For some of us nerdier H-T'ers, we like to understand the science behind making a car faster. Sometimes we talk about things like Moment of Inertia, Rotational Momentum, Centripetal Acceleration, Thermal Expansion, Drag, or other high-falutin scientific concepts, and not everyone is familiar with all of these concepts. I'd like for this thread to be a collection of some explanations about the above concepts and more.

MOMENT OF INERTIA

In a rotational system of motion, we can't directly use translational (aka straight line) quantities when talking about the motion. So in a straight line, where F=ma (Force = mass x acceleration), in rotational mechanics we have T=Ia (where T= torque, I=moment of inertia, and a=radial acceleration). If we consider the Moment of Inertia (or I) to be directly comparable to mass, we can then use I in a number of other equations to find out things like kinetic energy, momentum, etc.

Where this fits in with cars (specifically wheels and tires) is when discussing rim sizes and their effect on performance. Exactly calculating I for any object is a fairly complex affair (complete with integrals, density calculations, and other things that may be beyond our scope for this discussion) so for the sake of keeping it simpler, we will assume that I for a car wheel is calculated like this:

I=m x r^2, where m=mass, r=radius.

This is making the assumption that most of the wheels weight lies in the rim of the wheel (aka outermost edge from the hub) and that the wheel more or less resembles a hollow ring.

with all of that out of the way, let's plug in some #'s:

1) 16" OE 5th Gen wheel, mass = 19lbs.
I= 19lbs x 8"^2= 1216 lb-in^2

2) 17" Rota Subzero wheel, mass = 16.5 lbs.
I= 16.5lbs x 8.5"^2= 1192.1 lb-in^2

despite weighing 3.5lbs less (or 18% less) than the stock wheel, the Rota's moment of inertia is only ~2% lower than the OE wheel. Here's a more extreme example:

1) 15" Team Dynamics Pro Race I, mass = 13.2 lbs
I=13.2 x 7.5^2=742.5

2) 17"x7.5" SSR comps, mass = 13.0 lbs
I=13.0 x 8.5^2=939.25

so as we can see, even if the wheels are the same weight, diameter matters. in fact diameter (or radius) matters exponentially, since it is squared in the I=mr^2 equation!

now that we have our moment of inertia, we can use this figure to calculate things like rotational momentum or Torque. Why would we want to? we don't necessarily want to. Describing the motion of a car in mathematical and mechanical terms is a big headache, since there are tons of things to consider (heat transfer, a bunch of different kinds of friction, weight distribution, translational and rotational motion, kinetic and potential energy, etc.) But suffice it to say that even if it is just academic, there is a difference between 15" wheels and 18" wheels. You'd also be hardpressed to find a way to measure this difference with the millions of different variables that make it close to impossible. but in some of the sports we participate in, every little thing counts. Choose wheels and tires wisely!

 

<TABLE WIDTH="90%" CELLSPACING=0 CELLPADDING=0 ALIGN=CENTER><TR><TD>Quote &raquo;</TD></TR><TR><TD CLASS="quote">For some of us nerdier H-T'ers, we like to understand the science behind making a car faster.</TD></TR></TABLE>
As a nerdy guy, you should understand that "hardpressed" is not a word. You mean "hard pressed."


Dan

 

why doesn't the tire size/weight play any role in this? Rims with tires are around 30 something pounds correct (OEM)? Add that weight plus the actually radius of the whole wheel. Wouldn't it be a ton different? Please explain why the tire isn't included in the diameter or the weight

 

That's a good point, especially because tire width changes. But I think with regards to tire diameter, the assumption is that you would keep that as close to stock as possible, for obvious reasons.

Dan

 

usually tires weigh between 18 and 25lbs. Tire weight does have a large factor in moment of inertia...and it actually has a larger roll since its located furthest from the center of the rotating mass.


toyo usually has the lightest tires on the market...and bridgestone s03's, azenis sport tires are on the opposite spectrum being some of the heaviest tires on the market.


generally a small 15" wheel is the best for racing...since the tire choices in 15's is the best with R compound tires....and it has the lowest moment of inertia for acceleration/deccleration. overall tire diameter is usually kept the same.


I run 15" 8lb racing hart CP035 rims and 225/50/15 yoko A032R tires.

 

your numbers are wrong. The equations call for mass. you used weight. The proper units for moment of inertia's are slug-in or slug-ft etc.

 

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meh i hate using standard units, and didn't feel like converting to MKS, but i hate standard units because who knows what all of those arbitrary names and quantities are? if god wanted us to use the metric system he'd have given us 10 fingers...which is ironic b/c i still think of everything in feet. i'm just used to doing physics in MKS...

tires are excluded in this instance for the sake of simplicity and lack of definite tire weight listings. But when tires are added to the equation, rim size differences are exacerbated even more since the tire weight starts further away from the pivot, effectively lengthening the radius.

low profile tires weigh as much or more than regular series tires, but because the weight is concentrated further out on the rim, there's another exponential difference with every inch you plus size.

but tires are much more complicated than just weight/moment of inertia--compound, sidewall construction, tread all matter. and there's a tradeoff between some of the factors. also, throw in the fact that we can't custom build our rubber, so we're left choosing the best of what's offered.

(feel like i'm preaching to the choir)

 

The weight is always on the outside, large profile or not. They all almost have the same amount of tread. I am still missing your point bad-monkey..

There is too much **** involved to figure out which tire rim combo is most efficent for acceleration/turning. It's easier to use just the rim, but tires play a huge role.