Page:THEORY OF SHOCK WAVES AND INTRODUCTION TO GAS DYNAMICS.pdf/192

Here the impossibility of a strict similarity is obvious. The theory now includes acceleration of gravity $g$ expressed in terms of length/time$^{2}$. Together with the characteristic velocities of the explosion process, e.g., $c_{0}$, the presence of $g$ permits the plotting of the length, e.g., $c_{0}^{2}/g$ and time $c_{0}/g$. The absence of similarity is obvious: if we compare two charges of different size buried in the sand at an appropriate depth, we can see that the pressure of the soil at the level of the charge is proportional to the depth, and to the size of the charge. Likewise, minimum pressure required for the toppling of a wall in the second example is also proportional to the size. However, atmospheric pressure and blast pressure do not depend on the size.

Thus, with a change in size there is also a change in the ratio of soil pressure or the pressure required for the beginning of destruction to blast pressure, and similarity is therefore violated.

An excellent simulation method was proposed by Pokrovskiy [109]. To obtain similarity as we change the scale of the experiment, we must also change the length proportionally. Pokrovskiy obtains this by changing acceleration, and replacing gravity with centrifugal force. The model is exploded on a centrifuge and the dimensions are reduced with respect to nature at the same ratio of centripetal acceleration to acceleration of gravity. We can readily verify that soil pressure at similar depths will be similar.

Pokrovskiy made extensive use of his method for the purpose of modeling large scale explosions for excavation, and also for the purpose of studying the effect of various soils and different positions of the charge on the result of explosions. The linear modeling scale in his experiments reached 29, i.e., all the dimensions of the model were reduced bya factor of 29 as compared with the dimensions of the real object. The weight of the charge, which characterized the cost of the experiment, was reduced by a factor of 25,000.

Zel'dovich and Khariton proposed an approximate method for simulating the work of explosives against the forces of gravity. It is based on the fact that the new criterion