Crosswind aileron input at liftoff
 

Anyone able to explain the aerodynamics of why more aileron is required to maintain wings level at lift off during a crosswind?

It's never a good idea to establish a need for a specific control input for a given instant in time when dealing with aerodynamics. Flying an airplane is performed in a 3 dimensional fluid dynamic where absolutely nothing is static and the dynamic is in a state of constant change.
Rotation is an extremely complex moment of transition. Depending on the aircraft being flown there are many factors in play during rotation, the wind being only one of these factors.
The main thing as relates to control usage is in remembering that no two takeoffs will ever be EXACTLY the same as relates to wind. Of course there are certain "standards" we start out with for aileron use during the takeoff run but even these standards are subject to instant change as the run progresses.
The best way to look at control usage during takeoff and rotation is to accept that nothing is ever written in stone. The aircraft itself is the best indicator for what control pressures are required at any given instant in time. What you corrected for on takeoff A will be different either as necessary or in the amount of required pressure on takeoff B.
The aircraft is the best flight instructor a pilot will ever know.
Dudley Henriques

Consider a swept wing airliner, and the direction of the crosswind - the upwind wing "sees" the airflow coming at it more directly, as if there is less sweep; and the downwind wing "sees" its sweep angle effectively increased.
Next have a look at the effect of wing sweep on the CL vs angle of attack graph. The straight wing has the steepest gradient, and more sweep reduces the gradient of the graph.
Finally, realise that as you rotate, you are increasing the angle of attack from something near 0 to something near 10 or more. So it is obvious that the upwind "less swept" wing will generate more lift unless you do something about it. Hence into wind aileron input is required.
On the B747 I fly, the aileron input required on the runway should roughly double as you rotate (steady crosswind).

The weight of the airplane between the two mains, is mostly what keeps it from tipping over the downwind wheel. And when that's the only force in action, it works pretty good (have you ever felt like you were in danger of tipping over, while sitting still?)

But as you add more and more lift while gaining speed, you're cancelling this weight away, so better come up with something else (differential lift from the ailerons) instead.

Maybe rudder input to keep tracking straight on the runway, lift off and secondary effect of rudder, aileron to counter?

True, however this need for aileron is directly related to dihedral. The vast majority of aircraft will have positive dihedral (meaning total dihedral effect, not wing dihedral angle), as negative dihedral would make the aircraft behave very weirdly. It would make the aircraft very unstable on the roll axis, I'm not even sure this could be certified.

However for other inputs, you are more than right. For example roll input during a stabilized turn.
Also, for aerobatics, the controls are often reversed when flying reverted...

Adding to the geometry, if you take off with a steady crosswind component, you need a certain amount of rudder deflection to keep tracking straight. As soon as the wheels leave the ground, the opposing lateral force from the runway goes and the aircraft is free to yaw, which has the secondary effect of roll away from the direction of the crosswind. That’s why the standard technique is to rotate with crossed controls, then gently remove the aileron and rudder together to leave the airframe in coordinated flight tracking the centreline. Of course, if it’s gusty, you’ll be overlaying aileron input on top of the bias you already have.

It’s actually a very simple process. At least try to understand it or use basic rules to help you out. Crosswind = stick into the wind & opposite rudder is a good starting point to avoid you’re going to be chasing 😉

The basic explanation has been given and is part of an ATPL training. Relative wind changes, and aerodynamic characteristics change as the airflow hits along a different line. If the airflow would cut the wing into profile sections, you would see these cross-sections change and create different lift.

On modern jets you can actually ’measure’ exactly how much aileron is needed. In a crosswind takeoff you’ll find yourself giving rudder inputs (weathervane effect) in the roll. Gently bring in the aileron until the ’pumping’ stops and only a gentle rudder input remains. Keep this control wheel deflection steady during rotation and your wings will not roll an inch. Not going into spoiler deflection discussions... I don’t care. I don’t want to be the guy explaining wingtip or engine pod strikes because I was scared of spoiler drag.

I am beginning to notice here on these forums that we have an EXTREMELY wide range of pilot experience and expertise. This isn't a bad thing. It's actually a very good thing.
But when we engage in discussion concerning a training issue it can get a bit confusing when someone posts in the realm of basic flight training in the GA sense and someone else answers as an ATP dealing with specifics to flying an airliner.
Not that there is anything wrong with this. It's just notable that there are certain "differences" in the two planes of reference.
Take rotation for example; in the general aerodynamic sense referencing an average GA type airplane, the act of rotating into the transition between ground roll and flight contains elements of torque, gyroscopic precession, P Factor, slipstream forces, AND any wind correction required. Hardly a "simple process".
This by no means requires an instructor to teach all this while dual is being given. This is done through preflight and postflight instruction. In the airplane while in flight naturally the proper pedagogy involves a rote response. So in this sense "yes".........it's a "simple process". The airplane tells you what it wants you to do and you do it..........simple!
The overall goal of both approaches to the issue is in understanding it in theory and executing it in flight.
In the 60 odd years I've been directly involved with flight safety and training I've learned that there is seldom one magic bullet answer to any question involving training issues and procedural issues. Nothing is really complicated while at the same time nothing is really "simple".
Dudley Henriques

Good instructors always keep the theory out of the cockpit. The instructor briefs before the session, the student flies the airplane, the instructor debriefs, and the student then puts the theory and what was done by rote during the dual session together during that all important period between flights where the REAL comprehension occurs.
It's a constant circle of learning. The KISS principle in action !
Dudley Henriques