I think you will find the equations you refer to are the Navier-Stokes (not Napier-Stokes)!
AnthonyQ wrote:
Indeed….if lift was all about deflecting air downwards what would be the point of a camber?
Camber will result in air getting deflected downwards (downwash). A cambered airfoil will deflect more air downwards than a barn door at the same angle of attack.
Helicopters have cambered blades – try standing under a hovering helicopter some day and tell me that there aren’t vast quantities of air getting deflected downwards!
Let me try to understand that.
When I was a child, my parents used to travel by car a lot, to our respective holiday locations, and I was usually sitting in the backseat getting bored, no iPhones invented yet. So I frequently opened the window, and held my hand out.
It always seemed so easy to understand. When I tilt the hand slightly, the air which blows at the lower side is being compressed and deflected downwards. And of course, this creates a cushion of air on which the hand then glides upward. And, because the air which is being blocked from blowing over the upper side of the hand (which it does when the hand is level with the surface), automatically creates sort of a mini vacuum or area of lower pressure which helps the hand to move up. This, of course, works similar the other way round, when I tilt the hand down, it moves down because the cushion of air being created on the upper side.
I always thought planes are working the same way, at least my little paper gliders I used to fold and throw away. The air on the lower side acts like a cushion, on which the glider glides along. It just seems natural.
So, when turn the yoke i.e. to the left, I lower the right aileron, it creates an area of higher pressure underneath itself, a cushion of locally compressed air, on which the aileron glides upward, and because nothing stops it from doing that, it takes the whole wing with it. Vice versa on the other side.
What doesn’t seem so natural is explaining it from the other way around, and I was always unsure whether this Bernoulli stuff, where molecules of air want to meet their former colleagues at the end of the wing, was really correct. It doesn’t seem to be. Makes my world a little better :)
So, Alioth, I tend to disagree with you. The camber itself doesn’t create a downwash. It creates more negative pressure on the upper side of the wing (what I called mini vacuum as a child), so that the downwash (what I call cushion of air) results in an even better movement upwards.
alioth wrote:
Camber will result in air getting deflected downwards (downwash). A cambered airfoil will deflect more air downwards than a barn door at the same angle of attack.Helicopters have cambered blades – try standing under a hovering helicopter some day and tell me that there aren’t vast quantities of air getting deflected downwards!
And at the same time the camber will deflect the air up more (upwash) towards the advancing blade…
The large amounts of air moved down by a rotary wing, or sideways behind a propeller, is a side effect of the pressure changes caused by the lift, generated by the blades, i.e. you can still have the lift, measurable by the pressure change, but no net movement of air, if you trap the air…
Consider what would happen if your the helicopter was hovering in a sealed tube? You can find examples that might help answer this by looking at a hovercraft, with its ducted fan, or a fan in a vacuum cleaner… In the case of the vacuum cleaner (fan in a tube) if you place your hand over the tube, the airflow stops, but you still get a force which you can detect as a much lower pressure.
EuroFlyer wrote:
What doesn’t seem so natural is explaining it from the other way around, and I was always unsure whether this Bernoulli stuff, where molecules of air want to meet their former colleagues at the end of the wing, was really correct. It doesn’t seem to be. Makes my world a little better :)
But Bernoulli doesn’t say that at all! That is one of the biggest misconceptions – the “equal transit time” fallacy – that Bernoulli says that the air going over the top of the wing must meet their former colleagues at the end of the wing. In fact, the air over the top goes much faster relative to the air underneath, and gets to the trailing edge long in advance of the air at the bottom.
And this effect is present even with a barn door presented to the air with a positive angle of attack. The air over the top will get to the trailing edge long before the air at the bottom does. There is no equal transit time. A barn door just won’t do it as efficiently as a properly shaped airfoil.
Also if you took a flat bottomed wing (e.g. a TriPacer wing) and set it up in a wind tunnel, with the bottom of the wing parallel to the airflow, you would observe downwash.
What you describe as a “cushion” of air you felt when you put your hand out the window is the higher air pressure also described by other models – while you have lower pressure on top of the wing/hand …. It’s just a different way to express it.
But, i stand by it, the whole theory of lift is too complicated and has too many aspects to be discussed here successfully.
Ted wrote:
The large amounts of air moved down by a rotary wing, or sideways behind a propeller, is a side effect of the pressure changes caused by the lift, generated by the blades, i.e. you can still have the lift, measurable by the pressure change, but no net movement of air, if you trap the air…
The pressure difference is not in dispute. But air will still be getting moved and there will still be downwash.
alioth wrote:
downwash
and upwash… 
This video at about 1:05 as the aileron is lowered you can clearly see the increase in upwash! and of course the corresponding downwash 
Is quite remarkable how the deflection of the aileron affects the air approaching the wing.
At the end of the day the theories need to match the realities.
alioth wrote:
AnthonyQ wrote:
Indeed….if lift was all about deflecting air downwards what would be the point of a camber?
Camber will result in air getting deflected downwards (downwash). A cambered airfoil will deflect more air downwards than a barn door at the same angle of attack.Helicopters have cambered blades – try standing under a hovering helicopter some day and tell me that there aren’t vast quantities of air getting deflected downwards!
If you read my post I did not dispute that there is deflected air…my point was the misconception that Peter et al have that it is all about deflection…implying in some way that it is similar to the mass flux produced by a jet engine… the reduced pressure caused by the accelerated air has the major effect…
the misconception that Peter et al have that it is all about deflection
I never said it is “all” about deflection. I said the picture (of lift) is made up of several things, and all of them are required for it to work.
It doesn’t need to be an aerofoil and indeed ailerons rarely are aerofoils; they just move the airflow up or down.
