348 MOTION OF THE GAS SPHERE 



certain energy content of the charge. Measurements made at the Road 

 Research Laboratory (95) using one ounce polar ammon geUgnite 

 charges three feet below the surface and a single flash photographic 

 technique have been compared with calculations based on Taylor's 

 theory, corrected for surface effect according to Herring's analysis. 

 The observed maximum radius of 1.65 feet was sufficiently large com- 

 pared with the depth of 3 feet for a large, downward migration of the 

 bubble to occur. Measured displacements of the center as a function 

 of time agree with values calculated from theory moderately well up to 

 times near the minimum. The discrepancy at later times is most strik- 

 ingly shown if velocities are compared, the theory predicting a maxi- 

 mum value of 900 ft. /sec. while the maximum measured value was esti- 

 mated at 180 ft. /sec. This difference is to be attributed at least in part 

 to the greater hydrodynamic resistance of the flattened surface actu- 

 ally realized, as compared to a sphere assumed in the theory, and to 

 turbulence in the wake of this surface. 



Temperley (111) has modified the Taylor theory to include a first 

 approximation for the distortion expressed in surface harmonics (see the 

 discussion of section 8.7). The measured values of the harmonic co- 

 efficient, obtained by analysis of the observed bubble sphere, are in 

 qualitative agreement with calculated values based on Temperley's 

 results, the agreement being somewhat improved if observed rather 

 than computed values of vertical velocity are used in this calculation. 



Although photographic methods ideally offer the best means of ob- 

 taining information regarding the form of the bubble near its minimum, 

 there are numerous practical difficulties which have limited the quan- 

 tity and usefulness of such data. Some features of the observed motion 

 which have not been brought out in the discussion so far are the for- 

 mation of smoke-like streamers and narrow spiked projections on the 

 bubble periphery. These are not conspicuous when the bubble is large, 

 but become more evident as the bubble contracts and increasingly ob- 

 scure its outline, making determination of the shape and displacement 

 rather uncertain. An example of this is shown in the motion picture 

 frames of Plate IX for times near bubble minima. The general fog and 

 obscuration is probably due to the explosion products and stray foreign 

 matter such as charge case, if any, detonator fragments, and so on.^'' 

 The projections have been attributed by Penney to the effect of in- 

 creasing instability, as the bubble contracts, of high order harmonic 

 terms expressing local deviations from spherical form. 



The experimental difficulties of obtaining good underwater photo- 



^^ The difficulties with soUd products can be minimized by using an explosive 

 such as Polar Ammon Ciclignite, as has bcH'n done in Biitish work, the better oxygen 

 balance resulting in much less solid carbon. A further advantage is decreased con- 

 tamination of water in experimental tanks. 



