Piston acceleration---again!

[willeng]

Could somebody give the equation & an ( example ) for piston acceleration vs crank angle. I have made a search & found an equation in another post but i must be suffering from brain fade & just can't get my head around this.
Thanks.

 

[Brandnew]

Just look at one piston, the first piston. At TDC the first piston is at the top of it's travel (crank 0 deg). At BDC the piston is at the bottom of it travel (crank 180 deg). At TDC and BDC the piston is not moving, however brief that may be.

In between these two points the piston moves, and the piston moves quite fast.

When the piston moves away from TDC it accerlates rapidly. And when it comes to BDC it slows rapidly. Right in the middle of the "stroke" the piston goes from acceleration to deceleration, or an instant of zero acceleration. When this acceleration is zero, the speed is maximum. This occurs when the crank is at 90 degrees.

This moves the piston from top to bottom. Now these accelerations reverse from the 180-360 crank movement.

There are intense calculations out there to calculate the piston speed and acceleration at any point during the crank movement. Perhaps this is the equation(s) you where looking at.

There's also a simple equation that averages the speed of the piston, usually referred to as the "Mean Piston Speed" (MPS). This equation is simple but as the name indicates, it's just an average.

MPS = (stroke * RPM)/6

where,
MPS is in feet per minute
stroke is in inches

Say you have a car with a stroke of 3.75 inches and you want to know the MPS at 6000 RPM.

(375*6000)/2 = 3750 fpm

That's the simple equation. I'll let someone else do the "ugly" equations.

 

[aviat]

There are several calculators on the net such as the first site below that give you mean speed. The second site gives an example at different crank angles.
Brandnew,
I agree with what you say except that max velocity does not occur at 90 degrees ATDC. It occurs before 90 degrees and depends on the crank-rod ratio. The last two sites explains the reasons and gives some graphs. Max acceleration occurs at TDC.

http://www.davewin.com/tech/mean_piston_speed.shtml

http://www.rapidline.com/calc/engine/pcpiston.htm

http://www.epi-eng.com/ET-PstnMotion.htm

http://www.epi-eng.com/ET-PistnVelAccel.htm