Design of UAV Systems
Lesson objective - to discuss
Propulsion and propulsion
parametrics
including …
• Rationale
• Applications
• Models
Expectations - You will understand when and how
to use parametric propulsion relationships
c 2002 LM Corporation
Propulsion
18-1
Design of UAV Systems
Definitions
From Webster’s New Collegiate Dictionary
• Parameter – any set of physical properties whose
value determine the characteristics or behavior of a
set of equations
Our definition
• Propulsion parametric – fundamental design
parameter whose value determines the design or
performance characteristics of an engine
• Usually (but not always) a multi-variable relationship
- e.g., SFC (WdotF/Bhp), Bypass ratio (BPR), etc.
• Parametric model – Parametric based design
approach to define, size, estimate performance and
do trade offs on propulsion systems
- Different from the traditional approach
c 2002 LM Corporation
Lesson 5a - Air vehicle parametrics
18-2
Design of UAV Systems
Parametrics models
• Simple models that correlate thrust or power, weight,
fuel flow, speed and altitude
- Most based on historical and technology trend data
- Others based on simple definitions
- Some based on non-dimensional analysis (See
RosAP6.2.5)
• Internal combustion (IC) engines are easiest to model
- Simple (and generally independent) variables
- One complexity is fixed pitch propeller performance
• Jet engines are more difficult to model parametrically
- Many interrelated design and operating variables
• Turboprop (TBProp) parametric models are in between
Propulsion parametrics can be used for pre-concept design but engine
company models should be used as soon as they are available
c 2002 LM Corporation
Lesson 5a - Air vehicle parametrics
18-2a
Design of UAV Systems
Key parametrics
• Engine Power-to-weight ratio (HP0/Weng)
- HP0 = Maximum power (hp, uninstalled, sea level static)
or - Weng = Engine weight (lbm, uninstalled)
• Engine thrust-to-weight ratio (T0/Weng)
- T0 = Maximum thrust (lbf, uninstalled, sea level static)
- Weng = Engine weight (lbm, uninstalled)
• Specific Fuel Consumption (SFC)
SFC = Fuel flow/Power (WdotF/HP)
or SFC0 = WdotF0/ HP0 (lbm/hp-hr)
• Thrust Specific Fuel Consumption (TSFC)
TSFC = Fuel flow/Thrust available(WdotF/Ta)
TSFC0 = WdotF0/T0 (lbm/hp-hr)
Note - “0” postscript indicates
• Specific Thrust (Fsp)
sea level static (V=0)
- Fsp = Thrust/Airflow (T/WdotA)
conditions
- Fsp0 =T0/WdotA0 (lbf-sec/lbm)
c 2002 LM Corporation
Propulsion
18-3
Design of UAV Systems
Engine size
• Any number of performance requirements can
drive engine size (See RayAD 5.2)
- Takeoff
- Ground roll and distance over an obstacle
- And/or balanced field length (BFL)
- Time and/or distance to climb
- Cruise altitude and/or speed
- Acceleration and/or turn performance
- Engine out performance (for multi-engine aircraft)
• Historical thrust-to-weight or power-to-weight data
can be used for first pass sizing
- See RayAD Tables 5.1 and 5.2
• UAV historical data is limited and we will use
takeoff requirements for initial sizing
- See RayAD Figure 5.4
c 2002 LM Corporation
Lesson 5a - Air vehicle parametrics
18-4
Design of UAV Systems
Raymer (power-to-weight)
GA Single
GA Twin
Twin turboprop
Raymer (thrust-to-weight)
Trainer
Bomber
Transport
Sizing - manned vs. unmanned
0.07
0.17
0.20
0.4
0.25
0.25
UAV data from various sources including
Janes, Unmanned Air Vehicles
c 2002 LM Corporation
Propulsion
18-5
Design of UAV Systems
IC engines
• Engine power available (BHP)
• Output per unit size varies by type
- Small piston engines run at high RPM, have higher
output per unit size. Same for rotary engines
• For given engine at given altitude and RPM
- Almost no variation with speed
• At given RPM, manifold pressure varies with altitude
• Max power varies with air density ratio (see RayAD
Eqn13.10)
- Bhp = Bhp0*(8.55*-1)/7.55
(18.1)
• Engine SFC
• Runs high for small and rotary engines
• For given engine varies slightly with power available
- Typically 5-10% lower at cruise condition
• Engine power-to-weight varies with engine type
c 2002 LM Corporation
Lesson 5a - Air vehicle parametrics
18-6
Design of UAV Systems
IC engine parametrics
Compilation of data from various sources including: Roskam, Aerodynamics & Performance (RosAP); Janes, Aero Engines;
Janes, Unmanned Air Vehicles; www.tcmlink.com/producthighlights/www.lycoming.textron.com/main
c 2002 LM Corporation
Propulsion
18-7
IC engine size
Design of UAV Systems
Vol vs. Weight
Recip-air cooled
Recip-liquid cooled
Rotary-air cooled
Rotary-liquid cooled
all
20.00
= 30
= 40
10.00
0.00
0
100
(a)
200
50
= 20 pcf
300
400
500
Weight (lb)
Length (in)
30.00
Volume (cuft)
Length-to-Dequiv
40
Avg=1.3
L/De=2
L/De=1
30
Recip-air cooled
Recip-liquid cooled
Rotary-air cooled
Rotary-liquid cooled
all
20
10
10.00
(b)
20.00
30.00
40.00
Dequiv = sqrt[wh] (in)
Charts 18-7/8 show only
contemporary IC engines
• Earlier engines were
much larger
Compilation of data from various sources including:
- Roskam, Aerodynamics & Performance (RosAP)
- Janes, Aero Engines
- Janes, Unmanned Air Vehicles
-www.tcmlink.com/producthighlights/
(c)
c 2002 LM Corporation
-www.lycoming.textron.com/main
Propulsion
18-8
Design of UAV Systems
Propellers
• Two basic types of propellers (See RayAD10.4 & 13.6)
- Fixed pitch and Variable pitch
• Efficiency (p) varies with design and installation
- Blockage and flow “scrubbing” generate losses
• Fixed pitch efficiency varies with advance ratio (J)
- See RayADFig13.13
- Props generally designed for climb or cruise
• Variable pitch efficiency typically constant over
range of design speeds
- Use a nominal p = 0.8 for an initial guess
• Thrust horsepower (THP) defined by
- Thp = Bhp*p =Ta*V(fps)/550=Ta*V(KTAS)/325.6
Where ……….Ta = Thrust available
• Therefore……..
- Thrust available decreases with speed
Ta = 325.6*BHP*p /KTAS
(18.2)
c 2002 LM Corporation
Lesson 5a - Air vehicle parametrics
18-9
Design of UAV Systems
Propeller size
• Key sizing constraint is tip speed (Mach number)
- Linear function of engine RPM (V=R*)
• Lightest-most reliable design is direct drive
- No gear reduction
• Some UAVs use high RPM engines with belt
systems for speed reduction
- Manned aircraft prop
sizing can be used for
UAVs
- There will always be
exceptions for special
application aircraft
(e.g.Altus)
Compilation of data from unpublished
sources plus:
- Janes, Unmanned Air Vehicles
c 2002 LM Corporation
Lesson 5a - Air vehicle parametrics
18-10
Design of UAV Systems
Propeller parametrics
Nb = Number of blades
Rp = Prop radius (in)
Weight/Total blade length(in) ≈ 0.8 lb/in
Raw data from Janes All the Worlds
Aircraft
c 2002 LM Corporation
Propulsion
18-11
Design of UAV Systems
Turboprop engines
• Have typical prop characteristics (and constraints)
plus jet exhaust for thrust augmentation
• Thrust component is added for equivalent shaft HP, the
difference between Shp and EShp (see RayAD 13.7)
• Power available decreases with altitude
• Decreases with pressure  (see RayAD Table E.3)
• SFC variation with altitude less severe than jet
• Typical Lth/Dia = 2 - 3
• Typical density = 22 pcf
• Typical diameter = [4*Vol/(*L/D)]^1/3
- From Vol(cyl) = [/4][D^2]L[D/D]
c 2002 LM Corporation
Lesson 5a - Air vehicle parametrics
18-12
Design of UAV Systems
Typical TBProp
parametrics
Turboprop
engines
Data compiled from RosAP and Janes Aero Engines
c 2002 LM Corporation
Propulsion
18-13
Design of UAV Systems
Jet engines
• Includes turbojet (TBJet) and turbofan (TBFan) engines
• Thrust, weight, airflow and TSFC depend on design and
technology content and operating conditions
• Difficult to capture in general purpose parametrics
• Thrust available decreases with altitude - all engines
• TSFC decreases with altitude - all engines
• Effect of speed on thrust varies with bypass ratio (BPR)
• Low BPR - thrust generally increases with speed
• High BPR - thrust decreases with speed
• See RayAD Appendix E for specific examples
• Thrust-to-weight varies with engine size, BPR and
advanced technology content
• Physical geometry primarily a function of design BPR
• Physical installation reduces thrust by 5-20%
c 2002 LM Corporation
Propulsion
18-14
Generic jet engine
Design of UAV Systems
V
GG
Airflow
Gas Generator (GG)
Fan
GG thrust
Fan
Airflow
Fan thrust
Bypass ratio (BPR) = Fan airflow/total airflow
WdotAgg  WdotA*1/(BPR+1)
WdotAfn  WdotA*BPR/(BPR+1)
Turbojet (TBJ) BPR = 0, Turbofan (TBFan) BPR < 10; TBProp BPR >> 10
c 2002 LM Corporation
Propulsion
18-15
Design of UAV Systems
Typical TBJet parametrics
Data from Roskam, Aerodynamics & Performance (RosA)P and Janes, Aero Engines
SFC0 - Small turbojets
1.5
All engines (more later)
1
0.5
0
1000
2000
3000
T0 (lbf)
c 2002 LM Corporation
Propulsion
18-16
Typical TBFan parametrics
Design of UAV Systems
TSFC
1
(lbm/hr-lbf)
0.75
0.5
0.25
0
0
2
4
6
8
10
BPR
Data from Roskam, Aerodynamics & Performance (RosA)P and Janes, Aero Engines
c 2002 LM Corporation
Propulsion
18-17
TBJet and TBFan size
Design of UAV Systems
Database D (in)
• Despite its apparent simplicity, Raymer’s engine size
parametric correlates well with our database
- One difference is that Raymer bases his correlation on
engine inlet diameter
- Our data shows that it correlates with overall engine
diameter
Engine diameter
• Parametrics are for
uninstalled engine
150
weight
120
- Nominal TBFan
90
60
T0/Weng = 5.5
D^2 (ft) = WdotA/26
30
- An installation factor
0
of 1.3 is applied to
0
30
60
90
120
150
estimate installed
Raymer parametric (in)
engine weight
c 2002 LM Corporation
Propulsion
18-18
Design of UAV Systems
TBFan parametrics – cont’d
Data from Roskam, Aerodynamics & Performance (RosA)P and Janes, Aero Engines
c 2002 LM Corporation
Propulsion
18-19
Design of UAV Systems
Afterburning
• Way to augment jet engine performance to meet peak
thrust requirements such as…..
Takeoff….combat maneuvers….supersonic flight
• Works by injecting fuel into engine exhaust to react
residual oxygen and increase temperature/jet velocity
• Inefficient turbojet engines and turbofans can achieve
high augmentation ratios - lots of air to “burn”
• Efficient turbojets achieve low augmentation ratios
- Most of the air already “burned”
• Essentially a ramjet on the rear of the engine
• Only works for low-to-moderate BPR turbofans
- High BPR fans have insufficient overall pressure ratio
• Relatively light weight but very fuel inefficient
• High noise levels limit civil applications
c 2002 LM Corporation
Propulsion
18-20
Design of UAV Systems
A/B parametric data
Data from Roskam, Aerodynamics & Performance (RosAP) and Janes, Aero Engines
c 2002 LM Corporation
Propulsion
18-21
Design of UAV Systems
TBProp baseline
HP/W0 or T0/W0 (SLS)
• We will use parametric data to make a first pass engine
size estimate for our example UAV (see chart 15-40)
• We assume a nominal TBProp UAV wing loading
(W0/Sref) = 30 psf, a typical plan flap Clmax =1.8 (See
RayAD Fig 5.3) and a standard Vto/Vs = 1.1
• From RayAD Figure 5.4, required takeoff parameter
(TOP) for a 1500 ft takeoff
UAV sizing parametric
ground roll = 220 or:
0.5
220 =
Piston
Turboprop
0.4
Jet
[W0/Sref]/[Clto*T0/W0]
0.3
• For Clto = Clmax/(Vto/Vs^2)
0.2
= 1.49 and W0 = 1918 lbm
0.1
BHp0/W0 = 0.092
0
BHp0 = 176.5 BHp
60.00
40.00
20.00
0.00
• BHp0/W0 correlates well
Wing loading (psf)
with our parametric data
c 2002 LM Corporation
Propulsion
18-22
Design of UAV Systems
Application – TBProp
Chart 18-13 shows turboprops of this small size class
should be available at 2.25 Shp/lb
- Nominal weight would be 78.4 lbm
- At a density of 22 lb/cuft, volume would be 3.6 cuft
- At nominal Lth/Diam = 2.5, engine diameter (Deng) =
[4*Vol/(*Lth/Deng)]^1/3 ≈ 1.22ft and length (Leng) = 3ft
- SFC0 would about 0.65 lbm/hr-Bhp
In reality, however, there are no TBProps this small
c 2002 LM Corporation
Propulsion
18-23
TBFan alternative
Design of UAV Systems
HP/W0 or T0/W0 (SLS)
• We will also use parametric data to make a first pass
engine sizing for the TBFan alternative
• We assume a nominal TBFan UAV wing loading (W0/Sref)
= 40 psf, a typical plan flap Clmax =1.8 (See Raymer AD
Fig 5.3) and a standard Vto/Vs = 1.1
• From RayAD Figure 5.4, required takeoff parameter
(TOP) for a 1500 ft takeoff
UAV sizing parametric
ground roll = 100 or:
0.5
100 =
Piston
Turboprop
0.4
Jet
[W0/Sref]/[Clto*T0/W0]
0.3
• For Clto = Clmax/(Vto/Vs^2)
0.2
= 1.49 and W0 = 2939 lbm
0.1
T0/W0 = 0.269
0
T0 = 790 Lbf
60.00
40.00
20.00
0.00
• T0/W0 correlates well with
Wing loading (psf)
our parametric data
c 2002 LM Corporation
Propulsion
18-24
Design of UAV Systems
TBFan
From charts 18-16/17 we estimate T0/Weng ≈ 5.5
- Our TBFan would weigh 144 lbm
- At BPR = 5, WdotAmax = 790/30 = 26.3 pps
- From charts 18-16/17 Deng ≈ 12 in, Leng ≈ 24 in
From charts 18-17/19 TSFC0 ≈ 0.4 and TSFCcr ≈ 0.65
- But unfortunately, there are no BPR = 5 turbofans of
size class (see ASE261.Engine database.xls)
- However, there might be some under development
c 2002 LM Corporation
Propulsion
18-25
Design of UAV Systems
Overall results
The TBProp parametrics show the SFC0 value
assumed in the Lesson 15 example is low (0.4 vs 0.65)
- Small engines are less efficient than larger ones
- The performance impact will significant but it will make
make the results fit better with our sizing parametrics
- And there are no engines available at the size required
The TBFan parametrics show that Raymer’s values of
cruise TSFC are optimistic (which we already knew) and
that there are also no small BPR = 5 TBFan engines
- Size effects are likely to reduce TSFC also
However, we will continue our study as if engines were
available since we really don’t know yet what size air
vehicle we will end up with
- We will, however, note these issues as development risk
items and consider the implications when we select our
final configurations
c 2002 LM Corporation
Propulsion
18-26
Design of UAV Systems
Next subject
From Webster’s New Collegiate Dictionary
• Parameter – any set of physical properties whose
value determine the characteristics or behavior of
a set of equations
Our definition
• Propulsion parametric – fundamental design
parameter whose value determines the design or
performance characteristics of an engine
• Usually (but not always) a multi-variable relationship
- e.g., wing loading (W0/Sref), Swet/Sref, etc.
• Parametric model – Parametric based design
approach to define, size, estimate performance
and do trade offs on propulsion systems
- Different from the traditional approach
c 2002 LM Corporation
Propulsion
18-27
Design of UAV Systems
Parametric models
In the absence of real data, engine parametric models
can be used to provide reasonable trends for use in
pre-concept and conceptual design
- For example, Equation 5.4 (RayAD Eq. 13.10) captures
IC engine altitude effects and is useful for initial design
- No similar effects are captured in traditional jet engine
parametric models such as RayAD Eq. 10.5-10.15
- Mach and altitude effects are absent
- More general purpose thrust and fuel flow models are
needed and none exist
Therefore, we will have to develop our own jet engine
models (both TBJet and TBFan)
- We will use the engine performance charts in RayAD,
Appendix E as the basis for these models
c 2002 LM Corporation
Propulsion
18-28
Design of UAV Systems
IC parametric model
• Use Equation 18.1 (RayAD Eq. 13.10) to calculate
maximum power as a function of altitude
• BHP = BHP0*(8.55* -1)/7.55
(18.1)
where
• BHP0 = maximum power, SLS (sea level static)
•  = air density ratio
• Calculate cruise performance at 75% takeoff power
• Assume nominal 80% propulsion efficiency (p)
• Estimate thrust available from
• Ta = 325.6*BHP*p/KTAS
(18.2)
• Estimate fuel flow from
• WdotF = SFC*BHP
where
• SFC assumed constant (use SFC0 from chart 18-7)
• Estimate engine weight from chart 18-7
• For supercharged engine, assume pressure ratio/stage = 2
• See Raymer Figure 13.10 (page 394)
• Adjust engine weight as appropriate
c 2002 LM Corporation
Propulsion
18-29
Jet parametric model
Design of UAV Systems
V
GG
Airflow
Gas Generator (GG)
Fan
GG thrust
Fan
Airflow
Fan thrust
Assumptions
Bypass ratio (BPR)
WdotAgg  WdotA*1/(BPR+1)
WdotAfn  WdotA*BPR/(BPR+1)
GG Fsp = constant = Fsp-gg
Fan Fsp = (V0/V)*Fsp-fn(SLS)
BPR = Constant
Turbojet BPR = 0, Turbofan BPR < 10; Propfan BPR >> 10
c 2002 LM Corporation
Propulsion
18-30
Design of UAV Systems
Jet parametric model
• Assume jet engine thrust (subsonic) can be modeled as the
sum two (2) simplified components
- “Gas generator”(gg) - the core engine of a turbofan or
turboprop
- “Fan” (fn) - the fan or propeller
• Assume core engine thrust varies with core airflow
(constant core engine Fsp - a very simple approximation)
• Assume fan Fsp varies inversely with speed ratio (V0/V)
- Like a propeller
- Select non-zero V0 to fit data as appropriate
• Assume fan bypass ratio remains constant
• Assume all other engine parameters follow “corrected”
performance relationships (See P&W handbook, page 129)
- Ta = Ta0*
(18.3)
- WdotF = WdotF0**sqrt(^k)
(18.4)
- SFC = SFC0*sqrt( ^k)
(18.5)
k = f(cycle) but ≈ 0.5
- WdotA = WdotA0* /sqrt()
(18.6)
- f/a = (f/a0)*sqrt()*sqrt( ^k) ≈ (f/a0)* ^.75
(18.7)
c 2002 LM Corporation
Propulsion
18-31
Design of UAV Systems
Jet parametric model (cont’d)
• Using these simplifying assumptions, thrust available can
be estimated from:
Ta = WdotA*Fsp = WdotA*[Fsp-gg/(1+BPR) +
Fsp-fn*(V0/V)*(BPR/(1+BPR)] (18.8)
where
• WdotA = Total airflow (note :WdotA-gg = gg airflow)
• Fsp-gg = Core engine Fsp
• Fsp-fn = Fan Fsp (varies with number of fan stages)
• V0 = Non-zero reference speed (select to fit data)
• BPR - Fan bypass ratio (given by design)
• Estimate installation losses at 5-20% (more to follow)
• Estimate airflow from
WdotA = WdotA0*delta/sqrt()
(18.9)
where
•  = ( @h)*(1+.2M^2)^3.5
(18.10)
•  = (@h)*(1+.2M^2)
(18.11)
• Estimate fuel flow from WdotA-gg*corrected fuel/air ratio
= WdotA/(1+BPR)*(f/a0)* ^.75
c 2002 LM Corporation
Propulsion
18-32
Design of UAV Systems
RayAD model matching
RayAD Appendix E engines (Table E.1 - Low BPR,
Table E.2 - High BPR and Table E.3 - TBP) were
modeled parametrically using the following values:
LBPR
HBPR
TBP
Core Fsp (sec) 90
90
90
Fan Fsp (sec)
66
25
5
V0 (KTAS)
100
100
50
BPR
0.4
8
133
Fuel/air ratio
0.0292
0.0292
0.0292
Even though our parametric model is unique to this
course, engine companies often provide generic “cycle
decks” which produce similar (but more accurate) results
c 2002 LM Corporation
Propulsion
18-33
Design of UAV Systems
Model input rationale
Core engine Fsp - Value (90 sec) selected from chart
18-17 for BPR = 0
Fan Fsp - LBPR value selected to match data,
HBPR Fsp scaled based on fan
pressure ratio differences (1.6 vs.
4.3), TBP Fsp estimated at 20%
HBPR Fsp.
V0 - Values selected to match data
BPR - Given values used except for TBP
which was selected to match data
Fuel/air ratio - Value selected to match data
c 2002 LM Corporation
Propulsion
18-34
Model correlation - LBPR
Design of UAV Systems
Parametric model SFC
(sec)
(lbm/hr-lbf)
Low Bypass Ratio Turbofan
SFC Correlation
1.2
1.1
1.0
0.9
0.8
0.7
0.7
0.8
0.9
1.0
1.1
1.2
(lbm/hr-lbf)
Table E.1 SFC (sec)
c 2002 LM Corporation
Propulsion
18-35
Model correlation - HBPR
(lbm/hr-lbf)
Design of UAV Systems
(lbm/hr-lbf)
c 2002 LM Corporation
Propulsion
18-36
Model correlation - TBP
(lbm/hr-lbf)
Design of UAV Systems
(lbm/hr-lbf)
c 2002 LM Corporation
Propulsion
18-37
Database comparison - TBF
Design of UAV Systems
• Even though model Fan Fsp values generally match
Raymer’s models at BPR = 0.8 and 8.0 by definition
- We have no idea what Fan Fsp might look like at
intermediate BPR values
- And we have no idea how they correlate with real ones
• We can get answers by assuming values of Fsp-gg and
use Eq 18.18 to calculate Fan Fsp for typical engines
Fsp-fn parametric
(Assumed Fsp-gg = 90)
80
Fsp-fn parametric
(Assumed Fsp-gg = 80)
100
Calculated values
Calculated values
80
Model values
60
Est. upper bound
40
Model values
60
40
20
20
0
0
0
2
4
6
8
10
0
2
4
6
8
10
BPR
BPR
• The Fsp-gg = 80 data looks like it provides a better fit
c 2002 LM Corporation
Propulsion
18-38
Design of UAV Systems
Other data comparisons
• Actual engine performance data can also be used to
check and/or calibrate parametric model estimates
- For example, parametric model performance estimates
for typical TBProp and TBFan engines can be compared
to actual engines under the same flight conditions
- But because of design differences, even real engines
will show performance variations
- Nonetheless, the comparisons can be used to
generate multipliers to ensure the model estimates
match actual engine performance ranges
• Comparisons with database TBProp and TBFan engine
performance are shown in the following chart
- TBProp model thrust available and SFC are seen to fit
within the data spread, albeit somewhat optimistically
- TBFan thrust fits the data but TSFC is about 15% high
- A 0.87 TBFan TSFC multiplier will compensate for it
c 2002 LM Corporation
Propulsion
18-39
Performance correlations
Design of UAV Systems
TBProp SFC at 250 kts)
TBProp power ratio at 250 kts
0.60
1.1
TPE331-14
PT6A-41 (Flat rated)
Other
0.9
TPE331-14
PT6A-41 (Flat rated)
Other
0.55
0.7
0.50
0.5
0.45
0.40
0.3
10
20
30
40
10
50
20
30
40
50
Altitude (Kft)
Altitude (Kft)
TBFan Cruise TSFC (35-40Kft)
TBFan Cruise thrust ratio
(35-40Kft)
1
M = 0.7-0.85
0.3
0.9
M = 0.7-0.85
0.8
0.25
0.63/36Kft
0.7
0.2
0.6
0.63/36Kft
0.15
0.5
0
2
4
6
8
10
0
Data from Roskam, Aerodynamics & Performance (RosA)P and Janes, Aero Engines
c 2002 LM Corporation
2
4
6
8
10
BPR
BPR
Propulsion
- Propulsion model estimate
18-40
Design of UAV Systems
A note about Turboprops
• Raymer’s Appendix E.3 TPB model is somewhat unique
in that performance is expressed in terms of thrust and
TSFC, not Shp or Eshp and SFC = WdotF/Hp
- This makes us work the problem backwards
- In a traditional propeller aircraft analysis, we first
calculate Bhp available and then multiply by p to
determine thrust horsepower (Thp) available
- The Breguet range equation includes p in the
numerator and SFC is based on uninstalled Bhp
- In our model we calculate thrust and fuel flow directly
- We, therefore, have to calculate Thp from the
definition Thp = T*V(fps)/550 = T*V(kts)/325.6 and
then divide by p to get Shp
- Then we calculate SFC from fuel flow and Shp
c 2002 LM Corporation
Propulsion
18-41
Design of UAV Systems
Installation losses
• An important issue for any engine model or data is
installation losses
- All installations degrade power or thrust available
compared to engine company test stand-type data
- The differences are large enough to effect even preconcept design estimates
• Jet engine losses derive from multiple factors
- Inlet and nozzle losses
- Bleed air
- Power extraction
- Etc.
• Turboprops also have to deal with prop efficiency
• IC engine installations have similar losses (air
induction system, mufflers, generators and props)
We will capture these effects using simple installed performance
knock down factors
- We will use 0.8 - 0.95 for TBJ and TBF installations
- p will capture all losses for ICs and TBPs
During conceptual design, actual performance losses should be
calculated for the specific designs studied
c 2002 LM Corporation
Propulsion
18-42
Design of UAV Systems
Example - TBProp
1. Our TBProp UAV weighs 1918 lbm, has a balanced
field length requirement of 3000 ft (ground roll = 1500
ft) and Clto = 1.49 and wing loading of W0/Sref = 30
psf (qto = 20.2 psf , takeoff speed = 77.2 kts). We
assumed a nominal cruise of 180 kts at 27.4Kft, an
initial cruise weight (w4) = 1726 and a cruise lift-todrag ratio (LoDcr) of 23. What size engine is
required for takeoff and will it meet cruise
requirements?
2. From RayAD Figure 5.4, the required prop aircraft
ground roll takeoff parameter for is 220 where
TOP =[W0/Sref]/[CLt/o*(Bhp0/W0)] =
= qt/o/(Bhp0/W0)
or
Bhp0/W0 = qto/220 = 0.092
- Engine size, therefore, is
BHP0 = 1918Klb*0.092 = 176.5 Bhp
c 2002 LM Corporation
Propulsion
18-43
Design of UAV Systems
TBProp takeoff estimate
3. Because propeller models have singularities at V=0, the
TBProp is sized at V = V0 = 50 kts (M = 0.076)
- At an assumed p = 0.8*, takeoff thrust (T0) can be
calculated directly by definition of BHP or
T0  Bhp0*550*p/KTAS*1.689 = 919.6 lbf
- Equation 18.8 is solved for total airflow using chart
18.33 TBP model values or Wdota = 919.6/[90/134
+5*(50/50)*(133/134)] = 163.2 pps
- Knowing WdotA0, the TBP model can now predict
thrust, airflow and fuel flow at cruise conditions
- For simplicity, this will be done only once at Vcr =
180 kts and an altitude of 27.4 Kft (M=0.3)
- Then it will be programmed in a spreadsheet
* p is assumed to account for all installation losses
c 2002 LM Corporation
Propulsion
18-44
Design of UAV Systems
TBProp cruise estimate
4.Equations 18.9-11 provide estimates of total airflow
(WdotA) at cruise (M=0.302), where
 = (a@27.4Kft)*(1+.2M^2)^3.5 = 0.3556
 = (a@27.4Kft)*(1+.2M^2) = 0.8264
WdotA = WdotA0*/sqrt() = 64 pps
- Core airflow by definition of BPR is Wdota/(BPR+1) or
for BPR = 133, Wdota-gg = 0.48 pps
- Fuel flow is calculated using the model fuel-to-air ratio
value f/a = 0.0292 corrected for , or ….
WdotF = WdotA-gg*(f/a)* ^.75 = 0.012 pps or 43.4 pph
- Equation 5.8 is used to calculate Ta where
Ta = WdotA*(Fsp-gg/(1+BPR)+Fsp-fn*(V0/V)
*(BPR/(1+BPR))
= 64*(90/134+5*(50/180)*(133/134) = 130.9 lbf
c 2002 LM Corporation
Propulsion
18-45
Design of UAV Systems
TBProp cruise - cont’d
- Thp is calculated using Eq 18.2 or
Thp =130.9*180/325.6 = 72.4 Hp
while
Shp = 72.4/0.8 = 90.4 Bhp
- Finally SFCcr  WdotF/Shp is calculated and found
to be
SFCcr = 43.4pph/90.4Bhp = 0.48 pph/Bhp
- Next we need to compare thrust “available” against
thrust “required”  drag
- We get this by dividing weight by LoDcr or
D ≈ 1726lbm/23 = 75 lbf which is 57% of Ta and
shows that the TBProp meets cruise thrust
requirements at 180 kts
c 2002 LM Corporation
Propulsion
18-46
Design of UAV Systems
TBProp summary
TBP sizing
1. Select takeoff speed (Vto), calculate qto  [W/S]/Clto
2. Estimate takeoff Bhp0 required (RadAD Fig 5.4)
3. Select takeoff “sizing” speed = V0 (i.e. 50 kts)
4. Calculate Tavail at sizing speed (Ta0 = 325.6pBhp0/V0)
5. Calculate WdotA0 from Fsp and Ta0 at V0 (Eq 18-8, BPR = 133)
TBP performance
1. Select speed (KTAS) & and altitude (h)
2. Calculate ,  and M at h (atmosphere spreadsheet)
3. “Correct”  and  for M (Eqs 18-10 and 18-11)
4. Calculate total (prop+engine) WdotA (Eq 18-9)
5. Calculate engine airflow (WdotA-gg = WdotA/[BPR+1])
6. Calculate corrected fuel-to-air ratio (Eq 18.7)
7. Calculate fuel flow (WdotF= WdotA-ggcorrected fuel-to-air ratio)
8. Calculate thrust available (Eq 18-8)
9. Calculate uninstalled Bhp (= TaKTAS/[325.6 p)
10. Calculate uninstalled SFC [SFC = WdotF/Bhp(uninst)]
11. Check that Ta > D = W/LoD
c 2002 LM Corporation
Propulsion
18-47
Design of UAV Systems
Typical example - TBFan
1. Our TBFan alternative weighs 2914 lbm, has a
balanced field length requirement of 3000 ft (ground
roll = 1500 ft) and Clto = 1.49 and wing loading of
W0/Sref = 40 psf (qto = 26.9 psf , takeoff speed =
89.1 kts). We assumed nominal cruise at 300 kts at
27.4Kft, an initial cruise weight (w4) = 2645lbm and a
cruise lift-to-drag ratio (LoDcr) of 22.5.
2. From RayAD Figure 5.4, the required jet aircraft
ground roll takeoff parameter for is 100 where
TOP =[W0/Sref]/[CLt/o*(T0/W0)] =
= qt/o/(Bhp0/W0)
T0/W0 = qto/100 = 0.269
- Engine size, therefore, is
T0 = 2914*0.269 = 784 lbf
c 2002 LM Corporation
Propulsion
18-48
Design of UAV Systems where
TBFan performance
3. The TBF model also has a singularity at V=0 and is
sized at V = V0 by solving for WdotA0
where
Fsp0 = Fsp-gg/(1+BPR)+ Fsp-fn*(BPR/(1+BPR)
and
T0 = WdotA0*Fsp0
4. Therefore for BPR = 5.0, Fsp-gg = 90, Fsp-fn = 30
(vs. 25 at BPR = 8) and T0 = 784 lbf
WdotA0 = 784/(90/6+30*5/6) = 19.6 pps
5. Performance at other conditions is determined using
Equations 18.9-11 and V0 = 100 kts. For example, at
h = 27.4 Kft, V = 300 Kts (M = 0.503) :
 = (@27.4Kft)*(1+.2M^2)^3.5 = 0.37969
= (@27.4ft)*(1+.2M^2) = 0.8527
and
WdotA = WdotA0*delta/sqrt() = 8.4pps
c 2002 LM Corporation
Propulsion
18-49
Design of UAV Systems
TBFan performance - cont’d
- By definition core airflow (Wdota-gg) = Wdota/(BPR+1)
or for BPR = 5, Wdota-gg = 1.4 pps
- Fuel flow is calculated using the model fuel-to-air ratio
value f/a = 0.0292 corrected for , or WdotF =
WdotAgg*(f/a0)* ^.75 = 0.037 pps or 131 pph
- Equation 18.8 once again is used to calculate thrust
T = WdotA*[Fsp-gg/(1+BPR)+Fsp-fn*(V0/V)
*(BPR/(1+BPR)]
= 8.4*(90/6+30*(100/300)*(5/6)) = 197 lbf
and
TSFC = 131pph/197lbf = 0.67pph/lbf
- At a LODcr of 22.5 and initial cruise weight =2623 lbm, D
= 116.6 lbf compared to TBFan T (uninstalled) = 198 lbf.
If we assume a 5% installation loss, Ta = 188 lbf, which
is enough to meet the cruise thrust requirements
c 2002 LM Corporation
Propulsion
18-50
Design of UAV Systems
TBFan summary
1. Select BPR
2. Select Fsp-fn = f(BPR) Chart 5b-13
3. Select takeoff speed (Vto), calculate qto  [W/S]/Clto
4. Estimate takeoff T0 required (RadAD Fig 5.4)
5. Select takeoff “sizing” speed = V0 (i.e. 100 kts)
6. Calculate WdotA0 from Fsp and T0 at V0 (Eq 18-8)
TBF sizing
TBF performance
1. Select speed (KTAS) & and altitude (h)
2. Calculate ,  and M at h (atmosphere spreadsheet)
3. “Correct”  and  at M (Eqs 5-13 and 5-14)
4. Calculate WdotA (Eq 5-12)
5. Calculate core airflow (WdotA-gg = WdotA/[BPR+1])
6. Calculate corrected fuel-to-air ratio (Eq 5.10)
7. Calculate fuel flow (WdotF = WdotA-ggcorrected fuel-to-air ratio)
8. Calculate uninstalled thrust (Eq 5-11)
9. Calculate installed thrust (Tinst = Tuninstinstallation factor)
10. Calculate installed TSFC (TSFC = WdotF /Tinst
11. Check that Tinst > D = W/LoD
c 2002 LM Corporation
Propulsion
18-51
Design of UAV Systems
Concluding remarks
• Our parametric models predict reasonable performance
for a range of types, altitudes and subsonic speeds
• Although approximate, they capture effects not included
in traditional parametrics, e.g. RayAD equations 10.4-15.
- They can be used for pre-concept design studies until
better data is available
• The models are approximate and are valid only at
subsonic speeds
• The models do not capture temperature or RPM limits
obvious in RayAD Appendix E plots
• The models do the best job of predicting airflow
• The model do the worst job of predicting HBPR and TBP
performance at low-altitude and high-speeds.
- Typically, these engines are not operated under such
conditions and the errors have little practical effect
• During conceptual design engine company models
should be used
c 2002 LM Corporation
Propulsion
18-52
Design of UAV Systems
Expectations
You should now understand
• Propulsion parametrics and parametric models
• Where they come from
• How they are used
• The limits of their applicability
c 2002 LM Corporation
Propulsion
18-53
Design of UAV Systems
Homework
1. Write spreadsheet programs to calculate
uninstalled IC, TBProp and TBFan engine
performance with airspeed (or M) and altitude (or
delta & theta) as inputs - (team grade)
2. Run your TBProp and TBFan models for the
example problems (charts 18-43 through 18-50)
and compare results (team grade)
- Identify any errors in my example problems
3. Using a balanced field length criteria for takeoff,
size engines for your proposed air vehicle
(individual grades)
4. Use the team spreadsheets to calculate uninstalled
engine performance at takeoff and dash (target ID)
speeds for your proposed air vehicle (individual)
5. Compare TBProp and/or TBFan results to
ASE261.Engine.Models.xls and identify differences
(individual grades)
c 2002 LM Corporation
Propulsion
18-54
Week 2
Design of UAV Systems
c 2002 LM Corporation
Propulsion
Intermission
18-55