# Reciprocating weight in an engine

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.

#### Attachments

• recmass.zip
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## Answers and Replies

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
Science Advisor
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
Science Advisor
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
Science Advisor
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.

#### Attachments

• Comp Piston Acc.zip
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AlephZero
Science Advisor
Homework Helper
Piston acceleration is a linear acceleration along the axis of motion as opposed to the radial acceleration seen on the crankshaft.

Sure, but the accelerations at TDC and BDC are the sum and difference of two radial acclerations (the crank and the conrod - each with a different angular velocity because of the different radii) so the accelerations are the same order of magnitude as simple harmonic motion.

I thought the OP was questioning the big numbers, rather than the details of the calcs. THe formula in the first URL doesn't mean much, taken out of context.