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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 20, 2010

Going in Circles (Lift Part 3)

In 2 earlier posts (here and here), I've talked about the equal-transit-time principle (wrong), Bernoulli' equation (right), and Newton's Second Law (also right). I've also mentioned "circulation" a couple of times, but haven't discussed what that means.

Circulation is a description of the flow velocity around a lifting wing. It is based on the superposition (i.e. - addition) of two flows: the straight freestream flow over the wing, and a rotating flow around the wing. The result of adding these two flows is that the flow over the top of the wing is moving faster and the flow under the bottom of the wing is moving slower. Throw Mr. Bernoulli into the mix now, and we can see that there will be lower pressure on top of the wing and higher pressure below the wing—thus we get lift. A really good bathtub experiment to demonstrate circulation is found HERE

I'm not a big fan of using circulation to explain lift to pilots. It's not that circulation is wrong, it isn't. The problem lies in the fact that in order to really understand circulation, way too much math is required. By "too much math", I mean large amounts of vector calculus. Incidentally, the phrase "too much math" isn't something you'll hear from me very often, so enjoy it while it lasts!

When using circulation to describe lift (for pilots), there is no explanation of where the circulation (i.e. - the rotating flow) comes from—it's just assumed to be there. The circulation has a physical origin, or course, but describing that origin requires a great deal of math, or a significant amount of physical reasoning—both of which are necessary for aircraft designers, but a waste of resources (in this case) for pilots.

Circulation is a component of potential flow theory. Potential flow theory, in turn, is founded upon continuity as one of the key underlying principles. So circulation can be viewed as a more complicated form of continuity. It turns out that if we aren't worried about number crunching and just want to know physical origins, continuity is a quicker, simpler way to meet our objective.

Circulation has the added disadvantage that it doesn't (without LOTS of math) explain the presence of the "adverse pressure gradient" on top of the wing. This adverse gradient is important as the principle source of stalling phenomenon. In turn, understanding stalls is one of the key reasons we need to understand lift.

Using continuity directly doesn't give us a way to calculate lift. That's a problem for the engineering folk. But it does provide pilots with a description of the physical origins of lift—which makes it a good description for pilots.

When reasoning through the lift-production process, you can choose to use either circulation or continuity to explain the flow velocity difference above and below the wing. But regardless of which approach you prefer, you still need Bernoulli to explain the pressure difference—which is really the key to lift.

The bottom line here is that circulation is a valid description of the flow around the wing, and can be used (in conjunction with Bernoulli) to describe the production of lift. However, it is not the optimum approach to use for the training of pilots. For that, we have the simplified approach using continuity—which provides us with a description of physical origins, but no tools to calculate lift.

When we need specific numbers (i.e. - the results of calculation and/or testing), we can go to the flight manual. This document is provided to us by the good folks who designed and/or manufactured the aircraft. In other words, we can let them worry about the hard math so we can focus on physical origins and useful rules of thumb.

Happy Flying!

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