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Matlab codes for Sizing and Calculating the Aircraft Stability & Performance

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Ahmed Momtaz Hosny, PhD, profile picture
Ahmed Momtaz Hosny, PhD

The document details the estimation of UAV weights, sensitivity analysis of various parameters affecting takeoff weight, and preliminary sizing considerations based on design constraints such as lift-to-drag ratios and cruising speeds. It includes equations for calculating weights, fuel fractions, and performance metrics under different operational conditions. Additionally, it utilizes regression analysis and graphical representations to illustrate the sensitivities of takeoff weight to changes in payload, empty weight, specific fuel consumption, and other related factors.

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%%%%%%% UAV Weight Estimation and Sensitivity Analysis %%%%%%%%%%%% wwto=[330 440 451 418 443 584 451 339 661]; wwe=[110 220 304 275 324 328 275 200 473]; wwto=log10(wwto) wwe=log10(wwe) e1=[ones(size(wwto')) wwe']; C1=e1wwto' %%%%%%% UAV Weight Calculations %%%%%%%%%%%% Wto =160*2.2; %%%%%%%% Wto in LB Wpl = 30*2.2; %%%%%%%%% Wpl in LB a=0.04; %%%%%%%0.05; %C1(1); %%%%0.05; %%%%%%%%%%%%%%Light Airplane - 0.114; %%%%%%%%% Regression Line b=1.086; %%%%%%%%%%1.078; %C1(2); %%%%1.078; %%%%%%%% Light Airplane 1.1162; %%%%%%%%% Regression Line Vcr=75; %%%%%%%%% in mph %%%%%%% Regression Line for Allowable Value of Empty Weight %%%%%%%%%%% log10We = (log10(Wto)- a)/b Weall=10^(log10We) %%%%%%%%%%% We in LB W1_Wto = 0.97; W2_W1 = 0.985; W3_W2 = 0.988; W4_W3 = 0.999; W6_W5 = 0.988; W7_W6 = 0.995; Rcr=960/1.6 ;%%%%%%%%%%%%% in miles Eff_Pcr = 0.8; %%%%%%% between 0.75-0.8 Cpcr = 0.9 ; %%%%%%%%%%%%%%%%%%% Lbs/hp/hr
LDcr = 14 ; %%%%%%%%%%%% Selected According to Datcom Calculation lnW4_W5 = Rcr/(375*(Eff_Pcr/Cpcr)*LDcr); %%%%%%%%%Breguet's Range equation for propeller driven airplanes W5_W4 =1/exp(lnW4_W5); Mff=W1_Wto*W2_W1*W3_W2*W4_W3*W5_W4*W6_W5*W7_W6 %%%%%%%%%%Fuel Fraction Wfused=(1-Mff)*Wto ;%%%%%%%%%%% Used Fuel Wf = 1.25*Wfused %%%%%%%%%%%%%%% Total Fuel Weight Woe = Wto - Wf - Wpl ; %%%%%%%%%%%%% Operating Empty Weight We = Woe - 0.008*Wto %%%%%%%%%%%%% Empty weight %%%%%%%%%%%%%%%%%%%%% Sensitivity of TakeOff Weight to Payload %%%%%%%%%%%%%%%%%%%%%%%%%%%% c=1-(1+0.25)*(1-Mff)-0.008 %%%%%%%%%% WTO_To_WPL = b*Wto/(Wpl-c*(1-b)*Wto) %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Empty weight %%%%%%%%%%%%%%%%%%%%%%%%% WTO_TO_WE = b*Wto/(10^((log10(Wto)-a)/b)) %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Range%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% f = (-b*(Wto)^2*(1+0.25)*Mff)/(c*(1-b)*Wto-Wpl) RR = Cpcr/(375*Eff_Pcr*LDcr); WTO_TO_R = f*RR %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Cpcr %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% WTO_TO_Cpcr = f*Rcr/(375*Eff_Pcr*LDcr) %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Propeller Efficiency %%%%%%%%%%%%%%%%%% WTO_TO_Eff_Pcr= -f*Rcr*Cpcr/(375*(Eff_Pcr)^2*(LDcr)) %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to L/D %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
WTO_TO_LDcr = -f*Rcr*Cpcr/(375*Eff_Pcr*(LDcr)^2) %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Endurance %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% EE = Vcr*Cpcr/(375*Eff_Pcr*LDcr); WTO_TO_E = f*EE
%%%%%%% Sensitivity Analysis (Continuous) %%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% UAV Weight Calculations %%%%%%%%%%%% Wto = 80*2.25; %%%%%%%% Wto in LB Wpl = 15*2.25; %%%%%%%%% Wpl in LB Wto1=[57 77 96 115 133 150 167 184 200 217].*2.25; Wpl1=[10 15 20 25 30 35 40 45 50 55].*2.25; LD1=[10 11 12 13 14 15 16 17 18 19]; for j=1:1:10 for i=1:1:10 Wto = Wto1(i); %%%%%%%% Wto in Kg Wpl = Wpl1(i); %%%%%%%%% Wpl in Kg a=0.05; %%%%%%%%%%%%%%Light Airplane -0.114;%%%%%%%%% Regression Line b=1.078; %%%%%%%% Light Airplane 1.1162; %%%%%%%%% Regression Line Vcr=75; %%%%%%%%% in mph %%%%%%% Regression Line for Allowable Value of Empty Weight %%%%%%%%%%%5 log10We = (log10(Wto)- a)/b; Weall=10^(log10We) %%%%%%%%%%% We in LB W1_Wto = 0.97; W2_W1 = 0.997; W3_W2 = 0.998; W4_W3 = 0.992; W6_W5 = 0.993; W7_W6 = 0.993; Rcr=960/1.6 ;%%%%%%%%%%%%% in miles Eff_Pcr = 0.8; %%%%%%% between 0.75-0.8
Cpcr = 0.483 ; %%%%%%%%%%%%%%%%%%% Lbs/hp/hr LDcr = 10+j ; %%%%%%%%%%%%LDcr=14 Selected According to Datcom Calculation according to the proposed platform lnW4_W5 = Rcr/(375*(Eff_Pcr/Cpcr)*LDcr); %%%%%%%%%Breguet's Range equation for propeller driven airplanes W5_W4 =1/exp(lnW4_W5); Mff=W1_Wto*W2_W1*W3_W2*W4_W3*W5_W4*W6_W5*W7_W6 ; %%%%%%%%%%Fuel Fraction Wfused=(1-Mff)*Wto ;%%%%%%%%%%% Used Fuel Wf = 1.25*Wfused ; %%%%%%%%%%%%%%% Total Fuel Weight Woe = Wto - Wf - Wpl ; %%%%%%%%%%%%% Operating Empty Weight We = Woe - 0.008*Wto %%%%%%%%%%%%% Empty weight %%%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Payload %%%%%%%%%%%%%%%%%%%%%%%%%%%% c=1-(1+0.25)*(1-Mff)-0.008 %%%%%%%%%% WTO_To_WPL(j,i) = b*Wto/(Wpl-c*(1-b)*Wto); WTO_To_WPL_R(j,i) = (b*Wto/(Wpl-c*(1-b)*Wto))/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Empty weight %%%%%%%%%%%%%%%%%%%%%%%%% WTO_TO_WE(j,i) = b*Wto/(10^((log10(Wto)-a)/b)); WTO_TO_WE_R(j,i) = (b*Wto/(10^((log10(Wto)-a)/b)))/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Range%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% f = (-b*(Wto)^2*(1+0.25)*Mff)/(c*(1-b)*Wto-Wpl); RR = Cpcr/(375*Eff_Pcr*LDcr); WTO_TO_R(j,i) = f*RR; WTO_TO_R_R(j,i) = (f*RR)/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Cpcr %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% WTO_TO_Cpcr(j,i) = f*Rcr/(375*Eff_Pcr*LDcr); WTO_TO_Cpcr_R(j,i) =(f*Rcr/(375*Eff_Pcr*LDcr))/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Propeller Efficiency %%%%%%%%%%%%%%%%%%
WTO_TO_Eff_Pcr(j,i)= -f*Rcr*Cpcr/(375*(Eff_Pcr)^2*(LDcr)); WTO_TO_Eff_Pcr_R(j,i)= (-f*Rcr*Cpcr/(375*(Eff_Pcr)^2*(LDcr)))/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to L/D %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% WTO_TO_LDcr(j,i) = -f*Rcr*Cpcr/(375*Eff_Pcr*(LDcr)^2); WTO_TO_LDcr_R(j,i) = (-f*Rcr*Cpcr/(375*Eff_Pcr*(LDcr)^2))/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Endurance %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% EE = Vcr*Cpcr/(375*Eff_Pcr*LDcr); WTO_TO_E(j,i) = f*EE; WTO_TO_E_R(j,i) = (f*EE)/Wto; end end %mesh(Wto1,LD1,WTO_To_WPL) figure(1) surf(Wto1,LD1,WTO_To_WPL) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to PayLoad'); figure(2) surf(Wto1,LD1,WTO_TO_R) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to Range'); figure(3) surf(Wto1,LD1,WTO_TO_LDcr) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to (L/D)cr'); figure(4) surf(Wto1,LD1,WTO_TO_E) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to Endurance'); figure(5) surf(Wto1,LD1,WTO_To_WPL_R) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to PayLoad Relative to Take Off Weight'); figure(6)
surf(Wto1,LD1,WTO_TO_R_R) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to Range Relative to Take Off Weight'); figure(7) surf(Wto1,LD1,WTO_TO_LDcr_R) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to (L/D)cr Relative to Take Off Weight'); figure(8) surf(Wto1,LD1,WTO_TO_E_R) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to Endurance Relative to Take Off Weight'); %figure(1); %plot(Wto1,WTO_To_WPL) %xlabel('Take off weight in LB'); %ylabel('Sensitivity to PayLoad'); %figure(2); %plot(Wto1,WTO_TO_R) %xlabel('Take off weight in LB'); %ylabel('Sensitivity to Range'); %figure(3); %plot(Wto1,WTO_TO_Cpcr) %xlabel('Take off weight in LB'); %ylabel('Sensitivity to Specific Fuel Consumption'); %figure(4); %plot(Wto1,WTO_TO_LDcr) %xlabel('Take off weight in LB'); %ylabel('Sensitivity to (L/D)cr'); %figure(5); %plot(Wto1,WTO_TO_E) %xlabel('Take off weight in LB'); %ylabel('Sensitivity to Endurance');
%%%%%%%%%%%%%% Preliminary Sizing of UAV %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%% Sizing to Take Off Distance %%%%%%%%%%%%%%%%%%%%%%%% GL=300; %%%%%%%%%%%%%%%%%%%%%%% Ground Roll in feet..........Design Requirement GLP=solve('0.009*x^2+4.9*x-300');%%%%%%%%%%%%%%% Calculating Take Off Parameter TOP=GLP(2) ; %%%%%%%%%%%% Take Off Parameter row=0.002378 ; %%%%% Slugs/Cubic ft AR=12; %%%%%%%%%%%%% Aspect Ratio CD0=0.031; %%%%% at zero lift curve Oswald=0.8; %%%%%%%%%%%%%Oswald Effeiciency Factor Eff_Pcr=0.8 ; %%%%%%%%%%%% Propeller Efficiency row_rel=0.95; %%%%%%%%%%%%%%% Relative Density at 2000 meter altitude LDcr = 14 ; %%%%%%%%%%%% Selected According to Datcom Calculation W_P1=[1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8]; j=0; for CLmax =1.6:0.1:2.3 %%%%%%%%%%%%%%%%%%%%%%%%select CLmaxTO up to 2 in take off as it should be less than the CLmax in the normal case j=j+1; i=0; for W_S = 2:2:20 i=i+1; W_P1(i,j)=(TOP*row_rel*CLmax/W_S); end end W_S = 2:2:20; plot(W_S, W_P1(:,1)', W_S, W_P1(:,2)', W_S, W_P1(:,3)', W_S, W_P1(:,4)', W_S, W_P1(:,5)', W_S, W_P1(:,6)',W_S, W_P1(:,7)', W_S, W_P1(:,8)') %%%%%%%%%%%%%% Sizing to Stall Speed %%%%%%%%%%%%%%%%%%%%%%%% row=0.002378 ; %%%%% Slugs/Cubic ft j=0; forVstall =60:10:90 %%%%%%%%%% km/hr j=j+1; CLmax = 2.3;
W_S1(j)=(0.5*row*CLmax*Vstall^2)/1.204; end j=0; for j=0:1:3 j=j+1 i=0 for i=0:1:7 i=i+1 W_S2 (i,j)=W_S1(j) end end W_P2 = 0:10:70; plot(W_S2(:,1)', W_P2, W_S2(:,2)', W_P2, W_S2(:,3)', W_P2, W_S2(:,4)', W_P2, W_S, W_P1(:,1)', W_S, W_P1(:,2)', W_S, W_P1(:,3)', W_S, W_P1(:,4)', W_S, W_P1(:,5)', W_S, W_P1(:,6)',W_S, W_P1(:,7)', W_S, W_P1(:,8)') %%%%%%%%%%%%%% Sizing to Landing Limits %%%%%%%%%%%%%%%%%%%%%%%% CLmax = 2.3; row=0.002378 ; %%%%% Slugs/Cubic ft CLland=CLmax-0.2; %%%%%%%%%%% Landing Lift Coefficient CLmax=2.1 j=0; forVstall =60:10:90 %%%%%%%%%% km/hr j=j+1; W_S10(j)=(0.5*row*CLland*(Vstall*1.3)^2)/1.204; end j=0; for j=0:1:3 j=j+1 i=0 for i=0:1:7 i=i+1 W_S20 (i,j)=W_S10(j) end end %%%%%%%%%%%%%% Sizing to Cruise Speed %%%%%%%%%%%%%%%%%%%%%%%% row=0.002378 ; %%%%% Slugs/Cubic ft j=0; for Vcruise =100:10:200 %%%%%%%%%%%%%%% Vcruise in Km/hr j=j+1;
i=0; for W_S = 2:2:20 i=i+1; Ip=Vcruise/227; W_P3(i,j)=W_S/(row_rel*(Ip^3)); end end W_S = 2:2:20; %plot(W_S2(:,1)', W_P2, W_S2(:,2)', W_P2, W_S2(:,3)', W_P2, W_S2(:,4)', W_P2, W_S, W_P1(:,1)', W_S, W_P1(:,2)', W_S, W_P1(:,3)', W_S, W_P1(:,4)', W_S, W_P1(:,5)', W_S, W_P1(:,6)',W_S, W_P1(:,7)', W_S, W_P1(:,8)',W_S, W_P3(:,1)', W_S, W_P3(:,2)', W_S, W_P3(:,3)', W_S, W_P3(:,4)', W_S, W_P3(:,5)',W_S, W_P3(:,6)', W_S, W_P3(:,7)', W_S, W_P3(:,8)', W_S, W_P3(:,9)', W_S, W_P3(:,10)') %%%%%%%%%%%%%% Sizing to Rate of Climb %%%%%%%%%%%%%%%%%%%%%%%% row=0.002378 ; %%%%% Slugs/Cubic ft row_rel=0.95; %%%%%%%%%% Relative density CL32CD=(1.345*(AR*Oswald)^(3/4))/(CD0^(1/4)) j=0; for RC =0:100:600 j=j+1; RCP=RC/33000; i=0; for W_S = 2:2:20 i=i+1; W_P4=Eff_Pcr/(RCP+(W_S^0.5)/(19*CL32CD*(row_rel^0.5))) W_P5(i,j)=W_P4; end end W_S = 2:2:20; %plot(W_S2(:,1)', W_P2, W_S2(:,2)', W_P2, W_S2(:,3)', W_P2, W_S2(:,4)', W_P2, W_S, W_P1(:,1)', W_S, W_P1(:,2)', W_S, W_P1(:,3)', W_S, W_P1(:,4)', W_S, W_P1(:,5)', W_S, W_P1(:,6)',W_S, W_P1(:,7)', W_S, W_P1(:,8)',W_S, W_P3(:,1)', W_S, W_P3(:,2)', W_S, W_P3(:,3)', W_S, W_P3(:,4)', W_S, W_P3(:,5)',W_S, W_P3(:,6)', W_S, W_P3(:,7)', W_S, W_P3(:,8)', W_S, W_P3(:,9)', W_S, W_P3(:,10)',W_S, W_P5(:,1)', W_S, W_P5(:,2)', W_S, W_P5(:,3)', W_S, W_P5(:,4)', W_S, W_P5(:,5)', W_S, W_P5(:,6)',W_S, W_P5(:,7)') %plot(W_S, W_P5(:,1)', W_S, W_P5(:,2)', W_S, W_P5(:,3)') %%%%%%%%%%%%%% Sizing to of Climb Gradient %%%%%%%%%%%%%%%%%%%%%%%% row=0.002378 ; %%%%% Slugs/Cubic ft row_rel=0.95; %%%%%%%%%% Relative density CL32CD=(1.345*(AR*Oswald)^(3/4))/(CD0^(1/4));
CLClimb=1.4; %%%%%%%%%%%%CL Climb=CLmax-0.2%%%%%%%%%%%CLmax for clean configuration as it is a requirement Vstall=3298;%%%%%%% ft/min ===== 60 km/hr Vto=1.3*Vstall%%%%%%%%%%%Consider Vto=VRoCmax j=0; for RC =0:100:600 j=j+1; CGR=RC/Vto; CGRP=(CGR+LDcr^(-1))/(CLClimb^(0.5)); i=0; for W_S = 2:2:20 i=i+1; W_P6=(18.97*Eff_Pcr*row_rel^(0.5))/(CGRP*(W_S^(0.5))); W_P7(i,j)=W_P6; end end W_S =2:2:20; plot(W_S20(:,1)', W_P2, W_S20(:,2)', W_P2, W_S20(:,3)', W_P2, W_S20(:,4)', W_P2,W_S2(:,1)', W_P2, W_S2(:,2)', W_P2, W_S2(:,3)', W_P2, W_S2(:,4)', W_P2, W_S, W_P1(:,1)', W_S, W_P1(:,2)', W_S, W_P1(:,3)', W_S, W_P1(:,4)', W_S, W_P1(:,5)', W_S, W_P1(:,6)',W_S, W_P1(:,7)', W_S, W_P1(:,8)',W_S, W_P3(:,1)', W_S, W_P3(:,2)', W_S, W_P3(:,3)', W_S, W_P3(:,4)', W_S, W_P3(:,5)',W_S, W_P3(:,6)', W_S, W_P3(:,7)', W_S, W_P3(:,8)', W_S, W_P3(:,9)', W_S, W_P3(:,10)',W_S, W_P5(:,1)', W_S, W_P5(:,2)', W_S, W_P5(:,3)', W_S, W_P5(:,4)', W_S, W_P5(:,5)', W_S, W_P5(:,6)',W_S, W_P5(:,7)',W_S, W_P7(:,1)', W_S, W_P7(:,2)', W_S, W_P7(:,3)', W_S, W_P7(:,4)', W_S, W_P7(:,5)', W_S, W_P7(:,6)',W_S, W_P7(:,7)') grid on xlim([2 20]); ylim([2 30]); set(gca,'XTick',1:1:20) set(gca,'YTick',1:1:30) xlabel('Wing Loading lb/ft2'); ylabel('Power Loading lb/hr'); title('Matching Graph');
%%%%%%%%%%%%%%%%%%% Performance Program to calculate the Flight %%%%%%%%%%%%%%%%%%% Stability Derivatives of the Final Platform without %%Gimbal CLP=[-0.008304 -0.008555 -0.008720 -0.008913 -0.009090 -0.009250 -0.009392 -0.009517 -0.009600 -0.009699 -0.008722 -0.004094 -0.003643 -0.002706]; CNR=[-0.001342 -0.001365 -0.001381 -0.001401 -0.001426 -0.001455 -0.001488 -0.001526 -0.001585 -0.001616 -0.001788 -0.002072 -0.002086 -0.002098]; CM=[0.0632 0.0642 0.0382 0.0323 0.0271 0.0204 0.0131 0.0056 -0.0004 - 0.0103 -0.0346 -0.1037 -0.1088 -0.1141]; CMA=[-0.005988 -0.008453 -0.007224 -0.005474 -0.005967 -0.006980 -0.007399 -0.007662 -0.007903 -0.008077 -0.009225 -0.01029 -0.01038 -0.01076]; CLB=[-0.001326 -0.001319 -0.001316 -0.001313 -0.001310 -0.001308 -0.001307 -0.001305 -0.001304 -0.001303 -0.001300 -0.001232 -0.001222 -0.001211]; %%%%%%%%%%%%%%%%%%% Stability Derivatives of the Final Platform with Gimbal CLP1=[-0.008306 -0.008556 -0.008720 -0.008913 -0.009089 -0.009248 - 0.009390 -0.009515 -0.009598 -0.009697 -0.008721 -0.004099 -0.003648 - 0.002712]; CNR1=[-0.001519 -0.001544 -0.001562 -0.001584 -0.001609 -0.001639 - 0.001673 -0.001712 -0.001745 -0.001804 -0.001977 -0.002260 -0.002274 - 0.002286]; CM1=[0.0733 0.0546 0.0443 0.0367 0.0302 0.0227 0.0141 0.0053 -0.0017 - 0.0132 -0.0432 -0.1174 -0.1229 -0.1285]; CMA1=[-0.007302 -0.009955 -0.008920 -0.007031 -0.007006 -0.008051 - 0.008681 -0.008964 -0.009207 -0.009561 -0.01078 -0.01116 -0.01113 - 0.01128]; CLB1=[-0.001383 -0.001368 -0.001360 -0.001353 -0.001347 -0.001341 - 0.001335 -0.001329 -0.001325 -0.001319 -0.001304 -0.001213 -0.001201 - 0.001188];
%%%%%%%%%%%%%%%%%%% Equilibrium Diagram at different Re numbers.... %%%%%%%%%%%%%%%%%%%% CL, CD for different Re numbers / from DATCOM results Alfa=[-3 -1 0 1 2 3 4 5 5.8 7 10 16 16.5 17 18 19]'; %%%% AOA up to Maximum Lift Coefficient Alfa_1=[-3 -1 0 1 2 3 4 5 5.8 7 10 16 16.5 17 18 19]'; %%%%%%%%% AOA up to stall curve Alfa_2=[-3 -1 0 1 2 3 4 5 5.8 7 10 16 16.5 17]'; %%%%%%%%% AOA up to stall curve CD=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; CL=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; %%%%%%%%%%%%% Re number < 700000 CD0=[0.025 0.024 0.024 0.025 0.027 0.029 0.033 0.036 0.040 0.046 0.066 0.107 0.110 0.112 0.115 0.111]'; CL0=[-0.132 0.053 0.147 0.242 0.339 0.438 0.539 0.641 0.722 0.850 1.166 1.598 1.620 1.639 1.656 1.599]'; %%%%%%%%%%%%% Re number < 1400000 CD1=[0.022 0.021 0.021 0.022 0.024 0.027 0.030 0.033 0.037 0.043 0.064 0.104 0.107 0.109 0.112 0.108]'; CL1=[-0.132 0.053 0.147 0.242 0.339 0.438 0.539 0.641 0.722 0.850 1.167 1.598 1.620 1.639 1.656 1.599]'; %%%%%%%%%%%%% Re number < 3000000 CD2=[0.020 0.019 0.020 0.021 0.022 0.025 0.028 0.032 0.035 0.041 0.062 0.102 0.105 0.107 0.110 0.106]'; CL2=[-0.132 0.053 0.147 0.243 0.340 0.440 0.541 0.644 0.742 0.852 1.170 1.600 1.622 1.641 1.653 1.596]'; %%%%%%%%%%%%% Re number < %%%%%%%%%%%% CD3=[0.025 0.024 0.024 0.025 0.027 0.029 0.033 0.036 0.040 0.046 0.066 0.107 0.110 0.112 0.115 0.111]'; CL3=[-0.132 0.053 0.147 0.242 0.339 0.438 0.539 0.641 0.722 0.850 1.166 1.598 1.620 1.639 1.656 1.599]'; %%%%%%%%%%%%% Re number < %%%%%%%%%%%% CD4=[0.025 0.024 0.024 0.025 0.027 0.029 0.033 0.036 0.040 0.046 0.066 0.107 0.110 0.112 0.115 0.111]'; CL4=[-0.132 0.053 0.147 0.242 0.339 0.438 0.539 0.641 0.722 0.850 1.166 1.598 1.620 1.639 1.656 1.599]'; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Array Definitions D=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; TAS=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; %CLCD=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; P_av=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; P_av_1=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; P_req=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; %%%%%%%%%%%%%%% Efficiency of Propeller versus Advance Ratio J_R=[0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3]'; Eta_R=[0.48 0.6 0.7 0.8 0.9 0.97 1 0.95 0.85 0.6]'; e3=[ones(size(J_R)) J_R J_R.^2 J_R.^3 J_R.^4];
C3=e3Eta_R; z=polyfit(J_R,Eta_R,10) %%%%%%%%%%%% Engine Design Data J_Design=30/(7600*0.66); %%%%%%%%%% Advance Ratio at design condition Eff_Design=0.7; %%%%%%%%%%%%%%%% Efficiency at design condition bhp_sl=28; %%%%%%%%%%%%%%%% Brake Power at sea level %%%%%%%%%%%%%%%%%%%%% Input Conditions %%%%H=0; %%%%% Altitude in Km MAC=0.59; %%%%%%%% m Mean Aerodynamic Chord MTOW=160; %%%% Kg Maximum Take Off Weight of the UAV CLMAX=2.3; %%%%%%% Maximum Lift Coefficient with flaps CLMAX_noflaps=2.3; %%%%%%% Maximum Lift Coefficient without flaps / sometimes with flaps S=4.1; %%%%%%%%%% m^2 Wing Area %%%row=1.225; %%%%%%%%%% Kg/m^3 Density at Sea Level P0=101325; %%%%% Pa Pressure at Sea Level ISA T0=288.15; %%%%% deg K Temperature at Sea Level ISA g=9.80665; %%%%% m/s^2 gravity L=6.5; %%%% deg K/Km Lapse rate R=8.31432; %%%%% J/mol*deg K Gas Constant M=28.9644; %%%%%%%%%% gm/mol Molecular Weight miu=0.0000178934; %%%%%%%%%%%%%% Air Viscosity P_Dyn_Max=0.5*1.225*40*40; %%%%%%%%%%%% Pa Max Dynamic Pressure at Sea Level %%% 3 times the selected wing loading (980 Pa) x0=0; x1=0; x2=0; x3=0; x4=0; x5=0; x6=0; x7=0; x11=0; x12=0; x13=0; u=0; q=0; for H=0:0.125:10 %%%%%%%%%%%%%%% change 0.125 to 0.5 for EFD q=q+1 %%%%%%%%%%%%% Pressure, Temperature and Density Calculation at ISA T=T0-L*H; P=P0*(1-((L*H)/T0))^((g*M)/(R*L)); row=(P*M)/(R*T*1000); bhp=bhp_sl*((row/1.225)-((1-row/1.225))/7.55);
v_stall=((2*MTOW*g)/(row*S*CLMAX_noflaps))^(0.5) for i=1:1:640 %%%%%%%%%%% Speed Increment TAS(i)=2+0.0625*i; %%%%%%%%%%% Load Factor / Stalling Limit Calculation %%%%%%%%%%%%%%%% n(i,q)=(TAS(i)/v_stall)^2; %%%%%%%%%%% Re number Calculation %%%%%%%%%%%%%%%% Re=(row*TAS(i)*MAC)/miu if Re < 700000 %Rule CL=CL0; CD=CD0; elseif Re < 1400000 CL=CL1; CD=CD1; elseif Re < 3000000 CL=CL2; CD=CD2; end j=0; for j=1:1:16 CLCD0(j)=CL0(j)/CD0(j); CLCD1(j)=CL1(j)/CD1(j); CLCD2(j)=CL2(j)/CD2(j); end e1=[ones(size(Alfa)) Alfa]; C1=e1CL; e2=[ones(size(Alfa)) CL.^2]; C2=e2CD; %%%%%%%%%%%%%%%% Calculating Required and Available Power CL_Cal=MTOW*9.8/(0.5*row*TAS(i)^2*S); CD_Cal=[1 CL_Cal^2]*C2;
J_R_Cal=(TAS(i)/(7600*0.66))/J_Design; Eta_R_Cal=[1 J_R_Cal J_R_Cal^2 J_R_Cal^3 J_R_Cal^4]*C3; Eta_R_Cal_1=polyval(z,J_R_Cal); Eta_Cal=Eta_R_Cal*Eff_Design; Eta_Cal_1=Eta_R_Cal_1*Eff_Design; P_av(i)=Eta_Cal*bhp*743; P_av_1(i)=Eta_Cal_1*bhp*743; D(i)=0.5*row*TAS(i)^2*S*CD_Cal*1.5;%%%%%%%%%%%%%%%%%%%%%%%%% Adding 50% extra of total drag due to landing gear and antennas P_req(i)=D(i)*TAS(i); if abs(P_av(i) - P_req(i)) < 10 u=u+1; V_H(u,1)=TAS(i); V_H(u,2)=H; else end P_av_H(i,q)=P_av(i); P_req_H(i,q)=P_req(i); T_av_H(i,q)=P_av(i)/TAS(i); %%%%%%%%%%% Maximum Load Factor Limit %%%%%%%%%%%%%%%% C16=(0.5*row*((TAS(i))^2)*S)/(C2(2)*MTOW*g); C71=(0.5*row*((TAS(i))^2)*S*C2(1))/(MTOW*g); n_max(i,q)=(C16*((T_av_H(i,q)/(MTOW*g))-C71))^(0.5); r_min(i,q)=(4*C2(2)*(MTOW*g/S))/(g*row*(T_av_H(i,q)/(MTOW*g))*(1- (4*C2(2)*C2(1)/((T_av_H(i,q)/(MTOW*g))^2)))^(0.5)); n_r_min(i,q)=(2-(4*C2(2)*C2(1))/(T_av_H(i,q)/(MTOW*g))^2)^(0.5); CL_r_min(i,q)=(n_r_min(i,q)*MTOW*g)/(0.5*row*(TAS(i))^2*S); Fai_r_min(i,q)=57.3*acos(1/n_r_min(i,q)); TAS_r_min(i,q)=((4*C2(2)*(MTOW*g/S))/(row*(T_av_H(i,q)/(MTOW*g))))^(0.5); %%%%%%%%%%%%% Correct Turn Caculation
Thrust(i)=TAS(i)*10; r_min1(i,q)=(4*C2(2)*(MTOW*g/S))/(g*row*(Thrust(i)/(MTOW*g))*(1- (4*C2(2)*C2(1)/((Thrust(i)/(MTOW*g))^2)))^(0.5)); n_r_min1(i,q)=(2-(4*C2(2)*C2(1))/(Thrust(i)/(MTOW*g))^2)^(0.5); Fai_r_min1(i,q)=57.3*acos(1/n_r_min1(i,q)); TAS_r_min1(i,q)=((4*C2(2)*(MTOW*g/S))/(row*(Thrust(i)/(MTOW*g))))^(0.5); CL_r_min1(i,q)=(n_r_min1(i,q)*MTOW*g)/(0.5*row*(TAS_r_min1(i,q))^2*S); %%%%%%%%%%% Minimum Time Trajectory P_Excess_Sp=(P_av(i)-P_req(i))/(MTOW*9.8); ifP_Excess_Sp< 1 &&P_Excess_Sp>0.5 x0=x0+1; V_H_8(x0,1)=TAS(i); V_H_8(x0,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifP_Excess_Sp< 2 &&P_Excess_Sp>1.5 x2=x2+1; V_H_3(x2,1)=TAS(i); V_H_3(x2,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifP_Excess_Sp< 3 &&P_Excess_Sp>2.5 x3=x3+1; V_H_4(x3,1)=TAS(i); V_H_4(x3,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8);
%P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifP_Excess_Sp< 4 &&P_Excess_Sp>3.5 x4=x4+1; V_H_5(x4,1)=TAS(i); V_H_5(x4,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifP_Excess_Sp< 5 &&P_Excess_Sp>4.5 x5=x5+1; V_H_6(x5,1)=TAS(i); V_H_6(x5,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifP_Excess_Sp< 6 &&P_Excess_Sp>5.5 x6=x6+1; V_H_7(x6,1)=TAS(i); V_H_7(x6,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end end %%%%%%%%%%%%%Maximum Dynamic Pressure Limit V=((2*P_Dyn_Max)/row)^(0.5); V_H_1(q,1)=V; V_H_1(q,2)=H; %%%%%%%%%%%%% Stalling Limit V_min=((2*MTOW*9.8)/(row*CLMAX*S))^(0.5); V_H_2(q,1)=V_min; V_H_2(q,2)=H;
%%%%%%%%%%%%%%%%%%%%%% Performance Figures %figure(1) %plot(TAS,D) %xlabel('TAS'); %ylabel('Drag'); %figure(2) %plot(Alfa,CL,Alfa,e1*C1) %xlabel('Alfa'); %ylabel('CL'); %figure(3) %plot(Alfa,CLCD) %xlabel('Alfa'); %ylabel('CL/CD'); %figure(4) %plot(TAS,P_av,TAS,P_req) %xlabel('TAS'); %ylabel('Power'); end %%%%%%%%%%%%% Aircraft Energy Lines for z=0:0.0625:10 for i=1:1:2640 TAS1(i)=0+0.0625*i; AC_Energy=z*1000+(0.5*TAS1(i)*TAS1(i))/g; ifAC_Energy< 1040 &&AC_Energy>960 x1=x1+1; V_H_80(x1,1)=TAS1(i); V_H_80(x1,2)=z; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifAC_Energy< 3040 &&AC_Energy>2960 x11=x11+1; V_H_801(x11,1)=TAS1(i); V_H_801(x11,2)=z;
%P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifAC_Energy< 5040 &&AC_Energy>4960 x12=x12+1; V_H_802(x12,1)=TAS1(i); V_H_802(x12,2)=z; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifAC_Energy< 7040 &&AC_Energy>6960 x13=x13+1; V_H_803(x13,1)=TAS1(i); V_H_803(x13,2)=z; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end end end figure(3) plot(Alfa,CLCD0,Alfa,CLCD1,Alfa,CLCD2) xlabel('Alfa (deg)'); ylabel('CL/CD'); figure(4) plot(TAS,P_av_H(:,1)',TAS,P_req_H(:,1)',TAS,P_av_H(:,2)',TAS,P_req_H(:,2)' ,TAS,P_av_H(:,3)',TAS,P_req_H(:,3)',TAS,P_av_H(:,4)',TAS,P_req_H(:,4)',TAS ,P_av_H(:,5)',TAS,P_req_H(:,5)',TAS,P_av_H(:,6)',TAS,P_req_H(:,6)',TAS,P_a v_H(:,7)',TAS,P_req_H(:,7)',TAS,P_av_H(:,8)',TAS,P_req_H(:,8)',TAS,P_av_H( :,9)',TAS,P_req_H(:,9)',TAS,P_av_H(:,10)',TAS,P_req_H(:,10)',TAS,P_av_H(:, 11)',TAS,P_req_H(:,11)',TAS,P_av_H(:,12)',TAS,P_req_H(:,12)',TAS,P_av_H(:, 13)',TAS,P_req_H(:,13)',TAS,P_av_H(:,14)',TAS,P_req_H(:,14)',TAS,P_av_H(:, 15)',TAS,P_req_H(:,15)',TAS,P_av_H(:,16)',TAS,P_req_H(:,16)',TAS,P_av_H(:, 17)',TAS,P_req_H(:,17)',TAS,P_av_H(:,18)',TAS,P_req_H(:,18)',TAS,P_av_H(:, 19)',TAS,P_req_H(:,19)',TAS,P_av_H(:,20)',TAS,P_req_H(:,20)') xlabel('TAS (m/s)'); ylabel('Power (watt)'); figure(5)
plot(V_H(:,1),V_H(:,2),'*',V_H_1(:,1),V_H_1(:,2),'o',V_H_2(:,1),V_H_2(:,2) ,'o') xlabel('TAS (m/s)'); ylabel('Altitude (m)'); figure(6) plot(V_H_1(:,1),V_H_1(:,2),'o') xlabel('TAS (m/s)'); ylabel('Altitude (m)'); figure(7) plot(Alfa, CL0, Alfa, CL1, Alfa, CL2) xlabel('Angle of Attack (deg)'); ylabel('CL'); figure(8) plot(CD0, CL0, CD1, CL1, CD2, CL2) xlabel('CD'); ylabel('CL'); figure(9) plot(V_H_3(:,1)',V_H_3(:,2)','*',V_H_4(:,1)',V_H_4(:,2)','*',V_H_5(:,1)',V _H_5(:,2)','*',V_H_6(:,1)',V_H_6(:,2)','*',V_H_7(:,1)',V_H_7(:,2)','*',V_H _8(:,1)',V_H_8(:,2)','*',V_H_80(:,1)',V_H_80(:,2)','- ',V_H_801(:,1)',V_H_801(:,2)','-',V_H_802(:,1)',V_H_802(:,2)','- ',V_H_803(:,1)',V_H_803(:,2)','-') xlabel('TAS (m/s)'); ylabel('Altitude (Km)'); figure(10) plot(TAS,n(:,1)',TAS,n(:,2)') xlabel('TAS (m/s)'); ylabel('Load Factor '); figure(11) plot(TAS,n(:,1)',TAS,n_max(:,1)',TAS,n(:,21)',TAS,n_max(:,21)',TAS,n(:,41) ',TAS,n_max(:,41)',TAS,n(:,61)',TAS,n_max(:,61)',TAS,n(:,81)',TAS,n_max(:, 81)') xlabel('TAS (m/s)'); ylabel('Load Factor '); figure(12) plot(Alfa_2,CMA1,Alfa_2,CMA) xlabel('Angle of Attack (deg)'); ylabel('CMA1 '); figure(13) plot(Alfa_2,CM1,Alfa_2,CM) xlabel('Angle of Attack (deg)'); ylabel('CM '); figure(14) plot(Alfa_2,CNR1,Alfa_2,CNR)
xlabel('Angle of Attack (deg)'); ylabel('CNR '); figure(15) plot(Alfa_2,CLP1,Alfa_2,CLP) xlabel('Angle of Attack (deg)'); ylabel('CLP '); figure(16) plot(Alfa_2,CLB1,Alfa_2,CLB) xlabel('Angle of Attack (deg)'); ylabel('CLB '); figure(17) plot(TAS,r_min(:,1)',TAS,(n_r_min(:,1)*10)',TAS,(CL_r_min(:,1)*10)',TAS,Fa i_r_min(:,1)',TAS,TAS_r_min(:,1)') %plot(TAS_r_min(:,1)',r_min(:,1)',TAS_r_min(:,1)',(n_r_min(:,1)*10)',TAS_r _min(:,1)',(CL_r_min(:,1)*10)',TAS_r_min(:,1)',Fai_r_min(:,1)') xlabel('TAS (m/s)'); ylabel('Minimum Turn Radius '); figure(18) %plot(TAS,r_min(:,1)',TAS,(n_r_min(:,1)*10)',TAS,(CL_r_min(:,1)*10)',TAS,F ai_r_min(:,1)',TAS,TAS_r_min(:,1)') plot(Thrust',r_min1(:,1)',Thrust',(n_r_min1(:,1)*10)',Thrust',(CL_r_min1(: ,1)*10)',Thrust',Fai_r_min1(:,1)',Thrust',TAS_r_min1(:,1)') xlabel('TAS (m/s)'); ylabel('Minimum Turn Radius ');
Matlab codes for Sizing and Calculating the Aircraft Stability & Performance

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Matlab codes for Sizing and Calculating the Aircraft Stability & Performance

  • 1. %%%%%%% UAV Weight Estimation and Sensitivity Analysis %%%%%%%%%%%% wwto=[330 440 451 418 443 584 451 339 661]; wwe=[110 220 304 275 324 328 275 200 473]; wwto=log10(wwto) wwe=log10(wwe) e1=[ones(size(wwto')) wwe']; C1=e1wwto' %%%%%%% UAV Weight Calculations %%%%%%%%%%%% Wto =160*2.2; %%%%%%%% Wto in LB Wpl = 30*2.2; %%%%%%%%% Wpl in LB a=0.04; %%%%%%%0.05; %C1(1); %%%%0.05; %%%%%%%%%%%%%%Light Airplane - 0.114; %%%%%%%%% Regression Line b=1.086; %%%%%%%%%%1.078; %C1(2); %%%%1.078; %%%%%%%% Light Airplane 1.1162; %%%%%%%%% Regression Line Vcr=75; %%%%%%%%% in mph %%%%%%% Regression Line for Allowable Value of Empty Weight %%%%%%%%%%% log10We = (log10(Wto)- a)/b Weall=10^(log10We) %%%%%%%%%%% We in LB W1_Wto = 0.97; W2_W1 = 0.985; W3_W2 = 0.988; W4_W3 = 0.999; W6_W5 = 0.988; W7_W6 = 0.995; Rcr=960/1.6 ;%%%%%%%%%%%%% in miles Eff_Pcr = 0.8; %%%%%%% between 0.75-0.8 Cpcr = 0.9 ; %%%%%%%%%%%%%%%%%%% Lbs/hp/hr
  • 2. LDcr = 14 ; %%%%%%%%%%%% Selected According to Datcom Calculation lnW4_W5 = Rcr/(375*(Eff_Pcr/Cpcr)*LDcr); %%%%%%%%%Breguet's Range equation for propeller driven airplanes W5_W4 =1/exp(lnW4_W5); Mff=W1_Wto*W2_W1*W3_W2*W4_W3*W5_W4*W6_W5*W7_W6 %%%%%%%%%%Fuel Fraction Wfused=(1-Mff)*Wto ;%%%%%%%%%%% Used Fuel Wf = 1.25*Wfused %%%%%%%%%%%%%%% Total Fuel Weight Woe = Wto - Wf - Wpl ; %%%%%%%%%%%%% Operating Empty Weight We = Woe - 0.008*Wto %%%%%%%%%%%%% Empty weight %%%%%%%%%%%%%%%%%%%%% Sensitivity of TakeOff Weight to Payload %%%%%%%%%%%%%%%%%%%%%%%%%%%% c=1-(1+0.25)*(1-Mff)-0.008 %%%%%%%%%% WTO_To_WPL = b*Wto/(Wpl-c*(1-b)*Wto) %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Empty weight %%%%%%%%%%%%%%%%%%%%%%%%% WTO_TO_WE = b*Wto/(10^((log10(Wto)-a)/b)) %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Range%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% f = (-b*(Wto)^2*(1+0.25)*Mff)/(c*(1-b)*Wto-Wpl) RR = Cpcr/(375*Eff_Pcr*LDcr); WTO_TO_R = f*RR %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Cpcr %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% WTO_TO_Cpcr = f*Rcr/(375*Eff_Pcr*LDcr) %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Propeller Efficiency %%%%%%%%%%%%%%%%%% WTO_TO_Eff_Pcr= -f*Rcr*Cpcr/(375*(Eff_Pcr)^2*(LDcr)) %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to L/D %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  • 3. WTO_TO_LDcr = -f*Rcr*Cpcr/(375*Eff_Pcr*(LDcr)^2) %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Endurance %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% EE = Vcr*Cpcr/(375*Eff_Pcr*LDcr); WTO_TO_E = f*EE
  • 4. %%%%%%% Sensitivity Analysis (Continuous) %%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% UAV Weight Calculations %%%%%%%%%%%% Wto = 80*2.25; %%%%%%%% Wto in LB Wpl = 15*2.25; %%%%%%%%% Wpl in LB Wto1=[57 77 96 115 133 150 167 184 200 217].*2.25; Wpl1=[10 15 20 25 30 35 40 45 50 55].*2.25; LD1=[10 11 12 13 14 15 16 17 18 19]; for j=1:1:10 for i=1:1:10 Wto = Wto1(i); %%%%%%%% Wto in Kg Wpl = Wpl1(i); %%%%%%%%% Wpl in Kg a=0.05; %%%%%%%%%%%%%%Light Airplane -0.114;%%%%%%%%% Regression Line b=1.078; %%%%%%%% Light Airplane 1.1162; %%%%%%%%% Regression Line Vcr=75; %%%%%%%%% in mph %%%%%%% Regression Line for Allowable Value of Empty Weight %%%%%%%%%%%5 log10We = (log10(Wto)- a)/b; Weall=10^(log10We) %%%%%%%%%%% We in LB W1_Wto = 0.97; W2_W1 = 0.997; W3_W2 = 0.998; W4_W3 = 0.992; W6_W5 = 0.993; W7_W6 = 0.993; Rcr=960/1.6 ;%%%%%%%%%%%%% in miles Eff_Pcr = 0.8; %%%%%%% between 0.75-0.8
  • 5. Cpcr = 0.483 ; %%%%%%%%%%%%%%%%%%% Lbs/hp/hr LDcr = 10+j ; %%%%%%%%%%%%LDcr=14 Selected According to Datcom Calculation according to the proposed platform lnW4_W5 = Rcr/(375*(Eff_Pcr/Cpcr)*LDcr); %%%%%%%%%Breguet's Range equation for propeller driven airplanes W5_W4 =1/exp(lnW4_W5); Mff=W1_Wto*W2_W1*W3_W2*W4_W3*W5_W4*W6_W5*W7_W6 ; %%%%%%%%%%Fuel Fraction Wfused=(1-Mff)*Wto ;%%%%%%%%%%% Used Fuel Wf = 1.25*Wfused ; %%%%%%%%%%%%%%% Total Fuel Weight Woe = Wto - Wf - Wpl ; %%%%%%%%%%%%% Operating Empty Weight We = Woe - 0.008*Wto %%%%%%%%%%%%% Empty weight %%%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Payload %%%%%%%%%%%%%%%%%%%%%%%%%%%% c=1-(1+0.25)*(1-Mff)-0.008 %%%%%%%%%% WTO_To_WPL(j,i) = b*Wto/(Wpl-c*(1-b)*Wto); WTO_To_WPL_R(j,i) = (b*Wto/(Wpl-c*(1-b)*Wto))/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Empty weight %%%%%%%%%%%%%%%%%%%%%%%%% WTO_TO_WE(j,i) = b*Wto/(10^((log10(Wto)-a)/b)); WTO_TO_WE_R(j,i) = (b*Wto/(10^((log10(Wto)-a)/b)))/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Range%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% f = (-b*(Wto)^2*(1+0.25)*Mff)/(c*(1-b)*Wto-Wpl); RR = Cpcr/(375*Eff_Pcr*LDcr); WTO_TO_R(j,i) = f*RR; WTO_TO_R_R(j,i) = (f*RR)/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Cpcr %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% WTO_TO_Cpcr(j,i) = f*Rcr/(375*Eff_Pcr*LDcr); WTO_TO_Cpcr_R(j,i) =(f*Rcr/(375*Eff_Pcr*LDcr))/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Propeller Efficiency %%%%%%%%%%%%%%%%%%
  • 6. WTO_TO_Eff_Pcr(j,i)= -f*Rcr*Cpcr/(375*(Eff_Pcr)^2*(LDcr)); WTO_TO_Eff_Pcr_R(j,i)= (-f*Rcr*Cpcr/(375*(Eff_Pcr)^2*(LDcr)))/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to L/D %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% WTO_TO_LDcr(j,i) = -f*Rcr*Cpcr/(375*Eff_Pcr*(LDcr)^2); WTO_TO_LDcr_R(j,i) = (-f*Rcr*Cpcr/(375*Eff_Pcr*(LDcr)^2))/Wto; %%%%%%%%%%%%%%%%%%%% Sensitivity of Take Off Weight to Endurance %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% EE = Vcr*Cpcr/(375*Eff_Pcr*LDcr); WTO_TO_E(j,i) = f*EE; WTO_TO_E_R(j,i) = (f*EE)/Wto; end end %mesh(Wto1,LD1,WTO_To_WPL) figure(1) surf(Wto1,LD1,WTO_To_WPL) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to PayLoad'); figure(2) surf(Wto1,LD1,WTO_TO_R) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to Range'); figure(3) surf(Wto1,LD1,WTO_TO_LDcr) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to (L/D)cr'); figure(4) surf(Wto1,LD1,WTO_TO_E) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to Endurance'); figure(5) surf(Wto1,LD1,WTO_To_WPL_R) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to PayLoad Relative to Take Off Weight'); figure(6)
  • 7. surf(Wto1,LD1,WTO_TO_R_R) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to Range Relative to Take Off Weight'); figure(7) surf(Wto1,LD1,WTO_TO_LDcr_R) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to (L/D)cr Relative to Take Off Weight'); figure(8) surf(Wto1,LD1,WTO_TO_E_R) xlabel('Take off weight in LB'); ylabel('L/D cruise'); zlabel('Sensitivity to Endurance Relative to Take Off Weight'); %figure(1); %plot(Wto1,WTO_To_WPL) %xlabel('Take off weight in LB'); %ylabel('Sensitivity to PayLoad'); %figure(2); %plot(Wto1,WTO_TO_R) %xlabel('Take off weight in LB'); %ylabel('Sensitivity to Range'); %figure(3); %plot(Wto1,WTO_TO_Cpcr) %xlabel('Take off weight in LB'); %ylabel('Sensitivity to Specific Fuel Consumption'); %figure(4); %plot(Wto1,WTO_TO_LDcr) %xlabel('Take off weight in LB'); %ylabel('Sensitivity to (L/D)cr'); %figure(5); %plot(Wto1,WTO_TO_E) %xlabel('Take off weight in LB'); %ylabel('Sensitivity to Endurance');
  • 8. %%%%%%%%%%%%%% Preliminary Sizing of UAV %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%% Sizing to Take Off Distance %%%%%%%%%%%%%%%%%%%%%%%% GL=300; %%%%%%%%%%%%%%%%%%%%%%% Ground Roll in feet..........Design Requirement GLP=solve('0.009*x^2+4.9*x-300');%%%%%%%%%%%%%%% Calculating Take Off Parameter TOP=GLP(2) ; %%%%%%%%%%%% Take Off Parameter row=0.002378 ; %%%%% Slugs/Cubic ft AR=12; %%%%%%%%%%%%% Aspect Ratio CD0=0.031; %%%%% at zero lift curve Oswald=0.8; %%%%%%%%%%%%%Oswald Effeiciency Factor Eff_Pcr=0.8 ; %%%%%%%%%%%% Propeller Efficiency row_rel=0.95; %%%%%%%%%%%%%%% Relative Density at 2000 meter altitude LDcr = 14 ; %%%%%%%%%%%% Selected According to Datcom Calculation W_P1=[1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8;1 2 3 4 5 6 7 8]; j=0; for CLmax =1.6:0.1:2.3 %%%%%%%%%%%%%%%%%%%%%%%%select CLmaxTO up to 2 in take off as it should be less than the CLmax in the normal case j=j+1; i=0; for W_S = 2:2:20 i=i+1; W_P1(i,j)=(TOP*row_rel*CLmax/W_S); end end W_S = 2:2:20; plot(W_S, W_P1(:,1)', W_S, W_P1(:,2)', W_S, W_P1(:,3)', W_S, W_P1(:,4)', W_S, W_P1(:,5)', W_S, W_P1(:,6)',W_S, W_P1(:,7)', W_S, W_P1(:,8)') %%%%%%%%%%%%%% Sizing to Stall Speed %%%%%%%%%%%%%%%%%%%%%%%% row=0.002378 ; %%%%% Slugs/Cubic ft j=0; forVstall =60:10:90 %%%%%%%%%% km/hr j=j+1; CLmax = 2.3;
  • 9. W_S1(j)=(0.5*row*CLmax*Vstall^2)/1.204; end j=0; for j=0:1:3 j=j+1 i=0 for i=0:1:7 i=i+1 W_S2 (i,j)=W_S1(j) end end W_P2 = 0:10:70; plot(W_S2(:,1)', W_P2, W_S2(:,2)', W_P2, W_S2(:,3)', W_P2, W_S2(:,4)', W_P2, W_S, W_P1(:,1)', W_S, W_P1(:,2)', W_S, W_P1(:,3)', W_S, W_P1(:,4)', W_S, W_P1(:,5)', W_S, W_P1(:,6)',W_S, W_P1(:,7)', W_S, W_P1(:,8)') %%%%%%%%%%%%%% Sizing to Landing Limits %%%%%%%%%%%%%%%%%%%%%%%% CLmax = 2.3; row=0.002378 ; %%%%% Slugs/Cubic ft CLland=CLmax-0.2; %%%%%%%%%%% Landing Lift Coefficient CLmax=2.1 j=0; forVstall =60:10:90 %%%%%%%%%% km/hr j=j+1; W_S10(j)=(0.5*row*CLland*(Vstall*1.3)^2)/1.204; end j=0; for j=0:1:3 j=j+1 i=0 for i=0:1:7 i=i+1 W_S20 (i,j)=W_S10(j) end end %%%%%%%%%%%%%% Sizing to Cruise Speed %%%%%%%%%%%%%%%%%%%%%%%% row=0.002378 ; %%%%% Slugs/Cubic ft j=0; for Vcruise =100:10:200 %%%%%%%%%%%%%%% Vcruise in Km/hr j=j+1;
  • 10. i=0; for W_S = 2:2:20 i=i+1; Ip=Vcruise/227; W_P3(i,j)=W_S/(row_rel*(Ip^3)); end end W_S = 2:2:20; %plot(W_S2(:,1)', W_P2, W_S2(:,2)', W_P2, W_S2(:,3)', W_P2, W_S2(:,4)', W_P2, W_S, W_P1(:,1)', W_S, W_P1(:,2)', W_S, W_P1(:,3)', W_S, W_P1(:,4)', W_S, W_P1(:,5)', W_S, W_P1(:,6)',W_S, W_P1(:,7)', W_S, W_P1(:,8)',W_S, W_P3(:,1)', W_S, W_P3(:,2)', W_S, W_P3(:,3)', W_S, W_P3(:,4)', W_S, W_P3(:,5)',W_S, W_P3(:,6)', W_S, W_P3(:,7)', W_S, W_P3(:,8)', W_S, W_P3(:,9)', W_S, W_P3(:,10)') %%%%%%%%%%%%%% Sizing to Rate of Climb %%%%%%%%%%%%%%%%%%%%%%%% row=0.002378 ; %%%%% Slugs/Cubic ft row_rel=0.95; %%%%%%%%%% Relative density CL32CD=(1.345*(AR*Oswald)^(3/4))/(CD0^(1/4)) j=0; for RC =0:100:600 j=j+1; RCP=RC/33000; i=0; for W_S = 2:2:20 i=i+1; W_P4=Eff_Pcr/(RCP+(W_S^0.5)/(19*CL32CD*(row_rel^0.5))) W_P5(i,j)=W_P4; end end W_S = 2:2:20; %plot(W_S2(:,1)', W_P2, W_S2(:,2)', W_P2, W_S2(:,3)', W_P2, W_S2(:,4)', W_P2, W_S, W_P1(:,1)', W_S, W_P1(:,2)', W_S, W_P1(:,3)', W_S, W_P1(:,4)', W_S, W_P1(:,5)', W_S, W_P1(:,6)',W_S, W_P1(:,7)', W_S, W_P1(:,8)',W_S, W_P3(:,1)', W_S, W_P3(:,2)', W_S, W_P3(:,3)', W_S, W_P3(:,4)', W_S, W_P3(:,5)',W_S, W_P3(:,6)', W_S, W_P3(:,7)', W_S, W_P3(:,8)', W_S, W_P3(:,9)', W_S, W_P3(:,10)',W_S, W_P5(:,1)', W_S, W_P5(:,2)', W_S, W_P5(:,3)', W_S, W_P5(:,4)', W_S, W_P5(:,5)', W_S, W_P5(:,6)',W_S, W_P5(:,7)') %plot(W_S, W_P5(:,1)', W_S, W_P5(:,2)', W_S, W_P5(:,3)') %%%%%%%%%%%%%% Sizing to of Climb Gradient %%%%%%%%%%%%%%%%%%%%%%%% row=0.002378 ; %%%%% Slugs/Cubic ft row_rel=0.95; %%%%%%%%%% Relative density CL32CD=(1.345*(AR*Oswald)^(3/4))/(CD0^(1/4));
  • 11. CLClimb=1.4; %%%%%%%%%%%%CL Climb=CLmax-0.2%%%%%%%%%%%CLmax for clean configuration as it is a requirement Vstall=3298;%%%%%%% ft/min ===== 60 km/hr Vto=1.3*Vstall%%%%%%%%%%%Consider Vto=VRoCmax j=0; for RC =0:100:600 j=j+1; CGR=RC/Vto; CGRP=(CGR+LDcr^(-1))/(CLClimb^(0.5)); i=0; for W_S = 2:2:20 i=i+1; W_P6=(18.97*Eff_Pcr*row_rel^(0.5))/(CGRP*(W_S^(0.5))); W_P7(i,j)=W_P6; end end W_S =2:2:20; plot(W_S20(:,1)', W_P2, W_S20(:,2)', W_P2, W_S20(:,3)', W_P2, W_S20(:,4)', W_P2,W_S2(:,1)', W_P2, W_S2(:,2)', W_P2, W_S2(:,3)', W_P2, W_S2(:,4)', W_P2, W_S, W_P1(:,1)', W_S, W_P1(:,2)', W_S, W_P1(:,3)', W_S, W_P1(:,4)', W_S, W_P1(:,5)', W_S, W_P1(:,6)',W_S, W_P1(:,7)', W_S, W_P1(:,8)',W_S, W_P3(:,1)', W_S, W_P3(:,2)', W_S, W_P3(:,3)', W_S, W_P3(:,4)', W_S, W_P3(:,5)',W_S, W_P3(:,6)', W_S, W_P3(:,7)', W_S, W_P3(:,8)', W_S, W_P3(:,9)', W_S, W_P3(:,10)',W_S, W_P5(:,1)', W_S, W_P5(:,2)', W_S, W_P5(:,3)', W_S, W_P5(:,4)', W_S, W_P5(:,5)', W_S, W_P5(:,6)',W_S, W_P5(:,7)',W_S, W_P7(:,1)', W_S, W_P7(:,2)', W_S, W_P7(:,3)', W_S, W_P7(:,4)', W_S, W_P7(:,5)', W_S, W_P7(:,6)',W_S, W_P7(:,7)') grid on xlim([2 20]); ylim([2 30]); set(gca,'XTick',1:1:20) set(gca,'YTick',1:1:30) xlabel('Wing Loading lb/ft2'); ylabel('Power Loading lb/hr'); title('Matching Graph');
  • 12. %%%%%%%%%%%%%%%%%%% Performance Program to calculate the Flight %%%%%%%%%%%%%%%%%%% Stability Derivatives of the Final Platform without %%Gimbal CLP=[-0.008304 -0.008555 -0.008720 -0.008913 -0.009090 -0.009250 -0.009392 -0.009517 -0.009600 -0.009699 -0.008722 -0.004094 -0.003643 -0.002706]; CNR=[-0.001342 -0.001365 -0.001381 -0.001401 -0.001426 -0.001455 -0.001488 -0.001526 -0.001585 -0.001616 -0.001788 -0.002072 -0.002086 -0.002098]; CM=[0.0632 0.0642 0.0382 0.0323 0.0271 0.0204 0.0131 0.0056 -0.0004 - 0.0103 -0.0346 -0.1037 -0.1088 -0.1141]; CMA=[-0.005988 -0.008453 -0.007224 -0.005474 -0.005967 -0.006980 -0.007399 -0.007662 -0.007903 -0.008077 -0.009225 -0.01029 -0.01038 -0.01076]; CLB=[-0.001326 -0.001319 -0.001316 -0.001313 -0.001310 -0.001308 -0.001307 -0.001305 -0.001304 -0.001303 -0.001300 -0.001232 -0.001222 -0.001211]; %%%%%%%%%%%%%%%%%%% Stability Derivatives of the Final Platform with Gimbal CLP1=[-0.008306 -0.008556 -0.008720 -0.008913 -0.009089 -0.009248 - 0.009390 -0.009515 -0.009598 -0.009697 -0.008721 -0.004099 -0.003648 - 0.002712]; CNR1=[-0.001519 -0.001544 -0.001562 -0.001584 -0.001609 -0.001639 - 0.001673 -0.001712 -0.001745 -0.001804 -0.001977 -0.002260 -0.002274 - 0.002286]; CM1=[0.0733 0.0546 0.0443 0.0367 0.0302 0.0227 0.0141 0.0053 -0.0017 - 0.0132 -0.0432 -0.1174 -0.1229 -0.1285]; CMA1=[-0.007302 -0.009955 -0.008920 -0.007031 -0.007006 -0.008051 - 0.008681 -0.008964 -0.009207 -0.009561 -0.01078 -0.01116 -0.01113 - 0.01128]; CLB1=[-0.001383 -0.001368 -0.001360 -0.001353 -0.001347 -0.001341 - 0.001335 -0.001329 -0.001325 -0.001319 -0.001304 -0.001213 -0.001201 - 0.001188];
  • 13. %%%%%%%%%%%%%%%%%%% Equilibrium Diagram at different Re numbers.... %%%%%%%%%%%%%%%%%%%% CL, CD for different Re numbers / from DATCOM results Alfa=[-3 -1 0 1 2 3 4 5 5.8 7 10 16 16.5 17 18 19]'; %%%% AOA up to Maximum Lift Coefficient Alfa_1=[-3 -1 0 1 2 3 4 5 5.8 7 10 16 16.5 17 18 19]'; %%%%%%%%% AOA up to stall curve Alfa_2=[-3 -1 0 1 2 3 4 5 5.8 7 10 16 16.5 17]'; %%%%%%%%% AOA up to stall curve CD=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; CL=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; %%%%%%%%%%%%% Re number < 700000 CD0=[0.025 0.024 0.024 0.025 0.027 0.029 0.033 0.036 0.040 0.046 0.066 0.107 0.110 0.112 0.115 0.111]'; CL0=[-0.132 0.053 0.147 0.242 0.339 0.438 0.539 0.641 0.722 0.850 1.166 1.598 1.620 1.639 1.656 1.599]'; %%%%%%%%%%%%% Re number < 1400000 CD1=[0.022 0.021 0.021 0.022 0.024 0.027 0.030 0.033 0.037 0.043 0.064 0.104 0.107 0.109 0.112 0.108]'; CL1=[-0.132 0.053 0.147 0.242 0.339 0.438 0.539 0.641 0.722 0.850 1.167 1.598 1.620 1.639 1.656 1.599]'; %%%%%%%%%%%%% Re number < 3000000 CD2=[0.020 0.019 0.020 0.021 0.022 0.025 0.028 0.032 0.035 0.041 0.062 0.102 0.105 0.107 0.110 0.106]'; CL2=[-0.132 0.053 0.147 0.243 0.340 0.440 0.541 0.644 0.742 0.852 1.170 1.600 1.622 1.641 1.653 1.596]'; %%%%%%%%%%%%% Re number < %%%%%%%%%%%% CD3=[0.025 0.024 0.024 0.025 0.027 0.029 0.033 0.036 0.040 0.046 0.066 0.107 0.110 0.112 0.115 0.111]'; CL3=[-0.132 0.053 0.147 0.242 0.339 0.438 0.539 0.641 0.722 0.850 1.166 1.598 1.620 1.639 1.656 1.599]'; %%%%%%%%%%%%% Re number < %%%%%%%%%%%% CD4=[0.025 0.024 0.024 0.025 0.027 0.029 0.033 0.036 0.040 0.046 0.066 0.107 0.110 0.112 0.115 0.111]'; CL4=[-0.132 0.053 0.147 0.242 0.339 0.438 0.539 0.641 0.722 0.850 1.166 1.598 1.620 1.639 1.656 1.599]'; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Array Definitions D=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; TAS=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; %CLCD=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; P_av=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; P_av_1=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; P_req=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; %%%%%%%%%%%%%%% Efficiency of Propeller versus Advance Ratio J_R=[0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3]'; Eta_R=[0.48 0.6 0.7 0.8 0.9 0.97 1 0.95 0.85 0.6]'; e3=[ones(size(J_R)) J_R J_R.^2 J_R.^3 J_R.^4];
  • 14. C3=e3Eta_R; z=polyfit(J_R,Eta_R,10) %%%%%%%%%%%% Engine Design Data J_Design=30/(7600*0.66); %%%%%%%%%% Advance Ratio at design condition Eff_Design=0.7; %%%%%%%%%%%%%%%% Efficiency at design condition bhp_sl=28; %%%%%%%%%%%%%%%% Brake Power at sea level %%%%%%%%%%%%%%%%%%%%% Input Conditions %%%%H=0; %%%%% Altitude in Km MAC=0.59; %%%%%%%% m Mean Aerodynamic Chord MTOW=160; %%%% Kg Maximum Take Off Weight of the UAV CLMAX=2.3; %%%%%%% Maximum Lift Coefficient with flaps CLMAX_noflaps=2.3; %%%%%%% Maximum Lift Coefficient without flaps / sometimes with flaps S=4.1; %%%%%%%%%% m^2 Wing Area %%%row=1.225; %%%%%%%%%% Kg/m^3 Density at Sea Level P0=101325; %%%%% Pa Pressure at Sea Level ISA T0=288.15; %%%%% deg K Temperature at Sea Level ISA g=9.80665; %%%%% m/s^2 gravity L=6.5; %%%% deg K/Km Lapse rate R=8.31432; %%%%% J/mol*deg K Gas Constant M=28.9644; %%%%%%%%%% gm/mol Molecular Weight miu=0.0000178934; %%%%%%%%%%%%%% Air Viscosity P_Dyn_Max=0.5*1.225*40*40; %%%%%%%%%%%% Pa Max Dynamic Pressure at Sea Level %%% 3 times the selected wing loading (980 Pa) x0=0; x1=0; x2=0; x3=0; x4=0; x5=0; x6=0; x7=0; x11=0; x12=0; x13=0; u=0; q=0; for H=0:0.125:10 %%%%%%%%%%%%%%% change 0.125 to 0.5 for EFD q=q+1 %%%%%%%%%%%%% Pressure, Temperature and Density Calculation at ISA T=T0-L*H; P=P0*(1-((L*H)/T0))^((g*M)/(R*L)); row=(P*M)/(R*T*1000); bhp=bhp_sl*((row/1.225)-((1-row/1.225))/7.55);
  • 15. v_stall=((2*MTOW*g)/(row*S*CLMAX_noflaps))^(0.5) for i=1:1:640 %%%%%%%%%%% Speed Increment TAS(i)=2+0.0625*i; %%%%%%%%%%% Load Factor / Stalling Limit Calculation %%%%%%%%%%%%%%%% n(i,q)=(TAS(i)/v_stall)^2; %%%%%%%%%%% Re number Calculation %%%%%%%%%%%%%%%% Re=(row*TAS(i)*MAC)/miu if Re < 700000 %Rule CL=CL0; CD=CD0; elseif Re < 1400000 CL=CL1; CD=CD1; elseif Re < 3000000 CL=CL2; CD=CD2; end j=0; for j=1:1:16 CLCD0(j)=CL0(j)/CD0(j); CLCD1(j)=CL1(j)/CD1(j); CLCD2(j)=CL2(j)/CD2(j); end e1=[ones(size(Alfa)) Alfa]; C1=e1CL; e2=[ones(size(Alfa)) CL.^2]; C2=e2CD; %%%%%%%%%%%%%%%% Calculating Required and Available Power CL_Cal=MTOW*9.8/(0.5*row*TAS(i)^2*S); CD_Cal=[1 CL_Cal^2]*C2;
  • 16. J_R_Cal=(TAS(i)/(7600*0.66))/J_Design; Eta_R_Cal=[1 J_R_Cal J_R_Cal^2 J_R_Cal^3 J_R_Cal^4]*C3; Eta_R_Cal_1=polyval(z,J_R_Cal); Eta_Cal=Eta_R_Cal*Eff_Design; Eta_Cal_1=Eta_R_Cal_1*Eff_Design; P_av(i)=Eta_Cal*bhp*743; P_av_1(i)=Eta_Cal_1*bhp*743; D(i)=0.5*row*TAS(i)^2*S*CD_Cal*1.5;%%%%%%%%%%%%%%%%%%%%%%%%% Adding 50% extra of total drag due to landing gear and antennas P_req(i)=D(i)*TAS(i); if abs(P_av(i) - P_req(i)) < 10 u=u+1; V_H(u,1)=TAS(i); V_H(u,2)=H; else end P_av_H(i,q)=P_av(i); P_req_H(i,q)=P_req(i); T_av_H(i,q)=P_av(i)/TAS(i); %%%%%%%%%%% Maximum Load Factor Limit %%%%%%%%%%%%%%%% C16=(0.5*row*((TAS(i))^2)*S)/(C2(2)*MTOW*g); C71=(0.5*row*((TAS(i))^2)*S*C2(1))/(MTOW*g); n_max(i,q)=(C16*((T_av_H(i,q)/(MTOW*g))-C71))^(0.5); r_min(i,q)=(4*C2(2)*(MTOW*g/S))/(g*row*(T_av_H(i,q)/(MTOW*g))*(1- (4*C2(2)*C2(1)/((T_av_H(i,q)/(MTOW*g))^2)))^(0.5)); n_r_min(i,q)=(2-(4*C2(2)*C2(1))/(T_av_H(i,q)/(MTOW*g))^2)^(0.5); CL_r_min(i,q)=(n_r_min(i,q)*MTOW*g)/(0.5*row*(TAS(i))^2*S); Fai_r_min(i,q)=57.3*acos(1/n_r_min(i,q)); TAS_r_min(i,q)=((4*C2(2)*(MTOW*g/S))/(row*(T_av_H(i,q)/(MTOW*g))))^(0.5); %%%%%%%%%%%%% Correct Turn Caculation
  • 17. Thrust(i)=TAS(i)*10; r_min1(i,q)=(4*C2(2)*(MTOW*g/S))/(g*row*(Thrust(i)/(MTOW*g))*(1- (4*C2(2)*C2(1)/((Thrust(i)/(MTOW*g))^2)))^(0.5)); n_r_min1(i,q)=(2-(4*C2(2)*C2(1))/(Thrust(i)/(MTOW*g))^2)^(0.5); Fai_r_min1(i,q)=57.3*acos(1/n_r_min1(i,q)); TAS_r_min1(i,q)=((4*C2(2)*(MTOW*g/S))/(row*(Thrust(i)/(MTOW*g))))^(0.5); CL_r_min1(i,q)=(n_r_min1(i,q)*MTOW*g)/(0.5*row*(TAS_r_min1(i,q))^2*S); %%%%%%%%%%% Minimum Time Trajectory P_Excess_Sp=(P_av(i)-P_req(i))/(MTOW*9.8); ifP_Excess_Sp< 1 &&P_Excess_Sp>0.5 x0=x0+1; V_H_8(x0,1)=TAS(i); V_H_8(x0,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifP_Excess_Sp< 2 &&P_Excess_Sp>1.5 x2=x2+1; V_H_3(x2,1)=TAS(i); V_H_3(x2,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifP_Excess_Sp< 3 &&P_Excess_Sp>2.5 x3=x3+1; V_H_4(x3,1)=TAS(i); V_H_4(x3,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8);
  • 18. %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifP_Excess_Sp< 4 &&P_Excess_Sp>3.5 x4=x4+1; V_H_5(x4,1)=TAS(i); V_H_5(x4,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifP_Excess_Sp< 5 &&P_Excess_Sp>4.5 x5=x5+1; V_H_6(x5,1)=TAS(i); V_H_6(x5,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifP_Excess_Sp< 6 &&P_Excess_Sp>5.5 x6=x6+1; V_H_7(x6,1)=TAS(i); V_H_7(x6,2)=H; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end end %%%%%%%%%%%%%Maximum Dynamic Pressure Limit V=((2*P_Dyn_Max)/row)^(0.5); V_H_1(q,1)=V; V_H_1(q,2)=H; %%%%%%%%%%%%% Stalling Limit V_min=((2*MTOW*9.8)/(row*CLMAX*S))^(0.5); V_H_2(q,1)=V_min; V_H_2(q,2)=H;
  • 19. %%%%%%%%%%%%%%%%%%%%%% Performance Figures %figure(1) %plot(TAS,D) %xlabel('TAS'); %ylabel('Drag'); %figure(2) %plot(Alfa,CL,Alfa,e1*C1) %xlabel('Alfa'); %ylabel('CL'); %figure(3) %plot(Alfa,CLCD) %xlabel('Alfa'); %ylabel('CL/CD'); %figure(4) %plot(TAS,P_av,TAS,P_req) %xlabel('TAS'); %ylabel('Power'); end %%%%%%%%%%%%% Aircraft Energy Lines for z=0:0.0625:10 for i=1:1:2640 TAS1(i)=0+0.0625*i; AC_Energy=z*1000+(0.5*TAS1(i)*TAS1(i))/g; ifAC_Energy< 1040 &&AC_Energy>960 x1=x1+1; V_H_80(x1,1)=TAS1(i); V_H_80(x1,2)=z; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifAC_Energy< 3040 &&AC_Energy>2960 x11=x11+1; V_H_801(x11,1)=TAS1(i); V_H_801(x11,2)=z;
  • 20. %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifAC_Energy< 5040 &&AC_Energy>4960 x12=x12+1; V_H_802(x12,1)=TAS1(i); V_H_802(x12,2)=z; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end ifAC_Energy< 7040 &&AC_Energy>6960 x13=x13+1; V_H_803(x13,1)=TAS1(i); V_H_803(x13,2)=z; %P_Excess_Sp(i+(q-1)*640,1)=(P_av(i)-P_req(i))/(MTOW*9.8); %P_Excess_Sp(i+(q-1)*640,2)=TAS(i); %P_Excess_Sp(i+(q-1)*640,3)=H; else end end end figure(3) plot(Alfa,CLCD0,Alfa,CLCD1,Alfa,CLCD2) xlabel('Alfa (deg)'); ylabel('CL/CD'); figure(4) plot(TAS,P_av_H(:,1)',TAS,P_req_H(:,1)',TAS,P_av_H(:,2)',TAS,P_req_H(:,2)' ,TAS,P_av_H(:,3)',TAS,P_req_H(:,3)',TAS,P_av_H(:,4)',TAS,P_req_H(:,4)',TAS ,P_av_H(:,5)',TAS,P_req_H(:,5)',TAS,P_av_H(:,6)',TAS,P_req_H(:,6)',TAS,P_a v_H(:,7)',TAS,P_req_H(:,7)',TAS,P_av_H(:,8)',TAS,P_req_H(:,8)',TAS,P_av_H( :,9)',TAS,P_req_H(:,9)',TAS,P_av_H(:,10)',TAS,P_req_H(:,10)',TAS,P_av_H(:, 11)',TAS,P_req_H(:,11)',TAS,P_av_H(:,12)',TAS,P_req_H(:,12)',TAS,P_av_H(:, 13)',TAS,P_req_H(:,13)',TAS,P_av_H(:,14)',TAS,P_req_H(:,14)',TAS,P_av_H(:, 15)',TAS,P_req_H(:,15)',TAS,P_av_H(:,16)',TAS,P_req_H(:,16)',TAS,P_av_H(:, 17)',TAS,P_req_H(:,17)',TAS,P_av_H(:,18)',TAS,P_req_H(:,18)',TAS,P_av_H(:, 19)',TAS,P_req_H(:,19)',TAS,P_av_H(:,20)',TAS,P_req_H(:,20)') xlabel('TAS (m/s)'); ylabel('Power (watt)'); figure(5)
  • 21. plot(V_H(:,1),V_H(:,2),'*',V_H_1(:,1),V_H_1(:,2),'o',V_H_2(:,1),V_H_2(:,2) ,'o') xlabel('TAS (m/s)'); ylabel('Altitude (m)'); figure(6) plot(V_H_1(:,1),V_H_1(:,2),'o') xlabel('TAS (m/s)'); ylabel('Altitude (m)'); figure(7) plot(Alfa, CL0, Alfa, CL1, Alfa, CL2) xlabel('Angle of Attack (deg)'); ylabel('CL'); figure(8) plot(CD0, CL0, CD1, CL1, CD2, CL2) xlabel('CD'); ylabel('CL'); figure(9) plot(V_H_3(:,1)',V_H_3(:,2)','*',V_H_4(:,1)',V_H_4(:,2)','*',V_H_5(:,1)',V _H_5(:,2)','*',V_H_6(:,1)',V_H_6(:,2)','*',V_H_7(:,1)',V_H_7(:,2)','*',V_H _8(:,1)',V_H_8(:,2)','*',V_H_80(:,1)',V_H_80(:,2)','- ',V_H_801(:,1)',V_H_801(:,2)','-',V_H_802(:,1)',V_H_802(:,2)','- ',V_H_803(:,1)',V_H_803(:,2)','-') xlabel('TAS (m/s)'); ylabel('Altitude (Km)'); figure(10) plot(TAS,n(:,1)',TAS,n(:,2)') xlabel('TAS (m/s)'); ylabel('Load Factor '); figure(11) plot(TAS,n(:,1)',TAS,n_max(:,1)',TAS,n(:,21)',TAS,n_max(:,21)',TAS,n(:,41) ',TAS,n_max(:,41)',TAS,n(:,61)',TAS,n_max(:,61)',TAS,n(:,81)',TAS,n_max(:, 81)') xlabel('TAS (m/s)'); ylabel('Load Factor '); figure(12) plot(Alfa_2,CMA1,Alfa_2,CMA) xlabel('Angle of Attack (deg)'); ylabel('CMA1 '); figure(13) plot(Alfa_2,CM1,Alfa_2,CM) xlabel('Angle of Attack (deg)'); ylabel('CM '); figure(14) plot(Alfa_2,CNR1,Alfa_2,CNR)
  • 22. xlabel('Angle of Attack (deg)'); ylabel('CNR '); figure(15) plot(Alfa_2,CLP1,Alfa_2,CLP) xlabel('Angle of Attack (deg)'); ylabel('CLP '); figure(16) plot(Alfa_2,CLB1,Alfa_2,CLB) xlabel('Angle of Attack (deg)'); ylabel('CLB '); figure(17) plot(TAS,r_min(:,1)',TAS,(n_r_min(:,1)*10)',TAS,(CL_r_min(:,1)*10)',TAS,Fa i_r_min(:,1)',TAS,TAS_r_min(:,1)') %plot(TAS_r_min(:,1)',r_min(:,1)',TAS_r_min(:,1)',(n_r_min(:,1)*10)',TAS_r _min(:,1)',(CL_r_min(:,1)*10)',TAS_r_min(:,1)',Fai_r_min(:,1)') xlabel('TAS (m/s)'); ylabel('Minimum Turn Radius '); figure(18) %plot(TAS,r_min(:,1)',TAS,(n_r_min(:,1)*10)',TAS,(CL_r_min(:,1)*10)',TAS,F ai_r_min(:,1)',TAS,TAS_r_min(:,1)') plot(Thrust',r_min1(:,1)',Thrust',(n_r_min1(:,1)*10)',Thrust',(CL_r_min1(: ,1)*10)',Thrust',Fai_r_min1(:,1)',Thrust',TAS_r_min1(:,1)') xlabel('TAS (m/s)'); ylabel('Minimum Turn Radius ');