597 



In solving the equation of motion the parameters p and n of the pressure-time equation 



as given by Wood's formulae were u';ed viz. 



(A.1) 



= 12.0P°. ^l'?l Ibs./oq.ir 



6300 

 75777 



W in 



in ft. 



(6) 



giving 



wO.38 





(7) 



The results of solving the equation of motion for the maximum values of i are summarised 

 In Table 2 from which it will be seen that the calculated values are from 201 to ttOJ in excess of 

 the observed experimental values. 



( i i i ) Effect of dynamic loading . 



Undoubtedly, at least part of this discrepancy between calculated and observed volumes of 

 dishing is due to the assumption that the energy absorbed in deforming the diaphragm is the sajne 

 as that measured statically under uniform lateral pressure. To take account of dynamic loading 

 it is simplest to derive a hypothetical dynamic pressure-volume calibration curve from the static 

 calibration curve by increasing the pressure ordinates by a fixed percentage. In Table 3 are 

 shown the percentage increases required to bring the ciVculated values of volume of dishing to 

 within about 5t of the observed values. From this table it is seen that the percentage Increases 

 required vary from U0» to 60'?. 



That such large percentage increases really obtain in practice seems unlikely so that we 

 are next led to suspect that the discrepancy between theoretical and experimental volumes of 

 dishing may be at least partly accot'nted for by errors in the values assigned to the parameters 

 of the prcssur._^time equation by Wood's formulae. 



(iv) 



Effe ct of repl dicing Wood's formulae by the corresponding American formulae . 



To check whether the discrepancy between calculated and observed volumes of dishing in 

 Table 2 is due in part tc errors in Wood's formulae for the parameters of the pressure-time 

 equation the calculations were repeated replacing Wood's formulae by those published in American 

 reports (1). 



Impulse 



giving 



and 



20UX w"'^ 



d1.11' 



lbs. /sq. in. 

 lbs. secs./sq. in. 



:W 



.00 



w 

 a.u w' 



,0.38 



W in lbs. 



J D in ft. 



(8) 



TTVr 







1.39 



m 



The results of these calculations which were carried out by Admiralty Computing Service (2) 

 are summarised in Table 4. On average the values for the calculated volumes of dishing show a 

 reduction of about 9i on the values given by using Wood's fomiulae. Despite this Improvement, 

 however, the calculated volumes of dishing ire still 10» to 30» in excess of the observed values. 



(V) 



