A debate simmered in certain obscure quarters a couple of years ago over the relative merits of the Newton and Bernoulli explanations of lift, even though they’re just two sides of the same coin. An airplane produces many kinds of disturbances in the air as it passes by, and you can argue all day about causes and effects; but lift and drag ultimately boil down to what the airplane feels-that is, to the forces applied directly to its surface. Everything would become clear if we could just be airplanes for a little while, and feel on our skin the push here and the tug there whose end result is the miraculous levitation of thousands of pounds of deadweight. We can’t. But computers can make those feelings visible, and perhaps in that way make clearer just how it is that airplanes stay up. One type of representation has become a staple of sales brochures because it is graphically arresting and at the same time implies technical sophistication: It is the “spectrum plot,” in which some item of interest, like surface pressure or friction, is represented as a rainbow of colors. Here are two such plots, representing a 172RG in flight seen from above and below. In this case, the quantity being displayed is pressure or, more exactly, the pressure coefficient, or Cp. A pressure coefficient of zero represents ambient static pressure; a coefficient of 1.0 is the dynamic pressure of moving air at the flight speed, as the pitot tube would feel it.
The first choice you have to make when creating an analysis like this-this was done, by the way, with a program called CMARC, which is sold by a business in which I participate-is how you are going to map color to pressure. The full range of pressures on the airplane in the pictures is from 1.0 to maybe -1.5, with the lower figure representing the “suction” near the leading edge of the wing. (At large angles of attack, leading edge suction can get down to the neighborhood of -5.) The spectrum plot provides more useful detail, however, if you confine the available colors to a narrower band of numbers. In this case it runs from -0.4 to +0.4. In other words, any pressure lower than -0.4 reads as magenta, and any pressure higher than 0.4 reads as dark blue. Ambient pressure is a medium green.
You’ll notice that the spectrum used is not the true spectrum of visible light, which goes from red at one end to violet at the other. Violet looks reddish, confusing one end of the spectrum with the other, and so the color range used is from magenta (that is, fuchsia or deep pink), representing low pressure, to blue, representing high.
A recurrent pattern is visible in several parts of the airplane. Going from front to back, the color starts as blue, changes to pink, and then travels back through green to blue. The leading edges of the wings and the fuselage, for example, are dark blue, as is the base of the windshield; that is where the “total pressure” of the oncoming air is felt (and explains why cars often have their ventilation air intakes at the base of the windshield). Perhaps surprisingly, however, the same dark blue exists behind the rear window. This is the area of “pressure recovery,” and, although many people would suppose that pressure behind an airplane would be low, it is, unexpectedly, higher than ambient. This is due to a kind of bounce effect, whereby the energy stored as air speeds up to squeeze around an object is released as it converges behind. It’s never possible to recover all of that energy-if it were, things would have no drag – but part of the trick of designing low-drag bodies and airfoils is to get the most out of the pressure recovery.
Pressure is inversely proportional to speed – this is the principle famously associated with the 18th-century Dutch mathematician Daniel Bernoulli – and as air speeds up when it passes around obstacles, pressure drops. The drop is most conspicuous on the wings, where the large magenta area on the upper surface represents a significant part of the lift. The underside of the wing is also reddish, indicating lower-than-ambient pressure, but the effect there is much weaker. On the horizontal stabilizer the same phenomenon appears inverted, because in this case the horizontal tail is “lifting” downward to balance the airplane.
The magenta zone on the top of the wing grows less extensive toward the tip because the wing is twisted in order to ensure that the root works harder than the tip. The stall, when it occurs, will begin at the root and spread outward. Very near the tip, twist has gone so far that there is even a small patch of quite low pressure on the underside of the leading edge. Because of wing twist, the ailerons will be effective even when the inboard portion of the wing has stopped flying.
Looking up at the airplane from below, you can see a small magenta patch where the wing and fuselage meet. The fuselage is still bulging slightly here, and the combination of its curvature and the wing’s gives an extra kick to the air. This is an example of what causes interference drag, which occurs when flow speeds up because of the combined effects of two surfaces, or when one surface is simply immersed in the pressure field of another. The extra speed causes extra friction, and in the absence of a fillet or fairing may lead to flow separation and extra drag farther downstream. A similar pressure “shadow” can be seen on the side of the fuselage beneath the stabilizer.
One of the most powerful effects of the airplane’s passage is the pair of tip vortices that it leaves in its wake. But these are already behind the airplane, and have no effect on it. The only telltale sign of the tip vortex is the little patch of low pressure near the trailing edge of the wingtip; this is the core of the vortex, an area of intense low pressure produced as flow spills, like a breaking wave, around the wingtip. Spectrum plots like these can be used to investigate skin friction, boundary layer thickness and shape, laminar flow and turbulent separation. They have become a standard part of every aerodynamicist’s toolbox, but they can convey a great deal of knowledge and insight to nonspecialists as well.
Commenting upon February’s Aftermath, which involved a pilot who flew into the ground while approaching a lighted runway over dark terrain on a moonless night, a reader offered the following advice:
“The approach is on track to touchdown when the runway lights appear equidistant down the runway. Too high, and the lights on the approach end appear farther apart than the lights farther down. Too low, and the lights run together and appear as a line on the windscreen.”
That this letter was published in the May issue proves, if nothing else, that Flying is nondiscriminatory. We give equal treatment to truth and nonsense. (In another letter in the same issue, the waist canopy on a PBY was referred to as a “waste” canopy, perhaps because it was a good place to toss junk.) The crux of the problem is the phrase “appear equidistant.” First of all, does this mean that the sides of the runway appear equidistant from one another, or that successive lights along either side appear equidistant from one another? Actually, it doesn’t matter; neither is possible unless we are directly above the runway.
If we stand between railroad tracks and observe them converging to a point in the distance, we might nevertheless say that they “appear equidistant” from one another, simply because we know it to be the case. But if we locate, in remotest Amazonia, a person innocent of perspective convergence and we show him a photograph of those railroad tracks, he might well interpret it as a picture of two vertical sticks leaning toward one another.
It is quite impossible that from any point on the approach to a runway the lights appear equidistant from one another in any useful sense. We know for a fact that they are equidistant from one another, but they always appear farther apart at the closer end of the runway. The angle of the approach path, furthermore, has very little effect on the difference. If the lights at the far end of the runway subtend, left to right, an angle of one degree, and those at the near end two degrees, when we are on a three-degree ILS, they will subtend about the same angles if we are on a 10-degree STOL approach. The thing that changes the apparent convergence of the runway edges is not the height of the airplane, but its distance from the runway. The closer the airplane is to the threshold, the wider the near end of the runway looks compared with the far end.
(In case the phrase “subtends one degree” seems obscure, the sun and the moon each subtend an angle of one half degree in the sky; this is about half the width of a 150-foot-wide runway as viewed from a distance of two miles.)
The thing that will change with height is the vertical angle subtended by the runway ends. Viewed from an airplane a mile from the threshold on a three-degree glideslope, a mile-long runway subtends an angle of about 1.5 degrees; from a 10-degree glideslope, it subtends five degrees. The apparent vertical extent of the runway is almost directly proportional to the approach angle.
All this is very well, but it does not seem to prevent pilots from occasionally falling victim, on dark nights over unlighted terrain or water, to the illusion that they are higher up than they actually are. It happens not only to novices, but also to experienced professionals. Even though the runway must look abnormally wide and squat shortly before they hit the surface, it nevertheless appears correct-showing that verbal formulations like those offered by our correspondent are not only literally inaccurate, but also irrelevant to subjective experience.
Incidentally, carrier pilots occasionally report a different illusion which seems to support the tilted-verticals interpretation of our Amazonian friend: The deck appears to rear up and become vertical, like a flat photograph rather than a three-dimensional scene. If you reflect upon how this would look and feel and how difficult it would be to fly an approach to what appears like a string of lights framing a doorway, you may develop some sense of how much of our perception of a runway at night is supplied by our knowledge of what and where it must be, rather than by the direct evidence of our eyes. Approach illusions are most likely to occur on a long straight-in. Approach-slope lights are a great help, but not all runways have them. In their absence, it’s wise to avoid a straight-in approach at night over unlighted terrain or water. Flying a standard pattern makes it much less likely that you will drop below the proper approach slope.
