Averaging angles… Again

Question

I want to calculate the average of a set of angles, which represents source bearing (0 to 360 deg) - (similar to wind-direction)

I know it has been

Answer 1

This is incorrect on every level.

Vectors add according to the rules of vector addition. The "intuitive, expected" answer might not be that intuitive.

Take the following example. If I have one unit vector (1, 0), with origin at (0,0) that points in the +x-direction and another (-1, 0) that also has its origin at (0,0) that points in the -x-direction, what should the "average" angle be?

If I simply add the angles and divide by two, I can argue that the "average" is either +90 or -90. Which one do you think it should be?

If I add the vectors according to the rules of vector addition (component by component), I get the following:

(1, 0) + (-1, 0) = (0, 0)

In polar coordinates, that's a vector with zero magnitude and angle zero.

So what should the "average" angle be? I've got three different answers here for a simple case.

I think the answer is that vectors don't obey the same intuition that numbers do, because they have both magnitude and direction. Maybe you should describe what problem you're solving a bit better.

Whatever solution you decide on, I'd advise you to base it on vectors. It'll always be correct that way.