We watched a ship sail away for quite some time before it finally went out of sight. How far can we see until something actually goes over the horizon ?
nealjking
Favorite Answer
Pearlsaw has the right formula, but completely wrong numbers, because he has confused kilometers with meters.
How to figure this out:
- Draw a tangent from a point a distance h above the surface of the ocean (so radius = R + h) to the circle of radius R. The distance from the point at radius = R + h to the point at radius R is d, so by Pythagoras' theorem:
(R + h)^2 = R^2 + d^2
R^2 + 2Rh + h^2 = R^2 + d^2
d = sqrt(2Rh + h^2) ~ sqrt(2Rh)
where R = about 6350 km = 6.35e7 (m)
So d = sqrt(2*6.35e7*h)
= sqrt(1.27*e8*h)
= e4 * sqrt(1.27*h) (m)
If h = 1.5 (m),
d = e4 * sqrt(1.27*1.5) = 1.38e4 (m) = 13.8 (km)
(not 437 (m), as Pearlsaw calculated).
In general, if the height of the observation point is
height = h, the distance is:
d = e4*sqrt(1.27) * sqrt(h)
= 1.127*e4 *sqrt(h/(m))
= 11.27 (km) * sqrt(h/(m))
buford1111
It depends on how high you are above the waterline and what the visibility is. As a general rule, if visibility is good and you are at the waterline, you can see the mast of a ship come over the horizon at 12 miles and the whole ship at about 9 miles. If your vantage point is higher you can see farther.
deflagrated
Distance to the horizon = SQR(12740*height)
height in km (12470 is the diameter of the earth)
Pearlsawme
The distance is found using this formula
S = √ [2a h] where a is the radius of earth h is the height from sea level.
Near a beach supposing that one's eye level is a at a height of
1.5 m the distance that he can see is
√ [2*6378* 1.5] = 138.325 m
If h = 15 m
Distance is 437.42m
nathan
11 miles out. that's why international waters begin at 11 miles