Final Report

MAE 475

Flight Vehicle Design

Final Report

DESIGN OF A MULTI-ENGINE BUSINESS TURBOPROP AIRCRAFT

Submitted by:

The Left βrothersAnthony Donzella

Justin HruskaWyatt Trevithick

Joseph WongNels Lofgren

December 6th, 2016

Table of ContentsList of Symbols...............................................................................................................................iv

1 Mission Summary....................................................................................................................1

2 Comparative Aircraft...............................................................................................................1

2.1 Piper Cheyenne II XL.......................................................................................................22.2 Cessna 425 Corsair & Conquest 1....................................................................................32.3 Piper PA-42.......................................................................................................................42.4 Piaggio Avanti Evo...........................................................................................................52.5 Beechcraft King Air c90GTx............................................................................................6

3 Estimation of Gross Takeoff Weight.......................................................................................7

3.1 Mission Weight Estimates................................................................................................73.1.1 Determination of Regression Coefficients.................................................................7

3.1.2 Determination of Mission Weights............................................................................8

3.1.3 Determination of Parameters.....................................................................................8

3.1.4 Spreadsheet Calculation of Mission Weights............................................................9

3.2 Takeoff Weight Sensitivity Analysis..............................................................................123.3 Recommendations...........................................................................................................14

4 Wing Loading and Performance............................................................................................15

4.1 Performance Constraints.................................................................................................154.1.1 Takeoff Distance......................................................................................................15

4.1.2 Landing Distance.....................................................................................................16

4.1.3 Single Engine Climb................................................................................................16

4.1.4 Begin and End Cruise..............................................................................................17

4.1.5 Cruise Power Required and Power Installed...........................................................18

4.2 Recommendations...........................................................................................................185 Wing Design..........................................................................................................................19

5.1 Comparative Study of Similar Aircraft...........................................................................195.2 Main Wing Design..........................................................................................................20

5.2.1 Airfoil Selection.......................................................................................................20

5.2.2 Aspect Ratio.............................................................................................................20

5.2.3 Thickness.................................................................................................................20

5.2.4 Sweep.......................................................................................................................21

5.2.5 Taper Ratio..............................................................................................................21

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5.2.6 Incidence and Twist.................................................................................................21

5.2.7 Dihedral...................................................................................................................22

5.2.8 Stall..........................................................................................................................22

5.2.9 Results......................................................................................................................22

5.3 Drag Analysis..................................................................................................................245.4 Recommendations...........................................................................................................26

6 Layout and Design of Fuselage.............................................................................................27

6.1 Design of Fuselage..........................................................................................................276.2 Results and Spreadsheet Analysis...................................................................................296.3 Fuselage Layout..............................................................................................................306.4 Recommendations...........................................................................................................31

7 Empennage Design................................................................................................................31

7.1 Horizontal and Vertical Tail Design...............................................................................317.1.1 Airfoil Selection.......................................................................................................31

7.1.2 Aspect Ratio.............................................................................................................32

7.1.3 Thickness.................................................................................................................32

7.1.4 Sweep.......................................................................................................................32

7.1.5 Taper Ratio..............................................................................................................33

7.1.6 Tail Placement for Stall/Spin...................................................................................33

7.1.7 Results......................................................................................................................34

7.2 Drag Analysis..................................................................................................................377.3 Recommendations...........................................................................................................37

8 Engine Selection and Performance........................................................................................38

8.1 Engine Selection.............................................................................................................388.2 Performance....................................................................................................................428.3 Recommendations...........................................................................................................44

9 Takeoff and Landing Performance........................................................................................44

9.1 CDo Calculation................................................................................................................449.2 Takeoff Performance.......................................................................................................45

9.2.1 Thrust.......................................................................................................................46

9.2.2 Lift...........................................................................................................................47

9.2.3 Drag.........................................................................................................................47

9.3 Landing Performance......................................................................................................53

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9.4 Recommendations...........................................................................................................5510 Enhanced Lift Devices...........................................................................................................55

10.1 Types of Flaps.............................................................................................................5510.2 Leading and Trailing Edge Flap Design......................................................................5810.3 Recommendations.......................................................................................................63

11 Structural Design...................................................................................................................63

11.1 Refined Wing Analysis...............................................................................................6311.2 Wing Load Analysis....................................................................................................6511.3 Fuselage Load Analysis...............................................................................................6911.4 Fuselage Design..........................................................................................................7211.5 Recommendations.......................................................................................................72

12 Stability and Control..............................................................................................................73

12.1 Longitudinal Stability..................................................................................................7312.2 Lateral Stability...........................................................................................................7812.3 Directional Stability....................................................................................................7812.4 Rudder Sizing..............................................................................................................80

13 Engineering Conclusions and 3 View Drawings...................................................................82

References......................................................................................................................................84

Appendix A – Request of Proposal...............................................................................................85

Appendix B – Gross Takeoff Weight............................................................................................87

Appendix C – Weight Analysis.....................................................................................................90

Appendix D....................................................................................................................................93

Appendix E – Drag Calculations...................................................................................................96

Appendix F – Empennage Design.................................................................................................98

Appendix G – Power Requirements............................................................................................100

Appendix H – Engine Performance.............................................................................................102

Appendix I - Takeoff...................................................................................................................106

Appendix J - Landing..................................................................................................................117

Appendix L – Refined Weight.....................................................................................................121

Appendix M – Wing Loading......................................................................................................123

Appendix N – Structural Analysis...............................................................................................125

Appendix O – Stability Analysis.................................................................................................127

Appendix P – 3 view drawing.....................................................................................................131

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List of SymbolsSymbol Description Units

a Acceleration ft/s2

Aprop Area of propeller ft2

a.c Aerodynamic center --AR Aspect Ratio --b Wing span ftbf flap spanB Breguet range factor --

Bend Breguet endurance factor --c Chord length ft

CD0 Zero lift drag coefficient --Cdi Induced drag Coefficient --Cf Skin friction coefficient --Cfl Skin friction drag coefficient --Cl 2D lift coefficientCL 3D lift CoefficientCLα Lift curve slope --D Drag lbs

Dprop Diameter of propeller fte Oswald’s efficiency factor --E Hold time hoursF Form factor --Ff Friction force lbffn Fuel fraction at phase n of flight --H Placement Height ft

HT Horizontal tail --iw Incidence angle of wing deg.K Flap design constants --l length ftL Lift force lbLD n

Lift to drag ratio at phase n of flight --

LP Landing Parameter --M Mach number --

MAC/m.a.c Mean aerodynamic chord ftn Load factor --

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Symbol Description Units

P Power HPq Dynamic pressure lb/ft2

Q Interference factor --r radius of fuselage ft.R Range N.mi.Re Reynolds number --

ROC Rate of Climb ft/mins Structural factor --

Sref Planform area of wing ft2

Swet Wetted area of wing ft2

sfc Specific fuel consumption lbf /hrhp

Sn Ground roll at takeoff or landing ftT Thrust lbf

t/c Thickness ratio --TOGW Takeoff gross weight lbs.

Tvto Thrust at takeoff lbf

Δt Change in time hoursVn Velocity at n phase of flight fpsVT Vertical tail --Wn Weight at n phase of flight lbs.W/S Wing loading lbs/ft2

W/P Power loading lb/HPXac Aerodynamic center location ftXcg Center of gravity location ftΔy Leading edge sharpness --

αstall Stall angle of attack deg.α0L Zero lift angle of attack deg.flaps Flap deflection deg.

Γ Dihedral angle deg.ε Wing twist deg.

ηprop Propeller efficiency --λ Taper ratio --Λn Sweep angle at n location on wing deg. Coefficient of friction --ν Kinematic viscosity ft2/sρ Density sl/ft3

σTU Ultimate stress psi

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1 Mission SummaryThis is the final report in a series of reports that documents the conceptual design of a long

range, multi-engine turboprop aircraft in response to the RPF shown in Appendix A. The enclosed report shows the entire design process which includes comparative aircraft study, estimation of gross takeoff weight, wing loading/performance, wing design, layout and fuselage design, tail design, engine selection, takeoff and landing performance, enhanced lift selections, structural design, and stability and control. All calculations and raw data can be found in the appendix section presented at the end of the report.

Due to a recent marketing study, Beechcraft Inc. stated that there is a strong demand for a long range multi-engine turboprop business class propeller driven aircraft. The capabilities and specifications are shown below in Table 1.1.

Table 1.1: Mission RequirementsRange (NM) 1000

Holding (contingency) fuel 30 minutes

Reserve fuel 45 minutes

Design Cruise Speed (knots) 320 @ 25,000ft

Payload

6 passengers arranged in luxury seating (36" seat pitch) plus crew

(pilot and copilot)

FAR Takeoff Distance (ft) 2,000

FAR Landing Distance (ft) 2,000

As can be seen in the above table the aircraft must be spacious enough for luxury seating of 6 passengers as well as a 2 passenger crew. The aircraft must also be capable of achieving a cruise speed of 320 knots at an altitude of 25,000 feet. The desired range of the aircraft is to be 1000 nautical miles with a contingency fuel of 30 minutes and a reserve capacity of 45 minutes. The take-off and landing distances are set to be 2,000 feet in accordance with the Federal Aviation Regulations (FARs).

2 Comparative AircraftThe following aircraft have been chosen to be studied in order to provide a basis on which to

design a new aircraft given the mission specifications: Piper Cheyenne II XL, Rockwell Aero Commander 500 Series (500s Shrike Commander), Cessna 441 Conquest II, AAC Angel, and the Beechcraft King Air c90GTx. These particular aircraft were selected on their similarities in flight requirements and capabilities as an aircraft. Of each aircraft, pertinent data in regards to its performance, specifications, and components are discussed below.

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2.1 Piper Cheyenne II XL

Table 2.2: Manufacturing SpecificationsWTO (lbf) 9474WP (lbf) 4053WE (lbf) 5487WL (lbf) 7600

Pmax (HP) 1240

Powerplant Make/Modelx2 Pratt and Whitney (UACL) PT6A-135

VCruise (knts) 255VMax (knts) 275

Range (N.M) 1175Fuel Capacity (U.S. gal) 366

Table 2.3: Aircraft Geometry & Aerodynamic DataSREF (ft2) 229W/S (psf) 41.37

AR 7.95Wing Sweep (°) 5

Tail Config. ConventionalPower Loading

(lbf/HP) 7.64

Structure Factor 0.58

Figure 2.1: Piper Cheyenne II XL

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2.2 Cessna 425 Corsair & Conquest 1


Pmax (HP) 1000

Powerplant Make/Model 2x P&W PT6A-112






(lbf/HP) 8.60


Figure 2.2: Cessna 425 Corsair/Conquest 1

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2.3 Piper PA-42


Pmax (HP) 1440

Powerplant Make/Model x2 P&W PT6A-41





Tail Config. T-TailPower Loading

(lbf/HP) 7.78Structure Factor 0.57

Figure 2.3: Piper PA-42

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2.4 Piaggio Avanti Evo


Pmax (HP) 1630

Powerplant Make/Model 2 P&W PT6A-66B



Table 2.9: Aircraft Geometry & Aerodynamic SpecificationsSREF (ft2) 172.22W/S (psf) 70.26


Tail Config. T-TailPower Loading

(lbf/HP) 7.42Flap/Slat Config. CanardsStructure Factor 0.69

Figure 2.4: Piaggio Avanti Evo

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2.5 Beechcraft King Air c90GTx


Pmax (HP) 1100

Powerplant Make/Model2x Pratt & Whitney Canada PT6A-135A

@ 550 shp eachVCruise (knts) 226VMax (knts) 272


Table 2.11: Aircraft Geometry & Aerodynamics DataSREF (ft2) 295W/S (psf) 35.54

AR 9.76Wing Sweep (°) 5.69


(lbf/HP) 9.53

Flap/Slat Config. Flaps on Approach


Figure 2.5: Beechcraft King Air c90GTx

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3 Estimation of Gross Takeoff WeightThe purpose of this section is to provide an estimation for the gross takeoff weight of the

conceptual design aircraft. Fuel fraction method and Breguet equations will be used for the estimation of mission weights, and analyzed in a sensitivity analysis of the takeoff weight estimation.

3.1 Mission Weight EstimatesThe method used in calculating the amount of fuel burned during certain flight phases was the fuel fraction method. This approach uses a ratio defined as the weight entering a phase divided by the weight leaving that phase. Then the products of the individual fuel fractions for each phase is equal to the total fuel fraction for the entire mission. The Breguet Range Factor is a calculated value that is used in the determination of the weight of an aircraft in its cruise phase. Similarly, the Breguet Endurance Factor is a calculated Value used in the determination of the weight of the fuel consumed during the holding phase.

3.1.1 Determination of Regression Coefficients

A very vital part in the design process of an aircraft is the determination of the structure factor (s). s is defined as the ratio of the empty weight of the aircraft to the takeoff weight of the aircraft. This is represented in Equation 3.1.

(3.1)

Using this equation, a plot of the takeoff weight versus the structure factor was created by varying the structure factor of the aircraft and then determining the new takeoff weight for that specific structure factor. This plot is shown in Figure 3.1.

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0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.75500

10500

15500

20500

25500

30500

35500

f(x) = 52394893.8839223 x⁴ − 119027799.871473 x³ + 101440529.180396 x² − 38384237.4912745 x + 5442456.23697006

Iterated Takeoff Weight Iterated Takeoff Weight TrendlinePiper Cheyenne Piper Pa-42King Air c90gtx Cessna 425Piaggio Avanti

Structure Factor

WTO

(lbs

)

Figure 3.1: Structure factor calculations

Looking at the plot in Figure 3.1, the takeoff weight begins to rapidly increase proportionally to an increase in the structure factor. The structure factors of our comparable aircraft were also plotted onto this trend in order to determine the best structure factor to use. Looking at the points for the comparable aircraft as well as the takeoff weight trend line, a structure factor of 0.58 was chosen for the design.

3.1.2 Determination of Mission Weights

To determine the weights of the aircraft during the multiple phases of the missions, a spreadsheet analysis was carried out. This spreadsheet took the mission requirements as well as the calculated parameters to calculate useful values that would then be used in determining the mission weights of each phase via the fuel fraction method. This method is essentially the ratio of the aircraft leaving a phase to the weight of the aircraft at the beginning of that phase. Using the fuel fraction allowed the team to come up with a Takeoff Gross Weight (TOGW) through an iterative process in the spreadsheet.

3.1.3 Determination of Parameters

The determination of parameters was conducted after an in-depth look at aircraft comparable to that which is being designed. During the determination of the set parameters, the team selected values which correspond with the required payload, takeoff distance, and landing distance constraints outlined in the original RFP.

3.1.3.1 Determination of specific fuel consumption

When determining the specific fuel consumption to be used in the calculations, the team had to keep in mind that, per the RFP, the choice of engines for this aircraft were limited to the Pratt &

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Whitney PT6 series or Garrett TFE series. Therefore, for the given engines and their manufacturer’s data, a value of 0.58 was assigned to this variable.

3.1.3.2 Choosing the design Aspect Ratio

When analyzing similar long range, multi-engine turboprop business class propeller driven aircraft models, it was observed that the typical range was from seven, for smaller light aircraft such as the AAC Angel, up to roughly ten for larger payload aircraft such as the Beechcraft King Air c90GTx. When choosing the design aspect ratio, it was important to choose a wing large enough to meet the required takeoff distance constraint whilst also avoiding too large of a wing in order to avoid higher fuel consumption and efficiently cruise at the desired speed stated in the RFP. All variables considered, the team chose an aspect ratio of eight in order to meet all aforementioned design specifications.

3.1.3.3 Choosing of the zero lift drag coefficient

The dimensionless parameter CDo is directly related to the form drag, or zero lift drag of the aircraft, which is dependent on the geometry of the aircraft itself. Due to the complexity of the calculations involving the approximation of CDo, a range of typical values for similar aircraft was provided to the class, with values ranging from 0.0220 for clean, well-designed aircraft to 0.0260 for less aerodynamically clean aircraft. It was decided by the team to assume a value of 0.0230 allowing for a small degree of variation from the optimal value of 0.0220 or less.

3.1.3.4 Choosing of W/S

Before choosing a design wing loading, three specific situations were taken into consideration: takeoff and landing, single engine climb, and W/S for optimum cruise. Wing loading influences the landing parameter, LP, which is also found in the landing distance Equation 3.2

(3.2)

A higher wing loading, such as fifty, leads to longer takeoff distance which may conflict with the design requirement of a 2,000 foot takeoff distance. On the opposite side, too low of a wing loading, such as thirty, means a much larger wing area and significantly larger drag produced at the design cruise speed of 300 knots at 25,000 feet altitude. Due to fuel burn, the weight of the aircraft entering and exiting cruise will vary greatly meaning that the wing loading will ultimately affect the wing sizing as well. When considering the wing loading in a single engine situation one must keep in mind FAR pt. 135-187 in which it is stated that an aircraft in a single engine climb must be able to climb at a flight path angle of at least 2.4°, however for this design the flight path angle minimum will be considered at 3.3° instead.

3.1.4 Spreadsheet Calculation of Mission Weights

In this section, the flight phases and calculations leading to the weight of the aircraft at different phases as well as the final takeoff gross weight will be explained. To be able to come a final gross takeoff weight, a spreadsheet that calculates the weight of the aircraft at each section of the missions was created. The final TOGW is found through an iterative process. This means that the

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weight is guessed and then checked until a suitable value is reached. After the first TOGW was entered, Equation 3.3 was used to find the weight after takeoff.

W after ¿¿=W ¿ ∙ ff ¿ (3.3)

In this equation, the entered TOGW is multiplied by the fuel fraction at takeoff to come to a final weight after takeoff. A fuel fraction of 0.98 was selected based on similar values. After this weight was calculated, the weight of the fuel used during that phase could be calculated as the difference between the TOGW and the weight after the takeoff. This is shown in Equation 3.4.

W F , ¿¿=W ¿−W after ¿¿ (3.4)

The next phase was the climb and then acceleration to cruise. This phase is similar to the first phase and thus Equation 3.3 was modified to be used during this phase and is represented in Equation 3.5.

W After climb=W after ¿¿ ∙ ff climb (3.5)

The product of the weight after the takeoff and the fuel fraction for climb gives you the weight of the aircraft after the climb phase. A fuel fraction of 0.98 was selected based on similar values. Just like the previous phase, the fuel used during climb is the difference between the weight entering the phase and the weight leaving the phase shown in Equation 3.6.

W F , climb=W after ¿¿−W after climb (3.6)

The next phase of the flight was the cruise phase. In order to calculate the fuel used during the cruise section, the range and the Breguet Range Factor (B) were needed. The range is known to be 1000 nautical miles from the mission requirements and the Breguet Range Factor can be calculated using equation (3.7).

B=326 ∙ η¿ ∙LD Actual

∙ 1sfc (3.7)

In equation (3.7), η¿ is the efficiency of the propeller, LD Actual

is the actual Lift to Drag Ratio, 1

sfc

is the inverse of the engine’s standard fuel consumption, and 326 is a conversion factor from statute miles to nautical miles.

After B was found, the fuel used during cruise could be calculated using Equation 3.8.

W F , cruise=(1− 1

eRB

) ∙W start , cruise (3.8)

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In Equation 3.8, R is the range in nautical miles, B is the Breguet Range Factor, and the weight entering cruise is the same as the weight after the climb. Now with the fuel for cruise found, the weight after the cruise phase is just the difference of the weight entering cruise and the fuel used during the cruise expressed in Equation 3.9.

W after cruise=W enter cruise−W F, cruise (3.9)

The next phase entered is the Descent and Landing phase. This phase returns to using the fuel fraction method and is shown in Equation 3.10.

W after descent=W after cruise ∙ ff descent (3.10)

A fuel fraction of 0.975 was selected based on similar values. The fuel used during this phase is the difference between the weight after cruise and the weight after the descent. This is shown in Equation 3.11.

W F , descent=W after cruise−W after descent (3.11)

The next phase was the reserve phase, in order to calculate the fuel used in the reserve phase Equation 3.12 was used.

W F , Res=

sfc ∙ ΔtLD Max

∙ W Res ∙ V LD Max

550

(3.12)

In Equation 3.12, sfc is the engine’s standard fuel consumption, Δt is the time in reserve in

hours, LD Max

is the maximum lift to drag ratio, W Res is the weight entering the reserve, V LD Max

is the

velocity for the maximum lift to drag ratio, and the 550 is a conversion factor.

After the fuel of the reserve is found, the weight after the reserve can be found as the difference between the weight after descent and the weight of the fuel in reserve, shown in Equation 3.13.

W after res=W afterdescent−W F , res (3.13)

The last weight needed to be calculated is the fuel during the holding phase. The equation used to calculate this is expressed as Equation 3.14.

W F , Hold=(1− 1

eE

Bend

)∙ W enter hold (3.14)

In Equation 3.14, E is the time in hold in hours, Bendis the Breguet endurance factor, and W enter hold is the weight entering the hold which is the same as the weight leaving the reserve. The Breguet Endurance Factor is calculated using Equation 3.15.

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Bend=1

sfc∙ L

Dmax∙ 1

V hold (3.15)

In Equation 3.15, sfc is the engine’s standard fuel consumption, LDmax

is the maximum lift to drag

ratio, and V hold is the velocity in the hold.

Now with the weight of fuel used in hold the total fuel weight can be expressed as the sum of all the fuel used over the all the phases. And then the total fuel and payload weight is the weight of the fuel used added with the weight of the passengers and their baggage shown in Equation 3.16.

W F , Payload=W F+W payload (3.16)

Now the weight available for the structure of the aircraft could be calculated, shown as Equation 3.17.

W avail .=W ¿−W F , Payload (3.17)

Also the weight required to build the structure can be calculated using Equation 3.18.

W req .=W ¿ ∙ s (3.18)

Equation 3.18 is simply the TOGW multiplied by the structure factor s. and Equation 3.17 is the difference of the TOGW and the available structure. The difference between Equation 3.18 and Equation 3.17 will tell you whether you have a surplus of weight (positive) or a deficient of weight (negative). If you have a surplus, structure can be removed meaning the TOGW can be reduced, and if you have a deficient structure must be added increasing the TOGW. Using these equations and the given parameters, a final Gross Takeoff Weight of 9520 pounds was found.

3.2 Takeoff Weight Sensitivity AnalysisThis sensitivity analysis was conducted by varying range, aspect ratio, and zero lift drag coefficient. This was done in order to see how the listed parameters would affect the TOGW. The takeoff estimate calculations will be calculated using the values in TTaable 3.1.

Table 3.12: Sensitivity analysis parameters.CDo 0.0180 0.0210 0.0240 0.0270

Range (NM) 500 1000 1500

AR 5 7 9

A simple Matlab code (Appendix C) was constructed to vary each of the parameters while holding other values constant. This led to three graphs with three data sets on each graph. The different graphs correspond to the range of the aircraft; while the data sets on each graph correspond to the varying Aspect Ratio of the aircraft wing.

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Figure 3.2 shows aspect ratio and CDo varied while the range of the aircraft is held at 500 NM. This figure shows as CDo increases, the weight of the aircraft increases linearly due to rise in used fuel during cruise, which is caused by a decrease in L/Dmax from the increase of total drag on the aircraft. If an exponential trend line is added to the data for AR= 5 the slope can be expressed as y=4797.6e13.723x, this value can be used to compare the other two figures.

0.0170 0.0190 0.0210 0.0230 0.0250 0.027052005400560058006000620064006600680070007200

AR=5 AR=7 AR=9

CDo

TOG

W (l

bs)

Figure 3.2: Varying Aspect Ratio and Drag Coefficient at range of 500 NM

Figure 3.2 shows aspect ratio and CDo varied while the range of the aircraft is held at 1000 NM. A similar trend from figure 3.1 is shown in this figure. However, there are some differences. One difference is the increase in weight with increasing CDo changes with greater exponential. Another difference is the increase in range of TOGW. This is due to the need for more fuel to travel the increased range. If an exponential trend line is added to figure 3.3 for AR=5 the slope can be expressed as y=4492.8e34.303x, this shows that the slope has increased from e13.723 to e34.303.

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0.0170 0.0190 0.0210 0.0230 0.0250 0.02705800

6800

7800

8800

9800

10800

11800

AR=5 AR=7 AR=9

CDo

TOG

W (l

bs)

Figure 3.3: Varying Aspect Ratio and Drag Coefficient at range of 1000 NM

Figure 3.4 shows aspect ratio and CDo varied while the range of the aircraft is held at 1500 NM. Again, a similar trend from figure 3.3 is experienced, the main difference is the increase in weight with increasing CDo changes with greater exponential than figure 3.3 and figure 3.1. If adding an exponential trend line to Figure 3.4 is done again, the slope is shown as y=2762.9e82.498x, which is a greater increase from e34.303 previously seen between Figure 3.3 and Figure 3.2.

0.0170 0.0190 0.0210 0.0230 0.0250 0.02705800

10800

15800

20800

25800

30800

AR=5 AR=7 AR=9

CDo

TOG

W (l

bs)

Figure 3.4: Varying Aspect Ratio and Drag Coefficient at a range of 1500 NM

3.3 RecommendationsWith the initial comparative study of aircraft with similar mission specifications complete, the second stage of the design may begin. The first step towards building a functional aircraft is to

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find the gross takeoff weight available for the aircraft. The first step is to estimate an initial value for the gross takeoff weight. The fuel fraction method is then used to find the weight of the fuel burned in the phase. The fuel fraction method assigns each phase of flight an individual fuel fraction to compensate for the fuel burned. Of the given flight phases, the takeoff, climbing, and the descent and landing phases have fuel fractions assigned to be 0.99, 0.98, and 0.975 respectively. The two other phases, cruise and holding, involve calculations for the fuel consumed that involve the aerodynamics and aircraft geometry as well as the Breguet Range Factor and the Breguet Endurance Factor.

Following these steps will produce the total weight of fuel burned, which can then be used to find the available empty weight. A structure factor is then selected and used in order to find the required empty weight for the structure of the aircraft. With the calculations complete for both the available and required empty weights calculated, a comparison is done, and then the takeoff gross weight is then changed until the available and required empty weight have the same value.

The amount of fuel burned was found to be 2,398 pounds and the empty weight available was finalized at 5,522 pounds after taking the passengers, crew, and baggage into consideration. This led to the final take off gross weight to be 9,520 pounds.

4 Wing Loading and PerformanceThis section focuses on the calculations of the wing loading for the aircraft, as well as

other performance constraints such as: the wing loading, lift to drag ratio at both the beginning and end of cruise, the takeoff distance, the landing distance, and other performance constraints for the designed aircraft.

4.1 Performance Constraints In accordance with parameters laid out in the RFP, and in compliance with FAR requirements, the aircraft to be designed must be meet two specific criteria with respect to takeoff and landing distance respectively. The designed aircraft must meet the FAR specified requirement of being able to both land, and takeoff in a distance of 2,000 feet or less. In addition, the single engine climb must also be analyzed to ensure FAR criteria are met, thus allowing aircraft certification. One must take into consideration the design wing loading whilst optimizing the aircraft cruise.

4.1.1 Takeoff DistanceOne determining the estimated takeoff distance, one must collect several important quantities: the wing loading, W/S, the thrust to weight ratio for takeoff, T/W, the previously calculated CLmax, and the ratio of takeoff air density to standard sea level density, σ. One may calculate the thrust required at takeoff using the following formula,

T VTO=[ (SHP∗ηp )V ¿

]∗550(4.1)

Where SHP is the horsepower produced by a single engine on the aircraft, the 550 term is for conversion of units from horsepower, prop efficiency is a predetermined value for the selected propeller of the aircraft, and Vto is calculated using the following relation,

15

V ¿=1.2 (V stall ) (4.2)

The thrust to weight ratio is then obtained by dividing the calculated thrust value by the TOGW of the aircraft.

With this value in hand, one may progress to the calculation of the Takeoff Parameter of the aircraft, T.O.P, using Equation 4.3,

T . O . P .=[ (WS )( TW ) ]( 1

CLmax∗σ )

(4.3)

The resulting value is then substituted into the following relation for calculating takeoff distance,

S¿=[20.9 (T . O. P ) ]+87∗√T .O. P .( TW )

(4.4)

4.1.2 Landing Distance

Recalling from the RFP, the required landing distance is equal that of the required takeoff distance of 2,000 feet. As with the takeoff calculation, one must calculate a landing parameter, LP, using previously obtained values in the following equation,

LP=(WS )( 1

CLmax∗σ ) (4.5)

The closed form solution for determining the landing distance is far less complex than that of the takeoff distance, using only constant values in addition to the LP,

SL=118 LP+400 (4.5)

4.1.3 Single Engine Climb

Parameters involving and related to single engine climb are especially important since they affect the ability of the aircraft to be certified or not, specifically that in an engine out condition, per FAR Pt. 135-187, the aircraft, “...must be able to climb at =3.3 degrees.” To ensure the ability of the aircraft to meet this mandate, a minimum glide path slope of =3.3 degrees was used in the single engine calculations.

Primarily affect by single engine climb due to the loss of thrust, is the climb velocity, Vse,climb. The adjusted value is calculated using the following,

V se climb=V L

D max

−15 knts (4.6)

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And may then be used to calculate the adjusted single engine rate of climb, ROC, in units of feet per minute using,

ROC=(V seclimb) [sin (Γ )] (60 ) (4.7)

Where the outstanding constant of 60 is for version to the time units of minutes.By rearranging the total drag equation,

D=D i+D 0 (4.8)

And substituting in the following expressions for Di and Do, respectively,

Di=[(W

S )W ]q∗π∗AR∗e

(4.9)

D0=W∗q∗CD0

(WS ) (4.10)

It can be shown that a quadratic solution to the estimation of (W/S) may be found using the quadratic formula with respect to (W/S) as a variable, yielding the following expression,

1.2(WS )=

[( TW

−G)±√( TW

−G)2

−( 4 CD0

π∗AR∗e )]( 2

q∗π∗AR∗e )(4.11)

If one observes the two resulting solutions to this quadratic expression, a low value of (W/S) and high value of (W/S) are given. This range represents the range of wing loadings which will allow for satisfactory takeoff capability with a single engine. Any wing loading below the lowest value will not succeed because not enough lift will be generated by the wing to achieve takeoff. Any value selected which is higher than the max wing loading from the equation will also lead to failure since the wing will generate too much drag and keep the aircraft from successfully taking off.

4.1.4 Begin and End Cruise

In order to appropriately determine wing sizing, one must analyze the design aircraft at two points: starting cruise and ending cruise. Since the largest portion of fuel is burned while the

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aircraft is in cruise, the weight of the aircraft will fluctuate significantly when comparing the weight entering cruise to that of exiting cruise. For example, from the spreadsheet in Appendix A, the proposed aircraft enters cruise at a weight of approximately 9,143 pounds and exits cruise weighing 7,459 pounds. If one holds the wing loading, (W/S), constant for both weights, as shown in Appendix A, one would find two different ideal wing areas, Sw. However, the ideal wing sizes to optimize performance are not nearly large enough for an aircraft with the given design weight and payload capacity.

4.1.5 Cruise Power Required and Power Installed

With several power plant options provided in the RFP, including commercially available gas turbine motors such as Pratt & Whitney PT6 series or Garrett TFE series engines, a precise model has yet to be selected for the design aircraft. Nonetheless, performance calculations deem it necessary to estimate several parameters involving power in flight to compare with the required thrust to climb at a given flight path angle, Γ. One should investigate the Power required for cruise, Pcruise@altitude, Pinstalled, and the Single engine power required for climb at Γ.

To accurately determine the power required for cruise one must input the drag, propeller efficiency, and cruise velocity into the following formula,

Preq=1ηp

(D∗V cruise ) (4.12)

Notice as well that since the aircraft is flying at altitude and not in sea level conditions, the installed power may be found by multiplying the required power by the ratio of the local density to that of standard sea level air,

Pinstalled=Preq( ρactual

ρSSL) (4.13)

To find the single engine power required for climb at , only must simply divide the single engine horsepower in half and add a constant value as shown below,

Pse climb@ Γ=( SHP

2 )+40 (4.14)

When looking to compare the power installed per engine, one may derive the required thrust to climb at a flight path angle Γ from the following,

T req=( ηp∗PSEreq, climb@Γ

V SEclimb)550 (4.15)

This series of calculations allow for further comparison of the theoretical aircraft single engine performance to that which is required in the federal aviation regulation.

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4.2 RecommendationsBased on the calculations above, the design was determined to have design parameters consisting of the values listed in Table 4.1.

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Table 4.13: Key design parameters and ground rollWTO (lbs) 9520 Preq cruise end (HP) 909Sref (ft2) 226.67 Pinstall (HP) 2414T/W 0.339 W/S 42s ground roll landing (ft) 2223 s ground roll TO (ft) 2118

The given design restrains were taking off and landing within 2000ft, however with the design parameters chosen the ground roll on takeoff and landing are slightly higher than the design restraints. This can be fixed later in the design process by adding flaps and airbrakes, thus increasing the CL during landing and takeoff.

5 Wing DesignThis section documents the design of the Main wing of the aircraft. Components of the wing

design include: Airfoil selection, selection of the Aspect ratio, Thickness of the wing, Sweep angle, taper ratio, incidence and twist, Dihedral angle, as well as stall calculations. Included in this report as well, is the drag analysis of the selected airfoil and of the designed main wing. Including the zero lift drag, Induced drag, and the wing contribution to the total drag.

5.1 Comparative Study of Similar AircraftIn order to provide a basis on which to start the design of the wing for the aircraft, two of the five aircraft that were researched prior to the design phase were selected. These two aircraft, the Piper Cheyenne II XL and the Beechcraft King Air c90GTx, have similarities and differences when it comes to its wing configurations. This data and comparison of the data will provide a more accurate starting point for the wing design of the newly designed aircraft.

Table 5.1 is an in depth breakdown of the dimensions and different aspects of the wing. These dimensions include the span, aspect ratio, wing loading, wing reference area, and sweep angle. This table will provide an idea for an appropriate value for each different facet of the wing design.

Table 5.1: Wing Planform Data

Span, b (ft)

Aspect Ratio, AR

Sweep, Λ (°)

Reference Area, Sref (ft2)

Wing Loading, W/S (psf)

Piper Cheyenne II XL 42.69 7.95 5.00 229 41.37

Beechcraft King Air c90GTx 53.67 9.76 5.69 295 35.54

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5.2 Main Wing Design5.2.1 Airfoil Selection

For the design of the aircraft wing, a six series NACA airfoil was chosen. The six series was chosen because these airfoils were designed so the region over which the airflow remains laminar is maximized. This greatly decreases the drag over the wing. The airfoil chosen was the NACA 63-212. Table 5.2 displays the airfoil data and Figure 5.1 shows the airfoil.

Table 5.2: Design Airfoil dataName NACA 63-212 Cdo 0.0035

Clmax 1.35 rle 0.0024

Cla 0.1096 Cl minD 0a.c. 0.35 (t/c)max 35%

aoL (deg) -2 t/c 12%

Figure 5.1: 2D shape of the NACA 63-212 Airfoil

5.2.2 Aspect Ratio

For the wing design an aspect ratio of 8 was chosen. In choosing this value the length of the wing could be calculated using Equation 5.1

(5.1)

5.2.3 Thickness

To calculate thickness, t/c is used. This is the thickness over the total chord length. With the NACA 63-212 the thickness is 12% located at 35% back from the leading edge. Using these values the maximum thickness at the root and tip can be calculated using Equation 5.2

(5.2)

With tx being the thickness at 35% chord at any position on the wing with cx being the chord length at that position, x.

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5.2.4 Sweep

The purpose of adding sweep to an aircraft wing design is to lower the effective Mach number on the aircraft wing to reduce the overall load on the wing. Since this aircraft design will be traveling much slower than Mach 1, the design does not need any sweep at the leading edge. If sweep at the leading edge was brought into the design, the effective Mach speed would be described by Equation 5.3.

(5.3)

Since the leading-edge sweep will be considered to be zero for this design, the sweep at any location along the wing can be calculated using equation 5.4.

(5.4)

Listed in Table 5.3, values of sweep at important points along the wing can be found. This will be used to ensure the design of the wing is properly constructed.

Table 5.3 Sweep angle calculated at important locations along the wing.ɅLE 0

Ʌ1/4 chord -3.44420251

Ʌt/c max -4.81632341ɅTE -13.5358564

5.2.5 Taper Ratio

Taper ratio is described as the ratio between the length of the chord at the tip and of the root, as shown in equation 5.5. Adding taper ratio to the design minimizes the lift at the tips of the wing. This, in turn, minimizes the strength of the vortices developed at the wingtips of the aircraft. A perfect taper ratio design, is an elliptical wing. This design properly distributes the lift to minimize the effects of overflow at the tips of the wing. However, an elliptical wing is impractical and expensive. An alternative is a taper ratio with the range of [0.25~0.45]. For this aircraft wing, a value of 0.35 was selected.

(5.5)

5.2.6 Incidence and Twist

Incidence angle and twist both have a direct effect on the amount of lift that is generated. Twist also has an added benefit of allowing for smooth stall characteristics. This is because if a negative value of twist is added to the wing design, the tips of the wing will be at a lower angle of attack than that of the root, this ensures that the root of the wing will be stalling before the

22

tips. This is important because added twist limits the chances of a tip stall, which could result in an unrecoverable spin.

First, twist must be calculated using Equation 5.6 so that the value can be used in Equation 5.7 to calculate incidence angle.

(5.6)

(5.7)

In Equation 5.6, ε being the twist angle is chosen in order to achieve a change in angle of attack. For this wing design a twist of -2° was selected. This ensures that the coefficient of lift needed for cruise is achieved by changing α, which will be iw, or wing incidence. The value of twist can be manipulated to achieve a smaller, or higher angle of incidence. For this wing design the wing is at an angle of incidence of 1.86°.

5.2.7 Dihedral

Dihedral, ᴦ, can be added to a wing design to achieve sideslip stability. For this wing design a dihedral angle of 3.5° was used. Typical values range from [2~6°].

5.2.8 Stall

Considering the dihedral and twist added to the wing design of this aircraft, the aircraft should handle relatively well during a stall. Calculating the stall angle and speed of this aircraft can be done using Equations 5.8 and 5.9 respectively.

(5.8)

(5.9)

5.2.9 Results

After considering the above conditions, the final design of the aircraft wing is displayed in Table 5.4. The values that the team considered the most important are presented below, the rest can be seen in Appendix D.

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Table 5.4: Table of important values displaying wing properties

AirfoilNACA 63-212 S(ft2) 226.67 AR 8 ɅTE -13.5

b(ft) 42.58 iw(deg) 1.86 ε(deg) -2 L/D 22.062

cr (ft) 7.89 ɅLE 0.0 ᴦ(deg) 3.5 αstall (deg) 14.6

ct (ft) 2.76 Ʌ1/4 chord -3.4 ʎ 0.35Vstall

(ft/sec) 236.76m.a.c. (ft) 5.73 Ʌt/c max -4.8

A Solidworks model of the aircraft wing designed was created. Figures 5.2-5.5 display this.

Figure 5.2: Front view of the aircraft wing. In this view the dihedral angle and twist is clearly shown.

Figure 5.3: Side view of the aircraft wing. This shows the dihedral, as well as the taper of the wing.

Figure 5.4: Top view of the aircraft wing. This view clearly shows the sweep at the leading and trailing edges, as well as

the taper.

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Figure 5.5: 3D View of aircraft wing design

5.3 Drag AnalysisTo accurately model the drag produced by the wing planform, one must take into consideration all elements of the wing which directly affect the drag. However, the appropriate terms and atmospheric conditions must first be collected for proper inspection.

Table 5.5: Viscous DragV (ft/sec) 540.8q (lb/ft^2) 155.8836531Re 10276015.74

CF 0.002927452

Swet(ft2) 462.270798

F 1.439534461Q 1

Viscous Drag

As displayed in Table 5.5, the parameters considered are as follows, in order from top to bottom: cruise velocity, dynamic pressure, cruise Reynolds number, skin friction coefficient, wetted planform area, form correction factor, and interference factor.

Since the wing reaches a cruise Mach number of roughly 0.48, there is no need for a leading edge wing sweep since transonic speeds are not approached until near a cruise Mach of 0.7. The dynamic pressure at cruise is calculated using the well-known formula of,

25

(5.10)

And the cruise Reynolds number using the kinematic viscosity, nu, was determined via,

(5.11)

When determining the overall skin friction coefficient of the wing, one must consider both the laminar flow section and the section of the wing in which the flow trips to turbulent. Using the following relations for laminar flow skin friction and turbulent flow skin friction respectively, the overall coefficient is the sum of the two received values.

(5.12)

(5.13)

For an approximation of the wetted surface are of the wing, since the t/c ratio is greater than 5%, the team used,

(5.14)

The closed form solution for the computation of the form fact, F, was retrieved Design of Aircraft and is given by the following,

(5.15)

The design team also chose to affix a low wing, well filleted wing to the fuselage yielding an interference factor of 1.

With the necessary parameters allocated, one may delve further into the calculation for the total drag due to the wing by now determining the zero lift drag coefficient of the wing, C Do, and the induced drag coefficient of the wing at the beginning and end of cruise, CDibeg and CDiend

respectively, since the lift required changes as fuel is burned during cruise.

Using the collected terms, the zero lift drag coefficient of the wing may be found via,

(5.16)

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And the two induced drag coefficients may be calculated using the Munks relation,

(5.17)

Where the aspect ratio, Oswald’s efficiency, and cruise lift coefficients have already been determined in previous reports.

From this point, calculating the respective drags is done trivially by multiplying the drag coefficients times the cruise dynamic pressure, and wing area. The only difference is the usage of the Cdi and CD0 coefficients in the equation,

(5.18)

Table 5.6: Summary of DragCDO Wing 0.00859Cdi(begin cruise) 0.00313Cdi(end cruise) 0.00209Cd,total 0.01381Induced Drag(begin cruise) 110.745 lbfInduced Drag(end cruise) 73.6997 lbfZero Lift Drag 303.675 lbfTotal Drag 488.12 lbf

Diligently setting up the analysis as stated in this section, for the designed aircraft, one comes to the following numerical values seen in Table 5.6.

5.4 RecommendationsAfter comparable aircraft, such as Piper Cheyenne II XL and the Beechcraft King Air c90GTx, were studied, the team came up with a spreadsheet that was capable of predicting the parameters of the wing, as well as perform a beginning drag analysis on the aircraft. Selection of the Airfoil to be used was debated by the team and ultimately decided upon the NACA 63-212 to be used. A taper ratio of 0.35 was added to the wing design to minimize the lift at the tips and stop the aircraft from tip stalling. The team also decided that the addition of a dihedral angle of 3.5 degrees would help to combat any possible slide slip instability the aircraft may encounter.

With the wing parameters in place, a drag analysis was able to be performed. Using the calculations shown in section 4 of the report, the team came up with an induced drag of 110.745 pounds at the beginning of cruise, and 73.6997 pounds at the end of cruise. As well as the induced drag, a zero lift drag due to the wing with a magnitude of 303.675 pounds was calculated. With all of the values taken into consideration, the total drag on the aircraft was found to be 488.12 pounds.

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6 Layout and Design of FuselageWith the wing-design complete, the fuselage is the next step in the design of the aircraft;

then the drag forces on the fuselage can be found.

6.1 Design of FuselageIn order to properly design the fuselage for the concept aircraft, a myriad of considerations were taken into account. First and foremost, the aircraft must comfortably sit six passengers and two crewmembers along with their luggage. Additionally, the engine and avionics placement, payload accommodation, landing gear placement, fuel storage, wing attachment and carry through, and fuselage shape must all be considered. The team also chose to use the Sears-Haack relation, seen below, from Design of Aircraft to model the fuselage shape for drag calculation purposes:

[ r (x)r (0) ]

2

=[1−( 2xl )

2]3/2

(−l /2≤ x≤ l /2) (6.1)

Beginning with payload accommodation, the team chose to arrange the passengers in a conventional fashion: three rows of two seats with one seat on each side of the aisle. After deliberation the team felt this choice to be the most efficient arrangement of the payload due to its simplicity and optimization of personal space, as any other arrangement would require unnecessary elongation or widening of the fuselage. The crew manning the aircraft will be situated towards the nose of the aircraft with sufficient room for two individuals.

Following the deliberations on payload accommodation, the next topic discussed was the ideal placement of the landing gear for the aircraft. To allow for fuel storage in the wing, and provide uninhibited area for wing placement and carry through, the team chose to select a tripod configuration with a nose wheel and one outboard on each wing, as seen on the Piper Cheyenne III for example. Due to the large volume of space taken up by the carry through spar, the landing gear on the wings will be placed slightly aft of the main wing spar.

Since the model of engines to be used has been narrowed down to a select group, commercially available gas turbine motors such as the Pratt & Whitney PT6 series or Garrett TFE series engines, the only remaining issue to be resolved was the placement of the engines on the fuselage or body. After analyzing similar aircraft and their successes or failures respectively, such as the failure of the Antonov 28 and success of the Piper Cheyenne, the team decided upon wing mounted, streamlined nacelles for the engines.

As consistently seen in most aircraft, the nose of the aircraft will serve as the housing for the avionics package, with displays shown in the cockpit as seen below:

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Figure 6.1: Cockpit Display of Comparative Aircraft

Fuel storage is one of the paramount design considerations with respect to the fuselage. With various types of tanks, each with their own respective effectiveness, as seen in Table 6.1,

Table 6.1: Volume EffectivenessFuel Tank Type Fuselage WingDiscrete 100% -Bladder 83% 77%Integral 93% 85%

The team debated on the placement of the fuel storage container in either the wings or fuselage first. For safety concerns, in case of a crash to avoid any unnecessary fire hazard, the team sided with housing the fuel tanks in the wings. And though it requires more intricate containment, the team chose to select inboard, integral wing tanks to take advantage of the space available in the wing and to also take advantage of the higher effectiveness as compared to an amorphous bladder tank. With the adjustment from the 85% effectiveness of the integral wing tank, the total volume for fuel storage in the wing is 56.3 ft3.

Table 6.2: Ergonomic Dimensions of the Interior

Seat Width22.00

in

Seat Pitch34.00

in

Minimum Aisle Width

16.55

in

Using the minimum aisle width required as a basis and after comparing the average seat width and pitch provided, the team chose the values seen in Table 6.2 for the internal arrangement.

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Table 6.3: Fuel and Wing Volumetric PropertiesTotal Fuel used (lbs) 2398.227Total Fuel required (gal) 357.944Total Fuel required (ft3) 47.850

Volume Required (ft3) 56.295Wing Volume (ft3) 98.240

With a given range desired and the specific weight of the fuel being known, the total fuel required can be found by dividing the weight of fuel burned by the specific weight and is detailed in Table 6.3. Even with the additional volume needed due to integral wing tanks, there is sufficient space in the wing for the fuel to be stored.

6.2 Results and Spreadsheet AnalysisTo calculate the drag caused by the fuselage, the fuselage was broken down into ten sections; each with an equal width of 3.6 feet. At each section, the Reynolds number is calculated at the midpoint of each section. The skin friction for each section is then calculated using the equation:

(6.2)

Equation 3.1 is for turbulent flow and is used instead of the laminar flow skin friction equation due to the high Reynolds number at cruise velocity creating turbulent flow on the fuselage. The drag at each section is calculated using the equation:

(6.3)

The total drag on the fuselage is the summation of all the section drag forces. The full calculations can be seen in Appendix A. The calculated drag on the fuselage can be seen in Table 6.4.

Once the total drag is calculated, the fuselage zero lift drag can be calculated. This is done using the equation:

(6.4)

The result of this calculation is shown in Table 6.4.

Table 6.4: Drag SummaryDrag (lbs) 178.7CD0 0.005056

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6.3 Fuselage Layout Included in this section are; the fuselage dimensions, seating arrangement, and baggage area.

Figure 6.2: Top view of the seating arrangement and dimensions.

As displayed in Figure 6.2, the seating arrangement meets the required one foot aisle width, as described by the FAA, with an aisle width of 1.38 feet. This arrangement also features luxurious reclining leather seats in the front two seats, while the four in the rear have ample leg room, all having a seat pitch of 3.6’ or 43”. The luggage compartment is located in the rear of the aircraft so it does not limit the amount of head room for the passengers. This luggage compartment can hold six standard carry-ons (9” x 14” x 22”). The rear door is located directly in front of the baggage area, so that passengers can easily place their luggage in the compartment and continue onto the aircraft. Figures 6.3-6.4 show the fuselage layout, seating arrangement, and dimensions in feet.

Figure 6.3: Side view of the seating arrangement.

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34.27”

16.55”

17.44”

7.92”

Figure 6.4: Isometric view of the seating arrangement and baggage compartment.

6.4 RecommendationsAfter a complete design of the shape of the fuselage with the seating arrangements included, the drag analysis was conducted to determine the drag coefficient and the drag force on the fuselage alone. The drag force on the fuselage alone was calculated to be 178.7 pounds and the drag coefficient was 0.005056.

7 Empennage DesignThis section will include a detailed explanation of the horizontal and vertical tail design, which includes the airfoil, aspect ratio, thickness, sweep, taper, and placement. As well as the design of the empennage section, a drag analysis will be performed on the proposed design that includes the drag and zero lift drag on both the horizontal and vertical tail sections.

7.1 Horizontal and Vertical Tail DesignThe conventional layout of the horizontal and vertical tail was selected for the design of this aircraft. This design was selected due to the aircraft cruise velocity being subsonic. So a non-conventional design of the horizontal tail was not needed. This configuration was selected also due to the configuration requiring less structural support and having a lower overall weight as a result.

7.1.1 Airfoil Selection

For both the horizontal and the vertical tail, a symmetric airfoil was desired. Since a conventional design is used, a thin airfoil can be used since not as much structural is needed as compared to a configuration like the T-Tail configuration. The NACA 64-004 was selected as a

32

result of these requirements. Table 7.1 shows the properties for the NACA 64-004. This Airfoil was selected since the airfoil is symmetric and has a low thickness ratio.

Table 7.1: NACA 64-004 properties

Clmax 0.8Clalpha(/deg) 0.11

t/c 8%a.c. 0.26

αoL (deg) 0

7.1.2 Aspect Ratio

The aspect ratio for the horizontal and vertical tail was selected based from historical data of similar aircraft as provided by Corke. Using these ranges, the selected aspect ratios are shown in Table 7.2.

Table 7.2: Selected aspect ratiosARVT 2.0ARHT 3.0

7.1.3 Thickness

Due to the use of the conventional tail configuration, a thin airfoil can be used. As such, the airfoil selected has a maximum thickness of 4% of the chord length.

7.1.4 Sweep

The sweep angles for the horizontal tail were designed such that the trailing edge sweep angle is zero. These angles were calculated using the equation:

(7.1)

The results of the calculations are shown below in Table 7.3.

Table 7.3: Horizontal-tail sweep angles

Sweep AnglesΛLE (deg) 29.80Λ1/4 (deg) 23.26ΛTE (deg) 0.07

Λt/c max(deg) 18.99

The vertical tail sweep angles selected and calculated to have a negative trailing edge sweep angle. A leading-edge angle of 40.6 degrees was selected and equation 7.1 was used to calculate

33

the sweep angles throughout the vertical tail. The results of these calculations are shown below in Table 7.4.

Table 7.4: Vertical-tail sweep angles

Sweep AnglesΛLE (deg) 40.60Λ1/4 (deg) 32.73ΛTE (deg) 0

Λt/c max(deg) 27.21

7.1.5 Taper Ratio

The taper ratio was selected based off of the general range of similar aircrafts as provided by Corke. The selected aspect ratio for both the horizontal and vertical tail is 0.4. The Selected aspect ratio is then used to calculate the root and tip cord lengths of the horizontal and vertical tail. This is done using the equations:

(7.2)

(7.3)

(7.4)

Where:

(7.5)

(7.6)

The horizontal and vertical tail coefficients are selected based from values as described by Corke for a twin turboprop aircraft.

7.1.6 Tail Placement for Stall/Spin

To enhance stall control, the horizontal tail should be placed such that the horizontal tail in not inside the wake of the main wing. Based off the recommended placement of the horizontal tail from NACA, Table 7.5 shows the positions used for the placement of the horizontal tail. The horizontal distance is the distance from the mean aerodynamic center of the main wing to the mean aerodynamic center of the horizontal tail. The vertical distance is the distance above the mean aerodynamic center of the main wing.

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Table 7.5: Horizontal tail placementlHT (ft) 20.55HHT (ft) 0

To enhance spin control, the vertical tail should be placed such that the horizontal tail’s wake created during spin has the least amount of flow over the vertical tail. With a recommended minimum of 30% of the vertical tail outside of the horizontal tail wake. As such, the Vertical tail was positioned 18.55 feet behind the mean aerodynamic center of the main wing.

7.1.7 Results

The results of the calculations described for the horizontal tail and the vertical tail are shown in table 7.6 and table 7.7 respectively. Figures 7.1 through 7.8 show the top view, side view, front view, and an isometric view of the tail configuration to scale.

Table 7.6: Horizontal tail calculationsSweep Angles Viscous Drag Calculations

ΛLE (deg) 29.80 Cf 0.002871 SHT (ft2) 126.10Λ1/4 (deg) 23.26 RE 11609803 b (ft) 19.45ΛTE (deg) 0.07 Swet (ft2) 254.543 cr (ft) 9.26

Λt/c max(deg) 18.99 F 1.3002 ct (ft) 3.70Q 1 ARHT 3.00

CDo HT 0.0037 Xac HT (ft) 2.39D (lbf) 148.1205 β 0.76

CLα 0.0589m.a.c (ft) 6.88

Table 7.7: Vertical tail calculationsSweep Angles Viscous Drag Calculations

ΛLE (deg) 40.60 Cf 0.003 SHT (ft2) 65.79Λ1/4 (deg) 32.73 RE 10270618 b (ft) 11.47ΛTE (deg) 0 Swet (ft2) 132.805 cr (ft) 8.19

Λt/c max(deg) 27.21 F 1.278 ct (ft) 3.28Q 1 ARHT 2.00

CDo HT 0.0037 Xac HT (ft) 2.11D (lbf) 77.460 β 0.80

CLα 0.0456m.a.c (ft) 6.09

Figure 7.1: Front view of the horizontal tail

36

Figure 7.2: Isometric view of the horizontal tail

Figure 7.3: Right side view of the horizontal tail

Figure 7.4: Top view of the horizontal tail

37

Figure 7.5: Front view of the horizontal tail

Figure 7.6: Isometric view of the horizontal tail

Figure 7.7: Top view of the horizontal tail

38

Figure 7.8: Right view of the horizontal tail

7.2 Drag AnalysisWhen considering the zero lift drag of both the horizontal and vertical tails, that the previously used method for determining the zero lift drag coefficient of the wing planform may be adapted to these cases as well, after slight adjustment of parameters of course. Since symmetric airfoils are generally implemented for the horizontal and vertical tail shapes, the drag is directly dependent on the zero lift drag of the airfoil shape. The resulting simplifications yield the following expression, which is usable for both components,

D=q SW C f FQ (7.7)In this instance, q is the in-flight dynamic pressure, Sw is the wetted area for each respective surface, Cf is the skin friction coefficient, F is the form factor for each component, and Q is the interference factor of each component.

Having already solved for the in-flight dynamic pressure in the preliminary design phase, one may move forward to the determination of the wetted surface area. As with the wing planform, the wetted area is a function of the t/c of the selected area and the design reference area. The skin friction drag coefficient is a summation of the laminar flow and turbulent flow components of the previously stated equations for the skin friction drag coefficient. The form factor is determined from a closed form expression previously presented in the design of the wing planform, and also seen on page 75 in the Corke textbook Design of Aircraft. And finally, the interference factor is an assumption with a value of one for well-fileted members.

Table 7.8: Empennage Drag Analysis

Total Value Drag (lbs) CDo

Horizontal Tail 151.623 0.00380Vertical Tail 69.80865 0.00340

After careful deliberation, the following values, presented in Table 7.8, show the estimated drag and zero lift drag coefficient for each component of the empennage.

7.3 RecommendationsTaking into consideration the type of aircraft that is being designed, and the prior wing design and fuselage design, a conventional tail design was decided to be the best option for the aircraft. Based on the calculations above, the geometric parameters of the horizontal and vertical tail were determined and are presented in tables 7.9 and 7.10 respectively

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Table 7.9: Horizontal Tail Geometry

SHT (ft2) 153.40

b (ft) 21.45

cr (ft) 10.22

ct (ft) 4.09

ARHT 3.00

Table 7.10: Vertical Tail Geometry

SVT (ft2) 36.43

b (ft) 7.39

cr (ft) 7.04

ct (ft) 2.82

ARVT 1.50

Also following the aforementioned calculations, the contribution to zero lift drag from each tail and the total drag from the tails is shown in tables 7.11 and 7.12.

Table 7.11: Horizontal Tail Drag

CDo HT 0.0069

D (lbf) 166.0514

Table 7.12: Vertical Tail Drag

CDo VT 0.0073

D (lbf) 126.1305

8 Engine Selection and PerformanceThe performance of the engine will be calculated from the stall speed to the cruise speed

of 350 knots. This calculation will be carried out at four altitudes which include sea level, 8,000 feet, the cruise altitude of 25,000 feet, and 31,000 feet. In addition to these calculations an analysis of the rate of climb for a single engine will be carried out to ensure the aircraft is in accordance with FAR regulations.

8.1 Engine SelectionIn order to select an appropriate engine for the designed aircraft, the total drag, both zero lift drag and induced drag, while operating at cruise conditions must be computed. This has been a running calculation when each component of the aircraft is designed, making this a simple summation of the zero lift drag forces from the wing, fuselage, and the empennage. The only piece missing, is the nacelle; which can be found by using equation 8.1 and then multiplied by two since there are two engines on board.

40

(8.1)

Table 8.1: Total drag summationComponent D (lbs)Wing 312.3

Fuselage 141.1

Horizontal Tail 148.1

Vertical Tail 77.5Nacelle 29.4

Induced Wing 92.2Total 800.6

Zero

Lift

Table 8.1 shows the zero lift drag contribution from each of the previously discussed aspects of the aircraft design, as well as the induced drag from the wing. This results in a total drag force acting on the aircraft at cruise conditions. Table 8.2 reflects the drag coefficients for the same components.

Table 8.2: Total drag coefficient summationComponent CD

Wing 0.008838Fuselage 0.0039925

Horizontal Tail 0.003733

Vertical Tail 0.0037417Nacelle 0.000835


Zero

Lift

With the total drag, the power required at cruise can be found using Equation 8.2.

(8.2)

After calculating the power required at cruise, the shaft power can then be found by relating the power required, and the propeller efficiency, which is assumed to be 0.85. This relating is seen in Equation 8.3.

(8.3)

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With the shaft horsepower required at cruise known, the shaft horsepower at sea level can be found using Equation 8.4, which compensates for the change in power produced by the engine with the change in density. This trend in power drop with altitude increase is plotted in Figure 8.1.

(8.4)

0 5000 10000 15000 20000 25000 30000 35000 40000 450000

1000

2000

3000

4000

5000

6000

7000

8000

Altitude (ft)

Pshp

reqd

SSL

(HP)

Figure 8.1: Trend of shp required at SSL as a function of altitude

The next power requirement comes from the rate of climb. This is found using Equation 8.5 which relates the rate of climb to the power available and the power required in regards to the weight of the aircraft.

(8.5)

From here the additional power required to climb at 1,000 feet per minute can be found by using Equation 8.6 And then can be used to find the installed power for the aircraft in Equation 8.7.

(8.6)

(8.7)

42

The above calculations in Equations 8.6 and 8.7 are summarized in Table 8.3.

Table 8.3: Summary of power requirementsPreqd 25,000 ft (HP) 883.66

Pshp reqd 25,000 ft (HP) 1039.60Pshp SSL (HP) 2769.21

Preqd climb (HP) 2065.35Pinstall (HP) 2769.21

With an installed power of about 2800 HP, an engine selection of 1400 HP is selected. Given the list of engines and their performance provided, the T58-GE-100 engine is selected, which is produced by General Electric. Its shaft horsepower is 1500 HP which is an ideal selection for the design of the aircraft. Figure 8.2 shows the T58-GE-100, and Table 8.4 shows the dimensions and specific fuel consumption of the engine.

Table 8.4: T58-GE-100SFC at Full Power [lb/(HP*hr)] 0.61

Max Env. Diameter (in) 20.9Max Env. Length (in) 55

Figure 8.2: T58 Engine and its internal components (Goebel)

The next design consideration is with an engine out condition. As discussed in class, these type of aircraft have complications when climbing with only one engine operable. With an engine out and the specific engine selected, 1500 HP remains. Using equation 2.5 and solving for the power required using a rate of climb of 250 FPM, a required horsepower of 1200 HP is found. Which is lower than the HP available, meaning the aircraft meets the minimum requirements for climbing while operating at engine out conditions. The results for this calculation can be seen in Table 8.5.

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Table 8.5: Calculations at engine out conditionsROC (FPM) 250

ηP 0.85Pavail (HP) 1500

Preqd climb (HP) 1202.9

With the power requirements calculated, and an appropriate engine selected, the final thing necessary is the placement on the wing. Given an average 8-foot diameter propeller and a one-foot clearance from the tip of the propeller to the fuselage, this places each engine 5 feet from the fuselage, or 7.625 feet from the center of the wing (given the fuselage diameter of 5.25 feet. The placement can be seen in Figure 8.3.

Figure 8.3: Engine Placement on Wing

8.2 PerformanceUsing the parameters shown in table 8.6 and the performance parameters of the T58-GE-100, a spreadsheet was created to determine the required shaft horsepower as well as the Rate of climb. These were calculated using the equations:

(8.8)

(8.9)

The full spreadsheets for the calculations at standard sea level, 25000 ft., and 31000 ft. can be seen in Appendix H. Figure 8.4 shows the effect that the altitude has on the required shaft horse power. It can be seen that, in general, a higher altitude will require more horsepower. Figure 8.5 shows that a higher cruise velocity will result in a lower rate of climb. This is due to having less excess horsepower to climb since more is needed to cruise at a higher velocity. Figure 8.6 is like figure 8.5 however, figure 8.6 shows the rate of climb with one engine out.

Table 8.6: Aircraft parametersW (lbs) 9520Sref (ft2) 226.67E 0.85AR 8ηprop 0.85

44

Figure 8.4: Required shaft horsepower vs. Cruise velocity at sea level and altitudes

50 100 150 200 250 300 350-1000

0100020003000400050006000700080009000

10000

SSL 25000 ft

Vcr (fps)

ROC

(fpm

)

Figure 8.5: Rate of Climb vs. cruise velocity at sea level and 25000 ft

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50 100 150 200 250 300 350-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

SSL 25000 ft

Vcr (fps)

ROC

(fpm

)

Figure 8.6: Single engine rate of climb vs. cruise velocity

8.3 RecommendationsIt is important to note that for engine selection, one not only consider the cruise performance at altitude but also for takeoff and landing at standard sea level conditions, were the most power is required, in terms of the shaft horsepower. After considering both the zero lift drag and induced drag of all components on the aircraft, it was determined that the proposed aircraft will require 1039.60 shaft horsepower at 25,000 feet. Using provided equations, this determination was extrapolated to an installed horsepower requirement of 2769.21 horsepower. Rounding up to a total of 2800 horsepower, the team then sifted through the list of available engines and found multiple viable options. Ultimately, the T58-GE-100 was selected which provides a shaft horsepower of 1500 horsepower. The extra available thrust allows for the aircraft to comfortably meet the single engine climb requirements demanded by Federal Aviation Regulations for this type of aircraft.

9 Takeoff and Landing PerformanceThe goal of this section is to determine the overall takeoff and landing distances. Each

section will go into detail the exact process to determine these values. With the full spreadsheets shown in the appendices. Along with the takeoff and landing performance, the overall zero lift drag coefficient is calculated with and without the landing gear.

9.1 CDo CalculationThroughout the iterative design process of the aircraft, a crucial parameter that was calculated at every instance was the zero lift drag coefficient. Now that the design for the wing, fuselage, and empennage sections are completed, the total zero lift drag can be found by taking a total summation of each sections zero lift drag coefficient. This is shown in equation 9.1.

(9.1)

46

In this equation, the zero lift drag coefficients are for the fuselage, three-dimensional wing, horizontal tail, vertical tail, and the nacelles respectively. Two zero lift drag tables were created, one for the takeoff configuration which includes an estimate of the contribution of the landing gear on the aircraft, table 9.1, and one for the zero lift drag seen during flight with the landing gear retracted, table 9.2. Each table includes the sections zero lift drag coefficient, total zero lift drag coefficient, and the percentage contribution of that section to the total drag.

Table 9.14: Take-off Zero Lift Drag CoefficientCDof 0.0051 10.71%

CDoW 0.0088 18.49%

CDoHT 0.0039 8.19%

CDoVT 0.0038 7.98%

CDoNac 0.0010 2.10%

CDoGear 0.0250 52.52%

CDo TO 0.0476 100.00%

Table 9.2: Flight Zero Lift Drag Coefficient

CDof

0.0051 22.57%

CDoW

0.0088 38.94%

CDoHT

0.0039 17.26%

CDoVT

0.0038 16.81%

CDoNac

0.0010 4.42%

CDo Flight

0.0226 100.00%

Looking at the above tables, it can be seen that the landing gear practically doubles the value of the zero lift drag. Disregarding the landing gear, the aircraft’s wing provides the highest contribution to the zero lift drag at approximately 39%, and the total zero lift drag coefficient in flight being .0226. This total CDo is about 24 counts less than the initial guess at the beginning of the design process.

47

9.2 Takeoff PerformanceOnce all of the parameters such as engine power calculations and wing and empennage sizing have been completed a takeoff performance analysis can be created by using a numerically integrated spreadsheet in which takes into account all of the design parameters decided upon previously. There are many calculations that will go into this numerically integrated “flight simulator” in order to determine takeoff performance parameters such as ground roll.

9.2.1 Thrust

When creating the numerically integrated spreadsheet it is necessary to start with calculating static thrust. Static thrust is calculated using equation 9.2.

(9.2)

This equation for static thrust includes the area of the disk of the propeller. In this specific aircraft design the diameter of the propeller is 8 feet, which makes the area of the propeller 50.25 ft2. This static thrust calculation is used until the dynamic thrust calculation using equation 9.3 equals the static thrust condition. Once this occurs the dynamic thrust equation is adopted throughout the rest of the performance calculation. The thrust calculations can then be broken into x and y components using equations 9.4 and 9.5.

(9.3)

(9.4)

(9.5)

However, before dynamic thrust can be calculated the velocity of the aircraft must be determined. This is done using equation 9.6 and equation 9.7 for velocity in the x and y directions. The resultant velocity is determined using equation 9.8

(9.6)

(9.7)

(9.8)

In order to calculate the velocity components however, the aircraft acceleration will also need to be calculated. The acceleration calculations for x and y components are displayed in equations 9.9 and 9.10

(9.9)48

(9.10)

For the acceleration equations the thrust in the x and y directions is known for the static case, however the lift, drag, and friction force is still needed in order to calculate the acceleration. The friction force can be found using equation 9.11, however the lift force is still missing from this equation and will be explained in detail in the preceding section.

(9.11)

In this specific design, the coefficient Kspoiler is one since there are no spoilers being deployed during takeoff. In equation 3.1.10 the coefficient of friction is estimated to be 0.04. This equation is the frictional force due to the wheels touching the runway surface.

9.2.2 Lift

To calculate the acceleration, velocity, and position of the aircraft the lift must first be determined. This is done by first calculating the resultant lift for the speed given. This is shown in equation 9.12. In Equation 9.12, q, dynamic pressure and the coefficient of lift, must also be calculated. This is done using Equations 9.13 and 9.14.

(9.12)

(9.13)

(9.14)

Since CLα is known for the coefficient of lift equation it is necessary to calculate the effective angle of attack of the aircraft. This is done by using Equation 9.15. Once this is found, it can be applied to Equation 9.14 to find the coefficient of lift at a specific angle of attack.

(9.15)

Now that the lift force can be calculated, the resultant force will need to be broken into x and y components to apply them to equations 9.6 and 9.7, the acceleration x and y components. In order to do this the flight path angle, γ, must be found. The flight path angle can be calculated using equation 9.16 and applied to equations 9.17 and 9.18 to break the lift force into x and y components.

(9.16)

49

(9.17)

(9.18)

9.2.3 Drag

The next variable that is needed within the acceleration calculation in equations 9.9 and 9.10 is the drag force. To calculate this, first the coefficient of drag of the aircraft must be found.

(9.19)

Equation 9.20 can be used to find the change in the coefficient of drag when the landing gear are extended.

(9.20)

Equation 9.21 is used to find the induced drag.

(9.21)

Once the drag coefficient is calculated, then equation 9.22 can be used to find the drag force and then this can be broken down into x and y components using equations 9.23 and 9.24

(9.22)

(9.23)

(9.24)

Now that all of the necessary values are needed in order to calculated acceleration and velocity, equations 9.25 and 9.26 can be used in order to calculate position in x and y in order to determine takeoff distance and height.

(9.25)

(9.26)

50

Table 9.3 shows the static thrust, takeoff weight, ground roll to achieve takeoff, and distance in order to clear the FAA defined 35ft tree at the end of the runway.

Table 9.3: List of important takeoff parametersWTO 9520

Tstatic (lbs) 7079.2

W/S 42.0

Sx to clear obstacle (ft) 1373.4

Sx ground roll (ft) 1026.1

Table 9.4 shows the thrust on the aircraft at three speeds during takeoff. The speeds are 0, 50 knots, and 1.2Vstall

Table 9.4: Thrust for Certain Speeds during takeoffVelocity (ft/s) Thurst (lbs)

0 6505.183.39 6505.1176.8 6505.1

Figure 9.1 shows the change of use of the static thrust calculation against the dynamic thrust calculations and the velocity at which the two equations intersect. This also displays the change in thrust as the velocity increases.

0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.00.0

1000.02000.03000.04000.05000.06000.07000.08000.0

Airspeed (fps)

Thru

st (lb

s)

Figure 9.6: Thrust versus airspeed

Figure 9.2 displays the flight profile in the x and y direction and the rotation point of the aircraft can clearly be shown. The orange dot shows where the aircraft reaches 50 feet in height.

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0.0 1000.0 2000.0 3000.0 4000.0 5000.0 6000.00.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

900.0

1000.0

X position (ft)

Y P

ositi

on (f

t)

Figure 9.7: Displays the flight profile of the aircraft

Figure 9.3 displays the angle of attack, pitch, and flight path angle versus time. In this plot, the effective angle of attack decreases once the aircraft has established a positive rate of climb and the flight path angle increases due to the pitch and climb rate of the aircraft.

52

0 10 20 30 40 50 600.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

Pitch AngleAngle of AttackFlight Path Angle

Time (sec)

Ang

le (d

eg)

Figure 9.8: Angle of attack, pitch, and flight path angle versus time.

In Figure 9.4, it shows the acceleration components of the aircraft. Noticeably the Y acceleration peaks at the rotation time. This is accurate considering the aircraft will be gaining acceleration in the Y direction during takeoff.

53

0 10 20 30 40 50 600.0

5.0

10.0

15.0

20.0

25.0

30.0

X AccelerationY Acceleration

Time (sec)

Acc

eler

atio

n (ft

/sec2

)

Figure 9.9: X and Y components of acceleration with respect to time.

Figure 9.5 displays the velocity of the aircraft during takeoff operations. The velocity can clearly be seen to level off during climb.

0 10 20 30 40 50 600.0

50.0100.0150.0200.0250.0300.0350.0400.0450.0500.0

Time (sec)

Vel

ocity

(ft/s

ec)

Figure 9.10. Velocity of aircraft during takeoff with respect to time.

54

9.3 Landing PerformanceIn calculating the landing performance of this aircraft, it was paramount to keep in mind that per the RFP, the aircraft must be able to land on a 2000-foot runway. Keeping this parameter in mind, one must move on to analyzing the four primary stages of the landing sequence: approach, flare, free roll, and braking.

Beginning the approach, Federal Aviation Regulation requires aircraft to clear a 50-foot tall obstacle upon approach. Also, note that the standard glide path angle is roughly three degrees. From geometric and trigonometric inspection, one may produce the following equation for the distance covered in approach,

sA=HTR−50

tan γ approach(9.27)

In order to deduce the value for HTR, one must first calculate the radius of the transition via,

RTR=(1.23 V s )

2

0.19 g(9.28)

And with this in hand, the following expression may be used,

HTR=RTR (1−cos γapproach ) (9.29)

For the next sequence, the flare, one may see the distance covered in this sequence as an angular velocity. Accounting for radial components the following expression takes form,

sflare=RTR sin γapproach (9.30)

Once slightly hovering over the landing strip, an aircraft enters the third phase of landing called the “freeroll.” This is the time interval after the flare has been finished and before contact with the ground surface. This phase typically lasts 3 seconds and the distance covered may be calculated using,

sFR=3 V TD (9.32)

Entering the fourth and final phase, the breaking phase, one must numerically integrate basic equations of motion to find the total distance. Firstly, if one sets the datum at the point of contact in this phase, the initial position may then be left as zero feet. This also means that V final is equal to zero and Vinitial is equal to VTD. Now, one must collect the necessary terms in order to properly integrate the terms.

At the point of contact, the wing is still producing lift, the engines are no longer producing thrust, the aircraft still experiences a significant drag force, and there is also a new friction force introduced. For the drag, one must account for the lift induced drag as well as the zero lift drag of the aircraft and additional zero lift drag due to the flaps and the extended landing gear.

The zero lift drag of the aircraft has previously been estimated in prior reports, and the additional zero lift drag due to the flaps is dependent on the type of flaps chosen. This aircraft will use fifty degree deflecting fowler flaps, and the value given in Table 8.3 in Corke, page 164, is given as

55

0.0830 for the flaps. Referring to similar aircraft in the initial report, an estimated projected area for the landing gear was found and used to estimate the additional zero lift drag due to the landing gear. The equation used is as follows,

∆ CD 0LG=f LG

ALG

S(9.33)

When the total drag coefficient is determined, one may use the touchdown velocity and dynamic pressure to find the drag at the datum. The lift generated by the wing is proportional to the glide angle and touchdown speed, and the frictional force may be found as a result of finding the lift,

F f=μ (W ¿−LG ) (9.34)

Table 9.5: Additional ParametersμL Dry 0.6μL Wet 0.4CDo fl aps 0.0830CDo LG 0.0215

Table 9.5 shows the relevant terms discussed above.

Progressing onward to the equations of motion,

ax=∑ Forces

Mass(9.35)

sx=(V x 1

2−V x02 )

2ax

(9.36)

Note, since the engines provide no reverse thrust, the forces in the x-direction are only frictional, lift induced, and drag. Since we have already collected these terms for the first station, the datum, and all of these terms are zero at the second station, one may simplify the integration to the above equations.

Table 9.6: Landing DistanceSbraking (ft) 965.620Sapproach (ft) 827.103Sfl are (ft) 254.081SFR (ft) 483.398SL tota l (ft) 2530.203

Table 9.6 shows the calculated numerical values for the design aircraft with respect to each of the four phases of landing, and total distance covered.

56

9.4 RecommendationsThe total landing distance is under the required design takeoff distance by approximately six hundred feet. As of now, the aircraft has enough extra takeoff distance and does not currently use flaps during the takeoff. This means that the aircraft can be adjusted if needed and still easily be within the design parameters. This will be useful for the adjustment of the landing distance.

Currently the total landing distance is approximately four hundred feet above the landing distance required as shown in the RPF. This will need to be corrected for to reduce the overall landing distance. This can be done by either changing the trailing edge flaps to reduce the stall velocity. Resulting in a lower touchdown speed, thus reducing the distance needed to brake to a full stop. The other option would be to add a leading-edge device to the wing. This would have a similar effect on the stall speed, resulting in a reduction in the total landing distance.

Overall the aircraft design is proceeding well. All current parameters are within the nominal values. The only current parameter that needs to be adjust is the total landing distance. This will be corrected for as described earlier.

10 Enhanced Lift Devices

This section will serve to document the enhanced lift devices this conceptual aircraft may entail, with the primary goal to determine the leading edge and trailing edge flap design. The discussion section will delve fully into the exact process to determine the design of the flaps. All spreadsheets and complimentary documents will be shown in the appendices.

10.1 Types of Flaps

There are two categories of flaps that will be discussed in this section: they are trailing edge flaps and leading edge devices (LEDs). The trailing edge flaps are broken down into four types the plain flap, split flap, slotted flaps, and fowler flap. The first type, the plain flap, is simply the deflection of the trailing edge of the airfoil section, and is shown in figure 2.1.1. This is the most commonly used trailing edge flap on smaller aircraft.

Figure 10.11: Simple visualization of plain flap

The second type is known as the split flap. The split flap is very similar in design to the plain flap, only that on the split flap only the bottom of the airfoil section is deflected. This is illustrated in Figure 10.2. The lift enhanced lift produced by the split flap is essentially the same as a plain flap, but the drag is known to be larger. Due to this they were a popular addition to aircraft during World War II, but are not used as much in today’s industry.

57

Figure 10.2: Simple visualization of the split flap

The third type, the slotted flap, is again a redesign of the plain flap system, and is pictured in Figure 10.3. It includes the addition of a slot at the hinge point to allow for high-pressure air from the lower surface of the airfoil to pass to the upper surface of the flap. This is advantageous due to the boundary layer being able to have added momentum which will allow larger flap deflections before flow separation occurs. In addition, it can also be improved upon by adding more slots which would result in the creation of a double or triple slotted flap. These types of modifications lead to a higher lift coefficient, but can be detrimental to the time frame as they require a complicated construction process.

Figure 10.12: Simple visualization of the slotted flap

The final style flaps is known as the fowler flap. The fowler flap is a modified version of the slotted flap and is shown in Figure 10.4. This means that it includes the same slot and hinge system as the slotted flap, but is capable of translation reward of the airfoil section. This is an advantage because it can effectively increase the wing area of the aircraft.

Figure 10.13: Simple visualization of the fowler flap

The main advantage of these flap systems is that they are capable of increasing the lift coefficient for the aircraft by a sizeable percentage. This would be helpful during the takeoff and landing phases of flight in order to take off in a shorter distance and reduce the amount of distance needed when coming onto the runway for landing. It cannot go without mentioning that the flaps are not only advantageous, but like most things in the real world have disadvantages as well. While the system does increase the lift for a given angle of attack, it does not increase the angle

58

at which the aircraft will stall. It actually does the exact opposite and causes the stall angle to decrease. The results in changes in the location of the stagnation line and pressure gradient at the leading edge surface. This problem was ultimately solved by the creation of the aforementioned LEDs at the beginning of this section.

There are three types of LEDs that will be discussed in this section. They are the leading edge flap, the leading edge Krueger flap, and the leading edge slat. Basically what these devices do is they increase the radius of the leading edge to account for the changes done by the tailing edge flaps.

The first type, the leading edge flap, is essentially the same system and design of the tailing edge flap, but applied to the leading edge. The front of the leading edge would become capable of deflecting downwards. This type of configuration isn’t used all that often for general aviation aircraft, but is utilized in jet application such as on the F-18 due to the high sweep of the wing. Pictured in Figure 10.5 is an example of a leading edge flap.

Figure 10.14: Simple visualization of the leading edge flap

The second type is the Krueger flap. The Kruger flap utilizes and actuator system to deploy only a small surface on the bottom of the leading edge, keeping the main curvature of the leading edge the same, but increasing the camber of the airfoil section which will in turn increase the lift. This is illustrated below in Figure 10.6.

Figure 10.15: Simple visualization of the Kruger flap

The last type of LED, the slotted leading edge flap or slat, is essentially the slotted tailing edge applied to the leading edge, pictured in Figure 10.7. It allows a part of the leading edge to be translated out and the deflected which increases the effective wing area and camber of the airfoil section. From a theoretical stand point it utilizes the same idea of adding momentum to the boundary layer which was described in the slotted flap section earlier. These changes also cause a small change in the angle of attack for zero lift of the aircraft.

59

Figure 10.16: Simple visualization of the flat

A downside to the LEDs is they can require the plane to have more construction than was originally though upon. If a budget had been set, and this was not accounted for it could jeopardize the entire build. Another reason this is bad is it could push the structure factor up to a higher value which would change the entire design of the aircraft, so it is crucial to keep these things in mind when the choice of which LEDs will be used, if any.

10.2 Leading and Trailing Edge Flap Design

In the selection process of which types of trailing-edge flaps and leading edge devices, three main points were considered. The first came from comparative aircraft. Most turboprop aircraft utilize plane flaps, and this was one of the driving forces into the selection of plane flaps. The second reason is due to is due to its simplicity, both in design and mathematical computations associated with plane flaps. And the last reason is due to the amount of enhanced lift that’s actually necessary in the overall design of the aircraft. Last report contained calculations towards any necessary additional lift outside of the basic aerodynamics of the aircraft. It was found that there wasn’t a large necessity for enhanced lift, leading to the selection of plane flaps.

The first step in finding the change in the overall lift coefficient, is finding the change due to the trailing-edge flaps. The first step in doing so, involves determining whether the aspect ratio for the main wing is considered high or low. This is determined by Equation 10.1, where C 1 is a constant extracted from Figure 9.8 from Corke which related the constant value to the wings taper ratio.

AR> 4(C1+1 )cos (γ ¿)

(10.1)

If the given relation in Equation 10.1 is proven true, then the wings aspect ratio is considered to be high. The designed aspect ratio is high, which leads to the computation of maximum 3D lift coefficient using Equation 10.2 where the ratio between the maximum 3D and 2d lift coefficient is found using Figure 9.9 from Corke.

CLmax=[ CLmax

C lmax]C lmax

(10.2)

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Table 10.1 summarizes these two calculations and their required values from previous design work.

Table 10.1. 3D lift coefficient design

λ 0.35C1 0.48AR 8.00

Comparative Value 2.703ΛLE 0

CLmax/Clmax 0.9Clmax 1.52CLmax 1.368

Next, the stall angle is found using Equation 10.3 where the last term, change in alpha as a function of maximum lift coefficient, is found using Figure 9.11 in Corke.

α s=CLmax

CLα

+α 0L+∆ αC Lmax

(10.3)

The only missing piece is the leading-edge sharpness value,∆ y , which was found using Figure 9.10 in Corke. The above calculation is summarized in Table 10.2.

Table 10.2. Leading edge sharpness calculations

Δy/c (%) 8.5Δy 0.487Δ⍺CLmax 1.8⍺s (deg) 16.13

The next step is finding the stall angle while the flaps are deployed 40 degrees, which is the designed flap deflection. Equation 10.4 simply adds the change in stall angle, which is found from Figure 9.18 in Corke, to the “un-flapped” stall angle in order to find the “flapped” stall angle can be found, this calculation is summarized in Table 10.3.

α sflapped=αsbasic

+∆ α s (10.4)

Table 10.3. Stall angles of attack

δflap (deg) 40Δ⍺s (deg) -2.8

(⍺s) flapped (deg) 13.33

61

In order to find how the flap deflection effects the 2D lift coefficient, a few parameters are necessary; the mean aerodynamic chord, the designed flap chord length, and the percent thickness of the airfoil. Using these values are used in Figure 9.4 in Corke to find the rate of change in the 2D lift coefficient in regards to the flap deflection angle can be found; which will then be multiplied with the designed flap deflection angle to find the newly “flapped” 2D lift coefficient. These values are summarized in Table 10.4.

Table 10.4. Flap deflection angle calculations

mac (ft) 5.73cf (ft) 2cf/c 0.436t/c 12%dCl / dδf (rad)-1 5.35(Clmax)flapped 3.74

Then using Equation 10.5, the change in 2D lift coefficient can be calculated.

∆ C lmax=(C lmax )flapped−(C lmax )basic (10.5)

The final calculation for finding the change in the 3D lift coefficient is set by Equation 10.6, where K is defined in Equation 10.7.

∆ CLmax=∆C lmax

SWF

SWK∆

(10.6)

K∆=[1−0.08 cos2 ( Λc /4 ) ]cos3 /4 ( Λ c/4 ) (10.7)

The above calculations are summarized in Table 10.5

Table 10.5. Change in 3D lift coefficient

ΔClmax 2.22bf (ft) 8SWF 110.97SW 226.67KΔ 0.919ΔCLmax 0.997

The leading-edge devices are much simpler in the calculations. There is only one equation, Equation 10.8, which is fairly similar to the above equation for the trailing-edge flaps.

∆ CLmax=∆C lmax

SWF

SWcos ( Λ¿ )

(10.8)

Where the change in the 2D lift coefficient is a given value with a selected type of leading-edge device, which was selected as a fixed slot leading-edge device. Which leads to the total change in the overall lift coefficient of the aircraft which is a summation of the two values from the leading

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edge and trailing edge. These final calculations towards the change in lift coefficient are summarized in Table 10.6.

Table 10.6. Final lift coefficient changesΔClmax 0.2ΔCLmax 0.0979ΔCLmax 1.095

The increase in the drag coefficient, ΔCD0, is calculated at three different trailing edge flap deflection angles. The angles include a takeoff deflection of ten degrees, and two landing deflection angles of forty and fifty degrees. ΔCD0 is calculated using Equation 10.9:

(10.9)

K1 and K2 are found based off figures provided by Corke. These values can be seen in table 2.2.8. Swf/Sw is the ratio of planform area of the wing with the same span as the flap to the total planform area of the wing. With a flap span of 8ft positioned at the root of the wing, as shown in Figures 10.1-10.3, this ratio becomes 0.4896. Table 10.9 shows K1, K2 and the calculated ΔCD0.

Figure 10.1. Isometric view of the wing with the flaps deployed

Figure 10.2. Placement of flaps on wing

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Figure 10.3. Front view of the flaps deployed

Table 10.7: Calculated ΔCD0 at different flap deflection angles

δf 10o 40o 50o

K1 2 2 2k2 0.0125 0.0875 0.12ΔCD0 0.01223919 0.08567431 0.11749619

The change in the stall angle, Δαs, are determined based off figures provided by Corke. The Δαs

for each angle and the respective stall angles are shown in Table 10.7. The stall angles are calculated by adding the Δαs angle to the stall angle with flaps not deflected. The effect this, and the previously calculated ΔCLmax, has on the lift coefficient with respect to the angle of attack can be seen in Figure 10.4.

Table 10.4: Δαs and calculated αs at different deflection angles

δf 10o 40o 50o

Δαs -0.4o -2.82o -4.27o

αs 15.73o 13.31o 11.86o

-20 -16 -12 -8 -4 0 4 8 12 16 20

-0.5

0

0.5

1

1.5

2

2.5

No Flaps Flaps at 40 degrees

Angle of attack

CL

Figure 10.4: CL vs α with and without flaps

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10.3 Recommendations

All variables considered, the team decided upon the selection of plain flaps as the trailing edge flap design and slotted leading edge flaps, commonly known as flaps. Due to the previously determined landing distance, and noting that the aircraft satisfactorily meets the requirements per the RFP, the team felt simplicity was key. Since both leading edge and trailing edge devices increase the structural load the wing is exposed to minimizing the deadweight becomes key. The chosen arrangements are also much simpler to handle mathematically and mechanically.

11 Structural DesignThis section will serve to document the structural analysis of the wing and fuselage sections

of the aircraft. After the maximum moment for the fuselage is determined the skin thickness and material will be determined. The conclusions section will delve further into the structural analysis results. All spreadsheets and complimentary documents will be shown in the appendices.

11.1 Refined Wing AnalysisThe weight of each component of the aircraft are based off historical weights of the major components. The components to be calculated are the main wing, horizontal tail, vertical tail, installed engine, landing gear, and fuselage. These values are calculated using a multiplier times a factor for each component. These values are provided by Corke and can be seen in Table 11.1. These values provide a very accurate approximation the weight of each component on the aircraft.

Table 11.1: Weights of components of aircraft as multiple of the factorComponent Multiplier FactorMain Wing 2.5 Sw

Horizontal Tail 2.0 Sw

Vertical Tail 2.0 Sw

Installed Engine 1.4 Uninstalled Wengine

Landing Gear 0.057 Wto

Fuselage 1.4 Swet-fuse

When calculating the weight for the landing gear, the nose gear and main landing gear were calculated separately. The nose gear was estimated to be 60 pounds and the main landing gear was the remaining weight from the landing gear weight calculation. Table 11.2 shows the weights of each component as well as the payload, fuel, and “other”. Other is defined as all other minor components needed for the aircraft. These include things like avionics, navigation equipment, hydraulic equipment, and other small components. These were estimated to be evenly distributed throughout the entire aircraft.

Table 11.2: Component weightsComponent Weight

Fuselage 1855.50Wing 924.54

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Main Landing Gear 482.64Nose Landing Gear 60.00Engines 700.00other 1904.00Fuel Wing 2398.23Payload 1600.00Horizontal tail 509.0866Vertical tail 265.6097

The center of gravity for the entire aircraft is calculated using the standard one dimensional equation:

X cg=∑ Xn M n

∑M n

(11.1)

Each component is modeled as an evenly distributed load along the length of each component. With this assumption, the center of gravity for each component is easily determined. These values can be seen in Table 11.3 shown as the average percentage along the fuselage length. Also shown in Table 11.3 are the beginning and end locations of each component of the aircraft along with the overall calculated aircraft center of gravity. These as well are shown as a percentage of the fuselage length. The overall center of gravity is shown as the length back from the fuselage tip in feet.

Table 11.3: Component weight location and center of gravity

Load Type x/L Start x/L end x/L avgFuselage 0% 100% 0.5Wing 30% 55% 0.425Main LG 45% 45% 0.45Nose LG 5% 5% 0.05Engines 30% 45% 0.375other 0% 100% 0.5Fuel Fuselage 0% 100% 0.5Fuel Wing 35% 55% 0.45Payload 10% 60% 0.35H tail 80% 100% 0.9V tail 80% 100% 0.9Tail Lift 90% 90% 0.9

Xcg: 12.46 ft

Overall, the aircraft is stable with respect to the location of the center of gravity. With the location of the aerodynamic center of the wing located 13.5ft back from the nose of the aircraft, the aerodynamic center is behind the center of gravity and generates a static margin of 18%. This is well within the recommended static margin for stability.

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11.2 Wing Load AnalysisThe first step in calculating the shear and moment diagram is to find the load distribution across the wing. This load distribution has contributions from the lift generated by the wing, the landing gear, the engines, the structural weight of the wing, and the fuel that is stored within the wings. All of which are “negative” forces except that of the lifting force. The landing gear and the engines are treated as point loads, whereas the lift, fuel, and structural weights are distributed loads.

To find the lift distribution across the wing, Shrenck’s approximation is used, which averages an elliptical lift distribution with a trapezoidal lift distribution which is fairly accurate in real world modeling. The lift distribution for an elliptical wing is given by Equation 11.2, where the trapezoidal lift distribution is shown in Equation 11.3.

LE ( y )=4π

Lb √1−( y

b2 )

2

(11.2)

LT ( y )= 2(1+λ )

Lb [1−( y

b2 ) (1−λ )] (11.3)

In the above equations, L symbolizes the total load produced by the main wing and y is the half-span location where y = 0 signifies the root of the wing.

The total lift from the wing is found by first finding the lift, which is downforce, produced by the horizontal tail. This is found by Equation 11.4.

LT=W ¿

(xCG−xacw )(xacT

− xacw)

(11.4)

Then summing all the forces in the z-direction, the lift produced by the wing can be found through Equation 11.5.

LW=W ¿−LT (11.5)

The results from the combination of Equations 11.4 and 11.5 are shown in Table 11.4.

Table 11.4: Calculation of liftLT (lb) -1340LW (lb) 10860

With each contribution to the lift from the wing and the horizontal tail, both the elliptical and trapezoidal lift distributions can then be found and then averaged to provide a value for the lift. It is important to note that in the calculation for the lift and all the other distributed loads, the wing

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is broken into 21 sections to provide a rough integration of the loads over the wing. To increase the accuracy of the computations, the section count can be increased.

After the lift distribution is found, the next step is finding the structural distribution across the wing. This is found by Equation 11.6.

W structure ( y )=[2 W structure

(1+λ) ] [1− yb2

(1−λ)] (11.6)

The last distributed load across the wing is the fuels contribution. The fuel will be stored in between the main and rear spar in each wing. By using the chord length at each increment of the wing, after being discretized, the area between each of the spars can be found by estimating the area to be a rectangle. This is a two-dimensional calculation while looking at the “rib.” To make said area a volume, the subsequent ribs area between the main and rear spar will also be found, and then averaged to find an area that equally represents the two. By multiplying the average area between the two “ribs” by the distance between the segments, it provides a volume in which the fuel will be stored. Following this sequence of calculations up to the point between the eighth and ninth segment provides a volume of 20.27 ft3 which is just shy of the required volume of 22.86 ft3 per wing. To make up the remaining fuel storage, a bladder tank will be placed within the fuselage.

The engines weight, as well as the landing gear, are placed 7.98 feet from the root of the wing. As discussed this weight is treated as a point load within the spread sheet that calculates the total load distribution across the wing. After averaging the elliptical and trapezoidal lift, subtracting the fuel and structural load, and the two point loads from the engine and the landing gear; the following load distribution is found across the wing, Figure 11.1.

0 5 10 15 20 250

2

4

6

8

10

12

y (ft)

Load

(lb)

Figure 11.1: Total Wing Loading over the half-span

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It can easily be seen where the engines and landing gear are placed, y = 3.5 ft. It can also be seen where the fuel is placed, which is from the root to about 3 feet from the root. This is why the loading is slightly lower than that seen after the engine and landing gear. The entire spread sheet, which calculated the loads as well as the fuel volume can be seen in the Appendix.

After the total loading for the wing is found, the shear and moment values for each section can then be found. The shear diagram is simply the summation of the loads starting from the tip of the wing and working inwards. The moments at each segment can be found by multiplying each force in each segment by the distance to the segment being considered. Both the shear and moment values are then plotted to produce the shear and moment diagrams seen in Figures 11.2 and 11.3.

0 5 10 15 20 250.000

500.000

1000.000

1500.000

2000.000

2500.000

3000.000

3500.000

4000.000

y (ft)

Shea

r (lb

)

Figure 11.2: Shear Diagram for half-span

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0 5 10 15 20 250.000

5000.000

10000.000

15000.000

20000.000

25000.000

30000.000

35000.000

40000.000

y (ft)

Mom

ent(ft

-lb)

Figure 11.3: Moment Diagram for half-span

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11.3 Fuselage Load AnalysisWhen beginning the analysis of the fuselage structure, one must make sure to account for all weight sources and approximate them as point loads or distributed loads accordingly. These weights were determined analytically in a previous section. For this analysis the loads from the fuselage, wing structure, engines, extraneous entities, fuel, and payload were treated as distributed loads. The lift of the wing, lift of the tail, and weight of the landing gear were all treated as point loads at an interim point extrapolated from the 5% increments they fell between or near. In this analysis also, upward forces are treated as negative while downward forces have a positive sign convention.

Table 11.5: Component weights in (lbs)Component Weight (lbs)Fuselage 1855.50Payload 1600.00Wing 924.54Fuel 2398.23Tail 774.6963416main 482.64nose gear 60.00Engine 700.00Wing Lift Load 10860Tail Lift Load -1340Other 1428.00

Table 11.5 above shows the weights of each component.

In order to approximate the weight distribution of each component, the total weight of that respective component was spread across a predetermined number of stations in equal increments. The number of stations was determined form component placement,

Table 11.6: Starting and ending location for the weight of each componentLoad Type Load x/L Start x/L end x/L avgFuselage 1855.50 0% 100% 0.5Wing 924.54 30% 55% 0.425Main LG 482.64 45% 45% 0.45Nose LG 60.00 5% 5% 0.05Engines 700.00 30% 45% 0.375other 1428.00 0% 100% 0.5Fuel Fuselage 0.00 0% 100% 0.5Fuel Wing 2398.23 35% 55% 0.45Payload 1600.00 10% 60% 0.35

H tail 509.0866 80% 100% 0.9

V tail 265.6097 80% 100% 0.9

Tail Lift -1339.94 90% 90% 0.9

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The length of the fuselage was broken down into 20 increments in Table 11.6, each representing 5% of the total length of the aircraft, and loads were distributed accordingly. By summing the loads at each station one may easily produce the shear at a desired station. To find the moment at each station, one must add the moment of the previous station to the average of the shear at the desired station and the shear at the previous station, multiplied by 1.5 feet since this is representative of 5% of the fuselage length. However in the case of the point loads, a slight modification must be made to the moment calculation at the station immediately following the point load. The moment is found by adding the moment from the prior station to the average distance between the load location and following station multiplied by the load at that point.

Incorporating these approximations leads to a table as shown below which may also be viewed in the appendix,

Table 11.7: Excel sheet used to find the maximum shear and moment of the fuselagex/L x (ft) Wfuse (lbs) Wwing (lbs) Wlanding gear (lbs) Wengines (lbs) Wmisc (lbs) Wfuel (lbs) Wpayload (lbs) Wtail (lbs) L wing (lbs) L tail (lbs) Load (lbs) V (lbs) M (lb-ft)

0.000 0 0 0 0 0 0 0 0 0 0 0 0 0 00.0499 1.497 60 60 60 0

0.050 1.5 92.775 71.400 164.175 224.175 0.4260.100 3 92.775 71.400 164.175 388.350 459.8200.150 4.5 92.775 71.400 164.175 552.525 1165.4770.200 6 92.775 71.400 164.175 716.701 2117.3970.250 7.5 92.775 71.400 160.000 324.175 1040.876 3435.5790.300 9 92.775 154.090 233.333 71.400 160.000 711.599 1752.475 5530.5920.350 10.5 92.775 154.090 233.333 71.400 479.645 160.000 1191.244 2943.719 9052.7370.400 12 92.775 154.090 233.333 71.400 479.645 160.000 1191.244 4134.963 14361.748

0.4499 13.497 -10859.937 -10859.937 -6724.974 19670.7590.450 13.5 92.775 154.090 71.400 479.645 160.000 957.911 -5767.064 19654.4690.499 14.97 482.640 482.640 -5284.424 19560.7790.500 15 92.775 154.090 71.400 479.645 160.000 957.911 -4326.513 19488.6970.550 16.5 92.775 154.090 71.400 479.645 160.000 957.911 -3368.602 13717.3610.600 18 92.775 71.400 160.000 324.175 -3044.427 8907.5890.650 19.5 92.775 71.400 160.000 324.175 -2720.252 4584.0800.700 21 92.775 71.400 160.000 324.175 -2396.077 746.834

0.7257 21.7699998 1339.937 1339.937 -1056.139 -1811.3300.750 22.5 92.775 71.400 160.000 324.175 -731.964 -1322.2530.800 24 92.775 71.400 193.674 357.849 -374.115 -2151.8120.850 25.5 92.775 71.400 193.674 357.849 -16.266 -2444.5980.900 27 92.775 71.400 193.674 357.849 341.584 -2200.6090.950 28.5 92.775 71.400 193.674 357.849 699.433 -1419.8471.000 30 92.775 71.400 164.175 863.608 -247.567

As seen above in Table 11.7, the aircraft is has an excess of shear at the end of the fuselage. Further modifications will need to be made, and reduction of the weight of several components will need to be implemented. The moment however is small in comparison to the moments seen across the length of the fuselage. The aircraft will have a slight tendency to pitch down in its current state.

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Figure 11.4: Load distribution span wise across the fuselage

Figure 11.5: Shear distribution span wise across the fuselage

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Figure 11.6: Moment distribution span wise across the fuselage

Figures 11.4-11.6 are the produced plots for the aircraft in its current design status.

11.4 Fuselage DesignAfter the moment diagram for the fuselage was constructed, the design of the skin of the fuselage could be carried out. It is necessary to pick a thickness that would be suitable to withstand the maximum stresses that the aircraft could experience. Due to this, the maximum load factor was selected at a value of 5.8 and the maximum moment taken from the data was found to be 19670 foot pounds. With these values known, a material for the aircraft had to be selected. It was decided that due to its common use in aircraft that 2024-T3 Aluminum Alloy would be used for the skin of the fuselage. The minimum skin thickness was calculated using Equation 11.7 below.

(11.7)

Using the ultimate tensile strength for 2024-T3 found in Design of Aircraft, and with R being half of the largest distance in the fuselage, this yielded a skin thickness of approximately 0.0151 inches.

11.5 RecommendationsAll structural analyses considered, the team could predict the span-wise loading, shear, and moment on the wing, and the load, shear, and moment that the fuselage would experience in flight, through usage of a refined weight analysis. These calculations also allowed the design to pinpoint the center of gravity for the entire aircraft. It is important that care was taken in these calculations as they dictate the maximum loads that the aircraft will experience in flight. Taking into consideration these maximum loads and moments, the selection of 2024-T3 Aluminum

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Alloy was selected to be used for the fuselage due to its strength properties and common usage on similar aircraft of that type. 12 Stability and Control

Within this section, the longitudinal and lateral aircraft dynamics are calculated, plotted, and evaluated. Upon evaluations the aircraft must be open loop stable to provide a comfortable, and enjoyable aircraft to fly and be a passenger on.

12.1 Longitudinal StabilityIn the determination of the longitudinal stability of the aircraft various previously calculated parameters are needed. Table 12.1 displays the parameters that will be needed in the longitudinal stability. Along with these previously calculated variables, the downwash dε/dα must be found. This is determined via Figure 11.3 in Corke. In using this figure, taper ratio, the distance from the wing to the tail aerodynamic centers divided by the half-span of the aircraft, r, and finally the height of the horizontal tail divided by the half-span of the aircraft, m.

Table 12.1: Aircraft parameters.AR 8.0b (ft) 42.6

λ 0.4

iwing 1.4

SHT (ft2) 126.1

Sref (ft2) 226.7

mac (ft) 5.7

Vht 0.9

lht (ft) 9.3

Vstall (knots) 82.67

r 0.44H 2.00m 0.09dε/dα 0.45

Once these parameters are determined, the span-wise positions of the horizontal tail, main wing, and center of gravity must be found from previous calculations. These are displayed in Table 12.2, along with the non-dimensional span-wise positions described by Equation 12.1 with n being the position being described, and being the mean aerodynamic chord of the wing.

(12.1)

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Table 12.2: Span-wise positionsXcg (ft) 13.5

Xacwing(ft) 13.5

XacHT (ft) 22.8

Xbarcg 2.36

Xbaracwing 2.35

XbarHT 3.97

Figure 12.1: Visualization of the aerodynamic center and the center of gravity.

After all of the previously calculated parameters are tabulated, the stability analysis of the longitudinal aircraft dynamics can be performed.

First, the calculations that do not depend on angle of attack, such as the slope of the coefficient of lift and moment coefficient for the aircraft, are calculated and placed in a table. Equations 12.2-12.5 calculate these variables.

(12.2)

(12.3)

(12.4)

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(12.5)

Recall that static margin, S.M., must be positive in order to have longitudinal stability. Table 12.3 displays the calculated variables using the previously mentioned equations. Shown below, S.M., is indeed positive so longitudinal stability is achieved.

Table 12.3: Stability calculationsCLα_wing 0.086

CLα_HT 0.066

dCLair/dα 0.0654

dCM/dα -0.0326

xbarnp 16.94266192

S.M. 14.59

Now, varying angle of attack, the lift coefficient for the aircraft, and well as the moment coefficient of the aircraft can be determined for specific angles of attack. These are then used to determine the tail angle of incidence, iht, and the velocity of the aircraft. Equations 12.6-12.10 are used to determine the previously mentioned calculations.

(12.6)

(12.7)

(12.8)

(12.9)

(12.10)

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Figures 12.2 and 12.3 show the varying angle of attack versus the change in the moment coefficient of the aircraft. As seen, the slope of the moment curve is negative, this is characteristic of a longitudinally stable aircraft.

Figure 12.2: Decrease of moment coefficient with increase of angle of attack at iht=0°

Figure 12.3: Decrease of moment coefficient with increase of angle of attack at iht=5°

Analyzing these two plots, it is clear that with increase of horizontal tail incidence, the angle of attack at which the moment coefficient becomes zero increases.

Figure 12.4 displays the lift coefficient as it changes with respect to horizontal tail incidence.

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0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600 1.800 2.0000.000

5.000

10.000

15.000

20.000

25.000

30.000

CL

iht

Figure 12.4: Lift coefficient versus horizontal tail incidence.

As shown, with increasing lift coefficient, the incidence angle of the horizontal tail must also increase in order to produce the lift coefficient need for the aircraft to maintain level flight.

Figure 12.5 depicts the relation between aircraft velocity and horizontal tail incidence. As seen in the figure, as the aircraft increases to its designated cruise velocity, the tail incidence angle can be decreased. Once the aircraft starts to slow to its stall speed, the pilot must increase the tail incidence angle in order to hold steady level flight.

Figure 12.5: Relationship between velocity and tail incidence angle.

The excel table used to create Figures 12.2-12.5 can be seen in Appendix O.

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12.2 Lateral StabilityThe lateral motion of the aircraft is defined as the rolling motion about the fuselage longitudinal axis. The aircraft can witness a wind come in that is off the centerline of the aircraft. This wing would be known as a sideslip and the resulting angle that the wind comes in is the sideslip angle, β. The notation for the lateral stability is defined using the symbol C lβ. For ta aircraft, the right wing tip should rotate up to counter a positive side slip angle which would in turn cause C lβ to be less than zero. The total lateral stability of the aircraft is generally cut into section based on the wing section, vertical stabilizer, and wing-fuselage combination, shown in Equation 12.11.

(12.11)

Even further so, the contribution by the main wing is divided into three more subsections based on the wing position, sweep angle of the wing, and the dihedral of the wing. This is presented in Equation 12.12.

(12.12)

Taking each of these subdivisions into consideration, an estimate of the lateral stability of the aircraft can be determined via means of this equation. The wing mounting position to the fuselage has an effect with a high wing being good towards the lateral stability, a mid-wing having a neutral effect to the lateral stability, and a low wing being the less advantageous of the two. The lateral stability is also effected by the sweep angle of the wing as well. In the presence of a sideslip angle, the incoming velocity would be higher on one wing than the other causing a moment around the center of gravity of the aircraft. Lastly, the dihedral angle of the wing can have an effect of the lateral stability, with a positive dihedral angle increasing the lateral stability. In terms of the design aircraft, the dihedral of the wing will counteract the low wing positioning causing the lateral stability to be stable while in flight.

Seeing as how the lateral stability for an aircraft is a difficult parameter to calculate, it is usually taken as an approximation that the lateral stability is equal to the opposite of the directional stability. This is shown in Equation 12.13 and as thus, the lateral stability and directional values will be presented after the directional section.

(12.13)

12.3 Directional StabilityThe directional motion of an aircraft is a rotation about its vertical axis. Here, the directional moment about the center of gravity is defined as positive in a clockwise direction. A sideslip angle will cause the aircraft to what to yaw in a certain direction which is then counteracted by the lateral lift producing a moment around the center of gravity of the aircraft. The directional stability is denoted by the symbol Cnβ and is divided into three subsections as well shown in Equation 12.14

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(12.14)

The F, W, and VS in the above equation represent the fuselage, wing, and vertical stabilizer, respectively. In the terms of the directional stability, the aircraft should rotate in such a manner that the sideslip angle is reduced making Cnβ a positive value.

For the vertical stabilizer contribution, Equation 12.15 shows the calculation for this parameter.

(12.15)

Where is the vertical tail volume coefficient presented in Equation 12.16.

(12.16)

is the three dimensional lift curve slope for the vertical tail, and the quantity is the influence of the wing and fuselage on the vertical tail, and is shown in Equation 12.17.

(12.17)

The value for the wing’s contribution to the directional stability can be expressed in Equation 12.18.

(12.18)

The effect due to the fuselage was calculated using Equation 12.19.

(12.19)

Where the volume of the fuselage, (VOL)F was found using a solidworks model.

Using the above equations, the effect to directional stability could be calculated and in turn the l. These values are shown below in Table 12.4.

Table 12.4: Lateral and Direction StabilityCn VTβ 0.140763Cn Wβ 0.000672Cnβ F -0.05600

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According to Design of Aircraft, both of these values fall in the range to make the aircraft be stable.

12.4 Rudder SizingThe Rudder sizing is determined off two worst case scenarios. The first is considered the single engine condition, and the second is considering a cross wind with a sideslip of 11.5 degrees during takeoff and landing. Both of these cases assume that the rudder is capable of a maximum defection of 20 degrees.

First considering the engine out scenario in equilibrium, the value can be determined using Equation 12.20.

(12.20)

The secondary scenario considered is the cross-wind scenario where sideslip angle is considered to be 11.5 degrees. Equation 12.21 shows the equilibrium state for the cross wing section.

(12.21)

Using this value, the change in zero lift angle due to the rudder deflection can be calculated using Equation 12.22.

(12.22)

Using the aforementioned equations, the value for the zero lift angle change due to the rudder deflection was found to be -0.48. Using this value, and figure 11.9 in Design of Aircraft it was found that the size of the rudder was about 18% of the total vertical tail which comes out to be 11.84 square feet.

Table 12.5 below shows the stability derivatives along with the Rudder size below.

Table 12.5: Stability Derivatives and Rudder SizeCnβ 0.0854Clβ -0.0854SR (ft2) 11.84

Figure 12.5 below shows a drawing of the rudder attached to the vertical tail.

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Figure 12.6: Drawing of Rudder

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13 Engineering Conclusions and 3 View DrawingsUpon calculation of all the data throughout the design process the design team was capable

of reaching the ultimate goal in the design of this aircraft requested by Beechcraft Inc. Table 13.1 shows the pertinent design parameters that were calculated throughout the design process.

Table 13.1: Pertinent Design Parameters

Structure Factor 0.58 Fuel Req (gal) 358 Pinstall (HP) 2440

AR 8 bVT (ft) 8.51 CD0 0.0226

W/S (psf) 42 SVT (ft2) 65.79 STO (ft) 1026

TOGW (lbs) 9520 X ac VT (ft) 21 S clear obstacle (ft) 1374

bw (ft) 42.58 ΛLE VT (°) 57.5 S Land w/ flaps (ft) 1782

S (ft2) 226.67 bHT (ft) 19.45 ΔCL max 1.095m.a.c. (ft) 5.73 HT Airfoil NACA 64-004 Wing Lift (lb) 10078

ΛLE Wing (°) 0 SHT (ft2) 126.1 Tail Lift (lbs) -558.3

Xac W (ft) 13.5 Xac HT (ft) 22.77 Vmax Wing (lb) 3067.8

Wing Airfoil NACA-2412 ΛLE HT (°) 29.8 Mmax Wing (lb-ft) 33163.3

Dfuse (ft) 5.25 Xcg (ft) 13.5 Vmax fuse (lb) 5943.3

lfuse (ft) 30 VT Airfoil NACA 64-004 Mmax fuse (lb-ft) 19670.8

As well as the pertinent design parameters, below in Figure 13.1 is a three-view drawing showcasing the aircraft and its overall dimensions. This figure can also be viewed in the Appendix section of the report.

Figure 13.1: 3 view drawing for final aircraft design.

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Completion of the aircraft has the team rather pleased with the overall outcome of the aircraft and its design features. One feature the team feels could have been improved upon was the horizontal and vertical stabilizers. The empennage design of the aircraft called for a larger horizontal and vertical tail section due to the minimization of the fuselage in order to reach the target cruise speed of 320 knots, however; this minuet feature does not hinder the overall performance of the aircraft, and the design team is confident in the success of the aircraft’s final design. Without any further ado allow the Left βrothers to introduce the Gyrfalcon 536.

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ReferencesAngel Aircraft Corporation. AAC Brochure. Orange City: Angel Aircraft Corporation, n.d. Print.

"Angel Aircraft Corporation Photo Gallery2." Angel Aircraft Corporation Photo Gallery2. Angel Aircraft Corporation, 2008. Web. 29 Aug. 2016.

Graphiq. "AAC Angel Private Turboprop-driven Propeller Plane." Axlegeeks. Graphiq, 2016. Web. 29 Aug. 2016.

Mark, Robert P. "King Air C90 Ditching Still under Investigation." Aviation International News. AINOnline, 7 May 2012. Web. 29 Aug. 2016.

Textron Aviation. King Air C90GTx. N.p.: Textron Aviation, 2014. Print.

Corke, Thomas C. Design of Aircraft. Upper Saddle River, NJ: Prentice Hall, 2003. Print.

Abbott, Ira H., and Albert E. Von. Doenhoff. Theory of Wing Sections: Including a Summary of Airfoil Data. New York, NY: Dover Publ., 1982. Print.

Gjenvick, Paul K. "The Piper Cheyenne II XL - Specifications, Diagrams and Photo (1981)." Piper Cheyenne II XL. N.p., n.d. Web. 19 Sept. 2016.

"King Air C90GTx." King Air C90GTx. Textron Aviation, n.d. Web. 19 Sept. 2016.

Goebel, Greg. "Yet58_1b." Flickr. Yahoo!, n.d. Web. 17 Oct. 2016.

Image of Leading edge flaps. Digital image. N.p., n.d. Web. http://users.skynet.be/spotterfreak/flightcontrols2.html

Image of Trailing edge flaps. Digital image. N.p., n.d. Web. http://zoomaviation.com/programs/charts/flap_leading_edge_devices.png

86

http://zoomaviation.com/programs/charts/flap_leading_edge_devices.png

http://users.skynet.be/spotterfreak/flightcontrols2.html

Appendix A – Request of ProposalSpreadsheet showing request of proposal (RFP)

87

Range (NM) 1000

Holding (contingency) fuel 30 minutesReserve fuel 45 minutes

Design Cruise Speed (knots) 300 @ 25,00ft

Payload

6 passengers arranged in luxury seeting (36" seat pitch)

plus crew (pilot and copilot)

FAR Tafeoff Distance (ft) 2,000FAR Landing Distance (ft) 2,000

88

Appendix B – Gross Takeoff WeightSpreadsheet used in determining the gross takeoff weight

89

Cruise Altitude (ft) 25000Range (NM) 1000# of Passengers 6# of Crew 2Holding (min) 30Reserve (min) 45Vcr @ 25,000 feet (knots) 320

Structural Factor 0.58AR 8W/S (psf) 42CD0 0.0250Engine sfc (lbs/hr/HP) 0.57Prop Effi ciency 0.85ρ @ 25,000 Feet (sl/ft3) 0.001066Oswald's Effi ciency Factor 0.85

(L/D)max 14.62

CL (L/D)max 0.7308

CL act 0.2932

WCruise (lbf) 8317.46

VHold/Reserve (knots) 145

(L/D)Cruise 10.10Bregeut Range Factor 4911.19Bregeut Endurance Factor 60.04Avg. Passengers w/ bags (lbf) 200Total Payload Weight (lbf) 1600Iterated Final TOGW (lbs) 9520

Mission Requirements

Inpute Values

Calculations

MAE 475 Flight Vehcle Design

90

Flight Phase Fuel Fraction Used IterationTOGW 9520Start-Up & TO 0.98 190 9330Climb and Accel to Cruise 0.98 187 9143Cruise (Bregeut) 1684 7459Descent and Land 0.975 186 7272Reserve (Breguet Endurance) 91 7181Holding 60Total Fuel Weight 2398Total Fuel and Payload Weight 3998

Wt available for strucutre 5522Wt required for structure 5522Difference 0

91

Appendix C – Weight AnalysisMatlab code used for takeoff weight sensitivity analysis is displayed below.

92

clc

clear

data=xlsread('\desktop\MAE 475 Takeoff Estimate');

%Mission Requirements

cruise=data(1,1);

pass=data(3,1);

crew=data(4,1);

holding=data(5,1); %minutes

reserve=data(6,1); %minutes

V_cr=data(7,1); %@25,000ft Knots

% Input Values

S=data(9,1);

Wing_load=data(11,1);

sfc=data(13,1);

eff=data(14,1);

rho=data(15,1); %@25,000ft

os_eff=data(16,1);

%Variation Values

%

%

for Range=[500 1000 1500];

for AR=[5 7 9];

for C_Do=[0.0180 0.0210 0.0240 0.0270];

%Calculations

LD_max=0.5*sqrt((pi()*AR*os_eff)/C_Do);

C_L_LD_Max=sqrt(pi()*AR*os_eff*C_Do);

C_Lact=(2*Wing_load)/(rho*(V_cr*1.62)^2);

V_hold=145;

LD_cruise=LD_max*((2*C_Lact/C_L_LD_Max)/(1+(C_Lact/C_L_LD_Max)^2));

93

Bre_range=326*eff*LD_cruise*(1/sfc);

Bre_end=(1/sfc)*550*(LD_max)*(1/(V_hold*1.62));

Avg_pass=200;

total_payload=Avg_pass*(pass+crew);

diff=1;

while diff > 0.2

TOGW=randi([2000 28000]);

start=TOGW*0.98;

climb=start*0.98;

u1=TOGW-start;

u2=start-climb;

cruise_used=((1-(1/(exp((Range/Bre_range))))))*climb;

cruise=climb-cruise_used;

land=cruise*0.975;

land_used=cruise-land;

reserve_used=(((sfc*(45/60))/(LD_max))*land*(V_hold*1.62))/(550);

reserve_wgt=land-reserve_used;

hold_used=(1-(1/(exp(0.5/Bre_end))))*reserve_wgt;

total_fuel=(u1+u2+land_used+cruise_used+reserve_used+hold_used);

fuel_payload=total_fuel+total_payload;

Wt_ava=TOGW-fuel_payload;

WT_req=TOGW*S;

diff=Wt_ava-WT_req;

diff=abs(diff);

end

fprintf('TOGW for Range of %iNM ,AR of %i, and C_Do of %.4f = %ilbs',Range,AR,C_Do,TOGW);

fprintf('\n');

end

fprintf('\n');

end

fprintf('\n');

end

94

Appendix DThis appendix shows the spreadsheet used for determining the values in the report

95

Design Parameters AirfoilData Viscous DragVcruise (knots) 320 Name NACA

63-212Cdo 0.0035 V

(ft/sec)540.8

Vcruise (ft/sec) 540.8 Clmax 1.35 rle 0.0024 q (lb/ft^2)

155.88

M 0.48 Cla 0.1096 Cl minD 0 Re 1E10^7Meff 0.48 a.c. 0.35 (t/c)max 35% CF 0.002927S(ft2) 226.67 αoL (deg) -1.160 t/c 12% Swet(ft2) 462.27

AR 8 Sweep Angles Atmospheric Conditions

F 1.44

ɅLE(deg) 0 ɅLE 0 ν (cruise) 0.00030178 Q 1

W/S(lb/ft2) begin cruise

40.34 Ʌ1/4 chord -3.44 q(lb/ft2) 155.88

W/S(lb/ft2) after cruise

32.91 Ʌt/c max -4.82 ρ (sl/ft3) 0.001066

ε(deg) -2 ɅTE -13.54

ᴦ(deg) 3.5 Calculations

ʎ 0.35 b(ft) 42.58 C Ltrim 0.26

Drag Summary cr (ft) 7.89 CL (begin

cruise)

0.259

CDO Wing 0.00859 ct (ft) 2.76 CL (end cruise) 0.211Cdi(begin cruise) 0.00313 m.a.c. (ft) 5.73 CL (max) 1.350

Cdi(end cruise) 0.00209 iw(deg) 1.86 CLα 0.0856Induced Drag(begin cruise) (lb)

110.75 k 0.05 CLo 0.0993

Induced Drag(end cruise) (lb)

73.70 e 0.85 CD 0.012

Zero Lift Drag (lb) 303.67 Δαol 0.84 L/D 22.062Total Drag (lb) 488.12 αstall (deg) 14.6 Vstall

(ft/sec)236.76

96

AirfoilDataName NACA

63-212Cdo 0.0035

Clmax 1.35 rle 0.0024Cla 0.1096 Cl minD 0a.c. 0.35 (t/c)max 35%αoL (deg) -1.160 t/c 12%

Sweep Angles Atmospheric Conditions

ɅLE 0 ν (cruise)

0.00030178

Ʌ1/4 chord -3.44 q(lb/ft2) 155.88

Ʌt/c max -4.82 ρ (sl/ft3)

0.001066

ɅTE -13.54

Calculations

b(ft) 42.58 C Ltrim 0.26

cr (ft) 7.89 CL (begin

cruise)

0.259

ct (ft) 2.76 CL (end

cruise)

0.211

m.a.c. (ft) 5.73 CL (max) 1.350

iw(deg) 1.86 CLα 0.0856k 0.05 CLo 0.0993e 0.85 CD 0.012Δαol 0.84 L/D 22.062αstall (deg) 14.6 Vstall

(ft/sec)236.76

97

Appendix E – Drag CalculationsExcel spreadsheet showing the drag force and zero lift drag coefficient calculations.

98

99

Dimension Data

1 gal0.133681

ft^3Fuel Tank Type

FuselageW

inghcruise (ft)

25000D

fuse5.25

r(o)2.625

spec Vol, gas6.7

lbs/galDiscrete

100%-

V (knots)320.00

l/d5.714285714

Total Fuel used (lbs)2398.227

Bladder 83%

77%V (ft/sec)

540.80L (ft)

30Total Fuel required (gal)

357.9443Integral

93%85%

q (lbs/ft2)

155.884S (ft

2)226.67

Total Fuel required (ft^3)47.85035

ρ (sl/ft3)

0.00107Shape

Ojibe Cross Section, Sears-HaackVolum

e Required (ft^3)56.295

µ (sl ft/sec)3.22E-07

F1.480

ν (ft2/sec)0.000302

Q1

Low wing, well-filleted

x/Ldx

r(x)/r(o)r(x)

x (ft)xm

idpoint (ft)D

mid (ft)

Pmid (ft)

Awet (ft

2)Rex m

idCf

Drag (lb)0.00

00

00.0

00

00

00

00.10

30.464758

1.2199897543.0

1.82.43998

7.66522.996

32233110.003549

12.720640.20

30.715542

1.8782971016.0

5.43.756594

11.80235.405

96699340.002957

16.317230.30

30.877424

2.3032377629.0

94.606476

14.47243.415

161165560.002727

18.458190.40

30.969847

2.54584953612.0

12.65.091699

15.99647.988

225631790.00259

19.372810.50

31

2.62515.0

16.25.25

16.49349.480

290098010.002493

19.230050.60

30.969847

2.54584953618.0

19.85.091699

15.99647.988

354564240.00242

18.099820.70

30.877424

2.30323776221.0

23.44.606476

14.47243.415

419030460.002361

15.975860.80

30.715542

1.87829710124.0

273.756594

11.80235.405

483496690.002312

12.758240.90

30.464758

1.21998975427.0

30.62.43998

7.66522.996

547962910.00227

8.1373811.00

30

030.0

34.20

0.0000.000

612429140.002234

0Total

141.0702lbs

Cdo0.003992461

Fuselage DesignVolum

e EffectivenessDesign Param

eters

Viscuous Drag Calc

Appendix F – Empennage DesignThis section contains the spreadsheet used in the calculation the vertical and horizontal tail.

100

101

b (ft

)42.58

hcruise (ft

)25000

Wing Placem

ent45%

m.a.c. (ft

)5.73

V (ft/sec)

540.8X

acW13.5

Sr (ft

2)226.67

ρ (slugs/ft3)

0.001066X

ac VT (ft)

21.0029.19

Ʌ1/4 (deg)

-3.4442ν (ft

2/sec)0.000302

Xac HT (ft

)22.77

29.64

t/c12%

q (lbf/ft2)

155.88365λ

0.35M

0.48X

acW-0.53789

CVT

0.07N

ame

NACA 64-004

CHT

0.9N

ame

NACA 64-004

lVT (ft)

10.27Clm

ax0.8

Cf

0.002792lHT (ft

)9.27

Clmax

0.8C

f0.002871

ΛLE (deg)

35Clalpha (/deg)

0.11RE

13848898Λ

LE (deg)40

Clalpha (/deg)0.11

RE11609803

t/c8%

t/cmax

40%S

wet (ft

2)132.8048

t/c8%

t/c max

40%S

wet (ft

2)254.5433

λ0.4

a.c.0.26

F1.207603

λ0.4

a.c.0.26

F1.300171

αoL (deg)

0Q

1α

oL (deg)0

Q1

SVT (ft

2)65.79

CDo VT

0.0034S

HT (ft2)

126.10C

Do HT0.0037

b (ft)

8.51Λ

LE (deg)57.50

D (lbf)

69.80865b (ft

)19.45

ΛLE (deg)

29.80D

(lbf)148.1205

cr (ft

)11.05

Λ1/4 (deg)

49.72c

r (ft)

9.26Λ

1/4 (deg)23.26

ct (ft

)4.42

ΛTE (deg)

0.64c

t (ft)

3.70Λ

TE (deg)0.07

ARVT

1.10Λ

t/c max (deg)

43.42AR

HT3.00

Λt/c m

ax (deg)18.99

Xac VT (ft

)2.86

Xac HT (ft

)2.39

β0.86

β0.76

CLα

0.0283CL

α0.0589

m.a.c (ft

)8.21

m.a.c (ft

)6.88

Sweep Angles

Calculations

Sweep Angles

Air PropertiesM

ain Wing

Horizontal TailVertical Tail

Viscous DragViscous Drag

Calculations

Xac Locations

Appendix G – Power RequirementsSpreadsheet used to calculate the power requirements for the design.

102

Wing 303.7 Preqd 25,000 ft (HP) 883.66

Fuselage 178.7 Pshp reqd 25,000 ft (HP) 1039.60

Horizontal Tail 166.1 Pshp SSL (HP) 2769.21

Vertical Tail 126.1 Preqd climb (HP) 2065.35

Nacelle 33.1 Pinstall 2769.21Induced Wing 92.2

Total 899.9

Component CD

Wing 0.00859 ROC (FPM) 250Fuselage 0.005056 ηP 0.85

Horizontal Tail 0.006944 Pavail (HP) 1500

Vertical Tail 0.007331 Preqd climb 1202.9Nacelle 0.000939


SFC at Full Power [lb/(HP*hr)] 0.61Max Env. Diameter (in) 20.9Max Env. Length (in) 55

q 155.4780664

Zero

Lift

Ze

ro L

ift

103

Appendix H – Engine PerformanceFull spreadsheet data for calculation of engine performance parameters.

104

105

SSLV(knots)

W (lbs)

L (lbs)Sref (ft

2)h (ft

2)e

ARη

propC

D0ρ

qC

LC

DiD (lbs)

Vcr (fps)

Preq

Pshp req

Pshp avail

Pexcess

ROC (fpm)

γ (deg)60

9520#NUM

!226.67

00.85

80.85

0.0250.002377

12.188313.445873

0.5558271604.666

101.268295.4569

347.59633000

2704.54319374.9919

#NUM!

709520

#NUM!

226.670

0.858

0.850.025

0.00237716.58965

2.5316620.300022

1222.204118.146

262.5427308.8737

30002737.4573

9489.0853#NUM

!80

9520#NUM

!226.67

00.85

80.85

0.0250.002377

21.668111.938303

0.175867986.5614

135.024242.199

284.943000

2757.8019559.6042

#NUM!

909520

#NUM!

226.670

0.858

0.850.025

0.00237727.42371

1.5314990.109793

837.8911151.902

231.4133272.251

30002768.5867

9596.9916#NUM

!100

95203010.777

226.670

0.858

0.850.025

0.00237733.85643

1.2405140.072035

744.671168.78

228.5192268.8462

30002771.4808

9607.023771.56322

1109520

4839.258226.67

00.85

80.85

0.0250.002377

40.966281.025218

0.049201689.0177

185.658232.5848

273.62923000

2767.41529592.9308

59.44765120

95205880.672

226.670

0.858

0.850.025

0.00237748.75326

0.8614680.034739

660.1719202.536

243.1065286.0077

30002756.8935

9556.458551.85035

1309520

6591.781226.67

00.85

80.85

0.0250.002377

57.217370.734032

0.025222651.346

219.414259.8444

305.69933000

2740.15569498.4384

46.1785140

95207115.287

226.670

0.858

0.850.025

0.00237766.3586

0.6329150.018751

658.0861236.292

282.7282332.6214

30002717.2718

9419.114641.63399

1509520

7518.307226.67

00.85

80.85

0.0250.002377

76.176970.55134

0.014229677.3714

253.17311.8002

366.82383000

2688.19989318.3395

37.83896160

95207838.287

226.670

0.858

0.850.025

0.00237786.67246

0.4845760.010992

707.0946270.048

347.1809408.4481

30002652.8191

9195.696634.57849

1709520

8098.256226.67

00.85

80.85

0.0250.002377

97.845080.429244

0.008625745.7491

286.926389.0451

457.70013000

2610.95499050.5789

31.71678180

95208313.304

226.670

0.858

0.850.025

0.002377109.6948

0.3828750.006862

792.2351303.804

437.6076514.8325

30002562.3924

8882.242429.16191

1909520

8493.778226.67

00.85

80.85

0.0250.002377

122.22170.343633

0.005528845.7343

320.682493.1123

580.13213000

2506.88778689.8419

26.84853200

95208647.02

226.670

0.858

0.850.025

0.002377135.4257

0.3101290.004502

905.6275337.56

555.8247653.9115

30002444.1753

8472.456324.72847

2109520

8778.376226.67

00.85

80.85

0.0250.002377

149.30690.281296

0.003704971.4395

354.438626.0274

736.50283000

2373.97268229.1067

22.7652220

95208891.827

226.670

0.858

0.850.025

0.002377163.8651

0.2563050.003075

1042.801371.316

704.0156828.2536

30002295.9844

7958.769520.93033

2309520

8990.386226.67

00.85

80.85

0.0250.002377

179.10050.234502

0.0025741119.42

388.194790.0946

929.5233000

2209.90547660.3864

19.20141240

95209076.364

226.670

0.858

0.850.025

0.002377195.013

0.2153670.002171

1201.065405.072

884.57781040.68

30002115.4222

7332.871117.56038

2509520

9151.556226.67

00.85

80.85

0.0250.002377

211.60270.198482

0.0018441287.55

421.95987.7849

1162.13000

2012.21516975.1154

15.99248260

95209217.367

226.670

0.858

0.850.025

0.002377228.8695

0.1835080.001576

1378.723438.828

1100.0411294.166

30001899.9592

6585.993114.48554

2709520

9274.903226.67

00.85

80.85

0.0250.002377

246.81340.170167

0.0013551474.462

455.7061221.675

1437.2643000

1778.32546164.3634

13.0294280

95209325.039

226.670

0.858

0.850.025

0.002377265.4344

0.1582290.001172

1574.663472.584

1353.0191591.787

30001646.9812

5709.073611.61547

2909520

9368.468226.67

00.85

80.85

0.0250.002377

284.73260.147505

0.0010181679.241

489.4621494.409

1758.1283000

1505.59125218.9611

10.23645300

95209405.736

226.670

0.858

0.850.025

0.002377304.7079

0.1378350.000889

1788.127506.34

1646.1821936.685

30001353.8176

4692.85518.886049

3109520

9437.274226.67

00.85

80.85

0.0250.002377

325.36030.129086

0.000781901.26

523.2181808.679

2127.8583000

1191.32064129.5778

7.558835320

95209463.415

226.670

0.858

0.850.025

0.002377346.6898

0.1211440.000687

2018.59540.096

1982.2412332.048

30001017.7588

3527.94556.250056

3309520

9484.415226.67

00.85

80.85

0.0250.002377

368.69650.113913

0.0006072140.075

556.9742167.211

2549.663000

832.789332886.7697

4.955531340

95209500.461

226.670

0.858

0.850.025

0.002377391.3803

0.1073110.000539

2265.676573.852

2363.9322781.096

3000636.06801

2204.85763.671549

3509520

9511.686226.67

00.85

80.85

0.0250.002377

414.74130.101266

0.000482395.363

590.732572.75

3026.7653000

427.249711481.0127

2.394791

106

25000 ftV(knots)

W (lbs)

L (lbs)S

ref (ft2)

h (ft2)

eAR

ηprop

CD0

ρq

CL

CDi

D (lbs)V

cr (fps)P

req P

shp req P

shp availP

excessROC (fpm

)γ (deg)

609520

9140.348226.67

250000.85

80.85

0.0250.001066

5.4660267.683715

2.7636543455.098

101.268636.1652

748.42961126.24

490.074971698.7893

16.2355270

95209133.491

226.6725000

0.858

0.850.025

0.0010667.439868

5.6451781.491752

2557.842118.146

549.4524646.4146

1126.24576.78773

1999.369216.38246

809520

9156.249226.67

250000.85

80.85

0.0250.001066

9.7173794.322089

0.8744371981.135

135.024486.3651

572.19431126.24

639.875042218.0542

15.8896390

95209189.594

226.6725000

0.858

0.850.025

0.00106612.29856

3.4149840.545907

1591.525151.902

439.5562517.1249

1126.24686.68398

2380.312115.13935

1009520

9225.055226.67

250000.85

80.85

0.0250.001066

15.18342.766137

0.358171318.725

168.78404.6807

476.0951126.24

721.559442501.2039

14.29938110

95209259.08

226.6725000

0.858

0.850.025

0.00106618.37192

2.2860640.244635

1122.856185.658

379.0314445.9193

1126.24747.20872

2590.114213.44528

1209520

9290.341226.67

250000.85

80.85

0.0250.001066

21.86411.920929

0.172728979.9292

202.536360.8563

424.53681126.24

765.383892653.1164

12.61065130

95209318.502

226.6725000

0.858

0.850.025

0.00106625.65995

1.6367680.125405

874.8076219.414

348.991410.5776

1126.24777.24919

2694.246111.80929

1409520

9343.648226.67

250000.85

80.85

0.0250.001066

29.759471.411295

0.093234797.5601

236.292342.6492

403.11671126.24

783.590932716.2291

11.04542150

95209366.03

226.6725000

0.858

0.850.025

0.00106634.16266

1.2293940.07075

741.451253.17

341.2966401.5254

1126.24784.94353

2720.917710.31869

1609520

9385.943226.67

250000.85

80.85

0.0250.001066

38.869521.080522

0.054652701.7812

270.048344.572

405.37881126.24

781.668152709.564

9.626648170

95209403.677

226.6725000

0.858

0.850.025

0.00106643.88004

0.9571410.042884

675.1916286.926

352.2364414.3958

1126.24774.00374

2682.99628.965932

1809520

9419.493226.67

250000.85

80.85

0.0250.001066

49.194230.853746

0.034119659.2296

303.804364.1392

428.39911126.24

762.100932641.7364

8.332964190

95209433.62

226.6725000

0.858

0.850.025

0.00106654.81209

0.7662430.027484

652.0702320.682

380.1949447.2881

1126.24746.04527

2586.08137.724232

2009520

9446.25226.67

250000.85

80.85

0.0250.001066

60.733620.691534

0.022386652.3333

337.56400.3666

471.01961126.24

725.873542516.1583

7.136444210

95209457.545

226.6725000

0.858

0.850.025

0.00106666.95882

0.6272420.018417

658.9591354.438

424.6548499.5939

1126.24701.58532

2431.96596.566588

2209520

9467.641226.67

250000.85

80.85

0.0250.001066

73.487680.571516

0.01529671.1232

371.316453.0887

533.04551126.24

673.151482333.4033

6.011941230

95209476.647

226.6725000

0.858

0.850.025

0.00106680.32021

0.5228990.012799

688.1762388.194

485.7198571.435

1126.24640.5204

2220.29135.470065

2409520

9484.655226.67

250000.85

80.85

0.0250.001066

87.456410.480232

0.010796709.6013

405.072522.6175

614.84411126.24

603.622652092.3894

4.938779250

95209491.736

226.6725000

0.858

0.850.025

0.00106694.89628

0.4425820.009169

734.983421.95

563.8656663.3713

1126.24562.37456

1949.40764.416143

2609520

9497.95226.67

250000.85

80.85

0.0250.001066

102.63980.409192

0.007838763.9839

438.828609.5592

717.12841126.24

516.680981791.016

3.900426270

95209503.341

226.6725000

0.858

0.850.025

0.001066110.687

0.3794430.00674

796.3282455.706

659.8028776.2386

1126.24466.43737

1616.85223.390083

2809520

9507.945226.67

250000.85

80.85

0.0250.001066

119.03790.352824

0.005827831.7881

472.584714.7087

840.83371126.24

411.531491426.5272

2.883738290

95209511.787

226.6725000

0.858

0.850.025

0.001066127.6924

0.328910.005064

870.1748489.462

774.3954911.0534

1126.24351.84474

1219.62992.380156

3009520

9514.885226.67

250000.85

80.85

0.0250.001066

136.65060.307349

0.004422911.33

506.34838.9869

987.04351126.24

287.25322995.73068

1.87823310

95209517.251

226.6725000

0.858

0.850.025

0.001066145.9125

0.2878390.003878

955.1208523.218

908.61161068.955

1126.24217.62854

754.384651.376966

3209520

9518.889226.67

250000.85

80.85

0.0250.001066

155.47810.270131

0.0034161001.435

540.096983.4016

1156.9431126.24

142.8386495.13379

0.875467330

95209519.798

226.6725000

0.858

0.850.025

0.001066165.3473

0.2540070.00302

1050.176556.974

1063.4921251.167

1126.2462.748071

217.509070.372921

3409520

9519.975226.67

250000.85

80.85

0.0250.001066

175.52020.239285

0.002681101.262

573.8521149.021

1351.791126.24

-22.78106-78.96797

-0.13141350

95209519.409

226.6725000

0.858

0.850.025

0.001066185.9967

0.2258070.002387

1154.624590.73

1240.1291458.976

1126.24-113.8892

-394.7839-0.63819

107

31000 ftV(knots)

W (lbs)

L (lbs)Sref (ft

2)h (ft

2)e

ARη

propC

D0ρ

qC

LC

DiD (lbs)

Vcr (fps)

Preq

Pshp req

Pshp avail

Pexcess

ROC (fpm)

γ (deg)60

95209508.163

226.6731000

0.858

0.850.025

0.0008574.394357

9.5575734.275988

4284.08101.268

788.8003928.0004

876.18387.382711

302.902262.85747

709520

9475.852226.67

310000.85

80.85

0.0250.000857

5.9812087.02189

2.3080723163.086

118.146679.4654

799.371876.183

196.71766681.89946

5.52007280

95209452.824

226.6731000

0.858

0.850.025

0.0008577.812189

5.3761351.352949

2440.057135.024

599.0296704.7407

876.183277.1534

960.720816.810528

909520

9441.058226.67

310000.85

80.85

0.0250.000857

9.8873024.24781

0.844641948.997

151.902538.2846

633.276876.183

337.898451171.2867

7.383696100

95209437.218

226.6731000

0.858

0.850.025

0.00085712.20655

3.4407260.554168

1602.475168.78

491.756578.5365

876.183384.427

1332.57267.561408

1109520

9438.274226.67

310000.85

80.85

0.0250.000857

14.769922.843575

0.3785041350.891

185.658456.0067

536.4785876.183

420.17631456.4935

7.512968120

95209442.158

226.6731000

0.858

0.850.025

0.00085717.57743

2.3893930.267249

1164.401202.536

428.7876504.456

876.183447.3954

1550.84547.33202

1309520

9447.567226.67

310000.85

80.85

0.0250.000857

20.629062.035933

0.194031024.18

219.414408.5809

480.6834876.183

467.602151620.8898

7.072353140

95209453.704

226.6731000

0.858

0.850.025

0.00085723.92483

1.7554730.144254

917.874236.292

394.3387463.9279

876.183481.84432

1670.25876.765749

1509520

9460.088226.67

310000.85

80.85

0.0250.000857

27.464731.529212

0.109465837.1042

253.17385.3267

453.3255876.183

490.856341701.4978

6.431361160

95209466.434

226.6731000

0.858

0.850.025

0.00085731.24876

1.3440340.084559

776.0258270.048

381.0258448.2657

876.183495.15718

1716.40626.080875

1709520

9472.575226.67

310000.85

80.85

0.0250.000857

35.276921.190563

0.066351730.4605

286.926381.0693

448.3168876.183

495.113731716.2556

5.721441180

95209478.413

226.6731000

0.858

0.850.025

0.00085739.54921

1.0619530.05279

697.3575303.804

385.2453.1764

876.183490.98304

1701.9375.357404

1909520

9483.899226.67

310000.85

80.85

0.0250.000857

44.065630.95311

0.042523674.4469

320.682393.2418

462.6374876.183

482.941251674.0611

4.991345200

95209489.005

226.6731000

0.858

0.850.025

0.00085748.82618

0.8601820.034635

660.0118337.56

405.0792476.5638

876.183471.10379

1633.02784.624722

2109520

9493.72226.67

310000.85

80.85

0.0250.000857

53.830870.78021

0.028495652.7341

354.438420.6432

494.8743876.183

455.539831579.0771

4.258281220

95209498.041

226.6731000

0.858

0.850.025

0.00085759.07968

0.7108940.023657

651.5881371.316

439.9002517.5296

876.183436.28283

1512.32493.892306

2309520

9501.971226.67

310000.85

80.85

0.0250.000857

64.572630.650421

0.019803655.7665

388.194462.8447

544.5232876.183

413.338271432.7902

3.526789240

95209505.511

226.6731000

0.858

0.850.025

0.00085770.3097

0.5973480.016703

664.6261405.072

489.4935575.8747

876.183386.6895

1340.41533.161542

2509520

9508.665226.67

310000.85

80.85

0.0250.000857

76.290910.550516

0.014187677.6502

421.95519.8809

611.6246876.183

356.302131235.0809

2.796264260

95209511.435

226.6731000

0.858

0.850.025

0.00085782.51625

0.5089830.012127

694.4191438.828

554.0555651.83

876.183322.12749

1116.61842.430592

2709520

9513.823226.67

310000.85

80.85

0.0250.000857

88.985720.471979

0.010428714.5896

455.706592.0778

696.5621876.183

284.10526984.81865

2.064129280

95209515.827

226.6731000

0.858

0.850.025

0.00085795.69932

0.4388680.009016

737.8786472.584

634.0175745.9029

876.183242.16551

839.439281.696466

2909520

9517.446226.67

310000.85

80.85

0.0250.000857

102.65710.409123

0.007835764.051

489.462679.9526

799.9442876.183

196.23042680.2105

1.327194300

95209518.675

226.6731000

0.858

0.850.025

0.000857109.8589

0.3823030.006842

792.9101506.34

729.9675858.7853

876.183146.21555

506.839620.955916

3109520

9519.508226.67

310000.85

80.85

0.0250.000857

117.30490.358036

0.006001824.2905

523.218784.1521

922.5319876.183

92.030924319.01476

0.582247320

95209519.939

226.6731000

0.858

0.850.025

0.000857124.995

0.3360080.005285

858.0523540.096

842.6011991.2954

876.18333.581889

116.407810.205818

3309520

9519.956226.67

310000.85

80.85

0.0250.000857

132.92930.315953

0.004673894.0763

556.974905.4132

1065.192876.183

-29.23017-101.3231

-0.17372340

95209519.551

226.6731000

0.858

0.850.025

0.000857141.1077

0.2976410.004147

932.2607573.852

972.69031144.341

876.183-96.50724

-334.5314-0.55669

3509520

9518.71226.67

310000.85

80.85

0.0250.000857

149.53020.280876

0.003693972.5179

590.731044.537

1228.867876.183

-168.3542-583.5808

-0.94342

Appendix I - TakeoffValues used in the numerical integration of the takeoff performance spreadsheet.

108

HP 2769 AR 8.00 ΔCDflap 0

W (lbs) 9520 e 0.85 ΔCDgear 0.0215

Merit 0.8 CLα 0.09 CDo 0.0216

Dprop (ft) 8 iw 1.36 CLmax 1.8

ρ 0.002377 α0L -1.66 Δt 0.5

Aprop (ft2) 50.26548246 δflaps 0 μ3.62E-

07

Sref (ft2) 226.67 ηprop 0.85

W/S 42.00

W/P 3.43779954

Vstall 140.12 ft/sec 95.53 mph

1.2*Vstall 168.14 ft/sec114.6

4 mph

Takeoff Integration

Comments t Vx Vy V (fps)

Sx Sy (ft) γ Θ Tact Tx

0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7079.2 7079.2 0.5 11.3 0.0 11.3 2.8 0.0 0.0 0.0 7079.2 7079.2 1 22.7 0.0 22.7 11.3 0.0 0.0 0.0 7079.2 7079.2 1.5 34.0 0.0 34.0 25.5 0.0 0.0 0.0 7079.2 7079.2 2 45.3 0.0 45.3 45.3 0.0 0.0 0.0 7079.2 7079.2 2.5 56.7 0.0 56.7 70.8 0.0 0.0 0.0 7079.2 7079.2 3 68.0 0.0 68.0 102.0 0.0 0.0 0.0 7079.2 7079.2 3.5 79.3 0.0 79.3 138.8 0.0 0.0 0.0 7079.2 7079.2 4 90.7 0.0 90.7 181.3 0.0 0.0 0.0 7079.2 7079.2 4.5 102.1 0.0 102.1 229.5 0.0 0.0 0.0 7079.2 7079.2 5 113.4 0.1 113.4 283.4 0.0 0.0 0.0 7079.2 7079.2 5.5 124.8 0.1 124.8 343.0 0.0 0.0 0.0 7079.2 7079.2 6 136.2 0.1 136.2 408.2 0.0 0.0 0.0 7079.2 7079.2 6.5 147.7 0.1 147.7 479.2 0.0 0.0 0.0 7079.2 7079.2 7 159.1 0.1 159.1 555.9 0.0 0.0 0.0 7079.2 7079.21.2 Vstall 7.5 170.5 0.1 170.5 638.3 0.0 0.0 3.0 7079.2 7069.5 8 182.1 0.1 182.1 726.5 0.0 0.0 6.0 7079.2 7040.4

109

8.5 193.8 0.1 193.8 820.4 0.0 0.0 9.0 7079.2 6992.0 9 205.7 2.6 205.7 920.3 0.0 0.7 12.0 7079.2 6924.5 9.5 217.4 11.2 217.7 1026.1 3.5 3.0 15.0 6996.5 6758.1 10 227.8 24.3 229.1 1137.4 12.3 6.1 15.0 6648.9 6422.3 10.5 236.3 34.2 238.7 1253.4 27.0 8.2 15.0 6380.0 6162.635ft obs 11 243.7 41.6 247.2 1373.4 45.9 9.7 15.0 6161.5 5951.6 11.5 250.4 47.1 254.8 1496.9 68.1 10.

7 15.0 5977.0 5773.3

12 256.7 51.4 261.8 1623.7 92.7 11.3

15.0 5816.7 5618.5

12.5 262.7 55.0 268.4 1753.6 119.3 11.8

15.0 5674.8 5481.4

13 268.4 58.0 274.6 1886.3 147.6 12.2

15.0 5547.2 5358.2

13.5 273.8 60.7 280.4 2021.9 177.2 12.5

15.0 5431.5 5246.4

14 278.9 63.1 286.0 2160.0 208.2 12.8

15.0 5325.7 5144.2

14.5 283.9 65.4 291.3 2300.7 240.3 13.0

15.0 5228.4 5050.2

15 288.6 67.5 296.4 2443.9 273.5 13.2

15.0 5138.5 4963.4

15.5 293.2 69.6 301.3 2589.3 307.8 13.3

15.0 5055.0 4882.7

16 297.5 71.5 306.0 2737.0 343.1 13.5

15.0 4977.2 4807.6

16.5 301.8 73.3 310.5 2886.8 379.3 13.7

15.0 4904.5 4737.4

17 305.8 75.0 314.9 3038.7 416.4 13.8

15.0 4836.4 4671.6

17.5 309.8 76.7 319.1 3192.6 454.3 13.9

15.0 4772.4 4609.8

18 313.6 78.3 323.2 3348.5 493.0 14.0

15.0 4712.1 4551.5



18.5 317.3 79.8 327.2 3506.2 532.6 14.1

15.0 4655.1 4496.5

19 320.9 81.3 331.0 3665.7 572.9 14.2

15.0 4601.3 4444.5

19.5 324.3 82.7 334.7 3827.0 613.9 14.3

15.0 4550.2 4395.2

20 327.7 84.1 338.3 3990.0 655.6 14.4

15.0 4501.7 4348.3

20.5 331.0 85.4 341.8 4154.7 698.0 14. 15.0 4455.6 4303.8

110

5 21 334.2 86.7 345.2 4321.0 741.0 14.

5 15.0 4411.7 4261.4

21.5 337.3 88.0 348.5 4488.9 784.7 14.6

15.0 4369.8 4220.9

22 340.3 89.2 351.8 4658.2 829.0 14.7

15.0 4329.8 4182.3

22.5 343.2 90.3 354.9 4829.1 873.8 14.7

15.0 4291.6 4145.3

23 346.1 91.5 358.0 5001.4 919.3 14.8

15.0 4254.9 4110.0

23.5 348.9 92.6 360.9 5175.2 965.3 14.9

15.0 4219.8 4076.0

24 351.6 93.6 363.8 5350.3 1011.9 14.9

15.0 4186.1 4043.5

24.5 354.2 94.7 366.7 5526.7 1059.0 15.0

15.0 4153.8 4012.2

25 356.8 95.7 369.4 5704.5 1106.6 15.0

15.0 4122.7 3982.2

25.5 359.4 96.7 372.1 5883.5 1154.6 15.1

15.0 4092.7 3953.3

26 361.8 97.7 374.8 6063.8 1203.2 15.1

15.0 4063.9 3925.4

26.5 364.3 98.6 377.4 6245.3 1252.3 15.1

15.0 4036.1 3898.6

27 366.6 99.5 379.9 6428.1 1301.8 15.2

15.0 4009.3 3872.7

27.5 368.9 100.4 382.3 6611.9 1351.8 15.2

15.0 3983.5 3847.8

28 371.2 101.3 384.8 6797.0 1402.2 15.3

15.0 3958.5 3823.6

28.5 373.4 102.1 387.1 6983.1 1453.1 15.3

15.0 3934.4 3800.3

29 375.6 103.0 389.4 7170.4 1504.3 15.3

15.0 3911.0 3777.7

29.5 377.7 103.8 391.7 7358.7 1556.0 15.4

15.0 3888.4 3755.9

30 379.8 104.6 393.9 7548.1 1608.1 15.4

15.0 3866.5 3734.8

30.5 381.8 105.3 396.1 7738.5 1660.6 15.4

15.0 3845.3 3714.3

31 383.8 106.1 398.2 7929.9 1713.4 15.5

15.0 3824.7 3694.4

31.5 385.8 106.8 400.3 8122.3 1766.7 15.5

15.0 3804.8 3675.2

32 387.7 107.6 402.3 8315.7 1820.3 15. 15.0 3785.5 3656.5111

5 32.5 389.6 108.3 404.4 8510.0 1874.2 15.

5 15.0 3766.7 3638.3

33 391.4 109.0 406.3 8705.2 1928.5 15.6

15.0 3748.4 3620.7

33.5 393.3 109.7 408.3 8901.4 1983.2 15.6

15.0 3730.7 3603.6

34 395.0 110.3 410.1 9098.5 2038.2 15.6

15.0 3713.4 3586.9

34.5 396.8 111.0 412.0 9296.4 2093.5 15.6

15.0 3696.7 3570.7

35 398.5 111.6 413.8 9495.2 2149.2 15.6

15.0 3680.4 3555.0

35.5 400.2 112.3 415.6 9694.9 2205.1 15.7

15.0 3664.5 3539.6

36 401.8 112.9 417.4 9895.4 2261.4 15.7

15.0 3649.0 3524.7

36.5 403.5 113.5 419.1 10096.7 2318.0 15.7

15.0 3634.0 3510.2

37 405.1 114.1 420.8 10298.9 2374.9 15.7

15.0 3619.3 3496.0

37.5 406.6 114.7 422.5 10501.8 2432.1 15.7

15.0 3605.0 3482.2



38 408.2 115.2 424.1 10705.5 2489.6 15.8

15.0 3591.1 3468.7

38.5 409.7 115.8 425.7 10909.9 2547.4 15.8

15.0 3577.5 3455.6

39 411.2 116.4 427.3 11115.2 2605.4 15.8

15.0 3564.2 3442.7

39.5 412.6 116.9 428.9 11321.1 2663.7 15.8

15.0 3551.2 3430.2

40 414.1 117.4 430.4 11527.8 2722.3 15.8

15.0 3538.6 3418.0

40.5 415.5 118.0 431.9 11735.2 2781.2 15.9

15.0 3526.3 3406.1

41 416.9 118.5 433.4 11943.3 2840.3 15.9

15.0 3514.2 3394.5

41.5 418.3 119.0 434.9 12152.1 2899.6 15.9

15.0 3502.4 3383.1

42 419.6 119.5 436.3 12361.6 2959.3 15.9

15.0 3490.9 3372.0

42.5 420.9 120.0 437.7 12571.7 3019.1 15.9

15.0 3479.7 3361.1

43 422.2 120.5 439.1 12782.5 3079.3 15. 15.0 3468.7 3350.5112

9 43.5 423.5 120.9 440.5 12993.9 3139.6 15.

9 15.0 3457.9 3340.1

44 424.8 121.4 441.8 13206.0 3200.2 15.9

15.0 3447.4 3329.9

44.5 426.0 121.9 443.1 13418.7 3261.0 16.0

15.0 3437.1 3320.0

45 427.3 122.3 444.4 13632.1 3322.1 16.0

15.0 3427.0 3310.2

45.5 428.5 122.8 445.7 13846.0 3383.3 16.0

15.0 3417.1 3300.7

46 429.7 123.2 447.0 14060.5 3444.8 16.0

15.0 3407.5 3291.4

46.5 430.8 123.6 448.2 14275.6 3506.5 16.0

15.0 3398.0 3282.2

47 432.0 124.0 449.4 14491.4 3568.4 16.0

15.0 3388.8 3273.3

47.5 433.1 124.5 450.7 14707.6 3630.6 16.0

15.0 3379.7 3264.5

48 434.2 124.9 451.8 14924.5 3692.9 16.0

15.0 3370.8 3255.9

48.5 435.3 125.3 453.0 15141.9 3755.4 16.1

15.0 3362.1 3247.5

49 436.4 125.7 454.2 15359.8 3818.2 16.1

15.0 3353.5 3239.3

49.5 437.5 126.1 455.3 15578.3 3881.1 16.1

15.0 3345.2 3231.2

50 438.6 126.5 456.4 15797.3 3944.2 16.1

15.0 3337.0 3223.3

113

Ty αaircraft αeff CL q Lw Lwx Lwy CD D Dx Dy

0.0 1.4 3.0 0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00.0 1.3 3.0 0.3 0.2 8.9 0.0 8.9 1.8 63.8 0.0 63.80.0 1.3 3.0 0.3 0.6 35.5 0.0 35.5 2.3 321.5 0.1 321.50.0 1.3 3.0 0.3 1.4 79.8 0.0 79.8 2.3 716.7 0.3 716.70.0 1.3 3.0 0.3 2.4 142.0 0.1 142.0 0.5 278.4 0.1 278.40.0 1.3 3.0 0.3 3.8 221.9 0.1 221.9 0.0 2.7 0.0 2.70.0 1.3 3.0 0.3 5.5 319.6 0.1 319.6 0.0 3.8 0.0 3.80.0 1.3 3.0 0.3 7.5 435.2 0.2 435.2 0.0 5.2 0.0 5.20.0 1.3 3.0 0.3 9.8 568.8 0.3 568.8 0.0 6.8 0.0 6.80.0 1.3 3.0 0.3 12.4 720.2 0.3 720.2 0.0 8.7 0.0 8.70.0 1.3 3.0 0.3 15.3 889.7 0.4 889.7 0.0 10.7 0.0 10.70.0 1.3 3.0 0.3 18.5 1077.3 0.5 1077.3 0.0 12.9 0.0 12.90.0 1.3 3.0 0.3 22.1 1283.0 0.6 1283.0 0.0 15.4 0.0 15.40.0 1.3 3.0 0.3 25.9 1507.0 0.7 1507.0 0.0 18.1 0.0 18.10.0 1.3 3.0 0.3 30.1 1749.4 0.8 1749.4 0.0 21.0 0.0 21.0370.5 4.3 6.0 0.5 34.6 4021.3 1.8 4021.3 0.0 96.6 0.0 96.6740.0 7.3 9.0 0.8 39.4 6879.5 3.0 6879.5 0.0 248.0 0.1 248.01107.4 10.3 12.0 1.0 44.7 10392.1 4.6 10392.1 0.0 499.5 0.2 499.51471.8 12.6 14.3 1.2 50.3 13954.5 175.5 13953.4 0.1 799.5 10.1 799.41810.8 13.4 15.1 1.3 56.3 16462.1 848.7 16440.2 0.1 993.7 51.2 992.31720.9 10.3 11.9 1.0 62.4 14433.8 1531.8 14352.2 0.0 689.9 73.2 686.01651.3 8.1 9.8 0.8 67.7 12847.9 1842.4 12715.1 0.0 503.3 72.2 498.11594.7 6.7 8.3 0.7 72.6 11745.8 1976.1 11578.3 0.0 392.3 66.0 386.71547.0 5.7 7.4 0.6 77.2 11032.3 2039.6 10842.1 0.0 325.7 60.2 320.11505.5 5.0 6.7 0.6 81.5 10587.2 2079.1 10381.0 0.0 284.1 55.8 278.51468.7 4.5 6.2 0.5 85.6 10311.3 2111.2 10092.8 0.0 256.5 52.5 251.01435.7 4.2 5.8 0.5 89.6 10136.5 2140.6 9907.9 0.0 236.8 50.0 231.51405.8 3.9 5.5 0.5 93.5 10020.5 2168.1 9783.1 0.0 221.9 48.0 216.61378.4 3.6 5.3 0.5 97.2 9938.4 2193.8 9693.3 0.0 209.8 46.3 204.71353.2 3.4 5.0 0.4 100.9 9876.5 2217.6 9624.3 0.0 199.7 44.8 194.61329.9 3.2 4.9 0.4 104.4 9827.0 2239.3 9568.5 0.0 191.0 43.5 186.01308.3 3.0 4.7 0.4 107.9 9785.8 2259.2 9521.5 0.0 183.3 42.3 178.31288.2 2.9 4.5 0.4 111.3 9750.5 2277.4 9480.8 0.0 176.4 41.2 171.51269.4 2.7 4.4 0.4 114.6 9719.6 2294.1 9445.0 0.0 170.2 40.2 165.41251.8 2.6 4.2 0.4 117.9 9692.3 2309.4 9413.1 0.0 164.6 39.2 159.91235.2 2.5 4.1 0.4 121.1 9667.8 2323.5 9384.5 0.0 159.5 38.3 154.81219.6 2.3 4.0 0.3 124.2 9645.8 2336.6 9358.5 0.0 154.7 37.5 150.11204.8 2.2 3.9 0.3 127.2 9625.8 2348.8 9334.8 0.0 150.4 36.7 145.91190.9 2.1 3.8 0.3 130.2 9607.5 2360.1 9313.2 0.0 146.4 36.0 141.91177.7 2.1 3.7 0.3 133.2 9590.9 2370.7 9293.3 0.0 142.7 35.3 138.2Ty αaircraft αeff CL q Lw Lwx Lwy CD D Dx Dy

114

1165.1 2.0 3.6 0.3 136.0 9575.5 2380.5 9274.9 0.0 139.2 34.6 134.81153.2 1.9 3.5 0.3 138.9 9561.4 2389.8 9257.9 0.0 135.9 34.0 131.61141.8 1.8 3.5 0.3 141.7 9548.3 2398.6 9242.1 0.0 132.9 33.4 128.71131.0 1.7 3.4 0.3 144.4 9536.1 2406.8 9227.4 0.0 130.1 32.8 125.91120.6 1.7 3.3 0.3 147.1 9524.8 2414.5 9213.7 0.0 127.4 32.3 123.21110.7 1.6 3.3 0.3 149.7 9514.2 2421.9 9200.8 0.0 124.9 31.8 120.81101.3 1.6 3.2 0.3 152.3 9504.3 2428.8 9188.7 0.0 122.5 31.3 118.41092.2 1.5 3.2 0.3 154.8 9495.1 2435.4 9177.4 0.0 120.3 30.8 116.21083.5 1.4 3.1 0.3 157.3 9486.3 2441.7 9166.7 0.0 118.1 30.4 114.11075.1 1.4 3.1 0.3 159.8 9478.1 2447.7 9156.6 0.0 116.1 30.0 112.21067.0 1.3 3.0 0.3 162.2 9470.4 2453.3 9147.1 0.0 114.2 29.6 110.31059.3 1.3 3.0 0.3 164.6 9463.1 2458.8 9138.1 0.0 112.4 29.2 108.51051.8 1.3 2.9 0.2 166.9 9456.2 2463.9 9129.5 0.0 110.6 28.8 106.81044.6 1.2 2.9 0.2 169.2 9449.6 2468.9 9121.4 0.0 109.0 28.5 105.21037.7 1.2 2.8 0.2 171.5 9443.4 2473.6 9113.7 0.0 107.4 28.1 103.61031.0 1.1 2.8 0.2 173.7 9437.5 2478.1 9106.3 0.0 105.9 27.8 102.11024.5 1.1 2.8 0.2 175.9 9431.8 2482.5 9099.3 0.0 104.4 27.5 100.71018.3 1.1 2.7 0.2 178.1 9426.5 2486.6 9092.6 0.0 103.0 27.2 99.41012.2 1.0 2.7 0.2 180.2 9421.3 2490.7 9086.2 0.0 101.7 26.9 98.11006.4 1.0 2.7 0.2 182.3 9416.5 2494.5 9080.0 0.0 100.4 26.6 96.81000.7 1.0 2.6 0.2 184.4 9411.8 2498.2 9074.2 0.0 99.2 26.3 95.6995.2 0.9 2.6 0.2 186.5 9407.3 2501.8 9068.6 0.0 98.0 26.1 94.5989.9 0.9 2.6 0.2 188.5 9403.0 2505.2 9063.2 0.0 96.9 25.8 93.4984.8 0.9 2.5 0.2 190.4 9398.9 2508.5 9058.0 0.0 95.8 25.6 92.3979.7 0.9 2.5 0.2 192.4 9395.0 2511.7 9053.0 0.0 94.7 25.3 91.3974.9 0.8 2.5 0.2 194.3 9391.2 2514.8 9048.2 0.0 93.7 25.1 90.3970.2 0.8 2.5 0.2 196.2 9387.6 2517.8 9043.6 0.0 92.7 24.9 89.4965.6 0.8 2.4 0.2 198.1 9384.1 2520.7 9039.2 0.0 91.8 24.7 88.4961.1 0.8 2.4 0.2 199.9 9380.7 2523.4 9034.9 0.0 90.9 24.5 87.5956.8 0.7 2.4 0.2 201.7 9377.5 2526.1 9030.8 0.0 90.0 24.2 86.7952.6 0.7 2.4 0.2 203.5 9374.4 2528.7 9026.8 0.0 89.2 24.1 85.9948.4 0.7 2.4 0.2 205.3 9371.3 2531.3 9023.0 0.0 88.3 23.9 85.1944.4 0.7 2.3 0.2 207.1 9368.4 2533.7 9019.3 0.0 87.5 23.7 84.3940.5 0.7 2.3 0.2 208.8 9365.6 2536.1 9015.7 0.0 86.8 23.5 83.5936.7 0.6 2.3 0.2 210.5 9362.9 2538.4 9012.3 0.0 86.0 23.3 82.8933.0 0.6 2.3 0.2 212.1 9360.3 2540.6 9008.9 0.0 85.3 23.1 82.1929.4 0.6 2.3 0.2 213.8 9357.8 2542.8 9005.7 0.0 84.6 23.0 81.4925.9 0.6 2.2 0.2 215.4 9355.3 2544.9 9002.5 0.0 83.9 22.8 80.7922.5 0.6 2.2 0.2 217.0 9352.9 2546.9 8999.5 0.0 83.2 22.7 80.1919.1 0.5 2.2 0.2 218.6 9350.6 2548.9 8996.5 0.0 82.6 22.5 79.5Ty αaircraft αeff CL q Lw Lwx Lwy CD D Dx Dy

915.9 0.5 2.2 0.2 220.2 9348.4 2550.9 8993.6 0.0 82.0 22.4 78.9

115

912.7 0.5 2.2 0.2 221.7 9346.2 2552.7 8990.8 0.0 81.4 22.2 78.3909.5 0.5 2.2 0.2 223.2 9344.1 2554.6 8988.1 0.0 80.8 22.1 77.7906.5 0.5 2.1 0.2 224.8 9342.1 2556.4 8985.5 0.0 80.2 21.9 77.1903.5 0.5 2.1 0.2 226.2 9340.1 2558.1 8983.0 0.0 79.6 21.8 76.6900.6 0.5 2.1 0.2 227.7 9338.2 2559.8 8980.5 0.0 79.1 21.7 76.1897.8 0.4 2.1 0.2 229.1 9336.3 2561.4 8978.1 0.0 78.6 21.6 75.5895.0 0.4 2.1 0.2 230.6 9334.5 2563.0 8975.7 0.0 78.0 21.4 75.0892.2 0.4 2.1 0.2 232.0 9332.7 2564.6 8973.5 0.0 77.5 21.3 74.6889.6 0.4 2.1 0.2 233.4 9331.0 2566.1 8971.2 0.0 77.0 21.2 74.1887.0 0.4 2.0 0.2 234.8 9329.3 2567.6 8969.1 0.0 76.6 21.1 73.6884.4 0.4 2.0 0.2 236.1 9327.7 2569.1 8967.0 0.0 76.1 21.0 73.2881.9 0.4 2.0 0.2 237.4 9326.1 2570.5 8964.9 0.0 75.6 20.8 72.7879.5 0.4 2.0 0.2 238.8 9324.6 2571.9 8962.9 0.0 75.2 20.7 72.3877.1 0.3 2.0 0.2 240.1 9323.1 2573.2 8961.0 0.0 74.8 20.6 71.9874.7 0.3 2.0 0.2 241.4 9321.6 2574.5 8959.1 0.0 74.3 20.5 71.5872.4 0.3 2.0 0.2 242.6 9320.2 2575.8 8957.2 0.0 73.9 20.4 71.1870.2 0.3 2.0 0.2 243.9 9318.8 2577.1 8955.4 0.0 73.5 20.3 70.7868.0 0.3 2.0 0.2 245.1 9317.4 2578.3 8953.6 0.0 73.1 20.2 70.3865.8 0.3 1.9 0.2 246.4 9316.1 2579.5 8951.9 0.0 72.7 20.1 69.9863.7 0.3 1.9 0.2 247.6 9314.8 2580.7 8950.2 0.0 72.4 20.1 69.5

116

Ff ax ay

380.8 22.7 0.0380.4 22.7 0.0379.4 22.7 0.0377.6 22.7 0.0375.1 22.7 0.0371.9 22.7 0.0368.0 22.7 0.0363.4 22.7 0.0358.0 22.7 0.0352.0 22.8 0.0345.2 22.8 0.0337.7 22.8 0.0329.5 22.8 0.0320.5 22.9 0.0310.8 22.9 0.0219.9 23.2 0.0105.6 23.4 0.0-34.9 23.8 5.0-177.4 23.4 17.3-277.7 20.8 26.2-196.6 17.0 19.8-133.1 14.8 14.7-89.0 13.5 11.0-60.5 12.6 8.6-42.7 11.9 7.1-31.7 11.3 6.1-24.7 10.8 5.4-20.0 10.3 4.9-16.7 9.9 4.6-14.3 9.5 4.3-12.3 9.1 4.0-10.6 8.8 3.8-9.2 8.4 3.6-8.0 8.2 3.5-6.9 7.9 3.3-5.9 7.6 3.2-5.0 7.4 3.1-4.2 7.2 3.0-3.5 6.9 2.8-2.8 6.7 2.7Ff ax ay

117

-2.2 6.5 2.7-1.7 6.4 2.6-1.1 6.2 2.5-0.6 6.0 2.4-0.2 5.9 2.30.2 5.7 2.30.6 5.6 2.21.0 5.4 2.11.3 5.3 2.11.7 5.2 2.02.0 5.1 2.02.3 4.9 1.92.6 4.8 1.92.8 4.7 1.83.1 4.6 1.83.3 4.5 1.73.5 4.4 1.73.7 4.3 1.73.9 4.2 1.64.1 4.2 1.64.3 4.1 1.64.5 4.0 1.54.7 3.9 1.54.8 3.8 1.55.0 3.8 1.45.2 3.7 1.45.3 3.6 1.45.4 3.6 1.35.6 3.5 1.35.7 3.4 1.35.8 3.4 1.35.9 3.3 1.26.1 3.3 1.26.2 3.2 1.26.3 3.1 1.26.4 3.1 1.16.5 3.0 1.16.6 3.0 1.16.7 2.9 1.16.8 2.9 1.1Ff ax ay

6.9 2.8 1.17.0 2.8 1.0

118

7.0 2.7 1.07.1 2.7 1.07.2 2.7 1.07.3 2.6 1.07.3 2.6 0.97.4 2.5 0.97.5 2.5 0.97.6 2.5 0.97.6 2.4 0.97.7 2.4 0.97.8 2.3 0.97.8 2.3 0.87.9 2.3 0.87.9 2.2 0.88.0 2.2 0.88.0 2.2 0.88.1 2.1 0.88.2 2.1 0.88.2 2.1 0.8

119

Appendix J - LandingLanding Calculations

120

Landing PerformanceWlanding (lbf) 7272 γapproach (rads) 0.052359878 Dbraking

(lbf)1385.086

W/S (lbf/ft2) 32.083 RTR (ft) 4391.654326 LTD (lbf) 402.671Vstall (ft/sec) 133.264 HTR (ft) 6.018609624 Ff(lbf) 4121.701523V50 feet (ft/sec) 173.244 CL TD 1.216 ax (ft/sec2) -26.166VTD (ft/sec) 153.254 AReff 26.101 Sbraking (ft) 897.602q50 feet (lbf/ft2) 35.671 CDo 0.0250 Sapproach (ft) 839.215qTD (lbf/ft2) 27.914 CDi, braking 0.0212 Sflare (ft) 229.841μL Dry 0.6 CDo flaps 0.08300 SFR (ft) 459.762μL Wet 0.4 CDo LG 0.08969 SL total (ft) 2426.420

121

Appendix K – Enhanced LiftSpreadsheet of enhanced lift calculations

122

Trailing Edge Calculations Origin Leading Edge Device Origin

λ 0.35 Type Fixed Slot C1 0.48 Fig 9.8 ΔClmax 0.2 Table 9.1

AR 8.00 ΔCLmax

0.09791349

Comparative Value 2.703

Therefoe High AR Wing

ΛLE 0 TOTAL

CLmax/Clmax 0.9 Fig 9.9 ΔCLmax 1.095Clmax 1.52 CLmax 1.368 Eq 9.5Δy/c (%) 8.5 Fig 9.10Δy 0.487 Δ⍺CLmax 1.8 Fig 9.11

⍺s (deg) 16.13 Eq 9.6δflap (deg) 40 δf 10 40 50

Δ⍺s (deg) -2.8 Fig 9.18K1 (Fig 9.20) 2 2 2

(⍺s) flapped (deg) 13.33 Eq 9.10

k2 (Fig. 9.21) 0.0125 0.0875 0.12

c (ft) 5.73 ΔCD0

0.01223919

0.08567431

0.11749619

cf (ft) 2 cf/c 0.349 t/c 12% dCl / dδf (rad)-1 5.35 Fig 9.4(Clmax)flapped 3.74 ΔClmax 2.22 Eq 9.11bf (ft) 8

SWF

110.970259

SW 226.67 KΔ 0.919 Eq 9.12

ΔCLmax 0.997 Eq 9.9

123

Appendix L – Refined WeightRefined weight analysis

125

Load Type Load x/L Start x/L end x/L avg MFuselage 1855.50 0% 100% 0.5 927.751581 Aircraft CG 12.3Wing 924.54 30% 55% 0.425 392.930178Main LG 482.64 45% 45% 0.45 217.188Nose LG 60.00 5% 5% 0.05 3Engines 700.00 30% 45% 0.375 262.5 b (ft) 42.58other 1428.00 0% 100% 0.5 714 ʎ 0.35Fuel Fuselage 0.00 0% 100% 0.5 0 WTO 9520Fuel Wing 2398.23 35% 55% 0.45 1079.20206 AR 8.00Payload 1600.00 10% 60% 0.35 560 Croot (ft) 7.89

H tail 509.0866 80% 100% 0.9 458.177983 Ctip (ft) 2.76

V tail 265.6097 80% 100% 0.9 239.048725 Lfuse (ft) 30

Tail Lift -1339.94 90% 90% 0.9 -1205.94341 xacH (ft) 21.77

xacW (ft) 13.5X_cg_placement 12.3SM 21% Stable x/L 0.41062475

X_cg 12.3187426 LT -1340

LW 10860

Aircraft Data

Lift Calculations

126

Appendix M – Wing LoadingExcel sheet used to determine the wing loading of the aircraft.

127

128

V(shear)M

(mom

ent)

b (ft)

42.58station

y (ft)

y/(b/2)Lift

/unit spanLift/station

Lift/unit spanLift

/stationAverage

FuelEngine &

LGStructure

Total

ʎ0.35

10

0324.710

377.8173455.256

36608.736

WTO

95200.532

0.5320.025

345.466395.684

370.575-168.27282

-19.976182.3267

AR8.00

21.065

0.05324.304

365.5383272.929

33027.360Croot (ft

)7.89

1.5971.597

0.075344.600

382.612363.606

-157.42688-19.316

186.8633

Ctip ( ft)

2.763

2.1290.1

323.082353.259

3086.06629642.502

Lfuse (ft)

302.661

2.6610.125

342.861369.540

356.200-146.942239

-18.656190.6021

xacH (ft)

21.774

3.1940.15

321.036340.980

2895.46326458.567

xacW (ft)

13.53.726

3.7260.175

340.235356.467

348.351-136.818898

-17.996193.5365

delta y (ft)

1.0655

4.2580.2

318.149328.701

2701.92723479.106

delta y /2 (ft)

0.532294564.791

4.7910.225

336.702343.395

340.049-127.056856

-17.336195.6559

65.323

0.25314.399

316.4222506.271

22591.8075.855

5.8550.275

332.233330.323

331.278-117.656115

-16.676196.9460

LT-1339.94

76.388

0.3309.753

304.1432309.325

18143.495LW

108606.920

6.9200.325

326.789317.251

322.020-108.616673

-16.016197.3873

87.452

0.35304.172

291.8642111.938

15790.0817.984

7.9840.375

320.321304.179

312.250-99.9385308

-591.32-15.356

-394.36499

8.5170.4

297.601279.585

2506.30313331.817

9.0499.049

0.425312.764

291.107301.935

-14.696287.2391

109.581

0.45289.975

267.3062219.063

10816.53010.114

10.1140.475

304.037278.035

291.036-14.036

276.999611

10.6460.5

281.207255.026

1942.0648601.585

11.17811.178

0.525294.036

264.962279.499

-13.376266.1228

1211.710

0.55271.186

242.7471675.941

6675.74012.243

12.2430.575

282.624251.890

267.257-12.716

254.540713

12.7750.6

259.768230.468

1421.4005027.043

13.30713.307

0.625269.621

238.818254.220

-12.056242.1631

1413.840

0.65246.758

218.1891179.237

3642.73714.372

14.3720.675

254.781225.746

240.264-11.396

228.867215

14.9040.7

231.889205.910

950.3702509.159

15.43715.437

0.725237.757

212.674225.215

-10.737214.4789

1615.969

0.75214.775

193.631735.891

1611.57116.501

16.5010.775

218.029199.602

208.815-10.077

198.738417

17.0330.8

194.826181.352

537.153933.937

17.56617.566

0.825194.755

186.529190.642

-9.417181.2253

1818.098

0.85171.052

169.073355.927

458.55518.630

18.6300.875

166.390173.457

169.923-8.757

161.166719

19.1630.9

141.538156.794

194.761165.427

19.69519.695

0.925129.309

160.385144.847

-8.097136.7505

2020.227

0.95101.391

144.51558.010

30.87920.759

20.7590.975

53.97076.925

65.447-7.437

58.010221

21.2921

00

Aircraft Data

Lift Calculations

EllipticalTrapezoidal

Appendix N – Structural Analysis Excel sheet used to determine the shear and moment forces for the fuselage.

129

130

Tail774.6963416

main

482.64nose gear

60.00Engine

700.00W

ing Lift Load

10860Tail Lift

Load-1340

Other

1428.00x/L

x (ft)

Wfuse (lbs)

Ww

ing (lbs)W

landing gear (lbs)W

engines (lbs)W

misc (lbs)

Wfuel (lbs)

Wpayload (lbs)

Wtail (lbs)

L wing (lbs)

L tail (lbs)Load (lbs)

V (lbs)M

(lb-ft)

0.0000

00

00

00

00

00

00

00.0499

1.49760

6060

00.050

1.592.775

71.400164.175

224.1750.426

0.1003

92.77571.400

164.175388.350

459.8200.150

4.592.775

71.400164.175

552.5251165.477

0.2006

92.77571.400

164.175716.701

2117.3970.250

7.592.775

71.400160.000

324.1751040.876

3435.5790.300

992.775

154.090233.333

71.400160.000

711.5991752.475

5530.5920.350

10.592.775

154.090233.333

71.400479.645

160.0001191.244

2943.7199052.737

0.40012

92.775154.090

233.33371.400

479.645160.000

1191.2444134.963

14361.7480.4499

13.497-10859.937

-10859.937-6724.974

19670.7590.450

13.592.775

154.09071.400

479.645160.000

957.911-5767.064

19654.4690.499

14.97482.640

482.640-5284.424

19560.7790.500

1592.775

154.09071.400

479.645160.000

957.911-4326.513

19488.6970.550

16.592.775

154.09071.400

479.645160.000

957.911-3368.602

13717.3610.600

1892.775

71.400160.000

324.175-3044.427

8907.5890.650

19.592.775

71.400160.000

324.175-2720.252

4584.0800.700

2192.775

71.400160.000

324.175-2396.077

746.8340.7257

21.76999981339.937

1339.937-1056.139

-1811.3300.750

22.592.775

71.400160.000

324.175-731.964

-1322.2530.800

2492.775

71.400193.674

357.849-374.115

-2151.8120.850

25.592.775

71.400193.674

357.849-16.266

-2444.5980.900

2792.775

71.400193.674

357.849341.584

-2200.6090.950

28.592.775

71.400193.674

357.849699.433

-1419.8471.000

3092.775

71.400164.175

863.608-247.567

Appendix O – Stability Analysis Longitudinal and Lateral directional excel sheets used for stability analysis.

14

131

xcg - xac wing -1.181257 ftmac 5.73 ftXeng 8 ft

AR 8L 0 degl 0.35Sr 226.67 ft2

b 42.58 ftz 0 ftCL cruise 0.26

h 5.25 ftw 5 ftVol of fuselage 396.03 ft3

CL a VT 0.028 per deg

lVT 10.27 ftSVT 65.79 ft2

lVT 0.4 deg

VVT 0.070005(1+ds/db)q/q 1.240081 Eq[11.42]v. tail effect 0.140763 Eq[11.40] stablefuse. effect -0.056009 Eq[11.44] unstablewing effect 0.000672 Eq[11.43] stable

Cnb 0.0854 stable

CL b -0.0854 stable

Input Parametersr 20 degb 11.5 degAsym. T 1219.635 lbsSref 226.67 ft2

b 42.58 ftCnb 0.0854diam eng 5 ftVTO 200 ft/s

r 0.076 lbm/ft3

r 0.002378 sl/ft3

1.2 VTO 240 ft/s0.2 VTO 40 ft/s

q 68.0 lbs/ft2

Deng 1602 lbs

CN R

Asy. Power 0.098554 [rad]-1 Eq[11.47]Cross Wind -0.04912 [rad]-1 Eq[11.50]

daoL/dr -0.48 Eq[11.51]

Cr/CVT 18 % Fig. 11.9

Calculations

Calculations

Vertical Tail Parameters:

Wing Geometric Data

Directional Stability Coefficient:

Rudder Sizing

Wing Parameters:

Fuselage Parameters:

132

CMo -0.091

iht 0

α CLairplane CMcg iht dletaE V (Knots)0 0.209 0.026 4.751 11.88 362.4

1 0.315 -0.007 6.033 15.08 295.32 0.420 -0.039 7.315 18.29 255.53 0.526 -0.072 8.597 21.49 228.34 0.632 -0.104 9.880 24.70 208.45 0.738 -0.137 11.162 27.91 192.86 0.843 -0.169 12.444 31.11 180.37 0.949 -0.202 13.727 34.32 170.08 1.055 -0.234 15.009 37.52 161.29 1.161 -0.267 16.291 40.73 153.7

10 1.266 -0.300 17.574 43.93 147.211 1.372 -0.332 18.856 47.14 141.412 1.478 -0.365 20.138 50.35 136.213 1.584 -0.397 21.421 53.55 131.614 1.690 -0.430 22.703 56.76 127.415 1.795 -0.462 23.985 59.96 123.616 1.901 -0.495 25.267 63.17 120.117 2.007 -0.527 26.550 66.37 116.918 2.113 -0.560 27.832 69.58 113.919 2.218 -0.593 29.114 72.79 111.220 2.324 -0.625 30.397 75.99 108.621 2.430 -0.658 31.679 79.20 106.222 2.536 -0.690 32.961 82.40 104.023 2.641 -0.723 34.244 85.61 101.924 2.747 -0.755 35.526 88.81 99.925 2.853 -0.788 36.808 92.02 98.126 2.959 -0.820 38.090 95.23 96.327 3.065 -0.853 39.373 98.43 94.628 3.170 -0.886 40.655 101.64 93.029 3.276 -0.918 41.937 104.84 91.530 3.382 -0.951 43.220 108.05 90.131 3.488 -0.983 44.502 111.26 88.732 3.593 -1.016 45.784 114.46 87.433 3.699 -1.048 47.067 117.67 86.134 3.805 -1.081 48.349 120.87 84.935 3.911 -1.113 49.631 124.08 83.836 4.016 -1.146 50.914 127.28 82.637 4.122 -1.179 52.196 130.49 81.638 4.228 -1.211 53.478 133.70 80.5

133

AR 8.0b (ft) 42.6 Xcg (ft) 13.5 αol -1.7λ 0.4 Xacwing(ft) 13.5 Cm -0.055

iwing 1.4 XacHT (ft) 22.8 CLα_wing 0.086

SHT (ft2) 126.1 Xbarcg 2.36 CLα_HT 0.066

Sref (ft2) 226.7 Xbaracwing 2.35 dCLair/dα 0.0654

mac (ft) 5.7 XbarHT 3.97 dCM/dα -0.0326

Vht 0.9 xbarnp 16.94266192

lht (ft) 9.3 S.M. 14.59

Vstall (knots) 82.67

r 0.44H 2.00m 0.09dε/dα 0.45

Stability ParametersPositionsAircraft Parameters

15

134

Appendix P – 3 view drawingThree view drawing for final aircraft design.

16

135

Final Report

Documents

Transcript of Final Report