Optimal Design of a High-Altitude Solar-Powered Unmanned Airplane

ABSTRACT: This paper describes a multi-disciplinary design and optimization framework tailored for the conceptual development of high-altitude solar-powered unmanned aerial vehicles. The aircraft baseline configuration that the framework is able to handle is very similar to that of Zephyr, which is developed by the UK based company QinetiQ. The disciplines of aerodynamics, structures, stability, weight, and systems were considered and integrated into a modeFrontier® workflow, capable of providing a relatively simple sizing, but highly realistic airplane.


INTRODUCTION
The present work is concerned with the optimal design of unmanned high-altitude long-endurance (HALE) solar-powered airplanes.In order to accomplish this, a multi-disciplinary design framework was elaborated employing the modeFrontier ® (ESTECO, 2011) commercial optimization package.A brief technical retrospective of the development on solar-driven aircraft is provided in this section as well as the reasoning to address the utilization of such kind of airplane.
The first flight of a solar-powered aircraft took place on November 4 th , 1974, when the remotely controlled Sunrise I, designed by Robert J. Boucher of AstroFlight, Inc., flew after a catapult launch (Noth, 2008).The flight lasted 20 minutes at an altitude of around 100 m (Noth, 2008).
AeroVironment, Inc. was founded in 1971 by the ultralight airplane innovator Paul MacCready.Following the AstroFlight's airplane debut, AeroVironment undertook a more ambitious project to design a human-piloted, solarpowered aircraft.The firm initially based its design on the human-powered Gossamer Albatross II and scaled it down to three-quarters of its previous size for solar-powered flights.This was easier to accomplish because, in early 1980, the Gossamer Albatross aircraft had participated in a flight research program at NASA Dryden Research Center.Some of the Albatross flights were performed employing a small electric motor.The scaleddown aircraft was designated Gossamer Penguin (Fig. 1).It had a 71-ft wingspan compared to the 21.64-m (96-ft) span of the Gossamer Albatross (MacCready et al., 1983).Penguin's Empty Weight was just 31 kg, it had a low-power requirement and, therefore, it was an excellent test bed for testing of solar power systems (Noth, 2008).AstroFlight, Inc., of Venice, California, provided the power plant for the Gossamer Penguin, an Astro Cobalt 40 electric motor.Th is engine was designed to run at between 10,000 and 15,000 rpm, but the 11-ft diameter propeller of Penguin rotates between 120 and 130 rpm.Th e speed reduction was achieved with a three-stage gearbox with two timing pulley stages providing a reduction ratio of 5/1 each and a fi nal chain reduction stage delivering a 5.12/1 ratio.Robert Boucher, designer of the Sunrise II, worked as a key consultant for both aircraft and for the Solar Challenger.Th e power source for the initial fl ights of the Gossamer Penguin consisted of 25 nickelcadmium batteries and panels of 3,640 solar cells delivering 541W.Th e battery-powered fl ights took place at Shaft er Airport near Bakersfi eld, California.Paul MacCready's son, Marshall, was the test pilot.He was 13 years old and weighed approximately 80 lb (36 kg) at that time.Th e main targets of the test fl ights were the determination of required power to fl y the airplane, the optimization of the airframe/propulsion system, and pilot training.Flights took place on April 7 th , 1980, and a short solar-powered one on May 18 th .However, the offi cial project pilot was Janice Brown, a Bakersfi eld school teacher who weighed in at slightly less than 45 kg and was a charter pilot with commercial, instrument, and glider ratings.She checked out in the plane at Shaft er and made about 40 solar-powered fl ights.Wind direction, turbulence, convection, temperature and radiation at Shaft er in midsummer proved to be less than ideal for Gossamer Penguin because of crosswinds at takeoff and decreased solar power output due to higher ambient temperatures.Consequently, the project moved to Dryden in late July, although conditions there also were not ideal.Nevertheless, Janice fi nished the testing, and on August 7 th , 1980, she fl ew a public demonstration at Dryden in which she was able to cover 3.14 km in 14 minutes and 21 seconds.Th is was signifi cant as the fi rst sustained fl ight of an aircraft relying solely on direct solar power rather than batteries.It provided the designers with practical experience for developing a more effi cient solar-powered aircraft , taking into account that the Gossamer Penguin was fragile and had limited controllability.Th e Penguin fl ew preferably in the morning, when usually wind is minimal and consequently the turbulence level is still low.On the other hand, at this part of the day, the angle of the sun was low, requiring a tilting solar panel to capture properly the solar radiation (Noth, 2008).
From the lessons learned with Gossamer Penguin, AeroVironment engineering staff designed Solar Challenger, a piloted, solar-powered aircraft that was capable of highaltitude and long-endurance fl ights (Noth, 2008).
Th e last big step in aircraft powered by solar energy is the fi rst fl ight of twin-engine Solar Impulse airplane on December 3 rd , 2009 (Solar Impulse, 2013).Solar Impulse is a long-range solar powered plane project currently being undertaken at the École Polytechnique Fédérale in Lausanne, Switzerland.Th e project is promoted by Bertrand Piccard, who piloted the fi rst balloon that was able to circumnavigate the world nonstop.Th is project is expected to repeat that milestone in aviation history by employing a solar-powered airplane.Th e fi rst aircraft , offi cially named HB-SIA, is able to accommodate a single pilot, capable of taking off under its own power, and is intended to remain airborne up to 36 hours.Building on the experience of this prototype, a slightly larger follow-on design (HB-SIB) is planned to make circumnavigation of the globe in 20-25 days.On April 7 th , 2010, the HB-SIA underwent an extended 87 minutes test fl ight (Fig. 2).In contrast to earlier tests, the April fl ight reached an altitude of 1,200 m (3,937 ft ).In February 2012, Solar Impulse pilot Andre Borschberg spent more than 60 hours straight at the controls of the Solar Impulse fl ight simulator (Fig. 3).Granted, he was able to get some sleep, sometimes napping for a whole 20 minutes at a time (Solar Impulse, 2013).At that time, Borschberg was approaching the end of a 72-hour stint in the simulator, running through a series of tests and challenges to prepare for what lies ahead when he attempts to fl y around the world in a solar airplane in 2014 (Solar Impulse, 2013).
In recent years, European countries are taking a more central role in the development of High Altitude/Long Endurance solar-powered unmanned aerial vehicles (UAVs).Several projects are either ongoing or being planned for advanced solar powered vehicles.In the 2000-2003 period, a team from the Politecnico de Torino, in Italy, together with a team from the University of York in the UK, developed a concept for the Heliplat -a Very-Long Endurance Solar Powered Autonomous Aircraft (VESPAA) (Romeo and Frulla, 2004).Heliplat and other VESPAA UAVs could play the role of a "pseudo satellite", with the advantages of being closer to the ground, more fl exible and at a cost lesser than an actual satellite.Heliplat-like HALE fl ying above a major city will be able to cover a circular area of 1,000 km diameter, and process a predicted 425,000 cell phone conversations simultaneously (Romeo and Frulla, 2004).Th is means a user community of 8.5 million per unit (although this does not take into account data transmission).
Th e UAV platform of major interest to the present work is one that is capable to reach stratospheric altitudes and long endurance fl ights (HALE category) and powered by solar energy.In this context, the Zephyr, developed by the UK based QinetiQ (QinetiQ, 2013), is a confi guration that is very similar to that envisaged by the authors.Th e airplane carries a small payload and has no need for sophisticated assisted takeoff systems or prepared airfi elds (Fig. 4).Th e Zephyr is a lightweight airplane that uses a combination of a solar array and batteries to stay airborne.Th e plane weighs just 31 kg and has a wingspan of about 18 m (QinetiQ, 2013).Th e vehicle can circle over a particular area for extended periods.Th e military uses the vehicle for reconnaissance and communications platforms.Civilian and scientifi c programs use it for Earth observation.During the day, Zephyr uses its state-of-the-art solar cells spread across its wings to recharge high-power lithium-sulphur batteries and drive two propellers.At night, the energy stored in the batteries is suffi cient to keep Zephyr airborne.Th e batteries are supplied by Sion.In 2008, the airplane registered a recorded fl ight, staying airborne for a total of 82 hours and 37 minutes, which is a very impressive number for a solar powered air vehicle (QinetiQ, 2013).Th e Zephyr went for two straight nights without stopping for recharging and only relying on its solar powered batteries.Th e airplane is able to climb to altitudes up to 18 km (58,000 ft ) (QinetiQ, 2013).Missions conceived for Zephyr include forest and ocean monitoring, surveillance, and communication relay.Some highlights of Zephyr confi guration: • Zephyr's low-weight structure allows it to travel non-stop over long distances or to remain airborne in a desired station for a considerable long time.
• Th e unique propeller design provides the aircraft with a higher power-to-weight ratio.
• Th e aircraft fl ies day and night powered by solar energyrecharging its batteries along the day.• No complex launching mechanisms -the aircraft is launched manually by a ground crew of three people.• Silent fl ight -neither noise nor pollutant emissions.
• Th e wing design takes into account thermal air currents to lift the aircraft to higher altitudes.

METHODOLOGY
Before starting with the design of any solar-powered aerial vehicle, it is important to establish how the solar energy will be converted into vehicle motion (propulsion) and how to provide power for the airplane systems.Usually, the wing is an appropriate place to be covered with solar cells, which collect solar radiation and transform it into electrical energy.Batteries, propulsion and systems operate under diff erent conditions and thus a converter package is necessary.An appliance called Maximum Power Point Tracking (MPPT) enables the extraction of maximum power of solar cells and supplies the aircraft systems.During night, there is considerably less energy from solar cells and battery shall fulfi ll all power needs.Some modern solar cells are able to convert the infrared night radiation into electric power, enabling the batteries continuously to be loaded.Th is kind of solar cell was not considered in the present work.Figure 5 provides a scheme of the energy management inside the aircraft .

SolAR iRRAdiATion modelS
For a better understanding of the power system, it is necessary to describe the solar radiation model and the systems responsible for its transformation into useful energy.
In order to proceed with the calculation of the solar panel area required on the airplane, it is necessary to estimate the available solar radiation in a given location and date.For this, the relative movement of the Earth around the Sun and of our planet around its axis must be well understood.
Th e Earth has an elliptical orbit around the Sun, with an average distance of 150 million km.Period of revolution is of 365 days and 4 hours.On January 1 st , the nearest distance between our planet and the Sun takes place (perihelion); and on July 1 st , the remotest position, the distance is 3.3% farther than that of the closest position (aphelion).Considering that the incident solar radiation is inversely proportional to the square of the distance, the perihelion receives around 7% more radiation than when the Earth is at the aphelion.Another four points also are very important in the astronomy: the autumn and spring equinoxes; and summer and winter solstices (Fig. 6).Th e perihelion and the aphelion are the days of most and least intense radiation, respectively.Th e summer and winter solstices are the days with the longest and shortest time of solar radiation exposure.Being conservative, it is considered that the aircraft should able to fl y in any condition and so the point of project is the critical day of the year, in which it receives the least radiation along the day.Th e solar irradiance models found in the literature are based on data collected in the Northern hemisphere, mainly in the United States and Europe.For the present work, the model R.SUN was employed (IET, 2013).Th is sophisticated model was distributed by the Photovoltaic Geographical Information System (PVGIS) of the European Union.PVGIS provides online interactive maps of photovoltaic potentials in Europe and Africa.Figure 7 shows such a map considering the yearly sum of solar electricity generated by 1 kWp system with optimallyinclined modules.R.SUN was developed for the European and Africa environment and it is able to predict the direct and diff use irradiation and that refl ected by the Earth's surface.Th is last part of the solar irradiation is not taken into account in the present work, since the solar panels are located on the wing upper side of our solar-powered UAV. the irradiation model.Th e power demand should be easily achieved in the inter-tropical region, where Brazil is located, since the incident radiation is larger there.

eleCTRiCAl loAd
In the preceding paragraphs, the available power from solar irradiation was outlined.In this section, the concern is with the electrical power demand for the aircraft .
Power required for the payload package can vary.For this reason, an electrical demand of 100 and 200 W was considered.Power required for the control systems actuators is estimated to be 25.5 W. Th e engine power can be modeled in the following way (Eq.1; Anderson, 1989): QinetiQ's Zephyr presents an estimated electrical load of 174 W. Th is fi gure occurs close to the stall condition, being necessary to adopt a safety margin.Th ere are some power losses in the power plant system that increase the required power to operate the airplane.Such losses are caused by the propeller, the control box, the engine, and the gearbox, which present effi ciencies of 87, 95, 95, and 95%, respectively (Noth, 2008;Roskam, 2000).Taking into account such losses, the required weight-to-power ratio tops 100 kg/hp.Th us, the cruise is not the most critical condition to defi ne the required power.Some critical maneuvers must be addressed for such purpose.Th e airplane must be able to handle gusts and other severe operating conditions.However, in the present work, the used approach was based on similar weight-to-power ratios at cruise R.SUN is able to estimate the solar irradiation according to latitude, altitude, date and time of the day.In this way, it can be computed the radiation accumulated during an unclouded day.From this estimation, an example of density of energy per area is shown in Fig. 8.
According to the R.SUN model, for an aircraft at 40ºN latitude and fl ying 16 km above sea level, the critical day is December 21 st .In this day, the distribution of radiation is shown in Fig. 6.Th e chosen latitude is the reference for of some solar-powered planes (Table 1).Th e adopted value was slightly higher than that one of Zephyr: 25 kg/hp.
Typical cruise power for electrical driven airplanes is 56% of the engine nominal power.Th us, for the Zephyr airplane, this represents an increase of 140% and the adopted fi gure for the present work airplane was of 17.9 kg/hp.

ACTUAToRS
Actuators are employed in control surfaces like ailerons, rudder, and elevators.Th e airplane under development is confi gured with no high-lift devices and presents no landing gear.German company Volz is the actuator supplier for the Zephyr UAV (Volz Servos, 2013).Th e temperature of operation for usual actuator varies from 30 to 70ºC.However, in the tropopause, the typical temperature is -56.5ºC.For this reason, they developed a special actuator able to withstand temperatures below -70ºC -model DA 13-05-EXP 11859 (Fig. 9).
All actuators of the DA-13-05 Volz family have the same size (37.4x34.9x13.3mm), operating voltage (4.8 to 5 V), angle (130°), and casing mass (19 g) but they diff er by available output torque, device rotating speed and electrical current (power) (Volz Servos, 2013).Zephyr's actuator is the most advanced available on market in its class.However, there is no public data available and therefore we adopted the specifi cation of the DA 13-05-60 device.

SolAR pAnelS And BATTeRieS
Th e solar panels are extremely important components, considering that they are the unique source of energy, except the charged batteries in the fi rst day of operation.Th e impact of solar panels on the project is unquestionable.Th eir development was recorded to be slow and always has been a critical bottleneck for this kind of airplane.For example, Pathfi nder and Pathfi nder Plus were developed with the same characteristics, at the same time and using the same technology, and by the same team.However, they diff er in service ceiling, which is about 30,000 ft for the Plus version thanks to increased effi ciency of solar panels.
Several characteristics of state-of-art solar panels were compared, among them the effi ciency and weight per area.Flexible panels (Fig. 10) were then selected.Both specifi c weights are very similar and they can be considered as ultralight panels.Effi ciency is the factor that was taken into account for panel selection as well.In a conservative way, in this study we consider ISA+15 atmosphere conditions, as the effi ciency increases with decreasing temperature.As result, the panel

opTimizATion fRAmewoRK
The simulations for the airplane design under consideration were carried out by using the commercial software package modeFrontier ® V4.3 (ESTECO, 2011).The optimization framework modeFRONTIER provides a multi-objective optimization and design environment and it easily enables the coupling of CAD/computer aided engineering (CAE) tools, finite element structural analysis and computational fluid dynamics (CFD) software.It is developed by ESTECO SpA and provides an environment for product engineers and designers (ESTECO, 2011).ModeFRONTIER ® is a Graphical User Interface (GUI) driven software written in Java that wraps around the CAE tool, performing the optimization by modifying the value assigned to the input variables, and analyzing the outputs as they can be defined as objectives and/or constraints of the design problem.
In the present work, the airplane configuration that was select for study is very similar to that of the monoplane Qinetiq Zephyr, i.e., featuring a rectangular wing with a conventional tail, which is connected to the wing by a boom.The two engines are located at the inner wing.
The design variables of the present optimization framework are given in Table 2.No geometric wing twist was considered.Two electrical power requirements related to two different payloads were simulated: 100 and 200 W.It is reasonable to assume that a lighter airplane will be cheaper.Airplane size is proportional to weight, and if there are two airplanes, one small and one large, with the same payload, the smaller one is structurally more efficient, considering it requires a lighter structure to perform the same mission.Thus, airplane weight is an excellent indicator of configuration efficiency and it was considered the objective to be minimized in the mono-objective simulations.The constraints that were taken into account are: handling qualities, rudder shadowing at stall condition of the horizontal tail, and the area of solar panels, which have to be smaller than the available area on the wing.
Multi-objective simulations were run as well.In this case, weight and energy surplus were taken as objectives and an electrical demand of 200 W for the payload was considered.

diSCiplineS
The airplane under consideration in the present study must operate at high altitudes and its loiter is performed at very low speeds, which implies a low Reynolds number relative to wing mean aerodynamic chord.Typical Reynolds number lies in the 150,000 -200,000 range.Due to the low speed on station, high values of lift coeffi cient (C l ) are experienced by the airplane wing.Taken into account that energy supply is critical, a low-drag confi guration is mandatory.Based on Zephyr confi guration, a typical C l of 0.83 at 17 km of altitude was estimated, considering a speed of 60 km/h.In this condition, almost 80% of span operates at C l > 0.8, as shown in Fig. 11.Th us, the biggest aerodynamic issue was to fi nd out a lowdrag airfoil for high local lift coeffi cients.Due to low Reynolds number, a laminar airfoil was considered, with "drag bucket" covering the desired C l range (Fig. 12).Th e NACA 6-digit family to experimental results published by Abbott and Doenhoff (Abbott and Doenhoff , 1959) (Fig. 13).Table 3 contains some fi gures obtained with XFOIL and from experimental data.Th e correction for the polar curve was obtained by fi tting a parabola to the non-laminar portion of the polar curve (Eq.2): Where C d is the drag coeffi cient.off ers a variety of laminar airfoils and therefore the NACA 63412 profi le was selected to compose the wing.It combines all desired characteristics for the solar-powered UAV under consideration: high maximum lift coeffi cient (C lmax ); moderate to low value for the moment coeffi cient (C m ); and 12% relative thickness, an adequate one.All the polar curves were computed with the panel code XFOIL (Drela, 2000) and adjusted to fi t Th e NACA 63010 airfoil was chosen for the horizontal and vertical tailplanes (Fig. 14).Aerodynamic calculations for the complete confi guration were performed with the incompressible Athena Vortex Lattice (AVL) vortex-lattice code (Youngren and Drela, 1988).AVL handles lift ing surfaces, fuselages, and booms.All required aerodynamic and stability derivative coeffi cients can be quickly calculated with AVL (Youngren and Drela, 1988).
Concerning load calculation, there is no applicable certifi cation regulation for this kind of aircraft .Estimations that were carried out for the V-n diagram elaboration brought no realistic results.In this eff ort, FAA FAR-23 and JAR-VLA regulations were considered for a Zephyr-like airplane.For this reason, the present work considered a maximum a load factor of 3.8 for the structural sizing (Fig. 15).
analysis employed in the present study were very simple, as described by Megson (1999).Th e bending moment is supported by stringers only and torsion loads, by both stringers and skin.Th e structural layout is shown in Fig. 16, extending from leading edge to 25% of chord, where aerodynamic center is localized.Th e thickness of the wing skin is the same along the entire span, but stringers may vary for each wing station.
Th e cruise speed defi ned by the minimum required engine power for leveled and straight fl ight.Th e upper limit of the airplane dive speed was set to be 25% above the cruise speed.Th e maximum load factor 3.8 was applied for wing sizing; horizontal and vertical tail stabilizers sizing considered the cruise condition, C Lmax , and control surface defl ection of 15º; and boom was sized considering simultaneous tails forces.Fuselage and engines were not calculated.Th e methods of Ribs were not computed but it was assumed putting three of them per meter, with constant thickness.
Th e boom has a cylindrical form with constant radius and thickness, approximated by thin-walled tube.It can easily withstand the existing loads for this kind of airplane.Its defl ection was a constraint and used as sizing criteria.Carbon fi ber was the standard material for solar airplanes, except skin, which is built of Mylar.Biaxially-oriented polyethylene terephthalate (BoPET) is a polyester fi lm made from stretched polyethylene terephthalate (PET) and is used for its high tensile strength, chemical and dimensional stability, transparency, refl ectivity, gas and aroma barrier properties, and electrical insulation.A variety of companies manufacture BoPET and other polyester fi lms under diff erent brand names.In the UK and the United States, the most well-known trade names are Mylar, Melinex and Hostaphan (Staugaitis and Kobren, 1996).
Densities of the selected materials for the airplane structure are well known and thus the calculation of the mass distribution is an easy task.Th e fuselage and payload had fi xed weight; the weight of batteries depends on the capacity to supply all systems during night; and engine weight was estimated based on methodology described by Noth (2008).Th us, the weight and moment of inertia of each component can be estimated.Th ese calculations are performed through an iterative process   Nz: load factor.
until convergence is reached according to some stopping rules.Demand for electric power depends strongly on the drag, which, in turn, depends on the lift coeffi cient.Stability and control is a top issue in aircraft design, particularly hard for autonomous airplanes.Unplanned situations may happen and, in this case, there is no pilot to control and stabilize the airplane.Although an on-board computer can control an unstable airplane, this paves the way for accidents.For this reason, fl ying qualities levels 1 or 2 were imposed, according to MIL-F8785C (Department of Defence of United States of America, 1980), adapted for UAVs (Peters and Andrisano, 1997).Th is leads to the implementation of lateral-directional analyses in the design framework, addressing short-period, phugoid, roll, divergent spiral and Dutch-roll characteristics.

RESULTS
Th e modeFrontier ® workfl ow for the task under consideration is displayed in Fig. 17.Th ere are ten design variables in total.Th ey are related to the wing, horizontal tail (HT), and vertical tail (VT).Th e AVL panel code was employed to calculate the aerodynamic coeffi cients and stability derivatives.Some MATLAB ® routines then evaluated the C Lmax and dynamic behavior of the individuals that arise in the simulation process from data provided by AVL.
Th e simulations were run on a desktop computer fi tted with a single Intel Core2Quad Q6600 2.40 GHz processor, and 8.0 GB of installed Random Access Memory (RAM).
Th e initial population was generated with the SOBOL algorithm, available in the modeFrontier ® framework.SOBOL guarantees that any region of the design space does not become saturated, assuring that the entire domain be fulfi lled with a great variety of individuals.
Th e multi-objective MOGA-II genetic algorithm (ESTECO, 2011) was chosen for running the simulations.MOGA-II is an effi cient multi-objective genetic algorithm that uses a smart multi-search elitism.Th is new elitism operator is able to preserve some excellent solutions without bringing premature convergence to local-optimal frontiers.Th e effi ciency of this algorithm has been orderly proved on six well known test functions for multi-objective optimization.
For simplicity, MOGA-II requires only very few userprovided parameters; several other parameters are internally settled in order to provide robustness and effi ciency to the optimizer.Th e algorithm attempts a total number of evaluations that is equal to the number of points in the Design of Experiment (DOE) table (the initial population) multiplied by the number of generations.

mono-oBJeCTiVe SimUlATion
Th e fi rst runs revealed that a large number of individuals violated the posed restrictions.It is easy to understand, because in fi rst generations genetic algorithm searches in all

Variable Value
Generations 20

Repeated individuals 41
Total processing time 7h51m25s Average processing time for a single individual 1m19s Average processing time for four individuals 5m15s considered domain and more advanced generations are next to optimum.So, algorithm naturally reduced the domain to small range that offers good individuals, except mutations.
For the simulation tasks considering payload electrical demand of 100 W, 20 generations revealed to be enough to provide satisfactory convergence for obtaining an optimal airplane configuration (Table 4).The first runs recorded a large number of individuals that violated the prescribed constraints.Along the convergence process, the optimization framework naturally narrowed the band to generate individuals and most of them fulfilled the imposed constraints (Fig. 18).In other hand, mutation may generate unfeasible individuals along the simulation process.
The area and weight are consistent with data from Zephyr, but its required power supply is unknown.However, the wing loading of the best individual is very close to that of Zephyr.
Considering only the best individuals that did not violate restrictions, it is possible to state that a minimum wing area of 16 m 2 is required for obtaining a feasible configuration.Larger areas can feed systems with greater capacity during the day and must be turned off at night because the battery does not have sufficient storage capacity.For example, a system that requires 350 W can work under daylight conditions and must be turned off at night for airplanes with wing area set to 20 m 2 .The day chosen as the project point is very restrictive.If the same airplane flew in the summer, an 1,800 W of power could be generated during the day.
An overview of the best individual from the simulation is provided by Fig. 20.The optimal airplane presents 20 m 2 of wing area and wing aspect ratio of 25 (Table 5).All handling qualities were level 1 on station.The violation of power supply constraint is strongly associated with small wing area, while most of other violations are related to tail configuration parameters.Figure 19     Airplane gross weight amounts 30.1 kg.Th e weights of the airplane components are consistent and the battery weight fraction is huge (Fig. 21), revealing that this equipment presents an issue critical for the design of a solar-powered airplane.Typically, a battery generates 350 Wh/kg (265 Wh/kg considering the wrapper), but further development can increase this fi gure to 600 Wh/kg, which would have great benefi t for the confi guration of solar-powered aircraft .
As seen before, batteries are critical for design of solar powered airplanes.If the electrical power requirement for the payload is increased, the structural weight is also increased.Th is directly aff ects the weight of the engine and the required thrust to propel the airplane.

Multi-objective optimization
Weight minimization and power surplus maximization were taken as objectives for this task.Wing area was allowed to vary between 30 and 60 m 2 .Aft er 40 generations with 30 individuals each, the simulation was stopped.Figure 22 shows the feasible individuals of the present simulation and Fig. 23, its Pareto front.
Here, the available power from the optimal individuals is considerably higher than that of the optimal airplane from the previous simulation.Th is can be credited to the lower boundary that was set for the wing area, which was 50% higher than that of the optimal airplane from the mono-objective simulation.Th e confi guration from the Pareto front with the lowest available power weighs just 35.21 kg, slightly over the weight of the optimal airplane from the previous simulation.Table 6 contains some characteristics of this airplane.

CONCLUDING REMARKS
The development of solar-powered airplanes in the past was directly affected by the technology of solar panels.Nowadays, alongside with the solar panel efficiency issue, energy storage became a major concern for the design of solar air vehicles.In addition, considering that there are few airplanes flying in altitudes from 15 to 18 km, there are also few aircraft systems manufacturers able to deliver products capable of working under severe environmental conditions like the ones found in such altitudes.
The application of optimization tools proved to be quite appropriate, as provided in less than one day running a very large variety of airplanes, for which one can identify the strengths, weaknesses, and typical values of the variables for a good design.The case study proposed is an excellent example of this, because there are few semi-empirical mathematical models and built aircraft data, and even then with the application of simple theories, it was possible to design and verify the consistency with the few existing models.
Future work will encompass the wing and tail airfoils as design variables.

Figure 1 .
Figure 1.The fi rst piloted solar plane, the Gossamer Penguin.

Figure 5 .
Figure 5. Solar energy conversion system to power engine and other aircraft systems.

Figure 8 .
Figure 8. Yearly variation of accumulated daily radiation.

Figure 7 .
Figure 7. Photovoltaic solar electricity potential in European countries (Source: Photovoltaic Geographical Information System of European Union).

Figure 13 .
Figure 13.Adjusted polar curve for NACA 63412 airfoil according to experimental data.

Figure 14 .
Figure 14.Adjusted polar curve for NACA 63010 airfoil according to experimental data.
C d : drag coeffi cient; C l : lift coeffi cient.

Figure 15 .
Figure 15.Estimate V-n diagram for the Zephyr airplane.

Figure 18 .
Figure 18.Feasible individual progression along the simulation process.
provides an overview of the constraint violation by individuals for the entire simulation.

Figure 20 .
Figure 20.Optimal airplane configuration from the monoobjective simulation.

Figure 23 .
Figure 22.Feasible individuals from the multi-objective simulation.

Figure 21 .
Figure 21.The above pie chart provides a weight breakdown of the optimal airplane.EH: horizontal tail; EV: vertical tail.

Table 4 .
Information for the standard demand simulation.

Table 5 .
Optimal airplane from mono-objective simulation.
w : wing area; Y q : break position; AR w : wing aspect ratio; AR HT : horizontal tail aspect ratio; AR v : vertical tail aspect ratio; L v : vertical tail lever; L H : horizontal tail lever.

Table 6 .
Characteristics of the optimal lowest power airplane from the multi-objective simulation.S w : wing area; Y q : break position; AR w : wing aspect ratio; AR HT : horizontal tail aspect ratio; AR v : vertical Tail aspect ratio; L v : vertical tail lever; L H : horizontal tail lever.