calulate the indicated mean pressure with a p-v diagramm

Hello,

I have to calculate the indicated mean pressure. I have a p-v diagramm (in the attachements). I separated the two areas by finding the intersection. But know im not sure if the polyarea() function is the correct function to calculate the two areas.

The integral i have to implement is also in the attachements

(p: pressure in the cylinder; A: piston surface; V: volume of the cylinder; s: piston travel (path) as a function of the crank angle

Thanks for help!

Answer 1

[Mathieu NOE]

hello Julian

yes you can use polyarea, I believe you could also with trapz like in my example below (it uses this Fex submission : Fast and Robust Self-Intersections - File Exchange - MATLAB Central (mathworks.com))

results (two loops area) :

area = 71.3220 125.0467 (with trapz)

area2 = 72.5056 125.3691 (with polyarea)

code :

load('data.mat') 
[x0,y0,segments]=selfintersect(x,y); % fex : https://fr.mathworks.com/matlabcentral/fileexchange/13351-fast-and-robust-self-intersections
figure(1)
plot(x,y,'b',x0,y0,'dr','markersize',15);
axis square
hold on
% compute area for each loop 
for k = 1:numel(x0)
    ind = (segments(k,1):segments(k,2));
    x_tmp = x(ind);
    y_tmp = y(ind);
    % compute area 
    area(k) = trapz(x_tmp,y_tmp);
    area2(k) = polyarea(x_tmp,y_tmp);
    plot(x_tmp,y_tmp)
end

area
area2