Real-World Reference Constants
Findings from a survey of published combat research, operational analysis, and engineering data. Only what changes the design is recorded here — the full survey is far larger.
Every figure is from published or declassified sources and was cross-validated where possible. Where the underlying data is classified, unverifiable, or contested, that is stated. Numbers we adopt still get re-derived through our own models; nothing is transcribed into rules.
The fourteen things models usually get wrong
Ranked, and checked against C.A.T.S. as it stands.
| # | Error | C.A.T.S. status |
|---|---|---|
| 1 | Over-weighting weapon dispersion. It is a ~4% contributor for infantry at combat range | Clear. Measured: 88% of variance at 100 m, 17% at 500 m, 5% at 800 m, 1% at 1200 m |
| 2 | Treating wind drift as wind × time instead of wind × lag time. Over-predicts by 76% at extreme range | Clear. We use the lag-time rule |
| 3 | Using a drift exponent of 2.0. It is 2.1 inside 500 m rising to 2.4 beyond | Clear — emerges from the drag model rather than being assumed |
| 4 | Missing the exposure-time gate. Rounds available ≈ (t_exposed − 1.77 s) / 3.5 s | NOT MODELLED. A 2-second pop-up yields essentially zero aimed shots |
| 5 | Under-weighting range estimation. Irrelevant inside 400 m, dominant beyond 700 m | Clear. Ours crosses over at ~800 m |
| 6 | Applying the cosine rule to long-rod penetration. Effective thickness rises as cos^(−0.776)θ, slower than geometry — which is why modern tanks abandoned sloped glacis | Not yet modelled; matters for armour |
| 7 | Believing thermal sees through fog. Mid-wave IR barely beats the naked eye; only millimetre-wave genuinely penetrates | We have this wrong. Our visibility table gives thermal a flat recovery |
| 8 | Modelling a pilot as a fixed g ceiling rather than a depleting resource | Not yet modelled |
| 9 | Using advertised missile maximum range instead of the no-escape zone | Not yet modelled |
| 10 | Treating kill-probability errors as linear. They compound as (1−Pk)ⁿ | Relevant once we have multi-shot |
| 11 | Ignoring detection asymmetry. ~80% of aircraft losses were to pilots unaware they were attacked — the same figure from 1917 to 1991 | Not modelled, and it should dominate |
| 12 | Modelling space stealth | Clear. We already treat it as thermodynamics |
| 13 | Letting kinetic weapons fly unguided | Clear. Our lock-required threshold captures this |
| 14 | Modelling training as an accuracy multiplier | Directly affects OQ-25 — see below |
Training is not an accuracy multiplier
This is the most counter-intuitive well-supported finding in the survey, and it lands squarely on OQ-25 (how skill enters the roll).
| Condition | Expert vs average dispersion |
|---|---|
| Controlled range, unhurried | 1.5-1.6x |
| Time pressure, 3-second exposures, 100 yd | 1.7x |
| Time pressure, beyond 200 yd | 1.0-1.25x |
Under rapid fire against randomly presented targets, expert performance declined while average performance did not. Police data agrees: after 200+ comparisons of combat hit rate against range qualification score, no relationship was found.
Real-world combat hit rates run 17-19%, and drop to 18% when the target is shooting back versus 34% when it is not.
The mechanism is identified and it is not tremor: under threat, shooters execute significantly shorter goal-directed eye fixations, leaving less time to fine-tune the shot. It is a visual-attention failure. Critically, it is trainable — officers trained under anxiety stopped degrading, while controls did not.
Design consequence for OQ-25. Skill should have a large effect on time-to-first-shot, rate of aimed fire, and target discrimination, and only a modest effect on dispersion — roughly 1.7x at short range decaying toward 1.1x at long range. A flat "skill adds to the roll" model contradicts the data. The interesting resource is tempo and attention, not steadiness.
Suppression, with real numbers
Directly actionable for OQ-26, which the coverage survey already flagged as the most important missing military mechanic.
Measured suppression probability as a function of how far the round misses by:
| Miss distance | Probability the target is suppressed |
|---|---|
| 0.7 m | 90% |
| 6 m | 50% |
The published relationship is logarithmic in miss distance. Two things follow that matter more than the curve itself:
- Suppression does not require hits. It requires near misses, which is exactly the low-probability fire our lock threshold currently deletes.
- Volume matters through opportunity, not accuracy. At ~2% hit chance per round, 114 rounds are needed for 90% confidence of one hit — and most rounds fired in real engagements are suppressive rather than aimed.
Instrumented data gives 495 rounds per casualty for a machine gun in ambush and 1,310 in a bunker assault. The widely repeated "50,000 rounds per casualty" figure is a gross overestimate and should not be used.
Tempo constants
Three independent derivations converge on the same number, which is unusual enough to trust:
| Measure | Value |
|---|---|
| Minimum response time facing a threat | 1.5 s |
| Computed detect-decide-acquire-settle-break latency | 1.55 s |
| Measured lag to acquire and swing onto a new target | 1.77 s |
Use ~1.5-1.8 s as the universal "notice a new thing and put a round on it" constant.
Related: aimed semi-automatic fire runs 3.0-3.5 s per round in field conditions, not the ~1 s achievable against a known target. Combined with the constant above, rounds available during a brief exposure is (t_exposed − 1.77) / 3.5 — which is zero for any exposure under about two seconds.
Human factors
| Factor | Effect |
|---|---|
| Sleep deprivation | 17 h awake ≈ 0.05% blood alcohol; 24 h ≈ 0.10% — legally intoxicated. Roughly 0.004% BAC-equivalent per hour awake between 10 and 26 hours, accelerating non-linearly |
| Load carriage | A single 30-minute loaded march raised radial dispersion by 36% — comparable to dropping one firing position. The penalty persists for minutes after movement stops |
| Perceptual distortion under fire | Diminished sound 84% · tunnel vision 79% · acting on automatic 74% · time distortion 62% |
| Combat stress endurance | Infantry become combat-ineffective from cumulative stress in 60-240 days. Forward treatment returns 90% to duty within 72 hours; rearward treatment only 40% — evacuation is itself the damaging step |
The widely cited heart-rate bands for performance collapse are contested and should not be used as calibrated thresholds. The phenomenology above is well replicated; the specific numbers attached to it are not.
Lethality
| Mechanism | Time to incapacitation |
|---|---|
| Central nervous system hit | Instantaneous — the only reliably immediate stop |
| Complete cessation of cerebral blood flow | 10-15 seconds of wilful action remain |
| Massive haemorrhage without CNS involvement | Seconds to minutes, highly variable |
| Extremity hit | Often non-incapacitating |
The 10-15 second figure is the single most important number for small-arms lethality. Even a heart-destroying hit leaves a target able to act, and to shoot back, for about ten seconds. A system where a fatal hit ends participation immediately is modelling something that does not happen.
A head is roughly a quarter the height of a torso, so at any given dispersion its hit probability is about 6% of the torso's. Deliberate CNS targeting is not viable beyond very short range.
Sensors and obscurants — where we are currently wrong
| Finding | Consequence |
|---|---|
| Mid-wave infrared in fog is barely better than the naked eye. Long-wave retains a modest edge. Only millimetre-wave radar genuinely penetrates | Our visibility table gives thermal a flat 75% recovery in all conditions. That is wrong for fog specifically |
| Attenuation in thick fog: infrared ~100 dB/km vs 94 GHz ~3 dB/km | Roughly 33x better for millimetre-wave |
| Legacy smoke is transparent to thermal. At a screening density that blocks 99.97% of visible light, it blocks only 33% of long-wave IR. Multispectral smoke is required to defeat thermal | Smoke needs to be at least two materials, not one |
| Night-vision detection range scales as roughly illuminance^0.25-0.3, with a performance cliff below quarter moon | Gives us a real curve rather than a binary |
| Thermal crossover at dawn and dusk flattens the scene for 30-90 minutes twice daily. Optical observers outperform thermal in exactly those windows | A recurring, schedulable tactical window |
| Vegetation strongly favours thermal (47% vs 22% detection); open mixed terrain favours optical (58% vs 24%) | Terrain should select the sensor, not just modify it |
Space
| Finding | Consequence |
|---|---|
Radiator area = P / (εσT⁴). Halving radiator temperature multiplies area by 16 | Waste heat is a geometry problem, not a bookkeeping one |
| Carnot: efficiency and stealth are directly opposed. The high-efficiency cycle is the one with the enormous, fragile radiator | A genuine, physically forced design tradeoff |
| Radiators are large, thin, and impossible to armour. Adding 100 kg/m² of armour to a 1,960 m² radiator adds ~196 tonnes — likely more than the rest of the ship | Radiator sniping should be a dominant tactic. Track radiator area as its own hit location; losing a fraction forces a proportional power derate or a heat-sink countdown |
| Laser effective range ∝ √P · D / λ | Aperture beats power. Quadrupling power doubles range; doubling mirror diameter also doubles range, for far less mass and no extra waste heat. Any physically literate navy builds huge mirrors, not huge reactors |
| Beams are limited by intensity, not light-lag — by a factor of ~120 | Laser range is a power and aperture problem |
| Above ~3 km/s closing speed, a plain rock beats high explosive per kilogram, and the advantage grows as v² | Chemical warheads survive only for fragmentation patterns |
| Whipple shielding works by dispersing rather than stopping | Armour in space is spaced armour; the counter is a longer rod or a swarm |
| Plane change costs ~0.135 km/s per degree in low orbit. A 90° change costs more than reaching orbit | Cross-plane engagement is a multi-hour to multi-day strategic decision, not a manoeuvre |
| Displacing 100 km costs 1.16 m/s a day out, but 1,667 m/s in a minute | See below |
| Every breakup generates hundreds to thousands of fragments, each lethal | Orbital combat is strategically self-defeating: sinking a ship denies the enemy a ship, killing a satellite denies everyone the orbit |
The tension that should define space combat: you can be quiet and predictable, or loud and unpredictable, but never both. Slow unpredictability is nearly free; fast unpredictability is ruinous and every burn is a thermal flare. Not stealth, not armour — this trade.
Balance constants
| Constant | Value |
|---|---|
| Ceiling on quality substituting for quantity | 3:1. Even an elite formation with a per-sortie lethality edge over 20x achieved only 9:1 exchange, against a theoretical break-even near 3:1 |
| Detection asymmetry in air combat | ~80% of losses were to opponents who never saw the attacker — stable from 1917 to 1991 |
| Real combat hit rate, small arms | 17-19% |
The 3:1 ceiling is the most useful single balance number found: no amount of unit quality should let a force beat odds worse than about 3:1.
What is genuinely unknowable
Recorded so we do not chase it. All classified or unpublished: service armour-penetration figures (open estimates for the same round span 590-840 mm), thermal sight detection ranges, composite armour construction, all stealth-aircraft radar cross-sections, radar Doppler notch widths, and modern beyond-visual-range missile performance against a manoeuvring, jamming peer — for which zero public data exists, because every combat kill on record was against a non-manoeuvring, often unaware target.
Several widely repeated figures also trace to folklore rather than sources, including aircraft gun dispersion in mils, common rifle dispersion figures that trace back to game data, and the "ratio of fire" claim that a minority of soldiers fire their weapons — which is contested to the point of probable fabrication, though a participation rate below 100% is corroborated independently. Model the direction, not the magnitude.