"Sweet Spot"

[Greg Hermann]

>Force applied is a function of ( (area x pressure )  x lever arm )
>
>Picture a 1000 cc cylinder with a 100 cc chamber.  At top dead center this is
>a 10 to 1 ratio.
>
>Moving the piston downwards a small amount will increase the volume of the
>chamber from 100 cc to 200 cc - effectively halving the pressure.   If the
>pressure was 1000 psi at TDC - it is now 500 psi - with no other changes.

Right though, inaccurate thermodynamics. The gas loses temperature as it
expands, as well as losing pressure, so the drop in pressure is
considerably more precipitous than what you describe, Bob!

( V1 / V2 ) exp. (1.4) = ( P2 / P1)

(This equation assumes adiabatic expansion, which means no heat loss to the
piston crown or bore or chamber surfaces--which we all know just ain't so,
so the numbers from this equation are STILL giving too high a pressure!
(And the exponent given is for air, not exhaust gasses, and assumes that
their behavior is perfectly linear, which it isn't, but at least it gives
one a FAR better picture of what is going on!)

So: for double the volume, if the pressure started out at 1600 psia at TDC
(which is a much more realistic number for an NA engine than 1000 psia
is)--the pressure after a  2 : 1 volume expansion would be only 606 psia.
(Under IDEAL conditions, no heat loss to the water jackets, still lower in
the real world!)
>
>Moving the piston down another 100 cc increases the volume to 300 cc or 1/3
>what it was at TDC and a corresponding decrease in pressure.

And after a 3 :1  volume expansion from 1600 psia, the cylinder pressure
would be only  344 psia.

Now--add the kinematics of the engine into the picture--the fact that the
piston does not move very far at all down the bore during the first 15 or
20 degrees of crank rotation--and it is a bit easier to see why the "sweet
spot is so few degrees after TDC. The faster piston motion away from TDC
that happens with shorter con rods is a VERY interesting aspect of this
situation--and therefore of tuning!

Regards, Greg