[Eukie]

It is generally considered easy to spot something at the example 100 yards, but it should be remembered that this typically includes a search period.

The probability that a human eye's saccades passes over the object-of-interest can be given by the equation:

P(look at) = 1 - exp(-700/G*A_f/A_t*t)

Where A_f is the angular size of the eye search field, A_t is the angular size of the region being searched in, t is the search period in seconds, and G is a factor accounting for the environment typically equal to 10. The field of view of the eye that's actually active in searching/spotting is about 5 degrees wide. The full human field of view is 180 degrees horizontally and 135 degrees vertically, though for targeted searching this can be made smaller. This assumes the object being searched for is narrower than 5 degrees - for large objects replace A_f with the angular width of the target.

This is for a random search; trained searching makes the movement of the eyes less random, allowing for about a fourfold increase in searching efficiency.

In GURPS terms, most measurements are logarithmic, so the angular widths searching time, searching efficiency, and environmental factors can be described in terms of additive and subtractive factors, and the 3d6 curve roughly corresponds to the 1-exp(x) probability curve.

What makes visual search so "easy" in real life is that we usually have time to spot things, and furthermore, that movement will trigger the eye's wider field of view, greatly increasing A_f and the ability to spot in general. To account for the increased detectability of moving targets, multiply t by a factor (1+0.45*v)^2, where v is the angular velocity relative to the eye, in degrees per second. Sudden changes in brightness are also easy to spot because they benefit from more of the field of view.

In addition to this, there are two more factors to account for; when the eye passes over the target, it must be distinguished from the background, and when distinguished, it must be recognized.

The former depends on the target's contrast against the background; this is where darkness and camouflage comes into play. When a target has no contrast against the background in brightness or colour and must be recognized otherwise, it's considered to have a 50% chance of being distinguished. A blatant target, like man in a suit in a white room, has a 100% chance of being distinguished. The recognition is where the resolution comes into effect the greatest; the resolving power to tell which direction something is pointing must be about 3 times as great as to simply say something is there. The factor increases to 8-ish for telling what something is ("It's a tank", "It's a person", etc.) and 12-13 to tell exactly what it is. ("It's a T-72", "It's an enemy soldier", etc.)

Empirical data on the exact effects of camouflage (affecting contrast and colour contrast) and clutter (affecting G) is hard to find.

A very simple system to handle this would be three-part:

1: A Per-based roll against a relevant skill, affected by distance, target size, search field size, and search time.
2: A "defence roll" by the target, using their Stealth and/or Camouflage, aided by darkness and opposed by an unforgiving hiding place and good night vision.
3: Check how well the target is recognized by comparing Visual Acuity to Range+Size. Sometimes all you can say is "there's something in those bushes".

This is just some vague notes based on my memory of some papers I read once, mind.