# A summary of visibility? [closed]

Does anyone have a pointer to a good (plain and simple, quick to use) guide to visibility ranges, or could someone please give me (us) a brief, basic summary of visibility? (How far can you see on a clear day on a plain? In a forest? At dusk? At sea? Etc.)

Thanks,

• I'm voting to close this question as off-topic because it is not about RPGs, but real world biology research on what the human eye can do. Jun 1, 2015 at 22:27

One of the factors in visibility—at least, for “a clear day on a plain”—is the horizon. On an earth-sized and earth-shaped planet, using feet and miles, the horizon is the square root of the height of the eyes looking in feet; multiply by 1.346. That’s the horizon in miles. So on a perfectly clear day on perfectly “flat” land, a six foot tall person can see a little over three miles.

Usually, however, the question of how far someone can see is in reference to how far can they see something. For that, you add the horizon of the thing they’re looking toward to their own horizon.

Our hypothetical six-foot tall person could see another six-foot tall person start coming over the horizon six miles away. Of course, people are small, so it’s still going to be tough to see someone’s forehead six miles away. This is more useful for larger things, such as towers and mountains.

A 200 foot tower will start to come over the horizon from 19 miles away (plus the horizon of the person looking). A 10,000 foot mountain will start to come over the horizon 135 miles away (plus the horizon of the person looking).

And the math can be reversed as well. A 200 foot tower comes over the horizon at 19 miles away; at 16 miles away a 150 foot tower starts coming over the horizon. This means that at 16 miles, 50 feet of the 200 foot tower is now over the horizon. A 7,500 foot mountain starts coming over the horizon at 117 miles, so the 10,000 foot mountain has 2,500 feet showing at 117 miles.

And of course, spyglasses and other farseeing devices don’t change this, unless they can peer through the ground. That is, if something is below the horizon, a (non-magical, at least) spyglass can’t bring it above the horizon. The earth is in the way.

This is easier to use with a table, rather than doing square roots at the table. I don’t see how to put an HTML table here, but I have one in my game book either in the PDF or under Designing Adventures.

• Great info here, @JerryStratton. Do you have any input to address the question of low-light environments?
– Iszi
Mar 14, 2011 at 15:56
• Dim or hazy environments are very complex. Horizon is easy—is there line of sight to the thing or not? Low-light and haze involve a lot more variables, as you can see in Acedrummer_CLB’s weather service and wikipedia visibility links. I’d say find a couple of guidelines such as Acedrummer_CLB’s factoid that a candle flame is visible for ten miles in clear air, and use them as guidelines to set a simple difficulty of “easy”, “hard”, “impossible”, and so on, according to the game. Mar 15, 2011 at 0:44

W. H. Pick's 1932 monograph on visibility at sea.

His categories for observation under varying meteorological conditions:

0=Dense fog, objects not visible at 50 yards.

1=Thick fog, objects not visible at 1 cable (203 yards).

2=Fog, objects not visible at 3 cables (405 yards).

3=Moderate fog, objects not visible at 0.5 mile (nautical).

4=Thin fog or mist, objects not visible at 1 mile (nautical).

5=Visibility poor, objects not visible at 2 miles (nautical).

6=Visibility moderate, objects not visible at 5 miles (nautical).

7=Visibility good, objects not visible at 10 miles (nautical).

8=Visibility very good, objects not visible at 30 miles (nautical).

9=Visibility excellent, objects visible more than 30 miles (nautical).

Science!

• +1. But, just for seeing it clear (pun intended). On point 2=Fog, is visibility limited to 2 cables or 608 yards? Mar 29, 2011 at 13:19
• I guess you'd have to ask W.H. Pick. Apr 7, 2011 at 17:30

From wikipedia: Visibility A lot of math here but there is some good info.

From national weather service Visibilty.

From wikipedia: Human Eye.

These will take some reading and more than a little study to understand, so here is a summary:

The approximate field of view of a human eye is 95° out, 75° down, 60° in, 60° up. In game terms place your hands at 45° angles in each side of your face, by your eyes. That is the typical field of vision of a human.

It takes about 4 seconds for the eye to initially adjust to an abrupt change in lighting and as much as 30 minutes to fully adjust in very drastic lighting changes. (normal day light to normal night-time darkness - entering a cave.)

For viewing distances keep the following in mind; in clear air a candle flame is just visible at a distance of ten miles. This is the practical limit guide you can use for determining sight.

• Could you please throw in some relevant data to go with those links?
– Iszi
Mar 14, 2011 at 3:23

On a clear day far out to sea, you can see to the horizon.

Rain will limit visibility, but how much depends strongly on the amount of rain. I'd say that, at minimum, it cuts it in half. Even a light drizzle, stretched out far enough, will interfere with vision at that range.

If it's anything heavier than a drizzle (precipitation-wise) expect less than a mile. If there is strong wind, your visibility is cut by about 1/4 (waves in the distance interfere with horizon visibility).

Cloud cover in and of itself doesn't interfere with visibility.

Heavy rain and high winds? Your visibility cuts to nil very quickly. A big storm will make it difficult to see across the deck, let alone the ocean.

• On earth, from the deck or from the shore, the horizon would be about six miles away. From the crows nest, I think it is about fifteen miles, but I haven't done the math. Tall structures: Masts with sails, trees, mountains, etc. would be visible beyond the horizon depending on precipitation, fog, or haze due to humidity.
– Ron
Mar 15, 2011 at 11:54
• It's useful to think of many kinds of weather at sea not as ambient conditions, but as "cover" and "terrain". For example, you won't have "rain" unless it's right on top of you: you'll have "rain to the NNE obscuring the coastline and the traders who hug the shore". Mar 15, 2011 at 17:36

A rough formula for distance you can see is:

SquareRoot(height of eyes above surface in feet / 0.5736) = miles to horizon

or the equivalent in metric

SquareRoot(height of eyes above surface in centimeters / 6.752) = kilometers to horizon

So if you're roughly 6 feet tall and standing at the water's edge, you can see about 3 miles to the horizon on a clear day.

• Simple approximation is easier to remember for me: √(2 x feet) = miles. Or "The horizon is a the root of two feet!" Mar 15, 2011 at 14:06
• Well, sure, if you wanna make it easy... :) Mar 15, 2011 at 14:09