File:Mushroomcloud Size.png

1. Description: Final height h and radius r of a nuclear mushroom cloud as a function of the explosive yield W. The final height is approximately the height above the burst point for low and intermediate W and approx. the height above sea leval for high W.
2. Author: SiriusB
3. Date: Feb. 9 2005 (new version)
4. Sources: A figure in Glasstone/Dolan (1977), The effects of nuclear weapons. The values are fitted via the formulae

${\displaystyle H(W)=3.0\,\mathrm {km} \cdot 10^{0.006941{\mathit {LW}}^{4}-0.06216{\mathit {LW}}^{3}+0.1526{\mathit {LW}}^{2}+0.1878{\mathit {LW}}}}$,

${\displaystyle R(W)=0.6\,\mathrm {km} \cdot 10^{0.0137{\mathit {LW}}^{3}-0.0358{\mathit {LW}}^{2}+0.37{\mathit {LW}}}}$,

where LW = log₁₀(W/kT). For low yields the relation can be approximated by h ≈ 3000 m⋅(W/kT)^1/3. An interpolation to the cubic law is used for LW<1.5, i.e. W<32 kT in the new image version. The curve fits data from nuclear tests up to approx. 50 MT (the 'Tsar Bomba' test, 1961). The extrapolation to 100 MT is to be used with caution. For individual events there are large deviations in height; for example the mushroom cloud of the atomic bombings of Hiroshima and Nagasaki rose up to approx. 12 kilometres.

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