# Reciprocating weight in an engine

## Main Question or Discussion Point

I have been working on a small problem for a little while, and I so happen to find this forum. I was wondering if anyone can point me to the right direction with this.

I am trying to calculate very accurately how much the rod/piston assembly in an engine will weigh at a given RPM. I have been studying ARP's (Automotive Racing Products) equations from their website, but the numbers do not sound correct at all ( 228,742 kilo's @ 1000RPM? ). So I am kind of skeptical about their math or the way I am doing it.

this is the equation and graph
http://www.arp-bolts.com/Tech/T0_FastenerEng/T0_Images/FOSTERP1A-c.jpg [Broken]
http://www.arp-bolts.com/Tech/T0_FastenerEng/T0_Images/P1-CHARTS.jpg [Broken]

My thoughts about this is that the piston and rod are not changing direction instantly, but the rod slowly changes direction in about a 180 degree rotation of the crankshaft, but the change peaks at the bottom and top of the strokes. So I believe there has to be a much more detailed math to describe this.

I have an excel sheet i made that has all the work already there. So if anyone could take a look at it and steer me in the right direction with this, that would be cool.

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russ_watters
Mentor
There are 3600 seconds in a minute (acceleration is expressed in terms of m/s) and the answer is in Newtons, not kg. Via f=ma, 1kg=9.8N. So I calculate an answer of about 254N (1/3600th of 915,000) at 2000 rpm. I did calculate that from scratch and then compare/cross-check with your calculation, btw, so I'm pretty sure of the answer.

There is an additional issue of the acceleration not being constant in simple harmonic motion. I can't quite get my head around it, but I think that makes the answer off by a factor of pi/2, meaning the maximum force would be about 400 N. I'm not certain of that, though.

AlephZero
Homework Helper
If the position is A cos omega t, the acceleration is -omega^2 A cos omega t.

for your piston A = 0.0455 m.
A speed of 1000 rpm = 2 pi * 1000 / 60 radians/sec = 105 radians/sec

So the max acceleration of the piston at 1000 RPM is 500 m/sec or about 50 g.

So your piston will "weigh" 50 times more at 1000 RPM that at 0 RPM. The weight goes up as speed squared, so at 10000 RPM it "weighs" 5000 times as much as at 0 RPM.

An acceleration of 5000G in a rotating machine is quite a believable number - for example jet engine rotors go well beyond that G level.

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AlephZero
Homework Helper
There are 3600 seconds in a minute (acceleration is expressed in terms of m/s)
Oops ... that might explain why you got a rather small force.

Q_Goest
Homework Helper
Gold Member
Piston acceleration is a linear acceleration along the axis of motion as opposed to the radial acceleration seen on the crankshaft.

Attached is what I've used in the past for this. Hope that helps.

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AlephZero