The Energy Scales of Atomic Detonations

Vic Miller
March 11, 2012

Submitted as coursework for PH241, Stanford University, Winter 2012

Fig. 1: Number of nuclear US weapons tests and estimated yield for each year from 1945 to 1962.

Nuclear power and atomic weapons have been inextricably linked since the discovery of nuclear fission. Throughout the 1930's and 40's, scientists and engineers developed techniques to extract energy from the fission process, in both controlled and uncontrolled ways; their efforts culminated in Fermi's demonstration of the first nuclear reactor in 1942 and the Manhattan project's successful detonation of the Trinity device in July of 1945, the first supercritical fission explosion. After World War II, the Atomic Energy Commission oversaw US development and application of nuclear technologies for both weapons and power generation. Both atomic energy and atomic weapons are based in the same principles of nuclear physics, which dictate the process by which energy stored in the nuclear bonds of certain elements (e.g., uranium) is liberated; yet despite the fundamental similarity between nuclear weapons and power, the relevant scales of energy associated with weapons as compared to modern energy demands are surprisingly different. Recently, much attention has been given to foreign development of nuclear energy programs in the interest of monitoring nuclear technology proliferation, yet the destructive power of nuclear weapons lends credence to preventing the implementation of nuclear power programs, even in the interest of "clean", carbon-free, or "accessible" energy some believe nuclear power can offer.

The energy content of bombs and explosions is measured in equivalent tons of TNT. A one-kiloton explosion is equivalent to detonating one-thousand tons of TNT, and, similarly, a one-megaton event is equivalent to detonating one-million tons of TNT. The detonation of one ton of TNT releases about 4.2 × 1012 joules of energy; for comparison, it takes roughly 6.0 ×104 joules to warm up a cup of coffee. On July 16 of 1945, the US detonated the first nuclear device, known as Trinity, in the New Mexico desert. This plutonium fueled bomb had an estimated yield of 21 kilotons, and left a crater 2.9 meters deep and 335 meters wide. [1]

After the end of World War II, between 1946 and 1952, The US tested relatively low yield fission devices to study the performance of various weapon designs as well as the effects of nuclear blasts on buildings, boats, and the environment. The weapons tested in this period ranged in yield from less than 1 kiloton (e.g., the Buster-Jangle Able test) to weapons as big as 225 kilotons (the Greenhouse George test). During the fall of 1952, the first thermonuclear hydrogen fusion device, known as Ivy Mike, was detonated; it had an estimated yield of 10.4 megatons and infamously crated the Elugelab Island of the Enewak Atoll in the south Pacific. From 1952 to 1962, the US continued testing weapons of various sizes, with the largest being the 1954 Castle Bravo device, a 15 megaton thermonuclear device capable of being delivered as a weapon. [2] Devices were tested in the air, in the ocean, and underground during this time.

In 1963, the US signed the Partial Test Ban Treaty, which required all tests from that point on to be conducted underground to reducing the release of nuclear fallout resulting from atmospheric tests. Figure 1 displays the sum of all estimated yield for each year from 1945 to 1963 on the left ordinate, and the number of tests in each year on the right ordinate. Some tests that extended beyond 1963 were not included, and all yields were not available for all tests, but given the wide range of available US device yields, spanning five orders of magnitude, some tests obviously contribute more to our sum more than others. Nevertheless, we find that in total, the US detonated about 119 megatons of nuclear devices during this period from 1945 to 1963. If we recall that one kiloton of explosive is equivalent to about 4.2 × 1012 joules, the total number of joules released resulting from US nuclear weapons testing from 1945 to 1963 is 5 × 1017 joules. [2] All of this testing pales in comparison to the Soviet 58 megaton test, detonated at an altitude of 3500m at the Novaya Zemlya test site in October of 1961. This single soviet bomb's yield was reduced for testing from a designed yield of 100 megatons, which, as we just calculated, is nearly the entire US nuclear weapons cumulative yield detonated from 1945 to 1963. The fallout resulting from this explosion was recorded worldwide. [3]

Even so, all of these yields combined, are still dwarfed by the energy consumed by the world today. One gallon of gasoline contains about 1.3 × 108 joules of energy. So about 4 billion gallons of gasoline, or about 50 super tankers full of gasoline (capacity = 84 million gallons) is equivalent to all the US nuclear devices tested between 1945 and 1963. Furthermore, the world's energy use in 2008 was 5 ×1020 joules, or 1000 times more than our cumulative sum of kilotonnage. [4] This is the amount of the energy the world uses, on average, in about 8 hours. The scales of energy consumption are dizzying, and weapon yields seem laughably small in comparison, but become absolutely terrifying when one realizes that the weapons that leveled Hiroshima and Nagasaki had estimated yields of less than only 20 kilotons! Granted, the explosive yield of weapons does not translate directly into the power generating capacity of a nuclear power plant, but the scale to which weapons can be built once the nuclear technology and experience is acquired must make one question whether or not nuclear power is worth the risk of weapon proliferation.

©Victor Miller. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] "Project Trinity 1945-1946," U.S. Defense Nuclear Agency, DNA 6028F, December 1982.

[2] "For the Record - A History of the Nuclear Test Personnel Review Program, 1978-1993," U.S. Defense Nuclear Agency, DNA 6041F, March 1996.

[3] V. I. Khalturin et al., "A Review of Nuclear Testing by the Soviet Union at Novaya Zemlya, 1955-1990," Sci. Global Security 13, 1 (2005).

[4] "International Energy Outlook 2011," U.S. Energy Information Administration, DOE/EIA-0408(2011), September 2011.