# Torque required to launch a tennis ball

I am trying to find out if the 12 V DC electric motors that I have are powerful enough to launch a 100 g tennis ball 30 m away. The tennis ball is put down a pipe and ends up wedged in between 2 wheels (radius = 0.05 m) driven by the two 12 V DC electric motors. The picture below should hopefully clarify the situation:

• The electric motors are spinning at ~7000 RPM (no load), the motor specs are here: http://www.banebots.com/product/M5-RS555-12.html
• A wheel (with mass of 0.05 kg and radius of 50 mm) is connected to each motor
• The tennis ball is dropped down the pipe and ends up in between the two rotating disks
• The launching angle is 20 degrees

I calculated how far the ball flies if I keep the RPM constant based on the horizontal component of the linear velocity in combination with the flying time and launching angle. However, this does not account for the mass of the tennis ball.

When the ball passes through the two wheels, the electric motors will see an opposite moment. I guess I can calculate the moment by multiplying the mass * g * radius. However, it is not clear to me how I can then accurately calculate the effect on the RPM of the motors. I can optimize the location of wheels so that the ball isn't squeezed too much, so I was hoping to ignore this in the calculation and build in some margin instead. In the end, I would like the ball to fly at least 30 m.

Does anybody have an idea on how I can calculate if the motors are strong enough to launch the ball 30 m away?

• I very strongly doubt that any reasonble propulsion system can launch a tennis ball 30 m, because the ball has low density, high drag, and atmospheric effects will limit the range. Meanwhile, what you've drawn is a standard launcher used for baseball hitting practice. Take a look at the specs for commercial items. Dec 17, 2018 at 18:57
• @Feijo What specifications of motor did you go for in the end and how did they perform? May 17, 2019 at 11:21
• Were you able to figure out an answer to your design? I would love to talk more if possible. Nov 1, 2021 at 21:48
• The inertia of the wheels will matter quite a lot, I believe. Also, I’d suggest direct drive rather than right angle gears. Nov 2, 2021 at 23:50

Well, color me amazed. The work's been done for you, sort of. Here's a paper{dead link} new link that works that analyzes exactly your machine in excruciatingly precise mathematical and engineering detail... except I didn't see estimates of the achieved range, as they were more concerned with exit speed and covering an actual tennis court.

Now, I found a hands-on review of a tennis ball launcher which successfully does send a ball up to 90 feet, close to your 30 m goal. Granted, this is a dramatically different mechanism -- basically a large spring with a launch platform to propel the ball -- but it does suggest that your design can fire a ball that far if you can achieve similar exit velocities.

• thank you for the reference. That paper is indeed very detailed, but exactly what I needed. Appreciate the help. Dec 18, 2018 at 18:50
• @Carl The link to the paper is broken Nov 2, 2021 at 2:22
• @JamesA so it goes. I added another link which is working.... today at least. Nov 2, 2021 at 15:12
• Links go bad. If you include the title and first author, you make the citation searchable in the future in case the link fails. Nov 2, 2021 at 15:20
• For those who come in a few years when the new link dies, the paper is called Mathematical Analysis For A New Tennis Ball Launcher, WÓJCICKI. Nov 2, 2021 at 22:09

I'm using another type of 12 V motor (here's the link to it on eBay) that has 1.2 Kg of torque and 3000 rpm speed. I used two 5 inch diameter plastic wheels and tested how far the two motors can launch the ball. At about 45 degrees of angle, it can shoot the ball ~22-23 meters. I hope this info helps!

• Can the plastic wheels you used be found on amazon? May 23, 2022 at 17:18