#### Pertti Niukkanen

##### Member

Putting these values into Walter Bislin's calculator we must notice that in the View∠-box is the diagonal FOV. But 65° is the horizontal FOV. So you must type into the View∠-box the value 65*1.2018502 = 78.1203. http://walter.bislins.ch/bloge/inde...6-9-9-9-6~0.0343-10-11013.0098-114.987-9-31-1

Without refraction, we get the values as follows:

These calculations in the FlatEarth.ws -article are correct:

– Distance to the horizon = 5048 m (HorDistView v)

– Length of the visible horizon = 5425 m (HorLftRgtWidth)

The visible bulge (sagitta) of the horizon (HorLftRgtDrop) is 0.742757 m. But FlatEarth.ws says, "If the length of the horizon is 5048 m, then the bulge in the middle is 0.577 m." This is clearly not correct.

The bulge calculated by FlatEarth.ws is the sagitta of the circular segment of the Earth's great circle when the chord is 5425 m. You can see this with the Metabunk calculator when the distance is 5.425 km:

"Sagitta (or 'Bulge') is the amount of rise of the earth's curve from a straight line connecting two points on the surface. 'Sagitta' r-sqrt(4*r*r - d*d)/2, = 0.58 meters", https://www.metabunk.org/curve/?d=5.425&h=1000&r=6371&u=m&a=a&fd=60&fp=3264

This is the sagitta we have been talking about when trying to show the curvature of the Earth. It does not depend on the observer. The horizon bulge (HorLftRgtDrop) is the sagitta of the horizon ring, seen at a certain height above the center of the ring. These are two different things.

In this example the "Earth curve sagitta" is 58 cm and the "Horizon curve sagitta" is 74 cm. They are almost the same. So the sentence in the meme is right: "The bulge is only about 0.01% the length of the visible horizon". However, the reasoning is wrong.

At the observer height 5 m we get the chord 8577 m and the horizon curve sagitta 1.86 m. Then the bulge is about 0.02% the length of the visible horizon. Yet we might say that the conclusion is true: "We can’t see Earth’s curvature from the Earth surface itself, not because “there’s no curvature”, but because the curvature is too small for us to perceive."

Ultimately, the conclusion is based on a misconception that confuses the "Sagitta of the Horizon curve" with the "Sagitta of the Earth curve". So FlatEarth.ws should correct the meme and the article, especially since Erik Yde Lauritsen pointed out the error in the comment section already four years ago. (Although I don't know where he gets the bulge 62.6 cm from, instead of 74.3 cm.)