Internal ballistics

My object is to explain and illustrate a method which I have devised for obtaining the pressure-volume relation of the gases in the bore of a gun, from the instant of ignition of the charge to the instant when the shot leaves the gun. By the aid of the expressions given below, the pressure-volume curve, or the indicator diagram, of the charge can be plotted when the nature and weight of charge is given. The peculiarity of this problem, in comparison with similar problems of all kinds of internal combustion engines other than the gun, is that energy is produced in the gun by the burning of solid fuel within the gun itself during a considerable fraction of the expansion stroke. In other internal combustion engines, energy is added to the charge by combustion of the charge almost at constant volume, and no account need be taken of the rate of combustion of the fuel. In the gun problem, the rate at which the charge is burnt, that is the rate at which energy is produced, is fundamental to any investigation of the subject. There is the additional complexity that a discontinuity exists in the expansion of the gases at the point where the charge is just burnt. Up to this point expansion proceeds with the continuous addition of energy from the burning charge. After this point expansion proceeds nearly adiabatically. The influence of the resistance of the driving band on the subsequent expansion of the gases, and on the maximum pressure produced by the charge, is another vital element in the problem.