Final Report

MAE 475
Flight Vehicle Design
Final Report
DESIGN OF A MULTI-ENGINE BUSINESS TURBOPROP AIRCRAFT
Submitted by:
The Left βrothers
Anthony Donzella
Justin Hruska
Wyatt Trevithick
Joseph Wong
Nels Lofgren
December 6th, 2016

i
Table of Contents
List of Symbols ...............................................................................................................................iv
1 Mission Summary................................................................................................................... 1
2 Comparative Aircraft .............................................................................................................. 1
2.1 Piper Cheyenne II XL ...................................................................................................... 2
2.2 Cessna 425 Corsair & Conquest 1.................................................................................... 3
2.3 Piper PA-42...................................................................................................................... 4
2.4 Piaggio Avanti Evo .......................................................................................................... 5
2.5 Beechcraft King Air c90GTx ........................................................................................... 6
3 Estimation of Gross Takeoff Weight ...................................................................................... 7
3.1 Mission Weight Estimates................................................................................................ 7
3.1.1 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 ............................................................................. 12
3.3 Recommendations .......................................................................................................... 14
4 Wing Loading and Performance ........................................................................................... 15
4.1 Performance Constraints ................................................................................................ 15
4.1.1 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
5 Wing Design ......................................................................................................................... 19
5.1 Comparative Study of Similar Aircraft .......................................................................... 19
5.2 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

ii
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................................................................................................................. 24
6 Layout and Design of Fuselage............................................................................................. 27
6.1 Design of Fuselage......................................................................................................... 27
6.2 Results and Spreadsheet Analysis.................................................................................. 29
6.3 Fuselage Layout ............................................................................................................. 30
7 Empennage Design ............................................................................................................... 31
7.1 Horizontal and Vertical Tail Design .............................................................................. 31
7.1.1 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................................................................................................................. 37
8 Engine Selection and Performance ....................................................................................... 38
8.1 Engine Selection............................................................................................................. 38
8.2 Performance ................................................................................................................... 42
9 Takeoff and Landing Performance ....................................................................................... 44
9.1 CDo Calculation .............................................................................................................. 44
9.2 Takeoff Performance...................................................................................................... 45
9.2.1 Thrust ...................................................................................................................... 46
9.2.2 Lift........................................................................................................................... 47
9.2.3 Drag......................................................................................................................... 47
9.3 Landing Performance ..................................................................................................... 53

iii
10 Enhanced Lift Devices.......................................................................................................... 55
10.1 Types of Flaps............................................................................................................. 55
10.2 Leading and Trailing Edge Flap Design ..................................................................... 58
10.3 Recommendations....................................................................................................... 63
11 Structural Design................................................................................................................... 63
11.1 Refined Wing Analysis............................................................................................... 63
11.2 Wing Load Analysis ................................................................................................... 65
11.3 Fuselage Load Analysis.............................................................................................. 69
11.4 Fuselage Design.......................................................................................................... 72
11.5 Recommendations....................................................................................................... 72
12 Stability and Control............................................................................................................. 73
12.1 Longitudinal Stability................................................................................................. 73
12.2 Lateral Stability .......................................................................................................... 78
12.3 Directional Stability.................................................................................................... 78
12.4 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

iv
List of Symbols
Symbol Description Units
a Acceleration ft/s2
Aprop Area of propeller ft2
a.c Aerodynamic center --
AR Aspect Ratio --
b Wing span ft
bf flap span
B 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 coefficient
CL 3D lift Coefficient
CLα Lift curve slope --
D Drag lbs
Dprop Diameter of propeller ft
e Oswald’s efficiency factor --
E Hold time hours
F Form factor --
Ff Friction force lb
ffn 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 ft
L Lift force lb
𝐿
𝐷 𝑛
Lift to drag ratio at phase n of flight --
LP Landing Parameter --
M Mach number --
MAC/m.a.c Mean aerodynamic chord ft
n Load factor --

v
Symbol Description Units
P Power HP
q Dynamic pressure lb/ft2
Q Interference factor --
r radius of fuselage ft.
R Range N.mi.
Re Reynolds number --
ROC Rate of Climb ft/min
s Structural factor --
Sref Planform area of wing ft2
Swet Wetted area of wing ft2
sfc Specific fuel consumption 𝑙𝑏𝑓/ℎ𝑟
ℎ𝑝
Sn Ground roll at takeoff or landing ft
T Thrust lbf
t/c Thickness ratio --
TOGW Takeoff gross weight lbs.
Tvto Thrust at takeoff lbf
Δt Change in time hours
Vn Velocity at n phase of flight fps
VT Vertical tail --
Wn Weight at n phase of flight lbs.
W/S Wing loading lbs/ft2
W/P Power loading lb/HP
Xac Aerodynamic center location ft
Xcg Center of gravity location ft
Δy 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/s
ρ Density sl/ft3
σTU Ultimate stress psi

1
1 Mission Summary
This 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 Requirements
Range (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 Aircraft
The 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.

2
2.1 Piper Cheyenne II XL
Table 2.1: Manufacturing Specifications
WTO (lbf) 9474
WP (lbf) 4053
WE (lbf) 5487
WL (lbf) 7600
Pmax (HP) 1240
Powerplant Make/Model
x2 Pratt and Whitney
(UACL) PT6A-135
VCruise (knts) 255
VMax (knts) 275
Range (N.M) 1175
Fuel Capacity (U.S. gal) 366
Table 2.2: Aircraft Geometry & Aerodynamic Data
SREF (ft2) 229
W/S (psf) 41.37
AR 7.95
Wing Sweep (°) 5
Tail Config. Conventional
Power Loading
(lbf/HP)
7.64
Structure Factor 0.58
Figure 2.1: Piper Cheyenne II XL

3
2.2 Cessna 425 Corsair & Conquest 1
WTO (lbf) 8600
WP (lbf) 3652
WE (lbf) 4948
WL (lbf) 8000
Pmax (HP) 1000
Powerplant Make/Model 2x P&W PT6A-112
VCruise (knts) 251
VMax (knts) 263
Range (N.M) 1576
SREF (ft2) 225
W/S (psf) 38.2
AR 8.60
Wing Sweep (°) 0
Power Loading
(lbf/HP)
8.60
Figure 2.2: Cessna 425 Corsair/Conquest 1

4
2.3 Piper PA-42
WTO (lbf) 11200
WP (lbf) 4811
WE (lbf) 6839
WL (lbf) 10330
Pmax (HP) 1440
Powerplant Make/Model x2 P&W PT6A-41
VCruise (knts) 282
VMax (knts) 314
Range (N.M) 2241
SREF (ft2) 293
W/S (psf) 38.23
AR 6.43
Wing Sweep (°) 5
Tail Config. T-Tail
Power Loading
(lbf/HP) 7.78
Figure 2.3: Piper PA-42

5
2.4 Piaggio Avanti Evo
WTO (lbf) 12100
WP (lbf) 2300
WE (lbf) 8375
WL (lbf) 11500
Pmax (HP) 1630
Powerplant Make/Model 2 P&W PT6A-66B
VCruise (knts) 366
VMax (knts) 402
Range (N.M) 1370
Table 2.8: Aircraft Geometry & Aerodynamic Specifications
SREF (ft2) 172.22
W/S (psf) 70.26
AR 11.96
Wing Sweep (°) 1
Tail Config. T-Tail
Power Loading
(lbf/HP) 7.42
Flap/Slat Config. Canards
Figure 2.4: Piaggio Avanti Evo

6
2.5 Beechcraft King Air c90GTx
WTO (lbf) 10485
WP (lbf) 2108
WE (lbf) 5804
WL (lbf) 9832
Pmax (HP) 1100
Powerplant Make/Model
2x Pratt & Whitney
Canada PT6A-135A
@ 550 shp each
VCruise (knts) 226
VMax (knts) 272
Range (N.M) 1260
Table 2.10: Aircraft Geometry & Aerodynamics Data
SREF (ft2) 295
W/S (psf) 35.54
AR 9.76
Wing Sweep (°) 5.69
Power Loading
(lbf/HP)
9.53
Flap/Slat Config.
Flaps on
Approach
Figure 2.5: Beechcraft King Air c90GTx

7
3 Estimation of Gross Takeoff Weight
The 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 Estimates
The 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.
E
TO
W
s
W
 (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.

8
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 &
y = 52,394,893.88x4
- 119,027,799.87x3
+ 101,440,529.18x2
- 38,384,237.49x + 5,442,456.24
5500
10500
15500
20500
25500
30500
35500
0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7
WTO(lbs)
Structure Factor
Iterated Takeoff Weight Piper Cheyenne
Piper Pa-42 King Air c90gtx
Cessna 425 Piaggio Avanti
Iterated Takeoff Weight Trendline

9
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
max
1
L
L
W
s
S C
 
 
 
 (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

10
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.
𝑊𝑎𝑓𝑡𝑒𝑟 𝑇𝑂 = 𝑊𝑇𝑂 ∙ 𝑓𝑓𝑇𝑂 (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.
𝑊𝐹 ,𝑇𝑂 = 𝑊𝑇𝑂 − 𝑊𝑎𝑓𝑡𝑒𝑟 𝑇𝑂 (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.
𝑊𝐴𝑓𝑡𝑒𝑟 𝑐𝑙𝑖𝑚𝑏 = 𝑊𝑎𝑓𝑡𝑒𝑟 𝑇𝑂 ∙ 𝑓𝑓𝑐𝑙𝑖𝑚𝑏 (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.
𝑊𝐹,𝑐𝑙𝑖𝑚𝑏 = 𝑊𝑎𝑓𝑡𝑒𝑟 𝑇𝑂 − 𝑊𝑎𝑓𝑡𝑒𝑟 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 𝑝𝑟𝑜𝑝 ∙
𝐿
𝐷 𝐴𝑐𝑡𝑢𝑎𝑙
∙
1
𝑠𝑓𝑐
(3.7)
In equation (3.7), 𝜂 𝑝𝑟𝑜𝑝 is the efficiency of the propeller,
𝐿
𝐷 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.
𝑊𝐹,𝑐𝑟𝑢𝑖𝑠𝑒 = (1 −
1
𝑒
𝑅
𝐵⁄
) ∙ 𝑊𝑠𝑡𝑎𝑟𝑡,𝑐𝑟𝑢𝑖𝑠𝑒 (3.8)
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

11
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.
𝑊𝑎𝑓𝑡𝑒𝑟 𝑐𝑟𝑢𝑖𝑠𝑒 = 𝑊𝑒𝑛𝑡𝑒𝑟 𝑐𝑟𝑢𝑖𝑠𝑒 − 𝑊𝐹,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.
𝑊𝑎𝑓𝑡𝑒𝑟 𝑑𝑒𝑠𝑐𝑒𝑛𝑡 = 𝑊𝑎𝑓𝑡𝑒𝑟 𝑐𝑟𝑢𝑖𝑠𝑒 ∙ 𝑓𝑓𝑑𝑒𝑠𝑐𝑒𝑛𝑡 (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.
𝑊𝐹,𝑑𝑒𝑠𝑐𝑒𝑛𝑡 = 𝑊𝑎𝑓𝑡𝑒𝑟 𝑐𝑟𝑢𝑖𝑠𝑒 − 𝑊𝑎𝑓𝑡𝑒𝑟 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.
𝑊𝐹 ,𝑅𝑒𝑠 =
𝑠𝑓𝑐∙𝛥𝑡
𝐿
𝐷⁄
𝑀𝑎𝑥
∙𝑊 𝑅𝑒𝑠 ∙𝑉 𝐿
𝐷 𝑀𝑎𝑥
550
(3.12)
In Equation 3.12, 𝑠𝑓𝑐 is the engine’s standard fuel consumption, 𝛥𝑡 is the time in reserve in hours,
𝐿
𝐷⁄
𝑀𝑎𝑥
is the maximum lift to drag ratio, 𝑊𝑅𝑒𝑠 is the weight entering the reserve, 𝑉𝐿
𝐷 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.
𝑊𝑎𝑓𝑡𝑒𝑟 𝑟𝑒𝑠 = 𝑊𝑎𝑓𝑡𝑒𝑟 𝑑𝑒𝑠𝑐𝑒𝑛𝑡 − 𝑊𝐹 ,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.
𝑊𝐹,𝐻𝑜𝑙𝑑 = (1 −
1
𝑒
𝐸
𝐵 𝑒𝑛𝑑
⁄
) ∙ 𝑊𝑒𝑛𝑡𝑒𝑟 ℎ𝑜𝑙𝑑 (3.14)
In Equation 3.14, 𝐸 is the time in hold in hours, 𝐵 𝑒𝑛𝑑 is the Breguet endurance factor, and
𝑊𝑒𝑛𝑡𝑒𝑟 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.
𝐵 𝑒𝑛𝑑 =
1
𝑠𝑓𝑐
∙
𝐿
𝐷 𝑚𝑎𝑥
∙
1
𝑉ℎ𝑜𝑙𝑑
(3.15)

12
In Equation 3.15, 𝑠𝑓𝑐 is the engine’s standard fuel consumption,
𝐿
𝐷 𝑚𝑎𝑥
is the maximum lift to drag
ratio, and 𝑉ℎ𝑜𝑙𝑑 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.
𝑊𝐹,𝑃𝑎𝑦𝑙𝑜𝑎𝑑 = 𝑊𝐹 + 𝑊𝑝𝑎𝑦𝑙𝑜𝑎𝑑 (3.16)
Now the weight available for the structure of the aircraft could be calculated, shown as Equation
3.17.
𝑊𝑎𝑣𝑎𝑖𝑙. = 𝑊𝑇𝑂 − 𝑊𝐹,𝑃𝑎𝑦𝑙𝑜𝑎 𝑑 (3.17)
Also the weight required to build the structure can be calculated using Equation 3.18.
𝑊𝑟𝑒𝑞. = 𝑊𝑇𝑂 ∙ 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 Analysis
This 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 3.1: 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.
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

13
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.
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.
5600
5800
6000
6200
6400
6600
6800
7000
7200
0.0170 0.0190 0.0210 0.0230 0.0250 0.0270
TOGW(lbs)
CDo
AR=5 AR=7 AR=9

14
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.
Figure 3.4: Varying Aspect Ratio and Drag Coefficient at a range of 1500 NM
3.3 Recommendations
With 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
find the gross takeoff weight available for the aircraft. The first step is to estimate an initial value
5800
6800
7800
8800
9800
10800
11800
0.0170 0.0190 0.0210 0.0230 0.0250 0.0270
TOGW(lbs)
CDo
AR=5 AR=7 AR=9
5800
10800
15800
20800
25800
30800
0.0170 0.0190 0.0210 0.0230 0.0250 0.0270
TOGW(lbs)
CDo
AR=5 AR=7 AR=9

15
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 Performance
This 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 Distance
One 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,
𝑇𝑉𝑇𝑂 = [
( 𝑆𝐻𝑃 ∗ 𝜂 𝑝)
𝑉𝑡𝑜
]∗ 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,
𝑉𝑇𝑂 = 1.2( 𝑉𝑠𝑡𝑎𝑙𝑙) (4.2)

16
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.= [
( 𝑊
𝑆⁄ )
( 𝑇
𝑊⁄ )
](
1
𝐶𝐿 𝑚𝑎𝑥
∗ 𝜎
) (4.3)
The resulting value is then substituted into the following relation for calculating takeoff distance,
𝑆 𝑇𝑂 = [20.9( 𝑇. 𝑂. 𝑃)] + 87 ∗ √ 𝑇. 𝑂. 𝑃. (
𝑇
𝑊
) (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 = (
𝑊
𝑆
) (
1
𝐶 𝐿 𝑚𝑎𝑥
∗ 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 = 118𝐿𝑃 + 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,
𝑉𝑠𝑒𝑐𝑙𝑖𝑚 𝑏
= 𝑉𝐿
𝐷⁄
𝑚𝑎𝑥
− 15 𝑘𝑛𝑡𝑠 (4.6)
And may then be used to calculate the adjusted single engine rate of climb, ROC, in units of feet
per minute using,

17
𝑅𝑂𝐶 = ( 𝑉𝑠 𝑒 𝑐𝑙𝑖𝑚𝑏
)[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 = 𝐷𝑖 + 𝐷0 (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 ∗ 𝐶 𝐷0
( 𝑊
𝑆⁄ )
(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(
𝑊
𝑆
) =
[(
𝑇
𝑊
− 𝐺) ± √(
𝑇
𝑊
− 𝐺)
2
− (
4𝐶 𝐷0
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 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.

18
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 =
1
𝜂 𝑝
( 𝐷 ∗ 𝑉𝑐𝑟𝑢𝑖𝑠𝑒) (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 (
𝜌 𝑎𝑐𝑡𝑢𝑎𝑙
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,
𝑃𝑠𝑒𝑐𝑙𝑖𝑚𝑏@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,
𝑇𝑟𝑒𝑞 = (
𝜂 𝑝 ∗ 𝑃𝑆𝐸𝑟𝑒𝑞,𝑐𝑙𝑖𝑚 𝑏@𝛤
𝑉𝑆𝐸𝑐𝑙𝑖𝑚 𝑏
)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.
4.2 Recommendations
Based on the calculations above, the design was determined to have design parameters consisting
of the values listed in Table 4.1.

19
Table 4.1: Key design parameters and ground roll
WTO (lbs) 9520 Preq cruise end (HP) 909
Sref (ft2) 226.67 Pinstall (HP) 2414
T/W 0.339 W/S 42
s 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 Design
This 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 Aircraft
In 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

20
5.2 Main Wing Design
5.2.1 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 data
Name NACA 63-212 Cdo 0.0035
Clmax 1.35 rle 0.0024
Cla 0.1096 Cl minD 0
a.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
refb AR S  (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
@0.35x c x
t
t c
c
 (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.

21
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.
cos( )eff LEM M  (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.
1
/
2
tan tan (1 )r
x c LE
cx
c b
  
      
(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 -4.81632341
ɅTE -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.
t
r
c
c
  (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 tips. This is

22
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.
1 2
3 1
oL
 


 
     
(5.6)
, ,( )L cruise L oL oLC C        (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.
max
0
L
stall L
L
C
C 
   (5.8)
max
1
2
stall
L
W
SV
C


(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.

23
Table 5.4: Table of important values displaying wing properties
Airfoil
NACA
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 0.35
Vstall
(ft/sec) 236.76
m.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.

24
Figure 5.5: 3D View of aircraft wing design
5.3 Drag Analysis
To 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 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,
V (ft/sec) 540.8
q (lb/ft^2) 155.8836531
Re 10276015.74
CF 0.002927452
Swet(ft2
) 462.270798
F 1.439534461
Q 1
Viscous Drag

25
21
2
 cruiseq V (5.10)
And the cruise Reynolds number using the kinematic viscosity, nu, was determined via,
•cruiseV MAC
Re =
ν
(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.
1.328
For Laminar, C =
Reg
fl
L
(5.12)
22.58 0.65
10
455
For Turbulent, C =
(log (Re )) (1 0.144 ) 
fl
x crM
(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,
(1.977 0.52 ) wet ref
t
S S
c
(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,
max
4
0.18 .28
/
0.6
1 100 1.34 (cos( ))
( )
 
                  
 
t c
m
t t
F M
x c c
c
(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, CDo, 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,
0 ,
 
   
 
wet
D w f total
ref
S
C C FQ
S
(5.16)
And the two induced drag coefficients may be calculated using the Munks relation,

26
2
( Re)
 L
di
C
C
A
(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,
 D refD C qS (5.18)
Table 5.6: Summary of Drag
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 Recommendations
After 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.
CDOWing 0.00859
Cdi(begin cruise) 0.00313
Cdi(end cruise) 0.00209
Cd,total 0.01381
Induced Drag(begin cruise) 110.745 lbf
Induced Drag(end cruise) 73.6997 lbf
Zero Lift Drag 303.675 lbf
Total Drag 488.12 lbf
Drag Summary

27
6 Layout and Design of Fuselage
With 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 Fuselage
In 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 − (
2𝑥
𝑙
)
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:

28
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 Effectiveness
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 Width 22.00 in
Seat Pitch 34.00 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.
Table 6.3: Fuel and Wing Volumetric Properties
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
Fuel Tank Type Fuselage Wing
Discrete 100% -
Bladder 83% 77%
Integral 93% 85%
Volume Effectiveness
Total Fuel used (lbs) 2398.227
Total Fuel required (gal) 357.944
Total Fuel required (ft3
) 47.850
Volume Required (ft3
) 56.295
Wing Volume (ft3
) 98.240

29
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 Analysis
To 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:
2.58 2 0.65
10
0.455
( )
log (Re ) (1 0.144 )
f
x
C x
M


(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:
( ) ( ) ( )fF x qP x C x (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:
0D
D
C
qS
 (6.4)
The result of this calculation is shown in Table 6.4.
Table 6.4: Drag Summary
Drag (lbs) 178.7
CD0 0.005056

30
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.
34.27”
16.55”
17.44”
7.92”

31
Figure 6.4: Isometric view of the seating arrangement and baggage compartment.
6.4 Recommendations
After 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 Design
This 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 Design
The 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 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.

32
Table 7.1: NACA 64-004 properties
Clmax 0.8
Clalpha(/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 ratios
ARVT 2.0
ARHT 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:
4 (1 )
tan( ) tan( )
(1 )
x LE
x
AR



   

(7.1)
The results of the calculations are shown below in Table 7.3.
Table 7.3: Horizontal-tail sweep angles
Sweep Angles
ΛLE (deg) 29.80
Λ1/4 (deg) 23.26
ΛTE (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 the
sweep angles throughout the vertical tail. The results of these calculations are shown below in
Table 7.4.

33
Table 7.4: Vertical-tail sweep angles
Sweep Angles
ΛLE (deg) 40.60
Λ1/4 (deg) 32.73
ΛTE (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:
,
2
(1 )
VT
r VT
VT
S
c
b 


(7.2)
,
2
(1 )
HT
r HT
HT
S
c
b 


(7.3)
t
r
c
c
  (7.4)
Where:
VT w
VT
VT
C b S
S
l
 (7.5)
HT w
HT
HT
C c S
S
l
 (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.

34
Table 7.5: Horizontal tail placement
lHT (ft) 20.55
HHT
(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 calculations
Sweep Angles Viscous Drag Calculations
ΛLE (deg) 29.80 Cf 0.002871 SHT (ft2) 126.10
Λ1/4 (deg) 23.26 RE 11609803 b (ft) 19.45
ΛTE (deg) 0.07 Swet (ft2) 254.543 cr (ft) 9.26
Λt/c max(deg) 18.99 F 1.3002 ct (ft) 3.70
Q 1 ARHT 3.00
CDo HT 0.0037 Xac HT (ft) 2.39
D (lbf) 148.1205 β 0.76
CLα 0.0589
m.a.c (ft) 6.88
Table 7.7: Vertical tail calculations
Sweep Angles Viscous Drag Calculations
ΛLE (deg) 40.60 Cf 0.003 SHT (ft2) 65.79
Λ1/4 (deg) 32.73 RE 10270618 b (ft) 11.47
ΛTE (deg) 0 Swet (ft2) 132.805 cr (ft) 8.19
Λt/c max(deg) 27.21 F 1.278 ct (ft) 3.28
Q 1 ARHT 2.00
CDo HT 0.0037 Xac HT (ft) 2.11
D (lbf) 77.460 β 0.80
CLα 0.0456
m.a.c (ft) 6.09
Figure 7.1: Front view of the horizontal tail

35
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

36
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

37
Figure 7.8: Right view of the horizontal tail
7.2 Drag Analysis
When 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 = 𝑞𝑆 𝑊 𝐶𝑓 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 0.00380
Vertical 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 Recommendations
Taking 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

38
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 Performance
The 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 Selection
In 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.

39
2
0.0125
100
Nacelle
ft
D q
HP
 
  
 
(8.1)
Table 8.1: Total drag summation
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 summation
With the total drag, the power required at cruise can be found using Equation 8.2.
, @25,000req d ft cruiseP TV DV  (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.
, @25,000
_ @25,000
req d ft
p
shp reqd ft
P
P
  (8.3)
Component D (lbs)
Wing 312.3
Fuselage 141.1
Horizontal Tail 148.1
Vertical Tail 77.5
Nacelle 29.4
Induced Wing 92.2
Total 800.6
ZeroLift
Component CD
Wing 0.008838
Fuselage 0.0039925
Horizontal Tail 0.003733
Vertical Tail 0.0037417
Nacelle 0.000835
Induced Wing 0.00261
Total 0.0237503
ZeroLift

40
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.
_ @
25,000
25,000
1
1
7.55
shp reqd SSL
ft
ft SSL
SSL
P

 


  
  
  
 
  
 
(8.4)
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.
@ @ limshp SSL p reqd c b
TO
P P
ROC
W
 
 (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.
limc b TOP ROC W   (8.6)
@ liminstall shp SSL c bP P P   (8.7)
The above calculations in Equations 8.6 and 8.7 are summarized in Table 8.3.
0
1000
2000
3000
4000
5000
6000
7000
8000
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
PshpreqdSSL(HP)
Altitude (ft)

41
Table 8.3: Summary of power requirements
Preqd 25,000 ft (HP) 883.66
Pshp reqd 25,000 ft (HP) 1039.60
Pshp SSL (HP) 2769.21
Preqd climb (HP) 2065.35
Pinstall (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-100
SFC at Full Power [lb/(HP*hr)] 0.61
Max Env. Diameter (in) 20.9
Max 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.

42
Table 8.5: Calculations at engine out conditions
ROC (FPM) 250
ηP 0.85
Pavail (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 Performance
Using 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:
avail reqdP P
ROC
W

 (8.8)
( )reqd Do Di ref crP C C qS V  (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 parameters
W (lbs) 9520
Sref (ft2) 226.67
E 0.85
AR 8
ηprop 0.85

43
Figure 8.4: Required shaft horsepower vs. Cruise velocity at sea level and altitudes
Figure 8.5: Rate of Climb vs. cruise velocity at sea level and 25000 ft
-1000
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
50 100 150 200 250 300 350
ROC(fpm)
Vcr (fps)
SSL 25000 ft

44
Figure 8.6: Single engine rate of climb vs. cruise velocity
8.3 Recommendations
It 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 Performance
The 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 Calculation
Throughout 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.
Do Do Dof DoW DoHT DoVT DoNACC C C C C C C      (9.1)
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
5000
50 100 150 200 250 300 350
ROC(fpm)
Vcr (fps)
SSL 25000 ft

45
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 9.2: Take-off Zero Lift Drag Coefficient
CDof 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.
9.2 Takeoff Performance
Once 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.

46
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.
2/3
2static shp static diskT P A     (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.
shp pP
T
V

  (9.3)
cosxT T  (9.4)
sinyT T  (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
2 1 1y y y
V V a t   (9.6)
2 1 1x x x
V V a t   (9.7)
2 2
2 2x y
V V V  (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
 x x x x f
g
a T L D F
W
    (9.9)
 y y y y
g
a T L D W
W
    (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.

47
( )f spoilerF L K W  (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.
L refL C qS (9.12)
21
2
q V  (9.13)
L L effC C 
 (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.
0Leff w flapsi          (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.
1
tan y
x
V
V
   
  
 
(9.16)
sinxL L  (9.17)
cosyL L  (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.

48
0 0 0i Flaps GearD D D D DC C C C C    (9.19)
Equation 9.20 can be used to find the change in the coefficient of drag when the landing gear are
extended.
0
0.8
0.0032Gear
TO
D
ref
W
C
S
  (9.20)
Equation 9.21 is used to find the induced drag.
2
Rei
L
D
C
C
A
 (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
D refD C qS (9.22)
sinxD D  (9.23)
cosyD D  (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.
2 2
2 1
2 1
12
x x
x x
x
V V
s s
a

  (9.25)
2 2
2 1
2 1
12
y y
y y
y
V V
s s
a

  (9.26)
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 parameters
WTO 9520
Tstatic (lbs) 7079.2
W/S 42.0
Sx to clear obstacle (ft) 1373.4
Sx ground roll (ft) 1026.1

49
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 takeoff
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.
Figure 9.1: 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.
Velocity (ft/s) Thurst (lbs)
0 6505.1
83.39 6505.1
176.8 6505.1
0.0
1000.0
2000.0
3000.0
4000.0
5000.0
6000.0
7000.0
8000.0
0.0 100.0 200.0 300.0 400.0 500.0
Thrust(lbs)
Airspeed (fps)

50
Figure 9.2: 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.
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
900.0
1000.0
0.0 1000.0 2000.0 3000.0 4000.0 5000.0 6000.0
YPosition(ft)
X position (ft)

51
Figure 9.3: 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.
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
0 10 20 30 40 50 60
Angle(deg)
Time (sec)
Pitch Angle
Angle of Attack
Flight Path Angle

52
Figure 9.4: 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.
Figure 9.5. Velocity of aircraft during takeoff with respect to time.
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0 10 20 30 40 50 60
Acceleration(ft/sec2)
Time (sec)
X Acceleration
Y Acceleration
0.0
50.0
100.0
150.0
200.0
250.0
300.0
350.0
400.0
450.0
500.0
0 10 20 30 40 50 60
Velocity(ft/sec)
Time (sec)

53
9.3 Landing Performance
In 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 =
𝐻 𝑇𝑅 − 50
tan 𝛾𝑎𝑝𝑝𝑟𝑜𝑎𝑐ℎ
(9.27)
In order to deduce the value for HTR, one must first calculate the radius of the transition via,
𝑅 𝑇𝑅 =
(1.23𝑉𝑠)2
0.19𝑔
(9.28)
And with this in hand, the following expression may be used,
𝐻 𝑇𝑅
= 𝑅 𝑇𝑅(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
= 𝑅 𝑇𝑅 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,
𝑠 𝐹𝑅 = 3𝑉𝑇𝐷 (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 Vfinal 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.

54
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
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,
∆𝐶 𝐷0 𝐿𝐺
= 𝑓𝐿𝐺
𝐴 𝐿𝐺
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,
𝐹𝑓 = 𝜇( 𝑊𝑇𝑂 − 𝐿 𝐺 ) (9.34)
Table 9.5: Additional Parameters
Table 9.5 shows the relevant terms discussed above.
Progressing onward to the equations of motion,
𝑎 𝑥 =
∑ 𝐹𝑜𝑟𝑐𝑒𝑠
𝑀𝑎𝑠𝑠
(9.35)
𝑠 𝑥 =
(𝑉𝑥1
2
− 𝑉𝑥0
2
)
2𝑎 𝑥
(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 Distance
μL Dry 0.6
μL Wet 0.4
CDo flaps 0.0830
CDo LG 0.0215
Sbraking (ft) 965.620
Sapproach (ft) 827.103
Sflare (ft) 254.081
SFR (ft) 483.398
SL total (ft) 2530.203

55
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.
9.4 Recommendations
The 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 10.6: 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,

56
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.
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 10.7: 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 10.8: 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

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