PENGUIN AEROSPACEEmperor M160-3 Supersonic Business Jet

MAE 154A – Preliminary Design of Aircraft

Professor O.O. Bendiksen

Group Members:

Dylan Fagrey (Weights, CG, Layout)

Lowell Mansilla (Propulsion and Performance)

Cullen McAlpine (Aerodynamics)

Jason Ro (Stability and Control, CG)

1

Elmer Wu (Aerodynamics)

2

TABLE OF CONTENTSLIST OF FIGURES 3

LIST OF TABLES 3

INTRODUCTIONS 5

AIRCRAFT LAYOUT AND DESIGN 6

LAYOUT CONSIDERATIONS 6EXTERIOR LAYOUT 7INTERIOR LAYOUT 12CENTER OF GRAVITY 17

AERODYNAMICS 20

PLANFORM SELECTION 20SUBSONIC AERODYNAMICS 23

Cruise Performance 23Takeoff and Landing Performance 26

SUPERSONIC AERODYNAMICS 28Layout and Configuration 28Cruise Performance 29

PROPULSION AND PERFORMANCE 31

ENGINE SELECTION 31RATE OF CLIMB 31ABSOLUTE AND SERVICE CEILING 33CRUISING AND MAXIMUM MACH NUMBERS 35

STABILITY AND CONTROL 38

CENTER OF GRAVITY 39AERODYNAMIC CENTER 39NEUTRAL POINT AND STATIC MARGIN 40MOMENT COEFFICIENT WITH RESPECT TO ANGLE OF ATTACK 42TRIM ANALYSIS 43FUEL MANAGEMENT 46

STRUCTURES AND MATERIALS 47

CONCLUSION 48

RANGE BENEFITS 48LAYOUT AND CONFIGURATION 48

REFERENCES 50

APPENDIX 51

APPENDIX A: LAYOUT AND CONFIGURATION 51AIRCRAFT WEIGHT ESTIMATION EQUATIONS 53

APPENDIX B: AERODYNAMICS 55APPENDIX C: PROPULSION AND PERFORMANCE 60APPENDIX D: STABILITY AND TRIM 61

3

LIST OF FIGURESFigure 1: Side View 8Figure 2: Front View 8Figure 3: Top View 9Figure 4: Overturn Angle, Main Landing Gear (Sadraey, 2012) 11Figure 5: Interior Cabin Dimensions 12Figure 6: Interior Cabin Layout 13Figure 7: Fuel Tank Locations 15Figure 8: Transonic Area Plot 16Figure 9: L/D vs. sweep angle at various Mach numbers 20Figure 10: Lift coefficient vs. sweep angle for each Mach number 21Figure 11: Drag coefficient vs. sweep angle at each Mach number 21Figure 12: Optimized Wing Planform Dimensions 23Figure 13: Rate of Climb vs. Altitude 33Figure 14: Available and Required Thrust at Altitudes 34Figure 15: Trim Plot Subsonic Case 1 Loading Conditions 44Figure 16: Trim Plot Supersonic Case 1 Loading Conditions 44Figure 17: Engineering Drawing 51Figure 18: Maximum Cl Approximations by Nicolai 54Figure 19: Raymer Table B.1 (continued on next page) 57Figure 20: Empirical Pitching Moment Factor 62Figure 21: Downwash Estimation M = 0 63Figure 22: Subsonic Trim Plots M = .96 65Figure 23: Supersonic Trim Plots at M = 1.8 67

LIST OF TABLESTable 1: Similar Business Jet Dimensions 6Table 2: Landing Gear Wheel Track Calculations 11Table 3: Volumes and Surface Areas 16Table 4: Interior Cabin Volumes 17Table 5: Loading Conditions 18Table 6: Center of Gravity Locations 18Table 7: CFD Flight Parameters 24Table 8: Supersonic Interpolation Data 29Table 9: Rate of Climb 32Table 10: Absolute and Service Celing 34Table 11: Induced and Wave Drag Estimations 35Table 13: Static Margins for Loading Cases 41Table 14: CMα for Loading Cases 42Table 15: Angle of Attack and Elevator Deflections for Loading Cases 45Table 16: Weight Breakdown by Component 50

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Table 17: Iterative CFD Data (continued on next page) 55Table 18: Rate of Climb at Varying Altitudes 59Table 19: Weight Distribution Breakdown 60Table 20: Relevant Stability Coefficients 61Table 21: Subsonic Loading Conditions at M = .96 64Table 22: Supersonic Loading Conditions at M = 1.8 66

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INTRODUCTIONSIn a world of growing corporate connections and interdependence, the need for

supersonic business travel is growing significantly. While social media and internet related

technology can provide some solutions to problems involving long distance business operations,

often for general travel, supervising purposes and brokering critical business transactions,

physical travel is necessary. For busy CEOs, movie moguls, and other VIPs, time is often even

more important than money, and a supersonic business jet could provide a relaxing, efficient, and

most importantly, quick method of travel. There are a few popular concepts and current business

jets that provide luxury and speed, but few can accomplish both.

This report summarizes design considerations for a supersonic business jet based

primarily on the Aerion AS2 that would be optimized for both near sonic and supersonic cruise

while maintaining a high standard of comfort. The aircraft is designed to transport 8 to 12

executive passengers, including 2 passengers and a flight attendant. The business jet will cruise

between 45,000 and 49,000 feet and ideally would have a range of about 4000 nautical miles at a

subsonic speed of Mach .93, with the potential for supersonic cruise at Mach 1.8 with a range of

1900 nautical miles; maximum operating speed will be at Mach 1.9. Since FAA regulations do

not currently permit supersonic travel over the United States, the designed aircraft would utilize

the subsonic cruise specifications over the mainland and accelerate to supersonic speeds outside

of the mainland to uphold quick travel requirements.

The remainder of the report will describe a baseline design and aircraft layout as well as

discuss all aerodynamic, propulsion, performance, and stability calculations that pertain to the

required design parameters.

6

7

AIRCRAFT LAYOUT AND DESIGN Originally we based our aircraft design on the Aerion AS2, using its dimensions and

component locations. As we progressed with our calculations for aerodynamics, propulsion, and

stability we altered our layout based on functionality while maintaining a certain degree of

aesthetics.

Layout Considerations To begin the process of designing the Emperor, initial research was conducted of supersonic

and high-subsonic business jets in the market to get an idea of the sizing of the fuselage and the

dimensions of the passenger cabin. Basic measurements and weights were recorded for aircraft

such as the Aerion AS2 supersonic business jet, the Gulfstream G650 and G650ER high-

subsonic jets, and other, smaller business jets. The data found was used to size the fuselage of

our aircraft accordingly to provide maximum comfort and space for the passengers while also

minimizing negative performance effects. This research is compiled in Table 1.

Table 1: Similar Business Jet Dimensions

Aircraft Length (ft, in)

Width (ft, in)

Height (ft, in)

Cabin Length (ft, in)

Cabin Width (ft, in)

Cabin Height (ft, in)

Aerion AS2 160' 70' 27' 30' 7' 3" 6' 2"Gulfstream G650 99' 9" 99' 7" 25' 8" 53' 7" 8' 6" 6' 5"Gulfstream G650ER

99' 9" 99' 7" 25' 8" 47' 8' 6" 6' 5"

Gulfstream G550 96' 5" 93' 6" 25' 10" 43' 11" 7' 5" 6' 2"Bombardier Challenger 650

87' 10" 69' 7" 20' 5" 40' 3" 7' 11" 6'

Learjet 75 58' 50' 11" 14' 19' 9" 5' 1" 5'Hawker 800XP 51' 2" 51' 4" 18' 1" 21' 3" 6' 5' 9"

As the table shows, the Gulfstream G650 and G650ER have the largest cabin width and

standup height in the private business jet class. As a way of ensuring maximum comfort for our

passengers, we decided to imitate the interior dimensions of the G650 for our fuselage

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dimensions, while the exterior dimensions more closely resembled the Aerion AS2 due to the

supersonic capability and the need for fuel storage, wing sweep, and other factors. The

Emperor’s design predecessor was ultimately the Aerion, as it is the only supersonic business jet

that is far along in the design process. Other considerations that were necessary for supersonic

performance were also considered, such as highly swept wings and a tapered fuselage section,

which will be described in greater detail in the following section.

EXTERIOR LAYOUT The fuselage size was an estimate based on the Aerion AS2, and is set to 110 feet from the

nose to the back end of the tail cone, while the length from the nose to the end of the tail surfaces

is 120 feet. The total wingspan of the Emperor is 98.6 feet, and the total height from landing gear

to the tip of the T-tail is 35.4 feet. These dimensions are illustrated below in Figures 1, 2, and 3.

Engineering drawings of the Emperor are located in Appendix A. As is best shown in the top

view of the Emperor, the fuselage is tapered to attempt to follow the transonic area rule and

achieve better supersonic performance. The explanation and area-rule plots are located below, in

the Weights, Areas, and Volumes section.

9

Figure 1: Side View

Figure 2: Front View

110’ 0”

35’5”

98’ 7”

37’ 4”

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Figure 3: Top View

A 10 foot Von Karman nose cone was also chosen in order to reduce drag while satisfying the

FAR requirement of a 15° line-of-sight for the pilots on takeoff and landing. The Emperor’s

pilots have a 16.07° LOS, which eliminates the need for a “Pinocchio” nose or a droop-nose like

that of the Concorde. The Von Karman shape is the conventional nose used on most supersonic

fighters due to its ideality at higher Mach numbers.

The Emperor uses a low-mounted wing and high T-tail configuration, and the sizings for the

lifting bodies are located in the Aerodynamics and Stability Sections. Due to the presence of the

two fuselage-mounted engines, a T-tail is required to avoid unwanted downwash effects on the

horizontal stabilizers from the engine exhaust. Both the horizontal and vertical tails use a NACA

0012 symmetric airfoil. The tail planform area was determined to be 450 ft2 through stability

calculations, and the tail span was determined to be 37.35 feet with an aspect ratio of 3.1, a

sweep of 49°, and an incidence angle of -2.4°. The vertical stabilizer was sized using engine-out

estimations discussed in the Stability and Control Section, and was determined to be 14 feet in

span with a 0° trailing edge sweep.

120’ 0”

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In order to achieve enough thrust for supercruise, a tri-jet configuration was chosen for the

Emperor. Two BruinJet205 low-bypass turbofan engines are mounted on vibration-dampening

pylons to the fuselage behind the wings, at a distance of 92 feet from the nose. A third BJ205 is

mounted at the top of the fuselage above the tail, and the vertical stabilizer originates from the

top surface of that engine. The engines were placed where they are on the Emperor for a variety

of reasons. The main reason is that fuselage-mounted engines provide “clean” aerodynamics for

the wings, meaning that the wing can be optimally designed without having to take into account

mounting pylons or the additional weight of the engines on the wing. It also shortens the ground

clearance needed, which means that longer, complicated landing gear is not needed to

compensate for the wing mounts. Finally, by choosing the fuselage-mounted engines, it allows

for a quieter passenger cabin, and is the norm for most business jets on the market today.

The main landing gear of the Emperor was placed 79 feet from the nose, at a lateral spacing

of 5 feet from the centerline of the aircraft. In order to provide 11° of clearance for the takeoff

transition distance, the landing gear is set to hydraulically extend to 8 ft below the fuselage. The

wheel track of the main gear was determined using the equation involving the overturn angle of

the aircraft:

Y OT=HCG tanΦOT

where YOT is the wheel track, HCG is the vertical distance from the runway to the center of gravity

of the aircraft, and ΦOT is the overturn angle, as is illustrated in Figure 4.

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Figure 4: Overturn Angle, Main Landing Gear (Sadraey, 2012)

The recommended envelope for the overturn angle is ΦOT ≥25 ° .Because of the slender

fuselage of the Emperor, a conservative overturn angle of 26° was chosen, which resulted in a

wheel track of 4.66 feet. As 4.66 feet was the minimum wheel track for stable taxiing, it was

rounded up to 5 feet for safety. The calculations for HCG as well as the wheel track are located in

Table 2.

Table 2: Landing Gear Wheel Track Calculations

Component CG Height, ft Weight, lbsForward Engines 11.79 10722.44Fuselage 10.25 8654.02Wings 8.00 12754.93Aft Engine 17.33 5361.22Horizontal Stabilizers 35.00 1585.92Vertical Stabilizer 26.00 1036.67Payload 10.50 3120.00Systems 8.50 11816.82Fuel 8.00 64100.00 Total CG Height, ft Overturn Angle, rad Landing Gear Lateral Spacing, ft

9.56 0.45 4.66

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INTERIOR LAYOUT

Figure 5: Interior Cabin Dimensions

As shown in Figure 5, the main cabin fuselage has an interior centerline width of 8’2”

(allowing for 2” of exterior skin thickness) and has a height of 6’4” to accommodate taller

passengers. This allows for 2’ 2” of space under the cabin for controls, wiring, and structural

necessities. For the Emperor, we have chosen a sleek and streamlined double-club configuration:

on either side of the fuselage are three sets of two seats each, with a table for each set. In order to

provide adequate room for passengers to spread out, the cabin has been chosen at a length of 65

feet from the cockpit doors. A full galley and lavatory are also provided on the Emperor, fore

and aft of the passenger cabin, respectively. Finally, at the farthest aft in the cabin, is a luggage

compartment with a capacity of approximately 230 cubic feet. The configuration of the cabin is

outlined below in Figure 6.

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Figure 6: Interior Cabin Layout

An engineering drawing of the interior dimensions is also provided in Appendix A. The seats

that we have chosen provide top-of-the line luxury and comfort, at 24” wide and 48” tall,

allowing for an approximately 26” aisle in the seating area. At maximum passenger capacity, the

Emperor can carry 12 passengers, 1 crew member, and 2 pilots plus 60 lbs of luggage per

passenger.

WEIGHTS, AREAS, AND VOLUMES

Statistical weight estimations were used for each individual component of the aircraft.

Using Equations 15.46 - 15.49 and 15.52 - 15.58 from Raymer’s Aircraft Design: A Conceptual

Approach, as well as landing gear weight estimations found in Torenbeek’s Synthesis of

Subsonic Airplane Design and control systems estimates from Sadraey’s Aircraft Design: A

Systems Engineering Approach, the weight of each individual component was calculated and

summed to determine the total weight of the Emperor. The weight breakdown is contained in

Table 16 in Appendix A:

The statistical estimation equations are listed in the Appendix under Aircraft Weight

Estimation Equations. In order to compensate for the size of the Emperor and its capabilities,

composite materials were used extensively in the construction of our aircraft to reduce weight

15

where needed. Using so-called fudge factors located in the Weight Estimation section in Raymer,

the weights of components such as the wings, fuselage, tail surfaces, and engine housings were

reduced by factors of 10-20%. This allowed the Emperor to drop a significant amount of

structural weight (which could then be replaced with fuel) while remaining under the MTOW

conditions for the lifting surfaces and takeoff calculations. The Emperor also uses titanium

landing gear in order to reduce weight further. Titanium was chosen due to its high strength-to-

weight ratio, and it allowed a reduction in weight from traditional steel landing gear of 43%. The

high price of titanium is a non-issue in our case, as it will be negligible compared to the aircraft

price.

In the Emperor, the fuel is contained within two wing tanks as well as a reinforced tank

underneath the fuselage to protect against rupture. The fuel chosen for this aircraft is Jet A-1,

with a density of 6.71 lbs/gal. With 64,100 lbs of fuel, there are approximately 9,552 gallons of

fuel carried onboard in max range configuration. The wing tanks in the Emperor consist of 70%

of the wing volume, for a value of 426.17 ft3, or 3187.95 gallons per wing, which corresponds to

42782.34 lbs of fuel in the combined wing tanks. The remaining fuel is placed in the fuselage

tank, which has a volume of 424.70 ft3 (3177 gal) and a weight of 21317.65 lbs. The fuel was

placed under the wings and fuselage in order to avoid a large CG shift as fuel was expended, and

also eliminates the need for trim tanks. A fuel pumping plan is discussed in the Stability and

Control section. A diagram of the fuel tanks is located below in Figure 7:

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Figure 7: Fuel Tank Locations

Once the aircraft was assembled in SolidWorks, a series of surface area and volume

calculations were carried out. Firstly, the cross-sectional area was taken every 5 feet for the

entire length of the Emperor for transonic area rule calculations. The plot of these areas is shown

in Figure 8, plotted against the Sears-Haack body profile, which is argued to be the ideal drag-

reducing area distribution. The Sears-Haack equation for cross sectional area is

S ( x )=π Rmax2 [4 x (1−x ) ]

32 .

While this profile is impossible to obtain for any type of aircraft, it is considered a template for

the cross-sectional area of the aircraft. As the graph on the next page shows, the Emperor’s

cross-sectional area is vastly different than the Sears-Haack body. This is due to a number of

reasons. The wings on the Emperor are not only very large, but are also highly swept, meaning

that the area distribution is weighted towards the back of the aircraft, whereas the Sears-Haack

body begins to taper downward at its midpoint. Also, the Emperor has rear-mounted external

17

engines, and each of those adds a significant cross-section to the total profile. In the end, the

fuselage was necked down at the wing root wide enough to allow passengers to reach the

lavatory and luggage compartment in the aft section of the cabin, but structurally speaking, there

would be no way to taper the fuselage enough to make the aircraft more closely resemble the

Sears-Haack distribution.

0 20 40 60 80 100 1200

10

20

30

40

50

60

70

80

90

100Emperor Cross-Sectional Area vs. Sears-Haack Body Distribu-

tion

Emperor

Sears-Haack

Fuselage Stations, ft

Cros

s-Se

ction

al A

rea,

ft2

WingTaperedFuselage

Forward En-ginesFuselage

NoseTail

Figure 8: Transonic Area Plot

In addition, volume and surface area calculations were performed in SolidWorks, and the results

(including the total wetted area of the Emperor) are located in Table 3:

Table 3: Volumes and Surface Areas

Aircraft Component Volume, ft3 Surface Area, ft2

Fuselage 4871.65 3288.03Wings 1217.62 4590.71Engines (all three) 1086.12 1164.93Horizontal Tail 165.79 542.34Vertical Tail 65.83 224.55Total for Aircraft 7407.01 9810.56

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Also, volumes for the interior pressurized cabin were calculated, as the volume of the pressurized

cabin had an effect of the fuselage structural weight. These calculations are in Table 4:

Table 4: Interior Cabin Volumes

Cabin Component Volume, ft3

Cockpit 683.92Fuselage (Untapered) 2117.96Tapered Section 879.99Aft of Tapered Section 353.73Total Pressurized Volume 4035.60

CENTER OF GRAVITYThe center of gravity of the Emperor was determined by applying a moment equilibrium

on the aircraft. We estimated the location of each component of the aircraft with respect to a

coordinate system located at the nose. Table 19 in Appendix D displays these values as well as

the moment that is created by each component about the aircraft's nose.

All of the components generate a counterclockwise moment which, under trim conditions,

should be counterbalanced by the lift at the aircraft's center of gravity. Under trim, the force of

lift is equal to the aircraft’s weight, thus dividing the total moments by the aircraft's weight will

equal the distance of the Emperor’s center of gravity from its nose, as well as a percentage of the

mean aerodynamic chord. The center of gravity calculation is located below:

xcg=∑ M

W total

=76.93 ft=51.95 %MAC

An analysis of different loading conditions was considered as well. These loading conditions are

outlined in Table 5:

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Table 5: Loading Conditions

Loading Condition Payload FuelI Max MaxII Max MinIII Min MaxIV Min Min

For maximum load, all components will be on board while minimum load will exclude the

passengers, luggage, and flight attendant. Similarly, maximum fuel considers fuel tanks to be

completely full, while minimum fuel requires that the aircraft retain approximately 20% of the

total fuel capacity to allow for landing and remaining in a holding pattern. Applying this

methodology, we calculated the CG both from the nose and as a percentage of mean

aerodynamic chord for all load conditions considered, found in Table 6. During flight, the CG

does not remain constant because fuel is expended, reducing the weight and shifting weight

distribution in the wings and fuselage. The leading edge of the MAC was determined to be

located 69.36 ft from the nose, so the equation

%MAC=−(X ¿¿¿ , MAC−XCG )

MAC¿

is used to find the percentage shift in center of gravity.

Table 6: Center of Gravity Locations

Load Case CG Location from nose, ft

CG Location, %MAC

CASE I: Max Payload, Max Fuel 76.93 51.95CASE II: Max Payload, Min Fuel 75.45 41.81CASE III: Min Payload, Max Fuel 77.52 56.05CASE IV: Min Payload, Min Fuel 76.41 48.43

These CG shifts are fairly optimistic, as there is not much of a difference in the location of the

center of gravity as the Emperor expends fuel. However, this can be explained by the fact that

the largest component of the weight in the aircraft, the fuel, is located very close to the center of

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gravity. This was chosen on purpose to allow for maximum stability as the Emperor burns fuel.

This is a very common fuel placement scheme and is used by many aircraft in production and

use today. An additional discussion on the center of gravity shifts is located in the Stability and

Control section of the report.

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AERODYNAMICSPlanform Selection First and foremost, the wing planform geometry was optimized from the midterm report. This

was accomplished by examining the effects of sweep in the transonic region at three new leading

edge sweep conditions: 41, 45, and 49 degrees. For each new value for leading edge sweep, a

computational Excel sheet was used to determine the trailing edge sweep and tip chord length

required to maintain the aspect ratio and root chord length determined in the midterm report to

minimize changes to other aspects of the aircraft. Once these values were determined, the CFD

code was run for the cases of Mach 0.93 to Mach 1.08 at intervals of 0.03. At each interval, the

mesh was altered to reflect each new leading edge sweep and the corresponding plan form

conditions. This process provided the following graphs:

40 41 42 43 44 45 46 47 48 49 509

11

13

15

17

19

21

23

L/D vs. Sweep Angle

M=0.93M=0.96M=0.99M=1.02M=1.05M=1.08

Sweep Angle

L/D

Figure 9: L/D vs. sweep angle at various Mach numbers

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40 41 42 43 44 45 46 47 48 49 503.50E-01

3.70E-01

3.90E-01

4.10E-01

4.30E-01

4.50E-01

4.70E-01

4.90E-01

5.10E-01

5.30E-01

5.50E-01

Lift Coefficient vs. Sweep Angle

M=0.93M=0.96M=0.99M=1.02M=1.05M=1.08

Sweep Angle

Coeffi

cient

Figure 10: Lift coefficient vs. sweep angle for each Mach number

40 41 42 43 44 45 46 47 48 49 501.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

4.00E-02

4.50E-02

5.00E-02

Drag Coefficient vs. Sweep Angle

M=0.93M=0.96M=0.99M=1.02M=1.05M=1.08

Sweep Angle

Coeffi

cient

Figure 11: Drag coefficient vs. sweep angle at each Mach number

Data for these calculations, including percent reduction in various parameters, is presented in

Table 15 of Appendix B . While there is a notable reduction in lift coefficient, the reduction in

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drag coefficient is more than twice that of lift (even more in supersonic regions), so it was

decided that a leading edge sweep of 49 degrees would be adopted to significantly reduce drag.

Once the plan form was officially selected, the following calculations could be made; where A is

aspect ratio, b is wingspan, S is wing area, and cr and ct are the chord length at the root and tip

respectively.

Our aspect ratio is given by

A=b2

S=7.20

Therefore we can determine the wingspan to be

b=2√ AS ≈ 98.6 ft .

Similar to the specifications for the midterm report, we maintained that the chord at wing root

would be

b2=2.5 cr

As a result, the wing root chord length is

cr=b

2∗2.5= 98.6

2∗2.5≈ 19.72 ft .

In addition, the geometry based on the effects of wing sweep at transonic Mach numbers dictates

that the ratio of the tip chord length to the root chord length be:

λ=c t

cr

=.390

Thus, it can be shown that the tip chord would be 7.66 ft.

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Figure 12: Optimized Wing Planform Dimensions

SUBSONIC AERODYNAMICSCruise Performance A preliminary analysis was used to determine the achievable range of the plane. First, an

approximation was made with the assumption that if the range can be accomplished at cruise,

then other factors such as climb and descent can be modified from the preliminary analysis. To

calculate the range that can be achieved in nautical miles, the Breguet range equation will be

used, where a final conversion to nautical miles will be made at the end. Note that in this

equation, the velocity used is assumed to be the given cruise velocity of Mach .96, which is an

average of the range of prescribed Mach numbers in the requirements.

From Table B.1 in Raymer’s Aircraft Design, the cruise altitude of 41000 feet corresponds to

a speed of sound a = 968.1 fps. With the velocity at cruise determined, the Reynolds number can

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be found using the equation, ℜ= ρVDμ

, where the density and viscosity of air were determined

from altitude tables and the characteristic length D is the mean aerodynamic chord. This gave us

a subsonic cruise Reynolds number of just over 24 million. Thus, the velocity that will be used is

V = Ma = (968.1 fps)*(.96) = 929.37 fps. The assumption that trim flight equates weight and lift

yields the equation, L=W =qS C l, where q is the dynamic pressure, S is our wing planform area,

and Cl would be the coefficient of lift. Trim flight cruise conditions dictate the dynamic pressure

with the wing planform area being set in the Planform Selection Section of this report, and thus,

we can find the Cl of our plane during cruise trim conditions. The following equation shows this

analysis:

C l=WqS

= 123000(241.847)(1350)

=0.376

From this calculation of Cl, the given CFD code was used to iterate angles of attack with the

selected planform until the Cl approached the value required for trim. It was found that a

subsonic cruise of Mach 0.96 yielded a Cl of 0.372 at an angle of attack of 4 degrees. While this

is slightly lower than trim conditions, due to the iterative nature of the CFD calculations, for the

time constraints of this project it was concluded that the result was satisfactory. The following

table shows the results obtained from the CFD program.

Table 7: CFD Flight Parameters

α Cd, i+w CM,cr/4 LD i+w

CLα , avg . X%mac@CM=0

4 0.017 -0.66 20.97 5.33 45.94

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Using these parameters and trim conditions, it was determined that induced and wave drag on the

wing at subsonic trim is Di+w = 5550.4 lbs. In order to find the parasitic drag at subsonic

conditions, the following equations, dependent on wetted area, reference area, and skin

coefficient, are used:

CD P=

C f Swet

Sref

=(.00247)(3424.218)

(2735)=.00310

C f , subsonic=.074

ℜ.2≈ .00247

ℜ=ρV ( ct+cr

2 )μ

=(.00056)(929.376)(7.66+19.72

2)

2.97∗10−7 =2.4∗107

Utilizing the relevant parameters at Mach 0.96, the parasitic drag coefficient (CD p) was

determined to be .0031. Combining the parasitic and induced/wave drag coefficients, our total

drag was found to be D = 6,561.2 lbs. at subsonic cruise. We calculated range using

R=(Vc t

)( LD ) ln(W 0

W i)

where lift can be set equal to weight (since the aircraft is at trim), the velocity is constrained by

the Mach number, and the tip chord is provided as discussed in the plan form selection section.

Weights were discussed in the layout section, and were determined by estimates provided in

Raymer. Despite numerous iterations of the CFD code, in order to obtain sufficient lift to

maintain level flight at trim, the minimum induced drag was found to be insufficient to allow for

a range of 4500 nmi as requested in the design specifications. While the induced drag was

27

successfully minimized, the maximum range possible for our aircraft was found to be R = 3970

nmi.

Takeoff and Landing Performance Takeoff performance is a vital aspect of subsonic aerodynamics. If the plane cannot takeoff,

then the plane cannot fly. The prescribed runway length was given to be no more than 6000 ft.

As a result, our plane must be sized such that this take off length is possible. Total takeoff

distance required is determined through the sum of the ground roll distance, rotation distance,

transition distance, and climb out distance: Stotal=SG+SR+STR+SCL. First and foremost, the stall

speed at sea level must be determined in order to approximate takeoff speed. Figure 13 in

Appendix A taken from the Nicolai Aircraft Design book with our planform was used to

determine CL,max. Takeoff speed is defined as 1.2 times the stall speed, which can be found by

using CL,max of our wing from the figure at sea level.

V LOF=1.2V s=1.2√ Wρ seaC l ,max Sw

=1.2√ 123000 lbf .

(.00238slugs

ft3 )(1.35)(1350 ft2)=285.776 ft . s−1

The ground roll distance then becomes:

SG=12

Mass∗V LOF2

T e¿V LOF/√2

=2163.592 ft .

Where T e=T−D−μ(W −L)

There is also a rotation distance in which the plane begins to rotate to an angle that is

necessary to clear an obstacle of said amount of height. This is defined as the time it takes to

rotate the aircraft to an angle of attack such that a lift coefficient of 0.8CL,max is generated1. Since

1 Taken from Bendiksen’s Lecture Notes Chapter 2: Aircraft Performance eq. 2.159

28

there is no specific way estimate that time, we arbitrarily assigned a value of 2 seconds for this

period.

SR=V LOF tR=571.553 ft .

After rotation, the plane has “taken off” and begins to fly along an arc until the climb angle γcl

is reached. This expression is defined as:

sin γ CL=T−D

W

And the transition distance is shown to be equivalent to:

STR=R sin γ CL=3230.739 ft . where R=V LOF

2

0.152 g

There is also a climb out distance if the obstacle is taller than the plane’s altitude by the end

of the transition run, which is not applicable in this situation, but is defined as:

SCL=h−R (1−cosγ CL)

tan γCL

Therefore, our total takeoff distance given a 35 foot clearance at the end of the run comes out

to be 5965.885 feet. This value accounts for the total drag coefficient which includes parasitic

and wing drag. Attention was given to the rotation angle, which is approximately 11 degrees, in

order to ensure that there are no tail strikes at the end of the rotation run. Another final property

to note, is the requirement that throttle be at 75% for takeoff distance to not exceed runway

allotted. This is unfortunately due to excess thrust from the engine scaling as detailed in the

Propulsion Section. Too much thrust eventually causes the transition distance to increase at a

faster rate than ground roll decreases.

29

Landing is essentially the opposite of takeoff. Using a combination of equations from

Raymer’s Aircraft Design: A Conceptual Approach and Bendiksen’s Lecture Notes, the entire

distance for landing is calculated through the sum of flare, braking, and ground roll distance.

Since our climb-out height is higher than the obstacle, we do not need to worry about approach

distance. Flare speed is defined as:

V f =1.23∗V s=1.23 √ W f

ρC l S=1.23√ 71720

(.00238)(1.35)¿¿¿

Touchdown speed can be calculated similarly using 1.3 times the stall speed, which comes out to

be 236.41 feet.

s f=R sin γ=T−DW

V f2

.152 g=3452.262 ft .

Braking distance is a function of touchdown speed and delay, which we assumed to be 2 seconds

once again due to size of the aircraft: sbr=V TD t=472.809 ft . Finally the same equation used for

ground roll before is evaluated using the new touchdown speed, yielding sg = 844.581 ft. Total

ground distance is found to be 4769.65 feet.

SUPERSONIC AERODYNAMICSLayout and Configuration To accommodate supersonic cruising conditions, a variety of factors were employed in the

layout design and configuration of the plane. First of all, an aggressive wing sweep as proposed

in the Planform Selection Section will help reduce the perpendicular area as seen by the airflow,

and thus, reduce the supersonic drag. Since our operating speeds lie within the transonic and

supersonic region, the transonic area rule is utilized, which states that any cross sectional area to

the airflow must be smooth to reduce drag. Abiding by that rule, the fuselage has been necked

30

down near the wing attachment areas. In addition, the nose of the plane uses a less pronounced

von Karman cone in order to reduce the amount of drag from the nose of the fuselage.

Cruise Performance Using a method similar to that used in the Subsonic Cruise Performance section, the

supersonic drag on the plane can be determined. First and foremost, the Cl,max must be determined

for trim cruise conditions at high Mach numbers. Once again using Table B.1 from the Raymer

book, we can determine the speed of sound and air density at 41000 feet to be 968.1 fps

and .00056 slugs/ft3 respectively. Our cruise velocity thus corresponds to

V=Ma=(1.8 ) (968.1 )=1742.58 fps . With these numbers, we can determine that our dynamic

pressure q = 850.243 lb/ft.2. Below, the calculations are shown for the determination of Cl,max at

the cruise altitude:

C l ,max=√ WqS

=√ 123000(850.243)(1350)

=.10716

Once again, an iterative methodology was conducted to find a satisfactory Cl for the above

conditions. Since supersonic flight cannot be achieved legally in US airspace, flight conditions

for Mach 1.8 would be slightly different from that of subsonic speeds. The assumption was made

for a significant loss of fuel due to cruising at subsonic speed. Thus, a Cl = .0958 was deemed

satisfactory and within the bounds of error. The table below summarizes the data extrapolated

from the CFD output results for this new angle of attack and cruise condition.

Table 8: Supersonic Interpolation Data

α Cd, i+w CM,cr/4 LD i+w

CLα , avg . X%mac@CM=0

2 0.0197 -0.183 4.866 2.743 57.229

31

To find the parasitic drag at supersonic conditions, the following equations, dependent on

wetted area, reference area, and skin coefficient, are used:

CD P=

C f Swet

Sref

=(.00186)(3424.218)

2735.00233

ℜ=ρV ( ct+cr

2 )μ

≈ 4.5∗107

C f , supersonic=0.455 /¿

Note the similarities in this process and the one conducted in the Subsonic Cruise

Performance section. With these calculations made, the total drag, accounting for both induced

and parasitic, at supersonic trim conditions is 25,285 lbs. If a full tank of fuel was accounted for,

then a range of 1900 nautical miles can be reached at this condition.

32

PROPULSION AND PERFORMANCEEngine Selection We used three BruinJet BJ205 engines as the bases for our propulsion and performance

analysis with a given SLSD static thrust rating of 20,518 lbs for each engine, thus providing a

total SLSD static thrust of 61,554 lbs. From the subsonic and supersonic performance sections,

we have found that CD, subsonic = 0.02010 and CD, supersonic = 0.02203. After thorough drag

calculations that will be carried out in this section, we have found that the three BJ205 engines

cannot provide enough thrust to fly supersonically at both the cruising speed and at the

maximum operating speed especially because the available thrust decreases drastically with

altitude and speed. To compensate for this discrepancy, we chose to scale up the engines to

provide 163.1% more thrust which requires a 128% increase in the diameter of each engine. This

increases the overall drag of the aircraft, however, an increase in the amount of thrust available is

necessary to fly at high Mach numbers. After scaling the engine to meet drag requirements, we

have a new SLSD static thrust rating of 100,394.57 lbs.

Rate of Climb At sea-level conditions on a standard day, the aircraft must be able to climb at a rate of 3500

fpm with the maximum gross weight. We can solve for the steady rate of climb using the

following formula:

RC=(T AV−T Reqd ) V

W=√ 2 W

ρS CL(T AV

W−

C D

CL)

TReqd must be found by equating it to the drag at SLSD. In order to meet realistic and safe

standards, 50% engine throttle was used at SLSD conditions to yield the following data:

33

Table 9: Rate of Climb

W (lbs) 122,976.35TAV (lbs) 38,268.85V (fps) 428.72

TReqd (lbs) 5,927.64RC (fps) 112.75RC (fpm) 6765

According to our calculations, the jet will be able to fly at roughly 6765 fpm at 50% throttle,

which is well above 3500 fpm at SLSD conditions and maximum gross weight. This is naturally

high because the engines must be able to provide enough thrust to fly supersonically, so the

amount of available thrust greatly exceeds required thrust. To find the time it will take to reach

37,000 feet, we need to account for the change in thrust and density with increasing altitude. We

can approximate rate of climb values at certain points during the ascent and then take the average

rate of climb to find the estimated time to reach 37,000 feet. Again, we will perform this at 50%

throttle. These calculations are shown in Appendix C.

From standard sea level to an altitude of 40,000 feet, the average value of the rate of climb is

approximately RCavg = 4141.96 fpm. Dividing this value from 37,000 feet, we get the time it

takes to reach that altitude:

t 37,000ft=37000 feet

4243.11feetmin

=8.93 min

It will take about 9 minutes to reach an altitude of 37,000 feet, which is under the maximum

requirement of 20 minutes. This calculation was performed by using the TSFC to approximate

the amount of fuel burned in 5000-foot intervals of altitude. The required amount of thrust at

each altitude was equated to the amount of drag using the true airspeed at that altitude and CD,

subsonic = 0.02010.

34

Absolute and Service Ceiling The absolute ceiling is the uppermost altitude that the aircraft can theoretically attain, or

alternatively, the altitude at which rate of climb hits zero. However, aircrafts never can reach the

absolute ceiling, but instead, use the service ceiling as the maximum achievable altitude. For jets,

the service ceiling is the altitude at which rate of climb is 500 fpm. We can approximate both the

absolute ceiling and the service ceiling by plotting rate of climb versus altitude. We can also plot

required thrust and available thrust versus altitude and see that the two theoretically converge.

0 10000 20000 30000 40000 50000 600000

1000

2000

3000

4000

5000

6000

7000

Rate of Climb vs. Altitude

Altitude (feet)

Rate

of C

limb

(fpm

)

Figure 13: Rate of Climb vs. Altitude

35

0 10000 20000 30000 40000 50000 600000

10000

20000

30000

40000

50000

60000

70000

80000

Available and Required Thrust vs. Altitude

Available Thrust

Required Thrust

Altitude (feet)

Avail

able

/Req

uire

d Th

rust

(lbs

)

Figure 14: Available and Required Thrust at Altitudes

We approximated the trend between rate of climb and altitude to be linear, producing a

relatively strong correlation coefficient of R2 = 0.986. Using the trendline, we can obtain both the

absolute ceiling (RC = 0 fpm) and the service ceiling (RC = 500 fpm).

Table 10: Absolute and Service Celing

Absolute Ceiling 55,900 feet

Service Ceiling 54,100 feet

The minimum service ceiling is 51,000 feet, so our design clearly meets that expectation. We

have assumed full throttle to make ceiling calculations. In addition, we have assumed that once

the aircraft hits Mach 0.6 at an altitude of about 20,000 feet, it maintains that Mach number for

the rest of the climb.

36

Cruising and Maximum Mach Numbers The specified cruise Mach numbers are 0.90-0.95 for subsonic and 1.6-1.8 for supersonic.

The maximum operating Mach number is 1.9. To find the required thrust from our engines, we

need to find the drag at steady flight conditions:

T Reqd=D=12

ρ v2 CD S

We can approximate total drag by splitting it up into three components: induced, wave, and

parasite. Induced and wave drag coefficients can be interpolated from the CFD calculations:

Table 11: Induced and Wave Drag Estimations

Subsonic (Mach 0.96) Supersonic (Mach 1.8) Maximum (Mach 1.9)

V (ft/s) 929.38 1,742.58 1839.39q (lb/ft2) 241.85 850.24 947.34

CL 0.37673 0.10716 0.09618CD i+w 0.01700 0.01970 0.01950

Di+w (lbs) 5,550.39 22,612.23 24,938.71

It is clear from the table above that the thrust required will be dictated by the high amounts of

drag in supersonic cruising. Additionally, parasite drag also increases with speed. To estimate

parasite drag, we will take into account skin-friction effects since it comprises most of parasite

drag. Our approximation of parasite drag takes the following form:

CD P=

C f Swet

Sref

C f , subsonic=0.074

R e0.2

C f , supersonic=0.455 /¿,

37

ℜ=ρV ( ct+cr

2 )μ

From the Aerodynamic sections, a detailed analysis on drag gives us the following

information on parasite drag:

Subsonic (Mach 0.96) Supersonic (Mach 1.8) Maximum (Mach 1.9)

V (ft/s) 929.38 1,742.58 1839.39Re 2.400 x 107 4.500 x 107 4.750 x 107

Cf 0.00247 0.00186 0.00180CDp 0.00310 0.00233 0.00226Dp (lbs) 1,010.80 2,673.49 2,887.59

Like we predicted, the parasite drag increases with Mach number. Now that we have found

the parasite, induced, and wave drags, we can find the total drag and compare it to the available

thrust of three BJ205 engines at cruising altitude:

Subsonic (Mach 0.96) Supersonic (Mach 1.8) Maximum (Mach 1.9)Di+w (lbs) 5,550.39 22,612.23 24,938.71Dp (lbs) 1,010.80 2,673.49 2,887.59

DTOT (lbs) 6,561.19 25,285.72 27,826.30TBJ205 @ cruise per engine (lbs)

7,112.79 9,420.66 9,275.50

TAV @ cruise with 3 engines

(lbs)

21,338.37 28,261.97 27,826.49

A summary of the required thrusts at each cruising altitude along with the available thrusts

using the current engine configuration is shown:

Subsonic (Mach 0.96) Supersonic (Mach 1.8) Maximum (Mach 1.9)Required Thrust

@ Cruise (lbs)6,561.19 25,285.72 27,826.30

Available Thrust 21,338.37 28,261.97 27,826.49

38

@ cruise (lbs) We notice that with our engine specifications, we just have enough thrust to cruise at the

maximum operating Mach number of 1.9. Although the numbers are dangerously close at Mach

1.9, the aircraft is not designed to fly and cruise at this altitude. At the maximum supersonic

cruising speed of Mach 1.8, we have 10% more available thrust than required thrust, therefore

we are safe to cruise at these conditions. We have no problems cruising at subsonic speeds.

39

STABILITY AND CONTROLRevisions Several changes in terms of stability were made when the wings and layout were altered.

Some components were rearranged in order to control the shift in the center of gravity and the

location of the neutral point. Furthermore, many changes were applied to the tail to ensure

stability. The conversion to a T-tail significantly affected the effect of downwash on the tail, and

a tail incidence angle was introduced to attain proper trim conditions. Lastly, due to issues of

controllability, a fuel management outline, which is discussed later, was created to help balance

stability and maneuverability.

A critical component in aircraft design is stability: determining how well the aircraft can be

controlled. Numerous factors contribute to aircraft stability, thus we analyze four different load

conditions during for subsonic and supersonic trimmed flight, as was outlined in the Layout

Section above. Because our supersonic jet is relying on manual flight controls rather than an

electronic interface, we require our jet to have positive stability during trim conditions. The

analysis shown will only consider longitudinal stability and all calculations shown will be for the

first load case during subsonic and supersonic flight. Stable pitch is determined by two

calculations: a positive static margin and a negative moment coefficient with respect to angle of

attack (CMα).

Center of Gravity The stability of the aircraft is highly dependent on the location of its center of gravity. The

procedure for calculating the aircraft’s CG was described earlier in the report. Applying that

methodology, we calculated the CG for all load conditions being considered. During flight, the

CG does not remain constant as fuel is expended. It was essential to keep the center of gravity

from shifting drastically in order to keep the aircraft controllable. We aimed to keep our CG

40

shifts to within 2 ft. between our max fuel and min fuel loading conditions. The table of CG

locations was shown in the Layout Section.

According to the table, the maximum shift between the loading conditions is approximately

1.48 ft. which meets our goal. However, it is necessary to reiterate from earlier that the weights

used were estimated base on specs from other aircraft components, specifically existing business

jets, and equations from the textbook Aircraft Design: A Conceptual Approach. We realize that

our estimates will carry some degree of error.

Aerodynamic Center Similarly to an aircraft's center of gravity, the aerodynamic center of the wing and tail does

not stay constant during flight and are critical values in calculating stability. In general, most

airfoils have an aerodynamic center at the quarter-chord during subsonic flight but shifts to

approximately 45% of the mean aerodynamic chord during supersonic flight. However, utilizing

the CFD code we were able to find more realistic values for our wing and tail. We found that the

wing’s aerodynamic center is located approximately 38% MAC for low subsonic flight, 45.95%

MAC for subsonic cruise, and 57.23% MAC for supersonic cruise, leading to a total AC change

of 21.23%. Similarly, the tail’s aerodynamic center moves from 34.56% MAC to 53.23% MAC

between subsonic and supersonic conditions. This shift in AC is the result of the wing and tail

planform used. For comparison, a delta wing is beneficial for supersonic flight because it would

minimize this AC shift.

Neutral Point and Static Margin All aircraft have a center of gravity located at a point where there are no pitching moments,

regardless of angle of attack. This point is the aircraft's neutral point, or neutral stability, and is

the furthest CG location before the aircraft becomes unstable. The equation below was used to

41

locate the neutral point in our business jet, which is expressed as a percentage of the mean

aerodynamic chord.

xnp=CLα

x AC , wing−CM α , fuselage+ηh

S t

SW

C Lα ,tail x AC , tail(1− ∂ ϵ∂ α )+ F pα

qSw

(1− ∂ ϵ∂ α

) x p

C Lα+ηh

S t

Sw

CLα(1−∂ ϵ∂ α )+ Fpα

q Sw

Several assumptions were made when using this equation. The last term in the numerator and

denominator was neglected. According to Raymer, this term is typically ignored in the

calculation and is accounted for at the end with test data from similar aircrafts, usually a

reduction of the static margin by 1-3% for jets. While acceptable for subsonic flights, this

assumption would not be nearly as accurate for supersonic cases. Due to the scarcity of existing

supersonic business jets, more research will need to be done in order to account for the reduction

in stability in the supersonic flight regime. Besides the force term, other factors, such as

downwash effect, ηh, and moment coefficient for the fuselage were either given or calculated

based off estimates from graphs in the textbook. Below are the equations needed to solve for the

neutral point.

Downwash:

Subsonic:∂ ϵ∂ α

=( ∂ ϵ∂ α M =0)(

CLα

CLαM =0

)

Supersonic: ∂ ϵ∂ α

=1.62C Lα

πA

Fuselage Pitching Moment

CM α fuselage=K fuselageW f

2 Lf

c Sw

where

Wf = width of the fuselage Kf = empirical pitching-moment factor

42

Lf = length of fuselage

A sample calculation is for Case 1 subsonic loading configuration is carried out in Appendix B.

The static margin is the difference between the neutral point and the CG location. In order to

be stable in flight, the CG of the plane must be ahead of the neutral point. Thus static margin can

be expressed as the equation below.

Static Margin=xnp−xCG

Static margin is normally given as a percent and must be positive for the aircraft to be stable.

It is worth noting that too much stability reduces maneuverability. In other words, too stable

aircraft are uncontrollable since the pilot cannot not move from one trim condition to another.

Typical transport aircraft have a positive static margin of 5-10%, however since our aircraft’s

flight envelope includes supersonic conditions, compromises in terms of wing design and

performance have significant impacts on stability. The static margin for all load cases as well is

shown in the table below.

Table 12: Static Margins for Loading Cases

Load Case

Low subsonic M=0.33Cruise Subsonic M=0.96 Cruise Supersonic M=1.8

I 14.03% 19.57% 43.76%

II 24.18% 29.71% 53.91%

III 9.98% 15.52% 39.71%

IV 17.56% 23.10% 47.29%

Several things can be drawn from the values shown. The low subsonic column was placed in

to show that out plane is stable for lower speeds. The Mach number used was estimated to be the

speed of the plane after takeoff once all slats and flaps are retracted. All of the values in the table

43

are positive, thus the aircraft remains stable throughout its flight, however the static margin

drastically increases as Mach number increases. The largest contributors to this increase are the

placement of the wing and tail, the amount their AC shifts, reducing downwash, and the changes

in the lift-curve slopes. The high static margins during cruise conditions are not a critical issue

since as a transportation jet, maneuverability during cruise is not a priority.

Moment Coefficient with Respect to Angle of Attack The second criteria is to have a moment coefficient that opposes changes to angle of attack.

This pitching moment derivative is the moment coefficient with respect to angle of attack. It is

directly linked to the static margin by the equation below, along with the calculation results for

all load cases.

CM α=−CLα

( Xnp−XCG )

Table 13: CMα for Loading Cases

Loading Condition

Low subsonic

Subsonic Cruise

Supersonic Cruise

I -0.54551 -1.04401 -1.18741

II -0.94001 -1.58541 -1.46271

III -0.38801 -0.82791 -1.07751

IV -0.68271 -1.23231 -1.28321

As shown, as long as the lift curve slope is positive, the values will show the same conclusions

drawn from the static margin calculations.

Trim Analysis Enough information has been collected to determine what angle of attack and elevator

deflection angle is needed to maintain trimmed flight. We started with moment coefficient about

the CG and the total lift coefficient.

44

CM cg=CL (Xcg−X acw)+CM w

+CM wδfδ f +CM fus

−ηh

S t

Sw

CL t(X ¿¿act−Xcg)−

Tq Sw

Z t+D

q Sw

Z t+Fpα

q Sw

( Xcg−X p)¿¿

CLTotal=CLα

[α+iw ]+ηh

S t

Sw

CL t

The goal is to set the moment coefficient in terms of α and δ e. Several assumptions were made to

reduce this equation. The last term was neglected for the same reason explained above for the

neutral point. The moment coefficient and the drag component from the wing were neglected due

to their insignificant contribution to the overall moment. Flaps are not being used during trim

conditions. The tail lift coefficient can be found using eq. 16.32 from the textbook.

CL t=CLαt

[(α +iw)(1−∂ ϵ∂ α

)+(iw−it)−α 0 Lt ]

The incidence angle on the wing set to zero while tail incidence is at -2.4º. The last term in

the tail lift coefficient equation can be approximated using eq. 16.18 and Fig. 16.6 from the

textbook assuming an elevator area 20% of the tail area. Combining these equations and using

the values from the first load case for subsonic and supersonic trim, we get the equations below.

Subsonic:

CM cg=−1.46847 α−0.417307 δe+0.099331

CLTotal=6.50711α+0.180100δe−0.064570

Supersonic:

CM cg=−1.46766 α−0.227976 δe+0.064467

CLTotal=3.31761α+0.092873δ e−0.033297

Next, we set different values for the angle of attack and elevator deflection to solve for the

coefficients and plotted them to show graphically how they change. Below are the subsonic and

supersonic graphs for Case I.

45

-0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Trim Plot Subsonic Case I

4 degrees2 degrees0 degrees-2 degrees-4 degrees-6 degrees-8 degrees

Lift Coefficient

Mom

ent C

oeffi

cient

Figure 15: Trim Plot Subsonic Case 1 Loading Conditions

-0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

Trim Plot Supersonic Case I

4 degrees2 degrees0 degrees-2 degrees-4 degrees-6 degreesSeries13

Lift Coefficient

Mom

ent C

oeffi

cient

Figure 16: Trim Plot Supersonic Case 1 Loading Conditions

During trimmed flight, the moment about the CG should equal zero. Based on the graph, we

see several conditions where the aircraft can trim. According to the CFD calculations, during

subsonic and supersonic cruise our CL trim is 0.3767 and 0.1072 respectively. In order to meet

those conditions, we need to apply approximately 2º elevator deflection at an α of 3º for subsonic

46

and zero deflection at an α of 2º for supersonic. The table below shows approximated elevator

deflections and α needed to maintain trim. All data tables and graphs for each of the loading

conditions are shown in Appendix D.

Table 14: Angle of Attack and Elevator Deflections for Loading Cases

Subsonic Angle of Attack (deg) Elevator Deflection (deg)Case I 3 2Case II 3.6 -4Case III 3.6 4Case IV 3.9 -1.7

SupersonicCase I 2.1 0Case II 2.2 -2Case III 2 2Case IV 2 0

Fuel Management

One issue regarding the over-stability while flying at low Mach numbers must be addressed.

As seen in the static margin section, load case II displays a very high static margin. This type of

scenario would typically be associated with the aircraft arriving at its destination and needing to

land, making controllability a major concern. When experimenting with fuel placement for this

scenario, we found that as the fuel moved aft, the stability decreased. Thus to address the

problem, our fuel system, which was taken into account during our weight estimations, will have

a pump to move the remaining fuel out of the wings towards the back of the plane.

47

STRUCTURES AND MATERIALS In order to reduce the weight of our supersonic business jet and maximize customer comfort,

we will be taking advantage of newly available composite components. Using data from the

newly developed Boeing 787 Dreamliner, our primary fuselage will be constructed from a highly

durable composite fiberglass carbon laminate which is significantly lighter than aluminum (a

20% weight decrease) and will provide our passengers with a superior level of comfort due to a

higher available humidity level and leave them feeling invigorated and refreshed when they

reach their destination. In addition, this design decision will allow gourmet meals to be enjoyed

mid-flight, since sensory responses are enhanced at higher humidity levels. Our leading edge and

other critical aerodynamic surfaces will be constructed with aluminum to maintain compressive

structural integrity and reliability. Control surfaces, including ailerons, the fin, the tail cone, and

the flaps will also be constructed with carbon laminates and fiberglass to ensure durability and

minimize affects from fatigue. Engine components will utilize titanium for superior strength and

durability because it is less susceptible to fatigue and corrosion. The landing gear will be built

primarily from titanium parts that, while more expensive, offer a significant weight reduction

and strength increase over steel. Overall, these structural design considerations will result in a

more efficient, comfortable trip for the passengers and enhanced aerodynamic performance.

48

CONCLUSIONRange Benefits Given the parameters of this project, our plane was unable to meet the subsonic cruise range

requirements. However, the redeeming factor of this plane lies in both its supersonic range and

its maximum takeoff weight. Being fully loaded at 123,000 lbs. at takeoff offers numerous

advantages to business jets of similar class. This demonstrates a larger carrying capacity than

competing jets. The ability to cruise supersonically at Mach 1.8 for almost 2000 nautical miles

essentially allows for a trip between Los Angeles International Airport (LAX) to Chicago

O’Hare International Airport (ORD) to be cut down to a little less than 2 hours. This represents a

significant advantage for executives, as time is money. Thus, the Emperor allows businessmen a

high-speed efficient, direct flight with lax baggage restrictions to travel significant distances at

twice the speed of conventional jets.

As of right now, there are no supersonic business jets in use, and none are even close to

the testing and construction stages of development. As we discovered in compiling this report, it

is nearly impossible to meet all the prerequisites for a plane with those types of supersonic and

subsonic cruise abilities. Significant advances need to be made in various areas before an aircraft

like the Emperor can be realized, namely in drag reduction, composite materials, and propulsion

systems. One development that could help the Emperor achieve its maximum design potential

would be the use of variable-inlet engines, similar to those used on the SR-71 Blackbird high

supersonic jet. This would allow scaling of the thrust to compensate for different thrust

conditions throughout climb and cruise, while also decreasing the engine drag, that is a very

large component in terms of total aircraft drag. Also, fuel management is an issue as well.

Afterburners could not be used on the Emperor due to their massive fuel consumption, but are

49

used on most supersonic aircraft today. If engines could be developed with lower TSFC and

higher thrust, then maybe an aircraft like the Emperor M160-3 will become a reality sooner than

we think.

50

REFERENCESBendiksen, Oddvar. Lecture Notes. MAE 154A W15 UCLA.

Hale, Justin. Boeing: Boeing 787 From the Ground Up. Aero Qtr 4.06. 2008.

McCormick, B., Aerodynamics, Aeronautics, and Flight Mechanics. 2nd ed. Danvers: Wiley,

1992, Print.

Raymer, D., Aircraft Design: A Conceptual Approach.. 2nd ed. Washington, D.C.: American

Institute of Aeronautics and Astronautics.

Sadraey M., Aircraft Design: A Systems Engineering Approach, 2012, Wiley Publications

Torenbeek, E. Synthesis of Subsonic Airplane Design, Delft University Press, Martinus Nijhoff

Publishers, 1982.

51

APPENDIXAppendix A: Layout and Configuration

Table 15: Weight Breakdown by Component

Component Weight, lbsWing 12754.93Fuselage 7659.79Nose Landing Gear 880.03Main Landing Gear 2329.29Horizontal Tail 1585.92Vertical Tail 1036.67Installed Engines 16083.67Fuel Systems 2809.61Avionics 1082.19Controls 3320.95Hydraulic Systems 1194.50Air Conditioning/Anti-Ice 2557.82Electronics 851.75Total Fuel Weight 64100.00Passengers/Luggage 3120.00Furnishings 1990.00Pilot and Crew 615.00Aircraft Dry Weight (No Payload or Fuel) 55141.35Maximum Takeoff Weight MTOW (SLSD) 123000.00Total Aircraft Weight 122976.35

52

Figure 17: Engineering Drawing

53

AIRCRAFT WEIGHT ESTIMATION EQUATIONS

Raymer (15.46-15.49, 15.52-15.58):

W wing=(0.036 Sw0.758)∗(W fw

0.0035)∗( A

cos2 Λ )0.6

∗(q0.006)∗( λ0.04)∗( 100( tc )

cos Λ )−0.3

∗( N z W dg )0.49

W horiz tail=0.016 ( N z W dg )0.414∗(q0.168)∗(Sht0.896)∗( 100( t

c )cos Λht

)−0.12

∗( A

cos2 Λht)

0.043

∗λht−0.02

W vert tail=0.073(1+0.2H t

H v

)∗( N z W dg )0.376∗(q0.122)∗(Svt0.873)∗(100 ( t

c )cos Λ vt

)−0.49

∗( A

cos2 Λht)

0.357

∗(λvt0.039)

W fuselage=0.052(S f1.086)∗( N z W dg)0.177∗(Lt

−0.051)∗( LD )

−0.072

∗(q0.241)+W press

(Where W press=11.9∗(V pr Pdelta )0.271)

W installed engines=2.575 N en W en0.922

W fuel system=2.49(V t0.726)∗( 1

1+V i

V t)

0.363

∗N t0.242∗N en

0.157

W avionics=2.117W uav0.933

W hydraulics=K h(W0.8)(M 0.5)

W air−cond∧anti−ice=0.265(W dg0.52)∗(N p

0.68)∗(W avionics0.17 )∗M 0.08

W electronics=12.57 (W fuelsystem+W avionics )0.51

Torenbeek:

W main gear=40+0.16W ¿0.75+0.019 W ¿+1.5∗10−5 W ¿

1.5

54

W nose gear=20+0.1W ¿0.75+2∗10−5W ¿

1.5

Sadraey:

W controls=I sc∗(Sh+Sv+Swing) where Isc = 1.7 for full aerodynamic controls

55

Appendix B: Aerodynamics

Figure 18: Maximum Cl Approximations by Nicolai

56

Table 16: Iterative CFD Data (continued on next page)

Mach TE TTOL CL CMcr/4 CMmac/4 CD L/Di+w NSUP MACHmax

0.93 411.042

7 0.4844 -0.6627 0.0673 0.0287 16.888 11700 1.860

0.93 450.981

8 0.4147 -0.6364 0.0663 0.0205 20.244 10796 1.951

0.93 490.921

9 0.3570 -0.6300 0.0522 0.0161 22.161 10528 1.987

0.96 411.073

2 0.5142 -0.7474 0.0280 0.0365 14.070 14825 1.840

0.96 451.009

4 0.4412 -0.7005 0.0476 0.0250 17.636 13773 1.955

0.96 490.947

3 0.3725 -0.6641 0.0479 0.0178 20.973 13796 2.009

0.99 411.104

4 0.5238 -0.8085 -0.0179 0.0431 12.161 21988 1.909

0.99 451.037

7 0.4610 -0.7683 0.0138 0.0308 14.946 20328 1.933

0.99 490.972

6 0.3898 -0.7112 0.0341 0.0204 19.118 20267 2.016

1.02 411.135

6 0.5140 -0.8242 -0.0480 0.0463 11.102 39615 2.788

1.02 451.066

4 0.4702 -0.8231 -0.0247 0.0362 13.005 39775 1.946

1.02 490.998

2 0.4047 -0.7653 0.0089 0.0242 16.709 41071 1.975

1.05 411.166

5 0.4861 -0.7803 -0.0460 0.0461 10.556 48394 2.890

1.05 451.094

5 0.4665 -0.8404 -0.0481 0.0389 12.006 49557 2.917

57

1.05 491.023

9 0.4125 -0.8066 -0.0171 0.0278 14.844 52150 3.032

1.08 411.197

1 0.4570 -0.7296 -0.0392 0.0452 10.114 53567 2.981

1.08 451.122

8 0.4582 -0.8433 -0.0646 0.0405 11.311 55489 3.052

1.08 491.050

0 0.4155 -0.8357 -0.0401 0.0307 13.525 57567 3.087

58

Mach TE CL/Alpha X@CM=0 X%mac@CM=0% Decrease

CL% Decrease

CD% Increase

L/D

0.9341 6.94 1.260 44.94

0.9345 5.94 1.384 42.83 26.31% 43.84% 31.22%

0.9349 5.11 1.554 44.19

0.9641 7.37 1.322 53.36

0.9645 6.32 1.422 48.02 27.56% 51.41% 49.07%

0.9649 5.34 1.567 45.95

0.9941 7.50 1.388 62.22

0.9945 6.60 1.480 55.81 25.59% 52.67% 57.20%

0.9949 5.58 1.598 50.06

1.0241 7.36 1.431 68.11

1.0245 6.74 1.541 64.05 21.27% 47.69% 50.51%

1.0249 5.80 1.646 56.60

1.0541 6.96 1.432 68.23

1.0545 6.68 1.578 69.08 15.15% 39.66% 40.62%

1.05 4 5.91 1.693 62.93

59

9

1.0841 6.55 1.426 67.34

1.0845 6.56 1.606 72.86 9.08% 32.01% 33.72%

1.0849 5.95 1.734 68.43

60

Figure 19: Raymer Table B.1 (continued on next page)

61

62

Appendix C: Propulsion and PerformanceTable 17: Rate of Climb at Varying Altitudes

Altitude (ft) TAV (lbs) TReqd (lbs) W (lbs) ρ (slugs/ft3) V (fps) RC (fps) RC (fpm)

0 38,268.85 5,927.64 122,976.35 2.38E-03 428.72 112.75 6,764.91

5000 35,215.57 5,885.80 122,108.43 2.05E-03 460.24 110.55 6,632.88

10000 29,287.59 5,846.54 121,293.86 1.76E-03 495.38 95.74 5,744.16

15000 24,328.44 5,808.83 120,511.59 1.50E-03 534.97 82.21 4,932.68

20000 20,391.95 5,772.36 119,754.89 1.27E-03 579.48 70.74 4,244.55

25000 16,457.91 5,736.83 119,017.79 1.07E-03 629.81 56.73 3,403.97

30000 13,167.30 5,701.07 118,275.99 8.91E-04 686.74 43.35 2,601.03

35000 10,434.51 5,663.64 117,499.31 7.38E-04 752.09 30.54 1,832.25

40000 8,215.50 5,621.52 116,625.56 5.87E-04 840.15 18.69 1,121.20

63

Appendix D: Stability and TrimTable 18: Weight Distribution Breakdown

weight (lbs) cg location measured from nose (ft)

moments lbs*ft

total passengers 2340 47 109980

total luggage 780 76 59280

total crew 615 25 15375

wings, control surfaces 16075.88 73 1173539.24

tail 2622.59 110 288484.9

front gear 880.3 17 14965.1

rear gear 2329.29 79 184013.91

engine 1 and 2 10722.44667 92 986465.0936

engine3 5361.22333 100 536122.333

electronics,avionics 1933.94 25 48348.5

ani-ice system 2557.82 69 176489.58

furnishings 1990 47 93530

fuselage 6664.017 59 393177.003

fuel system 2809.61 81 227578.41

hydraulics 1194.5 75 89587.5

fuel 64100 79 5063900

64

Table 19: Relevant Stability Coefficients

*Values used are for Case 1 Loading conditions*

Terms needed SubsonicValueSupersonic

Values Comments

lift curve coefficient (wing) 5.33557 2.71318from eq. 12.6 (Raymer)

lift curve coefficient (tail) 5.13836 2.64971from eq. 12.6 (Raymer)

empirical fuselage factor 0.04estimated from Fig. 16.14 (Raymer)

width of fuselage 8.5

length of fuselage 110

moment coefficient (fuselage) 0.92561

ηh 0.9estimated between 0.85-0.95 (Raymer)

wing area 1350

tail area 450

aerodynamic center/MAC (wing) 5.216759

5.580546

aerodynamic center/MAC (tail) 7.594912

7.732120

downwash term 0.240 0.194 estimated using eq. 16.21a and Fig 16.12 (Raymer)

mean aerodynamic chord 14.5764324

xnp=(5.33557 ) (5.216759 )−0.92561+0.9 ( 450

1350)(5.13836)(7.594912)(1−0.240)

5.33557+0.9(450

1350)(5.13836)(1−0.240)

xnp=80.22 ft

65

Figure 20: Empirical Pitching Moment Factor

66

Figure 21: Downwash Estimation M = 0

67

Table 20: Subsonic Loading Conditions at M = .96

CASE I max payload max fuel elevator deflection

alpha 4 degrees 2 degrees 0 degrees -2 degrees -4 degrees -6 degrees -8 degrees

0 -0.0520 0.0702 -0.0583 0.0848 -0.0646 0.0993 -0.0709 0.1139 -0.0771 0.1285 -0.0834 0.1430 -0.0897 0.1576

2 0.1751 0.0189 0.1689 0.0335 0.1626 0.0481 0.1563 0.0626 0.1500 0.0772 0.1437 0.0918 0.1374 0.1063

4 0.4023 -0.0323 0.3960 -0.0178 0.3897 -0.0032 0.3834 0.0114 0.3771 0.0259 0.3709 0.0405 0.3646 0.0551

6 0.6294 -0.0836 0.6231 -0.0690 0.6169 -0.0544 0.6106 -0.0399 0.6043 -0.0253 0.5980 -0.0107 0.5917 0.0038

8 0.8566 -0.1348 0.8503 -0.1203 0.8440 -0.1057 0.8377 -0.0911 0.8314 -0.0766 0.8251 -0.0620 0.8188 -0.0474

10 1.0837 -0.1861 1.0774 -0.1715 1.0711 -0.1570 1.0648 -0.1424 1.0586 -0.1278 1.0523 -0.1133 1.0460 -0.0987

CASE II max payload min fuel elevator deflection

alpha 4 degrees 2 degrees 0 degrees -2 degrees -4 degrees -6 degrees -8 degrees

0 -0.0520 0.0755 -0.0583 0.0907 -0.0646 0.1059 -0.0709 0.1211 -0.0771 0.1363 -0.0834 0.1515 -0.0897 0.1667

2 0.1751 0.0012 0.1689 0.0164 0.1626 0.0316 0.1563 0.0468 0.1500 0.0620 0.1437 0.0772 0.1374 0.0924

4 0.4023 -0.0731 0.3960 -0.0579 0.3897 -0.0427 0.3834 -0.0275 0.3771 -0.0123 0.3709 0.0029 0.3646 0.0181

6 0.6294 -0.1474 0.6231 -0.1322 0.6169 -0.1170 0.6106 -0.1018 0.6043 -0.0866 0.5980 -0.0714 0.5917 -0.0562

8 0.8566 -0.2218 0.8503 -0.2066 0.8440 -0.1913 0.8377 -0.1761 0.8314 -0.1609 0.8251 -0.1457 0.8188 -0.1305

10 1.0837 -0.2961 1.0774 -0.2809 1.0711 -0.2657 1.0648 -0.2505 1.0586 -0.2352 1.0523 -0.2200 1.0460 -0.2048

CASE III min payload max fuel elevator deflection

alpha 4 degrees 2 degrees 0 degrees -2 degrees -4 degrees -6 degrees -8 degrees

0 -0.0520 0.0681 -0.0583 0.0824 -0.0646 0.0967 -0.0709 0.1110 -0.0771 0.1253 -0.0834 0.1397 -0.0897 0.1540

2 0.1751 0.0260 0.1689 0.0403 0.1626 0.0547 0.1563 0.0690 0.1500 0.0833 0.1437 0.0976 0.1374 0.1119

4 0.4023 -0.0160 0.3960 -0.0017 0.3897 0.0126 0.3834 0.0269 0.3771 0.0412 0.3709 0.0555 0.3646 0.0698

6 0.6294 -0.0581 0.6231 -0.0438 0.6169 -0.0295 0.6106 -0.0151 0.6043 -0.0008 0.5980 0.0135 0.5917 0.0278

8 0.8566 -0.1001 0.8503 -0.0858 0.8440 -0.0715 0.8377 -0.0572 0.8314 -0.0429 0.8251 -0.0286 0.8188 -0.0143

10 1.0837 -0.1422 1.0774 -0.1279 1.0711 -0.1136 1.0648 -0.0993 1.0586 -0.0850 1.0523 -0.0706 1.0460 -0.0563

CASE IV min payload min fuel elevator deflection

alpha 4 degrees 2 degrees 0 degrees -2 degrees -4 degrees -6 degrees -8 degrees

0 -0.0520 0.0720 -0.0583 0.0868 -0.0646 0.1016 -0.0709 0.1164 -0.0771 0.1312 -0.0834 0.1460 -0.0897 0.1608

2 0.1751 0.0128 0.1689 0.0275 0.1626 0.0423 0.1563 0.0571 0.1500 0.0719 0.1437 0.0867 0.1374 0.1015

4 0.4023 -0.0465 0.3960 -0.0317 0.3897 -0.0169 0.3834 -0.0022 0.3771 0.0126 0.3709 0.0274 0.3646 0.0422

6 0.6294 -0.1058 0.6231 -0.0910 0.6169 -0.0762 0.6106 -0.0614 0.6043 -0.0466 0.5980 -0.0319 0.5917 -0.0171

8 0.8566 -0.1651 0.8503 -0.1503 0.8440 -0.1355 0.8377 -0.1207 0.8314 -0.1059 0.8251 -0.0911 0.8188 -0.0763

10 1.0837 -0.2243 1.0774 -0.2096 1.0711 -0.1948 1.0648 -0.1800 1.0586 -0.1652 1.0523 -0.1504 1.0460 -0.1356

68

-0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

Trim Plot Subsonic Case II

4 degrees2 degrees0 degrees-2 degrees-4 degrees-6 degrees-8 degrees

Lift Coefficient

Mom

ent C

oeffi

cient

-0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Trim Plot Subsonic Case I

4 degrees2 degrees0 degrees-2 degrees-4 degrees-6 degrees-8 degrees

Lift Coefficient

Mom

ent C

oeffi

cient

-0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Trim Plot Subsonic Case III

4 degrees2 degrees0 degrees-2 degrees-4 degrees-6 degrees-8 degrees

Lift Coefficient

Mom

ent C

oeffi

cient

-0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Trim Plot Subsonic Case IV

4 degrees2 degrees0 degrees-2 degrees-4 degrees-6 degrees-8 degrees

Lift Coefficient

Mom

ent C

oeffi

cient

Figure 22: Subsonic Trim Plots M = .96

69

Table 21: Supersonic Loading Conditions at M = 1.8

CASE I max payload max fuel elevator deflection

alpha 4 degrees 2 degrees 0 degrees -2 degrees -4 degrees -6 degrees

0 -0.02681337 0.048554 -0.03006 0.05651 -0.03331 0.06451 -0.03651 0.07241 -0.03981 0.08041 -0.04301 0.08831

2 0.088993119 -0.00268 0.085751 0.005279 0.08251 0.01321 0.07931 0.02121 0.07601 0.02911 0.07281 0.03711

4 0.20479961 -0.05391 0.201558 -0.04595 0.19831 -0.03801 0.19511 -0.03001 0.19181 -0.02211 0.18861 -0.01411

6 0.320606102 -0.10514 0.317364 -0.09718 0.31411 -0.08921 0.31091 -0.08131 0.30761 -0.07331 0.30441 -0.06541

8 0.436412593 -0.15637 0.433171 -0.14841 0.42991 -0.14051 0.42671 -0.13251 0.42341 -0.12451 0.42021 -0.11661

10 0.552219085 -0.2076 0.548977 -0.19965 0.54571 -0.19171 0.54251 -0.18371 0.53931 -0.17581 0.53601 -0.16781

CASE II max payload min fuel elevator deflection

alpha 4 degrees 2 degrees 0 degrees -2 degrees -4 degrees -6 degrees

0 -0.02681337 0.051275 -0.03006 0.05956 -0.03331 0.06781 -0.03651 0.07611 -0.03981 0.08441 -0.04301 0.09271

2 0.088993119 -0.01184 0.085751 -0.00355 0.08251 0.00471 0.07931 0.01301 0.07601 0.02131 0.07281 0.02961

4 0.20479961 -0.07495 0.201558 -0.06666 0.19831 -0.05841 0.19511 -0.05011 0.19181 -0.04181 0.18861 -0.03351

6 0.320606102 -0.13806 0.317364 -0.12977 0.31411 -0.12151 0.31091 -0.11321 0.30761 -0.10491 0.30441 -0.09661

8 0.436412593 -0.20117 0.433171 -0.19288 0.42991 -0.18461 0.42671 -0.17631 0.42341 -0.16801 0.42021 -0.15971

10 0.552219085 -0.26428 0.548977 -0.256 0.54571 -0.24771 0.54251 -0.23941 0.53931 -0.23111 0.53601 -0.22291

CASE III min payload max fuel elevator deflection

alpha 4 degrees 2 degrees 0 degrees -2 degrees -4 degrees -6 degrees

0 -0.02681337 0.047468 -0.03006 0.055293 -0.03331 0.06311 -0.03651 0.07091 -0.03981 0.07881 -0.04301 0.08661

2 0.088993119 0.000979 0.085751 0.008804 0.08251 0.01661 0.07931 0.02451 0.07601 0.03231 0.07281 0.04011

4 0.20479961 -0.04551 0.201558 -0.03768 0.19831 -0.02991 0.19511 -0.02201 0.19181 -0.01421 0.18861 -0.00641

6 0.320606102 -0.092 0.317364 -0.08417 0.31411 -0.07631 0.31091 -0.06851 0.30761 -0.06071 0.30441 -0.05291

8 0.436412593 -0.13849 0.433171 -0.13066 0.42991 -0.12281 0.42671 -0.11501 0.42341 -0.10721 0.42021 -0.09941

10 0.552219085 -0.18498 0.548977 -0.17715 0.54571 -0.16931 0.54251 -0.16151 0.53931 -0.15371 0.53601 -0.14591

CASE IV min payload min fuel elevator deflection

alpha 4 degrees 2 degrees 0 degrees -2 degrees -4 degrees -6 degrees

0 -0.02681337 0.0495 -0.03006 0.057571 -0.03331 0.06561 -0.03651 0.07371 -0.03981 0.08181 -0.04301 0.08991

2 0.088993119 -0.00586 0.085751 0.002208 0.08251 0.01031 0.07931 0.01831 0.07601 0.02641 0.07281 0.03451

4 0.20479961 -0.06123 0.201558 -0.05316 0.19831 -0.04511 0.19511 -0.03701 0.19181 -0.02891 0.18861 -0.02091

6 0.320606102 -0.11659 0.317364 -0.10852 0.31411 -0.10041 0.31091 -0.09241 0.30761 -0.08431 0.30441 -0.07621

8 0.436412593 -0.17195 0.433171 -0.16388 0.42991 -0.15581 0.42671 -0.14771 0.42341 -0.13971 0.42021 -0.13161

10 0.552219085 -0.22732 0.548977 -0.21924 0.54571 -0.21121 0.54251 -0.20311 0.53931 -0.19501 0.53601 -0.18701

70

-0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

Trim Plot Supersonic Case I

4 degrees2 degrees0 degrees-2 degrees-4 degrees-6 degrees

Lift Coefficient

Mom

ent C

oeffi

cient

-0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

Trim Plot Supersonic Case II

4 degrees2 degrees0 degrees-2 degrees-4 degrees-6 degrees

Lift Coefficient

Mom

ent C

oeffi

cient

-0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

Trim Plot Supersonic Case III

4 degrees2 degrees0 degrees-2 degrees-4 degrees-6 degrees

Lift Coefficient

Mom

ent C

oeffi

cient

-0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

Trim Plot Supersonic Case IV

4 degrees2 degrees0 degrees-2 degrees-4 degrees-6 degrees

Lift Coefficient

Mom

ent C

oeffi

cient

71