This invention relates to landing mats, and is concerned with mats of the kind used for absorbing impact forces that result from the landing on the mat or other collision with it of a moving body. Mats of this kind have application as crash mats, fall arrestors and comparable items used in emergency rescue equipment, but have a principal application in gymnastics and other sports, where the term "landing mat" is used. However, the term "landing mat" is used in the description and claims herein to refer generally to mats of the above kind without limitation of application unless specifically stated.

According to the present invention there is provided a landing mat for absorbing impact forces, wherein a deformable force-distributing platform is backed by an array of compressible gas-springs each of which comprises a compressible resilient-body containing gas, the compressible bodies of the array are each coupled via an individual gas-flow path to a gas manifold that is common to the gas-springs, and wherein the incidence of impact force on the force-distributing platform compresses the compressible body of each of one or more of the gas-springs to bring about increase of gas pressure within that body for outflow of gas from it into the manifold via the respective gas-flow path at a faster rate than for consequential backflow of gas into it from the manifold via a gas-flow path that is more restrictive to gas flow than the outflow path.

The impact condition for which the mat should give most protection, referred to as the ^Λ rime condition' , is dependent on mass and impact velocity, and is where the mat is intended to exhibit maximum xforce efficiency' FE, defined by equation (1) as follows:

FE = [Impact Energy] /[ (Peak Force) x (Peak Deformation Depth) ]

For gymnastics mats it is probably best to ensure that male gymnasts landing from the maximum height commonly occurring, get best force efficiency, and that the mat does not 'bottom out' at this level of impact. For fall arrestors it may be best to ensure that small bodies do not exceed a certain peak value of G. Currently, lanyard- type fall arrestors must limit the force to 6 kilonewtons and this is dangerously high for a small person falling from 3 or more metres .

Impacts of equal energy do not necessarily have equal FE values. Thus an impactor of 20 kilograms hitting the mat at 5 metres per second will have significantly different FE from an impactor of 10 kilograms travelling at 7.07 metres per second although both have impact energy of 250 joules. This occurs because an initial

component of deceleration is dependent on the initial velocity of an impact and almost independent of the impactor mass, whereas a final decelerating force is mainly dependent on the incident impact energy. Landing mats according to the invention preferably have values of FE of at least 0.6 but more preferably greater than 0.7 for prime condition impacts . When a landing mat is to be used with a wide range of impactor masses (e.g. human bodyweights in the range 40 to 140 kilograms) the prime condition may be chosen to minimise the deceleration factor G for the 40 kilogram bodyweight. G is a dimensionless ratio defined by equation (2) as follows:

G = [Decelerating Force] / [Bodyweight x g]

where g is the acceleration due to gravity.

Alternatively, the prime condition may be chosen to minimise decelerating force for an average bodyweight at maximum expected impact energy.

The landing mat may be horizontal or slightly inclined and arranged to absorb the impact of falling objects. In other applications an upright landing mat is provided to absorb the impact of objects in horizontal motion. Typically, the gas-springs and the manifold comprise a sealed system containing normal atmospheric air and the air pressure within the sealed system is at or above the ambient atmospheric pressure. The gas-springs may be provided as individual air bellows arrangements or may be integrated together in a contiguous arrangement. The manifold provides a relatively unrestricted air passage that interconnects all the individual gas- spring elements.

For the case where the mat is horizontal, a downward impact

deformation may cause one, or more preferably several, gas-springs to compress vertically causing air to flow into the manifold before flowing into adjacent uncompressed gas-springs, thereby raising the pressure in these uncompressed gas-springs. As the impact

deformation recovers, air pressure in the uncompressed gas-springs forces air back into the manifold and then back into the compressed gas-springs, which start to expand vertically and regain equilibrium state. Flow restrictions on each gas-spring will be effective to regulate the relative rates of flow into and out of the manifold. For example, with the mat of the invention, the size of an orifice that is open for both outflow into the manifold and backflow from it may be smaller than an orifice that is open only for outflow from the gas-spring into the manifold. Furthermore, restriction may involve a valve that opens only during outflow from the gas-spring.

The present invention is especially applicable to landing mats used by gymnasts. The dismount at the final phase of a gymnastic exercise is critical. Performers have to take off and fly from an apparatus such as the horizontal bar and land safely but also remain still and upright after landing. Gymnastics landing mats must thus absorb high impact energies while reducing peak deceleration forces to safe levels without deforming deeply or unevenly. One method of reducing peak deceleration is to provide nearly constant deceleration throughout the landing.

The manifold may comprise a plurality of interconnected pipes or conduits but preferably it comprises an air-filled chamber extending the entire area of the mat in a single layer. Typically, the force- distribution platform, the gas-springs and the manifold are arranged in three separate layers of the mat, with the force distribution platform uppermost and the manifold underneath the gas-spring layer. Alternatively, the manifold may be positioned directly below the force- distribution platform with the gas-spring layer underneath. When a gymnast lands on the platform, it deforms below and around the gymnast's feet, and air in one or more gas-springs compresses, thus providing spring repulsion. The repulsion force is the product of the gauge pressure developed in the compressed gas-springs and the area of the gas-spring in contact with the force distributing platform. Each gas-spring will have a different degree of

compression, being a maximum directly below the gymnast's landing spot and diminishing in the gas-springs positioned radially outwards from the landing spot. It is useful to define an effective

deformation area AE as being equal to the cross-sectional area of a single cylindrical piston gas-spring that has the same initial volume and pressure as the sealed air volume of the landing mat and has the same static force displacement characteristic. For example, a male gymnast weighing 70 kilograms may compress a mat having AE equal to 0.36 square metres by 10 millimetres when standing

stationery on the mat. The piston head in a cylindrical piston gas- spring of cross-sectional area 0.36 square metres (that is a diameter of 0.68 metres), and the same air volume and initial pressure as the mat would move by 10 millimetres when a compressive force of 70 kilograms weight (687 newtons) is applied. The size of AE is dependent on the stiffness of the foam material, which in turn is strongly dependent on its thickness as well as on its elastic modulus. Preferably, the thickness of the force distribution platform is not less than 10% and not more than 30% of the overall mat height. The size of AE is also dependent slightly on the contact area of an impactor on the landing platform. A small test impactor may have an impact footprint of less than one hundred square centimetres whereas the impact footprint of a male gymnast is usually taken to be a 25 centimetre square, that is 625 square centimetres .

Initially, the gas springs may be pre-pressurised and the resulting repulsion force may be opposed by tethers that hold the platform in its quiescent state, which is preferably fairly flat and at uniform height above the floor where the mat is placed. The initial

decelerating force experienced by a gymnast on landing increases rapidly to a high value as the tension in the tethers quickly releases. It is however important that the initial force is not instantaneous as this would result in a very high jolt force. To avoid this, the inflated sealed system may be provided with slight bulges on the underside of the mat that flatten during initial impact. The tethers remain under tension until the bulges become flat. The force required to flatten the bulges increases gradually from zero to maximum over a deformation depth of a few millimetres. The gas-springs may not be pre-pressurised. Instead, the mat may be provided at ambient pressure with the gas-springs containing open- cell foam or a mixture of air and open-cell or closed-cell foam. As before, the gas-springs and the manifold may comprise a sealed system such that compression of gas-springs under an impact- deformation area gives rise to a rise in pressure in adjacent uncompressed gas-springs.

As the mat deforms and compresses, the rise in gauge pressure is determined by the reduction in overall volume of the gas-spring system and by the differential pressure opposing release of

compressed air into the manifold. The differential pressure quickly reaches a maximum when the downward velocity of the impacting body is still high and the flow of compressed air into the manifold is greatest. The differential pressure reduces to zero at the end of the deceleration when the impact zone is at maximum displacement and the flow of air from the gas-springs is zero. At the same time (at maximum displacement) , the ambient pressure due to overall volume change is a maximum. The two-pressure rise mechanisms have opposite rates-of-change slope and may be arranged to regulate the average rate of pressure change (and thus the deceleration force) to be nearly constant, which minimises the peak force sustained during landing. In this respect, the stiffness characteristics of the force-distribution platform, the size of the sealed enclosure and the flow restrictions are important and must be explicitly selected to achieve the required impact-absorbing performance.

The flow restrictions may involve flow-control valves that each comprise a flexible-flap valve arrangement that limits the backflow into the gas-spring from the air passage of the manifold when the flow reverses, and the impact zone starts to restore to its

equilibrium position. Each valve is open for air flow out of its associated gas-spring but may be closed or only partially closed to limit the rate of return flow and thereby control the degree of rebound. The valve mechanism is typically a flexible flap covering an aperture in the gas-spring at the interface to the manifold. The flap deflects outwards when the pressure in the gas spring exceeds a small threshold above the pressure in the manifold. The degree of outward deflection may increase with increasing pressure

differential .

The elastic modulus and thickness of the force-distribution platform may be chosen so that the impact-deformation is spread evenly and widely beyond the impact footprint (namely, the soles of the gymnast's feet) . This feature eliminates the tendency of a gymnast's foot to sink into the mat and possibly cause momentary foot

fixation. The platform can be fabricated from a mixture of materials and incorporate special stiffening members such as plates or rods or the like. Preferably, but without limitation, the platform

deformation caused by projectile impact is synclastic. Strongly anticlastic platforms should be avoided as they will distribute force unevenly and create undesirable asymmetric landing zones.

Suitable platform materials include high density foams and auxetic materials including auxetic honeycomb sandwich panels and auxetic foams . The platform may be located within the sealed enclosure or may be bonded or temporarily attached to the top surface of the sealed enclosure with re-closable fasteners such as hook-and-loop fasteners or the like. In any form of the invention, the indentation compression stiffness of the platform measured at 25% deformation should be at least twice but more preferably more than ten times the indentation compression stiffness of the sealed enclosure measured with a standard indenter.

Landing mats in accordance with the present invention will now be described, by way of example, with reference to the accompanying drawings, in which: Figure 1 is a schematic plan view of a first embodiment of a landing mat for gymnastics;

Figure 2 is a sectional side view of a first segment of the landing mat of Figure 1, the section being taken along line II-II of Figure 1;

Figure 3 is an internal sectional plan view of a gas-spring air- pocket of Figures 1 and 2, the plan view corresponding to shaded area 30 of Figure 2;

Figure 4 is a plan view and side view of a manifold interface used in second and third embodiments according to the invention of landing mats for gymnastics;

Figure 5 is a sectional side view of a segment of a second

embodiment of a landing mat for gymnastics, the sectional side view being taken along line V-V of Figure 4 with additional mat structure added;

Figure 6 is a sectional side view of an alternative arrangement of landing mat based on the corresponding segment of Figure 5;

Figure 7 is a schematic sectional side view illustrating aspects of the impact deformation caused by an impactor landing on the landing mat of Figure 5;

Figure 8 is a schematic plan view of a further embodiment of a gymnastics landing mat;

Figure 9 is a sectional view of the gymnastics landing mat of Figure 15, the section being taken on two planes along stepped line IX-IX of Figure 8;

Figures 10, 11 and 12 are graphs showing plots of pressure versus time for three configurations of a simulated model of a landing mat during identical incident impacts emulating the landing impact of a typical male gymnast;

Figure 13 is a graph showing three plots of force versus impact deformation depth corresponding to the three pressure versus time plots of Figures 8, 9 and 10 and a fourth plot demonstrating the effect of increasing the mat inflation pressure;

Figure 14 is a graph showing force versus impact deformation for two configurations of a simulated model of a landing mat during impacts emulating a standard test procedure for gymnastics landing mats;

Figure 15 is a schematic plan view of a cushioning assembly

according to the invention;

Figure 16 is a sectional view of a fall arresting safety cushion that uses the cushioning assembly of Figure 15 and includes a sectional side view of Figure 15, the section being taken along line XVI-XVI of Figure 15; and

Figure 17 is a graph showing force versus deformation depth for two test conditions of the fall arresting safety cushion of Figure 16.

The landing mat of Figures 1 to 3 is representative of a gymnastics landing mat according to the invention with, for example, overall dimensions of 2 metres length, 1.5 metres width and 0.2 metres height. This size of landing mat is frequently used in gymnastics competitions and is particularly suited to assembly using equipment used for standard king sized' bed mattresses.

Referring now to Figures 1 to 3, the gymnastics landing mat 1 represented comprises: a top foam platform 2, a side-by-side array of compressible gas-springs constituted by resilient air-pockets 3 formed as box-sections between foam divider sections 4, an air distribution manifold 5 extending below the air-pockets and formed between a semi-rigid sheet 6 and a base membrane 7, air-flow control parts 8 and 9, manifold spacers 10 that maintain the air-space between the semi-rigid sheet 6 and the base membrane 7, sets of tether components 11, 12 and 13, top cover 14, and side cover 15. The mat lies on a stable and relatively rigid floor 16, and the manifold airspace is typically between 10 to 30 millimetres high, as determined by the height of the spacers 10.

The mat 1 is inflated with air via an air inlet/outlet coupling on the manifold exterior wall (not shown) . This coupling is used to inflate and adjust the internal pressure. Advantageously, the operating pressure can be adjusted to optimise the landing

characteristics for different classes of gymnast, for example, low pressure for novice juniors and higher pressure for men's

competitions. The mat is preferably permanently maintained at operating pressure and only requires occasional pressure checks and adjustment. Optionally, a pressure monitor can be installed in each mat and programmed to 'wake up' periodically and wirelessly transmit data to a local computer. During use, continuous monitoring of the mat's internal pressure can provide valuable information. For example, as a gymnast walks or stands on the mat before or after an exercise, the average pressure rise in the mat is directly related to their bodyweight. On landing, the pressure versus time data is related to the deceleration experienced by the gymnast. This provides important information about the deceleration factor G experienced by gymnasts.

In order to maintain constant pressure, the mat must be sealed airtight. In this regard, and as illustrated in Figure 2, the outermost surfaces of the mat are clad with a top cover 14 and side cover 15, and a base membrane 7. These items are typically of heavy- duty polyester-reinforced polyvinyl chloride (PVC) sheet that provide a high degree of airtightness . The three PVC sheets may be separate and bonded to the outer foam parts, which may be closed- cell foam to maintain the air seal. This is convenient when the three materials are different. Thus, the top cover may be covered by carpet, whereas the base membrane may be a stiffer fabric than the side cover. Alternatively, the entire outer cover may be bonded or welded at the edge seams to form an overall sealed airbag. The side cover 15 may overlap onto the outer edges of the top cover 14 and the base membrane 7 to provide additional reinforcement. This increases the force distribution lengthwise along the edges of the mat and at the corners, and compensates for the loss of deformation- opposing force near the edges of the mat. Optionally, additional stiffening material can be inserted in the overlap areas. The outer foam sides 17 may be made from a grade of foam that is denser and harder than the foam dividers 4 to provide addition stiffness at the mat edges.

The foam platform 2 provides a flat, uniform landing surface that deforms under landing of the gymnast to form a wide indentation under the gymnast's feet such that the deformed volume is

significantly greater than the product of the gymnast's footprint and the deformation depth. Typically, the foam platform 2 is of a high-density stiff-grade urethane-foam, or similar relatively high modulus foam material and is preferably at least 20 millimetres thick, but more preferably 30 to 50 millimetres thick.

The dividers 4 that form the walls of the air-pockets are preferably made from lightweight, highly compressible open-cell foam with sufficient rigidity to maintain their required shape and dimensions within the mat. The dividers 4 are provided as individual sections with truncated wedge ends. When assembled, a hollow channel 18 is formed inside the foam at the four corners of each air-pocket. A sealing coat 19 is applied to one side of each foam divider section to block air flowing directly between adjacent air-pockets through the foam divider. The non-sealed side 20 allows air within the foam to expel into the air-pocket, when compressed. The arrangement is such that each air-pocket is enclosed by two sealed sides 19 and two non-sealed sides 20 and the foam walls with non-sealed sides contribute to the total volume of air within the air-pocket.

The sets of tether components 11, 12 and 13 comprise a top anchor 11, a restraining line 12 and a bottom anchor 13. The tethers are fitted at each intersect of the air-pocket walls, before the top cover 14 is bonded onto the foam platform 2. To facilitate assembly, the mat may be mounted and compressed on a standard mattress-tufting machine to reduce its overall thickness and give access to upper and bottom sides. The restraining cords 12 are each formed from a single looped length of line. The two ends of each line are then threaded into the top anchor 11 and knotted to fix the line onto the anchor 11, leaving a loop of precise length firmly attached to the centre of the anchor 11. At each tether position, a latch hook needle with pointed tip (not shown) is fed through a central clearance hole of the related bottom anchor 13 and through the hollow channel 18. It then pierces through the foam platform 2 and hooks onto the loop end of the appropriate restraining line 12. The loop is then pulled through the mat and out through the central clearance hole of the bottom anchor 13 and secured. Air sealing is formed between the closed-cell foam platform 2 and the restraining line but additional sealing compound can be applied. Sealing compound is applied on the interfaces between the bottom anchor 13 and the base membrane 7.

Each air-pocket 3 is provided with an air-flow control valve in the form of a flexible flap 8 held against the underside of the semirigid sheet 6, and a co-acting outflow orifice 9 (there may be more than one such orifice 9) that is cut out of the semi-rigid sheet 6. When the landing mat is inflated but quiescent (that is, not subject to dynamic load) the flap 8 covers the orifice 9 (or where there are more than one orifice 9, each of them) .

When a gymnast lands on the mat, at least one of the air-pockets 3, but preferably a plurality of them, are compressed. Pressure within each of the one or more compressed air-pockets 3 in consequence rises and pushes open its flap 8 to allow air to vent out of the compressed air-pocket through its orifice 9 (or each such orifice 9 where more than one is provided in the relevant air-pocket 3) . The air is vented into the airspace of the manifold 5.

The stiffness of the semi-rigid sheet 6 and the spacers 10 are chosen to ensure that the peak pressure differential developed during initial landing does not significantly compress the airspace of the manifold 5. Each orifice 9 should be large to provide a high rate of flow during the landing impact and reduce the pressure differential as required. Each air-pocket 3 is provided with at least one backflow orifice 21 (of smaller diameter than the orifice 9) to allow air to return to the air-pocket as it decompresses during the restoring phase when the landing deceleration ceases and the gymnast is lifted back to the final stationary level on the landing mat. Optionally, the backflow orifice 21 may be formed by an aperture through the flap 8. Landing mats according to the present invention can be significantly lighter than conventional mats since foam material is extensively replaced by air.

A second embodiment of the invention will now be described with reference to Figures 4 and 5.

Referring to Figure 4, a vacuum-formed manifold plate 40 is arranged to interface with eight gas-springs that are arranged side-by-side in four pairs. Dotted lines 41 indicate the positions of the gas- springs, which are bonded onto the plate at a later stage of manufacture. Sixteen spacers 42 raise the plate above its reference plane 43 by typically 15 to 25 millimetres. After vacuum forming, apertures are formed in the plate 40 to provide outflow orifices 44, backflow orifices 45 and fixing holes for push-on fasteners 46 used to attach valve flaps 47. In the configuration of Figure 4, the backflow orifices 45 are provided by openings left uncovered by the flaps 47 at rounded ends of the apertures in the plate 40, rather than by separate, discrete apertures in the plate.

Preferably, the effective aperture-area of each backflow orifice 45 is not more than 33% and not less than 5% of the maximum effective aperture-area of the outflow orifices 44, where effective-area' of the relevant orifice means the product of the physical area of the orifice and its coefficient of discharge. The different shapes and sizes of the two orifices lead to different values of discharge coefficient. The effective aperture-area of outflow orifice 44 initially increases as the operating pressure differential increases but quickly reaches a maximum. For gymnastics landing mats, it is found by simulation that when the ratio of the effective backflow aperture-area to the effective outflow aperture-area is greater than 0.33, the mat produces undesirable rebound. In this context

^outflow' means flow of air from a gas-spring into the manifold. However, if the ratio is less than 0.05 the air pressure in the manifold becomes undesirably high as the airflow into uncompressed gas-spring is too slow and this produces very high peak forces and high rebound. The plate 40 may be fabricated by vacuum forming a 1.5 millimetre thick sheet of thermoplastic such as high impact polystyrene (HIPS) , or other suitable polymer of suitable thickness; the holes and apertures may be cut with a laser knife or other suitable means. The plate 40 is typically 100 centimetres long by 50 centimetres wide and provides a convenient way of building different sizes of gymnastics landing mats such as 1.5 x 2.0 metres (requiring six plates) or 2.0 x 3.0 metres (requiring twelve plates) . Different overall sizes of plate and gas-spring array, and other forms of manufacture such as injection moulding, may be adopted. The valve flaps are typically made from spring steel shim or suitable polymer such as 0.25 millimetre thick film sold under the Registered Trade Mark ^x MYLAR' , or the like.

Referring now to Figure 5, the gymnastic landing mat 50 of the second embodiment of the invention is shown in part in sectional view, and comprises open-cell foam blocks 51 bonded to the manifold plate 40 of Figure 4. A manifold chamber 52 is formed between the manifold plate 40 and a base sealing membrane 53 that is bonded to the bases of the manifold spacers 42. A force-distributing foam platform 54 is bonded to the top surfaces of the foam blocks 51. The thickness of the foam platform 54 is preferably not less than 10% of the overall mat height and has a density greater than 70 kilograms per cubic metre.

The foam blocks are treated by dipping or spraying with liquid latex or other substance such that an air-impervious skin 55 is formed on the surface. In practice, a double height foam block is treated and then split in half to provide two blocks each with five air- impervious surfaces and one open surface that interfaces with the manifold plate 40. Other methods of forming an air-impervious skin may be used including a self-skinning process during manufacture of the foam. Optionally, reticulated foam may be used to reduce airflow resistance and a suitable method of forming an air-impervious skin applied. Figure 5 shows the foam blocks 51 as separate items for clarity but in practice the blocks may be bonded together. The lower surfaces of the blocks are bonded to the manifold plate along their peripheries only, so that air can flow freely through the foam surface contiguous with the orifices 44. Optionally, the foam block skins 55 can incorporate a non-stretch fabric scrim. Whatever form of construction is used, the gas-spring units must be able to withstand multiple compression from frequent impacts throughout its service life. Other fabrication procedures and other array

configurations and sizes can be adopted.

Each foam block 51, integral sealing skin 55 and co-acting air vent orifices 44 and 45 taken together form a gas-spring unit where the gas is contained within the cell structure of the open-cell foam blocks 51. The density of the foam blocks 51 should be preferably not more than 30 kilograms per cubic metre but more preferably not more than 20 kilograms per cubic metre. This ensures that most of the repelling force of the landing mat derives from the pneumatic forces of airflow into and out of the manifold chamber 52. The foam blocks provide slight additional impact absorption through their viscoelastic characteristic but more importantly provide geometric structure and dimensional accuracy without requiring inflation from an external pressurised air source. The overall mat volume should not be completely airtight to allow the air pressure inside the mat to settle slowly as the ambient pressure changes and as the

temperature of the mat changes. In particular, momentary pressure- increase due to a gymnast walking over, or jumping onto the mat should not result in contained air being expelled. This can be achieved by providing a flap valve near the centre of the base sealing-membrane 53 that closes tightly to prevent air escape but allows air to enter the mat if the ambient pressure exceeds the internal pressure; this occurs slowly since air must first seep underneath the lower membrane that lies flat and firm on the supporting floor.

Another embodiment of the invention in the form of a landing mat for gymnastics is illustrated in a sectional part view in Figure 6.

Referring to Figure 6, the illustrated landing mat 60 is constructed in similar manner to the landing mat of Figure 5 except that the foam blocks 51 are replaced by unfilled air-pockets 61. The air- pockets 61 have walls 62 of ripstop fabric formed into a rectangular cuboid. The upper surface of the cuboid is held in shape by a square or rectangular foam former 63 and the lower surface of the cuboid is held in shape using lengths of high-bond double-sided tape 64 to adhere the fabric to the surface of the manifold plate 40. Openings 65 in the square former 63 allow access to the inside of the air- pocket to complete the bonding operation. Once the lower ends of all the air-pockets have been bonded to the manifold plate, the square formers 63 are bonded together using joining tape or the like, and are then bonded to the underside of a foam platform 66. Other means of fabricating the fabric air-pockets can be adopted including stitching or fabric welding. This mat arrangement is not self- supporting but requires inflation to a gauge pressure that at least supports the weight of the foam platform, for example 690 pascals (0.1 pounds per square inch). The mat is held in shape when slightly pressurised by the fabric walls, which act as tethers similar to the tether lines 12 of Figure 2.

Figure 7 shows a test impactor 70 landing on the mat 50 of Figure 5 directly above a foam block 5la with the deformation in the upper layer 54 spread laterally from the impact footprint such that adjacent foam blocks 51b are also compressed. In this purely illustrative example, the force-distribution does not extend significantly beyond gas-springs 51b so there is negligible

compression in the adjoining outer gas-springs 51c. The diagram is a simplified two-dimensional representation and other gas-springs within a three by three sub-array are also compressed to varying extent. The deformation depth is measured from the initial top plane of the mat 71 to the bottom of the impactor 70. Shaded region 72 shows the cross-section of the deformation in an equivalent single gas-spring piston with piston area AE. Curved arrows 73 indicate the direction of airflow throughout the mat volume. In each gas-spring, the force opposing compression is proportional to its internal gauge pressure and to its cross-sectional area. When the impactor 70 first lands on the mat, the pressure differentials across the apertures and flow of air into the manifold chamber rise quickly but reduce to zero as the impactor velocity reduces to zero. Simultaneously, the average pressure throughout the mat increases as the impactor reaches maximum deformation-depth, thereby reducing the overall mat- volume .

On the rebound, the impactor 70 is propelled upwards and the pressure differentials reverse as the mat recovers shape and the pressure starts to return to its quiescent value. The quiescent gauge pressure is zero in the case where the mat is not pre- pressurised. The control flaps 47 close against the manifold plate 40 and against the exposed area of foam blocks, and the air now flows back into the foam blocks 51a and 51b via the backflow orifices 45. This high degree of flow restriction introduces large hysteresis in the force-deformation characteristic, reducing rebound from the mat surface to very small values.

Referring now to Figures 8 and 9, a gymnastics landing mat 80 comprises two separate halves joined together along the centre line 81 of a fabric carpet 82 that covers the overall upper surface of the mat 80. Thus, the mat 80 can be folded in half for storage or transport purposes. Typically, the full folded-out area of the mat of Figure 8 is 3 metres by 2 metres, with height of 0.2 metres. The left-hand half of mat 80 as viewed in Figure 8 comprises a 5x7 array of gas-springs 83 contained within an airtight skin 84. The gas- springs 83 are not contiguous but spaced slightly apart within an air-space occupying the same height as the gas-springs to provide a manifold 85 surrounding the gas-springs. A foam platform 86

distributes the impact force from a gymnast or other heavy object landing on the carpet 82 and compresses a group of gas-springs 83 over an effective area ΆΕ. Preferably, the effective area AE is not less than the area encompassing four gas-springs so that the mat absorbs impact forces uniformly irrespective of the point of impact relative to the centre of a gas-spring. The right-hand half of the mat is substantially identical in mirror image to the left-hand half, with gas-springs 87, manifold 89 and foam platform 90. The two halves are separately inflated via air inlet connectors 88.

Each gas-spring 83 or 87 comprises airtight fabric walls 91 formed around and adhesively bonded to a block of open-cell foam 92 at the bottom and to a semi-rigid former plate 93 at the top. Other means of attachment can be used including outward clinch staples (to the former plate) or stitching or welding. Preferably, the foam block 92 is made from reticulated foam that provides low airflow resistance. The fabric walls 91 are preferably made from lightweight ripstop fabric such as sailcloth or other highly flexible fabric with weight value not more than 70 grams per square metre. In order to

facilitate assembly of individual gas-springs, the reticulated foam block 92 and former plate 93 can be held in position on a mandrel pushed through the centre of the foam block 92 and the fabric walls 91 attached such that the fabric is pulled up to the requisite height uniformly round the perimeter of the gas-spring. The fabric walls act as tethers to hold the mat at known and consistent height throughout its extent when inflated above ambient air pressure.

Flap valves 94 are formed as integral parts of the fabric walls. These open outwards to allow air to vent out of a gas-spring 83, 87 when the air pressure inside the gas-spring is greater than the air pressure in the surrounding manifold chamber 85, 89. Optionally, a stiffening material such as film sold under the Registered Trade Mark ^MYLAR' , can be bonded onto the flaps to improve operation. When the pressure differential reduces to zero and reverses the flaps 94 close against the reticulated foam block surface leaving small gaps 95 to allow a controlled amount of backflow. The fabric walls 91 joined to the former plate 93 may have unintentional small gaps at the corners. This is acceptable provided the air escape through these gaps is small compared to the intended degree of backflow .

During gas-spring compression, the reticulated foam block 92 remains virtually undistorted until the compression reaches a maximum and it comes in contact with the former plate 93. The pressure in the gas- spring increases but the foam experiences little force across its thickness since it is almost open to airflow and thus does not experience the fairly high initial force required to compress it. Instead, the fabric walls 91 bulge outwards and reduce in height. This ensures that the flap valve apertures do not distort and reduce in size during initial compression. Also, the flaps close tightly against the reticulated foam when backflow occurs. On decompression, the fabric walls 91 are sucked in towards the centre of the gas- spring and this will initially diminish the required effect of removing the upward acceleration force and thereby reducing rebound. Once the gas-spring is partly decompressed the walls will start to regain shape and effectively limit the rate of expansion and upward force .

Stiffening members 96 are provided along the four edges of each of the two halves of the mat 80. These may be made from strips of glass-fibre composite or from polycarbonate or the like. The purpose of the stiffening members 96 is to increase the effective

deformation area AE for impacts on, or close to, the edges of each half of the mat. For optimum performance, the ratio of AE to overall mat area should preferable be not more than 0.25 and not less than 0.05 in mats according to the invention. For this reason it is preferable to divide a very large mat into two separate inflatable sections as illustrated in Figures 8 and 9. A very high ratio of AE to overall mat area results in excessive rise in manifold pressure with deformation depth, which dominates the force-deformation behaviour so that the gas-springs do not deform sufficiently to discharge sufficient air into the manifold and the mat exhibits excessive bounce irrespective of any combination of outflow and backflow apertures. In the other extreme, if the ratio of AE to overall mat area is less than 0.05 the mat becomes excessively soft and bottoms out at fairly low values of impact energy unless the outflow is severely restricted, which in turn causes very high peak forces .

The performance of landing mats for official gymnastic competition is specified by Federation Internationale de Gymnastique (FIG) . The FIG test procedure uses a standard test impactor comprising a 20 kilogram mass with a 10 centimetres diameter flat, circular impact footprint. The impactor is dropped onto specific impact locations on the mat from a height of 0.8 metres (thereby attaining landing velocity of 3.96m/s) and it is also a requirement that the mat is only 20 centimetres high. The FIG test specification requires that the average displacement of the impactor below the top plane of the landing mat is not more than 110 millimetres and any rebound above that plane is not more than 90 millimetres. A constant force of 1622 newtons applied for 52 milliseconds will bring the FIG impactor to rest in 110 millimetres. This represents the theoretical minimum force that could meet the FIG requirements. It is theoretically feasible to construct a landing mat that meets FIG test limits with peak deceleration force of slightly over 1622 newtons. However, such a landing mat would prove too soft for heavier gymnasts and result in bottoming out when the gymnast would effectively hit the floor, albeit at reduced velocity. ^' 'Bottoming out' occurs when the

deformation depth approaches the full available depth and the mat thickness reduces to a thin and almost incompressible layer. With the present invention, it is preferable to arrange that the maximum deceleration force obtained with the FIG impactor tests is slightly below the maximum conforming value of 3000 newtons. This ensures that the landing mat is firm enough to absorb all a gymnast's landing energy without bottoming out at an early stage of the impact .

Preferably a different form of impactor is used to evaluate

performance using simulation. Research has shown that a 24

kilograms impactor with 25 centimetres square footprint and drop velocities of up to 6.5 metres per second provides a close fit to the impact footprint and initial landing characteristics of a male gymnast (bodyweight 72 kilograms) on a representative landing mat (Pain, M. T. G. , Mills, C. & Yeadon, M.R. (2005) . Video analysis of the deformation and effective mass of gymnastics landing mats.

Medicine and Science in Sports and Exercise, 37, 1754-1760.) The 24 kilogram rigid mass with square footprint (referred to hereinafter as the 24kg impactor) provides an easily modelled stimulus with which to study landing mat performance.

Figure 10 shows plots of pressure versus time for a simulated model of a 24kg impactor landing with initial velocity of 6.5 metres per second on a single gas-spring equivalent of a typical air-filled landing mat. The control valve aperture adopted for the plotted results in Figure 10 was chosen to optimise the peak decelerating force on the 24kg impactor. Plot 101 (dotted trace) shows the response for the differential pressure across the control valve aperture. This peaks at 102 near the beginning of the collision when the impactor speed is still near maximum and pressure in the manifold chamber is low. This is followed by a negative slope as the impactor slows down and airflow rate reduces. Plot 103 (dash trace) shows the pressure in the manifold chamber, which distributes to all the uncompressed parts of the mat. This has a positive slope as air from the gas-spring transfers to the manifold chamber. Plot 104 (solid trace) shows the pressure in the gas-spring, which is the sum of the control valve differential pressure and the manifold chamber pressure. The two pressures combine to give almost constant pressure (and thus constant force) for most of the deceleration phase. The rate of backflow is a small fraction of the forward flow at a given pressure differential. When the impactor reverses direction and starts to rebound, the gas-spring gauge pressure rapidly falls to just above zero at point 105 and the impactor slowly returns to a final resting position. The impactor initially landing at 6.5 metres per second comes to rest with negligible rebound after approximately 270 milliseconds.

Figure 11 and 12 show plots from reruns of the simulation of Figure 10 demonstrating the effect of making the control valve aperture area smaller and larger respectively. In Figure 11, plots 111, 113 and 114 correspond to plots 101, 103 and 104 of Figure 10 with the effective valve control aperture reduced by 25%. This increases the differential pressure and the peak at 112 is significantly higher than peak 102. The initial pressure is much higher than the average pressure and this increases the impactor deceleration and reduces the deformation depth. Consequently, the change in volume of the mat is lower and thus the pressure rise in the manifold 113 is lower than the corresponding pressure 103 in Figure 10. In Figure 12, plots 121, 123 and 124 correspond to plots 101, 103 and 104 of Figure 10 with the effective valve control aperture increased by 25%. The modelled mat parameters exhibit a softer initial landing with deeper deformation but, because the deformed volume of the mat has increased, the overall pressure in the manifold chamber (plot 123) has also increased and is now higher than the corresponding pressure at 103 in Figure 10.

Figure 13 shows plots of force versus deformation depth of data computed from model simulation. Plots 131, 132 and 133 correspond to the pressure versus time plots displayed in Figures 10, 11 and 12 respectively. Plot 131 exhibits nearly constant force of just less than 5000 newtons over most of the response and maximum deformation depth of 126 millimetres. The value of FE as defined in Equation (1) is 0.81 for plot 131. The peak force in plot 132 is 6260 newtons, occurs early in the response and correlates with the high differential pressure 112 of Figure 11. The maximum deformation depth in plot 132 reduces to 111 millimetres as the mat gives harder overall stiffness due to more constricted outflow aperture and the FE value reduces to 0.73. In plot 133 the deceleration force is initially low and correlates with the low initial peak of the differential pressure plot 122 due to increased outflow aperture. The mat response is relatively soft and deformation depth increases to 136 millimetres. This

generates a relatively high peak force of 5350 newtons due to the mat being more compressed at the end of the deceleration phase compared to the optimum of plot 131 and FE is now only 0.71.

It can be seen from Figures 10 to 13 that FE is strongly dependent on the ratio of the differential pressure developed across the outflow orifices to the pressure increase in the manifold caused by overall compression (i.e. by reduction in volume). It is thus useful to adopt this pressure ratio as a calibrating parameter PR. It is found by analysis that highest FE is achieved in general when PR is equal to 0.7 or close to that value. For example, the PR ratio taken from plots 101 and 103 of Figure 10 show a value of 0.68 whereas the PR ratios in the corresponding plots of Figures 11 and 12 are 1.17 and 0.44 respectively. Thus, PR gives a sensitive indication of whether to increase or decrease the outflow orifice apertures for highest FE at a chosen prime condition. In developing and testing gymnastics landing mats it is standard practice to measure instantaneous force and deformation during test impacts using accelerometer and/or high speed video monitors. This and additional static force testing can be used to determine PR values without the need to monitor internal pressures. This in turn provides a means to optimise FE for a given prime condition by adjusting outflow apertures to achieve PR values at or near 0.7 or at a value within the range 0.4 to 1.4 or more preferably within the range 0.6 to 0.9 that results in high FE values. Plot 134 of Figure 13 shows the benefit of increasing inflation pressure from 690 pascals (which is the quiescent pressure in plot 131) to 6890 pascals (1.0 pound per square inch) and at the same time reducing AE by about 20% to approximately equalise the

resultant force (pressure times area) . The higher initial quiescent pressure increases the initial rate of decelerating force giving a flat force characteristic over a greater deformation range. FE for plot 134 increases to 0.87 and both peak force and deformation depth reduce relative to plot 131. However, very high inflation pressures prove detrimental to performance. These produce high rebound irrespective of the dampening effect of the flow restrictors.

Tension in internal tethers (e.g. in the restraining cords 12 of Figure 2) rise significantly so the mat becomes very hard and resilient. High pressure requires relatively small AE compared to low pressure so the variation in mat volume and pressure is minimal. The mat characteristic reverts to a constant force spring, which can result in high FE but at the cost of excessive rebound. It is thus preferable that gymnastics landing mats according to the invention are not inflated above 7000 pascals.

The model simulation presented in Figure 13 predicts negligible rebound in all four instances. The incident kinetic energy of the 24 kilogram mass landing at 6.5 metres per second (1014 joules) is totally expended by the work done (force x distance) during the deceleration phase and the steep downward slope of the plots shows that the restoring or rebound force reduces to zero almost

immediately after the maximum deformation is achieved. The plots presented in Figures 10 to 13 are useful as a guide to what happens in practice with real landing mats and is specific to pneumatic systems where impact force is generated by changes in air pressure in the inflated mat. The model computation includes the displaced mass and restoring force contributed by the foam upper layer but not its viscoelastic and compression rebound properties as these are insignificant compared to the pneumatic forces. The 24kg impactor only models the maximum impact force and displacement of a gymnast. In real-life, a male gymnast's bodyweight is typically three times the mass of the rigid impactor but he modulates the loading on the mat by joint flexion and spreads the duration of his landing phase to minimise peak forces.

Figure 14 shows calculated plots of force versus deformation depth for the FIG impactor. Plot 141 corresponds to mat characteristics identical to those of Figure 10. The peak force of 2.7 kilonewtons and maximum deformation of 91 millimetres are well within the FIG requirements although considerably more than would be achieved with a mat with smaller outflow apertures and designed for minimum force for FIG test conditions. The impactor comes to rest with minimal rebound and remains on the mat where its final deformation force 14,2 corresponds to its static deadweight of about 200 newtons . Plot 143 shows the effect of removing the flap valve control so that the outflow and backflow apertures are one and the same. The

deceleration phase follows plot 141 exactly until the full

deformation is reached and the flap valve of plot 141 starts to close near the end of the deceleration. The return phase shows the impactor accelerating quickly back to its start position. The much reduced enclosed area within plot 143 signifies much less absorbed energy, which results in the impactor flying off the mat with excessive rebound height.

Referring now to Figures 15 and 16, a fall arresting safety cushion 150 comprises a lower inflatable cushioning assembly 151 and an upper inflatable force distributing landing platform 152. The platform comprises a plurality of tubes 153 which are joined together extending longitudinally side by side and which are filled with air to a high pressure so that they strongly resist compression and bending deformation. Optionally, the tubes can be encased within top and bottom covers 154 and welded or adhesively bonded to the tubes to give additional rigidity. The platform 152 is preferably welded or otherwise fixed to the top surface of the cushioning assembly 151. Preferably, the height (i.e. the thickness) of platform 152 is not less than 5% of the overall height of the safety cushion 150 but more preferably at least 10% of the overall height.

The cushioning assembly 151 comprises a plurality of separate cylindrical gas-springs 155 within an inflatable airbag 156 and extending the full height of the airbag from the floor 157 to the ceiling 158. The gas-springs 155 are made from low-stretch and air- impervious material such as PVC coated polyester fabric or sailcloth or the like and provide vertical tethers to maintain the cushioning assembly at a required height. The air space around the gas-springs form the airflow distribution manifold 159. Outflow orifices 160 are provided at the junction of the gas-springs 155 and the airbag floor 157. Airflow control flaps 161 are attached above the outflow orifices 160. In the quiescent state, the flaps 161 cover about two- thirds of the outflow aperture areas and thus form backflow

apertures 162 comprising the remaining one-third of the outflow aperture that remains open.

In this application, the need for minimal rebound does not apply so the back flow apertures can be larger than the preferred maximum limit for gymnastics landing mats where very small rebound is required. The larger backflow ensures that the gas-springs can be rapidly inflated on first deploying the safety cushion and if preferred the size of the backflow aperture can be increased to 50% of the outflow aperture if rapid inflation has higher priority than low rebound.

As one or more of the gas-springs deform under strong impact, the cylindrical walls will collapse. To prevent this from interfering unduly with flap closure, the gas-spring walls below dashed line 163 in Figure 16 may be reinforced to retain their shape until the deformation approaches maximum depth. As the gas-springs decompress, the flaps fully regain their ability to close tightly against the outflow orifices 160.

A test impactor 164 is shown landing on and compressing gas-spring 155a and partially compressing gas-springs 155b. The remote gas- spring 155c is uncompressed. In gas-spring 155a the flaps are fully open so air vents into the manifold 159 at a high rate. In gas- springs 155b the flaps are open but the relative rate of compression is much lower so air vents into the manifold 159 at a lower rate. In gas-spring 155c and in all other uncompressed gas-spring 155, the flaps are fully closed so air flows from the manifold 159 via the backflow apertures 162 into the uncompressed gas-springs at

relatively very low rate. The air expelled from the compressed gas- springs 155a and 155b is distributed via the manifold to all the uncompressed gas-springs, which being much more numerous each share a very small portion of the total airflow out of gas-springs 155a and 155b. Since airflow is proportional to the square root of pressure across an orifice, the backflow apertures do not

significantly limit the flow rate from the manifold into the uncompressed gas-springs although smaller than the outflow

apertures .

The two assemblies are separately inflated, with the gauge pressure in the platform 152 being at least twice but more preferably ten times the gauge pressure in the cushioning assembly 151. Both assemblies 151 and 152 may be rapidly inflated from one high pressure air source by arranging a pressure relief valve on an air inlet to the platform 152 to vent into the cushioning assembly 151, with a second relief valve and co-acting control means ensuring that air supply stops once the cushioning assembly reaches its desired pressure. When both assemblies have reached operating pressure, the relief valves are manually or automatically closed so that the two inflated assemblies are isolated.

The safety cushion may be used to break the fall of a person jumping from a widow or for other applications such as landing from a high jump in athletics. In these applications the maximum drop height is accurately known but bodyweights will vary. Advantageously, the decelerating force increases with bodyweight so that the maximum value of G does not increase in inverse proportion to bodyweight (as occurs in constant force arrestors) .

Figure 17 shows plots of calculated force versus deformation depth for a safety cushion designed to minimise landing impacts to below 10G (see Equation (2)) with a drop to ground level of 4 metres and with a range of bodyweights from 40 to 140 kilograms. The height of the cushioning assembly is taken as 90 centimetres and the height of the landing platform 10 centimetres so the free-fall height is 3 metres .

Plot 171 shows the calculated force versus deformation depth for a rigid impactor of 40 kilograms with a free drop of 3 metres before it impacts the landing platform 152. For this application, the 40 kilogram impactor and 3 metre free drop is the preferred prime condition so the outflow orifices 160 are chosen to minimise peak force at this impactor mass and thereby provide a G factor of less than 10. From plot 171, it can be seen that the force versus deformation depth characteristic is flat at 3.8 kilonewtons over most of the deceleration phase and thus G is limited to about 9.7. Also, the calculated values for FE and PR are found to be 0.82 and 0.77 respectively. Unlike the plots of Figure 13, the force on the impactor does not quickly die away to zero once the maximum

deformation is reached. Instead, the force remains relatively high until about 20 centimetres from restoration and a rebound of over 30 centimetres occurs. The high rebound results from the backflow aperture being increased to 33% of the outflow aperture to allow quick initial inflation.

Plot 172 shows the force versus deformation depth characteristic for a 120 kilograms rigid impactor. Here, the initial deceleration due to restriction in the outflow orifices 160 is secondary to the gradual rise in pressure and gas-spring force as the cushioning assembly 151 deeply deforms and reduces overall air volume. The calculated peak force in plot 172 is just below 7 kilonewtons and thus the G factor is only 5.9. In this case the FE and PR values reduce to 0.58 and 0.38 respectively. The calculated rebound in this case is 22 centimetres.

At 120 kilograms the cushioning assembly approaches the bottoming out condition with calculated deformation depth of 87 centimetres. However, the system will remain safe as controlled decelerating capacity is still available since the landing platform 152 provides a buffer layer that combines with the cushioning assembly to limit peak force for several centimetres beyond the normal depth of operation. Thus, for bodyweights up to 140 kilograms the value of G increases above 5.9 but remains well below 10 although the

cushioning assembly 151 starts to bottom out. With this system, the calculated ratio of maximum to minimum G is only 1.64 whereas a constant force arrestor would result in a corresponding ratio of about 3.5, which would give unacceptably high G for low bodyweights and/or risk having lack of capacity for high bodyweights.