The earth is ENORMOUS. Even at the seemingly very high altitude of 120k feet, you are not very high up in terms of the size of the plant overall.

Earth has an average radius of 3959 miles. That's 21 million feet. 120k feet is 1/2 of 1% of that. If you take a basketball as a model of the earth, the balloon is less than 1/32 of an inch off the surface.

If you can see the "curvature" that is the horizon, then why does it not follow the same curvature should be expected to be seen horizontally along the horizon?

From near sea-level. there is absolutely no horizontal curvature of the horizon to be seen - nil!

Imagine being on an island in mid-ocean with a relatively calm sea.

All around you the horizon is exactly the same distance away and has to be the same height, just a few metres below eye-level. It does not matter which way you look, it's the same.

You can imagine looking at a very large circle around you. Seen edge on it looks perfectly flat.

From

1.5 m above sea-level, ideally the horizon is about 5 km away and 3 m below eye level. This makes the horizon only 0.03° below eye-level - quite imperceptible!

100 m above sea-level, the horizon is about 41 km away and 200 m below eye level. This makes the horizon 0.28° below eye-level - unnoticeable to the unaided eye, but measurable with good instruments!

10,000 m above sea-level, the horizon is about 412 km away and 20,000 m below eye level. The horizon is now 2.8° below eye-level - barely detectable to the unaided eye, but easily measurable!

even 20,000 m above sea-level, the horizon is about 582 km away and 40,000 m below eye level. Now the horizon is 3.9° below eye-level - detectable to the unaided eye, and easily measurable!

Now, what does this mean as far as visible curvature goes? So far I am guessing! But certainly

a 41 km circle only 0.28° below eye-level is not going to show any visible curvature, but when in comes to

a 412 km circle 2.8° below eye-level any visible curvature will be very small, especially looking out of a passenger plane window.

a 582 km circle 3.9° below eye-level any visible curvature will still be small, but probably quite noticeable from a pilots wider angle view..

What I will try to do is to work out just what would show on a flat photographic image - that's just geometry, once I get my head around the problem!

Maybe someone better at graphics than I can help.

There is this photo showing this "dip angle to the horizon" from an aircraft's instruments superimposed on the outside horizon.

The angle down to the visible horizon (somewhat blurred) looks to be 2.7° to 2.8°.

Before seeing that, I had done those calculations on the "dip angle to the horizon" and one line happened to be:

**Altitude**
| | **Dip Angle**
| | **Horizon Distance**
| |

**32,808 feet**
| | **2.8°**
| | **256 miles**
| |

It is certainly refreshing to see calculations work out like this.

I had not given a thought that flight instruments prove this horizon dip on every high altitude flight! There might be some curvature on that horizon, you have a look.

Then there is this video, which is aimed at "debunking" the idea that "The horizon always rises to eye-level", so it is certainly biased that way:

None of these are really aimed at showing "curvature", but at showing the "dip angle to the horizon", which is much easier to measure and much more definitive, besides being one way that the radius (of curvature) of the earth has been measured even from ancient times.

You could look at:

**Al Biruni measured the radius of the earth** by measuring the

*dip angle to the horizon* as in

**Al-Biruni's Classic Experiment: How to Calculate the Radius of the Earth?** *Sorry, this wasn't meant to go on so long, but it just grew - like Topsy!*