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  • Original Paper
  • Open Access

Long permanence high altitude airships: the opportunity of hydrogen

European Transport Research ReviewAn Open Access Journal20136:123

https://doi.org/10.1007/s12544-013-0123-z

  • Received: 9 September 2012
  • Accepted: 13 October 2013
  • Published:

Abstract

Introduction

MAAT cruiser/feeder airship system is a transport system financed by European 7th Framework programme 2011. The project aims to realize a cruiser/feeder airship system, which can connect major populated centres worldwide. The MAAT cruiser feeder system is based on two different airships, the cruiser, which remains airborne for long times, and the feeder, which connects the cruiser with the ground and vice versa. This paper traces a detailed bibliography about MAAT project showing the actual state of the art of the project. This bibliographic review allows understanding the level of innovation related to this project.

Methods

Starting from the results of the preceding literature, the authors present a model of the cruiser, in terms of both mass and energy. According to the preceding studies, they have assumed the following minimal set of hypothesis: the buoyant gas is hydrogen; the shape of the cruiser is a discoid; operative altitude is in the range 15-17 km. It is well known that the major showstopper to actual diffusion of airships is related to the initial costs related to the use of Helium. The problem is more accentuated in Europe than in USA and Russia, because of higher unitary prices. An economic comparison with the possibility of using Hydrogen has produced. A further comparison has performed in terms of operations, focusing on the necessity of replacing the gas, which disperses in the external atmosphere because of the porosity of the tissues of the balloon system. The on board generation of hydrogen as an energy system is very convenient on long permanence airships because the replacement buoyant gas can be produced on board. It has been also traced a complete energy balance of the cruiser airship assuming it as discoid. On one side it has been evaluated the hydrolysis process against batteries showing that an hydrolyser/fuell cell cycle has a lower efficiency in comparison of batteries but it looks less expensive and presents a lower weight than any battery type.

Results

This paper has clearly demonstrated that the use of hydrogen is much more convenient than the uoiuse of Helium, even if it require an accurate design to minimize the risks related to hydrogen potential flammability. It demonstrates the necessity of using hydrogen as buoyant gas in long endurance airships because of the easiness of replacement. An estimation of the necessary energy requirements for a discoid airship has produced demonstrating clearly that a discoid shaped airship is energetically inefficient. These results force to consider a different and more efficient cruiser system.

Conclusions

In conclusion this paper demonstrates clearly the necessity of using hydrogen to allow possible future airship renaissance, which could be a fundamental option for the future because of airships are the most energetically efficient aerial vehicles. This research activity has also clearly demonstrated that the initial discoid shaped cruiser hypothesis is not feasible on energetic point of view.

Keywords

  • Airship
  • Photovoltaic
  • Hydrogen
  • Dispersion
  • Energy balance

1 Introduction: the MAAT project

MAAT, Multibody Advanced Airship for Transport, aims to investigate aerial transportation possibility by airship based cruiser-feeder system [15]. MAAT is composed by two modules: The cruiser, named PTAH, (acronym of Photovoltaic Transport Aerial High altitude system); the feeder, named ATEN (Aerial Transport Elevator Network feeder), is a VTOL system (Vertical Take Off and Landing) which ensure the connection between the cruiser and the ground. They can lift up and down by the control of buoyancy force and displace horizontally to join to cruiser.

The project aims to:
  1. 1.

    identify and design the most functional cruiser/feeder airship architecture based on a discoid innovative airship able to remain airborne for long periods and to travel great distances;

     
  2. 2.

    design the best type of propulsion both for cruiser and feeder so they can contribute together to the propulsion of an innovative modular airship;

     
  3. 3.

    minimize the environmental air transport impacts by annulling the fossil fuels energy consumption by designing both cruiser and feeder are energetically autonomous by photovoltaic energy and innovative electric propulsion.

     
  4. 4.

    study the different possible ways of approaching and joining between ATEN and PTAH, and consequently, the release of ATEN from PTAH.

     
  5. 5.

    design the best procedure of docking operations thus identified in order to obtain the minimum disruption to passengers and the maximum safety for themselves and for goods

     
  6. 6.
    study the different architectures of PTAH and Athens, in such a way that :
    1. a.

      the lift up capacity guaranteed by the buoyancy force, may be integrated with the power of the engines;

       
    2. b.

      effective and safe procedures for docking;

       
    3. c.

      ATEN can land and take off from Airport Hubs named AHA located in major populated centres

       
    4. d.

      PTAH satisfies the better possible aerodynamic performances possible for the dimensions and the operative mission.

       
     
To study the transfer operations between ATEN and PTAH of goods and people and vice versa, to:
  1. 1.

    minimize distress conditions for passengers,

     
  2. 2.

    maximize performances especially for goods;

     
  3. 3.

    enhance safety of these operations to maximum possible level.

     

The objectives described are congruent with each other and to achieve this study of the system and components must be highly structured.

2 MAAT design activity

This project has started by a preliminary conceptual design activity. The historical milestone references for any author who approaches the design of airships are certainly Lewitt [5] and Warner [6]. Kreider [7] has defined the most comprehensible mathematical modeling of an High Altitude Balloon and allowed to predict the Performance during flight.

The fundamental guidelines about airship designs has synthesized by Khoury and Gillett [8].

The actual aeronautic guidelines has been defined by Raymer [9], with the conceptual design for innovation method. This methodology can be partially reassumed by the acronym KISS that means “keep it simple, stupid”. It is not a simple joke. In any breakthrough innovation it is important to adopt a step by step design starting from very basic model and then introducing individual modification, which can be tested individually inside the system.

The intrinsic difficulties related to the project has forced to produce a large conceptual and design innovation in different field starting from the basic principles. Krausman [10] has investigated various parameters affecting altitude performance of tethered aerostats. Colozza [11, 12] have studied several models of high altitude airships. In particular he has investigated the possibility of realizing high altitude photovoltaic airships. This studies has inspired the PSICHE project about photovoltaic energy production and conversion at high altitude [13], and the energetic design based of high-altitude airships by Dumas [14]. PSICHE can be considered the original cruiser/feeder high altitude system which has been the origin of the MAAT project constituted by two very specialized systems. The cruiser needs to be designed an airship with cruising capability, while the feeder is conceived by simplicity as an aerostat with possibility of control by propulsion. Similar results has been produced by Aglietti and others [15], who have studied the feasibility of solar power generation using high altitude platforms. Dumas and Trancossi [16] has formulated an improved mathematical model used for PSICHE energetic evaluation, estimating the photovoltaic energy, which can be produced at high altitude by an horizontal photovoltaic plant, both in terms of electric energy or hydrogen and oxygen. In particular this method has been also recently improved [17] by a more complete estimation of the plants and their energetic effects on the system.

Pascoa [17] has produced an effective analysis of possible propulsion concepts which can be adopted on unconventional airships defining an effective state of the art which can be starting point for future development of future airship design modes.

Trancossi and others [18] has presented a variable shape airship configuration, which permits to reduce both the risk of fire and presents also a variable frontal section increasing volume with altitude, such as a traditional aerostat. Dumas and others [19, 20] have presented two different studies on this airship concept, verifying also its optimal mission profile and its feasibility.

The difficulties related to the energetic balances related to unconventional high altitude airships has been analysed by Pshikhopov [21, 22] and confirmed by Dumas [23, 24] and Khoshnoud [20, 25]. The exigency of producing an effective optimization of the plants and the consequent design guidelines have been demonstrated by Smith [26, 27]. This problematic part of the project has been an exceptional opportunity for the future of the project development opening the road to a series of methodological innovations.

Two directions has then started: a traditional disciplinary process which aims to improve the results on the basis of specific disciplinary needs which has been produced an interesting series of minor improvements starting from the very interesting stability analysis by Voloshin [28]. Neydorf [29] has analysed the Stability issues of MAAT feeder airship during vertical movements with wind disturbances. Pshikhopov[30] has considered planning of energy-efficient trajectories for the feeder with implementation of evolution algorithms.

Vizinho [31] has performed an effective computational analysis of the propulsive nacelle which needs to be used for the MAAT cruised propulsion. Vucinic, Gaviraghi and others [32] have analysed in depth the connection system and passenger exchange modes between cruise and feeder.

Another direction of development of the project is looking at methodological issues such as optimization systems. Ceruti [33] is analyzing multi-disciplinary design optimization with Heuristic Algorithms. Cerruti [34] analyses also how to apply innovatively rapid prototyping tools to facilitate wind tunnel testing of unconventional unmanned airships. Tuveri [35] is developing an innovative mesh based approach for the estimate the added masses to an unconventional unmanned airship.

On the other side Trancossi [36] has focused on the conceptual design methodologies to perform an effective system design optimization. Starting from the generalized formulation of the second principle defined by Adrian Bejan and defined Constructal Law [37, 38], he have developed a novel design method which can overcome the theoretical limits of the bottom-up design approach. He has finally proposed final formulations based on a dual cycle design method with a preliminary design method: the first aims to the definition of the optimal system on the basis of Constructal principle and second principle of Thermodynamics, the second aims to produce an effective optimization of the internal subcomponents of the system. This design methodology - defined Constructal Design for Efficiency – aims to finalize an optimal design which can solve the energetic issues related to the MAAT cruiser-feeder system. It has been previously applied to transport airship shapes with interesting results [39, 40] and on MAAT system [41, 42]. In particular, Trancossi is also working inside standardization committees on photovoltaic focusing on the characterization of photovoltaic modules for extreme conditions [43].

3 Hydrogen use as buoyant gas

The use of hydrogen as buoyant gas is a defined technical choice of the MAAT project. This technical choice is necessary especially for airships with a long airborne permanence, because of simple replacement of the gas which disperses into the environment.

It is possible to evaluate the convenience of hydrogen use both as buoyant gas and as energy storage system comparing it to helium and batteries for a large electrically propelled airship.

It has been considered a high altitude long permanence airship, which is a part (cruiser) of the MAAT cruiser-feeder architecture. Three phenomena have considered initial volume inflating (at ground), energy production and storage, gas replacement during service. It has been also evaluated the energy balance of the system for the initial reference discoid shape. Safety considerations has been also taken into account.

4 General data

This paper considers a large airship with the capacity to lift 300 passengers plus baggage and 20 people crew at 16 km. An overall weight of 125 kg for passenger has estimated. A 5 % buoyant gas overpressure has estimated in the balloon to maintain the shape, even in presence of wind. The operative altitude has estimated at 16 km and maximum ceiling of the system at 17 km.

Atmospheric data have reported in Table 1.
Table 1

Atmospheric data

Altitude

Temperature

Pressure

Density

Pressure H2

[m]

[K]

[Pa]

[kg/m3]

[Pa]

0.00

288.15

101325.00

1.2250

106391.25

1000.00

281.65

89874.57

1.1116

94368.30

2000.00

275.15

79495.22

1.0065

83469.98

3000.00

268.65

70108.54

0.9091

73613.97

4000.00

262.15

61640.24

0.8191

64722.25

5000.00

255.65

54019.91

0.7361

56720.91

6000.00

249.15

47181.03

0.6597

49540.08

7000.00

242.65

41060.74

0.5895

43113.78

8000.00

236.15

35599.81

0.5252

37379.80

9000.00

229.65

30742.46

0.4663

32279.58

10000.00

223.15

26436.27

0.4127

27758.08

11000.00

216.65

22632.06

0.3639

23763.67

12000.00

216.65

19330.41

0.3108

20296.93

13000.00

216.65

16510.41

0.2655

17335.93

14000.00

216.65

14101.80

0.2268

14806.89

15000.00

216.65

12044.57

0.1937

12646.80

16000.00

216.65

10287.46

0.1654

10801.83

17000.00

216.65

8786.68

0.1413

9226.02

Bold indicates the valuesat optimal altitude

Main physical parameters of the airship have been evaluated in Table 2. An overpressure about 5 % has considered ensuring the possibility of the balloon system to keep the shape.
Table 2

Airship system weight

 

Number of persons

Mass (kg)

Passengers

480

48000

Crew

20

2500

Freight

12000

Total passengers and freights

 

62500

Structure

150000

Energy conversion

60000

Energy storage

50000

Propulsion

40000

Total System Weight

300000

Total Weight

362500

Both Hydrogen and Helium balloons has been estimated and it has been observed that helium balloons results about 1.084 times larger than hydrogen ones. The hydrogen mass has also been evaluated in 29.44 tons while helium mass in about 61.53 tons. A parameter, defined Veff, has defined for hydrogen and helium airships. It considers that the external volume of the system is larger than the volume of gas strictly necessary for buoyancy. A coefficient 1.1 has adopted in this evaluation because of the system is a cruiser/feeder. It presents more empty spaces than any other traditional airship system because of this architecture.

Changing shape airship architecture such as the ones evaluated in [19, 20] has evaluated. It has also evaluated an ellipsoid shape, which is characterised by the following relations:
(1)
(2)

Area expressed by Eq. 2 is expressed by the Knud Thomsen formula which has a maximum error of 1,061, where k is a numerical constant equal to 1.6075.

It is possible to compare Helium and Hydrogen volume. The comparison is reported in Table 3. The following conventions have assumed: V is the useful volume of buoyant gas for lift and V eff the effective volume used for aerodynamic calculations. The two semi axes on the horizontal plane (x, y) have been assumed a = b = 150 m. The constant c is considered variable with altitude. By this assumption, it is possible to evaluate the reference values used for calculation (Table 4).
Table 3

Volume comparison H2 vs. He

Altitude

Density H2

Density He

V(H2)

Veff (H2)

V(He)

Veff (He)

[m]

kg/m3

kg/m3

[m3]

[m3]

[m3]

[m3]

0.00

0.08953

0.17777

319251

351176

346150

380765

1000.00

0.08125

0.16132

351806

386986

381448

419593

2000.00

0.07356

0.14606

388561

427417

421300

463430

3000.00

0.06644

0.13193

430176

473194

466421

513064

4000.00

0.05987

0.11887

477437

525181

517665

569431

5000.00

0.05380

0.10682

531278

584406

576042

633647

6000.00

0.04821

0.09573

592821

652104

642771

707048

7000.00

0.04308

0.08555

663413

729754

719310

791241

8000.00

0.03838

0.07621

744681

819149

807425

888168

9000.00

0.03408

0.06767

838607

922467

909265

1000192

10000.00

0.03016

0.05989

947603

1042364

1027446

1130190

11000.00

0.02660

0.05281

1074645

1182109

1165191

1281710

12000.00

0.02272

0.04511

1258196

1384016

1364208

1500629

13000.00

0.01940

0.03853

1473098

1620408

1597218

1756939

14000.00

0.01657

0.03291

1724708

1897178

1870027

2057029

15000.00

0.01415

0.02811

2019282

2221211

2189421

2408363

16000.00

0.01209

0.02401

2364179

2600597

2563378

2819716

17000.00

0.01033

0.02050

2767981

3044779

3001202

3301323

Table 4

Reference values for calculation

Altitude

c(H2)

c(He)

A

Afront (H2)

Afront (He)

did (H2)

did (He)

V^2/3(H2)

V^2/3(He)

V^1/3(H2)

V^1/3(He)

[m]

[m]

[m]

[m2]

[m2]

[m2]

[m]

[m]

[m2]

[m2]

[m^2]

[m^2]

0.00

4.28

4.64

124920

1881.30

2039.81

5.02

5.41

4977.56

5253.37

70.55

72.48

1000.00

4.71

5.11

125016

2073.14

2247.82

5.50

5.92

5310.44

5604.70

72.87

74.86

2000.00

5.21

5.64

125130

2289.73

2482.66

6.02

6.49

5674.15

5988.56

75.33

77.39

3000.00

5.76

6.25

125268

2534.97

2748.56

6.61

7.12

6072.39

6408.86

77.93

80.06

4000.00

6.40

6.94

125435

2813.47

3050.52

7.27

7.83

6509.37

6870.06

80.68

82.89

5000.00

7.12

7.72

125637

3130.75

3394.54

8.01

8.62

6989.99

7377.31

83.61

85.89

6000.00

7.94

8.61

125883

3493.41

3787.76

8.84

9.51

7519.88

7936.57

86.72

89.09

7000.00

8.89

9.64

126185

3909.40

4238.79

9.78

10.50

8105.59

8554.72

90.03

92.49

8000.00

9.98

10.82

126557

4388.30

4758.04

10.83

11.63

8754.71

9239.82

93.57

96.12

9000.00

11.24

12.18

127018

4941.79

5358.17

12.02

12.89

9476.20

10001.28

97.35

100.01

10000.00

12.70

13.77

127592

5584.09

6054.59

13.36

14.32

10280.47

10850.11

101.39

104.16

11000.00

14.40

15.61

128311

6332.73

6866.31

14.87

15.93

11179.91

11799.40

105.74

108.63

12000.00

16.86

18.28

129439

7414.37

8039.08

16.98

18.16

12419.21

13107.37

111.44

114.49

13000.00

19.74

21.40

130884

8680.76

9412.17

19.35

20.66

13795.89

14560.33

117.46

120.67

14000.00

23.11

25.06

132731

10163.46

11019.80

21.97

23.43

15325.17

16174.36

123.79

127.18

15000.00

27.05

29.33

135089

11899.34

12901.95

24.89

26.49

17023.93

17967.24

130.48

134.04

16000.00

31.68

34.34

138091

13931.77

15105.62

28.09

29.86

18911.04

19958.91

137.52

141.28

17000.00

37.09

40.21

141901

16311.32

17685.66

31.61

33.53

21007.31

22171.34

144.94

148.90

5 Initial airship inflation

The initial inflation can be evaluated by assuming the masses of both helium and hydrogen.

In 2011, the Helium 99.9 % the average market price in the U.S. [44, 45] can be estimated between 50 and 70 USD/MCF. It means a price between 1.77 and 2.47 USD/m3. For such a volume of hydrogen it is necessary an initial expense between 613000 USD and 855000 USD excluding losses. Some China suppliers have similar prices also. Prices exclude storage cylinders and delivery costs, which lead in Europe to much higher prices.

In a preceding paper, Dumas [43] has estimated that the necessary hydrogen can be produced in one year with a large photovoltaic facility with the characteristics reported in Table 5. It has evaluated the economic feasibility of photovoltaic hydrogen production that making a conservative hypothesis on the prices of hydrolytic hydrogen (evaluated one-fifth of average helium cost). For advanced solid polymer or alkaline electrolyser, the electric efficiency [46] of the industrial process overcomes 75 %.
Table 5

Reference photovoltaic plant considered for hydrogen production

Module Properties

poly-Si

Module

Unit

Value

Power capacity

W

200

Efficiency

%

13.50 %

Area

m2

1.48

Nominal operating cell temp.

°C

45

Temperature coefficient

%/°C

0.40 %

Plant and Conversion Properties

 Plant

Unit

Value

 Miscellaneous losses

%

5.00 %

 Inverter

Unit

Value

 Efficiency

%

95.00 %

 Capacity

kW

1

 Distribution Losses

%

5.00 %

A possible market price of hydrogen for airship inflation can be estimated (prudentially) the 25 % of average helium cubic meter prices. It means that a cubic meter of Hydrogen is about 0.5 \$/m3 (a low price considering actual market standards). Considering that about 5 kWh are necessary to produce 1 m3 of compressed hydrogen, it means the price of electricity can be considered 0.1 \$/kWh.

Compressed hydrogen productivity has estimated in different locations and at different latitudes (Table 6). In particular sample locations has assumed on the northern hemisphere at 15° step.
Table 6

Considered geographic locations and climatic data

 

Lat.

Air temperature

Relative humidity

Daily solar radiation*

Wind speed

Earth temperature

deg

°C

%

kWh/m2/d

m/s

°C

Bjornoya Island

74.5

−1.3

88.3 %

1.81

7.0

3.0

Oslo

60

5.7

73.4 %

2.41

2.6

4.5

Torino

45

11.6

69.5 %

3.67

1.5

7.3

Cairo

30

21.4

58.1 %

5.38

4.0

24.5

Asmara

15

24.6

53.3 %

5.93

4.0

27.6

Singapore

0

26.7

83.3 %

4.45

1.7

26.6

* Average daily solar radiation on a horizontal plane

The hydrogen average annual productivity on a flat horizontal plan has estimated in terms of compressed hydrogen [20, 23, 24] and shown as a function of latitude in Fig. 1.
Fig. 1
Fig. 1

Cost of the plant at different latitudes and interpolating third order curve

It has also evaluated the plant dimensions (Table 7) according to the unitary costs specified in Table 5. The costs (Fig. 1) and payback times (Fig. 2) have been estimated. The dimensions have evaluated on the possibility of filling a large airship such as the one considered with the electrical production of a year.
Table 7

Photovoltaic plant dimensions

Latitude

Hydrogen productivity

Number of PV modules

Electric

Effective

Power

PV area

Deg.

m3/m2 year

kW

m2

Deg.

m3/m2 year

kW

m2

0

36.6

6959

1391.6

10298.69

15

48.5

5251

1050.2

7771.79

30

44.5

5723

1144.6

8470.38

45

32.1

7934

1586.8

11742.43

60

21.7

11737

2347.2

17370.14

75

19.2

13265

2652.8

19631.88

Fig. 2
Fig. 2

Payback times at various latitudes and interpolating curve

Considering European costs of Energy a similar photovoltaic plant, even if very large, can have a very similar payback time considering the possibility of selling the electricity on the market at the same evaluated price of 0.1 USD/kWh.

6 Buoyant dispersion

6.1 Permeability

An airship has continuous losses of gas by permeability. In scientific literature, different expressions can be found to describe permeability processes. The simplest way is to adopt the permeability coefficient [47], which can be defined as:

This representation of permeability is very comfortable for an initial evaluation and especially because it permit a temperature dependent formulation. The case of a high altitude airship can be described by temperature dependent coefficients, because of the extreme variation of thermal conditions during missions.

The permeation of molecules through flawless polymers is the combination of two effects: the solution of a permeant in the polymer and diffusion of the dissolved permeant. The permeability coefficient is the product of the diffusion coefficient D and the solubility coefficient S:
(3)
The permeability coefficient P, the diffusion coefficient D, and the solubility coefficient S can vary as a function of temperature, and exponential relations can express these relations:
(4)
where E p is the activation energy of permeation, E d the activation energy of diffusion, and Es the heat of solution that have in SI units the dimension [kJ/mol]. Those data are tabled for many polymers and for many gasses and liquids. P o , D o and S o are the multiplicative factors. R is the gas constant; T is the temperature.

The permeability coefficient is determined for a given temperature by means of the multiplicative factor P o and the activation energy of permeation E p . These data have been tabled by Pauly [47].

This permeability evaluation is important. Joints and defects need an accurate evaluation. In particular, data for some materials of interest for balloons are reported in Table 8.
Table 8

Estimated costs for the plant

Photovoltaic modules

\$/kW

1,000

Back-up system

\$/kW

300

Installation

\$/kW

200

Transmission lines

\$/kW

300

Inverter

\$/kW

100

Electrolysers

\$/kW

200

Compression plant and Storage

\$/kW

400

Total

\$/kW

2,500

7 Permeability evaluation of materials

The above-enunciated theory about permeability allows an effective application to the airship shape, both for helium and hydrogen. It can be assumed that the gas dispersion for permeability can be expressed as:
(5)

Gas dispersion for the three critical gasses has calculated for 1 m2 of balloon surface and per hour of steady service.

The choice of material must be a good compromise of mechanical properties and gas dispersions. The best compromise solutions between mechanical properties and porosity are Mylar A and or Nylon rip-stop-polyurethane dual layer balloons.

It is possible to find on the market high-quality proprietary fabrics. For example, it can be cited 3-ply rip-stop nylon 108.5 g/m2 made on rigorous standards with internal polyurethane balloon. It has not the typical problems of the polyurethane: the pinholes and the difficulties in reparation.

This material allows evaluating daily losses in STP conditions. Helium losses are about 2.5 10−4 m3 (273.15 K; 1,013 × 105 Pa)/(m2 day). Hydrogen losses about 3.5 10−4 m3 (273.15 K; 1,013 × 105 Pa)/(m2 day). The cited values do not consider an entire airship in service including losses due to the junctions among different textile sheets (Blimpworks Airship – USA). The considered overpressure is higher than the usual one 1–3 %).

8 Gas dispersion evaluation in service

The volume and surface defined in Table 4 allow evaluating the dispersion into service. An airship including junctions among sheets of the high-quality mentioned materials has been evaluated. Figure 3 shows the results. The overpressure has increased to 5 % instead 1 % evaluated by the producer.
Fig. 3
Fig. 3

Unitary losses as a function of operative altitude with high quality fabric

By the results in Figs. 4 and 5 it is possible to see that long permanence airships with mission times longer than a week it losses can be significant.
Fig. 4
Fig. 4

Losses [m^3/day] as a function of operative altitude with high quality fabric and interpolating functions

Fig. 5
Fig. 5

Temperature CIRA 86 average annual values vs. Standard Atmosphere values

The calculations show the losses because of permanence at high altitudes for a month. Helium losses are about 210 m3 and Hydrogen ones about 290 m3. These preliminary evaluations force to consider the impossibility to preserve the necessary overpressure and the shape geometry without any refill of gas. The losses increase also consistently in case of a lower quality fabric.

9 Daily thermal excursion effects

Another important volumetric effect is the daily thermal excursions and to location changes during travel. They have, with solar irradiance, large effects on the temperature and density of the buoyant gas. To compensate these daily thermal effects is necessary to preserve the operative altitude. The reference temperature of Standard Atmosphere model at stratospheric altitudes is about −56 °C.

The simplest regulation of the volume against temperature variations is to vary the mass of gas in the balloon. The same pressure and volume preceding the thermal variation can be restored and preserved. Thermal controls have often used but volumetric are less expensive and less complex. They need only a sufficient reserve of gas.

For example, Tables 9, 10, 11 and 12 shows the results of the calculations considering a thermal excursion of ±10°. This example shows clearly that it is necessary a gas reserve also in mass to keep the volume by buoyant gas addition or subtraction.
Table 9

Permeability coefficient of various materials

 

P(He)

(P(H2)

P(O2)

Poly(ethylene) density 0.914 g/cm^-3

7.40E-13

3.70E-13

2.20E-13

Polyvinilecloride plasticized 10 %

1.30E-13

3.83E-16

Polyvinilacetate

4.95E-13

2.99E-13

1.36E-14

Poly(trifluorochloroethylene) film 30 % cristallinity

7.05E-14

5.10E-13

3.00E-15

Mylar A

4.88E-14

2.44E-14

3.00E-15

Nylon 6

3.98E-14

2.85E-15

Nylon 11

1.34E-13

1.46E-13

Cellophane (relative humidity 43 %)

1.20E-15

5.36E-16

Table 10

Evaluation of dispersions for different polymers

Loses for a 20 μm membrane

Ground

16 km

 

V(H2)

V(He)

V(02)

V(H2)

V(He)

V(02)

 

[m3gas/m2 h]

[m3gas/m2 h]

[m3gas/m2 h]

[m3gas/m2 h]

[m3gas/m2 h]

[m3gas/m2 h]

Poly(ethylene) density 0.914 g/cm^-3

7.13E-05

3.56E-05

2.12E-05

1.07E-05

5.34E-06

3.18E-06

Polyvinilecloride plasticized 10 %

1.25E-05

 

3.69E-08

1.88E-06

 

5.53E-09

Polyvinilacetate

4.77E-05

2.88E-05

1.31E-06

7.15E-06

4.32E-06

1.96E-07

Poly(trifluorochloroethylene) film 30 % cristallinity

6.79E-06

4.91E-05

2.89E-07

1.02E-06

7.37E-06

4.33E-08

Mylar A

4.7E-06

2.35E-06

2.89E-07

7.05E-07

3.52E-07

4.33E-08

Nylon 6

    

5.75E-07

4.12E-08

Nylon 11

1.29E-05

1.41E-05

 

1.94E-06

2.11E-06

 

Cellophane (relative humidity 43 %)

1.16E-07

 

5.16E-08

1.73E-08

 

7.74E-09

Table 11

Example of massif regulation in the case of a thermal excursion in gas temperature ± 10°between day and night

Hydrogen

T [K]

V [m3]

ΔV [m3]

ΔM gas [kg]

206.65

2368397

−114609

1446

216.65

2483006

0

0

226.65

2597616

114610

−1318

Helium

T [K]

V [m3]

ΔV [m3]

ΔM gas [kg]

206.65

2579995

−124849

2865

216.65

2704844

0

0

226.65

2829692

124848

−3142

Table 12

Difference of average energy productivity and energy used for propulsion [kW]

Gray cells indicates negative values

This strategy of preserving the volume is interesting for hydrogen, because it is possible to avoid thermal actions on hydrogen lowering energetic costs and lessening the risks related to hydrogen thermal treatment plant.

Another thermal effect needs a serious evaluation: the changes in air temperature and density, moving from one location to another. Figure 5 shows average temperature by Standard Atmosphere model and average temperature at different latitudes by CIRA Model.

Figure 6 shows the temperature variation around the operative altitude.
Fig. 6
Fig. 6

Average temperature excursion around operative altitude of 16 km (North hemisphere)

It shows clearly that an average temperature jump about 25° must be considered. The daily thermal excursion has estimated in 10–12 ° C by considering data that are more accurate. By these values, the thermal effects on the system have estimated for this preliminary calculation.

In this case, the volume control by buoyant gas variation is easier than any other operation and much convenient for hydrogen airship.

10 Energy needs for flight

The energy production has estimated in a precedent paper [20] for square meter of photovoltaic surface at various latitudes. The photovoltaic surface has estimated about 61,000 m3. Daily average production has shown in Fig. 7 against latitude.
Fig. 7
Fig. 7

Electric Energy Production average daily value [MW] for different latitudes at an altitude of 16 km a

The considered discoid airship shape at 16.000 has shown in Fig. 8. The coefficient of drag of the shape CD and drag D has evaluated as a function of wind velocity at different diameters in a preceding paper [24]. It can be assumed conservatively a C d,V about 0.125 even if a lower one has been evaluated in the cited paper including their variation as a function of Reynolds number.
Fig. 8
Fig. 8

The configuration of the reference shape

Following the method presented in such paper the aerodynamic forces and necessary power has estimated. Figure 9 presents the needed power at 16 km against relative velocity of the airship and third order interpolating function.
Fig. 9
Fig. 9

Required power kW at different relative velocities

The held values allow verifying the average production of photovoltaic energy. The use of compressed hydrogen storage and fuel cells for conversions, together with batteries for emergency has assumed. A reference efficiency of the energy caption, storage and conversion has considered about 50 %.

Calculations have realised for 24 h of service at the annual mean relative speed of the considered airship. The energy needs have evaluated and subtracted to the needs for daily operations at constant velocity. The values are reported at an altitude of 16 km for different relative velocities. It has noted that the system must preferably move in the main direction of high altitude winds. In other cases, it can only remain in hovering conditions or being moved by high altitude winds passively.

The results force to consider a conservative hypothesis. The airship can move at an average velocity. It is equal to the average wind velocity in the selected location plus a seasonal value depending on photovoltaic energy high altitude caption.

Average speeds have evaluated by the results of these elementary calculations. Detailed calculations could be performed on daily, weekly or monthly photovoltaic productivity.

The operative velocity can then be plotted in Fig. 10 on average annual basis, taking data by the values of the velocity of winds by CIRA model.
Fig. 10
Fig. 10

Average velocity at an altitude of 16 Km at different latitudes

11 General considerations and future advances

This paper presents a problem and analyses it drawing a methodological model of work for the future activities related to the MAAT project.

The mission profiles require a more accurate analysis of the velocities of the winds at different altitude and an effective mapping of the jet streams. It will be one of the primary efforts of further activities, which will define the ideal shape of the cruiser and the mission profiles.

The optimization of the shape and operation connected problems. They are the core of the development of the MAAT cruiser/feeder project. This paper present a method for the calculations necessary to minimize of energy needs and volume through an effective step by step optimisation.

Future activity will require also a detailed study of adiabatic phenomena that takes place during vertical movements, especially relating the feeder behaviour. An airship is subject during vertical movement to heating and cooling phenomena. Considering the vertical motion of an airship or of a balloon, it can be easily demonstrated that it changes its average temperature during expansion/compression processes. Some hypothesis are required. They are in brief:
  1. 1.

    thermal exchanges of the balloon during the vertical movement are negligible,

     
  2. 2.

    the balloon can be considered as an air parcel.

     
  3. 3.

    changes in temperature result from either expansion or contraction

     
Such a process can be described by the first principle of thermodynamics and its governing equations are:
(6)
In particular it can be considered an adiabatic process described by Poisson Eq. (7), which can be obtained by ideal gas equation:
(7)

Using numerical interpolations of the Standard Atmosphere values it is possible to evaluate the theoretical adiabatic temperature reached by the balloon. It relates the initial conditions of temperature and pressure to the final temperature and pressure. In calculations it can be assumed the hydrogen gas constant R d = 4124 J/kg K and the specific heat c p = 14.25 J/kg K. It is in particular necessary to define an adequate model of the system and the heating/cooling apparatus to maintain the temperature of the gas in an acceptable range.

Adiabatic heating/cooling processes together with the heat transfer processes between the internal gas and the exterior one is an argument which needs to be analysed in depth. This activity will be interesting in the future especially to create an exact model of the vertical motion of the feeder.

Together it is necessary the job on controls.

12 Conclusions

This paper aims to show that hydrogen is fundamental for the future of airships. They are suffering large problems because of high costs of helium.

Hydrogen, which can be produced on board, simplifies the management of airship during long missions. It ensures the possibility of a continuous refilling of spread gas, even if hydrogen has higher dispersions than helium.

It has demonstrated that today prices of the photovoltaic hydrogen are the most economic choice for airship filling. Estimating a cost of electricity up to 0.1 USD/kWh it has shown that a photovoltaic plant for hydrogen production ensures a valid alternative to helium.

It has demonstrated that a mix of storage technologies can perform the best performances and flexibility. Hydrolyser and fuel cells can perform the basic needs and batteries ensure a fast acting and flexible system. Together they ensure acceptable performances even with non-optimised shapes.

In this paper it has been considered the possibility of using hydrogen for airship volume. It is another important development for the future hydrogen airships. It is necessary because it is needed to increase system safety by removing any air ballonet inside the volume of the hull.

Definitions and Abbreviations

A: 

Surface [m2]

a, b, c: 

Semi axes of an ellipsoid [m]

cp

specific heat at constant pressure [kJ/kg °C]

D: 

Diffusion coefficient [cm2/s]

d: 

diameter [m]

E: 

Energy [kWh]

H: 

Altitude [m, km]

M: 

Mass [kg, ton]

p: 

Pressure [Pa]

P: 

Permeation coefficient [cm3(273.15K; 1.013×105)/ (cm×s×Pa)]

R: 

Gas constant 8,3144 10−3 kJ/K mol

S: 

Solubility coefficient [cm3(273.15K; 1.013×105)/ (cm3×Pa)]

s: 

thickness [mm]

T: 

Temperature [K]

t: 

Time [s, h]

V: 

Volume [m3]

v: 

Wind velocity [m/s]

Acronyms

MAAT: 

Multibody Advanced Airship for Transport

PV: 

Photovoltaic

Declarations

Acknowledgments

The present work was performed as part of Project MAAT | Multibody Advanced Airship for Transport | with ref. 285602, supported by European Union through the 7th Framework Programme.

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors’ Affiliations

(1)
Università di Modena e Reggio Emilia, Di.S.M.I., Via Amendola, 2, 42100 Reggio Emilia, Italy
(2)
Reggio Emilia Innovazione scarl, Via Sicilia, 31, 42122 Reggio Emilia, Italy
(3)
Faculty of Engineering Sciences MECH-ETRO, Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium

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