A new scaling is developed for both air and underwater blast waves based on dimensional analysis. The new length, time, velocity, and pressure scales are based on three control parameters: the energy release of the explosive \(E_{_\mathrm {HE}}\), the density of the undisturbed ambient medium \(\rho _{_0}\), and the speed of sound in the undisturbed ambient medium \(C_{_0}\). The shock wave propagation is divided into two regimes based on its decay characteristics, and the resulting control parameters are different in each regime. For strong shocks with Mach numbers \(M_{_\mathrm {SW}} \gtrsim 5\), the increase in the shock wave radius R with time t is approximated by a power law with an exponent of 2/5 as previously described by G. I. Taylor. Shock propagation in this regime is shown to not be a function of the ambient medium sound speed, but only the ambient medium density, explosive energy release, and time. For weak shock waves with Mach numbers \(M_{_\mathrm {SW}} \lesssim 5\), the shock wave radius increase with time can be approximated by a linear function plus a logarithmic-type correction which decays to a sound wave at sufficiently long time. Shock propagation in this regime is scaled according to the medium’s ambient density, sound speed, explosive energy release, and time. The new scaling is compared to, and agrees well with, published experimental data for air and underwater blasts, from milligram explosions to nuclear blasts. The new scaling improves upon traditional Hopkinson and Sachs scaling by relating shock propagation in liquid and gas environments, allowing them to be scaled to a single functional relationship. The functional scaling relationships developed here are dimensionless.

基于尺寸分析，针对空中和水下爆炸波开发了一种新的缩放比例。新的长度，时间，速度和压力标度基于以下三个控制参数：爆炸物的能量释放\（E _ {_ \ mathrm {HE}} \），不受干扰的环境介质的密度\（\ rho _ {_0} \），以及在不受干扰的环境介质\（C _ {_ 0} \）中的声速。冲击波的传播根据其衰减特性分为两个区域，每个区域的控制参数都不同。对于马赫数\（M _ {_ \ mathrm {SW}} \ gtrsim 5 \）的强烈冲击，冲击波半径R随着时间t的增加而增加由幂定律近似，指数为2/5，如GI Taylor先前所述。示出了在这种情况下的冲击传播不是环境介质声速的函数，而是环境介质密度，爆炸性能量释放和时间的函数。对于马赫数\（M _ {_ \ mathrm {SW}} \ lesssim 5 \）的弱冲击波，冲击波半径随时间的增加可以通过线性函数加上对数型校正来近似，该校正会在足够长的时间内衰减为声波。根据介质的环境密度，声速，爆炸性能量释放和时间，可以确定这种情况下的冲击传播程度。新缩放比例与从毫克爆炸到核爆炸的空中和水下爆炸的实验数据进行了比较，并与之相吻合。通过将在液体和气体环境中的冲击传播关联起来，新的缩放比例在传统的Hopkinson和Sachs缩放比例的基础上进行了改进，从而可以将它们缩放为单个功能关系。此处开发的功能缩放关系是无量纲的。