K.M. Kiran Babu : Course Site

Exercise 5: Drag Analysis for a Typical Aircraft

Objective:

To Calculate the Zero-Lift Drag Coefficient and Lift Induced Drag Coefficient for a Aircraft
Plot the Variation of Zero-Lift Drag Coefficient and Lift Induced Drag Coefficient for a Aircraft Verus Velocity
To Determine the Velocity for Minimum Thrust Required from the Graph and Verify the results with the Analytical Formulas

Data for Generation of Drag Polar Curve

Fuselage Zero Lift Drag Coefficient

Wing Zero Lift Drag Coefficient

Lift Induced Drag Coefficient

Drag Variation with the Velocity

Program:

M_To = 600; %Maximum Takeoff Mass in Kg

% Wing Specifications

W_To = 600*9.81; %Maximum Takeoff Weight in NS_Wing = 11; %Wing Area in Sq.mb_Wing = 9; %Wing Span in mS_Wing = 11; %Wing Area in Sq.mb_Wing = 9; %Wing Span in mAR_Wing = 7.36; %Aspect Ratio of WingTR_Wing = 0.70; %Taper Ratio of WingMAC_Wing = 1.23; %Mean Aerodynamic Chord of Wing in mtc_Wing = 0.15; % Thickness - Chord Ratio of Wing

% Fuselage Specifications

L_Fuse = 7; %Length of the FuselageSWet_Fuse = 20; %Wetted Surface Area of FuselageMaxA_Fuse = 0.8; %Maximum Cross Section Area of FuselageD_Fuse = 1.009; %Equivalent Diameter of FuselageLtoD_Fuse = 6.936; %Length-Diameter Ratio of Fuselage

% Ambient Properties

Ph = 101325; %Ambient Pressure in N/sq.mrhoh = 1.225; %Ambient Density in kg/cu.mTh = 288.15; %Ambient Temperature in KMuh = 1.7894*10^-5; %Dynamic Viscosity of Air in Ns/sq.m

% Zero Lift Drag Coefficient of Fuselage

V = [50:5:200]; %Velocity in m/sRe_Fuse = (rhoh*L_Fuse.*V)/(Muh); %Reynolds Number Calculation of FuselageCf_Fuse = 0.00258 + (0.00102.*exp(-6.28*10^-9.*Re_Fuse)) + (0.00295.*exp(-2.01*10^-8.*Re_Fuse)); %Coefficient of Friction of FuselageRW_Fuse = 1; %Interference Factor of Wing Fuselage InteractionCD0_Fuse = RW_Fuse*Cf_Fuse*(1+(60/(LtoD_Fuse^3))+(0.0025*LtoD_Fuse))*(SWet_Fuse/S_Wing);

% Zero Lift Drag Coefficient of Wing

Re_Wing = (rhoh*MAC_Wing.*V)/(Muh); %Reynolds Number Calculation of WingCf_Wing = 0.00258 + (0.00102.*exp(-6.28*10^-9.*Re_Wing)) + (0.00295.*exp(-2.01*10^-8.*Re_Wing)); %Coefficient of Friction of WingRF_Wing = 1; %Interference Factor of Wing Fuselage InteractionCD0_Wing = RF_Wing*Cf_Wing*(1+(tc_Wing)+ (100*tc_Wing^4))*((2*S_Wing)/S_Wing); %Zero-Lift Drag Coefficient of Wing

% Zero Lift Drag Coefficient of Aircraft

CD0 = CD0_Fuse + CD0_Wing; %Zero Lift Drag Coefficient of Aircraft

% Lift Induced Drag Coefficient

eps = 0.85; %Oswald's Wing Efficiency FactorK = 1/(3.147*eps*AR_Wing); %Lift Induced Drag Coefficient FactorCL = (2*W_To)./(rhoh*S_Wing.*V.^2); % Coefficient of Lift of AircraftCDi = K*CL.^2; % Lift Induced Drag Coefficient

%Drag Polar

CD = CD0 + CDi; % Coefficient of Drag

% Drag Force

Drag_ZeroLift = (0.5*rhoh*S_Wing.*CD0.*V.^2); %Zero Lift Drag Force of the Aircraft in NDrag_LiftInduced = (0.5*rhoh*S_Wing.*CDi.*V.^2); %Lift Induced Drag Force of the Aircraft in NDrag = (0.5*rhoh*S_Wing.*CD0.*V.^2)+(0.5*rhoh*S_Wing.*CDi.*V.^2); %Drag Force of the Aircraft in N

Plots:

plot(V,CD0_Fuse,'-',V,CD0_Wing,'.-',V,CD), legend('CD0 - Fuselage','CD0 - Wing','CD0 - Aircraft'), xlabel('Velocity in m/s'),ylabel('Drag Coefficient'), axis ([50 200])

Variation of Zero Lift Drag Coefficient with Velocity

plot(V,CD0,'-',V,CDi,'.-',V,CD), legend('CD0 - Zero Lift Drag Coefficient','CDi - Lift Induced Drag Coefficient','CD - Drag Coefficient'), xlabel('Velocity in m/s'),ylabel('Drag Coefficient'), axis ([50 200])

Variation of Drag Coefficient with Velocity

plot(V,Drag_ZeroLift,V,Drag_LiftInduced,V,Drag), legend('Zero Lift Drag','Lift Induced Drag','Total Drag'), xlabel('Velocity in m/s'),ylabel('Drag Force in N'), axis ([10 200])

Variation of Drag Force with Velocity

Reference & Further Reading: https://aerotoolbox.net/drag-polar/#more-1325

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