Command Window OutputMichael MastromichalisAero 2200 DA-40 Performance AnalysisDr. Gregory11/16/2013 Task 1.Using the methods in class, the parasitic drag coefficient is .0.0398.The Oswald Efficiency Factor was calculated to be .763.L/Dmax is 14.38. Task 2The power required for sea level, 5000 ft, and 10000 ft is indicated on the graph. The following values for stall speed at sea level, 5000 ft, and 10000 ft, respectively, (in knots) are as follows: 53.1252

57.2295

61.8149

The following values for speed at minimum PR at sea level, 5000 ft, and 10000 ft, respectively, (in knots) are as follows: 101.1038

108.9147

117.6413

Task 3Maximum power available at sea level, 5000 ft, 10000 ft, respectively,(in hp) is as follows: 132.7560

110.6300

88.5040

According to the graph...Vmax_SL is approximately 137.7 knotsVmax_5000 is apporximately 133.825 knotsVmax_10000 is approximately 126.32 knots VTRmin for SL, 5000 ft, and 10000 ft, respectively, (in knots) are as follows 75.8672

81.7284

88.2768

The following Power Required for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at minimum speed are as follows: 31.3137

33.7329

36.4357

The following Power Available for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at minimum speed are as follows: 123.5745

104.9177

85.3150

The following Power Required for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at L/Dmax are as follows: 58.8536

63.4004

68.4803

The following Power Available for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at L/Dmax are as follows: 123.5745

104.9177

85.3150

The following Power Required for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at Vmmax are as follows: 140.0632

119.4555

99.3369

The following Power Available for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at Vmax are as follows: 131.3294

108.9971

86.4143

Task 4The maximum rate of climb values (in knots) for sea level, 5000 ft, and 10000 ft, respectively, are as follows: 8.4267

6.0733

3.5972

From the graph, the absolute ceiling is 17500 ft, and the service ceiling is 15450 ft. The time to climb (min) is as follows: 17.9224

According to the graph, the Best Climb Angle Condition Rate of Climb is 7.669 knotsThe climb angle Best Climb Angle Condition (in degrees is as follows: 6.5298

The velocity for Best Climb Angle Condition (in knots) is as follows: 67.4375

The Rate of Climb (knots fo)r Best Rate of Climb is as follows: 8.4060

According to the graph, the velocity for the Best Rate of Climb Condition is 83.58 knots The angle for the Best Rate of Climb Condition (in degrees) is as follows: 5.7432

Task 5The Endurance is 10.25 hours.The Range is 803.15 nautical miles. Task 6The maximum glide distance is 9.47 nauitcal miles.The indicated airspeed for maximum glide distance is 85.15 knots.The airspeed for maximum time aloft is 47.92 knots.The descent time is 0.20 hours. Task 7The maneuverability point is located at 103.56 knots.the minimum turn radius is 0.04 nautical miles.The maximum turn rate is 23.77 deg/s. Task 8The takeoff ground roll distance at maximum takeoff weight at standard sea level conditions is 1454.51 feet.The takeoff ground roll distance at maximum takeoff weight at 5000 ft is 1687.93 feet.The takeoff ground roll distance at 2400 lb at standard sea level conditions is 1172.26 feet.The landing ground roll distance at maximum weight at standard sea level conditions is 1110.43 feet.>>

Graphs

Scriptclear, clcdisp('Michael Mastromichalis')disp('Aero 2200 DA-40 Performance Analysis')disp('Dr. Gregory')disp('11/16/2013')disp(' ')%Determine the power curve for the Diamond DA-40 given takeoff weight, Power%available, and efficiency. W = 2645; %lb%e = .75; CDo = .0300;SHP_SL = 180; %hpSHP_5000 = 150; %hpSHP_10000 = 120; %hpS = 145.7; %ft^2b = 39.17; %ftAR = (b^2)/S;CLmax = 1.90; %Conditions at sea level, 5000 ft, and 10000 ftrho = 2.3769*(10^-3); %slug/ft^3rho_5000 = 2.0482 * (10^-3); %slug/ft^3rho_10000 = 1.7556 * (10^-3); %slug/ft^3

disp('Task 1.')disp('Using the methods in class, the parasitic drag coefficient is .0.0398.')disp('The Oswald Efficiency Factor was calculated to be .763.') %Now find the drag polar V_stall = sqrt(2*(W/S)/(rho*CLmax));V_assume = [V_stall : 500]; %ft/sCL = (2 * W)./(rho .* V_assume.^2 * S);CD = CDo +((CL.^2)./(pi*e*AR)); figure(1)C_L_min = min(CL);plot(C_L_min, CDo, '*')legend('CDo')hold on plot(CL, CD)title('CD vs. CL')xlabel('CL')ylabel('CD') L_over_D = CL./CD;figure(2)plot(CL, L_over_D)title('L/D vs. CL')xlabel('CL')ylabel('L/D')L_over_D_max = max(L_over_D);fprintf('L/Dmax is %.2f.' , L_over_D_max)disp(' ') disp('Task 2')disp('The power required for sea level, 5000 ft, and 10000 ft is indicated on the graph.')disp(' ') %To calculate airspeed for PR minB_SL = W^2/(.5 * rho * S * pi * AR * e);A_SL = .5 * rho * S * CDo; B_5000 = W^2/(.5 * rho_5000 * S * pi * AR * e);A_5000 = .5 * rho_5000 * S * CDo; B_10000 = W^2/(.5 * rho_10000 * S * pi * AR * e);A_10000 = .5 * rho_10000 * S * CDo; %Define a velocity vector and convert it to ft/s for the necessary%calculationsV = (40:150); %knotsV_calculation = V*6076/3600; %ft/s %Calculate Power RequiredPR_SL = A_SL * V_calculation.^3 + B_SL * V_calculation.^(-1); PR_5000 = A_5000 * V_calculation.^3 + B_5000 * V_calculation.^(-1); PR_10000 = A_10000 * V_calculation.^3 + B_10000 * V_calculation.^(-1); %Convert to hpPR_SL = PR_SL/550; %hp

PR_5000 = PR_5000/550; %hpPR_10000 = PR_10000/550; %hp %Calculate Vstall Vstall_SL = sqrt(2 * W / (rho * S * CLmax));Vstall_5000 = sqrt(2 * W / (rho_5000 * S * CLmax));Vstall_10000 = sqrt(2 * W / (rho_10000 * S * CLmax)); %Convert to knotsVstall_SL = Vstall_SL*3600/6076; %knotsVstall_5000 = Vstall_5000*3600/6076; %knotsVstall_10000 = Vstall_10000*3600/6076; %knots disp('The following values for stall speed at sea level, 5000 ft, and 10000 ft, respectively, (in knots) are as follows:')disp(Vstall_SL)disp(Vstall_5000)disp(Vstall_10000)disp(' ') %Calculate VminPROH_SL = 4 * W^2;IO_SL = rho^2*S^2*pi*AR*e*CDo;VPRmin_SL = (OH_SL/(3*IO_SL))^(1/4);%ft/s OH_5000 = 4 * W^2;IO_5000 = rho_5000 ^2 * S^2 * pi * AR * e * CDo;VPRmin_5000 = (OH_5000 / (3*IO_5000))^(1/4);%ft/s OH_10000 = 4 * W^2;IO_10000 = rho_10000 ^2 * S^2 * pi * AR * e * CDo;VPRmin_10000 = (OH_10000 / (3*IO_10000))^(1/4);%ft/s % Change V back to knotsV_plot = V_calculation*3600/6076; %knots figure(3)plot(V_plot, PR_SL, 'r')hold onplot(V_plot, PR_5000, 'b')hold onplot(V_plot, PR_10000, 'g')hold onxlabel('Velocity (knots)')ylabel('Power (hp)')legend('SL' , '5000 ft' , '10000 ft')title('Power vs. Velocity') disp('The following values for speed at minimum PR at sea level, 5000 ft, and 10000 ft, respectively, (in knots) are as follows:')disp(VPRmin_SL)disp(VPRmin_5000)disp(VPRmin_10000)disp(' ')

disp('Task 3') h = .78.*(1-(35./V_plot).^2); Pa_SL = SHP_SL * h; %hpPa_5000 = SHP_5000 * h; %hpPa_10000 = SHP_10000 * h; %hp maxPa_SL = max(Pa_SL);maxPa_5000 = max(Pa_5000);maxPa_10000 = max(Pa_10000); disp('Maximum power available at sea level, 5000 ft, 10000 ft, respectively,(in hp) is as follows:')disp(maxPa_SL)disp(maxPa_5000)disp(maxPa_10000) %For graphing purposes% Pa_SL = Pa_SL .* ones(1,length(V_plot));% Pa_5000 = Pa_5000 .* ones(1,length(V_plot));% Pa_10000 = Pa_10000 .* ones(1,length(V_plot)); figure(4)plot(V_plot, PR_SL, 'r')hold onplot(V_plot, PR_5000, 'b')hold onplot(V_plot, PR_10000, 'g')hold onplot(V_plot, Pa_SL, 'r')hold onplot(V_plot, Pa_5000, 'b')hold onplot(V_plot, Pa_10000, 'g')hold offxlabel('Velocity (knots)')ylabel('Power (hp)')legend('SL' , '5000 ft' , '10000 ft')title('Power vs. Velocity') disp('According to the graph...')disp('Vmax_SL is approximately 137.7 knots')disp('Vmax_5000 is apporximately 133.825 knots')disp('Vmax_10000 is approximately 126.32 knots')disp(' ') %Calculate power required at Vmin for the chartVPRmin_SL_calc = VPRmin_SL*3600/6076; %ft/sVPRmin_5000_calc = VPRmin_5000*3600/6076; %ft/sVPRmin_10000_calc = VPRmin_10000*3600/6076; %ft/s PRmin_SL = A_SL * VPRmin_SL_calc .^3 + B_SL * VPRmin_SL .^(-1);PRmin_5000 = A_5000 * VPRmin_5000_calc .^3 + B_5000 * VPRmin_5000 .^(-1);

PRmin_10000 = A_10000 * VPRmin_10000_calc .^3 + B_10000 * VPRmin_10000 .^(-1); %Convert to hpPRVmin_SL = PRmin_SL / 550; %hpPRVmin_5000 = PRmin_5000 / 550; %hpPRVmin_10000 = PRmin_10000 / 550; %hp %Find maximum L/D ratio%Calculate VTRmin%PR = TR*VTRmin_SL = (PRmin_SL)/VPRmin_SL; %lbTRmin_5000 = (PRmin_5000)/VPRmin_5000; %lbTRmin_10000 = (PRmin_10000)/VPRmin_10000; %lb %CD is known because CD = CDo + CDi and at this point, CDo = CDiCD2 = 2*CDo; %In steady, level flight, T = D%Now solve for V_TRmin as a function of T %T = .5 * rho * V^2 * S * CD VTRmin_SL = sqrt(2 * TRmin_SL / (rho * S * CD2)); %ft/s VTRmin_5000 = sqrt(2 * TRmin_5000 / (rho_5000 * S * CD2)); %ft/s VTRmin_10000 = sqrt(2 * TRmin_10000 / (rho_10000 * S * CD2)); %ft/s %Convert to knotsVTRmin_SL = VTRmin_SL*3600/6076; %knotsVTRmin_5000 = VTRmin_5000*3600/6076; %knotsVTRmin_10000 = VTRmin_10000*3600/6076; %knots disp('VTRmin for SL, 5000 ft, and 10000 ft, respectively, (in knots) are as follows')disp(VTRmin_SL)disp(VTRmin_5000)disp(VTRmin_10000) disp('The following Power Required for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at minimum speed are as follows:')disp(PRVmin_SL)disp(PRVmin_5000)disp(PRVmin_10000)disp(' ') %Calculate Power Available at Vminh = .78.*(1-(35./VPRmin_SL).^2);Pa_Vmin_SL_chart = SHP_SL * h; %hp h = .78.*(1-(35./VPRmin_5000).^2);Pa_Vmin_5000_chart = SHP_5000 * h; %hp h = .78.*(1-(35./VPRmin_10000).^2);Pa_Vmin_10000_chart = SHP_10000 * h; %hp disp('The following Power Available for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at minimum speed are as follows:')

disp(Pa_Vmin_SL_chart)disp(Pa_Vmin_5000_chart)disp(Pa_Vmin_10000_chart)disp(' ') %Do the same two steps as above, this time for L/Dmax (VTRmin)%Calculate power required at Vmin for the chartVTRmin_SL_calc = VTRmin_SL*6076/3600; %ft/sVTRmin_5000_calc = VTRmin_5000*6076/3600; %ft/sVTRmin_10000_calc = VTRmin_10000*6076/3600; %ft/s PRmin_SL_VTRmin = A_SL * VTRmin_SL_calc .^3 + B_SL * VTRmin_SL .^(-1);PRmin_5000_VTRmin = A_5000 * VTRmin_5000_calc .^3 + B_5000 * VTRmin_5000 .^(-1);PRmin_10000_VTRmin = A_10000 * VTRmin_10000_calc .^3 + B_10000 * VTRmin_10000 .^(-1); %Convert to hpPRVmin_SL_VTRmin = PRmin_SL_VTRmin / 550; %hpPRVmin_5000_VTRmin = PRmin_5000_VTRmin / 550; %hpPRVmin_10000_VTRmin = PRmin_10000_VTRmin / 550; %hp disp('The following Power Required for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at L/Dmax are as follows:')disp(PRVmin_SL_VTRmin)disp(PRVmin_5000_VTRmin)disp(PRVmin_10000_VTRmin)disp(' ') %Calculate Power Available at Vminh = .78.*(1-(35./VTRmin_SL_calc).^2);Pa_VTRmin_SL_chart = SHP_SL * h; %hp h = .78.*(1-(35./VTRmin_5000_calc).^2);Pa_VTRmin_5000_chart = SHP_5000 * h; %hp h = .78.*(1-(35./VTRmin_10000_calc).^2);Pa_VTRmin_10000_chart = SHP_10000 * h; %hp disp('The following Power Available for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at L/Dmax are as follows:')disp(Pa_Vmin_SL_chart)disp(Pa_Vmin_5000_chart)disp(Pa_Vmin_10000_chart)disp(' ') %Do the same for Vmax%Define VmaxVmax_SL = 137.7; %knotsVmax_5000 = 133.825; %knotsVmax_10000 = 126.32; %knots %Calculate power required at Vmin for the chartVmax_SL_calc = Vmax_SL*6076/3600; %ft/s

Vmax_5000_calc = Vmax_5000*6076/3600; %ft/sVmax_10000_calc = Vmax_10000*6076/3600; %ft/s PRmin_SL_Vmax = A_SL * Vmax_SL_calc .^3 + B_SL * Vmax_SL .^(-1);PRmin_5000_Vmax = A_5000 * Vmax_5000_calc .^3 + B_5000 * Vmax_5000 .^(-1);PRmin_10000_Vmax = A_10000 * Vmax_10000_calc .^3 + B_10000 * Vmax_10000 .^(-1); %Convert to hpPRVmin_SL_Vmax = PRmin_SL_Vmax / 550; %hpPRVmin_5000_Vmax = PRmin_5000_Vmax / 550; %hpPRVmin_10000_Vmax = PRmin_10000_Vmax / 550; %hp disp('The following Power Required for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at Vmmax are as follows:')disp(PRVmin_SL_Vmax)disp(PRVmin_5000_Vmax)disp(PRVmin_10000_Vmax)disp(' ') %Calculate Power Available at Vmin h = .78.*(1-(35./Vmax_SL).^2);Pa_Vmax_SL_chart = SHP_SL * h; %hp h = .78.*(1-(35./Vmax_5000).^2);Pa_Vmax_5000_chart = SHP_5000 * h; %hp h = .78.*(1-(35./Vmax_10000).^2);Pa_Vmax_10000_chart = SHP_10000 * h; %hp disp('The following Power Available for sea level, 5000 ft, and 10000 ft, respectively, (in hp) at Vmax are as follows:')disp(Pa_Vmax_SL_chart)disp(Pa_Vmax_5000_chart)disp(Pa_Vmax_10000_chart)disp(' ') %Task 4disp('Task 4')%Plot Pa-PR) vs. VRC_SL = (Pa_SL - PR_SL)/W;RC_5000 = (Pa_5000 - PR_5000)/W;RC_10000 = (Pa_10000 - PR_10000)/W; %Convert to ft/minRC_SL = RC_SL * 550 * 60; %ft/minRC_5000 = RC_5000 *550 * 60; %ft/minRC_10000 = RC_10000 * 550 * 60; %ft/min RC_SL_knots = RC_SL * 60 / 6076; %knotsRC_5000_knots = RC_5000 * 60 / 6076; %knotsRC_10000_knots = RC_10000 * 60 / 6076; %knots

%Plot R/C vs. Vinffigure(5)plot(V_plot, RC_SL_knots, 'r')hold on plot(V_plot, RC_5000_knots, 'b')hold onplot(V_plot, RC_10000_knots , 'g')hold offtitle('R/C vs. Velocity')ylim([0 10])ylabel('R/C(knots)')xlabel('Velocity (knots)') legend('Sea Level' , '5000 ft' , '10000 ft') RC_SLmax = max(RC_SL); %knotsRC_5000max = max(RC_5000); %knotsRC_10000max = max(RC_10000); %knots disp('The maximum rate of climb values (in knots) for sea level, 5000 ft, and 10000 ft, respectively, are as follows:')RC_SLmax_knots = max(RC_SL_knots); %knotsRC_5000max_knots = max(RC_5000_knots); %knotsRC_10000max_knots = max(RC_10000_knots); %knots disp(RC_SLmax_knots)disp(RC_5000max_knots)disp(RC_10000max_knots) %Find service and absolute ceilingsalt = [0, 5000, 10000];RCmax = [RC_SLmax, RC_5000max, RC_10000max];figure(6)plot(RCmax(1), alt(1) , 'd')hold onplot(RCmax(2), alt(2), 'x')hold onplot(RCmax(3), alt(3), '^')hold onplot(100,15450, '*')plot([100, 100], [0, 15450], '--')hold onP = polyfit(RCmax, alt, 1);RC_1 = (0 : 10 : max(RCmax));Alt = P(1)*RC_1+P(2);plot(RC_1, Alt)hold offtitle('Altitude vs. Rate of Climb')xlabel('Rate of CLimb (ft/min)')ylabel('Altitude (ft)')legend('Sea Level' , '5000 ft' , '10000 ft', 'Service Ceiling') disp('From the graph, the absolute ceiling is 17500 ft, and the service ceiling is 15450 ft.')disp(' ') %Plot RC vs. Altitude

figure(7)plot(alt(1), RCmax(1) , 'd')hold onplot(alt(2), RCmax(2), 'x')hold onplot(alt(3), RCmax(3), '^')P2 = polyfit(RCmax, alt, 1);Alt2 = P2(1)*RC_1+P2(2);plot(Alt2, RC_1)hold offtitle('Rate of Climb vs. Altitude')xlabel('Altitude (ft)')ylabel('Rate of Climb (ft/min)')legend('Sea Level' , '5000 ft' , '10000 ft') %Plot Time to Climbfigure(8)% plot(alt, RC_Inv)% RC_SL_Inv = (RCmax(1))^-1;% RC_5000_Inv = (RCmax(2))^-1;% RC_10000_Inv = (RCmax(3))^-1;RC_Inv = RC_1.^-1;RCmax_Inv = RCmax.^-1;plot(alt(1), RCmax_Inv(1), 'd')hold onplot(alt(2), RCmax_Inv(2), 'x')hold onplot(alt(3),RCmax_Inv(3), '^')hold on% P3 = polyfit(alt, RCmax_Inv,1);% Alt3 = P3(1)*RC_Inv + P3(2);% plot(Alt3, RC_Invplot(alt, RCmax_Inv)hold offtitle('Time To Climb: Inverse Rate of CLimb vs. Altitude')xlabel('Altitude (ft)')ylabel('Inverse Rate of Climb (ft/min)^-1')legend('Sea Level' , '5000 ft' , '10000 ft') T = trapz(alt, RCmax_Inv); %mindisp('The time to climb (min) is as follows:')disp(T) %Hodograph for Sea Level Climb at Max Takeoff WeightVv = RC_SL*60/6076; %knotsfigure(9)VH = sqrt(V_plot.^2-Vv.^2); %knotsplot(VH, Vv)hold onVmax = 0;for i = 1 : length(Vv) Vv_over_Vh(i) = Vv(i)/VH(i);if Vv_over_Vh(i) > Vmax Vmax = Vv_over_Vh(i);Vvtan_calc = [0, Vv(i)];Vhtan = [0, VH(i)];end

end plot(Vhtan, Vvtan_calc, '--o')hold offtitle('Rate of Climb vs. Velocity Hodograph')xlabel('Velocity (knots)')ylim([0 10])ylabel('Rate of Climb (knots)') disp('According to the graph, the Best Climb Angle Condition Rate of Climb is 7.669 knots') RC_calc = 7.669; %knotsRC_chart = RC_calc * 6076/60; %ft/minVh_theta = 67; %knotsarctan = RC_calc/Vh_theta;theta_RC = atand(arctan); %degrees disp('The climb angle Best Climb Angle Condition (in degrees is as follows:')disp(theta_RC) %Calculate the Velocity for Best Climb Angle ConditionV_theta= sqrt(RC_calc^2 + Vh_theta^2); %knotsdisp('The velocity for Best Climb Angle Condition (in knots) is as follows:')disp(V_theta)disp(' ') %Find the RC, angle, and velocity for Best Rate of ClimbRC_best = 8.406; %knotsRE_best_chart = RC_best * 6076/60; %ft/mindisp('The Rate of Climb (knots fo)r Best Rate of Climb is as follows:')disp(RC_best)%The Velocity for Best Rate of CLimb can be found by looking on the graph%based off of RC_Best.V_best = 83.58; %knotsdisp('According to the graph, the velocity for the Best Rate of Climb Condition is 83.58 knots')disp(' ') %Convert RC_best to knots%RC_best_calc = RC_best*60; %knotsarctan_best = RC_best/V_best;theta_best = atand(arctan_best); %degrees disp('The angle for the Best Rate of Climb Condition (in degrees) is as follows:')disp(theta_best)disp(' ') disp('Task 5')%Determine the maximum range and endurance.%At 10000ft, 90% fuelfuel = 50; %gallonsfuel_density = 6; %lb/galFuel_weight = fuel*fuel_density; %lb

Fuel_W = .9*Fuel_weight; %lbSFC = 0.49; %(lb/hr)/shp%Convert SFC to 1/ftSFC = SFC/550/3600; %1/fth2 = .78;W2 = W - Fuel_W; %lb cl = [.01 :.0001: CLmax];cd = CDo + cl.^2./(pi*AR*e); cl32 = cl.^(3/2); %CL^(3/2)/CD is VPRmin, and CL/Cd is the value for VTRmin. Conver it to ft/s for calculationsCL_to_the_3_over_2_divided_by_CD = cl32./cd;CL_to_the_3_over_2_divided_by_CD = max(CL_to_the_3_over_2_divided_by_CD);CL_over_CD = cl./cd; CL_over_CD = max(CL_over_CD); E = (h2/SFC)*(CL_to_the_3_over_2_divided_by_CD)*(sqrt(2*rho_10000*S))*(W2^(-1/2)-W^(-1/2)); %sec%Convert E to hoursE = E/3600; %hrfprintf('The Endurance is %.2f hours.\n' , E) %Calculate RangeR = (h2/SFC)*(CL_over_CD) * log(W/W2); %ft%Convert to nmiR = R/6076; %nmifprintf('The Range is %.2f nautical miles.\n' ,R)disp(' ') disp('Task 6')%Make a hodograph for Vv and Vh when gliding%Convert Vv and Vh to ft/scl = [.01 :.0001: CLmax];cd = CDo + cl.^2./(pi*AR*e);glide_angle = atan(1./(cl./cd)); %radiansglide_angle = glide_angle*180/pi*-1; %degreesV_descent = sqrt(2.*cosd(glide_angle)*(W/S)./(rho.*cl)); %ft/sVh = V_descent .* cosd(glide_angle); %ft/sVv2 = V_descent .* sind(glide_angle); %ft/s figure(10)plot(Vh, Vv2)title('Vv vs. Vh Hodograph for Gliding Speed')xlabel('Vh (ft/s)')ylabel('Vv (ft/s)') %Calculate max rangeHplane = 5000; %ftHbase = 1000; %ftH_useful = Hplane-Hbase; %ftRmax = H_useful*L_over_D_max; %ft%Comvert to nmi

Rmax = Rmax/6076; %nmifprintf('The maximum glide distance is %.2f nauitcal miles.\n' , Rmax) %Indicated airspeed to maximize glide distancecl2 = .83;new_angle = atand(Vv2/Vh); %degreesactual_new_angle = min(new_angle); %degreesactual_new_angle = abs(actual_new_angle); %degreesV_ind = sqrt(2*cosd(actual_new_angle)*W/(rho_5000*cl2*S)); %ft/sV_ind = V_ind*3600/6076; %knotsfprintf('The indicated airspeed for maximum glide distance is %.2f knots.\n' , V_ind) %At L/Dmax, CDo=CDiCLopt = sqrt(CDo*pi*AR*e); %for L/DmaxV_LDmax = sqrt(2*(W/S)/(rho_5000*pi*CLopt)); %ft/s%Convert to knotsV_LDmax = V_LDmax*3600/6076; %knotsfprintf('The airspeed for maximum time aloft is %.2f knots.\n' , V_LDmax) %Calculate the descent time%time = distance/velocitytime = Rmax/V_LDmax;fprintf('The descent time is %.2f hours.\n' , time)disp(' ') disp('Task 7')airspeedNE = 178; %knots V_inf = [0 : airspeedNE]; %knots% See_EL1 = linspace(0, CLmax, length(V_inf));% See_EL2 = linspace(0, -CLmax, length(V_inf));n = (.5 * rho .* V_inf.^2 .* S .* CLmax)/W;n2 = (.5 * rho .* V_inf.^2 * S .*-CLmax)/W; figure(11)plot(V_inf, n)hold onplot(V_inf, n2) n_max_P = 3.8;n_max_N = -1.53; ylim([n_max_N n_max_P]) %Find maneuver pointV_star = sqrt(((2 * n_max_P)/(rho * CLmax))*(W/S)); %ft/s%Convert to knotsV_star = V_star * 3600/ 6076; %knotsfprintf('The maneuverability point is located at %.2f knots.\n' , V_star)%At this point, he have the maneuvering point.%It is indicated on the graph by the following:hold onnmax = .5*rho*V_star^2*(CLmax/(W/S));plot(V_star,nmax, '*')hold onplot([V_star, V_star], [0, nmax], '--')hold on

VSTALL1 = sqrt(2 * (W/S)/(rho*CLmax)); %ft/sVSTALL1 = VSTALL1 * 3600 / 6076; %knotsplot(VSTALL1, .36, '^')hold onplot([VSTALL1, VSTALL1], [0,.36], '-.')hold onplot([V_star, airspeedNE] , [nmax, nmax], 'r')hold onplot([V_star, airspeedNE] , [-nmax, -nmax], 'r')hold onplot([airspeedNE, airspeedNE], [-nmax, nmax], 'r')hold offtitle('Load Factor vs. Velocity')xlabel('Velocity (knots)')ylabel('Load Factor') %Calculate minumum turn radius and maximum turn rate.g = 32.2; %ft/s^2Rmin = 2*(W/S)/(g*rho*CLmax); %ft%Convert to nautical milesRmin = Rmin/6076; %nautical milesfprintf('the minimum turn radius is %.2f nautical miles.\n' , Rmin)omegamax = g * sqrt(nmax*rho*CLmax/(2*(W/S))); %rad/s%Convert to degrees/somegamax = omegamax * 180/ pi; %deg/sfprintf('The maximum turn rate is %.2f deg/s.\n' , omegamax)disp(' ')disp(' ') disp('Task 8')%Takeoff ground roll distance at maximum takeoff weight at standard sea level conditionsVTO = 1.2 * sqrt(2 * (W/S)/ (rho * CLmax)); %ft/sVTO_knots = VTO * 3600/6076; %knotsVTO707_knots = .707 * VTO_knots; %knotsVTO707 = VTO* .707; %ft/sh_to = .78*(1-(35/VTO707_knots)^2); PASL = SHP_SL*h_to; %hpPASL_calc = PASL * 550; %lb*ft/sT707 = PASL_calc/VTO707; %lbmu = .02;H = 1.84; %ftphi = ((16*(H/b))^2)/(1+(16 * (H/b))^2);CLopt=(1/(2*phi))*pi*AR*e*mu; c__d = CDo + (phi * CLopt^2)/(pi*AR*e);Favg = T707 - .5 * rho * (VTO707)^2 * S * c__d - mu * (W - .5 * rho * (VTO707^2 * S * CLopt)); %lbSG = W * VTO^2/(2*g*Favg); %ft fprintf('The takeoff ground roll distance at maximum takeoff weight at standard sea level conditions is %.2f feet.\n' ,SG) %Same as above, only now for 5000 ftVTO_5000 = 1.2 * sqrt(2 * (W/S)/ (rho_5000 * CLmax)); %ft/sVTO_knots_5000 = VTO_5000 * 3600/6076; %knotsVTO707_5000_knots = .707 * VTO_knots_5000; %knots

VTO707_5000 = VTO707_5000_knots*6076/3600; %ft/sh_to = .78*(1-(35/VTO_knots_5000)^2); PA5000 = SHP_SL*h_to; %hpPA5000_calc = PA5000 * 550; %lb*ft/minT707_5000 = PA5000_calc/VTO707; %lb Favg_5000 = T707 - .5 * rho_5000 * (VTO707_5000)^2 * S * c__d - mu * (W - .5 * rho_5000 * (VTO707_5000^2 * S * CLopt)); %lbSG_5000 = W * VTO_5000^2/(2*g*Favg); %ft fprintf('The takeoff ground roll distance at maximum takeoff weight at 5000 ft is %.2f feet.\n' ,SG_5000) %Same but with takeoff weight of 2400 lb (at sea level)TOW = 2400; %lbVTO_2400lb = 1.2 * sqrt(2 * (TOW/S)/ (rho * CLmax)); %ft/sVTO707_2400lb = .707 * VTO_2400lb; %ft/sT707_2400lb = PASL_calc/VTO707_2400lb; %lbFavg_2400lb = T707 - .5 * rho * (VTO707_2400lb)^2 * S * c__d - mu * (TOW - .5 * rho * (VTO707_2400lb^2 * S * CLopt)); %lbSG_2400lb = TOW * VTO_2400lb^2/(2*g*Favg_2400lb); %ft fprintf('The takeoff ground roll distance at 2400 lb at standard sea level conditions is %.2f feet.\n' ,SG_2400lb) %Landing ground roll distance at maximum weight and standard sea level conditions. VTD = 1.3 * sqrt((2 * (W/S))/ (rho * CLmax)); %ft/sVTD707 = .707 * VTD; %ft/s %Use mu = .25mu2 = .25;Favg_TD = (-.5 * rho * VTD707^2 * S * c__d) - mu2 * (W - .5 * rho * VTD707^2 * S * CLopt); %lbSL = -W*VTD^2/(2*g*Favg_TD); %ft fprintf('The landing ground roll distance at maximum weight at standard sea level conditions is %.2f feet.\n' ,SL)