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Theses
12-1-2003
Aerodynamic force and moment balance design, fabrication, and testing for use in low Reynolds flow applications
Corey Abe
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This Thesis is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. Aerodynamic Force and Moment Balance Design, Fabrication, and Testing for use in Low Reynolds Flow Applications
by
Corey T. Abe
A Thesis Submitted In Partial Fulfillment ofthe Requirements for the
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
Approved by:
Dr. Kevin Kochersberger Department ofMechanical Engineering (Thesis Advisor)
Dr. Jeffrey Kozak Department ofMechanical Engineering (Committee Member)
Dr. Amitabha Ghosh Department ofMechanical Engineering (Committee Member)
Dr. Edward C. Hensel Department ofMechanical Engineering (Department Head)
DEPARTMENT OF MECHANICAL ENGINEERING COLLEGE OF ENGINEERING ROCHESTER INSTITUTUE OF TECHNOLOGY
DECEMBER 2003 Disclosure Statement
Permission Granted
Thesis Title: "Aerodynamic Force and Moment Balance Design, Fabrication, and Testing for use in Low Reynolds Flow Applications"
I, Corey T. Abe hereby grant permission to the Wallace Library ofthe Rochester Institute ofTechnology to reproduce my thesis in whole or in part. Any reproduction will not be for commercial use or profit.
Date:~
Corey T. Abe Aerodynamic Force and Moment Balance Design, Fabrication, and Testing for use in Low Reynolds Flow Applications
ABSTRACT:
The aerodynamic performance of airfoils operating at Reynolds numbers below
105 has been of interest due to its variety of applications in areas such as unmanned remotely piloted vehicles, small-scale machinery, and more recently, Micro Air Vehicles
(MAV's). Design and testing of airfoils to meet these applications is challenging due to the lack of experimental data in low Reynolds flow, compared to airfoils tested at higher
Reynolds numbers. Two mechanical balance devices are designed and evaluated to
provide a quick and simple method to test small airfoil aerodynamic loads. Each device measures two degrees of freedom; a force balance measures lift and drag forces and a moment balance measures pitch and roll moments.
Coefficients of lift and drag vs. angle of attack and coefficients of pitch and roll vs. angle of attack or sideslip angle data are obtained from the fabricated devices and
compared to literature results. A statistical evaluation is performed on various aspect ratio flat plate and cambered airfoils to test repeatability. Testing procedures are documented and an overall analysis oftesting methods and device designs are discussed.
u Table of Contents
LIST OF FIGURES IV
LIST OF TABLES V
LIST OF SYMBOLS VI
CHAPTER 1 INTRODUCTION 1
1.1 RIT Wind Tunnel Facility 2 1.2 Statement of the Problem 3
CHAPTER 2 LITERATURE REVIEW 6
CHAPTER 3 DESIGN 10
3.1 Requirements 10 3.2 Concepts 12 3.3 Balance Design 13 3.3.1 Reference System 13 3.3.2 Lift and Drag Balance 75 3.3.3 Pitch and Roll Moment Balance 24 3.4 Test Airfoil Design and Specifications 31
CHAPTER 4 EXPERIMENT METHODS AND DESIGN 33
4.1 Design of Experiment 33 4.2 Experiment Analysis 35 4.2.1 Lift and Drag Experiment 35 4.2.2 Pitch andRoll Moment Experiment 37 4.3 Computational Analysis 43 4.3.1 LinAir 43 4.3.2 Roll Moment Analysis 44 4.4 Statistical Analysis 46 4.5 Uncertainty Analysis 48
CHAPTERS RESULTS 52
5.1 Lift Results 52 5.2 Drag Results 55 5.3 Pitch Moment Results 58 5.4 Roll Moment Results 60 5.5 Uncertainty in Measurements 63
CHAPTER 6 SUMMARY 65
CHAPTER 7 FUTURE RECOMMENDATIONS 68
APPENDIX A: LIFT/DRAG BALANCE CAD DRAWINGS 71
APPENDIX B: PITCH/ROLL MOMENT BALANCE CAD DRAWINGS 77
APPENDIX C: EXPERIMENT PROCEDURES DOCUMENT 84
APPENDIX D: STATISTICAL ANALYSIS 88
APPENDIX E: EXCEL DATA CHARTS 92
REFERENCE 97
ill List of figures
Figure 1-1: RIT's Wind Tunnel Test Section 3 Figure 1-2: Diagram of RIT's Closed Circuit Wind Tunnel 5
Figure 2-1: Experimental apparatus used to measure three-dimensional hydrodynamic forces. (Sunada et. al. [5]) 6 Figure 2-2: Schematic of Balance used in experimental research [3] 8 Figure 3-1: Wind-Axis Reference Frame 14 Figure 3-2: Body-Axis Reference Frame 15 Figure 3-3: Assembly Diagram of Lift and Drag Balance 16 Figure 3-4: Balance Configuration to Measure Lift Force 17 Figure 3-5: Balance Configuration to Measure Drag Force 17
Figure 3-6: Moment Analysis Diagram -Lift Configuration 22 Figure 3-7: Moment Analysis Diagram for Drag Balance Configuration 23 Figure 3-8: Assembly Diagram ofthe Pitch and Roll Moment Balance 24 Figure 3-9: Assembly Diagram ofthe Test Platform for the Pitch and Roll Moment Balance 25 Figure 3-10: Fabricated Welding rod Test platform 26 Figure 3-11: Pitching Moment Balance Configuration 28 Figure 3-12: Rolling Moment Balance Configuration 28 Figure 3-13: Pitch Moment Analysis Diagram 29 Figure 3-14: Roll Moment Analysis Diagram 30
Figure 4-1: Diagram of Experiment Elements 34 Figure 4-2: Lift Configuration 36 Figure 4-3: Drag Configuration 36 Figure 4-4: Pitch Moment Configuration 38 Figure 4-5: Roll Moment Configuration 38 Figure 4-6: Flat Plate Moment Calibration Plot (Zero velocity and no airfoil) 40 Figure 4-7: Flat Plate Pitching Moment Data 40 Figure 4-8: Pitch Experiment Test Platform Setup 42 Figure 4-9: LinAir Vortex Panel Method Airfoil 44 Figure 4-10: Dihedral and Roll Moment Coefficient 45 Figure 5-1: Experimental Values of Lift Force and Coefficient 53 Figure 5-2: Comparison of Experimental Lift Data to Published Data 55 Figure 5-3: Experimental Drag Data 56 Figure 5-4: Comparison of Experimental Drag Data to Published Data 57 Figure 5-5: Experiment Pitching Moment Data 58 Figure 5-6: Pitching Moment Experimental and Published Values 60 Figure 5-7: Experimental Data; Rolling Moment 61 Figure 5-9: Roll Moment Coefficient Comparison to Analytical Models 62 Figure 7-1 : Balance design with added mass 68
iv List of Tables
Table 4.1: Uncertainty of measurement variables 50 Table 4.2: Summary ofpredicted uncertainty obtained from experimental methods 51 Table 5.1: Comparison ofUncertainty Analysis Techniques 63 Table 6.1: Summary of Lift and Drag Force Results 66 Table 6.2: Summary of Pitch and Roll Moment Results 67 Table E.l: Lift Data Spreadsheet 92 Table E.2: Drag Data Spreadsheet 93 Table E.3: Pitching Moment Spreadsheet (1 of 2) 94 Table E.4: Pitching Moment Spreadsheet (2 of 2) 95 Table E.5: Rolling Moment Spreadsheet 96 List of Symbols
AR Full-span aspect ratio
CD Drag coefficient (3D) Cl Lift Coefficient (3D)
Cm/4 Pitching moment coefficient about the quarter chord cr Rolling moment coefficient
Re Root-chord Reynolds number
Uo Free stream velocity ao 2D lift-curve slope b Wingspan c Root-chord length t Wing thickness a Angle of attack
P Sideslip angle r Dihedral angle
S Reference wing area
Q Dynamic pressure p Density
H Dynamic viscosity df degrees of freedom eg center of gravity subscript b Body axis frame subscript w Wind axis frame subscript min Minimum value subscript max Maximum value subscript ss sideslip
Vl Chapter 1 Introduction
105 The performance of airfoils operating at Reynolds numbers below has been of interest due to its variety of applications in areas such as sailplanes, small-scale machinery, and unmanned remotely piloted vehicles. The demand for very small, multi functional aircraft has come to the forefront of academic and military research. These small aircraft called micro-air vehicles (MAV's) are of interest due to potential applications in electronic surveillance, communications, and real-time data relay [1].
With the advances in miniaturizing electronics, these small aircraft can carry video and
advanced flight control devices. With this in mind, a general overview of MAV's is
outlined to provide some direction in the functionality and design of aerodynamic load balances.
Current designs of MAV's typically have wingspans of 6-8 inches (15-20cm) and weigh approximately 200 grams [2]. The endurance of such vehicles ranges from 20 to
30 minutes and operate at speeds of about 30 mph (18.5km/hr). At these values,
Reynolds numbers range from 20,000 to 200,000 [3]. The dependence on aerodynamic performance on the Reynolds number has been well documented in works by Jacobs and
106 Sherman [4], and aerodynamic performance at Reynolds numbers greater than are also readily available.
Conversely, little research has been done to investigate the aerodynamic properties of airfoils at relatively low Reynolds numbers, compared to traditional
106 Reynolds numbers greater than in magnitude. More specifically, there is a lack of such data for Reynolds numbers ranging from Re (10 < Re < 104). It is believed that wings and model airplanes exhibit unique characteristics at these low Reynolds numbers not observed in experiments of large airfoils and high Reynolds flow. More recently, works by Sunada, Sakaguchi, and Kawachi presented the study of aerodynamic
characteristics of selected airfoils measured at Reynolds numbers of 4000 [5] and has been used as a good starting point for further studies into aerodynamic characteristics under low Reynolds flows.
1. 1 RIT Wind Tunnel Facility
Rochester Institute of Technology's Wind Tunnel facility is located in the "Power
Wing" of the Mechanical Engineering department. The wind tunnel is a low speed, closed circuit system powered by a 60 hp motor. A student-designed chiller unit provides a stable temperature in the test section of +/- 0.5 degrees Fahrenheit. The modular test
(4' 2' section has been redesigned, providing a test section of x x 2') in dimensions and is accessible from all four side-panels (see Figure 1-1). By adjusting the fan blade pitch setting, a maximum allowable speed of 180 ft/sec (123 mph) and minimum sustained speed of approximately 20 ft/sec (13.6 mph) in the test section is achievable [6]. Figure 1-1: RIT's Wind Tunnel Test Section
In addition, a three-dimensional computerized traversing system offers motorized position of probes within the test section. Data acquisition systems include a six component spring balance which can measure a maximum of 50 lbf lift load, 75 in-lbf of pitching moment, and 25 in-lbf of rolling moment. The wind tunnel facility is also able to accommodate a variety of pitot-static tubes, pressure transducers, hot film anemometers, and a bubble generator for flow visualization applications. See Figure 1-2 for a schematic diagram ofthe RIT wind tunnel facility.
1.2 Statement ofthe Problem
The ability of the RIT wind tunnel facility to measure aerodynamic forces on
small-scale airfoils and model aircraft is limited. The desired forces and moments of
interest are of several magnitudes less that that of what the current wind tunnel instrumentation can measure. As previously mentioned, the current tunnel balance is capable of measuring forces in order of magnitude of 1 lbf, whereas forces on small-scale 10"4 airfoils at low Reynolds number are in the order of lbf. Similar scale insufficiency
occurs for moment measurements. At such low force and moment ranges errors in load
cell and strain amplifiers have a greater effect on data analysis of small airfoils [7]. This
dilemma illustrates the issues addressed in the prototype balance designs included in this
research.
The primary objective of this research is two fold. The first objective involves the
design and fabrication of two mechanical load balances. Two prototype balances, one
designed to measure aerodynamic forces of lift and drag, and another designed to
measure aerodynamic moments of pitch and roll, are included in this research. In total, the mechanical balances have the potential to resolve four degrees-of-freedom within
acceptable ranges ofuncertainty.
The second objective of this research is to experimentally evaluate the fabricated devices and compare experimental data to published values and documented sources.
Several flat plate and cambered airfoils have been incorporated in the wind tunnel experiments to meet this goal. In addition, repeatability is a major concern in the functionality of the device. Though statistical analysis and validation process in testing balance performance, prototype models are proven to be successful. The end goal is to eventually scale up the devices in order to accommodate a broader range of MAV
applications. Figure 1-2: Diagram of RIT's Closed Circuit Wind Tunnel
(Courtesy of Drew Walter) Chapter 2 Literature Review
Low Reynolds Number Aerodynamics
A wide range of research has been done on the performance of airfoil at Reynolds
104 105 numbers equal to or greater than 105. For example, wing characteristics at < Re < have been studied by Schmitz [8]. Recent research projects such as the development of small insect like flying machines and MAV's have presented opportunity to better understand aerodynamic behavior of centimeter sized airfoils operating at very low
103 105 Reynolds numbers, approximately < Re < [9].
Sunada et al. conducted systematic studies on aerodynamic characteristics of selected airfoils measured at Re = 4 x 10 [5]. Measurements by Sunada et al. were collected by water tunnel experiments in which a test airfoil is submerged underwater.
The collected data measured the hydrodynamic characteristics of the wings along with three-dimensional effects due to a finite model. Several flat plate, cambered, and NACA
profile airfoils were tested (see Figure 2-1 for test apparatus).
Side vievt O'cu-arcyln'iter LaadeeJI
-. A', 50 c - 40
Figure 2-1: Experimental apparatus used to measure three-dimensional hydrodynamic forces. (Sunada et al. [5]) Several conclusions were drawn by the work of Sunada et. al. [5]. It was found
103 = that airfoils at Re 4 x with low thickness ratios, a sharp leading edge, and about a
5% camber with a maximum camber position at mid-chord yielded high stall angle of
attack and high lift to drag ratios. Furthermore it was found that airfoil performance at
103 Reynolds numbers in the order of is strongly affected by flow separation and leading
edge vortices. Through flow visualization techniques leading edge vortices were
observed at an angle of attack of 6 degrees on tested airfoils [7]. The airfoil of particular
interest is the flat plate airfoil of aspect ratio 6.75 and 5% thickness. Sunada et. al.
103 published values of lift and drag at Re - 4 x from water tunnel experiments of the described airfoil and is used to evaluate experimental results contained in this research.
Another systematic investigation by Laitone E. V. examines airfoil aerodynamic loads with the use of a two-component beam balance rather than a typical strain gauge balance system [10]. Lift and drag data is measured on small models in the range of Re ~
104. Laitone's research focuses on the effect of aspect ratio on wing planform and annular airfoils. An interesting observation encountered from his research is the increase in the 3-D lift curve slope measured from experimental data compared to the analytical
values obtained from Glauert's calculation methods for rectangular planform wings. An apparent increase in induced drag and stall region of higher aspect ratio wings at approximately 12 to 14 degrees angle of attack was also observed.
Experimental work by Alain Pelletier and Thomas J. Mueller focuses on
about the quarter chord on series of measuring lift, drag, and pitching moment thin flat
and chambered plates at Reynolds numbers between 60,000 and 200,000 [3]. Results presented were obtained with a three-component platform force balance, which measures lift, drag, and pitching moment about the vertical axis simultaneously (see Figure 2-2).
This external balance transmits lift and drag forces through a sting which is connected to a moment sensor. The lift and drag platform are fitted with foil strain gauges while a moment sensor is rigidly mounted to an adjustable angle of attack mechanism on the top platform. The designed balance is an external device, which is positioned on top of the test section of a low speed wind tunnel. Refer to section 3.2 for a discussion on external
vs. internal balance designs.
Figure 2-2: Schematic of Balance used in experimental research [3] The focus of their study was to investigate the aerodynamic behavior on low aspect ratio wings down to Reynolds numbers of 20,000. In particular, flat plate and
= chambered airfoil profiles with an AR 1 .5 and root chord approximately 8 inches were tested at Reynolds number of 60,000. Results from these tests are used for comparison to results contained in the present research. Through research on low aspect ratio flat plates,
Mueller found that there is a thin region of separated flow near the trailing edge at low angles of attack. Flow reattachment was not observed in flow visualization experiments.
These flow observations may be a characteristic of low Reynolds flow not observed in conventional flow regimes. Chapter 3 Design
The purpose of collecting load measurements on scaled models is to gather data on forces and moments, which can be utilized to approximate the performance of a full-
scale vehicle or device. These forces and moments can be measured by four methods
[11]. This includes measuring stress distributions by means of pressure measuring devices or thin coatings, measuring the effect that the model causes on the air stream by runnel wall pressure analyses, and by measuring the model's motion caused by aerodynamic loads and computing the forces from equations of motion. The last and most frequently used method of measuring model loads is by directly measuring the force and moments which act on the complete model though the use of one or more balances.
This last method has been chosen as a means to collect experimental airfoil data of low
Reynolds flow research.
3.1 Requirements
There are many factors that must be accounted for in the design of a wind tunnel balance. For example, small difference in forces must be accurately resolved throughout
the range of operation from maximum to minimum airspeed. In addition, forces and moments can vary widely due to airspeeds and airfoil geometry.
The reason for designing and building a mechanical balance is to have a simple
mechanical device capable of measuring aerodynamic force and moments on small
airfoils. These airfoils range from cross-sections of approximately 2cm x 2cm to 9cm x
10 9cm (see section 3.4). For this reason, a simple small pendulum device is chosen as the
best design option.
Three objectives are considered in the design phase of a mechanical wind tunnel
balance: (1) the ability to resolve very small force and moments within an acceptable
range of accuracy, (2) the ability to accommodate small airfoils and test objects
(approximately 6 cm x 9 cm) and easily incorporated with the RIT wind tunnel facility,
and (3) device fabrication.
The first major concern of balance design is the challenge of accurately measuring
10"5 10"1 lift and drag forces in the order of magnitude of to lbf, pitching moments in the
10"1 10"4 10"2 range of 10 to in-lbf, and rolling moments in the range of to in-lbf.
Measuring these small force and moment values is highly dependent on the geometry of
the airfoils and the low wind tunnel velocities achieved during the experiment
(approximately 27 ft/sec or 18 mph).
The ease of incorporating such a device within a 2ft x 2ft test section area was
important for testing multiple airfoils without the need of setting up and extensively
calibrating each device. Lastly, the device is required to be easily machined and
reproducible. The reason for this is to provide a means to reproduce the device cost effectively on a larger scale. Though testing and validation of the small scale balance device it is expected that a larger scale device will provide similar results with the addition of accommodating larger test specimens.
11 3.2 Concepts
There are many techniques of producing balance devices for wind tunnel applications. Such devices are classified into two main categories, internal and external balances. Internal balances typically have force and moment elements and incorporate a cantilever beam or column arrangement. The two most commonly used transducer types for this application are strain gages and piezoelectric elements. Depending on the model geometry and test area, these elements can be arranged in differential or summing circuits to measure forces and moments [11].
Another design option is an external balance in which four classified designs are wire, platform, yoke, and pyramidal. A wire balance is one ofthe earliest designs used in aeronautics testing. Spring scales are used to obtain balance output. The model is usually mounted inverted to prevent unloading of the wires. The problem with this type of balance is the large tare drag associated with the wires. Also, due to the deflection of the springs the model attitude changed depending on the observed loads. Platform, Yoke,
and Pyramidal balance designs offer a better alternative to the issues associated with wire balance designs. Three or four columns support the platform balance. This design provides naturally orthogonal, however the resolving center of the balance is not at the center of the tunnel and additional data processing must be computed. In addition, forces
each column. are calculated as the sum of components acting on The yoke balance
center near the center of design solves this problem by having the moment resolving the
deflection compared to the platform tunnel, however there is typically larger balance
configuration.
12 The pyramidal balance measures moments about the resolving center and is able to
separate and read forces and moments directly vs. summing up components. Alignment
of this design is by far most challenging of the designs. These designs are usually
employed in large-scale wind tunnel facilities. However, through this background
research of basic balance concepts, the following design options have been chosen for the
prototype balances designed and tested in this thesis.
3.3 Balance Design
As discussed in the previous section there are many design option available in
building a mechanical balance. The following section details two prototype designs of a
knife and fulcrum system with each device measuring two degrees of freedom, lift/drag
and pitch/roll moment respectively. These designs incorporate the ideas of a yoke balance design along with the concept of a beam balance system to meet design
requirements.
3.3.1 Reference System
As this experimental investigation aims to study the validity of force and moment measurements of fabricated devices, it is important to assign a standard reference frame to the tunnel, balance, and airfoil system. To accomplish this, a fixed reference sign
convention is assigned to the tunnel test section with origin aligned with the balance
13 apparatus (see Figure 3-1). This reference frame corresponds to the standard definition of
a wind-axis system in which the x-axis points towards the oncoming free stream velocity.
z Tunnel Test Section
Freestream
- Velocity _-_!-
Figure 3-1: Wind-Axis Reference Frame
In addition to the wind-axis system, the industry standard sign convention for a
body-axis reference frame defines the airfoil coordinate system (see Figure 3-2). With
these two references lift, drag, pitching moment and rolling moment is measured. For
example, the x-axis for tunnel wind-axis reference and body-axis reference are always
aligned for both force and moment testing at level conditions (balance at the null/level position and zero degrees pitch and sideslip angle).
14 DRAG
9&$iWtt memsfAs. by defrtlion, mm RIGHT ROLL, NOSE UP KICK, and NOSE RIGHT YAW
tftfCHMG MOMnT CAUTlON-i are
AND HATS;
MOMENT AND RATI LP
Figure 3-2: Body-Axis Reference Frame
3.3.2 Lift and Drag Balance
The lift and drag balance design is based off the principles of a simple knife pendulum system (see Figure 3-3). The idea behind the design is that lift and drag forces may be statically measured by performing a moment analysis about the knife-edge pivot axis. By translating the swivel platform through 90 degrees, these forces can be measured through a sweep in angle of attack. Refer to Figure 3-4 and Figure 3-5 for balance setups.
15 Airfoil Vein Counter Mass
Tare Mass
Protractor
Base Plate
Figure 3-3: Assembly Diagram of Lift and Drag Balance
Three devices are used simultaneously to obtain a force measurement from the
balance. First a protractor indicates the angle of attack ofthe test airfoil. By rotating the
airfoil vein with a key, the angle of attack can be adjusted to an accuracy of 0.5
"inch" degrees. The second component is a graduated scale in units. The scale is
accurate to 1/64 of an inch. The last measuring device is a bubble level used to indicate the balance or null position. The primary components aside from the bolts and veins
were machined from 6061 aluminum through various lathe and milling processes. Refer to Appendix A: for balance detail drawings.
16 r Pivot Axis '^Hp
_. m 1 0
-) -
Vein translates Freestream Vein translates into and out of Freestream Velocity left to right the paper Velocity
Figure 3-4: Balance Configuration to Measure Figure 3-5: Balance Configuration to Measure Lift Force Drag Force
Note: Coordinate systems based on wind-axis reference frame. See section 3.3.1.
In order to size the components of the balance and assign a desired value of accuracy, several assumptions were required. First, the lever arms and veins of the
system were treated as simple beams with a uniform load distribution. The reason for this assumption is due to the simplification ofthe system and the ability to treat the center
of mass of components as point masses. This assumption simplifies the moment
contribution effects from multiple components. Furthermore the error associated with
this assumption is negligible due to the fact that data is always collected when the
"tared" balance is in the null or level position. The term refers to the balance being level
17 from a visual observation of a bubble level indicator. As long as the balance is tared, the effect ofmass distribution is negligible.
The second assumption made to size the balance is the size of the test airfoils. As previously mentioned, the smallest airfoil tested measures 0.394 x 2.657 inches (1 x 6.75) cm. However, to determine the effective range and precision of the balance a minimum test airfoil reference surface area of 1 sq. inch is assumed. Next, a precision on the coefficient of lift and drag is assumed. A value of 0.001 was chosen as a target precision design goal. This value is greater than one drag count ( 0.0001) and is taken to be a reasonable assumption due to the nature of wind tunnel application. Lastly, the minimum sustainable velocity of the RIT wind tunnel was assumed to be 27 ft/sec (8.23 m/sec). The coefficient of drag is
D QS
Equation 3.1
= If CDmin = 0.001, Smin = 1 sq. inch, and Uaomin 27 ft/sec then, the drag balance must be designed to resolve approximately 6.0E-06 lbf or have an accuracy of 3.0E-06 lbf.
= = - An upper limit of CDmax 1 was assumed, with Smax 8 sq. inches, and Uoomax 50 ft/sec
then the balance must have a precision of approximately 1 .6E-01 lbf. Thus the balance
lbf 8.0E-02 a ratio of has design requirements to measure loads from 3.0E-06 to lbf,
the same process is iterated for lift forces. The approximately 27,000:1. Similarly,
coefficient of lift is
18 QS
Equation 3.2
If = = = CLmin 0.001, Smin 1 sq. inch, Ua>min 27 ft/sec, then the balance design is required to
resolve 6.0-06 lbf or have an accuracy of 3.0E-06 lbf. Also, if CLmax = 1.5, Smax = 8
= sq. inch, Uoomax 50 ft/sec, then the balance design is required to resolve 2.5E-01 lbf or
have an accuracy of 1.25E-01 lbf. Thus the balance is required to measure loads from
3.0E-06 lbf to 1.25E-01 lbf, a ratio of approximately 42,000:1. These values of lift and
drag forces are theoretical limits of the intended balance design based on target precision
values.
In order to meet the requirements set by the above process, a sliding mass is used to achieve the desired accuracy and range of force measurements. For example, if a drag force is required to be measured to 2.4E-05 lbf, then a sliding mass of 3 grams will produce a resolution in force of approximately 1.6-05 lbf. These values are desired levels
ft/sec2 of accuracy and assume a standard gravitational field value of 32.2 and a
minimum scale resolution of 1/64 inches. Refer to Figure 3-6 for a pictorial view of lever
arm length description used in the moment summation analysis to obtain the range in force values. Depending on the size of the sliding mass, an appropriate maximum and minimum force range is obtained and may be chosen to meet test requirements.
19 A static moment summation about the pivot axis yields the lift or drag force
on the acting test subject's center of gravity (see Figure 3-6 and Figure 3-7). Therefore
the lifting force can be calculated by
+FL -F-L -R F,LF1l fl m m 2 F2 Lt t^Lift tare tare L_ift
Equation 3.3
the By taring system, i.e. the sum of moments from Fl, Fm, F2, and Ftare equal zero, then a simplified version of Equation 3.3 is
F I
c _ rmJj___ r,LiftM T
Equation 3.4
The benefit of this approach is that the force values can be directly obtained by the position of the sliding mass on the scale indicator at level position.
A similar analysis may be performed for the drag configuration (see Figure 3-7). The only addition is the contribution to vain drag induced by the free stream velocity. Vein drag is not a factor in lift moment summations because the freestream flow is parallel to the pivot axis. The drag moment is calculated by
ftareL^g _ f2LF2 F3LF3 p FjLpj+f-pL-jj rDrag t ^Drag
Equation 3.5
20 Again, taring the system and accounting for the addition of vein drag, a simplified version of Equation 3.5 is reduced to
_ *m^m p Drag j ^Drag
Equation 3.6
Drag forces are also directly obtained by the position of the sliding mass on the graduated scale at balance level position.
21 Lf2 -tare Lfi
*i ?
F L
F, tare *i ?
ir if V .r
O F2
Free stream velocity is into the plane ofthe paper.
-Lift
LFi = lever arm distance to eg (long) Lf2 = lever arm distance to eg (short) Lnft = lever arm distance to eg of airfoil Airfoil Lm - lever arm distance to sliding mass Ltare = lever arm distance to tare mass Fi = point mass force of lever arm (long) F2 = point mass force of lever arm (short) = FLift Fm Sliding mass force Ftare = tare mass force Fiift = lift force
Figure 3-6: Moment Analysis Diagram -Lift Configuration
22 Lf2 -tare
J_.F1
? *t ?
i m _L/m F, tare *t ?
^r \r "_ ]' S> ii ik
o F2
Lf3
Free stream velocity is parallel to the plane ofthe
paper.
Ldj'rag
Lfi = lever arm distance to eg (long) Lf2 = lever arm distance to eg (short) Lorag = lever arm distance to eg of airfoil Lm = lever arm distance to sliding mass Ltare = lever arm distance to tare mass Lf3 = lever arm distance to eg ofvein Fi = point mass force of lever arm (long) F2 = point mass force of lever arm (short) Fm = Sliding mass force Drag Ftare = tare mass force FDrag = lift force F3 = drag force of vein
Figure 3-7: Moment Analysis Diagram for Drag Balance Configuration
23 3.3.3 Pitch and Roll Moment Balance
The pitch and roll moment balance is also based on the principles of a simple knife-pendulum system (see Figure 3-8). By performing a static moment analysis of the
device at level position about the knife-edge axis, pitching and rolling moments of a test
airfoil is measured. The swivel platform is capable of rotating 90 degrees with a pitch
angle range of 0 to 12 degrees. Both pitching and rolling moment may be measured
through varying angles of attack or sideslip angles.
Figure 3-8: Assembly Diagram of the Pitch and Roll Moment Balance
74 The test platform is fabricated from welding rod arranged in a y-shape and is designed to accommodate a maximum size airfoil of 2.362 x 3.543 inches (6x9 cm). In
order to ensure that moments are summed about the airfoil quarter chord point the test platform is raised to the same pivot point as the test platform links. This helps to simplify calculations in taking moments about the quarter chord of an airfoil. In this case, the platform links are stainless steel snap swivels (see Figure 3-9and Figure 3-10 ). In order to adjust the pitch angle of a given airfoil, one of the three veins is adjusted by increasing or decreasing its length. An adjustable turnbuckle and threaded rod is capable of increasing or decreasing the pitch angle to a resolution of approximately 0.3 degrees per revolution. The turnbuckle has a 4-40 thread and can provide a range of angle deflection from 0 to 12 degrees (see Figure 4-8).
Platform Linksi Airfoil Mounting Vein \
Y-bar Test Platform
Figure 3-9: Assembly Diagram of the Test Platform for the Pitch and Roll Moment Balance
25 Figure 3-10: Fabricated Welding rod Test platform
Three devices are used simultaneously to obtain a force measurement from the
balance. First a protractor indicates the sideslip angle of the test airfoil. By translating the
swivel plate, the sideslip angle may be adjusted to an accuracy of 0.5 degrees (see
"inch" Figure 3-11 and Figure 3-12). The second device used is a graduated scale in
units and indicates the lever arm distance of the sliding mass. The scale is accurate to
1/64 of an inch. The last measuring device is a bubble level used to indicate the balance
null or level position. The primary components aside from the bolts and veins were
machined from 6061 aluminum and Plexiglas. Refer to Appendix B: for balance detail
drawings.
In order to size the components a similar process in sizing the lift and drag balance is implemented. The assumptions made are: 1) lever arms and veins of the
26 system may be treated as point masses at their respective eg, 2) the minimum geometry of a testable airfoil is approximately 2 sq. inch in reference planform area, 3) the precision of the coefficients of pitch and roll moments are desired to be accurate to 0.001, and 4) the minimum sustainable velocity of the RIT wind tunnel was assumed to be 27 ft/sec
(8.23 m/sec) with a maximum velocity of 50 ft/sec (15.24 m/sec). All measurements are taken at the balance null or level position. The coefficient of pitching moment about the
quarter chord is
M C - m"4 QSc
Equation 3.7
If Cmmin = 0.001, Smin = 2 sq. inch, and Uoomin = 27 ft/sec from the above assumptions then, the moment balance must be designed to resolve approximately 2.0E-06 ft-lbf or have
= of = 1 was assumed with 9 an accuracy of 1.0E-06 ft-lbf. An upper limit Cmmax Smax
= balance must be able to resolve sq. inch, and LUnax 50 ft/sec. For these values, the
1.96E-02 ft-lbf. Thus the balance has approximately 3.8E-02 ft-lbf or be accurate to
.9E-02 theoretical design requirements to measure loads from 1 .OE-06 ft-lbf to 1 ft-lbf, a
on the size of the an ratio of approximately 19,000:1. Depending sliding mass,
obtained and can be chosen to appropriate maximum and minimum moment range is
of and assume a meet test requirements. These values are desired levels accuracy
minimum scale resolution of 1/64 standard gravitational field value of 32.2 ft/sec and a inches.
27 The same analysis is iterated for the roll moment configuration seen in Figure
3-12. The coefficient of rolling moment is
R C = QSb
Equation 3.8
A minimum reference surface area of 2 sq. in, minimum free stream velocity of 27 ft/sec,
and Crmin = 0.001 was assumed. Upper limit values are a maximum reference surface
area of 9 sq. inches, maximum free stream velocity of 50 ft/sec, and Cmiax = 0.15. These
values yield a theoretical design load range from 1.0E-06 ft-lbf to 4.3E-03 ft-lbf or a ratio
of approximately 4300: 1 .
Veins iran-haia in ih< /firiicol clir^clion Alrfcil I'M otk. Lfjrfc.il pi:! [vint Veins U'.irtslijls -----^ Jp ond dciri Fr$sire-imv_J:iijr
iFrgceiream yc-tocEy |
Figure 3-12: Rolling Moment Balance Moment Balance Figure 3-11: Pitching Configuration Configuration
Note: Coordinate systems based on fixed tunnel reference frame. See section 3.3.1.
28 Due to the system design, the moment balance is self-centering meaning that it wants to find its level position. This is because the center of gravity is much lower than the knife-edge pivot axis. Because data is collected at the level position, moments can be easily summed and pitch or roll moments are directly measured and corrected due to tare
effects.
Fm = Sliding mass force x = distance to sliding mass from pivot M = Pitching moment about airfoil quarter chord
O = pivot point
UQ
Figure 3-13: Pitch Moment Analysis Diagram
29 Fm = Sliding mass force x = distance to sliding mass from pivot R = Rolling moment about airfoil quarter chord
O = pivot point
Ua> is into the
paper
Figure 3-14: Roll Moment Analysis Diagram
With the balance in the level position, pitching or rolling moments can be directly
mass and position relative to measured and are found to be the product of the sliding its
the knife edge pivot axis:
M or R = xFm
Equation 3.9
30 3.4 Test Airfoil Design and Specifications
There are several airfoil profiles used to test the functionality of the prototype balance devices. To begin, all airfoil profiles were cut from aluminum sheet metal to their appropriate geometries. Readily available sheet aluminum of various gauges is used
to produce the desired airfoil profiles. The following tables summarize the airfoils used
in this research:
Airfoil (1): Flat Plate la Airfoil (3): 4% Cambered Airfoil
c = 1cm c = 6cm
- = 0.0328ft 0.1969ft
b = 6.75cm b = 9cm
= 0.2215ft = 0.2953ft
0.0073ft2 0.0581ft2 S = S =
= AR = 6.75 AR 1.5
= thickness = 5% thickness 1%
= chamber = 0% camber 4%
10 Airfoil (2): Flat Plate lb Airfoil (4): Dihedral Airfoil
c = 6cm c = 1cm
= 0.1969ft = 0.0328ft
= b = 9cm b 6.75cm
= = 0.2953ft 0.2215ft
0.0073ft2 0.0581ft2 = S = S
= AR = 1.5 AR 6.75
= thickness = 1% thickness 5%
= camber = 0% camber 0% 10 r =
31 Airfoil (1) is used in lift and drag balance testing. The geometry matches that of published works by reference 5. Airfoil (2) is used to calibrate the pitch moment balance.
By collecting data at various angles of attack a theoretical tare moment as a function of angle of attack is approximated and used as a correction factor for cambered flat plate data (refer to section 4.2.2). Airfoil (3) is based on geometry data from published works from reference 21. Lastly, Airfoil (4) is used to test the rolling moment balance performance. This geometry was chosen due to the ease of approximating the rolling moment coefficient by analytical calculations and model simulations through a code
called "LinAir". All airfoil profiles are modeled as flat plates with blunt leading and
trailing edges.
32 Chapter 4 Experiment Methods and Design
4. 1 Design of Experiment
The problem addressed in this research is to evaluate the performance of two
prototype balance devices described in Chapter 3. In order to qualify the devices, a
systematic data collection approach and statistical evaluations are involved. The
evaluation process includes an assessment of data uncertainty and analysis of
repeatability in the data acquisition process. A comparison of experimental data to
published values and analytical results is also included as part of the qualification process.
A detailed experiment structure that outlines experiment parameters is the starting
point of experiment planning. Figure 4-1 shows a block diagram representation of the
wind tunnel experiment used as a foundation for the experiment described in this section
[12]. The input vector represents variables such as model angles of pitch and yaw. More
specifically, the angle of attack varies between 0 to 30 degrees in increments of 3 degrees
for both lift and drag experiments. The pitch angle varies between 0 and 12 degrees. And
lastly, the sideslip angle is variable from 0 to 90 degrees. The desired precision of
coefficients of lift and drag is 0.001 while the desired precision of the coefficients of
pitch and roll moment is 0.01 . Refer to section 3.3 for more details.
33 Figure 4-1: Diagram of Experiment Elements
The model size, model materials, and balance mass components are examples of controllable variables of this experiment. As previously mentioned, the design requirement goal is to have a device easy to incorporate with the RIT wind tunnel and easy to manufacture. The direct output values obtained by balance devices are length, measured from a graduated scale. From length measurement and static equilibrium equations described in chapter 3, output values of forces in the case of the lift/drag balance and moments, in the case of the pitch/roll balance may be computed. Examples
of components of the uncontrollable factors are the tunnel turbulence level of free stream velocity, tunnel air temperature and humidity, model deformation effects and human
errors associated in measurement observations. The tunnel operation limits were also
considered a factor of uncontrollable elements in experimental design even though
minimum and maximum ranges were assumed in the prototype design. With the
34 aforementioned variables accounted for, the following experiment methods were developed.
4.2 Experiment Analysis
Three basic principles in the design of experiments as identified by Montgomery focused on test planning [13]. These key principles are (1) Replication which refers to the requirement for much iteration, (2) Randomization which refers producing repeated iterations from independent random variables, and (3) Blocking which is in effect the opposite of randomization and used to isolate a particular effect such as power on/power off experiments. With these principles in mind the following section defines calculation methods and procedures of the data acquisition process.
4.2.1 Lift and Drag Experiment
To assess the performance of the lift/drag balance, published data and experiments by Sunada et. al. was chosen as a benchmark for comparison [5]. First, flow similarity parameters were calculated to meet the wind and water tunnel test parameters in the published papers. Also, similar profile airfoils were fabricated with matching aspect ratio, thickness ratio, and 2D profiles (refer to section 3.4). The experiment device
and Figure 4-3 below. setup for lift/drag testing is shown in Figure 4-2
35 Figure 4-2: Lift Configuration Figure 4-3: Drag Configuration
Ambient conditions were recorded prior to the start of data collection. The
ambient pressure recorded for each case of testing was the value observed at the local
airport. A temperature transducer positioned in the flow of the wind tunnel is used to check ambient temperatures. Due to the low speeds involved during testing, (Mach number ~ 0.03) static values were assumed to be approximately equal to the total value.
From these values the density of air may be calculated from the ideal gas law and dynamic viscosity is calculated from Sutherlands correlation. A Type 223 Baratron general purpose differential pressure transducer is used to measure the total dynamic pressure of the free stream velocity to an accuracy of approximately 5.3%. From this, a value of velocity is obtained. For lift testing, the test airfoil and balance apparatus setup is shown in Figure 4-2. The free stream velocity vector is parallel to the wind system x-
36 axis. The tunnel velocity is increased to match the published data's experiment value of approximately Re = 5500. With the balance tared, lift data is collected verses angle of attack at increments of 3 degrees from 0 to 30 degrees. Each run colleted 10 data points and a total of 20 runs were taken at angle of attacks of 0, 15, and 30 degrees for statistical analysis. Data was collected over a period of two to three days in which the devices as
assembled and disassembled for each test period. Refer to Appendix C: for detailed
outline of experiment procedures.
A similar process for data collection was performed for the drag tests with a setup as shown in Figure 4-3. Again data was collected at varying angles of attack from 0 to 30 degrees in increments of 3 degrees. Twenty runs were collected at angles of attack of 0,
15, and 30 degrees. The variation in drag testing vs. lift testing is the additional inclusion of the vein drag. To assess the tare drag from the vein, ten runs were measured without a test airfoil and an appropriate drag value is computed at a Reynolds number of 5500.
This tare value was applied to the moment analysis described in section 3.3.2 and used to
for a detailed outline of experiment correct the raw drag data. Refer to Appendix C:
procedures.
4.2.2 Pitch and Roll Moment Experiment
published data from To analyze the performance of the pitch/roll moment balance
Thomas J. Mueller and analytical models were chosen experiments by Alain Pelletier and
published these flat and as a benchmark for comparison. In the works by authors,
tested at Reynolds numbers cambered plate airfoil profiles with low aspect ratios were
37 between 60,000 to 140,000 [3]. Setting up flow similarity parameters involved collecting
ambient conditions data and setting up test parameters similar to the process used in
lift/drag experiment. Again, similar profile airfoils were fabricated with matching aspect
ratio, thickness ratio, and two-dimensional profiles. The experiment device setup for
pitch/roll moment testing is shown in Figure 4-4 and Figure 4-5 below respectively. The
free stream velocity ofthe wind tunnel is parallel to the wind axis x-axis.
Figure 4-4: Pitch Moment Configuration Figure 4-5: Roll Moment Configuration
collection. The Ambient conditions were recorded prior to the start of data
weather reports and assumed to be ambient pressure was obtained by local airport
conditions. A temperature transducer is used to approximately equal to tunnel ambient
38 check tunnel free stream velocity temperatures before, during, and after test runs. Due to the low speeds at testing static values were assumed to be approximately equal to the total value. To calibrate the pitch moment balance, a flat plate (airfoil(2) refer to section
3.4) is used. With the tunnel off condition, a calibration plot of moment vs. pitch angle is
used to approximate the moment at balance level position. These values provide a reference point for data collection at tunnel on condition. In other words, the difference between moment values calculated at pitch angles with the tunnel on and tunnel off, yields the raw moment data of the test airfoil. At zero degrees angle of attack, the pitching moment of a flat plate should be zero. Therefore the calibration of the balance using a flat plate also revealed a bias tare moment of the device whose value is used as a data correction factor (see Figure 4-6). Values for approximating the moments and data correction factor are obtained using methods described in section 4.3.
39 Flat Plate Moment Calibration - Zero Velocity (Value indicates the moment at level positon)
0.06
r--~.._ 0.05
c-
~- ^ ___ # 0.04
= + y -0.0023X 0.055 ^
R2 = 0.9843 0) ~__ 0.03 | i E J O) a oo2 b_
1 1 1 I
4 6 8
Angle of Attack, AoA (degrees)
? trial 1 trial 2 trial 3 x trial 4 x trial 5 average + theoretical Linear (average)
Figure 4-6: Flat Plate Moment Calibration Plot (Zero velocity and no airfoil)
Flat Plate Pitching Moment Analysis (Re = 40,000)
0.0100
0.0000 11 1 ' 1 (1 2 6 8 10 12 . fl
-0.0100 e > I
-0.0200
-0.0300 i ?
-0.0400
*> -0.0500
J -0.0600
Angle of Attack, AoA (degrees)
plate- Flat plate-no correction Linair Results . Flat data correction
Figure 4-7: Flat Plate Pitching Moment Data
40 The pitch balance zero angle bias error is found to be 0.015 in-lbf. This value was obtained from the flat plate pitching moment analysis. It is well known that the pitching moment about the quarter chord of a flat plate is zero. Knowing this theoretical value and comparing the difference from experimental values, the above stated difference in moment was computed and used to correct pitching moment data. Figure 4-7 compares the experimental pitching moment data corrected for zero angle bias error and LinAir results. It is promising to see that the balance bias correction factor improves the correlation between analytical LinAir model and experimental results. However there is great disagreement at six degrees angle of attack. This may be due to leading edge vortices and flow separation observed in literature works by Sunada et. al., not modeled in LinAir. This result is further discussed in Chapter 5.
With the calibration data in hand, the same procedure for a 4% cambered airfoil
(airfoil (3)) is iterated. This data provides a reference moment for data collection at tunnel on condition for airfoil(3). The input variable for pitch moment testing is pitch angle and is adjusted by lengthening or shorting a balance vein by the use of a swivel link
(see Figure 4-8). The measured output value is the distance of the sliding mass from the pivot axis ofthe knife edge. With these measurements twenty runs at pitch angles of 0, 6,
and 1 1 degrees were recorded. Refer to Appendix C: for procedure outline.
41 Figure 4-8: Pitch Experiment Test Platform Setup
A simple 10 degree dihedral flat plate, (airfoil (4)) is tested for roll moment
analysis. A single input variable, sideslip angle, is used to obtain an output moment from
the balance device with a zero degree angle of attack. Again, the distance of the sliding
mass from the pivot axis of the knife edge is recorded for various angles and a
corresponding moment calculated. The sideslip angle is adjusted by rotating the swivel plate through a desired angle deflection. From this information, a moment value is computed and corrected for balance tare due to drag effects. Data is collected for sideslip angles of 0, 6, and 9 degrees at an angle of attack of 0 degrees. Refer to Appendix C: for
experiment procedure outline.
42 The task of assessing the reliability in roll moment data is most challenging.
Published works on low Reynolds flow and roll moment of small airfoils is not yet
available. readily Therefore to test the reliability, analytical approaches outlined in
section 4.3 were implemented. The first method of analysis is a simplified linear
calculation of roll stability. LinAir is also used to provide an approximation to the roll
coefficient. These two methods will be discussed and compared to experimental values.
4.3 Computational Analysis
4.3.1 LinAir
"LinAir" A software code called is used to model and analytically obtain moment
coefficients as a function of input pitch and sideslip angles of flat plat airfoil geometries.
LinAir is a vortex lattice program for computing the aerodynamic characteristics of multi-element lifting surfaces. The program can be used to determine the appropriate wing twist for a new design, the expected performance of a given wing geometry, the proper angles of incidence for tail or canard surfaces, or the stability characteristics of a new configuration [14]. For the purpose of this research, LinAir is used to provide analytical models for the general behavior ofmoment coefficients of flat plate airfoils.
LinAir solves the Prandtl-Glauert equation, a linear partial differential equation describing inviscid, irrotational, subsonic flow. The flow is assumed to be (1) inviscid,
(2) fully attached; no separation, (3) low angles of deflection, and (4) thin plate airfoil geometry. Figure 4-2 is a sample output graphic from LinAir.
43 Reference Values
Sref: 0XJSB1 v bref: 0.2953 Xref: Oj0492 Panne I Yref: OXXXK) a-ef: 0.0000 Netem: 2 Control alpha: OjOOOOO Point beta: OjOCOOO pht-fc 0OCO00 fjhat 0.00000 rhat 0.00000 Mach: 000000 W*eLoc: 1.000 reflect: 1 CLRle: CL m.d_t I enent FdrceFilefdrces mdat ElemerrFileSem mxtat
Figure 4-9: LinAir Vortex Panel Method Airfoil
4.3.2 Roll Moment Analysis
The roll moment on an airplane when it starts to sideslip is a function of wing dihedral and wing sweep, wing position on the fuselage and vertical tail location.
However the greatest effect is from the wing dihedral angle T. A derivative of a roll stability derivation by Nelson [15] is used to derive an approximation formula for rolling moment coefficient. The incremental change in roll moment due to a change in lift can
be expressed as
AC, =(ALift)y
Equation 4.1
a summation of lift If the lifting surface is broken into i strips along the span, then
a contributions from zero to i can provide an approximation for wing lift assuming
uniform lift distribution.
44 Vv-rtical Wing profile
Vhoiizontal
Figure 4-10: Dihedral and Roll Moment Profile
= For ~ small sideslip angles and small angle approximation, Vss Vsin(P) ~vp, and Vssn
~ Vpr. The angle of attack is increased by a sin(a) ~ VverticaiA^. The effect of dihedral
angle is in effect to increase alpha, the angle of attack. Therefore, the new angle of attack
due to sideslip and dihedral angle is a + f3T. From this relationship, lift may be defined
as
Lift^Q,S,(Claa) i
Equation 4.2
where curve slope and a equal a + above Qa is the 2D lift is to BT , from the discussion.
Also for a dihedral wing, y-bar may be approximated as b/4. Therefore equation 5.2 may be shown in coefficient form as
45 2>.M(C/a/T)
___j ^ = ______4QSb 4
Equation 4.3
This equation was used to generate rolling moment coefficient values for a 10 degree dihedral angle, input sideslip angle, and an averaged 2D lift curve slope obtained from 3D lift data of a similar profile flat plate geometry (see Figure 5-8). A uniform lift distribution (2D) has been assumed in this analytical technique.
4.4 Statistical Analysis
Two methods are employed in analyzing the sets of experimental data. The first method is called a student-t analysis and is used to draw inferences of a sample's mean and standard deviation for small sample populations. As the sample size increases, the students-t distribution converges to the results of a normal distribution. For n > 100 the t- distribution and normal distribution are barely distinguishable. The quantity
t- y-vo
/7ry/n
Equation 4.4 [20]
is called the t-statistic and its distribution is called the student's t. The degrees of freedom parameter is defined as
46 df = n - 1 ; where n = number of observations
Equation 4.5
A two tail student's t distribution is applied to force and moment data to quantify a factor of repeatability. This method provides a 100(l-a)% confidence interval for a sample
population's unknown mean and standard deviation from each data set. The confidence interval is defined as
"
, s /2 Vn
Equation 4.6
Where, df = n-1 and the confidence coefficient is (1-a). A 95% confidence interval is
calculated from experimental data. Test procedures are outlined in Appendix C: and a summary of statistical results is found in Appendix D:.
A second method of analysis is a technique for measuring variability on a single variable coupled with curve fitting techniques used to approximate an unknown mean.
This method is ideal for small sample populations possessing a mound-shaped distribution. In most cases, a linear curve fit is adequate in approximating a sample data set. From the curve fit equation, a theoretical mean value is found and assumed to be the sample's mean. From this assumption, a sample variance is calculated. The equation for
sample variance is
y)2
,, . 2 = y Vanance= s > ivrz
, n \
Equation 4.7
47 where y-bar is the theoretical mean calculated from the curve fit equation, n is the
i* number of observations and y; is the observation in a sample population of size n. The
standard deviation for a sample is defined as
s = VVariance
Equation 4.8
The following is an example in determining a confidence interval for tare moment of a flat plate used in the pitching moment experiment. First, pitching moment vs. pitch angle data is approximated by a linear curve fit (see Figure 4-6). From the linear curve fit,
a theoretical mean value is calculated and used to estimate the sample's variance and standard deviation from Equation 4.7 and 4-5 at any pitch angle. Given a set of n measurements possessing a mound-shaped histogram the interval, y-bar 2s contains approximately 95% of the measurements [20]. Therefore a 95% confidence interval is calculated for linear or non-linear data sets of small sample sizes whose distribution is approximately normal.
4.5 Uncertainty Analysis
A method used in Mueller's analysis was developed by Kline and McClintock and is used to determine the uncertainties in experimental data [2]. This method involves
uncertainties associated with experimental measurements of pressure, temperature, lengths and the accuracy of measurement instruments [12]. From Equation 3.3 and
Equation 3.4 the following relation is developed for the uncertainty in the coefficient of
48 lift. "W" Capital in the following formulas represents error quantities, similar to notation used in reference 1 1 .
FI 1
LLift Qbc
Equation 4.9
From this equation the force uncertainty (W) is calculated as
2 2 2 (dC,WFm^ ^ rdCLWQ^ 2 L m fdcjvbX facjvc = rdCLWLm fdCLWL/ wc + + + | , , rrr db dc {\ 9Fm J \ SLmrn J K dLft j v dQ j [ Equation 4.10
By dividing by Cl equation 4.6 simplifies to
Wr (tistWL \ fWQ^ fWb^ fWc^ uft + + + + c, V Fm J \ L"ft J V ^ J \ o ) \c )
Equation 4.11
Similar equations are derived for drag, pitching moment, and rolling moment coefficients and are shown below.
Error function: Drag coefficient:
\2 V (nrr ( WL (Wb^ fWc^ Wr WL drag fWF^ + + + (WQ} + + F o c cr V ^drag J v Q-1 J V j \ J
Equation 4.12
49 Error function: Pitching moment coefficient:
2 ^z^V /x2 (Wc^1 Wn rWF.y (Wx WQ Wb + + + + 2 C x o , Fm J ^ ,Q J \ J V c )
Equation 4.13
Error function: Rolling moment coefficient
r \2 W, fWx^2 rWQ" (Wc^2 Cr rWbX . + + 2 + c x o c K Fm , V J \ j V )
Equation 4.14
As "W" previously mentioned, the capital represents uncertainty quantities associated
with equipment accuracy. The following table summarizes the precision in values of each
corresponding variable involved in the above equations.
Table 4.1: Uncertainty of measurement variables
Minimum Resolution/error Sliding mass = 0.05 Grams Ruler scale = 1/64 Inches Vein length = 1/64 Inches Dyn. Press. = 0.5%
= Span .001 Inches
= Chord .001 Inches
From the above derivation, uncertainties in force and moment coefficients are calculated based on the minimum resolution of experimental equipment shown in table
4.1. The values summarized in table 4.2 for force and moment coefficients assume a
standard gravitational field, a range of sliding mass deviation in length between .01 and 2 inches, and associated dynamic pressure during testing conditions. Similarly, the
50 minimum resolution in force and moments are obtained by moment analysis methods outlined in section 3.3. The values obtained from the analysis assume a minimum scale
l/64th resolution of inches and a standard gravitational field value. Refer to table 4.2 for a summary ofthe averaged uncertainty results.
Table 4.2: Summary of predicted uncertainty obtained from experimental methods
Uncertainty in. . . Coefficient Force or Moment Resolution*
Force 0.008 5.0E-05 lbf
Moment 0.002 1.5E-04 in-lbf
* Nominal Q = 0.8548 psf and S = 0.0073 sq. ft.
51 Chapter 5 Results
5.1 Lift Results
Lift data is collected by methods described in Chapter 4. Figure 5-1 shows the
collected of angle of data attack vs. lift coefficient curve for a flat plate of aspect ratio
6.75 and Reynolds number 5500. To provide perspective of the scale of forces measured
in this experiment (approximately in the order of 10"3lbf), lift force is shown on the
secondary axis and plotted as a solid line. Bright red data points represent the average of
20 runs collected at 3, 15, and 30 degrees. For these angles a 95% confidence interval for the coefficient of lift is found to be (0.27633, 0.29646), (0.66903, 0.68335), and (0.79533,
0.80734) respectively.
From Equation 4.11, the theoretical value of uncertainty for lift measurements is found by taking the average uncertainty over the range of eight test runs at angles of attack between 0 and 30 degrees. It was found that that there is an average deviation of
0.008 based on the values from Table 4.1. The deviation was found to slightly increases with higher angle of attack and may be attributed to the increased oscillation of the airfoil and vibration ofthe balance and wind tunnel system.
52 Plot of Lift Coefficient and Lift Force vs. Angle of Attack for a Flat Plate (AR = 6.75 & Re = 5500)
0.006
i 0.005
-sr
0.0004X3 3X2 y = + - 0.01 + 0.1 58x
R2 - = 0.9919 0.002
- 0.001
10 15 20 25
Angle of Attack (degrees)
Data Set 4 ? Data Set 1 Data Set 2 Data Set 3
- Set 8 X Data Set 5 Data Set 6 + Data Set 7 Data
- - Average Values ? avg. of 20 runs Lift Force Poly. (Average Values)
Figure 5-1: Experimental Values of Lift Force and Coefficient
In Figure 5-2, published data from Sunada et. al. [7] for a flat plate of aspect ratio
obtained in this research. 6.75 and Reynolds number 4,000 is superimposed with results
conditions Dark black circles represent the airfoil tested at the prescribed (Re=4000,
experimental data shows good agreement of the lift curve same geometry airfoil). The
there is a similar occurrence of a stall region profile with published values. By inspection
Sunada et. al. recorded a 3D lift curve at an angle of attack at approximately 12 degrees.
= at 5 degrees angle of attack. From slope of 5.8 per radian and (Cl/CdW 5.5
53 experimental data, a 3D lift curve slope of 4.98 per radian (a difference of 9.45%) and an
= approximated (CL/CD)max 5.7 at 5 degrees angle of attack (a difference of 5.56%) was calculated.
Glauert's calculations approximate the 3D lift curve slope for a rectangular planform wing with aspect ratio equal to the span divided by chord as
ln r - \ + (2IAR)(\ + r)
Equation 5.1
For an aspect ratio of 6.75 and a theoretical 2D lift curve slope value ao=27i, Glauert
~ ~ found x .165 and 8 0.05 [1 16]. With these values a 3D lift curve slope value of 4.67 per radian is calculated. The experimental value is greater than the theoretical value by
6.6%. Similar results of higher experimental 3D lift curve values were recorded in low
Reynolds flow experiments by Laitone [10].
54 Plot of Lift Co. fficisnt vt. Anyla of Attack for a Flat Plats (AR 6.75 8, P.a <* ESOO)
1 1 1
0 9
-~ *~*^r _- . O.B
-*-<"""^ 5 o_e> - 0.5 / y=-5-06..' 0 0004k'- 0 01 3x' 0.1 58x 0 4 - 0.3 - - '-_. 0 2 - Shaded circles represent a 5% thick flat plate AR = 6.75 / Shaded triangles represent a 2.5% thick flat plate AR=6.75 0 1 - 1 0 5 10 15 20 25 30 AiHjt*. ..r Attach .i.*.ji*<.s. ? Data Set 1 Data Set 2 Data Set 3 Data Set 4 Data8et5 - Data 8et 6 Data Set 7 Data8et8 Average Values ? avg of 20 runs Polv (Average Values) Figure 5-2: Comparison of Experimental Lift Data to Published Data (Experiment data- colored foreground & published values - black & white background) 5.2 Drag Results For the same airfoil, drag coefficient and force results are summarized in Figure 5-3. To provide perspective of the scale of forces measured in this experiment (approximately in the order of 10"3lbf), lift force is shown on the secondary axis and plotted as a solid line. Bright red data points represent the average of 20 runs collected at 0, 15, and 30 degrees. For these angles a 95% confidence interval for the coefficient of lift is found to be (0.02898, 0.03612), (0.26593, 0.27384), and (0.54818, 0.55887) respectively. 55 Coefficient of Drag and Drag Force vs. Angle of Attack for a Flat Plate (AR = 6.75 & Re = 5500) 0.60 i To 0 50 t .A. 0 0025 c 0 0020 o IL Ol ra - 0.0015 Q 0 0010 9E-05X" y = + 0.01 51 x + 0.0251 R2 ? = 0 9988 >o X 10 15 20 Angle of Attack (degrees) Data Set 1 Data Set 2 Data Set 3 x Data Set 4 Data Set 5 ? Data Set 6 Data Set 7 - Data Set 8 ? average value ? avg of 20 runs - Drag Force Poly, (average value) Figure 5-3: Experimental Drag Data Experiment results are superimposed with published data from Sunada et. al. [5] in Figure 5-4. The un-shaded white triangles represent an airfoil of aspect ratio 6.75 and Reynolds number of 4000. By observation there appears to be good agreement between experimental and published values. A zero lift CD was found to be 0.033 vs. 0.045 published by Sunada et. al. The theoretical drag coefficient error calculated from Equation 4.12, is found to be an average of 0.003 throughout the operation range of the average error from the first drag measurements. This value is obtained by taking eight test runs at angles of attack between 0 and 30 degrees. 56 Coefficient of Drag and Drag Force vs. Angle of Attack for a Flat Plate (AR = 6.75 8. Re = 5500) 0 50 -| 0.45 Un-shaded triangles represent a 5% thick flat plate AR = 6.75 Un-shaded circles represent a 2.5% thick flat plate AR=6.75 0 40 0 35 030 025 j . 020 0 15 -y^-g_Ki5' + C FP = 0.9988 0 10 0 05 ;-- 0 00 -I 8 10 12 20 i.nc)le of Attack (degrees) Data Set 1 Data Set 2 Data Set 3 . Data Set 4 - ? Data Set 5 ? Data Set 6 Data Set 7 Data Set 6 average value avg of 20 runs - - Poly, (average value) Figure 5-4: Comparison of Experimental Drag Data to Published Data (Experiment data-colored foreground & published values - black & white background) 57 5.3 Pitch Moment Results Pitching moment data was obtained by methods described in Chapter 4. Level moment tare values were subtracted from the total moment obtained during testing as a correction factor to account for the shift in the airfoil's center of gravity at respective angles of attack (see Figure 4-6 for moment tare calibration plot). Also, a correction factor for balance zero angle bias (refer to section 4.2.2) was applied to the raw data. Figure 5-5 is a summary of experimental results for pitching moment and coefficients. The secondary axis of Figure 5-5 shows the magnitude of moments analyzed in low Reynolds flow and small airfoil geometries. Pitching Moment and Coefficient vs. AoA for a 4% Chambered Flat Plate (AR = 1.5 and Re = 40,500) 0.00 0 & 2 4 6 8 10 12 14 16 18 2O -0.05 - -0.005 . ? * f E I i a c _ _ - -0 20 -0 02 - -0.25 -0.025 Angle of Attack (degress) ? Pitching moment coeff. a Pitching Moment Figure 5-5: Experiment Pitching Moment Data 58 Alain Pelletier and Thomas Mueller published data on a 4% chambered flat plate = with an aspect ratio of 1 .5 and Re 60,000. Figure 5-6 shows a comparison between corrected experimental results (blue diamonds) and published values (un-shaded white diamonds). The data comparison shows good agreement at the higher pitch angles tested however at a zero angle of attack there is approximately a 43% difference in value. This large deviation in value may be attributed to the setup of the airfoil prior to testing. A slight initial negative pitch angle may be attributed to a percentage in error of the first reading. A finer resolution in pitch angle data collection is required to better analyze effects at the zero angle location. It is promising however that data has been repeatedly collected by the prescribed process. It may be a fact that there is a bias factor not taken into consideration. The theoretical uncertainty analysis ofpitching moment values shows an average error of 0.002, computed by methods described in section 4.4. 59 Pitching Moment Coefficient vs. AoA for a 4% Chambered Flat Plate (AR ~ 1.5 and Re = 40.500) 0.00! 1B 20 -0.05 /\ -0.10 Un-shaded diamonds represent a 4% cambered airfoil -.20 AR=1.5 Un-shaded triangles represent a 4% cambered airfoil AR=3 0.26 Ali'lle 'tt An.uk lile tHeosl ?Avg. of 20 runs Figure 5-6: Pitching Moment Experimental and Published Values (Experiment data- colored foreground & published values - black & white background) 5.4 Roll Moment Results There is a lack of published information on low Reynolds flow and roll moment coefficients for very small airfoils. Therefore to assess the performance of the rolling moment balance, a 10 degree dihedral airfoil was chosen for several reasons. First, testing a similar flat plat airfoil profile with aspect ratio of 6.75 provided a means for calculating an approximate value of the rolling moment coefficient by use of the 2D lift curve slope obtained from experimental data. Secondly, the previously discussed computational "LinAir" program called provided another means to estimate the rolling moment 60 coefficient of flat plate airfoils (refer to section 4.3.2). Figure 5-7 shows the moment and coefficient ofroll for a 10 degree dihedral, 6.75 aspect ratio flat plate. Rolling Moment & Coefficient for a 10 Degree Dihedral Airfoil (AR = 6.75 & Re = 6800) - 0.005 -i 0.0002 -_ i ) - 2 3 4 5 6 7 8 9 10- 11 J 0 *^ "^ ^ -v V. - -0.0002 - - o v ^ - - ^ ^ T = ^ -0.004X + 0.0006 ^ y " R-* -> = 0.9935 a ,_, - -0.0006 ^^ "1 - 1 -0.0008 - -0.04 - - -0.001 -0.045 Angle , Sideslip (degrees) Roll Moment Coeff. Roll Moment Linear (Roll Moment Coeff.) Figure 5-7: Experimental Data; Rolling Moment experimental it is clear that By comparing hand calculations, LinAir, and values, increased. is apparent that the hand there is a huge deviation as the sideslip angle is It inaccuracies of the calculation overestimates the roll moment coefficient due to the assumption of a uniform lift distribution. formula at high angles of sideslip and the big obtained from lift of a high aspect Also, an unusually high 3D lift curve slope testing attribute to a percent ofthe deviation. ratio airfoil at low Reynolds number may 61 Conversely LinAir shows a better agreement to experimental values with a deviation of approximately 14% at the maximum sideslip angle tested compared to a 47% deviation from hand calculated values. It should be noted that the only calibration of the balance is the tare comparison conducted with the wind tunnel on and no airfoil, and with the tunnel on and airfoil present. This analysis investigates bias error in the balance design. An unknown bias error due to yaw effects may attribute to the deviation seen in the results. Flow separation and leading edge vortex effects as seen by Sunada et. al. in flow visualization experiments [5] may also cause discrepancies between experimental and analytical results. Rolling Moment for a 10 Degree Dihedral Airfoil 0.005 - oi () ^-T^r]--^^ 23456789 10 - -0.005 " ~~ """ ~ - - R2 - - = -^ -T _ 0.9935 - -0.01 " ^ = - . """""- -0.0024X a__. y 3E-05 ^ ~~--__ - R* -0.015 ' - . """--__. "---_ = 0.9999 o_ O - -0.02 - -0.025 ~_ " _k ^ * . - -0.03 - -0.035 R2=1 - -0.04 p, Sideslip Angle (degrees) Linear Linair Linear Linear (Hand Calc.) (Linair) 0 Experimental HandCalc. A (Experimental) Analytical Models Figure 5-8: Roll Moment Coefficient Comparison to 62 5.5 Uncertainty in Measurements Sections 4.4 and 4.5 outline the two methods employed to assess the uncertainty of experimental data. The target design goal was to design a force and moment balance with a precision of 0.001 for force and moment coefficients respectively. However from the post analysis of experimental data it was found that the target precision could not be achieved. At best, force coefficients were measurable to a precision of 0.006 and moment coefficients to a precision of 0.004. These values are obtained from the student-t analysis and 95% confidence interval with 19 degrees of freedom. These uncertainties correspond to a force resolution of 4.0E-05 lbf and a moment resolution of 2.2E-04 in-lbf, extremely small values. These force and moment values were found to be the minimum resolution of the sliding mass and beam system. Table 5.1 shows these measured uncertainties compared to the actual predicted uncertainties from equipment- specific error (discussed in section 4). The results show close agreement between predicted and actual error. Table 5.1: Comparison of Uncertainty Analysis Techniques Uncertainty 95% Confidence Interval (Average value) From Uncertainty (Student-t) Table 4.2 cF 0.008 0.006 ^m 0.002 0.004 The underlying principle in the acquisition of experimental data is that no measurement can be known to provide the true result. Thus the purpose for statistical analysis of data to draw inferences on the population mean and deviation is required and 63 provides a means to quantify error associated with experiment methods. However, the systematic or bias errors are sources that are most difficult to quantify. The best attempt to quantify contributions of bias error was done by comparing the lift coefficient at zero degrees angle of attack and the pitching moment coefficient at zero degrees of a plat plate. It is known that the theoretical value of both coefficients for a flat plate is zero. By comparing the deviation between experimental and theoretical values an approximation of bias error was calculated and assumed to influence the whole data set. Other contributions to bias error may be investigated from by a comparison of experimental data to published values. At best, the value obtained can be used as an approximate estimate of bias uncertainty. However, published values may or may not be correct. This may well be the case in comparing works that involve different fluid mediums for testing. For example, water tunnel data at high speeds are dominated by high pressure forces, whereas at low speeds viscous forces are dominant. The influence of these effects may not provide an appropriate basis for comparison. 64 Chapter 6 Summary Through research and experimental investigation, prototype models of aerodynamic load balances have been designed and tested. A series of wind tunnel experiments successfully provided data to evaluate the performance of each device. A brief overview of balance specifications and performance is summarized. The force balance has a design criterion to measure force coefficients of small airfoils to a resolution of 0.001 at a range of forces from approximately 3.0E-06 lbf to 1.25E-01 lbf. The uncertainty analysis of the collected data showed that the actual resolution in force coefficients was slightly higher, approximately in the order of 0.006. Theoretical design device precision was not achieved. However, through experimental data, it is found that there is good agreement with values published by Sunada et. al. There is at most, 12% deviation in lift coefficient values at the stall region angles of attack between 12 and 15 degrees. At all other angles tested the deviation was found to be less than 6%. An experimental value of 3D lift curve slope was found to deviate by 9.5% to published vales and 6.6% to numerical value derived by Glauert [16]. A similar drag analysis of revealed a maximum deviation between experimental and published values ratio from experimental data was found approximately 8%. Also, a maximum lift to drag 5.56% to a value of 5.5 at 5 to be 5.7 at 5 degrees angle of attack. This value deviates by et. al 5]. The simple knife/fulcrum system degrees angle of attack published by Sunada forces on small airfoils within designed is able to accurately measure lift and drag experimental uncertainty. 65 Table 6.1: Summary of Lift and Drag Force Results Max Drag Max Lift Coeff. 3D lift curve (L/D)max Coeff. Deviation Deviation slope Exp. 7% 12% at stall region 4.98/rad 5.7 @ 5 Data degrees AoA Published 5.8/rad 5.5 @ 5 Data degrees AoA The moment balance is designed to measure roll and pitching moments of test airfoils. It has a design target moment coefficient resolution of 0.001 and measure moments between a range of approximately 1.0E-06 ft-lbf to 1.9E-02 ft-lbf . It was found however that due to the vibration of the tunnel wall at higher velocities a minimum resolution of moment coefficient of 0.001 could not be met by adjusting the weight ofthe sliding mass. From the statistical analysis an uncertainty value of 0.004 was measured. Theoretical design coefficient uncertainty could not be achieved. However, comparison of experimental values with published works [21] showed good agreement at higher pitch angles (approximately 10% deviation). A large disagreement was found in the pitching moment coefficient at zero degrees pitch angle, approximately a 43% difference. This is coefficient profile for a flat plate (Figure puzzling due to the fact that the moment 4-7), coefficients published Pelletier at follows a similar pattern. In fact, pitching moment by 8xl04 Reynolds number of shows a similar pattern in which pitching moment is near zero about angle of attack at zero degrees angle of attack and a local maximum at 6 degrees confirm the pitch coefficient values for a flat plate [21]. More work is required to obtained near zero degrees angle of attack. 66 Comparison of roll moment data yielded results that need to be further investigated. The method used to approximate an analytical solution to the roll coefficient is far from perfect in comparing it to the actual data collected during tests. It is believed that flow separation and leading edge vortices are occurring in test experiments as seen by flow visualization tests by Sunada et al. These occurrences are not modeled in analytical methods. It is however promising to obtain a similar plot profile between experimental and analytical results. Refer the table below for a summary and comparison of results. Table 6.2: Summary of Pitch and Roll Moment Results Max pitching moment Max rolling moment deviation deviation Published Values 43% at low AoA N/A 10% at high AoA LinAir (3D) N/A 14% Calculated Values (2D) N/A 47% Lastly, the ability of the fabricated balance devices was found to be highly repeat-able in collecting data. Confidence interval obtained from a student's t statistical analysis was on the same order of magnitude of quantization error. For example, measuring a confidence interval of (0.2763, 0.2965) is on the same order of uncertainty obtained from analytical techniques described in section 4.5. This is a promising result that indicates a repeatable process. The initial alignment and setup is crucial in obtaining data with minimum bias errors good springboard and friction effects. The results contained in this thesis are a for the MAV's. next iteration goals ofmeasuring full scales 67 Chapter 7 Future Recommendations As previously mentioned, this thesis is a good starting point for continued research into modifying the balance prototypes for MAV applications. There are minor changes to be made to the aerodynamic load balances, which will allow for more accurate and easily operable devices. The ease of machinability and performance of the lift/drag balance is acceptable to within experimental uncertainty. However, there are design areas that may be improved upon. First, it is found that vibration becomes a problem as the angle of attack is increased beyond approximately 20 degrees. This observation is very apparent as the tunnel free stream velocity is increased beyond what was tested in this research. Depending on the range of testing, increasing the mass of the knife pendulum assembly may easily accommodate the levels of vibration disturbance. By adding mass below the center of gravity of the knife assembly, the system will also have a tendency to obtain a level position (see figure 7-1). Figure 7-1: Balance design with added mass 68 Other options to investigate include incorporating an oil pot-damping device to manage the dynamic motion of the system. Secondly, the bubble level used to indicate the null position, although functional, may be replaced by a more accurate measuring device. A laser and target indicator mounted on a far wall should provide better visual resolution and ease the data collection process. Linear differential transformers are another option, which is used in larger balance applications and can detect the equilibrium state. Lastly, if a finer visual resolution of angle of attack is required, the protractor can be replaced by an angle caliper or anglemometer to ease data collection. This will further provide accuracy in measuring changes in angle of attack to 0. 1 degrees if necessary. There are similar points to improve the design of the pitch/roll moment balance prototype. The level indicator and methods for increasing the mass of the knife pendulum assembly previously mentioned can be applied to this design. A notable effect in performance seems to be attributed to the increased drag seen by the balance veins. With the current setup, the device experiences a yawing effect due to the uneven of this effect be distribution of drag forces on the test assembly. A way countering may "T" effect to rearrange the y-bar test platform into a or equiangular formation. A second platform. Weight was added to the seen at higher tunnel velocities is the lifting ofthe test airfoils from floating. a denser metal y-bar test platform in order to keep the test Using problem. the vein used to hold the for the part fabrication can easily solve this Lastly, the cost of additional frictional effects. A airfoil into position is effective, however at height of the rod at various angles would be redesign of the vein to easily adjust the 69 beneficial in order to ease data collection. A mounting scheme in which the test platform is secured to the lower tunnel wall may prove to be a better support method. Pitch angle adjustment is controlled by rotating a clevis on a threaded rod. This clevis also introduces additional drag and is not able to accurately resolve pitch angles below 0.3 degrees. A more accurate angle indicator is required if finer angle adjustment is required. 70 Appendix A: Lift/Drag Balance CAD Drawings Figure A-l: Force Balance Assembly Drawing 71 : uj t i ^j o V -O Vfc < [ ___/ i ~~JL I- ~ ~^^^ j. f^j \ ' - -i i * t5h?i- ? t Hi i v ;. * Is .5 ti t 5 S I t r 1 i i * __ r j _. ? i j s ; rv T- i _____ 1 1 pig #5 1 Figure A-2: Lift & Drag Balance Knife Wedge 72 * S * _e o ., ^ j: o -l 5 5 ar -t | ri Q SJ Li Figure A-3: Lift & Drag Balance Swivel Plate 73 ij_i G-' i ' LU '-'"' I -i i - ' __ ' > C. _i - o T : i o 1 1 irf ir4 ~~& r Cl ii - -f ili\ JJ ~ = J . ' I3_A J*. ~: _i J- ___: = Figure A-4: Lift & Drag Balance V-Block 74 -, B =. 43 i:* si i ^ a f -3. $ = _i____I______ ->_: *L -crfc 7^ , & 0_ '~r ^ . X ^ v*- :s*. :S. <_.--*- ;"n* ._. " I JU ',-I-f 1 r <_. .**. J"B.> ~ __ S___ .1 . o * J _^ IX. >*" -5 ,, '< ;j -_. '- ''"' Figure A-5: Lift & Drag Balance Base Plate 75 X FT :: O 9 Si' .;'. . s _ n ]' o- I 1^ s o 191 / t- m 1 Figure A-6: Lift & Drag Balance Protractor Bracket 76 Appendix B: Pitch/Roll Moment Balance CAD Drawings Figure B-l: Moment Balance Assembly Drawing 77 X UJ -J < 1/J^-J < o < ______jj -o g . -___, X _n 1 i *< --. --> _j _l -.. i/*: _JU ___- i * \\ *"". Ll. rt. u- t~*l L.' ____ X *"""_: W & __L. e. -r .. 4 i! i"*. H' - _ Figure B-2: Pitch & Roll Moment Balance Base Plate 78 uC j^ E. e__ - i _ "V * _r . I U- / * \ < ;_ 1 P 1 ^ _> < _j a__ i_ c < :_". c: cn _s V * J \ *_/ " | - * i1 : *_ - J! ..- I ** ~ _. r i. '*' '' S - 0 3 | i? '.?.? fn ||f '"- r,0 M _=_ r_ -' *--_ *"** __r *____! / -ti r-i O _r ^ c - ^ _3 c ^* r^l * 1 __r JPLr .= _> ^*-fc_ '~ -J -^__f!_5lf u- ._. -__5W <_. V 1 _ -'. 2s. 53 _j f-. x _? r j& i f >.. -Si ;-- - "? _ Figure B-3: Pitch & Roll Moment Balance Swivel Plate 79 JJ "> _ v _ I ? r, - * : R*i _._.. ^ 3$. "-O 8 v-i --C- Q .0 r. *:_ __ Figure B-4: Pitch & Roll Moment Balance Knife Wedge 80 _i i -".UJ v-^ . _/\ . /? ___o /^ 5 /// <^ // X-J fi i< vv ^3- u/> -y \V7 < _____:xS W < * - h > 3 ?i _ i__ .. i S " _n __. ! '? . __ S h g - r"l er l**.^' !*i' * 0 I i*i _z -J^Tj* -C. "1/ U- U- r-. ~ *"_ LL. Q- -j r: " I?' ^-- '' i/. ": = -' %- fe :.! Sift ": _- is* >: .*.- < r. .^ i :: o -_r - / i i- 4 F j> ' [ on / i 1 T f~* C> "--. M Jm '-_"! "_< c^i *"" I"; '5. _ _~. ~ ~ H- r^-^__N* 41 ""- _ *T^i 1 ~_ 5; -.01 " Figure B-5: Pitch & Roll Moment Balance h-bar 81 X <5rv" V. v__ : ___ f _y jj" ;il r *' * ' - < ~ | s :; ., . ; r, .-i '_. - % : * .:. rt 3. j * : _ -} ~ 5 -.- fee 5 '?: -. i E J. Figure B-6: Pitch & Roll Moment Balance V-block 82 U _f *_> _l __;:__ < 2: __: -JJ *J b * i|#;' Figure B-7: Pitch & Roll Moment Balance Y-bar 83 Appendix C: Experiment Procedures Document Lift Data Collection Procedures 1 . Turn on the VLMX pressure transducer equipment at least 30 minutes prior to collection of data. Flip the big red lever, fan switch, and chiller switch to the on position. 2. Call airport information center to obtain ambient pressure and temperature. 3. Set-up the balance for lift data collection; see Figure 3-4. 4. Secure the balance device to the top ofthe wind tunnel panel and lock down the two machine screws such that the balance is zeroed at 90 degrees. 5. Use the small tare mass to level the balance (wind tunnel off). 6. Attach the airfoil to the knife and vein assembly; the airfoil should be parallel to the flow. 7. Check to ensure the balance level indicator is still centered. 8. Adjust the tunnel velocity to match the Reynolds number flow speed for testing. 9. Run the tunnel for 10 minutes; obtain a steady operation temperature. 10. Collect data starting at zero degrees angle of attack and incrementing by three degrees until 30 degrees is reached. At each angle, the position of the sliding mass on the scale is recorded at balance level position. the of collection. 1 1 . This is the last step in completing first iteration lift data Next repeat step 10 to collect 20 data points at 3, 15, and 30 degrees AoA. 12. Record at least 5 data points at all other AOAs. 13. Shut down equipment when done. 84 Drag Data Collection Procedures 1 . Turn on the VLMX pressure transducer equipment at least 30 minutes prior to collection of data. Flip the big red lever, fan switch, and chiller switch to the on position. 2. Call airport information center to obtain ambient density, temperature, and viscosity? 3. Set-up the balance for drag data collection; see Figure 3-5. 4. Use the small tare mass to level the balance (wind tunnel off). 5. Attach the airfoil to the knife and vein assembly; the airfoil should be parallel to the flow. 6. Adjust the tunnel velocity to match the Reynolds number desired for testing. 7. Run the tunnel for 10 minutes; obtain a constant operation temperature. 8. Collect data starting at zero degrees angle of attack and incrementing by 3 degrees until 30 degrees is reached. At each angle, the position ofthe sliding mass on the scale is recorded at balance level position. 9. This is the last step in completing the first iteration of drag data collection. Next repeat step 8 to collect 20 data points at 0, 15, and 30 degrees Angle of attack. 10. Record at least 5 data points at all other AOAs. when 1 1 . Turn off equipment done. Note: Vein drag tare data is assumed to be known prior to collecting drag data on test airfoils. 85 Pitching Moment Experimental Procedures Document 1 . Turn on the VLMX pressure transducer equipment at least 30 minutes prior to collection of data. Throw the big red lever, fan switch, and chiller switch. 2. Call airport information center to obtain ambient density, temperature, and viscosity? 3 . Set-up the balance for pitching moment data collection; see Figure 3-11. 4. Mount test airfoil and tare balance to indicate level position. (Wind tunnel off) 5. Adjust the tunnel velocity to match the Reynolds number for desired testing speed. 6. Run the tunnel for 10 minutes; obtain a constant operation temperature. 7. Collect data starting at zero degrees pitch angle, increment to 6 degrees, then lastly 1 1 degrees. May also alternate between maximum to minimum pitch angle to provide variability and assess hysteresis effects. At each angle, the position of the sliding mass on the scale is recorded at balance level position. 8. Repeat step 7 to collect 20 data points at 0, 6, and 1 1 degrees Angles of attack. 9. Turn off equipment when done. Note: Calibration data for pitch moment configuration is assumed to be known prior to collecting pitch moment data on test airfoils. Refer to section 4.2.2. 86 Rolling Moment Experimental Procedures Document 1 . Turn on the VLMX pressure transducer equipment at least 30 minutes prior to collection of data. Throw the big red lever, fan switch, and chiller switch. 2. Call airport information center to obtain ambient density, temperature, and viscosity? 3. Set-up the balance for rolling moment data collection; see Figure 3-12Figure 3-11. 4. Mount test airfoil and tare balance to indicate level position. (Wind tunnel off) 5. Adjust the tunnel velocity to match the Reynolds number for desired testing speed. 6. Run the tunnel for 1 0 minutes; obtain a constant operation temperature. 7. Collect data starting at zero degrees sideslip angle, increment to 6 degrees, then lastly 9 degrees. May also alternate between maximum to minimum pitch angle to provide variability and assess hysteresis effects. At each angle, the position ofthe sliding mass on the scale is recorded at balance level position. 8. Repeat step 7 to collect 20 data points at 0, 6, and 9 degrees sideslip angles. 9. Turn off equipment when done. Note: Calibration data for pitch moment configuration is assumed to be known prior to collecting pitch moment data on test airfoils. Refer to section 4.2.2. 87 Appendix D: Statistical Analysis Lift Data Statistical Analysis Drag Data Statistical Analysis Histogram ofLift- 3 AoA Histogram of Drag - 0 AoA (v_th 95% .-confidenceinterval meant forth* (with 95% .-confidenceInterval for the mean) S - I 7 6- 5 - 5- A ______ 0) 8- J LL 2- . 1 1 I il I 0 L_ [-.- i 3 25 0 26 0 27 0 2B 0 29 0 30 0 31 0 32 0 33 0 34 0 015 0 020 0 025 0 030 0 035 0 040 0 045 Drag - 0 AoA Figure D-l Figure D-4 Lift- Histogram of 1 5 AoA Histogram of Drag - 1 5 AoA (with 95% (-confidence interval for the mean) 6- | 5- | 4- u s 3- 3 i 2- J. i o ! J I .. i 1 1 1 r 6? 0 68 0 69 0 70 0 71 0 0.255 0 260 0.265 0 270 0.275 0.280 0 285 0 290 Drag - 1 5 AoA Figure D-2 Figure D-5 Histogram of Drag - 30 AoA Lift- Histogram of 30 AoA (with 95% .-confidenceinterval for the mean) 7- e- 5- 4- __ 3- i 2- I ,. 1 - 0- n n n~i 0 530 0 535 0 540 0 545 0 550 0 555 0 560 0 565 0 570 818 0 8_l 0 828 0 831 0 791 0 798 0 801 0 808 0 811 0 0 788 Drag - 30 AoA Figure D-6 Figure D-3 88 T Confidence Intervals Variable N Mean StDev SE Mean 95.0 % CI Lift - 3 20 0.28639 0.02151 0.00481 ( 0.27633, 0.29646) Variable N Mean StDev SE Mean 95.0 % CI Lift - 15 20 0.67619 0.01531 0.00342 ( 0.66903, 0.68335) Variable N Mean StDev SE Mean 95.0 % CI Lift - 30 20 0.80134 0.01283 0.00287 ( 0.79533, 0.80734) Variable N Mean StDev SE Mean 95.0 % CI Drag - 0 20 0.03255 0.00762 0.00170 ( 0.02898, 0.03612) Variable N Mean StDev SE Mean 95.0 % CI Drag - 1 20 0.26988 0.00845 0.00189 ( 0.26593, 0.27384; Variable N Mean StDev SE Mean 95.0 % CI Drag - 3 20 0.55353 0.01141 0.00255 ( 0.54818, 0.55887) Note: Minitab is used for statistical analysis. 89 Pitching Moment Statistical Analysis Rolling Moment Statistical Analysis Histogram of Pitch - 0 AoA Histogram of Roll - 0 (vsth 95% t-con_lef_e Nerval for the mean) (wrth 95% t-confldence Interval for the mean) I I 003 -0.003 41002 -0001 0.000 0.001 0.002 0 Roll-0 Figure D-10 Figure D-7 Histogram of Roll - 6 Histogram of Pitch - 6 AoA (vsrth 9Mb t-cor_der_e nterval tor the mean) (wth 95% t-ccrrtijence nerval for the mean) 1- "I 1 1 Figure D-8 Figure D-ll Histogram of Pitch - 1 1 AoA Histogram of Roll 9 for {with 95% t-confidence interval the mean) (with 95% t-confidence interval for the meen} g. 4- c 3 3" 2- ' ' 1 1 1 1 -0.080 -0.075 -0 070 0.095 -0.090 -0.085 Figure D-9 Figure D-12 90 T Confidence Intervals Variable N Mean StDev SE Mean 95.0 % CI - Pitch 20 -0.05750 0.00646 0.00144 (-0.06052,-0.05448) Variable N Mean StDev SE Mean 95.0 % CI - Pitch 20 -0.09169 0.00735 0.00164 (-0.09513,-0.08824) Variable N Mean StDev SE Mean 95.0 % CI - Pitch 20 -0.07622 0.00585 0.00131 (-0.07895,-0.07348) Variable N Mean StDev SE Mean 95.0 % CI Roll - 0 20 0.00003 0.00123 0.00027 (-0.00054, 0.00061) Variable N Mean StDev SE Mean 95.0 % CI Roll - 6 20 -0.01090 0.00176 0.00039 (-0.01173,-0.0100. Variable N Mean StDev SE Mean 95.0 % CI Roll 9 20 -0.01835 0.00176 0.00039 (-0.01917,-0.01752) Note: Minitab is used for statistical analysis. 91 Appendix E: Excel Data Charts US' igSlsg I 8 1 5 !58! : S2 ?! s S | 3 8 1 1 s F. laaic s s a S3 _ s S fi i 1 __ a * i s ji 5 __ 3 i s ! s s S 3 : 3 1 ": 1 1 S3 1 3 1 =T Pi :- 5 1 i s s s ?! _ E_ Si i I 1 ? . s 5 i i. 1 s _ S 5 " 5 a 1 l s s s fa i s i s 2 s s s. i S3 2 1 5 9 FS s s i 5 s 5 a 3 s 5 1 i S. 2 1 -: "- :: a B s ff _ s i 1 S3 II " s ' ?- c s _ 3 i V Pi g 3 s s ': S_ 5S 5 i. 2 5 1 i 1 1 3 K 3 !: s. s s a S 1 S3 1 ? SS 5 PI * s 1 C. 3 g SS s s _ | II s I 3 g _. s s S3 S ? _j E s 1 i I s E a S ff s s g r g 5 J. 5 2 2 I 5 I Ji 1 i s s s. 3 ^ _ s s . S3 g G. 1. : 1 I il I e ___ e -- 8- ;;. s S 5 g g iS 3 ff 8 ; S3 f 5 - _ 5 s _ lilt| i _ : i ?J I: 1([ -5 -lit IIIII-Ssb I f f Table E.l: Lift Data Spreadsheet 92 rSS. : i5gg 3 3} _ _ s: s. ?g ||. S 8 * IU. II k 3 a e fl In. S Q 5 Q. Q. t A \ I 5". Sift f_ __ Hill-: s js a a I S -| ^ 3 .e e e lllifl I! Table E.2: Drag Data Spreadsheet 93 S Sii si sa 3 S! I I t- to J * 1 i a I 1 'Hi 3 S 5 _ i 3 . 5 i 3 r | 1 1 | (= I |S ~ gl ll I _ * if, j i-i o_!!*._;4-_i-"!e_-_;iS-J || I 111, -e iii f!ij!f |_!8i8JHs____S_._.8 1 1 1 II |fl,.?j 3- i?e|s .g-^-o.gS^s^-o^-o-D.gs^s ffiiliifffi.saws;sa 111i I 111.8 c ai 111 | | I s i- i- ij c aa| gs 1 1 I 1 1 I __. i^liisi = s= il E o j _-__. s ? -S____Sc>io= 1EH__I ^^q a """ s Ii ! ?Il|sl|lslU|II5 Is 1 Iii ES a _a 111 ill Si is ill I S S 1 Sf ?: w s . ; i a 3 J i J 1 | | | | 1 Table E.3: Pitching Moment Spreadsheet (1 of 2) 94 se t s_ @ S 6 c? c? ^? I m 8 m _S m 1 s '% s s s -s S3 3 - 1 = -_j a 2 J Spreadsheet (2 of 2) Table E.4: Pitching Moment 95 *? a. SS 5 5 JgSSi illii 22 _ 9 =? 5 S ! gig' 88 __ r3 i ess I_3 " 2| o o o lis _F2 ess I o o | !- o g | is1. II 111000III i| si > 5.5 lljl!r ii i_D E il 4 e 1 J I ll a? i 1 | 9 S 9 __ J III ^ -__ a "S. Moment Spreadsheet Table E.5: Rolling 96 Reference 1 . Kroo, I., and Kunz, P. J., Meso-Scale Flight and Miniature Rotorcraft Development," Proceedings ofthe Conference on Fixed, Flapping and Rotary Vehicles at Very Low Reynolds Numbers, University ofNotre Dame, Notre Dame, IN, 2000, pp. 184-196. 2. Mueller, J. Thomas, "Aerodynamic Measurements at Low Reynolds Numbers for Micro- Fixed Wing Air Vehicles", University ofNotre Dame, Sept. 1999, pp. 1-30 3 . Pelletier, A., Mueller, J. T., "Low Reynolds Number Aerodynamics of Low-Aspect- Ratio, Thin/Flat/Cambered-Plate Wings". Journal of Aircraft, Vol. 37, No. 5, 2000, pp. 825-832. 4. Jacobs, E. N., Sherman, A. "Airfoil Section Characteristics as Affected by Number," Variations ofthe Reynolds NACA. TR-586 (1 937). 5. Sunada, S., Yasuda, T., Yasuda, K., Kawachi, K., "Comparison of Wing Characteristics at an Ultra-low Reynolds Number". Journal of Aircraft, Vol. 39, No. 2, 2002, pp. 331-338. 6. RITAero. 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