Response last updated by gtho4 on Apr 09 2023.
Jun 06 2007, 11:31 PM
davejacobs
Answer has 0 votes
davejacobs 22 year member
956 replies
Answer has 0 votes.
Or 3.29 real miles!
Jun 07 2007, 8:18 AM
gmackematix
Answer has 2 votes
gmackematix 21 year member
3206 replies
Answer has 2 votes.
The situation involves a right angled triangle involving the distances from the eyes to the centre of the Earth (R+h), from the horizon to the centre of the earth (R) and the required distance to the horizon x. Suppose all distances are in feet.
By Pythagoras, x = Sq rt ((R+h)^2 - R^2)
= Sq rt (2Rh + h^2)
Given that R is the radius of the Earth, then h^2 is so small compared to 2Rh ignoring it won't affect our approximate result.
So x ~ Sq rt (2Rh) = Sq rt (2R) * Sq rt h
The radius of the Earth is about 3,960 miles or 3,960 * 5,280 = 20,908,800 feet.
So Sq rt (2R) ~ 6,467.
So x in miles ~ 6,467/5,280 * Sq rt h ~ 1.22 * Sq rt h.
For h = 6 ft, I make x to be as near as dammit 3 miles.
I guess what I'm trying to say is yay, Mutch!
Jun 07 2007, 7:50 PM
markswood
Answer has 3 votes
markswood 17 year member
578 replies
Answer has 3 votes.
3,571.59 metres
This site is useful for calculating the distance at any given height above sea level.
Distance to horizon
In order to determine how far away the horizon is for any given observer, first determine how far above sea level the observer's eyes are. If the observer is standing on the surface of the ocean, his eyes might typically be somewhere between 140 and 200 centimeters above sea level. Look this number up in the first coloumn in the below table. The second coloumn then tells you how far away the horizon is.
Note that obstructions or poor visibility might further restrict how far an observer can see. The distance to the horizon is simply an upper limit to how far away it is physically possible to see - other circumstances may very well restrict this much further.
Example Ut'kikk has been placed in the tops of a sailing ship to keep a look out. The skies are clear and visibility is excellent. Ut'kikk is currently located up in the main mast, 12 metres above sea level. He can see as far away as 13 kilometers (approximately).
pvv.ntnu.no/~bcd/shadowworld/info/horizon.html no longer exists
Response last updated by gtho4 on Apr 09 2023.
Feb 19 2008, 9:46 AM
MonkeyOnALeash
Answer has 0 votes
MonkeyOnALeash
Answer has 0 votes.
This is dependent upon where on the Earth one is. The Earth IS an irregular Sphere and thusly Horizon will vary from Equator to Pole.
Feb 19 2008, 5:10 PM
gmackematix
Answer has 3 votes
gmackematix 21 year member
3206 replies
Answer has 3 votes.
Actually, the variation in curvature of the Earth at various points is too small to be greatly significant.
Note that the calculated distance to the horizon will be more than the actual distance due to the refraction of light through the atmosphere. https://en.wikipedia.org/wiki/Horizon
Feb 19 2008, 7:58 PM
zbeckabee
Answer has 4 votes
zbeckabee Moderator 19 year member
11752 replies
Answer has 4 votes.
AT SEA:
As you can see by the following, it varies (in part) by the height of the eye:
Height of eye (specify units): 5.6 (Decimal)
feet meters
Distance to the Horizon: 2.7663589065773806 (Nautical Miles) 3.1852173552208334 (Statute Miles)
Height of eyes: 5.0 feet
2.6139634656972545 Naut. Miles
3.0097474977147174 Stat. Miles
Presuming you are standing at sea level, not on an elevated piece of land, and you have an eye-level of 1.7 metres, then, ignoring possible hindrances to line-of-sight, the horizon will be 4.7 kms distant.
The horizon is where you see it, and a six-foot-tall man has eyes at about 5-1/2 feet. When you factor in the curvature of the Earth (remember it's spherical, not flat!) this is your answer:
SqrRt(man's eye-height in ft / 0.5736) = horizon's distance in mi
SqrRt(5.5 / 0.5736) ~= 3.1 miles
The formula will vary depending on the units of measure you use.