Every prompt-effect formula the engine uses, traced to the section of the handbook it comes from, with the computed values set beside the book’s own worked examples — including the places where the two disagree, and the places where the handbook declines to give a number at all.
A research dossier compiled for Grid/84. Every ring the atlas draws, every crater it digs and every plume it lays down comes from one book: Samuel Glasstone and Philip J. Dolan, The Effects of Nuclear Weapons, third edition, prepared by the United States Department of Defense and the Energy Research and Development Administration, 1977. This document says which section each formula comes from, what was done to it, and how far the result sits from the handbook’s own numbers.
Method. The tables below were produced by running the engine’s own functions and printing the output, not by transcribing figures into a page. Where a comparison against the book is shown, the book’s figure is quoted from the section named beside it. Several of the checks are also assertions in the test suite, so a formula cannot drift away from the source it was fitted to without a test failing.
Two things worth saying at the top. The handbook is not a model; it is a set of curves fitted to about fifteen years of atmospheric testing, and it carries its own uncertainties, some of them large — the initial-radiation curves are published with a stated reliability factor of one half to two. And where the book gives no number, this project gives none either. Section 06 lists what that leaves out.
DocumentedStated in the handbook at a named section, table or figure, and quoted from it.
Fitted or modelledA closed form fitted to the handbook’s curves, or a result the engine computes from the handbook’s constants that the handbook does not itself state.
Contested or uncertainThe handbook carries its own stated uncertainty here, or its two editions differ, or the figure depends on something the book leaves open.
No figure givenThe handbook names the effect and declines to quantify it. Nothing has been invented to fill the gap.
Every prompt-effect quantity the engine computes, and where it comes from. Each row is expanded in the section named.
| Quantity | Form | Source | Tier |
|---|---|---|---|
| Overpressure radius, air burst | r = c · W1/3 | Fitted to the handbook’s ch. III curves, at the height that maximises each ring | Fitted |
| Overpressure radius, surface burst | Z(Δp) · (2W)1/3 | §3.34, a contact burst as a free-air burst of twice the yield | Documented |
| Maximum fireball radius | 2 × 100 · W0.4 ft | §2.127 | Documented |
| Whether the fireball touches down | h ≤ Rfireball | §9.48, on which bursts make early fallout | Documented |
| Third-degree burn radius | 0.67 · W0.41 km | Fitted; mechanism at §7.96, outcome tabulated at Table 12.31 of the 1962 edition | Fitted |
| Initial radiation radius | 0.7 · W0.19 km, then one tenth-range per decade | §8.32 for the form; §8.34 for the one worked case | Fitted |
| Crater radius and depth | 60 and 30 ft · W0.3 | §6.09 | Documented |
| Lip crest and ejecta | 1.25× and 2.15× the radius | §6.71, §6.74 | Documented |
| Fallout contours | a · Wb, per contour | Table 9.93, with §9.94 for fission fraction and §9.97 for wind | Documented |
| Fallout decay | t−1.2 | §9.15 | Documented |
| Terrain factor on dose rate | 0.7 in the open | §9.95 | Documented |
| Structural collapse pressures | 3 and 5 psi | §5.53 for Japanese dwellings, §5.57 and §5.67 for the Nevada test houses | Documented |
| Aircraft in the open | 2 to 3 psi | §5.150 | Documented |
The cube-root law, the two burst geometries, and the one place where putting the weapon on the ground reaches further than putting it in the air.
FittedThe air-burst radii are a fit, and it is worth being clear whose. The closed forms are Carey Sublette’s, from the Nuclear Weapons Frequently Asked Questions §5.6, which are curve fits to the handbook’s chapter III. They give the radius at the height of burst that maximises that particular ring, over flat ground in clear air, and are stated as accurate to about ten per cent from 1 kt to 20 Mt. Each ring therefore stands at its own optimum height, which is a spread of altitudes rather than one weapon at one height. This matters when comparing against other instruments, and the comparison is in the project’s validation brief rather than here.
| Yield | 20 psi | 5 psi | 1 psi | Height for 5 psi |
|---|---|---|---|---|
| 1 kt | 0.28 | 0.71 | 2.20 | 298 m |
| 20 kt | 0.76 | 1.93 | 5.97 | 809 m |
| 100 kt | 1.30 | 3.30 | 10.21 | 1,384 m |
| 335 kt | 1.94 | 4.93 | 15.28 | 2,071 m |
| 1 Mt | 2.80 | 7.10 | 22.00 | 2,982 m |
| 10 Mt | 6.03 | 15.30 | 47.40 | 6,425 m |
DocumentedThe surface burst comes from the book directly, not from a fit. §3.34: over an ideal reflecting surface the shock from a contact burst “would correspond to that for a free air burst… with twice the energy yield”. The engine takes that at face value — the upper value, since real surfaces absorb some of the energy — and inverts the Kinney and Graham free-air fit of 1985 for the scaled distance. What comes out is not a uniform reduction.
| Overpressure | Air burst | Surface burst | Ratio of radii | Ratio of areas |
|---|---|---|---|---|
| 20 psi | 2.80 km | 3.01 km | 1.07 | 1.15 |
| 10 psi | 4.50 km | 4.10 km | 0.91 | 0.83 |
| 5 psi | 7.10 km | 5.77 km | 0.81 | 0.66 |
| 3 psi | 10.00 km | 7.69 km | 0.77 | 0.59 |
| 1 psi | 22.00 km | 16.94 km | 0.77 | 0.59 |
FittedAt twenty pounds a square inch the surface burst wins, and the reason is the whole logic of aiming. An air burst buys its reach from Mach reinforcement, where the incident and reflected shocks merge along the ground. That reinforcement is worth a great deal at low overpressure, far out, and very little close in, where the shock has not had room to merge. Doubling the effective yield helps everywhere. So at 1 psi the air burst covers nearly twice the area, and at 20 psi the surface burst covers fifteen per cent more. This is why a city is attacked from the air and a silo from the ground, and it falls out of the arithmetic rather than being asserted.
DocumentedThe pressures at which buildings fall are the book’s, and they are not one number. §5.53: Japanese-style wooden dwellings “collapsed at distances up to 7,500 feet (1.4 miles) from ground zero, where the peak overpressure was estimated to be about 3 pounds per square inch”. The American test houses of 1953 and 1955 collapsed or were damaged beyond repair at 5 psi (§5.57, §5.67), and 5 psi is the collapse pressure the 1979 Office of Technology Assessment casualty bands assume. The engine carries both, because applying an American suburb’s collapse pressure to Hiroshima counts the dead at the wrong radius.
Why the burn radius grows more slowly than the square root of the yield, and how the fit stands against the edition that tabulated the answer.
DocumentedThe mechanism, from §7.96. A target at distance D receives a radiant exposure of about Q ≈ 3.07 f W τ / D² calories per square centimetre, where f is the thermal partition and τ the atmospheric transmittance. A fixed exposure would therefore put the radius at the square root of the yield. The engine’s exponent is 0.41, below a half, and the reason is in the book too: the thermal pulse lengthens with yield, and a longer pulse delivers the same energy more slowly, so it takes more of it to do the same damage to skin.
UncertainThe 1977 edition draws the answer; the 1962 edition tabulates it. The third edition gives thermal effects as curves against slant range. The second edition’s Table 12.31 gives ranges from ground zero for burns to bare skin from air bursts, directly, in statute miles. The engine is fitted to the third edition and checked against the second, which is the only reason both editions are used at all.
| Yield | First-degree, book | Second-degree, book | Third-degree, engine | Fraction of second |
|---|---|---|---|---|
| 1 kt | 0.7 | 0.5 | 0.42 | 0.83 |
| 10 kt | 1.9 | 1.5 | 1.07 | 0.71 |
| 100 kt | 5.3 | 4.0 | 2.75 | 0.69 |
| 1 Mt | 14 | 11 | 7.07 | 0.64 |
| 10 Mt | >30 | 24 | 18.17 | 0.76 |
FittedThe check passes on both counts a check like this can pass on. The book’s tabulated second-degree ranges scale as W0.423 against the engine’s W0.41 — the same exponent to within three per cent across four decades of yield. And the engine’s third-degree radius sits inside the second-degree range at every yield, between 64 and 83 per cent of it, which is where a third-degree burn has to be: a deeper burn happens closer in. Independently, §12.66 of the 1977 edition puts 4.5 to 6 cal/cm² at nine to ten miles for a megatonne, which is the same place the engine puts 7.07. The comparison table is data in the test suite, so the fit cannot drift.
No figureAtmospheric transmittance is not modelled at all. The τ in §7.96 varies with visibility, humidity and slant path, and the handbook gives it as a family of curves rather than a number. The engine assumes clear air and says so on every readout. A hazy day, or cloud below the burst, changes the thermal radius more than any other single factor in this dossier.
One worked case in the whole chapter to check against — and a result that explains why prompt radiation stopped being how anyone expected to be killed.
DocumentedThe form, from §8.32. The dose falls as the inverse square of distance and then again by absorption in the air. Over the range that matters, those two together are what a fixed distance per factor of ten in dose amounts to — the tenth-range. The engine puts the 1,000-rad radius at 0.7 · W0.19 km and then steps outward one tenth-range per decade of dose, with the tenth-range interpolated in the logarithm of yield from 330 m at 1 kt to 700 m at 20 Mt.
DocumentedThe single anchor, and the engine sits four per cent inside it. The doses themselves are curves — Figure 8.33a and b — not a table, so there is nothing to check against row by row. But §8.34 works one case in the text: a 50 kt fission air burst gives “somewhat less than 300 rads” at 2,000 yards, which the book interpolates at about 250. The engine puts 250 rads at 1,922 yards, 3.9 per cent inside the book’s own figure. Against curves that carry a stated reliability factor of one half to two, that is well inside the source’s own uncertainty.
UncertainThe reliability factor is the largest stated uncertainty in this entire dossier, and it belongs to the book. The handbook’s initial-radiation curves are for a fission weapon at nine tenths of sea-level air density, and are published with a reliability factor of one half to two — that is, the true dose may be half the curve or twice it. A thermonuclear weapon of the same total yield gives less, because a smaller share of its energy is fission. None of that is modelled. The engine’s radiation ring is the least trustworthy ring it draws, and it is drawn anyway because leaving it out would imply the effect does not exist.
| Yield | 500 rad | 5 psi | Ratio | Third-degree burn |
|---|---|---|---|---|
| 1 kt | 799 m | 710 m | 1.13 | 670 m |
| 10 kt | 1,217 m | 1,530 m | 0.80 | 1,722 m |
| 20 kt | 1,374 m | 1,927 m | 0.71 | 2,288 m |
| 100 kt | 1,827 m | 3,296 m | 0.55 | 4,427 m |
| 335 kt | 2,271 m | 4,931 m | 0.46 | 7,267 m |
| 1 Mt | 2,769 m | 7,100 m | 0.39 | 11,378 m |
| 10 Mt | 4,230 m | 15,296 m | 0.28 | 29,247 m |
Running the engine’s own fits against each other: the 500-rad ring falls inside the 5 psi ring above 2.21 kt, and the 1,000-rad ring above 0.91 kt. Below those yields prompt radiation is the outer effect and reaches people the blast does not; above them, everyone who would have taken a fatal dose was already inside a radius where the buildings came down and the exposed skin burned.
The reason is in the exponents and nothing else. Blast radius goes as W1/3 and thermal as W0.41, but initial radiation goes as W0.19, because the air absorbs it: adding yield adds gamma rays, and the atmosphere takes almost all of the extra away before they arrive. This is the arithmetic behind the enhanced-radiation weapon — a weapon that wants prompt radiation to be the killing effect has to be small, and then deliberately shift its energy partition, because scaling up does not work.
At 1 kt the ordering inverts and the radiation ring is the outermost of the three. That is Hiroshima’s scale territory, and it is part of why the acute radiation syndrome is so prominent in the medical record of 1945 and so nearly absent from the projections for a modern exchange — not because modern weapons are gentler, but because at three hundred kilotonnes the blast has already reached everyone the gamma rays would have.
One constant from §6.09 reproduces the book’s own worked example and its lip statement at once — and the geometry decides, without being asked, which bursts make fallout.
Documented§2.127. The fireball radius at breakaway is about 100 · W0.4 feet, and the maximum “may be taken to be about twice that at the time of breakaway”. That is the whole of the fireball model: 200 feet at one kilotonne, 966 metres at a megatonne.
Documented§6.09, and the arithmetic checks out against the book’s own example. A one-kilotonne burst on the surface of dry soil or dry soft rock makes an apparent crater about 60 feet in radius and about 30 feet deep, with the crest of the lip some 15 feet beyond the crater’s edge; every dimension scales as W0.3. The book then works its own example: a hundred kilotonnes gives 60 × 1000.3 = 240 feet of radius and 120 of depth. The engine computes 238.9 and 119.4 — the book rounded, and the engine did not. The two are the same calculation.
DocumentedThe lip is stated twice, and one constant gives both. §6.71 puts the lip crest at 1.25 times the apparent radius and about a quarter of the apparent depth above the original surface. §6.09 separately says the crest stands 15 feet beyond a 60-foot crater. Those are the same statement: 1.25 × 60 = 75, and 75 − 60 = 15. The engine carries the factor and reproduces the fifteen feet exactly, which is a small thing but the right kind of small thing — two sentences sixty-two sections apart that have to agree, and do.
| Yield | Radius | Depth | Lip height | Ejecta to | Soil lifted |
|---|---|---|---|---|---|
| 15 kt | 41 m | 21 m | 5.2 m | 89 m | 0.09 Mt |
| 100 kt | 73 m | 36 m | 9.1 m | 157 m | 0.48 Mt |
| 335 kt | 105 m | 52 m | 13.1 m | 225 m | 1.44 Mt |
| 800 kt | 136 m | 68 m | 17.0 m | 292 m | 3.15 Mt |
| 1 Mt | 145 m | 73 m | 18.2 m | 312 m | 3.85 Mt |
FittedWhy the tonnage is worth computing at all. The volume is taken as a paraboloid of revolution, which is the shape of the book’s own crater profiles, at a bulk density of 1.6 tonnes per cubic metre for dry soil. A 335 kt surface burst therefore lifts about 1.4 million tonnes of ground. That mass is not a curiosity: it is the surface the fission products condense onto. Particles that heavy fall within hours rather than years, over a county rather than a hemisphere, and the plume the fallout model draws is that soil coming back down. The crater and the fallout pattern are two views of one event.
No figureTwo media the book names and does not quantify. In water-saturated soil the radius is appreciably greater and the final depth shallower, because the hole fills; in hard rock the dimensions are somewhat less. The handbook gives neither a number, so the engine gives neither, and the readout says the figure is the dry-soil case. A silo field in granite and a silo field in a river plain are not the same target, and this project cannot yet say by how much.
Nothing in the handbook says this, and the engine was not asked it; it falls out of putting two of the book’s sections beside each other. A weapon placed at the height that maximises the 5 psi area — the city case — has its fireball far above the ground at every yield: at a megatonne the fireball is 966 metres in radius and the burst is at 2,982. There is no crater and, by §9.48, no significant early fallout.
But a weapon placed at the height that maximises the 20 psi area — the hard-target case — is much lower, and the fireball is growing faster with yield (W0.4) than the height is (W1/3). The engine finds the two cross at about 323 kt: at 300 kt the fireball reaches 597 m and the burst sits at 600; at 335 kt the fireball reaches 624 m and the burst sits at 622. Above that, the fireball touches down.
The 335 kt W78 — the weapon the strike console fires most often at the Minuteman fields, two to a silo — is just over the line. A counterforce strike is described as the discriminate option, and at the yields actually deployed against silos the discrimination does not survive its own geometry: the burst digs, the soil goes up, and the plume goes downwind over whoever lives there. The heights of burst used here are the engine’s own rule rather than the handbook’s Figure 3.73 curves — see Section 06 — so the 323 kt figure is a modelled crossing, not a quoted one. The direction of the result does not depend on the rule.
The one chapter of the handbook that is a model rather than a set of measurements, and the one the engine leans on hardest.
DocumentedTable 9.93 is the whole pattern. The handbook gives idealized unit-time — that is, H+1 — reference dose-rate contours as downwind distance, maximum width and ground-zero width, each in the form a · Wb in statute miles, for a 15 mph effective wind with 15° of directional shear. The upwind extent is about half the ground-zero width (§9.93). Dose rates scale with the fission fraction (§9.94); downwind distances scale with wind speed by the factor at §9.97. The engine carries all eight contours of the table verbatim as data.
| Contour, 100% fission | Rate at H+1 here | Downwind | Maximum width |
|---|---|---|---|
| 1,000 rad/hr | 500 rad/hr | 25 mi | 3.0 mi |
| 100 rad/hr | 50 rad/hr | 122 mi | 12.4 mi |
| 10 rad/hr | 5 rad/hr | 328 mi | 30.5 mi |
| 1 rad/hr | 0.5 rad/hr | 547 mi | 53.8 mi |
DocumentedThe decay law, and what follows from it. §9.15 gives the dose rate as t−1.2, good to within about a quarter for two weeks. The engine computes a factor of 10 at seven hours and 107 at forty-nine, which is the seven-ten rule of chapter IX reproduced rather than asserted. Integrating that law from an arrival at one hour to infinity gives five times the H+1 rate, of which the forty-eight hours a study draws is 54 per cent. The consequence is the one that matters operationally: most of the dose anyone ever takes is taken early, so an evacuation begun after the plume arrives does not help those already under the heavy contours.
UncertainThe far contours are the least trustworthy thing the engine draws, and the book says why. This is an idealized pattern over a smooth plane in a simple wind with no rain. §9.95 states that real surfaces give 0.7 of these values in the open and 0.5 to 0.6 in rough terrain, and the engine carries the 0.7 as a terrain factor. Real patterns bend as the wind veers with height and over the hours; rain puts hotspots off the axis. By the time fallout has travelled to the 1 rad/hr contour, hundreds of miles downwind, the H+1 rate there has decayed a hundredfold. The shape at forty-eight hours is order of magnitude and general direction, and every readout says so.
Documented§9.48, and the half-truth it is usually reduced to. Air bursts produce no significant early fallout. That is not because they produce no fission products — they produce exactly as many — but because with no soil drawn into the fireball those products condense onto each other as sub-micron particles, which stay aloft for weeks or years and come down worldwide, much decayed, instead of over a county within a day. The same activity, distributed differently in space and time. The engine draws a plume for a surface burst and none for an air burst on this basis, and states the reason rather than letting the absence imply innocence.
No figureShelter is a control, not a model. The handbook gives protection factors of roughly two for an ordinary house, five for a ground-floor inner room, ten to forty for a basement and a hundred or more for a purpose-built shelter. Which of those applies to a given population is not a question the book can answer, and it is the single largest source of divergence between published casualty estimates for the same attack. The engine defaults to nobody sheltering — an upper bound, and labelled as one — and carries the protection factor as a slider so the sensitivity can be seen instead of argued about.
The gaps, stated as gaps. A model that quietly fills them is worse than one that does not have them.
UncertainOn the two editions. The 1977 third edition is the reference throughout. The 1962 second edition is used in exactly one place, for Table 12.31, because it tabulates a quantity the third edition only draws. Where the two differ on anything else, the third edition wins, and no figure in this project has been taken from the 1962 edition without the section being named.