A pilot wishes to fly on course 290 with an air speed of 300 knots when the wind blows from 224 at 18 knots. Find the drift angle to the nearest hundredth of a degree.
3.18
To find the drift angle, we need to consider the effect of the wind on the plane's course. The drift angle is the angle between the heading of the plane (which is directed along the desired course) and the ground track (the actual path of the plane over the ground).
To calculate the drift angle, follow these steps:
Step 1: Get the components of the wind vector
The wind is blowing from a direction of 224 degrees at a speed of 18 knots. We can represent the wind vector as (wind speed, wind angle). Convert the wind angle to radians:
wind_angle_rad = 224 * pi / 180
So, the wind vector components are:
wind_x = wind_speed * cos(wind_angle_rad)
wind_y = wind_speed * sin(wind_angle_rad)
Step 2: Get the components of the plane's velocity vector
The airspeed of the plane is given as 300 knots, and it is flying on course 290 degrees. Convert the course angle to radians:
course_angle_rad = 290 * pi / 180
So, the plane's velocity vector components are:
velocity_x = airspeed * cos(course_angle_rad)
velocity_y = airspeed * sin(course_angle_rad)
Step 3: Find the drift vector components
The drift vector represents the difference between the wind and the plane's velocity vectors. To find the drift vector, subtract the wind vector components from the velocity vector components:
drift_x = velocity_x - wind_x
drift_y = velocity_y - wind_y
Step 4: Calculate the drift angle
The drift angle θ is the angle whose tangent is given by:
tan(θ) = drift_x / drift_y
Since we have the drift vector components, we can find the drift angle using the atan2 function:
drift_angle_rad = atan2(drift_x, drift_y)
Finally, convert the drift angle to degrees:
drift_angle_deg = drift_angle_rad * 180 / pi
Therefore, by plugging in the values, the drift angle can be calculated to the nearest hundredth of a degree.