WO2009051793A1

WO2009051793A1 - Structures

Info

Publication number: WO2009051793A1
Application number: PCT/US2008/011867
Authority: WO
Inventors: Jayden David Harman
Original assignee: Pax Scientific, Inc.
Priority date: 2007-10-18
Filing date: 2008-10-17
Publication date: 2009-04-23
Also published as: WO2009051790A1

Abstract

A structure (10) subjected to stress wherein the structure (10) comprises a member upon which the stress is imposed wherein the stress within the member is distributed and wherein the configuration of at least a substantial portion of the member has curvature which conforms to a logarithmic curve to cause the stress to be distributed substantially evenly.

Description

Structures

Field of the Invention

The present invention relates to load bearing physical elements. The invention identifies a means to provide an element having at least one of its structural characteristics optimized or at least improved in comparison with a comparable conventional element. The improved characteristic may be drawn from the group including strength, shape, weight, space, stiffness and material usage. Frequently, economic benefits will also result from use of the invention.

The invention is described herein by reference to its use in respect to structures or mechanical components. However, the invention is more broadly applicable to any situation wherein a body experiences a stress as a result of the application of a' force. Hereinafter within this specification the term structure will be used to denote any such body. The term will be used to denote both a single member and a body comprising a group of sub-members which in composite form a member according to the invention.

Background Art

Structures have conventionally been designed according to perceived economies on the basis of simplicity of design and/or construction. Such perceptions have frequently adopted design parameters that are wasteful of material and wherein physical characteristics are selected that are far from an optimum leading to an overall design of a complete body that is inefficient or weak or overly heavy or subject to failure or poor strength to weight ratio or other problems. The perceived economy of initial simplicity is often overridden by a subsequent need to provide excessive support or other fix to the problem due to the inappropriate initial design. As an example, the use of a simple uniform beam or column may result in excessive weight or point loadings that require an excessively strong support. The structure required to support the support itself needs to be designed beyond fundamental requirements as a result, leading to further excess and wastage.

While it is known that efficiencies can be made in the design of structures where stress is distributed through a structure, the principles which govern such efficient design have eluded designers thus far.

Disclosure of the Invention

Accordingly, the invention resides in a structure subjected to stress wherein the structure comprises a member upon which the stress is imposed wherein the stress within the member is distributed and wherein the configuration of at least a substantial portion of the member has curvature which conforms to a logarithmic curve to cause the stress to be distributed substantially evenly.

According to a preferred feature of the invention, the radius of the logarithmic curve unfolds at a constant order of growth when measured at equiangular radii.

According to a preferred feature of the invention, the stress within the member is distributed substantially uniformly as a result of the shape of the member.

According to a preferred embodiment, the curvature of the configuration of the member is transverse to a central axis.

According to a further preferred feature of the invention the curvature of the profile of the member can be in the direction parallel to the central axis.

According to a further preferred feature of the invention the curvature of the configuration of the member is both transverse to the central axis and is parallel to the direction of the central axis to define a three dimensional surface conforming to the golden section

According to a preferred embodiment, the member comprises a form about a central axis about which the structure radiates where in the form has a configuration of logarithmic curve substantially conforming to the golden section.

According to a preferred embodiment, the member is provided from material of substantially constant thickness.

According to a preferred embodiment, the cross sectional area of the member varies logarithmically. According to a preferred embodiment, the cross sectional area of the member varies logarithmically in substantial conformity to the golden ratio.

According to a preferred embodiment, the member has a form generally conforming to the form of an egg. According to a preferred embodiment, the member has a form providing a shape generally conforming to the streamlines of a vortex. According to a preferred embodiment, the member has a form conforming to the form of a whorl.

According to a preferred embodiment, the member has a configuration conforming to the internal configuration of a shell of one of the phylum Mollusca, class Gastropoda or Cephalopoda.

According to particular forms of the invention the configuration conforms to the internal configuration of shells selected from the genera Volutidea, Argonauta, Nautilus, Conidea or Turbinidea.

According to a preferred embodiment, the structure has a configuration conforming to the external configuration of a shell of the aforementioned phylum Mollusca. According to a preferred embodiment, the structure comprises an elongate member subject to compressive loading. According to a preferred embodiment, the structure comprises an elongate member subject to tensile loading.

According to a preferred embodiment, the member comprises a blade of a rotor. According to a preferred embodiment, the blade is of substantially uniform thickness.

Accordingly, the invention resides in a hull of a water craft adapted to float on a body of water for traversal thereof, at least a substantial proportion of the hull being formed from a material of substantially uniform thickness wherein the material has curvature which conforms to a logarithmic curve.

It is a preferred feature that the radius of the logarithmic curve unfolds at a constant order of growth when measured at equiangular radii.

According to a preferred feature of the invention, the hull is formed without a frame for stiffening and/or strengthening the hull.

According to a further aspect the invention resides in a water craft comprising a hull as previously described.

According to a preferred feature of the invention, the water craft is provided with a cowling overlying the bow section of the hull, a substantial portion of the cowling taking the form of a compound curvature conforming with an equiangular spiral. According to a preferred embodiment, the curvature of the substantial portion of the cowling conforms with the Golden Section.

The invention will be more fully understood in the light of the following description of several specific embodiments. Brief Description of the Drawings

The description is made with reference to the accompanying drawings, of which: Figure 1 illustrates the form of the Golden Section;

Figure 2 is an elevation view of a structure according to the first embodiment;

Figure 3 is a elevation view of a structure according to the second embodiment;

Figure 4 is an elevation view of a structure according to the third embodiment;

Figure 5 is an isometric view of a fan according to the fourth embodiment;

Figure 6 is an isometric view of a tensile structure according to the fifth embodiment;

Figure 7 is an upper rear isometric of the sixth embodiment;

Figure 8 is an upper front isometric of the sixth embodiment;

Figure 9 is a lower front isometric of the sixth embodiment;

Figure 10 is a top plan view of the sixth embodiment;

Figure 11 is a lateral cross-section of the sixth embodiment through section line A-A as indicated on Figure 10;

Figure 12 is a lateral cross-section of the sixth embodiment through section line B-B as indicated on Figure 10;

Figure 13 is an upper front isometric of the seventh embodiment. Detailed Description of Specific Embodiments

Each of the embodiments comprises a structure subject to loading by one or more forces and is directed to distributing the stress imposed in the structure by the loading substantially evenly through the structure. In general, the shapes of the embodiments have been derived from shapes found in Nature which has evolved efficient and effective load distributing shapes over millions or billions of years.

It is found that the shapes used by Nature to distribute stress apply a common rule of design although the shapes that result may be extremely diverse. The shapes of the structures that result are found to have a curved form and it is further found that these forms have a curvature which conforms to an equiangular logarithmic curve. It is therefore a common feature of the shapes of the embodiments that they comprise a member which takes a shape which substantially conforms to a logarithmic curve. It is further found that Nature has evolved such shapes to be optimised when the logarithmic curve that is applied conforms to the celebrated Golden Section, that is . It is therefore a preferred feature of the embodiments that the said logarithmic curve of the member of the structure conforms to the Golden Section. The intention of the invention is to provide a structure which provides improved stress transfer by utilizing structures that have full or partial adherence to Nature's equiangular, logarithmic form. In general, it has been found that the optimum characteristics are achieved for a particular structure where the logarithmic curve substantially conforms to the Golden Section. In addition, it has been found that, where a structure conforms to these characteristics of the invention, such a structure distributes load and is able to distribute an impact loading substantially uniformly thorough the structure in a manner better than that achieved by structures of alternative shapes. The distribution of the load results in greater strength to weight or thickness rations and greater impact strength than is achieved in alternative structures. In Nature there are many examples of the use of such shapes. A hen's egg is often referred to as nature's strongest shape. It is also extremely economical in use of materials. Every part of a hen's egg, is part of a compound curve conforming to the golden section. Seashells, skeletons and animal horns also exhibit great strength to weight ratios. Additionally, these shapes are highly streamlined. An important benefit for living organisms where propulsion energy conservation is paramount. Seashells not only benefit from this Streamline Principle, they also have their centre of gravity optimally low, perfectly situated for their environment by protecting them from the forces of passing waves and currents. As an antelope's horns grow in spirals, the weight is always focused on the same point of the skull, thereby preventing the animal from being lopsided.

The characteristics of the Golden Section are illustrated in Figure 1 which illustrates the unfolding of the spiral curve according to the Golden Section. As the spiral unfolds the order of growth of the radius of the curve which is measured at equiangular radii (eg E, F, G, H, I and J) is constant. This can be illustrated from the triangular representation of each radius between each sequence which corresponds to the formula of a:b = b:a+b which conforms to the Fibonacci ratio of approximately 1 :1.618 and which is consistent through out the curve. An analysis of the Golden Section shows that it comprises a logarithmic curve wherein the radius of the logarithmic curve unfolds at a constant order of growth when measured at equiangular radii.

It is a further preferred characteristic of the embodiments that not only do the X and Y axis conform to Golden Section geometry, but also the Z axis or depth of the member conforms, to the Golden Section in three dimensions.

In the first embodiment, as shown in Figures 2, the structure comprises a member 10 having an apex 11 and a base 12. The structure is provided with ridges or profiles 13. All curves on the structure are compound curves designed, in every respect , in accordance with golden section progression. By tapering the structure, the minimum weight is incurred to obtain the desired strength. Loading at is distributed evenly throughout the entire structure.

In the second embodiment , as shown in Figure 3, a similar structure is provided but with larger ridges 13 for increased strength. The embodiment is particularly suited for use as a column for a structure subject wind loading or water flow around it. Not only is strength increased in this but wind loading, or in the case of a bridge pilings, water loading, is minimized.

The third embodiment as shown in Figure 4 is a similar structure to that of the first and second embodiments with two larger ridges 13 and 14 symmetrically opposed 180 degrees to each other. The structures may have one or multiple ridges dependent on user requirement.

The embodiments may be adapted significantly. For instance, the third embodiment may be provided with a much larger continuation of the ridge 3 following the same compound golden section curves. As the ridge is expanded in strict accordance with the golden section, it curls back on itself forming a shape somewhat similar to a seashell or an open sided cone.

Each of the above embodiments may be made from a wide variety of materials including, but not limited to concrete, metal, paper products and plastics, and from a variety of production methods according to the application, including to name but two, extruding and casting. The advantageous stress distribution and other benefits that result are not limited to a particular material.

As a result the wall thickness and material content can be minimized. As the material content and thus the weight is minimized, the strength to weight ratio is maximized. The fourth embodiment as shown in Figure 5 comprises a rotor such as a fan having a plurality of blades adapted to interact with fluid such as air. Fan blades, particularly for larger sized fans are usually made from sheet metal such as steel having a uniform thickness which is pressed into shape. The blades may also be made from plastics or other material and the comments below are equally applicable. Common problems with such blades are that they are subject to distortion during operation and also may flutter, that is the blades may establish a resonant oscillation. Distortion results in the fan not performing in accordance with the intended design, while flutter induces resonance and excessive noise and also affects performance. Where such problems are an issue, it is common practice by designs to incorporate reinforcement ribs into the blades. Such reinforcement ribs usually take the form of pressed or moulded elongate indentations in the blades. These indentations may be oriented radially, or arced or a combination of both. While such reinforcement ribs may reduce or overcome the distortion and/or flutter, by their nature, they tend to induce turbulence in the fluid flow over the blade. The turbulence decreases performance or efficiency of the blade and may result in noise, also.

An alternative means used to overcome the problem is to increase the thickness of the blade to thereby increase stiffness, but that solution raises it own problems. Thicker material increases the cost of the blade and also adds weight. The additional weight may require that the strength of bearings be increased, thereby further increasing cost.

According to the embodiment, the fan blades are formed as structures in accordance with the principles described above. In the embodiment, the blades 31 are formed having substantially ^■ uniform thickness. They have a configuration having a curvature substantially conforming to an equiangular logarithmic ratio. In the embodiment, that ratio is selected to conform to the Golden Section to optimize the stiffness for the particular blade having material of a particular thickness. As a result, the stiffness to weight ratio of the blade is maximized and thus the blade thickness can be minimized. At the same time the blade can be provided with a sufficient inherent stiffness that it does not require ancillary stiffening in the form of ribs. As a result, surface curvature of the blade 31 is uninterrupted and therefore turbulence is minimized. Performance is thereby maximized and noise minimized, while cost is minimized.

In a fifth embodiment, as shown in Figure 6, a structure is provided which is substantially egg shaped. This structure 40 has been devised for tensile loading. The structure 40 of this embodiment has a generally egg shaped appearance. The ends of the egg structure are formed with an end pieces 41 adapted to be secured by a generally conventional fixing 42, but which provides and expanding rim 43 to transmit the stress into wall of the egg shaped member 40. In this way, the point stress of the fixing 42 is distributed substantially evenly into the egg shaped member 40. The egg shaped member 40 distributes the stress evenly through its length due to its Golden Section profile. The arrangement enables the strength to weight ratio to be maximized.

In a sixth embodiment as shown in Figures 7 to 12 a structure is provided in the form of a boat.

The boat 111 comprises a hull 112, a cowling covering the bow section 115 of the hull to provide a foredeck 114, and a pair of flotation pontoons 116 disposed towards the rear and at each side of the hull 112. A windscreen 117 is provided at the rear of the foredeck in conventional manner.

The hull 112 is formed from a suitable material as is discussed below, in the first embodiment, the material having a generally uniform thickness. The hull 111 has a bow section 115, a stern 118 and an intermediate portion 119 between the bow 115 and the stern 118. The hull 111 is formed to provide an upper peripheral edge and an external surface in contact with the water having a three dimensional, compound curvature. The bow section 115 extends forwardly and upwardly from the intermediate portion 119 in a compound curve that leads to a forward-most point 121 at the peripheral edge. This forward-most point is merely a point on the curved peripheral edge and does not take a pointed form. Such a form could be taken if desired for aesthetic reasons but is not necessary, functionally.

The intermediate portion 119 extends with a slight curvature towards the stern 118, and is also curved towards the sides. The stern 118 acts to terminate the intermediate portion 119 and provide a transom 122 upstanding from the hull 112 to provide a support for an outboard motor. Alternatively, a jet-type motor can be used.

It is a feature of the embodiments that at least a substantial proportion of the hull is formed from a material of substantially uniform thickness wherein the material has curvature which conforms to a logarithmic curve. It is a preferred feature that the radius of the logarithmic curve unfolds at a constant order of growth when measured at equiangular radii, that is, that the curvature conforms to the Golden Section. As a result of this feature, it is a characteristic of the hull that it does not have a central, vee-shaped keel line. As will be discussed below, this compound curve conforming generally to an equiangular logarithmic curve provides the craft with improved characteristics of strength and stiffness.

The flotation pontoons 116 are engaged with the sides 123 of the hull to form the sides of the boat. The flotation pontoons 116 have a bulbous or pod shaped appearance as may be appreciated from the drawings. The lateral cross-sectional form of each pontoon is approximately circular throughout the length of the pontoon but the diameter varies from an apex 124 at the rear to a maximum 125 a little forwardly of the transom and receding to a small diameter somewhat forwardly of the centre of the hull. In the first embodiment, the forward end 126 of each pontoon flows forward integrally to form a rim 127 for the peripheral edge of the bow, thereby providing the first embodiment with a smooth, curved, streamlined appearance from the bow to the rear ends 124 of the pontoons. The pontoons are buoyant to provide the boat with lateral and longitudinal stability and in the first embodiment are formed from a floatation material such as a foamed plasties material. In adaptations of the first embodiment, the pontoons may be hollow or even inflatable to provide the form described. As a large amount of buoyancy is positioned behind the engine, the boat will not tip over backwards and will not flood from waves approaching from behind.

The form of the pontoons is configured to be coordinated with the compound curve of the hull through the length of contact with the hull, as shown by cross-sections in Figures 111 and 112. This coordinated formation provides the hull with an extremely streamlined and efficient form throughout its length, which minimizes turbulence. Nevertheless, the pontoons provide the boat with very great lateral stability and also longitudinal stability because of their extension behind the stern of the hull. The channel between the hull and pontoons entrains air to create additional buoyancy and further reduce drag.

The advantages of the hull arise from the form adopted for the hull, being a compound curve substantially conforming to an equiangular logarithmic curve, that curve preferably conforming to the Golden Section. The inventor has recognized that such forms provide a most advantageous structure. Firstly, that structures taking such a form have increased strength compared with other forms. Secondly, such structures facilitate the optimisation of the position of the centre of gravity.

The intention of the invention is to provide a boat structure which provides improved stress transfer by utilizing a structure that has full or partial adherence to equiangular, logarithmic form. In general, it has been found that the optimum characteristics are achieved for a particular structure where the equiangular logarithmic curve substantially conforms to the Golden Section. In addition, it has been found that, where a structure conforms to these characteristics of the invention, such a structure distributes load and is able to distribute an impact loading substantially uniformly thorough the structure in a manner better than that achieved by structures of alternative shapes. This is especially important for boats when they impact waves or strike obstacles. The distribution of the load results in greater strength to weight or thickness ratios and greater impact strength than is achieved in alternative structures. In particular, as in the first embodiment, this strength is achieved without the need for an internal frame and without the need for excessive use of material. This reduces overall weight which in turn reduces the potentially destructive forces of impact.

Thus, the application of such shapes to a boat hull provides a means of optimizing the strength of the hull, without use of an internal frame but with minimum material usage and therefore weight. This strength of the boat can be enhanced if the foredeck 114 also is formed with a curvature conforming to an equiangular logarithmic spiral, preferably conforming to the Golden Section. In the embodiment this is done, thereby not only providing protection to the bow from water spray but also increasing the strength at the bow, the region requiring greatest impact strength. All this is achieved without the need of an internal frame, thereby reducing, weight and cost. Where point source load are to be experienced, such as at anchor rope tethers and mountings for engine and the like they are accommodated by providing rigidising or reinforcing materials within and enclosed by outer foam to thereby progressively distribute the loading into the hull.

In the seventh embodiment, the foredeck 114 is formed as a separate piece from the hull 112, for assembly after forming. This arrangement not only enables the hull to be manufactured more easily, but also allows a group of hulls to be stacked within each other for transportation, thereby substantially simplifying manufacture of the hull and reducing transportation costs. A group of foredecks can also be stacked together. Optionally, the windscreen 117 may be shipped independently from the foredeck for assembly at the delivery point. The foredeck 114 is secured to the hull 112 by one of a range of by one of a range of fixing means well known to those skilled in the art. The hull 112 is formed from a suitable material as is discussed below, in the first embodiment, the material having a generally uniform thickness. The hull 111 has a bow section 115, a stern 118 and an intermediate portion 119 between the bow 115 and the stern 118. The hull 111 is formed to provide an upper peripheral edge and an external surface in contact with the water having a three dimensional, compound curvature. The bow section 115 extends forwardly and upwardly from the intermediate portion 19 in a compound curve that leads to a forward-most point 121 at the peripheral edge. As best shown in the bottom plan view, Figure 7, this forward-most point is merely a point on the curved peripheral edge and does not take a pointed form. Such a form could be taken if desired for aesthetic reasons but is not necessary, functionally.

A seventh embodiment illustrates one adaptation of the boat of the sixth embodiment which includes the inventive features of the sixth embodiment. The seventh embodiment is described with reference to Figure 13. The seventh embodiment includes many features which are substantially the same as those of the sixth embodiment and therefore in the drawings, like numerals are used to depict like features. The drawings provided are directed to identifying features that differ from those of the first embodiment, and therefore not all views are shown.

As shown in the drawings, the seventh embodiment comprises a boat 211 having a hull 212. The boat 211 comprises a hull 212 having a hull floor 217 and a cowling covering the bow section 115 of the hull to provide a foredeck 114 in the same manner as the first embodiment. The chief difference between the seventh embodiment and the sixth embodiment is that, instead of being provided with pontoons 116, the hull 212 of the second embodiment is formed with pontoon-like formations 216 which are integral with the hull 212. Externally, the appearance of the hull 212 is almost identical to that of the sixth embodiment, but instead of having the inner wall of the pontoons extending within the cockpit area, these are removed. The hull floor is upturned at the sides to form the external wall of the pontoon-like formation 216. While there are no longer enclosed pontoons to provide floatation, the rear portion 232 of the pontoon formations 216 may be filled with floatation material as necessary. It can be seen that the seventh embodiment maintains all the inventive advantages of the sixth embodiment while providing additional space in the cockpit.

As mentioned above, the use of a hull having a configuration conforming to an equiangular logarithmic curve and preferably conforming to the Golden Section not only provides the vessel with increased strength, but also functions to provide an external surface which has a curvature which conforms to an equiangular logarithmic curve and preferably conforms to the Golden Section. It is found that such a surface is more effective at providing a streamlined form which reduces drag by decreasing turbulence. The embodiments serves to, in the greater part, enable water to move in its naturally preferred way. As the boat is propelled through the water, the water is disturbed to some degree. However, because the hull surface follows the form of an equiangular logarithmic curve, preferably conforming to the Golden Section, the water is caused to be displaced in a more natural manner because the surface of the hull acts upon the water in a manner to cause it to flow in its naturally preferred way. The inefficiencies created through turbulence and friction, and thus the drag, which are normally found in a boat hull are significantly reduced. Previously developed technologies have generally been less compliant with natural water flow tendencies. The means of attachment of the pontoons of the first embodiment to the sides of the hull to provide a continuously curved surface between the hull and the pontoons also facilitates efficient passage of the vessel through the water.

It can be seen that a boat constructed in accordance with the embodiments enables a hull to be provided that is lighter than is conventionally the case. This will lead to a highly cost effective boat design when constructed from conventional materials such as wood, aluminium, fibreglass or polycarbonate. Because of its light weight, a small propulsion plant provides exceptional performance at very low fuel consumption, yet the pontoons and optimized centre of gravity ensure high stability.

It should be appreciated that the scope of the present invention need not be limited to the particular scope described above.

Throughout the specification, unless the context requires otherwise, the word "comprise" or variations such as "comprises" or "comprising", will be understood to imply the inclusion of a stated integer or group of integers but not the exclusion of any other integer or group of integers.

Claims

I claim

1. A structure subjected to stress wherein the structure comprises a member upon which the stress is imposed wherein the stress within the member is distributed and wherein the configuration of at least a substantial portion of the member has curvature which conforms to a logarithmic curve to cause the stress to be distributed substantially evenly.

2. A structure as claimed at claim 1 wherein the radius of the logarithmic curve unfolds at a constant order of growth when measured at equiangular radii.

3. A structure as claimed at claim 1 or claim 2 wherein the stress within the member is distributed substantially uniformly as a result of the shape of the member.

4. A structure as claimed at any one of claims 1 to 3 wherein the curvature of the configuration of the member is transverse to a central axis.

5. A structure as claimed at claim 4 wherein the curvature of the profile of the member can be in the direction parallel to the central axis.

6. A structure as claimed at claim 4 or claim 5 wherein the curvature of the configuration of the member is both transverse to the central axis and is parallel to the direction of the central axis to define a three dimensional surface conforming to the golden section

7. A structure as claimed at any one of claims 1 to 3 wherein the member comprises a form about a central axis about which the structure radiates where in the form has a configuration of logarithmic curve substantially conforming to the golden section.

8. A structure as claimed at any one of the previous claims wherein the member is provided from material of substantially constant thickness.

9. A structure as claimed at claim 8 wherein the cross sectional area of the member varies logarithmically.

10. A structure as claimed at claim 9 wherein the cross sectional area of the member varies logarithmically in substantial conformity to the golden ratio.

11. A structure as claimed at claim 9 or claim 10 wherein the member has a form providing a shape generally conforming to the streamlines of a vortex.

12. A structure as claimed at claim 9 or claim 10 wherein the member has a form conforming to the form of a whorl.

13. A structure as claimed at claim 9 or claim 10 wherein the member has a form generally conforming to the form of an egg.

14. A structure as claimed at any one of claims 1 to 3 wherein the member has a configuration conforming to the internal configuration of a shell of one of the phylum Mollusca, class Gastropoda or Cephalopoda.

15. A structure as claimed at any one of claims 1 to 3 wherein the configuration conforms to the internal configuration of shells selected from the genera Volutidea, Argonauta, Nautilus, Conidea or Turbinidea.

16. A structure as claimed at any one of claims 1 to 3 wherein the structure has a configuration conforming to the external configuration of a shell of the phylum

Mollusca.

17. A structure as claimed at any one of claims 1 to 12 wherein the member is elongate and subject to compressive loading.

18. A structure as claimed at any one of claims 1 to 12 wherein the member is elongate and subject to tensile loading.

19. A structure as claimed at any one of claims 1 to 12 wherein the member comprises a blade of a rotor.

20. A structure as claimed at claim 19 wherein the blade is of substantially uniform thickness.

21.A hull of a water craft adapted to float on a body of water for traversal thereof, at least a substantial proportion of the hull being formed from a material of substantially uniform thickness wherein the material has curvature which conforms to a logarithmic curve to thereby distribute stresses evenly within the hull.

22.A hull of a water craft as claimed at claim 21 wherein the radius of the logarithmic curve unfolds at a constant order of growth when measured at equiangular radii.

23.A hull of a water craft as claimed at claim 21 wherein the hull is formed without a frame for stiffening and/or strengthening the hull.

24. A water craft comprising a hull as claimed in any one of claims 21 to 23.

25. A water craft as claimed at claim 24 wherein the water craft is provided with a cowling overlying the bow section of the hull, a substantial portion of the cowling taking the form of a compound curvature conforming with an equiangular spiral.

26.A water craft as claimed at claim 25 wherein the curvature of the substantial portion of the cowling conforms with the Golden Section.