Simple Machine - Tennis Ball Catapult

A small remodel of our living room left me with some old 2x4 boards and some random scraps of 3/4 inch plywood. Rather than throw them out, my son and I decided to build an epic Science Fair Project. He wanted to test his hypothesis that more counterweights would increase the distance that his machine could throw a ball, but that it would not be a linear relationship between weight and distance. (Hint: He was right!)

This design can be made to any size and for him the most important measurement was that the length of the throwing arm be one (1) meter. Because he was building this as a Science Fair Project, he decided to use metric units were he could and one meter simplified many of the calculations for acceleration and force. Of course that leads to a mishmash of measurements since he was using US building materials, but since the materials are nominal sizes, it was not any more difficult.

For the main body:

6 - 2x4 studs,1.15m (or about 45 inches) long

12 - mending plates from scrap plywood (we cut ours into trapezoids to fit the corner)

1 - plywood base about 30 cm wide, 1 m long (about 1 ft x 3 ft)

2" wood screws and glue

For the throwing arm:

1 - 5/4 x 3 in straight-grain hardwood (such as oak), 2.5 m long

1 - 19mm (3/4 in) dowel rod (as an axle), 30 cm long (about 1 ft)

2 - 19mm dowel rod (to hang counterweights)

2 - mending plates from scrap plywood, about 250mm x 75mm

2 - roller bearing, 19mm inner diameter

1 - rope or paracord, 2m

1 - nail or cup hook

2" wood screws and glue

Misc:

variety of weight plates up to 7 kg (15 lb)

19mm drill bit (3/4 in Forstner or spade bit)

4 - cotter pins or lynch pins to secure weights and pendulum axle

Base:

Cut 2x4 studs to length(1.15m 0n longer edge) using 60 degree cuts to make 6 long trapezoids.

Lay 3 studs in a equilateral arrangement on a large flat table or floor and glue and screw (or brad nail) mending plates to each corner. Flip triangle over and repeat the mending plates on the other side. Repeat for other 3 studs.

On the top, inside mending plate of each triangle, bore a hole large enough to hold the outer races of the throwing arm axle bearings. With the axle and bearings in place between the tops, fasten the bottom sides of both triangles to the large 1 m x 30 cm base plate with glue and screws.

Cut the hardwood board to length, in our case 1.275 m. Pre-drill a small hole in the end of the arm to accept the nail or cup hook and install. Mark the throwing arm at 1.0 m from that end to locate the axle. Two short cut off lengths (about 150 mm) were glued parallel to the the tall sides centered on the axle location for additional strength. A 19 mm hole was bored perpendicular through the arm at the 1.0 m mark, then the axle dowel was inserted and glued in place. Another 19 mm hole was bored at 1.25 m from the end with the nail for the pendulum arm.

Note: Initial testing suggested that the axle was insufficient for the amount of weight we were applying. We added two more 100 mm lengths of the hardwood with 19 mm holes bored lengthwise to the axle, sandwiched in between two plywood layers. (shown in the pic)

With the remaining plywood or hardwood scraps and dowel, a pendulum arm is made from two 80 cm long boards with 19 mm holes bored 75 cm apart. A section of 25mm thick board can be sandwiched with glue and screws between the twin arms to space them to fit around the throwing arm. One dowel goes through the throwing arm counter-lever and cotter pins secure the pendulum arms to the dowel. The other dowel passes through the far holes of the pendulum arm and cotter pins secure weigh plates to the dowel. We added short pieces of PVC pipe to the dowel act as bushings but these may not be necessary.

Add the throwing arm and pendulum assembly to the base by slightly prying the tops of the base apart and inserting the axle into the bearings. Tie a sling knot 1 m from the end of your sling rope and fasten on end to the end of the throwing arm. Tie a small loop on the other end and pass over the nail in the end of the throwing arm.

Note: Several sling knot tutorials are available which are far better than I could do. We opted to make a sling pouch from a figure 8 loop of velcro because my son wanted to be able to easily adjust the length of the sling to study the impact on distance.

Warning! Do not stand behind or in front of the catapult. The arm will swing with sufficient force to easily break the thickest bones.

Load your projectile into the sling with the weights hanging straight down. While standing to the side, grab the pendulum arm and swing it back with one hand while holding the swing arm upright. As the pendulum arm is brought up, it will pinch the projectile to the throwing arm. At this point, you continue rotating the whole arm assembly until the weights are directly above the axle. Gently push the weights over the front of the axle and remove your body from the area. The weights will begin to fall, rotating the whole assembly. As the pendulum arm begins to separate from the throwing arm, the 4-to-1 ratio of the lever begins to significantly increase the speed of the throwing arm and the sling is released. The sling is accelerated through an arc, and if correctly adjusted, the loop of the sling is released as the projectile is fully extended and the throwing arm is 45 degrees to the horizontal.

This style of catapult is able to transfer more energy into the projectile than a traditional medieval trebuchet because the energy source is stored higher and the whole arm is accelerating for a longer time. When my son was trying higher weights (about 12 pounds), he was sending tennis balls over 256 ft, or 78 m. For reference, that is about as far as a professional can "serve" a tennis ball, trading raw speed for improved angle of launch. Higher weights tended to release the ball with a lot of spin which sent them off the mark. We didn't get to try baseballs or golf balls because we didn't have a safe place to shoot them.