-3- 541 



OuDble during the first oscillation, and has been calculated in a manner to be discussed presently. 

 It will br observed that in every case the observed minimum radius 'S considerably greater than the 

 calculated value, 



• Because of the observed luminosity of the bubble gases it seemed of interest to attempt some 

 calculation of the gas temperature at the instant of maximum compression. As data for the adiabatic 

 of the explosion products of polar Ammcn-gpl ignite were not available the adiabatic for the explosion 

 products of T.N.T. given by Jones (6) has been used to calculate the temperatures given in Table II. 

 These temperatures are rather lo* in view of the very great intensity of the "flash" produced by the 

 smallest bubbles - e.g. shot 124. It is noticeable that the region of luminosity only occupied a 

 fraction of the volume of the bubble, and in the shots which produced rather weak "flashes" this 

 luminous region was very small compared to the total volume. It might be argued that contrnry to the 

 assumption in the usual bubble theori.'S the pressure throughout the gas is not uniform, and this could 

 lead to some increase in pressure in parts of the bubble. sinci;, however, the temperature (absolute) 

 varies approximately as the one fifth power of the pressure, it does not appear likely that the 

 maximum tempersture will be much ibove the figures given in the Table. 



Di splace'T.ent - Time Curve s. 



The displacement of the centre of gravity of the bubble towards the target is plotted as a 

 function of time before and after the occurrence of the minimum radius in rigure 6 for a range of 

 values of the charge distance. as may be seen from Figure 5 this time is not very clearly defined 

 in the close shots. For the more distant shots the deflection time curve is roughly symmetrical 

 about the time of minimum radius. in the nearer shots the bubble approached very close to the target 

 plate, making contact with it soon after the minimum, so thjt a marked asymmetry of the displacement- 

 timt curve is to be expected. 



Compari son of Observed IhspLa c ement wx th The o ry . 



in c-ilculat ing the ^^ttr^.ctive efftct of the box model it has been assumed that the flat 

 target pl=ite surrounded Cy its riijid flat fl-n;f- mjy oe approximated by a rigid fixed disc of 

 equal area. Accordingly the "momentum constant" n, defined as one half the cube of the non- 

 dimcnsion-il minimum rddius multiplied by the maximum non-dimensional velocity, has been calculated 

 using the formul^'. fur the ittraction co-efficient for ?■. rigid disc given in reference (2). The 

 displaC'i-rai.nt at the minimum was then calculated. This curve was obtained by plotting the results 

 of all available .'uli integrations of the equations of bubble motion. The displacement thus 

 calcuiatt-d has been plotted in Figure 7 together with the observed values for all the photographic 

 shots. The results for both ^ inch and -^ inch plating do not appear to lie on separate curves, 

 nnd in plotting them in Figure 7 no distinction hus been made. This is to be expected since the 

 target plate is practically motionless, and therefore effectively rigid, during the period when 

 the- bubbK is l"'r^e, i.e. when it acquires most of its mofnentum, 



The agreement between the observed and predicted displacement of the bubble shown in Figure 7 

 requires to be interpreted with caution. in common with most experimental observations of the 

 bubble's behL^viour near its minimum, tnere arc rather wide discrepancies between theory and 

 '.s^rvat ion in regard to quantities such as minimum radius or maximum linear velocity. since, 

 •jwtvir, a considerable proportion of tn^- resultant displacement takes place some little time 

 oefore tne minimum, at least for the closer shots, the agreement in observed and calculated 

 displacements might still be expected, provided that the discrepancies arose only very close to the 

 time of minimum radius. It is thus reasonable to regard the observed agreement as indicating that 

 the theory provides a good estimate of the linear momentum of the bubble, except possibly during 

 a v.^ry short time near the occurrence of the minimum radius. Moreover, it should be remembered 

 that thf theory given in (2) was d^^rived on the assumption that the radius of the bubble when large 

 is small compared to its distancr from the target. For a one ounce charge the maximum radius Is 

 about 18 inches so that the thfory is here being used well beyond the region of validity of this 

 assumpt ion. 



