With air or foam in the tire, the AM will not pancake nearly as much as with no air. In our testing, we found that being able to adjust tire pressure and Frisbee compression (e.g. moving the wheel in and out) was beneficial. For that reason, we decided not to use foam.
Our shooter is mostly encased in 3/8" aluminum and the only exposed part of the wheel is covered by Lexan. So if it decides to grenade, the blast should be contained.
