Recently our team has been experimenting with the Grey-T 9.5" shooter and game piece kinematics for a Rapid React cargo. From my limited physics knowledge, I was able to create a decent simulation of a single-roller + hood shooter (similar to the Grey-T 7" shooter), using the Flywheel Physics Video by Lynbrook Robotics and basic 2D projectile motion.
However the Grey-T 9.5" shooter has a second flywheel roller on the end of the hood design, to control spin and add power to the launched game piece. I was stuck when trying to implement the physics of this version to account for spin and the extra momentum of the ball mainly because the top flywheel does not have the same amount of contact time as the bottom flywheel, leading to ambiguity with the momentum transfer calculations. Do you guys have any suggestions on how to model this?
You can treat this as two impulses on the ball. Basically a shooter shooting into a second shooter. The second shooter (dual flywheel) has to deal with all the various inertia from the first (single flywheel) stage.
Slip on the main flywheel will not be meaningfully changed as it transitions into the second shooter stage.
The hood flywheel will have to contend with a surface speed of the ball on contact of effectively 0 and the moment of inertia of the ball, depending on how much slip occurs this will modify how much rotation is pulled out of the ball.
Spring back of the ball as it decompresses and leaves both shooter wheels may not be negligible and depends on ball PSI, shooter stiffness, and probably most importantly final exit velocity. If rotation speed of the ball is 0 this may be easier to model.