Optimum

This is a dull and geeky update to my last post about pistons. I posted some diagrams for different ways to connect a rotor to a piston, like this:


The part labelled c1 is the connection from the rotor to the piston. I knew that the length of c1 had to be longer than the radius of the rotor, otherwise the machine would completely fail. To be safe, I noted on the diagrams to make c1 twice the radius at least. This is a good value, but I wanted to figure out the optimal length for c1.


The optimal length of c1 is about 1.5333r. This makes the optimal angle about 49.29°, not 45°. This is the point where you get the most angle increase for c1's length increase. This has nothing to do with the amount of force transferred, and if it does it's a coincidence. But I do think it's more efficient the greater the angle. Ideally the angle would be 90° at all times but obviously that's impossible. So, the longer c1 is the greater the angle, but 49.29° is the optimum trade between c1's length and the angle.

Here's a more accurate sketch:


Now you can sleep at night, eh?

Here's the working, if you're interested.