Making the Animation

Finally, we are ready to create an animation of the Wankel engine showing the triangular rotor turning inside the epitrochoidal bore. These movies are the best way to understand how the rotor and the epitrochoidal bore fit together in the Wankel engine.

Plot the Epitrochoidal Bore

Recall we chose the parameters r = 1, R = 2 and h = 1/2 for our engine design. Enter these into MATLAB now as well as the equations for an epitrochoid.

clear all;
clf;
r = 1;
R = 2;
h = 1/2;
for i = 1 : 41,
    th= 2*pi*(i-1)/41;
    x(i) = (r+R)*cos(th) - h*cos((r+R)/r*th);
    y(i) = (r+R)*sin(th) - h*sin((r+R)/r*th);
end
plot(x,y, 'b');
axis equal

Plot the Triangular Rotor

We shall enter the rotor in such a way that you can easily change the number of sides from three to any other value N. The rotor doesn't have to be triangular. For example, five sides are used in the Thomas engine. If the rotor has N sides, then the angle between its vertices is 2*Pi/N. Let 's not specify N until we are ready. At time t, the k^th vertex of the polygonal rotor lies at the angle (t + k*a). Thus the vertices of the rotor are given by entering the following command.

To test that we have entered everything correctly, let N = 3 and plot the rotor at time t = 0.

clear pointsx pointsy;
r=1; R=2; N=3; t=0;
for k =1:N,
    th=t+(k-1)*2*pi/N;
    x(k) = (r+R)*cos(th) - h*cos((r+R)/r*th);
    y(k) = (r+R)*sin(th) - h*sin((r+R)/r*th);
    pointsx = [pointsx, x(k)]; pointsy = [pointsy, y(k)];
end;
fill(pointsx, pointsy,'b');
axis equal

If everything in your code is correct (and the MATLAB computer gremlins aren't against you), you should get a nice blue triangle at this stage. If not, check your code for errors and knock on the monitor 3 times for luck.

Now we are ready to put the pieces together.