SIMPLIFIED METHOD FOR PARAMETRIC SURFACE GENERATION

Abstract

A method of designing an external geometry of an aircraft lifting surface, including the steps of defining a geometric shape corresponding to an initial lifting surface according to a planform, wherein the initial lifting surface is defined by at least five geometry parameters and a plurality of shape modifier parameters of the lifting surface, modifying the geometric shape of the initial lifting surface by applying a spanwise function to a shape modifier parameter of the initial lifting surface to obtain a modified lifting surface, defining a thickness of an airfoil at a given span position along the span of the modified lifting surface obtained in the modifying step based on a predefined airfoil, and defining the external geometry of the aircraft final lifting surface by interpolating the airfoil along the span of the modified lifting surface via a transition function.

Claims

1. A method of designing an external geometry of an aircraft lifting surface, the method comprising the steps of: defining a geometric shape corresponding to an initial lifting surface according to a planform, wherein the initial lifting surface is defined by at least five geometry parameters and a plurality of shape modifier parameters of said lifting surface; modifying the geometric shape of the initial lifting surface by applying a spanwise function to at least one shape modifier parameter of the initial lifting surface to obtain a modified lifting surface; defining a thickness of at least one airfoil at a given span position along a span of the modified lifting surface obtained in the modifying step based on at least one predefined airfoil; and defining the external geometry of the aircraft final lifting surface by interpolating the at least one airfoil along the span of the modified lifting surface by means of a transition function.

2. The method according to claim 1, wherein the geometric shape defined in the defining step is a trapezoid shape.

3. The method according to claim 1, wherein the at least five geometry parameters comprise at least one of a span, a root chord, a tip chord, a sweep angle at 25% and a dihedral angle.

4. The method according to claim 1, wherein the plurality of shape modifier parameters comprises at least a leading edge.

5. The method according to claim 1, wherein the plurality of shape modifier parameters comprises at least a trailing edge.

6. The method according to claim 1, wherein the plurality of shape modifier parameters comprises at least a sweep angle.

7. The method according to claim 1, wherein the plurality of shape modifier parameters comprises at least a thickness.

8. The method according to claim 1, wherein the plurality of shape modifier parameters comprises at least a twist.

9. The method according to claim 1, wherein the plurality of shape modifier parameters comprises at least a dihedral angle.

10. The method according to claim 1, wherein the modifying step comprises modifying the geometric shape of the initial lifting surface by applying a spanwise function to a plurality of shape modifier parameters.

11. The method according to claim 1, wherein the spanwise function applied in the modifying step is a function with a single input variable representing a span non-dimensional position in an interval [0,1].

12. The method according to claim 1, wherein the spanwise function is a mathematical model, such as polynomials, Nurbs, Nurbs-fit, splines, or any other real single-valued function defined over an interval [0,1], the mathematical model being configured to be controlled by control points and parameters depending on each of them.

13. The method according to claim 1, wherein the transition function applied in a final step is a mathematical function of a family of real single-valued functions.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0035] These and other characteristics and advantages of the invention will become clearly understood in view of the detailed description of the invention which becomes apparent from a preferred embodiment of the invention, given just as an example and not being limited thereto, with reference to the drawings.

[0036] FIG. 1A shows a first trapezoidal planform according to an embodiment of the present invention.

[0037] FIG. 1B shows a perspective view of two lifting surfaces each one corresponding to the trapezoidal planform of FIG. 1A.

[0038] FIG. 2A shows a first spanwise function according to an embodiment of the present invention.

[0039] FIG. 2B shows a lifting surface planform modified applying the spanwise function of FIG. 2A.

[0040] FIG. 2C shows a perspective view of two lifting surfaces each one corresponding to the lifting surface planform of FIG. 2B.

[0041] FIG. 3A shows a second spanwise function according to an embodiment of the present invention.

[0042] FIG. 3B shows a lifting surface planform modified applying the spanwise function of FIG. 3A.

[0043] FIG. 3C shows a perspective view of two lifting surfaces each one corresponding to the lifting surface planform of FIG. 3B.

[0044] FIG. 4A shows a third spanwise function according to an embodiment of the present invention.

[0045] FIG. 4B shows a lifting surface planform modified applying the spanwise function of FIG. 4A.

[0046] FIG. 4C shows a perspective view of two lifting surfaces each one corresponding to the lifting surface planform of FIG. 4B.

[0047] FIG. 5A shows a fourth spanwise function according to an embodiment of the present invention.

[0048] FIG. 5B shows a lifting surface planform modified applying the spanwise function of FIG. 5A.

[0049] FIG. 5C shows a perspective view of two lifting surfaces each one corresponding to the lifting surface planform of FIG. 4B.

[0050] FIG. 6A shows a fifth spanwise function according to an embodiment of the present invention.

[0051] FIG. 6B shows a lifting surface planform modified applying the spanwise function of FIG. 6A.

[0052] FIG. 6C shows a perspective view of two lifting surfaces each one corresponding to the lifting surface planform of FIG. 6B.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0053] The present invention provides a method to design an external geometry of an aircraft lifting surface by defining a plurality of geometry parameters, a plurality of shape modifier parameters and spanwise functions to modify the shape of an initial lifting surface to reach a desired final external geometry.

[0054] The method to design an external geometry of an aircraft lifting surface comprises the following steps: [0055] (a) defining the geometric shape corresponding to an initial lifting surface according to a planform, wherein the initial lifting surface is defined by at least five geometry parameters and a plurality of shape modifier parameters of the lifting surface; [0056] (b) modifying the geometric shape of the initial lifting surface applying a spanwise function to at least one shape modifier parameter of the initial lifting surface to obtain a modified lifting surface; [0057] (c) defining the thickness of at least one airfoil at given span position along the span of the modified lifting surface obtained in step (b) based on at least one predefined airfoil; and [0058] (d) defining the external geometry of the aircraft lifting surface by interpolating the at least one airfoil along the span of the modified lifting surface by means of a transition function.

[0059] FIGS. 1A to 6C depict the steps of an example of the present method starting from an initial lifting surface and applying different spanwise functions to design the external geometry of a final lifting surface. The method starts from a trapezoidal planform defined in step (a) that is modified by several spanwise functions that are applied to its corresponding shape modifier parameters independently in several iterations of step (b). Finally, steps (c) and (d) of the method are performed conforming the external geometry of the final aircraft lifting surface.

[0060] FIG. 1A shows a first lifting surface (1) conformed following step (a) of the present method, which is based on an initial geometric shape according to a lifting surface planform (1.1) that is defined by means of at least five geometry parameters and a plurality of shape modifier parameters. In this particular example, the geometric shape of the first lifting surface (1) according to a planform (1.1) is a trapezoid shape, which is considered to be one of the most effective and efficient shapes to begin with, as it is easily associated with the shape of a basic lifting surface planform. In particular, FIG. 1B shows a perspective view of two first lifting surfaces (1) corresponding to the trapezoidal planform (1.1) shown on FIG. 1A. The two first lifting surfaces (1) are axial symmetry of each other along a central axis along which their root chords (1.5) are placed next to each other.

[0061] First, a trapezoidal planform (1.1) is defined by means of at least five geometry parameters such as span (1.4), root chord (1.5), tip chord (1.6), sweep angle (1.7) at 25% and dihedral angle (not represented as it represents an elevation of the tip chord with respect to the plane of the figure to which the root chord belongs); and a plurality of shape modifier parameters such as leading edge (1.2), trailing edge (1.3), sweep angle, absolute thickness or relative thickness (ratio of maximum section thickness to local chord), twist and dihedral angle.

[0062] One of the shape modifier parameters is thickness (absolute thickness or relative thickness). This means that the thickness of the planform, at one point along the chord (usually the point of maximum thickness of the airfoil), is defined all along the span; and a spanwise function may be applied to the thickness so as to modify the thickness of the planform along span. According to the present invention, the perturbation functions (or spanwise functions) that are applied on step b) normally operate on the relative thickness of the lifting surface; however, if the thickness is an input for the present method, then the airfoil section is scaled.

[0063] Another shape modifier parameter could be the chord position of the maximum thickness, expressed in values between [0,1] on normalized chords, or as a percentage of the chord for each span position along the span. A spanwise function may also be applied to the chord position of the maximum thickness so as to modify the chord’s maximum thickness position along the span.

[0064] In other embodiments, in relation with the step c), the thickness of the planform along the chord at one predefined position of the span is defined by the choice of a specific predefined airfoil. This may be for example a NACA airfoil. The specific predefined airfoil is selected from a catalog or specifically designed, and the chord point with maximum thickness is defined by the geometry of the profile unless the perturbation function that modifies it is applied. Then, the step d) of defining the external geometry is performed.

[0065] Once the geometry of the first lifting surface planform (1.1) is defined in step (a), the plurality of shape modifier parameters are set up. The shape modifiers will be used in the subsequent steps of the method to modify the external geometry of the lifting surface planform (1.1) and therefore to obtain the external geometry of the final lifting surface.

[0066] FIGS. 2A-2C depict a first iteration of step (b) of the method, wherein the geometry of the first lifting surface (1) is modified by means of a first spanwise function (F1) applied to a first shape modifier parameter. The function (F1) is an example of a single-valued function, in this case continuous, defined in the interval [0,1] by control points and continuity conditions. The value of the parameters corresponding to the control points are the non-dimensional spanwise location in [0,1] and the non-dimensional chordwise perturbation (real-valued), non-dimensionalized with the local chord at the corresponding spanwise location. Specifically, as it is shown on FIG. 2A (and in the subsequent FIGS. 3A, 4A, 5A and 6A) the vertical axis (ordinate) corresponds to the interval [0,1] of the span from the root at y = 0 to the tip at y = 1; and the horizontal axis (abscissa) represents the local chord dimensionless with respect to the chord of the trapezoidal planform of the first lifting surface, wherein a negative value represents a point ahead of the leading edge of the first lifting surface and a value greater than 1 represents a point behind the trailing edge of the first lifting surface. For example, x = 0.5 corresponds to the midline of the trapezoidal planform at any point on the span; and x = 0.2 corresponds to the points at 20% of the local chord of the trapezoidal planform at any point of the span. If the sweep angle or the narrowing of the trapezoidal planform is changed, the geometry automatically adapts to the modification, which is, one of the main advantages of the invention, preserving the design intent against global disturbances of the trapezoidal planform geometry of the first lifting surface.

[0067] According to step (b), the trapezoidal planform (1.1) of the first lifting surface (1) is modified by means of applying the first spanwise function (F1) to the leading edge (1.2). That is, the first shape modifier parameter used to conform the external geometry of the final lifting surface (6) is the leading edge. The result of applying the first spanwise function (F1) to the leading edge (1.2) of the first lifting surface (1) can be observed on FIG. 2B. Particularly, FIG. 2B shows a planform (2.1) of a second lifting surface (2) with a second leading edge (2.2) as result of applying the first spanwise function (F1) to the leading edge (1.2) of the first lifting surface (1).

[0068] FIG. 2B shows the second lifting surface planform (2.1) obtained in a first iteration of step (b) wherein its geometry parameters (span (2.4), root chord (2.5), tip chord (2.6), sweep angle (2.7) at 25% and dihedral angle (not shown) compared to the first lifting surface planform (1.1) have been modified as consequence of applying the first spanwise function (F1) to the leading edge as shape modifier parameter.

[0069] A first spanwise function (F1) is defined, and then the function is applied to the shape modifier parameter. The result of applying the first spanwise function (F1) to the shape modifier parameter (leading edge) can be observed on the perspective view of the two second lifting surfaces present on FIG. 2C. In particular, FIG. 2C shows a perspective view of two second lifting surfaces (2) each one corresponding to the planform (2.1) shown on FIG. 2B. The two second lifting surfaces (2) are axial symmetry of each other along a central axis along which their root chords (2.5) are placed next to each other.

[0070] The value of the first perturbation function (F1) corresponds to a normalized variation of the local chord, i.e., actual shift of the leading or trailing edge divided by the local chord of the trapezoidal function. This is the effect of the perturbation functions at normalized values with the trapezoidal shape.

[0071] FIGS. 3A-3C show a second iteration of step (b) of the present method, wherein the geometry of the second lifting surface (2) is modified by means of a second spanwise function (F2), applied to a second shape modifier parameter. In this iteration of step (b) the planform (2.1) of the second lifting surface (2) is modified by applying the second spanwise function (F2) to the trailing edge (2.3), the second shape modifier parameter used to conform the external geometry of the final lifting surface (6). The result of applying the second spanwise function (F2) to the trailing edge (2.3) of the second lifting surface (2) can be observed in FIG. 3B. Particularly FIG. 3B shows a planform (3.1) of a third lifting surface (3) as a result of applying the second spanwise function (F2) to the trailing edge (2.3) of the second lifting surface (2).

[0072] FIG. 3B shows the third lifting surface planform (3.1) obtained in second iteration of step (b) wherein its geometry parameters (span (3.4), root chord (3.5), tip chord (3.6), sweep angle (3.7) at 25% and dihedral angle (not shown) compared to the first lifting surface planform (shown on FIG. 1A) have been modified as consequence of applying the second spanwise function (F2) to the trailing edge as shape modifier parameter.

[0073] One may note that the application of a second spanwise function to a second geometry parameter is entirely independent of the application of the first spanwise function to the first geometry parameter. In particular, the application of the second spanwise function does not impact the leading edge shape as defined by the first spanwise function. Moreover, the first spanwise function may be modified again without any impact on the trailing edge. The spanwise functions are completely independent from each other.

[0074] The result of applying the second spanwise function (F2) to the shape modifier parameter (trailing edge) can be observed on the perspective view of the third lifting surface (3) present on FIG. 3C. In particular, FIG. 3C shows a perspective view of two third lifting surfaces (3), each one corresponding to the planform (3.1) shown on FIG. 3B. These two third lifting surfaces (3) are axial symmetry of each other along a central axis along which their root chords (3.5) are placed next to each other.

[0075] FIGS. 4A-4C depict a third iteration of step (b) of the present method, wherein the geometry of the third lifting surface (3) is modified by means of a third spanwise function (F3) applied to a third shape modifier parameter. According to step (b), the planform (3.1) of the third lifting surface (3) present on FIG. 3C is modified by means of applying the third spanwise function (F3) to the dihedral. On this iteration the dihedral, a third shape modifier parameter, is used to conform the external geometry of the final lifting surface (6). The result of applying the third spanwise function (F3) to the dihedral of the third lifting surface (3) can be observed on FIG. 4B that shows a planform (4.1) of a fourth lifting surface (4) as a result of applying the third spanwise function (F3) to the dihedral of the third lifting surface (3).

[0076] FIG. 4B shows the fourth lifting surface planform (4.1) obtained in this third iteration of step (b) wherein its geometry parameters (span (4.4), root chord (4.5), tip chord (4.6) and sweep angle (4.7) at 25% and the dihedral angle (not shown) compared to the first lifting surface planform (shown on FIG. 1A) have been modified as consequence of applying the third spanwise function (F3) to the dihedral as shape modifier parameter.

[0077] The result of applying the third spanwise function (F3) to the third shape modifier parameter (dihedral) is presented on the perspective view of FIG. 4C. In particular, FIG. 4C shows a perspective view of two fourth lifting surfaces (4) each one corresponding to the planform (4.1) shown on FIG. 4B. The two fourth lifting surfaces (4) are axially symmetrical to each other along a central axis along which their root chords (4.5) are placed next to each other.

[0078] FIGS. 5A-5C show the fourth iteration of step (b) of the present method. In this last iteration of step (b) performed on this particular example, the fourth lifting surface (4) is modified by means of a fourth spanwise function (F4) applied to a fourth shape modifier parameter. According to step (b), the planform (4.1) of the fourth lifting surface (4) present on FIG. 4C is modified by means of applying the third spanwise function (F4) to the twist. On this iteration, the twist is used to conform the external geometry of the final lifting surface (6). The result of applying the fourth spanwise function (F4) to the twist is present on FIG. 5B that shows a planform (5.1) of a fifth lifting surface (5) as a result of applying the fourth spanwise function (F4) to the dihedral of the fourth lifting surface (4).

[0079] FIG. 5B depicts the fifth lifting surface planform (5.1) obtained in the fourth iteration of step (b) wherein its geometry parameters (span (5.4), root chord (5.5), tip chord (5.6), sweep angle (5.7) at 25% and dihedral angle (not shown) compared to the first lifting surface planform (shown on FIG. 1A) have been modified as consequence of applying the fourth spanwise function (F4) to the twist as shape modifier parameter.

[0080] The result of applying the fourth spanwise function (F4) to the fourth shape modifier parameter (twist) is presented on the perspective view of FIG. 5C. In particular, FIG. 5C shows a perspective view of two fifth lifting surfaces (5) each one corresponding to the planform (5.1) shown on FIG. 5B. The two fifth lifting surfaces (5) are axially symmetrical to each other along a central axis along which their root chords (5.5) are placed next to each other.

[0081] The mentioned spanwise functions (F1-F4) control the geometric shape of the lifting surface along the span, that is, changes the initial shape of a part of the planform acting on its corresponding shape modifier parameter. These changes on the shape are made independently, without causing any impact on other parts of the external geometry that are defined by other shape modifier parameters.

[0082] As already mentioned for FIG. 2B, in FIGS. 3B, 4B and 5B the geometry parameters (span (3.4, 4.4, 5.4), root chord (3.5, 4.5, 5.5), tip chord (3.6, 4.6, 5.6), sweep angle (3.7, 4.7, 5.7) at 25% and dihedral angle (not shown)) have been modified as consequence of applying the corresponding spanwise function (F2, F3, F4) to the corresponding shape modifier parameter.

[0083] As can be seen on the transition between FIGS. 2B-2C and 3B-3C, 3B-3C and 4B-4C, 4B-4C and 5B-5C, a different part of the external geometry of the planform is modified independently for each shape modifier parameter. Advantageously this feature allows the designer to modify different parts of the external geometry of the lifting surface based on the particular requirements of an aircraft, acting independently over each parameter without having to adjust the rest in every iteration.

[0084] After step (b) has been performed the required number of times to adjust the external geometry of the lifting surface according to the aircraft requirements, a fifth lifting surface (5) is obtained. In this particular example, the method iterates step (b) four times, applying four different spanwise functions (F1-F4) to four different shape modifier parameters (leading edge, trailing edge, dihedral and twist). As can be observed on the transition between FIGS. 2A-5C, each spanwise function only affects the chosen shape modifier parameter, and hence the part of the external geometry of the lifting surface that is purposely going to be modified, eliminating the drawback of having to adjust the rest of the parameters in every iteration.

[0085] The spanwise functions applied on the above mentioned iterations of step (b), are functions with a single input variable representing the span non-dimensional position f(span) span [0,1]. In addition, these spanwise functions are mathematical model, such as polynomials, Nurbs, Nurbs-fit, splines, or any other real single-valued function defined over the interval [0,1]. The mathematical model being configured to be controlled by control points and parameters depending on each of them.

[0086] FIGS. 6A-6C depict the steps (c) and (d) of the present method.

[0087] Once the fifth lifting surface (5) is obtained after iterating step (b) as many times as is needed to obtain the desired design, a new spanwise function (F5) is defined to be applied on step (c). This function provides the thickness of at least one airfoil along the span of the fifth lifting surface (5) based on at least one predefined airfoil at a given span position. This particular spanwise function (F5) can be observed on FIG. 6A. The result of applying the spanwise function (F5) to the thickness parameter, defines the thickness of the final lifting surface (6) along its span.

[0088] Finally, on step (d), the external geometry of the final lifting surface (6) is created by interpolating the at least one airfoil along the span of the modified lifting surface (5) by means of a transition function that is a mathematical function.

[0089] FIG. 6B shows the final lifting surface planform (6.1) obtained after performing steps (c) and (d), wherein its geometry parameters (span (6.4), root chord (6.5), tip chord (6.6), sweep angle (6.7) at 25% and dihedral angle) compared to the first lifting surface planform (shown on FIG. 1A) have been modified as consequence of applying the last spanwise function (F5) to obtain the thickness of the final lifting surface (6).

[0090] The result of applying the last spanwise function (F5) to obtain the thickness of the final lifting surface (6) is presented on FIG. 6C. In particular, FIG. 6C shows a perspective view of two final lifting surfaces (6) each one corresponding to the planform (6.1) shown in FIG. 6B. Each final lifting surface (6) corresponds with the final design of the external geometry of an aircraft lifting surface obtained after completing the present method.

[0091] While at least one exemplary embodiment of the present invention(s) is disclosed herein, it should be understood that modifications, substitutions and alternatives may be apparent to one of ordinary skill in the art and can be made without departing from the scope of this disclosure. This disclosure is intended to cover any adaptations or variations of the exemplary embodiment(s). In addition, in this disclosure, the terms “comprise” or “comprising” do not exclude other elements or steps, the terms “a” or “one” do not exclude a plural number, and the term “or” means either or both. Furthermore, characteristics or steps which have been described may also be used in combination with other characteristics or steps and in any order unless the disclosure or context suggests otherwise. This disclosure hereby incorporates by reference the complete disclosure of any patent or application from which it claims benefit or priority.