When a person stands at a beach, how many miles out to sea can a person see, until the curvature of the earth takes proper effect?
2006-12-26 23:24:28 · 12 answers · asked by Anonymous in Science & Mathematics ➔ Geography
Very interesting question!......
The answer depends on whether you define the distance as the straight, line-of-sight distance (from your eyes to the horizon), or as the distance along the planet's surface from the nearest point on the surface directly beneath your feet (well, straight down to sea level) to the horizon (i.e. the distance that you'd have to walk to get there).
At a height h above the surface of a spherical planet of radius rp:
The straight-line distance to the horizon:
ds=square root of h(2rp+h)
The curved distance along the planet's (sea-level) surface to the horizon:
dc=rp cos to the power of minus 1(rp over rp+h)
Where the height (h) above the surface of the earth is 1.8m
the straight line distance (ds) is 4.79180km and the curved surface distance (dc) is 4.79179km
2006-12-26 23:44:28 · answer #1 · answered by Princess415 4 · 0⤊ 0⤋
The distance d in kilometers to the true horizon on earth is approximately
d = \sqrt{13h},
where h is the height in meters of the eyes. Examples:
* Standing on the ground with h = 1.70 m (eye-level height), the horizon is at a distance of 4.7 km.
* Standing on a hill or tower of 100 m height, the horizon is at a distance of 36 km.
To compute to what distance the tip of a tower, the mast of a ship or a hill is above the horizon, add the horizon distance for that height. For example, standing on the ground with h = 1.70 m, one can see, weather permitting, the tip of a tower of 100 m height at a distance of 4.7+36 ≈ 41 km.
In the Imperial version of the formula, 13 is replaced by 1.5, h is in feet and d is in miles. Examples:
* Standing on the ground with h = 5 ft 7 in (5.583 ft), the horizon is at a distance of 2.89 miles.
* Standing on a hill or tower of 100 ft height, the horizon is at a distance of 12.25 miles.
The metric formula is reasonable (and the Imperial one is actually quite precise) when h is much smaller than the radius of the Earth (6371 km).
The curvature is the reciprocal of the curvature angular radius in radians. A curvature of 1 appears as a circle of an angular radius of 45° corresponding to an altitude of approx. 2640 km above the Earth's surface. At an altitude of 10 km (33.000 ft, the typical ceiling altitude of an airliner) the mathmatical curvature of the horizont is about 0.056, the same curvature of a the rim of circle with a radius of 10 metres that is viewed from 56 centimetres. However, the apparent curvature is less than that due to refraction of light in the atmosphere and due to the fact that the horizon is often masked by high cloud layers that reduce the altitude above the visual surface.
2006-12-26 23:37:14 · answer #2 · answered by Anonymous · 1⤊ 0⤋
On a clear day at sea level approx 21 miles,
answered by a 80 yr old Gentleman.
2006-12-27 00:03:16 · answer #3 · answered by alcatrass# 1 · 0⤊ 0⤋
so some distance the furthest we've long gone is around 3 hundred,000 kilometers that's a coarse determine for the gap from the Earth to the Moon. If we had the flexibility to holiday quicker in area or lengthen our nutrients and oxygen furnish could would desire to bypass lots further.
2016-12-18 19:46:55 · answer #4 · answered by sory 3 · 0⤊ 0⤋
If your eyes are 1.6 metres above sea level, then 4.66 kilometres (about 2.9 miles) is the horizon distance. If your eyes are 10 metres above sea level, then you'll be able to see 11.3km. Obviously, if there is something floating on the sea, like a ship, then you will see this when it's much further away than the figures given because the top of the ship will be above the horizon.
2006-12-26 23:32:15 · answer #5 · answered by JJ 7 · 2⤊ 1⤋
4 miles
2006-12-27 00:54:38 · answer #6 · answered by Anonymous · 0⤊ 0⤋
It depends how far you eyes are above the water. If your eyes are at sea level, a few inches. Typical 5 ft to 6 ft, it's about 15 miles, I think.
Work it our for yourself, simple trig.
2006-12-27 00:31:20 · answer #7 · answered by efes_haze 5 · 0⤊ 0⤋
At sea level, on a calm day, with good visibility, I think it's about 20 miles. However, without my specs, it's about 4 inches.
2006-12-26 23:28:37 · answer #8 · answered by Roxy 6 · 2⤊ 0⤋
that would depend on the persons vision, and wether they had 20/20 vision or not. when I stand at the beach i can only see about 2 feet in front of me.
2006-12-26 23:29:17 · answer #9 · answered by petal 3 · 0⤊ 0⤋
My Dad was a sailor and he said the horizon was 14 miles.
2006-12-27 09:34:15 · answer #10 · answered by Yeti 2 · 0⤊ 0⤋