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Old 08-23-2011, 08:45 AM   #6
grambles423
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Drives: 2008.5 BMP GTI
Join Date: Jun 2009
Location: Balls Deep
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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.

Overall, where are your gains seen most? You can consider sticking to the stock heavy wheels for some traction, however, the pros outweigh the cons.

Reference PDF
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Last edited by grambles423; 12-07-2011 at 09:47 AM.
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