Rob wrote: I think you are considering torque here rather than energy or power. You need to factor the rotation of the crank shaft into your integral. Then you will get the same result as the simple piston pressure/displacement annalysis.

 

I wish there was a way to express tone with the written language.  I'm intrigued by your thoughts...I'm not being argumentative.  If there was no friction....no momentum.... and the fuel burn was instantaneous...wouldn't the engine simply stop at TDC?  The force would be infinite straight down through the piston, rod and crank....??

If you want to get a head ache...contemplate moving the piston centerline to the ATDC side of the crank, thus producing a slight rod angle at TDC.