1 Introduction: the MAAT project

MAAT, Multibody Advanced Airship for Transport, aims to investigate aerial transportation possibility by airship based cruiser-feeder system [1–5]. 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
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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
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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
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Table 4 Reference values for calculation
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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
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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
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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
figure 1

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

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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
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Fig. 2
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Payback times at various latitudes and interpolating curve

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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
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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
figure 3

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

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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
figure 4

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

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Fig. 5
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Temperature CIRA 86 average annual values vs. Standard Atmosphere values

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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
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Table 10 Evaluation of dispersions for different polymers
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Table 11 Example of massif regulation in the case of a thermal excursion in gas temperature ± 10°between day and night
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Table 12 Difference of average energy productivity and energy used for propulsion [kW]
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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
figure 6

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

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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
figure 7

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

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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
figure 8

The configuration of the reference shape

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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
figure 9

Required power kW at different relative velocities

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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
figure 10

Average velocity at an altitude of 16 Km at different latitudes

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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.