Distance to the Horizon
The horizon is closer than you think.
Everyone over-estimates their distance from the horizon. If you look down a road in Kansas (a notably flat State), the road appears to go on forever … right to the horizon. You might think the road ahead is empty until an oncoming car pops up surprisingly quickly. Standing at the shore of a big lake, you assume you should be able to see things on the far shore. On the ocean, the horizon looks very far away indeed, until a boat steaming away from you disappears much too quickly. The curvature of the Earth is something we all know about, but we don’t take it into consideration in normal observations. The water in that lake is not flat, nor is the ocean or even Kansas. The horizon is surprisingly close to you unless you are at a great height.
The formula to calculate how far your horizon is from you is quite simple:
1.32 times the square root of your altitude in feet
is the distance to the horizon in miles.
Example 1:
Say you are six feet tall and standing on a dock three and a half feet high which places your eyes at nine feet above the water of a lake. The square root of nine feet is 3 feet. Multiply that by 1.32, like the formula says, and your horizon is only 3.96 miles away. If the lake was eight miles long and another tall person was standing on a similar dock at the far end of the lake, you could not see him. He would be hidden by the curvature of the Earth. That lake is not as flat as we assume.
Example 2:
Say you are on commercial airliner cruising at 35,000 feet. The square root of 35,000 is about 187. Using the formula, multiply that by 1.32 and your horizon is a little short of 250 miles away. Altitude makes an enormous difference.
Example 3:
Say you were on that dock again, but looking out on an ocean that appeared “a little choppy” with, perhaps one foot waves. You study the horizon and are astonished see really big waves moving way out there on the distance horizon. But if that horizon was only 3.96 miles away, the observed waves would be consistent with the one foot chop at the beach.
