So what’s a study of aerodynamics without starting out with how lift works? You would think this would be fairly simple and easy, considering how fundamental it is, but there’s a lot of different explanations out there that aren’t even compatible with each other. Although apparently, among people who actually know what they’re talking about, there’s not really a controversy – the problem lies in properly conveying it to us less-informed folk!
Everything I’ve come up with so far, wrong and right, tries to use Newton’s Laws, Bernoulli’s Principle, or both. Newton’s Third Law is the one that says that every action has an equal and opposite reaction – or, that if you hit one thing with another thing they will try to bounce off of each other in opposite directions. Bernoulli’s principle says that for an incompressible fluid, a) decreasing the area that the flow can go through must result in an increase in speed, and b) an increase in speed must come with a decrease in pressure. 1One doesn’t cause the other, they just have to happen together. The distinction is probably important eventually. First are some wrong ways to apply these concepts:
Misguided Theories of Lift Formation
Impact Lift
This theory says that lift can be explained simply by air molecules hitting the bottom of the airfoil – the force imparted by these molecules pushes the wing upward in a simple application of Newton’s Third Law; basically bouncing over an air “sea” like a rock skipping over water. But it is simple to see how this is not the whole story – there is no mention of the influence of the upper surface. By this explanation, any airfoil with the same weight and lower surface shape should function equally as well, and a cursory glance at the variety of different airfoils can show that that is not the case. If this theory were true it would not matter what the upper surface looked like – you could put all manner of instruments or spiky things on top with no harm done. But in fact engineers go to great lengths to do the exact opposite. In general they try to make the upper surface as smooth as possible, and big bulky things like engines can go underneath the wings, but never on top. Partly this is in order to keep the center of mass low (to help with stability), but mostly because disrupting airflow over the wing makes lift generation much more difficult. (Spoilers are flaps on the top surface of wings whose sole purpose is to “spoil” the lift generation, in order to descend faster without diving.)
Equal Transit-Time
This theory uses Bernoulli’s principle to start out in the right direction, but gets twisted in the execution. Bernoulli’s principle is relevant to explaining lift, but this theory applies it by saying that the air flowing over the curved upper surface of an airfoil must go faster in order to meet up again with the air over the (shorter) lower surface at the trailing edge. But there’s no reason that each “packet” of air has to stay with the “partner” it came with, and experiments with smoke have indeed shown that the air over the upper surface reaches the trailing edge far ahead of that on the lower surface.
Half-Venturi
From experiments disproving the equal-transit-time fallacy we know that the air over the top of the airfoil moves faster than that on the bottom. Another explanation for this is also from Bernoulli’s principle – the airfoil displaces the flow that comes at it, constricting its area in a sense. The air on top flows faster because it is displaced further – think of an airfoil with a curved top and flat bottom, for example. The faster-flowing air over the top half has a lower pressure and the difference pushes the wing up. This theory is getting closer, but the flaw lies in the reason that the air on top moves faster. It arises from thinking about Venturi tubes, which are simply tubes with a constriction in the middle, where the air moves faster in the constricted region and is therefore at a lower pressure. Some try to say that the wing forms two giant Venturi tubes, with the ground and the top of the atmosphere. But compared to the size of the atmosphere, the thickness of a wing is hardly going to constrict anything enough to get a sizable pressure difference. And this would also seem to imply that there is a minimum altitude for the wing to not produce lift in the opposite direction! Close to the ground, the “constriction” below the wing should cause a much lower pressure below the wing and run it into the ground. (In fact, at very low altitudes, a phenomenon called ground effect gives a boost in lift.)
The Better Ideas?
So it’s clear that lift is easy to misunderstand, but how should we actually go about thinking about it? So far I’ve found three ways2There may or may not also be a fourth way, but figuring out that will be a task in itself. Also I lost the source that referenced this fourth part., which are each valid and work together to explain lift. The first involves Newton’s laws. The shape and/or angle of the airfoil deflects air downwards, called downwash. From the 3rd law, the force pushing the air downward is countered by an equal force pushing the wing upward, which is lift. The wing has to either be at a nonzero angle or be curved (cambered) in order to deflect the air down at an angle. It’s easier to see on the bottom, but a lot of the air above the wing is also deflected, by the air higher up at the ambient pressure pushing down on the air in the lower pressure region right above the wing.
Another part involves circulation. Exactly how this works is still difficult, but some mechanism3something about downwash – turning is circulation (shape of airfoil)(but flat plates)(sideways flow?), when a plane takes off, causes rotation of the air about the wing. We can see that it exists because of the wingtip vortices – conservation of angular momentum says that a single vortex can’t just appear by itself. The wingtip vortices are the circulation (rotation) opposite of that on the wing, together keeping the net circulation of the system at 0, like it started with. The circulation about the wing is parallel to the freestream on the top surface, and opposite the freestream on the bottom. Adding the vectors of the circulation to that of the freestream, the top is moving much faster and you get a pressure differential (from Bernoulli’s principle). The lower pressure above and higher below also provides an upward force to the wing. This all seems reasonable, but in all honesty I still have trouble visualizing how these vortices are opposite of each other. Most diagrams seem to show the wingtip vortices rotating in a plane perpendicular to the chord, and I don’t understand how it comes to be like that if the source is to counteract the circulation on the wing. I suspect the fault lies in either how literally those depictions of vortices can be taken, or in my understanding of the physics behind the conservation of rotation.
A third way to visualize lift is found in this paper. The foundation of this way is the fact that there is a pressure gradient across curved streamlines, so that the pressure decreases as you move toward the center.4Although: “At the very centre, the assumption of frictionless flow is no longer justified (because streamlines in opposite directions get very close to each other, creating a strong shear flow) and the above arguments no longer hold (the ‘eye’ of the storm has low flow velocities and low pressure).” (Babinsky 2003) We know that friction/viscous effects cause the flow to curve around an airfoil, and this says that that curvature creates a pressure difference of below atmospheric pressure above the wing, and above atmospheric pressue below the wing, which again creates lift. This feels to me more of an explanation of what is rather than why it is, but it’s relatively easy to absorb, and one I didn’t come across the first couple of times I tried to write this post.
So there lies my understanding so far, (mathy) holes notwithstanding. Seems pretty okay as a start, but of course we’ll be back to this. And I haven’t even tried to tackle unsteady lift mechanisms yet… !
- Babinsky, Holger. 2003. “How Do Wings Work?” Physics Education, November. IOP Publishing, 497–503. doi:10.1088/0031-9120/38/6/001.