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Old 05-19-2011, 10:15 AM   #1
grambles423
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The Theory of Lighter Wheels and Better Tires

Being a vehicle design engineer, theres many questions that arise during development that get debated over for so long that you really lose time discussing and not actually doing. I will warn youo. This information is dry and will be boring, but its VERY VERY inclusive and detailed. It comes ver batim from one of my courses.

I'll premise this by saying, you do what you want at your own risk. I'm no way responsible for any wrong doings you do when modifying your car. Dont come to me complaining your rims warped and its my fault. I'm just creating a learning enviorment to better help understand our cars and help facilitate technical discussion over a forum that loses sight of its principles, sometimes.

Some vocbulary that will be mentioned:
Mass Moment of Inertia
Wheel Diameter (Not Rim Diameter)
Angular Velocity and Accleration
Frictional Forces
Lateral Forces
Tire Patch Width
Skid Ratio
Slip Ratio
Peak and Slide Coefficients
Slip Angle
Vertical Loads
Cornering Stiffness
Camber Angle

This thread will cover to theory and physics behind to a great debate:

Should I go lighter weight on my wheels?

The question I would then ask to you would be, well.....how much do you truly appreciate your suspension? Do you track a lot and really stretch the limits of your vehicle? Or do you just want better looking rims? If you want better looking rims, throw all caution to the wind and by the ones that you think look the best while the rest of us out perform you on the track. Nice 19s btw, how much do they weight?

Why does lighter wheels mean better performance?

A Few Facts to consider
  1. Weight
    • Wheelset and part of suspension are “unsprung weight”, which by definition cannot respond to the spring and damping of the suspension system (this is bad).
  2. Performance
    • Maintain Ground Contact
      • A tire that is not touching the ground is not accelerating the car or controlling the car.
      • Without ground contact a car is a projectile, losing speed and out of control
    • Limiting Lateral Load Transfer
      • A car in a turn puts more vertical load on its outside tires and less on its inside tires
      • The lateral resistance of a tire depends on the vertical load on that tire, but not linearly - the more and more vertical load on a tire, the less and less lateral load is generated as a result
      • Therefore, its best to keep the vetical load as evenly distributed as possible to maximize turning ability

Traction and braking forces
Longitudinal slipping and sliding
All tractions and braking forces are associated with slipping of the tire patch over the ground. The tire rubber deforms under friction load on the ground, this deformation integrates from the leading edge of the tire patch to the trailing edge, and resolves into slip (higher velocity than the vehicle for acceleration and steady driving, lower velocity than the vehicle for braking) as the tire patch lifts off.
If the local slip exceeds the locally-available coefficient of friction (velocity dependent), then the tire patch breaks loose and slides. Tire slide is a relative velocity between tire and ground at the leading edge of the tire patch.

Slip ratio (acceleration, driving)

i = 1 - [V/(Rw*ω)]

Angular Momentum

L = Iω

where i is slip ratio, V is vehicle speed, Rw is wheel radius (free – not compressed), and ω is wheel angular velocity.

Angular Momentum (L) is a function of wheel angular velocity and Mass Moment of Inertia, which ultimately is a function of the mass of your wheel.

For this case, we'll assume a wheel is a SOLID cylinder. Its a fortified assumption and will work well in our calculations. Theres actually two different mass moments of interia for this case, but we'll only take into consideration the axis about the wheel rotation.

Mass Moment of Intertia = [Mass of the wheel * (Radius of the entire WHEEL)^2] / 2

Simple? This is where the 17 vs 18 topic comes into play. Effectively, the entire wheel diameter remains the same between the two wheels, however, the bullk of your weight is 1" further into the axle with 17" rims, as opposed to 18s. Granted, if the mass of your 18s are lighter than stock, you might be able to perform better.

If you wanted, you could almost weigh both sets of tires, and detract that from your overall formula and find the effective 17 vs 18 calculations. You'll immediately see a difference.

Now, a heavier wheel would create a greater moment of interia and inevidtably create more angular acceleration, thus creating more downward force on the tire patch, THUS creating more traction THUS creating better acceleration times. A smaller diameter wheel would cause more wheel spin, because you've effectively reduced unsprung weight allowing for more torque to be transfered to the tire patch.

But thats only in a straight line. What about during a track event?

Well, thats where the lighter weight wheel shines. Every rotation aspect of the wheel whether it be turning, sliding, spinning, +/- camber is a function of rotation mass moment of intertia. The heavier the wheel the more reluctant it wants to rotate, spin, etc. etc. This causes more load and more forces traveling through the suspension and cause you to lose handling performance. Its always better to run lighter wheels if you have the opportunity.

Tires?? Well...I have a whole entire link to look at for that!

Thats as simple as I can make it for now. I'll update later.
Heres a few PDFs I made for classes long ago.
http://tinyurl.com/67xwp7p
http://tinyurl.com/6azyd6g

Check those out and it might give you a better idea of whats going on. I just got tired of typing LOL

PLEASE ask quetsions.
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Last edited by grambles423; 08-19-2011 at 12:53 PM.
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Old 05-19-2011, 10:25 AM   #2
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math hard

(p.s. thanks!)
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Old 05-19-2011, 10:42 AM   #3
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i actually understood that. for engineering courses

so basically you're saying heavier rims keep the car down on the floor better -> less wheel spin -> better acceleration etc. compared to lighter rims? that makes sense, but only at the very beginning of a drag race. I'm sure if you give both heavy and light rims some awesome tires the, the results would be different from what you're saying. But if you take it to the extreme comparing 10 inch rims vs 18 inch rims and each vehicle has 200+ hp 200+ tq, there will be a lot more wheel spin in the 10 inch rims vs the 18 inch rims.

nice write up
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Old 05-19-2011, 10:49 AM   #4
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Quote:
Originally Posted by fatty View Post
i actually understood that. for engineering courses

so basically you're saying heavier rims keep the car down on the floor better -> less wheel spin -> better acceleration etc. compared to lighter rims? that makes sense, but only at the very beginning of a drag race. I'm sure if you give both heavy and light rims some awesome tires the, the results would be different from what you're saying. But if you take it to the extreme comparing 10 inch rims vs 18 inch rims and each vehicle has 200+ hp 200+ tq, there will be a lot more wheel spin in the 10 inch rims vs the 18 inch rims.

nice write up
In a straightline, yes. But we're talking limits here though. You cant expect to find 50lb wheels performing better than 30lb wheels, you know? Most of these aspects have cut off points where they will actually hinder performance. A good starting point is stock wheel weight and go down from there.

Its REALLY hard to deteremine these limits, but a happy medium can always be found. VW did so using the 18" Detroits. Heavy as dirt, but perform nice.

But once up to speed the lightweight rims always will outperform.
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Old 05-19-2011, 11:31 AM   #5
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Aside from acceleration too, heavier unsprung will also hinder suspension performance in that the extra inertia of the assembly in moving up and down, translate to slower response. Your suspension can't follow the terrain as well, and shock absorber can't damp out the movement as effectively. This will dull response of the car(which may be even out by the reduced tire sidewall flex with the 18s vs 17s), and a car that might be suspect to uneven road profile. It will also reduce ride quality....

In the end though I have no money for wheel and tire upgrade...lol
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Old 05-19-2011, 11:40 AM   #6
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The way I see it, wheel spinning/tire slippage is affected by a) torque applied to the wheel and b) friction between tire and road. Friction is affected by weight and material's coefficient of friction. Even when you gun it and most of the weight shifts to the rear, youre still loading the front with decent weight (20% - 600lbs ish??). Reducing that weight by 20-30lbs shouldnt make much of a difference. So what I think causes proportionally more slippage is probably the greater ability for the torque to rotate the
lighter wheel. I think lighter wheel + better tire compound/tread pattern is the best combination.
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Old 05-19-2011, 11:49 AM   #7
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Quote:
Originally Posted by 4D17HY4 View Post
The way I see it, wheel spinning/tire slippage is affected by a) torque applied to the wheel and b) friction between tire and road. Friction is affected by weight and material's coefficient of friction. Even when you gun it and most of the weight shifts to the rear, youre still loading the front with decent weight (20% - 600lbs ish??). Reducing that weight by 20-30lbs shouldnt make much of a difference. So what I think causes proportionally more slippage is probably the greater ability for the torque to rotate the
lighter wheel. I think lighter wheel + better tire compound/tread pattern is the best combination.
Agreed. Tires are actually explain in depth in one of the links provided.
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Old 05-19-2011, 12:09 PM   #8
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Nice read, thanks
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Old 06-04-2011, 03:15 AM   #9
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Don't feel bad bumping this at all. We need more posts like this on the site. VW owners get a (deservedly) bad wrap for basically being tasteful ricers (looks over performance). Finding gems like this gives me hope.
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Old 06-04-2011, 06:03 AM   #10
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I would like to see a good example, or testimonial from someone who did as 1st mod: a set of top quality forged wheels. Something like VOLK RE30 (my favorite wheels), please?

I bought a set of enkei gtc 01 with michelin PS2, I weighted the detroit+continental CS2 3.4Kg heavier. So when I empty my hatch and do rear seat removal the car is jumping up when I accelerate. Should I work with new suspensions or motor mount? (I got the dcc)
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Old 06-04-2011, 08:21 AM   #11
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Oooh fun! moar engineers! subscribed...

i'll be back...
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Old 06-04-2011, 08:49 AM   #12
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Wow I was surprised to see that this thread was bumped. Not a lot of people appreciate the REAL physics behind what a vehicle is doing.

More to come......
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Old 06-04-2011, 08:20 PM   #13
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Quote:
Originally Posted by abusive View Post
Don't feel bad bumping this at all. We need more posts like this on the site. VW owners get a (deservedly) bad wrap for basically being tasteful ricers (looks over performance). Finding gems like this gives me hope.
I didnt realize we were getting that kind of bad wrap as tasteful ricers...
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Old 06-05-2011, 08:17 AM   #14
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I'm not a tasteful ricer. I'm a hipster. Difference, yah?
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