associated with the beginning of nuclear explo- sions, in comparison with corresponding rela~ _ tive velocities at the lower pressures associ- gard to the equation of state, the material velocity, u, is given by ‘ated with thebeginning of TNT explosions. uv? =(P- PV, - Vv) AIR SHOCK AIR SOIL. So GROUND SHOCK AIR SHOCK AIR SOL GROUND SHOCK Fig. 1.1 Schematic Comparison of Nuclear Explosion and Small~charge Explosion, Note the broad shallow character of the nuclear shock in soil, as shown above, with the relatively deep shock from TNT, shown below. The small energy transfer on nuclear explosions follows from the high density and incompressibility of soil relative to air at comparable pressures. The time rate of work per unit area of shock front in any substance is proportional to the product W= Pu where W = the rate of work per unit area and time P = the absolute pressure behind the shock u = material velocity Using only conservation of mass and momentum in the Rankine-Hugoniot equations, without re- where P = absolute pressure behind the shock P, = ambient pressure ahead of the shock 4 ' V = specific volume behind the shock ‘ Vy = ambient specific volume ahead of the shock It follows then that the rates of doing work by the shock in soil and the shock in air are related by tz) Vo/soil Pair (3 _wv} Psoil Vo air at the same pressure level in both media. The incompressibility of soil means that the quan- Hl