|MadSci Network: Engineering|
Well this is an interesting question. For fun, to be a little different and to limit friction, I would recommend a three-wheel design. Your vehicle will look a little like a tricycle, with two wheels in back and one wheel in front. With three wheels intead of four, you'll have a design that is a little easier and cheaper to build. Also, you'll have a little less friction than a four-wheel vehicle.
There are two ways to store energy in your elastic band and drive the wheels of your vehicle. You can twist the band to store energy in it (which is how many elastic band powered toy airplanes work) or you can stretch the band to store energy in it. I recommend you use the stretch strategy. There are a couple of other things to consider about your elastic band:
Design your vehicle, as I said above, as a tricycle. The two REAR wheels, however, should be larger than the front wheel. Make them about 4 to 8 cm in diameter and join them firmly to an axle. If the surface you're going to race on is slick (such as a concrete floor), make sure your rear wheels have good traction. Rubber wheels would be great, if you can work it out.
The front wheel isn't so important, and it can be smaller. Join the rear wheels to the front with some sort of frame that lets the rear wheels and axle turn freely. You will want to lubricate the axles where they rub against the frame with a drop or two of oil (or even a little Vasoline). The distance from the front wheel to the rear axle should be about 12-14 cm (you'll see why in a minute). You should place the egg on the frame towards the center of the vehicle. Don't let it ride too high, since it will take away from your overall stability.
To power the vehicle, attach the elastic band to the frame at the front, just behind the front wheel. Then, run the elastic band back to the rear axle. If the distance is just right, you will have a little slack in the band. Take this slack and start wrapping the band around the axle and lap it over itself. DON'T attach it to the rear axle, just wrap it around. Once you get the band started wrapping around the rear axle, you can keep turning the rear wheels to stretch the band and load up energy.
To release the vehicle, you'll put it on the floor and let loose of the rear wheels. The band will pull on the axle and drive the car. It's important that the rear wheels are large. If they're small, they'll just zip around without driving the vehicle. If they're large, they'll resist turning enough to keep the elastic band from delivering its power all at once.
As the elastic band unwinds, it will eventually reach the end. Since you haven't attached it to the rear axle, it will just drag along when it's done. If you had attached it, it would start to wind up in the other directions and take away from your speed.
Lastly, you're correct about building the vehicle from balsa wood. With the exception of the rear wheels, you want it to be as light as possible, to reduce friction. Still, you might want to look into building it from pre-fabricated materials. It will be a LOT easier to build from "Tinker Toys" or "K'Nex" or some other pre-fab parts. Even if you eventually decide to build it from balsa wood, you can use pre-fab parts to test out your design and get it right.
Remember: good engineers try out lots of designs and they test, test, test. If your car has problems at first, you can change your design to fix them.
Hope this helps,
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