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Tuesday, November 5, 2013

Lightweight Wheels - More Power to the ground and better 1/4 mile times - More Fun

My Calculations on Lightweight Wheels - More Power to the ground and better 1/4 mile times - More Fun

I did some calculations on how the wheel weight affects the inertia/momentum on the wheels. Most you probably know about this but never used any calculations to get the effect in numbers. I will basically show you how you can improve your 1/4mile time by at least 0.5sec.

PLEASE READ BELOW. This is the calculations I did years ago, but they still very much apply.

Since I previously owned 2000 VW Golf with 15" stock rims and 17" aftermarket rims, I can present all the calculations and the difference in 1/4mile ET. As we know, Inertia depends on the weight of the wheel and how far that weight is from the center of the wheel and it also depends on the weight of the tire. We know that the weight of wheel is distributed over the rim but the most of the weight is at the edge of wheel. Therefore, here is my assumption:

Assumption: Assume that all the weight is at the edge of wheel and at the edge of tire to make the formulas simpler and since we are dealing with relative values, it will not change our results.

General formula: I = mr^2 = mass * radius * radius
Inertia = Inerita of wheel + Inertia of the tire
Inertia = m1 * (r1^2) + m2 * (r2^2)

I will first explain it on my VW Golf example and then move to Civic 2001. With my VW, I actually lost horsepower to the ground because the aftermarket rims were much heavier. Just read the example below.

Car: VW Golf 2000stock wheel: steel 15x6
Mass of stock wheel: m1 = 20.2 lb
Radius of stock wheel: r1 = 7.5"
stock tire: Goodyear 195/65/15
Mass of stock tire: m2 = 20 lb
Radius of stock tire: r2 = 12.5"

Stock Inertia = 20.2 * (7.5^2) + 20 * (12.5^2)
Stock Inertia = 1136 + 3125
Stock Inertia = 4261 ********

New wheel: Enkei CDR9 17x7
Mass of new wheel: m1 = 21.6 lb
Radius of new wheel: r1 = 8.5"
new tire: Sumitomo HTR200 225/45/17
Mass of new tire: m2 = 24 lb
Radius of new tire: r2 = 12.5"

New Inertia = 21.6 * (8.5^2) + 24 * (12.5^2)
New Inertia = 1560 + 3750
New Inertia = 5310 *******

** Conclusion #1: New Inertia is 20% bigger than the Stock Inertia
** Conclusion #2: After testing the car at local drag track, the 1/4 mile time was 0.6sec worse with the bigger and heavier rims and put aside the numbers, the car felt much faster with the lighter stock rims.
** Conclusion #3: Try to get aftermarket wheel and tires that get your total inertia smaller than with stock wheels and tires.

Let's analyze 2001 Honda Civic with stock 14" wheels and aftermarket Kosei K1 TS wheels which are much lighter. You will see that the straight-line performance will be increased noticeably.

Car: 2001 Honda Civic LXstock wheel: steel 14x5.5
Mass of stock wheel: m1 = 18.6 lb
Radius of stock wheel: r1 = 7"
stock tire: Firestone 185/70/14
Mass of stock tire: m2 = 21 lb
Radius of stock tire: r2 = 12.15"

Stock Inertia = 18.6 * (7.0^2) + 21 * (12.15^2)
Stock Inertia = 911 + 3100
Stock Inertia = 4011 ********

New wheel: Kosei K1 TS 14x6
Mass of new wheel: m1 = 9.3 lb
Radius of new wheel: r1 = 7"
new tire: Yokohama AVID H4 195/65/14
Mass of new tire: m2 = 18 lb
Radius of new tire: r2 = 12.0"

New Inertia = 9.3 * (7.0^2) + 18 * (12.0^2)
New Inertia = 455 + 2592
New Inertia = 3047 *******

** Conclusion #1: New Inertia is 24% LESS than the Stock Inertia

** Conclusion #2: 1/4 mile times should be at least 0.5sec better and the 60 foot times much improved. That's probably better than most bolt-on performance parts. Also, it is not good to have too small inertia because that will give you too much power to the ground and cause too much wheel spin, but that can all be controlled by good sticky tires.

** Conclusion #3: Since these new wheels are lighter (wheels: 9.3lb vs. 18.6lb) (tires: 18lb vs 21lb), then it means that one new wheel/tire is about 12 pounds lighter and since the car has 4 wheels, that equals about 50 pounds. We all know that 50 pounds car-weight reduction means a gain of 0.1sec. Therefore, you improve performance by decreasing the Inertia and also by decreasing the overall weight of the car.

** Conclusion #4: Many of you will say that 14" wheel on Civic don't look good and the tires are too fat. Well it all depends what you like. For example, you can even go with lightweight 15x7 Kosei K1 TS wheels and 205/55/15 tires and that will give you around 10% better inertia (about 0.3sec in 1/4mile). Or if you want to go with lightweight 17x7 Kosei K1 TS wheels and 205/45/17 tires, then you might keep the inertia the same as stock, but you might improve the handling with low profile tires.

*** FINAL CONCLUSION: If you are going straight-line performance, then it would mean that you need to get smaller and lighter rims; however, if you are going road racing, then probably a compromise of light wheels and lower profile tires (not too low) is the best bet. Also, lighter wheels also improve handling besides straight-line performance. 

Many of you should ask yourself a question if you want to go BLING BLING with heavy 19" rims, or you want go with smaller and lighter wheels, or maybe a compromise of both. 

NOTE #1: Do not take this for granted. It is my opinion backed up with some physics calculations.
NOTE #2: This mostly applies to cars under 200hp. You are not going to able to notice the difference on powerful cars unless you are racing and milliseconds make difference.

Keywords: #wheels #rims #lightweight #racing #inertia #performance
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