MANY BIRDS ARE ABLE TO soar (fly without flapping their wings) by circling in rising air. A close observer of such a bird can learn much about the aerodynamics of the flight and much about how different species of birds accomplish the task of flying. Paul MacCready of AeroVironment Incorporated in Monrovia Calif., has developed a technique by which an amateur can calculate a bird's coefficient of lift, which is a measure of how efficiently the bird flies. The bird's speed and radius of circling can also be calculated.

MacCready is known for his construction of human-powered aircraft. His earliest observations of soaring birds inspired the construction of the Gossamer Condor, which in 1977 won the Kremer Competition by being the first man-powered aircraft to fly a figure-eight course. (The aircraft is now on display at the National Air and Space Museum.) The feasibility of the flight arose from MacCready's calculations on bird soaring, specifically his calculation of the output of power that is required.

MacCready began his observations and calculations on bird soaring in 1976 by watching turkey vultures (Cathartes aura) as they glided smoothly in circles. With the help of his children he measured the time a bird took to complete a circle and also the bird's angle of bank (the angle between the horizontal and the plane of the bird's wings). Holding a protractor at arm's length, MacCready measured the bank angle as a bird flew toward him and as it flew away. The average of the two measurements and the time of circling were recorded.

MacCready also observed the soaring of black vultures (Coragyps atratus) and of the best soarers of all frigate birds (Fregata magrifices). He again monitored frigate birds while he was on vacation in 1980 at La Paz in Mexico. In 1982 he videotaped the flights with a zoom-lens television camera. When the tape was reviewed, he measured the bank angle on the monitor's screen. A clock incorporated into the tape player recorded the time.

The results in 1980 and 1982 were surprisingly different. In 1980 the average bank angle was 23 degrees and the average time for a full circle was 9.1 seconds. In 1982 the average angle was 39 degrees and the average time was 9.4 seconds.

MacCready noted that the flights were at a much higher altitude in the second set of observations. The higher flights made measurements of the angles less accurate because of perspective. To correct for this problem he reduced the average bank angle to 36 degrees for the 1982 data. Still the puzzle remained. Why did the birds soar at a steeper angle in the higher flights? I shall return to this question after I introduce MacCready's calculations on flight efficiency.

A gliding bird descends slowly in relation to the air through which it flies If the air is rising faster than the bird descends, the bird gains altitude in relation to the ground. A circling bird usually maneuvers to stay within the rising air. The lift on the bird's wing is a force from the air that is perpendicular to a line connecting the wing tips. It is also perpendicular to the flight path. If the bird is flying level, the lift is entirely vertical and counters the bird's weight. When the bird banks, the lift is tilted from the vertical by the angle of bank and acquires a horizontal component. Only the vertical component of the lift is available to counter the bird's weight. If the component is too small, the bird sinks in relation to the rising air. If the component is too large, the bird rises. The horizontal component of the lift provides a centripetal force maintaining the circular motion. The size of the component depends on the strength of the lift and the bank angle.

MacCready derived a mathematical formulation whereby one can compute the speed of the bird once the bank angle and the time of circling are measured. His formula relies on three relations: (1) A bird soaring in a circle has matched the vertical component of lift to its weight. (2) The horizontal component of the lift generates circular motion and thus is equal to the bird's mass multiplied by the centripetal acceleration, which can be calculated as the square of the speed divided by the radius of the circle. (3) The speed of an object in circular motion is equal to the circumference of the circle divided by the time required to complete a circle.

Armed with these three relations, MacCready found that the speed of the bird is proportional to the circling time multiplied by the tangent of the angle of banking. Once the speed is known the radius can be computed from the relation between the speed and the circumference.

The full formulation is displayed in Figure 3. The relations are also plotted as a graph in the bottom illustration. The graph can be used in the field. First measure the bank angle of a bird soaring in a circle and the time it takes to complete a circle. Mark the time on the abscissa of the graph. Now move upward on the graph until you reach a straight line marked with the bank angle you measured. (You may have to interpolate between two such lines if the angle is not shown.) From that intersection move directly to the ordinate, from which you read the speed of the bird. For example, if a bird completes a circle in nine seconds at an angle of 20 degrees, its speed is about 5.1 meters per second.

You can also read the radius of the circle from the graph. When you have moved directly upward from the point representing the circling time to the intersection with a line of bank angle, determine the radius from the nearest curved line representing radii. In my example the radius is about 7.3 meters.

MacCready calculated on the basis of his field observations in 1980 that the birds glided at an average speed of S.9 meters per second in a circle with an average radius of 8.5 meters. The birds he observed in 1982 glided at 10.4 meters per second in a circle with a radius of 15.3 meters.

Another parameter is the bird's coefficient of lift, which is defined in terms of the loading of lift on the wings. The loading is the lift divided by the total surface area of the top surfaces of the wings. The coefficient of lift is the ratio of the lift loading to the excess pressure generated at the front of the bird by the forward movement. This excess pressure is equal to half of the density of the air multiplied by the square of the bird's speed.

The actual value for the coefficient of lift depends on the bird's angle of attack, the angle at which its wings meet the passing air. The largest useful value for the coefficient is obtained for the angle that results in stall, the instance in which the airflow over the top of the wing breaks away from the wing instead of moving smoothly to the rear edge. MacCready is interested in how large the coefficients can be for the soaring birds. Are they larger than the ill coefficients that aircraft built by human beings can achieve?

As it stands, the definition of the coefficient of lift is not useful for an amateur watching birds soar, because the lift is always unknown. Therefore MacCready has re-expressed the definition in terms of quantities an amateur can obtain. He replaces lift with the bird's weight. (The ratio of weight to the area of the top surfaces of the wings is termed the wing loading.) The bird's speed is replaced with the speed it would have if it were gliding in a straight line with the same coefficient of lift. This straight-line speed is the actual speed multiplied by the square root of the cosine of the bank angle. The ratio of the straight-line speed to the actual speed can be represented as a graph [see Figure 4]. The ratio is about 1 when the bank angle is small, but it can be appreciably smaller for larger angles.

To complete the calculation for the coefficient of lift one needs the ratio of weight to wing area (the wing loading) for the type of bird observed. (You can assume that the ratio is the same for all birds of the same type.) For the frigate birds observed by MacCready the ratio is about 35.1 newtons per square meter. (The newton is the metric unit of force. At one newton a body with a mass of one kilogram would be accelerated at a rate of one meter per second per second.) The density of air, which is also required in the calculation, depends on the air pressure and temperature. Assuming that the birds he observed as they soared were approximately at sea level and in air at a temperature of 15 degrees Celsius (59 degrees Fahrenheit), MacCready took the air density to be 1.225 kilograms per cubic meter.

With these values MacCready calculated a coefficient of lift of 1.79 from the 1980 data and .65 from the 1982 data. The two results are different because the straight-line speeds (which depend on actual speed and bank angle) are different.

The puzzle about the different bank angles in the two sets of observations in Mexico reappears in the calculations of the coefficients. When MacCready made his first observations of birds soaring in 1976, he expected to find that all birds would soar with the same coefficient of lift. His computations of that year for the turkey vulture, the black vulture and the frigate bird met this expectation. The surprise in the observations of 1980 and 1982 was that the same type of bird does not always soar with the same coefficient of lift. Because the winds in 1980 were smooth and gentle and the winds in 1982 were turbulent and strong, MacCready concluded that the birds made adjustments to change the coefficients of lift depending on the meteorological conditions.

In the same way, the pilot of a sailplane flies faster when he is circling in a turbulent thermal (a rising region of warm air) than he does when he is in a gentle one. The higher speed makes the craft less vulnerable to stall if turbulence momentarily increases the angle of attack of the wing. It also gives the pilot greater control. In addition to flying faster the pilot banks the sailplane more sharply in a strong thermal.

Soaring birds make such adjustments more effectively because they are more experienced and have better sensors and more ways of adjusting their wings. The videotapes MacCready made in 1982 reveal that in turbulence the birds were constantly altering their bank angle and the shape of their wings, particularly their twist.

The wing loading on some hang gliders is in the same range as that on some birds, such as the black vulture. Therefore the pilot of such a glider could utilize a thermal almost as small as the ones birds fly in. The bird, however, still has the edge in controllability. Colin J. Pennycuick of the University of Bristol, an expert in avian biology, once remarked: "I suspect that even if you could simulate a bird's control system, you would need a cockpit so full of levers that it would take an octopus to fly it." Moreover, since birds have shorter wings that take up less of the radius of turning, they avoid some of the wing twist needed to keep the lift the same over both wings. That adjustment is harder with the larger wings of a hang glider.

A sailplane has a greater wing loading than hang gliders or birds and flies much faster. It is also quite efficient and sinks through the air more slowly. Nevertheless, it cannot utilize a thermal as small as the ones birds exploit.

Because the turkey vulture has a substantially smaller wing loading than the black vulture, it can soar in smaller and weaker thermals. It can also soar earlier in the day (when the thermals are weaker). The frigate bird, with its long, slender wings, is the best ocean soarer of all. It can even make use of some of the gentle convective cells that develop in light wind when the water is warmer than the air.

The lift coefficient for frigates in calm conditions is 1.8. That is surprisingly large for the aerodynamic conditions of bird soaring. The high value indicates the frigate can glide with a low speed that normally would make other birds or a hang glider stall. MacCready suggests further observations might result in a lower coefficient for the frigate. If they do not, one must conclude that the frigates have a better engineering design than model airplanes of similar size operating at similar speeds and that aerodynamicists have something to aim at.

Last month I described how a peculiar afterimage can be generated in a dark room when one observes a scene briefly illuminated with a bright flash of light. You will see few details of the scene because of the dazzle of the light, but if you keep your gaze steady when the room is again dark, a detailed afterimage soon appears; it resembles a snapshot of the scene. The afterimage can be so vivid that details such as printed words can be recognized.

Part of the article was based on research by Edward H. Adelson of RCA's David Sarnoff Research Center. He offers another demonstration of this afterimage. An observer adapted to the dark views an apparently white card illuminated with a flash of light. In the afterimage he perceives the word RODS written on the card although there was no evidence of the word during the flash.

To set up this demonstration Adelson first writes RODS in thick block letters on the white card with a yellow highlighter pen. He then cuts a slit about a quarter of an inch wide in a red filter, covers the slit with a blue filter and attaches the composite to the flashgun. At the flash the gun sends out red light except from the slit, through which it sends blue light. When you set off the gun after you have adapted your eyes to darkness, you will see only a blank card bathed in red light. After a few tenths of a second the word RODS will appear.

Adelson explains the perception of the word in terms of the light absorbed by the yellow ink. In the red light the card is blank because the ink absorbs none of the light. In the blue light the card shows the word in dark gray because the ink absorbs blue. The cones of the retina are dominated by the bright red light, which masks the gray of the word formed in the dimmer blue light. The rods, insensitive to the red, record the presence of the word, but they are initially saturated by the blue light, and so the word is not perceived. As the rods become desaturated they eventually allow the perception of the word in the afterimage.

You may have to adjust the amount of blue from the flash. If there is too much blue, you will see the word during the flash of light and therefore will not be surprised to see it in the afterimage. If there is too little blue, you will not see the word in the afterimage.

You can also arrange the card so that the letters of the word are perceived one at a time. Hold the flashgun about six inches from the Sand angle it so that the entire word is illuminated The R is illuminated least by the flash. Rods receiving an image of the R are least saturated. Hence you perceive the R sooner than you do the other letters. The O is perceived next as the corresponding rods become desaturated. The S is the last letter to be perceived because the rods receiving its image were illuminated most and so require the greatest time to become desaturated.

Howard Brody of the University of Pennsylvania and Joseph P. Straley of the University of Kentucky have pointed out an error in my discussion of racquetball last September. I had written that in an elastic bounce of a ball from a floor the vertical velocity is reversed but unchanged in amount Thus each subsequent bounce should be equally high.

As obvious as this conclusion was to me, I forgot it when I watched a highly elastic ball bounce across my kitchen floor. When I put spin on the ball, it seemed to advance in a pattern of alternating high and low bounces. What I saw was an illusion: the height of each bounce was in fact virtually the same. Because of the spin, however, the ball came off the floor at different angles. If the horizontal velocity was low after a bounce, the ball rose at a steep angle. When the horizontal velocity was high, the angle was shallow. I misinterpreted the difference in angles as being a difference in height.

Brody also pointed out that in tennis the role of spin is more complex than it is in racquetball. "The high bounce of a topspin shot and the low bounce of a backspin shot result not from the interaction of the ball with the court surface but from the fact that the ball's vertical velocity is increased by topspin and decreased by backspin," he wrote. "This change is due to the Magnus effect." (The term refers to the unequal air pressure on opposite sides of the ball resulting from the interaction of the spinning surface with the passing air. Depending on the spin, the pressure difference can lift the ball or push it downward.) The effect is smaller on the racquetball because the ball is smoother.

Joseph W. Kennedy of Miami has written to me about several more unsolved puzzles that are associated with racquetball strokes. He delivers one of his strokes when he is near midcourt on the right-hand side. The ball hits the front wall, the rear of the left wall and the middle left of the back wall and then drops to the floor in front of the middle right of the back wall. An experienced opponent can anticipate this final position and return the ball.

Kennedy hits several of these shots and then makes a slight change, leading the stroke with his wrist. (He is right-handed.) Although the ball appears to hit the walls in the same places as before, it reaches the floor much closer to the back wall. The opponent is likely to be too far away from the wall to make a good return. Kennedy thinks he may be putting a spin on the ball by his wrist action.

Another peculiar (and rare) shot hits a front corner squarely at high speed. The ball drops to the floor and is unreturnable. Surely this results from the friction on the ball as it hits two walls simultaneously, but I do not know whether anyone has worked out the details of the collision.

A "kill shot" is directed horizontally and at high speed toward the bottom few inches of the front wall. The rebound is close to the floor and difficult to return. Yet sometimes, when the ball strikes the wall within two or three inches of the floor, it rises to a height of four or five inches on the rebound and is easier to return. Why does it rise? Perhaps it gains lift in the manner described by Brody.

Bibliography

SOARING BIRD AERODYNAMICS-CLUES FOR HANG GLIDING. Paul B. MacCready, Jr., in Ground Skimmer No. 45, pages 17-19; October, 1976.

SOARING AERODYNAMICS OF FRIGATE BIRDS. Paul B. MacCready, Jr., in Soaring, Vol. 48, No. 7, pages 2-22; July, 1984.

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