EP1905487A1

EP1905487A1 - A flyable object and a method of manufacturing the same

Info

Publication number: EP1905487A1
Application number: EP06020245A
Authority: EP
Inventors: Kristian Hohla; Martin Schottenloher; Ernst Hegels; Georg Korn
Original assignee: Friend for Golfers GmbH
Current assignee: Friend for Golfers GmbH
Priority date: 2006-09-27
Filing date: 2006-09-27
Publication date: 2008-04-02

Abstract

A flyable object (100,200,300,400,500,600) such as a golf ball, comprising a body (101) and a plurality of structures (102,201) such as dimples or protrusions formed on and/or in the body (101) in a non-periodic manner.

Description

The invention relates to a flyable object.
The invention further relates to a method of manufacturing a flyable object.
Moreover, the invention relates to a method of designing a flyable object.
Golf balls may comprise dimple structures to improve the aerodynamic properties of the golf ball.
US 4,925,193 discloses an aerodynamically symmetrical golf ball including a patterned outer surface having 492 dimples arranged in twenty triangles based upon an inscribed modified icosahedron lattice on the surface of the ball.
EP 0,587,285 discloses a golf ball having dimples formed in its outer spherical surface and arranged in a geodesic pattern defined by a plurality of imaginary grid lines which divide the outer spherical surface into an icosahedron having twenty triangular regions.
US 5,259,624 discloses a golf ball having dimples arranged as constrained by a plurality of geometric shapes, and the geometric shapes are located so that the sphere of the ball is symmetric about the origin.
EP 0,605,079 discloses a golf ball having dimples formed in its outer spherical surface and arranged in a geodesic pattern defined by a plurality of imaginary grid lines which divide the outer spherical surface into a truncated octahedron having six square regions and eight hexagonal regions.
US 5,308,076 discloses a golf ball characterized by enhanced flight distance and enhanced aerodynamic symmetry, the ball having a generally spherical surface with patterns of dimples thereon comprising a ball having a main axis and opposite surface polar regions associated with the axis.
US 5,415,410 discloses a golf ball having a spherical surface with a plurality of dimples formed therein, the spherical surface comprising eight spherical triangles delineated by three great circle parting lines not intersecting any dimples, said parting lines being formed by projecting the edges of an inscribed regular octahedron onto said spherical surface, each of said triangles having dimples located within parting lines.
US 5,562,552 discloses a method of laying out a dimple pattern on a golf ball comprising constructing a geodesically expanded icosahedron having 60 equal triangular faces. Each of the 60 triangular faces includes a substantially identical dimple pattern.
US 6,331,150 discloses a golf ball having a surface thereon with a plurality of dimples on the surface. The contour of each of the dimples is continuous from a first edge of each of the dimples to a second opposing edge of each of the dimples. The contour at the first edge may be equal to the contour of a sphere of the golf ball.
US 6,383,092 discloses a golf ball approaching zero land area having an inner sphere with a plurality of pyramidal projections.
US 2002/0010039 discloses a dimple pattern for a golf ball with multiple sets of dimples. Each of the multiple sets of dimples has a different diameter. A preferred set of dimples is seven different dimples. The dimples may cover as much as eighty-six percent of the surface of the golf ball. The unique dimple pattern allows a golf ball to have shallow dimples with steeper entry angles.
US 2002/0032081 discloses a dimple pattern for a golf ball with multiple sets of dimples. Each of the multiple sets of dimples has a different entry angle. A preferred set of dimples is eighteen different dimples. The dimples may cover as much as eighty-seven percent of the surface of the golf ball. The unique dimple pattern allows a golf ball to have shallow dimples with steeper entry angles.
However, conventional golf balls may suffer from the fact that there aerodynamic behavior is still insufficient.
It is an object of the invention to provide an object with proper aerodynamic properties.
In order to achieve the object defined above, a flyable object, a method of manufacturing a flyable object, and a method of designing a flyable object according to the independent claims are provided.
According to an exemplary embodiment of the invention, a flyable object is provided comprising a body and a plurality of structures formed on and/or in the body in a non-periodic manner.
According to another exemplary embodiment of the invention, a method of manufacturing a flyable object is provided, the method comprising forming a plurality of structures on and/or in a body in a non-periodic manner.
According to still another exemplary embodiment of the invention, a method of designing a flyable object is provided, the method comprising defining a pattern for forming a plurality of structures on and/or in a body of the flyable object in a non-periodic manner to thereby match a fluid dynamic property of the designed flyable object to a predetermined value of the fluid dynamic property.
In the context of this application, the term "flyable object" may particularly denote a physical structure which is adapted, designed, configured or foreseen to be operated in a fluidic (particularly a gas, but possibly also a liquid) environment in which it shall fly. Such an object may have the function to fly in a fluidic (particular gaseous) environment like air, so that fluid dynamic properties (particularly aerodynamic properties) are of relevance for such an object. Examples for flyable objects are sports devices like balls or frisbees, or any kind of vehicles like aircraft.
The term "non-periodic" may particularly denote a specific manner or rule according to which the structures (particularly indentations or protrusions) are arranged on a (spherical) surface of the object. Such a lack of periodicity may include a lack of any ordering scheme (like a random or statistical distribution scheme), but may also include an ordering scheme or algorithm which intentionally arranges the structures on the body so that it is avoided that sub-arrangements of the structures are repeated with identical motives and sizes again and again along or around the surface of the body. There may be repeated motives of structures even in a non-periodic arrangement, for instance similarities as known from fractional geometry, but these motives then should distinguish from one another at least partially with regard to at least one other ordering parameter like at least one dimension of the structure (length, width depth), a shape (geometry or relation between dimensions of the structure), etc. Periodicity may denote a pure repetition of basic building blocks B, for instance n times, yielding an arrangement -[B]_n-. In contrast to this, an example for a non-periodic ordering scheme would be an arrangement -[nB]_n-. since the basic building block nB would then vary along the structure. Thus, similarities may be found in an aperiodic pattern, but not a purely repeated arrangement of identical motives. For a three-dimensional object like a sphere, such a non-periodic arrangement may indicate a lack of periodicity along a (circular) closed line aligned along a surface of the sphere, and/or along an essentially cylindrical closed strip aligned along a circumferential surface portion of the sphere.
The term "asymmetric" may particularly denote a manner or rule according to which the structures (particularly indentations or protrusions) are arranged on a (particularly spherical) surface of the object, which manner or rule does not obey any symmetry operation or condition, like reflection of a part of the body with regard to a point, a line, or a plane. Again, lack of symmetry does not necessarily mean lack of any ordering scheme, but this ordering scheme will not lead to a highly symmetric arrangement of the dimples.
The term "similar pattern" may particularly denote a secondary pattern which has the same appearance like a primary pattern, but differs from the primary pattern with regard to at least one structural parameter (for instance with regard to the absolute size). For example, two triangles having identical angles may be similar, even if their side lengths differ. Such similarities can be found in geometrical structures as described in fractional geometry.
The term "Penrose tiling" may particularly denote a pattern of tiles which could completely cover an infinite (planar) plane, but only in a pattern which is non-repeating (aperiodic or non-periodic). Examples for such tiles are a thick rhombus and a thin rhombus, a dart and a kite, etc. Such tiles may be put together in accordance with a given rule. Even if the term "Penrose tiling" usually relates to planar surfaces, it might be considered as well in sufficient approximation for a "quasi"-planar surface like a surface of a sphere to be covered by tiles having dimensions which are significantly smaller than a radius of the sphere so that the curvature of the sphere may be neglectable for the sufficiently small tiles. In case of a curved surface, an adaptation of the shape of the structures to the curvature is possible, while generally maintaining the shape of the structures/basic units. Thus, curved basic units (like slightly curved kites) are possible.
The term "random" may particularly denote a pattern of structures of the flyable object which has no ordering structure at all, that is to say is purely statistical without any defined algorithm according to which the the arrangement is designed. An example for a random process is the pattern according to which rain drops impinge on the ground at a specific point of time.
The term "pseudo-random" may particularly denote a pattern of structures of the flyable object which appears to have no derivable ordering structure, that is to say looks phenomenally like a statistical arrangement. However, such a pseudo-random scheme may design the structures in accordance with a defined algorithm which generates a structure pattern, wherein a corresponding ordering scheme is not derivable without the knowledge of the algorithm. An example for a pseudo-random process may be the sequence of digits of the number π, when starting at a predefined position.
According to an exemplary embodiment of the invention, by arranging the structures (for instance dimples) non-periodically along a surface of the body, an intended asymmetry of the dimple arrangement along the surface of the body may result. Specifically such an asymmetry of a dimple distribution on a surface is believed to modify the aerodynamic behaviour of the flyable object in a desired manner. Consequently, for instance in an embodiment in which the flyable object is a golf ball, a stroke width of the golf ball may be increased compared to a conventional dimple pattern or compared to the omission of any dimples. Specifically the non-periodicity of the dimples may influence turbulent or laminar flow characteristics along a surface of the flyable object in a manner so as to improve (particularly to stabilize the desired trajectory or to shorten the stroke for the sake of security) the fluid dynamic properties. Thus, an interaction between a Magnus effect, a Bernoulli effect, and other physical impacts effecting the flying object may be significantly improved by selectively providing an aperiodic dimple pattern on the surface of the flying object.
When a golf ball is hit by a golf club actuated by a golf player, the stroke determines the ball's velocity, launch angle and spin properties, all of which influence its trajectory and its behavior when it hits the ground
A ball moving through air may experience various forces, particularly lift and drag. Drag slows the forward motion, whereas lift acts in a direction perpendicular to it. The magnitude of these forces may depend on the behavior of the boundary layer of air moving with the ball surface.
A golf ball may have dimples or protrusions which, according to exemplary embodiments of the invention, may be distributed aperiodically on the golf ball's surface. Their purpose is to shape (for instance increase or decrease) the lift and drag forces by modifying the behavior of the boundary layer. Drag and lift forces exist also on smooth balls and on balls having a symmetric dimple pattern. They may be, however, modified by asymmetrically arranged dimples. One effect of such dimples may be a reduction of drag, contributing to the increased length of flight of dimpled balls compared with smooth ones.
A spinning ball may deform the flow of air around it, creating lift in a way similar to an airplane wing. Backspin is imparted in many shots due to the golf club's loft (i.e. angle between the clubface and a vertical plane). A backspinning ball may experience an upward lift force which may make it fly higher and longer than a ball without spin would. Sidespin may occur when the clubface is not aligned perpendicularly to the direction of swing, leading to a lift force that makes the ball curve to one side or the other. These lift forces may be further increased through the presence of asymmetrically distributed dimples. Such an asymmetry of a dimple design may reduce or increase the effect of sidespin, and may have some kind of equillibrating or stabilizing effect.
In the light of these considerations, a non-periodic arrangement of the dimples may improve the flying characteristic and therefore the performance of the golf ball. This may allow also relatively moderate and poor golf players to obtain a sufficient large stroke width and/or a better control over a stroke.
By providing the golf ball surface with aerodynamically effective structures (particularly indentations and/or protrusions) in accordance with a pattern defining algorithm which deviates from a highly symmetric arrangement, a longer, equilibrated and more precise flight path of the ball may be made possible. Therefore, a distribution of the dimples in x-, y-and/or z-direction of a Cartesian coordinate system or with regard to r-, ϕ- and/or θ-coordinates of a spherical coordinate system may be appropriate to improve the aerodynamic characteristic.
The shape of the structures may be round, quadratic, pentagonal, hexagonal, kite-like, dart-like, etc. Thus, point-symmetric and non-point-symmetric forms are possible. The sizes of the individual dimples may vary. It may be advantageous to increase the number of dimples, or the dimple covered area per surface area of the flyable object. Individual structures may have different depths and shapes. With regard to these and other geometrical parameters, the dimples may be distributed asymmetrically along a surface of the flying object.
On the basis of a theory of Roger Penrose that an asymmetric tiling of a (planar and infinite) surface is possible using a plurality of tiles so that a plane can be tiled without the occurrence of long term periodicity structures, a similar tiling scheme, when applied for instance to the curved finite surface of a golf ball, may be taken as a basis for a rule or an algorithm according to which dimple structures are to be arranged along a surface of a flyable object. Namely, when such a tiling of a surface has been performed with or without significant gaps due to a non-planar property of a surface of the flying object, an algorithm may be formulated how to arrange dimples at specific portions of specific tiles of the Penrose tiling. By taking this measure, an ordered aperiodic structure in accordance with the Penrose tiling principle may be combined with the non-symmetric arrangement of the dimples, thereby involving intentional non-symmetry, improving the aerodynamic properties of the ball.
Such a Penrose tiling of a surface of a flying object may use two or more tiles, like kite and dart. The indentation area of a golf ball may therefore be made large in accordance with an aperiodic characteristics. However, exemplary embodiments of the invention may make use of a spherical packing of patterns. In this context, explicit reference is made to Eric Cockayne (1994), "Nonconnected atomic surfaces for quasicrystalline sphere packings", Phys. Rev. B, Vol. 49, No. 9, pages 5896-5910, and to Charles Radin (2004), "Orbits of Orbs: Sphere Packing Meets Penrose Tilings", The American Mathematical Monthly, February 2004, pages 137-149. The disclosure of these two documents with regard to efficient sphere packing schemes are explicitly referenced here, and are incorporated into the disclosure of this application by reference. Such efficient sphere packing schemes may ensure that a large surface portion of the flyable object is covered by dimples, which may guarantee proper flight characteristics of the flyable object.
According to an exemplary embodiment of the invention, it is possible that the aerodynamics of a golf ball is improved or optimized. However, according to another exemplary embodiment, the aerodynamics properties are selectively and intentionally deteriorated compared to an optimum distribution, so that it is possible to limit a maximum stroke length or distance of the golf ball by a specific dimple arrangement, for instance for security reasons. This may allow to restrict a maximum dimension over which the golf ball may fly even being hit essentially perfectly.
Particularly, for flying objects which have a spin during the fly, the aperiodic or asymmetric arrangement of the dimples according to exemplary embodiments may be of advantage as well, since it may stabilize the trajectory and may allow for an improved spin control.
Embodiments of the invention may be implemented in many technical fields, like golf balls, soccer balls, tennis balls, footballs, baseballs, but may also be used for designing bullets, projectiles, airplanes or other vehicles like cars.
Additionally or alternatively to the aperiodic arrangement of the dimples, the surface of the flying object may be designed with a structure as known as a shark skin structure. Similarly as the skin of a shark, the surface of the flying object may then be foreseen with physical structures which allow the flying object to have, in addition to the aerodynamically appropriate dimple structure, a proper aerodynamics due to the shark skin structure.
Additionally or alternatively to a shark skin structure and/or a dimple structure, the so-called Lotus effect may be taken into account for the surface design of the flyable object. By providing additional structures on the flying object which are in accordance with the so-called Lotus effect, namely protrusions/indentations in the order of magnitude of µm, the aerodynamics of the flying object may be further improved. By providing a surface of the flying object with structures in accordance with the Lotus effect, it may be prevented or suppressed that dirt or dust adheres to the ball, thereby improving particularly the rolling properties of the object. A golf ball comprising surface structures (in the order of magnitude of µm) in accordance with the Lotus effect is therefore disclosed with or without the provision of dimples/protrusions (in the order of magnitude of mm).
According to an exemplary embodiment, structures in accordance with schemes known from fractional geometry may be implemented.
It is also possible to modulate the depth of the dimples in an aperiodic manner. Therefore, an adjustment of the surface area of the dimples, and/or of the depth of the dimples, and/or of the size/length of the dimples, and/or of the shape of the dimples may be made possible. Therefore, asymmetric golf ball structures in accordance with a predefined ordering scheme may be provided.
Next, further exemplary embodiments of the flying object will be explained. However, these embodiments also apply to the methods.
The body may have an essentially spherical shape. For example, the body may be a sphere on and/or in which the plurality of structures are formed. Alternatively, the body may have a sphere-like structure, like a body having an oval cross-section. A sphere shape can be found in a golf ball, and an essentially spherical shape, like a shape with an oval cross-section, may be found in a baseball. However, completely other shapes are possible, for instance the shape of a car or a plane.
At least a part of the plurality of structures may be dimples. Dimples may be indentations formed in the body, for instance manufactured by an abrasive manufacturing process.
Additionally or alternatively, at least a part of the plurality of structures may be protrusions. Thus protrusions may be structures formed by applying or depositing material on the surface of the body, or by patterning a surface of the body (for instance using a lithography and/or an etching process). Such protrusions may be formed to extend radially outwardly from a spherical surface of the body.
It is possible that the object comprises both, dimples and protrusions, in a geometrically irregular structure.
The plurality of structures may have a number in the order of magnitude of 50 to 1000, more particularly may have a number between 100 and 500. For example, 400 may be an appropriate number of the structures on a golf ball.
The plurality of structures may be formed on and/or in the body in an asymmetric manner. Particularly, the plurality of structures may be formed on and/or in the body in a random manner. In such a random geometry, random numbers may be generated as a basis for a determination scheme at which positions of the surface of the body the structures are to be formed. Such random numbers may then define spherical coordinates of positions at which dimples are to be formed. This may include two angles and a radius.
The plurality of structures may form similar patterns of different sizes. Similar patterns may be patterns having for instance identical shape but differing with regard to a further structural parameter, like absolute size length, depth of the structure, extension direction of the structure (that is to say protrusions or dimples), etc.
The plurality of structures may be positioned based on patterns in accordance with a Penrose tiling. In other words, a surface of the flying object, for instance a spherical surface, may be tiled with tiles in accordance with a Penrose tiling scheme. Deviating from the situation of an essentially planar plane, a perfect Penrose tiling may be not possible on a spherical surface. However, in a case in which the tiles are sufficiently small as compared to a curvature of a surface of the flyable object, effects resulting from curvature of the surface and/or of the limited area of the surface may be neglectable in proper approximation, and a Penrose tiling may be approximately possible also along a finite spherical surface. It is further mentioned that even a non-perfect Penrose tiling does not necessarily influence embodiments of the invention in a negative manner, since small gaps between adjacent tiles may further increase the aperiodic characteristic. After having performed a (virtual) Penrose tiling, a specific rule or algorithm may be applied to the surface of the body covered with the (virtual) Penrose tiles. For example, one of these tiles (for instance kites) may be located on the surface of the object and may define a position at which dimples or other structures are formed. By taking this measure, the aperiodic pattern of the Penrose tiling may be mapped onto an aperiodic arrangement of the structures.
The plurality of structures may be positioned based on a virtual tiling of a surface of the body performed on the basis of at least two modular units, wherein a defined portion of at least one of the at least two modular units may serve as a position for at least a part of the plurality of structures. For example, the two modular units may comprise a kite modular unit (which may be a trapezoid). Furthermore, the modular units may comprise a dart modular unit which may be an arrow-like rectangular structure having one angle which is larger than 180° and having two sides of a first dimension and two sides of a second dimension, wherein the sides having the same dimension being adjacent to one another. It is also possible that, on the basis of these basic building components (kite and dart), larger modular units are formed by any desired combination. However, as an alternative to a kite and a dart Penrose tile, other Penrose tiles are possible, for instance a large rhombus and a small rhombus arrangement.
The plurality of structures may be positioned in centers of at least a part of the at least two modular units. It is also possible that the structures are positioned in corners of the modular units, or non-symmetrically with regard to a centre of the modular unit. Any desired design rule is possible in this respect.
The plurality of structures may be positioned in at least a part of the at least two modular units so as to fill a predetermined area portion of the at least two modular units. For example, such an area portion may be 1/3 or 30%. The determination of this area determines the entire area of the structures on the surface of the body, and may therefore also have an influence on the aerodynamic characteristics.
The plurality of structures formed on and/or in the body may define an ordered structure. Although the structures may lack any (long term) periodicity, an ordering scheme may be the basis of the arrangement of the plurality of structures. Such an ordering scheme may be defined by the above-discussed Penrose theory, or by other strategies.
A surface of the body and/or of the plurality of structures may have a Lotus effect surface property. This feature may be used in combination with an aperiodic arrangement of the structures, but also with conventional periodic structures or without structures. Therefore, more generally, a golf ball having a surface which is treated in accordance with the Lotus effect is disclosed here. For this purpose, at least a part of the surface of the flyable object may have a microstructure in accordance with the Lotus effect. By providing microstructures with special dimensions, a fluid repellant property as known from the Lotus plant may be used for a golf ball.
Additionally or alternatively, a surface of the body and/or of the plurality of structures may have a shark skin surface property. By making a surface functionalized in accordance with the Lotus effect and/or with a shark skin structure, impurities, dirt, mud, snow, rain, etc. may be securely prevented from adhering to the object, thereby improving the flying and/or rolling characteristics.
Different ones of the plurality of structures may differ with regard to at least one criteria of the group consisting of a size on a surface of the body, a shape on a surface of the body, a depth in a direction essentially perpendicular to a surface of the body, and a shape essentially perpendicular to a surface of the body. These or other parameters may be varied in an aperiodic manner, so that even a symmetric or periodic arrangement of the structures along a surface of the flying object may be considered as aperiodic as well, since these parameters may involve the aperiodicity.
At least a part of the plurality of structures may be shaped in at least one manner of the group consisting of a round shape, an oval shape, a triangle shape, a rectangular shape, a pentagonal shape, a hexagonal shape, and a polygonal shape (particularly with n = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,12, 13 or even more).
The object may be configured as one of the group consisting of a golf ball, a mini golf ball, a tennis ball, a table tennis ball, a squash ball, a soccer ball, a football, a basketball, a baseball, a volley ball, a bullet (for instance of a weapon), a vehicle (like an aircraft, a car, a ship, a bus, a helicopter, etc.).
The plurality of structures may have dimensions in the range between essentially 100 µm and essentially 1 cm, in particular in the range between essentially 0.5 mm and essentially 4 mm. The body itself may have dimensions in the range between essentially 1 cm and essentially 50 cm, particularly in the range between essentially 3 cm and essentially 30 cm.
The aspects defined above and further aspects of the invention are apparent from the examples of embodiment to be described hereinafter and are explained with reference to these examples of embodiment.
The invention will be described in more detail hereinafter with reference to examples of embodiment but to which the invention is not limited.
Figure 1 to Figure 6 show surface structures of golf balls according to exemplary embodiments of the invention.
Figure 7A, Figure 7B and Figure 8 show Penrose tilings as a basis for designing surface structures of golf balls according to exemplary embodiments of the invention.
Figure 9 shows a random dimple distribution generated by a corresponding random principle according to an exemplary embodiment of the invention.
Figure 10A, Figure 10B show Penrose tilings as a basis for designing surface structures of golf balls according to an exemplary embodiment of the invention.
The illustration in the drawing is schematically. In different drawings, similar or identical elements are provided with the same reference signs.
Fig. 1 shows a cross-section of a portion of a golf ball 100 according to an exemplary embodiment of the invention.
The golf ball 100 is formed on the basis of a spherical body 101. A plurality of structures 102 are formed as indentations/dimples at specific surface portions or positions of the plastics body 101. As can be taken from Fig. 1, a depth may vary for the individual indentations or dimples 102, particularly some of the indentations have a first depth d₁ which is smaller than a second depth d₂. Furthermore, there is no periodicity of the arrangement of the dimples 102 along the surface 103 of the body 101.
Fig. 2 shows a golf ball 200 according to an exemplary embodiment of the invention comprising indentations 102 and protrusions 201.
As can be taken from Fig. 2, the protrusions 201 all have a spherical or round shape, whereas a part of the indentations 102 are spherical, and others are of rectangular cross-sectional shape. However, also the protrusions 201 may be rectangular, or may have any other shape, for instance a cylindrical shape.
Fig. 3 shows a cross-section of a part of a golf ball 300 according to an exemplary embodiment of the invention in which only protrusions 201 are foreseen, which differ from one another with regard to shape (rectangular, half-spherical, triangular) and which are arranged in an asymmetric and aperiodic manner along a surface 103 of the golf ball 300.
Fig. 4 shows a plan view of a spherical golf ball 400 according to an exemplary embodiment of the invention having an aperiodic, random arrangement of triangular, round and rectangular protrusions 201.
In case of a golf ball 500 according to an exemplary embodiment of the invention shown in Fig. 5, indentations 102 are arranged in a circular manner around a spherical surface of the golf ball 500 on the basis of the geometrical structures triangle, circle and rectangle.
Although some ordered structures are present, the arrangement of the dimples 102 is non-symmetric along the circles.
Fig. 6 shows a golf ball 600 according to an exemplary embodiment of the invention having dimples 102 which are provided in a completely random manner along a surface of the golf ball 600. Such a random structure may also be formed by directing a random beam of material removing particles or radiation onto a surface of the golf ball 600, thereby generating dimples 102 at random positions.
In the following, referring to Fig. 7A, Fig. 7B and Fig. 8, a Penrose tiling 700, 800 will be explained which can be performed and taken as a basis to spatially define portions of dimples provided on a golf ball.
The tiling 700 of a portion of the plane shown in Fig. 7A can be taken as a starting point for a distribution of dimples on a sphere (more precisely on a surface of a sphere).
It is possible to interpret Fig. 7A as a tiling of a "cap" of a sphere, wherein the radius r of the cap is the 0.7-fold of the radius R of the sphere. Such a cap can be obtained by a planar cut (parallel to the XY-plane) in a height of 0.7 of the radius of the sphere. Then, the surface (content) of the cap is somewhat larger than 1/8 of the surface of the sphere (in the case R=1: 1/2π versus 4π).
The distortion caused by the curvature of the sphere will be neglected in the following (towards an exterior position, the darts and kites would have to become slightly smaller for a compensation of this effect). It is possible to interpret the cap to be flattened for the following considerations.
When, for instance, the distribution of altogether 400 dimples is desired, almost 50 dimples have to be distributed on the cap shown in Fig. 7A.
In order to generate such a distribution, the pattern (or other patterns) can be taken as a body of rules.
For instance, it is possible to place in the centre of each kite a circular dimple with a size so that the circle is a third of the area of the kite. In the middle or centre of each dart, it is possible to correspondingly place a circular dimple, which has an area of 1/3 (or somewhat more) of the area of the dart. As a result, a distribution of differently sized circular dimples may be obtained.
However, in such a manner the amount or area of the dimples may be too large. In the example it is however only intended to explain the general principle.
As an alternative to the above-mentioned scenario, it is possible to use other geometrical figures instead of circular dimples, for instance regular n polygons (n = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13), or irregular polygons.
It is further possible to vary the position and the size of the dimples. Increasing the size may be desirable when the entire area of the indentations should be larger. With regard to the position, it may then be reasonable to deviate from the centres, in order to avoid a too large deviation of a symmetric configuration.
In order to obtain the desired number of approximately 400 dimples altogether, it is possible to visualize in the above-mentioned Fig. 7A one of the plurality of decagons (almost circular) comprising approximately 40 darts and kites. Then, the procedure may be as described above, by taking this decagon as a basis for tiling the above-introduced cap as a starting point. The result is approximately 320 dimples. The differently tiles decagons already show the multifold and the asymmetry of the distribution of the dimples.
Fig. 7B shows the Penrose tiling 700 of Fig. 7A, wherein portions which may serve as locations for asymmetrically arranged dimple structures 750 are hatched.
Fig. 8 shows a detailed view 800 of a portion of the Penrose tiling 700 of Fig. 7A.
Another way of obtaining less dimples is as follows: In Fig. 8, a plurality of darts 702 and kites 701 may be grouped to form a new basic modular unit. For instance, such a combination may generate a decagon formed from 5 kites, or one big kite formed from two small kites and a dart, or to a star, etc. Then, the further procedure is as described above. A dimple may be assigned to all or to a part of these designed modular units.
Instead of the described tiling, there are other possible aperiodic tiling schemes which can be used to generate new distributions. For this purpose, it is also possible to use more than two basic modular units, in order to have more than only two different dimples.
A plurality of modifications of the above-described algorithms is possible. The distributions may be performed on the entire sphere and may be adapted, which may be a little bit difficult to visualize. There are further solutions in which from the very beginning aperiodic and/or asymmetric tilings of a sphere (or other compact oriented areas) can be used.
However, the described Penrose tiling 700, 800 is only an example. The important aspect for the arrangement of the dimples is not the tiling, but the aperiodic distribution which may be realized with many algorithms. There are degrees of freedom with regard to tilings, since (significant or non-significant) gaps between dimples may occur on a non-planar finite area. The tiling is only one opportunity to generate such distributions, whereas other concepts are possible and are within the scope of protection of the present invention. For example, in the above-mentioned reference of Cockayne, Fig. 2 shows a plurality of patterns which can be used as well as a basis for a golf ball dimple design.
In the following, random distributions of dimples and methods for generating such random distributions will be explained in more detail.
As an example for an aperiodic distribution of dimples (on a sphere or on any other curved or non-curved surface), it is possible to generate random distributions.
Generally, random distributions of dimples may be appropriate in order to obtain a better flight behaviour of a flying object, like a golf ball. In the following, exemplary methods will be explained how such a random pattern can be generated.
According to one method, the example of a rectangle R of a plane will be used. For example, such a rectangle may be a square with a side length of 1. A predetermined number of dimples or structures to be arranged on this area (for instance 400 dimples) as well as a shape of the structures (for instance circles) and dimensions characterizing this shape (for instance a radius of 0.02) may be pre-determined or pre-defined. In accordance with these selected parameters, the structures will be distributed on the rectangle.
A sufficiently long sequence of random pairs p_n=(x_n,y_n) of numbers may be generated, which describe points on the rectangle R. Such a generation may be carried out using any conventional method. The pairs may be candidates for centres of the desired dimples. The potential dimples are the circles K_n around P_n with a radius of 0.02.
In connection with the method, the following procedure may be carried out:

1. If p₁ is located at a distance from the edge of R (the rectangle) larger than 0.03, then p₁ is the centre of the first dimple. When the distance is smaller or equal to 0.03, then p₁ is disapproved, and the procedure continues with p₂.
2. When a first centre p_n,1 and therefore the first dimple D₁=K_n,1 is found in this manner after at the most a (predetermined) finite number of disapprovals, then p_n,2 is determined in an analog manner. For this purpose, the distance condition may be applied to R\D₁ instead of R: When the next element p_n,1+1 of the sequence (p_n) is within R\D₁, and when the edge condition dist(p_n,1+1, Rand (R\D₁)) > 0.03 id fulfilled, then P_n,1+1 is the next centre of a dimple D₂=K_n,1+1). Otherwise, P_n,1+1 is disapproved, until this condition is fulfilled.
3. This is performed in an analog manner for D₃.
4. In this manner, a sequence of dimples D_n is generated by induction, wherein all the dimples are within R, are pairwise disjunctive and have a distance of at least 0.01 from one another and from the edge. After, for instance, 400 steps, the procedure is finished.

Fig. 9 shows the rectangle R 900 and a plurality of randomly distributed dimples 901 generated in accordance with the described method after (approximately) 36 steps. Many variants are possible as alternatives to the described procedure:

1. Instead of the radius 0.02, a radius of 0.025 or any other radius may be selected, and instead of the distance 0.03 it is possible to select another distance, like 0.04.
2. It is possible to allow different radii, to thereby obtain a distribution of dimples having different sizes. The determination which radius is the present radius within the algorithm may be determined in a random manner or in a predetermined ordered manner.
3. It is possible to select a number of different shapes (circles, squares, hexagons, etc.) and may proceed as described above.

The described method may be extended to or substituted by arbitrary (finite and/or compact) areas, particularly on the surface of a sphere, the 2-sphere.
Another generation principle is based on a random walk principle. Again, it is possible to exemplary generate 400 circular dimples having a radius of 0.02 on a square R with a length of 1.
On R, a random walk may be generated (for instance with a step width of 0.01). When the random walk meets itself for the first time, the first dimple D₁ may be placed on the loop generated by this procedure, for instance in a manner that a centre of the dimple is positioned in a centre of gravity of the loop. Again, a random walk may be continued in the complement R\D₁, and the procedure is analog as described above. By induction, a suitable distribution of dimples may be generated, wherein the dimples may contact each others, or not.
The algorithm may be designed so that the dimples, pairwise, do not fall below a minimum distance from one another.
A large number of varieties is possible and can be implemented on compact areas and surfaces, particularly on golf balls.
According to an exemplary embodiment, it is possible to determine the shape of the respective dimple based on the shape of the respective loop. However, a predetermined maximum size should not be exceeded.
Another generation principle may be based on a Brownian motion model.
Further generation principles may use:

a) Percolation models
b) Exact models from statistical physics (Ising, Potts, and generalisations)
c) Stochastic Loewner Evolution.

These algorithms may generate relatively complex but suitable additional structures.
Fig. 10A shows a Penrose tiling 1000 which can be performed and taken as a basis to spatially define portions of dimples provided on a golf ball.
The tiling 1000 is formed based on three different tiles, namely squares 1001, hexagons 1002, and rhombuses 1003.
Fig. 10B shows the Penrose tiling 1000 of Fig. 10A, wherein (a part of the) portions which may serve as locations for asymmetrically arranged dimple structures 1050 are hatched.
It should be noted that the term "comprising" does not exclude other elements or features and the "a" or "an" does not exclude a plurality. Also elements described in association with different embodiments may be combined.
It should also be noted that reference signs in the claims shall not be construed as limiting the scope of the claims.

Claims

A flyable object (100, 200, 300, 400, 500, 600), comprising
a body (101);
a plurality of structures (102, 201) formed on and/or in the body (101) in a non-periodic manner.
The object (100, 200, 300, 400, 500, 600) of claim 1,
wherein the body (101) has an essentially spherical shape.
The object (100, 200, 300, 400, 500, 600) of claim 1 or 2,
wherein at least a part of the plurality of structures (102, 201) are dimples formed to extend into the body (101).
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 3,
wherein at least a part of the plurality of structures (102, 201) are protrusions formed to extend out of the body (101).
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 4,
wherein the plurality of structures (102, 201) are formed on and/or in the body (101) in an asymmetric manner.
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 5,
wherein the plurality of structures (102, 201) are formed on and/or in the body (101) in one manner of the group consisting of a random manner and a pseudo-random manner.
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 6,
wherein the plurality of structures (102, 201) are positioned on a surface of the body (101) based on similar patterns of different sizes.
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 6,
wherein the plurality of structures (102, 201) are positioned on a surface of the body (101) based on a pattern in accordance with a Penrose tiling (700, 800).
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 8,
wherein the plurality of structures (102, 201) are positioned based on a virtual tiling of a surface of the body (101) performed on the basis of at least two modular units (701, 702), wherein a defined portion or position of at least one of the at least two modular units (701, 702) serves as a portion or position for forming at least a part of the plurality of structures (102,201).
The object (100, 200, 300, 400, 500, 600) of claim 9,
wherein the at least two modular units comprise at least one of the group consisting of a kite (701), a dart (702), and a combination of a kite (701) and a dart (702).
The object (100, 200, 300, 400, 500, 600) of claim 9 or 10,
wherein the plurality of structures (102, 201) are positioned in or around centers of at least a part of the at least two modular units (701, 702).
The object (100, 200, 300, 400, 500, 600) of any one of claims 9 to 11,
wherein the plurality of structures (102, 201) are positioned in at least a part of the at least two modular units (701, 702) in a manner to fill a predetermined area portion of the respective modular unit (701, 702).
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 12,
wherein the plurality of structures (102, 201) are formed on and/or in the body (101) in accordance with a predetermined ordering scheme.
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 13,
wherein a surface of the body (101) and/or of the plurality of structures (102, 201) has a microstructure in accordance with the Lotus effect.
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 14,
wherein different ones of the plurality of structures (102, 201) differ with regard to at least one property of the group consisting of a size of the respective structure (102, 201) on a surface of the body (101), a shape of the respective structure (102, 201) on a surface of the body (101), a depth of the respective structure (102, 201) in a direction essentially perpendicular to a surface of the body (101), and a shape of the respective structure (102, 201) essentially perpendicular to a surface of the body (101).
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 15,
wherein at least a part of the plurality of structures (102, 201) is shaped at a surface of the body (101) in at least one manner of the group consisting of a round shape, an oval shape, a triangle shape, a rectangular shape, a pentagonal shape, a hexagonal shape, and a polygonal shape.
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 16,
configured as one of the group consisting of a golf ball, a mini golf ball, a tennis ball, a table tennis ball, a squash ball, a soccer ball, a football, a basketball, a baseball, a volley ball, a bullet, a vehicle, an aircraft, a car, and a ship.
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 17,
wherein the plurality of structures (102, 201) have dimensions in the range between essentially 100 µm and essentially 1 cm, particularly in the range between essentially 0.5 mm and essentially 4 mm.
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 18,
wherein the body (101) has dimensions in the range between essentially 1 cm and essentially 50 cm, particularly in the range between essentially 3 cm and essentially 30 cm.
The object (100, 200, 300, 400, 500, 600) of any one of claims 1 to 19,
wherein the plurality of structures (102, 201) are aerodynamically effective structures.
A method of manufacturing a flyable object (100, 200, 300, 400, 500, 600), the method comprising
forming a plurality of structures (102, 201) on and/or in a body (101) of the flyable object (100, 200, 300, 400, 500, 600) in a non-periodic manner.
A method of designing a flyable object (100, 200, 300, 400, 500, 600), the method comprising
defining a pattern for forming a plurality of structures (102, 201) on and/or in a body (101) of the flyable object (100, 200, 300, 400, 500, 600) in a non-periodic manner to thereby match a fluid dynamic property of the designed flyable object (100, 200, 300, 400, 500, 600) with a predetermined value of the fluid dynamic property.
The method of claim 22,
comprising forming dimples in a golf ball in a non-periodic manner to thereby limit a maximum stroke width of the golf ball.