# how far can two spinning wheels send a tennis ball [closed]

so lets say i have two spinning wheels above each other separated by a distance 'x' and I send a tennis ball between them- how do I find the distance the ball would go?

using Kinetic energy= Revolutions per minute

• Looks like you're thinking of using a pitching machine. Might want to research those. Oct 29, 2021 at 14:54

The trajectory of a tennis ball ejected from a machine gets a bit complicated due to the air resistance drag which is of second order. The typical speeds are in the range of 30-50m/s. Also, some machines' wheels rotate at different speeds spinning the ball that makes a difference.

Let's say your turning wheels are shooting the balls out at a speed of 30m/s. Assuming a radius of 20 cm they have a circumference of 125.6cm=1.256m. They need to rotate at $$30/1.256=23.83rps =60*23.83=1432.4rpm$$

The machine has to throw the balls at an angle of between 4 to 10 degrees depending on the wind and spin. The range can be around 80feet. Here is an article on the subject, range of the ball

Well, material limits tend to restrict edge-of-disk speeds to less than 1000 m/s. So what happens to a tennis ball if it is accelerated to Mach 2.9?

The stagnation temperature is about 540 F, so it will begin to melt, then explode. Plus the shock pressures would probably cause, um, spontaneous self disassembly.

So maybe take Mach 0.95 as a practical upper limit of launch speed that allows something resembling the thrown ball to return to earth.

The coefficient of drag can be taken to be 0.5 thanks to hundreds of experiments done on tennis balls by college kids.

The coefficient of lift will need to be iterated to find the best trajectory. But you probably want peak altitude of about 10% of the range and a launch angle of just a few degrees. Try 5 to start with.

Sadly, I couldn't find any record attempts for unrestricted tennis ball launchers. Something should be done about that. How about an X-Prize for the first 1500 m shot over level ground :)

• Someone's trying to be Randall's doppelganger! :-) Oct 29, 2021 at 14:55
• Going form memory, I think our "potato cannons" sent tennis balls about 800 yards across "the mines" when I was a kid growing up in Oakdale Pa near Pittsburg. Powered by lighter fluid in a stack of metal tennis ball cans inside a PVC pipe - about the same distance as my Ben Pearson 35# pull bow. With proper spin control, you should get double the flight time from a wheel thrower. Oct 29, 2021 at 19:32

It depends.

The main two factors (I can think of) that affect it are:

• the angle that the tennis ball is launched
• if there is any sliding between the bass and the spinning wheels (this actually translates to the actual speed at launch and the rotational speed of the ball).

• the $$C_D$$ coefficient of drag