This situation has been bugging me.
If I had two sets of flyerwheels where one had a 1:15 gear ratio and the other had a 1:25 and I ran the 1:15 geared flywheel at full power to achieve X rpm and I ran the flyer wheel with the 1:25 ratio at a lower power to achieve the SAME RPM, would there hypothetically be a difference in the initial velocity and acceleration of any balls shot out of the flyer wheels?
As long as both launchers are designed in the same way, I don’t think that there will be any significant difference.
However, there may be differences in other areas like recovery time between launches in non-hypothetical scenarios.
In theory, most likely. For the extremely short period of time that the ball is in contact with the wheels the motors are feeding energy to the ball through the wheels. With dfferent gear ratios you are most likely going to have the motors running at different powers (energy-wise) over the course of the shot. This translates into slightly diffferent amounts of energy transferred to the ball and therefore slightly different initial velocities.
However the time the ball is in contact with the wheels is very short and therefore the energy transfered to the ball from the motors is small. Generally we ignore this in our calculations because the amount of energy transfered to the ball from the wheels rotational energy is so much larger in comparison.
You could possibly quantify this amount of energy transfered to the ball from the motors if you could figure out the amount of time the ball is in contact with the wheels.
I think the only factor that might contribute significantly is the difference in angular momentum of your gear train. Different gears spinning at different velocities will have their own different contributions to the overall energy that is available to the ball. If the flywheels themselves are spinning at the same rate, then that’s probably about 95% of all the energy that will be available to the ball. You might see a little difference in the amount of kinetic energy that is stored in the gear trains but I doubt it would be worth worrying about. And the amount of energy that the motors are likely to contribute in the brief instant of ball-to-flywheel contact time is probably negligible.
So, long story short, I doubt having different gear trains would matter very much as long as you’re certain each flywheel is truly spinning at the same speed.