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Why does the velocity of air flowing over the top surface of aerofoil increase, when there is no contraction in area over the top?

user43704
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2 Answers2

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The aerofoil's angle of attack (angle of the wing to the airplane's path through the air) creates a low pressure area above the wing rearward from the leading edge that sucks in and accelerates air from the leading edge and circulates it upward. The lower surface of the wing tends to compress air, slows it down, and circulates it downward. The combination of low pressure on top and higher pressure on bottom lifts the airplane.

At some angles of attack, it's advantageous for an aerofoil's cross section to be convex on the top, and concave or flat on the bottom. The convex top path is longer than the concave or flat bottom path, which has given rise to the Longer Path or Equal Transit explanation of why air flow across the top is faster than air flow past the bottom.

The reasoning is that as the aerofoil moves at one speed through the air, if all the air meets at the trailing edge at the same time, but the top path is longer than the bottom path, then top air flow must move faster than bottom air flow, as the outside of a curve is longer than the inside of a curve. This assumption is incorrect and provides a misleading explanation. If both top and bottom air flows met at the same time, there would be little or no lift. Notice in the linked video that the angle of attack determines whether air flow is faster on top or on bottom.

Speed of air flow along the top of the wing is greater because the angle of attack creates an area of low pressure that sucks in air and circulates it upward. Speed of air flow along the bottom of the wing is less because the angle of attack creates pressure that slows the air and circulates it downward. This can be reversed if the angle of attack is reversed.

Ernie
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    I don't think this is correct. It seems like you are referring to the equal transit theorem, which is the basis of the common explanation of airplane flight, however this is not true. The seperating air flow must not connect at the other time. It has to do more with the geometry of the wing and yes you mentioned geometry, but it seems like you are using that in terms of the equal transit theorem. Correct me if I misinterpreted your answer. – Magnetar Mar 31 '17 at 16:55
  • @Ernie: You are repeating the "equal transit time fallacy", which has been taught for decades and is not true. In fact if it were true, wings would not work. There's an excellent e-book presenting all this. – Mike Dunlavey Mar 31 '17 at 18:20
  • There's nothing wrong with the equal transit time theory if it is expressed properly. see my answer. – JMLCarter Mar 31 '17 at 20:14
  • @Magnetar : I edited the answer, based on your comment and others, to make it clear that equal transit time as generally expressed is not a complete explanation. – Ernie Apr 01 '17 at 00:38
  • @JMLCarter : Thank you for your comment and your answer. I edited my answer based on your comment, and others. If it is misleading or incorrect, please let me know. – Ernie Apr 01 '17 at 00:51
  • @MikeDunlavey : I edited the answer and linked a video that may support your comment. If I misunderstood you, please let me know. – Ernie Apr 01 '17 at 00:53
  • @Ernie: I'm glad you're starting to get the idea. If you go and read the e-book I linked, you will understand that the fundamental concept is circulation. The shape of the wing is only an optimization for airplanes that don't normally need to fly inverted. (Aerobatic aircraft use symmetric airfoils.) The wing induces a circulation, a vortex, which with forward motion results in deflecting air downward, resulting in lift. The velocity difference is just that circulation. – Mike Dunlavey Apr 02 '17 at 13:20
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@Ernie "et al", There's nothing wrong with the equal transit time theory if it is expressed properly (In fact it is very good at explaining the thin, zero AoA aerofoil scenario).

Often it is not well expressed. Firstly I'd call it an approximation rather than a "theory".

Crucially the assertion is this:
That after the aerofoil has passed the air returns to its original state. This is modelled and approximated by considering that for that to happen the transit time of the air over and below the wing would need to be equal. It's an approximation. Then we consider what would happen if the air over the thin aerofoil maintains it's speed but not its velocity....
Since the over-wing path is longer it will have a longer transit time, or you could say there will be a path deficit. Essentially that's a kind of estimated vortex, from which can be calculated an approximate pressure deficit. As a result of this approximation we can estimate both
1) that the actual air speed over the aerofoil will increase as it is pushed into the low pressure region, and
2) the pressure differential above and below the wing gives an estimate of lift.

What's nice about this explanation is the horizontal (zero AoA) aerofoil can and does generate lift. It's an important solution because this mechanism is very drag efficient, so it's ideally the one we prefer wings to use in cruise mode. (Not during take-off an landing when the overriding concerns are power and control.)

What would be very, very, wrong is if any-one felt that 50 years ago people were significantly less capable of systematic thought than the current generation. Which is partly what compels my input.

JMLCarter
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  • You're mistaken. Look here. You say: "after the aerofoil has passed the air returns to its original state". It doesn't. The wing induces a vortex, which turns rearward off of each wingtip, forming a wake, which slowly dissipates by transferring its energy to the ambient air. The wake is easily seen in smoke or contrails. It is no different from a watercraft that surfs. It gets upward force by pushing the fluid downward, forming a wake. That wake cannot form if equal-time is true. Long-lived falsehoods are not rare. – Mike Dunlavey Apr 02 '17 at 13:32
  • No you need to follow the reasoning properly. The vortex is the conclusion of this thought process based on reasonable starting assumptions. It's a model that works to a certain level of accuracy. – JMLCarter Apr 02 '17 at 17:38