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Selection of Size of Battery for Solar Powered Aircraft
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Selection Selection of of Size Size of of Battery Battery for for Solar Solar Powered Powered Aircraft Aircraft IFAC PapersOnLine 51-29 (2018) 424–430 Selection Selection of of Size Size of of Battery Battery for for Solar Solar Powered Powered Aircraft Aircraft
* * ** ** Vijay Shankar Dwivedi Prashant Kumar *, Ajoy Kanti Ghosh **, G. M. Kamath** Vijay Shankar of Dwivedi Prashant Kumarfor , Ajoy Kanti Powered Ghosh , G. M. Kamath Selection Size*,, of Battery Solar Aircraft * * ** ** [[email protected], [email protected], [email protected], [email protected]] Vijay Shankar *, Prashant Kumar *, Ajoy Kanti Ghosh **, G. M. Kamath** [[email protected], [email protected]] Vijay Shankar Dwivedi [email protected], , Prashant [email protected], , Ajoy Kanti Ghosh , G. M. Kamath *Research scholar, *Research scholar, *Engineering, Indian * Institute of Technology, ** ** [[email protected], [email protected], [email protected]] Department of Kanpur, India. Vijay Shankar [email protected], , Prashant Kumar , Ajoy Kanti , G. M. Kamath Department of Aerospace Aerospace Engineering, Indian Institute of Ghosh Technology, Kanpur, India. [[email protected], [email protected], [email protected], [email protected]] ** *Research scholar, **Professor Professor *Research scholar, Department of Engineering, Indian Institute Kanpur, [[email protected], [email protected], [email protected]] Department of Aerospace [email protected], Engineering, Indian Institute of of Technology, Technology, Kanpur, India. India. ** **Professor *Research scholar, Professor Department Indian Department of of Aerospace Aerospace Engineering, Engineering, Indian Institute Institute of of Technology, Technology, Kanpur, Kanpur, India. India. ** Professor Department of work Aerospace Engineering, Indian Institute of Technology, Kanpur, India. trajectory Abstract: This research research proposes the methodology methodology for the the selection selection of battery battery and flight flight Abstract: This work proposes the for of and trajectory for a solar powered aircraft to achieve the maximum endurance. A mathematical model is for a solar powered aircraft to achieve the maximum endurance. A mathematical model is developed developed for for Abstract: This research work proposes the methodology for the selection of battery and flight trajectory the availability of irradiance at a particular geographical location on a given date and time. This work also the availability of irradiance at a particular geographical location on a given date and time. This work also Abstract: This research work proposes the methodology for the selection of battery and flight trajectory for aircraft to the endurance. mathematical model is constitutes the analysis of in with flight, of constitutes the detailed detailed analysis of variation variation in endurance endurance with the theA geographical location of flight, time timefor of for aa solar solar powered powered aircraft to achieve achieve the maximum maximum endurance. Ageographical mathematicallocation model of is developed developed for the availability of irradiance at a particular geographical location on a given date and time. This work also flight (relative position of Earth with respect to Sun), availability of solar irradiance, takeoff time, battery Abstract: This research work proposes the methodology for the selection of battery and flight trajectory flight (relative position of Earth respect to Sun), availability of asolar takeoff time, battery the availability of irradiance at a with particular geographical location on givenirradiance, date and time. This work also constitutes the analysis of in with location of flight, time of size, velocity, flight altitude, aerodynamic parameters of aircraft and propulsion for a flight solar powered aircraft to achieve the maximum endurance. mathematical model is developed size, flight velocity, flight altitude, aerodynamic parameters of the aircraft and aircraft aircraft propulsion system. constitutes the detailed detailed analysis of variation variation in endurance endurance with theAgeographical geographical location of flight, system. timefor of flight (relative position of Earth with respect to Sun), availability of solar irradiance, takeoff time, battery A case study is done for irradiance conditions on March 15 for the UAV MARAAL that is built at UAV the availability of irradiance at a particular geographical location on a given date and time. This work also A case(relative study isposition done forofirradiance March 15 for the MARAAL takeoff that is built UAV flight Earth withconditions respect toon Sun), availability ofUAV solar irradiance, time,atbattery size, velocity, flight altitude, aerodynamic parameters of aircraft aircraft propulsion system. laboratory This methodology can successfully during all seasons the constitutes the Kanpur. detailed analysis of variation in be endurance with the location ofof timefor of laboratory IIT Kanpur. This methodology can be successfully used during and all the the seasons offlight, the year, year, for size, flight flight IIT velocity, flight altitude, aerodynamic parameters of used the geographical aircraft and aircraft propulsion system. A case study is done for irradiance conditions on March 15 for the UAV MARAAL that is built at UAV all geographical locations on the Earth and for any solar powered aircraft. We can reduce the number of flight (relative position of Earth with respect to Sun), availability of solar irradiance, takeoff time, battery all geographical locations on the Earth and foron anyMarch solar 15 powered We can reduce number of A case study is done for irradiance conditions for theaircraft. UAV MARAAL that isthe built at UAV laboratory Kanpur. This methodology can successfully used during all the seasons of for cells to installed on UAV for operation or longer endurance for similar UAV if size, flight velocity, flight altitude, aerodynamic the aircraft aircraft propulsion system. cells to be be IIT installed on UAV for similar similar operation or we we can canofensure ensure longerand endurance for similar UAV if laboratory IIT Kanpur. This methodology can be beparameters successfully used during all the seasons of the the year, year, for all geographical locations on the Earth and for any solar powered aircraft. We can reduce the number of we take care of the proper selection of battery and the flight pattern for the operation to be performed. The A case study is done for irradiance conditions on March 15 for the UAV MARAAL that is built at UAV we take care of the proper selection of battery and the flight pattern for the operation to be performed. The all geographical locations on the Earth and for any solar powered aircraft. We can reduce the number of cells to installed on for or ensure longer endurance for UAV if objective this paper is to the battery to installed and selection of altitude profile laboratory Kanpur. This methodology can be capacity successfully used during all the seasons of the year, for objective ofIIT this paper is to estimate estimate theoperation battery capacity to be be installed and selection of similar altitude profile cells to be beof installed on UAV UAV for similar similar operation or we we can can ensure longer endurance for similar UAV if we take care of the proper selection of battery and the flight pattern for the operation to be performed. The during flight for a solar powered aircraft. all geographical locations on the Earth and for any solar powered aircraft. We can reduce the number of during forthe a solar powered aircraft. we takeflight care of proper selection of battery and the flight pattern for the operation to be performed. The objective of this paper is estimate the battery to be installed and selection of altitude profile cells to be on UAV for similar orControl) we can ensure longer endurance similar UAV if objective ofinstalled this paper is to to Federation estimate the battery capacity capacity to Hosting be installed and selection of altitude profile © 2018, IFAC (International ofoperation Automatic by Elsevier Ltd. Allfor rights reserved. during flight for a solar powered aircraft. we take care of the proper selection of battery and the flight pattern for the operation to be performed. The during flightSolar for aUAV; solar powered aircraft. Irradiance; Numerical simulation; Prolonged flight. Endurance Keywords: Battery selection; Keywords: UAV;isBattery selection; Irradiance; Numerical simulation; flight. Endurance objective ofSolar this paper to estimate the battery capacity to be installed andProlonged selection of altitude profile of solarflight UAV,forEnergy Energy management, Robotics, Flight Flight dynamics, dynamics, Altitude Altitude profile, profile, Solar Solar modelling. modelling. of solar UAV, Robotics, during a solarmanagement, powered aircraft. Keywords: Numerical Keywords: Solar Solar UAV; UAV; Battery Battery selection; selection; Irradiance; Irradiance; Numerical simulation; simulation; Prolonged Prolonged flight. flight. Endurance Endurance dynamics, of solar UAV, Energy management, Robotics, Flight Altitude profile, Solar modelling. of solar UAV, Energy management, Robotics, Flight dynamics, Altitude profile, Solar modelling. Keywords: Solar UAV; Battery selection; Irradiance; Numerical simulation; Prolonged flight. Endurance dynamics, of solar UAV, Energy management, Robotics, Flight Altitude profile, Solar modelling. In In most most of of the the parts parts of of the the world world the the solar solar energy energy is is available available 1. 1. INTRODUCTION INTRODUCTION all the seasons. Even in cloudy seasons the solar irradiance all the seasons. Even in cloudy seasons the solar irradiance is is In most the of world the solar is available aa certain day time. the The use available above certain altitude all the dayenergy time. Though Though the The use of of UAVs UAVs is is growing growing day day by by day day and and gaining gaining popularity popularity In most of ofabove the parts parts of the thealtitude world all the the solar energy is available available 1. INTRODUCTION 1. INTRODUCTION all the Even in seasons solar irradiance is installation of cells on adds extra weight to in installation of solar solar cells on aa UAV UAV addsthe extra weight to it, it, yet yet in both both civil civil and and military military applications. applications. In In conventional conventional UAVs UAVs all the seasons. seasons. Even in cloudy cloudy seasons the solar irradiance is available above a certain altitude all the day time. Though the it will be beneficial in terms of endurance if power harvested The use of UAVs is growing day by day and gaining popularity the endurance is limited by the energy carried with the aircraft In most of the parts of the world the solar energy is available it will be above beneficial in terms of endurance powerThough harvested theINTRODUCTION endurance is limited by the with the aircraft available a certain altitude all the dayiftime. the The use of UAVs is growing dayenergy by daycarried and gaining popularity 1. installation of cells on adds extra weight to yet cells is than the power required to in civil and military applications. In at the this is in all thesolar seasons. Even in cloudy solar irradiance is from solar cells is more more than theseasons power required to carry carry this at the time time of takeoff. Usually this energy energy is carried carried UAVs in the the from installation of solar solar cells on aa UAV UAV addsthe extra weight to it, it,this yet in both both civil of andtakeoff. militaryUsually applications. In conventional conventional UAVs it will be beneficial in terms of endurance if power harvested extra weight (solar cell, encapsulation, MPPT and wiring). the endurance is limited by the energy carried with the aircraft battery or in the form of fuel. In battery powered UAVs the available above a certain altitude all the day time. Though the The use of UAVs is growing day by day and gaining popularity extra weight (solar cell, encapsulation, MPPT and wiring). battery or in the form of fuel. In battery powered UAVs the it will be beneficial in terms of endurance if power harvested the endurance is limited by the energy carried with the aircraft solar cells is the to at the time Usually energy is in power in aa military very time this because there iscarried no supply supply of from installation of solar cells than on a UAV adds required extra weight to it,this yet in both civil of and applications. In there conventional UAVs power drains intakeoff. very short short time because no of from cells is more more than thetopower power required to carry carry this at the drains time of takeoff. Usually this energy is is carried in the the For aa solar fully solar powered aircraft meet the complete demand For fully solar powered aircraft to meet the complete demand extra weight (solar cell, encapsulation, MPPT and wiring). battery or in the form of fuel. In battery powered UAVs the power and the whole operation depends upon battery carried it will be beneficial in terms of endurance if power harvested the endurance iswhole limited the energy carried with the aircraft power and upon battery carried weight (solar cell, encapsulation, MPPT and wiring). battery or inthethe formoperation ofbyfuel. Independs battery powered UAVs the extra of supply from solar cells aa very large is of power power supply solar cellspower very large wingspan wingspan is power drains aa very time because there no supply of with UAV, there always structural limitation limits solar cells powered is from more than the required to shown carry this at thethe time ofin Usually this energy is is in the with the UAV, there isshort always structural limitation that limits power drains intakeoff. veryis short time because there iscarried nothat supply of from For a fully solar aircraft to meet the complete demand required. Wingspan of different solar aircrafts is in required. Wingspan of different solar aircrafts is shown in For a fully solar powered aircraft to meetMPPT the complete demand power and the whole operation depends upon battery carried the amount of battery that can be carried with the UAV. In extra weight (solar cell, encapsulation, and wiring). battery or in the form of fuel. In battery powered UAVs the the amount of whole batteryoperation that can be carriedupon withbattery the UAV. In Table power and the depends carried of supply from aa very large is 1. This This wingspan issolar largecells because the power power need 1. wingspan large because the need is is high high of power power supply from is solar cells very large wingspan wingspan is with UAV, always structural limitation that limits fuel-based UAVs the endurance depends and power drains in there a very short time becauseupon therefuel is nocarried supply of Table fuel-based UAVs the is endurance depends upon fuel carried and with the the UAV, there is always structural limitation that limits required. Wingspan of different solar aircrafts is shown in to carry the battery weight that is used during nights. The wing For a fully solar powered aircraft to meet the complete demand to carry the battery weight that is used during nights. The wing required. Wingspan of different solar aircrafts is shown in the of battery that can be carried with the UAV. In more fuel adds more weight payload has power and the depends upon carried moreamount fuel adds moreoperation weight where payload has always the amount of whole battery that can where be carried withbattery the always UAV. Inaa span Table 1. wingspan is large because the need is can besupply reduced significantly if athe thevery sizing of the the battery is of power from large wingspan span can be reduced significantly if sizing of battery is Table 1. This This wingspan issolar largecells because the power power need is high high fuel-based UAVs the endurance depends upon fuel carried and limitation. In recent past as the efficiency of solar cells is with the UAV, there is always structural limitation that limits limitation. UAVs In recent past as thedepends efficiency solar cellsand is done fuel-based the endurance uponoffuel carried to carry the battery weight that is used during nights. The wing in a well calculated manner. Apart from this, in a solar required. Wingspan of different solar aircrafts is shown in in the a well calculated Apart from this, in a wing solar to carry battery weight manner. that is used during nights. The more fuel adds more weight payload increasing is it become viable source the amount of cost battery that can where be carried withaahas the always UAV. Inaa done increasing and cost is decreasing decreasing it has has become viable source more fuel and adds more weight where payload has always span can be reduced significantly if the sizing of the battery is assisted UAVs also the endurance can be enhanced Table 1. This wingspan isthe largeendurance because thecan power need is high assisted UAVs also be enhanced span can be reduced significantly if the sizing of the battery is limitation. In recent past as the efficiency of solar cells is of power supply during the flight. A trend of improvement in fuel-based UAVs the endurance upon fuel carried of power supply during theasflight. A trend of of improvement in limitation. In recent past thedepends efficiency solar cellsand is significantly done in a well calculated manner. Apart from this, in a solar significantly if the battery is selected depending upon the to carry the battery weight that is used during nights. The wing if the battery is selected depending upon the done in a well calculated manner. Apart from this, in a solar increasing and cost is decreasing it has become a viable source the efficiency is shown in Fig. 1 and reduction in the price is more fuel and adds more weight payload ain has the efficiency iscost shown in Fig. 1where thealways price isa irradiance increasing is decreasing itand hasreduction become viable source assisted UAVs also the can pattern atsignificantly the siteendurance onif the given time andenhanced date of of span can be reduced sizing ofbe the battery is pattern at the on given time and date assisted UAVs also thesite endurance can be enhanced of power supply during the A improvement shown in limitation. In 2. recent past the efficiency solar cells in is irradiance shown in Fig. Fig. 2. of power supply during theasflight. flight. A trend trend of of of improvement in significantly if the battery is selected depending upon the operation and the aircraft characteristics. done in a well calculated manner. Apart from this, in a solar operation and the aircraft characteristics. significantly if the battery is selected depending upon the the is shown in Fig. 11 itand the is increasing and decreasing hasreduction become ain viable source the efficiency efficiency iscost shown incell Fig.has and reduction in the price price is irradiance pattern at on time date Apart from this aa is solar zero carbon emission assisted UAVs thesite Apart from this solarthe cellflight. has A zero carbon emission that that irradiance pattern also at the the siteendurance on given given can time beand andenhanced date of of shown in Fig. 2. of power supply during trend of improvement in shown this in Fig. 2. operation and the aircraft characteristics. makes a promising power source for future and therefore significantly ifthethe battery is selected depending upon the makes this a promising power source for future and therefore operation and aircraft characteristics. the efficiency is shown in focus Fig.has 1 and reduction in the price is Apart from this solar carbon emission this area that its this is is an an area thataaneeds needs focus onzero its efficient efficient utilization. Apart from this solar aacell cell hason zero carbon utilization. emission that that irradiance pattern at the site on given time and date of shown in Fig. 2. makes this a promising power source for future and therefore makes this a promising power source for future and therefore operation and the aircraft characteristics. this area that focus its Apart from solar aacell hason carbon utilization. emission that this is is an an areathis thataneeds needs focus onzero its efficient efficient utilization. makes this a promising power source for future and therefore this is an area that needs a focus on its efficient utilization.
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Table 2 MARAAL specifications Parameter Wing span Wing area Aspect ratio Empty weight Solar cells used
Value 5.35 m 2.04 m2 14 12 Kg Sunpower C60
Fig. 1. Solar cell efficiency with time.*
Fig 3. MARAAL Solar UAV 2. MATHEMATICAL MODELLING Fig. 2. Solar cell cost with time.* 2.1 Availability of Irradiance Table 1. Wingspan of different aircrafts Aircraft Solar Impulse Qinetiq Zephyr Helios HP03 NASA Centurion NASA Pathfinder
Earth revolves around the sun in an elliptical orbit whose eccentricity is such that the distance between the sun and the earth varies by 3.4 % above the sea. The mean distance between earth and sun is 1.495 x 1011 m, i.e. one astronomical unit (AU) (Duffie, John A., 1980).
Wing-span 63.4 m 22.5 m 75.3 m 62 m 36.3 m
Sun light is available only for limited number of hours therefore the utilization of this power should be done in an efficient way. Power consumed by UAV depends upon many factors such as speed at which we are flying, CL of UAV, duration of flight, rate of climb, how long we cruise at a particular altitude, payload etc. In a UAV there are two basic energy storing elements, the first battery and second the altitude i.e. the potential energy that we can trade for gliding. We dissipate energy during the flight. In solar UAV we have a supply of energy in form of solar energy. For a solar UAV to achieve maximum time of flight we need to focus aerodynamic aspects of flight in addition with the pattern we control the energy flow. Also depending upon the solar power availability we can optimize the endurance by selecting the optimal weight of battery and the cruise altitude where we charge our battery.
Fig. 4. Sun, Earth and Solar constant The solar constant (𝐺𝐺𝑠𝑠𝑠𝑠 ) is the power obtained from the sun on a unit area of surface perpendicular to the direction of propagation of the radiation at mean earth-sun distance (1 AU) outside the atmosphere. It is measured directly with the help of very high altitude aircraft, balloons, and spacecraft, which records the measurements of solar radiation outside the earth’s atmosphere. Resultant value of the solar constant Gsc was found to be 1367 W/m2 with an estimated error of 1.5%. (Duffie, John A., 1980; Jemaa, A BEN, 2013). (1) 𝐺𝐺𝑠𝑠𝑠𝑠 = 1367 𝑊𝑊/𝑚𝑚2 Since the distance between earth and sun is not constant, there is the periodic variation in extraterrestrial radiation flux.
In this paper an effort is made to find the best battery size and the flight pattern for maximum endurance. All study is done on solar UAV MARAAL, designed at UAV laboratory IIT Kanpur. Table 2 is representing the parameters associated with MARAAL and a visual of its flight is shown in Fig. 3. *https://sites.lafayette.edu/egrs352-sp14-pv/technology/history-of-pvtechnology/
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Variation is in the range of ±3.3 %. This change can be calculated using (2) (https://www.e-education.psu.edu/eme811/node/637). 𝐺𝐺𝑜𝑜𝑜𝑜 = 𝐺𝐺𝑠𝑠𝑠𝑠 (1.00011 + 0.034221 cos 𝐵𝐵 + 0.00128 sin 𝐵𝐵 + 0.000719 cos 2𝐵𝐵 + 0.000077 sin 2𝐵𝐵) 360 Where 𝐵𝐵 = (𝑛𝑛 − 1) 365
(2) (3)
Where 𝐺𝐺𝑜𝑜𝑜𝑜 is the extraterrestrial radiation incident on the plane normal to the radiation on the nth day of the year and this is shown in Fig. 5.
Fig. 6. Declination angle Latitude (ϕ): For Kanpur latitude is 26.5 N ΦKanpur = 26.50 Hour angle (ω): This is angular displacement of the sun either east or west of the local meridian because of the rotation of the earth on its axis at 150 per hour. Morning is considered to be negative and evenings positive *. cos ω = −tan ϕ tan δ (7) 2 (8) 𝑁𝑁 = cos −1 (−tan ϕ tan δ) 15 N is the number of daylight hours. Quantities ω and cos −1 (−tan ϕ tan δ) are in degree. For (7) beyond ϕ = ±66.55 deg: (tan δ − tan ϕ ) ≥ 1 there is no sunset, i.e. 24 hour daylight (tan δ − tan ϕ ) ≤ 1 there is no sunset, i.e. 24 hour darkness
Fig. 5. Extraterrestrial radiation incident on the plane normal to radiation To describe the hour-angle the local solar time (LST) is used, because the hour angle is zero at solar noon (LST: 12:00h), when the sun reaches its highest point in the sky. Using (4) the LST can be calculated from the local civil time (LCT) with the help of quantity called equation of time (EOT) (Rajendra, P., 2016; Keller, B. 2011). LST = LCT+EOT (4) EOT = 229.2(0.000075 + 0.001868cos(N) – 0.032077 sin(N) – 0.014615cos(2N) – 0.04089sin(2N)) (5) 360 Where, 𝑁𝑁 = (𝑛𝑛 − 1) , in deg 365 n = day number of the year The geometric relationships between a horizontal plane relative to the earth and the incoming beam solar radiation, that is, the position of the sun with respect to that plane, can be represented in terms of several angles. Declination(δ): It ranges from −23.45 degrees to +23.45 degrees with north to be positive (Keller, B. 2011). An approximate equation to find the declination is given in (6) (ElMghouchi Y., 2014). δ = 23.45 sin(A) (6) Where
A = 360 (
Fig. 7. Number of daylight hours The solar radiation that fills our sky are of three types: o Direct radiation, o Diffused radiation o Reflected radiation. "Direct radiation" also called as "beam radiation" or "direct beam radiation". It is used to describe solar radiation traveling on a straight line from the sun down to the surface of the earth.
284+n 365
) in degrees
"Diffused radiation", is the sunlight that has been scattered by molecules and particles in the atmosphere but that has still made it down to the surface of the earth.
* http://www.itacanet.org/the-sun-as-a-source-of-energy/part3-calculating-solar-angles/#3.2.-The-Hour-Angle
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Total radiation received (𝐺𝐺) is the summation of both, beam and diffused radiation (16) (ElMghouchi Y., 2014). (16) 𝐺𝐺 = 𝐺𝐺𝑐𝑐𝑐𝑐 + 𝐺𝐺𝑑𝑑 Direct and diffused irradiance on March 15 is shown in Fig 9.
Fig. 8. Types of radiation: Direct, diffused and reflected *. "Reflected radiation" On ground this has a contribution about 2% but for UAV at altitude this is negligible. Direct radiation is around 85% of the total insolation hitting the ground and diffuse radiation is about 15%. As the sun goes lower in the sky, the percent of diffuse radiation keeps going up until it reaches 40% when the sun is 10° above the horizon. Atmospheric conditions like clouds and pollution also increase the percentage of diffuse radiation. On an extremely overcast day, 100% of the solar radiation is diffuse radiation. The percentage of the sky's radiation that is diffuse is much greater in higher latitude, cloudier places than in lower latitude, sunnier places. Moreover, the percentage of the diffuse radiation tends to be higher in the winter than the summer in the higher latitude, cloudier places (Michele De Carli, 2012). Both of the radiations are considered and calculate the total amount of energy we receive. Hottel’s method is used to estimating the beam radiation transmitted through clear atmospheres which takes into account zenith angle (θz ) and altitude (Duffie, John A., 1980). Atmospheric transmittance for beam radiation is given by (9)
Fig. 9. Direct and diffused irradiance on a horizontal surface 2.2 Solar Cell In a solar UAV, solar cells are primary source of power. They convert photonic energy of available irradiance into electric energy. Their performance depends upon the materials used in the fabrication of it. In Table 4 the efficiency of different solar cells is given Table 4. Different types of solar cells with their maximum efficiencies available in market (Green, 2015) Type of solar cells Si Monocrystalline Si Polycrystalline Si Thin film GaAs thin film CIGS CdTe
−𝑘𝑘 ) cos 𝜃𝜃𝑧𝑧
(
(9) 𝜏𝜏𝑏𝑏 = 𝑎𝑎𝑜𝑜 + 𝑎𝑎1 𝑒𝑒 The constants 𝑎𝑎𝑜𝑜 , 𝑎𝑎1 and 𝑘𝑘 for the standard atmosphere with 23 km visibility are found from 𝑎𝑎𝑜𝑜 ∗ , 𝑎𝑎1 ∗ and 𝑘𝑘 ∗ using (10), (11) and (12). (10) . 𝑎𝑎𝑜𝑜 ∗ = 0.4237 − 0.00821(6 − 𝐴𝐴)2 (11) 𝑎𝑎1 ∗ = 0.5055 − 0.00595(6.5 − 𝐴𝐴)2 (12) 𝑘𝑘 ∗ = 0.2711 − 0.01858(2.5 − 𝐴𝐴)2 Where A is altitude of the observer in kilometers. Correction factors are applied to 𝑎𝑎𝑜𝑜 ∗ , 𝑎𝑎1 ∗ and 𝑘𝑘 ∗ to allow for change in climate types. The correction factors 𝑟𝑟𝑜𝑜 = 𝑎𝑎𝑜𝑜 /𝑎𝑎𝑜𝑜 ∗ , 𝑟𝑟1 = 𝑎𝑎1 /𝑎𝑎1 ∗ and 𝑟𝑟𝑘𝑘 = 𝑎𝑎𝑘𝑘 /𝑎𝑎𝑘𝑘 ∗ are given in Table 3 (Duffie, John A., 1980).
For solar UAV the GaAs is the best for performance point of view but due to the cost constrains Si monocrystalline (Sunpower C60) is used in MARAAL. Claimed efficiency by manufacturer of C60 is 23% but the achieved efficiency after installation on solar UAV was recorded about 20%. An ideal solar cell can be modelled by a current source (𝐼𝐼𝐿𝐿 ) in parallel with a diode; in practice no solar cell is ideal, so a shunt resistance (𝑅𝑅𝑆𝑆𝑆𝑆 ) and a series resistance (𝑅𝑅𝑆𝑆 ) component are added to the model (Lorenzo E, 1994). An equivalent circuit of solar cell is shown in Fig. 10 (Nishioka, K., 2007).
Table 3. Correction factors for climate types Climate Type Tropical Midlatitude summer Subarctic summer Midlatitude winter
𝐫𝐫𝐨𝐨 0.95 0.97 0.99 1.03
𝐫𝐫𝟏𝟏 0.98 0.99 0.99 1.01
Maximum efficiency achieved 22.9 ± 0.6 18.5 ± 0.4 8.2 ± 0.2 28.9 ± 1.0 15.7 ± 0.5 17.5 ± 0.7
𝐫𝐫𝐤𝐤 1.02 1.02 1.01 1.00
* http://bembook.ibpsa.us/index.php?title=Ground_Reflectance Clear sky beam radiation (𝐺𝐺𝑐𝑐𝑐𝑐 ) can be calculated using (13) (13) 𝐺𝐺𝑐𝑐𝑐𝑐 = 𝐺𝐺𝑜𝑜𝑜𝑜 𝜏𝜏𝑏𝑏 cos 𝜃𝜃𝑧𝑧
Fig. 10. Equivalent circuit of a solar cell
Clear sky diffuse radiation can be calculated using (14). (14) 𝐺𝐺𝑑𝑑 = 𝜏𝜏𝑑𝑑 𝐺𝐺0 Where 𝜏𝜏𝑑𝑑 = 0.271 − 0.294 𝜏𝜏𝑏𝑏 (15) And 𝐺𝐺0 is extraterrestrial beam radiation on horizontal plane. 427
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2.4 Propeller Propeller used in MARAAL is 30.5”x9.7 triple blade. The efficiency of a propeller is measured with respect to advance ratio (𝑗𝑗) (John B. Brandt, 2011). 𝑉𝑉 (17) 𝑗𝑗 = 𝑛𝑛𝑛𝑛 Where V = velocity n = rpm D = diameter A wind tunnel test was performed for the characterization of the propeller and an efficiency was recorded about 70 % for the advance ratio of 0.6 that is the condition of cruise. During climb the advance ratio drops to 0.4 and for this advance ratio the efficiency was recorded 58 %.
Fig. 11. V-I characteristic of a solar cell When a solar cell is short circuited the current is maximum (𝐼𝐼𝑠𝑠𝑠𝑠 ) but the voltage is zero, resulting in zero power. As the load impedance increases the current remains almost constant and then starts decreasing (from 𝐼𝐼𝑚𝑚𝑚𝑚 ), and voltage keeps increasing till (𝑉𝑉𝑚𝑚𝑚𝑚 ). At open circuit the voltage is maximum (𝑉𝑉𝑜𝑜𝑜𝑜 ) but the current is zero. The power that is delivered by solar cell to the load is the product of voltage and current and this pattern is shown in Fig. 11. The load impedance has always a value for which the power extracted is maximum, this maximum keeps changing with the irradiance, load and temperature. To utilize the solar cell most efficiently we need to operate about this maximum power point and the circuitry used for tracking the maximum power point is called MPPT (maximum power point tracking). The typical efficiency of MPPT is about 94 % to 98 % (Ezinwanne O., 2017; Karami N., 2017). Solar cells installed in MARAAL is Sunpower C60. Characteristics of Sunpower C60 is shown in Table 5.
2.5 Electronic Speed Control (ESC) and Motor ESC is used for the rpm control of the motor. It receives a pulse width modulated signal and changes the rpm of motor depending upon the duty cycle of received pulses. When the input and output voltages are very close to each other the efficiency of ESC is maximum and typically about 98 %, but this may drop up to 80 % when the input output voltage difference is more. In our operation the 6-cell battery is used so that the input voltage is close to operating voltage of motor and the efficiency of ESC is above 94 %. 2.6 Power Required
Table 5. Sunpower C60 specifications Parameter
Value
Peak Power
3.42 Watt
Efficiency
22.5 %
Peak Voltage
0.582 Volt
Peak Current
5.93 Amp
Open-circuit Voltage
0.687 Volt
Short-circuit Current Length Width Thickness
6.28 Amp 12.5 mm 12.5 mm 0.165 mm
Fig. 12. Force balance of an aircraft The calculation of power required for steady climb starts from the force balance equation of an aircraft (18) and (19) (Anderson, John D., 2010). T − D − mg sin γ = 0 (18) L − mg cos γ = 0 (19) Rate of climb can be given by (20) T−D (20) γ = sin−1 mg
Lift coefficient during climb is given by (21) (Perkins, 1949). mg cos γ CL climb = 1 2 (21)
2.3 Energy Model
Drag
The power generated by solar cell is given by (16) 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝜂𝜂𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ∗ 𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ∗ 𝑆𝑆𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ∗ 𝐺𝐺
2
1
ρV S
2
D = ρV SCD 2 CD = CD0 + kCL2
(22) (23)
Where CD is drag coefficient, CD0 is drag coefficient at zero lift, CL is lift coefficient and k is given by (24) (Etkin, 1996). 1 (24) k= π.AR.e AR is the aspect ratio of the wing and e is the span efficiency factor. Multiplying (18) by flight velocity V, gives d (25) TV = DV + mgV sin γ = DV + (mgh)
(16)
where 𝜂𝜂𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 is the efficiency of solar cells used, 𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 is the efficiency of MPPT, 𝑆𝑆𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 is the total area of the solar cells installed, G is the available irradiance and P is the power generated (Manuel H., 2013).
dt
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d
In (25) the term ‘TV’, ‘DV’ and ‘ (mgh)’ represents dt respectively, the power available, the energy dissipated in overcoming the drag and the rate of increase of potential energy. Thus while climbing the potential energy increases and a part of the propeller output is utilized for this gain of potential energy (Napolitano, 2012). Theoretically the energy required to climb from one altitude to another altitude is same for all velocities, but the propeller efficiency changes with advance ratio. Therefore, for initial climb the climb angle is kept about 2 degrees so that the advance ratio is about 65 % and the propeller is not losing efficiency.
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to cruise. After the sunset we start gliding with minimum sink rate and reach the altitude where power required to cruise is minimum. In Fig. 13 this is about 7:00 PM. Now the aircraft is at cruise altitude and the battery is fully charged and no solar power is available. This is the time to start the propeller and cruise until the battery is drained (about 11:PM). Now we have only the potential energy of the aircraft and this is the time to glide with minimum descend rate and land. The altitude pattern, Power required, solar power available, battery energy label and the flight path angle is shown in Fig. 14.
3. PATH PLANNING In the path planning it is assumed that the battery is fully charged at the time of takeoff. Through out the flight the battery energy (𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 ) at given time t can be calculated using (26) 𝑡𝑡
𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 𝐸𝐸0 − ∫𝑡𝑡
𝐷𝐷.𝑉𝑉
0 𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝑡𝑡
𝑑𝑑𝑑𝑑 − 𝑊𝑊(ℎ2 − ℎ1 ) + ∫𝑡𝑡 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑑𝑑𝑑𝑑 0
(26) Where 𝐸𝐸0 = Initial battery energy D = Drag V = Velocity W = Weight of aircraft ℎ1 = Takeoff Altitude ℎ2 = Altitude at time t 𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = Propeller efficiency The takeoff time is decided in such a way that at the time when solar energy is sufficient for cruise, the battery is drained. First we climb to the altitude (cruise altitude) where power requires to cruise is minimum for the given velocity and then we keep cruising until the the solar power is more than the power required to cruise.
Fig. 14. Altitude, power required, collected solar power, battery energy and flight path angle for a typical flight pattern.
5. RESULTS 5.1 Irradiance A mathematical model was developed for the availability of solar irradiance at Kanpur. This can be utilized for the study of many other performances related study of solar powered aircrafts at Kanpur and other places. Month wise available solar irradiance for MARAAL is shown in Fig. 15 assuming aircraft cruising less than 5 deg of angle of attack and no roll.
After sunrise when the battery is about to drain the solar power is more than the power required to cruise and now the charging of the battery starts keeping the altitude same. It is always advantageous to charge the battery at the altitude where power required to cruise is minimum. A typical flight path is shown in Fig. 13.
Fig. 13. A typical flight path Fig. 15 Global solar irradiance When the battery is fully charged, the climb starts till the time the solar power is available more than than the power required 429
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5.2 Battery Charging Altitude In above study for a given aircraft and irradiance conditions the size of battery is determined and for this battery the takeoff time is fixed. A future study is planned to determine the battery size is the takeoff time is given, how the endurance can be maximized for a takeoff time of our choice and what will be the corresponding battery size.
In Fig. 16 the effect of altitude on power required is shown for different velocities. In the curve for a given velocity where the power required is minimum is the best altitude for battery charging and cruising. Minimum altitude for cruise that can be used for operations is 1000m from sea level.
REFERENCES Anderson, John D.(2010), Aircraft Performance and Design. TATA McGraw-Hill. Duffie, John A., and William A. Beckman (1980), Solar engineering of thermal processes. Vol. 3. New York etc.: Wiley. Dwivedi Vijay Shankar, Jay Patrikar, Ghosh A. K., MARAAL: A Low Altitude Long Endurance Solar Powered UAV for Surveillance and Mapping Applications, submitted ElMghouchi Y., ElBouardi A., Choulli Z., Ajzoul T. (2014), Estimation of the Direct Diffuse and Global Solar Radiations, International Journal of Science and Research (IJSR), ISSN (Online) 2319-7064 Ezinwanne O., F Zhongwen (February 2017), Energy Performnce and Cost Comparison of MPPT Techniques for photovoltics and other Applications, Energy Procedia, Volume 107. Etkin, Bernard, and Lloyd Duff Reid (1996), Dynamics of flight: stability and control. Vol. 3. New York: Wiley. Green, Martin A., et al. (2015), Solar cell efficiency tables (Version 45), Progress in photovoltaics: research and applications 23.1: 1-9. Jemaa, A BEN, Souad RAFAb , Najib ESSOUNBOULI, Abdelaziz HAMZAOUI, Faicel HNAIEN, Farouk YALAOUI (2013), Estimation of Global Solar Radiation Using Three Simple Methods , Energy Procedia, Volume 42, Pages 406-415 John B. Brandt (January 2011), Propeller Performance Data at Low Reynolds Numbers. 49th AIAA Aerospace Sciences Meeting, 4-7, Orlando, FL. Keller, B. (March 2011), A Matlab GUI for calculating the Solar Radiation and Shading of Surface on the Earth, Computer Application in Engineering Education, Volume 19, Issue 1. Karami N. (February 2017), General review and classification of different MPPT Techniques, Renewable and Sustainable Energy Reviews, Volume 68, Part 1. Lorenzo E (1994), Solar Electricity: Engineering of Photovoltic Systems, PROGESNA. Michele De Carli (December 2012), Simulation and numerical methods Energy modeling for buildings and components, Kezirat lezarva. Manuel H. (2013), Design, Construction and Test of the Propulsion System of a Solar UAV. Napolitano, Marcello R. (2012), Aircraft dynamics: From Modeling to Simulation, John Wiley and Sons. Nishioka, K. (August 2007), Analysis of multicrystalline silicon solar cell by modified 3-diode equivalent circuit model taking leakage current through periphery into consideration, Solar Energy Materials and Solar Cells, Volume 91, Issue 13. Perkins, C. D., and R. E. Hage (1949), Airplane Performance Stability and Control, John Wiley & Sons, New York, p. 11. Rajendra, P., H Smith (2016), Modelling of solar irradiance and daylight duration for solar-powered UAV sizing, Energy Exploration & Exploitation, Vol. 34(2) 235-243
Fig. 16 Power required at different altitude for different velocities In Table 6 the charging as well as cruise altitude is given for different velocities Table 6. Velocity and charging altitude Velocity (m/sec) 12 14 16 18 20
Charging Altitude (m) 1000 1000 3000 5000 8000
The cruise speed of an aircraft can’t be less than the stall speed, therefore the power required for lesser speed is not calculated. Usually for aircrafts having larger aspect ratio the speed for power required minimum is less than the stall speed. 5.3 Endurance and Battery Size This was the main objective of this work and the results of the simulation are very useful for deciding the size of the battery of a solar powered aircraft. How the endurance is changing with the size of battery is shown in Fig 17. The endurance is maximum for 30 amp-hour battery and the takeoff time for this endurance will be 3 AM. And the endurance is 20 hours and 30 minutes.
Fig. 17. Battery capacity and endurance 430
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Selection Selection of of Size Size of of Battery Battery for for Solar Solar Powered Powered Aircraft Aircraft IFAC PapersOnLine 51-29 (2018) 424–430 Selection Selection of of Size Size of of Battery Battery for for Solar Solar Powered Powered Aircraft Aircraft
* * ** ** Vijay Shankar Dwivedi Prashant Kumar *, Ajoy Kanti Ghosh **, G. M. Kamath** Vijay Shankar of Dwivedi Prashant Kumarfor , Ajoy Kanti Powered Ghosh , G. M. Kamath Selection Size*,, of Battery Solar Aircraft * * ** ** [[email protected], [email protected], [email protected], [email protected]] Vijay Shankar *, Prashant Kumar *, Ajoy Kanti Ghosh **, G. M. Kamath** [[email protected], [email protected]] Vijay Shankar Dwivedi [email protected], , Prashant [email protected], , Ajoy Kanti Ghosh , G. M. Kamath *Research scholar, *Research scholar, *Engineering, Indian * Institute of Technology, ** ** [[email protected], [email protected], [email protected]] Department of Kanpur, India. Vijay Shankar [email protected], , Prashant Kumar , Ajoy Kanti , G. M. Kamath Department of Aerospace Aerospace Engineering, Indian Institute of Ghosh Technology, Kanpur, India. [[email protected], [email protected], [email protected], [email protected]] ** *Research scholar, **Professor Professor *Research scholar, Department of Engineering, Indian Institute Kanpur, [[email protected], [email protected], [email protected]] Department of Aerospace [email protected], Engineering, Indian Institute of of Technology, Technology, Kanpur, India. India. ** **Professor *Research scholar, Professor Department Indian Department of of Aerospace Aerospace Engineering, Engineering, Indian Institute Institute of of Technology, Technology, Kanpur, Kanpur, India. India. ** Professor Department of work Aerospace Engineering, Indian Institute of Technology, Kanpur, India. trajectory Abstract: This research research proposes the methodology methodology for the the selection selection of battery battery and flight flight Abstract: This work proposes the for of and trajectory for a solar powered aircraft to achieve the maximum endurance. A mathematical model is for a solar powered aircraft to achieve the maximum endurance. A mathematical model is developed developed for for Abstract: This research work proposes the methodology for the selection of battery and flight trajectory the availability of irradiance at a particular geographical location on a given date and time. This work also the availability of irradiance at a particular geographical location on a given date and time. This work also Abstract: This research work proposes the methodology for the selection of battery and flight trajectory for aircraft to the endurance. mathematical model is constitutes the analysis of in with flight, of constitutes the detailed detailed analysis of variation variation in endurance endurance with the theA geographical location of flight, time timefor of for aa solar solar powered powered aircraft to achieve achieve the maximum maximum endurance. Ageographical mathematicallocation model of is developed developed for the availability of irradiance at a particular geographical location on a given date and time. This work also flight (relative position of Earth with respect to Sun), availability of solar irradiance, takeoff time, battery Abstract: This research work proposes the methodology for the selection of battery and flight trajectory flight (relative position of Earth respect to Sun), availability of asolar takeoff time, battery the availability of irradiance at a with particular geographical location on givenirradiance, date and time. This work also constitutes the analysis of in with location of flight, time of size, velocity, flight altitude, aerodynamic parameters of aircraft and propulsion for a flight solar powered aircraft to achieve the maximum endurance. mathematical model is developed size, flight velocity, flight altitude, aerodynamic parameters of the aircraft and aircraft aircraft propulsion system. constitutes the detailed detailed analysis of variation variation in endurance endurance with theAgeographical geographical location of flight, system. timefor of flight (relative position of Earth with respect to Sun), availability of solar irradiance, takeoff time, battery A case study is done for irradiance conditions on March 15 for the UAV MARAAL that is built at UAV the availability of irradiance at a particular geographical location on a given date and time. This work also A case(relative study isposition done forofirradiance March 15 for the MARAAL takeoff that is built UAV flight Earth withconditions respect toon Sun), availability ofUAV solar irradiance, time,atbattery size, velocity, flight altitude, aerodynamic parameters of aircraft aircraft propulsion system. laboratory This methodology can successfully during all seasons the constitutes the Kanpur. detailed analysis of variation in be endurance with the location ofof timefor of laboratory IIT Kanpur. This methodology can be successfully used during and all the the seasons offlight, the year, year, for size, flight flight IIT velocity, flight altitude, aerodynamic parameters of used the geographical aircraft and aircraft propulsion system. A case study is done for irradiance conditions on March 15 for the UAV MARAAL that is built at UAV all geographical locations on the Earth and for any solar powered aircraft. We can reduce the number of flight (relative position of Earth with respect to Sun), availability of solar irradiance, takeoff time, battery all geographical locations on the Earth and foron anyMarch solar 15 powered We can reduce number of A case study is done for irradiance conditions for theaircraft. UAV MARAAL that isthe built at UAV laboratory Kanpur. This methodology can successfully used during all the seasons of for cells to installed on UAV for operation or longer endurance for similar UAV if size, flight velocity, flight altitude, aerodynamic the aircraft aircraft propulsion system. cells to be be IIT installed on UAV for similar similar operation or we we can canofensure ensure longerand endurance for similar UAV if laboratory IIT Kanpur. This methodology can be beparameters successfully used during all the seasons of the the year, year, for all geographical locations on the Earth and for any solar powered aircraft. We can reduce the number of we take care of the proper selection of battery and the flight pattern for the operation to be performed. The A case study is done for irradiance conditions on March 15 for the UAV MARAAL that is built at UAV we take care of the proper selection of battery and the flight pattern for the operation to be performed. The all geographical locations on the Earth and for any solar powered aircraft. We can reduce the number of cells to installed on for or ensure longer endurance for UAV if objective this paper is to the battery to installed and selection of altitude profile laboratory Kanpur. This methodology can be capacity successfully used during all the seasons of the year, for objective ofIIT this paper is to estimate estimate theoperation battery capacity to be be installed and selection of similar altitude profile cells to be beof installed on UAV UAV for similar similar operation or we we can can ensure longer endurance for similar UAV if we take care of the proper selection of battery and the flight pattern for the operation to be performed. The during flight for a solar powered aircraft. all geographical locations on the Earth and for any solar powered aircraft. We can reduce the number of during forthe a solar powered aircraft. we takeflight care of proper selection of battery and the flight pattern for the operation to be performed. The objective of this paper is estimate the battery to be installed and selection of altitude profile cells to be on UAV for similar orControl) we can ensure longer endurance similar UAV if objective ofinstalled this paper is to to Federation estimate the battery capacity capacity to Hosting be installed and selection of altitude profile © 2018, IFAC (International ofoperation Automatic by Elsevier Ltd. Allfor rights reserved. during flight for a solar powered aircraft. we take care of the proper selection of battery and the flight pattern for the operation to be performed. The during flightSolar for aUAV; solar powered aircraft. Irradiance; Numerical simulation; Prolonged flight. Endurance Keywords: Battery selection; Keywords: UAV;isBattery selection; Irradiance; Numerical simulation; flight. Endurance objective ofSolar this paper to estimate the battery capacity to be installed andProlonged selection of altitude profile of solarflight UAV,forEnergy Energy management, Robotics, Flight Flight dynamics, dynamics, Altitude Altitude profile, profile, Solar Solar modelling. modelling. of solar UAV, Robotics, during a solarmanagement, powered aircraft. Keywords: Numerical Keywords: Solar Solar UAV; UAV; Battery Battery selection; selection; Irradiance; Irradiance; Numerical simulation; simulation; Prolonged Prolonged flight. flight. Endurance Endurance dynamics, of solar UAV, Energy management, Robotics, Flight Altitude profile, Solar modelling. of solar UAV, Energy management, Robotics, Flight dynamics, Altitude profile, Solar modelling. Keywords: Solar UAV; Battery selection; Irradiance; Numerical simulation; Prolonged flight. Endurance dynamics, of solar UAV, Energy management, Robotics, Flight Altitude profile, Solar modelling. In In most most of of the the parts parts of of the the world world the the solar solar energy energy is is available available 1. 1. INTRODUCTION INTRODUCTION all the seasons. Even in cloudy seasons the solar irradiance all the seasons. Even in cloudy seasons the solar irradiance is is In most the of world the solar is available aa certain day time. the The use available above certain altitude all the dayenergy time. Though Though the The use of of UAVs UAVs is is growing growing day day by by day day and and gaining gaining popularity popularity In most of ofabove the parts parts of the thealtitude world all the the solar energy is available available 1. INTRODUCTION 1. INTRODUCTION all the Even in seasons solar irradiance is installation of cells on adds extra weight to in installation of solar solar cells on aa UAV UAV addsthe extra weight to it, it, yet yet in both both civil civil and and military military applications. applications. In In conventional conventional UAVs UAVs all the seasons. seasons. Even in cloudy cloudy seasons the solar irradiance is available above a certain altitude all the day time. Though the it will be beneficial in terms of endurance if power harvested The use of UAVs is growing day by day and gaining popularity the endurance is limited by the energy carried with the aircraft In most of the parts of the world the solar energy is available it will be above beneficial in terms of endurance powerThough harvested theINTRODUCTION endurance is limited by the with the aircraft available a certain altitude all the dayiftime. the The use of UAVs is growing dayenergy by daycarried and gaining popularity 1. installation of cells on adds extra weight to yet cells is than the power required to in civil and military applications. In at the this is in all thesolar seasons. Even in cloudy solar irradiance is from solar cells is more more than theseasons power required to carry carry this at the time time of takeoff. Usually this energy energy is carried carried UAVs in the the from installation of solar solar cells on aa UAV UAV addsthe extra weight to it, it,this yet in both both civil of andtakeoff. militaryUsually applications. In conventional conventional UAVs it will be beneficial in terms of endurance if power harvested extra weight (solar cell, encapsulation, MPPT and wiring). the endurance is limited by the energy carried with the aircraft battery or in the form of fuel. In battery powered UAVs the available above a certain altitude all the day time. Though the The use of UAVs is growing day by day and gaining popularity extra weight (solar cell, encapsulation, MPPT and wiring). battery or in the form of fuel. In battery powered UAVs the it will be beneficial in terms of endurance if power harvested the endurance is limited by the energy carried with the aircraft solar cells is the to at the time Usually energy is in power in aa military very time this because there iscarried no supply supply of from installation of solar cells than on a UAV adds required extra weight to it,this yet in both civil of and applications. In there conventional UAVs power drains intakeoff. very short short time because no of from cells is more more than thetopower power required to carry carry this at the drains time of takeoff. Usually this energy is is carried in the the For aa solar fully solar powered aircraft meet the complete demand For fully solar powered aircraft to meet the complete demand extra weight (solar cell, encapsulation, MPPT and wiring). battery or in the form of fuel. In battery powered UAVs the power and the whole operation depends upon battery carried it will be beneficial in terms of endurance if power harvested the endurance iswhole limited the energy carried with the aircraft power and upon battery carried weight (solar cell, encapsulation, MPPT and wiring). battery or inthethe formoperation ofbyfuel. Independs battery powered UAVs the extra of supply from solar cells aa very large is of power power supply solar cellspower very large wingspan wingspan is power drains aa very time because there no supply of with UAV, there always structural limitation limits solar cells powered is from more than the required to shown carry this at thethe time ofin Usually this energy is is in the with the UAV, there isshort always structural limitation that limits power drains intakeoff. veryis short time because there iscarried nothat supply of from For a fully solar aircraft to meet the complete demand required. Wingspan of different solar aircrafts is in required. Wingspan of different solar aircrafts is shown in For a fully solar powered aircraft to meetMPPT the complete demand power and the whole operation depends upon battery carried the amount of battery that can be carried with the UAV. In extra weight (solar cell, encapsulation, and wiring). battery or in the form of fuel. In battery powered UAVs the the amount of whole batteryoperation that can be carriedupon withbattery the UAV. In Table power and the depends carried of supply from aa very large is 1. This This wingspan issolar largecells because the power power need 1. wingspan large because the need is is high high of power power supply from is solar cells very large wingspan wingspan is with UAV, always structural limitation that limits fuel-based UAVs the endurance depends and power drains in there a very short time becauseupon therefuel is nocarried supply of Table fuel-based UAVs the is endurance depends upon fuel carried and with the the UAV, there is always structural limitation that limits required. Wingspan of different solar aircrafts is shown in to carry the battery weight that is used during nights. The wing For a fully solar powered aircraft to meet the complete demand to carry the battery weight that is used during nights. The wing required. Wingspan of different solar aircrafts is shown in the of battery that can be carried with the UAV. In more fuel adds more weight payload has power and the depends upon carried moreamount fuel adds moreoperation weight where payload has always the amount of whole battery that can where be carried withbattery the always UAV. Inaa span Table 1. wingspan is large because the need is can besupply reduced significantly if athe thevery sizing of the the battery is of power from large wingspan span can be reduced significantly if sizing of battery is Table 1. This This wingspan issolar largecells because the power power need is high high fuel-based UAVs the endurance depends upon fuel carried and limitation. In recent past as the efficiency of solar cells is with the UAV, there is always structural limitation that limits limitation. UAVs In recent past as thedepends efficiency solar cellsand is done fuel-based the endurance uponoffuel carried to carry the battery weight that is used during nights. The wing in a well calculated manner. Apart from this, in a solar required. Wingspan of different solar aircrafts is shown in in the a well calculated Apart from this, in a wing solar to carry battery weight manner. that is used during nights. The more fuel adds more weight payload increasing is it become viable source the amount of cost battery that can where be carried withaahas the always UAV. Inaa done increasing and cost is decreasing decreasing it has has become viable source more fuel and adds more weight where payload has always span can be reduced significantly if the sizing of the battery is assisted UAVs also the endurance can be enhanced Table 1. This wingspan isthe largeendurance because thecan power need is high assisted UAVs also be enhanced span can be reduced significantly if the sizing of the battery is limitation. In recent past as the efficiency of solar cells is of power supply during the flight. A trend of improvement in fuel-based UAVs the endurance upon fuel carried of power supply during theasflight. A trend of of improvement in limitation. In recent past thedepends efficiency solar cellsand is significantly done in a well calculated manner. Apart from this, in a solar significantly if the battery is selected depending upon the to carry the battery weight that is used during nights. The wing if the battery is selected depending upon the done in a well calculated manner. Apart from this, in a solar increasing and cost is decreasing it has become a viable source the efficiency is shown in Fig. 1 and reduction in the price is more fuel and adds more weight payload ain has the efficiency iscost shown in Fig. 1where thealways price isa irradiance increasing is decreasing itand hasreduction become viable source assisted UAVs also the can pattern atsignificantly the siteendurance onif the given time andenhanced date of of span can be reduced sizing ofbe the battery is pattern at the on given time and date assisted UAVs also thesite endurance can be enhanced of power supply during the A improvement shown in limitation. In 2. recent past the efficiency solar cells in is irradiance shown in Fig. Fig. 2. of power supply during theasflight. flight. A trend trend of of of improvement in significantly if the battery is selected depending upon the operation and the aircraft characteristics. done in a well calculated manner. Apart from this, in a solar operation and the aircraft characteristics. significantly if the battery is selected depending upon the the is shown in Fig. 11 itand the is increasing and decreasing hasreduction become ain viable source the efficiency efficiency iscost shown incell Fig.has and reduction in the price price is irradiance pattern at on time date Apart from this aa is solar zero carbon emission assisted UAVs thesite Apart from this solarthe cellflight. has A zero carbon emission that that irradiance pattern also at the the siteendurance on given given can time beand andenhanced date of of shown in Fig. 2. of power supply during trend of improvement in shown this in Fig. 2. operation and the aircraft characteristics. makes a promising power source for future and therefore significantly ifthethe battery is selected depending upon the makes this a promising power source for future and therefore operation and aircraft characteristics. the efficiency is shown in focus Fig.has 1 and reduction in the price is Apart from this solar carbon emission this area that its this is is an an area thataaneeds needs focus onzero its efficient efficient utilization. Apart from this solar aacell cell hason zero carbon utilization. emission that that irradiance pattern at the site on given time and date of shown in Fig. 2. makes this a promising power source for future and therefore makes this a promising power source for future and therefore operation and the aircraft characteristics. this area that focus its Apart from solar aacell hason carbon utilization. emission that this is is an an areathis thataneeds needs focus onzero its efficient efficient utilization. makes this a promising power source for future and therefore this is an area that needs a focus on its efficient utilization.
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Table 2 MARAAL specifications Parameter Wing span Wing area Aspect ratio Empty weight Solar cells used
Value 5.35 m 2.04 m2 14 12 Kg Sunpower C60
Fig. 1. Solar cell efficiency with time.*
Fig 3. MARAAL Solar UAV 2. MATHEMATICAL MODELLING Fig. 2. Solar cell cost with time.* 2.1 Availability of Irradiance Table 1. Wingspan of different aircrafts Aircraft Solar Impulse Qinetiq Zephyr Helios HP03 NASA Centurion NASA Pathfinder
Earth revolves around the sun in an elliptical orbit whose eccentricity is such that the distance between the sun and the earth varies by 3.4 % above the sea. The mean distance between earth and sun is 1.495 x 1011 m, i.e. one astronomical unit (AU) (Duffie, John A., 1980).
Wing-span 63.4 m 22.5 m 75.3 m 62 m 36.3 m
Sun light is available only for limited number of hours therefore the utilization of this power should be done in an efficient way. Power consumed by UAV depends upon many factors such as speed at which we are flying, CL of UAV, duration of flight, rate of climb, how long we cruise at a particular altitude, payload etc. In a UAV there are two basic energy storing elements, the first battery and second the altitude i.e. the potential energy that we can trade for gliding. We dissipate energy during the flight. In solar UAV we have a supply of energy in form of solar energy. For a solar UAV to achieve maximum time of flight we need to focus aerodynamic aspects of flight in addition with the pattern we control the energy flow. Also depending upon the solar power availability we can optimize the endurance by selecting the optimal weight of battery and the cruise altitude where we charge our battery.
Fig. 4. Sun, Earth and Solar constant The solar constant (𝐺𝐺𝑠𝑠𝑠𝑠 ) is the power obtained from the sun on a unit area of surface perpendicular to the direction of propagation of the radiation at mean earth-sun distance (1 AU) outside the atmosphere. It is measured directly with the help of very high altitude aircraft, balloons, and spacecraft, which records the measurements of solar radiation outside the earth’s atmosphere. Resultant value of the solar constant Gsc was found to be 1367 W/m2 with an estimated error of 1.5%. (Duffie, John A., 1980; Jemaa, A BEN, 2013). (1) 𝐺𝐺𝑠𝑠𝑠𝑠 = 1367 𝑊𝑊/𝑚𝑚2 Since the distance between earth and sun is not constant, there is the periodic variation in extraterrestrial radiation flux.
In this paper an effort is made to find the best battery size and the flight pattern for maximum endurance. All study is done on solar UAV MARAAL, designed at UAV laboratory IIT Kanpur. Table 2 is representing the parameters associated with MARAAL and a visual of its flight is shown in Fig. 3. *https://sites.lafayette.edu/egrs352-sp14-pv/technology/history-of-pvtechnology/
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Variation is in the range of ±3.3 %. This change can be calculated using (2) (https://www.e-education.psu.edu/eme811/node/637). 𝐺𝐺𝑜𝑜𝑜𝑜 = 𝐺𝐺𝑠𝑠𝑠𝑠 (1.00011 + 0.034221 cos 𝐵𝐵 + 0.00128 sin 𝐵𝐵 + 0.000719 cos 2𝐵𝐵 + 0.000077 sin 2𝐵𝐵) 360 Where 𝐵𝐵 = (𝑛𝑛 − 1) 365
(2) (3)
Where 𝐺𝐺𝑜𝑜𝑜𝑜 is the extraterrestrial radiation incident on the plane normal to the radiation on the nth day of the year and this is shown in Fig. 5.
Fig. 6. Declination angle Latitude (ϕ): For Kanpur latitude is 26.5 N ΦKanpur = 26.50 Hour angle (ω): This is angular displacement of the sun either east or west of the local meridian because of the rotation of the earth on its axis at 150 per hour. Morning is considered to be negative and evenings positive *. cos ω = −tan ϕ tan δ (7) 2 (8) 𝑁𝑁 = cos −1 (−tan ϕ tan δ) 15 N is the number of daylight hours. Quantities ω and cos −1 (−tan ϕ tan δ) are in degree. For (7) beyond ϕ = ±66.55 deg: (tan δ − tan ϕ ) ≥ 1 there is no sunset, i.e. 24 hour daylight (tan δ − tan ϕ ) ≤ 1 there is no sunset, i.e. 24 hour darkness
Fig. 5. Extraterrestrial radiation incident on the plane normal to radiation To describe the hour-angle the local solar time (LST) is used, because the hour angle is zero at solar noon (LST: 12:00h), when the sun reaches its highest point in the sky. Using (4) the LST can be calculated from the local civil time (LCT) with the help of quantity called equation of time (EOT) (Rajendra, P., 2016; Keller, B. 2011). LST = LCT+EOT (4) EOT = 229.2(0.000075 + 0.001868cos(N) – 0.032077 sin(N) – 0.014615cos(2N) – 0.04089sin(2N)) (5) 360 Where, 𝑁𝑁 = (𝑛𝑛 − 1) , in deg 365 n = day number of the year The geometric relationships between a horizontal plane relative to the earth and the incoming beam solar radiation, that is, the position of the sun with respect to that plane, can be represented in terms of several angles. Declination(δ): It ranges from −23.45 degrees to +23.45 degrees with north to be positive (Keller, B. 2011). An approximate equation to find the declination is given in (6) (ElMghouchi Y., 2014). δ = 23.45 sin(A) (6) Where
A = 360 (
Fig. 7. Number of daylight hours The solar radiation that fills our sky are of three types: o Direct radiation, o Diffused radiation o Reflected radiation. "Direct radiation" also called as "beam radiation" or "direct beam radiation". It is used to describe solar radiation traveling on a straight line from the sun down to the surface of the earth.
284+n 365
) in degrees
"Diffused radiation", is the sunlight that has been scattered by molecules and particles in the atmosphere but that has still made it down to the surface of the earth.
* http://www.itacanet.org/the-sun-as-a-source-of-energy/part3-calculating-solar-angles/#3.2.-The-Hour-Angle
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Total radiation received (𝐺𝐺) is the summation of both, beam and diffused radiation (16) (ElMghouchi Y., 2014). (16) 𝐺𝐺 = 𝐺𝐺𝑐𝑐𝑐𝑐 + 𝐺𝐺𝑑𝑑 Direct and diffused irradiance on March 15 is shown in Fig 9.
Fig. 8. Types of radiation: Direct, diffused and reflected *. "Reflected radiation" On ground this has a contribution about 2% but for UAV at altitude this is negligible. Direct radiation is around 85% of the total insolation hitting the ground and diffuse radiation is about 15%. As the sun goes lower in the sky, the percent of diffuse radiation keeps going up until it reaches 40% when the sun is 10° above the horizon. Atmospheric conditions like clouds and pollution also increase the percentage of diffuse radiation. On an extremely overcast day, 100% of the solar radiation is diffuse radiation. The percentage of the sky's radiation that is diffuse is much greater in higher latitude, cloudier places than in lower latitude, sunnier places. Moreover, the percentage of the diffuse radiation tends to be higher in the winter than the summer in the higher latitude, cloudier places (Michele De Carli, 2012). Both of the radiations are considered and calculate the total amount of energy we receive. Hottel’s method is used to estimating the beam radiation transmitted through clear atmospheres which takes into account zenith angle (θz ) and altitude (Duffie, John A., 1980). Atmospheric transmittance for beam radiation is given by (9)
Fig. 9. Direct and diffused irradiance on a horizontal surface 2.2 Solar Cell In a solar UAV, solar cells are primary source of power. They convert photonic energy of available irradiance into electric energy. Their performance depends upon the materials used in the fabrication of it. In Table 4 the efficiency of different solar cells is given Table 4. Different types of solar cells with their maximum efficiencies available in market (Green, 2015) Type of solar cells Si Monocrystalline Si Polycrystalline Si Thin film GaAs thin film CIGS CdTe
−𝑘𝑘 ) cos 𝜃𝜃𝑧𝑧
(
(9) 𝜏𝜏𝑏𝑏 = 𝑎𝑎𝑜𝑜 + 𝑎𝑎1 𝑒𝑒 The constants 𝑎𝑎𝑜𝑜 , 𝑎𝑎1 and 𝑘𝑘 for the standard atmosphere with 23 km visibility are found from 𝑎𝑎𝑜𝑜 ∗ , 𝑎𝑎1 ∗ and 𝑘𝑘 ∗ using (10), (11) and (12). (10) . 𝑎𝑎𝑜𝑜 ∗ = 0.4237 − 0.00821(6 − 𝐴𝐴)2 (11) 𝑎𝑎1 ∗ = 0.5055 − 0.00595(6.5 − 𝐴𝐴)2 (12) 𝑘𝑘 ∗ = 0.2711 − 0.01858(2.5 − 𝐴𝐴)2 Where A is altitude of the observer in kilometers. Correction factors are applied to 𝑎𝑎𝑜𝑜 ∗ , 𝑎𝑎1 ∗ and 𝑘𝑘 ∗ to allow for change in climate types. The correction factors 𝑟𝑟𝑜𝑜 = 𝑎𝑎𝑜𝑜 /𝑎𝑎𝑜𝑜 ∗ , 𝑟𝑟1 = 𝑎𝑎1 /𝑎𝑎1 ∗ and 𝑟𝑟𝑘𝑘 = 𝑎𝑎𝑘𝑘 /𝑎𝑎𝑘𝑘 ∗ are given in Table 3 (Duffie, John A., 1980).
For solar UAV the GaAs is the best for performance point of view but due to the cost constrains Si monocrystalline (Sunpower C60) is used in MARAAL. Claimed efficiency by manufacturer of C60 is 23% but the achieved efficiency after installation on solar UAV was recorded about 20%. An ideal solar cell can be modelled by a current source (𝐼𝐼𝐿𝐿 ) in parallel with a diode; in practice no solar cell is ideal, so a shunt resistance (𝑅𝑅𝑆𝑆𝑆𝑆 ) and a series resistance (𝑅𝑅𝑆𝑆 ) component are added to the model (Lorenzo E, 1994). An equivalent circuit of solar cell is shown in Fig. 10 (Nishioka, K., 2007).
Table 3. Correction factors for climate types Climate Type Tropical Midlatitude summer Subarctic summer Midlatitude winter
𝐫𝐫𝐨𝐨 0.95 0.97 0.99 1.03
𝐫𝐫𝟏𝟏 0.98 0.99 0.99 1.01
Maximum efficiency achieved 22.9 ± 0.6 18.5 ± 0.4 8.2 ± 0.2 28.9 ± 1.0 15.7 ± 0.5 17.5 ± 0.7
𝐫𝐫𝐤𝐤 1.02 1.02 1.01 1.00
* http://bembook.ibpsa.us/index.php?title=Ground_Reflectance Clear sky beam radiation (𝐺𝐺𝑐𝑐𝑐𝑐 ) can be calculated using (13) (13) 𝐺𝐺𝑐𝑐𝑐𝑐 = 𝐺𝐺𝑜𝑜𝑜𝑜 𝜏𝜏𝑏𝑏 cos 𝜃𝜃𝑧𝑧
Fig. 10. Equivalent circuit of a solar cell
Clear sky diffuse radiation can be calculated using (14). (14) 𝐺𝐺𝑑𝑑 = 𝜏𝜏𝑑𝑑 𝐺𝐺0 Where 𝜏𝜏𝑑𝑑 = 0.271 − 0.294 𝜏𝜏𝑏𝑏 (15) And 𝐺𝐺0 is extraterrestrial beam radiation on horizontal plane. 427
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2.4 Propeller Propeller used in MARAAL is 30.5”x9.7 triple blade. The efficiency of a propeller is measured with respect to advance ratio (𝑗𝑗) (John B. Brandt, 2011). 𝑉𝑉 (17) 𝑗𝑗 = 𝑛𝑛𝑛𝑛 Where V = velocity n = rpm D = diameter A wind tunnel test was performed for the characterization of the propeller and an efficiency was recorded about 70 % for the advance ratio of 0.6 that is the condition of cruise. During climb the advance ratio drops to 0.4 and for this advance ratio the efficiency was recorded 58 %.
Fig. 11. V-I characteristic of a solar cell When a solar cell is short circuited the current is maximum (𝐼𝐼𝑠𝑠𝑠𝑠 ) but the voltage is zero, resulting in zero power. As the load impedance increases the current remains almost constant and then starts decreasing (from 𝐼𝐼𝑚𝑚𝑚𝑚 ), and voltage keeps increasing till (𝑉𝑉𝑚𝑚𝑚𝑚 ). At open circuit the voltage is maximum (𝑉𝑉𝑜𝑜𝑜𝑜 ) but the current is zero. The power that is delivered by solar cell to the load is the product of voltage and current and this pattern is shown in Fig. 11. The load impedance has always a value for which the power extracted is maximum, this maximum keeps changing with the irradiance, load and temperature. To utilize the solar cell most efficiently we need to operate about this maximum power point and the circuitry used for tracking the maximum power point is called MPPT (maximum power point tracking). The typical efficiency of MPPT is about 94 % to 98 % (Ezinwanne O., 2017; Karami N., 2017). Solar cells installed in MARAAL is Sunpower C60. Characteristics of Sunpower C60 is shown in Table 5.
2.5 Electronic Speed Control (ESC) and Motor ESC is used for the rpm control of the motor. It receives a pulse width modulated signal and changes the rpm of motor depending upon the duty cycle of received pulses. When the input and output voltages are very close to each other the efficiency of ESC is maximum and typically about 98 %, but this may drop up to 80 % when the input output voltage difference is more. In our operation the 6-cell battery is used so that the input voltage is close to operating voltage of motor and the efficiency of ESC is above 94 %. 2.6 Power Required
Table 5. Sunpower C60 specifications Parameter
Value
Peak Power
3.42 Watt
Efficiency
22.5 %
Peak Voltage
0.582 Volt
Peak Current
5.93 Amp
Open-circuit Voltage
0.687 Volt
Short-circuit Current Length Width Thickness
6.28 Amp 12.5 mm 12.5 mm 0.165 mm
Fig. 12. Force balance of an aircraft The calculation of power required for steady climb starts from the force balance equation of an aircraft (18) and (19) (Anderson, John D., 2010). T − D − mg sin γ = 0 (18) L − mg cos γ = 0 (19) Rate of climb can be given by (20) T−D (20) γ = sin−1 mg
Lift coefficient during climb is given by (21) (Perkins, 1949). mg cos γ CL climb = 1 2 (21)
2.3 Energy Model
Drag
The power generated by solar cell is given by (16) 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝜂𝜂𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ∗ 𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ∗ 𝑆𝑆𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ∗ 𝐺𝐺
2
1
ρV S
2
D = ρV SCD 2 CD = CD0 + kCL2
(22) (23)
Where CD is drag coefficient, CD0 is drag coefficient at zero lift, CL is lift coefficient and k is given by (24) (Etkin, 1996). 1 (24) k= π.AR.e AR is the aspect ratio of the wing and e is the span efficiency factor. Multiplying (18) by flight velocity V, gives d (25) TV = DV + mgV sin γ = DV + (mgh)
(16)
where 𝜂𝜂𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 is the efficiency of solar cells used, 𝜂𝜂𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 is the efficiency of MPPT, 𝑆𝑆𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 is the total area of the solar cells installed, G is the available irradiance and P is the power generated (Manuel H., 2013).
dt
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d
In (25) the term ‘TV’, ‘DV’ and ‘ (mgh)’ represents dt respectively, the power available, the energy dissipated in overcoming the drag and the rate of increase of potential energy. Thus while climbing the potential energy increases and a part of the propeller output is utilized for this gain of potential energy (Napolitano, 2012). Theoretically the energy required to climb from one altitude to another altitude is same for all velocities, but the propeller efficiency changes with advance ratio. Therefore, for initial climb the climb angle is kept about 2 degrees so that the advance ratio is about 65 % and the propeller is not losing efficiency.
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to cruise. After the sunset we start gliding with minimum sink rate and reach the altitude where power required to cruise is minimum. In Fig. 13 this is about 7:00 PM. Now the aircraft is at cruise altitude and the battery is fully charged and no solar power is available. This is the time to start the propeller and cruise until the battery is drained (about 11:PM). Now we have only the potential energy of the aircraft and this is the time to glide with minimum descend rate and land. The altitude pattern, Power required, solar power available, battery energy label and the flight path angle is shown in Fig. 14.
3. PATH PLANNING In the path planning it is assumed that the battery is fully charged at the time of takeoff. Through out the flight the battery energy (𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 ) at given time t can be calculated using (26) 𝑡𝑡
𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 𝐸𝐸0 − ∫𝑡𝑡
𝐷𝐷.𝑉𝑉
0 𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝑡𝑡
𝑑𝑑𝑑𝑑 − 𝑊𝑊(ℎ2 − ℎ1 ) + ∫𝑡𝑡 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑑𝑑𝑑𝑑 0
(26) Where 𝐸𝐸0 = Initial battery energy D = Drag V = Velocity W = Weight of aircraft ℎ1 = Takeoff Altitude ℎ2 = Altitude at time t 𝜂𝜂𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = Propeller efficiency The takeoff time is decided in such a way that at the time when solar energy is sufficient for cruise, the battery is drained. First we climb to the altitude (cruise altitude) where power requires to cruise is minimum for the given velocity and then we keep cruising until the the solar power is more than the power required to cruise.
Fig. 14. Altitude, power required, collected solar power, battery energy and flight path angle for a typical flight pattern.
5. RESULTS 5.1 Irradiance A mathematical model was developed for the availability of solar irradiance at Kanpur. This can be utilized for the study of many other performances related study of solar powered aircrafts at Kanpur and other places. Month wise available solar irradiance for MARAAL is shown in Fig. 15 assuming aircraft cruising less than 5 deg of angle of attack and no roll.
After sunrise when the battery is about to drain the solar power is more than the power required to cruise and now the charging of the battery starts keeping the altitude same. It is always advantageous to charge the battery at the altitude where power required to cruise is minimum. A typical flight path is shown in Fig. 13.
Fig. 13. A typical flight path Fig. 15 Global solar irradiance When the battery is fully charged, the climb starts till the time the solar power is available more than than the power required 429
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5.2 Battery Charging Altitude In above study for a given aircraft and irradiance conditions the size of battery is determined and for this battery the takeoff time is fixed. A future study is planned to determine the battery size is the takeoff time is given, how the endurance can be maximized for a takeoff time of our choice and what will be the corresponding battery size.
In Fig. 16 the effect of altitude on power required is shown for different velocities. In the curve for a given velocity where the power required is minimum is the best altitude for battery charging and cruising. Minimum altitude for cruise that can be used for operations is 1000m from sea level.
REFERENCES Anderson, John D.(2010), Aircraft Performance and Design. TATA McGraw-Hill. Duffie, John A., and William A. Beckman (1980), Solar engineering of thermal processes. Vol. 3. New York etc.: Wiley. Dwivedi Vijay Shankar, Jay Patrikar, Ghosh A. K., MARAAL: A Low Altitude Long Endurance Solar Powered UAV for Surveillance and Mapping Applications, submitted ElMghouchi Y., ElBouardi A., Choulli Z., Ajzoul T. (2014), Estimation of the Direct Diffuse and Global Solar Radiations, International Journal of Science and Research (IJSR), ISSN (Online) 2319-7064 Ezinwanne O., F Zhongwen (February 2017), Energy Performnce and Cost Comparison of MPPT Techniques for photovoltics and other Applications, Energy Procedia, Volume 107. Etkin, Bernard, and Lloyd Duff Reid (1996), Dynamics of flight: stability and control. Vol. 3. New York: Wiley. Green, Martin A., et al. (2015), Solar cell efficiency tables (Version 45), Progress in photovoltaics: research and applications 23.1: 1-9. Jemaa, A BEN, Souad RAFAb , Najib ESSOUNBOULI, Abdelaziz HAMZAOUI, Faicel HNAIEN, Farouk YALAOUI (2013), Estimation of Global Solar Radiation Using Three Simple Methods , Energy Procedia, Volume 42, Pages 406-415 John B. Brandt (January 2011), Propeller Performance Data at Low Reynolds Numbers. 49th AIAA Aerospace Sciences Meeting, 4-7, Orlando, FL. Keller, B. (March 2011), A Matlab GUI for calculating the Solar Radiation and Shading of Surface on the Earth, Computer Application in Engineering Education, Volume 19, Issue 1. Karami N. (February 2017), General review and classification of different MPPT Techniques, Renewable and Sustainable Energy Reviews, Volume 68, Part 1. Lorenzo E (1994), Solar Electricity: Engineering of Photovoltic Systems, PROGESNA. Michele De Carli (December 2012), Simulation and numerical methods Energy modeling for buildings and components, Kezirat lezarva. Manuel H. (2013), Design, Construction and Test of the Propulsion System of a Solar UAV. Napolitano, Marcello R. (2012), Aircraft dynamics: From Modeling to Simulation, John Wiley and Sons. Nishioka, K. (August 2007), Analysis of multicrystalline silicon solar cell by modified 3-diode equivalent circuit model taking leakage current through periphery into consideration, Solar Energy Materials and Solar Cells, Volume 91, Issue 13. Perkins, C. D., and R. E. Hage (1949), Airplane Performance Stability and Control, John Wiley & Sons, New York, p. 11. Rajendra, P., H Smith (2016), Modelling of solar irradiance and daylight duration for solar-powered UAV sizing, Energy Exploration & Exploitation, Vol. 34(2) 235-243
Fig. 16 Power required at different altitude for different velocities In Table 6 the charging as well as cruise altitude is given for different velocities Table 6. Velocity and charging altitude Velocity (m/sec) 12 14 16 18 20
Charging Altitude (m) 1000 1000 3000 5000 8000
The cruise speed of an aircraft can’t be less than the stall speed, therefore the power required for lesser speed is not calculated. Usually for aircrafts having larger aspect ratio the speed for power required minimum is less than the stall speed. 5.3 Endurance and Battery Size This was the main objective of this work and the results of the simulation are very useful for deciding the size of the battery of a solar powered aircraft. How the endurance is changing with the size of battery is shown in Fig 17. The endurance is maximum for 30 amp-hour battery and the takeoff time for this endurance will be 3 AM. And the endurance is 20 hours and 30 minutes.
Fig. 17. Battery capacity and endurance 430