design and development of a three component strain gauge

Design and development of a three

component strain gauge wind tunnel

balance

by

Frederik Francois Pieterse

A dissertation submitted in partial fulfillment of the requirements for the degree of

MAGISTER PHILOSOPHAE IN MECHANICAL ENGINEERING

in the

FACULTY OF ENGINEERING

at the

RAND AFRIKAANS UNIVERSITY

R • A • U

Supervisor: Prof C Redelinghuys

November 2002

Abstract

Abstract

In today's world with its competitive environment there is a need to shorten product

development time by using CFD (Computational Fluid Dynamics) to design an object

for example a car, aeroplane or missile and to predict the forces that the wind will

have on the object (design). To evaluate the correctness of the CFD results, the design

or a scale model of the design must be tested in a wind tunnel by using a force

balance.

The wind tunnel balance is an apparatus used in the designing and testing of wings,

shapes and profiles. In general a balance can be used in all aerodynamic designs to

determine the forces on an object when it is moving through air.

The aim of this project was to design and manufacture a three-component external

balance for a low-speed wind tunnel using an axiomatic design method. It also covers

the installation of the external wind tunnel balance to a wind tunnel with a

computerized data acquisition capturing system, and performance evaluation of the

wind tunnel balance.

Acknowledgements ii

Acknowledgements

A special word of thanks goes out to the following people for their help, support,

patience and willingness to help in making this possible:

God, for the strength and guidance to complete this task.

Prof C. Redelinghuys, Supervisor, for all the support, expertise and time in his

busy schedule.

Prof. J. van Wyk, for all the support and expert advice on wind tunnels and wind

tunnel balances, pointing out the important factors in the design and keeping me

motivated.

•4. `Prof. L. Pretorius, for his input and time to keep me motivated.

Dr. I. W. Hofsajer, for his expert advice on data measurements, help, and teaching

on stepper motors.

Dr. R.F. Laubscher for this interest in the project and expert advice on

manufacturing of the NACA 23012 scale wing used for the test.

Mark Goossens, a colleague for his expert advice, help and teaching on load cell

design.

Walter Dott, for his expert advice, workmanship and patience during the

manufacturing of the wind tunnel balance.

Robbie de Wet Product Manager from RENOLD CROFTS for the donation of the

worm gearbox.

10. Dr. L. Liebenberg, a colleague for editing.

Wind Tunnel Balance

Design

APPENDEX A iii

Contents

Abstract

Acknowledgements ii

Contents iil

List of figures vii

List of tables xi

List of symbols xi i

1 Introduction 1 1.1 Aerodynamic forces 1 1.1.1 Lift 1 1.1.2 Drag 2 1.1.3 Pitching moment 2 1.2 Wind Tunnel balances 2 1.2.1 Wire balance 3 1.2.2 Platform Balance 4 1.2.3 Yoke balance 5 1.2.4 Pyramidal balance 6

Requirements and criteria for a wind tunnel balance 7 2.1 Introduction 7 2.2 Requirements for a wind tunnel balance design 7 2.3 Internal or external balance 7 2.4 Design for the wind tunnel balance design 10 2.4.1 Existing wind tunnel layout 10 2.4.2 Test section 11 2.4.3 Wind speed map in the high-speed test section 11 2.4.4 Determining the maximum model size 14 2.4.5 Rotation of the model 16 2.5 Accuracy of the measurements 17

Axiomatic design 19 3.1 Introduction 19 3.2 Axiomatic wind tunnel design parameters 20 3.3 Specification for the wind tunnel balance 21 3.4 Calculating lift and drag forces 22 3.4.1 Lift forces 22 3.4.2 Drag forces 23 3.4.3 Pitching forces 23

External wind tunnel balance concept design 24 4.1 Introduction 24 4.1 Preliminary ideas 24 4.1.1 External sting type wind tunnel balance (Concept 1) 24

APPENDEX A iv

4.1.2 External ring balance (Concept 2) 26 4.1.3 Wind tunnel balance (Concept 3) 27 4.3 Vertical strut concept design 28 4.3.1 Preliminary ideas 28 4.3.11 Shaft type 28 4.3.1.2 Half circle strut 29 4.3.1.3 Two-arm strut 30

5 Final wind tunnel design 32

5.1 Introduction 32 5.2 Forces diagram 32 5.2.1 Lift force 33 5.2.2 Drag force 34 5.2.3 Pitching moments 34 5.3 Wind tunnel base design 35 5.4 Wind tunnel two-arm strut design 38 5.4.1 Base top arm 40 5.4.2 Horizontal link arms 40 5.4.3 Vertical arms 45 5.4.4 The Headpiece 49 5.4.5 The Head vibration test 50 5.4.5 The worm gearbox assembly 52

6 Carbon fibre rods 55 6.1 Introduction 55 6.2 Manufacturing of carbon fibre rods 55 6.3 Comparison with Other Structural Materials 57 6.4 Deflection test of tubes 59

7 Worm gearbox design 61

7.1 Introduction 61 7.2 Worm gearbox design-Mechsoft computer software 61 7.3 Worm gear box verification 64 7.3.1 Centre distance 65 7.3.2 Pitch 65 7.3.3 Lead 66 7.3.4 Friction coefficient 67 7.3.5 Pressure angles 70 7.3.5 Worm Diameter 70 7.4 Wormgear dimensions 68 7.5 Face Width of the worm 72 7.6 Face Length of the worm 73 7.7 Forces on the worm gear 73 7.7.1 Axial Force on the worm 73 7.7.2 Efficiency of the worm gear set 75 7.8 Power to drive the worm 76 7.9 Angle of attack measurement 78 7.10 Donation of a commercial worm gearbox 78 8 Balance measuring devices 79 8.1 Introduction 79

APPENDEX A

8.2 Ring type load cell design theory 81 8.2.1 Maximum stress in curved beams theory 85

8.3 Lift load cell design 88

8.4 Pitch Load cell design 90

8.5 Drag Load cell design 93 8.6 Wheatstone bridge load cells 97 8.7 Load cell implementation 99

9. Electronic data capturing system 100

9.1 Introduction 100

9.2. Data capturing card 100

9.3 The Connection box 102

9.4 Strain gauge amplifier 102

9.5 Stepper motor driver 103

9.6 Angle sensor 104

9.7 Computer program 105

10 Installation of the wind tunnel balance 107


10.2 Installation in to the wind tunnel 107

11 Calibration of the wind tunnel balance 110


11.2 Calibration method 111 11.3 Load cells zero and gain setting procedure 112 11.3.1 Lift load cells zero and gain setting procedure 113 11.3.2 Drag Load cells zero and gain setting procedure 113 11.3.3 Pitch Load cells zero and gain setting procedure 114 11.4 Load cells calibration procedure 115

11.4.1 The lift calibration 116

11.4.2 The drag calibration 118

11.4.3 The pitch calibration 120 11.5 Load cell interference check 121

11.6 Angle sensor calibration 121 11.7 Evaluation of tare and interference 123

11.8 Data processing 124

12 Wind tunnel balance evaluation test 125


12.2 Set-up for the test 125

12.3 The test 126

12.3.1 Atmospheric air pressure 126

12.3.2 Air Density 127

12.3.3 Air speed 127

12.3.4 Reynolds number 127

12.4 Test results 129

12.4.1 Coefficient of lift 129

12.4.2 Coefficient of Drag 130

12.4.3 Coefficient of moment 131

12.5 Conclusion of the test results 133

APPENDEX A vi

13 Conclusion and recommendations 134 13.1 General Conclusions 134 13.2 Recommendations 134

14 Bibliography and references 135

APPENDIX A 137

APPENDIX B 140

APPENDIX C 171

APPENDIX D 176

APPENDIX E 180

APPENDIX F 197

APPENDIX G 202

APPENDIX H 204

APPENDIX I 206

List of Figures vii

List of Figures ,

Figure 1.1 Forces acting on an airfoil when moving through air 1

Figure 1.2 Pitching moment 2 Figure 1.3 Three component strain gage balance 3

Figure 1.4 Wire wind tunnel balance 3 Figure 1.5 Platform balance. 4

Figure 1.6 Yoke balance. 5 Figure 1.7 Pyamidal balance 6 Figure 2.1 Weighted objective tree 8 Figure 2.2 Existing wind tunnel layout at the RAU Mechanical Engineering

Department. 10 Figure 2.3 High-speed test section of the existing wind tunnel at the RAU Mechanical

Engineering Department. 11 Figure 2.5 Static pressure map layout of the test section 12 Figure 2.6 Boundary layer graph (20 to 200 mm from root) 13 Figure 2.7. Average horizontal distribution of wind speeds in test section 13 Figure 2.8. Average vertical distribution of wind speeds in test section 14 Figure 2.9 Aircraft model size 15 Figure 2.10. Frontal blockage area 15 Figure 2.11 Aspect ration of a wing 16 Figure 2.12 Stalling of a wing at high angles of attack 16 Figure 2.13 Angle of attack versus Lift Graph 17 Figure 2.14 Influence of tolerance (accuracy) on processing costs 18 Figure 3.1 Suh's concept of design as the process of mapping functional requirements

(FRs) to design parameters (DPs) 20 Figure 3.2 Hierarchy of function requirements (FRs) for a wind tunnel balance. 20 Figure 3.3 Hierarchy of design requirements (DPs) for a wind tunnel balance 21 Figure 4.1 Sting type external balance 25 Figure 4.2 FEA of the External sting type balance. 25 Figure 4.3 External ring arm balance 26 Figure 4.4 FEA External ring arm balance 27 Figure 4.5 Wind tunnel balance (concept 3) Preliminary idea of final design 28 Figure 4.6 Horizontal strut and vertical arm. 29 Figure 4.7 Halve circle arm 30 Figure 4.8 Two-arm strut 31 Figure 5.1 Sketch of forces and moments 32 Figure 5.2 Final concept design 35 Figure 5.2 Finite element mesh on the Wind Tunnel Balance base part. 36 Figure 5.4. Finite element analyses on the Wind Tunnel Balance base part. 38 Figure 5.5 Base Assembly 39 Figure 5.6 Sketch of the two-arm strut 40 Figure 5.7 FEA Deflection on the Base top arm 40 Figure 5.8 Horizontal link arm movement changes head angle 41 Figure 5.9 FEA Deflection on the Horizontal link arm 42 Figure 5.10 FEA Strength, Horizontal link arm 42 Figure 5.11 Horizontal link arms 43 Figure 5.12. Horizontal link arms fitted to the top base arm. 43 Figure 5.13 Screw studs 44 Figure 5.14 Bearing mounted 44

List of Figures viii

Figure 5.15 Screw studs in position 44 Figure 5.16 Sketch of forces on the arms 45 Figure 5.17 Special concentric holding tool 47 Figure 5.18 Special concentric holding tool in position 47 Figure 5.19 End caps aligned with concentric holding tools in position 48 Figure 5.20 Two-arm strut assembly 48 Figure 5.21 Bottom end cap mounted into horizontal arms 48 Figure 5.22 Top end cap mounted in head piece 48 Figure 5.23 FEA weak point at the neck 49 Figure 5.24 FEA Deflection if head part 49 Figure 5.25 Model wing mounted on headpiece for testing 50 Figure 5.26 Vibration frequency data monitored mounted on headpiece 52 Figure 5.27 Vibration sensor mounted on headpiece 51 Figure 5.28 Vibration frequency captured data 52 Figure 5.29. Worm gear cutaway 53 Figure 5.30. Worm gear in position 53 Figure 5.31 Worm gear Special mounting tool 54 Figure 5.32 Mounting of the worm gearbox with stepper motor 54 Figure 5.33 Head in +30° position 54 Figure 5.34 Head in -10° position 54 Figure 6.1 Carbon Fibre Process 56 Figure 6.2 Winding method 57 Figure 6.3 The strength to weight ratio 58 Figure 6.4 The stiffness to weight ratio 58 Figure 6.5 Tube test set-up 59 Figure 6.6 Carbon fibre deflection graph 59 Figure 7.1 Wind tunnel balance two-arm strut assembly 61 Figure 7.2 MechSoft-Profi Unitools Main page 62 Figure 7.3 Technical dialog page 62 Figure 7.4 Dimension dialog page 63 Figure 7.5 Load dialog page 64 Figure 7.6 Single-enveloping worm gear set 65 Figure 7.7 Forces on the worm exerted upon it by the worm gear 69 Figure 7.8 Efficiency shown as a fubction of lead and pressure angles 70 Figure 7.9 Worm and wormgear details 72 Figure 7.10 Forces diagram 74 Figure 8.1 Ring type Load Cell. 79 Figure 8.2 Sketch of a curved beam 81 Figure 8.3 Sketch of the curved beam 85 Figure 8.4 Ring bending forces 86 Figure 8.5 Sketch of curved beam 88 Figure 8.6 Pitch Load cell sketch 90 Figure 8.7 Line schematic of forces 91 Figure 8.8 Beam type load cell sketch 94 Figure 8.9 Strain gauge position in the drag load cell 97 Figure 8.10 Wire diagram of a Wheatstone strain gauge bridge 97 Figure 8.11 Drag load cell 99 Figure 8.12 Lift load cell 99 Figure 8.13 Drag load cell 99 Figure 8.14 Pitch load cell 99

List of Figures ix

Figure 9.1 PC mounted data acquisition card 101 Figure 9.2 PC mounted card, ribbon cable and connection box 101 Figure 9.3 Connection box 101 Figure 9.4 RS Strain gauge amplifiers PC board 102 Figure 9.5 Amplifiers mounted in control box 103 Figure 9.6 Stepper motor controller 103 Figure 9.7 Angle sensor mount 104 Figure 9.8 Angle control board inside control box 104 Figure 9.10 LabVIEW data capturing program 105 Figure 9.11 Motor control front panel 106 Figure 9.12 Data capturing front panel 106 Figure 10.1 Assembly of the wing tunnel balance 107 Figure 10.2 Testing wind tunnel balance outside the wind tunnel 107 Figure 10.3 Balance mounted in position underneath wind tunnel test section 108 Figure 10.4 Wind tunnel balance connected to data capturing system 108 Figure 10.5 Floor cut-away 109 Figure 10.6 Shroud fitted 109 Figure 10.7 Layout of computer and power supplies 109 Figure 11.1 I-Beam to eliminate Lift load cell 110 Figure 11.2 1-Beam to eliminate Drag load cell 110 Figure 11.3 I-Beam to eliminate Pitch load cell 111 Figure 11.4 Calibration rig in position 111 Figure 11.5 Measurement & Automation program 112 Figure 11.6. Lift amplifier setup, 80 N Max. 113 Figure 11.7. Drag amplifier setup, 7 N Max. 114 Figure 11.8. Pitch amplifier setup, 7 N Max 115 Figure 11.9 LabVIEW program for capturing data. 116 Figure 11.10 Positive lift calibration. 117 Figure 11.11 Negative lift calibration 117 Figure 11.12 Lift calibration graph. 117 Figure 11.13 Deflection measured 118 Figure 11.14 Deflection of two-arm strut under drag loads 118 Figure 11.15 Negative drag loads 119 Figure 11.16 Positive drag loads. 119 Figure 11.17 Drag calibration graph 120 Figure 11.18 Pitch calibration with drag loads 121 Figure 11.19 Pitch calibration with lift loads 121 Figure 11.20 Lift- drag interference graph 121 Figure 11.21 Angle calibration 122 Figure 11.22 Angle calibration graph 123 Figure 11.23 No shroud fitted 123 Figure 11.24 Shroud fitted 122 Figure 11.25 Tare graph 125 Figure 12.1 NACA 23012 airfoil filled to wind tunnel balance 125 Figure 12.2 Airfoil leveled 126 Figure 12.3 Drag minimized on brass-mounting 126 Figure 12.4 Vibration on angle sensors. 129 Figure 12.5 Vibration on the lift, drag and pitching moment sensors 129 Figure 12.6 Coefficient of lift graph comparison 130 Figure 12.7 Coefficient of Drag graph comparison 131

List of Figures x

Figure 12.8 Sketch of the forces and moments 132 Figure 12.9 Coefficient of moment graph comparison 133

List of Figures xi

List of Tables

Table 2.1 Evaluation charts for the wind tunnel balances 9 Table 2.2 Wind tunnel speed data 12 Table 2.3 Permissible measuring errors in the various aerodynamic coefficients 17 Table 6.1 Material strength and stiffens comparison 57 Table 7.1. Typical tooth dimensions for worm and wormgears 71 Table 11.1 Decrease of tare when the shroud as fitted. 123

List of Symbols xii

Lift of symbols

Symbol Description Units

On Pressure angle °

(Too Input torque worm no friction Nm

A h Height in water tube m

A pair Difference in air pressure Pa

A Blockage aria m2

a Distance m

A0 Angle change per step 0

ad Addendum m

AD maximum frontal Area m2

ax Distance m

Ai. Max. area lift m2

aw Aspect ratio m2

Aw Maximum wing aria m2

b Distance m

b Width of beam m

bg Distance m

bw Length of wing m

C Centre distance m

c Distance m

CD Coefficient of Drag

CL Coefficient of Lift

cw Chord length of the wing mm

d Distance m

Drag N

d Thickness of beam m

Dc Outside diameter centre m

der Dedendum m

DG Pitch diameter of the gear m

Dg Wormgear diameter m

Di Inside diameter m

Do Outside diameter m

List of Symbols xiii

Dow Outside diameter of worm m

DPs Design parameters

DrG Root diameter of gear m

Dr. Root diameter of worm m

Di Throat diameter of gear m

D. Worm diameter m

Young's Modules/Elastic Modules Pa

Eo Output voltage v

F Force N

Fg Face width of gear m

FMSTG Force strain gauge, (model and arm) N

Fn Normal force on the tooth N

FRs Functional requirement

FSGD Force strain gauge Drag N

FSGL Force strain gauge Lift N

FSGM Force strain gauge Moment N

Fw Face length of the worm gear m

Fwc Tangential force worm gear N

Fx Tangential force worm N

Fy Separating force on gear N

Fz Axial force on the worm N

g Gravitation (9.81) m/s2

h Height m

h Water difference m

/a Working depth m

hi Whole depth m

I Moment of inertia m4

IX Moment of inertia about x axis m4

Iy Moment of inertia about y axis m4

Temperature °K

8 Length m

L Lift N

Lg Lead worm gear N

List of Symbols xiv

Lst Load on strut N

M Moment Nm

Mo Pitching moment Nm

Mb Bending moment Nm

Mc Moment about c Nm

Mg Balance weight Nm

MG Moment force on the gear Nm

Mo Moment forces model Nm

Ms2g weight (model and arm) N

NG Number of teeth in the gear m

/sic Number of starts of on a gear

Load N

p Atmospheric pressure Pa

Circular pitch m

Pair Air pressure Pa

Pc Load on carbon fibre N

Pd Diametral pitch m

Pf Load N

R Radius of max. stress in bending beams m

RI, R2, R3, R4 Strain gauge resistance SI

rc centre radius of bending beam m

rc Centre radius of bending ring m

Rc Reynolds number

re radius worm gear m

ri Inside radius of bending beam m

ro Outside radius of bending beam m

S Surface area of a wing m2

Ti Input torque worm Nm

T2 Output torque worm Nm

Tti Temperature °K

Tt2 Temperature °K

v Deflection m

Wind speed m/s

W Weight of model N

List of Symbols xv

w width of test section m

xi Distance m

x2 Distance m

Y Beam deflection m

y Distance neutral axis m

a Angle of attack 0

ARI, AR2, AR3, AR4 Small changes in resistance i/

E Strain

X Lead Angle 0

P Friction coefficient Kg/ms

Pc Viscosity kg/ms

p Density of air kg/m'

pair Density of air kg/m'

pwater Density of water kg/m'

a Stress Pa

u Deflection m

Chapter 1: Introduction 1

1. Introduction

This chapter provides an overview of the aerodynamic forces and pitching moments

acting on a model when moving through air when designing a wind tunnel balance.

1.1 Aerodynamic forces

As air flows past an aeroplane, or any other body, air is diverted from its original path

and such deflections lead to changes in the speed of the air. Bernoulli's equation

shows that the pressure exerted by the air on the aeroplane is altered from that of the

undisturbed stream. Also the viscosity of the air leads to the existence of frictional

forces tending to resist its flow. As a result of these processes, the aeroplane

experiences a resultant aerodynamic force and moment. It is conventional and

convenient to separate this aerodynamic force and moment into three components

namely lift, drag and pitching moment, Houghton and Carpenter (1993).

chord line Angle o1 attack

Lift - - Total reaction

Centre of ► pressure

►

► ►

Drag

Relative airflow

Figure 1.1 Forces acting on an airfoil when moving through air.

1.1.1 Lift

This is the component of force acting upwards, perpendicular to the direction of flight

or to the undisturbed airflow acting through a point called the centre of pressure.

Pitching Moment


1.1.2 Drag

Drag is the component of force acting in the opposite direction to the line of flight or

in the same direction as the motion of the undisturbed air stream. It is the force that

resists the motion of the aircraft.

1.1.3 Pitching moment

This is the moment acting in the plane containing the lift and the drag, i.e. in the

vertical plane when the aircraft is flying horizontally. It is positive when it tends to

increase the incidence or raise the nose of the aircraft.

Figure 1.2 Pitching moment

1.2 Wind tunnel balances

A wind tunnel balance is an apparatus that measures forces and moments acting on an

model while the model is moving through the air. This can either be a very simple

device, such as a spring scale measuring the forces, to a complex measuring device

that feeds the information directly to a computer.

There are two main types of balances, namely, an internal strain gauge balance and an

external balance. External balances measure the forces externally with levers or wires

from outside the wind tunnel connected to a test piece inside the wind tunnel. Internal

strain gauge balance supported or "sting", is designed that the forces and moments

are measured by strain gauge bridges in a probe holding the test piece inside the wind

tunnel as shown in Figure 1.3, Rae and Pope (1984).

Normal tome (also on bottom)

Pithhing moment (also on bottom)

4

Model mounting surface

Axial force 3


Figure 1.3 Three component strain gage balance, Rae and Pope (1984).

The external wind tunnel balances used in wind tunnels can be divided in to four types

by the way it measures the forces on an object. These balances are named from their

main load-carrying members — Wire, platform yoke and Pyramidal, Rae and Pope

(1984).

1.2.1 Wire balance

The wire balance as shown in Figure 1.4 is one of the earliest types of wind tunnel

balances used to determine the forces on the model. Usually the model was mounted

inverted so that the lift adds to the weight of the model to prevent unloading the wires.

A large tare drag on the wires makes it difficult to assess accurate measurements.

Wires tend to break which can lead to the loss of the model. This type of balance is no

longer in use.

Figure 1.4 Wire wind tunnel balance, Rae and Pope (1984).

Calculation for wire balance

L (Lift) = C + D + E (Model is placed inverted -lift)

D (Drag) = A + B

Pitching M (Moment) = E x c


1.2.2 Platform balance

Platform balances as shown in Figure 1.5 are widely used. The platform balance

utilizes either three of four legs to support the main frame. They are constructed and

aligned with the minimum of difficulty. The disadvantages of these balances are:

Moments appear as small differences in large forces when

alignment is poor.

Balance resolving centre is not at the model centre and pitching

moments must be transformed.

Drag and side forces loads put pitching and rolling moments on the

load measuring sensors.

These interactions must be removed from the final data.

a

Figure 1.5 Platform balance, Rae and Pope (1984).

Calculation for a platform balance

L (Lift) = -(A+B+C)

D (Drag) = D + E

Pitching M (Moment) = C x m


1.2.3 Yoke balance

A yoke balance as shown in Figure 1.6 offers an advantage over the platform balance

because the moments are read about the model. The design leads to bigger deflections

than the platform balance, in pitch and side forces. Because the balance frame must

span the test section in order to get the two upper drag arms in their proper position,

the yaw lever arm is exceptionally long. The high supporting pillars are subject to

large deflections. The yoke balance brings out the pitching moment in the drag system

instead of in the lift. The drag forces being the smaller of the forces usually has to be

measured by three very sensitive sensors.

Figure 1.6 Yoke balance, Rae and Pope (1984).

Calculation Yoke balance

L (Lift) = -(A + B)

D (Drag) = C+D+E

Pitching M (Moment) = E x m


1.2.4 Pyramidal balance

The pyramidal balance as shown in Figure 1.7 read the moments about the resolving

centre and the six components are inherently separated and read directly by six

measuring units. No components need be added subtracted or multiplied. The

difficulties involved in reading the small differences in large forces are eliminated and

direct reading of the forces and moments simplify the calculations.

Figure 1.7 Pyamidal balance, Rae and Pope (1984).

Calculation Pyamidal balance

L (Lift) = Total weight on lowest table D (Drag) = D Pitching M (Moment) = -P x f

Accuracy art borer

0.16 0.4 04 0.4

018

000 Et■dy

.O'S

0.6 006

pure of Weighted Objective Tree 0.0375

0.25 100375

Goad traSEsrm

— Gras 0.0375

0.5 10.15 025 0 0375

7011ance le Oared

025 10075

We itor.na. om Md.

0 . 0 075

Reliable

0.3

0 075

Ord Sao b Tr Cafes

025 10.075

II 075

0.075

Ecombely

0.4 ma

01st Lil and Rich 00 1%

10

0.2 005

Mow booze

fnalbnM d

as 10.05

0.2

Day le innybckn

0.3 I 003

Era motors.

02

002

bow

d =wenn

aeote

Pito te

003

rr dry. bus

Reliable and Sinatal. Teslag Balance N a Wnaunnel

005

002

003

0.008

0004 qaeralrig

dare Cbarlsks

0.1 0.1

Elm so a

0.

En) le nlde.s

Elay

05 1 005 0.4 1 0 032

rEny la angle*

0.

Gad

0.1 I 0.1

04 1 Go

Ward croon

DKOISI oanpareeta

0.024

0.024

004

005

Tool ...I cO

Chapter 2: Requirements and criteria for a wind tunnel balance 8

The objectives were weighed and placed in a weighted objective tree (Figure 2.1). An

evaluation chart (Figure 2.3) was created for the wind tunnel balances to see the difference

between the balances.

Figure 2.1 Weighted objective tree

Ch

apte

r 2: R

equirem

ents and crit e

ria fo

r a

win

d tunn

el balan

ce

121V

H0

NO

LLAM

1VA

3 Table

2.1 Evaluation

charts for the

wind tunnel balances.

-1 0 ET ii

co co -4 a) cn a co N—, o CO ° -.1 ° al a l'a t1/4) -1'

No. D

escription

Weigh

t

Eval uatio

n criteria

[Num

ber o

f com

po

ne

nts

'Material co

st

[De

-cou

pled com

pone

nts

'Easy

to a

ccumulate d

ata

'Easy

to calib

rate

'Easy

to fit/chan

ge m

odel

'Quic

k ch

ang

e to

test conditio

ns

[Easy

mainten

ance

Easy

to m

anufactu

re

'Sim

ple as

sembly

'Sm

all no. o

f parts

[Steady sig

nal

Low h

ysteresis

[Sen

sitivity

Good tole

rance to te

st condition

s

Tole

rance to

ov

erlo

ad

Low

interf eren

ce fro

m outside

Low

vibratio

n

Low

wea

r of m

oving parts

1

0

0) 00

0

A.

0.02

4, [ 0

.008

1

0 6 0.) IQ

0 6 o CO

0 6 o CO

° 6 IV

° 6 Ch)

CD IV c"°

6 C.11

° 6 CO

P CD

P -, 01

0 6 4

01

0 6 -4 CT

0 6 -4 C.71

0.037

5]

0 O4 C.) 01 [N

atural Freq

. F

ri ction

Para

meters

...•

"co a) a 8 co co co CD -4 CC) -4 A OD CO --.1 --4 CT CO CO VI

Valu

e (1

-11)1

Exte

rnal w

ind

balance

-4 "0 9 co ca co co 01

P _.., co

, _0 " a

0 ,...,- — isi)

0.288

0 n• 0 T

0.048

_. A.

PPPo _> CO

_., A.

• "

0.64

1.2

8

_, 6 CT

0.525

0.37

5

0 -a) V cm

o 4.)

0.3675

* < CD f13 ar c CD a"'

CD O.

7

129

CO A a CT CO CD CO a CO -.4 -4 CO CO -4 CT CD CO CO

Valu

e (1

-11)

Internal w

ind balan

ce

(Sti ng

)

A ..D, co r,) CO

• .•,•3

6 co 0)

--4 00 949 0° 9. 400 6 co IV

8 6 co A

0 a CO

_,_, ON —

_, "

I 9

1:0

o • W Cn

o • Cli CI)

-, " Cn

' iQ

0.525

° i..) ,1

cn

0.675

° it)

0.588

Weigh

ted valu

e

II 1

LOW SPEED TEST AREA

L__ _J DOOR


In the elevation chart (Table 2.1) the objectives weights were multiplied with the values

(priorities generated between one and eleven) and a weighed value was obtained. The

weighed values were added. According to the weighed values the internal wind tunnel balance

is the more appropriate design to go for because of fewer moving parts and no friction.

Due to the assignment to build a wind balance according to the axiomatic design method and

the specialised equipment to manufacture a sting balance with a limited financial budget, it

was decided to build an external wind tunnel balance with a reasonable high accuracy.

2.4 Design criteria for the wind tunnel balance

To design a balance for a wind tunnel the following criteria must be taken in consideration:

The maximum wind speed in the test area

The wind tunnel projected area in test section

The maximum model size to be used as a test piece

Maximum rotation of the test piece

The increments of angle change

The accuracy of the measurements

Budget available for manufacture

Rigidity of the balance

2.4.1 Existing wind tunnel layout.

The wind tunnel in the RAU Mechanical Engineering department, is a close loop wind tunnel

with a low speed and high speed testing areas (Figure 2.2).

Figure 2.2 Existing wind tunnel layout at the RAU Mechanical Engineering Department


The low-speed area of the tunnel is 2.1 meters wide and 2 4 meters high and attains a

maximum average wind speed of 7.3 meters/second (26.3 km/h), mainly used for models of

size of 1-meter square such as buildings and wind energy models. The high-speed area of the

tunnel is 1 meter by 1 meter and used for high-speed testing with a maximum average wind

speed as explained in paragraph 2.4.3. The external wind tunnel balance was designed to fit in

the high-speed test area of the tunnel.

2.4.2 Test section

The test section is 1 m 2 and 3 meter long as shown in Figure 2.2. It is constructed from

pressed board and surrounded with a wooden frame. A disadvantage is the poor task lighting

in the test section, which needs to be upgraded.

Test area 3000

CrOSSSeCten of test area

SECTION A-A

Figure 2.3 High-speed test section of the existing wind tunnel at the RAU Mechanical

Engineering Department.

2.4.3 Wind speed map in the high-speed test section

The static pressure gradient along the test section must be known in order to make the

necessary corrections for linear flow through the section and boundary layer thickness. A

static tube with a water manometer was used to determine the static pressure in the high-speed

test section. Two vertical cross section 1 meter in front and another 1 meter behind the

balance were measured as shown in Figure 2.5.


Test area 3000

1 1 /

4--

From

Panel

CROSS SECTION GRID MAP

Wind tunnel

Balance area

Figure 2.5 Static pressure map layout of the test section.

The two cross sections were divided in to a grid 25mm to 100mm as shown in Figure 2.5. To

escape the effects of the flow boundary, measurements were taken at a point located at 25 to

100mm from the roof and the average wind speeds were plotted as shown in a graph Figure

2.6. The average wind speeds related to height were measured as shown in Table 2.2 and

plotted horizontally and vertically as shown in figure 2.7 and 2.8. (See appendix A)

Front Cross Section (speed m/s) Vertical

Distance (mm)

Hodzcotal distate (mm) Average speed (bath:Intel)

125 250 375 500 625 750 875 (Ms) Kroh

103 20.11 19.34 19.90 20.11 21.04 21.04 20.11 20. 24 72.85

200 2089 21.04 21.04 21.04 19.99 21.01 19.62 20.67 71.41

300 20.58 21.00 21.50 21.04 21.00 21.04 20.11 20.90 75.23

103 21.03 21.04 21.01 21.04 21.04 21.04 20.11 20.90 75.25

503 20.58 21.04 21.04 21.04 21.00 21.04 20.51 2091 75.26

e0) 20.00 21.01 21.04 21.04 21.00 21.04 21.04 20.811 75.20

700 20.80 21.04 21.04 21.04 21.60 20.11 21.04 20.84 7580

800 20.00 21.04 21.04 21.04 21.04 21.04 20.00 20.75 74.68

900 20.60 20.60 20.11 20.50 20.11 20.11 20.11 20.30 _ 73.10

1080

Average(m/s)

Average (Kolni)

20.42 20.80 20.86 20.88 20.87 20.84 213.30

7a51 74.88 7511 75.17 75.13 75.01 7309

Aft Cross Section (speed m/s) Viatica Horizontal distance (mm) Average Speed reerecoal)

DiSt34101 (mm) 125 250 375 500 625 750 875 (Ms) KnYh

100 20.03 20.11 20.11 20.11 20.11 21.04 20.11 20.23 72.81

280 20.58 21.04 20.58 21.04 21.30 21.04 19.62 20.75 74.68

300 20.58 21.00 21.04 21.04 21.04 20.70 20.70 20.87 75.14

400 20.58 21.04 21.00 21.00 21.00 21.04 20.70 20.91 75.28

500 20.58 21.01 21.00 21.45 21.23 21.04 21.03 20.93 75.35

600 20.00 21.04 21.00 21.01 21.00 21.00 21.00 20.87 75.13

700 20.58 21.04 21.03 21.01 21.03 21.00 20.11 20.83 74,97

s33 20.58 21.04 21.00 20.58 20.80 20.80 20.11 20.70 74.53

900 20.10 20.11 21.00 20.50 20.60 20.11 20.11 20.36 73.30

1080 0.03

Average(MS) 20.40 20.83 20.86 20.87 20.87 20.86 23.38

Average (Km/h) 73.44 74.99 75.09 75.12 75.11 75.11 73.38

Table 2.2 Wind tunnel speed data.


Average Wind speed in High-speed test section

25.0

20.0

•

--a—Front

—0—Aft

7 15.0

•

5.0

0.0

20 25 30 35 40 45 50 55 60 70 80 90 100 200

Distance from roof (mm)

Figure 2.6 Boundary layer graph (20 to 200 mm from roof).

Average Wind speed in High-speed test section

21.00

20.90

2080

20.70

.— 20 60

1 .1? 20.50

II 20.40

20.30

20.20

20.10

I

TUNNEL i CENTRE 1

—e—Front —o—ert

20.00 .

125 250 375 500 625 750 875

Distance from front panel (mm)

Figure 27. Average horizontal distribution of wind speeds in test section.


11 on

Average Wind speed In High-speed test section

(mis)

3 2

5 2

TUNNEL CENTRE

+Front

—o—Aft

20.00

19.80 . .

100 200 300 400 500 600 700

Distance Iron roof (mm)

800 900

Figure 2.8. Average vertical distribution of wind speeds in test section

From the graph in Figure 2.6 it can be seen that the friction from the side-walls (up to 200

mm) has an effect on the wind speed. A distance of 200 mm from the side-walls the wind

speed is uniformly with a little speed variation between the front and aft cross section as

shown in the graphs Figure 2.7 and Figure 2.8.

2.4.4 Determining the maximum model size

According to Barlow et al. (1999), the maximum model-span to tunnel-width ratio must be

between 0.3 - 0.7 for aircraft and —5% frontal area blockage of the test area for automobiles.

In a paper SAE Sp-1036 (1993), accurate test information were obtained from the model car

with a frontal blockage area of 7 - 9% of the tunnel area that gives a good correlation to a full-

scale car.

For the design of the wind tunnel balance a 0.25 to 0.7 model-span to tunnel-width ratio is

used for calculations (Figure 2.9) and a frontal area of —5% of the tunnel test area (Figure

2.10).

Test area

Test area


Width of model (b)

250 mm b 700mm

Figure 2.9 Aircraft model size.

Figure 2.10. Frontal blockage area

Blockage area for Cars

b = w and c = b

A =1/16 w2

A= 0.0625 m2 (6.25%)

Blockage area for airfoils

AD = b c sin 30° (max rotation of

model)

AD= 0.0625 x 0.5 m2

AD= 0.03125 m2 (3.12%)

According to Barlow et al. (1999), an aspect ratio of 7 or smaller is a good measure to use

when determining the area of an airfoil. Aspect ratio (aw) is the length of the wing (bw)

divided by the chord length (cw) as shown in Figure 2.11.


bw

Figure 2.11 Aspect ration of a wing

b a„, =

„, (2.1)

cw

Maximum wing area (Aw):

bw =0.7W =0.7rn

b 0.7 c = — =0.1m

w aw 7

A w = 0.7 x 0.1 = 0.07m 2

2.4.5 Rotation of the model

Automobile models seldom need to be rotated. In testing the wings and airfoils angel of

attack need to be changed. The drag and lift forces change as the angle of attack changes.

Figure 2.12 shows the airflow over a wing at high angle of attack. In Figure 2.13 the graph

shows a relation of a typical coefficient of lift versus the angle of attack. To change the

angle of attack the model needs to rotate about the horizontal axis.

Figure 2. 12 Stalling of a wing at high angles of attack, Houghton and Carpenter (1993).

14

12

O


15•

Ordinary ang es of flight

_ — I

,

1 A A

A IT rE,

__. FA - I— — A T1 _ I

I— — t -4" 0• 12•

16

Angle of attack

Figure 2.13 Angle of attack versus Lift Graph Houghton and Carpenter (1993).

2.5 Accuracy of the measurements

One of the problems of a wind tunnel balance is rigidity. Deflections in the balance can

move the model from centre and invalidate the moment data or nullify the balance

alignment so that part of the lift forces appears as drag or moment forces. To minimise

rigidity is to design the balance for minimum deflection to fit the accuracy for acceptable

errors listed in Table 2.3.

Low Angle of Attack High Angle of Attack

Lift CL = ±0.001, or 0.1% Cl, = =0.002, or 0.25% Drag CD = =0.0001, or 0.1% CD = ±0.0020, or 0.25% Pitching moment Cm = =0.001, or 0.1% C„, = ±0.002, or 0.25% Yawing moment C„ = ±0.0001, or 0.1% C„ = ±0.0010, or 0.25% Rolling moment C, = ±0.001, or 0.1% CI = =0.002, or 0.25% Side force Cy = =0.001, or 0.1% Cy = =0.002, or 0.25%

List 2.3 Permissible measuring errors in the various aerodynamic coefficients, Rae and

Pope (1984).


A trade-off between accuracy and money available allows for the accuracy of the wind

tunnel balance and influence the design objectives. Figure 2.13 shows the cost increases in

percentage as the accuracy increases.

400

300

200

00

0 30.030 30.015 30.010 30.003 30.001 30.0005 30.00025 Tolerance, In.

Incr

ease

in c

ost.

%

Figure 2.14 Influence of tolerance (accuracy) on processing costs, Dieter (2000).

Chapter 3: Axiomatic design 19

3. Axiomatic design

3.1 Introduction

Axiomatic design is a scientifically based design theory that provides designers with

decision-making criteria for the conceptual design process. The designer must clearly

define the design task in terms of what the customers need (Professor Nam Suh and

his colleagues at MIT have developed such a theoretical basis for design that is

focused around two design axioms, hence the name axiomatic design, Dieter (2000)).

Designers who have applied this theory to the creation of new designs or the diagnosis

of existing designs have produced better designs more quickly, maximising the

usefulness of their current design tools.

The methodology ensures that design decisions are based on customer needs that have

been thoroughly identified, and it provides a way to track that each function is

satisfied independently of every other function. The entire design is planned from its

highest functions to the smallest details before prototyping is considered.

Fundamental to this theory of design is the idea of functional requirements (FRs) and

design parameters (DPs). The design procedure is concerned with linking the two at

every hierarchical level of the design process. The design objectives are defined in

terms of specific requirements called functional requirements (FRs). In order to

satisfy these functional requirements a physical embodiment must be created in terms

of design parameters (DPs) as shown in Figure 3.1 by mapping the FRs of the

functional domain to the DPs of the physical domain to create a product or process to

satisfies the perceived need. Note from the mapping process (Figure 3.1) that one

design may result from the generation of DPs that satisfy the FRs, Dieter (2000).


Functional Requirements

Design Parameters

DP, DP 2 DP 3 DP4 DP5

FR, FR 2 FR3 FR 4 FR5

Mapping

Figure 3.1 Suh's concept of design as the process of mapping functional requirements

(FRs) to design parameters (DPs).

3.2 Axiomatic wind tunnel design parameters

From the DPs the external wind tunnel balance can be designed to meet FRs. The

balance must be capable to measure lift and drag forces as well as the pitching

moment on an object. Figure 3.2 shows the functional hierarchy for the external wind

tunnel balance.

Measure

Force and Moment

Measure LIFT

Force

Measure DRAG Force

PFTCH Moment

ANGULAR

Movement

Vertical Forces

Horizontal Force

Moment Measurirg

Control

DATA Capture

DATA Capture

DATA Capture Read-out

Figure 3.2 Hierarchy offunction requirements (FRs) for a wind tunnel balance,

Dieter (2000).


DATA LOOOER

Figure 3.3 Hierarchy of design requirements (DRs) for a wind tunnel balance.

3.3 Specification for the wind tunnel balance

From the requirements as discussed in chapter 2 the following specification was

defined.

Design requirements Specifications

1 Maximum wind speed in the test area 21.11 in/sec (75.99 km/h)

2 Projected test area Om wide and 1m high) I m2

3 Length of test section 3 m

4 Maximum model width (w) 250 - 600 mm

5 Maximum block area 0.0625 m2 or 6.25%

6 Pitch (Rotation of model in the horizontal axis) -10° to 30°

7 Accuracy to lift forces 0.1 % of full loads

8 Accuracy to drag forces 0.1 % of full loads

9 Accuracy to pitching moment 0.1 % of full loads

10 Accuracy on pitch angle 0.25° per step

11 Density of air (at mean sea level) 1.2 kg/m'

12 Density of air (Johannesburg 1740m above sea

level) 1.002 kg/m3

13 Coefficient of lift (CO 2.0 to 2.5

14 Coefficient of drag (CD) 0.2 to 0.35

Table 3.1 Design requirements for the wind tunnel balance.


3.4 Calculating lift and drag forces

3.4.1 Lift forces

Lift (L) is a force generated when an object such as an airfoil, airplane or object is

moving through air or water and the lift forces is always perpendicular to the flow.

The maximum lift force for the wind tunnel can be calculated by the lift formula.

L = —1

p.V 2 .CL .A L (3.1)

L= 1 x1.0x31.15 2 x 2.5x 0.07 2

L(max) = 84.9N

Where:

Density (p) = 1.0 kg/m'

Max wind velocity = 31.15 m/s (safety factor of 1.5)

Coefficient of Lift (CL) = 2.0

Maximum wing area (AL) = 0.07 m 2 (see section 2.4.4)

Tunnel width = I m

3.4.2 Drag forces

An object in airflow generates a drag force. The drag force is parallel and opposite to

the airflow and perpendicular to the lift force.

The maximum Drag force for the wind tunnel can be calculated by the drag formula.

D =—I p.V 2 .CD .A D (3.2) 2

D =-1

x1.0 x31.15 2 x0.35x 0.03125 2

D(max) = 5.306N

Where:

Density (p) =1.0 kg/m'

Maximum wind velocity = 31.65 m/s (safety factor of 1.5)


Coefficient of Drag (CD) = 0.35

Max frontal area (AD) = 0.03125 m2 (see section 2.2.4)

Tunnel width = 1 meter

3.4.3 Pitching forces

Pitching moment is dependent on the lift forces, drag forces and pitching moments on

the object as well as the geometry of the design.

Chapter 4: External wind tunnel balance concept designs 24

4. External wind tunnel balance concept designs

4.1 Introduction

One of the most common problems of a wind tunnel balance is lack of rigidity.

Deflection in a balance may move the model from the revolving centre and invalidate the

moment data so that part of the lift appears as drag or side forces. To conform to the list

as shown in Table 2.3, deflection and tolerances must be kept to a minimum.

The balance must also be designed to fit a budget and expensive components and

machining techniques must be kept to a minimum.

4.1 Preliminary ideas

To design the ideal wind tunnel balance a lot of preliminary ideas were generated and the

best of the ideas were used to design the wind tunnel balance. Preliminary ideas were

evaluated to the criteria list as shown in Chapter 2.4.

4.1.1 External sting type wind tunnel balance (Concept 1)

The external sting type balance concept as shown in Figure 4.1 was proposed to eliminate

the moving parts. The balance is to be machined from one solid part of aluminium. Due

to the complex design, forces interact with each other and a computer program is needed

to separate forces.

The advantage of this design is no moving parts, but the disadvantage of the proposed

design is the complex interaction between forces as shown in the finite element Figure

4.2. The pitching moment is not added because of the interaction between forces that

does not conform to the axiomatic design requirements.

Figure 4.1 Sting type external balance.

STRAIN GAUGES

t 100N

10N

Pet -Itp :: Sete Cespleternett

Unts


Figure 4.2 FEA of the External sting type balance.

LIFT


4.1.2 External ring balance (Concept 2)

The external ring arm balance concept as shown in Figure 4.3 was generated to allow the

object to rotate with out a deviation from its centre point. The advantage of the ring arm

is its stability, low vibration and minimum deflection. The disadvantage of this idea was

the large space for the arm to operate in, because of limited space the arm will not fit

below the existing wind tunnel test section. The weight of the arm in relation to the

forces is so big that small force or deviation in forces can not be detected. Further more

the mass centre of the ring arm will have an off balance effect on the lift force and

pitching moment.

Horizontal and vertical shafts with linear bearings separated the lift and drag forces. Pitch

sensor in the ring detects pitching moment. In the finite element analyse Figure 4.4 the

weak point in the arm is holding the model. In this design the way the lift and drag forces

were measured was further looked at and used in the final design concept.

ROTATION ANGLE

CENTRE OF

\

WIND TUNNEL

DRAG

111 1 selpio e 4, Mi.

3/4• %., KHiWI Figure 4.3 External ring arm balance.


m; Stt NSW Sten

Ural : W Ws)

Figure 4.4 FEA External ring arm balance.

4.1.3 Wind tunnel balance (concept 3)

From the above concepts a combination was used to design the balance as shown in

Figure 4.5. The lift and drag forces were separated by means of shafts. The lift force is

measured vertically and the drag force horizontally. Strain gauge load cells were used to

measure the forces. A shaft type arm is considered to allow angel changes. Pitching

moment is measured by means of strain gauge load cells.

The advantages of the In this design are:

Lift and drag forces do not interact.

Horizontally placed strain gauge load cell only measures lift forces.

Vertically placed strain gauge load cell only measures drag forces.

PITCH ANGLE

DRAG

Pivot STRAIN GAUGE

PITCH


Figure 4.5 Wind tunnel balance (concept 3) Preliminary idea offinal design.

4.3 Vertical strut concept design

4.3.1 Preliminary ideas

A few strut ideas were considered and the best of the ideas were used to design the wind

tunnel balance. Preliminary ideas were evaluated to the criteria list as shown in paragraph

2.4.

4.3.1.1 Shaft type

A vertical strut and horizontal arm as shown in Figure 4.6 were considered. The

horizontal strut can move form -10° to +30° with the aid of a motor that turns a threaded

shaft in to a threaded rod, acting as a push-pull cylinder.

0 0 CD

300

Chapter 4: External wind tunnel balance concept designs

29

Figure 4.6 Horizontal strut and vertical arm.

The disadvantage of this design is the length of the strut to accommodate the wind tunnel.

The horizontal strut diameter becomes very big to limit deflections that the weight and

size overwhelm the design.

4.3.1.2 Halve circle strut

A half circle type strut was looked at as shown in Figure 4.7. To limit the deflection to a

minimum the dimensions of the strut must be 100mm by 80mm cut on a radius of

750mm. Due to the space needed to operate in the weight of the arm and the cost for

manufacturing the arm, it was decided not to use this arm design idea.

Operating gear, motor

and load cells.

850

Chapter 4: External wind tunnel balance concept designs

30

Figure 4.7 Half-circle arm.

4.3.1.3 Two-arm strut

From the above ideas a new two-arm strut was designed. Using two struts that move up

and down and bolted to two horizontal arms allows the headpiece to rotate as shown in

Figure 4.8. A Company making small balances in the United States called AEROLAB

also uses this method of movement, but in training apparatus for school learners.

Due to the length of the struts, normal materials do not allow for small deflections and

thin diameters. As mentioned in paragraph 4.3.1.1 the problem with the shaft type, new

materials were looked at to satisfy the criteria for small deflections and thin diameters

that is light in weight.

31 Chapter 4: External wind tunnel balance concept designs

+10

Rotate I clockwise I

UP

Rotate anti-clockwise

Figure 4.8 Two-arm strut

-10°_

Down

The advantages of the two-arm strut mechanism are:

Bottom and top rotate together.

Two struts are more rigid than a single strut.

Rotation can be done from outside the wind tunnel and thus less drag.

Gearbox and stepper motor can be used to rotate accurately.

Lift force is in line with pivot point and this reduces couples.

The shafts behind the model have no interference effect on the model.

From this idea it was decided to develop the two-arm strut for the wind tunnel balance.

Wind Flow angle of` attack

Chapter 5: Wind tunnel balance design 32

5. Wind tunnel balance design

5.1 Introduction

From the conceptual designs discussed in Chapter 4 the final design were generated. An

external wind tunnel balance consists of a number of levers type parts that must be

designed for minimum deflection under maximum load. Because of the horizontal and

vertical shafts friction must be kept to a minimum.

5.2 Forces diagram

The sketch Figure 5.1 show the lift, drag and pitching moments forces acting on a model.

The wind tunnel balance must separate these forces and moments and accurately present

the small differences in large forces.

Lift

Figure 5.1 Sketch offorces and moments.


The balance is designed in such a manner so that the model moment reference centre,

point B, lies directly above the balance pivot point A, as shown in Figure 5.1.

In Figure 5.1 the lift force, drag force and pitching moment is shown with the relative

distances from the pivot point A.

5.2.1 Lift force

Lift is a force generated by the air when flow over an object such as an airfoil and is

perpendicular to the airflow. The weight of the model and the weight of the arm (Mstg)

affect the lift force (L) as shown in Figure 5.1.

Fsa = A I m g— L (5.1)

But for calibration L = 0 with no wind flow, Fms-rc (Force on the strain gauge due to

weight of the model and arm) is equal to Mstg.

— LFSG1. = FMS1U (5.2)

To get the lift (L) acting on an object, FMSTG must be subtracted from Fsa (Force strain

gauge lift). Thus lift can be written as

L = FSGL FMSTG (5.3)

The minus in front if the lift (L) refers to the direction of the force.

5.2.2 Drag force

An object in airflow generates a drag force. The drag force is parallel and opposite to the

airflow and perpendicular to the lift force. The force is measured at F SOD (Force strain

gauge drag)

Thus Drag can be written as:

D= FsGD (5.4)


5.2.3 Pitching moments

To calculate the pitching moment on the model, the moment (Mo) must be transferred to the pivot point A. Take moments about pivot point A. (+ clockwise, up -) as shown in Figure 5.1

The pitching moment (Mo) can be written as:

Mo (D x (Fsaw x c)+ (M s, g x a) — (FsGa x e) = (Mg x d)

Mo =(Mgxd)—(Dxb)—(F sGM xc)—(M„gxa)+(FsG,,xe) (5.5)

The balance weight (Mg) is added to counterbalance the weight of the strut arm and the model (Mszg)

(Mg x d) = (M SIG X a) (5.6)

Thus the moment is:

Mo = —(D x b)— (FsGm x c)+ (FsGo x e)

But from equation 5.4, FSGD = D, the moment can be written as:

M — FsGm xc+Dx (e — b) (5.7)

The lift component does not affect the pitch force because it lies directly above the pivot

point A as shown in Figure 5.1. Pitching moment (Mo) is defined with respect to the

model reference centre point B.

5.3 Wind tunnel base design

From the sketch in Figure 4.5 the lift and drag forces were separated and the lift force

defined in such a manner that it works through the pitch pivot point and thus has no effect

on the pitch force.

Pitch Strain gauge Laod cell


The lift force was separated from the drag forces by mounting two vertical shafts on the

drag plate as shown in Figure 5.2. The lift plate moves up and down with four linear

bearings on two vertical shafts. A strain gauge load cell mounted below the lift plate

measures the lift forces. The horizontal platform, drag plate, with the lift plate bolted on

top was designed to move on two horizontally mounted shafts located in a base plate

cradle as shown in Figure 5.2. A strain gauge load cell is mounted between the cradle and

the drag plate as shown in Figure 5.2 to measure the drag forces.

The base plate cradle hinges on the base plate via the pivot point. In the design as shown

in Figure 5.2 the pivot point (hinge) centre and the vertical arm of the lift plate centre

were in the same plane to minimise the effect of couples. A strain gauge load cell was

mounted between the base plate and the cradle to measure the pitch forces as shown in

Figure 5.2 and Figure 5.5.

CENTRE LINE OF OBJECT

CENTRE LINE OF OBJECT

Lift Strain gauge Load cell

Drag Plate

PITCH Base Plato Cradle

Base Plate

Figure 5.2 Final concept design.

Lift Plato

LIFT Vertical shafts

1. id- Horizontal shafts

Drag Strain gauge Load cell

gia=gra

r= I I Nil

As mentioned in the introduction paragraph 4.1, deflections are a main concern of a wind

balance. Due to the complex configuration of the design a finite element package

CosmosWorks Cosmos/works, (1999) was used to investigate deflections.


Figure 5.3 Finite element mesh on the Wind Tunnel Balance base part.

Figure 5.3 shows the mesh created by the finite element analysis (FEA). The mesh is

used to calculate the forces and determine the deflection of the part under certain

boundary conditions. Figure 5.4 shows the deflection of the shaft when a lift force of

100N and a drag force of ION are present on the arm with the base plated fixed in all

directions.

As shown in Figure 5.4, the maximum deflection that is predicted by the finite element

analysis (FEA) is 0.0427 millimetres. This is acceptable for a wind tunnel balance as

discussed by Barlow et al. (1999), in their book on low-speed wind tunnel testing.


100N

Windtunnel_balnew jem-tfp :: Static Displacement

Units : mm

10N

URES

277e-002

920e-002

b .564e-002

208e-002

851e-032

.495e-002

138e-002

782e-002

426e-002

069e-002

.128e-030

564e-030

000e-0313

Figure 5.4. Finite element analyses on the Wind Tunnel Balance base part.

Most of the base part components were made from aluminium for easy manufacturing.

The base top arm, horizontal and vertical shafts were made from stainless steel because

of its high strength and rigidity.


As shown in the Figure 5.4 the maximum defection is on the base top arm. This

deflection transfers to the strut and model 700 mm above that will enlarge the deflection

by up to lmin. (See Appendix B, Wind tunnel balance assembly. WTB-01-00.)

Figure 5.5 Base Assembly

5.4 Wind tunnel two-arm strut design

One of the problems of a wind tunnel balance could be rigidity. Deflections in the

balance can move the model from centre and invalidate the moment data or nullify the

balance alignment so that part of the lift forces appears as a drag force or as a pitching

moment.

The vertical arms are important components in the design, but also the longest but

weakest component of the design, because of their length the maximum deflection can be

Vertical arms

Worm Gearbox

12V Stepper Motor

Horizontal Link Arms

7-kr1/2:=

ICI

a-a Base Top Ann


expected at the top end of the strut. The ideal is to design for a maximum of 0.2 to

0.5mm. To achieve this carbon fiber material was selected for the struts, because of its

stiffens and weight advantage. More information on the carbon can be found in Chapter

6.

Figure 5.6 shows the two-arm strut design with a length of 690 millimeters from the

horizontal link arm to the top piece that is in the middle of the wind tunnel test section.

Headpiece

Figure 5.6 Sketch of the two-arm strut.

The advantage of the two-arm strut is that the point of rotation Of the headpiece (centre)

stays in line with the vertical centre of the wind tunnel balance no matter the angle of the

headpiece. As shown in Figure 5.8. (See Appendix B — drawing WTB-02-00.)


5.4.1 Base top arm

The base top arm is the connection between the base structure and the two-arm strut. It

transfers the loads from the model and two-arm strut to the load cells in the base. This

component must have the minimum deflection. As mentioned the base top arm is

manufactured from stainless steel and curries the gearbox and horizontal link arms,

shown in Figure 5.6.

Itiitpu•Ljr:Shis Diganarst

Ins:_

Figure 5.7 FEA Deflection on the Base top arm.

Figure 5.7 show a FEA of the base top arm with the mounting holes to the lift plate fixed

in all direction. A lift force of 100N and a drag forcelON were places on the bearing

mounting holes, as the forces transferred from the horizontal link arms to the base top

arm. As shown in Figure 5.12. A deflection of 0.01 mm is predicted by the FEA analysis.

(See Appendix B WTB-02-02)

5.4.2 Horizontal link arms

The horizontal link arms transfer the load from the carbon rods to the top base arm. This

component must be strong with the minimum deflection but also light in weight. The

1"tIlLigli

I

I

wndthnno! floor

jII

Windtunnel floor

_ —

Winctemnel floor


heavier the structure the less sensitive the balance becomes to small load changes. The

horizontal link arms are designed when moving up or down as shown in Figure 5.8 that

the model can change its angle relative to the oncoming airflow.

This movement allows changing the angle of the model from outside the wind tunnel as

shown in Figure 5.8.

Figure 5.8 Horizontal link arm movement changes head angle.

Figure 5.9 shows a FEA on the horizontal link arms with a deflection of 0.1nam. A cavity

was made in the component to reduce weight for better sensitivity of the lift

measurements.

Figure 5.10 shows that the cavity does not influence the strength of the link arm and that

the critical part of the design is the mounting holes. Figure 5.11 shows the parts after

manufacturing and Figure 5.12 shows the horizontal link arms fitted to the top base arm.


Figure 5.9 FEA Deflection on the Horizontal link arm.

waxrawlor. famc Moeda..

tit .NINI/900■1

L Figure 5.10 FEA Strength, Horizontal link arm.


Figure 5.11 Horizontal link arms.

Figure 5.12. Horizontal link arms fitted to the top base arm.


The horizontal link arm fits to the top base arm by means of a stud (Figure 5.13) that

screws through the link arm (Figure 5.15) into a bearing fitted in a cavity in the top base

arm as shown in Figure 5.12. This type of assembly allows for smooth operation with

very little friction. (See Appendix B, WTB-02-04 and WTB-02-03)

Figure 5. 13 Screw studs. Figure 5.14 Bearing mounted

Figure 5.15 Screw studs in position.

0 rn CD

A


5.4.3 Vertical arms

The vertical arms are an assembly of aluminium end caps and carbon fibre rods. The

carbon fibre rods were made from carbon fibre string and resin. Stiffness is achieved in

the way the strings were spun. Strings were spun in such a manner to achieve minimum

lateral deflection and for minimum twist. Chapter 6 explains the manufacturing of carbon

fibre and the curing process. Figure 5.16 shows the vertical arm as a cantilever beam with

the one end fixed and a force of 100 Newton on the other end.

Figure 5.16. Sketch offorces on the arms.

Diameters of the rods were chosen for minimum drag and interference as well as the

manufactures jig restrictions.


The maximum deflection on a beam can be calculated from, Hibbeler, (1993):

v— 3E1P1,5,3 (5.8)

Where: Deflection (u)

Load (P) = 100N

Length (Lst) = 690mm

Elastic Modules Carbon Fibre (E) = 690 GPa

Moment of inertia (L)

To calculate moment of inertia (kr):

la

Figure 5.16 Moments about the laa Axis.

/a = k + Axx2 I+ ky + AyY2] (5.9)

=[-g-64 (D 4 - d4 )+HR2 r22 ]]+[76i(D4 — t1 4 )+[74122 —r0y 2 ]1

Ia =[-L64 (0.0224 —0.010 4 )+[5-4 (0.011 2 —0.005 2 )0.021+

[:4-(0.022 4 —0.010 4 )+{4(0.011 2 —0.05 2 )1021

la =[ .10x10-8 +1.206x10-14.10x10 -8 +1.206x101

/c, = 1.3 x10-7 +1.3 x10-7

= 2.6x10-7m4


From the equation in 5.8 the minimum deflections that can be expected by the carbon

fibre rods are:

vPles, 3

— 3E1„

100N x 0.6903 v —

3x 400x109 x 2.6x10-7

v=1.05x1rm

v 0.105mm

The advantage of the carbon fibre rod is its stiffness to weight ratio when compare to the

same rod manufacture from steel.

The aluminium end caps were glued in position by using Pratley Ezeebond. To ensure

that the two opposite end caps were aligned and concentric, special concentric keeping

tools were made to align the two end caps as shown in Figures 5.17, 5.18 and 5.19

Figure 5.17 Special concentric holding toot. Figure 5.18 Special concentric holding

tool in position.


Figure 5.19 End caps aligned with concentric holding tools in position.

The two-struts were mounted in position as shown in Figure 5.20. The bottom end caps

were mounted into the two horizontal arms as shown in Figure 5.21. The top end caps were

mounted into the headpiece as shown in Figure 5.22. (See Appendix B, BTW-02-00)

Figure 5.20

Two-arm strut assembly.

Figure 5.21

Bottom end cap mounted into horizontal arms.

Figure 5.22 Top end cap mounted in head piece.


5.4.4 The Headpiece

The headpiece as shown in Figure 5.5 is the part used to mount the model. This part must

be strong to hold the model but small enough to reduce drag. Figure 5.23 shows a Finite

element analysis of the headpiece.

sniwid... Stdc Wei Strna

tier Wel Cleo)

Figure 5.23 FEA of the headpiece.

For strength and durability the head part was manufactured from stainless steel. Figure

5.24 shows a vertical deflection of 0.015 mm under maximum lift and drag forces.

LOOK emi.aide Dapisewnert

Ullb !wen

Figure 5.24 FEA, deflection of the headpiece.

Chapter 5: Wind tunnel balance design

50

Figure 5.25 show an airfoil mounted in position for testing.

Figure 5.25 Model wing mounted on headpiece for testing

5.4.5 The Head vibration test

Wind tunnel balance vibration can cause serious problems leading to inaccurate

measurements. Consequently FEA analysis was performed on the two-arm strut to

determine its natural frequency. The natural frequency predicted by the FEA analysis was

19.04Hz. (See Appendix C)

To evaluate the accuracy of the FEA analysis a vibration sensor was mounted on the

headpiece as shown in Figure 5.27. An oscilloscope was used to capture the data as

shown in Figure 5.26. The obtained natural frequency for the wind tunnel balance is

15.86Hz as shown in Figure 5.28.


Figure 5.26 Vibration frequency data monitored mounted on headpiece.

Figure 5.27 Vibration sensor mounted on headpiece.


_I i int ill.912 (FIIN1.2)- HPS 46DIB c I > CI x

108117!1002 OM Stt15 AN 48.8231z Ally c 244.114 SOO pts I)

E is

'I N:

1 0 on d 1 I file! ' .I

. . I • 1 I i I , , r' . 'l I

. . 1 11 !I 1 ,! ■

i

?I

i

--- -- — XI X2

Manes FIINI:2 j Y1 -35.088 dif X1 15.869 Hz Smace

FUNC2 rffil Y2 -75.000 c1BY X2 131.636 Hz

A -40.000 dBY A 115.967 Hz

Figure 5.28 Vibration frequency captured data.

The difference between the FEA frequency predictions and the real vibration test is that

the FEA was only performed on the two-arm strut assembly with the top base part fixed.

In the vibration sensor measurements the base part of the wind tunnel balance absorbs the

vibration and thus the lower frequency.

5.4.5 The worm gearbox assembly

The test model must be able to change its angle relative to the oncoming airflow. The

angle must be from -10° to +30° as listed in Table 5.1. A worm gearbox housing is fitted

to the top base shaft with the worm gear mounted to the upper horizontal shaft. Figure

5.29 and Figure 5.30 show how the worm gear is attached to the horizontal arm.


Figure 5.29. Worm gear cutaway. Figure 5.30. Worm gear in position.

To align and bolt the worm gear in position, a special tool was made that lines the centre

of the horizontal shaft mounting hole in to the centre of the worm gear as shown in

Figure 5.31.

Figure 5.31 Worm gear Special mounting tool.

The housing of the worm gearbox was designed to fit on the top base shaft with the worm

shaft and stepper motor as shown in Figure 5.32. In Chapter 7 the gearbox design are

discussed


Figure 5.32 Mounting of the worm gearbox with stepper motor.

The worm gearbox allows changing the angle of the head as shown in Figure 5.33 and

Figure 5.34.

Figure 5.33 Head in +30° position. Figure 5.34 Head in -10° position.

The stepper motor shaft steps 1.8° per step and this allows a 0.0257° change in head

angle or 38.89 steps per degree head angle change. Due to tolerance allowed for meshing

between the worm gear and worm shaft an accuracy of 0.25° is achieved.

Chapter 6: Carbon fiber rods

55

6. Carbon fibre rods

6.1 Introduction

Carbon fibre represents a new breed of high-strength material. Carbon fibre can be

described as a fibre containing at least 90% carbon obtained by the controlled pyrolysis

of appropriate fibres. The existence of carbon fibre came into being in 1879 when Edison

took out a patent for the manufacture of carbon filaments suitable for use in electric

lamps. However, it was in the early 1960s when successful commercial production was

started, as the requirements of the aerospace industry - especially for military aircraft —

for better and lightweight materials became of paramount importance. Carbon fibre

composites are ideally suited to applications where strength, stiffness, lower weight, and

outstanding fatigue characteristics are critical requirements.

6.2 Manufacturing of carbon fibre rods

Most carbon fibres are made from polyacrylonitrile (PAN) substances. Four processes were used to make the carbon fibre rods namely: http://www.users.globalnet.co.uk/carbon fibres.htm (2002).

Stretching the PAN fibres.

Stabilisation under tensions at 220° C.

Carbonisation in an inert atmosphere.

Graphitisation at temperatures varying up to 3000° C, in an inert atmosphere.

It is a costly process due to the high temperatures needed and the slow speed of the

conversions. By making alterations to the temperature during production, different

varieties of carbon fibre can be produced. The modulus of the fibre increases with

increase in temperature and reaches about 410 GPa after treatment at 2500° C. The fibre

strength is at its maximum at temperatures between 1200° C to 1700° C. Figure 6.1

shows a line chart of the process.

Liquid impregnation Thermosetting Resin Pitch

Chemical vapour Deposition Hydrocarbon Gas

1000 1200°C it-

1 - 3 Tints Carbonisation

500-100°C 1 -5 Times

Carbon-Carbon composite

Carbon fibre preform structure

Heat Treatment 2000 - 2800°C

Chapter 6: Carbon fiber rods 56

There are many different methods of manufacturing composite materials to produce the

desired properties and form for a component. Some of the methods currently used are:

Filament winding

Lay-up methods

Resin transfer moulding

Injection moulding

Vacuum bonding

Figure 6.1 Carbon Fibre Process htip:/Avww.callisto.myintu.edu.co.uk (2002).

The filament winding method was used to make the two vertical uprights. The process

uses continuous prepregnated fibres with resin that were pulled from a large spool and

wound at onto a rotating mandrel as shown in Figure 6.2. When the required diameter is

met the mandrel was removed and the wound tubes cured.


Pamto Mtge Wan =holed bi Wit ofer ClIMEO scam to romans OM

SC/ \

1111111 a Mp Raters

4— Rein ear

Rotating LWOW

• 171

Matta [anima

To Croat

Figure 6.2 Winding method, http://www.callisto.my.mtu.edu.co.uk (2002).

6.3 Comparison with Other Structural Materials

Due to the process methods described above, there is a very large range of mechanical

properties that can be achieved with composite materials. Even when considering one

fibre type on its own, the composite properties can vary by a factor of 10, Kotek et al.

(2001), with the range of fibre contents and orientations that are commonly achieved.

Table 6.1 shows the comparisons of the mechanical properties for the composite

materials.

Illibublipp Male BU. Ten0.1114490n MP.) 10h1

1899310884113

107441

Walk NSW

Carbca HS 3500 1811 - 270 1.8 80 -150

Carta IPA 5300 270.325 1.8 150.180

Caton IN 3500 325.410 Le tao - 240

Lew UM 2000 140. 2.0 200.

Air t at 3300 00 1.15 40 *rand tat 3100 120 0.45 80

Awl/ 1111M 3400 180 1.47 120

Grass • E 91m MO 89 23 27

GIus • 52 an 3450 35 23 34

Glass • quartz 3700 69 2.2 31

Muria= Agog 170218 400 1059 2.7 28

Tlanlurn 950 110 4.5 24

Mild Med (55 Glade) 450 205 7.8 26

69144443 Sled 05-801 800 193 7.8 25

145 9100 0774 18040 1241 197 73 25

Table 6.1 Material strength and stiffens comparison, Kotek et al. (2001).


The above figures clearly show the range of properties that different composite materials

can display. These properties can best be summed up as high strengths and stiffness

combined with low densities. It is these properties that give rise to the characteristic high

strength and stiffness to weight ratios that make composite structures ideal for so many

applications.

The strength and stiffness to weight ratio of composite materials can best be illustrated by

the following graphs Figure 6.3 and 6.4 that plot 'specific' properties Kotek et al. (2001).

These are simply the result of dividing the mechanical properties of a material by its

density.

=STEEL I■CARBON (high gamgth)

CARBON (high glithing) KEVLAR

C=i ALM/IRMA =I GLASS

STRENGTH I UNIT WEIGHT

Figure 6.3 The strength-to-weight ratio, Kotek et aL (2001).

=STEEL ∎CARBON (high cHISI) 1==1CAREION OliGH •Othinvi

KEVLAR ==s mumpaum =GLASS

STRIFFNESS I War WEIGHT

Figure 6.4 The stiffness-to-weight ratio, Kotek et aL (2001).

Carbon Fibre Bending graph

Load versus Deflection

2 ra n 2 2 8 r, :a 2 2 2 2 2 8 12 Si 2 2 8 2 2 6 ei n ai al ea ri vi ci co v.: .8 6

Deflection mica mInmeors

10000

9000

8000

7000

2 8000

11 5000

4000

3000

2000

1000

— Carta, and

A A v AN


6.4 Deflection test of tubes

Due to the process method used to manufacture the carbon tubes, it was decided to do a

deflection test on the tubes to determine the Elastic Modulus of the tubes.

An off-cut of a tube were placed on two supports and pressured with an hydraulic press

as shown in Figure 6.5 and a deflection graph was plotted as shown in Figure 6.6.

Figure 6.5 Tube test set-up.

Figure 6.6 Carbon fibre deflection graph.


From the graph as shown in Figure 6.6 the maximum Elastic Modulus can be calculated

by taking a straight line between two points. The non-linear line up to 5.73 mm is due to

some compressibility of the rod material and was ignored.

By using the deflection equation for beams from Hibbeler (1993), (See Appendix D):

A v — AP

'V (6.1)

48 El1

From the deflection graph the Elastic Modulus (E) can be determined.

E— AP X3

48A v11

E _ 4500N x 0.1503

48x5.6x10 -6 x1.1x10-8

E = 513GP a

Where Load (Pc ) = 4500N

Deflection (v) = 5.6 /re

Ix (See paragraph 5.4.3) =1.1x Hi s m4 ,

Length (X) = 150mm

As shown from the deflection graph and calculations that the used of carbon rods in the

two-arm strut is a good choice. For design on the two-arm strut see Chapter 5.

Wormgear body

Stepper Motor

Wormgear

Chapter 7: Worm gearbox design 61

7. Worm Gearbox design

7.1 Introduction

One of the design parameters (Table 3.1) is to rotate an headpiece (object attached)

horizontally in the wind tunnel between -10° to -35°. A worm gearbox was designed that

connects to vertical arms and base top arm to change the angle of the headpiece with the

aid of a stepper motor as shown in Figures 5.5 and 7.1. The worm gearbox is driven by a

stepper motor and can be accurately controlled by using of a computer program.

Figure 7.1 Wind tunnel balance two-arm strut assembly

7.2 Worm gearbox design-Mechsoft computer software

A partner of SolidWorks Corporation for designing gearboxes designed a computer

program Mechsoft. An icon used within the 3D Computer added design software

program, SolidWorks as shown in Figure 7.2, activated the computer program.


a a* tlib

' ila RS° :3 r%IvitilfitTA el b. o 9 !lc:a 9 I-O 3.rj

T.04

Gideon Pob

4 Mid covecisma. Mid amid= I Sayer*.

-6- Tina Sold. SD &W.

Ildb 0 kin

w. Wales filleivint* Leant

■- ihs. II.

p

[

17 enC PISS Ms is Rs is SeCtf re

a, Tito arcl Irma co keg

LCD Rims

0 111 SP/ Pm.

rMi III VW.

A ml

Chin 1W Mtge

in,

■

011.60-135e1W7

h M

11.41 pap

•

Z; ■

IPAI--...

■

thin 150 101111192 Spchact• Bob

A A •

Oa ISO 61010991

A EN

A Ds ISO 12751M

CALstca Swamping .emm swl4_

Worm Gearing Icon

Figure 7.2 MechSoft-Profi Unilools Main page.

When selection the icon a new technical dialog page appear as shown in Figure 7.3.

AVAJoe m Bearing: talmilalion : I BEIM Be CTCRond lora kleln

_ -Pislai@bealsi, , calculate Ralabase-

awrtiFOF I linerliotic_IT268timi,1 2-‘11 _ _ ___ -Type ol Geasim Maim Diameters

'Caw= -ZN 4 . Weans Diemen: coefficient q 11A3 Iv j

Lead Nadal Man I., , 191684c y 5 I, , 8 1 Al

Miking Part Worn () Weaning ei Warm Etch Damen, dl 18358 mm

-- , Banc Patameten WI:crown Uni1Conectiem m al ssit IN

' CerinDidance a 81.767 I., 1 mm Mn. Recamnarded Correction inin 85

Worm Length bl 38 Fa ! an . Um Ratio 93 I, I

Ninbes cl Teeth z Irn.:190 .... Woongaat Width b2 129 I a , mm

Ncernal ton -Ural Tooth Sizes r

Addendffn a' 1 I, .- Nodule in 1.6 I, 1.60M jinn

Banns Anglo a 20 I, 20.0703 II ji. SI' co....., c. 2 I,

Cana Ratio 22635 ' Root Ffial Uli8334 I, ...,‘

Figure 7.3 Technical dialog page .

In the technical dialog page the program leads you to select the geometry data needed to

design the gearbox, in the "Type of gearing" dialog section the program prompt you for

the lead direction and driving part. In the "Basic parameters section" dialog section, the

program requests the centre distances, gear ratio and number of teeth needed, to be filled

in. When selecting the module and pressure angle it is advise to go for standard settings


for easy manufacture and price. With this information given the program calculates main

diameters. The main diameters can be changed, but in turn the setup parameters will be

altered. So a compromise between main dimensions and basic parameters can be reached

to suit the design.

The dimensions dialog box as shown in Figure 7.4 shows all the sketches and dimensions

of the worm and worm gear as well as the work pitch diameter, circular pitch and other

information. The sizes given can be used to design the body of the worm gear. These

sketches and dimensions can also be exported to a drawing. (See Appendix B, Drawing

WTB-02-09 and WTB-02- 1 0).

)0Woun Geatiroj Calculation : I -. El

Ele Cleboard Ices licks -KliCa: &1 1 115 eiSICgil 1? II Labiate 1 L.P_alabqlt...1

geometry] Dimenlions I Tolerance I Lood t _ __ ass ineraions —

25133 27409 31.6123 ,v/

'

//..

1

(11;;;F)

1.4 // /1/2:5.n/2///1°

141 335 144.55 148175

21.558 149.975

Circular Pilch pn 5.027 _ Ji

Wak Pitch Diameter cAv 145.175 I Ten Cicular Pitch pa 5.046 I

Corporative Number at Teeth zv 41.035 Lead pz aas Base Helix Angle Yb 4.6978 I Base Gooier Pith pb 4.739

Figure 7.4 Dimension dialog page .

In the load section of the load dialog box (Figure 7.5), the power and speed can be added

to determine the forces in the worm and worm gear. From the forces on the worm and

worm gear the bearings can be selected.

Do w DRW

Throated wormgear

DG


rtaaWoim Gearing Calculation : I MCI El Eie actoced Mal Bab

134 0 121 5Pataigi 7 II EzbAte II 2atab.,e

$eat jth„rance 1 Lard I Load Sbeliti Celcilalim

Worm Wargeer co Ancordng to /3/J:7.1

Cy Acconfgato.&7

5 Accadrig W C5H 01 16%

rowel P 0.0 10.0192 0192 jpeno

Eipancy V W nu I. x Seed n 450 I __Vain

Toga Mk 01488 Nm 36.61326 I II

-Forces-- -

T eigennei Force Ft 924751 it 50517_126 IN F — —

I LI

Aid Face Fa 5051726 II 92_475101 fill Raid Force Fr 1910964 ii N ...I— Fn —

Nand Force Fn 559_4363 !I N Fr

CretantererViVelcciy v 64375 I CLID7_14 _ ji nth e"

Side Velcaly VI< 04342 rds

Figure 7.5 Load dialog page.

7.3 Worm gear box verification

To verify the Mechsoft computer software program, the worm and wormgear information

were checked by using standard formulas Mott, (1999), as shown in Figure 7.6 for the

gear set.

Figure 7.6 Single-enveloping worm gear set


7.3.1 Centre distance

The centre distances between the worm and the wormgear were selected as 80 mm due to

limited space available. With a fixed centre distance (C) for 80.767 mm and a worm

diameter (Dw) of 18.358 mm selected can the following formula be used to calculated the

wormgear diameter (Dg):

C = Dw+ Dg (7.1)

2

Dg = (2.C)— Dw

Dg =161.534-18.358

Dg = 143.176mm

7.3.2 Pitch

A basic requirement for a worm and wormgear set is that the axial pitch (Px) of the worm

must be equal to the circular pitch (p) of the wormgear in order to mesh, Mott, 1999.

Circular pitch (p) can be calculated by:

p = 7rDG

NG

Where Da = Pitch diameter of the gear (143.176 mm)

NG = Number of teeth in the gear (90 selected)

Wormgears are made according to circular pitch conventions, but commercially available

wormgears sets are usually made to a diametral pitch convention with the following

pitches readily available: 48, 32, 24, 16, 12, 10, 8, 6, 5, 4 and 3 (mm).

(7.2)


Pd = No (7.3)

DG

90 Pd 143.176

Pd = 0.628 /no?

Diametral pitch (Pa) can be defined as:

The conversion from diametral pitch (Pd) to circular pitch (p) can be made by substitute

7.3 into 7.4: Thus circular pitch (p):

Pd xp=ff (7.4)

P= P

P 0.628

p = 5.002 mm

7.3.3 Lead (Lg)

The lead (Lg ) ) of the worm is the axial distance that point on the worm would move as the

worm is rotated one revolution.

Thus, lead (L g) is equal to the number of starts on the worm multiply by the circular pitch

(p). Where the number of starts (Nw) =1

Lg = Nw x PT (7.5)

Lg =1x 5.002

Lg = 5.002 mm

P cos 5°

( 92.475 cos 20 ° sin 5°

559.436


7.3.4 Friction coefficient (E)

The computer program was designed according a CSN 01 4686 specification that uses a

friction coefficient when materials were selected, but not shown to the client. From the

computer data the friction coefficient can be calculated by using the following equation

from Burr and Cheatham, (1995).

F = F a (cos a sin p cos A) (7.6)

From the program data Figure 7.5:

Normal force on the tooth (Fe) = 559.436 N

Axial force (Fa) = 92.475 N (In Figure 7.5 it is shown as the tangential force - Ft

on the worm)

Lead angle (X) = 5 °

Pressure angle (0 = 20°

Friction coefficient (p.) from equation 7.6 can be written as:

(=JP- ) cos 0, sin A F„

cos 2

p = 0.0837

From the calculations a friction coefficient (g) of 0.0837 was used. Friction coefficient

(g) affects the efficiency (q) of the gearbox as shown in Appendix G.

The lead angle can be calculated using:

tan 2 — g (7.7) x Dv,

5.002 tan = 2

g x 18.358 = 4.95°


If friction is neglected, the only force exerted by the gear will be Fn. As shown in Figure

7.7 the normal force on the tooth Fn can be broken in to the three orthogonal components

namely, force in the x direction Fx (tangential force), force in the z direction Fz (axial

force) and the force in the y direction Fy (separating or radial force).

Figure 7.7 Forces on the Worm exerted upon it by the worm gear, -Shigley (1977).

Figure 7.7 shows the forces acting on the worm gear. The tangential force on the worm Fx

is the axial force on the worm gear and the axial force Fz on the worm is the tangential

force on the worm gear, assuming a 90°-shaft angle.

The forces can be written with no friction as:

= (Axial force, worm gear) = (Tangential force, worm) = F„cos0„ sin (7.8)

Fy (separating force) = F„ sin R (7.9)

F(Tangentail force, worm gear) = (Axial force, worm) = F„ cos 0 cos (7.10)

The relative motion between worm and worm gear teeth is pure sliding and so friction

plays an important role in the performance (efficiency ri) of worm gearing. By adding

friction to the worm tooth profile produces a frictional force (g Fn) as shown in Figure

7.7, having two components gFnCos k in the x direction and gFnSin A. in the z-direction.


Equations 7.8 and 7.11 can be written as:

FF = FAcosOn sin A + p cos A) (7.11)

F F„ (coscb, cosA — p sin A) (7.12)

If the friction force developed is large enough the gearset will be irreversible or self-

locking. From equation 7.12, if the friction force (p. Fn Sin A.) is bigger than the tangential

force on the gear Fz the gear cannot drive the worm.

Thus,

,u sin A) cos 0„ cos A

p ) ( cos 0„ cos A)

sin A

p ) cos0„ tan A

tan A ( (colls „)

(7.13)

However, small motions reduce the static coefficient of friction induced by vibrations,

Burr (1995). Test for self-locking by using equation 7.13 with a pressure angle of 20°.

tan A ( cos 0„

tanA ( 0.0837 cos20°

0.0837 tan 4.95

(0.0837

20°

0.0866(0.08907

From the equation 7.13, the friction force (LI Fn Sin X) is bigger than the tangential force

on the gear Fz, thus self-locking will occur.

Efficiency shown as a function of lead and pressure angles

(Constant friction coefficient of 0.0837)

-- Press. Male of 14.5 Deg.

Press. AV*, of 20 Deg.

Press. Angle of 25 Deg.

— Press. Mg!, of 30 Deg.

Press- Angle of 0 Deg

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

Lead Angle (Deg.)


Figure 7.8 shows the efficiency (q) (equation 7.14) as a function of lead and pressure

angles with a constant friction coefficient (is) of 0.0837. Burr and Cheatham, (1995). (See

Appendix G).

ri =100 tan t /1(cos 0„ — p tan A)

cos 0,, tan A. +,u (7.14)

Figure 7.8 Efficiency shown as a function of lead and pressure angles with a 0.0837

friction coefficient (p)

From the graph Figure 7.8 it can be seen that the efficiency On increases with the

increase of the lead angle and that the pressure angles have little effect on the efficiency

(1) of the gearbox.

7.3.5 Pressure angles (0 n)

Commercially available worm gears are made with pressure angles of 14.5°, 20°, 25° and

30°. Thus a pressure angle of 20° were used in the design.

7.3.5 Worm Diameter (Dw) (check)

The worm diameter affects the lead angle (X). Mott (1999) recommends that the worm

diameter should be approximately

D = c0 875 (7.15)

w 2.2


where the center distance (C) is between worm and the wormgear and the worm diameter

(Dw).

Because the Worm Diameter (Dw) was selected due to space restrictions, it was important

to check whether the lead angle (X) would affect the diameter, by using the equation from

Mott (1999). The worm diameter should fall between the range as shown:

C.875

1.6 < <3.0 (7.15) Dw

Where Worm Diameter (Dw) =18mni

Center distance (C) = 80mm

81 .767 0. 875

18 .358 = 2.568

Thus, the selected worm diameter can be used with a lead angle (X) of 4.95° because

equation 7.9 is satisfied

7.4 Wormgear dimensions

The wormgear design is a simple single-enveloping type and thus can the equations as

given in Table 7.1 be used.

Dimension Formula

Addendum a = 0.318 3P2 = I/Pd Whole depth h, = 0.686 6/3, = 2.157/P4

Working depth hk = 2a = 0.636 6Pa = 2/Pd Dedendum b = h, — a = 0.368 3p, = 1.157/Pd

Root diameter of worm Drw = Dw — 2b

Outside diameter of worm Dow = Dw + 2a = Dw + h t

Root diameter of gear 0,6 = Do — 2b

Throat diameter of gear D, = DG + 2a

SOURCE: Standard AGMA 341.02-1965 (R I970). Design of General Industrial Coarse-Pitch

Cylindrical Wormgearing, with the permission of the publisher. American Gear

Manufacturers Association, 1500 King Street. Suite 201. Alexandria. VA 22314.

Table 7.1. Typical tooth dimensions for worm and wormgears, Mott (1999).

0 Shi lmin)

I Pitch dia.

Outsidedia.

.■-

I I K-N I I

howhole depth

/

Figure 7.9 Worm and wormgear details, Mott (1999)

Outside dia. DOG

Throat dia. Or

Pitch dia. DG


By substituting values in the equation in Table 7.1 the following values obtained:

Addendum (aa):= 1.57mm

Dedendum (bd):= 1.827mm

Whole depth( lu):= 3.407mm

Working depth (hk):= 3.16mm

Root diameter of worm (Drw):= 14.34mm

Outside diameter of worm (Dow):= 14.86mm

Root diameter of gear (DrG):= 138.34mm

Throat diameter of gear (Dt):= 145.14mm

7.5 Face Width of the worm

The following equation can be used for the face width (Fg) of the wormgear:

22r FG = 2p = p (7.16)

FG = 2 x 4.95

FG = 9.9mm

Thus the face width were designed for 10 mm.


7.6 Face Length of the worm

The following equation can be used for the face length of the wormgear. This is the

length for the minimum load shearing between the worm and the wormgear.

2[( D 2, ) 2 _ ( D 2G 0)2 (7.17)

2[(145.14) (142_ 1.57n

2 2

F,„, = 41.7mm

A maximum length of 60mm was used to have a maximum intersect between the throat

diameter of the wormgear and the outside diameter of the worm.

7.7 Forces on the worm gear

The worm drive is subjected to separating forces that tend to force the worm and

wormgear out of mesh. The three forces, tangential force (Fx), axial force on the worm

(Fz) and Separating force (Fy), are shown in Figure 7.7.

7.7.1 Axial, tangential and separating force on the worm (Fz)

The axial force (Fz) on the worm is equal (see Figure 7.7) to on the tangential worm gear

force (Fx). The tangential force on the wormgear is dependent on the maximum force

generated by the object or wing that needs to be rotated.

From the sketch in Figure 7.10, lift does not affect on the gear because both works

through the centre of the gear, but drag and weight do. The moment forces (Mo ) in the

model were transferred to the worm gear shaft, thus the moment force (MG) on the gear,

output torque (T2) can be written as:

MG = T2 %•-• Mo -F(Dragx bg )+ (Weightx a g ) (7.18)

DRAG angle of attack

Wind Flow

FWD

f

Centre point model

Weight

ag

Centre point Gear


Where

Drag (max) = 50N

Weight (max) =100 N

bg = 0.7 meter

ag =100 mm

M 0 = 35 Nm

Thus the output torque (T2) is

T2 = 35 + (50 x 0.7)+ (100 x 0.1)

T2 = 80 Nm

LIFT

Figure 7.10 Forces diagram.


But the moment force (MG) on the gear can also be written as:

MG = FwG (7.19)

Where radius (rg) is halve the pitch diameter (DG) of the gear (142mm) and the tangential

force on the worm gear (FwG) = Axial force (F.) on the worm. Thus the axial force (Fz)

on the worm is:

M G = F = 978.39N

The normal force (Fn) on the teeth with friction (p = 0.0837) can be calculated using the

Equation 7.12.

Fz (cos0„ cos2 — p .1.) (7.20)

Fn (cos 20° cos 4.95° — 0.0837 sin 4.95°)

F„ =1053.20N

From Equation 7.9 and 7.11, the separating force (Fy) and tangential force (Fx) on the

worm can be calculated:

Separating force (Fy) = 90.87N

Tangential force (Fx) = 173.22N

7.7.2 Efficiency of the worm gear set

Efficiency (h) is the ratio of power required under the torque's and at the same speed.

The output torque (T2) is 80Nm from Equation 7.18. The required input torque (Ti) at

the worm shaft can be calculated by multiply Fx by the radius of the worm gear. By

substitute of Fn Equation 7.20 in to Equation 7.11, Fx can be written as

978.39

F F (

cos0,, sin 2,4-pcosA)

cosO"cos2 —p sin 2 (7.21)


Thus input torque (Ti) is.

T, =Dg

Fr = T2(D cos0„ tan), + p (7.22)

2 DG cos#,, —ptan2,

= 80(

0.0183) cos 20° tan 4.95° + 0.0837 0.1431) cos 20° — 0.0837 tan 4.95°

T, =1.809Nm

For no friction losses, corresponding to 100% efficiency, (g=0) the required input torque

(Ti)o can be written as equation 7.22 setting g = 0.

Thus the required input torque (Ti)o becomes:

(Ti )o T. T2 ( ft) tan (7.23)

(T,)= 80( 0.01831

tan 4.95 0.1431

VI = 0.886Nm

The efficiency is:

T q = 100

(

7;

) °

77=100x 0.8861.809

q = 48.97%

The minimum torque of 1.9 Nm needed to turn the wormgear.

7.8 Power to drive the worm

The minimum power needed to drive the gearbox can be written as:

2itnT P = (7.24) 60


Where: Torque (T) = 1.809

Number of revolutions per minute (n) =450 rpm

2nnT P =

60

P— 2ff x 450 x1.809

60 P = 85.24Wan

The minimum power required to drive the wormgear to change the angle of attack for

maximum drag on the model is 86 Watt.

Tablet 7.2 shows the comparison between the Mechsoft design software program and the

calculated values for the various criteria

Description

• Mechsoft design

software

Calculated from

formulas

Centre distance (C) 81,767 80 mm

Gear ratio 1:90 1:90

Circular pitch (p) 5.027 4.95

Lead (Lg) 5.046 4.96

Lead angle (X) 4.697° 4.95°

Face width worm 12.9mm 9.9mm

Face Length of worm 38mm 41.7mm

Power worm drive 0.04 kW 0.085kW

Torque worm gear 70Nm 80 Nm

Axial force worm 988.463 N 978.39N

Tangential Force worm 92.475 N 90.87N

Separating force worm 192.0964 N 173.22N

Tablet 7.2. Comparison between Mac soft computer program and calculated values

The minimum power needed to change the angle of attack is 85 watt. Thus a stepper

motor more than 85 watt must be used, but remember that weight is a limiting factor for

accurate measurements.


7.9 Angle of attack measurement

From the worm to worm gear ratio (1:90), the angle of attack will change by 4° for every

revolution of the worm or stepper motor. The stepper motor steps 1.8° per step, thus

gives 200 steps per revolution of the stepper motor.

The angle change per step (Ac) = Degrees per 1 revolution of worm

Number of steps per revolution of stepper motor

4° Ac =

200 Ac = 0.02°

Thus for every step increment of the stepper motor the angle of attack will change by

0.02°.

7.10 Donation of a commercial worm gearbox

Ronolds Croft donated a 1:70 commercial worm gearbox with the following

specifications:

Input

(r.p.m)

Output

(r.p.m) Gear ratings

1800 25.7

Input (kW) 0.574

Output (kW) 0.313

Output torque (Nm) 118

The angle change per step (Ac) = Degrees per 1 revolution of worm

Number of steps per revolution of stepper motor

Ac — 5.142°

200 Ac = 0.0257°

Thus for every step increment of the stepper motor the angle of attack will change by

0.0257°. The gearbox was stripped and the worm and wormgear were modified to suite

the wind tunnel-balance.

Chapter 8: Balance measuring devices 79

8. Balance measuring devices

8.1 Introduction

There are several methods for measuring forces or pressures, it can be done mechanically

by weights, scale devices or electrically where strain gauges are commonly used to

measure forces.

The load cell is the most critical part of the project and without the wind tunnel balance

cannot be used. Hoffmann (1989), discusses the importance of load cell accuracy and

specifies the following basic design requirements. These are:

The dimensions of the ring beam must suit the required maximum load whilst

not loosing sensitivity.

Any stress raising features such as holes, lugs, welds must be avoided to

prevent fatigue problems.

To reduce nonlinearly and hysteresis within the instrument, mechanical

connections must not be used or kept to a minimum.

Common safety factors of 150 to 200% to be used to prevent overload.

Using thin material sections can reduce temperature effects.

Figure 8.1 Ring type Load Cell.


The ring type load cell is approximately 50% more sensitive than the link type load cell.

This is because it acts in part as a cantilever providing a bending moment, witch

generates higher strain than a direct force alone. The ring allows the use of four strain

gauges as a full bridge circuit with its higher accuracy and temperature compensation

abilities. The thin section allows a more constant temperature profile through it and for

good temperature compensation.

The strain gauges are placed on the vertical apex of the load cell, which is almost a

constant distance from the applied load. This allows the gauges to operate to their full

potential.

The line of action of the applied force is on a line of symmetry of the ring and thus does

not allow for lateral movements. To prevent side forces due to misalignment of the load

cell, a universal type connection is used between the mounting base and load cell. (See

Appendix B, Drawing WTB-03-00, Strain gauge assembly.)

The max. strain (c) for brass is:

Cr

6 E (8:0

68.9x10 6

106x109

=650x10-3

Care must be taken not to exceed 650 micro strain in the load cell design. The load cells

were designed using the curved beam theory.


8.2 Ring type load cell design theory

In this section the Equations involved in the curved beams are explained.

Figure 8.2 Sketch of a curved beam, Popov 0978).

Consider the curved member as shown in Figure 8.2 (a) and (b). The outer surface of the

beam is a distance ro and the inner surface of the beam is a distance n from the centre of

curvature 0. The point 0 is the centre point of the beam curvature of the centroid axis re.

The stress distribution will be obtained by using the assumption as in a straight beam,

namely, that the sections perpendicular to the axis of the beam remain plane after a

bending moment M is applied. (The approximate theory developed by E. Winkler in

1958). Due to bending the angle I formed between the sides ad and bc. The small

deformation of the beam fibers described by the small angle d I .

Due to the bending of the beam, the length of the longitudinal fibres at gh depends upon

the distance r from the centre of curvature. Although the total deformation of beam fibres

follows the linear law, described by the small angle d I , strains do not follows the linear

law. Hooke's Law states that:


a = Ec (8.1)

The elongation of the fibres gh can be given as (R-0 d I , where R is the distance from 0

to the neutral surface and its length r I .

c (R — 0(10

n1) (8.2)

Substituting Equation 8.2 into Equation 8.1, the normal bending stress (a) becomes:

E (R — 0(10

n1) (8.3)

This can also be written as:

ar := E c14)

R — (I) (8.4)

Equation 8.3 contains two unknowns namely, R, the distance from 0 to the neutral

surface and d I the angle of rotation. To determine these quantities, a summation of all

the normal forces distributed over the cross section to be set equal to zero and the

moment of all these forces are equal to the external moment M. Thus:

F„ = 0

fcrdA = (E R - r)d# dA .0 (8.5)

A A 1'0


Because E, It, d I and I are constants at any one sections of a stressed beam the Equation

8.5 can be written as:

Ed0

r

i(1—Lc) E

0

d0[R fdA p A i = 0

0 A r A

A R — (8.6)

fdA A

In Equation 8.5, A is the cross-sectional area of the beam and R locates the neutral axis.

The summation of moments is made around the z-axis, which is normal to the plane

Figure 8.2 (a)

E M,

M= fadA(R r)— fE(R—

)

2 d0

dA (8 - 7) A A 1.0

Substitute Equation 8.4 into Equation 8.7

Ed0 rE(R — 0 2 or f(R — 0 2 M — j dA — -CA ±

0 r (R —r) r

or jR 2 —Rr—Rr+r 2 dA (R—r) A r

(8.8)

Chapter 8. Balance measuring devices 84

Thus substitute Equation 8.6 in place of the third term and the last term by definition

equals

Thus the moment can be given as:

M = (R— r) (rcA— RA) (8.9)

When the normal stress acting on a curved beam at a distance r from the centre of

curvature is:

o- M(R—r)

= rA(rc— R) (8.10)

Let

rc— R= e

and y the distance from the neutral surface Then Equation 10 can be written as:

My = Ae(R— y) (8.11)

The maximum stress is on the inside of a curved beam. In the curved bar the neutral axis

is pulled toward the centre of the curvature of the beam. This result from the higher stress

developed below the neutral axis at a distance R below the neutral axis. See Figure 8.2

(c).


• 8.2.1 Maximum stress in curved beam theory

Curved beam

dr

r

Figure 8.3 Sketch of the curved beam

Equation 8.6 is used to calculate the radius for maximum stress and Equation 8.10 to

determine

A R —

fdA

For the rectangular section, the elementary area is taken as (bdr) and integration is carried

out between ri and ro, the inner and outer radii and h the depth of the section.

b R=

rbdr l r A

R —

(

(8.12)

ln7)

90°

Pr. 2


According to Timoshenko (1955), the maximum bending moment in the ring can be

determine by the following equations, as shown in Figure 8.4.

Pt

Pt

Figure 8.4 Ring bending forces, Timoshenko (1955).

Figure 8.4 represent a thin circular ring submitted to two equal and opposite forces P

acting along the vertical diameter. Due to symmetry only one quadrant of the ring need

be considered. It is assumed that there are no shear stresses over the cross section mn and

that the tensile force on the cross section is equal to halve the force (P/2). It is further

more assumed that the cross section mn does not rotate during the bending of the ring.

The displacement corresponding to Mo is zero in Figure 8.4(b) and in which U is the

strain energy of the quadrant of the ring.

dU —0 dMo

(8.13)

For any cross section mn at an angle cp with the horizontal, the bending moment is:

M = Mo —t r,(1— cos yo) (8.14)


But Mo the initial bending moment equals M thus:

dM —1 dM0

(8.15)

But the strain energy for bending a straight beam is: (See Appendix H)

U - .1. 9 M 2 dc

0 2E1. (8.16)

Substitute Equation 8.16 and 8.14 into Equation 8.13, the potential energy is:

dM 2rd9 .0

dM0 I 2E1, z

1 2 1 , dM j In rug; = u

El, 0 dM0

IT 1 t

Mo— p

C rc a—cosc)14 = 0 El, 0 2

From witch

p x r 2 M — f c (1 ) o

2 it

(8.17)

Substituting Equation 8.17 in to 8.14, the bending moment M at any point in the ring can

be written as:

P xro M= '

2 (cow — —

2)

7/

But maximum bending is at the angle 9 = rt/2, thus M equals

M = Pf x r

` (cos—fr

— -1) 2 2 g


P xr M = f c

M =-0 .318 P f x rc (8.18)

The minus sign indicates that the bending moment at the point is anti-clockwise and tends

to increase the curvature of the beam at an angle p = n/2.

8.3 Lift load cell design

Lift load cell ring is designed using the curved beam theory as discussed in paragraph 8.2

b

Figure 8.5 Sketch of curved beam.

The minimum length b (seen Figure 8.10) can be calculated using the Equation 8.10. The

maximum stress is at the inner surface (ri).

= M(R —ri)

riA(rc — R)


From the Equation 8.18 the Maximum bending moment at the radius (rc) were calculated:

M = —0 .318P x r,

M = —0 .318x 300N x0.011

M = —1.0494Nm

Where the load P of 300 Newton, includes the weight of the model (±20N), weight of the

structure (±80N), maximum lift force (100N, worse case, wing mounted upside down), a

safety factor of 1.5 and rc (11.0mm) the distance from the centre of curvature to the

centroid.

The Equation (8.12) were used to calculate the radius R of the curved beam for maximum

stress is:

R =

in(ri) ri

3 R = 4112.5)

1 9.5))

R =10.93mm

ri =9.5mm

ro =12.5mm

h =3mm

h

From Equation 8.1) the area (A) can be calculated:

A— M (R — ri) rioi(rc — R)

Where:

M =1.0494Nm

R =10.93mm

ri = 9.5mm

rc =11mm

of = 68.9MPa

Thus cross-sectional area (A) =:

1.0494x(0.01093-0.0095) A=

0.0095x 68.9 x106 (0.011— 0.01093)

A =3.275x10-5 m 2


But area

A=bxh

b = A

= A 3.275x10

h (ro — ri) (0.0125-0.0095)

b = 0.01088m .10.91mm

The minimum length (b) for the Lift load cell ring, must not be less than 11 mm.

8.4 Pitch Load cell design

Figure 8.6 Pitch Load cell sketch.

The minimum length b (seen Figure 8.6) can be calculated using the Equation 8.10. The

maximum stress accurse at the inner surface (ri).

of — M(R — ri) riA(rc — R)

The force Fscisi was calculated around the pivot point A as shown in Figure 8.7.

(Drag x b)+ x a). c X FsGA4

(Drag x b)+ s, g x a) &AI =

Drag

Lift

angle of attack

Vind Flow

Mg


Figure 8.7 Line schematic of forces.

Where. Drag (D)= ION

b = 1.150 meter

c = 0.180 meter

a = 0.2 meter

(Drag x 1,,gx a) SGM

(I ON x 1.150 +(I CION X 0.2) P' SGM 0.180 Fsaw = Pi =175N


Thus, the maximum bending moment at the radius (re.) was calculated using Equation

8.18:

M = —0.318Pf xrc

M = —0.318x175N x0.011

M = —0.556Nm

Load Pr (175N) for drag was calculated for the maximum blockage area force of 10.0N in

the tunnel with a safety load factor of 1.5.

The Equation 8.12 were used to calculate the radius R of the curved beam for maximum

stress is:

R = In

1.5

11.0

R =11.734mm

Where

ri =11.0m

ro =12.5mm

h =1.5mm

From Equation 8.10 the area (A) can be calculated:

Where:

A— M(R— ri) ri °l(rt — R)

M = —0..556Nm

R =11.734mm

ri =11.0mm

rc =11.75mm

ai =68.9MPa


Thus cross-sectional area (A) =:

0.2234x (0.011734-0.011) A-

0.011x 68.9 x106 (0.01175— 0.011734)

A =3.365xle

But area A can be written as:

A=bxh

A A b = =

h (ro—ri)

3.365x10 b =

(0.0125 — 0.0011)

b = 0.0224m = 22.4mm

The minimum length (b) for the lift load cell ring, must not be less than 23mm.

8.5 Drag Load cell design

Due to the small drag forces on the model wing it was decided to make use of a beam

load cell in stead of a ring load cell because of the length of 5mm that cannot be

accommodated by the available strain gauges in use. (See Appendix B Drawing WTB-

01-15)

SECTION XX


Figure 8.8 Beam type load cell sketch.

The minimum deflection (e) as shown in Figure 8.8 can be calculated using the following

equation, (See appendix H):

But deflection can be written as:

? FA Y = — (8.19)

12E1

Where:

F = Force (N)

E = Young's Modulus

I = Inertia of beam

1 = Length of beam

Y = Deflection

Bending moment on the beam can be write as:

MA=Ms— 6E1

Y

(8.20)


Substituting Equation 8.19 into Equation 8.20 to calculate the bending at A, (Aappendix

H):

M _-6E1

x FX3

A.2 12E1

(8.21)

Stress (a) in a beam is:

My o- = — (8.22)

Substituting 8.21 into Equation 8.22, the stress at A is:

a = 0.5 Fky (8.23)

I

But inertia (I) and distance (y) can be substituted into the Equation 8.23 and the thickness

(d) can be written as:

bce

12 =

a = 0.5FA, 12d

bd3 x

2

d2 = 3FX bo-

d = 13nb (8.24)

Fk

2

In the Equation 8.25 the following dimensions were selected in order to determine the

thickness if the beam (d).

— (0.010x0.0012'

12

orml° 0.04 ( co° 2)


The length of the beam (1)= 140mm

The height if the beam (b) = 10mm

Load on the beam F = 10 Newton

Aluminium (a) =120 MPa

d = 13FX ba

d — 3x10x0.050

0.010x120x106

d=0.001118m=1.12mm

In the drag load cell the thickness (d) of the beam must not be less than 2mm.

Stress (a) in a beam (Equation 8.22) at the strain gauge position (x = 10mm):

F7t. But M = H—x) (see Appendix I)

2

Thus,

( FL

— xx y

o- —

a =104.16MPa

Stain at the strain gauge position is (see Figure 8.1):

104.166x106 e — —

E 73.1x109 rt rt. n • •


Strain gauge 10 101

LO Beam

Figure 8.9 Strain gauge positions in the drag load cell.

8.6 Wheatstone bridge load cells

The Wheatstone bridge is most commonly used for converting the small changes in the resistance of the strain gauges in to a voltage suitable for amplification and processing. Electric strain gauges have been used as measuring devices in several external balances with satisfactory degree of success.

A Wheatstone bridge can be constructed as a full bridge, quarter or a half bridge. The difference is in the way the stain gauges are wired and fitted to an object. A half bridge is constructed with two stain gauges, a quarter bridge with three-stain gauges and full bridge with four strain gauges.

In the design of the ring and beam type load cell, a complete Wheatstone bridge is used. Figure 8.8 shows the wire diagram of a full Wheatstone bridge.


Figure 8.10 Wire diagram of a Wheatstone strain gauge bridge.

In the Wheatstone bridge resistors RI, R2, R3 and R4 change , their value by an amount AR, then the bridge circuit becomes unbalanced the output voltage (Eo) can be calculated by the following equation, Window and Holister (1989):

E0 = RI + AR1 R4 + Rl+AR1+ R2+ AR2) (R3+AR3+R4 AR4+AR4

x Ei (8.25)

In the strain gauge the amount by which the resistance changes are very small and in the order of lr Volts. The approximation Equation 8.26 Window and Holister (1989), can be used for practical requirements.

1 I AR I AR 2 AR3 AR 4 ) E0 —

4 R1 R2 R3 R4 (8.26)

As mentioned, the load cell is a spring element. As shown in Figure 8.12 brass was used for the lift load cell and in Figure 8.11 aluminium for the drag load cell. (See Appendix B for information on the load cells.)

A full bridge circuit with its higher accuracy and temperature compensation abilities was used for the load cells. The thin section allows for good temperature compensation. The strain gauges are placed on the vertical apex of the lift and pitch load cell, which is


almost a constant distance from the applied load. This allows the gauges to operate to their full potential.

Four strain gauges were fitted on the beam of the drag load cell where the maximum deflection will occur as shown in Figure 8.10.

To prevent side forces due to misalignment of the lift and pitch load cells, a universal type connection is used between the mounting base and load cell. (See Appendix B, Drawing WTB-02-00, Strain gauge assembly.)

Figure 8.11 Drag load cell.

8.7 Load cell implementation

Figure 8.12 shows the lift, Figure 8.13 the pitch and Figure 8.14 the drag load cell in position.

Figure 8.12 Lift load cell. Figure 8.13 Drag load cell. Figure 8.14 Pitch load cell.

Chapter 9: Electronic data capturing system 100

9. Electronic Data Capturing System

9.1 Introduction

The quality and features of the data capturing system has a large impact on the quality

of the wind tunnel.

A good understanding of electronic signals is an advantage when designing a data

capturing system. The level of the signals (Volts) is generally quite low and requires

amplification. The electronic signals normally consist of data and noise. Noise can be

electrical or mechanical. Care must be taken to ensure that data if possible, noise free

or minimized.

9.2. Data capturing card

It was decided to use a Low-cost multifunction data acquisition card that plugs into a

PC to capture data from the external wind tunnel balance.

The low-cost multifunction data acquisition card PCI-6023E has the following

specification:

Bus:-PCI

Analog Inputs:-16 SE/8DI

Resolution:-12 bits

Sampling rate:- 200kS/s

Input range ± 0.05 to ± 0.10 V

Digital I/O:- 8

Counter/ Timers:- 2, 24-bit

Triggers:- Digital

The card fits into a slot in the PC as shown in Figure 9.1 and connects by means of a

ribbon cable to the connection box a shown in Figure 9.2. The load cells amplifiers

and stepper motor controller connects to the connection box as shown in Figure 9.3.

•teu.

504,L

......

. - • •

101 Chapter 9: Electronic data capturing system

Figure 9.1 PC mounted data acquisition card.

Figure 9.2 PC mounted card, ribbon cable and connection box.

Figure 9.3 Connection box.


9.3 The Connection box

The connection box is a platform between the instrumentation such as the load cell

amplifiers, motor controller, angle meter and the data acquisition PCI-6023E card. In

Appendix D more information about the connection box and wiring diagrams is given.

9.4 Strain gauge amplifier

Strain gauge amplifiers are used to enlarge the output signal from the stain gauge and

filters noise from the strain gauge output voltage. It is important to keep the strain

gauge output wires to the amplifier as short as possible, to avoid noise and to keep

resistance to a minimum. It is best to use twisted shielded wires and avoid alternating

current wires in the vicinity.

RS Strain gauge amplifiers PC board is used to enhance the signal as shown in Figure

9.4. The advantage of using these amplifiers is that the board is already designed and

tested. In Appendix D the circuit board diagrams are given.

A modification was done on the R1 (100-ohm) resistor to enhance the gain factor by

replacing it with a veritable 500-ohm resistor pot as shown in Figure 9.4. This allows

adjustment to the gain factor on the output signal to suite the PCI-6023E specification

of max input voltage of 10 volt.

Fra..w.

_ r.. ....... , Rs 435.-6.92--. STRAIN GAUGE AMPLIFIER • , 1 .C6 R7 ,....„ VR1 VR2 D1

is

• it I P. 0 .0% '4'

c (0 I :-.: 1 C+3 c -.-

' I. I .0 - . I .i. Ts

• (0 : , tit R6 ; --- R9 I

, ....-..■41 .......■J : T1 T, I + =lin awl 07 .0 10

+il CI in i CS i C1 "4-':-

t_114 1 1 C7

....1 R.3 -a —

. • 0

U A I L a. 1 R2 l 1— t--4

as _ liti r K

• . 1 7 ' ,--,

4 T3 T2 PE4 dt

+\-- C4 R5 Rp • R11

R1 (500-ohm pot)

Figure 9.4 RS Strain gauge amplifiers PC board


Figure 9.4 show the amplifiers of the load cells mounted in the control box with easy

access to the components.

Figure 9.5 Amplifiers mounted in control box

See Appendix D for more information on the RS Strain gauge amplifier PC boards

and wiring layout.

9.5 Stepper motor driver

A stepper motor, controlled by the computer, was connected to the worm gearbox to

change the angle of the object as discussed in chapter 5. The stepper motor driver card

was designed to drive the stepper motor and interface with the PCI-6023E card that

control the rotation. Figure 9.6 shows the stepper motor controller board. (See

Appendix D for the stepper motor controller-wiring diagram.)

Figure 9.6 Stepper motor controller.


9.6 Angle sensor

The electronic angle sensor is mounted on the top of the two horizontal arms as shown

in Figure 9.7 and measures the reverse angle of the model mounted to the head of the

wind tunnel balance. A control board as shown in Figure 9.8 is fitted inside the

control box next to the lift, drag and pitch amplifiers. The angle sensor is a gravity

orientated resistor sensor and angles are given out in volts. See Figure 11.22.

Figure 9.7 Angle sensor mount

Figure 9.8 Angle control board inside control box.

Graphic Functions

Front Panel

Control Blocks


9.7 Computer program

Data capturing software called LabVIEW 5.1 form National Instruments is used to

capture the data. LabVIEW is a graphical programming language that uses icons

instead of lines of text to create applications. In contrast to text-base programming

languages, where instructions determine program execution, LabVIEW uses dataflow

programming, where data determine execution.

A flow chart as shown in Figure 9.10 is created by code using graphical

representations of functions called blocks to control the program. The user interface as

shown in Figure 9.10 is known as the front panel.

Figure 9.10 Lab VIEW data capturing program.

ram mnarm-- CPU E _

400104004

F. non= Sri 44.V1W.,4441.001.4•an

BMW - it Wrsondwnlenich 161

OP 4444 bW6.d

Oat I

104 &MI 010 0 061 101 SIM CO

2065 6616 661 2035 EMS 46X1 200 016 032 650 US 011 4120 650 2(0 60 500 163 261 SW 4$. 60 2056 602 -00 1056 1$57 40 0 20 1540 665 651 2051 GS 010 GS IS 60 405 93

2061 197 665 61 104 (LW 035 6E1

2Q; 192 605 04 1051 658_6a _

4a4k Vyla

,12.02 __ i 44=


Two programs were created, one to control the stepper motor with an output to show

the angle of the head position, as shown in Figure 9.11 and the other program as

shown in Figure 9.12 to capture and save the data to file.

Figure 9.11 Motor control front paneL

Figure 9.12 Data capturing front panel.


9. Electronic Data Capturing System

9.1 Introduction

The quality and features of the data capturing system has a large impact on the quality

of the wind tunnel.

A good understanding of electronic signals is an advantage when designing a data

capturing system. The level of the signals (Volts) is generally quite low and requires

amplification. The electronic signals normally consist of data and noise. Noise can be

electrical or mechanical. Care must be taken to ensure that data if possible, noise free

or minimized.

9.2. Data capturing card

It was decided to use a Low-cost multifunction data acquisition card that plugs into a

PC to capture data from the external wind tunnel balance.

The low-cost multifunction data acquisition card PCI-6023E has the following

specification:

Bus:-PCI

Analog Inputs:-16 SE/8DI

Resolution:-12 bits

Sampling rate:- 200kS/s

Input range ± 0.05 to ± 0.10 V

Digital I/O:- 8

Counter/ Timers:- 2, 24-bit

Triggers:- Digital

The card fits into a slot in the PC as shown in Figure 9.1 and connects by means of a

ribbon cable to the connection box a shown in Figure 9.2. The load cells amplifiers

and stepper motor controller connects to the connection box as shown in Figure 9.3.

101 Chapter 9: Electronic data capturing system

Figure 9.1 PC mounted data acquisition card

Figure 9.2 PC mounted card, ribbon cable and connection box.

Figure 9.3 Connection box.

RS ft .C6 NJ,

13E R6 i __L

T1 11 fi

-ir 0 I C7

ns

• T3 T2

43-5-:692--, STRAIN GAUGE AMPLIFIER ID , . VR1 VR2 D1

11° 4- ∎S

N In 0- ry +NMI :1St .0 ),

C1 r"--. R3

R2 t1 -

RS RP • R11 •

R7 S + .1: C3

R9 I

CS -1-. I L :-.. 1 - I

N K,

R8 s‘. +.tit

C4


9.3 The Connection box

The connection box is a platform between the instrumentation such as the load cell

amplifiers, motor controller, angle meter and the data acquisition PCI-6023E card. In

Appendix D more information about the connection box and wiring diagrams is given.

9.4 Strain gauge amplifier

Strain gauge amplifiers are used to enlarge the output signal from the stain gauge and

filters noise from the strain gauge output voltage. It is important to keep the strain

gauge output wires to the amplifier as short as possible, to avoid noise and to keep

resistance to a minimum. It is best to use twisted shielded wires and avoid alternating

current wires in the vicinity.

RS Strain gauge amplifiers PC board is used to enhance the signal as shown in Figure

9.4. The advantage of using these amplifiers is that the board is already designed and

tested. In Appendix D the circuit board diagrams are given.

A modification was done on the RI (100-ohm) resistor to enhance the gain factor by

replacing it with a veritable 500-ohm resistor pot as shown in Figure 9.4. This allows

adjustment to the gain factor on the output signal to suite the PCI-6023E specification

of max input voltage of 10 volt.

R (500-ohm pot)

Figure 9.4 RS Strain gauge amplifiers PC board

- - „,,n}Cfl • ai

S eniarto r Val • 1/4•4 4' Lea 2/10. j

Chapter 9: Electronic data capturing system

103

Figure 9.4 show the amplifiers of the load cells mounted in the control box with easy

access to the components.

Figure 9.5 Amplifiers mounted in control box

See Appendix D for more information on the RS Strain gauge amplifier PC boards

and wiring layout.

9.5 Stepper motor driver

A stepper motor, controlled by the computer, was connected to the worm gearbox to

change the angle of the object as discussed in chapter 5. The stepper motor driver card

was designed to drive the stepper motor and interface with the PCI-6023E card that

control the rotation. Figure 9.6 shows the stepper motor controller board. (See

Appendix D for the stepper motor controller-wiring diagram.)

Figure 9.6 Stepper motor controller.


9.6 Angle sensor

The electronic angle sensor is mounted on the top of the two horizontal arms as shown

in Figure 9.7 and measures the reverse angle of the model mounted to the head of the

wind tunnel balance. A control board as shown in Figure 9.8 is fitted inside the

control box next to the lift, drag and pitch amplifiers. The angle sensor is a gravity

orientated resistor sensor and angles are given out in volts. See Figure 11.22.

Figure 9.7 Angle sensor mount

Figure 9.8 Angle control board inside control box.

Graphic Functions

Front Panel

Control Blocks


9.7 Computer program

Data capturing software called LabVIEW 5.1 form National Instruments is used to

capture the data. LabVIEW is a graphical programming language that uses icons

instead of lines of text to create applications. In contrast to text-base programming

languages, where instructions determine program execution, LabVIEW uses dataflow

programming, where data determine execution.

A flow chart as shown in Figure 9.10 is created by code using graphical

representations of functions called blocks to control the program, The user interface as

shown in Figure 9.10 is known as the front panel.

Figure 9.10 LabVIEW data capturing program.

pap .°2 la%i 10:0 5.33 201:0

203

.1103 301:0

Elm r. an Biwa It.b. tow Er:

Chapter 9: Electronic data capturing.system 106

Two programs were created, one to control the stepper motor with an output to show

the angle of the head position, as shown in Figure 9.11 and the other program as

shown in Figure 9.12 to capture and save the data to file.

Figure 9.11 Motor control front panel.

20$6 560 400 4604 20 1611 5E6 40% 100 MS 600 00 200 (CIS 601 40% 2161 015 107 00 20% Lill 603 401 201 4012 300 466) 10 002 400 11463 20% 002 140 460 20% 6517 0140 400 201 LW 650 400 201 LW 0580 SO 20% 602 405 403 20 497 605 00 200 4377 405 00 20% 55/2 405 400 =I 40_60 430 —

Figure 9.12 Data capturing front panel.

Chapter 10: Installation of the wind tunnel balance 107

10. Installation of the wind tunnel balance

10.1 Introduction

External balances are usually attached to a large mass of concrete to obtained

maximum stability and calibrated in position, while internal balances are calibrated

outside of the tunnel with only check loads applied to the model in position.

Care must be taken when aligning the external wind tunnel balance that the angle

movement relative to the horizon, is parallel to the to wind tunnel test section centre

line and perpendicular to the airflow.

10.2 Installation in the wind tunnel

The balance was assembled outside the wind tunnel to check if all parts are working

properly as shown in Figure 10.1 and 10.2. Load cells, stepper motor and angle sensor

were connected and tested to ensure working order. Data capturing software and

hardware were installed and provisionally calibrated to check that data transfers

correctly.

Figure 10.1 Assembly of the wind

tunnel balance.

Figure 10.2 Testing wind

tunnel balance outside the wind

tunnel.


After all the electronic components were connected and checked the balance was

mounted below the wind tunnel high-speed test section as shown in Figure 10.3. The

wind tunnel balance was bolted to the concrete floor with three concrete bolts for easy

alignment.

Figure 10.3 Balance mounted in position underneath wind tunnel test section.

To avoid interference and data loss, the control box was placed on the floor next to the

wind tunnel balance as shown in Figure 10.3. The lift, drag, pitch, angle sensor and

stepper motor control wires from the control box were connected to the connection

box as shown in Figure 10.4

Figure 10.4 Wind tunnel balance connected to data capturing system.


The floor of the test section was cut to accommodate the two-arm strut that penetrates

into the wind tunnel test section as shown in Figure 10.5.

Figure 10.5 Floor cut-away. Figure 10.6 Shroud fitted.

The headpiece of the wind tunnel balance was aligned to the centre of the wind

tunnel test section and bolted in position. A shroud was manufactured from stainless

steel, fitted around the two-arm strut to minimize the drag on the struts and bolted to

the wind tunnel test section floor as shown in Figure 10.6.

The two power supplies as shown in Figure 10.7 were mounted on top of the wind

tunnel to minimize interference and noise to data signals.

Figure 10.7 Layout of computer and power supplies.

Chapter 11: Calibration of the wind tunnel balance 110

11. Calibration of the wind tunnel balance

11.1 Introduction

Calibration of a wind tunnel balance is one on the important procedures of a wind

tunnel operation because from here on all test will depend on the graphs and data

accumulated. Secondly to see if the wind tunnel balance readings are in accordance

with the design specifications.

Because the wind tunnel balance was designed according to the axiomatic design

method the lift and drag forces should not interfere with each other. To evaluate this

theory, the lift, drag and pitching load cells must be eliminated and each load cell

must be calibrated on its own.

To eliminate a load cell an I-beam as shown in Figure 11.1, Figure11.2 and Figure

11.3 were bolted in the position of the load cell not calibrated at the time.

Figure 11.1 1-Beam to eliminate Lift Figure 11.2 1-Beam to eliminate Drag

load cell. load cell.


Figure 11.3 I-Beam to eliminate Pitch load cell.

11.2 Calibration method

Calibration was achieved by assembling the calibration rig around the wind tunnel

balance and bolted it to the floor of the wind tunnel test section as shown in Figure

11.4. Loads were applied using a pulley system, allowing individual loads and

moments to be applied to the balance. Calibration was carried out in the directions of

lift and drag in which aerodynamic loads were expected.

Figure 11.4 Calibration rig in position

Channel select Window

rci° cc"' Oro. Nutter

eflooer.o.. I MOSS 151..P.nd

Co ration

DeoceNtrolta

Stahl Med. 0d0

DAO Device Basics

Araakw Ica:ft uo Dpawl

Voltage readout Window

Wan

What do you wool to do?


11.3 Load cells zero and gain setting procedure

The load cells were calibrated by using the computer digital acquisition system. The

procedure to calibrate the system is explained below.

Connect all wires and cables needed to the computer digital acquisition

system.

Remove all interference that can cause misalignment or unwanted forces to

the load cells.

Switch on the power supply that supplies power to motor controller, load

cell amplifiers, angle sensor and computer.

Allow the system to warm up for 10 to 20 minutes and activate the

computer NI-DAQ program called Measurement & Automation, device

and interfaces as shown in Figure 11.5.

Check that the program reads the channels 1, 2 and 3.

Figure 11.5 Measurement & Automation program.


11.3.1 Lift load cells zero and gain setting procedure

(See Appendix E for strain gauge Amplifier settings)

Adjust VR1 pot on the lift strain gauge amplifier by turning it clockwise

till click.

Adjust VR2 pot on the lift strain gauge amplifier to read zero or as close to

zero.

Apply the maximum load of 80 Newton to lift as shown in Figure 11.6.

Figure 11.6. Lift amplifier setup, 80 N Maximum.

Adjust RI gain pot on the lift strain gauge amplifier by turning it till the

maximum full-scale range of 5 volts is reached.

Remove the 80 Newton-weight form lift.

Readjust the VR2 pot on the lift strain gauge amplifier to read zero or as

close to zero.

Lift load cell is set for calibration.

11.3.2 Drag Load cells zero and gain setting procedure

(See Appendix E for Amplifier settings)

1. Adjust VR1 pot on the drag strain gauge amplifier by turning it clockwise

till click.


Adjust VR2 pot on the drag strain gauge amplifier to read zero or as close

to zero.

Apply the maximum load of 7 Newton to drag as shown in Figure 11.7

Figure 11.7. Drag amplifier setup, 7 N Maximum.

Adjust RI gain pot on the drag strain gauge amplifier by turning it till the


Remove the 7 Newton -weight form drag.

Readjust the VR2 pot on the lift strain gauge amplifier to read zero or as

close to zero.

Drag load cell is set for calibration.

11.3.3 Pitch Load cells zero and gain setting procedure

(See Appendix E for Amplifier settings)

I Adjust VR1 pot on the pitch strain gauge amplifier by turning it clockwise

till click.

2 Adjust VR2 pot on the pitch strain gauge amplifier to read zero or as close

to zero.


3 Apply the maximum load of 7 Newton to drag as shown in Figure 11.8

Figure 11.8. Pitch amplifier setup, 7 N Max.

4 Adjust RI gain pot on the pitch strain gauge amplifier by turning it till the


5 Remove the 7 Newton -weight form pitch.

6 Readjust the VR2 pot on the pitch strain gauge amplifier to read zero or as

close to zero.

7 Pitch load cell is set for calibration.

11.4 Load cells calibration procedure

It is very important when doing the calibration procedure that it must be carried out

without interference and that care must be taken to ensure accurate alignment of the

calibration rig. It is wise to take notes of the calibration procedure because it can be

confusing when adding and removing weights.

The LabView computer program as shown in Figure 11.9 was used to capture data as

a mass was hung.

6404.010600411 2166 6621 4045 4650 2166 6621 8010 41721 2 161 6615 -56215 169 293 SOS 4661 46E3 2063 6615 -1603 4663 2031 6816 4520 ICJ 2050 6611 4072 4650 261 600 40513 46E3 261 60 84 469 206 GHQ 460 HU 2053 60 41340 169 2051 60 1040 169 2051 037 1040 4120

6102 1666 1® 20 6577 6135 169 2051 6577 035 4663 2062 6572 060 4650 201 190 00

a S05 10616W am

40 2E103 .1000 2501

4307 3111)


1000 readings were taken over a time period of 3 seconds for every mass added and

removed and logged to an ASCI files. The ASCI files are executed with Microsoft

excel program. Averages of the 1000 readings were computed and graphs created.

(See Appendix E.)

Figure 11.9 Lab VIEW program for capturing data.

11.4.1 The lift calibration

A shown in Figure 11.10 and 11.11 the lift load cell was calibrated for positive and

negative lift. The load cells were calibrated in position and measurements were taken

during both the loading and unloading phases to check for any hysteresis. Loads were

added from 5 to 75 Newton with increments of 5 Newton and data captured and

logged to files. Loads were reduced from 75 to 0 Newton with increments of 5

Newton and data captured and logged to files. Output Voltage (Eo) data from the

strain gauge amplifiers were plotted as shown in Figure 11.12. The deflection of the

two-arm strut as shown in Figure 11.13 was recorded and plotted as shown in Figure

11.14. (See Appendix E.)

Lift Load cell Calibration Graph Lift Load (N) = (Volts - 0.0397) / 0.0643

... .. .. ... .. ... ..

. . I . ._7 .. ! .. -••- .......

: . 4 4- i 4

0 i 4 " ' .. .. I ..

. ■ :-,PP:1*14

kr! • • : • : 4 : • 1 4 4-1-: • " • i.-4-4-1 ' .. ..

-

.

44-44- . ..

: f •

I

-

-r

... . -7 -H-4-±" 4'44' r-•! nil-1-r 1-4-71-

fl rr

Load (N)

Chapter 11: Calibration of the wind tunnel balance

117

Figure 11.10 Positive lift calibration. Figure 11.11 Negative lift calibration.

Figure 11.12 Lift calibration graph.

Two-arm strut Deflection

1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00

Load (N)

8 0.60

0.40

0.20

0.00

1.60

1.40

1.20

E 1 -a°

•

0.80

---7 .

" 1 •

1 ■ 4_44 L._ 4. I

•

-L.-4- ..... - ......

+ 1 1 4.-1 4

-""+ * .. .

- • ..... - --- 4 - --- - ;

• , • i * --- - 4---


Figure 11.13 Deflection measured

Figure 11.14 Deflection of two-arm strut under drag loads

11.4.2 The drag calibration

A shown in Figure 11.15 and 11.16 the drag load cell was calibrated for positive and

negative drag. The load cells were calibrated in position with measurements taken

during both the loading and unloading phases to check for any hysteresis. Loads were

added from 0.5 to 5 Newton with increments of 0.5 Newton and data captured and

logged to files. Loads were reduced from 5 to 0 Newton with increments of 0.5

Drag Calibration Graph Drag Load(N)+Volts(V)+ 0.370)/ 1.335

Load (N)

• j_ . . .

..+.1....4.-4-.4 4. .. 4... i.-4-4-4.-1-:- ... I .. r i .. -:--4-4.-i- i.-+ 4 ' . ' 4- i-i-±-i-4-i i -1'.. --t-h,--,-t --I- -s-t-r-t--i-t--1-1-i-t-t-i--1-t-4-,-rt. • 4--F-i.-t-t--r-i-t-i-t-

: r • - i- i--,---i-4- ; i-H-1-1*"--r-t- , .... , ... 4.

i

... 1...c...

: . .-4-

--t-r--;-. --t-i-

ei=.- ,--- ,

1- r-r- ,

- • 1- i ; ... 4.. : -1--

lT

-4--i--- -4. ... 1---t-i—t--1-44

i--# 41-

... t ... t•-•-+- H-1-1-4--•-t

- 44:: 1":21:t

. -1-1-

... _ ....

T.: Li:R.-: L.::::•:-.L_LI.:_r_E.-.. 4

4- - ---t- 1---1-4-1-4-4-1----+-1-i-1-4-1--•-r-4- 4--4--+- 4-

_ 7.1.::::,_; : . 4._;_"...._;_;_t_ •

-i-i-1-1-+-4-i-i-i-4- / 1 ii t.+-... t.

1- : : s h : : -rm : : : r : . ; ; : • : : • • : r--1 : :.

8.000

6.000

4.000

2.000

0.000 42 74, -2.009

-4.000

-6.000

-8.000

-10.000

-4- Load drag -o- Drag Unload

Chapter 11: Calibration of the wind tunnel balance

119

Newton and data captured and logged to files. Output Voltage (Eo) data from the

strain gauge amplifiers were plotted as shown in Figure 11.17.

Figure 11.15 Negative drug loads. Figure 11.16 Positive drag loads.

Figure 11. 17 Drag calibration graph

11.4.3 The pitch calibration

As shown in Figure 11.17 and 11.16 the drag pitch cell was calibrated for positive and

negative drag loads. The load cells were calibrated in position with measurements

taken during both the loading and unloading phases to check for any hysteresis. Loads

:74:tt±:1:4:44:±±±:t. ti-4:1 -4±±itti7.±-±i±±1::±±-itiatithtt:

,, 4 ... --- --- -- -- -- - 1 --- ' ' 144+44 : : :

- ....... , .. .. .

...

""1-44:PRP741114:1-7-

.. ; . ... ...

4..4.44:4444171.-4444.:7.4114:L=LE-' ''"`" • • ..

111:41::

.17:77.1-1-7 . 1117417.1:±:t4t:

.. ... . . ... 41--!

Pitch Calibration Graph Drag Load(NVolts(V) -0.0109)1-0.998

a-Drag Load

0-Drag Unload

Load Pitch

-w-Pitch Unload

8.000

6.000

4.000

2.000

0.000

-2.000

-4.000

-6.000

-8.000

-10.000

Load (N)

Pitch Calibration Graph Lift Load (N(volts(v) + 0.0276) /-0.002

6.000 ..... , . "

1„,„,,„

4.000

2.000

........ ; ; ; ; ; ........... ; ; ... ; ;

..... I .......

Lift Load

-0- Lift Unload

--:- Pitch Load

Pitch Unload 0.000

I : :

-2.000

• ' ...... ..........

I"' , , , , ,

-4.000 ..... .......

: I I ...... .. .. .. .

6.000

Load (N)


were added from 0.5 to 5 Newton with increments of 0.5 Newton and data captured

and logged to files. Loads were reduced from 5 Newton to 0 Newton with increments

of 0.5 Newton and data captured and logged to files. Output Voltage (Eo) data from

the strain gauge amplifiers were plotted as shown in Figure 11.18. As shown in Figure

11.19 lift forces have the minimum effect on the pitching moment. This is because the

lift force applied through the center of pivot point as shown in Figure 5.1.

Figure 11.18 Pitch calibration with drag loads.

Figure 11.19 Pitch calibration with lift loads.

Lift-Drag Interference Graph

6.0W

4.000

2.000

z a 0 000

-6-Lift load .

.... .... . . ...... • • : ' : : : .. . . . ......... .. -,. Lift unload

I A DragLoad

n , '''',',•:1?, , ,9 . ',, -.-Drad Unload , )7, 1,b , s?ur; ;

I I I

-6.000 I ... ....... ' "

-4000

Load (N)

4

....... • . .....

.. .... . : : .... .

..... ...... .... . . ii i..


11.5 Load cell interference check

Because the wind tunnel balance was designed by using the axiomatic design theory

Figure 11.20 shows very little interference between lift and drag forces.

Figure 11.20 Lift- drag interference graph

11.6 Angle sensor calibration

The angle sensor in an important component in the wind tunnel balance and is used to

monitor the angle of a wing or object relative to the oncoming airflow.

The angle sensor is mounted in a clamping bracket and can be adjusted to the horizon

(spirit level) or to an incline angle on a wing (chord) as shown in Figure 9.7.

The LabVIEW computer program was used in conjunction with the stepper motor

controller program to monitor the angle. (See Figure 9.11) The angle of the two-arm

was set at increments of 5° from —15° to +35° by using a variable angle spirit level as

shown in Figure 11.21 and recorded. Figure 11.22 shows the angle calibration graph.


Figure 11.21 Angle calibration

Angle Calibration Graph 0.028 Volts/deg

35

30

25

20

15

z 10

5

1

1

1

0 -5

-10

-15

4.16

I

4.0o 4.44 4.58 4.72 4.88 f 5.60

1—

4 5 •

5.42

I

20 Volts

Figure 11.22 Angle calibration graph.

11.7 Evaluation of tare and interference

In any wind tunnel the model has to be supported. This support will have an effect on

both the airflow about the model and have some drag and lift of its own. The direct


drag and lift on the support is called tare. The tare on the two-arm strut was measured

with a maximum wind speed of 20 m/s.

To eliminate the tare on the two-arm strut a shroud was made and fitted around the

strut as shown in Figure 11.23 and 11.24.

Figure 11.23 No shroud fitted Figure 11.24 Shroud fitted

The Table 11.1 shows the decrease in tare on the two-arm strut with and without the

shroud fitted.

Lift (V) Drag (V) No shroud fitted -0.062 -0.819 Shroud fitted -0.021 -0.340 Difference -0.041 -0.478 Decrease of tare (%) 65.423% 58.420%

Table 11.1 Decrease of tare when the shroud was fitted.

Figure 11.25 shows a tare chart that was created with the shroud in position as the

headpiece of the wind tunnel balance was rotated through —10 ° to +25°.


Figure 11.25 Tare graph.

11.8 Data processing

It is important to note that the data captured from the test needs to be processed. The

following procedure can be used as a guideline.

1 Capturing a set of data with the model in position with no wind.

2 Capture the data (maximum wind speed) and log it to file. (Remember to

take note of the file names and test conditions such as temperatures and

pressures)

3 Subtract the starting data (no wind) from the test data.

4 Subtract the tare data according to the angle from the new data as in 3

above.

5 Use this data for the graphs.

Chapter 12: Wind tunnel balance evaluation test 125

12. Wind tunnel balance evaluation test

12.1 Introduction

It was decided to evaluate the wind tunnel balance design by testing a NACA 23012

airfoil and compare the data measured to the actual data of a NACA 23012 airfoil.

Before a model is tested in a wind tunnel, a few considerations must be taken in account.

Clearly define the purpose of the test.

The wind tunnel and wind tunnel balance parameters.

Consideration on the accuracy and precision of the test results.

The size of the model to be tested.

12.2 Set-up for the test

A NACA 23012 airfoil with a chord length of I75mm and span of 600mm (aspect ratio

of 3.429) was cut from polystyrene and covered. A brass-mounting ring that slides onto

the headpiece bolts the wing in position as shown in Figure 12.1.

Figure 12.1 NACA 23012 airfoil filled to wind tunnel balance.

Chapter 12: Wind tunnel balance evaluation test

126

The wing was leveled with a spirit level as shown in Figure 12.2 and chord line set to

zero degrees. Clay was used to minimize the drag on the brass-mounting ring as shown in

Figure12.3.

Figure 12.2 Airfoil leveled

Figure 12.3 Drag minimized on

brass-mounting ring

All the electronic data acquisition system was checked, LabVIEW programs activated

and angle sensor adjusted to read zero degrees with the chord line.

12.3 The test

After all systems were checked the test conditions were noted, the wind tunnel was

started and wind speed was measured with a Pitot-static tube connected to a water

manometer.

Temperature:- 20° C.

Atmospheric pressure:- 634mm Hg.

Water manometer difference in water height (Ah).:- 20mm H20.

12.3.1 Atmospheric air pressure

From this information the atmospheric air pressure was calculated:

AP = PgAh (12.1)

Ap =13.6 x 103 x 9.81 x 0.634

AP = 84.58kPa


12.3.2 Air Density

The density of the air change with temperature and can be calculated by using the

equation:

3.483x10-3 x pa,,

t 0 K

3.483x10-3 x84.58x103

(12.2)

Pair — (21+ 273)

pair =1.002kg /m 3

12.3.3 Air speed

Apa, = —1 pV2 g (12.3)

12xAhxp,„,,,,,,xg V =

Paw

112 x 0.020 x1000x9.81 V =

1.002 V .19.79m/s = 71.89km/h

12.3.4 Reynolds number

The Reynolds number is physically a ratio measure of inertia forces to viscous forces in a

flow and is one of the most important parameter to compare test data with each other.

The Reynolds number was calculated from, Houghton and Carpenter (1993).

pVc. R = (12.4) •

Pc Where

Density (p) = 1.002 Kg' m 3

Speed (V) =19.78ml s

Chord (c,,)= 0.175m

But viscosity (µz) is temperature-related and the following equation stated

Houghton and Carpenter (1993), was used to determine viscosity at a 20°C.


3

Pc 0 Tt2i4

Pc20 T i

(12.5)

Where

Viscosity (tto) at 15°(288K) = 1.783E-5kg/ms

Temperature at

Temperature at

Ili

TO

(

= 20°C (297°K)

= 15°C (288°K)

3

Pc20

p 0

Tt 2) 4

TI 3

2 )4 2:

Pc20

Pc ° = 0.9771 Pc20

1.738x10-5 kg/ms Pc20 0.9771 pc20 =1.778x10 5 kg/ms

From Equation 12.4 the Reynolds Number (Re) was finally calculated as:

R = pVc„,

e Pc20

1.002x19.79x 0.175 R, —

1.778x10'

=19.517x106

The test model was rotated to -10° and data were captured using the IabVIEW program.

1000 readings were taken over a period of 3 seconds for every angle change from -10° to

+20° and logged to an ASCI file. See Appendix F for more information. Some vibration

was experience on the angle sensor, lift and drag data signals as shown in Figure 12.4 and

Figure 12.5 but this is compensated for by the 1000 readings over 3 seconds when the

average data were used.


Figure 12.4 Vibration on the angle sensor.

transposed waveform graph

10.4=

5.0--

.0.0--

=5.0-

'11.5 -1 r -

9 10

Figure 12.5 Vibration on the lift, drag and pitching moment sensors.

Lift data

Angle data

Drag data

Pitching moment data

12.4 Test results

The test data were captured to an ASCI file and imported into the Microsoft Excel

program, The data was processed as recommended in paragraph 11.8 and plotted.

12.4.1 Coefficient of lift

The Coefficient of lift (a) can be calculate by using the standard equation as stated in

Anderson, (1991).

2L C, =

pV 2 S (12.6)

Wind tunnel test Lift Coefficient of an NACA 23012 (114 chord)

- - -

Ht! I 71

• ...:44.44_1.144_144_1.

4 1.1444

model tested

-o-NACA-23012 Data

1.500

1.000

— 0.500 -u

...... : :

: •44 . 1;34-1. -1-4-1•4 .4440.1 -4

1-1•1+191-H'

'1-11

.. .. . ..

it: : , - ,-rt -t-r • r-

! ' I

fl f-i : .

0.000

H : H .. .

I : . 1-7

C ri -0.500 -

-1.000 -

-1.500

Angle of of Attack (Deg)


Lift (L) is measured in Volts and converted to Newton's by the equation as shown in the

graph Figure11.12. Density of the air was calculated (see Equation 12.2) and surface

area (S) the length of chord multiply by the span of the wing equals to 0.105 m 2.

Coefficient of lift (CO was calculated for every angle of attack and plotted as shown in

Figure 12.6. On the same graph the actual data of the NACA 23012-wing profile were

plotted to verify the test results. (See Appendix F).

Figure 12.6 Coefficient of lift graph comparison.

12.4.2 Coefficient of Drag

The Coefficient of drag (CD) was calculated by using the equation stated by Anderson,

(1991).

2D CD —

pv's (12.7)

Drag (D) is measured in Volts and converted to Newton's by the equation as shown in

the graph Figure11.17. Density of the air is calculated (see Equation 12.2) and

surface area (S) the length of chord multiply by the span of the wing equals to 0.105

m2.

1-1-E ' I

---- -- 1.•••• 7 -- : --

_14 - : I • ' I : • I • I •

-- - - - - 44. 3. • , • 41-41 ■ •14-- I-I-4 4' + I 4 ----- -

-- „ --

-- : ; 4

. ... ... • .

lAzdel tested

o— NACA-22012 Data

.4.

Wind Tunnel Test Drag Coefficient of an NACA 23012 (1/4 chord)

titt4Tiitiiiictii-km...0::;;;C4--c--0.--04-1: : ! . 4 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 8 7 8 9 10 11 12 13 14

Angle of Alien() (De g )

0.400

0.350

0.300

0.250

0.200

E 0.150 0

0.100

0.050

0.000

Chapter 12: Wind tunnel balance evaluation test

131

Coefficient of drag (CD) was calculated for every angle of attack and plotted as shown

in Figure 12.7. On the same graph the actual data of the NACA 23012-wing profile

were plotted to verify the test results. See Appendix F.

Figure 12.7 Coefficient of Drag graph comparison.

12.4.3 Coefficient of Moment

The Coefficient of moment (Cm) is taken about the wing quarter chord position and

calculated by using the equation stated in Anderson, (1991).

2M, C

u =

pv2s (12.8)

Moment (Mc) is calculated by taking moment around the point A as shown Figure

12.8.

Wind Flow angle of attack

T) t +


Lift

Figure 12.8 Sketch of the forces and moments.

Take moments about the pivot point A:

Mc + Db+ Lx2 + Mu ga— FsGne — M gd + FsGm C = 0

But FSGD = D and (Mstg x a) = (Mg x d)

Thus (Mc) can be written as:

Mc = D x(e—b)—(L x x 2 )— (FsGA, x c) (12.11)

Equation 12.2 was used to calculate the density of the air. The surface area of the

wing (S) (0.105m2) was calculated by multiplying the chord length (cw) of 175mm

with the span (bw) of 600mm.

Wind tunnel test Moment Coefficient of an NACA 23012 OM chord)


Coefficient of moment (Mc) was calculated using Equation 12.11 for every angle of

attack and plotted as shown in Figure 12.9. On the same graph the actual data of the

NACA 23012-wing profile was plotted to compare the test results. (See Appendix F.)

Figure 12.9 Coefficient of moment graph comparison.

12.5 Conclusion of the test results

From the graph (Figure 12.9) the test data differ from the actual NACA 23012-wing data

and the reason for this is:

The aspect ratio of the test wing is finite.

The test model was not on size or perfectly smooth because hot-wire cutting

methods are not ideal for these type of test models and shapes changes accrue.

The induced drag increase rapidly with a three-dimensional wing.

The mounting method has interference drag due to its shape and size.

Chapter 13:Conclusion and recommendations 134

13. Conclusion and recommendations

13.1 General Conclusions

External Wind tunnel balance design is not a design that can be taken lightly. A good

knowledge of aerodynamic principles and manufacturing methods need to be

mastered to comply with the international standards.

Data capturing is an art on its own and a good understanding is needed on how noise

can be eliminated and what instruments are to be used to capture data.

Because of time to design, build and install the external wind tunnel balance in to the

high-speed section of the wind tunnel the bare minimum computer programming in

the LabView was done to capture the data and this needs to be redesigned to make it

more user friendly.

In general the wind tunnel balance performs above expectations and can be used to do

provisional model testing.

13.2 Recommendations

There are a few changes and redesigns that can improve the external wind tunnel

balance and testing facility:

The LabVIEW data capturing program and LabVIEW stepper motor

control program should be combined.

The LabVIEW data capturing program can be made more user friendly.

Control of the wind tunnel fan motor can be automated and controlled via

the computer.

Wind speed measurements should be captured with the lift, drag and

pitching moment data in the LabView computer program

The backlash between the worm and worm gear should be improved.

Chapter 14. Bibliography and references 135

14. Bibliography and references

E L Houghton and P W Carpenter 1993, Aerodynamics for Engineering Students, 4 th Edition, Edward Arnold Hodder Headline London.

William Rae and Alan Pope 1984, Low-Speed Wind Tunnel Testing second edition, John Wiley & Sons New York.

Jewel B Barlow, William Rae and Alan Pope 1999, Low-Speed Wind Tunnel Testing Third Edition, John Wiley & Sons New York.

SAE Sp-1036 1993, Analysis of Vehicle Aerodynamics, Society of Automotive Engineers, Warrendale USA.

George E Dieter, 2000, Engineering Design 3RD Edition, Mc Graw Hill, Bostan.

http://www.aerolab.com/posit.htm, 2002, AEROLAB

Cosmos/works,1999, Structural Research and Analysis Corporation (SRAC), Los Angeles, California, USA.

R.0 Hibbeler, 1993, Static and Mechanics of Materials, Macmillan Publishing Company, New York, USA.

httu://www.usersslobalnet.co.uk/carbon fibres.htm, 2002, Fibres

http://www.callisto.my.mtu.edu.co.uk, 2002, Carbon Fibres

J Kotek, P Glogar and Mcemy, 2001, Interlaminar shear strength of textile rein forced carbon-carbon composite, 39th Experimental Stress Analysis 2001, Tabor, Czech Republic.

Robert L Mott, 1999, Machine Elements in Mechanical Design 3 RD Edition, Prentice Hall, London.

A D Deutschman, W Michels and C Wilson 1975, Machine design theory and practice, Macmillan Publishing Co. Inc., London.

A H Burr and J B Cheatham 1995, Mechanical Analysis and Design 2 nd edition, Prentice Hall, London.

J E Shigley 1977, Mechanical Engineering Design 3'd edition, Mc Graw Hill, New York, USA.

[16] P H Black and 0 E Adams, 1984, Machine Design, Mc Graw Hill, Bostan.

Chapter 14. Bibliography and references 136

Karl Hoffmann 1989, An Introduction to Measurements using Strain Gauges, Hottinger Baldwin Messtechnik GmgH Alsbach, Federal Republic of Germany.

E P Popov 1978, Mechanics of Materials 2nd Edition, Prentice-Hall, Inc Endlewood Cliffs, New Jersey.

S Timoshenko 1955, Strength of Materials 3rd Edition, Part I, D Van Nostrand company, Inc Princeton, New Jersey.

AL Window and GS Holister 1989, Strain Gauge Technology, Elsevier Science Publishers Ltd, Barking, Essex, England.

JF Douglas 1986, Fluid Mechanics Volume 1, Longman Science and Techical, John Wiley & Sons Inc., New York, USA.

E L Houghton and P W Carpenter 1993, Aerodynamics for Engineering Students, 4 th Edition, Edward Arnold , Hodder Headline London.

John D Anderson, JR 1991, Fundamentals of Aerodynamics rd edition, Mc Graw Hill, New York, USA.

APPENDIX A 137

APPENDIX A

Average Wind tunnel speed in high-speed test section

Front Cross Section (speed m/s) Veresal

Distance (m1/11)

Hortmedel *slants 00110 Anne, Semi 1021M°2*

125 250 375 500 625 750 675 (m/s) Krrub

1120 20.11 • 1934 19.03 20.11 21.04 21.04 20.11 2024 7285

200 20119 2104 21.04 21.04 19.99 21.04 1952 20.07 74.41

300 20.51 21 00 21.50 21.04 21.00 21.04 20.11 KM 7523

400 21.00 2104 21.04 21.04 21.04 21.04 20.11 20.03 7525

500 2055 2104 21.04 21.04 21.00 21.04 20.511 2001 7526

600 20.00 2104 21.04 21114 21.00 21.04 21.04 2029 75 20

700 20.00 2104 21.04 21.04 21.60 20.11 21.04 2014 75.03

BOO 20.00 2, 04 21.04 21.04 21.04 21.04 20.00 20.75 74.08

900 2000 2060 20.11 20.50 20.11 20.11 20.11 2020 73.10

1000

Avem(Pemis)

Avenge (NTT)

20.42 2000 2066 20.08 20.67 20.54 20.30

73.51 741111 75.11 75.17 75.13 75.01 73.09

Mt Cross Section (speed m/s) Venal Horizontal distance (mm) Ammo/ Speed Prorecatall

DiStallelt (MN 125 250 375 500 1125 750 675 (eft) Kren

100 20.00 20.11 20.11 20.11 20.11 21.04 20.11 2023 72.81

203 2056 21.04 20.56 21.04 21.30 21.04 10 62 2075 7458

300 2056 21.00 21.04 21.04 21.04 20.70 20.70 2057 75.14

400 20.58 21.04 21.00 21.00 21.00 21.04 20.70 2001 75.26

500 20.58 21.04 21.00 21.45 21.00 21.04 21.00 2003 75.35

600 20.00 2104 21.00 21.04 21.00 21.00 21.00 2017 75.13

700 20.50 21 04 21.00 21.04 21.00 21.00 20.11 2013 74.97

600 20.58 2104 71.00 2056 2000 20.60 2011 2070 74.53

900 20.10 20.11 21 00 20.50 20.60 20.11 20.11 2020 73.30

1000 0.00

Aversge(WS) 20.40 2083 30.80 20.87 20.87 20.1113 20.38

AVORIge (Killfh) 7344 7499 75 09 75.12 75.14 75.11 73.36

Average Boundary Layer in high-speed test section

Frontal Cross section Vertical Distance from the roof Distance

mm 41120

mm AP

Pa Speed (v)

m/s Speed (v)

Km/h 20 4.3 42.2 9.1 32.8 25 5.6 54.5 10.3 37.2 30 7.6 74.9 12.1 43.6 35 8.8 86.3 13.0 46.9 40 10.5 103.0 14.2 51.2 45 10.5 102.5 14.2 51.1 50 11.5 112.3 14.8 53.5 55 12.6 123.6 15.6 56.1 60 13.8 134.9 16.3 58.6 70 16.4 160.9 17.8 64.0 80 17.1 168.0 18.2 65.4 90 17.9 175.2 18.5 66.8 100 20.5 201.1 19.9 71.5 200 22.5 220.7 20.8 74.9

Rear Cross section Vertical Distance from the roof Distance

mm A 1120

mm AP

Pa Speed (v)

m/s Speed (v)

Km/h 20 4.0 39.2 8.8 31.6 25 5.2 51.0 10.0 36.0 30 8.0 78.5 12.4 44.7 35 9.0 88.3 13.2 47.4 40 10.3 101.0 14.1 50.7 45 11.0 107.9 14.6 52.4 50 12.0 117.7 15.2 54.7 55 12.6 123.6 15.6 56.1 60 13.5 132.4 16.1 58.0 70 16.4 160.9 17.8 64.0 80 17.0 166.8 18.1 65.1 90 18.0 176.6 18.6 67.0 100 20.0 196.2 19.6 70.6 200 22.0 215.8 20.6 74.1

TUNNEL

CENTRE

-4-Front

APPENDIX A

138

Average speed in high speed

test section (vertical distribution)

21.00

20.80

20.60

1 2040

g. w 20.20

20.00

19.80

-01

-.-- From

-0-Aft TUNNEL CENTRE

. .

100 200 300 400 500 600 700 800 900


Average speed in high speed test section (horizotal distribution)

21.00

zaso

20.80

20.70

20.60 E . 20.50

rn 20.40

20.30

20.20

20.10

125

250 375 500 625 750 875

Distance from front panel (mm)

• —.— Front

—o—Aft

a

......"....

APPENDIX A

139

Boundary layer in High-speed test section ( 20 to 100mm from roof)

C E

I cn

25.0

20.0

15.0

10.0

5.0

✓ 11.

a

0.0

20 25 30 35 40 45 50 55 60 70 80 90 100 200


APPENDIX 13 140

APPENDIX B

Drawings

Wind Tunnel Balance

liffilliffiffilli

APPENDIX B

141

k It At\ ' .111 1 r

Au .nn ll

' MI

LLI 9 9

a W ¢

O

APPENDIX 13

142

0

'6' t

4-

APPENDIX B 143

4

O

U

WT

B-0

1-0

2

SE

CTI

ON

B-B

t

144 APPENDIX B

SE

CT

ION

A-A

(2 9

cQM

Lift B

ase

Top

w cn m LL

DR

W N

o. V

VTB

-01-

05

LH L

IFT

BA

SE

BR

AC

KET

9 O

6

p

0

we 5 0. z

" `U\ti."W.‘.."t'saSs,:.N.ts ."` .%."Ma%•11

SE

CT

ION

A-A

war 01 01

C001 Oral

APPENDIX B 145

a

z

-r-' W a s co u = 2

00 11

c"•E.,

88 94

—r

8 .5da

28 99 03 a1

01 -01

09t

SE

CTI

ON

E-E

•—

APPENDIX B 146

4

_ It t"\\:\\ak, es \\xxx

:11/4 VI Olin- 4 lai sitam,....xt \ \

lig i ■

Oi

98 g2

2 r

. 111

..of i...(..

tii"

---•—•••----7. r 01 , on/II

cocci OMzi

SE

CT

ION

D-D

w

0

cc CD

N- 9

S

,z w RO

APPENDIX B 147

APPENDIX B 148

O “3/4„,

2 0V2 as

cy)

O 9

APPENDIX B 149

L/

00 91 0191.

SE

CTI

ON

C-C

BD

SE

CT

ION

B-B

0

a°

aW

p O

z

150 APPENDIX B

LP

O

UU

0

a_ LIJ

a:1

r

7

co

O

0

E E

O

.3 '3,e' zne z

Cl0101

0101

09

UJ LIT C or

<I ,0

—

RR

fifth II

01 ?V ()Val 1

APPENDIX B 151

UI

cr

I-

tEt, Lii

tI I

SE

CT

ION

A-A

1111C \if\

te,

121

O

I-

BALA

NC

E W

EIG

HT

0 0

rt

APPENDIX B 152

DR

AG

LO

AD

CEL

L

to

9

0 t OS

01 0 0

,̀0

N

4-4

o4

..:4;

09 • 0

08

001

O

CJ

APPENDIX B 153

*

I

APPENDIX B 154

1 ! c1

IiiiIMME 1:

ot i

s

:

APPENDIX B 155

t

APPENDIX B 156

vo % 000

E

■

0 • —ts-+

,StxS 000111 001'01

w w z

w co

co

•cl

1

g:

9

3:

APPENDIX B 157

O

5,

BEAR

ING

SCR

EW

9

U 096'9 5136.

03

ri rit

4-

7

§

N N

SE

CTI

ON

D-D

1Z

CO

H

P£

L 9P

NC) N

0

tr

a ce ce <C

r9

0

S Y

APPENDIX B

158

APPENDIX B 159

I-

.NitaabWeilea1/4:1% CD

8

I NI

1 I!

I I I

4

1

11

1 , A:

t

ka

k

DET

AIL

A-7\

• 60

.100

60

.000

a co

-H ©

i 1 11 1

tt

1 14,4

ocatz srp 00ZZZ

O

/

9Z

SE

CTI

ON

A-A

a

a

?rE O

fbr

aci U

0

0 co

J

si

APPENDIX B 160

rc

11 t O

9

sz

APPENDIX B 161

0

0 w

1

C

O

ce

a ) 9 N

ics 0

8

C

0

4

f

LIJ

SI

I

BI

rale— 0

SE

CT

ION

F-F

,f

t

APPENDIX

162

163 APPENDIX B

SE

CT

ION

D-D

09'9

O 0

9 rl 9 al

a o a

3:

L 9Z

U

APPENDIX B 164

0

V

S

WO

RM

MO

D

cr) On6 . 6

< 000* 01

Z66' I 0 000t

0

0

e

tla

o O .=

ie)E1 ;€2t1 Eogo

zF zo•rz z

t",

t 0

Z66'LL0 0001 I

006'60 000'01

i.

APPENDIX 8

Oq" L

OZ

165

' flra'e, 9.28f

166 APPENDIX B

O

In a ccW cc.

o

GE

AR

CO

UPL

IN

•

0019

SE

CT

ION

A-

an

APPENDIX B 167

CN

a vi7 N I') ci

z

w

N --- 00 (;) ci) 00

o o 1— 1— 1-- comwm

cn

0

in

z a Lu

z

z

re w z

0

h 0

•vt

0

w

z

H z 3 0

>- U)

w

3

0

a Fe U) Lu 0

8 831dVHD 33S

f..

2Z

APPENDIX B 0

168

0 0

0 z w 1--z 0 z

<

2

Z

00

7c= 4 4

II .

cN 5 2

c0

N

N

a LU

1.7Z In LU az) 0

UJ

cnUI

ge, o, =r,a

z = < 0

0 E - a z wz.

..0

<,, writs oz

z

V

1.44--1110-

169 APPENDIX B U

O

06

3

el

MI

1.0

7

0

2 ?131dVHO 33S

2

SE

E C

HA

PTER

8

9 0 a)

cx tu z a

rc

a tl

4—

APPENDIX B 170

OZ

00 LO

0 Os ',LT CO

APPENDIX C 171

APPENDIX C

Finite element buckling analysis

Mode shape Hertz Seconds 1 19.041008 0.052518 2 34.146515 0.029286 3 148.915970 0.006715 4 250.290665 0.003995 5 255.001358 0.003922

new en 20021est so12-41:: Frapancy

Mode Shape : 1 WiJe = 191:41 Hz

Z X *--•

Mode shape 1

APPENDIX C

172

new awn 2002de9so12-vb :: Frequency Mode Shape : 2 VS - 34.147 Hz

AY

Z X

Mode shape 2

new ern 2002les1_se12-nb z Frequency

Made Shove : 3 Value • 148.921t

V

Z x

APPENDIX C

173

Mode shape 3

Mode shape 4

new en 2W24est sca.vb:: Frequency

Mode Share : Value• 250.2!4

V

APPENDIX C 174

APPENDIX C

175

idodanew arm 2002dertso12-4):: Frequency

Shape : 5 Van 255 Hi

Mode shape 5

APPENDIX D 176

APPENDIX D

Strain Gauge and Data Acquisition System

ACHE 34 68 ACHO.

ACH1 33 67 AIGND

AIGND 32 66 ACH9

ACH10 31 65 ACH2

AC H3 30 64 AIGND

AIGND 29 63 ACH11

ACH4 28 62 AISENSE

AIGND 27 61 ACH12

ACH13 26 60 ACH5'.

ACH6 25 59 AIGND

AIGND 24 58 ACH14

ACH15 23 57 ACH7

DACOOUT 2 22 56 AIGND

DAC1OUT 2 21 55 AOGND2

EXTREF 2 20 54 AOGND 2

D104 19 53 DGND

DGND 18 52 D100 -,-

D101 17 51 D105

D106 16 50 DGND

DGND 15 49 D102

5V 14 48 D107

DGND 13 47 D103

DGND 12 46 SCANCLK

PF10/TRIG1 11 45 EXTSTROBE

PFI1/TRIG2 10 44 DGND

DGND 9 43 PFI2/CONVERT*

5V 8 42 PF13/GPCTR1_SOURCE

DGND 7 41 PF14/GPCTRLGATE

PF15/UPDATE* 40 GPCTRO_OUT

PF16/WFTRIG 5 39 DGND

DGND 4 38 PFI7/STARTSCAN

PFI9/GPCTRO_GATE 3 37 PFI8/GPCTRO_SOURCE

GPCTRO_OUT 2 36 DGND

FRED :OUT 1 35 DGND

-I' No Connect on Devices without Analog Output

68-Pin E Series 16 Al Channels

177 APPENDIX D

OUVO 3£Z0910d 01

Mffill111111111111111111111111111111111 ° 2 r•:: Poi S 2 2 °

0 WJ W

IND

TUN

NE

L 2

0

a

Cf

H3TIOILLNO0 1101011 1113dc131S

0 CM 2O- a 0. g N337:19 c11- k 6 MOTS).

3M8 _ j set &no

C31:1

.--. se

< 0. 7: N331:10 co.

c< 6 NtOTBA di+ 1 3778 _ j se.

'WO

OA VOA

d P8380 i- :3 1 6 MOTEIA

ame _4; dwo3

co co

-J

N3NLIO i N

032:1 c

APPENDIX D

178

A B D

F G

Figure 1. Circuit Diagram

A. + Bridge supply .B. Compensation

Set bridge supply + Input

Output G. - Bridge supply - Input H. Set zero

Components List

Component Value RS Stock No. Quantity Required

RI & R3 100Kf2 148-972 1pk R2 & R6 1000 148-269 1pk R4 oon 148-219 1pk

R5 & R8 ton 148-017 1pk R7 470 148-174 1pk R9 1KO 148-506 1pk R10 & R11 6800 148-461 1pk

VR1 & VR2 10K 186-520 2 D1 & D2 IN827 283-104 2 C1,C6 & O7 100nF 114-840 1pk C2 & C5 10nF 114-812 1pk C3 & C4 10pF 103-957 1pk T1 BD135 299-323 1pk T2 BD136 299-339 1pk T3 BC108 293-533 1pk

4-Way Connector 425-847 1pk

3-Way Connector 424-686 1 pk

IC Socket 24-pin 402-327 1pk

Strain Gauge Amp 846-171 1pk

APPENDIX D 179

Strain Gauge Amplifier PCB Stock No. 435-692

A printed circuit board to accept the RS Strain Gauge Amplifier and associated components to make an amplifier decoder for resistive bridge type sensors.

Assembly All components positions are marked on the PCB, shorting links are indicated by solid lines. C5, C6 and C7 are for reduction of noise and considerably slow

the output response. In some applications these components The components list below includes PCB mounting screw are best removed. terminals for ease of connection, however these need not be used as wires can be directly soldered to the board

The values of R1 and R2 given below set the gain to 1000. The gain can be set to other values and is defined by the equation.

R I Gain = 1 +-

2

RS Components Issued .luly 1995 7412

N`PG G - ;CIE "AM E":

VR1` 11R 2 D1

fl

Adjust to set Zero

Turn VR1 Clockwise till dick

;

R2

- RS R< RI-1 11

Adjust to set output gain

APPENDIX E

180

APPENDIX E

Wind Tunnel Balance Calibration

Strain gauge amplifier zero and gain setting

APPENDIX E 181

•

" - ' •

co = 17 :1:' --'

• : '••••!-*-t• .

+ --

_7; #_.,

"4-i- tt : .t_i_ir-•

-

• i- ' Ps• 1 :

E

. :

. : i-r - E -- “- • Er- 7

i-l-H-f 4-

-- • -t -- • :71- t_44.4e4-t--i-t-4 - • 1----re '--r: :

: :

-+E-Er --

1 r h. 4- -- • 4-

. . . . . . . .

-r- 4- 4. tJr - L -t- --f-i-l-H- ,-I- t-i -- i -- .-f.a.--- - - IL • •74 7 ••• 4-• 7_-_ .1._ I_ 4..

' 4- - -i-• - -f---1-i--4- -1-i-i-i-l -i.-l-le i- -i-t- ' :- .i l- -!---- ,--t- ,--t---■-,--:- ,---;!--4-t-t 1-•- e-- O.

it-•-• 1-1.t-4- i-4 - --

L . r - t

'-.1_i—i •_ 14..4 •_,1 z. _.- it. I__ .._ _I .1_ .. 1 : Li. • • _i - i 1— • : : : : - :if': • tilt, - I - - t . -r.1.-

-4-1.-i- t.: -- ' , i

IP -1-1- n--- :- -h-r h ' ---• - +- -H-4- : • • •

.,. • - 7 7 7 ; ; :. H-: : : : ; ; 7., ; -; 7. ; ; : 7. - : •

.- - ,- H- 1-1- -l---"-1 --- -}t -1 - --1--t -7 - t•-'--i-- -+- t - - . t - "i - --- 1 ' -r-i - r- -rt. 1- --- • - tie-v. -Hie -- I -- r. -4- +-• + --4 -1--, - .-- -4 - 4- -1-1- - I- 1-

"

1-1-;--i-i-l--

-r

: .

.

•

..--t- -1-- 4 4 -i--"- •---*- ::-.: • :--4-.-:- - 1 1-: -- --, 4- --i--L-1--i ' 4.._,___,...._ --- :al

I•• .1: • • : --t -1 --1-i-1-1--t-H- — ,- -(--

.__:. , „,, . I -4- i

' • ' z -1 • . ' 1 :

I 1 , 1 • : : , :

4-1-4.4-4-.4 -1-1-1-4 -4- -1. ..--

-f - :Li. II

— -

-4 -

•

1 - _ .

.- ; f-• .1-• ,-- t

1 4--

.

!

.. i-- -

--1' .t - 1 i. --

1

I 1 ■ 1-7'. ..ii-r"-t-i-

„„,„

- .. e, : : : : : • : ,

5 q 5 (A) Bon

a ci

O

9

O CO CD O

cc O

en

0

a 0 W) O CO

O

O

0

O

0

07

0707

0

a

1%.

O CO CO

0

O O 00 0

• CD 017

CD CO O CD

CO 0

147

0

07

0

CO CD

0 0 0

0 .c

a. 0 0 0 ci

TA

RE

CH

AR

T a

O

9

a

O

01

O co 9 9

07

O

4

W)

O 0

W)

O

O

O 4:3

O

O

O

O 0

8 9

O

O

9

O

O

O O 0

CU

O 0

O CI

CD

O O O

0 '7! 9

O

9 O O

9 O

9 O 0

O 0

O ci

O

9 O 0 O 0 O 0

O 0 a

a

en O

9

O cz. O O

0 O O ci

a

O O

OD

O O

.17

O O

LC) CD O O

04

O O

07 O O

O

O

9

CO O O O

07 04 O O

O

O O

07 04 O O

O

O O

<0

O O

CD O O

C

▪

4 O O

CD O O

IC) 147 O O

O O O

ci O

9 O

9 O O

0 O

O O

O O

O O

9 O O

O

9 O O iC

ra

a CO (17 a 07 C4

O eq

CD 9' O CY) O CO 0-• CO

0

•

O O

04

APPENDIX E 182

- t-

_;_a_E-, • 4 _ ,_,_ .4_ ,....1:::14.4-4—i-4-1—-1—;_i_;_;,

‘•::!::::::::::

:I: ..•::::::::::z:

-1-: -4-f-e-1-4:-

-I-4 - .

. , INI ; .. ... ...

. . .r.

.

. • •

-t- -r tt , :::::

—e

— A

ng

le s

en

sor

In co Cr) tn

CNI co

r in 0 U) O 0 0

• Ir.'

(saw 60a) ei6uy

.0

Co

a) C

0 T9 '47+ 03 z

To" Pi 0 a co

C

O

U)

CO CO

In

0

O 03

Cu

a

ibra

tion

Gra

.0

N r

(I)

O O Cr)

O O

CD O

N

ui N Lri

O U") It) O If)

r O O N

U) N

O C)

-o

N 0) C

APPENDIX E

183

O 0 co

O ci

G)

O

0

APPENDIX E

184

re

U) 2

u) 0 < I a. 0

-1 0 g

I- 0 LL Ey

LI z 0

z

LL

Def

lect

ion

0 0

cn r

le) r--

CJ CO

In r

0 CV N

CD IN

V" 01

0 01

E d a 0 0 0 6 6 r r r, E

cs o 0 0 0 0 0 0 0 0 0 0 O 10 . 0 . If) . 0 . I.0 . 0 . In . 0 . tt, . CD . 10 . 0 .

V ..--.. r C4 CNI Cr) 01 NI- -4- 1.0 in CO CO N- CO 2 0 ---., -I

Volts

142 L_ Volts . 55 A6-45544 65

4- :

. . . .

4=-1

6

4-

2-

2 0 : I ;

75:- ;65115 -2 - 1r4 4.4-±t

------ ---------

-- --

- - . s .

! 1-

-7.28

-4 -4- 4- - -

.4-

-1- -- --

r."-•

-4 - 4-

-6

-=- 7-1 1-7

APPENDIX E 185

LIFT LOAD CELL CALIBRATION

Mass till Load lilt Unbd Load(N) Volk Volts

-75 -4.763628 -4.944218 -70 -4447396 -4.484557 -65 -4.075764 -4232155 -80 -3.826167 -4.021289 -55 -3.495954 -3.879072 -50 -3103524 -3.281881 -45 -2.872159 -3.001145 -40 -2.523945 -2 879037 -35 -2.174253 -2.380191 -30 -1.855835 -201572 -25 -1.85111 -1.894231 - 20 -1.28446 -1.415887 -15 -0.943647 -1.030135 -10 -0825215 -0.836527 -5 -0.375071 -0.3089554 0 0 0 5 0.365023 0.28937 10 0.712805 0.612576 15 1.026372 0.91412 20 1.34155 1.237801 25 1.850335 1.54928 30 1.986515 1.85382 35 2 328814 2.18531 40 2.83975 2.477195 45 2.972535 2.775131 50 3237355 3.065412 55 3.531138 3.4061325 80 3.851905 3.711445 85 4.192938 4 04734 70 4.832665 4.338295 75 4.831895 4.657965

SUMMARY 01.1791.17 LET

Regression &statics Male R 0.9999091 R Spare 0 9998181 Abated R Sp 0.9998119 Standard Emu 0 0401062 Cteervabons 31

ANOVA 01 SS MS F weficence F

Regression Residal Total

1 29 30

256.457634 0.0468488

258504281

256.4578 0 001809

159438.7 8.57656

Coefficients Standard Eno: t Slat !Aisle. Loser 95%UPPer 95% one,' 99 °eloper 99.0%

Inerce91 X Variable 1

0039744 0.034315

0.00720328 0.00016107

5517493 399.2977

603E-06 8.57E-58

0.025012 0.054478 0.0839813 0.054844

0.019889 0.063871

0.059589 0.084759

Lift Load cell Calibration Graph Lift Load (N) = (Volts - 0.0397) 10.0643

Load (N)

APPENDIX E

186

-1111:47.7:24:77.:7. =17

Regression Statistics Multiple R 0.99776939 R Square 0 99554375 Adjusted R 54 0 99530921 Standard Ent 0 28447086 Observations 21

ANOVA at SS MS F forename F

Regression Residual Total

1 19 20

343 4943231 1.537549749 345 0318728

343 4943 0.080924

4244.671 8.37E-24

Coefficients Standard Error 'Stet P-value LOVAV 95% Upper95%MM)/ 99.051pper 99.0%

Intercept X Variable 1

-0.3703368 1.33580915

0.062076631 0.020503238

-5.965798 65.15114

9.66E-06 8.37E-24

-0.500265 -0.240409 1.292895 1.378723

4547934 1.277151

-0.192739 1.394488

Load Drag Load Drag Unload

(N) Volts Volts -5.00 -7442 -7442

4.50 -6.670 4.977 4.00 -6.110 4.547 -3.50 -5.330 -5.881 -3.00 4.280 4.720

-2.50 -3.440 -3.890 -2.00 -3.170

.1.50 -2.060 .2.400 4.09 -1.280 -1.670

-0.50 -0.670 -1.060 0.00 0.000 0.000 0.50 0.479 0.370 1.00 0.969 0.880 1.50 1.589 1.470

2.00 2.159 2.050 2.50 2.943 2.790 3.00 3.876 3.520

3.50 4.379 4.200 4.00 5.011 4.860 4.50 5.418 5.250

5.00 5.770 5.710

APPENDIX E

DRAG LOAD CELL CALIBRATION

SUMMARY OUTPUT DRAG

187

Drag Calibration Graph Drag Load(N)=(Volts(V) + 0.370) / 1.335

..... --• , t •

«- Drag Load 0- Drag Unload

8.000

6.000

4.000

2.000

0.000

- - - 1--1--rr

t i • I I- 4 1-i•-!!! ! • • t-t • . ' . . 4 4 . . ; : . . • . . : ! . : ! : : . : 4 . : . .

-4.000 -

-6.000

-8.000

-10.000

-2.000 -6 00i--4

-it

Load (N)

APPENDIX E 188

Dra

g C

alib

rati

on

Gra

ph

D

rag

Load

(N)=

(Vo

lts(V

) + 0

. 370

) / 1

.335

8.0

00

•

1 i

iii

ii

ii

■1

:1; lill m

ill

i i

iim

iIII

ifil

ill iirill

if fll

iii

Iiiii

iTh

lti ii! jjj

j .....

.. 4 i. I.

4...

...4 i

4 .

. I 1

4

Il

i! 1

---i

---i

'''''''''

'''''''

i!

il

ti

l i

jrn

iiiiIi

i j

li I li

''''''''

''''' 1

1 6.000-it

-----1-

-1

1i -1

''

11-m

-L-

--11

1-1

144

il

!;

1-• !

-Iii

si

'l

I'

It IJ 1

1 i

lli

l.m

l,

i t t

--.1

.......1

1._.

..l

1 -

1 1 i 1

1 t

1„

....1. 4

.1 '

1 1

' 11-

- I

r ......

Ft

I- .

... Hi .........

....

II1

11

1!

1 n I

4 I

1 I 1

1 1

' 1...

.t 1

i 1

_1

L 1

-.4 .

.... _I

1_...

. L.1

._..._"

,a'r

1 1

__

I._ ...L

..1 1 1

1..

._1_ 1._

i 1

1 1

! !

, 1

: . . .1

....

.....

f_ .

t ........ i 1

f._

;,••

•- --

L 1 I.

1.

4.000-

11'1*

H ti

ll

it

i 1

11

1:11i

II

-111.

1; ..

......

..

Li.

] __

,. I

it!! ....

.. ,ii 1

11i

Ii

i i

•r...

...1

illillitli

ttlill

I I

. I. i ..

.I 1

t 1

4 1

... 4

,__ i

4 4

4.. ..

4 ...1

t._

I_ i

1 .

1 1 1

1 i

r I.

- a

' i.

..-4_

1 4

_1-4

1 I

I

t

:F!i

tt;

1.1-1

11:[

it-

ii

ii

'ttt1

. •

I'i

til

!lir

:I

i 2.

000 -

_I-----

-t--1

i t i I

--1 t 4

-• ;1

1- i

ifti

l,....--"

;,if i

2:

:i

_4 .4

- ...

..... 1

_41 !

1 1

!, i

i :

, 1

4 i :

ti

,......altli

tt

lE

illi

'II

4:

11

Ii

il 1

.i

il

i.---1

;1

11

41 1

...ra

,-tir!

i I T

r! I

1

i , 1

i , i ,

, i

, ,

I I

l l

it i

i!l

i ■

rs>1.

..1

11

11

111

.....1

1M

I I i

i .

.....

-----iti

r-I

TI:

-tm

it

-ti,,,

.11

1 t

! 11 1

I

1 ...

...

-t-r-

t;-

1-1.-

Til

>

0.0

00

I , t I

t :

I 1

1'"'!;

''!

'.1.

.--r

!4

!t

!;,,,

....II

II

!.

i. . .!

..4..

1.}

... ! -.- D

rag

Lo

ad

2.1 •- 1

- i .1

I ! " ' ' '' " I

'1'"' ''' •

.4a

bol 1 . 41-6 ' ..

' Z' 1

f I '

I " 1

52.0

0.. I .

54:00 ri J

ra00.

L...

.472.

.. :00.

...1..

._..

. • e •

...4 . 4 4

0;

1 , 00

4 1 4

3 0

0i

1 A

00[ 1

15

00

o

...-

1-1 1

4 1

1 1

-1 1

1 -

I :

1 .

.-4 4

4 ...

. 4

1 h

....

F-

1. 1

4 1.

1 H

..

. 1 1

1 f

1 I 1

-0-

Dra

g U

nlo

ad

> -2

.000 -ii

ii

iiit

i•---

H t.

rt r

---i . -- -I-- 1-

1-

"111

t- ' H

4--

::-+

H.

H1

7,

1 I

r 4

11

11

-1

10000

"4

1[

141.

:14

••••-•ifii

irl

i_if M

IM

I

; ........... r i

I r

.......

-- • 4

-I_ .1.-

I_ 1

1 1

....4

. _L _

1 ...

. I

._ 4

......

....

I_ I

_ 1.

_I L

. I___

1 t_

__I _

__ .._

_ J..._

_1.....

.. itti-

1-

11

;11

-4.000 i

ti

./ 4

,-:

•1

1,

11•

1111

-4

1Til

lin

lin 1

1111

4---

1-1---1I

-1:t1

11

----4

----r

-tir

.---

'iT

H;

;;;1

71

-f I

riti

II-

11

11

r :I.

; ..... i[1

11

1.

1 m

ilm

iT

r :

11

1

. 1

11.ni ' II

.....

... i

!L■li!;

1--r

-t!

Tr

it-llti

i 't

il!

li

-6.0

00- lin

•,1

11

-1

. ■

I 4

-----r

i t ..

... -1---

--1----

-4---4

--r-

-T-

-r --

- _

.....

...._

...---1

.:Ti.-..

, i 7 i

' 1 1

14.11

iiii

in

iiii

m

li

r

ta,

1 I I

1 1

.111, .

. t .. 1:-

.1.-

1. .... -

1 i

ll?

i i r ..

.. 1 . __ .

. 1 ......

. I_ ....

'___

____ ..

..... i ; 1

IIntl

-8.0

00 -

.- ! ! I

1

1 1

-1- :

t

', t.

..1.

, i ,

I

, , 1

, , ,

I , , 1

it , , ,

, ,

-1r 1 . I. Ili!

1.1

111

iiii II '

II

I

ii

.- i lir Iii im

i

i !i

ll '-ii

i1.

1 I t

.._

. ii

•' m

!ii

! 1

II

II

II

II

-10. 0

00 " I

Li" I

I.I

TI i

iIii:

1 I

iiiii I

IT

II I Ilit

Load

(N

)

8.000

6.000

4.000 -

2.000

0.000 a

-4.000

-6.000

-8.000

-10.000

----

-9-4-

•

.

. . . . . . . . . . . . . . . .

. . . . . . . . . . . , . . . .

- --

APPENDIX E 189

PITCH LOAD CELL CALIBRATION DRAG LOAD

Load Drag Load Drag Unload Pitch Load Pitch Unload (N) Volts Volts Volts Volts

-500 -7.442 -7.442 4.973515 4.973515 -4.50 -6.670 -6.977 4.495633 4.434875 -4.00 -6.110 -6.547 4.012285 3.97297 -3.50 -5.330 -5.881 3.513475 3.49582 -3.00 -4.280 -4.720 2.955086 3.006785

-2.50 -3.440 -3.890 2.46514 2.418625 -2.00 -2.890 -3.170 1.97877 1,978656 -1.50 -2.060 -2.400 1.495001 1.484846 -1.00 -1.280 -1.670 1.032838 1.0085 -0.50 -0.670 -1.060 0,556635 0.54461 0.00 0,000 0.000 0 0 0.50 0.479 0.370 -0.539018 -0.445035 1.00 0.989 0.880 -0.930001 -0.82331 1.50 1.589 1.470 -1.308488

-1.915436 -1.317535

-1.7784 2.00 2.159 2.050 2.50 2.943 2.790 -2.419307 -2.286635 3.00 3.676 3.520 -2.992015 -2.796395 3,50 4.379 4.200 -3.476361 -3.302429 4.00 5.011 4.860 -4.001303 -3.833535 4.50 5.418 5.250 -4.516236 -4.33832 5.00 5.770 5.710 -5,149801 -5.149601

Pitch Calibration Graph Drag loads

Load (N)

--Drag Load

-0-Drag Unload

Load Pitch

Pitch Unload

APPENDIX E

190

Pitch Calibration Graph Lifts Loads

4.000

2.000

12 0.000 -6

-2.000

-4.000

0- Lift Load 0- Lift unload

Pitch Load m- Pitch Unload

6.000

-6.000

Load (N)

APPENDIX E 191

PITCH LOAD CELL CALIBRATION LIFT LOADS

Mass Lill Load Lift Unlod Pitch Load Pitch Unload Load(N) Volts Volts Volts Volts

-75 -4.76363 4.94422 0.110874 0.083125 -70 -4.4474 4.48456 0.076213 0.079798 -65 -4.07576 -4.23216 0.098594 0.114596 -60 -3.82617 4.02127 0.084935 0.070385 -55 -3.49595 -3.67907 0.081578 0.062948 -50 -3.18652 -3.28188 0.07555 0,048837 45 -2.87216 -3.00335 0.096684 0.035683 40 -2.52395 -2.67904 0.069927 0.050843 -35 -2.17425 -2.36019 0.028892 0.058435 -30 -1.85584 -2.03522 0.049903 0.060218 -25 -1.65111 -1.69423 0.051606 0.040077 -20 -1.28446 -1.41589 0.033636 0.033209 -15 -0.94385 -1.00014 0.014491 0.054377 -10 -0.62522 -0.63653 0.020884 0.033312 -5 -0.37507 -0.30896 0.013188 0.032385 0 0 0 0 5 0.365023 0.28937 -0.05061 0.003407 10 0.712605 0.612576 0.043385 -0.00603 15 1.026372 0.91412 -0.0134 -0,036196 20 1.34155 1.237801 -0.07702 -0.045565 25 1.650335 1.54928 -0.08861 -0.06456 30 1.988515 1.85382 -0.12383 -0,072258 35 2.328614 2.16531 -0.15305 -0.083963 40 2.63975 2.477195 -0.14608 -0.084161 45 2.972535 2.775131 -0.18338 -0,09053 50 3,237355 3 065412 -0.1718 -0.10461 55 3.531136 3.406132 -0.19076 -0,1197665 60 3.851905 3.711445 -0.18096 -0.121292 65 4.192936 4,04734 -0.15015 -0.127177 70 4.632665 4.336295 -0.13284 -0.135035 75 4.861895 4.657965 -0.1445 -0,130228

—m-

- Pitc

h U

nlo

ad

0 0 0

0 0 0

0 0 0

cci

0 0 0

ibra

tion

Gra

Li

fts

Loa

ds

V lC 0

(A) S3IOA

0 0 0 0 0 0 0 0 0

APPENDIX E

192

SUMMARY OUTPUT DRAG INTER

Regrassoon Staldtcs Mama R 0.903815 R Square 0.928554 Masted R 0.928091 Standard E 0.031842 Otaarabc 31

ANOVA a SS MS F ogreconce F

Regessios Residual Total

1 29 30

0.377357 0.029035 0.408392

0.377357 0.001001

378.8038 3.87E-18

En Star P-velue Lamm 95%0ppar 95%~4 99.01Mper 99.0% Intercept

Vadade 0.028322 0 002487

0.005643 0.000127

4.903815 19.41401

2115E-05 3.87E-18

0.010899 0.002207

0.039945 0.002727

0.012657 0.002117

0.043887 0.802817

......... .

....... : : H : : : : : :4 ::::::

APPENDIX E

193

Lift Interferance Draq

Load UR bad LA unbad DrapLoad Drag Unload -75 -4764 -4.944 -0.122 -0099 -70 -4.447 -4.485 -0.104 -0.097 -65 -4.076 -4232 -0.098 -0.079 -60 -3.820 -4.021 -0.092 -0.078 -55 -3.496 -3.679 -0.078 -04281 -50 -3.187 -3282 -0.039 -0.038 -45 -2.872 -3.003 -0.087 -0.029 -40 -2.524 -2.679 -0.076 -0018 -35 -2.174 -2.380 -0.085 -0.017 -30 -1.658 -2.035 -0.056 0.000 - 25 -1.651 -1.894 -0.052 0 005 -20 -1.284 -1.416 -0038 0.012 -15 -0.944 -1.030 -0.025 -0021 -10 -0.625 -0.637 -0.018 -0.018 -5 -0.375 -0.309 -0.010 -0.022 0 0.000 0.000 0.030 0.800 5 0385 02139 -0.019 0.020 10 0.713 0.613 -0.005 0.012 15 1.020 0.914 0.015 0.057 20 1.342 1.238 0.037 0.077 25 1.650 1.549 0.090 0.097 30 1.989 1.554 0.080 0.116 35 2.329 2.165 0.111 0.131 40 2.640 2.477 0.133 0.150 45 2.973 2.775 0.156 0.161 50 3.237 3.085 0.174 0.176 55 3531 3405 0.195 0.189 80 3 852 3.711 0.204 0.204 65 4.193 4.017 0.223 0.220 70 4.833 4.338 0.244 0.227 75 4.882 4.858 0.255 0.250

Lift Interferance Draq Graph Drag-(Lift(V)-0.0260/0.002]

6.000

4.000

4 :: t :: 44 :: i :: -44 : i-4 : 4 : 4 : 4 :: 1 :: i ' :: i :: ' :: - -a- Lift Load

.:i-- Lill Unload

-00-Drag Load

-.4- Drag unload

TTx r 7. , -,-, T -2 , ,--,-. ri" es tatrr-Pn .

0 4. -(ze +44-H-44-1-H-H-1-H-i-

2.000

E 0.000 0

-2.000'

-.000

-6.000 Load (N)

1-

4 .

— 1

—a—

Lift L

oad

Dra

g Lo

ad

,A

r. Li

ft U

nlo

ad

—)K—

Dra

g U

nlo

ad

Ca 0

—4—

-4—

(A ) slloA

o 0 0

0 0

0

0 0 00 O 0

csi 0

APPENDIX E

194

---------

8.000

6.000

4.000

2.000

0.030

V, 2.000 _

;I:Tt:-Lift.Effief-tilEff ir;t1EITEr

Load (N)

APPENDIX E

195

Drag Interferance Lift

Load Drag Load Drag Unload Let iM Load Let int Unload IN) Volts Volta Volts Volts

-5.00 -7.442 -7.442 0.102 0.000 .4.50 -8.670 -8.977 0.098 -0.028 .4.00 4.110 4.547 0.092 -0.001

-3.50 5.330 .5.881 0.088 0.006 -3.00 -4.280 -4.720 0.072 0.008

-2.50 -3.440 -3.890 0.072 0.022 -2.00 -2.890 -3.170 0.089 0.025

0.063 0.028 -1.00 -1.280 -1.670 0.052 0.028 -0.50 -0.870 .1.060 0.017 0.053 0.00 0.000 0.000 0.000 0.000 0.50 0.479 0.370 0.044 -0.050 1.00 0.969 0.880 -0.033 -0.068 1.50 1.589 1.470 0.002 -0.073 2.00 2.159 2.050 -0.079 -0.100 2.50 2.943 2.790 0.033 -0,114 3.00 3.676 3.520 -0.077 -0.114 3.50 4,379 4,200 -0.081 -0.151 4.00 5.011 4.880 -01351 -0,155 4.50 5.418 5.250 -0.051 -0.155 5.00 5.770 5.710 -0451 -0.155

SUMMARY OUTPUT LIFT INTER

Regression Statistics

Multiple R 0.905397

Square 0.819743 Adjusted F 0.810258 Standard 10.027988 Observant, 21

ANOVA

dl SS NS F ignincence F Regression 1 0.067578 0.087578 88.40501 1.68E48

Residual 19 0.01486 0.000782 Total 20 0.082438

Coarfictentrandand En t Stat P-value Lower 95% Lipper 95% user 99.01Ipper gee% Intercept 0.019474 0006103 3.191059 0.00481 0.008701 0,032247 0.002015 0.038934

X Variable -0.01874 0.002016 -9.29543 1.68E-06 -0.02296 -0.01452 -0.0245 -0.01297

Drag Interference Lift Graph Llf Hdrag (v)-0.0194)/-0.018]

-6.000

-8.000

-10.000

0- Drag Load

-a- Drag Unload

-)1- Lift Load

Unload

APPENDIX E

196

APPENDIX F 197

APPENDIX F

Wind Tunnel Balance Test Data

NACA 23012 Actual Data

Reynolds Number: 1000000

Angle(Deg) CI Cd Cm Up Tran(%c) Lo Tran(%c) -10 -0.9042 0.017373 -0.011959 0.9 0.01 -9 -0.82539 0.015167 -0.012297 0.89 0.01 -8 -0 72862 0.013386 -0.012427 0.86 0.01 -7 -0.62906 0.011574 -0.012545 0.86 0.02 -6 -0.527 0 010662 -0.012651 0.84 0.02 -5 -0.42271 0.009959 -0.012744 0.79 0.02 -4 -0.31354 0.009406 -0.012703 0.77 0.02 -3 -0.20437 0.009004 -0.01262 0.71 0.02 -2 -0.09761 0.008969 -0.012668 0.59 0.04 -1 0.01183 0.007013 -0.015121 0.53 0.5 0 0.11977 0.006834 -0.01292 0.44 0.65 1 0.22715 0.006815 -0.012791 0.38 0.77 2 0.33347 0.00729 -0.012705 0.32 0.79 3 0.44264 0.008383 -0.012744 0.18 0.82 4 - 0.5467 0.008924 -0.012648 0.16 0.84 5 0.65549 0.009308 -0.012676 0.16 0.86 6 0.75678 0.010048 -0.012571 0.14 0.89 7 0.86508 0010958 -0.012594 0.11 0.9 8 0.96309 0.011709 -0.012479 0.11 0.9 9 1.05804 0.01298 -0.012351 0.1 0.92 10 1.14969 0.014592 -0.012211 0.08 0.92 11 1.21781 0.016397 -0.011865 0.06 0.94 12 1.29931 0.018844 -0.011692 0.05 0.94 13 1.28917 0.023132 -0.010778 0.02 0.95

o Stagnation Point • Tiansition Point 0 9 epaiation Point

Airfoi 23012 Angle of Attack = 0 Deg. ReroIds Number =1000000

. . _

100% 9'0% L

0% 20%

40% do%

to 9 9 9 9 9 9

04

O O

O

O O

In

CD a a O O O

Coe

ffic

ient

and Mo

ment

0

-

10

APPENDIX F

198

9 E 0

et

4-4 9 9

a

•

0 CD

O 0 O

CI

O O

cc,

O

co 0 O O O

a O 0

a CV

O

O

O

cti O O 6

441

9 O

a

O O

O

O

0

O

to

CC O

to

O

a 40

O O O

N.

O

ul

O O 0

C O

a O O O O

CI O

In

O V

O

ar cl, O

a a O

C4 a a a

9 CO O O

a 9 • O • C a O C a co a a

Win

d Tu

nne l

Tes

t Mo

del

9 o 2 0 0

0, 2

,r) > O

a

C

LO CC

O

0 0 O

• O

co co

O

.e ? f, W.

a cc

Si co 9

§

9 v

9 9 wr 9

88-'12§88 a to 9 9

44- 9 9

CO 9

- Lc! -

2 9 '7

g 9 c;i

8 _co Cl o

9

,N. r- •

" 't

sg to 1.1:

g s "i

§ 9

A 9

E 9

a e .

.. . a 0 c, 0 a 0 333) ,t-'3AEREE-1,313A,T;i1 0 6 o o o 0 o 6 o N n tri 33A§E:33333E33

4, 4- 4- lc c. N. c- r-

— tom C!

-1,

^ 2 47

;I " 9

(.1 ,.. .

F. 9

sa'§ ca ca

g— wi

1 el - IC

§ 3 to 01

3 0 V

1 on

cr7, :41 Cii co; 3

Cl

:.' 3 g ,i n "

: el zzi

g ^-

?_, 9 R

g g

c 4

I' 91 ^: 9 1 7 o .- N n o . . . o a , a- -a a -9 9- 9 -a a- A

volts O.

c o o o n 8 9j cs si ..; 0 0 0 0 6 0 0 0 0

0 co 0 v 0 F cc r-- 44. 9 r- co

o te 49 1: o 9 9 9 a- E! ;

L a 0 a 9 9 4 q q 9 §. ce 44- co

8 8 'a 'a '8 8 S 8 G 8 c, -, S 4 4 9 9 4 4 4 9 9 9 6° 6 6 6

co co o cc 1.4- cc . tv to a, co to 0 to 0 8 8

• 4 a 9 9 19 / '7 o •-• Iv -, co Co I.- co co 9 e 8

Pitch

.si9 ,195,99 q4qq77 ,f ' (..i ,1 . ad s - 3 P.! n 1

.7i. 3 FE RI G ri „, ,

-2.8

1391

85

-2.9

9082

1

a a . 3

.

-4.1

3501

1

-5.8

75

24

9

A

•- • E

-7.1

8274

2 -7

.271

278

I.

-7.7

139

58

B cc .- • - ,. 0 9 ; 8 c. c, to o cl E t; o g

al iti gi g i--, 3 3 3 git' A 3^mrg °D A

° r... rg g 8, t g to-

7...99 q 9000odocioo .--..-. .-....- .-. na eV N cc lV ...

6 6 co 6 .: ca co 6 09 m 1V IV

c ri 3 A3M33,A33, 3 4- 4- -- I-- 0 14.

" 9 9 9 °11 01 ̀- A 8 n a 2 ,... A E.

4 I. 9' 9 n 9 9 1 9 N^ 0 4- 04 4.1 V 0 40 r- co 0 0 4_ el 9 V 9 0 4- 0 04

1 2

0

Lift

Coe

ffic

ient

of

an N

AC

A 2

3012

(1/

4 c

hor

d)

Ang

le of A

ttac

k (D

eg)

Win

d tu

nn

el t

est

ca I-.

cv 0

-a (NI -

N (53 N c‘i

< -o o 2

< z

N11---r- —i-- -1 ---

1 ri------t—r--- 71—r— r-- 1— --'— i co 1

j7 "F

1

•

- •

- -4 1

• I 1 I "--1-

.1_4_• 4._ I

• I 1

cla d.

O 0

0 0 0 r

APPENDIX F

199

o a c) o a o o a o c) in o u) a U) r r a ci a

(10) W013114000 #el

Win

d T

unn

el T

est

Dra

g C

oeff

icie

nt o

f an

NA

CA

230

12 (

1/4

cho

rd)

0.400

[II

" 1

F

It I 1

1 1

1 i

1 i

I !ii II

I m

ij

lt

Il

i I 1

ii! 1 1

.._

1

1 i

ll I i 1

1 1111

! !I ii

ll.

:111

11

11

.1,

i1

:1

11

1!! i 1

1111

i:1

M:i

ll M

il!

! i ill!

II

11

[1

1 i

ll

! 1

1111

11

i! ! i

iilli

1 1

■

II

0.3

50

!

II

!

i 1 I

i

II

I 1

I. 1

!

! 1 i

1 i!!1 1

1

1 1 i

I 1

I 1

1! i

ii :

: 1 1

:I

It '''i

i

:..,..

!

i 't

ilt ,

iim

il

i !

ill

l

i Illiiii

ll

i II

III

,111! 1 1

11"il

11

11

1 1

111 i

iiiiI

II!

!!!1

!

.•

11

11

1 !Ili i

111

!iii!!!!!!

11

111

1 !!

!!

!I

I!! il I j

Ili

fi

trilliiL

Iiiii

11

11

il

l 0.3

00

il 1

i,

I 1

1

, 1

lu

ti,

[1:1

1Eliiiii!

iliii 1

I

!H

i! i

i I 1 1

i

ll .n

. i

i I —

1,--1

- I 'I I m

nii

iii

ittli iii

iii: 1

-1 !II

ii

i!

' 11

.1i

ill Iii

it

it

it!iim

iTii

it'' i

ll

•s

i . 1, 1

1 (.3

11 1

illin

il ti

llriii

ii1

11

11

si

l I

_

...t.....

0.

25

0 1

i

I I

--I

liI

II

!I-I

I- m

i

l- 1

. —

1.i.

i11

11

: :

i l

l :

: I

li,

ir

t im

n;

1111

11.1

-1-1

-i

*T

il

itii117

17

1111

'111

1111

11

w

1

11111

1: 1

11

11

Hip

iti:

TH

-fl

ii1

11

11

1[1

11

11111

1 —

0—

Mod

el te

sted

ii

iii i

ti

ti

ii

l i

lii'l

l

i 1

111

1

1111

11

11

ill Il

itt

r t

fi

ft

ii

ii

-ii_i_

iiii

iir

itili

fill —

0— N

ACA

-230

12 D

ata

111

11

11

11,

11

1 I

lririff

iti

nIIII

Iii 4

-3 i

tig

1,--17 -11

:IL

I I:

1 1

, •

: it

littl

iiii

ll tri

l'---Iril

l

II

i

III

II

IIIIii Ilit

ti

ft

itt

ili

iii

ittilil

iIIIIII

I!

II

tar

0.150 I

1 1

1 i

ll 1

1 1

1

1

II tm

.1.

1.11

II

IIL

il

lim

ri

ll

! , i

ii ill

0

1 M

I i

II

li 1

1 I H

til

l-

4 1

if

1 1

14 1

1 1 I

4 1

il

4

4 I

1 i

I } i

i

I I,

I i

4 1

i! I ii

1.

1.-i.

ii1_

44!ilii

iii

iiii

i 1

.111

11

11

11

1 1

1,

.'1.

1.4.

;_i_

iiiii

i.1

.14

' -

44 !

li

i 1

i i i

iii 1

_1 i

0,10

0 ill!

in 1

I I

i ii

!!-

;-1-

1-1-

4-4-

iiiN

4

-Mt

!A

i iii

!1

1iin

-L

-1

il

ii

ii

ii

ll

i I il

-:i

-:4

11:

11

1+

444

I 1 4

.4.

4-1

111

11

1-1

4M

III: !

Ism

! 1

im

il

tri

i.

: i.

,i

ii i '1

1 I

I}

! 1.

11

11

1

!

!! 1

1

iii4

11

1

0.050 1.

....i.

...

I i 1.

- ' I

i ... i 1 1

1

H

LI 1

1.

1 i

I !

.....I

I....

,

1 1 1

, i!

I

it

1

1L

i '1

11

1 l i

i.i

lmil!!i

i 4 • i •

...1 1

1

i 1

! . I . t

t ■

. i :

i I i i i i i i I 1

1

i i i i 1 1 •

-IN

_i_

!....

-•

-iala

iiii

e!

"1

11 !

!!

!!

!!! !I :

"1

"1

"l

eja

• • :-•

': i

■ I I

, • : . ' • .. 7!"

" . .

0" .

• i :

. ; , :

. 1 :

: ! !

!! I ) / / i

I 0.000 4 I il il l e

'e iii I

iIII

Iii 1 1

I I I

-10

-9

-8 -

7 -

6 -

5 -

4 -

3 -

2 -1 0

1 2

3 4

5 6

7 8

9 1

0 1

1 12 1

3 14

Ang

le of

Att

ack

(Deg

)

is '— L.

o ci o o 0 0 il) 0 LO 0 CO CN/ CV r r

a ci ci ci a (p3) wapulao3 Gam

APPENDIX F

200

3 CNI < 0 Z <

(1) °

"017)

2

i I i 1 i I ! : : I I

I ,

, ; 1----t----. —'--

-r , ITT , ' i , • TI i _..),__ __L ,, , ,

,,,, , , , ,,,, , , , _r i 1 1 1- -, T ! I 1---- •4 •I• ! ! "

I 1 1 ! Mill!

±

1

1 - I- •t• t t : - I-

:

)

. I -1• ••44 ---

! ! r - - ---, -- t-

! ! 1 r I •

• ! • 4

I_ --

; ;;••1:::It

--f ---- i7-111 • : : : -

4 •

. .

Mom

ent

Coe

ffic

ien

t o

f an

NA

CA

2301

2 (1

/4 c

ho

rd)

CO

CO

CNI

0

(9

c9

O r

Win

d tu

nnel

test

APPENDIX F

201

-•-•:- 4• . lint! I: I

1 : ! : 1 : )- I- • ---1--r -i---t f -i—t----i--1-..--i--t--r---t—i-----r----

)

I

I ' 4, , I • " I . -r-E-I---1,- L -4 . I- 1 ' t--T-T--- 1--- - i i .--

i ! t• ! I : : : 1 i 1 1 : I

, . .

, 1 I

I'I

1---1 : : • 1 I

: : jr- L-i—.1--...1.--4- 1.i I

: I ■ 1 __4: ! "—t —• • • • - -1.: — 1- •-•4

I I 1 ! ! 1 I !

I1.

1I: --

iT: - 1

r. .-

; -

14I - I

i•-- --1,

T. - j -1-1

i -1

i -

1.-- -

--I1.--r

I--

--. .

:

:

1!rni I :

: !

r____f__ri _ : • i

; 3 - 7-17 .1■---11 - ii."1-1-1

_•L_•-•

1 -.--.1-4------■■■■ r -171 _

I ii 1 i Li ,i._ I 11

0

to O

r

(w3 )wammeo3 wewow

An

gle

of

atta

ck

(Deg

)

O

APPENDIX G

202

LL

APPENDIX G

8 i

Wit

_, 2

N

>.

OCC

5

20]

FEffic

lene

y

g8 g8g8g88

gg8gg8ggg88ggn88g

8g88

ggg88gg8ggg

88

ggg8g8g8g8g8g8g8g8g8ggg

8g8g88

gg8gg8ggg8g

8

Ln 0D

>,

,- C 9.,

g

88858888888888888888888888888888888888

Pre

ss

[L

ead

ang

r rim .r o co r- co 0) '- " V2 v tri @ .-- @P g I) R Cr .1 r1 74 P1 PI 'Ra 2 2 8 r; 2 2 g 8 8 MB

8 rgi W. 2 6

r in "

Vl

N-

r--:

Lri co

2 .-

co

41 8 S

E

0 >, <-,, 0

5

W n E w

CI r-

N

8 •

CD ,

en rn

o .- r.- LO

cg O rrr r-: c6 r- r-

'A

ni co

2 r R co

P- eo r-: co

er a r

CD >, N 0

C

E Ill

,- N,

..- CI CD N ,- ,-- rrr oi 0

... CV

2 seel 1,-- r- 4 n

es g co R r,

2e)

.-. op

(.48 8

co N g

Tr

CO

V

co 0

._

CO

Zr) R CO

._ N.

0 0 to

r- o co N 8 ai CO

o C d.,

Ew

0 N

0 CD

8

el CD n N

n4 N

0 .,r p CV

1 8

r.I.

2

g V2

c 8

o 1.2

0

0

E

a) •- S N ,-- 2

t

0 0 5 E

err r- (3) 6 v

§ .- N g en N o CD

0°3 N n

0 N,- R N.

§ N N r.

ni 0 co

el n el CD CO

tO r R co

al CO

CO Di

es ar Q g

li ft -1

e, n) 4 o o r- co o a ''- N @ @ @ @ @ ..- (0000040N N @ @ eiN DI CD 28 .- "PAL°8^8 CD CD

0 >,

0 (7 E W

C., C

N 0 0' N V tri 0 ,- N

IN

ZC1

g

r ro IN ci r-

0

nl 0

CD 0 N 0 R

r--

1- n CO

,..N 8 r: .-..J c000coo

or.- IT

.- CO S

..- ni co

r,Ln 6.. . 1,2 E W

rri ... 0? g

co

,,,,

;--

g ui .-

-a E ci

co r- N ni co co

VI

N 0 = or 5 E W

10 CV eg c4 0 ,-

Ivii .-

(4 r-

§ T,:e4 " ....

ui to r- r-

o nI

N CD N r- er ni co

/74 r- .- ri ao

ro

,,, 0

P d 5 5 E W

co 2 al N

ow ro I%-) 4 4-

fr- g ai 4

to r g IC o

o r- r71 ei co

co E el tr-

8 N N. co r--

l2 g ,- n4 0 N R al N-

2 (9 n CD 0 0 ci ai N- "-- g

P Or;

0 m IEr N co

'u- § .:

rol

2 Tr r-.

2

8 g

2

rt 0

r-: ,-

ZE, n .- ui 4

,_ " n) N 0 v. ci r-

N. n 0

t-

CD n P 2 0' V 4 tri I-- n-

CV r- o 0 ea I.-

o yr N .cr ori n

10 N N co ni CO

CO

Pre

ss.

Ang

les

(deg

) IL

ead

eng

e_

,- N cntrocr,00ar 0 - eg nnar. f m 0 0 1- 01 21

22

23

24

25

26

27

28

;71 2 2 35

36

en r-

el co

we! oupo 0 uonapd

1•••• o

o go co o o

o o

c7)

C) CV

Lead

Ang

le (

Deg

.)

I !

! t

01

O 0

(%) Aoualawa

0 CD

O 0 CV

O O

0 CV

r

0

APPENDIX G

203

APPENDIX H 204

APPENDIX H

Elastic strain energy in bending beams

(a)

(b)

Figure HI Bending of a build in beam

If a beam as shown in figure H1 is build in at one end, and bent by a couple M applied at the other end and acting in one of the principle planes, the angular displacement at the free end is:

MI V = El

(hi)

APPENDIX H 205

This displacement is proportional to the bending moment M and the work done during deflection by bending moment M is the area of the graph as shown in figure H1(b).

Thus the energy stored is:

U = Myo (h2)

2

By use of equation hl this energy may be expressed as:

Ell U —

2E (h3)

The energy stored in an element of the beam between two adjationt cross sections dx appart is:

2 dx dU = m

(h4)

2E1,

But the bending moment M is variable with respect to x and

d9 = dx— (h5) r

Thus the total energy in the beam is

u ,r 2

mdx (h6) Jo 2E1,

By replacing dx with in equation h4 with h5:

2 9 dU = 2E1

(h7) •

d

The energy due to an angular displacementis is

U — M2

J rdp (h8)

0 2 El

(a)

(c)

isA2(IA MI

\

+M2

0 \

B.M. diagram

B M2

B.M. diagram

+MI

APPENDEX I 206

APPENDIX I

Drag load cell Beam deflection

Figure 11 Deflection of a build in beam (Drag Load cell)

APPENDEX I 207

Deflection of the beam

The beam in Figure I I (a) can be desolved by two beams as shown in Figure 11 (b) and (c).

In Figure II (b) the beam is a fixed at point A with a force F pushing upwords at point B. the bending moment Mx at distance x is:

F x (t —x)

but

‘1 3 y M = El —th2 F(e x)

Thus

2

El —dy

= F(ex — 2

—X )4- C I dx

Using the boundaty conditions where x = 0 is dy/dx = 0, thus CI =0

But

3 Ely = F(L--

x — 3--)+ C2

6

If x = 0 then y = 0 and C2 becomes zero (C2 = 0)

At point B if x = I then

F e3 e Y = El ( 2 —

6)

Ft3 Y = 3E1

(r1)

APPENDEX I 208

Figure 12 Angle deflection of a build in beam (Drag Load cell)

The slope at point B 0 = dv/dx and max slope if x = / is:

98 2E1

F iv ‘ e B = El

FE2 (i2)

The displacement at C is:

Fx3

Y`' Y — 3E1 (i3)

The slope at point C is:

Fx 2 =

2E1 (i4)

Because there is no bending between point C and B, the displacement at B relative to point C can be be written as:

2 Yce =

x F

E1 x) 2 (i5)

APPENDEX I 209

Thus the total displacement at point B is the sum off equation i3 and i5.

Fx 2 Ye = 2E1 3E1

Fx3

3E1

Fx 2 Ye = = —6E1 (3e x)

In Figure Il (c) the beam is buit in at both ends. The deflection can be written as:

M2x2

Yz - 2E1

The deflections yi and y2 of the two beams can be added. Thus the total deflection is:

Y=Yi = Yz

Fx 2 Y = (3, —

M x2

6E1 2E1

But dY/dx = 0 at x = 0 and x = I from the diffenition of the beam.

Thus

dY x (— Fx rfi n

dx — El( 2 +A -±-2 ) =--

At x = 0 and

— Fx +FP+M2=0

If x = I the bending moment M2 is:

— Ft + FP + M2 =0

— FP M2 = 2

2

2

APPENDEX I 210

Replace M2 in Equation i8 and x =1, maximum deflection is:

, Fe b,„ t)+A (

2t)

1 = yt –

6E1 2E1

Fe Fe Y –

3E1 4E1

Fe Y - (i9)

12E1

Bending moment

The total bending moment is the sum of the moments MI and M2 is:

MI = Ft+ Fx= 0-9

– Ft M2 - 2 But

M = MI + M2

M = Ple – 44- – Fe 2

M = F(--€ 2

– x)

If x = / then is M can be written as:

t ) t =_ Ft

M = Fii-2

-Ft 2

+F/

APPENDEX I 211

B.M. diagram (c) B.M. diagram (b)

B FL A _m= 2

2

'fr

fro. "clr

4

-FL 2

Total B.M. diagram

Figure 1.3 Bending moment diagram (Drag Load cell)

."-/ 0 6

0 fri

CI cicici

CI

•

CI

•

O M

•

0 t-.. ------

0 ci

LID I'

0 (-; ri

E

0 =.-

0

0.004

0.003

0.002

0.001

0

-0.001

-0.002

-0.003

APPENDEX I 212

Drac Load cell Deflection

E= 73.1GPa 1= 1.44E-12 m^4

Load (F) 7 Newtons Deflection (m)_

Length / (m) Y 1 y2 V

0 0 0 0 0.005 2.77081E-06 2.07811E-06 6.92703E-07 0.010 2 21665E-05 -1.6625E-05 5.54162E-06 0.015 7.48119E-05 -5.6109E-05 1.8703E-05 0.020 0.000177332 -0.000133 4.4333E-05 0.025 0.000346351 -0.00025976 8.65878E-05 0.030 0.000598495 -0.00044887 0.000149624 0.035 0.000950388 -0.00071279 0.000237597 0.040 0.001418655 -0.00106399 0.000354664 0.045 0.002019921 -0.00151494 0.00050498 0.050 0.002770811 -0.00207811 0.000692703

Drag load cell Deflection graph

Length of beam (m)

design and development of a three component strain gauge

Documents