intersection from a plot and loop

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Alina Abdikadyr
Alina Abdikadyr 2023-3-31
编辑： Star Strider 2023-3-31
Hello everyone, could you please help me to find the intersection of two graphs, figure 1
My code is:
clear all; close all
W_takeoff = 10000;
W_landing=6000;
S = 20;
AR = 5;
cd0 = 0.02;
k = 1/pi/AR;
RC=0.51;
clalpha = 2*pi;
amin=2;
astall=12;
rho=1;
ct=0.001;
figure(1);hold on; xlabel('V');ylabel('D')
i=0;
for alpha = amin:0.001:astall
i=i+1;
cl(i) = clalpha * alpha * pi/180;
V_takeoff(i) = sqrt(2*W_takeoff/rho/S/cl(i));
V_landing(i) = sqrt(2*W_landing/rho/S/cl(i));
cd(i) = cd0 + k * cl(i) * cl(i);
D_takeoff(i) = 0.5 * rho * V_takeoff(i) * V_takeoff(i) * S * cd(i);
D_landing(i) = 0.5 * rho * V_landing(i) * V_landing(i) * S * cd(i);
p_takeoff(i) = D_takeoff(i)*V_takeoff(i);
p_landing(i) = D_landing(i)*V_landing(i);
P_takeoff(i)=20000+500*V_takeoff(i);
T_takeoff(i)=20000/V_takeoff(i)+500;
P_landing(i)=20000+500*V_landing(i);
T_landing(i)=20000/V_landing(i)+500;
cl_cd2(i)=cl(i)/(cd(i)*cd(i));
ang(i)=alpha;
end
figure(1); plot(V_takeoff,D_takeoff)
hold on
plot(V_takeoff,T_takeoff)
title(['Takeoff'])

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回答（2 个）

Antoni Garcia-Herreros
Ran in:
Hello Alina,
You can check the fzero function
clear all; close all
W_takeoff = 10000;
W_landing=6000;
S = 20;
AR = 5;
cd0 = 0.02;
k = 1/pi/AR;
RC=0.51;
clalpha = 2*pi;
amin=2;
astall=12;
rho=1;
ct=0.001;
figure(1);hold on; xlabel('V');ylabel('D')
i=0;
for alpha = amin:0.001:astall
i=i+1;
cl(i) = clalpha * alpha * pi/180;
V_takeoff(i) = sqrt(2*W_takeoff/rho/S/cl(i));
V_landing(i) = sqrt(2*W_landing/rho/S/cl(i));
cd(i) = cd0 + k * cl(i) * cl(i);
D_takeoff(i) = 0.5 * rho * V_takeoff(i) * V_takeoff(i) * S * cd(i);
D_landing(i) = 0.5 * rho * V_landing(i) * V_landing(i) * S * cd(i);
p_takeoff(i) = D_takeoff(i)*V_takeoff(i);
p_landing(i) = D_landing(i)*V_landing(i);
P_takeoff(i)=20000+500*V_takeoff(i);
T_takeoff(i)=20000/V_takeoff(i)+500;
P_landing(i)=20000+500*V_landing(i);
T_landing(i)=20000/V_landing(i)+500;
cl_cd2(i)=cl(i)/(cd(i)*cd(i));
ang(i)=alpha;
end
figure(1); plot(V_takeoff,D_takeoff)
hold on
plot(V_takeoff,T_takeoff)
title(['Takeoff'])
pp = spline(V_takeoff,D_takeoff); %Fit curve 1 to spline
pp2 = spline(V_takeoff,T_takeoff); %Fit curve 2 to spline
x1=xlim;
x0 = fzero(@(x) (ppval(pp,x)-ppval(pp2,x)), 50); % Find the root of the difference between the two curves
line([x1(1) x0],[ppval(pp,x0) ppval(pp,x0)],'LineStyle','--','Color','k')
y1=ylim;
line([x0 x0],[y1(1) ppval(pp,x0)],'LineStyle','--','Color','k')
Star Strider
Star Strider 2023-3-31
编辑：Star Strider 2023-3-31
Ran in:
clear all; close all
W_takeoff = 10000;
W_landing=6000;
S = 20;
AR = 5;
cd0 = 0.02;
k = 1/pi/AR;
RC=0.51;
clalpha = 2*pi;
amin=2;
astall=12;
rho=1;
ct=0.001;
% figure(1);hold on; xlabel('V');ylabel('D')
i=0;
for alpha = amin:0.001:astall
i=i+1;
cl(i) = clalpha * alpha * pi/180;
V_takeoff(i) = sqrt(2*W_takeoff/rho/S/cl(i));
V_landing(i) = sqrt(2*W_landing/rho/S/cl(i));
cd(i) = cd0 + k * cl(i) * cl(i);
D_takeoff(i) = 0.5 * rho * V_takeoff(i) * V_takeoff(i) * S * cd(i);
D_landing(i) = 0.5 * rho * V_landing(i) * V_landing(i) * S * cd(i);
p_takeoff(i) = D_takeoff(i)*V_takeoff(i);
p_landing(i) = D_landing(i)*V_landing(i);
P_takeoff(i)=20000+500*V_takeoff(i);
T_takeoff(i)=20000/V_takeoff(i)+500;
P_landing(i)=20000+500*V_landing(i);
T_landing(i)=20000/V_landing(i)+500;
cl_cd2(i)=cl(i)/(cd(i)*cd(i));
ang(i)=alpha;
end
Takeoffc = {D_takeoff; p_takeoff; P_takeoff; T_takeoff};
Landingc = {D_landing; p_landing; P_landing; T_landing};
L = numel(V_takeoff);
xidx = find(diff(sign(D_takeoff-T_takeoff))); % Approximate Index Of Intersection
for k1 = 1:numel(xidx)
idxrng = max(xidx(k1)-1,1) : min(xidx(k1)+1,L);
V_t(k1,:) = interp1(D_takeoff(idxrng)-T_takeoff(idxrng), V_takeoff(idxrng), 0);
X_t(k1,:) = interp1(V_takeoff(idxrng), D_takeoff(idxrng), V_t(k1));
end
figure;
plot(V_takeoff,D_takeoff)
hold on
plot(V_takeoff,T_takeoff)
xl = xlim;
yl = ylim;
for k = 1:numel(xidx)
hp = plot(V_t(k), X_t(k), 'sm', 'MarkerSize',10);
plot([xl(1) V_t(k)], [1 1]*X_t(k), ':', 'Color',hp.Color)
plot([1 1]*V_t(k), [yl(1) X_t(k)], ':', 'Color',hp.Color)
end
title(['Takeoff'])
xlabel('V')
ylabel('D')
text(V_t,X_t,compose(' (%.2f, %.2f)',[V_t X_t]), 'Horiz','left', 'Vert','middle')
I suspect that you want to do more than one of these comparisons. I created two cell arrays for the takeoffs and landings to make this easier. All that is necessary is to index into them, and then make the appropriate substitutions in the loops. So comparing ‘D_takeoff’ and ‘T_takeoff’ would only involve referencing ‘Takeoffc{1}’ and ‘Takeoffc{4}’ . To make this more efficient, build a matrix of the comparisons you want to make and then just index into it, so here the first row might be [1 4] and whatever other comparisons you want to make. The code shoud adapt eassily to it, and it is also set up to text for more than one intersection in each comparison, if necessary.
EDIT — (31 Mar 2023 at 15:56)
That might go something like this —
clear all; close all
W_takeoff = 10000;
W_landing=6000;
S = 20;
AR = 5;
cd0 = 0.02;
k = 1/pi/AR;
RC=0.51;
clalpha = 2*pi;
amin=2;
astall=12;
rho=1;
ct=0.001;
% figure(1);hold on; xlabel('V');ylabel('D')
i=0;
for alpha = amin:0.001:astall
i=i+1;
cl(i) = clalpha * alpha * pi/180;
V_takeoff(i) = sqrt(2*W_takeoff/rho/S/cl(i));
V_landing(i) = sqrt(2*W_landing/rho/S/cl(i));
cd(i) = cd0 + k * cl(i) * cl(i);
D_takeoff(i) = 0.5 * rho * V_takeoff(i) * V_takeoff(i) * S * cd(i);
D_landing(i) = 0.5 * rho * V_landing(i) * V_landing(i) * S * cd(i);
p_takeoff(i) = D_takeoff(i)*V_takeoff(i);
p_landing(i) = D_landing(i)*V_landing(i);
P_takeoff(i)=20000+500*V_takeoff(i);
T_takeoff(i)=20000/V_takeoff(i)+500;
P_landing(i)=20000+500*V_landing(i);
T_landing(i)=20000/V_landing(i)+500;
cl_cd2(i)=cl(i)/(cd(i)*cd(i));
ang(i)=alpha;
end
Takeoffc = {D_takeoff; p_takeoff; P_takeoff; T_takeoff};
Landingc = {D_landing; p_landing; P_landing; T_landing};
Lbl = {'D','p','P','T'};
Pairs = [1 4; 2 3];
L = numel(V_takeoff);
for k2 = 1:size(Pairs,1)
V1 = Takeoffc{Pairs(k2,1)};
V2 = Takeoffc{Pairs(k2,2)};
xidx = find(diff(sign(V1-V2))); % Approximate Index Of Intersection
for k1 = 1:numel(xidx)
idxrng = max(xidx(k1)-1,1) : min(xidx(k1)+1,L);
V_t(k1,:) = interp1(V1(idxrng)-V2(idxrng), V_takeoff(idxrng), 0);
X_t(k1,:) = interp1(V_takeoff(idxrng), V1(idxrng), V_t(k1));
end
figure;
plot(V_takeoff,V1)
hold on
plot(V_takeoff,V2)
xl = xlim;
yl = ylim;
for k = 1:numel(xidx)
hp = plot(V_t(k), X_t(k), 'sm', 'MarkerSize',10);
plot([xl(1) V_t(k)], [1 1]*X_t(k), ':', 'Color',hp.Color)
plot([1 1]*V_t(k), [yl(1) X_t(k)], ':', 'Color',hp.Color)
end
title(['Takeoff'])
xlabel('V')
ylabel(Lbl{Pairs(k2,1)})
text(V_t,X_t,compose(' (%.2f, %.2f)',[V_t X_t]), 'Horiz','left', 'Vert','middle')
end
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