I understood now that you are not a FETler defending FET as I thought in the beginning lol.

I cannot follow your calculation, but while searching for the formulas in the internet I found the amazing blog made by Walter Bislin. Did you know this?

No, I'm not a FEer.

The calculation is an approximation based upon Pythagoras for a great circle.

This image might help

Basically the horizon is a point on Earth (marked by a black h) which you can extend a line tangent to Earth towards the observer (marked by a black o).

This line has a length of d. The observer is at a height of h above the Earth, and Earth has a radius of R.

This gives a right angle triangle and thus by Pythagoras we know:

*R*^{2}+

*d*^{2}=(

*R*+

*h*)

^{2}*R*^{2}+

*d*^{2}=

*R*^{2}+2

*Rh*+

*h*^{2}*d*^{2}=2

*Rh*+

*h*^{2}*d*^{2}/(2

*R*)=

*h*+

*h*^{2}/(2

*R*)

If we now note that

*h*^{2}/(2

*R*) is basically nothing as R is much larger than h (unless you are very high, in space), this can be approximated as:

*d*^{2}/(2

*R*)=

*h*And this is where the FE saying of 8 inches per mile squared comes from.

I was being lazy and using excel solver to figure it out.

But to do it properly we really need a scaling factor, say k.

So to change the formula, now d and h are measured in px and k is in say m/px, we get:

(

*kd*)

^{2}/(2

*R*)=

*kh*k

*d*^{2}/(2

*R*)=

*h*k=2

*Rh*/(

*d*^{2})

That lets you figure out the scale factor and then find out what the dip and length would need to be.

Does that make sense?

The problem is that this focuses on the great circle which will be hidden by the horizon.

As for the site, while I haven't spent much time on it, I have seen it used here and had a cursory look at it before.

It does a much better job that what I have been doing as I have been focusing on the great circle, not the horizon.

I still dont really understand why I got this strong distortion at the beach and not at the kitchen Both were taken with 1x zoom and auto focus, while at the beach the focus point was most likely near infinity and in kitchen also not so far away from that. At least it looks sharp with at infinity and gets already unsharp by moving towards makro by around 10%.

There are a few possibilities.

Perhaps the simplest is that the tiles aren't actually that straight and you just can't easily tell by eye. Most people wouldn't notice a slight curve in the tiles, and depending upon how they were laid, there might be some curve.

Another is auto-correction by the software of the camera.

With some cameras, rather than trying to have the lens be perfect they choose to distort the image in software to try and make it look better. In some cases this will be applying a "simple" transformation based upon the known properties of the lens. Then there is the lazy way based upon a more complex algorithm which tries to fit something in the photo and then applies a distortion based upon that. It could be that it uses the latter algorithm and fitted the grid better than the horizon.

Another issue is distance. The actual distance to the object can affect what kind of distortion you have based upon the changing focal point.

The final issue I can think of (which I overlooked before) is that the line of the tiles doesn't quite match the line of the horizon.

The tiles are a straight line, the horizon is a circle. These get distorted differently.

Thanks for the lesson

Peace

Your welcome.

Glad I could help.