Question

Construct Your Own Problem Consider an airplane headed for a runway in a crosswind. Construct a problem in which you calculate the angle the airplane must fly relative to the air mass to have a velocity parallel to the runway. Among the things to consider are the direction of the runway, the wind speed and direction (its velocity), and the speed of the plane relative to the air mass. Also, calculate the speed of the airplane relative to the ground. Discuss any last-minute maneuvers the pilot might have to perform to land with its wheels pointing straight down the runway.

In your constructed problem, the angle the airplane must fly relative to the air mass is:

a) Less than 45 degrees
b) Exactly 45 degrees
c) Greater than 45 degrees
d) Insufficient information

Answer 1

An airplane must adjust its course northeast to counteract a westerly crosswind, using vector addition and trigonometry to calculate the necessary angle, which is typically greater than 45 degrees, and to determine ground speed. Before landing, the pilot must perform "crabbing" or "side-slipping" maneuvers.

Step-by-step explanation:

Let's construct a problem where an airplane is trying to land on a runway in the face of a crosswind. Suppose that the airplane can travel at a speed of 300 km/h relative to the air mass, and there's a crosswind blowing from the west at 90 km/h. The runway is oriented north to south. We need to calculate the angle that the airplane must fly relative to the air mass to ensure a ground velocity that is parallel to the runway, as well as the airplane's ground speed.

To calculate this, vector addition is used where the plane's velocity relative to the air and the wind velocity are combined to give the plane's velocity relative to the ground. Using trigonometric functions, we can deduce the required angle and ground speed. Let's assume the angle is greater than 45 degrees. The pilot must then set a heading that's northeast to counteract the western crosswind.

The plane's ground speed can be calculated using the Pythagorean theorem or a trigonometric approach. Typically, the ground speed will be different from the plane's speed through the air due to the influence of the crosswind.

As for the last minute maneuvers, before touchdown, the pilot must align the plane's wheels with the runway, a maneuver referred to as "crabbing" or "side-slipping".