Appendix D-1: The results from the modified Motor code.
Figure 1.1: Power, Efficiency and Torque of the major five candidates motors.
Figure 1.2: Motor Analysis of Astro CO25.
Figure 1.3: Motor Analysis of Aveox 1415/1.5.
Figure 1.4: Motor Analysis of Aveox 1415/2.
Figure 1.5: Motor Analysis of Maxcim N32-13D.
Figure 1.6: Motor Analysis of Maxcim N32-13Y.
Table 1.1: Efficiency and Power Output of Speed Controller.
Speed ControllerModel / Maxµ35B-21 / Maxµ35B-25NB
Efficiency (%) / 99.3 / 99.06
Resistance (Ohms) / 0.009 / 0.012
Power output (Watts) / 367.2 / 367.2
Power input (Watts) / 369.801 / 370.668
Power Dissipated (Watts) / 2.601 / 3.468
Appendix D-2: The results from Goldstein method code.
Table 2.1:The results from Goldstein Method for different Propeller.
Propeller / Analysis / (Gold) / 18 cellsGear ratio / 3.53 / 3.75 / 4
At Constant / Pitch Ratio
Thrust(lb)
Diameter / Pitch / 8 / 10 / 8 / 10 / 8 / 10
13 / 3.0742 / 3.7275 / 2.6927 / 3.2718 / 2.3349 / 2.8442
14 / 3.9316 / 4.7577 / 3.445 / 4.1774 / 2.9887 / 3.6327
15 / 6.1328 / 7.3879 / 5.3777 / 6.4902 / 4.6693 / 5.6475
16 / 4.9457 / 5.9718 / 4.3353 / 5.2449 / 3.7626 / 4.5625
18 / 9.0957 / 10.9022 / 7.9801 / 9.5819 / 6.934 / 8.3423
20 / 12.9713 / 15.4602 / 11.3853 / 13.5929 / 9.897 / 11.84
22 / 17.9158 / 21.2377 / 15.7336 / 18.678 / 13.6853 / 16.275
24 / 24.0945 / 28.4245 / 21.1696 / 25.0056 / 18.4238 / 21.7946
Power(kW) / Used
Diameter
13 / 0.2249 / 0.2938 / 0.1887 / 0.2467 / 0.1564 / 0.2047
14 / 0.2967 / 0.3863 / 0.2488 / 0.3242 / 0.2062 / 0.2689
15 / 0.4908 / 0.6347 / 0.4113 / 0.5323 / 0.3406 / 0.4412
16 / 0.3845 / 0.499 / 0.3223 / 0.4186 / 0.267 / 0.3471
18 / 0.7694 / 0.9878 / 0.6445 / 0.8279 / 0.5335 / 0.6858
20 / 1.156 / 1.4729 / 0.968 / 1.2339 / 0.8009 / 1.0216
22 / 1.6777 / 2.1213 / 1.4043 / 1.7765 / 1.1616 / 1.4703
24 / 2.366 / 2.9688 / 1.9799 / 2.4856 / 1.6371 / 2.0565
Efficiency
Diameter
13 / 0.4633 / 0.4301 / 0.4837 / 0.4496 / 0.5059 / 0.471
14 / 0.4493 / 0.4175 / 0.4695 / 0.4368 / 0.4914 / 0.4579
15 / 0.4236 / 0.3946 / 0.4432 / 0.4133 / 0.4647 / 0.4339
16 / 0.4361 / 0.4057 / 0.456 / 0.4247 / 0.4777 / 0.4456
18 / 0.4007 / 0.3742 / 0.4197 / 0.3923 / 0.4406 / 0.4124
20 / 0.3804 / 0.3558 / 0.3987 / 0.3734 / 0.4189 / 0.3929
22 / 0.362 / 0.3394 / 0.3798 / 0.3564 / 0.3994 / 0.3752
24 / 0.3452 / 0.3246 / 0.3625 / 0.341 / 0.3815 / 0.3593
Ct
Diameter
13 / 0.0506 / 0.0614 / 0.05 / 0.0608 / 0.0494 / 0.0601
14 / 0.0481 / 0.0583 / 0.0476 / 0.0577 / 0.047 / 0.0571
15 / 0.044 / 0.053 / 0.0436 / 0.0526 / 0.043 / 0.052
16 / 0.046 / 0.0555 / 0.0455 / 0.055 / 0.0449 / 0.0544
18 / 0.0408 / 0.0488 / 0.0404 / 0.0485 / 0.0399 / 0.048
20 / 0.0381 / 0.0455 / 0.0378 / 0.0451 / 0.0374 / 0.0447
22 / 0.036 / 0.0426 / 0.0357 / 0.0423 / 0.0353 / 0.042
24 / 0.0342 / 0.0403 / 0.0339 / 0.04 / 0.0335 / 0.0397
Cp
Diameter
13 / 0.0182 / 0.0238 / 0.0184 / 0.024 / 0.0185 / 0.0242
14 / 0.0166 / 0.0216 / 0.0167 / 0.0218 / 0.0168 / 0.0219
15 / 0.0141 / 0.0182 / 0.0142 / 0.0183 / 0.0142 / 0.0184
16 / 0.0152 / 0.0198 / 0.0153 / 0.0199 / 0.0154 / 0.02
18 / 0.0123 / 0.0157 / 0.0123 / 0.0158 / 0.0124 / 0.0159
20 / 0.0109 / 0.0139 / 0.0109 / 0.0139 / 0.011 / 0.014
22 / 0.0098 / 0.0124 / 0.0098 / 0.0124 / 0.0099 / 0.0125
24 / 0.0089 / 0.0112 / 0.009 / 0.0113 / 0.009 / 0.0113
Torque(ft-lb)
Diameter
13 / 0.191 / 0.2495 / 0.1702 / 0.2225 / 0.1506 / 0.197
14 / 0.2519 / 0.3281 / 0.2244 / 0.2925 / 0.1984 / 0.2588
15 / 0.4168 / 0.5391 / 0.3711 / 0.4803 / 0.3278 / 0.4246
16 / 0.3265 / 0.4238 / 0.2908 / 0.3777 / 0.2569 / 0.3341
18 / 0.6534 / 0.8389 / 0.5815 / 0.7469 / 0.5134 / 0.66
20 / 0.9817 / 1.2508 / 0.8733 / 1.1132 / 0.7708 / 0.9831
22 / 1.4248 / 1.8015 / 1.267 / 1.6028 / 1.1178 / 1.4149
24 / 2.0093 / 2.5213 / 1.7863 / 2.2424 / 1.5755 / 1.979
Advance Ratio
Diameter
13 / 0.167 / 0.167 / 0.1774 / 0.1774 / 0.1892 / 0.1892
14 / 0.155 / 0.155 / 0.1647 / 0.1647 / 0.1757 / 0.1757
15 / 0.1357 / 0.1357 / 0.1441 / 0.1441 / 0.1537 / 0.1537
16 / 0.1447 / 0.1447 / 0.1537 / 0.1537 / 0.164 / 0.164
18 / 0.1206 / 0.1206 / 0.1281 / 0.1281 / 0.1366 / 0.1366
20 / 0.1085 / 0.1085 / 0.1153 / 0.1153 / 0.123 / 0.123
22 / 0.0987 / 0.0987 / 0.1048 / 0.1048 / 0.1118 / 0.1118
24 / 0.0904 / 0.0904 / 0.0961 / 0.0961 / 0.1025 / 0.1025
Appendix D-3: Costs and Endurance test of Propulsion system.
Table 3.1: Cost Comparison of five major candidates motors and its components.
Table 3.2: The thrust required in each phase and the estimated throttle setting.
Table 3.3: The Available Energy from Different Battery Packs.
Motor / AstroCO25 / Aveox 1415/1.5 / Aveox 1415/2 / Maxcim N32-13Y / Maxcim N32-13DPrice / $180.00 / $247.95 / $247.95 / $177.95 / $177.95
Speed Controller
Maxµ35B-21 / $159.95 / Aveox L260 / $159.99 / Astro 204D / $100.00
Maxµ35B-25NB / $189.95 / Aveox M260 / $159.99
Gearbox
Maxcim / Aveox PG37 / Astro 713
$40.00 / $95.95 / $60.00
Table 3.4: Endurance Test for the Propulsion System.
Appendix D-4: Motor constant equations.
DC motors have the following constant parameters:
-Io: No load current. It is the lowest current to spin the motor.
-Rm: Terminal resistance: It is the resistance drawn by the motor structure.
-Kv: Voltage constant: It is a constant describing the relationship between RPM and voltage.
-Kt: Torque constant: It is a constant describing the relationship between torque and current drawn from the battery pack.
The current into a motor is,
I=Iin-Io[Eq. D-4.1]
Where Iin is the input current from the battery pack.
And the voltage into a motor is,
V=Vin-(Iin*Rm)[Eq. D-4.2]
Where Vin is the input voltage from the battery pack.
Then the power input and output from the motor can be calculated in the following way,
Pin = Vin*Iin [Eq. D-4.3]
Pout= V*I[Eq. D-4.4]
Pout = (Iin-Io)*(Vin-(Iin*Rm))[Eq. D-4.5]
The speed and torque of a motor can be obtained using Kv.
RPM=Kv*(Vin-Iin*Rm)[Eq. D-4.6]
Torque=(In-Io)/Kv[Eq. D-4.7]
The relationship between Kv and Kt is shown below,
Kt=1355/Kv[Eq. D-4.8]
These equations are used to analyze the motor, therefore, they do affect the rest of the propulsion system. These equations are implemented in the following codes [App. D-5, D-6, D-7].
Table 4.1: Motor Constants of Various Motors.
Appendix D-5: Motor Selection code
%Motor Selection
clear all
close all
%Prto= input('Enter Power required fot TO :');
%Prcl= input('Enter Power required for Climb :');
%if Prto > Prcl
% Pto=Prto;
%else
% Pto=Prcl;
%end
Pto=277.7344;
%Wtot=8.6;
%Pto=50*Wtot; % 50 W/lb for take off for rough estimation
I=[2:0.1:60];
cell=18;
vol=1.2;
Vin=vol*cell;
%Astroflight CO25
Io1=2.2;
Rm1=0.093;
kv1=971;
kt1=1.395;
rpm1=kv1.*(Vin-(I.*Rm1));
P1=(I-Io1).*(Vin-(I.*Rm1));
Pin1= I.*Vin;
eff1=P1./Pin1;
T1=kt1.*(I-Io1);
Idrpm1=kv1*Vin;
Noloadrpm1= kv1*(Vin-Io1*Rm1);
Istall1=Vin/Rm1;
Imax1=sqrt(Io1*Istall1);
nmax1=((Imax1-Io1)/Imax1)^2;
%Aveox 1415/1.5
Io2=2.5;
Rm2=0.01;
kv2=1568;
kt2=0.848;
rpm2=kv2.*(Vin-(I*Rm2));
P2=(I-Io2).*(Vin-(I.*Rm2));
Pin2= I.*Vin;
eff2=P2./Pin2;
T2=kt2.*(I-Io2);
Idrpm2=kv2*Vin;
Noloadrpm2= kv2*(Vin-Io2*Rm2);
Istall2=Vin/Rm2;
Imax2=sqrt(Io2*Istall2);
nmax2=((Imax2-Io2)/Imax2)^2;
%MaxCim N32-13Y
Io3=0.8;
Rm3=0.058;
kv3=1420;
kt3=0.946;
rpm3=kv3.*(Vin-(I*Rm3));
P3=(I-Io3).*(Vin-(I.*Rm3));
Pin3= I.*Vin;
eff3=P3./Pin3;
T3=kt3.*(I-Io3);
Idrpm3=kv3*Vin;
Noloadrpm3= kv3*(Vin-Io3*Rm3);
Istall3=Vin/Rm3;
Imax3=sqrt(Io3*Istall3);
nmax3=((Imax3-Io3)/Imax3)^2;
%Maxcim N32-13D
Io4=2.5;
Rm4=0.022;
kv4=2500;
kt4=0.548;
rpm4=kv4.*(Vin-(I*Rm4));
P4=(I-Io4).*(Vin-(I.*Rm4));
Pin4= I.*Vin;
eff4=P4./Pin4;
T4=kt4.*(I-Io4);
Idrpm4=kv4*Vin;
Noloadrpm4= kv4*(Vin-Io4*Rm4);
Istall4=Vin/Rm4;
Imax4=sqrt(Io4*Istall4);
nmax4=((Imax4-Io4)/Imax4)^2;
%Aveox 1415/2
Io5=1.8;
Rm5=0.022;
kv5=1190;
kt5=1.13;
rpm5=kv5.*(Vin-(I*Rm5));
P5=(I-Io5).*(Vin-(I.*Rm5));
Pin5= I.*Vin;
eff5=P5./Pin5;
T5=kt5.*(I-Io5);
Idrpm5=kv5*Vin;
Noloadrpm5= kv5*(Vin-Io5*Rm5);
Istall5=Vin/Rm5;
Imax5=sqrt(Io5*Istall5);
nmax5=((Imax5-Io5)/Imax5)^2;
%max efficiency of motors
disp('For Astro CO25')
nmax1
Imax1
P1(151)
eff1(151)
disp('For Aveox 1415/1.5')
nmax2
Imax2
P2(151)
eff2(151)
disp('For Aveox 1415/2')
nmax5
Imax5
P5(151)
eff5(151)
disp('For Maxcim N32-13Y')
nmax3
Imax3
P3(151)
eff3(151)
disp('For Maxcim N32-13D')
nmax4
Imax4
P4(151)
eff4(151)
figure(2)
subplot(311)
plot(I,P1,'k',I,P2,'b',I,P3,'g',I,P4,'m',I,P5,'y')
legend('AstroC025','Aveox1415/1.5','MaxcimN32-13Y','MaxcimN32-13D','Aveox1415/2')
hold on
plot(I,Pto,'r')
axis([2 25 100 500])
hold off
title('Power output by the Motors')
subplot(312)
plot(I,eff1,'k',I,eff2,'b',I,eff3,'g',I,eff4,'m',I,eff5,'y')
legend('AstroC025','Aveox1415/1.5','MaxcimN32-13Y','MaxcimN32-13D','Aveox1415/2')
title('Power efficiency of the Motors')
subplot(313)
plot(I,T1,'k',I,T2,'b',I,T3,'g',I,T4,'m',I,T5,'y')
legend('AstroC025','Aveox1415/1.5','MaxcimN32-13Y','MaxcimN32-13D','Aveox1415/2')
title('Torque produced by Motor')
%Gear box
m=3.75; %gear box ratio
rpmg1=rpm1/m;
rpmg2=rpm2/m;
rpmg3=rpm3/m;
rpmg4=rpm4/m;
rpmg5=rpm5/m;
ng= 0.95;
Pgout1=P1.*ng;
Pgout2=P2.*ng;
Pgout3=P3.*ng;
Pgout4=P4.*ng;
Pgout5=P5.*ng;
Tg1= m*ng*T1;
Tg2= m*ng*T2;
Tg3= m*ng*T3;
Tg4= m*ng*T4;
Tg5= m*ng*T5;
figure(3)
subplot(211)
plot(I,Pgout1,'k',I,Pgout2,'b',I,Pgout3,'g',I,Pgout4,'m',I,Pgout5,'y')
legend('AstroC025','Aveox1415/1.5','MaxcimN32-13Y','MaxcimN32-13D','Aveox1415/2')
title('Power output after gearbox')
subplot(212)
plot(I,Tg1,'k',I,Tg2,'b',I,Tg3,'g',I,Tg4,'m',I,Tg5,'y')
legend('AstroC025','Aveox1415/1.5','MaxcimN32-13Y','MaxcimN32-13D','Aveox1415/2')
title('Torque produced by gearbox')
%Speed controllers
%For maxcim's and Aveox: Maxu35B-21
Requi1 = 0.009;
Pd2345 = I.^2.*Requi1;
%For Astro Flight : 204D
Requi2 =0.002;
Pd1= I.^2.*Requi2;
%Battery
Poutn1 = Pin1 + Pd1;
Poutn2 = Pin2 + Pd2345;
Poutn3 = Pin3 + Pd2345;
Poutn4 = Pin4 + Pd2345;
Poutn5 = Pin5 + Pd2345;
%Speed Controller efficiency
%ns =output pwr/input pwr
ns1= Pin1./Poutn1;
ns2= Pin2./Poutn2;
ns3= Pin3./Poutn3;
ns4= Pin4./Poutn4;
ns5= Pin5./Poutn5;
figure(4)
subplot(211)
plot(I,Pd1,'k',I,Pd2345,'b')
legend('AstroC025','Rest')
title('Power dissipated by speed controller')
subplot(212)
plot(I,ns1,'k',I,ns2,'b',I,ns3,'b',I,ns4,'b',I,ns5,'b')
legend('AstroC025','Aveox1415/1.5','MaxcimN32-13Y','MaxcimN32-13D','Aveox1415/2')
title('Speed controller efficiency')
Appendix D-6: Motor Analysis Code
clear all
motordata21
[nmotor,col]=size(mxdata)
for ii=1:nmotor
ii
disp(' ')
disp('Start new motor')
titstr=mxname(ii,:);
disp(titstr)
Kv=mxdata(ii,1) %RPM/volt
Kt=mxdata(ii,2) % inch-ounce per ampere
R= mxdata(ii,3) % Ohms
Io=mxdata(ii,4) % amperes
Vin=mxdata(ii,6) % volt
Iin=Io:30;
[Pout,Poutfpps,PoutHp,Pin,Tout,Toutfp,RPM,eta]=motor(Vin,Iin,Kv,Kt,R,Io);
figure(ii)
motorplot(Iin,Pout,Tout,RPM,eta,titstr)
[PoutMax,PoutfppsMax,PoutHpMax,PinMax,ToutMax,ToutfpMax,RPMMax,etaMax]=...
motoranalysis(Pout,Poutfpps,PoutHp,Pin,Tout,Toutfp,RPM,eta,titstr)
pause
end
Function called motordata21
% Kv= RPM/volt
% Kt= inch-ounce per ampere
% R= Ohms
% Io= amperes
% m=gear ratio if motor is geared
% Vnom=volt (nominal motor voltage)
% HPnom=nominal horsepower at the conditions for max efficiency
% Kv Kt R Io m Vnom HPnom
mxdata=[1568 0.848 0.010 2.5 3.70 21.6 0.1371
1190 1.130 0.022 1.8 3.70 21.6 0.15877
1420 0.946 0.058 0.8 3.70 21.6 0.26647
2500 0.548 0.022 2.5 3.70 21.6 0.28592
971 1.390 0.093 2.2 1.63 21.6 0.28592 ]
mxname=['Aveox 1415/1.5 '
'Aveox 1415/2 '
'Maxcim N32-13Y '
'Maxcim N32-13D '
'Astro Cobalt-25 Sport Motor #625']
Appendix D-7 : Modified Goldstein Method code.
clear all
close all
echo off
format compact
clear
disp(' ')
disp('Start new run')
disp('Propeller Analysis using Goldsteins Classical Vortex Theory')
disp(' This code works for two bladed propellers only.')
disp(' ')
% Input constants
Diam = [13 14 16 15 18 20 22 24]';
n=size(Diam);
for i =1:n(1)
Din=Diam(i);
% propeller diameter (inches)
Pin=8; % pitch of the propeller (inches)
RPM= 7805.8; % RPM of propeller
Vmph=25*60/88 ;
%Vmph=0% airspeed in mph
rho=.002308; % air density (slug/ft**2) (sea level)
%rho=.002065; % air density (slug/ft**2) at 4750 feet
% Pin gives geometric angle to the flat part of the
% rear of the propeller
aoldeg=-6; % angle of zero lift of the propeller (degrees)
% measured from mean chord line (typically negative)
beta0deg=.5; % angle from flat part of the prop to mean chord line
a=2*pi; % lift curve slope of propeller
Cd0=.00655;% 2-d minimum drag coefficient
k=.01; % Cd = Cd0+k*Cl*Cl
B=2 ; % number of blades (2 for standard type propeller)
% input nondimensional properties at each radial location
% cR=c/R, x=r/R
x=[.3,.35,.4,.45,.5,.55,.6,.65,.7,.75,.8,.85,.9,.95,1.];
cR=.045*ones(size(x));
% END OF INPUTS
% Display inputs section
disp(['Diameter Din= ',num2str(Din),' inches'])
disp(['Pitch Pin= ',num2str(Pin),' inches'])
disp(['Angle of zero lift aoldeg= ',num2str(aoldeg),' degrees'])
disp(['Angle Flat side to mean chord beta0deg= ',num2str(beta0deg),' degrees'])
disp(['RPM= ',num2str(RPM),' rpm'])
disp(['2-d Lift curve slope a= ',num2str(a),' per rad'])
disp(['2-d Min drag coef Cd0= ',num2str(Cd0)])
disp(['k from 2-d drag polar= ',num2str(k)])
disp(['Number of blades B= ',num2str(B)])
disp(['air density rho= ',num2str(rho),' slug/ft^3'])
disp(['Airspeed Vmph= ',num2str(Vmph),' mph'])
% derived constants
V=Vmph*88/60; % airspeed in ft/sec
D=Din/12; % Diameter in feet
R=D/2; % Radius in feet
n=RPM/60; % propeller frequency (rev/sec) or (hz)
omega=2*pi*n; % frequency of revolution of the propeller (rad/sec)
lamda=V/(omega*R);
r2d=180/pi;
Vt=omega*R; % tip velocity (ft/sec)
J=V/(n*D); % advance ratio
% Output scalar constants
disp(['Airspeed V= ',num2str(V),' ft/sec'])
disp(['Propeller Diameter D= ',num2str(D),' feet'])
disp(['Propeller Radius R= ',num2str(R),' feet'])
disp(['propeller RPS n= ',num2str(n),' hertz'])
disp(['omega= ',num2str(omega),' rad/sec'])
disp(['lamda= ',num2str(lamda)])
disp(['r2d= ',num2str(r2d),' deg/rad'])
disp(['Tip speed Vt= ',num2str(Vt),' ft/sec'])
disp(['Advance Ratio J= ',num2str(J)])
disp(' ')
%derived section constants
c=R*cR; % chord in feet
cin=c*12; % chord in inches
%disp(' ')
%disp('x in r/R and is nondimensional, cR=c/R, cin in the chord in inches')
%echo on
%disp([x', cR', cin'])
%echo off
%disp(' ')
beta1=atan(((Pin/Din)/pi)./x);
beta=beta1+(beta0deg-aoldeg)/r2d;
sigma=B*c/(pi*R);
r=x*R;
Vr=Vt*sqrt(x.*x+lamda*lamda);
phi=atan(lamda./x);
WtVt=.02*ones(size(c)); %initial guess
nr=length(c);
nr1=nr-1;
aiold=zeros(size(c));
for ii=1:40
WaVt(1:nr1)=.5*(-lamda+sqrt(lamda*lamda+4*WtVt(1:nr1).*(x(1:nr1)-WtVt(1:nr1))));
ai(1:nr1)=atan(WtVt(1:nr1)./WaVt(1:nr1))-phi(1:nr1);
%ai(1:nr1)=atan((V+WaVt(1:nr1)*Vt)./(omega*r(1:nr1)-WtVt(1:nr1)*Vt))-phi(1:nr1);
e=sum(abs(ai(1:nr1)-aiold(1:nr1)));
iter=['Loop index= ',num2str(ii),' error= ',num2str(e)];
%disp(iter)
if e<.0001 ; break; end
aiold(1:nr1)=ai(1:nr1);
Cl(1:nr1)=a*(beta(1:nr1)-ai(1:nr1)-phi(1:nr1));
VeVt(1:nr1)=sqrt((lamda+WaVt(1:nr1)).^2+(x(1:nr1)-WtVt(1:nr1)).^2);
gamma(1:nr1)=.5*c(1:nr1).*Cl(1:nr1).*VeVt(1:nr1)*Vt;
sinphialp(1:nr1)=sin(phi(1:nr1)+ai(1:nr1));
kappa(1:nr1)=kappa2(x(1:nr1),sinphialp(1:nr1));
WtVt(1:nr1)=B*gamma(1:nr1)./(4*pi*Vt*r(1:nr1).*kappa(1:nr1));
end
Cl(nr)=0;
ai(nr)=beta(nr)-phi(nr);
VrVt=sqrt(lamda*lamda+1);
WaVt(nr)=VrVt*sin(ai(nr))*cos(ai(nr)+phi(nr));
WtVt(nr)=VrVt*sin(ai(nr))*sin(ai(nr)+phi(nr));
VeVt(nr)=sqrt((lamda+WaVt(nr))^2+(x(nr)-WtVt(nr))^2);
kappa(nr)=0;
Cd=Cd0+k*Cl.*Cl;
ZT=(pi/8)*(J*J+pi*pi*(x.*x)).*sigma;
ZP=pi*ZT.*x;
dCTdx=ZT.*(Cl.*cos(phi+ai)-Cd.*sin(phi+ai));
dCPdx=ZP.*(Cl.*sin(phi+ai)+Cd.*cos(phi+ai));
% Overall propeller performance
CT=trapi(dCTdx,x);
CP=trapi(dCPdx,x);
eta=CT*J/CP;
T=CT*rho*n^2*D^4;
P=CP*rho*n^3*D^5;
HP=P/550;
Pwatt=1.356*P;
torque=P/omega;
Clmax=max(Cl);
Toz=T*16;
PestWatts=1.31*D^4*(Pin/12)*(RPM/1000)^3;
% The above approximate formula works for
% Top Flite, Zinger and Master Airscrews reasonably well.
% For Rev Up props subract .5 in from the pitch.
% For APC props use constant 1.11 instead of 1.31.
% For thin carbon fiber folding props use 1.18 instead of 1.31.
% Ref: Electric Motor Handbook, by Robert J. Boucher,
% AstroFlight, Inc.
%echo on
%dat=[ x', beta', phi', kappa', ai', WtVt']
%disp(' ')
%dat2=[x', WaVt', VeVt', Cl', dCTdx', dCPdx']
%echo off
disp(' ')
disp(['Advance Ratio J= ',num2str(J)])
disp(['Thrust Coefficient CT= ',num2str(CT)])
disp(['Power Coefficient CP= ',num2str(CP)])
disp(['Propeller efficiency eta= ',num2str(eta)])
disp(['Speed V= ',num2str(V),' ft/sec'])
disp(['RPM= ',num2str(RPM),' rpm'])
disp(['Thrust T= ',num2str(T),' pounds'])
disp(['Thrust Toz= ',num2str(Toz),' ounces'])
disp(['Power used P= ',num2str(P),' ft*lbf/sec'])
disp(['Horsepower used HP= ',num2str(HP),' HP'])
disp(['Power used Pwatt= ',num2str(Pwatt),' watts'])
disp(['Torque used Q= ',num2str(torque),' ft*lbf'])
disp(['Torque used Q= ',num2str(torque*192),' in-oz'])
disp(['Clmax= ',num2str(Clmax)])
disp(' ')
disp(['Estimated power used, PestWatts= ',num2str(PestWatts),' watts, Ref: Boucher'])
disp(' ')
etaf(i)=eta;
Jf(i)=J;
Cp(i)=CP;
Ct(i)=CT;
Pw(i)=Pwatt;
Th(i)=T;
Tor(i)=torque;
end
Thrust=Th'
Power=Pw'
Efficiency=etaf'
Thrustcoeff=Ct'
Powercoeff=Cp'
Torqueis=Tor'
Advanceratio=Jf'
figure(1)
plot(Jf,etaf)
xlabel('J= V/nD = Advance Ratio')
ylabel('Propeller Efficiency')
title(' J vs. Eta at pitch=10, rpm=7012.5')
grid on
figure(2)
subplot(211)
plot(Jf,Cp)
xlabel('J= V/nD = Advance Ratio')
ylabel('Coefficient of Power Cp')
title(' J vs. Cp & Ct at pitch=10, rpm=7012.5')
grid on
subplot(212)
plot(Jf,Ct)
xlabel('J= V/nD = Advance Ratio')
ylabel('Coefficient of Thrust Ct')
grid on
figure(3)
subplot(211)
plot(x,dCTdx)
z=axis;
axis([0,1,0,z(4)])
xlabel('nondimensional radial location')
ylabel('dCTdx')
subplot(212)
plot(x,dCPdx)
z=axis;
axis([0,1,0,z(4)])
xlabel('nondimensional radial location')
ylabel('dCPdx')
disp(' For model aircraft propellers this code underestimates')
disp(' the power required. The underestimation is worse for RPM>10,000')
disp(' where it may underestimate by a factor of .5')
disp(' For RPM <10,000 the factor is about .75')