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Cited by 1,378Combustion and Detonation ProcessesComputational Fluid Dynamics and AerodynamicsStructural Response to Dynamic Loads

The formation of a blast wave by a very intense explosion I. Theoretical discussion

Taylor, Geoffrey Ingram·1950·Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
DOI 10.1098/rspa.1950.0049
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Abstract

This paper was written early in 1941 and circulated to the Civil Defence Research Committee of the Ministry of Home Security in June of that year. The present writer had been told that it might be possible to produce a bomb in which a very large amount of energy would be released by nuclear fission—the name atomic bomb had not then been used—and the work here described represents his first attempt to form an idea of what mechanical effects might be expected if such an explosion could occur. In the then common explosive bomb mechanical effects were produced by the sudden generation of a large amount of gas at a high temperature in a confined space. The practical question which required an answer was: Would similar effects be produced if energy could be released in a highly concentrated form unaccompanied by the generation of gas? This paper has now been declassified, and though it has been superseded by more complete calculations, it seems appropriate to publish it as it was first written, without alteration, except for the omission of a few lines, the addition of this summary, and a comparison with some more recent experimental work, so that the writings of later workers in this field may be appreciated. An ideal problem is here discussed. A finite amount of energy is suddenly released in an infinitely concentrated form. The motion and pressure of the surrounding air is calculated. It is found that a spherical shock wave is propagated outwards whose radius R is related to the time t since the explosion started by the equation R = S(γ)ttEtρ0-t, where ρo is the atmospheric density, E is the energy released and S(γ) a calculated function of of γ, the ratio of the specific heats of air.

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  • An AGN outburst with energy E_agn = 10^56 E_56 erg, assuming a blast-wave solution, would travel to ~18 kpc with a velocity of 236 km/s after ~30 Myr for E_56=6.

    “Following the previous example, we find that an outburst of E 56 = 6 (for an equivalent energy of SFR = 1 M ⊙ yr -1 over 30 Myr) would only travel to ∼ 18 kpc with a velocity of 236 km s -1 after a time of ∼ 30 Myr.”

    From The Fermi/eROSITA bubbles: a look into the nuclear outflow from the Milky Way (2024) · cites this paper as Taylor 1950

  • The general solution for a blast wave in an isotropic medium is self-similar, with shock radius and velocity given as power laws rs(t) ∝ t^η and vs(t) = η rs/t.

    “The general solution for a Blast-Wave (BW) in an isotropic medium is self-similar for which the radius and the velocity of the shock front, rs , at any time, t , is given as simple power laws, rs ( t ) ∝ t η and vs ( t ) = η rs / t .”

    From The Fermi/eROSITA bubbles: a look into the nuclear outflow from the Milky Way (2024) · cites this paper as Taylor 1950

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Authors
Taylor, G. I.
Corresponding author
Taylor, Geoffrey Ingram
Venue
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
Publisher
The Royal Society
Published
1950-03-22
Volume
201
Issue
1065
Pages
159-174
ISSN
  • 0080-4630 (ISSN-L)
  • 2053-9169
DOI
10.1098/rspa.1950.0049
OpenAlex
W2039232030
Cited by
1,378
References
0
Citations by year
2026: 35 · 2025: 65 · 2024: 51 · 2023: 39 · 2022: 57 · 2021: 84 · 2020: 79 · 2019: 58 · 2018: 62 · 2017: 59 · 2016: 56 · 2015: 55 · 2014: 60 · 2013: 49 · 2012: 39
FWCI
7.08
Type
journal article
Language
en
Open access
closed
Licence
royalsociety.org/journals/ethics-policies/data-sharing-mining/ (tdm)
Locations
Proceedings of the Royal Society of London A Mathematical and Physical Sciences (publishedVersion)
Topics
  • Physical Sciences › Engineering › Aerospace Engineering › Combustion and Detonation Processes
  • Physical Sciences › Engineering › Computational Mechanics › Computational Fluid Dynamics and Aerodynamics
  • Physical Sciences › Engineering › Civil and Structural Engineering › Structural Response to Dynamic Loads
Keywords
blast wave, shock wave propagation, nuclear explosions, atomic bomb, spherical shock, atmospheric pressure, adiabatic index, energy release, civil protection

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