To-Hit Physics

Angular size, dispersion, wind, lead error and visibility — modelled from real physics.

Angular size is the whole system

Every to-hit calculation reduces to one question: how large does the target appear, compared to how badly the shot scatters?

theta (mrad) = 1000 × size (m) ÷ range (m)

This is what makes the scales interrelate. Angular size is scale-free, so one equation covers a rifleman and a capital gun — there is no separate math for infantry and for ships. A human at 100 m and a frigate at 10 km are the same shot: a hundred times larger, a hundred times further, identical angle.

Careful with the claim, though: equal angular size means equal difficulty for the weapon dispersion term only, which really is range-invariant. It does not survive the environment — wind error grows with range, lead error grows with time of flight, and atmospheric distortion over 10 km is nothing like 100 m. This is a statement about the geometry of aiming, not a promise that scale never matters.

Both axes are logarithmic, so every line has the same slope — angular size falls off identically for everything. Any horizontal line you draw crosses engagements of equal difficulty. A standing human at 250 m is exactly as hard to hit as a capital ship at 300 km.

Hit probability

Targets are rectangles, not circles. A separable Gaussian over the presented profile:

P(hit) = erf( w ÷ 2√2·σx ) × erf( h ÷ 2√2·σz )

Fire control doesn't just tighten dispersion. It measures crosswind and tracks target motion, so it removes part of the bias terms too — which is most of what it buys.

Where the error actually comes from

The most common mistake in combat modelling is over-weighting the weapon. Its dispersion dominates at close range and becomes almost irrelevant past it — the shot is lost to wind you misjudged and range you estimated wrong, not to the rifle.

Trained rifleman, 10 m/s crosswind, 5% range error. Shares are of variance, since independent errors add as squares. Weapon dispersion falls from 88% of the problem at 100 m to 1% at 1200 m.

Movement and evasion

Lead error is bounded by what a target can physically do: displacement from a predicted path cannot exceed ½·a·t². Target Numbers at 500 m, stabilised autocannon.

What guidance actually buys

Against a jinking fighter at 500 m:

Guidance wins on two counts: it tightens dispersion and it corrects during flight, removing the lead-prediction error that dominates against a manoeuvring target. Notice how the unguided weapons converge — against a hard-manoeuvring target, precision stops mattering because the kinematic bound dominates. That is why point defence, ECM and decoys are the real battle: they attack guidance, not accuracy.

Suppression does not need hits

It needs near misses — which is exactly the low-probability fire a hit-only model throws away.

Crosswind drift at 500 m

Drift follows the lag-time rule — the gap between real and vacuum flight time, not flight time itself. But drift is a systematic bias, not random scatter: shooters dope it and fire-control computers measure it, so only the uncompensated residual hurts.

Light-speed weapons take no wind penalty at all — a real tactical difference, not a genre convention.

Visibility

Sensors recover most of the penalty, which is why they dominate real engagements and why sensor damage matters so much.