The explosive
yield of a nuclear weapon is the
amount of
energy that is discharged when a
nuclear weapon is detonated,
expressed usually in the equivalent
mass of
trinitrotoluene (TNT), either in
kilotons (thousands of tons of TNT) or
megatons (millions of tons of TNT), but
sometimes also in
terajoules (1 kiloton of
TNT = 4.184 TJ). Because the precise amount of energy released by
TNT is and was subject to measurement uncertainties, especially at
the dawn of the nuclear age, the accepted convention is that one kt
of TNT is simply defined to be 10
12 calories equivalent, this being very roughly equal
to the energy yield of 1,000 tons of TNT.
Examples of nuclear weapon yields
In order of increasing yield (most yield figures are
approximate):
| Bomb |
Yield |
Notes |
| kt TNT |
TJ |
| Davy Crockett |
|
variable yield tactical nuclear
weapon—mass only 23 kg (51 lb), lightest ever deployed by the
United States (same warhead as Special Atomic Demolition
Munition and GAR-11 Nuclear Falcon
missile) |
| Hiroshima's |
|
gun type uranium-235 fission bomb
(the first of the two nuclear weapons that have been used in
warfare) |
| Nagasaki's gravity bomb |
|
implosion type Plutonium-239
fission bomb (the second of the two nuclear weapons used in
warfare) |
| W76 warhead |
|
Twelve of these may be in a MIRVed Trident II missile; treaty limited to
eight |
| B61 nuclear bomb |
various |
- Mod 7—up to
- Mod 10—four yield options
- Mod 11—undisclosed yield
|
| W87 warhead |
|
Ten of these were in a MIRVed LG-118A Peacekeeper. |
| W88 warhead |
|
Twelve of these may be in a Trident II missile (treaty limited
to eight) |
| Ivy King device |
|
second most powerful pure fission bomb, 60 kg uranium,
implosion type |
| Orange Herald |
|
most powerful pure fission bomb, UK |
| B83 nuclear bomb |
variable |
up to ; most powerful US weapon in active service |
| B53 nuclear bomb |
|
most powerful US warhead; no longer in active service, but 50
are retained as part of the "Hedge" portion of the Enduring Stockpile; similar to the
W-53 warhead that has been used in the
Titan II Missile; decommissioned in
1987 |
Castle Bravo device |
|
most powerful US test |
| EC17/Mk-17, the EC24/Mk-24, and the B41 (Mk-41) |
various |
most powerful US weapons ever: ; the Mk-17 was also the largest
by size and mass: about ; the Mk-41 had a mass of 4800 kg; gravity
bombs carried by B-36 bomber (retired by
1957) |
| The entire Operation Castle
nuclear test series |
|
the highest-yielding test series conducted by the US |
Tsar
Bomba device |
|
USSR, powerful explosive device, mass of 27 short tons
(24,000 kg), in its "full" form (i.e. with a depleted uranium tamper instead of one made
of lead) it would have been . |
| All nuclear testing |
|
total energy expended during all nuclear testing.[202853] |
Comparative fireball radii for a selection of nuclear
weapons.
Note that full blast effects would extend many times beyond
the fireball itself.
Logarithmic scatterplot comparing the yield (in kilotons) and
weight (in kilograms) of all nuclear weapons developed by the
United States.
As a
comparison, the blast yield of the GBU-43 Massive Ordnance
Air Blast bomb is 0.011 kt, and that of the Oklahoma City
bombing
, using a truck-based fertilizer bomb, was 0.002
kt. Most
artificial
non-nuclear explosions are considerably smaller than even what
are considered to be very small nuclear weapons.
Yield limits
The yield-to-weight ratio is the amount of weapon yield compared to
the mass of the weapon. The theoretical maximum yield-to-weight
ratio for fusion weapons is 6 megatons of TNT per metric ton
(25 TJ/kg). The practical achievable limit is somewhat lower,
and tends to be lower for smaller, lighter weapons, of the sort
that are emphasized in today's' arsenals, designed for efficient
MIRV use, or delivery by cruise missile systems. The 25 MT yield
option reported for the Mk-41 would give it a yield-to-weight ratio
of 5.2 megatons of TNT per metric ton. While this would require a
far greater efficiency than any other U.S. weapon (at least 40%
efficiency in a fusion fuel of lithium deuteride), this was
apparently attainable. In 1963 DOE declassified statements that the
U.S. had the technological capability of deploying a 35 MT warhead
on the Titan II, or a 50-60 MT gravity bomb on B-52s. Neither
weapon was pursued, but either would require yield-to-weight ratios
superior to a 25 MT Mk-41. For current smaller US weapons, yield is
600 to 2200 kilotons of TNT per metric ton. By comparison, for the
very small tactical devices such as the Davy Crockett it was 0.4 to
40 kilotons of TNT per metric ton. For historical comparison, for
Little Boy the yield was only 4 kilotons of TNT per metric ton, and
for the largest Tsar Bomba yield was 2 megatons of TNT per metric
ton (deliberately reduced from about twice as much). The largest
pure-fission bomb ever constructed had a 500 kiloton yield, which
is probably in the range of the upper limit on such designs. Fusion
boosting could likely raise the efficiency of such a weapon
significantly, but eventually all fission-based weapons have an
upper yield limit due to the difficulties of dealing with large
critical masses. However there is no known upper yield limit for a
fusion bomb. Because the maximum theoretical yield-to-weight ratio
is about 6 megatons of TNT per metric ton, and the maximum achieved
ratio was apparently 5.2 megatons of TNT per metric ton, there is a
practical limit on air delivery of the weapon. Note that most later
generation weopons have eliminated the very heavy casing once
thought needed for the nuclear reactions to occur efficiently -
this greatly increases the achievable yield-to-weight ratio. For
example, the Mk-36 bomb as built had a yield-to-weight ratio of
1.25 megatons of TNT per metric ton. If the 12,000 pound casing of
the Mk-36 was reduced by 2/3s, the yield-to-weight ratio would have
been 2.3 megatons of TNT per metric ton which is about the same as
the later generation, much lighter 9 megaton Mk/B-53 bomb. Delivery
size limites can be estimated to acertain limits to delivery of
extremely high yield weapons. If the full 250 metric ton payload of
the Antonov An-225 could be used, a 1.3 gigaton bomb could be
delivered. Likewise the maximum limit of a missile-delivered weapon
is determined by the missile payload capacity. The large Russian
SS-18 ICBM has a payload capacity of 7200 kg, so the calculated
maximum delivered yield would be 37.4 megatons of TNT and a Saturn
V scale missile could deliver over 120 tons with a yield of about
700 megatons. Again, it is helpful for understanding to emphasize
that large single warheads are seldom a part of today's arsenals,
since smaller
MIRV warheads are far more
destructive for a given total yield or payload capacity. This
effect, which results from the fact that destructive power of a
single warhead scales approximately as the 2/3 power of its yield,
more than makes up for the lessened yield/weight efficiency
encountered if ballistic missile warheads are scaled-down from the
maximal size that could be carried by a single-warhead
missile.
Calculating yields and controversy
Yields of
nuclear explosions can
be very hard to calculate, even using numbers as rough as in the
kiloton or megaton range (much less down to the resolution of
individual
terajoules). Even under very
controlled conditions, precise yields can be very hard to
determine, and for less controlled conditions the margins of error
can be quite large. Yields can be calculated in a number of ways,
including calculations based on blast size, blast brightness,
seismographic data, and the strength of the shock wave.
Enrico Fermi famously made a (very) rough
calculation of the yield of the Trinity test
by dropping small pieces of paper in the air and
measuring at how far they were moved by the shock wave of the
explosion.
A good approximation of the yield of the Trinity test device was
obtained from simple
dimensional
analysis by the British physicist
G. I. Taylor. Taylor noted that the
radius R of the blast should
initially depend only on the energy
E of the explosion,
the time
t after the detonation, and the density ρ of the
air. The only number having dimensions of length that can be
constructed from these quantities is:
R=c\left( {\frac^{2}}{\rho}} \right)^{\frac {1} {5}}
Using the picture of the Trinity test shown here (which had been
publicly released by the U.S. government and published in
Life magazine), Taylor
estimated that at
t = 0.025 s the blast radius was 140
metres. Taking
ρ to be 1 kg/m³ and solving for
E,
he obtained that the yield was about 22 kilotons of TNT
(90 TJ). This very simple argument agrees within 10% with the
official value of the bomb's yield, , which at the time that Taylor
published his result was considered highly-
classified information. (See G. I.
Taylor,
Proc. Roy. Soc. London
A201, pp. 159, 175 (1950).)
Where this data is not available, as in a number of cases, precise
yields have been in dispute, especially when they are tied to
questions of politics. The weapons used in the
atomic bombings of
Hiroshima and Nagasaki, for example, were highly individual and
very idiosyncratic designs, and gauging their yield retrospectively
has been quite difficult.
The Hiroshima bomb, "Little Boy
", is estimated to have been between (a 20% margin
of error), while the Nagasaki bomb, "Fat Man
", is
estimated to be between (a 10% margin of error).
Such
apparently small changes in values can be important when trying to
use the data from these bombings as reflective of how other bombs
would behave in combat, and also result in differing assessments of
how many "Hiroshima bombs" other weapons are equivalent to (for
example, the Ivy
Mike
hydrogen bomb was equivalent to either 867 or 578
Hiroshima weapons — a rhetorically quite substantial difference —
depending on whether one uses the high or low figure for the
calculation). Other disputed yields have included the
massive Tsar
Bomba, whose yield was claimed between being "only" or at
a maximum of by differing political figures, either as a way for
hyping the power of the bomb or as an attempt to undercut
it.
See also
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