How far can the eye see?

[Mark]

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.

You could use the Greysmog Campaign setting from WoLA.

 

[The 1 and the Prime]

To find the horizon distance formula you need to use calculus. Briefly, you need to solve for where the tangent line to the circle curve intersects the Y axis at 1 + the height of the observer (relative to diameter). To find the arc length visible you use the following formula:

[90 - asin(1/(1+[h/R]))]*2R*pi/360= Visible arc length

That is, how far you'd need to walk to get to the horizon.

h is the height of the observer, R is the radius of the planet. Pi of course is the constant, and asin is the inverse sine function.

A person is about 1 five millionths of the radius of the Earth (he's a dwarf let's say, a tall one, or a short human, or an elf). For this approximate value the horizon is about 3.16 miles away. Halving the radius results in a horizon distance of 2.23 when standing on a "flat" part of the surface (like on the shore of the ocean and looking out to sea).

(90-Asin(1/1.0000002))/360*10000*3.141593=3.16

(90-Asin(1/1.0000004))/360*5000*3.141593=2.23

 

[Rechan]

You could use the Greysmog Campaign setting from WoLA.

I all ready have a setting I'm using. I odn't know why I'd want to use another setting?

The problem is just the PCs finding the things I've set out.

 

[Chris Knapp]

I all ready have a setting I'm using. I odn't know why I'd want to use another setting?

The problem is just the PCs finding the things I've set out.

I think he was making a funny, capping on us Angelenos and our perpetual smog. . .

 

[the Jester]

According to the 2e Players Handbook, under clear sky in daylight, the maximum range at which a man-sized object can be seen is about 1500 yards, if its moving. If it isn't, this drops to 1000 yards. At 500 yards, you can roughly identify the thing- shape, color, creature type, etc. At 100 yards, you can make out an individual's identity ("Hey, that's Bob!").

 

[Pbartender]

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.

To find the horizon distance formula you need to use calculus. Briefly, you need to solve for where the tangent line to the circle curve intersects the Y axis at 1 + the height of the observer (relative to diameter). To find the arc length visible you use the following formula:

[90 - asin(1/(1+[h/R]))]*2R*pi/360= Visible arc length

That is, how far you'd need to walk to get to the horizon.

What you're doing there isn't calculus. It's mostly trigonometry with a little geometry and algebra thrown in.

Also, unless you are dealing with an extreme case (a very, very small planet, or a very, very high observer), you don't really need to worry about figuring out the arc length. Just figure out the length of the tangent line drawn from the horizon to the observer.

The secant tangent theorem gives the following equation...

d=√(h(D+h)), where d is the distance to the horizon, h is the height of the observer off the ground, and D is the diameter of the planet.

Now, for when the observer is close to sea level (close meaning anything less than low orbit) on a reasonably earth-sized planet, h is going to be very, very small compared to D (compare the earth's diameter of ~7,900 miles to the top of Mount Everest at ~5.5 miles above sea level). So, to simplify further, ignore the "+h" part...

d=√(hD)

That's it. It's not perfectly precise, but for what we're doing it's good enough (meaning within 1% accuracy).

 

[Umbran]

If I recall correctly, human "20/20 vision" corresponds to being able to distinguish details that take up about 2 arcminutes (two-sixtieths of a degree) - I think that's something about 0.3 mm across, one meter away from you. The theoretical limit is down around 1 arcminute (so, something 0.15 mm across, held a meter away).

Lighting and other effects (haze, for example) can lessen acuity, of course.


Clarkvision Photography - Resolution of the Human Eye

 

[Primitive Screwhead]

I found the thread on this over in HRs...

Spotting Distance

 

[Bullgrit]

Well, I can see the sun, and it's over 90 million miles away.

Consider this: Would it help you or the game for them to be able to spot what they're looking for in the distance? Base your vision answer on this thought.

If you want them to go there, let them spot something. If you want them to continue wandering, don't let them spot anything.


Bullgrit

 

[Haffrung Helleyes]

complicated

You can see a long way if you're at elevation and the atmosphere isn't too hazy, but what you can make out diminishes quickly.

For example, I've been to the rim of Ngorogoro Crater in Tanzania. There's a wiki for it here:

Ngorongoro Conservation Area - Wikipedia, the free encyclopedia

It's about 10 miles across. There's a nice picture on the wiki that gives a pretty good idea of what you can see 10 miles out on a really clear day. When I was there, it was more hazy, and less detail was available.

Ken