Posted: Dec 22, 2010 5:13 pm
Winging it

The myth I want to talk about is something that I was taught in a physics class in high school many years ago. Being a science geek at the time, I read a lot of popular books and saw this myth repeated in print more than once. The myth goes like this:

“In order to ensure lift is created, and aircraft wing is curved at the top and flat at the bottom. This means that the air has further to travel over the top and hence has to travel faster than the air flowing past the bottom. The air travelling faster causes a reduced pressure at the top of the wing due to Bernoulli’s principle and hence lift is created”

I will present two counterexamples to refute this explanation, and then will discuss the contents of the myth and highlight the right and wrong statements.

Firstly the counterexamples. Figure 1 shows a picture taken at RIAT (the annual airshow at RAF Fairford) of a pair of F16s from the US Thunderbirds display team. Immediately we see a problem with the given explanation. If true, an aircraft flying upside down should experience negative lift, since the curved surface is now on the bottom. This would be problematic for the display team !

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Figure 1

Figure 2 shows a cheap little balsa wood model (it’s actually a glider, but I remember building models like that powered with an elastic band and propeller). The problem here is that the wing cross section is not aerofoil shaped – it’s flat on both top and bottom, so Bernoulli is not around to help us. (Incidentally, being a Brit I will use British terminology, i.e. aeroplanes and aerofoils rather than airplanes and airfoils).

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Figure 2

The Bernoulli Principle – Cause and Effect

Firstly let’s examine the feasibility of using the Bernoulli principle to explain lift. The idea is that the fast moving air over the upper surface causes a reduction in pressure there which “sucks” the wing upwards. Bernoulli’s equation says basically, in the case of aerodynamics that

P+(1/2) ρV2 = constant along a streamline

where P is air pressure, ρ is its density and V is the velocity of the flow. Note that, although this equation is applied along a streamline, is can be extended to compare pressures between streamlines if we make the assumption that the flow is irrotational and the height difference between the streamlines is small [1]. From this equation, we can see that if the velocity of the flow over the wing is higher than the velocity of the flow under the wing, then the pressure over the wing must be lower than the pressure under it.

It is important to see that this equation merely states an inverse relationship between the two quantities, i.e. regions of low pressure are correlated with regions of fast fluid flow and vice versa. It does NOT say “fast fluid flow causes low pressure” or “low pressure causes fast fluid flow”.

Fallacious Origin of the Faster Over-wing Flow

Perhaps the greatest fallacy in the popular explanation of lift is the following statement, which is a desperate attempt to explain the fact that the over-wing flow is faster than the under-wing flow. The statement goes like this:
“The air flowing over-wing has a greater distance to travel compared to the air flowing under-wing, and hence must flow faster”

The incorrect assumption here is that the pockets of air which got separated at the leading edge must somehow “meet up” again at the trailing edge. A picture of what really happens is shown in figure 3.

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Figure 3

Here the small coloured lines represent imaginary puffs of smoke injected by a vertical array of nozzles to the left of the leading edge. The puffs go off at regular time intervals, and each puff lasts a fixed duration. So at one time, the nozzles produce a band of red puffs. With no wing in the way, they would stay together forever. Fig 3 shows that, looking at earlier puffs, the orange ones have just hit the wing and started to separate top/bottom. In the green and blue cases, you can see that the top flow has moved much further along the wing than the corresponding-coloured bottom flow. It is clear that the top and bottom halves remain separated – they do not meet again, thus the requirement to meet again after travelling the longer over-wing distance as an explanation of the faster over-wing flow is false. Note there is a nice animation of this flow in the Wikipedia entry [2].

True Origin of Lift

There are two contributions to the lifting force:

(i) The pressure differential between the upper and lower wing surfaces.
(ii) The reaction force caused by the fact that the air leaving the wing has a downward component to its momentum

Looking at these in turn:

(i) Imagine a small cube of air passing along an over-wing streamline. Since the streamline is curved, the cube will exhibit a “desire” to move in the direction normal (and outwards) with respect to the wing upper surface (just as when whirling a bucket of water on a rope, the bucket desires to travel normal to the curve). This effect causes a reduction in pressure over-wing.

Conversely the pressure under-wing is increased due to the compression of the air resulting from the forward wing motion combined with the angle of attack.

The difference in pressure above and below the wing gives rise to a net force which contributes to the lift.

(ii) The airflow splits into two halves – one passes over-wing and one passes under. If there is a non zero angle of attack, or if the angle of attack is zero but the wing cross section has the classic curved aerofoil shape, the air leaving the wing will have gained a downward component to its momentum. Newton’s third law implies that the wing will, in turn, experience an upthrust, contributing to the lifting force.

The Counterexamples

Now that we know the true cause of lift, we can see how the counterexamples (flat wing cross section or inverted flight) fly.
Provided there is an angle of attack and the aircraft is propelled forward, the pressure differential between the upper and lower surfaces will exist regardless of the wing cross section (within reason!). Similarly, the angle of attack will ensure that the over-wing air has a downward vertical momentum component as it leaves the trailing edge, thus invoking the upthrust. Instrumental in this is the fact that the streamline closest to the upper side of the wing will try to follow the contour of the wing surface and hence will emerge downwards if the wing is angled upwards.

Why the Aerofoil ?

We have seen that the factors contributing to the generation of lift do NOT require the aerofoil cross section. Why, then, is this cross section almost universally employed in wing design ? The answer is efficiency. Although not absolutely necessary for lift, the aerofoil makes for a more efficient wing design.

To see this, consider a flat wing being propelled forwards. The angle of attack results in a downward momentum component of air flowing off the trailing edge and hence gives a contribution to lift. Increasing the angle of attack increases this lift, but there is a penalty. On the underside of the wing, the pressure build-up is greater with higher angles of attack. This pressure, of course, acts horizontally on the underside of the wing as well as vertically. The horizontal component of the force resulting from this pressure is experienced as drag, acting in the opposite direction to the driving force.

For normal (i.e. not takeoff or landing) flight, it is advantageous to reduce this drag as much as possible. To do this, we wish to reduce the angle of attack, but maintain a sufficiently high downward vertical momentum component of air flowing over the upper surface. The classic aerofoil design is efficient at achieving these objectives.

Stalling

Air flowing over the wing surface has a tendency to follow the contours of the surface [3]. To understand this, consider the fact that air has a small viscosity. The air layer “in contact” with the surface has a velocity relative to the surface of zero. As you look further out away from the surface this relative velocity will be higher, i.e. there is a velocity gradient. The consequence of this is that the flow will tend to curve towards the surface. This is known as the Coanda effect [4].
The layer of air immediately adjacent to the surface is known as the boundary layer. Under certain circumstances, the boundary layer separates from the surface. When this happens, the lift contribution from the upper wing vanishes and the aircraft stalls.

Summary

• The generation of lift from an aircraft wing is a complex process, which can only be comprehensively described using the principles and equations of fluid mechanics.
• There are two contributions to the lifting force – the downward momentum of air leaving the trailing wing edge, and the pressure difference between the underside and top side of the wing.
• The popular explanation of the faster over-wing flow velocity in terms of air above remaining correlated with air below is incorrect.
• In researching this issue using internet sources, great care must be taken to select sources which do not display any unreasonable bias. Amongst the popularisers, there is sometimes a tendency to endorse one ingredient in the explanation and refute all the others. To avoid this distortion, I’ve drawn my material from reputable authorities, such as NASA and Fermilab physicists.

References

[1] http://wright.nasa.gov/airplane/bern.html NASA Description of Bernoulli Equation

[2] http://en.wikipedia.org/wiki/Lift_%28force%29 Wikipedia Entry on Lift

[3] http://home.comcast.net/~clipper-108/lift.htm Anderson and Eberhardt “A Physical Description of Flight”

[4] http://en.wikipedia.org/wiki/Coanda_effect Wikipedia Entry on Coanda Effect

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