Average local density of air at different latitudes as a function of altitude and interpolating exponential functions 

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... paper presents important technical contents of the “cooperative” airship project named MAAT. This acronym stands for Multibody Advanced Airship for Transport. It is a novel airship concept based on the cruiser-feeder architecture. Photovoltaic and hydrogen productions have evaluated against altitude [1, 2], including energy needs for storage. The productivity for 1 square meter of flat photovoltaic plant has evaluated. It has verified that photovoltaic energy and Hydrogen production increase with altitude. It has demonstrated that hydrogen prices trends are encouraging the use of hydrogen as buoyant gas, instead of helium, on an economic point of view, even considering photovoltaic hydrogen [3]. It has also verified that a variable volume airship could present large advantages if compared to the constant shape and volume of a traditional airship [4]. It has also shown that an airship with variable volume is safer with Hydrogen than one equipped by ventilated air ballonets [5]. A novel variable volume architecture based on the defined idea has defined. Design guidelines have presented. This paper defines the energetic balance of a discoid airship with variable volume considering the results of these previous works [6]. This balance considers the atmospheric data and wind velocities at various latitudes and altitudes from U.S. Standard Atmosphere and CIRA Atmosphere models. General mathematical relations which could be applied to define airships behaviour has been obtained by well-known scientific literature [7, 8, 9, 10]. A mostly vertical profile mission of the feeder has been taken into account and a connection model between cruiser and feeder has been defined. Large CFD simulations have been performed to obtain the necessary basis of data to realize the necessary mathematical model that describes the energetic behaviour of the system. For atmospheric it has been considered two different hypotheses: the use of U.S. Standard Atmosphere model or the use of CIRA Model. The COSPAR International Reference Atmosphere [11, 12, 13] (CIRA) provides empirical models of atmospheric temperatures and densities as recommended by the Committee on Space Research (COSPAR). Since the early sixties, several different editions of CIRA have been published. CIRA-86 models consists of tables of the monthly mean values of temperature and zonal wind with almost global coverage (80°N - 80°S). They are compiled by Fleming et al. [14](1988), one in pressure coordinates including also the geopotential heights, and one in height coordinates including also the pressure values. These tables were generated from several global data compilations including ground-based and satellite (Nimbus 5, 6, 7) measurements (Oort (1983) [15] and Labitzke et al. [16] (1985)). The lower part was merged with MSIS-86 at 120 km altitude. In general, hydrostatic and thermal wind balances are maintained at all levels. The model accurately reproduces most of the characteristic features of the atmosphere such as the equatorial wind and the general structure of the tropopause, stratopause, and mesopause. The CIRA Working Group meets biannually during the COSPAR general assemblies. A global climatology of atmospheric temperature, zonal velocity and geopotential height derived from a combination experimental measurements by satellites, radiosondes and ground-based [17, 18]. The reference atmosphere extends from pole to pole and 0-120 km. The majority of the data are on a 5° latitude grid and approximately 2 km vertical resolution. This dataset is public. In particular, it has been compared different values from atmospheric models defining their possible range of validity. CIRA values have been considered. Average Temperature values have been plotted into Figure 1. Average pressure has been plotted into Figure 2. For both data series 4 th order interpolations has been calculated (R >0.99). By the above values, it has been possible to calculate atmospheric densities at various latitudes. They are plotted into Figure 3. Interpolating functions are exponential functions: In addition, wind speeds can be taken into account considering annual average wind speed (Figure 4) and annual maximum average monthly wind speed (Figure 5) at most significant latitudes. These values are very important for the further of the definition of the mission energetic profile. This assumption is done to the extreme variability of the wind values from point to point. It has been assumed because of the extreme geographic variations in the wind velocity. Even if a mainly vertical mission profile has been evaluated, it can be possible to predict the more calm wind operations. In this case it can be possible to accept different trajectories vertical motion. Some further considerations about atmospheric models can be performed by considering U.S. Standard Atmosphere Model. In particular, it can be verified that Standard Atmosphere Model describes the atmospheric conditions at latitude of 45°. It permits an ease of calculation of most physical parameters but it does not considers wind velocity in its description. Standard Atmosphere data are reported in the following table (Table 1). The NASA interpolation has been taken into account to simplify the results. Temperature T and pressure p can be fitted by the following curves: The lower stratosphere starts from 11,000 meters to 25,000 meters. To describe the atmospheric models in this region different methods have been created. The simplest is the one proposed by NASA with the following interpolating equations: In the lower stratosphere, the temperature is constant and the pressure decreases exponentially. The metric units curve fits for the lower stratosphere ...