Flywheel Physics: Power & Inertia Explained

[scotzur]

This may be a question better suited for the mech/aero engineering section, but I figure I'll start here.

MY question relates to a phenomenon that I just can't seem to figure out.
It has to do with a flywheel in a car.

With a lighter flywheel i would expect to see more horsepower at the wheels at ANY RPM. Although i personally have never seen this phenomenon firsthand, oftentimes on a dynometer (device for measuring horsepower and torque) a heavier flywheel will result in HIGHER power at low RPM's and eventually a lighter flywheel will yield higher results at higher RPM's.

I mean it would just stand to reason that a heavier flywheel would have more inertia than a lighter flywheel and would therefore need more energy to accelerate from (for examples sake) 1000 to 3000 RPM. The same "extra energy" would be required to accelerate the flywheel from 5000 to 7000 RPM. I don't see any reason why a heavier flywheel would show more power at lower RPM's.

The ONLY explanation I can think of is that with a heavier flywheel the individual "pulses" of force created during each combustion stroke of the motor are "smoothed out" and stored in the flywheel and released to the drive train over time. If this is the correct explanation, can anyone explain that in more mathematical terminology?
And if this is correct, is the car TRULY putting more power to the ground with a heavier flywheel, or is it just "tricking" the dynometer into seeing more power.

Here is a link to a website that discusses just this phenomenon, but does not go into any explanation:
the article is interesting, but more importantly, for a visual, you can click on the 6th picture down on the right hand side (it's a dyno chart) to enlarge it; then click on the image once it loads to zoom. This is a chart of a dyno pull done in first gear; Interestingly the dyno pull in second gear reveals that the phenomenon is almost completely gone.

http://www.europeancarweb.com/projectcars/0109ec_bmw_m3_clutch_flywheel/

 

[vanesch]

The ONLY explanation I can think of is that with a heavier flywheel the individual "pulses" of force created during each combustion stroke of the motor are "smoothed out" and stored in the flywheel and released to the drive train over time. If this is the correct explanation, can anyone explain that in more mathematical terminology?

Yes, that's the essential function of a flywheel: to act as a "reservoir" of rotational energy to which a pulsed source such as a combustion engine delivers energy in pulses, and which are smoothened out so as to speak, behind the flywheel.

Mathematically, this is simply shown by the equation which relates rotational speed (omega) to torque T:

I d omega/dt = T

The flywheel increases the moment of inertia I. If T is pulsed, then the derivative of omega (the changes in rotational speed) will be smaller if I is bigger.

 

[scotzur]

Thanks for the assistance in putting my words into math, and this makes perfect sense to me; you have the torque T, applied over a very short time, heavy flywheel doesn't change speed very much but stores the energy as rotational momentum.

Basically what you have said is that with an increased I (due to a heavier flywheel), to achieve the same (d omega/dt) you must input a larger T. or similarly, if you input the same T the (d omega/dt) will be smaller.

So, unless there is something i am missing, your equation only backs up my feeling that power should be higher across the WHOLE RPM range with a lighter flywheel.

i still don't see how a heavier flywheel will result in a higher power at the rear wheels at lower RPM. All this equation tells me is that the drive train will accelerate slower with a heavier flywheel. Basically since everything is accelerating slower, less energy/unit time (definition of power) is going to the wheels.

In the morning i am meeting with one of my professors; i will ask him about it then. Perhaps some face to face can help me out. I'll get back to you all if i get any answers.

 

[vanesch]

Thanks for the assistance in putting my words into math, and this makes perfect sense to me; you have the torque T, applied over a very short time, heavy flywheel doesn't change speed very much but stores the energy as rotational momentum.

Yes.

Basically what you have said is that with an increased I (due to a heavier flywheel), to achieve the same (d omega/dt) you must input a larger T. or similarly, if you input the same T the (d omega/dt) will be smaller.

Yes. So, for a given power (torque x rpm) you will accelerate slower with a bigger flywheel (but you can gain this back at the end: you can "freewheel" longer with no engine power before you come to a standstill). However, compared to the inertia of the total car, the flywheel is peanuts. So you won't notice any decrease in acceleration in a sportscar because of the flywheel.

So, unless there is something i am missing, your equation only backs up my feeling that power should be higher across the WHOLE RPM range with a lighter flywheel.

In principle, yes.

i still don't see how a heavier flywheel will result in a higher power at the rear wheels at lower RPM. All this equation tells me is that the drive train will accelerate slower with a heavier flywheel. Basically since everything is accelerating slower, less energy/unit time (definition of power) is going to the wheels.

It might be that the engine works more efficiently when running at a smoother rotation rate. Maybe the combustion and so on is more efficient that way. I'm no expert.

 

[scotzur]

It might be that the engine works more efficiently when running at a smoother rotation rate. Maybe the combustion and so on is more efficient that way. I'm no expert.

Thank you! This sounds like a very reasonable explanation. I will look into this.

So you won't notice any decrease in acceleration in a sportscar because of the flywheel.

I'm kind of digressing from my original subject of interest, but...I thought the same thing, and the truth is that the power difference is so small you don't really FEEL a difference. But the difference is there. In my particular case the regular flywheel weight is 35lbs, and the "lightweight" alternative is 13 lbs.

One person who personally switched flywheels said that he is experiencing better results at the track. From a dead stop to 60 feet, he can now consistently do it in 1.7 seconds where he could RARELY do that with the heavier flywheel. This may not have anything to do with the inertia you "gain" from switching to the lightweight flywheel, but instead could be due to the fact that with the heavier flywheel it is easier to spin the tires when you release the clutch because of all the extra momentum stored in the flywheel suddenly being transferred to the wheels. little or no spin = better coefficient of friction = better power transfer to the ground = better times.