Q&A for How to Calculate the Distance to the Horizon

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Can I see an object beyond the horizon?

Community Answer

Not the entire object, but you might be able to see part of it if it's tall enough. If something like a tree or a building is standing just beyond the horizon, you might be able to see the upper part of it.

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Question

Why wouldn't the formula for determining distance to the horizon work in a city or a forest?

Community Answer

The trees in the forest or the buildings in the city would affect the view.

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How many acres in 630 sq ft?

Donagan

Top Answerer

Because there are 43,560 square feet in an acre, 630 square feet equal 630 / 43,560 = 0.01446 acre.

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Is there a method of calculating distance from a visible object in the sky?

Community Answer

Yes. One modern way is by using radar, but a more traditional way is by using trigonometry and parallax. Measure out a straight baseline along the ground, and carefully measure the angle between this baseline and your distant object from each endpoint of your baseline. One then has two angles and their included side, so it is now possible to solve for the missing lengths: a = L * sin(A)/sin(A+B) where L is the length of your baseline, A and B are your two measured angles, and "a" at the distance along the side opposite angle A (i.e., between the point at angle B and the distant object).

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How many miles away is the horizon at an altitude of 30 feet above sea level?

Community Answer

1.17 X the square root of height of eye = distance to the horizon in nautical miles. Maybe 3 miles if you are standing in a boat and 9 feet above the water.

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Question

The formula is wrong. Should be d=R*Sin(arcCos(R/R+h).

Community Answer

You are correct that the formula seems to be missing a sin. Perhaps the authors intend to use the small angle approximation (sin x ~ x) which is good enough for this sort of calculation, but only works if your calculator is in radians mode when you do the arccos. To avoid misleading readers, they should have either explicitly specified radians, or used your formula where it doesn't matter how angles are measured.

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Why are you are saying the Horizon is about 89 miles away when other websites are saying its about 3 miles?

Community Answer

My statement was in error. The 89 mile reference pertained to a higher observation point above the ground or ocean. 3 miles is correct.

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Question

@Donagan, please elaborate your answer. Why it is 89 miles even if you use refraction it is not 89 miles?

Donagan

Top Answerer

You're right. It's 3 miles, not 89. The 89 mile reference related to a higher observation level. I apologize for the confusion.

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Question

How do I derive the formula to calculate the distance to the horizon?

Peter Porro Klinger

Community Answer

1.17 X the square root of height of eye = distance to the horizon in nautical miles.

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