WHEN AN AIRLINER IS AT cruising altitude, air sweeps past it at several hundred miles per hour. You look through the onrush of air every time you watch the passing landscape and clouds through an airplane window. Yet your view is normally so clear that you may well forget about the ferocious flow of air just outside the window.

The flow is quite noticeable, though, if you are sitting behind the wing and look at the landscape through the highly turbulent exhaust from a jet engine. The chaotic variations of air density within the exhaust alter the direction of the light rays reflected from the ground. The rays are refracted randomly by the turbulent gases and what you see is a wiggle dance of features in the landscape. The dancing is diminished when the plane is on the ground, because then much less air flows through the engine.

There are some less obvious clues that sometimes reveal the flow of air past an aircraft in flight. In her book Science from Your Airplane Window Elizabeth Wood describes one subtle tip-off: objects on the ground may appear distorted when light rays from them pass near the front of the wing. Wood first noted such distortion when she was seated near the leading edge of the wing and peered down at a long road that cut across the landscape at an angle to the wing. As the airplane proceeded over the landscape, the road seemed to slide gradually out of sight under the wing. Although the road was straight, the segment of it immediately in front of the wing always seemed to be bent toward the wing [see illustration below].

The kink in the road was an illusion. As a wing moves through the air some of the air is forced up over it; the speed of that air increases and its density decreases. The changes begin somewhat in front of the wing. When Wood viewed the road along the front edge of the wing, she intercepted rays that traversed the region of lower-density air there. The variation in density refracted the rays slightly upward. Now, when a light ray enters your eye, you automatically extrapolate it backward to perceive its source without considering any bending it may have undergone on its way to you. Such was the case with Wood and the refracted rays The deflection of the rays toward the vertical made part of the road seem to be nearer the wing than it , was. Since rays coming from the road farther from the wing did not pass I through the lower-density air and were not bent, their origins were seen correctly. The apparent kink in the road was the point where the undisplaced image of the road joined the displaced image.

Although this is certainly the right explanation of the illusion, one detail bothered me for some time: the reduction in air

density near a wing seemed to be too small to refract most of the rays by any perceptible amount. I assumed that the refraction works as follows. A ray is refracted when it crosses the boundary of the region of lower-density air. When it enters the lower part of the region, it is refracted somewhat toward the boundary. Since the ray is initially angled upward, the refraction makes it a little more vertical. Thereafter the ray travels in a straight line across the region until leaving it, whereupon it is refracted somewhat away from the boundary; again the refraction rotates the ray toward the vertical. What bothered me was the fact that if the air density is only moderately lower near the wing, refraction is significant only when a ray passes through the boundary at a glancing angle; the few rays that had that angle of approach hardly seemed capable of creating the illusion. I finally realized my error by taking a closeup view of the displaced bit of road. Starting at the kink position, the size of the illusionary shift of the road increases steadily with proximity to the wing, suggesting that the air density decreases steadily as the wing surface is approached. In the presence of such a density gradient, a light ray is refracted throughout its traversal of the region near the wing, and so it follows a curved path [Figure 3]. A ray that originates near the illusory kink has a short journey through the region and curves only slightly; a ray from the part of the road that is most displaced penetrates the region deeply, and so it curves more. The nonuniform deflection of the rays produces the non-uniform displacement of the road between the kink and the wing.

I can see a related illusion when I am seated just behind a wing and gaze over it. I pick out a large building in the approaching landscape and keep watching it as it seems to come closer to the wing. As it is about to disappear under the wing, it suddenly becomes distorted and seems to flow toward the wing, disappearing a little before it "should" disappear [see Figure 4]. By raising my head to bring the building back into view, I can repeat the disappearance act. At first I wondered if I was seeing only a confusing composite of my direct view of the building and a fleeting reflection of it out on the front edge of the wing. I checked by gradually raising my head to keep a building right at the edge, thus momentarily freezing the scene for study. There was no reflection: the image of the building was in fact distorted-stretched toward the wing.

The distortion was due to the same trick of refraction that kinked Wood's view of the road. When the lower part of the building's image neared the wing, it suddenly sank in my view because light rays from it were refracted into a curved path by the density gradient just above the wing. For a moment the image of the building elongated like drooping molten glass. When the top of the image also sank, because its light rays were curving through the density gradient, the entire building rapidly disappeared before it should have. The wing seemed to have sucked the building in like a vacuum cleaner.

How does your view of the wing itself escape distortion? After all, when you look down on it, you intercept rays that have climbed through the density gradient. There is no distortion because the rays traverse the density gradient for too short a distance and at too steep an angle to curve significantly. That may be a good thing: if wings were distorted much on airliners, flights would be more unnerving than they are now.

Wood suggested another way in which refraction might alter what is seen over the wing. Although most airliners fly slower than the speed of sound, the airflow over the top of the wing may actually exceed the speed of sound. When it does, a shock front forms that extends one or two meters upward from the wing. It is like a narrow, transparent, porous wall stretching out along the wing; it may extend the full length of the wing or be broken up into several short sections. The air density is low in front of a shock front and higher behind it. One cannot see the shock front on the wing, of course; after all, it is just air. Wood proposed, however, that one might be able to infer its presence because under some conditions its refraction of sunlight could cast a dark band on the wing.

An independent observation of such a band was reported in 1983 by Antony Hewish of the University of Cambridge. He had been flying at high altitude in a Boeing 727 with the sun about 25 degrees above the tip of the wing near him. The band ran along most of the length of the wing and was from one to two centimeters wide (he compared it to the diameter of the rivets on the wing). A narrower, bright band lay just behind the dark one. Mild turbulence jostled the bands, and sometimes multiple bands appeared. When the aircraft descended and slowed, the pattern slid toward the front of the wing, faded, narrowed and disappeared. Apparently the decrease in airspeed over the wing first diminished and then eliminated the shock front giving rise to the bands.

How were the bands Hewish saw formed? Consider a sun ray that pierces the front surface of the shock front at a glancing angle [see Figure 5]. Since the sun is 25 degrees above the wingtip, the ray is angled downward. As it passes through the shock front it is refracted slightly upward (and also slightly away from the fuselage), so that it reaches the wing somewhat closer to the trailing edge (and a bit farther out on the wing) than it would have in the absence of a shock front. The spot on the wing illuminated by the refracted ray is bright; the spot it would otherwise have illuminated is dim. If many rays along the length of the shock front are thus deflected, the bright spots form a bright band and the dim spots form a dark band. Bands could also be produced if sun rays pierced the rear of the shock front and so were deflected toward the leading edge of the wing.

The explanation is plausible but flawed: it ignores the possibility that the spots that should be dim may in fact be illuminated by other rays passing through somewhat lower points on the shock front. In order for bright and dark bands to form, the shock front must either be curved or have a steep density gradient across its narrow width. Either condition can focus the rays like a lens so that a bright band falls on the wing. The dark band then, is a strip where the focusing prevents rays from reaching the wing.

I searched for such bands on the wings of aircraft long and diligently but without luck. Then, on the day after I completed the first draft of this column, I saw them. I was seated well in front of the wing, the plane was at 38,000 feet. The sun was somewhat in front of the wing. When I looked back at the wing, I noticed an odd line on it. At first I thought the line was only an edge of one of the metal sheets on the wing, but then I saw that it shimmied slightly when the wing shook in the turbulence. Was the line due to a shock front? Suddenly the pilot banked the aircraft, bringing the wing up and turning us so that the sun was about 25 degrees above the wingtip. The line sharpened into distinct bright and dark bands. My excitement probably startled fellow passengers.

When the plane leveled out, the sun was still above the wingtip but at a larger angle. The bands were then less distinct. As I watched them for the next half hour, gradual changes in flight direction brought the sun somewhat behind the wing and the bands became fuzzy and finally disappeared.

This fortuitous experiment helped me to understand why the bands are so rare. For them to form, sun rays must skim through a shock front, because only then do the rays undergo appreciable deflection. That means the sun must be approximately above the wingtip; the ideal angle of elevation seems to be about 25 degrees, which must have something to do with the way the shock front curves vertically. When the sun is too far ahead of the wing or behind it, or too high above the wingtip, either the bands do not form or they are too faint to be seen by a casual observer.

The appearance of the bands may also depend on the air temperature. For a shock front to develop, the airflow over a wing must exceed the speed of sound. Since the speed of sound is lower in colder air, perhaps only fast planes flying through very cold air develop extensive shock fronts over the wings.

Recently I spotted another peculiar optical display that was probably caused by a shock front. I had the luxury of being on a nearly empty flight and could sample the view from several window seats over a wing. I happened to be on the opposite side of the aircraft from the sun when I noticed a dark vertical band near the leading edge of the wing. As I moved my head forward the band moved toward the wingtip. At first I thought the band was caused by an imperfection in the window, but when I moved forward to the next window seat, I saw the band again, this time out on the wingtip. Clearly its position was linked to the angle at which I viewed the wing. Still skeptical, I scrutinized the band while keeping my face pressed to the window. When the plane encountered mild turbulence that shook the wing gently, the band wiggled to and fro over the wing. Since my eyes were not moving with respect to the window, the dance had to be caused by something happening out on the wing and not by a blemish in the window.

From some points of view in the two window seats I saw two bands. By moving my head I could make one band pass the other one. I gradually began to realize that I was looking through one or two shock fronts that sat out on the wing. But how did the fronts form these bands? They differed from the bands seen by Hewish and predicted by Wood because they fell across my eyes (and presumably the nearby part of the fuselage) and not on the wing; from any window seat other than those two I would not have seen them. Also, since I was on the opposite side of the airplane from the sun, the bands could not be due to any refraction of direct sunlight.

After the flight I developed a plausible explanation for this second kind of band. Suppose there is a shock front that is curved horizontally, with a convex surface facing the leading edge of the wing. If I look at the wing almost tangentially along the shock front, I intercept rays that come from details on the wing beyond the shock front and may be refracted when they pass through the front. Consider two adjacent details. A ray from the one on my right might undergo only a small refraction because it enters the front at a large angle [see Figure 7]. A ray from the detail slightly to the left might be refracted more, because, owing to the front's curvature, it enters at a glancing angle.

When I mentally extrapolate the rays backward, the detail on my left appears to be displaced to the left of its true position. The detail on my right undergoes less displacement. The light rays from the region between the two details are then spread over a larger angle in my view than they should be, and that region appears to be dim. Since the shock front stands one or two meters high, I see a dark vertical band of about the same height out on the wing.

The model seems to explain two other aspects of what I saw. The leading edge of the wing and other features along the wing were warped upward near the dark band, apparently because when rays from those features passed upward through the shock front and into the higher air density, they were refracted slightly downward, away from the surface of the shock front. My mental extrapolation of them back onto the wing then produced the illusion that they originated slightly above their true origin. The model also explains why the dark band moved when I did. The band was visible only when I looked almost tangentially along the curved surface of the shock front, so that I intercepted rays that entered the front at a glancing angle and therefore underwent perceptible refraction; other angles of view through the front involved rays that were insignificantly refracted. If I moved my head forward, the place along the front where my view was almost tangential shifted toward the wingtip because of the horizontal curve of the shock front; so, consequently, did the dark band.

The next time you sit on the shady side, watch the plane's shadow soon after takeoff. At first the shadow is large, but it seems to shrink steadily as you ascend. The shrinkage is an illusion. Because the shadow is formed by almost parallel rays of light from the sun, it must be the same size regardless of your distance from the ground. (The rays are not precisely parallel because the sun is a disk in our field of view rather than a point, but I shall neglect that fact.)

The shadow seems to shrink when you ascend simply because its angular width decreases with distance. When the angle is too small and the shadow too faint, the shadow disappears. You might see the shadow again if you fly over a cloud that is not too far below the airplane. Recently I flew over an array of clouds scattered at many different altitudes below the plane. As the distance between me and the clouds kept rapidly changing, the apparent size of the airplane's shadow fluctuated wildly.

In the past several years Gordon Lundskow of Rochester, Minn., and Robert T. Chilcoat of the State University of New York at Syracuse have written to describe a peculiar feature that is sometimes seen at an aircraft's "shadow point." Lundskow had been watching the shadow on the ground until it disappeared when the plane had climbed to about 20,000 feet. In the shadow's place a bright spot appeared. Chilcoat observed a similar bright spot that traveled over the ground, always staying (as the shadow had stayed) diametrically opposite the sun. When a cloud below the airplane got in the way, the spot disappeared. You may sometimes see some such brightening even if the shadow is present; in that case the brightness surrounds the shadow.

The brightening at and near the shadow point is called heiligenschein. Its causes are varied, but in every case something on the ground scatters sunlight back in the general direction of the sun. When you look at the shadow point or close to it, you intercept some of the bright return of light.

Bibliography

SHOCK-WAVE PHOTOGRAPHY IN TUNNEL AND IN FLIGHT. F. E. Lamplough in Aircraft Engineering, Vol. 23, No. 266, pages 94-103; April, 1951.

SCIENCE FROM YOUR AIRPLANE WINDOW. Elizabeth A Wood. Dover Publications, Inc., 1975.

SUBSONIC FLOW. Milton Van Dyke in An Album of Fluid Motion. The Parabolic Press, 1982.

IN-FLIGHT MOVIES. A. Hewish in Nature Vol. 306, No. 5939, page 118; November 10, 1983.

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