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Subject:
Distance to horizon on ocean?
Category: Reference, Education and News > Education Asked by: jbt152001-ga List Price: $5.00 |
Posted:
26 Jan 2004 11:57 PST
Expires: 25 Feb 2004 11:57 PST Question ID: 300417 |
When standing on a beach approximately 10 feet above sea level how far in the distance is the horizon looking out at the ocean (assuming a flat ocean or no waves)? JT |
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Subject:
Re: Distance to horizon on ocean?
Answered By: omnivorous-ga on 26 Jan 2004 12:25 PST Rated: |
JBT -- The simple answer is about 5.5 km or 3.4 miles. The derived formula is indicated on this web page: Goddard Space Flight Center "Distance to the Horizon" (Stern, Dec. 13, 2001) http://www-istp.gsfc.nasa.gov/stargaze/Shorizon.htm The formula is: D = 112.88 km * h Where: D = distance to the horizon in kilometers 112.88 is actually the square root of the earth's diameter in km h = height in meters Since 10' is about 3 meters, D = 5.5 km. Now some caveats: * why can you see a ship that's further offshore? Because it's taller, rising above the horizon -- a fact known to seafarers even in Columbus' time (debunking the stories that Columbus' men believed in a "flat earth"). * atmospheric conditions can refract light over the horizon. Nathaniel Philbrick refers to this phenomenon called "looming" in his book "Sea of Glory." I've seen it on Lake Michigan and it's apparently quite common in Antarctica, as Philbrick says maps created by the Wilkes Expedition in 1838-1842 made some errors in judging distance when it made the first maps of the Antarctic coast. Here's an explanation of looming: SDSU "Distance to the Horizon" (Young, 2003) http://mintaka.sdsu.edu/GF/explain/atmos_refr/horizon.html Best regards, Omnivorous-GA |
jbt152001-ga
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Wow!! Can it get any better than this! |
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Subject:
Re: Distance to horizon on ocean?
From: redhoss-ga on 26 Jan 2004 19:21 PST |
Be sure that you add the distance from your feet to your eye to calculate "h" if the beach elevation is actually 10 feet above sea level. |
Subject:
Re: Distance to horizon on ocean?
From: jbt152001-ga on 26 Jan 2004 19:59 PST |
Thanks for the extra comment about adding the h of our height. |
Subject:
Re: Distance to horizon on ocean?
From: jameswh-ga on 27 Jan 2004 11:47 PST |
yes i think it can get any better than this... looking at the site referred to by omnivorous, you can see that the actual equation is: D = 112.88 * sqrt(h) where sqrt means 'square root' further, h is the height in kilometers, not metres. even further, the answer is actually 6.18km, i can't see where 5.5km came from, whatever way you organise the units or the formula. even further than that, 'perhaps' a more useful formula for working out the distance is this: D = acos(r/(r+h)) * ((2 * pi * r)/360) where: acos() is the inverse cosine function r is the radius of the earth in km (6370.9472km) h is the height above the earth in km (0.003km in this case) pi is about 3.142....something this gives the actual distance from the point where you stand to the horizon along the 'surface' of the planet, rather than in a straight line through the air. For this example, of 10' above the surface, the difference is negligible, it is still 6.18km, but scales up better for example if you were to look at the earth from the moon. the distance using the first simple method would be about 400,000km to the horizon, but using the second method, the distance along the surface of the earth from the point directly below you to the horizon would be more like 10,007km which is one quarter of the earths circumference (approx). i guess you wouldnt really gain much from using the second method, and i cant refer you to a site that explains it better, because i just worked it out myself. anyway, just thought that if you were planning on throwing something 5.5km in the hope that it landed on the horizon, you might be disappointed if it fell short. it's 6.18km away. and i did it for free... something wrong with me i think :) james |
Subject:
Re: Distance to horizon on ocean?
From: jbt152001-ga on 27 Jan 2004 16:55 PST |
James: Nothing wrong with a curious mind and a generous spirit...and besides I am beginning to understand the super complexity of the question!! JBT |
Subject:
Re: Distance to horizon on ocean?
From: jameswh-ga on 28 Jan 2004 07:34 PST |
well no, if you put it like that :) james |
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