Maximum visibility in air

[Huw]

Here's one for the atmospheric physicists

Situation came up recently - how far away can you see a mountain? A back-of-envelope calculation with Earth like curvature gives about 250km visibility for a 4km mountain.

But what if you have a flat or bowl shaped world or plane, with a large mountain range? Would it be visible from the entire world (and hence a useful navigational tool), or would the atmosphere render everything beyond a certain range a blurred haze?

Thanks in advance.

 

[Yalius]

The longest terrestrial line of sight is Mt. Sanford to Denali (Mt. Mckinley) at 270 miles, and cloud cover and haze make this one just baaaaarely visible. Pretty much anything beyond that wouldn't be visible in normal atmospheric conditions.

Edit: Here's a panoramic photo from Sanford. It's hard to pick out what's mountain and what's sky.

Photo

 

[Slife]

Let's see if this can be done with the game rules, because internal consistency is fun.

Given that Everest (9km) is about 450 times the height of a colossal creature, we can expand out the table of penalties to hide checks. The final number is . -16-4*450 =-1816 to hide checks. It automatically is considered to have rolled a 1 on its check, and has a dex of 0, giving a total of -1820 to hiding. Well, you get a -1 to spot something per 10 feet of distance. This translates to 18200 feet, or five miles if the mountain is hiding. It could only hide if it had concealment. Let's assume that it's behind fog (the only thing big enough for it to possibly hide behind), which reduces a normal 240 feet of sight (for an elf) to 5 feet. That's a factor of 48. So when not hiding, the mountain can be seen from 240 miles away.

A spyglass magnifies objects to twice their size, so by the inverse square rule you could see the mountain through a spyglass from 240*sqrt(2) = 340 miles away

Moral of the story: the rules don't work very well for modeling this kind of stuff, but you can fudge them so the numbers come out decently.

 

[Philodendron]

Let's see if this can be done with the game rules, because internal consistency is fun.

Given that Everest (9km) is about 450 times the height of a colossal creature, we can expand out the table of penalties to hide checks. The final number is . -16-4*450 =-1816 to hide checks. It automatically is considered to have rolled a 1 on its check, and has a dex of 0, giving a total of -1820 to hiding. Well, you get a -1 to spot something per 10 feet of distance. This translates to 18200 feet, or five miles if the mountain is hiding. It could only hide if it had concealment. Let's assume that it's behind fog (the only thing big enough for it to possibly hide behind), which reduces a normal 240 feet of sight (for an elf) to 5 feet. That's a factor of 48. So when not hiding, the mountain can be seen from 240 miles away.

A spyglass magnifies objects to twice their size, so by the inverse square rule you could see the mountain through a spyglass from 240*sqrt(2) = 340 miles away

Moral of the story: the rules don't work very well for modeling this kind of stuff, but you can fudge them so the numbers come out decently.

Bravo!

 

[Mishihari Lord]

I used to live in the San Fernando Valley a few years back. (My profile thinks I'm still there) I lived on the west end and the east end is something like 20 miles away. I could see those mountains maybe a score of times in the 5 years I lived there, usually after a very heavy rain. Those mountains were big, too, when you could see them. It's very odd to see a mountain range appear out of thin air.

So my take is going to be that atmospheric conditions are going to be way more important than actual line of sight in determining how far you can see. You may be able to see 300+ miles on a big planet with big mountains, but unless the air is crystal-clear, you're better off thinking about atmospheric opacity than geometry.