I am working on programming a simulation/model of a piston engine (steam, gas, etc). I have run into some trouble with the geometry. I need to calculate the torque T on the crankshaft as a function of the force F on the piston, the crankshaft angle theta, the connecting rod length L, and the crank length R (which is equal to half the stroke length). I should have no trouble getting the force from the pressure difference across the piston, butting getting the torque from that is more difficult. Heres an image that should clarify: http://web.mit.edu/~j_martin/www/pistonphysics.bmp The thing is, I actually already found the answer online on page 4 (1118) of this document: http://www.iop.org/EJ/article/0143-...quest-id=9d55429d-8fc3-428a-959e-33173d288def But I am really curious how this formula is derived. I can't seem to prove that formula myself. I can get a formula for it, but it is messy and involves lots of arcsin and arctan etc. Any help or insight would be greatly appreciated, thanks.