Conceptual Design of Hybrid Aerial Vehicle for Venus Exploration

Abstract

The conceptual design of a hybrid aerial vehicle for the exploration of the upper Venus atmosphere is presented. The vehicle will float like a balloon and harvest solar energy which is stored in batteries. The neutral buoyancy reduces the energy consumption and makes the vehicle robust and durable. Energy stored in the batteries can be used for powered flight with good horizontal and vertical mobility to explore aspects of the atmosphere. The vehicle is intended to operate near 55.3 km altitude and to explore the cloud layer of the planet. The vehicle takes its inspiration from the Stingray inflatable wing by Prospective Concepts. Based on a trade study, the wing span was set to 25 m. Equations are developed for the altitude, gas and skin temperature, and skin stress during neutrally buoyant flight. To keep the equations in a simplified analytical form, the complex compartmentalized gas pockets of the vehicle are lumped into a single gas sphere. The equations take into account the volumetric expansion of the structure and the requirement that the differential pressure needs to be large enough to allow for brief periods of powered flight without significant structural deformation. An aerodynamic analysis provides the lift and drag coefficient curves and indicates that the vehicle is pitch-stable. A powered flight analysis shows that an airspeed of 30 m/s can be maintained for 31 min at 55 km and 69 min at 69 km altitude.

1. Introduction

Despite the fact that Venus is Earth’s closest planetary neighbour, the present knowledge of the Venus atmosphere composition and physics is limited. The Venus atmosphere consists mainly of carbon dioxide, CO${}_2$. Dense sulphuric acid clouds obscure the surface and reflect most of the incoming sunlight. The pressure and temperature at 55 km altitude are similar to sea level conditions on Earth [1] and may support life. An improved understanding of the Venus atmosphere could potentially provide new insight into the Earth’s greenhouse effect and long-term climate change on Earth-like planets.

In-situ measurements for the stable layer above the middle clouds at about 50–53.5 km altitude were obtained by the Vega probes in 1985. Horizontal winds in the Venus atmosphere can be as high as 100 m/s. The rotation rate of Venus is the lowest of all planets in the solar system (243 Earth days). As a result super-rotation occurs, which refers to a situation where the wind speed exceeds the equatorial tangential velocity of the planet. An unstable region with strong vertical shear develops at night at an altitude of roughly 63 km. At low latitudes, the unstable region disappears in the morning. At higher latitudes, the unstable region may persist for most of the day. As a result of the extreme surface conditions, the lifetime of Venus landers has been very short [2] and new studies have proposed minimum requirements for future landers [3]. Navigation is challenging as Venus has no magnetic field.

New concepts have been proposed for in-situ measurements of the Venus atmosphere [2,4,5]. Buoyant vehicles such as balloons are robust and resilient, making them well suited for Venus missions. For example, a variable altitude balloon (or aerobot) was proposed by Hall et al. [6] for exploring the atmosphere between 52 and 62 km altitude. To alter the buoyancy of the vehicle (and hence the altitude), helium gas is exchanged between a high-pressure balloon and a zero-pressure balloon. the balloon trajectory was computed with a model by Carlson and Horn [7]. Agrawal et al. [8] proposed a variable altitude balloon-type aerobot that releases ballast and lifting gas to adjust its altitude. The objective is to explore the habitability of the planet’s cloud layer at 48–60 km altitude. Other balloon-type concepts were considered by the 2020 Venus Flagship Mission Study [5]. The general intent of the missions is to investigate the composition, physical processes, and meteorology of the atmosphere. Although balloons offer many advantages (such as simplicity and zero-power requirement for remaining afloat), more manoeuvrable vehicle designs are attractive for an active exploration of the atmosphere. A larger number of researchers investigated solar-powered aircraft for flight in the Venus atmosphere [9,10,11,12,13,14]. For example, Herkenhoff et al. [13] estimated the available solar power and Acosta et al. [14] computed the required wing and thrust loading. Dynamic soaring refers to a flight trajectory that extracts energy from velocity shear and this concept was explored by David [15] and Bullock et al. [16]. The proposed fixed-wing aircraft are often intended for operation above the clouds where the atmospheric conditions are more Earth-like. The large uncertainty with respect to the atmospheric conditions at such altitudes does however raise questions with respect to the stability and control of aircraft. Concepts with aerodynamic lift (that are manoeuvrable such as aircraft) and sufficient buoyancy to maintain altitude when floating, appear to be a good compromise for Venus exploration. They are potentially more resistant to gusts. Vertical or sheer wind gusts could have an effect on hybrid airships; however, they are believed to be less likely on Venus. The main effect would be on the control system, trying to maintain heading. Young et al. [17] proposed a twin-hull Venus airship concept for flight at low altitudes. The Venus atmospheric manoeuvrable platform (VAMP) was designed for operation between 55 and 70 km [18].

This paper addresses the conceptual design of a powered aerodynamic buoyant vehicle with horizontal and vertical mobility. The vehicle geometry was modelled after the Stingray inflatable wing by Prospective Concepts [19,20]. Efficient aerodynamics (low induced drag) make the Stingray efficient (low power consumption) and provide good horizontal and vertical mobility. Of relevance, a stingray-shaped buoyant inflatable flying wing with flapping wings was developed by Festo [21]. To summarize, the buoyant aircraft concept was chosen for the present study, because it offers many advantages over balloons and aircraft such as robustness and resilience (vehicle will not crash if propulsion system fails or vehicle looses flight control), manoeuvrability (compared to balloons), energy efficiency (low power consumption in forward flight), and compactness when deflated (to fit into aeroshell).

The paper is organized as follows: The atmospheric environment at the proposed cruise altitude of 55.3 km is characterized and the envisioned operational strategy is discussed. The vehicle geometry and component mass are discussed and the battery and solar cells are sized. Differential equations for the vehicle altitude and gas temperature are proposed and utilized to investigate the vehicle flight path. The skin thickness is obtained from a stress analysis. The lift, drag, and moment coefficient are computed over a relevant angle of attack range.

Based on the battery charge and airspeed, the maximum powered flight time for two different altitudes are computed. Finally, a brief paragraph outlining steps that can be taken for a more detailed analysis, as well as a summary and conclusions are offered.

2. Mission Environment

The Venus atmosphere density, pressure and temperature for altitudes between z = 50 km and 100 km are plotted in Figure 1. Near 55 km, an altitude of interest to atmospheric scientists [5], the pressure and temperature are similar to Earth at sea level. Therefore, the average cruise altitude for the present conceptual vehicle design was set to 55.3 km. This information is based on the Venus International Reference Atmosphere (VIRA) and other data, as described by Zasova et al. [1]. The data in this reference are provided for different solar latitudes. For the present analysis, the data were averaged over a day–night cycle. This approach is justified for a conceptual design. The solar irradiation, I, is plotted in Figure 1b. The experimental data (symbols) were obtained from Tomasko et al. [22]. The solid line constitutes a fourth-order polynomial fit.

Table 1. Atmospheric conditions and solar irradiation for 55.3 km altitude.

Temperature, T	299 K
Pressure, p	50.1 kPa
Density, $\rho$	0.887 kg/m${}^3$
Solar irradiation, I	318 W/m${}^2$

summarizes the atmospheric conditions and solar irradiation at 55.3 km.

The solar flux in Venus orbit can be as high as 2622 W/m${}^2$ [23]. The dense Venus clouds between 40 km and 70 km altitude reflect more than 75% of the solar radiation back into space [24] and make Venus the planet with the highest albedo, $r_e$, in the solar system. Here, albedo refers to the percentage of reflected solar radiation. For comparison, the albedo is 68.9% for Venus [25] and 43.4% for Earth [26]. The one-third of radiation that is not reflected is absorbed by Venus and remitted as infrared (IR) radiation (153 W/m${}^2$ according to the Spacecraft Thermal Control Book [27]). The IR radiation is absorbed by the clouds and scattered in all directions, including back down towards the surface. This causes a strong greenhouse effect. The clouds of Venus are composed of sulphuric acid and, as a result, all exposed surfaces of atmospheric vehicles need to be corrosion-resistant.

3. Envisioned Operational Strategy

The vehicle will float with the predominant winds and circumnavigate the planet near the equator. The vehicle will pass over the sunlit side and then enter the dark side (see Figure 2). Compared to aircraft, the vehicle will require no power for remaining airborne which will make it robust and tolerant to upset conditions. For flight at an altitude of 55.3 km and a wind speed of ≈60 m/s [28], it will take the vehicle ≈178 h to circumnavigate the planet. This time period must be considered a rough estimate as the uncertainty of the wind velocity measurements is high and the wind velocity will vary depending on environmental factors. To the best of the author’s knowledge, presently no reliable data on wind gusts in the Venus atmosphere are available.

The vehicle will receive direct solar irradiation from above, reflected (albedo) radiation from below, and IR radiation from the surface of the planet, all of which will increase the vehicle temperature. Natural and forced convection (in forward flight) as well as IR radiation from the vehicle into the environment will affect the vehicle temperature. Regarding the convective heat transfer, the skin temperature will increase when the surrounding air is warmer than the vehicle and decrease otherwise. When the vehicle emerges from the dark side, thermal expansion of the buoyant gas, as a consequence of solar heating, will make the vehicle climb. This change in volume will deform the geometry and affect the aerodynamic characteristics of the vehicle during powered flight. To minimize the deformation, the vehicle volume can be split up into buoyant gas pockets such as seen for the Prospective Concepts [20] and Festo [21] vehicles. The detailed analysis can be part of a later more detailed design. Figure 3 illustrates the resulting mission profile.

The vehicle geometry will resemble that of a flying wing. Solar cells will be mounted to the upper wing surface to harvest solar power during day time. The solar power will be stored in a battery and used for propulsion. This will allow the vehicle to change position or climb. The stored power will also be used for scientific measurements, communication and heating of critical components during night time.

4. Vehicle Conceptualization

4.1. Vehicle Geometry

As already mentioned, neutrally buoyant inflatable aerodynamic vehicles, such as the (VAMP) by Northrop Grumman [29], are promising for exploring the Venus atmosphere. Their compactness makes them potentially easier to store in rocket fairings and aeroshells. Planetary entry, inflation, and insertion in the target altitude are not considered in this paper. Inflatable aircraft have a long history that goes back to the Goodyear Inflatoplane of the 1950s. We based our design on the Stingray aircraft of the 1990s by Prospective Concepts [19,20]. The Stingray has a maximum takeoff weight of 840 kg, a maximum airspeed of 36 m/s, a wingspan of 13 m, and a volume of 680 m${}^2$. Based on published photos, we approximated the platform shape and airfoil geometry (Figure 4) and replicated the shapes using the computer-aided design (CAD) software SolidWorks 2021. The airfoil has 23% relative thickness which makes the vehicle voluminous. Artistic impressions of our CAD model are provided in Figure 5. The solar panels are highlighted in black and the propeller is modelled by a disk. Similar to the Prospective Concepts [20] and Festo [21] vehicles the drawings show chord-wise gas pockets that are aligned in the span-wise direction. The necessary supply of buoyant gas could be stored in a carbon-fibre gas tank.

Regarding the internal structure, larger structural members will be based on the tensairity concept (inflatable beams) [30]. A preliminary outline of the main structural members and control surfaces is shown in Figure 6. The ribs will be made from pockets that will be filled with buoyant gas similar to the chambers on parafoils. This will help maintain the airfoil shape of the inflatable wing during flight. The design of the gas pockets can be part of a later more detailed development effort.

4.2. Skin Materials

The skin will be made from a 0.025 mm thick fluorinated ethylene propylene (FEP) layer that is bonded to a 0.1 mm thick Kapton layer. A skin stress analysis shows that this bi-laminate film can withstand the expected maximum stresses without bursting. A similar film was proposed by Hall et al. [6]. To reduce absorption and provide oxidation resistance, the FEP layer is metallized on the back with silver and Inconel. The film has a low absorption and high emission coefficient. With a surface density area of 196 g/m${}^2$ [31,32], the film is relatively lightweight. The properties of the film are summarized in

Table 2. Properties of bi-laminate film.

Surface density, $\mathit{m}/\mathit{A}$ [31,32]	196 g/m${}^2$
Absorption coefficient, ${\alpha }_c$ [6]	0.09
Emission coefficient, $ϵ$ [6]	0.48
Specific heat, $c_p$ [33,34]	1047 J/(kg K)

.

4.3. Vehicle Sizing

The vehicle volume, V, and surface area, $S_f$, were obtained from the CAD model for different wingspans, b. A cubic regression for the volume,

$$V=-2.09\times {10}^{-5}-0.00025b-5.73\times {10}^{-6}{b}^2+0.053b^3,$$

(1)

and a quadratic regression for the surface area,

$$S_f=0.00051-0.00052b+1.16b^2,$$

(2)

were then used to approximate the data points (Figure 7).

The mass of the displaced atmospheric gas is,

$$m_a=V{\rho }_a,$$

(3)

where ${\rho }_a$ = 0.8868 kg/m${}^3$ is the density of the atmosphere at 55.3 km. The density of the buoyant gas, ${\rho }_g$, is obtained using the ideal gas law,

$${\rho }_g=\frac{p_g}{R_{s,g}{T}_g},$$

(4)

where $p_g$ and $T_g$ are the pressure and temperature. We chose helium with a gas constant of $R_{s,g}$ = 2076.9 J/(kg K) as buoyant gas. The mass of the buoyant gas is

$$m_g=V{\rho }_g.$$

(5)

The mass of the vehicle’s skin or film is obtained by multiplying the skin surface area, $S_f$, given by Equation (2), with the film surface density, m/A = 196 g/m${}^2$ (Table 2). The mass of the film is then

$$m_f=S_f\times 2\frac{m}{A}.$$

(6)

In Figure 8, $m_a$ (mass of displaced atmospheric gas), $m_f$ (skin mass), $m_g$ (buoyant gas), and $m_a-m_f-m_g$ (available mass for structure, instruments, battery, motor, etc.) are plotted versus the wingspan, b. For this analysis, $p_g$ and $T_g$ were taken as the atmospheric values, $p_a$ = 50.1 kPa and $T_a$ = 299.1 K at z = 55.3 km. Because of the different scaling of volume ($b^3$) and wing area ($b^2$), the available mass, $m_a-m_f-m_g$, increases sharply with wingspan.

During powered flight with horizontal airspeed u, the stagnation pressure must not exceed the internal pressure to prevent deformation of the wing shape,

$$p_g\ge p_a+\frac{1}{2}{\rho }_a{u}^2.$$

(7)

Keeping the volume constant, the internal gas pressure can be raised by increasing the gas temperature or total mass (see Equation (4)). For the latter case, the available mass will be reduced. These trends are illustrated in Figure 9 for a wingspan of b = 25 m.

From a mission perspective, a low skin mass is desirable as it allows for a larger payload mass or increased buoyancy and thus extended operating altitude range. Based on the previous analysis, we decided on a wingspan of b = 25 m. For this wingspan, the skin mass is $m_f$ = 141.7 kg and the available mass at cruise altitude is 530.1 kg for a total mass of 671.8 kg. This mass is similar to that of earlier missions, such as Venera 7 which had a launch mass of 1180 kg and a landing mass of 500 kg. The volume and surface area for this wingspan are V = 833.4 m${}^3$ and $S_f$ = 722 m${}^2$. The wing aspect ratio is 1.73. The maximum cruise velocity was set to 30 m/s, which is close to the nominal value for the VAMP [29]. From Figure 8, the mass of the displaced gas is $m_a$ = 739 kg, and the mass of the buoyant gas is $m_g$ = 67.2 kg.

4.4. Navigation, Communication, and Science Payload

Data published on the internet and in relevant reports [5,35,36,37] was utilized to estimate the mass of the different components. Necessary devices will include an on-board computer, an inertial navigation system, aerodynamic sensors, and equipment for communicating with a mother-ship in orbit. The science payload will likely include a mass spectrometer, a visible imager, and other cameras. The total mass of the equipment is estimated as 20 kg and the maximum power consumption is estimated as 55 W.

4.5. Solar Panel and Battery Sizing

Assuming that during night time only the navigation and communication instruments are active, the power consumption (on-board computer, inertial navigation system, aero-sensors, radio-communication devices, etc.) is roughly ≈16.7 W [5,35,36,37]. For transit over the dark side of the planet of ≈89 h (see Section 3), this will require E = 5.36 MJ of energy. Assuming that all instruments as well as the science payload are active during daytime, the power will be 55 W [5,35,36,37] and the energy consumed over 89 h will be E = 17.6 MJ. Consequently, a minimum of 23 MJ of energy must be generated while transiting the sunlit side of Venus to carry out a basic balloon-like science mission without powered flight. Since the intent is to actively explore aspects of the atmosphere, provisions are made to harvest a total of 68.9 MJ to allow for powered flight. The power harvested by solar cells is,

$$P_s={\eta }_s{C}_{s}SIsin\left[min\right(\theta ,\pi \left)\right],$$

(8)

where S is the wing platform area (approximated here as $S\approx S_f/2$ = 361 m${}^2$), $C_S$ is the percentage of the wing surface covered by solar cells, and I = 312 W/m${}^2$ is the average irradiation for the chosen cruise altitude (from Figure 1b). The angle $\theta$ is the sun angle with respect to the solar panel. When assuming that the bank and pitch angle are zero and that the solar panel surface is flat, the sun angle only depends on the longitude,

$$\theta =\omega t,$$

(9)

where t is the elapsed time. The angular velocity is,

$$\omega =\frac{u}{R_{planet}+z},$$

(10)

where $R_{planet}$ = 6051.8 km and z = 55.3 km are the radius of Venus and the cruise altitude, respectively. For an assumed wind speed of $u_w$ = 60 m/s, an angular velocity of $\omega$ = $9.82\times {10}^{-6}$ rad/s is obtained. The axial tilt of Venus is only 3 degrees and therefore not considered in this analysis. In Figure 10, the harvested solar power is plotted versus time. Time was normalized by the orbit period, $T_{\mathrm{orbit}}=2\pi /\omega$.

The energy harvested during the transit through the sunlit side is obtained by integration of Equation (8),

$$E={\int }_0^{T/2}{P}_{s}dt=\frac{2{\eta }_s{C}_{s}SI}{\omega }.$$

(11)

The conversion efficiency of flexible polymorphous solar cells can be as high as ${\eta }_s$ = 5 %. For an energy harvest of 68.9 MJ, Equation (11) suggests that the solar cells must cover at least 6% of the wing area, or $C_S=0.06$. Some types of flexible solar cells have density areas as low as 50 g/m${}^2$ [38]. Based on this number, the solar panel mass is estimated as 1.1 kg. To address design uncertainties as well as other issues, such as solar cell degradation and unfavourable sun incidence angles, a larger area of the wing may be covered with solar cells.

A commercial off-the-shelf 23 Ah lithium polymer (LiPo) battery with 22.2 V nominal voltage has a mass of 2.48 kg and can store approximately 510.6 Wh or 1.8 MJ of energy. A total of 38 batteries are required to collect all of the harvested energy. The total mass of the battery pack will then be 38 × 2.48 = 93.7 kg. LiPo batteries can operate over a temperature range of −20 ${}^{\circ }$C to 60 ${}^{\circ }$C. A thermal management system might be needed to ensure that the battery pack temperature remains within the operating range.

5. Thermal and Trajectory Analysis

5.1. Trajectory Model

Starting from the zero-pressure balloon equations by Carlson and Horn [7], differential equations for the altitude, film and gas temperature of pressurized balloons with flexible skin were developed. It is understood that the present analysis does at best provide guidance for the design of a buoyant flying wing. This approach was chosen for the conceptual analysis because the gas pockets of the vehicle have not yet been designed and an analysis in closed analytical form for a complex design with gas pockets is not possible.

5.1.1. Vertical Force Balance

Both buoyancy force and aerodynamic drag are acting in the vertical direction, z (positive up). The drag force is given by,

$$D=\frac{1}{2}{\rho }_a{C}_D\frac{dz}{dt}\left|\frac{dz}{dt}\right|S,$$

(12)

where ${\rho }_a$ is the density of the outside gas and S is the platform area. As the vertical motion is normal to the platform area, the drag coefficient is $C_D\approx 1$ (i.e., bluff body drag). The forces acting on the vehicle result in a vertical acceleration,

$$(m_t+C_m{\rho }_{a}V)\frac{d^{2}z}{d{t}^2}=g({\rho }_{a}V-m_t)-\frac{1}{2}{\rho }_a{C}_D\frac{dz}{dt}\left|\frac{dz}{dt}\right|S,$$

(13)

with total mass,

$$m_t=m_g+m_f+m_{P+S},$$

(14)

and gravitational acceleration, g = 8.7 m/s${}^2$. The combined payload and structure mass is $m_{P+S}$ = 470 kg and the virtual mass coefficient is $C_m=1$ [39]. The vehicle volume, V, is made up of the buoyant gas volume, $V_g$, and the components and structure volume. To simplify the analysis, the latter is neglected, and the gas volume is computed as,

$$V=V_g=\frac{m_g{R}_{s,g}{T}_g}{p_g}.$$

(15)

5.1.2. Volume Change

The outside air pressure decreases with altitude. If the inside gas pressure remains constant, during a climb the pressure difference, $\Delta p=p_g-p_a$, will increase. To allow for an analysis in closed analytical form, the skin is assumed to be a sphere with an equivalent radius of

$$R=\sqrt{\frac{3V}{4\pi }}.$$

(16)

As part of a more detailed design, this admittedly rather crude model could be replaced by a finite-element analysis for the actual geometry with gas pockets. The Laplace law for a thin-walled sphere provides the wall stress,

$${\sigma }_w=\Delta p\frac{R}{2t},$$

(17)

based on the wall thickness, t. From Hooke’s law,

$${\sigma }_w=Eϵ,$$

(18)

where E is Young’s modulus and

$$ϵ=\frac{\Delta r}{R},$$

(19)

is the strain. For the present analysis, the Young’s modulus was taken as E = 2.08 GPa (average for FEP and Kapton (see Section 6)). Equations (17)–(19) can be combined to

$$E\frac{\Delta r}{R}=\Delta p\frac{R}{2t}.$$

(20)

Then, the change in radius due to the pressure difference is

$$\Delta r=\Delta p\frac{R^2}{2Et},$$

(21)

and the equivalent volume is

$$V=\frac{4}{3}\pi {(R+\Delta r)}^3.$$

(22)

5.1.3. Heat Balance for Film

The film temperature, $T_f$, changes according to

$$m_f{c}_{p,f}\frac{d{T}_f}{dt}=\frac{d{Q}_f}{dt},$$

(23)

where $m_f$ and $c_{p,f}$ are the mass and heat capacity of the film, respectively, and

$$\begin{array}{ccc}\hfill \frac{d{Q}_f}{dt}& =& S\left[\underset{\begin{array}{c}\mathit{incoming}\mathit{solar}\\ \mathit{radiation}\mathit{and}\mathit{albedo}\end{array}}{\underbrace{I{\alpha }_c(1+r_e)}}+\underset{\begin{array}{c}\mathit{radiative}\mathit{and}\mathit{convective}\mathit{heat}\\ \mathit{transfer}\mathit{with}\mathit{buoyant}\mathit{gas}\end{array}}{\underbrace{2ϵ\sigma (T_g^4-T_f^4)+2h_g(T_g-T_f)}}\right.\hfill \\ & +& \left.\underset{\begin{array}{c}\mathit{convective}\mathit{heat}\mathit{transfer}\mathit{with}\\ \mathit{atmosphere}\mathit{and}\mathit{radiation}\mathit{to}\\ \mathit{outside}\end{array}}{\underbrace{2h_a(T_a-T_f)-2ϵ\sigma T_f^4}}+\underset{\mathit{Venus}\mathit{radiation}}{\underbrace{ϵ\sigma T_{BB}^4}}\right]\hfill \end{array}$$

(24)

is the heat flux to and from the film. Positive terms in Equation (24) signify incoming thermal fluxes and negative terms signify outgoing thermal fluxes. In Equation (24), I is the solar irradiation (Figure 1b), ${\alpha }_c=0.09$ is the absorption coefficient, $r_e=0.689$ is the albedo, $ϵ=0.48$ is the infrared radiation emissivity, $\sigma$ = $5.67\times {10}^{-8}$ W/(m${}^2$K${}^4$) is the Stefan–Boltzmann constant, $h_g$ and $h_a$ are the convective heat transfer coefficients from the film to the buoyant gas and the atmosphere, respectively, and $T_{BB}$ = 226.6 K is the black body temperature of Venus. All terms for which both the top and bottom surface contribute, scale with two times the platform area. The effect of the solar panel on the absorption and emission coefficient is neglected.

5.1.4. Convective Heat Transfer

During unpowered buoyant flight, the forced convective heat transfer is assumed to be zero and only natural convection is considered. The heat transfer coefficient from the film to the outside atmosphere is given by [40],

$$h_a=\frac{k_{a}Nu}{2R}.$$

(25)

The CO${}_2$ thermal conductivity is obtained from Sutherland’s law [41],

$$k_a=k_0{\left(\frac{T_a}{T_0}\right)}^{3/2}\frac{T_0+S_k}{T_a+S_k},$$

with $k_0$ = 0.0146 W/(mK), $T_0$ = 273 K, and $S_k$ = 1800 K [41]. In addition, R is the radius associated with the vehicle volume (see Equation (16)). Churchill et al. [42] provided a relationship for the Nusselt number,

$$Nu=2+\frac{0.589R{a}^{\frac{1}{4}}}{{\left[1+{\left(\frac{0.43}{P{r}_a}\right)}^{\frac{9}{16}}\right]}^{\frac{4}{9}}}.$$

(26)

The Prandtl number for CO${}_2$ is $P{r}_a$ = 0.726 and the Rayleigh number is,

$$Ra=GrP{r}_a,$$

(27)

with Grashof number,

$$Gr=\frac{g\beta (T_f-T_a){\left(2R\right)}^3}{{\nu }_a^2}.$$

(28)

The thermal expansion coefficient is computed as $\beta =1/(T_f-T_a)$. The dynamic viscosity of CO${}_2$ is obtained from Sutherland’s law,

$${\mu }_a={\mu }_0{\left(\frac{T_a}{T_0}\right)}^{3/2}\frac{T_0+S_{\mu }}{T_a+S_{\mu }},$$

(29)

with ${\mu }_0$ = $1.370\times {10}^{-5}$ Ns/m${}^2$, $S_{\mu }$ = 222 K, and $T_0$ = 273 K [41]. The kinematic viscosity is obtained from ${\nu }_a={\mu }_a/{\rho }_a$. The thermal conductivity and kinematic viscosity of helium are obtained from curve fits of published data over a relevant range of temperatures. The Prandtl number is taken as $P{r}_g=0.71$ and held constant.

5.1.5. Heat Balance for Lifting Gas

The temperature of the buoyant helium gas, $T_g$, changes according to

$$\frac{d{Q}_g}{dt}=S\left[\underset{\begin{array}{c}\mathit{radiative}\mathit{and}\mathit{convective}\mathit{heat}\\ \mathit{transfer}\mathit{with}\mathit{film}\end{array}}{\underbrace{-2ϵ\sigma (T_g^4-T_f^4)-2h_g(T_g-T_f)}}\right].$$

(30)

For the analysis it is assumed that the vehicle is not moving in the horizontal direction relative to the atmosphere. Therefore, in accordance with analyses for zero-pressure balloons (e.g., Carlson and Horn [7]) only natural convection is considered. The gas pressure is kept above the ambient pressure to allow for short segments of powered flight at a maximum airspeed of u,

$$p_g=p_a+\frac{1}{2}{\rho }_a{u}^2.$$

(31)

The change of the gas pressure is,

$$d{p}_g=d{p}_a+\frac{1}{2}{u}^{2}d{\rho }_a,$$

(32)

where the density derivative can be substituted with the ideal gas law,

$$d{p}_g=d{p}_a+\frac{1}{2}{\rho }_a{u}^2\left(\frac{d{p}_a}{p_a}-\frac{d{T}_a}{T_a}\right).$$

(33)

Making use of the expression for the change in atmosphere hydrostatic pressure, $p_a=-{\rho }_{a}gz$,

$$d{p}_g=\left(1+\frac{\frac{1}{2}{\rho }_a{u}^2}{p_a}\right)(-{\rho }_{a}gdz)-\frac{1}{2}{\rho }_a{u}^2\frac{d{T}_a}{T_a}$$

(34)

is obtained. The specific volume of the buoyant gas is,

$$\frac{1}{{\rho }_g}=\frac{R_{s,g}{T}_g}{p_g},$$

(35)

and the change of the specific volume is,

$$d\left(\frac{1}{{\rho }_g}\right)=\frac{1}{{\rho }_g}\left(\frac{d{T}_g}{T_g}-\frac{d{p}_g}{p_g}\right).$$

(36)

The first law of thermodynamics for the buoyant gas can then be formulated,

$$d{q}_g=c_{v,g}d{T}_g+\frac{p_g}{{\rho }_g}\left(\frac{d{T}_g}{T_g}-\frac{d{p}_g}{p_g}\right),$$

(37)

where $c_{v,g}$ is the specific heat at constant volume. Substitution of Equation (34) into Equation (37) gives,

$$d{q}_g=c_{v,g}d{T}_g+R_{s,g}{T}_g\left[\frac{d{T}_g}{T_g}+\left(1+\frac{\frac{1}{2}{u}^2}{R_{s,a}{T}_a}\right)\frac{{\rho }_a}{{\rho }_g}\frac{gdz}{R_{s,g}{T}_g}+\frac{{\rho }_a}{{\rho }_g}\frac{\frac{1}{2}{u}^2}{R_{s,g}{T}_g}\frac{d{T}_a}{T_a}\right].$$

(38)

Differentiation with respect to time and rearranging terms, Equation (38) becomes,

$$\frac{d{q}_g}{dt}=c_{v,g}\frac{d{T}_g}{dt}+R_{s,g}\frac{d{T}_g}{dt}+\left(1+\frac{\frac{1}{2}{u}^2}{R_{s,a}{T}_a}\right)\frac{{\rho }_a}{{\rho }_g}g\frac{dz}{dt}+\frac{{\rho }_a}{{\rho }_g}\frac{\frac{1}{2}{u}^2}{T_a}\frac{d{T}_a}{dt}.$$

(39)

This equation can be further simplified by making use of $c_{p,g}=c_{v,g}+R_{s,g}$ and substitutions for the vertical velocity,

$$v=\frac{dz}{dt},$$

(40)

and,

$$\frac{d{T}_a}{dt}=\frac{d{T}_a}{dz}\frac{dz}{dt}=\frac{d{T}_a}{dz}v.$$

(41)

Equation (39) then becomes

$$\frac{d{q}_g}{dt}=c_{p,g}\frac{d{T}_g}{dt}+\left(1+\frac{\frac{1}{2}{u}^2}{R_{s,a}{T}_a}\right)\frac{{\rho }_a}{{\rho }_g}gv+\frac{{\rho }_a}{{\rho }_g}\frac{\frac{1}{2}{u}^2}{T_a}\frac{d{T}_a}{dz}v.$$

(42)

This equation is combined with Equation (30) to obtain

$$\frac{d{q}_g}{dt}=\frac{1}{m_g}\frac{d{Q}_g}{dt}=c_{p,g}\frac{d{T}_g}{dt}+\frac{{\rho }_a}{{\rho }_g}\left[g+\frac{\frac{1}{2}{u}^2}{T_a}\left(\frac{g}{R_{s,a}}+\frac{d{T}_a}{dz}\right)\right]v.$$

(43)

For this approach, the amount of helium gas inside the vehicle has to be adjusted as will be shown later.

For $u=0$, Equation (43) simplifies to

$$\frac{1}{m_g}\frac{d{Q}_g}{dt}=c_{p,g}\frac{d{T}_g}{dt}+\frac{{\rho }_a}{{\rho }_g}gv=c_{p,g}\frac{d{T}_g}{dt}+\frac{p_a{\mathcal{M}}_a{T}_g}{p_g{\mathcal{M}}_g{T}_a}gv.$$

(44)

with molar masses ${\mathcal{M}}_a$ and ${\mathcal{M}}_g$. Assuming $p_g=p_a$, the expression for the zero-pressure balloon [7] is recovered,

$$\frac{1}{m_g}\frac{d{Q}_g}{dt}=c_{p,g}\frac{d{T}_g}{dt}+\frac{{\mathcal{M}}_a{T}_g}{{\mathcal{M}}_g{T}_a}gv.$$

(45)

The present model is built on simplifying assumptions. By definition, the solar array will absorb most of the impinging sunlight. Only a small portion of the absorbed sunlight will be converted to electricity. The rest is rejected as infrared heat which will heat up the airship and gas. Inefficiencies of the components within the airship also cause heating. If no thermal system is used to reject the waste heat, it will raise the equilibrium temperature of the airship and lifting gas. These effects have to be included in a more complete analysis.

5.2. Results

To obtain the vehicle trajectory over a complete orbit, Equations (13), (23) and (43) were integrated numerically with the implicit Euler backward scheme. The computational time step was $\Delta t$ = 10 s. Two cases were investigated: For the first case (variable mass), Equation (43) was solved and for the second case (fixed mass), Equation (44) was solved. The initial conditions were z = 55 km and $T_g$ = $T_f$ = 250 K for the first case and 55.3 km and $T_g$ = $T_f$ = 235.4 K for the second case. The combined structural and payload mass was set to $m_{P+S}$ = 520 kg. The pressure differential to the outside was chosen large enough to allow for cruise at u = 30 m/s (see Equation (7)).

5.2.1. Case 1: Variable Mass

Results obtained from Equation (43) for one orbit are illustrated in Figure 11. The film and gas temperature are directly related to the solar irradiation (Figure 11a). Because the film is very thin, the film temperature is very close to the gas temperature. During daytime, the vehicle climbs by a small amount and, as a result, the outside atmospheric temperature, pressure and density do not change much (Figure 11b). As expected, the inside gas pressure is $0.5{\rho }_a{u}^2$ above the outside atmospheric pressure. Buoyant gas has to be removed (about 3 kg per orbit) to regulate the inside gas pressure during the climb (Figure 11c). Gas also has to be removed during the descend. A practical approach for removing lifting gas is to pump it back into a gas tank. Alternatively, helium can be dumped into the atmosphere and then replenished from a gas tank which would, however, shorten the mission time. During the transit through the night, all variables remain constant.

5.2.2. Case 2: Fixed Mass

Releasing helium gas during each orbit reduces the total mission time. The cycling of helium between a reservoir tank and the vehicle requires a high-pressure pump which may not be practical or incur a mission penalty. Therefore, based on Equation (44) a scenario with constant amount of buoyant gas was analysed as well. Figure 12 shows results for one orbit.

Compared to case 1, the vehicle climbs up higher in the atmosphere (Figure 12a). As a result, the outside temperature as well as pressure and density drop more than for case 1 (Figure 12a,b). The difference between the inside and outside pressure remains large enough to satisfy Equation (7). As the vehicle climbs, the volume extends but the gas mass remains constant (Figure 12c).

6. Skin Stress Analysis

An annotated drawing of the bi-laminate skin material is provided in Figure 13. Assuming negligible surface curvature, when a force F is applied, the elongation, $\Delta l$, of the two layers and the strain, $ϵ=\Delta l/l_0$, will be identical. The force F is represented as the sum of two independent stresses ${\sigma }_1$ and ${\sigma }_2$ multiplied by the corresponding cross sectional areas $A_1$ and $A_2$,

$$F={\sigma }_1{A}_1+{\sigma }_2{A}_2.$$

(46)

The force F can also be represented as an average stress $\overline{\sigma }$ multiplied by the total cross sectional area of the bi-laminate film,

$$F=\overline{\sigma }(A_1+A_2).$$

(47)

By equating the two expressions for the force, the relation

$${\sigma }_1{A}_1+{\sigma }_2{A}_2=\overline{\sigma }(A_1+A_2)$$

(48)

is obtained. With the definition of axial stress, $\sigma =Eϵ$, where E is Young’s modulus, an average Young’s modulus for the bi-laminate film can be computed,

$$\overline{E}=\frac{E_1{A}_1+E_2{A}_2}{A_1+A_2}.$$

(49)

To prevent bursting of the skin, the stress in each layer needs to be kept below the material yield strength. The yield stress is 12 MPa for FEP [31] and 69 MPa for Kapton [32]. Based on Equation (17), the stress in the vehicle skin, $\overline{\sigma }$, was evaluated over one full orbit for both cases. The individual stresses were computed from $ϵ=\overline{\sigma }/\overline{E}$, ${\sigma }_1=E_1ϵ$, and ${\sigma }_2=E_2ϵ$.

We chose a 0.025 mm thick layer of FEP bonded to a 0.1 mm thick layer of Kapton. For case 1, the differential pressure, $p_g-p_a$, is constant and the stress is 1.85 MPa in the FEP material and 11.1 MPa in the Kapton. These values are well below the yield stress. For case 2, the differential pressure changes and the stress reaches a maximum of 11.2 MPa for the FEP and 66.9 MPa for the Kapton (Figure 14). Both values are high but below the yield stress. Ultimately, the present analysis provides initial guidance for a more detailed design. An accurate skin stress analysis for the actual skin geometry (and internal chambers or pockets similar to parafoils) will have to rely on finite element analysis and incorporate safety factors to account for uncertainty with regard to the atmospheric conditions (e.g., wind gusts).

7. Aerodynamic Analysis

The vehicle will be equipped with a propeller for powered flight (Figure 5 and Figure 6). Aerodynamic analyses were performed with XFLR5 and VSPAERO (part of the NASA open vehicle sketch pad, OpenVSP). The atmospheric conditions were obtained from VIRA. At 55.3 km altitude, the atmospheric density is ${\rho }_a$ = 0.887 kg/m${}^3$ and the dynamic viscosity is ${\mu }_a$ = $1.49\times {10}^{-5}$ Ns/m${}^2$. For an assumed airspeed of u = 30 m/s and mean aerodynamic chord of c = 16.11 m, the flight Reynolds number is $Re$ = $29\times {10}^6$.

7.1. Two-Dimensional Airfoil Section

The two-dimensional Stingray airfoil (see Figure 4) was analysed with XFLR5. The lift curve in Figure 15a has an almost constant slope between −10 and +5 degrees angle of attack. The zero-lift angle of attack is $\alpha \approx$−2 degrees. For $\alpha \approx$ 2.5 degrees, the lift coefficient is $C_l\approx 0.5$, and the drag coefficient is $C_d\approx 0.006$ (Figure 15b). Lift-drag polars for different Reynolds numbers are provided in Figure 15c. A low-Reynolds number effects result in a considerable drag increase for the smallest Reynolds number.

7.2. Three-Dimensional Vehicle

The geometries for the three-dimensional analysis in XFLR5 and VSPAERO are slightly different from each other (see Figure 16) but similar to that of the Stingray vehicle by Prospective Concepts [19,20]. Prospective Concepts carried out over 300 successful flight tests with the Stingray, giving us the confidence that the aerodynamics were sound.

VSPAERO provides the span-wise lift distributions, $d{C}_L/db$ (Figure 17a). The lift distributions peak near the wing tips and generally increase with the angle of attack, $\alpha$. A contour plot of the wall pressure coefficient, $C_p$, for the top surface at $\alpha$ = 2 degrees is shown in Figure 17b. The pressure is increased at the leading edge and reduced over much of the top surface.

The lift, drag, and moment coefficient obtained from XFLR5 and VSPAERO are plotted in Figure 18. In the figure, “VLM” refers to vortex lattice method and “Panel” refers to panel method. For the inviscid method, the boundary layers are disregarded. Both XFLR5 and VSPAERO predict a zero-lift angle of attack around ${\alpha }_0$ = −2 degrees. The lift coefficient slope and drag coefficient are smaller for VSPAERO compared to XFLR5. Both programs predict a negative moment coefficient slope, $d{C}_M/d\alpha <0$, which is required for the pitch stability of flying wings. Higher-fidelity computational fluid dynamics (CFD) approaches and/or wind tunnel experiments would allow us to evaluate the quality of the VSPAERO and XFLR5 results. A summary of some of the relevant aerodynamic parameters is provided in

Table 3. Aerodynamic parameters from VSPAERO.

Zero lift angle of attack, ${\mathit{\alpha }}_0$	−1.906 $\mathit{d}\mathit{e}\mathit{g}$
Drag coefficient at zero lift, $C_{D,C_L=0}$	0.00684
Lift coefficient at $\alpha$ = 10 degrees, $C_{L,\alpha =10\mathrm{degrees}}$	0.362
Drag coefficient at $\alpha$ = 10 degrees, $C_{D,\alpha =10\mathrm{degrees}}$	0.0277
Lift coefficient slope, $d{C}_L/d\alpha$	0.0399
Moment coefficient slope, $d{C}_M/d\alpha$	−0.0129

. The low lift coefficient slope can be explained by the low aspect ratio of only 1.9. The buoyancy requirement (large volume, thick airfoil, large mean aerodynamic chord, low aspect ratio) competes with the requirement for good aerodynamics (thin airfoil, large aspect ratio). The present design is a compromise between the two.

7.3. Powered Flight Analysis

The vehicle is intended to allow for dirigible powered flight. For the following analysis, the horizontal airspeed, u, is relative to the surrounding atmosphere which is moving with an unknown wind speed. Based on the results from the aerodynamic analysis (Section 7), the power required for straight and level neutrally buoyant flight at constant altitude (case 1) and the altitude and airspeed for flight with aerodynamic lift (case 2) were determined based on an available battery charge of E = 68.9 MJ. Higher performance can be achieved if the battery size is increased. The present analysis is preliminary in nature and only serves as a proof of concept. A deeper analysis that includes inefficiencies in power generation, charging and discharging, propulsion, etc., will be required for a more detailed vehicle design.

7.3.1. Case 1: Straight and Level Neutrally Buoyant Flight at Constant Altitude

For the following analysis, the vehicle is assumed to be neutrally buoyant and to cruise with a horizontal velocity, u, relative to the wind at 55.3 km. No lift is generated and as a result, the lift-induced drag is zero. To simplify the analysis, the effect of convective cooling on the gas temperature and thus buoyancy is neglected. The required power for straight and level flight at constant altitude is,

$$P_{req}=\frac{1}{{\eta }_p}Du=\frac{1}{{\eta }_p}{C}_{D,C_L=0}\frac{1}{2}{\rho }_a{u}^{3}S.$$

(50)

where ${\eta }_p=0.8$ is the assumed propulsive efficiency and ${\rho }_a$ = 0.8868 kg/m${}^3$ is the atmospheric density at cruise altitude. The drag coefficient is normalized by the platform area, S. The viscous drag coefficient at zero lift is obtained from the VSPAERO analysis, $C_{D,C_L=0}$ = 0.00684. As a “sanity check”, the drag coefficient was also computed based on an average skin-friction coefficient,

$$C_{D,C_L=0}=2C_{fr}.$$

(51)

Based on a correlation from Corke [43],

$$C_{fr}=\frac{0.455}{{\left(lo{g}_{10}Re\right)}^{2.58}},$$

(52)

where $C_{D,C_L=0}=$ 0.00509 is obtained for $Re=29\times {10}^6$. The difference between this number and the drag coefficient from VSPAERO is ≈34%. Therefore, the present results were based on the VSPAERO drag coefficient. The vehicle can cruise until the battery is completely drained, resulting in a flight time of

$$t_{flight}=\frac{E}{P_{req}}.$$

(53)

In Figure 19a, the required power and maximum flight time are plotted over the airspeed (i.e., the velocity relative to the wind). Flight at 30 m/s requires a power of 36.7 kW and can be sustained for around 31.2 min. The power consumption for lower airspeeds is less, thus allowing for longer flight times. For a more detailed analysis, the energy required for the acceleration to cruise speed can be included in the analysis.

7.3.2. Case 2: Altitude and Airspeed for Flight with Aerodynamic Lift

The lift force adds to the buoyancy force. The combined force is balanced by the weight of the skin, structure, and payload,

$$gV({\rho }_a-{\rho }_g)+\frac{1}{2}{\rho }_a{u}_{max}^2{C}_{L,\alpha =10\mathrm{degrees}}S=g(m_f+m_{P+S}).$$

(54)

For this analysis, the buoyant gas density and volume of the vehicle during the case 2 night flight at 55.3 km are held constant (i.e., ${\rho }_g$ = 0.1033 kg/m${}^3$ and V = 844.6 m${}^3$). The maximum lift force is obtained at the maximum airspeed, $u_{\max }$, and maximum lift coefficient, $C_{L,\max }$. Since the maximum lift coefficient is unknown, the value predicted by VSPAERO for $\alpha$ = 10 degrees was chosen, $C_{L,\alpha =10\mathrm{degrees}}=0.362$. For the following analysis, $m_{P+S}$ = 520 kg was assumed. The density of the atmosphere, ${\rho }_a$, decreases with altitude. This reduces the buoyancy force and the lift force. Assuming unaccelerated flight (thrust equals drag), Equation (50) can be used to obtain the maximum airspeed, $u_{\max }$, if $P_{req}$ is replaced by the maximum power, $P_{\max }$, and the drag coefficient (base drag and lift-induced drag) for $\alpha$ = 10 degrees is used, $C_{D,\alpha =10\mathrm{degrees}}=0.0277$. The power depends on the flight time via $P_{\max }=E/t_{\mathrm{flight}}$. The set of equations is solved for $u_{\max }$ and ${\rho }_a$ and the corresponding altitude is taken from Figure 1a. In Figure 19b, the altitude and airspeed are plotted versus the flight time. If all stored energy is consumed over 69 min, the vehicle can sustain an airspeed of ≈30 m/s in straight and level flight at an altitude of ≈69.2 km (≈13.9 km above neutrally buoyant altitude). Lower battery discharge rates increase the flight time but reduce the ceiling and maximum airspeed. The energy required for the climb from the cruise altitude to the higher altitude was not considered and can be included in a more detailed analysis.

8. Future Analysis

The present analysis is based on many simplifying assumptions. To assess the feasibility of the proposed vehicle with greater certainty, a more detailed design and first-principles-based analysis will be required. The external skin geometry and internal chambers or pockets will need to be designed. The operating environment (wind gusts, solar radiation, etc.) and aerodynamic loads have to be characterized with greater certainty. For the thermal analysis, the solar cells have to be included. The internal structure of the vehicle has to be designed. Both the skin and internal structure under load will have to be analysed with finite element analysis. The margin for the onset of the fluid–structure interaction, which can lead to flutter of the skin during powered flight, has to be investigated. The propulsion system has to be designed and analysed. This list is by no means exhaustive. Many other areas will have to be addressed and offer exciting opportunities for future research.

9. Conclusions

A buoyant flying wing vehicle is proposed for the exploration of the upper Venus atmosphere. This vehicle shares positive attributes of both balloons (simplicity, robustness) and aircraft (manoeuvrability). The vehicle geometry is similar to that of the Stingray by Prospective Concepts. Based on a sizing analysis, the wingspan was set to 25 m. For this size, it is expected that the deflated vehicle fits into the aeroshell of a typical launcher. The available combined structure and payload mass is 520 kg. Solar cells mounted to the upper surface of the wings will produce sufficient power for operation during transit through the night and for powered flight. Differential equations for the altitude, as well as skin and gas temperature, were developed and solved numerically. If helium is pumped back into a storage tank or dumped overboard during each orbit, the altitude can be maintained better, but the mission time is shortened. Therefore, the decision was made to maintain a constant helium mass. The vehicle will then climb and descend by about 500 m during each orbit. A stress analysis shows that a skin made from a 0.025 mm thick fluorinated ethylene propylene film that is bonded to a 0.1 mm thick Kapton film will be strong enough. An aerodynamic analysis was performed to obtain the lift, drag, and moment coefficient distributions. The moment coefficient slope was found to be negative, which is a requirement for tailless flying wings. If all solar energy harvested over one day is spent, neutrally buoyant powered flight at 30 m/s can be sustained for about 31.2 min at 55.3 km. Assuming that the volume and amount of buoyant gas remain the same, the vehicle can fly at 30 m/s for 69 min at an altitude of 69.2 km. A more detailed analysis, that includes the energy required for acceleration and climb as well as the energy consumed by the instruments and thermal management, is required for sizing the battery pack and solar panels. Future work will focus on a more detailed analysis of the aerodynamics and propulsion system and wind tunnel testing of a scaled model of the inflatable wing.