378 ME. J. E. PETAVEL ON THE PRESSURE OF EXPLOSIONS. 



factors : (1) on the surface of the explosive exposed to combustion and hence on the 

 radius of the cords at each instant during the reaction ; (2) on the radial speed at which 

 the zone of combustion is travelling towards the centre of each cord. This speed may 

 be taken as proportional to the pressure. The formula S = ap (where S is the speed 

 in centimetres per second, p the instantaneous pressure in tons per square inch, and a 

 an empirical constant equal to about 3 '5) may be of use where it is not possible to make 

 a direct experimental determination. 



The maximum pressure (P) developed by a given charge is usually well known, and 

 by aid of the above formula the curve of rise of pressure can therefore be obtained 

 The radius of the cordite for successive intervals of pressure (p = O'l P, p = 0'2P, 

 &c.) is first computed, and the time required to burn through the corresponding 

 distance at the average pressure (p = 0'5 P, p = 0'15 P, &c.) is then determined. In 

 calculating the radius, the volume of the unburnt explosive must, of course, be taken 

 into account, and this renders the work somewhat tedious. 



The formula does not take into account the fact that under experimental conditions 

 some time elapses while the flame is spreading before the normal rate of combustion is 

 set up. The zero of the calculated curve is, therefore, shifted somewhat to the right, 

 and a sharper slope given to the initial stage (a, fig. 10). 



It may with some truth be argued that the error occurring at a very low pressure 

 would not affect the results as applied to ballistics, the calculation arid experimental 

 curves being in agreement by the time the motion of the shot commences. It is 

 hoped, however, that the day is not far distant when we shall be able to obtain an 

 indicator card from a gun with the same ease as we now indicate other heat engines ; 

 approximate calculations such as the above will then cease to be of practical value. 



We have explained above the system used for firing the charge. When the key 

 is pressed, the atmosphere of oxyhydrogen, with which the enclosure has been filled, 

 explodes and the cordite is surrounded by a sheet of flame. The time at which this 

 takes place is recorded by a slight tremor of the gauge. The charge does not ignite at 

 once,* for though the explosive is surrounded by an intensely hot flame, a quite 

 appreciable time is required for its surface to rise to the temperature of ignition, t 



The ignition begins at the ends of each stick or at other parts, where, for instance 

 owing to a blister, the conductivity has been reduced. The last parts to be attacked 

 are those which were in contact with the walls of the enclosure or with some other 

 portion of the charge. These circumstances, together with a slow rate of combustion 

 which is characteristic of cordite under very low pressures, account for the gentle 

 slope of the first part of each curve. 



* In the appended tables and curves, time is counted from the instant the cordite ignites, as marked by 

 the first permanent rise of pressure. 



t A stick of cordite may under ordinary conditions be passed comparatively slowly through the flame 

 of a Bunsen burner without igniting. If, however, its surface has previously been scratched or scored, the 

 smaller particles will ignite at once and set fire to the mass. 



