FIELD OF THE INVENTION

The present invention relates to airfoils and lifting structures, such as wings, in particular to airfoils comprising a rigid surface contour leading edge flap and lifting structures comprising such airfoils. In particularly preferred embodiments, the airfoil is a double flap laminar airfoil.

BACKGROUND

In practice, it is known that laminar airfoils have low drag values in a certain range of angles of attack, corresponding to a range of lift coefficients. This lift coefficient range with low drag values is also referred to as the "laminar low drag bucket" and comes with long regions of laminar boundary layer flow on both sides of the airfoil before the flow becomes turbulent. It is a general goal for airfoil design to reduce overall drag of a wing. Airfoils may be optimized for reduced overall drag of the wing by reducing the profile drag coefficient within the laminar low drag bucket or by increasing the usable lift coefficient range of the airfoil, i.e. widening the laminar low drag bucket. The latter approach allows to reduce the wing area while maintaining equal maximum lift. The laminar low drag bucket is of particular importance in the design of sailplanes, as well as wings and airfoils therefor. During cross country flight, sailplanes operate by gaining altitude in atmospheric updrafts, such as thermal updrafts, and then use the gained altitude to glide a certain distance, such as a distance to another updraft, where the altitude expended for the glide can be regained. Atmospheric updrafts are typically small scale phenomena. In order to effectively use such atmospheric updrafts, i.e. maximize the altitude gained from the updraft, the time spent in the area of the updraft is to be maximized. This can for example be achieved by flying substantially straight and slow or by circling in the area of the updraft. While circling may extend the time spent in the area of the updraft at the pilot’s will, it is desired to minimize the circling radius and thus make use of even the smallest scale updrafts. Thus, even when circling in an updraft, a low speed is desired during such flight phases. Conversely, in order to maximize overall cross country flight distance, a high speed is desired when gliding between updrafts. Thus, a design conflict emerges in sailplane design, where wings and airfoils need to be optimized both for low profile drag coefficients at low speeds and low profile drag coefficients at high speeds.

A known technique to reduce overall drag of the wing at high speeds is to increase the wing loading of the sailplane. However, increased wing loading of a given wing results in an increase of the minimum air speed, thus adversely affecting the ability to maximize time spent in areas of atmospheric updrafts. Reducing the wing area while maintaining equal maximum lift, as can be achieved with an airfoil having a wide low drag bucket, is therefore particularly sought after in sailplane design. Thereby, a sailplane capable of high wing loading may be designed, thus reducing overall drag of the wing at high gliding speeds while at the same time maintaining a low minimum air speed for efficient thermalling.

As will be further detailed below with respect to the attached drawings, a number of airfoil designs have been proposed in the prior art in attempts to deal with the aforementioned design conflicts. However, there remains a need for improved airfoil designs, in particular such designs that overcome or at least mitigate drawbacks inherent with the known designs.

SUMMARY OF THE INVENTION

Underlying the present invention is the surprising finding that a leading edge flap having a rigid leading edge surface profile contour can be utilized to provide an airfoil with the desired properties. In particular, the invention relates to an airfoil as defined in appended independent claim 1 . The airfoil inter alia has a leading edge flap providing a rigid leading edge surface profile contour. The airfoil also comprises a central lifting section aft of the leading edge flap. The rigid leading edge surface profile is adapted to the central lifting section such that, at a first leading edge flap angle, a lower surface contour section of the airfoil is continuous in slope and/or curvature. Moreover, the rigid leading edge surface profile is adapted to the central lifting section such that, at a second leading edge flap angle, an upper surface contour section of the airfoil is continuous in slope and/or curvature. Preferred embodiments are defined in claims 2 to 15.

For the purposes of this description, a rigid surface profile contour is a surface profile contour that is configured to maintain its shape at least under conditions expected during operation. As such, the leading edge flap providing the rigid leading edge surface profile contour of the airfoil according to the invention is inherently different from morphing leading edge designs detailed below. Moreover, and as generally understood in the art of airfoil design, a continuous slope of a surface contour section, such as the upper or lower surface contour section of the airfoil of the present invention, means that the first order derivative of an airfoil’s surface function is mathematically continuous over the length of said section. Such continuity is also referred to as C1 continuity. As is also generally understood in the art of airfoil design, a continuous curvature of a surface contour section, such as the upper or lower surface contour section of the present invention, means that the second order derivative of the airfoil’s surface function is mathematically continuous over the length of said section. Such continuity is also referred to as C2 continuity.

In some embodiments, at the first leading edge flap angle, the upper surface contour section comprises a concave transition between the upper surface section of the leading edge flap and the top surface of the central lifting section. In some embodiments, at the second leading edge deflection angle, the lower surface contour section comprises a concave transition between the lower surface section of the leading edge flap and the bottom surface of the central lifting section. As a concave transition portion, a portion of the airfoil surface is understood, in which a straight line spanned between any two points on the airfoil’s surface extends outside of the airfoil, i.e. outside of a region enclosed by the airfoil’s surface. In other words, a straight line spanned between any two points of a concave transition on the top side of the airfoil extends above the airfoil, and a straight line spanned between any two points of a concave transition portion on the bottom side of the airfoil extends below the airfoil. In some embodiments, the concave transition comprises a concave kink. In other embodiments, the concave transition exhibits C1 continuity.

In some embodiments, the first leading edge flap angle corresponds to a low lift configuration of the airfoil. In the low lift configuration, the airfoil has a comparatively low lift coefficient. In some embodiments, the second leading edge flap angle corresponds to a high lift configuration of the airfoil. In the high lift configuration, the airfoil has a comparatively high lift coefficient. In particular, the airfoil’s lift coefficient in the low lift configuration is lower than the airfoil’s lift coefficient in the high lift configuration. In some embodiments, the leading edge flap comprises a hinge axis for pivoting in the plane of the airfoil at least between the first leading edge flap angle and the second leading edge flap angle. In particular, the leading edge flap is configured for performing a rigid body rotation around the hinge axis. In some embodiments, the leading edge flap angle is defined as an angle of rotation around the hinge axis. In some embodiments, the hinge axis is located between the top side of the airfoil and the bottom side of the airfoil, preferably equidistant to the top side and the bottom side. In some embodiments, the hinge axis is provided closer to the top side of the airfoil than to the bottom side of the airfoil. In other embodiments, the hinge axis is provided closer to the bottom side of the airfoil than to the top side of the airfoil. In other embodiments, the hinge axis is located outside of the airfoil, i.e. above the top side of the airfoil or below the bottom side of the airfoil. In such embodiments, the hinge axis can be a virtual hinge axis, in particular resulting from a kinematic guiding structure located within the airfoil. Alternatively, the hinge axis located outside of the airfoil can be a physical hinge axis.

In some embodiments, at the first leading edge flap angle, a flap gap is present in the lower surface contour section between the lower surface section of the leading edge flap and the bottom surface of the central lifting section. As a flap gap, a gap in the airfoil’s surface contour at a transition between a flap (e.g. the leading edge flap) and an undeflectable portion of the airfoil (e.g. the central section) is understood. In some embodiments, at the second leading edge flap angle, a flap gap is present in the upper surface contour section between the upper surface section of the leading edge flap and the top surface of the central lifting section. In some embodiments, sealing means for sealing the flap gap are provided. In some embodiments, at least one of the top side or bottom side of the airfoil is formed as a continuous shell, i.e. free of gaps at either flap angle. Preferably, the continuous shell comprises a flexible transition zone between the leading and/or trailing edge flap and the central lifting section.

In some embodiments, the airfoil further comprises a trailing edge flap providing a rigid trailing edge surface profile contour with an upper surface section and a lower surface section. In some embodiments, the trailing edge flap comprises a hinge axis for pivoting in a plane of the airfoil. In some embodiments, the trailing edge flap is configured to perform a rigid body rotation around the hinge axis. In some embodiments, a trailing edge flap angle is defined as an angle of rotation around the hinge axis. In some embodiments, at a first trailing edge flap angle, a transition between the bottom surface of the central lifting section and the lower surface section of the trailing edge flap is continuous in slope and/or curvature. In some embodiments, the first trailing edge flap angle corresponds to a low lift configuration of the airfoil. In some embodiments, at a second trailing edge flap angle, a transition between the top surface of the central lifting section and the upper surface section of the trailing edge flap is convex. In some embodiments, the convex transition comprises a convex kink. In other embodiments, the convex transition exhibits C1 continuity. As generally known in the art, convexity is the complement to concavity. In other embodiments, at the second trailing edge flap angle, the transition between the top surface of the central lifting section and the upper surface section of the trailing edge flap exhibits C1 and/or C2 continuity. In some embodiments, the second trailing edge flap angle corresponds to a high lift configuration of the airfoil.

In a particularly preferred embodiment, the first leading edge flap angle and the first trailing edge flap angle correspond to the low lift configuration of the airfoil. In a further preferred embodiment, the second leading edge flap angle and the second trailing edge flap angle correspond to the high lift configuration of the airfoil.

In other embodiments, in any of the high lift configuration and/or the low lift configuration, the leading edge flap is at an angle other than the first or second leading edge flap angle, in particular at an intermediate leading edge flap angle that is between the first leading edge flap angle and the second leading edge flap angle. In some preferred embodiments, in the low lift configuration, the leading edge flap is at a first intermediate leading edge flap angle that is closer to the first leading edge flap angle than to the second leading edge flap angle. In some preferred embodiments, in the high lift configuration, the leading edge flap is at a second intermediate leading edge flap angle that is closer to the second leading edge flap angle than to the first leading edge flap angle.

In some embodiments, in any of the high lift configuration and/or the low lift configuration, the trailing edge flap is at an angle other than the first or second trailing edge flap angle. In some embodiments, in any of the high lift configuration and/or the low lift configuration, the trailing edge flap is at an intermediate angle between the first and second trailing edge flap angle. In some embodiments, in the low lift configuration, the trailing edge flap is deflected at a negative angle greater than the first trailing edge flap angle. In some embodiments, in the high lift configuration, the trailing edge flap is deflected at a positive angle greater than the second trailing edge flap angle.

In some preferred embodiments, the airfoil is a laminar flow airfoil. In other embodiments, the airfoil is a conventional airfoil, i.e. configured such that airflow is turbulent over a substantial portion of the airfoil. In some embodiments, the airfoil is a cambered airfoil. In other embodiments, the airfoil is a symmetric airfoil.

In one embodiment of the present invention, a lifting structure with an airfoil according to the invention is provided, wherein the airfoil according to the invention extends at least along a portion of the span width of the lifting structure. In some embodiments, the airfoil according to the invention extends along the entire span width of the lifting structure. In some embodiments, the lifting structure is a rotor blade, such as a rotor blade of a wind turbine. In some embodiments, the lifting structure is a wing. In some embodiments, the lifting structure is an airplane wing, in particular a sailplane wing. In other embodiments, the lifting structure is a hydrofoil. In other embodiments, the lifting structure is a sail.

In another embodiment of the present invention, a vehicle comprising the airfoil according to the invention is provided, in particular with a lifting structure, such as a wing, as described above. In some embodiments, the vehicle is a boat. In some embodiments, the vehicle is an airplane. In some embodiments, the lifting structure comprising the airfoil according to the invention additionally or alternatively is an aerodynamic control surface, such as a horizontal or vertical stabilizer. In preferred embodiments, the airplane is a sailplane. In some embodiments, the sailplane comprises an auxiliary engine. As a sailplane, an airplane optimized for unpowered flight is understood. In particular, a sailplane is understood as an airplane designed for compliance with the Certification Specifications for Sailplanes and Powered Sailplanes CS-22 issued by the European Aviation Safety Agency and/or for compliance with Joint Aviation Requirements JAR-22 and/or for compliance with the acceptable means of compliance according to Advisory Circular 21.17-2A of the Federal Aviation Administration and/or comparable regulatory requirements.

The invention may provide a number of advantages. Compared to airfoil designs having a fixed leading edge, the wing area may be reduced while maintaining equal maximum lift, with the potential benefits discussed above. Compared to designs having a morphing leading edge, in which a surface contour of a leading edge flap has a differently shaped surface contour in a high lift configuration compared to a low lift configuration, a lifting structure comprising the airfoil of the invention may be of significantly reduced complexity. A reduction in complexity may also advantageously contribute to reducing technical risk involved in the development of new lifting structures, such as wings, and/or new vehicles, such as airplanes and in particular sailplanes.

In another embodiment of the present invention, a method for manufacturing a lifting structure, such as a wing, is provided. The method comprises providing an airfoil as defined in claim 1. In preferred embodiments of the present invention, the method comprises providing an airfoil as defined in any one of claims 2 to 15.

In another embodiment of the present invention, a method for using an airfoil is provided. In preferred embodiments of the present invention, the method comprises using an airfoil as defined in any one of claims 1 to 15 for flight. In preferred embodiments, the method comprises using the airfoil for unpowered flight, preferably for unpowered cross-country flight. Further and/or alternatively preferred embodiments will be described in detailed in the following together with the drawings listed below. The following description together with the drawings are therefore fully referenced for the purpose of detailing the previous description of the present invention. It has to be understood that any of the individual features described in the following and/or shown in the drawings can be combined with, or replace corresponding features of any of the aspects and/or embodiments described above. Moreover, it has to be understood that the fact that a certain feature is recited by an independent claim and/or the description of any of the aspects or embodiments, is not sufficient to indicate whether the feature is an essential feature.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 : shows a prior art design of a laminar airfoil with a camber changing trailing edge flap;

Figure 2: shows a prior art design of a laminar airfoil having a morphing leading edge system with continuous contour change;

Figure 3: shows an embodiment of a cambered airfoil according to the present invention;

Figure 4: shows an embodiment of a symmetric airfoil according to the present invention;

Figure 5: shows an inviscid pressure distribution of an airfoil according to the present invention on the low lift configuration;

Figure 6: shows an inviscid pressure distribution of an airfoil according to the present invention on the high lift configuration;

Figure 7: shows airfoil polars of a prior art laminar airfoil with camber changing flap compared to an airfoil of the present invention;

Figure 8: shows an embodiment of a lifting structure, such as a sailplane wing, according to the present invention; and

Figure 9: shows another embodiment of a lifting structure, such as a sailplane wing, according to the present invention. DETAILED DESCRIPTION OF THE DRAWINGS

It should be noted that the terms “upstream” and “downstream” refer to a direction of airflow relative to the airfoils depicted in the figures. Likewise, terminology such as “forward”, “aft”, “in front”, “behind” or analogous expressions for a relative position along a horizontal axis are defined with respect to the direction of airflow relative to the depicted airfoils. When oriented in reading direction and if not indicated otherwise, the direction of airflow in the appended figures with respect to the depicted airfoils is from left to right. If not indicated otherwise, a span width direction of the airfoils and/or lifting structures depicted in the figures is perpendicular to the drawing plane.

Moreover, if not indicated otherwise, expressions such as “up”, “down”, “above”, “below”, “on top”, “beneath”, “bottom”, “top” or analogous expressions for a relative spatial position along a vertical axis are defined in a direction generally perpendicular to the direction of airflow. For example, in line with common airfoil terminology and if not indicated otherwise, a top side of a depicted airfoil may also be referred to as a “suction side”. Likewise, a bottom side of a depicted airfoil may also be referred to as a “pressure side”.

Prior art

Figure 1 shows a prior art laminar airfoil 10 as proposed by Boermans and van Garrel (Boermans, L. M., and van Garrel, A., “Design and Windtunnel Test Results of a Flapped Laminar Flow Airfoil for High-Performance Sailplane Applications,” ICAS 19 - Proceedings of the 19th Conference of the International Council of Aeronautical Sciences, 1994, pp. 1241-1247). Airfoil 10 is also known under the designation DU89-134-14. It has a camber changing trailing edge flap 12 providing a rigid trailing edge surface profile contour 26 comprising a lower surface section 28 and an upper surface section 30. Trailing edge flap 12 is pivotable relative to a forward rigid airfoil section 14 around a hinge axis 16 indicated by a cross in Figure 1 . Trailing edge flap 12 has at least two distinct flap settings (i.e. flap angles), where either a top surface 18 or a bottom surface 20 is kink-free, i.e. exhibits C1 continuity. At these flap settings, the respective other surface has a concave kink 22A, 22B at the transition between forward rigid airfoil section 14 and trailing edge flap 12. A configuration, in which trailing edge flap 12 is at a first angle relative to forward rigid airfoil section 14 such that top surface 18 is continuous and kink-free and bottom surface 20 has kink 22A, is designated as a high-lift configuration (dashed line in Figure 1). A configuration, in which bottom surface 20 is continuous and kink-free and top surface 18 has kink 22B, is designated as a low-lift configuration (solid line in Figure 1).

In the high-lift configuration, kink 22A induces a pressure peak at bottom surface 20. Likewise, in the low-lift configuration, kink 22B induces a pressure peak at top surface 18. Such pressure peaks may disturb laminar airflow and are generally undesired. In particular, such pressure peaks may cause laminar-turbulent boundary layer transition potentially leading to a stark increase in drag. In airfoil 10, trailing edge flap 12 has a length of 14% of the total chord length (indicated by normalized x-coordinate in Figure 1), placing kinks 22A, 22B very close forward or even aft of a natural transition location common for modern laminar airfoils, which are typically at around 60-75% of total chord length on top surface 18 and up to 95% on bottom surface 20. Thereby, the benefits of change in camber significantly outweigh potential adverse effects of kinks 22A, 22B.

Airfoil 10 is a representative example of the class of airfoils discussed in the “BACKGROUND” section above that attempt to increase the usable lift coefficient range of the airfoil, i.e. to widen the laminar low drag bucket. While advantageous compared to earlier designs, in particular without a trailing edge flap, further optimization is desired. In particular, while airfoil 10 changes the camber at the trailing edge through trailing edge flap 12, the camber at a leading edge 24 remains unchanged. Changing the camber at leading edge 24 would allow to further reduce the wing area while maintaining equal maximum lift, potentially allowing for further increases in wing loading. However, since some form of kink (such as kinks 22A, 22B) is a necessary result of a rigid surface contour, applying the concept of trailing edge flap 12 to a rigid surface contour leading edge flap is commonly considered unsuited to the desired design goals in the art of airfoil design. In particular, resulting kinks of such a leading edge flap are thought to result in pressure peaks leading to laminar-turbulent boundary layer transition or - even worse - potentially to flow separation.

In view of the above discussed commonly accepted unsuitability of rigid surface contour leading edge flaps for the present design goals, significant research efforts have been and still are undertaken to develop leading edge flaps capable of continuous change in surface contour, by means of which changing airfoil camber in the leading edge section is achieved without introducing kinks. Such flaps are also referred to as morphing flaps. An exemplary cross-section of a sailplane wing 100 with a morphing leading edge 124 known from the prior art is shown in Figure 2. The depicted design is known in the art as MILAN and described in various research papers (e.g. Achleitner, J.; Rohde-Brandenburger, K.; Rogalla von Bieberstein, P.; Sturm, F.; and Hornung, M.: “Aerodynamic Design of a Morphing Wing Sailplane”, AIAA Aviation 2019 Forum, American Institute of Aeronautics and Astronautics, Reston, Virginia, 2019. doi:10.2514/6.2019-2816).

As indicated by the use of like reference numbers in Figures 1 and 2, sailplane wing 100 shares most features of airfoil 10 described above, but exchanges rigid leading edge section 24 for morphing leading edge flap 124. Morphing leading edge flap 124 comprises a flexible shell 126 surrounding an inner compliant mechanism 128. By application of force F to compliant mechanism 128, continuous changes in the shape of shell 126 are induced, thereby yielding the desired kink-free surface in high- and low-lift-configurations. However, the design’s complexity is a significant drawback. Moreover, flexible shell 126 encounters significant structural and mechanical challenges even under moderate external loads. As of yet, sailplane wing 100 with morphing leading edge flap 124 has therefore not advanced beyond the research stage and its application in a flying airplane is not expected in the near future.

Embodiments of the present invention

Figures 3 and 4 depict two preferred embodiments of airfoils 200, 300 according to the present invention. Axes x and y represent normalized profile coordinates in accordance with common convention in the field of airfoil design. The chord of airfoil 200 is indicated by dashed horizontal line 215. As indicated by like reference signs, the depicted preferred embodiments of airfoils 200, 300 each comprise a trailing edge flap 12 as known from the prior art discussed above. For the sake of brevity, it is fully referred to the foregoing description with regard to trailing edge flap 12, hinge axis 16 and kinks 22A, 22B. It has to be understood that the presence of a trailing edge flap 12 is not essential for the present invention. In other embodiments, airfoils 200, 300 may have a rigid trailing edge section instead of a trailing edge flap 12. However, and as will be further discussed below, the present invention may benefit from further advantages if combined with trailing edge flap 12.

In the following, it is primarily referenced to airfoil 200 shown in Figure 3. Except for the differences detailed below, the disclosure with respect to airfoil 200 fully applies to airfoil 300 shown in Figure 4. Airfoil 200 extends from leading edge 202 to trailing edge 204, with an upper surface or top side 206 and a lower surface or bottom side 208 forming respective aerodynamic surface contours of airfoil 200 between leading edge 202 and trailing edge 204. Airfoil 200 comprises a leading edge flap 210 forming a portion of airfoil 200 extending from leading edge 202, with leading edge flap 210 having a rigid surface profile contour 212 and a hinge axis 214. A central lifting section 220 is provided aft of leading edge flap 210, with a dashed vertical line 211 through hinge axis 214 indicating a boundary between leading edge flap 210 and central lifting section 220. Central lifting section 220 comprises a top surface 222 and a bottom surface 224, both providing a respective rigid surface contour forming a section of upper surface or top side 206 and lower surface or bottom side 208 of airfoil 200. In preferred embodiments, central lifting section 220 is a wing box as generally known in the prior art, and may in particular comprise structural components like spars, ribs and webs, as well as control systems. As mentioned, trailing edge flap 12 extends aft of central section 220 beginning at a boundary 213 and ending at trailing edge 204. Leading edge flap 210 comprises an upper surface section 230 forming a section of upper surface or top side 206 of airfoil 200, which extends from leading edge 202 to boundary 211 between leading edge flap 210 and central section 220. Leading edge flap 210 also comprises a lower surface section 228 forming a section of lower surface or bottom side 208 of airfoil 200, which extends from leading edge 202 to boundary 211 between leading edge flap 210 and central section 220. Similarly, trailing edge flap 12 comprises an upper surface section 30 forming a section of upper surface or top side 206 of airfoil 200, which extends from boundary 213 between central section 220 and trailing edge flap 12, and trailing edge 204. Moreover, trailing edge flap 12 comprises lower surface section 28 forming a section of lower surface or bottom side 208 of airfoil 200, which extends from boundary 213 between central section 220 and trailing edge flap 12, and trailing edge 204. The shape of upper surface or top side 206 and lower surface or bottom side 208 of airfoil 200 is thus defined by an envelope provided by the respective rigid surface profile contours of leading edge flap 210, central lifting section 220 and trailing edge flap 12.

As can be inferred from the position of the dashed vertical line on the x-axis in Figure 3, in the depicted embodiment, leading edge flap 210 has a length of 32% of the overall cord length. The transition between leading edge flap 210 and central lifting section 220 thus lies well within a region of laminar flow of laminar airfoil 200. It has to be understood, however, that the flap length is not limited to the aforementioned 32%, which is just an exemplary value chosen forthe depicted embodiment. In other embodiments the flap length is 10% or less, 15% or less, 20% or less, 25% or less, 30% or less, 35% or less, 40% or less, 45% or less, or 50% or less of the overall cord length.

Airfoil 200 has a low lift configuration indicated by solid black lines in Figure 3, and a high lift configuration indicated by dashed lines in Figure 3. As configurations, combinations of leading- and trailing edge flap deflection angles are understood. In the depicted embodiment, leading edge flap 210 is undeflected in the low lift configuration, i.e. has a deflection angle of 0° relative to central lifting section 220. When in the high lift configuration, leading edge flap 210 is deflected downwards at deflection angle 0 relative to central lifting section 220, thereby increasing the camber of airfoil 200. In the depicted preferred embodiment, trailing edge flap 12 is deflected downward relative to central section 220 at deflection angle p when in the high lift configuration, and undeflected when in the low lift configuration.

In the low lift configuration, a lower surface contour section 232 comprising at least lower surface section 228 of leading edge flap 210 and bottom surface 224 of central section 220 is continuous in slope and curvature. In the depicted preferred embodiment, this continuous lower surface contour section 232 also comprises lower surface section 28 of trailing edge flap 12 and thus extends over the entire length of airfoil 200. In the high lift configuration, an upper surface contour section 234 comprising at least upper surface section 230 of leading edge flap 210 and top surface 222 of central section 220 is continuous in slope and curvature, and as further detailed below, this continuous upper surface contour section 234 extends to a transition between top surface 222 and upper surface section 30 of trailing edge flap 12 where a convex kink 22C is located. Deflection angle p of trailing edge flap 12 has a slightly higher deflection than what would give a continuous slope and curvature over the entire length of airfoil 200, because as discussed below, resulting convex kink 22C further improves results in terms of lift and drag. In other embodiments, however, no convex kink 22C is present in the high lift configuration such that continuous upper surface contour section 234 extends over the entire length of airfoil 200.

Similar to what has been described above with reference to airfoil 10 shown in Figure 1 , concave kinks 226A and 226B are present at a transition between leading edge flap 210 and central section 220 in the respective configurations. In particular, when in the high lift configuration, concave kink 226A is present at a boundary between lower surface contour section 228 of leading edge flap 210 and bottom surface 224 of central section 220. Conversely, when in the low lift configuration, concave kink 226B is present at a boundary between upper surface contour section 230 of leading edge flap 210 and top surface 222 of central section 220. Conventional rigid leading edge flap airfoil designs on the other hand are designed such that, at a first leading edge flap deflection angle (typically 0° deflection in the low lift configuration), both the bottom and top airfoil surface exhibit C1 and/or C2 continuity. Consequently, at a second leading edge flap deflection angle (typically a downward, i.e. positive deflection angle in the high lift configuration) of these conventional rigid leading edge flap airfoil designs, a convex kink is present in a first airfoil surface (typically the upper surface) and a concave kink is present in an opposite, second airfoil surface (typically the bottom surface). These conventional airfoils are however not designed to achieve any significant laminar flow lengths, and thus the presence of kinks on both sides of the airfoil is uncritical. In some instances, these kinks and/or resulting gaps are even desired for such conventional turbulent airfoils.

Airfoil 300 depicted in Figure 4 is generally similar to airfoil 200 of Figure 3, except that airfoil 300 is a symmetric airfoil whereas airfoil 200 is a cambered airfoil. Black solid lines in Figure 4 indicate a symmetric or neutral configuration of airfoil 300, in which leading edge flap 310 and trailing edge flap 12 are undeflected relative to central section 320. In the symmetric configuration, an upper surface section 330 of leading edge flap 310 and a lower surface section 328 of leading edge flap 310 are symmetric to chord line 315. Likewise, in the symmetric configuration, lower surface section 28 of trailing edge flap 12 and upper surface section 30 of trailing edge flap 12 are symmetric to chord line 315. Being a symmetric airfoil, top surface 322 of central section 320 and bottom surface 324 of central section 320 are symmetric to chord line 315 in all configurations. Thus, a symmetric pair of concave kinks 331 is present at a boundary 311 between respective upper and lower surfaces of leading edge flap 310 and central section 320 in the symmetric configuration. Similarly, still in the symmetric configuration, a symmetric pair of concave kinks 23 is present at a boundary 313 between respective upper and lower surfaces of trailing edge flap 12 and central section 320.

Moreover, airfoil 300 comprises a low lift configuration (indicated in dotted lines in Figure 4) and a high lift configuration (indicated in dashed lines in Figure 4), with leading edge flap 310 and trailing edge flap 12 in the low lift configuration being deflected at respective equal absolute deflection angles as in the high lift configuration, but with opposite sign. Thus, in the depicted embodiment, leading edge flap 310 is deflected upward at a negative deflection angle -y when in the low lift configuration, and deflected downward at a positive deflection angle +y when in the high lift configuration. In the depicted embodiments, at deflection angle -y, a lower surface contour section comprising at least lower surface section 328 of leading edge flap 310 and bottom surface 324 of central section 320 is continuous in slope and curvature. Likewise, at deflection angle +y, an upper surface contour section comprising at least upper surface section 330 of leading edge flap 310 and top surface 322 of central section 320 is continuous in slope and curvature. In other embodiments however, in the low lift configuration, leading edge flap 310 is deflected upward at an intermediate angle that is less than deflection angle -y which would yield C1 and/or C2-continuity of the lower surface contour section. Moreover, in some embodiments, in the high lift configuration, leading edge flap 310 is deflected downward at an intermediate angle that is less than deflection angle +y which would yield C1 and/or C2-continuity of the upper surface contour section.

Similarly, in the depicted embodiment, trailing edge flap 12 is deflected upward at a negative deflection angle -6 when in the low lift configuration, and deflected downward at a positive deflection angle +6 when in the high lift configuration. As described above with reference to leading edge flap 310, in the depicted embodiment, negative deflection angle -6 is such that the transition between a lower surface contour section of trailing edge flap 12 and bottom surface 324 of central section 320 is continuous in slope and curvature. Likewise, in the depicted embodiment, positive deflection angle +6 is such that the transition between an upper surface contour section of trailing edge flap 12 and top surface 322 of central section 320 is continuous in slope and curvature. In other embodiments however, in the low lift configuration, trailing edge flap 12 is deflected upward at an intermediate angle that is less than deflection angle - 6 that would yield C1 and/or C2- continuity of the lower surface contour section. Alternatively, trailing edge flap 12 is deflected upward at an increased angle that is greater than deflection angle - 6 which would yield C1 and/or C2-continuity of the lower surface contour section. In some embodiments, trailing edge flap 12 is deflected downward at an intermediate angle that is less than deflection angle +6 that would yield C1 and/or C2-continuity of the upper surface contour section. Alternatively, trailing edge flap 12 is deflected downward at an increased angle that is greater than deflection angle +6 which would yield C1 and/or C2-continuity of the upper surface contour section.

Appropriate leading edge flap deflection angles are ranging from 1 ° up to 20°, preferably any 0.1 ° incremental angle between 1 ° and 20°. In the depicted embodiment of airfoil 200, leading edge flap deflection angle 0 of the high lift configuration is 5° and trailing edge flap deflection angle p of the high lift configuration is 23.8°, In the depicted embodiment of airfoil 300, leading edge flap deflection angle +y of the high lift configuration is 10° and trailing edge flap deflection angle +6 of the high lift configuration is 23.8°.

Tabular profile coordinates for airfoil 200 and airfoil 300 are provided in Table 1 below:

Table 1 : Profile coordinates for symmetric airfoil 300 and airfoil 200 in the low lift configuration and the high lift configuration

The airfoils of the present invention have been analysed numerically using XFOIL and XFOILSUC (Drela, M., “XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils,” Low Reynolds Number Aerodynamics Conf. Proc., 1989). Figure 5 shows a resulting inviscid pressure distribution for cambered airfoil 200 in the low lift configuration, whereas Figure 6 shows a resulting inviscid pressure distribution for airfoil 200 in the high lift configuration. As can be inferred from Figure 5, in the low lift configuration, a pressure distribution 250 on a bottom side of airfoil 200 is smooth and continuous. A pressure distribution 260 on a top side of airfoil 200 has respective dents 262, 264 at locations that substantially coincide with the location of hinges 16, 214 indicated by dashed vertical lines 211 , 213. In the high lift configuration, as shown in Figure 6, a pressure distribution 270 on the top surface of airfoil 200 is continuous, except at a position of hinge axis 16 of trailing edge flap 12, because flap deflection angle p is higher (more positive, i.e. trailing edge down) than what would give a continuous slope and curvature of the top surface of airfoil 200 over its entire length. Surprisingly, very low profile drag can be achieved with long regions of laminar flow on both the top and bottom surface of airfoil 200, even in the presence of kinks 226A and 226B. As discussed above, widening the laminar low drag bucket requires that contour kinks 226A and 226B and corresponding pressure dents do not cause laminar-turbulent boundary layer transition on respective sides of airfoil 200. In particular, when in the low lift configuration, no such transition should be caused on a bottom side of airfoil 200 at a boundary 213 between central section 220 and trailing edge flap 12. In any configuration, no such transition should be caused both on top and bottom sides of airfoil 200 at a boundary 211 between leading edge flap 210 and central section 220. Such transition is caused either by natural transition due to exponentially growing disturbance waves in the laminar boundary layer (Tollmien-Schlichting waves) or by artificial bypass transition. The Tollmien- Schlichting waves in the natural transition phenomenon are amplified by an adverse pressure gradient (pressure increase in streamwise direction), which could be caused by dent 262 in pressure distribution 260 on the top surface of airfoil 200 when in low lift configuration, and in high lift configuration by a dent 282 close to hinge axis 214 in a pressure distribution 280 on the bottom surface of airfoil 200. However, further numerical studies using the integral boundary layer analysis codes of XFOIL and XFOILSUC (Figure 7) have revealed that the adverse pressure regions at dents 262, 282 are uncritical inside the laminar low drag bucket and do not lead to premature laminar-turbulent boundary layer transition.

Airfoil drag polars resulting from numerical analysis conducted with the integral boundary layer and panel code XFOILSUC are provided in Figure 7 and show a comparison between airfoil 200 and a conventional flapped airfoil such as airfoil 10. In particular, Figure 7 shows resulting profile lift coefficients CL on the respective y axes over a range of profile drag coefficients CD on the x axis (left polar) and a range of angles of attack a (right polar). As can be inferred from Figure 7, compared to conventional flapped airfoils, the maximum lift within the laminar low drag bucket can be increased by 25 % using an airfoil according to the present invention in the high lift configuration, with only slightly increased drag and equal or better lift to drag values. This is achieved by extended regions of laminar flow and delayed turbulent flow separation on highly loaded top airfoil surface 206 in case of high lift coefficients due to the kink-free (C1 continuous) and curvature-steady (C2 continuous) upper surface contour section 234 in the high lift configuration. At angles of attack, where the high lift configuration is typically used, bottom airfoil surface 208 has a favorable pressure distribution 270, hence laminar-turbulent transition and turbulent flow separation are not an issue at these angles of attack. In the low lift configuration, bottom surface 208 is the critical one and top surface 206 is uncritical. Thus, dents 262 and 264 in pressure distribution 260 on top surface 206 do not lead to premature laminar-turbulent boundary layer transition in the low lift configuration, while the kink-free (C1 continuous) and curvature-steady (C2 continuous) contour of bottom surface 208 has favorable smooth pressure distribution 250.

The widened range of usable lift coefficients provided by an airfoil according to the present invention allows to reduce the wing area at equal maximum lift within the laminar low drag bucket of a wing, as compared to wings with conventional airfoils with a camber changing trailing edge flap only. The wing area could be reduced by the same percentage as the lift is increased, leading to a significant reduction in overall profile drag at equal induced drag, and thus also a significantly reduced total drag. Such a system could be used for (but is not limited to) aircraft or sailplane wings, hydrofoils or sails of sailboats or surfboards. Of course, the total drag reduction gives better overall performance for a system equipped with a wing using an airfoil according to the invention, be it in terms of fuel or energy usage for powered aircraft or boats, or increased glide ratio for sailplanes, or increased speed for sailboats/surfboards.

Figures 8 and 9 show two different embodiments of lifting structures W according to the present invention, both of which employ cambered airfoil 200 discussed above. The main difference between these two embodiments lies in the vertical position of hinge axes 214A, 214B. In the embodiment of Figure 8, hinge axis 214A is at a lower position and in the embodiment of Figure 9, hinge axis 214B is at an upper position. Again, the high lift configuration of leading edge flap 210 is indicated by a dashed line, whereas the low lift configuration of leading edge flap 210 is indicated by a solid black line. Since leading edge flap 210 has a rigid surface contour 212, an aft boundary 217 defined between the aft-most ends of upper surface section 230 and lower surface section 228 of leading edge flap 210, results either in a collision zone 219 with central section 220 (Figure 9), or a gap 221 forming in top airfoil surface 206 between central section 220 and leading edge flap 210 (Figure 8). When designing a lifting structure Wwith upper hinge axis 214B, collision zone 219 would for practical purposes be left free of material in either leading edge flap 210 or central section 220, thus leading of formation to an equally sized gap 223 in bottom airfoil surface 208 in the low lift configuration. Thus, a formation of a gap is expected independent of vertical hinge axis position, when a lifting structure W is provided with an airfoil according to the present invention.

Such gaps are also known as flap gaps and various seals and covers have been proposed in the prior art to avoid pressure venting therethrough. For example, Nylon foils may be used to seal these flap gaps. When used with an airfoil according to the present invention, bypass transition can be caused by a step necessarily introduced by the flap gap sealing at boundaries 211 and 213, which has to be avoided. An analysis based on the critical disturbance Reynolds number criterion by Braslow and Knox (Braslow, A. L., and Knox, E. C., “Simplified Method for Determination of Critical Height of Distributed Roughness Particles for Boundary-Layer Transition at Mach Numbers from 0 to 5,” NACA TN 4363, 1958) however indicates that both steps on the bottom surface of airfoil 200 at boundaries 211 and 213 are uncritical with respect to bypass transition for step heights of conventional Nylon flap sealing foils as normally used on sailplanes. A further analysis using a method even better suited for determining the influence of such steps („LAMINAR-TURBULENT TRANSITION PREDICTION IN THE PRESENCE OF SURFACE IMPERFECTIONS" in Int. J. Engineering Systems Modelling and Simulation, Vol. 6, Nos. 3/4, pp.162-170, doi: 10.1504/IJESMS.2014.063129) confirmed these results. At certain drag coefficients CD (such as close to the upper corner of the laminar low drag bucket shown in Figure 7), upper surface 206 of airfoil 200 may approach critical values in both the high and low lift configuration. In some embodiments of the present invention, upper surface 206 is thus formed as a single, continuous shell, preferably providing a flexible transition zone between leading edge flap upper surface contour section 234 and top surface 222 of central lifting section 220. In other embodiments of the present invention, an elastomeric sealing without a step is introduced at upper surface 206 and/or lower surface 208 at boundary 211 and/or 213. In other embodiments, a conventional Nylon flap sealing is used to seal gaps in upper surface 206 and/or lower surface 208 at boundary 211 and/or 213. It has to be understood, however, that the invention is not limited to a certain sealing technique. Any sealing means, like Nylon foil sealing, metal foil sealings, S-Tape sealings, elastomeric skins or continuous skins or shells comprising flexible transition zones like the Grob Speed Astir concept (Muller, M., “Grob G 104 Speed Astir II B: Erfahrungsbericht”, 2016. URL: https://www.segelflug.de/tests/SPEED-

ASTIR/Speed%20Flugbericht%200kt%202016.pdf) can be used in the present invention.

Placing hinge axis 214 closer to either of top airfoil surface 206 or bottom airfoil surface 208 leads to the respective closer airfoil surface undergoing little to no deformation upon deflection of leading edge flap 210. Thus, the shell forming the respective closer airfoil surface at boundary 211 may be able to sustain the resulting deformation through its inherent elasticity, without requiring any particular adaptation. The respective other airfoil surface, being further away from hinge axis 214, however, undergoes significant displacement leading to the formation of afore discussed gaps 221 , 223. When placing hinge axis 214A close to bottom airfoil surface 208, the formation of gap 221 may advantageously contribute to increasing the overall length of top airfoil surface 206, thus further increasing total lift. The increase in lift may in particular further be aided by sealing means, such as Nylon foil sealing, covering gap 221 as discussed above.

Hinge axis 314 of symmetric airfoil 300 on the other hand is located on chord line 315, i.e. equidistant to top side 306 and bottom side 308. Thus, in some embodiments of symmetric airfoil 300, when in the symmetric configuration, a first flap gap may be present in top side 306 and second flap gap may be present in bottom side 308. When in the high lift configuration, the flap gap in top side 306 increases in width and the flap gap in bottom side 308 decreases in width. In some embodiments, the flap gap in bottom side 308 is fully closed in the high lift configuration. When in the low lift configuration, the flap gap in bottom side 308 increases in width and the flap gap in top side 306 decreases in width. In some embodiments, the flap gap in top side 306 is fully closed in the low lift configuration. Of course, these flap gaps can be sealed using any of the sealing means and techniques discussed herein.

In particular in the context of the afore described flap gap sealing means and techniques does it become clear that the present invention is not limited to embodiments wherein in a configuration with a first airfoil surface exhibiting continuity in slope and curvature (C1 and C2 continuity), an opposite second airfoil surface exhibits a concave kink, such as concave kinks 226A, 226B discussed above. Other embodiments comprise convex transition portions in upper surface 206 and/or lower surface 208, for example provided at boundary 211 in the form of any of the flexible or elastic flap gap sealing means discussed above, configured to provide a C1 continuous, i.e. smooth and kink-free, contour of the corresponding airfoil surface, when the respective other airfoil surface is C1 and C2 continuous. In place of a kink, such embodiments thus exhibit an inflection point in the respective airfoil surface.