I have a problem with plotting two vectors, I want to vary 'z' by a certain amount and 'x' by another amount and plot versus each other, how can i make the matrix dimensions match?

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Ikenna Okoye
Ikenna Okoye 2018-11-24
评论： madhan ravi 2018-11-29
x = 2:1:25;
y = x^2;
z = 1:1:28;
plot(z,x)

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madhan ravi
madhan ravi 2018-11-25
编辑：madhan ravi 2018-11-25
Read about meshgrid() and ndgrid().

更多回答（2 个）

the cyclist
the cyclist 2018-11-24
Well, it's really up to you to decide. You have a 24-element vector, and a 28-element vector.
Which of those elements align with each other? The first 24 elements of both? Then you could just drop the last 4 elements of z.
Or maybe the two endpoints align, and you need to linearly interpret both vectors onto the same number of points?
It's really not clear from your question. I think you need to think more carefully about what makes sense.
  2 个评论
Ikenna Okoye
Ikenna Okoye 2018-11-24
Im trying to see if there is some variable x that varies, variable y that varies and variable z(x,y), that can take both vectors with different lengths and make them the same size in a code. I want to apply this to a more complex code.
the cyclist
the cyclist 2018-11-24
编辑：the cyclist 2018-11-24
Yes, there are an infinite number of ways to make these two vectors the same length. Here are three:
Method 1:
x = [x zeros(1,4)]; % Append 4 zeros to the end of x.
Method 2:
z = z(1:24); % Use only the first 24 elements of z.
Method 3:
x = [x nan(1,4004)]; % Append 4004 NaNs to the end of x.
z = [z nan(1,4000)]; % Append 4000 NaN to the end of z.
(The last one is almost certainly not useful, but who knows?)
My point is that the best method will depend on the relationship between the current elements of x and z. How do they "line up" with each other? That relationship is impossible to understand without more detailed information.

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Ikenna Okoye
Ikenna Okoye 2018-11-24
Heres my code: It plots thrust versus altitude and varies 'gamma'. I want to be able to create a carpet plot varying 'gamma', 'ex' and one other parameter i cannot remember right now. It runs fine, but as soon as i vary anything except altitude 'z', the error ''matrix dimentions do not agree'' pops up. The code has three parts: the main thrust code (Propulsion_rev3) and a funciton that it calls for altitude perameters , the code of atmosphere model (atmos0_100) and the function that calls the atmosphere model (Fun_atmos0_100).
%Propulsion_rev3
z = 0:1:100;
[T,P,rho,del,sig,the]= atmos0_100(z);
%% First stage: constants
r_o = 6.371e7; % earth radius, m
g_o = 9.81; % gravity, m/s^2
D = 100; % Drag, N, from aero
m_i = 12000; % initial wet mass, kg
P_c = 2.2339e7; % ambient pressure, Pa
g = 9.81; % gravitational acceleration, m/s^2
f = 6; % fuel to air ratio
I_sp = 363; % specific impulse, s
A_e = 4.104; % exit area, m^2
% From App.B
T_c = 3400; % temp, K
gamma = 1.21; % specific heat ratio
Mol = 13.5; % molecular mass, kg/kmol
v_o = 10; % inicial velocity, m/s
time = 80; % time to seperation, s, from performance
R = (8414/(1+f))*((1/28.97)+(f/Mol)); % gas constatnt, J/kg*K
cp = (R*gamma)/(gamma-1); % specific heat, J/kg*K
%% Inputs
F_req = 1334466; % required thrust, N (from Performance)
%% Engine characteristics/SSME design point
% assuming combustion efficiency of 1.0
ex = 77;
P_c = 2.2339e+7; % chamber pressure, Pa
A_t = (ex.^-1).*A_e; % throat area, m^2
epsilon = sqrt(gamma./(((gamma+1)./2).^((gamma+1)./(gamma-1))));
% Newton-Raphson method for finding exit mach number
b = 2.*(gamma-1)./(gamma+1);
c = ((gamma+1)./(gamma-1)).*((ex).^(b));
d = 2./(gamma-1);
Me_0 = 7.5;
original = (c .* (Me_0 .^ b)) - (Me_0 .^ 2) - d;
derivative = (b .* c .* (Me_0 .^ (b - 1))) - (2 .* Me_0);
Me_1 = Me_0 - (original ./ derivative);
while abs(original) > 10^-2
Me_0 = Me_1;
original = (c .* (Me_0 .^ b)) - (Me_0 .^ 2) - d;
derivative = (b .* c .* (Me_0 .^ (b - 1))) - (2 .* Me_0);
Me_1 = Me_0 - (original ./ derivative);
fprintf('Iteration: M_e = %.20f, error = %.20f \n', Me_1, original);
end
mf_f = 1-exp(-(sqrt(g_o*r_o))./(I_sp*v_o*((1-D)/F_req))); % fuel mass fraction
mf = mf_f *m_i; % mass of fuel, kg,
T_e = T_c./((1 + gamma.*R.*Me_1.^2)./(2.*cp));
P_e = P_c.*(1+((gamma-1)./2).*(Me_1.^2)).^(gamma./(1-gamma)); % exit static pressure, Pa (pg.144, Mattingly)
P_te = P_e./(1+((gamma-1)./(Me_1.^2))).^(-gamma./(gamma-1)); % exit total pressure, Pa
% using isentropic relations
% T_e = ((P_e./P_te).*T_c.^(gamma./(gamma-1))).^(1./(gamma./(gamma-1)));
v_e = Me_1.*sqrt(gamma.*R.*T_e);
a = (2*gamma)/(gamma-1);
coeff = gamma/(gamma-1);
Pr = ((2/(gamma+1))*(1+((gamma-1)/2))^(-gamma/(gamma-1)));
m_dot = ((P_c*A_t)/sqrt(T_c))*sqrt((2/R)*coeff*((Pr^(2/gamma))-(Pr^((gamma+1)/gamma))));
F_ava =((m_dot.*v_e) + (P_e-P).*(A_t.*ex));
S = (m_dot.*f)./F_ava; % specific fuel consumption, kg/s*N
f_t = (S.*F_ava).*time;
C_f = F_ava/(P_c*A_t);
R_thrusttoweight = (F_ava)/(f_t*9.81);
%C_f = epsilon*sqrt(a*(1-(P_e/P_c)^coeff))+(P_e/P_c - P/P_c)*ex;
%% engine sizing
D_e = 0.00357.*F_ava+14.48; % engine diameter, m
m_e = F_ava./(g*0.0006098.*F_ava+13.44); % engine mass, kg
L_e = 0.000030*F_ava+327.7; % engine length, m
Lstar = 1; % characteristic length, m
A_c = A_t*(8*((2*sqrt(A_t/pi))^(-0.6)) + 1.25); % average combustion chamber cx area, m^2
L_c = Lstar*(A_t/A_c); % combusiton chamber length, m
V_c = Lstar*A_t; % combustion chamber volume, m^3
d_e = sqrt((4.*ex.*A_t)/pi); % exit diameter, m
%% Tank sizing
V_f = (f_t/70.8)*(1/7); % fuel volume, m^3
V_o = (f_t/1141)*(6/7); % oxidizer volume, m^3
V_t = V_f + V_o; % total propellant volume, m^3
%% Plots/outputs
fprintf('m_dot = %f [kg/s] \n',m_dot)
fprintf('v_e = %f [m/s] \n',v_e)
fprintf('V_c = %f [m^3] \n,',V_c)
fprintf('A_c = %f [m^2] \n', A_c)
fprintf('m_e = %f [kg] \n',m_e)
fprintf('L_e = %f [m] \n', L_e)
fprintf('D_e = %f [m]',D_e)
fprintf('L_c = %f [m] \n', L_c)
fprintf('f_t = %f [kg]\n', f_t)
% fprintf('m_f = %f [kg]\n', m_f)
figure(1)
plot(z,F_ava,'linewidth',1.25)
title('Avalible thrust vs. Altitude')
xlabel('Altitude (km)')
ylabel('F_ava (N)')
figure(2)
plot(z,S,'linewidth',1.25)
title('Specific fuel consimption vs. Altitiude')
xlabel('Altitude (km)')
ylabel('S (kg/s*N)')
figure(3)
plot(z,C_f,'linewidth',1.25)
title('Thrust Coefficient vs. Altitiude')
xlabel('Altitude (km)')
ylabel('C_f')
%% Trade Studies
% plot(F_ava,gamma) % vary gamma from 1.2-1.4
%% Second stage: Constants
r_o = 6.371e7; % earth radius, m
% gravity, m/s^2
D = 100; % Drag, N, from aero
m_i = 12000; % initial wet mass, kg
P_c = 2.2339e7; % ambient pressure, Pa
g = 9.81; % gravitational acceleration, m/s^2
f2 = 6; % fuel to air ratio
I_sp = 363; % specific impulse, s
A_e2 = 4.104; % exit area, m^2
% From App.B
T_c2 = 3400; % temp, K
gamma2 = 1.21; % specific heat ratio
Mol2 = 13.5; % molecular mass, kg/kmol
R2 = (8414/(1+f2))*((1/28.97)+(f2/Mol2)); % gas constatnt, J/kg*K
cp2 = (R*gamma2)/(gamma2-1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% fun_atmos0_100
prompt = 'For SI select 1 for imperial select 2?';
unit = input(prompt);
if unit==1
prompt = 'What is your height value in kilometers?';
z = input(prompt);
else unit==2
prompt = 'What is your height value in feet';
zi = input(prompt);
z = convlength([zi],'ft','km');
end
[T,P,rho,del,sig,the]= atmos0_100(z)
fprintf('For altitude of z = %.3f [km] ',z);
fprintf(' SI Imperial Ratios \n');
fprintf('------------------------------------------------------------------------- \n');
fprintf('P = %.3f [Pa] del = %.5f \n',P,del);
fprintf('T = %.3f [K] the = %.5f \n',T,the);
fprintf('rho = %f [kg/m^3] sig = %f \n',rho,sig);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%atmos0_100
function[T,P,rho,del,sig,the]= atmos0_100(z)
global r R_o
%% Constants
% Sea level conditions
P_o = 101325; % (Pa)
rho_o = 1.225; % (Kg/m^3)
T_o = 288.15; % (K)
mu_o = 1.789*10^-5; % (Kg/m/s)
nu_o = 1.46*10^-5; % (m^2/s)
tc_o = 0.02596; % (W/m/K)
R_o = 287.053; % (J/Kg/K)
g_o = 9.80665; % (m/s^2)
Cp = 1005; % (J/Kg/K)
r_o = 6356.766; % (km)
r = 1.4;
%% Process
for i = 1:length(z)
h(i) = (r_o*z(i))/(r_o+z(i));
if h(i) == 0
P(i) = P_o;
T(i) = T_o;
rho(i) = rho_o;
elseif 0<h(i) && h(i)<=11
P(i) = P_o*(T_o/(T_o-6.5*h(i)))^(34.1632/-6.5);
T(i) = T_o-6.5*h(i);
rho(i) = P(i)/(R_o*T(i));
eps(i) = z(i)*10^3/(R_o*T(i));
del(i) = P(i)/P_o;
sig(i) = rho(i)/rho_o;
the(i) = T(i)/T_o;
elseif 11<h(i) && h(i)<=20
T(i) = 216.65;
P(i) = 22632.06*exp(-34.1632*(h(i)-11)/T(i));
rho(i) = P(i)/(R_o*T(i));
eps(i) = (z(i)-11)*10^3/(R_o*T(i));
del(i) = P(i)/P_o;
sig(i) = rho(i)/rho_o;
the(i) = T(i)/T_o;
elseif 20<h(i) && h(i)<=32
P(i) = 5474.889*(216.65/(216.65+(h(i)-20)))^34.1632;
T(i) = 196.65+h(i);
rho(i) = P(i)/(R_o*T(i));
eps(i) = (z(i)-20)*10^3/(R_o*T(i));
del(i) = P(i)/P_o;
sig(i) = rho(i)/rho_o;
the(i) = T(i)/T_o;
elseif 32<h(i) && h(i)<=47
P(i) = 868.0187*(228.65/(228.65+2*r*(h(i)-32)))^(34.1632/(2*r));
T(i) = 139.05+2*r*h(i);
rho(i) = P(i)/(R_o*T(i));
eps(i) = (z(i)-32)*10^3/(R_o*T(i));
del(i) = P(i)/P_o;
sig(i) = rho(i)/rho_o;
the(i) = T(i)/T_o;
elseif 47<h(i) && h(i)<=51
T(i) = 270.65;
P(i) = 110.9063*exp(-34.1632*(h(i)-47)/T(i));
rho(i) = P(i)/(R_o*T(i));
eps(i) = (z(i)-47)*10^3/(R_o*T(i));
del(i) = P(i)/P_o;
sig(i) = rho(i)/rho_o;
the(i) = T(i)/T_o;
elseif 51<h(i) && h(i)<=71
P(i) = 66.93884*(270.65/(270.65-2*r*(h(i)-51)))^(34.1632/(-2*r));
T(i) = 413.45-2*r*h(i);
rho(i) = P(i)/(R_o*T(i));
eps(i) = (z(i)-51)*10^3/(R_o*T(i));
del(i) = P(i)/P_o;
sig(i) = rho(i)/rho_o;
the(i) = T(i)/T_o;
elseif 71<h(i) && h(i)<=85
P(i) = 3.956420*(214.65/(214.65-2*(h(i)-71)))^(34.1632/-2);
T(i) = 356.65-2*h(i);
rho(i) = P(i)/(R_o*T(i));
eps(i) = (z(i)-71)*10^3/(R_o*T(i));
del(i) = P(i)/P_o;
sig(i) = rho(i)/rho_o;
the(i) = T(i)/T_o;
elseif 85<z(i) && z(i)<=91
T(i) = 186.8673;
P(i) = exp(2.159582*10^(-6)*z(i)^3 + -4.836957*10^(-4)*z(i)^2 + -.14251928*z(i) + 13.47530);
rho(i) = exp(-3.322622*10^(-6)*z(i)^3 + 9.111460*10^(-4)*z(i)^2 + -.2609971*z(i) + 5.944694);
eps(i) = (z(i)-85)*10^3/(R_o*T(i));
del(i) = P(i)/P_o;
sig(i) = rho(i)/rho_o;
the(i) = T(i)/T_o;
else
T(i) = 263.1905-76.3232*sqrt(1-((z(i)-91)/-19.9429)^2);
P(i) = exp(3.304895*10^-5*z(i)^3 + -.009062730*z(i)^2 + .6516698*z(i) + -11.03037);
rho(i) = exp(2.873405*10^-5*z(i)^3 + -.008492037*z(i)^2 + .6541179*z(i) + -23.6201);
eps(i) = (z(i)-85)*10^3/(R_o*T(i));
del(i) = P(i)/P_o;
sig(i) = rho(i)/rho_o;
the(i) = T(i)/T_o;
end
end
  3 个评论
显示 1更早的评论
Ikenna Okoye
Ikenna Okoye 2018-11-25
编辑：Walter Roberson 2018-11-25
Gotcha and gotcha, didnt know it was in the answers section.
% im trying to vary 'gamma' dimentions wont agree with 'F_ava', avalible thrust
gamma = 1.2:0.05:1.4;
ex = 60:4:76;
T_e = T_c./((1 + gamma.*R.*Me_1.^2)./(2.*cp));
P_e = P_c.*(1+((gamma-1)./2).*(Me_1.^2)).^(gamma./(1-gamma)); % exit static pressure, Pa (pg.144, Mattingly)
P_te = P_e./(1+((gamma-1)./(Me_1.^2))).^(-gamma./(gamma-1)); % exit total pressure, Pa
% using isentropic relations
% T_e = ((P_e./P_te).*T_c.^(gamma./(gamma-1))).^(1./(gamma./(gamma-1)));
v_e = Me_1.*sqrt(gamma.*R.*T_e);
a = (2*gamma)/(gamma-1);
coeff = gamma/(gamma-1);
Pr = ((2./(gamma+1)).*(1+((gamma-1)./2)).^(-gamma./(gamma-1)));
m_dot = ((P_c*A_t)./sqrt(T_c)).*sqrt((2/R).*coeff.*((Pr.^(2./gamma))-(Pr.^((gamma+1)./gamma))));
F_ava =((m_dot.*v_e)+ (P_e-P).*(A_t.*ex));
error message:
Error in Pro_rev3 (line 74)
F_ava =((m_dot.*v_e)+ (P_e-P).*(A_t.*ex)); Matrix dimensions must agree.
Most of the equaions depend on 'gamma' and that is the variable i want to vary. I want to do the same with 'ex' expansion ratio also to make a carpet plot similar to the image attatched.
the cyclist
the cyclist 2018-11-27
So, you are talking about a pretty major change in your code. You want to take something that was written as a function of one variable, and change it to now be a function two (or maybe three?) variables.
madhan ravi's idea that you will need to use meshgrid is likely part of the solution. Given input of two vectors, that function will create a 2-d grid of all possible combinations of the elements of them.
Then you would use the output of that to build the functions of those two variables. You will probably need to rewrite a lot of lines of code.

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