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Alina Abdikadyr on 10 Feb 2023
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https://support.mathworks.com/matlabcentral/answers/1910540-calculate-the-difference-between-minimum-values-of-a-parabola-and-straight-line-from-a-plot
Commented: Les Beckham on 10 Feb 2023
Accepted Answer: Les Beckham
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Hello everyone, please could you help me with a code.
How I can calculate the values from a plot? I need the difference between straight line (P) and between the minimum value of a parabola (P) for each curve.
So, for example in this curve, the difference between the straight blue curve and the first parabola, then the next straight line and green parabola and so on.
My code is:
clear all; close all
W = 60000;
S = 28.2;
AR=7;
cd0 = 0.02;
k = 0.04;
RC=0.51;
clalpha = 2*pi;
Psl=741000;
hv=0:1:10;
cdminp=4*cd0;
clminp=sqrt(3*cd0/k);
Vmin=sqrt(2*W/(1.225*28.2*clminp));
D=0.5*1.225*Vmin^2*S*cdminp;
Pminreq=D*Vmin;
deltaPgiven=RC*W;
figure(1);hold on; xlabel('V');ylabel('P')
hv=0:1:10;
for k1 = 1:numel(hv)
h = hv(k1);
i=0;
for alpha = 1:0.25:15
i=i+1;
rho(i)=1.225*exp(-h/10.4);
cl(i) = clalpha * alpha * pi/180;
V(i) = sqrt(2*W/rho(i)/S/cl(i));
L(i) = 0.5 * rho(i) * V(i) * V(i) * S * cl(i);
cd(i) = cd0 + k * cl(i) * cl(i);
D(i) = 0.5 * rho(i) * V(i) * V(i) * S * cd(i);
clcd(i) = cl(i)/cd(i);
p(i) = D(i)*V(i);
Ph(i)=Psl*(rho(i)/1.225).^0.75;
end
figure(1); plot(V,p)
hold on
plot(V,Ph);
end
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Accepted Answer
Les Beckham on 10 Feb 2023
Edited: Les Beckham on 10 Feb 2023
Open in MATLAB Online
Maybe this?
W = 60000;
S = 28.2;
AR=7;
cd0 = 0.02;
k = 0.04;
RC=0.51;
clalpha = 2*pi;
Psl=741000;
hv=0:1:10;
cdminp=4*cd0;
clminp=sqrt(3*cd0/k);
Vmin=sqrt(2*W/(1.225*28.2*clminp));
D=0.5*1.225*Vmin^2*S*cdminp;
Pminreq=D*Vmin;
deltaPgiven=RC*W;
figure(1);hold on; xlabel('V');ylabel('P')
hv=0:1:10;
for k1 = 1:numel(hv)
h = hv(k1);
i=0;
for alpha = 1:0.25:15
i=i+1;
rho(i)=1.225*exp(-h/10.4);
cl(i) = clalpha * alpha * pi/180;
V(i) = sqrt(2*W/rho(i)/S/cl(i));
L(i) = 0.5 * rho(i) * V(i) * V(i) * S * cl(i);
cd(i) = cd0 + k * cl(i) * cl(i);
D(i) = 0.5 * rho(i) * V(i) * V(i) * S * cd(i);
clcd(i) = cl(i)/cd(i);
p(i) = D(i)*V(i);
Ph(i)=Psl*(rho(i)/1.225).^0.75;
end
figure(1); plot(V,p)
hold on
plot(V,Ph);
[pmin, imin] = min(p); % find the min p
deltas(k1) = Ph(1) - pmin; % calculate the difference
tolerance = 5000; % or whatever you want
if (abs(deltas(k1) - 300000) < tolerance)
fprintf('delta = %8.1f at h = %4.1f, rho = %.5f, V = %.2f, Ph = %.1f, p = %.1f\n', ...
deltas(k1), h, rho(imin), V(imin), Ph(imin), p(imin))
end
end
delta = 302330.3 at h = 4.0, rho = 0.83387, V = 64.31, Ph = 555317.0, p = 252986.7
legend(compose('h = %.1f', hv), 'location', 'northwest')
grid on
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Alina Abdikadyr on 10 Feb 2023
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1910540-calculate-the-difference-between-minimum-values-of-a-parabola-and-straight-line-from-a-plot#comment_2610135
Yes, thank you! Also, how can I show points of P that brings me an exact delta on graph? For example, delta =3.0233. Also, can I display the values of h, rho, Vmin, Pmin for this exact delta in table?
Les Beckham on 10 Feb 2023
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1910540-calculate-the-difference-between-minimum-values-of-a-parabola-and-straight-line-from-a-plot#comment_2610155
See edited code above
Alina Abdikadyr on 10 Feb 2023
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1910540-calculate-the-difference-between-minimum-values-of-a-parabola-and-straight-line-from-a-plot#comment_2610170
Thank you very much! But If I will have more h values, so may I display the rows where delta is almost equal to 300000
Les Beckham on 10 Feb 2023
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1910540-calculate-the-difference-between-minimum-values-of-a-parabola-and-straight-line-from-a-plot#comment_2610230
Open in MATLAB Online
You are quite welcome.
I don't understand the new question. You can display whatever you want.
Maybe you mean to only display the results if delta is near 30000? How close?
You could put the fprintf statement inside an if condition. Something like
tolerance = 1000; % or whatever you want
if (abs(deltas(k1) - 30000) < tolerance)
fprintf('delta = %8.1f at h = %4.1f, rho = %.5f, V = %.2f, Ph = %.1f, p = %.1f\n', ...
deltas(k1), h, rho(imin), V(imin), Ph(imin), p(imin))
end
Alina Abdikadyr on 10 Feb 2023
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1910540-calculate-the-difference-between-minimum-values-of-a-parabola-and-straight-line-from-a-plot#comment_2610245
Open in MATLAB Online
Yes, you inderstand it correctly, where I should put this piece of code? I implmented it here:
clear all; close all
W = 60000;
S = 28.2;
AR=7;
cd0 = 0.02;
k = 0.04;
RC=0.51;
clalpha = 2*pi;
Psl=741000;
hv=0:1:10;
cdminp=4*cd0;
clminp=sqrt(3*cd0/k);
Vmin=sqrt(2*W/(1.225*28.2*clminp));
D=0.5*1.225*Vmin^2*S*cdminp;
Pminreq=D*Vmin;
deltaPgiven=RC*W;
figure(1);hold on; xlabel('V');ylabel('P')
hv=0:1:10;
for k1 = 1:numel(hv)
h = hv(k1);
i=0;
for alpha = 1:0.25:15
i=i+1;
rho(i)=1.225*exp(-h/10.4);
cl(i) = clalpha * alpha * pi/180;
V(i) = sqrt(2*W/rho(i)/S/cl(i));
L(i) = 0.5 * rho(i) * V(i) * V(i) * S * cl(i);
cd(i) = cd0 + k * cl(i) * cl(i);
D(i) = 0.5 * rho(i) * V(i) * V(i) * S * cd(i);
clcd(i) = cl(i)/cd(i);
p(i) = D(i)*V(i);
Ph(i)=Psl*(rho(i)/1.225).^0.75;
end
figure(1); plot(V,p)
hold on
plot(V,Ph);
[pmin, imin] = min(p); % find the min p
deltas(k1) = Ph(1) - pmin; % calculate the difference
tolerance = 1000; % or whatever you want
if (abs(deltas(k1) - 30000) < tolerance)
fprintf('delta = %8.1f at h = %4.1f, rho = %.5f, V = %.2f, Ph = %.1f, p = %.1f\n', ...
deltas(k1), h, rho(imin), V(imin), Ph(imin), p(imin))
end
legend(compose('h = %.1f', hv), 'location', 'northwest')
grid on
end
Les Beckham on 10 Feb 2023
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1910540-calculate-the-difference-between-minimum-values-of-a-parabola-and-straight-line-from-a-plot#comment_2610285
That's close to what I would do, but I would keep the legend and grid on outside of the for loop. I've edited my answer to reflect this change.
Alina Abdikadyr on 10 Feb 2023
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1910540-calculate-the-difference-between-minimum-values-of-a-parabola-and-straight-line-from-a-plot#comment_2610350
Thank you! What does the tolerance value mean?
Les Beckham on 10 Feb 2023
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1910540-calculate-the-difference-between-minimum-values-of-a-parabola-and-straight-line-from-a-plot#comment_2610355
It just represents how close to 300000 the delta has to be to make the code print the results. Adjust as desired.
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More Answers (1)
Torsten on 10 Feb 2023
Edited: Torsten on 10 Feb 2023
Open in MATLAB Online
syms h V W S rho cd0 k cl Psl
eqn = V == sqrt(2*W/rho/S/cl);
cl = solve(eqn,cl);
Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.
cd = cd0 + k * cl^2;
D = 0.5 * rho * V * V * S * cd;
p = D*V;
Vmin = solve(diff(p,V)==0,V);
pmin = subs(p,V,Vmin);
Ph = Psl*(rho/1.225)^0.75;
hnum = 0:0.01:10;
Wnum = 60000;
Snum = 28.2;
rhonum = 1.225*exp(-hnum/10.4);
cd0num = 0.02;
knum = 0.04;
Pslnum = 741000;
for i = 1:numel(hnum)
Phnum(i) = double(subs(Ph,[rho Psl],[rhonum(i),Pslnum]));
pm = double(subs(pmin,[W S rho cd0 k],[Wnum Snum rhonum(i) cd0num,knum]));
pminnum(i) = pm(end);
deltaP(i) = Phnum(i)-pminnum(i);
end
format long
deltaP.'
ans = 1001×1
1.0e+05 * 5.322767552311991 5.316422010284389 5.310079836471793 5.303741027866013 5.297405581460750 5.291073494251587 5.284744763235998 5.278419385413340 5.272097357784856 5.265778677353669
idx = deltaP > 2.8e5 & deltaP < 3.2e5; % select those deltaP with 2.8e5 <= deltaP < = 3.2e5
[hnum(idx).' deltaP(idx).'] % Show these values together with the corresponding h values
ans = 77×2
1.0e+05 * 0.000036700000000 3.196913122178178 0.000036800000000 3.191616062324753 0.000036900000000 3.186321382077705 0.000037000000000 3.181029079029593 0.000037100000000 3.175739150774377 0.000037200000000 3.170451594907418 0.000037300000000 3.165166409025479 0.000037400000000 3.159883590726722 0.000037500000000 3.154603137610705 0.000037600000000 3.149325047278384
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Alina Abdikadyr on 10 Feb 2023
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1910540-calculate-the-difference-between-minimum-values-of-a-parabola-and-straight-line-from-a-plot#comment_2610225
Thank you very much! But If I will have more h values, so may I display the deltaP values that are almost equal to 3?
Torsten on 10 Feb 2023
Direct link to this comment
https://support.mathworks.com/matlabcentral/answers/1910540-calculate-the-difference-between-minimum-values-of-a-parabola-and-straight-line-from-a-plot#comment_2610235
Edited: Torsten on 10 Feb 2023
Open in MATLAB Online
Add the lines
idx = deltaP > 2.8e5 & deltaP < 3.2e5; % select those deltaP with 2.8e5 <= deltaP < = 3.2e5
[hnum(idx) deltaP(idx)] % Show these values together with the corresponding h values
at the end of the code.
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