Final answer:
In crosswind conditions, the crab angle allows an airplane to maintain a velocity parallel to the runway. Last-minute maneuvers for alignment during landing include the 'side slip'. Angles can be determined through vector addition and component resolution of velocities.
Step-by-step explanation:
To safely land an airplane on a runway in crosswind conditions, one must calculate the crab angle to have a velocity parallel to the runway. Given the velocity of the wind (wind speed and direction), the speed of the airplane relative to the air mass, and the runway direction, we can apply vector addition to solve for the crab angle. Finally, we determine the ground speed of the airplane by combining the airplane's speed relative to the air mass with the wind's velocity vector.
Last minute maneuvers may include a 'side slip,' which involves angling the airplane's nose into the wind while dropping the upwind wing slightly. This allows the airplane to maintain its trajectory towards the runway while aligning its wheels for landing.
Example Problem:
Assume the runway is aligned north-south, the wind is coming from the west at 10 m/s, and the desired track of the airplane is due south at a speed of 50 m/s relative to the air mass.
- Calculate the angle to fly relative to the air mass.
- Calculate the speed of the airplane relative to the ground.
Let θ represent the crab angle needed. The equation for the component of the airplane's velocity that goes directly south is:
50 m/s × cos(θ) - 10 m/s.
The goal is to make sure the southern (parallel) component accounts for the wind speed, thus the equation simplifies to:
50 m/s × cos(θ) = 10 m/s.
By solving this equation, we can determine the necessary crab angle.