Question

How do you find the course speed and ground speed for the following, track 090°, air speed 300km/h, wind speed 060°, 50 km/h?

Answer 1

To find the course speed and ground speed given the track, airspeed, and wind speed, you can use vector addition. Here's how you can calculate them:

1. Convert all angles to a common reference frame (either true north or magnetic north) if necessary. For this example, we'll assume the angles are already in the same reference frame.

2. Draw a diagram representing the situation. You can draw a line to represent the track direction (090°) and another line to represent the wind direction (060°).

3. Calculate the wind component affecting the aircraft's motion. Since the wind is coming from 060° at a speed of 50 km/h, you can split it into two components: one along the track direction and another perpendicular to the track direction.

   • The component along the track direction can be found by multiplying the wind speed (50 km/h) by the cosine of the angle between the wind direction and the track direction. In this case, the angle is 090° - 060° = 30°. So, the component along the track is 50 km/h * cos(30°).

   • The component perpendicular to the track direction can be found by multiplying the wind speed (50 km/h) by the sine of the angle between the wind direction and the track direction. In this case, the angle is 090° - 060° = 30°. So, the component perpendicular to the track is 50 km/h * sin(30°).

4. Calculate the course speed. The course speed is the speed at which the aircraft is moving relative to the ground in the chosen track direction. It is equal to the airspeed minus the component along the track due to the wind. In this case, the airspeed is 300 km/h, and the wind component along the track is calculated in step 3.

   • Course speed = airspeed - component along the track

5. Calculate the ground speed. The ground speed is the actual speed of the aircraft over the ground, taking into account the wind. It is equal to the square root of the sum of the squares of the airspeed and the component perpendicular to the track due to the wind. In this case, the airspeed is 300 km/h, and the wind component perpendicular to the track is calculated in step 3.

   • Ground speed = sqrt(airspeed^2 + component perpendicular to the track^2)

By substituting the values obtained from the calculations, you can find the course speed and ground speed.