Contrails Fun 2 – Angles and Distances

After last years first episode with contrails, another one popped up today.  During a late afternoon walk, on a sunny Winter’s day, I saw a great contrail right over the Melbourne area:

[click on all pics to zoom in]

The FlightRadar24 app on the phone said NZ to South Africa and at about 34,000 ft (~ 10,000 m). So I continued the walk and a bit later I looked left (~West) and the day was so clear, I could still see it ‘miles’ away: I mean it making fresh trails. I firstly snapped a – zoomed in – picture:

Then I checked FlightRadar24 again. It was way over near Skipton:

I guessed its angle above the horizon, using the cool outstretched hand-fist rule. I’d estimated between 5 and 10 degrees.

So later on at home a bit of high-school maths. And some help from Google as I’d forgotten the basics! :

Skipton is about 130 km from me. The plane is 10 km off the ground. What is the angle (theta) from the horizon?

So, Tan(theta) = 10/130  [“opposite over adjacent”]

Tan(theta) = 0.0769

theta = 4.4 degrees

Very close to my 5 to 10 degrees. Yay me.