construction prototyping, flight dynamics modeling, and ......research article construction...

Research Article

Construction Prototyping Flight Dynamics Modeling andAerodynamic Analysis of Hybrid VTOL Unmanned Aircraft

Roman Czyba 1 Marcin Lemanowicz2 Zbigniew Gorol3 and Tomasz Kudala3

1Faculty of Automatic Control Electronics andComputer Science Department of Automatic Control SilesianUniversity of Technology16 Akademicka St Gliwice 44-100 Poland2Faculty of Chemistry Department of Chemical Engineering and Process Design Silesian University of Technology 16 Akademicka StGliwice 44-100 Poland3Faculty of Mechanical Engineering Silesian University of Technology 16 Akademicka St Gliwice 44-100 Poland

Correspondence should be addressed to Roman Czyba romanczybapolslpl

Received 17 July 2018 Accepted 30 August 2018 Published 1 October 2018

Academic Editor Jose E Naranjo

Copyright copy 2018 Roman Czyba et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A challenging issue associated with fixed-wing Unmanned Aerial Vehicles (UAVs) is that these vehicles are often not appropriatefor operating effectively in limited airspaceThis problem emerges especially in urban environment where the usage of a runway isnot possible and UAVs usually have to fly at a relatively low speed and altitude The development of a vertical take-off and landing(VTOL) fixed-wing plane is a promising trend which hopefully will solve this issue This paper presents the design process of anunmanned vertical take-off and landing aircraft including prototyping of the airframe construction and mathematical modelingas well as computational fluid dynamics (CFD) simulations The designed system is to be a hybrid platform for which differentoperating modes correspond to the vertical flight transition and spatial flight in the airframe system The paper discusses aniterative design process of the platform with emphasis on CAD design and aerodynamic analysis for particular flight modes Theoperating prototype is presented and future plans for platform improvement are discussed

1 Introduction

Aircraft technology has been developing for over a centurysince the Wright brothers built their first manned planethrough Sperryrsquos autopilot until the 21st century whenthe Unmanned Aerial Vehicles (UAVs) were invented [1ndash7] Generally there are three design structures fixed-wingaircraft rotorcrafts and aerostats However there are manyinnovative solutions in the form of aforementioned hybridconstructions giving interesting flight properties Each typeof UAV has its own advantages that predispose it to performspecific tasks Many UAVs [8] such as MQ9-Reaper RQ-2Pioneer RQ-5Hunter and RQ-4Global Hawkwere designedas fixed-wing type and their advantage is flight duration andthereby the area of operational activities Their disadvantageis the need to take-off and land from the runway whichsignificantly limits their functionality Another critical prob-lem associated with fixed-wing UAVs is that these vehicles

are often not appropriate for operating effectively in limitedairspace This is evident in urban environment where theusage of a runway is not possible and UAVs usually haveto fly at a relatively low speed and altitude This ldquoU-Spacerdquo[9] covers altitude up to 150 meters in the European Unionand is an area for the development of a strong and dynamicdrone services market [10] In turn multirotors [11 12] havethe capability of vertical take-off and landing (VTOL) whichincreases their operational flexibility But this constructionis unfortunately associated with a high energy demandwhich makes the flight relatively short A promising trend isdevelopment of a vertical take-off and landing (VTOL) fixed-wing plane or so-called hybrid UAV or VTOL aircraft whichcombines the advantages of both designs

Over the last five years many hybrid VTOL structureshave been created [1 13ndash16] One of them is Tilt-Rotor [17ndash20] where multiple rotors are mounted on rotating shafts ornacelles Another solution is the Tilt-Wing concept where

HindawiJournal of Advanced TransportationVolume 2018 Article ID 7040531 15 pageshttpsdoiorg10115520187040531

2 Journal of Advanced Transportation

Figure 1 The initial concept of the VTOL UAV

the transition between individual flight phases is obtained bytilting the wings with fixed rotors [17 21 22] Unfortunatelyduring take-off landing and hovering the wings will bedirected upwards which makes the aircraft more suscepti-ble to transverse winds Another type of convertiplane isDual-System [23] where multiple rotors are always directedupwards for vertical flight and another separate rotor forhorizontal flight This configuration is very simple to applyin terms of design and modeling because two flight phasescould be analysed separately But for most of the missionthe platform must transport unnecessary mass which canbe replaced by fuel or batteries Another solution is aconfiguration of Tail-Sitter [24 25] This platform takes offand lands vertically on its tail and the whole aircraft tiltsforward using differential thrust or control surfaces to achievehorizontal flight In conclusion it is true that today VTOLaircraft exist and operate in practice but they are burdenedwith various limitations and disadvantages

In this paper a novel design configuration in a formof hybrid of conventional aircraft and quadrotor with twoof four rotors mounted in nacelles with ability of rotationhas been proposed It will have a unique feature amongsimilar solutionsmdasha thrust vectoring of engines that ensurestheir usage in both vertical and horizontal flight Comparedto the above-mentioned designs an advantage of proposedapproach is an ability to rotate only the rotors themselvesnot the whole wing During take-off landing and hoveringthis solution makes the aircraftmore robust to cross winds Inthe airplane mode the advantage is also the usage of rotorsin the pushing system behind the trailing edge of the wingwhich ensures uniformity of the air stream flowing aroundthe airfoil In turn in VTOL mode the usage of pushingpropeller from underside of the rotor increases the efficiencyof the propulsion system [26 27]

The main purpose of this paper is to present the conceptof VTOL aircraft from scratch to final implementationcovering the individual stages of prototyping and thenderiving a mathematical model based on the physical modeland computational fluid dynamics CFD simulations [28]A mathematical model that can accurately describe the flightdynamics is exceedingly important in the design of a flightcontrol system In the case of hybrid UAVs the whole flightcan be divided into three phases namely vertical flightmode transition mode and horizontal flight mode As aconsequence the development of a real flight dynamicsmodel is much more difficult compared to the conventionalUAVs and causes many problems

The paper is organized as follows First the introductionis provided in Section 1 Then the concept of VTOL aircraftand construction prototyping are presented in Section 2The mechanical design and an explanation of flight phasesare shown in Section 3 A mathematical model includingforces and moments definition in individual flight phasesare determined in Section 4 Next the computational fluiddynamics (CFD) simulations are described together with adiscussion of received results The conclusions are brieflydiscussed in the last section

2 Mechanical Design andConstruction Prototyping

The initial concept of the UAV assumed that the constructionshould be efficient in terms of aerodynamics as far as itis possible Therefore the parts of the platform which arenecessary for the hovering flight mode (especially enginesand propellers) should not generate drag during standardflight mode which means that they should be hidden withinfuselage Simultaneously the minimum number of supportpoints which provides stable UAV hovering without necessityof applying any advanced and complicated control mecha-nisms is equal to three In the light of these assumptions theobvious choicewas a platform configurationwith two enginesmounted in the front of the wings and a ducted propellerplaced within the fuselage (Figure 1)

The front engines together with propellers were designedto tilt from vertical orientation used in standard flight modeto horizontal orientation used in hovering mode Togetherwith the ducted propeller they were arranged on a circularplan whose centre was located at the mass centre of construc-tion The advantage of such construction solution was thepossibility of hiding the fuselage propeller during standardflight mode and as a result to minimize generated dragOn the other hand the placement of the fuselage propellercomplicated significantly the tail construction Moreoverthe size of the fuselage had to be increased in order toaccommodate the mechanical construction As a result theaerodynamic properties of the platform were not satisfactoryIt was characterized by low lift with simultaneous high dragMoreover the thrust generated by fuselage propeller wastoo low and its mechanical construction was unnecessarilycomplicated In the initial design two separate autopilotswere considered both for hovering and standard flight modesconnected via mixer To conclude the concept with three

Journal of Advanced Transportation 3

Figure 2The second concept of the VTOL UAV

Figure 3 The optimization process of fuselage

M4

M3

M1

M2f1

f2

f3

f4xB

yB

zB

yE

zD

xN

yV

xV

zVxW

Figure 4 The final design of the VTOL aircraft

supporting points was rejected The disadvantages resultingfrom the placement of the third propeller overshadowed anyadvantages of this solution

The second iteration of the concept design was based onfour points of support (Figure 2) The first two engines withpropellers were placed in front of the wings as in the previousdesign Once again their tilt depended on the flight modeHowever another two propellers were drawn out from thefuselage on specially designed arms Due to the elimination ofthe ducted propeller the size of fuselage decreased Moreoverthe design of the tail changed from double ldquoTrdquo configurationinto ldquoHrdquo configuration

During the design process two different plane config-urations were considered ie centre-wing and high-wingMoreover the shape of the fuselage was optimized (Figure 3)

The biggest advantage of this design was the ease tocontrol hovering mode of flight The control characteristicswere identical to the characteristics of common quadcopterplatforms On the other hand still the aerodynamic proper-ties of the UAV were not satisfactory There were also sometechnical issues with moving arms for hovering mode Afterconstruction and tests of a prototype the third iteration ofdesign started

In the third and final iteration of design the wing profilewas changed Moreover the construction of the tail wassimplified further from ldquoHrdquo configuration into single ldquoTrdquoconfiguration with floating horizontal stabilizer (Figure 4)All four rotors were placed on two beams mounted belowwings which resulted in ldquoHrdquo propulsion configuration Inthe hovering flight mode all rotors were directed downward


fi

t

Figure 5 Tilt mechanism

(c) (b)

(a)

xbxwxV

fi

CoG

t

Figure 6 The flight envelope (a) VTOL mode (b) transition mode and (c) aircraft mode

In the transition mode the rear propellers (M1 M2) tiltedinto vertical position whereas the front rotors (M3 M4)were gradually turned off In the standard flight mode thespecial construction of front propellers allowed them to folddue to action of drag This resulted in the overall dragreduction The downward orientation of propellers as wellas placement of vertical propellers behind the wing resultedfrom aerodynamic optimization Comparing upward con-figuration downward configuration is characterized withhigher efficiency [26 27] and the pushing configuration ofpropulsion system does not influence the airflow over wingprofile

3 VTOL Aircraft Design

The developed VTOL prototype (Figure 4) allows verticaltake-off transition to forward flight travel to the destinationin cruise flight and transition back to hover flight as well aslanding vertically Finally the proposed design configurationis a hybrid of conventional aircraft in the high-wing systemand quadrotor with two of four rotors mounted in nacellesand having the ability to rotate

The transition mechanisms (Figure 5) which are appliedto achieve the conversion from vertical flight to horizontalflight and vice versa are based on the fact that rear rotors (M1 M2) are mounted on rotating nacelles During transition therotors tilt gradually towards flight direction providing theaircraft forward speedTheir interaction with the front rotors(M3 M4) ensures flight at a fixed height

The flight envelope of the UAV platform is divided intothe three following flight modes which was achieved by

means of the collective angular displacement of the two rearrotors (see Figure 6)

(i) VTOL mode this flight phase is intended for verticalclimbing descending and hovering The flying plat-formworks in amultirotormode and thewhole thrustis derived from the four rotors To minimize powerconsumption after reaching the required minimumaltitude the UAV platform immediately proceeds toflight in the aircraft mode

(ii) Transition mode two rear propellers are tilted syn-chronously towards the vertical direction whichin turn causes the horizontal speed of the aircraftto increase The angular position is controlled bychanging the thrust of particular rotors so that theairframe obtains a given angle of attack relative tothe incoming air streams With the increase of thehorizontal speed the fixed wings develop lift Beforethe angle of attack reaches a given value the roll angleis controlled by the difference in thrust between theleft and right rotors Yaw angle is regulated by thecounteractive moments generated by pairs of rotorsM1M3 andM2M4 In turn pitch angle is controlledby the difference in thrust between the front and rearrotors For horizontal-to-hover transition the reverseprocedure is performed

(iii) Aircraft mode at this flight phase the UAV has asufficient speed of translational movement whichallows generating lift force Under such conditionsthe platform behaves like a conventional airplaneand aerodynamic control surfaces such as rudder


Figure 7 VTOL aircraft

elevator and ailerons provide yaw pitch and rollmotions The required thrust force is generated bytwo rear rotors (M1 M2) tilted by an angle of 90degrees in relation to the initial position The othertwo front motors (M3 M4) are turned off and remainin initial position This flight phase is intended forenergy efficient long term operations

Such structure is characterized by high maneuverabilityin a limited area and the flight time is relatively long aboveone hour which is unachievable in the case of conventionalmultirotor carriers The advantage of proposed approach isan ability to rotate only the rotors themselves not the wholewing During take-off landing and hovering this solutionmakes that the aircraft more robust to cross winds In theairplane mode the advantage is also the usage of rotors inthe pushing system behind the trailing edge of the wing flapwhich ensures uniformity of the air stream flowing aroundthe airfoil The front engines are switched off because theyonly disturb the flow of air streams without significantlyincreasing the lift force generated on the wing In turn inVTOL mode the usage of pushing propeller from undersideof the rotor increases the efficiency of the propulsion system[26 27]

The technical specification of the designed and con-structed aircraft is included in Table 1

To ensure smooth switching between flight modes acertain error margin was provided as shown in Table 2

Figure 7 shows the final realization of the VTOL aircraft

4 Mathematical Modeling

The configuration of VTOL airplane is shown in Figure 4 Inthis paper 119909 119910 and 119911 axes of the inertial coordinate systemare defined as a right handed Cartesian coordinate systemwith North East and Downward directions abbreviated astheNEDcoordinate systemThemovement of the aircraftwillbe considered in relation to the following coordinates systems[29]

(i) inertial reference frame119865119864(119909119873 119910119864 119911119863)with the origindetermined on the surface of the Earth

(ii) inertial reference frame119865119881(119909119881 119910119881 119911119881)with the originin the centre of the mass of the aircraft

Table 1 VTOL aircraft specification

Parameter Value

Configuration VTOL aircraft

Wing span 2520 [mm]

Length 1600 [mm]

Wing area 54 [dm2]

Propeller diameter and pitch 16x8 [inch]

Minimum horizontal speed 10 [ms]

Maximum speed 30 [ms]

Table 2 VTOL flight modes

Flight Mode Horizontal Speed Vertical Speed

VTOL 0 divide 1ms 0 divide 5ms

Transition 0ms divide 12ms 0ms divide 1ms

Aircraft 10ms divide 30ms 0ms divide 5ms

(iii) body reference frame 119865119861(119909119861 119910119861 119911119861)(iv) wind reference frame 119865119908(119909119908 119910119908 119911119908)Assuming that VTOL airplane is a rigid body with six

degrees of freedom the state of aircraft motion is defined bytwelve coordinates The following state vector is adopted

119883 = [119880119881119882 120601 120579 120595 119875 119876 119877 119909 119910 119911]119879 (1)

where 119880119881119882 and 119875119876 119877 are projections of velocity andangular velocity onto the 119909119861 119910119861 and 119911119861 axes of the bodyaxis system 119865119861 respectively Three Euler angles roll angle 120601pitch angle 120579 and yaw angle 120595 are introduced to determinethe angular position of aircraft relatively to the Earth ie theorientation of the body coordinate system 119865119861 with respect tothe Earth coordinate system 119865119881

Whereas the control vector contains the following vari-ables their appropriate combinations allow effective platformcontrol in particular modes of flight119880 = [1199061 1199062 1199063 1199064 120575119905 120575119890 120575119903 120575119886]119879 (2)

where 119906119894 are PWMmotor inputs (119894 = 1 4) 120575119905 is deflectionof the rotor nacelle 120575119890 is elevator deflection 120575119903 is rudderdeflection and 120575119886 is ailerons deflection


Denoting the velocities as follows

(119881119864)119865119861 = [119880119881119882]119879 the aircraft velocity with respectto Earth(119881120572)119865119861 = [119881120572119909 119881120572119910 119881120572119911]119879 the aircraft velocity withrespect to air(119881119882)119865119882 = [119880119882 119881119882119882119882]119879 the wind velocity withrespect to Earth

the relationship between those velocities can be written as

(119881120572)119865119861 = (119881119864)119865119861 minus119863119861119882 (119881119882)119865119882 (3)

In order to determine the aerodynamic forces and momentsacting on the aircraft it is necessary to know the flight speedand two angles the angle of attack 120572 and the sideslip angle 120573These quantities are shown in Figure 4 which shows the flight

of the airplane taking into account the flow of air streamsfrom its left side They are defined based on the coordinatesvelocity vector

120572 = arctan119881120572119911119881120572119909 (4)

120573 = arcsin119881120572119910119881120572 (5)

(119881120572)119865119861 = (1198812120572119909 + 1198812

120572119910 + 1198812120572119911)12 (6)

Before introducing the appropriate equations describing theVTOL aircraftmovement the transformationmatrices whichinterconnect particular coordinate systems will be presentedin the following form

(i) The transformation matrix 119871119861119881 from the Earth coor-dinate system 119865119881 to the body coordinate system 119865119861

119871119861119881 = [[[cos 120579 cos120595 cos 120579 sin120595 minus sin 120579

sin 120601 sin 120579 cos120595 minus cos 120601 sin120595 sin 120601 sin 120579 sin120595 + cos120601 cos120595 sin 120601 cos 120579cos 120601 sin 120579 cos120595 + sin 120601 sin120595 cos120601 sin 120579 sin120595 minus sin 120601 cos120595 cos 120601 cos 120579]]] (7)

(ii) The transformation matrix119863119861119882 from the wind coor-dinate system 119865119882 to the body coordinate system 119865119861119863119861119882 = [[[

cos 120572 cos 120573 minus cos120572 sin 120573 minus sin 120572sin 120573 cos 120573 0

sin 120572 cos 120573 minus sin 120572 sin 120573 cos 120572 ]]] (8)

(iii) The matrix 119879120596 describes a relationship between theEuler angles and the angular velocity 119875 119876 119877 of theaircraft

119879120596 = [[[[[[1 sin 120601 sin 120579

cos 120579 cos 120601 sin 120579cos 1205790 cos 120601 minus sin 1206010 sin 120601

cos 120579 cos120601cos 120579

]]]]]](9)

In this paper air movements with respect to the Earth areassumed to be zero and the relationship between velocitiestakes the form

(119881120572)119865119861 = (119881119864)119865119861 = (119880119881119882) (10)

On this basis the VTOL airplane movement is describedby the following nonlinear system of twelve equations [29]119898( + 119876119882minus 119877119881 + 119892 sin 120579) = 119865119883 (11)

119898( + 119877119880 minus 119875119882 minus 119892 sin 120601 cos 120579) = 119865119884 (12)

119898( + 119875119881 minus 119876119880 minus 119892 cos120601 cos 120579) = 119865119885 (13)

119868119883 + 119876119877 (119868119885 minus 119868119884) minus (119875119876 + ) 119868119883119885 = 119871 (14)

119868119884 + 119875119877 (119868119883 minus 119868119885) + (1198752 minus 1198772) 119868119883119885 = 119872 (15)

119868119885 + 119875119876 (119868119884 minus 119868119883) + (119876119877 minus ) 119868119883119885 = 119873 (16)

( 120601120579) = 119879120596(119875119876119877) (17)

(119864119864119864) = 119871119879119861119881(119880119881119882) (18)

where

m is aircraft mass119892 is gravitational acceleration119865 = [119865119883 119865119884 119865119885]119879is force vector from aerodynamicforces and thrust119872 = [119871119872119873]119879is torque vector from aerodynamicforces and thrust119868 = [ 119868119909 0 minus119868119909119911

0 119868119910 0minus119868119909119911 0 119868119911

] is inertia matrix

Equations (11)ndash(18) allow describing spatial motion of aircraftin a body frame


41 Definition of Forces and Moments The forces andmoments at the aircraft centre of gravity have componentsdue to aerodynamic effects and to enginesrsquo thrust (thesecomponents will be denoted respectively by the subscripts119860 and 119879) The forces acting on the aircraft can be presentedin the form of the following vector equation expressed in the119865119861 system

119865119861 = [[[119865119883119865119884119865119885]]] = 119865119861119879 + 119865119861119860 =

[[[[119865119883119879119865119884119879119865119885119879

]]]] +[[[[119865119883119860119865119884119860119865119885119860

]]]]= [[[[

1198651198831198790119865119885119879]]]] + 119863119861119882

[[[minus119863119884minus119871]]]

(19)

The thrust component 119865119884119879 can be produced by unbalancedengine power in a multiengine aircraft However in our casethe applied thrust vectorization by using servos in the reargondolas eliminates this problem (119865119884119879 = 0)

In general form the thrust component 119865119861119879 has thefollowing form

119865119861119879 = [[[[1198651198831198790119865119885119879

]]]] =[[[

1198911 cos 120575119905 + 1198912 cos 12057511990501198913 + 1198914 + 1198911 sin 120575119905 + 1198912 sin 120575119905]]] (20)

where 120575119905 is tilt-rotor deflection and 119891119894 is 119894th rotor force (119894 =1 4)In the simplest form the relationship between the thrust119891119894 generated by the 119894th rotor and control signal 119906119894 has been

described as a square of the angular rotor velocity [30 31]A more detailed description taking into account dynamicsof BLDC motor propeller aerodynamics Electronic SpeedController (ESC) and batteries has been presented in [32]For the purposes of this paper it was assumed that 119891119894=f (119906119894)where 119894 = 1 4

The aerodynamic forces 119865119861119860 acting on the aircraft aredefined in terms of the dimensionless aerodynamic coeffi-cients [29 33]

119863 = 119902119878119862119863 ndash drag

119884 = 119902119878119862119884 ndash sideforce119871 = 119902119878119862119871 ndash lift(21)

where 119902 = 051205881198812120572 is free-stream dynamic pressure 120588 is air

density 119881120572 is aircraft velocity with respect to air S is wingarea 119862119863 119862119884 and 119862119871 are dimensionless force coefficients

The moments acting on the aircraft during the flight inthe 119865119861 system have the following form

119872 = [[[119871119872119873]]] = 119872119879 +119872119860 = [[[

119897119879119898119879119899119879]]] + [[[

119897119860119898119860119899119860]]] (22)

Torque component resulting from the engine thrust 119872119879consists of the action of the thrust difference of each pair andfrom the gyroscopic effect

119872119879 = [[[119897119879119898119879119899119879]]]

= [[[[119865119885119879998779119910119865119885119879998779119909119865119883119879radic9987791199092 + 9987791199102

]]]] + 120596

times [[[minus119869119903 (Ω1 minus Ω2) cos 1205751199050minus119869119903 (Ω1 sin 120575119905 + Ω3 minus Ω2 sin 120575119905 minus Ω4)

]]]

(23)

where 998779119909 998779119910 are distances from the force component to theaxis of rotation120596 = [ 0 minus119903 119902

119903 0 minus119901minus119902 119901 0

]119869119903 is rotor inertiaΩ119894 (119894 = 1 2 3 4) is angular speed of 119894th rotor

Taking into account the geometric arrangement of eachpropulsion unit in the considered airframe (Figure 8) thefollowing relationship was obtained

119872119879 =[[[[[[[[[[[

12 11989721198914 + 12 11989721198911 sin 120575119905 minus 12 11989721198913 minus 1211989721198912 sin 12057511990512 11989711198913 + 12 11989711198914 minus 12 11989711198912 sin 120575119905 minus 1211989711198911 sin 120575119905radic(121198971)2 + (12 1198972)21198911 cos 120575119905 sin 120575119892 minus radic(12 1198971)2 + (121198972)21198912 cos 120575119905 sin 120575119892

]]]]]]]]]]]


M1

xB

yB

M2

l2

l1

M4M3

g

Figure 8 Configuration of the propulsion system

+ [[[minus119869119903119902 (Ω1 sin 120575119905 + Ω3 minus Ω2 sin 120575119905 minus Ω4)minus119869119903119903 (Ω1 minus Ω2) cos 120575119905 + 119869119903119901 (Ω1 sin 120575119905 + Ω3 minus Ω2 sin 120575119905 minus Ω4)119869119903119902 (Ω1 minus Ω2) cos 120575119905 ]]]

(24)

Gyroscopic torque vector manifests itself in a form of arotation around unwanted axis which is perpendicular tothe axis of the propulsor and the axis around which thewanted rotation is achieved [34]Therefore themodel shouldalso include the gyroscopic effect resulting from the rotationof nacelles (11987211198722) by the 120575119905 angle However during thetransition phase the angular speed of the rotors Ω1 = Ω2and rotation angles of nacelles are also the same whereasthe direction of propellers rotation is opposite Thus thegyroscopic moments originating from the rotors 11987211198722during the rotation by the 120575119905 angle are canceled

The aerodynamic moment 119872119860 in (22) is composedof the moment defined by the dimensionless aerodynamiccoefficients and the moment resulting due to the differencein position of the centre of gravity and the centre of pressure

119872119860 = [[[119897119860119898119860119899119860]]]

= [[[119902119878119887119862119897119902119878119888119862119898119902119878119887119862119899

]]]+ [[[[

minus (119888119892119885 minus 119886119890119903119901119885) 119865119884119860(119888119892119885 minus 119886119890119903119901119885) 119865119883119860 minus (119888119892119883 minus 119886119890119903119901119883) 119865119885119860(119888119892119883 minus 119886119890119903119901119883) 119865119884119860]]]]

(25)

where 119902 = 051205881198812120572 is free-stream dynamic pressure 120588 is

air density 119881120572 is aircraft velocity with respect to air S is wingarea b is wing span c is mean aerodynamic chord of wing119862119897 119862119898 and 119862119899 are dimensionless moment coefficients 119888119892119895is centre of gravity in 119895-axis 119886119890119903119901119895 is aeroreference point inj-axis (119895 = 119909 119911)

The specificity of the VTOL aircraft flight causes thewhole flight envelope of the UAV platform to be divided intothree different flight modes VTOL transition and aircraft Itwas achieved bymeans of the collective angular displacementof the two rear rotors (Figure 4) The form of dimensionlessforce and moment coefficients depend also on the flightphase and therefore in the next part of the article the analysisof the model will be carried out in the individual modes

42 VTOL Mode In the case of vertical flight there arethe following conditions the inclination angle of the rotornacelles 120575119905 = 90∘ the angle of attack 120572 = 0∘ and the sideslipangle 120573 = 0∘ (see Figure 6)The control vector defined in (2)is reduced to the following form119880 = [1199061 1199062 1199063 1199064]119879 (26)

From the point of view of flight mechanics one cannottalk about the drag side force and lift as in the classic air-frame approach In the VTOL mode two main aerodynamiceffects are taken into consideration One concerns how thrustis generated while the other deals with the drag force whichis always opposite to the movement direction in z-axis

The aerial drag force is expressed in the same way as in(21) with the aircraft velocity reduced to the vertical speedW

119865119861 = [[[119865119883119865119884119865119885]]] =

[[[[[[004sum119894=1119891119894]]]]]]+ [[[

00minus119863]]]= [[[[[[

004sum119894=1119891119894]]]]]]+ [[[[[

00minus121205881198822119878119862119863

]]]]](27)


In vertical flight the VTOL airframe structure producesa large aerial drag therefore this force component hassignificantly large values compared to the classic multirotorconfiguration

The moments acting on the aircraft during the flightin the VTOL mode describe (22) (24) and (25) howeveraerodynamic moments in (25) are equal to zero (119897119860 = 119898119860 =119899119860 =0)43 Transition Mode During the transition phase (see Fig-ure 6) themain role in the generation of translational motionis played by the interaction between the angular speed ofrotors Ω119894 (119894 = 1 2 3 4) and deflection of the rotor nacelles120575119905 while the impact of the control surfaces is secondary Onlyat speeds close to stall velocity their participation becomessignificant Therefore the control vector takes the followingform 119880 = [1199061 1199062 1199063 1199064 120575119905]119879 (28)

The forces acting on the VTOL aircraft are determined by(19)ndash(21) However the dimensionless force coefficients 119862119863119862119884 and 119862119871 have the following form

119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119905 (120572) 120575119905119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119905 (120572) 120575119905

(29)

Themoments are described by (22)ndash(25) but the dimension-less moment coefficients 119862119897 119862119898 and 119862119899 take the form of

119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119905 (120572) 120575119905119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881

(30)

Particular aerodynamic derivatives 119862119894 = 119862119894(120572 120573) in (29)and (30) are calculated in ANSYS software using 3D analysisof the whole airframe

44 Aircraft Mode At this flight regime the aircraft hasgained enough velocity (above the stall speed) to generateaerodynamic forces to lift and control the flight In this modethe VTOL aircraft behaves like a common airplane and thecontrol vector contains the following variables119880 = [119906119905ℎ119905119897 120575119890 120575119903 120575119886]119879 (31)

where 119906119905ℎ119905119897 = 1199061 + 1199062When the platform reaches the minimum cruising speed

the motors1198723 and1198724 are switched off the inclination angle

of the rotor nacelles is set to 0 (120575119905 = 0∘) and the driving forceis given only by motors1198721 and1198722 (see Figure 6)

The forces acting in the aircraft mode are determined by(19)ndash(21) however the dimensionless force coefficients 119862119863119862119884 and 119862119871 have the following form

119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119890 (120572) 120575119890119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881+ 119862119884120575119903 (120572) 120575119903 + 119862119884120575119886 (120572) 120575119886119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119890 (120572) 120575119890

(32)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881+ 119862119897120575119903 (120572 120573) 120575119903 + 119862119897120575119886 (120572 120573) 120575119886119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119890 (120572) 120575119890119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881 + 119862119899120575119903 (120572 120573) 120575119903+ 119862119899120575119886 (120572 120573) 120575119886

(33)

As in the two previous flight modes the individualdimensionless forces and moments coefficients 119862119894 = 119862119894(120572 120573)in (32) (33) are calculated in the ANSYS software using 3DCFD analysis of the entire airframe

5 CFD Simulations

In order to evaluate the aerodynamic performance ofdesigned UAV the series of computational fluid dynam-ics simulations (CFD) were performed in the individualflight modes For that purpose ANSYS Workbench 172environment was used The geometry file was importedinto SpaceClaim software in which it was prepared forsubsequent processing (geometry repair and optimization forCFD analysis) Since nonsymmetrical interactions were tobe analysed like side wind or impact of steering surfacesposition it was necessary to create a full model of theplatform without any symmetry planes The computationaldomain was created on the basis of a paraboloid The modelof the UAV was placed in the centre of the domain (000)in order to seamlessly determine all desired coefficients Thedomain itself extended from -20m to 30m in X (platformlongitudinal) direction and from -30m to 30m in Y andZ directions Such prepared geometry was transferred intoANSYS Meshing software Due to the complexity of thegeometry an unstructural mesh was generated consisting oftetrahedral elements In order to correctly simulate gradients


at the surfaces (the y+ lt 1 condition) the inflation (boundarylayer) consisting of prism elements was generated Nextthe grid-independence study was performed As the optimalsolution 16 mln elements mesh was chosen with inflationlayer consisting of 15 sublayers Such prepared computationaldomain was exported into Fluent solver

Since low flight velocities (low Reynolds number) wereto be simulated and therefore no sudden changes in pressurewere expected the pressure-based solver was chosen [35] Inorder to determine all force and moment coefficients as wellas the dynamic interactions the simulations were made inthe steady state and transient However the data presentedin this section concern only the steady state cases so as theinterested reader could compare it more easily with otherpublications

All physicochemical properties of air were constant andaveraged for the weather conditions at which the UAV willbe tested Nowadays one may find publications in whichCFD analysis of the UAVs is performed using one-equationturbulence model (Spallart-Allmars) or two-equation turbu-lence model (usually SST k-120596) [36 37] However in order toachieve high accuracy of obtained results the four-equationTransitional SST turbulence model [38 39] was employedin the presented research The major disadvantage of thisdecision was significantly longer times of calculations TheLangtry-Menter four-equation Transitional SST turbulencemodel [40 41] originates from the SST k-120596 turbulencemodel [42 43] It couples its transport equations with theintermittency equation and the equation for the transitiononset criteria in terms of momentum-thickness Reynoldsnumber The transport equation for the intermittency 120574 isdefined as follows [35]

120597 (120588120574)120597119905 + 120597 (120588119880119895120574)120597119909119895 = 1198751205741 minus 1198641205741 + 1198751205742 minus 1198641205741+ 120597120597119909119895 [(120583 + 120583119905120590120574) 120597120574120597119909119895 ]

(34)

and for the transition momentum-thickness Reynolds num-ber

120597 (120588Re120579t)120597t + 120597 (120588UjRe120579t)120597xj= 119875120579119905 + 120597120597119909119895 [120590120579119905 (120583 + 120583119905) Re120579119905120597119909119895 ]

(35)

The transitionmodel interacts with the SST turbulencemodelby modification of the k-equation [35]

120597120597119905 (120588119896) + 120597120597119909119894 (120588119896119906119894)= 119866119896

lowast minus 119884119896lowast + 119878119896lowast + 120597120597119909119895 (Γ119896 120597119896120597119909119895)(36)

Finally the 120596-equation has the following form [35]120597120597119905 (120588120596) + 120597120597119909119895 (120588120596119906119895)= 119866120596 minus 119884120596 + 119863120596 + 119878120596 + 120597120597119909119895 (Γ120596 120597120596120597119909119895)

(37)

Due to the limited computational power Semi-ImplicitMethod for Pressure Linked Equations (SIMPLE) was usedinstead of coupled pressure-velocity coupling algorithm Alldiscretization schemes were set to the second-order up-wind whereas the gradients were evaluated using Green-Gauss Node-Based method As the convergence criteriathe values of all scaled residuals smaller than 1e-03 wereassumed Simultaneously the value of lift and drag coef-ficients were monitored The iterations were continued ifthese values did not achieve the constant level Three dif-ferent boundary conditions were used in simulations Theperipheral of paraboloid was set as velocity inlet for whichdirection vector and velocity magnitude were set The backsurface of paraboloid was set as pressure outlet Finallythe surface of the UAV was treated as wall with no slipcondition

In order to fulfil all requirements for which the UAVwas designed it should be characterized by high aerodynamicefficiency This feature will allow it not only to take off andland at any desired location but also more importantly totravel for long distances As one should expect the construc-tion modification of a classical plane for hovering mode offlight will always influence unfavourably the aerodynamicproperties of the platform Figure 9 presents the lift anddrag coefficients as the functions of angle of attack (AoA)for Re = 237 000 Although the maximal lift coefficient islow comparing to other conceptual studies [44] especiallydedicated for the same purpose [16] the designed UAVhas satisfactory parameters from the project aims point ofview The zero lift condition appears for AoA equal to minus1∘whereas the stall point is achieved for 12∘ The generatedlift and drag are sufficient to travel for the intended dis-tance

Figure 10 presents the pitching moment It changes itsvalue from positive to negative at approximately the sameangle of attack as for the zero lift condition After this pointit decreases steadily up to the stall region The negative slopeindicates positive static longitudinal stability of the UAV

Figure 11 represents lift to drag ratio as the functionof angle of attack Moreover the impact of side wind isanalysed As one may notice the designed platform behavesstably despite unfavourable conditions Although the impactof side wind on both the lift and drag is almost unnoticeablewhen considered separately if these two parameters arecombined some decrease in efficiency is visible As it shouldbe expected the biggest differences were noticed for 10∘ sidewind (maximal investigated value) for which lift to dragratio decreased by 27 22 and 18 for 0∘ 2∘ and 4∘respectively What is interesting in the case of 5∘ side windand AoA beyond 8∘ is that the lift to drag ratio increased by1


minus002

002

006

010

014

018

022

026

030

minus02

0

02

04

06

08

1

12

14

minus4 minus2 0 2 4 6 8 10 12 14 16 18

CD

[-]

CL

[-]

AoA [deg]

Lift coecientDrag coecient

Figure 9 Lift and drag coefficients versus angle of attack (AoA) for the final UAV design (Re = 237 000)

minus04

minus03

minus02

minus01

0

01

02

minus4 minus2 0 2 4 6 8 10 12 14 16 18

Cm

AoA [deg]

Figure 10 Pitching moment coefficient versus AoA for the final UAV design (Re = 237 000)

minus4

minus2

0

2

4

6

8

10

12

14

16

minus4 minus2 0 2 4 6 8 10 12 14 16 18

LD

AoA [deg]

Side wind (0 deg)

Side wind (5 deg)

Side wind (10 deg)

Figure 11 Impact of the side wind onto lift to drag ratio for the final UAV design (Re = 237 000)


(a) (b)

(c)

Figure 12 Velocity contour plots and wind velocity vectors (Re = 237 000) for (a) 0∘ AoA (b) 12∘ AoA and (c) 16∘ AoA

Figure 12 presents the process of wind streamlineddetachment from the wing surface during the increase ofAoA For the 0∘ AoA (Figure 12(a)) air steadily flows aroundthe wing A region of higher velocity is visible above the winggenerating small lift force (Figure 9)Moreover a thin laminarlayer may be noticed around solid surface When the AoAis increased up to 12∘ (Figure 12(b)) which corresponds tothe maximal lift force (Figure 9) one may notice a region ofsignificantly higher velocity above the wing Simultaneouslyfirst streamlines of air start to detach at the end of the surfaceAt this angle wing becomes a serious obstacle for the airflow Finally for AoA equal to 16∘ the detachment is clearlyvisible The lift force decreases and the drag force increasessubstantially

The impact of AoA value on the vorticity is presented inFigure 13The UAV is surrounded by an isosurface generated

for 100 sminus1 vorticity in order to depict the negative impactof nacelles on the lifting capabilities of the platform Thecolor of the isosurface represents local air velocity At 0∘ AoAthe vortices are generated mainly at the tips of winglets andbehind the nacelles and tail When the AoA was increased upto 12∘ some crucial changes may be noticed The constructionof nacelles in front of the wing generates vortices influencingaerodynamic performance of the wings Significantly higher

vorticity is visible behind the wing especially in the region ofnacelles and winglets Finally at AoA equal to 16∘ extremelyhigh vorticity is visible especially in the case of nacelles

The last step of the simulations involved the analysis ofaerodynamic properties of the VTOL during hovering andtransition stage of flight In these simulation the impact ofpropeller action on the air velocity profile around the wingsalso had to be included It was done by generation of fourvolumes of fluid which corresponded to the volumes createdduring rotational movement of propellers Next for each vol-ume appropriate momentum source was defined within thesolver As in the previous cases all simulations were made inthe steady state The simulations were performed for variousranges of velocities tilt angles and thrust values in order todetermine force and moments coefficients introduced in thefourth chapter of this work An exemplary result is presentedin Figure 14 in which the vortices generated by the propellersare depicted Of course the disturbance of air flow belowthe wing resulting from the action of front propellers has anegative influence on the overall aerodynamic properties ofthe platform Therefore the transition phase demands theoptimization of the flight scenario which will include thethrust of propulsion system and angle of attack value as wellas flight velocity


(a) (b)

(c)

Figure 13 Isosurface of vorticity (Re = 237 000) for 100 sminus1 (the color of isosurface represents wind velocity) for (a) 0∘ AoA (b) 12∘ AoAand (c) 16∘ AoA

6 Conclusions

In this paper the design process of a VTOL aircraft waspresented The evolution of the design from three supportpoints platform with ducted fuselage propeller into foursupport points ldquoHrdquo configuration was discussed An unusualconfiguration of propellers was proposed namely all fourpropellers directed downward during hovering mode andpropellers directed backward (pushing configuration) in thestandard flight mode As it was proven such design is moreefficient in aerodynamics terms The platform has fixed-wing configuration The rotors are mounted on beams placedbelow wings The front rotors have fixed position howevertheir construction allows them to fold due to action of dragIn the airplane mode they are switched off because theyonly disturb the flow of air streams without significantlyincreasing the lift force generated on the wingThe rear rotorsare mounted on nacelles that ensure the thrust vectoringof engines This provides their usage in both vertical andhorizontal flight The advantage of proposed approach is anability to rotate only the rotors themselves not the wholewing The proposed solution makes the aircraft more robustto cross winds The mathematical model of each of flightmodes was proposed and discussed Finally the results of

CFD simulations were presented for the final designThedegree of complexity of the aerodynamic properties of suchUAV obviously makes it impossible to control it in the openloop system and enforces regulation in a closed loop systemwith feedback Due to nonlinearities and instability resultingfrom the stall condition the transition mode is particularlydangerous and demanding in terms of reliability of thecontrol system CFD analysis results presented in this paperhave given a broad view on the aerodynamic properties of theaircraft in particular on the stall effect

Looking prospectively such constructions could be usedin an urban environment where the use of a runwayis not possible Such platforms will be useful when highmaneuverability in a limited area is demanded and the flighttime should be relatively long (above one hour) which isunachievable in the case of conventional multirotor carriers

Data Availability

All data used to support the findings of this study are includedwithin the article The CFD data used to support the findingsof this study are available from the corresponding authorupon request


Figure 14 Isosurface of vorticity (Re = 77 000) for 100 sminus1 (the color of isosurface represents wind velocity) for AoA=0∘ tilt of the rear rotornacelles 120575119905 = 45∘Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work has been granted by the Polish Ministry ofScience and Higher Education from funds of EuropeanUnion and national funds for years 2017-2018 [grant NoMNiSW2017110DIRNN2] The computational fluid sim-ulations were performed in ANSYS environment using ITinfrastructure of GeCONiI [grant NCBiR POIG 020301-24-099]

References

[1] R Austin Unmanned Aircraft Systems ndashUAVS Design Develop-ment and Deployment John Wiley amp Sons 2010

[2] M Logan T Vranas M Motter Q Shams and DPollock Technology Challenges in Small UAV DevelopmentInfotechAerospace 2005

[3] A C Watts V G Ambrosia and E A Hinkley ldquoUnmannedaircraft systems in remote sensing and scientific research

Classification and considerations of userdquo Remote Sensing vol4 no 6 pp 1671ndash1692 2012

[4] K P Valavanis Advances in Unmanned Aerial Vehicles vol 33Springer Netherlands Dordrecht 2007

[5] P Castillo R Lozano and A E DzulModelling and Control ofMini-flying Machines Springer-Verlag 2005

[6] K Nonami F Kendoul S Suzuki W Wang and D NakazawaldquoAutonomous flying robots Unmanned aerial vehicles andmicro aerial vehiclesrdquo Autonomous Flying Robots UnmannedAerial Vehicles and Micro Aerial Vehicles pp 1ndash329 2010

[7] R Czyba G Szafranski W Janusz M Niezabitowski ACzornik and M Błachuta ldquoConcept and realization ofunmanned aerial system with different modes of operationrdquoin Proceedings of the 10Th International Conference on Mathe-matical Problems in Engineering Aerospace And Sciences Icnpaa2014 pp 261ndash270 Narvik Norway 2014

[8] K Dalamagkidis ldquoAviation history and unmanned flightrdquoHandbook of Unmanned Aerial Vehicles pp 57ndash81 2015

[9] httpswwwsesarjueuU-Space

[10] httpswwwskyguidechenevents-media-boardu-space-live-demonstration

[11] R Czyba G Szafranski A Rys G Szafranski and A RysldquoDesign and control of a single tilt tri-rotor aerial vehiclerdquoJournal of Intelligent Robotic Systems vol 84 pp 53ndash66 2016


[12] R Czyba G Szafranski M Janik K Pampuch and MHecel ldquoDevelopment of co-axial Y6-Rotor UAV - designmathematical modeling rapid prototyping and experimentalvalidationrdquo in Proceedings of the 2015 International Conferenceon Unmanned Aircraft Systems (ICUAS) pp 1102ndash1111 DenverCO USA June 2015

[13] F Cakıcı and M K Leblebicioglu ldquoDesign and analysis of amode-switching micro unmanned aerial vehiclerdquo InternationalJournal of Micro Air Vehicles vol 8 no 4 pp 221ndash229 2016

[14] G R Flores-Colunga and R Lozano-Leal ldquoA nonlinear controllaw for hover to level flight for the Quad Tilt-rotor UAVrdquo IFACProceedings Volumes vol 47 no 3 pp 11055ndash11059 2014

[15] Y O Aktas U Ozdemir and Y Dereli ldquoRapid Prototyping ofa Fixed-Wing VTOL UAV for Design Testingrdquo JournalofIntelli-gentRoboticSystems vol 84 pp 639ndash664 2016

[16] D Orbea J Moposita W G Aguilar M Paredes R P Reyesand L Montoya ldquoVertical take off and landing with fixed rotorrdquoin Proceedings of the 2017 CHILEAN Conference on ElectricalElectronics Engineering Information and Communication Tech-nologies (CHILECON) pp 1ndash6 Pucon October 2017

[17] L Zhong H Yuqing Y Liying et al ldquoControl techniques oftilt rotor unmanned aerial vehicle systems A reviewrdquo ChineseJournal of Aeronautics vol 30 no 1 pp 135ndash148 2017

[18] A M Stoll E V Stilson J Bevirt and P Sinha ldquoA Multifunc-tional Rotor Concept for Quiet and Efficient VTOL Aircraftrdquoin Proceedings of the 2013 Aviation Technology Integration andOperations Conference Los Angeles CA USA

[19] J-T Zou and Z-Y Pan ldquoThe development of tilt-rotorunmanned aerial vehiclerdquo Transactions of the Canadian Societyfor Mechanical Engineering vol 40 no 5 pp 909ndash921 2016

[20] B Defense V-22 osprey Space and Security

[21] E Cetinsoy S Dikyar C Hancer et al ldquoDesign and construc-tion of a novel quad tilt-wing UAVrdquoMechatronics vol 22 no 6pp 723ndash745 2012

[22] R Udroiu and M Blaj ldquoConceptual design of a vtol remotelypiloted aircraft for emergencymissionsrdquo Scientific Research andEducation in the Air Force vol 18 no 1 pp 207ndash214 2016

[23] R Park Arcturus uav upgrades the jump15 vtol uav Airlines ampAviation Aerospace amp Defense December 2014

[24] M Hochstenbach C Notteboom B Theys and J De Schut-ter ldquoDesign and control of an unmanned aerial vehicle forautonomous parcel delivery with transition from vertical take-off to forward flight - VertiKUL a quadcopter tailsitterrdquo Inter-national Journal of Micro Air Vehicles vol 7 no 4 pp 395ndash4052015

[25] R Ritz and R DrsquoAndrea ldquoA global controller for flying wingtailsitter vehiclesrdquo in Proceedings of the 2017 IEEE InternationalConference on Robotics and Automation (ICRA) pp 2731ndash2738Singapore Singapore May 2017

[26] BTheys G Dimitriadis P Hendrick and J De Schutter ldquoInflu-ence of propeller configuration on propulsion system efficiencyof multi-rotor Unmanned Aerial Vehiclesrdquo in Proceedings of the2016 International Conference on Unmanned Aircraft Systems(ICUAS) pp 195ndash201 Arlington VA USA June 2016

[27] httpsnoveltyrpascomogar-mk2

[28] Y Jiang B Zhang and T Huang ldquoCFD study of an annular-ducted fan lift system for VTOL aircraftrdquo Aerospace vol 2 no4 pp 555ndash580 2015

[29] B L Stevens F L Lewis and E N Johnson Aircraft Controland Simulation Dynamics Controls Design and AutonomousSystems Wiley-Blackwell 3rd edition 2015

[30] A Abhishek ldquoTripathi Six-rotor UAV helicopter dynamicsand control theory and simulationrdquo International Journal ofAdvanced Research in Electrical Electronics and InstrumentationEngineering vol 2 no 11 pp 5747ndash5755 2013

[31] Z Chen Z Peng and F Zhang ldquoAttitude control of coaxialtri-rotor UAV based on Linear Extended State Observerrdquo inProceedings of the 2014 26th Chinese Control And DecisionConference (CCDC) pp 4204ndash4209 Changsha China May2014

[32] G Szafranski R Czyba andM Blachuta ldquoModeling and identi-fication of electric propulsion system for multirotor unmannedaerial vehicle designrdquo in Proceedings of the 2014 InternationalConference on Unmanned Aircraft Systems ICUAS 2014 pp470ndash476 USA May 2014

[33] Y Naidoo R Stopforth and G Bright ldquoRotor AerodynamicAnalysis of a Quadrotor forThrustrdquoCSIR Pretoria South Africa2011

[34] P Shao W Dong X Sun T Ding and Q Zou ldquoDynamicsurface control to correct for gyroscopic effect of propellerson quadrotorrdquo in Proceedings of the 2015 IEEE InternationalConference on Information and Automation (ICIA) pp 2971ndash2976 Lijiang China August 2015

[35] ldquoFluent Userrsquos Guiderdquo ANSYS INC 2016

[36] S G Kontogiannis and J A Ekaterinaris ldquoDesign performanceevaluation and optimization of a UAVrdquo Aerospace Science andTechnology vol 29 no 1 pp 339ndash350 2013

[37] P D Bravo-Mosquera L Botero-Bolivar D Acevedo-Giraldoand H D Ceron-Munoz ldquoAerodynamic design analysis ofa UAV for superficial research of volcanic environmentsrdquoAerospace Science and Technology vol 70 pp 600ndash614 2017

[38] SM Aftab A S MohdRafie NA Razak K A Ahmad and XWang ldquoTurbulenceModel Selection for LowReynolds NumberFlowsrdquo PLoS ONE vol 11 no 4 p e0153755 2016

[39] S M Aftab and K A Ahmad ldquoCorrection CFD study onNACA 4415 airfoil implementing spherical and sinusoidalTubercle Leading Edgerdquo PLoS ONE vol 12 no 11 p e01887922017

[40] R B Langtry and F R Menter ldquoCorrelation-based transitionmodeling for unstructured parallelized computational fluiddynamics codesrdquo AIAA Journal vol 47 no 12 pp 2894ndash29062009

[41] F R Menter R Langtry and S Volker ldquoTransition modellingfor general purpose CFD codesrdquo Flow Turbulence and Combus-tion vol 77 no 1ndash4 pp 277ndash303 2006

[42] F R Menter ldquoTwo-equation eddy-viscosity turbulence modelsfor engineering applicationsrdquo AIAA Journal vol 32 no 8 pp1598ndash1605 1994

[43] F R Menter M Kuntz and R Langtry ldquoTen Years of Indus-trial Experience with the SST Turbulence Model Turbu-lence HeatandMassTransferrdquo in Ten Years of Industrial Expe-rience with the SST Turbulence Model Turbulence Heatand-MassTransfer K Hanjalic Y Nagano and M Tummers Edspp 625ndash632 Begell House Inc HeatandMassTransfer 2003

[44] P Panagiotou S Fotiadis-Karras and K Yakinthos ldquoConcep-tual design of a Blended Wing Body MALE UAVrdquo AerospaceScience and Technology vol 73 pp 32ndash47 2018

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Submit your manuscripts at

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Figure 1 The initial concept of the VTOL UAV

the transition between individual flight phases is obtained bytilting the wings with fixed rotors [17 21 22] Unfortunatelyduring take-off landing and hovering the wings will bedirected upwards which makes the aircraft more suscepti-ble to transverse winds Another type of convertiplane isDual-System [23] where multiple rotors are always directedupwards for vertical flight and another separate rotor forhorizontal flight This configuration is very simple to applyin terms of design and modeling because two flight phasescould be analysed separately But for most of the missionthe platform must transport unnecessary mass which canbe replaced by fuel or batteries Another solution is aconfiguration of Tail-Sitter [24 25] This platform takes offand lands vertically on its tail and the whole aircraft tiltsforward using differential thrust or control surfaces to achievehorizontal flight In conclusion it is true that today VTOLaircraft exist and operate in practice but they are burdenedwith various limitations and disadvantages

In this paper a novel design configuration in a formof hybrid of conventional aircraft and quadrotor with twoof four rotors mounted in nacelles with ability of rotationhas been proposed It will have a unique feature amongsimilar solutionsmdasha thrust vectoring of engines that ensurestheir usage in both vertical and horizontal flight Comparedto the above-mentioned designs an advantage of proposedapproach is an ability to rotate only the rotors themselvesnot the whole wing During take-off landing and hoveringthis solution makes the aircraftmore robust to cross winds Inthe airplane mode the advantage is also the usage of rotorsin the pushing system behind the trailing edge of the wingwhich ensures uniformity of the air stream flowing aroundthe airfoil In turn in VTOL mode the usage of pushingpropeller from underside of the rotor increases the efficiencyof the propulsion system [26 27]

The main purpose of this paper is to present the conceptof VTOL aircraft from scratch to final implementationcovering the individual stages of prototyping and thenderiving a mathematical model based on the physical modeland computational fluid dynamics CFD simulations [28]A mathematical model that can accurately describe the flightdynamics is exceedingly important in the design of a flightcontrol system In the case of hybrid UAVs the whole flightcan be divided into three phases namely vertical flightmode transition mode and horizontal flight mode As aconsequence the development of a real flight dynamicsmodel is much more difficult compared to the conventionalUAVs and causes many problems

The paper is organized as follows First the introductionis provided in Section 1 Then the concept of VTOL aircraftand construction prototyping are presented in Section 2The mechanical design and an explanation of flight phasesare shown in Section 3 A mathematical model includingforces and moments definition in individual flight phasesare determined in Section 4 Next the computational fluiddynamics (CFD) simulations are described together with adiscussion of received results The conclusions are brieflydiscussed in the last section

2 Mechanical Design andConstruction Prototyping

The initial concept of the UAV assumed that the constructionshould be efficient in terms of aerodynamics as far as itis possible Therefore the parts of the platform which arenecessary for the hovering flight mode (especially enginesand propellers) should not generate drag during standardflight mode which means that they should be hidden withinfuselage Simultaneously the minimum number of supportpoints which provides stable UAV hovering without necessityof applying any advanced and complicated control mecha-nisms is equal to three In the light of these assumptions theobvious choicewas a platform configurationwith two enginesmounted in the front of the wings and a ducted propellerplaced within the fuselage (Figure 1)

The front engines together with propellers were designedto tilt from vertical orientation used in standard flight modeto horizontal orientation used in hovering mode Togetherwith the ducted propeller they were arranged on a circularplan whose centre was located at the mass centre of construc-tion The advantage of such construction solution was thepossibility of hiding the fuselage propeller during standardflight mode and as a result to minimize generated dragOn the other hand the placement of the fuselage propellercomplicated significantly the tail construction Moreoverthe size of the fuselage had to be increased in order toaccommodate the mechanical construction As a result theaerodynamic properties of the platform were not satisfactoryIt was characterized by low lift with simultaneous high dragMoreover the thrust generated by fuselage propeller wastoo low and its mechanical construction was unnecessarilycomplicated In the initial design two separate autopilotswere considered both for hovering and standard flight modesconnected via mixer To conclude the concept with three




M4

M3

M1

M2f1

f2

f3

f4xB

yB

zB

yE

zD

xN

yV

xV

zVxW








fi

t


(c) (b)

(a)

xbxwxV

fi

CoG

t























Parameter Value


Wing span 2520 [mm]

Length 1600 [mm]

Wing area 54 [dm2]











119883 = [119880119881119882 120601 120579 120595 119875 119876 119877 119909 119910 119911]119879 (1)








(119881120572)119865119861 = (119881119864)119865119861 minus119863119861119882 (119881119882)119865119882 (3)



120572 = arctan119881120572119911119881120572119909 (4)

120573 = arcsin119881120572119910119881120572 (5)

(119881120572)119865119861 = (1198812120572119909 + 1198812

120572119910 + 1198812120572119911)12 (6)









119879120596 = [[[[[[1 sin 120601 sin 120579


cos 120579 cos120601cos 120579

]]]]]](9)


(119881120572)119865119861 = (119881119864)119865119861 = (119880119881119882) (10)




119868119883 + 119876119877 (119868119885 minus 119868119884) minus (119875119876 + ) 119868119883119885 = 119871 (14)

119868119884 + 119875119877 (119868119883 minus 119868119885) + (1198752 minus 1198772) 119868119883119885 = 119872 (15)

119868119885 + 119875119876 (119868119884 minus 119868119883) + (119876119877 minus ) 119868119883119885 = 119873 (16)

( 120601120579) = 119879120596(119875119876119877) (17)

(119864119864119864) = 119871119879119861119881(119880119881119882) (18)

where


0 119868119910 0minus119868119909119911 0 119868119911

] is inertia matrix




119865119861 = [[[119865119883119865119884119865119885]]] = 119865119861119879 + 119865119861119860 =

[[[[119865119883119879119865119884119879119865119885119879

]]]] +[[[[119865119883119860119865119884119860119865119885119860

]]]]= [[[[

1198651198831198790119865119885119879]]]] + 119863119861119882

[[[minus119863119884minus119871]]]

(19)



119865119861119879 = [[[[1198651198831198790119865119885119879

]]]] =[[[

1198911 cos 120575119905 + 1198912 cos 12057511990501198913 + 1198914 + 1198911 sin 120575119905 + 1198912 sin 120575119905]]] (20)




119863 = 119902119878119862119863 ndash drag





119872 = [[[119871119872119873]]] = 119872119879 +119872119860 = [[[

119897119879119898119879119899119879]]] + [[[

119897119860119898119860119899119860]]] (22)


119872119879 = [[[119897119879119898119879119899119879]]]

= [[[[119865119885119879998779119910119865119885119879998779119909119865119883119879radic9987791199092 + 9987791199102

]]]] + 120596


]]]

(23)


119903 0 minus119901minus119902 119901 0



119872119879 =[[[[[[[[[[[


]]]]]]]]]]]


M1

xB

yB

M2

l2

l1

M4M3

g



(24)



119872119860 = [[[119897119860119898119860119899119860]]]

= [[[119902119878119887119862119897119902119878119888119862119898119902119878119887119862119899

]]]+ [[[[


(25)







119865119861 = [[[119865119883119865119884119865119885]]] =

[[[[[[004sum119894=1119891119894]]]]]]+ [[[

00minus119863]]]= [[[[[[

004sum119894=1119891119894]]]]]]+ [[[[[

00minus121205881198822119878119862119863

]]]]](27)





119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119905 (120572) 120575119905119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119905 (120572) 120575119905

(29)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119905 (120572) 120575119905119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881

(30)







119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119890 (120572) 120575119890119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881+ 119862119884120575119903 (120572) 120575119903 + 119862119884120575119886 (120572) 120575119886119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119890 (120572) 120575119890

(32)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881+ 119862119897120575119903 (120572 120573) 120575119903 + 119862119897120575119886 (120572 120573) 120575119886119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119890 (120572) 120575119890119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881 + 119862119899120575119903 (120572 120573) 120575119903+ 119862119899120575119886 (120572 120573) 120575119886

(33)


5 CFD Simulations






120597 (120588120574)120597119905 + 120597 (120588119880119895120574)120597119909119895 = 1198751205741 minus 1198641205741 + 1198751205742 minus 1198641205741+ 120597120597119909119895 [(120583 + 120583119905120590120574) 120597120574120597119909119895 ]

(34)


120597 (120588Re120579t)120597t + 120597 (120588UjRe120579t)120597xj= 119875120579119905 + 120597120597119909119895 [120590120579119905 (120583 + 120583119905) Re120579119905120597119909119895 ]

(35)


120597120597119905 (120588119896) + 120597120597119909119894 (120588119896119906119894)= 119866119896



(37)






minus002

002

006

010

014

018

022

026

030

minus02

0

02

04

06

08

1

12

14

minus4 minus2 0 2 4 6 8 10 12 14 16 18

CD

[-]

CL

[-]

AoA [deg]



minus04

minus03

minus02

minus01

0

01

02

minus4 minus2 0 2 4 6 8 10 12 14 16 18

Cm

AoA [deg]


minus4

minus2

0

2

4

6

8

10

12

14

16

minus4 minus2 0 2 4 6 8 10 12 14 16 18

LD

AoA [deg]

Side wind (0 deg)

Side wind (5 deg)

Side wind (10 deg)



(a) (b)

(c)








(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom




M4

M3

M1

M2f1

f2

f3

f4xB

yB

zB

yE

zD

xN

yV

xV

zVxW








fi

t


(c) (b)

(a)

xbxwxV

fi

CoG

t























Parameter Value


Wing span 2520 [mm]

Length 1600 [mm]

Wing area 54 [dm2]











119883 = [119880119881119882 120601 120579 120595 119875 119876 119877 119909 119910 119911]119879 (1)








(119881120572)119865119861 = (119881119864)119865119861 minus119863119861119882 (119881119882)119865119882 (3)



120572 = arctan119881120572119911119881120572119909 (4)

120573 = arcsin119881120572119910119881120572 (5)

(119881120572)119865119861 = (1198812120572119909 + 1198812

120572119910 + 1198812120572119911)12 (6)









119879120596 = [[[[[[1 sin 120601 sin 120579


cos 120579 cos120601cos 120579

]]]]]](9)


(119881120572)119865119861 = (119881119864)119865119861 = (119880119881119882) (10)




119868119883 + 119876119877 (119868119885 minus 119868119884) minus (119875119876 + ) 119868119883119885 = 119871 (14)

119868119884 + 119875119877 (119868119883 minus 119868119885) + (1198752 minus 1198772) 119868119883119885 = 119872 (15)

119868119885 + 119875119876 (119868119884 minus 119868119883) + (119876119877 minus ) 119868119883119885 = 119873 (16)

( 120601120579) = 119879120596(119875119876119877) (17)

(119864119864119864) = 119871119879119861119881(119880119881119882) (18)

where


0 119868119910 0minus119868119909119911 0 119868119911

] is inertia matrix




119865119861 = [[[119865119883119865119884119865119885]]] = 119865119861119879 + 119865119861119860 =

[[[[119865119883119879119865119884119879119865119885119879

]]]] +[[[[119865119883119860119865119884119860119865119885119860

]]]]= [[[[

1198651198831198790119865119885119879]]]] + 119863119861119882

[[[minus119863119884minus119871]]]

(19)



119865119861119879 = [[[[1198651198831198790119865119885119879

]]]] =[[[

1198911 cos 120575119905 + 1198912 cos 12057511990501198913 + 1198914 + 1198911 sin 120575119905 + 1198912 sin 120575119905]]] (20)




119863 = 119902119878119862119863 ndash drag





119872 = [[[119871119872119873]]] = 119872119879 +119872119860 = [[[

119897119879119898119879119899119879]]] + [[[

119897119860119898119860119899119860]]] (22)


119872119879 = [[[119897119879119898119879119899119879]]]

= [[[[119865119885119879998779119910119865119885119879998779119909119865119883119879radic9987791199092 + 9987791199102

]]]] + 120596


]]]

(23)


119903 0 minus119901minus119902 119901 0



119872119879 =[[[[[[[[[[[


]]]]]]]]]]]


M1

xB

yB

M2

l2

l1

M4M3

g



(24)



119872119860 = [[[119897119860119898119860119899119860]]]

= [[[119902119878119887119862119897119902119878119888119862119898119902119878119887119862119899

]]]+ [[[[


(25)







119865119861 = [[[119865119883119865119884119865119885]]] =

[[[[[[004sum119894=1119891119894]]]]]]+ [[[

00minus119863]]]= [[[[[[

004sum119894=1119891119894]]]]]]+ [[[[[

00minus121205881198822119878119862119863

]]]]](27)





119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119905 (120572) 120575119905119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119905 (120572) 120575119905

(29)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119905 (120572) 120575119905119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881

(30)







119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119890 (120572) 120575119890119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881+ 119862119884120575119903 (120572) 120575119903 + 119862119884120575119886 (120572) 120575119886119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119890 (120572) 120575119890

(32)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881+ 119862119897120575119903 (120572 120573) 120575119903 + 119862119897120575119886 (120572 120573) 120575119886119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119890 (120572) 120575119890119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881 + 119862119899120575119903 (120572 120573) 120575119903+ 119862119899120575119886 (120572 120573) 120575119886

(33)


5 CFD Simulations






120597 (120588120574)120597119905 + 120597 (120588119880119895120574)120597119909119895 = 1198751205741 minus 1198641205741 + 1198751205742 minus 1198641205741+ 120597120597119909119895 [(120583 + 120583119905120590120574) 120597120574120597119909119895 ]

(34)


120597 (120588Re120579t)120597t + 120597 (120588UjRe120579t)120597xj= 119875120579119905 + 120597120597119909119895 [120590120579119905 (120583 + 120583119905) Re120579119905120597119909119895 ]

(35)


120597120597119905 (120588119896) + 120597120597119909119894 (120588119896119906119894)= 119866119896



(37)






minus002

002

006

010

014

018

022

026

030

minus02

0

02

04

06

08

1

12

14

minus4 minus2 0 2 4 6 8 10 12 14 16 18

CD

[-]

CL

[-]

AoA [deg]



minus04

minus03

minus02

minus01

0

01

02

minus4 minus2 0 2 4 6 8 10 12 14 16 18

Cm

AoA [deg]


minus4

minus2

0

2

4

6

8

10

12

14

16

minus4 minus2 0 2 4 6 8 10 12 14 16 18

LD

AoA [deg]

Side wind (0 deg)

Side wind (5 deg)

Side wind (10 deg)



(a) (b)

(c)








(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom


fi

t


(c) (b)

(a)

xbxwxV

fi

CoG

t























Parameter Value


Wing span 2520 [mm]

Length 1600 [mm]

Wing area 54 [dm2]











119883 = [119880119881119882 120601 120579 120595 119875 119876 119877 119909 119910 119911]119879 (1)








(119881120572)119865119861 = (119881119864)119865119861 minus119863119861119882 (119881119882)119865119882 (3)



120572 = arctan119881120572119911119881120572119909 (4)

120573 = arcsin119881120572119910119881120572 (5)

(119881120572)119865119861 = (1198812120572119909 + 1198812

120572119910 + 1198812120572119911)12 (6)









119879120596 = [[[[[[1 sin 120601 sin 120579


cos 120579 cos120601cos 120579

]]]]]](9)


(119881120572)119865119861 = (119881119864)119865119861 = (119880119881119882) (10)




119868119883 + 119876119877 (119868119885 minus 119868119884) minus (119875119876 + ) 119868119883119885 = 119871 (14)

119868119884 + 119875119877 (119868119883 minus 119868119885) + (1198752 minus 1198772) 119868119883119885 = 119872 (15)

119868119885 + 119875119876 (119868119884 minus 119868119883) + (119876119877 minus ) 119868119883119885 = 119873 (16)

( 120601120579) = 119879120596(119875119876119877) (17)

(119864119864119864) = 119871119879119861119881(119880119881119882) (18)

where


0 119868119910 0minus119868119909119911 0 119868119911

] is inertia matrix




119865119861 = [[[119865119883119865119884119865119885]]] = 119865119861119879 + 119865119861119860 =

[[[[119865119883119879119865119884119879119865119885119879

]]]] +[[[[119865119883119860119865119884119860119865119885119860

]]]]= [[[[

1198651198831198790119865119885119879]]]] + 119863119861119882

[[[minus119863119884minus119871]]]

(19)



119865119861119879 = [[[[1198651198831198790119865119885119879

]]]] =[[[

1198911 cos 120575119905 + 1198912 cos 12057511990501198913 + 1198914 + 1198911 sin 120575119905 + 1198912 sin 120575119905]]] (20)




119863 = 119902119878119862119863 ndash drag





119872 = [[[119871119872119873]]] = 119872119879 +119872119860 = [[[

119897119879119898119879119899119879]]] + [[[

119897119860119898119860119899119860]]] (22)


119872119879 = [[[119897119879119898119879119899119879]]]

= [[[[119865119885119879998779119910119865119885119879998779119909119865119883119879radic9987791199092 + 9987791199102

]]]] + 120596


]]]

(23)


119903 0 minus119901minus119902 119901 0



119872119879 =[[[[[[[[[[[


]]]]]]]]]]]


M1

xB

yB

M2

l2

l1

M4M3

g



(24)



119872119860 = [[[119897119860119898119860119899119860]]]

= [[[119902119878119887119862119897119902119878119888119862119898119902119878119887119862119899

]]]+ [[[[


(25)







119865119861 = [[[119865119883119865119884119865119885]]] =

[[[[[[004sum119894=1119891119894]]]]]]+ [[[

00minus119863]]]= [[[[[[

004sum119894=1119891119894]]]]]]+ [[[[[

00minus121205881198822119878119862119863

]]]]](27)





119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119905 (120572) 120575119905119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119905 (120572) 120575119905

(29)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119905 (120572) 120575119905119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881

(30)







119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119890 (120572) 120575119890119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881+ 119862119884120575119903 (120572) 120575119903 + 119862119884120575119886 (120572) 120575119886119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119890 (120572) 120575119890

(32)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881+ 119862119897120575119903 (120572 120573) 120575119903 + 119862119897120575119886 (120572 120573) 120575119886119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119890 (120572) 120575119890119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881 + 119862119899120575119903 (120572 120573) 120575119903+ 119862119899120575119886 (120572 120573) 120575119886

(33)


5 CFD Simulations






120597 (120588120574)120597119905 + 120597 (120588119880119895120574)120597119909119895 = 1198751205741 minus 1198641205741 + 1198751205742 minus 1198641205741+ 120597120597119909119895 [(120583 + 120583119905120590120574) 120597120574120597119909119895 ]

(34)


120597 (120588Re120579t)120597t + 120597 (120588UjRe120579t)120597xj= 119875120579119905 + 120597120597119909119895 [120590120579119905 (120583 + 120583119905) Re120579119905120597119909119895 ]

(35)


120597120597119905 (120588119896) + 120597120597119909119894 (120588119896119906119894)= 119866119896



(37)






minus002

002

006

010

014

018

022

026

030

minus02

0

02

04

06

08

1

12

14

minus4 minus2 0 2 4 6 8 10 12 14 16 18

CD

[-]

CL

[-]

AoA [deg]



minus04

minus03

minus02

minus01

0

01

02

minus4 minus2 0 2 4 6 8 10 12 14 16 18

Cm

AoA [deg]


minus4

minus2

0

2

4

6

8

10

12

14

16

minus4 minus2 0 2 4 6 8 10 12 14 16 18

LD

AoA [deg]

Side wind (0 deg)

Side wind (5 deg)

Side wind (10 deg)



(a) (b)

(c)








(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom













Parameter Value


Wing span 2520 [mm]

Length 1600 [mm]

Wing area 54 [dm2]











119883 = [119880119881119882 120601 120579 120595 119875 119876 119877 119909 119910 119911]119879 (1)








(119881120572)119865119861 = (119881119864)119865119861 minus119863119861119882 (119881119882)119865119882 (3)



120572 = arctan119881120572119911119881120572119909 (4)

120573 = arcsin119881120572119910119881120572 (5)

(119881120572)119865119861 = (1198812120572119909 + 1198812

120572119910 + 1198812120572119911)12 (6)









119879120596 = [[[[[[1 sin 120601 sin 120579


cos 120579 cos120601cos 120579

]]]]]](9)


(119881120572)119865119861 = (119881119864)119865119861 = (119880119881119882) (10)




119868119883 + 119876119877 (119868119885 minus 119868119884) minus (119875119876 + ) 119868119883119885 = 119871 (14)

119868119884 + 119875119877 (119868119883 minus 119868119885) + (1198752 minus 1198772) 119868119883119885 = 119872 (15)

119868119885 + 119875119876 (119868119884 minus 119868119883) + (119876119877 minus ) 119868119883119885 = 119873 (16)

( 120601120579) = 119879120596(119875119876119877) (17)

(119864119864119864) = 119871119879119861119881(119880119881119882) (18)

where


0 119868119910 0minus119868119909119911 0 119868119911

] is inertia matrix




119865119861 = [[[119865119883119865119884119865119885]]] = 119865119861119879 + 119865119861119860 =

[[[[119865119883119879119865119884119879119865119885119879

]]]] +[[[[119865119883119860119865119884119860119865119885119860

]]]]= [[[[

1198651198831198790119865119885119879]]]] + 119863119861119882

[[[minus119863119884minus119871]]]

(19)



119865119861119879 = [[[[1198651198831198790119865119885119879

]]]] =[[[

1198911 cos 120575119905 + 1198912 cos 12057511990501198913 + 1198914 + 1198911 sin 120575119905 + 1198912 sin 120575119905]]] (20)




119863 = 119902119878119862119863 ndash drag





119872 = [[[119871119872119873]]] = 119872119879 +119872119860 = [[[

119897119879119898119879119899119879]]] + [[[

119897119860119898119860119899119860]]] (22)


119872119879 = [[[119897119879119898119879119899119879]]]

= [[[[119865119885119879998779119910119865119885119879998779119909119865119883119879radic9987791199092 + 9987791199102

]]]] + 120596


]]]

(23)


119903 0 minus119901minus119902 119901 0



119872119879 =[[[[[[[[[[[


]]]]]]]]]]]


M1

xB

yB

M2

l2

l1

M4M3

g



(24)



119872119860 = [[[119897119860119898119860119899119860]]]

= [[[119902119878119887119862119897119902119878119888119862119898119902119878119887119862119899

]]]+ [[[[


(25)







119865119861 = [[[119865119883119865119884119865119885]]] =

[[[[[[004sum119894=1119891119894]]]]]]+ [[[

00minus119863]]]= [[[[[[

004sum119894=1119891119894]]]]]]+ [[[[[

00minus121205881198822119878119862119863

]]]]](27)





119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119905 (120572) 120575119905119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119905 (120572) 120575119905

(29)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119905 (120572) 120575119905119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881

(30)







119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119890 (120572) 120575119890119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881+ 119862119884120575119903 (120572) 120575119903 + 119862119884120575119886 (120572) 120575119886119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119890 (120572) 120575119890

(32)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881+ 119862119897120575119903 (120572 120573) 120575119903 + 119862119897120575119886 (120572 120573) 120575119886119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119890 (120572) 120575119890119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881 + 119862119899120575119903 (120572 120573) 120575119903+ 119862119899120575119886 (120572 120573) 120575119886

(33)


5 CFD Simulations






120597 (120588120574)120597119905 + 120597 (120588119880119895120574)120597119909119895 = 1198751205741 minus 1198641205741 + 1198751205742 minus 1198641205741+ 120597120597119909119895 [(120583 + 120583119905120590120574) 120597120574120597119909119895 ]

(34)


120597 (120588Re120579t)120597t + 120597 (120588UjRe120579t)120597xj= 119875120579119905 + 120597120597119909119895 [120590120579119905 (120583 + 120583119905) Re120579119905120597119909119895 ]

(35)


120597120597119905 (120588119896) + 120597120597119909119894 (120588119896119906119894)= 119866119896



(37)






minus002

002

006

010

014

018

022

026

030

minus02

0

02

04

06

08

1

12

14

minus4 minus2 0 2 4 6 8 10 12 14 16 18

CD

[-]

CL

[-]

AoA [deg]



minus04

minus03

minus02

minus01

0

01

02

minus4 minus2 0 2 4 6 8 10 12 14 16 18

Cm

AoA [deg]


minus4

minus2

0

2

4

6

8

10

12

14

16

minus4 minus2 0 2 4 6 8 10 12 14 16 18

LD

AoA [deg]

Side wind (0 deg)

Side wind (5 deg)

Side wind (10 deg)



(a) (b)

(c)








(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom





(119881120572)119865119861 = (119881119864)119865119861 minus119863119861119882 (119881119882)119865119882 (3)



120572 = arctan119881120572119911119881120572119909 (4)

120573 = arcsin119881120572119910119881120572 (5)

(119881120572)119865119861 = (1198812120572119909 + 1198812

120572119910 + 1198812120572119911)12 (6)









119879120596 = [[[[[[1 sin 120601 sin 120579


cos 120579 cos120601cos 120579

]]]]]](9)


(119881120572)119865119861 = (119881119864)119865119861 = (119880119881119882) (10)




119868119883 + 119876119877 (119868119885 minus 119868119884) minus (119875119876 + ) 119868119883119885 = 119871 (14)

119868119884 + 119875119877 (119868119883 minus 119868119885) + (1198752 minus 1198772) 119868119883119885 = 119872 (15)

119868119885 + 119875119876 (119868119884 minus 119868119883) + (119876119877 minus ) 119868119883119885 = 119873 (16)

( 120601120579) = 119879120596(119875119876119877) (17)

(119864119864119864) = 119871119879119861119881(119880119881119882) (18)

where


0 119868119910 0minus119868119909119911 0 119868119911

] is inertia matrix




119865119861 = [[[119865119883119865119884119865119885]]] = 119865119861119879 + 119865119861119860 =

[[[[119865119883119879119865119884119879119865119885119879

]]]] +[[[[119865119883119860119865119884119860119865119885119860

]]]]= [[[[

1198651198831198790119865119885119879]]]] + 119863119861119882

[[[minus119863119884minus119871]]]

(19)



119865119861119879 = [[[[1198651198831198790119865119885119879

]]]] =[[[

1198911 cos 120575119905 + 1198912 cos 12057511990501198913 + 1198914 + 1198911 sin 120575119905 + 1198912 sin 120575119905]]] (20)




119863 = 119902119878119862119863 ndash drag





119872 = [[[119871119872119873]]] = 119872119879 +119872119860 = [[[

119897119879119898119879119899119879]]] + [[[

119897119860119898119860119899119860]]] (22)


119872119879 = [[[119897119879119898119879119899119879]]]

= [[[[119865119885119879998779119910119865119885119879998779119909119865119883119879radic9987791199092 + 9987791199102

]]]] + 120596


]]]

(23)


119903 0 minus119901minus119902 119901 0



119872119879 =[[[[[[[[[[[


]]]]]]]]]]]


M1

xB

yB

M2

l2

l1

M4M3

g



(24)



119872119860 = [[[119897119860119898119860119899119860]]]

= [[[119902119878119887119862119897119902119878119888119862119898119902119878119887119862119899

]]]+ [[[[


(25)







119865119861 = [[[119865119883119865119884119865119885]]] =

[[[[[[004sum119894=1119891119894]]]]]]+ [[[

00minus119863]]]= [[[[[[

004sum119894=1119891119894]]]]]]+ [[[[[

00minus121205881198822119878119862119863

]]]]](27)





119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119905 (120572) 120575119905119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119905 (120572) 120575119905

(29)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119905 (120572) 120575119905119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881

(30)







119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119890 (120572) 120575119890119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881+ 119862119884120575119903 (120572) 120575119903 + 119862119884120575119886 (120572) 120575119886119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119890 (120572) 120575119890

(32)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881+ 119862119897120575119903 (120572 120573) 120575119903 + 119862119897120575119886 (120572 120573) 120575119886119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119890 (120572) 120575119890119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881 + 119862119899120575119903 (120572 120573) 120575119903+ 119862119899120575119886 (120572 120573) 120575119886

(33)


5 CFD Simulations






120597 (120588120574)120597119905 + 120597 (120588119880119895120574)120597119909119895 = 1198751205741 minus 1198641205741 + 1198751205742 minus 1198641205741+ 120597120597119909119895 [(120583 + 120583119905120590120574) 120597120574120597119909119895 ]

(34)


120597 (120588Re120579t)120597t + 120597 (120588UjRe120579t)120597xj= 119875120579119905 + 120597120597119909119895 [120590120579119905 (120583 + 120583119905) Re120579119905120597119909119895 ]

(35)


120597120597119905 (120588119896) + 120597120597119909119894 (120588119896119906119894)= 119866119896



(37)






minus002

002

006

010

014

018

022

026

030

minus02

0

02

04

06

08

1

12

14

minus4 minus2 0 2 4 6 8 10 12 14 16 18

CD

[-]

CL

[-]

AoA [deg]



minus04

minus03

minus02

minus01

0

01

02

minus4 minus2 0 2 4 6 8 10 12 14 16 18

Cm

AoA [deg]


minus4

minus2

0

2

4

6

8

10

12

14

16

minus4 minus2 0 2 4 6 8 10 12 14 16 18

LD

AoA [deg]

Side wind (0 deg)

Side wind (5 deg)

Side wind (10 deg)



(a) (b)

(c)








(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom



119865119861 = [[[119865119883119865119884119865119885]]] = 119865119861119879 + 119865119861119860 =

[[[[119865119883119879119865119884119879119865119885119879

]]]] +[[[[119865119883119860119865119884119860119865119885119860

]]]]= [[[[

1198651198831198790119865119885119879]]]] + 119863119861119882

[[[minus119863119884minus119871]]]

(19)



119865119861119879 = [[[[1198651198831198790119865119885119879

]]]] =[[[

1198911 cos 120575119905 + 1198912 cos 12057511990501198913 + 1198914 + 1198911 sin 120575119905 + 1198912 sin 120575119905]]] (20)




119863 = 119902119878119862119863 ndash drag





119872 = [[[119871119872119873]]] = 119872119879 +119872119860 = [[[

119897119879119898119879119899119879]]] + [[[

119897119860119898119860119899119860]]] (22)


119872119879 = [[[119897119879119898119879119899119879]]]

= [[[[119865119885119879998779119910119865119885119879998779119909119865119883119879radic9987791199092 + 9987791199102

]]]] + 120596


]]]

(23)


119903 0 minus119901minus119902 119901 0



119872119879 =[[[[[[[[[[[


]]]]]]]]]]]


M1

xB

yB

M2

l2

l1

M4M3

g



(24)



119872119860 = [[[119897119860119898119860119899119860]]]

= [[[119902119878119887119862119897119902119878119888119862119898119902119878119887119862119899

]]]+ [[[[


(25)







119865119861 = [[[119865119883119865119884119865119885]]] =

[[[[[[004sum119894=1119891119894]]]]]]+ [[[

00minus119863]]]= [[[[[[

004sum119894=1119891119894]]]]]]+ [[[[[

00minus121205881198822119878119862119863

]]]]](27)





119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119905 (120572) 120575119905119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119905 (120572) 120575119905

(29)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119905 (120572) 120575119905119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881

(30)







119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119890 (120572) 120575119890119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881+ 119862119884120575119903 (120572) 120575119903 + 119862119884120575119886 (120572) 120575119886119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119890 (120572) 120575119890

(32)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881+ 119862119897120575119903 (120572 120573) 120575119903 + 119862119897120575119886 (120572 120573) 120575119886119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119890 (120572) 120575119890119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881 + 119862119899120575119903 (120572 120573) 120575119903+ 119862119899120575119886 (120572 120573) 120575119886

(33)


5 CFD Simulations






120597 (120588120574)120597119905 + 120597 (120588119880119895120574)120597119909119895 = 1198751205741 minus 1198641205741 + 1198751205742 minus 1198641205741+ 120597120597119909119895 [(120583 + 120583119905120590120574) 120597120574120597119909119895 ]

(34)


120597 (120588Re120579t)120597t + 120597 (120588UjRe120579t)120597xj= 119875120579119905 + 120597120597119909119895 [120590120579119905 (120583 + 120583119905) Re120579119905120597119909119895 ]

(35)


120597120597119905 (120588119896) + 120597120597119909119894 (120588119896119906119894)= 119866119896



(37)






minus002

002

006

010

014

018

022

026

030

minus02

0

02

04

06

08

1

12

14

minus4 minus2 0 2 4 6 8 10 12 14 16 18

CD

[-]

CL

[-]

AoA [deg]



minus04

minus03

minus02

minus01

0

01

02

minus4 minus2 0 2 4 6 8 10 12 14 16 18

Cm

AoA [deg]


minus4

minus2

0

2

4

6

8

10

12

14

16

minus4 minus2 0 2 4 6 8 10 12 14 16 18

LD

AoA [deg]

Side wind (0 deg)

Side wind (5 deg)

Side wind (10 deg)



(a) (b)

(c)








(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom


M1

xB

yB

M2

l2

l1

M4M3

g



(24)



119872119860 = [[[119897119860119898119860119899119860]]]

= [[[119902119878119887119862119897119902119878119888119862119898119902119878119887119862119899

]]]+ [[[[


(25)







119865119861 = [[[119865119883119865119884119865119885]]] =

[[[[[[004sum119894=1119891119894]]]]]]+ [[[

00minus119863]]]= [[[[[[

004sum119894=1119891119894]]]]]]+ [[[[[

00minus121205881198822119878119862119863

]]]]](27)





119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119905 (120572) 120575119905119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119905 (120572) 120575119905

(29)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119905 (120572) 120575119905119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881

(30)







119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119890 (120572) 120575119890119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881+ 119862119884120575119903 (120572) 120575119903 + 119862119884120575119886 (120572) 120575119886119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119890 (120572) 120575119890

(32)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881+ 119862119897120575119903 (120572 120573) 120575119903 + 119862119897120575119886 (120572 120573) 120575119886119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119890 (120572) 120575119890119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881 + 119862119899120575119903 (120572 120573) 120575119903+ 119862119899120575119886 (120572 120573) 120575119886

(33)


5 CFD Simulations






120597 (120588120574)120597119905 + 120597 (120588119880119895120574)120597119909119895 = 1198751205741 minus 1198641205741 + 1198751205742 minus 1198641205741+ 120597120597119909119895 [(120583 + 120583119905120590120574) 120597120574120597119909119895 ]

(34)


120597 (120588Re120579t)120597t + 120597 (120588UjRe120579t)120597xj= 119875120579119905 + 120597120597119909119895 [120590120579119905 (120583 + 120583119905) Re120579119905120597119909119895 ]

(35)


120597120597119905 (120588119896) + 120597120597119909119894 (120588119896119906119894)= 119866119896



(37)






minus002

002

006

010

014

018

022

026

030

minus02

0

02

04

06

08

1

12

14

minus4 minus2 0 2 4 6 8 10 12 14 16 18

CD

[-]

CL

[-]

AoA [deg]



minus04

minus03

minus02

minus01

0

01

02

minus4 minus2 0 2 4 6 8 10 12 14 16 18

Cm

AoA [deg]


minus4

minus2

0

2

4

6

8

10

12

14

16

minus4 minus2 0 2 4 6 8 10 12 14 16 18

LD

AoA [deg]

Side wind (0 deg)

Side wind (5 deg)

Side wind (10 deg)



(a) (b)

(c)








(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom





119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119905 (120572) 120575119905119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119905 (120572) 120575119905

(29)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119905 (120572) 120575119905119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881

(30)







119862119863 = 1198621198630 (120572 120573)119902=120575119890=0 + 119862119863119902 (120572) 1199021198882119881 + 119862119863120575119890 (120572) 120575119890119862119884 = 1198621198840 (120573)119901=119903=120575119903=120575119886=0 + 119862119884119901 (120572) 1199011198872119881 + 119862119884119903 (120572) 1199031198872119881+ 119862119884120575119903 (120572) 120575119903 + 119862119884120575119886 (120572) 120575119886119862119871 = 1198621198710 (120572 120573)119902=120575119890=0 + 119862119871119902 (120572) 1199021198882119881 + 119862119871120575119890 (120572) 120575119890

(32)


119862119897 = 1198621198970 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119897119901 (120572) 1199011198872119881 + 119862119897119903 (120572) 1199031198872119881+ 119862119897120575119903 (120572 120573) 120575119903 + 119862119897120575119886 (120572 120573) 120575119886119862119898 = 1198621198980 (120572)119902=120575119890=0 + 119862119898119902 (120572) 1199021198882119881 + 119862119898120575119890 (120572) 120575119890119862119899 = 1198621198990 (120572 120573)119901=119903=120575119903=120575119886=0 + 119862119899119901 (120572) 1199011198872119881+ 119862119899119903 (120572) 1199031198872119881 + 119862119899120575119903 (120572 120573) 120575119903+ 119862119899120575119886 (120572 120573) 120575119886

(33)


5 CFD Simulations






120597 (120588120574)120597119905 + 120597 (120588119880119895120574)120597119909119895 = 1198751205741 minus 1198641205741 + 1198751205742 minus 1198641205741+ 120597120597119909119895 [(120583 + 120583119905120590120574) 120597120574120597119909119895 ]

(34)


120597 (120588Re120579t)120597t + 120597 (120588UjRe120579t)120597xj= 119875120579119905 + 120597120597119909119895 [120590120579119905 (120583 + 120583119905) Re120579119905120597119909119895 ]

(35)


120597120597119905 (120588119896) + 120597120597119909119894 (120588119896119906119894)= 119866119896



(37)






minus002

002

006

010

014

018

022

026

030

minus02

0

02

04

06

08

1

12

14

minus4 minus2 0 2 4 6 8 10 12 14 16 18

CD

[-]

CL

[-]

AoA [deg]



minus04

minus03

minus02

minus01

0

01

02

minus4 minus2 0 2 4 6 8 10 12 14 16 18

Cm

AoA [deg]


minus4

minus2

0

2

4

6

8

10

12

14

16

minus4 minus2 0 2 4 6 8 10 12 14 16 18

LD

AoA [deg]

Side wind (0 deg)

Side wind (5 deg)

Side wind (10 deg)



(a) (b)

(c)








(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom





120597 (120588120574)120597119905 + 120597 (120588119880119895120574)120597119909119895 = 1198751205741 minus 1198641205741 + 1198751205742 minus 1198641205741+ 120597120597119909119895 [(120583 + 120583119905120590120574) 120597120574120597119909119895 ]

(34)


120597 (120588Re120579t)120597t + 120597 (120588UjRe120579t)120597xj= 119875120579119905 + 120597120597119909119895 [120590120579119905 (120583 + 120583119905) Re120579119905120597119909119895 ]

(35)


120597120597119905 (120588119896) + 120597120597119909119894 (120588119896119906119894)= 119866119896



(37)






minus002

002

006

010

014

018

022

026

030

minus02

0

02

04

06

08

1

12

14

minus4 minus2 0 2 4 6 8 10 12 14 16 18

CD

[-]

CL

[-]

AoA [deg]



minus04

minus03

minus02

minus01

0

01

02

minus4 minus2 0 2 4 6 8 10 12 14 16 18

Cm

AoA [deg]


minus4

minus2

0

2

4

6

8

10

12

14

16

minus4 minus2 0 2 4 6 8 10 12 14 16 18

LD

AoA [deg]

Side wind (0 deg)

Side wind (5 deg)

Side wind (10 deg)



(a) (b)

(c)








(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom


minus002

002

006

010

014

018

022

026

030

minus02

0

02

04

06

08

1

12

14

minus4 minus2 0 2 4 6 8 10 12 14 16 18

CD

[-]

CL

[-]

AoA [deg]



minus04

minus03

minus02

minus01

0

01

02

minus4 minus2 0 2 4 6 8 10 12 14 16 18

Cm

AoA [deg]


minus4

minus2

0

2

4

6

8

10

12

14

16

minus4 minus2 0 2 4 6 8 10 12 14 16 18

LD

AoA [deg]

Side wind (0 deg)

Side wind (5 deg)

Side wind (10 deg)



(a) (b)

(c)








(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom


(a) (b)

(c)








(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom


(a) (b)

(c)


6 Conclusions




Data Availability





Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom




Acknowledgments


References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of

Advances in

OptoElectronics

Hindawi

wwwhindawicom

Volume 2018



Volume 2018


Journal of


Hindawi

wwwhindawicom

Journal of


SensorsJournal of



RotatingMachinery

Hindawi






Propagation






Hindawi


Advances in

Multimedia


wwwhindawicom

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