ES1268359U - An aquatic device for sports and/or recreational activities (Machine-translation by Google Translate, not legally binding) - Google Patents

Abstract

An aquatic device (1) to carry out sports and / or recreational activities, comprising a floating hull (2), which has a bow end (6) and a stern end (5), characterized in that the hull (2) Floating provides a positive buoyancy between 30% and 60% of the weight of the user of the aquatic device (1), in which the live part of the hull (2) has a hydrodynamic configuration and is provided with a daggerboard (3), in which the deck comprises a depression (4) of greater depth in the vicinity of the stern (5) than in the vicinity of the bow (6) and ergonomically configured to support the human chin and torso on the surface of the depression (4), and in which the bow (6) is an inverted bow (6).

Description

DESCRIPTION

An aquatic device for sports and / or recreational activities

Technical sector of the invention

The present invention refers to a device for swimming and performing other sports and / or recreational water activities in a safe way, so it can be stated that it belongs to the nautical, sports, leisure and safety sectors.

The device object of the invention allows the partial buoyancy of a user in order to exercise, since it has been designed to swim safely and quickly by human traction either in the sea, lakes, swimming pools or rivers, for activities typical of divers, in even for other activities like gliding on the waves.

Background of the invention

In the current market there is a wide variety of devices or means for the practice of sports such as swimming or other aquatic recreational activities by which the buoyancy of users is increased, such as floats, mats and boards of various designs, such as known hard boards, called "boogie boards" in English, which help swimmers to increase their buoyancy when the current is stronger, that is, especially on the waves. The following documents show some of these devices for the practice of aquatic recreational activities: ES2252588, ES2161106, US20100273372 and US5389023.

The nautical devices currently available on the market do not offer users a hydrodynamic glide, nor do they allow them to face the waves with naturalness and performance, nor a glide with fluidity through traction of the human arm and that at the same time respects the human body from the head up to the hip.

The need to provide a versatile nautical device is highlighted, which allows use in more diverse circumstances, without the user having to choose different devices depending on the activity or environmental conditions, that is, that the same device serves to slide swimming with the only motor power of your arms and legs, to glide on load-bearing waves, and to simply float in more recreational or leisure activities, both in the absence or in the presence of significant currents.

Explanation of the invention

In order to provide a solution to the problems raised, an aquatic device is disclosed to carry out sports and / or recreational activities in a safe way, including swimming in water (swimming pool, lakes, rivers or sea), sliding through the waves, swimming in currents, serving as a support for divers while they swim, as a signaling buoy for their presence, etc. The aquatic device comprises a floating hull having a bow end and a stern end.

In essence, the aquatic device is characterized by the fact that the floating hull has a positive buoyancy comprised between 30% and 60% of the weight of the user of the aquatic device, because the live part of the hull has a hydrodynamic configuration and is provided with a centerboard, and because the hull deck comprises a depression of greater depth in the vicinity of the stern than in the vicinity of the bow, in which said depression has an ergonomic configuration to support the human chin and torso (of the user) on the surface of the depression. Furthermore, it is also characteristic of the aquatic device of the invention to have an inverted bow, that is, a bow that recedes towards the stern as it rises. The aquatic device has little sleeve at the height of the user's shoulder and torso placement so that the user can swim freely without obstacles.

Thus, the aquatic device of the invention has a singular hull shape that allows increasing the penetration of the bow or front part, allowing greater speed and maneuverability.

In addition, the aquatic device presents greater buoyancy than some hard boards, by increasing the contact surface, displacing a greater volume of water and allowing a better distribution of weights on the aquatic surface, even in the absence of significant currents. Likewise, it allows use in more diverse circumstances due to its characteristics, which provide it with certain properties comparable to floats and similar gadgets. Its hydrodynamic design allows optimal gliding during swimming or planing with load-bearing waves.

The aquatic device of the invention has been conceived and made in order to obtain numerous and notable advantages over other aquatic support means, providing intermediate buoyancy, and due to its hydrodynamic design it provides high performance in sliding over the water and a significant improvement in swimmer safety. It is designed so that the user can swim more easily because their feet and hands are free for the exercise of swimming. As will be explained later, it has between 2 to 3 anchor points to hold the swimmer, allowing him to freely exercise the appropriate movements for swimming and exercising. These anchors are quick release. In this way, due to its design, where it provides a buoyancy between 30% and 60% depending on the size model, the user remains "intermittent" in order to play sports. With the boards available on the market, in the absence of waves, if a user wants to swim with them they isolate him enough from the water, in the same way that happens with an inflatable mattress. In addition, given its hydrodynamic design, it offers greater performance in swimming and displacement that, together with the daggerboard of its live work, considerably increases the speed with the same impulse and therefore, the enjoyment. The centerboard converts the swing of the swim into a forward push, which is known as "pumping."

According to another characteristic of the invention, the cross section of the hull at the stern is a flattened U-shaped section.

According to another characteristic of the invention, the upper port and starboard edges of the deck extend parallel along a rear section of the deck adjacent to the stern until a change in level from which the edges extend convergent towards the bow inverted in an intermediate section and in a forward section of the deck. The ergonomic configuration of the depression is such that it allows the user to have their arms outside the cover with freedom to move them for swimming, since the arms are at the height of the intermediate section, before the change in level of the upper edges of the port and starboard. In a position of use of the aquatic device, the user leans on the cover, particularly on the surface of the depression, placing his waist and part of the thighs in the rear section of the cover, his chest in the middle section and his chin in the front section. The legs protrude from the stern so that the user has the freedom to move them while swimming.

According to another characteristic of the invention, the height of the upper port and starboard edges of the deck in the rear section measured with respect to the keel of the hull is greater than the height of said upper edges in the intermediate section measured with respect to the keel of the hull. This height difference allows the hip area to be protected laterally along the upper edges of the rear section, a section that preferably has a flattened U-shaped cross section, while the upper edges of the intermediate section, being lower in height, allow the movement of the arms outside the floating hull.

According to a preferred embodiment of the aquatic device object of the invention, the height of the upper port and starboard edges of the deck in the forward section adjacent to the inverted bow measured with respect to the keel of the hull is equal to or greater than the height of the Port and starboard upper edges on the rear leg measured relative to the keel of the hull.

As for the bow, when inverted, it generates an attack and breakage of the water with the advance of the device, in addition to positioning more volume in the bow, which causes more water to move and more buoyancy is generated in the bow.

According to another characteristic of the invention, the upper edge of the inverted bow comprises a first apical section with a positive slope followed by a second intermediate section with a positive slope but with less slope than that of the first section, and a third section with a negative slope arranged between the second span and the forward span of the upper port and starboard edges of the deck.

According to another characteristic of the invention, the hull deck comprises at least two anchor points suitable for securing a waist harness, located on the rear section of the deck separated from the end of the stern by the same distance. Preferably, the helmet cover comprises a third anchoring point located in the intermediate section of the cover, approximately at the height of where the sternum of the user of the aquatic device would be placed.

According to another embodiment of the invention, the aquatic device further comprises a harness for holding the torso of the user, movably anchored to the helmet cover by the two or three anchor points provided on the cover. The provision of the harness is optional, since there are users who may feel uncomfortable or imprisoned by the harness, for example, elderly people, and their objective when using the aquatic device object of the invention is to adequately transmit the moment that is generated when swim to the device and the device in turn to the daggerboard, to generate additional forward momentum. In fact, it is advisable to remove the daggerboard in the event that you do not want to use the harness.

On the other hand, those users with a more athletic profile will have the harness around their body so that the device and their body act as one when swimming at high speed. The use of the harness greatly improves the performance of the swimmer due to the effect of the torque exerted and transmitted to the daggerboard.

According to one embodiment of the invention, the daggerboard is formed by a vertical flat fin oriented according to a vertical plane from bow to stern, with a decreasing width from the keel to the lower end.

On the other hand, according to another embodiment of the invention, the daggerboard is made up of a vertical flat fin oriented according to a vertical plane from bow to stern, finished off at its lower end by two flat extensions that extend opposite and symmetrical with respect to the vertical fin and that form an angle greater than 90 ° with it.

In fact, in the aquatic device object of the invention, the daggerboard is removably coupled to the lower part of the hull, that is, a daggerboard can be removed and exchanged for another of a different configuration according to the user's needs.

According to a preferred embodiment of the aquatic device object of the invention, particularly suitable for an adult weighing about 80 kg, the total length of the hull measured between the ends from bow to stern is between 100 and 126 cm, preferably 113 cm, the maximum width of the helmet is between 40 and 46.8 cm, preferably being 42.4 cm, and the maximum height of the helmet without considering the daggerboard is between 20 and 30 cm, preferably being 25 cm. Preferably, the daggerboard has a length of between 10 and 20 cm.

According to another embodiment of the aquatic device of the invention, the daggerboard is foldable, which constitutes an advantage since its "pumping" effect can be regulated.

Other embodiments with the same or similar proportions are contemplated for users up to 40 kg, up to 70 kg and up to 100 kg, or embodiments for women and children.

According to the preferred embodiment of the invention, the lower edge of the hull, from which the daggerboard extends downwards, is an essentially straight edge.

Regarding the manufacture of the aquatic device object of the invention, several options of materials are contemplated. The weight of the aquatic device is very light, which allows it to be easily transported and stored.

Thus, the helmet according to a first variant is made of a composite material based on a plastic matrix and reinforcing fibers, that is, a material known as "composite".

In a second variant, the hull is made of marine plastic, which is the resulting material from recycled plastic recovered from coasts and seas, thus being able to give these plastics a second use and thus contributing to sustainability.

In a third variant, the helmet is made of a plastic envelope provided inside at least one inflatable chamber. In this variant, the helmet comprises at least a first inflatable chamber that forms the living work and a second inflatable chamber that forms the dead work, each provided with a valve, in which the pressure inside the first chamber is higher. to the pressure inside the second chamber. This variant allows, by means of a simple inflation and deflation, its transport and storage in an optimal way. It facilitates swimming on the water for both experts and amateurs, of various ages and both sexes.

In a fourth variant, the helmet is made entirely of carbon fiber.

Brief description of the drawings

The attached drawings illustrate, by way of non-limiting example, three preferred embodiments of the aquatic device object of the invention in three-dimensional representations, in order to better appreciate the shapes and volumes of the device. In these drawings:

Fig. 1 is a perspective view of a first preferred embodiment of the aquatic device object of the invention, with a daggerboard suitable for swimming, in which the port side of the hull of the aquatic device can be seen;

Fig. 2 is another perspective view of the device of Fig. 1;

Fig. 3 is another perspective view of the device of Fig. 1 in which the surface of the depression of the helmet cover can be seen;

Fig. 4 is the same view as Fig. 3 but in which the hidden lines have been represented with a finer and discontinuous line in order to appreciate the position of the anchor points and the arrangement of the daggerboard;

Fig. 5 is a perspective view of a second embodiment of the aquatic device object of the invention that, unlike the first embodiment, has a daggerboard for avoiding waves and gliding, that is, a daggerboard with hydrofoil;

Fig. 6 is another perspective view of the aquatic device of Fig. 5 in which the surface of the depression of the hull deck can be seen;

Fig. 7 is a side view of the aquatic device of Fig. 5;

Fig. 8 is the same view as Fig. 7 but in which the hidden lines have been represented with a broken line in order to appreciate the position of the anchor points and the arrangement of the daggerboard;

Fig. 9 is a perspective view of an embodiment of a harness that can form part of an embodiment of the aquatic device object of the invention;

Figs. 10 and 11 are schematic views of the detail of a folding daggerboard in a vertical position and in an inclined position; Y

Figs. 12 and 13 are perspective views of a third embodiment of the aquatic device object of the invention, in which the daggerboard is foldable, showing, respectively, in a vertical position and in a position inclined towards the stern.

Detailed description of the drawings

Figs. 1 to 4 show a first embodiment of an aquatic device 1 to carry out sports and / or recreational activities, such as swimming in water (swimming pool, lakes, rivers or sea), sliding through waves, swimming in currents, serving as support for divers to swim or as a signaling buoy of your presence, or simply to float resting on the water. The aquatic device 1 is provided so that the user can swim more easily due to the fact that his feet and hands are free for the exercise of swimming.

The aquatic device 1 comprises a floating hull 2, having a bow end 6 and a stern end 5. The floating hull 2 provides a positive buoyancy comprised between 30% and 60% of the weight of the user of the aquatic device 1. Thus, as buoyancy increases between 30% and 60%, depending on the size model, the user remains “half-water” in order to practice sports.

As can be seen in the drawings, the living part of the hull 2, which is the part of the hull that remains submerged, has a hydrodynamic configuration and is provided with a daggerboard 3. Given its hydrodynamic design, the aquatic device 1 offers a higher performance in the swimming and displacement that together with the keel of his living work increases considerably the speed with the same drive and enjoyment. Due to the arrangement of the centerboard 3 in its live work, in addition to increasing the stability and maneuverability of the helmet 2, the back and forth movement of the swimmer is transformed into a forward impulse, that is, the centerboard 3 allows a superior performance in swimming due to to the "pumping" effect, enjoying the swim more, since the performance of the user is increased. The centerboard 3 is approximately 10 to 20 cm long and varies according to the uses to be made of the aquatic device 1: prolonged swimming, playing with the waves, speed swimming, etc.

Thus, in the aquatic device 1 represented in Figs. 1 to 4, the centerboard 3 is indicated for when the user goes swimming, for which the centerboard 3 is made up of a vertical flat fin oriented according to a vertical plane from bow 6 to stern 5, with a decreasing width from keel to Lower end. The lower edge 21 of the hull 2 is an essentially straight edge, although with a certain inclination (not horizontal), as can be seen especially in Fig. 1, in which the forward-facing edge 6 of the fin moves only slightly away from the perpendicular to the lower edge 21 of hull 2, slightly exceeding 90 °.

The aquatic device 1 shown in Fig. 4 is like that of Figs. 1 to 3 but with the difference that the board 3 is designed to plan the waves, since its bearing force is used so that the board 3 with hydrofoil lifts the user and generates more speed. This centerboard 3 is made up of a vertical flat fin oriented according to a vertical plane from bow 6 to stern 5, finished off at its lower end by two flat extensions 31 that extend opposite and symmetrical with respect to the vertical fin and which form with it an angle greater than 90 °.

The daggerboard 3 is an element removably attached to the lower part of the hull 2, that is to say, a daggerboard 3 can be exchanged for another according to the needs of the user of the aquatic device 1. In Figs. 4 and 8 you can see the part 30 that remains inside the hull 2 and from which the daggerboard 3 starts.

Figs. 12 and 13 show an embodiment of the aquatic device 1 with the particularity that the daggerboard 3 is foldable, being able to adopt different inclinations and thus regulate what is known as the “pumping” effect, which is the forward thrust in which the daggerboard 3 converts the balance of the swim of the user of the aquatic device 1. In Figs. 10 and 11 it can be seen how the internal part 30 is configured with a housing to allow the rotation of the daggerboard 3 around a joint provided in said internal part 30.

Furthermore, in Figs. 1 to 8 it can be seen that the bow 6 is an inverted bow 6, that is, one that recedes towards the stern 5 as they go up. On the other hand, it is also appreciated that the cross section of the hull 2 at the stern 5 is a flattened U-shaped section.

The hull cover 2 comprises, as can be seen especially in Figs. 4 and 8, a depression 4 of greater depth in the vicinity of the stern 5 than in the vicinity of the bow 6 and has an ergonomic configuration for the support of the human chin and torso on the surface of the depression 4. Thus, it is possible to to say that the design of the helmet 2 in its part of dead work is adapted to the human torso.

In fact, three sections on the deck can be distinguished (see Figs. 2, 3 and 6: a rear section 70, adjacent to the stern 5, a forward section 72 adjacent to the bow 6 and an intermediate section 71 between said sections. The inverted bow 6 allows the chin to rest on an elastic and comfortable surface provided in the front section 72. The chest and belly are ergonomically tucked for greater comfort in the intermediate section 71 and in the rear section 70.

In Fig. 3 it can be seen that the upper port and starboard edges of the deck extend parallel along the rear span 70 until a change in level 8 from which the edges extend convergent towards the bow 6 inverted at the intermediate section 71 and in the front section 72 of the roof. In order that the above can be appreciated more clearly, they have been drawn in Figs. 3 and 6 discontinuous lines on the upper edges of the intermediate 71 and front 72 sections, since, since they are actually rounded edges in the figures, there may be some difficulty in appreciating the convergence of these sections.

The height of the upper port and starboard edges of the deck in the forward section 72 measured with respect to the keel of the hull 2 is equal to or greater than the height of the upper port and starboard edges in the rear section 70 measured relative to the hull keel 2.

In Fig. 7 it can be seen more clearly that the upper edge of the inverted bow 6 comprises a first apical section 61 with a positive slope, in the direction from bow 6 to stern 5, followed by a second intermediate section 62 with a positive slope but with a lower slope than that of the first section 61, and a third section 63 with a negative slope arranged between the second section 62 and the upper port and starboard edges of the forward section 72 of the

1

cover.

The hull deck 2 comprises at least two anchor points 80 and 81, suitable for securing a waist harness 9 (see Fig. 9), located in the rear section 70 of the deck separated from the end of the stern 5 by the same distance. Furthermore, a third anchor point 82 is additionally provided located in the intermediate section 71 of the roof. In this way, the aquatic device 1 has between two to three anchor points to hold the swimmer, allowing him to freely exercise the appropriate movements for swimming and exercising. The aquatic device 1 can have a harness 9 (for example, as represented in Fig. 9) made of rubber or neoprene that is placed around the human torso, which has two or up to three hooks 90 for two or up to three points. anchor: the two anchor points 80 and 81 at the waist and the third anchor point 82 at the level of the sternum. The anchoring is carried out by means of a system of hooks and loops, commercially known as industrial velcro®, which allows the force to be carried out, but which is easily detachable from the model. Another option is to do it with neodymium magnets. By hooking the harness 9 to the helmet cover 2, a very remarkable union with the human body is made, acting as a single entity, allowing intuitive, safe and natural swimming. It actively anchors the swimmer, leaving their hands and legs completely free for swimming. The user does not worry about the restraint and concentrates on swimming.

Regarding dimensions, in the drawings represented, according to a preferred option, the total length of the hull 2 measured between the ends of the bow 6 to the stern 5 is approximately 113 cm, the maximum beam of the hull 2 is approximately 42.4 cm , and the maximum height of the hull 2 without considering the daggerboard 3 is approximately 25 cm.

There are many plausible industrial manufacturing techniques for the aquatic device, from a mold to generate the product with composite materials (known as composites), for example, by a composite material with carbon fiber, rotational molding for its manufacture in marine plastics and its manufacture in inflatable plastics.

When the helmet 2 is made of a plastic envelope provided inside at least one inflatable chamber, it is advantageous that the helmet 2 comprises at least a first inflatable chamber that forms the living work and a second inflatable chamber that forms the dead work, each provided with a valve, in which the pressure inside the first chamber is higher than the pressure inside the second chamber. This variant of Inflated allows, by means of a simple inflation and deflation, its transport and storage in an optimal way.

Thus, it is shown that the hydrodynamic design of the hull 2 offers greater performance in swimming and displacement, which together with the daggerboard 3 of its live work considerably increases the speed with the same impulse and enjoyment. Its cover is soft, ergonomic and pleasant to the touch of human skin.

The aquatic device 1 allows great safety in swimming, since at any time it provides certain buoyancy to the user who, under any circumstance, can rest and resume swimming whenever he wishes. In the case of spearfishing divers, it allows, in addition to transferring the diver, to signal his position in front of other vessels while the diver is submerged, since the hull 2 or part of it can be produced with a special color.

In conclusion, the aquatic device 1 offers a solution in the nautical gadgets market, providing the user with the opportunity to glide fluently in the water with the traction of the human arm, being able to face small waves naturally, respecting the partially submerged human body. in the water from head to hip and taking advantage of the ocean currents you can find. It facilitates swimming on the water for both experts and amateurs, children included, in a safe way. It allows a swimmer to improve the speed and performance in swimming in a very substantial way and also to practice swimming for a longer time, since the swimmer tires less and can even rest leaning on the helmet 2. In addition, its weight is light, and allows to be transported and stored in a simple way.

Claims (19)

1. - An aquatic device (1) to carry out sports and / or recreational activities, which comprises a floating hull (2), which has a bow end (6) and a stern end (5), characterized in that the hull (2) floating provides a positive buoyancy comprised between 30% and 60% of the weight of the user of the aquatic device (1), in which the live part of the hull (2) has a hydrodynamic configuration and is provided with a daggerboard ( 3), in which the deck comprises a depression (4) of greater depth in the vicinity of the stern (5) than in the vicinity of the bow (6) and ergonomically configured to support the human chin and torso on the surface of the depression (4), and in which the bow (6) is an inverted bow (6). 2. - The aquatic device (1) according to claim 1, characterized in that the cross section of the hull (2) at the stern (5) is a flattened U-shaped section. 3. - The aquatic device (1) according to claim 1 or 2, characterized in that the upper port and starboard edges of the deck extend parallel along a rear section (70) of the deck adjacent to the stern ( 5) until a change in level (8) from which the edges extend convergent towards the inverted bow (6) in an intermediate section (71) and in a forward section (72) of the deck. 4. - The aquatic device (1) according to claim 3, characterized in that the height of the upper port and starboard edges of the deck in the rear section (70) measured with respect to the keel of the hull (2) is greater than the height of said upper edges in the intermediate section (71) measured with respect to the keel of the hull (2). 5. - The aquatic device (1) according to claim 4, characterized in that the height of the upper port and starboard edges of the deck in the forward section (72) adjacent to the inverted bow (6) measured with respect to the keel of the hull (2) is equal to or greater than the height of the upper port and starboard edges in the rear section (70) measured with respect to the keel of the hull (2). 6. - The aquatic device (1) according to claim 4 or 5, characterized in that the upper edge of the inverted bow (6) comprises a first apical section (61) with a positive slope followed by a second intermediate section (62) of positive slope but less slope than that of the first section (61), and a third section (63) with a negative slope arranged between the second section (62) and the upper port and starboard edges of the forward section (72) of the deck. 7. - The aquatic device (1) according to any one of claims 3 to 6, characterized in that the helmet cover (2) comprises at least two anchor points (80, 81) suitable for securing a harness (9 ) waist, located in the rear section (70) of the deck separated from the end of the stern (5) by the same distance. 8. - The aquatic device (1) according to claim 7, characterized in that the hull cover (2) comprises a third anchor point (82) located in the intermediate section (71) of the cover. 9. - The aquatic device (1) according to any one of the preceding claims, characterized in that the daggerboard (3) is formed by a vertical flat fin oriented according to a vertical plane from bow (6) to stern (5), width decreasing from keel to lower end. 10. - The aquatic device (1) according to any one of claims 1 to 8, characterized in that the daggerboard (3) is formed by a vertical flat fin oriented according to a vertical plane from bow (6) to stern (5), topped at its lower end by two flat extensions (31) that extend opposite and symmetrical with respect to the vertical fin and that form an angle greater than 90 ° with it. 11. - The aquatic device (1) according to any one of the preceding claims, characterized in that the daggerboard (3) is removably attached to the living work of the hull (2). 12. - The aquatic device (1) according to any one of the preceding claims, characterized in that the daggerboard (3) is foldable with respect to the keel of the hull (2). 13. - The aquatic device (1) according to any one of the preceding claims, characterized in that the total length of the hull (2) measured between the ends of bow (6) to stern (5) is between 100 and 126 cm, because the maximum beam of the hull (2) is between 40 and 46.8 cm, because the maximum height of the hull (2) without considering the daggerboard (3) is between 20 and 30 cm, and because the daggerboard (3) has a length comprised between 10 and 20 cm. 14. - The aquatic device (1) according to claim 13, characterized in that the total length of the hull (2) measured between the ends of bow (6) to stern (5) is approximately 113 cm, because the maximum beam of the hull (2) is approximately 42.4 cm, and because the maximum height of the hull (2) without considering the daggerboard (3), is approximately 25 cm. 15. - The aquatic device (1) according to any one of the preceding claims, characterized in that the lower edge (21) of the hull (2) is an essentially straight inclined edge. 16. - The aquatic device (1) according to any one of the preceding claims, characterized in that the hull (2) is made of a composite material based on a plastic matrix and reinforcing fibers, or a marine plastic material. 17. - The aquatic device (1) according to any one of claims 1 to 15, characterized in that the helmet (2) is made of a plastic envelope provided inside at least one inflatable chamber. 18. - The aquatic device (1) according to claim 17, characterized in that the helmet (2) comprises at least a first inflatable chamber that forms the living work and a second inflatable chamber that forms the dead work, each provided with a valve, in which the pressure inside the first chamber is higher than the pressure inside the second chamber. 19. - The aquatic device (1) according to any one of claims 7 or 8, characterized in that it also comprises a harness (9) to hold the torso of the user movably anchored to the helmet cover (2) by two or three points anchor bolts (80, 81, 82) provided on the cover. 1