Light cable net film airship main air bag and manufacturing method

Abstract

The manufacturing method comprises the steps of performing simulation analysis on a set two-dimensional bus and determining the arrangement position of circumferential reinforcing ribs and comprises the steps of starting from a mass point at the circumferential position of a fixed maximum section, obtaining the shape after deformation, then obtaining the mass point with the maximum transverse strain, and determining the arrangement position of the circumferential reinforcing ribs; the mass point is the obtained arc length position of the circumferential reinforcing rib; and fixing the mass point in the next calculation so as to continue segmentation until the positions of the circumferential reinforcing ribs with the set number are completed. And the step of determining the shape of the bump jointly restrained by the longitudinal reinforcing ribs and the circumferential reinforcing ribs comprises the steps that according to the positions of the reinforcing ribs, the elastic modulus of the reinforcing ribs and the elastic modulus of the spherical membrane, simulation calculation is conducted on the surface of the spherical membrane, and under the condition that the internal and external pressure difference of the airship is a set value, the three-dimensional shape of each small bump is determined. The problem that the main air bag of the polyethylene film airship is difficult to design is solved.

Description

Technical Field

[0001] The present application relates to the field of near-space aerostat design, and particularly focuses on the design of an aerostat capsule superpressure structure. Background Art

[0002] Aerostats fly by filling their interior with gas that is lighter than air, including airships, tethered balloons and free balloons. One of the current development directions of airships is stratospheric high-altitude airships. Stratospheric airships have received much attention among near-space flight platforms. Unlike free balloons, they can fly with power and obtain certain trajectory control capabilities, which makes them have important application value and broad development prospects. At present, stratospheric airships are mostly made of fabric skin materials, which obtain rigidity after withstanding the internal and external pressure difference at the ceiling altitude. However, the membrane surface density of traditional fabric airships is relatively large, and the design is simply similar to the early development of superpressure balloons, which rely on the film itself to resist the pressure difference.

[0003] The weight of the capsule is too large, which increases the cost of each process such as manufacturing, folding and transportation, pressure-maintaining and unfolding, and distribution. In addition, the fabric airship needs to overcome its own gravity, which leads to low volume and payload utilization. The speed v of the aircraft and the required energy P are in a cubic relationship. In order to increase the flight speed, more energy loads need to be carried, which further increases the volume of the airship. If the weight of the hull itself is large, the system weight and size design are prone to divergence.

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

[0005] Super-pressure balloons are made of linear low-density polyethylene (LLDPE) film material, which has the advantages of low cost, high flight altitude and large load. Super-pressure balloons are closed to the outside world, and the balloon membrane withstands the internal and external pressure difference to offset the impact of the temperature difference between day and night, achieving long-term flight at a stable altitude. At present, super-pressure balloons mostly adopt a "pumpkin-shaped" design, which uses a geometric configuration with an increased local curvature radius and reinforced ribs to jointly withstand the internal and external pressure difference. Super-pressure balloons have now become an important development target in projects including NASA, JAXA, CNES and Google Balloon.

[0006] The Chinese Academy of Sciences Institute of Space Information Innovation has carried out 7000m 3 The flight test of the pumpkin-shaped super-pressure balloon has accumulated sufficient technical experience. However, the super-pressure balloon does not have a streamlined shape and is subject to greater resistance in all directions.

[0007] In order to overcome the problem of instability during the deployment of super-pressure balloons and reduce the resistance encountered during the ascent of super-pressure balloons, the JAXA balloon group developed the Tawara "corn kernel" super-pressure balloon, which is formed by extending the equatorial part of the "pumpkin-shaped" balloon into an intermediate cylindrical shape.

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

[0009] The present application proposes a light-weight cable net film airship main airbag and a manufacturing method, which solves the problem that the polyethylene film airship main airbag is difficult to design.

[0010] The present invention provides an accurate and convenient structural optimal design method and processing technology for this polyethylene cable membrane structure airship. Based on the mass-particle method, the method discretizes a single airship membrane to obtain the spherical membrane bulge shape and reinforcing rib length under the condition of internal and external pressure difference, which is used as the plane film cutting shape input when making the PE airship.

[0011] The present application embodiment provides a method for manufacturing a main airbag of a lightweight cable net film airship, comprising the following steps:

[0012] The steps of performing simulation analysis on the set two-dimensional generatrix to determine the arrangement position of the circumferential stiffener include: starting from a mass point at a fixed circumferential position of the maximum cross-section, obtaining a deformed shape, and then obtaining a mass point with a maximum transverse strain, which mass point is the obtained arc length position of the circumferential stiffener; fixing the mass point in the next calculation to continue segmentation until the set number of circumferential stiffener positions are completed;

[0013] The step of determining the shape of the bulge after being constrained by the warp stiffeners and the circumferential stiffeners includes: simulating and calculating the surface of the spherical membrane according to the position of the stiffeners, the elastic modulus of the stiffeners 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 an embodiment of the present application, the airbag is in the shape of a corn-grain airship, with a front-to-back symmetrical busbar.

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

[0016] In one embodiment of the present application, the surface of the spherical membrane is discretized into triangular facets in numerical calculations to simulate the gravity of the mass point, the elastic force and damping force generated by the three-side mass segments of the facet, and the shape and in-plane force changes of the facet under the action of the internal and external pressure difference.

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

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

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

[0020] On the other hand, the present application also proposes a main airbag of a lightweight cable net film airship, which is made by the method of any embodiment of the present application. The airship has 2N+1 circumferential reinforcing ribs, N reinforcing ribs from the maximum cross-section circumference to the two ends, N+1 bulges, and the lengths of the bulges along the arc length are not equal, showing a distribution of short in the middle and long on both sides. N is a natural number.

[0021] At least one of the above technical solutions adopted in the embodiments of the present application can achieve the following beneficial effects:

[0022] At present, there is a lack of reference materials for the design of this type of polyethylene cable membrane structure hull. The present invention provides a detailed and reliable design method for the shape and force of the PE airship main airbag film. First, the optimal circumferential reinforcement rib position is calculated in sequence under two-dimensional conditions for the airship busbar. Then, using a single membrane as a calculation model, the design shape of each bulge and the plane film shape are obtained. Finally, the accuracy of the design method is verified through actual film processing, welding of each ball width and ground pressure resistance test. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0024] Figure 1 This is a schematic diagram of a lightweight cable-net membrane airship;

[0025] Figure 2 A flowchart of the method of the embodiment of the present application;

[0026] Figure 3 Solve for the circumferential reinforcement arrangement;

[0027] Figure 4 To solve the deformed shape of a single-sided single-width membrane;

[0028] Figure 5 The three-dimensional design of the corn-grain airship was solved;

[0029] Figure 6 is the stress state of the small drum;

[0030] Figure 7 is the stress state of the longitudinal and circumferential reinforcements;

[0031] Figure 8 The shape of the film cut for the main airbag of the corn-grain airship;

[0032] Fig. 9 This is the overall plan of the corn grain airship. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical solution and advantages of the present application clearer, the technical solution of the present application will be clearly and completely described below in combination with the specific embodiments of the present application and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present application.

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

[0035] Figure 1 It is a schematic diagram of a lightweight cable net film airship. In the embodiment of the present application, the airbag is made of polyethylene boat model material.

[0036] The present invention integrates the super-pressure balloon technology into the airship design, adopts polyethylene film as the airship bladder material, and adopts the warp reinforcement ribs 11 and the circumferential reinforcement ribs 12 to bear the stress in a similar way to the Tawara super-pressure balloon design, and the polyethylene film is squeezed into a bulge shape in the two orthogonal directions of the warp and the circumferential. And by modifying the shape of the hull into a water drop streamline to reduce resistance, a series of problems caused by the deadweight of the bladder during the manufacturing, pressure maintenance and release of the fabric airship are overcome, the flight altitude is increased, and the load carrying capacity is increased. The new polyethylene film airship (hereinafter referred to as "PE airship") can serve as an effective supplement to traditional fabric airships and super-pressure balloons, and has great application value in long-duration flight, regional residence, etc.

[0037] The corn grain airship is specifically an axisymmetric structure, with the axis horizontal, the left and right ends as poles, and the meridian lines intersecting at the poles. The circumferential line is a closed curve where the surface perpendicular to the axis intersects with the main airbag surface.

[0038] In terms of sphere design, unlike fabric airships, the polyethylene membrane material used in corn grain airships has low strength and cannot withstand large stresses. It is necessary to use warp and circumferential reinforcement ribs to assist in bearing the pressure difference between the inside and outside of the airship. During structural design, the strength analysis of the spherical membrane force should be carried out to obtain the spacing distribution of the circumferential reinforcement ribs and the shape of the plane membrane. In addition, in addition to ensuring the influence of the day and night temperature difference, the spherical pressure difference must also be able to resist the bending deformation when the bottom load is suspended, that is, it needs to have a certain stiffness. Since the film cannot withstand bending moments, the mass particle method can be conveniently used in engineering to discretize the spherical membrane and reinforcement rib structure of the corn grain airship to quickly solve the shape and force characteristics. The mass particle dynamics method is to carry out the design through the stable shape that can be achieved by the mass segment or triangular mass unit under the pressure difference force and elastic force. The result obtained satisfies the minimum potential energy deformation, which can also easily obtain the optimal force structure of the film or rope.

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

[0040] Table 1 Basic design parameters of corn grain airship

[0041] parameter value parameter value volume <![CDATA[264.07m 3 ]]> Surface Area <![CDATA[238.43m 2 ]]> Busbar length 18.86m Maximum section radius 2.64m Sphere length 17.04m Working pressure difference 300Pa Number of warp reinforcement bars 20 Polyethylene film thickness 38μm Film yield strength 10MPa Polyethylene film surface density <![CDATA[35.83g / m 2 ]]>

[0042] Figure 2 This is a flow chart of the method of the embodiment of the present application. The embodiment of the present application proposes a method for manufacturing a main airbag of a lightweight cable net film airship, including the following steps 10 to 40:

[0043] Step 10, simulate and analyze the set two-dimensional generatrix to determine the arrangement position of the circumferential reinforcement ribs, including: starting from the mass point at the fixed maximum cross-section circumferential position, obtain the deformed shape, and then obtain the mass point with the maximum lateral strain, which is the arc length position of the circumferential reinforcement ribs; fix the mass point in the next calculation to continue the division until the set number of circumferential reinforcement rib positions are completed.

[0044] In an embodiment of the present application, the airbag is in the shape of a corn-grain airship, with a front-to-back symmetrical busbar.

[0045] 270m 3 Taking the corn grain airship as an example for design, the generatrix equation is:

[0046]

[0047] in, and are the axial coordinate and radius of the airship, and the axial length of the airship is normalized to 1. is the axial coordinate normalized to the length of the airship, is the radius normalized to the length of the airship.

[0048] Therefore, the two-dimensional busbar is first simulated and analyzed to obtain the circumferential reinforcement rib layout position. In order to obtain the accurate circumferential reinforcement rib position as much as possible, the number of discrete points of the single-sided busbar is as dense as possible. 300 mass points are arranged in the single-sided busbar, and the calculation step size is 10^ (-5) s, and the calculation time is 3s to allow the deformation to reach a stable state. The busbar deformation and the corresponding mass point position of the maximum lateral strain are calculated in turn as follows: Figure 3 As shown in the figure, the airship has 15 circumferential stiffeners (7 stiffeners and 8 bulges from the maximum cross-section circumference to the ends), and the lengths of the bulges along the arc length are not equal, namely [0.9429, 1.0058, 1.0058, 1.0687, 1.0687, 1.2573, 1.3201, 1.5716] m, showing a distribution of short in the middle and long on both sides. This is also in line with the expectation that the deformation trend in the middle and the greater force require a more dense arrangement of circumferential stiffeners.

[0049] After the position of the circumferential reinforcement ribs is determined, the circumferential length of the airship cross section can be determined, so the length of the circumferential reinforcement ribs is determined.

[0050] Step 20, determining the shape of the bulge after being constrained by the warp stiffeners and the circumferential stiffeners, including: simulating and calculating the surface of the spherical membrane according to the position of the stiffeners, the elastic modulus of the stiffeners 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] How to determine the number of warp stiffeners. The warp stiffeners are determined by the designer based on the number of membranes of the hull. The more membranes there are, the closer the hull is to a body of revolution. If the number of membranes is small, the circumference of the airship is not round. In this example, the number of membranes of the hull is 20, which means the number of warp stiffeners is 20.

[0052] The shape and force of the bulge are designed after being constrained by the warp and circumferential reinforcements. The small bulge is the smallest unit of the corn grain airship. The force on the spherical membrane and the left and right pulling force on the circumferential reinforcement can be obtained by calculating the small bulge.

[0053] In one embodiment of the present application, the surface of the spherical membrane is discretized into triangular facets in numerical calculations to simulate the gravity of the mass point, the elastic force and damping force generated by the three-side mass segments of the facet, and the shape and in-plane force changes of the facet under the action of the internal and external pressure difference.

[0054] The points of the warp stiffeners are restricted to move only within the angular plane, the axial changes of the head section are fixed, and the end satisfies the geometric size constraints of the flange. The elastic modulus of the spherical membrane is 182MPa, the elastic modulus of the stiffener is 10GPa (the actual modulus is 180GPa), and the deformation of the spherical membrane is simulated. The design input is the above-obtained circumferential stiffener arrangement position, the pressure difference between the inside and outside of the airship is 300Pa, the initial spherical membrane elastic modulus is set to 10MPa to obtain the bulge shape, and then the spherical membrane modulus is set to the actual modulus of 182MPa to achieve the reduction of the spherical membrane stress. The three-dimensional shapes of each small bulge are solved as follows: Figure 4 shown. Figure 5 The three-dimensional shape of the main airbag.

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

[0056] The cut film edge of the corn grain airship is different from the smooth film petals of the previous zero pressure / super pressure airship. There is a lateral length contraction between the two bulge ball film materials, which is due to the constraint of the circumferential reinforcement ribs.

[0057] By curve fitting of the cut film shape, a smooth plane cut film shape is obtained. Figure 8 As shown. The outer contour in the figure is the final planar film shape of the corn grain airship; the edge shape 82 of the spherical film material required by the simulation calculation is similar to a wave shape and is not suitable for processing and manufacturing. Therefore, the first busbar 81 is fitted on the basis of the wave shape to facilitate processing. The second busbar 83 is the meridian reinforcement busbar after the surface of the tethered balloon is bulged under the action of the circumferential reinforcement line 85; the shape of the third busbar 84 is the shape of the balloon busbar of a smooth simple rotating body structure instead of a bulge configuration. It can be concluded that after the balloon is bulged due to the reinforcement ribs, the balloon needs more spherical film material, that is, the first busbar 81 has a lot more spherical film material than the third busbar 84.

[0058] The circumferential stress and the midline longitudinal stress along the airship are shown as follows: Figure 6 As shown, the dotted line is the circumferential stress of the center line; the solid line is the meridional stress of the center line. Figure 7 The stresses on the warp and circumferential reinforcements are recorded. The dashed line is the stress on the circumferential reinforcements; the solid line is the stress on the warp reinforcements. It can be concluded that the deformation of the sphere is small after the internal pressure is applied. And it conforms to the distribution trend of stress and deformation, with large stress in the middle and small stress at both ends. During the expansion and deformation process, there is no large stress caused by the flattening of the ball membrane at both ends. The stress and deformation of the entire sphere are well coordinated.

[0059] Based on the structural design, the area of ​​a single spherical membrane is 19.76m 2 (For comparison, the film cutting area of ​​pure rotary body is 11.92m 2). The total weight of the main airbag membrane of the corn grain airship is 14.1615kg. If the pressure difference is further increased, the maximum pressure difference that can be borne is about 1200Pa according to the yielding of the membrane stress when it is greater than 10MPa. The reinforcing rib rope set in the calculation is 3mm in diameter, so the maximum circumferential force is 216kg and the maximum longitudinal force is 100kg.

[0060] The lengths of the corresponding longitudinal reinforcement bars 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 stiffener on a single membrane are L = [0.03, 0.21, 030, 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 respectively.

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

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

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

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

[0066] Actual processing and production are used to verify the pressure-bearing capacity of the corn grain airship. The difference from the processing of the pumpkin balloon is that it is necessary to weld a circumferential reinforcement sleeve. After the processing is completed, a ground inflation experiment is carried out, and finally the ultimate pressure resistance of the corn grain airship is tested. During processing, the circumferential reinforcements tighten the warp reinforcements. Thickened film is used to seal both ends of the airship, and 20 warp reinforcements are tied at both ends. At the same time, holes are opened on the diagonal edges of the 8th film and the 8th bulge of the airship as inflation holes and pressure measuring ports. The diameter of the opening is 0.1m, or 10cm. And local reinforcement is carried out at the opening position, such as Fig. 9 Shown is the overall unfolded plan view of the corn grain airship.

[0067] After structural optimization design and actual processing and production, the polyethylene film airship has a design pressure difference of 300Pa and a standard stress of 2.5MPa. If the yield strength of polyethylene film is 10MPa, the theoretical pressure difference of the airship should reach more than 1000Pa. The pressure test of the airship shows that the airship structure is still intact when the pressure reaches 1081Pa, which verifies the reliability of the polyethylene airship structure designed in this paper.

[0068] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of further restrictions, the elements defined by the sentence "comprises..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0069] It will be understood by those skilled in the art that, unless expressly stated, the singular forms "one", "said", and "the" used may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the 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. In addition, the "connection" or "coupling" used herein may include wireless connection or wireless coupling. The term "and / or" used herein includes all or any unit and all combinations of one or more associated listed items.

[0070] Those skilled in the art will understand that unless otherwise defined, all terms (including technical, technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art to which this invention belongs.

[0071] The above is only an embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims

1. A method for manufacturing a main airbag of a lightweight cable net film airship, characterized in that: The following steps are involved: The steps of performing simulation analysis on the set two-dimensional generatrix to determine the arrangement position of the circumferential stiffener include: starting from a mass point at a fixed circumferential position of the maximum cross-section, obtaining a deformed shape, and then obtaining a mass point with a maximum transverse strain, which mass point is the obtained arc length position of the circumferential stiffener; fixing the mass point in the next calculation to continue segmentation until the set number of circumferential stiffener positions are completed; The step of determining the shape of the bulge after being constrained by the warp stiffeners and the circumferential stiffeners includes: simulating and calculating the surface of the spherical membrane according to the position of the stiffeners, the elastic modulus of the stiffeners 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. A method for manufacturing a main airbag of a lightweight cable net film airship as claimed in claim 1, characterized in that: The airbag is in the shape of a corn-grain airship and adopts a front-to-back symmetrical generatrix.

3. A method for manufacturing a main airbag of a lightweight cable net film airship as claimed in claim 1, characterized in that: The air bag is made of polyethylene boat model material.

4. A method for manufacturing a main airbag of a lightweight cable net film airship as claimed in claim 1, characterized in that: In numerical calculation, the surface of the spherical membrane is discretized into triangular facets to simulate the gravity of the mass point, the elastic force and damping force generated by the mass segments on the three sides of the facet, and the shape and in-face force changes of the facet under the action of the internal and external pressure difference.

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

6. A method for manufacturing a main airbag of a lightweight cable net film airship as claimed in claim 1, characterized in that: Under the condition of the maximum bearing pressure difference of the set value, determine the maximum circumferential and longitudinal forces of the reinforcement rope.

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

8. A main airbag of a lightweight cable net film airship, made by any method of claims 1 to 7, characterized in that: The busbar shape is: in, is the axial coordinate normalized to the length of the airship, is the radius normalized to the length of the airship.

9. A main airbag of a lightweight cable net film airship, made by the method of any one of claims 1 to 7, characterized in that: The airship has 2N+1 circumferential stiffeners, N stiffeners from the circumference of the largest cross-section to the head and tail ends, and N+1 bulges. The lengths of the bulges along the arc are not equal, showing a distribution of short in the middle and long on both sides.

10. A main airbag of a lightweight cable net film airship, characterized in that: The airship has 15 circumferential reinforcement ribs, 7 reinforcement ribs from the maximum cross-section circle to the head and tail ends, and 8 bulges. The lengths of each bulge along the arc are [0.9429, 1.0058, 1.0058, 1.0687, 1.0687, 1.2573, 1.3201, 1.5716] m.

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