Here’s a rather harrowing video I recently watched. It’s a commercial airliner on approach to a runway during a severe crosswind. The plane is attempting to perform a maneuver to keep itself flying over the runway without drifting off course, but this requires flying at an angle into the wind. It’s difficult and the pilot narrowly averts disaster by aborting the landing at about the last possible second.

The difficulty is one of relative motion. If you’re in a boat crossing a river to a point directly opposite your starting point, merely plowing straight ahead will result in your landing downstream from your destination. You have to angle upstream slightly to offset the drift. In particular, your angle is going to have to be such that the upstream component of your velocity with respect to the water is equal and opposite to the velocity of the water with respect to the shore.

Which is a slightly awkward way of saying that if the boat’s speed is v and the water’s speed is w, and the angle measured with respect to the straight line between the origin and destination,

More saliently,

Which says that the angle increases as the ratio of wind or water speed to vehicle speed ratio increases. If it goes over 1, the inverse cosine is undefined. Physically that means the wind/water is going faster than you and even a 90 degree angle can’t keep you on the straight and narrow. In practice I’m sure even considerably smaller angles are not possible to safely perform on an aircraft during landing.

On the other hand I have the luxury of sitting and thinking and typing about it. The associated situation in the plane probably became somewhat more difficult about the time the left wing sheared its tip off on the runway.