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.

Craig Berland

First, I have a pretty thick skin so I don't take offense till things get pretty blatent. I also tend to assume this of others, which isn't always the case. Besides, I rather enjoy a good argument. At least until it degrades into name calling.

 

Second, I'm not aware that I said that our theoretical Otto cycle engine had no momentum. If I did, then I was mistaken (and it wouldn't be the first time).

 

Third, with no friction and no momentum, the most likely place to stop would be bottom dead center. The power stroke, exhaust stroke and compression pressures all work in this direction. Precisely TDC is another potential point the system could stop, but without momentum or some other force, how was the compression stroke completed? I don't see that an instantaneous fuel burn rate is important here, so long as there are no shock waves or swirl forces to cause the piston to rock and disrupt the perfectly vertical crank and rod. Of course if we attached another 5 cylinders, then the power stroke of another piston would move the crank forward anyway.

 

Fourth, the force would not be infinite. Infinite force would require infinite pressure and that would require infinite energy... Then again, I suppose one could argue that perfect fuel would contain infinite energy, but this would make engine control somewhat difficult.

 

Fifth, I already have a head ache so I would rather not contemplate nonaligned cylinders. While I haven't come accross such an engine, I have seen a handfull of auto designs where the wrist pin was off center in the piston. My recollection is that this was done to reduce piston wear. (slant 6 ?) I never looked into it.

 

Finally, I was replying to George's comment about crank - rod geometry with respect to efficiency. I interpretted what he said as noting that the change in mechanical advantage as the rod and crank angles depart vertical (horizontal in a Lyconental) results in increased torque for a given pressure. (did I misread something?) This is certainly correct, however torque alone does not tell us much about either power or energy. One has to multiply the torque by the rotation or the rotational speed to compute these values. At the top and bottom of the stroke, the mechanaical advantage of the system is low, resulting in low torque values, but the angular dispalcement is high. At mid stroke just the opposite is true.

 

When we integrate the torque x angular displacement curve of the crankshaft, we find that it yields exactly the same energy as the integral of the pressure x piston displacement curve (ignoring friction). This makes sense because in a frictionless engine all of the  pressure force energy applied to the top of the piston is transfered through the rod to the crank shaft.

 

No offense taken and none intended,

 

Rob