Dry ice cannon
From Wikipedia, the free encyclopedia
A dry ice cannon is a recreational launching device, a variation on the spud gun where the energy comes from a dry ice bomb. Common projectiles include baseballs, tennis balls, and other objects.
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Common polyethylene two liter soft drink bottles have been tested to have a burst pressure between 140 and 180 PSI (9.65 - 12.4 bars). The volume of the bottle usually noticeably increases before this point, however data is currently unavailable for these increases in volume. Neglecting this increase of volume, 2 liters of gas compressed to 12.4 bars would have 15.2 kilojoules of potential energy at sea level, and at 9.65 bars, 9.2 kJ. The lower figure gives enough energy to theoretically propel a standard 142g baseball beyond the speed of sound (340m/s) (a sonic baseball has 8.22 kJ of kinetic energy); and the higher has enough energy to propel a baseball to 463m/s or mach 1.36.
However, since gas expansion cannot propel objects faster than the speed of sound in the working fluid, it is not actually possible to break the sound barrier with such a device.
Energy = Force * Distance
12.4 bars is about equal to 12.25 atmospheres, therefore, the gas can expanded by 24.5 liters. This means that it may expand 2.45 meters (a distance) along a cylinder with a cross sectional area of .01m^2. A force for that corresponding distance can now be calculated as well.
.01m2 * 12.4bars = 12,400N
Because the force decreases linearly with expansion this number is divided by two before multiplied by the distance to get energy.
6,200N * 2.45m = 15,190J
The principle of significant digits dictates that this should be rounded to 15.2 kJ.
Energy = (Mass * Velocity2) / 2
Simple algebra can be applied to this part of the equation. The above formula can be rearranged to read
Velocity = √(2*Energy/mass)
which works out to 463m/s.