A lightweight cable net membrane airship main envelope and method of manufacture

Abstract

The application discloses a light cable net film airship main gas bag and a manufacturing method. The steps for simulating and analyzing set two-dimensional generatrix and determining the arrangement position of the circumferential reinforcing rib include: starting from the quality point of the fixed maximum cross section circumferential position, obtaining the shape after deformation, and then obtaining the quality point with the maximum transverse strain, which is the obtained arc length position of the circumferential reinforcing rib; the quality point is fixed in the next calculation to continue segmentation until the positions of the set number of circumferential reinforcing ribs are completed. The steps for determining the bulge shape after being jointly constrained by the meridian reinforcing rib and the circumferential reinforcing rib include: according to the reinforcing rib position, the reinforcing rib elastic modulus and the spherical membrane elastic modulus, simulating and calculating the spherical membrane surface, and under the condition that the airship internal and external pressure difference is a set value, the three-dimensional shape of each small bulge. The application solves the problem that it is difficult to design a polyethylene film airship main gas bag.

Description

Technical Field

[0001] This application relates to the field of near-space airship design, with particular focus on the overpressure structure design of airship bladders. Background Technology

[0002] Aerostats rely on an internal gas lighter than air to fly, and include airships, tethered balloons, and free balloons. One current development direction for airships is the stratospheric high-altitude airship. Stratospheric airships have received considerable attention in near-space flight platforms. Unlike free balloons, they can perform powered flight, gaining a degree of trajectory control, making them of significant application value and broad development prospects. Currently, stratospheric airships are mostly made of fabric skin materials, gaining rigidity after withstanding the internal and external pressure differences at their service ceiling. However, traditional fabric airship membranes have a high density, relying solely on the membrane's own resistance to pressure differences, similar to the early development of overpressure balloons.

[0003] Excessive weight of the capsule increases costs in manufacturing, folding, transportation, pressure holding, deployment, and release. Furthermore, the fabric airship's own weight contributes to its low volume and payload utilization. The relationship between the aircraft's speed (v) and required energy (P) is cubic; increasing speed necessitates carrying more energy payload, further increasing the airship's size. A large hull weight also makes the system's weight and dimensions prone to design deviations.

[0004] At the same time, the service ceiling of current fabric airships is also limited.

[0005] Overpressure balloons are made of linear low-density polyethylene (LLDPE) film material, offering advantages such as low cost, high flight altitude, and large payload capacity. The overpressure balloon is sealed off from the outside environment, with the membrane bearing the pressure difference between the inside and outside to offset the effects of diurnal temperature variations, enabling stable altitude flight over long durations. Currently, most overpressure balloons adopt a "pumpkin-shaped" design, utilizing a geometric configuration with increased local curvature radii and reinforcing ribs to jointly withstand the pressure difference. Overpressure balloons have become an important development target for projects including NASA, JAXA, CNES, and Google's balloon program.

[0006] The Aerospace Information Research Institute of the Chinese Academy of Sciences has conducted 7000m research. 3 The flight tests of the pumpkin-shaped overpressure balloon yielded sufficient technological accumulation. However, the overpressure balloon lacked a streamlined shape and experienced significant drag in all directions.

[0007] To overcome the problem of instability during the deployment of overpressure balloons and to reduce the drag encountered during the ascent of overpressure balloons, the JAXA balloon group developed the Tawara "corn kernel" overpressure balloon, which forms a cylindrical shape in the middle by extending the equatorial portion of the "pumpkin-shaped" balloon.

[0008] However, the design steps and processing technology of the main airbag of this type of polyethylene film airship have not yet been studied, and there are no mature design steps on how to determine the shape of each bulge and the length of the reinforcing ribs. Summary of the Invention

[0009] This application proposes a lightweight cable-net film airship main airbag and its manufacturing method, solving the problem of the difficulty in designing polyethylene film airship main airbags.

[0010] For this type of polyethylene cable-membrane structure airship, this invention provides an accurate and convenient method for optimal structural design and processing. This method, based on the mass point method, discretizes a single-pane airship membrane to obtain the spherical membrane bulge shape and reinforcing rib length under internal and external pressure differential conditions, which serve as input for the planar membrane cutting shape during PE airship manufacturing.

[0011] This application provides a method for manufacturing the main airbag of a lightweight cable-net film airship, including the following steps:

[0012] The steps for performing simulation analysis on a set two-dimensional generatrix to determine the location of the circumferential stiffeners include: starting from the mass point at the fixed circumferential position of the largest cross-section, obtaining the deformed shape, and then obtaining the mass point with the largest transverse strain. This mass point is the arc length position of the obtained circumferential stiffener; in the next calculation, fix this mass point to continue dividing until the set number of circumferential stiffener positions are completed.

[0013] The steps for determining the shape of the bulge after being constrained by both the meridional and circumferential reinforcing ribs include: performing simulation calculations on the surface of the spherical membrane based on the position of the reinforcing ribs, the elastic modulus of the reinforcing ribs, and the elastic modulus of the spherical membrane, and determining the three-dimensional shape of each small bulge under the condition that the pressure difference between the inside and outside of the airship is a set value.

[0014] In the embodiments of this application, the airbag is shaped like a corn kernel airship and adopts a front-to-back symmetrical generatrix.

[0015] In one embodiment of this application, the airbag is made of polyethylene boat mold material.

[0016] In one embodiment of this application, the surface of the spherical membrane is discretized into triangular elements during numerical calculation. The simulation measures the changes in shape and in-plane forces under the influence of gravity on the mass point, the elastic and damping forces generated by the three mass segments of the element, and the internal and external pressure differential forces acting on the element.

[0017] In one embodiment of this application, a smooth planar cut-film shape is obtained by curve fitting of the cut-film shape.

[0018] In one embodiment of this application, the maximum circumferential and longitudinal forces on the reinforcing rope are determined under the condition of the maximum pressure difference under the set value.

[0019] In one embodiment of this application, the following steps are also included: setting the yield strength of the airship membrane, and determining the theoretical pressure difference that the airship body can withstand under the conditions of the meridional and circumferential reinforcing ribs and the three-dimensional shape of each small bulge.

[0020] On the other hand, this application also proposes a lightweight cable-net membrane airship main airbag, manufactured using the method of any embodiment of this application. The airship has 2N+1 circumferential reinforcing ribs, with N reinforcing ribs extending from the circumference of the largest cross-section to both ends, and N+1 bulges. The lengths of the bulges along the arc length are unequal, exhibiting a distribution that is shorter in the middle and longer at the sides. N is a natural number.

[0021] The above-described technical solutions adopted in the embodiments of this application can achieve the following beneficial effects:

[0022] Currently, there is a lack of design reference materials for this type of polyethylene cable-membrane structure hull. This invention provides a detailed and reliable design method for the shape and stress distribution of the main airbag membrane of a PE airship. First, the optimal circumferential reinforcing rib positions are calculated sequentially under two-dimensional conditions based on the airship's busbar. Then, using a single membrane as a calculation model, the design shapes of each bulge and the planar membrane cutting shape are derived. Finally, the accuracy of the design method is verified through actual membrane cutting and fabrication, welding of each spherical section, and ground pressure resistance tests. Attached Figure Description

[0023] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0024] Figure 1 Schematic diagram of a lightweight cable-net membrane airship;

[0025] Figure 2 This is a flowchart of the method in an embodiment of this application;

[0026] Figure 3 Solve for the arrangement of circumferential stiffeners;

[0027] Figure 4 To determine the shape of the single-sided, single-width membrane after deformation;

[0028] Figure 5 To obtain the 3D design drawing of the corn kernel airship;

[0029] Figure 6 This represents a small bulge stress state.

[0030] Figure 7 The stress state of the meridional and circumferential stiffeners;

[0031] Figure 8 The shape of the membrane is cut to fit the main airbag of the corn kernel airship.

[0032] Figure 9 This is a plan view of the entire corn kernel airship unfolded. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0034] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0035] Figure 1 This is a schematic diagram of a lightweight cable-net film airship. In the embodiments of this application, the airbag is made of polyethylene boat mold material.

[0036] This invention integrates overpressure balloon technology into airship design, using polyethylene film as the airship's body material. Similar to the Tawara overpressure balloon design, it employs warp and circumferential reinforcing ribs 11 and 12 to withstand stress, with the polyethylene film bulging in two orthogonal directions (warp and circumferential). Furthermore, the airship's shape is modified into a teardrop-shaped streamline to reduce drag, overcoming the problems caused by the airship's own weight during manufacturing, pressurization, and launch of fabric airships. This results in increased flight altitude and payload capacity. The novel polyethylene film airship (hereinafter referred to as "PE airship") can serve as an effective supplement to traditional fabric airships and overpressure balloons, with significant application value in long-endurance flight and area-based loitering.

[0037] The corn kernel airship has an axisymmetric structure, with the axis horizontal and the left and right ends as poles. The meridional lines intersect at the poles. The circumferential lines are closed curves formed by the intersection of a plane perpendicular to the axis and the surface of the main airbag.

[0038] In terms of spherical design, unlike fabric airships, the polyethylene membrane material used in corn kernel airships has lower strength and cannot withstand large stresses. Therefore, warp and circumferential reinforcing ribs are required to help bear the pressure difference between the inside and outside of the airship. During structural design, a strength analysis of the membrane stress should be conducted to determine the spacing of the circumferential reinforcing ribs and the shape of the planar membrane. In addition to ensuring the spherical pressure difference can withstand the effects of diurnal temperature variations, it must also resist bending deformation under bottom load suspension, requiring a certain degree of stiffness. Since the membrane cannot withstand bending moments, the mass point method can be conveniently used in engineering to discretize the spherical membrane and reinforcing rib structure of the corn kernel airship to quickly solve for its shape and stress characteristics. The mass point dynamics method designs based on the stable shape that mass segments or triangular mass elements can achieve under pressure difference and elastic force. The results satisfy the minimum potential energy deformation, thus easily obtaining the optimal stress structure of the membrane or rope.

[0039] The basic design parameters are shown in Table 1.

[0040] Table 1 Basic Design Parameters of the Corn Kernel Airship

[0041] parameter value parameter value volume <![CDATA[264.07m 3 ]]> Surface area <![CDATA[238.43m 2 ]]> bus length 18.86m Maximum cross-sectional radius 2.64m Length of sphere 17.04m Working pressure difference 300Pa Number of radial stiffeners 20 Polyethylene film thickness 38μm Thin film yield strength 10MPa Polyethylene film surface density <![CDATA[35.83g / m 2 ]]>

[0042] Figure 2 This is a flowchart of a method according to an embodiment of this application. This application proposes a method for manufacturing the main airbag of a lightweight cable-net film airship, including the following steps 10-40:

[0043] Step 10: Perform simulation analysis on the set two-dimensional busbar to determine the location of the circumferential stiffeners. This includes: starting from the mass point at the fixed maximum cross-sectional circumferential position, obtaining the deformed shape, and then obtaining the mass point with the maximum transverse strain. This mass point is the arc length position of the obtained circumferential stiffener. In the next calculation, fix this mass point to continue dividing until the set number of circumferential stiffener positions are completed.

[0044] In the embodiments of this application, the airbag is shaped like a corn kernel airship and adopts a front-to-back symmetrical generatrix.

[0045] At 270m 3 Taking a corn kernel airship as an example, the generatrix equation is:

[0046]

[0047] in, and These are the axial coordinates and radius of the airship, respectively. The axial length of the airship is normalized to 1. These are axial coordinates normalized to the length of the airship. It is the radius normalized according to the length of the airship.

[0048] Therefore, a simulation analysis of the two-dimensional busbar is first performed to determine the location of the circumferential stiffeners. To obtain the most accurate location of the circumferential stiffeners, the number of discrete points on a single-sided busbar is arranged as densely as possible. The simulation uses 300 mass points on a single-sided busbar, with a calculation step size of 10^... (-5) The calculation time is 3 seconds to allow sufficient deformation to reach a stable state. The deformation of the generatrix and the location of the mass point with the corresponding maximum lateral strain are calculated sequentially as follows: Figure 3 As shown, the airship has 15 circumferential reinforcing ribs (7 ribs from the circumference of the largest cross-section to both ends, and 8 bulges). The lengths of the bulges along the arc are not equal, and are [0.9429, 1.0058, 1.0058, 1.0687, 1.0687, 1.2573, 1.3201, 1.5716] m, showing a distribution that is shorter in the middle and longer at the sides. This is consistent with the expectation that the middle will deform and that the greater stress requires a denser arrangement of circumferential reinforcing ribs.

[0049] Once the location of the circumferential stiffener is determined, the circumferential length of the airship's cross-section can be determined, thus determining the length of the circumferential stiffener.

[0050] Step 20: Determine the shape of the bulge after being constrained by the meridional and circumferential reinforcing ribs, including: performing simulation calculations on the surface of the spherical membrane based on the position of the reinforcing ribs, the elastic modulus of the reinforcing ribs and the elastic modulus of the spherical membrane, and determining the three-dimensional shape of each small bulge under the condition that the pressure difference between the inside and outside of the airship is a set value.

[0051] Regarding the determination of the number of meridional stiffeners: The number of meridional stiffeners is determined by the designers based on the number of membranes in the hull. A higher number of membranes results in a hull that more closely resembles a body of revolution. A lower number of membranes results in a less rounded circumference for the airship. In this example, the hull has 20 membranes, meaning there are 20 meridional stiffeners.

[0052] The shape and stress of the bulge are designed based on the combined constraint of meridional and circumferential stiffeners. The corn kernel airship is represented by a small bulge as the smallest unit. Calculations on the small bulges reveal the stress on the spherical membrane and the lateral tensile forces on the circumferential stiffeners.

[0053] In one embodiment of this application, the surface of the spherical membrane is discretized into triangular elements during numerical calculation. The simulation measures the changes in shape and in-plane forces under the influence of gravity on the mass point, the elastic and damping forces generated by the three mass segments of the element, and the internal and external pressure differential forces acting on the element.

[0054] The points restricting the meridional stiffeners to move only within the angular plane are fixed, the axial variation of the front section is fixed, and the ends satisfy the geometric constraints of the flange. The elastic modulus of the spherical membrane is 182 MPa, and the elastic modulus of the stiffeners is 10 GPa (the actual modulus is 180 GPa). The deformation of the spherical membrane is simulated. The design input is the circumferential stiffener arrangement position obtained above, the pressure difference between the inside and outside of the airship is 300 Pa, the initial elastic modulus of the spherical membrane is set to 10 MPa to obtain the bulge shape, and then the spherical membrane modulus is set to the actual modulus of 182 MPa to reduce the stress of the spherical membrane. The three-dimensional shape of each small bulge is solved as follows. Figure 4 As shown. Figure 5 The main airbag has a three-dimensional shape.

[0055] Step 30: In one embodiment of this application, a smooth planar cut-film shape is obtained by curve fitting of the cut-film shape.

[0056] The edge of the corn kernel airship's membrane differs from the smooth membrane flaps of previous zero-pressure / overpressure airships. There is a lateral shrinkage between the two bulging spherical membrane materials, due to the presence of circumferential reinforcing ribs.

[0057] By curve fitting the cut-out shape, a smooth planar cut-out shape is obtained, such as... Figure 8 As shown in the figure, the outer contour is the final planar shape of the corn kernel airship. The edge shape 82 of the spherical membrane, calculated by simulation, is unsuitable for processing due to its wavy shape. Therefore, the first generatrix 81 is fitted based on the wavy shape to facilitate processing. The second generatrix 83 is the meridional reinforcing rib generatrix after the bulge is formed on the surface of the tethered balloon under the action of the circumferential reinforcing rib 85. The third generatrix 84 is the shape of the balloon generatrix if it were a smooth, simple rotating body structure without the bulge configuration. It can be concluded that after the bulge is formed by the reinforcing ribs, the balloon requires more spherical membrane material, that is, the first generatrix 81 requires much more spherical membrane material than the third generatrix 84.

[0058] The circumferential stress and the meridional stress along the centerline of the airship are as follows: Figure 6 As shown, the dashed line represents the circumferential stress along the center line; the solid line represents the meridional stress along the center line. Figure 7 The stresses on the meridional and circumferential stiffeners were recorded; the dashed lines represent the stress in the circumferential stiffeners, and the solid lines represent the stress in the meridional stiffeners. It can be concluded that the sphere deforms relatively little after the application of internal pressure. Furthermore, it conforms to the trend of higher stress in the middle and lower stress at both ends during the stress and deformation process. During the expansion deformation process, no significant stress caused by the flattening of the spherical membrane occurred at either end. The stress and deformation of the entire sphere are well coordinated.

[0059] Based on the structural design, the area of ​​a single spherical membrane was determined to be 19.76 m². 2 (For comparison, the area of ​​a pure rotating body-shaped film is 11.92 m²) 2The total weight of the main airbag membrane of the corn kernel airship is 14.1615 kg. If the pressure difference is further increased, assuming the membrane yields when the stress exceeds 10 MPa, the maximum withstand pressure difference is approximately 1200 Pa. The reinforcing ribs used in the calculation have a diameter of 3 mm, resulting in a maximum circumferential force of 216 kg and a maximum meridional force of 100 kg.

[0060] The corresponding lengths of the longitudinal reinforcing ribs are L = [1.57, 1.32, 1.26, 1.07, 1.07, 1.01, 1.01, 0.94, 0.94, 1.01, 1.01, 1.07, 1.07, 1.26, 1.32, 1.57] m. That is, the rope length is 18.49 m, and a total of 20 × 18.49 = 369.8 m is required.

[0061] The half lengths of each circumferential reinforcing rib on a single membrane are L = [0.03, 0.21, 0.30, 0.36, 0.39, 0.40, 0.41, 0.41, 0.42, 0.41, 0.41, 0.40, 0.38, 0.36, 0.30, 0.21, 0.03] m.

[0062] The total length of the circumferential stiffeners is 2 * 108.3 = 216.6 m. The sum of the lengths of the meridional and circumferential stiffeners is 369.8 m + 216.6 m = 586.4 m.

[0063] Step 40: Stress analysis and pressure resistance test.

[0064] In one embodiment of this application, the maximum circumferential and longitudinal forces on the reinforcing rope are determined under the condition of the maximum pressure difference of the set value.

[0065] In one embodiment of this application, the following steps are also included: setting the yield strength of the airship membrane, and determining the theoretical pressure difference that the airship body can withstand under the conditions of the meridional and circumferential reinforcing ribs and the three-dimensional shape of each small bulge.

[0066] The actual manufacturing process involved verifying the pressure-bearing capacity of the corn kernel airship. The difference from the pumpkin balloon manufacturing process is the need to weld circumferential reinforcing ribs. After manufacturing, a ground inflation test was conducted, followed by a final test of the corn kernel airship's ultimate pressure resistance. During manufacturing, the circumferential reinforcing ribs restrained the radial reinforcing ribs. Both ends of the airship were sealed with a thickened membrane, and 20 radial reinforcing ribs were tied at both ends. A hole was also made at the diagonal edge of the 8th membrane panel and the 8th bulge of the airship as an inflation port and pressure testing port. The hole diameter was 0.1m (10cm). Local reinforcement was applied at the hole locations, such as... Figure 9 The image shown is a plan view of the entire corn kernel airship when deployed.

[0067] After structural optimization design and actual fabrication, the polyethylene film airship has a designed pressure difference of 300 Pa and a standard stress of 2.5 MPa. If calculated based on the yield strength of polyethylene film of 10 MPa, the theoretical pressure difference the airship can withstand should reach over 1000 Pa. Pressure resistance tests were conducted on the airship; even at 1081 Pa, the airship structure remained intact, verifying the reliability of the polyethylene airship structure designed in this paper.

[0068] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0069] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when an element is “connected” or “coupled” to another element, it may be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein may include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.

[0070] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical, terminological, and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0071] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for manufacturing the main airbag of a lightweight cable-net film airship, characterized in that, Includes the following steps: The steps for performing simulation analysis on a set two-dimensional generatrix to determine the location of the circumferential stiffeners include: starting from the mass point at the fixed circumferential position of the largest cross-section, obtaining the deformed shape, and then obtaining the mass point with the largest transverse strain. This mass point is the arc length position of the obtained circumferential stiffener; in the next calculation, this mass point is fixed to continue the division until the set number of circumferential stiffener positions are completed. The steps for determining the shape of the bulge after being constrained by both the meridional and circumferential reinforcing ribs include: performing simulation calculations on the surface of the spherical membrane based on the position of the reinforcing ribs, the elastic modulus of the reinforcing ribs, and the elastic modulus of the spherical membrane, and determining the three-dimensional shape of each small bulge under the condition that the pressure difference between the inside and outside of the airship is a set value.

2. The method for manufacturing the main airbag of a lightweight cable-net film airship as described in claim 1, characterized in that, The airbag is shaped like a corn kernel airship and uses a symmetrical generatrix at the front and back.

3. The method for manufacturing the main airbag of a lightweight cable-net film airship as described in claim 1, characterized in that, The airbag is made of polyethylene boat mold material.

4. The method for manufacturing the main airbag of a lightweight cable-net film airship as described in claim 1, characterized in that, In the numerical calculation, the surface of the spherical membrane is discretized into triangular elements to simulate the changes in shape and in-plane forces under the influence of gravity on the mass point, elastic force and damping force generated by the three mass segments of the element, and internal and external pressure difference.

5. The method for manufacturing the main airbag of a lightweight cable-net film airship as described in claim 1, characterized in that, It also includes the following steps: obtaining a smooth planar cut-out shape by curve fitting of the cut-out shape.

6. The method for manufacturing the main airbag of a lightweight cable-net film airship as described in claim 1, characterized in that, Under the maximum pressure difference condition set at the set value, determine the maximum circumferential and longitudinal forces on the reinforcing rope.

7. The method for manufacturing the main airbag of a lightweight cable-net film airship as described in claim 1, characterized in that, It also includes the following steps: The yield strength of the airship membrane is set, and under the conditions of the meridional and circumferential reinforcing ribs and the three-dimensional shape of each small bulge, the theoretical pressure difference that the airship body can withstand is determined.

8. A lightweight cable-net film airship main airbag, manufactured by any one of claims 1 to 7, characterized in that, The busbar shape is as follows: in, These are axial coordinates normalized to the length of the airship. It is the radius normalized according to the length of the airship.

9. A lightweight cable-net film airship main airbag, manufactured by any one of claims 1 to 7, characterized in that, The airship has 2N+1 circumferential reinforcing ribs, with N reinforcing ribs from the circumference of the largest cross section to both ends, and N+1 bulges. The lengths of the bulges along the arc are not equal, showing a distribution that is shorter in the middle and longer on both sides.

10. A lightweight cable-net film airship main airbag, manufactured by any one of claims 1 to 7, characterized in that, The airship has 15 circumferential reinforcing ribs, 7 reinforcing ribs from the circumference of the largest cross section to each end, and 8 bulges. The lengths of each bulge along the arc length are [0.9429, 1.0058, 1.0058, 1.0687, 1.0687, 1.2573, 1.3201, 1.5716] m.

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