LouW
Posts: 804
Joined: 1/1/2003 From: Moreland, GA, USA Status: offline
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I will explain one more time (maybe if I speak slowly and distinctly……). First let me clarify a definition. The term “downwash” is technically defined as the angle through which air is deflected behind a wing and has units of radians. The only time I used the term earlier in this discussion I was referring to the downward acceleration of a mass of air by the passage of a wing, which units would be slugs/sec/sec. Even though they refer to the same phenomenon, they are not interchangeable. I will try to be more precise. There is a tendency of technical folk to sometimes confuse the mathematical model representing reality with reality itself. There are two concepts that make higher math possible. Without them we could only count and measure. They are the abstract concepts of zero and infinity. As absolutely indispensable as they are, if they are not carefully considered, results can be obtained that are at best misleading. The lift of an infinite span wing is one such example. From Newtons second law, F=ma Or transposing, a= F/m For a hypothetical wing of infinite span, the mass of air affected by its’ passage becomes infinite. Dividing F by infinity results in acceleration being zero (for any finite value of F). This is all very interesting, however it is also obvious, that for a real wing with a finite span affecting a finite mass of air, there must be a downward acceleration for any real value of F (lift). A high AR wing effects a large mass of air so the acceleration is small. A low AR wing affects a lessor quantity so the acceleration is more. I could go on with the development of circulation theory which is again the combination of several mathematical constructs to make the mathematical model represent more closely actual observed phenomenon. But I move on. All that has been said about the pressure being the only thing the wing “sees” is correct. The pressure distribution around the wing is the only direct force acting on the wing and is the proximate cause of lift. The argument comes with the analysis of a wing as a “free” body. Now this is a perfectly valid engineering technique for force analysis. It is used to isolate joints in trusses, beams, and other structural elements, as well as all manner of static and dynamic problems where things can be represented by vectors to simplify analysis. Lets look at an example of an airplane not moving but suspended from a rope. If the rope is represented by a vector acting on the airplane as a free body, it is easy to see that the weight is balanced by the tension in the rope, and the rope may be said to be the source of “lift”. However, a rope pulls two ways. (See Newton Law 3.) It is entirely appropriate to ask, what is supporting the other end of the rope? It could be a crane, a parachute, or a rafter in the Smithsonian museum. To fully understand what is supporting the airplane it is important to know what is happening on the other end of the rope. Back to the airplane flying through the air, there is an area of low pressure just above the wing, and its net effect on the wing is the lifting force supporting the wing. The net effect of that low pressure on the air is to cause the air above to flow downward toward the wing. The air thus set in motion continues to move downward after the wing (and its area of low pressure) has past (Newton 1.). The resulting downward flow is not some arbitrary side effect, but the direct result of the pressure (force) supporting the wing. In fact one simply cannot exist without the other. (Newton law 3.) It is the other end of the rope. In the above example it is OK to say that the rope is supporting the airplane but it is a more complete understanding to say that it is supported by the crane, or rafter, or whatever is on the other end of the rope. I agree completely that the net pressure distribution is the proximate cause of lift, but in a fluid there is simply no way to create a force on a body other than by accelerating a mass of the fluid. In the final analysis, when you cut through all the details, a wing is simply an air deflector.
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