Patent Publication Number: US-11659882-B2

Title: Helmet padding system

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of U.S. patent application Ser. No. 15/923,117, filed Mar. 16, 2018, which is a continuation-in-part of U.S. patent application Ser. No. 15/898,814, filed Feb. 19, 2018, which is a continuation-in-part of U.S. patent application Ser. No. 15/644,145, filed Jul. 7, 2017, which is a continuation in part of U.S. patent application Ser. No. 15/488,650, filed Apr. 17, 2017, which is a continuation-in-part of U.S. patent application Ser. No. 14/729,266, filed Jun. 3, 2015, which is a continuation-in-part of U.S. patent application Ser. No. 14/493,869, filed Sep. 23, 2014, which is a continuation-in-part of U.S. patent application Ser. No. 14/275,046, filed May 12, 2014. U.S. patent application Ser. No. 14/493,869 is also a non-provisional application of U.S. Patent Application No. 61/942,743, filed Feb. 21, 2014. The contents of each of the above applications are incorporated by reference herein in their entireties. 
    
    
     FIELD OF THE INVENTION 
     The invention relates generally to the field of protective headgear, and more particularly, to impact-resistant padding for protective headgear. 
     BACKGROUND OF THE INVENTION 
     Conventionally, participants in “contact” sports (e.g., wrestling, football, rugby) wear protective headgear to cushion the force of impacts that are regularly received during those events. In recent years, the negative health effects of the impacts to the head experienced during such contact sports have been a matter of focus. These negative health effects can be diminished or minimized by effectively cushioning participants from the forces of impacts. Accordingly, improved structures, such as impact-resistant headgear, are desired to lessen the impact forces experienced by those participants. 
     SUMMARY OF THE INVENTION 
     Aspects of the present invention are directed to helmet padding systems. 
     In accordance with one aspect of the present invention, a helmet padding system includes a rigid shell and a spacing pad. The rigid shell is configured to cover a top of a user&#39;s head and be worn under a piece of headgear. The rigid shell includes a first pair of slots configured to extend in a direction from a back of the user&#39;s head toward a front of the user&#39;s head when the rigid shell is worn on the user&#39;s head. The first pair of slots define a central portion and opposed side portions of the rigid shell. The central portion includes at least one flap extending from the central portion across one of the first pair of slots and covering a first region of one of the opposed side portions of the rigid shell. A spacing pad is positioned within the rigid shell. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention is best understood from the following detailed description when read in connection with the accompanying drawings, with like elements having the same reference numerals. When a plurality of similar elements are present, a single reference numeral may be assigned to the plurality of similar elements with a small letter designation referring to specific elements. When referring to the elements collectively or to a non-specific one or more of the elements, the small letter designation may be dropped. According to common practice, the various features of the drawings are not drawn to scale unless otherwise indicated. To the contrary, the dimensions of the various features may be expanded or reduced for clarity. Included in the drawings are the following figures: 
         FIG.  1    is an image illustrating an exemplary helmet padding system in accordance with aspects of the present invention; 
         FIG.  2    is an image illustrating an exemplary helmet shell of the helmet padding system of  FIG.  1   ; 
         FIG.  3    is an image illustrating exemplary absorption pads of the helmet padding system of  FIG.  1   ; 
         FIG.  4    is an image illustrating an exemplary spacing pad of the helmet padding system of  FIG.  1   ; 
         FIG.  5    is an image of the exemplary spacing pad of  FIG.  4    in a helmet shell; 
         FIG.  6    is an image Illustrating another exemplary spacing pad of the helmet padding system of  FIG.  1   ; 
         FIG.  7    is an image of the exemplary spacing pad of  FIG.  6    in a helmet shell; 
         FIG.  8    is an image illustrating yet another exemplary spacing pad of the helmet padding system of  FIG.  1   ; 
         FIGS.  9 A- 9 D  are images illustrating an exemplary impact-resistant pad in accordance with aspects of the present invention; 
         FIG.  10 A- 10 C  are images illustrating an exemplary protective headgear system in accordance with aspects of the present invention; 
         FIG.  11    is an image illustrating another exemplary protective headgear system in accordance with aspects of the present invention; 
         FIG.  12    is a cross-sectional diagram illustrating another exemplary helmet padding system in accordance with aspects of the present invention; 
         FIG.  13    is an image illustrating another exemplary spacing pad of the helmet padding system of  FIG.  1   ; 
         FIGS.  14 A- 14 D  are images illustrating another exemplary helmet padding system in accordance with aspects of the present invention; 
         FIGS.  15 A- 15 C  are images illustrating an alternative embodiment of the exemplary helmet padding system of  FIGS.  14 A- 14 D ; 
         FIGS.  16 - 18    are images Illustrating embodiments of another exemplary helmet padding system in accordance with aspects of the present invention; 
         FIGS.  19 A and  19 B  are images illustrating another exemplary helmet padding system in accordance with aspects of the present invention; 
         FIGS.  19 C and  19 D  are images illustrating a cross-sectional view of the exemplary helmet padding system of  FIGS.  19 A and  19 B ; 
         FIGS.  20 A and  20 B  are images illustrating an alternative embodiment of the helmet padding system of  FIGS.  19 A and  19 B ; 
         FIG.  21    is another image illustrating the embodiment of  FIGS.  20 A and  20 B  within a conventional cap; and 
         FIGS.  22  and  23    are images illustrating another exemplary helmet padding systems in accordance with aspects of the present invention; 
         FIGS.  24 A- 24 C  are images illustrating another exemplary helmet padding system in accordance with aspects of the present invention; 
         FIG.  25    is an image illustrating an exploded embodiment of the helmet padding system of  FIGS.  24 A- 24 C ; 
         FIG.  26    is an image illustrating an alternative embodiment of a cutout of the helmet padding system of  FIGS.  24 A- 24 C ; 
         FIG.  27    is an image showing an interior of the helmet padding system of  FIGS.  24 A- 24 C ; 
         FIGS.  28 A and  28 B  are images illustrating alternative embodiments of the helmet padding system of  FIGS.  24 A- 24 C ; 
         FIG.  29    is an image illustrating the helmet padding system of  FIGS.  24 A- 24 C  worn beneath a baseball cap; 
         FIGS.  30 A and  30 B  are images illustrating an alternative embodiment of the helmet padding system of  FIGS.  20 A and  20 B ; 
         FIGS.  31 A- 31 C  are images illustrating the helmet padding system of  FIGS.  30 A and  30 B  with a removable plate; 
         FIGS.  32 A and  32 B  are images illustrating an alternative embodiment of the helmet padding system of  FIGS.  24 A- 24 C ; 
         FIGS.  33 A and  33 B  are images illustrating another exemplary helmet padding system in accordance with aspects of the present invention; 
         FIG.  34    is an image illustrating a top view of the helmet padding system of  FIGS.  33 A and  33 B ; 
         FIG.  35    is an image showing an interior of the helmet padding system of  FIGS.  33 A and  33 B ; 
         FIGS.  36 A and  36 B  are images illustrating another exemplary helmet padding system in accordance with aspects of the present invention; 
         FIG.  37    is an image showing an interior of the helmet padding system of  FIGS.  36 A and  36 B ; 
         FIG.  38    is an image showing the helmet padding system of  FIGS.  36 A and  36 B  positioned within a cap; 
         FIGS.  39 A- 39 C  are images illustrating another exemplary helmet padding system in accordance with aspects of the present invention; 
         FIGS.  40 A and  40 B  are images illustrating an alternative embodiment of the helmet padding system of  FIGS.  39 A- 39 C ; 
         FIGS.  41 A- 41 C  are images illustrating another exemplary helmet padding system in accordance with aspects of the present invention; 
         FIG.  42    is an image showing the helmet padding system of  FIGS.  41 A- 41 C  positioned within a cap; 
         FIGS.  43 A- 43 C  are images illustrating another exemplary helmet padding system in accordance with aspects of the present invention; 
         FIG.  44    is an image showing the helmet padding system of  FIGS.  43 A- 43 C  positioned within a cap; 
         FIGS.  45 A- 45 C  are images illustrating another exemplary helmet padding system in accordance with aspects of the present invention; 
         FIG.  46    is an image showing the helmet padding system of  FIGS.  45 A- 45 C  positioned within a cap; 
         FIGS.  47 A- 47 D  are images illustrating another exemplary helmet padding system in accordance with aspects of the present invention; and 
         FIGS.  48 A and  48 B  are images illustrating another exemplary helmet padding system in accordance with aspects of the present Invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The embodiments of the invention described herein relate to helmet padding and protective headgear systems that incorporate impact-resistant pads beneath a user&#39;s helmet to cushion impacts on the helmet from the user&#39;s head. As used herein, the term “helmet” is not intended to be limited, but is meant to encompass any headgear worn for protection during an activity in which an impact to the head may occur. Additionally, as used herein, the term “impact-resistant” is intended to encompass any object that partially or fully lessens, diminishes, dissipates, deflects, or absorbs the mechanical force of an impact. 
     The exemplary systems and apparatus disclosed herein are configured to lessen the force of an impact on the user&#39;s head. This makes them particularly suitable for use by participants in athletic activities, and particularly suitable for participants in traditional “contact” sports, such as wrestling, American football, or rugby, where high-force impacts may be commonly experienced. While the exemplary embodiments of the invention are described herein with respect to athletic activities, it will be understood that the invention is not so limited. Suitable applications for the systems and apparatus of the present invention include, for example, military helmets or construction helmets. Other suitable applications will be readily understood by one of ordinary skill in the art from the description herein. 
     Referring now to the drawings,  FIG.  1    illustrates an exemplary helmet padding system  100  in accordance with aspects of the present invention. Helmet padding system  100  may be worn by a user during an athletic activity. As a general overview, system  100  includes a helmet shell  110 , a spacing pad  130 , and a plurality of absorption pads  150 . Additional details of system  100  are described herein. 
     Helmet shell  110  is configured to be positioned on a user&#39;s head. As shown in  FIGS.  1  and  2   , helmet shell  110  completely encloses the upper portion of the user&#39;s head. This may be desirable in order to ensure any impacts to the user&#39;s head are absorbed by helmet padding system  100 . Helmet shell  110  may include one or more straps  112  for securing helmet shell  110  to the user&#39;s head. The size of helmet shell  110  is selected such that helmet shell  110  can accommodate the remaining components of system  100  while still being securely positioned on the user&#39;s head. Where helmet shell  110  is a conventional helmet shell, it will be understood that helmet shell  110  may include its own integral, connected foam pads in addition to the pads described with respect to system  100 . It will be understood that the pads described with respect to system  100  may be pads provided in addition to the pads provided in conventional helmet shells  110 . Suitable helmet shells  110  for use with the present invention will be known to one of ordinary skill in the art from the description herein. 
     Spacing pad  130  is positioned within the interior of helmet shell  110 . As shown in  FIGS.  4 - 8   , spacing pad  130  comprises a central portion  132  and a plurality of extending portions  134  projecting outward from the central portion. Spacing pad  130  may or may not be coupled to the interior of helmet shell  110 . When spacing pad  130  is coupled to helmet shell  110 , central portion  132  is coupled to a central region of the interior of helmet shell  110 , such that extending portions  134  project toward the peripheral edges of helmet shell  110 . 
     Spacing pad  130  is formed from impact-resistant materials. For example, spacing pad  130  may include a layer of elastomeric material. The elastomeric material may provide impact-resistance by absorbing and dissipating the force of impacts laterally along the surface of the elastomeric material. In one exemplary embodiment, spacing pad  130  consists of only a single layer of elastomeric material. In another exemplary embodiment, spacing pad  130  comprises two or more layers of elastomeric material. Spacing pad  130  may include the layers of elastomeric material directly adjacent each other, or in a more preferred embodiment, may include a layer of high tensile strength fibrous material between the layers of elastomeric material. 
     Suitable materials for forming the elastomeric layer(s) include, but are not limited to, urethane rubbers, silicone rubbers, nitrile rubbers, butyl rubbers, acrylic rubbers, natural rubbers, styrene-butadiene rubbers, and the like. In general, any suitable elastomer material can be used to form the above-described elastomeric layers without departing from the scope of the present invention. Suitable materials for forming the layer of high tensile strength fibrous material include, but are not limited to, aramid fibers, fiberglass, or other high tensile strength fibers. The fibers may be woven to form a cloth layer that is disposed between and generally separates the opposing elastomeric layers. The high tensile strength fibrous material layer may desirably block and redirect Impact energy that passes through one of the elastomeric layers. Additional description of materials for forming spacing pad  130  may be found in co-pending U.S. patent application Ser. No. 13/331,004, the contents of which are incorporated herein by reference in their entirety. 
     As shown in  FIG.  4   , spacing pad  130  may comprise an array of raised portions  131  formed on a surface thereof. Raised portions  131  may have a rectangular shape, as shown in  FIG.  4   . However, one of ordinary skill in the art will understand that other shapes may be chosen. For example, raised portions  131  may have a square shape or a diamond shape. Raised portions  130  desirably enable air circulation across spacing pad  130  and concentrate the load from an impact on spacing pad  130 . An array of raised portions  131  having a diamond shape may be particular desirable, as these raised portions  131  may enable greater flexibility of spacing pad  130 . 
     As set forth above, spacing pad  130  may or may not be coupled to the interior helmet shell  110 . When spacing pad  130  is coupled to the Interior of helmet shell  110 , such coupling may be effected, for example, using adhesive. It may be desirable that the surface of spacing pad  130 , including the entire lengths of extending portions  134 , be adhered to the interior of helmet shell  110 . The lengths of extending portions  134  may be limited, to prevent separation of extending portions  134  from helmet shell  110  during an impact that deforms helmet shell  110 . 
     Absorption pads  150  may be coupled to spacing pad  130 . As shown in  FIG.  3   , the plurality of absorption pads  150  includes a first large absorption pad  152  and a number of remaining absorption pads  154 . As shown in  FIG.  1   , absorption pad  152  is configured to be coupled to the central portion of spacing pad  130 , and absorption pads  154  are configured to be coupled to the ends of the extending portions of spacing pad  130 . 
     Absorption pads  150  are desirably shaped such that they do not directly contact helmet shell  110  when spacing pad  130  is coupled to helmet shell  110 . Absorption pads  150  may be insulated from helmet shell  110  by the ends of spacing pad  130 , and/or may be formed with a preferential curve, in order to create a gap between the outer surfaces of pads  150  and the Interior of helmet shell  110 . Suitable materials for use in forming absorption pads  150  include, for example, conventional closed or open-cell foams, elastomeric and/or polymer materials. Other materials will be known to one of ordinary skill in the art from the description herein. 
       FIGS.  4 - 8  and  13    show different embodiments of spacing pads  130   a ,  130   b ,  130   c ,  130   d  for use with the present invention. Each spacing pad  130   a ,  130   b ,  130   c ,  130   d  Includes a respective central portion  132   a ,  132   b ,  132   c ,  132   d  and a respective plurality of extending portions  134   a ,  134   b ,  134   c ,  134   d . Features of these extending portions  134  will be described herein. It will be understood by one of ordinary skill in the art that any of the features described herein with respect to one embodiment of spacing pad  130  may be provided in any of the other embodiments. 
     As shown in  FIGS.  4 - 8   , extending portions  134  project outward at regular Intervals from their respective central portions  132 . As shown in  FIGS.  4  and  6   , the regular intervals may be approximately every 45°. As shown in  FIG.  8   , the regular intervals may be approximately every 90°. 
     As shown in  FIGS.  6  and  7   , extending portions  134   b  of spacing pad  130   b  have end portions  136   b . End portions  136   b  have a width greater than the width of the remainder of the respective extending portion  134   b . The wider end portions  136   b  of spacing pad  130   b  may be desirable in order to provide a large base for absorption pads  150 . The wide end portions  136   b  may be made sufficiently wide that the end portions  136   b  of adjacent extending portions  134   b  overlap with each other when spacing pad  130   b  is positioned within the helmet shell. 
     Additionally, as shown in  FIGS.  6  and  7   , spacing pad  130   b  may be contained in a liner  137 . Liner  137  may be configured to surround spacing pad  130   b  in order to provide a comfortable contact between the user and spacing pad  130   b.    
     As shown in  FIG.  8   , extending portions  134   c  may be arranged axially symmetrically relative to central portion  132   c . Alternatively, as shown in  FIG.  4   , extending portions  134   a  may be arranged axially asymmetrically. Additionally, as shown in  FIG.  4   , extending portions  134   a  may have varying lengths projecting from central portion  132   a.    
     The shapes and sizes of extending portions  134   a ,  134   b ,  134   c  may also be dependent on the configuration of helmet shell  110 , as set forth below. 
     As shown in  FIGS.  5  and  7   , the varying lengths of extending portions  134  may be selected to correspond to a peripheral contour of helmet shell  110 . In other words, if the periphery of the helmet shell  110  has a varying contour, the lengths of extending portions  134  may be selected such that, when spacing pad  130  is coupled to helmet shell  110 , the end of each extending portion  134  projects to within a specified distance of the periphery of helmet shell  110 . In an exemplary embodiment, extending portions  134  project to within 0.125-2.0 inches of the periphery of helmet shell  110 . 
     Helmet shell  110  may include features that would interfere with the path of extending portions  134 . Accordingly, as shown in  FIGS.  6  and  7   , extending portions  134   b  may be shaped to avoid interfering features in helmet shell  110 , i.e., by changing direction. As shown in  FIG.  6   , at least one of the extending portions  134   b  may have a first portion  138  extending in a first direction and a second portion  139  extending from the first portion  138  in a second direction different from the first direction. This may desirably ensure that the entire length of extending portion  134   b  is adhered to the interior of helmet shell  110 . 
     Additionally, as shown in  FIG.  13   , a spacing pad  130   d  may be intended for use in a baseball cap having a rear cut-out (e.g., for access to an adjustable strap). In this embodiment, one of extending portions  134   d  may be shortened and have a rounded edge relative to the other extending portions. This extending portion may be positioned to extend toward the rear cut-out of the baseball cap. This feature may desirably enable all of spacing pad  130   d  to fit comfortably within the baseball cap. 
     The width and number of extending portions  134  may be selected based on the circumference and size of helmet shell  110 . As shown in  FIGS.  4  and  6   , spacing pad  130  may include a relatively large number of thin extending portions  134 . Alternatively, as shown in  FIG.  8   , spacing pad  130  may include a relatively small number of thick extending portions  134 . In an exemplary embodiment, extending portions  134  have a width of approximately 1″ to approximately 4″. 
     It will be understood that the number, shape, and size of extending portions  134  in  FIGS.  4 - 8    is shown merely for the purposes of illustration, and is not intended to be limiting. Spacing pads  130  having different numbers of extending portions  134  or differently shaped and sized extending portions  134  may be used without departing from the scope of the present invention, as would be understood by one of ordinary skill in the art from the description herein. 
       FIGS.  9 A- 9 D  Illustrate an exemplary impact-resistant pad  200  in accordance with aspects of the present invention. Impact-resistant pad  200  may be worn by a user as part of a protective headgear system during an athletic activity, such as a wrestling match. As a general overview, impact-resistant pad  200  includes a top portion  220  and side portions  240  and  250 . Additional details of impact-resistant pad  200  are described herein. 
     Top portion  220  is configured to be positioned covering a top of the user&#39;s head. As shown in  FIGS.  9 A- 9 D  top portion  220  may be approximately circular, and is sized to cover substantially the entire top of the user&#39;s head. In an exemplary embodiment, top portion  220  includes a plurality of openings  222 . Openings  222  desirably provide ventilation to the user&#39;s head during use of impact-resistant pad  200 . As shown in  FIG.  9 D , openings  222  are formed around the periphery of top portion  220 . 
     Side portions  240  and  250  extend downward from top portion  220 . As used herein, the term “side portion” is not intended to mean that portions  240  and  250  are on the “side” of the user&#39;s head (as opposed to the front or back). To the contrary, portions  240  and  250  may be located on any side of the user&#39;s head. As shown in  FIGS.  9 B and  9 C  side portions  240  and  250  cover a front portion and a back portion of the user&#39;s head, respectively. As further Illustrated in  FIG.  9 A , back portion  250  extends a greater distance from top portion  220  than front portion  240 . This may be desirable in order to provide greater protection to the back of the user&#39;s head, and to prevent obstructing the user&#39;s view. 
     Side portions  240  and  250  are not directly connected to each other, as shown in  FIG.  9 A . In particular, a circumferential gap  260  is formed between side portions  240  and  250 . This may be particularly desirable so that impact-resistant pad  200  may be worn by users of different head sizes. For example, when a user has a relatively small head, the gap  260  will be relatively narrow, and side portions  240  and  250  will sit close to each other (or possibly in contact with each other) when placed on the user&#39;s head. However, when a user has a relatively large head, the gap  260  will be relatively large, and side portions  240  and  250  will sit far from each other when placed on the user&#39;s head. 
     It will be understood that the number, shape, and size of side portions  240  and  250  in  FIGS.  9 A- 9 D  is shown merely for the purposes of illustration, and is not intended to be limiting. Side portions  240  and  250  in different numbers or having different shapes or sizes may be used without departing from the scope of the present invention, as would be understood by one of ordinary skill in the art from the description herein. Impact-resistant pad  200  is formed from substantially the same materials described above with respect to spacing pad  130 . 
     Impact-resistant pad  200  is unconnected to any supporting structure. As will be discussed in further detail herein, impact-resistant pad  200  is configured to be worn under a helmet. To this end, impact-resistant pad  200  is desirably thin. In an exemplary embodiment, impact-resistant pad  200  has a thickness of no greater than approximately 23 mm, and even more preferably, a thickness of no greater than approximately 3 mm. The thickness of impact-resistant pad  200  may be selected based on a number of factors, including for example the type of helmet, the desired level of impact protection, and the type of material encasing the pad (such as moisture-wicking, moisture-absorbent, cloth, or neoprene). 
       FIGS.  10 A- 10 C  illustrate an exemplary protective headgear system  300  in accordance with aspects of the present invention. Protective headgear system  300  may be worn by a user during an athletic activity, such as a wrestling match. As a general overview, protective headgear system  300  includes an impact-resistant pad  320  and a helmet  340 . Additional details of protective headgear system  300  are described herein. 
     Impact-resistant pad  320  is formed from materials designed to dissipate the force of impacts on the user&#39;s head. In an exemplary embodiment, impact-resistant pad  320  is an impact-resistant pad substantially as described above with respect to impact-resistant pad  200 . In particular, impact-resistant pad  320  includes a top portion  322  configured to be positioned covering a top of the user&#39;s head, and side portions  324  and  325  extending downward from top portion  322 . Side portions  324  and  325  are not directly connected to each other, and define a circumferential gap (not shown) therebetween. 
     Helmet  340  is configured to be positioned on a user&#39;s head overtop of impact-resistant pad  320 . Helmet  340  is unconnected to impact-resistant pad  320 . When helmet  340  is positioned overtop of impact-resistant pad  320 , helmet  340  covers the circumferential portions of impact-resistant pad  320 . In an exemplary embodiment, helmet  340  comprises conventional wrestling headgear, as shown in  FIGS.  10 A- 10 C . Helmet  340  includes a plurality of straps  342  for securing helmet  340  to the user&#39;s head. Straps  342  extend over top portion  322  of impact-resistant pad  320 . Impact-resistant pad  320  may include guide portions (not shown) for receiving and properly positioning straps  342  of helmet  340 . 
     It will be understood by one of ordinary skill in the art that helmet  340  is not limited to the embodiment shown in  FIGS.  10 A- 10 C   FIG.  11    illustrates another exemplary protective headgear system  400  in accordance with aspects of the present invention. As a general overview, protective headgear system  400  includes an impact-resistant pad  420  and a helmet shell  440 , as shown in  FIG.  11   . Helmet shell  440  is configured to completely cover the user&#39;s head. This may be desirable in order to provide an additional layer of impact-resistance on top of impact-resistant pad  420 . The size of helmet shell  440  is selected such that helmet  440  can accommodate impact-resistant pad  420  therein while still being securely positioned on the user&#39;s head. In an exemplary embodiment, helmet shell  440  is a helmet shell substantially as described with respect to helmet shell  110 . Suitable helmet shells  440  for use with the present invention will be known to one of ordinary skill in the art from the description herein. 
       FIG.  12    illustrates an exemplary helmet padding system  500  in accordance with aspects of the present invention.  FIG.  12    shows an exploded cross-sectional diagram of helmet padding system  500  through a central portion thereof. Helmet padding system  500  may also be worn by a user during an athletic activity. As a general overview, system  500  includes a helmet shell  510 , a spacing pad  530 , and a deflection layer  570 . Additional details of system  500  are described herein. 
     Helmet shell  510  is configured to be positioned on a user&#39;s head. Helmet shell  510  may be a helmet shell substantially as described with respect to helmet shell  110 , or may be a helmet substantially as described above with respect to helmet  340 . The size of helmet shell  510  is selected such that helmet shell  510  can accommodate the remaining components of system  500  while still be securely positioned on the user&#39;s head. 
     Spacing pad  530  is positioned within the interior of helmet shell  510 . Spacing pad  530  may be a spacing pad substantially as described with respect to spacing pad  130 . Alternatively, spacing pad  530  may be an impact-resistant pad substantially as described above with respect to impact-resistant pad  200 . Likewise, spacing pad  530  may be formed from any of the materials set forth above with respect to spacing pad  130  or impact-resistant pad  200 , and may take any of the shapes described above with respect to spacing pad  130  and/or impact-resistant pad  200 . Alternatively, spacing pad  530  may have any other shape suitable for covering a space between the user&#39;s head and the helmet shell  510 . Spacing pad  530  may also comprise an array of raised portions  531  formed on a surface thereof, as described above with respect to raised portions  131 . 
     Spacing pad  530  is not adapted to be coupled to the interior of helmet shell  510 . In other words, spacing pad  530  remains unconnected to helmet shell  510  (or from any other component that is connected to helmet shell  510 , e.g., conventional helmet padding provided with helmet shell  510 ). This enables relative movement between spacing pad  530  and helmet shell  510 , which may be important to assist in dissipation of the force from impacts, as explained in further detail below with respect to deflection layer  570 . 
     Helmet padding system  500  may include a plurality of absorption pads  550  coupled to spacing pad  530 . Absorption pads  550  may be substantially the same as those described above with respect to absorption pads  150 . 
     Deflection layer  570  is positioned between helmet shell  510  and spacing pad  530 . Deflection layer  570  is formed from a material that is less flexible (i.e. stiffer) than spacing pad  530 . This enables the hard surface of deflection layer  570  to deflect a portion of the force from impacts along a surface thereof, rather than transmitting that force through deflection layer  570  to spacing pad  530 . In other words, it assists in converting forces from impacts into tangential forces (which propagate along the surface) as opposed to normal forces (which propagate through the surface to the user&#39;s head). In an exemplary embodiment, deflection layer  570  comprises a sheet of polycarbonate material. Deflection layer  570  may have a shape corresponding to the shape of spacing pad  530 , such that the deflection layer  570  completely covers the space between spacing pad  530  and helmet shell  510 . 
     Deflection layer  570  is also not coupled to the interior of helmet shell  510 . This creates a “slip plane” between deflection layer  570  and helmet shell  510 , and enables relative movement between the two components. Put another way, this allows independent movement of the user&#39;s head (with which spacing pad  530  and deflection layer  570  are in contact) and helmet shell  510 . 
     Helmet padding system  500  may also include a plurality of deflection plates  580 . Deflection plates  580  may be coupled to the interior of helmet shell  510  in positions such that they slidably abut deflection layer  570 . Deflection plates  580  may be coupled to helmet shell  510 , e.g., with an adhesive. Deflection plates  580  are formed from the same materials as deflection layer  570 . The use of deflection plates  580  coupled to helmet shell  510  may further promote a sliding Interface between deflection layer  570  and helmet shell  510 , and thereby promote deflecting the force of impacts in a tangential direction along deflection layer  570 , rather than through deflection layer  570  to spacing pad  530 . 
     Helmet padding system  500  may also include a deformation layer  590 . Deformation layer  590  may be positioned between deflection layer  570  and spacing pad  530 . Deformation layer  590  is configured to deform upon experiencing the force from an impact. Deformation layer  590  may undergo elastic (i.e. reversible) or plastic (i.e. irreversible) deformation. In an exemplary embodiment, deformation layer  590  comprises a sheet of corrugated plastic material configured to undergo plastic deformation. As shown in  FIG.  12   , the sheet of corrugated plastic material may comprise a pair of plastic surface layers separated by a plurality of plastic ridges defining air gaps therebetween. Like deflection layer  570 , deformation layer  590  may have a shape corresponding to the shape of spacing pad  530 , such that the deformation layer  590  completely covers the space between spacing pad  530  and deflection layer  570 . 
     Deformation layer  590  may undergo plastic deformation, for example, by crumpling, bending, fracturing, or other irreversible changes. Accordingly, deformation layer  590  may need to be periodically replaced following impacts to helmet padding system  500 , where such Impacts are sufficient to cause significant plastic deformation of deformation layer  590 . 
     The above components of helmet padding system  500  may be contained in a liner (not shown). In particular, a liner may be configured to surround and contain spacing pad  530 , deflection layer  570 , and deformation layer  590 , to maintain their relative positioning and arrangement. The liner may be formed, for example, from a cloth or nylon material to provide a comfortable contact between the user and the components of helmet padding system  500 . 
       FIGS.  14 A- 14 D  illustrate another exemplary helmet padding system  600  in accordance with aspects of the present invention. Helmet padding system  600  may be worn by a user during military activities, e.g., under a standard military helmet. As a general overview, system  600  includes a frame  610  and a spacing pad  630 . Additional details of system  600  are described herein. 
     Frame  610  is configured to be positioned on a user&#39;s head. Frame  610  comprises a rigid material such as, for example, a plastic or polycarbonate material. The size of frame  610  is selected such that helmet shell  610  can accommodate spacing pad  630  while still be securely positioned on the user&#39;s head. 
     Spacing pad  630  is coupled to frame  610 . Spacing pad  630  may be a spacing pad substantially as described with respect to spacing pad  130 , and/or may be formed from any of the materials described with respect to spacing pad  130 . In particular, spacing pad  630  comprises a central portion  632  and a plurality of extending portions  634  projecting outward from the central portion  632 . The plurality of extending portions  634  are fixed to frame  610 . 
     As shown in  FIGS.  14 A and  14 B , each extending portion  630  has an end portion with a greater width than a portion of the respective extending portion coupled to central portion  632 . Specifically, extending portions  630  get wider as they extend outwardly from central portion  632 . The end portions of extending portions  634  are fixed to frame  610 . 
     In an exemplary embodiment, frame  610  comprises a groove  612 , as shown in  FIG.  14 B . The end portions of each of the plurality of extending portions  634  are inserted within groove  612 . The end portions of the plurality of extending portions  634  may be additionally secured to the frame via one or more attachment mechanisms. Suitable attachment mechanisms  615  include, for example, rivets, adhesives, or stitching. 
     Frame  610  may be configured to be coupled to a helmet, as shown in  FIG.  14 D . In an exemplary embodiment, frame  610  is configured to be coupled to a standard-issue military helmet. The standard-issue military helmet includes a plurality (e.g. four) pre-arranged mounting points, such as drill holes, in the helmet. In this embodiment, frame  610  includes a plurality of through holes  614  positioned to align with the pre-arranged mounting points in the military helmet. This may desirably simplify the attachment of frame  610  to the helmet. Spacing pad  630  is fixed to frame  610  in such a way that spacing pad does not contact the helmet when frame  610  is coupled to the helmet. 
     In one exemplary embodiment, frame  610  has a ring shape, as shown in  FIGS.  14 B and  14 C . The plurality of extending portions  634  extend upward from frame  610 , such that central portion  623  is positioned above frame  610 . This creates a cavity within frame  610  in which the top of the user&#39;s head is positioned during use. 
       FIGS.  15 A- 15 C  illustrate another exemplary helmet padding system  700  in accordance with aspects of the present invention. The helmet padding system  700  is substantially the same as helmet padding system  600 , and only the differences between those two embodiments will be described hereinafter. 
     In an exemplary embodiment, frame  710  of helmet padding system  700  has a dome shape, as shown in  FIGS.  15 A- 15 C . The standard-issue military helmet includes a plurality (e.g. four) pre-arranged mounting points, such as drill holes, in the helmet. In this embodiment, frame  710  includes a plurality of through holes  714  positioned to align with the pre-arranged mounting points in the military helmet. 
     Spacing pad  730  is positioned within the dome, and may be adhered to an inner surface of the dome. The dome-shaped frame  710  includes a plurality of ridges  716  formed on an outer surface thereof. As shown in  FIGS.  15 A and  15 B , ridges  716  extend along frame  710  from edge to edge through a top portion of frame  710 . When dome-shaped frame  710  is coupled to a helmet, frame  710  contacts the helmet only along the outermost surfaces of the plurality of ridges  716 . This may be desirable in order to minimize the transfer of impact force from the helmet to frame  710 . In this embodiment, frame  710  may also include a plurality of straps  718  for enhancing fit and comfort of system  700  when worn by a user, as shown in  FIG.  15 C . 
     Helmet padding systems  600  and  700  may also include a deformation layer. The deformation layer may be a layer substantially as described with respect to deformation layer  590 . In one embodiment, the deformation layer is positioned between the frame and the spacing pad. In an alternative embodiment, the deformation layer is positioned such that it is between the frame and the helmet when the frame is coupled to the helmet. 
     As explained above with respect to  FIG.  13   , the helmet padding systems  800 ,  900 ,  1000  of the present invention may be used with baseball caps. In accordance with another aspect of the present invention, a helmet padding system usable with such a baseball-style cap is disclosed. New  FIGS.  16 - 18    disclose alternative embodiments of such a system. 
     The baseball cap of this system has the style of a normal baseball cap except on sides of the cap. The body of the cap may be formed from flexible material such as cotton or synthetic textiles. The rear of the cap may be fitted to the user&#39;s head, or may include a conventional adjustable strap. As shown in  FIG.  16   , the side  810  of the cap extends downward to cover the user&#39;s temple, and at least a portion (preferably at least 50%) of the user&#39;s ear. A downward extended portion is formed on both sides of the cap. As shown in  FIG.  16   , the downward extended portion may extend across the rear of the cap. Alternatively, as shown in  FIGS.  17  and  18   , the downward extended portion may end (or grow more narrow) across the rear of the cap. As shown in  FIG.  16   , the cap body may include an opening  820  in the area of the user&#39;s ear. The opening may be desirable in order to promote aeration within the cap, and to provide the user better hearing. 
     Within the cap, a spacing pad is provided. In an exemplary embodiment, spacing pad  130   d  illustrated in  FIG.  13    is provided. Alternatively, the cap may include any of the spacing pads and accompanying components described herein. Still further, this system may use conventional foam padding in place of the spacing pad. 
     The shape of the spacing pad may be selected to maximize coverage of the user&#39;s head while minimizing interference with the user&#39;s comfort (e.g., by obstructing the user&#39;s hearing). In an exemplary embodiment, the spacing pad has one extending portion that extends from the top of the cap to a position forward of the user&#39;s ear, to cover the user&#39;s temple, and another extending portion that extends from the top of the cap to a position rearward of the user&#39;s ear, to cover the base of the user&#39;s skull behind their ear. The spacing pad is shaped to leave a gap in the area of the user&#39;s ear, to avoid obstructing the user&#39;s hearing. 
     To protect the area of the user&#39;s ear, the cap may include a rigid frame. The rigid frame may be formed, for example, from rigid plastic. In an exemplary embodiment, the rigid frame comprises a plurality of rigid outer members extending along the periphery of the gap (adjacent the edges of the spacing pad). The frame may have a substantially round, rectangular, or triangular shape. The frame further comprises an open area between the rigid outer members. The open area in the central portion of the rigid frame is desirable in order to avoid obstructing the user&#39;s hearing. 
     The cap may also include a rigid liner around a peripheral edge of the cap. In an exemplary embodiment, the rigid liner comprises a thin, rigid structure extending around the peripheral edges of the cap. The rim may be formed, for example, from rigid plastic. The rim may desirably be positioned within a fold or pocket of the outer cloth body of the cap, in order to enhance the user&#39;s comfort. 
       FIGS.  19 A and  19 B  illustrate an exemplary helmet padding system  1100  in accordance with aspects of the present invention. Helmet padding system  1100  may be worn by a user during an athletic activity. Desirably, helmet padding system  1100  may be worn under another piece of headgear, such as a baseball cap. As a general overview, system  1100  includes a main portion  1110  and a removable portion  1180 .  FIG.  19 A  shows a view of helmet padding system  1100  with removable portion  1180  coupled to main portion  1110 , and  FIG.  19 B  shows a view of helmet padding system with removable portion  1180  separated from main portion  1110 . Additional details of system  1100  are described herein. 
     When system  1100  is worn under a baseball cap having a rear cut-out (e.g., for an adjustable strap), removable portion  1180  is desirably located at the same position as the rear cut-out. In normal use, removable portion  1180  remains coupled to main portion  1110 , and provides impact protection to the user in the area of the rear cut-out, in substantially the same manner as main portion  1110 . However, a user may also choose to remove removable portion  1180  during use. Removal of removable portion  1180  from main portion  1110  opens up an area of the user&#39;s head directly beneath the cut-out of the baseball cap. This may be particularly desirable for users of system  1100  having long hair, who for comfort or other reasons wish their hair to extend through the air of the rear cut-out of the baseball cap. In other words, removal of removable portion  1180  desirably allows certain users to utilize the rear cut-out of their baseball cap as they normally would if they were not wearing a helmet padding system underneath their baseball cap. 
     Main portion  1110  is configured to be positioned on a user&#39;s head. Main portion  1110  may include a plurality of different subcomponents similar to the layers of the various helmet padding systems described herein. In an exemplary embodiment, main portion  1110  includes a spacing pad (not shown), a plurality of absorption pads  1150 , and a deflection layer  1170 . 
     The spacing pad of main portion  1110  is positioned within the interior of main portion  1110 . The spacing pad may be a spacing pad substantially as described with respect to spacing pad  130 . Alternatively, the spacing pad may be an impact-resistant pad substantially as described above with respect to impact-resistant pad  200 . Likewise, the spacing pad may be formed from any of the materials set forth above with respect to spacing pad  130  or impact-resistant pad  200 , and may take any of the shapes described above with respect to spacing pad  130  and/or impact-resistant pad  200 . 
     In a particularly suitable embodiment, the spacing pad of main portion  1110  has a shape and structure corresponding to spacing pad  130   d , as shown in  FIG.  13   . As set forth above, both system  1100  and spacing pad  130   d  may be intended for use in a baseball cap having a rear cut-out (e.g., for an adjustable strap). In this embodiment, the spacing pad of main portion  1110  has a shortened extending portion having a rounded edge relative to the other extending portions, as shown in  FIG.  13   . In helmet padding system  1100 , this extending portion is positioned to extend toward the location of the removable portion  1180  of system  1100 . Accordingly, the spacing pad of main portion  1110  does not extend into or otherwise interfere with the area covered by removable portion  1180 . System  1100  may also include a separate spacing pad having the same material coupled to the interior of removable portion  1180   
     Helmet padding system  1100  may include a plurality of absorption pads  1150  coupled to the spacing pad and/or deflection layer  1170 . Absorption pads  1150  may be substantially the same as those described above with respect to absorption pads  150  (shown in  FIGS.  1  and  3   ). As shown in  FIG.  19 C , system  1100  may include absorption pads  1150  on both main portion  1110  and removable portion  1180 . One of ordinary skill in the art will understand that the number and positioning of absorption pads  1150  shown in  FIG.  19 C  is done for the purposes of illustration, and is not intended to be limiting. 
     Deflection layer  1170  is positioned along the exterior of main portion  1110 . Deflection layer  1170  may be a deflection layer substantially as described with respect to deflection layer  570  (shown in  FIG.  12   ). In an exemplary embodiment, deflection layer  1170  is formed from polycarbonate material. Deflection layer  1170  is shaped and sized so as to accommodate the components within (including the spacing pad and absorption pads  1150 ) while comfortably fitting on a user&#39;s head. Deflection layer  1170  includes a cut-out portion  1172  (similar to the spacing pad) having a shape corresponding to the shape of the conventional rear cut-out of a baseball cap. Cut-out portion  1172  is sized to accommodate the removable portion  1180  therein in order to form (with removable portion  1180 ) an approximately continuous dome shape on the top of the user&#39;s head. Deflection layer  1170  may further include one or more projecting sections  1174  to enhance the ability of system  1100  to dissipate the force of impacts to the user&#39;s head. 
     Deflection layer  1170  is not adapted to be coupled to the interior of the baseball cap. As with deflection layer  570 , this creates a “slip plane” between deflection layer  570  and the baseball cap, and enables relative movement between the two components. Put another way, this allows independent movement of the user&#39;s head (with which the spacing pad and deflection layer  1170  are in contact) and the baseball cap. 
     Removable portion  1180  is configured to be coupled to and removable from main portion  1110 . Removable portion  1180  may be formed from substantially the same materials as main portion  1110 . In particular, removable portion  1180  may include a spacing pad, absorption pad, and deflection layer the same as those used in the formation of main portion  1110 . Removable portion  1180  is shaped to correspond to the shape of the conventional rear cut-out of a baseball cap, and is sized to be received with the cut-out portion  1172  of the deflection layer  1170  of main portion  1110 . 
     Removable portion  1180  may be coupled to main portion  1110  by a number of different mechanisms. In an exemplary embodiment, removable portion  1180  is frictionally coupled to main portion  1110 , as shown in  FIGS.  19 A and  19 B . In this embodiment, removable portion  1180  includes tabs  1182  adapted to slide along the outer surface of main portion  1110 , and tabs  1184  adapted to slide along the inner surface of main portion  1110 . Tabs  1182  and  1184  sandwich main portion  1110  therebetween, thereby creating a friction fit that holds removable portion  1180  in place against main portion  1110 . 
     Alternatively or additionally, removable portion  1180  may be coupled to main portion  1110  using one or more snapping mechanisms, as shown in  FIGS.  19 C and  19 D . In this embodiment, removable portion  1180  includes a projection  1186  position to mate with a corresponding aperture  1188  on main portion  1110 . When removable portion  1180  is properly positioned against main portion  1110 , projection  1186  is received within aperture  1188 , thereby snapping removable portion  1180  in place against main portion  1110 . The snapping mechanism may be configured to frictionally maintain the connection until a predetermined pressure is applied to unsnap removable portion  1180  from main portion  1110 . 
     The above embodiments allow removable portion  1180  to be both uncoupled from and recoupled to main portion  1110 . However, in some embodiments, removable portion  1180  may not be permanently recoupled to main portion  1110 . In one embodiment, removable portion  1180  may be attached to main portion through one or more weakened, thinned, or perforated pieces of material (e.g., the material of deflection layer  1170 ). Removable portion  1180  may then be permanently removed from main portion  1110  by breaking this area of weakened material. 
       FIGS.  20 A and  20 B  illustrate an alternative embodiment  1200  of helmet padding system  1100 . As shown in  FIGS.  20 A and  20 B , the deflection layer of helmet padding system  1200  has a more streamlined outer surface, without the projecting sections of system  1100 . This may enable helmet padding system  1200  to more easily fit within or underneath a baseball cap, as shown in  FIG.  21   . 
     As shown in  FIG.  20 B , removable portion  1280  is frictionally coupled to main portion  1210  by a plurality of outer surface tabs  1282  and a plurality of inner surface tabs  1284  adapted to slide along the inner surface of main portion  1110 . Tabs  1282  and  1284  sandwich main portion  1210  therebetween, thereby creating a friction fit that holds removable portion  1280  in place against main portion  1210 . When system  1200  is used underneath a baseball cap having a rear cut-out, removable portion  1280  may optionally be removed to allow users with long hair to extend their hair out through the cap&#39;s rear cut-out. 
       FIGS.  22  and  23    illustrate another exemplary helmet padding system  1300  in accordance with aspects of the present invention. As with systems  1100  and  1200 , helmet padding system  1300  may be worn by a user during an athletic activity, and desirably, may be worn under another piece of headgear, such as a baseball cap. Generally, system  1300  includes the same components set forth above with respect to system  1100 . Additional features forming part of system  1300  are set forth below. 
     Main portion  1310  of system  1300  includes a cushioning portion  1390 . Cushioning portion  1390  extends into a cut-out area of deflection layer  1370 . In an exemplary embodiment, cushioning portion  1390  extends into a cut-out area along a centerline of deflection layer  1370  from a front-most edge of deflection layer  1370  toward a rearward portion of deflection layer  1370 . Cushioning portion  1390  separates opposed portions of deflection layer  1370  in order to enable movement of one side of deflection layer  1370  relative to the other side of deflection layer  1370 . Such movement may desirably assist system  1300  in dissipating the force of Impacts to a user&#39;s head. 
     Cushioning portion  1390  is formed from a material that is more flexible and/or compressible than the material of deflection layer  1370 . In an exemplary embodiment, cushioning portion is formed from the same materials as absorption pads  150  or  1150 . 
     The length of cushioning portion  1390  may be adjusted to optimize the force-dissipating effect provided. In one exemplary embodiment, cushioning portion  1390  extends along the entire length of deflection layer  1370 , from the front-most edge to the rear edge of cut-out portion, as shown in  FIG.  22   . In an alternative embodiment, cushioning portion  1390  does not extend along the entire length of deflection layer  1370 , but terminates before the rear edge, as shown in  FIG.  23   . Additionally, the width of cushioning portion  1390  may be adjusted to optimize the force-dissipating effect provided. In an exemplary embodiment, the width across cushioning portion  1390  may be from about 0.3 inches to about 3.0 inches. 
       FIGS.  24 A- 24 C  illustrate an exemplary helmet padding system  1400  in accordance with aspects of the present invention. Helmet padding system  1400  may be worn by a user during an athletic activity. Desirably, helmet padding system  1400  may be worn under another piece of headgear, such as a baseball cap, knit winter cap, beanie, or other piece of aesthetic headwear. As a general overview, system  1400  includes a rigid shell  1410  and a spacing pad  1440 . Additional details of system  1400  are described herein. 
     Rigid shell  1410  is configured to cover the top of a user&#39;s head. Rigid shell  1410  is sized to be worn under a baseball cap. Accordingly, it may be desirable that rigid shell  1410  be formed from a thin, rigid material. In an exemplary embodiment, rigid shell  1410  is formed from a polycarbonate material, as described above with respect to deflection layer  1170 . The material may have a thickness of less than approximately 5 mm, and more desirably, less than approximately 3.5 mm. Forming rigid shell  1410  with a low profile (i.e. thin size) is desirable to promote use of helmet padding system  1400  by eliminating interference with the aesthetic features of the headgear (e.g., baseball cap) worn on top of rigid shell  1410 . 
     Rigid shell  1410  includes a body portion  1420  and a pair of side portions  1430 . Body portion  1420  has a lower front edge  1421  extending between the pair of side portions  1430 . When worn under a baseball cap, lower front edge  1421  is positioned adjacent the brim of the baseball cap. Body portion  1420  further includes a lower rear edge  1422  extending between the pair of side portions  1430  opposite lower front edge  1421 . 
     In one embodiment, lower rear edge  1422  of body portion  1420  has approximately the same height as lower front edge  1421 , as shown in  FIG.  24 A . In this embodiment, lower rear edge extends along approximately the same circumferential line (around the user&#39;s head) as lower front edge  1421 . In this embodiment, when rigid shell  1410  is worn under a baseball cap (such as a fitted baseball cap) lower rear edge  1422  is positioned adjacent the lower edge of the cap. 
     In an alternative embodiment, lower rear edge  1422  extends down the user&#39;s head along with side portions  1430 , as shown in  FIGS.  25  and  26   . In this embodiment, lower rear edge  1422  extends along approximately a same circumferential line as the lower edges of side portions  1430 . In this embodiment, when rigid shell  1410  is worn under a baseball cap (such as a fitted baseball cap) lower rear edge  1422  extends below the lower edge of the cap. 
     Body portion  1420  may include at least one opening therein. The opening preferably allows breathability between the interior of rigid shell  1410  (i.e., the area adjacent the user&#39;s head) and the exterior of rigid shell  1410 . In an exemplary embodiment, body portion  1420  includes a plurality of openings  1423 , with at least one opening positioned between each side portion  1430  and an apex of rigid shell  1410 , as shown in  FIG.  24 A . 
     Body portion  1420  may also include one or more ridges along a surface thereof. In an exemplary embodiment, body portion  1420  includes an elevated ridge  1424  extending from an area adjacent lower front edge  1421  over the apex of body portion  1420  to an area adjacent lower rear edge  1422 , as shown in  FIG.  24 C . Ridge  1424  may provide additional structural stability to rigid shell  1410 , thereby allowing shell  1410  to better dissipate the force of impacts. Ridge  1424  may further provided additional space between rigid shell  1410  and the user&#39;s head, adding to comfort and breathability for the user. 
     Body portion  1420  may also include a pair of cutouts  1425  on ends of front edge  1421 , as shown in  FIG.  24 B . Cutouts  1425  are provided between front edge  1421  and side portions  1430 . Body portion  1420  may further include a pair of cutouts  1425  on the ends of rear edge  1422 , as shown in  FIG.  24 C . Cutouts  1425  desirably provide a path for coupling rigid shell  1410  to the interior of a baseball cap, as will be described below. It will be understood by one of ordinary skill in the art that the shape of cutouts  1425  shown in  FIG.  24 B  is provided for the purposes of illustration, and is not intended to be limiting. For example, cutouts  1425  may be formed with a triangular or round shape without departing from the scope of the present invention. 
     Side portions  1430  extend downward below the lower front edge  1421  of body portion  1420 , as shown in  FIGS.  24 A- 24 C . Side portions  1430  are sized to cover at least a portion (preferably at least 50%) of the user&#39;s ear when rigid shell  1410  is worn by the user. Side portions  1430  are also desirably sized to cover the user&#39;s temples when rigid shell  1410  is worn by the user. To this end, each side portion  1430  may have a circumferential length (along the side of the user&#39;s head) that is longer than the distance (or height) to which side portions  1430  extend below lower front edge  1421 . 
     Side portions  1430  may include at least one opening therein. The opening may preferably be positioned over the user&#39;s ear when rigid shell  1410  is worn by the user. Such positioning allows the user to hear his or her surroundings while maintaining protection to the user&#39;s ear area from impacts. In an exemplary embodiment, each side portion  1430  comprises a set of spaced apart, elongated openings  1431 , as shown in  FIG.  24 A . 
     Side portions  1430  may also include one or more flared portions. In an exemplary embodiment, side portions  1430  include flared portions  1432  extending outward relative to a surface of body portion  1420 , as shown in  FIG.  24 C . Flared portions  1432  may provide additional space between rigid shell  1410  and the user&#39;s head and ears, adding to the user&#39;s comfort. When rigid shell  1410  is worn beneath a baseball cap, flared portions  1432  may include all of side portions  1430  that are positioned below the baseball cap. 
     Side portions  1430  may also include one or more attachment points. During use of helmet padding system  1400 , it may be desirable to attach one or more accessories (such as straps, goggles, headphones or other accessories) to system  1400 . Accordingly, rigid shell  1410  may include one or more attachment points designed to facilitate the attachment of appropriate accessories to the user&#39;s athletic activity. Such attachment points are preferably positioned on side portions  1430  so that they can be accessed even when rigid shell  1410  is worn underneath a baseball cap. In an exemplary embodiments, side portions  1430  include a pair of through-holes  1433  on either end thereof, as shown in  FIG.  24 A . Through-holes  1433  provide attachment points for a strap (e.g., a chin strap) to be attached to rigid shell  1410 . 
     Spacing pad  1440  is positioned within the interior of rigid shell  1410 , as shown in  FIG.  27   . The spacing pad may be a spacing pad substantially as described with respect to spacing pad  130 . Alternatively, the spacing pad may be an impact-resistant pad substantially as described above with respect to impact-resistant pad  200 . Likewise, the spacing pad may be formed from any of the materials set forth above with respect to spacing pad  130  or impact-resistant pad  200 , and may take any of the shapes described above with respect to spacing pad  130  and/or impact-resistant pad  200 . 
     In a particularly suitable embodiment, the spacing pad  1440  includes a first portion  1441  extending circumferentially around a lower portion of rigid shell  1410 , e.g., adjacent lower front edge  1421  and lower rear edge  1422 , as shown in  FIG.  27   . In this embodiment, spacing pad  1440  includes a second portion  1442  extending from an area adjacent lower front edge  1421  over the apex of body portion  1420  to an area adjacent lower rear edge  1422 . 
     Where helmet padding system  1400  is used with a fitted baseball cap, rigid shell  1410  may have a continuous, uninterrupted rear body portion. However, when helmet padding system  1400  is used with an adjustable baseball cap, rigid shell  1410  may include a cutout as shown in  FIGS.  24 A- 26   , and as set forth below. 
     Rigid shell  1410  may include a cutout  1426  in an area of body portion  1420  opposite lower front edge  1421 . When rigid shell  1410  is worn beneath a baseball cap, cutout  1426  is provided in an area of body portion  1420  adjacent a rear of the baseball cap. In this embodiment, the baseball cap may be an adjustable baseball cap an opening for accommodating the adjustable strap. Accordingly, cutout  1426  has a shape corresponding to the shape of the opening in the rear of the adjustable baseball cap. 
     When rigid shell  1410  incorporates a cutout  1426 , helmet padding system  1400  may further comprise a removable portion  1460  configured to fit within cutout  1426  of rigid shell  1410 . Removable portion  1460  is formed from the same material as rigid shell  1410 , in order to provide similar protection from the force of impacts. Thus, when removable portion  1460  is coupled to rigid shell  1410 , the components form an approximately continuous dome shape on the top of the user&#39;s head. 
     Both cutout  1426  and removable portion  1460  may have a shape different from the semicircular cutout shape shown in  FIG.  25   . For example, as shown in  FIG.  26   , cutout  1426  and removable portion  1460  may cover a substantially larger portion of body portion  1420  of rigid shell  1410 . Providing a larger cutout  1426  and removable portion  1460  may be desirable in order to provide a size or contour adjustability to rigid shell  1410  to accommodate users having different sized heads. 
     Removable portion  1460  is configured to be coupled to and removable from rigid shell  1410 . Removable portion  1460  may be coupled to rigid shell  1410  by a number of different mechanisms, as described above with respect to removable portion  1180 . In an exemplary embodiment, removable portion  1460  is frictionally coupled to rigid shell  1410 , as shown in  FIG.  24 C . In this embodiment, removable portion  1460  includes tabs  1461  adapted to slide along the outer surface of rigid shell  1410 , and tabs  1462  adapted to slide along the inner surface of rigid shell  1410 , as shown in  FIG.  25   . Tabs  1461  and  1462  sandwich rigid shell  1410  therebetween, thereby creating a friction fit that holds removable portion  1460  in place against rigid shell  1410 . Removable portion  1460  may be coupled to rigid shell  1410  using alternative mechanisms as discussed above with respect to removable portion  1180 . 
     Where rigid shell  1410  does not include a cutout as set forth above, body portion  1420  may nonetheless include one or more slits in a lower portion thereof to accommodate users having different sized heads. The inclusion of slits in rigid shell  1410  may allow for adjustability of size between opposite sides of body portion  1420  without opening gaps that could negatively impact the protection provided by rigid shell  1410 . In an exemplary embodiment, body portion  1420  includes a vertical slit  1427  at an approximate midpoint of a rear portion of body portion  1420  extending upward from lower rear edge  1422 , as shown in  FIG.  28 A . In another exemplary embodiment, body portion  1420  includes a J-shaped slit  1428  along the rear portion of body portion  1420 , as shown in  FIG.  285   . As shown in  FIGS.  28 A and  28 B , body portion  1420  may include a tab  1429  on one side of the slit  1427  or  1428  that extends overtop a surface of the body portion on the other side of the slit  1427  or  1428 . Tab  1429  desirably allows the sides of body portion  1420  to move circumferentially with respect to one another (depending on the size of the user&#39;s head), while preventing relative inward or outward movement of the opposing sides of body portion  1420 . 
     As shown in  FIG.  29   , helmet padding system  1400  may further include a baseball cap  1480 . Baseball cap  1480  has a body portion  1481  and a brim portion  1482 . As set forth above, rigid shell  1410  is configured to be worn beneath baseball cap  1480 . Side portions  1430  of rigid shell  1410  are configured to extend downward below the lower edge of body portion  1481  of baseball cap  1480 , as shown in  FIG.  29   . In this embodiment, side portions  1430  provide protection for the user&#39;s head beneath the lower edge of conventional baseball caps, including the user&#39;s temples and ears, which are normally left uncovered by conventional baseball caps. 
     Additionally, the extension of side portions  1430  beneath the lower edge of baseball cap  1480  provides a visual indication to others that the user is wearing increased head protection relative to that offered by a normal baseball cap. Such visual indication may be useful, e.g., to promote compliance with requirements of head protection during athletic activities. 
     Baseball cap  1480  may include an interior flap of material adjacent the front or rear lower edges thereof. Such a flap of material may be used for providing a connection between baseball cap  1480  and rigid shell  1410 . In an exemplary embodiment, body portion  1420  may also include a pair of cutouts  1425 , as shown in  FIG.  24 B . In this embodiment, the flap on baseball cap  1480  passes through cutouts  1425 , such that a portion of the flap is positioned adjacent an interior surface of rigid shell  1410  (as opposed to outside of rigid shell  1410 ). Tucking a portion of the flap through cutouts  1425  may be useful to secure baseball cap  1480  to rigid shell  1410 , and to provide additional comfort and/or sweat absorbency to the user&#39;s forehead. 
       FIGS.  30 A and  30 B  illustrate an alternative embodiment  1500  of helmet padding system  1200  in accordance with aspects of the present invention. Helmet padding system  1500  may be worn by a user during an athletic activity. Like helmet padding system  1200 , helmet padding system  1500  may be worn under another piece of headgear, such as a baseball cap. As a general overview, system  1500  includes a main portion  1510  and an opening  1580 . Helmet padding system  1500  includes substantially the same features as helmet padding system  1100  and/or  1200 , except as described herein. 
     Main portion  1510  is configured to be positioned on a user&#39;s head. Main portion  1510  may include a plurality of different subcomponents corresponding to the layers of the various helmet padding systems described herein. In an exemplary embodiment, main portion  1510  includes a spacing pad, a plurality of absorption pads, and a deflection layer. Other components or layouts for dissipating the force of impacts may be selected based on the various embodiments described herein. 
     As shown in  FIG.  30 B , main portion  1510  of helmet padding system  1500  has a streamlined outer surface similar in design to helmet padding system  1200 . This streamlined outer surface may enable helmet padding system  1500  to more easily fit within or underneath a baseball cap, as described above. The streamlined outer surface may include one or more elevated ridges  1512  extending along the surface thereof. As shown in  FIG.  30 B , the elevated ridges  1512  extend in a direction from a front of the user&#39;s head to the back of the user&#39;s head. These ridges provide additional structural support to main portion  1510 , and assist in dissipating the force of impacts to the user&#39;s head. 
     Unlike systems  1100  and  1200 , the opening  1580  of helmet padding system  1500  does not extend down to the lower edge of main portion  1510 . Instead, main portion  1510  includes a bridge  1514  extending below opening  1580 , as shown in  FIGS.  30 A and  308   . Thus, opening  1580  is completely surrounded by parts of main portion  1510 . This layout improves the structural stability of helmet padding system  1500 , by limiting relative movement of the left and right sides of main portion  1510  relative to one another. For example, bridge  1514  may be formed from a substantially rigid material (such as the deflection layer material described above) in order to prevent inward and outward movement of the left and right sides of main potion  1510  relative to one another. 
     Bridge  1514  also allows helmet padding system  1500  to maintain a continuous, uninterrupted lower edge, as shown in  FIG.  30 B . This continuous lower edge may improve protection and comfort for the user. Moreover, bridge  1514  may include one or more of the interior padding layers described herein to improve impact resistance. For example, the main portion  1510  of helmet padding system  1500  may include a continuous padding layer along the entire lower circumferential edge thereof to improve protection of the user from impacts. 
     When system  1500  is worn under a baseball cap having a rear cut-out (e.g., for an adjustable strap), opening  1580  is desirably located at the same position as the rear cut-out. Thus, opening  1580  reveals an area of the user&#39;s head directly beneath the cut-out of the baseball cap. This may be particularly desirable for users of system  1500  having long hair, who for comfort or other reasons wish their hair to extend through the rear cut-out of the baseball cap. In other words, opening  1580  desirably allows certain users to utilize the rear cut-out of their baseball cap as they normally would if they were not wearing a helmet padding system underneath their baseball cap. 
     System  1500  may further include a removable plate  1582  sized to fit within opening  1580 , as shown in  FIGS.  31 A- 31 C . Removable plate  1582  may have an approximately oval shape corresponding to the shape of opening  1580 , in order to be easily received within and fill opening  1580 . When received within the opening, removable plate  1582  provides impact protection to the user in the area of opening  1580 , in substantially the same manner as main portion  1510 . To this end, removable plate  1582  may be formed from the same material as main portion  1510  of system  1500 , and may include one or more of the interior padding layers described herein to improve impact resistance. 
     Removable plate  1582  may be coupled to the main portion  1510  when it is received in opening  1580  using any of the attachment methods set forth above with respect to removable portions  1180  and  1280 . In an exemplary embodiment, the removable plate includes a plurality of snapping mechanisms  1584  that snap onto main portion  1510  of system  1500 , as shown in  FIG.  31 C . Snapping mechanisms  1584  may snap onto main portion  1510  on an outer surface thereof and/or on an inner surface thereof. To this end, snapping mechanisms may be formed as tabs that are configured to extend along an outer or inner surface of main portion  1510  when removable plate  1582  is positioned within opening  1580 . Removable plate  1582  can then be removed from main portion  1510  at the user&#39;s discretion. 
     In an exemplary embodiment, removable plate  1582  includes a pair of outer tabs  1586  extending from an upper edge, and an outer ridge  1588  extending along the lower edge thereof. Tabs  1586  and ridge  1588  are positioned to rest on or contact an outer surface of main portion  1510 , as shown in  FIG.  31 A . Removable plate  1582  further includes at least one inner tab  1589  extending from the upper edge and positioned to rest on or contact an inner surface of main portion  1510 . In this embodiment, to couple removable plate  1582  to main portion  1510 , plate  1582  is slid into opening  1580  from a lower angle, in order to sandwich main portion  1510  between tabs  1586  and  1589 , and allow ridge  1588  to rest on the lower edge of opening  1580 , as shown in  FIG.  31 C . 
       FIGS.  32 A and  32 B  illustrate an alternative embodiment  1600  of helmet padding system  1400  in accordance with aspects of the present invention. Helmet padding system  1600  may be worn by a user during an athletic activity. Like helmet padding system  1400 , helmet padding system  1600  may be worn under another piece of headgear, such as a baseball cap. As a general overview, system  1600  includes a rigid shell  1610 , a spacing pad, and a facemask  1690 . Helmet padding system  1600  includes substantially the same features as helmet padding system  1400 , except as described herein. 
     Rigid shell  1610  is configured to cover the top of a user&#39;s head. Rigid shell  1610  is sized to be worn under a baseball cap. Rigid shell  1610  includes a body portion  1620  and a pair of side portions  1630 . Body portion  1620  has a lower front edge  1621  extending between the pair of side portions  1630 . Body portion  1620  further includes a lower rear edge  1622  extending between the pair of side portions  1630  opposite lower front edge  1621 . 
     When worn under a baseball cap, lower front edge  1621  extends below the brim of the baseball cap. In an exemplary embodiment, lower front edge  1621  of rigid shell  1610  extends approximately one inch below the brim of the baseball cap. This protruding lower front edge  1621  may be desirable in order to provide added protection to the user, as well as to provide a location for attaching facemask  1690 , as will be discussed below. 
     As shown in  FIG.  32 A , lower rear edge  1622  of body portion  1620  extends down the user&#39;s head along with side portions  1630 . In this embodiment, lower rear edge  1622  extends along approximately a same circumferential line as the lower edges of side portions  1630 . In this embodiment, when rigid shell  1610  is worn under a baseball cap (such as a fitted baseball cap) lower rear edge  1622  extends below the lower edge of the cap, in order to provide additional protection to the neck of the user. 
     Body portion  1620  may also include a pair of cutouts  1625  on ends of front edge  1621 , one of which is shown in  FIG.  32 B . Cutouts  1625  are provided between front edge  1621  and side portions  1630 . It will be understood by one of ordinary skill in the art that the shape of cutouts  1625  shown in  FIG.  24 B  is provided for the purposes of illustration, and is not intended to be limiting. 
     Side portions  1630  extend downward below the lower front edge  1621  of body portion  1620 , as shown in  FIGS.  32 A and  32 BC . Side portions  1630  are sized to cover at least a portion (preferably at least 50%) of the user&#39;s ear when rigid shell  1610  is worn by the user. Side portions  1630  are also desirably sized to cover the user&#39;s temples when rigid shell  1610  is worn by the user. 
     Side portions  1630  may also include one or more attachment points. attachment points designed to facilitate the attachment of appropriate accessories to the user&#39;s athletic activity. Such attachment points are preferably positioned on side portions  1630  so that they can be accessed even when rigid shell  1610  is worn underneath a baseball cap. 
     In an exemplary embodiment, side portions  1630  include one or more grooves  1631 . Grooves  1631  provide attachment points for facemask  1690  to be coupled to rigid shell  1610 . In a preferred embodiment, lower front edge  1621  also includes one or more grooves  1631  for coupling facemask  1690  to rigid shell  1610 . Groove  1631  on lower front edge  1621  may be accessible to facemask  1690  without removing the user&#39;s cap due to lower front edge  1621  extending below the lower edge of the brim of the cap, as described above. 
     In another exemplary embodiment, side portions  1630  include one or more snaps  1633 . Snaps  1633  provide attachment points for a strap (e.g., a chin strap) to be attached to rigid shell  1610 . Snaps  1633  may be movable within slots on side portions  1630  in order to adjust the fitting of the chin strap. 
     Rigid shell  1610  may include a cutout  1626  in an area of body portion  1620  opposite lower front edge  1621 . When rigid shell  1610  incorporates a cutout  1626 , helmet padding system  1600  may further comprise a removable portion  1660  configured to fit within cutout  1626  of rigid shell  1610 . Removable portion  1660  is formed from the same material as rigid shell  1610 , in order to provide similar protection from the force of impacts. 
     Facemask  1690  is configured to protect the user&#39;s face from impacts or projectiles (such as baseballs or softballs) commonly in play during the course of an athletic activity. Facemask  1690  may be permanently coupled to rigid shell  1610 , or may be removably coupled to rigid shell  1610 . Preferably, facemask  1690  is removable from rigid shell  1610  without removable of rigid shell  1610  from the user&#39;s head, and without removing any components from rigid shell  1610 . In this manner, that facemask  1690  need not be worn throughout an entire athletic activity, and may be removed (e.g., when impacts to a user&#39;s face are not likely to occur) without removal of the user&#39;s baseball cap or the remaining components of system  1600 . 
     In an exemplary embodiment, facemask  1690  is formed from a plurality of rigid bars  1692  that protect the user&#39;s face without substantially obstructing the user&#39;s vision. Bars  1692  may have portions sized to mate with corresponding attachment points on rigid shell  1610  in order to couple facemask  1690  to rigid shell  1610 . In a preferred embodiment, one or more portions of bars  1692  are sized to mate with corresponding grooves  1631  formed on side portions  1630  and/or on lower front edge  1621 . Grooves  1631  are sized to provide a snug, secure fit to the portions of bars  1692 , while allowing facemask  1690  to be removed (e.g., by sliding) from grooves  1631  when facemask  1690  is not in use. 
     System  1600  may further include a chin strap  1694 . Chin strap  1694  is configured to secure system  1600  on the user&#39;s head during the course of an athletic activity. Chin strap  1694  has ends which are coupled to the respective side portions  1630  of rigid shell  1610 , and is sufficiently long to circle underneath the user&#39;s chin when rigid shell  1610  is worn by the user. Chin strap  1694  may be permanently coupled to rigid shell  1610 , or may be removably coupled to rigid shell  1610 . Preferably, chin strap  1694  is removable from rigid shell  1610  without removable of rigid shell  1610  from the user&#39;s head, and without removing any components from rigid shell  1610 . In this manner, that chin strap  1694  need not be worn throughout an entire athletic activity, and may be removed (e.g., when the user is not active engaged in the athletic activity) without removal of the user&#39;s baseball cap or the remaining components of system  1600 . 
     In an exemplary embodiment, chin strap  1694  is formed from a flexible material such as rubber or fabric that is flexible or soft enough to be comfortable to the user while remaining strong enough to secure system  1600  on the user&#39;s head. Chin strap  1694  has mating structures  1696  sized to mate with corresponding attachment points on rigid shell  1610  in order to couple chin strap  1694  to rigid shell  1610 . In a preferred embodiment, mating structures  1696  are configured to snap onto corresponding snaps  1633  formed on side portions  1630  of rigid shell  1610 . Snaps  1633  are configured to provide a snug, secure connection to the mating structures  1696  on chin strap  1694 . Snaps  1633  may also be positioned within slots on side portions  1630  to allow chin strap  1694  to be adjusted to ensure the user&#39;s comfort and security. 
       FIGS.  33 A- 35    illustrate an exemplary helmet padding system  1700  in accordance with aspects of the present invention. Helmet padding system  1700  may be worn by a user during an athletic activity. Desirably, helmet padding system  1700  may be worn under another piece of headgear, such as a baseball cap, knit winter cap, beanie, or other piece of aesthetic headwear. As a general overview, system  1700  includes a rigid shell  1710  and a spacing pad  1740 . Additional details of system  1700  are described herein. 
     Rigid shell  1710  is configured to cover the top of a user&#39;s head. Rigid shell  1710  is sized to be worn under a baseball cap. Accordingly, it may be desirable that rigid shell  1710  be formed from a thin, rigid material. In an exemplary embodiment, rigid shell  1710  is formed from a polycarbonate material, as described above. The material may have a thickness of less than approximately 5 mm, and more desirably, less than approximately 3.5 mm. Forming rigid shell  1710  with a low profile (i.e. thin size) is desirable to promote use of helmet padding system  1700  by eliminating interference with the aesthetic features of the headgear (e.g., baseball cap) worn on top of rigid shell  1710 . 
     Rigid shell  1710  includes a body portion  1720  and a pair of side portions  1730 . Body portion  1720  has a lower front edge  1721  extending between the pair of side portions  1730 . When worn under a baseball cap, lower front edge  1721  is positioned adjacent the brim of the baseball cap. Body portion  1720  further includes a lower rear edge  1722  extending between the pair of side portions  1730  opposite lower front edge  1721 . 
     In one embodiment, lower rear edge  1722  of body portion  1720  has approximately the same height as lower front edge  1721 , as shown in  FIG.  33 A . In this embodiment, lower rear edge extends along approximately the same circumferential line (around the user&#39;s head) as lower front edge  1721 . In this embodiment, when rigid shell  1710  is worn under a baseball cap (such as a fitted baseball cap) lower rear edge  1722  is positioned adjacent the lower edge of the cap. 
     Body portion  1720  may include at least one slot therein. The slot may preferably assist in the ability of rigid shell  1710  to protect against the force of impacts, e.g., by allowing portions of rigid shell  1710  to move relative to one another. The slot also preferably allows breathability between the interior of rigid shell  1710  (i.e., the area adjacent the user&#39;s head) and the exterior of rigid shell  1710 . 
     In an exemplary embodiment, body portion  1720  of rigid shell  1710  includes a pair of slots  1723  positioned between each side portion  1730  and an apex of rigid shell  1710 . As shown in  FIGS.  33 B and  34   , slots  1723  are positioned on either side of an apex of rigid shell  1710 . The pair of slots  1723  are configured to extend in a direction from a back of the user&#39;s head to the front of the user&#39;s head when rigid shell  1710  is worn on the user&#39;s head. 
     Body portion  1720  may also include one or more ridges along a surface thereof. In an exemplary embodiment, body portion  1720  includes an elevated ridge  1724  extending from an area adjacent lower front edge  1721  over the apex of body portion  1720  to an area adjacent lower rear edge  1722 , as shown in  FIG.  33 B . Ridge  1724  may provide additional structural stability to rigid shell  1710 , thereby allowing shell  1710  to better dissipate the force of impacts. Ridge  1724  may further provided additional space between rigid shell  1710  and the user&#39;s head, adding to comfort and breathability for the user. In this embodiment, the pair of slots  1723  are positioned on either side of ridge  1724 . 
     Side portions  1730  extend downward below the lower front edge  1721  and lower rear edge  1722  of body portion  1720 , as shown in  FIG.  33 A . Side portions  1730  are sized to cover at least a portion (preferably at least 50%) of the user&#39;s ear when rigid shell  1710  is worn by the user. Side portions  1730  are also desirably sized to cover the user&#39;s temples when rigid shell  1710  is worn by the user. In an exemplary embodiment, each side portion  1730  has a pair of sidewalls extending downward from body portion  1720  at a perpendicular angle to the lower front and rear edges  1721  and  1722  of body portion  1720 . Further, as shown in  FIG.  33 A , each side portion  1730  may have a rectangular shape. 
     Spacing pad  1740  is positioned within the interior of rigid shell  1710 , as shown in  FIG.  35   . The spacing pad  1740  may be a spacing pad substantially as described with respect to spacing pad  130 . Alternatively, the spacing pad  1740  may be an impact-resistant pad substantially as described above with respect to impact-resistant pad  200 . Likewise, the spacing pad may be formed from any of the materials set forth above with respect to spacing pad  130  or impact-resistant pad  200 , and may take any of the shapes described above with respect to spacing pad  130  and/or impact-resistant pad  200 . 
     In a particularly suitable embodiment, the spacing pad  1740  includes a first portion  1741  extending circumferentially around a lower portion of rigid shell  1710 , as shown in  FIG.  35   . In this embodiment, spacing pad  1740  includes a second portion  1742  positioned between slots  1723 , as set forth in greater detail below. 
     Where helmet padding system  1700  is used with a fitted baseball cap, rigid shell  1710  may have a continuous, uninterrupted rear body portion. However, when helmet padding system  1700  is used with an adjustable baseball cap, rigid shell  1710  may include a cutout as shown in  FIGS.  33 A- 33 B , and as set forth below. 
     Rigid shell  1710  may include a cutout  1726  in an area of body portion  1720  opposite lower front edge  1721 . When rigid shell  1710  is worn beneath a baseball cap, cutout  1726  is provided in an area of body portion  1720  adjacent a rear of the baseball cap. In this embodiment, the baseball cap may be an adjustable baseball cap an opening for accommodating the adjustable strap. Accordingly, cutout  1726  has a shape corresponding to the shape of the opening in the rear of the adjustable baseball cap. 
     When rigid shell  1710  incorporates a cutout  1726 , helmet padding system  1700  may further comprise a removable portion  1760  configured to fit within cutout  1726  of rigid shell  1710 . Removable portion  1760  is formed from the same material as rigid shell  1710 , in order to provide similar protection from the force of impacts. Thus, when removable portion  1760  is coupled to rigid shell  1710 , the components form an approximately continuous dome shape on the top of the user&#39;s head. Removable portion  1760  is configured to be coupled to and removable from rigid shell  1710 . Removable portion  1760  may be coupled to rigid shell  1710  by a number of different mechanisms, as described above with respect to removable portion  1180  or  1460 . 
     When rigid shell  1710  incorporates a cutout  1726 , both slots  1723  and ridge  1724  may extend to cutout  1726 . Likewise, the second portion  1742  of spacing pad  1740  may be coupled to the interior of ridge  1724  between slots  1723  and adjacent cutout  1726 . 
       FIGS.  36 A- 38    illustrate another exemplary helmet padding system  1800  in accordance with aspects of the present invention. Helmet padding system  1800  may be worn by a user during an athletic activity. Desirably, helmet padding system  1800  may be worn under another piece of headgear, such as a baseball cap, knit winter cap, beanie, or other piece of aesthetic headwear. As a general overview, system  1800  includes a rigid shell  1810  and a spacing pad  1840 . Additional details of system  1800  are described herein. 
     Rigid shell  1810  is configured to cover at least a portion of the top of a user&#39;s head. Rigid shell  1810  is sized to be worn under a baseball cap. Accordingly, it may be desirable that rigid shell  1810  be formed from a thin, rigid material. In an exemplary embodiment, rigid shell  1810  is formed from a polycarbonate material, as described above. The material may have a thickness of less than approximately 5 mm, and more desirably, less than approximately 3.5 mm. Forming rigid shell  1810  with a low profile (i.e. thin size) is desirable to promote use of helmet padding system  1800  by eliminating interference with the aesthetic features of the headgear (e.g., baseball cap) worn on top of rigid shell  1810 . 
     Rigid shell  1810  includes a body portion  1820  having a lower front edge  1821 . When worn under a baseball cap, lower front edge  1821  is positioned adjacent the brim of the baseball cap. Body portion  1820  further includes a rear edge  1822  opposite lower front edge  1821 . In one embodiment, rear edge  1822  of body portion  1820  is positioned in the vicinity of the middle of the user&#39;s head, as shown in  FIG.  36 A . In this embodiment, rear edge  1822  may be substantially positioned within a plane bisecting the user&#39;s head in an up-down direction. 
     Body portion  1820  may include at least one slot therein. The slot may preferably assist in the ability of rigid shell  1810  to protect against the force of impacts, e.g., by allowing portions of rigid shell  1810  to move relative to one another. The slot also preferably allows breathability between the interior of rigid shell  1810  (i.e., the area adjacent the user&#39;s head) and the exterior of rigid shell  1810 . 
     In an exemplary embodiment, body portion  1820  of rigid shell  1810  includes a pair of slots  1823  positioned on either side of an apex of rigid shell  1810 , as shown in  FIGS.  368  and  37   . The pair of slots  1823  are configured to extend in a direction from a back of the user&#39;s head to the front of the user&#39;s head when rigid shell  1810  is worn on the user&#39;s head. 
     Body portion  1820  may also include one or more ridges along a surface thereof. In an exemplary embodiment, body portion  1820  includes an elevated ridge  1824  extending from an area adjacent lower front edge  1821  over the apex of body portion  1820  to an area adjacent rear edge  1822 , as shown in  FIG.  368   . Ridge  1824  may provide additional structural stability to rigid shell  1810 , thereby allowing shell  1810  to better dissipate the force of impacts. Ridge  1824  may further provide additional space between rigid shell  1810  and the user&#39;s head, adding to comfort and breathability for the user. In this embodiment, the pair of slots  1823  are positioned on either side of ridge  1824 . 
     Spacing pad  1840  is positioned within the interior of rigid shell  1810 , as shown in  FIGS.  37  and  38   . The spacing pad  1840  may be a spacing pad substantially as described with respect to spacing pad  130 . Alternatively, the spacing pad  1840  may be an impact-resistant pad substantially as described above with respect to impact-resistant pad  200 . Likewise, the spacing pad may be formed from any of the materials set forth above with respect to spacing pad  130  or impact-resistant pad  200 , and may take any of the shapes described above with respect to spacing pad  130  and/or impact-resistant pad  200 . 
     In a particularly suitable embodiment, the spacing pad  1840  includes a first portion  1841  extending circumferentially around a lower portion of rigid shell  1810 , as shown in  FIG.  37   . In this embodiment, spacing pad  1840  includes a second portion  1842  positioned between slots  1823 . The second portion  1842  of spacing pad  1840  may be coupled to the interior of ridge  1824  between slots  1823  and adjacent rear edge  1822 . 
     As shown in  FIG.  38   , when rigid shell  1810  is worn under a baseball cap (such as a fitted baseball cap) rear edge  1822  is positioned at or immediately behind an apex of the baseball cap. In other words, rigid shell  1810  is positioned between the baseball cap and the user&#39;s head at a front portion of the user&#39;s head, and rigid shell  1810  is not positioned between the baseball cap and the user&#39;s head at a rear portion of the user&#39;s head. This structure may increase the comfort of the user wearing helmet padding system  1800  while still maintaining protection of the portion of front portion of the user&#39;s head, where impacts may be more likely. 
       FIGS.  39 A- 39 C  illustrate an exemplary helmet padding system  1900  in accordance with aspects of the present invention. Helmet padding system  1900  may be worn by a user during an athletic activity. Desirably, helmet padding system  1900  may be worn under another piece of headgear, such as a football helmet, baseball cap, knit winter cap, beanie, or other piece of aesthetic headwear. As a general overview, system  1900  includes a rigid shell  1910  and a spacing pad  1940 . Additional details of system  1900  are described herein. 
     Rigid shell  1910  is configured to cover the top of a user&#39;s head. Rigid shell  1910  is sized to be worn within a football helmet, between padding of the football helmet and the wearer&#39;s head. Accordingly, it may be desirable that rigid shell  1910  be formed from a thin, rigid material. In an exemplary embodiment, rigid shell  1910  is formed from a polycarbonate material, as described above. The material may have a thickness of less than approximately 5 mm, and more desirably, less than approximately 3.5 mm. 
     Rigid shell  1910  includes a body portion  1920 . Body portion  1920  has a lower front edge  1921 , lower side edges  1922 , and a lower rear edge  1923 . In one embodiment, lower side edges  1922  of body portion  1920  have approximately the same height as lower front edge  1921 . In this embodiment, lower side edges  1922  extend along approximately the same circumferential line (around the user&#39;s head) as lower front edge  1921 . 
     Lower rear edge  1923  may be formed by a cutout in an area of body portion  1920  opposite lower front edge  1921 , as shown in  FIG.  39 B . The cutout may have an approximately semicircular shape, or may have any other shape desired. 
     Alternatively, lower rear edge  1923  may extend along approximately the same circumferential line (around the user&#39;s head) as lower front edge  1921  and lower side edges  1922 , as shown in  FIGS.  40 A and  40 B . In this embodiment, lower front edge  1921 , lower side edges  1922 , and lower rear edge  1923  are all located in the same plane. 
     Body portion  1920  may include at least one slot therein. The slot may preferably assist in the ability of rigid shell  1910  to protect against the force of impacts, e.g., by allowing portions of rigid shell  1910  to move relative to one another. The at least one slot also preferably allows breathability between the interior of rigid shell  1910  (i.e., the area adjacent the user&#39;s head) and the exterior of rigid shell  1910 . 
     In an exemplary embodiment, body portion  1920  of rigid shell  1910  includes a first pair of slots  1924  and a second pair of slots  1925 . Slots  1924  and  1925  extend parallel to an apex line of rigid shell  1910 , the apex line extending in a direction of body portion  1920  from the front most point to a rearmost point (shown as a dashed line in  FIG.  39 A ). As shown in  FIG.  39 A , slots  1924  and  1925  are positioned on either side of the apex line of rigid shell  1910 , between the apex line and the lower side edges  1922  of body portion  1920 . 
     Slots  1924  extend from the lower front edge  1921  of body portion  1920 . As shown in  FIG.  39 A , slots  1924  may extend to a point forward of a midpoint of body portion  1920 , the midpoint being a line extending from side to side of rigid shell  1910  equidistant from the front most point to a rearmost point of body portion  1920  (shown as a dotted line in  FIG.  39 A ). Alternatively, slots  1924  may extend to a point closer to lower front edge  1921  than to the midpoint of body portion  1920 , as shown in  FIG.  40 A . In other embodiments, slots  1924  may extend to the midpoint of body portion  1920 , or to a point rearward of the midpoint of body portion  1920 . 
     Slots  1925  extend from lower rear edge  1923  of body portion  1920 . As shown in  FIG.  39 A , slots  1925  may extend to a point rearward of the midpoint of body portion  1920 . Alternatively, slots  1925  may extend to a point forward of the midpoint of body portion  1920 , as shown in  FIG.  40 A . In other embodiments, slots  1925  may extend to the midpoint of body portion  1920 . 
     As shown in  FIGS.  39 A and  40 A , slots  1925  may have a greater width than slots  1924 . In other embodiments, slots  1924  and  1925  may have the same width, or slots  1924  may have a larger width than slots  1925 . 
     As shown in  FIGS.  39 A and  40 A , slots  1925  may have a tapering width, while slots  1924  have a constant width. In other embodiments, either slots  1924  and/or  1925  may have constant or tapering widths. Likewise, either slots  1924  and/or  1925  may taper larger or smaller, i.e., may grow larger as they extend away from their respective edges, or may grow smaller as they extend away from their respective edges. 
     As shown in  FIGS.  39 A and  40 A , slots  1925  are positioned closer to the apex line of rigid shell  1910  than slots  1924 . In other embodiments, slots  1924  and  1925  may be positioned the same distance from the apex line of rigid shell  1910 , or slots  1924  may be positioned closer to the apex line than slots  1925 . 
     The variable lengths of slots  1925 , as well as the variable positioning of lower rear edge  1923 , allows the rigid material of shell  1910  to create a flexible tongue extending from the apex of rigid shell  1910  down to the lower rear edge  1923 . This flexible tongue enables helmet padding system  1900  to adjust to users of various head sizes, and further, allows better comfort for the user as well as better protection for all portions of the user&#39;s head, including the back of the user&#39;s head. 
     Body portion  1920  may also include one or more ridges along a surface thereof. In an exemplary embodiment, body portion  1920  includes a first ridge  1926  extending along the apex line of rigid shell  1910 , and a pair of second ridges  1927  extending along either side of ridge  1926 , as shown in  FIG.  39 A . Ridges  1926  and  1927  may provide additional structural stability to rigid shell  1910 , thereby allowing shell  1910  to better dissipate the force of impacts. Ridges  1926  and  1927  may further provided additional space between rigid shell  1910  and the user&#39;s head, adding to comfort and breathability for the user. 
     As shown in  FIG.  39 A , a portion of ridges  1927  may be interrupted or removed to create slots  1925 . In other embodiments, ridges  1926  and  1927  may be interrupted between the lower front edge  1921  and the lower rear edge  1923  of body portion  1920 , or portion(s) of ridges  1926  and/or  1927  may be removed to create slots  1924 . 
     Spacing pad  1940  is positioned within the interior of rigid shell  1910 , as shown in  FIG.  39 C . The spacing pad  1940  may be a spacing pad substantially as described with respect to spacing pad  130 . Alternatively, the spacing pad  1940  may be an impact-resistant pad substantially as described above with respect to impact-resistant pad  200 . Likewise, the spacing pad may be formed from any of the materials set forth above with respect to spacing pad  130  or impact-resistant pad  200 , and may take any of the shapes described above with respect to spacing pad  130  and/or impact-resistant pad  200 . 
     In an exemplary embodiment, the spacing pad  1940  includes a first portion  1941  extending circumferentially around a lower portion of rigid shell  1910 , and a second portion  1942  positioned between slots  1925 , as shown in  FIG.  39 C . 
     First portion  1941  of spacing pad  1940  is interrupted by slots  1924 , and thus forms separate sections following the lower front edge  1921  and lower side edges  1922  of body portion  1920 . Notwithstanding the interruptions caused by slots  1924 , first portion  1941  of spacing pad  1940  may follow a substantial portion (e.g., 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more) of the circumference of lower front edge  1921  and lower side edges  1922 , as shown in  FIG.  39 C . 
     Second portion  1942  of spacing pad  1940  extends along the apex line of body portion  1920  between slots  1925 . Second portion  1942  may cover a substantial portion (e.g., 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more) of a space between slots  1925 , as shown in  FIG.  39 C . 
     Spacing pad  1940  may further include one or more third portions  1943  contacting first portion  1941 . Third portions  1943  cover a space between first portion  1941  and slots  1925 , as shown in  FIG.  39 C . 
       FIGS.  41 A- 41 C  illustrate an exemplary helmet padding system  2000  in accordance with aspects of the present invention. Helmet padding system  2000  may be worn by a user during an athletic activity. Desirably, helmet padding system  2000  may be worn under another piece of headgear, such as a football helmet, baseball cap, knit winter cap, beanie, or other piece of aesthetic headwear. As a general overview, system  2000  includes a rigid shell  2010  and a spacing pad  2040 . Additional details of system  2000  are described herein. 
     Rigid shell  2010  is configured to cover the top of a user&#39;s head. Rigid shell  2010  is sized to be worn within a baseball cap, as shown in  FIG.  42   . Accordingly, it may be desirable that rigid shell  2010  be formed from a thin, rigid material. In an exemplary embodiment, rigid shell  2010  is formed from a polycarbonate material, as described above. The material may have a thickness of less than approximately 5 mm, and more desirably, less than approximately 3.5 mm. 
     Rigid shell  2010  includes a body portion  2020 . Body portion  2020  has a lower front edge  2021 , lower side edges  2022 , and a lower rear edge  2023 . In one embodiment, lower side edges  2022  of body portion  2020  have approximately the same height as lower front edge  2021 . In this embodiment, lower side edges  2022  extend along approximately the same circumferential line (around the user&#39;s head) as lower front edge  2021 . As shown in  FIG.  42   , when rigid shell  2010  is worn under a baseball cap, lower front edge  2021  and lower side edges  2022  may be tucked into the sweatband of the baseball cap, i.e., between the outer material of the cap and the sweatband. This configuration may increase the user&#39;s comfort in wearing rigid shell  2010 . 
     Lower rear edge  2023  may extend along approximately the same circumferential line (around the user&#39;s head) as lower front edge  2021  and lower side edges  2022 . Alternatively, as shown in  FIG.  41 B , lower rear edge  2023  may be formed by a cutout in an area of body portion  2020  opposite lower front edge  2021 . The cutout may have an approximately semicircular shape, as shown in  FIG.  41 B , or may have any other shape desired. 
     Body portion  2020  may include at least one slot therein. The slot may preferably assist in the ability of rigid shell  2010  to protect against the force of impacts, e.g., by allowing portions of rigid shell  2010  to move relative to one another. The at least one slot also preferably allows breathability between the interior of rigid shell  2010  (i.e., the area adjacent the user&#39;s head) and the exterior of rigid shell  2010 . 
     In an exemplary embodiment, body portion  2020  of rigid shell  2010  includes a pair of slots  2025 . Slots  2025  extend parallel to an apex line of rigid shell  2010 , the apex line extending in a direction of body portion  2020  from the front most point to a rearmost point (shown as a dashed line in  FIG.  41 A ). As shown in  FIG.  41 A , slots  2025  are positioned on either side of the apex line of rigid shell  2010 , between the apex line and the lower side edges  2022  of body portion  2020 . 
     Slots  2025  extend from lower rear edge  2023  of body portion  2020 . As shown in  FIG.  41 A , slots  2025  may extend to a point forward of a midpoint of body portion  2020 , the midpoint being a line extending from side to side of rigid shell  2010  equidistant from the front most point to a rearmost point of body portion  2020  (shown as a dotted line in  FIG.  41 A ). In other embodiments, slots  2025  may extend to the midpoint of body portion  2020 , or to a point rearward of the midpoint of body portion  2020 . 
     As shown in  FIG.  41 A , slots  2025  may have a tapering width. In other embodiments, slots  2025  may have a constant. Likewise, slots  2025  may taper larger or smaller, i.e., may grow larger as they extend away from lower rear edge  2023 , or may grow smaller as they extend away from lower rear edge  2023 . 
     Body portion  2020  may also include one or more ridges along a surface thereof. In an exemplary embodiment, body portion  2020  includes a ridge  2026  extending along the apex line of rigid shell  2010 , as shown in  FIG.  41 A . Ridge  2026  may provide additional structural stability to rigid shell  2010 , thereby allowing shell  2010  to better dissipate the force of impacts. Ridge  2026  may further provided additional space between rigid shell  2010  and the user&#39;s head, adding to comfort and breathability for the user. As shown in  FIG.  41 A , slots  2025  are positioned on either side of ridge  2026 . 
     Spacing pad  2040  is positioned within the interior of rigid shell  2010 , as shown in  FIG.  41 C . The spacing pad  2040  may be a spacing pad substantially as described with respect to spacing pad  130 . Alternatively, the spacing pad  2040  may be an impact-resistant pad substantially as described above with respect to impact-resistant pad  200 . Likewise, the spacing pad may be formed from any of the materials set forth above with respect to spacing pad  130  or impact-resistant pad  200 , and may take any of the shapes described above with respect to spacing pad  130  and/or impact-resistant pad  200 . 
     In an exemplary embodiment, the spacing pad  2040  includes a first portion  2041  extending circumferentially around a lower portion of rigid shell  2010 , and a second portion  2042  positioned between slots  2025 , as shown in  FIG.  41 C . 
     First portion  2041  of spacing pad  2040  may follow a substantial portion (e.g., 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more) of the circumference of lower front edge  2021  and lower side edges  2022 , as shown in  FIG.  41 C . Second portion  2042  of spacing pad  2040  extends along the apex line of body portion  2020  between slots  2025 . Second portion  2042  may cover a substantial portion (e.g., 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more) of a space between slots  2025 , as shown in  FIG.  41 C . 
     Spacing pad  2040  may further include one or more third portions  2043  contacting first portion  2041 . Third portions  2043  cover a space between first portion  2041  and slots  2025 , as shown in  FIG.  41 C . 
       FIGS.  43 A- 43 C  illustrate another exemplary helmet padding system  2100  in accordance with aspects of the present invention. Helmet padding system  2100  may be worn by a user during an athletic activity. Desirably, helmet padding system  2100  may be worn under another piece of headgear, such as a baseball cap, knit winter cap, beanie, or other piece of aesthetic headwear. As a general overview, system  2100  includes a rigid shell  2110  and a spacing pad  2140 . Additional details of system  2100  are described herein. 
     Rigid shell  2110  is configured to cover at least a portion of a user&#39;s head. Rigid shell  2110  is sized to be worn under a baseball cap. Accordingly, it may be desirable that rigid shell  2110  be formed from a thin, rigid material. In an exemplary embodiment, rigid shell  2110  is formed from a polycarbonate material, as described above. The material may have a thickness of less than approximately 5 mm, and more desirably, less than approximately 3.5 mm. Forming rigid shell  2110  with a low profile (i.e. thin size) is desirable to promote use of helmet padding system  2100  by eliminating Interference with the aesthetic features of the headgear (e.g., baseball cap) worn on top of rigid shell  2110 . 
     Rigid shell  2110  includes a body portion  2120  having a lower edge  2121  and an upper edge  2123  opposite lower edge  2121 . When worn under a baseball cap, lower edge  2121  is positioned adjacent the brim of the baseball cap. Lower edge  2121  extends around less than all of the user&#39;s head. In an exemplary embodiment, lower edge  2121  extends around no more than half of the user&#39;s head. In this embodiment, upper edge  2123  of body portion  2120  is positioned in the vicinity of the middle of the user&#39;s head. In this embodiment, upper edge  2123  may be substantially positioned within a plane bisecting the user&#39;s head in an up-down direction. 
     Body portion  2120  may include at least one slot therein. The slot may preferably assist in the ability of rigid shell  2110  to protect against the force of impacts, e.g., by allowing portions of rigid shell  2110  to move relative to one another. The slot also preferably allows breathability between the interior of rigid shell  2110  (i.e., the area adjacent the user&#39;s head) and the exterior of rigid shell  2110 . 
     In an exemplary embodiment, body portion  2120  of rigid shell  2110  includes a pair of slots  2125  positioned on either side of an apex line of rigid shell  2110 , the apex line extending in a direction of body portion  2120  from the front most point to a rearmost point (shown as a dashed line in  FIG.  43 A ). The pair of slots  2125  are configured to extend along the direction of the apex line from upper edge  2123  toward lower edge  2121 . 
     Body portion  2120  may also include one or more ridges along a surface thereof. In an exemplary embodiment, body portion  2120  includes an elevated ridge  2126  extending along the apex line, as shown in  FIG.  43 A . Ridge  2126  may provide additional structural stability to rigid shell  2110 , thereby allowing shell  2110  to better dissipate the force of impacts. Ridge  2126  may further provide additional space between rigid shell  2110  and the user&#39;s head, adding to comfort and breathability for the user. In this embodiment, the pair of slots  2125  are positioned on either side of ridge  2126 . 
     Spacing pad  2140  is positioned within the interior of rigid shell  2110 , as shown in  FIGS.  43 C and  44   . The spacing pad  2140  may be a spacing pad substantially as described with respect to spacing pad  130 . Alternatively, the spacing pad  2140  may be an impact-resistant pad substantially as described above with respect to impact-resistant pad  200 . Likewise, the spacing pad may be formed from any of the materials set forth above with respect to spacing pad  130  or impact-resistant pad  200 , and may take any of the shapes described above with respect to spacing pad  130  and/or impact-resistant pad  200 . 
     In an exemplary embodiment, the spacing pad  2140  includes a first portion  2141  extending circumferentially around a lower portion of rigid shell  2110 , as shown in  FIG.  43 C . In this embodiment, spacing pad  2140  includes a second portion  2142  positioned between slots  2125 . The second portion  2142  of spacing pad  2140  may be coupled to the interior of ridge  2126  between slots  2125  and adjacent upper edge  2123 . 
     As shown in  FIG.  44   , when rigid shell  2110  is worn under a baseball cap (such as a fitted baseball cap) upper edge  2123  is positioned at or immediately behind an apex of the baseball cap. In other words, rigid shell  2110  is positioned between the baseball cap and the user&#39;s head at a front portion of the user&#39;s head, and rigid shell  2110  is not positioned between the baseball cap and the user&#39;s head at a rear portion of the user&#39;s head. This structure may increase the comfort of the user wearing helmet padding system  2100  while still maintaining protection of the portion of front portion of the user&#39;s head, where impacts may be more likely. 
     As shown in  FIG.  44   , when rigid shell  2110  is worn under a baseball cap, lower edge  2121  may be tucked into the sweatband of the baseball cap, i.e., between the outer material of the cap and the sweatband. This configuration may increase the user&#39;s comfort in wearing rigid shell  2110 . 
       FIGS.  45 A- 45 C  illustrate another exemplary helmet padding system  2200  in accordance with aspects of the present invention. Helmet padding system  2200  may be worn by a user during an athletic activity. Desirably, helmet padding system  2200  may be worn under another piece of headgear, such as a baseball cap, knit winter cap, beanie, or other piece of aesthetic headwear. As a general overview, system  2200  includes a rigid shell  2210  and a spacing pad  2240 . Additional details of system  2200  are described herein. 
     Rigid shell  2210  is configured to cover at least a portion of a user&#39;s head. Rigid shell  2210  is sized to be worn under a baseball cap. Accordingly, it may be desirable that rigid shell  2210  be formed from a thin, rigid material. In an exemplary embodiment, rigid shell  2210  is formed from a polycarbonate material, as described above. The material may have a thickness of less than approximately 5 mm, and more desirably, less than approximately 3.5 mm. Forming rigid shell  2210  with a low profile (i.e. thin size) Is desirable to promote use of helmet padding system  2200  by eliminating interference with the aesthetic features of the headgear (e.g., baseball cap) worn on top of rigid shell  2210 . 
     Rigid shell  2210  includes a body portion  2220  having a lower edge  2221  and an upper edge  2223  opposite lower edge  2221 . When worn under a baseball cap, lower edge  2221  is positioned adjacent the brim of the baseball cap. Lower edge  2221  extends around less than all of the user&#39;s head. In an exemplary embodiment, lower edge  2221  extends around no more than half of the user&#39;s head. In this embodiment, upper edge  2223  of body portion  2220  is positioned at an approximate top of the user&#39;s forehead. 
     Upper edge  2223  extends along a line which is approximately parallel to lower edge  2221 , or extends in a plane which is approximately parallel to a plane of lower edge  2221 . Upper edge  2223  may maintain a predetermined from lower edge  2221 , for example, a distance of from one to four inches. Upper edge  2223  and lower edge  2221  are connected by a pair of curved ends  2222 , as shown in  FIG.  45 C . 
     Body portion  2220  has a generally arcuate shape designed to closely follow the contour of the user&#39;s forehead, as shown in  FIG.  45 B . In an exemplary embodiment, body portion  2220  is sized and shaped to extend from a region covering one of the user&#39;s temples, across the user&#39;s forehead, to a region covering the other one of the user&#39;s temples. 
     Body portion  2220  may include one or more ridges along a surface thereof. In an exemplary embodiment, body portion  2220  includes an elevated ridge  2226  extending from lower edge  2221  to upper edge  2223 , as shown in  FIG.  45 A . Ridge  2226  may provide additional structural stability to rigid shell  2210 , thereby allowing shell  2210  to better dissipate the force of impacts. Ridge  2226  may further provide additional space between rigid shell  2210  and the user&#39;s head, adding to comfort and breathability for the user. 
     Spacing pad  2240  is positioned within the interior of rigid shell  2210 , as shown in  FIGS.  45 C and  46   . The spacing pad  2240  may be a spacing pad substantially as described with respect to spacing pad  130 . Alternatively, the spacing pad  2240  may be an impact-resistant pad substantially as described above with respect to impact-resistant pad  200 . Likewise, the spacing pad may be formed from any of the materials set forth above with respect to spacing pad  130  or impact-resistant pad  200 , and may take any of the shapes described above with respect to spacing pad  130  and/or impact-resistant pad  200 . 
     In an exemplary embodiment, the spacing pad  2240  extending circumferentially between lower edge  2221  and upper edge  2223 , as shown in  FIG.  45 C . Spacing pad  2240  may cover a substantial portion (e.g., 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more) of an interior of body portion  2220 , as shown in  FIG.  45 C . 
     As shown in  FIG.  46   , when rigid shell  2210  is worn under a baseball cap (such as a fitted baseball cap), rigid shell  2210  does not cover the top or rear of the user&#39;s head. In other words, rigid shell  2210  is positioned between the baseball cap and the user&#39;s head only at a front portion of the user&#39;s head. This structure may increase the comfort of the user wearing helmet padding system  2200  while still maintaining protection of the portion of front portion of the user&#39;s head, where impacts may be more likely. 
     As shown in  FIG.  46   , when rigid shell  2210  is worn under a baseball cap, lower edge  2221  may be tucked into the sweatband of the baseball cap, i.e., between the outer material of the cap and the sweatband. This configuration may increase the user&#39;s comfort in wearing rigid shell  2210 . 
       FIGS.  47 A- 47 D  illustrate an exemplary helmet padding system  2300  in accordance with aspects of the present invention. Helmet padding system  2300  may be worn by a user during an athletic activity. Desirably, helmet padding system  2300  may be worn under another piece of headgear, such as a baseball cap, knit winter cap, beanie, or other piece of aesthetic headwear. As a general overview, system  2300  includes a rigid shell  2310 , a spacing pad  2340 , and straps  2370 . Additional details of system  2300  are described herein. 
     Rigid shell  2310  is configured to cover the top of a user&#39;s head. Rigid shell  2310  is sized to be worn within another piece of headgear. Accordingly, it may be desirable that rigid shell  2310  be formed from a thin, rigid material. In an exemplary embodiment, rigid shell  2310  is formed from a polycarbonate material, as described above. The material may have a thickness of less than approximately 5 mm, and more desirably, less than approximately 3.5 mm. 
     Rigid shell  2310  includes a body portion  2320 . Body portion  2320  has a lower front edge  2321 , lower side edges  2322 , and a lower rear edge  2323 . In one embodiment, lower side edges  2322  of body portion  2320  have approximately the same height as lower front edge  2321 . In this embodiment, lower side edges  2322  extend along approximately the same circumferential line (around the user&#39;s head) as lower front edge  2321 , as shown in  FIG.  47 B . 
     Lower rear edge  2323  may extend along approximately the same circumferential line (around the user&#39;s head) as lower front edge  2321  and lower side edges  2322 . Alternatively, as shown in  FIG.  47 B , lower rear edge  2323  may be formed by a cutout in an area of body portion  2320  opposite lower front edge  2321 , such that lower rear edge  2323  is positioned in a different plane than lower front edge  2321  and/or lower side edges  2322 . 
     In a particular embodiment, as shown in  FIG.  47 B , lower rear edge  2323  may be defined by opposed end sections  2323   a  extending upward from lower side edges  2322 , and a middle section  2323   b  extending to a point lower than the opposed sections. In this embodiment, the opposed end sections  2323   a  define a plane, and the middle section  2323   b  is positioned outside of the plane. In other embodiments, all of lower rear edge  2323  may be positioned in a single plane. 
     Body portion  2320  may include at least one slot therein. The slot may preferably assist in the ability of rigid shell  2310  to protect against the force of impacts, e.g., by allowing portions of rigid shell  2310  to move relative to one another. The at least one slot also preferably allows breathability between the interior of rigid shell  2310  (i.e., the area adjacent the user&#39;s head) and the exterior of rigid shell  2310 . 
     In an exemplary embodiment, body portion  2320  of rigid shell  2310  includes a pair of slots  2325 . Slots  2325  extend parallel to an apex line of rigid shell  2310 , the apex line extending in a direction of body portion  2320  from the front most point to a rearmost point (shown as a dashed line in  FIG.  47 A ). As shown in  FIG.  47 A , slots  2325  are positioned on either side of the apex line of rigid shell  2310 , between the apex line and the lower side edges  2322  of body portion  2320 . 
     Slots  2325  extend from lower rear edge  2323  of body portion  2320 . As shown in  FIG.  47 A , slots  2325  may extend to a point forward of a midpoint of body portion  2320 , the midpoint being a line extending from side to side of rigid shell  2310  equidistant from the front most point to a rearmost point of body portion  2320  (shown as a dotted line in  FIG.  47 A ). In other embodiments, slots  2325  may extend to the midpoint of body portion  2320 , or to a point rearward of the midpoint of body portion  2320 . 
     As shown in  FIG.  47 A , slots  2325  may have a tapering width. In other embodiments, slots  2325  may have a constant. Likewise, slots  2325  may taper larger or smaller, i.e., may grow larger as they extend away from lower rear edge  2323 , or may grow smaller as they extend away from lower rear edge  2323 . 
     Body portion  2320  may also include one or more elevated ridges along a surface thereof. In an exemplary embodiment, body portion  2320  includes a ridge  2326  extending along the apex line of rigid shell  2310 , as shown in  FIG.  47 A . Ridge  2326  may provide additional structural stability to rigid shell  2310 , thereby allowing shell  2310  to better dissipate the force of impacts. Ridge  2326  may further provided additional space between rigid shell  2310  and the user&#39;s head, adding to comfort and breathability for the user. As shown in  FIG.  47 A , slots  2325  are positioned on either side of ridge  2326 . 
     Spacing pad  2340  is positioned within the interior of rigid shell  2310 , as shown in  FIG.  47 C . The spacing pad  2340  may be a spacing pad substantially as described with respect to spacing pad  130 . Alternatively, the spacing pad  2340  may be an impact-resistant pad substantially as described above with respect to impact-resistant pad  200 . Likewise, the spacing pad may be formed from any of the materials set forth above with respect to spacing pad  130  or impact-resistant pad  200 , and may take any of the shapes described above with respect to spacing pad  130  and/or impact-resistant pad  200 . 
     In an exemplary embodiment, the spacing pad  2340  includes a first portion  2341  extending circumferentially around a lower portion of rigid shell  2310 , and a second portion  2342  positioned between slots  2325 , as shown in  FIGS.  47 C and  47 D , with  FIG.  47 D  being a cross-section showing a half of an interior of helmet padding system  2300 . 
     First portion  2341  of spacing pad  2340  may follow a substantial portion (e.g., 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more) of the circumference of lower front edge  2321  and lower side edges  2322 , as shown in  FIG.  47 C . Second portion  2342  of spacing pad  2340  extends along the apex line of body portion  2320  between slots  2325 . Second portion  2342  may cover a substantial portion (e.g., 50% or more, 60% or more, 70% or more, 80% or more, or 90% or more) of a space between slots  2325 , as shown in  FIG.  47 C . 
     Spacing pad  2340  may further include one or more third portions  2343  contacting first portion  2341 . Third portions  2343  cover a space between first portion  2341  and slots  2325 , as shown in  FIGS.  47 C and  47 D . 
     Straps  2370  are connected to respective sides of rigid shell  2310 . In an exemplary embodiment, a first strap portion  2370   a  extends downward from a forward portion of each lower side edge  2322 . and a second strap portion  2370   b  extends downward from a rearward portion of each lower side edge  2322 . 
     First and second strap portions  2370   a  and  2370   b  may be joined to form a single strap extending underneath the user&#39;s chin, as shown in  FIG.  47 B . Straps  2370  have a sufficient length to extend underneath a user&#39;s chin when helmet padding system  2300  is worn by the user. Straps  2370  may be adjustable in length in order to accommodate users having different head sizes. 
     Straps  2370  include one or more structures for connecting underneath the user&#39;s chin, to secure helmet padding system  2300  on the user&#39;s head. Suitable structures will be apparent to one of ordinary skill in the art, and may include, for example, buckles, clasps, or snaps. 
     Straps  2370  may be connected directly to rigid shell  2310  by, for example, bolts or snaps. As shown in  FIGS.  47 C and  47 D , spacing pad  2340  may include one or more cutouts  2344  to facilitate the direct connection of straps  2370  to rigid shell  2310 . 
       FIGS.  48 A and  48 B  illustrate a top and rear view, respectively, of an exemplary helmet padding system  2400  in accordance with aspects of the present invention. Helmet padding system  2400  may be worn by a user during an athletic activity. Desirably, helmet padding system  2400  may be worn under another piece of headgear, such as a football helmet, baseball cap, knit winter cap, beanie, or other piece of aesthetic headwear. As a general overview, system  2400  includes a rigid shell  2410  and a spacing pad (not shown). Additional details of system  2400  are described herein. 
     Rigid shell  2410  is configured to cover the top of a user&#39;s head. Rigid shell  2410  is sized to be worn within a baseball cap, as shown with respect to helmet padding system  2000 . Accordingly, it may be desirable that rigid shell  2410  be formed from a thin, rigid material. In an exemplary embodiment, rigid shell  2410  is formed from a polycarbonate material, as described above. The material may have a thickness of less than approximately 5 mm, and more desirably, less than approximately 3.5 mm. 
     Rigid shell  2410  includes a body portion  2420 . Body portion  2420  has a lower front edge  2421 , lower side edges  2422 , and a lower rear edge  2423 . In one embodiment, lower side edges  2422  of body portion  2420  have approximately the same height as lower front edge  2421 . In this embodiment, lower side edges  2422  extend along approximately the same circumferential line (around the user&#39;s head) as lower front edge  2421 . 
     Lower rear edge  2423  may extend along approximately the same circumferential line (around the user&#39;s head) as lower front edge  2421  and lower side edges  2422 . Alternatively, as shown in  FIG.  48 B , lower rear edge  2423  may be formed by a cutout in an area of body portion  2420  opposite lower front edge  2421 . The cutout may have any other shape desired. 
     Body portion  2420  may include at least one slot therein. The slot may preferably assist in the ability of rigid shell  2410  to protect against the force of impacts, e.g., by allowing portions of rigid shell  2410  to move relative to one another. The at least one slot also preferably allows breathability between the interior of rigid shell  2410  (i.e., the area adjacent the user&#39;s head) and the exterior of rigid shell  2410 . 
     In an exemplary embodiment, body portion  2420  of rigid shell  2410  includes a pair of slots  2425 . Slots  2425  extend parallel to an apex line of rigid shell  2410 . As shown in  FIG.  41 A , slots  2425  are positioned on either side of the apex line of rigid shell  2410 , between the apex line and the lower side edges  2422  of body portion  2420 . 
     Slots  2425  extend from lower rear edge  2423  of body portion  2420 . As shown in  FIG.  48 A , slots  2425  extend to a point forward of a midpoint of body portion  2420 . Slots  2425  may have a tapering width, or may have a constant width. Slots  2425  may taper larger or smaller, i.e., may grow larger as they extend away from lower rear edge  2423 , or may grow smaller as they extend away from lower rear edge  2423 . 
     As shown in  FIG.  48 A , slots  2425  define a central portion  2470  of the rigid shell  2410 . Central portion  2470  extends along the apex line of rigid shell  2410 . Central portion  2470  is movable relative to side portions of rigid shell  2410  due to the presence of slots  2425 . 
     In an exemplary embodiment, central portion  2470  includes a flap  2472  on one or both sides thereof. Flaps  2472  extend outward from the sides of central portion  2470 . Flaps  2472  extend across the respective slots  2425  and overlap with (i.e. cover) a region of the outer surface of the rigid shell  2410  on the opposite side of each slot  2425  from central portion  2470 , as shown in  FIGS.  48 A and  48 B . Flap  2472  is not directly coupled to the side portions of rigid shell  2410 , such that central portion  2470  remains movable relative to the side portions of rigid shell  2410 . The contact between the inner surfaces of flaps  2472  and the outer surface of the side portions of rigid shell  2410  may assist in transferring and dissipating the force from impacts received at central portion  2470  throughout the body of rigid shell  2410 . 
     In an exemplary embodiment, central portion  2470  includes a tail  2474  at a rear end thereof. Tail  2474  extends outward from the end of central portion  2470  in one or both directions around the circumference of rigid shell  2410 . Tail  2474  is not directly coupled to the side portions of rigid shell  2410 , such that central portion  2470  remains movable relative to the side portions of rigid shell  2410 . As shown in  FIG.  48 B , tail  2474  may define the lower rear edge  2423  of body portion  2420 . 
     Like flaps  2472 , tall  2474  extends across the respective slots  2425  and overlaps with a region of the outer surface of the rigid shell  2410  on the opposite side of each slot  2425  from central portion  2470 . The contact between the inner surfaces of tail  2474  and the outer surface of the side portions of rigid shell  2410  may assist in transferring and dissipating the force from impacts received at central portion  2470  throughout the body of rigid shell  2410 . 
     Flaps  2472  and/or tail  2474  may be formed from the same material as the rest of rigid shell  2410 , e.g., from polycarbonate. Flaps  2472  and/or tail  2474  may be integrally formed (e.g., molded in one piece) with the rest of rigid shell  2410 , or may be attached to central portion  2470 . The side portions of rigid shell  2410  may be provided with an impact-resistant coating, e.g. an elastomer coating, in the regions of contact with flaps  2472  and/or tail  2474 , in order to promote dissipation of force from impacts on central portion  2470 . The shape of flaps  2472  and/or tail  2474  in  FIGS.  48 A and  48 B  is not intended to be limiting. To the contrary, any shape may be used for flaps  2472  and tail  2474  that overlaps with one or both side portions of rigid shell  2410 . 
     A spacing pad is positioned within the interior of rigid shell  2410 . The spacing pad  2040  may be a spacing pad incorporating any of the materials, geometry, or features described with respect to spacing pad  2040 . 
     Although the invention is illustrated and described herein with reference to specific embodiments, the invention is not intended to be limited to the details shown. Rather, various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the invention. In particular, any of the features described herein with respect to one embodiment may be provided in any of the other embodiments.