Internal ballistics of a pneumatic potato cannon

Basic laws of thermodynamics and mechanics are used to analyse an air gun. Such devices are often employed in outdoor physics demonstrations to launch potatoes using compressed gas that is here assumed to expand reversibly and adiabatically. Reasonable agreement is found with reported muzzle speeds for such homebuilt cannons. The treatment is accessible to undergraduate students who have taken calculus-based introductory physics. Potato cannons are a popular construction project for physics demonstrations and science fairs [1]. They can be powered in three different ways: by a compressed gas (which is the type analysed in the present paper), by an explosive propellant [2] or by a sudden vacuum breaking [3, 4]. In the first, pneumatic case, the projectile can be modelled as a piston accelerating down the bore of a horizontal cylinder under the action of pressurized gas, taken to be ideal for simplicity. Three equations are used for the analysis: Newton’s second law, the ideal gas law and the first law of thermodynamics. Additional simplifying approximations are that the piston slides frictionlessly and no gas leaks around its edges (as should be appropriate for a thick, wet potato slice that is forcibly fit to the bore); atmospheric pressure is negligible compared to the gas pressure (while the piston is in the bore); the gas expansion occurs quasistatically (which will be valid provided the piston’s speed is small compared to the speed of sound) and adiabatically (i.e., without heat leakage to the surroundings) [5]. Some of these assumptions can be lifted by performing a numerical rather than an analytic analysis [6], and such extensions could become attractive classroom projects with different possible levels of sophistication. The ideal gas law for n moles of gas at pressure p, volume V and temperature T is pV = nRT (1) where R = 8.314 J mol−1 K−1 is the universal gas constant. The force on a piston of crosssectional area A is F = pA, as sketched in figure 1. Solving for p and substituting it into the left-hand side of equation (1) along with the volume of gas, V = Ax where x is the distance from the sealed end of the cylinder to the piston, leads to max = nRT, (2) 0143-0807/09/030453+05$30.00 c © 2009 IOP Publishing Ltd Printed in the UK 453 Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE JAN 2009 2. REPORT TYPE 3. DATES COVERED 00-00-2009 to 00-00-2009 4. TITLE AND SUBTITLE Internal ballistics of a pneumatic potato cannon 5a. CONTRACT NUMBER