# Bird flight speeds

## Homework Statement

Please bear with me. I'm a PhD student biologist struggling to remember some maths and physics, so I fear that this question may seem very simple to people using this forum.

The problem I have is with some data I have on bird flight, measured using a radar. I have bird ground speed (in metres per second) and heading (in degrees from north) and wind speed (in metres per second) and heading (also in degrees from north). I want to calculate airspeed. This would be simple if I had the angles between the two forces, but using bearings from north doesn't give me any of the internal angles of the triangle that I need to construct.

I can obviously use charts and marine navigational aides to work this out in practise, but I have 500,000 bird tracks, so need to be able to program the calculations.

One example track has bird ground speed of 15 m/s, with a heading of 136 degrees from north. Wind speed is 5 m/s with a heading of 295 degrees from north.

## Homework Equations

Sine Law
sin a/A = sin b/B = sin c/C

Cosine Law
c^2=a^2+b^2+(2abcosc)

## The Attempt at a Solution

I'm afraid that this is as far as I've got. My problem is really finding one of the internal angles of the triangle, in which case I can use the cosine law to calculate the length of the third side.

I've considered treating the two vectors seperately and looking at the displacement in x and y for each, but this doesn't deal with tracks and wind speeds that are in the opposite 180 degrees (you get problems with whether a speed should be added or subtracted).

Many thanks for any guidance you can give on how to treat this problem or on methods for finding one of the internal angles.

tiny-tim
Hi KLB! Welcome to PF! And remember cos(90º + x) = -sinx. 