Infinite Recharge Ballistics

I remain inspired by Ether and his apparent passion for mathematical modeling (PLEASE COME BACK!). In that light, please use this post to aggregate information related to modeling the ballistics of the Infinite Recharge POWER CELL shot.

My team has yet to measure the POWER CELL drag or lift coefficient so if anyone has made a ball drop experiment, I’d be particularly interested in that result!


i had a little fun with desmos last night

people who can do CAD and field modeling and cool stuff probably have better trajectory generators, but this is basic enough for us

as for drag and lift, I think it’s negligible for the sphere given, with smooth (undeformed) outer skin


(for this game) I agree drag and lift could be negligible, but I like including it in the math! This sheet was 100% inspired by previous posts by ETHER. Let’s continue to “Do the math” so we can “Save the World!”


This is a bad assumption for a spinning sphere, especially if you want to go for a 3/4 field shot.
The Apocyphal Wisdom is to slap some backspin on it for a flatter trajectory.
I’d love to see some real trajectory mapping and modeling, but I need to build our field first so we can run experiments.

Bit of a shaky cam, but this is some trajectory tracking we did today.
Its a bit fast on the gif, but Vx is dropping over a roughly 6m displacement. Roughly 16-19 m/s^2.
We did some lob throws as well and got much lower drag accelerations, but for those looking to shoot from a fair distance, expect to wrangle with the shooting dynamics.

Click to see rapidly looping GIF


A small part of me died to see your acceleration of gravity in imperial units. :slight_smile:

But thank you for for the cool post!

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Is there a way to document better what all the stuff is you have in your “DESMOS” sim? You know…asking for a friend? :slight_smile:

I can add quite a few notes on Desmos. They’ll be up in 6 minutes.

Also, I preferred to keep everything in feet because field dimensions are in feet-inches, not meters. As such, g is 32.15, not 9.81. :slightly_frowning_face:

@cmarley and @sgeckler, I added both of your resources to All the INFINITE RECHARGE resources. This is quite cool!

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did you use the updated link, @jaredhk? thanks for compiling everything!

@sgeckler there is an updated link btw

Not initially, but I just fixed it. If there are any future updates or additional resources you create, feel free to edit the post yourself, since it’s a wiki.

In computer science last semester, we built a ball launching simulator that took into account all factors, including the Magnus force, and used a genetic algorithm to determine optimal speed and launch angle to hit a goal. We’re currently working on adapting this solution for the game.


It’ll be interesting to see how well these 2 programs work in relation to this one

Mathematically I am assuming they should give similar results. I have not tested any of these but I intend to tomorrow.

@sgeckler’s calculator should be more accurate than mine because it takes into account drag and lift, which mine doesn’t. I’m curious to see how far off I was though. Also, magnus effect is definitely non-negligible on these balls! I’d love to see someone modeling magnus effect properly.

When I compared your calculator to @cmarley’s, the results were close. There was a little bit of variance but it was close.

I’ll likely try @sgeckler’s tomorrow and see how that compares given a similar scenario.

Also, what is ball velocity and how is it calculated? Is it essentially the surface speed of the shooter or is there more to it?

Ball velocity is just that, the velocity of the ball when it leaves the shooter. I’m essentially assuming that the ball appears at a specific location (0, y) traveling at the specified speed and angle. For a two-wheeled shooter (zero spin), the ball velocity is the surface speed of the wheels. For a single wheeled (hooded) shooter, the ball velocity is roughly half of the surface speed of the wheel (although it depends what the backing of the hood is made of).

This calculator is really cool! Any chance you could add units to the inputs? For example, “exit velocity of power cell” would be “exit velocity of power cell (m/s)”.

So looking at this, the curve represents the height of the ball and the lines represent the height of the goals. The places where the curve is in between the lines (the ones which determine the goals upper and lower bound) is from where you can shoot from and have the ball land into the target. Correct?

Which previous posts by Ether? Do you have a reading list? :slight_smile:

I made this semi-sloppy octave script that currently isn’t documented well.

Only considers a hooded shooter at the moment.

It takes into account:

  • What motors do you use, what RPM do you want to run them at, and how are they geared?
  • What is the MOI of the shooter wheels?
  • Magnus effect
  • Air resistance

And includes a handly single-variable bisection algorithm to find the right RPM or hood angle for a given shot. You can adapt to whatever…
And includes a handy rev-up-time simulator (so you can figure out how many motors you need, how adding inertia will help your shot but hurt your response time, etc…)