The under-$5 Vacuum Bazooka

This project consists of retrofitting a vacuum cleaner to fire a projectile through the usage of air pressure (or lack thereof). The parts:

Vacuum cleaner, obtained from a garage sale. Cost: $1
12" wooden dowel, from Home Depot. $1.12
10 feet PVC pipe, from Home Depot. $1.27
Tee fitting for the pipe, also from Home Depot. $1.05

Total: $4.44 (all prices include sales tax!)

That's right, you can make your own vacuum bazooka for less than $5! The first step was to attach the tee fitting onto the vacuum. This particular model had the floor piece detachable, so I took it off, leaving me with a round pipe, to which I screwed on the tee as shown in the picture. Then I cut down the 10' pipe to a shorter length, and pushed it in one end. The hardest part was sanding down the dowel (after cutting) to make it fit in the pipe. It has to fit perfectly, too large results in friction, and too small causes air leakage. I spent two hours sanding it by hand, and in the process I managed to sand down my fingers accidentally as well.

To launch, I turn on the vacuum to high, then put a small notecard over the end of the tee, and hold the wooden projectile halfway in the end of the pipe. When the vacuum has built, I let go of the projectile and it shoots about 30-40 feet.

My measurements have determined that it takes .006 seconds for the 6.6 cm projectile to pass a measuring point, thus the velocity as it leaves is 11 meters per second. The physics behind the operation is that of the power of air pressure. The vacuum cleaner creates a low-pressure area in the pipe, which the paper over the exit end prevents from being compromised. (The paper flies off harmlessly when the projectile hits it). Since there is lower pressure in the tube than outside, the air pressure pushes with a greater force on the projectile down the tube than the air in the tube can push out. The result is extremely rapid acceleration, which we can calculate.

• I measured the vacuum suction as being equivalent to an altitude of 2200 feet, which converts to 670.6 meters. The percentage of normal atmospheric pressure is measured by the equation P = P₀ * (1 - (h/44329 m))^5.255876. As a result, I determined that the vacuum pressure was .923 that of "sea level". The difference in pressure is 7802.025 N/m^2 of pressure.
• Because the pressure was exerted along the circular bottom of the projectile, the area being acted upon is area = pi * radius^2. The final equation for the force is F = 7802.025 N/m^2 * .00229 m^2. The force of air pressure accelerating the projectile is 17.867 N.
• By Newton's Second Law of Motion, Force = mass * acceleration. Thus, a = F / m. The mass of the projectile I measured to be one-half ounce, which is .0142 kg.
• A = 17.867 N / .0142 kg, so the acceleration of the projectile is 1258.24 m/s^2. Normal gravitional acceleration on Earth is 9.8 m/s^2, thus the acceleration in this case is 128.4 times that of gravity, known as 128 g.