Distant clouds

Well after sunset on Mauna Kea you can look out to the west and still see amazing colours in the sky and more often than not a dazzling display from very distant cirrus clouds. Sometimes these clouds aren't even on the IR satellite images although they always seem to be present on the western horizon. My guess is that they are a few hundred miles away and one day I'll sit down and try to calculate how far away they really are. It really ought to be a relatively simple geometry and trigonometry problem although I'll have to throw in the time of sunset as well and probably the odd assumption (such as how high the clouds are).

Atmospheric refraction probably ought to be taken into account as well - it becomes important when looking close to the horizon - I'm sure you've all seen those shots of a strangely-shaped sun just as it sets. When you look through a lot of our atmosphere, as you do when looking towards the horizon, it can do one or two odd things to the light - such as bend it.

There's a fairly simple formula you can use if you're ever on an aircraft looking out of the window and wondering how far you can see. I've often wanted to know this while flying over the US mainland, i.e., just how far can I see and what am I looking at way over there in the distance? It probably makes me a very boring passenger if you have the misfortune to sit next to me on a flight!

In the metric system the approximation is given by:

d = 3.6 * sqrt(h)

where d is the distance in kilometres and h your height above sea level in metres. Airliners typically cruise at around 11,000 metres (that's around 35,000 feet) which means the horizon is about 380 km away or approximately 235 miles distant. Give or take a few miles for haze and the exact altitude you're flying at, 200 miles is a good assumption on a clear day. The bit I need to work on is how far away those clouds might be given that they are probably 30,000 feet above the ocean.

A problem for a flu-ridden day I think...