# math

1. ### Contrail Angle with the Horizon - A Useful Distance Rule of Thumb?

The above diagram shows a grid of lines at 35,000 feet above the ground, viewed from ground level. Each line spacing is five miles apart. I've previously shown how to use the elevation of the horizontal lines to get a ballpark estimate of distance. But what about the sloped lines, what can they...
2. ### Let's imagine the actual area of the sky, above....

...OK. This is math that might be beyond me, and I'm hoping that others will feel free to chime in, and help. Here is the proposal (to dispute the myth of a concerted "spraying" effort, by showing how absurd it is, using math and geometry). I personally (amongst others) might be remembered...
3. ### Two planes at the "Same" Altitude, only one leaves a trail

Via Twitter: The first thing to notice here is that the planes are not actually the same type: But even if they were, the visual difference in size between a plane at 36,000 feet, and another at 38,000 feet is just 5%. In this image, the visually smaller plane on the left is 57 pixels long...
4. ### How far away can I see an aircraft?

I think the answer to this question might help people understand better what they are seeing in the sky. I live in Bristol in the UK. the road I live on is a few degrees off a straight North/South direction, so my lounge window is pointing slightly south West. I was looking out of my window...