The Blast Radius

Plate 7 speaks for itself: “Energy, read from a photograph and a ruler.”

The Physics

G. I. Taylor showed by similarity that a strong point blast grows as R ∝ t^(2/5). Fitting the radius in timed photographs of the 1945 Trinity fireball gave the energy of the explosion.

R = C (E t² / ρ)^(1/5)

• R: shock radius, m
• C: dimensionless constant ≈ 1.03 for γ = 1.4
• E: released energy, J
• t: time after detonation, s
• ρ: ambient air density, kg m⁻³
• γ: ratio of specific heats, dimensionless

C ≈ 1.03 for γ = 1.4. Taylor estimated E ≈ 16 800 t TNT.

Honest caveat: Taylor's figure is an estimate from a similarity solution; it lies within the range of yields later published for Trinity.

Sources

• G. I. Taylor, Proc. R. Soc. A 201, 159 and 175 (1950).

On the poster

Plate 007, “The Blast Radius”: the pixel-art plate with its slogan “Energy, read from a photograph and a ruler.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.