Tuesday, November 29, 2016

Distance to the visible horizon on a flat earth versus globe

If we live on a globe then the curvature of the earth goes with some distance quadruple downwards showing us a distinct curve. But if it is a flat earth or a plane then what you can see has a linear relationship. How can you calculate the distance to the visible horizon on a globe model and a flat earth? 

Globe model

We have been told that the earth is a globe with a radius of 6371 km. This means that from our point of view the edge of water or the horizon actually will block the waters that lie behind this line. But for the argument if it is a globe model then how do you calculate the distance to the horizon? So if you are on an outlook of 7,5 m then your horizon would be due to the curvature of the earth at (6371007,5^2-6371000^2)^(1/2) =  9,7 km.

Flat earth model

If you look at ongoing water such as the sea on a plane or flat earth there appears to be a mirror behind the visible horizon. This is caused due to perspective as all the lines of sight converge near the horizon. The visible horizon is created due to to much information or colours behind the horizon. It results in a mirroring effect. From our point of view also are line of sight is mirrored at the horizon. This is very typical as when you follow ships over the horizon, they seem to be disappearing from down to up. But they disappear above the visible horizon. Based on the theory of line of sight and a mirror after the visible horizon and the distance to the Sun you can find a relationship like this for the distance to the flat earth horizon: dh = distance horizon = ht/(tan(tan-1(6,35/15650))) = ht/0,40575 with in that ht = height of eye in m and dh in km. So if you are at an outlook-point of 7,5 m then your horizon would be at dh = 7,5/0,40575 = 18,5 km. Based on this theorised model you can see much further on a flat earth then you can do on a globe.

PS: I am not saying that the forgoing formula for the distance calculation of the visible horizon on a flat earth is completely correct, but it does give a direction on how much it might be.

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