What is the Sachs scaling law used to predict regarding nuclear weapon effects?

The Sachs scaling law is used to predict the effects of a nuclear explosion, specifically how the blast wave parameters (such as overpressure, dynamic pressure, and arrival time) scale with the yield of the weapon and the density of the atmosphere. It provides a way to estimate the extent and intensity of blast effects at different distances from the point of detonation, based on a reference explosion. In essence, Sachs scaling states that two explosions of different yields will produce the same blast effects at distances that are scaled proportionally to the cube root of their yields, and inversely proportional to the cube root of the atmospheric density. For example, if you double the yield of a nuclear weapon, the distance at which a specific overpressure (the pressure above normal atmospheric pressure) is experienced will increase by a factor of the cube root of two (approximately 1.26). Similarly, if the atmospheric density is higher (e.g., at sea level compared to a high altitude), the distance at which a certain overpressure is experienced will be reduced. The Sachs scaling law is a simplified model that assumes ideal conditions (such as a homogeneous atmosphere) and does not account for factors like terrain or thermal effects, but it provides a useful first-order approximation for estimating blast damage from nuclear explosions.