Infinite Recharge Ballistics

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.

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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?

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…)

My bad, it shall be updated again. I just assumed imperial units because the game manual, but it’s true most trajectories are international units.

As such, feet and seconds for all numbers.

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Yes, but account for the radius of the ball. There is an orange ball, and the play button at the bottom should move it.

How did you calculate the lift coefficient?

This is simply parabolic trajectory. I did not account for drag or lift. The ball does not rotate through the air. This is meant to provide a rough distance.

No offense to your calculator, but I was referring to sgecklers cause it has a tab that says lift coefficient.

The drag and lift coefficients are both determined by experimental methods. Team 4926 has not done either experiment yet this year. Maybe someone else can do it and post results here.

To determine drag, you would do a ball drop experiment from a high structure; we typically would use a multi-story parking garage. Usually in a stairwell to protect from wind disturbance, we tape a make on a wall 6 ft off the floor. Then someone goes to the top and drops the balls, without spin, while someone else captures the landing with slow mode video from a phone. Using the frame rate and distance you estimate the “Terminal Velocity” in ft/s. That is what goes in the sheet. Again, Team 4926 has not yet done this for the Infinite Recharge Power Cell.

After you have the drag coefficient estimated, you use the sheet to help you estimate the lift coefficient. We do this by shooting vertically. Using a single wheeled shooter puts a lot of back spin on the ball, which means the ball will actually not come directly down, but land ‘behind’ the shooter. We capture the exit velocity, the peak height, and how far behind the shooter the ball lands. Using those three pieces of information with the previously determined drag coefficient, you can use trial and error to in the sheet to get a trajectory that matches what you observed. It isn’t perfect, but it is close enough, usually.

If you do any of this please post your results here. It is a look of fun to see how closely your calculations can match your ´reality´!!!

P.S. We measure exit velocity using a white board and a cell phone camera. We draw small to large concentric circles 1” apart, from 2” diameter to 24” diameter on a big white board. We put this big white board on one side of the shooter and capture slow mo videos from the other. How many frames does it take to go, say 18”? There is your estimated/measured exit velocity! We have done this for our Infinite Recharge Power Cell shooter prototype. Here is an example. This particular example is 40 ft/s.