How far can the eye see?

[Rechan]

I'm running an exploration game. I fully anticipate that some player is going to climb a tree and look out over the horizon, to see if there are any structures that push past the canopy, etc etc. (They have yet to do this however).

So my question is: how far could they be able to see details by doing this? How far for instance would a village need to be for them to see the smoke of cookfires? How far would a 50'-60' high wall be before they can no longer see it?

 

[Pbartender]

I'm running an exploration game. I fully anticipate that some player is going to climb a tree and look out over the horizon, to see if there are any structures that push past the canopy, etc etc. (They have yet to do this however).

So my question is: how far could they be able to see details by doing this? How far for instance would a village need to be for them to see the smoke of cookfires? How far would a 50'-60' high wall be before they can no longer see it?

Largely, it'll depend on how good the eyesight of the observer is. Very often an object may be visible, even though fine details cannot be resolved.

However, what you seem to be looking for is the effective horizon distance, and how that is affected by tall objects. Wikipedia has a decent article on it, with all the relevant formulas, should you want to get that detailed.

Basically, the formula is roughly d=√1.5h. Where d is the distance that can be seen (horizon) in miles, and h is the height of the eyes of the observer in feet.

So, a 5' 7" tall person has a horizon of about 2.9 miles on level ground. At the top of a 100 foot tall tower, you'd have a horizon of 12.25 miles. At the top of a mountain a half mile high, you'd be able to see nearly 63 miles on a clear day.

When looking at something tall from something tall, you add the two together. So, a 5' 7" tall person on level ground could see the tippy-top of a 100' tall tower from a little more than 15 miles away. Someone in the tower could also see that 5' 7" person from the same distance, presuming they had good enough eyesight to distinguish something that small from that far away.

 

[MarkB]

It really does depend upon how much detail needs to be resolved. The Great Wall of China is visible from low orbit. On a clear night, the naked eye can see objects hundreds of light years away.

How far away something is no longer registered or recognised as a significant feature will depend upon how greatly it contrasts with its surroundings, and whether the observer is looking for it specifically.

 

[Piratecat]

It really does depend upon how much detail needs to be resolved. The Great Wall of China is visible from low orbit.

That's a myth, as it turns out.

NASA - China's Wall Less Great in View from Space

That being said, according to one web link:

At sea level the curvature of the earth limits the range of vision to 2.9 miles. The formula for determining how many miles an individual can see at higher levels is the square root of his altitude times 1.225. Thus on a clear day at 1,000 feet a person with normal vision can see 39 miles; at 10,000 feet, 123 miles; at 25,000 feet, 194 miles. With good visibility a pilot at 25,000 feet can see Germany from the English Channel; at the same altitude over Tunisia he can see the middle of Sicily.

Read more: Science: How Far Can You See? - TIME

 

[Pbartender]

At sea level the curvature of the earth limits the range of vision to 2.9 miles. The formula for determining how many miles an individual can see at higher levels is the square root of his altitude times 1.225. Thus on a clear day at 1,000 feet a person with normal vision can see 39 miles; at 10,000 feet, 123 miles; at 25,000 feet, 194 miles. With good visibility a pilot at 25,000 feet can see Germany from the English Channel; at the same altitude over Tunisia he can see the middle of Sicily.

I just ran across a nifty little reference chart that shows height vs. horizon distance in both metric and SI...

 

[The 1 and the Prime]

The article referenced above calculates the horizon distance, which is based on the curvature of the Earth's surface and would not necessarily be the same on your campaign world. If the PC's are on a larger planet the horizon distance will be larger since the surface doesn't curve as much (relative to height). If they are in some kind of fantastical flat world, there is no horizon. Consider also atmospheric interference that is not apparent at short distances, but is a noticeable haze over long distances due to hanging particulates and water vapor. This would again depend on your campaign world (and even the weather on that day).

However the OP's phrasing doesn't seem to be talking about this. The OP seems to be indicating that whatever it is, it is line of site visible (no mountains or curvature hiding it) and limits on vision will not be able to resolve it. I would point out that even my mortal communication device is able to see the local star and nearby planets with his naked eyes, and they are millions of miles away.

You can actually fairly easily approximate the effect of distance with a prop. Just remember that something twice as far away is half as high. Another useful fact is that 20/40 vision means you can see at 20 feet something someone with "perfect vision" can see at 40 feet. So if you want demihumans to have finer eyesight resolution you can adjust for that fairly easily (if they see at 20/10 they see it like a human would see something twice as close).

Here is how it works: Say you've got a 5000' high structure 100 miles away (say 100 miles= 500,000 feet). Then you could draw the structure 1.2 inches high in and amongst the other foreground and background material and hold up the picture 10 feet away from your players. Formula:

(Structure height)*(Drawing distance)/(Actual distance in world)=(Drawing Height)

Alternatively, if it is a needle in a haystack kind of problem, consider if the PCs had to notice a detail the size of the hypothetical drawn structure.

 

[Uder]

Hmm, my campaign world is half the size of Earth, but still a globe. How that would affect how far you can see? I've just been cutting the standard ballpark 3 miles down to 2 and not worrying about it... but it would be interesting to know the correct numbers.

 

[Rechan]

Well dang. I have put everything so far away that they're not going to see anything. And yet so close that travel to it wouldn't be too hard. Nothing is exceptionally tall, hence they're not going to see jack.

 

[PaulofCthulhu]

Hmm, my campaign world is half the size of Earth, but still a globe. How that would affect how far you can see? I've just been cutting the standard ballpark 3 miles down to 2 and not worrying about it... but it would be interesting to know the correct numbers.

I'm not even going to raise the whole 'Gravity' question. Fantasy worlds - whatever's good for your story!

 

[Primitive Screwhead]

On my other computer I have a 3e HR regarding encounter distance in which I built in the 'how far can you see' aspect. IIRC, I treated vision as a ranged weapon and used range increments. Terrain and atmosphere limited both the number of range increments as well as the length of an individual increment. Then the size of the 'target', if different than medium, would shift the increment level.

Fx, in a heavy forest the range increment was something like 10', meaning your encounters would be very close, but larger beasts would be easier to notice as they push through the trees.

Cooking fires and dust clouds would increase the 'size' of the target, making it easier to see.


If I remember to do so, I will post the full rules on Tuesday when I get back to that computer I need to adapt it to 4e anyway!