% Bootstrap Data Plate Cessna 182
format compact
close all
S=174;       % wing area (ft^2)
B=36;        % Wing span (ft)
BHPmax=230;  % Rated engine horsepower (hp), See Owner's Manual p. 4-2
RPM=2600;    % Rated engine speed, RPM
Din=82;      % Propeller diameter, in
CD0=.048662; % Paracite drag coefficient (from Step 1)
e=.7984;     % Airplane efficiency factor from Step 1
m=1.717;    % Slope of propeller polar (from Step 2)
b=-0.04032; % Intercept of propeller polar (from Step 2)

% Auxilary data
W0=2950;       % Standard weight and test day weight, lbf
AR=B*B/S       % Aspect ratio
k=1/(pi*AR*e) % Parameter of drag polar
nblades=2;     % Number of blades of propeller
C=.12;         % Altitude drop-off parameter for Gagg-Farrar Rule

rho=.002378 % Sea level
sigma=rho/.002378
Phi=(sigma-C)/(1-C)
BHP=BHPmax*Phi
n=RPM/60
D=Din/12
Cp=550*BHP/(rho*n^3*D^5)
J=.1:.01:1.2;


b=-0.04032;
Ct=b*J.*J+m*Cp;
CpVec=Cp*ones(size(Ct));
etap=J.^3*b/Cp+m*J;


subplot(311); hold on;  plot(J,Ct);
subplot(312); hold on;  plot(J,CpVec);
subplot(313); hold on;  plot(J,etap);

b=0
Ct=b*J.*J+m*Cp;
CpVec=Cp*ones(size(Ct));
etap=J.^3*b/Cp+m*J;
subplot(311); hold on; plot(J,Ct,'r')
subplot(312); hold on;  plot(J,CpVec,'r')
subplot(313); hold on;  plot(J,etap,'r')

b=0.04032
Ct=b*J.*J+m*Cp;
CpVec=Cp*ones(size(Ct));
etap=J.^3*b/Cp+m*J;
subplot(311); hold on;  plot(J,Ct,'g')
title('Propeller properties for various values of b')
legend('b=-','b=0','b=+')
ylabel('Thrust Coef Ct')
subplot(312); hold on;  plot(J,CpVec,'g')
ylabel('Power Coef, Cp')
subplot(313); hold on;  plot(J,etap,'g')
grid on
xlabel('Advance Ratio, J=V/nD')
ylabel('Prop Eff etap')
legend('b=-','b=0','b=+')
text2(.05,.9,'b of the propeller polar must be negative for the efficiency to fall off at high J')