# The Physics Behind the Flywheel Launcher

So I know this might be a lot to ask, but could anyone give me a brief overview of the physics behind the Flywheel launcher so that I know what exactly to research? Basically I’m trying to theoretically calculate the exact amount of speed, tourqe, momentum, etc. needed to accurately launch the fuel, and also know how long it will take for the flywheel to spin up again. Thanks.

Oh boy. There’s not just a simple answer… unless you can ensure the ball rolls, and does not slip, on the shooter hood, and the flywheel doesn’t slow down.

Then, that very non-real, physics classroom situation is pretty easy.

Wheel tangential speed = (RPM/60)2Pi*r_w
(RPM/60 to get rev/second, 2Pi to get in radians, r_w = radius of wheel)

Ball will rotate to match that tangential velocity. And since it is rolling, the center of mass of the ball will have 1/2 the tangential velocity.

Example: a 3-7/8" wheel rotating at 3600RPM will have a tangential speed of 37m/s. So the ball will have a forward speed of 18.5m/s… which we all know won’t actually happen.

Now, if you connect an RPM counter to your shooter, you can detect just how much it actually slows down during contact with the ball, and get a better look at ball speed. AND you can measure how long it takes to spin back up to full speed to avoid overloading the shooter.

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Great question!

I don’t have time to do a fuller run-down, but hopefully these few principles can help you get started:

1. If your shooter has single flywheel and a fixed outer gate, usually plan on shooting balls with your shooter having a surface velocity of 2x the desired linear velocity of the ball. Since the ball will (hopefully?) be rolling along the fixed outer plate with no slip against your shooter wheel by the time it exits, the shooter wheel will be contributing to the ball’s spin and linear velocity equally. In reality, I wouldn’t be surprised if its not pure rolling motion by the time it exits, but it’s hard to say what it will be…

This is a moot point if you’re using a pair of flywheels on opposite sides of the ball, as the ball won’t be rolling against a fixed outer plate.

1. For the spin-up time, I’d recommend calculating the energy that your flywheel has at your desired shooting velocity. The calculations aren’t hard… Wikipedia or an engineering resource would be helpful. Then you can look at the power output of your motor(s). Plan on half of the max power output, or less. Since power is energy per unit time, once you have the energy required and the power applied, the time is just the energy divided by power.

2. Try to gear your flywheel so that your motors are operating at half their free speed (or a little less?) when your flywheel is at its target speed (see #1 for what your target speed should be). This will allow your shooter to operate with the motor at its max power output so that you can recharge quickly if shooting many balls. This is good practice for any application where you want your system to operate at max power. See this post and thread for more details: https://www.chiefdelphi.com/forums/showpost.php?p=1630066&postcount=14.

I suspect you will make faster progress figuring this out experimentally.

However I have my fingers crossed this question interests Ether enough to get one of his detailed responses.

I wouldn’t be surprised if there’s some good threads from previous years… using the search tool should turn those up.

You should look into kinematics.

Most teams do not truly use a flywheel as intended.
A fw “stores” energy in angular momentum and is then transferred.

If you watch a fw metal stamp machine, you really see the effect.
The fw is brought up to speed.
When the stamp is engaged, the fw slows way down, because the energy is transferred to the press. More energy is then used to speed up the fw again. The reason it is done this way a lot is because you can use a small motor over a longer period on the fw then quickly transfer the stored energy to the press.

Most of the time the field pieces are so small (Fuel) that simply a wheel and motor is more than sufficient to “continually” throw.

Anyhow what you’ll want to look at are:

1. Projectile motion equations (terribly messy examples on the web. Use the attachment)
2. Treat initial velocity of fuel equal to the tangential velocity of the wheel
3. Rotations/second * circumference of the wheel

This will not get you perfectly perfect numbers, but close enough that you should be very happy with the results.

Good luck

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Look at conservation of momentum and conservation of angular momentum.

The amount of time to get back to speed depends what motor you’re using, how fast you’re firing your projectile, the inertia of your system, as well as where you’re operating at in the motor curve.

Lots and lots of variables. With wheeled shooters it’s usually best to do lots of prototyping.