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Line Of Sight With Regard To Altitude

THVGJP From Ukraine, joined Mar 2002, 158 posts, RR: 0
Posted (6 years 2 months 6 days 22 hours ago) and read 6272 times:

Approx how many statute ot nautical miles can one see for every 1000 feet gain in altitude? Assuming clear day no clouds flat or near flat terrain
Thanks
Glen

4 replies: All unread, jump to last

HaveBlue From United States of America, joined Jan 2004, 1936 posts, RR: 1
Reply 1, posted (6 years 2 months 6 days 21 hours ago) and read 6259 times:

I believe at sea level it is 12 miles before the horizon 'drops off', but I don't know how much that increases with altitude.

Here Here for Severe Clear!

Flyf15 From , joined Dec 1969, posts, RR:
Reply 2, posted (6 years 2 months 6 days 21 hours ago) and read 6255 times:

It is actually a fairly simple equation.

s = sqrt(2rh+h^2)

s = line of sight distance
r = radius of sphere (Earth = ~3959mi)
h = height viewed from

All have the same units... so make sure you use it correctly.

A few examples...with rough ideas of what might be there (yes, I know they're not accurate, but the right order of magnitude)

5.5ft: 2.9mi (Typical person's height to eyeballs)
2000ft: 54.8mi (General aviation aircraft / tall tower)
10000ft: 122.5mi (Mountain)
37000ft: 235.7mi (Airliner)
60000ft: 300.2mi (Concorde)
100000ft: 387.7mi (SR-71)
250000ft: 614.1mi (X-15)
500000ft: 871.1mi
1000000ft: 1239.1mi (Space Shuttle)

Timz From United States of America, joined Sep 1999, 6181 posts, RR: 8
Reply 3, posted (6 years 2 months 6 days 19 hours ago) and read 6227 times:

That's the distance to the horizon assuming no refraction, so the actual distance is slightly more. I've always wondered when Mt Shasta comes into view from a northbound airliner-- more than 300 miles away on a clear day, but dunno how much more.

SlamClick From United States of America, joined Nov 2003, 10019 posts, RR: 76
Reply 4, posted (6 years 2 months 6 days 18 hours ago) and read 6219 times:

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Quoting Timz (Reply 3):
I've always wondered when Mt Shasta comes into view from a northbound airliner

Actually saw Mount Hood in the sunset from over near Pocatello Idaho a distance of roughly 410 nautical miles.

The formula I always used was that distance to the horizon (or line-of-sight) in nautical miles is 1.23 X the square root of the altitude in feet. So in the case above I was at 33000' so:

The square root of thirty three thousand is 181.659
So 1.23 times 181.659 is 223.4 nautical miles to my horizon.

Thing is, though, that Mt. Hood, being near enough to fourteen thousand feet has a distance-to-horizon of its own of roughly 146 nautical miles. It is clear that I was observing the summit of Mt. Hood over the curve of the earth.

I think Bowditch gives 1.17 X the square root of your height but that might be for use down close to the surface of the water where there is thicker air.

Happiness is not seeing another trite Ste. Maarten photo all week long.

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