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A calculator (that can do on-ground or airburst, psi values between 1-10,000, yields up to 100 megatons).
A formula (that can do airburst, psi value of 20, and any arbitrary yield).
Another formula (that can do on-ground, any arbitrary psi value, and any arbitrary yield).
This leaves some holes; airburst explosions for particularly high yields but psis other than 20, and airburst explosions with psi values outside of the range 1-10,000 at any yield.
Is there any way that the airburst formula can be modified to account for these cases?
I find myself unequipped to debate space usability, but for that latter one, I disagreed with the usage of 20 psi, and created this thread to get a method to use lower psi for that.
I find myself unequipped to debate space usability, but for that latter one, I disagreed with the usage of 20 psi, and created this thread to get a method to use lower psi for that.
Yeah, I thought it was a bit of a stretch too. I think it's because of an oddity in your wording.
You said "Blast wave is bad, ordinary nuke formula is better, blast wave is inapplicable here for X, Y, Z...." While those reasons, considered seriously, would apply here too, because you focused them on the blast wave, and endorsed the nuke formula as better earlier, it got interpreted that way.
If you think it was misinterpreted in that sort of way, luckily it wasn't used anywhere, so all that needs to be done is mention in the comments that the calculation is wrong.
And we may want to write something into the explosion yield calculations page about this usability topic.
A calculator (that can do on-ground or airburst, psi values between 1-10,000, yields up to 100 megatons).
A formula (that can do airburst, psi value of 20, and any arbitrary yield).
Another formula (that can do on-ground, any arbitrary psi value, and any arbitrary yield).
This leaves some holes; airburst explosions for particularly high yields but psis other than 20, and airburst explosions with psi values outside of the range 1-10,000 at any yield.
Is there any way that the airburst formula can be modified to account for these cases?
Looked into it awhile ago, no you're just kind of screwed and will require shifting to a more nuanced explosion formula for those types of feats. In which you have many options so it's not actually that big a deal, in fact a few are actually better to use over the wiki standard to begin with, but that's besides the point.
tldr, is you can't, not in any simple or honest way anyway. This shit is fundamentally hard-coded to 20 psi; you can't just tack a psi onto it and have something that is actually precise or accurate. If you want general airburst coverage (other psis, any yield), you basically have to switch to a more complete blast-scaling model, which as said, we do have many other options.
Going step by step, our formula in actuality is: Y = ((x / 0.28)^3) / 1000
with Y in megatons and x in km. Rearranged for x = 2.8*Y^(1/3)
And this shit is just the cube-root scaling law for one specific overpressure level (20 psi, "urban areas completely levelled" at optimum height of burst). It's essentially a fit to numbers like those in the classic nuclear-effects table (1 kt, 20 kt, 1 Mt, 20 Mt at 20 psi). The problem you're running into lad, is the constant 0.28 itself already has airburst, optimal height of burst and 20 psi at the ground all factored in.
The moment you change the psi, the required constants also change. There is no hidden psi variable in that formula; it's just a one-point slice of a larger 2D relationship (pressure vs scaled distance). You could in theory figure it for every other psi, but that itself would be a calculation and a half.
The physics nerds over at idc actually use scaled distance in that they often define scaled distance Z.
Z = R / W^(1/3)
where you got R = distance from burst (m or km) and W = yield (kg TNT, tons, kt, whatever, you just gotta be consistent)
For any given overpressure P, there is a corresponding scaled distance Z(P) from blast data (Kingery-Bulmash is an example I've been ******* with lately).
From there the general relationship is something like R(P) = Z(P) * W^(1/3).
Invert that shit for yield; W = (R / Z(P))^3
That's the real "basic universal" formula ngl. From that point of view, the current airburst formula is just the 20-psi special case with Z(20 psi) encoded as "2.8 km / Mt^(1/3)". I'm actually not too sure why that's the standard.
So to generalize properly for airbursts you:
Get Z(P) for the overpressure you want (from Kingery-Bulmash or similar free-air/optimum-HOB data, like ya got options here), then use the same relation: W = (R / Z(P))^3.
This works for any yield; the 100 Mt limit in the calculator is just an arbitrary UI cap, not a physics limit, it can be worked around in extreme cases with ease.
But can we solve this otherwise? Only if you're willing to accept a sus af curve-fit, and even then it's not one neat constant change so like?
The serious blast slop does exactly this: it fits polynomials in log10(Z) and log10(P) (I dont have the funny symbols on hand to copy paste so deal with the manual write outs) so that log10(P) = poly(log10 Z) based on Kingery-Bulmash data.
Then you invert or pre-fit the inverse to get Z(P).
But caveats:
The fits are piecewise over different Z ranges.
They have 5 to 10+ coefficients per range.
They're not something you can compress or half ass into "(x / (A + B log P))^3 / 1000" without throwing away accuracy.
Which basically means there is no simple "replace 0.28 with f(psi) that is still grounded in actual blast data".
If you made up some f(psi) by eyeballing a couple of points, it'd be kind of bullshit, which like tbf, we already do that a lot, but here it'd be a tad worse, it's not a real generalization.
So fixing it, airburst explosions for particularly high yields but psis other than 20, airburst explosions with psi values outside of 1 to 10,000?
Well, high yields, psi =/= 20 psi, which in physics, is no problemo. The cube-root law doesn't care if the yield is 10 kilotons or 10 gigatons or even 10 fucktillitons; you just need Z(P) from a proper data source.
So you want a practical fix? Either use Kingery-Bulmash (or Jeon's simplified version idk) as the method. Then you just like, choose P and find Z(P) from the equation/table, W = (R / Z(P))^3.
Or, you could precalc a small table of constants k(P) = R / W^(1/3) for a few standard psis (1, 2, 3, 5, 10, 20 psi) from real nuclear-effects tables, then use W = (R / k(P))^3 as an approximate shortcut for those psis only. But you cannot honestly cover all psi with one tiny tweak of the current 20-psi formula, like you're just ****** there dude, there's nothing you can do really in that specific case.
As for psi outside 1 to 10,000. 1-50 psi is the usual structural damage range; mainstream data (Kingery-Bulmash, UFC, etc.) are good to go there. While 10,000+ psi (idk why you're asking for a value so high but eh) is basically inside or extremely near the fireball; the simple overpressure shit isn't a thing you should be using, you're into complete vaporization/near-ground-zero, where people normally use energy-density / temperature shit, not overpressure charts.
If you really want to take it into account, it's gon be a multi-step calc, not a one and done quickie meme.
So for over 10,000 psi at ground in an airburst, any neat overpressure radius formula is inherently sus af. That's not a missing feature or a thing we can work with; it's just not what those were designed for.
So how we fix that shit? If by solution you mean: "Can we modify the existing Y = ((x/0.28)^3)/1000 airburst formula to handle arbitrary psi in a physically sound way?"
Then no, not without basically throwing that formula away and replacing it with a full scaled-distance model (Kingery-Bulmash or equivalent) and its polynomial fits. But in that case if you do do that, there's a few caveats but they can be worked around last I checked.
If by "solution" you mean: "Is there a way, in principle, to handle arbitrary psi and yield for airbursts?"
Then yes, but the method to use is the same scaled distance setup above: Z = R / W^(1/3), get Z(P) from a real blast equation or table (Kingery-Bulmash, UFC 3-340-02, etc.) for your psi, and solve W = (R / Z(P))^3.
That's the correct generalization and about the simplest one you can do (there's other methods and formulas obviously, I looked over dozens when I was looking into a feat for [REDACTED], but those need extra steps I doubt others wanna **** with). Anything simpler than that is necessarily an approximation and not exactly a fair one, which like, eh.
Though, there's a slight caveat here; for incident (side-on) overpressure in free air, the Kingery-Bulmash polynomials are only defined for scaled distance, where Z = R / W^(1/3) in the range 0.05-40 m/kg^(1/3).
If you plug Z = 0.05 (the closest it lets you go normally) into the official polynomial, you get about
56,600 kPa or about 8,200 psi.
That's the maximum incident overpressure you can get within the validated range of Kingery-Bulmash. Anything above that is outside the calibration region. So there is no "Kingery value" for incident pressures above 8,200 psi without extrapolating, so yeah, using Kingery as a clean plug-and-plague source for over 10,000 psi incident isn't 100% valid (reflected overpressure curves do go way higher, but that's a different quantity and still bounded by the same Z-range tho). But it's a hell of a lot better than a 20 psi cap and has far more leeway and you're almost never gonna run into a 10k psi blast anyway for calc purposes.
BUT writing this I remembered another method that works in some situations. When you get into that near-field / very high pressure shit, people stop relying on simple empirical charts like Kingery and switch to either:
1. Strong-shock similarity (Sedov Taylor type) analytic models, or
2. Hydrocodes / CFD (AUTODYN, CTH, EUROPLEXUS, etc.) with proper EOS for explosive + air, which is what the JRC near-field work does.
For our purposes, the most useful closed-form thing you can actually use is the strong-shock similarity scaling.
So from the Sedov Taylor strong-shock solution for a point explosion in air, plus the Rankine-Hugoniot jump conditions, you can easily derive P = C*E / R^3.
Which is just:
P = peak overpressure at the shock front (Pa)
E = explosive energy (J)
R = distance from burst (m)
C = 0.19-0.22 for air (y = 1.4) depending on the exact similarity constant b used.
Using b = 1 (which is common in rough engineering use), you get P(Pa) = 0.19 * E(J) / R^3(m^3)
Then you convert that into psi and kilotons of TNT: 1 kt TNT = 4.184*10^12 J with 1 psi = 6894.757 Pa.
You end up with a very simple, actually useful for once rule of thumb: P(psi) = 115000000 * Wkt / R^3, where Wkt = yield in kilotons TNT and R = distance in meters because no shit, R is like always that.
And inverted: Wkt = P(psi) * R^3 / (115000000).
This is explicitly a strong-shock / near-field approximation, now it might not be a civil engineering Kingery value, but it does give us sensible numbers well above 10k psi.
In practice, say you want:
Peak overpressure P = 20,000 psi
At distance R = 10 m
Solve for yield Wkt
You just plug in:
R^3 = 10^3 = 1,000
A numerator = 20,000 * 1,000 = 2.0*10^7
Divide by around 115000000:
A quick example would be like 20000 psi * 10^3 / 115000000 = 0.17 kilotons.
And the fyi 115000000 is just all the fixed constants into one number so the formula stays simple (you could do it the long way but it's ******* obnoxious to read).
To explain, you start from the strong-shock relation in SI units:
P = 0.19 * EJ / R^3
where:
P is pressure in Pascals,
EJ is energy in Joules,
R is distance in meters,
0.19 comes from the strong-shock / Sedov stuff for air.
Now 1 kiloton TNT = 4,184,000,000,000 Joules, 1 psi = 6,894.76 Pascals
Thus, EJ = Wkt * 4,184,000,000,000, with psi = P / 6,894.76
Plug those into the first equation and simplify; you get like: psi = 115000000 * Wkt / R^3.
That 115000000 is basically just 115000000 = 0.19 * 4,184,000,000,000 / 6,894.76.
Nothing magical or some ass pulled value, just 0.19 + Joules per kiloton + Pascals per psi all rolled into one to save everyone some time.
And then you obviously divide that shit because you're just solving that same equation for Wkt instead of psi. So the divide by 115000000 is just the algebra rearrangement of that strong-shock relation with all the constants pre-multiplied, which is basically the 20 psi bullshit we already do but like, this formula's version of that.
So working off the above example, a 0.18 kiloton free-air burst, at 10m, gives you roughly 20,000 psi at the shock front in this model.
Check against the 1 kt / 20 m example btw, just for some number consistency,
R = 20m so R^3 = 8,000, Wkt = 1, P = 115000000 * 1 / 8,000 = 14,375 psi
which lines up with the = 14k psi shit from earlier.
So if you're trying to find some shit to use above 20 psi, you got:
Kingery-Bulmash, which is aight for 1 to 8,000 psi, but don't exactly reach 10k+ psi normally; going higher is extrapolation, while near-field over 10k psi you can use strong-shock scaling.
Again, there's more too, like there's dozens of models and methods but these the simplest. But you're not gonna be able to just go over 20 psi atm with the current formula, you'll need to dip into others, just how it is.
There are but it ain't gonna be like normal given, ya know, can't exactly have overpressure without air.
Ig it depends on what you mean by space though, let's say we got 3 categories for example.
You got "True" (or near) vacuum, so like a nuke or conventional charge in space, far from any atmosphere.
Explosion in a tenuous gas, so say a supernova in interstellar medium, or energy dumped into a low-density plasma. And then real-world high-altitude / space nukes near Earth where people care about radiation environments and EMP, and use semi-analytic plus code-based models like some MGS4 shit.
But one at a time.
In a vacuum: just treat it as a radiating point source as without air, there's no meaningful blast overpressure. What matters atm is:
Radiated energy (X-rays, gamma, optical/IR)
Kinetic energy of debris / fragments / plasma
In both cases, if you assume the explosion is roughly isotropic, the basic geometry is energy per unit area at radius r: F(r) = E / (4*pi*r^2)
With each being:
E is the energy in the shit we care about (Joules)
r is distance (m)
F is energy fluence (J/m^2 or whatnot)
For a nuclear weapon for example, total energy is: E(J) = Ykt * 4.184e12
And obviously Ykt is yield in kilotons TNT.
Glasstone & Dolan (it's been awhile) note that in the first microsecond of a nuclear detonation, roughly 70 to 80% of the yield appears as primary thermal radiation (soft X-rays) in vacuum, with the rest as kinetic energy of debris. So for radiation you can take: E rad = f rad * Ykt * 4.184e12
With f rad like 0.7-0.8 (rough order-of-magnitude) btw.
So you pick a damage threshold: say you want the radius where some material receives a fluence F thresh (J/m^2) that's enough to dissolve, ablate, or fry it or whatever else ya want.
You can then do:
F thresh = E rad / (4*pi*r^2)
Then you solve for r via r = sqrt(E rad / (4 * pi * F thresh))
Then you plug that shit for E rad: r = sqrt(f rad * Ykt * 4.184e12 / (4 * pi * F thresh))
So if you're willing to assume some benchmarks, which we already literally do for our current blast formulas (such as the psi values, basically just reasonable values that fit the feat and context), that being isotropic radiation, some fraction f rad of the yield in that band, and a material-dependent threshold, you can get a space kill zone for radiation. Note the scaling tho: r ∝ sqrt(Y) for a fixed fluence threshold.
That's very different from atmosphere blast overpressure, which gives r ∝ Y^(1/3).
Alternatively, kinetic / debris flux in vacuum might work. Same geometry if you treat the debris energy as a "kinetic fluence", in which you:
Let E kin be total kinetic energy of fragments/plasma, at radius r, average kinetic energy per unit area (which would look kind of like): Fkin(r) = E kin / (4 * pi * r^2).
If you care about penetration (lol), you might instead track: Total fragment mass, typical fragment speed, with number of fragments.
Simplest isotropic model would be: mass per unit area at r: mu(r) = M frag / (4*pi*r^2)
Plus kinetic energy per unit area: F kin(r) = (1/2) * M frag*v^2 / (4*pi*r^2)
Same 1/r^2 again. To get actual component damage tho you need: target area, material strength / areal density, and how you map that shit to "X J/m^2 of KE in lumps" to holes/penetration.
So for pure vacuum you're basically doing 1/r^2 and thresholds.
Shit you need boils down to:
Yield Y (or total energy E total)
Fractions into channels: f rad, f kin, etc. (design dependent, nuke vs HE)
Threshold fluences F thresh for whatever shit you care about
For dose, electronics failure, etc: stopping powers, material thickness, etc.
Now there's other options, but this ong might be the least pain in the ass.
But, say, explosion in a medium: Sedov-Taylor blast wave type deal, in that if there is some gas, like an interstellar medium, upper atmosphere, plasma, etc, and you're far enough in time that a shock has formed and energy losses are small, dudes use the Sedov-Taylor blast wave solution (Taylor von Neumann Sedov or whatever tf his name was) last I checked.
For a point explosion of energy E in a uniform medium of density rho, the shock radius is:
R(t) = beta * (E / rho)^(1/5) * t^(2/5) and the shock velocity is V(t) = dR/dt = (2/5) * R / t
So like:
E = explosion energy (J)
rho = ambient mass density (kg/m^3)
t = time since explosion
beta is a dimensionless constant at about 1 that depends weakly on the adiabatic index gamma (for gamma = 5/3, beta to 1.0-1.2 depending on convention) this bit is a tad beyond me tho atm, I haven't looked too deep into space stuff outside of wanting to calc some ZoE/Xeno slop.
But as examples, it'd be used for supernova remnants expanding into the interstellar medium or explosive waves from point explosions in gas in general, once you're past the very early free expansion phase of the blast, that is.
The big differences vs vacuum is this needs a medium: density rho, possibly cooling, magnetic fields, etc, whatever, you got a shit ton of options so it's decently versatile. And that it describes a shock front with pressure, density, and temperature jumps behind it.
To use this formula you need:
Total energy E you actually want in the blast wave (for nukes in high atmosphere, that's the portion that couples into the gas, not the whole yield obv).
Ambient density rho (for ISM: rho = n * m p; n in cm^-3).
Assumption that radiative losses are small (energy-conserving phase or whatever).
Anyway, from R(t) and the shock jump conditions, you can derive post-shock pressure and density profiles; that's what astrophysics and blast-physics papers do all the time, so like, you could use this to calc something like Cooler blowing up a star or something.
And then we got high-altitude / space nukes near Earth. For actual high-altitude nuclear explosions (HANE), things are a bit more ass:
Weapon goes off in thin air / near vacuum.
Soft X-rays and gammas stream out, dump energy into the upper atmosphere along their paths.
That heated atmosphere layer expands and drives shocks.
Gamma + geomagnetic field interactions create EMP (E1, E2, E3).
Ya'll can look up Glasstone & Dolan, "The Effects of Nuclear Weapons", to read more, given it has specific chapters on high-altitude and space bursts and EMP. I was looking into calcing Ocelot nuking JD from 4 so like, yeah.
But crucially: there is no single nice closed form formula the way there is for Sedov-Taylor or 1/r^2 fluence. Instead, goons use shit like radiation transport + hydro codes for X-ray/gamma deposition in the atmosphere (ATR, FLAIR codes) and EMP models like Meta-R-320's E1 EMP theory, which start from gamma-ray yield and directionality and integrate the induced currents to get peak fields.
The "formulas" you can actually write as a meme shortcut are mostly:
A. Energy partition / dose in HANE
Again, Glasstone & Dolan give energy partitions like:
Fraction to prompt gammas fgamma
Fraction to X-rays fx
Etc. as a function of altitude and design.
Then you still use 1/r^2 for fluence in the absence of scattering even still: fluence(r) = (f channel * Ykt * 4.184e12) / (4 * pi * r^2)
Then an extra step where you convert that to dose or fluence in particles using cross sections and material properties.
A braindead simple example would be like:
Photon energy be like E ph (J per photon).
Let mu en / rho be the mass energy-absorption coefficient of the material (m^2/kg).
Photon fluence Phi (photons/m^2) at r: Phi(r) = N_total / (4*pi*r^2)
Dose D (Gy = J/kg) roughly: D ~ (muen / rho) * Phi * E ph
Obviously, real codes integrate over spectrum and angles and all that fun shit, but conceptually that's what they do.
And then ya got B, which is EMP formulas (very rough because I haven't looked too deep into this one yet)
But uh, for the early-time E1 EMP, there are semi-analytic expressions of the form apparently:
"E peak ~ k * (Y eff / h) * f(geomagnetic latitude, line-of-sight)".
Where k is a constant with units, Y eff is gamma-ray effective yield, and h is burst height. The exact forms are messy and depend on the detailed model according to things like Savage et al. or Sandia; Taylor 1965.
In practice tho, governments and labs don't use a one-line formula; they use precalced parameter manuals and EM solvers that take:
Burst yield and height
Gamma-ray spectrum and angular distribution
Geomagnetic field model
Atmosphere density profile
and then vomit out peak fields vs location.
So what options do you actually have? If you want to do reasonable calcs for explosions in space and you can't do the usual wanky KE method, the standard tldr is:
1. Pure vacuum, no medium:
Use 1/r^2 geometry.
For each channel or whatever you want to call it (X-ray, gamma, kinetic debris), do:
E channel = f channel * Ykt * 4.184e12
F(r) = E channel / (4*pi*r^2)
And then solve for r where F(r) hits your chosen threshold F thresh.
This gives you "kill radii" for heating, ablation, electronics slop, etc, you get it.
2. Explosion in a gas/plasma (space but not vacuum):
If it's a point-like, short explosion and the medium is roughly uniform and energy-conserving:
Use Sedov-Taylor which as above: R(t) = beta * (E / rho)^(1/5) * t^(2/5).
Then use shock jump conditions to get pressure/density behind the shock.
Lastly, 3. High-altitude nuclear near Earth (real HANE):
For detailed stuff (EMP, belt formation, ionization profiles), you're realistically in code slop: radiation transport + MHD simulations (ATR, FLAIR, DNA codes, etc).
But you still fall back to: energy partition fractions from Glasstone & Dolan, 1/r^2 for fluence, maybe Sedov-Taylor for any shock in the residual atmosphere.
So yeah, there are formulas but that shit ain't blast wave based anymore.
tldr:
Vacuum: E / (4*pi*r^2) type stuff, plus material thresholds.
In a medium: Sedov-Taylor R(t) = beta*(E/rho)^(1/5)*t^(2/5).
High-altitude nukes: combo of those plus specialized EMP and radiation-transport models.
But uh, I guess for actual proof of concept I should show it in action. But I don't wanna I wanna play Metroid
And if ya'll like none of that shit, you got even more options, off the top of my head you have
For Air Blasts (Atmosphere):
Kingery-Bulmash (KB), good airbursts, roughly 1 to 8,200 psi, free-air or surface bursts. And it's the most trusted empirical dataset. Just the polynomial fits in terms of scaled distance for accurate peak pressure, impulse, etc, I explained this already.
Glasstone & Dolan curves. Decent quick reference for nuclear effects from about 1 kt to 20 Mt. And like, right from U.S. government nuclear-effects manuals. Gives tables/curves for multiple effects (overpressure, thermal, radiation, etc).
Brode's method, which is a simple spherical blast, rough 1 to 1000 psi estimates. Now this one is old but still decent for HE. A common form is P_psi = 0.975 / Z + 1.455 / Z^2 + 5.85 / Z^3 - 0.019, where Z is scaled distance in ft/lb^(1/3). Which is disgusting non metric units so secretly don't use it...
Sadovsky's formula, good conventional HE in air (TNT equivalent), especially mining/construction blasts.
Friedlander waveform model, which is best for pressure vs. time histories (not just peak psi), it lets you calc impulse, which matters for structural response, debris, glass breakage, etc, that type of shit.
UFC 3-340-02 / TM 5-1300, which is good for structural hardening, military design, protective structures, plus it contains curves and methods for reflected pressure, impulse, clearing effects, etc. Very useful for walls, bunkers, buildings and those types of feats.
For Very High Pressure / Near Field (over 10,000 psi)
Sedov-Taylor strong shock, already explained.
Gurney equations, aight fragment velocity from cased explosives. Good for bomb in a room or frag grenade–type effects when you give a shit about fragment speed rather than airblast. An example:
V = sqrt(2*E*(C/M) / (1+0.5*C/M))
V is fragment velocity, E is Gurney energy per unit mass of explosive, C is explosive mass, M is casing mass.
Though knowing this wiki people would just use KE which is like, aight Ig.
Jones Wilkins Lee (JWL) EOS, which is for high-fidelity modeling of detonation products and near-field blast. It's used inside hydrocodes (AUTODYN, CTH, etc). Ngl idk when this would come in handy, but needed when you want detailed pressure/volume behavior of explosive gases, so there's that, can't think of many feats that might use it tho.
And **** it, for underwater slop given I need to calc Pet Shop's feat eventually so may as well.
Cole's equations is useful, it's used for underwater nuclear/HE explosions. Classic empirical relations for peak pressure and decay. A typical peak-pressure form: P = K * ( W^(1/3) / R )^A.
Obviously P is pressure, W is charge weight, R is distance, and K, A come from data stuff and is dependent.
Geers-Hunter model, decent pressure-time history in water, it captures primary shock and bubble-pulse behavior, including gas cavity oscillation. Hell if I know why you'd use this over others but it's there.
Swisdak's (DDESB) charts is good for underwater safety distances for HE, plus it's based on actual test data for TNT and used for Navy/DoD safety standoffs.
For Ground Shocks / Cratering, which we'd prob never use given there's other viable common methods that would apply but eh
Depth-of-burst (DOB) scaling. Crater size from buried or surface bursts. It's a simple empirical relation like:
D = k * W^0.3, where D is crater dimension and k depends on soil/rock type. It's braindead, but we already have arguably just as good methods in play already.
Kinney & Graham, which is surface-burst airblast modified by ground reflection. It includes height-of-burst and reflection effects; bridges free-air to surface-burst behavior.
ConWep (US Army tool) fast standardized blast parameter predictions. But it implements Kingery-Bulmash and related models. Basically a half ass for airblast, reflected pressure, impulse, etc. Tbh you may as well use the actual formulas if you resort to this, just mentioning it for completion.
For Space / Vacuum
Inverse-square radiation, X-ray, gamma, or debris energy flux in vacuum. No air = no overpressure; damage is set by energy per unit area, I already explained this above, not doing it again.
Bethe-Bloch / stopping power. Energy deposition of charged particles in shields or materials. Needed for radiation damage to electronics and human tissue shit; tells you dose vs. material thickness. Pretty niche tho.
PLUS / HANE-type models (EMP slop)
High-altitude / exo-atmospheric nuclear bursts (EMP, trapped belts). Not exactly wiki friendly tho, but approximate rules exist where Y is yield and h is burst height, for early-time E1 EMP scaling.
For Exotic / High-Energy Feats you got uh
Taylor von Neumann Sedov. You'd use this for like supernova remnants, hypervelocity impacts, large point blasts in a uniform medium. It's a universal point-blast scaling too so that's nice.
Wong's radiation pressure model. You'd use this for photon propulsion, laser-driven ablation pressure, "light-based pushes". Relates light intensity/flux to pressure:
P = F / c (perfect reflection)
P = 2*I / c (for absorption/interaction)
F is radiant flux, I is intensity, c is speed of light. I legit ong can't think of a feat this would be used for though Except I just did, Metroid has like 3 things.
Gaussian energy deposition (pulsed lasers)
Beam weapon spot heating / vaporization shit. You either solve transient heat diffusion or compare fluence to a threshold (like Chaloner Goldman) to see if a material liquifies or ablates.
Personally, I'd do shit like this in cases the baby basic formula don't suffice.
Air blast, standard damage range (about 1–1000 psi)?
Use Kingery-Bulmash or Glasstone & Dolan.
Extreme close range, vaporization / near fireball, or over 10,000 psi)?
Use Sedov strong-shock scaling.
Underwater explosion? Cole's equations or Swisdak charts.
Explosion in vacuum / space?
Use inverse-square radiation with a relevant fluence threshold.
Your ass needs pressure–time history for structural damage?
Use Friedlander waveform or UFC 3-340-02 methods.
Don't want to do the math yourself because you're lazy af?
Don't. Actually do the work, but for argument's sake, use ConWep, but like, don't do that.
If Kingery-Bulmash feels excessive for your specific meme tho, these could work too:
Glasstone & Dolan tables (for nuclear airbursts), Brode / Sedov strong-shock (for very high-pressure, near-field), inverse-square radiation (for vacuum / space stuff).
But if you want accurate numbers across lots of scenarios, then KB polynomials + scaled distance (Z = R / W^(1/3)) is still the actual standard for airblast. Everything else is a special-case approximation layered on top of that shit and is case by case for when they'd apply so it just depends on the feat and context tbh. Assuming cases were our wiki's meme formula doesn't work right.
ALSO I ASKED TO POST, plus this shit took like 2 hours to write up and I had to dig for some old af pdfs be appreciative I also trimmed this, it was longer originally
You're right that stuff above 10k psi seems incredibly niche, I was more interested in stuff lower than 1 psi. We've got the nice 0.15 psi end for shattering window glass, but I ended up creating this thread hoping for an airburst value where the "shockwave" measured was merely shown jostling some clouds, and people still defaulted to 20 psi.
If the relevant papers decided not to bother going lower, that'd be quite unfortunate.
It's unfortunate to see (but makes sense that) space-based stuff seems to rely on either knowing the yield energy (while we'd usually be trying to find this), or knowing heating/radiation at a particular radius (which fiction would rarely ever establish).
In practicality, I think most of these cases would have to just fall to KE or inverse square.
I do wonder if we could hack something together. Going from previous similar talks we do often assume psi values of 20 at the frontier of explosions based on visuals which imo we see replicated in space-based feats. So could we tack the energy fluence that implies onto inverse square and say that works for these cases?
Just woke up, not really writing this in a fancy way, maybe clean it up later, anyway, for low shit the current formula still doesn't work, like being real, it's only for 20psi, we shouldn't even really be doing what we do with the other psi in the first place ngl.
KB in its normal engineering use, is good down to roughly 0.1 to 0.2 psi though as a ballpark.
Well, some extended standards (like DDESB/BEC-O) do push scaled distance further and implicitly go below 0.1 psi so there is actual values that do exist that can be plugged, but that’s not common for structural-damage work and the uncertainty goes up, for the wiki it could work as a rough approximate ballpark if we really wanted to **** with that so worse comes to worst, still got a decent option.
But at that low of value, realistically though, dudes usually stop calling it a "blast" and switch to acoustic / wave-propagation shit. As at that low of values it's not even really a proper blast wave anymore so you deal with it differently to begin with.
For example, at tiny overpressures (down around 0.1 psi or less), the disturbance is basically just sound. The nonlinearity is negligible (most explosive formulas deal with nonlinear slop hence the difference), and the wave obeys linear acoustics instead.
Wave-propagation models treat the thing as a sound wave that obeys the normal wave equation, has amplitude that drops with distance (1/r for spherical waves), has intensity related to pressure by standard acoustic relations. So instead of Z = R / W^(1/3) or the meme 20psi formula and blast tables, you use:
Speed of sound c
Air density rho
Acoustic intensity I
Energy / power spreading as 1 / (4*pi*r^2)
A rough example would for a simple spherical sound wave would be like
p peak = peak overpressure (Pa)
p rms = root-mean-square pressure (Pa)
rho = air density (kg/m^3), about 1.2 on average, but can change with context, take very important note of this though, I'll give a quick constant later down but if the feat differs, you change this, it's like doing a cloud feat without taking into account thinning, ya gotta.
c = speed of sound (m/s), about 343, obviously it changes depending on context like rho.
So say p rms = 0.7 * p peak (for a simple pulse / sinusoid), intensity I (W/m^2) = p rms^2 / (rho*c), acoustic power so P acoustic (W) = 4 * pi * r^2 * I (for spherical spreading), acoustic energy in the pulse would be E acoustic (J) = P acoustic * duration.
(in case you're wondering, 0.7 is just rounded from p rms = peak / sqrt(2) = 0.707).
So in practice, assuming you want some pissweak blast wave that jostled clouds, and you want to model something way below normal blast tables, say at r = 2000m, the peak overpressure from the feat is only psi = 0.01 psi (about sonic boom lv).
Treat it as a spherical acoustic pulse and ask what acoustic power/energy does this shit correspond to?
Well going step by step so people get what's happening, values rounded a bit, if you want more precision in a real calc simply don't round wen you do it.
First intensity:
psi = 0.01
1 psi = 6894.76 Pa
peak = P psi*6894.76
peak = 0.01*6894.76
peak = 68.9476 Pa
I = p rms^2 / (rho*c) = 48.26^2 / (1.2*343) = 5.66 W/m^2
Ok next acoustic shit at distance:
r = 2000m
P acoustic = 4*pi*r^2*I
r^2 = 2000*2000 = 4000000
4*pi*r^2 = 4*3.14159*4000000 = 50265472
P acoustic = 50265472*5.66
P acoustic = 284000000 W (which is like 284 million watts of acoustic power)
Need time though but that's easy to get in most cases so say, duration = 0.1s
E acoustic = P acoustic * duration
E acoustic = 284000000*0.1
E acoustic = 28400000 J
For tons of tnt, 1kg TNT is 4184000J so real quick
E acoustic / 4184000 = 28400000 / 4184000 = 6.8 kg TNT
Regardless:
A pulse that is only 0.01 psi at 2 km
Which lasts like 0.1 seconds
Is about 9-A for acoustic energy and only barely
Assuming 100% of the explosion’s energy went into sound (obviously this is a minimum, some energy would be dumped into the actual EXPLOSION part of things but, ya know, you're asking for overpressure specifically, this would be an approximate for the overpressure itself).
You basically switch to acoustic/wave-prop models, and stop treating it as "blast that breaks shit" and start using the sound-wave formulas (pressure, intensity, power, energy sequence) instead of blast tables and formulas.
For wiki though, I'd only ever dip into this under 0.1 to 0.2 psi, which at that point you’re kinda better off either ignoring it from a blast standpoint, or mapping it through acoustics, like this if you really want a number for that facet specifically for whatever reason (which as you can tell, the values kind of dogass, 2km boom to daze the weakest Robin...).
Ig I'll write up a quick shortcut formula for whoever wants it. I already elaborated a tad more above but ya need a constant.
EJ = K(rho, c)*P psi^2*r^2*t is a general equation for it.
Here's a standard value for general air, so 90% of calcs would use this. Already said what the shorthands mean so not doing it again.
K constant = 4*pi*0.7^2*6894.76^2 / (rho*c) = 711162.56 (For this, rho is 1.2 and c is 343).
Which you can then just use as a shortcut, obviously if the air pressure, c and all that is different for a specific feat, just plug in new values for the new constant, it's not hard and takes not even a second.
Which gives a general quickie as 711000*P psi^2*r^2*t.
Psi is psi obviously, r is distance, and t is time pulse duration, plug that in and you get a rough energy value for you weak overpressure.
Same values in the step by step obviously just a tad more precise; 711162.56*0.01^2*2000^2*0.1s = 28446502.4 joules, or about 6.8kg of TNT as said, same result, quick meme version.
There's other methods of course, but this one is easy af if you really want a formula for extremely weak overpressure, this is what most science goons use below a certain threshold after all.
Just woke up, not really writing this in a fancy way, maybe clean it up later, anyway, for low shit the current formula still doesn't work, like being real, it's only for 20psi, we shouldn't even really be doing what we do with the other psi in the first place ngl.
I mean DontTalkDT already pointed out that the airburst formula we got was just us reverse-engineering Nuclear Secrecy's nuclear formula using the 0.28 constant used for 20 psi. There are other constants for other psi values, albeit just the most common ones (1, 3, 5, and 10 psi).
I had previously tried working it out with stuff outside of the constants listed. Imo, it's less of a "hard coding" issue as it is an issue of answering the question "how the hell did they come up with the constants in the first place?" The source blog was initially grabbed by the OBD, but I don't think they exactly pinned out what goes in there at the time. If it comes down to a bunch of calculus, all I can really say to you and everyone else in the wiki is "Good luck with that one, buddy!" because I can hardly think about anyone particularly inclined towards that field.
I mean DontTalkDT already pointed out that the airburst formula we got was just us reverse-engineering Nuclear Secrecy's nuclear formula using the 0.28 constant used for 20 psi. There are other constants for other psi values, albeit just the most common ones (1, 3, 5, and 10 psi).
Well he just explained how to get other constants for airburst, the exact science behind it, and explained why theres an issue with the current way we do it so like... so I'm a bit confused since this reply doesn't really touch up on any of what was said in a meaningful way
