Shoe midsole with delayed energy return and lateral shear stability

Abstract

An energy return device for a midsole of a shoe comprises a resilient foam or matrix structure, such as a domed disk, around a cavity. The resilient structure is arranged to collapse into the cavity under foot strike pressure. The structure may initially resist the pressure primarily by compression forces directed around the cavity. As the cavity collapses these forces may provide decreasing vertical spring rate as the structure bends or as the forces become less vertical, causing the structure to stay more compressed through the midstride and energy return to be delayed until the user has moved further forward in their stance. At full collapse the material of the structure may resist further downward force of the user by direct compression. A lateral expansion limiter may resist lateral expansion to increase vertical force supplied by the compression forces around the cavity and reduce interference with other components.

Description

SHOE MIDSOLE WITH DELAYED ENERGY RETURN AND LATERAL SHEAR STABILITYTECHNICAL FIELD

[0001] Shoes with high travel, energy return and lateral shear stability.BACKGROUND

[0002] The inventors have previously disclosed footwear energy return devices, for example using a conical disk with a ring spring.

[0003] It is desirable for a shoe midsole to provide a wide and diverse range of performance benefits. This is very challenging with conventional solid foam midsole construction.

[0004] To achieve some desired characteristics there may be compromises that must be made to achieve them. High compression travel for a given stack height is desirable for the benefit of providing greater impact reduction by reducing the deceleration rate. However, higher travel will typically, with a solid foam midsole, have the compromise of reduced lateral shear stability because solid foams (or other geometries such as a foam cylinder) show reduced lateral shear stability if they are taller for a given diameter. A solid foam midsole will also demonstrate lower lateral shear stability the more it is compressed. This is undesirable for a shoe because lateral shear stability is typically more desirable when the midsole is compressed.

[0005] Lower durometer foam is desirable for the benefit of providing greater impact reduction by reducing the vertical deceleration rate during foot strike (partially as a result of providing greater travel) but it has the compromise of greater reduction in lateral shear stability because solid foams (or other geometries such as a foam cylinder) show reduced lateral shear stability if they are lower durometer.

[0006] In other words, it is expected, when designing a solid foam midsole, that increasing the travel, through the use of lower durometer foam and / or greater at-rest thickness, will decrease lateral shear stability of the midsole. This can lead to instability, poor ground feel and the risk of ankle roll. Shoe designers have been reticent to create midsoles with higher compression travel, by use of lower durometer foam, because it would lead to low lateral shear stability.

[0007] Additionally, common foam midsoles return a high percentage of foot-strike energy undesirably early in the stance phase of the gait cycle, before the user’s center of gravity (CG) is forward of their heel. This can be undesirable because energy returned before this point does not contribute as effectively to forward motion of the person. This problem can be partially addressed by using a thicker and / or softer foam. The thicker and / or softer foam reduces the bounce frequency so more of the energy can be released later in the stride than with a higher bounce frequency of a thinner conventional foam midsole. However, the thicker and / or softer foam may feel unstable, reduce ground feel, and increase the risk of an ankle roll-over due to the high lateral shearing propensity of the midsole.SUMMARY

[0008] A foam sole or midsole component within a range of geometries, provides for greater compression of the midsole for a given at-rest stack height as compared to a conventional solid foam midsole. Embodiments of the device also provide increased lateral shear stability (rather than decreased lateral shear stability) as they approach and reach full compression. This allows for the use of higher compression travel for a given starting thickness or stack height, without compromising lateral shear stability. Embodiments of the present device allow high midsole compression travel without sacrificing lateral shear stability.

[0009] In addition to improved impact reduction as a result of higher travel for a given at-rest thickness or stack height, embodiments of the device achieve a high level of propulsion by combining high travel with a spring rate that reduces through the mid-range of the compression, much more than with a conventional solid foam midsole. This allows the midsole to remain more compressed than a typical midsole, through the midstride, so there is more expansion travel available to return more energy to the user as they unweight the heel section and other parts of the midsole.

[0010] In an embodiment, a highly resilient material may include resilient foam, such as, but not limited to Pebax®, is configured as a conical disk shape, where the average OD of a section of the diagonal sidewall of a dome or linear or curved section of the device on a horizontal plane at 75% of the stack height (this OD is referred to as the functional upper OD or FUOD) has the following relationship to the ID of a section of the diagonal sidewall of a dome or linear or curved section of the device on a horizontal plane at 25% of the stack height (this ID is referred to as the functional lower ID or FLID): in cases where the FUOD is greater than the FLID, the FUOD can be <150%, <149%, <148%, <147%, <146%, <145%,<144%, <143%, <142%, <141%, <140% of the FLID and in cases where the FUOD is smaller than the FLID, the FUOD can be >70%, >71%, >72%, >73%, >74%, >75%, >76%, >77%, >78%, >79%, >80% of the FLID. The stack height is measured vertically from the bottom of the outsole to the top of the upper and does not include any removable insoles. In embodiments where the device is comprised of linear sections having the same cross-section as a conical disk, the FLID will correspond to the distance between the inner walls at 25% of the stack height, and the FUOD will correspond to the distance between the outer walls at 75% of the stack height.

[0011] In some embodiments, a conical disk may be used on its own with a portion of the benefit of the device. In some embodiments, a circumferentially (or horizontally) expandable conical disk or web member (or linear or curved diagonal web member) is secured to the inside surface, outside surface or is embedded inside of the foam conical disk. This circumferentially expandable conical disk may be of a solid material such as, but not limited to Delrin® (polyoxymethylene) or Pebax®, or polypropylene. It may also be constructed from a higher density foam than the conical foam disk with some of the same benefits. The circumferentially expandable conical disk increases the strain on the conical foam disk during compression in such a way as to further increase the effect of reducing the spring force and / or spring rate through the midrange of the travel. The circumferentially expandable conical disk will also further increase the lateral shear stability of the midsole.

[0012] In some embodiments, a linear or curved diagonal foam structure may be used on its own with a portion of the benefit of the device. In some embodiments, a horizontally expandable linear or curved diagonal web member is secured by one or more of being attached to the inside surface, being attached to the outside surface, or being embedded inside of the foam structure. This horizontally expandable web member may be of a solid material such as, but not limited to Delrin® (polyoxymethylene) or Pebax®, or polypropylene. It may also be constructed from a higher density foam than the linear or curved diagonal foam structure with some of the same benefits. The horizontally expandable linear or curved diagonal web member increases the strain on the linear or curved diagonal foam structure during compression in such a way as to further increase the effect of reducing the spring force and / or spring rate through the midrange of the travel and / or increase the lateral shear stability of the midsole.

[0013] Some embodiments of the present device provide higher than usual compression travel for a given stack height, as compared to a conventional foam midsole. This can provide improved impact reduction during ground strike. Some embodimentsdisclosed here provide a reduced spring rate partway through the travel, which results in a delayed energy return to increase propulsion. Some embodiments of the device disclosed here also provide increased lateral shear stability as they are compressed, as a result of the unique geometry, in comparison to a conventional foam midsole.

[0014] In various embodiments there is provided an energy return device for a midsole of a shoe for absorbing and returning energy from compression of the device under a downward force applied from a typical wearer to an upper of the shoe over a range of travel extending in a height direction from the upper of the shoe in an uncompressed state towards an outsole of the shoe, the energy return device comprising a resilient structure of compressible foam or matrix material supporting the upper in relation to the outsole, the resilient structure defining a cavity, the resilient structure defining an opening for air to enter the cavity or being permeable to air; the resilient structure being arranged to collapse, under the compression by the downward force applied to the upper by the typical user, into the cavity so that during a first part of the range of travel of the compression the structure deforms by bending of the resilient structure, the resilient structure collapsing into lateral bounds defined by the resilient structure at a height corresponding to a maximum lateral extent of the cavity, and during a second part of the range of travel of the compression at a further degree of compression than the first part the resilient structure deforms by direct compression of the material of the resilient structure between the insole and the outsole. The compression of the material of the resilient structure between the insole and the outsole may include the vertical compression of the now-horizontal sidewall (a lateral wall of the resilient structure) such that there remains no cavity or air gap between the now-horizontal sidewall and a base of the midsole device or the outsole of the shoe.

[0015] In various embodiments an energy return device there may be one or more of the features of: the energy return device comprises a lateral expansion limiter arranged to resist lateral expansion of the resilient structure; the resilient structure comprises a domed disk when not compressed under the downward force; the domed disk comprises a conical disk; the conical disk is a hollow frustum; the lateral expansion limiting structure comprises a ring about a base of the domed disk; the ring is a ring spring; the energy return device comprises a support structure extending along walls of the domed disk and having greater stiffness than the domed disk for shaping the collapse of the dome under the compression by the downward force; the support structure comprises a conical disk; the support structure comprises a web; the web comprises radially extending fingers; a first finger is circumferentially connected to a second finger with a bridge member at a first radial position and said second finger and a third finger are connected together at a second radial position and the second finger and the third finger are not connected together at the first radial position; the bridge member is thinner than the first finger member where it is attached to the first finger member and thinner than the second finger member where it is attached to thesecond finger member; successive circumferentially adjacent fingers of the radially extending fingers are not all circumferentially connected at an upper end of the web; the successive circumferentially adjacent radially extending fingers are not all circumferentially connected at a lower end of the web; under the compression of the structure under the downward force from the user the support structure compresses from conical to flat; under the compression of the structure under the downward force from the user the support structure compresses from conical to inverted conical; the support structure is attached to an inside surface of the domed disk; the support structure is attached to an outside surface of the domed disk; the support structure is embedded within the domed disk; the support structure has pockets or through holes that are radially aligned so as to make the insert conical disc insert more extensible or compressible in the circumstantial direction relative to the radial direction, such that under the compression by the downward force, the support structure flares out at a bottom end of the support structure increasing a strain deformation of and around a bottom of the domed disk; the domed disk when not compressed by the downward force has an upper average outer diameter at a plane perpendicular to the height direction at 75% of the stack height that is <150%, <149%, <148%, <147%, <146%, <145%, <144%, <143%, <142%, <141%, or <140% and >70%, >71%, >72%, >73%, >74%, >75%, >76%, >77%, >78%, >79%, or >80% of a lower average inner diameter at a plane perpendicular to the height direction at 25% of the stack height; the energy return device comprises an opening in the outsole, and the opening for air to enter the cavity is present and aligned with the opening in the outsole or the structure is permeable to air; the outsole has a tread design which allows air to flow in and out of the conical disk assembly and to the edges of the outsole when it is in contact with the ground; the opening for air to enter the cavity is present and aligned with the opening in the outsole and a ceiling of the cavity comprises a surface adapted to contact ground under the shoe in use; the lateral expansion limiter comprises the upper or the outsole; the energy return device comprises a compression biased damper made of a compressible material and adapted to begin compressing part way through the range of travel; the compression biased damper is located within the cavity; the energy return device has greater than 40%, or greater than 50% of a total energy return within a portion of the range of travel corresponding to the downward force being less than 50% of the downward force applied from the typical wearer; a portion of the resilient structure including at least parts of 80% or more, 70% or more, 60% or more, 50% or more, 40% or more, 30% or more, 20% or more, 10% or more of a height of the resilient structure, when not compressed under the downward force, vertically overlaps the cavity; when the resilient structure is compressed in the height direction, there is a degree of compression less than or equal to the compression of the device under the downward force applied from the typical wearer at which a set of points of the resilient structure forming, when the structure is not compressed under the downward force, a straight line in a vertical cross section of the resilient structure having an angle in relation to the height direction representing an outer wall angle of the resilient structure, are shifted under the degree ofcompression to form a curve that crosses a plane perpendicular to the height direction 3 times or more; a plane through which the S-curve passes 3 times or more is tilted by 1 to 2 deg, 2 to 3 deg, 3 to 4 deg, 4 to 5 deg, 5 to 6 deg, 6 to 7 deg, 7 to 8 deg, 8 to 9 deg, or 9 to 10 deg, 10 to 11 deg, 11 to 12 deg, 12 to 13 deg, 13 to 14 deg, 14 to 15 deg, 15 to 16 deg, 16 to 17 deg, 17 to 18 deg, 18 to 19 deg, 19 to 20 deg from being perpendicular to the height direction; an outer angle of the resilient structure, or the outer wall angle when dependent on a claim 31 or claim 32, measured from vertical is >15deg, >16deg, >17deg, >18deg, >19deg, >20deg, >21deg, >22deg, >23deg, >24deg, >25deg, >26deg, >27deg, >28deg, >29deg, >30deg, >31deg, >32deg, >33deg, >34deg, >35deg, >36deg, >37deg, >38deg, >39deg, >40deg, >41deg, >42deg, >43deg, >44deg, >45deg, >46deg, >47deg,>48deg, >49deg, >50deg, >51 deg, >52deg, >53deg, >54deg, >55deg measured over 40% or more, 50% or more, 60% or more, 70% or more of a height distance from the outsole to the upper; the opening for air to enter the cavity and in which the opening has a check valve biased to resist air flow out of the cavity; the resilient structure further defines a second opening to the cavity, the second opening having a restricted orifice; having the opening for air to enter the cavity in which the opening has an orifice restricted in size to cause greater resistance to compression, as compared to energy return in expansion from the energy return device; having the opening for air to enter the cavity and in which the opening is adapted to be restricted by the downward force applied from the typical wearer; the opening is located at a heel ward end of the resilient structure and adapted to be restricted by the downward force applied by a heel strike and become less restricted as the user moves forward in a stride; the opening is adapted to be less restricted by a foot strike that is not a heel strike than by a heel strike; the energy return device is shaped to conform to a tapering of the height between the upper and the outsole towards a front end of the midsole; the resilient structure is formed as one piece with the outsole; the resilient structure is formed of closed cell foam; where the compression of the material of the resilient structure between the insole and the outsole includes the vertical compression of the now-horizontal sidewall.

[0016] In some embodiments there is provided a shoe having a midsole comprising one or more energy return devices having one or more of the preceding features. In various further embodiments, the shoe may have any one or more of the following features: a single energy return device of the one or more energy return devices is used under a heel of the shoe in the midsole; the one or more energy return devices are multiple energy return devices; the shoe comprises at least an energy return device of the multiple energy return devices under the heel of the shoe and plural energy return device of the multiple energy return devices under the forefoot of smaller diameter and height than the at least an energy return device under the heel; the multiple energy return devices include two energy return devices in the forefoot and are collectively wider than the upper by 10% or more, 20%, or more, 30% or more, of a largest diameter of the two energy return devices; the shoe comprises a wedge of compressible foam or deformable material ahead of the forwardmost energy return deviceconnecting a botom surface of the upper with a top surface of the outsole, that shears as the stance progresses toward toe-off, and the resistance to shearing of this member un-shears the structure during toe-off; the multiple energy return devices are arranged from the heel to the forefoot so that a second energy return device of the multiple energy return devices begins to compress from foot strike pressure before a previous disk is fully compressed; one or more of the one or more energy return devices protrude into or through the outsole; the one or more of the one or more energy return devices contact the ground.

[0017] In various embodiments there is provided an energy return device for a midsole of a shoe for absorbing and returning energy from compression of the device under a downward force applied from a typical wearer to an upper of the shoe over a range of travel extending in a height direction from the upper of the shoe in an uncompressed state towards an outsole of the shoe, the energy return device comprising a resilient structure of compressible foam or matrix material supporting the upper in relation to the outsole, the resilient structure defining a cavity, the resilient structure defining an opening for air to enter the cavity or being permeable to air; the resilient structure being arranged to collapse, under the compression by the downward force applied to the upper by the typical user, into the cavity so that during a first part of the range of travel of the compression the structure deforms by bending of the resilient structure, the resilient structure collapsing by bucking into lateral bounds defined by the resilient structure at a height corresponding to a maximum lateral extent of the cavity, and during a second part of the range of travel of the compression at a further degree of compression than the first part the resilient structure deforms by direct compression of the material of at least a buckled portion of the resilient structure between the upper and the outsole and / or by direct compression of the material of the at least a buckled portion of the resilient structure between the upper and the ground. The compression of the material of the resilient structure between the upper and the outsole may include the vertical compression of the now-horizontal sidewall (a lateral wall of the resilient structure).

[0018] In some embodiments there is provided a guide support structure extending along walls of the domed structure and having a greater stiffness in a radial or diagonal direction than the domed structure for shaping the collapse of the dome under the compression by the downward force. In some embodiments, the guide support structure comprises a web, the web having an interrupted Outer Diameter (OD). In some embodiments a portion of the resilient structure forms 80% or more, 70% or more, 60% or more, 50% or more, 40% or more, 30% or more, 20% or more, or 10% or more of a height of the resilient structure, when not compressed under the downward force, is positioned within the horizontal footprint of the cavity. In some embodiments, the resilient structure has an outer surface and an angle of the outer surface of the resilient structure measured from vertical is >15deg, >16deg, >17deg, >18deg, >19deg, >20deg, >21deg, >22deg, >23deg, >24deg, >25deg, >26deg, >27deg, >28deg, >29deg, >30deg, >31deg, >32deg, >33deg, >34deg, >35deg, >36deg, >37deg, >38deg, >39deg, >40deg, >41deg, >42deg, >43deg, >44deg, >45deg,>46deg, >47deg,>48deg, >49deg, >50deg, >51deg, >52deg, >53deg, >54deg, >55deg measured over 40% or more, 50% or more, 60% or more, 70% or more of a height distance from the outsole to the upper. In some embodiments, the resilient structure when not compressed under the downward force comprises a domed structure, the energy return device further comprising a lateral expansion limiter arranged to resist lateral expansion of the domed structure, the lateral expansion limiting structure comprising a ring about a base of the domed structure.BRIEF DESCRIPTION OF THE FIGURES

[0019] Embodiments will now be described with reference to the figures, in which like reference characters denote like elements, by way of example, and in which:

[0020] Fig. 1 is a front cross-section view of a midsole device according to an embodiment.

[0021] Fig. 2 is a perspective cross-section view of supporting structural elements of a midsole device according to the embodiment of Fig. 1.

[0022] Fig. 3A is a perspective cross-section view of a midsole device comprising a higher density conical foam insert inside a lower density conical foam disk according to an embodiment.

[0023] Fig. 3B is a front cross-section view of a midsole device according to the embodiment shown in Fig. 3A.

[0024] Fig. 4A is a perspective view of a cylindrical array of coil springs demonstrating an operational principle of a block of foam under compression.

[0025] Fig. 4B is a perspective cross-section view of the cylindrical array of coil springs of Fig. 4A.

[0026] Fig. 4C is a front view of the cylindrical array of coil springs of Fig. 4A under compression.

[0027] Fig. 4D is a front view of the cylindrical array of coil springs of Fig. 4A shearing sideways.

[0028] Fig. 5A is a front cross-section view of a conical coil spring array demonstrating principles of operation of a conical foam disk according to some embodiments.

[0029] Fig. 5B is an isometric view of the conical coil spring array of Fig. 5 A.

[0030] Fig. 5C is a perspective view of the conical spring array of Fig. 5 A under compression.

[0031] Fig. 5D is a perspective cross-section view of the conical spring array of Fig.5 A under compression illustrating some of the lateral forces created by the conical shape.

[0032] Fig. 5E is a front cross-section view of the conical spring array of Fig. 5 A under compression illustrating the effect of a lateral shearing motion.

[0033] Fig. 6 is a front cross-section view of two midsole devices according to an embodiment in which the first midsole device is in an uncompressed state and situated behind the second midsole device which is in a compressed state.

[0034] Fig. 7 is a perspective cross-section view of a midsole device according to an embodiment in a compressed state.

[0035] Fig. 8 is a perspective cross-section view of supporting structural elements of a midsole device according to an embodiment in a compressed state.

[0036] Fig. 9 is a front cross-section view of a midsole device according to an embodiment with additional material above and below the web insert.

[0037] Fig. 10A is a perspective cross-section view of a web insert in an uncompressed state.

[0038] Fig. 10B is a perspective cross-section view of the web insert of Fig. 10A in a partially compressed state.

[0039] Fig. 10C is a perspective cross-section view of the web insert of Fig. 10C in a compressed state.

[0040] Fig. 11 is a front cross-section view of two midsole devices according to an embodiment in which the first midsole device is in an uncompressed state and situated behind the second midsole device which is in a compressed state, further illustrating the relative motion of guide support structure lower end during compression.

[0041] Fig. 12A is an isometric view of a guide support structure and an apex insert of a midsole device according to an embodiment in an uncompressed state.

[0042] Fig. 12B is an isometric view of the guide support structure of Fig. 12A in an uncompressed state.

[0043] Fig. 12C is an isometric view of the guide support structure of Fig. 12A in a compressed state.

[0044] Fig. 13A is a perspective view of the guide support structure of Fig. 12A in an uncompressed state.

[0045] Fig. 13B is a perspective view of the guide support structure of Fig. 12A in a partially compressed state.

[0046] Fig. 13C is a perspective view of the guide support structure of Fig. 12A in a compressed state.

[0047] Fig. 14A is a perspective cross-section view of the guide support structure of Fig. 12A in an uncompressed state.

[0048] Fig. 14B is a perspective cross-section view of the guide support structure of Fig. 12B in a partially compressed state.

[0049] Fig. 14C is a perspective cross-section view of the guide support structure of Fig. 12C in a compressed state.

[0050] Fig. 15 A is a perspective cross-section view of a midsole device comprising a according to an embodiment in a compressed state.

[0051] Fig. 15B is a perspective cross-section view of the apex insert, guide support structure and ring member of Fig. 15A in a compressed state.

[0052] Fig. 16A is a top view of reinforcing structures of an elliptic midsole device.

[0053] Fig. 16B is a perspective view of reinforcing structures of the elliptic midsole device of Fig. 16A

[0054] Fig. 17A is a side cross-section view of a non-round configuration of a midsole device including linear sections of diagonal wall shapes.

[0055] Fig. 17B is a perspective cross-section view from below of the non-round configuration of a midsole device of Fig. 17A.

[0056] Fig. 17C is a bottom view of the non-round configuration of a midsole device of Fig. 17 A.

[0057] Fig. 17D is a perspective from above of the non-round configuration of a midsole device of Fig. 17A.

[0058] Fig. 17E is a perspective exploded view of the non-round configuration of a midsole device of Fig. 17A.

[0059] Fig. 17F is a perspective cross-section exploded view of the non-round configuration of a midsole device of Fig. 17A.

[0060] Fig. 18A is a perspective cross-section view of a shoe midsole according to an embodiment.

[0061] Fig. 18B is a side cross-section view of the shoe midsole of Fig. 18A.

[0062] Fig. 19A is a side view of a shoe midsole according to an embodiment shown without sidewalls of the midsole, thereby revealing a multiplicity of midsole devices in the midsole.

[0063] Fig. 19B is a perspective view of the shoe midsole of Fig. 19A.

[0064] Fig. 20A is a perspective view of an outsole and midsole devices according to an embodiment.

[0065] Fig. 20B is a top view of the outsole and midsole devices of Fig. 20A.

[0066] Fig. 20C is a top view of support structures of the midsole devices as arranged for positioning on the outsole of Fig. 20 A.

[0067] Fig. 20D is a perspective view of the guide support structures of Fig. 20C.

[0068] Fig. 20E is a perspective view of the guide support structures of Fig. 20C positioned on an outsole.

[0069] Fig. 21 A is a bottom perspective view of midsole devices in a midsole according to an embodiment having holes in the outsole for flow of air.

[0070] Fig. 21B is a side cross-section view of the midsole of Fig. 21A.

[0071] Fig. 21C is a perspective cross-section view of the midsole of Fig. 21A

[0072] Fig. 21D is a bottom perspective cross-section view of the midsole of Fig. 21 A

[0073] Fig. 22 is a bottom perspective view of midsole devices projecting down from a midsole according to an embodiment.

[0074] Fig. 23 A is a graph of lateral shear stability of a conventional foam midsole as represented in an FEA analysis applied to a 2D planar representation of a cylindrical foam puck, as compared to a 2D planar representation of an exemplary conical foam disk of the present device, and a similar 2D planar representation of a conical foam disk with an exemplary web insert, in terms of lateral shear stability.

[0075] Fig. 23B is a graph of lateral shear stability of a conventional foam midsole as represented in an FEA analysis applied to a 3D cylindrical representation of a cylindrical foam puck, as compared to an exemplary conical foam disk of the present device, and a similar conical foam disk with an exemplary web insert.

[0076] Fig. 24A is a side cross section view of an embodiment of a midsole device including a biased damper.

[0077] Fig. 24B is a perspective cross section view of the embodiment of Fig. 24A.

[0078] Fig. 24C is a side cross section view of the embodiment of Fig. 24A with a domed disk of the midsole device shown in a compressed state in front of the same domed disk in an uncompressed state.

[0079] Fig. 25A is a plan view of a midsole according to an embodiment comprising tapered midsole devices.

[0080] Fig. 25B is a perspective view of the midsole of Fig. 25 A.

[0081] Fig. 25C is a perspective view of the midsole devices and outsole of Fig. 25B.

[0082] Fig. 25D is a side view of the midsole of Fig. 25A.

[0083] Fig. 25E is a side cross-section view of a midsole device of Fig. 25D.

[0084] Fig. 26A is a front view of a web structure according to an embodiment.

[0085] Fig. 26B is a perspective cross-section view of the web structure of Fig. 26A.

[0086] Fig. 26C is a perspective view from below of the web structure of Fig. 26 A.

[0087] Fig. 26D is a front cross-section view of a midsole device according to an embodiment comprising a foam apex insert.

[0088] Fig. 26E shows a magnified view of the bottom edge of a foam domed disk comprising an guide support structure and a ring spring with a downward extending flange.

[0089] Fig. 27A is a perspective view of a midsole device according to an embodiment comprising a plurality of air discharge ports.

[0090] Fig. 27B is a cross-section view of a midsole device according to an embodiment comprising air discharge ports.

[0091] Fig. 27C is a perspective view of a midsole device according to an embodiment comprising an open air discharge port and a one-way check valve port.

[0092] Fig. 27D is a perspective cross-section view of a midsole device according to an embodiment comprising a top one-way check valve in an apex insert.

[0093] Fig. 27E is a perspective cross-section view of a midsole device according to an embodiment comprising a top valve and one or more air discharge ports 360.

[0094] Fig. 27F is a perspective horizontal cross-section view of a midsole device according to an embodiment comprising a one-way check valve port and a non-occluding air discharge port.

[0095] Fig. 28 is a schematic illustration of a simplified representation of a dome disk illustrating geometric variables that may characterize embodiments of a domed disk structure.

[0096] Fig. 29 is a graph of estimated propulsive energy ratio of total energy return as a function of outer angle and bottom wall thickness according to an embodiment.

[0097] Fig. 30 is a graph of estimated propulsive energy ratio of total energy return as a function of outer angle and bottom wall thickness according to an embodiment.

[0098] Fig. 31 A is a schematic illustration of an approach to characterizing a simplified structural representation of a domed disk.

[0099] Fig. 3 IB is a schematic illustration of an approach to characterizing a simplified structural representation of a domed disk showing a simplified effective angle and effective width of a structure.

[0100] Fig. 31 Cis a schematic illustration of an approach to characterizing a simplified structural representation of a domed disk showing the identification of widths and angles of sections of material in a structure.

[0101] Fig. 32 is a graph showing a comparison of the load vs displacement profiles for a single device with and without the inclusion of compression-biased damping elements.

[0102] Fig. 33 is a top plan view of a midsole comprising four midsole devices in an exemplary configuration.

[0103] Fig. 34 is a graph showing an estimation of the load response provided by a distribution of midsole devices and the timing of their operations throughout stance.

[0104] Fig. 35 is a perspective view of a web structure comprising radial fingers with the fingers bridged at the inner diameter and the outer diameter in an alternating pattern.

[0105] Fig. 36 is a perspective view of a web structure comprising an accordion or wave web.

[0106] Fig. 37 is a perspective cross-section view of midsole device comprising a web structure on the outside of a foam domed disk.

[0107] Fig. 38 is a perspective cross-section partially-transparent view of a midsole device comprising web structure embedded within foam walls of a foam domed disk.

[0108] Fig. 39 is a perspective cross-section view of a midsole device comprising a foam apex insert.

[0109] Fig. 40 is a perspective cross-section view of a midsole device comprising an accordion-shaped ring around a foam apex insert.

[0110] Fig. 41 A is a front cross-section view of a schematic illustration of a foam domed disk including a material line representing either a straight bifurcation line (if a CAD model) or line between actual points (for an actual device).

[0111] Fig. 41B is a front cross-section view of the foam domed disk of Fig. 41 under compression exhibiting an S-shaped curve.

[0112] Fig. 41 C is a front cross-section view of the foam domed disk of Fig. 41 under compression exhibiting an S-shaped curve including a horizontal line (0°), and two lines at 15° from horizontal each passing through a nominal center point of the S-shaped curve.

[0113] Fig. 42A is a front cross-section view of a midsole device according to an embodiment comprising a web insert in an uncompressed configuration.

[0114] Fig. 42B is a front cross-section view of the midsole device of Fig. 42A in a compressed configuration exhibiting buckling of the web insert.

[0115] Fig. 43 A is a chart illustrating a region defined by desirable ranges of outer angles and aspect ratios.

[0116] Fig. 43B is the chart of Fig. 43 A excluding a set of outer angles and aspect ratios representing implausible geometries.

[0117] Fig. 43C is the chart of Fig. 43B further excluding outer angles and aspect ratios exhibiting an estimated Propulsive Energy Percentage (PEP) of less than 30%.

[0118] Fig. 44 is a side view of a buckling member oriented diagonally.

[0119] Fig. 45 is a side view of the buckling member of Fig. 44 under partial compression.

[0120] Fig. 46 is a side view of the buckling member of Fig. 44 under further compression.

[0121] Fig. 47 is a side view of a hinged buckling member with a live hinge.

[0122] Fig. 48 is a side view of a hinged buckling member with fabric hinges.

[0123] Fig. 49 is a side view of the hinged buckling member of Fig. 48 at full bending.

[0124] Fig. 50 is a side view a hinged buckling member with a single piece of fabric forming both bottom and top hinges.

[0125] Fig. 51 is a side view of a buckling member with a live hinge in the middle and a live hinge at the top.

[0126] Fig. 52 is an isometric view of the buckling member of Fig. 51.

[0127] Fig. 53 is a side view of multiple buckling members according to Fig. 51 with their upper blocks connected together.

[0128] Fig. 54 is an isometric view of the multiple buckling members of Fig. 53.

[0129] Fig. 55 is an isometric view of the buckling members of Fig. 53 but showing a surrounding structure in which the buckling members are embedded.

[0130] Fig. 56 shows the surrounding structure of Fig. 55 in isolation.

[0131] Fig. 57 is a side view of a hinged buckling member with a fabric hinge connecting to the top block.

[0132] Fig. 58 shows a side view of a hinged buckling member with an insert at the central hinge.

[0133] Fig. 59 shows a side view of a hinged buckling member with a rigid or flexible tube at the central hinge.

[0134] Fig. 60 is an isometric underside view of a midsole with buckling members arranged in a loop.

[0135] Fig. 61 is a section view of the midsole of Fig. 60.

[0136] Fig. 62 is a section view of the forefoot buckling member arrangement of Fig.61.

[0137] Fig. 63 is a section view of the heel buckling member arrangement of Fig. 61.

[0138] Fig. 64 is an isometric view of a reinforcement of a buckling member using a web structure.

[0139] Fig. 65 is a cross-section view of a midsole with diagonal buckling members according to an embodiment.

[0140] Fig. 66 is an isometric view of an embodiment of a midsole using the diagonal side members of Fig. 65.

[0141] Fig. 67 is a top view of the embodiment of a midsole of Fig. 65.

[0142] Fig. 68 is a cross-section view of a midsole with a single additional diagonal buckling member according to an embodiment.

[0143] Fig. 69 is an embodiment of a midsole with lengthwise diagonal buckling members in an inverted arrangement relative to outer diagonal members.

[0144] Figs. 70-72 show different section view of exemplary embodiments of arrays of lengthwise diagonal buckling members.

[0145] Fig.73 is an isometric view of a midsole with a reinforced diagonal buckling member connected to a portion of an outsole.

[0146] Fig. 74 is an isometric view of diagonal buckling member connected to a portion of an upper.

[0147] Fig. 75 is a simplified side cross-section of the arrangement of Fig. 74.

[0148] Fig. 76 is a side cross-section view a buckling member diagonally oriented as in the embodiments of Figs. 44-46 but with a narrow portion acting as a live hinge.

[0149] Fig. 77 is an illustration of a finite element analysis of the buckling member of the embodiment of Fig. 76 in an uncompressed state.

[0150] Fig. 78 is an illustration of a finite element analysis of the buckling member of the embodiment of Fig. 76 in a compressed state

[0151] Fig. 79 is an isometric view of a diagonal member as shown in Fig. 76 having a web insert as a reinforcing structure.

[0152] Fig. 80 is an isometric view of the diagonal buckling member of Fig. 79 in isolation.

[0153] Fig. 81 is an isometric view of the web insert of Fig. 79.

[0154] Fig. 82 is a side view of a midsole with plural diagonal buckling members as shown in Fig. 79.

[0155] Fig. 83 is a further side view of the embodiment of Fig. 82.

[0156] Fig. 84 shows an isometric view of an embodiment with diagonal buckling members in the arch that are less stiff.

[0157] Fig. 85 shows a side view of an embodiment of a midsole in which angled members are uniformly angled forward from the ground up and forward toward the front of the shoe.

[0158] Fig. 86 is an isometric view of the embodiment of Fig. 85.

[0159] Fig. 87 is a side view of an embodiment a midsole in which angled members are uniformly angled rearward from the ground up and rearward toward the rear of the shoe.

[0160] Fig. 88 is a second side view of the embodiment of Fig. 87.

[0161] Fig. 89 shows an exemplary force-displacement curve for a linear buckling member according to some embodiments.

[0162] Fig. 90 is an isometric view of an embodiment of an energy return device comprising an air damper.

[0163] Fig. 91 is an isometric cross-section view of the energy return device of Fig. 90.

[0164] Fig. 92 is a side cross-section view of the energy return device of Fig. 90.

[0165] Fig. 93 is a isometric transparent view of the energy return device with air damper of Fig. 90.

[0166] Fig. 94 is an isometric underside view of an embodiment of an energy return device comprising an air bladder with an air flow bypass.

[0167] Fig. 95 is a section view of the energy return device of Fig. 94.

[0168] Fig. 96 is an isometric view of the intermediate chamber of Fig. 94.

[0169] Fig. 97 shows an inflated cross-section in front of an uninflated profde of the embodiment shown in Fig. 94.

[0170] Fig. 98 is an isometric view of an embodiment of an energy return device with an airflow bypass adjustable with a dial.

[0171] Fig. 99 is a bottom view of the embodiment shown in Fig. 98.

[0172] Fig. 100 is an isometric view a dial and cam for restricting airflow within the channel of the energy return device of Fig. 98.

[0173] Fig. 101 is an isometric view of the dial and cam for restricting airflow within the channel of the energy return device of Fig. 98 with material cut away.

[0174] Fig. 102 is an isometric view of the dial and cam for restricting airflow within the channel of the energy return device of Fig. 98 with additional material cut away.

[0175] Fig. 103 is an isometric view embodiment of a two-chamber air damper including an entire upper.

[0176] Fig. 104 is an isometric view of the embodiment of a two-chamber air damper of Fig. 103 showing only the lower portion of the upper.

[0177] Fig. 105 is an isometric view of the two-chamber air damper of Fig. 103 without the upper.

[0178] Fig. 106 is an isometric view from below of the two-chamber air damper of Fig. 103 without the upper.

[0179] Fig. 107 is a side view of the multiple-chamber air damper according to an embodiment.

[0180] Fig. 108 is a top view of the multiple-chamber air damper of Fig. 107.

[0181] Fig. 109 is an isometric view from below of the multiple-chamber air damper of Fig. 107.

[0182] Fig. 110 is a side cross-section view of the multiple-chamber air damper of Fig. 107.

[0183] Fig. 111 is an isometric cross-section view of the multiple-chamber air damper of Fig. 107.

[0184] Fig. 112 is a cross-section view of the connection between the intermediate volume and the heel volume of Fig. 107.

[0185] Fig. 113 is a cross-section view of a midsole device including buckling members and an air bladder according to an embodiment.

[0186] Fig. 114 close-up view of the cross-section slice of the compressed shape of a vertical buckling member of the midsole device of Fig. 113.

[0187] Fig. 115 is a cross-section view showing the uncompressed geometry of the live hinge sections of the buckling members of the midsole device of Fig. 113.

[0188] Fig. 116 is a cross-section view of a variation of the midsole device of Fig.113 in which an elastic coating is continuous around par of the array of buckling members.

[0189] Fig. 117 is a simplified side cross-section view of a midsole device as it may be employed in a dress shoe incorporating low durometer outer foam.

[0190] Fig. 118 is an isometric view of a midsole device comprising sections of upright and inverted conical structure.

[0191] Fig. 119 is a cross-section along two planes showing sections of upright and inverted conical structure of Fig. 118.

[0192] Fig. 120 is a top view of the cross-section of Fig. 119.

[0193] Fig. 121 is a transparent isometric view of the cross-section of Fig. 119.

[0194] Fig. 122 is a isometric transparent view of the midsole device comprising sections of upright and inverted conical structure of Fig. 118.

[0195] Fig. 123 is a side cross-section view of a midsole device in which a resilient structure formed as a dome also acts as an air chamber.

[0196] Fig. 124 is a side cross-section view of a midsole device in which a damper seals off a fluid pathway during compression.

[0197] Fig. 125 is a isometric cross-section view of a web member with discontinuities.

[0198] Fig. 126 is a cross-section view of an energy return device comprising a resilient compressible structure of a cylindrical geometry.

[0199] Fig. 127 is a cross-section view of an energy return device comprising a resilient compressible structure of a conical shape inverted relative to the conical orientation of the web member.DETAILED DESCRIPTION

[0200] Immaterial modifications may be made to the embodiments described here without departing from what is covered by the claims. In the claims, the word “comprising” is used in its inclusive sense and does not exclude other elements being present. The indefinite articles “a” and “an” before a claim feature do not exclude more than one of the feature being present. Each one of the individual features described here may be used in one or more embodiments and is not, by virtue only of being described here, to be construed as essential to all embodiments as defined by the claims.

[0201] Throughout this specification, various structures with approximately circular, cylindrical or conical structure are described which have radial and axial dimensions for that structure. Embodiments of the invention may have multiple circular, cylindrical or conical structures in an article of footwear or part thereof, each structure having their own radial dimension and their own axial dimension. Each article of footwear has: a length which may be measured in the direction from heel to toe; a width, which may be measured in the direction from horizontal interior of the foot to horizontal exterior of the foot; and a depth, which may be measured in the direction downwards into the surface on which the footwear rests. The horizontal interior of the foot refers to the anatomical medial direction (i.e.laterally / horizontally towards the centerline of a human body wearing footwear containing or defined by the device) whereas the horizontal exterior of the foot refers to the anatomical lateral direction (i.e. laterally / horizontally away from the centerline of a human body wearing footwear containing or defined by the device).

[0202] An energy return device for a midsole of a shoe may absorb and return energy from compression of the device under a downward force applied by a wearer to an upper of the shoe in a height direction extending between an outsole of the shoe and the upper, which may be the depth direction defined above, or may be angled from the depth direction where compression occurs in a non-vertical direction. The energy return device may include a resilient structure such as a foam structure supporting the upper in relation to the outsole. The foam structure defines an opening for air to enter the cavity. The foam structure is arranged to collapse, under the downward force applied to the upper by the wearer, into the cavity so that as the compression begins, the foam structure deforms by bending of the foam structure, the foam structure collapsing into lateral bounds defined by the foam structure at a height corresponding to a maximum lateral extent of the cavity, and at a point near maximum compression under an exemplary downward force applied to the midsole by the user, the foam structure deforms by direct compression of the foam structure between the upper and the outsole. This latter deformation by direct compression may, depending on the embodiment, be very limited as the stiffness of the foam structure against direct compression may be much higher than the stiffness against the bending at the beginning of the compression. The compression of the material of the resilient structure between the insole and the outsole may include the vertical compression of the now-horizontal sidewall (a lateral wall of the resilient structure) such that there remains substantially no cavity or air gap between portions of the now substantially horizontal sidewall and a base of the midsole device or the outsole of the shoe. The exemplary downward force may be, for example, a downward force applied by a typical or exemplary user. In some embodiments, the resilient structure comprises a domed structure. The domed structure may comprise, for example, a domed disk, and the cavity is a volume cupped by the dome shape of the domed disk. The opening may be, for example, the entire interior of the base of the domed disk, although depending on the embodiments the base may be enclosed and other openings may be defined. The term “upper” refers to a portion of the shoe having a surface in contact with the bottom of the wearer’s foot (directly or via, for example, a sock and / or insole) and does not necessarily imply the presence or absence of a discrete insole component. The cavity may beempty (containing air only) or contain a low resistance air-permeable material or structure such as low durometer open cell foam.

[0203] A domed structure as used herein generally means a geometry that converges, in one orientation, upwards from a wide base to a top surface that may comprise a flattened or curved top and generally surrounds, via this curving shape, a cavity, typically with an opening at the base. While domed structures such as domed disks are typically contemplated as having the base at the bottom, an inverted orientation is not excluded. Also, while embodiments disclosed below have a circular base, other shapes, such as oval shapes or nonround or faceted shapes are also contemplated. Specific geometries of domed disks are described in greater detail later in this specification. The term ‘conical disk’ is understood to include truncated and approximately conical geometries including, but not limited, to truncated circular cones (i.e. a conical frustum) and truncated elliptic or faceted cones. A conical disk comprises a top surface and walls converging upwards towards a projected apex, which may for example be above or within the top surface. The top surface and bottom edges of the walls of a conical disk may have a circular, elliptic, or other approximately round shape. The term ‘frustum’ as used herein refers to a three-dimensional volume defined by the top surface and walls converging towards a projected apex above a top surface. As used herein, the walls of a frustum may generally converge uniformly towards the projected apex, but do not need to converge linearly; as a non-limiting example, a frustum as used herein may refer to a truncated elliptic paraboloid. Additionally, the top and bottom surfaces of a conical disk, including the top and bottom surfaces of a frustum, may or may not be flat and may or may not be parallel with each other.

[0204] In various embodiments of the device disclosed here, a midsole device 10 comprises a resilient compressible structure defining a cavity, for example arching over the cavity. An example of such a resilient compressible structure is a resilient domed structure, e.g. compressible foam domed disk 20, such as a conical disk 20A. Compressible foam domed disks 20 may be made of highly resilient materials such as highly resilient foam, such as, but not limited to, Polyurethane or Pebax®. Due to the converging (conical) geometry, flexibility, and compressibility of the foam, high travel can be achieved for a given stack height and maximum diameter of the base. In various embodiments, the compressible foam domed disk 20 is rigid enough, either due to the properties and shape of the foam or by support using a support structure such as the web support structure described below, to bend under the compression by the downward force applied to the upper in a manner that the downward force is initially resisted primarily by vertical / diagonal compression of the foamalong the vertical / diagonal length of the walls,. As compression continues, the spring rate may reduce, due to the parallel internal strain on the structure becoming less vertical as the structure collapses, due to buckling, or both. The compression of the sidewalls of the foam is then also vertically applied but is now compressing across the thickness of the walls. Toward the bottom of the travel, the internal compression stress along the length of the foam walls may be partially or fully retained in the radial direction by a lateral expansion limiter 60 at the base.

[0205] Some embodiments of the compressible foam domed disk 20 may be defined by specific ranges of geometries. The compressible foam domed disk 20 has a disk upper inner diameter (UID) 22, a disk upper outer diameter (UOD) 24, a disk lower inner diameter (LID) 26 and a disk lower outer diameter (LOD) 28. In the event of an inverted dome, the “upper” end is the narrower vertical end and the “lower” end, including the “base”, is the wider vertical end. These terms may be used even in non-round embodiments to describe inner and outer perimeters at narrower (“upper”) and wider (“lower”) vertical ends of generally dome-shaped embodiments. The foam domed disk also has a disk exterior surface 30 and a disk interior surface 32. Where a support structure extending along the walls of the dome, such as support structure 34 described below, is present, the diameters 22, 24, 26, 28 are of the dome inclusive of the support structure. For the purpose of this disclosure and the claims, where the foam structure flares out at the otherwise narrow end, the UOD will be taken as the smallest dimension in the top (i.e. in the vertical direction of general narrowing) 50% of the structure by height. Where there is no such flaring, any narrowing of the outer diameter above a highest point within the cavity will be excluded. The LID of the structure will be taken as the largest ID in the bottom (i.e. in the direction of general widening) half (in terms of height) of the structure.

[0206] A circumferentially expandable guide support structure 34 such as a web structure 36 may extend along the walls of the dome, for example adhered or otherwise attached to the inner surface of the foam domed disk 20, as is illustrated for example in Fig.1. In some embodiments, a guide support structure 34 may be on the inside or outside surfaces of the domed disk 20 or imbedded in the wall of the domed disk. Examples are shown in Figs 37 and 38. The web structure 36 is more rigid in the radial / diagonal direction than the foam and translates a portion of the vertically downward force on the web into a horizontally outward force on the base of the foam conical disk. This stores a portion of the foot strike energy in the compression of the foam in the radially outward direction and / or expansion of the bottom OD of the foam circumferentially as the OD expands radiallyoutward. While a web structure 36 is shown as the guide support structure 34 in the drawings, other comparably rigid structures may be used in place of a web structure 36, such as, for example, individual radial / diagonal spokes made of a rigid material. An interior web or spoked guide support structure 34 may have a guide support structure upper end 38 and a guide support structure lower end 40.

[0207] It has been observed that radially outward stretching of the base of the conical foam disk, past a certain amount, can be problematic because it becomes difficult to locate the base of the conical foam disc relative to the top of the outsole. For this reason, it is seen as beneficial to limit the radial expansion of the base of the conical foam disc. Lateral expansion of the cavity may also be limited, in dome or in non-dome embodiments, for example to increase compression of the foam around the cavity as the cavity collapses vertically, and thus the force supplied by such compression. Thus, the energy return device may comprise a lateral expansion limiter 60 arranged to resist lateral expansion of the foam structure. The lateral expansion limiter may be arranged to resist lateral expansion for example at the height corresponding to a maximum lateral extent of the cavity, for example at a height corresponding to the LID 26 in a dome embodiment. The expansion of the outer diameter (OD) of the conical foam disk may be controlled in several ways. In some embodiments, for example the embodiments shown in Figs. 3, 9, 25E or 26E, the base of the conical disk may be adhered to, embedded in or otherwise attached to the outsole to prevent it from radially expanding. In this case, most of the radial force component of the compression of the conical disk is taken up by horizontal tension in the outsole and the compression of the walls of the conical disk itself. Thus the outsole itself may act as the lateral expansion limiter 60. In Figs. 3 and 9, a cylindrical or L-shaped ring 61, which may be attached to the outsole, acts as the lateral expansion limiter on its own or in combination with the outsole.

[0208] As shown in Fig. 1, the base of the conical disk may have a rigid or flexible ring member 62 around the OD of the base to act as the lateral expansion limiter 60. This can be used to increase the spring force of the device and to achieve other effects as described in the disclosure.

[0209] Fig. 2, an assembly of an exemplary device is shown in cross-section with the conical foam disk removed. Each of the three remaining components may or may not be present in various embodiments. At the guide support structure upper end 38 of the web structure 36, an apex insert 50 is shown. The apex insert 50 may provide positioning and resistance to contraction of the guide support structure upper end 38. The apex insert may be made of any material such as, but not limited to, foam or a non-compressible plastic. If madeof a compressible or deformable material, it may allow a small amount of contraction of the guide support structure upper end 38, but less contraction than if there was no apex insert 50. This contraction may serve to reduce the stress on other parts of the foam domed disk 20 to prevent overstraining the foam in other areas. The apex insert may have flanged edges 52 that engage the surface of the guide support structure 34 at the guide support structure upper end 38. A lateral expansion limiter 60 may limit expansion of the LOD 28. In some embodiments, lateral expansion limiter 60 may comprise an exterior support ring 62 around the outside of the LOD 28, as illustrated in Fig. 1, which serve to increase the force needed to expand the outer diameter of the conical foam disk during vertical compression of the foam domed disk 20 and web structure 36.

[0210] As shown in Fig. 3, an embodiment of the device is shown as a conical resilient structure 110. There are many types of resilient materials, such as high resilience foam, which may be used for this construction. 35 durometer Pebax® foam is one nonlimiting example which may be used to construct embodiments of the conical resilient structure 110 disclosed here. Fig. 3 shows a higher density conical foam insert 130 as a support structure 34, inside a comparatively lower density conical foam disk 120. The device may be used without this conical foam insert 130 with a usable portion of the effects described here. In this embodiment, a lateral expansion limiter 60 is included and comprises a ring which may be an L-shaped ring 61 enclosing the lower outer diameter of the conical resilient structure 110, and which may be adhered or otherwise attached to the outsole.

[0211] In various such embodiments, as the user’s heel compresses a foam domed disk, e.g. a conical foam disc, the direction of force of compression of the walls of the conical disk proceeds initially in a diagonal direction which produces an outward force around the base of the conical foam disc. As the compression displacement (also referred to as “travel” in this disclosure) increases initially, the amount of bending / shearing of the foam walls of the conical disk increases. When constructed according to the principles disclosed here, this bending / shearing deformation results in a reduced rate of load-carrying capacity of the conical disk and results in a reduction of the spring rate as compression continues through the midrange of the compression travel. This falling off of the spring rate results in more of the foot strike energy being stored through the midstride, because the midsole is able to stay more compressed with less downward force of the user, through the midstride, so the midsole compression energy at the heel can be released later in the stride when it contributes more to forward propulsion. As the device nears full compression, the bending / shearing of the walls reduces due to collapsing of the walls and contact with the ground or top of the outsole. Afterthis contact, the compression of the walls across the thickness of the collapsed walls is increased and acts as a compressible bottom out bumper.

[0212] LATERAL SHEAR STABILITY

[0213] High thickness midsoles especially those comprising primarily low durometer foam without further structure via shaping of the foam or additional elements are inherently unstable in shear deformation. To illustrate this drawback of a high travel conventional foam midsole, Figs.4A-4D show a cylindrical array of coil springs 210, which will be used in this description to conceptually represent the forces at work in a block of foam under compression. At rest, as shown in Fig. 4A, the only force opposing the lateral shearing of the foam is the resistance to shear deformation of the foam, or in the case of these figures, the springs 220. This stabilizing force will be lower if the midsole is taller for a given width, other factors being held equal. As the springs 220 are compressed, for example approaching the state shown in Fig. 4C, it becomes increasingly unstable in the lateral shear direction. This is because the lowest energy position of the springs is in an elongated state which occurs when the springs shear sideways, as shown in Fig. 4D. This makes a conventional foam structure, as illustrated by the array of coil springs, less laterally stable as compression increases toward full compression. This can be detrimental to the performance and safety of a shoe midsole and is especially detrimental with tall stack height, low durometer conventional foam midsoles.

[0214] The graphs in Figs. 23A and 23B show the lateral shear stability of a conventional foam midsole as represented in an FEA analysis with a cylindrical foam puck, as compared to an exemplary conical foam disk of the present device, and a similar conical foam disk with an exemplary web insert, in terms of lateral shear stability. To create this graph,, the geometry was bonded to a flat plate on the top and bottom faces. The bottom plate was fixed in space, while the top plate underwent a series of consecutive deformations. The top plate was first shifted 5mm laterally, which develops a lateral “correcting” force in the geometry that pushes towards the centerline of the body. This lateral shift is maintained as the top plate is then compressed up to 15mm. The change in correcting force (referred to as lateral resistance in the graph) is then measured as a response of compression depth. A quadratic equation is then fitted to the first section of each curve, and extrapolated out to 25mm of compression, shown in the graphs with a smaller dotted line. This test was run twice for each geometry; once with axial-symmetry applied on the 2D surface (simulating a cylindrical shape), as illustrated in Fig. 23B, and a second time with an extruded planar shape, as illustrated in Fig. 23 A. An unexpected effect of the construction of embodimentsshown here is an increase in the lateral shear stability with greater compression, as compared to a decrease in the lateral shear stability of a conventional solid foam midsole. Additionally, the extrapolation of the puck geometry can be seen extending into negative force values. These negative values indicate that the lateral force is no longer pushing back towards the center of the geometry (stabilizing force), but is now applying additional force to shift the geometry further laterally (buckling force).

[0215] A conical array of coil springs 230 is illustrated in Figs. 5A-5E, for better visualization in three dimensions of the differences between a conventional foam block (as illustrated conceptually by the cylindrical array of springs 210 in Figs. 4A-4D) and a conical disk. The fully compressed lateral shear stability as shown in Fig 5C-5E of a conical array of coil springs (representing the conical foam disc) is greater than the cylindrical array of coil springs as shown in Fig 4A-4D (representing the conventional foam block) as a result of the compression of a far spring (in the leading direction of the shearing motion), and the extension of a near spring (in the trailing direction of the shearing motion) that is required in order to shear the top of the assembly, in a horizontal direction, relative to the bottom. In a conical foam disc of the present device, lateral shear on the conical foam disc results in compression of a first wall of the conical foam disc and extension of an opposing second wall of the conical foam disc that result in an opposing force against the lateral shearing force as the top of the device is translated laterally with respect to the base. The lateral shear stability increases with further compression of the conical resilient foam disk due to the increased spring force as the springs are compressed. At full compression, it can be seen in Figs. 5C- 5E, that all of the springs in the circular array are all highly loaded in the radially inward direction, even though the structure is providing minimal force, by comparison, in the vertical direction.

[0216] At full compression the springs 220 are essentially pre-loaded against each other in the horizontal direction. This creates high internal stress in the structure at full compression with a high force, pointing inward toward the center axis of the conceptual conical disk. The springs 220 are all partially in compression along a horizontal plane, which increases the inward force from all directions to dramatically increase the lateral shear stability of the portion of the midsole in which the device is situated when at full compression. By positioning one or more such devices through a midsole, the various regions or areas of the midsole may be provided with significantly improved lateral shear stability in that region or area.

[0217] The greater the compression of a midsole, the more important it is to have increased lateral shear stability. This is important because the highest lateral shear stability requirement will typically coincide with the highest vertical force of the user to compress the midsole. Additionally, when in motion and especially when accelerating, the highest vertical forces may coincide with moments of high lateral force (e.g. a sprinter running on the curve of a track). For example, an athlete using high-performance shoes requires lateral shear stability when their feet are applying significant force through the shoes to the ground surface; a decrease in lateral shear stability leaves the user at risk of sudden lateral motion that could result in an accident or injury. The construction of various embodiments of the present device provides increased lateral shear stability as the device approaches full compression, reducing these risks.

[0218] COMFORTABLE FORCE DISTRIBUTION GEOMETRY

[0219] In order to achieve a specific distribution of forces (such as but not necessarily an equally distributed force) upward on, for example, the user’s heel at full compression, it is useful for a conical disk as disclosed here to compress to a flat or concave shape at full compression. This allows a receiving disk 70, for example, to conform comfortably to a user’s heel at full compression. Fig. 6 shows an example of a shape which can achieve this requirement both at full compression and in anon-compressed state. A receiving disk 70 may comprise, for example, a heel disk that can be sized and shaped to receive a user’s heel. Multiple receiving disks 70 may be part of a plurality of midsole devices 10 in a single midsole. For example, a first receiving disk 70 may be a heel disk, while a second receiving disk 70 may be positioned under the ball of the foot and be shaped to receive the ball of the foot.

[0220] To achieve this, some embodiments may comprise a UOD 24 being approximately the same or smaller than the LID 26 of the foam domed disk 20. With this relative geometry principle, the compression and shearing of the conical walls of the foam results in a compressed shape which can be flat or concave or possibly convex, and less than half of the total at-rest foam height.

[0221] This configuration may allow for greater than 30%, greater than 40%, or greater than 50% compression travel in various embodiments. The configuration may also provide an integrated compressible bump stop, after full travel is reached, as a result of the vertical compressibility of the foam after full compression.

[0222] According to the principles of the device disclosed here, various exemplary configurations may have different conical wall angles, but have a geometry where the UOD24 of the conical disk is similar to the LID 26 of the bottom of the conical disk. The ceiling thickness of each disk may be similar to or thinner than the sidewall thickness, although a thicker ceiling may also be used. These two geometric relationships in various embodiments allow each of these disks to deform at full compression into a reasonably flat or concave shape to conform to the curved bottom of a user’s heel at full compression.

[0223] It should be noted that due to the compressibility of foam, the geometry does not need to be overly precise or accurate. Due to the many possible variations, a simplified section is defined between 25% and 75% of the stack height, where the total stack height is defined at the vertical distance from the bottom of the outsole to the top of the upper (not including any removable insole). The upper OD of this section is defined as the functional upper OD (FUOD) and the lower ID of this section is defined at the functional lower ID (FLID) with similar definitions for the functional lower OD (FLOD) and functional upper ID (FUID). FUODs that are larger than the FLID and <150%, <149%, <148%, <147%, <146%, <145%, <144%, <143%, <142%, <141%, <140% of the FLID as well as FUODs that are smaller than the FLID and >70%, >71%, >72%, >73%, >74%, >75%, >76%, >77%, >78%, >79%, >80% of the FLID have been shown to work with some portion of the benefit described here. In embodiments where the device is comprised of linear sections having the same cross-section as a conical disk, the FLID will correspond to the distance between the inner walls at 25% of the stack height, and the FUOD will correspond to the distance between the outer walls at 75% of the stack height.

[0224] Some embodiments of the device have extra material 64 around the UOD or LOD of the foam domed disk or inside of the UID or LID of the foam domed disk. In some embodiments, extra material 64 around the UOD 24 comprises a receiving disk 70. The UOD 24 and the LID 26 may, therefore, be measured below the additional structure around the top of the structure, as shown in Fig. 9 or above the extra material inside the ID at the bottom of the structure, also shown in Fig. 9.

[0225] In another way of measuring this relationship, the OD of the top may be taken as the smallest diameter in the top 50%, 40%, 30%, 10% of the structure or truncated section. The ID of the bottom of the structure may be taken as the largest ID in the lower 50%, 40%, 30%, 20%, 10% of the conical structure or truncated section.

[0226] The ceiling of the conical disk may be within 10% or more, 20% or more, 30% or more, 40% or more the thickness of the conical disk wall to provide a portion of the benefit of the device. The thickness of the conical disk wall may be measured at 50% of the stack height and perpendicular to the average angle of the ID and OD surfaces of the wall. Ifa wall is not a straight line or if it is curved or waved or if it has holes or other features or a combination of different materials or foam durometers, a person skilled in the art will be able to average a section of the wall and fit straight lines to it, to determine the effective angle.

[0227] The ceiling volume of the device may be of the same compressible foam or matrix material as the conical disk, or a different material, or combination of materials. An accordion section ceiling plug band / ring may be used to provide minimal radially inward compression of the ceiling plug / apex insert and at the same time allow for vertical compression of the plug and wave or accordion section band. This vertically compressible band allows the ceiling plug to be made from a lower density foam which may provide a greater level of comfort for some users at full compression. The ceiling may also comprise pockets or holes that allow the same material to be used but with a lower effective durometer in some areas to allow a more comfortable compliance with the user’s heel during compression and especially at or past full compression.

[0228] ENHANCING DELAYED ENERGY RETURN

[0229] The inherent properties of the conical disk disclosed here, provide for a delayed return of the energy stored during compression, as a result of the reduced spring rate part-way through the travel. This reduced spring rate allows the conical disk to stay more compressed through the midstride than if the spring rate continued to increase through the midpart of the travel, as is common with a conventional foam midsole.

[0230] Fig. 9 shows an embodiment of the device which allows for an even greater spring rate reduction or even a spring force reduction, if desired, part way through the compression travel.

[0231] RADIALLY RIGID CONICAL DISK (Web) INSERTS

[0232] The addition of a conical support structure on the inside or outside surfaces of the conical foam disk or embedded into the wall of the conical foam disk, with the web having greater stiffness in the radial / diagonal direction as compared to the horizontal / circumferential direction, can enhance the performance of the conical foam disk structure in several ways. In various embodiments, an internal support structure 34 can provide internal support as an insert within a foam domed disk 20. An exterior support ring 62 may provide exterior support for the foam domed disk 20. The web structure (interchangeably referred to as a web insert or web support structure) 36 can increase the total spring force of the assembly. The web insert can increase the lateral shear stability of the assembly, and the web structure can modify the force displacement curve of the assembly in abeneficial way. This component may be flat or semi-conical or fully conical when at rest and before assembly as shown in Figs 10A-10C.

[0233] A radially rigid and circumferentially expandible internal support structure 34 such as a conical disk (web) insert 36 is preferably adhered (or secured by some means such as, but not limited to, over-molding) to the inner surface of the foam conical disk 20A but may also be adhered or otherwise attached to the outside of the foam disk or embedded into the foam disk. The purpose of this radially rigid conical structure is to use the vertical compression of the device to radially compress and / or circumferentially expand the foam of the base of the conical disk.

[0234] . This allows this radially rigid internal support structure 34 to provide a portion of the total spring force, while also providing a greater reduction in the spring rate part-way through the compression as it deforms toward a more flattened shape, or even a past-flat shape as illustrated in Figs. 12A-12C, 13A-13C, and 14A-14C. This happens as a result of the OD of the web member pushing outward on the LOD 28 of the domed disk 20 to compress and / or stretch the foam in this area in the horizontal direction. When the web structure 36 is completely flat, for example, at or near full compression, the resulting force on the web is horizontally outward and does not add significantly to the total vertical force of the assembly

[0235] A removable radially rigid and circumferentially expandable conical disc insert is envisioned to allow different inner disk geometry's to be used with different effects on the spring rate, for fine tuning adjustment. In this case, the apex 50 of the disk can be secured to the top of the conical foam domed disk by many different means including, for example, fasteners such as Velcro™ or adhesives.

[0236] An internal support structure 34 such as a radially rigid web member 36 may be of many different constructions, including an array of separate fingers or spokes, that may or may not be connected. The non-limiting example shown in Figs. 10A-10C, 12A-12C, 13A-13C, and 14A-14C provides sufficient radial rigidity, which is used to radially compress part of the foam conical disk as will be described shortly, without creating a high level of spring force on its own. To test this during the design phase, the radially rigid conical disk should compress to flat on its own, with no support from the conical foam structure, with less than 50%, less than 40%, less than 30%, less than 20%, less than 10% of the total force required to compress the foam conical disk without the radially rigid conical disk included in the assembly.

[0237] An example of an internal support structure 34 comprising a radially rigid conical disk web structure 36 is shown in Figs. 10A-10C, 12A-12C, 13A-13C, and 14A-14C, all illustrating a section view with an array of radially elongated elliptical through-holes, overlapping circumferentially with an array of inner elongated through-holes and outer elongated through-holes. A bridge section of material exists between the radial members around these through-holes in such a way as to allow a high level of radial rigidity which allows the web to deform without unreasonably high internal strain to allow circumferential expansion during compression of this disk.

[0238] When the foam dome and web components are assembled together, the total force of the assembly will be greater than the sum of forces to compress the two components individually. This is because the preferred assembly of the components uses the radial expansion of the bottom of the radially rigid conical disk (web) to compress and / or stretch a portion of the bottom section of the foam conical disk structure.

[0239] Fig. 9 shows the lower end 40 of the radially rigid conical disk (web) embedded in a concave annular receiving feature on the ID of a plane near the bottom of a conical foam domed disk 20. As a result, when the assembly is compressed, the foam will compress and shear, while the radially rigid conical disk will undergo minimal radial compression along the radial fingers, as it deforms from conical to flat and pushes down and radially outward on the inner surface of the foam conical disk that it is adhered to.

[0240] As illustrated in Fig. 11, the internal support structure can provide vertical and radial forces that change in proportion during travel. The reaction force of the horizontal compression of the conical foam disk is a vertical force initially, when the radially rigid conical disc is still in a conical shape. The closer the radially rigid support structure conical disc is to flat, as compression of the assembly progresses, the lower the component of vertical force that the radially rigid conical disc will produce as it pushes radially horizontally outward on the foam. As a result, the force of compressing the foam conical disc will be augmented by the vertical force generated by the radially rigid support structure conical disc pushing outward on the base of the foam. The radially rigid support structure conical disk (web) spring rate can be designed to have a greater variation in the spring rate including an increasing spring rate initially and decreasing spring rate partway through the compression travel. By designing the radially rigid support structure conical disc (web) to provide a percentage of the total vertical force, the characteristic spring rate of the entire assembly can be designed to provide anywhere from a very slight reduction in the spring rate if the conical foam disk is providing a great majority of the total force, to a spring rate that falls off moredramatically, or even a spring force that falls off partway through the travel if the radially rigid conical disc provides very little vertical spring force of its own, and the web pushing out on the foam results in a greater portion of the total spring force (as compared to the vertical force of the web itself) throughout the mid-part of the travel.

[0241] The contribution of the radially rigid support structure conical disk to the total spring force can be modified or optimized by the use of a non-extensible or elastic ring of material around the outside of the base of the foam conical disc.

[0242] The use of a ring around the base of the foam conical disc will increase the spring force resistance on a horizontal plane which opposes the flattening of the radially rigid conical disc. Without this ring, the foam base of the foam conical disc will be caused to stretch radially. With the ring, the base of the foam conical disc will stretch less in the radial direction and will be forced to undergo more radial compression as a result of the radially expanding inner radially rigid support structure conical disk (web) as it flattens. Both of these scenarios have the advantage of storing energy in the foam either through compression or stretching or both.

[0243] COMPRESSIBLE FOAM CONICAL DISK INSERT

[0244] Figs. 3A-3B illustrate a compressible internal support structure 34 comprising a foam or elastic solid inner conical disc. This internal support disc may or may not comprise one or more pockets or through holes to increase circumferential expandability. By making this insert from a more compressible material (as compared to other embodiments using, e.g. solid plastic) such as a higher density foam, it is possible to provide some of the same benefits as the radially rigid conical disc web insert, but with less radial expansion of the bottom of the foam conical disk. The compressible foam or elastic solid inner conical disc may be adhered to the inner or outer surface of the main conical foam disk or embedded inside the wall of the main conical foam disk.

[0245] ANGULAR STABILITY EMBODIMENTS

[0246] Figures 3A-3B show an embodiment of a midsole device 10 with a larger upper section of material 64 to increase the area of the top of the conical foam disk. The angular stability of the device is also increased by having the larger OD of material on the top of the disk.

[0247] MIDSOLE DEVICES WITH NON-CIRCULAR GEOMETRIES

[0248] An example of a non-circular embodiment of a disk is illustrated in Figs. 16A and 16B which illustrate reinforcing structures of an elliptic midsole device 10. Figs. 17A- 17F show some examples of non-round configurations including linear sections 84 ofdiagonal wall shapes 82 of a midsole with non-round midsole devices comprising non-round discs 80. Note that diagonal walls 82 are typically opposed across the length or width of the midsole by one or more oppositely angled diagonal walls to prevent horizontal shifting of the upper during compression. The configurations shown in 17A-17F have an additional damping foam layer 86 inside the disc with an outsole portion 88 which contacts the ground at full compression, in addition to the outer foam damping layer 90 and corresponding outsole 92 over the rest of the sole including the bottoms of the walls of the disc. Also shown in Figs. 17A-17F are ring members 94 around the discs which act as lateral expansion limiters 60 analogous to ring 62 in Fig. 1.

[0249] COMPLETE MIDSOLE

[0250] Figs. 18A-18C, 19A-19B collectively illustrate exemplar complete midsoles 300 with embodiments of midsole devices 10 embedded. Figs. 20A-20D illustrate how a multiplicity of midsole devices 10 can be incorporated into a midsole 300.

[0251] Figs. 21A-Figs. 21D collectively illustrate embodiments in which holes 330 in the outsole 310 may be used to prevent air from sealing in the conical chambers, thus allowing the open bases of the domes to act as openings allowing air to enter and exit the cavities. Horizontal airflow channels 320 in the bottom of the outsole 310 are used to enable airflow if walking on a smooth flat surface. Other airflow channels may also be used above the outsole to prevent suction if walking in water or mud. Where airflow ports are located above the outsole, the conical or other shaped foam structure may be air sealed on the bottom.

[0252] Forefoot Outriggers.

[0253] Figs. 25A-25E show exemplary embodiments of the present device with one heel disk and two forefoot disks. The forefoot disks and heel disks may each comprise variations on midsole devices 10 as set out generally herein. The forefoot disks may be at a combined width of the top of two of them somewhat side-by-side, and preferably slightly staggered fore and aft to align with the user’s (MTP) joints, with an upper combined width which is approximately equal to the width of the bottom of the upper. The flared shape of the disks, is then shown to protrude to the left, and / or the right of the upper by 10% or more, 20%, or more, 30% or more of the largest diameter of each device.

[0254] Lateral protrusions on the outsole, provide a complete platform for the bottom of the conical disks. By following the general shape of the upper for other areas of the outsole, minimal weight is added to the outsole. These protrusions may be flat to the ground, but are preferably tapered upward in the laterally outward direction to prevent early contact of the protrusions with the ground when running around a comer.

[0255] Shearing foam toe area

[0256] A non-limiting exemplary embodiment is shown in Figure 25D. In this embodiment, the midsole in front of the forefoot domes has a structure, made of a compressible or deformable material such as foam or an elastomer which is able to deform in a shearing regime forward or rearward relative to the upper. When the user strikes their heel to the ground before striking the forefoot, a forward shearing of the midsole toe area, relative to the upper, has been observed in prototypes, and results from the high travel of the midsole under compression and the vertical travel of the top of the foam domes relative to the outsole and the taper that may exist in a midsole of the device. A shear-deflection block or blocks as shown here, store the fore-aft shearing energy and releases it back into the upper by propelling the upper forward during toe off as the toe of the midsole expands and returns from the shear-deflected shape to the original at-rest shape.

[0257] Tapered foam domes

[0258] The high compression ratio (the compression travel for a given stack height) of embodiments of the present device results in an unusually low profile midsole under full compression. It is typical, for large stack height in a conventional shoe, such as with a 40 mm stack height at the centre of the users heel, to have a maximum change in thickness, at rest, between the heel and the toe, of 4 mm to 10 mm.

[0259] It has been found by experimentation that a reduction in thickness, at rest, of the forefoot of device shown here, under the medial and lateral metatarsophalangeal (MTP) joints, of greater than 10 mm, greater than 11 mm, greater than 12 mm, greater than 13 mm, greater than 14 mm, greater than 15 mm, greater than 16 mm, greater than 20 mm, offers a better user experience for some users. This is because the unusually high percentage of compression travel from this technology would result in the toe being uncomfortably high, compared to the heel at full compression if a standard 4 to 10 mm, forefoot thickness difference was used when the shoe is at rest.

[0260] The total compression of the midsole under the heel is higher than the total compression of the midsole under the forefoot. When wearing the shoes, it takes less force than a conventional midsole to do the initial compression of the heel and forefoot, so the shoes will feel like they have a more conventional 4 to 10 mm reduction in thickness of the toe when they have a downward force applied to the them by the user, as long as they have a greater than 10mm drop from heel to toe when not weighted.

[0261] In Fig. 25E it is also shown that a slight taper on the top, and / or bottom of one or more foam domes may provide a more natural feel to the user and reduces pressure points along the leading edge of a non-tapered dome.

[0262] For some applications, it is considered beneficial to also taper the web inserts as well.

[0263] The domes and / or webs may be tapered on the top and / or the bottom of the dome.

[0264] ONE PIECE GUIDE SUPPORT STRUCTURES, FOAM DOMES AND OUTSOLE

[0265] In an embodiment, one or more of the foam domes are manufactured as a one- piece construction together with the outsole. The domes may also be of a one-piece construction with one or more other domes and a foam or other material layer above them and on the bottom of the upper. This may be more difficult to manufacture, however. The guide support structures and / or ring springs may all be one piece as well. Connection elements may be used. This may be beneficial for simplifying assembly and overall stability of the midsole.

[0266] COMPRESSION-BIASED DAMPING

[0267] A benefit provided by various embodiments of the conical foam domed disk 20 (with or without the internal web structure and with or without the ring spring) is the delay of energy return until later in the stance, which results from the device’s non-linear stiffness throughout its expansion (specifically that the expansion force will have a reducing spring force part way through the expansion or even an increase in spring force part way through the expansion). This is beneficial to delay the energy return, but this attribute is also seen in the device’s compressive stiffness, resulting in a reduction of the spring rate or even a reduction in the spring force, part-way through the compression loading. This falling off of the spring rate or possibly, the spring force, during compression, can cause the midsole to bottom out more abruptly than desired. As such, a construction which minimizes or eliminates the dropoff in stiffness during compression is desirable, but it is also desirable not to increase the spring force near the bottom of the travel during the expansion so the midsole can remain more compressed during midstride and return much of this energy later in the stance.

[0268] One solution to this issue is the inclusion of compression-biased damping elements 340 in the device 10, as illustrated in Figs. 24A-24C. After being compressed, the damping element / s are not caused to expand by the rest of the structure during midsole expansion, so the compression biased damper will contribute much more to the compressivephase than the expansive. This can be seen in Fig. 32, which displays a comparison of the load vs displacement profiles for a single device with and without the inclusion of compression-biased damping element / s. The more linear compression curve is desirable and provides greater comfort and impact reduction to the user. The more linear curve, however, translates to losses in efficiency because the damping element is dissipating the additional energy rather than storing it and releasing it later in the stride where it could provide additional propulsion. This loss of energy is only during compression, however, and is seen as a reasonable trade-off between performance and comfort.

[0269] Midfoot power dome (Alternative or in addition to damping)

[0270] In an embodiment, the integration of multiple conical foam disks into a single shoe, staggering their effects such that the variable spring rate of each disk complements the previous disk. Fig. 33 discloses a non-limiting example configuration of four conical foam disks according to the principles of this device: rearfoot device 370, midfoot device 372, lateral forefoot device 374, and medial forefoot device 376, though many other configurations are possible and anticipated by the inventors. In the exemplary configuration, contact is expected to begin at device 370, progress to device 372 before device 370 is fully compressed, then progress to begin compressing devices 374 and 376 in parallel before device 374 is fully compressed.

[0271] The graph in Fig. 34 depicts a non-limiting example of an estimation of the load response provided by each midsole device 10 and the timing of their operations throughout stance, as well as a trace of the load response provided by an exemplary independent rearfoot device for comparison. Fig. 34 shows estimated vertical load for a rearfoot device 460, a midfoot device 462, a forefoot lateral device 464 and a forefoot medial device 466. Total vertical load 468 is the sum of the loads of the four midsole devices.Independent rearfoot device load 470 represents the load response of an exemplary independent rearfoot device. The total vertical load line 468 is smoother than the single heel device comparison line (independent rearfoot device load 470) which has a more significant peak which would be felt by the user as a higher impact event at the end of the heel strike phase.

[0272] The rearfoot and forefoot devices are located to provide optimal support to a user’s foot, with the rearfoot unit supporting the heel and the two forefoot units supporting the medial and lateral metatarsophalangeal (MTP) joints. The midfoot device’s anteroposterior position is defined such that it begins compression just before the rearfoot unit’s load response flattens (Fig 34 - Point A). Accordingly, the rearfoot unit’s reduction instiffness is supplemented by the introduction of the upward force provided by the midfoot device so the user does not experience a decrease in support underfoot, as the spring rate of the heel device falls off, resulting in a smoother transition (known as “ride” in the industry) as the user’s weight transfers along the midsole from the heel to the forefoot. This effect can also be applied in the transition between midfoot to the forefoot (Fig 34 - Point B). The midfoot unit’s mediolateral position is typically defined such that it is centered under the arch of the foot, though this can be adjusted as desired to compensate for gaits exhibiting over / under-pronation, for example.

[0273] An advantage of this approach over an additional damping component, is that the compression energy of the midfoot disk is stored and released, to increase propulsion, rather than being dissipated with a damping element.

[0274] Damping element / s may still be used together with the midfoot disk configuration with various effects.

[0275] WEB MEMBER

[0276] The inventors have shown, through FEA analysis and empirical testing, that the performance of the device can be improved in several respects with the addition of a circumferentially and / or horizontally expandable member of a higher compression stiffness in the radial / diagonal cross section direction as compared to the conical foam disk. This web structure is adhered or otherwise attached to the inside, and / or outside of the conical foam disk or it may be embedded into the diagonal foam wall of the conical foam disk. A nonlimiting list of benefits of the addition of the web structure in some embodiments is to increase the internal strain in the foam during compression of the assembly to increase the spring force of the assembly, to increase the lateral shear stability of the assembly, and in some further embodiments, to increase the non-linearity of the spring force during compression as a result of the flattening of the web toward full compression to direct the vertical compression forces of the user into a horizontal force with decreasing vertical resistance toward and at full compression. The web structure may deform to a shape that is past horizontal, at full compression, such that some of the internal strain will be acting to push the ID of the web downward instead of upward. This may serve to further reduce the upward spring force of the assembly, part way through the compression travel for a more significant delay in the energy return during rebound.

[0277] While the web can increase the spring force and other performance aspects of the conical foam dome, there is a symbiotic structural relationship between the two where the foam dome also provides enough bending stiffness to the web structure to prevent it fromfully buckling in the radial / diagonal direction at full load. This allows the web to be a very lightweight structure because it does not need to prevent its own buckling. In fact, the web has been shown, in some configurations of the device, to experience a controlled buckling behavior where it is forced, by the deformation of the conical foam disk during compression travel of the assembly, to pass from a straight or concave shape through to a convex curved shape at full compression. This is a buckling motion, but it is controlled and limited in its extent by the stiffening effect of the foam. This effect is shown in Figs. 42A and 42B in which the web structure 36 buckles as the domed disk 20 compresses during travel.

[0278] The web may be of many shapes to achieve a range of desired effects. A nonlimiting exemplary web structure, shown here, has a non-continuous circumferential shape, preferably at any vertical plane, although a continuous shape at some, but not all vertical planes may work, as well as a continuous shape at any or all vertical plane positions as long as there is minimal or no uninterrupted circles of material. This could be true of, say, a circumferential or horizontal wave or accordion shape for all or part of the web structure, as illustrated in Fig. 36.

[0279] In the cross section of the web in Fig 26B, a first somewhat radial / diagonal finger is connected together at the top / ID to a second adjacent finger to one side of said first finger but not the other side of said first finger. The bottom of said first finger is also connected to an adjacent finger to one side but not the other. In this non-limiting example, every second finger is attached by a circumferential bridge structure to every third finger at a different radial / diagonal position such that the fingers can bend and twist during vertical compression of the web in a way that provides minimal resistance of the web to vertical compression. An exemplary representation of such a web structure is illustrated in Fig. 35. The result is a web structure which does not add a high level of spring force to the conical foam disk except by virtue of the radial forces which are transferred to the foam through the additional strain on the foam which is caused by the web.

[0280] It has been shown by experimentation that when the fingers (AKA spokes) of the web are thick enough to provide the required performance enhancement to the conical foam dome, the bridge members, if they are the same thickness of the fingers, become too stiff to allow flattening of the web without adding to much spring force to the conical foam disk part way through the travel. Circumferential bridge features may therefore be radially thinner than the adjacent conically / radially extending fingers. This thinner section allows the web to flatten with less force while still maintaining the radial / conical stiffness of the finger members.

[0281] Many different web geometries are possible and anticipated by the inventors. Structural principles that have been determined to be beneficial, are higher stiffness in the radial / conical direction and lower stiffness in the circumferential direction. An interrupted ID and OD of the web are also beneficial to allow the disk to flatten without exceeding a desired stress threshold in the web material. The web is preferably of a stiffer material than the foam dome material.

[0282] STACK HEIGHT

[0283] In a non-limiting exemplary embodiment, the conical foam disk has a total height of 35 mm.

[0284] The maximum legal stack height for a racing shoe in 2024 under some jurisdictions is 40 mm. This leaves 5 mm of material for the upper and the outsole, which may be considered to be quite thin for these two components combined.

[0285] To account for this, Fig 25E and 26E show the lower 2 to 5 mm or more of the device protruding into the outsole. The lower surface of the device may even contact the ground and may also be coated with a non-wearing material similar to the rest of the outsole.

[0286] Fig. 22 shows a partially disassembled outsole to show the domes and low ground contacting surface.

[0287] The ring spring may or may not be used and it, if used, it may be considered advantageous to create a flange on the ring spring as shown in Fig 26E, which can be used to provide additional surface area for adhering the dome to the outsole as shown in the image below.

[0288] In this case, it is considered advantageous to achieve some performance characteristics, to provide a ring of material on the top of the outsole and around the OD of the bottom of the dome. This ring may also include a cylindrical feature, which captures more of the dome material above and / or below the flat ring.

[0289] The dome or domes may be manufactured as one piece with the outsole, as shown in Figs. 17A and 17B.

[0290] Airflow.

[0291] If the bottom surface of the dome contacts the ground, it may be important, in some embodiments, to provide airflow channels, so air can be discharged and drawn back into the device with minimal or a predetermined resistance.

[0292] In a non-limiting exemplary embodiment, grooves, channels, or pockets 340, as illustrated for example in Fig. 22, are shown in the bottom of the dome, which communicate with grooves or channels or pockets in the outsole which are open toatmosphere around the ground contact of the outsole, as illustrated for example in Figs. 21A- 21D, to provide an air flow path to and from atmosphere during compression and rebound of the device

[0293] In embodiment, one or more airflow channels are provided above the outsole on the conical dome to allow air or water, etc. to be discharged from the dome during compression and for air to be drawn back into the dome during expansion.

[0294] All of these measures provide that a suction cup effect is not created under some conditions.

[0295] Also shown in Figs. 1 and 2 is a variation on the compressible foam insert at the apex of the dome and web. This insert 50 may be of the same or different foam than the dome 20 and may be a separate component as shown, or contiguous with the dome 20. This apex insert 50 provides resistance to the ID tips of the web fingers from moving radially inward, while still allowing them to move inward enough (as a result of the radially inward compression of the foam insert), to reduce the maximum stress on the foam dome at the opposite and outer ends of the radial / conical fingers. Two further embodiments illustrating a foam apex insert 50 are illustrated in Figs. 39 and 40. In Fig. 39, foam apex insert 50 may comprise the same, or higher or lower durometer foam than foam material of domed disk 20, or may be of a different material. In Fig. 40, foam apex insert 50 comprises an accordion shaped ring 51 around apex insert 50. An accordion shaped ring (or comparable structure) may compress vertically with minimal force while maintaining desired radial stiffness and, therefore, allow a lower durometer apex insert 50 to be used for more comfortable bottom out performance.

[0296] CHECK VALVE

[0297] The airflow channel or channels in Figs 27E and 27F may also be provided with means to achieve greater airflow restriction during compression than during rebound.

[0298] This includes a complete or partial occlusion of one or more airflow channels during compression such that an air damper is created.

[0299] In a non-limiting exemplary embodiment, airflow out of the cone volume is restricted during compression. During expansion of the cone, airflow is allowed into the cone for example through a one-way check valve 350 at the apex of the cone from the inside of the upper. This will promote one-way flow of air to cool the user’s foot without drawing in water or dirt from the ground. In this case, it is desirable to have one or more air discharge ports 360 in the wall of the conical dome. These can be constructed with an inserted, one-way check valve 360 A, or may simply be openings shaped with a sealing interface and optionallya taper which seals during compression and unseals during expansion due to the deformation of the dome and or the differential air pressure.

[0300] If one or more of these openings are situated at the back of the dome, they can be shaped to collapse as a result of the heel strike deformation and restrict airflow when the back of the dome is compressed. As the user’s heel rolls off of the back of the dome toward the forefoot, the shape of the back of the dome changes such that the openings open again, and airflow with or without minor restriction is allowed back into the dome.

[0301] It may be preferable for some applications, to have a separate, non-occluding air inlet and discharge port 360B. The purpose of this non-occluding airflow chamber is to provide a controllable and even adjustable (with some adjustment means by the user) discharge flow restriction that is not affected by the occluding valve or valves or opening or openings during compression. This allows for a controlled air damper during compression without requiring significant damping of the expansion of the disk due to the non-restricted airflow back into the dome from the valve or valves or opening or openings.

[0302] The volume inside the dome can be constructed to provide a small enough final volume that any water that could be drawn into the dome through the slots will be forced out mechanically through positive displacement and / or via the high flow rate of air exiting the dome. Airflow restriction in and out of the dome may be controlled by passive valves such as restriction valves and one-way check valves. Airflow restriction in and out of the dome may be controlled by active valves or restriction means such as a miniature electronic proportional valve such as but not limited to a MEMS device or a piezoelectric valve that can be controlled and adjusted by a CPU with inputs from an algorithm and / or the user.

[0303] GEOMETRIES

[0304] Several different geometrical definitions of various embodiments of a midsole device are described here, including methods of characterizing if a particular geometry is within a range of geometries to provide a significant portion of one or more performance benefits of the device.

[0305] DESIGN OF EXPERIMENTS (DOE)

[0306] A DOE was used to determine the range of geometries which provide one or more of the benefits of midsole device embodiments. The DOE used various geometries of midsole devices to evaluate how different geometry features contribute to different performance metrics. The DOE used statistical methods to evaluate the effects and interactions of geometric features on selected performance metrics. The following geometricvariables are applicable to various configurations of a foam domed structure: outer angle; maximum width from centerline; top wall thickness percentage of the max width; bottom wall thickness percentage of the max width; material stiffness scaling; functional height; and aspect ratio. A definition for each of these geometric variables is provided here for the case of a midsole device 10 comprising a foam domed disk. Various geometric parameters for are illustrated schematically for a foam domed disk in Fig. 28. In some variations of a midsole device which comprise different shapes and configurations for the foam structure, there may be corresponding variations upon the applicable geometric features and geometric variables: for example, a foam domed disc 20 with a curved exterior surface 30 may require a corresponding modified definition of the outer angle.

[0307] The outer angle 410 may be defined as the angle defined between the exterior surface 30 and the vertical centerline of the foam domed disk 20 of the midsole device 10. The maximum width 420 from centerline may be measured at the widest point of the hollow structure, perpendicular to the centerline. If the dome is a non-round shape, an average radius should be taken circumferentially at each height and the maximum average radius will be taken as the maximum width from centerline. The maximum width is held constant in this exemplary DOE and used as a scaling factor for the other variables to express them in dimensionless terms. Top wall thickness percentage of the maximum width is calculated from the top wall thickness 430 at the top of the midsole device expressed as a percentage of the maximum width from centerline. Bottom wall thickness percentage of the maximum width is calculated from the bottom wall thickness 440 at the bottom of the midsole device expressed as a percentage of the maximum width from centerline. Material stiffness scaling is calculated as a scaled stiffness of an exemplary material such as, but not limited to, a Pebax foam with a durometer of approximately 35Shore C. Functional height 450 was measured as 50% of the midsole device height 460 in which the midsole device height 460 is the separation between the lowest point of the outsole and the foot-receiving surface inside the upper. Aspect ratio is defined as the ratio of the functional height of the structure divided by the maximum width from centerline.

[0308] Each geometry specified in the DOE and described by the parameters above was modeled in a computer-aided design (CAD) program and imported into a finite element analysis (FEA) program. The FEA used a thin 2D cross-section with axisymmetric constraints to model the deformation behavior of the geometry as it was compressed by a rigid upper piece to measure the reaction forces. A target of 1100 N of reaction force was used.

[0309] Some performance metrics that were used for evaluation included: propulsive energy percentage of total energy return; slope of the curve at the inflection point; absolute energy return for a given force; absolute energy return for a given travel; travel for a given force; force at various points of the force displacement curve. Propulsive energy percentage of total energy return is the percentage of energy return that serves to propel the user forward at midstride. Midstride is approximately: (1) the point at which the center of mass of the user crosses the ankle after which energy returned by the device would contribute to propelling the user forward and (2) the point where the center of mass of the user reaches its lowest vertical point and begins moving upwards, after which energy returned by the device reduces the energy required by the user to move their center of mass upward.

[0310] These performance metrics were chosen as they reflect some critical metrics when evaluating shoe performance. The geometry variables were chosen as they were shown to provide the biggest effect to performance through testing. This combination of attributes can fully define the form of the device assuming a given max width.

[0311] The DOE takes a given range of geometries and specifies a series of experiments to conduct with various combination of the geometry. A response surface methodology (RSM) was used for defining the experiments and subsequent analysis. An RSM accounts for non-linear relationships between the geometry attributes and the performance metrics. Each of the following variables were varied through the ranges set out here. The outer angle was tested from a low of 1° to a maximum of 49°. The top wall thickness percentage of the max width was tested from 18% to 42%. The bottom wall thickness percentage of the max width was tested from 18% to 42%. Material stiffness scaling was tested from 0.5 to 1.5. Aspect ratio was tested from 0.46 to 0.94.

[0312] Key Geometry Parameters

[0313] In the DOE analysis, three geometric parameters were identified as having a statistically significant impact on the performance metrics: outer angle, bottom wall thickness percentage of the max width, and aspect ratio. Of these three parameters, bottom wall thickness only has a limited range of possible values as it is constrained by the angle and aspect ratio, and can be determined as a last step through FEA analysis or experimentation. Two geometric parameters identified by the DOE that can be used to define the regions of benefit of the device are therefore the aspect ratio and outer angle. Other parameters may also be used, and the significance of parameters will depend on the parameters studied.

[0314] Propulsive Energy

[0315] One of the key benefits of some embodiments of this device is that the geometry results in more of the energy return being delivered later in the user’s stride. This is a benefit as then a portion of the energy return acts on the user to propel them forward instead of pushing them backwards. For example, the propulsive energy portion of total energy return may be greater than 30%, 35%, 40%, 45% or 50%. When this occurs, the majority or at least a significant portion of the energy return of the device is used to propel the user forward. By comparison, for a simple spring following Hooke’s law, and stipulating a propulsive energy threshold of 50% of the max force as discussed below, would have a propulsive energy return of 25%.

[0316] Experimentation has shown that for a device that can compress approximately 70% of its total height when the user actuates with their heel, the propulsive energy threshold is believed, by the inventors, to occur when the force drops to about 50% of the max force of the compressed state. The propulsive energy threshold will vary based on the weight of the user and the size of the device and is not limited to specific compression ratios. While the definition provided here has proven to be a useful tool for helping to quantify the relative benefit of different geometries, it should be regarded as an indicator for which geometry ranges offer the most benefit, rather than an absolute measurement. The FEA analysis was further validated by comparing against force-displacement curves gathered during laboratory testing, giving the inventors confidence in the results.

[0317] Fig. 29 is a contour plot created from the results of the DOE showing the propulsive energy percentage of total energy return as a function of the outer angle and bottom section wall thickness percentage of the max width. These 2 variables were determined to have a statistically significant effect on the propulsive energy percentage in the DOE.

[0318] As can be seen in the contour plot, the technology crosses the 0.50 ratio of propulsive energy to total energy above 15° outer angle and various bottom wall thicknesses. A >15° outer angle may serve as the minimum outer angle for some embodiments for this aspect ratio because at this point the device has greater than 50% of its total energy return propelling the user forward. However, other target percentages of propulsive energy returned propelling the user forward may be used.

[0319] As previously described, the primary geometric parameters affecting the performance of a device are its outer angle and aspect ratio. Therefore, the combination of accepted values for these parameters can best be described in a plot showing aspect ratio against outer angle. Due to practical considerations, the outer angle of the device must beabove 10° and the aspect ratio must be below 1.0, as values outside these limits can compromise the device’s stability. Further, the outer angle of the device must be below 70° and the aspect ratio must be above 0. 17, as values outside these limits can result in devices which fail to exhibit one or more of the described benefits. Accordingly, the acceptable values of these two parameters can be plotted as shown in Fig. 43A. The shaded region 500A represents the region defined by having an outer angle greater than 10° and less than 70° and having an aspect ratio greater than 0. 17 and less than 1.0.

[0320] However, certain combinations of these parameters result in negative widths of critical components and as such are geometrically impossible. Removing the affected area yields the updated plot shown in Fig. 43B. The shaded region 500B represents the remaining acceptable values after the exclusion of implausible geometries from the shaded region 500A. Additionally, other combinations of these parameters do not produce geometries which provide the desired performance, as measured by the Propulsive Energy Percentage (PEP)ZPropulsive Energy Ratio (PER) metric previously described. Further limiting the space to those parameter sets which produce greater than 30 / 35 / 40 / 45 / 50% PEP results in the plot shown in Fig. 43C. Shaded region 500C represents the remaining portion of shaded region 500B after the exclusion of the parameter space which produces less than 30% PEP, i.e. falling below the 30% PEP line 502. Further limited regions could be defined by: excluding parameters which produce less than 35% PEP, i.e. falling below the 35% PEP line 504; excluding parameters which produce less than 40% PEP, i.e. falling below the 40% PEP line 506; excluding parameters which produce less than 45% PEP, i.e. falling below the 45% PEP line 508; and excluding parameters which produce less than 50% PEP, i.e. falling below the 50% PEP line 510.

[0321] The contours shown are defined by the following equation, derived using a parametric model developed from the results of FEA:

[0322] R = 5.5877 - 0.039980 -7O.OOO115302- 0.32460 + 31.0415 - 0.0960 / TPEP,

[0323] where R represents the aspect ratio, 0 represents the outer angle, and TPEPrepresents the PEP which the contour describes. Note that the final area depicted does not define the limits imposed on the parameters in the claims but instead serves to indicate the extent of what geometries may be considered viable and desirable according to some embodiments.

[0324] The DOE predictions were further validated by conducting tests of a sample and measuring force as a function of displacement on a test bench and calculating the propulsive energy ratio of the total energy and superimposing on the contour plot above to compare with the DOE prediction, as shown in Fig. 30.

[0325] The outer circle in Fig. 30 shows the calculated test results that indicated a propulsive energy ratio of -0.58 for a geometry with a 32° outer angle and 0.225 bottom wall thickness ratio. As can be seen the test data matches the DOE prediction denoted by the inner circle (-0.58). OUTER WALL ANGLE DEFINITION

[0326] Many examples given here are for a circular or non-circular dome structure. Similar principles may be applied to a linear or curved section of a diagonal foam structure. Assuming a flexible / compressible resilient foam dome structure, the outer angle is one of the key parameters for certain approaches of defining some geometries and some embodiments that achieve benefits of the present device. If a vertical cross section does not include a straight section of wall to measure the angle, an averaging method is described below under the heading “determining a simplified structural representation”; if a vertical cross section includes extraneous features or additional lower durometer foam, such as for aesthetic purposes, an approach to determining an equivalent angle of single durometer foam is described below under the same heading. One or more of these approaches may be used to identify if a device is within the claimed range of this disclosure, and a geometry and construction is considered to be within the range of this disclosure if it is described by at least one of these approaches. A typical shoe construction requires an upper to receive the user’s foot, a midsole and an outsole to interface with and grip the ground. The upper and outsole may have a wide range of constructions and use a wide range of materials; to keep these components from complicating these approaches the vertically measured center 50% of the device may be used for one or more of the approaches of determining if a geometry is within the range of geometries disclosed here. These approaches are guidelines that anticipate variations to the device which will still result in a functionally equivalent design. Many other variations are anticipated by the inventors such as holes or fins or textured surfaces or straight or spiraled slots that may or may not have a significant effect on the performance and that may or may not put a geometry inside the range of geometries disclosed here. Persons skilled in the art will be able to determine if variations not specifically listed here create a device with the functional equivalence of the range of midsole geometries and constructions disclosed here.

[0327] NON-INTERFERING COLLAPSING GEOMETERY

[0328] Another possible consideration, which may be used instead of, or in addition to, the outer angle consideration, is the degree to which the diagonal wall structure is free to collapse vertically downward. In an embodiment, the diagonal wall structure is free to collapse vertically downward without interference with another adjacent diagonal structure, for 80% or more, 70% or more, 60% or more, 50% or more, 40% or more, 30% or more, 20% or more, 10% or more of its vertical travel. In some embodiments a portion of the foam structure wholly forming, or including at least parts of, 80% or more, 70% or more, 60% or more, 50% or more, 40% or more, 30% or more, 20% or more, 10% or more of a height of the foam structure vertically overlaps the cavity.

[0329] DETERMINING A SIMPLIFIED STRUCTURAL REPRESENTATION

[0330] Assuming a flexible / compressible resilient foam domed disk such as a hollow frustum structure, the outer angle is a critical consideration used in defining embodiments achieving one or more benefits of the present device. It is anticipated by the inventors that variations to the outer wall shape are possible such as holes or fins or ribs or grooves or the addition of lower durometer compressible material, for example. The hollow frustum may also be irregularly shaped (such as but not limited to, non-round, faceted etc.) without a single consistent cross-section. An exemplary approach to characterizing a simplified structural representation is illustrated in Figs. 31A-31C.

[0331] To compute the outer angle (0eff) of an embodiment possessing both primary 470 and secondary 474 materials or having an irregular shape, the following is an example of a process that may be applied to generate a simplified structural representation (SSR) resembling a hollow conical frustum. The outer angle is given by the SSR’s conic half angle.

[0332] Truncate the device (an actual device or, for example, a CAD model of the device) by removing the top and bottom 25% by height, yielding the central region 474 with half the height of the original device. The height of the device is defined as the distance between the lowest point of the outsole and the foot-receiving surface inside the upper (under an insole if a removable insole is present) also referred to as the stack height, along the device's central vertical axis 476. This removes the complexity of accounting for the many possible variations in the outsole component and upper component and extracts the core geometry involved in deformation behavior. Identify the primary material, defined as the highest durometer compressible foam material which spans the full height of the truncated body, and remove all materials radially inward of it (this is to eliminate the effect of other foam materials inside the dome such as, but not limited to lower durometer damping foam). Extract a representative cross-section of the remaining body / s on a radial / axial vertical plane.For continuously rotationally symmetric devices, all cross-sections are equal by definition, so any radial vector can be used. For discretely rotationally symmetric devices, an average cross-section can be determined by someone skilled in the art of shoe design. Identify the angle of each material's outer wall with respect to the vertical axis. If a material's outer wall is linear, this angle can be identified by inspection. If a material's outer wall is not linear, this angle must be calculated using a least squares regression. The surface must be discretized using a sufficient number of points to capture all major features. The points must be distributed equally along the vertical axis, NOT along the path length of the surface. Identify the average radial width (w , height (h , and durometer (d of each material. For materials which don't span the full height of the truncated body, only compute the average radial width across the material’s actual height. Calculate the effective angle of the structure as the weighted average of each material, according to the following equation:

[0333]

[0334] Calculate the effective width of the structure as the weighted sum of each material, according to the following equation:

[0336] where hrefand dref represent the height of the truncated body and durometer of the primary material, respectively. Construct a trapezoid whose inner wall is described by the inner wall of the primary material and whose outer wall is described by the effective angle and width calculated above. The effective width should be applied at half the truncated body’s height, such that the resultant trapezoid yields an average radial width equal to the effective width.

[0337] Revolve the trapezoid about the central vertical axis to produce the device's SSR.

[0338] The outer angle of the SSR is used in the DOE to determine the useful range of geometries which produce one or more benefits of the device.

[0339] After the outer wall angle is determined, the inner wall angle can be determined by FEA or experimentation.

[0340] If a device has an outer wall angle when at rest of 15 degrees or less from vertical, the structure is unlikely to provide a high level of lateral shear stability which is preferred for comfort and performance on uneven terrain or when moving laterally, although it is believed by the inventors to be possible to provide lateral shear stability by anothermeans, so that an outer wall angle of less than 15 degrees from vertical may be usable for some applications.

[0341] With the above in mind, the device is shown to provide the most benefit at an outer wall angle from vertical of >10°, >11°, >12°, >13°, 14°, >15°, >16°, >17°, >18°, >19°, >20°, >21°, >22°, >23°, >24°, >25°, >26°, >27°, >28°, >29°, >30°, >31°, >32°, >33°, >34°, >35°, >36°, >37°, >38°, >39°, >40°, >41°, >42°, >43°, >44°, >45°, >46°, >47°, >48°, >49°, >50°, >51°, >52°, >53°, >54°, >55° measured over 40% or more, 50% or more, 60% or more,

[0342] S-CURVE DEFORMATION

[0343] In another way of defining examples of geometries that conform to the principle of the device disclosed here, an existing shoe or shoe CAD design is cross sectioned with a vertical plane such as, for a heel device a plane that crosses the center of a user’s heel position. This cross section is then further split across its symmetry line / central axis. A straight line can be plotted in-between the inner and outer walls of the geometry, with the line angle selected such that the line acts as a bifurcation line between the inner and outer wall angles. The top and bottom 25% of the geometry is to be excluded when generating the line angle, but the line is to be extended until it contacts the bounding edges of the cross section which includes the top of the foot or insole receiving surface and the bottom of the outsole. In cases where the inner and outer walls are curved and / or otherwise non-straight, and perfect bifurcation is therefore unachievable, the midpoint of the bifurcation line should be determined first, with an angle selected to create as close to a bifurcation line as possible. Fig. 41 A shows one example of this bifurcation line.

[0344] Two horizontal rigid plates extending beyond the bounds of the cross section are bonded to the body in the FEA program; with one bonded to the top face of the foam member, and the other to the base of the foam member. These bodies form surfaces that contact the deforming foam member at high compression. The top compression plate typically contacts the outer wall at high compression, while the bottom face contacts the inner wall as the device bottoms out. The diagonal foam member is then vertically compressed, or compressed in a height direction representing an actual likely direction of compression in use, to 70% of the member’s total height while constraining the top compression face and bottom face of the foam structure to zero lateral motion, such as in the FEA program, and the deformation of the FEA nodes comprising the straight bifurcation line (if a CAD model) or actual points (if an actual device) are used to describe the resulting curve. Material line 480 in Fig. 41 A represents either a straight bifurcation line (if a CAD model) or line between actual points (for an actual device). If an S-shaped curve in material line 480 results, and if thatcurve passes through a plane perpendicular to the height direction 3 times or more (as illustrated in Figs. 41B and 41C), or crosses through a plane that is angled relative to the height direction in the cross section plane, a total of three times or more (steeper in this example means rotated clockwise) such as 1 to 2 deg, 2 to 3 deg, 3 to 4 deg, 4 to 5 deg, 5 to 6 deg, 6 to 7 deg, 7 to 8 deg, 8 to 9 deg, or 9 to 10 deg, 10 to 11 deg, 11 to 12 deg, 12 to 13 deg, 13 to 14 deg, 14 to 15 deg, 15 to 16 deg, 16 to 17 deg, 17 to 18 deg, 18 to 19 deg, 19 to 20 deg, the device is determined to be within the bounds of an embodiment of the present device. In Fig. 41C, exemplary lines are shown at 0 deg, as well as at +15 degrees and -15 degrees to clarify the angle range referred to above.

[0345] Note that while the original straight line may extend above the midsole through the bottom of the upper (not shown in Fig. 41 A) and below the midsole to the bottom of the outsole (shown above) the S-shaped curve will cross the horizontal or angled line a minimum of three times within the midsole. This internal S-shaped curve is a beneficial feature in various embodiments of a midsole device. Embodiments with compression of a foam midsole producing this type of internal S curve, may provide increased compression travel for a given stack height. A conventional foam midsole that lacks the horizontal S-curve as described here, at full compression, might not provide the full delayed energy return which results from a reduced spring force or dramatically reduced spring rate part-way through the travel but may still provide other benefits such as high travel and lateral shear stability.

[0346] The inventors have found through FEA analysis and experimentation that many of the devices in the range of outer wall angles described here can be designed to exhibit this S-Shaped curve when compressed.

[0347] EXTRANEOUS GEOMETRY

[0348] It is anticipated by the inventors that the principles of the device disclosed here may be realized with the use of complex geometry such as by creating a diagonal foam wall member with vertical or horizontal or diagonal grooves or features on the inner or outer surfaces, or by creating fins or flanges or other protrusions, or by creating a waved shaped inner or outer surface, or by any other additional material or removal of patterned or nonpatterned material. In some cases, the cross section along a single vertical plane may not accurately represent the general construction of the diagonal member with regard to the performance characteristics it would provide. In such cases, the geometry can be represented by the average cross section of a linear or rotational array of planes with cross sections on each plane that are averaged together to reasonably represent the general construction of a section of a midsole diagonal foam structure. The number of arrayed planes and the spacingof the planes can be determined, by someone skilled in the art, to reasonably represent the characteristics of the midsole device structure with regard to the geometry of the device disclosed here. An example for a dome structure in the heel might be 10 planes spanning 180 degrees of a dome but more or less planes at greater or lesser angles may be used. An example for a more linear structure may be 10 planes spanning 40 mm along the length of a diagonal section but more or less planes at greater or lesser spacing may be used.

[0349] When an average geometry that someone skilled in the art would determine to be representative of the general structure, such as of the heel section of the midsole or the forefoot section of the midsole, any of the methods / ways of determining the geometry can be used to determine if a section of a shoe midsole falls within a range of geometries claimed for various embodiments.

[0350] Different embodiments may fall within the range of a different one or more of these ways of measurement without necessarily falling within the other(s). Different ways of determining the geometry of a device disclosed here are more suitable for specific embodiments of the device. These and other approaches to extraneous geometries are further detailed in the section Confounding Geometries, further below.

[0351] BUCKLING MEMBERS

[0352] In some embodiments, a shoe midsole may comprise plural buckling members which collectively provide a desired force response to compression of the midsole. Each buckling member may be formed of a resilient material such as resilient foam or a compressible matrix material. Each buckling member may have any shape suitable for buckling, for example a linear shape. The bucking members may extend between the upper and the outsole. As the midsole compresses, the buckling members buckle providing reducing resistance to compression. After the buckling occurs, further compression may occur by direct compression of the material of the buckling members between the upper and the outsole.

[0353] In some embodiments, the buckling members may include linear members which are oriented diagonally. A schematic diagram of such a buckling member 600 is shown in Fig. 44. As shown in Fig. 44, buckling member 600 extends diagonally between upper 602 and outsole 604. A vertical dashed line 606 indicates that the portion of the midsole on the other side of the dashed line is not shown. As the midsole compresses, the buckling member 600 first buckles as shown in Fig. 45 and then directly compresses as shown in Fig. 46. As shown in Fig. 44-46, the compression of the midsole is substantially vertical during this process. This is desirable not only for stability reasons but also for allowing the compressionto take the form of buckling. In particular, it is desired that the top 608 of the buckling member 600, typically connected to the upper 602, not move in an unconstrained manner to the right relative to the bottom 610 of the buckling member 600, typically connected to the outsole 604. If the top were free to slide to the right in the point of view of these figures, the buckling member would face a strong bending force from the start of the compression of the midsole and would thus provide less initial resistance. The vertical compression allows the buckling member to initially resist with compressive stress substantially oriented along the length of the member, which causes a stronger initial resistance to compression which becomes weaker or that increases at a lower rate for part of the travel as the buckling member bends as shown in Fig. 45.

[0354] Various methods may be used to constrain relative horizontal movement of the top and bottom of such a diagonal buckling member. In an embodiment, the dashed line 606 indicates a reflective symmetry such that a symmetric diagonal structure on the other side resists such horizontal motion. The tops of the complementary diagonal buckling members are connected by a compression resisting member (here the upper) and the bottoms are connected by a tension resisting member (here the outsole). If the diagonal members were tilting opposite to each other instead of toward each other, the bottoms would be connected in compression and the tops in tension. The plane of reflective symmetry represented by the dashed line 606 in this case may be, for example, at the center of the user's heel. The tension member may span the width of the outsole (for lengthwise members) and / or the length of the outsole (if the device is configured with laterally aligned diagonal members). It may be the outsole itself, or one or more less extensible members in or near the outsole such as plastic or fiber or rods that resist horizontal expansion of the wider parts of the angled members. In other embodiments, the horizontal displacement may be constrained by other means, which need not be symmetric. For example, in an embodiment with diagonal buckling members oriented across the breadth of the shoe and tilting forwards or backwards, relative motion of the upper and outsole may be constrained by a connection at one or both ends of the upper as shown for example in Figs. 85-88. Resistance to such relative motion may also be provided by other non-symmetric buckling members, such as buckling members oriented perpendicularly or obliquely, or by other types of buckling member.

[0355] An alternative form of buckling member 700 is shown in Fig. 47. In contrast to the diagonal buckling member 600 which buckles across its length into an S-curve, a biased buckling member 700 is biased, for example by initially being bent, to bend as it compresses. Optionally a top hinge 704 and / or a bottom hinge 706 may be included. Someresistance to bending is desired to enable the buckling member to provide initial resistance to compression of the midsole; thus, a central hinge 702, for example e, could be used if a source of resistance to bending of the hinge 702 is present. A live hinge provides an example of a hinge with a source of resistance, but external resistance may also be supplied, for example using an elastic reinforcement attached to the buckling member as shown in Fig. 114. The hinged buckling member 700 may buckle for example into a C-shaped curve. As the biased buckling member buckles, an upper part 708 and a lower part 710 may each remain relatively straight as the buckling may primarily occurs at the hinge(s) including the central biased portion. The hinged buckling member bends at or near the middle of its vertical length but may bend in other positions. In some embodiments, the linear buckling members may also be used in combination with a lateral shear stability member such as, but not limited to a conical powerdisk. In the embodiment shown in Fig. 47, the exemplary buckling member 700 has a slight curve or bend even when the midsole is not compressed, to ensure that it always buckles in the same predetermined direction. An exemplary strain reducing member 712 is shown here and may be a rod or tube such as, but not limited to a polyurethane tube but may be of many different materials and constructions. The strain reducing member 712 is adhered or otherwise attached to the foam at some central point and prevents a high-strain crease from forming at the bend during buckling. This reduces the strain at the bend area and increases the useful life of the midsole. The embodiment shown in Fig. 47 uses live hinges made of the same foam material at the top and bottom. Fig. 48 shows an embodiment using fabric hinges at the top and bottom instead of foam hinges, The fabric hinges may be made of a fdm of flexible plastic or a fabric material. The fabric hinges may be adhered as shown using the dashed lines.

[0356] Fig. 49 shows the hinged buckling member of Fig. 48 at full bending (buckling travel) but before the compression travel (direct compression of the material of the now-horizontal buckling member) that occurs near and at full travel.

[0357] Fig. 50 shows another embodiment of a hinged buckling member using fabric hinges where a single piece of fabric 714 forms both top and bottom fabric hinges. This fabric provides reinforcement of the buckling member, for example against shearing in the plane of the fabric.

[0358] A hinged buckling member as shown in Fig. 47, Figs. 48-49 or Fig. 50 may be connected to the bottom of the upper and to the top of the outsole along the full surface at the top and / or bottom of the vertical member. It may also be attached or adhered along one edge so that edge can act as a live hinge, or a flexible material such as a fabric can be used as a livehinge as shown in Figs. 48-49. Buckling members like this may be placed at any angle and anywhere in the midsole, in combination with diagonal members such as shown in Figs. 44- 46 or on their own with no diagonal members. In some embodiments, buckling members are spaced sufficiently far apart that they do not substantially overlap with other buckling members during compression.

[0359] In an embodiment shown in Figs. 51-56, a construction which allows moulding of foam material for the buckling members is shown. This multi part construction can be glued together, and allows an edge of the buckling member to act as a hinge to reduce resistance to Buckling while still locating the member. Material such as Pebax foam is well- suited for this function, because Pebax is used as a live hinge material. This hinge may be located on the top and / or bottom of the feature. The buckling member may be attached at only the top or the bottom. It is intended that some or preferably most of the area beside the hinge at the top and / or bottom of the structure, is not adhered to, and is able to move away from, the top and or bottom structure of the chamber.

[0360] Fig. 51 shows an embodiment of a buckling member. The partially connected buckling member 800 shown in Fig. 51 has a thinner portion 802, for example forming a live hinge, in the middle analogously to the biased buckling member 700, but at one end (in the embodiment shown in Fig. 51, the bottom end 804) is not connected to the upper or to the outsole. The connection at the upper end (here the top end 806) has a hinge 808, here a live hinge. Fig. 52 shows an isometric view of the buckling member 800 of Fig. 51. In the embodiment shown in Figs. 51-52, the upper hinge 808 does not connect to the upper directly, but to an upper block 810 that can connect to the upper and to other upper blocks from other buckling members. In an alternative embodiment, not shown, there could be a lower hinge connecting to a lower block. Any direct connection to the upper in any of the buckling members shown in this document may be replaced by a connection to an upper block, or other intermediate structure, and vice versa; and direct connection to the outsole in this document may be replaced by a connection to a lower block or other intermediate structure or vice versa.

[0361] The upper block 810 may be designed to allow multiple buckling members in a row to be assembled while maintaining the live hinge. The upper blocks may be connected for example by gluing them together. Care must be taken not to adhere the top of the buckling member 800 (next to the live hinges 808) to the upper block 810 during this gluing process. Figs. 52-56 illustrate an exemplary assembly of multiple buckling members with upper blocks. Fig. 53 shows a side view of multiple buckling members with their upper blocksconnected together. Fig. 54 shows an isometric view of the multiple buckling members and upper blocks along with a disconnected bottom support 812, for example the outsole. Fig. 55 shows another isometric view but also showing a surrounding structure 814 in which the upper blocks are embedded, which may for example be a portion of the upper of the shoe. Fig. 56 shows the surrounding structure on its own for better visibility.

[0362] As with other embodiments of the buckling members, the partially connected buckling member 800 may use a fabric hinge in place of a live hinge. Fig. 57 shows a version with a fabric hinge 808A at the top end 806. A flexible fabric or polymer is shown by line 816. Hash marks show adhesive. A material or insert 818 with higher stiffness than the foam may be used to prevent a crease from forming where the member compresses and bends, as shown in Fig. 58. This reduces strain at the bend and increases service life. A rigid or flexible tube or rod 820 can also be used to prevent creasing at the bending point, as shown in Fig. 59. A low profde material or insert as shown in Fig. 58 may be used in place of a tube or rod in any embodiment showing a tube or rod.

[0363] In some embodiments, multiple buckling members are arranged in a loop such as a circle. In an embodiment of a midsole 2700 shown in Figs. 60-61, buckling member arrangements 2705 and 2710 are added. A forefoot buckling member arrangement 2705 is shown in greater detail in the section view of Fig. 62 and the heel buckling member arrangement 2710 is shown in greater detail in the section view of Fig. 63. In this particular embodiment, the heel arrangement 2710 includes a ring spring 2715 which is not present in the forefoot arrangement 2705.

[0364] Axial slots 2720 separate the buckling member arrangement into plural buckling members to allow the buckling members to buckle as they compress without influence of hoop strength, which would alter the spring rate, or even prevent buckling altogether. In an embodiment (shown in Figs. 113 to 116), rather than the continuous (up to axial slots) elliptical structure shown in Figs. 60 and 61, a U-shaped structure is used. In this embodiment, the inner region of the U-shape is sized such that a user’s heel could fit within the concave region of the U-shape, allowing a greater amount of travel for a given shoe sole height, as the user’s foot could pass through the open side of the U-shape. In an embodiment, a deformable buckling structure having a cross-section similar to that of the buckling structure shown in Fig. 60 or Fig. 61 is arranged along at least a portion of the perimeter of a shoe sole. In an embodiment, a buckling structure runs along the entire perimeter of a shoe sole. In an embodiment, the thickness of the buckling structure varies about the perimeter of the shoe.

[0365] A higher durometer foam or solid material may be used as a coating or surface covering or web structure on the inner faces, outer faces or within the angled foam members or the more buckling members to provide increased spring force and / or lateral shear stability. These web structures may also be of a fabric material that is highly flexible while providing additional resistance to deformation along one or more planes or directions. A non-limiting example is a 45 degree cloth laminated to the outer or inner foam surface a laterally aligned forward and / or backwardly angled foam members. This diagonal fabric reinforcement may increase the lateral shear stability while having less effect on the vertical compression resistance. Fig. 64 shows an example of a reinforcement using a web structure; Fig. 50 provides another example using cloth reinforcement.

[0366] In an embodiment, elongated inwardly angled diagonal buckling members provide high travel as a result of a minimal vertical overlap of the top half of the structure with the bottom half of the structure on a plane that passes through the centerpoint of the user’s heel as shown in the cross section image of Fig. 65. The diagonal buckling members may deform for example as shown in Figs. 44-46 as the midsole is compressed. There are different ways to describe and define the shape of embodiments of the device. In the embodiment shown in Fig. 65 an imaginary vertical line extending downward from the upper leftmost point (E) on the diagonal cross section is within 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% (shown at 0% in this non-limiting example by the dashed line “A”) of the average thickness of the diagonal member (shown by dashed line “D”) (measured diagonally at half the stack height (as shown by the dashed line ”B”) of the lower and rightmost point of the diagonal structure. The non-limiting example shown here is at 0%.

[0367] The diagonal structure geometry of such embodiments has been shown by the inventors to have a sweet spot for some applications, of approximately 30 degrees outer surface average angle from vertical with an aspect ratio of approximately 2: 1 (stack height- to-wall thickness) with a range of angles and aspect ratios that have been shown to provide benefits for different shoe types and user weights and uses. As the outer angle approached vertical and as the aspect ratio becomes quite thin or quite thick, there are decreasing benefits because the potential maximum spring force may be reduced and comfort can also be negatively affected, although some degree of benefit may still be found at substantially different angles and aspect ratios.

[0368] Fig. 66 and Fig. 67 show respectively isometric side and top views of an embodiment using diagonal side members as shown in Fig. 65.

[0369] Between the diagonal side members, other buckling members may also be included. In some embodiments, one or more additional lengthwise buckling members may be used. Fig. 68 shows an example with a single additional lengthwise diagonal buckling member. Various features between two diagonal features may be used to provide additional compression resistance or damping resistance or any other function, for example a compression biased damper which could be a viscoelastic foam or an air bag.

[0370] Fig. 69 shows an example with two additional lengthwise diagonal buckling members. In the non-limiting exemplary embodiment shown in Fig. 69, these have an inverted arrangement relative to the outer diagonal members. These members may be of any geometry such as but not limited to steeper and thinner because lateral sheer stability is provided by the thicker and more horizontal outer diagonal members. The thinner and more vertical shape may provide more “pop” (“pop” is referred to here as the more pronounced S- curve of the expansion force which results in the delayed energy return of the device. When this curve is pronounced enough, the user will feel a momentary release of energy during the midsole expansion which is often described as a “pop”. The benefits of delayed energy return are still present below the noticeable “pop” level but some people prefer this effect and / or feeling in some use cases.

[0371] In other embodiments, an array of buckling members shaped to bend in the middle of the height of the buckling member may be used (for example having an internal live hinge as shown in the examples of Figs. 47-59. Such buckling members are typically characterized by a force displacement curve with a high relative initial vertical compression deformation but then fall off to a much lower spring rate or spring force partly into the travel as a result of a primarily bending deformation after buckling, followed by primarily compression deformation nearing, and at, full travel, to provide bottom-out impact reduction.

[0372] Figs. 70-72 show different views of an exemplary such embodiment with an array of such buckling members between lengthwise diagonal members.

[0373] WEB INSERT

[0374] In an embodiment, a higher durometer foam or solid plastic or other material web may be used to modify the characteristics of the diagonal foam components. Two benefits of the web component are to increase the lateral and or longitudinal shear stability. Another is to increase the spring force for a given foam durometer. Shear stability is a significant benefit that allows the present device to achieve high travel for a given stack height with much higher lateral shear stability than a conventional foam midsole of equivalent stiffness. The increase of spring force is a significant advantage because using astiffer foam to provide as much lateral shear stability as the web adds to the device, would increase the full compression bottom-out impact. The inventors have shown that a foam durometer of between 35 and 30 Shore A provides high enough spring force and also soft enough bottom-out compression comfort when the device is flattened, to provide a very comfortable and low impact midsole. Durometers of 40 and higher begin to lose this bottom out impact reduction for many users, although higher and lower durometer foam may work for certain types and styles of shoes and different weights of users. Figs. 73-75 show a midsole and outsole with a truss-shaped web adhered or otherwise attached to the inner surface of the diagonal foam structure. Fig. 73 is a simplified isometric view of such a reinforced diagonal member connected to a portion of an outsole; Fig. 74 shows the same diagonal member also connected to a portion of an upper, and Fig. 75 is a simplified image of a side cross section. The web may be made of, for example, Pebax plastic and adhered to the inside surface or outside surface or imbedded in the foam diagonal member. The web may be of many different shapes. This truss example allows lengthwise flexibility of the midsole while adding lateral shear stiffness to the diagonal foam structure. A cloth reinforcement as discussed above may provide a similar function.

[0375] LATERAL STRUCTURES

[0376] Fig. 76 shows another embodiment of a buckling member. This buckling member is diagonally oriented as in the embodiment of Figs. 44-46, but has a narrow portion that acts as a live hinge for buckling, as in the embodiments of Figs. 47-59. As with the embodiments of Figs. 44-46, a means of constraining horizontal motion of the upper end of this buckling member relative to the lower end is desired. An aspect ratio is measured as a function of the stack height E at the mid stack height position and the mid thickness position with a line (D) that is perpendicular to the average angle of line C which is the average of the angles of line A and B, to the thickness D which is approximately 3.2: 1 in this non-limiting example (or -2.5:1 if measured from the bottom of the upper to the top of the outsole). This has been shown to be an effective aspect ratio for excellent performance and the unique benefits of the device. Higher and lower angles (B) have been shown to provide benefits of the present device. Higher and lower aspect ratios have been shown to provide benefits of the present device.

[0377] Figs. 77 and 78 show a finite element analysis (FEA) of the collapse of a buckling member as shown in Fig. 76, in this embodiment also including a reinforcement material or structure on the lower side, for example as shown in Fig. 79.

[0378] The example shown in Figs. 77 and 78 uses the nodes in the FEA to plot a straight line from the bottom of the midsole, comprising the diagonal member, to the top of the diagonal member.

[0379] The diagonal foam member is then vertically compressed to full travel, such as in the FEA program or in a physical experiment, and the points of these nodes are used to describe the resulting curve. An S-shaped curve results, and if the curve passes through a line on the cross section plane that is horizontal or steeper, a total of three times or a total of a minimum of three times, or at least three times, or three times or more (steeper in this example means rotated clockwise) such as 1 to 2 deg, 2 to 3 deg, 3 to 4 deg, 4 to 5 deg, 5 to 6 deg, 6 to 7 deg, 7 to 8 deg, 8 to 9 deg, or 9 to 10 deg, the device is determined to be within the bounds of the present device. (An exemplary dotted white line is shown at 4 deg to clarify the angle range referred to above.)

[0380] While the line may extend above the midsole through the bottom of the upper (not shown above) and below the midsole to the bottom of the outsole (shown above) the S- shaped curve will cross the horizontal or angled line three times within the midsole. This internal S-shaped curve is a critical feature of the device. The compression of a conventional foam midsole will not produce this internal S curve, or if it does, it will be at a very steep (more vertical) angle than the range shown here, and will, as a result, not provide the desired compression travel for a given stack height. A conventional foam midsole that lacks the more horizontal S-curve at full compression, will not provide the delayed energy return which results from a reduced spring force or dramatically reduced spring rate part-way through the travel. At the same time, if the S-curve passes three times through a line within the ranges shown here, but has an outer wall angle, when at rest of 15 degrees or less from vertical, the structure will not provide a high level or lateral shear stability which is preferred for comfort and performance on uneven terrain or when moving laterally.

[0381] With the above in mind, the device is shown to provide the most benefit at a outer wall angle from vertical of <15deg, <16deg, <17deg, <18deg, <19deg, <20deg, <21deg, <22deg, <23deg, <24deg, <25deg, <26deg, <27deg, <28deg, <29deg, <30deg, <31deg, <32deg, <33deg, <34deg, <35deg, <36deg, <37deg, <38deg, <39deg, <40deg, <41deg, <42deg, <43deg, <44deg, <45deg, <46deg, <47deg, <48deg, <49deg, <50deg, <51deg, <52deg, <53deg, <54deg, <55deg measured over 40% or more, 50% or more, 60% or more, 70% or more of the height of the stack height preferably over a span with minimal outlying features, and with an internal S-curve at full compression as described above.

[0382] The initial straight line is completely inside the bounds of the cross section of the midsole diagonal member and extends to the top of the insole receiving surface and to the bottom of the outsole. In an embodiment in which the midsole has holes in it or other features that make it impossible to show a straight line that overlaps the entire midsole diagonal foam member, nodes in the FEA analysis can still be used to draw the straight line and the straight line will still create an S-shaped curve as shown below if the device is within the range of geometry of the present device as disclosed here.

[0383] ANGLE DEFINITIONS

[0384] With a simplified model with a cross section of a diagonal foam or flexible matrix structure having flat outer and inner surfaces such as B and A in Fig. 76, a suitable range of geometries may be defined by a range of angles of the outer surfaces along with a range of wall thicknesses. Experimentation has shown that an outer wall with an angle from vertical of <15deg, <16deg, <17deg, <18deg, <19deg, <20deg, <21deg, <22deg, <23deg, <24deg, <25deg, <26deg, <27deg, <28deg, <29deg, <30deg, <31 deg, <32deg, <33deg, <34deg, <35deg, <36deg, <37deg, <38deg, <39deg, <40deg, <41 deg, <42deg, <43deg, <44deg, <45deg, <46deg, <47deg, <48deg, <49deg, <50deg, <51 deg, <52deg, <53deg, <54deg, <55deg measured over 40% or more, 50% or more, 60% or more, 70% or more of the height of the stack height preferably over a span with minimal outlying features, can provide various benefits of the present device, with a preferred angle for some applications, based on testing and analysis, of between 25 and 35 degrees from vertical, although other angles may be preferable for other applications and uses. Lower angles such as <15deg, <16deg, <17deg, <18deg, <19deg, can provide some portion of the benefit of this device, however, the lateral sheer stability becomes lower at these lower angles and may require additional stability features. It is the belief of the inventors that angles in this lower range may be more likely to provide the needed stability when configured in a dome or partial dome shape (as compared to the more linear shapes described in this portion of this document). The inner surface angle and may have an angle from vertical of 20 degrees or more, 30 degrees or more, 40 degrees or more, 50 degrees or more, with a preferred angle for some applications being between 25 and 35 degrees from vertical, although higher and lower angles will also work for specific applications.

[0385] An exemplary diagonal structure is defined using this angle method below. The average angle of the outer surface of the device (B) may be <15deg, <16deg, <17deg, <18deg, <19deg, <20deg, <21deg, <22deg, <23deg, <24deg, <25deg, <26deg, <27deg, <28deg, <29deg, <30deg, <31deg, <32deg, <33deg, <34deg, <35deg, <36deg, <37deg,<38deg, <39deg, <40deg, <41deg, <42deg, <43deg, <44deg, <45deg, <46deg, <47deg, <48deg, <49deg, <50deg, <51deg, <52deg, <53deg, <54deg, <55deg measured over 40% or more, 50% or more, 60% or more, 70% or more of the height of the stack height preferably over a span with minimal outlying features. If there are anomalies or extra features or holes in the outer surface, someone skilled in the art will be able to determine an average outer surface angle over 40% or more, 50% or more, 60% or more, 70% or more of the height of the stack height to determine what angle of a simplified straight diagonal wall the outer surface would be functionally equivalent to.

[0386] For clarity, the angle of the outer wall will be easily measured if the cross section is a straight line over 40% or more, 50% or more, 60% or more, 70% or more of the height of the stack height. If the wall is curved or interrupted or has protruding features, a person skilled in the art will be able to determine, through FEA analysis, or other means, what angle a functionally equivalent simple straight cross section would be. If that simplified straight cross section functional equivalent wall is <15deg, <16deg, <17deg, <18deg, <19deg, <20deg, <21deg, <22deg, <23deg, <24deg, <25deg, <26deg, <27deg, <28deg, <29deg,<30deg, <31deg, <32deg, <33deg, <34deg, <35deg, <36deg, <37deg, <38deg, <39deg,<40deg, <41deg, <42deg, <43deg, <44deg, <45deg, <46deg, <47deg, <48deg, <49deg,<50deg, <51 deg, <52deg, <53deg, <54deg, <55deg it will be within the scope of the device described here in that respect.

[0387] Fig. 79 is an isometric view of a diagonal member as shown in Fig. 76, also having a web insert as a reinforcing structure to increase lateral and / or angular shear stability. Also shown in Fig. 79 is a tension member on top of the outsole, as well as portions of the outsole an upper. The tension member may be a plastic sheet or a length of fabric adhered to the outsole. Fig. 80 is another isometric view showing the diagonal buckling member alone, and Fig. 81 shows the web insert. The web member may be added to the assembly on one or more diagonal foam members. The web member provides three main functions. It may increase the magnitude of the force / displacement curve in that area. It may increase the lateral sheer stability of the midsole by virtue of the web material being higher durometer or a solid and more rigid or flexible plastic that provides additional resistance to lateral shearing of the diagonal member. It may also, depending on the geometry and materials it is constructed from, provide additional angular stability to the midsole by resisting twisting about a horizontal and lengthwise axis.

[0388] The web may be of many different designs. The one shown here is a nonlimiting example of a shape. It may be made of many different materials such as, but notlimited to, Pebax plastic. If such a web is adhered or otherwise attached to a diagonal member, it has been shown by the inventors to work with another opposing angle diagonal member also having such a web, although many different combinations of components in the midsole is anticipated by the inventors. In the non-limiting exemplary embodiment shown in Fig. 81, the X-shape of the web provides lateral shear stability and angular stability. Web structures of many different constructions may also be used on or in the more vertical buckling members described earlier such as shown in Fig. 64. The web structure illustrated here or in Fig. 64 may also represent an angled cloth laminate.

[0389] In embodiments of the device, a tension member is provided between the wider flared out surfaces of two or more angled buckling members. This tension member prevents the wider sections from moving apart and, for example, can prevent the upper from sliding horizontally relative to the ground as a result of compression or rebound forces and motion. The tensile member in some embodiments is the outsole or can comprise the outsole. The tension member may span the width of the outsole and / or the length of the outsole. It may be the outsole itself, or one or more less extensible members such as plastic or fiber that resists horizontal expansion of the outsole and prevents relative horizontal movement of the lower parts of the angled members during compression and rebound.

[0390] Fig. 82 shows an embodiment with a tension member on top of the outsole as well as plural diagonal buckling members such as shown in Fig. 79 that extend generally across the midsole from one side of the midsole toward the other side. The angled members provide high travel as a result of a minimal vertical overlap of the upper volume of material with the bottom volume of material such as, but not limited to, a cross section on a vertical plane that passes through the centerpoint of the user’s heel. In order to ensure a generally vertical compression of the midsole, in this embodiment for every forward or rearward angled diagonal member, there is one or more opposing and oppositely angled member / s within the length of the midsole. The horizontal tension member between the bottom of opposing compressible diagonal foam or compressible matrix structures prevents portions of the outsole from sliding apart on the ground during vertical compression of the midsole. This less-extensible horizontal tension member may be of many different designs and materials. Shown in Figs. 82-83, is a layer of nylon fabric 830 between the diagonal foam members and the outsole. The outsole itself could comprise the tensile member, or a thin plastic film or rods or fibers can be used instead of fabric. By using cloth or other tensile member that resists stretching, it allows the shoe designer to use a softer material for the outsole which increases vertical compression travel of the midsole and outsole.

[0391] In the non-limiting example shown in Figs 82-83, the diagonal members are scaled to match the height of the midsole from the heel to the toe. This reduces the magnitude of the force / displacement curve for each of these sets toward the toe. Other ways to adjust the force / displacement curve of different members is to use thinner or thicker diagonal feature walls or different angles or different foam densities within the range of geometries described here. It has been found, by the inventors, for example, that the diagonal features in the arch area may be less stiff (such as by reducing the wall thickness or increasing the outer wall angle, or using lower durometer foam) with beneficial effects with regard to comfort and a smooth transition from heel to toe during progression of stance. Fig. 84 shows an isometric view of this embodiment. The toe is shown attached to the upper with a toe wedge made of a material such as but not limited to foam. A heel wedge of a preferably compressible material can also be used.

[0392] COMBINATIONS

[0393] Many individual or combinations of lengthwise angled members, laterally aligned angled members, revolved or other shapes of angled members are possible and anticipated by the inventors.

[0394] ALL FORWARD OR BACKWARD

[0395] The inventors have shown it to be possible to have all or most of the foam angled members angled in the forward or backward directions, as shown in Figs. 85-88. This is made more effective by the use of one or more horizontal tension members that run for all or part of the length of the midsole. The upper acts as a first horizontal tension and / or compression member, and one or more substantially continuous outsole lines of material or tension members on or within the outsole and for all or part of the length of the midsole prevent the relative horizontal motion of the bottom of individual angled foam members relative to adjacent members during compression and rebound, and thus, preventing sliding of the outsole on the ground during compression and rebound.

[0396] This is important for outsole wear life and to preserve the stored energy in the midsole, because any sliding of the outsole on the ground during compression, results in wasted energy that does not contribute to rebound and propulsion.

[0397] It is the understanding of the inventors that a series of angled members that are angled forward from the ground up and forward toward the front of the shoe, can be used with benefits of the device disclosed here. Such an embodiment is shown in Figs. 85-86. This angled-forward configuration works well because the midsole is thinner at the toe and less prone to shearing deformation during compression and rebound when the forward-angledmembers are creating a rearward force on the outsole relative to the upper. The toe of the upper can, therefore, provide an effective shear-resistant anchor for the tensile member / s comprising the sole, preventing unwanted horizontal motion of the upper relative to the outsole. The toe of the outsole, in this non-limiting exemplary embodiment, is connected to the toe of the upper directly or with a shear-resistant member. The outsole comprises a generally horizontal tensile member which, together with the shear-resistant member at the toe, prevents undue rearward motion of all or parts of the outsole when the midsole is compressed. As shown in Figs. 76-80, the diagonal foam members are slightly curved and thicker at the top and comprise a “foot” section at the bottom. This is a non-limiting example of a diagonal member shape. Many other diagonal member shapes are possible and anticipated by the inventors.

[0398] The heel of the upper may also be used as an anchor for tensile members of the outsole and may be most useful if one or more diagonal members are angled backward in the midsole, as shown in Figs. 87-88. This member may be stiff enough to provide some impact reduction during heel strike and also to reduce horizontal forward motion of the outsole relative to the upper during compression of the midsole. As noted above, a tensile member can be the outsole itself or a separate structure.

[0399] Force response

[0400] The buckling discussed above, for example for linear buckling members or for buckling domes, results in a reduction in spring rate during at least part of the compression but does not necessarily result in a reduction in force at any point in the travel. Fig. 89 shows an exemplary force-displacement curve, with a rebound phase also shown. Buckling occurs in a primarily bending phase results and direct compression of the material in a primarily compression phase. The result of these sequential phases, of high bending deformation first, and then high compression deformation second, with a flexible and compressible foam or matrix material and within the range of geometries disclosed here, is a decreasing spring rate partway through the travel (as increased bending of the structure becomes less able to exert upward force to resist compression) and an increase of spring rate and force (as compression deformation increases) at full travel to prevent harsh bottom out. The combination of these two phases is able to provide a very high total travel for a given stack height. The use of a non-compressible material to form a diagonal or dome structure, as shown in some prior art, is not able to provide the low impact bottom-out characteristic of the compression phase at full compression. A foam structure that is not arranged to buckle and is generally vertical , as shown in some of the prior art, will be in a high % of vertical compression from thebeginning of the midsole travel and will not provide the falling off of the spring rate necessary to store a high % of foot strike energy for release later in the stride.

[0401] Generally linear compressible foam or matrix structures as disclosed throughout this document may be used, for example, within the same range of cross-sectional geometry as the rotationally revolved or arrayed geometry.

[0402] Selected numbered embodiments:

[0403] 1 - A midsole for a shoe with a diagonal structure comprised of a resilient and compressible foam or flexible / compressible matrix. The diagonal shape is swept along a straight or curved or open or closed path. A vertical cross-section plane passing through the centre of the user’s heel has an average outer wall angle of <15deg, <16 deg, <17 deg, <18 deg, <19 deg, <20 deg, <20 deg, <21 deg, <22 deg, <23 deg, <24 deg, <25 deg, <26 deg, <27 deg, <28 deg, <29 deg, <30 deg, <31 deg, <32 deg, <33 deg, <34 deg, <35 deg, <36 deg, <37 deg, <38 deg, <39 deg, <40 deg, <41 deg, <42 deg, <43 deg, <44 deg, <45 deg, <46 deg,<47 deg, <48 deg, <49 deg, <50 deg from vertical.

[0404] 2 - A flexible / compressible structure for a midsole with a diagonal crosssection on an actual or imaginary vertical plane passing through the center of the user’s heel. A minimum of four points on that plane describe a straight diagonal line when the structure is at rest. When the structure is at full compression (such as at a force of 1000N, 1500N, 2000 N of force on the heel structure for a size 10 shoe) the four or more points, describe a S or Z shaped curve that passes through an imaginary line 3 times and the imaginary line is between horizontal and 1°, 1° and 2°, 2° and 3°, 3° and 4°, 4° and 5°, 5° and 60°, 6° and 7°, 7° and 8°, 8° at 9°, 9° and 10°.

[0405] 3 - The device of 1 or 2 above, with a higher durometer insert to increase the lateral sheer stability of the foam structure, the insert being adhered or otherwise attached to the inner and / or outer surface of the diagonal foam structure and / or imbedded in the diagonal foam structure.

[0406] 4 - The device of 3 where the insert is more extensible or compressible in a first direction and less extensible or compressible in a second direction.

[0407] 5 - The device of 1 which undergoes a higher bending mode deformation earlier in the compression travel, as compared to later in the travel when the device is primarily in compressive deformation.

[0408] 6 - The device of any of 1-5 with linear or somewhat linear structures running

[0409] along all or part of the midsole.

[0410] 7 - The device of 6 with one or more opposing angled diagonal structures.

[0411] 8 - The device of any of 1-7 with linear or somewhat linear structures running

[0412] across the midsole.

[0413] 9 - The device of 8 with one or more opposing angle diagonal structures for one or more diagonal structures.

[0414] 10 - The device of 8 with more than half of the diagonal structures angled forward.

[0415] 11 - The device of 8 with more than half of the diagonal structures angled backward.

[0416] 12 - The device of 1-11 with a horizontal tension member to prevent relative horizontal motion of opposing or adjacent upper or lower portions of diagonal structures.

[0417] 13 - An insert structure with torsional twisting resistance to provide angular stability to the diagonal foam structure, with the torsionally resistant structure adhered to or imbedded in the diagonal foam structure.

[0418] 14 - The device of any of 1-13 with a lower durometer foam or other flexible member inside or outside or adjacent to the higher durometer diagonal foam structure, for the purpose of aesthetics, or for some other purpose.

[0419] 15 - The device of any of 1-14 with all or part of the diagonal structures being

[0420] AIR DAMPER

[0421] The reduction of spring rate in the present device results in a reduction of the force necessary from the user’s weight to keep the midsole compressed during the midstride. This allows the present device to stay more compressed during the midstride then a conventional foam midsole so that more travel is available after the midstride when the sole expands again.

[0422] In addition to bending / shearing / buckling of the foam during a first phase and compression of the foam during a second phased of travel, embodiments of the device also provide additional damping during compression by using air that is sealed inside the dome and by forcing it through a main air flow resistor, during all or part of the compression phase, for example as shown in Fig. 27F. This provides a tuneable or adjustable impact reduction effect from this air damper. A further embodiment using an air damper is shown in Figs. 90- 93. In the embodiment shown in Figs. 90-93, a single chamber 1105 is used for the entire foot of the user with flow control structures 1110 located at one or more positions in the chamber 1105 to change the pressure in one part of the chamber compared to another. The structure 1110, with a function similar to a check valve, is wide open during the beginning of the heel strike and increases in flow restriction as the heel 4015 is compressed. Fig. 92 shows the sole partway through compression at about 50% compression. In an embodiment, partway through the compression, such as, but not limited to, halfway through the heel zone compression, the flow control feature 1110 nearly closes, but due to the non-self-energizing shape, when the pressure in the heel zone 6015 is higher than the rest of the midsole chamber, air is still allowed to flow from the heel to the rest of the chamber, including forefoot region 1105, albeit with increased flow restriction. This feature may be a shape similar to that shown in the figure, or it could be a hole in the foam that closes partway through the compression of the heel zone.

[0423] As the user continues in the stance and begins to compress the air in the forefoot part of the chamber, the heel of the user lifts and the flow restriction element 1110 at the heel chamber, opens and allows air to rush back in to the heel chamber. The timing of this feature opening can be tuned or adjusted for the maximum propulsion benefit. I.e. the later it opens, the further forward the user’s centre of gravity will be and the more effect, up to a point, this pressurized air energy will have on the forward propulsion of the user. In the embodiment shown in Figs. 91 and 92, a forward structure 1115 similar to structure 1110 is provided in the forefoot part of the chamber such that when the user compresses the forefoot area of the chamber, air from the chamber moves rearward toward the heel zone of the chamber, where a portion of that energy is stored as increased pressure. As the user rolls forward onto their toes, the forward flow restriction element 1115 opens, and pressurized air from the rearward section of the chamber rushes back into the forefoot part of the chamber to help lift the forefoot of the user and propel them forward.

[0424] In an embodiment shown in Fig. 94, an air flow bypass 1410 may also be provided to communicate between a forefoot volume 1105 and a heel volume 6015, or between the forefoot volume 1105 and an intermediate volume 6010, so that air can still move from the forefoot part of the chamber rearward, even if the closable flow restriction element 1115 is closed. Thus, when the position sensitive closable air restriction element closes during compression of the heel, the tunable or adjustable bypass prevents the heel section of the chamber from sealing completely.

[0425] A section view of this embodiment is shown in FIG. 95. These bypass flow restriction features may also act to normalize the pressure from the heel to the forefoot sections of the chamber during slower compression and expansion movements such as slow walking or standing.

[0426] In an embodiment shown in FIG. 96, an intermediate chamber 6010 between the heel and forefoot sections of the chamber is designed from a material and a shape that is allowed to expand in volume when the heel and / or forefoot section are compressed. This expanding affect prevents the air pressure from increasing too much during a forefoot ground strike. This expandable chamber can be located under the arch of the user’s foot and shaped in such a way that it starts out with a non-circular cross-section and deforms into a more circular cross-section when pressurized, as shown FIG. 97 which shows an inflated crosssection shown in front of an uninflated profile. The walls of this chamber may also be thin enough that the walls can stretch if necessary to prevent over-pressurization.

[0427] By making the entire chamber out of a resilient, foam material, such as, but not limited to, Pebax, or TPU, the expandable midsection of the chamber, and the forefoot section of the chamber, can all be made of the same material.

[0428] In an embodiment shown in Figs.98-FIG. 99 a dial 1805 is shown which adjusts the flow restriction of the airflow bypass 1405. As shown in Fig. 101, the dial is connected to a cam 2105 which rotates along with the dial and is arranged to restrict airflow within channel 2110. Figs. 100 and 102 show this feature with less and more material cut away respectively.

[0429] Figs. 103-106 show a two-chamber air damper embodiment (for example as shown in Figs. 90-93) embedded in a shoe. Fig. 103 shows a simplified representation of a shoe including the entire upper, while Fig. 104 shows only a lower portion of the upper (which may alternatively be characterized as an upper midsole surface which supports the upper). Figs. 105 and 106 remove the upper (or upper midsole surface) entirely.

[0430] In an embodiment, multiple chambers are used in the heel and / or forefoot. Examples of multiple chambers in the forefoot are shown in Figs. 107-111. This has the advantage of preventing a single forefoot chamber from ballooning, when pressurized by air that is expelled from the heel section of the chamber. The shoe may feature a stiff plate arranged between an air chamber and the foot of the user to reduce the amount of expansion felt by the foot of the user. The air chambers may be arranged to expand downwards into a void within the outsole of the shoe, or in the radially outwards direction. The forefoot 4005, intermediate chamber 4010, and heel 4015 of a shoe sole are identified in FIG. 107. Fig. 109 shows forefoot volumes 6005, 6006 and 6007, intermediate volume 6010 and heel volume 6015. Fig. 112 shows a connection between the intermediate volume and the heel volume.

[0431] In various embodiments, the chambers may be for example each be a resilient structure formed for example as a dome as described elsewhere in this document. In various embodiments, buckling members can be included within the chambers, for example an arrangement as shown in Figs. 60 and 61 or an array as shown in Fig. 54.

[0432] The embodiment in FIG. 37-38 shows a foam cone arranged to compress in an axially shearing direction.

[0433] In an embodiment shown in Figs. 123-124, a resilient structure formed as a dome also acts as an air chamber. The outer diameter of a first vertical end 850 (here the top) is smaller than the inner diameter of the second vertical end 1010 (here the bottom). In an embodiment, the outer diameter of the first end 850 is within +-5%, +-10%, +-15%, +-20%, +-25% of the inner diameter of the second end 855. The second end may have radialexpansion limiting member 860 such as Kevlar thread to constrain the base 865 of the deformable member, causing it to transition to a buckling motion during compression. The base may have grooves (not shown) for retaining the radial expansion limiting member.

[0434] The deformable member may have a cylindrical base 865 which contributes to damping compression when the spring bottoms out. In an embodiment, the cone has a sealed region contained in part by a rigid cap 890. As the spring is compressed, a fluid pathway vents air, through vents such as a vent mesh 870 or air channel 875, to a port which communicates with ambient air. In an embodiment, the damper 880 shown in Fig. 124 is designed to seal off the fluid pathway at a predetermined point of compression. In the embodiment shown in Fig. 123, there is a vent mesh 870 along the base of the sealed region, so that air is not trapped within the volume of the foam spring. A buckling member 885 buckles during compression of the device.

[0435] Selected exemplary embodiments:

[0436] 1. A midsole for a shoe comprising a chamber with tapered walls. The chamber is constructed from a compressible and deformable material such as foam.

[0437] 2. The device of embodiment 1 where the OD of the upper surface is similar to the ID of the lower surface.

[0438] 3. The device of embodiment 1 where the wall thickness at the base of the chamber is, on average, radially larger than the wall thickness of the foam toward the top of the chamber.

[0439] 4. The device of embodiment 1 where the lower surface of the cone is allowed to peel up when the cone is compressed to allow a reduction in spring force at full compression as compared to if the lower surface was secured to the outsole and unable to peel up.

[0440] 5. The device of the previous embodiment which provides location for the lower surface by way of a thin section of contiguous material or different material, which is adhered to the bottom surface, but is not adhered to the outsole. Said thin layer of material, extending inward from the ID of the lower surface and attached to the outsole inside of the ID of the outer surface or near the ID of the surface in such a way that the OD of the bottom surface is able to peel upward as the chamber is vertically compressed.

[0441] 6. The device of embodiment 1 that is air sealed around the top of the chamber, and the bottom of the chamber with air flow features such as holes or tubes in and out of the chamber.

[0442] 7. The previous embodiment where one or more of these air flow features has a fixed or adjustable or tunable, airflow resistance orifice to act as an air damper during compression.

[0443] 8. Any of the above selected embodiments with an airflow feature which allows lower resistance airflow back into the chamber.

[0444] 9. The previous embodiment where the airflow feature which allows air to flow back into the chamber is closeable at some point in the compression of the chamber.

[0445] 10. The previous embodiment where the inflow feature is closed or more closed at full compression and becomes open or more open partway through expansion to allow air back into the chamber.

[0446] 11. Any of the above selected embodiments with a separate chamber or a different part of the same chamber, which contains the increased air pressure, resulting from air flowing out of the heel chamber.

[0447] 12. The previous embodiment where the additional chamber or other part of the same chamber comprises a forefoot chamber area.

[0448] 13. Any of the above selected embodiments where a heel chamber, or a heel part of a chamber, has a forefoot chamber or a forefoot area of the same chamber as the heel area chamber with an intermediate chamber or area of the same chamber as the heel and toe chamber, with the intermediate chamber providing storage of pressurized air, which is expelled from the heel and or toe chambers or chamber areas.

[0449] 14. The previous embodiment where the intermediate chamber has a shape or material property, which allows it to increase in volume when pressurized.

[0450] 15. Any of the above selected embodiments, where pressurized air in the intermediate chamber is allowed to flow to the heel part of the chamber, and or the toe part of the chamber.

[0451] 16. Any of the above selected embodiments where the wall thickness of a chamber is thicker at the base, than a layer of contiguous or different material at the ID of the top of the chamber. This layer of material prevents undue inward deformation of the upper part of the chamber as it is compressed. Once the chamber is compressed fully, the thinner, vertical cross-section of the upper layer compared to the thicker wall thickness of the bottom of the chamber walls, results in a concave foot receiving shape at full compression.

[0452] 17. Any of the above selected embodiments which comprise a compression biased damper, made of, for example, but not limited to a viscoelastic foam material insidethe chamber, which provides damping during compression, but does not detract from rebound energy during expansion of the chamber.

[0453] 18. Any of the above selected embodiments but with a vertically inverted structure as compared to any of the above selected embodiments.

[0454] 19. The device of embodiment 1, whereby foam walls of the structure are primarily in vertical compression initially, and then undergo increasingly more sheer deformation (e.g., due to buckling) for part of the range of travel toward full compression.

[0455] 20. Features for a mid sole comprised of a resilient foam material with an aspect ratio of height, to horizontal thickness of greater than 3 to 1, 4 to 1, 5 to 1, 6 to 1, 7 to 1, with said members being attached to the upper and or lower structures with a mid zone with lower cross-section than a top and or bottom surface of the member. Said hinged area, allowing the top and bottom of the member to peel away from the upper and lower chamber surfaces to provide a buckling effect.

[0456] 21. The previous embodiment with buckling members which are attached to the outside of the shoe upper at a large enough diameter that they do not significantly inhibit the full compression of the mid sole when they are buckled.

[0457] 22. The device of the previous embodiment, where a hinged section of material is located around the outside of the upper, and above the height of the bottom of the upper, such that the vertical length of these members is longer than the travel distance available between the bottom of the upper and the top of the outer sole.

[0458] 23. The device of the previous embodiment where the buckling members are arrayed around all or part of the shoe with gaps between them which allow buckling of the members with reduced circumferential expansion as compared to a similar structure with no vertical slots.

[0459] 24. The device of the previous embodiment, in which the buckling members are analogous to barrel staves which are hinged at the top and / or bottom, and are shaped to bend outward during compression, so that they buckle outward. Buckling inward is also contemplated.

[0460] 25. The device of the previous embodiment with an elastic member resisting outward buckling of the members wrapped around the outside of the waist of the barrel or otherwise attached to two or more staves to resist radial deflection of the mid-length (waist) of the staves.

[0461] A further embodiment of a midsole device 900 including buckling members 902 is shown in Figs. 113-115. In this embodiment, the buckling members 902 are arrayedaround the outside of a midsole heel section. They use a live hinge construction with live hinges (for example as shown in Fig. 47 or Fig. 51) and a reinforcement coating 906. In an embodiment, the reinforcement coating is an elastic coating instead of a non elastic fabric layer. By making it elastic, it will allow the outer layer of foam and elastic coating to stretch, which we have found to have a better effect. The same can be applied to any of the embodiments disclosed in this document using reinforcement coating.

[0462] The members may or may not have the pre-constructed slot 908 at the center bending point assisting in collapse of a central live hinge. But they preferably need a live hinge on the top (910) and bottom (912) hinge points. The elastic coating 906 is optional but is intended to extend the life of the hinged areas.

[0463] The embodiments of Figs. 113-115 also includes an air bladder 914 under the heel for damping. The air bladder may be omitted if desired and may be included in other embodiments that do not show an air bladder. The air bladder 914 may be designed with a one way valve 916 that has greater restriction to air leaving the bladder than to air coming back in. The bladder is preferably stiff enough to regain its shape between compression cycles, but it is also preferably flexible enough to allow it to collapse in on itself during expansion so as not to resist expansion and allow the buckling members to efficiently return the compression energy. The air in the bladder may vent to atmosphere or to a reservoir (not shown). The air bladder is shown including an internal damper 918 for further damping at full compression.

[0464] Fig. 114 is a close-up showing a cross section slice of the compressed shape of a vertical buckling member. Due to the buckling members being arrayed around the outside of the midsole and buckling outward as shown in Fig. 114, they are out of the way at full compression so greater travel is possible than if the buckling members were under the foot.

[0465] Fig. 115 shows the uncompressed geometry with the live hinge sections 910 and 912. The buckling members 902 form an array of individual sections. This allows circumferential expansion of the midline of the members.

[0466] Fig. 116 shows a variation of the embodiment of Figs. 113-115 in which the elastic coating 906 is continuous around part of the array. This will require the coating to stretch circumferentially, to store foot strike energy similar to a ring spring. The foam may or may not be continuous, and is preferably not continuous.

[0467] A midsole may comprise plural buckling members arranged to buckle to cause a reduction in spring rate as the midsole collapses under the weight of a user’s foot. This also delays the return of the stored energy to later in the user’s stride. At or near the full range oftravel, the material of the buckling members may be compressed directly to form a cushioning effect. Additional dampers, for example air dampers or dampers of a compressible material, may be included to provide this cushioning effect in addition to or instead of the material of the buckling members.

[0468] A buckling member can include a slight bend or other structural biasing to encourage the buckling member to bend in a particular direction, for example bending as a half-wavelength over its length. Such a buckling member typically is also arranged to hinge at the top and bottom, and may be disconnected from the upper or the outsole in one of those directions. Such a bent or biased buckling member may be, but need not be, vertically oriented.

[0469] A buckling member can be oriented diagonally to help it buckle, for example bending as a full-wavelength over its length. Such a buckling member may optionally be fixed to the upper at the top and / or fixed to the lower at the bottom, as these encourage the full-wavelength buckling as the upper and lower move closer vertically without moving horizontally. Typically, some restraint on horizontal motion of the upper relative to the lower is desired for such embodiments. The full-wavelength buckling may still use live hinges for one or both of the halves of the wavelength of buckling, for example the embodiment of Figs. 77-78 bends more significantly at the bottom half-wavelength where it is thinner, and less at the tip half-wavelength where it is thicker, but still bends in a full-wavelength s-curve as shown. Half-wavelength buckling members will not typically show such an s-curve. In some embodiments, live hinges on an angled buckling member may eliminate an s-curve.

[0470] Where a restraint on horizontal motion of the upper relative to the outsole is required, oppositely oriented diagonal buckling members may be used, or obliquely or perpendicularly oriented buckling members of any type. Alternatively, the horizontal motion may be constrained by connecting the outsole and the upper together, for example at one or both ends of the shoe. A tensioning member may be connected to the outsole or to the upper to bear horizontal forces applied to it by diagonal buckling members, or the outsole or the upper itself may bear the forces.

[0471] Live hinges may be reinforced using reinforcing material, which can include low profile reinforcement such as fabric or for example a rod or tube. Fabric may also be used for fabric hinges in place of live hinges. Reinforcing material may also be used to reinforce against lateral forces, for example using fabric or plastic webs. Elastic material may be used for a reinforcement coating to allow it to stretch.

[0472] Various arrangements of buckling members can be used, including circular arrangements of buckling members, arrays, and the use of buckling members with other mechanisms. For example, buckling members can be included inside a resilient dome or air bladder; an air bladder may also be included within an arrangement of buckling members. Typically, it is desirable to arrange buckling members so that they collapse in a nonoverlapping manner.

[0473] CONFOUNDING GEOMETRY

[0474] In some embodiments, the energy return device 10 may comprise complex or varied geometries that involve anomalies or deviations from the geometries specified. It is anticipated that the principles of the device disclosed herein may be realized with the use of complex geometries such as by creating a diagonal foam member with vertical or horizontal or diagonal grooves or features on the inner or outer surfaces, or by creating fins or flanges or other protrusions, or by creating a waved shaped inner or outer surface, or by any other additional material or removal of patterned or non-pattemed material. In some such cases, the cross section along a single vertical plane may not accurately represent the general construction of the diagonal member with regard to the performance characteristics it would provide. In such cases, the functional geometry of the device components can be represented by the average cross section of a linear or rotational array of representative planes with cross sections on each plane that are averaged together to approximately represent the general construction of a section of a midsole diagonal foam feature. The number of arrayed representative planes and the spacing of the planes can be determined, by someone skilled in the art, to reasonably represent the characteristics of the midsole with regard to the geometry of the device disclosed here. For example, for a dome structure in the heel, a representative set of planes might comprise 10 planes spanning 180 degrees of a dome; in other examples more or less planes at greater or lesser angles may be used to achieve a representative sample of the functional characteristics of the geometry of the energy return device. For an energy return device comprising linear structures, a representative set of planes may comprise 10 planes spanning 40 mm along the length of a diagonal section; in various embodiments more or fewer planes at greater or lesser spacing may be used.

[0475] When an average geometry that someone skilled in the art would determine to be representative of the general structure, such as of the heel section of the midsole or the forefoot section of the midsole, any of the methods of determining the geometry can be used to determine if a section of a shoe midsole falls within the range of geometries claimed as part of the device. Different embodiments may fall within the range of a different one ormore of these methods of measurement without necessarily falling within an other or others. Different methods disclosed herein may be more suitable for specific embodiments of the device.

[0476] DRESS SHOE EXAMPLE OF CONFOUNDING GEOMETRY

[0477] A simplified cross section of the device as could be used in a dress shoe (or various other kinds of shoe) is shown below in Fig. 117. In this dress shoe example, it is desirable for aesthetic reasons to encase the conical or linear diagonal structure 1160 in a low durometer foam outer member. If this outer foam component 1162 is low enough durometer or of a geometry which allows it to easily compress, it can be added with minimal affect on the performance of the diagonal structures. If the outer foam is high enough durometer, it may be necessary to steepen the angle or make other changes to the diagonal structure. Main diagonal structure and additional structures may be discrete parts or may be a variable durometer foam or matrix material. To determine if the total structure will behave as desired to provide benefits of the present device, the S-curve deformation method previously described can be used, for example, to determine if the midsole results in a straight line on a vertical plane that becomes an S-curve that passes through a horizontal or steeper line as described earlier, when fully compressed.

[0478] EXAMPLE OF NONSYMMETRIC ANGULAR SHAPE

[0479] In some embodiments, an energy return device employs a combination of geometries and / or utilizing features of multiple configurations of energy return devices. Such embodiments may involve, for example, non-symmetrical arrangements. Figs. 118-122 illustrates an energy return device combining first conical foam dome segments 1164 with second inverted conical dome segments 1166. In the event that both the first conical foam dome segments 1164 and the second inverted conical dome segments 1166 are configured with the geometries or properties recited elsewhere herein, such as falling into the ranges of angles described elsewhere herein, and even though the average angle of the complete device may not fall within the outer angle range, the combination may provide the benefits of the symmetric versions of the device. Someone skilled in the art will be able to determine if the benefits of sections of the diagonal structures fall within the bounds of the present device as described in this disclosure.

[0480] WEB ELEMENTS WITH DISCONTINUOUS RINGS

[0481] Some embodiments of guide support structures 34 may include discontinuities, for example to control or limit the distribution of force around the guide support structures. In some embodiments web structures 36 may include discontinuities or other spatial anomaliesin the geometry of the web element. An example of a web structure 36 with discontinuities is shown in Fig. 25. The web structure 36 a web structure ring 1250 of material around a web structure inner diameter of the web structure 36 with discontinuities 1252. These discontinuities 1252 can be gaps, grooves, cuts, slits or other breaks in the material. A given discontinuity may comprise a space between two segments of the material of the web structure ring 1250. If the web structure ring 1250 material is continuous or has few discontinuities, the strain on this ring, between the fingers, can be too high in some circumstances and can cause material failure, or can make the web too difficult to compress, resulting in a high pressure point under the users foot.

[0482] The discontinuities 1252 can be situated between one or more of the web structure 36 radial fingers, as shown in Fig. 125. These discontinuities 1252 can be defined by gaps separating sections of material of web structure ring 1250, or they can be defined by slits in web structure ring 1250 in which adjacent sections of material of web structure ring 1250 touch when the web structure 36 is at rest. With no space, the web structure ring ID maintains a similar diameter during compression and this can be beneficial for some configurations. Having gaps separating sections of material of web structure ring 1250 can allow the web structure ring ID to compress a small amount during the vertical compression of energy return device. The benefit of this is to reduce the outward expansion of the conical disk by a controlled amount which, in some configurations, can reduce the strain on the foam on the bottom of the foam disk where the web is pushing outward on it.

[0483] Web Structures Without a Domed Disk

[0484] In some embodiments of an energy return device, the compressible foam domed disk 20 may be replaced by a resilient compressible structure of a different geometry. In such embodiments, the web structure 36 and other elements of an energy return device may be embedded in a non-conical resilient structure. Exemplary illustrations of a nondomed resilient compressible structure are illustrated in Figs. 126 and 127. By using a circumferentially expandable web in a conical cavity but without a conical outer shape of a disk, the lateral shear stability of a midsole can be increased along with providing a softer midsole with more travel, as shown below. In Fig. 126, the expandable web structure 36 is embedded in a resilient disk structure 1260. The geometry of the resilient disk structure 1260A in Fig. 126 is cylindrical, but various geometries may be applicable, such as an inverted cone resilient disk structure 1260B, which is inverted relative to the orientation of the web structure 36, as illustrated in Fig. 128. Various geometries for a resilient disk structure 1260 may be employed, including, for example, curved geometries or a conicalshape for part of the disk and a non-conical or inverted conical or other combination of conical or curved shapes at different areas of the disk.

[0485] Some non-limiting embodiments are set out in the following clauses.

[0486] Clause 1. An energy return device for a midsole of a shoe for absorbing and returning energy from compression of the device under a downward force applied from a typical wearer via an upper of the shoe over a range of travel extending in a height direction from the upper of the shoe in an uncompressed state towards an outsole of the shoe, the energy return device comprising:

[0487] a resilient structure of compressible foam or matrix material supporting the upper in relation to the outsole, the resilient structure defining a cavity, the resilient structure defining an opening for air to enter the cavity or being permeable to air;

[0488] the resilient structure being arranged to collapse, under the compression by the downward force applied to the upper by the typical user, into the cavity so that during a first part of the range of travel of the compression the structure deforms by bending of the resilient structure, the resilient structure collapsing into lateral bounds defined by the resilient structure at a height corresponding to a maximum lateral extent of the cavity, and during a second part of the range of travel of the compression at a further degree of compression than the first part, the resilient structure deforms by direct compression of the material of the resilient structure between the upper and the outsole.

[0489] Clause 2. The energy return device of clause 1 further comprising a lateral expansion limiter arranged to resist lateral expansion of the resilient structure.

[0490] Clause 3. The energy return device of clause 1 or clause 2 in which the resilient structure when not compressed under the downward force comprises a domed disk.

[0491] Clause 4. The energy return device of clause 3 in which the domed disk comprises a conical disk.

[0492] Clause 5. The energy return device of clause 4 in which the conical disk is a hollow frustum.

[0493] Clause 6. The energy return device of any one of clauses 3-5 as dependent on clause 2 in which the lateral expansion limiting structure comprises a ring about a base of the domed disk.

[0494] Clause 7. The energy return device of clause 6 in which the ring is a ring spring.

[0495] Clause 8. The energy return device of any one of clauses 3-7 further comprising a guide support structure extending along walls of the domed disk and havinggreater stiffness than the domed disk for shaping the collapse of the dome under the compression by the downward force.

[0496] Clause 9. The energy return device of clause 8 in which the guide support structure comprises a conical disk.

[0497] Clause 10. The energy return device of clause 8 in which the guide support structure comprises a web.

[0498] Clause 11. The energy return device of clause 10 in which the web comprises radially extending fingers.

[0499] Clause 12. The energy return device of clause 11 in which a first finger is circumferentially connected to a second finger with a bridge member at a first radial position and said second finger and a third finger are connected together at a second radial position and the second finger and the third finger are not connected together at the first radial position.

[0500] Clause 13. The energy return device of clause 12 where the bridge member is thinner than the first finger member where it is attached to the first finger member and thinner than the second finger member where it is attached to the second finger member.

[0501] Clause 14. The device of any one of clauses 11-13 in which successive circumferentially adjacent fingers of the radially extending fingers are not all circumferentially connected at an upper end of the web.

[0502] Clause 15. The device of any one of clauses 11-14 in which the successive circumferentially adjacent radially extending fingers are not all circumferentially connected at a lower end of the web.

[0503] Clause 16. The device of any one of clauses 11-15 in which under the compression of the structure under the downward force from the user the guide support structure compresses from conical to flat.

[0504] Clause 17. The device of any one of clauses 11-15 in which under the compression of the structure under the downward force from the user the guide support structure compresses from conical to inverted conical.

[0505] Clause 18. The energy return device of any one of clauses 8-17 in which the guide support structure is attached to an inside surface of the domed disk.

[0506] Clause 19. The energy return device of any one of clauses 8-17 in which the guide support structure is attached to an outside surface of the domed disk.

[0507] Clause 20. The energy return device of any one of clauses 8-17 in which the guide support structure is embedded within the domed disk.

[0508] Clause 21. The energy return device of any one of clauses 8-19 in which the guide support structure has pockets or through holes that are radially aligned so as to make the insert conical disc insert more extensible or compressible in the circumstantial direction relative to the radial direction, such that under the compression by the downward force, the guide support structure flares out at a bottom end of the guide support structure increasing a strain deformation of and around a bottom of the domed disk.

[0509] Clause 22. The energy return device of any one of clauses 3-21 in which the domed disk when not compressed by the downward force has an upper average outer diameter at a plane perpendicular to the height direction at 75% of the stack height that is <150%, <149%, <148%, <147%, <146%, <145%, <144%, <143%, <142%, <141%, or <140% and >70%, >71%, >72%, >73%, >74%, >75%, >76%, >77%, >78%, >79%, or >80% of a lower average inner diameter at a plane perpendicular to the height direction at 25% of the stack height.

[0510] Clause 23. The energy return device of any one of clauses 3-22 further comprising an opening in the outsole, and in which the opening for air to enter the cavity is present and aligned with the opening in the outsole or the structure is permeable to air.

[0511] Clause 24. The energy return device of clause 23 in which the outsole has a tread design which allows air to flow in and out of the conical disk assembly and to the edges of the outsole when it is in contact with the ground.

[0512] Clause 25. The energy return device of clause 23 or clause 24 in which the opening for air to enter the cavity is present and aligned with the opening in the outsole and a ceiling of the cavity comprises a surface adapted to contact ground under the shoe in use.

[0513] Clause 26. The energy return device of any one of clauses 2-25 in which the lateral expansion limiter comprises the upper or the outsole.

[0514] Clause 27. The energy return device of any one of clauses 1-26 further comprising a compression biased damper made of a compressible material and adapted to begin compressing part way through the range of travel.

[0515] Clause 28. The energy return device of clause 27 in which the compression biased damper is located within the cavity.

[0516] Clause 29. The energy return device of any one of clauses 1-28 in which the energy return device has greater than 40%, or greater than 50% of a total energy return within a portion of the range of travel corresponding to the downward force being less than 50% of the downward force applied from the typical wearer.

[0517] Clause 30. The energy return device of any one of clauses 1-29 in which a portion of the resilient structure including at least parts of 80% or more, 70% or more, 60% or more, 50% or more, 40% or more, 30% or more, 20% or more, or 10% or more of a height of the resilient structure, when not compressed under the downward force, vertically overlaps the cavity.

[0518] Clause 31. The energy return device of any one of clauses 1-30 in which, when the resilient structure is compressed in the height direction, there is a degree of compression less than or equal to the compression of the device under the downward force applied from the typical wearer at which a set of points of the resilient structure forming, when the structure is not compressed under the downward force, a straight line in a vertical cross section of the resilient structure having an angle in relation to the height direction representing an outer wall angle of the resilient structure, are shifted under the degree of compression to form a curve that crosses a plane perpendicular to the height direction 3 times or more.

[0519] Clause 32. The energy return device of any one of clauses 1-30 in which, when the resilient structure is compressed in the height direction, there is a degree of compression less than or equal to the compression of the device under the downward force applied from the typical wearer at which a set of points of the resilient structure forming, when the structure is not compressed under the downward force, a straight line in a vertical cross section of the resilient structure having an angle in relation to the height direction representing an outer wall angle of the resilient structure, are shifted under the degree of compression to form a curve that crosses a plane 3 times or more where the plane is tilted by 1 to 2 deg, 2 to 3 deg, 3 to 4 deg, 4 to 5 deg, 5 to 6 deg, 6 to 7 deg, 7 to 8 deg, 8 to 9 deg, 9 to 10 deg, 10 to 11 deg, 11 to 12 deg, 12 to 13 deg, 13 to 14 deg, 14 to 15 deg, 15 to 16 deg, 16 to 17 deg, 17 to 18 deg, 18 to 19 deg, or 19 to 20 deg from being perpendicular to the height direction.

[0520] Clause 33. The energy return device of any one of clauses 1-32 in which an outer angle of the resilient structure, or the outer wall angle when dependent on clause 31 or clause 32, measured from vertical is >15deg, >16deg, >17deg, >18deg, >19deg, >20deg, >21deg, >22deg, >23deg, >24deg, >25deg, >26deg, >27deg, >28deg, >29deg, >30deg, >31deg, >32deg, >33deg, >34deg, >35deg, >36deg, >37deg, >38deg, >39deg, >40deg, >41deg, >42deg, >43deg, >44deg, >45deg, >46deg, >47deg,>48deg, >49deg, >50deg, >51 deg, >52deg, >53deg, >54deg, or >55deg measured over 40% or more, 50% or more, 60% or more, or 70% or more of a height distance from the outsole to the upper.

[0521] Clause 34. The energy return device of any one of clauses 1-33 having the opening for air to enter the cavity and in which the opening has a check valve biased to resist air flow out of the cavity.

[0522] Clause 35. The energy return device of clause 34 in which the resilient structure further defines a second opening to the cavity, the second opening having a restricted orifice.

[0523] Clause 36. The energy return device of any one of clauses 1-33 having the opening for air to enter the cavity in which the opening has an orifice restricted in size to cause greater resistance to compression, as compared to energy return in expansion from the energy return device.

[0524] Clause 37 The energy return device of any one of clauses 1-33 having the opening for air to enter the cavity and in which the opening is adapted to be restricted by the downward force applied from the typical wearer.

[0525] Clause 38. The energy return device of clause 37 in which the opening is located at a heelward end of the resilient structure and adapted to be restricted by the downward force applied by a heel strike and become less restricted as the user moves forward in a stride.

[0526] Clause s39. The energy return device of clause 38 in which the opening is adapted to be less restricted by a foot strike that is not a heel strike than by a heel strike.

[0527] Clause 40. The energy return device of any one of clauses 1-39 shaped to conform to a tapering of the height between the upper and the outsole towards a front end of the midsole.

[0528] Clause 41. The energy return device of any one of clauses 1-40 in which the resilient structure is formed as one piece with the outsole.

[0529] Clause 42. The energy return device of any one of clauses 1-41 in which the resilient structure is formed of closed cell foam.

[0530] Clause 43. A shoe having a midsole comprising one or more energy return devices of any one or more of clauses 1-42.

[0531] Clause 44. The shoe of clause 43 in which a single energy return device of the one or more energy return devices is used under a heel of the shoe in the midsole.

[0532] Clause 45. The shoe of clause 43 or clause 44 in which the one or more energy return devices are multiple energy return devices.

[0533] Clause 46. The shoe of clause 45 comprising at least an energy return device of the multiple energy return devices under the heel of the shoe and plural energyreturn device of the multiple energy return devices under the forefoot of smaller diameter and height than the at least an energy return device under the heel.

[0534] Clause 47. The shoe of clause 45 or clause 46 in which the multiple energy return devices include two energy return devices in the forefoot and are collectively wider than the upper by 10% or more, 20%, or more, 30% or more, of a largest diameter of the two energy return devices.

[0535] Clause 48. The shoe of any one of clauses 45-47 further comprising a wedge of compressible foam or deformable material ahead of the forwardmost energy return device connecting a bottom surface of the upper with a top surface of the outsole, that shears as the stance progresses toward toe-off, and the resistance to shearing of this member unshears the structure during toe-off.

[0536] Clause 49. The shoe of any one of clauses 45-48 in which the multiple energy return devices are arranged from the heel to the forefoot so that a second energy return device of the multiple energy return devices begins to compress from foot strike pressure before a previous disk is fully compressed.

[0537] Clause 50. The shoe of any one of clauses 44-49 in which one or more of the one or more energy return devices protrude into or through the outsole.

[0538] Clause 51. The shoe of clause 50 in which the one or more of the one or more energy return devices contact the ground.

[0539] Clause 52. The energy return device of any one of clauses 1-42 where the compression of the material of the resilient structure between the upper and the outsole includes vertical compression of a now-horizontal sidewall.

[0540]

Claims

AMENDED CLAIMS received by the International Bureau on 01 December 2025 (01.12.2025)1. An energy return device for a midsole of a shoe for absorbing and returning energy from compression of the device under a downward force applied from a typical wearer via an upper of the shoe over a range of travel extending in a height direction from the upper of the shoe in an uncompressed state towards an outsole of the shoe, the energy return device comprising: a resilient structure of compressible foam or matrix material supporting the upper in relation to the outsole, the resilient structure defining a cavity the resilient structure being arranged to collapse, under the compression by the downward force applied to the upper by the typical user, into the cavity so that during a first part of the range of travel of the compression the structure deforms by bending of the resilient structure, the resilient structure collapsing by buckling into lateral bounds defined by the resilient structure at a height corresponding to a maximum lateral extent of the cavity, and during a second part of the range of travel of the compression at a further degree of compression than the first part, the resilient structure deforms by direct compression of the material of at least a buckled portion of the resilient structure between the upper and the outsole and / or by direct compression of the material of the at least a buckled portion of the resilient structure between the upper and the ground.

2. The energy return device of claim 1 further comprising a lateral expansion limiter arranged to resist lateral expansion of the resilient structure.

3. The energy return device of claim 1 or claim 2 in which the resilient structure when not compressed under the downward force comprises a domed structure.

4. The energy return device of claim 3 further comprising a guide support structure extending along walls of the domed structure and having greater stiffness in a radial or diagonal direction than the domed structure for shaping the collapse of the dome under the compression by the downward force.

5. The energy return device of claim 4 as dependent on claim 2, in which the lateral expansion limiting structure comprises a ring about a base of the domed structure.

6. The energy return device of claim 4 or claim 5 in which the guide support structure comprises a conical disk.

7. The energy return device of claim 4 or claim 5 in which the guide support structure comprises a web, the web having an interrupted Outer Diameter (OD).

8. The energy return device of claim 7 in which the web comprises radially extending fingers.

9. The energy return device of any one of claims 5-8 in which the guide support structure is attached to an inside surface of the domed structure.

10. The energy return device of any one of claims 5-9 in which the guide support structure has pockets or through holes that are radially aligned so as to make the insert conical disc insert more extensible or compressible in the circumstantial direction relative to the radial direction, such that under the compression by the downward force, the guide support structure flares out at a bottom end of the guide support structure increasing a strain deformation of and around a bottom of the domed structure.

11. The energy return device of any one of claims 4- 10in which the domed structure when not compressed by the downward force has an upper average outer diameter at a plane perpendicular to the height direction at 75% of a stack height that is <150%, <149%, <148%, <147%, <146%, <145%, <144%, <143%, <142%, <141%, or <140% and >70%, >71%, >72%,>73%, >74%, >75%, >76%, >77%, >78%, >79%, or >80% of a lower average inner diameter at a plane perpendicular to the height direction at 25% of the stack height.

12. The energy return device of any one of claims 1-11 in which the resilient structure defines an opening for air to enter the cavity or is permeable to air.

13. The energy return device of any one of claims 3-11 further comprising an opening in the outsole, and in which at least one of a) the resilient structure defines an opening for air to enter the cavity, the opening for air to enter the cavity being aligned with the opening in the outsole, or b) the resilient structure is permeable to air.

14. The energy return device of claim 13 in which the outsole has a tread design which allows air to flow in and out of the conical disk assembly and to the edges of the outsole when it is in contact with the ground.

15. The energy return device of claim 13 or claim 14 in which the opening for air to enter the cavity is present and aligned with the opening in the outsole and a ceiling of the cavity comprises a surface adapted to contact ground under the shoe in use.

16. The energy return device of any one of claims 12-15 having the opening for air to enter the cavity and in which the opening has a check valve biased to resist air flow out of the cavity.

17. The energy return device of claim 16 in which the resilient structure further defines a second opening to the cavity, the second opening having a restricted orifice.

18. The energy return device of any one of claims 12-15 having the opening for air to enter the cavity in which the opening has an orifice restricted in size to cause greater resistance to compression, as compared to energy return in expansion from the energy return device.

19. The energy return device of any one of claims 12-15 having the opening for air to enter the cavity and in which the opening is adapted to be restricted by the downward force applied from the typical wearer.

20. The energy return device of claim 19in which the opening is located at a heelward end of the resilient structure and adapted to be restricted by the downward force applied by a heel strike and become less restricted as the user moves forward in a stride.

21. The energy return device of any one of claims 1-20 in which the energy return device has greater than 40%, or greater than 50% of a total energy return within a portion of the range of travel corresponding to the downward force being less than 50% of the downward force applied from the typical wearer.

22. The energy return device of any one of claims 1-21 in which a portion of the resilient structure forming 80% or more, 70% or more, 60% or more, 50% or more, 40% or more, 30% or more, 20% or more, or 10% or more of a height of the resilient structure, when not compressed under the downward force, is positioned within the horizontal footprint of the cavity.

23. The energy return device of any one of claims 1-22 in which, when the resilient structure is compressed in the height direction, there is a degree of compression less than or equal to the compression of the device under the downward force applied from the typical wearer at which a set of points of the resilient structure forming, when the structure is not compressed under the downward force, a straight line in a vertical cross section of the resilient structure having an angle in relation to the height direction representing an outer wall angle of the resilient structure, are shifted under the degree of compression to form a curve that crosses a plane perpendicular to the height direction 3 times or more.

24. The energy return device of any one of claims 1-23 in which, when the resilient structure is compressed in the height direction, there is a degree of compression less than or equal to the compression of the device under the downward force applied from the typical wearer at which a set of points of the resilient structure forming, when the structure is not compressed under the downward force, a straight line in a vertical cross section of the resilient structure having an angle in relation to the height direction representing an outer wall angle of the resilient structure, are shifted under the degree of compression to form a curve that crosses a plane 3 times or more where the plane is tilted by 1 to 2 deg, 2 to 3 deg, 3 to 4 deg, 4 to 5 deg, 5 to 6 deg, 6 to 7 deg, 7 to 8 deg, 8 to 9 deg, 9 to 10 deg, 10 to 11 deg, 11 to 12 deg, 12 to 13 deg, 13 to 14 deg, 14 to 15 deg, 15 to 16 deg, 16 to 17 deg, 17 to 18 deg, 18 to 19 deg, or 19 to 20 deg from being perpendicular to the height direction.

25. The energy return device of any one of claims 1-24 in which the resilient structure has an outer surface and an angle of the outer surface of the resilient structure measured from vertical is >15deg, >16deg, >17deg, >18deg, >19deg, >20deg, >21deg, >22deg, >23deg, >24deg, >25deg, >26deg, >27deg, >28deg, >29deg, >30deg, >31deg, >32deg, >33deg, >34deg, >35deg, >36deg, >37deg, >38deg, >39deg, >40deg, >41deg, >42deg, >43deg, >44deg, >45deg, >46deg, >47deg,>48deg, >49deg, >50deg, >51deg, >52deg, >53deg, >54deg, or >55deg measured over 40% or more, 50% or more, 60% or more, or 70% or more of a height distance from the outsole to the upper.

26. The energy return device of any one of claims 1-25 in which the resilient structure is formed of closed cell foam.

27. A shoe having a midsole comprising one or more energy return devices of any one of claims 1-26.

28. The shoe of claim 27 in which the one or more energy return devices are multiple energy return devices and the shoe comprising at least an energy return device of the multiple energy return devices under the heel of the shoe and plural energy return device of the multiple energy return devices under the forefoot of smaller diameter and height than the at least an energy return device under the heel.

29. The shoe of claim 26 or claim 27 further comprising a wedge of compressible foam or deformable material ahead of the forwardmost energy return device connecting a bottom surface of the upper with a top surface of the outsole, that shears as the stance progresses toward toe-off, and the resistance to shearing of this member un-shears the structure during toe-off30. The shoe of any one of claims 27-29 in which the one or more energy return devices are multiple energy return devices and in which the multiple energy return devices are arranged from the heel to the forefoot so that a second energy return device of the multiple energy return devices begins to compress from foot strike pressure before a previous disk is fully compressed.

31. The energy return device according to any one of claims 1-26 where compression of the compressible foam or matrix material of the resilient structure between the upper and the outsole during the second part of the range of travel includes vertical compression of a nowhorizontal sidewall.

32. A shoe comprising: an upper for receiving the foot of a wearer of the shoe; an outsole for contact with the ground; a midsole connecting the upper and the outsole, the midsole including a buckling member formed of a compressible foam or matrix material, the buckling member being connected to the upper at an upper end and to the outsole at a lower end; and a motion limiting connector connecting the upper and the outsole, the motion limiting connector limiting relative horizontal motion of the upper relative to the outsole sufficiently to cause the buckling member to buckle under vertical compression of the shoe by the foot of the wearer.

33. The shoe of claim 32 in which at least one of the connection of the buckling member to the upper at the upper end and the connection of the buckling member to the outsole at the lower end is via a first hinge.

34. The shoe of claim 33 in which another of the connection of the buckling member to the upper at the upper end and the connection of the buckling member to the outsole at the lower end is via a second hinge.

35. The shoe of claim 33 or claim 34 in which the first hinge comprises a live hinge formed of the compressible foam or matrix material.

36. The shoe of claim 33 or claim 34 in which the first hinge comprises a fabric hinge or a flexible hinge material.

37. The shoe of claim 36 in which the fabric hinge or the flexible hinge material comprises a sheet that extends over substantially a full surface of one side of the buckling member to act as a reinforcing structure.

38. The shoe of any one of claims 32-37 in which the buckling member is one of plural buckling members, the plural buckling members having different orientation such that one or more of the plural buckling members acts as the motion limiting connector for one or more others of the plural buckling members.

39. The shoe of any one of claims 32-38 in which the buckling member has a vertical- to-horizontal aspect ratio of 2 or greater, 2.5 or greater, 3 or greater, 4 or greater, 5 or greater, 6 or greater, or 7 or greater.

40. The shoe of any one of claims 32-39 in which the buckling member, when buckled under vertical compression of the shoe by the foot of the wearer, compresses to act as a bottom-out bumper for the vertical compression of the shoe by the foot of the wearer.

41. The shoe of any one of claims 32-40 in which the buckling member is biased to buckle in a buckling direction.

42. The shoe of claim 41 in which the buckling member is biased to bend in the buckling direction by being pre-bent or curved in that direction.

43. The shoe of claim 41 in which the buckling member is biased to bend in the buckling direction by being thinner near the midpoint of its height, and asymmetric such that a centre line is bent or curved in the buckling direction.

44. The shoe of any one of claims 41-43 further comprising a strain reducing member at a surface of the buckling member that is an inner surface relative to the buckling direction, the strain reducing member configured to prevent or reduce creasing of the buckling member as it buckles.

45. The shoe of claim 44 in which the strain reducing member is a tube or rod oriented substantially perpendicular to the buckling member and to the buckling direction.

46. The shoe of any one of claims 41-45 in which the buckling member buckles outwards such that the buckling member is not fully compressed between the upper and the outsole at full compression of the midsole.

47. The shoe of any one of claims 41-46 further comprising an elastic member connected to the buckling member that stores energy as the buckling member buckles.

48. The shoe of any one of claims 41-47 further comprising a guide support structure extending along the buckling member comprising a more rigid material than the compressible foam or matrix material of the buckling member.

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