Flexible shaft for hockey stick
By designing a multi-section structure carbon fiber composite ice hockey stick shaft, the existing ice hockey sticks are solved inadequate leverage and structural vulnerability in modern competitions, achieving more efficient energy storage and release, as well as a stronger structural design.
Patent Information
- Application Number
- CN202380050635.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2022-09-13
- Filing Date
- 2023-09-12
- Publication Date
- 2025-03-07
AI Technical Summary
Existing hockey sticks are difficult to meet the need for players to keep their strikes at a higher position when hitting the ball in a fast-moving modern game, resulting in insufficient leverage during fast hitting and the stick structure is prone to damage due to excessive bending and breakage.
A new type of hockey club shaft is designed, adopting a multi-sectional structure along its longitudinal axis, including upper, middle and lower sections, each with a different cross-sectional shape and wall thickness, ensuring that the shaft has a uniform wall thickness and mass distribution throughout the length through the use of carbon fiber composites.
The design allows players to exert force more easily in modern game styles and store and release more energy when hitting, providing a more ergonomic and lightweight design that reduces the risk of excessive bending and breaking of the stick in the hand.
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Figure CN119585023A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates generally to the field of ice hockey equipment and, more particularly, to ice hockey sticks. Background Art
[0002] Traditionally, ice hockey sticks have been made from wood. These solid wood sticks often lacked durability and sufficient rigidity, among other limitations. In an attempt to address these shortcomings, ice hockey stick construction has shifted from using solid wood for the shaft to using laminated wood, aluminum, and eventually carbon fiber composites.
[0003] Carbon fiber composites can reduce the weight of a stick. For example, a solid wood hockey stick might weigh between 650g and 700g, while a carbon fiber stick of the same size might weigh less than 400g. For players, having a lighter stick is advantageous because it can help with more agility and faster play. Carbon fiber composites can also increase the strength of the stick and allow for more shape changes along the shaft compared to a solid wood stick.
[0004] For example, due to common woodworking practices (and limitations), traditional wood sticks often have rectangular cross-sections with square corners. Carbon fiber composites allow for variations in geometry along the length of the shaft. This has led to the development of shafts with more rounded, asymmetrical shapes, which are considered more ergonomic than rectangular shafts with square corners.
[0005] Evolving technology has led to the development of more flexible shafts with engineered bend points that allow these shafts to store and release energy more efficiently than traditional ice hockey sticks. Areas of increased rigidity relative to the rest of the shaft are often created by adding additional layers of material to specific areas of the hockey stick. However, adding material to create rigidity can result in the adjacent unsupplemented sections being relatively thin. As a result, such unsupplemented shaft sections can result in structural deficiencies. Since the unsupplemented area is relatively soft compared to the stiffer, supplemented sections, more strain occurs in that area and it is more susceptible to damage and fracture.
[0006] In addition to changes in hockey stick construction, the mechanics of hitting the ball have also evolved over time, especially in the past two decades. Due to the increased speed of the game, players no longer have as much time as they once did to use a long swing and traditional swing shot. Specifically, the typical player is accustomed to holding the stick with their top hand (dominant hand) near the end or handle end during skating, and their bottom hand is placed below the top hand along the shaft. Players are trained to shift their bottom hand down to the midpoint area of the shaft when preparing to hit the ball. This practice increases the power and accuracy of the shot, but moving the bottom hand is time consuming in fast-moving games.
[0007] In the modern game, due to the increased speed of the game, players are now trained to keep their bottom hand higher on the stick shaft when striking the puck. This allows for a shorter, quicker release shot from a skating hand position. While this releases the puck quicker, the higher hand position may provide less leverage on the stick blade and puck. No commercially available stick has been designed to perform optimally in this new style of play.
[0008] Therefore, despite the progress made to date in the development of ice hockey sticks, there is still room for improvement in addressing the above-mentioned problems and shortcomings of the prior art. Summary of the invention
[0009] It is an object of the present invention to obviate or mitigate at least one of the above-mentioned disadvantages of the prior art.
[0010] Another object of the present invention is to provide a new hockey stick shaft.
[0011] Thus, in one aspect thereof, the present invention provides a hockey stick shaft comprising, along its longitudinal axis: (a) an upper section comprising four walls, each of which comprises a cross-sectional convex surface; (b) a middle section comprising four walls, three of which comprise a cross-sectional convex surface and one of which comprises a cross-sectional concave surface; and (c) a lower section comprising four walls, each of which comprises a cross-sectional convex surface.
[0012] In another aspect, the present invention provides a hockey stick shaft that is hollow and preferably formed of a carbon fiber composite material consisting of carbon fibers and a resin such as epoxy. However, other materials such as polyurethane, acrylic, and other forms of resins may be used. Likewise, one or more layers of carbon fibers may be replaced with other technical fibers such as aramid, PBO, etc. This construction allows the stick to be lightweight and effective for use in fast play.
[0013] In yet another aspect, the present invention is directed to a hockey stick shaft having no sharp or right angles along the length of the shaft, thereby improving the ergonomic comfort when gripping the shaft during intense play.
[0014] In yet another aspect, the present invention is directed to a hockey stick shaft formed from a sheet of carbon fiber composite material wrapped around an expandable membrane that is used to press the material outwardly into an inner cavity of a mold consisting of a shape without sharp corners or right angles. This also eliminates the need for the fibers to have sharp corners, thereby creating a stronger fiber-based structure.
[0015] In yet another aspect, the invention relates to a hockey stick shaft having at least three sections: a lower section terminating at the heel of the blade, a middle section connected to the lower section, and an upper section terminating at the tip or handle end of the stick, characterized in that the carbon fiber composite material along at least the lower section has a uniform wall thickness. In other words, the lower section has no areas where additional material has been added to increase its strength, and the lower section also has no areas where material has been removed to make the lower section more flexible. This makes the structure of the lower section stronger, reducing the risk of excessive bending and breaking.
[0016] In yet another aspect, the present invention is directed to a hockey stick shaft having at least five sections: a lower section terminating at the heel of the blade, a middle section connected to the lower section, and an upper section terminating at the tip or handle end of the stick, with transition zones between the lower section and the middle section and between the middle section and the upper section, and further characterized by a carbon fiber composite material having a uniform wall thickness along at least the lower region, the transition zone between the lower section and the middle section, and the middle section. The same benefits of increased strength along uniform wall sections as described above apply to this alternative embodiment.
[0017] In yet another aspect, the present invention is directed to a hockey stick shaft characterized in that the carbon fiber composite material has a uniform wall thickness along its entire length. This makes the overall shaft structure stronger, reducing the risk of excessive bending and breaking. The same benefits of increased strength for the uniform wall structure as described above apply to this alternative embodiment.
[0018] Therefore, the inventors have developed a hockey stick that allows players to use a modern grip, place the lower hand higher on the stick shaft to more easily apply power to the stick shaft and to store and release more energy during a shot compared to a traditional hockey stick. The hockey stick of the present invention provides a more ergonomic and lightweight design, allowing players to quickly adjust their grip position without affecting the fit of the stick shaft in the hand, as well as a preferred mass distribution along the length of the shaft.
[0019] To the best of the inventor's knowledge, a hockey stick having this combination of features is hitherto unknown.
[0020] Other advantages of the present invention will become apparent to those skilled in the art after reading this specification. BRIEF DESCRIPTION OF THE DRAWINGS
[0021] Embodiments of the present invention will be described with reference to the accompanying drawings, in which like reference numerals refer to like parts, and in which:
[0022] Figure 1 is a schematic diagram of an embodiment of the present hockey stick shaft, showing a side view of the hockey stick shaft.
[0023] Figure 2 yes Figure 1 Schematic diagram of a hockey stick shaft showing cross-sections of the (A) upper section, (B) middle section, and (C) lower section of the shaft.
[0024] Figure 3 is a graph showing flexibility measurements along the hockey stick shaft of the present invention using a standard flexibility testing method, the cantilever bend test. DETAILED DESCRIPTION
[0025] The present invention relates to a hockey stick shaft comprising, along its longitudinal axis: (a) an upper section comprising four walls, each of which comprises a cross-sectional convex surface; (b) a middle section comprising four walls, three of which comprise a cross-sectional convex surface and one of which comprises a cross-sectional concave surface; and (c) a lower section comprising four walls, each of which comprises a cross-sectional convex surface.
[0026] Preferred embodiments of the present invention will be described with reference to the following exemplary information, which should not be used to limit or interpret the present invention.
[0027] The present hockey stick comprises three main sections along the longitudinal axis of the stick. The three sections have different cross-sectional shapes, which create a double bending point in the shaft, as described herein. There are also two intermediate connecting transition areas, which are used to transition between the three main sections. The hockey stick preferably comprises a carbon fiber composite material, but can be made of any suitable material.
[0028] Figure 1 is a side view of a schematic diagram of an embodiment of the present hockey stick 100. The hockey stick shaft 100 is preferably hollow and, in this embodiment, includes a uniform wall thickness throughout.
[0029] The hockey stick shaft 100 includes an upper section 105 that is held by the player's upper hand and is located at the end of the shaft opposite the hockey blade (not shown). The upper section 105 includes a first upper section end 105a that is opposite a second upper section end 105b along the longitudinal axis of the stick. The second upper section end 105b is connected to a connecting region 115, which in turn is connected to the middle section 110 at its first middle section end 110a. In some preferred embodiments, the first connecting region 115 will have the same circumference measurement as the second upper section end 105b to the first middle section end 110a. This will allow a more seamless transition from shape to shape.
[0030] like Figure 2As shown in Figure A, the upper section 105 includes a convex-convex cross-sectional shape, including a top wall 130a, a front wall 130b, a bottom wall 130c, and a rear wall 130d, each of which includes a convex surface. Although not wishing to be bound by any particular theory or mode of action, the resulting curved shape of the upper section 105 can fit the palm of the player's upper hand, maximize the surface in contact with the player's hand, and allow the player to control the club efficiently. In addition, the curved shape allows the player to adjust their grip position without affecting the fit of the shaft in the hand.
[0031] The hockey stick shaft 100 also includes a middle section 110 including a first middle section end 110a opposite a second middle section end 110b along the longitudinal axis of the stick.
[0032] like Figure 2 B, middle section 110 comprises convex-concave cross-sectional shape.Specifically, middle section 110 comprises top wall 135a, bottom wall 135c and rear wall 135d (wherein each wall comprises convex surface) and front wall 135b (it comprises concave surface).Although do not wish to be constrained by any particular theory or mode of action, the resulting shape of top wall 135a, bottom wall 135c and rear wall 135d allows the club to fit the palm of the player's lower hand comfortably, and maximizes the contact between the player's hand and the club.The concave surface of front wall 135b also reduces the moment of inertia (I) for middle section 110, thereby produces more flexible district in the middle part of the club shaft.When using the club to hit a ball, the shape and position of middle section 110 produce upper bending area or " kick point (kick point)".The precise position of the upper kick point will depend on the position where the player's lower hand is placed along the shaft 100. However, as described above, in modern playing styles, the player's lower hand is placed higher on the shaft 100 than traditionally taught. The player's lower hand will likely fall in the area between the first middle section end 110a and the second middle section end 110b. The concave wall 135b then provides a convenient and secure grip for the player's fingers. Therefore, if the player uses a higher hand position (which is typical of modern playing styles), the upper reflex point will be located in the middle section 110 and close to the player's lower hand, which is preferred.
[0033] The hockey stick shaft 100 also includes a lower section 120 including a first lower section end 120a opposite a second lower section end 120b along the longitudinal axis of the stick. The second lower section end 120b of the lower section 120 is configured to be connected to a hockey stick blade (not shown). In some embodiments, the blade is replaceable. The blade may include any suitable material, including but not limited to wood, plastic, or a composite material.
[0034] like Figure 2As shown in Figure C, the lower section includes a convex-convex cross-sectional shape, including a top wall 140a, a front wall 140b, a bottom wall 140c, and a rear wall 140d, each of which includes a convex surface. Although not wishing to be bound by any particular theory or mode of action, the convex surface of the front wall 140b increases the overall moment of inertia (I), creating a more rigid zone in the club shaft. The relative stiffness compared to the middle section 110 helps to create the upper reflex point in the middle section as described above.
[0035] In some embodiments, the lower section preferably tapers from the first lower section end 120a to the second lower section end 120b. While not wishing to be bound by any particular theory or mode of action, the associated reduction in moment of inertia toward the lower end 120b creates an area of relatively low stiffness. This creates a lower "rebend point." Together with the upper rebend point, the result when using a stick containing a shaft of the present invention is a double-blow shot profile in which there are two rebend points that cooperate to transfer enhanced force to the puck when a swing shot is made.
[0036] As described above, the upper section 105 is separated from the middle section 110 by the first connection region 115. The upper section 105 is connected to one end of the first connection region 115 at the second upper section end 105b, and the middle section 110 is connected to the opposite end of the first connection region 115 at the first middle section 110a.
[0037] Similarly, the lower section 120 is separated from the middle section 110 by a second connection region 125. The lower section 120 is connected to one end of the second connection region 125 at a first lower section end 120a, and the middle section 110 is connected to the opposite end of the second connection region 125 at a second middle section 110b.
[0038] As described above, the hockey shaft 100 of the present invention is designed to fit a modern, faster style of play, in which the player's lower hand is kept higher on the stick during a shot so that no time is lost moving the lower hand. Some hockey sticks of the prior art are also designed to have multiple flexible zones along their shafts, such as a lower zone with a transition zone, a middle zone, and an upper zone. However, the ratios between their zones are different. Table 1 below illustrates the percentage of shaft lengths of sticks according to the prior art compared to the present invention.
[0039] Table 1 – Prior Art
[0040]
[0041]
[0042] As can be seen by comparing the above ratios, the stick of the prior art distributes approximately equal lengths to the upper section, the middle section, and the lower section. In the stick of the present invention, most of the length of the shaft is concentrated in the lower section and the middle section. This is because when using the stick of the prior art, in order to maximize the force on the ice hockey puck, the player's lower hand needs to slide down along the shaft, basically forming a cantilever that helps to transfer force to the ice hockey puck through the flexible shaft. There is no strategic benefit in deviating from the default configuration of three sections of approximately equal size. However, in the stick of the present invention, the player's hand remains at the height of the shaft, and there is no need to perform time-consuming hand position movement. On the contrary, by designing the shaft to have different cross-sectional profiles across different areas, the stick of the present invention allows the above-mentioned double return point to be generated, and even when the player's hands are both kept at a relatively high position on the shaft, a sharp force can be transferred to the ice hockey puck.
[0043] It should be noted that the transition zones of the present invention each occupy about 10% of the length of the shaft. This allows for a gradual transition between the different main lower, middle and upper sections. Particularly when using carbon fiber to make a club, the gradual transition prevents abrupt changes in cross-sectional profile and avoids associated structural stresses that may cause weak points along the shaft.
[0044] It should also be noted that the percentages allocated to each of the three major sections of the shaft 100 may vary within 20% of the percentages shown. Even with such variations, the advantages of the present invention are maintained.
[0045] Tables 2 to 9 below further illustrate examples of lengths for each component region of a hockey stick for an adult male player, the stick being 1544.3 mm in length. Additional valid ranges for the lengths of the segments are also outlined.
[0046] Table 2
[0047]
[0048]
[0049] Table 3
[0050]
[0051] Table 4
[0052]
[0053] Table 5
[0054]
[0055] Table 6
[0056]
[0057] Table 7
[0058]
[0059] Table 8
[0060]
[0061] Different sizes of clubs are designed for players (from children to seniors) based on height. However, the percentage of shaft length that corresponds to each of the three main sections and two connecting areas is consistent between different sizes of clubs.
[0062] Further advantageously, the shaft 100 can have a consistent wall thickness and quality along its length. In the prior art sticks, the bending area is made by scraping or otherwise subtracting material or with thinner walls. By increasing the amount of material in these areas, or by introducing additional structures, such as supports made of metal or wood and other similar reinforcement materials, the areas designed to be strong and reduced in bending are enhanced. This unevenness along the length of the hockey stick shaft makes the contrast between the flexible area and the non-flexible area greater, increasing the possibility of excessive bending and breaking of the shaft during the game. Advantageously, the shaft 100 of the present invention has an area of increased flexibility, which is designed using different geometric shapes, rather than manipulating the amount of material in these areas for the shaft 100. The result is that the shaft is uniformly strong and not easy to break, while providing a double bending point, which is converted into a sharp and enhanced force on the ice ball during the game.
[0063] Alternative embodiments of club shafts may also be prepared in which the wall thickness is uniform only in the areas of the club that are most susceptible to bending and strain (e.g., lower section 120, second connection area 125, and middle section 110). It may be desirable to use less carbon fiber material in portions of the shaft that are not typically subject to significant impact, bending, or strain (such as upper region 105). Having thinner walls in region 105 will reduce the weight of the club, and the club may be manufactured at a lower cost due to the savings in carbon fiber material in this region. This reduction in wall thickness in upper region 105 will not have a significant negative impact on the overall strength of shaft 100. Such alternative embodiments are within the scope of the present invention.
[0064] As described above, in a preferred embodiment, the hockey stick shaft 100 is hollow and formed from a carbon fiber composite material. When a hollow shaft is made using a carbon fiber composite material, a sheet of carbon fiber embedded in an epoxy resin "prepreg" can be wrapped around a cylindrical mandrel. The mandrel is then removed and an expandable membrane is placed within the uncured profile. The assembly is then placed within a heated mold that is formed in the desired outer shape of the stick. The membrane is then expanded and the carbon fiber composite material is pushed onto the inner cavity of the mold to form a cured composite structure. When this method is used to make the sharp angle shaft of the prior art, the strength is reduced because the fibers are stressed when used to form the sharp angle. Another advantage of this embodiment of the present invention is that the shaft angle is rounded, which allows the structure made of the carbon fiber composite material to have better structural integrity.
[0065] The above manufacturing method is not the only method for producing hollow shafts. However, it is preferred for forms with variable cross-sections. The use of an expandable membrane in conjunction with an external mold produces a more diverse cross-sectional shape than the prior art method of molding around an internal shape.
[0066] It should also be noted that if it is desired to achieve a consistent wall thickness across a variable cross-section, it may be necessary to use trimmed carbon fiber composite sheets in the area where the ball and stick shape tapers. Such adjustments in the manufacturing process are within the knowledge of those skilled in the art.
[0067] Figure 3 The results of flexibility testing using a standard test protocol called the cantilever bending test are shown. The stiffness of the club was measured every 5 cm along its shaft using a dynamometer and a test fixture, and every 2.5 cm along the last 40 cm of its lower section. The results were then plotted as shown, with the Y axis corresponding to the stiffness (measured in Newtons) and the X axis roughly corresponding to the length of the club (in inches). Two clubs of the present invention with different stiffness levels were tested; one was "85Flex", suitable for larger, taller adult male players, and the other was "75Flex", suitable for adult male players of medium height. It should be noted that the patterns between the clubs of different sizes are consistent, as shown in the substantially identical shapes of the two figures. There are also different levels of flexibility for clubs used for young players, such as 35Flex or 45Flex. The same pattern is also repeated for these different levels of clubs of the present invention.
[0068] From left to right, the flexibility measurements of the club from the blade end to the end are shown. It can be seen that in the lower section 120 of the shaft, especially toward the second lower section end 120b close to the connection with the blade, the stiffness decreases, which means that the flexibility increases. This is due to the geometry of the lower area 120, which consists of four convex walls that taper toward the blade. It can be seen that the stiffness of the lower section 120 decreases, and for the 85Flex club, the stiffness transitions from a maximum of 210 Newtons to a minimum of about 155 Newtons, a decrease of 26%. In the 75Flex club, the stiffness of the lower section 120 is similarly reduced, from a maximum of 185 to a minimum of 140, a decrease of 24%. Therefore, it can be seen that the reduction in stiffness of the lower section 120 of the shaft of the present invention is in the range of 24-26% from the first lower section end 120a toward the second lower section end 120b.
[0069] In the region of the plot corresponding to the middle section 110 (approximately decreasing from 29" to 39" in the figure), the stiffness decreases further. The middle section 110 has a combined convex-concave cross-sectional profile, which results in a decrease in stiffness and a corresponding increase in flexibility. From approximately 39" to 43" is the first connection zone 115, where a further decrease in stiffness can be observed. Moving toward the right side of the graph, the stiffness of the club increases again after exceeding the 43" point, which corresponds to the portion of the shaft that is the upper section 105, and returns to a cross-sectional profile consisting of four convex sides, which, due to the nature of their geometry, will be stiffer than the first connection area 115 or the middle section 110. For the 85Flex club, comparing the peak stiffness of the upper section 105, which is 209 Newtons, with the stiffness of the first connection area 115, which is 190 Newtons, it can be seen that the stiffness drops by 9%. For the 75Flex club, the peak stiffness of the upper section 105 is 178 Newtons, and the stiffness of the first connection area is approximately 165 Newtons, corresponding to a 7% drop in stiffness. It can therefore be seen that the reduction in stiffness between the upper section 105 and the first connection area 115 is in the range of 7-9%.
[0070] The regions of lower stiffness and higher stiffness that characterize the shaft of the present invention cooperate to provide a stick that is well suited for transferring forces to the puck during play, particularly when the player holds the stick with the lower hand and rests in the middle section 110. The adjacent region of lower stiffness in the first connection area 115 and the additional region of lower stiffness in the lower section 120 provide a double-return profile that helps transfer sharp forces to the puck during play.
[0071] It is also apparent that the transitions between the three sections, lower section 120, middle section 110 and upper section 105, are gradual. This further illustrates the benefit of designing gradual transition areas in the shaft between these major zones, reducing the abruptness of changes in flexibility that would otherwise introduce stress points in the shaft.
[0072] Thus, a new hockey stick shaft is provided that has a new ratio of flex zones along the shaft to better accommodate modern game speeds. Advantageously, zones of varying flexibility are designed through their cross-sectional geometry without the need to add or remove additional material from the shaft, which in the prior art results in the creation of stress points and increases the likelihood of over-bending and breaking. It is also preferred to use carbon fiber composite materials to manufacture the stick of the present invention in order to take advantage of the versatility of shapes and transitions that can be better achieved without compromising structural integrity.
[0073] Although the present invention has been described with reference to illustrative embodiments, the description is not intended to be interpreted in a limiting sense. Therefore, modifications to the illustrative embodiments and other embodiments of the present invention will be apparent to those skilled in the art after reference to this description.
Claims
1. A hockey stick having a shaft having a longitudinal axis and a first end and a second end defining a length therebetween and having a non-uniform cross-section along the shaft, the hockey stick comprising: a. an upper section along said longitudinal axis, terminating at said first end and comprising four walls, wherein each wall comprises a cross-sectional convex surface; b. a middle section along said longitudinal axis, comprising four walls, three of which comprise a cross-sectional convex surface, and one of which comprises a cross-sectional concave surface; c. a lower section along said longitudinal axis terminating at said second end and comprising four walls, wherein each wall comprises a cross-sectional convex surface; as well as d. a blade connected to the second end. 2 . The hockey stick of claim 1 , further comprising a first transition section between the upper section and the middle section.
3. The hockey stick of claim 2, further comprising a second transition section between the middle section and the lower section.
4. The hockey stick according to claim 1, wherein: The lower section tapers toward the edge.
5. The hockey stick of claim 1, the shaft having a hollow core surrounded by a wall, the shaft having a generally quadrilateral cross-section.
6. The hockey stick according to claim 5, wherein: The cross-section is generally rectangular.
7. The hockey stick according to claim 6, wherein: The concave wall is parallel to the edge.
8. The hockey stick according to claim 5, wherein: The wall has a constant thickness throughout the length of the shaft.
9. The hockey stick according to claim 5, wherein: The wall of the upper section of the shaft is thinner than the wall of the middle section.
10. The hockey stick of claim 3, wherein: a. the upper section is 11.2-16.8% of the length; b. The first transition section is 2-18% of the length; c. the middle section is 24-36% of the length; d. the second transition section is 2-18% of the length; and e. The lower section is 28.8-43.2% of the length.
11. The hockey stick according to claim 3, wherein: a. the upper section is 12.6-15.4% of the length; b. The first transition section is 6-14% of the length; c. the middle section is 27-33% of the length; d. the second transition section is 6-14% of the length; and e. The lower section is 32.4-39.6% of the length.
12. The hockey stick of claim 3, wherein: a. the upper section is 13.3-14.7% of the length; b. The first transition section is 8-12% of the length; c. the middle section is 28.5-31.5% of the length; d. the second transition section is 8-12% of the length; and e. The lower section is 34.2-37.8% of the length.
13. The hockey stick of claim 3, wherein: a. said upper section is 14% of said length; b. The first transition section is 10% of the length; c. the middle section is 30% of the length; d. the second transition section is 10% of the length; and e. The lower section is 36% of the length.
14. The hockey stick of claim 5, wherein: Adjacent walls are connected by corners, and each of the corners is arc-shaped.
15. The hockey stick of claim 3, wherein: The shaft has the highest flexibility in the lower section.
16. The hockey stick of claim 15, wherein: The shaft has a second highest flexibility in the second transition section.
17. The hockey stick of claim 15, wherein: The flexibility at the second end is 24-26% higher than the flexibility in the second transition section.
18. The hockey stick of claim 15, wherein: The flexibility in the first transition section is 7-9% higher than the flexibility at the first end.
19. The hockey stick of claim 1, made of wood, polymer, or carbon fiber composite.
20. The hockey stick of claim 19, made from a carbon fiber composite material.