Distance to Horizon (x) Versus Eye
Height (h) of Observer
Note
that the following applies for a ‘smooth’ earth surface such large
lakes, oceans and level plains or deserts — where surface
irregularities are small compared to height (h).
x² + R² =
(R + h)² = R² + 2Rh + h²
x² =
2Rh + h² = h(2R + h)
x = √[h(2R
+ h)]
R ≈ 4,000 miles ≈ 21,000,000
feet
For x in miles and h in
feet:
X = {√[h(42,000,000
+ h)}/5,280²
X = √[h(42,000,000
+h)/27,878,400]
For h < 50,000 feet,
h/27,878,400 is very small, and X ≈ √[42,000,000h/27,878,400]
or:
X ≈
√(3h/2)
|
h in feet |
6 |
10 |
20 |
50 |
100 |
200 |
500 |
1,000 |
2,000 |
5,000 |
10,000 |
20,000 |
50,000 |
|
x in miles |
3.0 |
3.9 |
5.5 |
8.7 |
12.2 |
17.3 |
27.4 |
38.7 |
54.8 |
86.6 |
122.5 |
173.2 |
273.9 |
11/9/2002 Fred Bohl
