An introduction to dimensional analysis focused on explosions

What's going on during an explosion?

In this series we show how the dynamics of explosions are due to the interplay between the energy output and a succession of resisting factors, from the mass of the bomb to the density and pressure of the swept-up ambient medium. Depending on the values of energy, mass, density and pressure, explosions can be tiny (as with laser-ablations), large (as with nuclear explosions) or humongous (as with supernovae).

This series on the physics of explosions is an introduction to dimensional analysis, a method which requires very limited mathematical background, while being surprisingly effective:

• From pairs of mechanical quantities emerge scaling laws that the explosion abides to.

• From trios of mechanical quantities emerge special events, turning points of the dynamics, which can be used as units of space and time, more objective than the traditional standards like meters and seconds.

• From the combination of the four mechanical parameters emerges a dimensionless number, which is the appropriate number base to quantify explosions, and to distinguish detonations from deflagrations.

Not only does dimensional analysis allows to predict the trajectories of explosions from microscopic to astronomical, but it also provides more objective ways to quantify spacetime and its relationship with mater as mediated by mechanical constants like energy, mass, density and pressure. Dimensional analysis reveals how explosions occurring on vastly different scales are actually similar if represented with the units and base implied by the mechanics at play.