Modeling Ball Shooters

[Tom Line]

This is actually a two part question with some observations from the past year. Initially, when we were discussing different ways to shoot the ball we modeled the system using basic Newtonian physics. You can find a very similar spreadsheet here using some of Ether's formulas.

While the ball flight characteristics follow the flight estimates very closely, what doesn't fit out expectations is the actual shooter mecahnism and the losses when shooting the ball.

In 2012, our shooter ran from 4000 to 6000 RPM using two 550's and a AM CimSim. That gave us a ballpark to setup for this year. However when you do the math and assume a minimum of slip, here are the number got:

Shooter Wheel Diameter .1016 M
Release Height .4064 M
Release Angle 75 degrees
RPM required to approximately hit the target: 2400 RPM.

In reality, we required an input RPM of 4675 to make this shot (from the defenses). These losses seem astoundingly high. We have close to 170 degrees of wrap on the wheels and we use 2.5" of compression. We have flywheels on the system - 2 .1016" diameter 3 kg aluminum disks with the centers lathed out.

Unfortunately I never captured the exit RPM of the shooter, but I did a simple energy conservation calculation (angular momentum etc) and those numbers also suggest we shouldn't need nearly that large an input RPM. I can only assume that the major loss in the system is the compression of the ball and friction - but I wouldn't know how to begin to model that.

My next question involves choosing the gear ratio for a shooter system. Obviously you want minimum spin-up to the maximum speed you're going to use. How do you make a guesstimate of what the unloaded speed of your shooter system is going to be, though? Clearly it will be much less than the gear-reduced free speed use to friction.

We got to where we needed to be through iteration of a number of motors and transmissions. However, I'd like to be able to make first approximations computationally.

[Chris is me]

Shooter wheels very noticeably slow down when a ball contacts them - you can see this if you take high speed video of a shot in progress (highly recommend doing this in development). Do you have any way of measuring the minimum speed a shooter wheel spins at during the shooting process? Perhaps the shooter is slowing down to that 2400 RPM mark just as the ball is leaving. I'm mostly spitballing here, but maybe there's something to this.

[Basel A]

Originally Posted by Chris is me

Shooter wheels very noticeably slow down when a ball contacts them - you can see this if you take high speed video of a shot in progress (highly recommend doing this in development). Do you have any way of measuring the minimum speed a shooter wheel spins at during the shooting process? Perhaps the shooter is slowing down to that 2400 RPM mark just as the ball is leaving. I'm mostly spitballing here, but maybe there's something to this.

Right. Assuming no energy input after the ball enters the shooter (a bad assumption), the initial energy of the flywheel needs to be equal to the total energy of flywheel+ball at the speed you want the ball to go, plus losses. Was your 2400 RPM number taking this into account? If not, I'd definitely expect a shooter speed significantly higher than the needed ball speed.

[ThaddeusMaximus]

Originally Posted by Basel A

Right. Assuming no energy input after the ball enters the shooter (a bad assumption)

Not sure this is a bad assumption. The work provided by the motors over 90 degrees of rotation seems pretty minute in comparison to the energy built up by several hundred rotations (Granted the torque falls off as angular velocity increases)...

Of course throwing numbers at this would be helpful.

We're also ignoring losses from ball compression.

[BBray_T1296]

Hard to understand your exact setup, but if you only have one wheel and a backplate you must account for spin.

The part of the ball touching the wheel can only have a linear speed equal to that of the wheel at best. Assuming zero slippage, the part of the ball contacting the wheel is at the wheel's speed, and the part of the ball touching the back/compression wall is zero, and thus the actual velocity of the center of mass is half the wheel speed.

Also your energy calculations need to include spin. If it has a large spin it has non-negligible rotational kinetic energy

[RoboChair]

Originally Posted by BBray_T1296

Hard to understand your exact setup, but if you only have one wheel and a backplate you must account for spin.

The part of the ball touching the wheel can only have a linear speed equal to that of the wheel at best. Assuming zero slippage, the part of the ball contacting the wheel is at the wheel's speed, and the part of the ball touching the back/compression wall is zero, and thus the actual velocity of the center of mass is half the wheel speed.

Also your energy calculations need to include spin. If it has a large spin it has non-negligible rotational kinetic energy

^^^^^^^^^^^^^^^^^
This.

With a one wheeled shooter (wheel surface speed)=/=(maximum ball speed).
Expect something more like (maximum ball speed)=1/2(wheel surface speed) before frictional, angular, and other efficiency losses.
A two wheeled shooter will fire at MUCH closer to the actual surface speed of the wheels because it eliminates that pesky rotational loss issue.

Our shooter this year had a surface speed of around 100 fps, but our shots were probably only in the range of 30-40 fps; far over 60% losses compared to the wheel speed but only an efficiency loss of 20-40% if you compare it to half wheel speed.

[Chris is me]

Originally Posted by ThaddeusMaximus

Not sure this is a bad assumption. The work provided by the motors over 90 degrees of rotation seems pretty minute in comparison to the energy built up by several hundred rotations (Granted the torque falls off as angular velocity increases)...

Of course throwing numbers at this would be helpful.

We're also ignoring losses from ball compression.

Based on some experience I've had with single wheel shooters this year, I think this is a really poor assumption. Shooter performance really seems to change a lot with more torque in the system - a world of difference between a mini-CIM versus two mini-CIMs in our shooter's performance for example. This seems to suggest the work being done by the motors while the shooter is under load helps keep the shooter up to speed. Now, how to account for this work in the model for a generic shooter is beyond me. I feel like this is a constant or series of constants that would have to be empirically derived.

[Steven Smith]

Originally Posted by Chris is me

Based on some experience I've had with single wheel shooters this year, I think this is a really poor assumption. Shooter performance really seems to change a lot with more torque in the system - a world of difference between a mini-CIM versus two mini-CIMs in our shooter's performance for example. This seems to suggest the work being done by the motors while the shooter is under load helps keep the shooter up to speed. Now, how to account for this work in the model for a generic shooter is beyond me. I feel like this is a constant or series of constants that would have to be empirically derived.

Alternatively, it could be that the additional rotating mass of the second motor provides a greater flywheel effect, decreasing the RPM drop of the system when the ball enters it. Not saying definitively this is the explanation, just offering an alternate reason to explain your observation.

This could be completely off base though, depending on how much of the energy is tied up in the shooting wheel versus motors, should probably just break out the math when I get a chance this evening :/

[Basel A]

Loving the discussion going on here so far!

Originally Posted by Chris is me

Based on some experience I've had with single wheel shooters this year, I think this is a really poor assumption. Shooter performance really seems to change a lot with more torque in the system - a world of difference between a mini-CIM versus two mini-CIMs in our shooter's performance for example. This seems to suggest the work being done by the motors while the shooter is under load helps keep the shooter up to speed. Now, how to account for this work in the model for a generic shooter is beyond me. I feel like this is a constant or series of constants that would have to be empirically derived.

This has been my experience as well.

There are a couple approaches that can be taken here. The method mentioned by Thaddeus above (Energy = Force x Distance) has a severe flaw in that it assumes the motor will only rotate the arc of the wheel path. However, because of the speed difference between the wheel and the ball, the wheel is absolutely going to slip, possibly for many revolutions, before it has matched speeds with the ball. One way to account for that is to determine the force during slip and measure the revolutions it takes for the wheel to stop slipping on the ball.

The approach I would take, and this is only marginally more feasible, is to look at the power output of the motor and subtract the amount of power going into the unloaded mechanical system. Then you can measure the amount of time it takes for the ball to enter and leave the shooter. Energy = Power x Time. This must be done empirically as well, but a system model could be developed to determine the power going into the unloaded system as a function of speed. A back of envelope calculation we performed midseason using this method suggested that the motors provided a comparable amount of energy to the ball during shooting as did the initial kinetic energy of the system (using the numbers from our shooter).

[Chris is me]

Originally Posted by Basel A

There are a couple approaches that can be taken here. The method mentioned by Thaddeus above (Energy = Force x Distance) has a severe flaw in that it assumes the motor will only rotate the arc of the wheel path. However, because of the speed difference between the wheel and the ball, the wheel is absolutely going to slip, possibly for many revolutions, before it has matched speeds with the ball. One way to account for that is to determine the force during slip and measure the revolutions it takes for the wheel to stop slipping on the ball.

I think you might be surprised how limited slip can be with the right shooter wheel. Zero slip isn't accurate but it might actually be close enough to be a workable assumption here. I really need to post some of my shooter's high speed videos when I can.

[Basel A]

Originally Posted by Chris is me

I think you might be surprised how limited slip can be with the right shooter wheel. Zero slip isn't accurate but it might actually be close enough to be a workable assumption here. I really need to post some of my shooter's high speed videos when I can.

Interesting. That would be great to see. Would love to hear more about those wheels too!

[ThaddeusMaximus]

Originally Posted by Chris is me

I think you might be surprised how limited slip can be with the right shooter wheel. Zero slip isn't accurate but it might actually be close enough to be a workable assumption here. I really need to post some of my shooter's high speed videos when I can.

Either way you slice it, I highly doubt we're accelerating the ball and flywheel instantaneously. There's some degree of slip (which I didn't think about).