[Treep Ravisarras]

At 47.9 km by calculation  136m should be hidden.

I tried your calculation, but shows 148m hidden at 47.9km, and 1.6m observer.

Same as my sine and cosine calculation, as expected. Not sure how you worked out the written 'theoretical' values in your link, but they do not come out of your formula.

Anyway, apparently we should allow for round earth refraction also.

[Treep Ravisarras]

Standard refraction occurs in average non-extreme case, bending light slightly downwards.
It is calculated simply by replacing Earth's radius in formulas by 7/6 * R.
So, instead of mean radius of 6371 km, you use 7432.833 km (or 7433 km).

Ok, thank you, easy enough. So, when I include this in my simple Round Earth assumption circle.

We get this result, quite interesting if I may say so myself.




Black dotted line is line of sight, rest below is hidden. Blue circle is ground.

Have to say that my calculation comes quite close to the video. Interesting. It simply is a Blue circle and some mathematics applied and I get result. Have included link so you can zoom in and out and play with it a little for who is interested.

[jimbob]

At 47.9 km by calculation  136m should be hidden.

I tried your calculation, but shows 148m hidden at 47.9km, and 1.6m observer.

Same as my sine and cosine calculation, as expected. Not sure how you worked out the written 'theoretical' values in your link, but they do not come out of your formula.

Anyway, apparently we should allow for round earth refraction also.

I looked at the video again and changed the observer height to an estimated 3m as he is not standing on the ground. I forgot to change it in the link.

[Treep Ravisarras]

Ah got it. Guy from video says height filmed at 2.1m. Maybe that why difference. So I used observer height 2.1m in last post.

But our mathematics same result I think, but different formula.