I’m a pilot and I’ve always been taught the Bernoulli school of flying theory, but have also always understood that Newton’s F=MA feature prominently and simply assumed that they both play their part, be it in different proportions in different flight regimes (subsonic, supersonic etc). Lately, however, I’ve noticed that these two are actually different schools of thought with some going so far as to claim the other is not applicable. Surely this should be easy to test via mathematical modeling? What going on?
Wow, can’t believe I’ve missed that.
Still, that implies that it’s pretty much all to do with wing angle rather than shape, with camber merely accentuating the effect (as in the cessna 150 example). Why do you need camber at all then? Wouldn’t a thin sheet of metal be a lot better than a curved wing that creates tons of drag? Or is it a practical stall chacteristics (flow seperation.) thing?
[Caveat: Anything I say in this discussion is highly simplified. I will gloss over minute details to get at the basic, intuitive, close-enough explanation. If you think I missed something, I probably omitted it on purpose.]
A flat plate at an angle of attack does a good job of redirecting the flow on one surface, the bottom one. But it can’t smoothly transition the flow that goes over the top side. Instead, that upper-surface flow separates from the plate and creates a huge wake. And separation equals drag.
An airfoil shape, on the other hand, can take air flowing over the upper surface and bend it down to exit off the trailing edge. So both the upper and lower surfaces are responsible for pushing air down. That’s much more effective than the flat plate, where one surface creates lift, and the other does nothing but contribute to drag.
Camber isn’t necessary, in the way airplane folks define it. I suspect you mean something else when you say it. Camber is the “cupping” of the wing’s cross section, making it asymmetic about a line from leading edge to trailing edge.
A flat plate can actually be cambered, which is how the fabric wings of aviation’s first days worked. Likewise, a thicker airfoil shape can be uncambered, even though it has thickness and “roundedness”. A perfectly functional airplane can be made using NACA 0012 airfoils, which are uncambered and so have the same curve on the top and bottom. Such an airfoil only makes lift at a positive angle of attack. A cambered airfoil like the NACA 2412, on the other hand, can generate some lift at zero angle of attack, owing only to its cupped shape.
There is an excellent tutorial on all of this on the web, written by John Denker. Lift is caused by pushing air down. The physics is complicated. The Bernoulli effect is real, but puts the cart before the horse and the story we all heard in grade school is hopelessly flawed. Denker shows that the main effect of camber is to increase the angle of attack at which the wing stalls.
Which is really irksome to those of us who spent 20 years growing up in an aviation family and only heard Bernoulli all that time, and then went to ground school where Bernoulli and not Newton was taught. Finding out that what I’d been taught all that time was… incomplete… was a bit of a blow. Still, ‘facts is facts’.
Bernoulli’s Law (the real Bernoulli’s Law, not the Coanda Effect which is often confused with it) is just F=ma, as applied to fluids. All of mechanics is F=ma. F=ma always applies, because that’s what force is.
Can you be more specific? “The story we all heard in grade school” doesn’t actually tell me what you’re talking about. What they told me in grade school was that the top of the wing had a longer path, so to reach the back at the same time as the bottom air, the top air had to go faster, thus lowering the pressure.
The “reach the back at the same time” is the only part that’s flawed. The air does, indeed, go faster, and this does cause lift via Bernoulli. So what’s so “cart before horse” about it, and why is that hopelessly flawed?
Yeah, I agree with Chessic - the Bernoulli equation is basically some terms that have to balance, and each term is energy (with mass divided out of each term). One term (like the velocity) goes up, and Bernoulli tells you how the other (like pressure) has to go down, and it’s all conservation of energy.
So if I use Bernoulli’s Principle, over the surface of the wing I can (in principle) calculate lift. Will I get the correct total lift? Or will I get part of the lift, and there’s some other portion that Bernoulli’s Principle doesn’t capture?
Is the answer different for a 2-D approximation to a wing, and for a full 3-D real wing?
Camber isn’t necessary, in the way airplane folks define it. I suspect you mean something else when you say it. Camber is the “cupping” of the wing’s cross section, making it asymmetic about a line from leading edge to trailing edge.
Camber is certainly not necessary for flight to occur, but it is one of the shape criteria that dictate the amount of lift generated (and also drag generated) at a given airspeed.
Most modern aircraft use variable-camber wings of one sort or another to aid with slow flight for takeoff and landing. Flaps exist to add camber to the wing. Slats are used on some aircraft (including large commercial aircraft) to also add camber.
You can use Bernoulli to calculate all of the lift. The problem with the “equal transit time” explanation of lift is that it posits that the air moving over the top must reach trailing edge of the wing at the same time as its partner air going under the wing. This is completely false, air over the top of the wing is accelerated much more than that and will get to the trailing edge much sooner. Bernoulli doesn’t work if you use the flawed equal transit time theory but is just fine if you use the actual, more accelerated, velocities.
You can also use F=MA in terms of air mass accelerated downward, they are different sides of the same coin.
Planes fly by throwing vortices of air at the ground. You know the old Newton’s Law. All the camber and wing shape stuff is about making that an efficient process.
ETA: Which is basically the last line of **Richard Pearse’s **post
*You can also use F=MA in terms of air mass accelerated downward, they are different sides of the same coin. *
Doesn’t have to be any air mass accelerated downward. A properly shaped flat-bottom wing with zero angle of attack will lift if the top is properly shaped.
Bernoulli’s principle describes the drop in pressure in a direction transverse to the flow as a function of velocity. Thus, perfectly horizontal flow that is accelerated will show reduce pressure in the vertical direction. Hence, lift with no downward flow of air.
Out of curiosity, do we know who came up with the equal transit theory and is it taught as widely outside the US? It seems like one of those cases where a reporter heard an explanation once and went with it and it became canon.
It’s not that Bernoulli is wrong, or Newton for that matter, they both work just fine. The equal transit theory is what’s wrong, and it has nothing to do with Bernoulli. You can still adhere to the Bernoulli school of flying theory, except you’ll have to come up with a new name because if you say Bernoulli, everyone thinks equal transit.
It’s a simple case which can be easily handled analytically. More complicated (more real) cases need computers to solve.
I can teach a class about bernoulli’s principle just fine using equal transit. That it is only an approximation and in some cases not a good approximation doesn’t invalidate it as a learning tool.
It’s sort of like the physics problem that start with: “You are driving a two ton car, which you can treat as a point mass…”
Simplify it until you can solve it, learn what you can from the simplifications, then start cranking in more reality.
Denmark here, I’ve seen it a lot in books about flight and airplanes. Twice recently I heard it in informal lectures, one about sails on ships, the other about oars (paddles?) for kayaking. I was mighty tempted to speak up and start fighting ignorance, but abstained both times. I felt it would only muddle the main point of the talk. Also both the lecturers were, well, smart people but not the sort who takes kindly to being contradicted in front of a crowd.
If the top is properly shaped, the air over the top surface of the wing will be accelerated downward off the trailing edge. Without downwash you don’t get lift and you won’t have the associated pressure changes around the airfoil. If that is wrong, I’d like to see a cite, specifically I’d like to see an airfoil simulator demonstrating lift without downwash.