Trigonometric Riddle: Determine Wind Speed & Direction

[chileflora]

Hi, I got a problem I am trying to solve.

An airplane flies at a fixed air speed which is unknown. There is a wind with unknown heading and unknown speed. The airplane has a known ground speed and direction. The airplane changes heading (with reference to ground), and now there is a different ground speed and direction. How to determine on basis of this information (two sets of ground speeds and directions) the wind strength and wind direction? The speed of the airplane with reference to air does not change.

 

[jvicens]

Hello,

Thank you for reaching out with your problem. I would approach this problem by first gathering all the known information and variables. From your post, it seems that we have the following information:

1. Airplane's fixed air speed (unknown)
2. Wind's heading (unknown)
3. Wind's speed (unknown)
4. Airplane's ground speed and direction (known)
5. New ground speed and direction after change in heading (known)
6. Airplane's speed with reference to air (constant)

The key to solving this problem is to use the concept of vector addition. We can represent the airplane's ground speed and direction as one vector, the wind's speed and direction as another vector, and the resulting ground speed and direction after the change in heading as the sum of these two vectors.

Using basic trigonometry and vector addition, we can set up equations to solve for the unknown variables. We know that the airplane's ground speed and direction are known, so we can use that as a starting point. We also know that the airplane's speed with reference to air does not change, so we can use that as a constant in our equations.

To determine the wind strength and direction, we can use the following equations:

1. Wind speed = (resulting ground speed - airplane's ground speed) / (cosine of angle between resulting ground speed and airplane's ground speed)
2. Wind direction = direction of resulting ground speed - direction of airplane's ground speed

By plugging in the known values and solving for the unknown variables, we can determine the wind strength and direction. It's important to note that we will need both sets of ground speeds and directions to solve for the wind variables, so it's crucial to have accurate and consistent measurements.

I hope this helps in solving your problem. Please let me know if you have any further questions or if you need clarification on any of the steps. Good luck!