This document provides specifications and calculations for an aircraft design. It estimates weights, wing loading, thrust-to-weight ratios, center of gravity locations, and landing gear specifications. Gross weight is estimated to be 295,660 lbs. Minimum wing loading is 38,977 lbs/ft^2. Maximum thrust-to-weight ratio is 0.3143. Preliminary center of gravity is at 50.175 ft. Secondary estimates incorporate wings and tails to obtain a center of gravity of 50.889 ft. Landing gear and wing placement locations are also calculated.

1. 1
Appendix A
Table of Contents
Specifications ..................................................................................................................... 1
Gross Weight Calculations ................................................................................................... 2
Wing Loading .................................................................................................................... 4
Cruise wing loading is least value ......................................................................................... 5
Thrust to Weight ................................................................................................................ 6
Mean aerodynamic chord ..................................................................................................... 7
1st CG Estimate ................................................................................................................. 8
2nd CG Estimate (Wing Addition) ........................................................................................ 8
Tail Addition ..................................................................................................................... 9
2nd Wing Placement and Landing Gear Specifications ............................................................ 12
Better Weight Estimates ..................................................................................................... 13
Convergence of Weight Estimates ....................................................................................... 16
Second Performance Analysis ............................................................................................. 18
Time calculations .............................................................................................................. 23
Specifications
clc,clear
% Passengers
% 10 family members (200 lbs.)
% 2 pilots (180 lbs.)
% 1 Flight attendant (180 lbs.)
% Baggage per crew (20 lbs.)
% Baggage per passenger (50 lbs.)
% Total Payload Weight
Wp = 10*200 + 20*3 + 10*50
% Total Crew Weight
Wc = 3*180
% Cruise Specifications
Vcruise = .75 * 659.8 * 5280 / 3600; % ft/s
Hcruise = 40000; % Altitude (ft)
% Stall Specifications
Vstall = 90 * 5280 / 3600; % ft/s
% Range Specifications (PHL to Bankok)
R = 8721 * 5280; % ft
% Loiter Specifications
Vloiter = .6 * 678.1 * 5280 / 3600; % ft/s
Hloiter = 30000; % ft
E = 1800; % seconds
% Rate of Climb Specifications

2. Appendix A
2
RC = 1500 / 60; % ft/s
% POWER PLANT
% More than 1 Turbofan
% MATERIAL SPECIFICATIONS
% Composite Material
% Load Limit Factor Sepcification
n = 4.0;
% Take Off and Landing Distance Specification
% s_T corresponds to Take-Off
% s_L corresponds to Landing
sgT = 6000; % ft
saT = 50; % ft
sgL = 4000; % ft
saL = 50; % ft
% Densities
rho40 = .00058727; % slugs/ft3
rho30 = .00089068; % slugs/ft3
rhoS = .0023769; % slugs/ft3
Wp =
2560
Wc =
540
Gross Weight Calculations
% Jet specific fuel consumptions (sfc) with respect to the cruise and
% loiter mission sections.
% Values are derived form Table 3.3 (Raymer) for high-bypass turbofans
% then converted to from lb/hr/lb to lb/s/lb
Ctcruise = .5/3600; % lb/s
Ctloiter = .4/3600; % lb/s
% Empy weight to gross weight ratio assumed from figure 8.1 (Anderson) for
% an approximate gross weight estimate according to previously designed
% aircraft depending upon their missions. NOTE: all ratios below are
% derived from historical data except for empty-gross.
WeW0 = .45;
W1W0 = .97;
W2W1 = .985;
W5W4 = .995;

3. Appendix A
3
% B-52 Bomber specificaitons, desired LDmax is 21 while in the loiter
% phase. The loiter phase will see the maximum lift to drag ratio while
% the cruise mission segment will see a slight reduction in the LD
% ratio according to page 22 (Raymer)
LDmaxL = 21;
LDmaxC = (.866).*LDmaxL;
% Cruise mission objective is for maximum range while loiter phase requires
% flying for endurance or specified time.
W3W2 = 1./(exp((R.*Ctcruise)./(Vcruise.*LDmaxC)))
W4W3 = 1./(exp((E.*Ctloiter)./LDmaxL))
W5W0 = W1W0.*W2W1.*W3W2.*W4W3.*W5W4
WfW0 = 1.06.*(1 - W5W0)
denom = 1- WfW0 - WeW0;
% Gross, Fuel and Empty Weights, Fcap = Fuel Capacity
W0 = (Wp + Wc)./denom %lbs
Wf = W0.*WfW0 %lbs
We = .45*W0 %lbs
Fcap = (Wf./5.64)*0.133681 %ft^3
W3W2 =
0.6160
W4W3 =
0.9905
W5W0 =
0.5800
WfW0 =
0.4451
W0 =
2.9566e+04
Wf =
1.3161e+04

4. Appendix A
4
We =
1.3305e+04
Fcap =
311.9510
Wing Loading
% Wing loading calculations for various mission segments of the flight. The
% The minimum wing loading will be selected.
% Take Off (Stall Velocity)
CL_airfoil = 1.6;
CL_highlift = .9;
CL_max = (CL_airfoil+CL_highlift)*.9
q = (0.5).*rhoS.*(Vstall.^2);
W1S = q.*CL_max
% Landing
g = 32.2;
Radius2 = ((1.23*Vstall)^2)/(.2*32.2);
hf = Radius2*(1-cosd(3));
sa2 = (50 -hf)/tand(3);
sf2 = Radius2*sind(3);
j = 1.15;
N = 3;
Ur = 0.4;
sg2 = sgL - sa2 - sf2;
A = j.*N.*sqrt(2./(rhoS.*CL_max));
B = (j.^2)./(g.*rhoS.*CL_max.*Ur);
C = B.^2;
D = (A.^2) + (2.*sg2.*B);
Z = sg2.^2;
x = [C -D Z];
W2S = roots(x)
% Cruise
Cdo = .012; % Taken from B-52
e = .6; % low wing from McCormick
K = 1./(4*(LDmaxC.^2).*Cdo)
W3S = (Vcruise.^2).*rho40./(2*sqrt((3.*K)./(Cdo)))

5. Appendix A
5
CL_max =
2.2500
W1S =
46.5920
W2S =
202.5173
115.6891
K =
0.0630
W3S =
38.9767
Cruise wing loading is least value
% Wing loading value selected as minimum from cruise flight and used to
% obtain wing area, and wing span thereafter. The aspect ratio is
% derived from induced drag and oswald efficiency factor.
WSmin = W3S
S = W0./WSmin
AR = 1./(pi.*e.*K)
b = sqrt(AR.*S)
WSmin =
38.9767
S =
758.5505
AR =
8.4220

6. Appendix A
6
b =
79.9281
Thrust to Weight
% Thrust to weight calculations for various mission segments. The highest
% value is to be selected.
% Take Off
n = 4;
CLadjust = .9*(1.7 + .5);
Radius = (6.96*(Vstall^2))/32.2;
ThetaOB = acosd(1-(50/Radius));
Sa = Radius*sind(ThetaOB);
y = (1.21*W3S)/(32.2*rhoS*CLadjust);
TW1 = y/(sgT - Sa)
% Rate of Climb
TW2 = (RC/Vstall)+(.5*rhoS*(Vstall^2)*(W3S^-1)*Cdo)+((2*W3S*K)/(rhoS*(Vstall^2)))
%Thrust Matching
a = .267;
c = .363;
TW3 = a.*(.75).^c
%Transport Statistical
TW4 = .25
%Sustained Turn
TWt = (.5*rho40*(Vcruise^2)*Cdo/W3S)+((W3S*K*(n^2))/(.5*rho40*(Vcruise^2)))
% Check
TWturnCheck = 2.*n.*sqrt(K.*Cdo)
TWcruiseCheck = 2*sqrt(K.*Cdo)
TW = TW2
T = W0.*TW
TW1 =
0.0578
TW2 =
0.3143
TW3 =

7. Appendix A
7
0.2405
TW4 =
0.2500
TWt =
0.3016
TWturnCheck =
0.2199
TWcruiseCheck =
0.0550
TW =
0.3143
T =
9.2936e+03
Mean aerodynamic chord
% cT = tip chord length, cR = root chord length, ybar = height of m.a.c.,
% cbar = spanwise location of m.a.c. and taper ratio lambda.
cT = 7.2;
cR = 12;
lambda = 0.6;
ybar = (b./6).*((1+2.*lambda)./(1+lambda))
cbar = (2/3).*cR.*((1+lambda+(lambda.^2))./(1+lambda))
ybar =
18.3169
cbar =
9.8000

8. Appendix A
8
1st CG Estimate
% Approximate locations and weights of all fuselage components. Used for
% moment calculation. (Refer to the AutoCAD sketch for better
% perspective).
% Engine
x1 = 80.8115;
w1 = 1.4*1644;
% Flight Attendant
x2 = 24.222;
w2 = 180;
% Bathroom
x3 = 28.972;
w3 = 130;
% Fridge & Food/ Drink
x4 = 28.972;
w4 = 400;
% Passengers
x5 = 56.157;
w5 = (10*200);
% Fuel Secondary and crew baggage
x6 = 36.7970;
w6 = 4767.5 + 20*3;
% Electrical System and Fuel Pump
x7 = 43.2970;
w7 = 200;
% Pilots
x8 = 20.472;
w8 = 2*180;
%Passenger Baggage
x9 = 70.342;
w9 = 50*10;
% Total Moment aabout Aircraft Nose
Mn = (x1.*w1) + (x2.*w2) + (x3.*w3) + (x4.*w4) + (x5.*w5) + (x6.*w6)...
+ (x7.*w7) + (x8.*w8) + (x9.*w9);
wn = w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 + w9;
% First center of gravity without wings
CG1 = Mn./wn
CG1 =
50.1750
2nd CG Estimate (Wing Addition)
% Wing mean aerodynamic center located at fuselage CG1 above
Wwing = (2.5).*S;
WwF = Wwing + (Wf - 4767.5)

9. Appendix A
9
% Distance from leading edge to aerodynamic center
cbar1 = (.25).*cbar
% Distance between aerodynamic center and the center of gravity
cbar2 = (.4).*cbar - cbar1
% Fuel weight had been incorporated in the wing weight value because of the
% significant amount of weight added to the wings from the fuel. Process
% follows that of Anderson.
CG2 = (Mn + WwF.*(CG1 + cbar2))./(wn + WwF)
WwF =
1.0290e+04
cbar1 =
2.4500
cbar2 =
1.4700
CG2 =
50.8889
Tail Addition
% Horizontal and Vertical tail volume ratios, values were averaged form data
% ranges of aircraft with good stability characterisitcs.
VHT = .5;
VVT = .0425;
% Measuring from the nose of the aircraft, PL = Plane Length, PL2 =
% approximate location of the mean aerodynmic center of the horizontal
% tail.
PL = 90;
PL2 = (.965250965).*PL
% Locations of the horizontal and vertical m.a.c. from the center of
% gravity of the aircraft (wings and fuselage). The horizontal is found
% by subtracting the fuselage/wing combination center of gravity from
% the overall length the Horizontal m.a.c. from the a/c nose.
lHT = PL2 - CG2
lVT = (.934033859).*lHT

10. Appendix A
10
% The planview area calculations for both horizontal and vertical sections.
SHT = (VHT.*cbar.*S)./lHT
SVT = (VVT.*b.*S)./lVT
% Assumed aspect ratio of the horizontal wing section ARH according to
% Anderson. The horizontal span, root cord length and tip chord length
% calculations are shown below respectively.
ARH = 4;
bt = sqrt(SHT.*ARH)
crt = (2.*SHT)./((lambda + 1).*bt)
ctt = lambda.*crt
% These are the coordinates for the location of the m.a.c. of the
% horizontal tail. cHT is the spanwise distance from the right-most edge,
% while yHT is distance away from the centerline. (Where the mirror of the
% tail occurs)
yHT = (bt./6).*(1 + 2.*lambda)./(1 + lambda)
cHT = (2/3).*crt.*(1 + lambda + (lambda.^2))./(1+lambda)
% Vertical tail section aspect ratio, averaged from data range found on
% page 441 (Anderson)
ARV = 1.65;
Lambda_Vtail = .85;
% In order below, the height of the vertical tail section, root chord
% length, and tip chord length.
hVT = sqrt(ARV.*SVT)
crVT = 2.*SVT./((Lambda_Vtail+1).*hVT)
ctVT = Lambda_Vtail.*crVT
% Similar to the horizontal tail section, cVT is the distance of the m.a.c.
% measured spanwise from the right of the airfoil, while zVT is height
% component of the m.a.c. location.
zVT = (2.*hVT./6).*(1+(2.*Lambda_Vtail))./(1+Lambda_Vtail)
cVT = (2/3).*crVT.*(1 + Lambda_Vtail + (Lambda_Vtail.^2))./(1 + Lambda_Vtail)
PL2 =
86.8726
lHT =
35.9837
lVT =
33.6100
SHT =

11. Appendix A
11
103.2940
SVT =
76.6663
bt =
20.3267
crt =
6.3521
ctt =
3.8113
yHT =
4.6582
cHT =
5.1876
hVT =
11.2472
crVT =
7.3692
ctVT =
6.2638
zVT =
5.4716
cVT =

12. Appendix A
12
6.8314
2nd Wing Placement and Landing Gear Specifi-
cations
% Static margin given as 10% (Anderson), calculation of the aerodynamic
% center of the wing body. Followed by calculation of the wing leading
% edge location, Crlead, and wing center location, Xc. NOTE: that Xc
% will be the location of the main landing gear for the aircraft.
% Measurements are made from the nose of the a/c.
SM = 0.1;
Xn = SM.*cbar + CG2;
Xacwing = Xn - VHT
Crlead = Xacwing - cbar1 - ((cR - cbar)./2);
Xc = Crlead + cR./2
Xnose = (0.086872587).*PL
% Distance calculation of each wheel from the known center of gravity (as
% opposed to the nose). Diagram can be seen on page 446 (Anderson). There
% are two location for the focus of all aircraft weight, being the nose and
% main landing gears. The main landing gear consists of a set of 2 wheels
% (left and right) and therefore it is necessary to split the load at that
% between between them.
X3 = Xc - Xnose;
X1 = CG2 - Xnose;
X2 = X3 - X1;
Fm = (W0.*X1)./X3
Fn = (W0.*X2)./X3
% Wheel Dimensions are calculated according to equation 8.82 (Anderson),
% where AD is the A diameter coefficient and AW is the A width
% coefficient, and so-on and so-forth.
AD = 1.51;
BD = 0.349;
AW = 0.715;
BW = 0.312;
% Main wheel diameter and width
MD = (AD.*((Fm./2).^BD))./12
MW = (AW.*((Fm./2).^BW))./12
% Nosewheel diameter and width
ND = (AD.*(Fn.^BD))./12
NW = (AW.*(Fn.^BW))./12
Xacwing =

13. Appendix A
13
51.3689
Xc =
53.8189
Xnose =
7.8185
Fm =
2.7683e+04
Fn =
1.8832e+03
MD =
3.5081
MW =
1.1673
ND =
1.7488
NW =
0.6265
Better Weight Estimates
%Front Cone Area
Front = pi*4*(4+sqrt(16.472^2+4^2))
%Main Cylinder Area
Center = (2*pi*4*56.476)+(2*pi*4^2)
%Rear Elipse Area

14. Appendix A
14
Back = pi*8*6.25*17.052
%Total Wetted Area
Wetted_area = Front+Center+Back
%Fuselage Weight
W_Fuselage = Wetted_area*1.4
%Main Wing Weight
W_Wings = 2.5*((7.2*36)+(36*2.4))
% Horizontal Tail Weight
W_HStab = 2*((4.1192*9.9822)+(1.25555*9.9822)+(.5*.9398*6.6303))
% Vertical Tail Weight
W_VStab = 2*((11.5656*5.2855)+(1.7618*11.5656))
% Landing Gear Weight
W_LGear = .057*W0
% W_Engine
W_Engine = 1.4*1644
% Other weight
W_Other = (.1*W0)
% Total Empty Weight
W_Empty = W_Fuselage+W_Wings+W_HStab+W_VStab+W_LGear+W_Engine+W_Other
Wf
% Take Off Weight
W_TO = Wc+Wp+Wf+W_Empty
Front =
263.2745
Center =
1.5199e+03
Back =
2.6785e+03
Wetted_area =
4.4617e+03

15. Appendix A
15
W_Fuselage =
6.2464e+03
W_Wings =
864.0000
W_HStab =
113.5348
W_VStab =
163.0125
W_LGear =
1.6853e+03
W_Engine =
2.3016e+03
W_Other =
2.9566e+03
W_Empty =
1.4330e+04
Wf =
1.3161e+04
W_TO =
3.0592e+04

16. Appendix A
16
Convergence of Weight Estimates
% Pluged the new W0 weight into the landing gear and other calculations and
% redetermined We (still using WeW0 ratio from the beginning and Wf.
% Repeated 16 times until all three weight values remianed steady.
W_LGear2 = .057*W_TO;
W_Other2 = (.1*W_TO);
W_Empty2 = W_LGear2+W_Other2+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf2 = WfW0*W_TO;
W_TO2 = Wc+Wp+Wf2+W_Empty2;
W_LGear3 = .057*W_TO2;
W_Other3 = (.1*W_TO2);
W_Empty3 = W_LGear3+W_Other3+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf3 = WfW0*W_TO2;
W_TO3 = Wc+Wp+Wf3+W_Empty3;
W_LGear4 = .057*W_TO3;
W_Other4 = (.1*W_TO3);
W_Empty4 = W_LGear4+W_Other4+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf4 = WfW0*W_TO3;
W_TO4 = Wc+Wp+Wf4+W_Empty4;
W_LGear5 = .057*W_TO4;
W_Other5 = (.1*W_TO4);
W_Empty5 = W_LGear5+W_Other5+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf5 = WfW0*W_TO4;
W_TO5 = Wc+Wp+Wf5+W_Empty5;
W_LGear6 = .057*W_TO5;
W_Other6 = (.1*W_TO5);
W_Empty6 = W_LGear6+W_Other6+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf6 = WfW0*W_TO5;
W_TO6 = Wc+Wp+Wf6+W_Empty6;
W_LGear7 = .057*W_TO6;
W_Other7 = (.1*W_TO6);
W_Empty7 = W_LGear7+W_Other7+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf7 = WfW0*W_TO6;
W_TO7 = Wc+Wp+Wf7+W_Empty7;
W_LGear8 = .057*W_TO7;
W_Other8 = (.1*W_TO7);
W_Empty8 = W_LGear8+W_Other8+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf8 = WfW0*W_TO7;
W_TO8 = Wc+Wp+Wf8+W_Empty8;
W_LGear9 = .057*W_TO8;
W_Other9 = (.1*W_TO8);
W_Empty9 = W_LGear9+W_Other9+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf9 = WfW0*W_TO8;
W_TO9 = Wc+Wp+Wf9+W_Empty9;

17. Appendix A
17
W_LGear10 = .057*W_TO9;
W_Other10 = (.1*W_TO9);
W_Empty10 = W_LGear10+W_Other10+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf10 = WfW0*W_TO9;
W_TO10 = Wc+Wp+Wf10+W_Empty10;
W_LGear11 = .057*W_TO10;
W_Other11 = (.1*W_TO10);
W_Empty11 = W_LGear11+W_Other11+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf11 = WfW0*W_TO10;
W_TO11 = Wc+Wp+Wf11+W_Empty11;
W_LGear12 = .057*W_TO11;
W_Other12 = (.1*W_TO11);
W_Empty12 = W_LGear12+W_Other12+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf12 = WfW0*W_TO11;
W_TO12 = Wc+Wp+Wf12+W_Empty12;
W_LGear13 = .057*W_TO12;
W_Other13 = (.1*W_TO12);
W_Empty13 = W_LGear13+W_Other13+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf13 = WfW0*W_TO12;
W_TO13 = Wc+Wp+Wf13+W_Empty13;
W_LGear14 = .057*W_TO13;
W_Other14 = (.1*W_TO13);
W_Empty14 = W_LGear14+W_Other14+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf14 = WfW0*W_TO13;
W_TO14 = Wc+Wp+Wf14+W_Empty14;
W_LGear15 = .057*W_TO14;
W_Other15 = (.1*W_TO14);
W_Empty15 = W_LGear15+W_Other15+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine;
Wf15 = WfW0*W_TO14;
W_TO15 = Wc+Wp+Wf15+W_Empty15;
W_LGear16 = .057*W_TO15;
W_Other16 = (.1*W_TO15);
W_Empty16 = W_LGear16+W_Other16+W_Fuselage+W_Wings+W_HStab+W_VStab+W_Engine
Wf16 = WfW0*W_TO15
W_TO16 = Wc+Wp+Wf16+W_Empty16
W_Empty16 =
1.4735e+04
Wf16 =
1.4308e+04
W_TO16 =

18. Appendix A
18
3.2143e+04
Second Performance Analysis
% 2nd analysis gross weight, empty weight, and fuel weight calculations.
W0v2 = W_TO16;
Wev2 = W_Empty16 ;
Wfv2 = Wf16;
% Lowest wing loading value, as well as the wing loading specific to climb,
% to be used in rate of climb calculations.
WSn = W0v2./S
WSclimb = (.97)*(.985).*WSn
% Rate of Climb
% The data series/ arrays shown below are for air densities according
% to their respective altitude, i.e. sea level, h = 0 and rho =
% 2.3769*10^-3. The rate of climb graph is derived from this data
% series being proportionally incorporated into thrut to weight
% caluclations. According to Anderson, as altitude increases, Thrust
% decreases proportional to rho^0.6 for turbofan engines.
rho_series = [2.3769 2.3423 2.3081 2.2743 2.2409 2.2079 2.1752 2.1429 ...
2.1110 2.0794 2.0482 2.0174 1.9869 1.9567 1.9270 1.8975 1.8685 ...
1.8397 1.8113 1.7833 1.7556 1.7282 1.7011 1.6744 1.6480 1.6219 ...
1.5961 1.5707 1.5455 1.5207 1.4962 1.4719 1.4480 1.4244 1.4011 ...
1.3781 1.3553 1.3329 1.3107 1.2889 1.2673 1.2459 1.2249 1.2041 ...
1.1836 1.1634 1.1435 1.1238 1.1043 1.0852 1.0663 1.0476 1.0292 ...
1.0110 .99311 .97544 .95801 .94082 .92387 .90716 .89068 .87443 ...
.85841 .84261 .82704 .81169 .79656 .78165 .76696 .75247 .73820 ...
.72413 .71028 .69443 .67800 .66196 .64629 .63100 .61608 .60150 ...
.58727 .41329 .39147 ] *(10^-3);
Altitude = [0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 ...
6000 6500 7000 7500 8000 8500 9000 9500 10000 10500 11000 11500 ...
12000 12500 13000 13500 14000 14500 15000 15500 16000 16500 ...
17000 17500 18000 18500 19000 19500 20000 20500 21000 21500 ...
22000 22500 23000 23500 24000 24500 25000 25500 26000 26500 ...
27000 27500 28000 28500 29000 29500 30000 30500 31000 31500 ...
32000 32500 33000 33500 34000 34500 35000 35500 36000 36500 ...
37000 37500 38000 38500 39000 39500 40000 47342 48475];
% Varying Thrust to Weight with increasing altitude. Note the sea level RC
% is estimated to be in the upper 90's (ft/s), well over 5400 ft/min
% which is 3.6 times shorter than desired specification.
TWnew = (T./W0v2).*(rho_series./rhoS)
% Equations 5.116 and 5.113 (Anderson) to solve for RCmaximum with 2nd
% analysis wing loading and thrust to weight specifications. The first
% three lines below utilize the data series above to plot a graph of
% the RCmax of the aircraft according to altitude. The following two
% lines of code are used to calculate time to climb using the sea level

19. Appendix A
19
% values of the array. Linies 413 - 428 combine equations 5.116 and
% 5.113 and then incorporate the change in thurst to weight with
% respect to altitude change. The "combined" equation then set to a
% a specific value of RCmax. According to Anderson, the absolute
% and service ceilings occur when RCmax = 0, 100 ft/min respectively.
% This translates to 0, and 5/3 ft/s. When plugged in and solved, x and
% y yield the absolute and service ceiling densities. Looking in the
% density tables in (Anderson), a corresponding height is found and
% manually typed into Absolute_Ceiling and Servvice_Ceiling below.
% (Values are interpolated by hand). These values were added to the
% arrays above after the fact.
Z = 1 + sqrt(1 + (3./((LDmaxL.^2).*(TWnew.^2))));
RCmax = sqrt((WSclimb.*Z)./(3.*rho_series.*Cdo)).*(TWnew.^1.5).*...
(1 - (Z./6) - (3./(2.*(TWnew.^2).*(LDmaxL.^2).*Z)));
% t_climb_min is converted to minutes
RCmaxSea = RCmax(1,1)
t_climb_min = (Altitude(1,81) - Altitude(1,1))./(RCmax(1,1));
syms x y
AC = solve( sqrt((WSclimb.*(1 + sqrt(1 + (3./...
((LDmaxL.^2).*(((T./W0v2).*(x./rhoS)).^2))))))./(3.*x.*Cdo)).*...
(((T./W0v2).*(x./rhoS)).^1.5).*(1 - ((1 + sqrt(1 + (3./...
((LDmaxL.^2).*(((T./W0v2).*(x./rhoS)).^2)))))./6) - (3./(2.*...
(((T./W0v2).*(x./rhoS)).^2).*(LDmaxL.^2).*(1 + sqrt(1 + (3./...
((LDmaxL.^2).*(((T./W0v2).*(x./rhoS)).^2)))))))) == 0, x);
Absolute_Density = vpa(AC(1,:))
Absolute_Ceiling = 48000 + (48500 - 48000)*((Absolute_Density - .00040045)/...
(.00039099 - .00040045))
SC = solve( sqrt((WSclimb.*(1 + sqrt(1 + (3./...
((LDmaxL.^2).*(((T./W0v2).*(x./rhoS)).^2))))))./(3.*x.*Cdo)).*...
(((T./W0v2).*(x./rhoS)).^1.5).*(1 - ((1 + sqrt(1 + (3./...
((LDmaxL.^2).*(((T./W0v2).*(x./rhoS)).^2)))))./6) - (3./(2.*...
(((T./W0v2).*(x./rhoS)).^2).*(LDmaxL.^2).*(1 + sqrt(1 + (3./...
((LDmaxL.^2).*(((T./W0v2).*(x./rhoS)).^2)))))))) == 5/3 , x);
Service_Density = vpa(SC)
Service_Ceiling = 47000 + (47500 - 47000)*((Service_Density - .00042008)/...
(.00041015 - .00042008))
% Plotting and Marking Ceiling Data
int = 0:1:100;
xx = Altitude(1,82).*(int./int);
yy = Altitude(1,83).*(int./int);
plot(RCmax, Altitude,RCmax(1,83),Altitude(1,83),'rs',RCmax(1,82),...
Altitude(1,82),'ks')
hold on
plot(xx,'k')
plot(yy,'r')
legend('RC vs. Altitude','Absolute Ceiling','Service Ceiling',...
'SC Marker','AC Marker')

20. Appendix A
20
grid on
xlabel('RCmax (ft/s)')
ylabel('Altitude (ft)')
title('RCmax Vs. Altitude')
axis([0 100 0 50000])
% 2nd Analysis Stall Velocity
Vstalln = sqrt((2./rhoS).*WSn./CLadjust)
% Landing Distance, where grv is gravity, AA is approach angle, Vf is flare
% velocity, R is flight path radius,hF is flare height. Determined valu
% is appr. 61% of the specified value 4000 ft. Well within constraints.
grv = 32.2;
AA = 3;
Vf = (1.23).*Vstalln;
Rv2 = (Vf.^2)./((0.2).*grv)
hF = Rv2.*(1 - cosd(AA))
SA = (50 - hF)./(tand(AA))
SF = (Rv2.*sind(AA))
SG = j.*N.*sqrt((2./rhoS).*WSn./CLadjust) + ...
((j.^2).*WSn./(grv.*rhoS.*CLadjust.*Ur))
SGn = SA + SF + SG
% 2nd Analysis Takeoff Distance, appr. 29% of specified value 6000 ft.
SGT = (1.21).*WSn./(grv.*rhoS.*CLadjust.*TW(1,:))
RR = (6.96).*(Vstalln.^2)./grv
OB = acosd(1 - saT./RR)
SAT = R.*sind(OB)
TOD = SGT + SAT
WSn =
42.3747
WSclimb =
40.4869
TWnew =
Columns 1 through 7
0.2891 0.2849 0.2808 0.2766 0.2726 0.2686 0.2646
Columns 8 through 14
0.2607 0.2568 0.2529 0.2491 0.2454 0.2417 0.2380

21. Appendix A
21
Columns 15 through 21
0.2344 0.2308 0.2273 0.2238 0.2203 0.2169 0.2136
Columns 22 through 28
0.2102 0.2069 0.2037 0.2005 0.1973 0.1942 0.1911
Columns 29 through 35
0.1880 0.1850 0.1820 0.1790 0.1761 0.1733 0.1704
Columns 36 through 42
0.1676 0.1649 0.1621 0.1594 0.1568 0.1542 0.1516
Columns 43 through 49
0.1490 0.1465 0.1440 0.1415 0.1391 0.1367 0.1343
Columns 50 through 56
0.1320 0.1297 0.1274 0.1252 0.1230 0.1208 0.1187
Columns 57 through 63
0.1165 0.1144 0.1124 0.1103 0.1083 0.1064 0.1044
Columns 64 through 70
0.1025 0.1006 0.0987 0.0969 0.0951 0.0933 0.0915
Columns 71 through 77
0.0898 0.0881 0.0864 0.0845 0.0825 0.0805 0.0786
Columns 78 through 83
0.0768 0.0749 0.0732 0.0714 0.0503 0.0476
RCmaxSea =
97.7624
Absolute_Density =
0.00039147049586455985078970718599533
Absolute_Ceiling =
48474.603812655400139974897115356

22. Appendix A
22
Service_Density =
0.00041329397068659587824712505735577
Service_Ceiling =
47341.693318902524126111895057413
Vstalln =
134.1931
Rv2 =
4.2304e+03
hF =
5.7977
SA =
843.4309
SF =
221.4038
SG =
1.3875e+03
SGn =
2.4523e+03
SGT =
1.0764e+03
RR =

23. Appendix A
23
3.8924e+03
OB =
9.1935
SAT =
7.3569e+06
TOD =
7.3580e+06
Time calculations
% Climb Segment
TCmin = (Hcruise - 0)./25
ThetaC = asind(RCmax(1,1)./Vstalln)
Rclimb = 39950./tand(ThetaC)

24. Appendix A
24
%Glide phase to loiter altitude
Thetamin1 = atan(1./LDmaxL);
Rglidemax1 = (Hcruise - Hloiter)./tan(Thetamin1)
VLDmax1 = sqrt(2*WSn.*sqrt(K./Cdo)./rho40);
VLDactual1 = sqrt(rho40./rho30).*VLDmax1;
Vsink1 = VLDactual1.*sin(Thetamin1);
Tglide1 = (Hcruise - Hloiter)./Vsink1
% Glide Phase 2 to sea level
Thetamin2 = atan(1./LDmaxL);
Rglidemax2 = (Hloiter - 0)./tan(Thetamin2)
VLDmax2 = sqrt(2*WSn.*sqrt(K./Cdo)./rho30);
VLDactual2 = sqrt(rho30./rhoS).*VLDmax2;
Vsink2 = VLDactual2.*sin(Thetamin2);
Tglide2 = (Hcruise - Hloiter)./Vsink2
T_Glide_Total = Tglide1 + Tglide2
% Loiter Time
Tloiter = E
% Cruise Time
Rnew = R - Rclimb - Rglidemax1 - Rglidemax2
Tcruise = Rnew./Vcruise
% Cumulative trip time
T_trip_total = TCmin + + Tcruise + T_Glide_Total + Tloiter
Thrs = T_trip_total./3600
TCmin =
1600
ThetaC =
46.7625
Rclimb =
3.7565e+04
Rglidemax1 =
210000
Tglide1 =

25. Appendix A
25
450.2751
Rglidemax2 =
630000
Tglide2 =
735.5675
T_Glide_Total =
1.1858e+03
Tloiter =
1800
Rnew =
4.5169e+07
Tcruise =
6.2236e+04
T_trip_total =
6.6821e+04
Thrs =
18.5615
Published with MATLAB® R2013a