# 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.

## Answers and Replies

tiny-tim
Science Advisor
Homework Helper
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.

Hi KLB! Welcome to PF!

You already have one of the internal angles - it's the ground speed heading minus the wind speed heading!

And remember cos(90º + x) = -sinx.

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