Patent Publication Number: US-6708424-B1

Title: Shoe with naturally contoured sole

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 08/479,779, filed Jun. 7, 1995, now U.S. Pat. No. 6,115,941, which is a continuation-in-part of application Ser. No. 08/162,962 filed Dec. 8, 1993 now U.S. Pat. No. 5,544,429, which is a continuation of Ser. No. 07/930,469 filed Aug. 20, 1992, now U.S. Pat. No. 5,317,819 issued Jun. 7, 1994 which is a continuation of Ser. No. 07/239,667 filed Sep. 2, 1988, now abandoned and application Ser. No. 07/492,360, filed Mar. 9, 1990, now U.S. Pat. No. 4,989,349 issued Feb. 5, 1991 which is a continuation of Ser. No. 07/219,387, filed Jul. 15, 1988, now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to a shoe, such as a street shoe, athletic shoe, and especially a running shoe with a contoured sole. More particularly, this invention relates to a novel contoured sole design for a running shoe which improves the inherent stability and efficient motion of the shod foot in a extreme exercise. Still more particularly, this invention relates to a running shoe wherein the shoe sole conforms to the natural shape of the foot, particularly the sides, and has a constant thickness in frontal plane cross sections, permitting the foot to react naturally with the ground as it would if the foot were bare, while continuing to protect and cushion the foot. 
     By way of introduction, barefoot populations universally have a very low incidence of running “overuse” injuries, despite very high activity levels. In contrast, such injuries are very common in shoe shod populations, even for activity levels well below “overuse”. Thus, it is a continuing problem with a shod population to reduce or eliminate such injuries and to improve the cushioning and protection for the foot. It is primarily to an understanding of the reasons for such problems and to proposing a novel solution according to the invention to which this improved shoe is directed. 
     A wide variety of designs are available for running shoes which are intended to provide stability, but which lead to a constraint in the natural efficient motion of the foot and ankle. However, such designs which can accommodate free, flexible motion in contrast create a lack of control or stability. A popular existing shoe design incorporates an inverted, outwardly-flared shoe sole wherein the ground engaging surface is wider than the heel engaging portion. However, such shoes are unstable in extreme situations because the shoe sole, when inverted or on edge, immediately becomes supported only by the sharp bottom sole edge where the entire weight of the body, multiplied by a factor of approximately three at running peak, is concentrated. Since an unnatural lever arm and force moment are created under such conditions, the foot and ankle are destabilized and, in the extreme, beyond a certain point of rotation about the pivot point of the shoe sole edge, forceably cause ankle strain. In contrast, the unshod foot is always in stable equilibrium without a comparable lever arm or force moment and, at its maximum range of inversion motion, about 200, the base of support on the barefoot heel actually broadens substantially as the calcaneal tuberosity contacts the ground. This is in contrast to the conventionally available shoe sole bottom which maintains a sharp, unstable edge. 
     It is thus an overall objective of this invention to provide a novel shoe design which approximates the barefoot. It has been discovered, by investigating the most extreme range of ankle motion to near the point of ankle sprain, that the abnormal motion of an inversion ankle sprain, which is a tilting to the outside or an outward rotation of the foot, is accurately simulated while stationary. With this observation, it can be seen that the extreme range stability of the conventionally shod foot is distinctly inferior to the barefoot and that the shoe itself creates a gross instability which would otherwise not exist. 
     Even more important, a normal barefoot running motion, which approximately includes a 7° inversion and a 7° eversion motion, does not occur with shod feet, where a 30° inversion and eversion is common. Such a normal barefoot motion is geometrically unattainable because the average running shoe heel is approximately 60% larger than the width of the human heel. As a result, the shoe heel and the human heel cannot pivot together in a natural manner; rather, the human heel has to pivot within the shoe but is resisted from doing so by the shoe heel counter, motion control devices, and the lacing and binding of the shoe upper, as well as various types of anatomical supports interior to the shoe. 
     Thus, it is an overall objective to provide an improved shoe design which is not based on the inherent contradiction present in current shoe designs which make the goals of stability and efficient natural motion incompatible and even mutually exclusive. It is another overall object of the invention to provide a new contour design which simulates the natural barefoot motion in running and thus avoids the inherent contradictions in current designs. 
     It is another objective of this invention to provide a running shoe which overcomes the problem of the prior art. 
     It is another objective of this invention to provide a shoe wherein the outer extent of the flat portion of the sole of the shoe includes all of the support structures of the foot but which extends no further than the outer edge of the flat portion of the shoe sole so that the transverse or horizontal plane outline of the top of the flat portion of the shoe sole coincides as nearly as possible with the loadbearing portion of the foot sole. 
     It is another objective of the invention to provide a shoe having a sole which includes a side contoured like the natural form of the side or edge of the human foot and conforming to it. 
     It is another objective of this invention to provide a novel shoe structure in which the contoured sole includes a shoe sole thickness that is precisely constant in frontal plane cross sections, and therefore biomechanically neutral, even if the shoe sole is tilted to either side, or forward or backward. 
     It is another objective of this invention to provide a shoe having a sole fully contoured like and conforming to the natural form of the non-load-bearing human foot and deforming under load by flattening just as the foot does. 
     It is still another objective of this invention to provide a new stable shoe design wherein the heel lift or wedge increases in the sagittal plane the thickness of the shoe sole or toe taper decrease therewith so that the sides of the shoe sole which naturally conform to the sides of the foot also increase or decrease by exactly the same amount, so that the thickness of the shoe sole in a frontal planar cross section is always constant. 
     These and other objectives of the invention will become apparent from a detailed description of the invention which follows taken in conjunction with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the drawings: 
     FIG. 1 is a perspective view of a typical running shoe known to the prior art to which the invention is applicable; 
     FIG. 2 shows, in FIGS. 2A and 2B, the obstructed natural motion of the shoe heel in frontal planar cross section rotating inwardly or outwardly with the shoe sole having a flared bottom in a conventional prior art design such as in FIG. 1; and—in FIGS. 2C and 2D, the efficient motion of a narrow rectangular shoe sole design; 
     FIG. 3 is a frontal plane cross section showing a shoe sole of uniform thickness that conforms to the natural shape of the human foot, the novel shoe design according to the invention; 
     FIG. 4 shows, in FIGS. 4A-4D, a load-bearing flat component of a shoe sole and naturally contoured stability side component, as well as a preferred horizontal periphery of the flat load-bearing portion of the shoe sole when using the sole of the invention; 
     FIG. 5 is diagrammatic sketch in FIGS. 5A and 5B, showing the novel contoured side sole design according to the invention with variable heel lift; 
     FIG. 6 is a side view of the novel stable contoured shoe according to the invention showing the contoured side design; 
     FIG. 7 shows, in FIGS. 7A-7D, a top view of the shoe sole shown in FIG. 6, wherein FIG. 7A is a cross-sectional view of the forefoot portion taken along lines  7 A of FIG. 6 or  7 ; FIG. 7B is a view taken along lines  7 B of FIGS. 6 and 7; and FIG. 7C is a cross-sectional view taken along the heel along lines  7 C in FIGS. 6 and 7; 
     FIG. 8 is a drawn comparison between a conventional flared sole shoe of the prior art and the contoured shoe design according to the invention; 
     FIG. 9 shows, in FIGS. 9A-9C, the extremely stable conditions for the novel shoe sole according to the invention in its neutral and extreme situations; 
     FIG. 10 shows, in FIGS. 10A and 10B, a side cross-sectional view of the naturally contoured sole side showing how the sole maintains a constant distance from the ground during rotation of the shoe edge; 
     FIG. 11 shows, in FIGS. 11A-11E, a plurality of side sagittal plane cross-sectional views showing examples of conventional sole thickness variations to which the invention can be applied; 
     FIG. 12 shows, in FIGS. 12A-12D, frontal plane cross-sectional views of the shoe sole according to the invention showing a theoretically ideal stability plane and truncations of the sole side contour to reduce shoe bulk; 
     FIG. 13 shows, in FIGS. 13A-13C, the contoured sole design according to the invention when applied to various tread and cleat patterns; 
     FIG. 14 illustrates, in a rear view, an application of the sole according to the invention to a shoe to provide an aesthetically pleasing and functionally effective design; 
     FIG. 15 shows a fully contoured shoe sole design that follows the natural contour of the bottom of the foot as well as the sides; 
     FIG. 16 is a diagrammatic side cross-sectional view of static forces acting on the ankle joint and its position relative to the shoe sole according to the invention during normal and extreme inversion and eversion motion; 
     FIG. 17 is a diagrammatic view of a plurality of moment curves of the center of gravity for various degrees of inversion for the shoe sole according to the invention, and contrasted to the motions shown in FIG. 2; 
     FIG. 18 shows, in FIGS. 18A and 18B, a rear diagrammatic view of a human heel, as relating to a conventional shoe sole (FIG. 18A) and to the sole of the invention (FIG.  18 B); 
     FIG. 19 shows, in FIGS. 19A-19F, the naturally contoured sides design extended to the other natural contours underneath the loadbearing foot such as the main longitudinal arch; 
     FIG. 20 illustrates, in FIGS. 20A-20E the fully contoured shoe sole design extended to the bottom of the entire non-load-bearing foot; 
     FIG. 21 shows the fully contoured shoe sole design abbreviated along the sides to only essential structural support and propulsion elements; 
     FIG. 22 illustrates, in FIGS. 22A and 22B, the application of the invention to provide a street shoe with a correctly contoured sole according to the invention and side edges perpendicular to the ground, as is typical of a street shoe; 
     FIG. 23 shows a method of establishing the theoretically ideal stability plane using a perpendicular to a tangent method; 
     FIG. 24 shows a circle radius method of establishing the theoretically ideal stability plane. 
     FIG. 25 illustrates, in FIGS. 25A and 25B, an alternate embodiment of the invention wherein the sole structure deforms in use to follow a theoretically ideal stability plane according to the invention during deformation; 
     FIG. 26 shows an embodiment wherein the contour of the sole according to the invention is approximated by a plurality of line segments; 
     FIG. 27 illustrates an embodiment wherein the stability sides are determined geometrically as a section of a ring; 
     FIG. 28 shows, in FIGS. 28A-28C, a shoe sole design that allows for unobstructed natural eversion/inversion motion by providing torsional flexibility in the instep area of the shoe sole; and 
     FIG. 29 illustrates a process for measuring the contoured shoe sole sides of the applicant&#39;s invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     A perspective view of an athletic shoe, such as a typical running shoe, according to the prior art, is shown in FIG. 1 wherein a running shoe  20  includes an upper portion  21  and a sole  22 . Typically, such a sole includes a truncated outwardly flared construction of the type best seen in FIG. 2 wherein the lower portion  22   a  of the sole heel is significantly wider than the upper portion  22   b  where the sole  22  joins the upper  21 . A number of alternative sole designs are known to the art, including the design shown in U.S. Pat. No. 4,449,306 to Cavanagh wherein an outer portion of the sole of the running shoe includes a rounded portion having a radius of curvature of about 20 mm. The rounded portion lies along approximately the rear-half of the length of the outer side of the mid-sole and heel edge areas wherein the remaining border area is provided with a conventional flaring with the exception of a transition zone. The Misevich, U.S. Pat. No. 4,557,059 also shows an athletic shoe having a contoured sole bottom in the region of the first foot strike, in a shoe which otherwise uses an inverted flared sole. 
     In such prior art designs, and especially in athletic and in running shoes, the typical design attempts to achieve stability by flaring the heel as shown in FIGS. 2A and 2B to a width of, for example, 3 to 3½ inches on the bottom outer sole  22   a  of the average male shoe size (10D). On the other hand, the width of the corresponding human heel foot print, housed in the upper  21 , is only about 2.25 in. for the average foot. Therefore, a mismatch occurs in that the heel is locked by the design into a firm shoe heel counter which supports the human heel by holding it tightly and which may also be re-enforced by motion control devices to stabilize the heel. Thus, for natural motion as is shown in FIGS. 2A and 2B, the human heel would normally move in a normal range of motion of approximately 15°, but as shown in FIGS. 2A and 2B the human heel cannot pivot except within the shoe and is resisted by the shoe. Thus, FIG. 2A illustrates the impossibility of pivoting about the center edge of the human heel as would be conventional for barefoot support about a point  23  defined by a line  23   a  perpendicular to the heel and intersecting the bottom edge of upper  21  at a point  24 . The lever arm force moment of the flared sole is at a maximum at 0° and only slightly less at a normal 7° inversion or eversion and thus strongly resists such a natural motion as is illustrated in FIGS. 2A and 2B. In FIG. 2A, the outer edge of the heel must compress to accommodate such motion. FIG. 2B illustrates that normal natural motion of the shoe is inefficient in that the center of gravity of the shoe, and the shod foot, is forced upperwardly, as discussed later in connection with FIG.  17 . 
     A narrow rectangular shoe sole design of heel width approximating human heel width is also known and is shown in FIGS. 2C and 2D. It appears to be more efficient than the conventional flared sole shown in FIGS. 2A and 2B. Since the shoe sole width is the same as human sole width, the shoe can pivot naturally with the normal 7° inversion/eversion motion of the running barefoot. In such a design, the lever arm length and the vertical motion of the center of gravity are approximately half that of the flared sole at a normal 7° inversion/eversion running motion. However, the narrow, human heel width rectangular shoe design is extremely unstable and therefore prone to ankle sprain, so that it has not been well received. Thus, neither of these wide or narrow designs is satisfactory. 
     FIG. 3 shows in a frontal plane cross section at the heel (center of ankle joint) the general concept of the applicant&#39;s design: a shoe sole  28  that conforms to the natural shape of the human foot  27  and that has a constant thickness (s) in frontal plane cross sections. The surface  29  of the bottom and sides of the foot  27  should correspond exactly to the upper surface  30  of the shoe sole  28 . The shoe sole thickness is defined as the shortest distance (s) between any point on the upper surface  30  of the shoe sole  28  and the lower surface  31  (FIGS. 23 and 24 will discuss measurement methods more fully). In effect, the applicant&#39;s general concept is a shoe sole  28  that wraps around and conforms to the natural contours of the foot  27  as if the shoe sole  28  were made of a theoretical single flat sheet of shoe sole material of uniform thickness, wrapped around the foot with no distortion or deformation of that sheet as it is bent to the foot&#39;s contours. To overcome real world deformation problems associated with such bending- or wrapping around contours, actual construction of the shoe sole contours of uniform thickness will preferably involve the use of multiple sheet lamination or injection molding techniques. 
     FIGS. 4A,  4 B, and  4 C illustrate in frontal plane cross section a significant element of the applicant&#39;s shoe design in its use of naturally contoured stabilizing sides  28   a  at the outer edge of a shoe sole  28   b  illustrated generally at the reference numeral  28 . It is thus a main feature of the applicant&#39;s invention to eliminate the unnatural sharp bottom edge, especially of flared shoes, in favor of a naturally contoured shoe sole outside  31  as shown in FIG.  3 . The side or inner edge  30   a  of the shoe sole stability side  28   a  is contoured like the natural form on the side or edge of the human foot, as is the outside or outer edge  31   a  of the shoe sole stability side  28   a  to follow a theoretically ideal stability plane. According to the invention, the thickness (s) of the shoe sole  28  is maintained exactly constant, even if the shoe sole is tilted to either side, or forward or backward. Thus, the naturally contoured stabilizing sides  28   a,  according to the applicant&#39;s invention, are defined as the same as the thickness  33  of the shoe sole  28  so that, in cross section, the shoe sole comprises a stable shoe sole  28  having at its outer edge naturally contoured stabilizing sides  28   a  with a surface  31   a  representing a portion of a theoretically ideal stability plane and described by naturally contoured sides equal to the thickness (s) of the sole  28 . The top of the shoe sole  30   b  coincides with the shoe wearer&#39;s load-bearing footprint, since in the case shown the shape of the foot is assumed to be load-bearing and therefore flat along the bottom. A top edge  32  of the naturally contoured stability side  28   a  can be located at any point along the contoured side of the foot  29 , while the inner edge  33  of the naturally contoured side  28   a  coincides with the perpendicular sides  34  of the load-bearing shoe sole  28   b.  In practice, the shoe sole  28  is preferably integrally formed from the portions  28   b  and  28   a.  Thus, the theoretically ideal stability plane includes the contours  31   a  merging into the lower surface  31   b  of the sole  28 . Preferably, the peripheral extent  36  of the load-bearing portion of the sole  28   b  of the shoe includes all of the support structures of the foot but extends no further than the outer edge of the foot sole  37  as defined by a loadbearing footprint, as shown in FIG. 4D, which is a top view of the upper shoe sole surface  30   b.  FIG. 4D thus illustrates a foot outline at numeral  37  and a recommended sole outline  36  relative thereto. Thus, a horizontal plane outline of the top of the load-bearing portion of the shoe sole, therefore exclusive of contoured stability sides, should, preferably, coincide as nearly as practicable with the load-bearing portion of the foot sole with which it comes into contact. Such a horizontal outline, as best seen in FIGS. 4D and 7D, should remain uniform throughout the entire thickness of the shoe sole eliminating negative or positive sole flare so that the sides are exactly perpendicular to the horizontal plane as shown in FIG.  4 B. Preferably, the density of the shoe sole material is uniform. 
     Another significant feature of the applicant&#39;s invention is illustrated diagrammatically in FIG.  5 . Preferably, as the heel lift or wedge  38  of thickness (s 1 ) increases the total thickness (s+s 1 ) of the combined midsole and outersole  39  of thickness (s) in an aft direction of the shoe, the naturally contoured sides  28   a  increase in thickness exactly the same amount according to the principles discussed in connection with FIG.  4 . Thus, according to the applicant&#39;s design, the thickness of the inner edge  33  of the naturally contoured side is always equal to the constant thickness (s) of the load-bearing shoe sole  28   b  in the frontal cross-sectional plane. 
     As shown in FIG. 5B, for a shoe that follows a more conventional horizontal plane outline, the sole can be improved significantly according to the applicant&#39;s invention by the addition of a naturally contoured side  28   a  which correspondingly varies with the thickness of the shoe sole and changes in the frontal plane according to the shoe heel lift. Thus, as illustrated in FIG. 5B, the thickness of the naturally contoured side  28   a  is equal to the thickness (s+s 1 ) of the shoe sole  28  which is thicker than the shoe sole (s) shown in FIG. 5A by an amount equivalent to the heel lift (s 1 ). In the generalized case, the thickness (s) of the contoured side is thus always equal to the thickness (s) of the shoe sole. 
     FIG. 6 illustrates a side cross-sectional view of a shoe to which the invention has been applied and is also shown in a top plane view in FIG.  7 . Thus, FIGS. 7A,  7 B and  7 C represent frontal plane cross-sections taken along the forefoot, at the base of the fifth metatarsal, and at the heel, thus illustrating that the shoe sole thickness is constant at each frontal plane cross-section, even though that thickness varies from front to back, due to the heel lift  38  as shown in FIG. 6, and that the thickness of the naturally contoured sides is equal to the shoe sole thickness in each FIGS. 7A-7C cross section. Moreover, in FIG. 7D, a horizontal plane overview of the left foot, it can be seen that the contour of the sole follows the preferred principle in matching, as nearly as practical, the load-bearing sole print shown in FIG.  4 D. 
     FIG. 8 thus contrasts in frontal plane cross section the conventional flared sole  22  shown in phantom outline and illustrated in FIG. 2 with the contoured shoe sole  28  according to the invention as shown in FIGS. 3-7. 
     FIG. 9 is suitable for analyzing the shoe sole design according to the applicant&#39;s invention by contrasting the neutral situation shown in FIG. 9A with the extreme situations shown in FIGS. 9B and 9C. Unlike the sharp sole edge of a conventional shoe as shown in FIG. 2, the effect of the applicants invention having a naturally contoured side  28   a  is totally neutral allowing the shod foot to react naturally with the ground  43 , in either an inversion or eversion mode. This occurs in part because of the unvarying thickness along the shoe sole edge which keeps the foot sole equidistant from the ground in a preferred case. Moreover, because the shape of the edge  31   a  of the shoe contoured side  28   a  is exactly like that of the edge of the foot, the shoe is enabled to react naturally with the ground in a manner as closely as possible simulating the foot. Thus, in the neutral position shown in FIG. 9, any point  40  on the surface of the shoe sole  30   b  closest to ground lies at a distance (s) from the ground surface  39 . That distance (s) remains constant even for extreme situations as seen in FIGS. 9B and 9C. 
     A main point of the applicant&#39;s invention, as is illustrated in FIGS. 9B and 9C, is that the design shown is stable in an in extremis situation. The ideal plane of stability where the stability plane is defined as sole thickness which is constant under all load-bearing points of the foot sole for any amount from 0° to 90° rotation of the sole to either side or front and back. In other words, as shown in FIG. 9, if the shoe is tilted from 0° to 90° to either side or from 0° to 90° forward or backward representing a 0° to 90° foot dorsiflexion or 0° to 90° plantarflexion, the foot will remain stable because the sole thickness (s) between the foot and the ground always remain constant because of the exactly contoured quadrant sides. By remaining a constant distance from the ground, the stable shoe allows the foot to react to the ground as if the foot were bare while allowing the foot to be protected and cushioned by the shoe. In its preferred embodiment, the new naturally contoured sides will effectively position and hold the foot onto the load-bearing foot print section of the shoe sole, reducing the need for heel counters and other motion control devices. 
     FIG. 10A illustrates how the inner edge  30   a  of the naturally contoured sole side  28   a  is maintained at a constant distance (s) from the ground through various degrees of rotation of the edge  31   a  of the shoe sole such as is shown in FIG.  9 . 
     FIG. 10B shows how a conventional shoe sole pivots around its lower edge  42 , which is its center of rotation, instead of around the upper edge  40 , which, as a result, is not maintained at constant distance (s) from the ground, as with the invention, but is lowered to 0.7(s) at 45° rotation and to zero at 90° rotation. 
     FIG. 11 shows typical conventional sagittal plane shoe sole thickness variations, such as heel lifts or wedges  38 , or toe taper  38   a,  or full sole taper  38   b,  in FIGS. 11A-11E and how the naturally contoured sides  28   a  equal and therefore vary with those varying thicknesses as discussed in connection with FIG.  5 . 
     FIG. 12 illustrates an embodiment of the invention which utilizes varying portions of the theoretically ideal stability plane  51  in the naturally contoured sides  28   a  in order to reduce the weight and bulk of the sole, while accepting a sacrifice in some stability of the shoe. Thus, FIG. 12A illustrates the preferred embodiment as described above in connection with FIG. 5 wherein the outer edge  31   a  of the naturally contoured sides  28   a  follows a theoretically ideal stability plane  51 . As in FIGS. 3 and 4, the contoured surfaces  31   a,  and the lower surface of the sole  31   b  lie along the theoretically ideal stability plane  51 . The theoretically ideal stability plane  51  is defined as the plane of the surface of the bottom of the shoe sole  31 , wherein the shoe sole conforms to the natural shape of the foot, particularly the sides, and has a constant thickness in frontal plane cross sections. As shown in FIG. 12B, an engineering trade off results in an abbreviation within the theoretically ideal stability plane  51  by forming a naturally contoured side surface  53   a  approximating the natural contour of the foot (or more geometrically regular, which is less preferred) at an angle relative to the upper plane of the shoe sole  28  so that only a smaller portion of the contoured side  28   a  defined by the constant thickness lying along the surface  31   a  is coplanar with the theoretically ideal stability plane  51 . FIGS.  12 C and  12 D show similar embodiments wherein each engineering trade-off shown results in progressively smaller portions of contoured side  28   a,  which lies along the theoretically ideal stability plane  51 . The portion of the surface  31   a  merges into the upper side surface  53   a  of the naturally contoured side. 
     The embodiment of FIG. 12 may be desirable for portions of the shoe sole which are less frequently used so that the additional part of the side is used less frequently. For example, a shoe may typically roll out laterally, in an inversion model to about 20° on the order of 100 times for each single time it rolls out to 40°. For a basketball shoe, shown in FIG. 12B, the extra stability is needed. Yet, the added shoe weight to cover that infrequently experienced range of motion is about equivalent to covering the frequently encountered range. Since, in a racing shoe this weight might not be desirable, an engineering trade-off of the type shown in FIG. 12D is possible. A typical running/jogging shoe is shown in FIG.  12 C. The range of possible variations is limitless. 
     FIG. 13 shows the theoretically ideal stability plane  51  in defining embodiments of the shoe sole having differing tread or cleat patterns. Thus, FIG. 13 illustrates that the invention is applicable to shoe soles having conventional bottom treads. Accordingly, FIG. 13A is similar to FIG. 12B further including a tread portion  60 , while FIG. 13B is also similar to FIG. 12B wherein the sole includes a cleated portion  61 . The surface  63  to which the cleat bases are affixed should preferably be on the same plane and parallel the theoretically ideal stability plane  51 , since in soft ground that surface rather than the cleats become loadbearing. The embodiment in FIG. 13C is similar to FIG. 12C showing still an alternative tread construction  62 . In each case, the load-bearing outer surface of the tread or cleat pattern  60 - 62  lies along the theoretically ideal stability plane  51 . 
     FIG. 14 shows, in a rear cross sectional view, the application of the invention to a shoe to produce an aesthetically pleasing and functionally effective design. Thus, a practical design of a shoe incorporating the invention is feasible, even when applied to shoes incorporating heel lifts  38  and a combined midsole and outersole  93 . Thus, use of a sole surface and sole outer contour which track the theoretically ideal stability plane does not detract from the commercial appeal of shoes incorporating the invention. 
     FIG. 15 shows a fully contoured shoe sole design that follows the natural contour of all of the foot, the bottom as well as the sides. The fully contoured shoe sole assumes that the resulting slightly rounded bottom when unloaded will deform under load and flatten just as the human foot bottom is slightly rounded unloaded but flattens under load; therefore, shoe sole material must be of such composition as to allow the natural deformation following that of the foot. The design applies particularly to the heel, but to the rest of the shoe sole as well. By providing the closest match to the natural shape of the foot, the fully contoured design allows the foot to function as naturally as possible. Under load, FIG. 15 would deform by flattening to look essentially like FIG.  14 . Seen in this light, the naturally contoured side design in FIG. 14 is a more conventional, conservative design that is a special case of the more general fully contoured design in FIG. 15, which is the closest to the natural form of the foot, but the least conventional. The amount of deformation flattening used in the FIG. 14 design, which obviously varies under different loads, is not an essential element of the applicant&#39;s invention. 
     FIGS. 14 and 15 both show in frontal plane cross section the essential concept underlying this invention, the theoretically ideal stability plane, which is also theoretically ideal for efficient natural motion of all kinds, including running, jogging or walking. FIG. 15 shows the most general case of the invention, the fully contoured design, which conforms to the natural shape of the unloaded foot. For any given individual, the theoretically ideal stability plane  31  is determined, first, by the desired shoe sole thickness (s) in a frontal plane cross section, and, second, by the natural shape of the individuals foot surface  29 . 
     For the special case shown in FIG. 14, the theoretically ideal stability plane for any particular individual (or size average of individuals) is determined, first, by the given frontal plane cross section shoe sole thickness (s); second, by the natural shape of the individual&#39;s foot; and, third, by the frontal plane cross section width of the individuals load-bearing footprint  30   b,  which is defined as the upper surface of the shoe sole that is in physical contact with and supports the human foot sole, as shown in FIG.  4 . 
     The theoretically ideal stability plane for the special case is composed conceptionally of two parts. Shown in FIGS. 14 and  4  the first part is a line segment  31   b  of equal length and parallel to  30   b  at a constant distance (s) equal to shoe sole thickness. This corresponds to a conventional shoe sole directly underneath the human foot, and also corresponds to the flattened portion of the bottom of the load-bearing foot sole  28   b.  The second part is the naturally contoured stability side outer edge  31   a  located at each side of the first part, line segment  31   b.  Each point on the contoured side outer edge  31   a  is located at a distance which is exactly shoe sole thickness (s) from the closest point on the contoured side inner edge  30   a.    
     In summary, the theoretically ideal stability plane is the essence of this invention because it is used to determine a geometrically precise bottom contour of the shoe sole based on a top contour that conforms to the contour of the foot. This invention specifically claims the exactly determined geometric relationship just described. It can be stated unequivocally that any shoe sole contour, even of similar contour, that exceeds the theoretically ideal stability plane will restrict natural foot motion, while any less than that plane will degrade natural stability, in direct proportion to the amount of the deviation. 
     FIG. 16 illustrates in a curve  70  the range of side to side inversion/eversion motion of the ankle center of gravity  71  from the shoe according to the invention shown in frontal plane cross section at the ankle. Thus, in a static case where the center of gravity  71  lies at approximately the mid-point of the sole, and assuming that the shoe inverts or everts from 0° to 20° to 40°, as shown in progressions  16   a,    16   b  and  16   c,  the locus of points of motion for the center of gravity thus defines the curve  70  wherein the center of gravity  71  maintains a steady level motion with no vertical component through 40° of inversion or eversion. For the embodiment shown, the shoe sole stability equilibrium point is at 28° (at point  74 ) and in no case is there a pivoting edge to define a rotation point as in the case of FIG.  2 . The inherently superior side to side stability of the design provides pronation control (or eversion), as well as lateral (or inversion) control. In marked contrast to conventional shoe sole designs, the applicant&#39;s shoe design creates virtually no abnormal torque to resist natural inversion/eversion motion or to destabilize the ankle joint. 
     FIG. 17 thus compares the range of motion of the center of gravity for invention, as shown in curve  75 , in comparison to curve  80  for the conventional wide heel flare and a curve  82  for a narrow rectangle the width of a human heel. Since the shoe stability limit is 28° in the inverted mode, the shoe sole is stable at the 20° approximate barefoot inversion limit. That factor, and the broad base of support rather than the sharp bottom edge of the prior art, make the contour design stable even in the most extreme case as shown in FIG.  16  and permit the inherent stability of the barefoot to dominate without interference, unlike existing designs, by providing constant, unvarying shoe sole thickness in frontal plane cross sections. The stability superiority of the contour side design is thus clear when observing how much flatter its center of gravity curve  75  is than in existing popular wide flare design  80 . The curve demonstrates that the contour side design has significantly more efficient natural 7° inversion/eversion motion than the narrow rectangle design the width of a human heel, and very much more efficient than the conventional wide flare design; at the same time, the contour side design is more stable in extremis than either conventional design because of the absence of destabilizing torque. 
     FIG. 18A illustrates, in a pictorial fashion, a comparison of a cross section at the ankle joint of a conventional shoe with a cross section of a shoe according to the invention when engaging a heel. As seen in FIG. 18A, when the heel of the foot  27  of the wearer engages an upper surface of the shoe sole  22 , the shape of the foot heel and the shoe sole is such that the shoe sole  22  conforms to the contour of the ground  43  and not to the contour of the sides of the foot  27 . As a result, the shoe sole  22  cannot follow the natural 7° inversion/eversion motion of the foot, and that normal motion is resisted by the shoe upper  21 , especially when strongly reinforced by firm heel counters and motion control devices. This interference with natural motion represents the fundamental misconception of the currently available designs. That misconception on which existing shoe designs are based is that, while shoe uppers are considered as a part of the foot and conform to the shape of the foot, the shoe sole is functionally conceived of as a part of the ground and is therefore shaped like the ground, rather than the foot. 
     In contrast, the new design, as illustrated in FIG. 18B, illustrates a correct conception of the shoe sole  28  as a part of the foot and an extension of the foot, with shoe sole sides contoured exactly like those of the foot, and with the frontal plane thickness of the shoe sole between the foot and the ground always the same and therefore completely neutral to the natural motion of the foot. With the correct basic conception, as described in connection with this invention, the shoe can move naturally with the foot, instead of restraining it, so both natural stability and natural efficient motion coexist in the same shoe, with no inherent contradiction in design goals. 
     Thus, the contoured shoe design of the invention brings together in one shoe design the cushioning and protection typical of modern shoes, with the freedom from injury and functional efficiency, meaning speed, and/or endurance, typical of barefoot stability and natural freedom of motion. Significant speed and endurance improvements are anticipated, based on both improved efficiency and on the ability of a user to train harder without injury. 
     These figures also illustrate that the shoe heel cannot pivot ±7 degrees with the prior art shoe of FIG.  18 A. In contrast the shoe heel in the embodiment of FIG. 18B pivots with the natural motion of the foot heel. 
     FIGS. 19A-D illustrate, in frontal plane cross sections, the naturally contoured sides design extended to the other natural contours underneath the load-bearing foot, such as the main longitudinal arch, the metatarsal (or forefoot) arch, and the ridge between the heads of the metatarsals (forefoot) and the heads of the distal phalanges (toes). As shown, the shoe sole thickness remains constant as the contour of the shoe sole follows that of the sides and bottom of the load-bearing foot. FIG. 19E shows a sagittal plane cross section of the shoe sole conforming to the contour of the bottom of the load-bearing foot, with thickness varying according to the heel lift  38 . FIG. 19F shows a horizontal plane top view of the left foot that shows the areas  85  of the shoe sole that corresponds to the flattened portions of the foot sole that are in contact with the ground when loadbearing. Contour lines  86  and  87  show approximately the relative height of the shoe sole contours above the flattened load-bearing areas  85  but within roughly the peripheral extent  36  of the load-bearing portion of sole  28   b  shown in FIG. 4. A horizontal plane bottom view (not shown) of FIG. 19F would be the exact reciprocal or converse of FIG. 19F (i.e., peaks and valleys contours would be exactly reversed). 
     FIGS. 20A-D show, in frontal plane cross sections, the fully contoured shoe sole design extended to the bottom of the entire non-load-bearing foot. FIG. 20E shows a sagittal plane cross section. The shoe sole contours underneath the foot are the same as FIGS. 19A-E except that there are no flattened areas corresponding to the flattened areas of the load-bearing foot. The exclusively rounded contours of the shoe sole follow those of the unloaded foot. A heel lift  38 , the same as that of FIG. 19, is incorporated in this embodiment, but is not shown in FIG.  20 . 
     FIG. 21 shows the horizontal plane top view of the left foot corresponding to the fully contoured design described in FIGS. 20A-E, but abbreviated along the sides to only essential structural support and propulsion elements. Shoe sole material density can be increased in the unabbreviated essential elements to compensate for increased pressure loading there. The essential structural support elements are the base and lateral tuberosity of the calcaneus  95 , the heads of the metatarsals  96 , and the base of the fifth metatarsal  97 . They must be supported both underneath and to the outside for stability. The essential propulsion element is the head of first distal phalange  98 . The medial (inside) and lateral (outside) sides supporting the base of the calcaneus are shown in FIG. 21 oriented roughly along either side of the horizontal plane subtalar ankle joint axis, but can be located also more conventionally along the longitudinal axis of the shoe sole. FIG. 21 shows that the naturally contoured stability sides need not be used except in the identified essential areas. Weight savings and flexibility improvements can be made by omitting the non-essential stability sides. Contour lines  85  through  89  show approximately the relative height of the shoe sole contours within roughly the peripheral extent  36  of the undeformed load-bearing portion of shoe sole  28   b  shown in FIG. 4. A horizontal plane bottom view (not shown) of FIG. 21 would be the exact reciprocal or converse of FIG. 21 (i.e., peaks and valleys contours would be exactly reversed). 
     FIG. 22A shows a development of street shoes with naturally contoured sole sides incorporating the features of the invention. FIG. 22A develops a theoretically ideal stability plane  51 , as described above, for such a street shoe, wherein the thickness of the naturally contoured sides equal the shoe sole thickness. The resulting street shoe with a correctly contoured sole is thus shown in frontal plane heel cross section in FIG. 22A, with side edges perpendicular to the ground, as is typical. FIG. 22B shows a similar street shoe with a fully contoured design, including the bottom of the sole. Accordingly, the invention can be applied to an unconventional heel lift shoe, like a simple wedge, or to the most conventional design of a typical walking shoe with its heel separated from the forefoot by a hollow under the instep. The invention can be applied just at the shoe heel or to the entire shoe sole. With the invention, as so applied, the stability and natural motion of any existing shoe design, except high heels or spike heels, can be significantly improved by the naturally contoured shoe sole design. 
     FIG. 23 illustrates a method of measuring shoe sole thickness in accordance with the present invention. The thickness (s) of the sole at a particular location is measured between the inner surface  30  and the outer surface  31  by the length of a line extending perpendicular to a line tangent to the sole inner surface at the measured location, all as viewed in a frontal plane cross section of the sole. This thickness (s) may also be referred to as a “radial thickness” of the shoe sole. 
     FIG. 24 illustrates another approach to constructing the theoretically ideal stability plane, and one that is easier to use, the circle radius method. By that method, the pivot point (circle center) of a compass is placed at the beginning of the foot sole&#39;s natural side contour (frontal plane cross section) and roughly a 90° arc (or much less, if estimated accurately) of a circle of radius equal to (s) or shoe sole thickness is drawn describing the area farthest away from the foot sole contour. That process is repeated all along the foot sole&#39;s natural side contour at very small intervals (the smaller, the more accurate). When all the circle sections are drawn, the outer edge farthest from the foot sole contour (again, frontal plane cross section) is established at a distance of “s” and that outer edge coincides with the theoretically ideal stability plant. Both this method and that described in FIG. 23 would be used for both manual and CADCAM design applications. 
     The shoe sole according to the invention can be made by approximating the contours, as indicated in FIGS. 25A,  25 B, and  26 . FIG. 25A shows a frontal plane cross section of a design wherein the sole material in areas  107  is so relatively soft that it deforms easily to the contour of shoe sole  28  of the proposed invention. In the proposed approximation as seen in FIG. 25B, the heel cross section includes a sole upper surface  101  and a bottom sole edge surface  102  following when deformed an inset theoretically ideal stability plane  51 . The sole edge surface  102  terminates in a laterally extending portion  103  joined to the heel of the sole  28 . The laterally-extending portion  103  is made from a flexible material and structured to cause its lower surface  102  to terminate during deformation to parallel the inset theoretically ideal stability plane  51 . Sole material in specific areas  107  is extremely soft to allow sufficient deformation. Thus, in a dynamic case, the outer edge contour assumes approximately the theoretically ideal stability shape described above as a result of the deformation of the portion  103 . The top surface  101  similarly deforms to approximately parallel the natural contour of the foot as described by lines  30   a  and  30   b  shown in FIG.  4 . 
     It is presently contemplated that the controlled or programmed deformation can be provided by either of two techniques. In one, the shoe sole sides, at especially the midsole, can be cut in a tapered fashion or grooved so that the bottom sole bends inwardly under pressure to the correct contour. The second uses an easily deformable material  107  in a tapered manner on the sides to deform under pressure to the correct contour. While such techniques produce stability and natural motion results which are a significant improvement over conventional designs, they are inherently inferior to contours produced by simple geometric shaping. First, the actual deformation must be produced by pressure which is unnatural and does not occur with a bare foot and second, only approximations are possible by deformation, even with sophisticated design and manufacturing techniques, given an individuals particular running gait or body weight. Thus, the deformation process is limited to a minor effort to correct the contours from surfaces approximating the ideal curve in the first instance. 
     The theoretically ideal stability can also be approximated by a plurality of line segments  110 , such as tangents, chords, or other lines. as shown in FIG.  26 . Both the upper surface of the shoe sole  28 , which coincides with the side of the foot  30   a,  and the bottom surface  31   a  of the naturally contoured side can be approximated. While a single flat plane  110  approximation may correct many of the biomechanical problems occurring with existing designs, because it can provide a gross approximation of the both natural contour of the foot and the theoretically ideal stability plane  51 , the single plane approximation is presently not preferred, since it is the least optimal. By increasing the number of flat planar surfaces formed, the curve more closely approximates the ideal exact design contours, as previously described. Single and double plane approximations are shown as line segments in the cross section illustrated in FIG.  26 . 
     FIG. 27 shows a frontal plane cross section of an alternate embodiment for the invention showing stability sides component  28   a  that are determined in a mathematically precise manner to conform approximately to the sides of the foot. (The center or load-bearing shoe sole component  28   b  would be as described in FIG.  4 ). The component sides  28   a  would be a quadrant of a circle of radius (r+r 1 ), where distance (r) must equal sole thickness (s); consequently the sub-quadrant of radius (r 1 ) is removed from quadrant (r+r 1 ). In geometric terms, the component side  28   a  is thus a quarter or other section of a ring. The center of rotation  115  of the quadrants is selected to achieve a sole upper side surface  30   a  that closely approximates the natural contour of the side of the human foot. 
     FIG. 27 provides a direct bridge to another invention by the applicant, a shoe sole design with quadrant stability sides. 
     FIG. 28 shows a shoe sole design that allows for unobstructed natural inversion/eversion motion of the calcaneus by providing maximum shoe sole flexibility particularly between the base of the calcaneus  125  (heel) and the metatarsal heads  126  (forefoot) along an axis  120 . An unnatural torsion occurs about that axis if flexibility is insufficient so that a conventional shoe sole interferes with the inversion/eversion motion by restraining it. The object of the design is to allow the relatively more mobile (in eversion and inversion) calcaneus to articulate freely and independently from the relatively more fixed forefoot, instead of the fixed or fused structure or lack of stable structure between the two in conventional designs. In a sense, freely articulating joints are created in the shoe sole that parallel those of the foot. The design is to remove nearly all of the shoe sole material between the heel and the forefoot, except under one of the previously described essential structural support elements, the base of the fifth metatarsal  97 . An optional support for the main longitudinal arch  121  may also be retained for runners with substantial foot pronation, although would not be necessary for many runners. The forefoot can be subdivided (not shown) into its component essential structural support and propulsion elements, the individual heads of the metatarsal and the heads of the distal phalanges, so that each major articulating joint set of the foot is paralleled by a freely articulating shoe sole support propulsion element, an anthropomorphic design; various aggregations of the subdivisions are also possible. An added benefit of the design is to provide better flexibility along axis  122  for the forefoot during the toe-off propulsive phase of the running stride, even in the absence of any other embodiments of the applicant&#39;s invention; that is, the benefit exists for existing conventional shoe sole designs. 
     FIG. 28A shows in sagittal plane cross section a specific design maximizing flexibility, with large nonessential sections removed for flexibility and connected by only a top layer (horizontal plane) of non-stretching fabric  123  like Dacron polyester or Kevlar. FIG. 28B shows another specific design with a thin top sole layer  124  instead of fabric and a different structure for the flexibility sections: a design variation that provides greater structural support, but less flexibility though still much more than conventional designs. Not shown is a simple, minimalist approach, which is comprised of single frontal plane slits in the shoe sole material (all layers or part): the first midway between the base of the calcaneus and the base of the fifth metatarsal, and the second midway between that base and the metatarsal heads. FIG. 28C shows a bottom view (horizontal plane) of the inversion/eversion flexibility design. 
     FIG. 29 is new in this continuation-in-part application and provides a means to measure the contoured shoe sole sides incorporated in the applicant&#39;s inventions described above. FIG. 29 is FIG. 27 modified to correlate the height or extent of the contoured side portions of the shoe sole with a precise angular measurement from zero to 180 degrees. That angular measurement corresponds roughly with the support for sideways tilting provided by the contoured shoe sole sides of any angular amount from zero degrees to 180 degrees, at least for such contoured sides proximate to any one or more or all of the essential stability or propulsion structures of the foot, as defined above in FIG.  21 . The contoured shoe sole sides as described in this application can have any angular measurement from zero degrees to 180 degrees. 
     Thus, it will clearly be understood by those skilled in the art that the foregoing description has been made in terms of the preferred embodiment and various changes and modifications may be made without departing from the scope of the present invention which is to be defined by the appended claims.