Grand Prix Racing - The Science of Fast Pinewood Cars

# Does cutting the tread help?

Once again, the answer must be a definite, MAYBE! As with many of these potentially time-saving techniques, the result depends on many factors. Here are some of the factors to consider:

1. Wheel moment of inertia - it is reduced by cutting the tread and that's good!
2. Wheel weight - it is reduced by cutting the tread and that's good!
3. Wheel tread friction - it may get worse if you can't smooth the wheel down again
4. Wheel edges - may contribute to drift if left sharp
5. Wheel balance - may cause vibration or wobble
6. Wheel torquing - the wheel may get jammed up against the bottom of the axle hub

The plan of attack here is this: First, we'll run a computer simulation of a car with cut treads and one with out to illustrate the possible advantage. That will take in the discussion of factors 1 and 2 while finding the right parameters to use in the simulation. Factors 3, 4 and 5 are covered elsewhere in this manual. So after some brief comments about them, we'll conclude with a discussion of factor 6.

## What Advantage is There?

In order to stage a virtual race of a tread cut car and a normal one, we need to find the moment of inertia of a cut tread wheel. First, how much tread is to be cut off? From the models it is clear that the more that is cut off the better. But there still has to be enough to support the car! Let's use 0.1 inch of tread left after cutting.

Now, we can apply the method used to calculate the moment of inertia for an AWANA kit wheel and just change the tread cylinder width from 0.315 inches to 0.1 inches. The worksheet looks like:

## An Estimate Of The Moment Of Inertia Of A Cut AWANA Kit Wheel

 Cylinder Radius (in) Width Volume %Mass Ii/mi Ii/m outer inner (in) (in3) (in2) (in2) 1 0.118 0.049 0.276 0.01001 13.953 0.008163 0.00113898 2 0.266 0.118 0.016 0.00284 3.959 0.042340 0.0016762 3 0.309 0.266 0.236 0.01835 25.578 0.083119 0.0212602 4 0.531 0.309 0.033 0.01939 27.028 0.188721 0.0510075 5 0.591 0.531 0.1 0.02115 29.481 0.315621 0.0930482 Totals V=0.07174 %m=100 I/m=0.16813108

to get the weight of the cut wheel, we need to assume the tread plastic has the same density as the rest of the wheel. It's volume was reduced from 0.11721 in3 to 0.07174 in3. The original weight was 0.08333 oz, so it is now 0.08333(0.07174)/0.11721 = 0.05100 oz.

Weight(_0.05100_ oz)/386.088 = Total Mass (0.0001321027 ozs2/in).

I/m (0.16813108) x Total Mass (0.0001321027) = I

Total Wheel Moment of Inertia, I = 0.000022211 ozins2.

An uncut AWANA kit wheel has a moment of inertia of 0.000048637 ozins2. so this is about 46% of that original value. With four wheels on the track, a car with tread cut like this should behave like one that has two uncut wheels lifted off the track (a tricky but possible balancing act). If one of these is lifted, the car should have even more advantage - as long as the other factors listed above prove beneficial in your situation.

Using the "typical" parameters for friction discussed in the question on the worst source of friction, we can run our race! With all four wheels on the track, the result is:

The car with cut treads wins in 2.8069 seconds by 4.661 inches!

That's fast!

Cutting a wheel doesn't reduce tread friction on a smooth surfaced track. However, it can reduce it on a bumpy one.

## Wheel Edges

If the edges of the narrowed wheel are sharp the wheel may tend to follow the wood grain in the track if it is not smoothed out. A rounded edge on the wheel may improve this tendency, but probably won't eliminate it.

## Wheel Balance

A wheel with more weight on one side than another will wobble. Cutting a wheel perfectly is not easy without the right high speed rotary tools. Wobbling raises and lowers the center of mass a minimum of a hundred times in the course of a race, multiples of that if there is more than one irregularity on your wheel. Most of the energy used during the up motion is returned on the downward motion. But some is lost to additional air movement and friction.

## Wheel Torquing

Wheel torquing happens when the wheel is no longer able to keep the axle on the bottom of its bore. One end tips up and the axle touches the wheel bore on the top at one end and the bottom at the other. Torquing is generally not good. It always increases axle friction by a factor of (n+1)/(n-1) but can be worth it in some cases.

A kit wheel cocked at 27 degrees from vertical will experience about three times more axle friction (n = 2). Axle friction reduces to the "normal" amount as the slanting angle decreases (n > 30 or so, O is less than 1 degree).

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 Grand Prix Racing - The Science of Fast Pinewood Cars Copyright © 1997, 2004 by Michael Lastufka, All rights reserved worldwide.