Although none of these three approaches is improper and each has its place, the fact is that lift isn't some irreducible arcane complexity, and describing why (or how) we can manage to fly can actually be made intuitive - or at least less mysterious. Richard Feynman once said that unless you have several different ways of looking at something, you don't really understand it. Actually, integrating your understanding is important because these different tactics are all related, and sparring over them makes about as much sense as the conflict of Gulliver's Lilliputians over which end of an egg to crack open first.
Let's start with Daniel Bernoulli, the eighteenth-century Swiss scientist, who although educated in medicine according to his father's wishes, remained interested in fluid flow and mathematics. He determined that, unlike traffic on the freeway when four lanes become two and our "car molecules" brake to a bumper-to-bumper crawl, when the path available to the molecular constituents of air becomes constricted, they don't crowd closer together (at subsonic speeds), but rather they speed up!
Actually, his observation was simply that as a fluid's velocity increases, its pressure decreases. The fact that velocity increases, as in the popular example of a venturi (an appropriately important constriction within a carbureted engine), is intuitive. Conservation of mass dictates that as the same number of molecules traverses a smaller cross-sectional area in the same amount of time without decreasing their separation (increasing the fluid's density), air will accelerate over our wings, its pressure simultaneously decreasing.
Just why this happens is about where most ground-school textbooks change the subject.
Look at a "wind tunnel" amalgamation of a venturi and an airfoil (see p. 36), using the NACA 2412 airfoil that you'll find on any Cessna 172. In real life, rather than an upper surface of a venturi, imagine instead a pressure disturbance "ceiling" some distance overhead, above which the airfoil doesn't affect the air it passes through, and imagine a series of vertically synchronized smoke pulses, each one an "air molecule." The result is the same: a differential pressure above and below the wing, providing lift. This only shows streamlines above the wing; how does this relate to what happens underneath the wing?
Airflow above a wing
Actually, the popular literature and even many texts to this day advance the oversimplified but erroneous notion that those molecules taking the high road meet up again with their former neighbors that passed beneath the wing. In fact, rather than having equal transit times, air passing above a wing (depending upon angle of attack) can travel almost twice as fast as that passing beneath. This was most effectively demonstrated nearly a half-century ago by the aerodynamicist Alexander Lippisch, using pulsed smoke streams. If distance alone were the primary determinant, the camber of our wings would have to take on cetacean proportions, with cross-sections much like a caricature of a whale! (Actually, the air traveling beneath the wing is also slowed down somewhat from the "free-stream" velocity.)
Why does the pressure drop? Here is one way to look at it: Molecules possess energy, expressed as random motion - and which, in one sense, we quantify by measuring heat, or temperature. Pressure and temperature drop because some energy is used up as the molecules accelerate, changing their motion from random to one with a more predominant horizontal component; hence, static pressure exerted (and measured "sideways," say by a static port) decreases. The faster the relative increase in velocity of air traveling over an airfoil, the greater becomes this differential pressure, and thus lift.
The upper wing's surface does most of the work, which is why, biplanes aside, you'll almost never see external structures mounted atop a wing. As an interesting historical aside, one exception was the "Channel Wing" of Willard Custer (incidentally, General Custer's great-grandnephew). With engines mounted within channels above U-shaped bends in the wing, greatly increasing the velocity of air above those sections, the pressure differential was enhanced so much that the aircraft reportedly had a power-on stall speed of about 20 mph. Because of a famous (possibly inherited) obstinacy and a certain lack of political finesse, however, Custer's design went the way of the Tuckerautomobile.
Although Bernoulli did not live to see anyone fly - he died the year before the first manned balloon ascent - and his method of measuring pressure within a moving fluid was first applied (somewhat painfully) to the measurement of arterial blood pressure, his principle still applies to any moving fluid. When water moves much faster than 27 knots at one atmosphere of pressure and room temperature, for example, its pressure drops below the vapor pressure of water, and bubbles of water vapor spontaneously form. In the case of propellers (boat propellers, that is), the sudden colapse of these bubbles, known as cavitation, can actually damage the propellers. (Fortunately,the supporting medium for aircraft ismore forgiving.)
The next view involves Newtonian mechanics. First, although impact forces do have some small effect, air cannot be exclusively viewed as innumerable microscopic "bullets" hitting the wing and imparting a reciprocal upward force. Aside from shear forces, lift is not simply a surface effect. Attributed to flow attachment as well as the viscosity of air, this momentum of downward-deflected air is the reason why cropdusters work so well. In addition to its beautiful depiction of wingtip vortices, the now-famous photo by Paul Bowen also shows a jet punching a huge furrow in the top of a fog bank as it climbs gracefully above it. That trench was formed from the diverted downwash of air, which as Newton's third law predicts, provides an upward force in return. Note that this downward-deflected air is not what causes lift, but rather is an effect of lift; the air exerts an upward force on the airfoil, and the airfoil reciprocates. In fact, huge masses of air, accelerated downward, and in accordance with Newton's second law, are involvedhere as well.
As air bends around the top of the wing, yes, vortices develop at the wing tips which to some extent counter lift, but as "nature abhors a vacuum" - at least here on Earth - the downward flow entrains air above, along with it. Air isn't terribly sticky stuff, but though small, its viscosity is not negligible, a fact to which anyone who acknowledges boundary layer effects will attest. This flow, combined with angle of attack, is what allows a pilot to shove the yoke well forward and fly upside-down in a Citabria, hanging from the shoulder straps. Even though the airfoil itself is upside-down and the angle of attack might need to be one and one-half times as much, it still flies. As with the oft-cited "flying barn door" that has no camber whatsoever, it is angle of attack, not just shape (see illustration, p. 38), that does it.
The proverbial "flying barn door"
Lastly we look, somewhat gingerly, at the mathematics of Bernoulli. Just as an object can trade the potential energy of altitude gain for kinetic energy and vice versa, a fluid conserves energy by exchanging its energy of motion for pressure (or altitude), according to the relationship [(1/2 x r x v2) + P + (r x g x h) = constant] where r (the Greek letter rho) is density, v is its velocity, P is pressure, g is the acceleration of gravity, and h is height. The first expression is what's known as the dynamic pressure; this is in fact what a pitot tube senses. The second term is the static pressure, and the third is just potential energy per unit volume. (In our case, we will assume a constant height and ignore that third term.) Although it was just another expression of the law of conservation of mechanical energy in a form convenient for fluid mechanics, its implications were, of course, profound.
Now, to explain this stuff with as little sleight of hand as possible, let's start out with something more familiar: first, pressure. This is a force per unit area (P = F / A). If we multiply both numerator and denominator (the "F" divided by the "A") by a length dimension [call it "D," for distance, in the equation P = (F x D) / (A x D)], we get work (or energy) divided by volume. (Energy refers to the ability to do work, and work is the quantity of energy used when we do it; the units are the same.) That's our "pressure" energy part.
Now for the kinetic contribution: Remember that "one-half times mass times velocity squared" equation from high school physics, the kinetic energy of a physical object in motion? This can be derived from a definition of work as force times distance, substituting mass times acceleration (Newton's second law) for force, and then replacing acceleration in turn by velocity per unit time, then average velocity (starting and ending, divided by two) multiplied by time for distance, which, after the time units cancel out:
W = F x D = (m x3 a) x D = (m x v/t) x (v/2 x t) = 1/2 x m x v2
yields the expression for kinetic energy: KE = 1/2 x m x v2
Well, since density (usually represented by a lower-case Greek letter, rho) equals mass per unit volume (r = m / V), if we solve for mass we get density times volume (m = r x V), or going one step further, density times area times length [m = r x (A x D)].
If we consider everything now, instead of one-half times mass times velocity squared, we get one-half times density times area times length times velocity squared [KE = 1/2 x r x (A x D) x v2]. And per unit of volume, it's just one-half times density times V-squared (KE = 1/2 x r x v2). There's the kinetic part.
The sum total - let's call it "E" - must never change. So if the sum of potential "pressure" energy and motion-induced kinetic energy is constant [E = P + (1/2 x r x v2)], when one goes up, the other must go down. (All of this stuff ignores compressibility, boundary layers, and all the other more sophisticated things).
So ... flight is still magical, but it doesn't have to be mysterious!
Jeff Pardo is an aviation writer in Maryland with a commercial pilot certificate for airplanes, and instrument, helicopter, and glider ratings. He has logged about 1,100 hours in 12 years of flying. An AirLifeLine mission pilot, Pardo also has flown for the Civil Air Patrol.
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