2018 Stats - Solar








Comments

Ryan said…
I have a question about the physics of pinewood derby cars. The Mark Rober pinewood derby video on YouTube says that you want your wheels to be light so that you do not waste a bunch of potential energy on angular momentum. Our pinewood derby car track, however, has a very steep start and a long flat portion. I was wondering if heavier wheels might help on a track shaped like ours, where the car accelerates quickly and then has to maintain that speed for a longer distance.


Brett said…
It was fun to crunch some numbers on this one. Sorry if I was too slow and you've already had your derby.

Having thinner wheels does appear to cause the car to slow down more quickly (deceleration between 4% and 8% greater depending on how much mass I estimated you could take off the wheels). About half of this difference is due to the smaller rotational inertia of the thinned wheels, but the other half is due to increased weight of the non-wheel portion of the car (assuming you add the weight to the car that you remove from the wheels) which increases the friction between the axles and the wheels.

But that still wasn't enough to negate the effects of the greater speed you achieve at the bottom of the ramp by having the thinner wheels. You start the flat part of the track at 1% to 2% greater speed with the thin wheels and end up with a finishing time that is 0.8% to 1.6% less than the fat wheeled vehicle.

There is one more factor that might tip the balance in favor of the fat wheels though, and that is rolling friction. This is the force between the track and the outer part of the wheel that slows the wheel through microscopic deformations in the materials leading to forces that act off-center of the wheel and result in a torque in the opposite direction of the rotation of the tire. This is not something that is easily modeled so I wouldn't trust any sort of ball-park estimate I could come up with, other than to say that the fatter tire would certainly spread the weight of the car over a larger area, thus decreasing material deformation and reducing rolling friction. Whether it's enough to make fat wheels the better strategy, I have no idea. Sorry I couldn't give you something more conclusive.

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