I have been thinking about this lately, and was wondering if the community had anything to say about it. So, if we know the max total torque Is 1.67 N-mper motor, and we know the smallest needed energy to throw a nbn ball into the high goal from about 14 feet away, we should be able to calculate the fastest fire rate possible assuming we have no friction. Because angular momentum is hard to calculate, we might have to be test how fast the ball leaves the launcher.

Although the rate is not going to be accurate due to friction and actual motor torque at given RPM’s, I think it could give a sense as too how much energy is lost due to friction or not being taken advantage of. I will see what I can come up with. Please post if you have comments or findings.

If there was no friction or drag, couldn’t you accelerate your flywheels to an infinitely high speed, in which case you could aim straight at the back of the net and have an infinitely fast rate of fire?

I guess what you mean is the max fire rate with a certain design and calculated using a certain method while still ignoring friction.

You are right that (assuming you had the transmission to do so) the wheels could keep accelerating infinitely without friction, but you can never have infinite fire rate even without friction (not including friction required and energy spent to fire the ball) because we do not have nor can have infinite power and the balls do not weigh nothing.
The most important thing to calculate first would probably be how much energy is spent when a ball is fired. This is going to be different depending on the design, but the numbers should not differ too much. One way to calculate this is by using momentum. This may be the most accurate, but to do this, we would first have to find the total angular velocity of the wheel and then graph how much the speed changed after each shot.
The other way is to find speed and plug in mass. I was thinking this could be done with a frame by frame camera that you knew the fps of. Video tape the robot shooting with a ruler behind the ball as it is firing and figure out how much distance it moves per frame.

Besides hardware, the fastest rate of fire is also limited by how fast the human can move to load the balls. I feel that the human speed is actually a bigger problem then hardware

I feel this way too. I’ve seen catapult style launchers that are so fast that students just about lose a hand trying to load the thing. (which is one thing I don’t like about NbN, the human element shouldn’t be a factor)

Angular momentum and linear momentum are different quantities. Both are conserved in a closed system, but they are conserved separately rather than together. Within a closed system, the amount of angular momentum stays constant AND the amount of linear momentum stays constant.

This is not a closed system because there can be significant forces acting between the robot and the playing surface. The robot can push pretty hard on a ball without moving relative to the ground, so in that case what is happening is that the change in momentum of the ball is matched by a (negligible) change in momentum of the Earth.

There is a good video trilogy explaining some of these concepts on YouTuber Veritasium’s channel. Not all of it is relevant here, but it might be interesting to someone.

You can get an upper bound that assumes 100% efficiency by using an energy approach - there is a minimum amount of energy required to get a ball into the net which you can calculate using ballistic formulas, and there is a maximum power output from a 393 motor (the maximum power output is something like 4.4 watts per motor, but cortex PTCs will be a problem if you try to do this with too many motors for too long). (number of motors * max power) / (min energy) = (theoretical maximum fire rate), but of course there are a LOT of reasons why you can’t get anywhere near this rate in practice.