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The specific "sub questions" I'm asking are:

  1. When you are looking at clouds just on the horizon, how far away would they be?
  2. How wide (in km) is that total field of vision at roughly cloud height.

    • Let's assume that the clouds being viewed are of the high family form which range from 5-12.2km (16,500 to 40,000 feet) in altitude.
    • Let's assume flat or nearly flat ground at an elevation of 0-100 metres (328 feet) above sea level.
    • Let's also assume the viewer is human and approx 170cm tall (5'7").

I understand if the answers can only be approximates. Looking for both a general way to think about this question as well as how to measure the field of view in question. If it's difficult to take all the variables into account then can anyone explain what the absolute maximum distance would be in a best case scenario?

Similar but not the same question: How much sky do we see at any one moment?

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I would appreciate revisions to the question that keep to the spirit of the two "sub questions" that make it more useful or precise. Also would appreciate any other appropriate tags. Thanks. –  Lisa Oct 15 '12 at 21:51
    
Take a look at en.wikipedia.org/wiki/Horizon –  gerrit Nov 14 '12 at 23:18

1 Answer 1

Your question may be more than simple geometry, but it is worth having the geometry as a baseline:

Head and cloud

The distance from Head to Ground is $\sqrt{r_1^2-r_2^2}$ where $r_2$ is about 6,371km and $r_1$ is about 1.7m more, which is about 4.65km.

Similarly the distance from Ground to Cloud is $\sqrt{r_3^2-r_2^2}$ which, if $r_3-r_1$ is 10km, is about 357.1km.

So Head to Cloud is about 360km, and more if the cloud is higher. But things like hills getting in the way or other factors will also make a difference.

If a human's field of vision is about a half circle, then you might double that for side-to-side distance.

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I think in practice, it's very considerably less than that. There's actually an atmosphere in between... –  gerrit Nov 14 '12 at 23:09

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