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UCLA Mechanical and Aerospace Engineering Department

MAE 154A – Preliminary Design of Aircraft

Professor O. O. Bendiksen

March 18, 2013

Karl Balitaan – Aerodynamics & Layout

Filip Kik – Stability and Trim & Layout

Christian Pineda – Propulsion and Performance

Final Design Review of the Sonic Cruiser

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Table of Contents

I. Introduction – pg 5

II. Summary of Sonic Cruiser Specifications – pg 6

III. Aircraft Design and Layout – pg 7-17

IV. Aerodynamics – pg 18-35

V. Propulsion and Performance – pg 36-50

VI. Stability and Trim – pg 51-63

VII. Conclusions – pg 64-65

VIII. References – pg 66

IX. Appendix – pg 67-74

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List of Figures and Tables

Aircraft Design & Layout Table D1 - Final Weight Breakdown for Aquila, our Optimized Sonic Cruiser at Load Condition I – pg 9 Table D.2 - Fuselage Exterior Dimensions – pg 10 Table D3 - Fuselage’s Nose Section – pg 10 Table D4 - Fuselage’s Center Section – pg 10 Table D5 - Fuselage’s Tail Section – pg 11 Table D6 - Fuselage Dimensions – pg 11 Table D7 - Fuel Tank Capacity of Aquila – pg 12 Table D8 - Summary of Aircraft Weight and CG for Load Condition I – pg 13 Table D9 - Summary of Aircraft Weight and CG for Load Condition II – pg 13 Table D10 - Summary of Aircraft Weight and CG for Load Condition III – pg 13 Table D11 - Summary of Aircraft Weight and CG for Load Condition IV – pg 13 Figure D1 – Aquila Seating Layout – pg 14 Figure D2 – Fuselage Cross Section Interior View – pg 15 Figure D3 – Front View of Aquila with Landing Gears Deployed – pg 16 Figure D4 – Front View of Aquila with Landing Gears Retracted – pg 16 Figure D5 – Side View of Aquila with Landing Gears Deployed – pg 16 Figure D6 – Side View of Aquila with Landing Gears Retracted – pg 17 Figure D7 – Top View of Aquila – pg 17

Aerodynamics:

Table A1 - Initial CFD Code Parameter Sweeps for 0.95Ma and CL = 0.3 – pg 19 Table A2 - Possible Optimized Wing Configuration – pg 20 Table A3 - Wing A Fixed Geometric Relationships – pg 21 Table A4 - Starting Cruise Conditions for Sonic Cruiser – pg 22 Table A5 - NACA 64-006 Lift Polar – pg 23 Table A6 - NACA 64-006 Drag Polar – Parasite Drag Formula – pg 23 Table A7 - Planform Area Summary – pg 24 Table A8 - Sonic Cruiser’s Optimized Wing Geometry Relationships – pg 25 Table A9 - Optimized Wing Dimensions – pg 25 Table A10 - Aileron Dimensions – pg 25 Table A11 - Canard Dimensions – pg 26 Table A12 - Dimensions for 1 Vertical Stabilizer – pg 27 Table A13 - Rudder Dimensions – pg 27 Table A14 - Reynolds Number for Cruise Conditions at 0.95Ma – pg 27 Table A15 - Induced Drag Formula – pg 27 Table A16 - Total Drag Coefficient for the Sonic Cruiser’s Wing and Canard for CL = 0.3 – pg 28 Table A17 - Lift-to-Drag Ratio for Wing and Canard at Cruise Lift Coefficient of CL = 0.3 – pg 29 Table A18 - Fuselage Skin Friction Drag Coefficient – pg 30 Table A19 - Vertical Stabilizer Skin Friction Drag Coefficient – pg 30 Table A20 - External Geometry of Engine and Nacelles – pg 31 Table A21 - Properly-Designed Engine and Nacelle Skin Friction Drag Coefficient – pg 31 Table A22 - Total Aircraft Lift Coefficient for Cruise at CL = 0.3 for Load Condition I at Start of Cruise – pg 32 Table A23 - Aerodynamic Center and Moment Calculations with respect to MAC for CL = 0.3 – pg 34 Table A24 - Fowler Flaps Dimensions – pg 35 Table A25 - Maximum Lift Coefficients for Airfoil and Wing without Addition of Flaps – pg 35 Table A26 - Maximum Lift Coefficients for Airfoil and Wing with Addition of Flaps – pg 35 Table A27 - Parasite Drag Contribution from Fully Extended Fowler Flaps – pg 36

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Figure A1 – Comparison of L/D vs. Ma between Baseline and Optimized Wing – pg 21 Figure A2 – Comparison of Drag Coefficient vs. Ma between Baseline and Optimized Wing – pg 22 Figure A3 – Comparison of total L/D vs. Ma between Baseline and Optimized Wing – pg 28 Figure A3 – Comparison of total Drag Coefficient vs. Ma between Baseline and Optimized Wing – pg 30

Performance:

Table P1 – GE90-94B Specifications – pg 37 Table P2 – Climb Performance – pg 44 Table P3 – Maximum Mach – pg 46 Table P4 – Absolute Ceiling – pg 46 Table P5 – Parameters in Determining Maximum Range – pg 47 Table P6 – Rate of Descent – pg 48 Table P7 – Fuel Weight Breakdown – pg 48 Table P8 – Performance Summary – pg 51 Figure P1 – Landing Gear Drag Coefficient Factor – pg 39 Figure P2 – Takeoff Parameters – pg 40 Figure P3 – Takeoff Performance – pg 41 Figure P4 – Takeoff Distance – pg 41 Figure P5 – Thrust Map Scaling: PW4056 to GE90-94B – pg 43 Figure P6 – Climb Altitude vs. Time – pg 44 Figure P7 – Climb Cruise Altitude Variation – pg 45 Figure P8 – Complete Mission Profile – pg 47 Figure P9 – Maximum Climb Performance Scaling from JTD9-7 – pg 49

Stability and Trim:

Table S1.a – CG Location for all Loading Conditions at Start of Cruise – pg 55 Table S1.b – CG Location for all Loading Conditions at Takeoff – pg 56 Table S1.c – CG Location for Load Condition I at End of Cruise and After Descent – pg 57 Tables S2 – Parameters and Respective Values for Calculation of Static Margin – pg 59-61 Table S3 – Static Margin and Pitch Stability for all Load Conditions and Flight Scenarios – pg 61 Tables S4 – Trim Calculations – pg 63 Figures S1: Plot of Pitch Stability for all Load Conditions at Start of Cruise and Takeoff – pg 62

Appendix:

Table AP1 – Statistics of Original Sonic Cruiser Design – pg 68 Table AP2 – Statistics of Boeing 787-8 Dreamliner – pg 68 Table AP3 – Baseline Sonic Cruiser Design Dimensions – pg 68 Table AP4 – Standard Atmosphere – pg 68 Table AP5 – Optimized Wing’s Aerodynamic Stats for CL = 0.3 – pg 69 Table AP6 – Optimized Wing’s Aerodynamic Stats for CL = 0.4 – pg 70 Table AP7 – Optimized Wing’s Aerodynamic Stats for CL = 0.5 – pg 70 Table AP8 – Climb Excel Spreadsheet – pg 73 Table AP9 – Cruise Excel Spreadsheet – pg 74 Table AP10 – Descent Excel Spreadsheet – pg 75 Figure AP1 – Comparison of Total L/D vs. Ma for Baseline and Optimized Wing – pg 69 Figure AP2 – Comparison of Total L/D vs. Ma for Baseline and Optimized Wing – pg 69 Matlab Code for Thrust Lapse – pg 71-72

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Introduction

The Sonic Cruiser concept originally devised by Boeing was aimed to exploit the commercially

uncharted altitudes greater than 40,000 feet. There are several advantages and disadvantages to

operating in this range. At higher altitudes, the air density is lower, inducing a lower drag for the same

speed. At the same time, the thrust capabilities of engines generally decrease at altitude and at higher

speeds. Aerodynamically, a wing of small thickness is ideal for the transonic regime, but structurally, it is

a nightmare to manufacture and maintain its integrity. Had this concept been successfully implemented,

the speed increase near sonic flight might have paved way for a new breed of commercial aircraft, the

Sonic Cruiser.

We improved upon the performance of our baseline design for the Sonic Cruiser. We named

our optimized Sonic Cruiser the Aquila, which is Latin for “the eagle.” Aquila has a range greater than

7,600 nautical miles and can fly at a maximum cruise velocity faster than Mach 1. Moreover, it cruises

alone for altitudes greater than 40,000ft. With its sleek design of the fuselage and lifting surfaces, its

cruise velocity near the speed of sound, and its impressive range capabilities, the Aquila flies swiftly

above its competitors. Just like the eagle is the undisputed king of the birds, we believe our design has

the necessary performance to become the future leader of the current commercial aviation fleet.

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Summary of Sonic Cruiser Design Specifications

Number of Passengers

200

Start of Cruise Conditions

h [ft] V [Ma] V [mph]

40,000 0.95 627.052

Takeoff

CL, total stall speed Vstall [mph]

liftoff speed VLO

[mph]

climb out speed V2

[mph]

ground roll [ft]

air distance

[ft]

takeoff distance

[ft] Time [s]

1.47 150.73 190.31 193.36 7073.03 611.03 7648.06 42.60

Climb

Mach average RC [ft/min] time to cruise conditions from

standstill [min]

0.95 1663.09 24.73

Maximum Cruise Altitude

hmax [ft]

~50,000

Maximum Velocity

h [ft] V [Ma] V [mph]

41,000 1.023 991

Landing

VL=1.15Vstall [mph]

173.34

Range

Distance [nm]

7638.39

Note: the cruise altitude was determined using the spreadsheet in the Appendix for Climb Cruise. As weight decreases, the amount of lift needed decreases. Maximum cruise altitude is the altitude at which the aircraft burns off all fuel during climb cruise.

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Aircraft Design and Layout

Optimized Weight Sizing for Sonic Cruiser

For our optimized Sonic Cruiser, Aquila, we performed an iterative process using spreadsheets in

order to determine its weight and required planform area. We sized Aquila using Load Condition I (Max

Payload & Max Fuel) since this condition will replicate its business life cycle in order to become feasible

and profitable. MTOW is the maximum takeoff weight and is the sum of the structural weight, fuel

weight, and payload. OEW is the operating empty weight and is the aircraft’s structural weight.

In summary, we used the range equation as our starting point in order to determine MTOW,

OEW, fuel weight, and the planform area of the canard and wing. We set our design condition for the

start of cruise at 40,000ft and a speed of 0.95Ma for Load Condition I. Moreover, we will design our

aircraft such that the lift coefficients of the canard and wing are both equal to CL,W = CL,C = 0.3 since this

leads to the lowest drag coefficient for its cruise flight envelope. To ensure that the lift coefficients are

equal at the start of cruise, we will orient the wing and canard at a given incidence angle to compensate

for interference effects. Furthermore, we will determine the required total planform area such that

Aquila can generate enough lift to overcome its weight at the start of its cruise and not for MTOW. Thus,

we also estimated the fuel burned from takeoff to reach 40,000ft altitude.

After calculating a possible total planform area, we found the individual planform area for both

the wing, SW, and canard, SC by utilizing the same 12% area ratio as our original Sonic Cruiser. A more

detailed explanation for the planform area determination is presented in the Aerodynamics portion of

this report. Afterwards, we needed to determine the necessary fuel fraction required in order to satisfy

the minimum range specification of 7,500 nautical miles. Lastly, we calculated the total lift to drag ratio

(L/D) of the Sonic Cruiser that is required for the range equation. The equations for the total aircraft lift

and drag are provided in the aerodynamics portion of this report. It is important to note that the range

calculated is a first order estimate and provides a highly optimistic value. A more thorough calculation of

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the range is presented in the performance portion of this report. The table below shows the final results

of our iterative process.

Table D1 - Final Weight Breakdown for Aquila, our Optimized Sonic Cruiser at Load Condition I

MTOW = OEW + Wfuel + Wpayload

MTOW [lbs] OEW [lbs] Wfuel [lbs] Wpayload [lbs] Wfuel,max/MTOW [%]

480,000 215,600 218,400 46,000 45.5

With these values above, we found a required total planform area of S = 6,350ft2. The wing has a

planform area of SW = 5,670ft2 and the canard has a planform area of SC = 680ft2. Identical to our original

model, Aquila will still carry 200 passengers for a payload weight of 46,000lbs. Second, we estimated

that it would burn approximately 8,000lbs of fuel to reach its starting cruise altitude of 40,000ft. Thus,

we calculated a first order range of 7,800 nautical miles.

A table detailing the weights and range of our original Sonic Cruiser and the Boeing 787-8

Dreamliner is located in the Appendix of this report for comparison. Our optimized aircraft’s MTOW is

4% less than our original design. Moreover, our optimized aircraft has a smaller fuel fraction than our

first design. Our new aircraft has a fuel percentage weight of 45.5% compared to 46.8%. Lastly, our

optimized Sonic Cruiser’s OEW is approximately 2% less than our initial design and 11% less than the

Boeing Dreamliner’s OEW. We foresee an improvement in the research and manufacturing of composite

materials in the next 10 years for this lightweight structure to become feasible.

The reason we chose a large wing planform area is due to the effects of drag at the start of our

cruise at 40,000ft altitude at 0.95Ma. The reason our wing planform area is large is because Aquila will

be flying at a small lift coefficient of CL = 0.3. However, we found a potential solution for the optimized

Sonic Cruiser for CL = 0.4. At this higher CL, our Sonic Cruiser will have a smaller wing planform area of SW

= 4465 ft2. Unfortunately, increasing the lift coefficient from CL = 0.3 to CL = 0.4 yields a 57% increase in

the total drag coefficient. With this large increase in drag, we found the drag to equal approximately

40,180 lbs at the start of cruise with this smaller wing. Our current engines and their more powerful

derivative cannot generate enough thrust at cruise to overcome this drag. Also, our estimated range

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decreased sharply from 7800 nautical miles to 7500 nautical miles if we chose to fly at a higher lift

coefficient using a smaller wing planform area. Thus, we chose a larger planform area in order to avoid

this sharp increase in drag and increase our range.

Final Sizing for Fuselage

The table below shows the final dimensions we agreed upon for Aquila’s fuselage. We used the

dimensions of the Boeing 787 Dreamliner as our starting and primary reference. Here, λ is the fineness

ratio that determines the slenderness of our Sonic Cruiser.

Table D.2 - Fuselage Exterior Dimensions

Dfus,in [ft] Dfus,out [ft] Lfus [ft] λfus (Lfus/Dfus,out)

16 17 200 11.765

We sized our aircraft’s fuselage section using the sizing guide from Appendix B of Torenbeek.

The nose and tail sections of the fuselage can be described in terms of a parabolic equation. The

fuselage has a circular cross section but tapers inward at the nose and tail sections. The term “b”

corresponds to the radius of the cross section and “a” corresponds to the length of each section.

[ ( ( ⁄ ) )] ⁄

The table below provides the values of the constants (b, a, n, m) for the nose and tail sections.

Also, the factors φ and k account for the curvature of the nose and tail sections compared to a normal

cylindrical body.

Table D3 - Fuselage’s Nose Section

ln [ft] a [ft] b [ft] m n

15 15 8.5 2 1

φ kA,n kW,n kV,n kC,n

0.6180 0.6667 0.6833 0.5167 0.7417

Table D4 - Fuselage’s Center Section

lc [ft] kA,c kC,c

145 1.00 1

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Table D5 - Fuselage’s Tail Section

lt [ft] a [ft] b [ft] m n

40 40 8.5 2 1

φ kA,t kW,t kV,t kC,t

0.6180 0.6667 0.6833 0.5167 0.7417

We can now determine the external dimensions of the fuselage section using the equations

below. AC is the cross sectional area, Cf is the circumference, Vf is the interior volume, and Sf,wet is the

wetted area of the fuselage. We did not perform transonic area ruling for the Sonic Cruiser by tapering

the fuselage section where the wings are located. We focused more on passenger comfort and safety

since a cylindrical fuselage provides an even stress distribution when the cabin is pressurized. The final

dimensions of the fuselage are summarized in the table below.

⁄

( )

( )

Table D6 - Fuselage Dimensions

Ac [ft2] Cfus [ft] Vfus [ft

3] Sfus,wet [ft2]

226.980 53.407 39362.127 9751.242

Fuel Tank Determination

We assumed a fuel density of 6.6 lbs/gallon. The primary fuel tanks for Aquila are located inside

the wing and canard. The volume for the amount of fuel that can fit inside each structure is expressed in

the equation below. S is the planform area, b is the wingspan, (t/c) is the thickness-to-chord ratio, λ is

the taper ratio of the wing or canard, and Vtank (%) is the percentage of the tank volume to the total

volume. A chart summarizing the dimensions for the wing and canard is located in the Aerodynamics

portion of this report.

( ⁄ )( ⁄ ) [(

) ( ) ⁄ ] ( )

Furthermore, Aquila contains two additional fuel tanks that are used to maintain trim flight and

a favorable static margin. The trim tanks are located in the nose and tail section of the aircraft. Thus,

Aquila will utilize a fuel management plan. The volume of each section was found by multiplying the

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cross sectional area of the fuselage by the appropriate length and curvature factor for each section.

These values are given in the previous table. We also determined a percentage ratio, Vtank (%), of the

tank size for each section. The nose trim tank has a CG moment arm of 8 ft measured from the nosetip.

The tail trim tank consists of smaller individual tanks such that the CG moment arm can range from 165-

195ft. The table below summarizes the total amount of fuel that can fit in each section.

Table D7 - Fuel Tank Capacity of Aquila

Vtank (%) Vtank [gallons] Wfuel [lbs]

Wing 85 23809.4 157142.3

Canard 90 1047 6910.4

Nose 36 4737.2 31265.5

Tail 75 26317.8 173697.3

Based on our performance calculations, we cannot store the maximum fuel that Aquila can carry

(218,400lbs) in the wing and canard alone. We need to store the remaining fuel in either the nose or tail

trim tanks. This fuel storage plan is presented in the Stability and Trim portion of this report.

Aquila’s Final Weight Estimates

Aquila’s wing, canard, tail fins, and fuselage weights are based off Hepperle’s conceptual

analysis, and we designed our aircraft utilizing a 20% increase in composite material use. The respective

weights of our wing, canard, tails fins, and fuselage are 67,756.8lbs, 8,187.3lbs, 7,215.5lbs, and

37,642.7lbs respectively. Our front landing gear weighs 3,086.4lbs, and our rear landing gears weigh

13,345.7lbs. This is based off Hepperle’s total landing gear approximation and the Dreamliner’s

configuration with 2 wheels located in the front and 8 wheels in the rear, split into two quads, one

under each wing. Our aircraft systems and flight instruments weigh 33,377.6lbs. Since we decided to

downsize our engines for the final report, we save significantly on our structural weight. The new

engines weigh a total of 33,288lbs where each GE90-94B weighs 16,644lbs. The engines are 14 feet in

diameter and 18 feet long. The nacelles have a total weight of 11,700lbs, and it was computed using an

equation in Torenbeek that depended upon the maximum thrust output by the engine at sea level.

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We analyzed the Sonic Cruiser’s stability for all 4 loading conditions at two scenarios. The first

scenario corresponds to takeoff at sea level, standard day for V = 0.25Ma. The second scenario

corresponds to the start of cruise at 40,000ft altitude for V = 0.95Ma. Moreover, we added two new

scenarios for Loading Condition I to model its full performance for its intended business life cycle. The

first new condition corresponds to the end of cruise at 48,000ft for V = 0.95Ma. The second new

condition corresponds to the end of descent from a cruising altitude of 48,000ft to 5,000ft for V =

0.36Ma. The table below briefly summarizes the weight of the aircraft and CG location for each loading

condition. The fuel weight for each scenario was calculated by our performance lead and a detailed

explanation is provided in the Performance section of this report. A more detailed chart of each

individual component’s placement and weight along with CG calculations for each loading condition can

be found in Table S.1 of the Stability and Trim section. The CG moment arm is taken with respect to the

datum which is placed at the tip of the nose.

Table D8 - Summary of Aircraft Weight and CG for Load Condition I

CG [ft] Wa/c [lbs] Wfuel [lbs] Wpayload [lbs]

Takeoff 144.676 479018 217418 46000

Start of Cruise 145.843 471142 209542 46000

End of Cruise 132.210 267600 6000 46000

Descent 131.037 262449 849 46000

Table D9 - Summary of Aircraft Weight and CG for Load Condition II

CG [ft] Wa/c [lbs] Wfuel [lbs] Wpayload [lbs]

Takeoff 135.975 285583 23983 46000

Start of Cruise 134.386 277707 16107 46000

Table D10 - Summary of Aircraft Weight and CG for Load Condition III

CG [ft] Wa/c [lbs] Wfuel [lbs] Wpayload [lbs]

Takeoff 144.652 433018 217418 0

Start of Cruise 145.907 425142 209542 0

Table D11 - Summary of Aircraft Weight and CG for Load Condition IV

CG [ft] Wa/c [lbs] Wfuel [lbs] Wpayload [lbs]

Takeoff 144.567 239583 23983 0

Start of Cruise 143.225 231707 16107 0

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Figure D1 – Aquila’s seating layout and interior arrangement where L stand for lavatories and G stand for galleys

Passenger and Payload Design and Fuselage Interior

Aquila has a finalized maximum payload of 46,000lbs carrying 200 passengers. Using Raymer as

our primary reference, we assumed each passenger plus their carry-on baggage weighed an average of

180lbs. We then assumed that each passenger brought aboard 1 luggage which weighed an average of

50lbs each. Thus 10,000lbs corresponds to luggage weight and 36,000lbs is divided evenly into the 200

passengers. Our 200 passengers can purchase tickets to sit in their choice of the economy, business, or

first class sections. The layout, seating arrangement, and placement of each section of the aircraft can

be seen in the figure below.

The first class passengers weigh approximately 2,340lbs with a moment arm of 21ft from the

datum, the nose tip. The business class passengers weigh 7,920lbs with a moment arm of 44.5ft from

the nose. Finally, the economy class passengers weigh a total of 25,740lbs with a moment arm of 111ft.

The exterior diameter of the fuselage is 17ft, and the interior diameter is 16ft. The top 9.75ft of

the cabin interior is for the passenger seating area, and the bottom 6.25ft of the fuselage’s cross section

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Figure D2 - Scaled Cross Section cutout of fuselage and respective class seating

is the undercarriage and holds the systems, fuel lines, and luggage. The luggage is stored in a container

that is 5ft by 7ft by 138ft with a total volume of 4,830ft3 and a CG arm of 87.5ft. The location and

placement of the luggage container can be seen in the figure below along with the seating arrangement

and spacing for each of the passenger classes.

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Figure D4 - Front View of Aquila with landing gears retracted

Figure D5 - Side View of Aquila with landing gear deployed

Aquila’s 3-View Drawings

The finalized layout and design of Aquila can be seen in the following figures below. Front, side,

and top views are included with landing gear both deployed and retracted.

Figure D3 - Front View of Aquila with landing gears deployed

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A more detailed explanation for the dimensions of the various structures such as the wing

and canard is presented in Tables A9 and A11 of the Aerodynamics portion of this report. A chart for the

Figure D6 - Side View of Aquila with landing gear retracted

Figure D.7: Top View of Aquila

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distances between the nose and the various aircraft structures is presented in Figure S.1 of the Stability

and Trim portion of this report.

We decided to use a low wing and high canard configuration for our Sonic Cruiser. A low

wing is commonly used on most passenger planes today for structural strength and passenger comfort

and safety. Moreover, we can retract and store the landing gears inside the fuselage after takeoff with a

low wing design. We used a high canard placement in order to reduce the interference effects of

downwash and upwash between the wing and canard. Also, this placement of the wing and canard adds

to the aesthetic appeal of Aquila. Briefly, we decided to use twin vertical tails for aesthetic appeal and

directional stability and control. A more detailed explanation for the use of two vertical tails is provided

in the Aerodynamics portion of this report.

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Aerodynamics

Since the Aquila will be operating in the transonic flow regime, special aerodynamic

considerations must be taken into account for this challenging region. Most current commercial aircraft

do not cruise at Mach numbers greater than 0.8 due to the onset of wave drag at velocities close to the

speed of sound. Wave drag occurs due to the formation of shock waves on the surfaces of the aircraft

such as its wing and fuselage. If a shock develops on the surface of an aircraft, a sudden pressure drop

occurs downstream of the shockwave which leads to flow separation. This separation reduces the lift of

the aircraft but increases its drag. Thus, we must design Aquila to delay the onset of wave drag as late as

possible through special aerodynamic designs like the use of swept wings and thin airfoils. This section

will detail the unique aerodynamic characteristics and design for Aquila that will allow it to successfully

cruise in the transonic flow regime.

CFD Wing Optimization

With the use of the CFD code, we attempted to increase the aerodynamic performance of the

Sonic Cruiser’s baseline wing. Our main focus was to decrease the induced and wave drag coefficient

(CD,i+w) experienced in the cruise flight envelope of 0.95Ma – 0.98Ma. In the CFD code, we were only

allowed to vary the following 3 wing geometries: wing span to root chord ratio ((b/2)/cr), taper ratio (λ),

and leading edge sweep angle (ΛLE). We first ran three trial runs to observe how the drag coefficient

(CD,i+w) and lift-to-drag ratio (L/Di+w) varied when we modified each of these parameters relative to the

baseline wing. We ran the CFD code for a speed of 0.95Ma at the appropriate angle of attack in order to

achieve a lift coefficient of 0.3. Our results from the trial runs are shown in the table below.

Table A1 - Initial CFD Code Parameter Sweeps for 0.95Ma and CL = 0.3

Baseline Wing Varying λ Varying (b/2)/cr Varying ΛLE

CL 0.3 0.29994 0.29999 0.30008 0.29919 0.30191 0.30005

α [°] 2.04463 2.006 2.060 2.045 2.045 1.818 2.322

(b/2)/cr 2.5 2.5 2.5 2.25 2.75 2.5 2.5

ΛLE [°] 37 37 37 37 37 34 40

λ 0.3886 0.36 0.40 0.3886 0.3886 0.3886 0.3886

A 7.201498 7.352941 7.142857 6.481348 7.921648 7.201498 7.201498

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CD,i+w 0.014106 0.013941 0.014141 0.015243 0.013038 0.016889 0.012172

% CD,i+w - -1.17% +0.25% 8.06% -7.57% 19.73% -13.71%

L/Di+w 21.2665 21.5243 21.214 19.6862 22.9465 17.8761 24.6513

% L/Di+w - +1.17 -0.25% -7.43% 7.90% -15.94% 15.92%

CLα [rad-1] 8.40677 8.56693 8.34387 8.40759 8.38243 9.51487 7.40371

Based upon the results of the CFD code, we observed a trend. Increasing the wingspan and

leading edge sweep angle increased L/D. Plus, reducing the taper ratio increased L/D. These results

agree with the results we learned in class about improving the aerodynamic characteristics of a wing.

Increasing the wingspan and reducing the taper ratio effectively increased the aspect ratio. A larger

aspect ratio corresponded to a decrease in the induced drag. Moreover, increasing the sweep angle

delayed the formation of shocks on the wing’s surfaces and the onset of transonic drag divergence. This

decreased the wave drag coefficient. With these results, we proceeded to optimize our wing. We did not

use a taper ratio less than 0.3 and a leading edge sweep angle greater than 45° based upon

recommendations from Professor Bendiksen. We settled upon 4 possible new wing configurations

whose dimensions and CFD results are given in the table below. We compared the drag coefficient, L/D,

and lift curve slope, CLα, to the baseline wing whose aerodynamic stats are located in the table above.

Table A2 - Possible Optimized Wing Configuration

Wing A Wing B Wing C Wing D

CL 0.30007 0.29987 0.29979 0.2996

α [°] 2.260 2.782 2.767 2.237

(b/2)/cr 3 3 2.75 2.75

ΛLE [°] 40 45 45 40

λ 0.3 0.3 0.3 0.3

A 9.230769 9.230769 8.461538 8.461538

CD,i+w 0.010476 0.010089 0.010340 0.011054

% CD,i+w -25.73% -28.48% -26.70% -21.64%

L/Di+w 28.6438 29.7228 28.9940 27.1038

% L/Di+w +34.69% +39.76% +36.34% +27.45%

CLα [rad-1] 7.60740 6.17578 6.20768 7.67361

% CLα -9.51% -26.54% -26.16% -8.72%

All 4 configurations improved the lift-to-drag ratio by at least 27%. Additionally, each wing

reduced the drag coefficient by at least 21% compared to the baseline wing. Each wing had the same

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10.0

14.0

18.0

22.0

26.0

30.0

34.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

L/D

i+w

Mach

Figure A1 - Optimized vs. Baseline Wing - L/Di+w vs. Ma

0.3 CL - Optimized

0.4 CL - Optimized

0.5 CL - Optimized

0.3 CL - Baseline

0.4 CL - Baseline

0.5 CL - Baseline

taper ratio of 0.3. We varied the wing span ratio between 2.75 and 3.00 and the leading edge sweep

angle from 40° and 45°. For the two wings with the 45° sweep, they had the largest increase in L/D

compared to the 40° sweep. However, sweeping the wing to this large extent drastically reduced the lift

curve slope of the wing, CLα. For both wings, CLα decreased by more than 26% compared to the baseline

wing. This sharp reduction would lead to problems during stability and trim since static margin is

inversely proportional to the lift curve slope, CLα. Additionally, for a smaller CLα, the plane would have to

fly at a higher angle of attack in order to generate the same lift coefficient. During cruise, we wish the

aircraft to fly trim at a reasonable angle of attack for both passenger’s and flight crews’ convenience.

We settled upon Wing A as our optimized wing for Aquila.

Table A3 - Wing A Fixed Geometric Relationships

(b/2)/cr λ (ct/cr) A (b2/S) S/cr2 c cr

3 0.3 9.230769 3.9 0.712821

ΛLE [°] ΛTE [°] y c/cr xc /cr Airfoil

40 31.206 1.230769 1.032738 NACA 64A-006

We then ran more CFD code to obtain the full aerodynamic performance of the optimized wing

for all flight velocities and likely lift coefficients. We obtained the aerodynamic performance of the wing

for CL = 0.3, 0.4, and 0.5 for the same velocity range in the midterm report. From the plots below, we

shifted the peak of the L/D curve from 0.85Ma in the baseline wing to 0.90Ma in our optimized wing.

21

Initial Cruise Design Conditions for Aquila

For our starting point, we set the initial cruise parameters of Aquila at the minimum

requirements. Aquila will start its cruise at an altitude of 40,000ft at a velocity of 0.95Ma. The Mach

number will correspond to the speed of sound at 40,000ft altitude. We selected a cruise lift coefficient

of CL = 0.3 since this condition corresponded to the maximum lift-to-drag ratio from CFD. Moreover, we

will design Aquila so at the start of its climb cruise, CL,W = CL,C = 0.3.

Table A4 - Starting Cruise Conditions for Sonic Cruiser

h [ft] ρ [slug ft3] a [ft/s] 0.95Ma [ft/s] CL.W = CL,C

40,000 5.8727E-04 968.08 919.68 0.3

Throughout this report, a lowercase subscript “l” corresponds to 2D parameters of the airfoil. An

uppercase subscript “L” corresponds to the 3D parameters of the wing. Furthermore, the subscripts

“W,” “C,” and “a c” refer to the parameters of the wing, canard, and entire aircraft respectively.

Airfoil Selection

We selected the NACA 64A-006 airfoil for Aquila. Since the aircraft will be operating in the

transonic flow regime, a thin, symmetric airfoil is necessary in order to delay the formation of shocks on

the aircraft’s surfaces. These shock waves cause the aircraft to experience wave drag as it approaches

the speed of sound. The NACA 64A-006 airfoil has a thickness-to-chord ratio of 6%. Based upon our CFD

results for the optimized wing, a sharp increase in drag does not occur until 0.95Ma.

0.008

0.012

0.016

0.020

0.024

0.028

0.032

0.036

0.040

0.044

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

CD

,i+w

Mach

Figure A2 - Optimized vs. Baseline Wing - CD,i+w vs. Ma

0.3 CL - Optimized

0.4 CL - Optimized

0.5 CL - Optimized

0.3 CL - Baseline

0.4 CL - Baseline

0.5 CL - Baseline

22

Since we were unable to locate wind tunnel data for the NACA 64A-006 airfoil, we decided to

use a similar airfoil, the NACA 64-006, in order to evaluate the airfoil’s properties. We located wind

tunnel data of the NACA 64-006 airfoil from NACA Report no. 824, Summary of Airfoil Data.

We applied a curve-fit equation to the lift and drag polar of the NACA 64-006 airfoil and

assumed the equations we obtained to be identical for the NACA 64A-006 airfoil. We determined the

lift curve slope, Clα, from the lift polar and the parasite drag, Cd,p, as a function of lift from the drag polar.

We neglected the laminar bucket present in the airfoil’s drag polar due to our aircraft’s cruising

conditions. Since our aircraft will fly in the transonic regime, we assumed fully turbulent flow over all of

Aquila’s surfaces. Our curve-fitting results are shown in the tables below. We used these equations to

model the parasite drag of the wing and to size the flaps for takeoff.

Table A5 - NACA 64-006 Lift Polar

Clα [rad-1] Cl,max α stall[°]

5.8330 0.800 9.00

Table A6 - NACA 64-006 Drag Polar – Parasite Drag Formula

Cd,p = ACl2 + BCl + C

A B C

0.005152732 1.32E-05 0.004920273

Wing and Canard Planform Area Determination

As explained in the Initial Weight Sizing portion of this report, we sized the required total

planform area required by Aquila based upon its weight at the start of its climb cruise at 40,000ft

altitude. For load condition I, MTOW equaled 480,000 lbs. We estimated that the aircraft would burn

8,000lbs of fuel to reach its starting altitude of 40,000ft so Wa/c at start of cruise = 472,000lbs. Moreover, we

designed Aquila so at the start of its climb cruise, the lift coefficients of the wing and canard, CL,W and

CL,C, would both be equal to 0.3. We also decided to use the same area ratio between the canard and

wing of 12% from our midterm report. Using this 12% area split, the combined lift coefficient of Aquila,

23

CL,a/c, is 0.336. Lastly, Aquila will fly at a velocity of 0.95Ma. Using these assumptions for our design

condition, we solved the lift equation below for the required total planform area of Aquila.

⁄ ( ) ( )

In order to generate enough lift with the desired conditions satisfied, we required a total

planform area of 6,335ft2. However, we decided to use a larger planform area of 6,350ft2 as a safety

measure in case Aquila burns less than 8,000lbs of fuel to reach its cruising altitude. Using the finalized

total planform area of 6,350ft2, Aquila must burn more than 7,000lbs of fuel in order to generate

enough lift to overcome its weight at the start of its climb cruise. This condition was forwarded onto the

performance lead as a needed goal.

Since we chose a 12% area split between the wing and canard, the wing has a planform area, SW

= 5,670ft2 and the canard has a planform area, SC = 680ft2. The canard will utilize the same overall

geometry as the main wing. Thus, its aerodynamic properties like CD and CLα are identical to the wing.

The actual dimensions of the wing, canard, and other aircraft structures are chronicled in the next

section. Lastly, our original Sonic Cruiser’s geometry from the midterm report is located in the Appendix.

Table A7 - Planform Area Summary

Stotal [ft2] SW [ft2] SC [ft2] SC/SW [%]

6350 5670 680 12

Aircraft Lifting and Control Surfaces Dimensions

We used the equations below to calculate the dimensions of the various aircraft structures. Taper Ratio: ⁄ (ct corresponds to chord at the wingtip; cr corresponds to chord at the wing root)

Aspect Ratio: ⁄

Mean Aerodynamic Chord, MAC: ̅ ( ) ( )⁄

Sweep Angle: [ ( )( ) ( )⁄ ] (e1 and e2 are the chord fractions)

Spanwise Location of MAC: ̅ ( ⁄ )[( ) ( )⁄ ]

Location of Center of Gravity measured from Leading Edge:

[ ( )

] [ ( )]⁄

Location of Center of Gravity measured in Spanwise Direction:

24

[( )( )] [ ( )]⁄

Wing & Ailerons

The CFD data we obtained for the optimized wing of the Aquila provided us with relationships

between the various wing geometries. These are summarized in the table below. To determine the

center of gravity of the wing, we modeled the wing as a trapezoid and assumed that the geometric

center and the center of gravity of the wing coincided.

Table A8 - Sonic Cruiser’s Optimized Wing Geometry Relationships

(b/2)/cr λ (ct/cr) A (b2/S) ΛLE [°] ΛTE [°] c cr t/c [%]

3.0 0.3 9.230769 40 31.206 0.712821 6

Using the wing planform area of 5670ft2 and the relationships above, we calculated the wing’s

additional geometries. The table below displays our results.

Table A9 - Optimized Wing Dimensions

SW [ft2] bW [ft] bw/2 [ft] cr,w [ft] ct,w [ft] c W [ft] xcg [ft] ycg [ft]

5670 228.776 114.388 38.129 11.439 27.179 52.967 46.928

Furthermore, for roll and yaw control, we designed ailerons on the wings. Its dimensions are

given below. Since our new wingspan is greater than the original Sonic Cruiser, we decided to increase

the span of the ailerons by 4 ft. We used the same aileron chord length of 8 ft from the baseline Sonic

Cruiser. This led to a chord ratio between the ailerons and wing of approximately 30% which agrees with

recommendations from Raymer for an approximate 25% chord ratio between the wing and aileron.

Table A10 - Aileron Dimensions

ba [ft] ca [ft] ca ( cw) [%] Sa [ft2] δa [°]

36 8 29.434 288 30

Spanwise Location from Aircraft’s Centerline [ft] Spanwise Location from Aircraft’s Centerline [%]

68ft ≤ y ≤ 104ft 65.426% ≤ y ≤ 92.366%

Canard Since Aquila’s canard is essentially a scaled-down version of the main wing, the same

relationships between the planform area and the other geometries are valid. Its dimensions are given

below based upon the canard’s planform area of 680 ft2.

25

Table A11 - Canard Dimensions

SC [ft2] bC [ft] bC/2 [ft] cr,C [ft] ct,C [ft] c C [ft] xcg [ft] ycg [ft]

680 79.227 39.614 13.205 3.961 9.412 18.343 16.252

We sized the canard’s planform area to be 12% of the wing’s planform area based upon

recommendations from Raymer and Professor Bendiksen. However, the actual lift produced by the

canard depends upon a force and moment balance with the lift produced by the main wing about the

wing’s center of gravity. This calculation is given in the Stability and Trim portion of this report.

Since Aquila lacks a horizontal tail, the canard must provide both lift and trim control during

flight. Therefore, we designed the canard to rotate like an elevator on a horizontal tail to provide pitch

control. Aquila’s canard can rotate as a single surface with a ±20° range of motion to provide variable

trim during its transonic flight.

Fin & Rudder

The vertical stabilizer or fin uses the same NACA 64A-006 airfoil. The Aquila’s fin has the same

leading edge sweep angle as the wing but has no sweep on its trailing edge. We based this design on

modern passenger planes today whose vertical stabilizer is shaped like a right-angle trapezoid.

We employed two smaller vertical stabilizers instead of a large vertical stabilizer like current

passenger planes. We agreed upon this configuration to reduce the parasite and wave drag experienced

by Aquila during its transonic flight. Unlike a large vertical stabilizer that protrudes out of the narrow

fuselage, twin vertical fins will still provide effective attitude control and directional stability for their

smaller size. However, due to mass constraints, we reduced the area of the twin vertical tails which

decreased the vertical tail coefficient, a measurement of their effectiveness to trim the aircraft.

However, we overlooked this setback since Aquila’s canard will be the primary trim control surface. The

table below shows the dimensions of one vertical stabilizer for Aquila. We measured the vertical tail

moment arm, LVT, as the distance from 25% of the mean aerodynamic chord of the wing to the vertical

26

fin. The combined area of the two vertical tails corresponds to a 10% ratio to the wing planform area

which is comparable to modern day passenger planes like the Boeing 7 series.

Table A12 - Dimensions for 1 Vertical Stabilizer

λ (ct/cr) A (h c ) SVT [ft2] hVT [ft] cr,VT [ft] ct,VT [ft]

0.1609 1.467 284.139 22.125 22.125 3.560

xcg [ft] ycg [ft] ΛLE,VT [°] ΛTE,VT [°] LVT [ft] cVT

14.586 8.397 40 0 11.557 0.00506

Vertical Tail Volume Coefficient for Twin Tails: ⁄

Furthermore, for yaw control and directional stability, the fins have rudders. The dimensions are

given below based on recommendations in Raymer for a 50% area ratio of the rudder to the fin.

Table A13 - Rudder Dimensions

cr,rud [ft] ct,rud [ft] hrud [ft] Srud [ft2] Srud/SV[%] δrud [°]

11 1.770 22.125 141.267 49.718 ±30

Aircraft Structures Drag

The table below displays the Reynolds number based on Aquila’s mean aerodynamic chord. The

Reynolds number allowed us to calculate the corresponding skin friction drag coefficient, CF, for

turbulent flow from a friction diagram located in Appendix F of Torenbeek.

Table A14 - Reynolds Number for Cruise Conditions at 0.95Ma

h [ft] V [ft/s] ν [ft2/s] c [ft] Re CF

40,000 919.68 5.06E-04 27.179 5.6E+07 0.0018

Wing & Canard

Using the drag polar of the NACA 64-006 airfoil, we added the parasite drag of the airfoil to the

induced and wave drag calculations obtained from the CFD code. The parasite drag equation is located

in the section titled, Airfoil Selection. Additionally, we estimated the induced drag formula using the

optimized wing’s aspect and taper ratio to determine δ from the Professor Bendiksen’s lecture slides.

Our results for the induced drag formula are given in the table below.

Table A15 - Induced Drag Formula, Cd,i = Cl2(1+δ) (πA)

δ λ A

0.016 0.3 9.230769

27

The total drag coefficient for Aquila can now be computed for a given lift coefficient. The table

below shows the total drag versus Mach number for our cruise condition of CL = 0.3.

Table A16 - Total Drag Coefficient for the Sonic Cruiser’s Wing and Canard for CL = 0.3

CD,p+i+w = CD,p + CD,i + CD,w

M CD,p CD,i CD,w CD,i+w+p

0.20 0.0053881 0.0031538 0.0128962 0.0214381

0.30 0.0053879 0.0031523 0.0097917 0.0183319

0.50 0.0053860 0.0031395 0.0073075 0.0158330

0.70 0.0053879 0.0031528 0.0069342 0.0154749

0.75 0.0053881 0.0031538 0.0068449 0.0153868

0.80 0.0053878 0.0031521 0.0066709 0.0152108

0.85 0.0053885 0.0031565 0.0064594 0.0150044

0.90 0.0053896 0.0031641 0.0063177 0.0148714

0.92 0.0053876 0.0031504 0.0063971 0.0149351

0.95 0.0053882 0.0031546 0.0073214 0.0158642

0.96 0.0053879 0.0031530 0.0082130 0.0167539

0.97 0.0053879 0.0031525 0.0092255 0.0177659

0.98 0.0053881 0.0031538 0.0104452 0.0189871

0.99 0.0053879 0.0031525 0.0118435 0.0203839

Furthermore, a graph of the optimized wing’s lift-to-total drag ratio is shown below in the

transonic velocity regime. With the addition of parasite drag, the lift-to-drag ratio is greatly reduced

compared to Figure A1. The plot below also compares our optimized wing with the baseline wing.

9.0

12.0

15.0

18.0

21.0

0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99

L/D

i+w

+p

Mach

Figure A3 - Optimized vs. Baseline Wing - L/Di+w+p vs. Ma

0.3 CL - Optimized

0.4 CL - Optimized

0.5 CL - Optimized

0.3 CL - Baseline

0.4 CL - Baseline

0.5 CL - Baseline

28

The table below shows the lift-to-drag ratio for Aquila’s optimized wing with the addition of

parasite drag. In the transonic Mach number range of 0.90Ma – 0.99Ma, the L/D ratio for our optimized

wing is greater than the baseline wing from the midterm report. Thus, we will be able to increase the

range of our Sonic Cruiser since L/D for a cruise speed of 0.95Ma is nearly 23% greater for the optimized

wing than the baseline wing.

Table A17 - Lift-to-Drag Ratio for Wing and Canard at Cruise Lift Coefficient of CL = 0.3

M L/Di+w+p for Baseline Wing L/Di+w+p for Optimized Wing % L/Di+w+p

0.20 13.8662 13.9952 +0.93%

0.30 15.7419 16.3628 +3.94%

0.50 18.8253 18.9068 +0.43%

0.70 19.4768 19.3849 -0.47%

0.75 19.6818 19.4992 -0.93%

0.80 20.0059 19.7195 -1.43%

0.85 20.3891 20.0048 -1.88%

0.90 20.1469 20.2079 +0.30%

0.92 18.8135 20.0782 +6.72%

0.95 15.3894 18.9149 +22.91%

0.96 14.1784 17.9056 +26.29%

0.97 13.0121 16.8846 +29.76%

0.98 11.9142 15.8018 +32.63%

0.99 10.9234 14.7160 +34.72%

Aquila’s canard will have the same lift and drag characteristics as the wing since we are using

the same airfoil but scaled down the wing geometry.

Moreover, we can estimate the drag divergent Mach number for the wing and airfoil. From the

plot of total drag coefficient versus Mach number below, we observed a sudden increase in the drag at a

Mach number past 0.92. Hence, we concluded that the drag divergent Mach number for this optimized

wing and airfoil combination is 0.95.

29

Fuselage

Using the dimensions of the fuselage in the Aircraft Layout Section, we calculated the skin

friction drag coefficient, CD,fuselage, according to the equation below provided from Torenbeek. The

parameter, φfus is a correction factor that accounts for the curvature of the nose and tail section of the

fuselage. The skin friction drag coefficient, CF, was given in the beginning of this section on Aircraft Drag.

( ) ⁄

Table A18 - Fuselage Skin Friction Drag Coefficient

φfuselage Sfuselage,wet [ft2] CD,fuselage

0.2101 9751.242 0.003746

Fins

The skin friction drag coefficient for a single vertical stabilizer, CD,VT, can be determined using the

equation below from Torenbeek. The thickness to chord ratio of the vertical stabilizer is equal to the

wing and canard since all three surfaces employ the same NACA 64A-006 airfoil. Λcr/2,V is the sweep angle

of the vertical stabilizer measured from the midpoint of the root chord to the tip chord.

( ( ⁄ ) )

Table A19 - Vertical Stabilizer Skin Friction Drag Coefficient

(t/c)VT [%] Λcr/2,VT [°] CD,VT

6 4.600 0.000209982

0.012

0.016

0.020

0.024

0.028

0.032

0.036

0.040

0.044

0.048

0.052

0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99

CD

,i+w

+p

Mach

Figure A4 - Optimized vs. Baseline Wing - CD,i+w+p vs. Ma

0.3 CL - Optimized

0.4 CL - Optimized

0.5 CL - Optimized

0.3 CL - Baseline

0.4 CL - Baseline

0.5 CL - Baseline

30

Engines & Nacelles

The table below shows the dimensions of the engine and nacelles as one unit. We determined

the wetted area of the engines and nacelles using Solidwork’s measurement tool.

Table A20 - External Geometry of Engine and Nacelles

hengine [ft] lengine [ft] Dengine [ft]

13.708 25.094 13.25

We determined the skin friction drag coefficient of the engines and nacelles, CD,engine, using the

assumption that they have been properly designed by our performance engineers. Thus, we can use the

following formula provided to us from Torenbeek.

⁄

Table A21 - Properly-Designed Engine and Nacelle Skin Friction Drag Coefficient

Sengine,wet [ft2] CD,engine

1262.322 0.000500921

Total Aircraft Lift

In this section, we will derive the combined lift contributions from the wing and canard. The

canard is in the upwash field of the wing so its lift curve slope, CLα,C, will increase. However, the wing is in

the downwash field of the canard so its lift curve slope, CLα,W, will decrease.

The upwash term for the canard is ̅̅ ̅̅ ( )⁄ .

The downwash term for the wing is ( )( ̅̅ ̅̅ ⁄ )⁄ . Thus, the lift coefficient for each structure can be rewritten to include these interference effects.

The wing’s lift coefficient becomes [( ) ].

The canard’s lift coefficient becomes [( ) ].

The last term in the two equations above accounts for the incidence angle, i, of the lifting

surface with respect to the centerline of the fuselage. A positive incident angle corresponds to a

clockwise rotation of the wing or canard about the fuselage’s centerline.

Using the equations above, we can rewrite the total lift of the aircraft as .

31

CL,a/c is the lift coefficient of the aircraft that takes into account the interference between the canard and

wing. CL,a/c can be rewritten as the following equation where the terms have been previously introduced

above. ( )⁄

We can rewrite the equation above in terms of the lift-curve slope of the aircraft, CLα,a c.

( ) ( ⁄ )( )

( ⁄ )

We included the destabilizing effects of downwash and upwash in this final report. Furthermore,

based upon the outcome of stability and trim calculations, we will utilize an incidence angle for both the

wing and canard. This determination of the incidence angle is located in the Stability and Trim portion of

this final report.

We can extend these results in order to determine the lift coefficient of Aquila for its cruise lift

coefficient of CL = 0.3. We will now formalize our desired lift coefficient for Load Condition I at start of

cruise. We will attempt to have either CL,W = CL,C = 0.3 or CL,a/c = 0.336 in order to maximize our range.

Both options yield the same final result of CL,a/c = 0.336. However, we can achieve CL,a/c = 0.336 if CL,W

does not equal CL,C only if we obtain the appropriate CL ratios from our trim analysis. The table below

shows the design lift coefficient of Aquila. The terms and equations used to calculate our results have

been previously defined in this section.

Table A22 - Total Aircraft Lift Coefficient for Cruise at CL = 0.3 for Load Condition I at Start of Cruise

SW [ft2] CL,W SC [ft2] CL,C CL,a/c

5670 0.3 680 0.3 0.336

In order to calculate the lift curve slope of the wing, canard, and Aquila as a whole, we need to

perform trim calculations for each loading condition because the lift curve slope depends on the

individual lift coefficient for each structure. Moreover, we will need to include both upwash and

32

downwash effects, ε, for the determination of the lift curve slopes. This calculation and its results will be

shown in the Stability and Trim portion of this report.

Total Aircraft Drag

Similar to the total lift equation for the aircraft, we can write an equation for the total drag of

Aquila as a function of the various structures.

We can rewrite this equation in terms of the drag coefficient where the reference area is the

wing’s planform area, SW. Moreover, we will rewrite the interference drag term as an ad-hoc drag

percent increase. We decided to add a 5% drag coefficient increase to account for interference effects

between the various aircraft structures. The results are given below where the terms have been

previously introduced and calculated.

( ( ⁄ ) )

The purpose of the preceding two sections was to find an expression for the total aircraft lift-to-

drag ratio which is required for performance calculations mainly in the determination of the range. The

equation is given below where the terms have been previously defined.

⁄

⁄

Aerodynamic Center and Moment Calculations

Using the results of our optimized wing from the CFD code, we were able to locate the

aerodynamic center and observe its migration further aft as the velocity increased. For a fixed speed,

the aerodynamic center remains constant and does not depend upon the angle of attack.

We can locate the aerodynamic center on the mean aerodynamic chord, c or MAC, using

trigonometric relations. The distance from the leading edge of the root chord of the wing or canard to

33

the leading edge of MAC is given by the following equation, . We can now

proceed to determine the location of the aerodynamic center on the MAC using the output, xac/cr, from

the CFD code and the following equation, ( ⁄ ) .

Our results for our design lift coefficient of 0.3 are given in the table below. For subsonic

velocities below 0.5Ma, the aerodynamic center was already located at 40% of the MAC. As the velocity

increased, the aerodynamic center moved further aft past the midpoint of the MAC for velocities near

the speed of sound. Furthermore, we can compute the pitch moment coefficient about the aerodynamic

center using the equation below.

(( ̅⁄ ) )

Table A23 - Aerodynamic Center and Moment Calculations with respect to MAC for CL = 0.3

M xac,MAC [ft] xac c [%] CM,cr/4 CM,ac

0.20 10.491 38.598% -0.44587 0.105311

0.30 10.506 38.655% -0.44581 0.105281

0.50 10.522 38.713% -0.44690 0.105251

0.70 10.724 39.456% -0.45190 0.105145

0.75 11.085 40.785% -0.45362 0.105229

0.80 11.234 41.333% -0.45565 0.105242

0.85 11.428 42.047% -0.45893 0.105227

0.90 11.695 43.028% -0.46454 0.105261

0.92 12.152 44.709% -0.46754 0.105312

0.95 12.513 46.039% -0.48200 0.105218

0.96 13.787 50.726% -0.48945 0.105239

0.97 14.468 53.232% -0.49910 0.105228

0.98 15.338 56.434% -0.51097 0.105226

0.99 16.397 60.330% -0.52451 0.105216

Flap Design for Low-Speed Takeoff

As a starting point to size the flaps, we first determined what lift coefficient and takeoff velocity

was required for Aquila. We decided to set CL,W = 0.85, CL,C = 0.60, and V = 0.25Ma at sea level conditions

for takeoff. Plugging these parameters into the lift equation, Aquila generated enough lift to overcome

MTOW and takeoff from the ground. Thus, we needed to design and size flaps that will provide us with

the desired lift coefficient of 0.8 at takeoff.

34

Our Sonic Cruiser, Aquila, will employ single-slotted flaps commonly known as Fowler flaps in

order to generate enough lift for takeoff. The span of the flaps is 32ft, and they are located at a

spanwise direction of 16ft to 48ft measured from the wing’s root chord. When the flaps are retracted

into the wing, they have an 8ft chord. At takeoff, they are fully extended to 4.48ft past the trailing edge

of the wing. The total planform area for one set of flaps is 256 ft2 and they are 9% of the planform area

for one half of the wing. Also, we designed the flaps to deflect 30° downwards at takeoff. A summary of

the flap’s geometry and dimensions is given in the table below.

Table A24 - Fowler Flaps Dimensions

bf [ft] cf [ft] cf ( cw) [%] Sf [ft2] Sf /(Sw/2) [%] δf [°]

32 8 29.43 256 9.03 30

Spanwise Location from Aircraft’s Centerline [ft] Spanwise Location from Aircraft’s Centerline [%]

16ft ≤ y ≤ 48ft 13.99% ≤ y ≤ 41.96%

Now, we will briefly summarize the design and sizing process for the Fowler flaps. The maximum

lift coefficient for the NACA 64A-006 airfoil was determined using the lift-curve slope of the NACA 64-

006 airfoil obtained through wind tunnel testing. We then estimated the maximum lift coefficient for

the 3D wing by employing a correction factor from Appendix E of Torenbeek. Our results are given

below. Without the addition of Fowler Flaps, our wing cannot reach the ideal takeoff lift coefficient of

0.85 without stalling on the runway.

Table A25 - Maximum Lift Coefficients for Airfoil and Wing without Addition of Flaps

Cl,max Clα [rad-1] CL,max,W Clα [rad-1] for M = 0.25

0.8 5.83300 0.599 4.63293

Using the design process outlined in Appendix E of Torenbeek, we first determined the

additional lift the slotted flaps will provide for the airfoil. Afterwards, we used a correction factor to

transform our results for the airfoil into the wing. The final calculations are given below.

Table A26 - Maximum Lift Coefficients for Airfoil and Wing with Addition of Flaps

C'l,max ΔfCL,max CL,max

0.932 0.480 1.412

35

From the table above, the maximum lift coefficient of the wing is approximately 1.4 which will

allow Aquila to successfully takeoff and climb from the runway without stalling.

Although flaps allow the aircraft to generate enough lift for takeoff, they generate an excessive

amount of drag while fully extended. We can model this increase in drag as a parasite drag term added

to the overall drag equation of the wing. We programmed this lengthy ad-hoc drag factor into a

spreadsheet since it depended upon the current lift coefficient during the aircraft’s takeoff and climb

from the runway. The table below summarizes the flap’s parasite drag factor for the wing’s maximum lift

coefficient, CL,max = 1.412. Using this programmable value, our propulsion and performance lead can

accurately determine their calculations for takeoff and climb.

Table A27 - Parasite Drag Contribution from Fully Extended Fowler Flaps

CL ΔfCD,p

1.412 0.0074

36

Performance

Engine Selection, Background, and Motivation GE90-94B

From our Midterm Report we have determined that our previous engine selection, the GE90-

115B was too powerful for the application of the Sonic Cruiser. The excess thrust provided by the 115B

over the 94B is outweighed by weight savings we would gain from choosing a smaller engine. This

smaller engine, with a lower thrust rating than the 115B, boasts the same thrust specific fuel

consumption of 0.53 lb/lbf/hr at the 777-200ER's cruising conditions. This lower weight for the engines

helped in reducing the maximum takeoff weight to 480,000 lb.

Basic Engine Specifications

static thrust bypass ratio weight length fan diameter T/W ratio

93,700 lbf 8.33 16,644 lb 217 in 123 in 5.6:1

Takeoff Performance and Calculations

For the final report we have included the drag coefficients from all aircraft components. We

have now included the drag contributions of the canard, fuselage, engines, and vertical tails. The

procedures below for takeoff calculations follow the same format as the Midterm Report.

Given the manufacturer's rated takeoff rating for an engine we had to consider thrust lapse as a

function of Mach number up to about Mach 0.3. A MATLAB script was devised to incorporate lift, drag,

velocity, the thrust lapse formula, and basic equations of motion. Starting from the thrust lapse

equation

[ ( )

√( ) (

) ]

Table P.1 GE90-94B specifications

37

and knowing the static takeoff of our engine TTO, we found the thrust corresponding to Mach number,

and then converted that to velocity. In the preceding relation λ is the bypass ratio (8.33) and G is the gas

generator function (1.1).

During the ground roll before takeoff, we had to consider the friction of the tarmac on the

wheels and incorporated it into the following equation:

∑ ( )

where μ was set to 0.03 for a cement runway. Once the aircraft lifts off the ground, we used the more

general form:

∑

Then the acceleration can be tabulated using Newton's Second Law by dividing by mass

∑

By incrementing velocity in the MATLAB program and determining acceleration using the

previous relation, the time between each velocity step was found.

Using this incremental time, the specific fuel consumption at sea level, and the thrust from the

thrust lapse equation, we determined the fuel burned at each step.

Our takeoff ct is 0.377. This was then subtracted from our weight. As velocity increases, so does lift

where the dynamic pressure is

and the updated value for drag is

(( ) )

38

keeping in mind the drag from the landing gear and the additional drag from extended flaps. The

landing gear contribution depends on the frontal area, the area of the wing, and a factor dependent on

the weight and the type of landing gear configuration.

where the factor Δflg is from Perkins and Hage

With a takeoff weight of 480,000 pounds and using a tricycle configuration for our landing gear,

we can extrapolate the graph to find a Δflg of about 70.

We determined the aircraft's stall speed at CL,max of 1.4 with flaps deployed and added a safety

factor of 26% to our takeoff speed so that VTO = 1.26 Vstall. This safety factor was increased from the

midterm report in order to accommodate the new stability and aerodynamic requirements from the

addition of upwash and downwash effects. The stall speed was when the lift equaled not maximum

takeoff weight but more accurately the weight of the aircraft, taking into account the fuel burned up

until this point. The distance covered between each time step is then computed by

The ground roll distance is then the distance covered up until takeoff velocity. At takeoff speed

the aircraft will start to climb at a rate

Figure P.1 Landing Gear Drag Coefficient factor

39

The MATLAB script took this into consideration by setting the rate of climb equal to zero at

velocities lower than 1.26Vstall. Once the aircraft starts to climb, the altitude is given using

The total takeoff distance is when the aircraft clears the 35 foot obstacle as dictated by FAR

regulations. The velocity at this point is the V2 or climb out speed. The air distance is the ground covered

from takeoff until the 35 foot clearance. The results from plotting in MATLAB are shown in the figures

below.

From the figure above, we note that with the landing gear deployed, the drag comes very close

to equaling the thrust. When optimizing the MATLAB code we found that if the landing gear were left

deployed for too long, the drag would exceed thrust and the aircraft would start to descend. We

observe that the drag decreases drastically once the landing gears are retracted. As a result, the thrust

excess becomes larger and our rate of climb increases accordingly.

00000

100000

200000

300000

400000

500000

600000

700000

800000

900000

0 10 20 30 40 50

Forc

e (

lbf)

Time (s)

Takeoff Parameters using Thrust Lapse Equation up to Mach 0.3

Lift

Weight

Thrust

Drag

Thrust Excess

Landing Gear Up

Figure P.2 Takeoff Parameters

40

The graph above shows that our Sonic Cruiser, Aquila, compares favorably with current

commercial airliners in terms of takeoff time. Once it achieves liftoff however, the climb rate increases

radically once the landing gears are retracted due to a large excess thrust and high CL.

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50

Alt

itu

de

(ft)

Time (s)

Takeoff: Altitude vs. Time

Height

ClearanceHeight of 35 ftLanding Gear retracted

Takeoff time to clear obstacle : 42.604s

Climb out Speed: 193.36 mph

0

50

100

150

200

250

300

350

400

450

500

0 2000 4000 6000 8000 10000

Alt

itu

de

(ft

)

Distance (ft)

Takeoff: Altitude vs. Distance

Altitude

Air Distance: 611.03ft

Landing Gear retracted (Drag greatly reduced)

Ground Roll Distance: 7073.03ft

Figure P.4 Takeoff Distance

Figure P.3 Takeoff Performance

41

Considering that LAX has a runway length of over 12,000ft, our Sonic Cruiser's required takeoff

field length at CLmax= 1.4 (wing) of 7,684ft allows it to takeoff from San Diego Airports comfortably,

whose runway lengths can vary from 7,200ft to 8,800ft depending on the direction of approach. This

new takeoff field length is more reasonable than the previous length of 5,700ft using the GE90-115B.

Climb Performance and Calculations

In determining the climbing performance of our aircraft, we performed a similar analysis as the

takeoff portion using lift, drag, and the equations of motion. However, in the Mach range above 0.3, the

thrust lapse formula previously utilized is no longer valid. In addition, we do not have access to the

manufacturer specifications in terms of how the thrust and specific fuel consumption vary with altitude

and Mach number. Instead, we performed a simple scaling method using available data from an engine

with a similar bypass ratio. From McCormick, this data is available for the Pratt & Whitney 4056, which

has a bypass ratio of about 5 compared to the bypass ratio of 8.33 of the GE90-94B. First, we know that

the PW engine is rated for 56,700lbf of thrust. Looking at the thrust map, the highest value at sea level

is 44,000lbf. We took the ratio between the rated thrust of the Pratt& Whitney engine and highest value

on the graph in McCormick and applied it to the GE90. This value, which is lower than the rated thrust of

the GE90-94B, serves as the highest point in the thrust map. This process was then applied to the

remaining axes values. To find the SFC values, we had to have a known reference point of our engine on

which to base our SFC variation. From data on the Boeing 777-200ER, the specific fuel consumption of

the engine is 0.53 lb/lbf/hr at Mach 0.89 and 35,000ft. Noting this point on the graph and its

corresponding value for the PW4056, we can apply a simple scaling to the rest of the points in the graph

as we did for the thrust.

42

Using a similar process as the takeoff calculations, we can find the height and Mach attained at

discrete points. With a target speed and height we determined the SFC at each point as well. With the

rate of climb from the end of the takeoff section and setting a target height, we solved for the time it

took for the Sonic Cruiser to reach altitude. The velocity at each point is also computed to determine if

and when the aircraft would reach cruise mach at our desired cruising altitude of 40,000 feet.

The following altitude graph is a summary of the values determined in Excel using the

aforementioned procedure. This includes the altitude and time at the very end of the takeoff section.

The raw data is presented later in the Appendix. The calculations showed that while the Sonic Cruiser

did not reach Mach 0.95 right when it reached cruise height, it was able to reach cruising speed 1.56

minutes later.

Mach

Figure P.5 Thrust Map Scaling: PW 4056 to GE90-94B

43

A climb time of almost 25 minutes is reasonable considering that Boeing's baseline design is

about the same. This value compares much more favorably than our tabulated number of 9 minutes

from the Midterm Report. We accomplished this using a thrust setting of 65% of the available thrust

from the Pratt and Whitney scaling graph instead of the maximum available thrust. For the Midterm

Report, the maximum available thrust was used.

Climb Performance Summary

Mach Average RC time to cruise conditions from standstill

0.95 1,663.09 fpm 24.73 min

Climb Cruise Performance In order for the range equation

( )⁄

√ ⁄ ( )

to hold valid, we have to set L/D, v, and ct as constant. As fuel is burned, weight decreases and so lift has

to decrease accordingly. In the lift and drag equations we hold CL or CD, v, and Swing constant. This leaves

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 5 10 15 20 25 30

Alt

itu

de

(ft

)

Time (min)

Climb Performance: Altitude vs. Time

reach climb cruise and altitude at 24.73 min

Figure P.6 Climb Altitude vs. Time

Table P.2 Climb Performance

44

us with changing ρ, or the altitude. As weight decreases we must increase altitude. Knowing our design

CL to be 0.336, we can set CL/CD to equal L/D. The only unknown is then CD, which incorporates the wave

drag. The drag values calculated included a 5% ad hoc value from interference between aircraft

components. Thrust is set equal to drag, and knowing the weight at each altitude we can solve for the

fuel burned between each altitude increment (since altitude dictates ρ which dictates L). Knowing the

TSFC (ct) we can then solve for the time it takes to burn that amount. The following graph shows how

the altitude changes over time over the entirety of the cruise segment.

Using the Pratt and Whitney scaling graph for our new engine, the GE90-94B, we found that we

are short in thrust after incorporating the wave drag once we reached cruising conditions. Looking back

at the PW4056 scaling graph, we inspect that the thrust value at sea level was not actually rated at

56,750 pounds of thrust but started at a lesser rating of 44,000lbf. We note that this ratio between the

actual rated thrust and the thrust given at sea level in the graph is 1.28977. For the purposes of our

cruise segment, we can theoretically increase the thrust by up to 28.977% and still be within the

capabilities of the engine for a thrust rating of 88.3%. In this way, we can achieve enough thrust to

overcome drag without changing our engines or redesigning our entire wing. Using our original scaling

for the new engine and the new wave drag incorporated into our drag calculations, the thrust falls short

35000

40000

45000

50000

0 3 6 9 12 15

Alt

itu

de

(ft

)

Time (hr)

Climb Cruise: Variation of Altitude vs. Time

Figure P.7 Climb cruise altitude variation

45

by about 3,000lbf. This small difference, we believe, does not warrant changing our engine nor

redesigning our wing to achieve a lower drag.

We also note that if we did not impose an altitude restriction for the climb cruise segment, our

aircraft would continue to climb to an altitude of about 50,000 ft by the end of cruise. In order for the

range formula to hold true for a constant altitude, CL has to decrease with decreasing weight. CD

decreases in turn, and we were able to achieve a constant L/D value of about 13.9 for cruise.

We determined the maximum mach number achievable by Aquila during its cruise. Maximum

velocity was iterated by determining if the available thrust at that velocity and altitude equaled the drag

at that velocity. From our force equation in Takeoff Performance and Calculations, the aircraft cannot

accelerate once the available thrust from the engines is not enough to overcome drag. It is important to

note that we utilized 100% of the available thrust for our sonic cruiser to reach this speed. This is a

hypothetical situation to test the engine performance and is not indicative of a normal mission.

at 100% thrust setting Mach Max Mmax 1.023 Mach

Max Velocity Vmax 675.68 mph

altitude h 41,000 ft

Next, we determined the absolute ceiling of our aircraft. In our Excel spreadsheet, we set the

thrust setting to 88.3% and determined the rate of climb. Previously for cruise, we set the thrust to

88.3% to verify that we have enough thrust to at least equal drag. With this verified, the rate of climb

was determined at each increment of altitude. The results are in the following table.

at 88% thrust setting Absolute Ceiling habs ~50,000 ft

Rate of Climb at habs

~6 fpm

Table P.3 Maximum Mach

Table P.4 Absolute Ceiling

46

Range Performance and Calculations

( )⁄

√ ⁄ ( )

a0 is the speed of sound at sea level, ct is the thrust specific fuel consumption, and θ is the

corrected temperature. In the range calculation we included the effects of wave drag since cruise is the

majority of the flight segment.

CL a0 ct M L/Di+p+w Max fuel MTOW

0.336 1,116.5 ft/s 0.54 0.95 13.9 218,400 lb 480,000 lb

The actual CL was 0.335 which was close to the design CL of 0.336. The corresponding L/D ratio,

took into account the induced, parasite, and wave drag. The specific fuel consumption was estimated

from the PW4056 scaling graph. Initially this value seems optimistic for the given cruising altitude of

40,000ft and velocity. However, with the trend of increasingly powerful and fuel efficient turbofan

engines, this number is reasonable. For comparison, Hepperle estimated a TSFC of about 0.55 for the

baseline sonic cruiser design to have a feasible range. These conditions lead to a predicted range of

Rpredicted=7991.7 nmi

0 2 4 6 8 10 12 14 16

0

10000

20000

30000

40000

50000

60000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Time (hr)

Alt

itu

de

(ft)

Distance (nmi)

Mission Profile: Altitude vs. Time and Distance Traveled

Range: 7638.9 nmi

Cruise Time: 14 hr

Table P.5 Parameters in Determining Maximum Range

Figure P.8 Complete Mission Profile

47

The overall mission profile is shown above. We see that the tabulated range is more than 300

nmi short of the value dictated by the range equation. This is because the range equation is a first order

approximation. The actual distance calculated above involved calculating the distance traveled by the

beginning of cruise and subtracting this value from that at the end of cruise.

Descent

For descent, we set a target rate of descent that agreed with modern airlines. Setting a target

velocity and performing the same calculations as the climb portion, our Excel spreadsheet gives the

following numbers. We start descent at the altitude at the end of cruise, 48,000 ft.

Rate of Descent RD 2,000 fpm

Average Velocity

384.32 mph

Time to Descend to 5,000 ft 21.5 min

Fuel Weight Calculations

max fuel weight fuel after descent

Range for Cruise: 218,400 lb 4,902.459 lb

7,638.89 nmi fuel burned by beginning of cruise fuel for 30min loiter at 5000 ft, 400 ft/s

T/O and Climb to cruise 8,858.374 lb 4,053.55 lb

24.73 min fuel burned by end of cruise fuel after loiter

Cruise time 203,541.6 lb 848.91 lb

14.01 hr fuel reserved for descent

Descent time to 5000 ft 6,000 lb

21.5 min fuel burned during descent to 5000 ft

Total Time to mission end 1,097.541 lb

14.78 hr

Table P.6 Rate of Descent

Table P.7 Fuel Weight Breakdown

48

From the takeoff, climb, and cruise segments, we determined the fuel burned at discrete points,

taking into consideration that thrust and SFC vary with altitude and mach number. We are then left with

the remaining fuel for descent and loiter. With the thrust pulled far back, the amount of fuel burned

from the end of cruise is about 1,100lbs. We chose this height and a speed of 272.73 mph (400 ft/s) as

reasonable for our loiter conditions. For 30 minutes of loitering at these conditions, a fuel weight of

4,053.55lb is burned.

Maximum Climb Performance

Instead of utilizing the PW4056 graph, we scaled the maximum climb thrust data given in the

JT9D-7 engine. The data gave the thrust values at discrete mach numbers and altitudes. The JT9D-7

engine is rated at 47,900 lbs of thrust while the GE90-94B is rated at 93,700 lbs. The ratio between these

two values was used to scale our the GE90-94B engine. It is important to note that the following graph

assumed a constant weight MTOW. In this way, the graph underestimates climb performance in order to

simplify calculations. Lift was set equal to weight, and at a given altitude and speed, we solved for CL.

Using CL and Mach number, we estimated the corresponding CD, i+w+p using the baseline values given for

the NACA 64-006 airfoil. Rate of climb was determined as usual.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

RC

(fe

et

pe

r m

inu

te)

Mach

Rate of Climb Vs. Mach Number (Maximum Performance)

Sea Level

5000 ft

10000 ft

20000 ft

30000 ft

40000 ft

Figure P.9 Maximum Climb Performance scaling from JTD9-7

49

Looking at the graph we note that the rate of climb at 40,000ft is less than what we tabulated

for cruise. This discrepancy can be attributed to different sources being used to scale our engine. In the

mission profile for takeoff, cruise, and climb, we scaled the PW4056 engine. This section of the report

was completed before the JT9D-7 data was posted. The summary of our performance calculations are

shown below.

50

Takeoff

Stall Speed Vstall 150.73 mph Ground Roll Distance SG 7073.026 ft

Liftoff Speed VL/O 190.31 mph Air Distance SA 611.0307 ft

Safety Factor VL/O/Vstall SF 1.26 Takeoff Distance ST/O 7684.057 ft

Climb out Speed (V2)* VV2 193.36 mph Takeoff Time tT/O 42.604 s

Safety Factor between L/O and stall speed dictated by stability and aerodynamic requirements

*defined as the speed when the aircraft passes the 35 foot obstacle. V2 is also Takeoff Speed

Climb

Average Rate of Climb RCavg 1663.09 fpm Distance Covered Sclimb 176 nmi

Speed at Start of Climb VV2 193.36 mph Height at start of Climb 35 ft

0.3 Mach

Speed at End of Climb 615.7766 mph Height at End of Climb 40000 ft

0.933 Mach

Climb Time 24.02 min

Total Time to Mission End 24.73 min

Time to Mission End is the time, from standstill on the runway, to the end of this segment. Average Rate of Climb was by taking the height climbed from takeoff to cruising altitude and dividing by the climb time.

Transition between End of Climb and Start of Cruise

When we reach our cruising altitude of 40000 feet, we don’t quite reach our cruising speed of Mach 0.95.

We need to accelerate in order to reach this design Mach.

Time to accelerate from Mach 0.933 to Design Mach 0.95 1.56 min

Cruise

Cruise Speed Vcruise 919.68 mph Altitude at Cruise start 40000 ft

0.95 Mach Altitude at Cruise end 48000 ft

Range R 7638.39 nmi Cruise Time tcruise 14 hr

Total Time to Mission End 14.217 hr

Cruise speed was kept constant for cruise to satisfy the constant L/D requirements for the range equation. Range is the distance covered by the end of cruise minus the distance covered up until the start of cruise. The range equation, as a first order approximation, provided us with an optimistic value for the range. The excel spreadsheet used in tabulating the value offered a more realistic number.

Descent to 5000 ft

Rate of Descent RD 2000 fpm Altitude at Descent start 48000 ft

Average Descent Speed VD 384.32 mph Descent time to 5000 ft 21.5 min

Total Time to Mission End 14.78 hr

Table P.8 Performance Summary

51

Stability and Trim

Stability and control are vital characteristics of any aircraft. An aircraft that is stable will be easy

to maintain in flight as there will be a restoring force for every movement; however if an aircraft is

excessively stable, then it will be too difficult to control and too much force will be needed in order to

induce a change in its movement. There will also be a sufficient lag time between the control input and

the aircraft’s actual execution of the desired control. In contrast, for an unstable aircraft, the pilot can

easily control the flight motion; however once such a motion is induced, there will be no natural

restoring force to damp the motion. Without the use of electronic flight controls, such as a fly-by-wire

system, the plane will continue along its current input direction, which may eventually lead to a crash if

the pilot fails to correct it. Thus for commercial civil transport aviation, it is best to have a slightly stable

aircraft so that there is an optimal combination of safety and maneuverability.

Our Sonic Cruiser, the Aquila, is designed to be stable under all flight conditions. The initial step

in designing an aircraft for stability is determining the placement and weight of each individual

component, which was accomplished in our aircraft layout and design process. This allows us to

determine the aircraft’s center of gravity (CG), which lies at the root of all future stability calculations.

First, each individual aircraft component is assigned an initial weight estimate in ‘lbs’ and a moment arm

for its CG. A datum line is arbitrarily drawn at the tip of the aircraft’s nose, and the placement of each

component is then measured as the distance of its CG in ‘ft’ from the datum line. This distance is the

arm of each component. The arm of the entire aircraft as a whole is known as the CG of the aircraft. To

find the CG of the whole aircraft we find the moment, in ‘lbf-ft’, of each individual component by

multiplying the weight by its respective arm. The total weight is then found by summing the individual

weights, and the total moment is found by summing all the individual moments. The total moment is

then divided by the total weight, which gives the total arm (CG) of the aircraft. The CG was calculated in

this fashion for four different loading conditions, for both flight at start of cruise at Mach 0.95 at an

52

altitude of 40,000ft, and at takeoff at Mach 0.25 at sea level on a standard day. For the sake of

completion, the CG was also calculated for flight at the end of cruise at Mach 0.95 at a height of

48,000ft, and after the end of descent and loitering for 30mins at Mach 0.36 at a height of 5,000ft, for

the most common loading condition, in order to ensure that the Aquila is compliant within the entire

flight envelope.

The loading conditions encompass different combinations of payload and fuel. Loading

Condition I is the state when the Aquila is loaded to its maximum payload and maximum fuel. Load

Condition II is with max payload and minimum fuel. Load Condition III is when the Aquila is at minimum

payload and maximum fuel. Finally, Load Condition IV is when the Aquila is loaded with the minimum

payload and minimum fuel. Load Condition I is the most common loading condition because the Aquila

will be flying at maximum payload and maximum fuel for the overwhelming majority of its business life

in order to maximize its business revenue. The CG at each loading condition will be different and their

locations are important, as a further aft CG decreases stability while increasing controllability, while a

further forward CG increases stability while decreasing controllability. A CG aft of the neutral point

means the aircraft is unstable, while a CG in front of the neutral point means the aircraft is stable.

The Aquila had to be stable at all four loading conditions for both beginning of cruise and

takeoff. As an extra, we also had to make sure the Aquila was stable at the end of cruise and after

descent and loitering, for Load Condition I. Knowing the CGs of our Sonic Cruiser for all conditions,

preliminary stability calculations were completed. Pitch moments about the center of gravity ( )

were calculated, and the 3D lift curve slope for the aircraft as a whole ( ) was established (The

details of each calculation will be explained later in the text). Dividing the moment about the center of

gravity by the negative total aircraft 3D lift curve slope ( ) gave us the preliminary Static Margins

(SM), which is the distance between the aircraft’s CG and its neutral point. It is a measure of how stable

or unstable an aircraft is. The SM is often expressed as a percentage of the mean aerodynamic chord

53

(MAC). A positive percentage means the aircraft is stable, and a negative percentage implies an unstable

aircraft. Commercial transport aviation recommends a minimum SM of 5%, and a range of 5-10%

between all flight conditions is ideal.

The preliminary static margins indicated that our Sonic Cruiser was excessively stable for all Load

Conditions at both takeoff and start of cruise. Knowing that only a minimum SM of 5% is required, we

went back and solved for the appropriate CG location that would satisfy this minimum SM requirement

for all load conditions at takeoff and start of cruise, as well as for the two extra conditions. Knowing that

Load Condition III has the furthest aft CG, we redesigned the Aquila by relocating its fixed components,

so that with the added fuel, it would have a CG as far aft as possible in order to assure a SM as close to

5% as possible during Takeoff. Also, by making sure that the Aquila was as close to the minimum

required stability as possible at LC III during takeoff, we knew the Aquila would be stable, with

minimized excessive stability, for all loading conditions. It was found through calculation that at Load

Condition III, the maximum required distance between the aircraft CG and the datum should be

144.652ft at takeoff and 145.908ft at start of cruise, for a stability margin of exactly 5%. Knowing this,

we went back to the drawing board and redesigned the aircraft so that each individual component

would be located at the proper distance from the datum in order to ensure our total aircraft CG would

not exceed the calculated limits. The finalized individual component location from the datum can be

seen in the tables below, along with the corresponding CG calculations for each loading condition at

start of cruise and at takeoff, and for loading condition I at end of cruise and after loiter & descent. Start

of cruise conditions were calculated at Mach 0.95 at 40,000ft and takeoff conditions were calculated at

Mach 0.25 at sea level on a standard day. End of cruise conditions were calculated at Mach 0.95 at

48,000ft, and conditions after end of descent and loitering for 30mins were calculated at Mach 0.36 at

5,000ft.

54

Component Weight (lbs) Arm (ft) Moment (lb-ft)

Wing 67756.8 169.467 11482541.63

Canard 8187.3 28.343 232052.6439

Tail Fins 7215.5 178 1284359

Fuselage 37642.7 100 3764270

Front Landing Gear 3086.4 15 46296

Rear Landing Gear 13345.7 152 2028546.4

Systems 33377.6 100 3337760

Engines 33288 176 5858688

Nacelles 11700 176 2059200

Fuel in Canard 6910.4 28.343 195861.4672

Fuel in Wing 157142.3 169.467 26630434.15

Fuel in Tail Trim Tank 42413.3 180 7634394

Fuel in Nose Trim Tank 3076 8 24608

Luggage 10000 87.5 875000

First Class Passengers 2340 21 49140

Business Class Passengers 7920 44.5 352440

Economy Class Passengers 25740 111 2857140

Total 471142 145.842933 68712731.29

CG (distance from nose in ft)

Load Condition I (Max Payload:Max Fuel)

Start of Cruise @ Mach 0.95 @ 40,000ft.

145.8429333

Component Weight (lbs) Arm (ft) Moment (lb-ft)

Wing 67756.8 169.467 11482541.63

Canard 8187.3 28.343 232052.6439

Tail Fins 7215.5 178 1284359

Fuselage 37642.7 100 3764270

Front Landing Gear 3086.4 15 46296

Rear Landing Gear 13345.7 152 2028546.4

Systems 33377.6 100 3337760

Engines 33288 176 5858688

Nacelles 11700 176 2059200

Fuel in Canard 0 28.343 0

Fuel in Wing 0 169.467 0

Fuel in Tail Trim Tank 16107 192 3092544

Fuel in Nose Trim Tank 0 8 0

Luggage 10000 87.5 875000

First Class Passengers 2340 21 49140

Business Class Passengers 7920 44.5 352440

Economy Class Passengers 25740 111 2857140

Total 277707 134.386161 37319977.67

CG (distance from nose in ft)

Start of Cruise @ Mach 0.95 @ 40,000ft.

Load Condition II (Max Payload:Min Fuel)

134.3861612

Component Weight (lbs) Arm (ft) Moment (lb-ft)

Wing 67756.8 169.467 11482541.63

Canard 8187.3 28.343 232052.6439

Tail Fins 7215.5 178 1284359

Fuselage 37642.7 100 3764270

Front Landing Gear 3086.4 15 46296

Rear Landing Gear 13345.7 152 2028546.4

Systems 33377.6 100 3337760

Engines 33288 176 5858688

Nacelles 11700 176 2059200

Fuel in Canard 6910.4 28.343 195861.4672

Fuel in Wing 157142.3 169.467 26630434.15

Fuel in Tail Trim Tank 27599.3 180 4967874

Fuel in Nose Trim Tank 17890 8 143120

Luggage 0 87.5 0

First Class Passengers 0 21 0

Business Class Passengers 0 44.5 0

Economy Class Passengers 0 111 0

Total 425142 145.90655 62031003.29

CG (distance from nose in ft)

Start of Cruise @ Mach 0.95 @ 40,000ft.

Load Condition III (Min Payload:Max Fuel)

145.9065519

Component Weight (lbs) Arm (ft) Moment (lb-ft)

Wing 67756.8 169.467 11482541.63

Canard 8187.3 28.343 232052.6439

Tail Fins 7215.5 178 1284359

Fuselage 37642.7 100 3764270

Front Landing Gear 3086.4 15 46296

Rear Landing Gear 13345.7 152 2028546.4

Systems 33377.6 100 3337760

Engines 33288 176 5858688

Nacelles 11700 176 2059200

Fuel in Canard 0 28.343 0

Fuel in Wing 0 169.467 0

Fuel in Tail Trim Tank 16107 192 3092544

Fuel in Nose Trim Tank 0 8 0

Luggage 0 87.5 0

First Class Passengers 0 21 0

Business Class Passengers 0 44.5 0

Economy Class Passengers 0 111 0

Total 231707 143.2251 33186257.67

CG (distance from nose in ft)

Start of Cruise @ Mach 0.95 @ 40,000ft.

Load Condition IV (Min Payload:Min Fuel)

143.2250975

Tables S.1.a: CG of each individual component and the aircraft as a whole, for each loading condition

at start of cruise.

55

Component Weight (lbs) Arm (ft) Moment (lb-ft)

Wing 67756.8 169.467 11482541.63

Canard 8187.3 28.343 232052.6439

Tail Fins 7215.5 178 1284359

Fuselage 37642.7 100 3764270

Front Landing Gear 3086.4 15 46296

Rear Landing Gear 13345.7 152 2028546.4

Systems 33377.6 100 3337760

Engines 33288 176 5858688

Nacelles 11700 176 2059200

Fuel in Canard 6910.4 28.343 195861.4672

Fuel in Wing 157142.3 169.467 26630434.15

Fuel in Tail Trim Tank 45475.3 180 8185554

Fuel in Nose Trim Tank 7890 8 63120

Luggage 10000 87.5 875000

First Class Passengers 2340 21 49140

Business Class Passengers 7920 44.5 352440

Economy Class Passengers 25740 111 2857140

Total 479018 144.67599 69302403.29

CG (distance from nose in ft)

Takeoff @ Mach 0.25 @ Sealevel on Standard Day

Load Condition I (Max Payload:Max Fuel)

144.6759898

Component Weight (lbs) Arm (ft) Moment (lb-ft)

Wing 67756.8 169.467 11482541.63

Canard 8187.3 28.343 232052.6439

Tail Fins 7215.5 178 1284359

Fuselage 37642.7 100 3764270

Front Landing Gear 3086.4 15 46296

Rear Landing Gear 13345.7 152 2028546.4

Systems 33377.6 100 3337760

Engines 33288 176 5858688

Nacelles 11700 176 2059200

Fuel in Canard 0 28.343 0

Fuel in Wing 0 169.467 0

Fuel in Tail Trim Tank 23983 192 4604736

Fuel in Nose Trim Tank 0 8 0

Luggage 10000 87.5 875000

First Class Passengers 2340 21 49140

Business Class Passengers 7920 44.5 352440

Economy Class Passengers 25740 111 2857140

Total 285583 135.975074 38832169.67

CG (distance from nose in ft)

Takeoff @ Mach 0.25 @ Sealevel on Standard Day

Load Condition II (Max Payload:Min Fuel)

135.9750744

Component Weight (lbs) Arm (ft) Moment (lb-ft)

Wing 67756.8 169.467 11482541.63

Canard 8187.3 28.343 232052.6439

Tail Fins 7215.5 178 1284359

Fuselage 37642.7 100 3764270

Front Landing Gear 3086.4 15 46296

Rear Landing Gear 13345.7 152 2028546.4

Systems 33377.6 100 3337760

Engines 33288 176 5858688

Nacelles 11700 176 2059200

Fuel in Canard 6910.4 28.343 195861.4672

Fuel in Wing 157142.3 169.467 26630434.15

Fuel in Tail Trim Tank 30755.3 180 5535954

Fuel in Nose Trim Tank 22610 8 180880

Luggage 0 87.5 0

First Class Passengers 0 21 0

Business Class Passengers 0 44.5 0

Economy Class Passengers 0 111 0

Total 433018 144.65182 62636843.29

CG (distance from nose in ft)

Takeoff @ Mach 0.25 @ Sealevel on Standard Day

Load Condition III (Min Payload:Max Fuel)

144.6518235

Component Weight (lbs) Arm (ft) Moment (lb-ft)

Wing 67756.8 169.467 11482541.63

Canard 8187.3 28.343 232052.6439

Tail Fins 7215.5 178 1284359

Fuselage 37642.7 100 3764270

Front Landing Gear 3086.4 15 46296

Rear Landing Gear 13345.7 152 2028546.4

Systems 33377.6 100 3337760

Engines 33288 176 5858688

Nacelles 11700 176 2059200

Fuel in Canard 383 28.343 10855.369

Fuel in Wing 0 169.467 0

Fuel in Tail Trim Tank 23600 192 4531200

Fuel in Nose Trim Tank 0 8 0

Luggage 0 87.5 0

First Class Passengers 0 21 0

Business Class Passengers 0 44.5 0

Economy Class Passengers 0 111 0

Total 239583 144.566889 34635769.04

CG (distance from nose in ft)

Takeoff @ Mach 0.25 @ Sealevel on Standard Day

Load Condition IV (Min Payload:Min Fuel)

144.5668893

Tables S.1.b: CG of each individual component and the aircraft as a whole, for each loading condition at

takeoff.

56

Component Weight (lbs) Arm (ft) Moment (lb-ft)

Wing 67756.8 169.467 11482541.63

Canard 8187.3 28.343 232052.6439

Tail Fins 7215.5 178 1284359

Fuselage 37642.7 100 3764270

Front Landing Gear 3086.4 15 46296

Rear Landing Gear 13345.7 152 2028546.4

Systems 33377.6 100 3337760

Engines 33288 176 5858688

Nacelles 11700 176 2059200

Fuel in Canard 0 28.343 0

Fuel in Wing 0 169.467 0

Fuel in Tail Trim Tank 6000 192 1152000

Fuel in Nose Trim Tank 0 8 0

Luggage 10000 87.5 875000

First Class Passengers 2340 21 49140

Business Class Passengers 7920 44.5 352440

Economy Class Passengers 25740 111 2857140

Total 267600 132.21014 35379433.67

CG (distance from nose in ft)

End of Cruise @ Mach 0.95 @ 48,000ft.

Load Condition I (Max Payload:Max Fuel)

132.2101408

Component Weight (lbs) Arm (ft) Moment (lb-ft)

Wing 67756.8 169.467 11482541.63

Canard 8187.3 28.343 232052.6439

Tail Fins 7215.5 178 1284359

Fuselage 37642.7 100 3764270

Front Landing Gear 3086.4 15 46296

Rear Landing Gear 13345.7 152 2028546.4

Systems 33377.6 100 3337760

Engines 33288 176 5858688

Nacelles 11700 176 2059200

Fuel in Canard 0 28.343 0

Fuel in Wing 0 169.467 0

Fuel in Tail Trim Tank 849 192 163008

Fuel in Nose Trim Tank 0 8 0

Luggage 10000 87.5 875000

First Class Passengers 2340 21 49140

Business Class Passengers 7920 44.5 352440

Economy Class Passengers 25740 111 2857140

Total 262449 131.03666 34390441.67

CG (distance from nose in ft)

End of Descent and Loiter for 30mins @ Mach 0.36 @ 5,000ft.

Load Condition I (Max Payload:Max Fuel)

131.0366649

As one can see, the location of each fixed component was placed, such that at LC III, the CG

would be the furthest aft as possible without surpassing the 5% SM limit of 144.652ft for takeoff and

145.908ft for cruise. This would ensure a minimization of the excessive stability that could be found in

the furthest forward CG positions. In order to achieve a SM as close as possible to the 5% minimum, and

to reduce the excessive stability at the most forward CG conditions, a fuel management plan had to be

implemented. We implemented a 31,625.507lb capacity nose fuel trim tank and a 157,142.337lb

capacity tail trim tank. The tail trim tank is composed of smaller tanks such that the effective moment

arm from the datum can be located anywhere from 165-195ft. Through pumping various amounts of

fuel to the nose and tail trim tanks for each loading condition, the CG, and thus the SM of the aircraft,

could be further optimized to ensure minimum stability and to reduce excessive stability. These tanks

were also implemented since the maximum amount of fuel required for certain conditions would not fit

solely in the canard and wing fuel tanks. The nose and tail trim tanks for LCs I and III, for both start of

Tables S.1.c: CG of each individual component and the aircraft as a whole, for loading condition I, at end of cruise and after end

of descent and loiter for 30mins.

57

cruise and takeoff conditions, have various amount of fuel in them in order to optimize the SM. During

flight the fuel will be managed by a computer system so that it is pumped between all available tanks

and burned accordingly, in order to maintain optimum Stability Margins. For LCs II and IV, for start of

cruise and takeoff conditions, and also for LC I at end of cruise and after end of descent and loiter for

30mins, all of the remaining fuel is placed solely in the tail trim tank. This ensures the reduction of the

SM down to 5% as close as possible in order to increase controllability.

As mentioned earlier, the first step in calculating stability is determining the pitch moment

about the CG ( ) for each of the loading conditions. The following equation is used to calculate :

(

) (

) ( ) (

) { (

) } (

) (S1)

where Sc and Sw are the canard and wing areas respectively; ac and aw are the canard and wing 3D lift

curve slopes; Vf is the fuselage volume; k1 and k2 are fuselage slenderness ratios; ‘l’ is the distance

between the canard’s aerodynamic center and the wing’s aerodynamic center, which changes under

different flight conditions; and lw is the distance between the wing’s aerodynamic center and the

aircraft’s CG. To calculate Static Margin, we used the equation below.

(S2)

CL ,a/c is the 3D lift curve slope of the aircraft as a whole, and its value changes with respect to

each loading and flight condition. In order to account for wing and canard interference, downwash and

upwash effects had to be taken into account. Both downwash and upwash create a destabilizing effect,

and they affect the canard and wing 3D lift curve slopes as can be seen in equation S3 below.

ac → ac (1 + εc)

aw → aw (1 – εw)

εc and εw are the combined interference, factoring in the downwash and upwash, for the canard

and wing respectively. They can be found by utilizing the equations below:

(S3)

58

Condition LC I LC II LC III LC IV

Takeoff 144.676 135.975 144.652 144.567

Start of Cruise 145.843 134.386 145.907 143.225

End of Cruise 132.21 - - -

After Descent 131.037 - - -

CG Distance from Nose [ft]

SW [ft2] 5670

SC [ft2] 680

c ͞W [ft] 27.179

Vfuselage [ft3] 39362.127

k1 1.724E-02

k2 9.667E-01

Aircraft Dimensions

(zero for supersonic flow) (S4)

(

) (S5)

where bc is the canard span, and ‘c’ is the wing mean aerodynamic chord. The revised canard and wing

3D lift curve slopes which were then found in equation (S3) were then input into the original pitching

moment about the CG equation (S1), in order to find the new for the aircraft.

Utilizing equation (S1-S5) above, we calculated the maximum allowable CG moment arm for a

5% SM for each condition. Plugging in 0.05 for SM, and the respective 3D lift curve slope for the aircraft

as a whole for CL ,a/c, for each condition, would give us the necessary pitch moment about the center of

gravity. We would plug that pitch moment about the CG value into CMα in equation S1 above and solve

for lw, given the necessary canard and wing 3D lift curve slopes for each condition. Then, given the

desired lw value in order to reach a minimum SM of 5%, the optimized CG was found by subtracting the

moment arm of the wing aerodynamic center by lw, for each condition. The fixed component locations

and aircraft layout were then modified to meet the optimized CGs as closely as possible. The new

modified and finalized CG for each loading condition was then used to calculate the respective finalized

‘lw’ (finalized component layout and CG calculations can be seen in the previously mentioned tables

above S.1.a-S.1.c). Plugging in the necessary respective unknowns for each case into equations S1 and S2

above gave us the CM and SM for each of the loading and flight conditions. The respective values of

each input parameter (as determined by aerodynamics, performance, and aircraft design) can be seen in

the tables below.

59

LC I LC II LC III LC IV

CL,W 0.770 0.425 0.696 0.385

CLα,W [rad-1

] 4.56970 4.63056 4.58133 4.63876

εW 0.11798 0.11878 0.11845 0.12041

CL,C 1.186 0.991 1.073 0.596

CLα,C [rad-1

] 4.50448 4.53510 4.52216 4.59701

εC 0.07106 0.07201 0.07124 0.07213

CL,a/c 0.912 0.544 0.825 0.456

CLα,a/c [rad-1

] 4.60917 4.66358 4.61967 4.67131

dnose to wing's ac [ft] 166.357 166.357 166.357 166.357

lw [ft] 21.681 30.382 21.705 21.790

dnose to canard's ac [ft] 27.266 27.266 27.266 27.266

lC [ft] 117.410 108.709 117.386 117.301

l [ft] 139.091 139.091 139.091 139.091

Takeoff at Sea Level, Standard Day

LC I LC II LC III LC IV

CL,W 0.278 0.148 0.251 0.134

CLα,W [rad-1

] 7.59479 7.51963 7.57919 7.51142

εW 0.20238 0.20122 0.20147 0.19860

CL,C 0.470 0.411 0.423 0.257

CLα,C [rad-1

] 7.72685 7.68249 7.69192 7.58247

εC 0.11629 0.11514 0.11605 0.11501

CL,a/c 0.335 0.197 0.302 0.165

CLα,a/c [rad-1

] 7.09217 7.03396 7.08177 7.03359

dnose to wing's ac [ft] 169.664 169.664 169.664 169.664

lw [ft] 23.821 35.278 23.757 26.439

dnose to canard's ac [ft] 28.411 28.411 28.411 28.411

lC [ft] 117.432 105.975 117.496 114.814

l [ft] 141.253 141.253 141.253 141.253

Start of Cruise at 40,000 ft

CL,W

CLα,W [rad-1

]

εW

CL,C

CLα,C [rad-1

]

εC

CL,a/c

CLα,a/c [rad-1

]

dnose to wing's ac [ft]

lw [ft]

dnose to canard's ac [ft]

lC [ft]

l [ft]

LC I

0.205

7.55242

End of Cruise at 48,000 ft

0.20471

0.616

7.81576

0.11564

0.279

7.05208

169.664

37.454

28.411

103.799

141.253

60

Tables S.2: Parameters and respective values utilized in calculation of CM and SM for all four loading

conditions at both start of cruise and takeoff and also for loading condition I at the two extra flight

conditions: end of cruise and after descent & loiter for 30mins.

Table S.3: Calculated CM and Static

Margin, for each respective loading and

flight condition.

CL,W

CLα,W [rad-1

]

εW

CL,C

CLα,C [rad-1

]

εC

CL,a/c

CLα,a/c [rad-1

]

dnose to wing's ac [ft]

lw [ft]

dnose to canard's ac [ft]

lC [ft]

l [ft]

35.327

27.268

103.769

139.096

4.56316

0.07277

0.283

4.70770

166.364

LC I

0.211

4.67996

0.11952

0.598

After Descent to 5000ft and Loiter for 30 mins

Condition LC I LC II LC III LC IV

Takeoff -0.2307152 -1.7443222 -0.23105 -0.2351652

Start of Cruise -0.3548658 -3.3052624 -0.35452 -1.0875094

End of Cruise -3.7983112 - - -

After Descent -2.6294552 - - -

Condition LC I LC II LC III LC IV

Takeoff 0.0500557 0.3740308 0.050014 0.0503424

Start of Cruise 0.0500363 0.4699008 0.05006 0.1546165

End of Cruise 0.5386083 - - -

After Descent 0.5585439 - - -

Condition LC I LC II LC III LC IV

Takeoff 5.01% 37.40% 5.00% 5.03%

Start of Cruise 5.00% 46.99% 5.01% 15.46%

End of Cruise 53.86% - - -

After Descent 55.85% - - -

Static Margin

Static Margin [%]

CMα

Plugging in the above respective values for the respective loading and flight conditions into the

necessary equations yields the pitching moments and static margins seen in the tables below.

61

Figures S.1: CM plotted against ‘(lw/c)’ for all loading conditions at start of cruise and takeoff. The slopes are

linear, and the x-intercept is the neutral point.

CM is negative for every loading condition at both start of cruise and takeoff. This includes the

two extra flight conditions at LC I, which signifies the Aquila’s stability throughout the entire flight

envelope. It is also clear that we have a minimum SM of 5% for each condition, which is compliant with

commercial transport aviation recommendations. The two graphs below help visualize the data.

One can see that at Load Condition II our aircraft is very stable, which may show some difficulty

in controllability. However LC II corresponds to the maximum payload, minimum fuel condition. This

load condition will never be seen in the life cycle of the Aquila, as a fully loaded plane with passengers

and their luggage will never have a reason to be loaded with minimum fuel. Fuel will always be at a

maximum in order to achieve the required range to transport the passengers and to maximize

profitability. Fuel at such low levels would signify a range in which other modes of transport such as a

car, bus, or train would be more feasible.

It is important that the Aquila is stable at all load conditions. However it is also imperative that it

is trimmable under all flight conditions within its flight envelope without the use of active controls or

trim tabs which would cause too much drag. At trim flight, the weight of the aircraft is balanced by the

lift produced from the wings and canard. Also, the moment about the aircraft’s center of gravity is zero.

For our calculations, pitch-up moments were considered positive. Our trim calculations resulted in the

following two equations for the lift produced by the wing and canard.

62

Table S.4: Trim calculations for all load conditions at both takeoff and start of cruise and also for Load Condition I at end

of cruise and after descent to 5000ft and loiter for 30 minutes.

aSLSD [ft/s] Vtakeoff [Ma] Vtakeoff [ft/s] ρSLSD [slug/ft3] qtakeoff [lbs/ft

2]

1116.5 0.25 279.125 2.3769E-03 92.59

LC I LC II LC III LC IV

Wa/c [lbs] 479018 285583 433018 239583

Wfuel[lbs] 217418 23983 217418 23983

l [ft] 139.091 139.091 139.091 139.091

lW [ft] 21.681 30.382 21.705 21.790

lC [ft] 117.410 108.709 117.386 117.301

CL,W 0.770 0.425 0.696 0.385

CL,C 1.186 0.991 1.073 0.596

CL,a/c 0.912 0.544 0.825 0.456

LC/(LW +LC) [%] 15.588 13.366 14.319 8.494

LW/(LW +LC) [%] 84.412 78.157 84.395 84.334

CLα,W [rad-1

] 4.56970 4.63056 4.58133 4.63876

CLα,C [rad-1

] 4.50448 4.53510 4.52216 4.59701

εW 0.11798 0.11878 0.11845 0.12041

εC 0.07106 0.07201 0.07124 0.07213

αW [°] 9.815 4.835 8.741 4.267

αC [°] 12.683 10.277 11.293 5.531

CLα,a/c [rad-1] 4.60917 4.66358 4.61967 4.67131

αa/c [°] 10.175 5.515 9.062 4.427

Takeoff at Sea Level, Standard Day

a40k [ft/s] Vcruise [Ma] Vcruise [ft/s] ρ40k [slug/ft3] qcruise [lbs/ft

2]

968.08 0.95 919.676 5.8727E-04 248.36

LC I LC II LC III LC IV

Wa/c [lbs] 471142 277707 425142 231707

Wfuel[lbs] 209542 16107 209542 16107

l [ft] 141.253 141.253 141.253 141.253

lW [ft] 23.821 35.278 23.757 26.439

lC [ft] 117.432 105.975 117.496 114.814

CL,W 0.278 0.148 0.251 0.134

CL,C 0.470 0.411 0.423 0.257

CL,a/c 0.335 0.197 0.302 0.165

LC/(LW +LC) [%] 16.864 24.975 16.819 18.718

LW/(LW +LC) [%] 83.136 75.025 83.181 81.282

CLα,W [rad-1

] 7.59479 7.51963 7.57919 7.51142

CLα,C [rad-1

] 7.72685 7.68249 7.69192 7.58247

εW 0.20238 0.20122 0.20147 0.19860

εC 0.11629 0.11514 0.11605 0.11501

αW [°] 1.377 0.159 1.125 0.025

αC [°] 1.781 1.402 1.482 0.395

CLα,a/c [rad-1] 7.09217 7.03396 7.08177 7.03359

αa/c [°] 1.436 0.341 1.177 0.079

Start of Cruise at 40,000 ft

a48k [ft/s] Vcruise [Ma] Vcruise [ft/s] ρ48k [slug/ft3] qcruise [lbs/ft

2]

968.08 0.95 919.676 4.0051E-04 169.38

Wa/c [lbs]

Wfuel[lbs]

l [ft]

lW [ft]

lC [ft]

CL,W

CL,C

CL,a/c

LC/(LW +LC) [%]

LW/(LW +LC) [%]

CLα,W [rad-1

]

CLα,C [rad-1

]

εW

εC

αW [°]

αC [°]

CLα,a/c [rad-1]

αa/c [°]

2.704

7.05208

0.994

7.55242

7.81576

0.20471

0.11564

0.696

0.205

0.616

0.279

26.516

73.484

LC I

267600

141.253

37.454

103.799

6000

End of Cruise at 48,000 ft

a5k [ft/s] Vend [Ma] Vend [ft/s] ρ5k [slug/ft3] qend [lbs/ft

2]

1097 0.3646 400 2.0482E-03 163.83

Wa/c [lbs]

Wfuel[lbs]

l [ft]

lW [ft]

lC [ft]

CL,W

CL,C

CL,a/c

LC/(LW +LC) [%]

LW/(LW +LC) [%]

CLα,W [rad-1

]

CLα,C [rad-1

]

εW

εC

αW [°]

αC [°]

CLα,a/c [rad-1]

αa/c [°]

849

2.270

0.11952

0.07277

1.795

5.605

4.70770

After Descent to 5000 ft and Loiter for 30 minutes

LC I

262449

139.096

35.327

103.769

0.211

0.598

0.283

25.398

74.602

4.67996

4.56316

⁄ (S6.a)

⁄ (S6.b)

The trim calculations and the necessary lift coefficients for both the wing and canard that result

in a total moment about the CG equal to 0, for each loading condition are shown in the tables below.

We interpolated the lift curve slopes for all flight conditions from the optimized aerodynamic data.

63

As one can see, we were able to achieve our desired total lift coefficient for the Aquila for Load

Condition I at the start of its cruise. From our trim analysis, we achieved a CL,a/c = 0.335 which is in

agreement to the design CL,a/c of 0.336. Utilizing the equations from the total aircraft lift section in the

Aerodynamics portion of the report, a small incidence angle was applied to the wing and canard to

compensate for the effects of upwash and downwash, in order to reduce the effective angle of attack.

At takeoff the Aquila’s canard has a stall angle of 7.6°, and the wing has a stall angle of 17.5° since it has

deployed its flaps. For all loading conditions at takeoff, the wing’s effective angle of attack is smaller

than the stall angle. However for LC I-III the canard’s effective angle of attack is greater than the stall

angle. However utilizing flaps, our wing has a CLmax of 1.4 at takeoff and is more than capable of carrying

the entire load of the aircraft on its own, which only requires a CL,w of 0.82. For the start of cruise flight

condition, both the wing’s and canard’s stall angles of attack are 4.56° and for every load condition the

effective angles of attack are far below the stall angle. Also, for the end of cruise the wing and canard

have the same stall angles and both effective angles of attack are below the stall angle. Finally at the

end of descent to 5,000ft and loitering for 30 minutes, the stall angles of the canard and wing are both

7.6°, and our calculated effective angles of attack at that flight condition are below that. Thus it is

evident that the aircraft is trimmable under all load conditions for all flight conditions. In conclusion, the

Aquila is stable under all flight and load conditions, and it is trimmable for those conditions as well.

64

Conclusion

We greatly improved upon the aerodynamic performance of our original Sonic Cruiser design

with the use of the CFD code. We increased the aspect ratio of our wing by increasing the sweep angle

and decreasing the taper ratio. As a result, we lowered the drag coefficient of our optimized wing by

more than 25% compared to the baseline wing. Furthermore, we lowered the maximum takeoff weight

for our new Sonic Cruiser design through an iterative process. Thus, we were able to decrease the

required planform area for our new design by 5.5%. Also, we incorporated the destabilizing effects of

upwash and downwash for our trim and stability calculations. Despite these interference effects, we

were able to prove that our Sonic Cruiser, Aquila, can remain in trim and stable flight for all load

conditions. Despite the challenge of flying in the transonic flow regime, Aquila has the necessary

aerodynamic characteristics to cruise safely in this region.

For the Final Report, we have improved the performance of our Sonic Cruiser, Aquila, to meet

the requirements outlined by the baseline specifications. In addition we downsized our engine from the

GE90-115B, rated at 115,300lbs of thrust, to the GE90-94B, rated at 93,700lbs of thrust. This reduction

in thrust comes with a weight savings that contributed in decreasing our maximum takeoff weight from

500,000lbs to 480,000lbs. Aerodynamic optimization of the wing and canard using the given Euler code

helped minimize our drag and maximized our L/D ratio for cruise, increasing our range from just above

7,500 nmi to 7,638 nmi. This improvement is significant considering that wave drag was unaccounted for

in the range equation in our preliminary design. Downsizing the engine also gave us reasonable takeoff

and climb values in terms of takeoff time and time to cruise to altitude. Our initial value of climb time of

9 minutes, while more than optimistic from a performance standpoint, is dubious in terms of passenger

comfort and stressing the aircraft structure (and thus lifetime). Extending this time to 25 minutes places

our Sonic Cruiser in agreement with the baseline design. With the exception of the maximum operating

65

Mach number, which is outside the typical mission regime of our aircraft, we have successfully achieved

the performance requirements of the Sonic Cruiser design.

Overall the Aquila is stable for all four loading condition at both beginning of cruise and at

takeoff. It is also stable for its most common loading condition (LC I), at both end of cruise, and after

descent and loiter for 30mins. Furthermore it achieves a static margin as close to 5% as possible for

most of the loading conditions, which is compliant with commercial transport aviation

recommendations. Also, for its most common loading condition in its operable business life, the Aquila

has a static margin of 5% at start of cruise and takeoff, which provides ample stability while maximizing

controllability. This is achieved through a fuel management plan that is managed by a computer, in

which appropriate amounts of fuel are pumped into the nose and tail trim tanks throughout the entire

flight envelope. In addition to its stability, the Aquila is trimmable at all load and flight conditions. Except

for loading conditions I-III at takeoff, where the wing extends its flaps to carry the entire load of the

aircraft, the effective angles of attack for the wing and canard never exceed their respective stall angles

for their respective flight condition. Despite the challenges faced in flying in the transonic region, the

Aquila maintains its balance of controllability and minimum stability, along with its trimability in flight.

Comparing our Aquila to the Boeing Dreamliner, it is no wonder why developing a passenger

aircraft operating in the transonic regime is such a daunting task. Several complications must be

considered for this particular aircraft. First is combatting the effects of wave drag near the sonic mach

range. This additional non-linear behavior of wave drag necessitates a powerful engine. Consequently,

to achieve a feasible range, the fuel efficiency required would be pushing the boundaries of the most

efficient turbofans currently in production. Also, the speed at which the aircraft should operate adds

another layer of complication to the drag problem. For this reason we chose a cruising speed at the

lower bound of the design requirements. All else considered, even with these complications, we have

satisfactorily designed an aircraft that meets these formidable specifications with aplomb.

66

References

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

Publishers, 1982

2. Raymer, D. P., Aircraft Design: A Conceptual Approach, AIAA Education Series

3. Abbot, I. H., von Doenhoff, A.E., and Stivers, L.S., Jr., Summary of Airfoil Data, NACA Report 824,

1945

4. McCormick, B.W., Aerodynamics, Aeronautics, and Flight Mechanics, 2nd Ed., John Wiley & Sons,

1995

5. Bendiksen, O.O., MAE 154A Preliminary Design of Aircraft, Department of Mechanical and

Aerospace Engineering, UCLA, Los Angeles, 2013

6. Hepperle, Martin. "The Sonic Cruiser - A Concept Analysis." Aviation Technologies of the XXI

Century: New Aircraft Concepts and Flight Simulation. Berlin: Print.

7. http://www.boeing.com/commercial/airports/acaps/787sec2.pdf

8. "Sample Aircraft Weight Statements." Sample Aircraft Weight Statements. N.p., n.d. Web. 15

Feb. 2013.

9. "Weight and Balance." Weight and Balance. N.p., n.d. Web. 15 Feb. 2013.

10. "Aircraft Weight and Balance." Weight and Balance of Aircraft. N.p., n.d. Web. 15 Feb. 2013.

11. "A Sample Atmosphere Table (US Units)." A Table of the Standard Atmosphere to 65,000 Feet.

N.p., n.d. Web. 15 Feb. 2013.

12. "Commercial Airplanes." Boeing:. N.p., n.d. Web. 15 Feb. 2013.

67

Appendix

The table below shows the original weight and range of our Sonic Cruiser from the midterm report.

Table AP1 – Statistics of the Baseline Sonic Cruiser from the Midterm report

MTOW [lbs] OEW [lbs] Wfuel [lbs] Wfuel/MTOW [%] Range [nm]

500,000 220,074 233,926 46.8 7508

The table below shows the Dreamliner’s weight and range which we used for comparison.

Table AP2 – Boeing 787-8 Dreamliner’s Statistics

MTOW [lbs] OEW [lbs] Wfuel [lbs] Wfuel/MTOW [%] Range [nm]

502,000 242,000 229,330 45.7 7650

The table below shows the dimensions of the wing from our Sonic Cruiser from the Midterm Report.

Table AP3 - Baseline Sonic Cruiser Dimensions

SW [ft2] bW [ft] bw/2 [ft] cr,w [ft] ct,w [ft]

6000 207.868 103.934 41.574 16.155

c W [ft] λ (ct/cr) A (b2/S) ΛLE [°] ΛTE [°]

30.730 0.3886 7.2015 37 26.98

The table below shows the standard atmosphere table we used to calculate the dynamic

pressure and velocity throughout Aquila’s flight.

Table AP4 – Standard Atmosphere

Altitude [ft] ρ [slug ft3] a [ft/s]

0 2.3769E-03 1116.50

5000 2.0482E-03 1097.10

10000 1.7555E-03 1077.40

15000 1.4962E-03 1057.40

20000 1.2673E-03 1036.90

25000 1.0663E-03 1016.10

30000 8.9070E-04 994.80

35000 7.3820E-04 973.10

40000 5.8727E-04 968.08

41000 5.5976E-04 968.08

42000 5.3361E-04 968.08

43000 5.0866E-04 968.08

44000 4.8489E-04 968.08

45000 4.6227E-04 968.08

46000 4.4068E-04 968.08

47000 4.2000E-04 968.08

48000 4.0051E-04 968.08

68

The plot below shows the lift to total drag (induced, wave, and parasite) ratio of our optimized wing for a larger Mach number range outside of the transonic flow regime.

The plot below shows the total drag coefficient (induced, wave, and parasite) of our optimized wing for a larger Mach number range outside of the transonic flow regime.

The following 3 tables show the optimized drag and lift curve slope values of our optimized wing obtained from the CFD code.

Table AP5 - Optimized Wing’s Aerodynamic Stats for CL = 0.3

M CD,i+w+p Avg CLα [rad-1]

0.20 0.0214381 4.63606

0.30 0.0183319 4.66384

0.50 0.0158330 4.86847

0.70 0.0154749 5.32955

0.75 0.0153868 5.51682

0.80 0.0152108 5.75933

9.0

12.0

15.0

18.0

21.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

L/D

i+w

+p

Mach

Figure AP1 - Optimized vs. Baseline Wing - L/Di+w+p vs. Ma

0.3 CL - Optimized

0.4 CL - Optimized

0.5 CL - Optimized

0.3 CL - Baseline

0.4 CL - Baseline

0.5 CL - Baseline

0.012

0.016

0.020

0.024

0.028

0.032

0.036

0.040

0.044

0.048

0.052

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

CD

,i+w

+p

Mach

Figure AP2 - Optimized vs. Baseline Wing - CD,i+w+p vs. Ma

0.3 CL - Optimized

0.4 CL - Optimized

0.5 CL - Optimized

0.3 CL - Baseline

0.4 CL - Baseline

0.5 CL - Baseline

69

0.85 0.0150044 6.09215

0.90 0.0148714 6.60721

0.92 0.0149351 6.91401

0.95 0.0158642 7.60740

0.96 0.0167539 7.77034

0.97 0.0177659 8.00523

0.98 0.0189871 8.23695

0.99 0.0203839 8.44568

Table AP6 - Optimized Wing’s Aerodynamic Stats for CL = 0.4

M CD,i+w+p Avg CLα [rad-1]

0.20 0.0312459 4.62687

0.30 0.0261839 4.64666

0.50 0.0234626 4.85497

0.70 0.0243075 5.30198

0.75 0.0240141 5.49378

0.80 0.0234862 5.75214

0.85 0.0228525 6.12802

0.90 0.0223534 6.73844

0.92 0.0228336 7.07103

0.95 0.0249028 7.67456

0.96 0.0259397 7.88551

0.97 0.0271528 8.08897

0.98 0.0285178 8.27575

0.99 0.0301210 8.43416

Table AP7 - Optimized Wing’s Aerodynamic Stats for CL = 0.5

M CD,i+w+p Avg CLα [rad-1]

0.20 0.0445452 4.60426

0.30 0.0391728 4.61993

0.50 0.0374542 4.80274

0.70 0.0380041 5.22477

0.75 0.0376203 5.41486

0.80 0.0363801 5.69352

0.85 0.0347827 6.13549

0.90 0.0340571 6.83057

0.92 0.0347571 7.18372

0.95 0.0372460 7.74875

0.96 0.0384978 7.92969

0.97 0.0396458 8.10013

0.98 0.0411036 8.24099

0.99 0.0426555 8.29253

70

Performance Code for Thrust Lapse (Takeoff until Mach 0.3)

%downgraded engine to GE90-94B

cl_w = 1.4;

cl_c = .582;

s_c = 680;

s_w = 5670;

cl_max = 1.16;

cl = cl_w+(cl_c*s_c/s_w);

S = s_w;

B = 8.33;

sfc = 0.377288136; %sea level tsfc up to mach 0.3

cl(1) = cl;

M(1) = 0; %mach

T(1) = 93700*2; %lbf

D(1) = 0;

v(1) = 0;

W(1) = 480000; %lbf

fburn(1) = 0;

totfburn(1) = 0;

d(1) = 0;

t(1) = 0;

time(1) = 0;

RC(1) = 0;

dh(1) = 0;

h(1) = 0;

n(1) = 0;

v_to(1) = 0;

%Thrust Lapse, Equations of Motion, and

%Numerical Integration

%Ground Roll to Takeoff

for i = 1:300

%assume constant cl for now

cl(i) = cl_w+(cl_c*s_c/s_w);

%parasite

A = 0.005152732;

B = 0.000013187062627979;

C = 0.00492027293173902;

cd_p = A*cl(i)^2+B*cl(i)+C;

%induced

delta = 0.016;

lambda = 0.3;

Ar = 9;

cd_i = cl(i)^2*(1+delta)/(pi*Ar);

%gear and flaps

lg_fa = 13.89; %drag from landing gear reduces excess thrust until retraction

%assuming same landing gear as boeing 787, frontal area of

%two 50x20.0R22 tires is 13.89 ft^2

cd_lg = 70*lg_fa/S;

%cd_f = 0.0043289499-0.0028446659*(cl(i)-1.828152044);

psi = 0.009351116;

xi = 0.003036426;

phi = 0.771406825;

cd_f = psi-xi*(cl(i)-phi);

%canard

cd_c=(cd_i+cd_p)*s_c/s_w;

%fuselage

cd_fus = 0.00354*6000/5670;

%tails

cd_vt = 0.000209982*2;

%engine and nacelle

71

cd_eng = 0.00050092142857*2*6000/5670;

%total drag coefficient

cd = cd_p+cd_i+cd_f+cd_lg+cd_vt+cd_eng+cd_fus+cd_c;

if i > 253 %with landing gear down, drag eventually exceeds thrust so must retract before

this point to reduce drag 245

cd = cd-cd_lg;

end

%increment using velocity

M(i+1) = M(i)+0.001;

v(i+1) = 761.25*5280/3600*M(i+1);

v(i) = 761.25*5280/3600*M(i);

L(i) = 0.5*0.0023769*S*cl(i)*v(i)^2;

L(i+1) = L(i);

D(i) = 0.5*0.0023769*S*cd*v(i)^2;

D(i+1) = D(i);

T(i) = 2*93700*(1- (0.454*(1+B))*M(i)/sqrt((1+0.75*B)*1.1)+(0.6+0.13*B/1.1)*M(i)^2);

T(i+1) = T(i);

if L(i) < W(i)

h(i+1) = 0;

end

if L(i) > W(i) %when lift exceeds weight the following must be

considered

v_mu(i) = v(i); %define minimum unstick speed

if v(i)<=279

h(i+1) = 0;

end

if v(i)>279 %the first nonzero value in this array is the takeoff

speed

v_to(i) = v(i); %the first nonzero value in this array is the takeoff

speed

Te(i) = T(i)-D(i); %ground drag disappears from thrust excess relation

RC(i) = Te(i)*v(i)/W(i); %when lift > weight and when thrust > drag, aircraft

can start climb

dh(i) = RC(i)*t(i);%-0.5*32.174*t(i)^2; %takes into account the height

climbed at each respective RC

h(i+1) = h(i)+dh(i); %current height

end

end

Te(i) = T(i)-D(i)-0.03*(W(i)-L(i));

Te(i+1) = Te(i);

%assume acceleration is always positive

acc(i) = Te(i)/W(i)*9.80665*3.28084; %a=F/m. 1lbf/lbm=9.80665 m/s^2. 1 m = 3.28084 ft

t(i+1) = (v(i+1)-v(i))/acc(i);

time(i+1) = time(i)+t(i+1);

fburn(i) = T(i)*sfc*t(i)/3600;

W(i+1) = W(i)-fburn(i);

d(i+1) = v(i)*t(i)+0.5*acc(i)*t(i)^2+d(i);

totfburn(i+1) = fburn(i)+totfburn(i);

n(i) = L(i)/W(i);

end

72

Table AP 8 CLIMB

GE90-115b Tav lbf 164216 146284 125967 109713 93459 81269 71517 65015 48761 45510.4 44698 40634.3 38196.2 37383.5 37383.5

Speed of sound ft/s 1116.5 1116.5 1097.1 1077.4 1057.4 1036.9 1016.1 994.8 973.1 972.096 971.092 970.088 969.084 968.08 968.08

V ft/s 334.95 390.775 405.927 430.96 475.83 518.45 558.855 596.88 681.17 729.072 776.8736 776.0704 872.1756 903.139 919.676

M

0.3 0.35 0.37 0.4 0.45 0.5 0.55 0.6 0.7 0.75 0.8 0.8 0.9 0.932918 0.95

V kts 198.4524 231.5277 240.5051 436.2665 442.7631 450.1927 462.895 479.343 460.461 433.3617 457.6205 482.7431 481.2445 535.095 544.8952

V mph 228.375 266.4375 276.7684 502.0468 509.5229 518.0727 532.6903 551.6183 529.8893 498.7039 526.6205 555.5311 553.8066 615.7766 627.0545

V ft/s 334.95 390.775 405.927 736.3353 747.3003 759.84 781.2792 809.0401 777.171 731.4324 772.3768 814.779 812.2497 903.139 919.68

ρ slugs/ft^3 0.002377 0.002308 0.002048 0.001756 0.001496 0.001267 0.001066 0.000891 0.000738 0.00071 0.000678 0.000646 0.000616 0.000587 0.000587

h ft 478.7951 994.5409 5000 10000 15000 20000 25000 30000 35000 36000 37000 38000 39000 40000 40000

T lbf 112100.1 99859.05 85989.89 74894.29 63798.69 55477.33 48820.24 44381.72 33286.12 31067.14 30512.56 27738.53 26074.19 25519.41 25519.41

tsfc 1/hr 0.377288 0.377288 0.377288 0.46918 0.477869 0.417049 0.425738 0.451803 0.46918 0.483255 0.497753 0.512686 0.512686 0.53 0.54

Cl_tot

0.64 0.5 0.5 0.52 0.5 0.5 0.51 0.53 0.49 0.45 0.41 0.43 0.36 0.35 0.336

Cd_c (i+p) 0.002188 0.001532 0.001532 0.001616 0.001532 0.001532 0.001573 0.001659 0.001491 0.001336 0.001195 0.001264 0.001037 0.001007 0.000968

Cd_fus

0.003746 0.003746 0.003746 0.003746 0.003746 0.003746 0.003746 0.003746 0.003746 0.003746 0.003746 0.003746 0.003746 0.003746 0.003746

Cd_fins

0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042

Cd_eng

0.00106 0.00106 0.00106 0.00106 0.00106 0.00106 0.00106 0.00106 0.00106 0.00106 0.00106 0.00106 0.00106 0.00106 0.00106

Cd_wing (i+p) 0.02139 0.014974 0.014974 0.015794 0.014974 0.014974 0.01538 0.016216 0.014576 0.013064 0.011681 0.012357 0.010133 0.009848 0.009462

Cd_tot

0.030244 0.022818 0.022818 0.023768 0.022818 0.022818 0.023288 0.024256 0.022358 0.020608 0.019007 0.019789 0.017216 0.016886 0.016439

Lift lbf 483842.4 499610.1 478400.2 480652.5 480193.6 482854.5 481505.1 476798 475810.7 481668.5 475627.9 474523.7 478315.7 475324.6 473175.3

Drag lbf 22864.65 22800.54 21832.58 21969.07 21914.43 22035.87 21987.1 21821.22 21710.26 22058.44 22049.95 21838.25 22874.01 22931.72 23149.79

Weight lbf 479014.3 478916.9 478342.8 477446.4 476560 475791.6 474999.4 474117.3 473353.6 473103.2 472799.3 472515.2 472132.1 471496.5 471138

Fx (or Te) lbf 89235.45 77058.51 64157.31 52925.22 41884.26 33441.46 26833.13 22560.51 11575.86 9008.698 8462.61 5900.279 3200.179 2587.69 2369.615

Acceleration ft/s^2 5.993695 5.176858 4.315316 3.566513 2.827736 2.261383 1.81754 1.530978 0.786816 0.612649 0.575882 0.401756 0.21808 0.176579 0.161821

Time from prev. s

9.313954 63.70376 91.83647 104.6634 119.5597 137.2128 158.3772 176.0435 60.03117 72.03167 71.91544 103.1911 169.1552 93.67456

Fuel Burned lb

97.47476 574.0941 896.398 886.366 768.3963 792.1988 882.1524 763.6953 250.3527 303.888 284.0889 383.1789 635.52 358.5779

Tot Fuel Burned lb 981.9919 1079.467 1653.561 2549.959 3436.325 4204.721 4996.92 5879.072 6642.767 6893.12 7197.008 7481.097 7864.276 8499.796 8858.374

Gamma RC degrees 9.472057 9.218985 7.684746 3.717252 3.206362 2.747741 2.315228 2.01142 1.228087 1.087489 1.031505 0.68146 0.417011 0.314453 0.288171

R/C ft/min 3322.407 3772.58 3266.676 2866.33 2509.206 2186.385 1894.213 1704.125 999.4808 832.967 834.3132 581.4456 354.7039 297.3991 277.5338

time elapsed s 53.0766 62.39055 126.0943 217.9308 322.5942 442.154 579.3668 737.7439 913.7874 973.8186 1045.85 1117.766 1220.957 1390.112 1483.786

time elapsed min 0.88461 1.039843 2.101572 3.63218 5.37657 7.369233 9.656113 12.29573 15.22979 16.23031 17.43084 18.62943 20.34928 23.16853 24.72977

distance traveled ft 10729.64 14593.85 49209.06 103826.8 169116.9 247265.4 341057.2 454790.3 586898.1 631769 689222.5 746072.9 837234.7 992531.6 1079392

distance traveled nmi 1.767069 2.403466 8.104259 17.09927 27.85193 40.72223 56.16884 74.89959 96.65647 104.0463 113.5083 122.871 137.8845 163.4604 177.7655

73

Table AP 9 CRUISE

GE90-115b Tav lbf 37383.5 36018.2 34652.9 33287.6 31922.3 30557 29126.6 27696.2 26265.8 26265.8 26265.8 26265.8 26265.8 26265.8

Speed of sound ft/s 968.08 968.08 968.08 968.08 968.08 968.08 968.08 968.08 968.08 968.08 968.08 968.08 968.08 968.08

V ft/s 919.676 919.676 919.676 919.676 919.676 919.676 919.676 919.676 919.676 919.676 919.676 919.676 919.676 919.676

M

0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95

ρ slugs/ft^3 0.000587 0.00056 0.000534 0.000509 0.000485 0.000462 0.000441 0.00042 0.000401 0.000401 0.000401 0.000401 0.000401 0.000401

h ft 40000 41000 42000 43000 44000 45000 46000 47000 48000 48000 48000 48000 48000 48000

Tav lbf 25519.41 33368.61 32103.75 30838.88 29574.02 28309.15 26983.98 25658.8 24333.62 24333.62 24333.62 24333.62 24333.62 24333.62

tsfc 1/hr 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54

Cl_tot

0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.336 0.325587 0.315174 0.304761 0.294348 0.283935

Cd_tot

0.016439 0.02422 0.02422 0.02422 0.02422 0.02422 0.02422 0.02422 0.02422 0.023419 0.02267 0.021921 0.021172 0.020423

Lift lbf 473175.3 451019.1 429910.3 409848.9 390673.7 372465.4 355062.7 338465.8 322674.4 312674.4 302674.4 292674.4 282674.4 272674.4

Drag lbf 23149.79 32511.16 30989.56 29543.46 28161.24 26848.71 25594.26 24397.89 23259.59 22490.41 21771.11 21051.82 20332.53 19613.24

Weight lbf 471138 451019.1 429910.3 409848.9 390673.7 372465.4 355062.7 338465.8 322674.4 312674.4 302674.4 292674.4 282674.4 272674.4

Time from prev. s 93.67456 4125.529 4541.054 4526.983 4539.374 4521.221 4532.96 4535.088 4526.106 2964.227 3062.161 3166.788 3278.818 2114.125

Fuel Burned lb 358.5779 20118.86 21108.79 20061.41 19175.16 18208.35 17402.67 16596.99 15791.31 10000 10000 10000 10000 6219.727

Tot Fuel Burned lb 8858.374 28977.23 50086.02 70147.43 89322.59 107530.9 124933.6 141530.6 157321.9 167321.9 177321.9 187321.9 197321.9 203541.6

time elapsed s 1483.786 5609.315 10150.37 14677.35 19216.73 23737.95 28270.91 32806 37332.1 40296.33 43358.49 46525.28 49804.1 51918.22

time elapsed hr 0.412163 1.558143 2.819547 4.077042 5.337979 6.593874 7.85303 9.112777 10.37003 11.19342 12.04403 12.92369 13.83447 14.42173

distance traveled ft 1079392 4873542 9049840 13213197 17387951 21546010 25714864 29885676 34048228 36774356 39590552 42502972 45518422 47462732

distance traveled nmi 177.7655 802.6254 1490.422 2176.087 2863.628 3548.421 4234.991 4921.883 5607.416 6056.383 6520.183 6999.831 7496.446 7816.655

74

Table AP10 DESCENT

GE90-94b Tav lbf 26265.8 30557 37383.5 65015 81269 109713 125967

Speed of sound ft/s 968.08 968.08 969.08 994.8 1036.9 1077.4 1097.1

V ft/s 919.676 814.7237 617.2699 550 500 450 400

M

0.95 0.841587 0.636965 0.552875 0.482207 0.417672 0.364598

V mph 627.0518 555.4934 420.8658 375 340.9091 306.8182 272.7273

Tav lbf 21345.28 24832.59 30380.25 52835.39 66044.44 89159.87 102368.9

ρ slugs/ft^3 0.000401 0.000462 0.000587 0.000891 0.001267 0.001756 0.002048

h ft 48000 45000 40000 30000 20000 10000 5000

T lbf 10567.59 8693.564 3529.876 6316.645 8695.154 3205.722 656.342

tsfc 1/hr 0.54 0.53 0.49 0.45 0.445 0.445 0.377

Cl_tot

0.283935 0.3 0.4 0.35 0.3 0.26 0.23

Cd_c (i+p+w) 0.001722 0.001884 0.00252 0.00264 0.00264 0.00192 0.00192

Cd_fus

0.003746 0.003746 0.003746 0.003746 0.003746 0.003746 0.003746

Cd_fins

0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042

Cd_eng

0.00106 0.00106 0.00106 0.00106 0.00106 0.00106 0.00106

Cd_wing (i+p+w) 0.014347 0.0157 0.021 0.022 0.022 0.016 0.016

Cd_tot

0.021295 0.02281 0.028746 0.029866 0.029866 0.023146 0.023146

Lift lbf 272674.4 260987 253760.1 267348.6 269459.7 262030.8 213684.6

Drag lbf 20450.58 19843.84 18236.56 22813.35 26825.74 23326.93 21504.24

Weight lbf 272674.4 272531.8 272339.8 272195.7 271958.8 271636.3 271576.9

Fx (or Te) lbf -9882.99 -11150.3 -14706.7 -16496.7 -18130.6 -20121.2 -22631.4

Acceleration ft/s^2 -1.16614 -1.31636 -1.73744 -1.94994 -2.14494 -2.38326 -2.68117

Time from prev. s

90 150 300 300 300 150

Fuel Burned lb

142.6625 191.9829 144.1366 236.8742 322.4453 59.43943

Tot Fuel Burned lb 204579 204721.7 204913.6 205057.8 205294.7 205617.1 205676.5

R/D ft/s -33.3333 -33.3333 -33.3333 -33.3333 -33.3333 -33.3333 -33.3333

R/D ft/min -2000 -2000 -2000 -2000 -2000 -2000 -2000

time elapsed s 51918.22 52008.22 52158.22 52458.22 52758.22 53058.22 53208.22

time elapsed hr 14.42173 14.44673 14.4884 14.57173 14.65506 14.7384 14.78006

distance traveled ft 47462732 47536057 47628648 47793648 47943648 48078648 48138648

distance traveled nmi 7816.655 7828.731 7843.98 7871.154 7895.858 7918.091 7927.972

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