Physics of a piston engine

1. Oct 24, 2008

cjmdjm

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.

2. Oct 26, 2008

gmax137

Well your second link doesn'twork for me so I cant see the equation the book gets. The mathematical description of the motion of a crank-rod-piston device is indeed a messy beast full of arc-functions. And it isnt symmetrical between top & bottom (like a sine function) because the motion as the big-end bearing goes over the top is different than as it comes around the bottom. Maybe the (simpler??) formula I cant see is an average over the power stroke, or something like that? The "standard" torque equations typically have terms like "BMEP" which is a kind of average cylinder pressure.

3. Oct 26, 2008

cjmdjm

Ok, I attached the formula that they come up with in that document. I am just curious how it is derived, because it is somewhat simpler than the formulas I can come up with. Lol, in the document they say, "From simple geometry." I wouldn't really call it simple though.

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