154 MEASUREMENT OF PRESSURES 



The piston gauge in the form described thus measures the impulse of 

 the wave up to an unknown time t. In order to make a more direct 

 interpretation of the pressure-time curve it is evidently necessary to 

 determine the time of piston motion. If this is known one could obtain 

 an approximation to the pressure-time curve by writing I{t) = Pav-t 

 where Pav is an average of the pressure over the time of action. The 

 exact meaning of such an average depends of course on the form of the 

 curve P(t) but the difficulty can be resolved by using several piston- 

 crusher units each acting over successively greater intervals. If each 

 added interval is made small enough the average pressures over the 

 added intervals represent good stepwise approximation to a continuous 

 curve. If the pressure changes comparatively little over the first such 

 interval the time of action of the piston can be computed assuming its 

 acceleration to be uniform. The time h for the first piston is then 



where Li is the length of free travel and Vi the final velocity computed 

 from the crusher deformation. The average pressure over this interval 

 is then 



/p; im p = ^^^1^1 ^ miVi"^ _ mi Eel — PiSi 



^ ^ "^' At, 2AU 1 + mi/M' 2AU 



All the quantities in this equation are known except for the final pres- 

 sure Pi which must be estimated. Its effect is not very large and can 

 be estimated by judicious guessing, or if necessary a second approxima- 

 tion correcting an initially assumed value. 



A second piston is designed to have a longer free travel Li and if 

 necessary a larger mass ???2 in order to increase its travel time h. The 

 extra travel time for this piston, again assuming an interval t^ — h short 

 enough that the acceleration can be considered uniform, is 



, . 2(7.2 - L,) 



''-''== TTTfT 



The average pressure over the interval t-i — ii is then given by 



^272 - wiFi {W2V2 - wiFi) (F2 + Vi) 



(5.11) Pa.2 = 



A{t2- h) 2(L2 - Li)A 



Again all the quantities can be calculated from known gauge constants 

 and the average pressure over the interval ^1 < ^ < ^2 determined. 



