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One of my team members asked if they could use a rubber balloon to propel the car -- a balloon is a non-metallic elastic material, and the energy to propel the car would be stored in it. Thoughts?

You mean they want to use rocket propulsion with an air-filled balloon, rather than they want to use a stretched balloon to somehow turn the wheels, I suppose?

The balloon and the air inside it are both "non-metallic elastic materials". I can't see a reason that the balloon-rocket car wouldn't be legal.

But remember that the vehicle must remain stationary while armed, and then start moving when you push vertically down on the trigger. That's going to be a challenge to do with a rocket balloon.

Although now I think a little more about it, if you took the view that the compressed air inside the balloon was part of the vehicle, then using it as the rocket propellant would breach rule 3h.

I'm not sure whether this violates the rules, but either way, FAI Tan SS is probably going to be better than a rubber balloon.