Determine flywheel velocity for ball exit velocity

Agreed, especially when you throw in the first approximation phrase ( I would say “general rule of thumb” but I’m a simple guy). Besides slippage there is the ball compression which changes the effective ball diameter. Lets say you compress this ball 3 inches. Now your rolling a 4 inch ball that has a skin of a 7 inch ball. So the surface speed is of a 7 inch ball but the core is spinning like a 4 inch ball spun at a 7 inch ball rate which I’m sure screws the calculation up. Hurts my brain. We have witnessed “ball windup” which can be described as similar to what a dragster tire sidewall does. The inertia of getting the ball up to rotational speed seems to play into this. This stuff all changes with the type of ball (whiffle ball vs. this “rubber bag filled with foam”. Etc. ,etc…

At the end of the day, start with ball speed = wheel surface speed/2.

1 Like

It’s going to be “driven” by the driving wheel(s) so in a perfect world, the circumference of the ball doesn’t matter.

Since we’re accelerating real actual balls, the weight of the ball and the gripiness of the roller, hood (if applicable), and ball all come into play. You can only accelerate a foam filled ball so quickly before the thing starts to come apart…


I made a spreadsheet last year that attempted to quantify this, adapting a paper I found on CD I believe from 846: Shooter_Calculations_Document.pdf (549.2 KB) . It was pretty accurate with all of the data I was able to obtain from mine and other teams. I used Tracker Video Analysis and Modeling Tool for Physics Education to calculate launch speed. It failed in a few instances:

  • Slippery hood or low compression
  • Incorrect wheel MOI input (very sensitive to this.) Best guesses came when getting the wheel MOI from CAD.

I’ve been meaning to redo the math to address these and make the analysis more rigorous, but it works as a rough guess or at least to get a sense of how different variables can affect your shot.

If anyone has side-shot videos of launching balls and knows their shooter parameters I’d love to get the additional data to refine this.

Why wouldn’t circumference matter?

Screw it, next time I build a shooter I’ll just slap a few falcons on and call it a day


Never a bad plan.


To first order, ball circumference doesn’t affect the speed of the ball on launch, as it will be the average of the speeds of the drive wheels [zero on one side for a hooded launcher]. It will affect the rotation rate - a larger ball will spin more slowly in terms of rpm than a small one for the same speed differential. Circumference will certainly matter when it comes to figuring out how far the drive wheels should be from the hood or each other.

It does, however, at least in theory, affect the trajectory via the Magnus effect (think how a spinning ping-pong ball can curve). However, at least with the parameters of the Infinite Recharge game it doesn’t seem to be a large enough effect that I’ve been able to visually discern it. NASA has a nice description and formula for computing the resulting lift here [ Ideal Lift of a Spinning Ball ]. If I’ve done the math right (which I quite possibly didn’t) that seems to be ~400 N of force (which seems like it should be more than enough to effect the trajectory). It would be interesting to then go from the generated lift to just how much that actually changes the trajectory.

I’m with @john3928 , here is what we were able to find with our testing:
We have a hood shooter powered by 3x775s. It has 2x4" polyurethane wheels and has 1.5" of compression. As stated above, we also have PTFE on the hood to make it more slick.

This graph represents the difference in the angle that our shooter was designed to release vs what it actually did. All of them are positive, which makes sense as there would be some flex in the structure of our shooter and kickback once the ball comes out, meaning that the ball exits on a tangent line that’s more vertical than designed. It is interesting how the deviation goes down as the speed increases, not sure why that is happening.

Either out data is wrong or there is little to no relation between the speed and angle error:

It should be noted that I defined error as the standard deviation, so it isn’t based on our theoretical velocity.

This was a lot of fun to mess around with, although I’m not exactly sure how profound the benefits were to our shooter performance. I did plug in these values into a trajectory optimization spreadsheet that helped us define the optimal angles for our two position hood in each zone, but not sure how much this helped us overall. In a normal season this would have taken way too long to do.


If one side of the ball is travelling at the surface speed of the wheel and the other side of the ball is travelling at 0 speed (because it is in non-slipping contact with the shooter hood) then the center of the ball will be travelling at the average of those two speeds. To be precise (as others have noted) you would need to assume that the hood is a flat wall and the shooter wheel is infinite diameter, and the ball was not being compressed to get exactly 1/2 the wheel surface speed. The more precise answer will take into account the ratio of the shooter wheel diameter and the hood diameter. But, for a first order approximation, you can start with 1/2 and it will get you reasonably close.

Now, in theory, you can solve this using the ball’s diameter, by putting in the circumference into an equation that solves for the rotational speed of the ball and then put the radius into an equation that solves for the speed of the center of the ball given a rotational speed and an non-slipping contact with a fixed wall. When you substitute that the circumference is 2piR, then R will cancel out of both sides of the equation and you will be left with Vball = 1/2 Vwheel_surf. So, if it makes you feel better to solve it using the circumference, go for it!