Patent Publication Number: US-2019184250-A1

Title: Hockey Stick with Variable Stiffness Shaft

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of U.S. patent application Ser. No. 15/842,033, filed Dec. 14, 2017, which is incorporated herein by reference in its entirety for any and all non-limiting purposes. 
    
    
     FIELD 
     This disclosure relates generally to fabrication of molded structures. More particularly, aspects of this disclosure relate to molded hockey shafts having non-uniform cross-sectional geometries along the shaft length, as well as hockey stick blades molded from foam and wrapped with one or more layers of tape. 
     BACKGROUND 
     Hockey stick shafts may be constructed from one or more layers of synthetic materials, such as fiberglass, carbon fiber or Aramid. Aspects of this disclosure relate to improved methods for production of a hockey stick shaft with increased bending stiffness and/or decreased mass. 
     SUMMARY 
     This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. The Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. 
     Aspects of the disclosure herein may relate to fabrication of a formed hockey stick structure. In one example, the formed hockey stick structure may include shaft that has a variable cross-sectional geometry. A method of fabricating a formed hockey stick structure that has variable shaft geometry may include forming a shaft structure. The formation of the shaft structure may include wrapping a mandrel with fiber tape to form a wrapped shaft structure, removing the mandrel from the wrapped shaft structure to form an internal shaft cavity, and inserting an inflatable bladder into the shaft cavity. The wrapped shaft structure may be positioned within a mold, and the mold may be heated and the bladder may be expanded within the cavity to exert an internal pressure on the cavity to urge the fiber tape toward the walls of the mold. The mold may be cooled and the bladder contracted and removed. The method of fabricating a formed hockey stick structure may additionally include forming a hockey stick blade structure, and coupling the shaft structure to the blade structure. The walls of the mold may impart an outer geometry on the shaft structure that includes a portion having a cross-sectional geometry with at least five sides along a length of the shaft structure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure is illustrated by way of example and not limited in the accompanying figures in which like reference numerals indicate similar elements and in which: 
         FIG. 1  depicts a front side of a hockey stick structure, according to one or more aspects described herein. 
         FIG. 2  depicts a more detailed view of a front side of the hockey stick blade structure and a portion of the shaft structure of  FIG. 1 , according to one or more aspects described herein. 
         FIG. 3  depicts a more detailed view of a back side of the hockey stick blade structure and a portion of the shaft structure of  FIG. 1 , according to one or more aspects described herein. 
         FIG. 4  depicts a front side of a hockey stick structure, according to one or more aspects described herein. 
         FIG. 5  depicts an example hockey stick shaft, according to one or more aspects described herein. 
         FIGS. 6-13  schematically depict cross-sectional views of the hockey stick shaft of  FIG. 5 , according to one or more aspects described herein. 
         FIG. 14  depicts an example hockey stick shaft, according to one or more aspects described herein. 
         FIGS. 15-23  schematically depict cross-sectional views of the hockey stick shaft of  FIG. 14 , according to one or more aspects described herein. 
         FIGS. 24-28  schematically depict stages of one or more hockey stick shaft molding processes, according to one or more aspects described herein. 
         FIG. 29  graphs the bending stiffness of a five-sided hockey stick shaft compared to a conventional hockey stick shaft having a uniform rectangular cross-sectional geometry, according to one or more aspects described herein. 
         FIG. 30  graphs the bending stiffness of a seven-sided hockey stick shaft compared to a conventional hockey stick shaft having a uniform rectangular cross-sectional geometry, according to one or more aspects described herein. 
         FIG. 31  schematically depicts another view of a hockey stick blade structure, according to one or more aspects described herein. 
         FIG. 32  schematically depicts another implementation of a blade structure that has a stiffened top portion, a flexible bottom portion, and a slot, according to one or more aspects described herein. 
         FIG. 33  schematically depicts another implementation of a blade structure that has a stiffened top portion, a flexible bottom portion, and a slot, according to one or more aspects described herein. 
         FIG. 34  schematically depicts another implementation of a blade structure that includes a slot support element, according to one or more aspects described herein. 
         FIG. 35  schematically depicts an alternative implementation of a hockey stick blade structure, according to one or more aspects described herein. 
         FIG. 36  depicts a hockey stick blade structure with a schematic cutting plane, according to one or more aspects described herein. 
         FIG. 37  depicts a cross-sectional view of a hockey stick blade structure, according to one or more aspects described herein. 
         FIG. 38  depicts two form core portions that are used in a hockey stick blade structure, according to one or more aspects described herein. 
         FIG. 39  schematically depicts abridge element between two form core portions that are used in a hockey stick blade structure, according to one or more aspects described herein. 
         FIG. 40  schematically depicts a plan and an elevation view of a first bending test carried out on a hockey stick blade structure, according to one or more aspects described herein. 
         FIG. 41  schematically depicts a plan and an elevation view of a second bending test carried out on a hockey stick blade structure, according to one or more aspects described herein. 
         FIG. 42  schematically depicts a plan and an elevation view of a third bending test carried out on a hockey stick blade structure, according to one or more aspects described herein. 
     
    
    
     Further, it is to be understood that the drawings may represent the scale of different component of one single embodiment; however, the disclosed embodiments are not limited to that particular scale. 
     DETAILED DESCRIPTION 
     In the following description of various example structures, reference is made to the accompanying drawings, which form a part hereof, and in which are shown by way of illustration various embodiments in which aspects of the disclosure may be practiced. Additionally, it is to be understood that other specific arrangements of parts and structures may be utilized, and structural and functional modifications may be made without departing from the scope of the present disclosures. Also, while the terms “top” and “bottom” and the like may be used in this specification to describe various example features and elements, these terms are used herein as a matter of convenience, e.g., based on the example orientations shown in the figures and/or the orientations in typical use. Nothing in this specification should be construed as requiring a specific three-dimensional or spatial orientation of structures in order to fall within the scope of this invention. 
     Aspects of this disclosure relate to systems and methods for production of a hockey stick structure using variable cross-sectional geometries. 
       FIG. 1  depicts a front side of a hockey stick structure  100 , according to one or more aspects described herein. In one example, the hockey stick structure  100  includes a shaft structure  102  that is rigidly coupled to a blade structure  104 . In one example, the shaft structure  102  may include a hollow structure formed from one or more fiber-reinforced materials. For example, the shaft structure  102  may be formed from a carbon fiber material. The shaft structures described throughout this disclosure may use materials in addition to or as an alternative to carbon fiber, including fiberglass, Aramid, and/or other composite or fiber-reinforced materials, among others. It is further contemplated that any of the structures described throughout these disclosures may use one or more materials in a tape form, or formed as discrete elements prior to one or more molding processes. Additionally or alternatively, the tape and/or discrete elements, and may be preimpregnated with resin or another adhesive, or may have resin or another adhesive applied to the tape and/or discrete pieces. In one specific implementation, the shaft structure  102  may be formed from one or more layers of carbon fiber tape that are preimpregnated with resin and heated and cooled in a mold in order to impart the desired geometries of the final shaft structure  102 . Additionally, the shaft structure  102  may include one or more internal foam core structures around which the fiber tape is wrapped and molded in order to give the shaft structure  102  its final form. The blade structure  104  may be molded separately to the shaft structure  102 , and subsequently rigidly coupled to the shaft structure  102 . Alternatively, the blade structure  104  may be co-molded with the shaft structure  102 . In another implementation, the blade structure  104  may be removably coupled to the shaft structure  102 . As such, the blade structure  104  and the shaft structure  102  may be interchangeable and replaceable. 
       FIG. 2  depicts a more detailed view of a front side of the hockey stick blade structure  104  and a portion of the shaft structure  102 , according to one or more aspects described herein. Further,  FIG. 3  depicts a more detailed view of a back side of the hockey stick blade structure  104  and a portion of the shaft structure  102 , according to one or more aspects described herein. In one example, the blade structure  104  may be formed from one or more layers of fiber reinforced material, similar to the shaft structure  102 . In particular, the blade structure  104  may be formed from one or more layers of carbon fiber tape that are preimpregnated with resin, and wrapped around a foam core before being heated and cooled in a mold to form the desired geometries of the final blade structure  104 . Additionally, the blade structure  104  may include one or more fiber pins extending through one or more layers of fiber tape and an internal foam core of the blade structure  104  between a front face  106  and a back face  108 . Advantageously, the pins, when molded along with the fiber tape of the blade structure  104 , may reinforce the blade structure  104 . 
     Additionally, the blade structure  104  may include a slot  114  that extends through the blade from the front face  106  to the back face  108 , and extends along a portion of a length of the hockey stick blade structure  104  between a heel side  110  and a toe side  112  of the blade structure  104 . In one example, the slot  114  may be positioned at a distance  116  from a top edge  118  of the blade structure  104 . In another example, the slot  114  may be substantially parallel to the top edge  118  of the blade structure  104 . The distance  116  may range between 10 mm and 20 mm. Additionally or alternatively, distance  116  may be a percentage of an overall blade height  120 . For example, distance  116  may be approximately or exactly 10%, 15%, 20%, 25%, 30%, 33%, 35% or 40% of height  120 . It is further contemplated, however, that the distance  116  may have any value, without departing from the scope of these disclosures. Similarly, the slot  114  may have a slot height  122 . This slot height  122  may range between 2 mm and 20 mm and/or may be a percentage of the overall blade height  120 . For example, slot height  122  may be approximately or exactly 1%, 2%, 5%, 10%, 15%, 20%, 25%, 30%, 33%, 35% or 40% of height  120 . Further, the slot  114  may be positioned at a distance  124  from the toe side  112  of the blade structure  104 , and at a distance  126  from the heel side  110  of the blade structure  104 . Distance  124  and distance  126  may range between 15 mm and 80 mm and between 20 mm and 150 mm, respectively, and/or may each be a percentage of an overall blade length  128 . As such, the slot  114  may have a length  130  that measures between 70 mm and 270 mm, and/or as a percentage of the overall blade length  128 . For example, slot length may be approximately or exactly 30%, 33%, 35% or 40%, 50%, 60%, 70%, 80%, or 90% of length  128 . Further, it is contemplated that any of the distances  124 ,  126 , and/or  130  may have any value, without departing from the scope of these disclosures. 
     Advantageously, the slot  114  may reduce the mass of the blade structure  104 . Additionally or alternatively, the slot  114  may allow more material to be added to the blade structure  104  toward the bottom edge  132  prior to molding. As such, the slot  114  may essentially allow the mass in the blade  104  to be shifted toward the bottom edge  132 . This additional material may include added layers of fiber tape used prior to molding, and/or one or more inserts being used within the blade structure  104 . This additional material/structural elements may increase the hardness, and hence the durability, of the bottom edge  132  of the blade structure  104  and/or the overall strength and stiffness of the blade  104 . 
       FIG. 4  depicts a front side of a hockey stick structure  400 , according to one or more aspects described herein. In one example, the hockey stick structure  400  may include a shaft structure  102  similar to that of a hockey stick structure  100 , as previously described. The hockey stick structure  400  may additionally include a blade structure  402  that may be co-molded with the shaft structure  102 , or may be formed as a separate structure and rigidly coupled to the shaft structure  102 . It is contemplated that the blade structure  402  may be formed using one or more molding processes similar to those of blade structure  104 , as described in relation to hockey stick structure  100 . Accordingly, the blade structures  104  and  402  may include any hockey blade curve geometries. Additionally, the blade structures  104  and  402  may include pin reinforcement elements that are inserted into a foam core of the blade structures  104  and  402  prior to one or more molding processes. These pin reinforcement elements are described further in U.S. patent application Ser. No. 15/280,603, filed 26 Sep. 2016, the entire contents of which is incorporated herein by reference in its entirety for any and all non-limiting purposes. 
     In one example, shaft structure  102  may include a variable cross-sectional geometry that is configured to provide a prescribed variable stiffness along the length of the shaft. Advantageously, the variable cross-sectional geometry may allow the hockey stick shaft  102  to be constructed using less material, while still maintaining a desired and high flexural rigidity. In particular, the variable cross-sectional geometry may allow the stick shaft  102  to be constructed using comparatively fewer layers of fiber tape and/or using comparatively fewer or no reinforcement inserts within the hollow core of the stick shaft  102  This decreased amount of material may result in a hockey stick structure  100  and/or  400  having a comparatively reduced mass when compared with a hockey stick constructed using conventional methods. 
     In another example, the mass of the hockey stick structure  100  and/or  400  may be reduced when compared to a conventional hockey stick structure that includes a shaft having a rectangular cross-sectional geometry. However, the hockey stick structures  100  and/or  400  may use an increased number of lighter fiber layers when compared to a conventional hockey stick structure. In one example, a conventional hockey stick shaft may include 8-13 fiber layers that result in a total mass of a stick being approximately 422 grams. However, the hockey stick structure  100  and/or  400  may use 11-20 layers, but a total mass of a stick may be approximately 376 grams. In certain examples, the mass of hockey stick structures  100  and/or  400  may be reduced by 7-20% relative to conventional hockey stick structures. In other examples, the processes described herein may be used to reduce the mass of a hockey stick by 25-30% or more, when compared to a similar hockey stick constructed using conventional methodologies. In certain examples, the fiber layers used to construct the hockey stick structures  100  and/or  400  may have low densities than fiber layers used in conventional hockey stick structures. As a result, the hockey stick structures  100  and/or  400  may use an increased number of fiber layers, but have a resultant mass that is lower than conventional hockey stick structures due to the comparatively lower material densities. It is contemplated that any material densities may be used for the fiber layers of hockey stick structures  100  and/or  400 , without departing from the scope of these disclosures. 
     Advantageously, an increased number of fiber layers may result in a stronger hockey stick structure since the layers may be oriented relative to one another, such that any mechanical properties (e.g., strength, hardness, stiffness, among others) that are greater along one axis or a limited number of axes of a given layer of fiber tape (e.g., an anisotropic material) may result in an aggregate layered material with increased mechanical properties in multiple directions (in one example this methodology may be used to form a hockey stick structure that tends toward an isotropic material). In other examples, the increased number of fiber layers of the hockey stick structures  100  and/or  400  may be used to impart one or more structural properties in one direction, and one or more different structural properties in a second direction. 
     In particular, the hockey stick shaft  102  may be considered a beam subject to a bending force during a shooting or passing motion (e.g. a slap shot, wrist shot among others). The flexural rigidity, or “bending stiffness” of a hockey stick shaft includes two components, and is given by the formula: 
       Flexural rigidity= E·I    (Equation 1)
 
     From Equation 1, E represents a contribution of the material of the hockey stick shaft  102  to the flexural rigidity. E is the Young&#39;s Modulus, or elastic modulus, and is a measure of the stiffness of a hockey stick shaft  102 . E has SI units of Pascals (Pa). 
     Also from Equation 1, I represents a contribution of the cross-sectional geometry of the hockey stick shaft  102  to the flexural rigidity. I is the Second Moment of Inertia, or Second Moment of Area, and is a measure of the efficiency of a shape to resist bending. I has SI units of m̂4. 
     With reference to Equation 1, the hockey stick shaft  102  is configured to increase the Second Moment of Area, I, component of the flexural rigidity by using a non-standard cross-sectional geometry. In certain examples, the hockey stick shaft  102  may be configured with a cross-sectional geometry that varies along a length of the shaft  102 , and thereby varies the flexural rigidity of the shaft  102  with position along the shaft&#39;s length. Advantageously, this may allow a the hockey stick shaft  102  to be manufactured with flexing characteristics that are tuned to a specific position type, player type (weight, height, strength, among others) or a specific player (e.g. a specific professional player). 
     In one example, increasing the Second Moment of Area, I may allow the Young&#39;s Modulus, E, to be decreased, while maintaining a same overall flexural rigidity. In one example, the Young&#39;s Modulus, E, may be decreased by reducing an amount of material used to form all or part of the hockey stick shaft  102 , and hence, reducing the overall mass of the hockey stick shaft  102 . 
     In one implementation, the Second Moment of Area, I, of the hockey stick shaft  102  may be increased by using a non-rectangular cross-sectional geometry. Specifically, the hockey stick shaft  102  may include portions with pentagonal and/or heptagonal cross-sectional geometries.  FIG. 5  schematically depicts an example hockey stick shaft  502 , according to one or more aspects described herein. In one implementation, the hockey stick shaft  502  may include one or more portions with pentagonal (5-sided) geometries. It is contemplated that the cross-sectional geometry of hockey stick shaft  502  may vary along the longitudinal length  504 . In this regard, multiple cross-sections of the hockey stick shaft  502  are provided in  FIGS. 6-13 , as described in the following portions of this disclosure. However,  FIGS. 6-13  refer to one implementation of variable cross-sectional geometry of hockey stick shaft  502 , and it is contemplated that alternative cross-sectional geometries may be used, without departing from the scope of these disclosures. In one example, as described in relation to  FIGS. 6-13 , the hockey stick shaft  502  may include a first portion with a first cross-sectional geometry and a second portion with a second cross-sectional geometry. The first cross-sectional geometry may be pentagonal in shape, and the second cross-sectional geometry may have another pentagonal cross-sectional geometry, or may be rectangular in shape. It is contemplated that the description of the various geometries used throughout these disclosures may be refer to geometries with rounded edges/corners, such that pentagonal and a rectangular geometries may have respective five and four sides with rounded corners with any radius of curvature. It is further contemplated that the geometries may or may not have two or more sides of equal length. Additionally, it is contemplated that the sides of the various cross-sectional geometries may have inner and/or outer surfaces that are substantially planar, or may be partially uneven, including convex and/or concave geometries. 
       FIGS. 6-13  include various dimensional values. As such, it is contemplated that these dimensions may be implemented with any values, without departing from the scope of these disclosures. It is further contemplated that the hockey stick shaft  502  may have increased bending stiffness when compared to a conventional shaft that uses rectangular cross sections. This increased bending stiffness may result from non-standard pentagonal geometry, without an increase in Young&#39;s modulus, E, resulting from an increased material/shaft wall thickness, and the like. In another example, an increase in bending stiffness may result from a combination of increased second moment of inertia, I, and Young&#39;s Modulus, E. 
       FIG. 6  schematically depicts a cross-sectional view corresponding to arrows  6 - 6  from  FIG. 5 , according to one or more aspects described herein. In one example, the cross section of  FIG. 6  includes five sides  616   a - 616   e.  The cross-section includes an apex  618  formed at the intersection of side  616   d  and  616   e.  This apex  618  is positioned on the back of the hockey stick shaft  502 , and the side  616   b  provides a substantially flat surface on the front of the hockey stick shaft  502 . The cross-section of  FIG. 6  additionally depicts carbon-fiber walls  622  that surround the internal cavity  814 . In one specific implementation, the cross-section of  FIG. 6  includes the following specific dimensional values, such that length  602  may equal 0.671 inches. In another example, length  602  may range between 0.6 and 0.8 inches, among others. Length  604  may equal 0.362 inches. In another example, length  604  may range between 0.3 and 0.5 inches, among others. Length  610  may equal to 0.458 inches. In another example, length  610  may range between 0.4 and 0.6 inches, among others. Length  608  may equal 1.671 inches. In another example, length  608  may range between 1.5 and 1.8 inches, among others. Length  606  may equal 0.445 inches. In another example, length  606  may range between 0.35 and 0.6 inches, among others. The radius of curvature  618  may equal 0.12 inches. In another example, the radius of curvature  618  may range between 0.08 and 0.16 inches. The radius of curvature  614  may equal 0.197 inches. In another example, the radius of curvature  614  may range between 0.18 and 0.21 inches. 
       FIG. 7  schematically depicts a cross-sectional view corresponding to arrows  7 - 7  from  FIG. 5 , according to one or more aspects described herein. In one example, the cross section of  FIG. 7  includes five sides, similar to  FIG. 6 . The cross-section of  FIG. 7  additionally depicts carbon-fiber walls  622  that surround an internal cavity  814 . In one specific implementation, the cross-section of  FIG. 7  includes the following specific dimensional values, such that length  702  may equal 0.532 inches. In another example, length  702  may range between 0.5 and 0.6 inches, among others. Length  704  may equal 0.365 inches. In another example, length  704  may range between 0.3 and 0.5 inches, among others. Length  706  may equal to 0.531 inches. In another example, length  706  may range between 0.4 and 0.65 inches, among others. Length  708  may equal 1.437 inches. In another example, length  708  may range between 1.3 and 1.55 inches, among others. The radius of curvature  712  may equal 0.12 inches. In another example, the radius of curvature  712  may range between 0.08 and 0.16 inches, among others. The radius of curvature  714  may equal 0.206 inches. In another example, the radius of curvature  714  may range between 0.19 and 0.22 inches, among others. 
       FIG. 8  schematically depicts a cross-sectional view corresponding to arrows  8 - 8  from  FIG. 5 , according to one or more aspects described herein. In one example, the cross section of  FIG. 8  includes five sides, similar to  FIG. 6 . The cross-section of  FIG. 8  additionally depicts an internal cavity  814  formed within the carbon-fiber walls  622 . In one example, the internal cavity  814  may have a substantially rectangular cross-sectional shape. In another example, the internal cavity  814  may have a substantially pentagonal shape, such that the thickness of the sidewall  622  is substantially uniform around the perimeter of the hollow shaft  502 . It is further contemplated that the internal cavity  814  may have additional or alternative cross sectional geometries in addition to or as alternatives to the pentagonal and/or rectangular geometries described herein. In one specific implementation, the cross-section of  FIG. 8  includes the following specific dimensional values, such that length  802  may equal 0.412 inches. In another example, length  802  may range between 0.39 and 0.43 inches, among others. Length  804  may equal 0.393 inches. In another example, length  804  may range between 0.37 and 0.42 inches, among others. Length  806  may equal to 0.681 inches. In another example, length  806  may range between 0.6 and 0.8 inches, among others. Length  808  may equal 1.21 inches. In another example, length  808  may range between 1.1 and 1.4 inches, among others. The radius of curvature  810  may equal 0.12 inches. In another example, the radius of curvature  810  may range between 0.08 and 0.16 inches, among others. The radius of curvature  812  may equal 0.216 inches. In another example, the radius of curvature  812  may range between 0.19 and 0.24 inches, among others. 
       FIG. 9  schematically depicts a cross-sectional view corresponding to arrows  9 - 9  from  FIG. 5 , according to one or more aspects described herein. In one example, the cross section of  FIG. 9  includes five sides, similar to  FIG. 6 . The cross-section of  FIG. 9  additionally depicts an internal cavity  814  formed within the carbon-fiber walls  622 . In one specific implementation, the cross-section of  FIG. 8  includes the following specific dimensional values, such that length  902  may equal 0.402 inches. In another example, length  902  may range between 0.38 and 0.43 inches, among others. Length  904  may equal 0.405 inches. In another example, length  904  may range between 0.38 and 0.43 inches, among others. Length  906  may equal to 0.795 inches. In another example, length  906  may range between 0.7 and 0.9 inches, among others. Length  908  may equal 1.174 inches. In another example, length  908  may range between 1.0 and 1.3 inches, among others. The radius of curvature  910  may equal 0.12 inches. In another example, the radius of curvature  910  may range between 0.08 and 0.16 inches, among others. The radius of curvature  912  may equal 0.197 inches. In another example, the radius of curvature  912  may range between 0.18 and 0.22 inches, among others. 
       FIG. 10  schematically depicts a cross-sectional view corresponding to arrows  10 - 10  from  FIG. 5 , according to one or more aspects described herein. In one example, the cross section of  FIG. 10  includes five sides, similar to  FIG. 6 . The cross-section of  FIG. 10  additionally depicts an internal cavity  814  formed within the carbon-fiber walls  622 . In one specific implementation, the cross-section of  FIG. 10  includes the following specific dimensional values, such that length  1002  may equal 0.388 inches. In another example, length  1002  may range between 0.37 and 0.42 inches, among others. Length  1004  may equal 0.388 inches. In another example, length  1004  may range between 0.37 and 0.42 inches, among others. Length  1006  may equal to 0.842 inches. In another example, length  1006  may range between 0.7 and 1.0 inches, among others. Length  1008  may equal 1.168 inches. In another example, length  1008  may range between 1.0 and 1.3 inches, among others. The radius of curvature  1010  may equal 0.12 inches. In another example, the radius of curvature  1010  may range between 0.08 and 0.16 inches, among others. The radius of curvature  1012  may equal 0.197 inches. In another example, the radius of curvature  1012  may range between 0.18 and 0.22 inches, among others. 
       FIG. 11  schematically depicts a cross-sectional view corresponding to arrows  11 - 11  from  FIG. 5 , according to one or more aspects described herein. In one example, the cross section of  FIG. 11  includes five sides, similar to  FIG. 6 . The cross-section of  FIG. 11  additionally depicts an internal cavity  814  formed within the carbon-fiber walls  622 . In one specific implementation, the cross-section of  FIG. 11  includes the following specific dimensional values, such that length  1102  may equal 0.389 inches. In another example, length  1102  may range between 0.37 and 0.42 inches, among others. Length  1104  may equal 0.389 inches. In another example, length  1104  may range between 0.37 and 0.42 inches, among others. Length  1106  may equal to 0.864 inches. In another example, length  1106  may range between 0.7 and 1.0 inches, among others. Length  1108  may equal 1.165 inches. In another example, length  1108  may range between 1.0 and 1.3 inches, among others. The radius of curvature  1110  may equal 0.12 inches. In another example, the radius of curvature  1110  may range between 0.08 and 0.16 inches, among others. The radius of curvature  1112  may equal 0.197 inches. In another example, the radius of curvature  1112  may range between 0.18 and 0.22 inches, among others. 
       FIG. 12  schematically depicts a cross-sectional view corresponding to arrows  12 - 12  from  FIG. 5 , according to one or more aspects described herein. In one example, the cross section of  FIG. 12  includes five sides, similar to  FIG. 6 . The cross-section of  FIG. 12  additionally depicts an internal cavity  814  formed within the carbon-fiber walls  622 . In one specific implementation, the cross-section of  FIG. 12  includes the following specific dimensional values, such that length  1202  may equal 0.384 inches. In another example, length  1202  may range between 0.36 and 0.41 inches, among others. Length  1204  may equal 0.384 inches. In another example, length  1204  may range between 0.36 and 0.41 inches, among others. Length  1206  may equal to 0.819 inches. In another example, length  1206  may range between 0.7 and 1.0 inches, among others. Length  1208  may equal 1.165 inches. In another example, length  1208  may range between 1.0 and 1.3 inches, among others. The radius of curvature  1210  may equal 0.12 inches. In another example, the radius of curvature  1210  may range between 0.08 and 0.16 inches, among others. The radius of curvature  1212  may equal 0.197 inches. In another example, the radius of curvature  1212  may range between 0.18 and 0.22 inches, among others. 
       FIG. 13  schematically depicts a cross-sectional view corresponding to arrows  13 - 13  from  FIG. 5 , according to one or more aspects described herein. In one example, the cross section of  FIG. 13  includes five sides, similar to  FIG. 6 . The cross-section of  FIG. 13  additionally depicts an internal cavity  814  formed within the carbon-fiber walls  622 . In one specific implementation, the cross-section of  FIG. 13  includes the following specific dimensional values, such that length  1302  may equal 0.358 inches. In another example, length  1302  may range between 0.34 and 0.38 inches, among others. Length  1304  may equal 0.358 inches. In another example, length  1304  may range between 0.34 and 0.38 inches, among others. Length  1306  may equal to 0.756 inches. In another example, length  1306  may range between 0.65 and 1.0 inches, among others. Length  1308  may equal 1.165 inches. In another example, length  1308  may range between 1.0 and 1.3 inches, among others. The radius of curvature  1312  may equal 0.197 inches. In another example, the radius of curvature  1312  may range between 0.18 and 0.22 inches, among others. 
       FIG. 14  depicts an example hockey stick shaft  1402  that may be similar to hockey stick shaft  102 . In one implementation, the hockey stick shaft  1402  may include one or more portions with heptagonal (7-sided) geometries. It is contemplated that the cross-sectional geometry of hockey stick shaft  1402  may vary along the longitudinal length  1404 . In this regard, multiple cross-sections of the hockey stick shaft  1402  are provided in  FIGS. 15-23 , as described in the following portions of this disclosure. However,  FIGS. 15-23  refer to one implementation of variable cross-sectional geometry of hockey stick shaft  1402 , and it is contemplated that alternative cross-sectional geometries may be used, without departing from the scope of these disclosures. In one example, as described in relation to  FIGS. 15-23 , the hockey stick shaft  1402  may include a first portion with a first cross-sectional geometry and a second portion with a second cross-sectional geometry. The first cross-sectional geometry may be heptagonal in shape, and the second cross-sectional geometry may have another heptagonal cross-sectional geometry, or may be rectangular in shape. It is contemplated that the description of the various geometries used throughout these disclosures may be refer to geometries with rounded edges/corners, such that pentagonal and a rectangular geometries may have respective five and four sides with rounded corners with any radius of curvature. It is further contemplated that the geometries may or may not have two or more sides of equal length. Additionally, it is contemplated that the sides of the various cross-sectional geometries may have inner and/or outer surfaces that are substantially planar, or may be partially uneven, including convex and/or concave geometries. 
     It is noted that  FIGS. 15-23  include various dimensional values. As such, it is contemplated that these dimensions may be implemented with any values, without departing from the scope of these disclosures. It is further contemplated that the hockey stick shaft  1402  may exhibit increased bending stiffness when compared to a conventional shaft that uses rectangular, or rounded rectangular cross sections. This increased bending stiffness may result from non-standard heptagonal geometry, without an increase in Young&#39;s Modulus, E, resulting from an increased material/shaft wall thickness, and the like. In another example, an increase in bending stiffness may result from a combination of increased second moment of inertia, I, and Young&#39;s Modulus, E. 
       FIG. 15  schematically depicts a cross-sectional view corresponding to arrows  15 - 15  from  FIG. 14 , according to one or more aspects described herein. In one example, the cross section of  FIG. 15  includes seven sides  1520   a - 1520   g.  The cross-section of  FIG. 15  additionally depicts an internal cavity  1720  and carbon-fiber walls  1524  that surround the internal cavity  1720 . The walls  1524  may otherwise be referred to as shaft structure sidewalls  1524 . In one specific implementation, the cross-section of  FIG. 15  includes the following specific dimensional values, such that length  1502  may equal 0.460 inches. In another example, length  1502  may range between 0.35 and 0.6 inches, among others. Length  1504  may equal 0.590 inches. In another example, length  1504  may range between 0.45 and 0.75 inches, among others. Length  1506  may equal 0.457 inches. In another example, length  1506  may range between 0.35 and 0.6 inches, among others. Length  1508  may be 1.675 inches. In another example, length  1508  may range between 1.45 and 1.9 inches, among others. The radius of curvature  1510  may equal 0.216 inches. In another example, the radius of curvature  1510  may range between 0.19 and 0.23 inches. The radius of curvature  1512  may equal 0.16 inches. In another example, the radius of curvature  1512  may range between 0.12 and 0.2 inches. The radius of curvature  1514  may equal 0.197 inches. In another example, the radius of curvature  1514  may range between 0.18 and 0.22 inches. 
       FIG. 15  schematically depicts a cross-sectional view corresponding to arrows  15 - 15  from  FIG. 14 , according to one or more aspects described herein. In one example, the cross section of  FIG. 15  includes seven sides  1520   a - 1520   g.  The cross-section of FIG.  15  additionally depicts an internal cavity  1720  and carbon-fiber outer walls  1524  that surround the internal cavity  1720 . In one specific implementation, the cross-section of  FIG. 15  includes the following specific dimensional values, such that length  1502  may equal 0.460 inches. In another example, length  1502  may range between 0.35 and 0.6 inches, among others. Length  1504  may equal 0.590 inches. In another example, length  1504  may range between 0.45 and 0.75 inches, among others. Length  1506  may equal 0.457 inches. In another example, length  1506  may range between 0.35 and 0.6 inches, among others. Length  1508  may be 1.675 inches. In another example, length  1508  may range between 1.45 and 1.9 inches, among others. The radius of curvature  1510  may equal 0.216 inches. In another example, the radius of curvature  1510  may range between 0.19 and 0.23 inches. The radius of curvature  1512  may equal 0.16 inches. In another example, the radius of curvature  1512  may range between 0.12 and 0.2 inches. The radius of curvature  1514  may equal 0.197 inches. In another example, the radius of curvature  1514  may range between 0.18 and 0.22 inches. 
       FIG. 16  schematically depicts a cross-sectional view corresponding to arrows  16 - 16  from  FIG. 14 , according to one or more aspects described herein. The cross-section of  FIG. 16  additionally depicts an internal foam core  1522  and carbon-fiber outer walls  1524  that surround the internal foam core  1522 . In one specific implementation, the cross-section of  FIG. 16  includes the following specific dimensional values, such that length  1602  may equal 0.349 inches. In another example, length  1602  may range between 0.25 and 0.45 inches, among others. Length  1604  may equal 0.404 inches. In another example, length  1604  may range between 0.38 and 0.43 inches, among others. Length  1606  may equal 0.22 inches. In another example, length  1606  may range between 0.19 and 0.25 inches, among others. Length  1608  may be 0.566 inches. In another example, length  1608  may range between 0.45 and 0.7 inches, among others. Length  1610  may be 1.337 inches. In another example, length  1610  may range between 1.1 and 1.6 inches, among others. The radius of curvature  1612  may equal 0.216 inches. In another example, the radius of curvature  1612  may range between 0.19 and 0.23 inches. The radius of curvature  1614  may equal 0.16 inches. In another example, the radius of curvature  1614  may range between 0.12 and 0.2 inches. 
       FIG. 17  schematically depicts a cross-sectional view corresponding to arrows  17 - 17  from  FIG. 14 , according to one or more aspects described herein. In one example, the cross section of  FIG. 17  includes seven sides, similar to  FIG. 15 . The cross-section of  FIG. 17  additionally depicts an internal cavity  1720  formed within the carbon-fiber walls  1524 . In one specific implementation, the cross-section of  FIG. 17  includes the following specific dimensional values, such that length  1702  may equal 0.341 inches. In another example, length  1702  may range between 0.3 and 0.4 inches, among others. Length  1704  may equal 0.396 inches. In another example, length  1704  may range between 0.37 and 0.43 inches, among others. Length  1706  may equal to 0.27 inches. In another example, length  1706  may range between 0.15 and 0.45 inches, among others. Length  1708  may equal 0.082 inches. In another example, length  1708  may range between 0.06 and 0.1 inches, among others. Length  1710  may equal 0.082 inches. In another example, length  1710  may range between 0.06 and 0.1 inches, among others. The radius of curvature  1716  may equal 0.16 inches. In another example, the radius of curvature  1716  may range between 0.12 and 0.2 inches, among others. The radius of curvature  1718  may equal 0.197 inches. In another example, the radius of curvature  1718  may range between 0.18 and 0.22 inches, among others. 
       FIG. 18  schematically depicts a cross-sectional view corresponding to arrows  18 - 18  from  FIG. 14 , according to one or more aspects described herein. In one example, the cross section of  FIG. 18  includes seven sides  1520   a - 1520   g,  similar to  FIG. 15 . The cross-section of  FIG. 18  additionally depicts an internal cavity  1720  formed within the carbon-fiber walls  1524 . In one specific implementation, the cross-section of  FIG. 18  includes the following specific dimensional values, such that length  1802  may equal 0.351 inches. In another example, length  1802  may range between 0.3 and 0.4 inches, among others. Length  1804  may equal 0.409 inches. In another example, length  1804  may range between 0.38 and 0.43 inches, among others. Length  1806  may equal to 0.38 inches. In another example, length  1806  may range between 0.3 and 0.5 inches, among others. Length  1808  may equal 0.133 inches. In another example, length  1808  may range between 0.1 and 0.16 inches, among others. Length  1810  may equal 0.974 inches. In another example, length  1810  may range between 0.8 and 1.2 inches, among others. Length  1812  may equal 1.231 inches. In another example, length  1812  may range between 1.0 and 1.4 inches, among others. The radius of curvature  1814  may equal 0.16 inches. In another example, the radius of curvature  1814  may range between 0.12 and 0.2 inches, among others. The radius of curvature  1816  may equal 0.216 inches. In another example, the radius of curvature  1816  may range between 0.19 and 0.24 inches, among others. 
       FIG. 19  schematically depicts a cross-sectional view corresponding to arrows  19 - 19  from  FIG. 14 , according to one or more aspects described herein. The cross-section of  FIG. 19  additionally depicts an internal cavity  1720  formed within the carbon-fiber walls  1524 . In one specific implementation, the cross-section of  FIG. 19  includes the following specific dimensional values, such that length  1902  may equal 0.357 inches. In another example, length  1902  may range between 0.3 and 0.4 inches, among others. Length  1904  may equal 0.404 inches. In another example, length  1904  may range between 0.38 and 0.43 inches, among others. Length  1906  may equal to 0.41 inches. In another example, length  1906  may range between 0.3 and 0.5 inches, among others. Length  1908  may equal 0.135 inches. In another example, length  1908  may range between 0.12 and 0.17 inches, among others. Length  1910  may equal 0.968 inches. In another example, length  1910  may range between 0.8 and 1.2 inches, among others. Length  1912  may equal 1.233 inches. In another example, length  1912  may range between 1.0 and 1.4 inches, among others. The radius of curvature  1914  may equal 0.197 inches. In another example, the radius of curvature  1914  may range between 0.18 and 0.22 inches, among others. The radius of curvature  1916  may equal 0.16 inches. In another example, the radius of curvature  1916  may range between 0.12 and 0.20 inches, among others. 
       FIG. 20  schematically depicts a cross-sectional view corresponding to arrows  20 - 20  from  FIG. 14 , according to one or more aspects described herein. The cross-section of  FIG. 20  additionally depicts an internal cavity  1720  formed within the carbon-fiber walls  1524 . In one specific implementation, the cross-section of  FIG. 20  includes the following specific dimensional values, such that length  2002  may equal 0.357 inches. In another example, length  2002  may range between 0.3 and 0.4 inches, among others. Length  2004  may equal 0.404 inches. In another example, length  2004  may range between 0.38 and 0.43 inches, among others. Length  2006  may equal to 0.41 inches. In another example, length  2006  may range between 0.3 and 0.5 inches, among others. Length  2008  may equal 0.135 inches. In another example, length  2008  may range between 0.12 and 0.17 inches, among others. Length  2010  may equal 0.972 inches. In another example, length  2010  may range between 0.8 and 1.2 inches, among others. Length  2012  may equal 1.233 inches. In another example, length  2012  may range between 1.0 and 1.4 inches, among others. The radius of curvature  2014  may equal 0.197 inches. In another example, the radius of curvature  2014  may range between 0.18 and 0.22 inches, among others. The radius of curvature  2016  may equal 0.16 inches. In another example, the radius of curvature  2016  may range between 0.12 and 0.20 inches, among others. 
       FIG. 21  schematically depicts a cross-sectional view corresponding to arrows  21 - 21  from  FIG. 14 , according to one or more aspects described herein. The cross-section of  FIG. 21  additionally depicts an internal cavity  1720  formed within the carbon-fiber walls  1524 . In one specific implementation, the cross-section of  FIG. 21  includes the following specific dimensional values, such that length  2102  may equal 0.329 inches. In another example, length  2102  may range between 0.3 and 0.36 inches, among others. Length  2104  may equal 0.395 inches. In another example, length  2104  may range between 0.38 and 0.43 inches, among others. Length  2106  may equal to 0.41 inches. In another example, length  2106  may range between 0.3 and 0.5 inches, among others. Length  2108  may equal 0.181 inches. In another example, length  2108  may range between 0.16 and 0.20 inches, among others. Length  2110  may equal 0.840 inches. In another example, length  2110  may range between 0.7 and 1.0 inches, among others. Length  2112  may equal 1.203 inches. In another example, length  2112  may range between 1.0 and 1.4 inches, among others. The radius of curvature  2114  may equal 0.173 inches. In another example, the radius of curvature  2114  may range between 0.16 and 0.19 inches, among others. The radius of curvature  2116  may equal 0.16 inches. In another example, the radius of curvature  2116  may range between 0.12 and 0.20 inches, among others. 
       FIG. 22  schematically depicts a cross-sectional view corresponding to arrows  22 - 22  from  FIG. 14 , according to one or more aspects described herein. The cross-section of  FIG. 22  additionally depicts an internal cavity  1720  formed within the carbon-fiber walls  1524 . In one specific implementation, the cross-section of  FIG. 22  includes the following specific dimensional values, such that length  2202  may equal 0.753 inches. In another example, length  2202  may range between 0.6 and 0.9 inches, among others. Length  2204  may equal 1.163 inches. In another example, length  2204  may range between 1.0 and 1.3 inches, among others. The radius of curvature  2206  may equal 0.173 inches. In another example, the radius of curvature  2206  may range between 0.16 and 0.19 inches, among others. 
       FIG. 23  schematically depicts a cross-sectional view corresponding to arrows  23 - 23  from  FIG. 14 , according to one or more aspects described herein. The cross-section of  FIG. 23  additionally depicts an internal cavity  1720  formed within the carbon-fiber walls  1524 . In one specific implementation, the cross-section of  FIG. 23  includes the following specific dimensional values, such that length  2302  may equal 0.750 inches. In another example, length  2302  may range between 0.6 and 0.9 inches, among others. Length  2304  may equal 1.160 inches. In another example, length  2304  may range between 1.0 and 1.3 inches, among others. The radius of curvature  2306  may equal 0.173 inches. In another example, the radius of curvature  2306  may range between 0.16 and 0.19 inches, among others. 
     In addition to, or as an alternative to the variable pentagonal and heptagonal cross-sectional geometries described in relation to hockey shaft structures  502  and  1402 , the thicknesses of the sidewalls  622  and  1524  may vary along the lengths  504  and  1404  of the shafts  502  and  1402 . In one example, it is contemplated that the sidewall thickness of sidewalls  622  and/or  1524  may vary by up to 20% along the lengths  504  and  1404  of the respective shafts  502  and  1402 . In another example, the sidewall thickness of sidewalls  622  and/or  1524  may be approximately constant along the lengths  504  and  1404  of the respective shafts  502  and  1402 . 
       FIGS. 24-28  schematically depict stages of a process for molding a shaft having variable cross-sectional geometry, similar to shafts  102 ,  502 , and  1402 .  FIG. 24  schematically depicts a wrapped shaft structure  2400  that includes one or more layers of carbon fiber tape (or a polymeric tape that uses an additional or alternative fiber material)  2402 . The carbon fiber tape  2402  is wrapped around a mandrel  2404 . The mandrel  2404  may have a cross-section that is a rough approximation of the desired cross-section of the hockey stick shaft once molded. As such, the mandrel  2404  may have an approximate rectangular, pentagonal, and/or heptagonal cross-section, among others. In one implementation, the mandrel  2404  is constructed from a metal and/or alloy, such as steel, iron, aluminum, or titanium, among others. It is contemplated that any metal or alloy may be used, in addition to or as an alternative to any ceramic, polymer, or composite material, such as a fiber-reinforced material. The mandrel  2404  may additionally include compressible elements or portions that may allow the wrapped carbon fiber tape  2402  to be removed from the mandrel  2404  prior to molding. Additionally or alternatively, a removal agent, such as a lubricant, may be included in an outer layer of the mandrel  2404  (such as a layer of solid lubricant) or may be added to the mandrel  2404  each use before wrapping with the carbon fiber tape  2402  (such as a liquid lubricant). It is contemplated that the carbon fiber tape  2402  may be wrapped around the mandrel  2404  by one or more machines, or may be manually wrapped. It is contemplated that the carbon fiber tape  2402  may include any number of layers, and that the layers may be oriented in any manner relative to one another, without departing from the scope of these disclosures. In one example, the carbon fiber tape  2402 , when removed from the mandrel  2404 , may be referred to as a wrapped shaft structure. 
       FIG. 25  schematically depicts another stage of a molding process of a hockey stick shaft that has variable cross-sectional geometry, similar to shafts  102 ,  502 , and  1402 . As depicted in  FIG. 25 , the carbon fiber tape  2402  has been removed from the mandrel  2404  to reveal an internal shaft cavity  2502 . An inflatable bladder  2504  is schematically depicted within the cavity  2502 , and the wrapped carbon fiber tape  2402  is schematically depicted within two mold halves  2506  and  2508  of mold  2500 . The mold halves  2506  and  2508  are schematically depicted as being partially separated from one another. In the depicted implementation, the mold halves  2506  and  2508  are both female molds. It is contemplated, however, that more than the two depicted mold halves  2506  and  2508  may be used to mold the hockey stick shaft having variable cross-sectional geometry. Alternatively, a male-female mold may be used in place of the female-female mold depicted in  FIG. 25 . 
       FIG. 25  schematically depicts the mold halves  2506  and  2508  as partially separated from one another.  FIG. 26  schematically depicts the mold  2500  once the halves  2506  and  2508  have been closed together. As such,  FIG. 26  schematically depicts the five-sided mold geometry  2602  that is to be imparted on the wrapped carbon fiber tape  2402 . It is contemplated that the mold geometry  2602  is merely one schematic implementation, and the mold  2500  may have any internal geometry in order to form the variable geometries of hockey stick shafts  102 ,  502 , and  1402 . 
       FIG. 27  schematically depicts a further step in the molding process of a hockey stick shaft having variable cross-sectional geometry, similar to hockey stick shafts  102 ,  502 , and  1402 . In one example,  FIG. 27  schematically depicts one or more processes associated with heating the mold halves  2506  and  2508 . The mold  2500  may be heated in order to activate/melt one or more resins preimpregnated within, or applied to, the wrapped fiber tape  2402 . Simultaneously or subsequently, the inflatable bladder  2504  is inflated, as depicted in  FIG. 27 , which imparts a force on the internal walls of the hockey stick shaft and urges the wrapped carbon fiber tape  2402  toward the walls of the mold  2500 . As depicted in  FIG. 27 , the inflatable bladder  2504  may completely fill the internal cavity  2502 . It is contemplated that the inflatable bladder  2504  may be used in combination with one or more insert elements configured to apply force to the internal walls of the wrapped carbon fiber tape  2402 . 
     Following the heating and expansion of the bladder  2504  that mold  2500  may be cooled in order to allow the resin on and/or within the wrapped carbon fiber tape  2402  to solidify. The bladder  2504  is deflated and may be removed from the cavity  2502  in order reveal the molded hockey stick shaft.  FIG. 28  schematically depicts one example of molded hockey stick shaft  2800 , similar to one or more of shafts  102 ,  502 , and  1402 . As depicted the bladder  2504  has been removed in order to reveal the internal cavity  2502  that extends along at least a portion of a longitudinal length of the shaft  2800 . 
     As previously described, the use of non-standard geometry in the cross-section of a hockey shaft (i.e. geometry that is not rectangular or rounded rectangular) the hockey shaft may have its flexural rigidity increased by increasing the value of the second moment of inertia, I (see, e.g., Equation 1). By using cross-sectional geometries that vary along the length of the hockey stick shaft (e.g., along the longitudinal length  504  of shaft  502 , and/or the longitudinal length  1404  of shaft  1402 , otherwise referred to as the shaft lengths  504  and  1404 ), the flexural rigidity or bending stiffness of a given shaft can vary at different points along the shaft.  FIGS. 5-13  and  FIGS. 14-23  depict examples of five-sided and seven-sided cross-sectional shaft geometries. It is contemplated, however, that the specific geometries may be varied beyond those described in  FIGS. 5-13  and  FIGS. 14-23 , without departing from the scope of these disclosures. 
     Further advantageously, the use of cross-sectional geometries that vary along the length of a stick shaft (e.g., along the longitudinal length  504  of shaft  502 , and/or the longitudinal length  1404  of shaft  1402 ) may allow the position of a kick point of a shaft to be specified for a given shaft. As such, it is contemplated that the structures and processes described herein for the production of a hockey stick shafts having variable cross-sectional geometries may be used to position the kick point at any location along a hockey stick, such as hockey stick  100  and/or  400 . 
       FIG. 29  depicts the bending stiffness of the five-sided hockey stick shaft  502  compared to a conventional hockey stick shaft having a uniform rectangular cross-sectional geometry. In particular, graph  2908  depicts how the bending stiffness (y-axis,  2904 ) varies along the hockey stick shaft length (x-axis,  2902 ) for a conventional hockey stick shaft having a uniform rectangular cross-sectional geometry. Graph  2906  depicts how the bending stiffness (y-axis,  2904 ) varies along the hockey stick shaft length (x-axis,  2902 ) for the hockey stick shaft  502  of  FIG. 5  having pentagonal cross-sectional geometries. In one example,  FIG. 29  schematically depicts that the bending stiffness of the pentagonal cross-sectional geometry of shaft  502  represented in graph  2906  may be increased over that of the conventional hockey stick shaft cross-sectional geometry represented in graph  2908  by the difference indicated as  2910 . In one example, the variable bending stiffness depicted in graph  2906  may result from a variable shaft geometry, and hence, second moment of inertia, along the shaft length. As such, a first portion of a hockey stick shaft may have a first cross-sectional geometry associated with a first bending stiffness and a second portion of the hockey stick shaft may have a second cross-sectional geometry associated with a second bending stiffness. In one example, a maximum increase in bending stiffness  2910  may be at least 20% or at least 25%. In another example, the increase in bending stiffness  2910  may range between 0% and 40% along the length of the hockey stick shaft. 
     In another example, a first portion of a hockey stick shaft, such as shaft  502 , may have a first bending stiffness, which may be increased over a conventional stick shaft by amount  2912 . In one implementation, the amount  2912  may range between 0 and 20%. A second portion of the hockey stick shaft, such as shaft  502 , may have a second bending stiffness, which may be increased over a conventional stick shaft by amount  2914 . In one implementation, the amount  2914  may range between 0 and 30%. A third portion of the hockey stick shaft, such as shaft  502 , may have a third bending stiffness, which may be increased over a conventional stick shaft by amount  2910 . In one implementation, the amount  2916  may range between 0 and 40%. A fourth portion of the hockey stick shaft, such as shaft  502 , may have a fourth bending stiffness, which may be increased over a conventional stick shaft by amount  2916 . In one implementation, the amount  2916  may range between 0 and 35%. 
       FIG. 30  depicts the bending stiffness of the seven-sided hockey stick shaft  1402  compared to a conventional hockey stick shaft having a uniform rectangular cross-sectional geometry. In particular, graph  3008  depicts how the bending stiffness (y-axis,  3004 ) varies along the hockey stick shaft length (x-axis,  3002 ) for a conventional hockey stick shaft having a uniform rectangular cross-sectional geometry. Graph  2906  depicts how the bending stiffness (y-axis,  3004 ) varies along the hockey stick shaft length (x-axis,  3002 ) for the hockey stick shaft  1402  of  FIG. 14  having heptagonal cross-sectional geometries. In one example,  FIG. 30  schematically depicts that the bending stiffness of the heptagonal cross-sectional geometry of shaft  1402  represented in graph  3006  may be increased over that of the conventional hockey stick shaft cross-sectional geometry represented in graph  3008  by the difference indicated as  3010 . In one example, the variable bending stiffness depicted in graph  3006  may result from a variable shaft geometry, and hence, second moment of inertia, along the shaft length. As such, a first portion of a hockey stick shaft may have a first cross-sectional geometry associated with a first bending stiffness and a second portion of the hockey stick shaft may have a second cross-sectional geometry associated with a second bending stiffness. In one example, this maximum increase in bending stiffness  3010  may be at least 25%, or at least 30%. In another example, the increase in bending stiffness  3010  may range between 0% and 40% along the length of the hockey stick shaft. 
     In another example, a first portion of a hockey stick shaft, such as shaft  1402 , may have a first bending stiffness, which may be increased over a conventional stick shaft by amount  3012 . In one implementation, the amount  3012  may range between 0 and 35%. A second portion of the hockey stick shaft, such as shaft  1402 , may have a second bending stiffness, which may be increased over a conventional stick shaft by amount  3010 . In one implementation, the amount  3010  may range between 0 and 50%. A third portion of the hockey stick shaft, such as shaft  1402 , may have a third bending stiffness, which may be increased over a conventional stick shaft by amount  3014 . In one implementation, the amount  3014  may range between 0 and 40%. A fourth portion of the hockey stick shaft, such as shaft  1402 , may have a fourth bending stiffness, which may be increased over a conventional stick shaft by amount  3016 . In one implementation, the amount  3016  may range between 0 and 35%. 
       FIG. 31  schematically depicts another view of the hockey stick blade structure  104 , according to one or more aspects described herein. As depicted, the molded blade structure  104  may be coupled to an end  3102  of a stick shaft  102 . In one example, this end  3102  may be referred to as a proximal end  3102  of the stick shaft  102 . The second end  3104  of shaft  102  is depicted in  FIG. 1 , and may be referred to as a distal end  3104 . The molded blade structure  104  may include a top edge  118  that is spaced apart from a bottom edge  132  by a blade height  120 . Additionally, the blade structure  104  may include a heel  110  spaced apart from a toe  112  by a blade length  128 . Further, the blade structure  104  may include a front face  106  that is spaced apart from a back face  108  (not depicted in  FIG. 31 ) by a blade thickness (not depicted in  FIG. 31 ). It is contemplated that any of the dimensions described throughout this disclosure may have any values. Further, indicated lengths are merely schematic representations, and the start and end points of the depicted dimensions may vary from those depicted in the accompanying figures. Additionally, a given dimension, such a thickness of the blade structure  104 , may be non-uniform. For example, a thickness of the blade structure  104  may vary along the blade height  120 , and/or along the blade length  128 , without departing from the scope of these disclosures. 
     The blade structure  104  additionally includes a slot  114 , which forms an aperture that extends through the blade thickness between the front face  106  and the back face  108 . The slot  114  has a length  130  and a height  122 . Additionally, the slot has a bottom edge  3108 , a top edge  3110 , a toe end  3112 , and a heel end  3114 . As depicted, the slot  114  has rounded toe end  3112  and heel end  3114 . However, alternative end geometries may be utilized, such as square ends, among others. 
     Advantageously, the slot  114  allows the blade structure  104  to exhibit enhanced flexing and energy transfer capabilities. In particular, the slot allows the blade structure  104  to have flexing characteristics similar to a “slingshot” during a shooting or other puck-striking (or ball-striking) motion. In one example, the slot  114  separates a first area (portion) of the blade structure  104  that has a first stiffness from a second area (portion) of the blade structure  104  that has a second stiffness. In one example, the differential is blade stiffness across the blade height  120 , facilitated by the presence of the slot  114 , allows the blade to behave in a manner comparable to a slingshot, and result in more energy being transferred to the puck/ball. When described herein, the comparatively stiffer portion  3120  may be comparatively stiffer than an equivalent area of a hockey stick blade that does not include a slot  114 . Similarly, the comparatively more flexible portion  3122  may be comparatively more flexible than an equivalent area of a hockey stick blade that does not include a slot  114 . Accordingly the comparatively stiffer portion of the blade structure  104  may brace against the flexing of the comparatively less stiff portion of the blade structure  104  during a shooting action. As such, the interaction between the comparatively stiff and flexible portions of the blade structure  104  may result in more energy being transferred to a puck/ball, when compared to a conventional hockey stick blade implementation. In turn, this increased energy transfer may result in faster puck/ball motion. 
       FIG. 31  schematically illustrates the stiffened top portion  3120  and the flexible bottom portion  3122  of the blade structure  104 . In the depicted implementation, the blade structure  104  includes two areas (portions  3120  and  3122 ) having differing stiffness characteristics. However, in alternative implementations, the blade structure  104  may be broken up into additional areas with additional stiffness characteristics. As depicted, the stiffened top portion  3120  extends along the full blade length  128  between the heel  110  and the toe  112 . Additionally, the stiffened top portion  3120  includes a toe portion  3124  that extends between the top edge  118  and the bottom edge  132  at the toe  112  of the blade structure  104 , and a heel portion  3126  that extends substantially between the top edge  118  and the bottom edge  132  at the heel  110  of the blade structure  104 . 
     The slot  114  may additionally include an edge reinforcing material  3130  that extends around a perimeter of the slot  114 . In one example, the edge reinforcing material  3130  is formed by adding one or more additional layers of fiber material around the perimeter of the slot  114  prior to molding of the blade structure  104 . 
     It is noted that the schematic geometries of the stiffened top portion  3120  and the flexible bottom portion  3122  depicted in  FIG. 31  are merely one example configuration of the blade structure  104  that has areas of differing stiffness separated by the slot  114 . Indeed,  FIG. 32  schematically depicts another example implementation of the blade structure  104  having a stiffened top portion  3120 , a flexible bottom portion  3122 , and a slot  114  separating at least a portion of those areas  3120  and  3122  from one another. As depicted, the stiffened top portion  3120  and the flexible bottom portion  3122  have different geometries to those depicted in  FIG. 31 . In particular, the toe portion  3124  of the stiffened top portion  3120  extends only partially between the top edge  118  and the bottom edge  132 . Similarly, the heel portion  3126  extends only partially between the top edge  118  and the bottom edge  132 . 
       FIG. 33  schematically depicts another example implementation of the blade structure  104  having a stiffened top portion  3120 , a flexible bottom portion  3122 , and a slot  114  separating at least a portion of those areas  3120  and  3122  from one another. In particular,  FIG. 33  depicts the stiffened top portion  3120  as having a larger heel portion  3126  than that depicted in  FIG. 31  and  FIG. 32 . Accordingly, it will be appreciated that the geometries of the top portion  3120  and the bottom portion  3122  depicted in  FIGS. 31-33  merely represent a limited number of possible variations in the size and shape of the portions  3120  and  3122 . It is contemplated that any geometries of these portions  3120  and  3122  may be utilized, without departing from the scope of these disclosures. 
     In one example, the hockey stick blade structure  104  includes the described stiffened top portion  3120  and flexible bottom portion  3122 . As such, the stiffened top portion  3120  may have a stiffness that is comparatively higher than the flexible bottom portion  3122 . In another example, the bottom portion  3122  may have a comparatively higher stiffness than the top portion  3120 . Accordingly, the stiffness of the flexible bottom portion  3122  may be higher than that of the stiffened top portion  3120 . However, the flexible bottom portion  3122  may have a stiffness that is still lower than an equivalent area of a hockey stick blade that does not include a slot  114 . Similarly, the stiffened top portion  3120  may have a stiffness value that is lower than the flexible bottom portion  3122 , but comparatively higher than an equivalent area of a hockey stick blade structure that does not include a slot  114 . 
     In another implementation, and as schematically depicted in  FIG. 34 , the hockey stick blade structure  104  may include a slot support element  3134  that extends through the slot  114 . This slot support element  3134  may serve to reinforce the blade structure  104 . In one example, the slot support arm  3134  is connected between the top edge  3110  and the bottom edge  3108  of the slot  114 . As schematically depicted in  FIG. 34 , the slot support element  3134  may form part of the stiffened top portion  3120  of the blade structure  104 . As such, the slot support element  3134  may be formed from materials similar to the rest of the stiffened top portion  3120 . In particular, the slot support element  3134  may include a foam core onto which one or more layers of fiber tape are layered and molded. Additionally or alternatively, the slot support element  3134  may be formed of a solid material (such as a metal, alloy, polymer, fiber-reinforced material, or combination thereof, among others). However, in an alternative implementation, the slot support element  3134  may form part of the flexible bottom portion  3122 . As depicted, the slot support element  3134  divides the slot  114  into two portions: a toe slot portion  114   a  and a heel slot portion  114   b.  In alternative implementations, additional slot support elements, similar to element  3134 , may be utilized, without departing from the scope of these disclosures. 
       FIG. 35  schematically depicts an alternative implementation of a hockey stick blade structure  104 . In particular,  FIG. 35  schematically depicts slot tie elements  3140   a  and  3140   b  that connect the top edge  3110  to the bottom edge  3108  of the slot  114 . The slot tie elements  3140   a  and  3140   b  may be formed from one or more of a fiber-reinforced material, a metal, an alloy, or a polymer, among others. The depicted slot tie elements  3140   a  and  3140   b  are merely one exemplary implementation, and different geometries may be utilized, without departing from the scope of these disclosures. In one example, the slot tie elements  3140   a  and  3140   b  do not form part of the stiffened top portion  3120  or the flexible bottom portion  3122  of the blade structure  104 . The slot tie elements  3140   a  and  3140   b  may be utilized to prevent the slot  114  from excessive deformation during a shot motion. As depicted in  FIG. 35 , the blade structure  104  includes two slot tie elements  3140   a  and  3140   b  that divides the slot  114  into three portions:  114   a,    114   b,  and  114   c.  However, the blade structure  104  may use a single slot tie element, or three or more slot tie elements, without departing from the scope of these disclosures. 
       FIG. 36  depicts the hockey stick blade structure  104  with a schematic cutting plane between arrows  37 - 37 . This cutting plane corresponds to the cutting plane of the cross section depicted in  FIG. 37 . 
       FIG. 37  depicts a cross-sectional view of the hockey stick blade structure  104  along the cutting plane depicted in  FIG. 36 . Further,  FIG. 37  depicts the hockey stick blade structure  104  after it has been molded. Accordingly,  FIG. 37  depicts a cross-sectional view of the stiffened top portion  3120  and the flexible bottom portion  3122 , separated by the slot  114 . In one example, the front face  106  of the hockey stick blade structure  104  separated from the back face  108  by a blade thickness  3702 . It is contemplated that this blade thickness  3702  may have any value. Additionally, it is contemplated that the blade thickness  3702  will vary across the blade height  120  and/or blade length  128 . In one example, the blade structure  104  includes a foam core. This foam core may include two foam core portions  3704  and  3706 . In alternative implementations, a single foam core portion, or three or more portions may be used, without departing from the scope of these disclosures. In one example, a top foam core portion  3704  may form the core of the stiffened top portion  3120 , and a bottom foam core portion  3706  a form the core of the flexible bottom portion  3122 . The hockey stick blade structure  104  may be formed by layering fiber reinforced material (e.g., carbon fiber tape that may be preimpregnated with resin, or may have resin separately applied) onto the foam cores  3704  and  3706 . In order to stiffen the top portion  3120  of the blade structure  104 , additional layers of fiber material may be added to the top portion  3120 . As such, the top portion  3120  may have a greater sidewall thickness than the bottom portion  3122 . Additionally, the stiffness differential between the stiffened top portion  3120  and the flexible bottom portion  3122  may result from the larger cross-sectional area of the flexible bottom portion  3122 . As previously described, the perimeter of the slot  114  may be reinforced with an edge reinforcing material  3130 . This edge reinforcing material  3130  may include one or more additional layers of fiber-reinforced material when compared to the sidewalls of the front face  106  and back face  108 . These additional layers may result in an increased sidewall thickness, and comparatively higher strength and/or hardness at the edge of the slot  114 . 
       FIG. 38  depicts two form core portions that are used in the hockey stick blade structure  104 . As depicted, when the top foam core portion  3704  is positioned proximate the bottom foam core portion  3706 , the geometries of the foam core portions include an aperture for the slot  114 . Seam  3802  represents the intersection of the top foam core portion  3704  with the bottom foam core portion  3706 . In order to couple the top foam core portion  3704  to the bottom foam core portion  3706 , a bridge is positioned between the foam core portions  3704  and  3706  along the seam  3802 . This bridge is schematically depicted in  FIG. 39  as element  3902 , and may be formed from one or more layers of a fiber-reinforced material that extend between the foam core portions  3704  and  3706 . In one example implementation, one or more top bridge fiber layers  3904  of fiber-reinforced material are positioned between the foam core portions  3704  and  3706  along the top foam core portion  3704 , and one or more bottom bridge fiber layers  3906  of fiber-reinforced material are positioned between the between the foam core portions  3704  and  3706  along the bottom foam core portion  3706 . Additionally or alternatively, a bridge structure may be formed between the foam core portions  3704  and  3706  using an adhesive or an epoxy (including an epoxy strip or epoxy core), among others. Further, a bridge structure may be formed between the foam core portions  3704  and  3706  using one or more materials in addition to or as an alternative to the fiber-reinforced material described above. These additional or alternative materials may include one or more polymers, ceramics, metals or alloys, among others. Subsequently, additional layers of fiber-reinforced material may be added to the foam core portions  3704  and  3706  and this pre-mold structure, otherwise referred to as a wrapped preform blade structure, may be molded to form the final geometry of the blade structure  104 . It is contemplated that the foam core portions  3704  and  3706  may be formed of any foam material with any foam density. In another example, the blade structure  104  may be constructed without the seam  3802  and bridge structure. Alternatively, the blade structure  104  may be constructed with the seam  3802 , but without the bridge structure The blade structure  104  may alternatively include a partially or fully hollow core, such that one or more of the foam core potions  3704  and  3706  are not utilized. Accordingly, the blade structure  104  may be constructed by wrapping fiber-reinforced material around an inflatable bladder element. As such, the bladder element may be inflated during a molding process to urge the sidewalls of the blade structure  104  to conform to the geometries of the mold. The bladder may be removed or deflated and left within the molded blade structure  104  after one or more molding processes have been completed. 
       FIGS. 40-42  schematically depict tests performed on the blade structure  104  that includes a slot  114  to determine the bending/stiffness characteristics of the blade  104  when compared to a conventional stick blade that does not include a slot. In particular, three different types of bending tests were carried out. The first test is schematically depicted in  FIG. 40 , and is a measurement of the force required to give rise to a 5 mm displacement of the flexible bottom portion  3122  of the blade structure  104 . Specifically,  FIG. 40  depicts a plan and elevation view of the blade structure  104 . Elements  4004  and  4006  represent support points, and element  4002  is the point at which a force is applied to the flexible bottom portion  3122  to result in a displacement of the flexible bottom portion  3122  by 5 mm. 
       FIG. 41  schematically depicts a plan and an elevation view of a second bending test carried out on the blade structure  104 . In particular,  FIG. 41  schematically depicts a test of the force required to displace the stiffened upper portion  3120  by 5 mm. In this case, the force is applied at point  4102 . 
       FIG. 42  schematically depicts a plan and an elevation view of a third bending test carried out on the blade structure  104 . In particular,  FIG. 42  schematically depicts a test of the force required to displace the whole blade  104  by 5 mm. In this case, the force is applied along line  4202 . 
     The testing results of the bending tests carried out on the blade structure  104  that includes a slot  114  are compared to testing results of a conventional hockey stick blade structure that does not include a slot. In this regard, the flexible bottom portion  3122  is found to have a stiffness that is approximately 3% lower than an equivalent area of a hockey stick blade structure that does not include a slot  114 . In another example, the flexible bottom portion  3122  is found to have a stiffness that is lower than an equivalent area of a hockey stick blade structure that does not include a slot  114 , with the comparative decrease in stiffness ranging between 0% and 15%. The testing described in relation to  FIG. 41  indicated that the stiffened top portion  3120  has a stiffness that is approximately 11% higher than an equivalent area of a hockey stick blade structure that does not include a slot  114 . In another example, the stiffened top portion  3120  is found to have a stiffness that is higher than an equivalent area of a hockey stick blade structure that does not include a slot  114 , with the comparative increase in stiffness ranging between 5% and 25%. The testing described in relation to  FIG. 42  indicated that the whole blade structure  104  has a stiffness that is approximately 32% higher than an equivalent hockey stick blade structure that does not include a slot  114 . In another example, the hockey stick blade structure  104  is found to have a stiffness that is higher than an equivalent area of a hockey stick blade structure that does not include a slot  114 , with the comparative increase in stiffness ranging between 25% and 45%. In one example, the stiffness of the flexible bottom portion  3122  may differ from the stiffness of the stiffened top portion  3120  by at least 2%. 
     In certain examples, the various structures described throughout this disclosure may be manufactured using additional or alternative manufacturing techniques. In one implementation, one or more of the structures of the hockey stick structure  100  may be manufactured using one or more resin transfer molding processes. In particular, one or more of the molded structures of the hockey stick structure  100  may be formed by positioning fiber-reinforced material (e.g., fiber braids or woven elements) into a mold, whereby the fiber-reinforced material is referred to as “dry fiber,” and has not been preimpregnated with resin or had resin or another bonding agent applied. Subsequently, resin is injected into the tooling to complete the molding processing. 
     In another example, one or more of the structures of the hockey stick  100  may be manufactured using additive manufacturing processes. In certain examples implementations, these additive manufacturing processes may be referred to as 3-D printing processes. For example, the blade structure  104 , or another portion of the hockey stick  100 , may be formed using one or more additive manufacturing techniques that facilitate the production of complex internal lattice structures within the blade structure  104 , or another portion of the hockey stick structure  100 . These additive manufacturing processes may include one or more of the following types of processes, including: VAT polymerization, material jetting, binder jetting, material extrusion, powder fusion, sheet lamination, or directed energy deposition. The various manufacturing processes described throughout this disclosure may additionally be used to form microlattice structures within the hockey stick structure  100 , such as with the blade structure  104 . These microlattice structures are described in further detail in U.S. Pat. No. 9,925,440, filed 13 May 2014, the entire contents of which are incorporated herein by reference. 
     It is contemplated that any combination of the various manufacturing processes and techniques described in this disclosure may be used to form any of the blades or shafts discussed herein including the hockey stick structure  100 , or portions thereof. In particular, the described manufacturing processes may be utilized to impart variable flexing characteristics on the blade structure  104  by defining the stiffness characteristics of one or more portions of the blade structure (e.g., portions  3120  and  3122 , among others). Further, any combination of the described manufacturing processes may be used to produce the bridge structures of the described blade  104 . In one specific implementation, a microlattice structure or another structural geometry may be formed as a bridge element within the blade  104 , similar to bridge  3902 . The structural features (e.g., microlattice structure) formed by the use of, among others, additive manufacturing processes, may allow for the stiffness characteristics of the blade structure  104  to be varied between different portions of the blade  104 , and in some cases may allow the stiffness to be increased without an increase in structural mass, when compared to structures formed by alternative processes. Additionally, the use of additive manufacturing may facilitate mass reduction in combination with increased stiffness by forming internal supports scaffolding (lattices) within, for example, the blade  104 , that are stiffer and lighter than alternative structures. 
     A formed hockey stick structure may include a shaft that has a variable cross-sectional geometry. In one aspect, a method of fabricating a formed hockey stick structure that has variable shaft geometry may include forming a shaft structure. The formation of the shaft structure may include wrapping a mandrel with fiber tape to form a wrapped shaft structure, removing the mandrel from the wrapped shaft structure to form an internal shaft cavity, and inserting an inflatable bladder into the shaft cavity. The wrapped shaft structure may be positioned within a mold, and the mold may be heated and the bladder may be expanded within the cavity to exert an internal pressure on the cavity to urge the fiber tape toward the walls of the mold. The mold may be cooled and the bladder contracted and removed. The method of fabricating a formed hockey stick structure may additionally include forming a hockey stick blade structure, and coupling the shaft structure to the blade structure. The walls of the mold may impart an outer geometry on the shaft structure that includes a first portion having a cross-sectional geometry with at least five sides along a length of the shaft structure, and the second portion. The first portion of the shaft structure may have a first bending stiffness that is greater than a second bending stiffness of the second portion, due to the first portion having a greater second moment of inertia than the second portion. 
     In one example, the first portion of the shaft structure may have a first shaft sidewall thickness and the shaft structure may also include a third portion with a second shaft sidewall thickness, less than the first shaft sidewall thickness. 
     In one example, the cross-sectional geometry of the first portion of a hockey stick shaft structure with at least five sides includes a flat surface facing a front of the hockey stick, and an apex facing a back of the hockey stick. 
     In another example, the second portion of the shaft structure may have a rectangular cross-section along the length of the shaft structure. 
     In one example, the first portion and the second portion of the shaft structure may have approximately a same elastic modulus. 
     In another example, the first portion and the second portion of the shaft structure may have approximately a same sidewall thickness. 
     In another example, the first portion may have a heptagonal cross-sectional geometry. 
     In another example, the hockey stick blade structure may include a slot extending from a front face to a back face along a portion of the length of the hockey stick blade structure. 
     In one example, the slot may be substantially parallel to a top edge of the hockey stick blade structure. 
     In another aspect, a shaft structure of a hockey stick may be formed by a method that includes the steps of wrapping a mandrel with fiber tape to form a wrapped shaft structure, and removing the mandrel from the wrapped shaft structure to reveal an internal shaft cavity. An inflatable bladder may be inserted into the internal shaft cavity, and the wrapped shaft structure may be positioned within a mold. The mold may be heated and the bladder expanded within the cavity to urge the fiber tape toward the walls of the mold. The mold may be cooled, the bladder contracted, and the bladder removed from the shaft structure. The walls of the mold may impart an outer geometry on the shaft structure that includes a first portion having a cross-sectional geometry with at least five sides along a length of the shaft structure, and a second portion. The first portion of the shaft structure may have a first bending stiffness that is greater than a second bending stiffness of the second portion, due to the first portion having a greater second moment of inertia than the second portion. 
     In one example, the first portion of the shaft structure may have a first shaft sidewall thickness and the shaft structure further includes a third portion with a second shaft sidewall thickness, less than the first shaft sidewall thickness. 
     In one example, the cross-sectional geometry of the first portion of the shaft structure with at least five sides includes a flat surface facing a front of the hockey stick, and an apex facing a back of the hockey stick. 
     In another example, the second portion of the shaft structure has a rectangular cross-section. 
     In another example, the first portion and the second portion of the shaft structure may have approximately a same elastic modulus. 
     In another example, the first portion and the second portion of the shaft structure have approximately a same sidewall thickness. 
     In one example, the first portion may have a heptagonal cross-sectional geometry. 
     In another aspect, a hockey stick apparatus may include a hollow shaft structure molded from wrapped fiber tape, with the hollow shaft structure further including a longitudinal length of first portion of which may have a cross-sectional geometry with at least five sides and a first flexural rigidity. A second portion of the longitudinal length of the hollow shaft structure may have a second flexural rigidity less than the first flexural rigidity. A molded blade structure may be rigidly coupled to a proximal end of the hollow shaft structure. 
     In one example, the first flexural rigidity of the first portion may be higher than the second flexural rigidity due to a higher second moment of area of the cross-sectional geometry of the first portion, and the elastic moduli of the materials of the first portion and the second portion may be approximately the same. 
     In another example, the first portion and the second portion of the hollow shaft structure may have an approximately same sidewall thickness. 
     In yet another example, the first portion may have a heptagonal cross-sectional geometry. 
     In another example, the molded blade structure may include a slot extending from a front face to a back face along a portion of a length of the molded blade structure. 
     In another example, the slot may be substantially parallel to a top edge of the molded blade structure. 
     In another aspect, a hockey stick apparatus may include a hollow shaft structure that has a proximal end and a distal end. The hockey stick apparatus may additionally include a molded blade structure that is coupled to the proximal end of the hollow shaft structure. The molded blade structure may additionally include a top edge that is spaced apart from a bottom edge by a blade height, a heel that is spaced apart from a toll by a blade length, a front face that is spaced apart from a back face by a blade thickness, and a slot that defines an aperture that extends through the blade thickness between the front face and the back face. The slot may extend along a portion of the blade length, and the slot may have a top edge, a bottom edge, a toe end and a heel end. The molded blade structure may additionally include a stiffened top portion that extends between the top edge of the blade structure and the top edge of the slot along a portion of the blade length. The molded blade structure may also include a flexible bottom portion that extends between the bottom edge of the blade structure and the bottom edge of the slot along a portion of the blade length. The stiffened top portion may have a first stiffness and the flexible bottom portion may have a second stiffness that is different to the first stiffness. The stiffened top portion may brace against flexing of the flexible bottom portion of the blade structure. 
     In one example, the stiffened top portion extends along a fold length of the blade. 
     In another example, the stiffened top portion has a toe portion that extends between the top edge of the blade and the bottom edge of the blade structure at a toe of the blade structure. The stiffened top portion may additionally have a heel portion that extends between the top edge of the blade structure and the bottom edge of the blade structure at the heel of the blade structure. 
     The molded blade structure may be formed from layers of fiber-reinforced tape, and the flexible bottom portion of the blade structure may include fewer layers than the stiffened top portion of the blade structure. 
     The top edge, the bottom edge, the toe end, and the heel end of the slot may include an edge reinforcement material. 
     The top edge of the slot may be substantially parallel to a top edge of the hockey stick blade structure. 
     The slot may extend along at least 60% of the blade length. 
     The slot height between the top edge and the bottom edge of the slot may measure at least 10% of the blade height. 
     The molded blade structure may include a foam core, and the foam core may extend through the flexible bottom portion and the stiffened top portion of the blade structure. 
     In another aspect, a hockey stick blade may include a top edge spaced apart from a bottom edge by a blade height, a heel spaced apart from a toe by a blade length, a front face spaced apart from a back face by a blade thickness, and a slot that defines an aperture that extends through the blade thickness between the front face and the back face. The slot may extend along a portion of the blade length, and have a top edge, a bottom edge, a toe end and a heel end. A top portion of the blade structure may extend between the top edge of the blade structure and the top edge of the slot along a portion of the blade length. A bottom portion of the blade structure may extend between the bottom edge of the blade structure and the bottom edge of the slot along a portion of the blade length. 
     The slot may extend along at least 60% of the blade length. 
     A slot height between the top edge and the bottom edge of the slot may measure at least 10% of the blade height. 
     The top portion may have a first stiffness and the bottom portion may have a second stiffness, different to the first stiffness, and the top portion may brace against flexing of the bottom portion of the blade structure. 
     The first and second stiffness values may differ by at least 2%, or at least 1%, or at least 5%, or at least 10%. 
     The top portion may extend along the full blade length. 
     In another aspect, a method of fabricating a formed hockey stick blade structure may include forming a pre-mold blade structure by adding layers of fiber tape to a form core,. The pre-mold blade geometry may have a bottom edge spaced apart from a top edge by a blade height, a heel spaced apart from a toe by a blade length, a front face spaced apart from a back face by a blade thickness, and a slot defining an aperture that extends between the front face and the back face through the full blade thickness. The slot may have a top edge, a bottom edge, a toe end and a heel end. The method may additionally include positioning the pre-mold blade structure within a mold, heating and cooling the mold, and removing the formed hockey stick blade structure from the mold. 
     The present disclosure is disclosed above and in the accompanying drawings with reference to a variety of examples. The purpose served by the disclosure, however, is to provide examples of the various features and concepts related to the disclosure, not to limit the scope of the invention. One skilled in the relevant art will recognize that numerous variations and modifications may be made to the examples described above without departing from the scope of the present disclosure.