AIRPLANE WING WITH AT LEAST TWO WINGLETS

The present invention relates to an airplane and a wing for an airplane.

Airplanes are one of the most important transportation apparatus both for persons and for goods as well as for military applications, and they are almost without alternative for most long-distance travels. The present invention is related to airplanes in a sense that does not include helicopters, and it relates to a wing for an airplane in a sense that does not include rotor blades for helicopters. In particular, the invention relates to airplanes having fixed wings and to such fixed wings themselves.

The basic function of a motorized airplane and its wings is to produce a certain velocity by means of a propulsion engine and to produce a required lift by means of wings of the airplane in the airflow resulting from the velocity. This function is the subject of the aerodynamic design of the wings of the airplane, for example with regard to their size, profile etc.. It is generally known to use so-called wing tip devices or winglets at the outer ends of the main wings of airplanes, i.e. of those wings mainly or exclusively responsible for the lift. These winglets are meant to reduce so-called wing tip vortices which result from a pressure difference between a region above and a region below the wing, said pressure difference being the cause of the intended lift. Since there is some end of the wing, the airflow tends to compensate the pressure difference which results in a vortex. This wing tip vortex reduces the lifting effect of the wing, increases the noise produced, increases energy loss due to dissipation in the airflow, and can be detrimental for other aircrafts closely following the airplane. The winglets mentioned are so to speak a baffle against the wing tip vortex.

The problem of the present invention is to provide an improved wing having a winglet and an improved respective airplane. In order to solve this problem, the invention is directed to a wing for an airplane, said wing comprising an outer wing end on an opposed side of said wing with regard to an inner side of the wing for mounting to the airplane, at least two winglets on said outer wing end connected to said wing, an upstream first one of said winglets preceding a downstream second one of said winglets in a flight direction of said wing, said first winglet and said second winglet being mutually inclined, as seen against the flight direction, by a relative dihedral angle deltal ,2 in an interval from 5° to 35°, wherein said first winglet is upwardly inclined relative to said sec- ond winglet, wherein said relative dihedral angle is defined as the opening angle at said winglets' root of an isosceles triangle having one vertex on the root, namely at a splitting point of both winglets in horizontal direction and in the middle of the positions of leading edges of said winglets in vertical direction, one vertex on the leading edge of said first winglet and one vertex on the leading edge of said sec- ond winglet, as seen in a projection against said flight direction, said triangle having a variable length of the two equal triangle sides and said dihedral angle interval being valid for at least 70 % of the equal side length along a shorter one of said first winglet and said second winglet, and to an airplane having two such wings mutually opposed as well as to a use of an upgrade part comprising respective winglets for mounting to an airplane in order to produce such a wing or airplane.

The invention relates to a wing having at least two winglets wherein these winglets are fixed to an outer wing end of the wing. To avoid misunderstandings, the "wing" can be the main wing of the airplane which is (mainly) responsible for the required lift; it can, however, also be the horizontal stabilizer wing which is normally approximately horizontal as well. Further, the term "wing" shall relate to the wing as such as originating at the airplane's base body and extending therefrom outwardly. At an outer wing end of this wing, the at least two winglets are fixed and extend further, but not necessarily in the same direction. As principally already known in the prior art, a winglet can be inclined relative to the wing and/or bent. Preferably, the winglets do not extend inwardly from the outer wing end, however.

The inventors have found that a mutual inclination of the two winglets as seen against the flight direction, leads to advantageous results in a quantitative assessment by computer fluid dynamics calculations. In particular, it has proven to be advantageous to incline the upstream first winglet relative to, for example and preferably, more upwardly than, the second winglet. Therein, the difference in inclination, the difference in the so called dihedral angle (relative dihedral angle) should be moderate, namely not more than 35°. On the other hand, a certain relative dihedral angle should be observed and should thus not be smaller than 5°. More preferred lower limits of the relative dihedral angle interval are (in the following order) 7°, 9°, 1 1 °, 13°, and 15°, whereas more preferred upper limits are 33°, 31 °, 29°, 27°, and 25°. Thus, an optimum should be in the region of 20°.

The results of the inventors show that this relative dihedral angle is more important than the absolute dihedral angels of both winglets which might be due to the fact that the air flow geometry has a certain degree of rotational symmetry about an axis parallel to the flight direction at the end of the main wing and thus at the root of the winglets. This is, naturally, only an approximative statement but nevertheless, the relative dihedral angle is regarded to be more important than the absolute one.

The relative dihedral angle is defined herein in an average sense, namely by means of an isosceles triangle between vertices. One vertex shall be on the root and one respective vertex on each winglet. More precisely, the triangle is defined in a projection against the flight direction and the vertex on the root shall be, as regards the horizontal dimension, at a splitting point of both winglets, i. e. where both winglets are separated in the horizontal dimension as seen vertically. As re- gards the vertical dimension, the root vertex shall be in the middle of the positions of the leading edges (the most upstream edges) of both winglets at the just mentioned horizontal location or, if they coincide there, at that position. Since this re- gion is subject to smooth transition shapes in order to avoid aerodynamic disturbance, the leading edge so to say loses its identity in this transition region (the so called fairing between the winglets and the main wing end). Therefore, the leading edges shall be extrapolated in the following manner: an inner portion of 10 % of the spanwise length of the winglet (defined in more detail in the following) is disregarded and an outer portion between 90 % and 100 % is disregarded as well for other reasons (namely possible roundings as explained in the embodiment). The remaining 10 % - 90 % represent a proper leading edge which can be extrapolated. Should the leading edge not be straight, an average line can be used for extrapolation.

The vertices on the winglets themselves shall be on their leading edges, respectively. Consequently, the opening angle of this triangle, namely the angle between the two equal sides, is the relative dihedral angle.

The triangle definition includes a variable length of the equal sides within the limits imposed by the shorter one of both winglets. In terms of this variable side length concept, the defined relative dihedral angle intervals shall be valid for at least 70 % of the side length, more preferably for at least 75 %, 80 %, 85 %, or even 90 % of the side length. In other words: If a minor portion of the winglets does not obey to the relative dihedral angle interval, this is not too detrimental for the invention, whereas, of course, 100 % within the interval are the best case.

The variable side length concept takes into account that the winglets need not be straight (in the perspective against the flight direction) but can also be completely or partially bent, e. g. along a circular portion as shown for the first winglet in the embodiment. The winglets could also be polygonal (with limited angles) or shaped otherwise so that the relative dihedral angle varies along their spanwise length. Further, even with straight winglets (as seen against the flight direction), their lead- ing edge lines need not necessarily meet at the root vertex as defined above which could lead to slight variations of the relative dihedral angle along their length. However, with straight winglets, the relative dihedral angle as defined by the triangle concept is at least approximately just the angle visible against the flight direction.

The above and all following descriptions of the geometric shape of the wing and the winglets relate to what the expert understands as an "in-flight" shape. In other words, these explanations and definitions relate to the flight conditions in which the aerodynamic performance is actually meant to be and is relevant, which basically is the typical travel velocity (on distance) at the typical travel altitude. The expert is familiar with that there is another "jig shape" which is meant to be the shape of the wing and the winglets in a non-flying condition, i. e. without any aerodynamic forces acting thereon. Any difference between the jig shape and the in-flight shape is due to the elastic deformation of the wing and the winglets under the aerodynamic forces acting thereupon. The precise nature of these elastic deformations depends on the static mechanical properties of the wing's and winglets' construc- tion which can be different from case to case. This is also a familiar concept to the mechanical engineer and it is straightforward to calculate and predict such deformations for example by finite element calculations with standard computer simulation programs. A reference to the jig shape in this description would thus not make much sense because the aerodynamic performance is the relevant category. Further, the mechanical structure of a wing and a winglet according to the invention may vary from case to case so that any assumptions about how the jig shape transforms into the in-flight shape would be speculative.

Further, the terms "horizontal" and "vertical" relate to a mounted state of the wing at an airplane, wherein "vertical" is the direction of gravity and "horizontal" is perpendicular thereto.

The inclinations of the winglets relative to each other as explained above have proven to be advantageous in terms of a trade-off between two aspects. On the one hand, a relative dihedral angle of zero or a very small quantity leads to that a downstream winglet, here the second winglet, is subject to an airstream not only influenced by the upstream (here first) winglet, but also to a turbulent or even diffuse airflow in the wake of the upstream winglet, inhibiting a proper and pronounced aerodynamic performance such as the production of a lift and/or thrust contribution as discussed below. In contrast, a downstream winglet might produce too much drag compared to what it is actually intended for, this being lift, thrust, vortex cancellation or whatever.

On the other hand, too large relative dihedral angles so to say "decouple" the winglets from each other whereas the invention intends to use a synergetic effect of the at least two winglets. In particular, the invention preferably aims at conditioning the airflow by the upstream winglet for the downstream winglet. In particular, one aspect of the invention is to use the inclined airflow in the region of the tip vortex of the wing in a positive sense. A further thought is to produce an aerodynamic "lift" in this inclined airflow having a positive thrust component, i.e. a forwardly directed component parallel to the flight direction of the airplane. Herein, it should be clear that the "lift" relates to the aerodynamic wing function of the winglet. It is, however, not necessarily important to maximize or even create a lifting force in an upwardly directed sense, here, but the forward thrust component is in the centre of interest.

In this respect, the inventors found it advantageous to "broaden" the inclined airflow in order to make an improved use thereof. This makes sense because a wing- tip vortex is quite concentrated so that substantial angles of inclination of the air- flow direction (relative to the flight direction) can be found only quite near to the wingtip. Therefore, the invention provides for at least two winglets, one upstream winglet being intended for "broadening" the region of inclined airflow and a downstream winglet being intended for producing a thrust component therefrom, according to a preferred aspect.

The upstream winglet is thus intended for "splitting" the wingtip vortex of the wing by "shifting" a part thereof to the winglet tip, i.e. outwardly. Consequently, a super- position of the winglet-induced tip vortex (winglet tip vortex) and the vortex of the "rest of" the wing (said wing being deeper in the direction of flight than the winglet) results. In this sense, the above relative dihedral angle interval is advantageous.

Preferably, the winglets as represented by their respective chord line (the line between the leading edge and the most downstream point of the airfoil) shall also be inclined in a certain manner as regards a rotation around a horizontal axis perpen- dicular (instead of parallel) to the flight direction. The rotation angle is named angle of incidence and shall be positive in case of a clockwise rotation of the winglet as seen from the airplane's left side and vice versa from its right side. In this sense, an angle of incidence interval for the first winglet from -15° to -5° is preferred, more preferably in combination with an angle of incidence interval for the second winglet from -10° to 0°. These intervals relate to the root of the winglets and the angle of incidence interval is defined in a variable sense in linear dependence of the position along the spanwise length of the winglet. It shall be shifted from the root to the tip of the respective winglet by +2° which leads to an interval from -13° to -3° for the first winglet and from -8° to +2° for the second winglet at their respective tip. This does not necessarily imply that the actual angle of incidence of a certain implementation must be "twisted" which means show a varying angle of incidence in this sense. An actual implementation can also be within the intervals defined without any twisting. However, since the inventors take into regard the variation of the airflow in dependence of the distance from the root of the winglets, a moderate dependence of the interval definition in this sense is appropriate (in other words: the centre of the interval and the borders thereof are "twisted").

The angle of incidence is defined as above between the respective winglet's chord line and a chord line of the wing as such (the main wing). This latter chord line is referred to near to that position (in horizontal direction perpendicular to the flight direction) where the wing is split into the winglets, in other words where the wing- lets separate when going more outwardly. Since at the splitting position, also the main wing can already be deformed somewhat (in terms of a fairing) in order to provide for a smooth transition to the winglets, the chord line shall be referred to a little bit more inward, namely 10 % of the main wing spanwise length more inward. The same applies vice versa to the winglet so that the chord line is referred to 10 % more outward of the splitting position.

More preferred lower limits of the incidence angle interval for the first winglet at its root are -14°, -13°, -12°, and -1 1 °, and at its tip +2° additional to these values, whereas more preferred upper limits at the root of the first winglet are -6°, -7°, -8°, -9° and, again, +2° more at the tip. Analogously, more preferred lower limits for the second winglet at the root are -9°, -8°, -7°, -6°, and more preferred upper limits are -1 °, -2°, -3°, -4°, and again +2° more at the tip, respectively. Again, the angle intervals defined shall be valid for at least 70 %, more preferably at least 75 %, 80 %, 85 %, and even 90 %, of the spanwise length of the respective winglet. In other words: minor portions of the winglets not obeying to these criteria are not of essence. As regards the angle of incidence of the first winglet, it is favourable to use the interval defined in order to minimize the drag thereof and to produce not too much downwash of the airstream downstream of the first winglet. Too much downwash would hinder the function of the second winglet which is based on the inclination of the airflow due to the already described vortex. The interval given for the second winglet has proven to be advantageous in terms of an optimized thrust contribution. In many cases, the actual angle of incidence of the first winglet will be smaller than that of the second winglet as can also be seen from the intervals given, because the airstream downstream of the first winglet has already been changed thereby. In any case, the intervals defined and, in most cases, a somewhat smaller angle of incidence of the first winglet compared to the second winglet are general results of the computer fluid dynamics simulations performed. Preferably, the invention also comprises a third winglet downstream of the second winglet, and more preferably, the invention is limited to these three winglets (per wing). More preferably, the third winglet obeys to a relative dihedral angle interval relative to the second winglet as well, namely from 5° to 35° with the same more preferred lower and upper limits as for the relative dihedral angle between the first and the second winglet (but disclosed independently thereof). This dihedral angle difference is to be understood in the second winglet being (preferably more upwardly) inclined relative to the third winglet. The definition of the relative dihedral angle is analogous to what has been explained above but, naturally, relates to a second and a third winglet, here.

As already explained with regard to the relation between the first and the second winglets and their relative dihedral angle, also here, in the retrospective relation between the second and the third winglets, it is neither favourable to position the third winglet directly "behind" the upstream second winglet, nor is it favourable to decouple them in an aerodynamic sense. Instead, by means of a relative dihedral angle in the interval given, the third winglet will again be in the position to produce a synergetic effect downstream of the first and the second winglets, and in particular, as preferred in this invention, to produce a thrust contribution once more.

Still more preferred, the third winglet also is subject to a limitation of the angle of incidence in an analogous manner as explained above for the first and for the sec- ond winglet including the explanations as regards a definition of the chord line. Here, for the third winglet, the intervals shall be from -7° to +3° at the root and, again, +2° more at the tip and the linear interpolation therebetween of the interval. More preferred lower limits for the interval of the incidence angle for the third winglet are -6°, -5°, -4°, -3°, and more preferred upper limits are +2°, +1 °, 0°, -1 °, at the root and +2° more at the tip. Again, the intervals for the relative dihedral angle and the angle of incidence shall be valid for preferably at least 70 % of the shorter one of the second and third winglet and for the spanwise length of the third winglet, respectively. Again, more preferred limits are at least 75 %, 80 %, 85 %, 90 %.

The function of the above choice of the angle of incidence of the third winglet is similar to that one of the second winglet, namely that the airstream to which the third winglet is subjected, has already been changed by the upstream two wing- lets, and that the third winglet is intended to produce a thrust contribution therein together with a minimized drag of the complete system. In a further preferred implementation, a so called sweepback angle of the two or three winglets is in an interval from -5° to 35°, respectively, relative to the sweep- back angle of the main wing (a positive value meaning "backwards"). In other words, the winglets can be inclined in an arrow-like manner backwardly, as airplane wings usually are, preferably at least as much as the main wing or even stronger. Therein, the sweepback angle need not be the same for all three winglets. More preferred lower limits are -4°, -3°, -2°, -1 °, whereas more preferred upper limits are 30°, 25°, 20°, 15°. As just noted, the sweepback angle is related to the inclination of the leading edge of the respective winglet compared to a horizontal line perpendicular to the flight direction. This can be defined in a fictious hori- zontal position of a winglet (the dihedral angle and the angle of incidence being zero and in an unrolled condition of any bending). Alternatively, the sweepback angle can be defined by replacing the actual extension of the winglet in the horizontal direction perpendicular to the flight direction (as seen vertically) by the spanwise length b thereof defined somewhere else in this application.

Should the leading edge not be linear, the sweepback angle relates to an average line with regard to the non-linear leading edge in the range from 20 % to 80 % of the respective span of the winglets. This limited span range takes into account that the leading edge might be deformed by rounded corners (such as in the embodi- ment) at the outward end and by transitions at the so called fairing at their inner end. Since the sweepback angle is very sensitive to such effects, 20 % instead of 10 % are "cut off" at the borders. As regards the reference, the leading edge of the main wing, the range from 50 % to 90 % of its span and an average line in this range shall be taken into account. This is because the spanwise position of 0 % relates, as usual, to the middle of the base body and thus is not in the main wing itself, and there is a so called belly fairing at the transition from the base body to the main wing which is not only configured to be a proper airfoil but is more a transition to the airfoil. Still further, an adaption of a sweepback angle of the winglets to the outer portion of the main wings is appropriate anyway.

The simulations done have shown that the results can be optimized by a somewhat enhanced sweepback angle of the winglets but that this angle should not be exaggerated. Since the sweepback angle has a connection to the usual speed range of the aircraft, it is a pragmatic and technically meaningful reference to start from the sweepback angle of the main wing.

The above explanations with regard to the relative dihedral angle are intentionally open with regard to their "polarity", in other words to whether a downstream wing- let is inclined upwardly or downwardly with regard to an upstream winglet. In fact, the inventors have found that the aerodynamic performance is rather insensitive in this respect. However, it is preferred that the upstream first winglet is inclined more upwardly than the second winglet (with and without a third winglet). It is, further and independently, preferred that the third winglet, if any, is inclined more downwardly than the second winglet. The best results achieved so far are based on this concept as shown in the embodiment.

Although it has been explained above that the relative dihedral angle between the first and the second winglet (and also that between the second and the third winglet) is more important than the absolute values of the respective dihedral angles of the winglets, they are also preferred choices for the latter. For the first winglet, the respective dihedral angle interval is from -45° to -15°, more preferred lower limits being -43° -41 ° -39° -37° and -35° whereas more preferred upper limits are - 17° -19° -21 ° -23° and -25°.

For the second winglet, all these values are shifted by +20° including the more preferred limits. The same applies to the third winglet, if any, in relation to the second winglet. Again, these angle intervals shall be valid for at least 70 %, preferably at least 75 %, 80 %, 85 %, or even 90 % of the respective spanwise length of the winglet. For the sake of clarity: The limitations of the relative dihedral angle explained above apply in this context. If, for example, the dihedral angle of the first winglet would be chosen to be -35°, the interval for this dihedral angle of the second winglet would be automatically limited to be not more than 0°. The relative dihedral angle definitions are dominant, thus. Further, the absolute dihedral angle is defined in a similar manner as the relative dihedral angle, the difference being that one of the equal sides of the isosceles triangle is horizontal instead of on the leading edge of one of the winglets.

It has been found that too low absolute values of the dihedral angle such as below -45°, and thus winglets oriented more or less upwardly can be disadvantageous because it is more difficult to provide for a proper and smooth transition (fairing) between the main wing's outer end and the winglet. Further, the numerical simulations have not shown any advantage for such very low dihedral angles. On the other hand, very large values, i. e. winglets directed strongly downwardly such as with a dihedral angle of more than 25°, can have the detrimental effect of reducing the ground clearance. Of course, the effect described for very low values is also valid for the very large values but, as can be seen from the difference between the borders of -45° and +25°, the ground clearance is usually a dominant aspect (whereas exceptions are existent, such as so called high-wing aircrafts being less sensitive with regard to ground clearance). Thus, dihedral angles from one of these limits to the other are generally preferred and even more preferred in the intervals defined above for the first, the second, and the third winglet. As regards the respective length and spanwise direction of the winglets, certain proportions to the spanwise length of the (main) wing are preferred, namely from 2 % to 10 % for the first winglet, from 4 % to 14 % for the second winglet and from 3 % to 1 1 % for the third winglet, if any. Respective preferred lower limits for the first winglet are 2.5 %, 3.0 %, 3.5 %, 4.0 %, 4.5 %, 5.0 %. Preferred upper limits for the first winglet are 9.5 %, 9.0 %, 8.5 %, 8.0 %, 7.5 %, 7.0 %. For the second winglet, the more preferred lower limits are 5.0 %, 6.0 %, 6.5 %, 7.0 %, 7.5 %, 8.0 %, and more preferred upper limits for the second winglet are 13 %, 12 %, 1 1 .5 %, 1 1 .0 %, 10.5 %, 10.0 %. Finally, the more preferred lower limits for the third winglet are 3.5 %, 4.0 %, 4.5 %, 5.0 %, 5.5 %, 6.0 %, and more preferred upper limits are 10.5 %, 10.0 %, 9.5 %, 9.0 %, 8.5 %, and 8.0 %.

The spanwise length is herein defined as the distance from the root of the wing- lets, namely at the separation of the winglet from the neighbouring winglets (in case of the second winglet between the first and the third winglet, the innermost separation) to their outward end in a direction perpendicular to the flight direction and under the assumption of an angle of incidence and a dihedral angle of zero, i. e. with the winglet in a horizontal position. In case of an non-linear shape of the winglet, such as a curved part as with the first winglet in the embodiment, the spanwise length relates to a fictious straight shape (an "unrolled" condition) since such a bending is an alternative to a dihedral inclination. More precisely, it relates to a projection plane perpendicular to the flight direction and, therein, to the length of the wing in terms of a middle line between the upper and the lower limitation line of the projected winglet. For the main wing, the same definition holds but starting in the middle of the base body (in the sense of a half span). The length of the main wing is measured up to the separation into the winglets; it is not the length of the complete wing including the winglets. As regards the above relative length intervals for the winglets, these sizes have proven to be practical and effective in terms of the typical dimensions of the tip vortex of the main wing which is of essence for the function of the winglets. Too small (too short) winglets do not take advantage of the full opportunities whereas too large winglets reach into regions with their respective winglet tips where the main wing's tip vortex is already too weak so that the inclined airflow cannot be taken advantage from for the full length of the winglets (in particular the second and third) and the broadening effect discussed above, as a particularly preferred concept of the invention, will possibly more produce two separated than two superposed vortex fields.

Further, there are preferred relations between the spanwise lengths of the wing- lets, namely that the second winglet preferably has a length from 105 % to 180% of the first winglet. Likewise, it is preferred that the third winglet length is from 60% to 120% of the second winglet. Therein, more preferred lower limits for the first interval are 1 10 %, 1 15%, 120 %, 125 %, 130 %, 135 %, and 140%, whereas more preferred upper limits are 175 %, 170 %, 165 %, and 160 %. More preferred lower limits for the second interval are 65 %, 70 %, 75 %, whereas more preferred upper limits are 1 15 %, 1 10 %, 105 %, 100 %, 95 %, and 90 %.

In a more general sense, it is preferred that the second winglet is at least as long (spanwise) as the third winglet, preferably longer, and the third (and thus also se- cond) winglet is at least as long and preferably longer as the first winglet. This is basically due to the fact that the second winglet should take full advantage of the broadened inclined airstream region as broadened by the first winglet in order to produce a maximum effect, and the third winglet shall, again, produce an analogous or similar effect, but will not be able to do so since energy has already been taken out of the airstream. Thus, it should be limited in size in order not to produce too much drag.

Still further, the aspect ratio of the winglets is preferably in the interval from 3 to 7 wherein more preferred lower limits are 3.5 and 4.5 and more preferred upper lim- its are 6.5, 6.0, and 5.5. This relates, as any of the quantitative limitation herein, individually to each winglet and relates to a two winglet embodiment where there is comparatively much space in the chord line direction. For a three winglet embodi- ment, the aspect ratios can be somewhat higher and are preferably in the interval from 4 to 9 wherein preferred lower limits are 4.5 and 5.0 and more preferred upper limits are 8.5, 8.0, and 7.5. This relates, again, to each winglet individually. Although higher aspect ratios are more efficient in an aerodynamic sense, they have a smaller area and thus, produce smaller forces (and thus a small thrust). In other words, within the already-described length limitation, a substantial winglet area is preferred. On the other hand, a too low aspect ratio increases the drag and decreases the efficiency in an amount that finally reduces the effective thrust by means of an increased drag. All in all, the CFD simulations repeatedly showed optimum values around 5.

The aspect ratio is defined as the double spanwise length of a wing (i. e. the full span of the airplane in case of a main wing), and likewise the double spanwise length of a winglet, divided by the chord line length, namely as an average value. To be precise, the definition in this application to cut-off the outer 10 % of the spanwise length when assessing the chord line length, is valid also here to exclude an influence of a fairing structure and/or roundings of a winglet. Preferred implementations of the invention can have certain root chord lengths for the winglets. The values are defined for two cases, namely for a set of exactly two and another set of exactly three winglets. For two winglets, the root chord length for the first winglet can be in the interval from 25 % to 45 % of the chord length of the main wing next to the splitting into the winglets (not at the root of the main wing).

In this case, for the second winglet, the respective preferred interval is from 40 % to 60 %. More preferred lower limits for the first winglet are 27 %, 29 %, 31 %, and for the second winglet 42 %, 44 %, 46 %, more preferred upper limits for the first winglet are 43 %, 41 %, 39 %, and for the second winglet 58 %, 56 %, 54 %. The case of exactly three winglets has a preferred interval for the first winglet from 15 % to 35 % of the chord length of the main wing next to the splitting, and from 25 % to 45 % for the second winglet, and from 15 % to 35 % for the third winglet. More preferred lower limits for the first winglet are 17 %, 19 %, 21 %, for the se- cond winglet 27 %, 29 %, 31 %, and for the third winglet 17 %, 19 %, 21 %. More preferred upper limits for the first winglet are 33 %, 31 %, 29 %, for the second winglet 43 %, 41 %, 39 %, and for the third winglet 33 %, 31 %, 29 %. The respective tip chord length of the winglets is preferably in an interval from 40 % to 100 % of the respective root chord length, wherein more preferred lower limits are 45 %, 50 %, 55%, 60 %, and the more preferred upper limits are 95 %, 90 %, 85 %, 80 %.

Generally, these chord lengths take into account the available overall length, the advantageous size distribution between the winglets and the desired aspect ratio thereof. Further, a certain intermediate distance between the winglets in the flight direction is desired to optimize the airflow. As can be seen from the centers of the above intervals for the respective chord lengths, a length from 5 % to 25 %, preferably at least 10 %, preferably at most 20 %, of the available length are approximately used for this distance even near the root of the winglets, in total. This means that the respective chord lengths of the winglets preferably do not add up to 100 %.

Still further, it is clear to the expert that some fairing (as the so called belly fairing at the transition between the base body and the main wing) is used in the transi- tion region between the main wing's end and the winglets' roots. Therefore, also the chord length at the end of the main wing is referred to at a distance 10 % inward from the splitting into the winglets (relative to the length in terms of the half span of the main wing) to be clearly out of this transition. In the same manner, the root chord length of the winglets is referred to at a position 10 % outward of the separation into the winglets to be well within the proper airfoil shape of the winglets. The same applies to the position of the chord line in relation to for example the angle of attack. Still further, in some wings and winglets, the outer front corner is "rounded" as in the embodiment to be explained hereunder. This rounding can be done by a substantial reduction of the chord length in the outermost portion of the winglet but is not regarded to be a part of the above-mentioned feature of the relative chord length at a winglet tip in relation to a winglet root. Therefore, the chord length of the winglet at 10 % of the winglet's length inward of its tip is referred to, here.

As already mentioned, the invention is preferably used for two wings of the same airplane mutually opposed. In particular, the respective two wings and the winglets according to the invention on both sides can be antisymmetrical with regard to a vertical centre plane in the base body of the airplane. In this sense, the invention also relates to the complete airplane. A preferred category of airplanes are so called transport category airplanes which have a certain size and are meant for transportation of substantial numbers of persons or even goods over substantial distances. Here, the economic advantages of the invention are most desirable. This relates to subsonic airplanes but also to transonic airplanes where supersonic conditions occur locally, in particular above the main wings and possibly also above the winglets. It also relates to supersonic airplanes having a long distance travel velocity in the supersonic region.

Further, the invention is also contemplated in view of upgrade parts for upgrading existing airplanes. For economic reasons, it can be preferred to add such an up- grade part including at least two winglets at a conventional wing (or two opposed wings) rather than to change complete wings or winglets. This is particularly reasonable because the main advantage of the invention cannot be to increase the lift force of the wings which could exceed limitations of the existing mechanical structure. Rather, the invention preferably aims at a substantial thrust contribution to improve efficiency and/or speed. Consequently, the invention also relates to such an upgrade part and its use for upgrading an airplane or a wing in terms of the invention. In both cases, with regard to the complete airplane and with regard to the upgrade of existing airplanes, a first simulated choice for the airplane has been the Airbus model A 320. Therein, an outward part of the conventional wings, a so called fence, can be demounted and replaced by a structure according to the invention having two or three winglets.

The invention will hereunder be explained in further details referring to exemplary embodiments below which are not intended to limit the scope of the claims but meant for illustrative purposes only.

Figure 1 shows a plan view of an airplane according to the invention including six winglets schematically drawn; Figure 2 is a schematic diagram for explaining the creation of a thrust by a winglet;

Figure 3a, b are schematic illustrations of the air velocity distribution in a tip vortex;

Figure 4 is a schematic perspective view of a wing according to the invention;

Figure 5 is a schematic front view of a wing tip according to the invention including two winglets;

Figure 6 is a diagram showing two graphs of an inclination angle dependency on distance relating to figure 5;

Figure 7 is a schematic side view to explain the gamma angles of two winglets of an embodiment;

Figure 8 is a front view of the same winglets to explain the delta angles; Figure 9 is a plan view of an Airbus A320 main wing; Figure 10 is a front view of said wing;

Figure 1 1 is a side view of said wing;

Figure 12 is a side view to explain reference lines used for simulations in the embodiment;

Figure 13 is a top view to illustrate the same reference lines; Figure 14 to 17

are diagrams illustrating beta angles at varying distances from the main wing tip for various simulations in the embodiment;

Figure 18 is a front view of three winglets according to an embodiment of the invention showing their dihedral angles; Figure 19 is another front view of two winglets for explaining a relative dihedral angle;

Figure 20 is a schematic drawing for explaining a bending of a first winglet; Figure 21 is a side view of sections of a main wing and three winglets for explaining angles of inclination;

Figure 22 combines a front view and a top view for explaining a sweepback angle of a winglet;

Figure 23 is a top view onto three winglets in a plane for explaining the shape; Figure 24 is a perspective drawing of a complete airplane according to the invention;

Figure 25 is a top view onto three winglets at a main wing tip of said airplane;

Figure 26 is a side view of the three winglets of figure 25; and

Figure 27 is a front view thereof. Figure 1 is a plan view of an airplane 1 having two main wings 2 and 3 and two horizontal stabilizers 4 and 5 as well as a vertical tail 6 and a fuselage or base body 7. Figure 1 shall represent an Airbus model A 320 having four propulsion engines, not shown here. However, in figure 1 , the main wings 2 and 3 each have three winglets 8, 9, 10, respectively. Two respective winglets sharing a reference numeral are mirror symmetrical to each other in an analogous manner as both main wings 2 and 3 and the base body 7 are mirror symmetric with regard to a vertical plane (perpendicular to the plane of drawing) through the longitudinal axis of the base body. Further, an x-axis opposite to the flight direction and thus identical with the main airflow direction and a horizontal y-axis perpendicular thereto are shown. The z- axis is perpendicular and directed upwardly.

Figure 2 is a schematic side view of an airfoil or profile (in figure 2 a symmetric standard wing airfoil, in case of the A 320 an asymmetric airfoil) of a main wing 2 and an airfoil (for example NACA 2412, a standard asymmetric wing airfoil or RAE 5214, an asymmetric wing airfoil for transonic flight conditions) of an exemplary winglet W which is just for explanation purposes. A solid horizontal line is the x-axis already mentioned. A chain-dotted line 13 corresponds to the chord line of the main wing 2 (connecting the front-most point and the end point of the profile), the angle alpha there between being the angle of attack of the main wing.

Further, a bottom line 14 of the profile of winglet W (which represents schemati- cally one of winglets 8, 9, 10) is shown and the angle between this bottom line 14 and the bottom line of the main wing profile is gamma, the so-called angle of incidence. As regards the location of the definition of the chord lines along the respective span of the wing and the winglets reference is made to what has been explained before.

Figures 3a and b illustrate a tip vortex as present at any wing tip during flight. The fields of arrows at the right sides symbolize the component of the airflow velocity in the plane of drawing as regards direction and magnitude (arrow length). Figure 3a shows a point of x = 2.5 m (x = 0 corresponding to the front end of the wing tip) and figure 3b relating to a downstream location of x = 3.4 m. It can be seen that the tip vortex "develops with increasing x" and that the vortex is quite concentrated around the wing tip and quickly vanishes with increasing distance therefrom. This statement relates to almost any direction when starting from the wing tip with no qualitative but also small quantitative differences.

Further, figures 3a and b illustrate that the wing tip vortex principally adds some upward component to the airflow velocity together with some outward component in the lower region and some inward component in the upper region. With this in mind, it can be understood that figure 2 shows a local flow direction having an an- gle beta to the flight direction x. This local flow direction (components perpendicular to the plane of drawing of figure 2 being ignored) attacks the symbolic winglet W and causes a lift L _n thereof as shown by an arrow. This lift is perpendicular to the flow direction by definition. It can be seen as a superposition of a vertically upward component and a positive thrust component F _xn ,L.

Principally the same applies for the drag D _n of the winglet W. There is a negative thrust component of the drag, namely F _xniD . The thrust contribution of the winglet W as referred to earlier in this description is thus the difference thereof, namely xn = F _xniL - F _xniD and is positive here. This is intended by the invention, namely a positive effective thrust contribution of a winglet. Figure 4 shows the main wing 2 and exemplary two winglets of figure 2, namely 8 and 9. Wing 2 is somewhat inclined relative to the y-axis by a so called sweepback angle and has a chord line length decreasing with the distance from the base body 7 from a root chord line length cr to a tip chord line length ct. At a wing outer end 15, winglets 8 and 9 are mounted, compare also figure 5.

Figure 5 shows the wing 2 and the winglets 8 and 9 in a projection on a y-z-plane and the length b of main wing 2 (b being measured from the centre of base body 7 at y = 0 along the span of main wing 2 as explained before) and respective lengths b1 and b2 of winglets 8 and 9, respectively. For simplicity, wing 2 and winglets 8 and 9 are shown straight and horizontal, only. However, an inclination relative to wing 2 around an axis parallel to the x-axis would not lead to qualitative changes.

Figure 6 shows a diagram including two graphs. The vertical axis relates to beta (compare figure 2), namely the angle of inclination of the local airflow direction in a projection on a x-z-plane.

The horizontal line shows "eta", namely the distance from outer wing end 15 divided by b, the length of main wing 2. A first graph with crosses relates to the condition without winglets 8 and 9 and thus corresponds to figures 3a and b, qualitatively. The second graph showing circles relates to an airflow distribution downstream of first winglet 8 and thus upstream of second winglet 9 (the first graph relating to the same x-position). The graphs result from a computer simulation of the airflow distribution (such as figures 3a and b).

It can easily be seen that the first graph shows a maximum 16 closely to outer wing end 15 whereas the second graph has a maximum 17 there, an intermediate minimum at around eta = 1 .025 and a further maximum 18 at around eta = 1 .055, and decreases outwardly therefrom. Further, the second graph drops to a value of more than 50 % of its smaller (left) maximum and more than 40 % of its larger (right) maximum whereas it drops to a value of still more than 25 % of its larger maximum at about eta = 1 .1 , e.g. at a distance of about 10 % of b from outer wing end 15. This angle distribution is a good basis for the already described function of winglet 9, compare figure 2.

Simulations on the basis of the airplane type Airbus A320 have been made. They will be explained hereunder. So far, the inventors achieve around 3 % reduction of the overall drag of the airplane with three winglets as shown in figurel by means of the thrust contribution of the winglets and a small increase of the overall lifting force (in the region of maybe 1 % lift increase). The lift increase enables the airplane to fly with a somewhat lower inclination (compare alpha in figure 2) which leads to a further reduction of the overall drag. These simulations have been made by the computer programme CFD (computational fluid dynamics) of ANSYS.

As a general basic study, computer simulations for optimization of the thrust contribution of a two winglet set (first and second winglet) with a standard NACA 0012 main wing airfoil and a NACA 2412 winglet airfoil and without any inclination of the winglet relative to the main wing (thus with a setup along figures 4 and 5) have shown that an aspect ratio 5 is a good choice. Although higher aspect ratios are more efficient in an aerodynamic sense, they have a smaller area and thus, produce smaller forces (and thus a small thrust). In other words, within the limitation of a length b2 (span) of 1 .5 m (for the A320), a substantial winglet area is preferred. On the other hand, a too low aspect ratio increases the drag and decreases the efficiency in an amount that finally reduces the effective thrust by means of an increased drag. All in all, the CFD simulations repeatedly showed optimum values around 5.

On this basis, the length b1 of the upstream first winglet 8 for the A320 has been chosen to be 2/3, namely 1 m in order to enable the downstream second winglet 9 to take advantage of the main part of the broadened vortex region, compare again the setup of figures 4 and 5 and the results in figure 6.

The mean chord length results from the length of the fingers and from the fixed aspect ratio. As usual for airplane wings, there is a diminution of the chord line length in an outward direction. For the first upstream winglet 8, the chord line length at the root is 400 mm and at the top is 300 mm, whereas for the downstream second winglet 9 the root chord length is 600 mm and the tip chord length 400 mm. These values have been chosen intuitively and arbitrarily.

For the winglets, instead of the above mentioned (readily available) NACA 2412 of the preliminary simulations, a transonic airfoil RAE 5214 has been chosen which is a standard transonic airfoil and is well adapted to the aerodynamic conditions of the A320 at its typical travel velocity and altitude, compare below. The Airbus A320 is a well-documented and economically important model airplane for the present invention.

The most influential parameters are the angles of incidence gamma and the dihedral angle delta (namely the inclination with respect to a rotation around an axis parallel to the travel direction). In a first coarse mapping study, the mapping steps were 3° to 5° for gamma and 10° for delta. In this coarse mapping, a first and a second but no third have been included in the simulations in order to have a basis for a study of the third winglet. Figure 7 illustrates the angle gamma, namely gamma 1 of winglet 8, the first winglet, and gamma 2 of winglet 9, the second winglet, both shown as airfoils (compare figure 2) and with their chord lines in relation to the main wing airfoil and its chord line. Figure 8 illustrates the angle delta in a perspective as in figure 5, but less schematic. Again, delta 1 is related to the first winglet 8 and delta 2 to the second winglet 9. The structures in the left part of figure 8 are transient structures as used for the CFD simulations. These structures do not correspond to the actual A320 main wing to which the winglets, the slim structures in the middle and the right, have to be mounted but they define a pragmatic model to enable the simulation.

Figure 9 shows a plan view onto a main wing of the A320, the wing tip is oriented downward and the base body is not shown but would be on top. Figure 9 shows a main wing 20 of the A320 which actually has a so called fence structure, namely a vertical plate, at the end of the wing which has been omitted here, because it is to be substituted by the winglets according to the invention. Figure 10 shows the main wing 20 of figure 9 in a front view, in figure 1 1 shows the main wing 20 in a side view (perspective perpendicular to the travel direction - X). The somewhat inclined V geometry of the main wings of the A320 can be seen in figures 10 and 1 1 . A typical travel velocity of 0.78 mach and a typical travel altitude of 35,000 feet has been chosen which means an air density of 0.380 kg/m ³ (comparison: 1 .125 kg/m ³ on ground), a static pressure of 23.842 Pa, a static temperature of 218.8 K and a true air speed (TAS) of 450 kts which is 231 .5 m/s. The velocity chosen here is reason to a compressible simulation model in contrast to the more simple incom- pressible simulation models appropriate for lower velocities and thus in particular for smaller passenger airplanes. This means that pressure and temperature are variables in the airflow and that local areas with air velocities above 1 Mach appear which is called a transsonic flow. The total weight of the aircraft is about 70 tons. A typical angle of attack alpha is 1 .7° for the main wing end in in-flight shape. This value is illustrated in figure 2 and relates to the angle between the chord line of the main wing at its tip end to the actual flight direction. It has been determined by variation of this angle and calculation of the resultant overall lifting force of the two main wings. When they equal the required 70 to, the mentioned value is approximately correct. In this mapping, a certain parameter set, subsequently named V0040, has been chosen as an optimum and has been the basis for the following more detailed comparisons. The gamma and delta values of winglets 8 and 9 ("finger 1 and finger 2") are listed in table I which shows that first winglet 8 has a gamma of -10° and a delta of -20° (the negative priority meaning an anti-clockwise rotation with regard to figure 7 and 8) whereas second winglet 9 has a gamma of -5° and a delta of -10°. Starting therefrom, in the third and fourth line of table I, gamma of the first winglet 8 has been decreased and increased by 2°, respectively, and in the fifth and sixth lines, delta of first winglet 8 has been decreased and increased by 10°, respectively. The following four lines repeat the same schedule for second winglet 9. For comparison, the first line relates to a main wing without winglet (and without fence). In the column left from the already mentioned values of gamma and delta, the numbers of the simulations are listed. V0040 is the second one.

From the sixth column on, that is right from the gamma and delta values, the simulation results are shown, namely the X-directed force on an outward section of the main wing (drag) in N (Newton as all other forces). In the seventh column, the Z- directed force (lift) on this outward section is shown. The outward section is defined starting from a borderline approximately 4.3 m inward of the main wing tip. It is used in these simulations because this outward section shows clear influence of the winglets whereas the inward section and the base body do not. The following four columns show the drag and the lift for both winglets ("finger 1 and 2" being the first and second winglet). Please note that the data for "finger 1 " in the first line relates to a so-called wing tip (in German: Randbogen) which is a structure between an outward interface of the main wing and the already mentioned fence structure. This wing tip is more or less a somewhat rounded outer wing end and has been treated as a "first winglet" here to make a fair comparison. It is substituted by the winglets according to the invention which are mounted to the same interface. The following column shows the complete lift/drag ratio of the wing including the outward and the inward section as well as the winglets (with the exception of the first line).

The next column is the reduction achieved by the two winglets in the various configurations with regard to the drag ("delta X-force") and the respective relative value is in the next-to-last column. Finally, the relative lift/drag ratio improvement is shown. Please note that table I comprises rounded values whereas the calculations have been done by the exact values which explains some small inconsistencies when checking the numbers in table I. It can easily be seen that V0040 must be near a local optimum since the drag reduction and the lift drag ratio improvement of 2.72 % and 6.31 %, respectively, are with the best results in the complete table. The small decrease of gamma of the first winglet 8 (from -10 to -8) leads to the results in the fourth line (V0090) which are even a little bit better. The same applies to a decrease of delta of the second winglet 9 from -10° to 0°, compare V0093 in the next-to-last line. Further, a reduction of delta of the first winglet 8 from -20° to -30° leaves the results almost unchanged, compare V0091 . However, all other results are more or less remarkably worse. Figure 12 shows a side view in the perspective of figure 1 1 but with the two winglets added to the main wing in figure 1 1 and, additionally, with two hatched lines for later reference (reference lines for air velocity angle) and figure 13 shows a plan view onto the main wing tip and the two winglets with the same reference lines as in figure 12. Both reference lines are upstream of the respective leading edge of the winglet by 10 cm and are parallel to said leading edge. Figure 14 is a diagram comparable to figure 6, namely showing the angle beta on the vertical axis and the distance from the main wing tip along the reference lines just explained. The basic parameter set and simulation V0040 is represented by circles, V0046 is represented by triangles, and V0090 is represented by diamonds. The solid lines relate to the reference line upstream of the first winglet 8 and the dotted lines to the other one, upstream of the second winglet 9 and downstream of the first winglet 8. Table I clarifies that V0046 has a reduced gamma of the first winglet 8 and V0090 an increased gamma of the first winglet 8 with a step size 2 °. First of all, the graphs show that the first winglet 8 produces a significantly "broadened" vortex region, even upstream of the first winglet 8 as shown by the solid lines. In contrast to figure 6, there is no pronounced second maximum (18 in figure 6) but a more or less constant beta angle between 0.5 m and about 1 .2 m. The respective length of the main wing is 16.35 m which means for example an eta of 1 .031 for 1 .5 m and of 1 .07 for 1 .2 m, approximately (compare figure 6).

This beta value is in the region of 9° which is in the region of 70 % of the maximum at 0° (both for the reference line between both winglets, i. e. the dotted graph). Further, with the reduced gamma value, V0046 (triangles) shows an increased beta upstream of the first winglet 8 and a decreased beta downstream thereof. Contrary to that, with increased gamma, V0090 shows an increased beta downstream of the first winglet 8 and a decreased beta upstream thereof. Thus, the inclination gamma (angle of incidence) can enhance the upwards tendency of the airflow in between the winglets, in particular for places closer to the main wing tip than 1 m, compare figure 14. In this case, the beta values above a distance of 1 m are not deteriorated thereby. The results in table I show, that the overall performance of this parameter set is even a little bit better than V0040. This is obviously due to a reduced overall drag (although the angle of incidence has been increased), i. e. by a stronger contribution to the overall thrust.

On the other hand, a reduction of the gamma value from 10° to 8° and thus from V0040 to V0046 clearly leads to substantially deteriorated results, compare table I. Consequently, in a further step of optimization, gamma values higher, but not smaller than 10° and possibly even a little bit smaller than 12° could be analyzed.

Further, figure 15 shows an analogous diagram, but for V0040 in comparison to V0092 and V0091 . Here, the angle delta of the first winglet 8 has been varied from -20° to -10° and to -30°, compare table I and figure 8. Obviously, this has little impact on the air velocity angle (beta) distribution upstream of the fist winglet 8 (solid lines) but it has an impact on the airstream angles downstream thereof (dotted lines). Again, the beta values increase a little bit for distances below 1 m by in- creasing the delta value, namely for V0091 . The respective performance results in table I are almost identical with those of V0040 and obviously the beta values in figure 15 as well.

On the other hand, decreasing the delta value to -10 and thus bringing both wing- lets in line (as seen in the flight direction) qualitatively changes the dotted graph in figure 15. The beta values are reduced up to about 1 m, namely the length of the first winglet 8, and are clearly increased above that distance value. Seemingly, the second winglet 9 is somewhat in the lee of the first winglet 8 up to 1 m and "sees" the winglet tip vortex thereof at distances above 1 m. In summary, this does not improve the results but leads to some deterioration, as table I shows. The inventors assume that the beta increase at distances above 1 m does not compensate for the beta decrease at smaller distances.

Figure 16 shows another analogous diagram, now relating to a variation of the gamma angle of the second winglet 9. Again, this obviously has not much impact on the beta values upstream of the first winglet 8 (solid lines), but has a substantial impact on the beta values in between both winglets (dotted lines). Here, the beta values increase with a small decrease of gamma from 5° to 3° and, in the opposite, they decrease with an increase of gamma from 5° to 7°. In a similar manner as the solid lines in figure 14, a turning into the airstream of the winglet obviously decreases the inclination of the airstream upstream of the winglet. The results in table I clearly show that both variations, V0038 and V0042 decrease the perfor- mance results. In particular, the reduction of beta between both winglets by an increase of gamma of the second winglet 9 substantially deteriorates the lift/drag improvement. Further, a too strong inclination of the winglet does produce more lift but also produces over-proportionally more drag and thus leads to a deterioration.

Obviously, with a next step of optimization, the gamma value of the downstream winglets should be left at 5°.

Finally, figure 17 relates to a variation of the delta angle of the second winglet 9 and leads to similar results as figure 15: for V0094, the delta values of both winglets are -20° and again the second 9 winglet seems to be in the lee of the upstream winglet and shows a strong impact by the winglet tip vortex thereof which leads to comparatively bad results, in particular with regard to the lift drag ratio. Increasing the delta difference between both winglets by V0093 does not change much in the beta values and leads to similar (somewhat improved) results in table I. Again, with a next step of optimization, the range of delta for the second winglet 9 between 0° and -10° is interesting.

On the basis of the above results, further investigations with three winglets and again based on what has been explained above in relation to the A320 have been conducted. Since the number of simulations feasible in total is limited, the inventors concentrated on what has been found for two winglets. Consequently, based on the comparable results with regard to the drag reduction of more than 2.7 % and the lift/drag ratio for the complete wing (compare the fourth-last and second- last column in table I), the parameters underlying V0040, V0090, V0091 , and V0093 were considered in particular. Consequently, simulations with varying values for the angle of incidence gamma and the dihedral angle delta of the third winglet were performed on the basis of these four parameter sets and were evaluated in a similar manner as explained above for the first and second winglet.

Simultaneously, data with regard to the in-flight shape of the main wing of the A320 were available with the main impact that the chord line at the wing end of the main wing is rotated from the so-called jig shape underlying the calculations explained above by about 1 .5°. This can be seen by the slightly amended gamma values explained below. Still further, data relating to the drag of the complete airplane for different inclinations thereof were available, then, so that the impact of an improvement of the overall lift (by a lift contribution of the winglets as well as by an increase of the lift of the main wing due to a limitation of the vortex-induced losses) on the overall drag due to a variation of the inclination of the airplane could be assessed. The results (not shown here in detail) showed that the V0091 basis proved favourable. The respective embodiment will be explained hereunder.

Figure 18 shows a front view of the winglets 8, 9, 10 of this embodiment as seen in the x-direction and illustrates the dihedral angles delta 1 , 2, 3 of the three winglets. The upper most winglet is the first one, the middle winglet is the second one, and the lowest winglet is the third downstream one. Figure 18 shows qualitatively, that a substantial, but limited relative dihedral angle between the succeeding winglets has proven to be advantageous also for the three winglet embodiment. Taking this opportunity, figure 19 explains the definition of the relative dihedral angle along the claim language. In the same perspective as figure 18, the first and the second winglet are shown together with two radii r1 and r2 of different size. The meeting point of a vertical and the horizontal line is the root R (at the splitting point horizontally and the meeting of the leading edges vertically) and one vertex of an isosceles triangle shown, the other two vertices of which are on the leading edges of the two winglets and referred as V1 and V2. The angle between the line R-V1 and the line R-V2 is the relative dihedral angle if taken as an average over all radii ri possible within the shorter one of the two winglets, namely the first one. The visible difference between the line R-V1 from the leading edge of the first winglet is connected to the bending of the first winglet to be explained hereunder which is also the background of the deviation between the line for delta 1 and the first winglet in figure 18.

Figure 20 illustrates the above mentioned bending of the first winglet which is so to say a distribution of a part of the dihedral angle along a certain portion of the spanwise length. Actually, in figure 20, a leading edge L is schematically shown to start from a root R and to be bent along a circular arch shape B extending over one third (330 mm) of its length with a radius of 750 mm and an arch angle of -15°. Already at the start of R the leading edge of the first winglet has a dihedral angle of -20°. This means that outwards of the bending, the dihedral angle for the second and third third of the length of the first winglet is actually -35°. In an average along the complete spanwise length of the first winglet from R to its outward end, an average dihedral angle of about -30° results, -15° of which have been "distributed" along the arch as described.

The reason is that in this particular embodiment, a straight leading edge of the first winglet with a dihedral angle of -30° has made it somewhat difficult to provide for a smooth transition of a leading edge to that one of the main wing end (in the so- called fairing region) whereas with -20° dihedral angle, the smooth transition has not caused any problems. Therefore, in order to enable an average value of -30°, the solution of figure 20 has been chosen.

In general, it is within the teaching of this invention to use winglet shapes that are not straight along the spanwise direction such as shown in figure 20. They could even be arch shaped along the complete length as pointed out before. What is most relevant in the view of the inventors, is the relative dihedral angle in an average sense. If for example, a first and a second winglet would both be arch shaped in a similar manner so that the isosceles triangle construction explained earlier with a fixed vertex at the root would be inclined more and more with increasing length of the equal sides thereof due to the curvature of the winglet leading edges, the relative dihedral angle according to this construction might even remain almost constant along the leading edges. Still, at a certain portion along the spanwise length of for example the second winglet, the proximate portion along the span- wise length of the first winglet would be positioned relative to the second winglet in a manner that is well described by the relative dihedral angle (remember the somewhat rotationally symmetrical shape of the vortex at the wing end) and is well described by the triangle construction.

The absolute dihedral angles of the second and the third winglet in this embodiment are delta 2 = -10° and delta 3 = +10° wherein these two winglets of this embodiment do not have an arch shape as explained along figure 20. Consequently, the relative dihedral angle between the first and the second winglet is 20°, is the same as the relative dihedral angle between the second and the third winglet, and the first winglet is more upwardly inclined than the second winglet, the second winglet being more upwardly inclined than the third winglet, compare figure 18. The angle delta 1 shown in figure 18 is the starting dihedral angle at the root of the first winglet, namely -20 ° instead of the average value of -30 °.

As regards the angles of incidence, reference is made to figure 21 showing a side view and sections through the three winglets 8, 9, 10, and the main wing 2. The sectional planes are different, naturally, namely 10 % outward of the spanwise length of the winglets from the respective splitting positions, and 10 % inward in case of the main wing 2, as explained earlier, to provide for undisturbed chord lines. The chord lines and the respective angles gamma 1 , 2, 3 are shown in figure 21 . The angles are gamma 1 = -9° for the first winglet, gamma 2 = -4° for the second winglet and gamma 3 = -1 ° for the third winglet, all being defined relative to the main wing chord line at the described outward position and in the in-flight shape of the winglets and of the main wing (all parameters explained for this embodiment relating to the in-flight shape).

Figure 21 also shows the respective rotating points on the chord line of main wing 2 as well as on the chord line of the respective winglet 8, 9, 10. In terms of the respective chord line length of the winglets, the rotating points are approximately at a third thereof. In terms of the chord line length of main wing 2, the rotating point of the first winglet is at 16.7 % (0 % being the front most point on the chord line), the rotating point of the second winglet is at 54.8 %, and the rotating point of the third winglet is at 88.1 %. Figure 22 illustrates the sweepback angle epsilon of a representative winglet 9, namely the angle between the leading edge thereof and a direction (y in figure 22) being horizontal and perpendicular to the flight direction. Herein, winglet 9 is thought to be horizontal (delta and gamma being zero in a fictious manner), alternatively, the spanwise length of winglet 9 could be used instead of its actual ex- tension in the y-direction when being projected onto a horizontal plane. Please note that also the arch shape of winglet 8 as explained along figure 22 would be regarded to be unrolled. In other words, the spanwise length includes the length of the arch. In the present embodiment, the sweepback angle of the main wing 2 is 27.5°. Variations starting from this value showed that an increased sweepback angle of 32° is preferable for the winglets, in other words 4.5° sweepback angle relative to the main wing's sweepback angle. This applies for the second and for the third winglets 9, 10 in this embodiment whereas for the first winglet 8, the sweepback angle has been increased slightly to 34° in order to preserve a certain distance in the x-direction to the leading edge of the second winglet 9, compare the top view in figure 25 explained below.

Figure 23 is a fictious top view onto the three winglets 8, 9, 10, to explain their shape. It is fictious because the dihedral angles and the angles of incidence are zero in figure 23 and the arch shape of the first winglet 8 is unrolled. Figure 23, thus, shows the respective spanwise length b1 , 2, 3. It further shows the chord line lengths cr1 , 2, 3, at 10 % of the spanwise length outward of the splitting points (these being at the bottom of figure 23) as well as the tip chord line lengths ct1 , 2, 3, at 10 % inward of the winglets' tips. The actual values are (in the order first, second, third winglet): a root chord length cr of 0.4 m, 0.6 m, 0.4 m; a tip chord length ct of 0.3 m, 0.4 m, 0.25 m; a spanwise length b of 1 m, 1 .5 m, 1 .2 m. This corresponds to a root chord length cr of approximately 25 % of the main wing chord length at its end (as defined), approxi- mately 37 % and approximately 25 %; a tip chord length relative to the root chord length of 75 %, 67 % and 63 %; and a spanwise length relative to the spanwise main wing length (16.4 m) of 6.1 %, 9.2 %, 7.3 %, respectively.

Please note that the angle of sweepback as shown in figure 23 is no rotating oper- ation result. This can be seen in that the chord line lengths cr and ct remain unchanged and remain in the x-z-plane, in other words horizontal in figure 23. This is necessary in order not to disturb the airfoil by the introduction of the sweepback angle. Still further, figure 23 shows a rounding of the respective outer forward corner of the winglets' shape. This rounding relates to the region between 90 % and 100 % of the spanwise length wherein the chord line length is continuously reduced from 90 % to 100 % spanwise length by 50 % of the chord line length such that in the top view of figure 23 an arch shape is generated. It is common practice to use roundings at the outer forward corners of wings to avoid turbulences at sharp corner shapes. By the just explained reduction of the chord line length in the outer 10 % of the spanwise length, the qualitative nature of the airfoil can be preserved.

The airfoil used here is adapted to the transonic conditions at the main wing of the A320 at its typical travel velocity and travel altitude and is named RAE 5214. As just explained this airfoil is still valid in the outer 10 % of the spanwise length of the winglets.

Still further, this trailing edge (opposite to the leading edge) of the winglets is blunt for manufacturing and stability reasons by cutting it at 98 % of the respective chord line length for all winglets. The transformation of the shapes shown in figure 23 to the actual 3D geometry is as follows: first, the sweepback angles are introduced which are already shown in figure 23. Second, the bending of the first winglet along the inner third of its spanwise length with the radius of 750mm and the angle of 15° is introduced. Then, the winglets are inclined by a rotation by the angle of incidence gamma. Then, the dihedral angles are adjusted, namely by inclining the first winglet by 20° upwardly (further 15° being in the bending), the second winglet by 10° upwardly and the third winglet by 10° downwardly. Please note that the above transformation procedure does not relate to the jig shape and to the geometry as manufactured which is slightly different and depends on the elastic properties of the main wing and the winglets. These elastic properties are subject of the mechanical structure of the wing and the winglets which is not part of the present invention and can be very different from case to case. It is, however, common practice for the mechanical engineer to predict mechanical deformations under aerodynamic loads by for example finite elements calculations. One example for a practical computer program is NASTRAN.

Thus, depending on the actual implementation, the jig shape can vary although the in-flight shape might not change. It is, naturally, the in-flight shape that is responsible for the aerodynamic performance and the economic advantages of the invention.

Table II shows some quantitative results of the three winglet embodiment just ex- plained (P0001 ). It is compared to the A320 without the invention, but, in contrast to table I, including the so-called fence. This fence is a winglet-like structure and omitting the fence, as in table I, relates to the improvements by the addition of a (two) winglet construction according to the invention to a winglet-free airplane whereas table II shows the improvements of the invention, namely its three winglet embodiment, in relation to the actual A320 as used in practice including the fence. This is named B0001 . The lift to drag ratios for both cases are shown (L/D) in the second and third column and the relative improvement of the invention is shown as a percentage value in the forth column. This is the case for six different overall masses of the airplane between 55t and 80t whereas table I relates to 70t, only. The differences between the masses are mainly due to the tank contents and thus the travel distance.

Table II clearly shows that the lift to drag improvement by the invention relative to the actual A320 is between almost 2 % in a light case and almost 5 % in a heavy case. This shows that the invention is the more effective the more pronounced the vortex produced by the main wing is (in the heavy case, the required lift is much larger, naturally). In comparison to table I, the lift to drag ratio improvements are smaller (around 6.3 % for the best cases in table I). This is due to the positive effect of the conventional fence included in table II and to the in-flight deformation of the main wing, namely a certain twist of the main wing which reduces the vortex to a certain extend. For a typical case of 70t, the drag reduction of an A320 including the three winglet embodiment of the invention compared to the conventional A320 including fence is about 4 % (wing only) and 3 % (complete airplane), presently. This improvement is mainly due to a thrust contribution of mainly the second winglet and also due to a limited lift contribution of the winglets and an improved lift of the main wing by means of a reduction of the vortex. As explained earlier, the lift contributions allow a smaller inclination of the complete airplane in travel flight condition and can thus be "transformed" into a drag reduction. The result is about 3 % as just stated. For illustration, figure 24 to 27 show the 3D shape of the A320 and three winglets, namely a perspective view in figure 24 of the complete airplane, a top view onto the main wing end and the winglets in figure 25 (against the z-direction), a side view (in y-direction) in figure 26, and finally a front view (in x-direction) in figure 27. The figures show smooth transitions in the fairing region between the main wing end and the winglets and also some thickening at the inward portion of the trailing edges of the first and second winglets. These structures are intuitive and meant to avoid turbulences.

POOOl vs BOOOl - wing only

Ratio Lift/Drag

POOOl L/D BOOOl L/D improvement m [t] [%]

55.0 27.7 27.1 1.9

60.0 27.1 26.3 2.8

65.0 25.8 24.9 3.5

70.0 24.1 23.1 4.1

75.0 22.3 21.3 4.5

80,0 20.5 19.6 4.7