Min Chang1,2, Zhou Zhou1, Rui Wang1, Xiaoping Xu1 1 Science and Technology on UAV Laboratory, Northwestern Polytechnical University 2 Xi’an Institute of Modern Control Technology

Keywords: Solar-powred UAV, , design methodology, energy performance

Abstract A design methodology for configuration sizing 1 General Introduction of -powered UAVs is established, which could be equally applied to all configurations The has attracted many researchers capable of year-round operations in the in the last 40 years due to its clearness and stratosphere at low and middle latitudes. In eternity for high altitude long endurance (HALE) general, the configurations are classified into unmanned aerial vehicles (UAV). Solar- two representative types—the conventional and powered UAVs show their superiorities in the the wing-sail. The wing-sail configuration civil or military fields. Higher altitude means employs sail tails that can rotate around wider covering area of interest and higher individual roll axes to maximize solar energy survivability, and longer endurance means more absorption, and photovoltaic (PV) modules are timely intelligence and information. coupled to the wing and only one side of each References[1-3] mainly focused on sail tail. The configuration sizes are treated as traditional design processes of solar-powered key design variables, including wingspan, airplanes and validated the feasibility of solar- ratio of wing, and area ratio of sail tails powered flight. Bailey[4] generally discussed to the wing. component parameters determination, presented The established methodology mainly and analyzed a high-altitude solar-powered contains two parts. The first part parameterizes platform for a proposed mission. Steven[5] energy absorption and energy consumption, studied the energy characteristics for solar- mass components and aerodynamic efficiency. powered flying wing, tandem wing and airship The second part employs an optimal approach under the constraint of energy balance. to obtain a group of optimized solutions. Then, Romeo[6, 7] carried out research activities on the methodology is applied to analyze HALE platforms to achieve persistent conceptual parameters at different latitudes for operations for several months in the northern both configurations. Finally, a solar powered latitudes of 36°~45° at the altitudes of 15~20 stratospheric UAV concept of wing-sail km in Europe. Noth[8] developed a conceptual configuration, PoXiao, is proposed for year- design methodology, and successfully achieved round operation at middle latitudes. Its energy continuous flight of 27 h by solar-powered Sky- performance is investigated to validate the Sailor near the solstice at the latitude of operational altitude and latitude capabilities 44 °N in 2008. Rizzo[9] proposed a throughout a whole year and demonstrate the mathematical model for conceptual design and utility of the design methodology. The compared 4 representative configurations based characteristics of stability and control for the on energy characteristics. Comprehensively wing-sail configuration is also preliminary speaking, these design methodologies above are analyzed. merely focused on continuous operation near

1 Min Chang, Zhou Zhou, Rui Wang, Xiaoping Xu

the equator or continuous flight for a single day proposed the configurations which incorporated or several weeks at higher latitudes when the rotatable -trackers into solar-powered solar radiation is rich, and are scarcely focused airplanes of conventional configuration to on year-round operation at higher latitudes. In achieve longer flight duration at higher latitudes. the history of solar-powered flight, solar- However, they did not systematically present powered and Zephyr respectively the methods for sizing the wing and non- produced records of absolute altitude of 29,531 horizontal sun-trackers. Ref. [15] also proves m for 4 hours on August 13, 2001 in Hawaii the superiorities of sun-trackers with variable (18 °N) [10] and endurance of 336 hours from orientations when applied to high-altitude solar- 15 km to 18 km in July 23, 2010 in Yuma powered UAVs at wide latitudes. (32 °N) verified by Fédération Aéronautique In general, the configurations for solar- Internationale. Their PV modules are both powered airplanes can be categorized into two horizontally mounted only on their wings representative types—the conventional and the conventionally. With conceptual parameters of wing-sail, as shown in Fig.2. For the flying-wing Helios prototype (HP01) from Ref. conventional, PV modules are mainly [10], Fig. 1 shows its achievable persistent horizontally disposed on the wing. For the altitudes from low to middle latitudes wing-sail, a portion of PV modules is throughout a whole year. horizontally disposed as the conventional, and 20 the rest are mounted on the sail tails that can

16 rotate around body axes. The conventional is a 0° special case of the wing-sail when the total area 12 10°N of sail tails is zero, and the all-wing design like 20°N 8 30°N Helios with no fuselages and tails belongs to the 40°N conventional. 4 60°N


Achievable Persistent Altitude (km) Altitude Persistent Achievable 0 0 50 100 150 200 250 300 350 Day from Jan. 1 Fig. 1 Persistent altitude capability of the Helios prototype (HP01) The HP01 could fly continuously within the region bounded by each curve and the (y = 0). It is obvious that the HP01 could not maintain station keeping at high altitudes and higher latitudes during the months. It is due to the fact that both the solar elevation on average and the day length near winter decrease with increasing latitude, leading to the decreasing of the solar in the projected on a surface disposed horizontally, i.e. Fig. 2 Perspective views of exemplary embodiments of on the wing[11, 12]. It is also the key reason conventional and wing-sail configurations why to date solar-powered UAVs with PV Thus, this paper aims to define a modules only mounted on the wing have limited mathematical model of design methodology for operational values, especially at high altitudes configuration sizing of solar-powered and higher latitudes near winter. stratospheric UAVs for year-round mission Inspired by the solar collector “tracking” requirements from low to middle latitudes. This the Sun to minimize the angle of incidence of design methodology is under the constraints that beam radiation on the surfaces with PV modules, energy consumption is balanced by energy Keidel[13] from Germany and Gerald[14] from absorption within the daytime, the nighttime and the Boeing Company both innovatively a whole day of 24 hours. As to energy

2 A GENERAL DESIGN METHODOLOGY FOR YEAR-ROUND SOLAR POWERED STRATOSPHERIC UAVS FROM LOW TO MIDDLE LATITUDES absorption, area density of PV modules is airplane. The solar-powered airplane does not modeled, considerations including PV modules’ change its weight in operation. In general, the orientation, thermodynamics of PV modules, total weight can be divided into eight parts. propagation of solar radiation, flight direction, Equation (1) summaries the total-weight buildup: operational altitude, operational latitude, mtot m pld  m af  m pm  m mppt  different , etc. As to energy consumption, (1) m m  m  m each mass component is parameterized and bat p av lg aerodynamic efficiency model based on Here mpld, maf, mpm, mmppt, mbat, mp, mav and mlg configuration parameters is built. Besides, represent the mass of payload, airframe Quantum-Behaved Particle Swarm (QPSO) structure, PV modules, MPPT, secondary algorithm and Kriging surrogate model are batteries, propulsion systems, avionics and employed to achieve an optimal group of landing gear, respectively. configuration parameters efficiently. A fitness Secondly, the energy balance means that function of AR of wing, cruise velocity and the total energy collected from onboard PV payload weight fraction is defined to link the modules must be equal to or higher than the optimization and the QPSO algorithm. Finally, electrical energy consumed for mission the established design methodology is put into execution in a whole day of 24 hours. The applications. Firstly, the key conceptual relationship is defined by: parameters obtained by the design methodology SKHHPHHw pm d n  tot d n c dc  (2) for both configurations are compared from the Here Sw donates the reference area of wing, Kpm equator to the latitude of 50°N. Secondly, a donates daily-averaged total power of solar powered stratospheric UAV concept of photovoltaic modules per Sw, Hd and Hn donate wing-sail configuration, PoXiao, is designed at day period and night period, c and dc donate the latitude of 45°N. Then, the flight the efficiencies of charging and discharging of performance, power characteristics, and secondary batteries, and Ptot donates total power tracking of PoXiao concept on the consumption of solar-powered aircraft. summer solstice and the winter solstice are During the nighttime period, there is explored, and operational persistent altitude and another balance between the energy stored in payload power capabilities are further secondary batteries and the total power investigated at middle latitudes throughout a consumption multiplied by night duration. whole year. In addition, the impacts of the mP H  (3) installation and the rotation of sail tails of the bat bat dc tot n wing-sail configuration from a stability and Here bat donates gravimetric energy density of control point of view are preliminary analyzed. secondary batteries. Equations (1) to (3) are the basic equations for determining configuration parameters, which 2 Basic Equations: Energy Balance and distinguish continuous-operation solar-powered Mass Balance airplanes from conventional-powered HALE Based on the potential application listed at the airplanes. In level flight, the total power beginning, steady level flight acts as the single consumption contains three parts. design point for solar-powered stratospheric PPPPPPPtot pld  p  av  pld  lev p  av (4) UAVs as other HALE airplanes. The following Here Ppld, Pp, Pav and Plev donate the power study is only concentrated on level flight at consumption of payload, propulsion systems, constant altitude and storing the diurnal surplus avionics and level flight, respectively. Also, p of solar energy only in secondary batteries. The donate the efficiency of propulsion systems. basic equations contain mass balance and The first part comes from payload energy balance. instruments given in the design mission Firstly, the mass balance means that the requirements. The second part is for propelling lifting force has to be equal to or higher than the mechanisms to maintain level flight at a certain total weight of every component constituting the altitude as shown in Eq. (5). 3 Min Chang, Zhou Zhou, Rui Wang, Xiaoping Xu

mgtot W 2 CD PVlev  W  1.5 (5) CL CS Dw C L 

Here V donate flight velocity, CL and CD donate coefficients of lift and drag, r donate air density, W donate total weight. The last part is avionics power required for Fig. 3 Top and side views of the wing-sail type and its flight control, communication and navigation, configuration variables etc. It is estimated as a constant fraction of the Fig. 4 is a schematic representation of the avionics mass: flight course for the wing-sail configuration to track the sun's and elevation angle. The Pmavav  av (6) Statistically, the power-to-mass ratio of flight course comprises a semicircle end and a straight leg, and both the length of the leg and avionics is estimated about 6.0 W/kg in av the diameter of the end are far longer than the Ref.[4]. wingspan.

3 Introduction of the Design Methodology The configuration sizing of solar-powered UAVs differs significantly from traditional HALE airplanes. It can be generalized by two aspects with the energy-centered design guideline[12]. Firstly, all energy in operation only comes from PV modules mounted on the wing or sail tails. Secondly, these surfaces are highly coupled with the aerodynamic characteristics, and their weights of airframe Fig. 4 schematic representation of two adjacent flight structures and PV modules occupies a large courses of Azimuth-Elevation tracking method amount of total weight and then influences the In Fig. 4, there are two adjacent flight total power consumption as shown in Eq. (4) courses for two adjacent periods. In the first and Eq. (5). Without taking into account course, it starts from the point A1 to the point B1 geometric sizes of fuselages, horizontal and with the heading direction and corresponding vertical tails of small wetted areas, there are rotating angle of sail tails to maximize solar four characteristic configuration variables for energy absorption, and then turns right 180 the wing-sail configuration, including wingspan, degrees along the semicircle end to the point C1. aspect ratio (AR) of wing (bw/cw), chord ratio At this moment, the sensor onboard detects the (ct/cw) and area ratio (St/Sw) of sail tails to the and solar elevation angle, wing, as shown in Fig. 3. Accordingly, there are and then recalculates the next heading direction. two variables of wingspan and AR of wing for During the period from the point C1 to the point the conventional. The platform shapes of the A2, the solar azimuth angle is tracked, named wing and sail tails need to be rectangular with "Azimuth tracking" method. At the same time, constant chord designs for ease of PV modules sail tails rotate and track the solar elevation integration and ease of manufacture, and all sail angle in the way of "Elevation tracking" method. tails are considered to be with unified lengths The second period begins at the point A2. In and widths. In Fig. 3, the shadowed parts Fig.4, arc B1C1 and arc C1A2 are concentric, and represent PV modules. The chord ratio (ct/cw) is the length of the legs and the radius of the ends chosen by design experience at the beginning are termed Lov and Rov, respectively. It is not for the wing-sail configuration. necessary for the conventional configuration with no sail tails to track the Sun, so its flight course is not constrained by the sun's position.


Then, as the theoretical core of this work, aerodynamic efficiency formulation, QPSO the sizing process for the conventional and algorithm and its fitness function, and Kriging wing-sail configurations is shown in Fig. 5. surrogate model.

4 Power Characteristics Model of Photovoltaic Modules It is well known that PV modules absorb solar radiation effectively if their surfaces point to the direction of solar propagation, while the related to each PV module varies at all times. Here introduces a fixed right- handed gravitational Cartesian coordinate system S, with Sx pointing to the south, Sy pointing to the west, Sz pointing to the nadir, and with the origin in the center of each PV module. The geometric relationships between the beam solar radiation and a plane of any orientation relative to the at any time are described in terms of two angles and two Fig. 5 Sizing process for both configurations vectors as illustrated in Fig. 6. The design process starts from the top- architecture mission requirements, which include operational altitudes, operational latitudes, flight seasons, mass and power of the payload, and tracking method and configuration type. Firstly, the approximate range of each configuration parameter is obtained with design experience. Then, a software package DACE (Design and Analysis of Computer Experiments) in MATLAB® is employed to obtain a Kriging approximation model relating configuration parameters to corresponding power absorption Fig. 6 Position of the Sun relative to an arbitrarily of PV modules in order to save computational oriented PV module costs[16]. With this Kriging approximation Only the part of total solar radiation model and a group of configuration values projected on the normal direction of PV randomly selected, conceptual parameters modules can be absorbed effectively. The total related to the mass and energy are then obtained. power from all PV modules of Npm, termed Ppm, If all mass balance and energy balance is defined as: equations are satisfied, then the fitness value is PPPpm pm.w  pm.t  obtained by the fitness function that links the Npm (7) optimization problem and QPSO algorithm[17]. IStot pmcosnn s , pm pm   i If the fitness value is optimal, it achieves a i group of final configuration sizes. If not, a new The total power Ppm contains two parts: group is generated by QPSO algorithm again one part from the wing, termed Ppm.w, and the until the stop criterion is reached. Section IV to other part from sail tails, termed Ppm.t. The total section VII will describe the key parts of the power from all PV modules varies all the time configuration design methodology in detail, in operation. In a whole day, including the including power characteristics model of PV daytime and nighttime, the daily average total modules, mass components parameterization, power per unit wing area is calculated below:

5 Min Chang, Zhou Zhou, Rui Wang, Xiaoping Xu

P Here cs and ss are constants, valued 0.357 and Kt pm d (8) pm  0.678, respectively. hb and hs are height SHHw d n  Hd constants, valued 40 km and 7 km, respectively. RE is the Earth radius, valued 6,356.8 km. dep is 4.1 Total Solar Radiation at High Altitude depression angle, an altitude correction to solar elevation angle. Equation (11) and (12) for the The radiation spectrum changes in the beam radiation prove sufficiently accurate course of its path through the atmosphere, results in Ref. [13] for the intended application, depending on a number of parameters, such as especially at high altitudes and at shallow angles distance from the Earth to the Sun, altitude, of incidence. Only at altitudes below about 10 cover, haze content, moisture content, and km could significant deviations occur for soil pollution. The total solar radiation contains current weather conditions. mainly beam radiation, (also called direct Another radiation component is diffuse radiation), diffuse radiation and reflected radiation, the solar radiation whose direction is radiation. Due to low- and cloud-free scattered by the atmosphere. Under the atmosphere in the stratosphere, the reflected hypothesis that the diffuse radiation for all radiation component is negligible. Therefore, directions and radiation angles are considered to the total solar radiation is expressed by: be constant, the diffuse radiation, sharing 8% of the beam radiation, is defined by[13]: IIItotbeamdif (9) h Here Ibeam donates beam radiation, and Idif IIdifbeam0.08 exp (13) diffuse radiation. hs Solar at mean earth-sun distance, Here h donate flight altitude. Ion, outside the atmosphere is nearly constant, with variation range of ±3.3% in a whole year. 4.2 Orientations of PV Modules and the Line The World Radiation Center has adopted a from PV Modules to the Sun value of 1,367 W/m2 for the , termed Gsc. The dependence of extraterrestrial Solar-powered airplanes has variable flight radiation on time of year with sufficient paths in operation, and the position relationships accuracy for most engineering calculations is between the Sun and PV modules vary all the given by[11]: time, leading to the fact that the composition of the incident cos(n , n ) changes at any I Gn 1 0.033cos 360 365 (10) s pm on scd  time. Figure 1 shows that only the solar There are several methods for modeling the elevation angle, termed s, and the solar beam radiation [11, 13, 18], the solar radiation azimuth angle, termed s, geometrically received without scattered by the atmosphere. determine the unit vector of the direction of Taking into consideration the environment in radiation propagation, ns: the stratosphere, modeling accuracy, and T n cos cos  ,cos  sin  , sin  (14) calculating difficulties, an empirical radiation s s s s s s  model is employed in Ref. [13], the radiation The variables s and s are expressed and of which is defined as a function of obtained as: altitude and solar elevation angle: sins sin  lat sin  s cos  lat cos  s cos  h (15)   cossh sin h sin s  cs exp  coss h  (16) IIexps (11) sin sin  sin  beam on h  s lat s ss  cos s  hb  s dep  coss cos lat sin  1 90 The terms of the ,  , and the dep s , h, above are defined as follows[11]: dep0.57  arccos R E R E  h (12)


n  284 d cosb sin  pm cos  pm sin  b sin  pm s  23.45sin 360 (17)  365 npmb sin pm sin pm  cos  b cos pm  sin   1512H  (18)  h s cospm cos pm LLst ct  E (22) HH  t (19) s ct 1560 EBB0.0172 4.28cos 7.35sin 4.3 PV Modules Model t (20) 3.35cos 2BB 9.732sin 2 Based on the operating principles of solar 360 cells, its absorption efficiency depends on its Bn 1 (21) 365 d surface temperature and rarely on total irradiance. Therefore, it is necessary to integrate Here, Hs and Hct are solar time in hours and standard clock time in hours for local time zone, the thermodynamic model into the design methodology, since the atmosphere in the respectively. Lst and Lct are standard meridian for the local time zone in degrees and the stratosphere is significantly rare and thin, of the location in degrees, respectively. leaving less air for either conduction or Similarly, only attitude angles of the solar- to carry the excess heat away. The powered UAVs and mounting angles of PV experimental data in Ref. [19] show that total modules determine the normal unit vectors of irradiance received slightly affects the efficiency of Si-cell PV modules in the range any PV module, npm. The body-axis system, B, 2 2 is rigidly fixed to the solar-powered UAV, with from 180 W/m to 1300 W/m , which is in accordance with the irradiance range in the Bx pointing forward, By pointing to the right stratosphere. However, the experimental data wing, and Bz being the cross product of Bx and for Si-cell PV modules in both Ref. [19] and By. The attitude angles are based on the body- axis system relative to the frame S, which Ref. [20] show that surface temperature of PV include yawing, pitching and rolling angles, modules from about -80°C to 50°C approximately exhibit linear relationship with termed b, b and b, respectively. The mounting angles of PV modules are based on absorption efficiency. Low temperature leads to the local coordinate system of each PV module high efficiency, while high temperature leads to relative to the body-axis system. The local right- low efficiency. For other materials, the handed coordinate system P is rigidly fixed to temperature characteristics still exist. When the surface temperature of a PV module is Tsur, its any PV module, with Pz normal to its plane and efficiency is defined by: Px paralleling to any boundary. The mounting angles include yaw-deviation, pitch-deviation pm pm01 CTT T sur  sur0  (24) and rotate-deviation angles, termed pm, pm and Here, CT represents the temperature coefficient pm, respectively. Then, npm is derived by of a PV module and pm0 represents the standard transformation: efficiency of a PV module at the standard T surface temperature T , usually 25°C . Two npm L g2b L b2pm 0, 0, 1 (22) sur0 sides of the wing and sail tails are rigidly Here Lg2b is the transformation matrix from body-axis coordinate system to fixed connected together through internal supports, such as ribs and beams as illustrated in Fig. 7. gravitational coordinate system, and Lb2pm is the transformation matrix from local coordinate Because these connections are of relatively system to body-axis coordinate system. small cross-sectional area, heat transfer through them by conduction is negligible. In addition, In level flight, the attitude angles of  and b both the insides of the wing and sail tails are  are approximately zero. In addition, the yaw- b hollow and closed, filled with only air. As the deviation angle of pm is also approximately low conductance through air for internal heat zero in order to avoid projected surface area transfer between two sides of the wing and sail along the freestream. Therefore, the final npm is tails is also negligible, the control volume for derived from Eq. (22):

7 Min Chang, Zhou Zhou, Rui Wang, Xiaoping Xu

thermodynamic model is limited for the side  14 41 35 5 2 exposed to direct sunlight. In Fig. 7, the control Nufor  PrRe0.0370.664  ReRexx volumes are indicated by dashed lines.    Rex  rlam Re (28) 23  g  Tsur T a c pm Ra  2  Ta    cpm 2 W Re  (29)   CSLw  cp   Pr  a  k

Here Ra, Re, Nu and Pr denote Rayleigh Fig. 7 Control volumes and structures of cross sections for wing and vertical sun-trackers number, Reynolds number, Nusselt number and Prandtl number respectively.  denotes the Therefore, the heat-balance equation could dynamic viscosity of the atmosphere. (cp)a be expressed as[21-23]: denotes specific heat for the atmosphere, valued -1 -1 dTsur E in E out q sun  q elec  q rad  q conv 1,004 J·kg ·K . rlam denotes the ratio of   dt m cc  laminar flow and Rex denotes local Reynolds  pmpm pppmpm    number at the transition point. Equations (26) to qsun q elec  pm  pm Is cosnn s , pm (25) (28) for heat transfer analysis are limited under  the conditions of incompressible flow,  44kNu 8 qrad q conv  pm T sur  T a  T sur  T a  0.6≤Pr≤60, and Rex≤Re≤10 [21].  c  pm Here, E and E represent the rate of energy in out 5 Mass Components Parameterization transfer entering and leaving any control volume. q'' represents the heat flux. (c ) As listed in Eq. (1), the total mass is p pm divided into eight parts. In this section, it will go represents the specific heat for PV modules.  pm through all the parts and establish their mass and  represent the absorptivity and emissivity pm models respectively. The payload mass is given of PV modules, respectively. c represents the pm in the design requirements, not dependent upon local chord of the surface with PV modules. k the configuration parameters. represents the thermal conductivity of atmosphere. Tsur and Ta represent the surface temperature of PV modules and atmosphere, 5.1 Airframe Structure respectively.  represents the Stefan-Boltzmann Usually, the statistical weights methods are constant, valued 5.67×10−8 W·m-2·K -4. used in conceptual design. However, with a Convection heat transfer is a mixture of small number of solar-powered airplanes in the free (or natural) convection and forced history[8], researchers mostly used sailplanes' convection as expressed in Eq. (27) and Eq. (28), structure mass estimation instead [4, 8]. For respectively. large-wingspan and high aspect-ratio wing, the 7/2 7/2 7/2 Nu Nufor Nu fre (26) structure mass estimated by those models results 2 in high wing loading, leading to no feasibility of  0.387Ra1/6 continuous flight in the stratosphere[12]. From Nufre 0.825 (27) the Pathfinder up to the Helios prototype, the 9/16 8/27 1 0.492 Pr structure mass per unit wing area has been kept   under control through the span-loader guideline[10, 24]. It means that total mass is

8 A GENERAL DESIGN METHODOLOGY FOR YEAR-ROUND SOLAR POWERED STRATOSPHERIC UAVS FROM LOW TO MIDDLE LATITUDES distributed along the wingspan, and it is likely the operation with an approximate constant that the whole airplane is connected wingtip-to- power-to-mass ratio, termed mppt. The MPPT wingtip together by a series of small airplanes. mass can be defined by: Therefore, the airframe structure mass per unit mPmpptpmmppt    (32) wing area has little relevance to the wingspan max and AR of wing. Then, the structure mass is proportional to the area: 5.4 Secondary Batteries

mrSSafaf.w1  af.w w  af.t t Concerning the battery, its mass is directly (30) 1 rr  S proportional to the energy storage needed in the af.w af.w s af.t w nighttime, which is proportional to total power The raf.w term represents the weight ratio of consumption and night duration, and inversely fuselages, horizontal tails, and nacelles for proportional to its gravimetric energy density propulsion systems to the wing. The af.w term and discharging efficiency. andaf.t term respectively represent surface HPn tot densities of airframe structure for the wing and mbat  (33)  sail tails. Statistically, the total structure mass bat dc per unit wing area of several HALE solar- powered airplanes is estimated: Pathfinder's 5.5 Propulsion Systems 1.95 kg/m2[25], Zephyr's 1.1 kg/m2, HeliPlat's 2 2 A propulsion system usually contain three 2.0 kg/m [6], and Solar Impulse's 3.5 kg/m [26]. subparts (motor and its control electronics, propeller), usually not including gearbox owing 5.2 PV Modules to the reliability in long-endurance operation The solar cells are interconnected and the extreme environment in the stratosphere. electrically and then encapsulated between two As a whole, the propulsion systems mass is non-reflective transparent layers to obtain a PV proportional to the maximum continuous shaft module. Therefore, the surface density of PV power, termed (Pp)max, and inversely modules includes both solar cells and the proportional to the power-to-mass ratio, termed encapsulation. The surface density of PV p. Although the main flight condition is in the quiescence flight, higher power should be modules on the wing, termed pm.w, is relatively considered for taking-off, climbing, and flying higher than that on sail tails, termed pm.t, in that the flexibility and aerodynamic loads of the against prevailing in the stratosphere and former are higher than those are on the latter. turbulence in low altitudes. Generally, the ratio The PV modules mass can be estimated by: of maximum continuous shaft power to shaft power in level flight, termed p, is about 2 to 3. mpm S pm.w pm.w2 S pm.t pm.t (31) The propulsion systems mass is defined by: pm2w  pm.w2rS S  pm2t  pm.t w   Pp   P m max p lev (34) Here Spm.w and Spm.t represent total areas of PV p    modules on the wing and sail tails respectively, p p p and pm.w and pm.t represent surface densities of PV modules on the wing and sail tails 5.6 Avionics and Landing Gear respectively. pm2w and pm2t represent area The contributions of avionics and landing ratios of PV modules to their mounted wing and gear to the total mass buildup are of relatively sail tails, respectively, which are both lower small magnitude, but should be included for than 1.0. completeness. Avionics and landing gear are estimated as constant fractions of gross mass:

5.3 Maximum Power Point Tracker mav m lg  r av m tot  r lg m tot (35) Generally, the MPPT mass is proportional Statistically, the avionics weight fraction, to the peak power of all PV modules throughout termed rav, is estimated about 0.03 in Ref.[4] ,

9 Min Chang, Zhou Zhou, Rui Wang, Xiaoping Xu

and the landing gear weight fraction, termed rlg, 22Sw Cff .w FF w S t C .t FF t is estimated about 0.00725 in Ref.[18]. CD0  rf r LP Sw (40)

2rf r LP C ff.w FF w r s C .t FF t  6 Aerodynamic Efficiency Formulation 1.3280.455 1.5 Crrf .wlam.wlam.w 2.58 1  (41) The CCDLterm in Eq. (5) is named as Rew log10Re w  endurance parameter for solar-powered UAVs, 1.3280.455 whose terms CD and CL are correlated in Ref.[27] Crrf .tlam.tlam.t 2.58 1  (42) by: Ret log10Re t  C 2 L Rertcw Re (43) CCDD0 (36)  Aew For the wing-sail configuration, the Here CD0 donate the coefficient of parasite drag. component form factors of the wing and sail The Oswald efficiency factor e in Eq. (36) tails, termed FFw and FFt, are equal to 1.25 and varies with wing aspect ratio. Solar-powered 1.1 empirically, respectively. The chord ratios UAVs usually use rectangular wing with the of laminar flow of the wing and sail tails, same cross sections and with little twist in order termed rlam.w and rlam.t, are equal to 0.2 and 0.0 to maximize PV modules and reduce empirically, respectively. The scaling factor rf is manufacturing costs. To obtain the actual e for equal to 1.25 based on the wetted area ratios of rectangular wing of high aspect ratio, a series of fuselages and nacelles to reference wing area. wings with aspect ratios from 10 to 60 are rLP donates the interference drag by distributed calculated with classic lifting-line theory using propellers, valued 1.07 in Ref.[6]. nonlinear section lift data[28]. The airfoils used There are two efficient conditions for level are E387 and FX 63-137, representative of low flight from flight mechanics theory: the Reynolds airfoils. The section lift data are minimum thrust required and the minimum obtained by XFOIL[29] in the conditions of power required. In real flight, the minimum Mach number of 0.15, and Reynolds number of power required is preferred for solar-powered 500,000, as shown in Fig. 8. The first-order airplanes. However, the minimum thrust exponential decay fit of all the calculation result required is considered in the design for e is: methodology. In this flight condition, the lift

eA0.303exp w 30.9  0.695 (37) coefficient CL is defined as: 0.95 CA eCmin, C (42) E387( =4°) Lw D0 L  up  0.90 FX 63-137( =4°) Here (C ) is the upper limit of the cruise lift E387( =8°) L up 0.85 FX 63-137( =8°) coefficient, valued by 1.25 with design Fit curve experience. 0.80

Oswald factor 0.75 Ma=0.15, Re =0.5×106 7 Optimization Formulations w 0.70 10 20 30 40 50 60 It is obvious that configuration sizes and AR of Wing other conceptual parameters are nonlinearly Fig. 8 Tendency of Oswald factor for rectangular coupled by energy. Besides, under the wings with aspect ratios from 10 to 60 constraints of both energy balance and mass Then, the Component Buildup Method[27] balance, the solution space for configuration is used to calculate the parasite-drag coefficient sizes is wide. Therefore, it is necessary to CD0 in Eq. (36), which is mainly built up by the employ multi-objective optimization method to wing and sail tails. The parasite drag from achieve the optimal matching of conceptual fuselages, distributed propulsion nacelles and parameters. Here, QPSO algorithm and Kriging other miscellaneous components are considered surrogate model are employed. by a scaling factor, termed rf, in Eq. (38):


7.1 QPSO algorithm (3). Evaluate the desired fitness function for Particle Swarm Optimization, first each particle and compare with the particle’s previous best values, and then set the best value introduced by Kennedy and Eberhart[30] in 1995, is a population based optimization to the current value if the current value is better. technique inspired by social behavior of bird (4). Determine the current global best position flocking or fish schooling. Due to the fact that among the particle’s best positions. Compare the PSO algorithm is simpler and more feasible the current global position to the previous, and than other non-gradient based algorithms, it is then set the global position to the current global widely applied in the areas of airfoil[31] and if the current global position is better. wing [32]optimization and preliminary aircraft (5). Generate M new particles by Eq. (43) configuration optimization[33]. However, in restricted by the Euclidean distance, and each this algorithm, each particle moves along a new particle must fit basic equations. determined trajectory in Newtonian mechanics, (6). Repeat steps (2)-(5) until a stop criterion is lacking global-convergence guarantee. Then, satisfied OR a pre-specified number of Sun[17, 34] presented an improved PSO generations are completed. algorithm in 2004, called Quantum-Behaved If a QPSO particle fit basic equations, it Particle Swarm Optimization (QPSO). Its can obtain a group of conceptual parameters. individual particle can appear in any position of Three conceptual parameters of payload weight the whole solution space, and QPSO have more fraction, wing AR and cruise velocity are excellent global searching ability. The chosen for fitness calculation of each particle. formulations of QPSO algorithm are given Higher payload weight fraction means better payload-carrying ability and lower costs, lower by[17]: jj AR of wing Aw means less flexible, and larger Xj1 X p u  X g 1  u   cruise velocity V has more advantages to go ii  11  (43) against prevailing . The fitness function j j 1 employs a multi-objective nonlinear weighting  mbest  X i ln  u2 method, which is expressed by: M j 1 j  p f   mbestX  i (44)  i   Ffit i 2 M i1   i Here, each particle, X, in QPSO algorithm has  exp1 two variables of configuration parameters,  ii f  i   (45) including wing AR, the area ratio of sail tails to  exp 1ii >1 j the wing. In Eq. (43) and Eq. (44), X i is the  p CC    position of particle i at generation j. X is the  newii bad i  i =1 2 best position found by particle i so far, and X g is  CC     goodi bad i the best position among all the particles in the The term Cnew corresponds to the present population. values of evaluation parameters, the term Cbad The design ranges for two variables are corresponds to the given unacceptable values, determined experientially before optimal design. and the term Cgood corresponds to the given The process can be outlined as follows: satisfying values. If the ith evaluation parameter (1). Create an initial randomly distributed (Cnew)i is near its (Cbad)i, the intermediate swarm of M particles with initial position variable i is large, leading to the fact that its information restricted by an appropriate contribution to F is also large. If the i Euclidean distance, and each particle must fit fit th evaluation parameter (Cnew)i is near its (Cgood)i, basic equations of energy balance and mass it contributes little to F . Therefore, the less the balance. fit term Ffit is, the better the group of configuration (2). Calculate the Mean Best Position mbest values is. among the particles by Eq. (44).

11 Min Chang, Zhou Zhou, Rui Wang, Xiaoping Xu

7.2 Kriging surrogate model newly added samples, termed q, is 20, and the When solving the basic equations for each number of iterations is about 3 to 5. That is, the total number of whole samples ranges from 80 group of configuration parameters in each QPSO particle, it has to recalculate the daily to 100. As the particles generated in QPSO, the averaged total power per unit wing area and the samples are also randomly distributed in the maximum total power of PV modules by minor design sites by an appropriate Euclidean time step. It leads to expensive calculations. distance. Therefore, the Kriging approximation model is utilized as a surrogate to estimate power 8 Application of the Design Methodology characteristics of PV modules quickly and precisely. As depicted in the flow chart of Fig. 9, Until now, the design methodology for year- the processes of Kriging surrogate model round solar-powered stratospheric UAVs has construction is based on the data from the been established. The following researches are computer experiment. focused on its applications for both configurations, especially the wing-sail type.

8.1 Mission Requirements and Input Parameters There are about forty parameters contained in the formulations of the methodology. It is necessary to distinguish among four different groups. The first group is composed of configuration variables, including AR of wing, Fig. 9 Flow chart for building Kriging Surrogate wing chord, chord ratio and area ratio of sail model tails to the wing. At the beginning, the design The input samples contain four parameters space for each configuration size is generally in design sites: rc, rS, cw and Rew. The ranges of given by experience: Aw on [20, 60], cw on [2 m, the first three parameters are given 6 m] and rs on [0, 1]. The chord ratio of sail tails experientially. The range of Rew is derived from to the wing, rc, is valued 5.0 by design its definition expression in Eq. (46), and the experience. In addition, wing loading and lift ranges of lift coefficient and wing loading in Eq. coefficient statistically ranges from 20 N/m2 to 2 (46) are given statistically. 80 N/m and 0.6 to 1.4, respectively. Then, Rew ranges from 0.22×106 to 2.1×106 by Eq. (46) for cww V c 2 W Rew  (46) Kriging surrogate model construction. CS Lw The second group is composed of True responses can be obtained from input parameters linked to the design mission, which samples by true simulation, and the input are operational altitude, seasons, operational samples and true responses are used for latitude, mass and power consumption of the constructing the Kriging approximation model payload, and the configuration type. A top- with the software package DACE. Then, architecture design mission in the stratosphere predicted responses can be obtained from any for year-round operation is given as follows. input sample by this approximation model as a  Operational altitude: 20 km surrogate. If the differences between predicted  Operational longitude: 120 °N responses and true responses are within the  Flight duration: > one year (continuous given criterion, the construction procure is over. operation) If not, it is necessary to add more input samples  Payload weight: 300 kg and true responses. In this paper, the number of  Payload power: >3000 W initial samples, termed Q, is 20. The number of


 Operational latitude and Configuration: increasing. The evaluation parameters of the defined in the following fitness function are summarized in Table 2. The third group comprises of parameters In Table 2, Vw donates the chosen wind that are linked to the technology levels and are velocity. Usually, solar-powered stratospheric constant or can be considered as constants. A UAVs should be able to against 90-percentile or list of these parameters is presented in Table 1. 95-percentile winds. Based on year-round wind The parameters related to PV modules are from data at the altitudes of 18 km to 20 km in silicon solar cells in Ref.[22] , which are Ref.[4] , the wind velocity of 35 m/s is chosen practically mature and used by most solar- to constraint the design speed. powered airplanes. The parameters for secondary batteries are from Lithium-Sulfur (Li- 8.2 Comparative Analysis on Conceptual S) Batteries of high specific energy and maturity. Parameters of Both Configurations Table 1 Input constants for each component Firstly, daily averaged power area densities Parameter Value Parameter Value of PV modules mounted on the wing and sail -2 af.w 1.1 kg·m p 0.72 tails as a function of operational latitudes at the -2 af.t 0.5 kg·m pm0 0.21 altitude of 20 km are compared as shown in Fig. -2 pm.w 0.6 kg·m pm2w 0.85 10. pmh refers to the wing and pmt refers to 0.45   0.95 tracking sail tails. Four typical days are chosen, pm.t kg·m-2 pm2t 2200 including the sprint , the summer   C -0.0045 K-1 mppt W·kg-1 T solstice, the autumn equinox and the winter 400 W·kg- 712 solstice.   (c ) p 1 p pm J·K·kg-1 90 -1 ) av 6 W·kg pm 0.8 2 60 p 2.5 pm 0.85

(W/m Spring equinox 600 30 pmh Summer solstice r 0.00725    lg bat W·h·kg-1 0 Autumn equinox

180 ) rav 0.03 c 0.95 2 Winter solstice r 0.15   0.95 150

af.w dc 120 (W/m

rf 1.25 rLP 1.07 90 pmt  h=20 km 60 Table 2 Parameters for fitness function 0 10 20 30 40 50 60  (°N) lat Evaluation (Cgood)i (Cbad)i i parameters Fig. 10 Comparisons between pmh and pmt at 20 km

rpld 0.18 0.12 1 From the equator to 60 °N, the changing V 1.1×Vw 0.9×Vw 0.25 tendencies of both pmh and pmt with the Aw 25 45 0.2 increasing of operational latitudes are the same. The last group comprises of parameters Higher latitudes near the winter seasons lead to from the Kriging surrogate model, the QPSO smaller values, while higher latitudes near the algorithm and its fitness function. As to the summer seasons lead to largervalues. At low Kriging surrogate model construction, the latitudes, the variations in both pmh and pmt Euclidean distance is 0.5, the number of initial throughout a whole year are of slight degree, samples and newly added samples of every and pmt of sail tails is generally higher than iteration step are 20 and 20 respectively, and the pmh of the wing by 52~93 percent. However, at number of iterations to achieve the stop criteria middle latitudes, their variations throughout a -3 of 1×10 in Fig. 9 is usually 3~5. As to the whole year show significant and pmt of sail tails QPSO algorithm, the Euclidean distance is is higher than pmh of the wing by 93~898 equal to 0.4, a swarm size of 80 particles is used, percent in that pmh is closer to zero near the the total number of generations is 40, and the winter seasons if the operational latitude is Contraction-Expansion Coefficient  linearly closer to the Arctic Circle of 66.5 °N. decrease from 1.0 to 0.5 with the generation

13 Min Chang, Zhou Zhou, Rui Wang, Xiaoping Xu

Then, with input parameters and mission 1.3 requirements in the section A, optimized 1.2

L 1.1 conceptual parameters for both configurations C 1.0 0.9 from the latitudes of the Equator to 50 °N are 0.8 compared in Fig. 11. Two days of the summer 48

D Tropic of Cancer solstice (n =173) and the winter solstice /C 40

d L C (nd=356) are chosen. In Fig. 11, the researched 32 parameters contain the configuration sizes (bw 24 0 10 20 30 40 50  (°N) and Aw), power absorption (pm), aerodynamic e) lat efficiency (CL and CL/CD) and payload-carrying 0.30 capacity (rpld). 0.25 350 Conventional@n =173 d 300 Conventional@n =356 0.20

d pld 250 Wing-sail@n =173 r d 0.15 Wing-sail@n =356 200 d 150 0.10 Tropic of Cancer Wingspan (m) 100 0.05 0 10 20 30 40 50 50  (°N) Tropic of Cancer f) lat 0 0 10 20 30 40 50  (°N) Fig. 11 Comparisons of conceptual parameters for lat a) both configurations 60

50 As to the conventional configuration depicted by dash-dot lines with hollow triangles 40 and circles, from low to middle latitudes, bw and 30 Aw decrease during summer and increase during 20 winter, pm increase during summer and

Aspect ratio of wing 10 Tropic of Cancer decrease during winter, CL and CL/CD decreases 0 during summer and increase during winter, and 0 10 20 30 40 50  (°N) rpld increases during summer and decrease b) lat 0.45 during winter. With the energy-centered guideline, pm acts as the key influential factor. 0.40 Higher pm leads to smaller total areas of PV

s 0.35 modules required and then saves the weights of

r structure, PV modules and secondary batteries, 0.30 and finally leads to higher rpld because of the 0.25 smaller total weight. Meanwhile, bw decreases Tropic of Cancer 0.20 because of the smaller wing area required. In 0 10 20 30 40 50  (°N) addition, higher pm also leads to less demand c) lat 200 for aerodynamic efficiency of CL and CL/CD and then lower Aw by the fitness function. On the

150 ) contrary, lower pm leads to larger total areas of 2 PV modules required and then increases the

(W/m 100 weights of structure, PV modules and secondary


 batteries, and finally leads to lower rpld because 50 of the larger total weight. In addition, lower pm Tropic of Cancer leads to more demand for higher aerodynamic 0 10 20 30 40 50  (°N) efficiency of CL and CL/CD and then higher Aw. d) lat As to the wing-sail configuration depicted by solid line with solid triangles and circles, the


changing tendencies of bw, Aw, CL, CL/CD and the operational latitude and flight duration. With rpld from low to middle altitudes are the same as other input parameters in section A, the the conventional for the similar reasons. In optimized design specifications of PoXiao are addition, rs increases continuously during winter listed in Table 3. with increasing latitudes, but decreases from the Table 3 Optimized design specifications equator to the Tropic of Cancer and then increases subsequently during summer. It is Parameter Value Parameter Value bw 152.3 m maf 689.0 kg because that the improved amplitude of pmt cw 3.06 m mpm 322.2 kg compared to pmh as depicted in Fig. 10 is the Aw 49.8 mbat 783.3 kg lowest on the summer solstice on the Tropic of 2 Cancer and increases from low to middle Sw 466.0 m mmppt 51.3 kg altitudes on the winter solstice. Comparatively rs 0.42 mp 168.6 kg S 2 speaking, the installation of sail tails increase pm 582.0 m mlg 17.6 kg CL 1.25 m 72.7 kg the parasite drag coefficient CD0, so higher Aw av C /C for the wing-sail at the same latitude is L D 38.1 mpld 300 kg Re 6 m employed leading to larger CL to cover the loss w 0.58×10 tot 2404.7 kg V -1 -2 of CL/CD. 29.9 m·s W/Sw 50.62 N·m -2 Comprehensively speaking, at low latitudes, pm 63.4W·m rpld 0.125 the conventional and the wing-sail are both As mentioned during the weight estimation suitable for year-round operation and the latter for airframe structure, a lower structural weight does not show much superiority over the former. for a platform with high aspect ratio wing can At middle latitudes, two typical design points of be obtained by the span-loader guideline. It is the summer solstice and the winter solstice likely that a series of modular units is fixed differ greatly for both configurations. However, together in a wingtip-to-wingtip manner, the employment of the tracking sails by the forming a single flying surface of great size. wing-sail can bridge the gap to some degree, The planforms of PoXiao is illustrated in Fig. 12. and shorten the wingspan, reduce the total area Only one side of each sail tail is placed with PV of PV modules and the overall weight. Thus, it modules. In the Fig. 12 c), the terms pm.t and is obvious that the wing-sail outperforms the pm.h donate the rotation-deviation angles of PV conventional for year-round operation at middle modules on sail tails and the wing with dihedral latitudes. The higher the latitude, the more angles. When the local dihedral angle is positive, remarkable the superiority is. pm.h is positive on the left wing and negative on the right wing. 8.2 Application of Design Methodology on the Wing-Sail Configuration at Middle Latitudes The design methodology developed from section III to section VII could be equally applied to the conventional and the wing-sail configurations. In view of limited researches to explore the year-round operational potentials at Fig. 12 Configuration sizes of PoXiao concept middle latitudes by , following sections are focused on the application of design From the point of view of geometry sizes, methodology on the wing-sail configuration. PoXiao is divided into five equal units. The The following proposed concept is named volume coefficients of horizontal tails and "PoXiao" which means breaking dawn after vertical tails are 0.6062 and 0.00711, flight throughout the whole night. The latitude respectively. The three-dimensional view of of 45 °N within middle latitudes and the winter PoXiao concept and the enlarged view of its solstice poorest in solar radiation at middle single unit are illustrated in Fig. 13. latitudes are chosen for design requirements of

15 Min Chang, Zhou Zhou, Rui Wang, Xiaoping Xu



) 2

80 (W/m

w 60


/ pm.t

P 40

20 Fig. 13 PoXiao optimized configuration 0

In the following, the energy performance 0 3 6 9 12 15 18 2145 2448 Clock time [h] and characteristics of stability and control of c)  : Winter solstice Summer solstice wing-sail PoXiao concept are investigated, 180 s respectively. 120

60 (°) 8.4 Analysis on Energy Characteristics of b 0  PoXiao Concept -60 The winter solstice and the summer -120 solstice are selected for the energy simulations -180 0 3 6 9 12 15 18 2145 4824 that start at sunrise and last 40 hours as depicted Clock time (h) d) in Fig. 14. PoXiao takes off at the sea level with  : Winter solstice Summer solstice 180 s 60% of batteries capacity, and climbs to the operational altitude of 20 km with the maximum 120

continuous shaft power of 67.5 kW. During 60 (°)

0 pm.t taking off and climbing, the overall efficiency  of the propelling system is assumed constant. -60 The length of straight leg Lov is 40 km, and the -120 radius of the semicircle end Rov is 2 km. -180 30 0 3 6 9 12 15 18 4521 4824 V [m/s] Clock time (h) e) 25 500 peak plateau h [km] 20 400 15

300 10 200 5 Winter solstice

Summer solstice (kW·h) storage Battery 0 100 Lower limit of discharging 0 6 12 18 24 306 3612 4218 2448 Clock time (h) 0 a) 0 6 12 18 24 30 6 3612 1842 2448 Clock time (h) 350 f) 300 Fig. 14 Continuous flight simulation of PoXiao concept

) 250 2 Figure 14 contains six parts. The first part, 200

(W/m Fig. 14 a), includes the performances of flight


/S 150 altitude and flight velocity. The climb phases

pm P 100 last about 3.2 hours on both days, and the climb 50 rate is less than 2 m/s. The second and the third

0 parts respectively show power absorption of PV 0 6 12 18 24 30 6 1236 4218 4824 modules per unit wing area for PoXiao concept Clock time (h) b) and for its tracking sails, respectively. For clarity, the period from 21 o'clock on the first day to 21 o'clock on the second day is hidden in Fig. 14 c) to e) because of repetition. PV

16 A GENERAL DESIGN METHODOLOGY FOR YEAR-ROUND SOLAR POWERED STRATOSPHERIC UAVS FROM LOW TO MIDDLE LATITUDES modules on the tracking sails oriented normal to drag ratios at different altitudes are calculated the sun's elevation angle can collect a maximum with Eq. (38) ~ Eq. (41) according to Reynolds of solar energy in the daytime as compared to number. The efficiency of the propulsion system PV modules horizontally disposed, i.e. those at different altitudes is assumed constant. In Fig. mounted on wing upper surfaces. Tracking sails 15 a), the payload power is a constant of 3 kW, contribute significantly to total power and continuous-operation simulations are absorption, especially at dawn when PoXiao has carried out to obtain the achievable station- exhausted most of stored energy in secondary keeping altitudes at different middle latitudes. In batteries. The fourth part, Fig. 14 d), includes Fig. 15 b), the operational altitude is fixed at 20 solar azimuth angle, s, and flight-heading km, and continuous-operation simulations are direction of PoXiao, b. The fifth part, Fig. 14 carried out to obtain maximum continuous e), includes solar elevation angle, s, and rotate- power consumption of payload at different middle latitudes. deviation angle of sail tails, pm.t, for tracking 30 P =3kW the Sun. On the purpose of maximizing power 28 pld collection, the heading direction is 26 24 perpendicular to the direction of solar 22 propagation, i.e., s=b±90° or s=b±270°, the 20 18 rotate-deviation angle of sail tails is adapted  = 30°N 16 lat  = 45°N related to the heading direction, i.e., pm.t =- Operational altitude (km) 14 lat 12  = 55°N 90°s or pm.t =90°s. The adaptation of lat 10 0 50 100 150 200 250 300 350 rotate-deviation angle is finished during the n (d) turnaround of the prescribed course. The final a) d 35 part, Fig. 14 f), displays the cycles of h=20 km discharging and charging of secondary batteries. 30 The peak plateaus mean that the battery is fully 25 20 charged, while the lowest points mean the 15 battery capacity margins. For the critical design 10 condition of the winter solstice, PV modules can 5 collect enough solar energy for mission flight

Operational payload power (kW) 0 and fully charging secondary batteries in the 0 50 100 150 200 250 300 350 n (d) daytime, and the stored energy in secondary b) d batteries can fit mission flight in the nighttime. Fig. 15 Mission capabilities at middle latitudes It validates the proposed design methodology. In Fig. 14 f), wide peak plateaus indicate that In general, mission capabilities in Fig. 15 the power absorption is surplus, which usually are highly dependent on solar flux distributions occurs near summer. In addition, large battery in different latitudes. As to altitude capability, capacity margin allows the platform to either operational altitudes in or near summer are increase operational altitude or increase the higher than those in or near winter are. From electrical load of mission payload. 30 °N to 45 °N and to 55 °N , the differences of Experientially, higher payload power and higher operational altitude between the summer altitude means larger covered area of interest solstice and the winter solstice change from 4 and higher mission effectiveness for solar- km to 7 km and to 17 km. As to payload power powered platforms. capability, payload instruments are allowed to Further, the mission capabilities of consume much more power in or near summer operational altitude and payload power at than in or near winter. At the latitude of 55 °N , middle latitudes throughout a whole year are the payload power reaches 10 times that of explored respectively, as illustrated in Fig. 15. design value in summer. However, PoXiao The selected latitudes are 30 °N , 45 °N and cannot maintain station keeping at 20 km 55 °N . The lift coefficient is 1.25 and the lift-to- though the payload power is zero during the periods from nd=0 to nd=31 and from nd=311 to 17 Min Chang, Zhou Zhou, Rui Wang, Xiaoping Xu

nd =365, and it is necessary to decrease the pm.t=45° are opposite to those for pm.t=-45°, operational altitude. while the other parameters are approximately the same. Assuming that propulsion systems do 8.4 Preliminary analysis on Stability and not generate unbalanced moments on the Control of PoXiao Concept aircraft, each elevator deflects the same angle to trim the pitching moment and each rudder Stability and control derivatives in deflects the same angle to trim the yawing longitudinal and lateral directions are estimated moment. by an extended vortex-lattice model modified based on Athena Vortex Lattice (AVL) code Table 4 Aerodynamic parameters in equilibrium from MIT. The wing incidence is 4 deg, and the Parameter No sails -90° -45° 0° horizontal tails incidences are 1 deg. The wing e 0.798 0.797 0.794 0.798 -1 employs an optimized low Reynolds airfoil CL (rad ) 6.13 6.13 6.19 6.25 -1 based on FX 63-137, and the airfoils of Cm (rad ) -0.96 -0.96 -1.04 -1.12 horizontal, vertical and sail tails are all treated SM (%) 15.73 15.73 16.77 18.00 -1 as flat plates. The lifting surfaces are Cn (rad ) 0 0 1.7E-3 0 -1 represented as single-layer vortex sheets Cmq (rad ) -20.65 -20.65 -22.58 -24.71 -1 discretized into horseshoe vortex filaments, and Cnq (rad ) 0 0 0.041 0 -1 fuselages like prolate spheroids are modeled via Cme (rad ) -1.220 -1.220 -1.243 -1.278 source-doublet filaments. The number of -1 Cm (rad ) 0 0 -0.05 0 horseshoe vortices is 18×94 for the wing, is -1 Cl (rad ) -0.17 -0.17 -0.17 -0.17 12×12 for each horizontal tail, is 12×12 for each -1 Cn (rad ) -1.3E-2 -9.4E-3 -1.1E-2 -1.3E-2 vertical tail, and is 25×10 for each sail tail. The -1 Clp (rad ) -0.94 -0.94 -0.945 -0.954 total number of horseshoe vortices is 4382. The -1 Cnp (rad ) -0.16 -0.16 -0.16 -0.16 modeling fuselages do not extend backwards -1 Clr (rad ) 0.40 0.40 0.40 0.40 and pass through sail tails. The 3D model of the -1 vortex lattice method is illustrated in Fig. 15, Cnr (rad ) -0.0127 -0.0143 -0.0134 -0.0125 -1 the rotate-deviation angle of which is -45 deg. Cnr (rad ) -1.4E-2 -1.5E-2 -1.5E-2 -1.4E-2 The reference point in the input file is located at e (°) 0.3 0.29 0.12 -0.06 the center of gravity that does not change during r (°) 0 0 -0.23 0 rotation of sail tails. The hinges of each elevator Longitudinally, the rotation of sail tails is located at 60% of local chords and that of brings little effect on aerodynamic efficiency at each rudder is located at 40%. small angles of attack in equilibrium. However, the aerodynamic center moves backwards when rotation-deviation angles are gradually close to 0°, resulting moderate increasing of longitudinal static and dynamic stability. Laterally, static directional stability donated as Cnand yawing- directional damping increases of slight degree

Fig. 15 3D model for vortex-lattice method(pm.t=-45°) when rotation-deviation angle closer to ±90°, Aerodynamic parameters in equilibrium for while the installation and rotation of sail tails the conventional configuration with no sails and bring little effect on roll stability derivatives. the wing-sail configuration with the rotate- Particularly, when the rotation-deviation angle deviation angles equal to -90°, -45°, and 0° are of sail tails is not equal to 0° or ±90°, coupling displayed in Table 3, which include stability and between longitudinal and lateral-directional control derivatives, static margins, elevator and derivatives was of slight degree, and three of rudder deflections for trim, and Oswald cross-coupling derivatives are bold in Table 4. It efficiency factors. Aerodynamic parameters for brings control law complexity. In addition, deflection of each elevator and rudder used for  =90° are the same as those for  =-90°. pm.t pm.t trim is little and differs of slight degree for Aerodynamic parameters of Cn, Cnq, Cm for 18 A GENERAL DESIGN METHODOLOGY FOR YEAR-ROUND SOLAR POWERED STRATOSPHERIC UAVS FROM LOW TO MIDDLE LATITUDES different configurations. In conclusion, the the latter does not show much superiority over influence brought by the installation and the former. rotation of sail tails is slight, though the area In view of limited investigations on year- ratio of sail tails to the wing is considerable. It is round operational potentials at middle latitudes because that the aspect ratio of sail tails, only by solar energy, a wing-sail concept named expressed by bt/ct, is equal to 0.19, which results PoXiao is developed by the design methodology in so small normal forces that generated at the latitude of 45°N, and its energy moments are of slight degree. When five sail performance at middle latitudes and sails are united as one sail tail with the aspect characteristics of stability and control ratio of about 1.0, it is further investigated that influenced by tracking sail tails are also its influence of installation and rotation of the investigated preliminarily. From an energy point sail tails augment significantly on stability and of view, the winter solstice acts as the critical control, and most of them are negative. From design condition at middle latitudes in the this point of view, tracking sails divided into northern hemisphere. During year-round several equal units with span-loader guideline operation, it is practicable to increase station- can moderate the influence rotating sail tails on keeping altitude or augment payload power stability and control of the wing-sail consumption to enhance the mission capability configuration. in the period from spring to autumn when solar energy absorption is surplus. In addition, the addition and rotation of sail tails of PoXiao have 9 Conclusion slight influence on the characteristics of stability A design methodology of year-round solar- and control, and the degree of influence will powered stratospheric UAVs at low to middle increase if the aspect ratio of sail tails increase. latitudes is developed, which can be equally Future research work will focus on four applied to configurations with or without non- aspects, mainly for the wing-sail configuration. horizontal sun-trackers. The configurations are Firstly, the tracking method for sail tails is not generally categorized into the conventional type limited on Azimuth-Elevation tracking method. and the wing-sail type. Based on traditional Further investigations will be focused on design methodology, the proposed methodology sensitivity analyses of conceptual parameters to comprehensively comprises formulations for explore flight principles of the wing-sail power absorption of PV modules, each mass configuration with different kinds of tracking component, and aerodynamic efficiency. methods. Secondly, if the gravimetric energy Particularly, the thermodynamics and density of secondary batteries is not higher orientations of PV modules at all latitudes and enough, a portion of the diurnal surplus of solar stratospheric altitudes throughout a whole year energy by tracking sails can be stored in are considered. Besides, the QPSO algorithm potential energy by gaining a certain altitude. and Kriging surrogate model are integrated into The guideline will be incorporated into the the methodology in order to obtain a group of methodology. 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19 Min Chang, Zhou Zhou, Rui Wang, Xiaoping Xu

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