Professional Development
Short Course on
Tactical Missile Design
Eugene L. Fleeman
Tactical Missile Design
E-mail: GeneFleeman@msn.com
Web Site: http://genefleeman.home.mindspring.com
2/24/2008
ELF
1
Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
2/24/2008
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2
Emphasis Is on Physics-Based, Analytical Sizing
of Aerodynamic Configuration
Area
Emphasis
Aero Configuration Sizing
Aero Stability & Control
Aero Flight Performance
Propulsion
Structure
Weight
Warhead
Miss Distance
Cost
Additional Measures of Merit
Launch Platform Integration
Primary Emphasis
Seeker, Sensors, and Electronics
Secondary Emphasis
Power Supply
Tertiary Emphasis
-
Safe, Arm, and Fuzing
2/24/2008
ELF
Not Addressed
3
Tactical Missiles Are Different from Fighter Aircraft
Tactical Missile
Characteristics
Example of
State-of-the-Art
Axial Acceleration
Maneuverability
Speed / altitude
Dynamic pressure
Size
Weight
Production cost
Observables
Range
Kills per use
Target acquisition
Superior
2/24/2008
Comparison With
Fighter Aircraft
AGM-88
AA-11
SM-3
PAC-3
Javelin
FIM-92
GBU-31
AGM-129
AGM-86
Storm Shadow
LOCAAS
Better
Comparable
ELF
–
–
–
– Inferior
4
Aero Configuration Sizing Parameters
Emphasized in This Course
Nose Fineness
Propulsion Sizing /
Propellant or Fuel
Diameter
Stabilizer
Geometry / Size
Wing Geometry / Size
Thrust
Profile
Flight Conditions ( α, M, h )
Flight Control
Geometry / Size
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Length
5
Conceptual Design Process Requires Evaluation
of Alternatives and Iteration
• Mission / Scenario
Definition
Update
Initial
• Weapon
Requirements,
Trade Studies
and Sensitivity
Analysis
• Launch Platform
Integration
Revised
Trades / Eval
Initial
Reqs
Alt
Concepts
Initial Carriage /
Launch
Effectiveness / Eval
Baseline
Selected
Iteration
Refine
Weapons
Req
• Weapon Concept
Design Synthesis
Alternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine
• Technology
Assessment and
Dev Roadmap
Initial Tech
Tech Trades
Initial
Revised
Roadmap Roadmap
Note: Typical conceptual design cycle is 3 to 9 months. House of Quality may be used to translate customer requirements
to engineering characteristics. DOE may be used to efficiently evaluate the broad range of design solutions.
2/24/2008
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6
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Define Mission Requirements
Alt Mission
Establish Baseline
Alt Baseline
Aerodynamics
Propulsion
Weight
Resize / Alt Config / Subsystems / Tech
Trajectory
Meet
Performance?
No
Yes
Measures of Merit and Constraints
No
Yes
2/24/2008
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7
Examples of Air-Launched Missile Missions /
Types
Air-to-air
Example SOTA
• Short range ATA. AA-11.
Maneuverability
• Medium range ATA. AIM-120.
Performance / weight
• Long range ATA. Meteor.
Range
10 feet
Air-to-surface
• Short range ATS. AGM-114.
Versatility
• Medium range ATS. AGM-88.
Speed
• Long range ATS. Storm Shadow. Modularity
Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved
2/24/2008
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8
Examples of Surface-Launched Missile Missions /
Types
Surface-to-surface
Example SOTA
• Short range STS. Javelin.
Size
• Medium range STS. MGM-140.
Modularity
• Long range STS. BGM-109.
Range
10 feet
Surface-to-air
2/24/2008
• Short range STA. FIM-92.
Weight
• Medium range STA. PAC-3.
Accuracy
• Long range STA. SM-3.
High altitude
Permission of Missile.Index. Copyright 1997©Missile.Index All Rights Reserved
ELF
9
Aero Configuration Sizing Has High Impact on
Mission Requirements
Impact on Weapon Requirement
Aero Measures of Merit
Aero Configuration
Sizing Parameter
Other Measures of Merit
Range / Time to RobustMiss ObservWeight Maneuver Target
ness
Lethality Distance ables Survivability Cost
Constraint
Launch
Platform
Nose Fineness
Diameter
Length
Wing Geometry / Size
Stabilizer Geometry / Size
Flight Control
Geometry / Size
Propellant / Fuel
Thrust Profile
Flight Conditions
( α, M, h )
Very Strong
2/24/2008
Strong
Moderate
ELF
–
Relatively Low
10
Example of Assessment of Alternatives to
Establish Future Mission Requirements
Measures of Merit
Alternatives for Precision Strike
Cost per
Shot
Number of
Launch Platforms
TCT
Required
Effectiveness
Future Systems
Standoff platforms / hypersonic missiles
Overhead loitering UCAVs / hypersonic missiles
Overhead loitering UCAVs / light weight PGMs
Current Systems
Penetrating aircraft / subsonic PGMs
–
Standoff platforms / subsonic missiles
Note:
Superior
–
–
Good
Average
– Poor
Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivity
time of less than 2 m and target location error ( TLE ) of less than 1 m for motion suspended target.
2/24/2008
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11
C4ISR Tactical Satellites and UAVs Have High
Impact on Mission Capability
LaunchPlatforms
Platforms
Launch
Off-boardSensors
Sensors
Off-board
•FighterAircraft
Aircraft
•Fighter
•Bomber
•Bomber
•TacticalSatellite
Satellite
•Tactical
•UAV
•UAV
•Ship/ Submarine
/ Submarine
•Ship
•UCAV
•UCAV
PrecisionStrike
StrikeWeapons
Weapons
Precision
•HypersonicSOW
SOW
•Hypersonic
•SubsonicPGM
PGM
•Subsonic
•SubsonicCM
CM
•Subsonic
TimeCritical
CriticalTargets
Targets
Time
•TBM/ TEL
/ TEL
•TBM
•SAM
•SAM
•C3
•C3
•OtherStrategic
Strategic
•Other
Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivity
time of less than 2 m and target location error ( TLE ) of less than 1 m for motion suspended target.
2/24/2008
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12
Example of System-of-Systems Analysis to
Develop Future Mission Requirements
t1
TBM Launch
Launch Pt Rcvd
t2
100
t3
Hypersonic
Missile Launch
HM Intercept
at XXX nm
Altitude – 1000 ft
t0
3. Alt / Speed / RCS Required
For Survivability
60
40
20
0
4. Lethality
W/H W3 > W2
W/H W2 > W1
Warhead W1
Lethality / Concrete
Penetration ( ft )
Time, Min
Range 3 > R2
Range 2 > R1
Range 1
3-4
1-2
120
100
80
60
40
20
0
4000
6000
2000
Average Speed to Survive, fps
0
2- 3
Cruise Missile Launch
2. Time To Target
RCS1
80
5. Campaign Model Weapons
Mix ( CM, Hypersonic
Missile ) Results
RCS2 > RCS1
( eg., Korean Scenario )
4-5
1. Compare Targeting of Subsonic Cruise Missile
Versus Hypersonic Missile
50
40
30
20
10
0
2/24/2008
1000
2000
3000 4000
Average Speed, fps
5000
0
0
ELF
1000 2000
3000
Impact Velocity, fps
4000
Selected For All:
• Value of Speed /
Range
• Time Urgent Targets
• High Threat
Environments
• Buried Targets
• Launch Platform
Alternatives
• Operating and
Attrition Cost in
Campaign
• Weapon Cost in
Campaign
• Mix of Weapons in
Campaign
• Cost Per Target Kill
• C4ISR Interface
13
Example of Technological Surprise Driving
Immediate Mission Requirements
Sidewinder AIM-9L ( IOC 1977 )
Performance
•+/- 25 deg off boresight
Archer AA-11 / R-73 ( IOC 1987 )
•6.5 nm range
Performance
•> +/- 60 deg off boresight
•20 nm range
New Technologies
•TVC
•Split canard
•Near-neutral static margin
•+/- 90 deg gimbal seeker
•Helmet mounted sight
2/24/2008
ELF
Note: AIM-9L maneuverability shortfall compared to
Archer drove sudden development of AIM-9X.
14
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Define Mission Requirements
Alt Mission
Establish Baseline
Alt Baseline
Aerodynamics
Propulsion
Weight
Resize / Alt Config / Subsystems / Tech
Trajectory
Meet
Performance?
No
Yes
Measures of Merit and Constraints
No
Yes
2/24/2008
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15
Baseline Design Benefits and Guidelines
Benefits of Baseline Design
Allows simple, conceptual design methods to be used with good
accuracy
Well documented benchmark / configuration control / traceability
between cause and effect
Balanced subsystems
Gives fast startup / default values for design effort
Provides sensitivity trends for changing design
Baselines can cover reasonable range of starting points
Baselines can normally be extrapolated to ±50% with good accuracy
Guidelines
Don’t get locked-in by baseline
Be creative
Project state-of-the-art ( SOTA ) if baseline has obsolete subsystems
Sensors and electronics almost always need to be updated
2/24/2008
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16
Example of Missile Baseline Data
Configuration Drawing
Weight / Geometry
11.6
37°
11.5
Body
16.5
Transport Air Duct
Payload Bay
Fore-body
Aftbody
Engine
Tail ( Exposed )
126.0
76.5
Mid-body
Aft-body
Area ( 2 panels ), ft2
Wetted area ( 4 panels ), ft2
Aspect ratio ( exposed )
Taper ratio
Root chord, in
Span, in. ( exposed )
L.E. sweep, deg
M.A.C., in
Thickness ratio
X MAC, in
Y MAC, in ( from root chord )
Tail Cone
159.0
171.0
Note: Dimensions are in inches
Reference values:
Source: Bithell, R.A. and Stoner, R.C. “Rapid Approach for Missile Synthesis”, Vol. II, Air-breathing
Synthesis Handbook, AFWAL TR 81-3022, Vol. II, March 1982.
Reference area, ft2
Reference length, ft
Aerodynamics
C
0
0
1
3
2
M, Mach Number
4
C
D
0
4.0
.40
-.4
.1
0
-.8
-1.2
Mach
.30
1.5
0
.20
1
2
3
4 2.0
M, Mach Number
3.0
4.0
4.0
3.0
2.0
0
4
8
12
1.5
16
α, Angle of Attack ~ deg
0
Mach
.10
0
-1.6
1.2
4
8
12
α, Angle of Attack ~ deg
1.2
Mach
1.2
1.5
2.0
3.0
3.0
4.0
2.0
Isp, Specific Impulse, sec
.05
SRef = 2.264 ft2
LRef = Dref = 1.698 ft
Xcg @ Sta 82.5 in.
.2
Axial Force Coefficient, CA
Pitching Moment Coefficient, Cm
C
N ~ per deg
δ
.10
•
1,000
15,000
•
•
500
Note:
φ =1
••
142.5
142.5
31.6
31.0
37.0
70.0
1,262.6
476.0
1,738.6
31.0
11.5
1,781.1
449.0
2,230.1
165.0
165.0
164.0
157.2
81.8
87.0
83.2
164.0
126.0
84.9
142.5
96.5
Ramjet Engine Station Identification
0
1.0
0
0
4
8
12
16
4
3
5
6
Rocket Propulsion
•
h = SL
•
Note:
φ =1
••
1
10
2
3
4
M, Mach Number
α, Angle of Attack ~ deg
0
0
1
•
•
h = 40K ft
•
•
•
•
•
2
1.0
2.0
Note: Constant altitude flyout
•
•
0
( ISP )Booster = 250 sec
20
0
h = 20K ft •
•
3
h = 60K ft
•
•
h = 80K ft
2.0
ML = 0.80
constant altitude flyout
1.0
0
0
20
40
h, Altitude 1,000 ft
4
60
3.0
Time ~ sec
4.0
5.0
6.0
3.0
2.5
2.0
0
20
40
60
h, Altitude 1,000 ft
80
M, Mach Number
House of Quality
60,000 ft
300
200
40,000 ft
20,000 ft
h = SL
Note:
• ML = 0.8, Constant Altitude Flyout
0
0
1
2
3
Example:
• Breguet Range for Mach 3 / 60 Kft flyout:
M, Mach Number
Rmax = V ISP ( L / D )Max ln [ WBC / ( WBC - Wf )]
= 2901 ( 950 ) ( 3.15 ) ln ( 1739 / ( 1739 - 476 )) = 2,777,192 ft or 457 nm
•
•
5,000
0
2
1
Free Stream
Inlet Throat
Subscripts
0
Free stream conditions ( Ramjet Baseline A0 = 75.4 in2 at Mach 4, α = 0 deg, Note: AC = 114 in2 )
1
Inlet throat ( Ramjet Baseline A1 = AIT = 41.9 in2 )
2
Diffuser exit ( Ramjet Baseline A2 = 77.3 in2 )
3
Flame holder plane ( Ramjet Baseline A3 = 287.1 in2 )
4
Combustor exit ( Ramjet Baseline A4 = 287.1 in2 )
20.375 in diameter
5
Nozzle throat ( Ramjet Baseline A5 = 103.1 in2 )
6
Nozzle exit ( A6 = 233.6 in2 )
Ref
Reference Area ( Ramjet Baseline Body Cross-sectional Area, SRef = 326 in2 )
0
400
Range ~ nm
44.5
33.5
10,000
500
2/24/2008
101.2
80.0
112.0
121.0
121.0
30
16
Flight Performance
100
95.2
103.0
30.0
20.0
5.0
20,000
SRef = 2.264 ft2
LRef = DRef = 1.698 ft
Xcg @ Sta 82.5 in.
.3
0
33.5
33.5
60.0
60.0
1,500
.4
-.2
Normal Force Coefficient, CN
m ~ per deg
δ
SRef = 2.264 ft2
LRef = DRef = 1.698 ft
Xcg @ Sta 82.5 in.
0
2.264
1.698
15.7
64.5
510.0
Inlet capture area
Ac = 114 in2
Inlet throat area
Reference area
120°
Nozzle throat area
Specific impulse
Equivalence ratio – operating fuel / air ratio divided by fuel / air ratio for stochiometric combustion
Ramjet Propulsion
-.4
+ .4
Tailcone2.24
Exit Duct
8.96
Controls
1.64
Fins ( 4 )0.70
End of 16.5
Cruise
23.0
Ramjet Fuel ( 6.9 ft3 )
37.0
Start of Cruise
14.2Nozzle ( Ejected )
Boost
0.04 Port
Frangible
150.5
End of Boost
5.4
Boost Propellant
Booster Ignition
15.9
42.4
129.0
Ac
AIT
SRef
A5
Isp
φ
Boost Thrust ~ 1000 lbs
43.5
28.33
Midbody
Inlet68.81
0.58
Electrical
N/A
Hydraulic
Fuel15.0
Distribution
CG Sta, In.
Boost Range ~ nm
23.5
Nose
Boost Propellant
Booster, and
Ramjet Engine
20.375
Payload
Bay
8.39
Warhead
Weight, lb
Paredo Sensitivity for DOE
Nondimensional Range Sensitivity
to Parameter
Sta 0.
Ramjet Fuel
Warhead
Forebody
171.0
Guidance
T, Net Thrust, lb
Guidance
( CD0 )Nose Corrected = ( CD0 )Nose Uncorrected x ( 1 - Ac / SREF )
17.7
8.36
Component
0.52
Nose 0.29
Length, in
Diameter, in
Fineness ratio
Volume, ft3
Wetted area, ft2
Base area, ft2 ( cruise )
Boattail fineness ratio
Nose half angle, deg
Boost Nozzle
Chin
Inlet
Conical forebody angle, deg
Ramp wedge angle, deg
Capture area, ft2
Throat area, ft2
Burnout Mach Number
Sta 150.3
20.375 dia
Flow Path Geometry
Inlet
1.5
1
0.5
0
ISP
-0.5
Fuel
Weight
Thrust
-1
CD0, Zero- CLA, LiftCurveLift Drag
Slope
Coefficient
Coefficient
Inert
Weight
Parameter
4
Sea Level Flyout at Mach 2.3
40 Kft Flyout at Mach 2.8
ELF
20 Kft Flyout at Mach 2.5
60 Kft Flyout at Mach 3.0
17
Baseline Design Data Allows Correction of
Computed Parameters in Conceptual Design
PCD, C = ( PB, C / PB, U ) PCD, U
PCD, C
PB, C
PB, U
PCD, U
Example
Parameter of conceptual design, corrected
Parameter of baseline, corrected ( actual data )
Parameter of baseline, uncorrected ( computed )
Parameter of conceptual design, uncorrected (computed )
• Ramjet Baseline with RJ-5 fuel ( heating value = 11,300,000 ft-lbf / lbm )
• Advanced Concept with slurry fuel ( 40% JP-10 / 60% boron carbide =
18,500,000 ft-lbf / lbm )
• Flight conditions: Mach 3.5 cruise, 60k ft altitude, combustion temperature
4,000 R
• Calculate specific impulse ( ISP )CD,C for conceptual design, based on corrected
baseline data
( ISP )B, C = 1,120 s
– ( ISP )B, U = 1387 s
– ( ISP )CD, U = 2,271 s
– ( ISP )CD, C = [( ISP )B, C / ( ISP )B, U ] ( ISP )CD, U = [( 1120 ) / ( 1387 )] ( 2271 ) = 0.807 ( 2271 )
= 1,834 s
–
2/24/2008
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18
Summary of This Chapter
Overview of Missile Design Process
Examples
Tactical missile characteristics
Conceptual design process
SOTA of tactical missiles
Aerodynamic configuration sizing parameters
Processes that establish mission requirements
Process for correcting design predictions
Discussion / Questions?
Classroom Exercise
2/24/2008
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19
Introduction Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
2/24/2008
The missile design team should address the areas of mission / scenario
definition, weapon requirements, launch platform integration, design, and
t_______ a_________.
The steps to evaluate missile flight performance require computing
aerodynamics, propulsion, weight, and flight t_________.
Air-to-air missile characteristics include light weight, high speed, and high
m______________.
Air-to-surface missiles are often versatile and m______.
Four aeromechanics measures of merit are weight, range, maneuverability,
and t___ to target.
The launch platform often constrains the missile span, length, and w_____.
An enabling capability for hypersonic strike missiles is fast and accurate
C____.
An enabling capability for large off boresight air-to-air missiles is a h_____
m______ sight.
A baseline design improves the accuracy and s____ of the design process.
ELF
20
Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
2/24/2008
ELF
21
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Define Mission Requirements
Alt Mission
Establish Baseline
Alt Baseline
Aerodynamics
Propulsion
Weight
Resize / Alt Config / Subsystems / Tech
Trajectory
Meet
Performance?
No
Yes
Measures of Merit and Constraints
No
Yes
2/24/2008
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22
Missile Diameter Tradeoff
Drivers toward Small Diameter
• Decrease drag
• Launch platform diameter constraint
Drivers toward Large Diameter
• Increase seeker range and signal-to-noise, better resolution and tracking
• Increase blast frag and shaped charge warhead effectiveness ( larger diameter
⇒ higher velocity fragments or higher velocity jet )
• Increase body bending frequency
• Subsystem diameter packaging
• Launch platform length constraint
Typical Range in Body Fineness Ratio 5 < l / d < 25
• Man-portable anti-armor missiles are low l / d ( Javelin l / d = 8.5 )
• Surface-to-air and air-to-air missiles are high l / d ( AIM-120 l / d = 20.5 )
2/24/2008
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23
Small Diameter Missiles Have Low Drag
D = CD q SRef = 0.785 CD q d2
D / CD, Drag / Drag Coefficient, lb
100000
Note: D = drag in lb, CD = drag coefficient, q = dynamic pressure in psf,
d = diameter ( reference length ) in ft
10000
Dynamic Pressure =
1,000 psf
Dynamic Pressure =
5,000 psf
Dynamic Pressure =
10,000 psf
1000
100
Example for Rocket Baseline:
d = 8 in = 0.667 ft
10
Mach 2, h = 20k ft, ( CD )Powered = 0.95
4
8
12
16
20
q = 1/2 ρ
0
V2
= 1/2 ρ ( M a )2
= 1/2 ( 0.001267 ) [( 2 ) ( 1037 )]2 = 2,725 psf
d, Diameter, in
D0 / CD = 0.785 ( 2725 ) ( 0.667 )2 = 952
0
D0 = 0.95 ( 952 ) = 900 lb
2/24/2008
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24
Large Diameter Radar Seeker Provides Longer
Detection Range and Better Resolution
RD = { π σ n3/4 / [ 64 λ2 K T B F L ( S / N ) ]}1/4 Pt 1/4 d
100
θ3dB = 1.02 λ / d, θ3dB in rad
Assumptions: Negligible clutter, interference, and
atmospheric attenuation; non-coherent radar ( only
signal amplitude integrated ); uniformly illuminated
circular aperture; receiver sensitivity limited by
thermal noise
Symbols:
σ = Target radar cross section, m2
n = Number of pulses integrated
λ = Wavelength, m
K = Boltzman’s constant = 1.38 x 10-23 J / K
T = Receiver temperature, K
B = Receiver bandwidth, Hz
1
F = Receiver noise factor
0
5
10
15
20 L = Transmitter loss factor
S / N = Signal-to-noise ratio for target detection
d, Diameter, Inches
Pt = Transmitted power, W
d = Antenna diameter
Example Seeker Range for Transmitted Power Pt = 100 W, nm
Example: Rocket Baseline
Example Seeker Range for Transmitted Power Pt = 1,000 W, nm
d = 8 in = 0.20 m, Pt = 1000 W, λ = 0.03 m ( f = 10 GHz )
Example Seeker Range for Transmitted Power Pt = 10,000 W, nm
RD = Target detection range = { π ( 10 ) ( 100 )3/4 / [ 64 (
Example Seeker Beam Width, deg
0.03 )2 ( 1.38 x 10-23 ) ( 290 ) ( 106 ) ( 5 ) ( 5 )( 10 )]}1/4 (
Note for figure: σ = 10 m2, n = 100, λ = 0.03 m ( f = Transmitter
1000 )1/4 ( 0.203 ) = 13,073 m or 7.1 nm
frequency = 10 x 109 Hz ), T = 290 K, B = 106 Hz ( 10-6 s pulse ), F θ3dB = 3-dB beam width = 1.02 ( 0.03 ) / 0.203 = 0.1507
= 5, L = 5, S / N = 10
rad or 8.6 deg
10
2/24/2008
ELF
25
Large Diameter IR Seeker Provides Longer
Detection Range and Better Resolution
RD = Target detection range, m
( IT )Δλ = Target radiant intensity between λ1 and λ2= ε
IFOV = dp / [ ( f-number ) do ]
Lλ ( λ2 - λ1 ) AT, W / sr
ηa = Atmospheric transmission
Ao = Optics aperture area, m2
10
D* = Specific detectivity, cm Hz1/2 / W
Δfp = Pixel bandwidth, Hz
Ad = Detectors total area, cm2
( S / N )D = Signal-to-noise ratio required for detection
1
ε = Emissivity coefficient
0
2
4
6
8
10 L = Spectral radiance ( Planck’s Law ) = 3.74 x 104 / {
λ
4
do, Optics Diameter, Inches
λ5 { e[ 1.44 x 10 / ( λ TT )] – 1 }}, W cm-2 sr-2 μm-1
λ2 = Upper cutoff wavelength for detection, μm
Example Seeker Range for Exo-atmospheric, km
λ1 = Lower cutoff wavelength for detection, μm
Example Seeker Range for Humidity at 7.5 g / m3, km
AT = Target planform area, cm2
Example Seeker Range for Rain at 4 mm / hr, km
λ = Average wavelength, μm
Example Seeker IFOV, 10-5 rad
TT = Target temperature, K
IFOV = Instantaneous field-of-view of pixel, rad
Example: do = 5 in = 0.127 m, exo-atmospheric
4
f-number = dspot / ( 2.44 λ )
Lλ = 3.74 x 104 / { 45 { e{ 1.44 x 10 / [ 4 ( 300 ) ]} – 1 }} = 0.000224 W cm-2 sr-2
dp = Pixel diameter, either μm
μm-1, ( IT )Δλ = 0.5 ( 0.000224 ) ( 4.2 – 3.8 ) 2896 = 0.1297 W / sr, Ad =
256 x 256 x ( 20 μm )2 = 0.262 cm2, f-number = 20 / [ 2.44 ( 4 ) ] = 2.05 dspot = Spot resolution if diffraction limited = dp, μm
RD = { 0.1297 ( 1 ) ( 0.01267 ) { 8 x 1011 / [( 250 )1/2 ( 0.262 )1/2 ]} ( 1 )-1
Figure: dT = 2 ft ( 60.96 cm ), TT = 300 K, λ1 = 3.8 μm,
}1/2 = 12, 740 m
λ2 = 4.2 μm, ε = 0.5, λ = 4 μm, FPA ( 256 x 256, 20 μm
IFOV = 0.000020 / [ 2.05 ( 0.127 )] = 0.0000769 rad
), D* = 8 x 1011 cm Hz1/2 / W, ( S / N ) = 1, Δf = 250 Hz.
100
RD = { ( IT )Δλ ηa Ao { D* / [( Δfp )1/2 ( Ad )1/2 ]} ( S / N )D-1 }1/2
D
2/24/2008
ELF
p
26
First Mode Body Bending Frequency, rad / s
Missile Fineness Ratio May Be Limited by
Impact of Body Bending on Flight Control
ωBB = 18.75 { E t / [ W ( l / d
10000
Assumes body cylinder structure, thin skin, high
fineness ratio, uniform weight distribution, free-free
motion. Neglects bulkhead, wing / tail stiffness.
ωBB = First mode body bending frequency, rad / s
E = Modulus of elasticity in psi
t = Thickness in inches
W = Weight in lb
l / d = Fineness ratio
) ]}1/2
E t / W = 1,000 per in
E t / W = 10,0000 per in
E t / W = 100,000 per in
1000
Example for Rocket Baseline:
100
0
10
20
30
l / d, length / diameter
l / d = 18
EAVG = 19.5 x 106 psi
tAVG = 0.12 in
W = 500 lb
E t / W = 19.5 x 106 ( 0.12 ) / 500 = 4680 per in
ωBB = 18.75 ( 4680 / 18 )1/2 = 302 rad / sec = 48 Hz
ωActuator = 100 rad / sec = 16 Hz
ωBB / ωActuator = 302 / 100 = 3.02 > 2
Derived from: AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993.
2/24/2008
ELF
27
Nose Fineness Tradeoff
High Nose Fineness Superior Aerodynamically, Low Observables
Example: lN / d = 5 tangent ogive
d
Low Nose Fineness Ideal Electromagnetically, High Propellant Length / Volume
Example: lN / d = 0.5 ( hemisphere )
d
Moderate Nose Fineness Compromise Dome
Examples: lN / d = 2 tangent ogive
lN / d = 2 faceted
lN / d = 2 window
lN / d = 2 multi-lens
d
ow
Wind
2/24/2008
ELF
28
Faceted and Flat Window Domes Can Have Low
Dome Error Slope, Low Drag, and Low RCS
Firestreak
Mistral
SLAM-ER
Faceted Dome ( Mistral ) Video
JASSM
THAAD
2/24/2008
ELF
29
Supersonic Body Drag Driven by Nose Fineness
while Subsonic Drag Driven by Wetted Area
( CD0 )Body = (CD0 )Body,Friction + ( CD0 )Base + ( CD0 )Body, Wave
(CD0 )Body,Friction = 0.053 ( l / d ) [ M / ( q l )]0.2. Based on Jerger reference, turbulent boundary layer, q in psf, l in ft.
( CD0 )Base,Coast = 0.25 / M, if M > 1 and (CD0 )Base,Coast = ( 0.12 + 0.13 M2 ), if M < 1
( CD0 )Base,Powered = ( 1 – Ae / SRef ) ( 0.25 / M ), if M > 1 and ( CD0 )Base,Powered = ( 1 – Ae / SRef ) ( 0.12 + 0.13 M2 ), if M < 1
( CD0 )Body, Wave = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( lN / d )]}1.69, for M > 1. Based on Bonney reference, tan-1 in rad.
Note: ( CD )Body,Wave = body zero-lift wave drag coefficient, ( CD )Base = body base drag coefficient, ( CD )Body, Friction = body skin
0
0
0
friction drag coefficient, ( CD )Body = body zero-lift drag coefficient, lN = nose length, d = missile diameter, l = missile body
0
length, Ae = nozzle exit area, SRef = reference area, q = dynamic pressure, tan-1 [ 0.5 / ( lN / d )] in rad.
Example for Rocket Baseline:
10
1
0.1
0.01
0
1
2
3
4
5
(CD0)Body,Wave;
lN / d = 0.5
(CD0)Body,Wave;
lN / d = 1
(CD0)Body,Wave;
lN / d = 2
(CD0)Body,Wave;
lN / d = 5
(CD)Base,Coast
( CD )Body, Wave ( CD )Body, Friction
0
0
( CD )Base
lN / d = 2.4, Ae = 11.22 in2, SRef = 50.26 in2, M =
2, h = 20k ft, q = 2725 psf, l / d = 18, l = 12 ft
( CD )Body, Friction = 0.053 ( 18 ) { ( 2 ) / [( 2725 )
0
( 12 ) ]}0.2 = 0.14
( CD )Base Coast = 0.25 / 2 = 0.13
( CD )Base Powered = ( 1 - 0.223 ) ( 0.25 / 2 ) = 0.10
( CD )Body, Wave = 0.14
0
( CD )Body, Coast = 0.14 + 0.13 + 0.14 = 0.41
M, Mach Number
0
( CD )Body, Powered = 0.14 + 0.10 + 0.14 = 0.38
0
2/24/2008
ELF
30
Moderate Nose Tip Bluntness Causes a
Negligible Change in Supersonic Drag
Steps to Calculate Wave Drag of a Blunted Nose
1.
Relate blunted nose tip geometry to pointed nose tip geometry
lN
dNoseTip
2.
dRef
Compute (CD0 )Wave,SharpNose for sharp nose, based on the body reference area
( CD )Wave,SharpNose = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( lN / d )]}1.69
0
3.
Compute ( CD0 )Wave,Hemi of the hemispherical nose tip ( lNoseTip / dNoseTip = 0.5 ), based on the
nose tip area
( CD0 )Wave,Hemi = ( 1.59 + 1.83 / M2 ) {[ tan-1 ( 0.5 / ( 0.5 )]}1.69 = 0.665 ( 1.59 + 1.83 / M2 )
4.
Finally, compute ( CD0 )Wave,BluntNose of the blunt nose, based on the body reference area
( CD0 )Wave,BluntNose = ( CD0 )Wave,SharpNose ( SRef - SNoseTip ) / SRef + ( CD0 )Wave,Hemi SNoseTipi / SRef
Example Rocket Baseline ( dRef = 8 in ) with 10% Nose Tip Bluntness at Mach 2
2/24/2008
•
•
•
( CD0 )Wave,SharpNose = [ 1.59 + 1.83 / ( 2 )2 ] [ tan-1 ( 0.5 / 2.4)]1.69 = 0.14
dNoseTip = 0.10 ( 8 ) = 0.8 in
SNoseTip = π dNoseTip2 / 4 = 3.1416 ( 0.8 )2 / 4 = 0.503 in2 = 0.00349 ft2
•
( CD0 )Wave,Hemi = 0.665 [ 1.59 + 1.83 / ( 2 )2 ] = 1.36
•
( CD0 )Wave,BluntNose = 0.14 ( 0.349 - 0.003 ) / 0.349 + ( 1.36 ) ( 0.003 ) / ( 0.349 ) = 0.14 + 0.01 = 0.15
ELF
31
Boattail Decreases Base Pressure Drag Area
Base Pressure Drag Area
Without Boattail
dRef
θBT
With Boattail
During Motor Burn After Motor Burnout
dBT
Note: Boattail angle θBT and boattail diameter dBT limited by propulsion nozzle packaging, tail flight
control packaging, and flow separation
Reference: Chin, S. S., Missile Configuration Design, McGraw-Hill Book Company, New York, 1961
2/24/2008
ELF
32
Boattailing Reduces Drag for Subsonic Missiles
CDO, Example Zero-Lift Drag Coefficient
0.45
Nose
0.40
3.00
0.35
Center body
Boattail
6.00
10.50
1.50
0.30
0.25
0.20
dBT / dRef = 1.0
dBT / dRef = 0.9
dBT / dRef = 0.8 Note:
dBT / dRef = 0.6
dBT = Boattail Diameter
dBT / dRef = 0.4
dRef = Body Reference Diameter
0.15
0.10
0.05
0.0
0.5
1.0
1.5
2.0
2.5
M∞
3.0
3.5
4.0
4.5
5.0
5.5
Note: Boatail half angle should be less than 10 deg, to avoid flow separattion.
Source: Mason, L.A., Devan, L. and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWC TR 81-156, July
1981
2/24/2008
ELF
33
Lifting Body Has Higher Normal Force
⏐ CN ⏐ = [⏐( a / b ) cos2 φ + ( b / a ) sin2 φ ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]
Note:
If α negative, CN negative
Based on slender body theory ( Pitts, et al ) and cross flow theory ( Jorgensen ) references
Valid for l / d > 5
Example l / d = length / diameter = 20
a/b=3
1/2
d=2 (ab)
φ = 0°
150
CN,
100
Example
Normal
Force
Coefficient
for l / d = 20 50
0
CN
2b
a/b=2
φ
2a
0
20
a/b=1
40
60
80
100
α, Angle of Attack, Deg
2/24/2008
ELF
34
L / D Is Impacted by CD0, Body Fineness, and
Lifting Body Cross Section Geometry
L / D = CL / CD = ( CN cos α – CD0 sin α ) / ( CN sin α + CD0 cos α )
For a lifting body, ⏐ CN ⏐ = [⏐( a / b ) cos2 ( φ ) + ( b / a ) sin2 ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]
4
L / D,
Lift / Drag
3
High drag, low fineness body ( a / b = 1, l / d = 10, CDO = 0.5 )
Low drag nose ( a / b = 1, l / d = 10, CDO = 0.2 )
High fineness, low drag ( a / b = 1, l / d = 20, CDO = 0.2 )
Lifting body, high fineness, low drag ( a / b = 2 @ φ = 0°, l / d =
20, CDO = 0.2 )
2
CN
1
0
0
20
40
60
80
100
φ
2b
2a
α, Angle of Attack, Deg
Note:
• If α negative, L / D negative
•d = 2 ( a b )1/2
•Launch platform span constraints ( e.g., VLS launcher ) and length constraints ( e.g., aircraft compatibility )
may limit missile aero configuration enhancements
2/24/2008
ELF
35
Lifting Body Requires Flight at Low Dynamic
Pressure to Achieve High Aero Efficiency
L / D = CL / CD = ( CN cos α – CDO sin α ) / ( CN sin α + CDO cos α )
⏐ CN ⏐ = [⏐( a / b ) cos2 ( φ ) + ( b / a ) sin2 ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]
Example L / D, Lift / Drag
4
Example:
q = 500 psf
3
•a / b = 1 ⇒ L / D = 2.40
•a / b = 2 ⇒ L / D = 3.37
2
q = 5,000 psf
•a / b = 1 ⇒ L / D = 0.91
1
•a / b = 2 ⇒ L / D = 0.96
0
100
1000
10000
100000
q, Dynamic Pressure, lb / ft2
Circular Cross Section ( a / b = 1 )
2/24/2008
Lifting Body ( a / b = 2 )
Note. Example figure based on following assumptions:
Body lift only ( no surfaces ), cruise flight ( lift = weight ), W = L = 2,000 lb, d = 2 ( a b )1/2, S = 2 ft2,
l / d = 10, CD0 = 0.2
ELF
36
Trade-off of Low Observables and ( L / D )Max
Versus Volumetric Efficiency
( L / D )Max, ( Lift / Drag )Max
6
Tailored
Weapons
5
Conventional
Weapons
( circular
cross section )
Advantages:
• ( L / D )Max
• Low RCS
Lower
Advantages:
• Payload
• Launch Platform
Integration
4
Radar
Cross
Section
3
2
Circular
4
Cross Section
6
Body Planform Area
8
10
( Body Volume )2/3
2/24/2008
ELF
37
Δ Cm / Δ α and Static Margin Define Static
Stability
xAC
Statically Stable: ΔCm / Δα < 0,
with xac behind xcg
Statically Unstable: ΔCm / Δα > 0,
with xac in front of xcg
xCG
Cm
δ2
α
α
α
δ2
Non-oscillatory
Divergent
Non-oscillatory
Convergent
Oscillatory
Convergent
xCG
δ1
Cm
δ1
xAC
α
t
t
Oscillatory
Divergent
Note: Statically unstable missile requires high bandwidth autopilot.
Autopilot negative rate feedback provides stability augmentation.
2/24/2008
ELF
38
Body Aerodynamic Center Is a Function of Angle
of Attack, Nose Fineness, and Body Length
Distance to Body Aerodynamic
Center / Length of Nose
( xAC )B / lN = 0.63 ( 1 - sin2 α ) + 0.5 ( lB / lN ) sin2 α
5
4
total length of body /
length of nose = 1
total length of body /
length of nose = 2
total length of body /
length of nose = 5
total length of body /
length of nose = 10
3
2
1
Example:
0
19.2
143.9
Rocket Baseline Body
0
20
40
60
80
Angle of Attack, Deg
100
lB / lN = 143.9 / 19.2 = 7.49
α = 13 deg
( xAC )B / lN = 0.81
Note: Based on slender body theory ( Pitts, et al ) and cross flow theory ( Jorgensen ) references. No flare.
( xAC )B = Location of body aerodynamic center, lN = length of nose, α = angle of attack, lB = total length of body.
2/24/2008
ELF
39
Flare Increases Static Stability
CNα = ( CNα )B + ( CNα )F
( C N )B
α
+M
( CNα )F
d dF
9
+α
x=0
( xac )B
lN
xAC xCG
Based on Slender Body Theory:
xF l B
( xac )F
( CNα )F = 2 [( dF / d )2 – 1 ]
( xac )F = xF + 0.33 lF [ 2 ( dF / d ) + 1 ] / [ ( dF / d ) + 1 ]
( CNα )B = 2 per rad
( xac )B = 0.63 lN
ΣM = 0 at Aerodynamic Center. For a Body-Flare:
( CNα )B {[ xCG – ( xAC )B ] / d } + ( CNα )F [ xCG – ( xAC )F ] / d = - [( CNα )B + ( CNα )F ]
[( xAC – xCG ) / d ]
Static Margin for a Body-Flare
( xAC – xCG ) / d = - {( CNα )B {[ xCG – ( xAC )B ] / d } + ( CNα )F {[ xCG – ( xAC )F ] / d }} /
[( CNα )B + ( CNα )F ]
2/24/2008
ELF
40
Flare Increases Static Stability ( cont )
Example of Static Margin for THAAD ( Statically Unstable Missile )
CNα = ( CNα )B + ( CNα )F
(C )
Nα B
( CNα )F
14.6 18.7 in
9
( xac )B = 57.7
91.5
146.9
xAC = 140.9
230.9 242.9
( xac )F = 237.1
( CNα )F = 2 [( 18.7 / 14.6 )2 – 1 ] = 2 [(1.28)2 – 1 ] = 1.28 per rad
( xac )F = 230.9 + 0.33 ( 12.0 )[ 2 ( 18.7 / 14.6 ) + 1 ] / [ ( 18.7 / 14.6 ) + 1 ] = 237.1 in
( xac )B = 0.63 ( 91.5 ) = 57.7 in
xCGLaunch = 146.9 in
( xAC – xCG )Launch / d = - { 2 {[ 146.9 – 57.7 ] / 14.6 } + 1.28 {[ 146.9 – 237.1 ] / 14.6 }}
/ [ 2 + 1.28 ] = - 0.41
2/24/2008
ELF
41
Tail Stabilizers Have Lower Drag While Flares
Have Lower Aero Heating and Stability Changes
Type Stabilizer
Drag
Span
Heating
ΔCNα Tail Control
Flare ( e.g., THAAD )
–
–
Tails ( e.g., Standard Missile )
–
Note:
2/24/2008
Superior
Good
ELF
–
Average
– Poor
42
Wing Sizing Trades
Advantages of Small Wing / Strake / No Wing
•
•
•
•
•
Range in high supersonic flight / high dynamic pressure
Max angle of attack
Launch platform compatibility
Lower radar cross section
Volume and weight for propellant / fuel
Advantages of Larger Wing
•
•
•
•
•
•
•
•
Range in subsonic flight / low dynamic pressure
Lower guidance time constant*
Normal acceleration*
High altitude intercept*
Less body bending aeroelasticity ( wing stiffens body )
Less seeker error due to dome error slope ( lower angle of attack )
Less wipe velocity for warhead ( lower angle of attack )
Lower gimbal requirement for seeker
*Based on assumption of aerodynamic control and angle of attack below wing stall
2/24/2008
ELF
43
Most Supersonic Missiles Are Wingless
2/24/2008
Stinger FIM-92
Grouse SA-18
Grison SA-19 ( two stage )
Gopher SA-13
Starburst
Mistral
Kegler AS-12
Archer AA-11
Gauntlet SA-15
Magic R550
Python 4
U-Darter
Python 5
Derby / R-Darter
Aphid AA-8
Sidewinder AIM-9X
ASRAAM AIM-132
Grumble SA-10 / N-8
Patriot MIM-104
Starstreak
Gladiator SA-12
PAC-3
Roland ( two stage )
Crotale
Hellfire AGM-114
ATACM MGM-140
Standard Missile 3 ( three stage )
THAAD
Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved
ELF
44
Wings, Tails, and Canards with Large Area and
at High Angle of Attack Have High Normal Force
⏐( CN )Surface ⏐ = [ 4⏐sin α’ cos α’⏐ / ( M2 – 1 )1/2 + 2 sin2α’ ] ( SSurface / SRef ), if M > { 1 + [ 8 / ( π A )]2 }1/2
⏐( CN )Surface ⏐ = [ ( π A / 2) ⏐sin α’ cos α’⏐ + 2 sin2α’ ] ( SSurface / SRef ), if M < { 1 + [ 8 / ( π A )]2 }1/2
( CN )Wing SREF / SW,
Wing Normal Force Coefficient
for Rocket Baseline
Note: Linear wing theory applicable if M > { 1 + [ 8 / ( π A )]2 }1/2, slender wing theory applicable if M < { 1 + [ 8 / ( π A )]2 }1/2,
A = Aspect Ratio < 3, SSurface = Surface Planform Area, SRef = Reference Area
M < 1.35, based on slender wing theory + Newtonian impact theory
M = 2, based on linear wing theory + Newtonian impact theory
M = 5, based on linear wing theory + Newtonian impact theory
4
Example for Rocket Baseline
Wing
AW = 2.82
SW = 2.55 ft2
SRef = 0.349 ft2
δ = 13 deg, α = 9 deg
3
M=2
{ 1 +[ 8 / ( π A )]2 }1/2 = 1.35
2
1
0
0
30
60
Since M > 1.35, use linear wing
theory + Newtonian theory
α’ = αW = α + δ = 22°
( CN )Wing SRef / SW = 4 sin 22°
cos 22° / ( 22 – 1 )1/2 + 2 sin2 22°
= 1.083
( CN )Wing = 1.08 ( 2.55 ) / 0.349 =
90
7.91
α’ = αW = α + δ , Wing Effective Angle of Attack for Rocket Baseline, Deg
2/24/2008
ELF
45
Aerodynamic Center of a Thin Surface ( e.g.,
Wing, Tail, Canard ) Varies with Mach Number
( xAC / cMAC )Surface = [ A ( M2 – 1 )1/2 – 0.67 ] / [ 2A ( M2 –1 )1/2 – 1 ], if M > ~ 2
XAC / CMAC, Surface Non-dimensional
Aerodynamic Center
( xAC / cMAC )Surface = 0.25, if M < ~ 0.7
0.5
0.4
Note: Based on linear wing theory
Thin wing ⇒ M ( t / c ) << 1
( xAC )Surface = Surface aerodynamic
center distance from leading
edge of ( cMAC )Surface
cMAC = Mean aerodynamic chord
A = Aspect ratio = b2 / S
A=1
A=2
A=3
0.3
0.2
Example: Rocket Baseline Wing
0.1
A = 2.82
xMAC
cMAC = 13.3 in
0
0
1
2
3
M, Mach Number
4
5
xAC
cMAC
( xMAC )Wing = 67.0 in
M=2
( xAC / cMAC )Wing = 0.481
( xAC )Wing = 6.4 in from mac leading
edge = 73.4 in from nose tip
2/24/2008
ELF
46
Hinge Moment Increases with Dynamic Pressure
and Effective Angle of Attack
HM = NSurface ( xAC - xHL )Surface
q = 436 psf ( M = 0.8 )
q = 2725 psf ( M = 2 )
Note: Based on linear wing
theory, slender wing theory,
and thin wing ( M ( t / c ) << 1 )
NSurface = Normal force on surface
( two panels )
( xAC - xHL )W = distance from
surface aerodynamic center to
hinge line of surface
q = 1242 psf ( M = 1.35 )
q = 17031 psf ( M = 5 )
HM, Example Hinge Moment, in - lb
30000
25000
Example for Rocket Baseline
Wing Control
N
x
20000
cmac = 13.3 in
xHL = 0.25 cmac
15000
xH
AC
W
L
SRef = 0.349 ft2
cm
ac
SW = 2.55 ft2
10000
δ = 13 deg, α = 9 deg
α’ = αW = α + δ = 22°
M = 2, h = 20k ft, q = 2725 psf
5000
NW = [ CN ( SRef / SW )] qSW =
W
1.083 ( 2725 ) ( 2.55 ) = 7525 lb
0
0
10
20
30
xAC / cmac = 0.48
α’ = αW = α + δ , Wing Effective Angle of Attack of Rocket Baseline, Deg HM = 7525 ( 0.48 – 0.25 ) ( 13.3 )
= 23019 in – lb for two panels
2/24/2008
ELF
47
Wings, Tails, and Canards Usually Have Greater
Skin Friction Drag Than Shock Wave Drag
( CD0 )Surface,Friction = nSurface { 0.0133 [ M / ( q cmac )]0.2 } ( 2 SSurface / SRef ), q in psf, cmac in ft
( CDO )Surface,Wave = nSurface ( 1.429 / MΛLE2 ){( 1.2 MΛLE2 )3.5 [ 2.4 / ( 2.8 MΛLE2 – 0.4 )]2.5 – 1 } sin2 δLE cos ΛLE
tmac b / SRef , based on Newtonian impact theory
nSurfaces = number of surface planforms ( cruciform = 2 )
( CDO )Surface = ( CDO )Surface,Wave + ( CDO )Surface,Friction
q = dynamic pressure in psf
0.4
cmac = length of mean aero chord in ft
0
Example ( CD )Surface,Friction
γ = Specific heat ratio = 1.4
MΛ = M cos ΛLE = Mach number ⊥ leading edge
0.3
LE
δLE = leading edge section total angle
ΛLE = leading edge sweep angle
0.2
tmac = max thickness of mac
b = span
Example for Rocket Baseline Wing:
0.1
nW = 2, M = 2, h = 20k ft ( q = 2,725 psf ), cmac = 1.108
ft, SRef = 50.26 in2, SW = 367 in2, δLE = 10.01 deg, ΛLE =
45 deg, tmac = 0.585 in, b = 32.2 in, MΛ = 1.41 ( M = 2 )
LE
0
0
10
20
n SSurface / SRef
M / ( q cmac ) = 0.00001 ft / lb
M / ( q cmac ) = 0.001 ft / lb
30
40
50
M / ( q cmac ) = 2 / [ 2725 ( 1.108 )] = 0.000662 ft / lb
n SSurface / SRef = 2 ( 367 ) / 50.26 = 14.60
( CD )Wing,Friction = 0.090
M / ( q cmac ) = 0.0001 ft / lb
M / ( q cmac ) = 0.01 ft / lb
O
( CD )Wing,Wave = 0.024
0
( CD )Wing = 0.024 + 0.090 = 0.11
O
2/24/2008
ELF
48
Examples of Wing, Tail, and Canard Panel
Geometry Alternatives
Parameter
Triangle
Aft Swept LE
( Delta )
Trapezoid
Variation xAC
Double
Bow Tie
Swept LE
Rectangle
–
Bending Moment / Friction
–
–
Supersonic Drag
–
RCS
–
Span Constraint
–
Stability & Control
Aeroelastic Stab.
–
λ = Taper ratio = cT / cR
A = Aspect ratio = b2 / S = 2 b / [( 1 + λ ) cR ]
yCP = Outboard center-of-pressure = ( b / 6 ) ( 1 + 2 λ ) / ( 1 + λ )
cMAC = Mean aerodynamic chord = ( 2 / 3 ) cR ( 1 + λ + λ 2 ) / ( 1 + λ )
2/24/2008
ELF
Note: Superior
Good
Average
Poor
–
Based on equal surface area and equal span.
Surface area often has more impact than geometry.
49
Examples of Surface Arrangement and
Aerodynamic Control Alternatives
Two Panels
( Mono-Wing )
Three
( Tri-Tail )
Folded
Wraparound
Four
( Cruciform )
Extended
Interdigitated
Six*
Eight*
Balanced Actuation Flap Control
Control
In-line
Note: More than four tails are usually free-to-roll pitch / yaw stabilizers, for low induced roll.
2/24/2008
ELF
50
Most Missiles Use Four Control Surfaces with
Combined Pitch / Yaw / Roll Control Integration
Control Integ
Control Surfaces Example
Control Effect Cost Packaging
Pitch / Yaw
2
Stinger FIM-92
–
Pitch / Roll
2
ALCM AGM-86
–
Pitch / Yaw / Roll
3
SRAM
–
Pitch / Yaw / Roll
4
Adder AA-12
Pitch + Yaw + Roll
5
Kitchen AS-4
–
–
Pitch / Yaw + Roll
6
Derby / R-Darter
–
–
Note:
2/24/2008
Superior
Good
ELF
Average
–
Poor
51
There Are Many Flight Control Configuration
Alternatives
Control Design
Alternatives
Control
Tail
Cruciform ( 4 )
Tri-tail ( 3 )
Not Compressed
Folded
Wraparound
Switchblade
Canard
Wingless
Wing
Strake / Canard
In Line with Controls
Interdigitated with Controls
Number ( 2, 3, 4 )
Above
Tail ( 3, 4, 6, 8 )
Rolling Airframe ( 2 ) Tail + Wing
In Line with Controls
Interdigitated with Controls
Wing
TVC or
Reaction Jet
Control
2/24/2008
Fixed Surface
Alternatives
ELF
Above
Tail ( 3, 4, 6, 8 )
Strake / Canard & Tail
In Line with Controls
Interdigitated with Controls
Movable Nozzle
Jet Tab
Jet Vane
Axial Plate
Secondary Injection
Normal Jet / JI
Spanwise Jet / JI
Tail ( 3, 4, 6, 8 )
Tail + Canard / Strake
Tail + Wing
52
Tail Control Is Efficient at High Angle of Attack
CN Trim
( assumed statically stable )
CN at δ = 0
α
V∞
CNC at δ = 0
cg
CNC
☺ Efficient Packaging
☺ Low Hinge Moment / Actuator
Torque
☺ Low Induced Rolling Moment
☺ Efficient at High α
2/24/2008
ΔCN
Negative δ
Decreased Lift at Low α if
Statically Stable
ELF
53
Tail Control Is More Effective Than Conventional
Canard Control at High Angle of Attack
+δ
• Assumed static stability
• Control surface local
angle of attack α’ = α + δ
• Panel stalled at high α*
• Assumed static stability
• Control surface local
angle of attack α’ = α – δ
• Panel not stalled at high α
α
V∞
α
–δ
V∞
Tail Control
1.0
Conven
Canard
Control
Clδ / ( Clδ )α = 0°
Cmδ / ( Cmδ )α = 0°
Conventional Canard Control
Tail
Control
☺
0
10 – 20°
1.0
Conven
Canard
Control
0
20 – 30°
Ø = 0°
Tail
Control
☺
10 – 15° 15 – 30°
α ~ Angle of Attack ( deg )
α ~ Angle of Attack ( deg )
*Note: Additional forward fixed surfaces ( such as Python 4 ) in front of movable canards alleviate stall
at high α. Free-to-roll tails ( such as Python 4 ) alleviate induced roll from canard control at high α.
2/24/2008
ELF
54
About 70% of Tail Control Missiles Also Have Wings
JASSM AGM-158
Maverick AGM-65
CALCM
JSOW AGM-154
Tomahawk BGM-109
Taurus KEPD 350
Storm Shadow / Scalp
Popeye AGM-142
Exocet MIM40
TOW2-BGM71D
AMRAAM AIM-120
Sunburn SS-N-22
Standard RIM-66 / 67
RBS-70 / 90
Shipwreck SS-N-19
Super 530
Sea Dart ( two stage )
FSAS Aster
R-37 ( AA-X-13 )
Mica
Adder AA-12
Rapier 2000
SD-10 / PL-12
Seawolf
Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved
2/24/2008
ELF
55
Tail Control Alternatives: Conventional Balanced
Actuation Fin, Flap, and Lattice Fin
Control
Type of Tail Control
Hinge
Effectiveness
Drag
Moment RCS
Balanced Actuation Fin ( Example: ASRAAM AIM-132 )
Flap ( Example: Hellfire AGM-114 )
–
Lattice Fin ( Example: Adder AA-12 / R-77 )
Note:
2/24/2008
Superior
–
Good
ELF
Average
–
Poor
56
Lattice Fins Have Advantages for Low Subsonic
and High Supersonic Missiles
Advantages
High control effectiveness at
low subsonic and high
supersonic Mach number
Low hinge moment
Short chord length
Disadvantages
High RCS ( cavities, normal
leading edges )
High drag at transonic Mach
number ( choked flow )
Low Subsonic
☺
2/24/2008
ELF
Transonic
Low Supersonic High Supersonic
☺
57
Conventional Canard Control Is Efficient at Low
Angle of Attack But Stalls at High Alpha
δ
ΔCN
CN Trim ( assumed statically stable )
C
NC
CN at δ = 0
α
cg
V∞
☺ Efficient Packaging
☺ Simplified
Manufacturing
☺ Increased Lift at Low α
if Statically Stable
Stall at High α if
Statically Stable
Induced Roll
Note:
= CNC at δ = 0°
= CNC at δ = δ
2/24/2008
ELF
*Note: Additional forward fixed surface in
front of movable canard alleviates stall at
high α. Free-to-roll tails alleviate induced
roll at high α. Dedicated roll control
surfaces avoid roll control saturation and
simplify autopilot design.
58
Canard Control Missiles Are Wingless and Most
Are Supersonic
Stinger FIM-92
Grouse SA-18
Grison SA-19 ( two-stage )
Gopher SA-13
Starburst
Gauntlet SA-15
Mistral
AIM-9L
Archer AA- 11
Magic R 550
Python 4
U-Darter
Python 5
Derby / R-Darter
Aphid AA-8
Kegler AS-12
GBU-12
GBU-22
2/24/2008
GBU-27
GBU-28
Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved
ELF
59
Missiles with Split Canards Have Enhanced
Maneuverability at High Angle of Attack
δ
ΔCN
C
α’ ~ α
α
α’ ~
NC
δ
Note: α’ = Local angle of attack
Kegler AS-12
Archer AA-11
Aphid AA-8
Magic R 550
Python 4
U-Darter
Note: Forward fixed surface reduces local angle-of-attack for movable canard, providing higher stall angle of attack. Forward
surface also provides a fixed, symmetrical location for vortex shedding from the body.
Python 4 also has free-to-roll tails and separate roll control ailerons.
2/24/2008
ELF
60
Wing Control Requires Less Body Rotation But
Has High Hinge Moment, Induced Roll and Stall
Δ CN ~ CN Trim
δ
V
( α small )
cg
☺ Low Body α / Dome Error Slope
☺ Fast Response ( if skid-to-turn )
2/24/2008
Poor Actuator Packaging
Large Hinge Moment
Larger Wing Size
Induced Roll
Wing Stall
ELF
61
Wing Control Missile Susceptible to High Vortex
Shedding
Strong vortices from wing interact with tail
Video of Vortices from Delta
Wing at High Angle of Attack
Source: University of Notre Dame web site:
http://www.nd.edu/~ame/facilities/SubsonicTunnels.html
2/24/2008
Source: Nielsen Engineering & Research ( NEAR ) web site:
http://www.nearinc.com/near/project/MISDL.htm
ELF
62
Wing Control Missiles Are Old Technology
Sparrow AIM-7: IOC 1956
Skyflash: IOC 1978
Alamo AA-10 / R-27: IOC 1980
HARM AGM-88: IOC 1983
Aspide: IOC 1986
Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved
2/24/2008
ELF
63
TVC and Reaction Jet Flight Control
Liquid Injection
Hot Gas Injection
Jet Vane*
± 12°
± 7°
± 10°
Note: Jet vanes provide roll control and share
actuators with aero control, but have reduced ISP
Axial Plate
Jet Tab
Movable Nozzle
± 20°
± 15°
± 7°
Note:
•TVC and reaction jet flight control provide
high maneuverability at low dynamic pressure
Reaction Jet
•TVC usually has lower time constant and
miss distance than aero control
M∞
Jet Flow
•Reaction jets usually have lower time
constant and miss distance than TVC
•Reaction jets can be either impulse jets or
controlled duration jets
2/24/2008
Jet inter.
ELF
Thrust
Jet interaction
64
Most Tactical Missiles with TVC or Reaction Jet
Control Also Use Aero Control
Jet Vane + Aero Control:
Sea Wolf GWS 26
Mica
Sea Sparrow RIM-7
AIM-9X
IRIS-T
A-Darter
Javelin
Jet Tab + Aero Control:
Archer AA-11
Reaction Jet + Aero Control:
PAC-3
Movable Nozzle + Aero Control + Reaction Jet:
SM-3 Standard Missile
Aster FSAF 15
Movable Nozzle + Reaction Jet:
THAAD
Reaction Jet:
LOSAT
2/24/2008
ELF
Example Video of TVC ( FSAF-15 and Javelin ) 65
Skid-to-Turn Is the Most Common Maneuver Law
Skid-To-Turn ( STT )
• Advantage: Fast response
• Features
–
–
STT
LO S
Does not require roll commands from autopilot
Works best for axisymmetric cruciform missiles
Maneuver w / o Roll Command
Bank-To-Turn ( BTT )
• Advantage: Provides higher maneuverability for planar
wing, noncircular / lifting bodies, and airbreathers
• Disadvantages
–
–
–
Target
BTT ( with
Planar Wing )
LO S
Time to roll
Requires fast roll rate
May have higher dome error slope
Target
Step 1: Roll Until
Wing ⊥ LOS
• Features
–
–
Roll attitude commands from autopilot
Small sideslip
LO S
Rolling Airframe ( RA )
Step 2: Maneuver @ Roll
Rate = 0 and Wing ⊥ LOS
• Advantage: Requires only two sets of gyros /
accelerometers / actuators ( packaging for small missile )
• Disadvantages for aero control
–
–
–
Reduced maneuverability for aero control
Requires high rate gyros / actuators
Requires precision geometry and thrust alignment
• Features
2/24/2008
–
–
–
Bias roll rate and roll moment
Can use impulse steering ( e.g., PAC-3, LOSAT )
Compensates for thrust offset
ELF
Target
RA
LO S
Target
Maneuver with Bias Roll
Moment
Bias Roll Rate ( e.g., 3 Hz )
66
Asymmetric Inlets Require Bank-to-Turn
Maneuvering
Examples of Twin Inlet Missiles with Bank-to-Turn
Twin Side Inlets Ramjet: ASMP
Twin Cheek Inlets Ducted Rocket: HSAD
Twin Cheek Inlets Ducted Rocket: Meteor
Examples of Single Inlet Missiles with Bank-to-Turn
Chin Inlet Ramjet: ASALM
Bottom Inlet Turbojet: BGM-109 Tomahawk
Bottom Inlet Turbojet: Storm Shadow / Scalp
Top Inlet Turbofan: AGM-86 ALCM
2/24/2008
Note: Bank-to-turn maneuvering maintains low sideslip for better inlet efficiency.
ELF
67
X Roll Orientation Is Usually Better Than + Roll
Orientation
Trailing edge
deflection
+ Roll Orientation with Four Tail Surfaces Control of Pitch / Yaw / Roll, Looking Forward from Base
Fin 1
Fin 4
Pitch Up
Fin 2
Yaw Right
Roll Right
Fin 3
X Roll Orientation with Four Tail Surfaces Control of Pitch / Yaw / Roll, Looking Forward from Base
4
1
Pitch Up
3
Note:
2/24/2008
Yaw Right
Roll Right
2
+ roll orientation usually has lower trim drag, less static stability and control effectiveness in pitch and yaw, and
statically unstable roll moment derivative ( Clφ > 0 ).
X roll orientation has better launch platform compatibility, higher L / D, higher static stability and control
effectiveness in pitch and yaw, and statically stable roll moment derivative ( Clφ < 0 ).
ELF
68
Trimmed Normal Force Is Defined at Zero
Pitching Moment
Normal Force, CN
δ = δ Trim for either statically unstable tail
control or statically stable canard control
δ=0
δ = δ Trim for either statically stable tail
control or statically unstable canard control
Pitching Moment, Cm
Angle of Attack ( Deg )
2/24/2008
δ = δ Max
αTrim @ Cm = 0
Angle of Attack ( Deg )
δ=0
ELF
69
Relaxed Static Margin Allows Higher Trim Angle
of Attack and Higher Normal Force
Note: Rocket Baseline
XCG = 75.7 in.
Mach 2
( α + δ )Max = 21.8 deg, ( CN
16
)
Trim Max
α / δ = 0.75, ( Static Margin = 0.88 Diam )
α / δ = 1.5, ( SM = 0.43 Diam )
( CN, Trim )max, Max
Trimmed Normal
Force Coefficient of
Rocket Baseline
α / δ = ∞, ( SM = 0 )
12
8
4
0
0
4
12
8
16
20
24
( αTrim )max, Μax Trim Angle of Attack, deg
2/24/2008
ELF
70
Tails Are Sized for Desired Static Margin
CN
( CN ) W
α
α
( CN ) T
α
( CN ) B
α
+M
+α
x = lN
( xAC )B
x=0
( xAC )W
ΣM = 0 at aerodynamic center
xCG xAC
x = lB
( xAC )T
( CN )B {[ xCG – ( xAC )B ] / d } + ( CN )W {[ xCG – ( xAC )W ] / d } SW / SRef + ( CN )T {[ xCG – ( xAC )T ] / d } ST / SRef
α
α
α
= - [( CN )B + ( CN )W SW / SRef + ( CN )T ST / SRef ] [( xAC – xCG ) / d ]
α
α
α
Static margin for a specified tail area is
( xAC – xCG ) / d = - {( CN )B {[ xCG – ( xAC )B ] / d } + ( CN )W {[ xCG – ( xAC )W ] / d } SW / SRef + ( CN )T {[ xCG – ( xAC )T ] / d } ( ST / SRef )} /
α
α
α
[(CN )B + (CN )W SW / SRef + ( CN )T ST / SRef ]
α
α
α
Required tail area for a specified static margin is
ST / SRef = ( CN )B {[ xCG – ( xAC )B ] / d } + ( CN )W {[ xCG – ( xAC )W ] / d } ( SW / SRef ) + {[( CN )B + ( CN )W SW / SRef ][( xAC – xCG ) / d ]}
α
α
α
α
/ {( CN )T [( xAC )T – xCG ] / d - ( xAC – xCG ) / d }
α
2/24/2008
ELF
71
Larger Tail Area Is Required for Neutral Stability
at High Mach Number
(ST)Neutral / SRef = { (CNα)B [ xCG – (xAC)B ] / d + (CNα)W {[ xCG – (xAC)W ] / d } ( SW / SRef )} / {{[ (xAC)T – xCG ] / d } (CNα)T }
5
0.2
=
)
Assumptions for figure:
•XCG ≈ l / 2, (XAC)B ≈ d, ( XAC )T ≈ l – d
f
/ S Re
•α < 6 deg, turbulent boundary layer
( SW
}
l
/
0 •(CNα)B = 2 per rad
)C W]
)=
f
xA
g)
•(CNα)T = (CNα)W = 4 / [ M2 –1 ]1/2, if M
–(
/ S Re
n
i
G
w
> { 1 + [ 8 / ( π A )]2 }1/2
}( S W
{[ x C ard
l
/
rw
) W]
( fo
C
5 •(CNα)T = (CNα)W = π A / 2, if M < { 1 +
xA
2
(
.
–
- 0 [ 8 / ( π A )]2 }1/2
G
=
x
C
)
{[
f
Example Rocket Baseline:
/ S Re
W
S
(
l = 144 in, d = 8 in, SW = 2.55 ft2, SRef =
/l}
]
)W
0.349 ft2, AW = 2.82, (cMAC)W = 13.3 in,
x AC
(
–
xMAC = 67.0 in from nose tip, burnout
)
G
x
C
g
( xCG = 76.2 in from tip ), Mmax = 3
n
{[
wi
t
f
(a
(xAC)W = 0.49 ( 13.3 ) = 6.5 in from
leading edge of MAC
(ST)Neutral / SRef, Neutral Stability Tail Area /
Reference Area
3
2
1
(xAC)W = 6.5 + 67.0 = 73.5 in from nose
0
0
1
2
3
4
M, Mach Number
5
{[ xCG – (xAC)W ] / l } ( SW / SRef ) = 0.14
( forward wing )
(ST)Neutral / SRef = 1.69 provides neutral
stability
(ST)Neutral = 1.69 ( 0.349 ) = 0.59 ft2
2/24/2008
ELF
72
Stability and Control Derivatives Conceptual
Design Criteria
| Clδr / Clδa | < 0.3 ( Roll Due to Rudder Deflection ) | Clφ / Clδa | < 0.5 ( Roll Due to Roll Angle )
Clδr
z
x
Clδa
x
Clδa
Clφ
y
z
y
| Cnδa / Cnδr | < 0.2 ( Yaw Due to Aileron Deflection ) | Cmα / Cmδ | < 1 ( Pitch Due to α )
x
Cnδa
Cnδr
z
Cmα
Cmδ
y
z
2/24/2008
y
z
| Clβ / Clδa | < 0.3 ( Roll Due to Sideslip )
Clβ
x
x
| Cnβ / Cnδr | < 1 ( Yaw Due to Sideslip )
x
Cnβ
Clδa
Cnδr
y
z
y
Note: The primary control derivative ( larger bold font ) should be larger than the undesirable stability and control derivative.
ELF
73
Most of the Rocket Baseline Body Buildup Normal
Force Is Provided by the Wing
( CN )Total = ( CN )Wing-Body-Tail ≅ ( CN )Body + ( CN )Wing + ( CN )Tail
15
CN, Normal Force
Coefficient of
Rocket Baseline
Body + Wing + Tail
10
Body + Wing
5
Body
0
0
5
10
15
α, Angle of Attack, Deg
20
25
Note for figure: M = 2, δ = 0
Note: ( CD0 )Total = ( CD0 )Wing-Body-Tail ≅ ( CD0 )Body + ( CD0 )Wing + ( CD0 )Tail
( Cm )Total = ( Cm )Wing-Body-Tail ≅ ( Cm )Body + ( Cm )Wing + ( Cm )Tail
2/24/2008
ELF
74
Summary of Aerodynamics
Conceptual Design Prediction Methods of Bodies and Surfaces
Normal force coefficient
Drag coefficient
Aerodynamic center / pitching moment coefficient / hinge moment
Design Tradeoffs
Diameter
Nose fineness
Boattail
Lifting body versus axisymmetric body
Wings versus no wings
Tails versus flares
Surface planform geometry
Flight control alternatives
Maneuver alternatives
Roll orientation
Static margin / time to converge or diverge
Tail sizing
2/24/2008
ELF
75
Summary of Aerodynamics ( cont )
Stability and Control Design Criteria
Static stability
Control effectiveness
Cross coupling
Body Buildup
New Aerodynamics Technologies
Faceted / window / multi-lens domes
Bank-to-turn maneuvering
Lifting body airframe
Forward swept surfaces
Neutral static margin
Lattice fins
Split canard control
Free-to-roll tails
Discussion / Questions?
Classroom Exercise
2/24/2008
ELF
76
Aerodynamics Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
2/24/2008
Missile diameter tradeoffs include consideration of seeker range, warhead
lethality, structural mode frequency, and d___.
Benefits of a high fineness nose include lower supersonic drag and lower
r____ c____ s______.
Three contributors to drag are base drag, wave drag, and s___ f_______
drag.
To avoid flow separation, a boatail or flare angle should be less than __ deg.
A lifting body is most efficient at a d______ p_______ of about 700 psf.
At low angle of attack the aerodynamic center of the body is on the n___.
Subsonic missiles often have w____ for enhanced range.
The aerodynamic center of the wing is between 25% and 50% of the m___
a__________ c____.
Hinge moment increases with the local flow angle due to control surface
deflection and the a____ o_ a_____.
Increasing the surface area increases the s___ f_______ d___.
ELF
77
Aerodynamics Problems ( cont )
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2/24/2008
Leading edge sweep reduces drag and r____ c____ s______.
A missile with six control surfaces, four surfaces providing combined pitch /
yaw control plus two surfaces providing roll control, has an advantage of
good c______ e____________.
A missile with two control surfaces providing only combined pitch / yaw
control has advantages of lower c____ and good p________.
A tail control missile has larger trim normal force if it is statically u_______.
Lattice fins have low h____ m_____.
Split canards allow higher maximum angle of attack and higher
m______________.
Two types of unconventional control are thrust vector control and r_______
j__ control.
The most common type of TVC for tactical missiles is j__ v___ control.
Three maneuver laws are skid to turn, bank to turn, and r______ a_______.
Bank to turn maneuvering is usually required for missiles with a single wing
or with a_________ inlets.
ELF
78
Aerodynamics Problems ( cont )
21.
22.
23.
24.
25.
2/24/2008
A missile is statically stable if the aero center is behind the c_____ o_
g______.
Tail stabilizers have low drag while a f____ stabilizer has low aero heating
and a relatively small shift in static stability.
If the moments on the missile are zero the missile is in t___.
Total normal force on the missile is approximately the sum of the normal
forces on the surfaces ( e.g., wing, tail, canard ) plus normal force on the
b___.
Increasing the tail area increases the s_____ m________.
ELF
79
Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
2/24/2008
ELF
80
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Define Mission Requirements
Alt Mission
Establish Baseline
Alt Baseline
Aerodynamics
Propulsion
Weight
Resize / Alt Config / Subsystems / Tech
Trajectory
Meet
Performance?
No
Yes
Measures of Merit and Constraints
No
Yes
2/24/2008
ELF
81
High Specific Impulse Is Indicative of Lower Fuel /
Propellant Consumption
ISP, Specific Impulse, Thrust / ( Fuel or Propellant
Weight Flow Rate ), S
4,000
Turbojet: ISP typically constrained by turbine temperature limit
3,000
Ramjet: ISP typically constrained by
combustor insulation temperature limit
2,000
Scramjet: ISP typically
constrained by thermal choking
1,000
Solid Rocket: ISP typically constrained
by safety
Ducted Rocket
0
0
2
4
6
8
10
12
Mach Number
2/24/2008
ELF
82
Cruise Range Is Driven by L/D, Isp, Velocity, and
Propellant or Fuel Weight Fraction
R = ( L / D ) Isp V In [ WL / ( WL – WP )] , Breguet Range Equation
Typical Value for 2,000 lb Precision Strike Missile
Parameter
Subsonic Turbojet
Missile
Liquid Fuel
Ramjet Missile
Hydrocarbon Fuel
Scramjet Missile Solid Rocket
L / D, Lift / Drag
10
5
3
5
Isp, Specific Impulse
3,000 s
1,300 s
1,000 s
250 s
VAVG , Average Velocity
1,000 ft / s
3,500 ft / s
6,000 ft / s
3,000 ft / s
WP / WL, Cruise Propellant or
Fuel Weight / Launch Weight
R, Cruise Range
0.3
0.2
0.1
0.4
1,800 nm
830 nm
310 nm
250 nm
Note:
2/24/2008
Ramjet and Scramjet missiles booster propellant for Mach 2.5 to 4 take-over speed not included in WP
for cruise. Rockets require thrust magnitude control ( e.g., pintle, pulse, or gel motor ) for effective cruise.
Max range for a rocket is usually a semi-ballistic flight profile, instead of cruise flight. Multiple stages may
be required for rocket range greater than 200 nm.
ELF
83
( T / W )Max , ( Thrust / Weight )Max
Solid Rockets Have High Acceleration Capability
1,000
Solid Rocket
.
TMax = 2 Pc At = m Ve
100
10
Ramjet
Turbojet
TMax = (π / 4 ) d2 ρ0 V02 [( Ve / V0 ) 1]
1
0
1
TMax = (π / 4 ) d2 ρ0 V02 [( Ve / V0 ) 1]
2
3
4
5
M, Mach Number
Note:
.
Pc = Chamber pressure, At = Nozzle throat area, m = Mass flow rate
d = Diameter, ρ0 = Free stream density, V0 = Free stream velocity,
Ve = Nozzle exit velocity ( Turbojet: Ve ~ 2,000 ft / s, Ramjet: Ve ~ 4,500 ft / s, Rocket: Ve ~ 6,000 ft / s )
2/24/2008
ELF
84
Turbojet Nomenclature
Inlet
Compressor
Combustor
Turbine
Nozzle
0
Free Stream
1
2
3
Compressor Entrance
Compressor Exit
Inlet Entrance
2/24/2008
5
4
Turbine Exit
Turbine Entrance
ELF
85
High Temperature Compressors Are Required to
Achieve High Pressure Ratio at High Speed
T3, Compressor Exit Temperature, R
T3 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M02 }( p3 / p2 )( γ3 - 1 ) / γ3
p3 / p2 = 1
p3 / p2 = 2
p3 / p2 = 5
p3 / p2 = 10
γ0 = 1.4, γ3 ≈ 1.29 + 0.16 e-0.0007 T3
3000
Note: Ideal inlet; ideal compressor; low subsonic,
isentropic flow
2000
T3
1000
Example:
M0 = 2, h = 60k ft ( T0 = 398 R )
p3 / p2 = 5 ⇒ T3 = 1118 R, γ3 = 1.36
0
0
1
2
3
4
M0, Free Stream Mach Number
T3 = Compressor exit temperature in Rankine, T0 = free stream temperature in Rankine, γ = specific heat
ratio, M0 = free stream Mach number, p3 = compressor exit pressure, p2 = compressor entrance pressure
2/24/2008
ELF
86
High Turbine Temperature Is Required for High
Speed Turbojet Missiles
T4,Turbojet Turbine Temperature, R
T4 ≈ T3 + ( Hf / cp ) f / a, T in R
T3 = 500 R
T3 = 1000 R
T3 = 2000 R
T3 = 4000 R
cp4 ≈ 0.122 T40.109, cp in BTU / lb / R
5000
4000
3000
T4
2000
Example:
M0 = 2, h = 60K ft ( T0 = 398 R ),
p3 / p2 = 5 ⇒ T3 = 1118 R
1000
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
RJ-5 fuel ( Hf = 14,525 BTU / lb ),
cp = 0.302 BTU / lb / R , f / a =
0.067 ( stochiometric ) ⇒ T4 =
1118 + ( 14525 / 0.302 ) 0.067 =
4,340 R
f / a, Fuel-to-Air Ratio
T4 = Turbojet turbine entrance temperature in Rankine, T3 = compressor exit temperature in Rankine,
Hf = heating value of fuel, cp = specific heat at constant pressure, f / a = fuel-to-air ratio
2/24/2008
ELF
87
Turbine Material Temperature Limit Is a
Constraint for a High Speed Turbojet Missile
Max Short
Duration Temp
Turbine Material
Temperature Constrained
Turbines for Mach 4 Cruise
ISP for Mach
4 Cruise
≈ 3,000R
Nickel Super Alloys
Very Highly Constrained Turbojet,
Air Turbo Rocket, Turbo Ramjet
≈ 1,000 s
≈ 3,000R
Titanium Aluminides ( lighter
weight than nickel super alloys )
Very Highly Constrained Turbojet,
Air Turbo Rocket, Turbo Ramjet
≈ 1,000 s
≈ 3,500R
Single Crystal Nickel
Aluminides
Highly Constrained Turbojet
≈ 1,200 s
≈ 4,000R
Ceramic Matrix Composites
Moderately Constrained Turbojet
≈ 1,500 s
≈ 4,500R
Rhenium Alloys
Moderately Constrained Turbojet
≈ 2,000 s
≈ 5,000R
Tungsten Alloys
Slightly Constrained Turbojet
≈ 2,500 s
Note: Constrained turbojet for Mach 4 cruise imposes a limit on turbine temperature that is less than ideal. Constraints
could consist of a combination of:
• Constraint on compressor pressure ratio to limit turbine temperature
• Constraint on fuel-to-air ratio to limit turbine temperature
• Use of afterburner to limit turbine temperature
2/24/2008
ELF
88
Turbine-Based Missiles Are Capable of Subsonic
to Supersonic Cruise
Turbojet
SS-N-19 Shipwreck
Firebee II
Turbo Ramjet
Regulus II
SR-71
Air Turbo Rocket
2/24/2008
ELF
89
Compressor Pressure Ratio for Maximum Thrust
Turbojet Is Limited by Turbine Temperature
( p3 / p2 )@Tmax ≈ {( T4 / T0 )1/2 / { 1 + [( γ0 - 1 ) / 2 ] M02 }}γ4 / ( γ4 - 1 )
( p3 / p2 )@Tmax
Assumptions: Ideal turbojet ( isentropic inlet, compressor, turbine, nozzle; low subsonic and constant pressure
combustion; exit pressure = free stream pressure )
100
10
Example:
M0 = 2.0, h = 60k ft (T0 = 390 R ) , T4 = 3,000 R,
γ4 = 1.31
( p3 / p2 )@Tmax = {{ ( 3000 / 390 )1/2 / { 1 + [( 1.4 1 ) / 2 ] 2.02 }}1.31/ ( 1.31 – 1 ) = 6.31
1
Note:
0
0.5
1
1.5
2
2.5
3
M0, Mach Number
T4 = 2000 R
T4 = 4000 R
3.5
4
T0 = Free stream temperature
T4 = Turbine entrance temperature
T4 = 3000 R
T4 = 5000 R
γ = Specific heat ratio
Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974
2/24/2008
ELF
90
Turbojet Thrust Is Limited by Turbine Maximum
Allowable Temperature
.
Note:
.
( T / m )IdealMax = Ve – V0
Assumption: Ideal turbojet
20
Ve = { 2 cp T5t [ 1 – ( p0 / p5t )( γ5 - 1 ) / γ5 ]}1/2
T5t ≈ T4 – T3 + T2
T3 ≈ T2 ( p 3 / p 2 ) ( γ 3 - 1 ) / γ 3
15
=1
)
T2 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M02 }
/p
2
p5t ≈ p4 ( T5 / T4 )γ4 / ( γ4 - 1 )
p4 = p 3
je t
(p
3
10
p2 ≈ p0 { 1 + [( γ0 - 1 ) / 2 ] M02 }γ0 / ( γ0 - 1 )
Ram
Tmax / [( p0 ) ( A0 )], Nondimensional Maximum
Thrust
TIdealMax / ( p0 A0 ) = ( γ0 M0 / a0 ) ( T / m )IdealMax
p0 = Free stream static pressure
5
A0 = Free stream flow area into inlet
T4 = Turbine entrance temperature
0
0
1
2
3
M0, Mach Number
T4 = 2000 R
T4 = 4000 R
T4 = 3000 R
T4 = 5000 R
4
Example: M0 = 2, h = 60 k ft ( T0 = 390 R, p0
= 1.047 psi ), T4 = 3,000 R, γ4 = 1.31, ( p3 /
p2 )@Tmax = 6.31, p2 = 8.19 psi, p3 = 51.7 psi,
A0 = 114 in2, T2 = 702 R, T3 = 1133 R, γ3 =
1.36
p5t = 23.0 psi, Ve =
T5t = 2569 R, γ5 = 1.32,
.
4524 ft / s, ( T / m )IdealMax = 2588 ft / s,
TIdealMax / p0 A0 = 7.49
TIdealMax = 7.49 ( 1.047 ) ( 114 ) = 894 lb
2/24/2008
ELF
91
Turbojet Specific Impulse Decreases with
Supersonic Mach Number
( ISP )Ideal@Tmax gc cp T0 / ( a0 Hf ) = TIdealMax T0 / [( p0 A0 γ0 M0 ) ( T4 – T3 )]
( ISP )Ideal ( gc ) ( cp ) ( T0) / [ ( a0 ) ( Hf )],
Nondimensional Ideal Specific Impulse
Assumptions: Ideal turbojet ( isentropic inlet, compressor, turbine, nozzle; flow, low subsonic, constant pressure combustion;
exit pressure = free stream pressure), max thrust
Example:
0.8
0.6
Ra
mje
M0 = 2, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s
), RJ-5 fuel ( Hf = 14,525 BTU / lbm ), T4 =
3,000 R, cp = 0.293 BTU / lbm / R, γ0 = 1.4
t(p
3
/p
0.4
2
=1
Calculate ( ISP )Ideal@Tmax gc cp T0 / ( a0 Hf ) =
0.559
( ISP )Ideal@Tmax = 0.559 ( 968 ) ( 14525 ) / [ 32.2
( 0.293 ) ( 390 )] = 2136 s
)
Note:
gc = Gravitational constant = 32.2
0.2
cp = Specific heat at constant pressure
T0 = Free stream temperature
0
0
1
2
3
M0, Mach Number
T4 = 2000 R
T4 = 4000 R
4
a0 = Free stream speed of sound
Hf = Heating value of fuel
TIdealMax = Ideal maximum thrust
T4 = 3000 R
T4 = 5000 R
γ = Specific heat ratio
T4 = Combustor exit temperature
T3 = Compressor exit temperature
2/24/2008
ELF
92
Tactical Missile Ramjet Propulsion Alternatives
Liquid Fuel Ramjet
Rocket Boost Inboard Profile
Ramjet Sustain Inboard Profile
Note:
Booster Propellant
Fuel
Solid Fuel Ramjet
Boost
Sustain
Solid Ducted Rocket
Boost
Sustain
2/24/2008
ELF
93
High Specific Impulse for a Ramjet Occurs Using
High Heating Value Fuel at Mach 3 to 4
( ISP )Ideal gc cp T0 / ( a0 Hf ) = { M0 {{( T4 / T0 ) / { 1 + [( γ0 - 1 ) / 2 ] M02 }}1/2 - 1 } / {{ 1 + [( γ0 - 1 ) / 2 ] M02 } {( T4 / T0 ) / {
1 + [( γ0 - 1 ) / 2 ] M02 }} – 1 }
( ISP )Ideal ( gc ) ( cp ) ( T0) / [ ( a0 ) ( Hf )],
Nondimensional Ideal Specific Impulse
Assumptions: Ideal ramjet, isentropic inlet and nozzle, low subsonic and constant pressure combustion, exit pressure = free
stream pressure, φ ≤ 1
Example for Ramjet Baseline:
0.6
M = 3.5, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s ),
RJ-5 fuel ( Hf = 14,525 BTU / lbm ), T4 = 4,000 R,
cp = 0.302 BTU / lbm / R, γ0 = 1.4
Calculate ( ISP )Ideal gc cp T0 / ( a0 Hf ) = { 3.5 {{(
4000 / 390 ) / { 1 + [( 1.4 - 1 ) / 2 ] 3.52 }}1/2 - 1 } / {{
1 + [( 1.4 - 1 ) / 2 ] 3.52 } {( 4000 / 390 ) / { 1 + [(
1.4 - 1 ) / 2 ] 3.52 }} – 1 } = 0.372
0.4
( ISP )Ideal = 0.372 ( 968 ) ( 14525 ) / [ 32.2 ( 0.302 ) (
390 ) = 1387 s
0.2
Note:
gc = Gravitational constant = 32.2
cp = Specific heat at constant pressure
0
0
1
2
3
4
M0, Free Stream Mach Number
T4 / T0 = 3
T4 / T0 = 10
T4 / T0 = 5
T4 / T0 = 15
5
T0 = Free stream temperature
a0 = Free stream speed of sound
Hf = Heating value of fuel
γ = Specific heat ratio
T4 = Combustor exit temperature
Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974
2/24/2008
ELF
94
High Thrust for a Ramjet Occurs from Mach 3 to
5 with High Combustion Temperature
TIdeal / ( φ p0 A0 ) = γ0 M02 {{[ T4 / T0 ] / { 1 + [( γ0 - 1 ) / 2 ] M02 }}1/2 - 1 }
Assumptions: Ideal ramjet, isentropic inlet and nozzle, low subsonic and constant pressure
combustion, exit pressure = free stream pressure, φ ≤ 1
T / [ PHI ( p0 ) (A0 ) ], Nondimimensional
Thrust
25
Note: T4 and T0 in R
Example for Ramjet Baseline:
20
M0 = 3.5, α = 0 deg, h = 60k ft ( T0 = 390 R, p0 =
1.047 psi ), T4 = 4,000 R, ( f / a ) = 0.055, φ =
0.82, A0 = 114 in2, γ0 = 1.4
15
TIdeal / ( φ p0 A0 ) = 1.4 ( 3.5 )2 {{[ 4000 / 390 ] / { 1
+ [( 1.4 – 1 ) / 2 ] ( 3.5 )2 }}1/2 – 1 } = 12.43
TIdeal = 12.43 ( 0.82 ) ( 1.047 ) ( 114 ) = 1216 lb
10
Note:
( T )Ideal = Ideal thrust
p0 = Free stream static pressure
5
A0 = Free stream flow area into inlet
γ0 = Free stream specific heat ratio
0
0
1
2
3
4
M0, Free Stream Mach Number
T4 / T0 = 3
T4 / T0 = 10
T4 / T0 = 5
T4 / T0 = 15
5
M0 = Free stream Mach number
T4 = Combustor exit temperature
T0 = Free stream temperature
φ = Equivalence ratio = fuel-to-air ratio /
stochiometric fuel-to-air ratio
Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974
2/24/2008
ELF
95
Ramjet Combustor Temperature Increases with
Mach Number and Fuel Flow
T4 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M02 } + ( Hf / cp ) ( f / a )
T4, Combustor Exit Temperature for RJ-5
Fuel, Rankine
Assumptions: Low subsonic combustion. No heat transfer through inlet ( isentropic
flow ). φ ≤ 1.
T4 = combustor exit temperature in Rankine, T0 = free stream temperature in Rankine,
γ = specific heat ratio, M0 = free stream Mach number, Hf = heating value of fuel, cp =
specific heat at constant pressure, f / a = fuel-to-air ratio.
6000
Example:
•M0 = 3.5
4000
•h = 60k ft ( T0 = 390 R )
•RJ-5 fuel ( Hf = 14,525 BTU / lb / R )
•f / a = 0.055
2000
•γ0 = 1.4
•cp = 0.122 T0.109 BTU / lbm / R.
Note: cp ≈ 0.302 +/- 5% if 2500 R < T < 5000 R
0
0
1
2
3
4
5
•Then T4 = 390 { 1 + [( 1.4 – 1 ) / 2 ] ( 3.5 )2 } +
[( 14525 ) / ( 0.302 )] 0.055 = 3,991 R
M0, Free Stream Mach Number
f / a = 0.01
2/24/2008
f / a = 0.03
f / a = 0.05
f / a = 0.067
Note: ( f / a )φ = 1 ≈ 0.067 for stochiometric combustion of liquid hydrocarbon fuel, e.g., RJ-5.
ELF
96
Ramjet Combustor Entrance Mach Number
Should Be Low, to Avoid Thermal Choking
( M3 )TC = {{ - b + [ b2 – 4 γ32 ]1/2 } / ( 2 γ32 )}1/2
b = 2 γ3 + ( T4t / T0 )( 1 + γ4 )2 / {( 1 + 0.2 M02 )[ 1 + ( γ4 – 1 ) / 2 ]}
Assumptions: Constant area combustion, [( γ 3 – 1 ) / 2 ] M32 << 1, isentropic inlet
( M3 )TC, Combustor Entrance Mach
Number with Thermal Choking
0.4
Example:
M0 = 2, h = 60k ft ( T0 = 390 R ), T4t = 4,000 R, γ0 = 1.4
γ4 = 1.29 + 0.16 e-0.0007 ( 4000 ) = 1.300
0.3
T0t = ( 1 + 0.2 M02 ) T0 = 702 R
γ 3 = 1.29 + 0.16 e-0.0007 ( 702 ) = 1.388
b = 2 ( 1.388 ) + ( 4000 / 390 )( 1 + 1.300 )2 / {( 1 + 0.2
( 22 )[ 1 + ( 1.300 – 1 ) / 2 ]} = - 24.211
0.2
( M3 )TC = {{ 24.211 + [( -24.211 )2 – 4 ( 1.3882 )
]1/2 } / [ 2 ( 1.3882 )]}1/2 = 0.204
0.1
Note:
( M3 )TC = Combustor entrance Mach number with
thermal choking ( M4 = 1 )
0
0
1
2
3
4
5
M0 = Free stream Mach number
M0, Free Stream Mach Number
T4t / T0 = 3
T4t / T0 = 10
2/24/2008
γ3 = Specific heat ratio at combustor entrance
T4t / T0 = 5
T4t / T0 = 15
ELF
T4t = Combustor exit total temperature
T0 = Free stream static temperature
γ4 = Specific heat ratio in combustion
97
A Ramjet Combustor with a Low Entrance Mach
Number Requires a Small Inlet Throat Area
AIT / A3 = [( γ + 1 ) / 2 ]( γ + 1 ) / [ 2 ( γ - 1 )] M3 {[ 1 + ( γ - 1 ) / 2 ] M32 }-( γ + 1 ) / [ 2 ( γ - 1 )] = ( 216 / 215 ) M3 ( 1 + M32 / 5 )-3
Assumptions: Isentropic inlet, MIT = 1, γ = 1.4
Note:
M3, Combustor Entrance Mach Number
1
AIT = Inlet throat area
A3 = Combustor entrance area
0.8
M3 = Combustor entrance Mach number
γ = Specific heat ratio
Example:
0.6
Ramjet Baseline
AIT = 41.9 in2
0.4
A3 = 287 in2
AIT / A3 = 41.9 / 287 = 0.1459
0.2
Assume sonic flow ( M = 1 ) at AIT
M3 = 0.085
M3 = 0.085 < ( M3 )TC = 0.204
0
0
0.2
0.4
0.6
0.8
1
( A )IT / A3, Inlet Throat Area to Combustor Area Ratio
2/24/2008
ELF
98
Typical Ramjet Has Nearly Constant Pressure
Combustion
Assume Rayleigh Flow, with Heat Addition at
Constant Area
Negligible Friction
Pressure Loss in Combustor is Given by
p4 / p3 = ( 1 + γ3 M32 ) / ( 1 + γ4 M42 )
Mach Number Increase in Combustor Is Given by
T4t / T0 = [( 1 + γ3 M32 ) / ( 1 + γ4 M42 )]2 ( M4 / M3 )2 { 1 + [( γ4 – 1 ) / 2 ] M42 } / { 1 + [( γ3 – 1 ) / 2 ] M32 }
From Prior Example
M0 = 2, h = 60k ft ( T0 = 390 R ), T4t = 4,000 R, γ0 = 1.4, γ4 = 1.300, and γ 3 = 1.388
Assume Ramjet Baseline with Sonic Inlet Throat
AIT / A3 = 41.9 / 287 = 0.1459 ⇒ M3 = 0.085
Solving Above Equations
M4 = 0.304
p4 / p3 = 0.902
Assumption of Nearly Constant Pressure Combustion Is Reasonably Accurate
10% error
2/24/2008
ELF
99
Minimum Length for the Combustor Is a
Function of Combustion Velocity
( lcomb )min = tcomb Vcomb
Minimum Combustor Length, ft
10
tcomb = 0.001 s
tcomb = 0.002 s
tcomb = 0.004 s
1
Example for tcomb = 0.002 s and
Subsonic Combustion Ramjet:
•Vcomb = 200 ft / s
0.1
•( lcomb )min = 0.002 ( 200 ) = 0.4 ft
100
1000
10000
Vcomb, Combustion Velocity, ft / s
Example for tcomb = 0.002 s and
Scramjet:
•Vcomb = 3,000 ft / s
•( lcomb )min = 0.002 ( 3000 ) = 6.0 ft
2/24/2008
ELF
100
Ramjet Engine / Booster Integration Options
Fuel
Boost Propellant
Low Cruise Drag ( Modern Ramjets )
Integral-Rocket Ramjet ( IRR )
Aft Drop-off Booster
Forward Booster
Podded Drop-off Booster
High Cruise Drag
Podded Ramjet
Podded IRR
Podded Ramjet, Aft Drop-off Booster
Source: Kinroth, G.D. and Anderson, W.R., “Ramjet
Design Handbook,” CPIA Pub. 319, June 1980
2/24/2008
ELF
101
Inlet
Compatibility
Cost
Carry Drag
Cruise Drag
Ejectables
Weight
Diameter
Length
Selection Factors
Cycle
Compatibility
Ramjet Engine / Booster Integration Trades
Integral Rocket – Ramjet ( IRR )
Aft Booster ( Drop-off )
–
–
Forward Booster
–
Podded Booster ( Drop-off )
–
Podded Ramjet
–
–
–
–
–
–
Podded IRR
Podded Ramjet
Aft Booster ( Drop-off )
–
Superior
–
–
–
Above Average
–
–
–
Average – Below average
Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980
2/24/2008
ELF
102
Ramjets with Internal Boosters and No Wings
Have Low Drag
1.2
• Podded Ramjet
CD0 = DO / ( q SREF ), Zero-Lift Drag
Coefficient
• Podded IRR
• Podded Ramjet, Aft Drop
Off Booster
• IRR
• Aft Drop Off Booster
• Forward Booster
• Podded Drop Off Booster
• IRR
• Aft Drop-off Booster
0.8
With Wings
CD0
Without Wings
0.4
• Forward Booster
• Podded Drop-off Booster
0
Note:
Nose Fineness Ratio ≥ 2.25
Nose Bluntness Ratio ≤ 0.20
2
3
4
5
M, Mach Number
Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980
2/24/2008
ELF
103
Ramjet Inlet Options
Type Inlet
Sketch
Placement
Nose
Nose-full axisymmetric
Forward underside in nose compression fieldpartial axisymmetric
Forward in nose compression field-cruciform ( four )
axisymmetric
Chin
Forward Cruciform
Axisymmetric
Aft Cruciform
Axisymmetric
Aft-cruciform ( four ) axisymmetric
Under Wing Axisymmetric
In planar wing compression field-twin axisymmetric
Twin Two-dimensional
Aft-twin cheek-mounted two dimensional
Underslung Axisymmetric
Aft underside-full axisymmetric
Underslung Twodimensional
Aft underside-belly mounted two dimensional
Cruciform Two-dimensional
Aft-cruciform ( four ) two dimensional
Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980.
2/24/2008
ELF
104
Ramjet Inlet Concept Trades
Prime
Mission
Suitability
–
STT
W, C
ATS, STA
–
BTT
STT
T
T
ATS, ATA, STA
ATS, ATA, STA
STT
T
ATS
BTT
T
ATS, ATA, STA
BTT
T
ATS, ATA, STA
BTT
T
ATS
BTT
T
ATS, ATA, STA
STT
T
ATS
inlet Cost
Preferred
Control
Warhead
Shrouding
Preferred
Steering
–
Drag
Weight
Alpha
Capability
Carriage
Envelope
Recovery
Type Inlet
Pressure
Selection Factors
–
–
–
–
–
Note:
BTT = Bank to Turn
STT = Skid to Turn
W = Wing C = Canard
T = Tail
Superior
Above Average
–
Average – Below average
Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980
2/24/2008
ELF
105
Current Supersonic Air-breathing Missiles Have
Either a Nose Inlet or Axisymmetric Aft Inlets
United Kingdom
Sea Dart GWS-30
France
ASMP
ANS
AS-17 / Kh-31
Kh-41
SS-N-22 / 3M80
SA-6
SS-N-19
SS-N-26
C-101
C-301
Russia
China
Taiwan
Hsiung Feng III
India
BrahMos
• Aft inlets have lower inlet volume and do not degrade lethality of forward located warhead.
• Nose Inlet may have higher flow capture, pressure recovery, smaller carriage envelope, and lower drag.
2/24/2008
ELF
106
Shock on Inlet Cowl Lip Prevents Spillage
Inlet w/o External Compression
Inlet Swallows 100% of the Free
Stream Flow
External Compression Required for
Efficient Pressure Recovery if Mach
Number > 2 and Inlet Start at Low
Supersonic Mach number
External Compression Inlet ( with
Spillage )
Spillage
Shocks
Shocks Converge Outside Inlet Lip
( Results in Spillage Air )
External Compression Inlet ( w/o
Spillage )
Shocks
Inlet Swallows 100% of the Free
Stream Flow
2/24/2008
Shocks Converge at Inlet Lip ( Inlet
Captures Maximum Free Stream
Flow )
ELF
107
Shock Wave Angle Increases with Deflection
Angle and Decreases with Mach Number
tan ( α + δ ) = 2 cot θ2D ( M2 sin2 θ2D – 1 ) / [ 2 + M2 ( γ + 1 – 2 sin2 θ2D )] , for 2D flow, perfect gas
Theta, 2D Shock Wave Angle @ Gamma =
1.4, Degrees
Note: θ2D = 2D shock wave angle, M = Mach number, α = angle of attack, δ = body deflection angle, γ = specific heat
ratio, θconical ≈ 0.81 θ2D
50
Example for Ramjet Baseline:
40
α
30
θ
20
δ = 17.7 deg, M = 3.5, α = 0 deg, γ = 1.4
⇒ θ2D = 32 deg
10
θconical ≈ 0.81 θ2D = 0.81 ( 32 ) = 26 deg
Approximate estimate of θ:
0
0
5
10
15
20
Alpha + Delta, Deflection Angle, Degrees
Mach 2 ( Deltamax = 23 deg )
Mach 5 ( Deltamax = 41 deg )
2/24/2008
δ
θ2D ≈ μ + α + δ = sin-1 ( 1 / M ) + α + δ
θconical ≈ 0.81 θ2D = 0.81 [ sin-1 ( 1 / M ) +
α+δ]
Mach 3 ( Deltamax = 34 deg )
ELF
108
Capture Efficiency of an Inlet Increases with Mach
Number
( A0 / Ac )conical = ( h / l ) ( 1 + δ M + αM ) / [( 1 – 0.23δM + αM )( δ + h / l )] , conical nose with forward inlet
( A0 / Ac )2D = ( h / l ) ( 1 + δ M + αM ) / [( 1 + αM )( δ + h / l )] , 2D nose with forward inlet
Note: A0 / Ac ≤ 1, AC = inlet capture area, A0 = free stream flow area, δ = defection angle in rad, h = inlet height, l =
distance from nose tip to inlet
A0 / Ac, Baseline Ramjet Inlet Capture
Efficiency
1
α
δ
stream
lin
A0
streamline
Ac
streamline
0.8
e
oblique shock
0.6
body
h inlet
stream
lin
e
Example for baseline ramjet ( conical
nose )
0.4
h = 3 in
0.2
l = 23.5 in
h / l = 0.1277
AC = 114 in2
0
0
1
2
3
4
Alpha = 0 Deg
5
δ = 17.7 deg ( 0.3089 rad )
M = 3.5, α = 0 deg
M, Mach Number
2/24/2008
nose
Alpha = 10 Deg
ELF
A0 / Ac = 0.81 ⇒ A0 = 92 in2
Spillage = Ac - A0 = 114 - 92 = 22 in2
109
Isentropic Compression Allows Inlet Start at
Lower Mach Number
AIT / A0 = 1.728 ( MIE )start [ 1 + 0.2 ( MIE )start2 )-3, Assumptions: 2-D inlet, Isentropic flow through inlet ( n = ∞ ), γ = 1.4
AIT / A0 = ( MIE )start {[ 0.4 ( MIE )start2 + 2 ] / [ 2.4 ( MIE )start2 ]3.5 }{[2.8 ( MIE )start2 – 0.4 ] / 2.4 }2.5 {[ 1.2 / ( 1 + 0.2 (
MIE )start2 ]}3, Assumptions: 2-D inlet, single normal shock ( n = 1 ), γ = 1.4
( M )IE, Inlet Entrance Start Mach
Number
Note: AIT = inlet throat area, A0 = free stream flow area, ( MIE )start = inlet entrance start Mach number, γ = specific heat
ratio, n = number of shocks
4
Example for ramjet baseline
n=∞
3
AIT = 0.29 ft2
n=1
Ac = 114 in2 = 0.79 ft2 ⇒ AIT / Ac = 0.367
Process:
1. Assume ( MIE )start
2
2. Compute capture efficiency AIT / A0
3. Compute ( MIE )start and compare with
assumed ( MIE )start
1
4. Iterate until convergence
Limit for isentropic compression
0
0
0.2
0.4
0.6
0.8
AIT / A0
Inlet Start for Isentropic Compression
Inlet Start for Single Normal Shock
2/24/2008
ELF
1
- From Prior Figure, A0 / Ac = 0.53
- Compute AIT / A0 = ( AIT / Ac ) / ( A0 / Ac ) =
0.367 / 0.53 = 0.69 ⇒ ( MIE )start = 1.8
Ramjet baseline has mixed compression
with n = 5. Actual inlet start Mach
number is ( MIE )start > 1.8
110
Forebody Shock Compression Reduces the Inlet
Entrance Mach Number
( MIE )2D = {{ 36 M04 sin2 θ2D - 5 [ M02 sin2 θ2D - 1 ][ 7 M02 sin2 θ2D + 5 ]} / {[ 7 M02 sin2 θ2D - 1 ][ M02 sin2 θ2D + 5 ]}}1/2
tan ( α + δ ) = 2 cot θ2D ( M02 sin2 θ2D – 1 ) / [ 2 + M02 ( 2.4 – 2 sin2 θ2D )]
Assumptions: 2D flow, perfect gas, γ = specific heat ratio = 1.4
Note: MIEt= inlet entrance Mach number, M0 = free stream Mach number, θ = oblique shock angle, α = angle of attack, δ = body
deflection angle
( M )IE, Inlet Entrance Mach Number
4
Example for ramjet baseline
3
δ = 17.7 deg
( MIE )start = 1.8 ( from prior example )
2
Compute M0 = 2.55
Note: Ramjet baseline forebody is
conical, not 2D
1
0
0
10
20
30
40
Alpha + Delta, Local Angle of Attack at Inlet Entrance, Deg
M0 = 2
2/24/2008
M0 = 3
M0 = 5
ELF
111
Optimum Forebody Deflection Angle(s) for Best
Pressure Recovery Increases with Mach Number
Note: δTotal = Total deflection angle,
δ1 = 1st deflection angle, δ2 = 2nd
deflection, δ3 = 3rd deflection.
First External Shock
Second External Shock
Optimum Total Deflection Angle, Deg
δ2
60
Optimum deflection angle provides
equal loss in total pressure across
each shock wave.
δTotal
Optimum deflection angles are
nearly equal for M > 4.
δ1
12.1, 15.2, 19.4
11.1, 13.0, 15.5
40
16.1, 22.1
15.0, 18.8
7.6, 8.2, 8.2
10.4, 11.2
20
Example: Optimum forebody deflection angles for
double wedge ( n = 3 ) at Mach 2: δ1 = 10.4 deg, δ2
= 11.2 deg ⇒ δtotal = 10.4 + 11.2 = 21.6 deg
0
0
1
2
3
4
M0, Free Stream Mach Number
n=1
2/24/2008
n=2
n=3
n=4
Isentropic Compression
Reference: “Technical Aerodynamics Manual,” North American Rockwell Corporation, DTIC AD 723823, June 1970.
ELF
112
Oblique Shocks Prior to the Inlet Normal Shock
Are Required to Satisfy MIL-E-5008B
MIL-E-5008B Requirement: ptInlet / pt0 = 1 – 0.075 ( M – 1 )1.35
PtInlet / pt0, Inlet Total Pressure
Ratio
1
n = 1 ( Normal Shock )
n = 2 ( 1 Optimum Oblique
Shock + Normal Shock )
n = 3 ( 2 Opt Oblique
Shocks + Normal Shock )
n = 4 ( 3 Opt Oblique
Shocks + Normal Shock
Ideal Isentropic Inlet
0.1
MIL-E-5008B
0.01
Note: 2D flow assumed
0
1
2
3
4
M, Mach Number
5
pt
Inlet
= Inlet total pressure
pt = Free stream total pressure
0
Example: MIL-E-5008B requirement for Mach 3.5 ( pt / pt = ηinlet = 0.74 ) can be satisfied only if there are more
Inlet
0
than three oblique shocks prior to inlet normal shock.
Source for Optimum 2D Shocks: Oswatitsch, K.L., “Pressure Recovery for Missiles with Reaction Propulsion at High
Supersonic Speeds”, NACA TM - 1140, 1947.
2/24/2008
ELF
113
High Density Fuels Provide Higher Volumetric
Performance but Have Higher Observables
Type Fuel
Density,
lb / in3
Volumetric
Performance,
BTU / in3
Low
Observables
Turbine ( JP-4, JP-5, JP-7, JP-8, JP-10 )
~ 0.028
559
Liquid Ramjet ( RJ-4, RJ-5, RJ-6, RJ-7 )
~ 0.040
581
HTPB
~ 0.034
606
Slurry ( 40% JP-10 / 60% carbon )
~ 0.049
801
Solid Carbon ( graphite )
~ 0.075
1132
–
Slurry ( 40% JP-10 / 60% aluminum )
~ 0.072
866
–
Slurry ( 40% JP-10 / 60% boron carbide )
~ 0.050
1191
–
Solid Mg
~ 0.068
1200
–
Solid Al
~ 0.101
1300
–
Solid Boron
~ 0.082
2040
–
2/24/2008
Superior
Above average
ELF
Average
– Below average
114
Ducted Rocket Design Implications
Excess Fuel from Gas Generator
~ 30 % ⇒ Behaves more like a rocket ( higher burn rate, higher burn
temperature, lower ISP )
~ 70 % ⇒ Behaves more like a ramjet ( higher ISP, lower burn rate, lower
burn temperature )
Choice of Fuel
Metal ( e.g., B, Al, Mg ) ⇒ Higher ISP, higher density, deposits, higher
observables
Carbon based ( e.g., C, HTPB ) ⇒ Lower observables, higher reliability,
lower ISP
Choice of Oxidizer
AP ⇒ Higher burn rate, lower hazard, HCl contrail
Min Smoke ( e.g., HMX, RDX ) ⇒ Lower Observables, lower heating value,
lower burn rate, hazardous
Thrust Magnitude Control Approaches
Pintle or valve in gas generator throat
Retractable wires in grain
2/24/2008
ELF
115
High Propellant Fraction Increases Burnout
Velocity
5000
ΔV = -gc Isp ln (1 - Wp / Wi)
Assumption: T >> D, T >> W sin γ, γ = const
4000
Isp = 250 s
ΔV, Missile
3000
Isp = 200 s
Incremental
Burnout Velocity,
2000
ft / s
Example: Rocket Baseline
Wi,boost = WL = 500 lb, Wp, boost = 84.8 lb
ISP, boost = 250 s
WP, boost / Wi = 84.8 / 500 = 0.1696
ΔV = -32.2 ( 250 ) ln ( 1 - 0.1696 ) = 1496 ft / s
1000
0
0
0.1
0.2
0.3
0.4
0.5
WP / Wi, Propellant Weight / Initial Missile Weight
2/24/2008
ELF
116
High Specific Impulse Requires High Chamber
Pressure and Optimum Nozzle Expansion
ISP = cd {{[ 2 γ2 / ( γ - 1 )] [ 2 / ( γ + 1 )] ( γ + 1 ) / ( γ - 1 ) [ 1 – ( pe / pc ) ( γ - 1 ) / γ ]}1/2 + ( pe / pc ) ε - ( p0 / pc ) ε } c* / gc
.
T = w p ISP = ( gc / c* ) pc At ISP
Isp, Specific Impulse of Rocket Baseline, s
ε = {[ 2 / ( γ + 1 )]1 / ( γ - 1 ) [( γ -1 ) / ( γ + 1 )]1/2 } / {( pe / pc )1 / γ [ 1 - ( pe / pc ) ( γ - 1 ) / γ ]1/2 }
Note:
ε = nozzle expansion ratio
pe = exit pressure
pc = chamber pressure
p0 = atmospheric pressure
.
w P = propellant weight flow rate
At = nozzle throat area ( minimum, sonic, choked )
γ = specific heat ratio = 1.18 in figure
cd = discharge coefficient = 0.96 in figure
c* = characteristic velocity = 5,200 ft / s in figure
h = 20k ft, p0 = 6.75 psi in figure
Example for Rocket Baseline:
300
250
ε = Ae / At = 6.2 ⇒ pe / pc = 0.02488, At = 1.81 in2
200
0
10
20
30
Nozzle Expansion Ratio
pc = 300 psi
pc = 2000 psi
( pc )boost = 1769 psi, pe = 44 psi, ( ISP )boost = 257 s
( ISP )ε = 6.2 / ( ISP )ε = 1 = 257 / 200 = 1.29
( T )boost = ( 32.2 / 5200 ) ( 1769 ) (1.81 )( 257 ) = 5096 lb
pc = 1000 psi
pc = 3000 psi
( pc )sustain = 301 psi, pe = 7.49 psi, ( ISP )sustain = 239 s
( ISP )ε = 6.2 / ( ISP )ε = 1 = 240 / 200 = 1.20
( T )sustain = ( 32.2 / 5200 ) ( 301 ) (1.81 )( 240 ) = 810 lb
2/24/2008
ELF
117
High Propellant Weight Flow Rate Requires High
Chamber Pressure and Large Nozzle Throat
.
(pc)At, Chamber Pressure x Nozzle
Throat Area, lb
w p = gc pc At / c*
100000
10000
c* = 4800 ft / s
c* = 5200 ft / s
c* = 5600 ft / s
1000
Rocket Baseline At for Boost:
c* = 5200 ft / s
( pc )boost = 1,769 psi
100
.
w p = Wp / tb = 84.8 / 3.69 = 23.0 lb / s
1
10
100
Propellant Weight Flow Rate, lb / s
.
pc At = c* w p / gc = 5200 ( 23.0 ) / 32.2
= 3,714 lb
At = 3714 / 1769 = 2.10 in2
.
2/24/2008
Note: At = nozzle throat area, c* = characteristic velocity, w p = propellant weight flow rate, gc = gravitational constant,
pc = chamber pressure
ELF
118
Ab, Rocket Baseline Propellant Burn Area, in2
High Chamber Pressure Requires Large
Propellant Burn Area and Small Nozzle Throat
600
Ab = gc pcAt / ( ρc*r )
Example Ab for Rocket
Baseline:
r = rpc=1000 psi ( pc / 1000 )n
At= 1.81 in2
ρ = 0.065 lb / in3
n = 0.3
rp
400
c = 1000 psi
= 0.5 in / s
c* = 5,200 ft / s
Tatmosphere = 70 °F
For sustain ( pc = 301 psi ):
•r = 0.5 ( 301 / 1000 )0.3 = 0.35
in / s
200
•Ab = 149 in2
For boost ( pc = 1,769 psi )
•r = 0.59 in / s
•Ab = 514 in2
0
0
500
1000
1500
2000
Pc, Rocket Baseline Motor Chamber Pressure, psi
Note: Ab = propellant burn area, gc = gravitation constant, At = nozzle throat area, ρ = density of propellant, c* = characteristic velocity,
r = propellant burn rate, rp =1000 psi = propellant burn rate at pc = 1,000 psi, pc = chamber pressure, n = burn rate exponent
c
2/24/2008
ELF
119
Conceptual Design Sizing Process for a Rocket
Motor
1. Define Altitude and Required Thrust-time
New Value ( s )
2. Assume Propellant ( Characteristic Velocity, Nominal
Burn Rate, Burn Rate Exponent ), Chamber Pressure, Burn
Area, and Nozzle Geometry ( Expansion Ratio, Throat Area )
New Value ( s )
3. Compute ISP and
Thrust
OK?
Yes
No
4. Compute Propellant Weight Flow Rate and Propellant Used
OK?
Yes
No
5. Determine Diameter and Length to Satisfy wp and Ae
OK?
Yes
2/24/2008
ELF
No
120
Conventional Solid Rocket Thrust-Time Design
Alternatives with Propellant Cross-Section
•Climb at ≈
constant
dynamic
pressure
•Fast launch –
≈ cruise
•Fast launch –
≈ cruise – high
speed terminal
Thrust ( lb ) Thrust ( lb )
•Dive at ≈
constant
dynamic
pressure
Thrust ( lb )
•≈ Cruise
Thrust Profile
Thrust ( lb ) Thrust ( lb )
Example Mission
Example Web Cross Section / Volumetric Loading
Constant
Thrust
~ 82%
Burning Time ( s )
End Burner
~90%
Radial Slotted Tube
~ 79%
Regressive
Thrust
Burning Time ( s )
~ 87%
Progressive
Thrust
Burning Time ( s )
Production of Star Web Propellant.
~ 85% Photo Courtesy of BAE
Boost-Sustain
Burning Time ( s )
Boost-Sustain-Boost
~ 85%
Burning Time ( s )
Note: High thrust and chamber pressure require large surface burn area.
2/24/2008
~95%
ELF
Medium Burn Rate Propellant
High Burn Rate Propellant
121
Conventional Rocket Has Fixed Burn while
Thrust Magnitude Control Can Vary Burn Interval
Conventional Fixed Burn Interval ( Boost )
End Burning
Radial Burning
Conventional Fixed Burn Interval ( Boost – Sustain )
Concentric Radial Burning
High Burn Rate Boost
Low Burn Rate Sustain
Radial Boost
End Burning Sustain
Simultaneous Burning
Pulse Motor TMC Variable Burn Interval ( Boost – Coast – Boost / Sustain - Coast )
1st Pulse: Radial Boost
2nd Pulse: End Burning Sustain
Separate Burning ( Pulsed Motor )
1st Pulse: Radial Boost
2nd Pulse: Radial Sustain / Boost
Separate Burning ( Pulsed Motor )
Note: Each pulse increases motor cost approximately 40%.
2/24/2008
ELF
Boost Propellant
Sustain Propellant
122
Tactical Rocket Motor Thrust Magnitude Control
Alternatives
Solid Pulse Motor
☺ High ISP
Limited Pulses
Solid Pintle Motor
Thermal or Mechanical Barriers
☺ Continuously Select Up to
40:1 Variation in Thrust
☺ Reduce MEOP on Hot Day
Good ISP Only If Burn Rate
Exponent n → 1
Pintle
Bi-propellant Gel Motor
☺ High ISP
Pressurization
☺ Duty Cycle Thrust
Gelled Oxidizer
Gelled Fuel
Combustion
Chamber
☺ Insensitive Munition
Lower Max Thrust
Toxicity
2/24/2008
ELF
123
Solid Rocket Propellant Alternatives
Burn
ρ,
ISP,
Rate @
Specific Density, 1,000 psi,
Safety Observables
Impulse, s lb / in3
in / s
Type
• Min Smoke. No Al fuel or AP
oxidizer. Either Composite with
Nitramine Oxidizer ( CL-20, ADN,
HMX, RDX ) or Double Base. Very low
contrail (H2O).
–
–
–
220 - 255
0.055 - 0.062
250 - 260
0.062
0.25 - 2.0
• Reduced Smoke. No Al ( binder
fuel ). AP oxidizer. Low contrail ( HCl ).
0.1 - 1.5
–
• High Smoke. Al fuel. AP oxidizer.
High smoke ( Al2O3 ).
Superior
2/24/2008
260 - 265
Above Average
0.065
Average
ELF
0.1 - 3.0
– Below Average
124
Steel is the Most Common Motor Case Material
Type
Temperature
Volumetric
Efficiency
Weight
IM
Airframe /
Launcher
Attachment
Cost
Steel
Aluminum
–
–
Strip Steel /
Epoxy Laminate
–
–
Composite
Titanium
Superior
2/24/2008
Above Average
ELF
–
–
–
–
Average – Below Average
125
Heat Transfer Drives Rocket Nozzle Materials,
Weight, and Cost
Dome Closeout
Exit Cone
Housing
Throat
2/24/2008
Rocket Nozzle Element
High Heating ( High Chamber
Pressure or Long Burn ) ⇒
High Cost / Heavy Nozzle
Low Heating ( Low Chamber
Pressure or Short Burn ) ⇒
Low Cost / Light Weight Nozzle
♦ Housing Material
Alternatives
♦ Steel
♦ Cellulose / Phenolic
♦ Aluminum
♦ Throat Material
Alternatives
♦ Tungsten Insert
♦ Rhenium Insert
♦ Molybdenum Insert
♦
♦
♦
♦
♦ Exit Cone, Dome Closeout,
and Blast Tube Material
Alternatives
♦ Silica / Phenolic Insert
♦ Graphite / Phenolic Insert
♦ Silicone Elastomer Insert
♦ No Insert
♦ Glass / Phenolic Insert
ELF
Cellulose / Phenolic Insert
Silica / Phenolic Insert
Graphite Insert
Carbon – Carbon Insert
126
Summary of Propulsion
Emphasis
Turbojet propulsion
Ramjet propulsion
Rocket propulsion
Conceptual Design Prediction Methods
Thrust
Specific impulse
Design Trades
Turbojet turbine material, compressor ratio, and cycle
Ramjet engine / booster / inlet integration
Ramjet fuel
Propellant burn area requirement
Nozzle throat area
Nozzle expansion ratio
Rocket motor grain
Thrust magnitude control
2/24/2008
ELF
127
Summary of Propulsion ( cont )
Design Trades ( cont )
Solid propellant alternatives
Motor case material alternatives
Nozzle materials
New Propulsion Technologies
Hypersonic turbojet
Ramjet / ducted rocket
Scramjet
Combined cycle propulsion
High temperature turbine materials
High temperature combustor
Oblique shock airframe compression
Mixed compression inlet
Low drag inlet
High density fuel / propellant
Endothermic fuel
2/24/2008
ELF
128
Summary of Propulsion ( cont )
New Propulsion Technologies ( cont )
Solid rocket thrust magnitude control
High burn exponent propellant
Low observable fuel / propellant
Discussion / Questions?
Classroom Exercise ( Appendix A )
2/24/2008
ELF
129
Propulsion Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
2/24/2008
An advantage of turbojets compared to ramjets is s_____ thrust.
The specific impulse of a turbojet is often limited by the maximum
allowable temperature of the t______.
The specific impulse of a ramjet is often limited by the maximum allowable
temperature of the c________.
Ducted rockets are based on a fuel-rich g__ g________.
A safety advantage of solid rocket propulsion over liquid propulsion is less
t_______.
A rocket boost to a take-over Mach number is required by ramjets and
s________.
Parameters that enable the long range of subsonic cruise turbojet missiles
are high lift, low drag, available fuel volume, and high s_______ i______.
High thrust and high acceleration are achievable with s____ r_____
propulsion.
In a turbojet the power to drive the compressor is provided by the t______.
ELF
130
Propulsion Problems ( cont )
10.
11.
12.
13.
14.
15.
16.
17.
2/24/2008
The compressor exit temperature is a function of the flight Mach number
and the compressor p_______ r____.
Compressor exit temperature, fuel heating value, and fuel-to-air ratio
determine the turbojet t______ temperature.
Three types of turbine based propulsion are turbojet, turbo ramjet, and a__
t____ r_____.
Mach number and fuel-to-air ratio determine the ramjet c________
temperature.
An example of a ramjet with low drag and light weight is an i_______ r_____
ramjet.
Russia, France, China, United Kingdom, Taiwan, and India are the only
countries with currently operational r_____ missiles.
100% inlet capture efficiency occurs when the forebody shock waves
intercept the i____ l__.
Excess air that does not flow into the inlet is called s_______ air.
ELF
131
Propulsion Problems ( cont )
18.
19.
20.
21.
22.
23.
24.
25.
26.
2/24/2008
Starting a ramjet inlet at lower supersonic Mach number requires a larger
area of the inlet t_____.
Optimum pressure recovery across shock waves is achieved when the total
pressure loss across each shock wave is e____.
The specific impulse and thrust of a ramjet are a function of the efficiency
of the combustor, nozzle, and i____.
High density fuels have high payoff for v_____ limited missiles.
The specific impulse of a ducted rocket with large excess fuel from the gas
generator can approach that of a r_____.
High speed rockets require large p_________ weight.
At the throat, the flow area is minimum, sonic, and c_____ .
For an optimum nozzle expansion the nozzle exit pressure is equal to the
a__________ pressure.
High thrust and chamber pressure are achievable through a large propellant
b___ area.
ELF
132
Propulsion Problems ( cont )
27.
28.
29.
30.
31.
2/24/2008
Three approaches to solid rocket thrust magnitude control are pulse motor,
pintle motor, and g__ motor.
A high burn exponent propellant allows a large change in thrust with only a
small change in chamber p_______.
Three tradeoffs in selecting a solid propellant are safety, observables, and
s_______ i______.
A low cost motor case is usually based on steel or aluminum material while
a light weight motor case is usually based on c________ material.
Rockets with high chamber pressure or long burn time may require a
t_______ throat insert.
ELF
133
Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
2/24/2008
ELF
134
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Define Mission Requirements
Alt Mission
Establish Baseline
Alt Baseline
Aerodynamics
Propulsion
Weight
Resize / Alt Config / Subsystems / Tech
Trajectory
Meet
Performance?
No
Yes
Measures of Merit and Constraints
No
Yes
2/24/2008
ELF
135
Designing Light Weight Missile Has High Payoff
Production cost
Logistics cost
Size
Firepower
Observables
Mission flexibility
Expeditionary warfare
2/24/2008
ELF
136
Flight Performance ( Range, Speed,
Maneuverability ) Sensitive to Subsystem Weight
Dome -
Seeker -
Structure
Guidance and
Control -
Power
Supply
High Sensitivity
2/24/2008
Propulsion
Warhead
Low Sensitivity
ELF
Wings
Insulation
Data
Link -
Stabilizers
Flight
Control
- Minor Sensitivity
137
Missile Range is a Function of Launch Weight,
Propellant Weight, and Specific Impulse
ΔV ≈ -gc Isp ln ( 1 - WPropellant / Wi )
1000
Assumptions:
θI = Launch Incidence Angle = 45 deg for max
range
R ≈ V2 sin ( 2θi ) / gc
Rmax, Maximum Range, nm
Thrust Greater Than Drag and Weight
Flat, Non-rotating Earth
For Two-Stage Missile with ( Wi )Min : ΔV1 = ΔV2
Example: Two-Stage Missile with Minimum
Weight and Rmax = 200 nm = 1.216 x 106 ft
100
Assume ISP = 250 sec, WPayload = 500 lb, WInert =
0.2 WPropellant
V = [( 32.2 ) ( 1.216 x 106 )]1/2 = 6251 ft / s
ΔV1 = ΔV2 = V / 2 = 3125 ft / s
Wi,SecondStage = WPayload + WInert + WPropellant = 814 lb
Wi, FirstStage = WInert + WPropellant = 85 + 427 = 512 lb
10
100
1000
Wi, Example Initial Launch Weight, lb
Single-Stage Missile
2/24/2008
10000 Wi = Wi,FirstStage + Wi,SecondStage = 1326 lb
Compare: Single-Stage Missile, R = 200 nm
Two-Stage Missile
ELF
ΔV = 6251 = - 32.2 ( 250 ) ln [ 1 – WPropellant / (
WPropellant + 0.2 WPropellant + 500 )] ⇒ Wp = 767 ⇒
Wi = 1420 lb
138
Missile Weight Is a Function of Diameter and
Length
WL = 0.04 l d2
WL, Missile Launch Weight, lb
10000
Units: WL( lb ), l ( in ), d ( in )
1000
100
10
100
1000
10000
100000
1000000
ld2, Missile Length x Diameter2, in3
2/24/2008
FIM-92
SA-14
Javelin
RBS-70
Starstreak
Mistral
HOT
Trigat LR
LOCAAS
AGM-114
Roland
RIM-116
Crotale
AIM-132
AIM-9M
Magic 2
Mica
AA-11
Python 3
AIM-120C
AA-12
Skyflash
Aspide
AIM-9P
Super 530F
Super 530D
AGM-65G
PAC-3
AS-12
AGM-88
Penguin III
AIM-54C
Armat
Sea Dart
Sea Eagle
Kormoran II
AS34
AGM-84H
MIM-23F
ANS
MM40
AGM-142
AGM-86C
SA-10
BGM-109C
MGM-140
SSN-22
Kh-41
ELF
139
Most Subsystems for Tactical Missiles Have a
Density of about 0.05 lb / in3
Guidance: Flight Control:
0.04 lb / in3 0.04 lb / in3
Dome Material:
0.1 lb / in3
2/24/2008
Warhead:
0.07 lb / in3
Propellant:
0.06 lb / in3
Structure and Motor Case:
0.10 ( Al ) to 0.27 ( steel ) lb / in3
ELF
Data Link:
0.04 lb / in3
Aero Surfaces:
0.05 ( built-up Al ) to 0.27 ( solid
steel ) lb / in3
140
Modeling Weight, Balance, and Moment-of-Inertia
Is Based on a Build-up of Subsystems
Example Missile Configuration
Nose G&C
Wing Section
With Fuel
Inlet Section
Engine
With Fuel
Fuel
Plug
Warhead
Inlet
Model
+z
+x
Legend
Assume Uniform Weight Distribution For a Given Segment
Structure and Subsystems
Engine Structure and Subsystems
Warhead and Structure
Fuel
Inlet Structure and Subsystems
Aero Surfaces
xCG = Σ ( xsubsystem1 Wsubsystem1 + xsubsystem2 Wsubsystem2 + … ) / Wtotal
2/24/2008
IY = Σ [ ( Iy,subsystem1 )local + Wsubsystem1 ( xsubsystem1 - xCG )2 / gc + ( Iy,subsystem2 )local + Wsubsystem2 ( xsubsystem2 - xCG )2 / gc + … ]
ELF
141
( Iy,local ) g / ( W d2 ), Nondimensional Yaw Local Momen
of Inertia
Moment-of-Inertia Is Higher for High Fineness
Ratio Body
( Iy,cylinder )local = [ W d2 / gc ] [( 1 / 16 ) + ( 1 / 12 ) ( l / d )2 ]
100
( Iy,cone )local = [ W d2 / gc ] [ ( 3 / 80 ) + ( 3 / 80 ) ( l / d )2 ]
er
d
n
i
l
Cy
Cone
10
Example for Ramjet Baseline at Launch ( xcg = 8.04 ft )
Assume missile can be approximated as a conical nose-cylinder
1
For the cone, d = 1.25 ft, l / d = 1.57, Wcone = 15.9 lb, xcg,cone = 1.308 ft
For the cylinder, l / d = 7.22, d = 1.698 ft, Wcylinder = 2214 lb, xcg,cylinder = 8.09 ft
Iy = ( Iy,cone )local + Wcone ( xcg,cone - xCG )2 / gc + ( Iy,cylinder )local + Wcylinder ( xcg,cylinder xCG )2 / gc
0.1
( Iy,cone )local = [ 15.9 ( 1.25 )2 / 32.2 ] [ 0.0375 + 0.0375 ( 1.57 )2 ] = 0.10 slug-ft2
( Iy,cylinder )local = [ 2214 ( 1.698 )2 / 32.2 ] [ 0.0625 + 0.0833 ( 7.22 )2 ] = 872 slug-ft2
Iy = 0.10 + 22.4 + 872 + 0.16 = 895 slug-ft2
0.01
0
10
20
30
l / d, Length / Diameter
2/24/2008
ELF
142
Structure Design Factor of Safety Is Greater for
Hazardous Subsystems / Flight Conditions
Pressure Bottle ( 2.50 / 1.50 )
Ground Handling Loads ( 1.50 / 1.15 )
3.0
Captive Carriage and Separation Flight Loads ( 1.50 / 1.15 )
Motor Case ( MEOP ) ( 1.50 / 1.10 )
Free Flight Loads ( 1.25 / 1.10 )
2.0
FOS,
Factor of Safety
( Ultimate / Yield )
Δ Castings ( 1.25 / 1.25 )
Δ Fittings ( 1.15 / 1.15 )
Thermal Loads ( 1.00 / 1.00 )
1.0
Note:
0
• MIL STDs include environmental ( HDBK-310, NATO STANAG 4370, 810F, 1670A ), strength and rigidity ( 8856 ), and captive
carriage ( 8591 ).
•The entire environment ( e.g., manufacturing, transportation, storage, ground handling, captive carriage, launch separation,
post-launch maneuvering, terminal maneuvering ) must be examined for driving conditions in structure design.
•FOS Δ for castings is expected to be reduced in future as casting technology matures.
•Reduction in required factor of safety is expected as analysis accuracy improves will result in reduced missile weight / cost.
2/24/2008
ELF
143
Structure Concepts and Manufacturing
Processes for Low Parts Count
Structure Manufacturing Process Alternatives
Composites
Metals
Structure
Vacuum
Vacuum
Concept
Compression
Filament
Thermal
Assist
Bag /
Alternatives RTM
Mold
Wind Pultrusion Form Autoclave Cast
Geometry
Alternatives
High
Speed
Strip
Machine Forming Laminate
Monocoque
Lifting Body
Airframe
Axisymmetric
Airframe
Integrally Hoop
Stiffened
–
Integrally
Longitudinal
Stiffened
–
Monocoque
Integrally Hoop
Stiffened
Integrally
Longitudinal
Stiffened
Surface
Solid
Sandwich
Note: Manufacturing process cost is a function of recurring cost ( unit material, unit labor ) and non-recurring cost ( tooling ).
Note:
2/24/2008
Very Low Parts Count
Low Parts Count
ELF
Moderate Parts Count – High Parts Count
144
Low Parts Count Manufacturing Processes for
Complex Airframes
Vacuum Assisted RTM
Resin
Pump
3D Fiber Orientation
Filament Wind
Helical wind versus
radial wind
Pultrusion ………………………………….
2D Fiber Orientation ( 0-±45-90 deg )
Pour Cup Vent
Metal Casting
Riser
Mold Cavity
Parting Line
2/24/2008
ELF
145
Tactical Missile Airframe Material Alternatives
Type
Tension
( σTU / ρ )
Material
Metallic
Aluminum 2219
Increasing
Steel PH 15-7Mo
Cost
Buckling
Max
Stability
Short – Life
Temp
( σBuckling / ρ )
–
Thermal
Stress
Joining
Cost
Weight
–
–
–
Titanium 6Al-4V
–
Composite S994 Glass /
Increasing Epoxy and S994
Glass / Polyimide
Cost
Glass or
Graphite Reinforce
Molding
–
Graphite / Epoxy
and Graphite
Polyimide
Note:
2/24/2008
–
Superior
Above Average
ELF
Average
–
– Below Average
146
Strength – Elasticity of Airframe Material Alternatives
σt = P / A = E ε
Kevlar Fiber
w / o Matrix
Graphite Fiber
w / o Matrix
( 400 – 800 Kpsi )
400
Glass Fiber
w / o Matrix
300
Very High Strength Stainless Steel
( PH 15-7 Mo, CH 900 )
High Strength Stainless Steel
( PH 15-7 Mo, TH 1050 )
σt, Tensile Stress,
103 psi
200
Titanium Alloy ( Ti-6Al-4V )
100
Aluminum Alloy ( 2219-T81 )
0
0
1
2
3
4
ε, Strain, 10-2 in / in
2/24/2008
ELF
5
Note:
• High strength fibers are:
– Very small diameter
– Unidirectional
– High modulus of
elasticity
– Very elastic
– No yield before failure
– Non forgiving failure
• Metals:
– Ductile,
– Yield before failure
– Allow adjacent structure
to absorb load
– Resist crack formation
– Resist impact loads
– More forgiving failure
E, Young’s modulus of elasticity, psi
P, Load, lb
ε, Strain, in / in
A, Area, in2
Room temperature
147
Structural Efficiency at High Temperature of
Short Duration Airframe Material Alternatives
Graphite / Polyimide ( ρ = 0.057 lb / in3 ), 0-±45-90 Laminate
Graphite / Epoxy
( ρ = 0.065 lb / in3 )
0-±45-90 Laminate
Ti3Al ( ρ = 0.15 lb / in3 )
σTU / ρ, Ultimate Tensile Strength /
Density, 105 In.
12.0
10.0
Ti-6Al-4V Annealed Titanium ( ρ = 0.160 lb / in3 )
8.0
PH15-7 Mo Stainless Steel ( ρ = 0.277 lb / in3 ). Note:
Thin wall steel susceptible to buckling.
6.0
Graphite
4.0
Glass
Chopped Epoxy
2219-T81
Composites,
Random Orientation Aluminum
( ρ = 0.101 lb / in3 )
( ρ = 0.094 lb / in3 )
2.0
0
0
200
400
600
800
1,000
Short Duration Temperature, ° F
2/24/2008
ELF
148
Hypersonic Missiles without External Insulation
Require High Temperature Structure
( Tmax )Titanium Aluminide ≈ 2,500 °F )
r=
1
r=
0
r = .9
0 .8
Tr = T0 ( 1 + 0.2 r M2 )
Tr, Recovery Temperature, °F
2,000
( Tmax )Single Crystal Nickel Aluminides ≈ 3,000 °F
( Tmax )Ceramic Matrix Composite ≈ 3,500 °F
( Tmax )Nickel Alloys ( e.g., Inconel, Rene,
Hastelloy, Haynes )
1,500
Note:
• (T )
max Steel
• γ = 1.4
•
•
•
1,000
• Tr = Recovery Temperature, R
( Tmax )Ti Alloy
• T0 = Free stream temperature, R
• Tmax = Max temperature capability
( Tmax )Graphite Polyimide
• No external insulation assumed
•
•
• ( Tmax )Al Alloy
500
•
•
•
•
•
•
( Tmax )Graphite Epoxy
0
2/24/2008
0
1
2
3
4
M, Mach Number
ELF
5
6
r is recovery factor
h = 40k ft ( TFree Stream = 390 R )
Stagnation r = 1
Turbulent boundary layer r = 0.9
Laminar boundary layer r = 0.8
Short-duration flight ( less than
30 m ), but with thermal soak
149
Structure / Insulation Trades for Short Duration Flight
Example Structure / Insulation Concepts
Mach Tmax
Increasing
k
c
ρ
α
Hot Metal Structure ( e.g., Al ) without
Insulation
600
0.027
0.22
0.101
0.000722
Hot Metal Structure ( e.g., Al )
600
0.027
0.22
0.101
0.000722
Internal Insulation ( e.g., Min-K )
2000
0.0000051 0.24
0.012
0.00000106
Self-insulating Composite Structure
( e.g., Graphite Polyimide )
1100
0.000109
0.27
0.057
0.00000410
Ext Insulation ( e.g., Micro-Quartz Paint )
1200
0.0000131 0.28
0.012
0.00000226
Cold Metal Structure ( e.g., Al )
600
0.027
0.22
0.101
0.000722
Internal Insulation ( e.g., Min-K )
2000
0.0000051 0.24
0.012
0.00000106
Note:
•
•
•
•
2/24/2008
Tactical missiles use passive thermal protection ( no active cooling )
Small thickness allows more propellant / fuel for diameter constrained missiles ( e.g., VLS launcher )
Weight and cost are application specific
Tmax = max temp capability, ° F; k = thermal conductivity, BTU / s / ft2 / ° F / ft; c = specific heat or thermal
capacity, BTU / lbm / ° F; ρ = density, lbm / in3; α = thermal diffusivity = k / ( ρ c ), ft2 / s
ELF
150
External Insulation Has High Payoff for Short
Duration Flight
1,000
Example Airframe Temperature with No External
Insulator – Steel Airframe Selected.
Example Temperature ° F
900
800
4.0
Mach
700
3.0
600
Mach
Number
500
2.0
400
300
Example Airframe Temperature with 0.012 in Insulator –
Aluminum Airframe Acceptable for Short Duration.
200
Note: Short Range Air-to-Air Missile
Launch ~ 0.9 Mach at 10k ft Altitude
Atmosphere ~ Hot Day ( 1% Risk ) Mil-HDBK-310
100
0
1.0
0
2
4
6
8
10
12
14
Time After Launch ~ s
2/24/2008
ELF
151
Phenolic Composites Are Good Insulators for
High Temperature Structure and Propulsion
Graphites
• Burn
• ρ ~ 0.08 lb / in3
• Carbon / Carbon
6,000
5,000
Bulk Ceramics
• Melt
• ρ ~ 0.20 lb / in3
• Zirconium Ceramic,
Hafnium Ceramic
4,000
Tmax, Max
Temperature
Capability,
R
Porous Ceramics
• Melt
• Resin Impregnated
• ρ ~ 0.12 lb / in3
• Carbon-Silicon
Carbide
3,000
2,000
Low Density
Composites
• Char
• ρ ~ 0.03 lb / in3
• Micro-Quartz
Paint, GlassCork-Epoxy,
Silicone Rubber
Plastics
• Sublime
• Depolymerizing
• ρ ~ 0.06 lb / in3
• Teflon
1,000
0
Medium Density Phenolic
Composites
• Char
• ρ ~ 0.06 lb / in3
• Nylon Phenolic, Silica
Phenolic, Glass
Phenolic, Carbon
Phenolic, Graphite
Phenolic
0
1
2
3
4
Insulation Efficiency, Minutes To Reach 300° F at Back Wall
2/24/2008
Note:
Assumed Weight Per Unit Area of Insulator / Ablator = 1 lb / ft2
ELF
152
A “Thermally Thin” Surface ( e.g., Metal
Airframe ) Has Uniform Internal Temperature
Example for Rocket Baseline Airframe:
( dT / dt )t = 0 = ( Tr - Tinitial ) h / ( c ρ z )
Aluminum skin w/o external insulation
dT / dt, Initial Skin Temperature Rate for
Rocket Baseline, Deg F / sec
T = Tr – ( Tr – Tinitial ) e – h t / ( c ρ z )
c = 0.215 BTU / lb / R, ρ = 0.10 lb / in3 = 172.8 lb / ft3,
z = 0.16 in = 0.0133 ft, k = 0.027 BTU / s / ft2 / R / ft
h = k NNU / x
1000
x = 1.6 ft
Thermally thin ⇒ h ( z / k )surface < 0.1
Assume Mach 2 sustain flight, 20k ft altitude ( T0 =
447 R , k = 3.31 x 10-6 BTU / s / ft2 / R / ft ), Turbulent
boundary layer, x = 1.6 ft
100
Rex = ρ0 M a0 x / μ0 = 12.56 x 106
NNU = 0.0271 Re0.8 = 12947
h = k NNU / x = 0.0268 BTU / s / ft2 / R
10
Test: h ( z / k )surface = 0.0132 < 0.1 ⇒ thermally thin
Calculate Tr = T0 [ 1 + 0.2 r M2 ] = 447 [ 1 + 0.2 ( 0.9 )
( 2 )2 ] = 769 R
1
0
1
2
3
4
5
M, Mach Number
6
At t = 0, Assume Tinitial = 460 R, or 0° F
( dT / dt )t = 0 = ( 769 - 460 ) ( 0.0268 ) / [( 0.215 )
(172.8 ) ( 0.01333 )] = 17°F / s
At a sustain time t = 10 s, T = 769 - ( 769 – 460 ) e –
0.0268 ( 10 ) / [ 0.215 ( 172.8 ) ( 0.0133 )] = 589 R, or 129° F
Note: No external insulation; thermally thin structure ( uniform internal temperature ); “Perfect” insulation behind airframe; 1-D
heat transfer; Turbulent boundary layer; Radiation neglected; dT / dt = Temperature rate, R / s; Tr = Recovery ( max )
temperature, R; h = Convection heat transfer coefficient, BTU / s / ft2 / R; c = Specific heat, BTU / lb / R; ρ = Density, lb / ft3; z =
Thickness, ft; k = Conductivity, BTU / s / ft2 / R / ft; Re = Reynolds number; NNU = Nusselt number
Reference: Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design,
D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960
h = sea level
2/24/2008
h = 20K ft
h = 50K ft
h = 80K ft
ELF
153
A “Thermally Thick” Surface ( e.g., Radome ) Has
a Large Internal Temperature Gradient
[ T ( z, t ) - Tinitial ] / [ Tr – Tinitial ] = erfc { z / [ 2 ( α t )1/2 ]} – e( h z / k ) + h2 α t / k2 erfc { z / [ 2 ( α t )1/2 ] + h ( α t )1/2 / k }
[ T ( 0, t ) - Tinitial ] / [ Tr – Tinitial ] = 1 - eh2 α t / k2 erfc [ h ( α t )1/2 / k ]
Applicable for thermally thick surface: z / [ 2 ( α t )1/2 ] > 1
Example: Rocket Baseline Radome
.1
=0
Mach 2, 20k ft alt ( T0 = 447 R ), Turbulent boundary layer,
x = 19.2 in = 1.6 ft, t = 10 s, Tr = 769 R, Tinitial = 460 R
/k1
0
k=1
00
⇒ h = 0.0268 BTU / s / ft ⇒ ( h / k )( α t )1/2 = 0.491
Test: z / [ 2 ( α t )1/2 ] = 0.0208 / { 2 [ 1.499x10-5 ( 10 )]1/2 } =
0.849 < 1 ⇒ not quite thermally thick
Inner wall ⇒ h z / k = 0.935
hz/
hz
0.5
α = 1.499 x 10-5 ft2 / s
/k
k=
1 hz
hz
/k
=0
X = 1.6 ft
z = 0.25 in = 0.0208 ft, k = 5.96 x 10-4 BTU / s / ft / R,
hz/
[ T ( z, t ) - ( T )initial ] / [( T )r – ( T )initial ]
1
[ T ( 0.0208, 10 ) - Tinitial ] / [ Tr – Tinitial ] = 0.0608
T ( 0.0208, 10 ) = 479 R ( Note: Tinner ≈ Tinitial )
Surface ⇒ h z / k = 0
0
0.1
1
( h / k )( α t )1/2
10
100
[ T ( 0, 10 ) - Tinitial ] / [ Tr – Tinitial ] = 0.372
T ( 0, 10 ) = 575 R
Note: T ( z,t ) ∼ ( T )initial; 1-D heat transfer; Radiation neglected; Turbulent boundary layer; Tr = Recovery temperature, R; h =
Heat transfer coefficient, BTU / ft2 / s / R; k = Thermal conductivity of material, BTU / s / ft2 / R / ft; α = Diffusivity of material,
ft2 / s; zmax = Thickness of material, ft; erfc = Complementary error function
Reference: Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design,
D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960
2/24/2008
ELF
154
Internal Insulation Temperature Can Be Predicted
Assuming Constant Flux Conduction
[ T ( z, t ) – Tinitial ] / [ T ( 0, t ) – Tinitial ] = e- z2 / ( 4 α
t)–
Applicable for thermally thick surface: z / [ 2 ( α t )1/2 ] > 1
1
( π / α t )1 / 2 ( z / 2 ) erfc { z / [ 2 ( α t )1/2 ]}
Example for Rocket Baseline Airframe Insulation:
[ T ( z, t ) – Tinitial ] / [ T ( 0, t ) – Tinitial ]
0.10 in Min-K Internal Insulation behind 0.16 in aluminum
Skin
Aluminum
0.16 in
X = 1.6 ft
0.10 in
Min-K
z
Assume M = 2, 20k ft alt, x = 1.6 ft, Tinitial = 460 R, t = 10 s,
zMin-K = 0.10 in = 0.00833 ft, αMin-K = 0.00000106 ft2 / s, k =
5.96 x 10-4 BTU / s / ft, h = 0.0268 BTU / s / ft
0.5
Test: z / [ 2 ( α t )1/2 ] = 0.00833 / {2 [ 0.00000106 ( 10 )]1/2} =
1.279 > 1 ⇒ thermally thick
( α t )1/2 / z = [ 0.00000106 ( 10 ) ]1/2 / 0.00833 = 0.3907
[ TMin-K ( 0.0217, 10 ) – 460 ] / [ TMin-K ( 0, 10 ) – 460 ] = 0.0359
Assume ( Tinner )aluminum = ( Touter )Min-K
From prior example, ( Tinner )aluminum = 569 R at = 10 s
Then, ( Touter )Min-K = 569 R at t = 10 s
0
0.1
1
( α t )1/2 / z
10
100
Compute, ( Tinner )Min-K = 460 + ( 569 – 460 ) 0.0338 = 460 + 4
= 464 R
Note: 1-D conduction heat transfer, Radiation neglected, Constant heat flux input, T ( z,t ) = Inner temperature of insulation
at time t, Tinitial = Initial temperature, T ( 0, t ) = Outer temperature of insulation at time t, α = Diffusivity of insulation material,
ft2 / s; zmax = Thickness of insulation material, ft; erfc = Complementary error function
Reference: Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, 1989
2/24/2008
ELF
155
A Sharp Nose Tip / Leading Edge Has High
Aerodynamic Heating
hr, Stagnation Heat Transfer Coeff for
Rocket Baseline at h = 20k ft, BTU / ft2 / s / R
hr = NNUr kr / dNoseTip
0.6
Example for Rocket Baseline Nose Tip:
NNUr = 1.321 RedNoseTip0.5 Pr0.4
Assume M = 2, 20k ft alt, stagnation ( Tr = 805
R ) for a sharp nose tip ( e.g., 1% blunt )
0.5
0.4
dNoseTip / dRef = 0.01 ⇒ dNoseTip = 0.01 ( 8
in ) = 0.08 in = 0.00557 ft
0.3
RedNoseTip = ρ0 V0 dNoseTip / μr = 3.39 x 104
0.2
NNUr = 223
hr = 0.1745 BTU / ft2 / s / R
0.1
Outer surface temperature after 10 s heating
in sustain flight ( M = const, Tr = const ):
0
2
0
1
2
3
4
5
M, Mach Number
1% Bluntness
5% Bluntness
2% Bluntness
10% Bluntness
6
2
[ T ( 0, t ) - Tinitial ] / [ Tr – Tinitial ] = 1 – e h αt / k
erfc { h ( α t )1/2 / k }
[ T ( 0, 10 ) - 460 ] / [ 805 – 460 ] = 1 – e [( 0.1745 )
( 1.499 x 10-5 ) ( 10 ) / ( 5.96 x 10-4 )2 ] erfc { ( 0.1745 ) [
1.499 x 10-5 ( 10 )]1/2 / ( 5.96 x 10-4 )]} = 0.845
2
T ( 0, 10 ) = 460 + 345 ( 0.845 ) = 752 R
Note: 1-D conduction heat transfer; Laminar boundary layer; Stagnation heating; Radiation neglected; hr = Convection
heat transfer coefficient for stagnation recovery, BTU / s / ft2 / R; NNUr = Nusselt number for stagnation recovery; kr =
Air thermal conductivity at stagnation recovery ( total ) temperature, BTU / s / ft / R; dNoseTip = Nose tip diameter, ft;
RedNoseTip = Reynolds number based on nose tip diameter, Pr = Prandtl number
Reference: Allen, J. and Eggers, A. J., “A Study of the Motion and Aerodynamic Heating of Ballistic
Missiles Entering the Earth’s Atmosphere at High Supersonic Speeds”, NACA Report 1381, April 1953.
2/24/2008
ELF
156
Tactical Missile Radiation Heat Loss Is Usually
Small Compared to Convective Heat Input
QRad = 4.76 x 10-13 ε T4
100
QRad in BTU / ft2 / s, T in R
Example: Ramjet Baseline
Assume:
10
Radiation Heat
Flux at
Equilibrium
Temperature,
BTU / ft2 / s
•Titanium skin with emissivity ε =
0.3
•Long duration ( equilibrium )
heating at Mach 4
1
•h = 80k ft, T0 = 398 R
•Turbulent boundary layer ( r =
0.9 ) ⇒ T = Tr = T0 ( 1 + 0.2 r M2 ) =
1513 R
0.1
Calculate:
QRad = 4.76 x 10-13 ( 0.3 ) ( 1513 )4
= 0.748 BTU / ft2 / s
0.01
0
1
2
3
4
5
6
Cruise Mach Number
Emissivity = 0.1
2/24/2008
Emissivity = 1
ELF
157
Design Concerns for Localized Aerodynamic
Heating and Thermal Stress
Flare / Wedge Corner Flow
Body Joints
Hot missile shell
Cold frames or bulkheads
Causes premature buckling
Shock wave – boundary layer
interaction
Separated Flow
High heating at reattachment
Leading Edges
IR Domes / RF Radomes
Hot stagnation temperature on leading edge
Small radius prevents use of external insulation
Cold heat sink material as chord increases in thickness
leads to leading edge warp
Shock wave interaction with adjacent body structure
Large temp gradients due to low thermal conduction
Thermal stress at attachment
Low tensile strength
Dome fails in tension
Note: σTS = Thermal stress from restraint in compression or tension = α E ΔT
α = coefficient of thermal expansion, E = modulus of elasticity, ΔT = T2 – T1 = temperature difference.
Example: Thermal Stress for Rocket Baseline Pyroceram Dome, α = 3 x 10-6, E = 13.3 x 106 psi
Assume M = 2, h = 20k ft alt, t = 10 s. Based on prior figure, ΔT = TOuterWall – TInnerWall = 102 R
Then σTS = 3 x 10-6 ( 13.3 x 106 ) ( 102 ) = 4,070 psi
2/24/2008
ELF
158
Examples of Aerodynamic Hot Spots
Nose Tip
Leading Edge
Flare
2/24/2008
ELF
159
WBS,Body Structure Weight, lb
Tactical Missile Body Structure Weight Is about
22% of the Launch Weight
WBS / WL ≈ 0.22
1000
100
Example for 500 lb missile
WL = 500 lb
WBS = 0.22 ( 500 ) = 110 lb
10
100
1000
10000
WL, Launch Weight, lb
Hellfire ( 0.22 )
Sidewinder ( 0.23 )
Sparrow ( 0.18 )
Phoenix ( 0.19 )
Harpoon ( 0.29 )
SM 2 ( 0.20 )
SRAM ( 0.21 )
ASALM ( 0.13 )
SETE ( 0.267 )
Tomahawk ( 0.24 )
TALOS ( 0.28 )
Note: WBS includes all load carrying body structure. If motor case, engine, or warhead case carry external
loads then they are included in WBS. WBS does not include tail, wing, or other surface weight.
2/24/2008
ELF
160
Body Structure Thickness Is Based on
Considering Many Design Conditions
Structure Design Conditions That May Drive Airframe Thickness
Manufacturing
Transportation
Carriage
Launch
Fly-out
Maneuvering
Contributors to Required Thickness for Cylindrical Body Structure
Minimum Gage for Manufacturing: t = 0.7 d [( pext / E ) l / d ]0.4. t ≈ 0.06 in if pext ≈ 10 psi
Localized Buckling in Bending: t = 2.9 r σ / E
Localized Buckling in Axial Compression: t = 4.0 r σ / E
Thrust Force: t = T / ( 2 π σ r )
Bending Moment: t = M / ( π σ r2 )
Internal Pressure: t = p r / σ
High Risk ( 1 ), Moderate Risk ( 2 ), and Low Risk ( 3 ) Estimates of Required Thickness
1.
2.
3.
2/24/2008
t = FOS x Max ( tMinGage , tBuckling,Bending , tBuckling,AxialCompression , tAxialLoad , tBending , tInternalPressure )
t = FOS x ( t2MinGage + t2Buckling,Bending + t2Buckling,AxialCompression + t2AxialLoad + t2Bending + t2InternalPressure )1/2
t = FOS x ( tMinGage + tBuckling,Bending + tBuckling,AxialCompression + tAxialLoad + tBending + tInternalPressure )
ELF
161
Localized Buckling May Be A Concern for
Thin Wall Structure
σBuckling,Bending / E ≈ 0.35 ( t / r )
Nondimensional Buckling Stress
σBuckling,AaxialCcompression / E ≈ 0.25 ( t / r )
t
r
Bending
Axial Compression
Note: Thin wall cylinder with local buckling
0.1
σBuckling / E = Nondimensional buckling stress
σBucklingBending = Buckling stress in bending
σBucklingAxialCompression = Buckling stress in axial
compression
0.01
E = Young’s modulus of elasticity
t = Airframe thickness
0.001
r = Airframe radius
Min thickness for fab and handling ≈ 0.06 in
0.0001
0.001
Example for Rocket Baseline in Bending:
0.01
0.1
t / r, thickness / radius
4130 steel motor case, E = 29.5 x 106 psi
σyield = 170,000 psi
t = 0.074 in, r = 4 in
t / r = 0.0185
Note: Actual buckling stress can vary +/- 50%, depending upon typical
imperfections in geometry and the loading.
2/24/2008
ELF
σBuckling,Bending / E ≈ 0.35 ( 0.0185 ) = 0.006475
σbuckling,Bending ≈ 191,000 psi
σbuckling,Bending ~ σyield
162
Process for Captive and Free Flight Loads
Calculation
Captive Flight
Free Flight
Max Aircraft Maneuver
Per MIL-A-8591
Maneuver Per
Design Requirements
Carriage Load
Weight load
of bulkhead
section
Air Load
Weight load
of bulkhead
section
Air Load
Obtained
By Wind
Tunnel
2/24/2008
Air Load
Note: MIL-A-8591 Procedure A assumes max air
loads combine with max g forces regardless of
angle of attack.
Example of αmax Calculated by MIL-A-8591 Using
Procedure A for F-18 Aircraft Carriage:
αmax = 1.5 nz,max Wmax / ( CLα q SRef )aircraft
αmax = 1.5 ( 5 ) ( 49200 ) / [ 0.05 ( 1481 ) ( 400 )] =
12.5 deg
ELF
163
Maximum Bending Moment Depends Upon Load
Distribution
Example for Rocket Baseline:
c = 4, ejection load
l = 144 in
MB = N l / c
C = 8 for uniform loading
w = load per unit length
⇒
N = 10,000 lb ( 20 g )
⇒
MB = 360,000 in-lb
Total
Load 100,000
N
50,000
40,000
30,000
20,000
10,000
Length l Max Bending
Moment MB
Coefficient C
8
7.8
6
4
100
2,000
3,000
4,000
5,000
2,000
10,000
1,000
20,000
30,000
40,000
50,000
500
400
300
10
100
4
2/24/2008
0
l
C = 4 for load at center ( e.g., ejection load )
N = Normal Force
l/2
100,000
200,000
300,000
400,000
500,000
200
1
3
100
1,000,000
200
2,000,000
2
5
l
C = 6 for linear loading to center
w
1,000
5,000
4,000
3,000
C = 7.8 for linear loading
w
0
200
300
400
500
1
l = length
0
ELF
0
l
C = 1 for load at end ( e.g., control force )
N = Normal Force
l
0
l
164
Bending Moment May Drive Body Structure
Weight
t
t
r
MB
t = MB ( FOS ) / [ π r2 σMax ]
A=2πrt
Iz = IY = π r3 t
Note / Assumptions:
Thin cylinder
Circular cross section
Example for Rocket Baseline:
• Body has circular cross section
• 2219-T81 aluminum skin ( σult = 65,000 psi )
• r = 4 in
• Ejection load = 10,000 lb ( 20 g )
• MB = 360,000 in ⋅ lb
• FOS = 1.5
• t = 360,000 ( 1.5 ) / [ π ( 4 )2 ( 65,000 )] = 0.16 in
2/24/2008
ELF
Solid skin
Longitudinal strength
Axial load stress and thermal
stress assumed small compared
to bending moment stress
σ = MB r / IZ = MB r / (π r3 t )
= MB / (π r2 t )
165
Tactical Missile Propellant Weight Is about 72%
of Rocket Motor Weight
WP / WM ≈ 0.72
WP, Propellant Weight, lb
10000
1000
100
Example for Rocket Baseline
WM = 209 lb
WP = 0.72 ( 209 ) = 150 lb
Increased propellant fraction if:
High volumetric loading
10
10
100
1000
WM, Total Motor Weight, lb
Note: WM includes propellant, motor case, nozzle, and insulation.
2/24/2008
Hellfire ( 0.69 )
Sidewinder ( 0.61 )
Sparrow ( 0.64 )
Phoenix ( 0.83 )
ASALM ( 0.86 )
SM-2 ( 0.76 )
SRAM ( 0.71 )
TALOS ( 0.66 )
ELF
10000
Composite case
Low chamber pressure
Low flight loads
Short burn time
166
Motor Case Weight Is Usually Driven By Stress
from Internal Pressure
Assume motor case is axisymmetric, with a front ellipsoid dome
and an aft cylinder body
Motor Case
Cylinder
Hoop
Stress
Case Dome
Nozzle
Case Cylinder
π/2
p
p
b
Motor Dome
Ellipsoid
Longitudinal
Stress
σt t = - 0∫ p r sinθ dθ
( σt )Hoop Stress = p r / t
( σt )Longitudinal Stress
= [ 2 + ( a / b )2 ] p ( a b )1/2 / ( 6 t )
2a
If a = b ( hemi dome of radius r ),
then ( σt )Longitudinal Stress = p r / ( 2 t )
With metals – the material also reacts body bending
In composite motor designs, extra ( longitudinal ) fibers must usually be
added to accommodate body bending
2/24/2008
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167
A Composite Motor Case Is Usually Lighter
Weight
Calculate Maximum Effective Operating Pressure ( Burst Pressure )
pburst = pBoost, Room Temp x eπk Δ T x ( Design Margin for Ignition Spikes, Welds, Other Design Uncertainty )
Assume Rocket Motor Baseline: diameter = 8 in., length = 55 in, ellipsoid dome a / b = 2, pBoost,RoomTemp =
1769 psi, πk = ( Δp / ΔT ) / pc = 0.14% / °F
Assume Hot day T = 160° F ⇒ eπk ΔT = e0.0014 ( 160 - 70 ) = 1.134. Uncertainty factor is 1.134, 1σ
Assume a 3σ uncertainty design margin is provided by, pburst ≈ 1769 x ( 1.134 )3 = 2,582 psi
Assume Ultimate Factor of Safety FOS = 1.5
Rocket Baseline Steel Case ( σt )ult = 190,000 psi
tHoop = ( FOS ) x pburst x r / σt = 1.5 x 2582 x 4.0 / 190,000 = 0.082 in
tDome = ( FOS ) x pburst x ( a b )1/2 x [ 2 + ( a / b )2 ] / ( 6 σt ) = 1.5 x 2582 x [ 4 x 2 ]1/2 x [ 2 + ( 2 )2 ] / [ 6 x 190,000 ]
= 0.058 in
Weight = WCylinder + WDome = ρ π d tHoop l + ρ ( 2 π a b ) tDome = 30.8 + 0.8 = 31.6 lb for steel case
Try Graphite Fiber at σt = 450,000 psi Ultimate, Assume 60% Fiber / 40% Epoxy Composite
tHoop = 1.5 x 2582 x 4.0 / [ 450,000 ( 0.60 )] = 0.057 in radial fibers for internal pressure load
tDome = 0.041 in, for internal pressure load
Weight = 11.1 lb for composite case ( w/o insulation, attachment, aft dome, and body bending fiber )
Must also add about 0.015 in of either longitudinal fibers or helical wind to counteract body bending load
2/24/2008
ELF
168
WSurface σmax1/2 / ( ρ S Nmax1/2 ), Non-dimensional Weight
A Low Aspect Ratio Delta Wing Allows Lighter
Weight Structure
3
WSurface σmax1/2 / [ ρ S Nmax1/2 ] = [ A ( 1 + 2 λ )]1/2
Note:
WSurface = ρ S tmac
Surface is 2 panels ( Cruciform wing has 4 panels )
WSurface = Surface weight sized by bending moment
troot = [ FOS Nmax A ( 1 + 2 λ ) / σmax,]1/2
ρ = Density
Assumption: Uniform loading
σmax = Maximum allowable ( ultimate ) stress
tmac = Thickness of mean aero chord cmac
2
troot = Thickness of root chord croot
Nmax = Maximum load
A = Aspect ratio
λ = Taper ratio
1
Example for Rocket Baseline Wing ( 2219-T81
Aluminum ): A = 2.82, λ = 0.175, cr = 19.4 in, σmax =
σult = 65k psi
Assume M = 2, h = 20k ft, α + δ = 22 deg
From prior example, Nmax = 7525 lb
0
0
1
Calculate t = [ 1.5 ( 7525 ) ( 2.82 ) [ 1 + 2 ( 0.175 ) /
3 65000 ]1/2 =root0.813 in
2
A, Aspect Ratio
Taper Ratio = 0
2/24/2008
Taper ratio = 0.5
troot / croot = 0.813 / 19.4 = 0.0419 = tmac / cmac
Taper Ratio = 1
ELF
tmac = 0.0419 ( 13.3 ) = 0.557 in
Wwing σmax1/2 / [ ρ S Nmax1/2 ] = [ A ( 1 + 2 λ )]1/2.= 1.95
Wwing = 20.6 lb for 1 wing ( 2 panels )
169
Dome Material Is Driven by the Type of Seeker
and Flight Environment
Seeker
Dome
Material
RF-IR Seeker
Zinc Sulfide
( ZnS )
Zinc Selenide
( ZnSe )
Sapphire /
Spinel
Quartz / Fused
Silica ( SiO2 )
Silicon Nitride
( Si3N4 )
Diamond ( C )
RF Seeker
Pyroceram
Polyimide
IR Seeker
Mag. Fluoride
( MgF2 )
Alon
( Al23O27N5 )
Germanium
( Ge )
2/24/2008
Density
( g / cm3 )
Dielectric
Constant
MWIR /
LWIR
Bandpass
Transverse
Strength
( 103 psi )
Thermal
Expansion
( 10-6 / ο F )
Max ShortErosion,
Knoop ( kg
Duration
2
/ mm )
Temp ( ο F )
4.05
8.4
18
4
350
700
5.16
9.0
8
4
150
600
3.68
8.5
28
3
1650
1800
2.20
3.7
8
0.3
600
2000
3.18
6.1
90
2
2200
2700
3.52
5.6
400
1
8800
3500
2.55
1.54
5.8
3.2
25
17
3
40
700
70
2200
400
3.18
5.5
7
6
420
1000
3.67
9.3
44
3
1900
1800
5.33
- 16.2
15
4
780
200
Superior
-
-
Above Average
ELF
Average
Below Average
-
Poor
170
topt / ( N λ0 ), Non-dimensional Optimum Thickness
Radome Weight May Be Driven by Optimum
Thickness Required for Efficient Transmission
1
WOptTrans = ρ Swet tOptTrans
Note:
tOptTrans = 0.5 n λ0 / ( ε - sin2 θi )1/2
WOptTrans = Weight at Optimum Transmission
θ
δ
ρ = Density
90 deg
θi
Swet = Surface wetted area
tOptTrans = Optimum thickness for 100% transmission
d
n = Integer ( 1, 2, … )
l
λ0 = Wavelength in air
ε = Dielectric constant
θi = Radar signal incidence angle = 90 deg - δ - θ
θ = Surface local angle
δ = Seeker look angle
Example for Rocket Baseline Pyroceram Radome:
ε = 5.8, ρ = 0.092 lb / in3, λ0 = 1.1 in, n = 1, tangent
ogive, l = 19.2 in, d = 8 in, Swet = 326 in2
10
δ = 0 deg ⇒ ( θI )avg ≈ 90 – 0 - 11.8 = 78.2 deg
0.1
1
ε, Dielectric Constant
Incidence Angle = 0 deg
Incidence Angle = 80 deg
Incidence Angle = 40 deg
tOptYtans = 0.5 ( 1 ) ( 1.1 ) / ( 5.8 – 0.96 )1/2 = 0.25 in
WOptTrans = 0.092 ( 326 ) ( 0.25 ) = 7.5 lb
2/24/2008
ELF
171
Missile Electrical Power Supply Alternatives
W = WE E + WP P
Measure of Merit
Power Supply
Generator
Lithium Battery
Thermal Battery
Storage Life
Cost
WE, Weight /
Energy
( kg / kW-s )
0.0007
0.0012
0.0125
WP, Weight / Power
( kg / kW )
1.4
1.5
0.3
Voltage Stability
Superior
Above Average
Average
Below Average
Example for Thermal battery: If E = 900 kW–s, P = 3 kW ⇒ W = WEE + WPP = 0.0125 ( 900 ) + 0.3 ( 3 ) = 12.2 kg
Note: Generator provides highest energy with light weight for long time of flight ( e.g., cruise missile ).
Lithium battery provides nearly constant voltage suitable for electronics. Relatively high energy with light weight.
Thermal battery provides highest power with light weight ( may be required for actuators ).
2/24/2008
ELF
172
Electromechanical Actuators Are Light Weight
and Reliable
W = WT TS
Measure of Merit
EM
Cold Gas Pneumatic
Hydraulic
WT, Weight / Stall Torque ( lb /
in-lb )
0.0025
0.0050
0.0034
Rate ( deg / s )
Up to 800
Up to 600
Up to 1000
Bandwidth ( Hz )
Up to 40
Up to 20
Up to 60
Reliability
Cost
Superior
Above Average
Average
Note:
Below Average
Schematic of Cold Gas Pneumatic Actuation
•Actuation system weight based on four actuators.
•Cold gas pneumatic actuation weight includes actuators, gas bottle,
valves, regulator, and supply lines.
•Hydraulic actuation weight includes actuators, gas generator or gas
bottle, hydraulic reservoir, valves, and supply lines.
•Stall torque ≈ 1.5 maximum hinge moment of single panel.
Example weight for rocket baseline hydraulic actuation at Mach 2, 20k ft alt, α = 9 deg, with max control deflection of wing ( δ
= 13 deg ) ⇒ Hinge moment of one panel = 11,500 in-lb. TS = 1.5 ( 11500 ) = 17,250 in-lb ⇒ W = WTTS = 0.0034 ( 17250 ) = 59 lb
2/24/2008
ELF
173
Examples of Electromechanical Actuator
Packaging
Canard ( Stinger ) ……………
Tail ( AMRAAM ) …………………………………………………………………
Jet Vane / Tail ( Javelin ) ……
Movable Nozzle ( THAAD ) ……………………………………………………………
2/24/2008
ELF
174
Summary of Weight
Conceptual Design Weight Prediction Methods and Weight
Considerations
Missile system weight, cg, moment of inertia
Factors of safety
Aerodynamic heating
Structure
Dome
Propulsion
Insulation
Power supply
Actuator
Manufacturing Processes for Low Parts Count, Low Cost
Precision castings
Vacuum assisted RTM
Pultrusion / Extrusion
Filament winding
2/24/2008
ELF
175
Summary of Weight ( cont )
Design Considerations
Airframe materials
Insulation materials
Seeker dome materials
Thermal stress
Aerodynamic heating
Technologies
MEMS
Composites
Titanium alloys
High density insulation
High energy and power density power supply
High torque density actuators
Discussion / Questions?
Classroom Exercise ( Appendix A )
2/24/2008
ELF
176
Weight Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
2/24/2008
Propulsion system and structure weight are driven by f_____ o_ s_____
requirements.
For a ballistic range greater than about 200 nautical miles, a t__ s____ missile
is lighter weight.
Tactical missile weight is proportional to v_____.
Subsystem d______ for tactical missiles is about 0.05 lb / in3
Modeling weight, balance, and moment-of-inertia is based on a build-up of
s_________.
Missile structure factor of safety for free flight is usually about 1.25 for
ultimate loads and about 1.10 for y____ loads.
Manufacturing processes that can allow low parts count include vacuum
assisted resin transfer molding of composites and c______ of metals.
Low cost airframe materials are usually based on aluminum and steel while
light weight airframe materials are usually based c________ materials.
Graphite fiber has high strength and high m______ o_ e_________.
ELF
177
Weight Problems ( cont )
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
2/24/2008
The recovery factors of stagnation, turbulent boundary layer, and laminar
boundary layer are 1.0, 0.9, and ___ respectively.
The most popular types of insulation for temperatures greater than 4,000 R
are charring insulators based on p_______ composites.
Tactical missiles experience transient heating, and with increasing time
the temperature approaches the r_______ temperature.
The inner wall temperature is nearly the same as the surface temperature
for a t________ t___ structure.
A thermally thick surface is a good i________.
A low conductivity structure is susceptible to thermal s_____.
The minimum gauge thickness is often set by the m____________ process.
A very thin wall structure is susceptible to localized b_______.
Ejection loads and flight control loads often result in large b______
moment.
An approach to increase the tactical missile propellant / motor weight
fraction over the typical value of 72% would be c________ motor case.
ELF
178
Weight Problems ( cont )
20.
21.
22.
23.
24.
2/24/2008
The required rocket motor case thickness is often driven by the
combustion chamber p_______.
A low aspect ratio delta wing has reduced w_____.
For low speed missiles, a popular infrared dome material is z___ s______.
A thermal battery provides high p____.
The most popular type of actuator for tactical missiles is an
e________________ actuator.
ELF
179
Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
2/24/2008
ELF
180
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Define Mission Requirements
Alt Mission
Establish Baseline
Alt Baseline
Aerodynamics
Propulsion
Weight
Resize / Alt Config / Subsystems / Tech
Trajectory
Meet
Performance?
No
Yes
Measures of Merit and Constraints
No
Yes
2/24/2008
ELF
181
Flight Envelope Should Have Large Max Range,
Small Min Range, and Large Off Boresight
Off Boresight Flyout Envelope / Range
•Max
•Min
Forward Flyout Envelope / Range
•Max
•Min
Examples of Max / Min Range Limitations:
Fire Control System Range and Off Boresight
Seeker Range, Gimbal Angle, and Tracking Rate
Maneuver Capability
Time of Flight
Closing Velocity
2/24/2008
ELF
182
Conceptual Design Modeling Versus Preliminary
Design Modeling
Conceptual Design Modeling
1 DOF [ Axial force ( CDO ), thrust, weight ]
2 DOF [ Normal force ( CN ), axial force, thrust, weight ]
3 DOF point mass [ 3 aero forces ( normal, axial, side ),
thrust, weight ]
3 DOF pitching [ 2 aero forces ( normal, axial ), 1 aero
moment ( pitching ), thrust, weight ]
4 DOF [ 2 aero forces ( normal, axial ), 2 aero moments
( pitching, rolling ), thrust, weight ]
CDO
CN
CA
CN
CA
CN
2/24/2008
ELF
Cm
CA
CN
Cm
Cl
CN
Cm
Cl
CA
Preliminary Design Modeling
6 DOF [ 3 aero forces ( normal, axial, side ), 3 aero
moments ( pitching, rolling, yawing ), thrust, weight ]
CY
CA
Cn
CY
183
1-DOF Coast Equation May Have Good Accuracy
Near Zero Angle of Attack
2.0
1.5
•
•
( V )2-DOF / ( V )1-DOF,
Predicted Deceleration
1.0
Comparison for Rocket
Baseline
0.5
0
Note:
–
–
–
–
–
2/24/2008
0
2
4
6
8
αTrim, Trim Angle of Attack, Deg
10
.
( V. )2-DOF = Two-degrees-of-freedom deceleration
( V )1-DOF = One-degree-of-freedom deceleration
Rocket baseline during coast
Mach 2, h = 20,000 ft
αTrim ≈ 0.3 deg for 1-g flyout
ELF
184
3-DOF Simplified Equations of Motion Show
Drivers for Configuration Sizing
+ Normal Force
+ Thrust
+ Moment
θ
α << 1 rad
V
γ
W
δ
+ Axial Force
..
Configuration Sizing Implication
..
Ιy θ ≈ Ιy α ≈ q SRef d Cmα α + q SRef d Cmδ δ
.
( W / gc ) V γ ≈ q SRef CNα α + q SRef CNδ δ - W cos γ
( W / gc
.
)V ≈T-C
A SRef
q - CNα α2 SRef q - W sin γ
High Control Effectiveness ⇒ Cmδ >
Cm , Iy small ( W small ), q large
α
Large / Fast Heading Change ⇒ CN
large, W small, q large
High Speed / Long Range ⇒ Total
Impulse large, CA small, q small
Note: Based on aerodynamic control
2/24/2008
ELF
185
For Long Range Cruise, Maximize V Isp, L / D,
and Weight Fraction of Fuel / Propellant
R = ( V Isp ) ( L / D ) ln [ WBC / ( WBC - WP )] , Breguet Range Equation
R, Cruise Range, ft
1.00E+08
ith Wing
w
t
e
j
o
b
r
onic Tu
s
b
rframe
i
u
A
S
l
c
i
a
r
c
t
i
e
Typ
xisymm
A
h
t
i
w
t
Ramje
Typical
Airframe
c
i
r
t
e
m
th Axisym
i
w
t
e
k
c
o
Typical R
1.00E+07
1.00E+06
Example: Ramjet Baseline at Mach 3 / 60k ft alt
R = 2901 ( 1040 ) ( 3.15 ) ln [ 1739 / ( 1739 - 476 )]
= ( 9,503,676 ) ln [ 1 / ( 1 - 0.2737 )] = 3,039,469 ft
= 500 nm
1.00E+05
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
WP / WBC, Propellant or Fuel Weight / Weight at Begin of Cruise
( V ISP )( L / D ) = 2,000,000 ft
( V ISP )( L / D ) = 25,000,000 ft
( V ISP )( L / D ) = 10,000,000 ft
Note: R = cruise range, V = cruise velocity, ISP = specific impulse, L = lift, D = drag,
WBC = weight at begin of cruise, WP = weight of propellant or fuel
2/24/2008
ELF
186
Efficient Steady Flight Is Enhanced by High L / D
and Light Weight
Steady Level Flight
L
D
T=D
L=W
T
Steady Climb
T–D
L γC
D
W
T=W/(L/D)
Note:
D–T
T
V∞
L
γD
D
γC
W
SIN γc = ( T – D ) / W = Vc / V∞
Vc = ( T – D ) V∞ / W
RC = Δh / tan γC = Δh ( L / D )
• Small Angle of Attack
• Equilibrium Flight
• VC = Velocity of Climb
• VD = Velocity of Descent
• γC = Flight Path Angle During Climb
• γD = Flight Path Angle During Descent
• V∞ = Total Velocity
• Δh = Incremental Altitude
• RC = Horizontal Range in Steady Climb
• RD = Horizontal Range in Steady Dive ( Glide )
2/24/2008
Steady Descent ( Glide )
VC
T
W
VD
γD
V∞
SIN γD = ( D – T ) / W = VD / V∞
V D = ( D – T ) V ∞/ W
RD = Δh / tan γD = Δh ( L / D )
Reference: Chin, S.S., “Missile Configuration Design,”
McGraw Hill Book Company, New York, 1961
ELF
187
Flight Trajectory Lofting / Shaping Provides
Extended Range
Apogee or Cruise
Climb
Altitude
Glide
Rapid Pitch Up
Line-Of-Sight Trajectory
RMAX
Range
RMAX
Lofted Trajectory Design Guidelines for Horizontal Launch:
– High thrust-to-weight ≈ 10 for safe separation
– Rapid pitch up minimizes time / propellant to reach efficient altitude
– Climb at α ≈ 0 deg with thrust-to-weight T / W ≈ 2 and q ≈ 700 psf to minimize drag /
propellant
– Apogee at q ≈ 700 psf, followed by either ( L / D )MAX cruise or ( L / D )MAX glide
2/24/2008
ELF
188
Small Turn Radius Using Aero Control Requires
High Angle of Attack and Low Altitude Flight
.
RT = V / γ ≈ 2 W / ( gc CN SRef ρ )
Assumption: Horizontal Turn
RT, Example Instantaneous Turn Radius, ft
1000000
Note for Example Figure:
W = Weight = 2,000 lb
a / b = 1 ( circular cross section ), No wings
CN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2 α
l / d = Length / Diameter = 10
SRef = 2 ft2
CDO = 0.2
( L / D )Max = 2.5
q( L / D ) ≈ 700 psf
Max
α( L / D ) = 15 deg
Max
T( L / D ) = 740 lb
100000
10000
Max
Example:
Δ α = 10 deg
CN = 0.94
1000
0
5
10
15
Delta Alpha, Deg
h = sea level
h = 60k ft
2/24/2008
h = 20k ft
h = 80k ft
20 h = 40k ft ( ρ = 0.000585 slug / ft3 )
RT = 2 ( 2,000 ) / [( 32.2 ) ( 0.94 ) ( 2 ) (
0.000585 )] = 112,000 ft
h = 40k ft
ELF
Note: Require ( RT )Missile ≤ ( RT )Target, for
small miss distance
189
High Turn Rate Using Aero Control Requires
High Angle of Attack and High Velocity
.
γ = gc CN ρ V SRef / ( 2 W ), rad / s
Assumption: Horizontal Turn
n=
g
100
Example Gamma Dot, Turn Rate, deg / s
20
15
10
5
0
0
1000
2000
3000
Velocity, ft / s
Alpha = 15 deg
Alpha = 90 deg
2/24/2008
Alpha = 30 deg
ELF
Example for Lifting Body at Altitude h = 20,000 ft:
Assume:
• W = Weight = 2,000 lb
• a / b = 1 ( circular cross section )
• No wings
• Negligible tail lift
• Neutral static stability
CN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2 α
• SRef = 2 ft2
• l / d = Length / Diameter = 10
• α = 15 deg
• V = 2000 ft / s
Then:
• N = Normal Force = CN q SRef
CN = sin [ 2 ( 15 )] cos ( 15 / 2 ) + 2 ( 10 ) sin2 ( 15 ) =
0.50 + 1.34 = 1.835
q = Dynamic Pressure = 0.5 ρ V2 = 0.5 ( 0.001267 ) (
2000 )2 = 2534 psf
N = 1.835 ( 2534 ) ( 2 ) = 9,300 lb
N / W = 9300 / 2000 = 4.65 g
.
γ = 32.2 ( 1.835 ) ( 0..001267 ) ( 2000 ) ( 2 ) / [ 2 ( 2000 )]
= 0.0749 rad / s = 4.29 deg / s
190
For Long Range Coast, Maximize Initial Velocity
and Altitude and Minimize Drag Coefficient
V / Vi = { 1 – [( gc sin γ ) / Vi ] t } / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }
{[ gc ρAVG SRef ( CD0 )AVG ] / ( 2 W )} R = ln { 1 – [ gc2 ρAVG SRef ( CD0 )AVG / ( 2 W )] [ sin γ ] t2
+ {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }
1
V / Vi @ γ = 0 deg
Note: Based on 1 DOF coast
0.8
dV / dt = - gc CD0 SRef q / W – gc sin γ
Assumptions:
0.6
• γ = constant
0.4
• α ≈ 0 deg
0.2
{[ gc ρAVG SRef (CD0 )AVG ] / ( 2 W )} R
• D > W sin γ
@ γ = 0 deg
V = velocity during coast
0
Vi = initial velocity ( begin coast )
0
0.5
1
1.5
[( gc ρ SRef CD Vi ) / ( 2W )] t, Non-dimensional Coast Time
0
2 R = coast range
Vx = V cos γ, Vy = V sin γ
Rx = R cos γ, Ry = R sin γ
Example for Rocket Baseline:
•W = WBO = 367 lb, SRef = 0.349 ft2, Vi = 2,151 ft / s, γ = 0 deg, ( CD )AVG = 0.9, h = 20,000 ft ( ρ = 0.00127 slug / ft3 ), t = 10 s
0
•[( gc ρ SRef ( CD )AVG Vi ) / ( 2 W )] t = {[ 32.2 ( 0.00127 ) ( 0.349 ) ( 0.9 ) ( 2151 )] / [ 2 ( 367 ) ]} 10 = 0.376
0
•V / Vi = 0.727 ⇒ V = 0.727 x 2151 = 1564 ft / s, {[( gc ρ SRef ( CD )AVG )] / ( 2 W )} R = 0.319 ⇒ Rcoast = 18,300 ft or 3.0 nm
0
2/24/2008
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191
For Ballistic Range, Maximize Initial Velocity,
Optimize Launch Angle, and Minimize Drag
Vx / Vi = cos γi / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }
( Vy + gc t ) / Vi = sin γi / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }
1.2
{[ gc ρAVG SRef (CD0 )AVG ] / ( 2 W cos γi )} Rx
1
0.8
= ln { 1 + [ gc ( ρ )AVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }
0.6
{[ gc ρAVG SRef (CD0 )AVG ] / ( 2 W sin γi )} ( h – hi + gc t2 / 2 )
= ln { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W ) t }
0.4
Assumptions: Thrust = 0, α = 0 deg, D > W sin γ, flat earth
0.2
0
0
0.5
1
1.5
2
Nomenclature: V = velocity during ballistic flight, Vi = initial
velocity, Rx = horizontal range, h = altitude, hi = initial altitude,
Vx = horizontal velocity, Vy = vertical velocity
{[ gc ρAVG SRef ( CD )AVG Vi ] / ( 2 W )} t, Non-dimensional Time
0
Example for Rocket Baseline:
•W = 367 lb, SRef = 0.349 ft2, Vi = VBO = 2,151 ft / s, γi = 0 deg, ( CD )AVG = 0.9, hi = 20,000 ft, ρAVG = 0.00182 slug / ft3, t = 35 s
0
•[ gc ρ SRef ( CD )AVG Vi / ( 2 W )] t = { 32.2 ( 0.00182 ) ( 0.349 ) ( 0.9 ) ( 2151 ) / [ 2 ( 367 ) ]} 35 = 1.821
0
•Vx / Vi = 0.354 ⇒ Vx = 762 ft / s, ( Vy + 32.2 t ) / Vi = 0.354 ⇒ Vy = - 1127 ft / s, {[ gc ρ SRef ( CD )] / ( 2 W cos γi )} Rx = 1.037 ⇒
0
Rx = 42,900 ft or 7.06 nm, {[ gc ρAVG SRef ( CD )AVG ] / ( 2 W sin γi )} ( h – hi + 16.1 t2 ) = 1.037 ⇒ h = 0 ft
2/24/2008
0
ELF
192
High Propellant Weight, High Thrust, and Low
Drag Provide High Burnout Velocity
Delta V / ( g ISP ), Nondimensional
Incremental Velocity
ΔV / ( gc ISP ) = - [ 1 – ( DAVG / T ) – ( WAVG sin γ / T )] ln ( 1 - Wp / Wi )
0.7
Example for Rocket Baseline:
0.6
Assume γ = 0 deg
Assume Mi = 0.8, h = 20k ft
0.5
Wi = WL = 500 lb
0.4
For boost, WP = 84.8 lb
WP / WL = 0.1696
0.3
ISP = 250 s
0.2
TB = 5750 lb
0.1
Assume D = DAVG = 635 lb
0
DAVG / T = 0.110
0
0.1
0.2
0.3
0.4
0.5
Wp / Wi, Propellant Fraction
DAVG / T = 0
DAVG / T = 0.5
ΔV / [( 32.2 ) ( 250 )] = - ( 1 - 0.110 )
ln ( 1 - 0.1696 ) = 0.1654
ΔV = ( 0.1654 ) ( 32.2 ) ( 250 ) =
1331 ft / s
DAVG / T = 1.0
Note: 1 DOF Equation of Motion with α ≈ 0 deg, γ = constant, Wi = initial weight, WAVG = average weight, WP =
propellant weight, ISP = specific impulse, T = thrust, Mi = initial Mach number, h = altitude, DAVG = average drag,
ΔV = incremental velocity, gc = gravitation constant, Vx = V cos γ, Vy = V sin γ, Rx = R cos γ, Ry = R sin γ
2/24/2008
Note: R = ( Vi + ΔV / 2 ) tB, where R = boost range, Vi = initial velocity, tB = boost time
ELF
193
High Missile Velocity and Lead Are Required to
Intercept High Speed Crossing Targets
VM sin L = VT sin A, Proportional Guidance Trajectory
4
VM
Note:
Proportional Guidance
VM = Missile Velocity
VT = Target Velocity
A = Target Aspect
L = Missile Lead Angle
≈Seeker Gimbal
3
VM / VT
L A
VT
2
A = 90°
Example:
1
0
A = 45°
L = 30 deg
A = 45 deg
VM / VT = sin ( 45° ) / sin ( 30° ) =
1.42
0
10
20
30
40
50
L, Lead Angle, Deg
2/24/2008
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194
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Define Mission Requirements
Alt Mission
Establish Baseline
Alt Baseline
Aerodynamics
Propulsion
Weight
Resize / Alt Config / Subsystems / Tech
Trajectory
Meet
Performance?
No
Yes
Measures of Merit and Constraints
No
Yes
2/24/2008
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195
Summary of Flight Performance
Flight Performance Activity in Missile Design
Compute range, velocity, time-to-target, off boresight
Compare with requirements
Discussed in This Chapter
Equations of motion
Flight performance drivers
Propulsion alternatives range comparison
Steady level flight required thrust
Steady climb and steady dive range prediction
Cruise prediction
Boost prediction
Coast prediction
Ballistic flight prediction
Turn radius and turn rate prediction
Target lead for proportional homing guidance
2/24/2008
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196
Summary of Flight Performance ( cont )
Flight Performance Strongly Impacted by
Aerodynamics
Propulsion
Weight
Discussion / Questions?
Classroom Exercise ( Appendix A )
2/24/2008
ELF
197
Flight Performance Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
2/24/2008
Flight trajectory calculation requires input from aero, propulsion, and w_____.
Missile flight envelope can be characterized by the maximum effective range,
minimum effective range, and o__ b________.
Limitations to the missile effective range include the fire control system,
seeker, time of flight, closing velocity, and m_______ capability.
1 DOF simulation requires modeling only the thrust, weight, and a____ f____.
A 3 DOF simulation that models 3 aero forces is called p____ m___ simulation.
A simulation that includes 3 aero forces ( normal, axial, side ), 3 aero moments
( pitch, roll, yaw ), thrust, and weight is called a _ DOF simulation.
..
The pitch angular acceleration θ is approximately equal to the second time
derivative of the a____ o_ a_____.
Cruise range is a function of velocity, specific impulse, L / D, and f___ fraction.
If thrust is equal to drag and lift is equal to weight, the missile is in s_____
l____ flight.
Turn rate is a function of normal force, weight, and v_______.
ELF
198
Flight Performance Problems ( cont )
11.
12.
13.
14.
15.
16.
17.
18.
2/24/2008
Coast range is a function of initial velocity, weight, drag, and the t___ of flight.
Incremental velocity due to boost is a function of ISP, drag, and p_________
weight fraction.
To intercept a high speed crossing target requires a high speed missile with a
high g_____ angle seeker.
An analytical model of a rocket in co-altitude, non-maneuvering flight can be
developed by patching together the flight phases of boost and c____.
An analytical model of a rocket in a short range, off-boresight intercept can be
developed by patching the flight phases of boost and t___.
An analytical model of a guided bomb in non-maneuvering flight can be
developed from the flight phase of a steady d___.
An analytical model of an unguided weapon can be developed from the
b________ flight phase.
An analytical model of a ramjet in co-altitude, non-maneuvering flight can be
developed by patching the flight phases of boost and c_____.
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199
Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
2/24/2008
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200
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Define Mission Requirements
Alt Mission
Establish Baseline
Alt Baseline
Aerodynamics
Propulsion
Weight
Resize / Alt Config / Subsystems / Tech
Trajectory
Meet
Performance?
No
Yes
Measures of Merit and Constraints
No
Yes
2/24/2008
ELF
201
Measures of Merit and Launch Platform
Integration Should Be Harmonized
Launch Platform
Integration /
Firepower
Robustness
Lethality
Cost
Balanced Design
Miss Distance
Reliability
Other
Survivability
Considerations
2/24/2008
Carriage and
Launch
Observables
ELF
202
Tactical Missiles Must Be Robust
Tactical Missiles Must Have Robust Capability to
Handle
Robustness
Launch Platform
Integration /
Firepower
Robustness
Cost
Lethality
Reliability
Miss Distance
Other
Survivability
Considerations
Carriage and
Launch
Observables
Adverse Weather
Clutter
Local Climate
Flight Environment Variation
Uncertainty
Countermeasures
EMI / EMP
This Section Provides Examples of Requirements for
Robustness
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203
Adverse Weather and Cloud Cover Are Pervasive
North Pole
Region
North Atlantic
NOAA satellite image
of earth cloud cover
Annual Average 1.0
Fraction of
Cloud Cover
0.8
Rising Air Rising Air
Descending
Air
South Pole
Region
0.6
0.4
Argentina, Southern
Africa and Australia
Note: Annual Average Cloud Cover
Global Average
= 61%
Global Average Over Land
= 52%
Global Average Over Ocean = 65%
0.2
0.0
65°N
45°N
25°N
5°N
Cloud
Cover
Over Land
Descending
Air
Deserts ( Sahara,
Gobi, Mojave )
85°N
Cloud Cover
Over Ocean
0°
5°S
25°S
45°S
65°S
85°S
Latitude Zone
Reference: Schneider, Stephen H. Encyclopedia of Climate and Weather. Oxford University Press, 1996.
2/24/2008
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204
Radar Seekers Are Robust in Adverse Weather
O2, H2O
1000
ATTENUATION (dB / km)
100
Note:
H2O H2O
O2
EO attenuation through
cloud at 0.1 g / m3 and 100
m visibility
EO attenuation through
rain at 4 mm / h
Humidity at 7.5 g / m3
Millimeter wave and
microwave attenuation
through cloud at 0.1
gm / m3 or rain at 4 mm / h
CO2
10
H2O
O2
H2O, CO2
CO2
1
H2O
20° C
1 ATM
H2O
EO sensors are ineffective
through cloud cover
O3
0.1
X Ku K Ka Q V W
MILLIMETER
RADAR
0.01
10 GHz
3 cm
100
3 mm
Radar sensors have good to
superior performance
through cloud cover and rain
Very Long Long Mid Short
1 THz
0.3 mm
VISIBLE
INFRARED
SUBMILLIMETER
10
30 µm
100
3.0 µm
1000
0.3 µm
Increasing Frequency
Increasing Wavelength
Source: Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997
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205
Radar Seekers Are Desirable for Robust
Operation within the Troposphere Cloud Cover
40
Cumulonimbus ( 2 – 36k ft )
Cirrus ( 16 – 32k ft )
30
h,
Altitude,
103 ft
20
Altostratus ( 8 – 18k ft )
Altocumulus ( 9 – 19k ft )
10
Stratus ( 1 – 7k ft )
Cumulus ( 2 – 9k ft )
Fog
0
Note:
•IR seeker may be able to operate “Under the Weather” at elevations less than 2,000 ft using GPS / INS midcourse guidance
•IR attenuation through cloud cover greater than 100 dB per km. Cloud droplet size ( 0.1 to 50 μm ) causes resonance.
•mmW has ~ 2 dB / km attenuation through rain. Typical rain drop size ( ∼ 4 mm ) is comparable to mmW wavelength.
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206
Precision Strike Missile Target Sensors Are
Complemented by GPS / INS / Data Link Sensors
Sensor
Adverse
Weather
Impact
ATR / ATA
in Clutter
Range
Moving
Target
Volume
Search
Time
Hypersonic
Dome
Compat.
Diameter
Required
Weight and
Cost
• SAR
-
• Active
Imaging
mmW
• Passive
Imaging
mmW
• Active
Imaging IR
(LADAR)
• Active Nonimage IR
(LADAR)
• Active Nonimage mmW
• Passive
Imaging IR
• Acoustic
-
-
2/24/2008
-
-
• GPS / INS /
Data Link
Note:
-
-
-
Maturity
-
-
Superior
Good
Below Average
ELF
- Poor
207
Imaging Sensors Enhance Target Acquisition /
Discrimination
Imaging LADAR
Passive Imaging mmW
2/24/2008
Imaging Infrared
Video of Imaging Infrared
ELF
SAR
Video of SAR Physics
208
Example of Mid Wave – Long Wave IR Seeker
Comparison
Assume Exo-atmospheric Intercept with
Target diameter DT = 2 ft ( AT = 2919 cm2 ), temperature TT = 300 K, emissivity ε = 0.5
Diameter of seeker aperture do = 5 in ( Ao = 0.01267 m2 )
Diameter of pixel detector dp = 40 μm
Spot resolution if diffraction limited = dspot = dp = 40 μm
Temperature of pixel detector Td = 77 K
Focal plane array size 256x256 FPA ( Ad = 1.049 cm2 )
Pixel detector bandwidth Δfp = 50 Hz ( tinteg = 0.00318 s )
Required signal-to-nose ratio for detection ( S / N )D = 5
First Calculate MWIR Seeker Detection Range
RD = { ( IT )Δλ ηa Ao { D* / [( Δfp )1/2 ( Ad )1/2 ]} ( S / N )D-1 }1/2, m
Radiant intensity of target within seeker bandwidth ( IT )Δλ = ε Lλ ( λ2 - λ1 ) AT, W sr-1
Spectral radiance of target Lλ = 3.74 x 104 / { λ5 { e[ 1.44 x 104 / ( λ TT )] – 1 }}, W cm-2 sr-2 μm-1
Assume λ = 4 μm, λ2 = 5 μm, λ1 = 3 μm, then
Lλ = 0.000224 W cm-2 sr-2 μm-1, ( IT )Δλ = 0.643 W sr-1
Assume Hg0.67Cd0.33Te detector at λ = 4 μm and 77 K ⇒ D* = 8 x 1011 cm Hz1/2 W-1
RD = { ( 0.643 ) ( 1 ) ( 0.01267 ) {( 8 x 1011 ) / [( 50 )1/2 ( 1.049 )1/2 ]} ( 5 )-1 }1/2 = 13,480 m
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209
Example of Mid Wave – Long Wave IR Seeker
Comparison ( cont )
Next, Calculate LWIR Seeker Detection Range
RD = { ( IT )Δλ ηa Ao { D* / [( Δfp )1/2 ( Ad )1/2 ]} ( S / N )D-1 }1/2, m
( IT )Δλ = ε Lλ ( λ2 - λ1 ) AT, W sr-1
Lλ = 3.74 x 104 / { λ5 { e[ 1.44 x 104 / ( λ TT )] – 1 }}, W cm-2 sr-2 μm-1
Assume λ = 10 μm, λ2 = 13 μm, λ1 = 7 μm, then
Lλ = 0.00310 W cm-2 sr-2 μm-1, ( IT )Δλ = 26.7 W sr-1
Assume Hg0.80Cd0.20Te detector at λ = 10 μm and 77 K ⇒ D* = 5 x 1010 cm1/2 Hz1/2 W-1
RD = { ( 26.7 ) ( 1 ) ( 0.01267 ) {( 5 x 1010 ) / [( 50 )1/2 ( 1.049 )1/2 ]} ( 5 )-1 }1/2 = 21,600 m
( λ )( Lλ )max = 2898 / TT, Wein’s Displacement Law, TT in K
15
Subsonic Airframe
I
LW
10
Mach 4 Airframe
R
Wavelength for Max Spectral
Radiance, Microns
MWIR Seeker Versus LWIR Seeker Selection Depends Upon Target Temperature
MW
IR
5
Jet Engine
Rocket Plume
Flare
Example: TT = 300 K
0
0
500
1000
1500
TT, Target Temperature, K
2/24/2008
ELF
2000
( λ )( Lλ )max = 2898 / TT
= 2898 / 300 = 10.0 μm
210
GPS / INS Provides Robust Seeker Lock-on in
Adverse Weather and Clutter
Target Image
480 Pixels
•
640 Pixels ( 300 m )
175 m
Seeker Lock-on @ 850 m to go ( 1 pixel = 0.47 m )
Seeker Lock-on @ 500 m to go ( 1 pixel = 0.27 m )
3 m GPS / INS error ⇒ nM
3 m GPS / INS error ⇒ nM
req
= 0.15 g, σ < 0.1 m
req
88 m
= 0.44 g, σ < 0.1 m
44 m
Seeker Lock-on @ 250 m to go ( 1 pixel = 0.14 m )
Seeker Lock-on @ 125 m to go ( 1 pixel = 0.07 m )
3 m GPS / INS error ⇒ nM
3 m GPS / INS error ⇒ nM
req
2/24/2008
= 1.76 g, σ = 0.9 m
req
= 7.04 g, σ = 2.2 m
Note:
= Target Aim Point and Seeker Tracking Gate, GPS / INS Accuracy = 3 m, Seeker 640 x 480 Image, Seeker
FOV = 20 deg, Proportional Guidance Navigation Ratio = 4, Velocity = 300 m / s, G&C Time Constant = 0.2 s.
ELF
211
Data Link Update at Seeker Lock-on Reduces
Moving Target Error
Target Error at Seeker Lock-on, m
TESeekerLock-on = [ TLE2 + ( VT tLatency )2 ]1/2
1000
VT = 1 m / s
VT = 10 m / s
VT = 100 m / s
VT = 1000 m / s
100
10
0.1
1
10
100
Target Latency at Seeker Lock-on, s
1000
Example:
TLE = 10 m
tSeekerLock-on = 100 s
tUdate = 90 s
VT = 10 m / s
tLatency = tSeeker- tUdate = 100 – 90 = 10 s
TESeekerLock-on = [ TLE2 + ( VT tLatency )2 ]1/2
= { 102 + [ 10 ( 10 )]2 ]1/2
= 100.5 m
Note: tSeekerLock-on = Seeker Lock-on time, tUdate = Data Link Update Time, VT = Target Velocity, TLE = Target Location
Error at Update = 10 m
2/24/2008
ELF
212
Optimum Cruise Is a Function of Mach Number,
Altitude, and Planform Geometry
120
Scramjet
h, Altitude, kft
100
q = 200 psf
q = 500 psf
q = 1,000 psf
q = 2,000 psf
q = 5,000 psf
q = 10,000 psf
q = 20,000 psf
Ramjet
80
60
40
Subsonic Turbojet with Low Aspect Ratio Wing
20
Note: q = 1 / 2 ( ρ V2 )
Wingless Subsonic Turbojet
0
0
1
2
3
4
5
6
7
M, Mach number
Note:
• U.S. 1976 Standard Atmosphere
• For Efficient Cruise, ( L / D )Max for Cruising Lifting Body Typically Occurs for 500 < q < 1,000 psf
• ( L / D )Max for Cruise Missile with Low Aspect Ratio Wing Typically Occurs for 200 < q < 500 psf
2/24/2008 • q ≈ 200 psf lower limit for aero control
ELF
213
Missile Guidance and Control Must Be Robust
for Changing Events and Flight Environment
Level Out
Engine Start Transient
Cruise
Example High Performance Missile Has
• Low-to-High Dynamic Pressure
• Negative-to-Positive Static Margin
• Thrust / Weight / cg Transients
• High Temperature
• High Thermal Load
• High Vibration
• High Acoustics
Booster Shutdown
Transient at High Mach
Pitch-Up at High Alpha
Engine Shutdown
Transient
Climb
Booster Ignition
Air Launch at Low
Mach ( high α ) /
Deploy
Compressed
Carriage Surfaces
2/24/2008
Pitch-Over at High Alpha
Pitch-Over at
High Alpha
Dive
Terminal at High
Dynamic Pressure
Precision Impact
at α ≈ 0 Deg
Vertical Launch in Cross Wind ( high α )
/ Deploy Compressed Carriage Surfaces
ELF
214
Design Robustness Requires Consideration of
Flight Altitude
Troposphere ( h < 36,089 ft )
Stratosphere ( h > 36089 ft )
T / TSL = 1 – 6.875 x 10-6 h, h in ft
T = constant = 390 R
p / pSL = ( T / TSL )5.2561
p / pSL = 0.2234 e - ( h – 36089 ) / 20807
ρ / ρSL = ( T / TSL )4.2561
ρ / ρSL = 0.2971 e - ( h – 36089 ) / 20807
Characteristic at Altitude /
Characteristic at Sea Level
1
0
20
40
60
80
100
Troposphere Stratosphere
Temperature Ratio
Pressure Ratio
Density Ratio
Speed of Sound Ratio
0.1
0.01
h, Geometric Altitude, kft
U.S. Standard Atmosphere, 1976
– TSL = 519 R
– pSL = 2116 lb / ft2
– ρSL = 0.00238 slug / ft3
– cSL = 1116 ft / s
Note: TSL = Temperature at sea level, pSL = pressure at sea level, ρSL = density at sea level, cSL = speed
of sound at sea level, h = altitude in ft.
2/24/2008
ELF
215
Variation from Standard Atmosphere
Design Robustness Requires Consideration of
Cold and Hot Atmospheres
Ratio: Cold-to-Standard
Atmosphere
Ratio: Hot-to-Standard
Atmosphere
Ratio: Polar-to-Standard
Atmosphere
Ratio: Tropic-to-Standard
Atmosphere
1.5
( + 30 % )
1
( - 23% )
0.5
0
Temp
Density Speed of
Sound
Note:
• Based on properties at sea level
•U. S. 1976 Standard Atmosphere: Temperature = 519 R, Density = 0.002377 slug / ft3, Speed of sound = 1116 ft / s
2/24/2008
ELF
216
Design Robustness Is Required to Handle Uncertainty
Narrow Uncertainty ( e.g.,
SDD Flight Performance )
Example Normalized PDF
1
Broad Uncertainty ( e.g.,
Conceptual Design Flight
Performance )
Skewed Uncertainty ( e.g.,
Cost, Weight, Miss
Distance )
Bimodal Uncertainty ( e.g.,
Multi-mode Seeker Target
Location )
Uniform Bias Uncertainty
( e.g., Seeker Aim Point
Bias )
0.5
0
-20
-10
0
10
20
Typical % Error from Forecast Value
Note for normal distribution: PDF = { 1 / [ σ ( 2 π )1/2 ]} e {[( x - μ ) / σ ]
2/24/2008
ELF
2/2}
217
Counter-Countermeasures by Missile Enhance
Design Robustness
Examples of CCM ( Missile )
Examples of CM ( Threat )
Imaging Seeker
Multi-spectral / Multimode Seeker
Temporal Processing
Hardened GPS / INS
EOCM
directed laser
flare
smoke
RFCM
active radar
jammer
chaff
standoff acquisition
Integrated GPS / INS
directional antenna
pseudolite / differential
GPS
Decoy
Low Observables
Speed
Altitude
Maneuverability
Lethal Defense
2/24/2008
ATR / ATA
Speed
Altitude
Maneuverability
Low Observables
Saturation
ELF
218
Examples of Countermeasure-Resistant Seekers
IIR ( I2R AGM-130 ) ………………………………………………
Two Color IIR ( Python 5 )
Acoustic - IIR ( BAT ) …………………………………………..
IIR – LADAR ( LOCAAS ) ………………………………………
ARH – mmW ( AARGM )
ARH - IIR ( Armiger ) …………………………………………….
2/24/2008
ELF
219
A Target Set Varies in Size and Hardness
Lethality
Example of Precision Strike Target Set
Air Defense ( SAMs,
AAA )
Launch Platform
Integration /
Firepower
Robustness
Cost
Lethality
Reliability
Miss Distance
Other
Survivability
Considerations
Carriage and
Launch
Observables
Armor
TBM/ TELs
Artillery
Naval
C3II
Counter Air
Aircraft
Transportation Choke
Points ( Bridges,
Railroad Yards, Truck
Parks )
Oil
Refineries
Examples of Targets where Size and Hardness Drive Warhead Design
/ Technology
•Small Size, Hard Target: Tank ⇒ Small Shaped Charge, EFP, or KE
Warhead
•Deeply Buried Hard Target: Bunker ⇒ KE / Blast Frag Warhead
•Large Size Target: Building ⇒ Large Blast Frag Warhead
2/24/2008
Video Example of Precision Strike Targets
ELF
220
76% of Baghdad Targets Struck First Night of
Desert Storm Were C3 Time Critical Targets
Targets: 1. Directorate of Military Intelligence; 2, 5, 8,
13, 34. Telephone switching stations; 3. Ministry of
Defense national computer complex; 4. Electrical transfer
station; 6. Ministry of Defense headquarters; 7. Ashudad
1
4
2
3
6 5
7
23 25
8 24 26
9
10
27
11
21
22
12
13 14
15
20
16
17
28
31
32
29
30
33
34
35
37
36
19
2/24/2008
18
highway bridge; 9. Railroad yard; 10. Muthena airfield ( military
section ); 11. Air Force headquarters; 12. Iraqi Intelligence
Service; 14. Secret Police complex; 15. Army storage depot;
16. Republican Guard headquarters; 17. New presidential
palace; 18. Electrical power station; 19. SRBM assembly
factory ( Scud ); 20. Baath Party headquarters; 21.
Government conference center; 22. Ministry of Industry and
Military Production; 23. Ministry of Propaganda; 24. TV
transmitter; 25, 31. Communications relay stations; 26.
Jumhuriya highway bridge; 27. Government Control Center
South; 28. Karada highway bridge ( 14th July Bridge ); 29.
Presidential palace command center; 30. Presidential
palace command bunker; 32. Secret Police headquarters;
33. Iraqi Intelligence Service regional headquarters; 35.
National Air Defense Operations Center; 36. Ad Dawrah oil
refinery; 37. Electrical power plant
Source: AIR FORCE Magazine, 1 April 1998
ELF
221
Type of Target Drives Precision Strike Missile
Size, Speed, Cost, Seeker, and Warhead
Anti-Fixed Surface Target Missiles ( large size, wings, subsonic, blast frag warhead )
AGM-154
Storm Shadow / Scalp
KEPD-350
BGM-109
AGM-142
Anti-Radar Site Missiles ( ARH seeker, high speed or duration, blast frag warhead )
AGM-88
AS-11 / Kh-58
ARMAT
Armiger
ALARM
Anti-Ship Missiles ( large size, KE / blast frag warhead, and high speed or low altitude )
MM40
AS-34 Kormoran
AS-17 / Kh-31
BrahMos
SS-N-22 / 3M80
Anti-Armor Missiles ( small size, hit-to-kill, low cost, shape charge, EFP, or KE warhead )
Hellfire
LOCAAS
MGM140
AGM-65
LOSAT
Anti-Buried Target Missiles ( large size, high fineness, KE / blast frag warhead )
2/24/2008
CALCM
GBU-28
GBU-31
ELF
Storm Shadow
MGM-140
Permission of Missile Index. 222
Examples of Light Weight Air Launched MultiPurpose Precision Strike Weapons
Weapon
Fixed
Surface
Targets(1)
Moving
Targets(2)
Time
Critical
Targets(3)
Buried
Targets(4)
Adverse
Weather(5)
Firepower(6)
Example New Missile
AGM-65
Small Diameter Bomb
AGM-88
–
–
–
–
Hellfire / Brimstone /
Longbow
LOCAAS
–
–
–
–
(1) – Multi-mode warhead desired. GPS / INS provides precision ( 3 m ) accuracy.
(2) - Seeker or high bandwidth data link required for terminal homing.
Note:
Superior
(3) - High speed with duration required ⇒ High payoff of high speed / loiter and powered submunition.
2/24/2008
(4) - KE penetration warhead required ⇒ High impact speed, low drag, high density, long length.
Good
(5) - GPS / INS, SAR seeker, imaging mmW seeker, and data link have high payoff.
Average
(6) - Light weight required. Light weight also provides low cost ELF
–
Poor
223
Blast Is Effective at Small Miss Distance
Delta p / p0, Overpressure Ratio to Undisturbed Pressure
Δ p / p0 = 37.95 / ( z p01/3 ) + 154.9 / ( z p01/3 )2 + 203.4 / ( z p01/3 )3 + 403.9 / ( z p01/3 )4
1000
z = r / c1/3
Note:
Based on bare sphere of pentolite ( Ec1/2 = 8,500 ft / s )
Δp = overpressure at distance r from explosion
100
p0 = undisturbed atmospheric pressure, psi
z = scaling parameter = r / c1/3
r = distance from center of explosion, ft
c = explosive weight, lb
10
Example for Rocket Baseline Warhead:
c = 38.8 lb
h = 20k feet, p0 = 6.8 psi
r = 10 ft
z = 10 / ( 38.8 )1/3 = 2.95
1
0
2
4
6
8
10
z p01/3 = 5.58
Δp / p0 = 13.36
z ( p0 )1/3
Δp = 90 psi
Reference: US Army Ordnance Pamphlet ORDP-2—290-Warheads, 1980
2/24/2008
ELF
224
Guidance Accuracy Enhances Lethality
Rocket Baseline Warhead
Against Typical Aircraft Target
PK > 0.5 if σ < 5 ft ( Δ p > 330 psi,
fragments impact energy > 130k
ft-lb / ft2 )
PK > 0.1 if σ < 25 ft ( Δp > 24 psi,
fragments impact energy > 5k ftlb / ft2 )
Note: Rocket Baseline 77.7 lb warhead
C / M = 1, spherical blast, h = 20k ft.
Video of AIM-9X Flight Test Missile Impact on Target
( No Warhead )
2/24/2008
ELF
225
Warhead Blast and Fragments Are Effective at
Small Miss Distance
2.4 m
witness
plate
Roland 9 kg explosively formed warhead
multi-projectiles are from preformed case
Hellfire 24 lb shaped charge warhead
fragments are from natural fragmenting case
Video of Guided MLRS 180 lb blast fragmentation warhead
2/24/2008
ELF
226
Maximum Total Fragment Kinetic Energy
Requires High Charge-to-Metal Ratio
( KE / Mwh ) / Ec, Non-dimensional Kinetic Energy
KE = ( 1 / 2 ) Mm Vf2 = Ec Mc / ( 1 + 0.5 Mc / Mm )
0.4
Low K
Note:
Based on Gurney Equation
Cylindrical Warhead
KE = Total Kinetic Energy
Mm = Total Mass Metal Fragments
Vf = Fragment Velocity
Ec = Energy Per Unit Mass Charge
Mc = Mass of Charge
Mwh = Mass of Warhead = Mm + Mc
KE
High
E
0.3
0.2
Example:
Rocket Baseline Warhead
0.1
Mc = 1.207 slug
Mm = 1.207 slug
Mc / Mm = 1
0
0
0.5
1
1.5
2
Mc / Mm, Charge-to-Metal Ratio
2.5
3
Ec Mc = 52,300,000 ( 1.207 ) =
63,100,000 ft-lb
KE = 63100000 / [1 + 0.5 ( 1 )]
= 42,100,000 ft-lb
Reference: Carleone, Joseph (Editor), Tactical Missile Warheads (Progress in Astronautics and Aeronautics, Vol 155), AIAA, 1993.
2/24/2008
ELF
227
Multiple Impacts Are Effective Against Threat
Vulnerable Area Subsystems
Pk, Probability of Kil
PK = 1 - ( 1 - Av / Atp )nhits
Note:
• Av = Target vulnerable area
• Atp = Target presented area
1
0.9
0.8
0.7
0.6
0.5
0.4
Av / Atp = 0.1
Av / Atp = 0.5
Av / Atp = 0.9
0.3
0.2
0.1
0
Example:
If Av / Ap = 0.1, nhits = 22 gives PK = 0.9
If Av / Ap = 0.9, nhits = 1 gives PK = 0.9
0
5
10
15
20
25
30
nhits, Number of Impacts on Target
2/24/2008
ELF
228
Small Miss Distance Improves Number of
Warhead Fragment Hits
nhits = nfragments [ AP / ( 4 π σ2 )]
Number of Fragment Hits
100
Wwh = 5 lb
Wwh = 50 lb
Wwh = 500 lb
80
60
Example for Rocket Baseline:
WWH = 77.7 lb
40
Mc / Mm = 1, Wm = 38.8 lb = 17,615 g
Average fragment weight = 3.2 g
20
nfragments = 17615 / 3.2 = 5505
AP = Target presented area = 20 ft2
0
0
20
40
60
80
Sigma, Miss Distance, ft
2/24/2008
100
σ = Miss distance = 25 ft
nhits = 5505 { 20 / [( 4 π ) ( 25 )2 ]} = 14
Kinetic energy per square foot. = KE
/ ( 4 π σ2 ) = 42100000 / [ 4 π ( 25 )2 ] =
5,360 ft-lb / ft2
Note:
• Spherical blast with uniformly distributed fragments
• nhits = nfragments [ AP / ( 4 π σ2 )]
• Warhead charge / metal weight = 1
• Average fragment weight = 50 grains ( 3.2 g )
• AP = Target presented area = 20 ft2
ELF
229
High Fragment Velocity Requires High Charge-toMetal Ratio
Vf = ( 2 Ec )1/2 [ ( Mc / Mm ) / ( 1 + 0.5 Mc / Mm )]1/2
Vf, Fragment Velocity, ft / s
10000
HMX Explosive
TNT Explosive
8000
6000
Note: Based on the Gurney equation for a
cylindrical warhead
Example:
Baseline Rocket Warhead
4000
HMX Explosive
MC / Mm = 1
2000
Vf = 8,353 ft / s
HMX Explosive ( 2 EC )1/2 = 10,230 ft / s
TNT Explosive ( 2 EC )1/2 = 7,600 ft / s
Vf = Fragment initial velocity, ft / s
Ec = Energy per unit mass of charge, ft2 / s2
Mc = Mass of charge
Mm = Total mass of all metal fragments
Mwh = Mass of warhead = Mm + Mc
0
0
1
2
3
Mc / Mm, Charge-to-Metal Ratio
2/24/2008
ELF
230
Small Miss Distance Improves Fragment
Penetration
Steel Perforation by Fragment ( in )
.5
150 Grains ( 9.7 g )
.375
50 Grains
( 3.2 g )
.25
.125
10
2/24/2008
20
30
40
50
60
70
80
Miss Distance ( ft )
90
100
110
120
Note: Typical air-to-air missile warhead
• Fragments initial velocity 5,000 ft / s
• Sea level
• Average fragment weight 3.2 g
• Fewer than 0.3% of the fragments weigh more than 9.7 g for nominal 3.2 g preformed warhead fragments
• Small miss distance gives less reduction in fragment velocity, enhancing penetration
ELF
231
Hypersonic Hit-to-Kill Enhances Energy on Target
for Missiles with Small Warheads
ET / EC, Total Energy on Target / Warhead
Charge Energy
ET / EC = [( 1 / 2 ) ( WMissile / gc ) V2 + EC ( WC / gc )] / [ EC ( WC / gc )]
9
Weight of
missile /
Weight of
charge = 20
Example for Rocket Baseline:
8
WMissile = 367 lb
7
WC = 38.8 lb
6
WMissile / WC = 9.46
5
Weight of
missile /
Weight of
charge = 10
V = 2,000 ft / s
4
( 1 / 2 ) ( WMissile / gc ) V2 = 22.8 x 106 ft-lb )
3
EC ( WC / gc ) = 63.1 x 106 ft-lb
2
ET / EC = 1.36
Weight of
missile /
Weight of
charge = 5
1
0
0
1000
2000
3000
4000
5000
Missile Closing Velocity, ft / s
6000
Weight of
missile /
Weight of
charge = 2
Note: Warhead explosive charge energy based on HMX, ( 2 EC )1/2 = 10,230 ft / s.
1 kg weight at Mach 3 closing velocity has kinetic energy of 391,000 J ⇒ equivalent chemical energy of 0.4 lb TNT.
2/24/2008
ELF
232
Kinetic Energy Warhead Density, Length, and
Velocity Provide Enhanced Penetration
P / d = [( l / d ) – 1 ] ( ρP / ρT )1/2 + 3.67 ( ρP / ρT )2/3 [( ρT V2 ) / σT ]1/3
P / d, Target Penetration / Penetrator Diameter for
Steel on Concrete
60
50
40
30
20
10
0
0
1000
2000
3000
V, Velocity, ft / s
l/d=2
l/d=5
l / d = 10
4000
Note:
V > 1,000 ft / s
l/d>2
Non-deforming ( high strength, sharp nose )
penetrator
l = Penetrator length
d = Penetrator diameter
V = Impact velocity
ρP= Penetrator density
ρT = Target density
σT= Target ultimate stress
Example for 250 lb Steel Penetrator
l / d = 10
l = 48 in ( 4 ft )
d = 4.8 in ( 0.4 ft )
Concrete target
ρP = 0.283 lb / in3 ( 15.19 slug / ft3 )
ρT = 0.075 lb / in3 ( 4.02 slug / ft3 )
V = 4,000 ft / s
σT = 5,000 psi ( 720,000 psf )
P / d = [ 10 – 1 }( 15.19 / 4.02 )1/2 + 3.67 ( 15.19
/ 4.02 )2/3 [ 4.02 ( 4000 )2 / 720000 ]1/3 = 57.3
P = ( 57.3 ) ( 0.4 ) = 22.9 ft
Source: Christman, D.R., et al, “Analysis of High-Velocity Projectile Penetration,” Journal of Applied Physics, Vol 37, 1966
2/24/2008
ELF
233
Examples of Kinetic-Kill Missiles
Standard Missile 3 ( NTW )
PAC-3
LOSAT
2/24/2008
THAAD
LOSAT Video
ELF
234
CEP Approximately Equal to 1σ Miss Distance
Miss Distance
Launch Platform
Integration / Robustness
Firepower
Missile Circular Error Probable ( 50%
of shots within circle )
Extreme Missile
Trajectory
Cost
Lethality
Reliability
Miss Distance
Survivability
Observables
Missile 1σ Miss Distance ( 68%
of shots within circle for a
normal distribution of error )
Median
Trajectory
Target
Presented Target Area
Extreme Missile
Trajectory
For a normal distribution of error:
Probability < 1σ miss distance = 0.68
Probability < 2σ miss distance = 0.95
Probability < 3σ miss distance = 0.997
Hypothetical Plane
Through Target
Source: Heaston, R.J. and Smoots, C.W., “Introduction to Precision Guided Munitions,” GACIAC HB-83-01, May 1983.
2/24/2008
ELF
235
A Collision Intercept Has Constant Bearing for a
Constant Velocity, Non-maneuvering Target
Example of Collision Intercept
( Line-of-Sight Angle Constant )
.
( Line-of-Sight Angle Rate L = 0 )
Example of Miss
( Line-of-Sight Angle Diverging )
.
( Line-of-Sight Angle Rate L ≠ 0 )
Overshoot Miss
t2
( LOS
L
)1 > (
LO S
t1
)0
Seeker Line-of-Sight
Missile
t1
A
Target
t0
Missile
( LOS )1 = ( LOS )0
L
Seeker Line-of-Sight
A
t0
Target
Note: L = Missile Lead
A = Target Aspect
2/24/2008
ELF
236
A Maneuvering Target and Initial Heading Error
Cause Miss
Target
A
Missile
Collision
Point
L
γM
0
+Z
Maneuvering : τ d2Z + dZ + N’ Z = – N’ cos A 1 a t2
T
dt
to – t to – t cos L 2
Target
dt2
Initial Heading : τ d2Z + dZ + N’ Z = – VM γM
0
dt
to – t
Error
dt2
Reference: Jerger, J.J., Systems Preliminary Design
Principles of Guided Missile Design, D. Van Nostrand
Company, Inc., Princeton, New Jersey, 1960
2/24/2008
Note: to - t = 0 at intercept, causing discontinuity in above equations.
N’ = Effective navigation ratio = N [ VM / ( VM - VT cos A )]
N = Navigation ratio = ( dγ / dt ) / ( dL / dt )
τ = Missile time constant, VM= Velocity of missile, γM = Initial flight
0
path angle error of missile, to = Total time of flight, aT = Acceleration
of target, VT = Velocity of target
ELF
237
Missile Time Constant Causes Miss Distance
τ is a measure of missile ability to respond to
target condition changes
τ equals elapsed time from input of target
return until missile has
completed 63% or ( 1 – e-1 ) of corrective
maneuver ( t = τ )
τ also called “rise time”
Contributions to time constant τ
Control effectiveness ( τδ )
Control dynamics ( e.g., actuator rate ) ( τδ. )
Dome error slope ( τDome )
Guidance and control filters ( τFilter )
Other G&C dynamics ( gyro dynamics,
accelerometer, processor latency, etc )
Seeker errors ( resolution, latency, blind range,
tracking, noise, glint, amplitude )
Approach to estimate τ
τ = τδ +
2/24/2008
τδ.
Input
Time
ti
63%
Output
ti
τ
Time
Acceleration Achieved
= 1 – e- t / τ
Acceleration Commanded
Example for Rocket Baseline:
M = 2, h = 20k ft, coast
τ = τδ + τδ. + τDome
+ τDome
= 0.096 + 0.070 + 0.043 = 0.209 s
ELF
238
Time Constant τδ for Control Effectiveness Is
Driven by Static Margin
Assumptions for τδ
Control surface deflection limited
Near neutral stability
αMax, δMax
Equation of motion is
..
αMax
α = [ ρ V2 S d Cmδ / ( 2 Iy ) ] δMax
Integrate to solve for αMax
τδ / 2
αMax= [ ρ V2 S d Cmδ / ( 8 Iy ) ] δMax τδ2
τδ is given by
τδ
– δMax
τδ = [ 8 Iy ( αMax / δMax ) / ( ρ V2 SRef d Cmδ )]1/2
Contributors to small τδ
Example for Rocket Baseline:
Low fineness ( small Iy / ( SRef d ))
High dynamic pressure ( low altitude / high
speed )
Large Cmδ
2/24/2008
W = 367 lb, d = 0.667 ft, SRef = 0.349 ft2, Iy = 94.0 slug-ft2,
M = 2, h = 20k ft ( ρ = 0.001267 slug / ft3 ),
αMax = 9.4 deg, δMax = 12.6 deg, Cmδ = 51.6 per rad,
τδ = { 8 ( 94.0 ) ( 9.4 / 12.6 ) / [ 0.001267 ( 2074 )2 ( 0.349 )
( 0.667 ) ( 51.6 ) ]}1/2 = 0.096 s
ELF
239
Time Constant τδ. for Flight Control System Is
Driven by Actuator Rate Dynamics
α Max, δ Max
Assumptions for τδ.
.
.
δ
Control surface rate limited ( δ = δ Max )
Near neutral stability
.
1
.
Equation of motion for δ = +/- δ Max
α Max
α Max
.
τδ
τδ.
.
...
α = [ ρ V2 S d Cmδ / ( 2 Iy ) ] δ Max
Equation
of motion for “perfect” response
.
δ = ∞, δ = δMax
..
α = [ ρ V2 S d Cmδ / ( 2 Iy ) ] δMax
τδ. is difference between actual response
to αMax and “perfect” ( τδ ) response
Then
.
• δ Max = 360 deg / s, δMax = 12.6 deg
Note:
.
• τδ. = 2 ( 12.6 / 360 ) = 0. 070 s
Response for control rate limit
Response for no control rate limit
τδ. = 2 δMax / δ Max
2/24/2008
- δ Max Example for Rocket Baseline
ELF
240
Time Constant τDome for Radome Is Driven by
Dome Error Slope
| R | = 0.05 ( lN / d – 0.5 ) [ 1 + 15 ( Δ f / f ) ] / ( d / λ )
τDome = N’ ( VC / VM ) | R | ( α / γ. )
α / γ. = α ( W / gc ) VM / { q SRef [ CN + CN / ( α / δ )]}
α
δ
Example for Rocket Baseline at M = 2, h = 20k ft, q =
2725 psf
Assume VT = 1,000 ft / s, giving VC = 3,074 ft / s
Assume N’ = 4, f = 10 GHz or λ = 1.18 in, Δ f / f = 0.02
Configuration data are lN / d = 2.4, d = 8 in, SRef = 0.349
ft2, W = 367 lb, CN = 40 per rad, CN = 15.5 per rad, α / δ
α
δ
= 0.75
Compute | R | = 0.05 ( 2.4 – 0.5 ) [ 1 + 15 ( 0.02 )] / ( 8 /
1.18 ) = 0.0182 deg / deg
τDome = 4 ( 367 ) ( 3074 ) ( 0.0182 ) / [ 32.2 ( 2725 ) ( 0.349 )
( 40 + 15.5 / 0.75 )] = 0.043 s
2/24/2008
|R| @ d / λ = 10, Radome Error Slope,
Deg / Deg
Substituting gives τDome = N’ W VC | R | / { gc q SRef [ CNα + CNδ / ( α / δ )]}
ELF
0.03
Δ f / f = 0.05
0.02
Δ f / f = 0.02
Δf/f=0
Faceted or
Window
Dome
0.01
0
Tangent
Ogive
Dome
0
1
2
3
lN / d, Nose Fineness
Multi-lens
Dome
241
High Initial Acceleration Is Required to Eliminate
a Heading Error
aM t0 / ( VM γM ) = N’ ( 1 – t / t0 ) N’ – 2
6
6
4
aM t0 / ( VM γM ),
Non-dimensional
Acceleration
4
Note: Proportional Guidance
τ=0
t0 = Total Time to Correct
Heading Error
aM = Acceleration of Missile
VM = Velocity of Missile
γM = Initial Heading Error of
Missile
N’ = Effective Navigation Ratio
3
2.5
2 N’ = 2
0
0
2/24/2008
Example: Exoatmospheric Head-on Intercept, N’ = 4
Midcourse lateral error at t = 0 ( seeker lock-on ) =
200 m, 1 σ
Rlock-on = 20000 m ⇒ γM = 200 / 20000 = 0.0100 rad
VM = 5000 m / s, VT = 5000 ⇒ t0 = Rlock-on / ( VM + VT ) =
20000 / ( 5000 + 5000 ) = 2.00 s
aM t0 / ( VM γM ) = 4
aM = 4 ( 5000 ) ( 0.0100 ) / 2.00 ) = 100 m / s2
nM = 100 / 9.81 = 10.2 g
0.2
0.6
0.4
t / t0, Non-dimensional Time
ELF
0.8
1.0
242
Missile Minimum Range May Be Driven By 4 to 8
Time Constants to Correct Initial Heading Error
σHE = VM γM t0 e-( t0 / τ ) j = 1∑N’ – 1 {( N’ - 2 )! [ - ( t0 / τ )]j / [( j – 1 )! ( N’ – j – 1 )! j! ]}
If N’ = 3, σHE = VM γM t0 e-( t0 / τ ) [ ( t0 / τ ) - ( t0 / τ )2 / 2 ]
If N’ = 4, σHE = VM γM t0 e-( t0 / τ ) [( t0 / τ ) - ( t0 / τ )2 + ( t0 / τ )3 / 6 ]
If N’ = 5, σHE = VM γM t0 e-( t0/ τ ) [( t0 / τ ) – ( 3 / 2 ) ( t0 / τ )2 + ( t0 / τ )3 / 2 – ( t0 / τ )4 / 24 ]
If N’ = 6, σHE = VM γM t0 e-( t0 / τ ) [( t0 / τ ) - 2 ( t0 / τ )2 + ( t0 / τ )3 - ( t0 / τ )4 / 6 + ( t0 / τ )5 / 120 ]
0.3
N’ = 3
0.2
Note: Proportional Guidance
( σHE )Max shown in figure is the envelope of adjoint solution
( σHE )Max = Max miss distance ( 1 σ ) from heading error, ft
VM = Velocity of missile, ft / s
γM = Initial heading error, rad
t0 = Total time to correct heading error, s
τ = Missile time constant, s
N’ = Effective navigation ratio
N’ = 4
| ( σHE )Max / ( VM γM to ) |
N’ = 6
0.1
Example: Ground Target, N’ = 4, τ = 0.2, GPS /
INS error = 3 m, Rlock-on = 125 m, γM = 3 / 125 =
0.024 rad, VM = 300 m / s, t0 = 125 / 300 = 0.42 s
t0 / τ = 0.42 / 0.2 = 2.1, (σHE )Max / ( VM γM to ) = 0.12
( σHE )Max = 0.12 ( 300 ) ( 0.024 ) ( 0.42 ) = 2.2 m
0
References:
0
2
tO / τ
4
6
8
10
•Donatelli, G.A., et al, “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-82-0364, January 1982
•Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952
2/24/2008
ELF
243
Required Maneuverability Is about 3x the Target
Maneuverability for an Ideal ( τ = 0 ) Missile
nM / nT = [ N’ / ( N’ – 2 )] [ 1 – ( 1 – t / t0 )N’ – 2 ]
Where
t = Elapsed Time
t0 = Time to Target
N’ = Effective Navigation Ratio
6
nM
,
nT
Assumptions:
τ=0
VM > VT
N’ = 2 ∞
↑
N’ = 2.5
Example:
τ = 0, N’ = 3, t / t0 = 1
4
⇒ nM / nT = 3
3
Missile-to-Target
Acceleration 2
Ratio
0
4
6
0
0.2
0.4
0.6
0.8
1.0
t / t0, Non-Dimensional Time
2/24/2008
ELF
244
Target Maneuvers Require 6 to 10 Time
Constants to Settle Out Miss Distance
0.3
σMAN = gc nT τ2 e-( t0 / τ ) j = 2∑N’ – 1 {( N’ - 3 )! [ - ( t0 / τ )]j / [( j – 2 )!
( N’ – j – 1 )! j! ]}
If N’ = 3, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 ]
If N’ = 4, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 6 ]
If N’ = 5, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 3 + ( t0 /
τ )4 / 24 ]
If N’ = 6, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 2 + ( t0 /
τ )4 / 8 - ( t0 / τ )5 / 120 ]
N’ = 3
0.2
( σMAN )Max
gc nT τ2
Note: Proportional Guidance
( σMAN )Max is the envelope of adjoint solution
( σMAN )Max = Max miss ( 1 σ ) from target accel, ft
nT = Target acceleration, g
gc = Gravitation constant, 32.2
τ = Missile time constant, s
N’ = Effective navigation ratio
τ0 = Time of flight, s
N’ = 4
0.1
N’ = 6
0
References:
0
2
tO / τ
4
6
8
10
•Donatelli, G.A., et al, “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-82-0364, January 1982
•Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952
2/24/2008
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245
An Aero Control Missile Has Reduced Miss
Distance at Low Altitude / High Dynamic Pressure
Note: Proportional guidance
Target maneuver initiated for max miss ( t0 / τ = 2 )
( σMan )Max in figure = Envelope of adjoint miss
distance
τ = Missile time constant, s
N’ = Effective navigation ratio = 4
nT = Target acceleration, g
gc = Gravitation constant = 32.2
Rocket Baseline Maximum Miss Due to Maneuvering
Target, ft
( σMan )Max = 0.13 gc nT τ2 @ N’ = 4, t0 / τ = 2
100
10
h = SL
h = 20k ft
h = 40k ft
h = 60k ft
h = 80k ft
1
Example for Rocket Baseline at Mach 2, coasting
Assume:
• nT = 5g, VT = 1,000 ft / s, head-on intercept
•h = 20k ft ⇒ τ = 0.209 s
0.1
0
2
4
6
8
10
( σMan )Max = 0.13 ( 32.2 )( 5 )( 0.209 )2 = 0.9 ft
•h = 80k ft ⇒ τ = 1.17 s
Target Maneuverability, g
( σMan )Max = 0.13 ( 32.2 )( 5 )( 1.17 )2 = 28.7 ft
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246
Glint Miss Distance Driven by Seeker Resolution,
Missile Time Constant, and Navigation Ratio
Sigma / ( bT )Res, Nondimensional Miss Distance
from Glint @ 2 Hz Bandwidth
σGlint = KN’ ( W / τ )1/2
Note:
Proportional guidance
Adjoint miss distance
σGlint = Miss distance due to glint noise, ft
W = Glint noise spectral density, ft2 / Hz
τ = Missile time constant, s
N’ = Effective navigation ratio
( bT )Res = Target span resolution at seeker blind range, ft
B = Noise bandwidth, Hz ( 1 < B < 5 Hz )
KN’ = 0.5 ( 2 KN’ = 4 )N’ / 4
0.8
KN’ = 4 = 1.206
W = ( bT )Res2 / ( 3 π2 B )
0.6
0.4
Example: Rocket Baseline at Mach 2, h
= 20k ft altitude ⇒ τ = 0.209 s
Assume:
0.2
•N’ = 4
•B = 2 Hz
•( bT )Res = bt = 40 ft ( radar seeker beam
width resolution of target wing span )
0
0
0.2
0.4
0.6
0.8
Tau, Missile Time Constant, s
N' = 3
N' = 4
N' = 6
1
Calculate:
W = ( 40 )2 / [ 3 π2 ( 2 )] = 27.0 ft2 / Hz
σGlint / ( bT )Res = KN’ ( W / τ )1/2 / ( bt )Res
= 1.206 ( 27.0 / 0.209 )1/2 / 40 = 0.343
σGlint = 0.343 ( 40 ) = 13.7 ft
Reference:
Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952
2/24/2008
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247
Minimizing Miss Distance with Glint Requires
Optimum Time Constant and Navigation Ratio
σ = [( σMAN )Max2 + ( σGlint )2 ]1/2
Note:
Proportional guidance
Adjoint miss distance
( σMAN )Max = Max miss distance from
target maneuver, ft
σGlint = Miss distance from glint noise, ft
τ = Missile time constant, s
N’ = Effective navigation ratio
Rocket Baseline Miss Distance, ft
50
40
30
Example for Rocket Baseline at Mach 2,
h = 20k ft altitude ⇒ τ = 0.209 s
20
Assume:
10
N’ = 4
•B = 2 Hz
•( bT )Res = 40 ft
0
0
0.2
0.4
0.6
0.8
Tau, Missile Time Constant, s
N' = 3
N' = 4
N' = 6
1
•nT = 5g, VT = 1,000 ft / s, Head-on
From prior figures:
( σMAN )Max = 0.9 ft, σGlint = 13.7 ft
Calculate:
σ = [( σMAN )Max2 + ( σGlint )2 ]1/2 = 13.7 ft
Reference:
Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952
2/24/2008
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248
Missile Carriage RCS and Launch Plume Are
Considerations in Launch Platform Observables
Launch Platform
Integration /
Firepower
Carriage and
Missile Carriage Alternatives
Robustness
Cost
Lethality
Reliability
Miss Distance
Survivability
Observables
Launch Observables
Internal Carriage: Lowest Carriage RCS
Conformal Carriage: Low Carriage RCS
Conventional External Pylon or External Rail Carriage: High Carriage RCS
Plume Alternatives
Min Smoke: Lowest Launch Observables ( H2O Contrail )
Reduced Smoke: Reduced Launch Observables ( e.g., HCl Contrail from AP
Oxidizer )
High Smoke: High Launch Observables ( e.g., Al2O3 Smoke from Al Fuel )
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249
Examples of Weapon Bay Internal Carriage and
Load-out
Center Weapon Bay Best for Ejection Launchers
F-22 Bay Loadout: 3 AIM-120C, 1 GBU-32
Video
AMRAAM Loading in F-22 Bay
2/24/2008
F-117 Bay Loadout: 1 GBU-27, 1 GBU-10
B-1 Bay Loadout: 8 AGM-69
Side Weapon Bay Best for Rail Launchers
F-22 Side Bay: 1 AIM-9 Each Side Bay
ELF
RAH-66 Side Bay: 1 AGM-114, 2 FIM92, 4 Hydra 70 Each Side Bay
250
Minimum Smoke Propellant Has Low Observables
High Smoke Example: AIM-7
Reduced Smoke Example: AIM-120
Minimum Smoke Example: Javelin
Particles ( e.g., metal fuel ) at all
atmosphere temperature.
Contrail ( HCl from AP oxidizer ) at T < -10° F
atmospheric temperature.
Contrail (H2O ) at T < -35º F
atmospheric temperature.
High Smoke Motor
Reduced Smoke Motor
Minimum Smoke Motor
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251
High Altitude Flight and Low RCS Enhance
Survivability
Pt, Radar Transmitted Power
Required for Detection, W
Launch Platform
Integration /
Firepower
Other Survivability
Considerations
Pt = ( 4 π )3 Pr R4 / ( Gt Gr σ λ2 )
10000000
Robustness
Cost
Lethality
Reliability
Miss Distance
Survivability
Observables
1000000
100000
Example for Pt = 50,000 W:
10000
Not detected if:
h > 25k ft for σ = 0.001 m2
1000
h > 77k ft for σ = 0.1 m2
100
0
20
40
60
80
100
h, Geometric Altitude, kft
RCS = 0.1 m2
2/24/2008
RCS = 0.01 m2
RCS = 0.001 m2
Note:
Range Slant Angle = 20 deg, Gt = Transmitter Gain = 40 dB, Gr = Receiver Gain = 40 dB, λ = Wavelength = 0.03
m, Pr = Receiver Sensitivity = 10-14 W, σ = radar cross section ( RCS )
Based on Radar Range Equation with ( S / N )Detect = 1 and Unobstructed Line-of-Sight
ELF
252
Mission Planning and High Speed Enhance
Survivability
Flyby
texp ( V / Rmax ), Non-dimensional Threat
Exposure Time
texp = 2 ( Rmax / V ) cos [
sin-1
( yoffset / Rmax )] – treact
2
x
R ma
SAM
Site
yoffset
texp V
1
Example:
yoffset = 7 nm, Rmax = 10 nm = 60750 ft,
yoffset / Rmax = 0.7, treact = 15 s
0
0
0.2
0.4
0.6
0.8
1
yoffset / Rmax, Non-dimensional Offset Distance from
Threat
treact ( V / Rmax ) = 0
treact ( V / Rmax ) = 1.0
Note: Based on assumption of constant altitude, constant heading flyby of
threat SAM site with an unobstructed line-of-sight. texp = exposure time to
SAM threat, Rmax = max detection range by SAM threat, V = flyby velocity,
yoffset = flyby offset, treact = SAM site reaction time from detection to launch
2/24/2008
treact V
ELF
If V = 1000 ft / s, treact ( V / Rmax ) = 0.247
•texp ( V / Rmax ) = 2 cos [ sin-1 ( 7 / 10 )] –
15 ( 1000 / 60746 ) = 1.428 – 0.247 = 1.181
•texp = 1.181 ( 60746 / 1000 ) = 71.7 s
If V = 4000 ft / s, treact ( V / Rmax ) = 0.988
•texp ( V / Rmax ) = 0.440
•texp = 0.440 ( 60746 / 4000 ) = 6.7 s
253
Low Altitude Flight and Terrain Obstacles
Provide Masking from Threat
hmask = ( hmask )obstacle + ( hmask )earth = hobstacle ( Rlos / Robstacle ) + ( Rlos / 7113 )2
hmask, Altitude that Masks Line-of-Sight
Exposure to Surface Threat, ft
2000
hmask = altitude that allows obstacle and earth
curvature to mask exposure to surface threat LOS, ft
hobstacle = height of obstacle above terrain, ft
1500
Rlos = line-of-sight range to surface threat, ft
Robstacle = range from surface threat to obstacle, ft
1000
Height of low hill or tall tree ≈ 100 ft
Height of moderate hill ≈ 200 ft
Height of high hill ≈ 500 ft
500
Height of low mountain ≈ 1000 ft
Example:
0
0
10
20
30
Rlos, Line-of-Sight Range to Surface Threat, nm
Rlos ( hobstacle / Robstacle ) = 100 ft
Rlos ( hobstacle / Robstacle ) = 200 ft
Rlos ( hobstacle / Robstacle ) = 500 ft
Rlos ( hobstacle / Robstacle ) = 1000 ft
2/24/2008
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40
hobstacle = 200 ft
Robstaacle = 5.0 nm = 30395 ft
Rlos = 10.0 nm = 60790 ft
Rlos ( hobstacle / Robstaacle ) = 60790 ( 200 /
30395 ) = 400 ft
hmask = 200 ( 60790 / 30395 ) + ( 60790 /
7113 )2 = 400 + 73 = 473 ft above terrain
254
Insensitive Munitions Improve Launch Platform
Survivability
Critical Subsystems
Rocket motor or fuel tank
Warhead
Severity Concerns Ranking of Power Output - Type
1.
2.
3.
4.
5.
Detonation ( ~ 0.000002 s rise time )
Partial detonation ( ~ 0.0001 s rise time )
Explosion ( ~ 0.001 s rise time )
Deflagration or propulsion rise time ( ~ 0.1 s rise time )
Burning ( > 1 s )
Design and test considerations ( MIL STD 2105C )
2/24/2008
Fragment / bullet impact or blast
Sympathetic detonation
Fast / slow cook-off fire
Drop
Temperature
Vibration
Carrier landing ( 18 ft / s sink rate )
ELF
255
High System Reliability Is Provided by High
Subsystem Reliability and Low Parts Count
Typical System Reliability
Rsystem ≈ 0.94 = RArm X RLaunch X RStruct X RAuto X
RAct X RSeeker X RIn Guid X RPS X RProp X RFuze X RW/H
Arm ( 0.995 – 0.999 )
Launch Platform
Integration /
Firepower
Robustness
Cost
Lethality
Reliability
Miss Distance
Survivability
Observables
Reliability
Launch ( 0.990 – 0.995 )
Structure ( 0.997 – 0.999 )
Autopilot ( 0.993 – 0.995 )
Typical Event /
Subsystem
Actuators ( 0.990 – 0.995 )
Seeker ( 0.985 – 0.990 )
Inertial Guidance ( 0.995 – 0.999 )
Power Supply ( 0.995 – 0.999 )
Propulsion ( 0.995 – 0.999 )
Fuze ( 0.987 – 0.995 )
Warhead ( 0.995 – 0.999 )
0.90
0.92
0.94
0.96
0.98
1.00
Typical Reliability
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256
Sensors, Electronics and Propulsion Drive
Missile Production Cost
Cost
Dome
Seeker
Structure
•Rocket –
•Airbreather
Guidance and
Control
Power –
Supply
Very High
( > 25% Production Cost )
Propulsion
•Rocket
•Airbreather
Warhead –
and Fuzing
High
( > 10% )
Wings –
Robustness
Lethality
Reliability
Miss Distance
Survivability
Observables
Stabilizers –
Aerothermal – Data
Link
Insulation
Moderate
( > 5% )
Launch Platform
Integration /
Firepower
Cost
Flight
Control
– Relatively Low
( < 5% )
Note:
System assembly and test ~ 10% production cost
Propulsion and structure parts count / cost of airbreathing missiles are higher than that of rockets
2/24/2008
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257
Sensors and Electronics Occupy a Large Portion
of a High Performance / High Cost Missile.
Example: Derby / R-Darter Missile
Source: http://www.israeli-weapons.com/weapons/missile_systems/air_missiles/derby/Derby.html
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258
Cost Considerations
Life Cycle
System Development and Demonstration ( SDD )
Production
Logistics
Culture / processes
Relative Emphasis of Cost, Performance, Reliability, Organization Structure
Relaxed Mil STDs
IPPD
Profit
Competition
2/24/2008
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259
SDD Cost Is Driven by Schedule Duration and
Risk
CSDD = $20,000,000 tSDD1.90, ( tSDD in years )
CSDD, SDD Cost in Millions
10000
1000
Example:
5 year ( medium risk ) SDD program
100
Low
Moderate
High
Risk
Risk
Risk
SDD
SDD
SDD
CSDD = $20,000,000 tSDD1.90
= ( 20,000,000 ) ( 5 )1.90
= $426,000,000
10
0
2
4
6
8
10
12
14
tSDD, SDD Schedule Duration in Years
AGM-142
SLAM
AIM-120A
TOW 2
JDAM
JSOW
SLAM-ER
AGM-130
HARM
MLRS
Harpoon
Javelin
LB Hellfire
ATACMS
BAT
JASSM
Tomahawk
PAC-3
Hellfire II
ESSM
Patriot
Note: SDD required schedule duration depends upon risk. Should not ignore risk in shorter schedule.
-- Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Associates, 1999
– SDD cost based on 1999 US$
2/24/2008
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260
Light Weight Missiles Have Low Unit Production
Cost
C1000th ≈ $6,100 WL0.758, ( WL in lb )
C1000th, Cost of Missile Number 1000, U.S.$
10000000
Javelin
Longbow Hellfire
AMRAAM
MLRS
HARM
JSOW
Tomahawk
1000000
100000
Example:
10000
2,000 unit buy of 100 lb missile:
10
100
1000
WL , Launch Weight, lb
10000 C1000th ≈ $6,100 WL0.758 = 6100 ( 100 )0.758 =
$200,000
Cost of 2,000 missiles = 2000 ( $200000 ) =
$400,000,000
Note:
-- Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Associates, 1999
– Unit production cost based on 1999 US$
2/24/2008
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261
Learning Curve and Large Production Reduce
Unit Production Cost
Cx / C1st, Cost of Unit x / Cost of First Unit
Cx = C1st Llog2x, C2x = L Cx , where C in U.S. 99$
1
L = 1.0
L = 0.9
0.1
Example:
For a learning
curve coefficient
of L = 80%, cost of
unit #1000 is 11%
the cost of the first
unit
0.01
1
10
100
L = 0.8
L = 0.7
1000
10000 100000 1E+06
x, Number of Units Produced
Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book,
1999,” Data Search Associates, 1999
2/24/2008
ELF
Javelin ( L = 0.764, C1st = $3.15M,
Y1 = 1994 )
Longbow HF ( L = 0.761, C1st =
$4.31M, Y1 = 1996 )
AMRAAM ( L = 0.738, C1st =
$30.5M, Y1 = 1987 )
MLRS ( L = 0.811, C1st = $0.139M,
Y1 = 1980 )
HARM ( L = 0.786, C1st = $9.73M,
Y1 = 1981 )
JSOW ( L = 0.812, C1st = $2.98M,
Y1 = 1997 )
Tomahawk ( L = 0.817, C1st =
$13.0M, Y1 = 1980 )
Labor intensive learning curve: L < 0.8
Machine intensive learning curve: L > 0.8 )
Contributors to the learning curve include:
• More efficient labor
• Reduced scrap
• Improved processes
262
Parts Count, Hours, or Cost ( US$ )
Low Parts Count Reduces Missile Unit
Production Cost
1000000
100000
10000
1000
100
10
Parts
Fasteners
Circuit Cards Connectors
Current Tomahawk
Assembly /
Test Hours
Unit
Production
Cost ( US$ )
Tactical Tomahawk
Note: Tactical Tomahawk has superior flexibility ( e.g., shorter mission planning, in-flight retargeting, BDI / BDA,
modular payload ) at lower parts count / cost and higher reliability. Enabling technologies for low parts count include:
casting, pultrusion / extrusion, centralized electronics, and COTS.
2/24/2008
ELF
263
Tactical Missile Culture Is Driven by Rate
Production of Sensors and Electronics
Copperhead Seeker and Electronics Production
Patriot Control Section Production
Video of Hellfire Seeker and Electronics Production
2/24/2008
ELF
264
Logistics Cost Considerations
Wartime Logistics Activity
Peacetime Logistics Activity
•Contractor Post-production Engineering
•Training Manuals / Tech Data Package
•Simulation and Software Maintenance
•Configuration Management
•Engineering Support
•System Analysis
•Launch Platform Integration
•Requirements Documents
•Coordinate Suppliers
•Deployment Alternatives
•Airlift
•Sealift
•Combat Logistics
•Storage Alternatives
•Wooden Round ( Protected )
•Open Round ( Humidity, Temp, Corrosion, Shock )
•Reliability Maintenance
•Launch Platform Integration
•Mission Planning
•Field Tests
•Reliability Data
•Maintainability Data
•Effectiveness Data
•Safety Data
•Surveillance
•Testing
•Maintenance Alternatives
•First level ( depot )
•Two level ( depot, field )
•Disposal
2/24/2008
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265
Logistics Cost Lower for Simple Missile Systems
Simple: Stinger More Sophisticated: Hawk and SLAMRAAM
Very Complex: THAAD
2/24/2008
Complex: PAC-3
Video of Logistics Alternatives
ELF
266
Logistics Is Simpler for Light Weight Missiles
Support Personnel required
for Installation
Support personnel for installation with 50 lb lift limit per person
Support personnel for installation with 100 lb lift limit per person
Machine lift for installation
6
4
2
0
10
100
1000
10000
Missile Weight, lb
Predator ( 21 lb )
2/24/2008
Sidewinder ( 190 lb )
Sparrow ( 500 lb )
ELF
Video of Simple Logistics for a
Light weight Missile
Laser Guided Bomb ( 2,500 lb )
267
Small MEMS Sensors Can Provide Health
Monitoring, Reducing Cost and Weight
Micro-machined Electro-Mechanical Systems ( MEMS )
Small size / low cost semiconductor manufacturing process
2,000 to 5,000 sensors on a 5 in silicon wafer
Wireless ( RF ) Data Collection and Health Monitoring
Distributed Sensors Over Missile
Stress / strain
Vibration
Acoustics
Temperature
Pressure
Reduced Logistics Cost and Improved Reliability
Health monitoring
Reduced Weight and Production Cost
More Efficient Design
2/24/2008
ELF
268
Missile Carriage Size, Shape, and Weight Are
Driven by Launch Platform Compatibility
Launch Platform Integration / Firepower
US Launch Platform
Launcher
Carriage Span / Shape
Length
Weight
Launch Platform
Integration /
Firepower
”
22
Submarines
263”
3400 lb
263”
3400 lb
~168”
~500 lb to
3000 lb
158”
3700 lb
70”
120 lb
Miss Distance
Survivability
Observables
22
”
~
VLS
Lethality
Reliability
~
Surface Ships
Robustness
Cost
CLS
22”
2/24/2008
”
28
Helos
~
Vehicles
Launch
Pods
~24” x 24”
Rail
ELF
28
”
Ground
Rail /
Ejection
~
Fighters /
Bombers /
UCAVs
∼13” x 13”
269
F-18 C / E
5,000 lb
4,000 lb
E, carry 1
E, carry 2
C, carry 1
C, carry 2
E, carry 3
C, carry 3
E, carry 2
Configuration for Day Operation
with Bring-Back Load
2/24/2008
ELF
+ 2 Inbd Tk + 2 AIM-9
C, carry 2
+ CL Tk + 2 AGM-88
+ 2 Inbd Tk + 2 AIM-9
+ CL Tk + 2 AGM-88
+ CL Tk + 2 AIM-9
+ 2 Inbd Tanks
+ CL Tank
1,000 lb
Clean
Outboard Asymmetric
Bring-Back Load Limit
E, carry 1
+ CL Tk + 2 AIM-9
2,000 lb
C, carry 1
+ 2 Inbd Tanks
Inboard Asymmetric
Bring-Back Load Limit
+ CL Tank
3,000 lb
Clean
Max Strike Weapon
Weight
Light Weight Missiles Enhance Firepower
Configuration for Night Operation
with Bring-Back Load
270
Launch Envelope Limitations in Missile / Launch
Platform Physical Integration
Off Boresight
Seeker field of regard ⇒ potential obscuring from launch platform
Minimum Range
Launcher rail clearance and aeroelasticity ⇒ miss at min range
Helo rotor downwash ⇒ miss at min range
Safety
Launcher retention ⇒ potential inadvertent release, potential hang-fire
Launch platform local flow field α, β ⇒ potential unsafe separation
Launch platform maneuvering ⇒ potential unsafe separation
Handling qualities with stores ⇒ potential unsafe handling qualities
Launch platform bay / canister acoustics ⇒ missile factor of safety
Launch platform bay / canister vibration ⇒ missile factor of safety
2/24/2008
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271
Store Separation Wind Tunnel Tests Are
Required for Missile / Aircraft Compatibility
F-18 Store Compatibility Test in AEDC 16T
AV-8 Store Compatibility Test in AEDC 4T
Types of Wind Tunnel Testing for Store Compatibility
- Flow field mapping with probe
- Flow field mapping with store
- Captive trajectory simulation
- Drop testing
Example Stores with Flow Field Interaction: Kh-41 + AA-10
2/24/2008
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272
Examples of Rail Launched and Ejection
Launched Missiles
Example Rail Launcher: Hellfire / Brimstone
Example Ejection Launcher: AGM-86 ALCM
Video of Hellfire / Brimstone Carriage / Launch
Video of AGM-86 Carriage / Launch
2/24/2008
ELF
273
Examples of Safe Store Separation
Laser Guided Bombs Drop from F-117
AMRAAM Rail Launch from F-16
2/24/2008
Video of Rapid Drop ( 16 Bombs ) from B-2
ELF
274
Examples of Store Compatibility Problems
Unsafe Separation
2/24/2008
Hang-Fire
ELF
Store Aeroelastic Instability
275
MIL-STD-8591 Aircraft Store Suspension and
Ejection Launcher Requirements
Store Weight / Parameter
30 Inch Suspension
14 Inch Suspension
♦ Weight Up to 100 lb
• Lug height ( in )
• Min ejector area ( in x in )
Not Applicable
Yes
0.75
4.0 x 26.0
♦ Weight 101 to 1,450 lb
• Lug height ( in )
• Min lug well ( in )
• Min ejector area ( in x in )
Yes
1.35
0.515
4. 0 x 36.0
Yes
1.00
0.515
4.0 x 26.0
♦ Weight Over 1,451 lb
• Lug height ( in )
• Min lug well ( in )
• Min ejector area ( in x in )
Yes
1.35
1.080
4.0 x 36.0
Not Applicable
Ejection Stroke
2/24/2008
ELF
276
MIL-STD-8591 Aircraft Store Rail Launcher
Examples
Rail Launcher
Forward Hanger
LAU-7 Sidewinder Launcher
2.260
LAU 117 Maverick Launcher
1.14
Aft Hanger
2.260
7.23
Note: Dimensions in inches.
• LAU 7 rail launched store weight and diameter limits are ≤ 300 lb, ≤ 7 in
•LAU 117 rail launched store weight and diameter limits are ≤ 600 lb, ≤ 10 in
2/24/2008
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277
Compressed Carriage Missiles Provide Higher
Firepower
Baseline AIM-120B AMRAAM
Compressed Carriage AIM-120C AMRAAM ( Reduced Span Wing / Tail )
Baseline AMRAAM: Loadout
of 2 AMRAAM per F-22 SemiBay
Compressed Carriage
AMRAAM: Loadout of 3
AMRAAM per F-22 Semi-Bay
17.5 in
17.5 in
12.5 in 12.5 in 12.5 in
Video of Longshot Kit on CBU-97
Note: Alternative approaches to compressed carriage include surfaces with small span, folded surfaces, wrap
around surfaces, and planar surfaces that extend ( e.g., switch blade, Diamond Back, Longshot ).
2/24/2008
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278
Example of Aircraft Carriage and Fire Control
Interfaces
Folding
Suspension
Lug
Wing Deploy
Safety Pin
Wing
Folding
Suspension
Lug
Fire Control /
Avionics
Umbilical
Connector
Flight Control
Access Cover
Electrical
Safety Pin
Example: ADM-141 TALD ( Tactical Air-Launched Decoy )
Carriage and Fire Control Interfaces
2/24/2008
ELF
279
Example of Ship Weapon Carriage and Launcher,
Mk41 VLS
Cell
Cell
Before After
Firing Firing
Canister Cell Hatch
Exhaust Hatch
Ship Deck
Missile Cover
Plenum
8 Modules / Magazine
Tomahawk Launch
2/24/2008
Module Gas Management
8 Canister Cells / Module
ELF
Standard Missile Launch
280
Robustness Is Required for Carriage, Shipping,
and Storage Environment
Environmental Parameter Typical Requirement
Surface Temperature
-60° F* to 160° F
Surface Humidity
5% to 100%
Rain Rate
120 mm / h**
Surface Wind
100 km / h steady***
Video: Ground / Sea Environment
150 km / h gusts****
Salt fog
3 g / mm2 deposited per year
Vibration
10 g rms at 1,000 Hz: MIL STD 810, 648, 1670A
Shock
Drop height 0.5 m, half sine wave 100 g / 10 ms: MIL STD 810, 1670A
Acoustic
160 dB
Note: MIL-HDBK-310 and earlier MIL-STD-210B suggest 1% world-wide climatic extreme typical requirement.
* Lowest recorded temperature = -90° F. 20% probability temperature lower than -60° F during worst month of worst location.
** Highest recorded rain rate = 436 mm / h. 0.5% probability greater than 120 mm / h during worst month of worst location.
*** Highest recorded steady wind = 342 km / h. 1% probability greater than 100 km / h during worst month of worst location.
**** Highest recorded gust = 378 km / h. 1% probability greater than 150 km / h during worst month of worst location.
2/24/2008
ELF
281
Summary of Measures of Merit and Launch
Platform Integration
Measures of Merit
Robustness
Warhead lethality
Miss distance
Carriage and launch observables
Other survivability considerations
Reliability
Cost
Launch Platform Integration
Firepower, weight, fitment
Store separation
Launch platform handling qualities, aeroelasticity
Hang-fire
Vibration
Standard launchers
Carriage and storage environment
Discussion / Questions?
Classroom Exercise ( Appendix A )
2/24/2008
ELF
282
Measures of Merit and Launch Platform
Integration Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
2/24/2008
IR signal attenuation is greater than 100 dB per km through a c____.
GPS / INS enhances seeker lock-on in adverse weather and ground c______.
A data link can enhance missile seeker lock-on against a m_____ target.
An example of a missile counter-counter measure to flares is an i______
i_____ seeker.
Compared to a mid-wave IR seeker, a long wave IR seeker receives more
energy from a c___ target.
High fineness kinetic energy penetrators are required to defeat b_____
targets.
For the same lethality with a blast fragmentation warhead, a small decrease in
miss distance allows a large decrease in the required weight of the w______.
For a blast / frag warhead, a charge-to-metal ratio of about one is required to
achieve a high total fragment k______ e_____.
A blast fragmentation warhead tradeoff is the number of fragments versus the
individual fragment w_____.
ELF
283
Measures of Merit and Launch Platform
Integration Problems ( cont )
10.
11.
12.
13.
14.
15.
16.
17.
18.
2/24/2008
Kinetic energy penetration is a function of the penetrator diameter, length,
density, and v_______.
In proportional homing guidance, the objective is to make the line-of-sight
angle rate equal to z___.
Aeromechanics contributors to missile time constant are flight control
effectiveness, flight control system dynamics, and dome e____ s____.
Miss distance due to heading error is a function of missile navigation ratio,
velocity, time to correct the heading error, and the missile t___ c_______.
A missile must have about t_____ times the maneuverability of the target.
Minimizing the miss distance due to radar glint requires a high resolution
seeker, an optimum missile time constant and an optimum n_________ r____.
Weapons on low observable launch platforms use i_______ carriage.
Weapons on low observable launch platforms use m______ smoke propellant.
For an insensitive munition, burning is preferable to detonation because it
releases less p____.
ELF
284
Measures of Merit and Launch Platform
Integration Problems ( cont )
19.
20.
21.
22.
23.
24.
25.
26.
27.
2/24/2008
Missile system reliability is enhanced by subsystem reliability and low p____
count.
High cost subsystems of missiles are sensors, electronics, and p_________.
Missile SDD cost is driven by the program duration and r___.
Missile unit production cost is driven by the number of units produced,
learning curve, and w_____.
First level maintenance is conducted at a d____.
A standard launch system for U.S. Navy ships is the V_______ L_____ S_____.
Most light weight missiles use rail launchers while most heavy weight missiles
use e_______ launchers.
Higher firepower is provided by c_________ carriage.
The typical environmental requirement from MIL-HDBK-310 is the _% worldwide climatic extreme.
ELF
285
Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
2/24/2008
ELF
286
Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
2/24/2008
ELF
287
Air-to-Air Engagement Analysis Process and
Assumptions
F-pole range provides kill of head-on threat outside of
threat weapon launch range
Aircraft contrast for typical engagement
C = 0.18
Typical visual detection range by target ( Required F-pole
range )
RD = 3.3 nm
Typical altitude and speed of launch aircraft, target aircraft,
and missile
h = 20k ft altitude
VL = Mach 0.8 = 820 ft / s
VT = Mach 0.8 = 820 ft / s
VM = 2 VT = 1,640 ft / s
2/24/2008
ELF
288
Assumed Air-to-Air Engagement Scenario for
Head-on Intercept
RL= VM tf + VT tf
t = 0 s (Launch Missile)
RF-Pole = VM tf - VL tf
Blue Aircraft
( 820 ft / s )
Red Aircraft
( 820 ft / s )
Blue Missile
( 1640 ft / s )
RL= Launch Range = 10.0 nm
RF = Missile Flight Range = 6.7 nm
t = tf = 24.4 s ( Missile Impacts Target )
Blue Aircraft
( 820 ft / s )
Red Aircraft
Destroyed
R F-pole = 3.3 nm
2/24/2008
ELF
289
R, Visible Range for 50 ft2 Target, nm
Target Contrast and Size Drive Visual Detection
and Recognition Range
2/24/2008
8
RD = 1.15 [ Atp ( C – CT )]1/2, RD in nm, Atp in ft2
RR = 0.29 RD
Visual Detection Range,
nm
Visual Recognition
Range, nm
6
Note:
RD = Visual detection range for
probability of detection PD = 0.5
C = Contrast
CT = Visual threshold contrast = 0.02
Atp = Target presented area = 50 ft2
RR = Visual recognition range
θF = Pilot visual fovial angle = 0.8 deg
Clear weather
Pilot search glimpse time = 1 / 3 s
4
2
Example:
If C = 0.18
RD = 3.3 nm
RR = 1.0 nm
0
0.01
C = 0.01 C = 0.02
0.1
1
C, Contrast
C = 0.05 C = 0.1 C = 0.2
ELF
C = 0.5 C = 1.0
290
High Missile Velocity Improves Standoff Range
RF-Pole / RL = 1 – ( VT + VL ) / ( VM + VT )
Note: Head-on intercept
RF-Pole = Standoff range at intercept
RL= Launch range
F-Pole Range / Launch Range
1
VM = Missile average velocity
VT = Target velocity
0.8
VL = Launch velocity
VL / VM = 0
VL / VM = 0.2
VL / VM = 0.5
VL / VM = 1.0
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
Target Velocity / Missile Velocity
2/24/2008
ELF
1
Example:
• VL = VT
• VM = 2 VT
• Then VT / VM = VL / VM = 0.5
• RF-Pole / RL = 0.33
• RF-Pole = RD = 3.3 nm
• RL = 3.3 / 0.33 = 10.0 nm
291
Missile Flight Range Requirement Is Greatest for
a Tail Chase Intercept
RF / RL, Missile Flight Range / Launch Range
( RF / RL )Head-on = ( VM / VT ) / [(VM / VT ) + 1 ]
3
( RF / RL )TailChase = ( VM / VT ) / [(VM / VT ) - 1 ]
2.5
2
( RF / RL ) Head-on
( RF / RL ) Tail Chase
1.5
Examples:
1
•Head-on Intercept
0.5
0
0
1
2
3
4
VM / VT, Missile Velocity / Target Velocity
2/24/2008
ELF
5
• VM = 1,640 ft / s, VT = 820 ft / s
• VM / VT = 1640 / 820 = 2
• RF / RL = 2 / ( 2 + 1 ) = 0.667
• RL = 10.0 nm
• RF = 0.667 ( 10.0 ) = 6.67 nm
•Tail Intercept at same conditions
• RF / RL = 2 / ( 2 – 1 ) = 2.0
• RF = 2.0 ( 10.0 ) = 20.0 nm
292
Drawing of Rocket Baseline Missile Configuration
STA 60.8
19.4
LEmac at
STA 131.6
BL 8.0
3.4
LEmac at STA 67.0
BL 10.2
Λ = 45°
16.1
8.0 d
cgBO
STA 125.4
18.5
12.0
cgLaunch
Λ = 57°
Rocket Motor
40.2
STA 0
19.2
Nose
46.1
Forebody
62.6
84.5
Payload
Midbody
Bay
Aftbody
138.6 143.9
Tailcone
Note: Dimensions in inches
Source: Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis, Vol. 1, Rocket Synthesis
Handbook,” AFWAL-TR-81-3022, Vol. 1, March 1982.
2/24/2008
ELF
293
Mass Properties of Rocket Baseline Missile
Component
1
3
2
4
5
6
2/24/2008
Weight, lb.
C.G. STA, in.
4.1
12.4
46.6
7.6
77.7
10.2
61.0
0.0
47.3
23.0
6.5
5.8
26.2
38.6
12.0
30.5
32.6
54.3
54.3
73.5
75.5
–
107.5
117.2
141.2
141.2
137.8
75.5
Burnout Total
Propellant
367.0
133.0
76.2
107.8
Launch Total
500.0
84.6
Nose ( Radome )
Forebody structure
Guidance
Payload Bay Structure
Warhead
Midbody Structure
Control Actuation System
Aftbody Structure
Rocket Motor Case
Insulation ( EDPM – Silica )
Tailcone Structure
Nozzle
Fixed Surfaces
Movable Surfaces
ELF
294
Rocket Baseline Missile Definition
Body
Dome Material
Airframe Material
Length, in
Diameter, in
Airframe thickness, in
Fineness ratio
Volume, ft3
Wetted area, ft2
Nozzle exit area, ft2
Boattail fineness ratio
Nose fineness ratio
Nose bluntness
Boattail angle, deg
Pyroceram
Aluminum 2219-T81
143.9
8.0
0.16
17.99
3.82
24.06
0.078
0.38
2.40
0.0
7.5
Material
Planform area, ft2 ( 2 panels exposed )
Wetted area, ft2 ( 4 panels )
Aspect ratio ( 2 panels exposed )
Taper ratio
Root chord, in
Tip chord, in
Span, in ( 2 panels exposed )
Leading edge sweep, deg
Aluminum 2219-T81
2.55
10.20
2.82
0.175
19.4
3.4
32.2
45.0
Movable surfaces ( forward )
2/24/2008
ELF
295
Rocket Baseline Missile Definition ( cont )
Movable surfaces ( continued )
Mean aerodynamic chord, in
Thickness ratio
Section type
Section leading edge total angle, deg
xmac, in
ymac, in ( from root chord )
Actuator rate limit, deg / s
13.3
0.044
Modified double wedge
10.01
67.0
6.2
360.0
Material
Modulus of elasticity, 106 psi
Planform area, ft2 ( 2 panels exposed )
Wetted area, ft2 ( 4 panels )
Aspect ratio ( 2 panels exposed )
Taper ratio
Root chord, in
Tip chord, in
Span, in ( 2 panels exposed )
Leading edge sweep, deg
Mean aerodynamic chord, in
Thickness ratio
Section type
Section leading edge total angle, deg
xmac, in
ymac, in ( from root chord )
Aluminum 2219-T81
10.5
1.54
6.17
2.59
0.0
18.5
0.0
24.0
57.0
12.3
0.027
Modified double wedge
6.17
131.6
4.0
Fixed surfaces ( aft )
2/24/2008
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296
Rocket Baseline Missile Definition ( cont )
References values
Reference area, ft2
Reference length, ft
Pitch / Yaw Moment of inertia at launch, slug-ft2
Pitch / Yaw Moment of inertia at burnout, slug-ft2
0.349
0.667
117.0
94.0
Rocket Motor Performance ( altitude = 20k ft, temp = 70° F )
Burning time, sec ( boost / sustain )
Maximum pressure, psi
Average pressure, psi ( boost / sustain )
Average thrust, lbf ( boost / sustain )
Total impulse, lbf-s ( boost / sustain )
Specific impulse, lbf-s / lbm ( boost / sustain )
3.69 / 10.86
2042
1769 / 301
5750 / 1018
21217 / 11055
250 / 230.4
Propellant
Weight, lbm ( boost / sustain )
Flame temperature @ 1,000 psi, °F
Propellant density, lbm / in3
Characteristic velocity, ft / s
Burn rate @ 1000 psi, in / s
Burn rate pressure exponent
2/24/2008
84.8 / 48.2
5282 / 5228
0.065
5200
0.5
0.3
ELF
297
Rocket Baseline Missile Definition ( cont )
Propellant ( continued )
Burn rate sensitivity with temperature, % / °F
Pressure sensitivity with temperature, % / °F
0.10
0.14
Rocket Motor Case
Yield / ultimate strength, psi
Material
Modulus of elasticity, psi
Length, in
Outside diameter, in
Thickness, in (minimum)
Burst pressure, psi
Volumetric efficiency
Grain configuration
Dome ellipse ratio
170,000 / 190,000
4130 Steel
29.5 x 106 psi
59.4
8.00
0.074
3140
0.76
Three slots + web
2.0
Nozzle
Housing material
Exit geometry
Throat area, in2
Expansion ratio
Length, in
Exit diameter, in
2/24/2008
4130 Steel
Contoured ( equiv. 15° )
1.81
6.2
4.9
3.78
ELF
298
Rocket Baseline Missile Has Boost-Sustain
Thrust - Time History
8
Boost Total Impulse = ∫Tdt = 5750 ( 3.69 ) = 21217 lb-s
6
Thrust – 1,000 lb
4
2
Sustain Total Impulse = ∫Tdt = 1018 ( 10.86 ) = 11055 lb-s
0
2/24/2008
0
4
Time – seconds
ELF
8
12
16
Note: Altitude = 20k ft, Temperature = 70° F
Total impulse drives velocity change
299
Normal Force ~ CN
Pitching Moment – Cm
Rocket Baseline Missile Aerodynamic
Characteristics
0
-4.0
0.6
4.60
M = 1.2 and 1.5
-8.0
3.95
-12.0
2.35
2.0
-16.0
20
M
1.5
16
2.0
2.35
2.87
3.95
4.60
1.2
0.6
12
8
4
0
2/24/2008
SRef = 0.349 ft2, lRef = d = 0.667 ft, CG at STA 75.7, δ = 0 deg
0
4
8
12
16
α, Angle of Attack – Deg
ELF
20
24
300
K1, K2 ~ Per Deg2
K2
.004
0.2
K1
.002
0.1
CA = CAα = 0 + K1 δ2 + K2 α δ
0
0
1.2
Power Off
0.8
Power On
1.2
0.8
0.4
δ
0.4
0
2/24/2008
.006
0.3
Cm at α = 0 deg, Per Deg
CA at α = 0 deg
δ
CN at α = 0 deg, Per Deg
Rocket Baseline Missile Aerodynamic
Characteristics ( cont )
0
1
2
3
4
M, Mach Number
0
5
ELF
0
1
2
3
4
M, Mach Number
5
301
High Altitude Launch Enhances Rocket Baseline
Range
Burnout
Vmax = 2524 ft / s
40
Altitude ~ 103 ft
30
Boost /
Sustain
Termination
Mach = 1.5
Coast
Vmax = 2147 ft / s
20
ML = 0.7
CD
10
AVG
Vmax = 1916 ft / s
= 0.65
Constant Altitude Flight
0
0
5
10
15
20
25
Range ~ nm
2/24/2008
ELF
302
Low Altitude Launch and High Alpha Maneuvers
Enhance Rocket Baseline Turn Performance
25
Alt.
α
1 10k ft 15°
2 10k ft 10°
3 40k ft 15°
4 40k ft 10°
Cross Range 1,000 ft.
20
15
4
10
3
5
1
Termination at M = 1.0
Marks at 2 s intervals
2
0
-10
-5
0
5
10
Down Range 1,000 ft.
Note: Off boresight envelope that is shown does not include the rocket baseline seeker field-of-regard limit ( 30 deg ).
2/24/2008
ELF
303
Paredo Shows Range of Rocket Baseline Driven
by ISP, Propellant Weight, Drag, and Static Margin
1.5
Note: Rocket baseline:
1
hL = 20k ft, ML = 0.7, MEC = 1.5
R@ ML = 0.7, hL = 20k ft = 9.5 nm
Nondimensional 0.5
Range
Sensitivity to
0
Parameter
Example: 10% increase in propellant
weight ⇒ 8.8% increase in flight range
Isp
Prop.
Weight
CD0
-0.5
Drag- Static Thrust Inert
Due-to- Margin
Weight
Lift
-1
Parameter
2/24/2008
ELF
304
Boost - Sustain Trajectory Assumptions
Assumptions
1 degree of freedom
Constant altitude
Simplified equation for axial acceleration based on thrust,
drag, and weight
nX = ( T – D ) / W
Missile weight varies with burn rate and time
W = WL – WP t / tB
Drag is approximated by
D = CDO q S
2/24/2008
ELF
305
Example of Rocket Baseline Axial Acceleration
nX = ( T - D ) / W
15
Note:
tf = 24.4 s
ML = 0.8
hL = 20,000 ft
TB = 5750 lb
tB = 3.69 s
TS = 1018 lb
tS = 10.86 s
D = 99 lb at Mach 0.8
D = 1020 lb at Mach 2.1
WL = 500 lb
WP = 133 lb
nx, Axial Acceleration, g
Boost
10
5
Sustain
0
0
5
10
15
Coast
20
25
-5
t, Time, s
2/24/2008
ELF
306
Example of Rocket Baseline Missile Velocity vs
Time
ΔV / ( gc ISP ) = - ( 1 - DAVG / T ) ln ( 1 - Wp / Wi ), During Boost-Sustain
V / VBO = 1 / { 1 + t / { 2 WBO / [ gc ρAVG SRef ( CD )AVG VBO ]}}, During Coast
0
V, Velocity, ft / s
3000
Sustain
2000
Coast
Boost
1000
Note:
ML = 0.8
hL = 20k feet
0
0
5
10
15
20
25
t, Time, s
2/24/2008
ELF
307
Range and Time-to-Target of Rocket Baseline
Missile Meet Requirements
10
R = Δ Rboost + Δ Rsustain + Δ Rcoast
R, Flight Range, nm
8
Coast
6
(RF)Req = 6.7 nm @ t =24.4 s
4
Sustain
Note:
2
ML = 0.8
Boost
hL = 20k ft
0
0
5
10
15
20
25
t, Time, s
2/24/2008
ELF
308
Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
2/24/2008
ELF
309
Example of Wing Sizing to Satisfy Required
Maneuver Acceleration
Size Wing for the Assumptions
( nZ )Required = 30 g to counter 9 g maneuvering target )
( nZ ) = Δ ( nZ )Wing + Δ ( nZ )Body + Δ ( nZ )Tail
Rocket Baseline @
Mach 2
20,000 ft altitude
367 lb weight ( burnout )
From Prior Example, Compute
αWing = α’Max = ( α + δ )Max = 22 deg for rocket baseline
Video of Intercept of Maneuvering Target
α = 0.75δ, αBody = αTail = 9.4 deg
Δ ( nZ )Body = q SRef ( CN )Body / W = 2725 ( 0.349 ) ( 1.28 ) / 367 = 3.3 g ( from body )
Δ ( nZ )Tail = q STail [( CN )Tail ( SRef / STail )] / W = 2725 ( 1.54 ) ( 0.425 ) / 367 = 4.9 g ( from tail )
Δ ( nZ )Wing = ( nZ )Required - Δ ( nZ )Body - Δ ( nZ )Tail = 30 – 3.3 – 4.9 = 21.8 g
( SW )Required = Δ ( nZ )Wing W / { q [( CN )Wing (SRef / SWing )]} = 21.8 ( 367 ) / {( 2725 ) ( 1.08 )} = 2.72 ft2
Note: ( SW )RocketBaseline = 2.55 ft2
2/24/2008
ELF
310
Wing Sizing to Satisfy Required Turn Rate
Assume
.
( γ )Required > 18 deg / s to counter 18 deg / s maneuvering aircraft
Rocket Baseline @
Mach 2
20,000 ft altitude
367 lb weight ( burnout )
γi = 0 deg
Compute
.
γ = gc n / V = [ q SRef CNα α + q SRef CNδ δ - W cos ( γ ) ] / [( W / gc ) V ]
α / δ = 0.75
α’ = α + δ = 22 deg ⇒ δ = 12.6 deg, α = 9.4 deg
.
γ = [ 2725 ( 0.349 )( 0.60 )( 9.4 ) +2725 ( 0.349 )( 0.19 )( 12.6 ) – 367 ( 1 )] / ( 367 / 32.2 )( 2074 ) = 0.31
rad / s or 18 deg / s
Note: ( SW )RocketBaseline ⇒ 18 deg / s Turn Rate
2/24/2008
ELF
311
Wing Sizing to Satisfy Required Turn Radius
Assume Maneuvering Aircraft Target with
.
γ = 18 deg / s = 0.314 rad / s
V = 1000 ft / s
.
( RT )Target = V / γ = 1000 / 0.314 = 3183 ft
Assume Rocket Baseline @
Mach 2
20,000 ft altitude
367 lb weight ( burnout )
Compute
.
γ = 18 deg / s ( prior figure )
.
( RT )RocketBaselinet = V / γ = 2074 / 0.314 = 6602 ft
Note: ( RT )RocketBaselinet > ( RT )Target ⇒ Rocket Baseline Can Be Countermeasured by Target in a Tight Turn
Counter-Countermeasure Alternatives
Larger Wing
Higher Angle of Attack
Longer Burn Motor with TVC
2/24/2008
ELF
312
Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
2/24/2008
ELF
313
Combined Weight / Miss Distance Drivers: Nozzle
Expansion and Motor Volumetric Efficiency
Parameter
Baseline
Fixed surface number of panels
Movable surface number of panels
Design static margin at launch
Wing movable surface sweep ( deg )
Tail fixed surface sweep ( deg )
Wing movable surface thickness ratio
Nose fineness ratio
Rocket chamber sustain pressure ( psi )
Boattail fineness ratio ( length / diameter )
Nozzle expansion ratio
Motor volumetric efficiency
Propellant density ( lb / in3 )
Boost thrust ( lb )
Sustain thrust ( lb )
Characteristic velocity ( ft / s )
Wing location ( percent total length )
4
4
0.40
45.0
57.0
0.044
2.4
301
0.38
6.2
0.76
0.065
5,750
1,018
5,200
47.5
Sensitivity
Variation
3
2
0.30
49.5
60.0
0.034
2.6
330
0.342
6.82
0.84
0.084
6,325
1,119
5,720
42.75
Note:
Baseline: Weight = 500 lb, Miss distance = 62.3 ft
W* = weight sensitivity for parameter variation = ΔW / W
σ* = miss distance sensitivity for parameter variation = Δ σ / σ
2/24/2008
ELF
W*
σ*
+0.054
+0.071
+0.095
-0.205
+0.027
+0.041
-0.016
-0.076
+0.096
-0.114
-0.136
-0.062
+0.014
+0.088
-0.063
+0.181
+0.100
+0.106
+0.167
+0.015
+0.039
+0.005
-0.745
-0.045
+0.140
-0.181
-0.453
+0.012
-0.018
+0.246
-0.077
-0.036
Strong impact with synergy
Strong impact
Moderate impact with synergy
Moderate impact
314
A Harmonized Missile Can Have Smaller Miss
Distance and Lighter Weight
Parameter
Judicious changes
Boost thrust ( lb )
Wing location ( percent missile length to 1/4 mac )
Wing taper ratio
Nose fineness ratio
Nose blunting ratio
Nozzle expansion ratio
Sustain chamber pressure ( psi )
Boattail fineness ratio
Tail leading edge sweep ( deg )
Technology limited changes
No. wing panels
No. tail panels
Wing thickness ratio
Wing leading edge sweep ( deg )
Static margin at launch ( diam )
Propellant density ( lb / in3 )
Motor volumetric efficiency
Measures of Merit
Total weight ( lb )
Miss distance ( ft )
Time to target ( s )
Length ( in )
Mach No. at burnout
Weight of propellant ( lb )
Wing area ( in2 )
Tail area ( in2 )
2/24/2008
*Note:
Value of driving parameter
Baseline Value
Missile Configured for
Minimum:
Weight
Miss Distance
Harmonized
5,750
47.5
0.18
2.4
0.0
6.2
301
0.38
57
3,382
47
0.2
3.2
0.05
15
1,000
0.21
50
3,382
44
0.2
2.55
0.05
15
1,000
0.21
50
3,382
46
0.2
2.6
0.05
15
1,000
0.21
50
4
4
0.044
45
0.4
0.065
0.76
2
3
0.030
55
0.0
0.084
0.84
2
3
0.030
55
0.0
0.084
0.84
2
3
0.030
55
0.0
0.084
0.84
500
62.3
21.6
144
2.20
133
368.6
221.8
385.9
63.1
23.8
112.7
2.08
78.3
175.5
109.1
395.0
16.2
23.6
114.7
2.09
85.4
150.7
134.5
390.1
16.6
23.8
114.9
2.07
85.9
173.8
112.0
ELF
315
Baseline Missile vs Harmonized Missile
144”
57°
45°
2.4
Nose
Fineness; 2.6
Weight ( lb ); 500
390
Propellant Density 0.065
0.084
( lb / in3 );
55°
Surfaces;
{ 2 wings / 3 tails
4 wings / 4 tails
50°
115”
2/24/2008
ELF
316
Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
2/24/2008
ELF
317
Lofted Glide Trajectory Provides Extended Range
Using Rocket Baseline, Compare
Lofted Launch-Coast-Glide Trajectory
Lofted Launch-Ballistic Trajectory
Constant Altitude Trajectory
Assume for Lofted Launch-Coast-Glide Trajectory:
γi = 45 deg
γ = 45 deg during boost and sustain
γ = 45 deg coast
Switch to ( L / D )max glide at optimum altitude
( L / D )maxg glide trajectory after apogee
hi = hf = 0 ft
Velocity, Horizontal Range, and Altitude During Initial Boost @ γ = 45 deg
ΔV = - gc ISP [ 1 – ( DAVG / T ) - ( WAVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 250 ) [ 1 - ( 419 /
5750 ) – 458 ( 0.707 ) / 5750 ] ln ( 1 - 84.8 / 500 ) = 1,303 ft / s
ΔR = ( Vi + ΔV / 2 ) tB = ( 0 + 1303 / 2 ) 3.69 = 2,404 ft
ΔRx = ΔR cos γi = 2404 ( 0.707 ) = 1,700 ft
ΔRy = ΔR sin γi = 2404 ( 0.707 ) = 1,700 ft
h = hi + ΔRy = 0 + 1700 = 1,700 ft
2/24/2008
ELF
318
Lofted Glide Trajectory Provides Extended
Range ( cont )
Velocity, Horizontal Range, and Altitude During Sustain @ γ = 45 deg
ΔV = - gc ISP [ 1 – ( DAVG / T ) – ( WAVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 230.4 ) [ 1 – ( 650 /
1018 ) – 391 ( 0.707 ) / 1018 ] ln ( 1 - 48.2 / 415.2 ) = 81 ft / sec
VBO = 1303 + 81 = 1,384 ft / s
ΔR = ( Vi + ΔV / 2 ) tB = ( 1303 + 81 / 2 ) 10.86 = 14,590 ft
ΔRx = ΔR cos γi = 14590 ( 0.707 ) = 10,315 ft
ΔRy = ΔR sin γi = 14,590 ( 0.707 ) = 10,315 ft
h = hi + ΔRy = 1700 + 10315 = 12,015 ft
Velocity, Horizontal Range, and Altitude During Coast @ γ = 45 deg to h@( L / D )max
Vcoast = Vi { 1 – [( gc sin γ ) / Vi ] t } / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t } = 1384 { 1 –
[( 32.2 ( 0.707 )) / 1384 ] 21 } / { 1 + {[ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))}
21 } = 674 ft / s
Rcoast = { 2 W / [ gc ρAVG SRef ( CD0 )AVG )]} ln { 1 – [ gc2 ρAVG SRef ( CD0 )AVG / ( 2 W )] [ sin γ ] t2 +
{[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t } = { 2 ( 367 ) / [ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 )] ln
{ 1 – [ (32.2)2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) / (( 2 ( 367 ))] [ 0.707 ] ( 21 )2 + {[ 32.2 ( 0.001338 )
( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))} 21 } = 17148 ft
( Rx )coast = ( Ry )coast = Rcoast sinγ = 17148 ( 0.707 ) = 12124 ft
2/24/2008
ELF
319
Lofted Glide Trajectory Provides Extended Range
( cont )
Flight Conditions At End-of-Coast Are:
t = 35 s
V = 674 ft / s
h = 24,189 ft
q = 251 psf
M = 0.66
( L / D )max = 5.22
α( L / D )max = 5.5 deg
Initiate α = α( L / D )max = 5.5 deg at h = 24,189 ft
Incremental Horizontal Range During ( L / D )max Glide Is
ΔRx = ( L / D ) Δh = 5.22 ( 24189 ) = 126,267 ft
Total Horizontal Range for Elevated Launch-Coast-Glide Trajectory Is
Rx = ΣΔRx = ΔRx,Boost + ΔRx,Sustain + ΔRx,Coast + ΔRx,Glide = 1700 + 10315 + 12124 + 126267 =
150406 ft = 24.8 nm
2/24/2008
ELF
320
Lofted Glide Trajectory Provides Extended
Range ( cont )
Note: Rocket Baseline
30
z End of boost
0
γ = 45
de g
Ballis
t ic
Gli
de
s, h = 21,590 ft
ÊLofted coast apogee, t = 35 s, V = 674 ft / s, h = 24,189 ft
@
(L
/D
®Lofted ballistic impact, t = 68 s,
)m
²Lofted
ax
istic
Coas
t@
20
γ = - 71 deg, V = 1368 ft / s
glide impact, t = 298 s, γ = - 10.8 deg, V = 459 ft / s
Ä Co-altitude flight impact, t = 115 s, V = 500 ft / s
„
Susta
in
10
ÈLofted ballistic apogee, t = 35 s, V = 667 ft /
Ø
È
Ball
h, Altitude, k ft
„ End of sustain
z
z
0
Co-altitude
„
®
Ä
²
10
20
30
R, Range, nm
2/24/2008
ELF
321
Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
2/24/2008
ELF
322
Ramjet Baseline Is a Chin Inlet Integral Rocket
Ramjet ( IRR )
Sta 150.3
37°
11.6
11.5
16.5
Boost Nozzle
20.375 dia
Guidance
Chin
Inlet
Sta 0.
Ramjet Fuel
Warhead
Boost Propellant
Booster, and
Ramjet Engine
Transport Air Duct
23.5
43.5
Forebody
126.0
76.5
Payload Bay
Mid-body
Nose
Aft-body
Tail Cone
159.0
171.0
Note: Dimensions are in inches
Source: Bithell, R.A. and Stoner, R.C. “Rapid Approach for Missile Synthesis”, Vol. II, Air-breathing
Synthesis Handbook, AFWAL TR 81-3022, Vol. II, March 1982.
2/24/2008
ELF
323
Mass Properties of Ramjet Baseline Missile
Component
Weight, lb
Nose
CG Sta, in
15.9
15.7
Forebody Structure
Guidance
42.4
129.0
33.5
33.5
Payload Bay Structure
Warhead
64.5
510.0
60.0
60.0
Midbody Structure
Inlet
Electrical
Hydraulic System for Control Actuation
Fuel Distribution
95.2
103.0
30.0
20.0
5.0
101.2
80.0
112.0
121.0
121.0
Aftbody Structure
Engine
44.5
33.5
142.5
142.5
Tailcone Structure
Ramjet Nozzle
Flight Control Actuators
Fins ( 4 )
End of Cruise
Ramjet Fuel ( 11900 in3 )
Start of Cruise
Boost Nozzle ( Ejected )
Frangible Port
End of Boost
Boost Propellant
2/24/2008 Booster Ignition
31.6
31.0
37.0
70.0
1,262.6
476.0
1,738.6
31.0
11.5
1,781.1
449.0
2,230.1
ELF
165.0
165.0
164.0
157.2
81.8
87.0
83.2
164.0
126.0
84.9
142.5
96.5
324
Ramjet Baseline Missile Definition
Inlet
Type
Material
Conical forebody half angle, deg
Ramp wedge angle, deg
Cowl angle, deg
Internal contraction ratio
Capture area, ft2
Throat area, ft2
Mixed compression
Titanium
17.7
8.36
8.24
12.2 Percent
0.79
0.29
Dome Material
Airframe Material
Combustor Material
Length, in
Diameter, in
Fineness ratio
Volume, ft3
Wetted area, ft2
Base area, ft2 ( cruise )
Boattail fineness ratio
Nose half angle, deg
Nose length, in
Silicon nitride
Titanium
Insulated Inconel
171.0
20.375
8.39
28.33
68.81
0.58
N/A
17.7
23.5
Body
2/24/2008
ELF
325
Ramjet Baseline Missile Definition ( cont )
Tail ( Exposed )
Material
Planform area ( 2 panels ), ft2
Wetted area ( 4 panels ), ft2
Aspect ratio ( 2 panels exposed )
Taper ratio
Root chord, in
Span, in. ( 2 panels exposed )
Leading edge sweep, deg
Mean aerodynamic chord, in
Thickness ratio
Section type
Section leading edge total angle, deg
xmac, in
ymac, in ( from root chord )
Titanium
2.24
8.96
1.64
0.70
16.5
23.0
37.0
14.2
0.04
Modified double wedge
9.1
150.3
5.4
Reference values
Reference area, ft2
Reference length, ft
2/24/2008
2.264
1.698
ELF
326
Engine Nomenclature and Flowpath Geometry for
Ramjet Baseline
( CD0 )Nose Corrected = ( CD0 )Nose Uncorrected x ( 1 - Ac / SREF )
Ac = Inlet capture area
SRef = Reference area
20.375 in
Ac = 114 in2
120°
Ramjet Engine Station Identification
SRef
0
1
2
3
4
5
6
Subscripts
0
Free stream flow into inlet ( Example, Ramjet Baseline at Mach 4, α = 0 deg ⇒ A0 = 104 in2. Note: AC = 114 in2 )
1
Inlet throat ( Ramjet Baseline A1 = AIT = 41.9 in2 )
2
Diffuser exit ( Ramjet Baseline A2 = 77.3 in2 )
3
Flame holder plane ( Ramjet Baseline A3 = 287.1 in2 )
4
Combustor exit ( Ramjet Baseline A4 = 287.1 in2 )
5
Nozzle throat ( Ramjet Baseline A5 = 103.1 in2 )
6
Nozzle exit ( Ramjet Baseline A6 = 233.6 in2 )
Ref
Reference Area ( Ramjet Baseline Body Cross-sectional Area, SRef = 326 in2 )
2/24/2008
ELF
327
Aerodynamic Characteristics of Ramjet Baseline
SRef = 2.264 ft2
lRef = dRef = 1.698 ft
Xcg @ Sta 82.5 in
δ = 0 deg
4.0
Normal Force Coefficient, CN
Axial Force Coefficient, CA
.40
Mach
.30
1.2
1.5
2.0
.20
3.0
4.0
.10
0
0
4
8
12
16
α, Angle of Attack ~ deg
Mach
3.0
1.2
1.5
2.0
2.0
3.0
4.0
1.0
0
0
4
8
12
16
α, Angle of Attack ~ deg
Source: Reference 27, based on year 1974 computer program from Reference 32.
2/24/2008
ELF
328
Aerodynamic Characteristics of Ramjet Baseline
( cont )
Pitching Moment Coefficient, Cm
+ .4
SRef = 2.264 ft2
lRef = dRef = 1.698 ft
Xcg @ Sta 82.5 in
δ = 0 deg
0
-.4
Mach
4.0
-.8
3.0
-1.2
2.0
1.5
-1.6
1.2
0
4
8
12
α, Angle of Attack ~ deg
16
Source: Reference 27, based on year 1974 computer program from Reference 32.
2/24/2008
ELF
329
-.4
SRef = 2.264 ft2
lRef = dRef = 1.698 ft
Xcg @ Sta 82.5 in
δ= 0 deg
α = 0 deg.
.4
-.2
.3
C
D
0
C
δ
m ~ per deg
Aerodynamic Characteristics of Ramjet Baseline
( cont )
0
.2
.1
.05
0
δ
N ~ per deg
.10
1
2
3
4
C
M, Mach Number
0
0
2/24/2008
0
1
2
3
M, Mach Number
4
Source: Reference 27, based on year 1974 computer program from
Reference 32.
ELF
330
Thrust Modeling of Ramjet Baseline
Tmax, Max Thrust, lb
100000
10000
h = Sea Level
h = 20k ft
h = 40k ft
h = 60k ft
h = 80k ft
Example: M = 3.5, h = 60k ft, ϕ
= 1 ⇒ Max Thrust = 1,750 lb
1000
Note:
Standard atmosphere
T = Tmax ϕ
100
0
1
2
3
4
φ = 1 if stochiometric ( f / a = 0.0667 )
α = 0 deg
M, Mach Number
Figure based on Reference 27 prediction
2/24/2008
ELF
331
Specific Impulse Modeling of Ramjet Baseline
ISP, Specific Impulse, s
1,500
•
Example: M = 3.5 ⇒ ISP = 1,120 s
1,000
•
•
••
••
Note:
500
•
•
•
Standard atmosphere
ϕ≤1
ISP based on Reference 27 computer prediction.
0
0
1
2
3
4
M, Mach Number
2/24/2008
ELF
332
Rocket Booster Acceleration / Performance of
Ramjet Baseline
Boost Thrust ~ 1000 lb
30
( ISP )Booster = 250 s
20
10
0
1.0
2.0
3.0
Time ~ s
Standard atmosphere
ML = 0.80
Constant altitude flyout
2.0
Burnout Mach Number
Boost Range ~ nm
0
1.0
0
0
20
40
60
h, Altitude 1,000 ft
2/24/2008
ELF
4.0
5.0
6.0
0
20
40
3.0
2.5
2.0
60
h, Altitude 1,000 ft
80
333
Ramjet Baseline Has Best Performance at High
Altitude
500
400
Range ~ nm
60,000 ft
300
200
40,000 ft
100
20,000 ft
h = SL
0
0
1
2
3
4
M, Mach Number
Note: ML = 0.8, Constant Altitude Fly-out
Example, Mach 3 / 60k ft flyout ⇒ 445 nm. Breguet Range Prediction is R = V ISP ( L / D ) ln [ WBC / ( WBC - Wf )] = 2901 ( 1040 )
( 3.15 ) ln ( 1739 / ( 1739 - 476 )) = 3,039,469 ft or 500 nm. Predicted range is 10% greater than baseline missile data.
2/24/2008
ELF
334
From Paredo Sensitivity, Ramjet Baseline Range
Driven by ISP, Fuel Weight, Thrust, and CD0
Nondimensional Range Sensitivity
to Parameter
1.5
Example: At Mach 3.0 / 60k ft altitude
cruise, 10% increase in fuel weight
⇒ 9.6% increase in flight range
1
0.5
0
ISP
-0.5
Fuel
Weight
Thrust
-1
CD0, Zero- CLA, LiftLift Drag
CurveCoefficient
Slope
Coefficient
Inert
Weight
Parameter
Sea Level Flyout at Mach 2.3
40k ft Flyout at Mach 2.8
2/24/2008
ELF
20k ft Flyout at Mach 2.5
60k ft Flyout at Mach 3.0
335
Ramjet Baseline Flight Range Uncertainty Is +/- 7%, 1 σ
Parameter
Baseline Value at Mach 3.0 / 60k ft
Uncertainty in Parameter
ΔR / R from Uncertainty
1. Specific Impulse
1040 s
+/- 5%, 1σ
+/- 5%, 1σ
2. Ramjet Fuel Weight
476 lb
+/- 1%, 1σ
+/- 0.9%, 1σ
3. Cruise Thrust ( φ = 0.39 )
458 lb
+/- 5%, 1σ
+/- 2%, 1σ
4. Zero-Lift Drag Coefficient
0.17
+/- 5%, 1σ
+/- 4%, 1σ
5. Lift Curve Slope Coefficient
0.13 / deg
+/- 3%, 1σ
+/- 1%, 1σ
6. inert Weight
1205 lb
+/- 2%, 1σ
+/- 0.8%, 1σ
Level of Maturity Based on Flight Demo of Prototype, Subsystem Tests, and Integration
Wind tunnel tests
Direct connect, freejet, and booster firing propulsion tests
Structure test
Mock-up
Hardware-in-loop simulation
Flight Test
Total Flight Range Uncertainty at Mach 3.0 / 60k ft Flyout
ΔR / R = [ (ΔR / R )12 + (ΔR / R )22 + (ΔR / R )32 + (ΔR / R )42 + (ΔR / R )52 + (ΔR / R )62 ]1/2 = +/- 6.9%, 1σ
2/24/2008
R = 445 nm +/- 31 nm, 1σ
ELF
336
Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
2/24/2008
ELF
337
Slurry Fuel and Efficient Packaging Provide
Extended Range Ramjet
Propulsion / Configuration
Fuel Type / Volumetric
Performance (BTU / in3) /
Density (lb / in3)
Fuel Volume (in3) /
Fuel Weight (lb)
ISP (s) / Cruise
Range at Mach 3.5,
60k ft (nm)
Liquid Fuel Ramjet
RJ-5 / 581 / 0.040
11900 / 476
1120 / 390
Ducted Rocket ( Low Smoke )
Solid Hydrocarbon / 1132 / 7922 / 594
0.075
677 / 294
Ducted Rocket ( High
Performance )
Boron / 2040 / 0.082
7922 / 649
769 / 366
Solid Fuel Ramjet
Boron / 2040 / 0.082
7056 / 579
1170 / 496
Slurry Fuel Ramjet
40% JP-10, 60% boron
carbide / 1191 / 0.050
11900 / 595
1835 / 770
2/24/2008
Note:
Flow Path
Available Fuel
ELF
Rcruise = V ISP ( L / D ) ln [ WBC / ( WBC - Wf )]
338
Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket, Design, Build, and Fly
2/24/2008
ELF
339
Example of Ramjet Velocity Control Through Fuel
Control
Ramjet Baseline
Equivalence Ratio
Ramjet Baseline Fuel
Flow Rate, lb / s
10
T
Example for Ramjet Baseline:
Mi = 4, h = sea level, T0 = 519R
T+W-D=0
W
1
D
W = WBO = 1263 lb
D = CD q SRef = 3353 CD MI2 = 3353 ( 0.14 )
0
0
( 4 )2 = 7511 lb
Trequired = D - W = 7511 - 1263 = 6248 lb
.
wf = T / ISP = 6248 / 1000 = 6.25 lb / s
φ = Trequired / Tφ = 1 = 6248 / 25000 = 0.25
0.1
0
1
2
3
4
Note: Excess air provides cooling of
combustor
Mi, Impact Mach Number at Sea Level
Note: Ramjet baseline, vertical impact at sea level, steady state velocity at impact, T = thrust, W = weight, D = drag,
WBO = burnout. weight, CD = zero-lift drag coefficient, Mi= impact Mach number, Trequired = required thrust for steady
0
state flight, wf = fuel flow rate, ISP = specific impulse, φ = equivalence ratio ( φ = 1 stochiometric )
2/24/2008
ELF
340
Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Surface impact velocity
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
2/24/2008
ELF
341
Computer Sizing Code Should Have Fast
Turnaround and Be Easy to Use
Objective of Conceptual Design
Search Broad Solution Space
Iterate to Design Convergence
Characteristics of Good Conceptual Design Sizing Code
Fast Turnaround Time
Easy to Use
Directly Connect Predictions of Aeromechanics and Physical
Parameters to Trajectory Code
Simple, Physics Based Methods
Includes Most Important, Driving Parameters
Provides Insight into Relationships of Design Parameters
Stable Computation
Imbedded Baseline Missile Data
Human Designer Makes the Creative Decisions
2/24/2008
ELF
342
Example of DOS-Based Conceptual Sizing
Computer Code – ADAM
Conceptual Sizing Computer Program
Advanced Design of Aerodynamic Missiles ( ADAM )
PC compatible
Written in DOS
Aerodynamic Module Based on NACA 1307 Calculates
Static and dynamic stability derivatives
Control effectiveness and trim conditions
3, 4, 5, and 6-DOF Simulation Modules
Proportional guidance
Input provided automatically by aerodynamic module
Configurations Benchmarked with Wind Tunnel Data
Greater than 50 Input Parameters Available
Defaults to benchmark configuration ( s )
2/24/2008
ELF
343
Example of Spreadsheet Based Conceptual
Sizing Computer Code - TMD Spreadsheet
Conceptual Sizing Computer Code
Tactical Missile Design ( TMD ) Spreadsheet
PC compatible
Windows Excel spreadsheet
Based on Tactical Missile Design Short Course and Textbook
Aerodynamics
Propulsion
Weight
Flight trajectory
Measures of merit
2/24/2008
ELF
344
Example of Spreadsheet Based Conceptual
Sizing Computer Code, TMD Spreadsheet
Define Mission Requirements [ Flight Performance ( RMax, RMin, VAVG ) , MOM, Constraints ]
Establish Baseline ( Rocket
, Ramjet
)
Aerodynamics Input ( d, l, lN, A, c, t, xcg )
Aerodynamics Output [ CD , CN, xac, Cm , L / D, ST ]
δ
0
Propulsion Input ( pc, ε, c*, Ab, At, A0, Hf, ϕ, T4, Inlet Type )
.
Propulsion Output [ Isp, Tcruise, pt / pt , w , Tboost, Tsustain, ΔVBoost ]
2
Alt Mission
Alt Baseline
Resize / Alt Config /
Subsystems / Tech
0
Weight Input ( WL, WP, ρ, σmax )
Weight Output [ WL, WP, h, dT / dt, T, t, σbuckling, MB, σ, Wsubsystems, xcg, Iy ]
Trajectory Input ( hi, Vi, Type ( cruise, boost, coast, ballistic, turn, glide )
Trajectory Output ( R, h, V, and γ versus time )
Meet
Performance?
Yes
Measures of Merit and Constraints
Yes
2/24/2008
ELF
No [ RMax, RMin, VAVG ]
No [ pBlast, PK, nHit,
Vfragments, PKE,
KEWarhead, τTotal,
σHE, σMAN, Rdetect,
CSDD, C1000th, Cunit x ]
345
Example of TMD Spreadsheet Sizing Code
Verification: Air-to-Air Range Requirement
Example Launch Conditions
hL = 20k ft
ML = 0.8
Example Requirement
RF = 6.7 nm with tf < 24.4 s
Solutions for Rocket Baseline
ADAM: RF = 6.7 nm at tf = 18 s
TMD Spreadsheet: RF = 6.7 nm at tf = 19 s
3 DOF using wind tunnel aero data: RF = 6.7 nm at tf = 21 s
Differences in Flight Time to 6.7 nm Mostly Due to Zero-Lift Drag Coefficient.
For Example:
ADAM prediction at Mach 2.0: ( CD0 )coast = 0.53
TMD Spreadsheet prediction at Mach 2.0: ( CD0 )coast = 0.57
Wind tunnel aero data at Mach 2.0: ( CD0 )coast = 1.05
Wind Tunnel Data / Baseline Missile Data Correction Required to Reduce
Uncertainty in CD
0
2/24/2008
ELF
346
Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Surface impact velocity
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
2/24/2008
ELF
347
Example of Design, Build, and Fly Customer
Requirements
Objective – Design, Build, and Fly Soda Straw Rocket with:
Flight Range Greater Than 90 ft
Weight Less Than 2 g
Furnished Property
Launch System
Distance Measuring Wheel
Weight Scale
Micrometer Scale
Engineer’s Scale
Scissors
Furnished Material
1 “Giant” Soda Straw: 0.28 in Diameter by 7.75 in Length, Weight = 0.6 g
1 Strip Tabbing: ½ in by 6 in, Weight = 1.4 g
1 Ear Plug: 0.33 – 0.45 in Diameter by 0.90 in Length, Weight = 0.6 g
1 “Super Jumbo” Soda Straw: 0.25 in Diameter by 7.75 in Length
2/24/2008
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348
Example of Design, Build, and Fly Customer
Requirements ( cont )
Furnished Property Launch System with Specified Launch Conditions
Launch Tube Diameter: 0.25 in
Launch Tube Length ( e.g., 6 in )
Launch Pressure ( e.g., 30 psi )
Launch Elevation Angle ( e.g., 40 deg )
Predict Flight Trajectory Range and Compare with Test
2/24/2008
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349
Soda Straw Rocket Launcher and Targeting
9. Rocket on Launcher
8. Launch Tube
7. Inclinometer
6b. Manual Valve
Launcher ( 0.1 s
average response )
6a. Solenoid Valve
Launcher ( 0.025 s
average response )
5. Launch Switch
4. Pressure Gauge
3. Air Hose
2. Pressure Tank
1. Pump
11. Rockets with Various Length, Tail Geometry, Nose Geometry, and Other Surfaces
2/24/2008
10. Laser Pointer Targeting Device
ELF
350
It Is Easy to Make a Soda Straw Rocket
1. Cut Large Diameter “Giant” Soda Straw to Desired
Length
2. Twist and Squeeze Ear Plug to Fit Inside Soda
Straw
3. Slide Ear Plug Inside Soda Straw
4. Cut Adhesive Tabs to Desired Height and Width of Surfaces
5. Apply Adhesive Tabs to Soda Straw
6. Wrap Front of Ear Plug and Straw with Tape
7. Slide Giant Soda Straw Rocket Over Smaller
Diameter “Super Jumbo” Soda Straw Launch Tube
2/24/2008
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351
Soda Straw Rocket Baseline Configuration
Ear Plug
Soda Straw
Strip Tabbing
0.25 in
0.28 in
0.5 in
lc = 6.0 in
l = 7.0 in
2/24/2008
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352
Soda Straw Rocket Baseline Weight and Balance
Component
Nose ( Plug )
Body ( Soda Straw )
Fins ( Four )
Total
2/24/2008
Weight, g
0.6
0.5
0.5
1.6
ELF
cg Station, in
0.5
3.5
6.75
3.39
353
Soda Straw Rocket Baseline Definition
Body
Material Type
Material density, lb / in3
Material strength, psi
Thickness, in
Length, in
Diameter, in
Fineness ratio
Nose fineness ratio
HDPE Plastic
0.043
4,600
0.004
7.0
0.28
25.0
0.5
Material
Planform area, in2 ( 2 panels exposed )
Wetted area, in2 ( 4 panels )
Aspect ratio ( 2 panels exposed )
Taper ratio
Chord, in
Span ( exposed ), in
Span ( total including body ), in
Leading edge sweep, deg
xmac, in
Plastic
0.25
1.00
1.00
1.0
0.5
0.5
0.78
0
6.625
Fins
2/24/2008
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354
Soda Straw Rocket Baseline Definition ( cont )
Nose
Material Type
Material density, lb / in3
Average diameter
Length
Foam
0.012
0.39 in
0.90 in
Reference Values
Reference area, in2
Reference length, in
0.0616
0.28
Thrust Performance
Inside cavity length, in
Typical Pressure, psi
Maximum thrust @ 30 psi pressure, lb
Time constant, s ( standard temperature )
2/24/2008
6.0
30
1.47
0.025
ELF
355
Soda Straw Rocket Baseline Static Margin
( xAC )B
xCG
d
xAC
l
( xAC )T
For body-tail geometry, static margin given by
( xAC – xCG ) / d = - {( CN α )B {[ xCG – ( xAC )B ] / d } + ( CNα )T {[ xCG – ( xAC )T ] / d }( ST /
SRef )} / [( CNα )B + ( CNα )T ST / SRef ]
For baseline soda straw configuration
xCG = 3.39 in, d = 0.28 in, ( CNα )B = 2 per rad, ST = 0.25 in2, SRef = 0.0616 in2
( xAC )B = [( xAC )B / lN ] lN = 0.63 ( 0.14 ) = 0.09 in
( CNα )T = π AT / 2 = π ( 1 ) / 2 = 1.57
( xAC )T = 6.5 + 0.25 ( cmac )T = 6.63
Substituting
( xAC - xCG ) / d = - { 2 ( 3.39 – 0.09 ) / 0.28 + [ 1.57 ( 3.39 – 6.63 ) / 0.28 ] [( 0.25 ) /
0.0616 ]} / [ 2 + 1.57 ( 0.25 ) / 0.0616 ] = 6.00 ( statically stable )
xAC = 6.00 ( 0.28 ) + 3.39 = 5.07 in from nose
2/24/2008
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356
Soda Straw Rocket Has High Acceleration Boost
Performance
T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) A
a ≈ 32.2 T / W, V = ∫ a dt, s = ∫ V dt
100
V, Velocity, fps
80
60
Note: Time Tics
Every 0.01 s
40
20
0
0
2
4
6
8
10
s, Distance Traveled During Launch, Inches
pgauge = 15 psi
pgauge = 60 psi
2/24/2008
pgauge = 30 psi
ELF
Thrust ( T ) from Pressurized Tube of Area A
T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) A
A = ( π / 4 ) ( 0.25 )2 = 0.0491 in2, τ = Valve Rise Time
Example:
Assume pgauge = 30 psi, lt = 6 in, τ = 0.025 s ( Average
for Solenoid Valve ), s = lc = 6 in
Thrust Equation Is:
T = 30 ( 1 - e – t / 0.025 ) ( 0.0491 ) = 1.4726 ( 1 - e – 40.00 t )
Note: Actual Boost Thrust Lower ( Pressure Loss,
Boundary Layer, Launch Tube Leakage, Launch
Tube Friction )
Equations for Acceleration ( a ), Velocity ( V ), and
Distance ( s ) During Boost Are:
a ≈ 32.2 T / W = 32.2 ( 1.4726 ) ( 1 - e – 40.00 t ) / 0.00352
= 13471.1 ( 1 - e – 40.00 t )
V = ∫ a dt = 13471.1 t + 336.78 e – 40.00 t – 336.78
s = ∫ V dt = 6735.57 t2 – 8.419 e – 40.00 t – 336.78 t +
8.419
End of Boost Conditions Are:
s = lc = 6 in = 0.500 ft ⇒ t = 0.0188 s
a = 7123 ft / s2 = 221 g
V = 75.2 ft / s
q = ½ ρ V2 = ½ ( 0.002378 ) ( 75.2 )2 = 6.72 psf
M = V / c = 75.2 / 1116 = 0.0674
357
Most of the Soda Straw Rocket Drag Coefficient
Is from Body Skin Friction
CD0 = ( CD0 )Body,Friction + ( CD0 )Base,Coast + ( CD0 )Tail,Friction
= 0.053 ( l / d ) [ M / ( q l )]0.2 + 0.12 + nT { 0.0133 [ M / ( q cmac )]0.2 } ( 2 ST / SRef )
CD0, Zero-Lift Drag Coefficient
1.5
1
0.5
0
0
2
4
6
8
10
ST / SRef, Tail Planform Area / Reference Area
V = 40 fps
2/24/2008
V = 80 fps
ELF
Example: V = 75.2 fps, ST = 0.00174 ft2, SRef =
0.000428 ft2 ⇒ ST / SRef = 4.07
Compute:
CD0 = 0.053 ( 25.0 ){ 0.0674 / [( 6.72 ) ( 0. 583 )]}0.2 +
0.12 + 2 { 0.0133 { 0.0674 / [( 6.72 ) ( 0.0417 )]}0.2 }[ 2
( 4.07 )] = 0.58 + 0.12 + 0.16 = 0.86
Note:
• Above Drag Coefficient Not Exact
• Based on Assumption of Turbulent Boundary
Layer
• Soda Straw Rocket Small Size and Low Velocity ⇒
Laminar Boundary Layer ⇒ Large Boundary Layer
Thickness on Aft Body at Tails
Compute Drag Force:
Dmax = CD qmax SRef = 0.86 ( 6.72 ) ( 0.000428 ) =
0.00247 lb
Compare Drag Force to Weight:
Dmax / W = 0.00247 / 0.00352 = 0.70
Note: Drag Force Smaller Than Weight
358
Soda Straw Rocket Baseline Has a Ballistic Flight
Range Greater Than 90 Feet
Rx = { 2 W cos γi / [ gc ρ SRef CD0 ]} ln { 1 + t / { 2
W / [ gc ρ SRef CD0 Vi ]}}
h - hi, Height above Initial Launch
Height, ft
h = { 2 W sin γi / [ gc ρ SRef CD ]} ln { 1 + t / { 2
0
W / [ gc ρ SRef CD0 Vi ]}} + hi - gc t2 / 2
Horizontal Range At Impact = Rx = { 2 (
40
Note: Time Tics
every 0.5 s
30
0.00352 ) cos γi / [ 32.2 ( 0.002378 ) (
0.000428 ) ( 0.86 )]} ln { 1 + t / { 2 (
0.00352 ) / [ 32.2 ( 0.002378 ) (
0.000428 ) ( 0.86 ) ( 75.2 )]}}
= 249.8 cos γi ln ( 1 + 0.301 t )
= 249.8 ( 0.866 ) ln [ 1 + 0.301 ( 1.8 )] =
93.7 ft
20
Height At Impact = h = { 2 ( 0.00352 )
10
0
0
20
40
60
80
100
Rx, Horizontal Range, ft
Gamma = 10 Deg
2/24/2008
Example, Assume lt = 6 in, pgauge = 30 psi, γi
= 30 deg, τ = 0.025 sec, Soda Straw
Baseline, t = timpact = 1.8 s
Gamma = 30 Deg
Gamma = 50 Deg
ELF
sin γi / [ 32.2 ( 0.002378 ) ( 0.000428 ) (
0.86 )} ln { 1 + t / { 2 ( 0.00352 ) / [ 32.2
( 0.002378 ) ( 0.000428 ) ( 0.86 ) ( 75.2
)]}} + hi – 32.2 t2 / 2
= 249.8 sin γi ln ( 1 + 0.301 t ) + hi –
32.2 t2 / 2 = 249.8 ( 0.5 ) ln [ 1 + 0.301 (
1.8 )] + hi – 32.2 ( 1.2 )2 / 2
= hi + 1.9 ft
359
Soda Straw Rocket Range Driven by Inside
Chamber Length and Launch Angle
0.8
Example: 10% decrease in
inside chamber length ⇒
7.7% decrease in range at t =
1.8 s. Note: Result is
nonlinear because inside
chamber length = launcher
length. Increase in lc also
leads to decrease in range.
0.6
Nondimensional
Range
Sensitivity to
Parameter
0.4
Note: Decreased chamber length ⇒
shorter duration thrust ( decreased
total impulse ) ⇒ decreased end-ofboost velocity
Soda Straw Rocket Baseline:
W = Weight = 0.00423 lb
lc = inside chamber length = 6 in
τ = Time constant to open solenoid
valve = 0.025 s
pgauge = gauge pressure = 30 psi
0.2
γi = Initial / launch angle angle = 30 deg
lt = 7 in
0
V = Launch velocity = 75.2 fps
lc
Gamma pgauge
W
tau
CD0
CD0 = Zero-lift drag coefficient = 0.86
timpact = Time from launch to impact =
1.8 s
-0.2
Rx = Horizontal range = 94 ft
2/24/2008
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360
Soda Straw Rocket Baseline Flight Range
Uncertainty Is +/- 2.4%, 1 σ
Parameter
Baseline Value
Uncertainty in
Parameter
ΔR / R Due to
Uncertainty
1. Inside Chamber Length
6 in
+/- 2%, 1 σ
+/- 1.5%, 1σ
2. Launch Angle
30 deg
+/- 3%, 1σ
+/- 1.7%, 1σ
3. Gauge Pressure
30 psi
+/- 3%, 1σ
+/- 0.5%, 1σ
4. Weight
1.6 g
+/- 6%, 1σ
+/- 0.4%, 1σ
5. Solenoid Time Constant
0.025 s
+/- 20%, 1σ
+/- 0.2%, 1σ
6. Zero-Lift Drag Coefficient
0.86
+/- 20%, 1σ
+/- 0.2%, 1σ
Estimate of Level of Maturity / Uncertainty of Soda Straw Rocket Baseline Parameters Based on
Wind tunnel test
Thrust static test
Weight measurement
Prediction methods
Total Flight Range Uncertainty for 30 psi launch at 30 deg
ΔR / R = [ (ΔR / R )12 + (ΔR / R )22 + (ΔR / R )32 + (ΔR / R )42 + (ΔR / R )52 + (ΔR / R )62 ]1/2 = +/- 2.4%, 1σ
R = 94 ft +/- 2.3 ft, 1σ
2/24/2008
ELF
361
House of Quality Translates Customer
Requirements into Engineering Emphasis
0
Chamber Length
Tail Planform Area
Flight Range
7
8
2
Weight
3
6
4
74 = ( 7x8 + 3x6 )
26 = ( 7x2 + 3x4 )
1
2
Note: Based on House of Quality, inside chamber length most important design parameter.
Note on Design Characteristics Sensitivity
Matrix: ( Room 5 ):
1 - Customer Requirements
2 – Customer Importance Rating ( Total = 10 )
3 – Design Characteristics
4 – Design Characteristics Importance Rating ( Total = 10 )
5 – Design Characteristics Sensitivity Matrix
6 – Design Characteristics Weighted Importance
7 – Design Characteristics Relative Importance
++ Strong Synergy
+ Synergy
0 Near Neutral Synergy
- Anti-Synergy
- - Strong Anti-Synergy
2/24/2008
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362
DOE Explores the Broad Possible Design Space
with a Reasonably Small Set of Alternatives
Design Space for Design of Experiments ( DOE )
Engineering
Characteristics Range
lc, Inside Chamber
Length, in
ST, Tail Planform Area,
in2
Lower Value
4
0.125
Upper Value
6
0.25
Full Factorial DOE Based on Upper / Lower Values of k = 2 Parameters:
Number of Combinations = 2k = 22 = 4
Concept
Sketch
lc, Inside Chamber
Length, in
ST, Tail Planform Area,
in2
“Big Kahuna”
6
0.25
“Shorty”
4
0.25
“Stiletto”
6
0.125
“Petite”
4
0.125
Note: DOE concepts should emphasize customer driving requirements and the driving engineering characteristics.
2/24/2008
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363
Engineering Experience Should Guide the DOE
Set of Alternatives and the Preferred Design
As an Example, for the Soda Straw Rocket, from
Experience We Know That
Soda Straw Rocket Must Fit on Launcher
Maximum Boost Velocity Occurs When Chamber Length = Launch
Tube Length
Three or Four Tails Best for Stability
Tails That Are Too Small May Result in an Unstable Flight
Tails That Are Too Large Add Weight and Cause Trajectory
Dispersal
Canards Require Larger Tails for Stability, Add Weight, and Cause
Trajectory Dispersal
Wings Add Weight, Add Drag, and Cause Trajectory Dispersal
2/24/2008
ELF
364
Engineering Experience Should Guide the DOE
Set of Alternatives and Preferred Design ( cont )
As an Example, Soda Straw Rocket Geometry Should Be Comparable to an Operational
Rocket with Near-Neutral Static Stability ( e.g., Hydra70 )
Concept
Sketch
l / d,
Total Length /
Diameter
b / d,
Total Tail Span /
Diameter
c / d,
Tail Chord /
Diameter
“Big Kahuna”
25
2.79
2
“Shorty”
17.9
2.79
2
“Stiletto”
25
1.89
2
“Petite”
17.9
1.89
2
Hydra 70
15.1
2.66
1
Note: For a subsonic rocket with the center-of-gravity in the center of the rocket, slender body theory and slender
surface theory give total tail span and chord for neutral stability of bNeutralStability ≈ 2 d and cNeutralStability > ≈ d
respectively.
2/24/2008
ELF
365
Optimum Design Should Have Balanced
Engineering Characteristics
As an Example, for the Soda Straw Rocket Design We
Should
Reflect Customer Emphasis of Requirements for
Range
Weight
Provide Balanced Emphasis of Most Important Engineering
Characteristics
Chamber Length
Tail Size / Span
2/24/2008
ELF
366
Summary of Sizing Examples
Rocket Powered Missile ( Sparrow Derived Baseline )
Standoff range requirement
Wing area sizing requirements for maneuverability, turn rate, and
turn radius
Multi-parameter harmonization
Ballistic versus lofted glide flight range
Ramjet Powered Missile ( ASALM Derived Baseline )
Robustness in range uncertainty
Propulsion and fuel alternatives
Surface target impact velocity
Computer Aided Sizing Tools for Conceptual Design
ADAM
Analytical prediction of aerodynamics
Numerical solution of equations of motion
2/24/2008
ELF
367
Summary of Sizing Examples ( cont )
Computer Aided Sizing Tools for Conceptual Design ( cont )
TMD analytical sizing spreadsheet ( based on this text )
Analytical prediction of aero, propulsion, and weight
Closed form analytical solution of simplified equations of motion
Soda Straw Rocket Design, Build, and Fly
Static margin
Drag
Performance
Sensitivity study
House of Quality
Design of Experiment ( DOE )
Discussion / Questions?
Classroom Exercise ( Appendix A )
2/24/2008
ELF
368
Sizing Examples Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
2/24/2008
Required flight range is shorter for a head-on intercept and it is longer
for a t___ c____ intercept.
The rocket baseline center-of-gravity moves f______ with motor burn.
The rocket baseline is an a_______ airframe.
The rocket baseline thrust profile is b____ s______.
The rocket baseline motor case and nozzle are made of s____.
The rocket baseline flight range is driven by ISP, propellant weight
fraction, drag, and s_____ m_____.
Contributors to the maneuverability of the rocket baseline are its body,
tail, and w___.
Although the rocket baseline has sufficient g’s and turn rate to
intercept a maneuvering aircraft, it needs a smaller turn r_____.
Compared to a co-altitude trajectory, the rocket baseline has extended
range with a l_____ glide trajectory.
The ramjet baseline has a c___ inlet.
The Mach 4 ramjet baseline has a t_______ airframe.
ELF
369
Sizing Examples Problems ( cont )
12.
13.
14.
15.
16.
17.
18.
19.
2/24/2008
Although the ramjet baseline combustor is a nickel-based super alloy, it
requires insulation, due high temperature. The super alloy is i______.
The flight range of the ramjet baseline is driven by ISP, weight, thrust,
zero-lift coefficient, and the weight fraction of f___.
Extended range for the ramjet baseline would be provided by more
efficient packaging of subsystems and the use of s_____ fuels.
A conceptual design sizing code should be based on the simplicity,
speed, and robustness of p______ based methods.
The House of Quality room for design characteristics weighted
importance indicates which engineering design characteristics are most
important in meeting the c_______ r___________.
Paredo sensitivity identifies the design parameters that are most
i________.
DOE concepts should emphasize the customer driving requirements and
the driving e__________ characteristics
If the total tail span ( including body diameter ) is twice the body
diameter, the missile is approximately n________ s_____.
ELF
370
Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
2/24/2008
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371
Relationship of Technology Assessment /
Roadmap to the Development Process
Technology Roadmap Establishes Time-phased
Interrelationships for
Technology development and validation tasks
Technology options
Technology goals
Technology transition ( ATD, ACTD, DemVal, PDRR, SDD )
Technology Roadmap Identifies
Key, enabling, high payoff technologies
Technology drivers
Key decision points
Critical paths
Facility requirements
Resource needs
2/24/2008
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372
Relationship of Design Maturity to the US
Research, Technology, and Acquisition Process
Research
Technology
Acquisition
6.1
6.2
6.3
6.4
6.5
Basic
Research
Exploratory
Development
Advanced
Development
Demonstration
& Validation
System
Development
and
Demonstration
Production
System
Upgrades
~ $0.1B
~ $0.3B
~ $0.9B
~ $0.5B
~ $1.0B
~ $6.1B
~ $1.2B
Maturity Level
Conceptual Design
Drawings ( type ) < 10 ( subsystems )
Technology
Development
~ 10 Years
2/24/2008
Preliminary Design
Detail Design
Production Design
< 100 ( components )
> 100 ( parts )
> 1000 ( parts )
Technology
Demonstration
~ 8 Years
Prototype
Demonstration
~ 4 Years
Full Scale
Development
~ 5 Years
First
Limited Block
~ 2 Years ~ 5
Years
1-3 Block
Upgrades
~ 5-15 Years
Production
Note:
Total US DoD Research and Technology for Tactical Missiles ≈ $1.8 Billion per year
Total US DoD Acquisition ( SDD + Production + Upgrades ) for Tactical Missiles ≈ $8.3 Billion per year
Tactical Missiles ≈ 11% of U.S. DoD RT&A budget
US Industry IR&D typically similar to US DoD 6.2 and 6.3A
ELF
373
Technology Readiness Level ( TRL ) Indicates
the Maturity of Technology
TRL 1- 3
TRL 4
TRL 5
TRL 6
TRL 7
Category 6.1
Category 6.2A
Category 6.2B
Category 6.3
Category 6.4
Basic
research
Exploratory
development
of a
component,
conceptual
design
studies, and
prediction
methods
Exploratory
development
of a
subsystem
Advanced tech
demo of a
subsystem
Prototype
demonstration
Initial assessment ⇒ component test ⇒
2/24/2008
subsystem test ⇒ integrated subsystems ⇒ integrated missile
ELF
374
Typical Number of Alternative Concepts
or Number of Design Drawings
Conceptual Design Has Broad Alternatives
While Detail Design Has High Definition
1000
100
Number of Concepts
Number of Drawings
10
1
0
5
10
15
Time ( Years )
2/24/2008
Conceptual
Prelim.
Detail
Production
Design
Design
Design
Design
ELF
375
US Tactical Missile Follow-On Programs Occur
about Every 24 Years
Short Range ATA, AIM-9, 1949 - Raytheon
AIM-9X ( maneuverability ), 1996 - Hughes
Medium Range ATA, AIM-7,1951 - Raytheon
AIM-120 ( autonomous, speed,
range, weight ), 1981 - Hughes
Anti-radar ATS, AGM-45, 1961 - TI
Hypersonic Missile, > 2007
AGM-88 ( speed, range ), 1983 - TI Hypersonic Missile > 2007
PAC-3 (accuracy), 1992 - Lockheed Martin
Long Range STA, MIM-104, 1966 - Raytheon
Man-portable STS, M-47, 1970 - McDonnell Douglas Javelin ( gunner survivability,
lethality, weight ), 1989 - TI
Long Range STS, BGM-109, 1972 - General Dynamics
Long Range ATS, AGM-86, 1973 - Boeing
AGM-129 ( RCS ), 1983 - General Dynamics
Medium Range ATS, AGM-130, 1983 - Rockwell
1950
2/24/2008
1965
1970
1975
1980
1985
Year Entering SDD
ELF
Hypersonic Missile > 2007
1990
JASSM ( cost, range,
observables ), 1999 - LM
1995
> 2000
376
Missile Design Validation / Technology
Development Is an Integrated Process
Propulsion
Propulsion Model
•Rocket Static
•Turbojet Static
•Ramjet Tests
-Direct Connect
-Freejet
Airframe
Aero Model
Guidance
and Control
Wind Tunnel
Tests
Model Digital Simulation
Seeker
Lab Tests
IM Tests
Structure
Test
Hardware
In-Loop
Simulation
Tower
Tests
Flight Test Progression
( Captive Carry,Jettison,
Separation, Unpowered
Guided Flights, Powered
Guided Flights, Live
Warhead Flights )
Actuators / Initiators
Sensors
Lab Tests
Autopilot / Electronics
Power
Supply
Warhead
2/24/2008
Ballistic Tests
Environment
Tests
•Vibration
•Temperature
Witness / Arena Tests
ELF
IM Tests
Sled Tests
377
Examples of Missile Development Tests and
Facilities
Airframe Wind Tunnel Test ………………………………………………………
Propulsion Static Firing with TVC ……..
Propulsion Direct Connect Test …………………………………….
Propulsion Freejet Test …………
2/24/2008
ELF
378
Examples of Missile Development Tests and
Facilities ( cont )
Warhead Arena Test ……………………………………………………….
Warhead Sled Test ………………………
Insensitive Munition Test ……………………………………………..
Structure Test …………………………………………..
2/24/2008
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379
Examples of Missile Development Tests and
Facilities ( cont )
Seeker Test ……………………………………………………….
Hardware-In-Loop ………
Environmental Test ……………………………………………..
Submunition Dispenser Sled Test ……………………
2/24/2008
ELF
380
Examples of Missile Development Tests and
Facilities ( cont )
RCS Test ……………………………………………………………….
Store / Avionics Test
Flight Test ……………………………………………………………………….
Video of Facilities and Tests
2/24/2008
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381
Missile Flight Test Should Cover Extremes of
Flight Envelope
Example: Ramjet Baseline Propulsion Test Validation ( PTV )
High L / D Cruise
Flight 7
Flight 3
Booster
Transition:
Thrust - Drag
w
Lo
m
na
y
D
ic
su
s
e
Pr
re
High Aero Heating
Flight 7
Flight 1
Flight 7
Flight 7
Flight 3
Flight 7
a
yn
D
h
Hig
cP
i
m
re
su
s
re
Flight 3
Note: Seven Flights from Oct 1979 to May 1980.
Flight 1 failure of fuel control. As a result of the high thrust, the flight Mach number exceeded the design Mach number.
2/24/2008
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382
Example of Aero Technology Development
Conceptual Design ( 5 to 50 input parameters ) Prediction
Preliminary Design ( 50 to 200 input parameters ) Prediction
Missile DATCOM. Contact: AFRL. Attributes include: Low cost
MISL3. Contact: NEAR. Attributes include: Modeling vortex shedding
SUPL. Contact: NEAR. Attributes include: Paneling complex geometry
AP02. Contact: NSWC. Attributes include: Periodic updates
CFD. Contact: Georgia Tech. Attributes include: Model runs on Parallel
Processing PCs
Preliminary Design Optimization
Response Surface Model: Contact: Georgia Tech. Attributes include
10x more rapid computation
Probabilistic Analysis: Contact: Georgia Tech. Attributes include an
evaluation of design robustness
2/24/2008
ELF
383
Example of Aero Technology Development
( cont )
Wind Tunnel Test Verification
Body buildup force and moment
Control effectiveness and hinge moment
Store carriage and separation
Flow field ( may be required )
Pressure distribution ( may be required )
Plume, heat transfer, and dynamic stability ( usually not
required )
Inlet ( if applicable )
3 to 6-DOF Digital Simulation
Hardware-in-loop Simulation
Detail Design ( over 200 input parameters )
Flight Test Validation
2/24/2008
ELF
384
Example of Missile Technology State-of-the-Art
Advancement: Air-to-Air Missile Maneuverability
Operational Angle of Attack, Deg
60
50
Controls Augmented
with Propulsion
Devices ( TVC,
Reaction Jet )
40
30
20
10
0
1950
1960
1970
1980
Year IOC
2/24/2008
ELF
1990
2000
2010
AIM-7A
AM-9B
R530
AA-8
AIM-54
R550
Skyflash
Python 3
AA-10
Aspide
Super 530D
AA-11
AIM-120
Python 4
AA-12
MICA
AIM-132
AIM-9X
385
Mcruise, Cruise Mach Number
Example of Missile Technology State-of-the-Art
Advancement: Ramjet Propulsion
7
6
Scramjet
Ramjet
5
4
3
2
1
0
1950
1960
1970
1980
1990
2000
2010
Year Flight Demonstration
Cobra
RARE
D-21
ALVRJ
ANS
HyFly
2/24/2008
X-7
Bloodhound
CROW
3M80
Kh-41
SED
Vandal/Talos
BOMARC
SA-6
ASALM
SLAT
ELF
St-450
Typhon
Sea Dart
AS-17 / Kh-31
BrahMos
SE 4400
STATEX
LASRM
ASMP
Meteor
386
Enabling Technologies for Tactical Missiles
Dome
Faceted / Window
Multi-mode
Multi-spectral
Multi-lens
Electronics
G&C
GPS / INS
In-flight Optimize
α, β Feedback
ATR
Insulation
Hypersonic
High Density
COTS
Central
Power
Data Link
BDI / BDA
In-flight Retarget
Moving Target
Phased Array
Flight Control
EM and
Piezoelectric
TVC / Reaction Jet
Dedicated Roll
MEMS
Seeker
Multi-mode
Multi-spectral
SAR
Strapdown
Uncooled Imaging
High Gimbal
Warhead
High Energy Density
Multi-mode
High Density Penetrator
Boosted Penetrator
Smart Dispenser
Powered Submunition
2/24/2008
Airframe
Lifting Body
Neutral Static Margin
Lattice Fins
Split Canard
Low ΔxAC Wing / Low Hinge Moment Control
Free-to-Roll Tails
Compressed Carriage
Low Drag Inlet
Mixed Compression Inlet
Single Cast Structure
VARTM, Pultrusion, Extrusion, Filament Wind
High Temperature Composites
Titanium Alloy
MEMS Data Collection
Low Observable Shaping and Materials
ELF
Propulsion
Hypersonic Turbine-Based
Liquid / Solid Fuel Ramjet
Variable Flow Ducted Rocket
Scramjet
Combined Cycle Propulsion
High Temperature Turbine
High Temperature Combustor
High Density Fuel / Propellant
High Throttle Fuel Control
Endothermic Fuel
Composite Case
Pintle / Pulsed / Gel Motor
High Burn Rate Exponent Propellant
Low Observable
387
Summary of Development Process
Development Process
Technology roadmap
Development activities
Time frame
Level of Design Maturity Related to Stage of Development
Missile Follow-on Programs
Subsystems Development Activities
Subsystems Integration and Missile System Development
Flight Test Activities
Missile Development Tests and Facilities
State-of-the-Art Advancement in Tactical Missiles
New Technologies for Tactical Missiles
Discussion / Questions?
Classroom Exercise ( Appendix A )
2/24/2008
ELF
388
Development Process Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
2/24/2008
A technology roadmap establishes the high payoff technologies g____.
The levels of design maturity from the most mature to least mature are
production, detail, preliminary, and c_________ design.
Technology transitions occur from basic research to exploratory
development, to advanced development, to d____________ and v_________.
Approximately 11% of the U.S. RT&A budget is allocated to t_______
m_______.
In the U.S., a tactical missile has a follow-on program about every __ years.
Compared to the AIM-9L, the AIM-9X has enhanced m______________.
Compared to the AIM-7, the AIM-120 has autonomous guidance, lighter
weight, higher speed, and longer r____.
Compared to the PAC-2, the PAC-3 has h__ t_ k___ accuracy.
Guidance & control is verified in the h_______ in l___ simulation.
Airbreathing propulsion ground tests include direct connect tests and
f______ tests.
Aerodynamic force and moment data are acquired in w___ t_____ tests.
ELF
389
Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
2/24/2008
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390
Evaluate Alternatives and Iterate the System-ofSystems Design
• Mission / Scenario
Definition
Update
Initial
• Weapon
Requirements,
Trade Studies
and Sensitivity
Analysis
• Launch Platform
Integration
Revised
Trades / Eval
Initial
Reqs
Alt
Concepts
Initial Carriage /
Launch
Effectiveness / Eval
Baseline
Selected
Iteration
Refine
Weapons
Req
• Weapon Concept
Design Synthesis
Alternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine
• Technology
Assessment and
Dev Roadmap
Initial
Tech
Tech
Trades
Initial
Revised
Roadmap Roadmap
Note: Typical design cycle for conceptual design is usually 3 to 9 months
2/24/2008
ELF
391
Exploit Diverse Skills for a Balanced Design
Customer ( requirements pull )
⇒ mission / MIR weighting
Operations analysts
⇒ system-of-systems analysis
System integration engineers
⇒ launch platform integration
Missile design engineers
⇒ missile concept synthesis
Technical specialists ( technology push )
⇒ technology assessment / roadmap
2/24/2008
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392
Utilize Creative Skills
Use Creative Skills to Consider Broad Range of Alternatives
Ask Why? of Requirements / Constraints
Project into Future ( e.g., 5 – 15 years )
State-of-the-art ( SOTA )
Threat
Scenario / Tactics / Doctrine
Concepts
Technology Impact Forecast
Recognize and Distill the Most Important, Key Drivers
Develop Missile Concept that is Synergistic within a
System-of-Systems
Develop Synergistic / Balanced Combination of High
Leverage Subsystems / Technologies
2/24/2008
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393
Identify and Quantify the High Payoff Measures
of Merit
Max / Min
Range
Lethality
Time to
Target
Reliability
Miss Distance
Observables
Survivability
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Robustness
ELF
Weight
394
Start with a Good Baseline
I would have
used the wheel
as a baseline.
2/24/2008
ELF
395
Conduct Balanced, Unbiased Tradeoffs
Propulsion
Aerodynamics
Production
Structures
Seeker
Guidance and
Control
Warhead – Fuze
2/24/2008
ELF
396
Evaluate Many Alternatives
AA- 8 / R-60
Python 4
Magic 550
U-Darter
Python 5
Derby / R-Darter
AIM-9L
Aspide
AA-10 / R-27
Skyflash
AIM-7
R-37
AA-12 / R-77
AIM-9x
Super 530D
AIM-132
AA-11 / R-73
AIM-54
AIM-120
Mica
IRIS-T
Meteor
A-Darter
Taildog
Note: Although all of the above are supersonic air-to-air missiles, they have different configuration geometry
2/24/2008
ELF
397
Search a Broad Design Solution Space ( Global
Optimization vs Local Optimization )
Local Optimum ( e.g., Lowest Cost
Only in Local Solution Space )
Local Optimum ( e.g., Lowest Cost
Only in Local Solution Space )
Global Optimum ( e.g., Lowest Cost in
Global Solution Space ) within Constraints
2/24/2008
ELF
398
Evaluate and Refine as Often as Possible
2/24/2008
ELF
399
Provide Balanced Emphasis of Analytical vs
Experimental
Thomas Edison: "Genius is 1%
inspiration and 99% perspiration."
Albert Einstein: "The only real
valuable thing is intuition."
2/24/2008
ELF
400
Use Design, Build, and Fly Process, for
Feedback That Leads to Broader Knowledge
Prediction Satisfies
Customer
Requirements?
No
Build
Is it Producible?
No
2/24/2008
Wisdom
Where is the wisdom we have lost in
knowledge? Where is the knowledge
we have lost in information?--T. S.
Eliot ( The Rock )
Understanding
Knowledge comes by taking things
apart: analysis. But wisdom comes by
putting things together.--John A.
Morrison
Knowledge
Information
Failure /
Success
Fly ( Test )
Test Results Satisfy
Customer Requirements
and Consistent with
Prediction?
Climb Ladder of Kn
owledge
Design
No
We are drowning in information but
starved for knowledge.--John Naisbitt
( Megatrends: Ten New Directions
Transforming Our Lives )
We learn wisdom from failure much
more than from success. We often
discover what will do, by finding out
what will not do; and probably he who
never made a mistake never made a
discovery.--Samuel Smiles ( Self Help )
Data
Yes
ELF
401
Evaluate Technology Risk
2/24/2008
ELF
402
Keep Track of Assumptions and Develop RealTime Documentation
It’s finally
finished ! . . .
2/24/2008
ELF
403
Develop Good Documentation
Technology
Roadmap
Unit production
cost
and developmen
t cost
Weight and balanc
e
Three-view drawing of
preferred concept( s )
Traceability of
system driving MIRs
Sensitivity of system /
subsystem parameters
Mission flight profiles of
preferred concept( s )
Aero and propulsion
characteristics
Justification of
ept(s)
recommended conc
rnative
Sketches of alte
concepts
eighting
MIRs W
2/24/2008
ELF
404
Utilize Group Skills
Preliminary Design – 8%
Detail /
Production
Design –
30%
Conceptual Design – 2%
Other Than
Design –
60%
(Test, Analysis,
Configuration
Management, Software,
Program Management,
Integration,
Requirements,
etc.)
Source: Nicolai, L.M., “Designing a Better Engineer,” AIAA Aerospace America, April 1992
2/24/2008
ELF
405
Balance the Tradeoff of Importance vs Priority
Production Programs /
Detail Design
SDD Programs /
Preliminary Design
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ELF
Advanced Programs /
Conceptual Design
406
Evaluate Alternatives and Iterate the
Configuration Design
Define Mission Requirements
Alt Mission
Establish Baseline
Alt Baseline
Aerodynamics
Propulsion
Weight
Resize / Alt Config / Subsystems / Tech
Trajectory
Meet
Performance?
No
Yes
Measures of Merit and Constraints
No
Yes
2/24/2008
ELF
407
Configuration Sizing Conceptual Design
Guidelines: Aeromechanics
Configuration Sizing Parameter
Aeromechanics Design Guideline
Body fineness ratio
Nose fineness ratio
Boattail or flare angle
Efficient cruise dynamic pressure
Missile homing velocity
Ramjet combustion temperature
Oblique shocks prior to inlet normal
shock to satisfy MIL-E-5008B
Inlet flow capture
Ramjet Minimum cruise Mach number
Subsystems packaging
2/24/2008
ELF
5 < l / d < 25
lN / d ≈ 2 if M > 1
< 10 deg
q < 1,000 psf
VM / VT > 1.5
> 4,000° F
> 2 oblique shocks / compressions if M >
3.0, > 3 shocks / compressions if M > 3.5
Shock on cowl lip at Mmax cruise
M > 1.2 x MInletStart , M > 1.2 MMaxThrust = Drag
Maximize available volume for fuel /
propellant
408
Configuration Sizing Conceptual Design
Guidelines: Guidance & Control
Configuration Sizing Parameter
G&C Design Guideline
ωBB > 2 ωACT
α/δ>1
If low aspect ratio, b / d ≈ 2, c / d > ≈ 1
< 30%
τ < 0.2 s
n M / nT > 3
3 < N’ < 5
< btarget
.
.
γM> γT
RTM < RTT
Body bending frequency
Trim control power
Neutral stability tail-body
Stability & control cross coupling
Airframe time constant
Missile maneuverability
Proportional guidance ratio
Target span resolution by seeker
Missile heading rate
Missile turn radius
2/24/2008
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409
Wrap Up ( Part 1 of 2 )
Missile design is a creative and iterative process that includes
System considerations
Missile concepts and sizing
Flight trajectory evaluation
Cost / performance drivers may be “locked in” during
conceptual design
Missile design is an opportunity for a diverse group to work
together for a better product
Military customer ⇒ mission / scenario definition
Operations analysts ⇒ system-of-systems modeling
System integration engineers ⇒ launch platform integration
Missile design engineers ⇒ missile concept synthesis
Technical specialists ⇒ technology assessment / technology roadmap
2/24/2008
ELF
410
Wrap Up ( Part 2 )
The missile conceptual design philosophy requires
Iteration, iteration, iteration
Evaluation of a broad range of alternatives
Traceable flow-down allocation of requirements
Starting with a good baseline
Paredo sensitivity analysis to determine the most important, driving
parameters
Synergistic compromise / balanced subsystems and technologies
that are high leverage
Awareness of technology SOTA / technology assessment
Technology impact forecast
Robust design
Creative design decisions made by the designer ( not the computer )
Fast, simple, robust, physics-based prediction methods
2/24/2008
ELF
411
Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
2/24/2008
ELF
412
References
1. “Missile.index,” http://missile.index.ne.jp/en/
2. AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993
3. Bonney, E.A., et al, Aerodynamics, Propulsion, Structures, and Design Practice, “Principles of Guided Missile Design”,
D. Van Nostrand Company, Inc., 1956
4. Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, “Principles of Guided Missile Design”, D.
Van Nostrand Company, Inc., 1960
5. Chin, S.S., Missile Configuration Design, McGraw-Hill Book Company, 1961
6. Mason, L.A., Devan, L., and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWCTR 81-156, 1981
7. Pitts, W.C., Nielsen, J.N., and Kaattari, G.E., “Lift and Center of Pressure of Wing-Body-Tail Combinations at Subsonic,
Transonic, and Supersonic Speeds,” NACA Report 1307, 1957
8. Jorgensen, L.H., “Prediction of Static Aerodynamic Characteristics for Space-Shuttle-Like, and Other Bodies at Angles
of Attack From 0° to 180°,” NASA TND 6996, January 1973
9. Hoak, D.E., et al., “USAF Stability and Control DATCOM,” AFWAL TR-83-3048, Global Engineering, 1978
10. “Nielsen Engineering & Research (NEAR) Aerodynamic Software Products,” http://www.nearinc.com/near/software.htm
11. Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., 1974
12. Anderson, John D. Jr., “Modern Compressible Flow,” Second Edition, McGraw Hill, 1990
13. Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319 and AFWAL TR 80-2003, June 1980
14. “Technical Aerodynamics Manual,” North American Rockwell Corporation, DTIC AD 723823, June 1970
15. Oswatitsch, K.L., “Pressure Recovery for Missiles with Reaction Propulsion at High Supersonic Speeds”, NACA TM 1140, 1947
16. Carslaw, H.S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, 1988
2/24/2008
ELF
413
References ( cont )
17. Allen, J. and Eggers, A.J., “A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth’s
Atmosphere at High Supersonic Speeds”, NACA Report 1381, April 1953.
18. Schneider, S.H., Encyclopedia of Climate and Weather, Oxford University Press, 1996
19. Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997
20. US Army Ordnance Pamphlet ORDP-20-290-Warheads, 1980
21. Carleone, J. (Editor), Tactical Missile Warheads, “AIAA Vol. 155 Progress in Astronautics and Aeronautics,” American
Institute of Aeronautics and Astronautics, 1993
22. Christman, D.R. and Gehring, J.W., “Analysis of High-Velocity Projectile Penetration Mechanics,” Journal of Applied
Physics, Vol. 37, 1966
23. Heaston, R.J. and Smoots, C.W., “Precision Guided Munitions,” GACIAC Report HB-83-01, May 1983
24. Donatelli, G.A. and Fleeman, E.L., “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-820364, January 1982
25. Bennett, R.R. and Mathews, W.E., “Analytical Determination of Miss Distances for Linear Homing Navigation
Systems,” Hughes Tech Memo 260, 31 March 1952
26. Nicholas, T. and Rossi, R., “US Missile Data Book, 1996,” Data Search Associates, 1996
27. Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis,” AFWAL TR 81-3022, March 1982
28. Fleeman, E.L. and Donatelli, G.A., “Conceptual Design Procedure Applied to a Typical Air-Launched Missile,” AIAA 811688, August 1981
29. Hindes, J.W., “Advanced Design of Aerodynamic Missiles ( ADAM ),” October 1993
30. Frits, A.P., et al, “A Conceptual Sizing Tool for Tactical Missiles, “ AIAA Missile Sciences Conference, November 2002
31. Bruns, K.D., Moore, M.E., Stoy, S.L., Vukelich, S.R., and Blake, W.B., “Missile DATCOM,” AFWAL-TR-91-3039, April
1991
2/24/2008
ELF
414
References ( cont )
32. Moore, F.G., et al, “The 2002 Version of the Aeroprediction Code”, Naval Surface Warfare Warfare Center, March 2002
33. Nicolai, L.M., “Designing a Better Engineer,” AIAA Aerospace America, April 1992
2/24/2008
ELF
415
Bibliography of Other Reports and Web Sites
System Design
Fleeman, E.L., “Tactical Missile Design,” American Institute of Aeronautics and Astronautics, 2006
“DoD Index of Specifications and Standards,” http://stinet.dtic.mil/str/dodiss.html
“Periscope,” http://www.periscope1.com/
Defense Technical Information Center, http://www.dtic.mil/
NATO Research & Technology Organisation, http://www.rta.nato.int/
“Missile System Flight Mechanics,” AGARD CP270, May 1979
Hogan, J.C., et al., “Missile Automated Design ( MAD ) Computer Program,” AFRPL TR 80-21, March 1980
Rapp, G.H., “Performance Improvements With Sidewinder Missile Airframe,” AIAA Paper 79-0091, January 1979
Nicolai, L.M., Fundamentals of Aircraft Design, METS, Inc., 1984
Lindsey, G.H. and Redman, D.R., “Tactical Missile Design,” Naval Postgraduate School, 1986
Lee, R.G., et al, Guided Weapons, Third Edition, Brassey’s, 1998
Giragosian, P.A., “Rapid Synthesis for Evaluating Missile Maneuverability Parameters,” 10th AIAA Applied
Aerodynamics Conference, June 1992
Fleeman, E.L. “Aeromechanics Technologies for Tactical and Strategic Guided Missiles,” AGARD Paper
presented at FMP Meeting in London, England, May 1979
Raymer, D.P., Aircraft Design, A Conceptual Approach, American Institute of Aeronautics and Astronautics, 1989
Ball, R.E., The Fundamentals of Aircraft Combat Survivability Analysis and Design, American Institute of
Aeronautics and Astronautics, 1985
“National Defense Preparedness Association Conference Presentations,” http://www.dtic.mil/ndia
2/24/2008
ELF
416
Bibliography of Other Reports and Web Sites ( cont )
System Design ( continued )
Eichblatt, E.J., Test and Evaluation of the Tactical Missile, American Institute of Aeronautics and Astronautics,
1989
“Aircraft Stores Interface Manual (ASIM),” http://akss.dau.mil/software/1.jsp
“Advanced Sidewinder Missile AIM-9X Cost Analysis Requirements Description (CARD),”
http://deskbook.dau.mil/jsp/default.jsp
Wertz, J.R and Larson W.J., Space Mission Analysis and Design, Microprism Press and Kluwer Academic
Publishers, 1999
“Directory of U.S. Military Rockets and Missiles”, http://www.designation-systems.net/
Fleeman, E.L., et al, “Technologies for Future Precision Strike Missile Systems,” NATO RTO EN-018, July 2001
“The Ordnance Shop”, http://www.ordnance.org/portal/
“Conversion Factors by Sandelius Instruments”, http://www.sandelius.com/reference/conversions.htm
“Defense Acquisition Guidebook”, http://akss.dau.mil/dag/
Aerodynamics
“A Digital Library for NACA,” http://naca.larc.nasa.gov/
Briggs, M.M., Systematic Tactical Missile Design, Tactical Missile Aerodynamics: General Topics, “AIAA Vol.
141 Progress in Astronautics and Aeronautics,” American Institute of Aeronautics, 1992
Briggs, M.M., et al., “Aeromechanics Survey and Evaluation, Vol. 1-3,” NSWC/DL TR-3772, October 1977
“Missile Aerodynamics,” NATO AGARD LS-98, February 1979
“Missile Aerodynamics,” NATO AGARD CP-336, February 1983
“Missile Aerodynamics,” NATO AGARD CP-493, April 1990
“Missile Aerodynamics,” NATO RTO-MP-5, November 1998
Nielsen, J.N., Missile Aerodynamics, McGraw-Hill Book Company, 1960
2/24/2008
ELF
417
Bibliography of Other Reports and Web Sites ( cont )
Aerodynamics ( continued )
Mendenhall, M.R. et al, “Proceedings of NEAR Conference on Missile Aerodynamics,” NEAR, 1989
Nielsen, J.N., “Missile Aerodynamics – Past, Present, Future,” AIAA Paper 79-1818, 1979
Dillenius, M.F.E., et al, “Engineering-, Intermediate-, and High-Level Aerodynamic Prediction Methods and
Applications,” Journal of Spacecraft and Rockets, Vol. 36, No. 5, September-October, 1999
Nielsen, J.N., and Pitts, W.C., “Wing-Body Interference at Supersonic Speeds with an Application to
Combinations with Rectangular Wings,” NACA Tech. Note 2677, 1952
Spreiter, J.R., “The Aerodynamic Forces on Slender Plane-and Cruciform-Wing and Body Combinations”, NACA
Report 962, 1950
Simon, J.M., et al, “Missile DATCOM: High Angle of Attack Capabilities, AIAA-99-4258
Burns, K.A., et al, “Viscous Effects on Complex Configurations,” WL-TR-95-3060, 1995
Lesieutre, D., et al, “Recent Applications and Improvements to the Engineering-Level Aerodynamic Prediction
Software MISL3,’’ AIAA-2002-0274
Moore, F.G., Approximate Methods for Weapon Aerodynamics, American Institute of Aeronautics and
Astronautics, 2000
“1976 Standard Atmosphere Calculator”, http://www.digitaldutch.com/atmoscalc/
“Compressible Aerodynamics Calculator”, http://www.aoe.vt.edu/~devenpor/aoe3114/calc.html
Ashley, H. and Landahl, M., Aerodynamics of Wings and Bodies, Dover Publications, 1965
John, James E.A., Gas Dynamics, Second Edition, Prentice Hall, 1984
Zucker, Robert D., Fundamentals of Gas Dynamics, Matrix Publishers, 1977
Propulsion
Chemical Information Propulsion Agency, http://www.cpia.jhu.edu/
St. Peter, J., The History of Aircraft Gas Turbine Engine Development in the United States: A Tradition of
Excellence, ASME International Gas Turbine Institute, 1999
2/24/2008
ELF
418
Bibliography of Other Reports and Web Sites ( cont )
Propulsion ( continued )
Mahoney, J.J., Inlets for Supersonic Missiles, American Institute of Aeronautics and Astronautics, 1990
Sutton, G.P., Rocket Propulsion Elements, John Wiley & Sons, 1986
“Tri-Service Rocket Motor Trade-off Study, Missile Designer’s Rocket Motor handbook,” CPIA 322, May 1980
Humble, R.W., Henry, G.N., and Larson, W.J., Space Propulsion Analysis and Design, McGraw-Hill, 1995
Jenson, G.E. and Netzer, D.W., Tactical Missile Propulsion, American Institute of Aeronautics and Astronautics,
1996
Durham, F.P., Aircraft Jet Powerplants, Prentice-Hall, 1961
Bathie, W.W., Fundamentals of Gas Turbines, John Wiley and Sons, 1996
Hill, P.G. and Peterson, C.R., Mechanics and Thermodynamics of Propulsion, Addison-Weshley Publishing
Company, 1970
Mattingly, J.D., et al, Aircraft Engine Design, American Institute of Aeronautics and Astronautics, 1987
Materials and Heat Transfer
Budinski, K.G. and Budinski, M.K., Engineering Materials Properties and Selection, Prentice Hall, 1999
“Matweb’s Material Properties Index Page,” http://www.matweb.com
“NASA Ames Research Center Thermal Protection Systems Expert (TPSX) and Material Properties Database”,
http://tpsx.arc.nasa.gov/tpsxhome.shtml
Harris, D.C., Materials for Infrared Windows and Domes, SPIE Optical Engineering Press, 1999
Kalpakjian, S., Manufacturing Processes for Engineering Materials, Addison Wesley, 1997
MIL-HDBK-5J, “Metallic Materials and Elements for Aerospace Vehicle Structures”, Jan 2003
“Metallic Material Properties Development and Standardization ( MMPDS )”, http://www.mmpds.org
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Bibliography of Other Reports and Web Sites ( cont )
Materials and Heat Transfer ( continued )
Mallick, P.K., Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Second Edition, Maecel
Dekker, 1993
Chapman, A.J., Heat Transfer, Third Edition, Macmillan Publishing Company, 1974
Incropera, F.P. and DeWitt, D.P., Fundamentals of Heat and Mass Transfer, Fourth Edition, John Wiley and
Sons, 1996
Guidance, Navigation, Control, and Sensors
Zarchan, P., Tactical and Strategic Missile Guidance, “AIAA Vol. 124 Progress in Astronautics and
Aeronautics,” American Institute of Aeronautics and Astronautics, 1990
“Proceedings of AGARD G&C Conference on Guidance & Control of Tactical Missiles,” AGARD LS-52, May 1972
Garnell, P., Guided Weapon Control Systems, Pergamon Press, 1980
Locke, A. S., Guidance, “Principles of Guided Missile Design”, D. Van Nostrand, 1955
Blakelock, J. H., Automatic Control of Aircraft and Missiles, John Wiley & Sons, 1965
Lawrence, A.L., Modern Inertial Technology, Springer, 1998
Siouris, G.M., Aerospace Avionics Systems, Academic Press, 1993
Stimson, G.W., Introduction to Airborne Radar, SciTech Publishing, 1998
Lecomme, P., Hardange, J.P., Marchais, J.C., and Normant, E., Air and Spaceborne Radar Systems, SciTech
Publishing and William Andrew Publishing, 2001
Wehner, D.R., High-Resolution Radar, Artech House, Norwood, MA, 1995
Donati, S., Photodetectors, Prentice-Hall, 2000
Jha, A.R., Infrared Technology, John Wiley and Sons, 2000
Schlessinger, M., Infrared Technology Fundamentals, Marcel Decker, 1995
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Follow-up Communication
I would appreciate receiving your comments and
corrections on this text, as well as any data,
examples, or references that you may offer.
Thank you,
Gene Fleeman
Tactical Missile Design
E-mail: GeneFleeman@msn.com
Web Site: http://genefleeman.home.mindspring.com
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Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
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