Primaryﬂightcontroldesign fora4-seatelectricaircraft

Primary flight control designfor a 4-seat electric aircraft

CYRIL LACHAUME

Master in Aerospace EngineeringDate: March 5, 2021Supervisor: Rolf StuberExaminer: Raffaello MarianiSchool of Engineering Sciences (SCI), Dpt. Of EngineeringMechanics, unit of Aerospace and Vehicle EngineeringHost company: Smartflyer AGSwedish title: Primär flygkontrolldesign för ett 4-sits elektrisktflygplan

iii

AbstractThis thesis work is part of a design process which aims to develop a four-seathybrid-electric aircraft at Smartflyer (Grenchen, Switzerland). In that scope,various mechanisms of the plane had to be developed, including the systemactuating the control surfaces. The objective of this thesis work is to designthe primary flight controls which will be implemented in the first prototypebuilt at Smartflyer.Firstly, the work investigates the calculation of the aerodynamic loads appliedto the control surfaces through the use of three different methods which areanalytical calculations, VLM analysis and CFD simulation. Then, the workconsists in defining the kinematic mechanisms of the flight control to handlethe deflection of the horizontal stabiliser, the ailerons and the rudder. Lastly,the calculation of the forces to which are submitted the components of theflight control is conducted. This step allows to determine the pilot controlforces and ensures to take into account the ergonomic aspect during the designphase. The results of this work highlight the limits of the different methodsused and serves as a basis for a future sizing work and detailed conception.

iv

SammanfattningDetta uppsatsarbete är en del av en designprocess som syftar till att utvecklaett fyrsitsigt hybridelektriskt flygplan vid Smartflyer (Grenchen, Schweiz). Idetta omfång måste olika mekanismer i planet utvecklas, inklusive systemetsom manövrerar kontrollytorna. Syftet med detta uppsatsarbete är att utformade primära flygkontrollerna som kommer att implementeras i den första pro-totypen som byggdes på Smartflyer.För det första undersöker arbetet beräkningen av de aerodynamiska belastning-arna som appliceras på kontrollytorna genom användning av tre olika metodersom är analytiska beräkningar, VLM-analys och CFD-simulering. Därefter be-står arbetet i att definiera de kinematiska mekanismerna för flygkontrollen föratt hantera avböjningen av den horisontella stabilisatorn, kranarna och rodret.Slutligen genomförs beräkningen av de krafter till vilka komponenterna i flyg-kontrollen överförs. Detta steg gör det möjligt att bestämma pilotstyrkrafternaoch säkerställer att man tar hänsyn till den ergonomiska aspekten under de-signfasen. Resultaten av detta arbete belyser gränserna för de olika metodersom används och tjänar som grund för ett framtida storleksarbete och detalje-rad uppfattning.

Contents

1 Introduction 11.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Smartflyer and the SFX1 development . . . . . . . . . . . . . 21.3 Thesis aim and delimitation . . . . . . . . . . . . . . . . . . . 2

2 Background 32.1 Aircraft primary flight controls . . . . . . . . . . . . . . . . . 32.2 Sources of the aerodynamic loads over a body . . . . . . . . . 32.3 Determination of the aerodynamic loads over an airfoil or a

three-dimensional body . . . . . . . . . . . . . . . . . . . . . 52.3.1 XFLR5 and The Vortex Lattice Method . . . . . . . . 62.3.2 CFD . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 Regulation CS-23 . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Methods 83.1 Determination of the aerodynamic loads . . . . . . . . . . . . 8

3.1.1 Horizontal tail unit . . . . . . . . . . . . . . . . . . . 83.1.2 Ailerons and Rudder . . . . . . . . . . . . . . . . . . 18

3.2 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.1 Primary flight controls kinematics . . . . . . . . . . . 243.2.2 Differential ailerons . . . . . . . . . . . . . . . . . . 27

3.3 Pilot control forces . . . . . . . . . . . . . . . . . . . . . . . 29

4 Results 314.1 Horizontal tail unit . . . . . . . . . . . . . . . . . . . . . . . 31

4.1.1 Tail and AST deflections . . . . . . . . . . . . . . . . 314.1.2 Tail aerodynamic loads . . . . . . . . . . . . . . . . . 33

4.2 Ailerons and rudder . . . . . . . . . . . . . . . . . . . . . . . 364.2.1 Aileron deflections and rate of roll . . . . . . . . . . . 364.2.2 Aileron and rudder aerodynamic loads . . . . . . . . . 37

v

vi CONTENTS

4.3 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.3.1 Horizontal stabiliser . . . . . . . . . . . . . . . . . . 404.3.2 Ailerons . . . . . . . . . . . . . . . . . . . . . . . . . 404.3.3 Rudder . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.4 Primary flight control loads . . . . . . . . . . . . . . . . . . . 424.4.1 Horizontal stabiliser . . . . . . . . . . . . . . . . . . 434.4.2 Ailerons . . . . . . . . . . . . . . . . . . . . . . . . . 434.4.3 Rudder . . . . . . . . . . . . . . . . . . . . . . . . . 45

5 Discussion 465.1 Aerodynamic loads . . . . . . . . . . . . . . . . . . . . . . . 465.2 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6 Conclusions 49

Bibliography 51

Chapter 1

Introduction

1.1 ContextAir transport is a major economic and societal player worldwide. In the past 40years the volume of air travel has expanded tenfold and air freight has grownby a factor of fourteen. The world’s economies have grown three to four timesover the same period. Air transport has been one of the world’s fastest grow-ing economic sectors [1]. The total number of passengers carried on airplanesreached 4.3 billion in 2018, and around 9 billion are expected by 2050, mean-ing that the current passenger volume will be doubled.At the same time, climate change consideration has been an omnipresent sub-ject during the last years andwill bemore than ever themain topic of the future.The contribution of aviation towards climate change is highly criticized. In2008, a report from the International Air Transport Association (IATA) statedthat aviation accounts for 3 percent of the total human made contribution toclimate change [2], and this number will grow with the rise of passenger vol-ume.With the expected increase in global air travel over the next decades, the relia-bility and environmental impact of aviation are becoming critical issues for thefuture of flight. Such assessments pushed a number of companies and startupsto develop new technologies aiming for more sustainable and efficient vehi-cles regarding air transportation. Numerous new solutions are under devel-opment and involving various fields in aviation. Some solutions focus on theaircraft philosophy itself, including blended wing body, laminar flow aircraft,or even drones and VTOL concepts. Propulsion represents another major fieldof research from new fuel technologies with bio fuels and hydrogen, to moreefficient turbo-machines and solar, fully electric, or hybrid power-train [3].

1

2 CHAPTER 1. INTRODUCTION

1.2 Smartflyer and the SFX1 developmentSmartflyer AG is an aeronautical company based in Grenchen, Switzerland.Founded in April 2016, Smartflyer aims to develop a hybrid-electric aircraftwith four seats offering General Aviation a more sustainable solution and openthe path for regional hybrid-electric airliners. Called SFX1, the first prototypebeing built by Smartflyer consists in a high wing fuselage with an electricalengine mounted on the vertical stabiliser. Such propulsion configuration issupposed to allow laminar flow around the fuselage further downstream thanallowed on conventional propeller layout. Furthermore, the accelerated airmass can flow freely away without experiencing blockage effect by the fuse-lage. Consequently, such propulsion layout helps decreasing drag and improv-ing the propeller’s efficiency. As a result, it is claimed that the aircraft achievesan efficiency increase of plus 30% compared to a conventional propulsion con-figuration [4].The SFX1 relies on a hybrid drive train featuring an electric motor for thepropulsion and an internal combustion engine coupled to an electric generatorwhich is used as a range extender. During take-off and landing, the aircraftis powered by the batteries present in the wings, allowing to decrease noisedisturbances in the vicinity of the airports. During flight, the range extenderenables battery charging to extend the flight distance covered by the plane.The prototype must demonstrate that such design can emit 50% less CO2, be60% quieter than conventional designs and still be able to fly over a distanceof 750 km. The last advantage claimed for the electric drive is its efficiencyand smaller maintenance cost, so that the operating costs of the aircraft couldbe lowered by 33% [4].

1.3 Thesis aim and delimitationThe overall content of this thesis is about the design and the calculation of theprimary flight controls for the prototype SFX1. More specifically, one part ofthe thesis focuses on the determination of the aerodynamic loads on each con-trol surfaces. A second part consists in the definition of the Kinematics of theprimary flight controls to ensure the desired mobility of the control surfaces,while keeping the stick forces within the regulation limit. Finally, amechanicalanalysis is carried out to define the forces exerted on each component formingthe primary flight controls.

Chapter 2

Background

2.1 Aircraft primary flight controlsThe concept of primary flight controls refers to the complete system allowingthe aircraft to change its flight attitude, and thus be controlled to follow thedesired flight path. The system is composed of a yoke or a pilot stick that willinput the pilot’s command and transmit it to the primary control surfaces. Thetransmission of the pilot’s command can be achieved mechanically thanks to acable/pulley or push/pull rod system. It can also be transmitted electrically tohydraulic actuators in the case of a fly-by-wire aircraft. The primary controlsurfaces include the ailerons, the elevator, and the rudder. It consists in hingedor movable lifting surfaces designed to change the attitude of the aircraft bychanging the airflow over the aircraft’s surface during flight. They respectivelyinfluence the roll, pitch and yaw [5].In the case of the first prototype built by Smartflyer, the primary flight controlsconsists in a pilot stick linked mechanically to the control surfaces.

2.2 Sources of the aerodynamic loads overa body

An airfoil is a section of a streamlined body which is generally designed tooptimise the ratio of lift over drag produced when placed into airflow. The ge-ometry of the profile is defined through conventional parameters like its chord,thickness, camber or leading edge radius[6].No matter the complexity of the geometry of the body shape, the aerodynamicforces and moments acting on the body are entirely due to the pressure and

3

4 CHAPTER 2. BACKGROUND

shear stress distribution over the surface. By integrating the pressure and shearstress distributions over the complete surface of the body, it is possible to de-termine a resultant aerodynamic force and a moment. Lift is determined bytaking into account the angle of attack of the airfoil and by projecting the aero-dynamic resultant on the axis perpendicular to the free-stream direction. Theprojection along the free-stream direction results in drag determination [7].These projections of the aerodynamic resultant are illustrated in appendix Bby Figure 1.Non-dimensional coefficients are widely used in engineering, and this is espe-cially true in aeronautics. Three major benefits come from their use. Firstly, itsimplifies the equations used by reducing the number of parameters. Secondly,the use of dimensionless parameters reduces drastically the number of exper-iments to study a phenomena which includes a high number of parameters.Finally, it provides scaling laws allowing to explore full-scale applications bycarrying out experiments on a smaller and cheaper scaled model [8]. Basedon these assessments, it is possible to express the pressure and the shear stressacting on a body with dimensionless coefficients, respectively :

Cp = (p− p∞)/q∞ (2.1)

Cf = τ/q∞ (2.2)

With the dynamic pressure defined by :

q∞ = ρ.V 2/2 (2.3)

Figure 2 in Appendix B illustrates the nomenclature for the integration ofpressure and shear distribution over a two-dimensional body surface, resultingin the following equations [7] :

Cn =1

c

[ ∫ c

0

(Cp,l − Cp,u)dx+

∫ c

0

(Cf,udyudx

+ Cf,ldyldx

)dx]

(2.4)

Ca =1

c

[ ∫ c

0

(Cp,udyudx

− Cp,ldyldx

)dx+

∫ c

0

(Cf,u + Cf,l)dx]

(2.5)

CmLE =1

c2

[ ∫ c

0

(Cp,u − Cp,l)xdx−∫ c

0

(Cf,udyudx

+ Cf,ldyldx

)xdx

+

∫ c

0

(Cp,udyudx

+ Cf,u)yudx+

∫ c

0

(−Cp,ldyldx

+ Cf,l)yldx] (2.6)

CHAPTER 2. BACKGROUND 5

Cn and Ca are respectively the normal and axial force coefficients appliedat any point of the two-dimensional body. The pitching moment coefficient ofthe body due to axial and normal forces taken at the leading edge as applicationpoint is denotedCmLE . These equations hold for the case of a two-dimensionalbody but the samemethod can be applied to obtain the equations representativeof a three-dimensional case. Finally, equations (2.7) and (2.8) express how toobtain the lift and drag coefficients Cl and Cd :

Cl = Cncos(α) − Casin(α) (2.7)

Cd = Cnsin(α) + Cacos(α) (2.8)

2.3 Determination of the aerodynamic loadsover an airfoil or a three-dimensional body

The previous section underlines that evaluating the aerodynamic loads exertedon a body consists in determining the shear and pressure distribution over itssurface. Several flow models are available in order to describe flow behaviourin space, all of them being based on the elementary notion of mass, energyandmomentum conservation. Depending on the initial hypothesis made, theselaws will be translated through equations that will differ and lead to differentflow models. Each of them having a different complexity level with their re-spective advantages and drawbacks.Some models are linear such as the Panel Methods, the Lifting Line Theory(LLT) or the Vortex LatticeMethod (VLM). Others are non-linear, for examplethe Finite DifferenceMethod (FDM), the Finite ElementMethod (FEM) or theFinite Volume Method (FVM). Having the highest fidelity, the Navier-Stokesmodels are mainly used in the field referred to as Computational Fluid Dy-namics (CFD), with Reynolds-Averaged-Navier-Stokes (RANS) model beingwidely spread, especially for aircraft aerodynamics. However, the accuracyof the Navier-Stockes models is paid at a high computational cost, which maytranslate also to a high financial cost [9]. Aiming to determine the aerody-namic forces applied on the control surfaces of the SFX1, two softwares basedon different flow models will be used: XFLR5 and OpenFoam.

6 CHAPTER 2. BACKGROUND

2.3.1 XFLR5 and The Vortex Lattice MethodXFLR5 is an analysis tool for airfoils, wings and planes operating at lowReynolds Numbers. It features airfoil direct and inverse analysis capabilities.It also includes wing design and analysis capabilities based on the LifitingLine Theory, on the Vortex Lattice Method, and on a 3D Panel Method [10].The aerodynamic results extracted from XFLR5 are obtained with the Vor-tex Lattice Method. The basis of the method is formed by the Biot-SavartLaw, Prandtl’s lifting line theory, the Kutta-Jukowski theorem and Hermanvon Heimholtz vortex filament theory [11]. In VLM, the wing surface is splitup in quadrilateral panels on which a horseshoe vortex is placed at the quarter-chord line as illustrated in figure 3 in Appendix B. Assuming a flow tangencycondition across the surface to represent the impossibility to have flow throughit, the strength of each vortex is computed using the Biot-Savart law. Once thevortex strengths are determined, it is possible to obtain lift and drag [9].In order for VLM results to be meaningful, some key assumptions are to bemade. This method assumes the flow field to be incompressible, inviscid andirrotational. It also considers that the lifting surfaces are thin and the con-ditions depicts small angles of attack and sideslip [12]. The Vortex LatticeMethod and the theoretical concepts behind are well covered and extensivelyexplained in the available literature [13–15].

2.3.2 CFDComputational fluid dynamics (CFD) refers to computer-based simulationsused to solve problems involving fluid flow, heat transfer, acoustics or evenchemical reactions. The Navier-Stokes equations are the fundamental govern-ing equations behind CFD solvers, and are currently considered as the most ac-curate flow model able to describe viscous, compressible and rotational flows.These equations translate the fundamental physic principles of mass, energyand momentum conservation [16].One of the current key issue in CFD remains turbulence modelling, especiallysince most of the engineering applications encounter turbulent flows. In orderto get acceptable results for the simulation, turbulence can either be simulatedor approximated by a model.Direct numerical simulation (DNS) consists in simulating the integrity of theeddies from the largest to the smallest vortical structure. In consequence, thisrequires an extremely fine meshing, resulting in very accurate solutions al-though coming at an extensively high computational cost. For this reason DNScurrently only belongs to research, but the evolution of computer capabilities

CHAPTER 2. BACKGROUND 7

in the future could allow industrial use.Reynolds-averaged Navier-Stokes methods, on the other hand, do not simulateturbulent flow but estimates it through a model considering an averaged flow.This method allows to considerably decrease the computational cost comparedto DNS, but the accuracy of the results is also affected. Nevertheless, it yieldsto results accurate enough to be used in the most advanced commercial appli-cations such as aeronautics or automotive.Finally, Large Eddy Simulation (LES) represents a compromise between thetwo previous models. The largest eddies are simulated and only the onessmaller than the finest mesh aremodeled. A detailed description of eachmodelis available in literature [17–20].In the scope of this thesis, results obtained from the CFD software OpenFoamwill be used. OpenFoam, standing for “Open Source Field Operation and Ma-nipulation”, is a free and open source CFD software, renown for the accuracyof its results. It is used by a large community, including F1 teams and premiumbrands such as Aston Martin [21].

2.4 Regulation CS-23Before a newly developed aircraft model may enter into operation, it must ob-tain a type certificate from the responsible aviation regulatory authority. Since2003, the European Aviation Safety Agency (EASA) is responsible for the cer-tification of aircraft in the EU and for some European non-EU Countries. Thiscertificate testifies that the type of aircraft meets the safety requirements set bythe European Union. The CS-23 (certification specifications) provide the tech-nical requirements for certification of small aeroplanes. This includes Normal,Utility, Aerobatic and Commuter category aeroplanes [22]. Even if the SFX1is currently a prototype and consequently does not need to be certified, thefinal goal at Smartflyer is to have the opportunity to produce this aircraft in aseries. Based on that goal, the development of the prototype follows closelythe guidelines provided by CS-23 documents.

Chapter 3

Methods

3.1 Determination of the aerodynamic loadsIn accordance to CS-23, calculations must be done to define the maximal aero-dynamic loads a control surface that could experience inside the entire flightenvelope of the aeroplane. Consequently, calculations are carried out accord-ing to regulation at maneuvering speed VA and ISA conditions at sea level,with the considered control surface deflected to its extreme position. In thecase of the SFX1, VA = 65.2 m/s.

3.1.1 Horizontal tail unitDue to the unconventional and high position of the thrust line, the SFX1 fea-tures an all-movable horizontal stabilizer, also called stabilator. In order toimprove the handling qualities of the aircraft along the pitch axis, this hori-zontal stabilizer needs to be equipped with an anti-servo tab (AST), a hingedsurface mounted at the trailing edge of the stabilizer. Its main role is to in-crease the hinge-moment of the horizontal tail unit (HTU) in order to increasethe pilot stick forces when the tail deflection increases. This provides a betterfeeling for the pilot and limits the risk of over controlling the aircraft. Next toit, the AST deflection increases the camber of the HTU airfoil. Consequently,it results in a lift increment compared to a configuration with only a clean air-foil profiled tail deflected at the same incidence.Finally, the AST will be used as a trim device for the SFX1 regarding pitch.

8

CHAPTER 3. METHODS 9

Determination of the maximum deflection angles for the horizontal tail

At this stage, the geometric sizing of the tail is assumed to be correctly doneand will serve as basis for the tail aerodynamic loads calculation. The tail pos-itive deflection, resulting in a nose-down moment, has been set to +5°. Thetail negative deflection, however, is yet to be determined.Two phases are considered to be the most critical regarding the necessary tailloads that will ensure the safe handling of the aircraft: the go-around and thetake-off rotation cases. In order to determine which of these situations is themost critical, the tail lift coefficient CLt is used as a comparison criterion andis as well the target parameter of the study.

A - Take-off and rotationThe method described hereby aims to determine the minimum lift coefficientthat is required for the horizontal stabilizer during take-off. This assures thatthe tail produces enough down force to allow the rotation of the airplane aroundits main landing gear. The results are obtained by calculating the sum of theaerodynamic and mechanical moments exerted on the aircraft. In this situa-tion, the calculation is carried around the main landing gear axis, being theaxis of rotation. This method requires some initial hypothesis, which follows:

• When the rotation is initiated, the normal reaction force of the nose land-ing gear is null. Consequently, the nose landing gear does not create anymoment around the considered rotation axis

• The drag of the tail is neglected due to its relatively small influence onthe results

• An equilibrium state is considered, leading to a static analysis

The different forces exerted on the airplane as well as their application pointand direction are illustrated in picture 4 in appendix.The static analysis results in the following set of equations:

• Moment equation in A for the equilibrium case:∑MA = −MACWB

+LW .a+DW .e−T. cosα.c+T. sinα.b+Lt.d−W.XCG = 0

(3.1)

• Translation of equation (3.1) in term of tail lift:

Lt =W.XCG +MACWB

− LW .a−DW .e+ T. cosα.c− T. sinα.b

d(3.2)

10 CHAPTER 3. METHODS

• Translation of equation (3.2) in terms of tail lift coefficient:

CLt =W.XCG + T. cosα.c− T. sinα.b+ q.SW (CMACWB

.CRef − CLW .a− CDW .e)

d.q.ST(3.3)

From equation (3.3), it is possible to determine the tail lift coefficient CLtthat leads to equilibrium. By slightly increasing the value found to include asafety margin, the minimum CLt required for rotation is obtained.

B - Go-aroundThe method used for the Go-around case is identical to the one used for therotation at take-off, excepted that the moment balance is now considered at thecenter of gravity (CG) and not the main landing gear. The hypotheses are alsoidentical, exception made for the nose landing-gear which is no longer part ofthe analysis, and the considered airspeed being replaced by the approach speedVF.

The equations obtained by the static analysis are identical to the set ofequation (3.1-3.3) found previously excepted for the definition of the differentlengths a, b, c and d which are now defined with respect to the CG.

C - Tail deflectionsThe minimum tail lift coefficient required being known, it is possible to deter-mine the tail incidence it that will allow to reach the necessary down-force. Ifat is the tail lift curve slope, the tail incidence is defined by:

CLt = at · it (3.4)

At this stage, as the deflection angles of the AST are not already defined, a liftcurve slope at=5/rad is assumed, knowing from CFD simulation that the samestabilator without any AST gives at=4/rad.

Anti-servo tab deflections

The deflection of the anti-servo tab is directly linked to the deflection of theHTU through a mechanical linkage. Figure 5 illustrates the AST kinematics.The AST is linked to a push-pull rod through a control horn. The rod is con-nected to a linear servo. The servo, fixed to the vertical tail of the aircraft,is used for the longitudinal trim of the aircraft. Thus, outside of the trimmingphase, the push-pull rod can be considered attached to a fixed point at the fuse-lage. In such conditions, there is a kinematic law that directly gives the AST


deflection regarding the HTU angle of incidence.The deflections of the AST were defined as follows:

• At maneuvering speed VA, the aircraft must be in trimmed flight withthe servo trim centered.

• The HTU maximum deflection TE down being it=+5°, the deflection ofthe AST needs to be found in order to have the HTU moment at its pivotaxis not exceeding the moment allowed by the maximum stick forces.

• Due to the mechanical linkages, the characterisation of the two previ-ous points defines the rest of the AST deflections covering the completeHTU movement range.

Aerodynamic loads on the horizontal tail and the anti-servo tab

The aerodynamic loads exerted on the horizontal tail and the anti-servo tabdepend on the deflection of each device with respect to the free-stream direc-tion. In order to carry out the structural analysis of the aircraft, the forces ofinterest are the highest ones in term of magnitude. They are generated at therespective extreme deflections of each device, trailing edge up and down.The loads necessary for the development of the aircraft are illustrated in Figure6 and listed below:

• XHTU and XAST : Refer to the aerodynamic forces exerted on the lon-gitudinal axis X of the frame of reference, which is also the free streamdirection. These values correspond to the drag of each devices and aremainly used for the structural analysis

• ZHTU andZAST : Refer to the aerodynamic forces exerted on the verticalaxis Z of the frame of reference, that is perpendicular to the free streamdirection. These values correspond to the lift force of each device andare mainly used for the structural analysis

• MHTU and MAST : Refer to the aerodynamic moments exerted on thetail devices. MHTU is calculated around the quarter chord axis of theHTU andMAST around its hinge axis. These values are mainly used forthe determination of the pilot stick forces along the longitudinal axis

In the scope of this work, only ZHTU ,MHTU andMAST will be examinedin tail loads determination. Three different methods will be investigated tocalculate the aerodynamic forces exerted on the tail unit. The first one cor-responds to the analytical calculations based on two major reference books in


aeronautics: the "DATCOM" fromMcDonnel Douglas [23] and the "AirplaneDesign Part VI: Preliminary Calculation of Aerodynamic, Thrust and PowerCharacteristics" from Jan Roskam [24].The other methods are software based: XFLR5 will be used for the VLManalysis and OpenFoam to run CFD simulations. A comparison of the resultsbetween the different methods will be further proceeded.

A - Analytical methods

1 - ZHTUZHTU is determined by the lift produced by the horizontal stabilizer. The mainbody is a NACA 0012 profile. The aerodynamic characteristics of such airfoilarewell documented and the lift curve slope is estimated to beClα0012=6.165/radfor a Reynolds number Re=4.5e6 [25]. The lift curve slope of the associatedfinite wing of aspect ratio AR is approximated according to reference [26] bythe formula:

CLα0012 =Clα0012

1 +Clα0012πeAR

(3.5)

In equation (3.5), Clα0012 must be expressed per radian and e stands for theOstwald efficiency factor.To qualify the influence of the AST, it is possible to calculate the lift incrementdue to its deflection. According to [23], the lift increment developed by thedeflection of a control surface is given by :

∆CL = ∆cl(CLαclα

)[(αδ)CL

(αδ)cl

]Kb (3.6)

Where :

• ∆cl is the section lift increment due to control deflection, which includesthe flap deflection

• CLα is the lift curve slope of the wing with flap retracted

• clα is the section lift-curve slope of the basic airfoil, including compress-ibility effects

• (αδ)CL(αδ)cl

is the ratio of three-dimensional flap-effectiveness parameter tothe two dimensional flap-effectiveness parameter

• Kb is the flap-span factor


Once ∆CL is determined, the HTU lift coefficient corresponds to the sumof the lift created by the main body and by the AST :

CLHTU = Clα0012 · it + ∆CL (3.7)

The method is applicable in the high-flap-deflection range and limited tothe low speed regime, to which belongs the SFX1.

2 -MHTU

The pitching moment of the all-movable tail isMHTU . It is calculated at the1/4 chord and then transposed at the hinge axis when calculating the pilotstick forces. Instead of working with the forces and moments, working withthe coefficients offers more flexibility. The pitching moment coefficient for theHTU is defined in equation (3.8):

CMHTU=

∆Cm∆CL

· CL + Cm0θ=0(3.8)

CL was determined from the previous section. Cm0θ=0corresponds to the

pitching moment at 0°angle of attack and no twist. Consequently, Cm0θ=0=0

for a symmetrical airfoil. Calculation of Cm0θ=0is made through equation

(3.9)[23]:

Cm0θ=0=

A · cos2(Λc/4)

A+ 2 · cos(Λc/4)· Cm0 (3.9)

In this equation, A refers to the aspect ratio,Λc/4 to the quarter chord sweepand Cm0 the pitching moment at 0°angle of attack.∆Cm∆CL

correspond to the slope of the wing pitching moment increment. Refer-ence [24] clarifies its calculation:

∆Cm∆CL

= (nref −Xac

Cr) · Cr

c(3.10)

In equation (3.10), nref stands for distance between the leading edge vertexat the root and the desired point of calculation for the moment of reference,expressed in % of root chord. The ratio Xac

Crrepresents the location of the

aerodynamic center in % of root chord, Cr the root chord and c the mean aero-dynamic chord.

Finally, the ratio XacCr

can be calculated for a tapered wing thanks to thefollowing formula:

Xac

Cr=

23(1 − λ) + 1

2· [1 − λ2

1+λ] · π · log(1 + A

5)

1 + π · log(1 + A5)

(3.11)


The parameter λ being the taper ratio, the ratio of the tip chord over the rootchord of the wing.

3 -MAST

For the calculation of the AST hinge-moment, this device can be consideredas a deflected control surface such as a flap or aileron. The general equationfor the hinge-moment coefficient of such item is:

ch = chα · α + chδa · δa + chδt · δt (3.12)

In equation (3.12), chα stands for the variation of hinge-moment due tothe aircraft angle of attack, chδa is the variation of hinge-moment due to thesurface control deflection and chδt corresponds to the change in hinge-momentdue to tab deflection. It is important to mention that this equation is valid onlyin the linear hinge-moment range, encountered for small deflections. In thecase of the anti-servo tab, the previous equation is reduced to :

chAST = chα · α + chδa · δa (3.13)

The complete method is taken from the USAF Stability and Control DAT-COM [23], in the part "Section hinge-moment of high-lift and control device".The first step is the calculation of the trailing edge angle φTE at 90%, 95% and99% of the chord in order to check if the thickness condition described by theequation underneath is respected:

tan(φTE

2) = tan(

φ′TE2

) = tan(φ′′TE

2) =

t

c(3.14)

The trailing edge angle φTE is generally given for an airfoil. The angles at95% and 99% chord are obtained by measuring the thickness Y at the desiredchord location. Equations (3.15) and (3.16) define these angles, and Figure 8in appendix B exemplifies this calculation method.

tan(φ′TE

2) =

Y902

− Y992

9(3.15)

tan(φ′′TE

2) =

Y952

− Y992

4(3.16)

If the thickness condition is respected, the hinge-moment derivative C ′hαis calculated with equation (3.17):

C ′hα =[ C ′hα(Chα)theory

]· (Chα)theory (3.17)


However, if the thickness condition previously cited is not respected, acorrection to account for a particular thickness distribution is required, leadingto equation (3.18):

C ′′hα = C ′hα + 2(Clα)theory[1 − Clα

(Clα)theory

]· (tan(

φ′′TE2

− t

c) (3.18)

Finally, the hinge-moment derivative needs to be corrected to account fornose-shape and nose-balance effects, which is done by the following equation:

(Chα)balance = C ′′hα ·[(Chα)balance

C ′′hα

](3.19)

A final correction for the Mach-number effects is available but will notbe used in the scope of this thesis due to the flight regime of the SFX1. Thevarious terms present in the equation (3.17) until (3.19) are described hereby:

• C′hα

(Chα)theory

is the ratio of the actual to the theoretical hinge-moment deriva-tive for a radius-nose, sealed-gap, plain trailing-edge flap

• (Chα)theory is the theoretical hinge-moment derivative for airfoils re-specting the thickness condition

• Clα)theory is the theoretical section lift-curve slope

• Clα(Clα )theory

is an empirical correction factor that accounts for the devel-opment of the boundary layer towards the airfoil trailing edge

• (chα )balanceCh′′α

is a correction factor that accounts for the balance ratio of thecontrol surface

The same methodology applies for the determination of chδa with the fol-lowing equations, the use of (3.21) being necessary only if the thickness con-dition is not respected :

C ′hδ =[ C ′hδ(Chδ)theory

]· (Chδ)theory (3.20)

C ′′hδ = C ′hδ + 2(Clδ)theory[1 − Clδ

(Clδ)theory

]· (tan(

φ′′TE2

− t

c) (3.21)

(Chδ)balance = C ′′hδ ·[(Chδ)balance

C ′′hδ

](3.22)


Each term of these equations can be defined by analogy with chδa .

Finally, reusing the notations of the method described in this subsection,the hinge-moment coefficient for the anti-servo tab becomes:

chAST = (chα)balance · α + (chδa )balance · δa (3.23)

B - XFLR5

The first phase necessary to run XFLR5 is to define all the airfoil profilesthat will be necessary to further investigate the aerodynamic loads. The mainprofile is the one of the HTU, a NACA0012 airfoil. The other profiles corre-spond to the NACA0012 airfoil fitted with a flap of 15% chord length whosehinge is located at mid thickness, and whose deflection corresponds to the ASTdeflection for each angle of incidence of the HTU.Once the profiles are defined, they are analysed for a range of Reynolds numberfrom 50 000 to 5,5 Million, determining the 2D aerodynamic characteristicsof each profile. The last step consists in modelling in 3D the HTU plan-formas a wing with a flap representing the AST, based on the profiles defined pre-viously. Figure 7 exemplifies a modelling of the tail with XFLR5.Finally, it is possible to realise a VLM analysis for a range of tail angles ofincidence, the AST deflection being changed by changing the wing profile.Such simulation leads to the lift, drag and pitching moment of the tail as wellas the hinge-moment of the AST. From these results, it is possible to obtainthe forces of interest expressed earlier, exception made forXAST and ZAST . Itis important to note that some corrections need to be applied to the results inorder to have a realistic simulation.The first correction concerns the tail surface used in the simulation, whichdoes not account for the presence of the fuselage. The tail fairings of SFX1covers about 7% of the simulated stabilizer area.This consequently reducesapproximately by the same amount the forces generated by the HTU.The second crucial parameter that is not simulated directly with such mod-elling is the downwash effect of the wing. To correct it, the downwash angleneeds to be beforehand calculated for the desired flight condition and the VLManalysis must be carried out for the local angle of incidence, which includesdownwash.

C - CFD

A CFD simulation is carried out closely resembling an experiment.


The first step is called pre-processing, it corresponds to the preparation ofthe simulation and establishes the basis required for the analysis. During pre-processing, the user initially defines the flow problem and the geometry to bestudied. Generally, a CAD (Computed Aided Design) model is employed todefine the geometry, and after, it is downloaded in the pre-processor where theuser can define a flow region and identify the fluid domain of interest. Duringthe development of the SFX1, a parametric CAD model was designed, allow-ing to control the deflection of each control surface. It will be used for theCFD analysis.Another major aspect of pre-processing is setting up all the analysis controlparameters. These can be simulation parameters such as the time step, thenumber of iterations or the residual controls. It also implies to define the tur-bulencemodel used, which highly depends on the flow behavior expected. Theuser also needs to fill in the physical conditions of the domain boundaries,which are described by the boundary and initial conditions. For this study, anincompressible model with second-order solver is used. A see level and ISAflow conditions are assumed. The chosen turbulence model is kω − SST .Finally, pre-processing is also about generating a mesh. The flow domain isdiscretized in smaller cells or elements. The partial differential equations thatdescribe mathematically the problem are transformed into a set of algebraicequations, which can now be solved thanks to the space discretization of thedomain. This method assumes that the behavior of the variables of interest(pressure, temperature, velocity, etc) is linear within each cell. Various typeof cells are available for meshing: tetrahedral, hexahedral, pyramidal, etc. Forthe purpose of this study, hexahedral cells have been chosen. Their use is ad-vised when dealing with flow-aligned problems as they provide higher qualitysolutions for fewer cells and nodes compared to tetrahedral, and features lowernumerical diffusion in such context.To take profit of the symmetry physics of the problem, only one half of theaircraft will be studied, allowing to decrease the computational cost of thesimulation for the same quality level in the results. This leads to a 5.3 Millioncells meshing.

Carrying out the simulation is the second step, realised by the computerthrough the chosen CFD solver. At this stage, the user can often observe theevolution of the convergence criteria and check for any errors during solving,but not much interaction is expected.

The final step is the post-processing. It consists in analysing the results


obtained during the simulation and plotting them in order to extract the flowproperties of interest. Results can be visualised and interpreted in an easierway with the help of post-processing tools such as streamlines, vector plots orcontour plots.

3.1.2 Ailerons and RudderThe ailerons on the SFX1 cover the span between the flaps and the winglets,with a width of 25% chord. In order to reduce adverse yaw, the aircraft featuresdifferential ailerons. It means that the deflection of the aileron going down andthe one going up will not be symmetrical.Indeed, when an aileron is deflected downward, it creates an increase of lift thatcomes with an increase of induced drag. Consequently, the wing being raisedup is experiencing a higher drag than the wing being lowered, which will tendto rotate the aircraft around its yaw axis. To minimise this phenomenon, theidea is to minimise the global imbalance of drag created by the aileron deflec-tion. Several technical solutions have been developed such as Frise ailerons,the use of spoiler or differential ailerons. In the case of the latter, the drag im-balance reduction is realised by significantly increasing the deflection of theaileron deflected upwards with respect to the one deflected downwards. Thedifferential ratio can usually reach 1:2 in general aviation, meaning that up-ward deflection will be twice larger than the downward one. This ratio caneven reach 1:3 for some airliners such as the Boeing 777-200 [27].The SFX1’s rudder is quite conventional, covering the height of the verticaltail. Its deflection has already been set to ± 25 with respect to the verticalstabiliser’s chord line.

Determination of the required aileron deflection

The surface of the ailerons has been defined and the sizing had been done pre-viously, and its surface area is assumed to be final. However, the deflectionsare not yet determined and the process leading to their definition is explainedin this section.The presence of ailerons on an aircraft ensures the manoeuvrability of the ve-hicle around its roll axis. The quality criteria to assess the good behavior ofthe machine is called the rate of roll, or roll rate. It corresponds to the angulardisplacement that the aircraft is able to reach during a given time, generallyexpressed in degrees or radians per second, and is directly linked to the ailerondeflection.


The method explained hereby is based on the theory described in Gudmunds-son [28], chapter 23. It starts with defining the rolling moment La:

La = Faup · yup − Fadown · ydown= clδα · δaup · yup − clδα · δadown · ydown

(3.24)

The forces Fa represent the variation of lift created by the deflection δa ofthe ailerons and y the span location of the application of these forces. Bysymmetry, ydown and yup are equal and can simply be noted y. The coefficientclδα represents the change in lift coefficient with aileron deflection.The infinitesimal rolling moment can consequently be expressed such as:

dLa = (dFaup − dFadown ) · y= (δaup − δadown) · clδα · q · c · y · dy

(3.25)

The variable q stands for the dynamic pressure and c the wing chord at thespan location y. If the infinitesimal rolling moment is now expressed throughan infinitesimal moment coefficient, it results in the following equation:

dCl =dLa

q · s · b

=(δaup − δadown) · clδα · q · c · y · dy

q · S · b

= (δaup − δadown) · clδα ·c · y · dyS · b

(3.26)

In equations (3.25), b is the wingspan and S the wing surface delimited by theailerons’ span. By integrating between the most inner and outer span of theaileron, the rolling moment coefficient can be expressed as:

Cl =(δaup − δadown) · clδα

S · b

∫ b2

b1

c(y) · y · dy (3.27)

The different parameters present in the previous equation are illustrated in Fig-ure 9 in appendix B. In the case of a straight tapered wing, of taper ratio λ, rootchord CR and wingspan b, the equation describing the chord length accordingto the span position is:

c(y) = CR(1 +2(λ− 1)

b· y) (3.28)

Thanks to this definition, it is possible to express the aileron authority Clδα ,with a capital "C", which must not be confused with clδα used previously:


Clδα =dCldδα

=clδαS · b

·∫ b2

b1

CR(1 +2(λ− 1)

b· y)y · dy

=clδα · CR2 · S · b

·[(b2

2 − b21) +

4(λ− 1)

3b(b3

2 − b31)]

(3.29)

Finally, the roll rate p is expressed through equation (3.29) by:

p = −2 · Clδα · VClp · b

(δaup − δadown) (3.30)

The term V is the airspeed andClp refers to the damping in roll coefficient.In the case of the SFX1 which features a straight tapered wing, the formuladetermining the damping in roll coefficient is:

Clp = −(clα + cd0) · CRb24S

[1 + 3λ] (3.31)

The coefficient cd0 corresponds to the zero-lift drag.

It is important to mention that this calculation leads to the steady roll-rate,when the angular motion is no longer accelerated. Indeed, the roll motionconsists in a transient acceleration which decreases as the roll rate increasesand finally vanishes once the steady state is reached, as shown in Figure 10.Being interested in the pilot-desired responsiveness, the steady roll rate is thecriteria to consider. It is often mentioned in the literature that for a generalaviation aircraft to be pleasurable to fly, the roll helix angle condition shouldbe respected. This condition being:

pb

2V> 0.07 radians (3.32)

Based on the equation (3.24) to (3.32), it is henceforth possible to deter-mine the aileron deflection in both directions to achieve the desired rate of roll,keeping in mind that the deflection of one aileron is linked to the other by thedifferential ratio.

Determination of the aerodynamic loads

On the SFX1, the ailerons have a simple design. Their shape is obtained byslicing the wing profile with a semi-circle in the inner side of the profile. The


center of the circle is located at mid-thickness and 75% chord from the LE, asdepicted in Figure 11. The same method was used to define the rudder shape.The control surface aerodynamic loads are directly linked to their respectivedeflection. The determination of these loads is essential to ascertain the pilotstick forces and ensure that the aircraft is not too sensitive or requires too muchforce to be maneuvered. Additionally, it will contribute to the sizing of theflight control mechanism.In this subsection, the aim is to determine the hinge-moment coefficient of theailerons and the rudder. As mentioned previously, this coefficient is a linearfunction of the control surface deflection under small angles condition. For theailerons, it is also a linear function of the aircraft angle of attack αwhile beinga linear function of the angle of sideslip β for the rudder. As the SFX1 doesnot feature any tab on the aileron, the formula describing the aileron hinge-moment coefficient cha can be approximated by:

cha = chα · α + chδa · δa (3.33)

Likewise, for the rudder hinge-moment coefficient chr :

chr = chβ · β + chδa · δa (3.34)

Hence, the possibility to determine cha and chr by finding chα , chβ and chδawith the different manners described underneath.

A - Analytical methods

The analytical methodology which is used to determine the hinge-momentof the ailerons and the rudder is identical to the one described in section 3.1.1to determine the moment exerted on the AST. For conciseness, it will not fur-ther be discussed here.

B - XFLR5

The wing and vertical stabiliser profiles, in clean configuration and withdeflected control surface, are defined in XFLR5. They are analysed for a rangeof Reynolds number which lays between 3,2 and 6,5 Millions. Once the sec-tion analysis is finished, a half wing is modeled and can be used to perform aVLM analysis for various deflections of the aileron as well as different anglesof attack of the wing. A second model representing the vertical tail is analysedfor different rudder deflections and sideslip angles.


The result given by XFLR5 is directly the hinge-moment of the control sur-face, that can afterward be converted in terms of hinge-moment coefficient.By running the analysis for different aileron deflections and interpolating lin-early the results, it is possible to directly obtain chδa . If the same method isapplied with no aileron deflections and different angles of attack, it leads tochα . This also works for chβ and chδa in the rudder case.


C - CFD

The simulation described in the horizontal tail section is used as well forthe determination of the ailerons and the rudder loads. The settings are con-sequently the ones defined previously. The results are accessed by definingthe surfaces of interest and defining a point at which the calculation is ran.For both surfaces, the calculation is made at the hinge axis, giving directly thehinge-moment as well as the normal and axial forces.


3.2 KinematicsKinematics is a branch of mechanics that studies rigid body motions, outsidetime or force considerations. It relies on purely geometrical considerationsand can be used to describe the motion of a point, a solid body, or a systemof solid bodies. One of the main assumption for kinematics use is that solidbodies cannot deform and will conserve their initial shape under any circum-stances. In the scope of this thesis, kinematics theory is used to link the con-trol surface deflections to the pilot stick or pedals displacement. A deeper andmore complete description of the field is available in the literature [29–31].

3.2.1 Primary flight controls kinematicsThe primary flight control system is divided in three different sub-assemblies,each of them being related to the control of one axis of the aircraft.The kinematics analysis focuses on calculating the linear and angular displace-ments of the various components constituting the primary flight controls. Tothat end, two hypothesis are formulated. The first assumption considers thatthe motion of a pushrod is always described in a plan. The second assumesthat the pushrods are always oriented parallel to the horizontal or vertical plan.

The figure below is used as an example to illustrate the methodology used:

Figure 3.1: Kinematics illustration of angle and displacement

For calculation, the initial input is the desired control surface deflectiongiven as an angle compared to neutral position, noted α at point A. This hingeangle induces a displacement a of the first attachment point of the pushrodconnecting the control surface to the next bell-crank. Considering no defor-mation of the pushrod and the previously mentioned hypothesis, it is possibleto consider the displacement on the pushrod attachment in point B being equal


to the one in A. This means that in B, the pushrod attachment to the lever oflength L2 has moved horizontally by a distance a. This motion leads to theangle β, which through the lever of length L3, results in a displacement b forthe next pushrod. The equations linked to these geometrical considerationsare the following:

a = L1 · sin(α) (3.35)

β = sin−1(a

L2) (3.36)

b = L3 · sin(β) (3.37)

The application of this method to the other components of the kinematicchain allows to find the resulting stick or pedal displacement. By playing withthe length of the various bell-crank’s arms, it is possible to adjust the dis-placement ratio between the control surfaces and the pilot commands so thatthe aircraft does not require to much efforts to fly but meets the required con-trol deflections for safe handling.

A - Pitch controlThe first mechanism deals with the control of pitch, being formed by twopushrods and one bell-crank in between. It is represented in the kinematicsdraw underneath :

Figure 3.2: Kinematic chain of the pitch axis control mechanism


B - Roll controlThe roll control mechanism is the most complicated one of the primary flightcontrol systems. Also constituted with pushrods and bell-cranks, its kinemat-ics chain is illustrated by Figure 3.3.

Figure 3.3: Kinematic chain of the roll axis control mechanism

C - Yaw controlYaw control system is handled by a pulley-cable system directly linked to thepilot pedals.

Figure 3.4: Kinematic chain of the yaw axis control mechanism


3.2.2 Differential aileronsAsmentioned earlier, the SFX1 features differential ailerons in order to reduceadverse yaw during roll. The difference in aileron deflection is obtained purelymechanically thanks to a crank-bell which arms are oriented at an angle Ω

smaller or greater than 90°. This crank-bell is located just after the pushrodconnecting the ailerons and the rest of the kinematic chain, as it is possibleto observe in the kinematics drawing of the roll flight control mechanism. Bythe non linearity of the trigonometric functions, an input displacement d1 willlead to an output displacement d2 or d3, depending on which side the lever isdeflected with respect to its original position, as exemplified by the drawingbelow:

Figure 3.5: Exemplification of differential ailerons mechanism

The original position of the levers is represented by the continuous lines,while the dash lines represent a deflected position obtained after an input dis-placement d1. From this displacement, the crank-bell rotates around its axisby an angle α. In that configuration of the levers, a vertical displacement ofd1 above the original position leads to a horizontal displacement d3 while aninitial input in the other direction leads to d2.Mathematically, the interest is in determining the displacements d2 and d3

as a function of the input displacement d1 and the opening angle Ω. This istranslated in terms of equations by the system of equation (3.38):


d1 = L1 · sin(α)

d2 = b− a

d3 = c− b

(3.38)

Based on trigonometry, the lengths a, b and c are:a = −L2 · cos(Ω − α)

b = −L2 · cos(Ω)

c = −L2 · cos(Ω + α)

(3.39)

Finally, by substituting the previous results in the first system, d2 and d3 canbe found:

α = sin−1( d1L1

)

d2 = L2[cos(Ω − α) − cos(Ω)]

d3 = L2[cos(Ω) − cos(Ω + α)]

(3.40)

Using the equation system (3.40), the final differential ratio for the aileronscan be adjusted by playing with the value of the angle Ω.


3.3 Pilot control forcesAsmentioned inKinematics and Dynamics of Mechanical Systems [31], struc-tural forces analysis often follow a kinematics analysis. The pilot control forcesrefer to the stick forces and to the pedal forces since the pitch and roll motionsof the aircraft are managed through the stick and the yaw is managed by thepedals. The determination of these forces is based on the work described pre-viously in section (3.1).The origin of the command forces is the aerodynamic loads exerted on the con-trol surfaces when they are deflected. Since all the control surfaces are hinged,this is translated to a hinge-moment for each surfaces. This hinge-moment isafterwards transmitted until the pilot commands through the complete kine-matic chain forming the primary flight controls. Finally, the intensity of thepilot control forces depends on the intensity of the hinge-moment and the kine-matic ratio between the surface deflection and the stick or pedal displacement.To find the pilot control forces, a static load analysis is considered for a givencontrol surface deflection, assuming that the pilot is strong enough to lock thestick or the pedals into the desired position. Under such conditions, the forcesand torques are considered for each mechanism and link according to New-ton’s first law.On the physical mechanism, pushrods will be attached to the bell-crank withrod-ends. This can be modeled, in terms of kinematics, by a spherical joint.The bell-crank will be mounted over ball-bearing, which can be modeled as arevolute or hinged joint [31]. From such modelling, it can be deduced that theforces acting on the pushrods are aligned with them, and that the pushrods areonly experiencing pull or push stress. Finally, the force F exerted at a distanceh from the rotational axis of a lever by a pushrod creates a torque T in thecrank-bell as shown in Figure 3.6:

Figure 3.6: Representation of a force and a torque applied to a levermechanismin equilibrium for a static analysis


The application of Newton’s first law leads to equation (3.41):

T = F · h (3.41)

If the torque is the input, reversing this equation leads to the force trans-mitted to a pushrod. While carrying such calculation, it is important to takeinto account the variation of the projected lever arm if the mechanism forcesare calculated for different deflection angles. Figure (3.7) highlights this phe-nomenon :

Figure 3.7: Variation of the projected lever arm according to the deflectionangle of a lever

If L is the length of the lever, the lever-arm distance originally noted hbecomes h′ when the mechanism is deflected by and angle α. The equationdescribing the value of h′ according to α is:

h′ = L · cos(α) (3.42)

Finally, starting with the hinge-moment of the desired control surface and ap-plying these equations at each pushrod and crank-bell allows the determinationof the pilot control forces for all axis.

Chapter 4

Results

4.1 Horizontal tail unit

4.1.1 Tail and AST deflectionsA - HTU

For the estimation of the tail lift coefficient CLt required in the rotationcase, the ISA conditions at see level are considered. The flaps are deflected intake-off position by an amount of 15°. The value of the chosen parameters forthis study case are described in table (4.1):

Parameters Take-offweight (W)

Aircraft rotationspeed (Vr)

MotorThrust (T)

Air density(ρ)

Dynamicspressure (q)

Thrust lineangle (α)

Value 13 734 N 33 m/s 2500 N 1.225 kg/m3 729 Pa 2°

Table 4.1: Parameters used to determine CLt required during rotation

The resulting value of CLt is dependent of the position of the center ofgravity. Calculations show that the most forward CG position is the most crit-ical with regard to the tail lift required. The same assessment is made for thego-around phase of flight.

In the go-around situation, ISA conditions at see level are also considered.The flaps are deflected for landing configuration at 30°, increasing the aero-dynamic pitching moment. The aircraft is assumed to be flying in trimmedcondition with an angle of attack of 2.89°. The value of the chosen parametersare described in table (4.2):

31

32 CHAPTER 4. RESULTS

Parameters Take-offweight (W)

Aircraftairspeed (Vr)

MotorThrust (T)

Air density(ρ)

Dynamicspressure (q)

Thrust lineangle (α)

Value 13 734 N 36.8 m/s 3017 N 1.225 kg/m3 829 Pa 2°

Table 4.2: Parameters used to determine CLt required during go-around

Based on the previously described simulation parameters, the resulting val-ues for CLt are:

Rotation case Go-around case

CLt 0.967 0.574

Table 4.3: Values of CLt resulting of the rotation and go-around cases consid-eration

Consequently, the rotation case is the most critical in terms of down-forcerequired from the tail. For the determination of the tail trailing-edge up deflec-tion, the previously found value is increased by 10%. Assuming a lift curveslope of at = 5/rad (or at = 0.0873/°), it results in a required tail deflectionof it=12.18°. In order to have a conservative approach, the final deflectionselected for the tail is it=13°.

B - AST

The deflections of the AST were defined as follows:

• At maneuvering speed VA, the aircraft must be in trimmed flight with theservo trim centered.

In such circumstances, the aircraft has an AoA α=1.41°, the HTU angleof incidence being it=-4.74°. In that configuration, the AST is alignedwith the HTU (δAST=0).

• The HTU maximum deflection TE down being it=+5°, the deflection ofthe AST needs to be found in order to have the HTU moment at its pivotaxis not exceeding the moment allowed by the maximum stick forces.

An initial gearing ratio between the pilot stick and the horizontal tail of2 is assumed. This ratio, characterised by the kinematics of the mech-anism, translates the amount of force that the pilot needs to produce to

CHAPTER 4. RESULTS 33

counteract a given hinge-moment at the HTU pivot axis. In such situ-ation, it means that if the pilot produces 1 Nm of torque at the stick, 2Nmwill be applied at the HTU. According to CS-23 regulation [32], themaximum stick force advised for the pitch control is 267 N (see Figure12 in Appendix B). Based on such assessment, an initial maximal pilotforce of 267 N was considered, leading to around 110 Nm of torque atthe end of the 425 mm long pilot stick. Afterwards, different AST de-flections were tried on the XFLR5 model to reach a pitching moment ofapproximately 220 Nm at the hinge axis. It finally resulted in an ASTdeflection of δAST=+9.35°.

• Due to the mechanical linkages, the characterisation of the two previouspoints defines the rest of the AST deflections covering the complete HTUrange of movement.

The use of the CAD software Solidworks allowed to draw the kinemat-ics of the AST system as shown in appendix B with Figure 13. Thanksto this, the deflection of the AST can be known for any tail deflection.As a result, when the HTU is deflected with 13°trailing-edge up, δAST=-14.54°.This is illustrated by Figure 14 in Appendix B. In addition, it is pos-sible to obtain the equation ruling the AST deflection (y) with respectto the tail angle of incidence (x). The equation that approximates thismechanical law is the following:

y = 0.0009x3 − 0.0254x2 + 1.0009x+ 4.9122 (4.1)

The angles considered are expressed in degrees.

4.1.2 Tail aerodynamic loadsThe use of XFLR5 and CFD directly leads to the value of the forces and mo-ments investigated. For the analytical method, the dimensionless coefficientfirstly needs to be determined.

A -ZHTU

From the method section, the equation leading to ZHTU is:

CLHTU = CLα0012 · it + ∆CL (4.2)


The term∆CL is detailed in equation (3.5). The value of the different termsin this equation are found from the diagrams present in the Datcom [23]. Table4.4 summarises these values:

δAST 9.35 ° -14.54 °

∆cl 0.2727 0.4229(CLαclα

) 0.678 0.678(αδ)CL(αδ)cl

1.12 1.12Kb 0.8 0.8

CLα0012 (/°) 0.0749 0.0749

∆CL 0.166 0.257CLHTU without AST -0.375 0.974CLHTU with AST - 0.541 1 .231

Table 4.4: Lift increment due to AST deflection

B -MHTU

From the method section, the equation leading toMHTU is:

CMHTU=

∆Cm∆CL

· CL + Cm0θ=0(4.3)

The various terms are detailed by the equations (3.9) to (3.11). In theSFX1 case, the deflection of the AST is not 0 when the tail is not deflected.It has been found that Cm0 = -0.01736 (equation 3.9) for an anti-servo tabdeflection of -0.87°. As for ZHTU , the value of the different terms comes fromthe diagrams present in the Datcom [23]. Table 4.5 summarises these values:

δAST 9.35 ° -14.54 °XacCr

0.414 0.414Cm0θ=0

-0.015 -0.015∆Cm∆CL

-0.0626 -0.0626

CMHTU- 0.049 0 .062

Table 4.5: HTU pitching-moment including AST deflection effects


C -MAST

As mentioned in the chapter 3, the hinge-moment coefficient of the AST isgiven by the equation (3.23). The detail of all the terms implicated is presentedin the relatedmethod part and only the value of themain results (extracted fromthe Datcom’s diagrams) is presented in the table 4.6:

δAST 9.35 ° -14.54 °

chα (/°) -0.001306 -0.001306chδa (/°) -0.010479 -0.010479

Tail angle of incidence it (°) 5 -13

chAST 0.105 0.139

Table 4.6: AST hinge-moment coefficient

D -Tail results for all the methods

The results of the three investigated methods are expressed in terms ofmoments and forces. The considered airspeed is VA = 65.2 m/s, resultingin a dynamic pressure of 2604 Pa at see-level and ISA conditions. For thedimensionless coefficient, the surface of the complete HTU is used for ZHTUandMHTU . ForMAST , the surface of the AST is taken.For a tail incidence it = −13, the associated forces and moments are:

Forces and Moments ZHTU (N) MHTU (Nm) MAST (Nm)

analytical method -9 359 361 14.81XFLR5 -9 785 471 12.81CFD -6 140 325 13.67

Table 4.7: Value of the aerodynamic loads exerted on the horizontal tail for adeflection it=-13°


For a tail incidence it = 5, the forces and moments are:

Forces and Moments ZHTU (N) MHTU (Nm) MAST (Nm)

analytical method 4113 -285 -10.03XFLR5 4554 -332 -8.22CFD 3492 -195 -9.45

Table 4.8: Value of the aerodynamic loads exerted on the horizontal tail for adeflection it=5°

The important difference in the results obtained will be discussed in thechapter 5.

4.2 Ailerons and rudder

4.2.1 Aileron deflections and rate of rollThe aileron maximal deflection is a compromise between handling qualitiesand pilot stick forces. In the scope of the SFX1, three airspeeds have to beconsidered. The first one is the maneuvering speed VA, which will conditionthe pilot stick forces. The second and third speeds are the take-off speed VTOand stall speed VS1 . According to CS-23 [32], the aircraft must feature a rollrate of 12°/s and 15°/s at respectively VTO and 1.2VS1 .

To determine the desired rate of roll, it is aimed to respect the roll helixangle condition described in equation (3.32), which results at VA in a roll rateof p = 41.5/s.The coefficient clδα , representing the change in lift coefficient with aileron de-flection, was determined by CFD analysis of the ailerons. The parameters usedto carry out the calculation are summed up in the table underneath:

Parameters Value

clδα (/rad ) 2.909Clδα (/rad ) 0.239Taper ratio λ 0.615Clp (/rad ) -0.839

Table 4.9: Parameters and their respective value used for roll-rate calculation


Based on these parameters, the smallest aileron deflection allowing tomeetthe roll helix angle condition is 12° for the aileron going downwards, and 17.9°for the one going upwards. These values are linked by the aileron differentialratio. As a result, the SFX1 will feature a roll rate of p = 44.1/s at VA.

These deflections rely on the assumption that the control system mecha-nism is made of rigid bodies that will not deform during use. However, thisassumption generally does not hold in general aviation aircraft. Indeed, asexplained by S.Gudmundsson [28], the deflections of the control surfaces inflight are typically 25% smaller than ground deflections where no loads are ap-plied. According to this book, on some poorly designed systems, it could evenbe so critical that only 25% of the maximum deflection could be achieved.Consequently, the ailerons maximum deflection is increased by about 25% andthe final results are the following:

Parameters Value

VTO (m/s) 33Estimated roll rate at VTO (°/s) 22.33

1.2 VS1 (m/s) 29.7Estimated roll rate at 1.2 VS1 (°/s) 20.1Maximum downward deflection (°) 15Maximum upward deflection (°) -22.4Estimated roll rate at VA (°) 44.1

Table 4.10: Maximum aileron deflections and aircraft rate of roll at differentairspeeds

The maximum aileron deflections presented in the table 4.10 allow to meeta rate of roll in line with the roll helix condition at any considered airspeed andallow the SFX1 to respect the criterion given by the CS-23 regulation [32].

4.2.2 Aileron and rudder aerodynamic loadsA -Aileron aerodynamic loads

The hinge-moment derivatives for the ailerons chα and chδ were obtainedfor the analytical method with the same procedure described in section 4.1.2for the horizontal tail.Regarding the XFLR5 and CFD analysis, a grid of points for different angles


of attack and aileron deflections have been established. The derivative chα wasobtained by interpolating linearly the hinge-moment coefficient with respectto α with no deflection δ. With such method, the derivative is the curve slopeof the interpolation curve. The same was performed to determine chδ , but withα = 0. Table 4.11 summarizes the values obtained:

Method chα (/°) chδ (/°)

analytical method (DATCOM) -0.0063 -0.0145XFLR5 -0.0066 -0.0126CFD -0.0054 -0.0105

Table 4.11: Aileron hinge-moment derivative for the different calculationmethods

The calculation of the aerodynamic loads for the ailerons are carried outfor an aircraft angle of attack α = 0.64, which is the lowest AoA at whichthe SFX1 could be trimmed for an airspeed equal to VA. This is also the AoAwhich results in the highest aerodynamic loads for the ailerons.To verify if the linearisation hypothesis of the hinge-moment coefficient canhold, the values obtained directly from XFLR5 and CFD will be compared tothe ones coming from the hinge-moment derivative described in table 4.11.The aerodynamic loads for the ailerons are found to be:

Aileron hinge-moment (Nm) Aileron deflecteddownward (15°)

Aileron deflectedupward (-22.4°)

analytical method -47.4 67.4Linearized hinge-moment for XFLR5 -41.3 58.4

XFLR5 -68.2 36.0Linearized hinge-moment for CFD -34.4 48.7

CFD -52.6 24.8

Table 4.12: Ailerons hinge-moments for the different calculation methods

B -Rudder aerodynamic loads

The hinge-moment derivatives for the rudder chβ and chδ were found in theexact same manner than the ones of the ailerons. It results in table 4.13:


Method chβ (/°) chδ (/°)

analytical method (DATCOM) -0.0017 0.0112XFLR5 -0.0046 -0.0124CFD -0.0047 -0.0055

Table 4.13: Rudder hinge-moment derivative for the different calculationmethods

The calculation of the aerodynamic loads for the rudder are carried outfor an aircraft angle of sideslip β = 20/s. This sideslip angle results in thehighest aerodynamic loads for the rudder.As for the ailerons, the values obtained directly from XFLR5 and CFD willbe compared to the ones coming from the the hinge-moment derivatives de-scribed in the table 4.13. It leads to the following results :

Rudder hinge-moment for adeflection of 25° and sideslip angle of 20° Hinge-moment(Nm)

analytical method -241.0Linearized hinge-moment for XFLR5 -308.5

XFLR5 -271Linearized hinge-moment for CFD -177.7

CFD -164.2

Table 4.14: Rudder hinge-moments for the different calculation methods

4.3 KinematicsThis section presents the linear and angular displacements of the primary flightcontrol mechanisms obtained from applying the methodology described insection 3.2. The naming of the angles and displacements, even if not explicitlydescribed by a draw, is straightforward.Using figures (3.2), (3.3) and (3.4), the name of the kinematic parameters ischosen such that the angle αi corresponds to the angle created at the pivot axisonto which the torqueMi is applied. With the same reasoning, a displacementdi corresponds to a displacement of the rod which sees the force Fi.The results calculated under the hypotheses formulated in the method are com-pared to the values determined in 3D by the mechanism definition in the CADsoftware. For a better visualisation of the overall primary flight controls, a


CAD modelling of the mechanisms is presented by figure 15 in Appendix B.

4.3.1 Horizontal stabiliserThe deflection of the pilot stick to control the horizontal stabiliser is not sym-metrical when pushing or pulling the stick. For use convenience, a stick travelof 65mm was defined for pushing the stick and 160mm for pulling it.The length of each considered lever arm and geometric angle is summarizedin table 4.15:

Geometric parameter L1 L2 L3 L4 L5 Ω

Value (mm or °) 425 70 60 54 100 180

Table 4.15: Geometric parameters for the horizontal tail kinematics

The resulting kinematic displacements for a trailing-edge up deflection ofthe HTU are:

Parameter Formula Calculated value Value from CAD

d1 (Stick travel) (mm) Chosen value 160 160α1 (rad) sin−1( d1

L1) -0.39 -0.39

d2 (mm) L2 · sin(α1) -26.35 -26.35α2 (rad) sin−1( d2

L3) -0.45 -0.46

d3 (mm) L4 · [sin(Ω − α2) − sin(Ω)] -23.72 -23.78αHTU (°) sin−1( d3

L5) -13.72 -13.17

Table 4.16: Horizontal tail kinematics for trailing-edge up deflection

For the trailing-edge down deflection of the HTU, the results are the fol-lowing:

4.3.2 AileronsThe deflection of the pilot stick to control the ailerons is symmetrical for a leftor right bank input. Consequently, the displacement of the kinematic chain isgiven for one configuration.The length of each considered lever arm and geometric angle is summarizedin table 4.18:

The resulting displacement for the considered lever arms and angles aresummarized in table 4.19:



d1 (Stick travel) (mm) Chosen value 65 65α1 (rad) sin−1( d1

L1) 0.15 0.15

d2 (mm) L2 · sin(α1) 10.71 10.71α2 (rad) sin−1( d2

L3) 0.18 0.18

d3 (mm) L4 · [sin(Ω − α2) − sin(Ω)] 9.64 9.63αHTU (°) sin−1( d3

L5) 5.53 5.72

Table 4.17: Horizontal tail kinematics for trailing-edge down deflection

Geometric parameter L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L12effective L13 Ω

Value (mm or °) 325 100 70 50 80 80 80 77 80 50 55 45 39.70 38.53 61.91

Table 4.18: Geometric parameters for the aileron kinematics


αailerondown (°) Chosen value 16.24 16.24d7down (mm) L13 · sin(αailerondown) 10.68 10.51α6down (rad) Ω − cos−1(cos(Ω) − d7

L12) 0.30 0.32

αaileronup (rad) sin−1(d7upL13

) -19.19 -23.61d7up (mm) L12 · [cos(Ω) − cos(Ω + α6)] 12.66 15.25α6up (rad) sin−1( d6

L11) 0.30 0.34

d6 (mm) L11 · sin(Ω − cos−(αaileronup)) 16.24 17.02α5 (rad) sin−1( d6

L10) 0.33 0.33


L8) 0.34 0.34


L6) 0.34 0.34


L4) 0.57 0.56


L2) 0.39 0.38

d1 (Stick travel) (mm) L1 · sin(α1) 122.8 121.7



Table 4.19: Aileron kinematics

4.3.3 RudderFor the rudder kinematics, the considered lever arms are defined hereby:

Geometric parameter L1 L2 L3

Value (mm) 140 46 63.25

Table 4.20: Geometric parameters for the rudder kinematics

This leads to the following displacements, with the assumption that thecables will not elongate under the load:

4.4 Primary flight control loadsIn this section are presented the forces exerted on each pushrods or cables ofthe primary flight control mechanism, with the respective torques generatedat each axis of rotation. The naming of the moments and forces respect thefigures (3.2), (3.3) and (3.4) in section 3.2.1.Based on Smartflyer’s experience, the aerodynamic loads obtained from CFDsimulation are supposed to be the most reliable and will thus be used as inputfor the calculations in this section.The different lengths of the lever arms used for the calculations are the onespresented in the Kinematics section 4.3. The results for each flight control axisare presented in the next subsections.



αrudder (°) Chosen value 25 25d2 (mm) L3 · sin(αrudder) 23.49 23.26α1 (rad) sin−1( d2

L2) 0.54 0.55

Pedal displacement (mm) L1 · sin(α1) 72.48 73.14

Table 4.21: Rudder kinematics

4.4.1 Horizontal stabiliserResults for a trailing-edge up deflection:

Parameter Formula Calculated value

MHTUup (Nm) Defined by aerodynamic loads 232F3 (N)

MHTUup

L5·cos(αHTU )2388

M2 (Nm) F3 · L4cos(α2) 116F2 (N) M2

L3·cos(α2)2149

M1 (Nm) F2 · L2cos(α1) 139F1 (Stick Force) (N) M1

L1·cos(α1)354

Table 4.22: Horizontal stabilizer flight control forces andmoments for trailing-edge up deflection

Results for a trailing-edge down deflection:

4.4.2 Ailerons


Mailerondown (Nm) Defined by aerodynamic loads -52.61

F7down (N)Mailerondown

L13·cos(αailerondown )-1422

M6down (Nm) F7down · L12effectivecos(α6down) -53.9

F6down (N)M6down

L11·cos(α6down)

-1027



Maileronup (Nm) Defined by aerodynamic loads 23.95

F7up (N)Maileronup

L13·cos(αaileronup )658

M6up (Nm) F7up · L12effectivecos(α6down) 25

F6up (N)M6up

L11·cos(α6up )475

M5 (Nm) (F6up − F6down) · L10cos(α5) 71

F5 (N) M5

L9·cos(α5)939

M4 (Nm) F5 · L8cos(α4) 68

F4 (N) M4

L7·cos(α4)903

M3 (Nm) F4 · L6cos(α3) 68

F3 (N) M3

L5·cos(α3)903

M2 (Nm) F3 · L4cos(α2) 38

F2 (N) M2

L3·cos(α2)645

M1 (Nm) F2 · L2cos(α1) 60

F1 (Stick Force) (N) M1

L1·cos(α1)199

Table 4.24: Aileron flight control forces and moments



MHTUdown (Nm) Defined by aerodynamic loads -143F3 (N)

MHTUdown

L5·cos(αHTU )-1437

M2 (Nm) F3 · L4cos(α2) -76F2 (N) M2

L3·cos(α2)-1293

M1 (Nm) F2 · L2cos(α1) -89F1 (Stick Force) (N) M1

L1·cos(α1)-213

Table 4.23: Horizontal stabilizer flight control forces andmoments for trailing-edge down deflection

4.4.3 Rudder


Mrudder (Nm) Defined by aerodynamic loads 164

F2 (N) M2

L3·cos(α2)2597

M1 (Nm) F2 · L2cos(α1) 119

F1 (Pedal Force) (N) M1

L1·cos(α1)853

Table 4.25: Rudder flight control forces and moments

Chapter 5

Discussion

5.1 Aerodynamic loadsThe determination of the aerodynamic loads for the control surfaces of interesthas been carried out by the use of three methods which lead to the resultspresented in chapter 4. From the results expressed in table 4.7 and 4.8, severalobservations can be made:

• The value of the vertical force exerted on the HTU is found to be highlydependant on the method used. A difference up to 37% is observedbetween CFD and XFLR5 results for the HTU deflected at it = −13,and 34% with the analytical method. What is more, both XFLR5 andthe analytical method are overestimating this value compared to CFD,although they are in agreement with each other.

• The hinge-moment estimation for the HTU features high variations de-pending on the method used. The difference can reach 31% betweenCFD and XFLR5. In both cases, XFRL5 seems to overestimate thehinge-moment. That is in line with the first assessment since the HTUhinge-moment comes mainly from the lift generated, which is also beingoverestimated by XFLR5 and the analytical method.

• The hinge-moment estimation for the AST leads globally to close resultsfor all the methods.

To explain such a difference in the results, multiple parameters have tobe taken into account. The first assessment is that the analytical and XFLR5methods do not consider the change in local angle of attack at the HTU due

46

CHAPTER 5. DISCUSSION 47

to the downwash of the wing. In the considered situations, the downwash an-gle is estimated to reach about 1°, which decreases the value found with bothmethods.A second explanation is the presence of a tail fairing located at the junctionof the fuselage and the horizontal tail which covers approximately 7% of theHTU surface. To simplify the analytical model, the tail fairing has not beenaccounted in the calculation. The aerodynamic forces being directly linkedto the HTU area, the results of this method should consequently be decreasedby the same amount to obtain a more realistic value. The same assessmentcan be made on XFLR5. Although the software is able to generate a fuselageshape, it was not done because it is not recommended by its developer for twomain reasons. The first one is directly linked to the theoretical aspect of thepanel method, which requires that the union of the panels defines one or moreclosed volumes. These volumes must be neither intersecting nor overlapping,implying that the wing and fuselage cannot be defined separately and com-bined, otherwise resulting in overlapping panels. The software handles thisproblem by representing the wing as thin surfaces if a fuselage is present, butthis leads to the second problem: numerical issues and the difficulty to dealwith the wake and fuselage interaction. In the case of VLM, the trailing vor-tices are extended infinitely behind the wing panels. If the distance betweena vortex and the wake line tends towards zero, strong numerical influence ap-pears on the fuselage panels leading to numerical instability. Consequently,in the XFLR5 analysis, the aircraft fuselage has not been modelled, resultingin the same issue faced with analytical method. The CFD does not face suchproblem, working directly with the CAD model on which all the surfaces aredefined.Another important explanation is the presence of separated flow over the HTUwhich is only predicted by CFD. Indeed, one important hypothesis formulatedfor the use of VLM method and analytical calculation is the presence of at-tached flow all over the surface. The CFD simulation highlighted the presenceof separated flow over the AST, as illustrated in Figure16 in Appendix B. OnFigure16is plotted the wall shear stress along the longitudinal axis of the air-craft. As long as the flow is attached, it produces a shear stress over the skindue to friction forces, which disappears when the flow separates. This is illus-trated in this case during the post-processing by the area colored in red.Finally, with the methodology employed, only the CFD is able to consider anyinteraction effects between fuselage and horizontal stabiliser. For XFLR5, theimpossibility to implement reliably the fuselage in the analysis does not al-low to investigate the interaction HTU/fuselage, and consequently to bring

48 CHAPTER 5. DISCUSSION

any correction to the results regarding this aspect. On the analytical side, thisaspect has not been covered but represents an interesting subject to investigateif only this method is available. These wing-fuselage interactions are known todecrease the value of the aerodynamic forces generated and lead to the devel-opment of the fillets at the California Institute of Technology in the 1930s [26].

Regarding the hinge-moment calculation of the ailerons and the rudder,the same conclusions can be drawn regarding the overestimation of the aero-dynamic loads applied to the control surfaces for the analytical method andXFLR5. This can again be attributed mainly to the impossibility of thesemethods to predict detached flow that is encountered once the control surfacedeflection is too important. This phenomena also explains why the hypothesisof the linear behavior of the hinge-moment with respect to the deflection angleis not valid in the investigated cases. Indeed, this linear relation is only validfor small angles of deflection (generally considered inferior or equal to 10°).It is possible to observe in table 4.12 that the hinge-moment determined fromthe linear relation is overestimated for the 15°deflection while underestimatedfor the one of -22.4°.

5.2 KinematicsThe kinematic analysis was carried out under the assumption that themotion ofa pushrod is always described in a plane and that the pushrods are always ori-ented parallel to the horizontal or vertical plane. The results presented in table4.16, 4.17, 4.19 and 4.21 highlight a good matching of this method comparedto the CAD values, which can be considered as a reference. An error rangebetween 1 and 2% is observed for most of the values calculated. However,a difference of about 17% has been found for αaileronup , d7up and α6up . Thisdifference is explained by the three-dimensional orientation of the pushrodlinking the aileron to the last crank-bell, which is also being angled comparedto the frame of reference. The specific orientation of these pieces introducesangles that are not taken into account and modifies the value of the displace-ments.Building an accurate model based on the coordinates of each pushrod-endpoints at their neutral position is possible and would account for the real ori-entation of each component of the mechanism. However, for such calculationmethod, all the components of the kinematic chain need to be defined spatially,which was not the case by the beginning of this work.

Chapter 6

Conclusions

The goal of this thesis was to determine the aerodynamic loads applied on theprimary flight control surfaces of an aircraft and design the kinematics of theprimary flight control system. This, ensuring to obtain the desired deflectionsfor a safe handling of the prototype SFX1. Linked to the kinematics definition,a section was dedicated to the determination of the forces in each componentsof the kinematic chain to ensure reasonable stick forces and prepare bucklingcalculation for sizing.

The aerodynamic loads were investigated with the help of three differentmethodologies. One was based over the widely referenced book "DATCOM"fromMcDonnell Douglas Corporation, the second relied on the VLMmethodand the third consisted in computational fluid dynamicswith Reynolds-averagedNavier-Stokesmethods. The results underlined the limits of the two firstmethod-ologies to cope with the study case, especially to deal with separated flow andto properly consider the real geometry of the aircraft. Thus, the aerodynamicloads obtained by analytical and XFLR methods were found to be in agree-ment with each other but overestimated by about 35% compared to CFD.

The kinematics was initially handledwith the analyticalmethodology basedon kinematics drawings and trigonometrical formulas, with the hypothesis ofplanar motion of the pushrods. A good reliability of the method was illustratedthrough the results which were compared to CAD values serving as reference.However, it also illustrated the limit of the method when three-dimensionalmovements are encountered.

Finally, the work achieved in terms of aerodynamic loads and kinemat-

49

50 CHAPTER 6. CONCLUSIONS

ics was used to determine the forces to which is submitted each componentof the flight control mechanisms. Pilot control forces were calculated as wellto verify that a human pilot is capable to fully deflect the control surfaces atmaneuvering speed. An optimisation of the gearing ratio in the kinematicsrepresents a possible future work on that topic to take into consideration theergonomic aspect of the flight controls.

In a broader scope, this work can be used with the aim of sizing the variouselements forming the flight controls and contribute to the detailed design of theaircraft subsystem. This is especially important for the sizing of the pushrodswhich are prone to buckling. The determination of the resulting load in eachpivot axis can also serve as an input for the sizing of the ball-bearings and inthe design of the anchor points to the fuselage.

Bibliography

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[15] McBain G.D. Theory of Lift: Introductory computation aerodynamicsin Matlab/Octave. Fifth Edition. John Wiley and Sons, Ltd, 2012. isbn:9781119952282.

[16] Wendt John F. et al. Computational Fluid Dynamics: An Introduction.Third Edition. Springer, 2009. isbn: 9783540850557.

[17] Versteeg H K and Malalasekera W. An Introduction to ComputationalFluidDynamics. Second Edition. Pearson Education, 2007. isbn: 9780131274983.

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[20] LarsDavidson.An Introduction to TurbulenceModels. Tech. rep. ChalmersUniversity of Technology, Department of Thermo and Fluid Dynamics,August 16, 2018.

[21] Why choose OpenFOAM® instead of STAR-CCM+® or ANSYS® Flu-ent? https://www.totalsimulation.co.uk/choose-openfoam-instead-star-ccm-ansys-fluent/. Accessed:2020-01-15.

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54 BIBLIOGRAPHY

Appendix A

Glossary

Abbreviation Elaboration

IATA International Air Transportation Association

AoA Angle of Attack

LLT Lifting Line Theory

VLM Vortex Lattice Method

FDM Finite Difference Method

FEM Finite Element Method

FMV Finite Volume Method

CFD Computational Fluid Dynamics

RANS Reynolds-averaged-Navier-Stokes

DNS Direct Numerical Simulation

EASA European Aviation Safety Agency

HTU Horizontal Tail Unit

AST Anti Servo Tab

CG Center of Gravity

CAD Computer Aided Design

ISA International Standard Atmosphere

BIBLIOGRAPHY 55

Appendix B

Figure 1: Resultant aerodynamic force and the components into which it splits[7]

Figure 2: Nomenclature for the integration of pressure and shear distributionover a two-dimensional body surface [7]

56 BIBLIOGRAPHY

Figure 3: Distributed horseshoe vortices over a swept wing with 12 panels [9]

Figure 4: Forces exerted on the SFX1 during rotation at take-off with theirrespective application point

BIBLIOGRAPHY 57

Figure 5: Illustration of the Anti-servo tab and the trim mechanism

Figure 6: Forces of interest resulting of the tail aerodynamic loads

58 BIBLIOGRAPHY

Figure 7: Illustration of the HTU modelling with XFLR5

Figure 8: Illustration of the calculation of the TE angle for a control surface

BIBLIOGRAPHY 59

Figure 9: Definition of aileron geometry [28]

Figure 10: Aircraft roll rate response to an aileron deflection [27]

Figure 11: Section view of the wing profile with the aileron

60 BIBLIOGRAPHY

Figure 12: Maximal pilot forces advised in CS-23, amendment 4 [32]

Figure 13: AST deflection for a tail deflection of 5°

BIBLIOGRAPHY 61

Figure 14: AST deflection for a tail deflection of -13°

Figure 15: CAD model of the flight control kinematics

62 BIBLIOGRAPHY

Figure 16: CFD simulation: wall shear stress along longitudinal axis illustrat-ing flow separation at the AST

Documents

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