The fastest serve ever recorded by a ping-pong player moved at about 70 mph (113 km/h). Professor Mark French of Purdue University's Mechanical Engineering Technology department and his graduate students, Craig Zehrung and Jim Stratton, have built an air gun for classroom demonstrations that fires a ping-pong ball at over Mach 1.2 (900 mph or 1,448 km/h). As the picture above shows, that's fast enough for the hollow celluloid balls to blow a hole through a standard paddle.

There are plans all over the internet for ping-pong guns that use stored pressure one way or another to shoot ping-pong balls at velocities from 100-300 mph (161-483 km/h). In the simplest cases, these guns consist of an open-ended tube (usually PVC plumbing pipe) into which a ping-pong ball fits loosely. The tube is sealed at each end by a membrane strong enough to withstand atmospheric pressure, and the air in the tube is removed.

To fire, the gun is mounted so that the ping-pong ball is near the rear membrane, which is then nicked (typically by a knife or sharp point). The ping-pong ball is accelerated by the inrush of air, which also blows out the front membrane. Even though some designs include a compressed air chamber, the laws of gas flow limit the velocity of the air in the tube to considerably less than the speed of sound.

How a de Laval (convergent-divergent) nozzle works (Image: Wikipedia)

Professor French and his students wanted to develop a demonstration of how a de Laval nozzle (also called a convergent-divergent nozzle) converts subsonic gas flow into supersonic flow. As you can see above, there is a pressure source at the inlet (on the left) of the nozzle. At that point, the pressure and temperature are large, but the velocity is low, as expansion of the gas is driven not by the total pressure, but by the local gradient of pressure. Another way of seeing this is that at the nozzle inlet, the gas is not expanding into a vacuum, but into a region whose pressure is nearly as large.

As the gas flows through the converging part of the nozzle, its speed increases. There is nowhere else for the gas to go, so to compress the flow through a smaller diameter requires that the velocity increases. At the throat (smallest diameter) of the nozzle, the gas velocity reaches the speed of sound. At this point, larger inlet pressures will not drive the gas any faster, a condition called choked flow. Now as the gas at the throat expands into the diverging (outlet) part of the nozzle, it expands, converting temperature and pressure into larger supersonic velocities.

Schematic diagram of the supersonic ping-pong gun (Image: Mark French)

To demonstrate the conversion of subsonic to supersonic flow, Prof. French and his team designed the gun shown above. The end of the pressure vessel is sealed with laminating tape. Both the nozzle and the barrel are evacuated so the the gas flow is unobstructed. Overall, the gun is a bit less than 12 feet (3.65 m) in length.

To fire the gun, the pressure is increased in the pressure vessel until the tape breaks. French found that two layers of tape ruptured at about 60 psi (414 kPa), and three layers at about 90 psi (620 kPa). The speed of the ball was measured using a high-speed camera viewing the ball moving against a calibrated scale. A typical velocity was a bit over 1,448 km/h (900 mph) – nominally a velocity of Mach 1.23, which is about the top speed of the Soviet-era MIG-19 fighter.

The lead photo should convince the reader that this ping-pong gun is not a toy. The energy and momentum of the ping-pong ball is roughly the same as that of a .32 caliber ACP pistol – not the best choice for defense, to be sure, but quite lethal under the right circumstances.

Prof. French gives a good explanation of the physics and design of the supersonic ping-pong gun in the video below. If you want to skip to the firing of the gun, it begins at about 5:40.

Source: arXiv.com (PDF) via MIT Technology Review