Abstract:
A lifting foil for an aircraft, a hydrofoil or the like having a pair of courses or wings. Vortex losses due to spanwise fluid flow are substantially reduced by joining the tips of the courses with flow guides configured for jointly terminating the undesired flows. Termination is effected by providing the flow guides with crossections cambered for reducing the dynamic pressure of fluid flowing in a spanwise direction across flow guide surfaces.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     This invention relates generally to the field of fluid dynamics with emphasis on aerodynamic drag phenomena. A particular object of the invention is to reduce energy losses suffered by an aircraft in flight due to induced drag. It is known that this particular type of drag is accompanied by a shedding of vortices from the tips of the wings. It is believed that these vortices result from a spanwise flow of air from a relatively high pressure condition on the lower wing surface to a relatively low pressure condition on the upper wing surface. Similar phenomena occur around hydrofoils employed for underwater use. It might be remarked that air behaves much as a perfect fluid when acting against an airfoil at speeds below about 200 mph and at altitudes below about 100,000 ft. Within that regimen the mathematical tools employed for analysis of airfoils are substantially the same as those for hydrofoils General teachings regarding aircraft drag may be found in classical reference books such as “Foundations of Aerodynamics”, Kuethe and Schetzer, © 1950 by John Wiley &amp; Sons, Inc; “Aerodynamics of a Compressible Fluid”, Liepmann and Puckett, © 1947 by John Wiley &amp; Sons, Inc; “Airplane Performance Stability and Control”,  1949  by Perkins and Hage, publisher John Wiley &amp; Sons, Inc; and in “The Dynamics and Thermodynamics of compressible Fluid Flow”, two volumes by Ascher H. Shapiro, The Ronald Press Company, New York, N.Y., 1953. Reference may also be made to a well known earlier work “Hydrodynamics”, Sir Horace Lamb, 1879, Sixth Ed. by Dover Publications, New York, N.Y., 1945.  
         [0002]     The prior art shows numerous techniques for dealing with induced drag, but none are fully satisfactory. Following are some typical examples. 
        Miranda, U.S. Pat. No. 3,834,654, teaches a box-wing aircraft having a fuselage which is centrally positioned and encircled by six adjoining wing sections.     Wenzel, U.S. Pat. No. 4,146,199 shows an aircraft having a lifting body fuselage surrounded by fore mounted aft swept and aft mounted forward swept wings. The patent describes means for inducing translation of tip-generated vortices.     Wajnikonis, U.S. Pat. No. 4,949,919 discloses hydrofoil families which partially suppress induced vorticity by introducing a longitudinal component of the flow directed by the lifting foil tip towards the hydrofoil base.     Gratzer, U.S. Pat. No. 5,348,253 teaches the attachment of a blended winglet to each wing tip.     Eger U.S. Pat. No. 5,503,352 relates to a box-wing aircraft having wing segment tips connected with arrow-shaped pylons.     Nosenchuck et al. U.S. Pat. No. 5,492,289 has a perturbation proximate to the tip end of the wing planform trailing edge.     McCarthy U.S. Pat. No. 5,634,613 generates beneficial wing tip vortices which are said to rotate in a direction opposite to that of induced drag vortices. The patent asserts that the beneficial vortices create upwash fields which neutralize induced drag. The reference discusses numerous other references dated earlier than 1994.     Frediani U.S. Pat. No. 5,899,409 discloses a large passenger plane having a pair of rearwardly swept wings arranged in tandem with a pair of forwardly swept wings.     Vanmoor U.S. Pat. No. 6,095,457 teaches an airfoil which is reversely curved in accordance with a trigonometric function.     Meschino U.S. Pat. No. 6,340,134 B1 shows an aircraft having a drag reduction system which includes a high aspect ratio, supplementary wing for providing at least 65% of the total lift. The main wing provides structural integrity.     Carlow U.S. Pat. No. 6,474,604 B1 teaches a mobius-like joining structure which is said to reduce vortex-induced drag on a foil.     Huenecke U.S. Pat. No. 6,513,761 B2 discloses the use of vortex generators at the trailing edge of each wing for partly dissipating the vortices responsible for induced drag,     Cox et al. U.S. Pat. No. 6,626,398 B1 teaches an unmanned reconnaissance biplane having staggered and gapped wings.        
 
         [0016]     While much has been accomplished by others in reducing drag losses of lifting foils, much still remains to be done. It is an undeniable fact that commercial and governmental air transportation expenditures are very high and are steadily increasing. These costs ultimately are passed on to an already overburdened public A substantial proportion of that expenditure pays for fuel which is burned in overcoming induced drag. Even small reductions in that drag may have the potential to create enormous savings for the public.  
       SUMMARY OF THE INVENTION  
       [0017]     This invention provides a novel lifting foil configured generally in the form of an endless band having a plurality of exposed surfaces which meet at common boundary lines. The lifting foil comprises a generally horizontal upper course, a generally horizontal lower course parallel to and spaced apart from the upper course and a pair of opposed, vertically extending flow guides. A first one of these flow guides joins a first end of the upper course to a corresponding first end of the lower course, while a second flow guide joins a second end of the upper course to a corresponding second end of the lower course.  
         [0018]     The joinder of the upper and lower courses to the flow guides occurs at four margins, referred to herein as an upper starboard margin, an upper port margin, a lower starboard margin and a lower port margin. The flow guides are blended into the courses at those margins so as to avoid discontinuities in the fluid flow across the inner and outer surfaces of the foil.  
         [0019]     In the use of the invention a working fluid, such as water or air, flows from fore to aft through a large central passage, where it exerts dynamic pressure outwardly against an exposed first surface of the foil. The working fluid also flows around the exterior of the foil, exerting dynamic pressure inwardly against a second surface thereof. The region between the first and second surfaces defines a cambered lifting body which reacts to the dynamic pressure on its first and second surfaces by generating a net upwardly directed lifting force. Preferably the lifting foil has a third surface for dividing the large central passage into a pair of smaller, spaced apart, passages having generally elliptical crossections and a fuselage therebeween.  
         [0020]     The flow guides are designed to avoid generation of spanwise fluid flow by balancing the pressure at the upper starboard margin against the pressure at the lower starboard margin, and concomitantly balancing the pressure at the upper port margin against the pressure at the lower port margin. Preferably the pressure balancing is accomplished by configuring the starboard flow guides to have a cross section which will reduce a dynamic pressure from a maximum value at the upper starboard margin to a midpoint value of zero, while simultaneously increasing the dynamic pressure from a midpoint value of zero to a maximum value at the lower starboard margin. A similar process is carried out on the port side of the foil.  
         [0021]     The lifting foil is unexpectedly stable and easily controllable in flight. It is believed that the performance of the foil is due, at least in part, to the tendency of the flow guides to stabilize the dynamic pressure at the ends of the upper and lower courses. This reduces the flow of fluid in the spanwise direction and makes the courses behave in the manner expected for 2-dimensional lifting bodies. It is believed that a lifting foil in accordance with the present invention enjoys reduced spanwise fluid flow and that this in turn eliminates, or at least substantially reduces, the generation of drag-producing vortices.  
         [0022]     It is therefore an object of the present invention to provide an apparatus and method for improving the dynamic performance of a lifting foil.  
         [0023]     It is another object of the invention to reduce induced drag vortices to zero.  
         [0024]     A further object of the invention is to reclaim vortex energy while reducing tailplane aerodynamic balancing drag to zero.  
         [0025]     A still further object of the invention is to increase lift with no substantial drag penalty.  
         [0026]     Other objects of the invention are to increase lift and decrease drag for very low speed flight, to reduce spanwise fluid flow in a lifting foil, to decrease aircraft drag and improve aircraft stability, as well as other and further objects and advantages as will be apparent from the following description, the accompanying drawings and the appended claims.  
     
    
     BRIEF DESCRIPTION OF THE DRAWING  
       [0027]      FIG. 1  is a perspective view of a lifting foil.  
         [0028]      FIG. 2  is a top view of the lifting foil of  FIG. 1 .  
         [0029]      FIG. 3  is a front view of the lifting foil of  FIG. 1 .  
         [0030]      FIG. 4  is a side view of the lifting foil of  FIG. 1 .  
         [0031]      FIG. 5A  is a schematic illustration of pressure forces against a pair of flow guides.  
         [0032]      FIG. 5B  is a partially cut away perspective drawing of a flow guide.  
         [0033]      FIG. 5C  is a diagram of a cambered airfoil.  
         [0034]      FIG. 6  is a schematic side view of a lifting foil according to the invention.  
         [0035]      FIGS. 6A-6I  are cross sections of ribs located at angularly displaced positions on  FIG. 6 .  
         [0036]      FIG. 7  illustrates a range of elliptical crossections having major axis/minor axis ratios which are deemed useful for configuring a lifting foil.  
         [0037]      FIG. 8  is a top view of an alternative embodiment of the invention.  
         [0038]      FIG. 9  is a front view of the embodiment of  FIG. 8 .  
         [0039]      FIG. 10  is a side view of the embodiment of  FIG. 8 .  
         [0040]      FIGS. 11-18  are front views of second through ninth alternative embodiments of the invention.  
         [0041]      FIG. 19  is a graphical plot of calculated performance characteristics for the lifting foil of this invention and comparative calculated characteristics for a typical prior art lifting foil.  
         [0042]      FIG. 20  is a perspective view of a tenth alternative embodiment of the invention.  
         [0043]      FIG. 21  is a top view of the embodiment of  FIG. 20 .  
         [0044]      FIG. 22  is a front view of the embodiment of  FIG. 20 .  
         [0045]      FIG. 23  is a side view of the embodiment of  FIG. 20 . 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0046]     A preferred embodiment of the subject invention may have a form as generally illustrated by lifting foil  10  in  FIGS. 1-4 .  FIG. 1  is a perspective drawing of the lifting foil with a coordinate system attached. The coordinate system has its origin at the center-of-gravity of foil  10 . It is right-handed and employs conventional 3-axis, X,Y,Z Cartesian coordinate designations. Directions may also be referred to as “starboard” (+Y), “port” (−Y), “fore” (+X), “aft” (−X), “up” (−Z) and “down” (+Z). The term “spanwise” is used to refer to sideward motion in either the +Y or −Y direction. The lifting foil is laterally symmetrical across the X-Z vertical plane.  FIG. 2  is a top view of lifting foil  10  while  FIGS. 3 and 4  are front and side views respectively.  
         [0047]     Lifting foil  10  comprises four basic elements, blended end-to-end to form a closed loop surrounding an open interior These elements are an upper course  14 , a lower course  15 , a starboard flow guide,  16  and a port flow guide  18 . Upper course  14  is positioned generally in an X-Y plane and has an upper starboard margin  52  and an upper port margin  54 . Lower course  15  is geometrically similar to upper course  14  and is situated parallel thereto. Lower course  15  has a lower starboard margin  56  and a lower port margin  58 . Margins  52 ,  54 ,  56 , and  58  are best shown by phantom lines in  FIG. 1  Starboard flow guide  16  is joined to upper course  14  at upper starboard margin  52  and is joined to lower course  15  at lower starboard margin  56 . Port flow guide  18  is joined to upper course  14  at upper port margin  54  and is joined to lower course  15  at lower port margin  58 . It should be understood that the margins  52 ,  54 ,  56  and  58  merely define the geometric limits of the four principal elements and do not have any particular structural significance. Upper course  14  and lower course  15  generate lift in the −Z direction when traveling in the +X direction through a surrounding fluid or when held stationary against a surrounding fluid moving in the −X direction. Flow guides  16 ,  18  are configured in the form of an arc having a center portion  69  of substantially circular curvature and end portions  68 ,  70  of a curvature which causes a blending with the surfaces of upper course  14  and lower course  15 . (See  FIG. 6 ).  
         [0048]     Preferably upper course  14  is rearwardly offset by a distance ΔX from lower course  15 , as illustrated in  FIGS. 2 and 4 . This offset is a design feature which may be selected in such a way as to provide a cargo carrying capability appropriate for the intended use of the lifting foil. By way of example,  FIG. 10  shows a side view of a cargo carrier  130  having a somewhat extended offset ΔX′.  FIGS. 8 and 9  are a top view and a front view, respectively of cargo carrier  130 .  
         [0049]     Upper course  14  may be swept rearward, and lower course  15  may be swept forward. If lifting foil  10  happens to be an aircraft, then it may be desirable to incorporate a fuselage  20  into the structure. As illustrated in  FIG. 1 , fuselage  20  may be positioned midway between flow guides  16  and  18  and extend upwardly from lower course  15  to upper course  14 . Fuselage  20  may house a suitable power supply, controls and one or more passenger compartments. Most conveniently a cockpit and crew quarters may be located in a nose area designated by reference numeral  12 . Ample space is available for placement of aerodynamic control surfaces. The entire surface of lifting foil  10  is smooth, and its four principal elements are blended together so as to minimize vortex generation.  
         [0050]     Lifting foil  10  has four boundary lines  31 ,  32 ,  33  and  34  as illustrated in  FIG. 2 . The configuration of lifting foil  10  may be established by stretching a warped surface in the area outside the four boundary lines  31 - 34 . Three surfaces, including a first surface  37 , a second surface  38  and a third surface  39  meet at these boundary lines. In its most preferred embodiment lifting foil  10  has a fuselage  20  within an interior region extending rearwardly and upwardly from reference point  12  and exteriorly bounded by first surface  37 , second surface  38  and third surface  39 .  
         [0051]     Lifting foil  10  has a starboard flow passage  22  and a port flow passage  24 , as best illustrated in  FIG. 3 . These flow passages are generally symmetrical. As fluid flows through passages  22 ,  24 , it experiences point-to-point variations in the magnitude and direction of the velocity. These velocity variations cause variations in dynamic pressure (commonly called “q”) throughout the moving fluid. According to the well known Bernoulli equation, 
 
 q= ½ ρV   2  
 
 where: 
        ρ is the density of the fluid, and     V is the fluid velocity.        
 
         [0054]     Lifting foil  10  experiences a net force having a magnitude and direction depending upon the size of its wetted area and the variations in dynamic pressure thereacross.  FIG. 5A  illustrates a pattern of incremental forces  63   a - 63   h  applied against the surfaces of flow guides  16 ,  18  as a result of dynamic pressure variations. Incremental forces  63   a - 63   h  are represented by vectors oriented normal to the surfaces of flow guides  16 ,  18  and having lengths corresponding to the magnitudes of the incremental forces being represented. For ease of illustration vectors  63   a - 63   h  represent vector sums of incremental forces operating at the same aspect angle against second surface  38  and third surface  39 . As used herein, reference numeral  63  applies generally to any of the illustrated vectors, specific ones of vectors  63  being designated  63   a  through  63   g . The total force exerted by the fluid against flow guide  16  is given by the expression: 
 
 F=ΣqΔA  
 
 where ΔA is an elemental area wetted by the fluid. 
 
         [0055]     The vertical component of the vector F is the lift.  
         [0056]     Still referring to  FIG. 5A , attention is directed at vectors  63   a  and  63   b . These vectors are of equal magnitude, horizontal and oppositely directed. Vectors  63   a  and  63   b  are therefore self-cancelling. Other vectors  63  have vertical components in addition to any horizontal component. The horizontal components are self-cancelling, but the vertical components of these vectors are commonly directed. Therefore the vertical components are additive, and lift-contributing. Similarly port flow guide  18  is subjected to pressure forces represented by vectors  63   c  and  63   d  having self-cancelling horizontal components. Vectors  63   e - 63   h  represent pressure forces at margins  52 ,  56  of flow guides  16 ,  18  and have no horizontal component.  
         [0057]     As indicated previously, the inboard boundaries of starboard flow guide  16  are delineated by upper starboard margin  52  and lower starboard margin  56 . These two margins are shown schematically in  FIG. 5A  by a single, vertical phantom line. Similarly, a single vertical phantom line represents upper port margin  54  and lower port margin  58 , the inboard boundaries of port flow guide  18 . It will be understood that upper course  14  extends between upper starboard margin  52  and upper port margin  54  and has a uniform pressure pattern shown by the length of pressure vectors  63   f  and  63   h . Similarly lower course  15  extends between lower starboard margin  56  and lower port margin  58  and has a uniform pressure indicated by vectors  63   e  and  63   g.    
         [0058]     Starboard and port flow guides  16 ,  18  create blended bridges between upper course  14  and lower course  15 . And while their operation is not yet fully understood, it is believed that Starboard and port flow guides  16 ,  18  connect courses  14 ,  15  together in such a way as to cause each to function as a terminator for the other. It appears that they provide equalizing fluid flows which balance out spanwise pressure variations, thereby making courses  14 ,  15  behave like virtual two-dimensional wings. However, regardless of the precise process taking place within starboard and port flow guides  16 ,  18 , the lifting foil of this invention inherently obtains remarkable results, as hereinafter described.  
         [0059]      FIG. 5B  illustrates one possible structure for a starboard flow guide  16 . The structure of a port flow guide  18  would be identical, except for left and right hand parts differences. Referring now to  FIG. 5B , flow guide  16  is seen to comprise a series of stiffening ribs secured between second surface  38  and third surface  39 . For additional stiffness, the illustrated ribs may be tied together by one or more spars (not illustrated). Surfaces  38  and  39  have been introduced above and serve as covering for a large area of lifting foil  10 . By way of example, surfaces  38  and  39  may be fabricated from thin aluminum sheet material.  
         [0060]      FIG. 5B  illustrates flow guide  16  with second surface  38  partially cut away to reveal five typical ribs  83 - 87 . Two end ribs  81  and  89  are also exposed. These latter two ribs are welded or otherwise secured to structure (not illustrated) at margins  52 ,  56 . This creates blended connections between starboard flow guide  16  and adjoining ends of courses  14 ,  15 . Two more ribs  82  and  88  are not illustrated in  FIG. 5B  but will be discussed below in connection with the description of  FIGS. 6B and 6H . Port flow guide  18  is similarly joined to courses  14 ,  15  at margins  54 ,  58  respectively.  
         [0061]      FIG. 5C  serves as an aid in understanding the geometry involved in the achievement of coordinated lift at both upper and lower ends of flow guide  16 . Shown there is a side view of a rib, being generic in nature and labeled for identification with reference numeral  64 . Rib  64  has an upper surface  90 , a lower surface  91 , a chord line  92  and a mean camber line  93 . The chord line runs between the ends of the rib, while the mean camber line follows a locus of positions midway between upper surface  90  and lower surface  91 . The area between chord line  92  and mean camber line  93  represents the lift available from a surface wrapped around the rib. That lift may be increased by changing the curvature of surfaces  90  and/or  91  to increase or decrease the area between chord line  92  and mean camber line  93 . The lift may also be changed by modifying the angle of attack, “a”, the angle between chord line  92  and the relative fluid velocity “V”.  
         [0062]     The operation of flow guide  16  is explained diagrammatically in  FIG. 6 . That figure has nine placement lines,  6 A- 6 A through  6 I- 6 I, indicating the locations and viewing directions for nine cuts across flow guide  16 . Sketches of those nine cuts are appear on  FIGS. 6A-6I , as indicated by reference numerals  81 - 89 .  
         [0063]     It is desired to produce substantially uniform lift along the lengths of courses  14 ,  15  between their respective margin pairs. It is also desired to have that lift drop substantially to zero at the course margins. Those desires substantially are met by placing flow guides  16 ,  18  between courses  14 ,  15 , at margins  52 ,  54 ,  56  and  58  as described above. The flow guides have cambered crossections which provide lift ranging from a maximum value down to a minimum value, preferably zero, and then increasing from the minimum value back to the maximum. The maximum value for the lift is the same as the value of the lift at margins  52 ,  54 ,  56  and  58  of courses  14 ,  15 . For present purposes it should be understood that the term “lift” is being used loosely as a shorthand for “lift per unit span”.  
         [0064]      FIG. 6  assumes that lifting foil  10  is moving in the +X direction, thereby creating an apparent fluid motion in the −X or aft direction and producing lift in the −Z direction. Also appearing on the figure is a vector diagram  175 . Shown there are the above-described net force vector, F, a lift vector, L and a horizontal vector, H. V and L meet at an angle, “g”. H is perpendicular to L, so the three vectors define a right triangle. L is always vertical and is the vertical component of F. F may be positioned such that g may have any value between 0 and II radians. The camber of the crossections illustrated in  FIGS. 6A-6E  may be made proportional to COS(g), so that the lift generated by the first II/2 rad. goes from max to 0. However, the camber of the crossections illustrated in  FIGS. 6E-6I  should be made proportional to COS(II−g), so that the lift over that angular range goes from 0 to max. This matches the terminating pressure conditions at margins  52 ,  56 . In a similar manner the pressure conditions at margins  54 ,  58  are matched by flow guide  18 . In this manner I am able to avoid a negatively directed lift by either of courses  14 ,  15  This invention provides flow guides in matching pairs such that each member views a termination of the other as a continuation of itself, thereby reducing pressure imbalances in the spanwise direction.  
         [0065]     Referring now to  FIGS. 6A-6I  there are shown, by way of example, nine rib crossections  81 - 89 . Ribs  81 ,  89  are substantially identical and are cambered to provide the above described maximum lift. Rib  85  ( FIG. 6E ) is perfectly symmetrical about a horizontal plane and generates no lift. Ribs  82 - 84  ramp the lift from the maximum down to zero, while ribs  86 - 88  ramp the lift from zero back to the maximum.  
         [0066]     It will be observed that the underside of lifting foil  10  is keel-shaped, extending symmetrically upward at an angle “b” on both sides of a baseline extending in the X-direction through reference point  12 . This provides a small dihedral for minimizing adverse effects of sideslip. For an embodiments as illustrated in  FIG. 3 , a suitable dihedral angle may be about 5 degrees, applied symmetrically to passages  22 ,  24 . One of ordinary skill in the art may easily determine an appropriate dihedral angle for other embodiments of the invention. See Chapter 9 of Perkins and Hage, Sixth Printing, February, 1957.  
         [0067]     Cross sections of lifting foil  10  which are taken across the Y-Z plane have a generally elliptical appearance, as illustrated in  FIG. 7 . The elliptical shape seems to play a beneficial role in the performance of the lifting foil. However, it is not known how much of the benefit is attributable to the elliptical shape and how much is due to other factors, such as flow guides  16 ,  18 .  
         [0068]     There are a number of ways of specifying the ellipticity of a closed line. For present purposes it is convenient to use the major-axis/minor-axis ratio. Referring now to  FIG. 7 , there is shown a family of ellipses having a common major axis  40 . The family members have minor axes falling at various positions along line  41 . Four such ellipses  42 ,  44 ,  46 ,  48  have ratios of 3.0, 10.5, 1.6 and 1.0, respectively. Ellipse  48  is a special case where the ellipse becomes a circle. That is not of interest herein. Also not of interest is a case where the ratio goes to infinity, and the ellipse collapses against the major axis. The three remaining cases are of interest in the practice of this invention.  
         [0069]     It has been found that the lifting foil performs best when the major-axis/minor-axis ratio is around 3.0. Maximum and minimum values are about 10.5 and 1.6 respectively. The region occupied by ellipses within that range is cross-hatched in  FIG. 7 . I am able to identify that region as a result of information acquired during a flight test program involving many flight tests of scale model lifting foils, variously configured in accordance with this invention. Those models exhibited remarkable stability for both powered and unpowered flight, and were found to be amazingly easy to control.  
         [0070]      FIGS. 8-10  are top, front and side views respectively of a first alternative embodiment of the invention, a cargo-carrying “stretch” version. This version is identical to the version of  FIGS. 2-4 , except for the offset distance which has been increased from ΔX to ΔX′.  
         [0071]      FIGS. 11-18  are front views, respectively, of second through ninth alternative embodiments  0 ,  170 ,  180 ,  190 ,  200  and  210  of the invention.  
         [0072]     A tenth alternative embodiment of the invention  220  is shown in perspective in  FIG. 20 , top, front and side views, respectively, being shown in  FIG. 21 . Lifting foil  220  is similar to lifting foil  10 , except for the substitution of a facilities bay  225  for fuselage  20 . The functions of fuselage  20  are all handled inside facilities bay  225 . This eliminates some supporting structure, but it likewise reduces weight and drag. The courses and flow guides of this tenth alternative embodiment operate in like manner as their counterparts in the version of  FIG. 1 . Note that lifting foil  220  has only one passage  222 , two boundary lines  241 ,  243  and two exposed surfaces  238 ,  239 .  
         [0073]     Key performance parameters for an hypothetical lifting foil according to my invention have been calculated with the aid of a digital computer. The computer ran a simplified program. Employing a well known procedure which models a cambered lifting foil as a series of panels, or Flat plates at varying angles of attack The same program was run for a typical prior art standard Wing of the same span and area. The resulting data are plotted in  FIG. 19  as a series of curves identified by reference numerals as follows: 
         102  Lift Coefficient (This Invention)      103  Lift Coefficient (Standard Wing)      104  Drag Coefficient (Same for both)      105  Moment Coefficient (This Invention)      106  Stability Coefficient (This Invention)      107  Span Efficiency (This Invention)      108  Span Efficiency (Standard Wing)        
 
         [0081]     Referring now to  FIG. 19 , the computer calculations indicate that the lifting foil of this invention is a substantial improvement over the standard wing. In particular, there is an improvement of about 35% in span efficiency, an improvement of about 30% in lift coefficient and an improvement of about 25% in moment coefficient. While not plotted in  FIG. 19 , the standard wing stability coefficient, d(C M )/d(C L ) went from −0.350711 to −0.345073 or a value of about −0.35 throughout the angle of attack range from 0 to 10 deg. That compares with a value of about −0.64 for my lifting foil, thereby indicating that I have achieved a stability margin improvement of about 5% The lifting foil of this invention is expected to achieve such results with no significant increase in drag.  
         [0082]     It will be appreciated that this invention has application to a number of significantly different situations where fluid drag is encountered; for example to fixed wing aircraft, rotary wing aircraft, submarines and hydrofoils. Those skilled in the art will understand that many modifications may be made to structures, materials, proportions, arrangements, components and methods described herein, without departing from the scope of the invention claimed below.