# The Naked Scientists Forum

### Author Topic: how far is the horizon?  (Read 5201 times)

#### paul.fr

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##### how far is the horizon?
« on: 12/10/2007 22:58:10 »
this may seem like a silly question, but: Say i stood on the sand at the edge of the sea and looked out, would the distance to the horizon be the same as if i was in a desert and look accross as far as i could see to the horizon?

hope that makes sense.

#### lyner

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##### how far is the horizon?
« Reply #1 on: 13/10/2007 00:00:18 »
It depends entirely how high your vantage point is.
Let's assume we are talking about a perfectly smooth, spherical globe.
If your eye is exactly at ground level, your horizon is zero distance from you. - you can look only along a tangent to where your eye is.
If you raise your viewpoint, your horizon will be   a circle which is the locus of all tangents from your eye to the sphere. The higher, the bigger. Climb to the crow's nest Jim lad and see if you can see Treasure Island.
If you are talking about  the effect on land - then the surface is not smooth - and the geometry gets more complicated but it's the same principle.

#### chris

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##### how far is the horizon?
« Reply #2 on: 13/10/2007 01:02:03 »
You can use the "123" rule - the distance to the horizon in miles is (roughly) given by multiplying the square root of the height of your eyes above the ground, in feet, by 1.23. Therefore, if there's nothing in the way (such as a large sand dune) and you're at the same elevation, you should see a horizon an equivalent distance away in a desert or at the beach.

Chris
« Last Edit: 09/12/2007 22:25:35 by chris »

#### Bass

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##### how far is the horizon?
« Reply #3 on: 13/10/2007 01:33:33 »
Depends on whether or not you're a member of the flat-earth society

#### JimBob

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##### how far is the horizon?
« Reply #4 on: 13/10/2007 03:43:32 »
Here, here!! Another member! I can't drink no mo' but lift one for me.

#### lyner

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##### how far is the horizon?
« Reply #5 on: 13/10/2007 13:48:03 »
Quote
the height of your eyes above the ground
in imperial or metric units?

#### Pumblechook

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##### how far is the horizon?
« Reply #6 on: 08/12/2007 23:08:12 »
Distance km = Sq root (13h)..  h is height of your eyes or camera in metres above the surrounding land.

Someone with their eyes 1.7 metres above the sand (standing on the sand) could see 4.7 km out to sea.

In practice it is far more complicated than that because light tends to curve and you tend to see  further.

When you are much higher up your rarely see over the calculated distance because it tends not to be clear enough.   From a height of 500 metres the calculated distance is 80 km.

From one 500 metre hill it should be possible to see another 500 metre hill over the sea at nearly 160 km.

#### turnipsock

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##### how far is the horizon?
« Reply #7 on: 09/12/2007 22:10:43 »
There are tables in most nautical almanacs for this sort of thing.

#### chris

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##### how far is the horizon?
« Reply #8 on: 09/12/2007 22:26:25 »
Quote
the height of your eyes above the ground
in imperial or metric units?

Sorry - my mistake - it's in feet.

Chris

#### Pumblechook

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##### how far is the horizon?
« Reply #9 on: 09/12/2007 22:41:03 »
km = sq rt (13 x height(metres)) does agree with miles = 1.23 sq rt height(feet).

e.g ..  1.8 metres gives 4.8 km.... 6 ft gives 3 miles (4.8 km).

#### The Naked Scientists Forum

##### how far is the horizon?
« Reply #9 on: 09/12/2007 22:41:03 »