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# Formula for peak piston acceleration at top/bottom of stroke?

## Formula for peak piston acceleration at top/bottom of stroke?

(OP)
I found the formula for mean piston speed on this forum, and that was useful.  But I want to be able to figure out how much more stress I'm putting on a piston (due to rapid change in acceleration) if I shorten the rods.

I remember a formula from Physics class:
Final velocity =(Initial velocity)+((acceleration)x(time)^2)

Should I be using some from of this equation? If so, how do I find the max velocity of the piston (is it always in the middle of the stroke?)

Lots of questions...trying to learn.

Thanks,
MazdaJim
Replies continue below

### RE: Formula for peak piston acceleration at top/bottom of stroke?

Jim,

The instantaneous speed of the piston at a given crank angle (q)is as follows:  Sp=pi/2*sin(q)[1+cos(q)/((R^2-sin^2(q))^.5)*ave. piston speed.  (R is the ratio of con. rod length to crank radius)  If you know the speed of the engine, you can calculate the time required to slow the piston from max velocity to zero (at TDC or BDC), which will be 1/2 stroke.  Your ave acceleration should be (Sp(max)-Sp(TDC))/T(1/2 stroke) or you can take the derivative of the speed eqn w.r.t (q) and calculate instantaneous accleration.

You might want to pick up a copy of Internal Combustion Engine Fundamentals by John Heywood, it has alot of useful information regarding basic engine design.

### RE: Formula for peak piston acceleration at top/bottom of stroke?

Jim..do you have the "BobWeights" 's card data from your balance-job ???
and what rpm ranges are you looking for ?
Bore in inches
Stroke in inches
Rod C-C length
Pin offset ..

Larry Meaux  (meauxrace2@aol.com)
MaxRace Software
ET_Analyst for DragRacers

### RE: Formula for peak piston acceleration at top/bottom of stroke?

I thought I'd mention that the aforementioned "speed equation" is an approximation only, but that it's usually within +-0.5% of what you'd get from a closed-form mathematical solution.  (The closed-form solution for acceleration is a bit long to type in here, but if you'd like, I can email you a mathcad sheet with the eqns in it).

### RE: Formula for peak piston acceleration at top/bottom of stroke?

IvyMike ..could you Email me those equations also ???

i'm sort of an "equation collector " and "software collector"

if anyone here programs in some of the older versions
of BASIC , QBasic 1.0-1.1 , QuickBASIC 1.0 to 7.1,
or VBDOS 1.0 STD or Pro versions, some of Borland's
Turbo Pascal versions TPWIN , etc. and are missing some files or need something in particular , email me and i'll
send it to you !

Also have rare Visual Basic 1.0 for Windows professional version , VB2.0, 3.0, 4.0-16 and 32 bit, vb5.0, vb6.0 pro versions files

Larry Meaux  (meauxrace2@aol.com)
MaxRace Software
ET_Analyst for DragRacers

### RE: Formula for peak piston acceleration at top/bottom of stroke?

sure thing.  Do you like Mathcad, or would you prefer .pdf?

### RE: Formula for peak piston acceleration at top/bottom of stroke?

could you send it as a .PDF ??
Thanks, Larry

Larry Meaux  (meauxrace2@aol.com)
MaxRace Software
ET_Analyst for DragRacers

### RE: Formula for peak piston acceleration at top/bottom of stroke?

Will do, first thing in the am.

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