Design of a Light-Weight Vertical Tail for a Hybrid High-Altitude Pseudo-Satellite ^†

Abstract

The interest in high-altitude pseudo-satellites (HAPSs) has significantly increased in recent years due to the great versatility of these platforms, which allows them to be employed in a wide variety of applications in civilian and military fields. This study focuses on the design of an innovative hybrid airship vertical tail. The empennage proposed is internally sustained with a light-weight structure and coated with a thin film, avoiding any leakage that would occur with inflated structural elements. The design of the vertical tail and its structural analysis through a detailed finite element (FE) model are presented to show its overall behavior subjected to the aerodynamic loads.

1. Introduction

HAPSs have seen a remarkable increase in recent decades as a valid complementary solution to satellites and RPASs (Remotely Piloted Aerial Systems) [1]. These types of structures can include free-floating balloons, airships, or powered fixed-wing aircrafts that use either solar power or an on-board energy source. High-altitude pseudo-satellites are employed in a wide variety of applications in civilian and military fields, such as for improvements in telecommunications, astronomy, emergency applications, remote sensing, scientific explorations, cargo transportation, observation, and surveillance [2,3]. Typically, these platforms fly at an altitude of about 18–20 km, which is characterized by weak winds and the absence of meteorological phenomena [4,5]. These conditions facilitate mission operations. The aim of this paper is to describe the design process of a vertical tail (VT) for a hybrid airship. This type of vehicles can generate aerodynamic forces like a fixed-wing and aerostatic ones like balloons and airships [6,7]. An example of a hybrid platform is shown in Figure 1. Taking part in the lateral–directional stability of the platform, the design of the tail assembly is essential to guarantee safety during flight. Indeed, the lateral–directional degree of freedom are strictly coupled. The tail provides the main contribution to the directional stability. When the side-slip angle is not equal to zero, it generates a force and, thus, a yaw moment, which restores the attitude of the platform. This tendency is named positive weathercock stability [8,9,10]. The design process is carried out pursuing the right compromise among multiple constraints of different nature, with the aim of achieving a solution that weighed as low as possible because a low structural weight allows the mass of the entire airship to be contained. Moreover, this implies the following: (1) less material is needed to create the different parts that make up the platform; (2) and there is reduced energy consumption for flight, consequently limiting the environmental impact and economic expenses.

2. Materials and Methods

2.1. Design Process

The proposed tail empennage is characterized by a dihedral angle close to 90°, allowing us to treat it, for all intents and purposes, as a vertical aerodynamic surface. The design process begins with the evaluation of the vertical tail volume coefficient $C_{VT}$. This parameter concerns the hybrid airship volume, center of gravity, and length to the tail surface, particularly in the following:

$$C_{VT}={\displaystyle \frac{l_{VT}·S_{VT}}{l_b·Vo{l}^{2/3}}}$$

(1)

where $l_{VT}$ is the distance between the center of gravity of the platform and the quarter chord of the VT mean aerodynamic chord; $l_b$ is the airship body length; $S_{VT}$ is the previously mentioned tail surface; and $Vol$ is the platform volume. A considerable amount of $C_{VT}$ values, as a function of volume platforms, can be found in [9]. Interpolating these values, the VT volume coefficient is obtained as described in [9]. At this stage, $S_{VT}$ can be calculated by imposing a reasonable assumption for the position of the vertical tail aerodynamic center, which is not fully defined. The planform vertical tail area is then employed to estimate the weight of vertical empennage and to define an updated value of the center of gravity, knowing the weight of all the remaining platform structures. During the preliminary design phase, a prediction of the mass value of the light-weight vertical tail can be obtained as follows [9]:

$$W_{VT}=F_{PSQ}·S_{VT}·F_{AF}$$

(2)

where $F_{AF}$ takes into account the tail external attach fittings, and $F_{PSQ}$ is the surface density (kg/m²) used to fabricate the tail surface out of light-weight structural materials. As shown in Figure 2, the process is iterative. Finally, the area and layout of the tail are refined through aerodynamic, flight mechanics and stability/control analyses. The forward step is the CAD/CAE design phase, based on the restrictions reported in the “Constraints” block of Figure 2 and the results of the FE analysis. The structural design loads, applied to the finite element model, are derived from the subpart C-structure of JARUS CS-LUAS considering the flight profile of the platform. The choice falls on these recommendations because, at the moment of writing, the specific regulation for HAPS is not yet well-assessed. A safety factor of 1.5 is imposed to the limit loads, as specified in CS-LUAS 303, while the sections considered to evaluate the loads under different flight conditions are CS-LUAS 441 and CS-LUAS 443 [11]. This phase is also characterized by an iterative procedure.

In

Table 1. Geometrical parameters of the vertical tail.

Geometrical Parameter	Value
Geometric mean chord	1.3 [m]
$\mathrm{Dihedral}\mathrm{angle}\Gamma$	75.0°
$\mathrm{VT}\mathrm{swept}\mathrm{angle}{\Lambda }_{LE}$/ $\mathrm{Wing}\mathrm{swept}\mathrm{angle}{\Lambda }_{LE}$	1.2

, the geometrical features of the aerodynamic surface are listed. The vertical empennage is characterized by a symmetrical airfoil which responds in a symmetric manner to positive and negative side-slip angles.

2.2. CAD Model

In Figure 3, the CAD model, representative of the vertical tail, is shown. The employed software is Autodesk Fusion 2024.

A configuration with a light-weight structure and coated with a thin film was preferred over an inflated one. Generally, the latter is pressurized like the envelope, requiring a heavier fabric skin to avoid leakage, thus with a more sophisticated manufacturing technique and additional weight increase. The used material for the different components is indicated between the brackets in Figure 3. The external skin, made of fabric material, has the function of containing the internal structure and transmitting the aerodynamic forces to the ribs. The chosen material is subjected to mechanical and thermal stress, deteriorating actions of external agents such as ultraviolet rays and ozone. Clearly, no single material is capable of offering all the desired characteristics; consequently, multi-layer one is adopted, in which each layer performs a certain function [12]. The inner structure of the vertical tail features two circular carbon fiber tubes that act as empennage spars, which ensure the desired high torsional rigidity, maintaining the weight to be as low as possible. The arrangement of these tubes is dictated by the necessity to support aerodynamic loads, conventionally applied to a quarter chord. The ribs, sustained by the spars, have the aim to maintain the external shape of the tail. Furthermore, a carbon fiber tube is inserted in the LE and TE to support them. The above-mentioned parts are bonded together with an epoxy resin, giving the required compactness. The spars are constrained to the platform structure by means of polyether ether ketone (PEEK) supports and connected together by means of screws, allowing for the fitting, the replacement, and the removal of VT in the event of damage. Two dyneema cables connect the lower bracing support with the bracing upper supports (which are glued to the spars). This link is crucial to prevent excessive deformation of the aerodynamic surface, resulting in a loss of efficiency. The Young modulus of dyneema is obtained following the hypothesis of linear elastic material and the data provided by the manufacturer. In

Table 2. Material properties.

Material	Young Module ${\mathit{E}}_{\mathit{l}}$ [MPa]	Young Module ${\mathit{E}}_{\mathit{t}}$ [MPa]	Poisson’s Ratio $\mathit{\nu }$	Density $\mathit{\rho }$ [kg/m3]
Prepreg	163,000.0	12,000.0	0.28	1570.0
PEEK	3600.0	-	0.35	1320.0
Polystyrene	3200.0	-	0.35	1021.0
Dyneema	44,000.0	-	-	970.0

, the characteristics of the adopted materials are shown [13,14,15].

2.3. FE Model

An FE model of the vertical tail, based on the previous CAD model, is created to investigate the mechanical behavior. The used software for the pre- and post-processing phases is Simcenter FEMAP 2306. MSC Nastran 2024.1 is employed as solver. Considering their shape, the spars, the external plies of ribs, and the LE and TE tubes are discretized through quadrilateral 2D linear shell elements. A laminate structure is adopted to represent the orthotropic composite material they are made of. In particular, three different properties are created, considering the thickness of plies that characterize these parts. The spar tube supports, the core of ribs, the polystyrene LE/TE parts, and the bracing supports are meshed with parabolic tetrahedral elements, comprising an elastic linear isotropic material. To simulate the bonding between the different parts of the vertical tail, connectors based on glue contact type are implemented in the FE model. This contact type blocks relative displacements between the involved surfaces, allowing the interaction between multiple bodies. The dyneema cable is modeled using rod-type elements with an associated axial stiffness. The direction and the verse of the aerodynamic load only induces tension in the bracing. The assigned value to the stiffness is the result of the expression.

$$K_{rod}={\displaystyle \frac{E·A}{L}}$$

(3)

in which A and L represent the cable section and length, respectively. The cable section is chosen to avoid failures. The lower bracing support and the spar tube supports are constrained in all six degrees of freedom (DOFs). According to the JARUS CS-LUAS regulations, the aerodynamic load L is expressed as follows:

$$\begin{array}{c}L={\displaystyle \frac{1}{2}}\rho V_{fin}^2({cos}^2\beta {cos}^2\alpha +{sin}^2\beta {sin}^2\Gamma +{cos}^2\beta {sin}^2\alpha {cos}^2\Gamma \pm \hfill \\ \hfill 2sin\beta cos\beta sin\alpha cos\Gamma sin\Gamma )S_{VT}·C_{l_{\alpha }}{[arctan({\displaystyle \frac{tan\beta sin\Gamma }{cos\alpha }}\pm tan\alpha cos\Gamma )]}_{rad}\end{array}$$

(4)

where $\rho$ is the air density, $V_{fin}$ is the air velocity impacting the vertical tail, and $C_{l_{\alpha }}$ is the lift coefficient gradient. The sign ± is related to the vertical tail under consideration, i.e., the right or the left empennage. L, acts orthogonally to the vertical tail planform area, and it is the result of the flight conditions, characterized by an angle of attack $\alpha$ and a side-slip angle $\beta$. Depending on the values of $\alpha$, $\beta$, the approximation $sinx\simeq x_{rad}$, $cosx\simeq 1$ can be adopted. An expression of $C_{l_{\alpha }}$ that is consistent with CFD analysis is expressed as follows [16]:

$$\begin{array}{c}\hfill C_{l_{\alpha }}={\displaystyle \frac{\pi }{2}}AR\left[{\displaystyle \frac{1}{rad}}\right]\end{array}$$

(5)

The Equation (5) is reasonable for an aspect ratio $AR$ smaller than 1.5. The vector load in Equation (4) must be added with the lateral gust $F_g$, which is defined as follows:

$$F_g={\displaystyle \frac{1}{2}}\rho V_{fin}{S}_{VT}{\displaystyle \frac{\pi }{2}}AR·K·U_{de}{sin}^2\Gamma$$

(6)

where the projection of empennage in the vertical aircraft plane of symmetry $x_B$− $z_B$ is considered. $U_{de}$ is the intensity of lateral gust, while K is the attenuation gust factor, with a definition that can be found in [11]. A series of load cases are derived according to the regulations; consequently, the loads in Equations (4) and (6) are calculated. The worst-case scenario, in terms of loads, is examined to understand the size of the internal structures of the empennage. It is worth noting that, in the analyzed configuration, the loads, due to the projection of empennage in the horizontal aircraft plane $x_B$− $y_B$, are negligible compared to those of the vertical projection because of the high value of angle $\Gamma$. For structural purposes, the load (4) and (6) must be distributed over the vertical tail area and vector-summed in the directions orthogonal and parallel to the empennage planform area. The lift per unit span is assumed to be located at one quarter chord, and the intensity can be derived by means of the Schrenk method [17,18] which is a semi-graphical approach to calculate $c{C}_l$, with c and $C_l$, which represent the chord and the section lift coefficient, respectively. Then, this parameter is adjusted to take into account the effect of dihedral and swept angles. Therefore, the lift-section distribution is written as follows:

$$\begin{array}{c}\hfill L_{Schrenk}^{\prime }={\displaystyle \frac{1}{2}}\rho V_{fin}^2{\left[c{C}_l\right]}_{\Lambda }cos\Gamma \end{array}$$

(7)

where ${\left[c{C}_l\right]}_{\Lambda }$ represents the lift distribution considering the swept angle. The regulations specify how to distribute gust $L_g^{\prime }\left({\displaystyle \frac{x}{c}}\right)$ along the chord (Figure 4).

The parameter H is derived by imposing the value of $F_g$ calculated through Equation (6). It is easy to demonstrate that the point of application of $L_g^{\prime }\left({\displaystyle \frac{x}{c}}\right)$ is at the quarter chord, and the gust distribution along the span $F_g^{\prime }$ is expressed as follows:

$$\begin{array}{c}\hfill F_g^{\prime }=Hc\end{array}$$

(8)

where c is a function that describes the variation in the chord along the span of the empennage. The span-wise distributions in the orthogonal and parallel directions to the planform vertical tail area are expressed as follows:

$$F_{\perp }^{\prime }=L_{Schrenk}^{\prime }+F_g^{\prime }sin\Gamma$$

(9)

$$F_{\Vert }^{\prime }=F_g^{\prime }cos\Gamma$$

(10)

In the treated case study, $F_{\Vert }^{\prime }$ is negligible compared to $F_{\perp }^{\prime }$. Figure 5 shows the non-dimensional orthogonal force, increased by a factor of 1.5, compared to the non-dimensional span-wise direction. The dimensionless factor includes the maximum values.

The distribution, applied at one-quarter of the chord, is redistributed on each rib and, through RBe3 elements, divided among the elements of the lateral surfaces of the ribs. This way, the load is transmitted to the spars. The load acting on each rib is derived from the following equation:

$$P_{rib}={\int }_{z_i}^{z_{i+1}}{F}_{\perp }^{\prime }dz$$

(11)

where i goes from 0 to 4, and z is the coordinate along the span-wise direction of the vertical tail. $z_1$ and $z_4$ represent the coordinates of the root and tip ribs, while the other $z_i$ describes the coordinate of the middle point between two consecutive ribs. Figure 6 shows the non-dimensional values of the applied forces, dimensionless with respect to the maximum value.

3. Results and Discussion

Figure 7A shows the maximum displacement of the vertical tail with the adoption of the bracing. This permits the reduction in the effect of the gust load, as seen in Figure 7B, in which the bracing cables are absent. Indeed, in the latter case, the maximum displacement is 21.39 mm instead of 3.85 mm. Furthermore, there is also a variation in the trend of displacement along the span-wise direction. Figure 7C reports the maximum stress (23.73 MPa) calculated with the von Mises yield criterion. This value is reached in the bracing upper support. For the chosen material, the yielding strength is equal to 70 MPa. Consequently, the safety factor is ≃2.95. Due to the nature of the CFRP laminate, the adoption of a failure criterion is necessary. Among the available options, the Tsai–Wu criterion is selected, as it can describe complex failure modes under both tension and compression, providing a more accurate prediction of failure behavior under combined loading conditions [19]. The criterion indicates that the material will not fail if the following expression is fulfilled:

$$F_1{\sigma }_1+F_2{\sigma }_2+F_{11}{\sigma }_1^2+F_{22}{\sigma }_2^2+2F_{12}{\sigma }_1{\sigma }_2+F_6{\tau }_{12}+F_{66}{\tau }_{12}^2\le 1$$

(12)

In Figure 7D, the laminate failure index is illustrated; the maximum value is reached in the front spar, at the location where it connects to the support.

Finally, the weights of the innovative structure and of the light-weight classical structure is calculated and compared.

Table 3. Weight comparison.

Structure	Weight [kg]
Light-weight classical	3.47
Innovative proposed	1.10

highlights that the proposed structure results in a saving of almost 70% of the predicted weight.

4. Conclusions

This work presents the design of a vertical tail for a hybrid airship. The aim is to provide guidelines for the design of structures based on parts made of materials such as polystyrene, fabrics, and thermoplastics that can be of great interest for the HAPS. The FE analysis results show that the designed structure can withstand external loads without compromising the shape and the aerodynamic efficiency of the vertical tail. The selected materials and the arrangement of various components enabled the design to meet the constraints that guided the design process. The weight reduction in the vertical tail impacts the overall design of the hybrid airship structure, enabling the reduction in the maximum take-off weight (MTOW). This is in accordance with the environmental sustainability policies that the aviation field is heading towards. The next steps will be the manufacturing phase of the described assembly and the testing of it. The acquired data will be used to validate the FE model, comparing the numerical results with experimental measurements.