AAE 451 Spring 2006
Preliminary Design Review
(Group II)
Mike Dumas
Adam Naramore
Ben Scott
Gaetano Settineri
Tim Sparks
David Wilson
TABLE OF CONTENTS
1
2
3
4
Executive Summary .................................................................................................... 3
Introduction ................................................................................................................. 5
Concept Justification................................................................................................... 6
Final Design ................................................................................................................ 7
4.1
Aircraft Specifications ........................................................................................ 7
4.2
Design Mission & Flight Envelope..................................................................... 9
5 Cabin Layout ............................................................................................................. 10
6 Flops Analysis ........................................................................................................... 13
7 Aerodynamics ........................................................................................................... 18
7.1
Airfoil Selection ................................................................................................ 18
7.2
Raymer Analysis ............................................................................................... 21
7.3
FLOPS Comparison .......................................................................................... 24
8 Structural Design and Analysis ................................................................................. 25
8.1
Material Selection ............................................................................................. 26
8.2
Load factors ...................................................................................................... 27
8.3
Forward Wing Structure ................................................................................... 28
8.4
Aft Wing Structure ............................................................................................ 28
8.5
Wing connection ............................................................................................... 29
8.6
Rib Spacing ....................................................................................................... 29
8.7
Fuselage Structure ............................................................................................. 30
8.8
Landing Gear .................................................................................................... 31
9 Propulsion ................................................................................................................. 31
9.1
Fuel Selection.................................................................................................... 31
9.2
Emissions .......................................................................................................... 33
9.3
ONX Analysis ................................................................................................... 35
10
Stability ................................................................................................................. 38
10.1 Control Surface Sizing ...................................................................................... 38
10.2 CG, Static Margin and Fuel Burn ..................................................................... 41
11
Weight Estimation ................................................................................................ 43
12
Cost Analysis ........................................................................................................ 46
12.1 Direct Operating Cost ....................................................................................... 46
12.2 Acquisition Cost................................................................................................ 49
13
Conclusion ............................................................................................................ 50
14
References ............................................................................................................. 52
15
Appendix .............................................................................................................. 54
15.1 Aerodynamics ................................................................................................... 54
15.1.1
Airfoil Selection ........................................................................................ 54
15.1.2
Raymer Analysis ....................................................................................... 64
15.2 Structures .......................................................................................................... 71
15.2.1
Composite material properties calculation code ....................................... 71
15.3 Propulsion ......................................................................................................... 73
15.4 Cost Analysis .................................................................................................... 77
15.4.1
Direct Operating Cost ............................................................................... 77
1
Executive Summary
EcoJet has designed a joined wing aircraft that runs on 100% bio-diesel fuel. An
isometric view of the designed aircraft can be seen in Figure 1. This aircraft was designed
to target fractional ownership operators such as NetJets or FlexJets. Over the next 5
years, EcoJet has projected to capture 2.5% of the total business jet market through the
sales of 25 aircraft. As the cost of aviation fuel increases, EcoJet plans to become a strong
competitor in the alternative fuel market for business jets. By 2022, EcoJet projects to
have captured 7% of the light-medium business jet market which is 260 aircraft.
Figure 1: Isometric View of Concept Aircraft
The aircraft fuselage is 50 ft in length and has a wing span of 55 ft. The sweep of
both wings is 30 degrees and the dihedral/anhedral is 10 degrees. Fuel will be stored in
both the forward and aft wing eliminating the need for external fuel tanks. During flight
fuel will be drawn from both wings in junction with a designed fuel schedule in order to
ensure aircraft stability. The two aft mounted engines generate a combine take off thrust
of approximately 10,600 lbs.
Table 1
below shows the target design parameters and the actual parameters of the final
design. From this table, it can be shown that EcoJet met all of its design targets except the
gross take-off weight and acquisition cost. The aircraft was designed to have a
particularly spacious cabin layout that focused on the comfort of its passengers.
Table 1: Target and Actual Design Parameters
Parameters:
Targets:
Actual
GTOW (lbs)
20,000
26,144*
Cruise Mach
0.85
0.85
TO Field Length
3500ft
3400ft
Passenger Cap:
6
6
Range
1700 nm
1700 nm
Acquisition Cost
$10 million
$14.5 million
Operating Cost
$1,000/hr
$1,062/hr
While the final acquisition cost did not meet the target value is still remained
within the established threshold of $15 M. The gross take of weight of the aircraft
exceeded the establish threshold of 25,000 lbs. This was deemed acceptable due to the
aircraft meeting all other critical performance requirements.
2 Introduction
The goal of this project was to design a business aviation (BA) or a general
aviation (GA) aircraft that uses a non-petroleum based fuel in its power plant. This
mandated market research into the future of BA and GA aircraft sales. Research was also
required to determine which alternative fuels would be most applicable to BA or GA
aircraft power plants currently in existence and would be FAA approved for use. The
selected market for this design project was the BA market, specifically fractional
ownership operators, and the fuel selected was B100 bio-diesel. The final concept was a
light-medium business jet that employed a joined wing design. The design requirements
for this concept are listed below in Table 2.
Table 2: Concept Design Requirements
Parameters:
Targets:
Thresholds:
GTOW (lbs)
20,000
< 25,000
Cruise Mach
.85
> .77
TO Field Length
3500ft
< 4000ft
Passenger Cap:
6
≥4
Range
1700 nm
≥ 1500 nm
Acquisition Cost
$10 million
≤ $15 million
Operating Cost
$1,000/hr
≤ $1,500/hr
These design requirements were compiled after a comparative analysis of current
BA aircraft on the market and consultation from representatives from fractional
ownership companies such as NetJets and FlexJets. The market selection also required
this design to conform to IFR requirements. This was critical in the estimation of the
necessary fuel needed for a nominal mission.
3 Concept Justification
With the predicted limited supply of petroleum based fuels the introduction of bio
fuels in aviation is soon expected. It was judged that the time of introduction of new bio
fuels would also be an opportunity to introduce new aircraft concepts that have been
researched but yet to be pursued for full scale design and construction. Of the concepts
researched, the joined wing concept had the most potential benefits over a traditional
aircraft design.
Credited to Julian Wolkovitch, the proposed benefits of the joined wing design
are listed as follows:
1. Light weight
2. High stiffness
3. Low induced drag
4. Good transonic area distribution
5. High trim CLmax
6. Reduced wetted area and parasite drag
7. Direct lift control capability
8. Direct sideforce capability
9. Good stability and control
Based on the proposed benefits along with the use of bio fuels in this aircraft, the
joined wing design has the potential to transform the image of business aviation.
4 Final Design
4.1 Aircraft Specifications
The final design of the aircraft was a bio-diesel powered BA jet employing a
joined wing configuration. The aircraft carries 6 passengers and has a 2 person flight
crew. The fuselage length was set at 50 ft with an outside diameter of 7 ft. The wing
span is 55 ft with the aft and forward sweep of the wings being 30 degrees. The dihedral
of the forward wing is equal to the anhedral of the aft wing at 10 degrees. The root chord
of the forward wing is 6ft and the root chord of the aft wing is 5 ft. Both wings have a
taper ratio of 0.32, and the aspect ratio is 8.5 which is calculated with the total planform
area of both the forward and aft wing. The vertical tail is 13 ft tall from the center line of
the fuselage with a root chord of 9.3 ft and has a taper ratio of 0.45 and an aspect ratio of
2. A 3-view drawing of the aircraft can be seen on the next page in Figure 2.
Cabin Door
55ft
7 ft
300
300
13ft
50ft
100
100
Figure 2: 3-view of aircraft
The aircraft uses two turbofan engines that are mounted on the side of the aft
section of the fuselage. Each engine produces approximately 5,300 lbs of thrust at take
off using B100 bio-diesel. The aircraft range is 1,700 nmi with a standard IFR reserve
capability. The cruise altitude is 41,000 ft with a maximum service ceiling of 45,000 ft.
The cruise Mach number at cruise altitude is 0.85.
The final gross take off weight is 26,144 lbs with 10,000 lbs of fuel and 1,500 lbs
of payload. The estimated acquisition cost is $14.5M and the direct operating cost is
$1,062/hr.
4.2 Design Mission & Flight Envelope
A representation of a typical mission for the aircraft is shown below. This
mission also includes a missed landing and reserve fuel flight and landing at an alternate
airport, in order to meet the reserve flight requirements. The mission profile is shown
below in Figure 3.
Figure 3: Mission Profile
The flight performance envelope for the aircraft was developed based off of
equations from the Dan Raymer Aircraft Design textbook. Equation 5.6 was used to
calculate the stall velocity at certain intervals in flight. Estimates for the wing loading
were used along with a Matlab program that decreases the CL value as the aircraft climbs
higher during take off and decreases the density of air at the correct intervals. Equation
5.6 was used along with these other constraints to produce Figure 4 below. The same
process was used to produce the cruise portion of the envelope. This figure represents the
slowest possible speed that the aircraft can maintain at certain points in the design
mission.
Figure 4: Flight Performance Envelope
5 Cabin Layout
The cabin was designed to luxury in mind. The designed aircraft has a spacious
fuselage layout for the comfort of its passengers. The length of the cabin is a long 27.5
feet. The width of cabin is 6.5 ft window to window and an aisle to ceiling height of 6 ft.
This has given the passengers plenty of room to stand up and walk around during the
flight.
Figure 5 shows the layout of the cabin. The door is located at the back of the
cabin. A full lavatory with a closing door is located directly across from the cabin entry
door. The cockpit can be seen at the front of the cabin. A large refreshment center,
serving drinks, snacks, and possibly even full meals, is located next to the cockpit. A
large closet for coats and baggage is across the aisle from the refreshment center. Both
the closet and the refreshment center measure 5 feet by 2.2 feet.
The useable floor width of the cabin including the seats and the aisle is 5.6 feet.
The width of the aisle is 1.27 feet. The aisle is sunk approximately 6 inches below the
main floor which allows for 6 ft of clearance from floor to ceiling in the aisle of the
aircraft.
Figure 5: Cabin and Cockpit Layout
There are 6 passenger seats in the cabin. The 4 seats in the rear of the cabin are
arranged for conference style seating with one row of seats facing the other. The
dimensions of the seats are 2.5 feet long and 2.167 feet wide as seen in Figure 6. In
addition to the spacious dimensions of the seats, there is also 3 feet between seats. This
provides passengers with plenty of leg room for comfort. Figure 6 below shows the
dimensions of the aft cabin seats with the spacing between the seats.
Figure 6: Close-up of the geometry of the 4 aft passenger seats in the cabin
Another benefit to the spacious cabin of the designed aircraft is that a conference
table is installed in the cabin. The table folds out in two pieces from the sides of the cabin
in between the passenger seats. The pieces extend to connect in the middle of the aisle.
The seats can also swivel to allow passengers to better face each other during
conversation.
The two front passenger seats are sleeper seats. When upright, these seats sit the
same as the 4 aft passenger seats. These seats have the ability to fold down into sleeper
seats with 6 feet of sleeping room as seen in Figure 7. This feature of the cabin adds to
the comfort of the aircraft. Passengers can comfortably sleep during cross-country flights
if they choose.
Figure 7: Close-up of the two forward passenger sleeper seats
6 Flops Analysis
After conducting the initial trade studies based on the most important design
attributes, and historical aircraft data; using tools like the QFD matrix, and Pugh’s
method, provided good benchmarks for beginning the design process. This also gave
insight into the competition and market into which the product will enter, providing
information to make the aircraft as competitive as possible. Once the design goals and
thresholds had been established using more rudimentary design tools a more detailed
sizing code, FLOPS (Flight Optimization System), was employed to analyze more
specific design configurations. FLOPS utilizes a combination of set design requirements
and thresholds such as gross takeoff weight, wing loading, aspect ratio, thrust to weight
ratio, and a detailed mission, etc. With better estimates of the ranges in which the basic
design requirements fall, FLOPS can make more detailed predictions of the performance
characteristics and critical sizing values such as gross take off weight and fuel weight,
which make up the defining characteristics of an aircraft. FLOPS can also make
predictions for costs of development, acquisition, and operation; however the cost
prediction in FLOPS proved to be unreliable as it was designed for sizing larger
commercial transport aircraft.
Before sizing a bio-diesel powered aircraft, FLOPS was calibrated with a similar
size benchmark aircraft in order to gage the accuracy of the results. The Citation XLS is
a competing aircraft in the medium business jet market. The important design values
characterizing the XLS and the FLOPS subsequent performance predictions are shown
below in Table 3:
Table 3: FLOPS results - Cessna Citation XLS Calibration
Citation XLS, input
GTOW
Aircraft values
20200
Design Range
Cruise Mach #
Wing loading
1798
0.75
54.6
lb
nm
lb/ft^2
fuselage length
51
ft.
width fuselage
PAX capacity
AR
Number of crew
Max cruise alt.
Take off field
length
6
8
8.3
2
41,000
ft.
3560
ft.
Engine/fuel Values
Thrust/engine
3991 Lbf
Overall pres.
Ratio
15.7
Fan pres. Ratio
1.59
Bypass ratio
4.12
Fuel heating
value
18400
lb/(hrSFC max
0.5 lbf)
Fuel price
2.57 $/gal
ft.
Citation XLS, output
Aircraft values
GTOW
19,144
Design Range
1885
Cruise Mach #
0.761
Fuel Weight
4179
lb
nm
Acquisition
DOC
Costs
8.073
1423
$million
$/hr
The most noticeable discrepancy is in the cost of the aircraft. A Citation XLS
today would cost $10.5 million given by reference 2. Therefore, the $8.073 million
FLOPS prediction is an obvious under-estimate. The gross take off weight prediction
from FLOPS appears to be accurate within a few percent of the given specification as
does the design range and cruise Mach #. This calibration proved FLOPS to be reliable
for performance predictions of the aircraft, but significantly inaccurate for cost
estimations.
With initial design parameters determined, entering these values into FLOPS
yielded a detailed description of the aircraft’s size, performance and costs. The design
mission had a large effect on the output of the results, especially with the aggressive
design goal of the aircraft being able to fly 1700 nmi at 0.85 Mach, including IFR range
of 200 nmi. At cruise, a fixed-altitude, fixed-Mach number analysis was used. To adhere
to the design goals this type of analysis was a necessity. Trade studies were performed
varying thrust to weight ratio (T/W) and wing loading (W/S), to verify FLOPS provided
expected trends. A sample of the results from the FLOPS analyses can be seen below in
Table 4:
Table 4: FLOPS Results from Varying Wing Loading and Thrust-to-Weight Ratio
W/S = 65
W/S = 70
W/S =
Wto=
26182 Lb
Wto=
25071.3 lb
Wto=
Takeoff =
3006 ft.
Takeoff =
3602 ft.
Takeoff =
T/W = .4
Oper cost =
2351.3 $/hr
Oper cost =
2262.93 $/hr Oper cost =
Price =
9.681 $M
Price =
9.487 $M
Price =
Wto= 26334.4 Lb
Wto=
25541.5 lb
Wto=
Takeoff =
3177 ft.
Takeoff =
3360 ft.
Takeoff =
T/W = .45
Oper cost = 2315.96 $/hr
Oper cost =
2258.6 $/hr Oper cost =
Price =
9.775 $M
Price =
9.613 $M
Price =
Wto= 27434.2 Lb
Wto=
26504.1 lb
Wto=
Takeoff =
3000 ft.
Takeoff =
3170 ft.
Takeoff =
T/W = .5
Oper cost = 2363.09 $/hr
Oper cost =
2300.44 $/hr Oper cost =
Price =
9.972 $M
Price =
9.789 $M
Price =
75
24226.5
3805
2200.4
9.335
24950.2
3544
2216.63
9.483
25815.2
3338
2254.2
9.646
lb
ft.
$/hr
$M
lb
ft.
$/hr
$M
lb
ft.
$/hr
$M
. The predictions for the current design follow the expected trend in that the
acquisition cost increases (with respect to the XLS); due to the aircrafts significantly
higher cruise speed and larger cabin. The acquisition cost, however, is still grossly
under-estimated considering this is new technology. As expected the GTOW in the
current design is also larger due to the need for more fuel (flying faster and using and
alternative fuel) and the larger fuselage. This information was also used to establish the
Plot
design space with a carpet plot in FigureCarpet
8:
28000
27500
T/W = .4
27000
Takeoff Weight (lb)
T/W = .45
T/W = .5
26500
Takeoff
Constraint
26000
25500
25000
24500
24000
63
65
67
69
71
73
75
77
W/S (lb/ft^2)
Figure 8: Carpet Plot
The final design iteration through FLOPS was a combination of all the previous
analysis mentioned. Wing loading was determined from the carpet plot and aerodynamic
analysis of required wing area. GTOW was determined from FLOPS making sure to
account for the required fuel taking into consideration a bio-fuel powered engine. Not
accounted for in the FLOPS analysis was an actual joined wing analysis as shown below
in Table 5 (engine values were obtained from ONX analysis).
Table 5: FLOPS Results for Current Design
Current Design, input
GTOW
Aircraft values
30,000
Design Range
Cruise Mach #
Wing loading
1700
0.85
73
Lb
nm
Lb/ft^2
fuselage length
50
ft.
width fuselage
PAX capacity
Wing sweep
AR
Number of crew
Max cruise alt.
Take off field
length
7
6
30
8.5
2
41,000
ft.
4000
ft.
Engine/fuel Values
Thrust/engine
5000 lbf
Overall pres.
Ratio
20
Fan pres. Ratio
2.9
Bypass ratio
3.2
Fuel heating
value
16108
lb/(hrSFC max
0.65 lbf)
Fuel price
3.63 $/gal
deg
ft.
Current Design, output
Aircraft values
GTOW
26144.3
Design Range
1802.2
Cruise Mach #
0.85
Takeoff Length
3405
Fuel Weight
9885.6
Costs
Lb
nm
Acquisition
DOC
Airframe R&D
9.486
2194.95
41.211
$million
$/hr
$million
Lb
GTOW has exceeded design threshold, but there has been a welcome increase in
range. All other output values held to the design goals. The block of time in which the
aircraft will perform its design mission is quite good, at 4.06 hrs. Speedy and
comfortable travel was a key design requirement and FLOPS verified that this goal was
met with our high cruise speed and large cabin. Several scaling factors had to be
implemented for the Joined wing concept that could not be taken into account in the
FLOPS analysis, due to not being familiar enough with the FLOPS code and were taken
into consideration by other analyses. FLOPS has shown significant inaccuracies in
predicting the acquisition and operating costs from the calibration model due to the fact
that the FLOPS cost model was designed for commercial transport as mentioned above.
Additional cost models were developed to take into account the use of new technology
and the development of the Joined wing design.
7 Aerodynamics
7.1 Airfoil Selection
Over forty-five airfoils were looked at from Dr. Michael Selig’s airfoil database at
the University of Illinois. The airfoils listed in Table 16 are in the NACA 63-Series,
NACA 64-Series, NACA 66-Series, Sikorsky Rotorcraft Series, and the NASA
Supercritical Series. Figure 19-Figure 23 show examples of the airfoils analyzed. The
NACA 6-Series airfoils are used frequently on business aircraft for their high
performance in the low transonic Mach range and their ease of manufacturing. The
Sikorsky Rotorcraft Series was looked at for their ability to have high lift coefficient
values in the transonic range. The NASA Supercritical Series is used on transonic
aircraft, because the airfoils minimize the transonic wave drag by reducing the shock
magnitude along the upper surface.
A cambered airfoil is needed for all of the forward wing and the aft wing after the
elevators to the tip. A symmetrical airfoil is needed for the vertical stabilizer and the
elevator region of the aft wing to create some downwash for stability. For a look at
current production aircraft, airfoil selections were obtained from Mr. David Lednicer’s
“Incomplete Guide to Airfoil Usage.” The majority of the early Cessna Citation Jets used
NACA 5-Series airfoils; however, these aircraft do not meet our required cruise Mach
number. The Bombardier Learjet’s in our class use NACA 64-Series airfoils while also
having similar cruise Mach numbers.
The airfoils selected were run through Dr. Mark Drela’s X-FOIL code developed
at the Massachusetts Institute of Technology. This analysis was run at a Reynolds
Number of 1 million to account for the maximum possible root chords of the wings at
lower than cruise altitudes. The actual Reynolds Number for the forward wing is 274,000
and 219,000 for the aft wing at 41,000 feet and at 480 knots. The fuselage Reynolds
Number is 75.9 million at these same conditions, but was factored into the airfoil
analysis. The airfoils that converged fully in X-FOIL over a specified angle of attack
range of -10° to 20° had their data compiled in MATLAB and further analysis was done.
The goal in the airfoil selection was to obtain the lowest drag at low angles of
attack while obtaining a high CLmax at an angle of attack of at least 15° with soft stall
characteristics. Also, the airfoils selected had to be structurally capable to fit around a
wing box and encompass a flap/aileron/elevator section. With these parameters set,
several airfoils were eliminated from the database.
Figure 9 shows the drag polar for the 4 best airfoils that met all of the specified
parameters. The NACA 64212, shown in Figure 10, was chosen due to its very low drag
at small CL values for the forward wing and the aft wing without the elevator section.
The SC 20010, shown in Figure 11, was chosen for the elevator section of the aft wing
and the vertical stabilizer, because it had the lowest drag for a symmetrical airfoil.
Comparison of CD vs. CL for 4 best airfoils
0.025
0.02
CD
0.015
0.01
0.005
NACA 64212
NACA 64012A
SC 20010
SC 20614
0
-2.5
-2
-1.5
-1
-0.5
0
CL
0.5
1
1.5
2
2.5
Figure 9: CD vs. CL Plot for 4 Best Airfoils
Figure 10: NACA 64212 Airfoil chosen for the forward wing and the aft wing without the elevator
section
Figure 11: NASA SC 20010 Airfoil chosen for vertical stabilizer and the elevator section of the aft
wing
Section 15.1.1 in the Appendix shows plots of some of the airfoils analyzed and
then just the top 4 airfoils with their lift, drag, and transition characteristics.
7.2 Raymer Analysis
Chapter 4 “Airfoil and Geometry Selection,” Chapter 12 “Aerodynamics,” and
Chapter 21 “Conceptual Design Examples” from the Raymer textbook were used in the
aerodynamic sizing of the joined wing aircraft. The MATLAB code used to do this
analysis along with the code that generated the V-N diagram found in the Structures
Analysis section of this paper can be found in the Appendix section 15.1.2.
The aircraft was sized for a traditional mono-wing design initially. To transform
the design to the joined wing, we took the required planform area output from the code
and split the wing. The forward wing was sized to produce 60% of the required lift,
while the aft wing was sized to produce the other 40% of the required lift without the
elevator section that will produce significantly less lift. The actual wing area is larger
than the required area. In later design phases the wing areas could be optimized for best
structural and aerodynamic performance, however, at this stage no optimization was
done. The airfoil inputs for the Raymer analysis code are listed on the next page in Table
6. The mission inputs were the same for the design mission (i.e. Mach Cruise Number of
0.85).
Table 6: Airfoil / Wing Inputs into Raymer Aerodynamic Analysis Code
Aspect Ratio
Airfoil Efficiency
Wing Sweep @ Quarter Chord
Hinge-Line Angle of Flaps
Wing Sweep @ Max Thickness
Wing Loading
Taper Ratio
CLmax (airfoil)
Thickness to Chord Ratio
dy ~ Leading Edge Sharpness Ratio (Raymer p329)
CLmax/Clmax (aircraft/airfoil) (Raymer p330)
ΔCL for Cruise Mach of 0.8 at dy=2.3
Slotted Flap Additional Lift CL
Cfe ~ estimated (Raymer p341)
Flap Angle at Takeoff
Flap Angle at Landing
Estimated Oswald Span Efficiency Factor
Mean chord location of Maximum Thickness
Flap Coverage Reference Area
8
95%
30°
30°
28°
7
0.32
2.0
10%
20.3*t/c
0.89
-0.5
1.3
0.0030
30°
70°
1.05
0.4
30%
An elliptical lift distribution was assumed for this initial analysis of the aircraft.
Normally, the Oswald Span Efficiency Factor for traditional mono-wing aircraft ranges
from 60% to 80% with a fully elliptical lift distribution. However, the out-of-plane
effects felt by the joined wing, winglets, a bi-wing, or a c-wing aircraft have the ability to
push the span efficiency above 100%. The calculated span efficiency for our aircraft for
a mono-wing is 60%. The same airfoil and wing inputs for a bi-wing give a span
efficiency of 160%. The average span efficiency then is 110%. From Dr. John
Sullivan’s course notes of AAE 415 “Aerodynamic Design,” the span efficiency for a
joined wing aircraft with a wing spread height to span ratio of 0.2 is 105%. Thus, this
number was used in our analysis.
Figure 12 on the next page shows a plot of the coefficient of lift versus the angle of
attack required from the Raymer Analysis. The horizontal lines between CL values of
1.5-2.0 are the maximum lift coefficient values for this aircraft based on Raymer’s
correlations. It was stated in class that the average flight angle of attack for climb is 3°,
so for this values, the CL required is 0.45 at takeoff. The CLmax value for cruise is 1.75.
2
1.5
Cruise
Takeoff
Landing
1
0.5
CL
Cruise
0
Takeoff
-0.5
Landing
-1
-1.5
-2
-25
-20
-15
-10
-5
0
5
10
15
20
 (deg)
Figure 12: CL and CLmax versus Angle of Attack from Raymer Analysis with Cruise, Takeoff, and
Landing Requirements
Figure 13 on the next page shows the drag polar determined from the Raymer
analysis for cruise, takeoff, and landing. This plot correlates well with the airfoils chosen
for the design aircraft.
2
Cruise
Takeoff
Landing
1.5
1
CL
0.5
0
-0.5
-1
-1.5
-2
0
0.01
0.02
0.03
0.04
0.05
CD
0.06
0.07
0.08
0.09
0.1
Figure 13: Drag Polar from Raymer Analysis showing Cruise, Takeoff, and Landing Requirements
7.3 FLOPS Comparison
The drag polar received from the FLOPS analysis in section 6 was compared with
the data received from the Raymer analysis done above section 7.2. Figure 14 on the
next page shows the comparison between these separate analyses.
The drag found from Raymer is lower than the drag found in FLOPS for a few
reasons. First, the FLOPS code does not have an input to change the Oswald span
efficiency factor. This value is calculated from aspect ratio and taper ratio, and for the
same lift, the total drag will be higher in the FLOPS analysis. The second reason for the
drag differential is the fact that transonic wave drag was not included in the Raymer
analysis. The design cruise Mach number is at the bottom threshold for transonic flow.
Thus, even though some flow over the top of the wings will be supersonic, the majority
of the aircraft will be at a cruise Mach number of 0.85. The understanding that the
Raymer analysis will consistently under predict the drag was utilized throughout the
aerodynamic analysis and sizing.
Drag Polar
1
0.9
0.8
0.7
CD
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.01
0.02
0.04
0.03
0.05
0.06
0.07
CL
Raymer - M=.84
Flops M=.825
Flops M=.850
Figure 14: Drag Polar Comparison between the Raymer and FLOPS Analysis
8 Structural Design and Analysis
One of the proposed benefits of the joined wing design is a reduction in the
structural weight of the wings compared to a traditional mono-wing and horizontal tail
configuration. This reduction in weight involves significant optimization of the wing
structure based on the aerodynamic loading. Due to the limited time frame for analysis
this optimization could not be performed. The forward wing and aft wing structure were
designed separately for different loading conditions. The forward wing structure was
sized similar to a mono-wing designed for bending due to lift. The aft wing was sized for
column buckling due to compression. This is due to the lift and torsion loads on the
forward wing being transferred into the aft wing at the wing tip. The fuselage structure
was sized for shear loading at trim and cabin pressurization. The basic equations for the
structural analysis were found in chapter 14 of reference 1.
8.1 Material Selection
For the internal wing box structure and ribs Aluminum 2017 was chosen.
Aluminum 2017 is a widely used material in aircraft structures and allows for a low
fabrication cost. For the wing skin AS4/3501-6 Graphite Epoxy was used. The use of
composites allows for a reduction of weight while maintaining high strength in the
structure. For ease of analysis a symmetric ply lay-up was used. This results in the
composite having quasi-isotropic material properties. The ply stack orientation was
[±45/0/90]s2 for a total of 16 plies. Each ply is 5 mils thick resulting in a total skin
thickness of 0.08 inches. Fiber orientations at ±45 degrees provide torsional stiffness in
the skin alleviating part of the torsion stress in the wing box. This same composite lay-up
was also used for the fuselage skin. The overall material properties for the composite
were calculated using a Matlab code developed in AAE 555: Mechanics of Composites
Materials and Laminates taught by Professor C.T. Sun at Purdue University. This code
can be found in Appendix 15.2. A summary of the material properties is given in Table 7
below.
Table 7: Material Properties
Material
Ex
Ey
Gxy
υxy
Al 2017
10.4 Msi
--
3.95 Msi
0.33
AS4/3501-6
[±45/0/90]s2
16.2 Msi
16.2 Msi
6.27 Msi
0.29
8.2 Load factors
The load factors that the aircraft structure is required to withstand are mandated
by the FAA. For this class of aircraft the limit load factors are 3 positive gs and -1.5
negative gs. A V-N diagram was constructed for this aircraft to determine the load
factors during different segments of the flight. The diagram can be seen on the next page
in Figure 15.
Stall Speed
Figure 15: V-N Diagram
The aircraft structure was sized for an ultimate load factor which is 1.5 times the
limit load factor. This was done to increase survivability of the aircraft in a worst case
scenario.
8.3 Forward Wing Structure
From the aerodynamic analysis, the total lift was distributed between the forward
and aft wing 60/40 (60% of the lift on the forward wing 40% on the aft). For a final
design GTOW of 26,144 lbs this results in a nominal lift of 15,686 lbs generated by the
front wing. For an ultimate load factor of 4.5 the forward wing would have to withstand
70,588 lbs of lift. For a simple, conservative design of the wing box structure, the lift
was split in half and placed as a point load at both tips. This was used to size the cross
section of the wing box at the root. Based on analysis from reference 19, the wing box
spanned from 7% of the chord length to 70% of the chord length which left 30% of the
chord for control surfaces on the trailing edge. With the root chord of the forward wing
being 6 ft in length this resulted in a wing box height of 5 inches and a span of 44 inches
at the root. The web thickness was set at 0.25 inches and the resulting flange thickness
was 0.5 inches using the ultimate stress of Al 2017 as the failure criteria for sizing the
cross section. The wing box carries through at the bottom of the fuselage below the cabin
deck. This was done to minimize stress concentrations at load path intersections.
8.4 Aft Wing Structure
The wing box design in the aft wing spanned the same chord percentage as the
forward wing box. With the root chord of the aft wing being 5 ft in length the wing box
span was 36 inches and 4.2 inches tall. The aft wing box was sized for compression and
failure due to buckling. A worst case scenario of a complete transfer of the forward wing
load into compression of the aft wing for a 4.5 ultimate load factor was used as the design
loading condition. Again the ultimate stress of Al 2017 was used as the failure criteria.
The boundary condition used was a fixed-fixed column with riveted or bolted ends
reducing the effecting column length to 82% of the original length. An average inertia of
the root and tip cross sections was taken for calculation of the critical buckling load. The
web thickness was set to 0.25 inches which resulted in a required flange thickness of 0.25
inches. This provided the necessary compression stiffness and also the necessary shear
stiffness to handle the lifting load. There is very little carry through structure for the aft
wing because of the root connections at the mid-span of the vertical tail.
8.5 Wing connection
Reference 25 suggests a connection of the aft wing with the forward wing at 70%
of the semi-span of the forward wing from the center line of the fuselage. This would
ideally minimize the structural weight of the wing. The result of a wing connection at
this point would be reduction in the span efficiency factor and a more complicated
analysis of the loading condition on the wing. For better aerodynamic performance and
ease of structural analysis, the forward and aft wings were connected at the tip resulting
in both wings having an equal span. The leading edge of the aft wing is lined up behind
the trailing edge of the forward wing and a simple wing pod structure is used to connect
the wing tips together.
8.6 Rib Spacing
The rib spacing was determined using sheet buckling of the skin. The boundary
condition employed was simply supported on all sides. The distance between the ribs at
the root of the forward wing was calculated and was then maintained throughout the rest
of the forward wing and the aft wing for uniform rib spacing. The resultant spacing was
30 inches between ribs. The thickness of the ribs was 0.25 inches and the material
selected was Al 2017. The complete wing structure layout is show in Figure 16 on the
next page.
Figure 16: Wing Structure Layout
8.7 Fuselage Structure
The composite lay-up used for the skin of the wings was also used for the
fuselage skin. This lay-up was analyzed to determine if additional structural support such
as longerons would be needed. This was done by calculating the max shear force at trim
conditions for ultimate loading of the aircraft and then calculating the resultant shear
stress in the fuselage cross section. The maximum shear force was estimated to be
130,720 lbs which results in a shear stress of 6.2 ksi at ultimate loading. This was an
acceptable stress level therefore it was determined that no addition support structure was
needed. The fuselage also had to withstand a 9.3 psi pressure differential between the
cabin pressure and the external pressure. The resulting hoop stress was 5.6 ksi, also an
acceptable stress level for the fuselage.
8.8 Landing Gear
A critical component of the overall aircraft is the landing gear system. Based on
the discussion of landing gear from Raymer’s text the nose gear for this aircraft will be
placed 7.5 feet back from the nose along the center line of the aircraft, and the main gear
will be 32.5 feet back from the nose. In order to assure that the tail will not strike the
ground during rotation at take-off the gear will have to be at least 3.25 feet tall. The
horizontal spacing needs to be adequate to prevent the aircraft from tipping over. For this
aircraft configuration this spacing will be 18 feet. The main gear will have two tires per
strut, and the nose gear will also have two tires two provide control of the aircraft in the
event of a flat tire. Tire selection is as follows; main gear: 37 x 14.0-14, nose gear: 21 x
7.25-10. This tire selection was made from the list of landing gear tires provided in
Raymer chapter 11 Table 11.2.
9 Propulsion
9.1 Fuel Selection
The basis for choosing an adequate alternate fuel source was put upon the
maturity, the availability, and the amount of fuel available and any evidence of the wear
effects the fuel might have on certain parts of the aircraft. Three fuels were studied as
possible candidates for this task. These fuels included bio-diesel, liquid methane, and
bio-kerosene.
Through research bio-diesel has shown it is able to meet all the requirements
deemed necessary in an alternate fuel. The use of bio-diesel has been researched in the
science community and test data is readily available for a number of different cases. This
research has shown that bio-diesel is currently the most mature fuel of all the proposed
fuels. Because the proposed market entrance would be in relatively soon five year period,
bio-diesel has a large advantage over the other, less tested fuels. The availability of biodiesel is much greater than that of the other two fuels especially liquid methane. New
government proposals to use mixed diesel fuel instead of standard number 2 diesel fuel
and to offer tax benefits for people using bio-diesel will result in the increased
production. The supply of bio-diesel will begin to rise as the market demand for it also
rises.
During the preliminary analysis of the proposed aircraft the assumption was made
that because bio-diesel has a lower fuel heating value, 16,108 BTU/lbm (National Biodiesel Board), more fuel would be required to fly the same distance as an aircraft using
Jet-A fuel. Jet-A fuel in comparison has a fuel heating value of about 18,300 BTU/lbm.
After research on tests performed to study the fuel flow rate it was found that this
assumption was not entirely accurate. Research by the Purdue Aviation Department has
found just this in Table 8. The aviation facility ran these tests at a ground stationed
engine at about 600ft above sea level with no applied load. If this proves true for 100%
bio-diesel, this will translate into weight savings for the estimated gross takeoff weight of
the aircraft. The density of bio-diesel is greater then that of Jet-A. This translate into a
few things, less volume is needed of bio-diesel for the same mass of fuel which can effect
the CG travel as fuel is consumed from the wing fuel tanks. It should be noted however
that not all studies have found this. A 2nd study from a Baylor University found
inconclusive evidence whither this would hold true while flying at cruise altitude. Further
analysis and research into this area will be necessary considering most of the flight time
will be spent cruising at the proposed 41,000 ft
Table 8: Fuel Consumption of Jet-A versus Bio-Diesel Mixes
9.2 Emissions
A number of studies have also been done on the emissions of bio-diesel fuels.
These studies have had fairly consistent results. The trends found show that in a
comparison of straight Jet-A versus blends of bio-diesel, emissions are not significantly
different at engine idle, but the emissions from the bio-diesel decrease as the engine is
throttled up. Particle emissions and carbon monoxide emissions are reduced but some
tests have shown that there can be a slight increase in NOx production. Some test results
have shown the opposite, however, which may be due to the manufacturing process of the
bio-diesels themselves. Shown on the next page are two studies on emissions from
turbine engines. Figure 17 was produced through a study done at Baylor University,
while Table 9 was produced through a study done by the American Society of
Mechanical Engineers. In this particular study at 500Hp the more bio-diesel used in the
fuel mixture the lower all of the emissions were measured at, with the exception of CO
which was measured less then Jet-A for the 2% bio-diesel mix, but measured higher for
the 20% mix.
Figure 17: Baylor University Turbine Engine Emission Study
Table 9: American Society of American Engineers Study on Turbine Engine Emission
The largest decrease in hydrocarbons occurs at the higher levels of bio-diesel and
Jet-A mixes. The study by Baylor University was performed using a PT6 engine and used
two types of bio-diesel fuel. One type was produced by NOPEC in Lakeland Florida and
was derived from waste cooking oils. The 2nd was produced by Griffin Industries of Cold
Springs Kentucky. The 2nd oil was derived from rendering plant animal wastes. The other
two studies were done using a soy methyl ester blend with Jet-A.
9.3 ONX Analysis
The heating value of bio-diesel varies slightly depending on the additives mixed
into it along with the Jet-A. The estimate that was used for all of the engine calculations
was a heating value of 16108 Btu/lbm (National Bio-diesel Board). In order to choose a
suitable engine for the proposed alternately fueled aircraft a number of factors were
considered. The required fuel flow was a concern as well as the thrust produced by the
aircraft. In order to determine these values an on-design engine program was used called
ONX. This program was developed by Jack Mattingly (aircraftenginedesign.com). To
calibrate the ONX code baseline data from three engines was used. One of these engines
is the Garrett TFE731-5BR engine which is used on aircraft such as the Hawker 800XP
and the Falcon 900. The engine compressor specifications inputted into the ONX code
was found from www.jetengine.net/civtfspec.html. ONX results on the TFE731-5BR can
be seen in Table 10 and Table 11 along with a comparison of the actual values. The info
on the other two engines can be found in the appendix in Table 19 through Table 22.
There is a small discrepancy between the two, 2.5% for the SFC and 7% for the thrust,
but these values seem very reasonable considering some inputs needed to be estimated
such as the turbine inlet temperature and other more advanced inputs that ONX may not
consider that were not available in the engine database.
Table 10: Baseline Engine TFE731-5BR
Component
Cruise Mach
Cruise Alt
Overall Pressure Ratio (OPR)
Value
.8
40000 ft
15.1
Bypass Ratio (Beta)
3.5
Fan Pressure Ratio (FPR)
3.48
Turbine Inlet Temp (TIT)
Jet-A Heating Value
2600 R
18400 BTU/lbm
Table 11: ONX Comparison for Baseline Engine TFE731-5BR
Parameter
SFC
Cruise Thrust
ONX Value
.7748
1122 lbf
Actual Value
.756
1052 lbf
In order to predict the performance of the new bio-diesel engine the only input
values that were changed was the fuel heating value and the OPR. The higher the OPR
the less fuel is needed to burn therefore an OPR of 20 was used. In new engines an OPR
of 20 is a very obtainable figure due to the new technologies being incorporated into new
engines that increase compressor efficiencies. Two different trade studies were done to
calculate an optimal bypass ratio and fan pressure ratio. These studies can be found in the
appendix in Figure 34. The trade study shows the bypass and fan pressure ratios. At high
bypass ratios less fuel is needed with the cost of more drag and less thrust. A middle
value was chosen that gave a good thrust and a reasonable SFC. The fan pressure ratio
affects the thrust much less then the bypass ratio therefore the value which gave the
lowest SFC was chosen. The results of the ONX code for the alternately fueled engine
can be found in Table 13. A more complete list of the ONX inputs and results can be
found in the appendix.
Table 12: Bio-Diesel Engine Results
Component
Cruise Mach
Cruise Alt
Overall Pressure Ratio (OPR)
Bypass Ratio (Beta)
Fan Pressure Ratio (FPR)
Turbine Inlet Temp (TIT)
Jet-A Heating Value
Value
.85
41000 ft
20
3.2
2.9
2600 R
16108 BTU/lbm
Table 13: Bio-Diesel Design Point and Threshold Point Operation
Output Parameters
Thrust
SFC
f (fuel fraction)
M= .85 Value
1151 lbf (cruise)
.882
.0331
M = .77 Values
1206 lbf (cruise)
.852
.0337
It can be seen in Table 13 that the fuel flow fraction is not significantly higher
than that of the baseline engine using Jet-A, but it is still larger. The SFC value, however,
is much higher in the bio-diesel engine but the same amount of thrust is produced which
is very important for proper cruise speeds.
A number of assumptions were made while using the ONX code due to the
complexity of the code and the limitations of the different requirements of the aircraft at
this point. Efficiencies for each component play a large role in the fuel required and the
amount of thrust that can be produced. Compressor efficiencies are always less than the
turbine efficiencies, which is reflected in the ONX code. Bleed air and cooling air values
are not often published for engines, so the program default values were used. Based on
research a conservative turbine inlet temperature value was set at 2600°R. This has
already been achieved in the marketplace so there would be a possibility that this could
be increased as new technology is introduced into the market. The Cp values also needed
to be estimated for the engine. Finding accurate Cp values after the combustion of the
bio-diesel has occurred yielded no results, so the program default values were used. The
last assumption made was the amount of air flow through the engine. The engine
database used reported static flow rates, but to find the thrust at cruise the air flow at
cruise is needed. These values were found using the baseline data at static conditions and
the thrust at cruise. For the baseline and the bio-diesel engine at mass flow rate of
40 lbm/s was used. All the exact values entered into ONX can be found in Appendix 15.3
in Table 17 and Table 18.
10 Stability
10.1 Control Surface Sizing
Every control surface was sized separately for this design (i.e. no control surface
serves a dual function). The aircraft has ailerons and flaps located on its forward wing. It
has ailerons, flaps, and elevators located on its aft wing. The rudder on the vertical tail
was sized for directional stability during a one engine out scenario.
The forward wing has 175 ft2 of surface area which does not include the area
through the fuselage. Single slot flaps were used to provide maximum lift during take off
and landing. The surface area of the flaps on the forward wing is 50 ft2 overall or 25 ft2
on each wing. This takes up about 28% of the lifting surface of the forward wing. The
surface area of the ailerons is relatively small with only 6 ft2 total or 3 ft2 per wing. This
results to about 3.5% of the lifting surface of the forward wing.
The aft wing has 178 ft2 of surface area available for lift. The aft wing also has 6
ft2 of aileron surface area, 3 ft2 per wing. The elevators take up 26 ft2 of the aft wing or
13 ft2 per wing. To increase the lift of the aircraft, small flaps were also added to the aft
wing. The flaps are only 12 ft2, but they will enhance the lifting capacities of the aircraft.
The percent used of the total lifting surface of the stability surfaces for the aft wing are
3.4% for the ailerons, 15% for the elevators, and 7% for the flaps.
The tail has a total surface area of 91 ft2. The aircraft has a very large rudder that
is 41 ft2. This is 45% of the total surface area of the tail. A large rudder will establish
better control of the aircraft especially in a one engine out or heavy crosswind situation.
The total surface area of the forward wing, aft wing, and tail is 444 ft2. The total surface
area of the control surfaces is 141 ft2. These control surfaces provide the aircraft with
adequate ability to control itself in a one engine out or 20% of takeoff speed crosswind
situation.
To solve for a one engine out configuration for the designed aircraft, the moment
caused by the one engine was calculated. The engines are located aft of the center of
gravity with a moment arm of 5.5 feet. One engine generates approximately 5300 lbs of
thrust. This generates a moment of 29,150 ft-lbs.
If the aircraft is to be trimmed in this configuration, this moment of 29,150 ft-lbs
must be offset by the rudder. To ensure stability, spin recovery equations were used to
size the rudder. Equation 1 for spin recovery criterion is:
Ixx  Iyy
W
b2
g
where:
(1)
b 2WRx2
Ixx 
4g
(2)
and:
Iyy 
L2WRy2
4g
(3)
The spin recovery criterion for the designed aircraft was determined to be 0.0164.
This is a dimensionless parameter and is a threshold value. The designed aircraft is
above this value. The airplane relative density parameter was determined to be 19.17,
another dimensionless parameter, based on equation 5 below:
W
 S
gb
(5)
Based on Figure 16.32 of the reference 1, the TDPF, or minimum allowable taildamping power factor for the designed aircraft is 0.0015. The TDPF is determined by
multiplying the tail damping ratio and the unshielded rudder volume coefficient together.
Based on the minimum value of TDPF, the tail damping ratio will be above 0.05 and the
volume coefficient should be above 0.03.
The designed aircraft will be above these factors for takeoff, landing, and cruise.
This spin recovery criterion was used to determine the amount of rudder area needed to
recover from a one engine out configuration.
10.2 CG, Static Margin and Fuel Burn
The location of the CG of the aircraft is critical to the static stability and the
calculation of the static margin of the aircraft through out the design mission. Equation
(6), shown below, was used to estimate the CG location where W is the weight of each
component and x is the perpendicular distance from the tip of the aircraft to the center of
mass of the component. Locating the CG of the aircraft will help to determine whether
the aircraft is stable or not based on the location of the neutral point. For the aircraft to
be statically stable the CG must be located in front of the neutral point.
The static margin of an aircraft is a value used to describe the stability of the
aircraft. The static margin was determined using Equation (7) shown below. The static
margin calculation was done as a percent of the front wing mean aerodynamic chord
(MAC in the equation). Raymer states that a static margin of 5-10% is typical of
transport aircraft. Based on the estimations made for weight and CG, the minimum static
margin during the design mission is 7 %. This static margin occurs after the descent into
the destination airport before landing maneuvers take place.
CG
W x
W
i i
(6)
i
SM 
( x np  xcg )
MAC
(7)
One of the most critical factors in determining the static margin travel and the
aircraft stability is the fuel burn schedule. In order to maintain a positive static margin
the fuel consumption must occur on a strict schedule. The schedule that has been used in
the calculations of the static margin throughout the flight is shown in Table 14. Based on
this fuel burn schedule a static margin travel diagram was created to show the location of
the static margin throughout a max passenger, max range mission with the required IFR
alternate. A diagram of the static margin travel is show on the next page in Figure 18.
Table 14: Estimated Fuel Burn Schedule for Design Mission
Fuel Burn Schedule
Mission Segment
Take-off
Climb
Cruise
Descend
Missed Approach
Climb to Alt Cruise
Reserve Cruise
45 Minute Loiter
Descend to Alt
Land at Alt
Total Fuel Burned
Total Fuel
Fuel from Forward
Fuel from Aft
Used
Tanks
Tanks
500
1250
3705
3710
795
800
250
750
750
750
750
450
450
500
110
9700
5820
500
1250
250
750
750
390
3890
Static Margin Travel
27000
Full Fuel, Full
Passengers
Take off
Gross Weight [lbs]
25000
Lower Static
Margin Limit
23000
Climb
Cruise Segment
Upper Static
Margin Limit
21000
Descent
Reserve Cruise
19000
Landing at
Destination
Airport
17000
zero fuel
full payload
15000
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Static Margin as % of MAC
Figure 18: Static Margin Travel
11 Weight Estimation
In order to assess the accuracy of the FLOPS gross take-off weight estimation a
method developed by Raymer was utilized to develop a 2nd weight estimation. Chapter
15 discusses this method in detail and utilizing Equations 15.25– 15.59 a basic estimation
of the weight of the aircraft was made. The unique design of the aircraft made changes to
Raymer’s structural weight estimations necessary. Both of the wings weights were
calculated with Raymer’s equation as main lifting wings. The dimensions of each wing
were used in the equation to arrive at individual final wing weights. In order to properly
account for the use of advanced composites in the construction of the aircraft structures
the weighting factors shown in Table 15.4 of Raymer’s text were utilized. The low-end
of these factors was used based on the assumption that the aircraft will utilize composites
to the maximum possible extent.
The equations provided in Raymer’s text are given for military aircraft,
cargo/transport aircraft, and general aviation aircraft. A business class aircraft does not
fit into any of these categories, so an average prediction of the weight of each component
was taken from the cargo/transport aircraft and general aviation aircraft estimates. There
were also some components (installed APU, hydraulics, etc.) that were listed in the
cargo/transport category that did not appear in the general aviation aircraft category. The
weights for these components were taken directly from the cargo/transport aircraft
component weight equations; no averaging or adjustments were made. Lastly, the
weights of components such as the pilot seats, passenger seats, refreshment center,
lavatory, and appliances, and other furnishings were taken from historical data and
estimations.
The weights for the passengers, pilots, and baggage were originally based on FAA
passenger weight requirements, but were changed based on an adjusted view of the
typical C.E.O. type passenger that would utilize this aircraft. The weight for each
passenger was set at 200 pounds and the average weight of luggage for each passenger
was set at 35 pounds. The total weight for each pilot was set at 200 pounds (this weight
includes any luggage brought by the pilots). The complete weight breakdown is shown
on the next page in Table 15.
Table 15: Aircraft component weight breakdown
Structures
Forward wing
Aft Wing
Fuselage
Nose gear
Main landing gear
Tail
Nacelles
Weight (lbs)
1231.8
1025.6
2224.5
115.7
609.5
815.8
146.7
Propulsion
Installed Engines
Engine Starter
Engine Controls
Fuel System/Tanks
3004.7
48.8
41.2
90.2
Equipment
Flight Controls
Avionics
Instruments
APU Installed
Electrical
Air Conditioning
Hydraulics
581.6
1982.7
134.4
220
676
471.9
125.6
Accommodations
Seats (6 total)
Lavatory
Refreshment center
Appliances (Fridge,
Microwave, Coffee Pot)
Other Furnishings
300
45
300
110
105.1
Based on the estimations described above the manufacturing empty weight of the
aircraft is 14,137 pounds. The fuel weight required to complete the max range, max
payload mission with the necessary reserves, was determined using FLOPS. Based on
this FLOPS analysis the aircraft will need to carry 10,000 pounds of fuel. This fuel will
be stored entirely in the wings of the aircraft with 6,000 pounds being housed in the
forward wing and 4,000 pounds being housed in the rear wing. With the addition of the
fuel the maximum gross take-off weight of the aircraft is estimated at 26,147 pounds.
Assuming that 3% of the fuel in each tank cannot be used zero-fuel weight will be 16,447
pounds. This includes the weight of the flight crew and 6 passengers with baggage in the
aircraft
These weight estimates correlate well with the output from FLOPS. This
correlation serves to validate the data received from FLOPS and therefore validates the
input used to reach this gross take-off weight. Another purpose for estimating these
various weights is to determine the location of the center of gravity (CG) of the aircraft,
and this data will in-turn be used to determine the static stability of the aircraft.
12 Cost Analysis
12.1 Direct Operating Cost
The direct operating cost of an aircraft is one of the most important points to a
potential buyer. Calculating the direct operating cost can be more difficult then it sounds.
Different companies use different criteria for what is included in a direct operating cost.
Some companies factor in costs of engine overhauls and of repainting basic surfaces.
Upgrades and aircraft inspections are two more examples of costs that may be considered
into the direct operating cost. The direct operating cost for the EcoJet alternatively fueled
aircraft is based off of the variable cost estimates done by AMSTAT Corporation. Three
different aircraft were used as a baseline in order to properly estimate the cost of the
EcoJet aircraft. The breakdown used by AMSTAT of the variable operating cost is based
off of four main categories. The fuel expense is calculated by multiplying the average
hourly aircraft fuel consumption by the current average nationwide fuel price. The hourly
fuel consumption is found from actual operator experience and includes fuel burn
throughout the entire flight operation. The maintenance labor expense represents the
combined costs of internal and contractor labor and includes both scheduled and
nonscheduled maintenance. This figure is also based off of operator experience. The parts
expense includes costs for all the replacement parts for the airframe, avionics, and
engines if the aircraft is not enrolled in an engine maintenance plan. Finally the
miscellaneous trip expense includes all trip-related expenses including crew overnight
expenses, catering, cabin supplies, and landing / parking fees. This expense is the same
for all aircraft in a particular category or class. Table 23 shows the operating cost of three
baseline aircraft in comparison with the EcoJet aircraft. The data on the three baseline
aircraft is directly from the AMSTAT Corporation’s database.
The fuel expense is dependant on two factors as mentioned before, the cost of fuel
and the consumption rate. To calculate the fuel consumption of EcoJet the SFC was used
at cruise as the average fuel consumption. A majority of the time spent is at cruise in
comparison with the 30 to 40 min it may require to takeoff, climb, and land. Due to the
different type of fuel and the variety of results from studies done on the fuel consumption
of bio-diesel based fuels this number is a rough estimate. Just as important in the fuel
expense is the cost of bio-diesel. The cost of bio-diesel can be almost a dollar less then
Jet-A. Marin Biofuels sells B100 bio-diesel for $3.62 per gallon in Los Angeles. To try
and account for the estimate of the fuel consumption rate of the EcoJet aircraft, the higher
cost of bio-diesel in California was used instead of a national average. The fuel expense
is about $500 for the EcoJet aircraft which is significantly less then the Jet-A fueled
aircraft. Again, the cheaper cost of fuel is a large part of this cost. With more testing
results could show that the fuel consumption may actually be less then expected or could
show the opposite. In either respect the fuel expense of EcoJet will be less then the
aircraft that use Jet-A fuel.
The maintenance expense was a hard expense to estimate. Estimating this cost
from the weight is not possible due to the costs shown in the baseline. The Learjet 45
weighs in the over 20,000lbs category but has the cheapest maintenance labor expense.
This cost was overestimated to be more expensive then all of the baseline aircraft.
Maintenance is going to be more costly due to the new technology involved in this
aircraft as well as the lack of methods to perform labor on a diamond wing aircraft.
The parts expense for the EcoJet was grossly overestimated in comparison with
the baseline aircraft. Bio-diesel is known to corrode rubber fuel lines in automobiles as
well as test aircraft that have used bio-diesel (Soy-Diesel blends use in aviation turbine
engines, Purdue Ave-Tech Department). This effect will require different types of hosing
to be used which may cost more then the standard fuel lines. The effect that the bio-diesel
has on the engine is also a young science. Some testing has shown that due to the
lubricity improvements of bio-diesel the wear of some critical engine components could
be reduced, thus increasing the life and time between overhaul of the engine (The Use of
Bio-Fuels as additives and extenders for aviation turbine fuels, The American Society of
Mechanical Engineers). More research could show that parts last longer then the baseline
aircraft which could drive this parts expense down.
The miscellaneous trip expense for EcoJet was calculated based on the class of
the aircraft. The EcoJet aircraft is more similar to the Citation Excel and the Learjet 45
baseline aircraft therefore the design aircraft would be a class three aircraft. Class three
aircraft have a miscellaneous trip expense of about $165. The EcoJet cost was rounded up
to $170 for this section, to include the possibility of forgotten factors in this section.
Overall the total operating cost of the EcoJet aircraft is about $1062 per hour.
This is comparable to all three of the baseline aircraft. It is neither the cheapest nor the
most expensive, but as mentioned above this value is very flexible once more research is
done on using bio-diesel in aircraft turbine engines. Ideally this cost could be driven
down but even if the cost were to increase due to inaccurate fuel consumption value or an
underestimate of one of the expenses the direct operating cost would still be competitive
in comparison with the three baseline aircraft, especially the citation excel which is the
most similar aircraft to EcoJet.
12.2 Acquisition Cost
The final acquisition cost of the aircraft was estimated to be 14.5 million dollars.
This was still within the threshold limit established in the design criteria, but still
relatively high in terms of making this design competitive with current aircraft on the
market. This acquisition cost was determined based on adjusted predictions from FLOPS
which included a set offset that was determined in the calibration. This was then
validated by calculating an acquisition cost from a linear regression curve that predicted
acquisition cost as a function of gross take off weight. The equation for this curve was
found by plotting the acquisition cost of current BA aircraft against their gross take off
weight and then curve fitting the data. This value compared well with the estimate from
FLOPS. Finally a research and development factor was included for the use of the joined
wing concept that accounted for approximately an extra $2.5M in the acquisition cost.
13 Conclusion
Of the seven design objectives created in the initial research phase of the project
only one was not met within the created design thresholds: the maximum gross takeoff
weight design target was set at 20,000 lbs with a threshold value of 25,000lbs. The
calculated gross takeoff weight was a little over 26,100lbs, exceeding the threshold limit
by 1,100 lbs. Even though the GTOW threshold was exceeded, the take off length and the
cruise Mach number targets were met. The excessive gross takeoff is not considered a
failure of the design since all other design parameters were within the specified
thresholds. The gross takeoff weight is linked to the large acquisition cost which is a
critical aspect of marketing the aircraft.
The excessive weight was a driving factor in the acquisition cost of the aircraft and
drove this value up significantly. The target cost was set during preliminary design to $10
million with a threshold value of $15 million. The cost calculated was found at $14.5
million, which is within the threshold value but is slightly out of a competitive cost range
for aircraft of this size. The low direct operating cost of about $1100 per hour will
become a good selling point for the aircraft due to its very competitive nature in
comparison to other aircraft.
The excessive gross take off weight is driven primarily by the large fuselage and
the cruise speed of the aircraft, both of which substantially exceed the performance of
current BA aircraft in this class. The lack of optimization of the aerodynamics and the
structure also is a significant factor that drove the gross take off weight outside the
threshold. Given more time for analysis, an optimization code could have been
developed for the structure and aerodynamics of the aircraft which most likely would
have led to a reduced GTOW. The predicted extra weight of fuel needed for using biodiesel instead of Jet-A also contributed to the increased weight of the aircraft. If future
research proves bio-diesel to burn with the same efficiency as Jet-A the amount of biodiesel needed will decrease.
Overall this design was considered to successfully meet the requirements of the
design project. With the exception of the gross take off weight and acquisition cost, all
other performance parameters of the aircraft met or exceeded the design specifications
established. The estimated direct operating cost is competitive with existing aircraft and
will be even more competitive as the price of petroleum fuels rises. A reduction in the
gross take off weight would lead to a reduction in the acquisition cost making it more
attractive to fractional operators wishing to recover their expenses as soon as possible.
14 References
1. Raymer, Daniel P. “Aircraft Design: A Conceptual Approach”, Third Edition,
AIAA Inc. Reston, Virginia 1999.
2. investor.textron.com/downloads/03-08-2006_Citigroup.pdf
3. Samuels, Mary F. Structural Weight Comparison of a Joined Wing and a
ConventionalWing. AIAA paper 81-0366R, Vol. 19 No. 6 June, 1982
4. Mattingly, J., On-Design analysis of gas turbine engines V3.23
5. www.Aircraftenginedesign.com
6. Renewable Aviation Fuels Development Center (RAFDC), Baylor University
7. http://www.baylor.edu/bias/
8. Lopp Denver, Stanley Dave., “Soy-Diesel blends use in aviation turbine engines”
9. Purdue University School of Technology, 1995
10. Kimble-Thom, M., Cholis, J., Stanley, D., Lopp., D. “The use of bio-fuels as
additives and extenders for aviation turbine fuels.” The American Society of
Mechanical Engineers 1999.
11. http://www.biodiesel.org, “Energy Content,” National Biodiesel Board
12. “Cessna, Citation Excel, CE-560-XL Aircraft Operating Cost Report”
13. AMSTAT Corporation, January 13th, 2006
14. “Hawker 400XP, Model 400A Aircraft Operating Cost Report”
15. AMSTAT Corporation, January 13th, 2006
16. “Learjet 45, Model 45 Aircraft Operating Cost Report”
17. AMSTAT Corporation, January 13th, 2006
18. Wolkovitch, J., “The Joined Wing: An Overview” AIAA -45285-385
19. Samuels, M., “Structural Weight Comparison of a Joined Wing and a
Conventional Wing.” AIAA-81-0366R, Journal of Aircraft. Vol. 19, No. 6, June
1982
20. Gallman, John W., Kroo, Ilan M., Smith, Stephen C., “Design Synthesis and
Optimization of Joined-Wing Transports,” AIAA-90-3197, Sept. 17-19, 1990.
21. Burkhalter, John E., Spring, Donald, J., Kent, M., “Downwash for Joined-Wing
Airframe with Control Surface Deflections,” Journal of Aircraft. Vol. 29, No. 3,
May-June 1992.
22. Wolkovitch, Julian, “Joined-Wing Research Airplane Feasibility Study.” AIAA84-2471, Oct 31-Nov2, 1984.
23. Smith, S. C., Cliff, S. E., “The Design of a Joined-Wing Flight Demonstrator
Aircraft,” AIAA-87-2930, Sept. 14-16, 1987.
24. Gallman, John W., “Optimization of an Advanced Business Jet,” AIAA-94-4303CP.
25. Kroo, Ilan, Gallman, John, Smith, Stephen. “Aerodynamic and Structural Studies
of Joined-Wing Aircraft,” Journal of Aircraft, Vol. 28, No. 1.
26. Kroo, Ilan, Gallman, John, Smith, Stephen. “Optimization of Joined-Wing
Aircraft,” Journal of Aircraft Vol. 30, No. 6, Nov-Dec 1993.
27. Wolkovitch, Julian, “Joined Wing Aircraft,” U.S. Patent 3,942,747, March 1976.
28. Selig, Michael. “UIUC Airfoil Coordinates Database – Version 2.0 (over 1550
airfoils”, http://www.ae.uiuc.edu/m-selig/ads/coord_database.html, University of
Illinois Urbana-Champaign Department of Aerospace Engineering.
29. Lednicer, David, “The Incomplete Guide to Airfoil Usage,”
http://www.ae.uiuc.edu/m-selig/ads/aircraft.html, University of Illinois UrbanaChampaign Department of Aerospace Engineering.
30. AAE 415: Aerodynamic Design, Instructor: J.P. Sullivan, Purdue University
31. AAE 555: Mechanics of Composite Materials and Laminates, Instructor: C.T.
Sun, Purdue University
15 Appendix
15.1 Aerodynamics
15.1.1
Airfoil Selection
Table 16: Airfoils Analyzed
Sikorsky Rotorcraft
63215B
SC1012r8 SC1094r8
63412
SC1095
63415
NASA Supercritical
NACA 64-Series
20010
20412
64008A 64015A 64212ma 20012
20414
64012
64108
64212mb 20402
20503
64012A 64110
64215
20403
20518
64015
64212
20404
20606
20406
20610
NACA 66-Series
20410
20612
66021
NACA 63-Series
63010A 63210A
63012A 63212
63015A 63215
SC1095r8
20614
20706
20710
20712
20714
21006
21010
Figure 19: Example NASA Supercritical Airfoil
Figure 20: Example NACA 63-Series Airfoil
Figure 21: Example NACA 64-Series Airfoil
Figure 22: Example NACA 66-Series
Figure 23: Example Sikorsky Rotorcraft Airfoil
Comparison of CL vs.  for all airfoils
2.5
N63A010
N63015A
N64012A
N64015
N64108
N64212
N66021
sc1012r8
sc20010
sc20012
sc20610
sc20612
sc20614
sc20714
sc20710
sc20712
sc21006
sc21010
2
1.5
1
0
-0.5
-1
-1.5
-2
-2.5
-25
-20
-15
-10
-5
0
5
10
15
20
25
 (deg)
Figure 24: C_L vs. Angle of Attack for all airfoils
Comparison of CL vs.  for 4 best airfoils
2.5
2
1.5
1
0.5
CL
CL
0.5
0
-0.5
-1
-1.5
NACA 64212
NACA 64012A
SC 20010
SC 20614
-2
-2.5
-25
-20
-15
-10
-5
0
5
10
15
 (deg)
Figure 25: CL vs. Angle of Attack for 4 Best Airfoils
20
25
Comparison of CD vs.  for all airfoils
0.03
N63A010
N63015A
N64012A
N64015
N64108
N64212
N66021
sc1012r8
sc20010
sc20012
sc20610
sc20612
sc20614
sc20714
sc20710
sc20712
sc21006
sc21010
0.025
0.015
0.01
0.005
0
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
 (deg)
Figure 26: CD vs. CL for all Airfoils
0.03
NACA 64212
NACA 64012A
SC 20010
SC 20614
0.025
0.02
CD
CD
0.02
0.015
0.01
0.005
0
-2.5
-2
-1.5
-1
-0.5
0
CL
0.5
1
Figure 27: CD vs. CL for 4 Best Airfoils
1.5
2
2.5
200
N63A010
N63015A
N64012A
N64015
N64108
N64212
N66021
sc1012r8
sc20010
sc20012
sc20610
sc20612
sc20614
sc20714
sc20710
sc20712
sc21006
sc21010
150
100
L/D
50
0
-50
-100
-150
-25
-20
-15
-10
-5
0
5
10
15
20
25
 (deg)
Figure 28: Lift to Drag Ratio versus Angle of Attack for all Airfoils
200
150
100
NACA 64212
NACA 64012A
SC 20010
SC 20614
L/D
50
0
-50
-100
-150
-25
-20
-15
-10
-5
0
5
10
15
20
 (deg)
Figure 29: Lift to Drag Ratio versus Angle of Attack for 4 Best Airfoils
25
200
N63A010
N63015A
N64012A
N64015
N64108
N64212
N66021
sc1012r8
sc20010
sc20012
sc20610
sc20612
sc20614
sc20714
sc20710
sc20712
sc21006
sc21010
150
100
L/D
50
0
-50
-100
-150
-2.5
-2
-1.5
-1
-0.5
0
CL
0.5
1
1.5
2
2.5
Figure 30: Lift to Drag Ratio versus Coefficient of Lift
200
NACA 64212
NACA 64012A
SC 20010
SC 20614
150
100
L/D
50
0
-50
-100
-150
-2.5
-2
-1.5
-1
-0.5
0
CL
0.5
1
1.5
2
Figure 31: Lift to Drag Ratio versus Coefficient of Lift for 4 Best Airfoils
2.5
25
20
[Negative Slope - Top Transition, Positive Slope - Bottom Transition]
15
10
 (deg)
5
0
-5
-10
-15
-20
-25
0
0.1
0.2
0.3
0.4
0.5
X/C
0.6
0.7
0.8
0.9
N63A010
N63A010
N63015A
N63015A
N64012A
N64012A
N64015
N64015
N64108
N64108
N64212
N64212
N66021
N66021
sc1012r8
sc1012r8
sc20010
sc20010
sc20012
sc20012
sc20610
sc20610
sc20612
sc20612
sc20614
sc20614
sc20714
sc20714
sc20710
sc20710
sc20712
sc20712
sc21006
1
sc21006
sc21010
sc21010
Figure 32: Transition Location Percentage for All Airfoils with Angle of Attack
25
NACA 64212
20
[Negative Slope - Top Transition, Positive Slope - Bottom Transition]
NACA 64012A
15
SC 20010
10
SC 20614
 (deg)
5
0
-5
-10
-15
-20
-25
0
0.1
0.2
0.3
0.4
0.5
X/C
0.6
0.7
0.8
0.9
1
Figure 33: Transition Location Percentage for 4 Best Airfoils with Angle of Attack
%AAE451 EcoJet Inc
%Comparison Code for airfoils
clear;close all;clc
load 'set1.mat'
load 'set2.mat'
load 'set3.mat'
load 'set4.mat'
load 'set5.mat'
load 'set6.mat'
load 'set7.mat'
load 'set8.mat'
load 'set9.mat'
load 'set10.mat'
load 'set11.mat'
load 'set12.mat'
load 'set13.mat'
load 'set14.mat'
load 'set15.mat'
load 'set16.mat'
load 'set17.mat'
load 'set18.mat'
load 'set19.mat'
%set_...=[alpha,Cl,CD,L/D,Top_Xtr,Bot_Xtr]
%Compare CL vs. alpha for all airfoils
figure (1)
plot(set_n63A010(:,1),set_n63A010(:,2), set_n63015A(:,1),set_n63015A(:,2),
set_n64012A(:,1),set_n64012A(:,2),
set_n64015(:,1),set_n64015(:,2),set_n64108(:,1),set_n64108(:,2),set_n64212(:,1),set_n64212(:,2
),set_n66021(:,1),set_n66021(:,2),set_sc1012r8(:,1),set_sc1012r8(:,2),set_sc20010(:,1),set_sc20
010(:,2),set_sc20012(:,1),set_sc20012(:,2),set_sc20610(:,1),set_sc20610(:,2),set_sc20612(:,1),s
et_sc20612(:,2),set_sc20614(:,1),set_sc20614(:,2),set_sc20714(:,1),set_sc20714(:,2),set_sc207
10(:,1),set_sc20710(:,2),set_sc20712(:,1),set_sc20712(:,2),set_sc21006(:,1),set_sc21006(:,2),set
_sc21010(:,1),set_sc21010(:,2))
xlabel('\alpha (deg)');ylabel('CL');grid
title('Comparison of CL vs. \alpha for all airfoils')
legend('N63A010','N63015A','N64012A','N64015','N64108','N64212','N66021','sc1012r8','sc2001
0','sc20012','sc20610','sc20612','sc20614','sc20714','sc20710','sc20712','sc21006','sc21010',-1);
%Compare CL vs. alpha for 4 best airfoils
figure (2)
plot(set_n64212(:,1),set_n64212(:,2),set_n64012A(:,1),set_n64012A(:,2),set_sc20010(:,1),set_sc
20010(:,2),set_sc20614(:,1),set_sc20614(:,2))
xlabel('\alpha (deg)');ylabel('CL');grid
title('Comparison of CL vs. \alpha for 4 best airfoils')
legend('NACA 64212','NACA 64012A','SC 20010','SC 20614',-1)
%Compare CD vs. CL for all airfoils
figure (3)
plot(set_n63A010(:,2),set_n63A010(:,3),set_n63015A(:,2),set_n63015A(:,3),set_n64012A(:,2),set
_n64012A(:,3),set_n64015(:,2),set_n64015(:,3),set_n64108(:,2),set_n64108(:,3),set_n64212(:,2),
set_n64212(:,3),set_n66021(:,2),set_n66021(:,3),set_sc1012r8(:,2),set_sc1012r8(:,3),set_sc2001
0(:,2),set_sc20010(:,3),set_sc20012(:,2),set_sc20012(:,3),set_sc20610(:,2),set_sc20610(:,3),set_
sc20612(:,2),set_sc20612(:,3),set_sc20614(:,2),set_sc20614(:,3),set_sc20714(:,2),set_sc20714(:
,3),set_sc20710(:,2),set_sc20710(:,3),set_sc20712(:,2),set_sc20712(:,3),set_sc21006(:,2),set_sc
21006(:,3),set_sc21010(:,2),set_sc21010(:,3))
xlabel('\alpha (deg)');ylabel('CD');grid
title('Comparison of CD vs. \alpha for all airfoils')
legend('N63A010','N63015A','N64012A','N64015','N64108','N64212','N66021','sc1012r8','sc2001
0','sc20012','sc20610','sc20612','sc20614','sc20714','sc20710','sc20712','sc21006','sc21010',-1);
%Compare CD vs. CL for 4 best airfoils
figure (4)
plot(set_n64212(:,2),set_n64212(:,3),set_n64012A(:,2),set_n64012A(:,3),set_sc20010(:,2),set_sc
20010(:,3),set_sc20614(:,2),set_sc20614(:,3))
xlabel('CL');ylabel('CD');grid
title('Comparison of CD vs. CL for 4 best airfoils')
legend('NACA 64212','NACA 64012A','SC 20010','SC 20614',-1)
%Compare L/D vs. alpha for all airfoils
figure (5)
plot(set_n63A010(:,1),set_n63A010(:,4),set_n63015A(:,1),set_n63015A(:,4),set_n64012A(:,1),set
_n64012A(:,4),set_n64015(:,1),set_n64015(:,4),set_n64108(:,1),set_n64108(:,4),set_n64212(:,1),
set_n64212(:,4),set_n66021(:,1),set_n66021(:,4),set_sc1012r8(:,1),set_sc1012r8(:,4),set_sc2001
0(:,1),set_sc20010(:,4),set_sc20012(:,1),set_sc20012(:,4),set_sc20610(:,1),set_sc20610(:,4),set_
sc20612(:,1),set_sc20612(:,4),set_sc20614(:,1),set_sc20614(:,4),set_sc20714(:,1),set_sc20714(:
,4),set_sc20710(:,1),set_sc20710(:,4),set_sc20712(:,1),set_sc20712(:,4),set_sc21006(:,1),set_sc
21006(:,4),set_sc21010(:,1),set_sc21010(:,4))
xlabel('\alpha (deg)');ylabel('L/D');grid
title('Comparison of L/D vs. \alpha for all airfoils')
legend('N63A010','N63015A','N64012A','N64015','N64108','N64212','N66021','sc1012r8','sc2001
0','sc20012','sc20610','sc20612','sc20614','sc20714','sc20710','sc20712','sc21006','sc21010',-1);
%Compare L/D vs. alpha for 4 best airfoils
figure (6)
plot(set_n64212(:,1),set_n64212(:,4),set_n64012A(:,1),set_n64012A(:,4),set_sc20010(:,1),set_sc
20010(:,4),set_sc20614(:,1),set_sc20614(:,4))
xlabel('\alpha (deg)');ylabel('L/D');grid
title('Comparison of L/D vs. \alpha for 4 best airfoils')
legend('NACA 64212','NACA 64012A','SC 20010','SC 20614',-1)
%Compare L/D vs. CL for all airfoils
figure (7)
plot(set_n63A010(:,2),set_n63A010(:,4),set_n63015A(:,2),set_n63015A(:,4),set_n64012A(:,2),set
_n64012A(:,4),set_n64015(:,2),set_n64015(:,4),set_n64108(:,2),set_n64108(:,4),set_n64212(:,2),
set_n64212(:,4),set_n66021(:,2),set_n66021(:,4),set_sc1012r8(:,2),set_sc1012r8(:,4),set_sc2001
0(:,2),set_sc20010(:,4),set_sc20012(:,2),set_sc20012(:,4),set_sc20610(:,2),set_sc20610(:,4),set_
sc20612(:,2),set_sc20612(:,4),set_sc20614(:,2),set_sc20614(:,4),set_sc20714(:,2),set_sc20714(:
,4),set_sc20710(:,2),set_sc20710(:,4),set_sc20712(:,2),set_sc20712(:,4),set_sc21006(:,2),set_sc
21006(:,4),set_sc21010(:,2),set_sc21010(:,4))
xlabel('CL');ylabel('L/D');grid
% title('Comparison of L/D vs. CL for all airfoils')
legend('N63A010','N63015A','N64012A','N64015','N64108','N64212','N66021','sc1012r8','sc2001
0','sc20012','sc20610','sc20612','sc20614','sc20714','sc20710','sc20712','sc21006','sc21010',-1);
%Compare L/D vs. CL for 4 best airfoils
figure (8)
plot(set_n64212(:,2),set_n64212(:,4),set_n64012A(:,2),set_n64012A(:,4),set_sc20010(:,2),set_sc
20010(:,4),set_sc20614(:,2),set_sc20614(:,4))
xlabel('CL');ylabel('L/D');grid
title('Comparison of L/D vs. CL for 4 best airfoils')
legend('NACA 64212','NACA 64012A','SC 20010','SC 20614',-1)
%Compare alpha vs. transistion x/c for all airfoils
figure (9)
plot(set_n63A010(:,5),set_n63A010(:,1),set_n63A010(:,6),set_n63A010(:,1),set_n63015A(:,5),set
_n63015A(:,1),set_n63015A(:,6),set_n63015A(:,1),set_n64012A(:,5),set_n64012A(:,1),set_n6401
2A(:,6),set_n64012A(:,1),set_n64015(:,5),set_n64015(:,1),set_n64015(:,6),set_n64015(:,1),set_n
64108(:,5),set_n64108(:,1),set_n64108(:,6),set_n64108(:,1),set_n64212(:,5),set_n64212(:,1),set_
n64212(:,6),set_n64212(:,1),set_n66021(:,5),set_n66021(:,1),set_n66021(:,6),set_n66021(:,1),set
_n642415(:,5),set_n642415(:,1),set_n642415(:,6),set_n642415(:,1),set_sc1012r8(:,5),set_sc1012
r8(:,1),set_sc1012r8(:,6),set_sc1012r8(:,1),set_sc20010(:,5),set_sc20010(:,1),set_sc20010(:,6),s
et_sc20010(:,1),set_sc20012(:,5),set_sc20012(:,1),set_sc20012(:,6),set_sc20012(:,1),set_sc206
10(:,5),set_sc20610(:,1),set_sc20610(:,6),set_sc20610(:,1),set_sc20612(:,5),set_sc20612(:,1),set
_sc20612(:,6),set_sc20612(:,1),set_sc20614(:,5),set_sc20614(:,1),set_sc20614(:,6),set_sc20614
(:,1),set_sc20714(:,5),set_sc20714(:,1),set_sc20714(:,6),set_sc20714(:,1),set_sc20710(:,5),set_s
c20710(:,1),set_sc20710(:,6),set_sc20710(:,1),set_sc20712(:,5),set_sc20712(:,1),set_sc20712(:,
6),set_sc20712(:,1),set_sc21006(:,5),set_sc21006(:,1),set_sc21006(:,6),set_sc21006(:,1),set_sc
21010(:,5),set_sc21010(:,1),set_sc21010(:,6),set_sc21010(:,1))
xlabel('X/C');ylabel('\alpha (deg)');grid
title('Comparison of \alpha vs. transistion along x/c for all airfoils')
legend('N63A010','N63A010','N63015A','N63015A','N64012A','N64012A','N64015','N64015','N64
108','N64108','N64212','N64212','N66021','N66021','sc1012r8','sc1012r8','sc20010','sc20010','sc2
0012','sc20012','sc20610','sc20610','sc20612','sc20612','sc20614','sc20614','sc20714','sc20714','
sc20710','sc20710','sc20712','sc20712','sc21006','sc21006','sc21010','sc21010',-1);
text(.25,14,'[Negative Slope - Top Transition, Positive Slope - Bottom Transition]')
%Compare alpha vs. transistion x/c for 4 best airfoils
figure (10)
plot(set_n64212(:,5),set_n64212(:,1),set_n64212(:,6),set_n64212(:,1),set_n64012A(:,5),set_n640
12A(:,1),set_n64012A(:,6),set_n64012A(:,1),set_sc20010(:,5),set_sc20010(:,1),set_sc20010(:,6),
set_sc20010(:,1),set_sc20614(:,5),set_sc20614(:,1),set_sc20614(:,6),set_sc20614(:,1))
xlabel('X/C');ylabel('\alpha (deg)');grid
title('Comparison of \alpha vs. transistion along x/c for 4 best airfoils')
legend('NACA 64212',' ','NACA 64012A',' ','SC 20010',' ','SC 20614',' ',-1)
text(.25,14,'[Negative Slope - Top Transition, Positive Slope - Bottom Transition]')
15.1.2
Raymer Analysis
%AAE 451 ECOJET
%Aerodynamic Analysis
%--------------------------------------------------clear;close all;clc;
%Wing Inputs
AR=8;
eta=.95;
swpc4=30*pi/180;
swphl=30*pi/180;
%Aspect Ratio
%airfoil efficiency
%Wing Sweep at C/4
%Hinge Line Angle of high-lift surface
swpm=28*pi/180;
%Wing Sweep at max thickness
WS=70;
%Wing Loading (lbs/sqft)
tpr=0.32;
%Taper Ratio = C_tip/C_root
Clmax=2.0;
%Airfoil max Cl
tc=0.10;
%Thickness to Chord Ratio
dy=20.3*tc;
%Leading Edge Sharpness Ratio (p329)
CLratio=0.89;
%(CLmax/Clmax) for 30 deg sweep (p330)
CLdelta=-0.5;
%Delta CLmax for M=.8 at dy=2.03 Approximation
CLdelta2=1.3;
%Slotted Flap additional lift gain
Cfe=0.0030;
%Estimated Skin Friction Coefficient (p341)
dflapto=30;
%Flap Angle for Takeoff (deg)
dflapla=70;
%Flap Angle for Landing (deg)
Fflap=0.0074;
%Flap coefficient for slotted flaps (p349)
e=1.05;
%Oswald Span Efficiency Factor for a Diamond Wing of Height/Span=0.2
xcm=.4;
%mean chordwise location of the maximum thickness position
%Mission Inputs
Vcr=480*1.68780986; %Velocity at Cruise (kts to ft/s)
W=25000;
%Weight of Aircraft (lbs)
l=50;
%Fuselage Length (ft)
d=7;
%Fuselage Diameter (ft)
Swet_fuse=1000;
%Fuselage Wetted Area (sqft)
Swet_tail=180;
%Tail Wetted Area (sqft)
l_eng=6;
%Engine Length (ft)
r_eng=2.5/2;
%Engine Radius (ft)
unit=1;
%Atmosphere Flag: 0=Metric, 1=English
alt=0;
%Altitude (ft)
g=32.17;
%Acceleration due to Gravity (ft/sec^2)
alfa=(-20:.01:20)*pi/180;
%Angle of Attack
alfa0=(-4.25+.7)*pi/180;
%Angle of Attack for Zero Lift
Re_fuse=7.59e7;
%Reynold's Number - Fuselage
Re_fwing=2.74e5;
%Reynold's Number - Fore Wing
Re_awing=2.19e5;
%Reynold's Number - Aft Wing
Re_wing=(Re_fwing+Re_awing)/2; %Reynold's Number - Average Wing
%--------------------------------------------------%Calculations
[t, p, rho, a] = atmosphere(alt, unit);
Speed of Sound]
%Atmosphere Data [Temperature, Pressure, Density,
q=.5*rho/g*Vcr^2;
%Dynamic Pressure at Cruise
Sref=W/WS;
%Reference Area
b=sqrt(AR*Sref);
%Wing Span
croot=2*Sref/(b*(1+tpr));
%Chord at Root (ft)
ctip=tpr*croot;
%Chord at Tip (ft)
cbar=(2/3)*croot*(1+tpr+tpr^2)/(1+tpr);
%Mean Aerodynamic Chord (ft)
cflap=.3*cbar;
%Flap Chord (ft)
Ybar=(b/6)*((1+2*tpr)/(1+tpr));
%Position of MAC
Sexp=Sref-d*croot;
%Exposed Area - Approximation
Sflap=.30*Sexp;
%Flap Reference Area (sqft)
Swet_wing=2.003*Sexp;
%Wetted Surface Area
swple=atan(tan(swpc4)+((1-tpr)/(AR*(1+tpr))));
%Sweep Angle at Leading Edge (rad)
swple_deg=swple*180/pi;
%Sweep Angle at Leading Edge (deg)
Mcr=Vcr/a;
Cl=1/q*WS;
%Cruise Mach Number
%1st Approximation of Cl
F=1.07*(1+d/b)^2;
%Fuselage Lift Factor
beta=sqrt(1-Mcr.^2);
%Mach number Correction Factor
Clalf=(2*pi*AR)/(2+sqrt(4+AR^2*beta^2/eta^2*(1+tan(swpc4)^2/beta^2)))*(Sexp/Sref)*F;
per alfa (rad)
CLmax=0.9*Clmax*cos(swpc4);
%Cl
%CLmax for Clean Aircraft
%Parasite Drag
%Fuselage
f=l/d;
Cf_fuse=.455/((log10(Re_fuse))^2.58*(1+.144*Mcr^2)^.65); %Skin Friction Coefficient
FF_fuse=1+60/f^3+f/400;
CDo_fuse=Cf_fuse*FF_fuse*Swet_fuse/Sref;
%Parasite Drag
%Engines
f_eng=l_eng/sqrt(4*r_eng^2);
FF_eng=1+.35/f_eng;
%Wings
FF_wing=(1+.6/xcm*tc+100*tc^4)*(1.34*Mcr^.18*cos(swpm)^.28);
Cflam=1.328/sqrt(Re_wing);
%Skin Friction Coefficient for Laminar Flow
Cfturb=0.455/((log10(Re_wing))^2.58*(1+0.144*Mcr^2)^0.65); %Skin Friction Coefficient for
Turbulent Flow
Cfe=(0.20*Cflam+0.80*Cfturb)/2;
%Weighted Average Skin Friction Coefficient
(20% Laminar)
CDo_wing=Cfe*FF_wing*(Swet_wing/Sref)
%Parasite (zero-lift drag)
%Vertical Tail
FF_tail=(1+.6/xcm*tc+100*tc^4)*(1.34*Mcr^.18);
CDo_tail=Cfe*FF_tail*Swet_tail/Sref;
%Total
CDo=CDo_fuse+CDo_wing+CDo_tail
CDleak=0.05*CDo;
CDi=(Clalf*alfa).^2/(pi*AR*e);
%Parasite Drag
%Leakage and Protuberance Drag 2-5% (p350)
%Induced Drag
CLmax2=CLmax*CLratio+CLdelta;
number and leading edge sharpness
DCLmax=0.9*CLdelta2*(Sflap/Sref)*cos(swphl);
devices
DCLmax_to=0.8*DCLmax;
DCLmax_la=0.6*DCLmax;
Dalf_la=15*pi/180*Sflap/Sref*cos(swphl);
Dalf_to=10*pi/180*Sflap/Sref*cos(swphl);
%High Aspect Ratio Correction for Mach
%Change in CLmax due to high-lift
%Change in CLmax at takeoff
%Change in CLmax at landing
%Change in alfa at zero lift for landing
%Change in alfa at zero lift for takeoff
DCDoflap_to=Fflap*(cflap/cbar)*(Sflap/Sref)*(dflapto-10); %CDo Change due to flaps at Take-off
DCDoflap_la=Fflap*(cflap/cbar)*(Sflap/Sref)*(dflapla-10); %CDo Change due to flaps at Landing
[x,y]=size(CDi);
CDo=CDo*ones(x,y);
CDleak=CDleak*ones(x,y);
CD=CDo+CDleak+CDi;
CDto=CD+DCDoflap_to;
CDla=CD+DCDoflap_la;
Srqd=W/(q*.45)
%Total CD @ Cruise
%Total CD @ Takeoff
%Total CD @ Landing
%Required Wing Planform Area
%V-n Diagram Creation
rhosl=.0023
Ve=0:.1:1200;
L=1.755*.5*rhosl*Ve.^2*Sref;
L3=-.68*.5*rhosl*Ve.^2*Sref;
n_mlift=L/W
Vmax=1116.4*.95
n2=1.5/(Vmax-Vcr)*Ve-6.35
n3=L3/W;
figure (1)
plot(Ve,n_mlift,Ve,3,Vmax,n_mlift, Ve,-1.5,Ve,n2,Ve,n3,Ve,0);grid
xlabel('Velocity (ft/sec)');ylabel('load factor (g''s)')
AXIS([0 1100 -2 3.5])
figure (2)
plot((alfa+alfa0)*180/pi,Clalf*alfa,alfa*180/pi,CLmax, (alfa+alfa0+Dalf_to)*180/pi, Clalf*alfa,
alfa*180/pi, CLmax+DCLmax_to, (alfa+alfa0+Dalf_la)*180/pi, Clalf*alfa, alfa*180/pi,
CLmax+DCLmax_la);grid
hold on; plot(3,-2:.01:2);
xlabel('\alpha (deg)');ylabel('C_L')
legend('Cruise','Cruise CLmax','Takeoff','Takeoff CLmax','Landing','Landing CLmax')
figure (3)
plot(CD,Clalf*alfa,CDto,Clalf*alfa,CDla,Clalf*alfa);grid
xlabel('C_D');ylabel('C_L')
AXIS([0 0.1 -2.0 2.0])
Atmosphere Subroutine
% function [t, p, rho, a] = atmosphere(height, unit)
% Richard Rieber
% rrieber@gmail.com
% Updated 3/17/2006
%
% Function to determine temperature, pressure, density, and speed of sound
% as a function of height. Function based on US Standard Atmosphere of
% 1976. All calculations performed in metric units, but converted to
% english if the user chooses. Assuming constant gravitational
% acceleration.
%
% Input o h (feet or meters)
%
o unit - optional; default is metric;
%
boolean, True for english units, False for metric
% Output o t - Temperature (K (default) or R)
%
o p - Pressure (pa (default) or psi)
%
o rho - Density (kg/m^3 (default) or lbm/ft^3)
%
o a - speed of sound (m/s (default) or ft/s)
function [t, p, rho, a] = atmosphere(height,unit)
if nargin < 1
error('Error: Not enough inputs: see help atmosphere.m')
elseif nargin > 2
error('Error: Too few inputs: see help atmosphere.m')
elseif nargin == 2
unit = logical(unit);
elseif nargin == 1
unit = 0;
end
if height < 0
error('Height should be greater than 0')
end
m2ft = 3.2808;
K2R = 1.8;
pa2psi = 1.450377377302092e-004;
kg2lbm = 2.20462262184878;
if unit
height = height/m2ft;
end
g = 9.81;
%Acceleration of gravity (m/s/s)
gamma = 1.4; %Ratio of specific heats
R = 287;
%Gas constant for air (J/kg-K)
%Altitudes (m)
Start = 0;
H1 = 11000;
H2 = 20000;
H3 = 32000;
H4 = 47000;
H5 = 51000;
H6 = 71000;
H7 = 84852;
%Lapse Rates (K/m)
L1 = -0.0065;
L2 = 0;
L3 = .001;
L4 = .0028;
L5 = 0;
L6 = -.0028;
L7 = -.002;
%Initial Values
T0 = 288.16; %(k)
P0 = 1.01325e5; %(pa)
Rho0 = 1.225; %(kg/m^3)
if height <= H1
[TNew, PNew, RhoNew] = Gradient(Start, height, T0, P0, Rho0, L1);
elseif height > H1 & height <= H2
[TNew, PNew, RhoNew] = Gradient(Start, H1, T0, P0, Rho0, L1);
[TNew, PNew, RhoNew] = IsoThermal(H1, height, TNew, PNew, RhoNew);
elseif height > H2 & height <= H3
[TNew, PNew, RhoNew] = Gradient(Start, H1, T0, P0, Rho0, L1);
[TNew, PNew, RhoNew] = IsoThermal(H1, H2, TNew, PNew, RhoNew);
[TNew, PNew, RhoNew] = Gradient(H2, height, TNew, PNew, RhoNew, L3);
elseif height > H3 & height <= H4
[TNew, PNew, RhoNew] = Gradient(Start, H1, T0, P0, Rho0, L1);
[TNew, PNew, RhoNew] = IsoThermal(H1, H2, TNew, PNew, RhoNew);
[TNew, PNew, RhoNew] = Gradient(H2, H3, TNew, PNew, RhoNew, L3);
[TNew, PNew, RhoNew] = Gradient(H3, height, TNew, PNew, RhoNew, L4);
elseif height > H4 & height <= H5
[TNew, PNew, RhoNew] = Gradient(Start, H1, T0, P0, Rho0, L1);
[TNew, PNew, RhoNew] = IsoThermal(H1, H2, TNew, PNew, RhoNew);
[TNew, PNew, RhoNew] = Gradient(H2, H3, TNew, PNew, RhoNew, L3);
[TNew, PNew, RhoNew] = Gradient(H3, H4, TNew, PNew, RhoNew, L4);
[TNew, PNew, RhoNew] = IsoThermal(H4, height, TNew, PNew, RhoNew);
elseif height > H5 & height <= H6
[TNew, PNew, RhoNew] = Gradient(Start, H1, T0, P0, Rho0, L1);
[TNew, PNew, RhoNew] = IsoThermal(H1, H2, TNew, PNew, RhoNew);
[TNew, PNew, RhoNew] = Gradient(H2, H3, TNew, PNew, RhoNew, L3);
[TNew, PNew, RhoNew] = Gradient(H3, H4, TNew, PNew, RhoNew, L4);
[TNew, PNew, RhoNew] = IsoThermal(H4, H5, TNew, PNew, RhoNew);
[TNew, PNew, RhoNew] = Gradient(H5, height, TNew, PNew, RhoNew, L6);
elseif height > H6 & height <= H7
[TNew, PNew, RhoNew] = Gradient(Start, H1, T0, P0, Rho0, L1);
[TNew, PNew, RhoNew] = IsoThermal(H1, H2, TNew, PNew, RhoNew);
[TNew, PNew, RhoNew] = Gradient(H2, H3, TNew, PNew, RhoNew, L3);
[TNew, PNew, RhoNew] = Gradient(H3, H4, TNew, PNew, RhoNew, L4);
[TNew, PNew, RhoNew] = IsoThermal(H4, H5, TNew, PNew, RhoNew);
[TNew, PNew, RhoNew] = Gradient(H5, height, TNew, PNew, RhoNew, L6);
[TNew, PNew, RhoNew] = Gradient(H6, height, TNew, PNew, RhoNew, L7);
else
error('Height is out of range')
end
t = TNew;
p = PNew;
rho = RhoNew;
a = (R*gamma*t)^.5;
if unit
t = t*K2R;
p = p*pa2psi;
rho = rho*kg2lbm/m2ft^3;
a = a*m2ft;
end
function [TNew, PNew, RhoNew] = Gradient(Z0, Z1, T0, P0, Rho0, Lapse)
g = 9.81;
%Acceleration of gravity (m/s/s)
gamma = 1.4; %Ratio of specific heats
R = 287;
%Gas constant for air (J/kg-K)
TNew = T0 + Lapse*(Z1 - Z0);
PNew = P0*(TNew/T0)^(-g/(Lapse*R));
% RhoNew = Rho0*(TNew/T0)^(-(g/(Lapse*R))+1);
RhoNew = PNew/(R*TNew);
function [TNew, PNew, RhoNew] = IsoThermal(Z0, Z1, T0, P0, Rho0)
g = 9.81;
%Acceleration of gravity (m/s/s)
gamma = 1.4; %Ratio of specific heats
R = 287;
%Gas constant for air (J/kg-K)
TNew = T0;
PNew = P0*exp(-(g/(R*TNew))*(Z1-Z0));
% RhoNew = Rho0*exp(-(g/(R*TNew))*(Z1-Z0));
RhoNew = PNew/(R*TNew);
%Ben Scott
%Senior Design
%Flight Performance envelope calculation
clc
clear
close all
%Creates atmosphere data needed
Homework5part1;
clc
Densitytakeoff = TropoDens(1:7);
DensityClimb = TropoDens(7:37);
Densitycruise = [TropoDens(37) StrataDens(1:9)];
CruiseAlt = [TropoAlt(37) StrataAlt(1:9)];
%Assign different Cl values to different portions of the flight mission
Cltakeoff = linspace(1.5,1.2,length(Densitytakeoff));
ClClimb = linspace(1.2,.8,length(DensityClimb));
Clcruise = linspace(.8,1,length(Densitycruise));
%Assign Wing Loading
WingLoad = 73;
%Calculate Vstall using Raymer equation
VstallCruise = sqrt(2*WingLoad./(Densitycruise.*Clcruise)); %ft/s
VstallTakeoff= sqrt(2*WingLoad./(Densitytakeoff.*Cltakeoff)); %ft/s
VstallClimb = sqrt(2*WingLoad./(DensityClimb.*ClClimb));
%ft/s
%Set Cruise Altitude at 410000 ft
CruisAlt = 41000+0*Alpha;
%Plot All Three Stall Conditions
plot(VstallCruise,[CruiseAlt],'b'...
,VstallTakeoff,TropoAlt(1:7),'g',VstallClimb,TropoAlt(7:37),'r')
xlabel('V_s_t_a_l_l (ft/s)')
ylabel('Altitude (ft)')
title('Stall Speed Performance Plot')
legend('Cruise','Take Off','Climb')
grid on
hold on
%Plot Cruise Altitude
plot((linspace(0,700,length(CruisAlt))),CruisAlt,'g')
text(280,42000,'Cruise Altitude')
15.2 Structures
15.2.1
Composite material properties calculation code
%Gaetano Settineri
%AAE 451
%This will calculate the effective moduli for SYMMETRIC LAMINATES ONLY
%Units are english standard
clear all
close all
clc
%Lamina Properties
E1=20305283.3; %psi
E2=1450377.38 ; %psi
G12=1015264.16 ; %psi
nu12=0.3;
t=0.005; %Ply thickness (inches)
z=[-7.5 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 45 5.5 6.5 7.5]*t; %Distance from midplane
of layup to ply centroids
theta=[pi/4 -pi/4 0 pi/2 pi/2 0 -pi/4 pi/4 pi/4 -pi/4 0 pi/2 pi/2 0 -pi/4 pi/4]; %Orientation angles for
layup 1
A=zeros(3,3);
B=zeros(3,3);
D=zeros(3,3);
for j=1:1:length(theta)
A=A+Q_matrix(E1,E2,G12,nu12,theta(j))*t;
B=B+Q_matrix(E1,E2,G12,nu12,theta(j))*t*z(j);
D=D+Q_matrix(E1,E2,G12,nu12,theta(j))*(t*z(j)^2+t^3/12);
end
A=A^-1;
Ex=1/(8*t*A(1,1));
Ey=1/(8*t*A(2,2));
nu_xy=-A(1,2)/A(1,1);
nu_yx=-A(1,2)/A(2,2);
Gxy=1/(8*t*A(3,3));
eta_xyx=A(1,3)/A(3,3);
eta_xyy=A(2,3)/A(3,3);
%Gaetano Settineri
%This function calculates the Q matrix of a single composite ply based on
%its orientation
function [Q_bar]=Q_matrix(E1,E2,G12,nu12,theta)
nu21=E2/E1*nu12;
Q11=E1/(1-nu12*nu21);
Q12=nu12*E2/(1-nu12*nu21);
Q22=E2/(1-nu12*nu21);
Q66=G12;
Q_11=Q11*cos(theta)^4+2*(Q12+2*Q66)*sin(theta)^2*cos(theta)^2+Q22*sin(theta)^4;
Q_12=(Q11+Q22-4*Q66)*sin(theta)^2*cos(theta)^2+Q12*(sin(theta)^4+cos(theta)^4);
Q_22=Q11*sin(theta)^4+2*(Q12+2*Q66)*sin(theta)^2*cos(theta)^2+Q22*cos(theta)^4;
Q_26=(Q11-Q12-2*Q66)*sin(theta)^3*cos(theta)+(Q12-Q22+2*Q66)*sin(theta)*cos(theta)^3;
Q_16=(Q11-Q12-2*Q66)*sin(theta)*cos(theta)^3+(Q12-Q22+2*Q66)*sin(theta)^3*cos(theta);
Q_66=(Q11+Q22-2*Q12-2*Q66)*sin(theta)^2*cos(theta)^2++Q66*(sin(theta)^4+cos(theta)^4);
Q_bar=[Q_11 Q_12 Q_16; Q_12 Q_22 Q_26; Q_16 Q_26 Q_66];
15.3 Propulsion
Engine Trade Study
1.4
1.2
1
0.8
SFC
Fan Pressure
Bypass
0.6
Reasonable SFC with
higher cruise thrust
Best SFC value but low
cruise thrust
0.4
0.2
0
0
1
2
3
4
5
Pressure / Bypass Ratio
Figure 34: Pressure / Bypass Ratio Trade Study
6
Table 17: ONX Inputs for sea level thrust
ONX V3.23 - On-Design Calculations File: C:\Program Files\AED/onx.onx
Turbofan Engine with Two Exhausts & Conv. Nozzles
**********************
Input Data
**********************
Mach No = 0.010
Alpha
= 3.200
Alt (ft) = 1
Pi C'
= 2.900
T0 (R) = 518.69
Pi D (max) = 0.980
P0 (psia) = 14.695
Pi B
= 0.980
Density = .0023773
Pi N
= 0.980
(Slug/cuft)
Pi N'
= 0.980
Efficiency
Cp C
= 0.2380 Btu/lbm-R
Burner
= 0.980
Cp T
= 0.2950 Btu/lbm-R
Mech Hi Pr = 0.950
Gamma C = 1.4000
Mech Lo Pr = 0.950
Gamma T = 1.3800
LP Comp (Fan)= 0.920 (ec')
Tt4 max = 2600.0 R
HP Comp
= 0.920 (ecH)
h - fuel = 16108 (Btu/lbm)
HP Turbine = 0.890 (etH)
CTO Low = 0.0100
LP Turbine = 0.890 (etL)
CTO High = 0.0000
Pwr Mech Eff L = 0.890
Cooling Air #1 = 5.000 %
Pwr Mech Eff H = 0.850
Cooling Air #2 = 5.000 %
Bleed Air
= 1.000 %
************************* RESULTS *************************
Tau R = 1.000
a0 (ft/sec) = 1116.3
Pi R
= 1.000
V0 (ft/sec) = 11.2
Pi D
= 0.980
Mass Flow = 135.0 lbm/sec
Tau L = 6.213
Area Zero =158.108 sqft
PTO Low = 175.84 KW
Area Zero* = 2.732 sqft
PTO High = 0.00 KW
Tau C' = 1.3919
Pt5'/P0
= 2.842
Eta C' = 0.9073
Tt5'/T0
= 1.3919
Pt9'/P9' = 1.8929
P0/P9'
= 0.6796
M9 ' = 1.0000
V9'/V0
=107.6998
Pi C
= 20.000
Tau M1
= 0.9694
Pi CH = 6.897
Tau M2
= 0.9769
Tau CH = 1.8216
Eta CH
= 0.8961
Pi TH = 0.3887
Eta TH
= 0.9023
Tau TH = 0.7933
Pi TL = 0.1465
Eta TL
= 0.9141
Tau TL = 0.6245
V9/V0 = 52.565
P9/P0 =
M9/M0 = 31.890
Pt9/P0 = 1.072
A9/A0 = 0.0127
f
= 0.03023
Thrust = 5273 lbf
fo
= 0.00641
F/mdot = 39.056 lbf/(lbm/s)
S
= 0.5904 (lbm/hr)/lbf
T9/T0 = 2.3073
Table 18: ONX Inputs for cruise level thrust
ONX V3.23 - On-Design Calculations File: C:\Program Files\AED/onx.onx
Turbofan Engine with Two Exhausts & Conv. Nozzles
**********************
Input Data
**********************
Mach No = 0.850
Alpha
= 3.200
Alt (ft) = 41000
Pi C'
= 2.900
T0 (R) = 390.00
Pi D (max) = 0.980
P0 (psia) = 2.602
Pi B
= 0.980
Density = .0005598
Pi N
= 0.980
(Slug/cuft)
Pi N'
= 0.980
Efficiency
Cp C
= 0.2380 Btu/lbm-R
Burner
= 0.980
Cp T
= 0.2950 Btu/lbm-R
Mech Hi Pr = 0.950
Gamma C = 1.4000
Mech Lo Pr = 0.950
Gamma T = 1.3800
LP Comp (Fan)= 0.920 (ec')
Tt4 max = 2600.0 R
HP Comp
= 0.920 (ecH)
h - fuel = 16108 (Btu/lbm)
HP Turbine = 0.890 (etH)
CTO Low = 0.0100
LP Turbine = 0.890 (etL)
CTO High = 0.0000
Pwr Mech Eff L = 0.890
Cooling Air #1 = 5.000 %
Pwr Mech Eff H = 0.850
Cooling Air #2 = 5.000 %
Bleed Air
= 1.000 %
************************* RESULTS *************************
Tau R = 1.145
a0 (ft/sec) = 968.0
Pi R
= 1.604
V0 (ft/sec) = 822.8
Pi D
= 0.980
Mass Flow = 40.0 lbm/sec
Tau L = 8.263
Area Zero = 2.699 sqft
PTO Low = 39.17 KW
Area Zero* = 2.644 sqft
PTO High = 0.00 KW
Tau C' = 1.3919
Pt5'/P0
= 4.558
Eta C' = 0.9073
Tt5'/T0
= 1.5930
Pt9'/P9' = 1.8929
P0/P9'
= 0.4238
M9 ' = 1.0000
V9'/V0
= 1.3555
Pi C
= 20.000
Tau M1
= 0.9665
Pi CH = 6.897
Tau M2
= 0.9726
Tau CH = 1.8216
Eta CH
= 0.8961
Pi TH = 0.4496
Eta TH
= 0.9005
Tau TH = 0.8221
Eta TL
= 0.9094
Pi TL = 0.2172
A9/A0 = 0.2501
Tau TL = 0.6878
Thrust = 1151lbf
P9/P0 =
Pt9/P0 = 1.881
f
= 0.0333
fo
= 0.00702
F/mdot = 28.971 lbf/(lbm/s)
S
= 0.8825 (lbm/hr)/lbf
T9/T0 = 2.9779
Table 19: Baseline Engine TFE731-5AR
Component
Cruise Mach
Cruise Alt
Overall Pressure Ratio (OPR)
Bypass Ratio (Beta)
Fan Pressure Ratio (FPR)
Turbine Inlet Temp (TIT)
Jet-A Heating Value
Value
.8
40000 ft
14.6
3.65
3.48
2600 R
18400 BTU/lbm
Table 20: ONX Comparison for Baseline Engine TFE731-5AR
Parameter
SFC
Cruise Thrust
ONX Value
.777
1088 lbf
Actual Value
.771
986 lbf
Table 21: Baseline Engine TFE731-3B-100
Component
Cruise Mach
Cruise Alt
Overall Pressure Ratio (OPR)
Bypass Ratio (Beta)
Fan Pressure Ratio (FPR)
Turbine Inlet Temp (TIT)
Jet-A Heating Value
Value
.8
40000 ft
14.6
2.8
2.8
2600 R
18400 BTU/lbm
Table 22: ONX Comparison for Baseline Engine TFE731-3B-100
Parameter
SFC
Cruise Thrust
V9/V0 = 2.203
M9/M0 = 1.176
ONX Value
.817
1042 lbf
Actual Value
.816
844 lbf
15.4 Cost Analysis
15.4.1
Direct Operating Cost
Table 23: Direct Operating Cost
Variable Cost (Hourly)
Citation Excel Hawker 400 LearJet 45
EcoJet
Fuel Expense
$907.97
$801.76
$828.15
$492.94
Cost of Fuel (per gal)
$4.18
$4.18
$4.18
$3.62
Fuel Consumption (gal/h)
217
102.4
198
136
Maintenance Labor Expense
$182.33
$102.40
$47.30
$200.00
Parts Expense
$147.26
$59.11
$68.00
$200.00
Misc. Trip Expense
$165.46
$93.48
$165.46
$170.00
Jet Category
< 20,000 lbs < 20,000 lbs > 20,000 lbs > 20,000 lbs
Class
3
2
3
3
Total Variable Costs
$1,403.02
$1,056.75
$1,108.91
$1,062.94