Aerodynamic devices and satellites

Abstract

To provide an aerodynamic device and satellite that can reduce launch costs while reducing atmospheric drag. [Solution] The aerodynamic device is an aerodynamic device that reduces the effect of atmospheric drag on the satellite, and comprises an aerodynamic shaping section provided at the tip of the satellite body, the aerodynamic shaping section is configured to be deformable between a first state in which it is conical in shape and a second state in which it is folded from the first state.

Description

Technical Field

[0001] The present disclosure relates to an aerodynamic device and a satellite.

Background Art

[0002] Artificial satellites orbiting around planets in the upper atmosphere of the Earth decelerate due to the influence of atmospheric drag. Therefore, an artificial satellite needs to increase its speed by the amount of deceleration using a propulsion device or the like to maintain its orbit. At this time, if the atmospheric drag received by the artificial satellite can be reduced, the thrust of the propulsion device or the like and the amount of propellant can be reduced, so that the cost associated with the development and operation of the artificial satellite can be reduced.

[0003] In order to reduce the atmospheric drag received by an artificial satellite, for example, Patent Document 1 discloses a configuration in which the satellite body has a shape such that the cross-sectional area in the traveling direction is reduced. Further, Patent Document 2 discloses a configuration in which a conical structure that tapers toward the traveling direction is provided at the tip portion.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, in the configuration described in Patent Document 1, since the surface affected by the atmospheric drag is a flat surface, there is a possibility that the atmospheric drag cannot be effectively reduced. Further, in the configuration described in Patent Document 2, since the overall dimensions of the satellite body are large, the volume when mounted on a rocket becomes large, so there is a possibility that the constraints on the mounting location will increase. Therefore, there is a problem that the launch cost of the satellite increases due to a decrease in the number of satellites mounted when multiple satellites are mounted.

[0006] The purpose of this disclosure is to provide an aerodynamic device and satellite that can reduce the launch cost of a satellite while reducing atmospheric drag. [Means for solving the problem]

[0007] The aerodynamic device relating to this disclosure is An aerodynamic device that reduces the effects of atmospheric drag on a satellite, The satellite body is equipped with an aerodynamic shaping section located at its tip. The aerodynamically shaped section is configured to be deformable between a first state in which it is conical in shape and a second state in which it is folded from the first state.

[0008] The satellite related to this disclosure is The satellite body and The aerodynamic shaping section provided at the tip of the satellite body, Equipped with, The aerodynamically shaped section is configured to be deformable between a first state in which it is conical in shape and a second state in which it is folded from the first state. [Effects of the Invention]

[0009] According to this disclosure, it is possible to reduce the cost of satellite launches while reducing atmospheric drag. [Brief explanation of the drawing]

[0010] [Figure 1] This figure shows a satellite equipped with an aerodynamic device according to an embodiment of the present disclosure. [Figure 2A] This is a diagram showing the aerodynamic device in its first state. [Figure 2B] This is a diagram showing the aerodynamic device in its second state. [Figure 3] This is a simplified diagram showing the folded frame section. [Figure 4] This is a diagram illustrating the inclination angle of a cone shape. [Figure 5] This graph shows an example of analysis results illustrating the change in CDS for each angle. [Figure 6] It is a graph showing an example of an analysis result indicating the change in CDS for each angle when the thermal adaptation coefficient is changed. [Figure 7] It is a diagram for explaining the fold line when folding the aerodynamic shaping part. [Figure 8] It is a diagram for explaining the fold line when folding the aerodynamic shaping part. [Figure 9] It is a diagram simply showing a modification example of the folded frame part. [Figure 10] It is a diagram simply showing a modification example of the folded frame part. [Figure 11A] It is a diagram showing an example of a configuration having no frame part. [Figure 11B] It is a diagram showing an example of a configuration having no frame part.

Mode for Carrying Out the Invention

[0011] Hereinafter, embodiments of the present disclosure will be described in detail based on the drawings. FIG. 1 is a diagram showing a satellite 1 equipped with an aerodynamic device 100 according to an embodiment of the present disclosure. Also, in explaining the structure of the aerodynamic device 100 of the present embodiment, the orthogonal coordinate system shown in each figure is used. The aerodynamic device 100 is arranged such that, for example, when the satellite 1 is flying in a horizontal attitude, the X direction is the traveling direction of the satellite 1, the Y direction is parallel to the horizontal plane and perpendicular to the traveling direction, and the Z direction is the vertical direction.

[0012] As shown in FIG. 1, the satellite 1 is an artificial satellite orbiting around a planet or the like in space above the earth. The satellite 1 includes a satellite body 11 and an aerodynamic device 100. The satellite body 11 is a part constituting the main body of the satellite 1 and is configured, for example, in a rectangular parallelepiped shape. The aerodynamic device 100 is provided at the tip (the + side end in the X direction) of the satellite body 11.

[0013] As shown in FIGS. 2A and 2B, the aerodynamic device 100 is a device for reducing the influence of atmospheric resistance received by the satellite 1, and includes an aerodynamic shaping part 110 and a lock part 120.

[0014] The aerodynamic shaping part 110 is provided at the tip of the satellite main body 11 (+ side end in the X direction) and is configured to be deformable between a first state and a second state. The first state is the state of the aerodynamic shaping part 110 shown in FIG. 2A, in which the aerodynamic shaping part 110 has a tapered cone shape that tapers toward the + side in the X direction. The cone shape in the present embodiment is a square pyramid shape. The second state is the state of the aerodynamic shaping part 110 shown in FIG. 2B, in which the aerodynamic shaping part 110 is in a folded state from the first state.

[0015] The aerodynamic shaping part 110 has a bottom surface part 111, a frame part 112, a linear part 113, and a surface part 114.

[0016] The bottom surface part 111 constitutes the bottom surface of the above cone shape and is configured in a shape that matches the end surface on the + side in the X direction of the satellite main body 11. In the present embodiment, the bottom surface part 111 is composed of a rectangular plate-like member. The bottom surface part 111 is, for example, attached to the satellite main body 11. Note that the bottom surface part 111 may be a part of the satellite main body 11.

[0017] The frame part 112 constitutes a part of the side surface of the cone shape (the side surface on the - side in the Z direction) and is configured to be foldable. The frame part 112 has three frame members 112A, 112B, 112C and three hinge members 112D, 112E, 112F.

[0018] The three frame members 112A, 112B, 112C are joined together by each hinge member to form, as a whole, one triangular side surface in the cone shape.

[0019] The frame member 112A is arranged at the most tip side (the + side in the X direction) of the three frame members and is configured in a triangular shape. The frame member 112A is also referred to as the first frame member.

[0020] Frame member 112B is positioned in the middle of the three frame members and is configured in a trapezoidal shape. Frame member 112B is also referred to as the second frame member 112B.

[0021] Frame member 112C is positioned at the bottommost side (the negative side in the X direction) of the conical shape among the three frame members, and is configured in a trapezoidal shape. Frame member 112C is also referred to as the third frame member 112C.

[0022] The X-side end of the first frame member 112A and the X-side end of the second frame member 112B are connected by a hinge member 112D. The hinge member 112D connects the first frame member 112A and the second frame member 112B in such a way that, for example, when the first frame member 112A and the second frame member 112B are folded, they become convex toward the Z-side (see also Figure 3).

[0023] The negative end of the second frame member 112B in the X direction and the positive end of the third frame member 112C in the X direction are connected by a hinge member 112E. The hinge member 112E connects the second frame member 112B and the third frame member 112C in such a way that, for example, when the second frame member 112B and the third frame member 112C are folded, the hinge member 112E becomes convex toward the positive side in the Z direction (see also Figure 3).

[0024] The X-side end of the third frame member 112C and the bottom surface 111 are connected by a hinge member 112F. The hinge member 112F connects the third frame member 112C and the bottom surface 111 in such a way that it is convex toward the Z-side when the bottom surface 111 and the third frame member 112C are folded (see also Figure 3).

[0025] In this way, the frame portion 112 is configured to be foldable by folding it at each hinge member.

[0026] Furthermore, the inclination angle θ of the conical shape formed by the aerodynamic shaping section 110 is set to a predetermined angle. This predetermined angle is, for example, an angle at which the atmospheric resistance experienced by the aerodynamic shaping section 110 during the flight of satellite 1 is sufficiently small, and is, for example, 80 degrees.

[0027] The inclination angle θ of the conical shape is, for example, the angle θ between the line 110A connecting the tip of the aerodynamic shaping section 110 and the Z-direction + end of the aerodynamic shaping section 110, and the Z-direction, when the satellite 1 is positioned along the horizontal direction (X-direction), as shown in Figure 4. Furthermore, the inclination angle θ of the conical shape may be an angle other than the angle between the line 110A and the Z-direction (for example, the angle between the X-direction and line 110A), as long as it is an angle related to the inclination of the conical shape.

[0028] It has been analytically confirmed that the drag coefficient (CD value) of the surface portion 114 decreases as the inclination angle θ increases.

[0029] The atmospheric drag of the cone-shaped aerodynamic section 110 is calculated by the product of the drag coefficient CD, the surface area S, and the atmospheric dynamic pressure. Since the surface area S of the aerodynamic section 110 correlates with the reciprocal of the cosine value of the inclination angle θ, the CDS (product of CD and S), which takes into account the drag coefficient CD and the surface area S, changes with respect to the change in inclination angle θ, as shown in Figure 5. In Figure 5, the product of the drag coefficient and the surface area is shown as CDS, and it has been analytically confirmed that CDS is minimized when the inclination angle θ is 80 degrees. That is, focusing only on the cone shape of the aerodynamic section 110, the inclination angle θ is preferably, for example, 75 to 85 degrees. Furthermore, considering the thermal adaptation coefficient α described later, the inclination angle θ is preferably in the range of 45 to 80 degrees.

[0030] As shown in Figure 2A, the linear portion 113 connects the base portion 111 to the tip of the conical shape, that is, the positive end in the X direction of the first frame member 112A. Specifically, the linear portion 113 connects the portion of the base portion 111 other than the portion to which the frame portion 112 is attached to the positive end in the X direction of the first frame member 112A. In this embodiment, the linear portion 113 has two linear members 113A and 113B.

[0031] The two linear members 113A and 113B are, for example, cables with a shape-retaining function that can be bent and deformed. The two linear members 113A and 113B are attached to each of the two vertex portions of the bottom portion 111 that do not include the edge to which the frame portion 112 is attached, and have a restoring force to maintain the aerodynamic shaping portion 110 in a first conical shape.

[0032] By providing the linear portion 113 in this way, the aerodynamically shaped portion 110 is maintained in the first state unless any external force is applied.

[0033] The surface portion 114 constitutes the surface of the aerodynamically shaped portion 110 and is composed of a foldable thin film material such as a film, cloth, tape, or laminate. The surface portion 114 has a first portion 114A and a second portion 114B.

[0034] The first part 114A constitutes the side surface of the aerodynamic shaping section 110 other than the frame section 112. The first part 114A corresponds to the range from the positive end in the Y direction of the frame section 112 to the negative end in the Y direction of the frame section 112, via two linear members 113A and 113B. The two linear members 113A and 113B are attached to the back side of the first part 114A.

[0035] The second part 114B corresponds to the frame part 112 and is attached to the surface of each of the multiple frame members 112A, 112B, and 112C. The second part 114B is connected to the first part 114A.

[0036] The surface portion 114 is made of a material that has resistance to atomic oxygen (AO). Preferably, the atomic oxygen-resistant material is, for example, an organic material or inorganic material containing silicon. Alternatively, the atomic oxygen-resistant material may be silicon dioxide, aluminum oxide, zinc oxide, titanium oxide, tin oxide, indium oxide, etc.

[0037] In this way, the surface portion 114 has atomic oxygen resistance, which helps to prevent damage to the aerodynamic device 100 from atomic oxygen.

[0038] Furthermore, it is preferable that the surface portion 114 is formed of a material that has specular reflectivity of gas molecules that collide with the surface during the flight of the satellite 1. The material that has specular reflectivity of gas molecules is a material that has a sufficiently smooth surface, and may be, for example, a material in which the thermal adaptation coefficient of the surface portion 114 is less than or equal to a predetermined value.

[0039] The thermal adaptation coefficient is an index that represents the change in energy. Specifically, the thermal adaptation coefficient is a value from 0 to 1 that indicates the degree of compatibility between gas molecules and the surface 114 when they collide with the surface 114 and are scattered. The thermal adaptation coefficient can be defined, for example, by the following equation (1).

[0040] α = (Tf - Ti) / (Ts - Ti) ... (1)

[0041] In equation (1), α is the thermal adaptation coefficient. Ti is the temperature of the colliding gas molecules. Ts is the temperature of the surface 114 that is collided with by the gas molecules. Tf is the temperature of the gas molecules at temperature Ti after they are scattered by the surface 114 at temperature Ts.

[0042] According to equation (1), the smaller the temperature change of the gas molecules (Tf-Ti), the smaller the thermal adaptation coefficient α becomes. In other words, the reduction in the velocity of satellite 1 due to collisions of gas molecules is suppressed.

[0043] Figure 6 is a qualitative graph showing the change in CDS with respect to the change in the inclination angle θ of the cone shape when the thermal adaptation coefficient α is changed in three stages. E1 in Figure 6 shows the change in CDS when the thermal adaptation coefficient α is the highest of the three stages. E2 in Figure 6 shows the change in CDS when the thermal adaptation coefficient α is the second highest of the three stages. E3 in Figure 6 shows the change in CDS when the thermal adaptation coefficient α is the lowest of the three stages.

[0044] As the thermal adaptation coefficient α increases (closer to 1), gas molecules colliding with the surface of the aerodynamically shaped section 110 become thermally adapted and scattered randomly. This prevents the gas molecules from being reflected in the appropriate direction, reducing the effectiveness of the shape in reducing CDS. Therefore, the CDS for E1, which has the largest thermal adaptation coefficient α in Figure 6, is almost independent of the inclination angle θ of the cone shape. As the thermal adaptation coefficient α decreases (closer to 0), gas molecules colliding with the surface of the aerodynamically shaped section 110 are reflected specularly, thus allowing the shape to exert its effect in reducing CDS. Therefore, the CDS for E3, which has the smallest thermal adaptation coefficient α in Figure 6, changes significantly depending on the inclination angle θ of the cone shape.

[0045] As shown in Figure 6, it can be confirmed that as the tilt angle θ increases beyond 45 degrees, a smaller thermal adaptation coefficient α results in a smaller CDS. From this result, it is preferable that the tilt angle θ is greater than 45 degrees.

[0046] Furthermore, materials with specular reflectivity, that is, materials with a relatively small thermal adaptability coefficient α (materials with a thermal adaptability coefficient α of, for example, 0.5 or less), include nickel and gold. It is desirable that the surface portion 114 be made of a material that has atomic oxygen resistance and reflectivity. For the surface portion 114, a material with a substantially smooth surface whose thermal adaptability coefficient α does not change over time can be used, for example, a member coated with a metal film can be used. A coating film formed by PVD, sputtering, vapor deposition, ion plating, CVD, or ALD can also be used.

[0047] As shown in Figures 2A and 2B, the locking part 120 is for locking the aerodynamic shaping part 110 into a second state (a folded state from a conical shape), and is, for example, a pin puller. The locking part 120 is provided at the positive Z-side end of the bottom surface part 111, and is configured to lock the aerodynamic shaping part 110 into the second state by engaging the tip of the frame part 112 (frame member 112A) with the pin of the pin puller.

[0048] The operation of the aerodynamic device 100 configured as described above will now be explained.

[0049] Before the launch of satellite 1, the aerodynamic device 100 is folded so that the aerodynamic shaping section 110 is in the second state.

[0050] The aerodynamic shaping section 110 is folded inward in a conical shape at the side portion adjacent to the frame section 112 in the Y direction. The fold in the side portion may be at any position, but for example, as shown in Figure 7, it may be at a position P corresponding to the connection portion between frame member 112B and frame member 112C. P is shown, for example, by a line perpendicular to the connection portion between frame member 112B and frame member 112C on the side portion. For example, the fold may be the lines L1, L2, L3 that connect each vertex of the triangle constituting the side portion to any position on the line corresponding to P.

[0051] L1 corresponds to the vertex of the triangle forming the side surface located on the tip side of the frame portion 112. L2 and L3 correspond to the two vertices of the triangle forming the side surface located on the bottom portion 111 side.

[0052] Furthermore, the aerodynamic shaping section 110 is folded at L4 and L5 on the side portion facing the frame section 112 in the Z direction. L4 is a line indicating a fold at a position corresponding to the connection between frame member 112A and frame member 112B. L5 is a line indicating a fold at a position corresponding to the connection between frame member 112B and frame member 112C.

[0053] As shown in Figure 8, the aerodynamic shaping section 110 is folded so as to be convex to the negative side in the Z direction at L4, and folded so as to be convex to the positive side in the Z direction at L5.

[0054] The position of the tip of the folded aerodynamic shaping section 110 corresponds to the positive Z-side end of the bottom surface section 111. A locking section 120 is provided at the positive Z-side end of the bottom surface section 111, allowing the tip of the aerodynamic shaping section 110 to be locked by the pin puller's pin. In this way, the aerodynamic shaping section 110 is locked to the second state (see Figure 2B).

[0055] The rocket carrying satellite 1 is launched when the aerodynamic shaping section 110 is in the second state. In other words, at the time of satellite 1's launch, the aerodynamic shaping section 110 is locked in the second state.

[0056] Thus, when satellite 1 is launched, the aerodynamic shaping section 110 is folded, which reduces the dimensions (volume) of satellite 1 when it is mounted on the rocket. As a result, the degree of freedom in mounting satellites on the rocket is increased, and various launch opportunities can be utilized, such as rideshares with other satellites. In addition, when launching multiple satellites, more satellites can be mounted on the rocket, which contributes to reducing launch costs.

[0057] After the rocket carrying satellite 1 is launched, the lock on the locking mechanism 120 is released at an appropriate time. When the locking mechanism 120 is released, the restoring force of the hinge members 112D, 112E, and 112F causes the aerodynamic shaping mechanism 110 to unfold from the second state to the first state (see Figure 2A). In other words, the aerodynamic shaping mechanism 110 deforms from the second state to the first state when the locking mechanism 120 is released.

[0058] An appropriate timing could be, for example, after satellite 1 has separated from the rocket and its attitude has stabilized.

[0059] This allows satellite 1 to have a shape that reduces atmospheric drag, thereby reducing the atmospheric drag it experiences during flight. As a result, the thrust of the propulsion system and the amount of propellant used on satellite 1 can be reduced, thus lowering the development and operation costs of satellite 1. This effect is particularly pronounced when applied to very low-altitude satellites orbiting the Earth (below 300 km altitude) where atmospheric drag is significant, or to artificial satellites orbiting Mars in low orbit.

[0060] Based on the above, this embodiment makes it possible to reduce the cost of satellite launch while reducing atmospheric drag.

[0061] Furthermore, the provision of the frame portion 112 and the linear portion 113 makes it easier to fold the aerodynamic shaping portion 110, and also makes it easier to form the conical shape of the aerodynamic shaping portion 110.

[0062] Furthermore, since the surface portion 114 is made of a material resistant to atomic oxygen, damage to the components of the satellite 1 due to atomic oxygen can be reduced.

[0063] Furthermore, since the surface portion 114 is made of a material that has specular reflectivity of gas molecules, the effect of atmospheric resistance can be further reduced.

[0064] In the above embodiment, the aerodynamic shaping section 110 was folded so that the tip of the frame section 112 (the first frame member 112A) was located on the + side in the X direction of the satellite 1, but the disclosure is not limited thereto. For example, as shown in Figure 9, the first frame member 112A may be folded so that it is sandwiched between the second frame member 112B and the third frame member 112C. In this case, the connection portion between the first frame member 112A and the second frame member 112B may be configured to be locked by the locking section 120.

[0065] Furthermore, although the above embodiment shows that the frame portion is composed of three frame members, this disclosure is not limited thereto, and it may be composed of four or more frame members, or even just two frame members.

[0066] Furthermore, in the above embodiment, the aerodynamic shaping section was folded on the tip surface of the satellite body, but this disclosure is not limited thereto. For example, as shown in Figure 10, the aerodynamic shaping section 110 may be folded so that the frame member follows the side portion of the satellite body 11. In the example shown in Figure 10, the frame portion is composed of two frame members 112G and 112H, and the frame member 112H located at the tip of the frame portion is folded along the side portion of the satellite body 11.

[0067] Furthermore, although the above embodiment included a frame section having multiple frame members, this disclosure is not limited thereto, and a frame section may not be provided.

[0068] An example of a configuration without a frame is a configuration having a surface portion 114 and a spiral biasing member 115, as shown in Figures 11A and 11B.

[0069] The biasing member 115 is a spring member that biases the surface portion 114 toward the + side in the X direction, and constitutes the framework of the surface portion 114. The surface portion 114 is the same material as in the above embodiment, and is configured to be conical in shape by the biasing member 115 unless any external force is applied (see Figure 11A).

[0070] For example, by compressing the biasing member 115 and locking the end of the biasing member 115 located at the tip of the surface portion 114 with a locking part (not shown), the surface portion 114 and the biasing member 115 become folded (see Figure 11B). Then, when the locking by the locking part is released, the biasing member 115 deforms the surface portion 114 into a conical shape (see Figure 11A).

[0071] Another configuration that does not have a frame is one in which the surface portion 114 is inflated with air.

[0072] In this configuration, for example, when the surface portion 114 is folded, air is injected from the inside of the surface portion 114 to deform it into a cone shape.

[0073] Furthermore, although the cone shape in the above embodiment was a square pyramid, this disclosure is not limited to this, and the cone shape does not have to be a square pyramid as long as it matches the shape of the satellite body. For example, if the satellite body is constructed as a cylinder, the cone shape may be a cone. Also, if the satellite body is constructed as a triangular prism, the cone shape may be a triangular pyramid.

[0074] Furthermore, in the above embodiment, the material having specular reflectivity was defined as a material with a small thermal adaptation coefficient α, but this disclosure is not limited thereto. For example, a material determined based on an index other than the thermal adaptation coefficient may be determined as a material having specular reflectivity.

[0075] Furthermore, the embodiments described above are merely examples of how this disclosure may be implemented, and the technical scope of this disclosure should not be limited by them. In other words, this disclosure can be implemented in various ways without departing from its essence or its main features. [Industrial applicability]

[0076] The aerodynamic device of this disclosure is useful as an aerodynamic device and satellite capable of reducing launch costs while reducing atmospheric drag. [Explanation of Symbols]

[0077] 1 satellite 11 Satellite body 100 Aerodynamic devices 110 Aerodynamic Shaping Section 111 Bottom part 112 Frame section 112A First frame member 112B Second frame member 112C Third frame member 112D Hinge Member 112E Hinge component 112F Hinge component 113 Linear part 114 Surface part 120 Locking part

Claims

1. An aerodynamic device that reduces the effects of atmospheric drag on a satellite, The satellite body is equipped with an aerodynamic shaping section located at its tip. The aerodynamically shaped section is configured to be deformable between a first state in which it is conical in shape and a second state in which it is folded from the first state. Aerodynamic device.

2. The aerodynamic shaping portion is further provided with a locking portion for locking it in the second state, The aerodynamic shaping section deforms from the second state to the first state when the lock on the locking section is released. The aerodynamic device according to claim 1.

3. The locking mechanism locks the aerodynamic shaping mechanism during the launch of the satellite and unlocks the aerodynamic shaping mechanism after the launch of the satellite. The aerodynamic device according to claim 2.

4. The aerodynamic shaping portion comprises a base portion that constitutes the bottom surface of the conical shape, a surface portion that constitutes the surface of the side portion of the conical shape, and a linear portion that connects the base portion and the tip of the conical shape and has a restoring force for maintaining the aerodynamic shaping portion in the first state. The aerodynamic device according to claim 1.

5. The aerodynamic shaping section further comprises a plurality of frame members that form part of the side surface of the conical shape and are foldably attached to the bottom surface, The linear portion is provided on the bottom surface at locations other than where the plurality of frame members are attached. The aerodynamic device according to claim 4.

6. The aforementioned surface portion is The first portion, which is made of a foldable member, constitutes the sides of the conical shape other than the plurality of frame members, A second portion is attached to the surface of the plurality of frame members, Having, The aerodynamic device according to claim 5.

7. The surface portion is made of a material that has resistance to atomic oxygen. The aerodynamic device according to claim 4.

8. The surface portion is made of a material that has specular reflectivity of gas molecules that collide with the surface during the satellite's flight. The aerodynamic device according to claim 4.

9. The satellite body and The aerodynamic shaping section provided at the tip of the satellite body, Equipped with, The aerodynamically shaped section is configured to be deformable between a first state in which it is conical in shape and a second state in which it is folded from the first state. satellite.

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