256 



SHOCK WAVE MEASUREMENTS 



increases with pressure ahead of the front, and the pressure difference 

 across the front is large if the wave advances into fluid already under 

 compression. The form of a shock wave therefore changes as it enters 

 a region through which another shock wave has passed, and the pattern 

 of Fig. 7.16a is modified into the scheme corresponding to Fig. 7.16b. 

 This condition is described as regular reflection by von Neumann (116), 

 as discussed in section 2.10. The case considered here, of intersecting 

 shock waves of equal strength, is equivalent to a shock wave and its 



MACH 

 STEM 



SLIPSTREAMS 



PENTOUTE 

 STICKS 



REFLECTED 

 FRONTS 



Fig. 7.17 Mach reflection of intersecting shock waves from pentolite sticks 

 detonated at one end. 



reflection in a rigid surface below the line of symmetry in Fig. 7.16, and 

 so the analysis of this latter case is directly applicable here. 



Detailed calculation, based on the Rankine-Hugoniot conditions, 

 shows that the differences from the geometrical reflection increase with 

 the strength of the shocks and increasing angle between the shock fronts, 

 as measured by the half angle a between either shock and the plane of 

 symmetry. For pressures less than about 10,000 Ib./in.^ the dif- 

 ferences are not large, but become so rapidly at higher pressures, par- 

 ticularly for values of a approaching 90°. For sufficiently large values 

 of Pm and a, the equations at the shock fronts cannot be satisfied by the 

 regular reflection scheme of Fig. 7.16b. Instead, the so-called Mach 

 region reflection shown in Fig. 7.16c is found as discussed in section 

 2.10, with much higher pressures behind the advancing discontinuity 



