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Southport, Manitoba, Canada
Steve Pomroy is a professional flight instructor and aviation writer. He has been teaching since 1995 and holds an Airline Transport Pilot License, Class 1 Instructor and Aerobatic Instructor Ratings, military QFI, and an undergraduate degree in Mechanical Engineering. He's written and published three flight training books through his company, SkyWriters Publishing, and has several other books under development. Steve currently teaches RCAF pilot candidates on their Primary Flight Training course.

Monday, December 13, 2010

Wherefore Art Thou Lift?! (Lift Part 2)

In my second-to-last post, I looked at the equal-transit-time concept of lift production (and, for those who didn't read the post, pointed out that it's incorrect). I also mentioned a few things that I hear in theory-of-flight "discussions" that annoy me. The equal-transit-time concept and associated remarks were on that list. Some other important pet peeves included:
  1. Bernoulli is "just a theory" and has never been proven,
  2. If Bernoulli were right, it wouldn't be possible to fly inverted, and
  3. 80% of lift comes from Bernoulli, 20% comes from Newton (or some other set of false numbers).
First things first. "Prove: to test, prove worthy" (from www.etymonline.com. To say that something is "just a theory" and "has never been proven" is a contradiction. If an idea has never been proven (as in tested), it isn't a theory, it's a hypothesis. Theories have been tested, repeatedly, against logical consistency and empirical evidence. To become a theory, a hypothesis must survive this repeated testing and never be "disproved". The "just a theory" nonesense gets used a lot by people who have a personal preference or political agenda that is contradicted by the facts. It shows up all the time in the ongoing religion-v-evolution "debate", but I digress...

Based on this (proper) definition, Bernoulli's Equation indeed qualifies as a 'theory'. It is not a hypothesis. Has Bernoullis' equation been tested against logical consistency? Yes. Has it been tested against empirical evidence? Yes. Has it ever failed a test (i.e. - been disproved)? No. So, is Bernoulli's equation right? Yes, within the limits of the approximations made to get it (no friction and no compressibility). Can it be used to calculate (or explain the physical mechanism of) pressure changes around a wing? Yes, at low Mach numbers (where compressibility is unimportant) and low angles of attack (where friction effects are low and there is no airflow separation).

At higher Mach numbers and in the presence of friction, Bernoulli can still be used if we ("we" being the engineers who do these types of calculations) apply the appropriate corrections. From the standpoint of describing the physical mechanism of lift (i.e. - no number crunching), Bernoulli is useful right up until shock waves start to appear in the high-speed range, and until large amounts of separation result in stalling in the low-speed range.

Beyond empirical testing in the physical world, Bernoulli's equation can be derived from Newton's Second law of Motion. Applying Newton's Law to a fluid element traveling along a streamline in the absence of friction (i.e. - outside the boundary layer) will yield Euler's Equation. Applying this equation further to an incompressible fluid (i.e. - a fluid of constant density) will yield Bernoulli's equation. So the argument that lift comes from Newton, and not Bernoulli is silly, since they are both ultimately the same thing: Newton describes the conservation of momentum, and Bernoulli describes the conservation of energy (as applied to a flowing fluid).

Bernoulli's Equation tells us that as fluid's velocity increases, static pressure decreases. This is ultimately the source of lift on an aircraft wing. The question, then, is, "Where does the velocity change come from?" (Answer: Not equal-transit-time!). Bernoulli's equation says nothing about this. It just states that given a velocity change, there will be a corresponding pressure change.

The velocity change comes from the shape and angle of attack of the wing. The flow of a fluid is governed by the principle of continuity, which, boiled down to it's most fundamental form, is the conservation of mass applied to a flowing fluid. Without getting into details (maybe in a future post), continuity will result in increased velocity over the top of a positively cambered wing at a positive angle of attack.

Ok, so what about downwash and Newton's Third Law? Forces occur in equal and opposite pairs. So if the air exerts a force on the wing, the wing exerts an equal and opposite force on the air. As the wing gets pushed up, the air gets pushed down. How does this all come about? The pressure differnces above and below the wing result in the formation of wingtip vortices. These vortices create an imbalance between the upwash (ahead of the wing) and the downwash (behind the wing) so that there is an excess of downwash. The net effect is for the air in the vicinity of the wing to be deflected downward. But this deflection ultimatly requires the pressure difference above and below the wing—which is calculated/explained by Bernoulli's equation.

This addresses the (non-existent) 80/20 split between Newton and Bernoulli. The physical mechanism of lift can be described in terms of Newton (redirected airflow and action-reaction force pairs) or Bernoulli (velocity changes resulting in pressure changes). Both descriptions are valid, but they don't share the labor. If you know the velocity change and mass flow in the downwash, you could calculate the lift being produced. On the other hand, if you know the velocity changes, and therefore the pressure changes, over the wing, you could calculate the lift being produced. Both approaches would give you the same result, and that result would match measurements of the lift on the wing in question.

What about flying inverted? Well, to quote myself from above, "The velocity change comes from the shape and angle of attack of the wing", and "...will result in increased velocity over the top of a positively cambered wing at a positive angle of attack" [emphasis added in both quotes]. What about at negative angles of attack? The positive camber will induce higher velocities on top of the wing even at low and zero AOA. But if the AOA gets sufficiently negative, the wing will produce negative lift due to increased flow velocity over the bottom of the wing. Positively cambered wings aren't very efficient at producing negative lift, but they can do it—and this is indeed consistent with Bernoulli's equation (or, more correctly, continuity/circulation as a source of velocity change).

Great. Now, what about "Circulation"? It's been mentioned a little bit here, but the details will have to wait till next post! Till Then:

Happy Flying!

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