- Email: [email protected]
Aerodynamic influences on a tethered high-altitude lighter-than-air platform system to its behavior
JID:AESCTE AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.1 (1-7)
Aerospace Science and Technology ••• (••••) •••–•••
1
67
Contents lists available at ScienceDirect
2
68
3
69
Aerospace Science and Technology
4
70
5
71
6
72
www.elsevier.com/locate/aescte
7
73
8
74
9
75
10
76
11 12 13
77
Aerodynamic influences on a tethered high-altitude lighter-than-air platform system to its behavior
78 79
14 15 16 17 18 19 20
80
Kazuhisa Chiba
a,∗
a
b
c
, Ryosuke Nishikawa , Masahiko Onda , Shin Satori , Ryojiro Akiba
d
a
84 85 86 87
a r t i c l e
i n f o
88
a b s t r a c t
23 24 25 26 27 28 29 30 31 32 33
82 83
The University of Electro-Communications, Tokyo 182-8585, Japan b Sky Platform Technologies Co. Ltd., Tochigi 320-0855, Japan c Hokkaido University of Science, Sapporo 006-8585, Japan d Hokkaido Aerospace Science and Technology Incubation Center, Sapporo 001-0010, Japan
21 22
81
89
Article history: Received 17 February 2017 Received in revised form 21 August 2017 Accepted 21 August 2017 Available online xxxx Keywords: Tethered platform system Lighter-than-air hull Rockoon system High altitude Aerodynamics
34
The goal of this study was to investigate the influence of aerodynamic factors on the static behavior of a tethered high-altitude lighter-than-air platform. The system design comprised a lighter-than-air vehicle and a tether cable, and the conceptual platform configuration of such a system is studied herein. Governing equations were derived to model the static behavior of the system, and the effects of aerodynamic lift and buoyancy were parametrically analyzed based on the advection distance of the platform under storm conditions. The aerodynamic lift and buoyancy of the hull were shown to have nonlinear effects. We further analyzed the influence of the aerodynamic drag created by the tether. Since this was shown to have a significant influence, we concluded that the cable should ideally have a crosssectional shape resembling the airfoil of a heavier-than-air aircraft. However, it is sufficient to ensure that the drag coefficient is of the order of 10−1 . © 2017 Elsevier Masson SAS. All rights reserved.
90 91 92 93 94 95 96 97 98 99 100
35
101
36
102
37
103
38
104
39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
1. Introduction A firm lighter-than-air (LTA) vehicle for use in the lower stratosphere would provide a platform for a wide range of space activities. In the early 2000s, Japan Aerospace Exploration Agency (JAXA) conducted R&D on a free-flying LTA stratospheric platform. This was aborted because appropriate propulsion units with sufficient thrust were not available, and the high-altitude performance was inadequate. However, the potential merits of such a platform remain. A stratospheric platform would be the ideal launchpad for rocket-powered space transportation systems. An alternative approach is the tethered high-altitude platform, comprising an LTA vehicle1 and a tether cable. This is similar to the rockoon systems [1] that were successfully used for space observation in the 1950s and 60s. Stratospheric platforms could replace rockoon systems as highfrequency, high-load capacity space launch facilities. Fixed wing heavier-than-air (HTA) aircrafts have been tested [2,3], in which
58 59 60 61 62 63 64 65 66
*
Corresponding author. E-mail address: [email protected] (K. Chiba). 1 As general definitions, LTA vehicle (or LTA hull) refers to an unpowered aircraft, airship shows a powered one, and aerostat (or LTA aircraft) includes both. The terms are used accordingly. http://dx.doi.org/10.1016/j.ast.2017.08.029 1270-9638/© 2017 Elsevier Masson SAS. All rights reserved.
the rocket is released in the lower stratosphere. Current aircrafts have an upper payload weight limit of approximately 100 [t], but launch velocities near the speed of sound can be achieved in the lower stratosphere. However, rocket installation on and separation from HTA aircraft remains technically challenging. As rockoon systems have been successfully deployed in the past, the moored LTA platform is a promising alternative to HTA aircraft launch systems. A tethered lower-stratospheric platform might also find applications in fields such as agriculture [4], defense [5], meteorology [6], environmental science [7], and telecommunications [8,9]. This type of platform offers a useful bridge between space and ground, as the influence of cloud cover can be ignored even at altitudes above 10 [km]. Such a system would have the following advantages:
• No thrust is required to maintain the altitude of the platform (thus, the system uses an LTA vehicle instead of an airship); no maintenance on the ground is also required. • The tethered platform can hold the mooring position within the length of the rope.
105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
The tether cable can be used to transmit electricity, and replenish the buoyancy gas. A cargo carrier called “a climber” can ascend and descend the cable, supplying payloads.
127 128 129 130 131 132
JID:AESCTE
2
AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.2 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
1
67
2
68
3
69
4
70
5
71
6
72
7
73
8
74
9
75
10
76
11
77
12 13
78
Fig. 1. Typical geometries of (a) axisymmetric [24] and (b) hybrid [22] airships.
79
14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
80
Mooring is based on the aerostat principle, which has been extensively researched since the 1970s [10–13]. Recent research efforts have addressed both practical low altitude applications by replacing balloons with weathervaning aerostats, and research into mooring of balloons at high altitudes. The TCOM Corporation continues to conduct research on the first of these [14,15]. Advanced research is being carried out on the design of aerostats with novel conformations [16–18]. Attempts are being made to develop an airborne wind energy turbine system [19]. The altitude that can be achieved by tethered systems is limited by the weight of the tether, and this must be addressed if high-altitude systems are to be realized. Mooring at an altitude of 20 [km] has been reported [20], making lower stratospheric LTA platforms a practical proposition. In addition, hybrid aerostats have been developed [21,22] that take advantage of both buoyancy and aerodynamic lift. These are expected to replace conventional balloons in high-altitude applications. The goal of the current study was to develop a high-altitude LTA platform. Our design is for an LTA vehicle geometry for lower stratospheric use. The body has a membrane structure, offering a flexible aerodynamic shape that is responsive to winds. To investigate the static response of the tethered system to wind pressure, we used the relationship between aerodynamic performance and the advection distance of the platform as the index. The study made a quantitative comparison of the aerodynamic performance of tethered high-altitude LTA platform systems to investigate the hull geometry. The full research project involved the following steps:
44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
1. We investigated the static behavior of the system under storm conditions to confirm the practicality of the proposed system [23]. 2. We investigated the optimal geometry of the platform and produced a design concept for the LTA vehicle geometry. To minimize the weight while achieving the necessary volume, the hull was given a membrane structure. The research clarified the technical challenges that this poses in manufacture. 3. We defined a set of missions and developed the necessary equipment: the avionics and a climber. This next step will be to define practical manufacturing methods. 4. We explored the marketing and business models that would be needed to bring the system to market. This work is as necessary as the engineering stage.
59 60 61 62 63 64 65 66
In this paper, we discuss only the first of these steps. We start by introducing the static response to the drag on the tether and the aerodynamic lift and buoyancy of the LTA vehicle. Section 2 describes each component of the system. Section 3 derives the governing equations for the static response and provides the problem definition. Section 4 reports the analytical results. We present our conclusions in Section 5.
81
2. Tethered high-altitude platform system
82
2.1. Platform configuration
83
2.1.1. Selection of hybrid-LTA hull configuration If the mooring point is set to the lower stratosphere, a spherical platform is practically enough. In this research, however, the LTA hull was designed to allow active control of the platform, efficient operation, and use in a wide range of applications. JAXA’s stratospheric platform has an axisymmetric airship shape [24–26] as shown in Fig. 1(a). In the mid-1990s, an alternative hybrid airship design concept was proposed. This is shown in Fig. 1(b). The hybrid LTA hull combines the aerodynamic lift of an HTA aircraft with the buoyancy of an LTA vehicle. Since this produces a greater upward force than an axisymmetric hull, the hybrid LTA vehicle has outstanding stability and excellent aerodynamic performance, even at low speeds. In a conventional axisymmetric design, complex ballast loading and unloading operations are needed to adjust buoyancy, but the hybrid design renders that unnecessary. However, as the hybrid LTA hull is unstable under roll, measures must be taken to ensure stability when exposed to crosswinds. A steerable platform may require thrusters and control surfaces when operated in the lower stratosphere.
85
84 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
2.1.2. Aerodynamic performance of the aerostats Fig. 2 compares the aerodynamic performance of the axisymmetric oval and hybrid aerostats. These approximate values provided the inputs to the governing equations for the static response (hull) of the system. The reference area of the LTA hull S ref was given by Eq. (1):
106 107 108 109 110 111 112
(hull)
S ref
2
= V 3.
(1)
Here, V is the volume of an LTA hull filled with buoyant gas. The LTA vehicle is assumed to have the similar operational conditions, with a Reynolds number Re 107 and a Mach number M 0.2. Both ranges are used when controlling an LTA vehicle near the ground. If we assume that the operation takes place in the lower stratosphere, the ranges should be extended as follows: 6
Re 10 , M 0.5.
(2)
The aspect ratio A R for an axisymmetric LTA hull is given by Eq. (3):
AR =
4
πFR
.
(3)
Here, F R is the aspect ratio when seen in plan and K is the induced drag, given by the following equation using the induced drag coefficient C D L :
K=
C DL C L2
.
(4)
113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
JID:AESCTE AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.3 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
3
1
67
2
68
3
69
4
70
5
71
6
72
7
73
8
74
9
75
10
76
11
77
12
78
13
79
14
80
15
Fig. 4. Coordinate system for behavioral analysis of a tethered high-altitude platform with an LTA vehicle and tether. The blue curve is the cable. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
16 17 18 19 20 21
88 89 90
First, we derive the governing equations for the static behavior of a tethered system comprising an LTA vehicle and a tether cable. The coordinate system adopted is shown in Fig. 4. The wind velocity vector w is defined in the x– y plane. w is the aerodynamic drag on the tether rope, θ [deg] is the elevation angle on the plane of the tether cable, and φ [deg] is the azimuth of the wind direction in the x– y plane, which increases counterclockwise from the x axis. The unit tangent vector for the tether cable t is given by the following equation:
25 26 27 28 29 30 31 32 33 34 35
dx
t=
36
ds
37 39 40
Fig. 3. Comparison of breaking lengths of high strength materials.
42
46 47 48 49
Fig. 2 shows that as the A R of the axisymmetric aerostat increases, K decreases. In the case of the axisymmetric aerostat, K declines linearly as C L α increases. However, the K of the hybrid aerostats is not on the extended line, and the C L α of the hybrid aerostats instead rises abruptly. It can be seen from Fig. 2 that the hybrid aerostat has a greater aerodynamic lifting capacity than the axisymmetric design.
50 51
2.2. Tether strength
54 55 56 57 58 59 60 61 62 63 64 65 66
dy ds
j+
dz ds
A key challenge is to ensure that the tether has sufficient strength. We next investigated candidate materials. Fig. 3 shows example materials with specific strength data. The figure shows the breaking length, calculated by dividing the specific strength by the gravitational acceleration. This gives the maximum length of a tether that can support its own weight. We assumed the cross-section of the tether to be fixed. As the chemical composition of each material can be varied, the breaking length falls within a range. Since all the breaking lengths shown in Fig. 3 would allow lower-stratospheric altitudes, to be achieved, all five materials could be used to tether a vehicle at an altitude of 10 [km] to 20 [km]. In the upcoming selection, we will decide other material properties: weight, cost, surface roughness, and ease of manufacture.
d y = ds cos θ sin φ,
(6b)
dz = ds sin θ.
(6c)
t = cos θ cos φ i + cos θ sin φ j + sin θ k.
= D w xy sin θ cos θ − W sin θ, ds
97 98 99 100 102 104 105 106 107 108 110
113 114 115 116 117 118 120 121
⎡
D w xy cos θ − W
⎤
⎥ ⎢ D w xy sin θ + W cot θ ⎥ ⎢ θ ⎢ ⎥ − ⎥ ⎢ d ⎢ ⎥ ⎥. T ⎢x⎥=⎢ ⎥ ⎢ dz ⎣ ⎦ ⎢ cot θ cos φ ⎥ y ⎦ ⎣ cot θ sin φ s
96
119
(8b)
Here, D w xy [N/km] is the aerodynamic drag created by the wind per unit length of cable in the x– y plane, and W [N/km] is the specific weight per unit length. When combined with Eqs. (6) and (8), the governing equations are therefore as follows:
T
95
112
(7)
(8a)
= D w xy sin2 θ + W cos θ.
⎡ ⎤
94
111
The tension on the tether T [N] can be expressed by θ [deg] as follows:
dθ
93
109
As a result, t can be expressed as follows:
−T
92
103
(6a)
dT
91
101
(5)
k.
dx = ds cos θ cos φ,
ds
52 53
i+
Here, ds represents an infinitesimal length of cable, allowing the following equations to be obtained geometrically:
38
45
84
87
24
44
83
86
3. The static response of the system 3.1. Derivation of the governing equations
23
43
82
85
Fig. 2. Aerodynamic characteristics of the axisymmetric and hybrid airships [24–26, 21,22].
22
41
81
csc θ
122 123 124 125 126 127 128
(9)
129 130 131 132
JID:AESCTE
AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.4 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
4
1
67
2
68
3
69
4
70
5
71
6
72
7
73
8
74
9
75
10
76
11
77
12
78
13
79
14
80
15
81
16
82
17
83
18
84
19
85
20
86
21
87
22 23 24 25
88
Fig. 5. Wind data used in the analysis. (a) Instantaneous wind speed and direction under storm conditions. The plot is based on data from the Meteorological Agency of Japan. The black curve is the B-spline, approximated data. (b) Mapping of the data onto a two-dimensional plane. Length represents wind speed. North is at 90 [deg]. Altitude is given by color.
26 27
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
(tether)
D w xy = C d
w is derived as
2
.
(10)
(tether)
of the altitude z [m]. S ref [m2 ] is the reference area of the cable. The initial condition at the point connecting the tether with the LTA hull is needed to solve the differential equations for T and θ in Eq. (9). By defining T and θ at the upper end of the tether cable as T 0 and θ0 respectively, the initial condition can be determined geometrically as follows:
T 0 = ( L + B )2 + D 2 , L+B tan θ0 = . D
(11a) (11b)
Here, L, B, and D are the aerodynamic lift, the buoyancy, and the aerodynamic drag of the LTA hull, respectively. Below, we demonstrate that the optional wind vector becomes a unit vector when any vector of the tether in the x– y plane is supplied in the above governing equations. For an arbitrary wind vector w in the x– y plane, w has two components in the x and y directions (Eq. (12)).
w = w cos φ i + w sin φ j .
(12)
The normal and tangent vectors of a wind are respectively defined as w ⊥ and w . Since the wind direction is φ [deg], w ⊥ is given as follows:
w ⊥ = (t × w ) × t
= w − t(w · t)
(13)
= w sin2 θ cos φ i + w sin2 θ sin φ j − w sin θ cos θ k.
63
66
(tether)
Here, is the aerodynamic drag coefficient of the cable. In cross-section, the tether is assumed to be a circle of diameter 50 [mm] and can be treated as a two-dimensional cylinder. Both the wind speed w ( z) and air density ρair ( z) [kg/m3 ] are functions
62
65
1
· ρair ( z) w 2 ( z) · S ref
(tether) Cd
61
64
90 91 92
D w xy is defined as
28 29
89
94
w = t(w · t) 2
2
= w cos θ cos φ i + w cos θ sin φ j + w sin θ cos θ k.
(14)
(15)
(16a)
|| w || = w cos θ,
(16b)
so w ⊥ is the unit normal vector and w is the unit tangent vector. Thus, w is a unit vector of the governing equations.
100 101 102 103 104 106
The static response generally depends on the input wind data. To simplify the comparison, the wind under storm conditions was held constant, as shown in Fig. 5. Next, we give the computational assumptions made for the (tether)
cable. C d was set to 1.5, based on the maximum drag coefficient around a two-dimensional cylinder under Re values from 105 to 107 . By spline interpolation and based on wind data supplied by the Meteorological Agency of Japan, we generated a wind dataset for w ( z). Since the diameter of the tether was assumed to (tether) be 50 [mm], S ref was 50 [m2 ]. The specific weight of the tether cable was set to 3 × 103 [kg/km]. The following parameters were assumed for the LTA vehicle. The drag coefficient of the vehicle was set to 0.06 [21]. A buoyancy of 160 [t] was assumed, based on the volume of the hull and the use of gaseous hydrogen (H2 (g)) as the LTA gas. H2 (g) was selected as it provides maximum buoyancy. It is not commonly used in LTA aircraft because of its flammability. However, we assume that the use of appropriate materials in the gas bearing hull can reduce the risk to acceptable levels because safety is ensured unless sparks are emitted. Given the above, B can be derived from the difference between the density of air ρair , the density of H2 (g) ρH2 , and the volume of the gas envelope V :
is then given by Eq. (18), based on Eq. (1):
99
105
3.2. Computational parameters
(hull)
96 98
|| w ⊥ || = w sin θ,
S ref
95 97
Finally,
B = V (ρair ( z) − ρH2 ( z)),
As
w = w ⊥ + w ,
93
(17)
107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
JID:AESCTE AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.5 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
1 2
(hull)
S ref
=
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
2
B
67
3
ρair (z) − ρH2 (z)
The aerodynamic drag of when the ratio between spheroid is approximately axis is approximately 40 mately 1.4 × 106 [m3 ].
5
.
(18)
68 69
an axisymmetric LTA hull is minimized the major and the minor axes of the 3.9:1 [27]. Since in this design the minor [m], when B is 160 [T], V is approxi-
70 71 72 73 74 75
3.3. Problem definition
76 77
To confirm the stability of a tethered high-altitude platform system under the influence of strong winds, we analyzed the advection distance of the platform dadv . The tether was assumed to be of unrestricted length, and the platform to be at a constant altitude of 20 [km]. dadv was therefore defined by the distance in the x– y plane from the point at which the tether was attached to the ground surface. This provided the origin (0, 0, 0) of the node to the platform (x0 , y 0 , 20 [km]), as follows:
dadv
x20
+
y 20 .
78 79 80 81 82 83 84 85 86
(19)
The length of the tether and the path taken are important elements of the system design. However, in this study, we assumed the length to be the distance of the platform from the nodal point on the ground when no force was applied to the tether at the origin. If the tether is in contact with the ground at all points except the origin, that is, if the platform is unable to lift the tether by L and B, the system will not be functional. We considered the following three relationships:
87 88 89
Fig. 6. Comparison of static behavior of the systems with different geometries. Thin lines show the results for the axisymmetric geometry (L = 0), and thick lines show those for the hybrid geometry (L = B). Red shows the behavior of the tether in three-dimensional space. The x– y, x–z, and y–z planes are shown in green, blue, and cyan. The origin is the point at which the tether connects to the ground. (For interpretation of the colors in this figure, the reader is referred to the web version of this article.)
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
90 91 92 93 94 95 96
(tether)
1. The sensitivity of the static response to L when B and C d are held constant at 160 [T] and 1.5 [–], respectively. (tether) 2. The sensitivity of the static response to B when L and C d are held constant at 0 [T] and 1.5 [–], respectively. (tether) when L and B 3. The sensitivity of the static response to C d are both set to 160 [T]. 4. Results and discussion 4.1. Sensitivity of the aerodynamic lift on the LTA hull Fig. 6 shows the system behavior when L = 0 (axisymmetric geometry) and L = B (hybrid geometry). Even when the hull had no lift L under storm conditions, dadv was approximately 8 [km]. As can be seen from Fig. 6, the L generated by the hybrid geometry reduced dadv . Fig. 7 shows the effect of varying L on the static behavior of the system. The effect of the tether tension T is shown in Fig. 7(a) and appeared to be linear with T . However, nonlinearities appeared when the change in lift L and tension T varied from their initial settings. From Eq. (11a), T showed a small but significant nonlinear relationship with L. T reached a minimum at an altitude of 0 [km], then rose in line with altitude, at a rate depending on the wind speed. As a result, the highest tension occurred at the point where the tether connected with the platform. This suggested that special attention must be paid to the connectors between the hull and the tether. Fig. 7(b) shows the nonlinearity of the change in θ . Equation (11b) introduces a nonlinearity between L and θ . When projected onto the x– y plane, the tether also became nonlinear, as shown in Fig. 7(c). This is expected from the nonlinearity appearing in T and θ . Furthermore, as L increased, dadv decreased. The effect of shortening dadv was more pronounced in the case of the hybrid hull than the axisymmetric one, suggesting that the hybrid hull is a promising design for a platform of this type.
4.2. Sensitivity of the buoyancy on the LTA hull
97 98
Next, we analyzed the axisymmetric LTA vehicle without taking account of L to isolate the effect of B on the static behavior of the system. The results shown by the black lines in Fig. 8 are the same as those in Fig. 7. As B changed, the volume of the LTA hull V also changed, which in turn affected D. Fig. 8 shows the sensitivity of B to the static response of the system. When B was set to 40 [T], part of the tether cable dragged on the ground. This was deemed to be a system failure, and the result is not shown. Fig. 8(a) shows the behavior of T as B was changed. When B decreased, T also decreased. Since V responded to the change in (hull) B, the change in hull size caused S ref to vary. The change in T
99
also declined, so that was nonlinear with B. As B declined, S ref ∂ T /∂ z (representing the gradient of T for altitude z) decreased close to the hull. This confirmed that, as B declined, the distribution of T was related to the wind speed shown in Fig. 5(a). Fig. 8(b) describes the effect on θ of varying B. Since the tether itself was assigned a weight of 40 [T], when B = 40 [T], the tether rope became slack close to the ground. When B was increased to 80 [T], the system was marginally able to lift the tether. This determined the minimum volume of the platform. The projection of the tether onto the x– y plane is shown as Fig. 8(c). Reducing B introduced an abrupt nonlinear rise in dadv . Clearly, B must be sufficient to lift at least the weight of the whole system. Since there is a tradeoff between T and dadv , the optimal compromise between maximizing T and the size of the LTA platform must be established at an early stage in the design.
110
(hull)
100 101 102 103 104 105 106 107 108 109 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
4.3. Sensitivity of the aerodynamic drag on the tether rope
127 128
In this study, we did not examine the influence of aerodynamic drag on the hull on the static response of the system. Assuming a constant B, the same wetted area is set with the same degree of V regardless of the geometry of the LTA platform. The
129 130 131 132
JID:AESCTE
AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.6 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
6
1
67
2
68
3
69
4
70
5
71
6
72
7
73
8
74
9
75
10
76
11
77
12
78
13
79
14
80
15 16 17 18
81
Fig. 7. Influence on the static response by L variation of the LTA hull. (a) Tension T of the tether cable vs. altitude. (b) Elevation angle of the tether rope θ vs. altitude. (c) The tether cable silhouette projected onto the ground (x– y plane). The origin is the connecting point of the tether cable to the ground. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
82 83 84
19
85
20
86
21
87
22
88
23
89
24
90
25
91
26
92
27
93
28
94
29
95
30
96
31
97
32
98
33
99
34 35 36
100
Fig. 8. Influence on the static response due to B variation of the LTA vehicle. (a) Tension T of the tether rope vs. altitude. (b) Elevation angle of the tether cable θ vs. altitudes. (c) The tether rope silhouettes projected onto the ground.
101 102
37
103
38
104
39
105
40
106
41
107
42
108
43
109
44
110
45
111
46
112
47
113
48
114
49
115
50
116
51
117
52
(tether) Cd
118
53
Fig. 9. Influence on the static response of
variation on the tether cable. (a) Tension of the tether rope T vs. altitude. (b) Elevation angle of the tether cable θ vs.
54
altitude. (c) The tether rope silhouettes projected onto the ground. Note that C d in the legend denotes C d
(tether)
in the text.
55 56 57 58 59 60 61 62 63 64 65 66
axisymmetric and hybrid geometries will therefore exhibit similar aerodynamic drag characteristics. By contrast, since the tether has a length of at least 20 [km], it is important to investigate the (tether)
influence of C d
. (tether)
to the static behavior of Fig. 9 shows the sensitivity of C d the system. Since the L was set equal to B, the result in Fig. 7 is identical to that when same cyan color. Since
(tether) Cd = 1.5, and they are (tether) Cd can fall in a range
shown in the from 10−2 to (tether)
100 , the four values of 1.5, 1.0, 0.1, and 0.01 are shown. A C d of 0.01 is close to the C d of the airfoil of an HTA aircraft. Fig. 9
120 (tether)
shows the strong effect that C d
121
has on the static behavior of (tether)
the system when the tether is long. As C d increased, the sensitivity to T , θ , and dadv increased. By contrast, the influence of (tether) Cd
on the static response of the system decreased markedly when the value was set low. (tether) Fig. 9(a) shows the effect of C d on T . T was little affected (tether)
119
(tether)
by the wind when C d was small, but increased as C d increased. As with the wind speed shown in Fig. 5(a), the distribution of T was nonlinear. But the distribution of T can be regarded as almost linear. The gradient of the line depended on
122 123 124 125 126 127 128 129 130 131 132
JID:AESCTE AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.7 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
1
the initial conditions of the governing equations. Fig. 9(a) shows
2
that the distribution of T was almost the same when C d was set at 0.1 and 0.01. As the cross-sectional shape of the tether ca-
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
(tether) Cd
is of the order of 10−1 , it
ble largely determines T when is not necessary to consider the surface roughness or accuracy of the cross-section of the cable. (tether) on θ . As can be seen, Fig. 9(b) shows the influence of C d (tether) Cd
the trend was similar to that for T . When increased, the distribution of θ became increasingly nonlinear. As with T , the gradient of θ depended on the initial conditions set for Eq. (11b). (tether)
At C d values of 0.01 and 0.1, the difference in θ was less than 1 [deg], suggesting that it is unnecessary to strictly mini(tether)
mize C d
. (tether) Cd
to dadv . These results Fig. 9(c) shows the sensitivity of confirmed those reported in Figs. 9(a) and (b). To minimize the effect of wind on the system, the cross-section of the tether ca(tether) Cd
ble must be carefully designed. Taking cost into account, should be of the order of 10−1 . The material of the tether should be flexible, and the cross-section should ideally resemble that of the airfoil of an HTA aircraft. However, unlike in HTA aircraft design, it is not necessary to have an order of one count (representing a C d of 0.0001). A design that maintains an order of 10−1 (1000 counts) is sufficient. 5. Conclusions
28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62
We have quantitatively investigated the influence of the aerodynamics of a tethered lighter-than-air system on the static response. The goal was to investigate the practicality of a high-altitude platform comprising a lighter-than-air vehicle and a tether cable. We considered conventional axisymmetric and hybrid hull geometries. The results showed that, even when the platform was axisymmetric, the advection distance of the platform under storm conditions was of the order of 10−1 [km]. The advection distance could be shortened nonlinearly by having the hybrid vehicle generate aerodynamic lift. The study quantitatively demonstrated the aerodynamic sensitivity of the lighterthan-air hull and the tether to the static behavior of the system.
• As the aerodynamic lift was increased, the tension on the tether cable increased nonlinearly, whereas the advection distance decreased also nonlinearly. The tension on the tether also declined nonlinearly. The advection distance reflected the tension on the cable. • As the buoyancy of the hull was reduced, the advection distance increased significantly. The volume of the hull is determined by the buoyancy required. The upper limit of the buoyancy is given by the allowable cable tension, and the lower limit by the allowable advection distance, which reflects the environment into which the system is to be inserted. • To minimize the advection distance, it is necessary to reduce the aerodynamic drag of the tether. The design target aerodynamic drag coefficient of the cross-section of the tether is enough to be of the order of 10−1 . In further research, we will investigate the optimal sizing of a lighter-than-air platform.
63 64
Conflict of interest statement
65 66
Acknowledgement
(tether)
26 27
7
There is no conflict of interest.
67 68
Part of this study was supported by Grant-in-Aid for Scientific Research (C) 16K00295, Japan Society for the Promotion of Science as well as the Collaborative Research Project (J15010, J16007, and J17L050) of the Institute of Fluid Science, Tohoku University, Japan.
69 70 71 72 73
References
74 75
[1] W.R. Corliss, NASA Sounding Rockets, 1958–1968 – a Historical Summary, NASA SP-4401, 1971. [2] N. Sarigul-Klijn, M. Sarigul-Klijn, C. Noel, Air-launching earth to orbit: effects of launch conditions and vehicle aerodynamics, J. Spacecr. Rockets 42 (3) (2005) 569–575. [3] I.R. McNab, A research program to study airborne launch to space, IEEE Trans. Magn. 43 (1) (2007) 486–490. [4] C. Yang, J.H. Everitt, Q. Du, B. Luo, J. Chanussot, Using high-resolution airborne and satellite imagery to assess crop growth and yield variability for precision agriculture, Proc. IEEE 101 (3) (2013) 582–592. [5] D.E. Bar, K. Wolowelsky, Y.S.Z. Figov, A. Michaeli, Y. Vaynzof, Y. Abramovitz, A. Ben-Dov, O. Yaron, L. Weizman, R. Adar, Target detection and verification via airborne hyperspectral and high-resolution imagery processing and fusion, IEEE Sens. J. 10 (3) (2010) 707–711. [6] F. Werner, M. Wendisch, H. Siebert, T. Schmeissner, P. Pilewskie, R.A. Shaw, New airborne retrieval approach for trade wind cumulus properties under overlying cirrus, J. Geophys. Res., Atmos. 118 (16) (2013) 3634–3649. [7] J.E. Garabedian, R.J. McGaughey, S.E. Reutebuch, B.R. Parresol, J.C. Kilgo, C.E. Moorman, M.N. Peterson, Quantitative analysis of woodpecker habitat using high-resolution airborne lidar estimates of forest structure and composition, Remote Sens. Environ. 145 (6) (2014) 68–80. [8] M. Kong, O. Yorkinov, S. Shimamoto, TCP/IP performance evaluations based on elevation angles for mobile communications employing stratospheric platform, IEICE Trans. Commun. 92 (11) (2009) 3335–3344. [9] R.S. Pant, N. Komerath, A. Kar, Application of lighter-than-air platforms for power beaming, generation and communications, in: Proceedings on International Symposium on Electronic System Design, 2011. [10] J.D. DeLaurier, A stability analysis for tethered aerodynamically shaped balloons, J. Aircr. 9 (9) (1972) 646–651. [11] L.T. Redd, R.M.B. Bland, R.M. Bennett, Stability Analysis and Trend Study of a Balloon Tethered in a Wind; with Experimental Comparisons, NASA TN D-7272, 1973. [12] G.S. Aglietti, Dynamic response of a high-altitude tethered balloon system, J. Aircr. 46 (6) (2009) 2032–2040. [13] A. Rajani, R.S. Pant, K. Sudhakar, Dynamic stability analysis of a tethered aerostat, J. Aircr. 47 (5) (2010) 1531–1538. [14] S.P. Jones, J.A. Krausman, Nonlinear dynamic simulation of a tethered aerostat, J. Aircr. 19 (8) (1982) 679–686. [15] J. Krausman, D. Miller, The 12M™ Tethered Aerostat System: Rapid Tactical Deployment for Surveillance Missions, AIAA Paper 2015-3351, 2015. [16] R.S. Pant, Methodology for determination of baseline specifications of a nonrigid airship, J. Aircr. 45 (6) (2008) 2177–2182. [17] C.V. Ram, R.S. Pant, Multidisciplinary shape optimization of aerostat envelopes, J. Aircr. 47 (3) (2010) 1073–1076. [18] S.R. Mistr, R.S. Pant, Design and fabrication of a quick dismantlable remotely controlled semirigid finless airship, in: Innovative Design and Development Practices in Aerospace and Automotive Engineering, in: Lecture Notes in Mechanical Engineering, 2017. [19] N. Deodhar, A. Bafandeh, J. Deese, B. Smith, T. Muyimbwa, C. Vermillion, P. Tkacik, Laboratory-scale flight characterization of a multitethered aerostat for wind energy generation, AIAA J. 55 (2017), http://dx.doi.org/10.2514/1.J054407. [20] S.S. Badesha, SPARCL: a high-altitude tethered balloon-based optical spaceto-ground communication system, Proc. SPIE Int. Soc. Opt. Eng. 4821 (2002) 181–193, http://dx.doi.org/10.1117/12.450641. [21] G.E. Carichner, L.M. Nicolai, Fundamentals of Aircraft and Airship Design, vol. 2 – Airship Design and Case Studies, AIAA, Reston, VA, 2013. [22] L.M. Nicolai, G.E. Carichner, Airplanes and Airships Evolutionary Cousins, AIAA Paper 2012-1178, 2012. [23] K. Chiba, S. Satori, R. Mitsuhashi, J. Sasaki, R. Akiba, Motion Analysis of Captive Platform System Constructed from Airship and Tether, in: 53rd AIAA Aerospace Science Meeting, 2015, 2015, AIAA Paper 2015-0713. [24] I.H. Abbott, Airship Model Tests in the Variable Density Wind Tunnel, NACA TR-394, 1931. [25] H.B. Freeman, Force Measurements on a 1/40 Scale Model of the U.S. Airship Akron, NACA TR-432, 1933. [26] S.A. Ross, H.R. Liebert, LTA Aerodynamics Handbook, Goodyear Aircraft Corp., Akron, OH, 1954. [27] J.S. Parsons, R.E. Goodson, F.R. Goldschmied, Shaping of axisymmetric bodies for minimum drag in incompressible flow, J. Hydronaut. 8 (3) (1974) 100–107.
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
[m5G; v1.221; Prn:29/08/2017; 8:45] P.1 (1-7)
Aerospace Science and Technology ••• (••••) •••–•••
1
67
Contents lists available at ScienceDirect
2
68
3
69
Aerospace Science and Technology
4
70
5
71
6
72
www.elsevier.com/locate/aescte
7
73
8
74
9
75
10
76
11 12 13
77
Aerodynamic influences on a tethered high-altitude lighter-than-air platform system to its behavior
78 79
14 15 16 17 18 19 20
80
Kazuhisa Chiba
a,∗
a
b
c
, Ryosuke Nishikawa , Masahiko Onda , Shin Satori , Ryojiro Akiba
d
a
84 85 86 87
a r t i c l e
i n f o
88
a b s t r a c t
23 24 25 26 27 28 29 30 31 32 33
82 83
The University of Electro-Communications, Tokyo 182-8585, Japan b Sky Platform Technologies Co. Ltd., Tochigi 320-0855, Japan c Hokkaido University of Science, Sapporo 006-8585, Japan d Hokkaido Aerospace Science and Technology Incubation Center, Sapporo 001-0010, Japan
21 22
81
89
Article history: Received 17 February 2017 Received in revised form 21 August 2017 Accepted 21 August 2017 Available online xxxx Keywords: Tethered platform system Lighter-than-air hull Rockoon system High altitude Aerodynamics
34
The goal of this study was to investigate the influence of aerodynamic factors on the static behavior of a tethered high-altitude lighter-than-air platform. The system design comprised a lighter-than-air vehicle and a tether cable, and the conceptual platform configuration of such a system is studied herein. Governing equations were derived to model the static behavior of the system, and the effects of aerodynamic lift and buoyancy were parametrically analyzed based on the advection distance of the platform under storm conditions. The aerodynamic lift and buoyancy of the hull were shown to have nonlinear effects. We further analyzed the influence of the aerodynamic drag created by the tether. Since this was shown to have a significant influence, we concluded that the cable should ideally have a crosssectional shape resembling the airfoil of a heavier-than-air aircraft. However, it is sufficient to ensure that the drag coefficient is of the order of 10−1 . © 2017 Elsevier Masson SAS. All rights reserved.
90 91 92 93 94 95 96 97 98 99 100
35
101
36
102
37
103
38
104
39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
1. Introduction A firm lighter-than-air (LTA) vehicle for use in the lower stratosphere would provide a platform for a wide range of space activities. In the early 2000s, Japan Aerospace Exploration Agency (JAXA) conducted R&D on a free-flying LTA stratospheric platform. This was aborted because appropriate propulsion units with sufficient thrust were not available, and the high-altitude performance was inadequate. However, the potential merits of such a platform remain. A stratospheric platform would be the ideal launchpad for rocket-powered space transportation systems. An alternative approach is the tethered high-altitude platform, comprising an LTA vehicle1 and a tether cable. This is similar to the rockoon systems [1] that were successfully used for space observation in the 1950s and 60s. Stratospheric platforms could replace rockoon systems as highfrequency, high-load capacity space launch facilities. Fixed wing heavier-than-air (HTA) aircrafts have been tested [2,3], in which
58 59 60 61 62 63 64 65 66
*
Corresponding author. E-mail address: [email protected] (K. Chiba). 1 As general definitions, LTA vehicle (or LTA hull) refers to an unpowered aircraft, airship shows a powered one, and aerostat (or LTA aircraft) includes both. The terms are used accordingly. http://dx.doi.org/10.1016/j.ast.2017.08.029 1270-9638/© 2017 Elsevier Masson SAS. All rights reserved.
the rocket is released in the lower stratosphere. Current aircrafts have an upper payload weight limit of approximately 100 [t], but launch velocities near the speed of sound can be achieved in the lower stratosphere. However, rocket installation on and separation from HTA aircraft remains technically challenging. As rockoon systems have been successfully deployed in the past, the moored LTA platform is a promising alternative to HTA aircraft launch systems. A tethered lower-stratospheric platform might also find applications in fields such as agriculture [4], defense [5], meteorology [6], environmental science [7], and telecommunications [8,9]. This type of platform offers a useful bridge between space and ground, as the influence of cloud cover can be ignored even at altitudes above 10 [km]. Such a system would have the following advantages:
• No thrust is required to maintain the altitude of the platform (thus, the system uses an LTA vehicle instead of an airship); no maintenance on the ground is also required. • The tethered platform can hold the mooring position within the length of the rope.
105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
The tether cable can be used to transmit electricity, and replenish the buoyancy gas. A cargo carrier called “a climber” can ascend and descend the cable, supplying payloads.
127 128 129 130 131 132
JID:AESCTE
2
AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.2 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
1
67
2
68
3
69
4
70
5
71
6
72
7
73
8
74
9
75
10
76
11
77
12 13
78
Fig. 1. Typical geometries of (a) axisymmetric [24] and (b) hybrid [22] airships.
79
14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
80
Mooring is based on the aerostat principle, which has been extensively researched since the 1970s [10–13]. Recent research efforts have addressed both practical low altitude applications by replacing balloons with weathervaning aerostats, and research into mooring of balloons at high altitudes. The TCOM Corporation continues to conduct research on the first of these [14,15]. Advanced research is being carried out on the design of aerostats with novel conformations [16–18]. Attempts are being made to develop an airborne wind energy turbine system [19]. The altitude that can be achieved by tethered systems is limited by the weight of the tether, and this must be addressed if high-altitude systems are to be realized. Mooring at an altitude of 20 [km] has been reported [20], making lower stratospheric LTA platforms a practical proposition. In addition, hybrid aerostats have been developed [21,22] that take advantage of both buoyancy and aerodynamic lift. These are expected to replace conventional balloons in high-altitude applications. The goal of the current study was to develop a high-altitude LTA platform. Our design is for an LTA vehicle geometry for lower stratospheric use. The body has a membrane structure, offering a flexible aerodynamic shape that is responsive to winds. To investigate the static response of the tethered system to wind pressure, we used the relationship between aerodynamic performance and the advection distance of the platform as the index. The study made a quantitative comparison of the aerodynamic performance of tethered high-altitude LTA platform systems to investigate the hull geometry. The full research project involved the following steps:
44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
1. We investigated the static behavior of the system under storm conditions to confirm the practicality of the proposed system [23]. 2. We investigated the optimal geometry of the platform and produced a design concept for the LTA vehicle geometry. To minimize the weight while achieving the necessary volume, the hull was given a membrane structure. The research clarified the technical challenges that this poses in manufacture. 3. We defined a set of missions and developed the necessary equipment: the avionics and a climber. This next step will be to define practical manufacturing methods. 4. We explored the marketing and business models that would be needed to bring the system to market. This work is as necessary as the engineering stage.
59 60 61 62 63 64 65 66
In this paper, we discuss only the first of these steps. We start by introducing the static response to the drag on the tether and the aerodynamic lift and buoyancy of the LTA vehicle. Section 2 describes each component of the system. Section 3 derives the governing equations for the static response and provides the problem definition. Section 4 reports the analytical results. We present our conclusions in Section 5.
81
2. Tethered high-altitude platform system
82
2.1. Platform configuration
83
2.1.1. Selection of hybrid-LTA hull configuration If the mooring point is set to the lower stratosphere, a spherical platform is practically enough. In this research, however, the LTA hull was designed to allow active control of the platform, efficient operation, and use in a wide range of applications. JAXA’s stratospheric platform has an axisymmetric airship shape [24–26] as shown in Fig. 1(a). In the mid-1990s, an alternative hybrid airship design concept was proposed. This is shown in Fig. 1(b). The hybrid LTA hull combines the aerodynamic lift of an HTA aircraft with the buoyancy of an LTA vehicle. Since this produces a greater upward force than an axisymmetric hull, the hybrid LTA vehicle has outstanding stability and excellent aerodynamic performance, even at low speeds. In a conventional axisymmetric design, complex ballast loading and unloading operations are needed to adjust buoyancy, but the hybrid design renders that unnecessary. However, as the hybrid LTA hull is unstable under roll, measures must be taken to ensure stability when exposed to crosswinds. A steerable platform may require thrusters and control surfaces when operated in the lower stratosphere.
85
84 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
2.1.2. Aerodynamic performance of the aerostats Fig. 2 compares the aerodynamic performance of the axisymmetric oval and hybrid aerostats. These approximate values provided the inputs to the governing equations for the static response (hull) of the system. The reference area of the LTA hull S ref was given by Eq. (1):
106 107 108 109 110 111 112
(hull)
S ref
2
= V 3.
(1)
Here, V is the volume of an LTA hull filled with buoyant gas. The LTA vehicle is assumed to have the similar operational conditions, with a Reynolds number Re 107 and a Mach number M 0.2. Both ranges are used when controlling an LTA vehicle near the ground. If we assume that the operation takes place in the lower stratosphere, the ranges should be extended as follows: 6
Re 10 , M 0.5.
(2)
The aspect ratio A R for an axisymmetric LTA hull is given by Eq. (3):
AR =
4
πFR
.
(3)
Here, F R is the aspect ratio when seen in plan and K is the induced drag, given by the following equation using the induced drag coefficient C D L :
K=
C DL C L2
.
(4)
113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
JID:AESCTE AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.3 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
3
1
67
2
68
3
69
4
70
5
71
6
72
7
73
8
74
9
75
10
76
11
77
12
78
13
79
14
80
15
Fig. 4. Coordinate system for behavioral analysis of a tethered high-altitude platform with an LTA vehicle and tether. The blue curve is the cable. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
16 17 18 19 20 21
88 89 90
First, we derive the governing equations for the static behavior of a tethered system comprising an LTA vehicle and a tether cable. The coordinate system adopted is shown in Fig. 4. The wind velocity vector w is defined in the x– y plane. w is the aerodynamic drag on the tether rope, θ [deg] is the elevation angle on the plane of the tether cable, and φ [deg] is the azimuth of the wind direction in the x– y plane, which increases counterclockwise from the x axis. The unit tangent vector for the tether cable t is given by the following equation:
25 26 27 28 29 30 31 32 33 34 35
dx
t=
36
ds
37 39 40
Fig. 3. Comparison of breaking lengths of high strength materials.
42
46 47 48 49
Fig. 2 shows that as the A R of the axisymmetric aerostat increases, K decreases. In the case of the axisymmetric aerostat, K declines linearly as C L α increases. However, the K of the hybrid aerostats is not on the extended line, and the C L α of the hybrid aerostats instead rises abruptly. It can be seen from Fig. 2 that the hybrid aerostat has a greater aerodynamic lifting capacity than the axisymmetric design.
50 51
2.2. Tether strength
54 55 56 57 58 59 60 61 62 63 64 65 66
dy ds
j+
dz ds
A key challenge is to ensure that the tether has sufficient strength. We next investigated candidate materials. Fig. 3 shows example materials with specific strength data. The figure shows the breaking length, calculated by dividing the specific strength by the gravitational acceleration. This gives the maximum length of a tether that can support its own weight. We assumed the cross-section of the tether to be fixed. As the chemical composition of each material can be varied, the breaking length falls within a range. Since all the breaking lengths shown in Fig. 3 would allow lower-stratospheric altitudes, to be achieved, all five materials could be used to tether a vehicle at an altitude of 10 [km] to 20 [km]. In the upcoming selection, we will decide other material properties: weight, cost, surface roughness, and ease of manufacture.
d y = ds cos θ sin φ,
(6b)
dz = ds sin θ.
(6c)
t = cos θ cos φ i + cos θ sin φ j + sin θ k.
= D w xy sin θ cos θ − W sin θ, ds
97 98 99 100 102 104 105 106 107 108 110
113 114 115 116 117 118 120 121
⎡
D w xy cos θ − W
⎤
⎥ ⎢ D w xy sin θ + W cot θ ⎥ ⎢ θ ⎢ ⎥ − ⎥ ⎢ d ⎢ ⎥ ⎥. T ⎢x⎥=⎢ ⎥ ⎢ dz ⎣ ⎦ ⎢ cot θ cos φ ⎥ y ⎦ ⎣ cot θ sin φ s
96
119
(8b)
Here, D w xy [N/km] is the aerodynamic drag created by the wind per unit length of cable in the x– y plane, and W [N/km] is the specific weight per unit length. When combined with Eqs. (6) and (8), the governing equations are therefore as follows:
T
95
112
(7)
(8a)
= D w xy sin2 θ + W cos θ.
⎡ ⎤
94
111
The tension on the tether T [N] can be expressed by θ [deg] as follows:
dθ
93
109
As a result, t can be expressed as follows:
−T
92
103
(6a)
dT
91
101
(5)
k.
dx = ds cos θ cos φ,
ds
52 53
i+
Here, ds represents an infinitesimal length of cable, allowing the following equations to be obtained geometrically:
38
45
84
87
24
44
83
86
3. The static response of the system 3.1. Derivation of the governing equations
23
43
82
85
Fig. 2. Aerodynamic characteristics of the axisymmetric and hybrid airships [24–26, 21,22].
22
41
81
csc θ
122 123 124 125 126 127 128
(9)
129 130 131 132
JID:AESCTE
AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.4 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
4
1
67
2
68
3
69
4
70
5
71
6
72
7
73
8
74
9
75
10
76
11
77
12
78
13
79
14
80
15
81
16
82
17
83
18
84
19
85
20
86
21
87
22 23 24 25
88
Fig. 5. Wind data used in the analysis. (a) Instantaneous wind speed and direction under storm conditions. The plot is based on data from the Meteorological Agency of Japan. The black curve is the B-spline, approximated data. (b) Mapping of the data onto a two-dimensional plane. Length represents wind speed. North is at 90 [deg]. Altitude is given by color.
26 27
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
(tether)
D w xy = C d
w is derived as
2
.
(10)
(tether)
of the altitude z [m]. S ref [m2 ] is the reference area of the cable. The initial condition at the point connecting the tether with the LTA hull is needed to solve the differential equations for T and θ in Eq. (9). By defining T and θ at the upper end of the tether cable as T 0 and θ0 respectively, the initial condition can be determined geometrically as follows:
T 0 = ( L + B )2 + D 2 , L+B tan θ0 = . D
(11a) (11b)
Here, L, B, and D are the aerodynamic lift, the buoyancy, and the aerodynamic drag of the LTA hull, respectively. Below, we demonstrate that the optional wind vector becomes a unit vector when any vector of the tether in the x– y plane is supplied in the above governing equations. For an arbitrary wind vector w in the x– y plane, w has two components in the x and y directions (Eq. (12)).
w = w cos φ i + w sin φ j .
(12)
The normal and tangent vectors of a wind are respectively defined as w ⊥ and w . Since the wind direction is φ [deg], w ⊥ is given as follows:
w ⊥ = (t × w ) × t
= w − t(w · t)
(13)
= w sin2 θ cos φ i + w sin2 θ sin φ j − w sin θ cos θ k.
63
66
(tether)
Here, is the aerodynamic drag coefficient of the cable. In cross-section, the tether is assumed to be a circle of diameter 50 [mm] and can be treated as a two-dimensional cylinder. Both the wind speed w ( z) and air density ρair ( z) [kg/m3 ] are functions
62
65
1
· ρair ( z) w 2 ( z) · S ref
(tether) Cd
61
64
90 91 92
D w xy is defined as
28 29
89
94
w = t(w · t) 2
2
= w cos θ cos φ i + w cos θ sin φ j + w sin θ cos θ k.
(14)
(15)
(16a)
|| w || = w cos θ,
(16b)
so w ⊥ is the unit normal vector and w is the unit tangent vector. Thus, w is a unit vector of the governing equations.
100 101 102 103 104 106
The static response generally depends on the input wind data. To simplify the comparison, the wind under storm conditions was held constant, as shown in Fig. 5. Next, we give the computational assumptions made for the (tether)
cable. C d was set to 1.5, based on the maximum drag coefficient around a two-dimensional cylinder under Re values from 105 to 107 . By spline interpolation and based on wind data supplied by the Meteorological Agency of Japan, we generated a wind dataset for w ( z). Since the diameter of the tether was assumed to (tether) be 50 [mm], S ref was 50 [m2 ]. The specific weight of the tether cable was set to 3 × 103 [kg/km]. The following parameters were assumed for the LTA vehicle. The drag coefficient of the vehicle was set to 0.06 [21]. A buoyancy of 160 [t] was assumed, based on the volume of the hull and the use of gaseous hydrogen (H2 (g)) as the LTA gas. H2 (g) was selected as it provides maximum buoyancy. It is not commonly used in LTA aircraft because of its flammability. However, we assume that the use of appropriate materials in the gas bearing hull can reduce the risk to acceptable levels because safety is ensured unless sparks are emitted. Given the above, B can be derived from the difference between the density of air ρair , the density of H2 (g) ρH2 , and the volume of the gas envelope V :
is then given by Eq. (18), based on Eq. (1):
99
105
3.2. Computational parameters
(hull)
96 98
|| w ⊥ || = w sin θ,
S ref
95 97
Finally,
B = V (ρair ( z) − ρH2 ( z)),
As
w = w ⊥ + w ,
93
(17)
107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
JID:AESCTE AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.5 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
1 2
(hull)
S ref
=
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
2
B
67
3
ρair (z) − ρH2 (z)
The aerodynamic drag of when the ratio between spheroid is approximately axis is approximately 40 mately 1.4 × 106 [m3 ].
5
.
(18)
68 69
an axisymmetric LTA hull is minimized the major and the minor axes of the 3.9:1 [27]. Since in this design the minor [m], when B is 160 [T], V is approxi-
70 71 72 73 74 75
3.3. Problem definition
76 77
To confirm the stability of a tethered high-altitude platform system under the influence of strong winds, we analyzed the advection distance of the platform dadv . The tether was assumed to be of unrestricted length, and the platform to be at a constant altitude of 20 [km]. dadv was therefore defined by the distance in the x– y plane from the point at which the tether was attached to the ground surface. This provided the origin (0, 0, 0) of the node to the platform (x0 , y 0 , 20 [km]), as follows:
dadv
x20
+
y 20 .
78 79 80 81 82 83 84 85 86
(19)
The length of the tether and the path taken are important elements of the system design. However, in this study, we assumed the length to be the distance of the platform from the nodal point on the ground when no force was applied to the tether at the origin. If the tether is in contact with the ground at all points except the origin, that is, if the platform is unable to lift the tether by L and B, the system will not be functional. We considered the following three relationships:
87 88 89
Fig. 6. Comparison of static behavior of the systems with different geometries. Thin lines show the results for the axisymmetric geometry (L = 0), and thick lines show those for the hybrid geometry (L = B). Red shows the behavior of the tether in three-dimensional space. The x– y, x–z, and y–z planes are shown in green, blue, and cyan. The origin is the point at which the tether connects to the ground. (For interpretation of the colors in this figure, the reader is referred to the web version of this article.)
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
90 91 92 93 94 95 96
(tether)
1. The sensitivity of the static response to L when B and C d are held constant at 160 [T] and 1.5 [–], respectively. (tether) 2. The sensitivity of the static response to B when L and C d are held constant at 0 [T] and 1.5 [–], respectively. (tether) when L and B 3. The sensitivity of the static response to C d are both set to 160 [T]. 4. Results and discussion 4.1. Sensitivity of the aerodynamic lift on the LTA hull Fig. 6 shows the system behavior when L = 0 (axisymmetric geometry) and L = B (hybrid geometry). Even when the hull had no lift L under storm conditions, dadv was approximately 8 [km]. As can be seen from Fig. 6, the L generated by the hybrid geometry reduced dadv . Fig. 7 shows the effect of varying L on the static behavior of the system. The effect of the tether tension T is shown in Fig. 7(a) and appeared to be linear with T . However, nonlinearities appeared when the change in lift L and tension T varied from their initial settings. From Eq. (11a), T showed a small but significant nonlinear relationship with L. T reached a minimum at an altitude of 0 [km], then rose in line with altitude, at a rate depending on the wind speed. As a result, the highest tension occurred at the point where the tether connected with the platform. This suggested that special attention must be paid to the connectors between the hull and the tether. Fig. 7(b) shows the nonlinearity of the change in θ . Equation (11b) introduces a nonlinearity between L and θ . When projected onto the x– y plane, the tether also became nonlinear, as shown in Fig. 7(c). This is expected from the nonlinearity appearing in T and θ . Furthermore, as L increased, dadv decreased. The effect of shortening dadv was more pronounced in the case of the hybrid hull than the axisymmetric one, suggesting that the hybrid hull is a promising design for a platform of this type.
4.2. Sensitivity of the buoyancy on the LTA hull
97 98
Next, we analyzed the axisymmetric LTA vehicle without taking account of L to isolate the effect of B on the static behavior of the system. The results shown by the black lines in Fig. 8 are the same as those in Fig. 7. As B changed, the volume of the LTA hull V also changed, which in turn affected D. Fig. 8 shows the sensitivity of B to the static response of the system. When B was set to 40 [T], part of the tether cable dragged on the ground. This was deemed to be a system failure, and the result is not shown. Fig. 8(a) shows the behavior of T as B was changed. When B decreased, T also decreased. Since V responded to the change in (hull) B, the change in hull size caused S ref to vary. The change in T
99
also declined, so that was nonlinear with B. As B declined, S ref ∂ T /∂ z (representing the gradient of T for altitude z) decreased close to the hull. This confirmed that, as B declined, the distribution of T was related to the wind speed shown in Fig. 5(a). Fig. 8(b) describes the effect on θ of varying B. Since the tether itself was assigned a weight of 40 [T], when B = 40 [T], the tether rope became slack close to the ground. When B was increased to 80 [T], the system was marginally able to lift the tether. This determined the minimum volume of the platform. The projection of the tether onto the x– y plane is shown as Fig. 8(c). Reducing B introduced an abrupt nonlinear rise in dadv . Clearly, B must be sufficient to lift at least the weight of the whole system. Since there is a tradeoff between T and dadv , the optimal compromise between maximizing T and the size of the LTA platform must be established at an early stage in the design.
110
(hull)
100 101 102 103 104 105 106 107 108 109 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
4.3. Sensitivity of the aerodynamic drag on the tether rope
127 128
In this study, we did not examine the influence of aerodynamic drag on the hull on the static response of the system. Assuming a constant B, the same wetted area is set with the same degree of V regardless of the geometry of the LTA platform. The
129 130 131 132
JID:AESCTE
AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.6 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
6
1
67
2
68
3
69
4
70
5
71
6
72
7
73
8
74
9
75
10
76
11
77
12
78
13
79
14
80
15 16 17 18
81
Fig. 7. Influence on the static response by L variation of the LTA hull. (a) Tension T of the tether cable vs. altitude. (b) Elevation angle of the tether rope θ vs. altitude. (c) The tether cable silhouette projected onto the ground (x– y plane). The origin is the connecting point of the tether cable to the ground. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
82 83 84
19
85
20
86
21
87
22
88
23
89
24
90
25
91
26
92
27
93
28
94
29
95
30
96
31
97
32
98
33
99
34 35 36
100
Fig. 8. Influence on the static response due to B variation of the LTA vehicle. (a) Tension T of the tether rope vs. altitude. (b) Elevation angle of the tether cable θ vs. altitudes. (c) The tether rope silhouettes projected onto the ground.
101 102
37
103
38
104
39
105
40
106
41
107
42
108
43
109
44
110
45
111
46
112
47
113
48
114
49
115
50
116
51
117
52
(tether) Cd
118
53
Fig. 9. Influence on the static response of
variation on the tether cable. (a) Tension of the tether rope T vs. altitude. (b) Elevation angle of the tether cable θ vs.
54
altitude. (c) The tether rope silhouettes projected onto the ground. Note that C d in the legend denotes C d
(tether)
in the text.
55 56 57 58 59 60 61 62 63 64 65 66
axisymmetric and hybrid geometries will therefore exhibit similar aerodynamic drag characteristics. By contrast, since the tether has a length of at least 20 [km], it is important to investigate the (tether)
influence of C d
. (tether)
to the static behavior of Fig. 9 shows the sensitivity of C d the system. Since the L was set equal to B, the result in Fig. 7 is identical to that when same cyan color. Since
(tether) Cd = 1.5, and they are (tether) Cd can fall in a range
shown in the from 10−2 to (tether)
100 , the four values of 1.5, 1.0, 0.1, and 0.01 are shown. A C d of 0.01 is close to the C d of the airfoil of an HTA aircraft. Fig. 9
120 (tether)
shows the strong effect that C d
121
has on the static behavior of (tether)
the system when the tether is long. As C d increased, the sensitivity to T , θ , and dadv increased. By contrast, the influence of (tether) Cd
on the static response of the system decreased markedly when the value was set low. (tether) Fig. 9(a) shows the effect of C d on T . T was little affected (tether)
119
(tether)
by the wind when C d was small, but increased as C d increased. As with the wind speed shown in Fig. 5(a), the distribution of T was nonlinear. But the distribution of T can be regarded as almost linear. The gradient of the line depended on
122 123 124 125 126 127 128 129 130 131 132
JID:AESCTE AID:4171 /FLA
[m5G; v1.221; Prn:29/08/2017; 8:45] P.7 (1-7)
K. Chiba et al. / Aerospace Science and Technology ••• (••••) •••–•••
1
the initial conditions of the governing equations. Fig. 9(a) shows
2
that the distribution of T was almost the same when C d was set at 0.1 and 0.01. As the cross-sectional shape of the tether ca-
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
(tether) Cd
is of the order of 10−1 , it
ble largely determines T when is not necessary to consider the surface roughness or accuracy of the cross-section of the cable. (tether) on θ . As can be seen, Fig. 9(b) shows the influence of C d (tether) Cd
the trend was similar to that for T . When increased, the distribution of θ became increasingly nonlinear. As with T , the gradient of θ depended on the initial conditions set for Eq. (11b). (tether)
At C d values of 0.01 and 0.1, the difference in θ was less than 1 [deg], suggesting that it is unnecessary to strictly mini(tether)
mize C d
. (tether) Cd
to dadv . These results Fig. 9(c) shows the sensitivity of confirmed those reported in Figs. 9(a) and (b). To minimize the effect of wind on the system, the cross-section of the tether ca(tether) Cd
ble must be carefully designed. Taking cost into account, should be of the order of 10−1 . The material of the tether should be flexible, and the cross-section should ideally resemble that of the airfoil of an HTA aircraft. However, unlike in HTA aircraft design, it is not necessary to have an order of one count (representing a C d of 0.0001). A design that maintains an order of 10−1 (1000 counts) is sufficient. 5. Conclusions
28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62
We have quantitatively investigated the influence of the aerodynamics of a tethered lighter-than-air system on the static response. The goal was to investigate the practicality of a high-altitude platform comprising a lighter-than-air vehicle and a tether cable. We considered conventional axisymmetric and hybrid hull geometries. The results showed that, even when the platform was axisymmetric, the advection distance of the platform under storm conditions was of the order of 10−1 [km]. The advection distance could be shortened nonlinearly by having the hybrid vehicle generate aerodynamic lift. The study quantitatively demonstrated the aerodynamic sensitivity of the lighterthan-air hull and the tether to the static behavior of the system.
• As the aerodynamic lift was increased, the tension on the tether cable increased nonlinearly, whereas the advection distance decreased also nonlinearly. The tension on the tether also declined nonlinearly. The advection distance reflected the tension on the cable. • As the buoyancy of the hull was reduced, the advection distance increased significantly. The volume of the hull is determined by the buoyancy required. The upper limit of the buoyancy is given by the allowable cable tension, and the lower limit by the allowable advection distance, which reflects the environment into which the system is to be inserted. • To minimize the advection distance, it is necessary to reduce the aerodynamic drag of the tether. The design target aerodynamic drag coefficient of the cross-section of the tether is enough to be of the order of 10−1 . In further research, we will investigate the optimal sizing of a lighter-than-air platform.
63 64
Conflict of interest statement
65 66
Acknowledgement
(tether)
26 27
7
There is no conflict of interest.
67 68
Part of this study was supported by Grant-in-Aid for Scientific Research (C) 16K00295, Japan Society for the Promotion of Science as well as the Collaborative Research Project (J15010, J16007, and J17L050) of the Institute of Fluid Science, Tohoku University, Japan.
69 70 71 72 73
References
74 75
[1] W.R. Corliss, NASA Sounding Rockets, 1958–1968 – a Historical Summary, NASA SP-4401, 1971. [2] N. Sarigul-Klijn, M. Sarigul-Klijn, C. Noel, Air-launching earth to orbit: effects of launch conditions and vehicle aerodynamics, J. Spacecr. Rockets 42 (3) (2005) 569–575. [3] I.R. McNab, A research program to study airborne launch to space, IEEE Trans. Magn. 43 (1) (2007) 486–490. [4] C. Yang, J.H. Everitt, Q. Du, B. Luo, J. Chanussot, Using high-resolution airborne and satellite imagery to assess crop growth and yield variability for precision agriculture, Proc. IEEE 101 (3) (2013) 582–592. [5] D.E. Bar, K. Wolowelsky, Y.S.Z. Figov, A. Michaeli, Y. Vaynzof, Y. Abramovitz, A. Ben-Dov, O. Yaron, L. Weizman, R. Adar, Target detection and verification via airborne hyperspectral and high-resolution imagery processing and fusion, IEEE Sens. J. 10 (3) (2010) 707–711. [6] F. Werner, M. Wendisch, H. Siebert, T. Schmeissner, P. Pilewskie, R.A. Shaw, New airborne retrieval approach for trade wind cumulus properties under overlying cirrus, J. Geophys. Res., Atmos. 118 (16) (2013) 3634–3649. [7] J.E. Garabedian, R.J. McGaughey, S.E. Reutebuch, B.R. Parresol, J.C. Kilgo, C.E. Moorman, M.N. Peterson, Quantitative analysis of woodpecker habitat using high-resolution airborne lidar estimates of forest structure and composition, Remote Sens. Environ. 145 (6) (2014) 68–80. [8] M. Kong, O. Yorkinov, S. Shimamoto, TCP/IP performance evaluations based on elevation angles for mobile communications employing stratospheric platform, IEICE Trans. Commun. 92 (11) (2009) 3335–3344. [9] R.S. Pant, N. Komerath, A. Kar, Application of lighter-than-air platforms for power beaming, generation and communications, in: Proceedings on International Symposium on Electronic System Design, 2011. [10] J.D. DeLaurier, A stability analysis for tethered aerodynamically shaped balloons, J. Aircr. 9 (9) (1972) 646–651. [11] L.T. Redd, R.M.B. Bland, R.M. Bennett, Stability Analysis and Trend Study of a Balloon Tethered in a Wind; with Experimental Comparisons, NASA TN D-7272, 1973. [12] G.S. Aglietti, Dynamic response of a high-altitude tethered balloon system, J. Aircr. 46 (6) (2009) 2032–2040. [13] A. Rajani, R.S. Pant, K. Sudhakar, Dynamic stability analysis of a tethered aerostat, J. Aircr. 47 (5) (2010) 1531–1538. [14] S.P. Jones, J.A. Krausman, Nonlinear dynamic simulation of a tethered aerostat, J. Aircr. 19 (8) (1982) 679–686. [15] J. Krausman, D. Miller, The 12M™ Tethered Aerostat System: Rapid Tactical Deployment for Surveillance Missions, AIAA Paper 2015-3351, 2015. [16] R.S. Pant, Methodology for determination of baseline specifications of a nonrigid airship, J. Aircr. 45 (6) (2008) 2177–2182. [17] C.V. Ram, R.S. Pant, Multidisciplinary shape optimization of aerostat envelopes, J. Aircr. 47 (3) (2010) 1073–1076. [18] S.R. Mistr, R.S. Pant, Design and fabrication of a quick dismantlable remotely controlled semirigid finless airship, in: Innovative Design and Development Practices in Aerospace and Automotive Engineering, in: Lecture Notes in Mechanical Engineering, 2017. [19] N. Deodhar, A. Bafandeh, J. Deese, B. Smith, T. Muyimbwa, C. Vermillion, P. Tkacik, Laboratory-scale flight characterization of a multitethered aerostat for wind energy generation, AIAA J. 55 (2017), http://dx.doi.org/10.2514/1.J054407. [20] S.S. Badesha, SPARCL: a high-altitude tethered balloon-based optical spaceto-ground communication system, Proc. SPIE Int. Soc. Opt. Eng. 4821 (2002) 181–193, http://dx.doi.org/10.1117/12.450641. [21] G.E. Carichner, L.M. Nicolai, Fundamentals of Aircraft and Airship Design, vol. 2 – Airship Design and Case Studies, AIAA, Reston, VA, 2013. [22] L.M. Nicolai, G.E. Carichner, Airplanes and Airships Evolutionary Cousins, AIAA Paper 2012-1178, 2012. [23] K. Chiba, S. Satori, R. Mitsuhashi, J. Sasaki, R. Akiba, Motion Analysis of Captive Platform System Constructed from Airship and Tether, in: 53rd AIAA Aerospace Science Meeting, 2015, 2015, AIAA Paper 2015-0713. [24] I.H. Abbott, Airship Model Tests in the Variable Density Wind Tunnel, NACA TR-394, 1931. [25] H.B. Freeman, Force Measurements on a 1/40 Scale Model of the U.S. Airship Akron, NACA TR-432, 1933. [26] S.A. Ross, H.R. Liebert, LTA Aerodynamics Handbook, Goodyear Aircraft Corp., Akron, OH, 1954. [27] J.S. Parsons, R.E. Goodson, F.R. Goldschmied, Shaping of axisymmetric bodies for minimum drag in incompressible flow, J. Hydronaut. 8 (3) (1974) 100–107.
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132