Ever wonder how far away a guard on a sentry tower of a given height can see someone coming?

If you have binoculars that can spot a man at 10 miles, how high up do you have to be to fully use them?

Your radio has enough power to broadcast a signal 20 miles away, how tall an antenna do you need to keep the horizon from cutting your range?

How far away is the horizon on a planet with a size notably different that earth?

Questions like this can come up in various games, from fantasy to SF to modern settings. In most cases a GM might just handwave it off andf be done.

If you want more accurate, consistent answers, or you don't want to be shown up by a player who knows the answers, here's a formula you might want to jot down.


To determine the horizon for an observer and object of a given height, take the square root of: (( D x 1760 x H) + (H x H)) to get the answer in yards.

Where D = the diamater of the planet you're on in miles (~7915 for earth) and H is the combined height, in yards, of the observer and the target.

Using this we see that a man who is 2 yards tall can see another man 2 yards tall on earth at about (square root of) (7915 x 1760 x 4) + (4 x 4) at up to about 7,480 yards, or roughly 4.25 miles befoe the horizon blocks LOS between them.

Likewise we see that a 2 yard tall man on a 15 foot (5 yard) sentry tower can see a 2 yard tall man at 6.3 miles assuming he has a good visual aid.

A radio tower 60 feet tall can broadcast directly to a hand held or helmet reciever 2 yards off the ground at a distance of 9.9 miles before the horizon cuts if off.

These are rough figures but generally accurate enough. You can adjust the value of 7915 (earth's diameter in miles) for horizon distances on planets of different sizes.

It's useful in some cases in varios games, so the equation belongs in the notebooks of most gamers.

"what do you see with your elf eyes?"

Good to know just how far that would be.

Probably less if it's not a clear day / there's moisture in the atmosphere.

Quote from: Stuart"what do you see with your elf eyes?"

Good to know just how far that would be.

Probably less if it's not a clear day / there's moisture in the atmosphere.

Well, all this formula does is give you the distance to the horizon where the curvature of earth (or another spherical body) would block LoS regsardless of any other considerations, such as visual aids, atmospheric conditions, etc.

It basically establishes a rough absolute limit on vivibility which other facotrs may further degrade but could not really enhance.

One use of this might be to establish what I call the "Man horizon" on various planets. It would be the distance at which a man 2 yards tall could see another man 2 yards tall assuming both were on a flat plain.

On earth it seems to be about 4.25 miles, on a planet with a diameter of 4, 956 miles as opposed to earth's 7915 miles it was like 3.3 miles.

Thean again, this assumes a world in which real-world science and physics apply.  If Tolkien were to tell you Legolas could see 50 miles, I doubt it would break your suspension of disbelief.

This would be more in keeping with a "traveller" type game than LotR....

One of the things I've always wondered was how to derive the gravity of a planet using Traveller's planetary notation. They give density, as I recall, but I don't know how to get gravity from that.

Quote from: ColonelHardissonOne of the things I've always wondered was how to derive the gravity of a planet using Traveller's planetary notation. They give density, as I recall, but I don't know how to get gravity from that.

G=Di x De

G = planet's surface gravity

Di = the planets diameter expressed in relation to earth's.

De = the density of a planet in relation to earths.

I was just making a planet for a scenario and wanted it to be small, barely habitable and have lower gravity than earths. I also wanted it to be dense with metals and such.

I set the density at 1.2 x that of earth's and wanted the gravity to be about 75% that of earth.

I ended up with a diameter of 4,956 miles. I rechecked that thru the above equation, divindig earth's diameter of 7915 miles by the diameter of the planet i'd determmined as being 4956, multiplied the result be the density of 1.2 and got .7488% of earth's gravity, which I rounded off to 75%.

So you can use that if you want.

Colonel Hardisson,
 If you have college textbook store near you - hit that place between semesters and see if you can get a used physics or astrophysics text  book.
 Should give you all the useful formulas.
 When I worked in a store like that ...years ago... most used textbooks were 30 to 40% off the original cover price.

 There might also be some kind of 9 by 12 cheat sheet card there for those kinds of formulas.

- E.W.C.

Sniff* sniff* Pyew, what's that stench in my thread? Oh, it's the breath of an ass kissing tokhest straave. Gak.

Quote from: Dominus NoxThis would be more in keeping with a "traveller" type game than LotR....

There aren't any elves in Traveller.  Well, excluding the Darrians.

This is actually neat information, Nox.  A bit fiddly for the everyday campaign, but this sort of thing has come up in the past.  Thanks.

!i!

Quote from: Dominus NoxSniff* sniff* Pyew, what's that stench in my thread? Oh, it's the breath of an ass kissing tokhest straave. Gak.

Nox. Shut the fuck up. Shut the fuck up now.  You don't like the guy, IL him. Don't threadcrap (your own thread!  How the Hel you can threadcrap your own thread I'll never know - but you managed it).

Bad enough when it was anyone with brown skin or anyone who might not agree with you on the nature of just about anything, but to single out a new poster because you have a(n imagined) history with the guy goes beyond Noxism and into stalker territory.

So do everyone a favour and just IL the guy.