FlyingMoggy2
How is the pitching moment of the lift-weight couple balanced?
"Lift forward of weight has a nose-up pitching moment, which is counterbalanced by the downward deflection of the horizontal tailplane, which creates a nose-down counterpitch. Therefore, lift aft of weight requires the opposite balance."
Personally I think it is sloppy teaching to try and explain what is happening to the “Deflection” of the air. It is much clearer to talk about the resultant force. In this case if you had the center of lift ahead of the center of gravity, the coupling of these two resultant force would require a tail up force to balance them out. If the lift and weight is the other way around, you would require a tail down force. Pretty simple really.
How does a crosswind affect the critical engine?
A crosswind, depending on its direction, can either help to restore or aggravate the yawing moment of an aircraft with a failed critical engine. For instance, a failed critical number 1 engine will cause a yaw to the left. A crosswind component from the left will apply a restoring force to the aircraft's fuselage, whereas a crosswind from the right will aggravate the yawing moment further to the left due to the sideways force experienced on the right side of the aircraft's fuselage (which is from the right to the left). Therefore, a crosswind landing is of even greater importance with a critical engine failure.
I have highlighted the word “from” for a good reason. If it said “to” it would be correct. I’m not sure if it is a typo but it is clearly wrong. A crosswind from the same direction as an engine that has failed is going to make the yaw worse, period. Think about a crosswind take off and the rudder input that is required to keep it straight. Now imagine an engine failing and what effect this will have.