Rajkumar Project Report Copy

A Project Report Entitled

Design, Optimizationand Calibration of 6-Component External

Wind Tunnel Balance

Submitted to

VISVESVARAYA TECHNOLOGICAL UNIVERSITY, BELGAUM

In partial fulfilment of requirements for the award of the degree of

MASTER OF TECHNOLOGY

In

MACHINE DESIGN

By

RajkumarKhot

(USN: 1BM13MMD10)

Project work carried out at

Indian Institute of Science Bangalore 560012

Under the guidance of

POST GRADUATE AND RESEARCH CENTRE

DEPARTMENT OF MECHANICAL ENGINEERING

B. M. S. COLLEGE OF ENGINEERING

BANGALORE- 560019

July, 2015

Internal Guide

Dr. J. SharanaBasavaraja

Associate Professor

Dept. of Mechanical Engineering

BMS College of Engineering

Bangalore

External Guide

Dr. S B Kandgal Principal Research Scientist

Dept. of Aerospace Engineering

Indian Institute of Science

Bangalore

POST GRADUATE AND RESEARCH CENTRE

DEPARTMENT OF MECHANICAL ENGINEERING

B. M. S. COLLEGE OF ENGINEERING

BANGALORE- 560019

July, 2015

CERTIFICATE

Certified that the project work entitled Design, Optimization and Calibration of 6-

Component External Wind Tunnel Balancecarried out atIndian Institute of

Science, Bangaloreby Mr.RajkumarKhotbearing the University Seat Number

1BM13MMD10, a bonafide student of B M S College of Engineering is in partial fulfilment

for the award of Master of Technology in Machine Design of Visvesvaraya Technological

University, Belgaum during the year 2014-2015. It is certified that all correction/suggestions

indicated for the internal assessment have been incorporated in the report deposited in the

departmental library. The project report has been approved as it satisfies the academic

requirement in respect of project work prescribed for the said Degree.

Dr. J. SharanaBasavaraja

Associate Professor



Bangalore -560019

Dr. L Ravikumar

Professor and Head



Bangalore -560019

Dr. K MallikarjunBabu

Principal


Bangalore -560019

External Viva

Name of the Examiner Signature with date

1.

2.

DECLARATION

I, RajkumarKhot (1BM13MMD10), student of IV semester M.Tech Machine Design, B

M S College of Engineering, Bangalore, hereby declare that the work being presented in the

dissertation entitled Design, Optimization and Calibration of 6-Component

External Wind Tunnel Balancesubmitted to the Visvesvaraya Technological

University during the academic year 2014-15, is an authentic record of the work done under

the academic guidance of Dr. J. SharanaBasavaraja, Associate Professor, Department of

Mechanical Engineering, B M S College of Engineering, Bangalore. This project work is

submitted in partial fulfilment of the requirements for the award of the degree Master of

Technology in Machine Design. The work contained in thesis has not been submitted to any

other University or Institute for the award of any degree.

Place: Bangalore

Date: (RajkumarKhot)

ACKNOWLEDGEMENT

While bringing out this thesis to its final form, I came across a number of people whose

contributions in various ways helped my field of research and they deserve special thanks. It is a

pleasure to convey my gratitude to all of them.

First and foremost, I would like to express my deep sense of gratitude and indebtedness to my

supervisors Dr. S B Kandagal(External guide) Principal Research Scientist,Dept. of Aerospace

Engineering,IISc, Bangalore and Dr. J. SharanaBasavaraja(Internal guide)Associate

ProfessorBMS College of EngineeringBangalore. And for their invaluable encouragement,

suggestions and support from an early stage of this research and providing me extraordinary

experiences throughout the work. Above all, their priceless and meticulous supervision at each

and every phase of work inspired me in innumerable ways

I specially acknowledge them for their advice, supervision, and the vital contribution as and

when required during this research. Their involvement with originality has triggered and

nourished my intellectual maturity that will help me for a long time to come. I am proud to

record that I had the opportunity to work with an exceptionally experienced Professors like them.

I am highly grateful to Dr. S B Kandagaland Dr. D. Ghose, Chairman, Aerospace Engineering

Dept. IISc Bangalore for giving me opportunity to carry out my thesis work at this reputed

institute, which has given me exposure various methodologies of research. I also thank Mr. V

Surendranath and Staff of OCWT, IISc, Bangalore for giving their valuable suggestion and

time whenever asked for.

I am greatly indebted to Dr. B. S. Suresh, Professor and Co-ordinator, PG (Machine Design),

B. M. S. College of Engineering, Bangalore for theencouragement he has given during the

course of this project work.

I wish to express my sincere thanks to Dr. L Ravi Kumar, Professor & Head, Department of

Mechanical Engineering, B. M. S. College of Engineering, Bangalore for supporting throughout

the duration of project.

I take immense pleasure in thanking Dr. K. MallikharjunaBabu, Principal, B. M. S. College

of Engineering, Bangalore, for providing the right kind of milieu.

I extend my thanks to my friendsManjunathMelagiri, Vishal G.P, Ramesh

Sarangamath,Guru Brahmam, Shiva Shankar, Guru Raja, at Vibration and Acoustics lab,

Aerospace department, IISc, Bangalore, for supporting and tolerating me for the past one year

Finally, I extend my thanks to the entire faculty of the Department of MechanicalEngineering,

BMSCE, Bangalore, for their continued co-operation and support during the tenure of this

project work.

RajkumarKhot

ABSTRACT

A six component platform balance was designed and fabricated in the dept. of Aerospace

Engineering, IISc, Bangalore, for measuring aerodynamic forces and moments on models. This

balance utilizes load cells for transducing forces into electrical signals. The platform balance

consists of a leveled platform constrained by six load cells for measuring forces in vertical, axial

and sideward directions. The project work includes the detailed study of wind tunnel balance

types, mounting methods, design concepts, materials used for fabrication of external strain gauge

balances, derivation for calibration, transformation and user matrices.

Project work also includes the FEM analysis of 6-component external force balance,

optimization of force measuring elements and load cells. To study the static and dynamic

coupling of balance when model is attached to force balance by studying individual and coupled

behavior and finally Validating the dynamic characteristics in wind tunnel for a typical model

and study the error in responses of individual components with increased loads. The present

study uses the CATIA to modeling the force balance configuration, Finite Element Analysis

(FEA) extensively to find forces developed in the load cells and optimization of force measuring

elements. MATLAB used during the generation of calibration, transformation and user matrices.

CONTENTS

List of Figures

List of tables

Notations

1 Introduction ............................................................................................................................. 9

1.1 Wind Tunnels ................................................................................................................... 9

1.2 Working method of Wind Tunnel .................................................................................... 9

1.3 Types of Wind Tunnel.................................................................................................... 10

1.3.1 Based on Flow Speed .............................................................................................. 10

1.3.2 Based on Shape: ...................................................................................................... 11

1.4 Balance Types ................................................................................................................ 13

1.4.1 External balances .................................................................................................... 13

1.4.2 Internal balances ..................................................................................................... 15

1.5 Advantages of external balance over internal balance ................................................... 16

1.6 Drawbacks of external balance over internal balance .................................................... 16

1.7 Model Mounts ................................................................................................................ 16

2 Literature Review .................................................................................................................. 19

3 Platform Balance Description ................................................................................................ 22

4 Load Cell ............................................................................................................................... 24

4.1 What is a Load Cell? ...................................................................................................... 24

4.2 Working of Load Cell .................................................................................................... 25

Load Cells - How They Work? .............................................................................................. 25

5 Calibration of the platform balance ....................................................................................... 27

5.1 Objectives of the calibration .......................................................................................... 27

5.2 Force and moment concepts ........................................................................................... 31

5.3 Calibration procedure ..................................................................................................... 32

5.3.1 Negative normal force: ........................................................................................... 32

5.3.2 Positive rolling moment: ......................................................................................... 32

5.3.3 Negative axial force: ............................................................................................... 33

5.3.4 Positive pitching moment: ...................................................................................... 33

5.3.5 Positive side force: .................................................................................................. 34

5.3.6 Positive yawing moment: ........................................................................................ 34

6 Derivation of Calibration Matrix, Transformation Matrix and User matrix of the platform

balance .......................................................................................................................................... 36

7 Balance calibration data and errors ....................................................................................... 40

8 The Concept of I-Beam and Spring Element ......................................................................... 43

8.1 I-Beam ............................................................................................................................ 43

8.2 FE Analysis of Force Measuring element without and with I-beam.............................. 44

8.3 Spring Element in place of Load cell ............................................................................. 45

9 FEM analysis of external force balance ................................................................................ 46

9.1 Normal Force, Rolling moment and pitching moment measurement ............................ 46

9.2 Side Force and Yawing moment measurement .............................................................. 47

9.3 Axial Force Measurement .............................................................................................. 48

9.4 Combined forces and Moments: .................................................................................... 49

9.5 Stress and Deformation plot ........................................................................................... 50

10 Conclusions and Recommendations .................................................................................. 51

10.1 Conclusions .................................................................................................................... 51

10.2 Recommendations .......................................................................................................... 51

11 References .......................................................................................................................... 52

12 Appendix ............................................................................................................................ 54

12.1 Appendix A .................................................................................................................... 54

LIST OF FIGURES

FIGURE 1-1SCHEMATIC REPRESENTATION OF A WIND TUNNEL....................................................... 10

FIGURE 1-2SCHEMATIC REPRESENTATION OF AN OPEN CIRCUIT WIND TUNNEL ............................. 11

FIGURE 1-3SCHEMATIC REPRESENTATION OF A CLOSED CIRCUIT WIND TUNNEL ............................ 12

FIGURE 1-46-COMPONENT EXTERNAL BALANCE AND SUPPORT SYSTEM AT IISC OPEN CIRCUIT

WIND TUNNEL. ........................................................................................................................ 13

FIGURE 1-5TYPICAL SCALED MODELS INSIDE THE WIND TUNNEL ................................................... 14

FIGURE 1-6TYPICAL INTERNAL BALANCE USED IN LOW SPEED WIND TUNNELS .......................... 15

FIGURE 1-7STING AND STRUT MOUNTING METHODS ...................................................................... 16

FIGURE 1-8TYPICAL MODELS INSIDE THE WIND TUNNEL TEST SECTION ......................................... 18

FIGURE 3-1DIFFERENT VIEWS OF PLATFORM BALANCE .................................................................. 22

FIGURE 4-1TYPICAL LOAD CELL USED IN PLATFORM BALANCE AT IISC OPEN CIRCUIT WIND TUNNEL

............................................................................................................................................... 24

FIGURE 4-2SPECIFICATION OF LOAD CELL ..................................................................................... 25

FIGURE 4-3WHEATSTONE BRIDGE NETWORK ................................................................................ 26

FIGURE 5-1PLATFORM BALANCE WITH CALIBRATION SETUP (A) .................................................... 28

FIGURE 5-2PLATFORM BALANCE WITH CALIBRATION SETUP (B).................................................... 29

FIGURE 5-3AXES SYSTEM .............................................................................................................. 30

FIGURE 5-4FORCE AND MOMENT CONCEPT .................................................................................... 31

FIGURE 5-5CALIBRATION FOR NF AND RM .................................................................................... 32

FIGURE 5-6CALIBRATION FOR AF AND PM ..................................................................................... 33

FIGURE 5-7CALIBRATION FOR SF AND YM ..................................................................................... 34

FIGURE 6-1FORCE AND MOMENT VECTORS AT CC AND BC ........................................................... 38

FIGURE 8-1CONCEPT OF I-BEAM.................................................................................................... 43

FIGURE 8-2FORCE MEASURING ELEMENT WITHOUT AND WITH I-BEAM .......................................... 44

FIGURE 8-3FE ANALYSIS OF FORCE MEASURING ELEMENTS ........................................................... 44

FIGURE 8-4FE ANALYSIS OF FORCE MEASURING ELEMENT BY REPLACING SRING INPLACE OF LOAD

CELL ....................................................................................................................................... 45

FIGURE 9-1NF, RM, PM MEASUREMENT ......................................................................................... 46

FIGURE 9-2SF, YM MEASUREMENT ............................................................................................... 47

FIGURE 9-3AF MEASUREMENT ....................................................................................................... 48

FIGURE 9-4COMBINED FORCES AND MOMENTS MEASUREMENTS ................................................... 49

FIGURE 9-5STRESS AND DEFORMATION PLOT ................................................................................ 50

LIST OF TABLES

TABLE 3-1 THE RATING OF THE BALANCE IS GIVEN IN THE ABOVE TABLE. .................................... 23

TABLE 7-1CALIBRATION DATA (1) TABLE 7-2 CALIBRATION DATA (2) ......... 40

TABLE 7-3 CALIBRATION DATA (3) TABLE 7-4CALIBRATION DATA (4) ......... 41

TABLE 7-5CALIBRATION DATA (5) TABLE 7-6 CALIBRATION DATA (6) .............. 42

TABLE 9-1NF MEASUREMENT ........................................................................................................ 46

TABLE 9-2SF MEASUREMENTS ....................................................................................................... 47

TABLE 9-3AF MEASUREMENT ........................................................................................................ 48

TABLE 9-4COMBINED FORCES AND MOMENTS MEASUREMENTS..................................................... 49

TABLE 9-5EN24 STEEL PROPERTIES ............................................................................................... 50

NOTATIONS

E..Youngs modulus

G..Shear modulus

..Poissons ratio

x, y, z Cartesian coordinates

Fx, Fy, Fz Forces in Cartesian coordinate system

Mx, My, Mz Moments in Cartesian coordinate system

AF.Axial force

NF.Normal force

SfSide force

Mx..Rolling moment

My..Pitching moment

Mz .Yawing Moment

Stress at a point

Strain at a point

M ............Mach number

[C].Calibration Matrix

[T].Transformation matrix

[U].User Matrix

RPerpendicular distance between CC and BC

CC.Calibration centre

BC....Balance centre

a..Eccentricity

F.....Force

Design, Optimization and Calibration of 6-Component External Wind Tunnel Balance

Department of Mechanical Engineering, B M S College of Engineering, Bangalore. Page 9

1 Introduction

The aim of wind tunnel tests is the simulation of the flow around bodies or their scaled models.

In aeronautical applications, the measurement of aerodynamic loads in a wind tunnel, forces and

momentums, is a very difficult task due to the required accuracy. The wind tunnel balances,

comprised by several hardware and software components, provides directly the pursued

measurements, with high accuracy and reliability. For these reasons, among others, wind tunnel

balances have become a common tool in testing facilities.

1.1 Wind Tunnels Wind tunnel is a physical instrument used to test scale models of aircraft and spacecraft. Wind

tunnel is used to predict the amount of forces and moments generated by the solid objects. This

helps designers to choose the proper size for things such as wings, spoilers, and parachutes.

Information obtained in wind tunnels is used to improve the design of anything affected by wind.

In the tunnel; the engineer can carefully control the flow conditions which affect forces on

the aircraft. Some wind tunnels are big enough to hold full-size versions of vehicles. Typically,

there are sensors and instruments inside wind tunnels that give scientists hard data regarding an

object's interaction with wind. And often, there are windows that let those same scientists

observe experiments visually. With those data and observations, engineers grapple with variables

of aerodynamics such as pressure, velocity, temperature and density. In addition, these tunnels

can help engineers figure out how wind interacts with stationary objects, such as locomotives,

buildings, missiles, spacecrafts and bridgesand find ways to make them stronger and safer.

1.2 Working method of Wind Tunnel Most of the time, powerful fans move air through the tunnel. The object to be tested is fastened

in the tunnel so that it will not move. The object can be a small model of a vehicle. It can be a

full-size aircraft or spacecraft. The air moving around the still object shows what would happen

if the object were moving through the air. How the air moves can be studied in different ways.



Smoke or dye can be placed in the air and can be seen as it moves. Threads can be attached to the

object to show how the air is moving. Special instruments are often used to measure the force

and moments of the air on the object.

1.3 Types of Wind Tunnel Wind tunnels are designed for a specific purpose and speed range. Therefore, there are many

different types of wind tunnels and several different ways to classify wind tunnels.

1.3.1 Based on Flow Speed

Figure 1-1Schematic representation of a wind tunnel

1.3.1.1 Subsonic or low speed wind tunnels

Maximum flow speed in this type of wind tunnels can be 135m/s. Flow speed in wind tunnels is

generally preferred in terms of Mach number which comes out to be around 0.4 for this case.

These types of wind tunnels are most cost effective due to the simplicity of the design and low

wind speed. Generally low speed wind tunnels are found in schools and universities because of

low budget.



1.3.1.2 Transonic wind tunnels

Maximum velocity in test section of transonic wind tunnels can reach up to speed of sound i.e.

340m/s or Mach number of 1. These wind tunnels are very common in aircraft industry as

most aircrafts operate around this speed.

1.3.1.3 Supersonic wind tunnels

Velocity of air in test section of such wind tunnel can be up to Mach 5. This is accomplished

using convergent-divergent Nozzles. Power requirements for such wind tunnels are very high.

1.3.1.4 Hypersonic wind tunnels

Wind velocity in test section of such type of wind tunnels can measure between Mach 5 and

Mach 15. This is also achieved using convergent - divergentnozzles.

1.3.2 Based on Shape:

1.3.2.1 Open circuit wind tunnel:

Figure 1-2Schematic representation of an open circuit wind tunnel

This type of wind tunnel is open at both ends. The chances of dirt particles entering with air are

more so more honeycombs (mesh to clean incoming air) are required to clean the air. Open type

wind tunnels can further be divided into two categories:



A) Suck down tunnel

With the inlet open to atmosphere, axial fan or centrifugal blower is installed after test section.

These types of wind tunnels are not preferred because incoming air enters with significant swirl.

B) Blower tunnel

A blower is installed at the inlet of wind tunnel which throws the air into wind tunnel. Swirl is a

problem in this case as well but blower tunnels are much less sensitive to it.

1.3.2.2 Closed circuit wind tunnel

Figure 1-3Schematic representation of a closed circuit wind tunnel

Outlet of such wind tunnel is connected to inlet so the same air circulates in the system in a

regulated way. The chances of dirt entering the system are also very low. Closed wind tunnels

have more uniform flow than open type. This is usually a choice for large wind tunnels as these

are more costly than open type wind tunnels.



1.4 Balance Types

Balance types are distinguished by the number of force/moment components which are measured

simultaneously one to six are possible and the location at which they are placed. If they are

placed inside the model they are referred to as internal balancesand if they are located outside of

the model or the wind tunnel, they are referred to as external balances. And rotary balances are

used for propellers, helicopter blades and other rotating models.

1.4.1 External balances

Figure 1-46-component External Balance and Support system at IISc Open circuit wind tunnel.



Figure 1-5Typical scaled models inside the wind tunnel

They are placed outside the model, inside or outside the wind tunnel chamber test section, there

are two types of external balances exist. The first is the one-piece external balance, which is

constructed from one single piece of material and which is equipped with strain gauges. Such

balances are also referred to as sidewallbalancesas used in half-model tests. The second type of

external balance comprises single force transducers which are connected by a framework. Such a

design can be built very stiff but needs more space compared to the one-piece design. However,

there is usually plenty of space available around the wind tunnel for such a balance, and so the

construction can be optimized with respect to measurement requirements, such as optimized

sensitivity, stiffness and decoupling of load interactions. But they always introduce some

interference in the wind flow. However the possibility to change test models with almost no

effort provides a high flexibility to the wind tunnel facility. There are several degrees of

complexity for these balances, depending mainly on the number of measurement channels, which

can vary between 1 and 6.



1.4.2 Internal balances

Figure 1-6Typical Internal Balance Used in Low Speed Wind Tunnels

They are placed inside the model, thus no interferences are introduced in the wind flow by the

balance components, but a mechanical support for the model is always needed to maintain it in

the test chamber and change the model orientation if desired. There is limited space inside the

model itself, so internal balances have to be relatively small in comparison to external balances.

There are two main types of internal balances. The monolithic type, in which the balance body

consists of a single piece of material, is designed in a way such that certain areas are primarily

stressed by the applied loads. The other internal balance type uses small transducers which are

orientated with their sensing axes in the direction of the applied loads. Such a balance is

combined into a solid structure. A balance measures the total model loads and therefore is placed

at the center of gravity of the model and is generally constructed from one solid piece of

material. The number of measured components can also vary between 1 and 6. Above Figure

shows an example of internal balance.



1.5 Advantages of external balance over internal balance 1. They are placed outside the model, inside or outside the wind tunnel chamber test section.

2. High flexibility to the wind tunnel facility.

3. Multi-purpose test facility (Aircrafts, automobiles, locomotives, Buildings etc.).

4. The external balance placed outside the wind tunnel test chamber so, their dimensions

and weight are not important.

1.6 Drawbacks of external balance over internal balance 1. Drawback is always introduces some interference in the wind flow, interference problem

doesnt arise in internal balance as the balance placed inside the model.

2. Aerodynamic interference between the model support system and the model itself

3. Interference between tunnel and model.

4. Inertia loads on the balance.

1.7 Model Mounts

Figure 1-7Sting and strut mounting methods



There are several different methods for mounting the model inside the test section. The choice of

mounting system in a particular wind tunnel is often driven by the type of balance being

employed. For an external balance, measuring devices are located outside of the model and the

tunnel. For an external balance, the mount must transmit the aerodynamic loads on the model to

the external balance, and hold the model securely at the desired flight condition of angle of

attack and angle of yaw. For an internal balance, the measuring devices are located inside the

model. The mount does not have to transmit forces, but must provide a path for information to be

passed from the model to data recording devices.

On the above figure, four different methods for mounting a fighter aircraft model in a tunnel and

for all of the mounting systems, the struts are normally shielded from the air in the tunnel so that

the drag of the struts themselves is not included in the drag of the aircraft. At the upper right, we

have a three strut mount that connects to the model near both wing tips and at the aft end. The

three strut mount is used most often with external balances; the bottom of the three struts

connects to a platform that is instrumented with strain gages. With three movable struts,

the angle of attack and roll angle can be accurately set and sustained while yaw is provided by

turning the model on the circular section of the platform. The disadvantage of this system is the

expense, complexity and maintenance for three movable struts. Aerodynamic interference

between the struts and the model and flow blockage in the tunnel are also concerns for a three

strut mount. Less expense, interference, and blockage can be obtained by the two strut mount at

the upper left. But the two strut mount is less rigid than the three strut in pitch and roll. Even less

expensive and with a minimum of interference and blockage is the single strut mounting system

shown at the bottom. The single strut can be attached to the top or bottom of the model as shown

at the left bottom, or it can be attached to the rear of the model, as a sting mount, as shown at the

right bottom. The sting mount has less interference with the model flow field than the one strut

mount, but the aft end of the model may be distorted to accept the sting mount. Single strut

mounts are less rigid than multiple strut mounts. The single strut mounts works very well with

internal balances and flow diagnostics.



Figure 1-8Typical models inside the wind tunnel test section

We now focus our attention in the 6 components external balances, as they provide 3 forces and

3 momentums measurement and a high flexibility for a multi test wind tunnel.



2 Literature Review

Miguel A. Gonzalez, Jose Miguel Ezquerro, Victoria Lapuerta, Ana Laveron,

and Jacobo Rodriguez [1]

This paper gives the general description of wind tunnel balances. The number of measuring

components and the position of the balance with relation to the model and wind tunnel chamber

determines the wind tunnel balances designs. The most flexible ones in terms of usability are the

six components external balances, so these will be referenced for introducing the calibration

process; this is one of the key points to achieve the required aerodynamic tests results accuracy

and reliability. Because of its influence on the drag measurement accuracy, the coupling effect

between lift and drag measurements is analyzed very deeply as well. The analysis of the non-

stationary effects are finally done taking into account the wind tunnel balance requirements and

constraints, with special attention on an issue not commonly mentioned, the inertia forces

generated on the balance by the model vibrations, and their influence on the aerodynamic forces

to be measured. Several mentions to signal processing and acquisition are done, as this is the

other key point on the measurements accuracy. However, it is easy to extrapolate these

procedures to other types of balances, as the main intention is to shows which are the critical

points that make wind tunnel balances such a special and complex hardware. They do not intend

here to describe the design and calibration procedures of the industrial manufacturers. This is the

result of a work done in the University Polytechnica de Madrid (UPM), and the

InstitutoTechnologico y de EnergiasRenovables (ITER, Tenerife, Canary Island, Spain,

www.iter.es).

AnkitSoni&PankajPriyadarshi[2]

The important design principles were learnt during the study of this paper, which are described in

this paper. Measurement of forces and moments on aerodynamic models has always been an

important part of wind tunnel experiments. A study was carried out on various beam type load

cells using Finite Element Analysis. It was found that a parallelogram beam type load cell met all



requirements and was found to be sensitive only to the normal loading and insensitive to all other

loads and moments. The final configuration of the load cell was arrived at by carrying out a non-

linear constrained optimization of the configuration parameters for two materials, namely

Aluminum and Stainless Steel. These load cells were used to configure different designs of six

components External Strain Gauge Balance. Static FE analysis of the complete assembly was

carried out. An attempt was made to reduce the coupling between various forces & moments and

to make the components sensitive only to their respective normal loads.

HosseinNabipour[3]

This paper aims to fully put the wind tunnel of Memorial University back into service which

requires equipping the tunnel with its old force balance and flow visualization equipment. The

major part of the project will be the calibration and modernization of the force balance for force

and moment measurements on the test model. The balance will be equipped with a data

acquisition system and a computer to monitor and analyze the test results simultaneously. Also

there will be some flow measurements across the test section and finally the smoke generator

needs to be prepared and installed in the tunnel.

Marin SANDU, Adriana SANDU [4]

This paper describes the design of a six-component force/moment sensor which is compact, has

high measuring sensitivities, and can be used either as internal or as external balance in the

aerodynamic testing. The measurement of steady and fluctuating forces acting on a body in a

flow is one of the main tasks in wind-tunnel experiments. Usually, a multi-component strain

gauge force and moment sensor (also known as balance) is used to generate signals which are

processed by means of an adequate instrumentation. To design a wind-tunnel balance, the

specifications of the load ranges and the available space (for the placement of the balance inside

or outside the model) are required. The main challenge is to conceive the elastic element of the

sensor as a monolithic part with a relative simple geometry and to identify the adequate



placement of strain gauges to maximize the measuring sensitivities and to diminish the inter-

influence of the components.

S. M. GORLIN and I. I. SLEZINGER [5]

Some of the measuring techniques and instruments are described in this book. In this textbook

for advanced measuring techniques and instruments are described. R. C. Pankhurst and D. W.

Holder discuss a wide range of experimental problems in their textbook "Wind -Tunnel

Technique" (1952), but the treatment is general and sometimes superficial. Since the publication

of these works the technology of aerodynamics has advanced greatly. In this book systematically

certain modern techniques of aerodynamic measurement are described. They have made wide

use of experience in the USSR and abroad, selecting material to enable readers with knowledge

of theoretical aerodynamics to become familiar with experimental practice and with the

instruments and apparatus used in practice. The book is intended mainly for experimental-

research works in aerodynamics and for those using their results and also for students of fluid

dynamics. This book is useful for engineers and technicians designing and constructing

aerodynamic installations, and developing measuring equipment.

Tropea C, Yarin A L, Foss J F [6]

The aim of this paper is to give an impression of the possibilities, advantages and limitations

offered by the use of piezoelectric balances. Several types of external balances are discussed for

wall mounted models, which can be suspended one-sided or twin-sided. Additionally an internal

sting balance is described, which is usually applied inside the model. Reports are given on

selected measurements performed in very different wind tunnels, ranging from low-speed to

transonic; from short- to continuous running time and encompassing cryogenic and high pressure

principles. The projects span from a wing/engine combination in a low-speed wind tunnel to

flutter tests with a swept-wing performed in a Transonic Wind Tunnel, and include bluff

bodiesin a high pressure and cryogenic wind tunnel, as well. These tests serve as examples for

discussing the fundamental aspects that are essential in developing and applying piezo balances.



3 Platform Balance Description

A six component platform balance was designed and fabricated in the dept. of Aerospace

Engineering, IISc, Bangalore, for measuring aerodynamic forces and moments on models. This

balance utilizes load cells for transducing forces into electrical signals. The platform balance

consists a leveled platform constrained by six load cells for measuring forces in vertical, axial

and sideward directions. Fig.1to Fig. 4 shows the different views of the balance. In Fig.1 two

load cells (H1, H2) are indicated which were used for measuring side force and yawing moment.

In Fig.2 one load cell (H3) is indicated to measure axial force. In fig.3 three load cells (V1, V2,

and V3) are fixed to measure normal force, rolling moment and pitching moment. In Fig.4 all

the six load cells are fixed to form the complete platform balance system.

Figure 3-1Different views of platform balance



A hexagonal shaped rigid plate (Fig.4) is used as the metric platform. A circular flange fitting is

bolted at the center of this platform (Fig.4) for the purpose of fixing the model support adopter.

The center of the flange coincides with the vertical center line of the platform balance.

The vertical components of the load on the model are sensed by the three load cells fitted

vertically as indicated in the Fig.3. These loads cells are designated as V1, V2 and V3. For

sensing side force and yawing moment, there are two load cells fitted horizontally. In the same

plane for sensing axial force one load cell is provided. These load cells are designated as H1, H2

and H3. From these six load cells the six-components of forces and moments are obtained.

With the direction of axial force aligned parallel to the tunnel axis, we have the following main

components referred to the balance Centre.

1. Normal Force (NF) = V1+V2 +V3

2. Rolling Moment (RM) = (V1-V2)*a

3. Pitching Moment (PM) = V3*a

4. Side Force (SF) = H1+H2

5. Yawing Moment (YM) = (H1-H2)*b

6. Axial Force (AF) = H3

Where a and b are the corresponding length of the moment arm.

Table 3-1The rating of the balance is given in the above Table.

Axial force 136 kg

Side force 250 kg

Normal force 700 kg

Rolling moment 200 kgm

Pitching moment 50 kgm

Yawing moment 70 kgm



4 Load Cell Load: The word loadwill be used to describe both the applied forces and moments. The task of a

balance is to measure the aerodynamic loads, which act on the model or on components of the

model itself. In total there are six different components of aerodynamic loads, three forces in the

direction of the coordinate axes, and the moments around these axes themselves.

Thesecomponents are measured in a certain coordinate systemwhich can be either fixed to the

model or to the wind tunnel.

4.1 What is a Load Cell? A load cell is a sensor or a transducer that converts a load or force acting on it into an electronic

signal. This electronic signal can be a voltage change, current change or frequency change

depending on the type of load cell and circuitry used.

Figure 4-1Typical load cell used in Platform balance at IISc open circuit wind tunnel

Load cells or Load sensors as they are commonly called - can be made using resistive,

capacitive, inductive or other techniques. Most commonly available load cells are based on the



principle of change of resistance in response to an applied load. This is termed piezo-resistive

i.e. something that changes in response to an applied pressure (or squeezed).

One of the most popularly used types of the load cells is the strain gauge load cell. In fact

amongst all the types of load cells, the strain gauge type ones are used most commonly. These

load cells are used for the measurement of very large compressive and tensile forces. This load

cell is the special application of the strain gauges.

4.2 Working of Load Cell

Load Cells - How They Work?

Load cells are traditionally built using resistive bonded foil strain gauges (as shown in the picture

below). Strain gauges are essentially resistors built using standard semiconductor etching

techniques and are bonded to a metallic member such as a cantilever beam or diaphragm.

Figure 4-2 Specification of load cell



Usually at least four strain gauges are configured in a Wheatstone Bridge configuration with four

separate resistors connected as shown below in what is called a Wheatstone Bridge Network. An

excitation voltage - usually 10V is applied to one set of corners and the voltage difference is

measured between the other two corners. At equilibrium with no applied load, the voltage output

is zero or very close to zero when the four resistors are closely matched in value. That is why it

is referred to as a balanced bridge circuit.

Figure 4-2Wheatstone bridge Network

When the metallic member to which the strain gauges are attached, is stressed by the application

of a force, the resulting strain - leads to a change in resistance in one (or more) of the resistors.

This change in resistance results in a change in output voltage. This small change in output

voltage can be measured and digitized after careful amplification of the small milli-volt level

signals to a higher amplitude 0-5V or 0-10V signal.



5 Calibration of the platform balance

The goal of calibration is to minimize any measurement uncertainty by ensuring the accuracy of

test equipment. Calibration quantifies and controls errors or uncertainties within measurement

processes to an acceptable level.

5.1 Objectives of the calibration

1. To determine the interaction components

2. To check accuracy, repeatability and linearity.

3. To determine the calibration constant for each component.

For calibration purpose a vertical tubular column with suitable fittings on its both ends need to

fabricate. One end of the bar will have a flange fitting and will be bolted on the platform balance

to the corresponding holes provided for the purpose. The other end of the bar will also have

flange fitting clamped to the vertical column by a pinch fitting thus permitting rotation about a

vertical axis. This will be used for supporting the loading bar and pans. Fig shows a typical

arrangement made for calibration. The loading bar and pans can be aligned with the axial or

lateral directions to calibrate respective components. This arrangement is used for calibration of

the following components.



Figure 5-1Platform balance with calibration setup (a)



Figure 5-2Platform balance with Calibration setup (b)



Axes System

Figure 5-3Axes system

For the platform balance, we choose the balance centre to be at the centre of the mounting flange

which mates with the model/calibration column. The directions of axes are chosen as follows:

Axial force direction coincides with wind direction and is horizontal (X direction).

Normal force direction is vertical positive upwards (Z direction).

Side force direction is horizontal and at right angle to the tunnel axis (Y Direction).



5.2 Force and moment concepts

Figure 5-4Force and moment concept

1. Axial force: The force Parallel to the wind flow and to the tunnels walls.

2. Normal force: Upward/Downward force normal to Drag and Side force.

3. Side force: Applied to the sides of the test model and normal to drag and lift.

4. Yawing moment: Moment caused by Drag and Side force about an axis parallel to Lift

5. Pitching moment: Moment caused by Drag and Lift about an axis parallel to side force

6. Rolling moment: Moment caused by Lift and Side force about an axis parallel to Drag



5.3 Calibration procedure

5.3.1 Negative normal force: This is obtained by loading equal weights on both the pans.

5.3.2 Positive rolling moment:

In the negative normal force loading setup, rolling moment is obtained by transferring weights

from one pan to another keeping the total weights same.

Figure 5-5Calibration for Nf and Rm

Normal force = Nf =Fz = F1+ F2

Rolling moment = Rm= Mx= F1*a-F2a

Remaining forces (fx, Fy) and moments (My, Mz) are zero



[Nf] = [1 0 0 0 0 0] [Rm] = [0 0 1 0 0 0]

5.3.3 Negative axial force:

This requires pulley-string arrangement. The loading on the pan gives axial force.

5.3.4 Positive pitching moment: The loading arm will be rotated by 90 degree to the original position and loading pans will be

hung. Both loading pans loaded equal loads. Now transferring loads from one pan to another,

the pitching moment is obtained.

Figure 5-6Calibration for Af and Pm

Axial force = Af = Fx = F

Mz

Fx

Fy

Mx

My

Fz

Mz

Fx

Fy

Mx

My

Fz



Pitching moment = Pm = My = F*a

Remaining forces (Fy, Fz) and moments (Mx, Mz) are zero

[Af] = [0 0 0 0 1 0] , [Pm] = [0 1 0 0 0 0]

5.3.5 Positive side force: This requires pulley-string setup for loading in side direction.

5.3.6 Positive yawing moment: This is obtained by pulley-string setup, the string being tied to the loading bar at a distance from

the center.

Figure 5-7Calibration for Sf and Ym

Side force = Sf = Fy = F

a= 25cm

F

Mz

Fx

Fy

Mx

My

Fz

Mz

Fx

Fy

Mx

My

Fz



Yawing moment = Ym = Mz = F*a

Remaining forces (Fx, Fz) and moments (Mx, My) are zero

[Sf] = [0 0 0 1 0 0] [Ym] = [0 0 0 0 0 1]

Mz

Fx

Fy

Mx

My

Fz

Mz

Fx

Fy

Mx

My

Fz



6 Derivation of Calibration Matrix, Transformation Matrix

and User matrix of the platform balance

Before use, any balance needs a calibration to establish the relationship between the balance

output vector in millivolts per volt of excitation and the load vector (forces and moments relative

to a balance centre suitably defined with respect to the balance). For the platform balance, we

choose the balance centre to be at the centre of the mounting flange which mates with the

model/calibration column. The directions of axes are chosen as follows: axial force direction

coincides with wind direction and is horizontal. Normal force direction is vertical positive

upwards and side force direction is horizontal and at right angle to the tunnel axis.

It would be most convenient to calibrate the balance by applying one component of the load

vector at a time and record the balance output vector for each component. However, in this

particular case, it is difficult to apply only a single component of the load vector at a time due to

constraints associated with the balance location. Therefore an alternative scheme using a

generalized loading method is employed and is described below.

Let the balance output vector (written as a row vector for convenience) be associated with a

generalized load vector F. Assuming linearity, we may relate R to F by a calibration matrix C as,

In the above, the calibration matrix is easily obtained by the conventional method of applying

one component of F at a time and recording the balance output vector.

Inverting the above relation, one obtains

654321 RRRRRR 654321 FFFFFF

6661

1611

....

......

......

......

......

....

CC

CC

=



Above equation gives the components of any applied load resolved into generalized forces

1 6 one may transform this to set of forces into forces relative to balance Centre

(Normal force NF, Pitching moment PM, Rolling moment RM, Side force SF, Axial force AF

and Yawing moment YM) by a simple transformation.

We may write

Above equation resolves the generalized forces 16 into forces relative to balance

Centre. The transformation matrix [T] is obtained by using equilibrium considerations.

Let CC= calibration Centre, BC= balance Centre; CC and BC are co-linear at a distance of R.

654321 RRRRRR 654321 FFFFFF =

6661

1611

....

......

......

......

......

....1

cc

cc

YMAFSFRMPMNF = 654321 FFFFFF

6661

1611

....

......

......

......

......

....

TT

TT



R

Figure 6-1Force and moment vectors at CC and BC

Force and moment vectors at CC and BC will be

F

= Fxi + Fyj + Fzk; M

= Mxi + Myj + Mzk

Force and Moment vectors at BC wii be

F

= Fxi + Fyj + Fzk; M

= Mx i + Myj + Mzk

The procedure to evaluate forces (Fx, Fy, fz) and moments (Mx, My, Mz) at Balance centre is

Cleary explained in calibration procedure chapter.

Fx = Axial force (Af), Fy = Side force (Sf), Fz = Normal force (Nf)

Mx = Rolling moment (Rm), My = Pitching moment (Pm),

Mz = Yawing moment (Ym)

. (4)

YM

AF

SF

RM

PM

NF

aR

R

R

0100

01000

00100

000100

000010

000001

Mz

Fx

Fy

Mx

My

Fz

=



R=Column length= 101.4cm

a= eccentricity = 25cm

. (5)

In equation (4) and (5) the middle 6*6 matrix is called Transfer matrix [T]

Using above equation we have,

. (6)

. (7)

Here [U] is the user matrix and is obtained by post multiplying with [T].

1004.0056.400

01004.1010

0014.10100

000100

000010

000001

YM

AF

SF

RM

PM

NF

Mz

Fx

Fy

Mx

My

Fz

=

YMAFSFRMPMNF 654321 RRRRRR= C1 T

U YMAFSFRMPMNF = 654321 RRRRRR

C 1



7 Balance calibration data and errors

Table 7-1Calibration data (1) Table 7-2 Calibration Data (2)

Applied Load

(NF)(kg)

Measured

load (kg) % Error

-20 -20.0185 -0.0925

-40 -40.011 -0.0275

-60 -59.9901 0.0165

-80 -79.9745 0.031875

-100 -99.9979 0.0021

-80 -79.9973 0.003375

-60 -59.9925 0.0125

-40 -40.0086 -0.0215

-20 -19.9924 0.038

Applied

Load (AF)

(kg)

Measured load

(kg) % Error

-5 -5.0072 -0.144

-10 -9.9546 0.454

-15 -14.9527 0.3153

-20 -19.8777 0.6115

-25 -24.9131 0.3476

-30 -29.853 0.49

-25 -25.2144 -0.858

-20 -20.2068 -1.034

-15 -15.0998 -0.665

-10 -10.049 -0.49

-5 -5.0138 -0.276



Table 7-3Calibration data (3) Table 7-3Calibration Data (4)

Applied

Load

(SF)(kg)

Measured load

(kg) % Error

10 10.0333 -0.333

20 19.933 0.335

30 29.9616 0.128

40 39.9879 0.0302

50 49.8957 0.2086

40 40.1149 -0.2872

30 30.1812 -0.604

20 20.0187 -0.0935

10 9.9803 0.197

Applied Load

(RM)(kg-m)

Measured load

(kg-m) % Error

10 10.0333 -0.333

20 19.933 0.335

30 29.9616 0.128

40 39.9879 0.0302

50 49.8957 0.2086

40 40.1149 -0.2872

30 30.1812 -0.604

20 20.0187 -0.0935

10 9.9803 0.197



Table 7-4Calibration data (5) Table 7-5 Calibration Data (6)

The calibration data shows that the balance behaves in a linear fashion in the range of loads

applied. The transformation matrix obtained is almost a diagonal matrix as expected. Percentage

error is less than 1% of maximum load in each component.

Applied

moment

(YM)(kg-m)

Measured

moment

(kg-m)

% Error

-2 -1.9638 1.81

-4 -3.934 1.65

-6 -5.9076 1.54

-8 -7.8926 1.3425

-6 -5.9025 1.625

-4 -3.9642 0.895

-2 -1.9769 1.155

Applied moment

(PM)(kg-m)

Measured

moment

(kg-m)

% Error

1.2 1.1882 0.9833

2.4 2.3997 0.0125

3.6 3.6198 -0.55

4.8 4.8037 -0.0771

6 6.0227 -0.3783

4.8 4.8202 -0.4208

3.6 3.6155 -0.4306

2.4 2.4208 -0.8667

1.2 1.1992 0.0667



8 The Concept of I-Beam and Spring Element

8.1 I-Beam

Figure 8-1Concept of I-Beam

When an I-beam bends the top of the beam is in compression and the bottom is in tension. These

forces are greatest at the very top and very bottom. So to make the stiffest beam with the least

amount of material you would want the material to be only at the top and bottom sides. However

still need to connect them together or they would just be two separate plates and would not be

stiff at all. So need to put a web in the middle to connect them and make them work together.

The idea is to remove material that is not carrying much load and concentrating the material

where the load is highest. Its an extremely efficient shape for resisting bending.



Figure 8-2Force measuring element without and with I-beam

8.2 FE Analysis of Force Measuring element without and with I-

beam

Figure 8-3FE analysis of force measuring elements

A study was carried out on various configurations of force measuring elements using Finite

Element Analysis. It was found that an I- beam induced in-between type of force measuring

element met all requirements and was found to be sensitive only to the normal loading and

insensitive to all other loads and moments. Static FE analysis of the force measuring element was

carried out. An attempt was made to reduce the coupling between various forces & moments and

to make the components sensitive only to their respective normal loads and to protect the load

cells.



8.3 Spring Element in place of Load cell

Figure 8-4FE analysis of force measuring element by replacing sring inplace of load cell

The static FE analysis of the complete assembly force balance was carried out by replacing

spring element in place of load cells, because there are no options to create and simulate load

cells like elements in Ansys and some other available analysis softwares. When a spring is

compressed or stretched from its initial position after applying force on an element, the force or

reaction it exerts is approximately proportional to its change in length.



9 FEM analysis of external force balance

9.1 Normal Force, Rolling moment and pitching moment measurement

Figure 9-1Nf, Rm, Pm measurement

The vertical components of the load on the model are sensed by the three load cells fitted

vertically. These loads cells are designated as V1, V2 and V3.

Applied NF (N) V1 (N) V2 (N) V3 (N)

-100 50.98 50.08 0.180

-200 100.29 100.26 0.554

-300 150.15 149.85 0.205

-400 200.20 200.15 0.340

Table 9-1Nf measurement



9.2 Side Force and Yawing moment measurement

Figure 9-2Sf, Ym Measurement

For sensing side force and yawing moment, there are two load cells fitted horizontally. These

load cells are designated as H1, H2.

Applied SF (N) H1 (N) H2 (N)

50 -24.99 24.99

100 -49.99 49.99

150 -74.99 74.99

200 -99.99 99.99

Table 9-2Sf measurements



9.3 Axial Force Measurement

Figure 9-3Af measurement

In the horizontal plane for sensing axial force one load cell is provided in axial direction and is

designated as H3.

Table 9-3Af measurement

Applied AF (N) H3 (N)

25 24.99

50 49.99

75 74.99

100 99.99



9.4 Combined forces and Moments:

Figure 9-4Combined forces and moments measurements

From V1, V2, V3, H1, H2 and H3 load cells the six-components of forces and moments are

obtained.

Table 9-4Combined forces and moments measurements

Applied

load

(N) V1 (N) V2 (N) V3(N) H1(N) H2(N) H3(N)

Af 50 -0.00004 -0.0038 -0.0019 -0.0049 -0.00027 49.99

Sf 100 -0.00035 -0.00098 -0.00037 -49.99 49.99 -

0.00022

Nf 200 -100.001 -100.001 0.544 -0.0002 -0.0009 -0.0003



9.5 Stress and Deformation plot

Figure 9-5Stress and Deformation plot

The static FE Analysis shows that, stresses and deformations in a designed external balance are

within the limits for specified range of forces and moments.

Material Used: EN24 Steel.

Table 9-5EN24 steel properties

EN24 Mechanical Properties

Max Stress 850-1000 MPa

Yield Stress 680 MPa

0.2% Proof Stress 665 Mpa

Elongation 13%

Hardness 248-302 Brinell

EN24 Chemical composition

Carbon 0.36-0.44%

Silicon 0.10-0.35%

Manganese 0.45-0.70%

Sulphur 0.040 Max

Phosphorus 0.035 Max

Chromium 1.00-1.40%

Molybdenum 0.20-0.35%

Nickel 1.30-1.70%



10 Conclusions and Recommendations

10.1 Conclusions 1. Calibration procedure is explained in detail and data obtained is presented.

2. The calibration data shows that the balance behaves in a linear fashion in the range of

loads applied. The transformation matrix obtained is almost a diagonal matrix as

expected. Percentage error is less than 1% of maximum load in each component.

3. The balance can be utilised to determine aerodynamic loads within the specified range

of forces and moments.

4. The FE Analysis shows that, stresses and deformations of the designed external

balance are within the limits as.

10.2 Recommendations

Recommendations for future works into developing the external force balance include:

1. Alter the balance so that two or more struts can be used to support models which will

allow for additional stability.

2. Install vibration isolators that support the force balance to reduce vibration and increase

stability

3. Create a software program that enables easier calibration, better display, that will reduce

the impact of vibrations on readings

4. The present work could be extended for developing a design package for complete design

of the balance and preparation of design data that would further help in the design of

actual wind tunnel balances.



11 References

[1] Miguel A. Gonzalez, Jose Miguel Ezquerro, Victoria Lapuerta, Components of a Wind

Tunnel Balance: Design and Calibration (2012).

[2] AnkitSoni, PankajPriyadarshi,Finite Element Analysis and Optimization of a Beam Type

Load cell for an External Balance design Aerospace Engg. Dept. Indian Institute of Space

Science and Technology, Trivandrum-695547

[3] HosseinNabipour,Wind Tunnel revitalization project, Memorial University, Mechanical

Engg. Dept. (2006)

[4] M. Sandu, A. Sandu, Analytic-numerical approach in a multicomponent strain gauge

transducer design, Scientific Bulletin of University politehnica of Bucharest, vol67, no. 3,

pp. 37- 44( 2005).

[5] Gorlin S.M &Slezinger,Wind Tunnels and Their Instrumentation, Israel Program for

Scientific Translations, No 1680, Israel Jerusalem (2009).

[6] Tropea. C, Yarin.A.L, Foss.J.F,Force and Moment Measurements, Springer (2007).

Retrived from

[7] Frederick Francois Pieterse, Design and Development of a six Component Strain Gauge

Wind Tunnel Balance, Rand Afrikaans University (2010).

[8] Design of a six component External strain gage balance, NASA Website

[9] Engler R.H, Klein C, Wind Tunnels and Wind Tunnel Test Techniques, Cambridge, UK,

Paper 43 (1997).

[10] Robinson, M.J. Mee, D.J Tsai, C.Y. Bakos, Measurement of three components of Force on

a large scramjet in a shock tunnel Journal of Spacecraft and Rockets 41(2004).

[11] J.B. Barlow, W.H. Rae Jr and A.Pope, Low-Speed wind Tunnel, 3rd Ed. John Wiley &

Sons, New York (1999).

[12] G. Schewe, Force measurements in aerodynamicsusingpiezo-electric multicomponent force

transducers, Proc. 11th iciasf, 85 Record, Stanford University (1985)



[13] Beginners Guide to Wind Tunnels, Glenn learning technologies project, NASA, Retrieved

from

[14] B. Ewald, Multi-component force balances for conventional and cryogenic wind tunnels,

Meas. Sci.Technol. 11, 8194 (2000)

[15] Tiffany. A, Wind Tunnel Instrumentation, Electronic Engg. Vol 29, No.3, (1957)

[16] Pollok. N, The optimum design of stain gauge sting balance for wind tunnel models,

Report 133, aeronautical research laboratories, Australia (1979)

[16] Levvy .L.E and Saunders.C.G, A modern wind tunnel balance, J.roy.Aero.Soc. vol 57,

512-520 (1953)

[17] Alonpope and John.J.Harpus,Low wind tunnel testing, John Wiley & Sons N.Y (1966).

[18] Reston, Assessment of Experimental Uncertainty with Application to Wind Tunnel

Testing, AIAA S-071A (1999).

[19] G Schewe, Force measurement in aerodynamics using peizo-electric multicomponent force

transducer, 11th ICIASF 85 Record, Stanford University, (1985).

[20] Reston, Calibration and Use of External Strain Gauge Balance with Application to Wind

Tunnel Testing, AIAA R-091(2003)



12 Appendix

12.1 Appendix A

The modeling of the external force balance with the required configuration is designed using

CATIA V5 software. The front, top, side and isometric views of the balance is shown in the

following figures.

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