AeroPlus wrote:
On a cross-wind take-off, right after you break ground, you can for just a few seconds feel the sideways shoving of the air, shouldering you over, accompanied by a weathercocking tendency. However, this lasts just seconds and once the airplane has yielded to this force, it is flying and cannot feel the wind. This shoving tendancy right after take-off has to do because of the force that just was acting on it.
An aircraft isn’t a leaf with close to zero mass and huge “wing” area. It is the relative components that’s of interest, and the effect of wind gradients and momentum of the aircraft cannot simply be ignored. Yes, the ideal and rather naive version for an aircraft in a moving piece of air is that it moves relative to the air -always, thus ground speed is irrelevant and all that. This is “mostly true”, and probably all that a pilot flying a SEP need to care about, but it is NOT the whole truth, very far from it 
In certain situations the wind gradients and momentum of the aircraft plays major parts. Taking off (and landing for that matter) in a cross wind is such a situation, although mostly theoretical because gust associated with strong winds is often a more important factor to care about. Birds utilize these effects all the time, one of the finest examples is the albatross, using the gradients of the air close to the sea as the only “engine” for flight. These wind gradients would have no effect whatsoever if it wasn’t for the mass/momentum of of the bird. The whole point of the albatross flying is that it does NOT become “as one” with the air. To put it in other words, the reason it is able to fly as it does, is because what you are saying is positively wrong (just an ideal assumption when the mass of the aircraft is zero and the wind is constant all the time, everywhere).
An airplane flying through a moving airmass (wind) behaves a lot like walking in a moving train. The train is moving at a certain speed (the moving airmass). You get up from your seat and move to the front of the train to eat lunch, then move back to your seat. That movement in the train is as the aircraft flying within a moving air mass. Fly a circle when there is wind. On the ground that circle will not be perfectly round, but in the moving airmass, you might end up again pretty close to the air that you initially disturbed when you started the turn to fly the circle around.
I am no engineer and took this understanding from reading the Stick and Rudder book as written in 1944 by Wolfgang Langewiesche and still considered a good book on the topic. That book helped me to better understand the principles of flight and I had wished that I would have read that book earlier on at the beginning of my flight training. Langewiesche makes a few bold statements about the principles of flight in his book. One of them is that the reason airplanes fly has mainly to do with the wing as deflector of the air being pushed (deflected) down, thus as opposite effect that the aircraft must go up. It is an old book written over 60 years ago, but I don’t think it is considered outdated and the principles of flight haven’t changed.
The reason that a crosswind enroute at 90 degrees to your intended track behaves as a headwind is that you must use some of the aircraft’s speed to counter the sideways push and remain on the intended track. If your heading remained at 90 degrees you would not see a headwind but would be pushed sideways.
The sailing example is not relevant as the wing (sail) is oriented a completely different way
And the reason an ABA flight with any wind takes longer than one in still air even with AB lined up in the wind direction is that you spend longer in the headwind than with the tailwind so it affects you more.
A change in stall speed leads to an increase in weight automatically just due to the relationship between weight and stall speed. I am afraid I also don’t think this has anything to do with the present problem.
I accept there may be a momentary couple of knots increase in IAS when airborne before the inertia is overcome and the aircraft is accelerated by the crosswind. But that again doesn’t help you use less runway. Unless you takeoff in a diagonal way across the runway I don’t see a crosswind as possibly helping you shorten your roll and due to crossed controls etc needed to remain straight on centreline it probably lengthens it.
You don’t get more pure headwind; that remains at 70kt. But you get more wind, if slightly off-axis, and I think 73kt at 16 deg off-axis does produce more lift than 70kt on-axis.
5% more airspeed is about 10% more lift.
The confusion comes from our focus on how the aircraft moves with relation to the ground.
AeroPlus wrote:
One of them is that the reason airplanes fly has mainly to do with the wing as deflector of the air being pushed (deflected) down, thus as opposite effect that the aircraft must go up. It is an old book written over 60 years ago, but I don’t think it is considered outdated and the principles of flight haven’t changed.That’s exactly right. The wing achieves the upward (lifting) force, by exerting a downward force on the air. Newton’s third law in action.
AeroPlus wrote:
An airplane flying through the wind behaves a lot like walking in a moving train
Yes. But what happens when the train is turning or accelerating and breaking ? Imagine two trains moving side by side at slightly different speed, one at 100 kts and one at 110. Jumping from the fastest one to the slowest slowest, you will land on the other train at 110 kts, 10 kts faster than it moves, when you started zero relative velocity on the first train. So, from zero relative energy on the first train, you suddenly have 10 kts of relative energy (speed) on the second train.
When taking off in a cross wind (90 deg), you are essentially jumping on to the train that is moving perpendicular to your direction. Obviously there are lots of energy that needs to be “even out” before you are in sync with the wind. That energy differential can be used (maybe only in theory for us, but used all the time by birds).
To summarise (?)…
A crosswind won’t affect the takeoff run or the takeoff speed, but as soon as the aircraft is airborne it will weathervane into the wind and then gain some extra airspeed. So the performance of the first 50 feet or so of climb is slightly improved.
A crosswind won’t affect the takeoff run or the takeoff speed
I reckon it will make you reach the takeoff point a bit sooner. The takeoff AIRspeed itself won’t change.
After take-off it will weathervane into the wind but with no increase in airspeed. The ground speed changes but not the airspeed :-)
