Alice’s White Queen claimed she could believe ‘six impossible things before breakfast’. Pilots come a close second. What about that most basic bit of aeronautical knowledge, how an aeroplane flies? In the English speaking world the usual demonstration is to blow over a sheet of paper and watch it rise..
lower pressure than stationary.
Let’s admit it, it is impressive, and quite counter-intuitive, and there is no denying that the sheet does rise. What about the explanation? The instructor announces that this proves that ‘moving air’, i.e. the jet he has blown over the top, has lower pressure than the stationary air underneath. He then explains that the curved top surface of the wing (shows a picture of the cross section of a wing at this point) is longer than the lower surface, and so air molecules going ‘over the top’, a bit of first world war imagery there, have to travel faster to catch up with their fellows taking the shorter route. In doing so, they get further spaced out which means their pressure is reduced. Two claims, both not quite right. Of course if you blow under the sheet, it rises even more enthusiastically, but our demonstrator never shows you that. And this explanation tells us nothing about how much lift is generated.
The jet of air blown over the top of the sheet is in fact at the same pressure as that underneath… let’s just say that again, the same pressure. Why, well the boundary condition for the air coming out of your lungs via your mouth is that it is at the same pressure as the air around it. It is indeed at a lower pressure than the air inside your lungs (otherwise it wouldn’t come out), and you raise the pressure in your lungs when you blow.. So moving air does have lower pressure than non moving, but you have to specify which non moving air you mean.
Now what about all these little molecules trying to catch up with their friends, like children in double file going to class, do they? Er, no. There is no invisible rubber band between two molecules forced by the wing to take different paths. So they don’t link up again. In fact, those going over the upper surface finish up ahead of those taking the lower, shorter, route (by an amount that depends on the lift coefficient if you want to know) , but we are getting ahead of ourselves.
travel faster to catch up and are more spaced out = lower pressure.
Both there is no link between the molecules above and below, they don't rejoin at the trailing edge.
The simpler way to look at a wing is to just regard it as a device for deflecting air downwards. To do that you have to tilt it relative to the air flow. And if the air is pushed down, it, by Newton’s Laws, must push the wing back up, which we call lift. The clever aerofoil shape isn’t necessary to generate lift (which it is under the explanation above), though it is necessary to do it efficiently over a wide range of angles and speeds, and to provide thickness for the wing structure. Not only does this way of looking at the problem give the right answer, it also tells us, in a simplified way, how the lift varies with angle, speed and air density. The more the wing is angled to the flow, the greater the force applied to the air and the greater the lift; similarly the more molecules arriving at the wing, the greater their mass and the greater their speed, the greater the lift. So we finish up with the relation
L =f(αρV2)
Where:
α = angle of incidence
ρ = density, and
V = speed ( and it is V2 because the higher the speed, the more molecules arrive in a given time, and the greater the momentum they carry.
Not bad for a moment’s thought
There is just the little mystery of the rising sheet of paper to explain. If it isn’t because the jet going over the top surface is a lower pressure than the air underneath, then what is it? The answer is entrainment. Air either side of the jet tends to get caught up in it, to be entrained by it; the surrounding air is in effect being pumped away by the jet, so the pressure either side of the jet itself tends to be slightly lower than that further away. Any surface near the jet will feel that lower pressure and be sucked towards it, If there is only one such surface close by, the jet curves towards the surface, and the surface feels a corresponding force towards the jet. This is of course the famous Coanda effect, which causes a shower curtain to be dragged into the centre of the bath when the shower is turned on, and keeps those ping-pong balls balancing on a jet of water at the fairground. Ironically, this actually is the origin of the circulation around the wing without which there would be no lift, and it takes the viscous nature of fluids to get it started. No viscosity, no lift (readers with a background in aerodynamics will recall that lift is possible in inviscid flow, and we often assume no viscosity to make calculation easier; the snag is there is no way to get it going, but not to worry, all fluids other than those weird superconducting ones near absolute zero are viscous to some extent).
Please don’t misunderstand, the pressure over the top of a lifting wing really is lower than that underneath, it is just that blowing over the top doesn’t prove it. I think the real explanation is easier to understand and it is a pity books continue to peddle this half truth. Let’s not be too hard on the poor instructors, though. It took a good few years after the Wrights first flew before scientists and engineers could agree on what was going on.