a preliminary design for a unmanned long range strike vehicle

A Preliminary Design Analysis for an Uninhabited Long Range Supersonic Strike Vehicle

Instructors: Neil Weston and Carl Johnson

By Michael Lopez

December 5, 2014

I certify that I have abided by the honor code of the Georgia Institute of Technology and followed the collaboration guidelines as specified in the project description for this assignment

Abstract

This document is a preliminary design for the creation of an uninhabited long range strike

vehicle. The design process used for the creation of this vehicle was primarily taken from Dr.

Jan Roskam’s series of aircraft design books. A figure of merits analysis was performed to

determine to best component configuration. Using these configuration choices, a weight

sizing analysis was performed based on the mission profile, mission fuel fractions, and the

class I drag polar to produce a takeoff weight for the vehicle. Subsequently, a constraint

analysis was performed on each segment of flight in order to produce an optimal thrust to

weight ratio at sea level takeoff and an optimal wing loading at takeoff. These ratios

produced preliminary values for thrust and wing area. Using all of this information, a

preliminary component design of the fuselage, wing, tail, high lift devices, and control

surfaces was performed. Finally, landing gear were attached to the aircraft and the entire

configuration was weighed and balanced to produce a finalized initial aircraft design. In

addition to this design process, trade studies were performed on key assumptions and design

decisions throughout the process to provide justification of various choices and demonstrate

the impact that changing these values would have on important design parameters.

Nomenclature

α = thrust lapse

β = vehicle weight over vehicle takeoff weight

Λ = quarter chord sweep angle

Γ = dihedral angle

λ = taper ratio

ρ = density

μ = turn bank angle

μto = ground friction coefficient

AR = main wing aspect ratio

b = wing span

c = chord

CD,o = coefficient of zero lift drag

CD = coefficient of drag

Cf = coefficient of skin friction

CL = coefficient of lift

d = diameter

e = Oswald’s efficiency factor

2

g0 = gravitational acceleration

h = altitude

KΛ = sweep coefficient

K1 = 1st order drag polar coefficient

K2 = 2nd order drag polar coefficient

kL = approach speed safety factor

kTO = takeoff speed safety factor

M = vehicle Mach number

n = load factor

q = dynamic pressure

R = vehicle range

RC = vehicle rate of climb

S = component area

SG = takeoff distance

Swet = vehicle wetted area

Tmax = maximum engine thrust

TSL = thrust at sea level

TSFC = thrust specific fuel consumption

t/c = thickness to chord ratio

T/W = thrust to weight ratio

v = vehicle speed

V = volumetric coefficient

WE = empty weight

WF = maximum fuel weight

WP = payload weight

WTO = maximum takeoff weight

W/S = wing loading

List of Figures

Figure 1: Final Vehicle Configuration..........................................................................................................................10

Figure 2: Vehicle Payload Location.............................................................................................................................11

Figure 3: Mission Profile..............................................................................................................................................12

Figure 4: Similar Vehicle Weight Regression..............................................................................................................13

Figure 5: Aspect Ratio Trade Study

Figure 6: Thickness to Chord Ratio Trade Study

3

Figure 7: Vehicle Accleration Trade Study

Figure 8: Thrust Specific Fuel Consumption Trade Study

Figure 9: Supercruise Mach Number Trade Study

Figure 10: Takeoff Assumption Comparison

Figure 11: Constraint Analysis

Figure 12: Descent Rate Trade Study

Figure 13: Load Factor Trade Study

Figure 14: Maximum Lift Coefficient on Approach Trade Study................................................................................33

Figure 15: Takeoff Distance Trade Study.....................................................................................................................34

Figure 16: Fuselage Top View......................................................................................................................................36

Figure 17: Fuselage Side View.....................................................................................................................................36

Figure 18: Fuselage Front View

Figure 19: Coefficient of Lift versus Angle of Attack for NACA 64-204

Figure 20: Coefficient of Drag versus Angle of Attack for NACA 64-204

Figure 21: Coefficient of Moment about the Leading Edge versus Angle of Attack for NACA 64-204.....................39

Figure 22: 2-D Drag Polar for NACA 64-204..............................................................................................................40

Figure 23: Main Wing Top View..................................................................................................................................43

Figure 24: Main Wing Side View.................................................................................................................................43

Figure 25: Main Wing Front View

Figure 26: Tail Top View

Figure 27: Tail Side View

Figure 28: Tail Front View...........................................................................................................................................47

Figure 29: Vehicle Top View.......................................................................................................................................48

Figure 30: Vehicle Subsonic Leading Edge..................................................................................................................49

Figure 31: Neutral Point Location................................................................................................................................50

Figure 32: Center of Gravity Range

Figure 33: Weight-C.G. Excursion Diagram

Figure 34: Landing Gear Side View

4

Figure 35: Final Design Top View

Figure 36: Final Design Side View

Figure 37: Final Design Front View

List of Tables

Table 1: Analysis of Alternatives...................................................................................................................................7

Table 2: Wing Layout Selection.....................................................................................................................................8

Table 3: Wing Attachment Selection..............................................................................................................................8

Table 4: Number of Fuselages Selection........................................................................................................................9

Table 5: Tail Type Selection...........................................................................................................................................9

Table 6: Tail Attachment Selection................................................................................................................................9

Table 7: Number of Engines Selection.........................................................................................................................10

Table 8: Weight Sizing Assumptions...........................................................................................................................13

Table 9a: Mission Fuel Fractions..................................................................................................................................14

Table 9b: Mission Fuel Fractions (cont.) 14

Table 10: Additional Fuel Fractions

Table 11: Weight Sizing Analysis Results

Table 12: Drag Polar Assumptions

Table 13: Lift to Drag Ratios

Table 14: Simple Takeoff Analysis Values

Table 15: Frictional Takeoff Analysis Values

Table 16: Climb Analysis Values.................................................................................................................................25

Table 17: Descent 1 Analysis Values...........................................................................................................................25

Table 18: Descent 2 Analysis Values...........................................................................................................................25

Table 19: Supercruise Analysis Values........................................................................................................................26

Table 20: Dash 1 Analysis Values................................................................................................................................26

Table 21: Dash 2 Analysis Values................................................................................................................................26

Table 22: Subcruise Analysis Values...........................................................................................................................26

Table 23: Zoom Analysis Values..................................................................................................................................27

5

Table 24: Acceleration Analysis Values.......................................................................................................................27

Table 25: Delivery Analysis Values

Table 26: Approach Analysis Values

Table 27: Service Ceiling Analysis Values

Table 28: Fuselage Component Weight and Volume

Table 29: Main Wing Specifications

Table 30: Maximum Lift Coefficients

Table 31: Flap Sizing Values........................................................................................................................................42

Table 32: Volumetric Coefficient Method....................................................................................................................44

Table 33: Tail Sizing Values.........................................................................................................................................45

Table 34: Neutral Point Analysis Values

Table 35: Neutral Point Calculations

Table 36: Gross Weight Ratios

Table 37: Vehicle Component Weights

Table 38: Component Centers of Gravity

Table 39: Vehicle Centers of Gravity

Table 40: Gear Strut Load Values

6

I. Introduction

The purpose of this RFP is to detail one potential configuration and design of an uninhabited long range strike

vehicle. This vehicle would be designed with the capability of performing high altitude, sustained supersonic flight,

delivering a weapons payload, and returning back to land. This vehicle would be used by the military to perform

strike missions on targets in potentially hazardous areas, thus making the unmanned nature of this vehicle highly

desirable. In addition, a vehicle without a pilot is capable of performing more hazardous and dangerous maneuvers

without considering the safety and health of the pilot. The primary design influences for this vehicle come from the

Northrop Grumman B-2 Spirit bomber and the Lockheed Martin F-22 Raptor. Many of the decisions made in the

configuration selection and subsequent analysis of the vehicle were made based on these or similar aircraft.

II. Preliminary Configuration Selection

A. Analysis of Alternatives

For the configuration of this aircraft, many different design choices were possible. However, by using the F-22

Raptor and B-2 Spirit as base points, the choices for this unmanned supersonic bomber became somewhat simpler.

In order to analyze and select the best layout and component configuration, a figure of merits analysis for each

important component choice was performed. The table of these alternatives is shown below in Table 1. The eventual

choices for the aircraft configuration have been highlighted.

Table 1: Analysis of Alternatives

Components AlternativesWing Layout Flying wing Conventional Tandem wing

Wing Attachment Low Middle High BlendedFuselage Shape Blended Rounded Circular Square

Number of Fuselages 0 1 2 3Tail Type V-tail Conventional H-tail T-tail

Tail Attachment One boom Two booms On fuselageNumber of Engines 1 2

B. Figures of Merit Analysis

In order to obtain the best choice for each component, a figure of merit analysis was done to analyze the benefits

of each possibility. The analysis was done on using a scale of important from one to five with one being an

unimportant design point and five being a crucial design point. The weighting is assigned to each figure of merit

based on its relative importance to the overall configuration. These weightings are arbitrary but they are made with

consideration to the preliminary design process first and the subsequent design with lesser importance. The possible

7

choices for each component are then graded on another scale of one to five with one being inferior and five being

superior.

The first design choice in the configuration of this vehicle was the wing chosen. The figure of merit analysis for

the various wing layouts is shown below in Table 2.

Table 2: Wing Layout Selection

Wing Layout

FOM Weight Flying wing Conventional Tandem wing

Size 5 3 4 2

Drag 4 3 4 2

Manufacturing 2 3 4 3

Maintenance 3 3 3 2

Total 13 42 53 36

Due to its superior performance on the most important figure of merit, the weight, the conventional wing was

chosen as the wing layout.

The next design choice was where to mount the wing. The analysis for this choice is shown in Table 3.

Table 3: Wing Attachment Selection

Wing Attachment

FOM Weight Low Middle High Blended

Size 5 4 4 4 3

Drag 4 4 4 4 3

Manufacturing 2 2 3 2 3

Maintenance 3 2 4 3 3

Total 13 46 54 49 42

The blended wing offers the lowest weight possible due to the fact that much of the weight of the fuselage is

incorporated into the wing as well as exceptional high speed performance. This allows it to outperform the standard

middle attachment and is the reason it was selected. As a consequence of the wing attachment being selected as

blended, the fuselage shape was automatically chosen to be blended as well.

The next step of the configuration selection was to choose the number of fuselages that would be incorporated

into the vehicle. That figure of merit analysis is shown below in Table 4.

8

Table 4: Number of Fuselages Selection

Number of Fuselages

FOM Weight Zero One Two Three

Size 5 5 4 3 2

Drag 4 5 4 3 2



Total 13 70 56 42 28

While it may appear that zero fuselages is the best configuration, the reason one fuselage is selected is due to the

fact that zero fuselages does not meet the mission design requirements. If there is no fuselage, there is no room to

store the payload that the vehicle will be dropping.

Next, the type of tail that will be used is analyzed. The analysis of tail types is shown in Table 5.

Table 5: Tail Type Selection

Tail Type

FOM Weight V-tail Conventional H-tail T-tail

Size 5 5 4 3 4

Drag 4 5 4 3 3



Total 13 63 53 42 49

Here, a somewhat unconventional V-tail is seen to be the best configuration choice. This is due to the fact that it

is simpler in structure and performs better than the other options in high speed supersonic flight. As that is the most

strenuous design requirement for the vehicle, that means the major design choices will be made to optimize that

condition.

Once the V-tail configuration is chosen, the placement of the tail is decided. The analysis of tail attachment

locations is shown in Table 6.

Table 6: Tail Attachment Selection

Tail Attachment

FOM Weight One boom Two booms On Fuselage

Size 5 4 3 5

Drag 4 4 3 5

Manufacturing 2 3 2 4

9

Maintenance 3 3 2 4

Total 13 51 37 65

As would be expected, the design clearly favors a tail attached to the fuselage. Booms are used primarily by

helicopters and are not optimal for high speed flight.

The final component to consider is the engines. First, the number of engines must be decided. Table 7 shows the

figure of merit analysis for number of engines.

Table 7: Number of Engines SelectionNumber of Engines

FOM Weight One Two

Size 5 5 4

Drag 4 4 3

Manufacturing 2 4 4

Maintenance 3 3 3

Total 13 58 49

While one engine is lighter, it would have to be larger and heavier than each of the two engines individually in

order to produce the same thrust. This can create structural issues and in general, it is much safer to fly with two

engines in case one engine fails. Therefore, two engines are selected for this design.

In summary, the figure of merits analysis determined that a flying wing aircraft, with a blended wing body shape,

one fuselage, a V-tail mounted to the fuselage, with two engines would be the best design to meet the given

requirements.

C. Final Configuration

The final configuration choices for the vehicle were compiled and a modeling sketch was created using the

OpenVSP software. The result of this sketch can be seen below in Fig. 1. In addition, the location of the 4,000 lbs of

required payload can be seen in Fig. 2. All components except the location of the payload have been de-shaded in

order to emphasize the area where the payload will be located.

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Figure 1: Final Vehicle Configuration

Figure 2: Vehicle Payload Location

III. Weight Sizing Analysis

Now that the configuration for the airplane has been determined, the vehicle must be sized using an iterative

weight sizing analysis. This analysis takes into account the various requirements, mission segments, and design

choices made and allows for an initial value of takeoff weight to be determined. In addition, a constraint analysis is

then performed to determine a proper wing loading and thrust to weight ratio which gives a thrust value for engine

sizing and a wing area for structural sizing.

A. Mission Profile

To begin the weight sizing process, a mission profile was created for use throughout the entire analysis. This

mission profile shows each segment of the flight, the altitude at which each segment was performed, and the range

for each segment of flight. This mission profile will be used for all subsequent analysis regarding the various phases

of flight. A diagram of this mission profile is shown below in Fig. 3.

11

0 200 400 600 800 1000 1200 1400 1600 1800 20000

10000

20000

30000

40000

50000

60000

Start, Taxi, and Takeoff

Climb

Supercruise Dash 1

Delivery

Dash 2AccelerateZoom

Descent 1

Subcruise

Descent 2

Landing

Distance Traveled (nm)

Altit

ude

(ft)

Figure 3: Mission Profile

B. Weight Regression

The next step in the weight sizing process was to create a weight regression based on vehicles of similar

approximate size and design mission. Using these vehicles, a trendline was created in order to determine the values

of the A and B coefficients used to create a relationship between maximum takeoff weight, W TO, and maximum

empty weight, WE. The relationship between these two parameters is given by the following equation:

log10 W E=log10 W ¿−A

B (1)

In addition, in order to incorporate the effects of the improvements of technology by the eventual in-service data of

2025, a technology correction factor of .75 was used to generate the A value for the weight sizing. With this in mind,

the linear regression line created was analyzed to produce values of .815 and .910 for A and B respectively. The

graph showing this regression is displayed in Fig. 4 below.

12

Figure 4: Similar Vehicle Weight

Regression

C. Initial Weight Sizing

After obtaining A and B coefficients, the estimated WTO for the vehicle could be calculated. This is achieved by

creating a step by step analysis for each segment of the mission and approximating the fuel used in each segment.

The assumptions made during this step of the analysis include the rate of climb of the vehicle, RC, the thrust specific

fuel consumption, TSFC, of the engines, and the optimum subsonic cruise altitude and Mach number. All of these

assumptions were chosen to be conservatively within the range of current technology. These assumptions are shown

below in Table 8.

Table 8: Weight Sizing Assumptions

Rate of Climb (ft/s) Rate of Descent (ft/s) TSFC (lb/(lb*hr)) Msubcruise hsubcruise (ft) Acceleration (ft/s2)

2,750 12,000 .95 .8 40,000 9.28

The main purpose of these assumptions was to help with the calculation of the mission fuel fractions. These fuel

fractions are percentages of the takeoff weight which will be used to calculate the total fuel weight of the vehicle.

These assumptions are made in order for the analysis of the vehicle to be made possible. The effect of the choices of

RC and TSFC are analyzed later on during the trade studies. Depending on whether the mission segment is a change

in altitude segment or a constant altitude segment, two different equations for mission fuel fraction are used. These

equations are shown below in Eqns. 1 and 2.

M ff=1

e

E∗TSFCLD

(1)

13

10000 1000001000

10000

100000

Takeoff Weight (lbs)

Empt

y W

eigh

t (lb

s)

M ff=1

e

R∗TSFC

v∗( LD

) (2)

The calculated values of the mission fuel fractions for each segment of flight are shown below in Tables 9a and

9b.

Table 9a: Mission Fuel Fractions

Start Taxi Takeoff Climb Supercruise Dash 1 Zoom

.99 .995 .995 .965 .803 .976 .997

Table 9b: Mission Fuel Fractions (cont.)

Delivery Accelerate Dash 2 Descent 1 Subcruise Descent 2 Landing

.996 .997 .972 .995 .842 .996 .992

These fuel fractions were then multiplied together to get a final mission fuel fraction. This value along with the

chosen values for the fraction of trapped fuel and oil and the fraction of reserve fuel are shown below in Table 10.

Table 10: Additional Fuel Fractions

Mff Mff_tfo Mres

.590 .005 .055

Using these calculated and chosen fuel fractions, the weight of the fuel needed for the flight of the mission was

calculated. Using the initial guess for takeoff weight and subtracting the calculated fuel weight, the known payload

weight, and the crew weight, a value for empty weight of the vehicle was calculated using Eq. 3 below.

W E, calculated=W ¿ , guess−W fuel−W payload−W crew (3)

The empty weight can also be calculated using the initial takeoff weight guess and the previously calculated A

and B coefficients. This calculation is shown in Eq. 4 below.

W E, allowable=10log10 W ¿ , guess−A

B (4)

These two values of WTO are then compared to determine the difference between the two. For the takeoff weight

guess to be an accurate value for the vehicle, the difference between the two calculated empty weights must be very

low. Using Microsoft Excel’s goal seek operator, the two values of WE are converged by varying the initial WTO

guess value. In order to obtain a truly converged value of WE, the lift to drag ratio, L/D, for each segment is also

14

converged during the class I drag polar analysis in the next section. The results of the weight sizing convergence for

this vehicle are shown below in Table 11.

Table 11: Weight Sizing Analysis Results

WTO (lbs) A B WF (lbs) WP (lbs) WC (lbs) WE (lbs)

36,711 .815 .910 19,591 4,000 0 13,121

D. Class I Drag Polar Analysis

In order for the weight sizing analysis to be completed accurately, one factor, the lift to drag ratio, is needed

from a class I drag polar analysis for each segment of the mission. The L/D for each segment is a crucial factor in

the range or endurance equations that determine segment fuel fractions. In order for this analysis to be possible,

factors such as the Oswald efficiency factor, e, the aspect ratio, AR, the thickness to chord ratio, t/c, and the skin

friction coefficient, Cf, are chosen. The choice of AR and t/c are based on military fighter aircraft such as the F-22.

The effect of these choices will be explored later during trade studies on the vehicle. The c and d coefficients needed

to calculate the wetted area of the vehicle are taken from Roskam’s Part II1. Finally, a wing loading, W/S, is roughly

guessed for the purposes of generating a wing area. These values are shown below in Table 12.

Table 12: Drag Polar Assumptions

AR e t/c W/S c d Cf

2.5 .85 .04 98 .2263 .6977 .0026

Using the takeoff weight and the c and d coefficients, the wetted area of the vehicle can be calculated using Eqn. 5.

Swet=10c+d log10 W ¿ (5)

This value of wetted area is then used with the area computed using the wing loading guess and the skin friction

coefficient to calculate a zero lift drag coefficient. This process is shown in Eqn. 6.

CD ,0=C f

Swet

S (6)

For the supersonic cruise segments of the mission, the t/c ratio and the supersonic Mach number are used to

approximate a coefficient of wave drag, CD,wave using the following Eqn. 7:

1 Roskam, Jan. Preliminary Sizing of Airplanes. Lawrence: DARcorporation, 2005. Print.

15

CD ,wave=5.3∗( t

c)

2

√ M2−1

(7)

The coefficient of lift for the vehicle is calculated for each segment using the weight at the beginning of the

segment, the density at that altitude, the velocity of the vehicle, and the wing area approximation as shown in Eqn. 8.

CL=W

.5 ρ v2 S (8)

The induced drag of the vehicle is calculated using the coefficient of lift and the lift factor. The lift factor is

calculated using Oswald’s efficiency factor and the aspect ratio of the aircraft as shown in Eqn. 9.

K1=1

πeAR (9)

The coefficient of drag for the vehicle is then calculated according to Eqn. 10.

CD=CD, 0+CD, wave+K1CL2 (10)

Finally, the lift to drag ratio can be determined by dividing the coefficient of lift by the coefficient of drag. This

final calculation is shown in Eqn. 11.

LD

=CL

CD

(11)

Similarly to the overall WTO, the values for L/D calculated for each segment are then converged with the values

guessed for L/D for use in the weight sizing spreadsheet. Each value must be converged separately and the iterative

convergence process repeated until all values of L/D and the value of WE have been converged at the same time. The

L/D results of this convergence are shown below in Table 13.

Table 13: Lift to Drag Ratios

Climb Supercruise Dash 1 Zoom Deliver

y

Accelerat

e

Dash 2 Descent 1 Subcruis

e

Descent 2

5.58 3.62 5.31 9.31 8.53 9.28 5.10 2.28 9.67 7.67

16

IV. Weight Sizing Trade Studies

In order to solidify some of the assumptions made during the sizing process, trade studies were performed on

some of the key design choices. These trade studies show how the final value of WTO varies as the design variable is

changed.

A. Aspect Ratio Trade Study

One main contributing factor to the design of the vehicle was the chosen value for the aspect ratio. The aspect

ratio has a large impact on the class I drag polar analysis of the aircraft. The variation of the aspect ratio and its

effect on the takeoff weight are shown below in Fig. 5.

1 1.5 2 2.5 3 3.5 430000

35000

40000

45000

50000

55000

60000

Aspect Ratio (~)

Take

off W

eigh

t (lb

s)

Figure 5: Aspect Ratio Trade Study

The graph of takeoff weight versus aspect ratio shows a steady decrease in the takeoff weight as the aspect

ratio is increased. An increased aspect ratio would mean some combination of a decreased wing area or an increased

wing span. The most direct result of varying the aspect ratio is a change in the K 1 value used to calculate the induced

drag in the class I drag polar. As the aspect ratio is increased, the value of K 1 decreases. This results in a decrease in

the coefficient of drag and an increase in the L/D of the vehicle. While this may seem to be an infinitely good result,

the larger and larger aspect ratio puts a much larger stress on the internal structure of the vehicle. As the wing

becomes longer, it becomes very difficult to support the wing, especially in supersonic flight. In addition, due to the

extremely high speeds of supersonic flight, a large L/D is not necessary in order to maintain the lift needed for

steady flight. Thus, for the purposes of this supersonic ULRSV, an L/D of 2.5 was chosen.

B. Thickness to Chord Trade Study

One of the most important phases of the design of this vehicle is the supersonic flight. The supersonic flight

introduces a new source of drag, the wave drag, which as Mach number is increased, begins to greatly impact the

17

overall drag on the vehicle. The equation used to relate the thickness to chord ratio of the wing to the wave drag

created is shown in the class I drag polar discussion section of this report. The variation of t/c and its effect on the

WTO of the vehicle is shown below in Fig. 6.

0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.06530000

35000

40000

45000

50000

55000

Thickness to Chord Ratio (~)

Take

off W

eigh

t (lb

s)

Figure 6: Thickness to Chord Ratio Trade Study

The analysis of WTO versus t/c shows a somewhat quadratic relationship between t/c and takeoff weight. As the

t/c is increased, the WTO increases steadily. This makes sense because as the thickness of the wing is increased,

clearly the weight of the wing will increase as well. This also has implications on the supersonic performance of the

wing. For supersonic flight, wings are desired to be as thin as possible in order reduce the disturbance on the flow at

such high speeds. However, this ratio cannot be so small as to make the wing difficult to manufacture and

potentially impossible to support. Therefore, for the purposes of this vehicle design, a t/c of .04 was chosen for the

vehicle.

C. Vehicle Acceleration Trade Study

Some of the most stressful structural segments are those that require an acceleration of the aircraft. These

segments put the maximum stress on the vehicle and require the greatest output from the engines. By varying the

acceleration requirement for the vehicle, different values of the potential WTO were generated. The results of this

analysis are shown below in Fig. 7.

18

4 5 6 7 8 9 10 11 12 13 1436200

36400

36600

36800

37000

37200

37400

37600

Acceleration (ft/s2)

Take

off W

eigh

t (lb

s)

Figure 7: Vehicle Acceleration Trade Study

The results of this analysis of takeoff weight versus acceleration show a somewhat quadratic relationship

between the two values. As the acceleration requirement in increased, the subsequent converged WTO value is

decreased down to a minimum where it appears to level out. By this analysis, the higher the acceleration, the lower

the takeoff weight. However, higher and higher accelerations put very high stress on the vehicle and place great

demands on the vehicle’s engines. Therefore, an acceleration of 9.28 ft/s2 was chosen to give a low value of WTO

without putting an overly large stress on the vehicle.

D. Thrust Specific Fuel Consumption Trade Study

One of the main sources of weight in the vehicle is the weight due to fuel. Therefore, one of the most important

parameters chosen for the design of this vehicle was the thrust specific fuel consumption, TSFC, of the engines. The

higher the value of TSFC, the more rapidly the fuel is consumed by the engines and the more the range is reduced.

Therefore, an engine design team will always strive to decrease the TSFC of the engines they are creating.

However, due to the design mission of this vehicle to fly in high altitude supersonic flight, the TSFC for the engine

is unavoidably large. Current technology has made great strides in the reduction of TSFC in transonic flight but in

order to maintain supersonic flight, the fuel consumption of an aircraft is still very high. To demonstrate the large

impact that the TSFC has on the WTO, a trade study analysis was done of TSFC. The results of this analysis are

shown below in Fig. 8.

19

0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.220000

25000

30000

35000

40000

45000

50000

55000

60000

Thrust Specific Fuel Consumption (lb/(lb*hr))

Take

off W

eigh

t (lb

s)

Figure 8: Thrust Specific Fuel Consumption Trade Study

As can be clearly seen from this graph, the TSFC has an enormous impact on the converged value of W TO. When

the value of TSFC increases from .75 to .1.15, the value of WTO more than doubles from 25,000 lbs to over 50,000

lbs. This relationship is why the focus of engine design is always on reducing the TSFC as much as possible.

However, for this design, in order to take into account the high fuel burn of supersonic flight, a TSFC of .95 was

chosen for design analysis.

E. Supercruise Mach Number Trade Study

The final design point considered for the trade study analyses of this vehicle design was the choice of supersonic

cruise Mach number. As discussed previously, the supersonic requirement for this vehicle results in a large fuel burn

and reduced overall range of the vehicle. In order to demonstrate the large effect of the fuel weight on the W TO of the

aircraft, the supersonic cruise Mach number was varied and then the WTO was re-converged. The results of this

analysis are shown below in Fig. 9.

20

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 234000

35000

36000

37000

38000

39000

40000

41000

Supercruise Mach Number (~)

Take

off W

eigh

t (lb

s)

Figure 9: Supercruise Mach Number Trade Study

The graph of takeoff weight versus supercruise Mach number shows a very clear quadratic relationship. With a

higher supercruise Mach number though the aircraft is flying the same distance over a shorter amount of time, the

amount of fuel necessary for this flight goes up considerably. This results in a 4,000 pound increase between a cruise

Mach number of 1.5 and 1.9. For this parameter, however, the design requirements for the vehicle clearly specified a

supercruise Mach number of 1.5. Therefore, the requirements of the customer outweigh any efficiency gains from

flying at a different speed.

V. Constraint Analysis

The goal of this analysis is to further the design of the uninhabited long range strike vehicle previously created

during the weight sizing process. In order to determine important design features such as the thrust to weight ratio

and the wing loading of the vehicle, a constraint analysis was performed on the initial design. These two ratios are

important parameters because using these values as well as the takeoff weight from the weight sizing process, the

sea level thrust required to power the vehicle and the wing area of the vehicle can be determined. With the takeoff

weight, the empty weight, the thrust required, and the wing area of the vehicle as well as conceptual configuration

choices, specific decisions about engines, internal structure, and materials to be used can be considered in order to

move into a more detailed design.

For each mission segment, a constraint analysis was performed to determine the relationship between the thrust

to weight ratio and the wing loading for that segment of the flight. The primary foundation for this analysis is the

energy based constraint equation. This equation is shown below in Eqn 12.

21

T SL

W ¿

=βα { qS

βW ¿[K1( nβ

qW ¿

S )2

+K2( nβq

W ¿

S )+CD0+ R

qS ]+ 1V

ddt (h+ V 2

2 g0)} (12)

The energy based constraint equation applies to all segments of the flight. However, in order to make the analysis

easier, simplifying assumptions are made for each case in order to simplify the equation to a more manageable form.

For example, in all segments of flight except takeoff and landing, R = 0 because the aircraft is not on the ground and

there is no ground friction. In order to do the constraint analysis, several assumptions made during the weight sizing

process were reused. These include the vehicle aspect ratio, the zero lift drag coefficient, the Oswald’s efficiency

factor, and the first and second order drag polar coefficients. The aspect ratio of 2.5 was chosen because both the F-

22 Raptor and the F-35 Lightning have similar aspect ratios. The F-22 has an aspect ratio of 2.35 while the F-35 has

an aspect ratio of 2.662. Both of these aircraft are similar in design and have the capability to fly at high supersonic

speeds. The wing area, the lift factor, and the zero lift drag coefficient are taken from the previous analysis done

during the class I drag polar.

The other factors of great importance for this analysis are the thrust lapse and weight correction. The thrust lapse

is calculated using the density ratio of the density at the altitude of that segment to the density at sea level as shown

in Eqn. 13. The thrust lapse at altitude is then calculated using this density ratio and the Mach number of the desired

segment as shown in Eqn. 14. The weight correction, beta, is defined as the weight at the start of the segment over

the takeoff weight as shown in Eqn 15.

σ= ρρSL

(13)

α= TT SL

=.72 [ .88+.245 (|M−.6|)1.4 ] σ .7 (14)

β= WW ¿

(15)

These values are used in each segment of the flight to calculate the thrust to weight values needed to maintain

stable flight. For the purposes of this design analysis, the final design point was required to be at a thrust to weight

ratio between .6 and 1.2 and a wing loading between 60 and 100 pounds per square foot.

A. Takeoff

The first segment of the vehicle operation that was analyzed was the takeoff performance of the vehicle. Two

different takeoff possibilities were analyzed: takeoff with friction and takeoff assuming that friction is negligible.

First, the case that assumes that the thrust force is much greater than the drag due to friction was analyzed. For this

case, the overall energy based constraint equation is reduced to the following form shown in Eqn. 16:

2 Hunter, Jamie. Jane's All the World's Aircraft: In Service: 2012-2013. Coulsdon: IHS Jane's, 2012. Print.

22

T SL

W ¿=β2

αk¿

2

sG ρ g0CL ,max(W ¿

S ) (16)

The takeoff performance was analyzed at an altitude of 5,000 ft on a 90° F day, the takeoff distance was given to

be 10,000 ft and the takeoff speed safety factor was chosen to be 1.2. The values used for this analysis are shown in

Table 14.

Table 14: Simple Takeoff Analysis Values

α β CL,max, TO rho (slugs/ft3) kTO STO (ft)

.608 .985 1.8 .001866 1.2 10,000

After performing this analysis, the thrust to weight is shown to vary from .1 at 50 lbs per square ft to .4 at 170 lbs

per square ft. This shows that a takeoff without friction has very little impact on the overall performance

requirements of the vehicle. The takeoff case does not drive the design point decision.

The assumption that friction plays a very small role in the takeoff performance is a very oversimplifying one.

Therefore, an analysis of the takeoff was performed that also takes into consideration the rolling friction. For this

analysis, the energy based constraint equation was modified to the following:

T SL

W ¿=

βα {ξ¿

qβ ( S

W ¿)+μ¿+

1g0

dVdt } (17)

The variable, ξTO, is defined as shown in Eqn. 18.

ξ¿=(CD+CD , R−μ¿CL ) (18)

In this analysis, the most important chosen factor is the ground friction coefficient. This value was chosen to

be .025 based on data for various surfaces taken from Roskam.3 The values used for this analysis are shown below in

Table 15.

Table 15: Frictional Takeoff Analysis Values

α β CL,max, TO rho (slugs/ft3) μ dv/dt (ft/s2) q (lbs/ft2) CD,R

.608 .985 1.8 .001866 .025 4 44.92 .0458

The results of this analysis proved that the frictionless assumption drastically changes the resulting thrust to

weight ratio required. Whereas the frictionless case produced thrust to weight ratios ranging from .1 to .4, the case


23

including friction resulted in thrust to weight ratios from 1.3 at 50 lbs per square ft wing loading to .55 at 170 lbs per

square ft wing loading. This relationship shows that at lower wing loading, the frictionless assumption is very poor,

but at higher values of wing loading, the error due to the assumption decreases dramatically. The comparison of

these two curves is plotted below in Fig. 10.

50 70 90 110 130 150 1700

0.2

0.4

0.6

0.8

1

1.2

1.4

Simple TakeoffFriction Takeoff

Wing Loading at Takeoff (lbs/ft2)

Thru

st to

Wei

ght a

t Sea

Leve

l Tak

eoff

(~)

Figure 10: Takeoff Assumption Comparison

B. Climb and Descent

The next important flight segment to be considered was the climb and descent of the aircraft. For the segments of

flight involving constant speed climb or descent, the energy based constraint equation was simplified to the

following form shown in Eqn. 19:

T SL

W ¿=

βα {K1

βq (W ¿

S )+K2+CD0

βq (W ¿

S )+

1V

dhdt } (19)

The necessary assumptions to perform this analysis were the vehicle speed and the vehicle climb rate. The

vehicle is assumed to be in a state where time to climb is not important. Therefore, the climb speed was chosen to be

250 knots and the both descent speeds were chosen to be 200 knots in order to reduce the thrust necessary. The rate

of climb was chosen to be 2,750 feet per minute. As the F-22 Raptor has a potential climb rate of over 50,000 feet

24

per minute4, this value is well within the possible range for an aircraft of similar performance and is chosen to be

low in order to reduce the thrust to weight ratio necessary for this segment of flight. The rate of descent was chosen

to be 12,000 feet per minute. The values used for the climb, descent 1, and descent 2 segments of flight are shown

below in Tables 16, 17, and 18.

Table 16: Climb Analysis Values

α β v (ft/s) rho (slugs/ft3) dh/dt (ft/s) q (lbs/ft2)

.386 .98 421.95 .000974 45.83 86.73

Table 17: Descent 1 Analysis Values


.192 .685 337.56 .000408 -200 23.25

Table 18: Descent 2 Analysis Values


.426 .522 337.56 .001267 -200 72.16

The resulting thrust to weight values for the climb segment increased linearly from .57 at 50 lbs per square ft

wing loading to 1.05 at 170 lbs per square ft wing loading. The values of thrust to weight for the first descent

increased rapidly from -1.28 to .66 while the values for the second descent increased from -.60 to -.48. The reason

for the difference is due to the second descent occurring after the subcruise phase and at a much lower altitude. The

lighter aircraft and the lower density make the requirements much lower for the vehicle. As these segments of climb

and descent are only to change altitude for the mission and do not need to be executed in a rapid timeframe, the

values were intentionally chosen so that this segment of flight would not drive the design.

C. Cruise

Based on the weight sizing analysis, the phases of flight that consume the most fuel are the supersonic and

subsonic cruise. Therefore, it is important to analyze these flight segments to ensure that the thrust to weight ratio

required does not put a high strain on the vehicle over a long period of time. Since the cruise is assumed to be steady

level flight, both of the terms in the energy based strain equation involving change in velocity or change in height

become zero and the equation simplifies to the following form shown in Eqn. 20. In addition the two supersonic

dash segments are also analyzed using this equation.


25

T SL

W ¿=

βα {K1

βq (W ¿

S )+K2+CD0

βq (W ¿

S )} (20)

The only assumption that is made for the either cruise segment is the subsonic cruise takes place at a chosen

altitude and Mach number. For the purposes of this mission, an altitude of 40,000 feet and Mach .8 were chosen.

The values for each of these segments of flight are shown in tables 19, 20, 21 and 22 below.

Table 19: Supercruise Analysis Values

α β v (ft/s) rho (slugs/ft3) q (lbs/ft2)

.178 .945 1452.11 .000285 300.03

Table 20: Dash 1 Analysis Values


.163 .748 1936.15 .000285 533.38

Table 21: Dash 2 Analysis Values


.207 .713 1936.15 .000285 533.38

Table 22: Subcruise Analysis Values


.244 .680 774.46 .000585 175.49

The values of thrust to weight ratio for the supersonic cruise that resulted from this analysis varied from .73

to .55 and increased again to .61 as the wing loading was increased from 50 to 170 lbs per square ft. The subsonic

cruise had an even smaller range from .34 down to .29 and increasing back to .36. The values for the thrust to weight

ratio of the dash 1 segment decreased from 1.22 to .50 and the values for the thrust to weight of the dash 2 segment

decreased from .95 to .38. As the design range is between .6 and 1.2, it is clear that neither of the cruise mission

segments has a large impact on the design point selection while the dash segments would only have influence on the

design point at low wing loading.

D. Zoom and Acceleration

The mission segment that involves the greatest amount of thrust for this mission was the acceleration segment.

The vehicle was required to increase its speed from Mach .85 to Mach 2 in two minutes. In order to achieve this, a

26

substantial dive was needed to decrease the thrust load placed on the engines. Without a dive maneuver, the thrust

required for this acceleration would have far exceeded the design requirements for the vehicle. The zoom maneuver,

on the other hand, required a substantial increase in altitude in order to rapidly slow down the vehicle. For these

purposes, the energy based strain equation was modified to include both a change in altitude as well as a change in

velocity. The resulting equation is shown below in Eqn. 21:

T SL

W ¿=

βα {K1

βq (W ¿

S )+K2+CD0

βq (W ¿

S )+

1V

dhdt

+1g0

dVdt } (21)

For these segments of flight, the critical assumptions that are made include the velocity, the rate of climb, and

the acceleration. As this analysis can only be done using a single velocity, the velocity was chosen as the average

between the values of Mach 2 and Mach .85. This resultant velocity was 817 knots. The acceleration was derived

from a simple calculation of the change in velocity over the given two minutes to be 9.28 ft/s 2. Finally, the rate of

climb was given in the requirements to be 200 fps.

Table 23: Zoom Analysis Values

α β v (ft/s) rho (slugs/ft3) dv/dt (ft/s2) q (lbs/ft2) dh/dt (ft/s)

.174 .724 1379.51 .000285 -9.28 270.78 200

Table 24: Acceleration Analysis Values

α β v (ft/s) rho (slugs/ft3) dv/dt (ft/s2) q (lbs/ft2) dh/dt (ft/s)

.174 .716 1379.51 .000285 9.28 270.78 -200

Taking rate of climb to be positive and acceleration to be negative, the values of thrust to weight ratio for the

zoom segment of flight were calculated to range from .04 down to -.15. This shows that the deceleration has a much

greater impact on the thrust required than the change in height. For the acceleration flight segment, a negative rate of

climb and positive acceleration produced thrust to weight values ranging from 1.23 at 50 lbs per square ft wing

loading decreasing down to 1.04 at 170 lbs per square ft. These values are very important to the overall analysis

because it can be clearly seen that this segment of flight will be very influential in the determination of the overall

design point. The acceleration puts a great load on the vehicle’s engines and it is only through a dive maneuver that

this segment of flight is able to be contained within the required parameters.

E. Delivery

When designing a vehicle for a specific purpose such as this uninhabited long range strike vehicle, one of the

obviously important segments of the mission is the segment involving the actual execution of the mission objective

itself. In this case, this involves releasing a payload weapon at a desired military target. For the purposes of this

27

analysis, the payload delivery segment has been modeled as a constant speed and constant altitude turn. However,

for the purposes of assuming a worst case scenario, it is assumed that the vehicle does not deliver its payload. The

result of these assumptions is the following energy based strain equation shown in Eqn. 22:

T SL

W ¿=

βα {K1 n2 β

q (W ¿

S )+K2 n+CD0

βq (W ¿

S ) } (22)

The major difference with this equation and the previous equations used for steady level flight is the inclusion of

the load factor. In all previous cases, the load factor, n, was assumed to be approximately one and therefore not

important in the calculation of the thrust to weight ratios. In this case, the execution of a turning maneuver makes

that assumption invalid and the load factor must be included. The load factor is defined by the following equation

shown in Eqn. 23:

n= 1cosθ

(23)

Theta is defined as the turn bank angle in degrees. Therefore, the larger the turn bank angle, the greater the load

factor and the greater the resultant stress on the vehicle. The design requirements for the vehicle initially specified a

load factor of two, but indicated that this parameter could be adjusted in order to maintain the desired thrust to

weight and wing loading.

Table 25: Delivery Analysis Values

α β v (ft/s) rho (slugs/ft3) n q (lbs/ft2)

.176 .721 822.86 .000362 1.6 122.51

The initial value of two for load factor proved to be excessive for the vehicle and produced thrust to weight

values that were outside the desired range. Therefore, in order to obtain values that were more suitable, the load

factor was decreased from 2 to 1.6. This modification resulted in thrust to weight values that increased linearly

from .71 up to 1.68 as wing loading increased. The intersection of this curve with the curve previously determined

from the acceleration segment created the corner where the design point was later placed.

F. Approach

The last segment of flight, the approach, is important to the mission because although the thrust to weight value

is not a factor, the calculated wing loading for the approach defines the absolute maximum wing loading possible for

the vehicle. To determine this value, the equation for stall speed was rearranged to the following form in Eqn. 24:

28

W ¿

S=

ρ vapp2C L,max

2 kapp2 β

(24)

The stall speed has been replaced by the approach speed divided by the approach safety factor. The approach

safety factor is an important parameter and has been chosen to be 1.3. The other important assumptions for this

analysis are the approach speed and the maximum lift coefficient of the vehicle. The approach speed is given by the

requirements to be 170 knots. However, this value proved to be slightly large when examining the resultant wing

loading value and was reduced to 160 knots in order to provide a more reasonable value. The maximum coefficient

of lift on approach was assumed to be 2.2 based on data taken from Roskam about the increase in maximum C L due

to non-clean configurations.5 The vehicle was assumed to land at the same location and conditions that it initially

took off from. The values for this approach analysis are shown in Table 25.

Table 26: Approach Analysis Values

β CL,max,L vapp (ft/s) rho (slugs/ft3) kapp

.518 2.2 270.05 .001866 1.3

The result of this analysis of the approach of the vehicle was a maximum wing loading of 170.86 lbs per square

ft. This high value of wing loading means that there is a wide range of possibilities for design points and the landing

segment of flight will not have a heavy impact on this design point.

G. Service Ceiling

The final energy based constraint that was analyzed was the service ceiling of the vehicle. It is important to

know the maximum altitude possible at specific velocities for the purpose of maneuverability as well as the risk of

exceeding the service ceiling and approaching the dangerous absolute ceiling. The form of the energy based

constraint equation used to analyze this requirement is no different from the one used earlier to analyze the constant

speed climb. The equation is shown below in Eqn. 25:

T SL

W ¿=

βα {K1

βq (W ¿

S )+K2+CD0

βq ( W ¿

S )+

1V

dhdt } (25)

What makes this analysis different from the original climb analysis is the rate of climb used for the analysis. The

service ceiling for a military aircraft is defined to be the altitude at which the vehicle’s rate of climb is equal to 100


29

feet per minute. For this analysis, the desired ceiling has been defined to be 60,000 feet and the Mach number for

this ceiling has been given as Mach 2.0. At that altitude and Mach number, the velocity is calculated to be 1,147

knots. The values used for this analysis are shown in Table 26.

Table 27: Service Ceiling Analysis Values


.175 .945 1936.15 .000224 1.67 419.44

Using these values, the resultant thrust to weight values required to reach this service ceiling range from .95

down to .57 as wing loading is increased. Therefore, the given service ceiling requirement is not a factor when

considering the overall design point.

H. Design Point

The purpose of this entire constraint sizing analysis was to determine a point on the graph of wing loading vs

thrust to weight ratio that satisfied all the individual mission segment requirements. This design point would

minimize the thrust to weight ratio necessary while maximizing the wing loading. This point is the most design point

because a minimized thrust to weight ratio expands the range of possible engines that can provide the necessary

thrust. The less thrust that is required, the lighter the engine can be. In addition, a maximized wing loading

minimizes the necessary wing area required for the vehicle and reduces the structural load placed on the fuselage as

well as the inner spars and ribs needed. After doing the energy based constraint analysis on all of the segments of

flight, the two segments that define this design point are shown to be the acceleration and the delivery of the

payload. The intersection of these two curves defines the location with the minimum thrust to weight ratio while still

attempting to maximize the wing loading. Therefore, for this constraint analysis, the resultant thrust to weight ratio

was determined to be 1.06 with a wing loading of 98 lbs per square ft. Using these values as well as the initially

determined takeoff weight value of 36,711 lbs, the sea level thrust necessary and the wing area of the vehicle were

calculated to be 39,031 lbs and 375.7 ft2 respectively. All of the different thrust to weight ratio curves as well as the

design point can be seen below in Fig. 11.

30

Figure 11: Constraint Analysis

VI. Constraint Analysis Sensitivity Studies

Now that a design point has been determined for the vehicle, the requirements of the design call for sensitivity

studies in order to determine the impact of both performance requirements as well as the assumptions made

throughout the analysis.

A. Descent Rate Trade Study

The first performance parameter that was analyzed was the descent rate during the accelerated dive of the

vehicle. The acceleration segment of the flight was one of the determining factors of the design point. Therefore, the

descent rate was chosen in order to determine how relaxing or increasing the dive performed would affect the

overall design of the vehicle. The result of this trade study is shown below in Fig. 12.

31

50 70 90 110 130 150 170

-1.5

-1

-0.5

0

0.5

1

1.5

2Simple Takeoff

Friction Takeoff

Climb

Supercruise

Dash 1

Zoom

Delivery

Acceleration

Dash 2

Descent 1

Subcruise

Descent 2

Landing

Service Ceiling

Design PointWing Loading at Takeoff (lbs/ft2)

Thru

st to

Wei

ght a

t Sea

Lev

el T

akeo

ff (~

)

50 70 90 110 130 150 170

-1.5

-1

-0.5

0

0.5

1

1.5

2

150 ft/s

175 ft/s

200 ft/s

225 ft/s

250 ft/s


Thru

st to

Wei

ght a

t Sea

Lev

el T

akeo

ff (~

)

Figure 12: Descent Rate Trade Study

The results of this sensitivity study show the strong impact that the descent rate has on the overall thrust to

weight value of the acceleration segment. The steeper the dive, the greater the acceleration due to gravity and the

less acceleration that the engines themselves are required to put out. Therefore, from a performance perspective, it is

always desireable to dive as steeply as possible in order to both reduce the time necessary for the desired

acceleration as well as reduce the necessary output of the engines of the vehicle.

B. Load Factor Trade Study

The other mission segment that defined the design point for this vehicle was the delivery of the payload modeled

as a constant speed and constant altitude turn. The driving factor in the thrust to weight ratio of this analysis was the

load factor of the vehicle. The greater the load factor, the steeper the turn being performed and the greater the load

on the vehicle itself. The sensitivity study with respect to the load factor is shown in Fig. 13 below.

32

50 70 90 110 130 150 170

-2

-1

0

1

2

3

4

0.8

1.2

1.6

2

2.4


Thru

st to

Wei

ght a

t Sea

Lev

el T

akeo

ff (~

)

Figure 13: Load Factor Trade Study

This sensitivity study shows just how large an impact the load factor has on the resulting thrust to weight values.

For the initially suggested load factor of two, the maximum wing loading of the vehicle would be very small in order

to maintain the desired maximum of 1.2 on the thrust to weight ratio. Increasing the load factor to 2.4 results in a

very steep curve with thrust to weight ratios well beyond the acceptable range. Therefore, for this design, the load

factor was decreased to 1.6 in order to expand the range of possible wing loading values that would meet the

specified requirements.

C. Maximum Lift Coefficient on Approach Trade Study

One of the most important assumptions in this analysis was the assumption regarding the maximum lift

coefficient during the final approach and landing of the vehicle. This assumption is important because the approach

segment of flight determines the maximum wing loading possible for the vehicle. The values of the lift coefficient

vary depending on the amount of extra surfaces and wing area that are added by the use of devices such as flaps and

slats. The greater the wing area that is increased during landing, the larger the resulting maximum lift coefficient

will be. A sensitivity study was performed on this lift coefficient in order to determine the magnitude of its effect on

the resulting wing loading value. The results of this sensitivity study are shown below in Fig. 14.

33

50 70 90 110 130 150 170 190 210 230

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1.6

1.9

2.2

2.5

2.8


Thru

st to

Wei

ght a

t Sea

Lev

el T

akeo

ff (~

)

Figure 14: Maximum Lift Coefficient on Approach Trade Study

The results of this sensitivity confirm that the lift coefficient on approach has a strong impact on the maximum

wing loading possible for the vehicle. An increase in the lift coefficient of .3 results in an increase in the maximum

wing loading by approximately 23. For this design analysis, a lift coefficient of 2.2 was chosen due to data shown in

Roskam detailing the lift coefficient due to flaps at landing.

D. Takeoff Distance Trade Study

The final design assumption that was analyzed for a sensitivity study was the requirement for takeoff distance.

While the takeoff segment did not have an impact on the design point chosen for the vehicle, the length of takeoff is

still a very important parameter as it defines the set of possible runways this vehicle is capable of using. The shorter

the necessary distance for takeoff, the greater possible takeoff and landing locations the vehicle can use. This can be

highly desirable for possible uses on an aircraft carrier or rapidly assembled bases near military front lines. The

results of this sensitivity study are shown below in Fig. 15.

Figure 15: Takeoff Distance Trade Study

The results of this sensitivity study show that the required distance for takeoff does have a strong impact on the

thrust to weight ratio necessary for the vehicle. The shorter the allowable takeoff distance, the greater the slope of

the relationship between wing loading and thrust to weight ratio. Should the takeoff distance be reduced even

34

further, it could become a design point consideration. However, for the purposes of this design analysis, the takeoff

performance was not a priority and so a distance of 10,000 feet was used to ensure that the takeoff performance did

not affect the overall design choices.

VII. Component Design

After performing the constraint analysis on the desired vehicle, the next step in the design process is to begin

designing individuals components of the overall vehicle. Each component was designed using a specific process

detailed in Roskam’s Part II design book. Previous analysis and configuration choices resulted in a vehicle with one

fuselage, a conventional, mid mounted wing, and a v-tail. This paper will explain the design choices made and show

their impact on the final design of each component. Throughout the report, many of the design choices made were

taken from Roskam’s data regarding the F-16 military fighter. This is due to the fact that the F-16 shares a similar

speed and capability and overall size to that of the vehicle designed for this long range strike mission.

VIII. Fuselage Design

The primary component of this supersonic vehicle that must be designed first is the fuselage. The preliminary

configuration choices resulted in a single fuselage aircraft. This fuselage would contain the weapons payload, the

avionics, and as much of the necessary mission fuel as possible.

35

50 70 90 110 130 150 170

-1.5

-1

-0.5

0

0.5

1

1.5

2

5,000 ft

7,500 ft

10000 ft

12,500 ft

15,000 ft


Thru

st to

Wei

ght a

t Sea

Lev

el T

akeo

ff (~

)

A. Weight

The first step in the design process of the fuselage involved compiling a list of all the various components that

would be placed inside the fuselage. The fuselage must be sized in order account for all the weights and volumes of

these components. In order to determine the weight of the avionics equipment necessary in the aircraft, a simple

relationship shown in Eqn. 26 is used. The density of the avionic equipment is assumed to be 30 lbs per square feet.

The list of these weights and sizes is shown in Table 27 below.

W avionics

W E

=.03 (26)

Table 28: Fuselage Component Weight and Volume

Weight (lbs) Volume (ft3)

Avionics 395 13.2

Military Payload 4,000 42.9

Mission Fuel 19,657 408.8

As can be seen from the table, the mission fuel requirement easily dominates both the weight and the volume

requirements. The avionics weight and volume were taken from simple relations from Raymer’s design book based

on the empty weight of a fighter aircraft which can be used for preliminary design purposes. The weight of the

avionics was taken to be 3% of the empty weight of the aircraft and the density of the avionics was taken to be 30

lbs/ft3.6 The military payload weight was given by the requirements in the early design phase of the aircraft while the

volume was taken from the known dimensions of a GBU-32 smart bomb7. Finally, the fuel volume needed for the

aircraft was calculated using the previously known fuel weight of 19,657 lbs and the density of JP-8 military fuel

taken to be .775 kg/L8.

B. Design Choices

Using the known volumes of the various components inside the fuselage, the fuselage cross section and length

can be considered. The most important parameter in the design of the fuselage itself is fineness ratio. This ratio is

defined as the length of the fuselage divided by the diameter. Using Roskam’s table of values for fineness ratio

found in Table 4.1 of Part II of his design book series, a fineness ratio of 10 was selected for this aircraft9. Due to the

supersonic requirements of the vehicle’s mission, a longer, thinner fuselage section is desired because it will

6Raymer, Daniel P. Aircraft Design: A Conceptual Approach. Reston, VA: American Institute of Aeronautics and Astronautics, 1999. Print.7 "Joint Direct Attack Munition (JDAM) GBU-29, GBU-30, GBU-31, GBU-32."Joint Direct Attack Munition (JDAM) GBU-31. N.p., n.d. Web. 6 Nov. 2014. http://fas.org/man/dod-101/sys/smart/jdam.htm. 8 Schmigital, Joel, and Jill Tebbe. JP-8 and Other Military Fuels. Rep. N.p., 12 Jan. 2011. Web. 8 Nov. 2014. www.dtic.mil%2Fcgi-bin%2FGetTRDoc%3FAD%3DADA554221. 9 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.

36

http://fas.org/man/dod-101/sys/smart/jdam.htm

produce less drag in the high speed flow. In addition to this fineness ratio, Roskam also gives values for the

structural thickness of the fuselage wall. This chosen thickness of 2 inches must be taken into account when the

fuselage itself is designed and modeled.

C. Fuselage Model

Using the internal component volumes as well as the parameters taken from Roskam’s data10, a three-view of one

potential fuselage design was created using SolidWorks modeling software. These views are shown in Fig. 16, Fig.

17, and Fig. 18 below. All dimensions shown are in feet.

Figure 16: Fuselage Top View

Figure 17: Fuselage Side View

10 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.

37

Figure 18: Fuselage Front View

D. Final Fuselage Design Summary

As the three views of the final fuselage model show, a circular cross section with a diameter of 6 feet was chosen

for the main section of the fuselage. Using this choice and the fineness ratio, the final length of the fuselage can be

easily calculated to be 60 feet long. This is a reasonable value because it is comparable to current military aircraft

such as the F-22 Raptor which has a length of 72 feet11. The entire fuel necessary for the mission has been placed

inside the fuselage, thus allowing the wings to be of a minimal thickness and overall weight. This fuel is stored in

one large central tank in the center of the aircraft. This tank has a diameter of 5 feet and a length of 22 feet. These

dimensions give a tank volume of 431.9 ft3 which is more than adequate to store the 19,657 lbs of fuel. The military

payload of the four GBU-32 bombs has been placed near the rear of the aircraft, with the four bombs being stacked

vertically on top of one another for rapid deployment in a combat situation. The avionics of the aircraft has been

placed at the front of the fuselage in place of a cockpit. Finally, the small object placed between the avionics and the

main fuel tank is the Jet Fuel Starter, JFS, which is used to power up the vehicle’s engines until they can maintain

their rotation themselves.


38

IX. Wing Design

Now that the fuselage has been designed, the next component to be designed was the wing. The wing provides

the vast majority of the lift for this aircraft as well as being the location of the vehicle flap and ailerons as well as

the engines which are not included in this version of the design. The preliminary configuration choices previously

decided that this wing would be a traditional wing mounted in the middle of the fuselage.

A. Configuration Choices

Throughout the wing design process, many assumptions and design choices were made using historical data

taken from Roskam’s design book. While these choices do not have numerical explanations, they have been

previously verified by design engineers and analysts using complex finite element analysis, FEA, as well as

computational fluid dynamics, CFD. Therefore, it possible to use these assumptions and values created for other

aircraft in the design of this vehicle provided that the two vehicles share similar traits.

Due to the mission requirements of the vehicle, the wing was chosen to be a cantilevered wing mounted the

middle of the fuselage. The mid wing attachment point was selected due to its strong supersonic performance with

respect to minimizing drag on the aircraft.

B. Airfoil Selection

One critically important factor in the design of the wing is the airfoil chosen to be the cross section of the wing

along the span. This airfoil drives the vehicle’s lift, drag, and moment response through all phases of flight. For the

purposes of this supersonic strike vehicle, the NACA 64-204 airfoil was chosen. This design choice was based on

similar aircraft such as the F-22 Raptor which used this type of airfoil in their design. This airfoil was analyzed in

the XFOIL program to determine these important responses. The graphs of these responses are shown in Figs. 19,

20, 21, and 22.

-4 -2 0 2 4 6 8 10 12 14-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Angle of Attack (°)

Coeffi

cient

of L

ift (~

)

Figure 19: Coefficient of Lift versus Angle of Attack for NACA 64-204

39

The coefficient of lift versus angle of attack shows the .177 offset of the c l due to camber. The initial portion of

the graph shows a very linear relationship with a dc l/dα of .1098. The stall characteristics of the airfoil can be seen

beginning around 8 degrees angle of attack. Immediately the cl decreases and becomes very unsteady.

-4 -2 0 2 4 6 8 10 12 140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18


Coeffi

cient

of D

rag

(~)

Figure 20: Coefficient of Drag versus Angle of Attack for NACA 64-204

The coefficient of drag versus angle of attack response shows very favorable drag at low angles of attack.

Between -2 and 6 degrees angle of attack, the coefficient of drag is nearly constant at a value of .004. This means

that the cl can be increased for added lift without a drastic penalty in the increase in drag. At an angle of attack

beyond 6 degrees, the drag begins to increase dramatically and at the stall point, makes a near vertical increase.

-4 -2 0 2 4 6 8 10 12 14

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0


Coeffi

cient

of M

omen

t

Figure 21: Coefficient of Moment about the Leading Edge versus Angle of Attack for NACA 64-204

The coefficient of moment about the leading edge of the vehicle is shown to be negative regardless of the angle

of attack chosen. This is a desirable outcome because it means that when the vehicle will naturally resist any upward

40

change in its angle of attack and attempt to prevent increasing angle of attack up to the stall region. For the range of

angles of attack which will be used by this vehicle, the Cm,LE is nearly constant at a value of -.043.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Coefficient of Drag (~)

Coeffi

cient

of L

ift (~

)

Figure 22: 2-D Drag Polar for NACA 64-204

Finally, the drag polar for the NACA 64-204 airfoil shows a very high L/D ratio for all values of c l up to almost

one. This behavior means that the range performance will be very strong at all angles of attack before stall.

However, in supersonic flight, the velocity is so high that in order to produce the lift necessary for steady level

flight, the cl does not need to be very high. Therefore, to maintain level flight, a lower angle of attack than the

optimum will be used.

C. Wing Geometry Specification

Having decided upon the airfoil shape to be used for the wing, the next step is to determine the geometric

properties of the wing. These properties are taken from previous sizing and constraint analysis and Roskam’s

historical data as well as design choices with regards to drag and vehicle control. The chosen specifications are

displayed below in Table 28.

Table 29: Main Wing Specifications

structure placement airfoil Area (ft2) AR Span (ft) Sweep,c/4 (°) t/c taper incidence (°) dihedral (°)

cantilevered mid-wing NACA 64-204 374.0 2.5 30.6 45 .04 .3 0 0

The properties such as the wing area, aspect ratio, span of the wing, and thickness to chord ratio come from

previous weight sizing and constraint sizing analysis. The incidence angle and dihedral angle of the wing are chosen

to be zero in order to optimize performance and control of the aircraft during high speed flight. Finally, the sweep

41

angle and taper ratio of the wing were chosen based on the F-16 data displayed in Roskam’s Table 6.9 in Part II of

his design series.12

D. Flap Design

Before the full wing can be designed and modeled, the control surfaces that will be placed on the wing must be

sized and located. The first of these control surfaces that must be designed is the flaps on the wing. During takeoff

and landing, the vehicle requires a large cL,max than can be produced by a plain wing. Therefore, flaps are needed to

increase the lift on the vehicle and either help it get in the air on takeoff or help it slow down upon landing. In order

to decide which flaps to use and how to size these flaps, a process was used to determine the change in C l,max that

each flap would produce. First, the change in cL at takeoff and landing was calculated using Eqn. 27. The values of

CL,max for takeoff and landing were taken from the previously assumed values during the constraint analysis.

Table 30: Maximum Lift Coefficients

CL,max,TO CL,max,L

1.8 2.2

ΔC Lmax ¿ /L

=1.05(CLmax¿ / L

−CLmax) (27)

Then, the required increase in cl,max due to the flaps being lowered was calculated using Eqn. 28.

Δcl max=

ΔC Lmax∗S

Swf

K Λ

(28)

The value KΛ accounts for the effect of sweep angle when the flaps are down and can be calculated using Eqn. 29.

K Λ=(1−.08 cos Λ c4

2)cos Λc /43/4

(29)

The ratio of the main wing area to the flap area can be estimated using multiple values between zero and one and

running the calculations multiple times. The necessary increase in c l due to flap deflection can be calculated by Eqn.

30.

Δcl=1K

Δclmax(30)


42

The factor K can be found for each type of flap using Fig. 7.4 in Roskam’s Part II13. Finally, the increase in cl due to

the flaps can be calculated using Eqn. 31.

Δcl=c l∝∝δ f

δ f (31)

The value of αδ,f is the section lift effectiveness parameter and can be found using Fig. 7.8 in Roskam 14. The δf

represents the flap deflection. For this aircraft, Swf/S of .84 and a flap chord to main wing chord ratio, c f/c, of .30

were chosen. Due to the high change in lift needed, Fowler flaps were chosen to be placed on the wing. The result of

these calculations is shown in Table 30 below.

Table 31: Flap Sizing Values

KΛ Swf/S bf/b K αδ,f δf (°)

Takeoff .74 .4 .75 .92 .53 25

Landing .74 .4 .75 .92 .46 40

The result of these calculations was a Fowler flap covering 75% of the span and 40% of the wing area. The flap

would be deflected 25° at takeoff and 40° at landing.

E. Aileron Design

The other necessary control surface to place on the wing is the ailerons. Unlike the flaps, for this initial design,

the aileron sizing was taken from historical data provided by Roskam for fighter aircraft in Table 8.9b in his Part

II.15 Using the values in this table as a base point, the aileron was chosen to be at the tip of the wing. The size is

shown in the final 2D modeling.

F. Wing Mode

With the flaps and the ailerons designed, the wing was then designed and modeled in three different views. One

half of the wing is shown with the other half being symmetrical with respect to the midline of the aircraft. The three

views of the main wing are shown in Figs. 23, 24, and 25.




43

Figure 23: Main Wing Top View

Figure 24: Main Wing Side View

Figure 25: Main Wing Front View

G. Final Wing Design Summary

The result of this wing analysis and design was a wing of span 30.6 ft, area of 374 ft 2, 45° quarter chord sweep,

with Fowler flaps along 75% of the span and ailerons near the wing tips. Two spars were added into the wing as can

44

be seen in the top view of the wing. The leading edge spar is placed at .5% of the chord while the second spar is

placed just before the control surfaces.16 In many aircraft, fuel is stored in the wings but for this design, all the

mission fuel necessary was placed inside the fuselage. This design choice was made in order to minimize the weight

and thickness of the wing with the goal of maximizing supersonic performance. In the future, this wing may need to

be altered slightly to account for the position and weight of the vehicle’s engines. However, at this time, the wing

meets all requirements and design choices and can be used for a preliminary modeling layout.

X. Tail Design

The final vehicle component that must be designed during this stage is the vehicle’s tail. This part of the vehicle

is critical for its contribution to stability and control, future weight and balance of the vehicle, as well as a lesser

contribution to lift. In the preliminary configuration analysis, a v-tail was chosen for its high velocity performance

and minimal drag.

A. Tail Configuration

The process by which the tail was designed was the volume coefficient method. Assumptions were made about

the moment arm of the horizontal and vertical tail as well as the volume coefficient of the horizontal and vertical tail

in order to determine the area of the tail required. The area of the horizontal and vertical tail can be calculated

separately using Eqns. 32 and 33.

Sh=V h S c

xh

(32)

Sv=V v Sb

xv

(33)

Because the tail is a v-tail, the horizontal and vertical surface areas must then be combined into one surface with a

dihedral angle that can be calculated easily using Eqn. 34.

Γh=tan−1 Sv

Sh

` (34)

The final values from these calculations are shown in Table 31.

Table 32: Volumetric Coefficient Method

x V S dihedral (°)

Horizontal 20 0.3 68.60 38.1


45

Vertical 20 0.094 53.74 38.1

B. Tail Geometry Specifications

After the surface areas and dihedral angle for the tail have been calculated, the next step in the process was to

choose the geometric parameters which would define the shape of the tail. These parameters include the incidence

angle, the aspect ratio, the sweep angle, the thickness ratio, the airfoil, and the taper ratio. These choices were made

based on the previously designed main wing as well as values taken from Roskam’s Tables 8.13 and 8.14 in Part II. 17The final values chosen for the tail geometry are shown in Table 32.

Table 33: Tail Sizing Values

AR Sweep (°) taper t/c airfoil incidence (°)

3 40 .3 .04 NACA 64-204 0

C. Tail Control Surfaces

Similarly to the design of the main wing, before the tail can be fully designed and modeled, the control surfaces

that will be placed on the tail must be sized and located. Due to the designed tail being a v-tail, the two control

surfaces normally on the horizontal and vertical tail of an airplane, the elevators and the rudder, were combined into

one control surface which controlled both pitch and yaw motion. The basis for the these sizing and locating

decisions was the data provided in Roskam’s Table 8.9a and 8.9b in Part II18. The v-tail control surfaces for this

aircraft were based on the control surfaces of similar style fighter aircraft. By this reasoning, the entire length of the

span of the v-tail was used for the ruddervator. The final control surface design and placement can be seen in the

design model of the tail.

D. Tail Model

With finalized values for the tail and control surface sizing, the final tail can be designed and modeled. Only one

tail is shown in these models with the other tail being a reflection across the center of the aircraft. The three views of

the tails are shown in Figs. 26, 27, and 28.

17 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.18 Roskam, Jan. Preliminary Configuration Design and Integration of the Propulsion System. Lawrence, Kan.: DARcorporation, 2004. Print.

46

Figure 26: Tail Top View

Figure 27: Tail Side View

47

Figure 28: Tail Front View

E. Final Tail Design Summary

The result of the tail design process is a v-tail on each side of the midline of the aircraft with a height of 4.31 ft, a

width of 5.50 ft, and a length of 5.86 feet. The ruddervator is located at the back of this v-tail and will be used to

control both pitch and yaw of the vehicle. While this may require a more complicated feedback response controller

and sensors, the v-tail gives much better performance in the conditions required for this mission. This tail will likely

be moved and resized in the weight and balance process but for this preliminary design, the v-tail meets all

requirements and chosen parameters and can be used to model the first stage of the design.

XI. Final Design Summary

Once all three major vehicle components had been sized, designed, and modeled, they could be combined to

create the first working visual model of the full aircraft. This aircraft will need much more analysis and repetitive

iteration through all steps of the design but with this model, the design can proceed into more detailed design work.

F. Final Model

The final model of the preliminary design for the uninhabited long range strike vehicle is shown in Fig. 29.

48

Figure 29: Vehicle Top View

The result of combining the three components designed in this initial design phase is a vehicle that somewhat

resembles a large missile. This is realistic because at the high supersonic speeds this vehicle is designed for, the

vehicle shape needs to be streamlined and narrow to reduce the impact of the wave drag. One important parameter

that must be analyzed with the final configuration is the supersonic or subsonic leading edge of the vehicle. A

supersonic leading edge results in shocks forming on the surface of the wing. In order to greatly reduce the

disturbances across the wing, the leading edge must be contained within the Mach cone that the vehicle creates in

flight. All flow within this cone is initially subsonic so the leading edge of the vehicle wing will interact with

subsonic flow. The relationship to calculate the Mach cone of the vehicle is shown in Eqn. 35.

μ=sin−1 1M

(35)

At Mach 2, this cone is 30° on either side of the line of symmetry of the aircraft. The angle between the nose of

the aircraft and the leading edge of the tip chord is shown in Fig. 30.

49

Figure 30: Vehicle Subsonic Leading Edge

G. Neutral Point

One crucial point on the aircraft to determine from this initial design is the neutral point. The neutral point is the

point on the aircraft which defines the location of the center of gravity which would be statically neutral. The neutral

point is a critical factor in computing the longitudinal static stability of the entire aircraft. The distance between the

center of gravity and the neutral point is called the static margin and is a measure of this stability. If the neutral point

is not behind the center of gravity, then the vehicle is unstable. In order to find the neutral point for this

configuration, the coefficients of lift, coefficients of moment, and other geometric factor were used. The

relationships used to find the neutral point are shown below in Eqns. 36, 37, 38 and 39.

CL ,α , w=C l , α , w

1+Cl , α ,w

π ARw

(36)

CL ,α ,t=Cl , α ,t

1+C l ,α , t

π AR t

(37)

dεdα

=2CL, α ,w

π ARw

(38)

xNP

c=

x AC

c+η V H

cL ,α ,t

cL ,α , w

(1− dεdα

) (39)

50

The values used in these calculations are shown in Table 33. The results of the neutral point calculations are

shown in Table 34.

Table 34: Neutral Point Analysis Values

c xac/c CM,α,f Cl,α,w Cl,α,t η VH ARw ARt

12.2 .25 -.24 6.11 6.11 1 .3 2.5 3

Table 35: Neutral Point Calculations

de/dα cL,α,t cL,α,w XNP/c c XNP

.875 3.71 3.44 .360 12.2 5.54

Using these values, the neutral point of the aircraft is calculated to be 5.54 ft past the leading edge of the main

wing. This means that the center of gravity of the wing must be in front of this point in order for the vehicle to be

stable. The location of the neutral point on the vehicle is shown in Fig. 31 below.

Figure 31: Neutral Point Location

XII. Landing Gear and Weight and Balance

The final step in the preliminary design process is the design and addition of landing gear to the aircraft and

then the process of determining the weights of each component to determine the center of gravity of the vehicle.

51

This step allows for a finalized preliminary design of the vehicle to be completed with basic consideration for

important factors like stability. It is possible, during this process, to determine that the entire designed aircraft is

unfeasible and cannot be fixed without major redesign of one or more of the components.

A. Component Weight Breakdown

The first step in this process was to determine the weights of each of the individual components being placed

into the fuselage. This step is necessary because a weighted center of gravity for each of these components will

produce the center of gravity for the overall aircraft. Weights were calculated for the various systems and then

specific components by using data taken from Roskam’s Part V19. The values chosen for this analysis were taken

from the F-18 Hornet due to its similar style and performance capabilities. The most important value for this

analysis was the flight design gross weight, WG. The ratios used to determine these weights are shown in Table 35

below.

Table 36: Gross Weight Ratios

WTO/WG Wstructure/WG Wpower/WG Wfixed/WG Wwing/WG Wempennage/WG Wfuselage/WG Wengine/WG Wgear/WG

0.623 0.357 0.194 0.158 0.117 0.029 0.145 0.684 0.062

Using these ratios, the weights of each component were calculated. These weights are shown in Table 36 below.

Table 37: Vehicle Component Weights

WG Wstructure Wpower Wfixed Wwing Wempennage Wfuselage Wengine Winduct Wgear

22,887 8,171 4,440 3,616 2,678 664 3,319 3,307 299 1,149

B. Component Center of Gravity

Using these calculated weight values for each component, the individual center of gravity for each component

was calculated based on both its distance from the nose of the aircraft, xcg, and its distance from a reference point

well below the nose of the aircraft, zcg. This reference point was chosen to be 20 feet below the nose of the aircraft

so that with the later addition of the landing gear, the center of gravity location would still be positive. Because the

vehicle is intentionally designed to be perfectly symmetrical, the ycg of the aircraft is known to be 0. Each individual

center of gravity was found using SolidWorks area centroid.

19 Roskam, Jan. Component Weight Estimation. Lawrence, Kan.: DARcorporation, 2003. Print.

52

Table 38: Component Centers of Gravity

Component xcg (ft) zcg (ft)

fuselage 35.3 20.0

wing 46.2 20.0

tail 55.3 24.8

engine 47.0 22.0

air induct 41.0 22.0

fixed equipment 7.0 20.0

fuel 24.0 20.0

payload 40.5 20.0

nose gear 6.0 13.0

main gear 37.7 13.0

The information shown in Table 35, Table 36, and Table 37 includes the landing gear of the aircraft which will

be designed in a later step.

C. Vehicle Center of Gravity

Using the weights and individual centers of gravity for the components of the aircraft, the overall center of

gravity for this configuration can be calculated. There are multiple centers of gravity of interest for this design

process depending on which weights are included in the center of gravity calculation. The five points of interest can

be calculated using Eqns. 40, 41, 42, 43, and 45 as shown below20.

xcgW E

=∑i=1

6

W i x i

W E

(40)

xcgW OE

=∑i=1

8

W i x i

W 0 E

(41)


53

xcgW ¿

=∑i=1

13

W i x i

W ¿

(42)

xcgW F

=∑i=1

9

W i xi

W OE+W F

(43)

xcgW P

=∑i=1

6

W i x i

W OE+W P

(44)

The resulting centers of gravity from these equations are shown below in Table 38.

Table 39: Vehicle Centers of Gravity

WE (ft) WOE (ft) WTO (ft) WF (ft) WP (ft)

xcg 37.8 37.3 30.7 29.4 38.1

zcg 22.9 22.6 21.0 21.0 22.0

The front-most and aft-most centers of gravity are shown in Fig. 31 below.

Figure 32: Center of Gravity Range

54

D. Weight-C.G. Excursion Diagram

The purpose of calculating all of these different values for the center of gravity was to analyze the potential

movement of the center of gravity during the various flight segments. This is represented graphically using a weight-

c.g. excursion diagram as shown in Fig. 33.

0.4 0.5 0.6 0.710000

15000

20000

25000

30000

35000

40000

We

Payload

Wto

Fuel

Fuel

Woe

Payload

C.G. Location (F.S.)

Wei

ght (

lbs)

Figure 33: Weight-C.G. Excursion Diagram

This diagram shows that the fuel is by far the dominating factor in the determination of the movement of the

center of gravity. This makes sense because in supersonic flight, a large amount of fuel will be burned at a rapid

rate. Initially, the center of gravity will be much further forward. However, as the fuel is burned, the center of

gravity will move backwards. This results in a center of gravity range of 8.7 ft. This is a reasonable value for the

range because of the large changes that occur during sustained supersonic flight. In addition, all of these values are

in front of the previously calculated neutral point position at 38.2 ft behind the nose. This means that the vehicle will

always be statically stable.

E. Landing Gear Configuration

The final component that must be designed for this aircraft is the landing gear. The landing gear must be

designed such that the vehicle is capable of easily taking off and landing safely, the vehicle will not tip over in either

the longitudinal or the lateral direction, and that the gear can be folded up inside the aircraft structure after takeoff.

This is particularly important because in supersonic flight, every exposed piece of the aircraft creates a large amount

of a vehicle with fixed landing gear would create a very large amount of excess, wasteful drag. Therefore, for this

design, the landing gear configuration has been chosen to be a traditional tricycle with retractable gear. This

configuration is the simplest and most commonly used for this style of aircraft.

55

F. Gear Design

When designing the landing gear for this aircraft, four criteria must be met: the gear must prevent the entire

vehicle from touching the ground when the vehicle is landed, the gear must prevent longitudinal tip over, the gear

must prevent lateral tip over, and the gear must retractable into the vehicle structure. Due to the thin nature of the

wings, the main gear may be attached to the lower surface of the wing but the bulk of the gear and the tires must be

stored inside the fuselage.

In order to prevent the vehicle from touching the ground at any time, the center of the tires have been placed 7

feet below the nose of the aircraft. This ensures that the vehicle will not hit the ground at any point while it is on the

ground. One strut and one tire have been chosen for the nose landing gear because this vehicle is relatively light and

does not need a large amount of reinforced landing gear. The location of the nose landing gear has been chosen to be

6 feet behind the nose of the aircraft. This is done because the nose landing gear is located very near to the nose of

the aircraft and in this location, the vehicle can be retracted backwards into the fuselage. In the fuselage, they will be

retracted beneath the fixed equipment placed near the front of the aircraft. The nose landing gear tires have a

diameter of 2 feet and can easily be placed in the structure as can be seen in the fuselage side view in Fig. 17.

The main landing gear have been placed 39.9 feet behind the nose of the wing. The height of the gear is the

same as the nose gear and the distance behind the nose is determined by a 15 degree angle between the landing gear

and the most aft center of gravity. The gear is attached on the wing at 8.5 feet on either side of the axis of symmetry.

This location is determined by a 50 degree angle that is determined by the line between the nose and main gear,

passing through the front most center of gravity and ending at the opposite side main gear. The main gear of the

aircraft is designed to be retracted laterally into the fuselage on either side of the payload at the rear of the aircraft.

Sufficient space for these landing gear can be seen in the top view of the fuselage in Fig. 16. Similarly to the nose

gear, the main gear at the rear of the aircraft have been chosen to have on strut and one tire. The final configuration

and implementation of the landing gear is shown below in Fig. 34.

Figure 34: Landing Gear Side View

G. Landing Gear Loads

56

In the design of the landing gear, it is important to calculate the loads that the landing gear will be placed under.

This load analysis can help determine the number of tires, the tire size, the number of struts, and the materials

chosen for the manufacturing. The load on the nose wheel strut and main gear strut are calculated according to Eqns.

45 and 46 respectively.

Pn=W ¿ lm

lm+ln

(45)

Pm=W ¿ lm

ns(l¿¿m+ ln)¿ (46)

The value of ln is defined as the distance between the nose gear and the center of gravity and the value of l m is

defined as the distance between the center of gravity and the main gear. The value of n s is chosen to be 1 for both

sets of gear. The values used for these calculations and the results are shown in Table 39 below.

Table 40: Gear Strut Load Values

WTO (lbs) ln (ft) lm (ft) ns Pn (lbs) Pm (lbs)

36,711 32.1 1.9 1 2,031 34,679

In order to size the tires of the landing gear, two ratios of Pn/WTO and nsPm/WTo are used. Using the calculated

values, these ratios are found to be .055 and .944 respectively. Using Table 9.2 in Roskam Part II 21, these ratios are

then used to size the main gear to be 24x8 inches with a pressure of 210 psi and the nose gear to be 18x6.5 inches

with a pressure of 120 psi. This results in a volume of 2.09 ft3 for the main gear and .96 ft3 for the nose gear.

XIII. Conclusion

The result of this analysis was to produce a preliminary model of a vehicle with a fuselage, a wing with flaps and

ailerons, simple engines, and a v-tail with ruddervators. In the future of this design, more detailed design

considerations like the wing tips, material selection, and internal structure may be added to create a more complete

airplane. The purpose of this RFP was to create an uninhabited, long range strike vehicle capable of executing a

strike mission and returning back to base. This design went through the process detailed in Roskam’s design book

series to create this vehicle one component at a time and eventually combine all of these components together into a

full aircraft model. All of these individually designed components and choices work together in order to create a

vehicle capable of carrying out the design mission in the most effective and efficient manner. The final three views

of the design for this RFP are shown below in Figs. 35, 36 and 37.


57

Figure 35: Final Design Top View

Figure 36: Final Design Side View

Figure 37: Final Design Front View

58

In the models shown above, the vehicle is assumed to be in flight and the landing gear in the retracted position.

The design process requires large numbers of iteration and a large amount of very detailed analysis and this is only

the first step. One major consideration in any design that was not considered for this analysis was the cost of the

vehicle. This is always one of the most important things to consider throughout the entire design process. While with

enough time and resources, an aircraft with truly superior qualities might be developed and manufactured, the cost to

the company would be so high that the vehicle would never be produced. However, for the purposes of preliminary

design, cost is not an important factor for this considered RFP and the finalized vehicle has been created for the

purposes of future detailed design.

59

References

1. Hunter, Jamie. Jane's All the World's Aircraft: In Service: 2012-2013. Coulsdon: IHS Jane's, 2012. Print.

2. Jackson, Paul A. Jane's All the World's Aircraft: Development & Production: 2012-2013. Coulsdon: IHS Jane's, 2012. Print.

3. "Joint Direct Attack Munition (JDAM) GBU-29, GBU-30, GBU-31, GBU-32."Joint Direct Attack Munition (JDAM) GBU-31. N.p., n.d. Web. 6 Nov. 2014. http://fas.org/man/dod-101/sys/smart/jdam.htm.

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a preliminary design for a unmanned long range strike vehicle

Documents

vehicle weight

vehicle takeoff weight

vehicle speed v

final vehicle configuration

design process

weight ratio v

vehicle range rc

preliminary design analysis