Richard KLINE & Floyd FOGLEMAN
Omni
(1984)
The
Ultimate Paper Airplane (Excerpt)
US Patent
# 3,706,430
US Patent
# 4,046,338
"Fancy Flights"
by Scot Morris
The sleek and silvery airplane shown here, flying in formation with its creators, Richard Kline and Floyd Fogleman, isn’t just any paper airplane. It is a paper airplane so remarkable and original that it is protected by two separate US patents.
It is a paper airplane so revolutionary that mockups of its wing have been put through wind-tunnel tests by NASA, the Navy, the Air Force, and the Army.
It is a paper airplane so unconventional that it drives aerodynamics experts crazy. It seems to violate one of the major laws of flight: the Bernoulli principle, which explains, theoretically, what keeps all ordinary planes aloft. And it is a paper airplane whose plans are made public, for the first time, in this issue.
Most wings are round on top, flat on the bottom, so air plows over the top. This means the air is less dense on top and more dense on the bottom. As a result there is greater pressure on the bottom, which provides lift.
This wing, however, is flat on top and notched --- partially hollowed out --- on the bottom. Because it has more area on its underside, its "lift" should propel it toward the ground; it should sink like a rock.
It soars. So much for Bernoulli.
Richard Kline, a New York advertising-firm art director, had no idea he was about to start such a stir when, in 1968, he sat in his kitchen table in Mount Vernon, NY to make a paper airplane for his 6-year old son, Gary. He folded back the leading edge of a delta-wing design in such a way that he left an open slot on the underside of each wing. The plane flew straighter and farther than any paper airplane he had ever seen before. Even a living room was too small for a fair flight test.
More significant, when balanced and launched properly, the plane wouldn’t stall. Stalling is on of the principle causes of airplane accidents: the plane turns at too great an angle to the wind, loses its lift, and crashes into the ground. Some crashes can be traced to engine failure or an onboard fire or explosion, but most are tied to stalling. The plane suddenly loses its lift, and all the pilot’s controls become worthless.
Kline’s little paper plane simply refused to stall. "I was just trying different things", Kline said later. "I had this idea that I wanted to make a glider that would reach its apogee and automatically level off."
"One day I cut this thing out of paper, and it did exactly that, and I said, ‘That’s what I’m looking for’."
Kline noticed that the plane was more stable when he opened the slots under the wings, but it was really his friend and advertising colleague, Floyd Fogleman, a weekend pilot and model builder, then realized that the notch under the wing represented "a whole new concept in aerodynamics". A partnership was born, and the men kept the discovery to themselves until their first patent was granted in December 1972. Soon after that, the articles began appearing in magazines and newspapers. There were stories in Time, The London Daily Telegraph, and The Paris Express. A 1973 feature on CBS’s 60 Minutes proved so popular that it was repeated three years later.
Kline and Fogleman remained cautious about revealing the instructions for folding their marvelous plane. Hobbyists studied pictures of the plane and footage of the few seconds of the 60 Minutes segment during which Kline shows TV interviewer Morley Safer the first few folds. Viewers tried to reconstruct the design, but most failed miserably.
The fold, in fact, isn’t simple; you’ll probably make a few mistakes before you get it right. You can make two planes from our master designs --- one to practice on one to get exactly right. Even so, you might want to practice first on an ordinary sheet of heavy typing paper. Cut the paper down to the dimensions in our diagrams, and use the fold lines on the master designs to get all the proportions correct.
A few flying hints: Before each launch, view the plane head-on and make sure the tops of each wing are horizontal and that both wings are of equal thickness. Check to see that the vertical stabilizer is pointing straight up and that the tape on the nose has no loose ends. You can wedge a paper clip into the fuselage just behind the nose to balance the plane and extend its flights. Experiment with clips of different sizes. And when you find one that works, use a small piece of tape to reinforce the fuselage just in front of the tail. Fogleman reports some exceptionally long glides after tossing the plane up into the wind. If properly launched, the craft gains altitude rapidly and then flies with the breeze.
Aerodynamics experts who looked at the plane said it would never fly --- not with that notch, or "step", on the underside of the wing. "They would tell me, ‘Forget it. It won’t work’, Kline says. "But me, I never heard of Bernoulli, so what do I know? It works, that’s all."
How does it work? The inventors didn’t know. So with patent papers safely in hand, they set out to find someone who could tell them. They took it to one of America’s leading aerodynamics experts, John Nicolaides, a former NASA official and onetime head of the aerospace-engineering departments at both Notre Dame and California Polytechnic State University at San Luis Obispo.
Nicolaides, whose "flying flivver" was the subject of a story in one of Omni’s first issues ["A Flyer for the Masses", Dec. 1978], was skeptical at first. He became a believer, however, when the men visited him at Notre Dame and tested a paper model in the campus’s athletic center. "One of my throws went into the lights of the arena, struck the roof, and then glided clear across the building and into the seats", says Kline. "Nicolaides couldn’t believe it."
This one flight, more than anything else, convinced the aerodynamics expert that the toy deserved some serious wind-tunnel tests. "The data were strange", Nicolaides said, "not like any wind-tunnel data I had ever seen". Nicolaides confirmed that the wing was a true breakthrough in design and that it greatly resists stalling.
But why? "I don’t know", Nicolaides told Safer on 60 Minutes. "A conventional wing, with increasing angle of attack, increases its lift. But eventually, at a steep critical angle the wing can suddenly lose its lift, causing the plane to crash. The Kline-Fogleman wing doesn’t do that. It has good lift for small angles of attack, but a t larger angles, the lift declines and the plane just levels off. This happens even at very large angles of attack, which allows it to avoid the tragic stall phenomenon."
Wind tunnel tests showed that the Kline-Fogleman wing was stable at angles well over 16 to 18 degrees. That’s the inclination at which ordinary wings lose their lift and begin to stall. In fact, the Kline-Fogleman wing stubbornly resists stalling all the way up to a 45 degree angle of attack.
Fogleman says that the tests complement observations he made using a homebuilt radio-controlled model plane with a 6-foot wingspan. "I tested our design with different curvatures on the top and the bottom of the wing", he says, "and the most impressive thing about them all is that they don’t want to spin. There is a spinning maneuver in competitions. You take the normal radio-controlled plane and fly it up to a stall angle, and it will suddenly snap over and go into a spin. Our plane won’t do that. You have to cut the throttle and control the ailerons and rudder all at once to force it to spin. And you can spin it in either direction, which is unusual. Most planes will spin only in the direction of their torque, opposite the way the propeller is turning. Our plane seems to resist that torque, so you can spin it either way. When you take your hands off the controls, the plane comes out of the spin in less than half a turn and returns to straight and level flight."
Just as when you have to force the plane to spin, you also have to force it to stall. "You can’t get it to stall like an ordinary plane", Fogleman says. "It just keeps on porpoising on ahead. When you cut power on landing, it doesn’t stall either, as other planes do, but just keeps going flat ahead. Also, other planes will tip stall --- one wingtip goes down, and the plane spins out of control and crashes --- if they are brought in for a landing at too slow a speed or too high an angle. Our plane just refuses to tip stall."
One would think that the Air Force and NASA would be eager to perform exhaustive tests on the Kline-Fogleman wing and its variations. Apparently that hasn’t happened. "We know NASA tested it", Fogleman says, "but we couldn’t get any results from them, and neither could Nicolaides."
In 1979, P.K. Pierpont, then manager of the airfoil-research program at NASA’s Langley Research Center in Virginia, told Omni about three studies, one of them partially funded by NASA. All had come up with the same results: The Kline-Fogleman wing was found to have a poor lift-to-drag (L/D) ratio --- a standard measure of wing efficiency. These results indicated that the airfoil had no practical application, Pierpont said, so no further tests were made.
And according to Bud Bobbitt, chief of NASA’s transonic-aerodynamics division, test showed that the Kline-Fogleman wing was inefficient. The L/D numbers weren’t encouraging, so studying the wing’s resistance to stalling became a low priority.
Max Davis, of the Air Force Flight Dynamics Lab at Wright-Patterson Air Force Base in Dayton, OH, told a similar story. A few tests were performed after all the publicity in 1973, he said, but preliminary studies indicated that the wing was not suitable for a full-size aircraft because it has too much drag and not enough lift.
"All that is true", Nicolaides says, "but it misses the point. This airfoil doesn’t have great lift at low angles, I grant that. But at high angles, where most planes spin out of control and crash, this one keeps flying."
Furthermore, Nmicolaides found that at subsonic speeds, the wing worked even better when it was turned upside down, with the notch on the top instead of on the bottom. In the notch-up mode, the wing’s lift improved by 44% and its L/D ratio improved by about 30%. And it still refused to stall.
That was enough to convince Nicolaides that the Kline-Fogleman wing deserved serious study by the US government.
In April 1973 Nicolaides wrote letters to NASA, the Air Force, and the Navy, urging them to test the Kline-Fogleman wing in all conceivable configurations: notch down, notch up, rounded leading edge, curved wing surfaces, varied curvature and placement of the notch, and so on. Nicolaides enclosed copies of his encouraging wind-tunnel data.
Apparently, the government experts with the big testing facilities generally ignored most of Nicolaides recommendations. Even when they put the Kline-Fogleman wing through its paces, they concentrated on the lift and drag data, not the resistance to stalling, or they studied only the razor edge version, not the rounded, more winglike variation. In explaining the space agency’s lack of interest, Pierpont said in 1979 that the flight characteristics of the Kline-Fogleman wing were no better than those of a flat plate. But this assertion was disputed by the wind-tunnel data in Nicolaides’s 1973 letter to NASA.
All of this would seem to indicate a marked lack of interest in exploring an idea that could save lives and airplanes. At worst, it suggests that the government did test wings that qualify as Kline-Fogleman variations but won’t reveal the test results.
It boils down to this: If the suggested tests weren’t done, why not? And if they were done, why weren’t the results made known to Nicolaides, Kline, Fogleman, or an inquiring reporter from Omni?
One line of speculation is that the government is withholding the data for national security reasons. Another is that officials perceive a possible overlap between the Kline-Fogleman idea and the do-called Whitcomb supercritical wing. This wing, invented by Richard Whitcomb and patented by NASA in 1976, permits planes to fly close to the sound barrier without being buffeted by turbulence on top of the airfoil. This feat is made possible by the wing’s unusual shape. It’s relatively flat on the top, with a concavity on the undersurface, The hollowed section isn’t the abrupt notch of the Kline-Fogleman patent drawings, but it is well within the range of variations that Nicolaides suggested for testing (When I asked Nicolaides to describe the Whitcomb wing, he called it "a regular wing with a smoothed-out Kline-Fogleman notch on the bottom.")
It’s possible that Kline and Fogleman were awarded a patent on an idea that includes features of the Whitcomb wing. If so, government officials, firmly wedded to Whitcomb’s design, may be trying to sharpen the distinction between the two ideas by downplaying the airworthiness of the Kline-Fogleman prototype.
"I don’t know whether the whole story will ever come out", Nicolaides says. "But the important thing to remember is that the Kline-Fogleman wing doesn’t stall. If the government tsters say that it is not quite as good as other wings in terms of lift-to-drag ratios, they are neglecting to say that it is infinitely better in terms of not killing people. That’s what the Kline-Fogleman wing is all about."
"What I keep coming back to", says Kline, "is the whole question of what makes our airfoil so stable. We believe that the notches cause pockets of air tubulence to be trapped on the underside of the wings and that these pockets somehow support the aircraft at steep angles of attack. No one, as far as I know, has studied what’s going on in these pockets."
Until proper tests are conducted, it is hard to tell what promise the Kline-Fogleman wing holds. So far the most encouraging findings have come from model plane hobbyists, backyard testers and small aircraft companies.
Amerijet, Inc., an Ohio firm producing single-engine planes, is testing a Kline-Fogleman wing to be used on a two-seater aircraft. If the stress-analysis and wind-tunnel tests go as expected, the company will build the first full-scale Kline-Fogleman aircraft in about two years.
J.B. Mitroo, president of Amerijet, told Omni that preliminary tests indicate that the wing will actually improve the efficiency of flight, bringing about a 25 to 35% saving s in fuel.
On the model-airplane front, findings continue to be impressive. Pete Reed, of Avon, CT, tried a Kline-Fogleman wing on a radio-controlled model plane that had a habit of stalling. "It solved the problem", he says. "The plane doesn’t stall anymore, and the difference is spectacular. It flies better than any other plane I have used. With my old plane, if you slowed it down it would stop flying and it would tip stall to one side or the other. I can haul the Kline-Fogleman model up to a very high angle of attack or slow it way down, and the plane still won’t tip stall. The only problem is that the wing adds a lot of drag and the plane flies slower than before."
Reed thinks the drag problem might be corrected if the Kline-Fogleman shape were used only on the outer quarter or third of each wing, rather than along its full length. "If a stall starts at the base of the wing, next to the fuselage, you have time to correct it. But if it starts at the wingtip, it spreads to the rest of the wing before you know it, and there is nothing you can do but watch the thing crash."
Reed suggests another promising variation: carving the blades of a propeller into a Kline-Fogleman profile. "I tried it once. I didn’t take any hard measurements, but the plane seemed to fly faster", he says.
In another test on the idea of a Kline-Fogleman propeller, George Leu, of South Orange, NJ, cut a Kline-Fogleman notch into the two blades of an 11-inch diameter model airplane propeller.
When he attached a fish scale to a plane equipped with an ordinary propeller and revved the engine, he got a maximum pull of about 10 pounds. "When I put the Kline-Fogleman prop on the same plane, I got 11 pounds of pull. It was amazing. The people I was flying with could hardly believe it. Fish scales aren’t the most accurate devices, but the one I used did measure a positive difference, and that sure makes me think this design has possibilities. When I flew the plane with its Kline-Fogleman prop, it seemed to have a lot more vertical power than before, and I needed to give it less correction than usual to get it to do such standard maneuvers as rolling and looping."
The romantic in us would like to think that a significant breakthrough in aerodynamics had its beginning on a kitchen table in New York. That a father making a toy for his son hit upon just the right combination of paper glue, scotch tape and luck. Whether this is a tale of genuine discovery or just a fantasy of what might have been has not yet been answered. We’re rooting for the kitchen table.
Paper Plane Instructions:Page 1 ~ Page 2
Paper Plane Plans: Page 1 ~ Page 2
Excerpt: The Ultimate Paper Airplane by R. Kline & F. Fogleman (1985, Simon & Schuster; ISBN 0-671-55551-0) ~
A friend of Floyd's George Leu of South Orange, NJ, was one of the recipients of an experimental set of propeller blades. Leu had many years' experience flying radio-controled aircraft with Floy, and he agreed to conduct the propeller-blade test. The experimental blades were 11 inches long and had a 7 degree angle of pitch; the engine used was a Webra Speed 0.60 cubic inch.
Leu conducted a simple static test with a radio-controlled plane anchored to the ground. A spring-loaded fish scale was used to determine the mount of pull or thrust prodcued by both a conventional blade adn the Kline-Fogleman prop. The results were striking. The conventional blade pulled a maximum of 10 pounds. But when Leu put the Kline-Fogleman prop on, he got 11 pounds of thrust, or a 10% increase in thrust with slightly fewer RPMs (a 200 RPM drop in a 13,500 RPM run). The test was repeated a second time, adn teh results remained the same.
Then Leu put the Kline-Fogleman prop on his radio-controlled plane and flew it. he noticed that it climbed vertically with much more power than with the conventional prop that he had flown before...
Below: The conventional airofoil (top) shows the four major forces that act upon a wing during flight: lift, thrust, drag adn gravity. The Kline-Fogleman airfoil (bottom) traps seom of the displaced air molecules, reverses their direction, adn produces a forward "push". this action will support the airfoil up to a 45 degree angle of attack, whether it is used with the step on teh bottom or on the top.
Airfoil for Aircraft
Richard
L. Kline & Floyd F. Fogleman
(Dec. 19, 1972)
Background of the Invention
The invention relates to airfoils, especially airfoils having lift and drag characteristics suitable for aircraft wing sections and the like. In the comparatively low or subsonic speed range, the conventional airfoil has cambered surfaces that define a profile of gradually decreasing thickness from the leading edge to the trailing edge. For high or supersonic speeds, the airfoil camber is comparatively small and the wing thin so that the upper and under surfaces tend to be substantially planar.
It follows therefore, that the drag characteristics of the subsonic airfoil are not suitable for supersonic speed, whereas the lift characteristics of the supersonic airfoil are not well suited for low airspeeds. The present invention is concerned with providing a new and basic airfoil design that can be readily varied to meet the requirements of a wide range of airspeeds.
Summary of the Invention
In accordance with the invention, an air foil having a basic design that lends itself to use in aircraft throughout a wide range of airspeeds, comprises a continuous upper surface, and a stepped under surface. The leading edge of the airfoil is defined by the apex of a wedge-shaped section that is formed by angular convergence of the upper surface and a generally planar portion of the under surface. Starting at the leading edge, the diverging under surface terminates abruptly in advance of the leading edge to form on the airfoil under surface a step-like discontinuity that extends spanwise of the airfoil. Rearward of the discontinuity, i.e., the base of the wedge-shape section, the airfoil has a comparatively thin cross-section that terminates as the trailing edge of the airfoil proper.
For varying drag and lift characteristics according to airspeed, the apex angle of the wedge-shape section can be varied, and the diverging under side can be shortened or lengthened to vary the location of the defined step with respect to the trailing edge.
A principal object of the invention therefore, is a new and improved airfoil for aircraft having a minimum of design parameters for adapting the airfoil to a wide variety of airspeeds.
A further object of the invention is an airfoil of the character above having a continuous upper surface and a lower surface having a stepped discontinuity, the surfaces being angularly and spacially related to define a chord section that increases in thickness from the leading edge of the airfoil to the discontinuity.
A related object is an improved airfoil as defined above, having advantageously combined lift, drag and stability characteristics.
These and other objects, features and advantages will become apparent from the following description with reference to the accompanying drawings.
Brief Description of the Drawings
Figure 1 is a side view, in partial perspective, of high speed fixed wing aircraft having airfoils embodying the invention;
Figure 2 is a cross-sectional view of one of the airfoils taken at the indicated junction of the airfoil and aircraft fuselage as shown in Figure 1;
Figure 3 is a front half-section view of aircraft showing a wing airfoil typical of the invention;
Figure 3A to 3D inclusive, are sectional views of the airfoil taken respectively, at the correspondingly lettered section location of Figure 3;
Figure 4 is a front half-section view of aircraft showing the airfoil in modified form;
Figure 4A to 4D inclusive, are sectional views taken respectively at the correspondingly lettered section locations of Figure 5;
Figure 5 is a plan view of the airfoil shown in Figure 3;
Figure 5A to 5D inclusive, are sectional views of the airfoil taken respectively, at the correspondingly lettered section locations of Figure 5;
Figure 6 is a leading edge view of the airfoil of Figure 5 taken from the right as shown;
Figure 7 is a perspective view of a cross-section taken along the line 7-7 of Figure 6;
Figure 8 is a perspective view of a rotary wing type aircraft embodying the invention, and
Figure 9 is an enlarged view of the peripheral edge section of a rotary airfoil as shown in Figure 8.
Description of Preferred Embodiment
The airfoil of the invention is illustrated in Figures 1 and 2 as applied by way of example, to fixed-wing aircraft of the high speed type. It will be understood, however, from the following description that the invention is not limited to high speed or even fixed wing types, and that it can be used advantageously in rotary wing aircraft, and also in comparatively small, low-speed aircraft of the propeller-driven type, as well as in intermediate speed types.
Referring first to Figure 1, the aircraft 10 comprises a conventional streamlined fuselage 12 with empennage 14 and swept-back wings 16 and 18 that constitute the improved airfoils of the invention. The lateral edges of the wings converge toward the rear of the fuselage so that as viewed from above, the composite area of the wings is of generally diamond configuration. Since descriptions of remaining equipment, such as thrust engines, landing gear, etc., are unnecessary for understanding the invention, these items are not shown in the drawings; it is sufficient to mention that conventional jet engines can be carried by the wing structure in suitable manner (suspension, cantilever, etc.) according to aircraft CG and other factors.
The airfoils constituting the wings 16 and 18 in Figure 1, are mounted on the fuselage so as to have a small angle-of-attack according to usual practice when the aircraft is on the runway. Each wing, taking for example wing 16 and referring now to Figure 2, comprises an extensive main section 24 that extends from along the wing leading edge 26 toward the wing trailing edge. The section 24 terminates to form a step 28 that defines a discontinuity in the under surface of the wing between the leading and trailing edges. As indicated in figure 1, the step 28 extends outwardly from the fuselage, its root section at, or spanwise of the wing in the general direction of the wing Y-axis, in contrast with the angular direction of the swept-back leading edge 26 of the wing. As in the general case of airfoils that constitute aircraft wings, the relative air flow with respect to the airfoil is from the leading edge in direction generally parallel to the root section and rearwardly to the free trailing edge, and thence downstream in substantially the same general direction.
As best shown in Figure 2, the underside of the wing is basically formed by the main section 20 and the undersection 24 that is of wedge-shape with its apex coinciding with the leading edge of the wing. The wedge-like section 24 is joined to the main section 20 beneath the forward part thereof, with the wedge apex as indicated above merging with the front edge of the main section to form the leading edge 26 of the wing, and the wedge base forming the "riseR" of the step at 28.
The design angle made between the sections 20 and 24, i.e., the apex angle, can be varied in accordance with aerodynamic considerations, lift, drag, etc., as also can the location of the step with respect to the trailing edge that determines the ratio between the wing top and surface area (section 20) and the under surface area of section 24. The "riser" portion at 28 of the step (indicated by dotted line in Figure 1) can be either sealed or left open, depending on preferred construction of section 24, aerodynamic stresses, etc. For low airspeeds, the riser portion may remain comparatively open, as desired.
Reference will now be made to Figures 3 to 7 for a more detailed description of the new airfoil embodying the invention. As the aircraft is symmetrical with respect to its main axes, the half-sections shown in Figures 3 and 4 are sufficient for illustrating possible variations in the airfoil configuration. Figure 3 indicates a conventional fuselage 30 with one wing 32 constituting an airfoil of the basic character illustrated by Figures 1 and 2. The view, looking toward the swept-back leading edge at 34, shows the continuous upper surface 36 of the airfoil as slightly convex between the fuselage and outer wing tip 38, as is also the lower surface 40 of the wedge-like under section 42.
For illustrating the structural form of the airfoil 32, Figures 3A to 3D are cross-sectional views taken at the section lines A-A, B-B, etc., respectively, of Figure 3. The section nearest the fuselage (Figure 3A) shows the wedge-like under portion 42 as shaving a small apex angle and extending to the step 44 at somewhat less than half the distance to the trailing edge 46. The apex angle increases somewhat at the mid-section of the airfoil, Figures 3B and 3C, to about 10 degrees with the step distance from the leading edge decreasing as shown by Figure 1. Neat the wing tip, Figure 3D, the wedge apex angle decreases for gradual tapering-off at the wing tip. The upper wing section shortens, generally according to distance from wing tip so as to conform with the wing shape of Figure 1.
Figure 4 illustrates the invention as embodied in a modified airfoil 50 especially adapted for high speeds, such as in the supersonic range. Here, the apex angle of the wedge under portion 52 remains substantially constant at a small angle, such as 5-6 degrees, throughout the leading edge 54 from the fuselage 30 to the wing tip 56. The under-surface discontinuity or step, is located with reference to the trailing edge as illustrated in Figure 1. Accordingly, the thickness of the airfoil 50 is materially reduced as compared with Figure 3 and the upper wing surface, as well as the lower surface of the wedge are substantially planar. The airfoil cross-sections at the transversely spaced sections A, B, C, and D, are shown by Figures 4A to 4D respectively, and further description thereof is unnecessary in view of Figures 3A to 3D for an understanding of this aspect of the invention.
Figure 5 is a plan view of the airfoil shown in Figure 3;
Figure 5A to 5D inclusive,
are sectional views of the airfoil taken respectively, at the
correspondingly lettered section locations of Figure 5;
Figure 6 is a leading edge view of the airfoil of Figure 5 taken from the right as shown;
Figure 7 is a perspective view of a cross-section taken along the line 7-7 of Figure 6;
Figure 8 is a perspective view of a rotary wing type aircraft embodying the invention, and
Figure 9 is an enlarged view of the peripheral edge section of a rotary airfoil as shown in Figure 8.
Description of Preferred Embodiment
The airfoil of the invention is illustrated in Figures 1 and 2 as applied by way of example, to fixed-wing aircraft of the high speed type. It will be understood, however, from the following description that the invention is not limited to high speed or even fixed wing types, and that it can be used advantageously in rotary wing aircraft, and also in comparatively small, low-speed aircraft of the propeller-driven type, as well as in intermediate speed types.
Referring first to Figure 1, the aircraft 10 comprises a conventional streamlined fuselage 12 with empennage 14 and swept-back wings 16 and 18 that constitute the improved airfoils of the invention. The lateral edges of the wings converge toward the rear of the fuselage so that as viewed from above, the composite area of the wings is of generally diamond configuration. Since descriptions of remaining equipment, such as thrust engines, landing gear, etc., are unnecessary for understanding the invention, these items are not shown in the drawings; it is sufficient to mention that conventional jet engines can be carried by the wing structure in suitable manner (suspension, cantilever, etc.) according to aircraft CG and other factors.
The airfoils constituting the wings 16 and 18 in Figure 1, are mounted on the fuselage so as to have a small angle-of-attack according to usual practice when the aircraft is on the runway. Each wing, taking for example wing 16 and referring now to Figure 2, comprises an extensive main section 24 that extends from along the wing leading edge 26 toward the wing trailing edge. The section 24 terminates to form a step 28 that defines a discontinuity in the under surface of the wing between the leading and trailing edges. As indicated in figure 1, the step 28 extends outwardly from the fuselage, its root section at, or spanwise of the wing in the general direction of the wing Y-axis, in contrast with the angular direction of the swept-back leading edge 26 of the wing. As in the general case of airfoils that constitute aircraft wings, the relative air flow with respect to the airfoil is from the leading edge in direction generally parallel to the root section and rearwardly to the free trailing edge, and thence downstream in substantially the same general direction.
As best shown in Figure 2, the underside of the wing is basically formed by the main section 20 and the undersection 24 that is of wedge-shape with its apex coinciding with the leading edge of the wing. The wedge-like section 24 is joined to the main section 20 beneath the forward part thereof, with the wedge apex as indicated above merging with the front edge of the main section to form the leading edge 26 of the wing, and the wedge base forming the "riser" of the step at 28.
The design angle made between the sections 20 and 24, i.e., the apex angle, can be varied in accordance with aerodynamic considerations, lift, drag, etc., as also can the location of the step with respect to the trailing edge that determines the ratio between the wing top and surface area (section 20) and the under surface area of section 24. The "riser" portion at 28 of the step (indicated by dotted line in Figure 1) can be either sealed or left open, depending on preferred construction of section 24, aerodynamic stresses, etc. For low airspeeds, the riser portion may remain comparatively open, as desired.
Reference will now be made to Figures 3 to 7 for a more detailed description of the new airfoil embodying the invention. As the aircraft is symmetrical with respect to its main axes, the half-sections shown in Figures 3 and 4 are sufficient for illustrating possible variations in the airfoil configuration. Figure 3 indicates a conventional fuselage 30 with one wing 32 constituting an airfoil of the basic character illustrated by Figures 1 and 2. The view, looking toward the swept-back leading edge at 34, shows the continuous upper surface 36 of the airfoil as slightly convex between the fuselage and outer wing tip 38, as is also the lower surface 40 of the wedge-like under section 42.
For illustrating the structural form of the airfoil 32, Figures 3A to 3D are cross-sectional views taken at the section lines A-A, B-B, etc., respectively, of Figure 3. The section nearest the fuselage (Figure 3A) shows the wedge-like under portion 42 as shaving a small apex angle and extending to the step 44 at somewhat less than half the distance to the trailing edge 46. The apex angle increases somewhat at the mid-section of the airfoil, Figures 3B and 3C, to about 10 degrees with the step distance from the leading edge decreasing as shown by Figure 1. Near the wing tip, Figure 3D, the wedge apex angle decreases for gradual tapering-off at the wing tip. The upper wing section shortens, generally according to distance from wing tip so as to conform with the wing shape of Figure 1.
Figure 4 illustrates the invention as embodied in a modified airfoil 50 especially adapted for high speeds, such as in the supersonic range. Here, the apex angle of the wedge under portion 52 remains substantially constant at a small angle, such as 5-6 degrees, throughout the leading edge 54 from the fuselage 30 to the wing tip 56. The under-surface discontinuity or step, is located with reference to the trailing edge as illustrated in Figure 1. Accordingly, the thickness of the airfoil 50 is materially reduced as compared with Figure 3 and the upper wing surface, as well as the lower surface of the wedge are substantially planar. The airfoil cross-sections at the transversely spaced sections A, B, C, and D, are shown by Figures 4A to 4D respectively, and further description thereof is unnecessary in view of Figures 3A to 3D for an understanding of this aspect of the invention.
Figure 5 which is a plan view, referring to Figure 3, shows more explicitly the spacial relation between the under-surface discontinuity and the leading and trailing edges. Here, the airfoil 60 is in top plan view, with the sectional views Gigs. 5A to 5D taken as before at spaced points between the fuselage junction edge 62 and the wing tip 64. The step 66, as generally shown in Fig. 1 (and in Fogs. 5A to 5D) extends from the fuselage edge to the wing tip at a swept-back angle materially smaller than that of the leading edge 68. The apex angle in this instance can be comparatively small, i.e., ranging between 4 and 6 degrees, so that the wing is sufficiently thin for high air speeds. Although the upper wing surface and the under surface of the wedge portion are preferably slightly convex with respect to the generally linear leading edge, these surfaces for practical purposes may be considered planar.
Figs. 6 and 7 are different views of sections of the airfoil, Fig. 5, wherein the upper and lower wing surfaces are slightly convex with respect to the horizontal center line, Fig. 6, rather than linear as in Fig. 4. In Fig. 6 the airfoil 70 has an upper surface 72 that increases in convexity from the root or fuselage end, to the wing tip, Fig. 7. The apex angle of the under-surface wedge portion 78 varies in the manner described above for defining convex wedge surfaces as shown in Figs. 6 and 7. The resulting airfoil is of moderate thickness suitable for lower airspeeds than those for Fig. 4; also the convex surface provides for increased stability. Fig. 7 which shows a perspective view of the airfoil at the section line 7-7 of Fig. 6 illustrates the relationship between the varying apex angle and height of step 79 to the convexity of the upper and lower wing surfaces.
The comparatively thin trailing portion resulting from the abrupt undersurface discontinuity as described above, is intended to be aerodynamically functional throughout full utilization of the airfoil; that is, the space beneath the thin portion downstream of the step is not intended to be occupied, as for housing auxiliary equipment, flaps, etc., that would in effect, tend to eliminate or markedly reduce the aerodynamic effect of the discontinuity.
Figs. 8 and 9 show the invention as embodied in the airfoils of rotating wing type aircraft. In Fig. 8 a helicopter 80 is provided with rotating airfoils or blades 82 wherein at least the outer portion of each blade is constructed according to the basic configuration described above. Fig. 9 is an enlarged view of the outer (or peripheral speed) end of the rotor blade wherein the continuous upper surface 84 is substantially planar and the under surface is characterized by a wedge-like portion 86 defining a step-like discontinuity 88 intermediate the leading edge 90 and the trailing edge 92. The apex or leading edge angle is a function of rotor rpm and required lift characteristics, and as shown is approximately 10 degrees.
Since the major part of the lift produced by helicopter blades is at the outer third of the blade length by reason of the greater swept area and higher blade velocity thereat, the under-surface step can be terminated as desired by gradual merging with the blade at an intermediate point as indicated by dotted lines 88 in Fig. 8. An important consideration in the use of the present airfoil for helicopter blades is that the blades can be efficiently rotated at speeds for bringing the tip speeds into the supersonic range by reason of the improved lift and drag characteristics of the thinner high speed airfoil. It will also be apparent that where desired, the invention can readily be incorporated in airfoil control sections such as elevators and rudders, as well as in the main lifting or wing sections.
Referring further to the airfoil configuration of Fig. 9, it will become apparent that the basic geometry of the airfoil can be varied to considerable extent while retaining the essential novel concept of the invention. For example, the apex or wedge angle can be varied from several degrees as described above, to as much as 30 degrees for obtaining lift and stability characteristics under lower airspeed conditions. Also, the ration of the upper or camber surface area at 84 to the under-surface area at 94 of the wedge portion (always greater than unity) can be varied by location of the discontinuity (step) with reference to the trailing edge, according to aerodynamic characteristics desired.
The upper and lower camber surfaces of the airfoil can be substantially planar, as in Fig. 4, or slightly convex as in Figs. 3 and 6. Preferable, the convexity of these surfaces is limited at the point of maximum bow with respect to a horizontal reference to about 2 percent of the fore-aft length of the surfaces at 84 and 94 respectively. The so-called riser portion of the step at 88 is not limited to an approximately right angle as shown for convenience in Figs. 3A, etc., and 5A, etc., but may be inclined to a greater or lesser extent than that shown in Fig. 9 for example.
As regards aerodynamic theory, the technical reasons for the improved performance of the present airfoil are unknown to the inventors. Small-scale airplanes constructed according to the configurations of Figs. 1 and 3 were tested in flight and demonstrated unusually good lift, stability, and pitching moment characteristics; further, the airfoil parameters thereof were found by modern computer technique, to be suitable for both high speed and low speed conditions, and to have lift, drag and moment characteristics within the limits of modern aerodynamic design criteria.
Although the invnetion in its preferred form is shown applied to the airfoils of aircraft, application as well to guided-entry type spacecraft, missiles, etc., in instances where airfoils are used, is implicit.
Having set forth the invention in what is considered to be the best embodiment thereof, it will be understood that changes may be made in the apparatus as above set forth without departing from the spirit of the invention or exceeding the scope thereof as defined in the following claims: [Claims not included here].
