Calculate RPM for Launching Ball by Flywheel

[SMKJ]

TL;DR Summary

I need help calculating the RPM needed to launch a cricket ball from a ball launcher driven by a flywheel.

Assume the top image to be the simple version of the wheel configuration and the lower one to be the proposed way of wheel arrangement. In the newer version i want to use a heavy metal plate of approx 200gms and a wheel of 50gm instead of a heavy 200gm wheels due to sourcing issues.

This is what the metal plate looks like. The metal plate is about 100mm in diameter and the wheel is 114mm in diameter. My calculations are as follows:
wt_metal = 200gm = 0.2kg
wt_wheel = 50gm = 0.05kg
desired exit velocity of ball = v = 70kmph = approx 20m/s
wt_ball = 70gm = 0.07kg
Assume that the wheel and the metal plate is just a disk so as to ease calculations:
Moment of Inertia of wheel = 1/2 m_wheel r^2
Moment of inertia of metal plate = 1/2 m_plate r^2
Total moment of inertia = 3.31E-4 kgm^2 = I
Applying Energy conservation:
1/2 m_ball v_ball^2 = 1/2 I w^2
w^2/V_ball^2 = m_ball/I = 211.3
w/v_ball = 14.53
v_ball being 20 m/s
w = 290 rad/s
converting this to RPM = approx 3000 RPM
Driving this setup with 5010, 750Kv motors at 16V i expect a driving RPM range of 0 - 12000
Can someone please validate/correct my theories!!!

Solidworks files for the motor to wheel adapter and the 2 designs of the metal plate are attached:
https://drive.google.com/drive/folders/1XR9uy64MSJkxj9szRVHWCp2k7mFUlYS2?usp=sharing

 

[scottdave]

I haven't checked everything, but it looks like you are saying ALL of the wheels energy converts to ball kinetic energy? Is the motor on or off during launch? What is the wheel speed after the ball is launched?

 

[SMKJ]

I haven't checked everything, but it looks like you are saying ALL of the wheels energy converts to ball kinetic energy? Is the motor on or off during launch? What is the wheel speed after the ball is launched?

I have designed the control electronics to detect the moment of the energy transfer and immediately cut off power(the motor stops immediately) and after the ball is launched they spin up again.
Or I can also do the motors spinning at a constant RPM throughout.
I'm asking for advice about what should I do to achieve the best results.
(I'm an electrical Engineer and thus have very little knowledge about the mechanical aspects; thanks for your help)

 

[Juanda]

Just to make sure I understood correctly. Are you trying to build something like this?

 

[Juanda]

From @berkeman 's like I understand my assumption was correct.

@SMKJ you have mentioned conservation of energy. Although it's true energy will always be conserved (in classical physics) there need to be the right conditions for the transfer of energy to happen as you intend.

First of all, you system will be governed by friction. It is through friction that the kinetic energy will travel from the wheel to the ball. Make sure there is enough friction so you can make some simple assumptions such as the rim velocity of the wheel being the same as the rim velocity of the ball. You may achieve that by increasing the pressure or the friction coefficient. Also, if you prolong the contact between the ball and the wheel you will give the ball more time to accelerate. That'd be achieved either by not trying to accelerate the ball too much or by having a very big wheel so it's in contact for a longer time.

Secondly, having a stationary wall might give you some trouble because the ball will come out with a spin and because the output velocity will be decreased. Here is a simplification of a system like that:

If you have two wheels you won't have to deal with those problems. Your velocity profile will be constant instead of a triangle so the center of mass will move at the same speed as the rim speed of the wheels. Also, the ball will come out without spinning. You don't necessarily need 2 motors. You can simply link them mechanically with gears.

I would keep the motor running at a constant RPM. As you supply power to the motor, the wheels will stabilize at a certain speed. You then feed the ball and the sudden load might decrease the wheel' speed a little but the effect would be minimized by having bigger wheels with greater inertia.

Here is a related and recommended watch for your problem. In that video, he's accelerating Frisbies but the overall physics are very similar.


Good luck with your project.

 

[berkeman]

From @berkeman 's like I understand my assumption was correct.

I was confused from the start of this thread when I seemed to see the OP asking about a single-wheel pitching machine, which I'd never seen before. I'm pretty sure all the pitching machines I've seen use 2 wheels, so when I saw your video, I went "Oh, I guess they do exist after all..."

 

[Juanda]

Beisball isn't too common in Spain so I don't really know what's common. I wrote Beisball throwing machine on YouTube or something along those lines and that's one of the shortest videos that showed up at the top.
Maybe they did it like that to save on cost and complexity although it certainly carries some cons as mentioned in post #5.

 

[SMKJ]

From @berkeman 's like I understand my assumption was correct.

@SMKJ you have mentioned conservation of energy. Although it's true energy will always be conserved (in classical physics) there need to be the right conditions for the transfer of energy to happen as you intend.

First of all, you system will be governed by friction. It is through friction that the kinetic energy will travel from the wheel to the ball. Make sure there is enough friction so you can make some simple assumptions such as the rim velocity of the wheel being the same as the rim velocity of the ball. You may achieve that by increasing the pressure or the friction coefficient. Also, if you prolong the contact between the ball and the wheel you will give the ball more time to accelerate. That'd be achieved either by not trying to accelerate the ball too much or by having a very big wheel so it's in contact for a longer time.

Secondly, having a stationary wall might give you some trouble because the ball will come out with a spin and because the output velocity will be decreased. Here is a simplification of a system like that:
View attachment 345751

If you have two wheels you won't have to deal with those problems. Your velocity profile will be constant instead of a triangle so the center of mass will move at the same speed as the rim speed of the wheels. Also, the ball will come out without spinning. You don't necessarily need 2 motors. You can simply link them mechanically with gears.

I would keep the motor running at a constant RPM. As you supply power to the motor, the wheels will stabilize at a certain speed. You then feed the ball and the sudden load might decrease the wheel' speed a little but the effect would be minimized by having bigger wheels with greater inertia.

Here is a related and recommended watch for your problem. In that video, he's accelerating Frisbies but the overall physics are very similar.


Good luck with your project.

Hi, thank you so much for your help. I'm indeed working with 2 wheels but calculated with 1 wheel to keep things simple as i figured that if calculations show that it works with 1 wheel then it sure shall work with 2.
Well, my inspiration of the metal plate came directly from this stuffmadehere video.
I shall get to extensive experimentation and get back to you all in a few days to report my findings.

 

[SMKJ]

Just to make sure I understood correctly. Are you trying to build something like this?

Yes exactly, but the with a lighter cricket ball of about 70-100gms instead of a 150gm baseball.

 

[sophiecentaur]

it looks like you are saying ALL of the wheels energy converts to ball kinetic energy?

Machines often have flywheels to give high instant power from a lower power. You do not want the speed to drop as the load of the ball is applied so you have high angular momentum somewhere to achieve this.

There is an extra problem of spin that's needed for a convincing launch of the ball. How is that achieved in commercial ball launchers?

 

[Tom.G]

A side note:

As a kid, we would occassionally play 'sand lot' baseball. One day I was pitching to a very good hitter.

Normally when pitching I would release the ball by releasing my thumb pressure. This would impart a little spin to the ball as it left my hand/fingers. One day I tried releasing both thumb and fingers, thereby putting no spin on the ball.

The good hitter suddenly wasn't good any more, and shouted
"What are you doing? I can't hit anything!"

So pay attention to spin, it is important.

Cheers,
Tom

 

[SMKJ]

Machines often have flywheels to give high instant power from a lower power. You do not want the speed to drop as the load of the ball is applied so you have high angular momentum somewhere to achieve this.

There is an extra problem of spin that's needed for a convincing launch of the ball. How is that achieved in commercial ball launchers?

My concept of spin is using 2 wheels with the ball sandwiched in between and when the 2 wheels have different speeds the ball shall come out having some spin to it.
This 2 wheel solution is a good approximation of a 2D spin model. But if you want to provide spin in 3D like a top spin/bottom spin the you shall need 3 wheels griping the ball in a triangular form.
Also instead of doing all the complex math of the ball coming out and its spin and stuff I plan to shoot a hell lot of balls with varying speed and collect its data and simply train a machine learning model and make that do all the complex physics computations.

 

[Juanda]

My concept of spin is using 2 wheels with the ball sandwiched in between and when the 2 wheels have different speeds the ball shall come out having some spin to it.
This 2 wheel solution is a good approximation of a 2D spin model. But if you want to provide spin in 3D like a top spin/bottom spin the you shall need 3 wheels griping the ball in a triangular form.
Also instead of doing all the complex math of the ball coming out and its spin and stuff I plan to shoot a hell lot of balls with varying speed and collect its data and simply train a machine learning model and make that do all the complex physics computations.

How is this going? It sounded interesting.