Math CentralQuandaries & Queries


Question from Will:

the formula for figuring the earth's curve goes against logic, looking at a fixed point and backup 1mi. the point drops 8" then 16" in the next mi. and 32" in the third mi. why shouldn't it be 24" why is the 8" per mi. squared can you tell me in laymen's terms why this is it goes against logic it would seem the correct way would be to add up 8" per mile as you back up from the fixed point 8"- 16"- 24"- 32" not 8/16/32/64"

Hi Will,

Let me try with some diagrams. In the diagram below you are at the green dot on the surface of the Earth and the horizontal line is your line of sight. The horizontal scale is in miles.

line of sight

The vertical scale is in inches and the red dot below the 1 mile indicator is 8 inches below the line of sight. The red dot below the 2 mile indicator is 16 inches below the line of sight. The remaining red dots are 24, 32 and 40 inches below the line of sight respectively.

If you look carefully you will see that the red dots lie on a straight line.

The problem with your reasoning is that, because of the curvature of the surface of the Earth, the surface of the Earth drops away from the line of sight more quickly than linearly.

line of sight 3

I hope this helps,

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