Science Questions

How does elevation affect how far away the horizon appears?

Sun, 28th Nov 2010

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Question

Des Enright asked:

How much further can you see beyond the horizon as you go up each floor of a skyscraper building?

Answer

Chris -   Well letís assume your skyscraper is standing in isolation, so itís not going to get your view blocked by an adjacent building for instance, so thereís no get out clauses like that. Itís a building in isolation in the middle of nowhere. 

Thereís a sort of approximation for distance to the horizon, which is 1.23 times the square root of the height of your eyes above the ground in feet. 

So you could work out, using that little rule, how much further you're going to see if you go up the height, in feet, of one storey in a building, and then you could keep doing that to work out how much further you're going to be able to see to the horizon from the top of the building than the bottom, for example.

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That rule of thumb would be better for the addition of a unit or two. Bored chemist, Sun, 5th Dec 2010



Which part of "in feet" did you not understand? Geezer, Sun, 5th Dec 2010

r=radius of earth = 6.3675◊10^6 meters = 2.0891◊10^7 feet
h=height above the ground
d=distance to horizon

r^2 + d^2 = (r + h)^2
r^2 + d^2 = r^2 + 2rh + h^2
         d^2 = 2rh + h^2

since h^2 is so much smaller than the others it can be ignored

d = √2 * √r * √h
d = 1.414 * 2523.39 * √h (all in meters)
d = 3568.61 * √h (all in meters)

d = 1.414 * 4570.67 * √h (all in feet)
d = 6463.90 * √h (all in feet) granpa, Sun, 5th Dec 2010


Which part of "in feet" did you not understand?


In BC's defense, I omitted the word "MILES" - which I've now added.

C

chris, Sun, 5th Dec 2010



LOL. I'm quite sure BC is entirely capable of defending himself  Geezer, Sun, 5th Dec 2010



Which part of "in feet" did you not understand?


None.
What variety of esp let you know what units he was using for the distance to the horizon.

I suspect the rule breaks down for silly distances like a skyscraper that reaches the moon.

While I'm at it, what the OP asked for is actually the first derivative of that estimate with respect to height, measured in storeys.
That's a mess of a set of units.
Bored chemist, Mon, 6th Dec 2010



None.
What variety of esp let you know what units he was using for the distance to the horizon.



I confess was deliberatley misinterpreting your point to mean that thare were no units mentioned at all .

You were quite correct though. Additional units were required. Geezer, Mon, 6th Dec 2010

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