Tuesday, December 16, 2008

Thinking about lift

I've been thinking a lot about lift lately. Not the kind of lift that glider pilots seek out (upward moving air), but the kind of lift that both airplane and glider pilots care about: the lift generated by the wing.

All pilots, and most passengers, at some level want to know "What makes an airplane fly?" The wing, obviously! Since I want to be an instructor, I should be able to explain what enables a wing to fly. I've read a number of sources, and am still unsatisfied with the explanations.

Most sources talk about Bernoulli's principle (why the top of the wing causes lift) and/or Newton's law of reaction (why the bottom of the wing causes lift). Some synthesize the two, and speculate on what proportion of each effect causes the most lift. Some introduce "circulation". Eventually they all start getting vague and say that the reason a wing accelerates air that flows over the top surface can't be easily explained and mumble something about Euler's equations, as if that will help.

Stick and Rudder, otherwise a fantastic book, simply says "It shoves the air down with its bottom surface, and it pulls the air down with its top surface; the latter action is the more important." Langeweische says a lot about how lift varies with Angle of Attack - he is much more concerned with how to fly the wing than with why the wing flies.

See How It Flies Section 3, Airfoils and Airflow, is filled with wonderful diagrams of stream lines:

and talks a lot about the timing of the parcels of air. Like other books, it tries to correct the false notion that the air flowing over the top of the wing "must" move faster in order to meet up with corresponding parcels flowing below. That makes sense - there's nothing tying the two flows together.

Later, Denker talks about circulation but never explains it. He starts with the idea of air circulating around a stationary wing on the ground (artificially stirred by a paddle), then expects us to accept that circulation continues during flight. I'm sorry, but I don't think there's any air making its way around the trailing edge from the top to the bottom and flowing forward - it's all flowing past the trailing edge. In fact he makes that point himself by discussing the stagnation point at the trailing edge. He and other sources seem to say that circulation is a mathematical construct to explain pressure differences, not a real circulation around the wing. Huh?

Aerofoils and Wings explains a lot about how different wings behave, but as far as lift generation goes, Brandon just refers us to Denker. Later, "As the air accelerates away from the stagnation line, the local airflow over the upper surface gains a greater speed than the lower." We're supposed to take this on faith? What makes it accelerate so much? OK, it accelerates upward because the leading edge forces the air up over the top surface. But why would air flowing below the wing not also accelerate? It's being pushed down, just as the air over the top is being pushed up (due to the Angle of Attack), but I suppose not as much.

In the January 2009 issue of AOPA Flight Training, "The Magic of Lift" can't seem to decide whether or not air meets up at the trailing edge at the same time. Christensen spends some time trying to explain why air traveling faster has lower pressure, using a car-traffic analogy. That's a useful analogy, but only if you assume that the air above must move faster because it has to get to the trailing edge at the same time as the air below. He starts to debunk that idea and then reverts back to it.

But at least Christensen considers the wing from what I think is a better point of view. Most texts describe a stationary wing, and a moving flow of air. I think that's because wind tunnels have been used for years to study airfoils (it's easier than observing airflow by looking down the tip of a moving wing!). But in flight, the wing moves and the air is still. Most texts would claim that the two situations can be described by the same laws. But I'm not so sure... I think the behavior of the air may be different, primarily because of inertia and ambient pressure.

The air has stationary inertia (it must be shoved out of the way by the wing), it doesn't have inertia of motion. As the air is shoved out of the way, wouldn't its pressure be increased, rather than decreased as is assumed in the air-moving-faster-over-the-wing model? He states that as the air comes back down after the wing has passed, it "now possesses momentum, causing the air to overshoot ... resulting in the downwash." I get that. But what started it moving downward - isn't it the ambient pressure of the air above it that is being shoved against? I think of the air as squishy, and once the wing gets out of the way, the air is squished back downward.

According to Bernoulli, moving air has lower pressure. But it seems to me that it may not have lower pressure in all directions. A parcel of air moving upward, being shoved out of the way by the top surface of the leading edge, may have lower pressure horizontally, but wouldn't it have higher pressure vertically? After all, it's being squeezed between the wing and the air above it. Once it gets moving at a constant rate, maybe... but as it's accelerating, it seems to me the pressure in the vertical direction would be higher. (I remember reading a description of pitot tubes and venturis that made me think of it this way... I'll have to look for it.)

NASA cops out and fails to provide a good explanation, too. They spend a lot of time explaining flow patterns and have some great interactive illustrations, but in the end they just say "The real details of how an object generates lift are very complex and do not lend themselves to simplification. For a gas, we have to simultaneously conserve the mass, momentum, and energy in the flow. ... To truly understand the details of the generation of lift, one has to have a good working knowledge of the Euler Equations."

But equations merely quantify physical phenomena. Mass is moved around by energy, not by numbers. There must be a way to explain what the air is doing, without getting into the details of how much. Langeweische did such a tremendous job of explaining phenomena and behaviors without invoking mathematics - I wish he had tackled this aspect as well.

Some texts also get into bound vortices (the full extension of what we pilots usually call "wingtip vortices"), and I think this aspect is far more important in explaining lift than most authors do. To put it as simply as I can, if some air is shoved downward (whether by Bernoulli and suction on the top, or Newton and deflection on the bottom), that displaced air must be replaced by air from above. You can't leave a hole in the air - that's a vacuum, and as we all know, Nature hates vacuuming. The most natural way for the ambient air to fill it is from a circular region above and around the hole. Then that gap is filled by air from below the circular region (all around the original hole). Then that circular gap is filled by the original shoved-down air spreading out. Viola - a donut-shaped flow of air - like a smoke ring. And due to inertia, it keeps on vortexing until it's diluted.

I have to think about this a little more, and find some good diagrams of it. It's almost got me believing in circulation again. The BGA Gliding: Theory of Flight has a good diagram of the donut shape of the bound vortex (Chapter 3 Figure 40), but again I think the bound vortex is partly a mathematical abstraction. I really don't think air flows forward under the wing!

So, writing this out, I think I've arrived at a conclusion. Why does the air accelerate over the top of the wing? Because it's been given energy by the leading edge, shoving it out of the way. Where did it get that energy? In the case of an airplane, it comes from the engine shoving the wing forward. In the case of a glider, it comes from gravity pulling the glider and wing downward-forward. The ultimate purpose of the wing is to transfer energy from the (engine or falling fuselage) into downward-moving air at the trailing edge, which shoves the wing upward. Most texts talk about the flow of the air over a stationary wing, as if the air has the energy. I think the wing has the energy, the leading edge forces the air up, then the compressed air above forces the displaced air back down past the trailing edge. The displaced air takes the energy with it, causing a vortex. Somehow Newton's action-reaction law gets invoked to cause the wing to go up - still not sure why. I think air moves the wing up, not old Newton. I'll have to think on this some more.

I have no aerodynamic training, just what I've read along the way to becoming a pilot and an instructor. If you have some insight into this topic, please comment! If I'm all wet, I'd like to know where I've got it wrong. But I really care about what mass and energy do. Analogies don't hold wings up. Equations quantify but don't explain. It has to make sense.


Anonymous said...



Roger Worden said...

Thanks, that's very helpful. Too bad it doesn't say who wrote it!

This fits very well with some things I thought about after the original post. Here's a key statement about the contribution of the top surface: "A similar, but reversed, process operates if the surface moves away from the fluid, creating a low-pressure region." It seems to me that the air moving into that low-pressure region will have lost some energy due to compression, expansion, and motion. The air directly moved downward by the lower surface should be more energetic, and probably contributes more to the lift than the upper air. The "similar, but reversed, process" is less efficient.

Yet various texts showing pressure area measurements say the upper low-pressure area is stronger than the lower high-pressure area and is more important. Seems to me the reason the lower high-pressure area appears weaker is that the wing itself is moved up into that space as well, relieving some of the pressure below. That's the whole point - to get the wing to move UP.

All this happens simultaneously, so it's hard to say exactly what causes what.

Another thing I thought of: my comments about the energy transfer to the air are off a bit. In the case of an airplane, the engine contributes enough energy to cause the lift to be strong enough to actually RAISE the airplane, i.e. lift in excess of the wing loading. In the case of a glider, the conversion of gravity to forward energy contributes only enough energy to cause the lift to SLOW DOWN THE SINKING to the familiar 150 or so feet per minute. It's not enough to overcome the wing loading and RAISE the glider. There's no free lunch.

Julien said...

Thanks for the discussion and the links. I went through the same process when studying for PPL.

It all became clearer for me when I realised that the shape of the wing had nothing to do with lift generation. Blasa gliders generate lift. Aircrafts can fly inverted and still generate lift that points skyward.

The way I tell myself the story of how planes fly is as follows:

The propeller is here to pull the plane forward. The wings translate this forward motion into an upward force which we call lift. It works by deflecting the airstream downwards which, by action and reaction, pushes the wing upwards. Anyone can verify that by sticking their hand out of the window in a car, or running while holding a solid sheet of cardboard.

The more air hits the wing, the more the wing gets pushed up (lift). But also the more drag gets created. This is why drag and lift increase initially with angle of attack.

The whole idea with different wing designs is about obtaining the nicest-looking lift-to-angle of attack and drag-to-angle of attack plots.

Remember that you could fly an airplane by using barn doors as wing, as long as the engine is strong enough to pull the plane forward. The stall characteristics may be quite interesting to observe though :-)

In the case of a glider, replace propeller with gravity and the story still holds.