Naked Science Forum
General Science => General Science => Topic started by: thedoc on 05/12/2010 00:13:55
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How much further can you see beyond the horizon as you go up each floor of a skyscraper building?
Asked by Des Enright
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Chris - Well let’s assume your skyscraper is standing in isolation, so it’s not going to get your view blocked by an adjacent building for instance, so there’s no get out clauses like that. It’s a building in isolation in the middle of nowhere.
There’s a sort of approximation for distance to the horizon in miles 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.
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That rule of thumb would be better for the addition of a unit or two.
Which part of "in feet" did you not understand?
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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)
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That rule of thumb would be better for the addition of a unit or two.
Which part of "in feet" did you not understand?
In BC's defense, I omitted the word "MILES" - which I've now added.
C
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In BC's defense, I omitted ......
LOL. I'm quite sure BC is entirely capable of defending himself [;D]
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That rule of thumb would be better for the addition of a unit or two.
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.
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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.
[/quote]
I confess was deliberatley misinterpreting your point to mean that thare were no units mentioned at all [:D].
You were quite correct though. Additional units were required.