Motorcycle Cornering Improvement: An AerodynamicalApproach based on Flow Interference

A Master Thesis in Fluid Mechanics

Author: Vojtech Sedlak

Supervisor/Examiner: Alessandro TalamelliTechnical Advisor: Stefan Wallin

Department of Mechanicsand

Department of Aeronautical and Vehicle Engineering

Royal Institute of Technology KTH 2012

Contents

Nomenclature 1

1 Introduction 31.1 Early History of Motorcycle Aerodynamics . . . . . . . . . . . . . . . . . . . 31.2 Focus on cornering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Serious Attempts on Wing Use . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Project Overview 82.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Mechanical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Evaluating the Effect of Interference . . . . . . . . . . . . . . . . . . . 122.2.3 Anhedral angle effect on Vertical and Horizontal Forces . . . . . . . . 142.2.4 Overall performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 Speed estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3.1 Airfoil Selection: NACA 23015 . . . . . . . . . . . . . . . . . . . . . . 18

3 Problem Specification 193.1 Identifying Variables - The Buckingham Pi Theorem . . . . . . . . . . . . . . 193.2 Problem Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Predicting Near-wall Cell Size . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Numerical Approach 234.1 Work Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Numerical Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5 Preliminary 2D test-case 265.1 Geometrical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.3 Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.4.1 Airfoil Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.4.2 Interpretation of Interfered Airfoil results . . . . . . . . . . . . . . . . 305.4.3 Interfered Airfoil at α = 0◦ . . . . . . . . . . . . . . . . . . . . . . . . 315.4.4 Interfered Airfoil at α = 4◦ . . . . . . . . . . . . . . . . . . . . . . . . 325.4.5 Interfered Airfoil at α = 8◦ . . . . . . . . . . . . . . . . . . . . . . . . 34

6 Simple 3D case 386.1 Geometrical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396.3 Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

7 Final Concept 43

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8 Discussion 458.1 Additional Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458.2 Further improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

8.2.1 Higher top speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

9 Conclusion 47

Acknowledgments 48

A Appendix: Data 49A.0.2 Data for 2D cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49A.0.3 Data for 3D cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

B MotoGP Regulations 2012 52

2

Abstract

A new aerodynamic device, based on flow interference effects, is studied in order to signifi-cantly improve the cornering performance of racing motorcycles in MotoGP.After a brief overview on why standard downforce devices cannot be used on motorcycles,the new idea is introduced and a simplified mechanic analysis is provided to prove its effec-tiveness. The concept is based on the use of anhedral wings placed on the front fairing, withthe rider acting as an interference device, aiming to reduce the lift generation of one wing.Numerical calculations, based on Reynolds-averaged Navier-Stokes equations, are performedon simplified static 2D and 3D cases, as a proof of concept of the idea and as a preparationfor further analysis which may involve experimental wind-tunnel testing. The obtained re-sults show that the flow interference has indeed a significant impact on the lift on a singlewing. For some cases the lift can be reduced by 70% to over 90% - which strengthens thepossibility of a realistic implementation.

Abstract in Swedish: Sammanfattning

Ett nytt aerodynamisk koncept som nyttjar effekter av flodesinterferenser ar utvarderat isyfte att pa ett noterbart satt forbattra en roadracing-motorcykels kurtagningsmojligheter.Efter en kort genomgang av varfor diverse klassiska “downforce” losningar ej ar applicerbarapa motorcyklar, presenteras det nya konceptet. Varpa en mekanisk analys genomfors i syfteatt se over dess tillampbarhet. Konceptet bygger pa anhedrala vingar som placeras pa denframre kapan, dar foraren agerar som ett interferensobjekt, och forsoker stora ut lyftkraftensom den ena vingen genererar. Numeriska berakningar baserade pa RANS-ekvationer arutforda i forenklade statiska 2D och 3D fall. Som ett vidare steg rekommenderas vindtun-neltester. Resultaten visar att flodesinterferenser ar ytterst markbara for vingar och i vissafall kan lyftkraften reducerats med 70–90%. Detta forstaker mojligheten for en realistiskimplementering.

Nomenclature

Symbols

Aw area of a wing [m2]bw half-span of a wing [m2]Cd, CD drag coefficient for 2D, 3D case [-]Cf friction coefficient [-]CI interference coefficient [-]Cl, CL lift coefficient for 2D, 3D case [-]cr airfoil chord length [m]dc diameter of interference device[m]~F , F force vector, force [N]g0 sea level gravity constant, 9.81 [m/s2]K turbulence kinetic energy [m2/s2]k number of fundamental dimensions [-]l∗ viscous length scale [m]~M , M moment vector, moment [Nm]M∞ free stream Mach number [-]m mass [kg]m0 mass motorcycle [kg]mr mass rider [kg]N normal force [N]n number of independent physical variables [-]P mean static pressure [N/m2]p static pressure [N/m2]p′ fluctuating pressure part [N/m2]~R, R reaction force vector, reaction force [N]rc radius of a corner [m]~r distance vector [m]Recr Reynolds number for an airfoil chord[-]ReL Reynolds number for specific lenght[-]Sij mean strain rate tensor [s−1]T temperature [K]U mean velocity [m/s]u′ fluctuating velocity part [m/s]uτ friction velocity [m/s]v velocity [m/s]xc position of interference device in x-direction [m]yc position of interference device in y-direction [m]yn wall-distance [m]y+ normalized wall-distance [-]α angle of attack [◦]δij Kronecker delta [-]µ dynamic viscosity [kg/(m s)]µs static friction coefficient [-]ν kinematic viscosity [m2/s]νt turbulence eddy viscosity [m2/s]Π dimensionless product [-]Πcount number of dimensionless products [-]ρ density [kg/m3]τw wall shear stress [N/m2]φwing anhedral angle of wing [◦, rad]ϕlean lean angle of motorcycle [◦, rad]

1

Acronyms

CAD Computer Aided DesignCFD Computational Fluid DynamicsFIM Federation Internationale de MotocyclismeFL Finish LineRANS Reynolds-averaged Navier-Stokes equationVLM Vortex Lattice Method

Constant values

To avoid any misconceptions, due to different definition-style in various literature, followingvalues yield throughout this document. They are mainly based upon the standard values providedby Ansys Fluent.

g0 9.81 [m/s−2]ρ∞ 1.225 [kg/m3]µ∞ 1.7894e-05 [kg/(m · s)]T∞ 288.16 [K]

2

Chapter 1

Introduction

A first thing to identify is what motorcycle type should be subjected for improvement.Clearly when aerodynamics is the topic, the fast going road racing machines are the oneswith most to gain. The road racing motorcycle is a definition that includes all types ofmotorcycles that may compete by doing laps or sprint races on paved, closed down, purposebuilt race tracks. These tracks have a high number of corners, thus making cornering speedand agility a key element for success.Within road racing, there are several different categories in which motorcycles may compete.Mainly there are two premier classes. One that is referred to as MotoGP - a category purelyfocused on prototype racing with less strict regulations in an attempt to encourage creativethinking and development. The other category is Superbike World Championship where thefocus is to get as much racing for as small cost as possible. This results in production bikesthat are heavily regulated.As this thesis aims to provide a plausible aerodynamic cornering improvement, the aim isto be within the more lenient MotoGP regulations. However, the aim is not to present afinal concept, but merely to provide some basic analysis whether the idea is at all realisticor not.

1.1 Early History of Motorcycle Aerodynamics

In the early years much of the focus regarding aerodynamics for motorcycles, was simplyfocused on streamlining. And very much so, various concepts that were brought to light,would challenge different speed-records of the day. The idea was basically to create a tear-drop shaped faring that would cover the rider as much as possible. They also tried to buildthe motorcycle as low and narrow as possible to reduce the frontal area.

Figure 1.1: Left: In early 1950’s the typical “dustbin” fairing were popular as shown byGiulio Carcano’s Moto Guzzi. Right: In 1957 FIM banned these types of fairings and the“dolphin” shape quickly became the norm. [5]

However, these massive fairings turned soon out to be dangerous in crosswinds and cumber-some when cornering. It soon became clear, that to make fast and safe motorcycles, which

3

can go around twisting race tracks, many other considerations had to be taken into account.This led to motorcycles with more open, yet sleek, fairings. A concept which seems to havestood the time, since the basics layout, appears to be similar to even todays machines.Knowing this, raises the question whether the industry is reluctant to change or if this basicconcept is actually so good, that any radical changes will most likely fail. What is known, isthat countless attempts have been made to improve on this classic design. How many andwith which ideas, is something one can only speculate, since these sort of things are usuallyclose guarded secrets.

1.2 Focus on cornering

It is clear that if one would find a way of how to improve cornering, the advantage would besubstantial. A typical MotoGP track consists of a high number of sweeping corners. Eventhe majority of road sections that are between corners, that may look like straights, areactually no real straights since the motorcycle has to prepare for the next corner right away.In section 2.3, an example is given of the traditional racing track TT circuit Assen. Noticehow turn 1 to 4 can be considered as a one sweeping corner.Cornering can obviously be improved by aerodynamic means. Placing a wing that createsnegative lift (downforce) increases the normal force, thus enabling the static friction forceto reach higher values.

v [km/h]

C = –2L

In�uence of Lift coe�cient during Corneringon a vehicle for unbanked turns

r [m]c

C = –1L

C = 0L

equation: μ mg – C ρ v A =s 0 L ∞( (12

2 mvrc

2

values: μ = 1

m = 600 kg

A = 1.47 m

s

2

50 100 150 200 250 300

100

200

300

400

500

600

w

w

Figure 1.2: Visualization of the great speed advantage a higher downforce can provide. Insome cases the speed can be more than doubled.

In figure 1.2 an example is given where a simplified vehicle is cornering at various cornerradii. The figure shows that if the downforce is increased (CL = -2) the vehicle may go morethan twice as fast through corners with low curvature.There are some radical concepts that have been implement in the past, based on this way ofthinking and some of them reached the public attention and curiosity. One of these conceptswas conceived by a university student, Rodger Freeth in 1977 (figure 1.3). He added twohorizontal wings, in the front and back with the hope that it would create extra downforceon the tires in mid-turn, to improve cornering speed. The largest wing was placed behindthe rider, mounted on the back of the rear sub-frame and had a span of 700 mm with achord of 245 mm. The front wing was attached to the lower fork sliders and had a span of660 mm and chord of 130 mm. [10]

4

Figure 1.3: Rodger Freeth and his concept “Aerofoil Viko TZ750A” from 1977 [10]

Naturally, when a motorcycle is leaned into a corner, this wing will generate negative lift(downforce) at the angle at which the bike is leaning. This will not only generate a verticalforce component which will make the bike stick to the ground. It will also add to the lateralforce component, pushing the bike of the track. Perhaps back in 1977, when Freeth wasracing his bike the lean angles were not so great, maybe not even scraping his knees. Todaythese lean angles can typically reach over 50◦. In such case the lateral force componentbecomes greater than the desired vertical one. On top of all that this concept got bannedby the controlling body, due to the great risk of entanglement in close racing.As many have pointed out over the years a far better concept would be to mount the wingson a gyroscopic tilting device. Thus making sure that no matter what lean angle, the wingswould always be parallel to the ground. This way the lateral force component would beeliminated. Even if such device would be allowed, the placement would remain a problem.It is important to place the wings in the undisturbed free-stream. That would mean eitherplacing it above the bike or on the sides. The bike itself is usually about ∼500 mm wide(excluding handlebars), so to put them on the sides would add major width (since they haveto be of a significant size). On top of all that they would have to be movable, which addsadditional level of complexity to the design and makes them unusable in competitive racingas MotoGP due to regulations (Appendix B).

Wing

Vertical force

component

Lateral force

component Tilting Wing

Vertical force

component

Front/rear view Front/rear view

N

μ N

Fx

Fy

N

μ N

Fy

s s

Figure 1.4: These are the forces generated by a fixed- and a tilting-wing, during cornering.The idea is that a tilting wing is stabilized and is always positioned parallel to the ground.This way it would not produce any lateral force components.

5

1.3 Serious Attempts on Wing Use

However, there are applications where small wings (or devices more similar to bulges) in thefront of a bike can make themselves useful. It is when there is a need to reduce front-endlift at high speeds. A phenomenon which occurs due to the fact that a motorcycle alwayshas a relatively high profile in the vertical direction compared to its wheelbase. Thereforea pitching moment, created by the drag of the airflow is far more noticeable than for e.g alow car. [5]

Figure 1.5: This type of front wing is made to reduce front-end lift. Here it can bee seen onBarry Sheene’s Suzuki RG500 from 1979. [10] [11]

This type of device can be seen on motorcycles as the BMW R100RS (1977) and on GrandPrix road-racing machines as the Suzuki RG500 from 1979 (see figure 1.5). This trend hasapparently not made the desired impact, since this concept was dropped only a short timelater, or at least Suzuki did not implement them on GP bikes the following seasons. Mostlikely, the trade-off was an inferior cornering ability, which simply was not worth it.At the end of the 2009 season, in Sachsenring, Ducati introduced a similar concept. Here thewings were far more distinctive and placed in the front of the fairings. They also featuredsmall winglets. The concept only lasted though the rest of that season and was abandonedafter the next years pre-season testing.

Figure 1.6: From 2009 to 2010 Ducati attempted to use straight small wings at the front ofthe fairings. Unfortunately the idea was abandoned. [2]

6

Regarding the Ducati wings, there are also some unofficial claims and speculations, thatthe mounting of such wings also creates a low pressure area where the radiator outflowis normally situated. This will then increase the flow through the radiator and helps thecooling. One can argue if there perhaps are not easier ways to achieve the same effect.Another difficulty that aerodynamic concepts, as the ones mentioned, has to face is thateventually the rider is the one who has to feel all the advantages. This is the only way itmay be added to the motorcycle and incorporated into the riding. A good example of howa good theoretical idea can end up in a blind alley is the Hossack suspension concept. Itshowed a lot of promise in theory. In the end it did not become a success due to its higherweight with combination of the riders dislike towards the different front-end feel. The thingis that riders spend most of their careers adapting, getting used to and trying to understanda certain system (e.g. telescopic-forks). A change can throw them of too much if the gain isnot clear.

7

Chapter 2

Project Overview

This thesis aims to present an idea – a concept – and provide initial estimations of whatit might be like, when it has reached a prototype stage. As is usually the case, this idea isfairly simple in theory, but to attain it practically may be a bit of a challenge.

First stage will be to present an overall theoretical idea, on which this concept is build upon.In a brief way it will show the advantages and the weak points. To give a quantitative firstlook, simple mechanical estimations will be given to see what can be achieved in an idealscenario.The main phase will then be to see if these mechanical goals can be achieved by the useof certain aerodynamic hypotheses. These hypotheses will be put to test in several CFDcalculations and their prospective validity will be obtained and quantified.Conclusively, all of the above considerations will be put together in a final concept. It willshow what it is all about, but there will obviously be room for plenty of further improvements.

2.1 Concept

To begin with, when a motorcycle is cornering it will do so at a significant lean-angle. Withthe rider hanging-out, which is typically done to reduce the lean angle, the airflow aroundthe rider and the bike becomes asymmetric.On one side the flow is moving relatively smoothly and on the other, the rider acts as asort of interference mechanism. The rides is interfering with the streamlined flow, makingit deviate which in turn alters the resulting reaction forces. Since the flow is subsonic andacts in streamlines, it is highly sensitive to interactions occurring up and downstream.The great thing about this is that in practically all motor racing, mechanically movableaerodynamic devices are prohibited. However the rider on a motorcycle, is to some extentmovable and is affecting the flow around the motorcycle.

What this concept is all about, is that one could greatly improve cornering by placing highlyanhedral wings on both sides of the motorcycle (see figure 2.1). Making sure they are placedclose to the rider – at such an anhedral angle, when the bike is cornering, one of the wingswill become horizontal and the other, vertical. This way, the horizontal wing is generatingnegative-lift (downforce) and the other one is adding to the unwanted lateral force.However, with the rider acting as a movable interference device (see figure 2.2), the wingwhich is generating the lateral force, is now partially disturbed. Thus there will only be asmall addition to the lateral force.An important thing to note here is that the wings will have to be placed on the front fairing,after the radiator inlet and in front of the riders knee and/or elbow. To place wings behindthe rider is not recommended due to low maximum width restrictions and the high risk ofthe rider getting tangled up in it during a crash.When the motorcycle is going down the straight at full throttle, the increased drag on thewings will naturally deprive it of its maximum speed. The wings will however be of useduring the acceleration and braking by pressing the front to the ground.The most important question is, whether this interference effect is significant enough. Aquestion which will be evaluated in this report.

8

Front view Front view, while cornering

Anhedral wings

on both sides

While cornering,

one is horizontal

...the other one

is vertical

Figure 2.1: The idea is to place anhedral wings on each side of the motorcycle, which willgenerate lift in the direction of the arrows. When the bike is leaned into a corner, ideallyone wing is horizontal and the other one is vertical...

but, the rider may

interfere the !ow

around the vertical wing

Figure 2.2: ...The rider will then interfere with the flow around the vertical wing, reducingthe horizontal force component.

Furthermore, there are other areas which may have a crucial impact on the actual appli-cability. One of them is stability during transition from uninterfered state to a interferedone. The risk is that too sudden movements or changes of rider’s position may unsettlethe bike. Similar risk may occur when the rider enters someone else’s slipstream. Theslipstream problem is a well known phenomenon in F1 racing, at least a well debated one.The solution there, seems to simply cope with it. To be aware, but not to concern too greatly.

Advantages:

- Downforce increased during cornering, i.e increased cornering speed.

- Acceleration improved by decreasing pitching and roll moment.

- Breaking distance shortened.

Downsides:

- Higher drag will reduce top speed.

- Interference effect may not be significant enough.

- Due to geometry restrictions, wings may have to be small in size.

- The motorcycle might get unstable when the rider moves into cornering positionquickly.

- Slipstreaming may disrupt stability.

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2.2 Mechanical aspects

To get a more clear understanding of how this idea may be of use, a simple clarificationof the mechanical forces is in order. What will be looked at is how the cornering may beaffected with such wings mounted. This suggests that a 2D example with a frontal view ofthe bike is in order. Where the horizontal x-axis is pointing in the direction of the centripetalacceleration and the y-axis is the vertical component (see figure 2.3). The z-axis is pointingout of the plane and is only used to show the moment. To simplify things even more, straightline flow is assumed.

c0 = 6

00c1 = 7

00

c2 = 8

00

c3 =

200

c4 =

70

b = 300w

x

yφlean

Fm Fr

Fw2

Fw1

mass centermotorcycle

mass centerrider

downforce point 2

downforce point 1

rr

rw1

rw2

rm

ϕwing

N

M0

μ Ns

Figure 2.3: A simplified model of a cornering motorcycle.

This figure introduces a fair amount of variables which all follow a very simple system. Allvectors denoted ~F contains forces in x and y direction and in the same manner, vectorsdenoted ~r contains positions. When trying to obtain the moment (see equation 2.11) thecrossproduct of these two vector types will give the result.The most fundamental force components are the ones acting on the bike and rider. Thesetwo forces could have been merged together, but it is more flexible to keep them separatedshould one desire to investigate other rider positions.

Force vector ~Fm is acting on the motorcycle and ~Fr on the rider. Both are affected bycentripetal acceleration and gravity, only the mass is different. 160 kg estimated for themotorcycle [4, §2.5] and 70kg for the rider (it should be noted that some of the MotoGPriders weigh closer to 60 kg)

~Fm = m0

−v2/rc−g00

(2.1)

~Fr = mr

−v2/rc−g00

(2.2)

For a standard bike – here, referred to as the “reference case” – these forces would be theonly ones acting on it in this simple example (if one excludes resultant normal forces). Abike equipped with anhedral wings, will also get contributions from the force componentscaused by lift.

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~Fw1 =1

2CLρ∞v

2Aw

cos(φw1)sin(φw1)

0

(2.3)

~Fw2 =1

2(1− CI)CLρ∞v2Aw

cos(φw2)sin(φw2)

0

(2.4)

These equation introduce a new set of variables and to make estimations easier to follow,these are the values they have been set to.

Used values for wings

CL = 1.7 (lift coefficient)bw = 0.3 m (span of one wing-part)cr = 0.2 m (root chord of the wing)Aw = cr · bw = 0.06 m2 (area of one wing)

What differentiates the interfered wing with the other one is the interference coefficient CI .This variable may typically attain values between 0 and 1. Where 0 is no interference – thewing is generating lift in an undisturbed fashion. If the value reaches 1, the wing generatesno lift, i.e. it is fully interfered. Further details are explained in section 3.1.

CI =∆CLCL

= 0 . . . 1

The angle for the uninterfered wing φw1 and the interfered wing φw2 is the resulting angleof both the lean angle ϕlean and the anhedral angle of the wings φwing.

φw1 = −ϕlean + φwing −1

2π (2.5)

φw2 = −ϕlean − φwing +3

2π (2.6)

It is clear that the above approach results in a complex geometry which can be significantlysimplified. This can be done by creating a “center of pressure”. A point where all of thedifferent lift forces intersect and can be converted into a single force (figure 2.4).

A new vector is formed ~Fw and replaces the old force vectors acting on the wings. Thisvector can be describes as a function of the lean angle and of the interference coefficient.The ~Fw vector will then point from the center of pressure, rcp, in a direction ϕcp.

~Fw = f (CI , ϕlean) (2.7)

The problem here is that if the anhedral angle φwing is changed, both the position of thecenter of pressure rcp will be moved and the angle ϕcp will be affected. Therefore, if oneintends to keep the geometry fixed, the simplification by the use of center of pressure issuggested. In following sections however, different choices of anhedral angles are investigatedthus making the initial setup more flexible, despite its greater complexity.

2.2.1 Calculations

To establish a resultant force, denoted ~F0 in the both the x and y direction is fairly straightforward. Summarize all the force vectors and introduce normal forces. The resultant forcefor a bike with no wings has the index “ref ”, suggesting it is a reference case. Equilibriumis reached when the resultant force, ~F0 is equal to zero.

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c0 = 6

00c1 = 7

00

c2 = 8

00

c3 =

200

c4 =

70

b = 300w

rcp

x

yφlean

Fm Fr

Fw2

Fw1

mass centermotorcycle

mass centerrider

downforce point 2

downforce point 1

rr

rw1

rw2

rm

ϕwing

N

F = f(C ,φ )w

φcp

I lean

center ofpressure

M0

μ Ns

Figure 2.4: The same model with the use of center of pressure.

~F0,ref = ~Fm + ~Fr +

µsNN0

(2.8)

~F0,concept = ~Fm + ~Fr + ~Fw1 + ~Fw2 +

µsNN0

(2.9)

Next step is to set the equation for the moment. This way the roll-moment of the bike canbe established. The result is simply obtained by adding crossproducts of distance vectors ~rand force vectors ~F .

~M0,ref = ~rm × ~Fm + ~rr × ~Fr (2.10)

~M0,concept =(~rw1 × ~Fw1 + ~rw2 × ~Fw2

)+ ~rm × ~Fm + ~rr × ~Fr (2.11)

These equations are then combined, solved and used for all of the following mechanicalestimations in this chapter.

2.2.2 Evaluating the Effect of Interference

Primarily, the idea behind the anhedral wings is to give the motorcycle additional down-force. The downforce increases the vertical normal force N , which will give it the ability togo through a corner faster. It will also reduce the needed static friction coefficient µs if thecornering characteristics are kept the same.

Another interesting feature is that the anhedral wings can help to reduce the lean angle bygenerating a negative roll moment. It counteracts the moment caused by centripetal forcesacting on the mass center of the motorcycle and the rider.This advantage can give two different favorable outcomes. It can either let the rider go fasterthrough the corner, yet keeping the same lean angle as the standard bike. A very usefuladvantage when going through very long sweeping corner (figure 2.5).The other option is to maintain the same speed through the corner, but with the bike moreupright thus enabling more aggressive throttle roll-on and braking, enabling faster entranceand exit of the corner. This is refered to in motorcycle terms as “squaring it off” (figure 2.6).

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v [km/h]

C = 1 (ideal case)I

C = 0.9I

C = 0.7 (realistic case)I

reference case

Cornering speed over radius of curvatureat const. lean angle of 50°

r [m]c

100 200 300 400 500

100

150

200

250

300

Figure 2.5: A noticeably increase of speed in long sweeping corners is noted if the interferenceeffect is high. rc is the curvature radius of the corner.

0 10 20 30 40 50

100

150

200

250

300

350

v [km/h]

C = 1 (ideal case)I

C = 0.9I

C = 0.7 (realistic case)I

reference case

φ [°]

Cornering speed over lean angleat const. radius of curvature r = 600 m

lean

Figure 2.6: With a high interference effect, the lean angle is noticeably decreased.

A noticeable detail is the significant difference between the reference case and the conceptbike, when reaching high speeds. This is simply due to the fact that a wing generatesmore lift when the dynamic pressure is higher. As a result the advantages of the wingsbecomes more apparent. Unfortunately at low speeds, where the bike usually does a lot ofits cornering, the help of the wing is very small. A characteristic which all wings have incommon and is far from ideal in any motor racing.It is also clear that the higher interference coefficient CI we have, the better is the result.If however the interference would not be there, i.e. CI = 0, the curve would be exactly thesame as for the reference case. Even though there would not be a difference in moment, onehas to take into consideration that these wings also affects the lateral force. With the the

13

vertical wing undisturbed, the result would be far from favorable.Here it is also suggested that value of CI = 0.7 is consider realistic. This has not beenverified but it is nonetheless an unwritten goal in further chapters. If better values can beachieved it will only be favorable, but this value will be referred to when doing estimations.

2.2.3 Anhedral angle effect on Vertical and Horizontal Forces

An essential part of the wing layout is the selection of the anhedral angle. The initial proposalwas to use an anhedral angle which matches the maximum lean angle of the bike, typicallyaround 50◦. A reason is that if the anhedral angle is too small, even the uninterfered wingwill provide a certain negative lateral force component and work in a similar way as RodgerFreeth’s wing (see figure 1.3, left picture).Too high anhedral angle and the downforce during straight line braking and accelerationwill be reduced. Since the wings may not be mechanically movable (Appendix B), one hasto make compromises.

Beginning with the vertical forces (see figure 2.7) it is clear that a high anhedral angle isfar from the best choice. An interesting detail is also how all of these different setups havetheir own peak points regarding downforce. The very high anhedral angle setups naturallyhave their peak points far behind the maximum lean angle of the motorcycle.

lean

0 10 20 30 40 50

2300

2350

2400

2450

2500

N [N]

Vertical force on tiresat velocity 65 m/s (234 km/h), r = 600 m, C = 0.7

φ [°]

ϕ = 40°wing

ϕ = 50°wing

ϕ = 60°wing

reference case

ϕ = 70°wing

c I

Figure 2.7: A high anhedral angle provides a lower vertical force component

In this case the interference effect CI has been kept constant at a realistic value of 0.7, butif reduced further, the peak point of the curve will move to the left and drop off very quickly.

For the horizontal force, however, the aim is to keep this force as small as possible (figure 2.8).A lower horizontal force means less force pushing the bike of the track. In this case it israther the setup with the high anhedral angle which shows best results. If CI would bereduced, all of the the curves would increase in value and cut the reference curve at a lowerlean angle.

2.2.4 Overall performance

Thus far the force components and moments have been examined individually, showingdifferent characteristics. The next step is to put them together so that a complete overviewcan be visualized.

14

0 10 20 30 40 50

1450

1500

1550

1600

1650

1700

μ N [N]

Horizontal force on tiresat velocity 65 m/s (234 km/h), r = 600 m, C = 0.7

ϕ = 40°wing

ϕ = 50°wing

ϕ = 60°wing

reference case

ϕ = 70°wing

c I

leanφ [°]

s

Figure 2.8: Horizontal component will be lower with a high anhedral angle.

A good way to illustrate the total advantage of a certain setup, is to look at the total staticfriction coefficient µs, which will keep one from loosing grip, when the friction force is atits maximum. If one can manage with a lower µs, one can conclude that the rider on thatparticular bike can use a bit worse or more deteriorated tires.

140 160 180 200 220 240

0.4

0.6

0.8

1.0

1.2

1.4

ϕ = 40°wing

ϕ = 50°wing

ϕ = 60°wing

reference case

ϕ = 70°wing

Friction coe�. for di�erent velocitiesup to maximum lean angle (50°), r = 300 m, C = 0.7c I

v [km/h]

μ [-]s

Figure 2.9: Comparing the speed and the friction coeff. required to go through a fast corner

To bring this to a conclusion it is of interest to plot the friction coefficient over speed. Thisway all of the mentioned equations can be satisfied. The corner radius is 300 m which couldbe estimated to a 5th gear corner doing 230+ km/h through the apex. This scenario issimilar to the 8th corner of the TT Circuit in Assen, which is mentioned in the upcomingsection (see figure 2.11).What one can tell from this, is that if one can go through the corner at the maximum leanangle, the reference bike is 9 km/h slower, and requires a bit higher static friction coefficient

15

Figure 2.10: Jonathan Rea’s (WSBK) rear tire after race one in Misano 2010, shows greatsigns of deterioration. Notice that most of the deterioration occurs out on the edges of thetire, suggesting it has been exposed to very high loads at high lean angles. [3]

(better tires) to stay on the track. Since one may expect the tires to be completely finishedafter a race (which in MotoGP may last over 40 minutes), it should be considered a greatadvantage if one can stay competitive even on worse tires.An important detail to keep in mind, is that this mechanical model is very simple, so noconsiderations has been taken to the fact that the friction coefficient changes over lean angledue to the shape of the tire. This model is only intended for comparison with the referencecase.

16

2.3 Speed estimation

A very important factor to clarify, is in which speed spectrum the motorcycle may typicallytravel, when doing a lap of a generic road-racing circuit, in this case TT Circuit Assen. Thiscircuit has a good mix of slow and fast corners and will show what Reynolds numbers arerelevant and what dynamic pressure one may expect.Since the variation of speed is usually great it is helpful to divide it up in different categories.A typical procedure is to split it up, to see which gear is used for which corner. That wayone can separate the fast corners from the slow ones. Obviously this entire process is merelyan estimation, but should provide general characteristics.

N

TT Circuit AssenMotoGP 2012, Qualify, V.Rossi

1

2

3

4

5

6 7

8

9

10

1112

13

14

15

16

17

18

19

20

21

#2:119 km/h

#4:195 km/h

#3:110 km/h

#3:116 km/h

#2:70 km/h#4:219 km/h

#5:246 km/h

max 309 km/h

#4:162 km/h

#3:130 km/h

#2:111 km/h#2:106 km/h

#3:153 km/h

#5:227 km/h

#4:184 km/h

#2:103 km/h

#2:143 km/h

ma

x 2

40

km

/h

ma

x 285 km/h

max 291 km

/h

Figure 2.11: Current gear and lowest corner speed at the TT Circuit Assen. The values arefrom Valentino Rossi’s qualify lap 2012. It was not his fastest lap, but shows the genericcharacter of given sections.

TT Circuit Assen, 2012, qualify rossi

Corner Gear Speed– 291 (max speed in section i1/FL)1 2 1192 4 1953 3 1104 3 1165 2 707 4 219– 309 (max speed in section i2)8 5 2469 4 16210 3 130– 240 (max speed in section i3)11 2 11112 2 10613 3 15314 5 227– 285 (max speed in section i4)17 4 18418 2 10320 2 143

17

From previous table one can get an idea of the average speed for each corner-type basedon gears and the minimum corner speed. This will give an estimation of relevant Reynoldsnumber if the chord length of the used airfoil is cr = 0.2 m.

Summary of velocities for each corner type

Definition km/h m/s Recr Commentvc2g 109 30.2 4.13e5 Average 2nd gear cornervc3g 127 35.3 4.84e5 3rd gear cornervc4g 190 52.8 7.23e5 4th gear cornervc5g 237 65.7 8.99e5 5th gear corner

2.3.1 Airfoil Selection: NACA 23015

v∞

x

y cr

cr14

Figure 2.12: A standard NACA 23015 positioned upside-down.

This generic type of airfoil is good for low Reynolds numbers, especially around mentionedvelocity regions. It has a small camber which gives it a very standard feel, with a typi-cal stall point at 14◦. Another advantage is that it is a very well tested airfoil and offersno surprises. Simply ideal for initial test cases when one would like to test the validity ofa theory. Following velocities were obtained from available Reynolds numbers. [1, pp500-501]

Summary of available velocities for NACA 23015

Definition Recr km/h m/s Commentvref1 2.6e5 68.4 19.0 ∼1st or 2nd gear corner speed.vref2 6.0e5 157.8 43.8vref3 8.9e5 234.00 65.0 ∼5th gear corner speed.

The vref3 is particularly interesting due to the fact that that will be the speed region wherethe anhedral wings will be most helpful. For those reasons it is extensively used throughoutthis document.

18

Chapter 3

Problem Specification

In the previous chapter it has been concluded that there is much to gain from a conceptutilizing anhedral wings in terms of improved cornering. What has also been concluded, isthat this concept fully relies on whether the flow around the wings can be interfered.The greater this change, between a normal and an interfered wing, can be made, the moresubstantial will the effects of this concept be.

As a result of this, the main focus of this work will be to fully identify the effects of theinterference. By knowing what causes it and how it can be fully maximized, a well workingconcept can be derived.To archive this the best approach is to start with a very simple static examples and identifyall the variables that are important.

3.1 Identifying Variables - The Buckingham Pi Theo-rem

First question one may ask when trying to quantitatively identify the cause of a certaineffect, is which variables it depends on. Then the next step is to isolate them , except forone variable – which is being systematically manipulated. This manipulation will reveal thecause and effect of the specific variable.In this case there is a body which is being subjected to aerodynamic forces. The body is inthe most simplified case, an airfoil or a wing and some device which is interfering the wing.This device will in this text be referred to as an interference device and will in its mostsimple case be modeled as a cylinder (sized approximately as a human knee to represent therider).

These aerodynamic forces can be simplified to a one single force, a reaction force ~R. [7, §1.7]

~R = f(ρ∞, v∞, cr, µ∞, α, dc, xc, yc) (3.1)

This force is then a function of several different physical variables. Many of them may lookvery familiar, apart from the last 3 ones. These are related to the interference device andare the size dc (which may be the diameter size if the device is a cylinder), position inx-direction xc and y-direction yc.The strength of the Buckingham Pi Theorem is that both the amount of independent vari-ables can be reduced and they can also be made dimensionless which will significantlysimplify further calculations.A first step is to rearrange the previous equation (3.1) so that the function equals 0. Thisresults in a new function definition.

g(ρ∞, v∞, cr, µ∞, α, dc, xc, yc, ~R) = 0 (3.2)

Now the new function also depends on the reaction force, thus there is a total of 9 indepen-dent physical variables. This amount is here referred to as n, i.e. n = 9.The other value k, equals the number of fundamental dimensions. In mechanics, all physicalvariables can be expressed in terms of the dimensions of mass, length, and time. Thus thevalue k = 3.

19

This gives a relation for the amount of dimensionless Π products.

Πcount = n− k = 6 (3.3)

By setting up and solving all of the 6 dimensionless Π products it is possible to obtain acoefficient of the reaction force. The exact procedure is well explained in literature. [7, §1.7]

CR = f

(Recr ,M∞, α,

dccr,xccr,yccr

)(3.4)

The same procedure can be done for the other coefficients, of lift, drag, moment etc.

CL = f

(Recr ,M∞, α,

dccr,xccr,yccr

)(3.5)

CD = f

(Recr ,M∞, α,

dccr,xccr,yccr

)(3.6)

CM = f

(Recr ,M∞, α,

dccr,xccr,yccr

)(3.7)

This paves the way for the definition of the Interference coefficient. It has been said thatthis coefficient simply goes, in most cases between 0 and 1. Here it becomes clear that thedefinition is a bit more complex.

CI =∆CLCL

(3.8)

It is defined as the change of lift coefficient ∆CL, divided by the lift coefficient CL of theuninterfered wing. The ∆CL represents the difference in lift coefficient between the interferedand uninterfered wing.The interference coefficient may typically go between 0 and 1, but is not limited to onlythat. If the values are negative it will mean that not only has the reduction of lift failed,but it has done the complete opposite – it has made it increase. Assume on the other handthat the value is larger than 1. This will mean that not only has the wing been completelyinterfered, but now a lift force, going in the other direction has been created. This lattereffect may never happen for wings at high angles of attack with high lift coefficients, butrather for wings generating low lift in the uninterfered state.

3.2 Problem Overview

As the variables are identified, the next step is to have a plan on how to proceed. The bestthing to do would be to make a model and test it in a wind tunnel. This is however a greatundertaking which may consume a lot of time. Therefore it is a good idea to start withsome calculations and establish if this idea works in theory.

First thing to notice that this problem is in the region of high Reynolds numbers. Assum-ing the chord of the wing is 2 decimeters, the Reynolds numbers may vary from 200 000to up over 1 million (see section 2.3). This with the combination of a bluff body, therider, interfering the aerodynamic device, the wing, results in an unsteady problem. Whatthis means is that there are no analytical solution methods that can be used on this problem.

The approach is naturally use some form of numerical method on both the continuity equa-tion and Momentum equation, also known as Navier-Stokes equation. The Energy equationis not needed, since we can assume incompressible flow due to low Mach numbers. A goodchoice is to use the Reynolds-averaged Navier-Stokes equation which is a time averaged mo-mentum equation that uses Reynolds decomposition. The turbulence model was chosen tobe Spalart-Allmaras which is a very simple model, yet sufficient since the main task is todetermine lift and not drag.

20

Wind tunnel

ideaCalculations

• Reynolds Number too high

• Unsteady problem

• No analytical solution

RANS

• Good for lift estimations

• Can not resolve drag correctly

Fluid Domain

• Domain size restrictions

• Cell count restrictions

Simpli!cations

• Focusing only on the principle

• Setting up a static problem

Proof of Concept

Numerical Methods

To be on the safe side, key points have been solved using a more advanced viscous model,the SST (Menter’s Shear Stress Transport).As a numerical approach is used it also means that a fluid domain has to be defined andmeshed. This brings limitations to both the sizing of the domain and the amount of cellsthat can be computed.All the limitations mentioned will force one to try simplifying the problem as much as it ispossible and only focus on the basic principles. This also means to set up a static problemeven thou we know that the real problem will be a dynamic one. The rider is moving intothe interference position and this movement could cause some Hysteresis effects. For nowone may neglect such effects to see if the concept even works at this stage.

3.3 Predicting Near-wall Cell Size

The following section may be considered as slightly unnecessary, due to the fact that theaim of this project is not to resolve any turbulent vorticity which is needed for any accuratevalues of drag. However it is a good idea to have the knowledge of the desired mesh sizingand to know how far off, the actual mesh is.To figure this out one may evaluate the mesh grid type, which is used to resolve the viscoussublayer, and to consider the normalized wall-distance, y+.The normalized wall-distance can be expressed as a ratio between the wall distances yn andthe inner viscous length scale l∗. At the first grid cell, y+ needs to have the value of 1. [6,§12] [14, L06] If this can not be achieved the grid should be remeshed.Since the inner viscous length scale can be rewritten as kinematic viscosity divided by frictionvelocity, the equation becomes as following.

y+ =ynl∗

=ρ∞uτynµ∞

(3.9)

Where the uτ is the friction velocity, defined by the wall shear stress, τw. Also note thatthe kinematic viscosity has been replaced by the dynamic viscosity µ∞ divided by densityρ∞ to prepare the equation for further steps and also because these specific variables haveknown values.

uτ =

√τwρ∞

(3.10)

The wall shear stress, τw can be obtained from the friction coefficient, Cf , which in turncan be found in various literature. The one here is for the skin friction of a plate. [14, L06]

21

τw =1

2Cfρ∞v

2 (3.11)

Cf = 0.058Re−0.2L (3.12)

ReL =ρ∞vL

µ∞(3.13)

With following values,y+ = 1v = vref3L = cr

Then the yn = 5.19e-6 m. In the preliminary 2D test-case (chapter 5) the value that hasbeen used is 1e-5. In the following 3D case the first grid cell has a size of 5e-6, but herethe inflation (or prism-layer as it is called) uses wb-exponential growth rate which has a bitdifferent characteristics. The total thickness of the inflation layer is about 1 cm. [15, L5]

22

Chapter 4

Numerical Approach

The solver for the fluid dynamics part in this study is Ansys Fluent. A platform usedby many companies in the automotive industry which makes it the ideal working tool. Itprovides a wide variety of different solver settings which will be considered.An important thing to note is that the author only has access to one workstation and nota powerful cluster of any kind. This somewhat limits the number of details, precision andthe amount of different types of calculations that can be made. Fortunately the task isto investigate lift and not drag, which means that a coarser mesh and lot more simplecalculations are required.

4.1 Work Flow

Within each solver package, that one may choose, there are certain compability consider-ations. Usually there is one program to generate the geometry, another one to mesh it,another one to solve it and finally a program to present all the results. Naturally none ofthese programs communicate with each other very well and one may consider it a great featif one program can read what the other one has produced.Despite this there are ways of how go through all these steps in a fairly efficient manner.Obviously different users have their own preferences and may rather do most of the workin a single application, rather than split it all up. It is typically possible to do most of thesimple geometry building in a meshing applications, if one prefers to do so.Nevertheless, the process is to start with the generation of an airfoil and place it in a fluiddomain. Then generate a mesh from the domain and then solve it.

Airfoil generator(XFLR5)

CAD(e.g. Solid-Works/Edge)

2D-Mesh(Ansys Mesh)

3D-Mesh(Ansys ICEM CFD)

CFD Solver(Ansys Fluent)

Figure 4.1: Schematics of the work flow.

When generating airfoils it is recommended to use XFLR5, a freeware aimed at model-plane builders and provides features to quickly calculate simple incompressible flow. Thisapplication is especially useful when there is a need to generate standard NACA airfoils, asit has a build-in generator for those. Once the airfoil is generated it is exported to a DAT filewhich is then converted to a curve-geometry file. This part is made using a own developedconverting application, which has not only a capability to transform it, but also to projectit onto a desired plane.The curve-file is then imported into a CAD-program to create the surrounding fluid domainand add additional geometrical details that might be needed for the simulation.

23

As the geometry is set, it is necessary to mesh it. Depending on if it is a 2D or a 3D problem,different approaches are suitable. For the simple 2D case a more easy-to-do approach isto use the Ansys Workbench and set up a project schematics. Starting with importingthe geometry to the Ansys Geometry and then move to Ansys Mesh. Using the projectschematics is actually very convenient since all parts are connected and can be updatedfrom changes made upstream.For 3D cases the Ansys Mesh is just not practical enough. To have full control over inflationsizing and other elements it is preferable to use Ansys ICEM CFD, which provides far moreoptions and control. However, to import something into ICEM the best format to use turnedout to be IGS. Note that this format has a tendency to flip normal vectors of surfaces. Alsowhen the mesh is exported to a Fluent CAS file it can sometimes be corrupted. This is usuallycaused by corrupt mesh orientation, which may occur during volume mesh generation. Eachof these meshing approaches are discussed extensively in respective chapters.Eventually the mesh is imported into Fluent where it is solved using desired schemes. For3D cases it is convenient to use the CFD-Post tool to clearly see the different contour plotsand other visualizations.

4.2 Meshing

When dealing with airfoils the typical meshing approach is to have a coarse structure nearthe edges of the fluid domain and increase the quality near the objects, which are to beinvestigated.The first step is to decide whether to use structured or unstructured mesh. The advantagedof the structured mesh is that it can be solved much faster and there is rarely a noticeabletransition between the free stream an the boundary layer. In fact, when using structuredmesh one may even skip the process of creating a inflation layer (to properly resolve theboundary layer) and merely dense the mesh near a given surface.A clear disadvantage is the creation of a structured mesh, which usually is a tedious work.The cells get easily skewed and to fix this can be very tiresome. In this case there will bea lot of moving around of a certain interference device which will undoubtedly present newchallenges for each position.It is much more manageable to to use the flexibility of an unstructured mesh together withinflation layers, despite the extra solving time.

Figure 4.2: The unstructured mesh between the trailing edge of the airfoil and the interfer-ence device.

For those reasons an unstructured mesh is chosen and to resolve the boundary layer, whichforms at the wall of a given object, a inflation layer is constructed. The inflation layer istypically smallest in thickness near the wall and then it grows exponentially (or in any other

24

desired way) in the normal direction from the wall. It should do so until it covers the entireboundary layer. To achieve this one may have to go back after obtain the solutions fromthe solver and modify the specific mesh.If one uses a standard exponential grow, starting at reasonably small value (see section 3.3)with at least 30 layers, there is usually no problem to enclose the boundary layer.Then there is also the question of necessity, since this work mainly focuses on lift and notdrag. Lift is typically much less sensitive to a poorly made mesh, thus one may not have tobe all that concerned with the details.

4.3 Numerical Solver

Since only the lift is of the main interest, this part is way more easier than it normally wouldhave been. Because drag force is of little use, the vorticity generated mainly by the bluffbody does not need to be resolved in high detail. Also the Mach number is low which meansthat the flow can be treated as incompressible.The main problem with vorticity is that in reality it is transient, which means that thereis a need to incorporate times-steps into the solution process for good accuracy. However ifone uses time averaged solution models as the Reynolds-averaged Navier-Stokes equations(RANS), which uses Reynolds decomposition, one will get a time-averaged approximationof the problem. Here is the incompressible version:

ui = Ui + u′i and p = P + p′

∂Ui∂t

+ Uj∂Ui∂xj

= −1

ρ

∂P

∂xi+

∂

∂xj

(ν∂Ui∂xj− u′iu′j

)(4.1)

To further simplify the problem one may use Boussinesq expression for the turbulent stresstensor, which is used in Spalart-Allmaras one-equation model.

u′iu′j = 2νtSij −

2

3Kδij (4.2)

Here the Sij is the mean strain rate tensor, K is the turbulence kinetic energy and δij isthe Kronecker delta. All of these variables used standard values provided by Fluent andare described in the user manual. There are naturally many details to this, that could bediscussed further. Unfortunately such topics are also out of the scoop of this thesis, buthopefully the provided references will encourage further reading [6, §4] [13, §4.2].Nevertheless, this gives a low-cost RANS model which is known to give good results forboundary layers subjected to adverse pressure gradients. To validate the results a numberof key-points have also been solved by the use of a more complex solution model, the 4-equation model SST (Menter’s Shear Stress Transport). This more complex version ofRANS has the ability to predict transition from laminar to turbulent flow.The solution method is selected to Coupled Pressure-Velocity scheme with the use of 2ndOrder Upwind for Momentum and Modified Turbulent Vicosity. A coupled scheme uses upmore memory but converges faster. In some cases the convergence was improved with theuse pseudo-transient settings where correct length-scales were provided. This is particularlythe case for 3D problems.

25

Chapter 5

Preliminary 2D test-case

In this part, initial tests will be made using CFD. The focus will be on the positioning ofthe interference device behind a generic airfoil. Initially values for the uninterfered case willbe obtained (a case where you only have the wing and nothing is disrupting it). The nextstep is to place an interference device behind it and see what will happen to the interferencecoefficient CI or as it also can be referred to, ∆CL/CL.To gain a deeper understanding, the angle of attack α of the wing will be varied to see howthis affects the outcome.

5.1 Geometrical Setup

The geometry has been made with simplicity in mind. A 2-dimensional C-grid fluid domainaround an airfoil of standard type, NACA 23015 and a 2-dimensional cylinder. The dimen-sions of the fluid domain are 20 times the size of the airfoil chord, cr in all directions. Witha value of cr = 0.2 m, the domain is 4 m in all directions from the center of the airfoil.

x

y

v∞

�ow in

let

�o

w o

utl

et

4 m (20·c )r

4 m

(2

0·c

) r

airfoil 2D cylinder

Figure 5.1: A C-grid fluid domain containing an airfoil (NACA 23015) and a 2-dimensionalcylinder.

The center of the airfoil is defined at the 1/4 cr (one quarter of the chord length) and ispitched around that point to acquire the desired α. From the trailing edge of the airfoil

26

(when at α = 0 position) the distance to the center of the cylinder are measured. Thedistance is then defined as xc in the horizontal direction and yc in the vertical. Since theinterference device is a cylinder, it has a diameter defined as dc.Due to the criteria of having dimensionless values, all the cylinder diameter and distancevalues are divided by the chord length of the airfoil (details are in section 3.1). This way itwill be easier to compare values in graphs.

v∞

x

yxc

yc

α

Ø = dc

crcr1

4

Figure 5.2: A close up of the internal relations between the NACA 23015 airfoil and the2-dimensional cylinder.

With the given geometry and the flow velocity of v∞ = vref3 = 65 m/s. (see section 2.3.1)the next phase is to go through all of the different changes to obtain the comparable results.Following table shows which values are altered and with how much at each step.

Variables Min Step Maxα 0◦ +4◦ 8◦

xc/cr 0.5 +0.25 1yc/cr -0.2 +0.1, (+0.05) 0.4

Table 5.1: Variable Manipulation

5.2 Mesh

As stated before, the 2D meshing is done using Ansys Mesh and is accessed through Work-bench. The Mesh-method is set to Triangles since an unstructured mesh will be used. It isalso important to set all of the general mesh parameters:

Relevance center = FineSmoothing = highMin.Size = 1e-4

Next step is to define the Edge Sizing for the airfoil and the cylinder. For the top andbottom side of the airfoil, the element size is set to 8e-4 m. There is also a Bias Factor,which is set to 10 and a Bias Type that is specified so that the smallest cell-spacing is at theleading and trailing edge of the airfoil. Since the airfoil has a blunt trailing edge it workedbest just to set the Number of Divisions for that part to 8 with no bias. For the cylinder aEdge Sizing of 1e-3 is sufficient.For both the airfoil and the cylinder, following Inflation settings yield.

27

Inflationfirst layer height = 1e-5 mmax layer = 30growth rate = 1.15

After this is done, the next step is to let the Fluent solver iterate a few time (see the followingsection, 5.3). About 50 iterations should do the work and provide some information on howthe grid can be adapted.With the obtained results in Fluent a recommended next step is to adapt the velocity gra-dient. Let Fluent calculate the maximum velocity magnitude and then refine the thresholdby 0.001.Boundary adaptation is also a good improvement and a distance threshold 0.4 m for airfoiland cylinder is of good use.

Figure 5.3: The mesh improvement after adaptation between the trailing edge of the airfoiland the interference device.

The change of mesh by the use of adaptation brings new complications. Typically the gridsize increases and the Orthogonal Quality gets worse. In this case the quality is good enoughnot to be regarded as unacceptably low by Fluent, but one should keep in mind to be con-servative with the adaptation process. Note that Orthogonal Quality ranges from 0 to 1,where values close to 0 correspond to low quality. A value of 1e-2 is the lowest acceptablevalue by the solver, here the value for the adapted case is 2.60e-1.

Mesh Cells Faces Nodes Min Orth. Quality Max Aspect RatioInitial 37041 68575 31533 3.94e-1 2.05e2Adapted 157296 288754 131457 2.60e-1 2.06e2

5.3 Solver

With the use Spalart-Allmaras one-equation model the flow is then solved, using Coupledscheme and Second Order Upwind to solve both the Momentum and Modified TurbulentViscosity. In the figure below it is very clear that good results can be obtained fairlyquickly. Thus it is not necessary to extend the calculation, since even 400 iteration aresufficient enough for an uninterfered wing (see figure 5.4).The situation is a bit different for the interfered cases. It evidently requires more time tosolve due to a larger count of cells and more complex geometry. A good approach is to doapproximately 200 iterations and to get some preliminary results and then to adapt the gridbased on velocity gradient and near wall grid refinement. This will reduce the OrthogonalQuality but will however improve the quality of the result. From figure 5.5 it is also clear

28

Figure 5.4: Residuals for an undisturbed wing at α = 0◦, v∞ = 65 m/s.

that the residuals are struggling a bit more to reach low values. For those reasons it is goodto do about 2000 iterations to be on the safe side.

Figure 5.5: Residuals for an interfered case. α = 8◦, v∞ = 65 m/s, xc/cr = 0.5, yc/cr = 0

5.4 Results

The first step is to verify that the method works by comparing its results with the onesobtained from literature. Next step is then to do calculations for different variable manipu-lations as seen in the table 5.1. To reduce the amount of workload, the idea was to initiallyonly try a very limited amount of positions for the interference device. Initially only 4 posi-tions in vertical directions and only 3 in the horizontal. Since the vertical direction is moreinteresting this part was then refined for higher airfoil α.

5.4.1 Airfoil Properties

The verification of the standard NACA 23015, which is used throughout this thesis, under-went as expected. As seen in table 5.2, some of the values correspond very closely to thereference values obtained from literature [1, pp500-501].

α Cl Cd L/D0◦ -0.122 (-0.12) 0.0139 (0.006) -8.7514◦ -0.548 (-0.55) 0.0171 (0.007) -32.108◦ -0.952 (-0.97) 0.0178 (0.0085) -53.5712◦ -1.286 (-1.38) 0.0301 (0.013) -42.79

Table 5.2: Results for NACA 23015. Reference values in parenthesis.

29

It is mainly the lift coefficient Cl, which is very close to the reference case, but only forreasonable angle of attacks, α. As the angle α for the airfoil is increased, the airfoil isgetting closer to the stall-angle (which in literature is about 14◦). Even before this angleis reached, a separation bubble is starting to to form on the trailing edge of the airfoil andis noticeable at 12◦. Since the numerical model, which has been used, has a poor abilityto resolve vorticity in the wake of the airfoil, the lift at those angles is somewhat under-predicted. It should also be noted that the wake-thickness is significantly larger at α = 12◦

than at 8◦.For the drag coefficient Cd there is a systematic over-prediction which is due to the fact thatthe Spalart-Allmaras is a one-equation model which lacks the ability to predict transition.The entire flow is treated as turbulent, but in reality about one third of the airfoil should besubjected to laminar flow before the transition occurs. This can actually be visualized withthe use of SST, the 4-equation model. However, since only the lift interference coefficient isof interest the one-equation model is good enough for angles α up to 8◦.

Figure 5.6: Pressure over an undisturbed wing at α = 0◦, v∞ = 65 m/s

5.4.2 Interpretation of Interfered Airfoil results

To better illustrate how the position (of the interference device) affects the interferencecoefficient, there will be 3 main types of different figures/plots at disposal. At an initialstage only a results at a few selected few points will be obtained to get an idea of what maybe o interest. Then some of the more interesting cases will be refined and evaluated to geta better understanding.

Interference coefficient over distance xc/cr

This will show the change of interference coefficient as the distance between the airfoil andthe interference device is increased. On the x-axis of the plot, is a dimensionless distancevariable, xc/cr and on the y-axis is the interference coefficient. Different curves are thenshowed for different yc/cr positions. The idea is to clearly see what happens to the interfer-ence coefficient as you move away.

Interference coefficient over vertical position yc/cr

It is similar to the figure above, with difference that now the vertical position is of maininterest. Here the x-axis of the plot is used for plotting the changes of the interferencecoefficient, while the y-axis shows the vertical position. This type of figure is the one thatreceived most attention, since the changes in vertical positioning has shown some reallyinteresting results.

30

Contour plot for the Interference coefficient

Contour plots has 3 axises and here the x and y-axis has been reserved to the x and yposition of the interference device. The remaining z-axis shows the interference coefficientby the use of different contour colors.

5.4.3 Interfered Airfoil at α = 0◦

The first case to look into is when the angle of attack of the airfoil is α = 0◦. In these teststhe velocity is kept at v∞ = vref3 = 65 m/s, which corresponds to 234 km/h and could beseen as the speed though a 4th or a 5th gear corner.Since the airfoil has a little bit of camber it generates lift even at 0◦. The lift is smallhowever, which means that the resulting interference coefficient is a bit sensitive to changes,as will be seen.

0.5 0.6 0.7 0.8 0.9 1−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

ΔC /C over xl l c

{ v = 65.00 [m/s], α = 0°, d /c = 0.5 }c r

ΔC

/C

l

l

x /cc r

y /c = −0.10c r

y /c = 0c r

y /c = 0.10c r

y /c = 0.20c r

∞

Figure 5.7: There is a reduction of interference coefficient as the x-distance increases. Alsonote the huge interference spread at close distances.

Initially in figure 5.7 one may see the reduction of interference as the x-distance increases.It shows that it does not take much before all of the interference is mostly reduced. Onlya half length step in x-direction. This shows that if the rider wants to interfere the wingeffectively, he must be positioned close to the airfoil.In the vertical position only a few values has been marked out, to merely give an idea ofwhat is happening. It is clear that to position the interference device below the centerlineis to prefer.As mentioned before, at α = 0◦, the interference coefficient is very sensitive in the verticaldirection. This results in very high deviations, from -3 to 1.5 for the coefficient. When theinterference coefficient has a positive value higher than 1 it shows that there is actually alift force generated in the opposite direction. This would be very good if it was not for thefact that the airfoil is not generating much lift in the first place.In the contour plot all these values are put together and visualized with the help of differentcolors. The blue colors show low values for the interference coefficient while the red onesshow high. If one would place a interference device somewhere, it should be in the red area.

31

−3 −2 −1 0 1 2−0.1

−0.05

0

0.05

0.1

0.15

0.2

ΔC /C over yl l c

ΔC /Cl l

y /

cc

r

x /c = 0.50c r

x /c = 0.75c r

x /c = 1.00c r

{ v = 65.00 [m/s], α = 0°, d /c = 0.5 }c r∞

Figure 5.8: The interference coefficient may change rapidly for low α.

0.5 0.6 0.7 0.8 0.9 1

−0.05

0

0.05

0.1

0.15

0.2

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

y /

cc

r

ΔC /C contourl l

{ v = 65.00 [m/s], α = 0°, d /c = 0.5 }c r∞

x /cc r

Figure 5.9: The red colored area is the optimal place for the interference device.

5.4.4 Interfered Airfoil at α = 4◦

As the angle of attack for the airfoil is increased, the behavior of the interference becomesmore predictable. The old rule, that it decreases over horizontal distance remains unchangedas seen in figure 5.10.What becomes more clear, is the shape of the interference coefficient for the vertical positions(figure 5.11). The points at which results has been obtained, are still a bit too scarce to givea full view of the actual behavior. Despite this one may see that there is a clear build upon the lower side of the upside-down airfoil. Naturally it is impossible, with only 4 points

32

0.5 0.6 0.7 0.8 0.9 1−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

ΔC /C over xl l c

{ v = 65.00 [m/s], α = 4°, d /c = 0.5 }c r∞

y /c = −0.10c r

y /c = 0c r

y /c = 0.10c r

y /c = 0.20c r

x /cc r

ΔC

/C

l

l

Figure 5.10: Now the interference spread becomes lower at close distances.

at hand, to estimate where the actual maximums and minimums are, but for now it will do.From previous results it stems that the ideal position to place the interference device isslightly below the airfoil. This statement is based on a low number of points but gives inthis case a small overview. In the contour plot this ideal position can be spotted.

−0.2 0 0.2 0.4 0.6 0.8

x/dc = 1.00

xc/c

r = 1.50

xc/c

r = 2.00

−0.1

−0.05

0

0.05

0.1

0.15

0.2

ΔC /C over yl l c

{ v = 65.00 [m/s], α = 4°, d /c = 0.5 }c r∞

y /

cc

r

ΔC /Cl l

Figure 5.11: The interference coefficient becomes more predictable.

33

0.5 0.6 0.7 0.8 0.9 1

−0.05

0

0.05

0.1

0.15

0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

y /

cc

r

x /cc r

ΔC /C contourl l

{ v = 65.00 [m/s], α = 4°, d /c = 0.5 }c r∞

Figure 5.12: The ideal position does not change, but becomes more clear.

5.4.5 Interfered Airfoil at α = 8◦

This angle of attack is the most relevant of them all. It is an angle which is high enough togenerate significant downforce, yet is not so high that there are separations forming at thetrailing edge with a thick wake as a result. This is in fact the most relevant study and hasbeen subject for high refinement.

0.5 0.6 0.7 0.8 0.9 1−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

y /c = −1c r

y /c = −0.8c r

y /c = −0.6c r

y /c = −0.4c r

y /c = −0.2c r

y /c = −0.1c r

y /c = −0.05c r

y /c = 0c r

y /c = 0.05c r

y /c = 0.075c r

y /c = 0.1c r

y /c = 0.2c r

y /c = 0.4c r

y /c = 0.6c r

y /c = 0.8c r

y /c = 1c r

ΔC

/C

l

l

x /cc r

ΔC /C over xl l c

{ v = 65.00 [m/s], α = 8°, d /c = 0.5 }c r∞

Figure 5.13: Reduction of interference coefficient over the x-distance offers no surprises.

As before the interference coefficient decreases over horizontal distance as can be seen infigure 5.13. Now when so many points are being investigated in the vertical direction, a

34

more clear idea of the true behavior can be obtained.To fully understand this, the figure 5.14 is presenting very detailed results for when a in-terference device is at different positions behind the upside-down airfoil (which is trying togenerate downforce). On the right side of the figure are the contour-plots of the velocity,pointing at specific important results and are trying to illustrate the behavior and interac-tion between the wake of the airfoil and the interference device. There are 4 main positionsof interest.

1) Above the airfoil When the interference device is above the airfoil, interference is ac-tually the opposite of what one would hope for. It is the combination of the additionof higher pressure above the airfoil and the fact that the airfoil’s wake seems to bedrawn into the wake of the cylindrical interference device, which is being used here.Naturally if the shape of the interference device would have been different, so wouldthe wake interaction.

2) In the wake As the interference device is moved downward, the interference coefficientis increased and reaches a maximum point when the wake of the airfoil is hitting theinterference device straight on.

3) Sudden dip Moving the interference device further down will result in a sudden dipin interference coefficient. It is because now, the wake of the airfoil is being curvedaround the top of interference device and drawn into its wake.

4) Below the airfoil When the interference device is placed further below the airfoil, an-other peak-point is reached. It is due to the interaction of the wakes, but now in theopposite direction and the pressure buildup under the wing.

35

−0.4 −0.2 0 0.2 0.4 0.6 0.8 1−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

ΔC /C over yl l c

ΔC /Cl l

y /

cc

r

{ v = 65.00 [m/s], α = 8°, d /c = 0.5 }c r

x /c = 0.50c r

x /c = 0.75c r

x /c = 1.00c r

1)

2)

3)

4)

Figure 5.14: The change of interference coefficient and velocity contour plots at each position.

36

This clearly gives more insight into the true nature of interference in the purpose of reducinglift. What can be seen is that it has two main peak points and some unwanted points thatcan actually do the opposite of what is being attempted to achieve.

0.5 0.6 0.7 0.8 0.9 1−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

ΔC /C contourl l

{ v = 65.00 [m/s], α = 8°, d /c = 0.5 }c r∞

x /cc r

y /

cc

r

Figure 5.15: This contour plot shows the ideal (red) and less ideal (blue) positions to placethe interference device.

To summarize this entire case a contour plot is showing what it looks like when it is all puttogether. Interesting thing to notice is the clear discontinuity when the wake of the airfoilis trying to hit interference device.

37

Chapter 6

Simple 3D case

After the 2D case is complete the next step is to see if the same theory is valid for a 3D case.The setup is very similar to the one used in the previous chapter, only now the airfoil hasturned into a finite wing. With this in mind it will be interesting to see how the interferencecoefficient will fare with the somewhat changed situation. Typically when a airfoil is turnedinto a wing, there are losses connected to the wing-tip vortices. The question is how theinterference will be affected by this.

6.1 Geometrical Setup

A fluid domain of the same type as the one used for the 2D problem is used. That means aunstructured C-grid with inflow going in the positive x-directions and outflow on the otherside.

Upside-down Wing

(NACA-23015)

Stationary Wall

(no slip)

Interference Device

(Flat cigar or rounded cylinder)

x

z

y

Figure 6.1: The 3D fluid domain with a wing and a semi-infinite flat-cigar.

An important detail here is that nor the wing or the interference device have a span thatgoes all across the width of the fluid domain which is 2 m. The 3D fluid domain in totalis smaller than the 2D domain. About half as long and half as high. The reason for this isthat if a properly sized domain would be used, the semi-infinite flat-cigar would be just too

38

long which would complicate the meshing. If one would use full resolution the high numberof cells would be inconvenient and if coarsened, the rounded features of the geometry wouldsuffer.The decision is to use a domain that has at least 2 m in all directions from the pivotal pointof the wing. The wingspan is 4 dm for the wing and the interference device is just as wide.Other sizing values are kept the same.This small sizing of the fluid domain has evidently a bad effect on the quality of the re-sults. However if one considers other influences which may come in to effect, it is still verymanageable. One contributing factor is the low ability to resolve wingtip vortices.Either way, there are 2 different types of interference devices that will be used.

A 3D cylinder which is almost identical to the 2D cylinder, but has completely roundededges, meaning that the fillet radius is half of the cylinder diameter.

The 3D flat-cigar has basically the shape of a horizontally extended cylinder. The flatcigar is semi-infinite to show what kind of effects will be occurring when there is nowake interaction.

To make it more real the far side of the domain is modeled as a stationary wall with noslip condition, just like the airfoil and the interference device. All walls are meshed withinflation layers.

6.2 Mesh

For the 3D mesh it is preferable to use the Ansys ICEM CFD to have more control over thecomplex geometry. The surface meshing has been done using All Tri mesh type wich wasset to Patch Dependent for all surfaces, excluding the airfoil, interference device and the farwall. Those were set to Autoblock.The volume meshing was done using Tetra/Mixed mesh type with the help of Quick (De-launay) method which uses the TGlib scheme. In the volume mesh there are also inflationlayers, or prism layers are they are called in this application. The prism layers were appliedto all wall elements.

Inflationgrowth law = wb-exponentialinitial height = 5e-6 mheight ration = 1.2number of layers = 30approx. prism layer thickness = ∼9.1e-3 mMin prism quality = 1e-7

With all the mesh parameters set, both the 3D cylinder and the flat-cigars are meshed. Ascan be seen in figure 6.2 and 6.3.

Figure 6.2: The finished mesh result for the 3D cylinder

39

Figure 6.3: A similar meshing result for the semi-infinite flat-cigar.

It is worth noticing the level of details on both elements. On the flat-cigar the detail levelcontinues the same way throughout its semi-infinite length. It is not so good from a mesh-size perspective, but the problem is that when one tries to make these smooth reductions asone moves further way, the geometry gets torn. Instead of having smooth edges they nowbecome choppy. It is always a difficult task to decide what may be optimal.

Mesh Cells Faces Nodes Min Orth. Quality Max Aspect Ratio3D cylinder 1141991 2710274 472205 1.14e-2 8.08e4Flat-cigar 2687563 6434550 1148948 1.24e-2 9.39e4

As the skewness and quality of the cells was very poor to begin with there was no idea todo further cell adaptations since that usually only make things worse. One solution couldbe to adapt the mesh and then convert the mesh to Polyhedral. That is a very powerful andreliable way get to get rid of skewness problems.

6.3 Solver

The solution method was identical to the 2D with the exception that no cell adaptationswere made and in some cases the pseudo-transient settings were used, with a length-scalemanually set to the chord of the airfoil.

Figure 6.4: Residuals for a typical 3D case.

Even when the mesh was not refined and the amount of iterations was only set to 500, itstill took 8 hours on the available computer to perform calculations for one case. Despitethis it is possible to get residuals close to 1e-7.

40

6.4 Results

As before the fist step is to see what values can be obtained for an uninterfered case. In thiscase the only way to obtain some realistic values to compare with is to do some calculationboth by hand and by the use of some panel method application. The wing has a 2 dm chordand a 4 dm span with no winglets. This makes for a very stocky wing with high amount ofwingtip vortices.The Methods used were the application XFLR5, Vortex Lattice Method (VLM) and thenobviously Fluent. For the Fluent case one method involved a symmetry plane instead of avertical wall. This was done to neglect the drag and other influences caused by the wall, sothat the comparison would be more real. Obviously the mesh was done a bit differently forthe symmetry plane case (no inflation on the vertical wall). [9, pp221-226]

Method CL CD L/DXFLR5 -0.6046 0.0286 -21.14VLM -0.5762 0.0264 -21.83Fluent (symmetry) -0.5896 0.0491 -12.01Fluent (wall) -0.5733 0.5177 -1.107

Table 6.1: Results for a wing (NACA 23015) using different methods for calculation

The results for the uninterfered 3D case show a similar shortcomings as for the 2D case.The lift is close in comparison, but the drag is not. It is worth pointing out that neither theXFLR5 or the VLM have any reliable drag models, so the comparison should be viewed asa basic indication.

−0.4 −0.2 0 0.2 0.4 0.6 0.8 1−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

ΔC /C and ΔC /CL L l l

y /

cc

r

3D flat−cigar x /c = 0.50c r

x /c = 0.75c r

x /c = 1.00c r

3D cylinder

2D cylinder

ΔC /C and ΔC /C over yL L l l c

{ v = 65.00 [m/s], α = 8°, d /c = 0.5 }c r

Figure 6.5: Close similarities between the 2D and the 3D case are shown. Also the goodresults for the flat-cigar are unmistakable.

As a final test the 3D cylinder and the flat-cigar has been compared with the 2D cylinderand with each other. This has been done to see the differences when going from 2D to3D and also to see what happens when the flat-cigar is reducing the wake interaction. Itshould be mentioned that there is as a difference between the interference coefficient in the3D and in the 2D environment. The definition for the 2D version is ∆Cl/Cl where the Clis obviously the 2D case lift coefficient and is defines as the lift force divide by the dynamicpressure and chord. In the 3D case it is the 3D lift coefficient CL that is used, which has

41

wing area as a variable instead of chord. Thus, in the 3D case the interference coefficient is∆CL/CL.The interesting part is that the interference coefficient is not very different in the 3D casecompared with the 2D. Naturally the geometry is slightly different and there is an influencefrom the wing tip vortices. Overall the results are very similar.As expected the flat-cigar has due to its semi-infinite length obtained the most favorablevalues for the interference coefficient. It also has much lower dips or fluctuations and istherefor more predictable. The main explanation is that there is no wake behind the semi-infinite flat-cigar in which the flow could get tangle up in and produce unwanted effects.This is very good news, since if the goal is to make a rider interfere a wing with his knee(shaped as a cylinder/sphere), the knee is attached to a leg which is more of a flat-cigarshape. Combining this knowledge will tell us that this method of interference has some realpotential in a static case.

42

Chapter 7

Final Concept

Throughout this document the focus has been to see if the interference effect has any poten-tial to make any difference. Preliminary CFD tests in a static environment has shown thatthere is indeed some promise that the entire concept might work. A lot of work still needsto be done, but as a matter or of interest, let us see what this concept might look like whenit is done.

Front view

Simple

Anhedral wings

Front view

Bi-plane wings

Front view

Multiple

Anhedral angles

Figure 7.1: Possible wing geometry for the final concept.

One major problem that might come up is where and how to attach the wings onto themotorcycle fairing. A simple solution would be just to place the wings at some given anglein a position where they could be easily interfered. The problem here is that there is not allthat much space to play with.A motorcycle is already about 0.4 to 0.5 m wide and the maximum limit is 0.6 m. Thisdoes not give much room for wing placing. From previous initial estimations (in section 2.2)it shows that the wings have to be quite large to make significant changes. A wing with0.3 m span and 0.2 m chord and a reasonable lift coefficient of 1.7, will produce about 200to 300 N through a fast 4 or 5th gear corner. This may not seem as much but a MotoGPrider usually weights between 50 to 70 kg. So, this wing will produce almost a half of whatthis rider produces with his weight – which is to make the bike lean into a corner (also withthe help of counter steering), keep that lean angle throughout the corner and to move frontand back, so that the front or back wheel are loaded during acceleration or braking.Another solution is to place several wing sections that could be interfered by the use of eitherone or several body-parts. This way a larger total wing area could be obtained resulting inmore downforce. The downside is the higher drag that can be expected.Finally, the idea that may have the greatest potential is the use of curved wings. Herethe initial anhedral angle at the wing root could be something in the range of 50◦ and thenchanging into an anhedral angle closer to 80◦. This way one may take the benefit of multipleanhedral angles (as explained in previous section 2.2.3) and also squeeze in as much wingarea as possible into the tight space. Additionally various struts and winglets could be usedto strengthen the design or to curve or funnel the flow in desired direction.

43

Figure 7.2: A concept using curved wings with multiple anhedral angles. The CFD per-formed here is very approximative.

Figure 7.3: Front view of he motorcycle with the curved wings.

44

Chapter 8

Discussion

Despite showing a lot of promise thus far, this new concept still has a long way to gobefore reaching a final concept stage. The positive surprise has been that the interferenceeffect is there and shows a significant contribution. However the problem of the conceptimplementation is still an unsolved case.

8.1 Additional Work

The next step on the the way to reach a working prototype, is to verify that all of theseresults that has been presented here are valid. This means testing all of the simplifiedconcepts in a wind tunnel and then compare them with the CFD results in this thesis.A severe limitation of the calculations performed here, is that in reality, it is mainly adynamical problem since the body of the rider is moving into the position of the idealinterference. This can give hysteresis effects. Basically a case when a previous positionhas an influence on the current position. How to deal with this and what to expect canbe complex problem to solve. In many ways due to the very complex geometry of themotorcycle, it may be severely difficult to do a simplified case test of this.

8.2 Further improvements

When it comes to the actual design there are many complications that may be difficult toovercome. One them is the placement of the wings and adapting the fairing so that theoncoming air comes in as smoothly as possible (see figure 8.1).The problem is that when a motorcycle is cornering the air moves around the motorcyclein a curved way. If the fairing of the motorcycle is too narrow one may have separationson the outer side of the bike. This means that the fairings have to be designed in such waythat the air is smoothly directed at the wings.Another problem with the curved flow during cornering, is that the inner wing (which therider is trying to block) is actually experiencing higher angle of attack (if the anhedral angleis very high), thus being more effective. So, the outer wing does not only suffer from possibleseparation bubbles disturbing the flow, but also has a lower angle of attack. None of thesedetails work in favor for the concept.

8.2.1 Higher top speed

One problem that all wings are having is the high lift-induced drag they create. A problemmost noticeable when the vehicle is trying to reach the top speed. This problem has howeverbeen reduced by Mercedes in Formula 1 and could be applicable for wing configurations inMotoGP (figure 8.2).It works with the help of static pressure, which typically increases when the speed does. At aspecific moment the static pressure becomes so large, that with the help of clever channeling,a separation occurs and the wing is rid of lift-induced drag. This is obviously at the cost ofhigh separation drag, but nevertheless the total drag is smaller.[8]The best part is that it is legal by the (current) MotoGP regulations of 2012.

45

Figure 8.1: The relatively wide cooler does not simplify the wing implementation. This couldhowever be resolved with some redesigning. The question is at what consequences. [12]

Figure 8.2: The Mercedes-Horn is using static pressure to stall the wing at high speeds toreduce drag. This type of device is legal by the MotoGP regulations (2012).[8]

46

Chapter 9

Conclusion

A concept has been suggested which has the capacity to significantly improve the corner-ing abilities of road racing motorcycles. This idea is also compliant with the road racingregulations of MotoGP 2012.This concept suggest the use of highly anhedral wings for use during cornering, where oneof the wings would have its lift generations reduced, as the rider is leaning of the bike inthe corners. The ideal result would be that the other wing alone would generate all of thenecessary downforce and make the bike perform better than the existing ones.After doing simplified numerical calculations, only focusing on the basic principles in staticcases, it has shown the the principle of interference effect is existing and is a very significantone. The search for an optimal positioning of an interference device, also shows a complexbehavior where several peak points can be identified, as well as positions that have a veryundesired effect.Even with these initial positive results there are still many issues that need to be addressed.The main one is how this interference effect will actually behave in a wind tunnel test and ifthe results will be the same. Then there is the question of what will happen in reality wherethe problem is highly dynamical and there is a great risk of unwanted hysteresis effects.Even when all this is dealt with the question is how all this can be applied on a realmotorcycle with a real rider trying to set the best lap of the race.Despite all of these unresolved concerns, the fact remains that this concept has a lot ofpromise, with ideas that can surely deepen the understanding of other fields in aerodynamics.

47

Acknowledgments

An early idea of this concept came to the author’s mind when taking a course in vehi-cle aerodynamics. This idea was then told, in its very basic form to the course lecturer,Alessandro Talamelli. This sparked a discussion which evolved this basic idea into a fulltheory, described in this thesis. Without the help and support from Alessandro, this ideawould likely never been anything more than a sketch on a piece of jagged paper, forgottendeep down in a drawer. Thus, it is fully in order to express sincere gratitude to AlessandroTalamelli for his time, effort and ideas which moved the work forward.As the thesis was underway Stefan Wallin was the one who provided support and help forthe CFD tools. His help was very appreciated and brought forward some great results.Also the author would like to thank the “Department of Mechanics” and “Department ofAeronautical and Vehicle Engineering” at KTH for all their help an support, making thisthesis possible.Finally the author would like to thank Michal Sedlak for bringing up ideas and thoughtsregarding the work and what could be improved.

48

Appendix A

Appendix: Data

A.0.2 Data for 2D cases

Details of these cases are explained in Chapter 5.

Table A.1: Uninterfered Reference Case for NACA-23015 in 2D

v∞ α Nx Ny Nz xc/cr yc/cr Cl Cd L/D ∆Cl/Cl

65.00 0◦ 7.22 -63.16 0 - - -0.122 0.014 -8.751 -65.00 4◦ 8.83 -283.42 0 - - -0.548 0.017 -32.095 -65.00 8◦ 9.20 -493.10 0 - - -0.953 0.018 -53.573 -65.00 12◦ 15.56 -665.72 0 - - -1.286 0.030 -42.794 -

Table A.2: Interference Case for NACA-23015 and a Cylinder (dc/cr = 0.5)

v∞ α Nx Ny Nz xc/cr yc/cr Cl Cd L/D ∆Cl/Cl

65.00 0◦ 106.24 34.76 0 0.5 -0.1 0.067 0.205 0.327 1.55065.00 0◦ 105.57 -9.10 0 0.5 0 -0.018 0.204 -0.086 0.85665.00 0◦ 106.10 -112.67 0 0.5 0.1 -0.218 0.205 -1.062 -0.78465.00 0◦ 106.75 -236.62 0 0.5 0.2 -0.457 0.206 -2.217 -2.74665.00 0◦ 108.71 -0.05 0 0.75 -0.1 0.000 0.210 -0.001 0.99965.00 0◦ 109.77 -54.64 0 0.75 0 -0.106 0.212 -0.498 0.13565.00 0◦ 108.24 -101.75 0 0.75 0.1 -0.197 0.209 -0.940 -0.61165.00 0◦ 109.67 -148.23 0 0.75 0.2 -0.286 0.212 -1.352 -1.34765.00 0◦ 110.40 -24.03 0 1 -0.1 -0.046 0.213 -0.218 0.61965.00 0◦ 112.45 -63.48 0 1 0 -0.123 0.217 -0.565 -0.00565.00 0◦ 110.11 -85.71 0 1 0.1 -0.166 0.213 -0.778 -0.35765.00 0◦ 111.80 -113.26 0 1 0.2 -0.219 0.216 -1.013 -0.79365.00 4◦ 107.01 -64.37 0 0.5 -0.1 -0.124 0.207 -0.602 0.77365.00 4◦ 107.00 -84.95 0 0.5 0 -0.164 0.207 -0.794 0.70065.00 4◦ 102.48 -197.71 0 0.5 0.1 -0.382 0.198 -1.929 0.30265.00 4◦ 103.87 -328.78 0 0.5 0.2 -0.635 0.201 -3.165 -0.16065.00 4◦ 111.24 -162.73 0 0.75 -0.1 -0.314 0.215 -1.463 0.42665.00 4◦ 106.18 -183.05 0 0.75 0 -0.354 0.205 -1.724 0.35465.00 4◦ 107.75 -249.00 0 0.75 0.1 -0.481 0.208 -2.311 0.12165.00 4◦ 109.71 -302.08 0 0.75 0.2 -0.584 0.212 -2.754 -0.06665.00 4◦ 113.51 -211.17 0 1 -0.1 -0.408 0.219 -1.860 0.25565.00 4◦ 110.20 -230.44 0 1 0 -0.445 0.213 -2.091 0.18765.00 4◦ 112.47 -250.33 0 1 0.1 -0.484 0.217 -2.226 0.11765.00 4◦ 111.71 -297.49 0 1 0.2 -0.575 0.216 -2.663 -0.05065.00 8◦ 126.50 -319.34 0 0.5 -1 -0.617 0.244 -2.524 0.35265.00 8◦ 127.17 -270.13 0 0.5 -0.8 -0.522 0.246 -2.124 0.45265.00 8◦ 118.26 -216.38 0 0.5 -0.6 -0.418 0.228 -1.830 0.56165.00 8◦ 112.37 -160.02 0 0.5 -0.4 -0.309 0.217 -1.424 0.675Continued on Next Page. . .

49

Table A.2 – Continuedv∞ α Nx Ny Nz xc/cr yc/cr Cl Cd L/D ∆Cl/Cl

65.00 8◦ 107.43 -149.98 0 0.5 -0.2 -0.290 0.208 -1.396 0.69665.00 8◦ 105.78 -183.53 0 0.5 -0.1 -0.355 0.204 -1.735 0.62865.00 8◦ 104.61 -197.83 0 0.5 -0.05 -0.382 0.202 -1.891 0.59965.00 8◦ 100.91 -163.90 0 0.5 0 -0.317 0.195 -1.624 0.66865.00 8◦ 102.02 -147.27 0 0.5 0.05 -0.285 0.197 -1.444 0.70165.00 8◦ 102.44 -132.91 0 0.5 0.075 -0.257 0.198 -1.298 0.73065.00 8◦ 96.51 -195.34 0 0.5 0.1 -0.377 0.186 -2.024 0.60465.00 8◦ 98.74 -355.30 0 0.5 0.2 -0.686 0.191 -3.598 0.27965.00 8◦ 103.08 -590.79 0 0.5 0.4 -1.141 0.199 -5.731 -0.19865.00 8◦ 102.46 -672.26 0 0.5 0.6 -1.299 0.198 -6.561 -0.36365.00 8◦ 102.60 -672.91 0 0.5 0.8 -1.300 0.198 -6.558 -0.36565.00 8◦ 103.23 -651.74 0 0.5 1 -1.259 0.199 -6.313 -0.32265.00 8◦ 124.19 -340.18 0 0.75 -1 -0.657 0.240 -2.739 0.31065.00 8◦ 121.51 -313.62 0 0.75 -0.8 -0.606 0.235 -2.581 0.36465.00 8◦ 118.21 -289.07 0 0.75 -0.6 -0.558 0.228 -2.445 0.41465.00 8◦ 115.01 -276.38 0 0.75 -0.4 -0.534 0.222 -2.403 0.43965.00 8◦ 111.85 -290.46 0 0.75 -0.2 -0.561 0.216 -2.597 0.41165.00 8◦ 109.96 -307.60 0 0.75 -0.1 -0.594 0.212 -2.797 0.37665.00 8◦ 110.50 -317.49 0 0.75 -0.05 -0.613 0.213 -2.873 0.35665.00 8◦ 107.52 -324.93 0 0.75 0 -0.628 0.208 -3.022 0.34165.00 8◦ 103.59 -319.49 0 0.75 0.05 -0.617 0.200 -3.084 0.35265.00 8◦ 101.93 -320.89 0 0.75 0.075 -0.620 0.197 -3.148 0.34965.00 8◦ 102.87 -361.46 0 0.75 0.1 -0.698 0.199 -3.514 0.26765.00 8◦ 98.30 -418.24 0 0.75 0.2 -0.808 0.190 -4.255 0.15265.00 8◦ 107.14 -500.15 0 0.75 0.4 -0.966 0.207 -4.668 -0.01465.00 8◦ 106.71 -566.94 0 0.75 0.6 -1.095 0.206 -5.313 -0.15065.00 8◦ 106.50 -594.78 0 0.75 0.8 -1.149 0.206 -5.585 -0.20665.00 8◦ 106.41 -599.69 0 0.75 1 -1.159 0.206 -5.636 -0.21665.00 8◦ 122.42 -365.16 0 1 -1 -0.705 0.237 -2.983 0.25965.00 8◦ 120.58 -351.70 0 1 -0.8 -0.679 0.233 -2.917 0.28765.00 8◦ 118.52 -343.13 0 1 -0.6 -0.663 0.229 -2.895 0.30465.00 8◦ 116.29 -344.82 0 1 -0.4 -0.666 0.225 -2.965 0.30165.00 8◦ 113.81 -358.58 0 1 -0.2 -0.693 0.220 -3.151 0.27365.00 8◦ 112.27 -370.25 0 1 -0.1 -0.715 0.217 -3.298 0.24965.00 8◦ 106.98 -376.09 0 1 -0.05 -0.727 0.207 -3.516 0.23765.00 8◦ 110.16 -384.59 0 1 0 -0.743 0.213 -3.491 0.22065.00 8◦ 108.52 -391.66 0 1 0.05 -0.757 0.210 -3.609 0.20665.00 8◦ 99.34 -369.46 0 1 0.075 -0.714 0.192 -3.719 0.25165.00 8◦ 100.79 -400.71 0 1 0.1 -0.774 0.195 -3.976 0.18765.00 8◦ 98.77 -461.33 0 1 0.2 -0.891 0.191 -4.671 0.06465.00 8◦ 109.21 -482.49 0 1 0.4 -0.932 0.211 -4.418 0.02265.00 8◦ 109.18 -522.24 0 1 0.6 -1.009 0.211 -4.783 -0.05965.00 8◦ 109.18 -548.25 0 1 0.8 -1.059 0.211 -5.021 -0.11265.00 8◦ 108.73 -561.08 0 1 1 -1.084 0.210 -5.160 -0.138

A.0.3 Data for 3D cases

Details of these cases are explained in Chapter 6.

Table A.3: Uninterfered Reference Case for NACA-23015 in 3D

v∞ α Nx Ny Nz xc/cr yc/cr CL CD L/D ∆CL/CL

65.00 8◦ 107.19 -118.69 -140.08 - - -0.573 0.518 -1.107 -

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Table A.4: Interference Case for NACA-23015 and a 3D Cylinder (dc/cr = 0.5)

v∞ α Nx Ny Nz xc/cr yc/cr CL CD L/D ∆CL/CL

65.00 8◦ 143.49 -49.42 -144.67 0.5 -0.4 -0.239 0.693 -0.344 0.58465.00 8◦ 141.53 -39.85 -146.26 0.5 -0.1 -0.192 0.684 -0.282 0.66465.00 8◦ 143.50 -34.11 -150.99 0.5 0 -0.165 0.693 -0.238 0.71365.00 8◦ 139.36 -41.70 -144.40 0.5 0.05 -0.201 0.673 -0.299 0.64965.00 8◦ 142.84 -37.54 -144.08 0.5 0.1 -0.181 0.690 -0.263 0.68465.00 8◦ 143.69 -98.76 -150.47 0.5 0.2 -0.477 0.694 -0.687 0.168

Table A.5: Interference Case for NACA-23015 and a Flat-Cigar (dc/cr = 0.5, length issemi-infinite)

v∞ α Nx Ny Nz xc/cr yc/cr CL CD L/D ∆CL/CL

65.00 8◦ 119.85 -14.88 -337.95 0.5 -0.4 -0.072 0.579 -0.124 0.87565.00 8◦ 120.05 -11.87 -336.85 0.5 -0.3 -0.057 0.580 -0.099 0.90065.00 8◦ 119.40 -10.14 -337.87 0.5 -0.2 -0.049 0.577 -0.085 0.91565.00 8◦ 119.94 -9.20 -342.43 0.5 -0.1 -0.044 0.579 -0.077 0.92265.00 8◦ 120.30 -9.00 -338.55 0.5 -0.05 -0.043 0.581 -0.075 0.92465.00 8◦ 120.43 -9.06 -338.94 0.5 0 -0.044 0.582 -0.075 0.92465.00 8◦ 120.05 -8.38 -336.58 0.5 0.05 -0.040 0.580 -0.070 0.92965.00 8◦ 115.47 -9.77 -322.70 0.5 0.1 -0.047 0.558 -0.085 0.91865.00 8◦ 121.56 -16.01 -338.01 0.5 0.2 -0.077 0.587 -0.132 0.86565.00 8◦ 121.96 -26.14 -338.11 0.5 0.3 -0.126 0.589 -0.214 0.78065.00 8◦ 123.99 -37.66 -339.85 0.5 0.4 -0.182 0.599 -0.304 0.683

51

Appendix B

MotoGP Regulations 2012

Since the aim of this work is to provide a viable concept, which can be used for motorcycleroad racing (e.g Grand Prix), it is of interest to know the specific limitations and options.Only the relevant rules are presented here and the ones of extra interest are emphasized. [4]

2.7.7 Bodywork

2.7.7.1 The windscreen edge and the edges of all other exposed parts of the streamliningmust be rounded.

2.7.7.2 The maximum width of bodywork must not exceed 600mm. The width of the seator anything to its rear shall not be more than 450mm (exhaust pipes excepted).

2.7.7.3 Bodywork must not extend beyond a line drawn vertically at the leading edge ofthe front tyre and a line drawn vertically at the rearward edge of the rear tyre. Thesuspension should be fully extended when the measurement is taken.

2.7.7.4 When viewed from the side, it must be possible to see:

a. At least 180 degrees of the rear wheel rim.

b. The whole of the front rim, other than the part obscured by the mudguard, forks,brake parts or removable air-intake.

c. The rider, seated in a normal position with the exception of the forearms.

Notes: No transparent material may be used to circumvent the above rules. Coversfor brake parts or wheels are not considered to be bodywork obstructing the view ofwheel rims in regard to the above rules.

2.7.7.5 No part of the motorcycle may be behind a line drawn vertically at the edge of therear tyre.

2.7.7.6 The seat unit shall have a maximum height of the (approximately) vertical sectionbehind the riders seating position of 150mm. The measurement will be taken at a 90angle to the upper surface of the flat base at the riders seating position, excluding anyseat pad or covering. Any on-board camera/antenna mounted on the seat unit is notincluded in this measurement.

2.7.7.7 Mudguards are not compulsory. When fitted, front mudguards must not extend:

a. In front of a line drawn upwards and forwards at 45 degrees from a horizontal linethrough the front wheel spindle.

b. Below a line drawn horizontally and to the rear of the front wheel spindle.

The mudguard mounts/brackets and fork-leg covers, close to the suspension leg andwheel spindle, and brake disc covers are not considered part of the mudguard.

2.7.7.8 Wings may be fitted provided they are an integral part of the fairing or seat and donot exceed the width of the fairing or seat or the height of the handlebars. Any sharpedges must be rounded. Moving aerodynamic devices are prohibited.

52

2.7.7.9 The lower fairing has to be constructed to hold, in case of an engine breakdown,at least half of the total oil and engine coolant capacity used in the engine (minimum5 litres for MotoGP and Moto2, minimum 2.5 litres for Moto3). The lower fairingshould incorporate a maximum of two holes of 25mm. These holes must remain closedin dry conditions and must be only opened in wet race conditions, as declared by theRace Director.

2.7.8 Clearances

2.7.8.1 The motorcycle, unloaded, must be capable of being leaned at an angle of 50 degreesfrom the vertical without touching the ground, other than with the tyre.

2.7.8.2 There must be a clearance of at least 15mm around the circumference of the tyreat all positions of the motorcycle suspension and all positions of the rear wheel ad-justment.

53

References

[1] I. H. Abbott and A. E. V. Doenhoff. Theory of Wing Sections. Dover Publications,inc., dover edition, 1958.

[2] J. Beeler. First shots of valentino rossi on the ducati. http://www.asphaltandrubber.com/news/valentino-rossi-ducati-valencia-test/. 2010–11–09, visited 2012–09–18.

[3] J. Black. Aprilia’s max biaggi wins the double to extend his world superbikelead as carlos checa crashes. http://www.foxsports.com.au/motor-sports/

superbikes/aprilias-max-biaggi-wins-race-one-at-misano-from-carlos

-checa-to-extend-his-world-superbike-lead/story-fn5k3gtw-1226390545446.11th June 2012, visited 2012–09–18.

[4] F. I. de Motocyclisme. FIM Road Racing World Championship Grand Prix Regulations.2012 1st edition.

[5] T. Foale. Motorcycle Handling and Chassis Design, the art and science. Tony FoaleDesigns, 2011.

[6] A. Johansson. Turbulence - SG2218, Lecture notes. KTH Mechanics, 2011.

[7] J. John D. Anderson. Fundamentals of Aerodynamics. McGraw-Hill, Inc., 2nd edition,1991.

[8] D. Madier. The F1-Forecast.com Technical Files - Aerodynamical & Mechanical Updates2010. F1-Forecast, 12 2010.

[9] A. Rizzi. Aerodynamic Design, a Computational Approach. KTH Aeronautical & Ve-hicle Engineering, 2002.

[10] T. Stevenson. Rodger freeths aerofoil viko tz750a. http://www.motorcycletrader.co.nz/View/Article/Rodger-Freeths-Aerofoil-Viko-TZ750A/236.aspx?Ne=145&N=

4294967266&No=135, http://www.classicyams.com/special-yamaha-bikes/

special-yamaha-bikes/yamaha-tz750a-aerofoil.html. visited 2012–07–16.

[11] various. The magnificent seven - british racing legend barry sheene.https://theselvedgeyard.wordpress.com/2010/12/20/the-magnificent-seven

-british-racing-legend-barry-sheene/. December 20, 2010, visited 2012–09–18.

[12] various. Pit lane sportbike news (fastdates.com): Ducati’s monocoque design dilemma.http://www.fastdates.com/PitLaneNews2012.01.03.HTM. Bologna, Italy, Dec 15th,visited 2012–09–18.

[13] various. ANSYS Help - Fluent. SAS IP, Inc., 2011.

[14] various. Introduction to ANSYS FLUENT 14.0. ANSYS, inc., 2012, January 25.

[15] various. Introduction to ANSYS ICEM CFD 14.0. ANSYS, inc., 2012, March 21.

54