Nuke Simulator / Methods

How It Works

This page explains how the Nuke Simulator turns a yield and a burst type into the rings on the map: which sources it uses, how each effect is calculated, how the results are checked, and where the method stops being reliable.

Overview

The simulator estimates six distances for one explosion: the maximum fireball radius, the 20, 5, and 1 psi blast overpressure radii, the distance for a 50% chance of third-degree burns on bare skin, and the distance at which the initial radiation dose is 500 rem. Everything is calculated in your browser. Each effect uses its own relationship from the literature, because blast, heat, and radiation do not scale with yield in the same way.

Method for each effect

Fireball

Glasstone and Dolan give the maximum fireball of a 1-megaton explosion as about 5,700 feet across (§2.05) and state that fireball radius scales with about the 0.4 power of the yield (§2.127). The simulator uses that rule. For a surface burst, where the fireball meets the ground, it follows the book's guidance to treat the explosion as having twice the yield.

Blast overpressure

Blast uses an analytic curve fit by H. L. Brode (1986) for peak overpressure on the ground as a function of distance and burst height, ported from the open-source glasstone library. Distances scale with the cube root of the yield, as described in Glasstone and Dolan chapter III. The simulator searches for the distance at which the overpressure falls to 20, 5, and 1 psi. A sea-level atmosphere and flat, open ground are assumed.

Thermal radiation (burns)

The heat model reads the curves in Glasstone and Dolan Fig. 7.42, which give the distance at which the ground receives a given amount of heat for air bursts with 12 miles of visibility. The amount of heat needed for a 50% chance of third-degree burns comes from Fig. 12.65; it rises from about 6 calories per square centimeter at 1 kiloton to about 11 at 10 megatons (our reading of the figure), because a larger explosion delivers its heat over a longer pulse. For surface bursts the model uses a thermal fraction of 0.18 instead of the air-burst 0.35 (§7.101). The distance along the line of sight is converted to a distance along the ground using the burst height.

Initial nuclear radiation

Initial radiation is the radiation released within the first minute. The model adds three parts: neutrons, secondary gamma rays, and gamma rays from fission products, using digitized curves from Glasstone and Dolan chapter VIII (Figs. 8.123, 8.127, 8.130, and 8.132) provided by the glasstone library. Yields up to 100 kilotons use the fission weapon curves; larger yields use the thermonuclear curves. Neutron and gamma doses are counted equally, which is a simplification. As with heat, the line-of-sight distance is converted to a ground distance.

The fixed airburst height

The simulator has exactly two burst options. A surface burst happens at ground level. An airburst always uses one example from the literature: Hiroshima, where Glasstone and Dolan give a burst height of 1,670 feet for a yield of about 12.5 kilotons (§2.24).

To apply that one example to other yields, the height is scaled with the cube root of the yield, the same scaling the book uses for burst height in its blast charts. That works out to about 720 feet times the cube root of the yield in kilotons, so the geometry looks the same as the historical example at every size. For example:

• Little Boy (15 kt): about 0.54 km (0.34 mi) above the ground.
• B83 (1.2 Mt): about 2.3 km (1.4 mi) above the ground.
• Tsar Bomba (50 Mt): about 8.1 km (5.0 mi) above the ground.

The height is not chosen to increase any effect, and the simulator does not offer a height setting or any "optimum height" calculation. This is a deliberate boundary for an educational tool. One visible result is that for the largest yields the burst is so high that the 500 rem initial radiation dose does not reach the ground at all, so that ring has no size.

Sources

Every number the simulator shows comes from published, public literature. No code from NUKEMAP or any other unlicensed project is used.

• Glasstone, Samuel, and Philip J. Dolan, eds. The Effects of Nuclear Weapons. 3rd ed. Washington, D.C.: U.S. Department of Defense and U.S. Energy Research and Development Administration, 1977 (sold by the Superintendent of Documents, U.S. Government Printing Office). Used for:
  • Fireball size: §1.32 and §2.05 (1-megaton fireball about 5,700 ft across), §2.127, eqs. (2.127.1) and (2.127.2) (radius scales as yield^0.4; a surface burst behaves like twice the yield).
  • The fixed airburst example: §2.24 (Hiroshima: burst height 1,670 ft, yield about 12.5 kilotons), scaled with the cube root of yield as in the notes to Figs. 3.73a to 3.73c.
  • Blast (chapter III): Figs. 3.72 and 3.73a to 3.73c and their worked examples, used as reference cases for the blast model; §2.34 and §2.35 and §5.53 as further checks.
  • Thermal radiation (chapters VII and XII): Fig. 7.42 (distance for a given heat dose vs. yield, air bursts, 12-mile visibility), Table 7.88 and §7.101 (heat fraction 0.35 for air bursts, 0.18 for surface bursts), Fig. 12.65 (heat dose for 50% probability of third-degree burns).
  • Initial nuclear radiation (chapter VIII): Figs. 8.123a and b, 8.127a and b, 8.130a and b, and 8.132 with §8.124 and §8.131 (neutron, secondary gamma, and fission-product gamma doses); Figs. 8.33a and b split fission (up to 100 kt) and thermonuclear weapons.
  • Fallout background (chapter IX), used for the explanations on the nuclear fallout map page only.
• GOFAI, glasstone: nuclear weapons effects modelling in Python, github.com/GOFAI/glasstone, Copyright © 2016 GOFAI, released under the MIT License. The blast model (a curve fit by H. L. Brode, Airblast From Nuclear Bursts: Analytic Approximations, Pacific-Sierra Research Corporation, 1986, as cited by glasstone) and the digitized initial-radiation curves from Glasstone and Dolan chapter VIII are ported from this library. The MIT license text ships with our source code (LICENSES/glasstone-MIT.txt).

Fallout is not modelled. A simplified fallout model (the "Miller" scaling mentioned by other simulators) was considered, but we could not locate and fully cite the original report, so we leave it out rather than show numbers we cannot trace.

How the numbers are checked

The model is tested automatically against about thirty values printed in Glasstone and Dolan (1977): worked examples in the text and readings taken from its figures. Each check has a tolerance of ±10% for numbers printed in the text and ±15% for values read from graphs. Values the model itself produces are never used as reference values.

Three cases fall outside those tolerances, and they are kept in the test file (tests/effects.test.ts) as known deviations rather than hidden. For example, the 1 psi distance of a small surface burst is about 20% larger than one of the book's graphs, although it agrees with the book's own "twice the yield" rule. The fireball has no independent check, because the book's one clear fireball figure was used to set the formula.

The distances quoted in the text and tables on this site are generated from the same model when the site is built, so they always match what the map shows.

Limitations

These are rough, idealized estimates for education. Real outcomes could be quite different.

• Flat, open ground and a standard sea-level atmosphere are assumed. Hills, buildings, and weather are ignored, and they can change results a lot.
• Heat (burn) distances assume a clear day with 12 miles (about 19 km) of visibility and bare skin facing the flash. Haze, cloud, smoke, or any shade reduce them; snow or cloud above the burst can increase them.
• Radiation distances assume a typical weapon design; the source rates its curves as reliable only to within roughly a factor of two (0.5 to 2 times for fission weapons, 0.25 to 1.5 times for thermonuclear weapons). The 500 rem contour counts neutron and gamma doses equally. Yields up to 100 kt use fission-weapon curves, larger yields use thermonuclear curves, so there is a small jump at 100 kt.
• The airburst option always uses one fixed example burst height: Hiroshima's (1,670 ft for about 12.5 kt), scaled to the chosen yield. No burst height optimization or damage-maximizing features are offered, by design.
• Very small (below 1 kt) and very large (above 10 to 20 Mt) yields go beyond the source charts; results there are extrapolations and are flagged in the results panel.
• Rings are sharp lines, but real effects fade gradually with distance.
• Fallout is not modelled.
• Population figures (when available) show people living inside a zone, never casualty estimates.
• Not affiliated with NUKEMAP or any government agency.

Data and attribution

• Map tiles and buildings:OpenFreeMap, using data © OpenStreetMap contributors (Open Database License). The attribution is also shown in the corner of the map.
• City search: GeoNames (cities15000 dataset), licensed under CC BY 4.0, trimmed by us to cities with a population of at least 500,000.
• Effects model: blast fit and radiation curve data ported from GOFAI/glasstone, MIT License, Copyright © 2016 GOFAI.
• Map rendering: MapLibre GL JS (BSD 3-Clause License).
• Population layer: GHSL GHS-POP (CC BY 4.0) is planned and not yet integrated.

Want to see the methods in action? Try the nuke simulator, or read the nuclear blast radius guide for a table of every preset.