A More Comprehensive Database for Propeller Performance Validations at Low Reynolds Numbers

A MORE COMPREHENSIVE DATABASE FOR PROPELLER PERFORMANCE VALIDATIONS AT LOW REYNOLDS NUMBERS

A Dissertation by

Armin Ghoddoussi

Master of Science, Wichita State University, 2011

Bachelor of Science, Sojo University, 1998

Submitted to the Department of Aerospace Engineering and the faculty of the Graduate School of Wichita State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

May 2016

A MORE COMPREHENSIVE DATABASE FOR PROPELLER PERFORMANCE VALIDATIONS AT LOW REYNOLDS NUMBERS

The following faculty members have examined the final copy of this dissertation for form and content, and recommend that it be accepted in partial fulfillment of the requirement for the degree of Doctor of Philosophy with a major in Aerospace Engineering.

L. Scott Miller, Committee Chair

Klaus Hoffmann, Committee Member

Kamran Rokhsaz, Committee Member

Charles Yang, Committee Member

Hamid Lankarani, Committee Member

Accepted for the College of Engineering

Royce Bowden, Dean

Accepted for the Graduate School

Dennis Livesay, Dean

iii

ACKNOWLEDGEMENTS

I would like to express my deepest gratitude to my advisor and mentor, Professor L. Scott

Miller for his guidance throughout this project. Also, I am sincerely grateful for the opportunity and help that the department of Aerospace Engineering, NIAR W. H. Beech Wind Tunnel, NIAR

Research Machine Shop, NIAR CAD/CAM Lab, Cessna Manufacturing Lab and their generous staff provided.

Above all, none of this would be possible without the love and care of my parents, brother and friends. This is dedicated to my family members, Akhtar, Ali and Elcid Ghoddoussi. Thank you for your constant support and patience.

ABSTRACT

Validation is the essential process of evaluating the precision and reliability of analytical or computational solutions. In this dissertation, a series of comprehensive propeller wind tunnel tests were designed for validation of propeller design and analysis techniques. This work focused primarily on small propellers operating at lower Reynolds numbers in the range of 90,000 to

120,000, which is particularly helpful for unmanned aerial vehicle applications. Extensive propeller and experimental apparatus geometries along with test section spatial dimensionality are described. An open-source computer-aided design (CAD) method was used to create the propeller blades, nacelle, and spinner surface outlines, aiming for easy reproduction. Two different propeller designs were tested: a simple propeller with a constant pitch-to-diameter ratio, chord length, and thickness; and a complex propeller with a pitch-to-diameter ratio and chord length as a function of blade radius. Both propellers with a variable pitch of five degrees increment were tested at several angle settings. Critical test section flow field and geometry information that can be used as boundary conditions are also presented in this study. In addition to classical propeller performance plots of thrust and torque coefficients and efficiency against the advance ratio, nacelle surface pressure distribution in terms of coefficients and propeller wake survey results are provided. Two different wind tunnels were utilized to evaluate the experimental and facility bias. Known errors, uncertainties, and instrumental accuracies are quantified and presented here.

TABLE OF CONTENTS

Chapter Page

1. INTRODUCTION ...... 1

1.1 Propulsive Efficiency in Propeller Design ...... 1 1.2 Challenges in Propeller Design and Analysis ...... 3 1.3 Development in Analysis and Design Methods ...... 4

2. MODERN PROPELLER ANALYSIS AND DESIGN ...... 9

2.1 Momentum-Blade Element Theory ...... 9 2.2 JavaProp ...... 15 2.3 Vortex Theory ...... 21 2.4 Computational Fluid Dynamics ...... 26 2.4.1 CFD Example 1...... 26 2.4.2 CFD Example 2...... 29

3. PROBLEMS AND GOALS ...... 31

3.1 Problems in Propeller Validation ...... 31 3.2 Statement of Objective ...... 35 3.3 Methods of Approach ...... 35

4. EXPERIMENTAL APPARATUS ...... 37

4.1 Geometry Descriptions ...... 37 4.1.1 Wind Tunnels and Model Installations ...... 37 4.1.2 Model Propellers ...... 42 4.1.3 Model Nacelle-Spinner ...... 48 4.1.4 Model Setup Assessment ...... 50 4.1.5 System Performance Prediction ...... 52 4.2 Data Measurement and Process ...... 57 4.2.1 System Calibration ...... 60 4.2.2 Data Corrections and Tares ...... 63 4.2.3 Test Procedure ...... 64 4.3 System Evaluations ...... 66

5. RESULTS ...... 74

5.1 Propeller Performance ...... 74 5.1.1 PD1 Results of Propeller Performance ...... 74 5.1.2 COMP Results of Propeller Performance ...... 82 5.2 Nacelle Pressure Distribution ...... 88 5.2.1 PD1 Results of Nacelle Pressure Distribution ...... 89

TABLE OF CONTENTS (continued)

Chapter Page

5.2.2 COMP Results of Nacelle Pressure Distribution ...... 103 5.3 Wake Survey ...... 119 5.4 Nacelle-Spinner Effect ...... 131 5.5 Dynamic Tare ...... 137

6. CONCLUSIONS...... 144

REFERENCES ...... 146

APPENDIXES ...... 152

Appendix A……………………………………………………………………………….153 Appendix B……………………………………………………………………………….157

vii

LIST OF TABLES

Table Page

1. Summary of System Accuracy, Precision, and Errors…………………………….……. 67

viii

LIST OF FIGURES

Figure Page

1. Rotating propeller: (a) front view, (b) velocities and forces on blade element looking toward hub...... 10

2. BART data vs. M-BE analysis of APC Thin-E propellers [24]...... 14

3. Synthetic drag polar of Clark Y airfoil at different Reynolds numbers [22]...... 18

4. JavaProp validation results compared with NACA TR-594, designated blade angle at 0.75R [22]...... 21

5. Vortex theory, JavaProp, and propeller 5868-9 experimental results [39] comparison, with designated blade angle at 0.75R...... 25

6. Combined propeller/nacelle/wing grid domain [28]...... 27

7. Propeller/nacelle pressure distribution at Mach 0.15, 6650 rpm: (a) α = 0°, (b) α = 10°, data digitized from [26]...... 28

8. Propeller/nacelle/wing slipstream dynamic pressure survey behind the propeller [28] ... 29

9. Propeller wind tunnel model and grid domain [30]...... 30

10. Sensitivity analysis of pitch angle using JavaProp...... 32

11. Sensitivity analysis of chord length using JavaProp...... 32

12. Sensitivity analysis of propeller section airfoil using JavaProp...... 33

13. Sensitivity analysis of airfoil aerodynamics for ClarkY using JavaProp...... 33

14. Photo (top) and description (bottom) of 3×4 LSWT at Wichita State University...... 38

15. Model installation (top) and side view (bottom) in 3×4 LSWT...... 39

16. Description of Beech wind tunnel and C-mount assembly in 7×10 NIAR...... 41

17. Model installation and side view in 7×10 NIAR...... 42

18. PD1 propeller in OpenSCAD interface...... 43

19. PD1 Propeller blade assembly...... 44

20. 3D scan of PD1 propeller blade, within ±0.002 inch accuracy...... 45

LIST OF FIGURES (continued)

Figure Page

21. COMP propeller blade design and assembly without nacelle and spinner...... 47

22. 3D scan results of COMP blade within -0.007 inch accuracy...... 47

23. Nacelle assembly CAD design (dimensions in inches)...... 49

24. Nacelle bottom side modification for 7×10 NIAR setup...... 49

25. Top and bottom of PD1 blade 3D scan set at β0.75 = 23°, within +0.015 inch accuracy. .. 50

26. Top and bottom of COMP blade 3D scan at β0.75 = 15°, within ±0.020 inch accuracy. .... 51

27. Both sides 3D scan of the nacelle-spinner assembly, within +0.070 inch accuracy...... 51

28. PD1 propeller performance analysis...... 54

29. COMP propeller performance analysis...... 55

30. PD1 blade radial distribution of angle of attack, lift and drag coefficients at J = 0.2 and β0.75 = 23°...... 56

31. COMP blade radial distribution of angle of attack, lift and drag coefficients at J = 0.2 and β0.75 = 20°...... 56

32. PD1 and COMP blades local Reynolds number distributions at J = 0.2...... 57

33. Data measurement and processing block diagram...... 58

34. Load cell calibration for thrust...... 60

35. Test section velocity and temperature variations of 7×10 NIAR (courtesy of NIAR). .... 62

36. Five-hole probe wake survey at 7×10 NIAR wind tunnel...... 64

37. Inside the nacelle in each tunnel: 7×10 NIAR (left) and 3×4 LSWT (right)...... 66

38. Thrust coefficient repeatability test of 12×12 APC Thin-E propeller in 3×4 LSWT...... 68

39. Power coefficient repeatability test and efficiency of 12×12 APC Thin-E tests in 3×4 LSWT...... 69

40. Reynolds number (Re0.75) repeatability test of 12×12 APC Thin-E in 3×4 LSWT...... 70

41. Tunnel data comparison of 3×4 LSWT and 7×10 NIAR for 12×12 APC Thin-E...... 71

LIST OF FIGURES (continued)

Figure Page

42. Tunnel data comparison from WSU, BART [24], and UIUC [58] for 10×7 APC Thin- E propeller...... 72

43. Tunnel data comparison from WSU, BART [24] and UIUC [58] for 12×12 and 8×8 APC Thin-E...... 73

44. Coefficients CT, CP, and η against J for PD1 at 5,000 rpm, where β0.75 = 23°...... 77

45. Coefficients CT, CP, and η against J for PD1 at 5,000 rpm, where β0.75 = 28°...... 78

46. Coefficients CT, CP, and η against J for PD1 at 5,000 rpm, where β0.75 = 33°...... 79

47. Coefficients CT, CP, and η against J for PD1 at 4,000 ~ 6,000 rpm, where β0.75 = 23°. ... 80

48. Eppler 387 airfoil wind tunnel results comparison at two Reynolds numbers, data digitized from [47]...... 81

49. Coefficients CT, CP, and η against J for COMP at 6,000 rpm, where β0.75 = 15°...... 83

50. Coefficients CT, CP, and η against J for COMP at 6,000 rpm, where β0.75 = 20°...... 84

51. Coefficients CT, CP, and η against J for COMP at 6,000 rpm, where β0.75 = 25°...... 85

52. Coefficients CT, CP, and η against J for COMP at 6,000 rpm, where β0.75 = 30°...... 86

53. Coefficients CT, CP, and η against J for COMP at 4,000 ~ 6,000 rpm, where β0.75 = 20°...... 87

54. Nacelle coordinate system...... 88

55. Nacelle surface pressure distribution for PD1 at 3×4 LSWT for different Φ, where β0.75 = 23° (continued)...... 90

56. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 23° (continued)...... 92

57. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 23°...... 93

58. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 28° (continued)...... 94

59. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 28° (continued)...... 96

LIST OF FIGURES (continued)

Figure Page

60. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 28°...... 97

61. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 33° (continued)...... 98

62. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 33°...... 100

63. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 33°...... 101

64. Nacelle surface pressure distribution at 7×10 NIAR for different Φ without propeller (continued)...... 101

65. Test section side wall pressure distribution at 7×10 NIAR without propeller...... 102

66. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 15° (continued)...... 103

67. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 15° (continued)...... 105

68. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 15°...... 106

69. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 20° (continued)...... 107

70. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 20°...... 109

71. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 20°...... 110

72. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 25° (continued)...... 110

73. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 25° (continued)...... 112

74. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 25°...... 113

75. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 30° (continued)...... 114

76. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 30°...... 116

xii

LIST OF FIGURES (continued)

Figure Page

77. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 30°...... 117

78. Nacelle surface pressure distribution at 7×10 NIAR without propeller (continued)...... 117

79. Test section side wall pressure distribution at 7×10 NIAR without propeller...... 118

80. Slipstream velocity components for PD1 at Φ = 0°, x/L = 0.02, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR)...... 120

81. Slipstream velocity components for PD1 at Φ = 90°, x/L = 0.02, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR)...... 121

82. Slipstream velocity components for PD1 at Φ = 270°, x/L = 0.02, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR)...... 121

83. Slipstream velocity components for PD1 at Φ = 0°, x/L = 0.49 where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR)...... 122

84. Slipstream velocity components for PD1 at Φ = 90°, x/L = 0.49 where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR)...... 122

85. Slipstream velocity components for PD1 at Φ = 270°, x/L = 0.49, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR)...... 123

86. Slipstream velocity components for PD1 at Φ = 0°, x/L = 0.843 where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR)...... 123

87. Slipstream velocity components for PD1 at Φ = 90°, x/L = 0.843, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR)...... 124

88. Slipstream velocity components for PD1 at Φ = 270°, x/L = 0.843, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR)...... 124

89. Swirl angle at different longitudinal locations and azimuth angles for PD1, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR)...... 125

90. Slipstream velocity components for COMP at Φ = 0°, x/L = 0.02, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR)...... 126

91. Slipstream velocity components for COMP at Φ = 90°, x/L = 0.02, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR)...... 126

xiii

LIST OF FIGURES (continued)

Figure Page

92. Slipstream velocity components for COMP at Φ = 270°, x/L = 0.02, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR)...... 127

93. Slipstream velocity components for COMP at Φ = 0°, x/L = 0.49, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR)...... 127

94. Slipstream velocity components for COMP at Φ = 90°, x/L = 0.49, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR)...... 128

95. Slipstream velocity components for COMP at Φ = 270°, x/L = 0.49, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR)...... 128

96. Slipstream velocity components for COMP at Φ = 0°, x/L = 0.843, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR)...... 129

97. Slipstream velocity components for COMP at Φ = 90°, x/L = 0.843, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR)...... 129

98. Slipstream velocity components for COMP at Φ = 270°, x/L = 0.843, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR)...... 130

99. Swirl angle at different longitudinal locations and azimuth angles for COMP, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR)...... 131

100. Nacelle-spinner effect on PD1 β0.75 = 23° performance tested at 3×4 LSWT...... 132

101. Nacelle-spinner effect on PD1 β0.75 = 28° performance tested at 3×4 LSWT...... 132

102. Nacelle-spinner effect on PD1 β0.75 = 33° performance tested at 3×4 LSWT...... 133

103. Nacelle-spinner effect on PD1 β0.75 = 23° performance tested at 7×10 NIAR...... 133

104. Nacelle-spinner effect on PD1 β0.75 = 28° performance tested at 7×10 NIAR...... 134

105. Nacelle-spinner effect on PD1 β0.75 = 33° performance tested at 7×10 LSWT...... 134

106. Nacelle-spinner effect on COMP β0.75 = 15° performance tested at 7×10 NIAR...... 135

107. Nacelle-spinner effect on COMP β0.75 = 20° performance tested at 7×10 NIAR...... 135

108. Nacelle-spinner effect on COMP β0.75 = 25° performance tested at 7×10 NIAR...... 136

109. Nacelle-spinner effect on COMP β0.75 = 30° performance tested at 7×10 NIAR...... 136

xiv

LIST OF FIGURES (continued)

Figure Page

110. Dynamic tare for spinner-nacelle configurations in loads and coefficient forms and corresponding trend line equations...... 138

111. Dynamic tare for no-spinner no-nacelle (nsnn) configurations in loads and coefficient forms, and corresponding trend line equations...... 139

112. Dynamic tare results (“D”) for configurations with and without spinner-nacelle for PD1 β0.75 = 23° at 3×4 LSWT compared with vortex theory analysis results...... 140

113. Dynamic tare results (“D”) for configurations with and without spinner-nacelle for PD1 β0.75 = 28° at 3×4 LSWT compared with vortex theory analysis results...... 140

114. Dynamic tare results (“D”) for configurations with and without spinner-nacelle for PD1 β0.75 = 33° at 3×4 LSWT compared with vortex theory analysis results...... 141

115. Dynamic tare results (“D”) for configurations with and without spinner-nacelle for COMP β0.75 = 15° at 7×10 NIAR compared with vortex theory analysis results...... 141

116. Dynamic tared results (“D”) for configurations with and without spinner-nacelle for COMP β0.75 = 20° at 7×10 NIAR compared with vortex theory analysis results...... 142

117. Dynamic tared results (“D”) for configurations with and without spinner nacelle for COMP β0.75 = 25° at 7×10 NIAR compared with vortex theory analysis results...... 142

118. Dynamic tared results (“D”) for configurations with and without spinner-nacelle for COMP β0.75 = 30° at 7×10 NIAR compared with vortex theory analysis results...... 143

LIST OF ABBREVIATIONS

2D Two-Dimensional

3D Three-Dimensional

AGARD Advisory Group for Aerospace Research and Development

BART Basic Aerodynamics Research Tunnel

CAD Computer-Aided Design

CFD Computational Fluid Dynamics

CMM Coordinate Measuring Machine

CNC Computer Numerical Control

COMP Complex Propeller

CPU Central Processing Unit

FFA Flygtekniska Försöksanstalten (Aeronautical Research Institute of Sweden)

FS Full Scale

LSWT Low-Speed Wind Tunnel

LTPT Low-Turbulence Pressure Tunnel (at Langley Research Center) mV Millivolts

NACA National Advisory Committee for Aeronautics nsnn No-Spinner No-Nacelle (Configurations)

NIAR National Institute for Aviation Research

PLA PolyLactic Acid psf Pounds per Square Foot psid Pounds per Square Inch Differential

RD Readings

xvi

LIST OF ABBREVIATIONS (continued)

RO Rated Output rpm Revolutions per Minute

UAVs Unmanned Aerial Vehicles

UTRC United Technologies Research Center

VWT Vertical Wind Tunnel (at Air Force Research Laboratory)

WSU Wichita State University

WOZ Wind-Off-Zero

xvii

LIST OF SYMBOLS

° Degree

α Angle of attack

αi Induced angle of attack

α0l Zero-lift line angle of attack relative to the chord line

β Geometric pitch angle

β0.75 Pitch angle at 75% of radius

 u ε Swirl angle,   tan 1 t ux ϕ Angle of resultant flow CJ η Efficiency,   T CP U λ Tip speed ratio,   VT μ Viscosity

ρ Density Bc σ Propeller solidity for rectangular blades,    R ω Angular velocity

Γ Bound circulation around any blade station

Φ Azimuth angle a Lift-curve slope c Local chord length

pp  cpr Pressure coefficient, cpr  q d 2D drag or differential dL, dD Differential lift and drag, respectively

xviii

LIST OF SYMBOLS (continued) l 2D lift l’ Non-dimensional axial location of wall pressure port to 7×10 test section

length where l’ = 0 at entrance and l’ = 1 at exit n Revolutions per second p Pitch, distance p Local pressure p∞ Freestream static pressure q Dynamic pressure

1 2 q∞ Freestream dynamic pressure, qU   2 r Radial location t Blade thickness ux, ut, ur Flow velocity components (axial, radial, and tangential, respectively) v Velocity vector and/or magnitude v’ Vortex displacement velocity w Induced velocity wa Axial component of induced velocity wt Tangential component of induced velocity r x Non-dimensional radial location, x  R x, y, z Nacelle/tunnel fixed coordinate system or distances

xix

LIST OF SYMBOLS (continued)

A Disk area

B Number of blades

CL 3D lift coefficient (lower case subscript: 2D design lift coefficient)

CD 3D drag coefficient (lower case subscript: 2D design drag coefficient) P CP Power coefficient, C  P nD35 Q CQ Torque coefficient, C  Q nD25 T CT Thrust coefficient, C  T nD24 D Propeller diameter

Dhub Propeller hub diameter

DC Direct Current

F Prandtl’s tip loss factor

HP Horsepower U J Advance ratio, J  nD L Nacelle length

M Mach number

P Shaft power

Q Propeller shaft torque

R Propeller radius Uc Re Reynolds number, Re   Vc R0.75 0.75 2 2 Re0.75 Reynolds number at 75% of radius, Re0.75  , where VUR   R0.75 0.75

LIST OF SYMBOLS (continued)

T Thrust

U Freestream velocity

V Voltage (mV = millivolts)

VE Effective freestream velocity

VR Resultant freestream velocity

VT Tip velocity, VT = ωR

xxi CHAPTER 1

INTRODUCTION

1.1 Propulsive Efficiency in Propeller Design

A propeller is a device that generates thrust or force in a fluid medium such as water or air.

A mass of fluid medium driven by the propeller causes a reaction in the opposite direction, that is, the craft’s forward thrust. An airscrew propeller, commonly used on aircraft, screws or twists its way through the air, pushing or pulling the aircraft forward as it turns. The rotational kinetic energy increment added by the shaft power in the air moving backward, also called the slipstream, cannot be regained and is considered a power loss [1, 2]. Another type of energy loss may be the friction between the air and propeller blades. Therefore, the thrust available or power produced by the propeller is less than the power provided by the engine. A propeller designer aims to increase the ratio of useful power to engine power in order to obtain greater propulsive efficiency.

During World War II, propeller propulsion achieved a standard that was quite high. With the debut of jet engines, the progress in propeller propulsion struggled for a period of a time. But with the increase in the price of oil, there has been great demand for optimally improving the efficiency of propeller propulsion, hence making it the most economical means of propulsion [3].

Most aircraft propellers are run by internal combustion engines, and the best propeller performance is at a certain speed of revolutions whereby the engine is designed to operate at its highest efficiency. With recent improvement in lithium-ion battery technology, the use of electrical motors with innovative propeller designs has increased rapidly, especially in small unmanned aerial vehicles (UAVs). This requires a large shift in design from traditional propellers to a new propeller design and analysis method for different environments. In addition to its aerodynamic efficiency,

a propeller must also show its structural trustworthiness with sufficient strength, that is, longer fatigue life [4].

A variety of elements are considered in propeller selection. Interestingly, propeller performance is not always the only priority in choosing propellers. For instance, it may be necessary to have wide blades with a low tip speed to lower the noise level of a propeller. Also, the propeller diameter can be limited based on of ground clearance or the distance from the nacelle to the fuselage. Propeller and motor dynamics also need to be in compliance. Furthermore, the impulse response of the engine should not match the natural frequency of the first bending mode or harmonics of the blade. This will lead to excessive vibration and ultimately fatigue failure [5].

From an aircraft performance and designer point of view, it might be important to choose a propeller with a high static thrust for takeoff and a high efficiency at cruise. With an appropriate propeller mechanism, these are relatively easy to achieve if the propeller pitch is variable. A fixed- pitch propeller requires settling for something between these two extremes. The pitch of the propeller defines the distance it translates through the air in one revolution without slipping. The rotation of the whole blade about its long axis determines if the blade has a fixed or variable pitch.

A constant-pitch propeller has the same twist throughout the radius of the entire blade and refers to the propeller geometry.

The design procedure of a propeller is not well defined [5]. Generally, one must first decide on the number of blades, which may be based on experience or could be an arbitrary number, for starting its design and the analysis iteration process. Similarly, pitch distribution contributes essentially to the efficiency and performance of the propeller. The results of stress calculations determine whether the thickness distribution needs to be changed or not. Finally, a radial distribution of pitch and blade thickness may be prescribed.

The propeller analysis and design process and its historical development will be discussed in detail in sections to follow. As explained, each method has its advantages and disadvantages.

An attempt has been made to provide additional detailed information, especially for low Reynolds numbers that will eventually improve the methods of both analysis and design.

1.2 Challenges in Propeller Design and Analysis

As discussed briefly in this section, three main concerns are involved in the propeller design process. These issues, in order of their importance and difficulty level, are introduced here.

The first issue in this process is to design a propeller according to the rotational speed desired by the engine or motor. A rotating propeller causes resistance as it turns around the shaft axis. This resistance, also known as torque, Q, increases as the rotational speed increases.

Therefore, the speed of revolution is decided by the power available to spin the propeller. In contrast, engines and motors operate most efficiently at their designated rate of revolution.

Designing a propeller for a certain rate of revolutions that are suitable for a motor is a relatively easier task, but the speed of the aircraft for which it is designed to perform must also be considered, and this has considerable impact on the torque or power settings. Consequently, it is difficult to design a propeller based only on its engine performance without knowing the aircraft operating speed. In other words, an individual propeller must be designed for each combination of aircraft and engine, which makes the effort challenging. Therefore, it is essential to develop a reliable theory on which to base the design.

The second issue in the design process is to create an efficient propeller. Only a portion of power, P, generated by the engine is converted into thrust, T, and the remainder primarily disperses into the slipstream. Efficiency (η) is the ratio of the useful power delivered by the propeller and power provided by the motor (shaft power):

TU   (1.1) P where U is the velocity of the aircraft. Typically, the efficiency of the propeller is shown by a percentage, and a designer aims to maximize this value by applying a reliable and accurate analysis method.

The final issue in the design process is to develop a dependable and safe propeller. A series of forces and bending moments act on a rotating propeller due to centrifugal forces and thrust.

Also, vibration and torque of the engine or motor cause severe wear and tear on the blades, shifting the blade into thicker and heavier designs. In the meantime, it may be challenging to increase the efficiency and reliability of a propeller because they are mutually opposing matters, but achievable.

However, the toughest obstacle for a designer is the first problem—to design a propeller for a particular engine and aircraft operating speed combination [4].

1.3 Development in Analysis and Design Methods

Early propeller studies conducted by Rankine [6] and Froude [7] in the 19th century established the fundamentals of momentum theory for a propeller in a fluid medium, such as air or water. In this theory, an actuator disk replaces the propeller geometry, thus neglecting the geometric features and the slipstream rotation. In 1900, Drzewiecki [8] introduced the blade element method, including section lifting surfaces set to an optimum angle of attack. Although

Drzewiecki was the first to introduce the blade element theory, this work failed to account for the induced velocity at each element. It seems that Wilbur and Orville Wright were the first who combined the momentum and blade element theories and successfully introduced highly efficient propellers [9].

In 1925, Weick [10] published the empirical method, “a simple system” for small airplane designers and builders derived from wind tunnel models and in-flight full-scale tests. Here, design

steps are made through easy calculations and charts for a baseline propeller with an average fuselage. To increase accuracy, it is necessary to provide precise horsepower, revolutions per minute (rpm), and velocity of the operating condition, otherwise performance diminishes. This method is sufficient only for low-power engines, that is, engines that have a little less than one horsepower to about fifty horsepower.

With the application of Prandtl’s lifting line theory [11] to propellers, a new era of propeller development began. Circulation over a finite wing was shown, which is applicable to the propeller blade as a lifting surface incorporated by the bound vorticity and a vortex sheet shed from the trailing edge of the blade. Betz [12] showed that a propeller with optimum-induced velocity distribution causes undeformed or rigid helical vortex sheets to move downstream of the propeller.

This occurs where each point of the radius in a helical wake has the same velocity in axial distance from the propeller, that is, parallel to the rotation axis, so that the induced loss is minimal. Betz assumed that the propeller would be lightly loaded, or the slipstream would roll up as wake contraction occurred. The helicoidal vortex sheet is assumed to move as a rigid body, but that is not the case in reality. The averaged axial and swirl velocity components between the vortex sheets of the slipstream are less than the sheet velocities by a factor F. Also, the swirl component of the velocity varies throughout slipstream radius. Prandtl provided an approximation method, also called Prandtl’s tip loss factor F, using a series of semi-infinite plates. This factor becomes more exact as the number of blades increases or the advance ratio becomes smaller.

Goldstein [13] found the exact solution to the ideal Betz wake problem. His vortex theory resulted in the geometry of a propeller rather than predicting its performance. Lock et al. [8] applied Goldstein solutions to a design and conducted high-speed aircraft propeller performance analyses from 1941 to 1945; this work is published in an Aeronautical Research Council report

[14]. Throughout a series of National Advisory Committee for Aeronautics (NACA) reports [15-

18], Theodorsen showed that the same light-loading assumption made by Betz, Prandtl, and

Goldstein was not necessary and could be removed. Due to contraction, instead of Goldstein’s solution concentrating right behind the propeller, Theodorsen proved that this solution was effective even far downstream. Theodorsen’s theory, like Goldstein’s solution, resulted in the geometry of the propeller but with an ideal wake far downstream.

In 1949, Crigler [19] applied Theodorsen’s theory to propeller design. The optimum propeller efficiency can be described from a number of graphs for any design condition. In a more recent work in 1994, Adkins and Liebeck [20] modified Larrabee’s [21] method by removing the light-loading assumption and small-angle approximation. They presented an iterative design procedure to calculate the axial velocity of the vortex filament and flow-angle distribution.

Parameters required for analysis and design are the number of blade elements, number of blades, propeller diameter, hub diameter, revolution speed, freestream velocity, and particularly lift and drag coefficients of the section design. Accurate airfoil geometry specifications and its aerodynamic characteristics lead to better propeller performance predictions. In addition, for design, thrust or power inputs must be provided in order to obtain chord length and pitch distribution along the radial direction for an optimum wake or inverting the process for propeller performance analysis. An open-source program called JavaProp [22], written by Hepperle using a

Java application, is available using Adkins, Liebeck, and Larrabee’s blade element methods, which is discussed in Chapter 2.

Despite the evolution of the lifting line theory and its robustness, the limitations of this theory must be considered. First, it is only applied to conventional blades with a large aspect ratio, not wide-chord propfan blades, for instance. Next, and importantly, high Mach numbers and low

Reynolds number effects are not incorporated into basic theories that require corrections to section airfoil data [23, 24]. Furthermore, the theory does not account for three-dimensional effects, such as sweep angle or cross flow, since the bound vorticity is assumed to be straight.

Progress in computational capabilities makes complex numerical analyses, such as solving

Euler or Navier-Stokes equations, more affordable and accurate. Although still computationally more expensive than traditional momentum-blade element theory, these methods can implement viscous phenomena like turbulence and flow separation. Unprecedented details of the propeller flow field and its interaction with a wing or fuselage are some of the greatest advantages of computational fluid dynamics (CFD) [23, 25-33]. It appears that the future of CFD methods is promising; however, some issues need to be addressed. As mentioned above, computational costs are significant. But with advancement in computer technologies, this problem should be solved eventually. Another important concern is the lack of validated code to prove that the method is authentic with a certain level of confidence. When accuracy and limitations of experimental measurements and CFD codes, grid-density effects, and physical basics are equally known, they can be compared over a range of specified parameters. A detailed surface and flow-field comparison with experimental data justifies the code’s ability to accurately model the critical physics of the flow. Precision in geometric measurements of the actual model is imperative, especially when operating at low Reynolds numbers. This is because any small defect in fabrication or change in geometry affects aerodynamic characteristics at lower Reynolds numbers, thus making the propeller performance even more unpredictable.

Previous discussions have suggested procedures for assessing the accuracy and credibility of CFD techniques [34-36]. The scope of this study is to provide comprehensive propeller experimental data designed for validating analysis and design tools at low Reynolds numbers.

Without a doubt, this is the first step in improving tools and processes of modern propeller analysis and design, in hopes of ultimately enhancing propeller efficiency. The goal here is to provide extensive measurements of the performance, geometries, flow field, and boundary conditions required for validation and development of analysis and design tools, particularly for UAV applications operating at lower Reynolds numbers. Prediction and eventually agreement in analysis results with experimental data capturing Reynolds number effects potentially lead to establishment of the code’s ability. In Chapter 2, we will further discuss the recent analysis methods and design process with corresponding problems and inquiries.

CHAPTER 2

MODERN PROPELLER ANALYSIS AND DESIGN

Aerodynamically, a designer struggles to deliver a propeller with maximum efficiency in order to satisfy all performance expectations. Hence, an accurate analytical method is required to achieve this goal. Modern analysis and design processes have evolved over the years, as previously reviewed in the historical development section of Chapter 1. The different propeller analysis and design tools that are dominantly used in the field will be examined in this chapter. Any prediction method must be validated, typically using existing experimental results, in order to endorse its credibility. The detailed experimental data can verify the tool’s ability and accuracy.

2.1 Momentum-Blade Element Theory

The momentum-blade element theory is a relatively simple means to approximate the induced angle of attack αi by combining two different methods. This approach allows the prediction of propeller performance more accurately by examining the aerodynamics of the blade section. This theory does not particularly account for the flow rotation and tip loss factor, unless it has been imposed. Approximation of the induced effects gives only a rough estimate for the analysis. Although this is one of the original blade element methods that accounts for the induced velocity, with the improvement in computers, the use of this method has diminished [5]. Yet, it is useful to be familiar with this theory because of its applications to other models, which can be found in numerous literature reviews.

In general, if the propeller with radius r screws itself through the air without slipping, then the distance it would travel in one revolution is the pitch, p:

pr 2 tan (2.1)

assuming the pitch is constant throughout the blade radius, where the pitch angle β is the angle between the plane of rotation and the section chord line. However, for the following analysis, it is more convenient to define it relative to the zero-lift line instead of the chord line. Figure 1(a) shows the front view of a rotating propeller with two blades and an angular velocity ω rad/s with incoming freestream velocity U. The notation on this figure is similar to that of McCormick [5]. Note that the induced velocity w, shown in Figure 1(b), is much smaller in scale than indicated here.

(a) (b)

Figure 1. Rotating propeller: (a) front view, (b) velocities and forces on blade element looking toward hub.

Each blade is divided into several radial elements, dr, which contribute to thrust T and torque Q resulting from section lift and drag. From Figure 1, these values can be calculated as

dTdLcosiidDsin() (2.2)

dQ r dLsin   ii  dD cos(    ) (2.3) where the differential lift dL and the section lift coefficient Cl will be, respectively,

1 dLVcC  dr 2 (2.4) 2 El

Cali()     (2.5)

Similarly the differential drag dD can be found as

1 dD V c C dr 2 (2.6) 2 Ed

To find the induced angle of attack αi in equations (2.2) and (2.3) for the following analysis, assume that αi and the drag-to-lift ratio are small. This assumption is not valid at high disc loadings or when flow separation occurs, thus causing a deviation in results. Now, the resultant velocity VR and the effective velocity VE in Figure 1(b) are almost equal, that is, VR ≈ VE. As a result, for B blades, equation (2.2) can be rewritten as

B dTVca 2 ()cos dr (2.7) 2 Ri

Note that blade section lift-curve slope a, has a direct impact on the thrust obtained in this equation.

At this point, linear lift with angle of attack (i.e., i ) is assumed. From the momentum principle, thrust is

T2 A U w  w (2.8)

For small αi, the induced velocity can be approximated as w ≈ VR αi, and equation (2.8) can be written for dT as

dTrdrUVV2 Ri cos2cos Ri (2.9)

By equating equations (2.7) and (2.9), the induced angle of attack can be determined as

1/2 2 1  aV aV  aV    R  R R    i 2 2 2   (2.10) 2x 8 x VT  x8 x VT 8 x VT  where U   VVx22 R RT

Bc       tan 1  R x

r VR  x  T R

The dimensionless characteristics of propellers are defined by thrust coefficient CT and power coefficient CP obtained from experiment results as

T C  (2.11) T nD24

P C  (2.12) P nD35

In momentum-blade element theory, these are functions of the advance ratio J and expressed as

 1  222   CJxCT   [ l cos id Cdxsin()] i (2.13) 8 xh

 1  22 2  CxP JxC  [sinl  id C cos()] i dx (2.14) 8 xh where U J  (2.15) nD

Hence, the propeller efficiency in equation (1.1) can be written in terms of CT, CP, and J as

CJ   T (2.16) CP

Inevitably, the efficiency increases as the advance ratio increases until the windmill condition approaches. This is because of how the term is defined in equation (2.16). Note that section lift and drag coefficients directly affect CT and CP, as shown in equations (2.13) and (2.14). Hence, it is critical to provide precise section airfoil aerodynamic characteristics in order to obtain accurate thrust and power predictions. Torque coefficient CQ and power coefficient CP result in a relationship of

CCPQ 2 (2.17)

Assumptions made in this theory of a small induced angle of attack and drag-to-lift ratio are not necessarily true but convenient for the sake of simple calculations. Ol et al. [24] presented an analytical-experimental comparison for a range of small propellers using the momentum-blade element theory for the analysis. The XFOIL interactive program was applied to predict the section airfoil characteristics and low Reynolds number effects. Sectional coefficient analysis results for

Re ≤ 60,000 vary significantly and hence are unpredictable. High sensitivity to twist, chord length distribution, and Reynolds number effects is predicted. Especially, low Reynolds numbers highly affect the results when the propeller rpm varies throughout advance ratio sweeps. The variation in rpm causes scattered thrust and torque measurements in the wind tunnel test data. However,

Reynolds number effects cannot be demonstrated well in traditional coefficient plots [24]. Analysis results for uniform compared to non-uniform induced velocity for the entire blade show a small difference in thrust coefficients, except at low advance ratios. Uniform induced velocity is preferred for the analytical method to avoid calculation complexity. Thrust and torque coefficients as well as efficiency against a series of advance ratio are shown in Figure 2. Wind tunnel tests were performed in the Basic Aerodynamics Research Tunnel at the NASA Langley Aerospace Research

Center in Virginia and the Vertical Wind Tunnel at the U.S. Air Force Research Laboratory in Ohio.

Six “Thin-Electric” propellers, APC series, were considered by Ol et al. [24] for wide- range selections of the pitch-to-diameter ratio including square propellers (pitch = diameter). Some wind tunnel results were compared with the experimental data of Brandt and Selig [37], showing significantly higher efficiency due to “discrepancies” in twist measurements. In Ol’s study, each blade segment was sliced with a band saw or digitally scanned to render the airfoil, and then input to the XFOIL program to analyze the section’s aerodynamic performance. A significant uncertainty in twist angle was observed with an estimate of +/–1 degree. As a result, an inconsistency in twist

distribution was detected in comparison with Brandt’s [37] cross section measurements for the same propeller. An offset of ±2° in analytical predictions shows a substantial shift in thrust and torque coefficients and efficiency in Ol’s report. Lack of information on propeller geometry is a common issue when approaching analytical predictions, since the manufacturer does not provide any information on geometric characteristics [26, 36].

The momentum-blade element analysis results mostly under-predict the experimental data, as shown in Figure 2.

Figure 2. BART data vs. M-BE analysis of APC Thin-E propellers [24]. Uncertainty remains on the selection of the correct twist angle for blade sections in the analytical attempts. Nevertheless, it can be argued that the other reason for such a discrepancy is possibly the

“Reynolds number effects” as the result of not choosing the appropriate rpm used in the analytical method. Small propellers operating at such low Reynolds numbers may produce a massive separation bubble, thus altering entire section aerodyanmic characteristics, hence occasionally unpredictable.

2.2 JavaProp

JavaProp is a new version of the SimProp program written by Hepperle in Java on an open source domain [22]. It is a simple, user-friendly code incorporating blade element theory introduced by Adkins and Liebeck in designing an optimum propeller [20]. Ignoring the three- dimensional effects of the blade, it has the additional ability of finding circumferential and axial velocities added to the incoming flow of each blade element. This simplified method agrees relatively well with experimental data when disk loading is small but is not accurate under static conditions, as mentioned in Chapter 1.

The blade element theory with additional Prandtl’s tip loss factor is integrated into

JavaProp to account for the effect of number of blades and tip loss. Yet, this approximation loses accuracy with fewer blade numbers or at high advance ratios. A series of off-design analyses for a full range of propeller operating conditions and a detailed analysis for a specific advance ratio can be executed by the program. These analysis modes predict the propeller performance, if the local twist and chord distribution as well as the number of blades, propeller diameter, and rpm are known. Furthermore, the design lift-to-drag ratios of four radial segments must be specified.

The “Multi Analysis” mode in JavaProp computes a full range of thrust and power coefficients against the advance ratio from static to windmill conditions. Here, the only detailed description shown is the stalled percentage of the airfoil. For a fixed-pitch propeller operating at lower freestream velocities, the blade section is mostly stalled since it performs at high angles of

attack or beyond the maximum lift. As the advance ratio increases, which is a function of the freestream velocity, efficiency also increases. However, it is not very clear if the designer intentionally reached the target efficiency or it may be only because of how the term is defined, as shown in equation (1.1). The “Single Analysis” mode in JavaProp performs an analysis based on a given advance ratio or velocity in addition to previous given values. This mode allows for studying aerodynamic characteristics along the radius. In addition to lift and drag coefficient radial distributions, the locally induced velocity by the propeller wake is presented as an interference factor. This factor, in terms of axial and swirl components, is coupled to the incoming flow velocity.

Force and bending moment coefficients are also included for structural stress calculations. The

“Flow-Field Card ” in JavaProp offers a convenient study of the slipstream for a specific advance ratio. The color spectrum describes the axial acceleration of the flow field before and after the propeller in the form of the axial velocity-to-freestream velocity ratio [22].

On the other hand, the propeller design process results in the chord length distribution and geometric pitch angle β along the radius r. The design lift coefficient Cl or lift-to-drag ratio L/D, which affects the local chord length c, needs to be specified in advance. It is important to emphasize that the aerodynamic characteristics of an airfoil depend on its chord and thickness. The geometry of a blade section or an airfoil consists of the airfoil profile, thickness, and chord length, and all contribute to its performance, although the contribution of each may vary. It is critical that all necessary geometry details are provided in advance.

The “Airfoil Card” in JavaProp offers a limited airfoil selection along with synthetic airfoil data which are reproduced considering parameters such as zero lift, maximum lift and minimum drag coefficients. Randomly choosing the highest L/D airfoil consequently means sacrificing the off-design performance as well as overall accuracy of the prediction. Smaller design lift coefficient

values result in wider blades. Decreasing the L/D at the tip widens only the tip chord length. For off-design performance at a lower speed or high disk loadings, it is necessary to reduce the lift coefficient for inboard sections to delay the stall when the blade sections are wider and set at lower angles. The engine/motor and propeller combination may influence system performance, which can be derived from the power coefficient and rpm curve. To satisfy the optimum propeller theory originally presented by Betz and Prandtl, the following design parameters [22] need to be prescribed:

Number of Blades

A propeller with more blades increases the uniform distribution of thrust and power in the wake of the propeller but with a small improvement in efficiency. For a constant power or thrust, an increase in the number of blades causes shortening of the chord length. Reducing the propeller diameter is the tradeoff for maintaining the chord length, although this will usually decrease efficiency if the tip speed is less than Mach one. The number of blades B also contributes to the propeller solidity σ, which represents the ratio of blade area to disk area as defined, and directly contributes to the thrust and power coefficients—see equations (2.13) and (2.14).

Velocity

Freestream velocity along with rotational speed defines the pitch distribution of the propeller. The desired efficiency might be obtained by increasing the pitch of the propeller but causes the blade to stall at certain incoming flow speeds or rotational speeds.

Diameter

The diameter of the hub determines the effective propeller diameter. The effect of the propeller diameter on performance is significant: the larger the propeller diameter, or consequently the propeller area, from the continuity equation, the more thrust that can be obtained for a constant

velocity along the control volume. On the other hand, the same effect can be observed on high- aspect-ratio wings on sailplanes that produce more lift with less drag or L/D. In general, the best performance is attained when the pitch-to-diameter ratio is one.

Lift and Drag Distributions

The prescription of drag polar and design angle of attack at each radial location is more convenient than section design lift and drag coefficients. Figure 3 shows an example of a canned or artificial airfoil drag polar used in JavaProp, which characterizes essentially zero lift, maximum lift coefficient, and minimum drag coefficient. Usually, a propeller maximum efficiency can be obtained when the section lift-to- drag ratio is at its peak. Lower angle of attack settings work better for the overall design aspects that include off-design conditions since the stall occurs gently.

Regardless of how one delays stall by controlling the lift-to-drag ratio, analysis results are unreliable at very low advance ratios.

Figure 3. Synthetic drag polar of Clark Y airfoil at different Reynolds numbers [22]. Desired Thrust or Power Available

Based on the total drag or the available motor, either the desired thrust of the propeller or a given useful shaft power can be specified.

Density

Fluid density does not have any influence on the power or thrust coefficients as well as efficiency, but it greatly impacts the propeller size and shape. For example, hydro-propellers have smaller dimensions compared to airscrews. Moreover, the air density determines whether the tip has reached supersonic speed. Values for power and thrust are calculated directly from the fluid density.

The Adkins and Liebeck design method used in JavaProp is intended to correct Larrabee’s difficulties and find the exact solution. With specifications of the previous terms, the following iterative design procedure is used to find the pitch and chord-length distribution.

a. Select an initial estimate for the ratio of vortex displacement velocity to the freestream

velocity v’/U, or select v’/U = 0 to start.

b. Find Prandtl’s momentum loss factor and flow angle at each element.

c. Calculate the product of the local total velocity and blade section chord along with the local

Reynolds number.

d. Determine the airfoil section drag-to-lift ratio and angle of attack from the airfoil data.

e. For the minimum drag-to-lift ratio, revise Cl, and repeat step c.

f. Calculate the axial and rotational interference factors as well as local total velocity.

g. Determine the blade chord length using step c results, and twist β.

h. Find the four derivatives as defined, and integrate them over the blade region.

i. Find v’/U and either the non-dimensional power or thrust coefficients.

j. If the new value for v’/U is different from the old value (e.g., 0.1%), then return to step b.

k. Determine the propeller efficiency and other parameters, such as propeller solidity.

These steps usually take more than a few iteration cycles to converge. Also, the viscous loss term can be added for more accurate results.

Although JavaProp is a fast and user-friendly code, it has its limitations, as discussed previously. Predictions where flow separation occurs are poor, e.g., at high disk loadings or low advance ratios. Furthermore, restrictions limit the section blade aerodynamic characteristics that can be implemented. Finally, boundary layer interactions with complex phenomena in cases such as three-dimensional effects, Mach number effects, etc., are ignored in JavaProp. Users must agree on whether to sacrifice accuracy in order to obtain a quick and fairly reasonable estimate.

Hepperle presented validation results of his code in comparison with Theodorsen’s experimental data [38]. The geometry was imported by the JavaProp “Geometry Card” feature using a three-bladed propeller and Clark Y section airfoil at Re = 500,000. However, it is not clear if the airfoil data used appropriately represented the exact tested propeller blade characteristics.

Figure 4 shows all validation results obtained in coefficient forms and efficiency against advance ratio J.

Angles settings show the pitch angle at 75% radius, or 0.75R. The thrust coefficient (shown in the upper left portion of Figure 4) only agrees with the trend of the linear region of the curve with a systematic shift, but not as much where the flow is mostly separated. Here, a similar trend is apparent, as the analysis results underpredict the experimental data, as was shown in momentum- blade element theory validations. The power coefficient curves (right side of Figure 4) show an identical trend to the thrust coefficient graph, with large deviations at the lower advance ratios.

Note that the experimental data has some discontinuities as well, depending on each test condition.

Generally, a propeller operates at the linear region of this regime, except for takeoff and landing. The efficiency curve may cancel out practical errors since it depends on both the thrust and power coefficients. It may not be wise to validate a method with the efficiency plot.

Nonetheless, the more accurate it becomes, the better its assessment on overall aircraft performance.

Figure 4. JavaProp validation results compared with NACA TR-594, designated blade angle at 0.75R [22].

2.3 Vortex Theory

Unlike the previous momentum-blade element theory, vortex theory incorporates the induced effect. A complex iterative process and, therefore, an increase in calculation time is inevitable for obtaining considerably more accurate results. The vortex theory starts with consideration of the ultimate wake of the optimum propeller, or Betz’s condition, as discussed previously in Chapter 1.

Studies have been conducted to justify the assumption that the normality condition holds between the effective velocity VE and the induced velocity w (see Figure 1). Prandtl’s tip loss factor F is an approximation for Goldstein’s kappa factor, which becomes more exact as J decreases or the number of blades increases, and can be expressed as

2 1 Bx(1) F cosexp  (2.18) 2sin T where ϕT is the tip helix angle of the blade. For a lightly loaded propeller,

1 T  t a n (2.19)

With Prandtl’s tip-loss approximation of Goldstein’s vortex theory, the bound circulation Γ and the tangential velocity component wt of the induced velocity can be related in

BГ ≈ 4π rFwt (2.20)

From the Kutta-Joukowski theorem,

1   cC V (2.21) 2 lE

Substituting equation (2.21) into equation (2.20) yields

VE wt CxFl  8 (2.22) VVTT

Now VE /VT can be shown in terms of wt /VT as

1 2 V w   w w  E x22 t  x   4 t x  t  (2.23) VV 2 VV T T  TT 

Solving for wt /VT will determine the induced angle of attack αi as

1 Uw a i tan  (2.24) rw t

The axial component of induced velocity wa can also be found as a function of wt. From the geometry above,

2 2 2 VVE Rcos  i (2.25)

Hence, it is possible to derive

2 2 VE 2 2 2  (Jx )cos i (2.26) VT which shows the vortex theory and momentum-blade theory differences in CP and CT equations

(2.13) and (2.14). The left-hand side of equation (2.26) is used in vortex theory, and the right-hand

2 side of the equation is used in the momentum-blade element, where cos αi ≈ 1, since αi is assumed to be a small angle. Other refinements to the angle of attack and the lift coefficient in vortex theory may increase the accuracy.

Validation of vortex theory was attempted by Moffitt et al. [36] for UAV-scale propellers using similar method to measure blade-section geometry, as described in section 2.1. A given full- scale propeller was also designated by McCormick [5] to exercise vortex theory applications and compare with wind tunnel data for validations. This three-blade 5868-9 propeller has a Clark Y section with chord, twist, and thickness distribution, as provided by previous researchers [38-40].

Although details on other geometric features and test conditions are not specified, results are used in different validation examples, such as JavaProp. McCormick’s vortex theory approach is relatively easy to utilize since the computer programming procedure is provided to predict the performance of this specific propeller. Software Maple 16 was used for developing this program.

Results for thrust and torque coefficients in addition to efficiency are shown in Figure 5.

Most airfoil characteristics, except post-stall lift coefficient behavior, are estimated with a no-detail description of the approximation process. The Cl range is limited between –0.8 and 1.2

for this calculation. As discussed, a major portion of the propeller blade stalls at a lower advance ratio. Evidently results for the thrust coefficient in this region are poor; however, it becomes astonishingly accurate in the linear region (see Figure 5). As discussed previously, the blade twist angle β needs to be adjusted to the zero-lift line instead of the chord line. McCormick estimates the zero-lift line angle α0l to the chord line for this particular airfoil as

t   46 (2.27) 0l c

The slope of the section lift coefficient a for the Clark Y airfoil is taken to be

t a 0 . 1 1 . 0 (2.28) c

Cl can be determined from equation (2.5), and Cd is also expected to be

2 CCC 0.0100.15 dd min  l (2.29) where t C 0.0040.017 (2.30) dmin c

Note that parameters α0l, a, and Cdmin are a function of the thickness-to-chord length ratio t/c. It is convenient to use t/c in these equations, since the blade’s radial distribution is presented in the report. To find both Cl and Cd as a function of angle of attack, an iterative process needs to be implanted to simultaneously calculate all the unknown parameters, primarily wt /VT and the induced angle of attack αi in equations (2.22) and (2.24).

0.2 JP-15 0.25 JP-25 JP-35 VT-15 0.16 VT-25 0.2 VT-35 Exp-15 0.12 Exp-25 0.15 Exp-35 T P C C 0.08 0.1

0.04 0.05

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

0.8

0.6 η

0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 5. Vortex theory, JavaProp, and propeller 5868-9 experimental results [39] comparison, with designated blade angle at 0.75R.

Close agreement of vortex theory predictions is clear when the blade is at lower angles or not stalled. This is because the airfoil characteristics are fairly known in this region. As the advance ratio decreases, the section angle of attack increases, and the blade starts to stall from the inboard section of the blade. The results of vortex theory prediction show linear behavior for the thrust coefficient throughout the advance ratio (shown in left top of Figure 5). No post-stall treatment is

applied for the airfoil lift coefficient. The power coefficient and efficiency curves coincide rather well with the test data. However, JavaProp analysis has a systematic under-prediction for most regions. This deviation possibly indicates that the zero-lift line of the airfoil might be off and not well prescribed in JavaProp validations, according to Hepperle [22]. Despite the offset of the results, it appears that the overall outcome of JavaProp is acceptable for the initial design for such a simple and fast tool. One can argue whether the time and effort used in the programming of vortex theory is worth the sacrifice of obtaining a more reasonable overall result.

2.4 Computational Fluid Dynamics

Without a doubt, the most sophisticated and potentially accurate analysis and design tool is computational fluid dynamics. Solving Euler and Navier-Stokes equations also requires extensive calculation and central processing unit (CPU) time when compared with previous analytical methods. This is not the only concern; CFD codes also need to be verified. CFD validation is a principle that must be coordinated between computational and experimental constraints. Lack of knowledge in physical modeling, limited computer resources, and mathematical approximation increase the uncertainties in the CFD application [34]. As a result, the extension of CFD into the design process depends on the credibility of how the code is validated through experiments, that is, how the code is an essential part of its evolutionary progress. Two examples are introduced here to show the extent of CFD applications in propeller analysis and in the existing validation problems.

2.4.1 CFD Example 1

An analysis of propeller wake interference effect was conducted by Strash et al. [26]. Their results are compared with wind tunnel test data obtained by the Flygtekniska Försöksanstalten

(FFA) or Aeronautical Research Institute of Sweden [41, 42] in the late 1980s. The extensive

experimental data consist of four nacelle/wing combinations where axisymmetric nacelle and axisymmetric nacelle/wing combinations were used for validations (see Figure 6). Time-averaged pressure distribution over the nacelle and wing, a velocity components survey on the propeller slipstream, and typical thrust and torque measurements for a single advance ratio of 0.70 were investigated. The propeller used was a one-fifth scale model of a Dowty Rotol R243 propeller on a SAAB 340 powered nacelle.

Figure 6. Combined propeller/nacelle/wing grid domain [28].

It seems that the vast amount of experimental data is best suited for CFD validations as used in other studies [28, 33]. Nonetheless, despite specifications of nacelle/wing geometry and wind tunnel model installation, no information on the propeller geometry is available except for the diameter of 0.64 m. Reluctantly, Strash et al. [26] compromised the R243 propeller to a similar one but with a different section chord and twist distribution than the Dowty Rotol R212 propeller that was apparently available. Therefore, credibility of the validation of this study is questionable since the exact propeller geometry is unknown. It seems like this is a common issue in most

validation processes, as explained in previous examples, before examining the credibility of the code.

The calculated thrust coefficient was 12% off from the test data. The surface pressure coefficient distribution along the x-axis of nacelle is presented in Figure 7 at an advance ratio of

0.7. Figure 7 (a) represents the propeller/nacelle combination with no wing interaction at a

0-degree angle of attack, and Figure 7 (b) shows this for a 10-degree angle of attack. Strash et al. concluded that with the “qualitatively quite good” comparison results, the numerical simulation is

“feasible” for preliminary design applications.

0.8 0.8 Test Data Test Data Upper Surface Upper Surface Lower Surface 0.4 0.4 pr

0 pr 0 c c

-0.4 -0.4

-0.8 -0.8 -15 0 15 30 45 -15 0 15 30 45 x x

(a) (b)

Figure 7. Propeller/nacelle pressure distribution at Mach 0.15, 6650 rpm: (a) α = 0°, (b) α = 10°, data digitized from [26].

The same FFA wind tunnel data was applied for validation purposes in numerical simulations [28], although there was no indication of whether the exact propeller geometry was used or not. A wake survey in terms of non-dimensionalized dynamic pressure immediately behind the propeller where x/R = 0.14 is shown in Figure 8. Time-averaged data match well in comparison with two other time-accurate pressure profiles.

Figure 8. Propeller/nacelle/wing slipstream dynamic pressure survey behind the propeller [28]

2.4.2 CFD Example 2

Another dilemma in CFD validation is when the code developer only holds details of the propeller model geometry and tunnel boundary conditions, which have not been disclosed to the public. Moffitt et al. [30] compared the experimental data of a sub-scale six-bladed propeller designed by Aero Composites Inc. to the solution of a Reynolds-averaged Navier-Stokes CFD flow solver. Geometry descriptions of this investigation exclusively belong to the United Technologies

Research Center (UTRC). Generally, readers are not able to verify and compare a code’s ability to any other published test data for this reason. Eventually, analysts must run a series of wind tunnel tests for the purpose of individual validation. In addition to feasibility of the facility and cost of the wind tunnel testing, the experiment needs to be designed and scaled for a validation goal.

The results of propeller testing and CFD analysis were compared by Moffitt using the prescribed traditional vortex theory [36]. Figure 9 shows the UTRC wind tunnel settings and computational domain for the tunnel boundaries and propeller geometry. To assess the fabricated blade geometry, a white light scan was used on three of the six propeller blades made with

maximum variations of a few thousandths of an inch. Moffitt et al. concluded that the CFD codes agreed better than the classical vortex theory, especially in predicting thrust and torque as a function of blade pitch angle. Also, they argued that the code has the ability to overcome the effects of a low Reynolds number, wall blockage, and other measurement difficulties in the predictions.

Figure 9. Propeller wind tunnel model and grid domain [30].

Another CFD propeller analysis problem is using an inadequate validation method. The experiment chosen by Westmoreland et al. [29] for code validations consisted of two untwisted symmetric rotor blades at hover [43]. Although this test was comprised of a pair of rotating blades set at a five-degree angle of attack, the helicopter rotor model did not fully replicate the complex propeller geometry. Moreover, the pressure coefficients of the rotor blade surfaces were compared, not the expected propeller thrust and torque coefficients. Recognizing the existing problems in

CFD propeller analysis, especially in its validation methods, the urgency to solve these issues and build confidence in CFD results is high. Chapter 3 presents a summary of the problems and goals, including the approach taken to obtain these objectives.

CHAPTER 3

PROBLEMS AND GOAL

Validation is the primary means to examine the precision and reliability in analytical and computational solutions [35]. The basic method of validation is to quantify error and uncertainty of prediction in simulation and compare this with experimental data. As the examples in Chapter

2 describe, propeller analysis and prediction methods suffer from lack of extensive experimental data designed specifically for validation purposes. This chapter provides a summary of the problems and difficulties in existing propeller analysis. Furthermore, the objectives of this project and considerations made to approach the challenge are explained.

3.1 Problems in Propeller Validation

Geometry Details

For most validation experiments, few details on propeller, spinner, nacelle, and tunnel test section geometry are available. The absence of any of these geometric features or even accurate confirmation of the constructed model dimensions causes a severe failure in the essential physics of modeling. Especially, the complex geometry of the propeller blade requires a comprehensive instruction of reproduction or modeling procedure. Accessibility of wind tunnel data for section aerodynamic characteristics at various Reynolds numbers is also very important.

A series of analysis was executed to evaluate the influence of each critical factor in design, fabrication, and testing environment. JavaProp was utilized for its convenience and its broad setup flexibility in model selections to compare results. 17×12 APC Thin-Electric propeller twist and chord distribution was used as the baseline. Factors found to have the most impact on the propeller performance are, in order, the following: pitch angle, chord length, section airfoil, and airfoil aerodynamics characteristics used based on its operating Reynolds number. Figure 10 to Figure 13

show sensitivity comparisons of individual variable as indicated for a generic propeller. An additional measurement of the blade deformation or calculated load of deformed components can also be helpful. Spatial dimensionality of the wind tunnel test section, as well as geometric specifications of the nacelle, spinner, and model mount, etc., must be fully documented.

0.2 0.2 Δβ = 0° Δβ = 0° Δβ = 10° 0.16 0.16 Δβ = 10° Δβ = 20° Δβ = 20°

0.12 0.12 T P C C 0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J Figure 10. Sensitivity analysis of pitch angle using JavaProp.

0.2 0.2

c/R = 0.10 @ .75R c/R = 0.10 @ .75R 0.16 c/R = 0.13 @ .75R 0.16 c/R = 0.13 @ .75R c/R = 0.15 @ .75R c/R = 0.15 @ .75R 0.12 0.12 T P C C 0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J Figure 11. Sensitivity analysis of chord length using JavaProp.

0.2 0.2

Clark Y Clark Y 0.16 0.16 Flat Plate Flat Plate Eppler 193 Eppler 193 0.12 0.12 T P C C 0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

Figure 12. Sensitivity analysis of propeller section airfoil using JavaProp.

0.2 0.2 Re=25,000 Re=25,000 Re=100,000 Re=100,000 0.16 0.16 Re=500,000 Re=500,000

0.12 0.12 T P C C 0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

Figure 13. Sensitivity analysis of airfoil aerodynamics for ClarkY using JavaProp.

Test Conditions

Boundary conditions of the experiment are also critical parameters for computational simulations that are frequently missed in validation reports. Typically, these consist of average quantities of test section freestream velocity, dynamic pressure or total pressure with static pressure, and total temperature. Essentially, all measurements are required to be calibrated for wind tunnel testing. Turbulence intensity, boundary layer thickness, and boundary layer transition are also supplemental quantities. Although it is important for CFD turbulence codes to reference these data as accurately as possible, some wind tunnel facilities are reluctant to measure or disclose detailed flow quality. Furthermore, the position of all instrumentation needs to be specified for

CFD boundary condition settings.

Results

Lack of collective global and local measurements is evident in previous work. These are fundamental requirements in CFD validation experiments. Global quantities may be classical propeller thrust and torque coefficients, and efficiency as a function of the advance ratio. Local measurements may include nacelle surface pressure coefficients, slipstream local velocity distribution and its components, and wing surface pressure distribution. Also valuable are revolution speed, local Reynolds numbers, and freestream velocity, since they can identify the effects of coupled parameters against each other. Similarly, accuracy and limitations of individual instruments are recommended to be introduced. In addition, methods of dynamic and/or static tare and blockage corrections applied in the results must be recognized.

Measurement Repeatability and Error

Experimental errors, such as random and bias uncertainties in measurements, are suggested to be evaluated. An Advisory Group for Aerospace Research and Development (AGARD)

document [44] on standard wind tunnel testing has procedures for error estimation; however, they are not widely used in validation experiments. Finally, repeatability tests on the model and facility are advised, for example, duplicating the test on a different day with the same test conditions. Also, repeatability on a reconstructed model can be beneficial if cost and time allow. Exercising another wind tunnel facility with the equivalent test conditions proves that the results are independent from instrumentation bias.

3.2 Statement of Objective

The objectives of this dissertation are as follows:

 To provide a universal geometric description as well as comprehensive experimental data

on two propellers, primarily for low Reynolds number propeller performance validations.

 To capture critical elements of the experiment in the results.

3.3 Methods of Approach

The primary purpose of this effort is to provide a database for analysts to assess the validity and accuracy of a computational analysis by providing crucial information. Considering the existing problems discussed above, the following steps were taken to achieve the objectives above:

Geometry

Primarily, a simple blade propeller with a constant pitch-to-diameter ratio, chord length, and thickness was tested. Then, a practical blade propeller with a varying pitch-to-diameter ratio and chord length as functions of the propeller radius was evaluated. The applied blade section airfoil profile and experimental data is well documented for a range of Reynolds numbers, particularly lower Reynolds numbers by different sources. All critical geometries are reproducible via simple programming or an accessible computer-aided design (CAD) file. The test section

geometry, nacelle, spinner, and model mount geometries are presented. The coordinate measuring machine (CMM) or 3D scan (point cloud) measured accuracy of the blades’ actual fabrication.

Test Conditions

The freestream flow was calibrated at the test section by measuring the average freestream velocity, total and static pressures, and tunnel temperature. The experimental procedure and apparatus descriptions were provided from the work of Merchant and Miller [45]. The test section inlet and outlet pressures, test section pressure gradient, and instrumentation positions were determined. Known wind tunnel flow quality, such as turbulence intensity and flow angularity, are provided.

Collective Results

Thrust coefficient, power or torque coefficients, and revolutions per minute for an adjustable pitch propeller with five degrees increment were obtained as global quantities. In addition, nacelle surface pressure distribution and propeller wake velocity components were measured as local quantities. Some crucial low Reynolds number effects on results were captured using a variety of rpm and freestream velocity tests. Corrected and uncorrected wind tunnel blockage data and the method of dynamic and static tares are provided.

Experimental Errors

Repeatability tests on the propeller model, test condition, test facility (wind tunnel), and testing procedure were implemented. Known instrumentation bias and error as well as uncertainties in measurements are quantified and documented in the report.

CHAPTER 4

EXPERIMENTAL APPARATUS

As previously explained, the initial objectives and considerations were implemented in model selections and wind tunnel testing methods. Accordingly, apparatus geometries and specifications are described in detail in this chapter. The measurement system and experimental procedures are also documented in detail by Merchant and Miller [45].

4.1 Geometry Descriptions

This section provides all the geometry details necessary for modeling and reproduction purposes. This includes the wind tunnel, model installation apparatus, and all critical components such as nacelle, spinner, and propeller blade specifications.

4.1.1 Wind Tunnels and Model Installations

3×4 LSWT at Wichita State University

Tests were carried out in two separate low-speed wind tunnel facilities with different test section geometries. Initially, all tests were conducted in the 3-foot by 4-foot low-speed wind tunnel

(3×4 LSWT) at Wichita State University (WSU). This open-return tunnel has a rectangular eight- foot-long test section that can reach a maximum dynamic pressure of 38 pounds per square foot

(psf). However, results are obtained at a dynamic pressure of no higher than 20 psf. The total pressure ring is located at the tunnel pre-section inlet, which is 20 feet long and has a cross section of 7 feet by 10 feet. The static pressure ring is at the test section entrance, and the difference of the two pressure measurements gives the tunnel dynamic pressure reading that is calibrated to the center of the test section. However, the indicated dynamic pressure is neither compensated nor corrected for the presence of the C-strut mount (also referred to as C-mount) since its blockage is

estimated to be less than 0.4% increase in the tunnel dynamic pressure readings. A picture of the tunnel and its geometry details including the C-mount are presented in Figure 14.

Figure 14. Photo (top) and description (bottom) of 3×4 LSWT at Wichita State University.

The model was mounted on a sensor/motor platform attached to the C-mount and described in Figure 15 along with a full-model assembly photograph. The model nacelle front edge was set at 18.29 ± 0.03 inches from the tunnel C-mount tip, the geometry of which is shown in Figure 14.

The rotation axis coincides with the nacelle center line, and the distances to the plane of rotation presented here. All tests were conducted at a zero-degree angle of attack and yaw angle within accuracy of ±0.2 degree.

Figure 15. Model installation (top) and side view (bottom) in 3×4 LSWT.

7×10 Wind Tunnel at the National Institute for Aviation Research

To minimize the tunnel blockage effect and assess facility bias error in results, more tests were performed in the Walter Beech Memorial 7-foot by 10-foot low-speed wind tunnel at the

National Institute for Aviation Research (7×10 NIAR). This unique facility has a rectangular test section that is 7 feet high, 10 feet wide, and 12 feet long, with a contraction area ratio of 6 to 1 from a circular pre-section. A 2,500 horsepower (HP) fan can generate a test speed up to 240 mph and a maximum dynamic pressure of 125 psf. The closed-loop tunnel has an active heat exchanger temperature control that allows continuous full-speed operation all day long. Flow conditioning tools were implemented to reduce the turbulence intensity of the tunnel as low as 0.07% at 3.8 psf tunnel q in core flow regions, that is, at least a foot from any wall. The tunnel total pressure ring is located at the pre-section where the static pressure ring is at the inlet of the test section. The tunnel dynamic pressure was calibrated to the center of the test section and corrected for the presence of the C-mount. In addition to uncorrected and corrected tunnel q for blockage, two pitot- static tubes located at the entrance and exit of the test section provide the total and static pressures for boundary condition settings. Moreover, pressure gradients along the test section are measured via pressure transducers connected to both test-section side walls. All pressure ports measured the pressure differential to the tunnel barometric pressure.

The geometry details of the 7×10 NIAR wind tunnel and the model installation on the C- mount are provided in Figure 16. The model was installed far ahead of the mount so that the flow affected by its existence was minimal, as shown in Figure 17.

For easy reproduction and modeling purposes, considerations were made not to expose any wiring or tubing at the vicinity of the model or the test section in both wind tunnels.

Figure 16. Description of Beech wind tunnel and C-mount assembly in 7×10 NIAR.

Figure 17. Model installation and side view in 7×10 NIAR.

4.1.2 Model Propellers

PD1 Propeller

Two different propeller blade geometries were designed and tested. Initially, a basic propeller geometry was considered for wind tunnel testing, which was expected to simplify the modeling and analysis effort for validations. Propeller blade PD1 was selected to have a constant pitch-to-diameter ratio (p = 12 inches, D = 12 inches, or p/D = 1), chord length, and thickness.

Hence, the geometric twist angle β at 75% blade radius, β0.75, was 23° calculated from equation (2.1). For the blade profile, an Eppler 387 (E387) airfoil was utilized for its high lift-to- drag aerodynamic characteristics in addition to the extensive experimental data available, especially at low Reynolds numbers [46-51]. This airfoil is designed for model gliders operating at Re = 2.0 × 105 where theoretical predictions and empirical drag polar agree surprisingly well

[51]. The maximum thickness of this airfoil is 9.06% of the chord length and the maximum camber of 3.2%. The XFOIL program was used to extrapolate 200 profile coordinates from the original 61

points, as presented by Somers and Maughmer [46], which are tabulated in Appendix A. For its manufacturing feasibility, 5% of an inch chord length trailing edge was omitted, as presented in the coordinates. This was necessary to ensure a reasonable trailing-edge thickness.

An open source CAD software written in C++ language, OpenSCAD, was used for the initial design and outline drawings [52]. Figure 18 shows the software interface. The left-hand side describes the script file that generates an object, or in this case, the propeller. Initial designs of critical geometries were rendered by OpenSCAD, the program files of which are provided in

Appendix A. The advantage of this program is that it is capable of producing complex-defined shapes. The profile coordinates were imported into OpenSCAD’s propeller file, and then

Figure 18. PD1 propeller in OpenSCAD interface.

extruded and twisted to build the blade shape using simple scripted functions. Note that the blade was twisted at its profile’s centroid, that is, x/c = 40.04% and y/c = 2.95% of an inch chord length

NOT 0.95 inch.

A detailed design was performed using SolidWorks software. The blade file exported in

STL format by OpenSCAD in a metric unit system was imported into SolidWorks. Sixteen profile segments were extracted, and loft function was used to recreate the geometry for the fabrication purposes. Figure 19 shows the CAD design of the propeller blade assembly and final computer numerical control (CNC) machined products. The assembly consisted of the blade, blade root, pitch angle control plate, and pin for blade pitch angle adjustments with five degrees increment at three different β0.75 settings: 23°, 28°, and 33°. The blade was connected to the root through two stainless pins perpendicular to the longitudinal blade axis. The blade was machined from an aluminum alloy 7075-T6 block. Stress analysis results show that the blade deflection under maximum loads at β0.75 = 33° is 0.05 inch at the tip in the thrust direction. For the analysis, centrifugal force, thrust, and torque were simultaneously applied.

Figure 19. PD1 Propeller blade assembly.

A 3D scan on both sides of each blade was performed to verify the accuracy of the constructed models. Figure 20 shows a very good match when comparing the final fabricated blade to the design CAD geometry, indicating that the variation is within ±0.002 inch, where the accuracy of the scan system is ±0.001 ~ 0.002 inch.

Figure 20. 3D scan of PD1 propeller blade, within ±0.002 inch accuracy.

COMP Propeller

Likewise, for practical and advanced analysis efforts in validations, a complex propeller geometry “COMP” was considered. This propeller blade has a twist and chord length as functions of the blade radius with a constant thickness. Similar to the previous PD1 blade, the E387 airfoil was utilized. However, contrary to the 5% reduction in the PD1’s trailing edge, 10% was omitted.

The coordinates of this propeller blade are presented in Appendix A. This reduction was necessary

to ensure a reasonable trailing-edge thickness of the blade since it has shorter chord length at the tip of the blade. Since OpenSCAD operates in a metric system, equations are written accordingly.

However, the U.S. unit system is adopted in this document. The blade design was inspired by

Hartman’s 5868-R6 blade form curves, though simplified to fit equivalent polynomial functions

[39]. The twist distribution β is a function of the local blade radius r as

β = 1714.5/r (4.1) where the propeller radius R = 6.0 inches—or 152.4 mm for equation (4.1)—and β is calculated in degrees, where the reference β0.75 = 15°. The chord length c (mm) is also described as

c = - 0.0033r2 + 0.6r - 4.5 (4.2) where the blade thickness remains constant relative to the chord length of 9.06% to avoid unnecessary complexity.

Figure 21 shows the OpenSCAD blade design, detailed design, and fully assembled COMP aluminum blades. Twenty-four profile sections were exported as an STL file and used for the detailed design in SolidWorks. This propeller also has a variable five-degree increment pitch with four angle settings that can be manually set at the hub. The blade pitch angles can be adjusted at

β0.75 = 15°, 20°, 25°, and 30°. Structural analysis shows each blade can withstand a maximum centrifugal force of 77.1 lbf, 1.5 lbf thrust, and 3.1 in-lbf torque loads applied simultaneously with less than 0.1 inch of deflection at the tip in the thrust direction (at β0.75 = 30°). Figure 22 shows the 3D scan results for one of the blades. The CNC machining accuracy is satisfactory for such a small and thin blade and kept mostly under -0.007 inches variation showed in dark purple color.

Figure 21. COMP propeller blade design and assembly without nacelle and spinner.

Figure 22. 3D scan results of COMP blade within -0.007 inch accuracy.

4.1.3 Model Nacelle-Spinner

Similar steps were taken for the nacelle and spinner designs using OpenSCAD. The geometry script files are available in Appendix A. These components were constructed using a 3D printer using polylactic acid (PLA) filaments. The nacelle was divided into halves for easy accessibility and strapped to the sensor/motor platform. The nacelle surface had a total of 62 orifices—eight around the perimeter and eight in the longitudinal direction—which were connected to a pressure transducer to measure static pressure. Figure 23 shows the full CAD model assembly including important dimensions. Two pressure ports are omitted as a slot was made on the rear bottom of the nacelle for 3×4 LSWT C-mount, as shown in Figure 23. This slot was sealed for the 7×10 NIAR testing with the original design curvature part shown in Figure 24.

Hub components were also constructed using the 3D printer enclosing the blade root and the angle control plate, which was installed on the motor shaft. The hub consisted of two parts— top and bottom—and a U-hold to tighten the propeller blades and hold the hub parts together on the motor shaft. A magnetic pickup tab was located between the hub and the nacelle. The spinner enclosed the hub assembly. The spinner was aligned carefully with the nacelle to replicate the design geometry. The gap between the spinner and the nacelle was 0.05 inch. Two screws were used to attach the spinner to the hub, and screw caps were designed to fill the holes and render the geometry. Considerations were made to increase the stiffness of the spinner, in order for it to withstand high rpm centrifugal forces without deflection. The blades were balanced where the center of gravity deviated within ±1.0% of the blade length in order to decrease system vibration.

The motor shaft and nacelle alignment were also important to reduce vibration. The gap between the motor shaft, magnetic pickup, and nacelle were sealed with brushes and tapes. The nacelle and spinner surfaces were painted and polished several times to achieve a smooth finish.

Figure 23. Nacelle assembly CAD design (dimensions in inches).

Figure 24. Nacelle bottom side modification for 7×10 NIAR setup.

4.1.4 Model Setup Assessment

Sensitivity analysis in the previous chapter showed that the pitch angle setting significantly influences performance. Here, a 3D scan was performed to evaluate the hub setup accuracy for a pitch that is true to the design criteria. The PD1 pitch angle set to β0.75 = 23° is shown in Figure 25 for one blade’s top and bottom sides. Both sides have nominal differences of less than a fifteen thousandth of an inch when compared to the CAD models. The same results are shown for the

COMP blade in Figure 26. Note that the spinner and nacelle are excluded from the picture to focus on the pitch setting accuracy. In addition, Figure 27 shows the 3D scan image of the nacelle-spinner assembly when compared with the CAD design. The overall setup and manufacturing accuracy were satisfactory for such a large-scale and complex model. Maximum offset appeared in the nacelle mid-section at approximately +0.07 inch that is less than 1.0% of the nacelle diameter. It also shows that alignment of the spinner/hub with the nacelle was excellent, which requires an extensive setting effort.

Figure 25. Top and bottom of PD1 blade 3D scan set at β0.75 = 23°, within +0.015 inch accuracy.

Figure 26. Top and bottom of COMP blade 3D scan at β0.75 = 15°, within ±0.020 inch accuracy.

Figure 27. Both sides 3D scan of the nacelle-spinner assembly, within +0.070 inch accuracy.

4.1.5 System Performance Prediction

Numerical analyses were performed for the designed propellers to predict the performances, integrating JavaProp and vortex theory, as discussed in previous chapters. This also helped to set an appropriate test matrix. The results are shown in Figure 28 and Figure 29 for the two models PD1 and COMP, respectively. Since JavaProp does not have the E387 airfoil in its database, the drag polar of the E193 profile was selected with section L/D set at 30. E193 was slightly thicker with 10.2% thickness and the maximum camber of 3.0% compared to the E387

9.06% and 3.2% respectively. However, XFOIL aerodynamics analysis showed identical results for both airfoils. Geometry descriptions of the chord length and blade twist distribution as a function of the radius were imported into JavaProp for both propellers. The spinner area covered

30% of the propeller diameter. In addition, vortex theory was utilized based on self-written program with E387 aerodynamics data obtained from the low-turbulence pressure tunnel (LTPT) at the Langley Aerospace Research Center [47].

A linear curve estimated the Cl as a function of angle of attack α and a fourth-order polynomial curve for Cd as a function of Cl obtained from a range of α = -3° ~ 8°. Hence, post-

stall treatment on the Cl curve was not implemented. The Cl -α and Cl -Cd relations are, respectively,

Cl 0.097520.39195 (4.3)

4 3 2 CCCCCd 0.169940.486770.466850.16239l l l 0.03413 l (4.4)

However, JavaProp airfoil database had a drag polar with several key parameters implemented, such as maximum lift, minimum drag coefficients in addition to post stall trend which is similar to

Figure 3.

As shown, performance analysis results between the two methods vary for the PD1 model as opposed to the COMP propeller. Both thrust and torque predictions have large differences between the two analysis methods for the PD1 model. This may suggest a large flow separation, especially when the propeller is highly loaded or at lower advance ratios. On the other hand, surprisingly, both methods match very well for the COMP model for a range of advance ratios for thrust and power coefficients as well as efficiency curves. Regardless of the conclusion, analysis results provide a good estimation of the expected values.

A detailed analysis at a certain test condition was also performed using same methods to study the aerodynamics characteristics along the radius for both propellers as shown in Figure 30 to Figure 31. The angle of attack, lift and drag coefficients at local radius locations were presented for one advance ratio where J = 0.20, and the PD1 was set to β0.75 = 23°, and β0.75 = 20° for the

COMP. Although the angle of attack curves had a similar trend for both propellers, the difference between the two methods was significant for the PD1 propeller. A substantial portion of the blade was at stall where α > 12° for the PD1, according to the E387 wind tunnel results showed in

Chapter 5. Thus, the difference in post-stall treatment between the two methods was clear in lift and drag coefficient plots which also explains the PD1 performance plots disagreements.

Finally, Figure 32 shows the local Reynolds number along the radius for the same advance ratio calculated by JavaProp. The Reynolds number of a significant portion of the blade was under

100,000 (i.e., r/R ≤ 0.75) which can be considered as low Reynolds number. Furthermore, this was less than 60,000 where r/R was 0.45 or less. Hence, low Reynolds number effect could cause discrepancy in the wind tunnel results as shown in Chapter 5.

0.32

0.28 JavaP Vortex 33° 0.24 28°

0.2 0.2 JavaP 23°

33° Vortex 0.16 28° P 0.16 23° C

0.12 0.12 T C 0.08 0.08

33° 33° 0.04 28° 0.04 28° β = 23° β = 23°

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

0.8

33° 0.6 28° η β = 23° 0.4

JavaP Vortex 0.2

0 0 0.4 0.8 1.2 1.6 2 J Figure 28. PD1 propeller performance analysis.

0.2 0.2 JavaP JavaP Vortex Vortex 0.16 0.16

0.12 0.12 P T C C 0.08 0.08 30° 30° 25° 25° 20° 0.04 0.04 β = 15° 20° β = 15° 0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

1 JavaP Vortex 0.8

0.6 30° 25° η 20° 0.4 β = 15°

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 29. COMP propeller performance analysis.

32 3.2 JavaP Cl JavaP Cl Vortex Vortex Cd JavaP 24 2.4 Cd Vortex d C (deg)

16 , l 1.6 α C

8 0.8

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 r/R r/R

Figure 30. PD1 blade radial distribution of angle of attack, lift and drag coefficients at J = 0.2 and β0.75 = 23°.

32 3.2 JavaP Cl JavaP Cl Vortex Vortex Cd JavaP 24 2.4 Cd Vortex d C

16 , l 1.6 (deg) C α

8 0.8

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 r/R r/R

Figure 31. COMP blade radial distribution of angle of attack, lift and drag coefficients at J = 0.2 and β0.75 = 20°.

2 PD1

1.6 COMP ) 5

10 1.2 × ( Re Re 0.8

0.4

0 0 0.2 0.4 0.6 0.8 1 r/R

Figure 32. PD1 and COMP blades local Reynolds number distributions at J = 0.2.

4.2 Data Measurement and Process

As documented by Merchant and Miller [45], the measurement system consisted of three divisions: the sensor/motor platform, instrument and power unit, and data processing devices as shown in Figure 33. The sensor/motor platform was mounted directly on the C-mount in the 3×4

LSWT and fixed at the nacelle’s center line, concentric with the motor shaft. In the 7×10 NIAR, it was connected to the C-mount via an adaptor steel pipe, as shown previously in Figure 16.

The sensor or balance measured two components—tension/compression and torque—and had a combined nonlinearity and hysteresis of ±0.5% for a rated output of 2 mV/V. The capacity of the balance was 500 lb for thrust and 500 in-lb for torque directions. Two 1,200-watt DC brushed electric motors with identical specifications were randomly switched between tests to include motor performance bias in results. The motor was set on a rigid adaptor specifically designed to connect the motor to the load cell. The motor holder also encased a 10-VDC magnetic-pickup to measure and record the propeller rpms in proximity of a spinning metallic

Figure 33. Data measurement and processing block diagram. tab measuring a maximum of 20,000 targets/s. The motor temperature was monitored by a thermocouple attached to the surface of the motor. An insulated adaptor isolated the balance from the motor’s thermal effects. However, minor heat transfer to the balance may have been picked up as loads when a high shaft power was required. Although these thermal effects on measurements are insignificant, they are quantified as thermal error in the following section.

Signals from the balance were sent to a conditioner/amplifier located outside the test section and then to an array of optical isolators. Finally, the signal processing and reduction was implemented in the computer and Microsoft Excel® software sheet via a 16-bit analog-to-digital card. The data acquisition and reduction system, or DAQ, established by Merchant and Miller [45] in 2006, was written in Visual Basic language. The reduction process incorporated the tunnel blockage correction for a given propeller diameter and tunnel cross section as described by Glauert

[53]. In addition to the load calculations, the DAQ generated non-dimensionalized propeller performance properties, such as propeller efficiency, coefficients of thrust and torque, etc. Based on sensitivity studies performed by Merchant, the sample rate was set to 5,000 Hz per channel with a sample period of 8 seconds. Details of the DAQ are discussed in Merchant’s master’s thesis

[54].

The tunnel dynamic pressures were measured and recorded differently for the two tunnels.

At the 3×4 LSWT, the tunnel dynamic pressure recording was integrated into the DAQ and readouts were obtained directly from a high precision ±1 psid pressure transducer into the data reduction system. The tunnel dynamic pressure from the DAQ was compared with the test section pitot-static probe for a range of dynamic pressure and found to be within ±5.0% of the readings.

For the nacelle pressure port measurements, a 16-channel Scanivalve with a full scale of ±10 in

H2O differential was used. The Scanivalve was set to a different DAQ with a sample rate of 40 Hz and sample period of 5 seconds, which measured the differential of the local pressure and tunnel static ring pressure. Data were synchronized with tunnel dynamic pressure measurements after the test was completed to obtain the pressure coefficients.

In the case of the 7×10 NIAR, the tunnel dynamic pressure was recorded through the tunnel system separately but collected simultaneously with the load measurements. Data were added into the DAQ once the testing ended. All pressure transducers read the differential to the tunnel barometric pressure including tunnel dynamic pressure, nacelle pressure, test section wall pressure, test section inlet, and outlet pitot tubes. The nacelle pressure ports were connected to a 32-channel electronic pressure scanner embedded inside the nacelle with a full scale of ±2.5 psid at a 15 Hz sample rate. The same rate was used for the wall measurements. Entrance and exit probes as well as a five-hole probe used for the wake survey were sampled at 50 Hz via a ±1.0 psid Scanivalve.

The sample period for all tests was 5 seconds, except for the wake survey five-hole probe, which was 1 second. The cone head five-hole probe had a 60° flow angle receptivity.

4.2.1 System Calibration

The load cell was calibrated for thrust and torque using known weights, as shown in Figure

34 for the thrust direction. The balance had a linear trend when loads were applied or removed from the apparatus. Interactions between the load readings were accounted for in the final balance behavior matrix. The calibration procedure frequently was performed to ensure the accuracy of the load cell and DAQ. When a 5 lb load was applied in the thrust direction, the accuracy of the system was +1.5% of thrust readings, and for a 1 lb load, this was +1.0% of thrust readings. Based on balance specifications, the total error for hysterisis, nonlinearity, and nonrepeatability was +0.55% of rated output. Similar results were observed in the torque measurements. The rpm sensor measurements were also cross-checked with a calibrated strobe light. The DAQ rpm readouts had an accuracy of ±0.3%.

Figure 34. Load cell calibration for thrust.

The two tunnel dynamic pressures are also calibrated to the one measured at the center of the test sections. For the tunnel total pressure and temperature in the 3×4 LSWT, the ambient readouts were input into the DAQ to calculate air density where the deviation was ±1.0% of readings in a standard day similar test conditions. The indicated dynamic pressure was not corrected for the blockage of the C-mount, which is estimated to be less than 0.4% increase in the tunnel dynamic pressure readings. The angle of attack offset was within ±0.2° from zero.

At the 7×10 NIAR wind tunnel, an instant tunnel barometric pressure and ambient temperature was measured internally for each tunnel dynamic pressure. All pressure measurements are the differential to the barometric pressure, and system transducers and gauges were calibrated frequently. The accuracy of the 7×10 tunnel dynamic pressure was 0.1 psf or better when q > 2.5 psf. The tunnel dynamic pressure can be cross-checked with the readouts of two pitot-static probes located at the entrance and the exit of the test section, especially for q < 2.5 psf. Flow uniformity and temperature variation across the 7×10 test section is plotted in Figure 35. The highest investigated tunnel dynamic pressure at 100 psf is where the temperature variation is at peak because of the wall friction.

The tunnel cross section velocity distribution varies the most at the lowest tunnel dynamic pressure. However, results show an excellent flow quality at q = 3.8 psf with variation less than

±1.0% of the velocity readings. Corrected tunnel dynamic pressure due to existence of the C-mount is used for the 7×10 tunnel data comparisons. Although the difference between uncorrected and corrected data for the presence of the C-mount was very small, both data are available in Appendix

B. The angle of attack α was measured by a calibrated inclinometer prior to each test and a zero- degree offset was expected to be within ±0.02°. The five-hole probe was also calibrated at two flow speeds of 16 ft/s and 3280 ft/s or Mach = 3.0 by the Aeroprobe Corporation. The measurement

accuracy for the flow angles was up to 0.4°, and 0.8% of the total flow velocity readings. The five- hole probe calibration details and manual were accessible through the Aeroprobe website [55].

Measurement errors and accuracy are also summarized and tabulated in the following data analysis section.

Figure 35. Test section velocity and temperature variations of 7×10 NIAR (courtesy of NIAR).

4.2.2 Data Corrections and Tares

As explained, corrections due to the propeller blockage were incorporated into the results for the presented global quantities and tunnel data comparisons. Although an increase in the velocity increment due to propeller blockage of the tunnel test section should be less than a few percent except for the static runs, corrections due to the effect are considered. Nevertheless, uncorrected data for the blockage are provided for the reader’s discretion for validation purposes.

Since the propeller diameter was the same for both propellers, the only variable for the blockage correction in DAQ was the tunnel cross section. According to the study by Merchant [54], other tunnel corrections such as solid blockage are negligible, since the total uncertainty is less than

0.3%.

The effect of instruments or support or even parts of a wind tunnel model on measurements is called tare or interference. Two different types of tare were considered here: static tare and dynamic tare. Static tare, which was integrated into the DAQ Wind-Off-Zero (WOZ) module, was considered for the weight of the system attached to the sensor and also for the minor temperature effects. The average of two WOZ readings, the beginning and the end of each run with ten measurements, was subtracted from each collected data. The difference of these two readings in terms of load was treated as thermal effect error since weight distribution variation before and after runs is zero.

On the other hand, dynamic tare was investigated to mainly exclude the drag effect of the spinner and study the actual loads generated by the propeller, mainly thrust. A similar method as that of Ol et al. [24] was used here. Sweeps of tunnel dynamic pressure with all models except the propeller were tested at certain rpms. Drag was measured and curve-fitted as a function of the tunnel dynamic pressure, and then added to the specified propeller’s thrust data. This approach

makes it applicable to a wide range of tunnel speeds. The results were also calculated and presented in coefficient forms. Dynamic tare for torque measurements, which is caused by spinner/hub and shaft power only, was neglected, since it was less than 1% of the readings at maximum with the propeller on. The same method was taken for the no-spinner no-nacelle models for comparison.

Note that dynamic tare is only applied to the data in the “Dynamic Tare ” section in Chapter 5. The intrusive effect of the five-hole probe on the flow was not considered here (see Figure 36). These effects are believed to be most severe in the vicinity of the slipstream boundaries and “quite difficult to estimate,” according to Samuelsson [42]. Nonetheless, pressure values in other regions, that is, between the blade tip and the root, are considered true.

Figure 36. Five-hole probe wake survey at 7×10 NIAR wind tunnel.

4.2.3 Test Procedure

A sweep of tunnel dynamic pressure at each run, which consists of ten data collections, was set to cover the propeller performance curves for a range of advance ratio. The rpm was pre-set by a fixed voltage on the power supply to the motor, and variation of the amperage was logged in order to monitor the shaft power delivered for the operator’s reference. Shaft power varied,

depending on the individual system wiring setup and motor electrical efficiency. The maximum voltage and amperage delivered were set to the motor specifications in order to avoid extreme motor heat or damage. Note that the rpm increases slightly as the tunnel q increases for the constant voltage delivered, although the effect was nominal for the non-dimensionalized propeller performance parameters. The tunnel q step size was predetermined by Merchant; nonetheless, supplementary data may comply to fill the voids in the performance curves. In those cases, repeated runs were performed with a shift in the tunnel q set. For the static thrust measurements, the initial tunnel dynamic pressure was set to 0 < q ≤ 0.1 psf, in order to create a gentle airflow so the propeller was not rotating in its own wake.

The spinner and nacelle must be disassembled in order to obtain access to the hub and propeller pitch angle setting. The spinner has two screw caps to maintain the designated curvature.

All exposed small gaps such as ones between the blade and spinner or nacelle screw holes were covered with Scotch tape to avoid any flow disturbances. Scotch tape is a convenient and inexpensive tool and found to be almost as effective as clay for small hole treatments in laminar regions [56]. Model gaps must be re-taped prior to the next run. Meanwhile, an air tube was ducted into the nacelle; this tube can inject compressed air towards the motor, in order for it to cool down as the following test preparations are made. Note that the cooling system was shut off and did not operate while testing was in progress.

For pressure measurements in the 3×4 LSWT, a total of 62 nacelle pressure ports were divided into four test runs for each pitch angle setting since the Scanivalve has only 16 channels.

The Scanivalve is located right outside and underneath the test section to increase the system sensitivity in pressure perturbation measurements. In the 7×10 NIAR, a smaller 32-channel pressure scanner was enclosed inside the nacelle, thus allowing twice as much data acquired per

run. For test time constraints, only half of the nacelle pressure survey was performed. In both tunnels, the reference pressure port was connected to the tunnel static ring to measure freestream static pressure, p∞, and each channel to the local nacelle pressure ports, p, to obtain the differential pressures. The final results are presented in the form of pressure coefficients. All wiring and tubing were run internally through the C-mount to maintain the overall simplicity in geometry (see Figure

37).

Figure 37. Inside the nacelle in each tunnel: 7×10 NIAR (left) and 3×4 LSWT (right).

4.3 System Evaluations

System evaluations were performed prior to the model experimentation in order to quantify and qualify the reliability of the data presented in the following chapter. It was critical to analyze the total amount of experimental error in the system especially for this study. The aim of this section is to identify all the known errors and reveal them to the readers. By using the 3D-scanning method, the model fabrication quality was also demonstrated and compared to the design geometry. Additionally, predictions for the designated propellers performance were made utilizing

JavaProp and vortex theory analysis.

Instrument accuracy is addressed in the system calibration section. Other uncertainties in measurements can also affect results, thus increasing the overall experimental error. Bias in the

facility or system measurement or test procedure can cause systematic or fixed error, which is typically proportional to the true value and can be eliminated by identifying the accuracy of the system. On the other hand, random error is usually unpredictable and depends on repeatability of the system measurement. Typically, a large number of repeated tests may quantify random error, providing a normal distribution and standard deviation. Table 1 provides a summary of the accuracy and error that is known. The statistical measurements shown are the maximum value in each data set. Therefore, typically the system is more accurate than listed here.

A commonsense analysis of the data suggests that error in the final results equal the combined maximum error of all parameters in the most detrimental way [57]. Accuracy, standard deviation, and thermal errors for thrust and torque measurements are based on observed readouts or readings (RD). Other parameters refer to the model specifications from the manufacturer based on the rated output (RO) or the full scale (FS).

TABLE 1

SUMMARY OF SYSTEM ACCURACY, PRECISION, AND ERROR

Instrument Unit Accuracy RD STDV RD Thermal Error Errors Thrust lb +1.5% ±0.15% ±1.5% RD ±0.55% RO Torque in-lb +1.0% ±0.10% ±1.0% RD ±0.55% RO rpm rpm ±0.3% ±1.0% - ±0.05% 3×4 LSWT ±5.0% ±1°C ±0.10% FS lb/ft2 ±9.0% Tunnel q where q > 5.0 psf (at sensing element) (1.0 psid) 3×4 LSWT ±0.2% FS lb/ft2 - ±5.0% ±0.001% FS Scanivalve (±10 in H2O) 7×10 NIAR ±4.0% lb/ft2 N/A - - Tunnel q where q > 2.5 psf 7×10 NIAR ±0.06% FS lb/ft2 - N/A ±0.004% FS/°C Scanner (±2.5 psid) < 0.4° angles, Five-Hole ±0.12% FS ft/s < 0.8% total N/A ±0.001% FS/°C Probe (±1.0 psid) velocity

Note that the standard deviation of the 3×4 LSWT Scanivalve is high. This is due to the rapid pressure fluctuations of the nacelle surface that is located behind the propeller caused by the presence of the propeller wake. The 7×10 wind tunnel DAQ is not set to output standard deviation for the pressure systems.

Initial tests demonstrate the quality and repeatability of data obtained at the 3×4 LSWT to assess the random error in the system. Tests were executed by different operators on separate days.

Figure 38 to Figure 40 show four test performances of the same off-the-shelf 12×12 APC Thin-

Electric propeller. The first number in the APC propeller specification indicates its diameter in inches and the second number is its pitch in inches. The efficiency η, along with CT and CP, are plotted against J at approximately 7,500 ~ 8,500 rpm, and each compares well, showing system repeatability. The Reynolds number at 75% of the radius (Re0.75) is also plotted as a function of J to show the test conditions of each run. By default, all data shown are corrected only for tunnel blockage.

0.2 WSU Run 324 WSU Run 368 0.16 WSU Run 371 WSU Run 418

0.12 T C

0.08

0.04

0 0 0.4 0.8 1.2 1.6 2 J

Figure 38. Thrust coefficient repeatability test of 12×12 APC Thin-E propeller in 3×4 LSWT.

0.2 WSU Run 324 WSU Run 368 WSU Run 371 0.16 WSU Run 418

0.12 P C

0.08

0.04

0 0 0.4 0.8 1.2 1.6 2 J

1 WSU Run 324 WSU Run 368 0.8 WSU Run 371 WSU Run 418

0.6 η

0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 39. Power coefficient repeatability test and efficiency of 12×12 APC Thin-E tests in 3×4 LSWT.

WSU Run 324 WSU Run 368 1.6 WSU Run 371 WSU Run 418 ) 5

10 1.2 × ( 0.75

Re 0.8

0.4

0 0 0.4 0.8 1.2 1.6 2 J

Figure 40. Reynolds number (Re0.75) repeatability test of 12×12 APC Thin-E in 3×4 LSWT.

The WSU 3×4 LSWT and 7×10 NIAR data are compared for the same 12×12 APC Thin-

E propeller in Figure 41. Results show a good comparison indicating nominal bias error from the two facilities and partially different DAQ systems, as explained previously. Figure 42 compares the 3×4 LSWT results with two other wind tunnel test data for a 10×7 APC thin-E propeller at

6,500 rpm. Data from the Basic Aerodynamics Research Tunnel (BART) at Langley Aerospace

Research Center, which is digitized from the Ol et al. study [24], did not specify the rpm. Although the results seem scattered, the authors state that no drastic variation resulted between 6,000 and

8,000 rpm. WSU’s data agrees with BART data and also data from the University of Illinois at

Urbana-Champaign (UIUC), which are plotted in Figure 42 and Figure 43 for APCs 10×7, 8×8, and 12×12 Thin-E. It is shown that the integrated DAQ is repeatable and comparable with other wind tunnel measurements throughout a series of testing.

0.2

3x4 LSWT Run 368

0.16 7x10 NIAR Run 659

0.12 T C

0.08

0.04

0 0 0.4 0.8 1.2 1.6 2

3x4 LSWT Run 368

0.8 7x10 NIAR Run 659

0.6 η

0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 41. Tunnel data comparison of 3×4 LSWT and 7×10 NIAR for 12×12 APC Thin-E.

0.2

WSU 6,500 rpm

0.16 UIUC 6,500 rpm BART

0.12 T C

0.08

0.04

0 0 0.4 0.8 1.2 1.6 2 J

WSU 6,500 rpm

0.8 UIUC 6,500 rpm BART

0.6 η

0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J Figure 42. Tunnel data comparison from WSU, BART [24], and UIUC [58] for 10×7 APC Thin-E propeller.

0.2

12x12 WSU 12x12 BART 0.16 8x8 BART 8x8 UIUC

0.12 T C

0.08

0.04

0 0 0.4 0.8 1.2 1.6 2 J

1 12x12 WSU 12x12 BART 0.8 8x8 BART 8x8 UIUC

0.6 η

0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J Figure 43. Tunnel data comparison from WSU, BART [24] and UIUC [58] for 12×12 and 8×8 APC Thin-E.

CHAPTER 5

RESULTS

Test results for the model propellers are presented in this chapter. The plotted results are reduced data, which account for the blockage corrections and thermal-static tares, as discussed in the previous chapter for tunnel comparisons. Load measurements, nacelle pressure distributions, and a wake survey were performed on two propeller blades in two different wind tunnels.

Application of the dynamic tare (spinner drag effect) and nacelle-spinner effects on performance will be discussed later in this chapter. Finally, the performance results are compared with the predicted values.

5.1 Propeller Performance

This section shows traditional performance plots such as thrust and torque coefficients with efficiency curves against a range of advance ratios. Two different propeller blades were examined and results are separated into subsections. However, results for the two wind tunnels are compared in the same corresponding graphs.

5.1.1 PD1 Results of Propeller Performance

As discussed earlier, a PD1 propeller blade has a constant twist, p/D = 1, as well as constant chord length and thickness throughout its six-inch radius. Hence, the design twist angle at 75% radius, β0.75 is 23°. Additional tests were conducted at 28° and 33° pitch angles at approximately

5,000 rpm (i.e., 4,800 to 5,600 rpm), which is equivalent to Re0.75 = 90,000 to 120,000 for a range of advance ratios. Thrust and power coefficients as well as efficiency results are shown for the 3×4

LSWT and 7×10 NIAR wind tunnels in Figure 44 to Figure 46. Figure 47 shows PD1 performance at three different revolution speeds, i.e., 4,000, 5,000 and 6,000 rpms, in order to evaluate the

Reynolds number (Re0.75 = 75,000 ~ 130,000) dependency, where β0.75 = 23°. Runs were repeated

on two or three different days for both tunnels, with test apparatus disassembled and reassembled, to check the system repeatability. For such a low Reynolds number range, data repeatability can be confirmed for each tunnel. Thrust coefficients for higher pitch angles agree well for both wind tunnels, that is, except for β0.75 = 23°, where the 7×10 NIAR results are about 4% on average higher than 3×4 LSWT (Figure 44 to Figure 47). Also, power coefficients results in the 7×10 NIAR for all pitch settings are 5 ~ 6% higher than the 3×4 LSWT on average. Several reasons may be causing this outcome.

First, the total uncertainty of the system at its worst is estimated to be about 5%, which includes the accuracy, thermal error, and other instrument and random errors. However, this is unlikely the case, since COMP blade results shown in the next section are consistent for both tunnels.

Next, and most likely, the tunnel systematic bias was caused by the difference in tunnel flow characteristics at certain test conditions. As presented previously, the flow quality of the 7×10

NIAR tunnel is well known, reducing the tunnel turbulence intensity. On the other hand, the 3×4

LSWT is expected to have higher turbulence intensity than the 7×10 NIAR tunnel. Blade’s local

Reynolds number depends on the advance ratio and the section location and chord length, nonetheless, the higher flow turbulence intensity increases the overall effective Reynolds number.

Higher turbulence intensity causes earlier transition by tripping the flow, and as a result, the effective Reynolds number is higher than lower turbulence flow. Figure 48 shows E-387 airfoil data among three different wind tunnels at two Reynolds numbers [47]. The airfoil aerodynamic characteristics vary between tunnels at Re = 60,000 with a possible separation bubble at α ≈ 6° for

LTPT and Delft results. This demonstrates the effect of the tunnel flow characteristics on the aerodynamics performance, especially at lower Reynolds numbers. Moreover, post stall behavior

varies at higher angles of attack for each tunnel (i.e., α ≥ 12°) which is also possibly caused by the reason explained above. The vast majority of the blade section operates at Re ≤ 100,000 at lower advance ratios as explained in previously. For example, Re0.45 ≈ 60,000 at J = 0.20, that is the local

Reynolds number at 45% of the blade radius. In addition, both JavaProp and vortex theory analysis results indicated that blade section angles of attack were higher than 12° at lower advance ratios

(i.e., J ≤ 1.0) especially for r/R = 0.7 or less regions. This implies that separation or stall, at least for a portion of the blade. Also shown in Figure 28 and Figure 29, vortex theory and JavaProp predictions did not match well for the PD1 as opposed to the COMP results. The reason can be explained by the post stall treatment, that is, the difference in the drag polar of the two methods which may cause a similar outcome by operating at different effective Reynolds numbers produced at individual wind tunnels.

As will be discussed in the following sections, the wake survey results show a possible flow separation region in the vicinity of the root for β0.75 = 23°. This region can be smaller or rather different in the 3×4 LSWT based on the tunnel flow characteristics or at the higher Reynolds numbers causing a change in performance curves. Higher pitch settings thrust coefficients are more consistent between the two tunnels because the section angles of attack are dominantly at post stall. Therefore, tunnel flow characteristics have minimal impact on the results. The gap between the tunnels data diminishes at higher advance ratios also supports this argument, resulting lower section angles of attack for the same pitch settings. Nonetheless, it is fair to say that the efficiency curves are consistent for both tunnels. In contrast, propeller performances are consistent for the

COMP blade in both tunnels. This is caused by significantly lower pitch setting throughout the blade sections and relatively low section angles of attack. The COMP results are shown in the following section.

0.32 3x4 Run 1 3x4 Run 2 0.28 3x4 Run 3 7x10 Run 1 7x10 Run 2 0.24 7x10 Run 3

0.2 0.2 3x4 Run 1 3x4 Run 2 0.16 3x4 Run 3 P 0.16 C 7x10 Run 1 7x10 Run 2 0.12 7x10 Run 3 0.12 T C

0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

1 3x4 Run 1 3x4 Run 2 0.8 3x4 Run 3 7x10 Run 1 7x10 Run 2 0.6 7x10 Run 3 η

0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 44. Coefficients CT, CP, and η against J for PD1 at 5,000 rpm, where β0.75 = 23°.

0.32

3x4 Run 1 3x4 Run 2 0.28 3x4 Run 3 7x10 Run 1 0.24 7x10 Run 2

0.2 0.2 3x4 Run 1 3x4 Run 2

0.16 3x4 Run 3 P 0.16 C 7x10 Run 1 7x10 Run 2 0.12 0.12 T C 0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

0.8

0.6 η

3x4 Run 1 0.4 3x4 Run 2 3x4 Run 3 0.2 7x10 Run 1 7x10 Run 2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 45. Coefficients CT, CP, and η against J for PD1 at 5,000 rpm, where β0.75 = 28°.

0.32 3x4 Run 1 3x4 Run 2 0.28 3x4 Run 3 7x10 Run 1 7x10 Run 2 0.24

0.2 0.2 3x4 Run 1 3x4 Run 2

0.16 3x4 Run 3 P 0.16 7x10 Run 1 C 7x10 Run 2 0.12 0.12 T C

0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2

J J

0.8

0.6 3x4 Run 1

η 3x4 Run 2 3x4 Run 3 0.4 7x10 Run 1 7x10 Run 2

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 46. Coefficients CT, CP, and η against J for PD1 at 5,000 rpm, where β0.75 = 33°.

0.32 3x4 4000 rpm

3x4 5000 rpm 0.28 7x10 4000 rpm

7x10 5000 rpm

0.24 7x10 6000 rpm

0.2 0.2 3x4 4000 rpm 3x4 5000 rpm 0.16 7x10 4000 rpm P 0.16 C 7x10 5000 rpm 7x10 6000 rpm 0.12 0.12 T C

0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

1 3x4 4000 rpm 3x4 5000 rpm 7x10 4000 rpm 0.8 7x10 5000 rpm 7x10 6000 rpm 0.6 η

0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 47. Coefficients CT, CP, and η against J for PD1 at 4,000 ~ 6,000 rpm, where β0.75 = 23°.

Re = 60,000 Re = 100,000

1.2 1.2

0.8 0.8 l l C

C 0.4 0.4

0 0 Stuttgard Stuttgard Delft Delft LTPT LTPT

-0.4 -0.4 -4 0 4 8 12 16 -4 0 4 8 12 16 α (deg) α (deg)

Figure 48. Eppler 387 airfoil wind tunnel results comparison at two Reynolds numbers, data digitized from [47].

5.1.2 COMP Results of Propeller Performance

This propeller blade has a varying twist distribution and chord length as a function of radius with a constant thickness ratio, which was specified previously. The design blade twist angle at

75% radius, β0.75 is 15°. The blade’s variable pitch was set at additional three different angles: 20°,

25°, and 30° at 0.75R. Figure 49 to Figure 52 show CT, CP, and η as a function of J at approximately

6,000 rpm (i.e., between 5,800 and 6,400 rpm), which is also equivalent to Re0.75 = 90,000 to

120,000. All tests are repeated at the two facilities on different days. Results shown in Figure 53 verify the Reynolds number (Re0.75 = 65,000 ~ 120,000) independency for β0.75 = 20° for a range of advance ratio.

In contrast to the PD1 results, the COMP performance curves agree well for both wind tunnels. This is an ideal outcome for validations purposes. In general, the COMP propeller consumes significantly less power relative to the PD1. Also, a higher efficiency of 85% is obtained for β0.75 = 25° and 30°. Note that a few percent shift in the power coefficient is detected between the tunnel results for a blade pitch at β0.75 = 30°. It appears that a systematic gap between two tunnels increases as the pitch angle increases. Consequently, the torque measured has increased, as shown in Figure 52. Overall, the COMP performance curves are consistent and repeatable throughout all pitch settings.

0.2 0.2 3x4 Run 1 3x4 Run 1 3x4 Run 2 3x4 Run 2 0.16 3x4 Run 3 0.16 3x4 Run 3 7x10 Run 2 7x10 Run 1 7x10 Run 2 7x10 Run 2 0.12 0.12 P T C C 0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

1 3x4 Run 1 3x4 Run 2 0.8 3x4 Run 3 7x10 Run 1 7x10 Run 2 0.6 η

0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 49. Coefficients CT, CP, and η against J for COMP at 6,000 rpm, where β0.75 = 15°.

0.2 0.2 3x4 Run 1 3x4 Run 1 3x4 Run 2 3x4 Run 2 0.16 3x4 Run 3 0.16 3x4 Run 3 7x10 Run 1 7x10 Run 1 7x10 Run 2 7x10 Run 2 0.12 0.12 P T C C 0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2

J J

1 3x4 Run 1 3x4 Run 2 0.8 3x4 Run 3 7x10 Run 1 7x10 Run 2 0.6 η

0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 50. Coefficients CT, CP, and η against J for COMP at 6,000 rpm, where β0.75 = 20°.

0.2 0.2 3x4 Run 1 3x4 Run 1 3x4 Run 2 3x4 Run 2 0.16 0.16 3x4 Run 3 3x4 Run 3 7x10 Run 1 7x10 Run 1

0.12 7x10 Run 2 0.12 7x10 Run 2 T P C C

0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

1 3x4 Run 1 3x4 Run 2 0.8 3x4 Run 3 7x10 Run 1 0.6 7x10 Run 2 η 0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 51. Coefficients CT, CP, and η against J for COMP at 6,000 rpm, where β0.75 = 25°.

0.2 0.2 3x4 Run 1 3x4 Run 1 3x4 Run 2 3x4 Run 2 0.16 0.16 3x4 Run 3 3x4 Run 3 7x10 Run 1 7x10 Run 1 7x10 Run 2 0.12 7x10 Run 2 0.12 T P C C

0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

1 3x4 Run 1 3x4 Run 2 0.8 3x4 Run 3 7x10 Run 1 7x10 Run 2 0.6 η

0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 52. Coefficients CT, CP, and η against J for COMP at 6,000 rpm, where β0.75 = 30°.

0.2 0.2 3x4 4000rpm 3x4 4000rpm 3x4 5000rpm 3x4 5000rpm 0.16 3x4 6000rpm 0.16 3x4 6000rpm 7x10 4000rpm 7x10 4000rpm 7x10 5000rpm 7x10 5000rpm 0.12 0.12 7x10 6000rpm 7x10 6000rpm P T C C 0.08 0.08

0.04 0.04

0 0 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 J J

1 3x4 4000rpm 3x4 5000rpm 0.8 3x4 6000rpm 7x10 4000rpm 7x10 5000rpm 0.6 7x10 6000rpm η

0.4

0.2

0 0 0.4 0.8 1.2 1.6 2 J

Figure 53. Coefficients CT, CP, and η against J for COMP at 4,000 ~ 6,000 rpm, where β0.75 = 20°.

5.2 Nacelle Pressure Distribution

This section presents the nacelle surface pressure distribution along the longitudinal axis in non-dimensional forms, i.e., pressure coefficient cpr , and x/L. The origin of the coordinate system is the nacelle upstream leading edge at x/L = 0, as shown in Figure 54. This coordinate system is applied to all the following results. Longitudinal stations were divided into eight segments with x/L = 0.118 increments, where x is the local distance from the nacelle upstream leading edge, and L is the length of the nacelle. Both side walls of the 7×10 NIAR entire test section pressure coefficients are also plotted against non-dimensional distance l’ from the entrance of the test section showing the test section pressure gradient at different advance ratios. The azimuth angle Φ represents the nacelle pressure port angle, where 12 o’clock is at Φ = 0°, and has an increment of 45° in the clockwise direction about the longitudinal axis or the axis of rotation when looking downstream. Note that both propellers also rotate clockwise when looking downstream. All static pressure ports are perpendicular to the nacelle surface.

Figure 54. Nacelle coordinate system.

5.2.1 PD1 Results of Nacelle Pressure Distribution

Nacelle surface pressure coefficients are plotted against the longitudinal position for the three pitch angles—23°, 28°, and 33°—for several advance ratios. Results of the 3×4 LSWT and

7×10 NIAR wind tunnels are shown in Figure 55 to Figure 65. 7×10 NIAR side wall pressure gradients are also plotted for boundary condition applications. Pressure measurements in the 3×4

LSWT are limited to 16 channels at each run; hence, only two rows of azimuth angles are measured at the same condition (e.g., Φ = 0° and 45°, etc.). On the other hand, 7×10 NIAR results are obtained at a single test run but only for half of the nacelle at four azimuth angles—0°, 45°, 90°,

135°—except at β0.75 = 23° and 28°, with an additional 180° and 225°, as shown in Figure 56.

Only first and last plot’s legend are displayed for the same 7×10 NIAR runs to avoid redundancy.

Each pressure port was checked prior to the test, but a few did not work properly because of clogs, tube disconnections, or leakages. These are omitted from the presented data.

The 3×4 LSWT nacelle setup has a two-inch gap in front of the C-mount. This nacelle surface discontinuity creates flow separation on the lower half towards the end of the nacelle, as shown for Φ = 135° and 225°. The last two measurements downstream at Φ = 180° are omitted for the existence of the C-mount. However, this section was sealed with a part that replicated the original surface curvature for the 7×10 NIAR runs, although no pressure ports were added.

Pressure distribution curves appear smooth in most cases, that is, at peaks behind the propeller due to the induced pressure by the propeller and lowest at the nacelle maximum diameter, and they tend to increase at the pressure recovery regions. Also the pressure coefficients seem to be axis-symmetrical on both sides of the nacelle. The pressure distribution of the nacelle surface without a propeller is shown in Figure 64 with the spinner rotating at the same 5,000 rpm in order to study the spinner effect. Although the 3×4 and 7×10 results are not precisely comparable, since

the test conditions and tunnel cross section sizes are different, they show identical behavior.

However, the 7×10 NIAR results show less separated regions, mainly because of the C-mount location. Wall pressure gradient slopes are mostly consistent despite of the advance ratio.

Φ = 0°, β0.75 = 23° Φ = 45°, β0.75 = 23° 0.5 0.5 J=0.44 J=0.44 J=0.55 J=0.55 J=0.64 J=0.64 0.25 J=0.72 0.25 J=0.72 J=0.88 J=0.88 J=1.03 J=1.03 J=1.15 J=1.15 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 90°, β0.75 = 23° Φ = 135°, β0.75 = 23° 0.5 0.5 J=0.40 J=0.40 J=0.53 J=0.53 J=0.58 J=0.58 0.25 J=0.70 0.25 J=0.70 J=0.89 J=0.89 J=0.99 J=0.99 J=1.10 J=1.10

pr 0 pr

c c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 55. Nacelle surface pressure distribution for PD1 at 3×4 LSWT for different Φ, where β0.75 = 23° (continued).

Φ = 180°, β0.75 = 23° Φ = 225°, β0.75 = 23° 0.5 0.5 J=0.43 J=0.43 J=0.50 J=0.50 J=0.61 J=0.61 0.25 J=0.70 0.25 J=0.70 J=0.86 J=0.86 J=1.02 J=1.02 J=1.12 J=1.12 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 270°, β0.75 = 23° Φ = 315°, β0.75 = 23° 0.5 0.5 J=0.44 J=0.44 J=0.49 J=0.49 J=0.58 J=0.58 0.25 J=0.72 0.25 J=0.72 J=0.88 J=0.88 J=1.01 J=1.01 J=1.11 J=1.11 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 55 (continued). Nacelle surface pressure distribution for PD1 at 3×4 LSWT for different Φ , where β0.75 = 23°.

Φ = 0°, β = 23° Φ = 45°, β = 23° 0.5 0.5 J=0.45 J=0.58 J=0.68 0.25 J=0.81 0.25 J=0.98 J=1.13 J=1.32 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 90°, β = 23° Φ = 180°, β = 23° 0.5 0.5

0.25 0.25 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 56. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 23° (continued).

Φ = 225°, β = 23° Φ = 270°, β = 23° 0.5 0.5

0.25 0.25 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 56 (continued). Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 23°.

North Side Wall Pressure Coeff, β = 23° South Side Wall Pressure Coeff, β = 23° 0.5 0.5 J=0.45 J=0.58 J=0.68 0.25 0.25 J=0.81 J=0.98 J=1.13 J=1.32 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 l' l'

Figure 57. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 23°.

Φ = 0°, β = 28° Φ = 45°, β = 28° 0.5 0.5 J=0.39 J=0.39 J=0.49 J=0.49 J=0.61 J=0.61 0.25 J=0.72 0.25 J=0.72 J=0.89 J=0.89 J=1.03 J=1.03 J=1.13 J=1.13 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 90°, β = 28° Φ = 135°, β = 28° 0.5 0.5 J=0.38 J=0.38 J=0.54 J=0.54 J=0.61 J=0.61 0.25 J=0.70 0.25 J=0.70 J=0.88 J=0.88 J=0.99 J=0.99 J=1.14 J=1.14 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 58. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 28° (continued).

Φ = 180°, β = 28° Φ = 225°, β = 28° 0.5 0.5 J=0.41 J=0.41 J=0.56 J=0.56 J=0.64 J=0.64 0.25 J=0.72 0.25 J=0.72 J=0.88 J=0.88 J=1.02 J=1.02 J=1.14 J=1.14 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 270°, β = 28° Φ = 315°, β = 28° 0.5 0.5 J=0.43 J=0.43 J=0.56 J=0.56 J=0.62 J=0.62 0.25 J=0.72 0.25 J=0.72 J=0.90 J=0.90 J=1.03 J=1.03 J=1.12 J=1.12 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 58 (continued). Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 28°.

Φ = 0°, β = 28° Φ = 45°, β = 28° 0.5 0.5 J=0.43 J=0.55 J=0.66 0.25 J=0.79 0.25 J=0.97 J=1.10 J=1.34 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 90°, β = 28° Φ = 135°, β = 28° 0.5 0.5

0.25 0.25 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 59. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 28° (continued).

Φ = 180°, β = 28° Φ = 225°, β = 28° 0.5 0.5

0.25 0.25 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 59 (continued). Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 28°.

North Side Wall Pressure Coeff, β = 28° South Side Wall Pressure Coeff, β = 28° 0.5 0.5 J=0.43 J=0.55 J=0.66 0.25 0.25 J=0.79 J=0.97 J=1.10 J=1.34 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 l' l'

Figure 60. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 28°.

Φ = 0°, β = 33° Φ = 45°, β = 33° 0.5 0.5 J=0.46 J=0.46 J=0.51 J=0.51 J=0.59 J=0.59 0.25 J=0.73 0.25 J=0.73 J=0.90 J=0.90 J=1.03 J=1.03 J=1.15 J=1.15 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 90°, β = 33° Φ = 135°, β = 33° 0.5 0.5 J=0.41 J=0.41 J=0.56 J=0.56 J=0.65 J=0.65 0.25 J=0.74 0.25 J=0.74 J=0.88 J=0.88 J=1.04 J=1.04 J=1.16 J=1.16 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 61. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 33° (continued).

Φ = 180°, β = 33° Φ = 225°, β = 33° 0.5 0.5 J=0.47 J=0.47 J=0.63 J=0.63 J=0.74 J=0.74 0.25 0.25 J=0.89 J=0.89 J=1.03 J=1.03 J=1.15 J=1.15 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 270°, β = 33° Φ = 315°, β = 33° 0.5 0.5 J=0.45 J=0.45 J=0.52 J=0.52 J=0.64 J=0.64 0.25 J=0.77 0.25 J=0.77 J=0.91 J=0.91 J=1.06 J=1.06 J=1.17 J=1.17 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 61 (continued). Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 33°.

Φ = 0°, β = 33° Φ = 45°, β = 33° 0.5 0.5 J=0.46 J=0.58 J=0.67 0.25 J=0.80 0.25 J=0.97 J=1.11 J=1.35 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 90°, β = 33° Φ = 135°, β = 33° 0.5 0.5

0.25 0.25 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 62. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 33°.

100

North Side Wall Pressure Coeff, β = 33° South Side Wall Pressure Coeff, β = 33° 0.5 0.5 J=0.46 J=0.58 J=0.67 0.25 0.25 J=0.80 J=0.97 J=1.11 J=1.35 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 l' l'

Figure 63. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 33°.

Φ = 0°, Tare (5000 rpm) Φ = 45°, Tare (5000 rpm) 0.5 0.5 J=0.46 J=0.59 J=0.69 0.25 J=0.83 0.25 J=1.02 J=1.17 J=1.43 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 64. Nacelle surface pressure distribution at 7×10 NIAR for different Φ without propeller (continued).

101

Φ = 90°, Tare (5000 rpm) Φ = 135°, Tare (5000 rpm) 0.5 0.5

0.25 0.25 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 64 (continued). Nacelle surface pressure distribution at 7×10 NIAR for different Φ without propeller.

North Test Section Wall Pressure Coeff, Tare South Test Section Wall Pressure Coeff, Tare 0.5 0.5 J=0.46 J=0.59 J=0.69 0.25 0.25 J=0.83 J=1.02 J=1.17 J=1.43 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 l' l'

Figure 65. Test section side wall pressure distribution at 7×10 NIAR without propeller.

102

5.2.2 COMP Results of Nacelle Pressure Distribution

A similar method was used to measure the pressure distribution for the COMP blade at four pitch angles of 15°, 20°, 25°, and 30° at 0.75R. The results are presented in Figure 66 to Figure 79.

The pressure distribution for this propeller somewhat differs from the PD1 results, mostly at the vicinity of the maximum nacelle diameter at lower pitch angles in the 3×4 LSWT. It appears the minimum pressure coefficients are not sensitive to the advance ratios at lower pitch angle settings for the 3×4 LSWT results. The pressure gradient of the 7×10 NIAR test section side walls are also plotted for boundary condition references. The pressure distribution of the nacelle surface and wall pressure without a propeller and with the spinner rotating at the same 6,000 rpm in order to study the spinner effect is shown in Figure 78 and Figure 79.

Φ = 0°, β = 15° Φ = 45°, β = 15° 0.5 0.5 J=0.34 J=0.34 J=0.46 J=0.46 J=0.51 J=0.51 0.25 J=0.60 0.25 J=0.60 J=0.72 J=0.72 J=0.81 J=0.81 J=0.89 J=0.89 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 66. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 15° (continued).

103

Φ = 90°, β = 15° Φ = 135°, β = 15° 0.5 0.5 J=0.34 J=0.34 J=0.44 J=0.44 J=0.49 J=0.49 0.25 J=0.61 0.25 J=0.61 J=0.71 J=0.71 J=0.85 J=0.85 J=0.90 J=0.90 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 180°, β = 15° Φ = 225°, β = 15° 0.5 0.5 J=0.37 J=0.37 J=0.43 J=0.43 J=0.50 J=0.50 0.25 J=0.61 0.25 J=0.61 J=0.72 J=0.72 J=0.81 J=0.81 J=0.88 J=0.88 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 66 (continued). Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 15° (continued).

104

Φ = 270°, β = 15° Φ = 315°, β = 15° 0.5 0.5 J=0.36 J=0.36 J=0.46 J=0.46 J=0.54 J=0.54 0.25 J=0.62 0.25 J=0.62 J=0.73 J=0.73 J=0.83 J=0.83 J=0.90 J=0.90 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 66 (continued). Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 15°.

Φ = 0°, β = 15° Φ = 45°, β = 15° 0.5 0.5 J=0.38 J=0.48 J=0.56 0.25 J=0.66 0.25 J=0.78 J=0.87 J=0.93 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 67. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 15° (continued).

105

Φ = 90°, β = 15° Φ = 135°, β = 15° 0.5 0.5

0.25 0.25 pr pr c c 0 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 67 (continued). Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 15°.

North Side Wall Pressure Coeff, β = 15° South Side Wall Pressure Coeff, β = 15° 0.5 0.5 J=0.38 J=0.48 J=0.56 0.25 0.25 J=0.66 J=0.78 J=0.87 J=0.93 pr pr c c 0 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 l' l'

Figure 68. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 15°.

106

Φ = 0°, β = 20° Φ = 45°, β = 20° 0.5 0.5 J=0.35 J=0.35 J=0.43 J=0.43 J=0.51 J=0.51 0.25 J=0.59 0.25 J=0.59 J=0.73 J=0.73 J=0.84 J=0.84 J=0.92 J=0.92 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 90°, β = 20° Φ = 135°, β = 20° 0.5 0.5 J=0.31 J=0.31 J=0.43 J=0.43 J=0.51 J=0.51 0.25 J=0.61 0.25 J=0.61 J=0.74 J=0.74 J=0.84 J=0.84 J=0.91 J=0.91 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 69. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 20° (continued).

107

Φ = 180°, β = 20° Φ = 225°, β = 20° 0.5 0.5 J=0.35 J=0.35 J=0.44 J=0.44 J=0.50 J=0.50 0.25 J=0.60 0.25 J=0.60 J=0.73 J=0.73 J=0.85 J=0.85 J=0.92 J=0.92 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 270°, β = 20° Φ = 315°, β = 20° 0.5 0.5 J=0.38 J=0.38 J=0.46 J=0.46 J=0.51 J=0.51 0.25 J=0.63 0.25 J=0.63 J=0.75 J=0.75 J=0.85 J=0.85 J=0.93 J=0.93 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 69 (continued). Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 20°.

108

Φ = 0°, β = 20° Φ = 45°, β = 20° 0.5 0.5 J=0.37 J=0.48 J=0.56 0.25 J=0.67 0.25 J=0.80 J=0.89 J=1.08 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 90°, β = 20° Φ = 135°, β = 20° 0.5 0.5

0.25 0.25 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 70. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 20°.

109

North Side Wall Pressure Coeff, β = 20° South Side Wall Pressure Coeff, β = 20° 0.5 0.5 J=0.37 J=0.48 J=0.56 0.25 0.25 J=0.67 J=0.80 J=0.89 J=1.08 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 l' l'

Figure 71. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 20°.

Φ = 0°, β = 25° Φ = 45°, β = 25° 0.5 0.5 J=0.36 J=0.36 J=0.43 J=0.43 J=0.51 J=0.51 0.25 J=0.61 0.25 J=0.61 J=0.73 J=0.73 J=0.83 J=0.83 J=0.93 J=0.93 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 72. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 25° (continued).

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Φ = 90°, β = 25° Φ = 135°, β = 25° 0.5 0.5 J=0.36 J=0.36 J=0.44 J=0.44 J=0.51 J=0.51 0.25 J=0.61 0.25 J=0.61 J=0.74 J=0.74 J=0.83 J=0.83 J=0.94 J=0.94 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 180°, β = 25° Φ = 225°, β = 25° 0.5 0.5 J=0.36 J=0.36 J=0.44 J=0.44 J=0.52 J=0.52 0.25 J=0.60 0.25 J=0.60 J=0.76 J=0.76 J=0.84 J=0.84 J=0.95 J=0.95 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 72 (continued). Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 25° (continued).

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Φ = 270°, β = 25° Φ = 315°, β = 25° 0.5 0.5 J=0.35 J=0.35 J=0.46 J=0.46 J=0.54 J=0.54 0.25 J=0.61 0.25 J=0.61 J=0.76 J=0.76 J=0.86 J=0.86 J=0.95 J=0.95 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 72 (continued). Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 25°.

Φ = 0°, β = 25° Φ = 45°, β = 25° 0.5 0.5 J=0.37 J=0.47 J=0.55 0.25 J=0.66 0.25 J=0.80 J=0.91 J=1.07 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 73. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 25° (continued).

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Φ = 90°, β = 25° Φ = 135°, β = 25° 0.5 0.5

0.25 0.25 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 73 (continued). Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 25°.

North Side Wall Pressure Coeff, β = 25° South Side Wall Pressure Coeff, β = 25° 0.5 0.5 J=0.37 J=0.47 J=0.55 0.25 0.25 J=0.66 J=0.80 J=0.91 J=1.07 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 l' l'

Figure 74. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 25°.

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Φ = 0°, β = 30° Φ = 45°, β = 30° 0.5 0.5 J=0.36 J=0.36 J=0.43 J=0.43 J=0.51 J=0.51 0.25 J=0.61 0.25 J=0.61 J=0.75 J=0.75 J=0.86 J=0.86 J=0.96 J=0.96 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 90°, β = 30° Φ = 135°, β = 30° 0.5 0.5 J=0.36 J=0.36 J=0.45 J=0.45 J=0.52 J=0.52 0.25 J=0.61 0.25 J=0.61 J=0.74 J=0.74 J=0.86 J=0.86 J=0.95 J=0.95 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 75. Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 30° (continued).

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Φ = 180°, β = 30° Φ = 225°, β = 30° 0.5 0.5 J=0.35 J=0.35 J=0.46 J=0.46 J=0.52 J=0.52 0.25 J=0.60 0.25 J=0.60 J=0.73 J=0.73 J=0.86 J=0.86 J=0.96 J=0.96 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 270°, β = 30° Φ = 315°, β = 30° 0.5 0.5 J=0.35 J=0.35 J=0.46 J=0.46 J=0.53 J=0.53 0.25 J=0.62 0.25 J=0.62 J=0.76 J=0.76 J=0.86 J=0.86 J=0.97 J=0.97 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 75 (continued). Nacelle surface pressure distribution at 3×4 LSWT for different Φ, where β0.75 = 30°.

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Φ = 0°, β = 30° Φ = 45°, β = 30° 0.5 0.5 J=0.38 J=0.48 J=0.56 0.25 J=0.67 0.25 J=0.81 J=0.94 J=1.11 pr pr c c 0 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Φ = 90°, β = 30° Φ = 135°, β = 30° 0.5 0.5

0.25 0.25 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 76. Nacelle surface pressure distribution at 7×10 NIAR for different Φ, where β0.75 = 30°.

116

North Side Wall Pressure Coeff, β = 30° South Side Wall Pressure Coeff, β = 30° 0.5 0.5 J=0.38 J=0.48 J=0.56 0.25 0.25 J=0.67 J=0.81 J=0.94 J=1.11 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 l' l'

Figure 77. Test section side wall pressure distribution at 7×10 NIAR, where β0.75 = 30°.

Φ = 0°, Tare (6000 rpm) Φ = 45°, Tare (6000 rpm) 0.5 0.5 J=0.44 J=0.62 J=0.75 0.25 J=0.89 0.25 J=1.02 J=1.15 J=1.46 pr pr

c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 78. Nacelle surface pressure distribution at 7×10 NIAR without propeller (continued).

117

Φ = 90°, Tare (6000 rpm) Φ = 135°, Tare (6000 rpm) 0.5 0.5

0.25 0.25 pr pr c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x/L x/L

Figure 78 (continued). Nacelle surface pressure distribution at 7×10 NIAR without propeller.

North Side Wall Pressure Coeff, Tare South Side Wall Pressure Coeff, Tare 0.5 0.5 J=0.44 J=0.62 J=0.75 0.25 0.25 J=0.89 J=1.02 J=1.15 J=1.46 pr pr c 0 c 0

-0.25 -0.25

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 l' l'

Figure 79. Test section side wall pressure distribution at 7×10 NIAR without propeller.

118

5.3 Wake Survey

A five-hole probe traverse system, as described in the Chapter 4, was utilized to perform the propeller wake survey in the 7×10 NIAR wind tunnel. Slipstream velocities of both propellers were examined at a certain test condition for each propeller at three azimuth angles of 0°, 90°, and

270° and three nacelle longitudinal locations of x/L = 0.02, 0.49, and 0.843. The PD1 blade pitch angle was set at β0.75 = 23° and the freestream velocity at 67 ft/s and 5,000 rpm, i.e., an advance ratio of 0.804. Results are shown in Figure 80 to Figure 88. Swirl angle plots for PD1 at three different nacelle longitudinal locations and three azimuth angles are shown in Figure 89. The

COMP pitch angle was set to β0.75 = 20°, U = 67 ft/s, and 6,000 rpm, i.e., J = 0.670. Results for the

COMP are shown in Figure 90 to Figure 98. Slipstream velocities were obtained on x-y-z components of the tunnel Cartesian coordinate system and transferred into the polar coordinate system, as shown previously in Figure 54. Results are plotted in non-dimensional form by dividing the velocity components into the freestream velocity magnitude. Also, projections of the two velocity vectors are plotted; one being the superimposed axial and radial components and the other being the tangential and radial velocity components. The PD1 first run was repeated to assess system repeatability. Swirl angles plots for the COMP at three different nacelle longitudinal locations and three azimuth angles are shown in Figure 99.

Vortex theory analysis results show that blade elements from the root to 0.7R are at high angles of attack for the PD1 propeller for the same test condition. Axial velocity component results show a drop in magnitude immediately behind the propeller that may suggest a partial stall in this region. The velocity magnitude gradually transfers into a uniform distribution at the end of the nacelle. The maximum axial velocity component of 1.3 times larger than the freestream velocity was detected at the nacelle mid-section. The COMP was at lower angles of attack for the entire

119

blade sections, according to results of the vortex theory analysis. A relatively uniform velocity for this blade was measured with the maximum axial velocity component a little less than 1.3 times larger than the freestream. Different azimuth angle results show, on average, a symmetrical flow distribution around the nacelle over a period of time.

Φ = 0°, x/L = 0.02, PD1

(ux-U)/U ut/U 1.5 ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 80. Slipstream velocity components for PD1 at Φ = 0°, x/L = 0.02, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR).

120

Φ = 90°, x/L = 0.02, PD1

(ux-U)/U ut/U 1.5 ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 81. Slipstream velocity components for PD1 at Φ = 90°, x/L = 0.02, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR).

Φ = 270°, x/L = 0.02, PD1

(ux-U)/U ut/U 1.5 ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 82. Slipstream velocity components for PD1 at Φ = 270°, x/L = 0.02, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR).

121

Φ = 0°, x/L = 0.49, PD1

(ux-U)/U ut/U 1.5 ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 83. Slipstream velocity components for PD1 at Φ = 0°, x/L = 0.49 where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR).

Φ = 90°, x/L = 0.49, PD1

(ux-U)/U ut/U 1.5 ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 84. Slipstream velocity components for PD1 at Φ = 90°, x/L = 0.49 where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR).

122

Φ = 270°, x/L = 0.49, PD1

(ux-U)/U 1.5 ut/U ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 85. Slipstream velocity components for PD1 at Φ = 270°, x/L = 0.49, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR).

Φ = 0°, x/L = 0.843, PD1

(ux-U)/U ut/U 1.5 ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 86. Slipstream velocity components for PD1 at Φ = 0°, x/L = 0.843 where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR).

123

Φ = 90°, x/L = 0.843, PD1

(ux-U)/U 1.5 ut/U ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4 v / U

Figure 87. Slipstream velocity components for PD1 at Φ = 90°, x/L = 0.843, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR).

Φ = 270°, x/L = 0.843, PD1

(ux-U)/U ut/U 1.5 ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4 v / U

Figure 88. Slipstream velocity components for PD1 at Φ = 270°, x/L = 0.843, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR).

124

x/L = 0.02, PD1 x/L = 0.49, PD1 x/L = 0.843, PD1

Φ = 0° Φ = 0° Φ = 0° Φ = 90° Φ = 90° Φ = 90° 1.5 Φ = 270° 1.5 Φ = 270° 1.5 Φ = 270°

1 1 1 r / R r / R r r / R r

0.5 0.5 0.5

0 0 0 -4 0 4 8 12 -4 0 4 8 12 -4 0 4 8 12 Swirl Angle ε (deg) Swirl Angle ε (deg) Swirl Angle ε (deg)

Figure 89. Swirl angle at different longitudinal locations and azimuth angles for PD1, where β0.75 = 23°, U = 67 ft/s, 5,000 rpm (7×10 NIAR).

125

Φ = 0°, x/L = 0.02, COMP

(ux-U)/U ut/U 1.5 ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 90. Slipstream velocity components for COMP at Φ = 0°, x/L = 0.02, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR).

Φ = 90°, x/L = 0.02, COMP

(ux-U)/U 1.5 ut/U ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 91. Slipstream velocity components for COMP at Φ = 90°, x/L = 0.02, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR).

126

Φ = 270°, x/L = 0.02, COMP

(ux-U)/U ut/U 1.5 ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4 v / U

Figure 92. Slipstream velocity components for COMP at Φ = 270°, x/L = 0.02, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR).

Φ = 0°, x/L = 0.49, COMP

(ux-U)/U ut/U 1.5 ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 93. Slipstream velocity components for COMP at Φ = 0°, x/L = 0.49, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR).

127

Φ = 90°, x/L = 0.49, COMP

(ux-U)/U 1.5 ut/U ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 94. Slipstream velocity components for COMP at Φ = 90°, x/L = 0.49, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR).

Φ = 270°, x/L = 0.49, COMP

(ux-U)/U 1.5 ut/U ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 95. Slipstream velocity components for COMP at Φ = 270°, x/L = 0.49, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR).

128

Φ = 0°, x/L = 0.843, COMP

(ux-U)/U 1.5 ut/U ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 96. Slipstream velocity components for COMP at Φ = 0°, x/L = 0.843, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR).

Φ = 90°, x/L = 0.843, COMP

(ux-U)/U ut/U 1.5 ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 97. Slipstream velocity components for COMP at Φ = 90°, x/L = 0.843, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR).

129

Φ = 270°, x/L = 0.843, COMP

(ux-U)/U 1.5 ut/U ur/U

1 r / R r /

0.5

0 -0.2 0 0.2 0.4

v / U

Figure 98. Slipstream velocity components for COMP at Φ = 270°, x/L = 0.843, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR).

130

x/L = 0.02, COMP x/L = 0.49, COMP x/L = 0.843, COMP

Φ = 0° Φ = 0° Φ = 0° Φ = 90° Φ = 90° Φ = 90° 1.5 Φ = 270° 1.5 Φ = 270° 1.5 Φ = 270°

1 1 1 r / R r / R r r / R r

0.5 0.5 0.5

0 0 0 -4 0 4 8 12 -4 0 4 8 12 -4 0 4 8 12 Swirl Angle ε (deg) Swirl Angle ε (deg) Swirl Angle ε (deg) Figure 99. Swirl angle at different longitudinal locations and azimuth angles for COMP, where β0.75 = 20°, U = 67 ft/s, 6,000 rpm (7×10 NIAR).

5.4 Nacelle-Spinner Effect

Effects of the nacelle and spinner on the propeller performance are studied in this section.

Thrust and power coefficients plus efficiency curves, configurations with and without nacelle- spinner are compared for different pitch angles on PD1 propeller at the 3×4 LSWT in Figure 100 to Figure 102. Similar comparisons are made for PD1 propeller results obtained at the 7×10 NIAR wind tunnel in Figure 103 to Figure 105. This study shows that propeller performance drops significantly at higher advance ratios due to drag from the hub and other exposed parts. The maximum efficiency decreases 10 ~ 15% on average for all pitch angle settings. Likewise, the

COMP propeller data are compared in Figure 106 to Figure 109 for the 7×10 NIAR tunnel only, since the data was similar for both tunnels. No-spinner no-nacelle configurations are presented as nsnn in these figures.

131

0.3 1

CT CT nsnn CP 0.24 0.8 CP nsnn eta eta nsnn 0.18 0.6 P ,C η T C 0.12 0.4

23°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2 J

Figure 100. Nacelle-spinner effect on PD1 β0.75 = 23° performance tested at 3×4 LSWT.

0.3 1 CT CT nsnn CP 0.24 CP nsnn 0.8 eta eta nsnn

0.18 0.6 P ,C η T C 0.12 0.4

28°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2 J

Figure 101. Nacelle-spinner effect on PD1 β0.75 = 28° performance tested at 3×4 LSWT.

132

0.3 1 CT CT nsnn CP 0.24 CP nsnn 0.8 eta eta nsnn

0.18 0.6 P ,C η T C 0.12 0.4

33°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2 J

Figure 102. Nacelle-spinner effect on PD1 β0.75 = 33° performance tested at 3×4 LSWT.

0.3 1 CT CT nsnn CP 0.24 CP nsnn 0.8 eta eta nsnn

0.18 0.6 P ,C η T C 0.12 0.4

23°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2 J

Figure 103. Nacelle-spinner effect on PD1 β0.75 = 23° performance tested at 7×10 NIAR.

133

0.3 1

0.24 0.8

CT CT nsnn 0.18 CP 0.6

P CP nsnn ,C eta η T

C eta nsnn 0.12 0.4

28°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2

Figure 104. Nacelle-spinner effect on PD1 β0.75 = 28° performance tested at 7×10 NIAR.

0.3 1

0.24 0.8

0.18 0.6 P ,C η T C 0.12 0.4 33°@0.75R CT CT nsnn 0.06 CP 0.2 CP nsnn Series6 Series7 0 0 0 0.4 0.8 1.2 1.6 2

Figure 105. Nacelle-spinner effect on PD1 β0.75 = 33° performance tested at 7×10 LSWT.

134

0.3 1

CT CT nsnn CP 0.24 0.8 CP nsnn eta eta nsnn 0.18 0.6 P η ,C T C 0.12 0.4

15°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2

J Figure 106. Nacelle-spinner effect on COMP β0.75 = 15° performance tested at 7×10 NIAR.

0.3 1 CT CT nsnn CP 0.24 CP nsnn 0.8 eta eta nsnn

0.18 0.6 P η ,C T C 0.12 0.4

20°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2 J

Figure 107. Nacelle-spinner effect on COMP β0.75 = 20° performance tested at 7×10 NIAR.

135

0.3 1 CT CT nsnn CP 0.24 CP nsnn 0.8 eta eta nsnn

0.18 0.6 P ,C η T C 0.12 0.4

25°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2 J

Figure 108. Nacelle-spinner effect on COMP β0.75 = 25° performance tested at 7×10 NIAR.

0.3 1 CT CT nsnn CP 0.24 CP nsnn 0.8 eta eta nsnn

0.18 0.6 P ,C η T

C 30°@0.75R 0.12 0.4

0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2 J

Figure 109. Nacelle-spinner effect on COMP β0.75 = 30° performance tested at 7×10 NIAR.

136

5.5 Dynamic Tare

While the propeller generates thrust, the presence of the spinner by itself causes drag, which is also measured by the load cell. These two forces act against each other, unless the spinner is designed to have a positive effect on the propeller performance. Here, to separate the propeller thrust value, the individual spinner/hub drag was measured and added to the thrust value acquired with the combination of the propeller and with/without nacelle as the dynamic tare. Results for the dynamic tare are shown in Figure 110 for configurations with spinner and nacelle in both tunnels at 5,000 and 6,000 rpms. Similar tare results are presented in Figure 111 for no-spinner no-nacelle configurations. The data is shown as drag coefficient against advance ratio, based on propeller diameter and revolution speed, as well as drag versus tunnel dynamic pressure. Finally, the trends are estimated and given in equations that can be interpolated to the corresponding test condition.

Results show slightly different drag between the two tunnels, which may explain the thrust and power coefficient discrepancies, especially in the PD1 performance plots shown previously in

Figure 44. Note that dynamic tare for torque caused by spinner and motor shaft power is not presented, since it is less than 1% of the readings and therefore considered negligible. Figure 112 to Figure 114 show PD1 results in which the dynamic tare is applied to the thrust measurement and as a result to the efficiency curves for the 3×4 LSWT. The same method is used for the two configurations, with and without the spinner-nacelle. Interestingly, results for both configurations are identical to each other, which may refer to actual propeller performance. In another words, the results exclude the effect of spinner/hub and nacelle. The same comparisons are made for COMP results, as shown in Figure 115 to Figure 118. Unlike the PD1 results, it seems that the presence of the spinner-nacelle has positive effect on the COMP thrust and as a result on the efficiency. In

137

addition, vortex theory analysis results are added and compared, showing a reasonable match with efficiency curves, and thrust and power coefficients when the propeller is lightly loaded.

0.024

3x4 5000 rpm 7x10 5000 rpm 7x10 6000 rpm 0.018

y = 2.94E-03x2 + 8.43E-04x + 3.80E-03 R² = 9.96E-01 (7x10 6000rpm)

D 0.012 C y = 2.58E-03x2 + 2.33E-03x + 3.76E-03 R² = 9.98E-01 (7x10 5000rpm)

0.006

y = 2.19E-03x2 + 9.02E-05x + 3.93E-03 R² = 9.98E-01 (3x4 5000rpm)

0 0 0.4 0.8 1.2 1.6 2 J

0.5

3x4 5000 rpm 7x10 5000 rpm 0.4 7x10 6000 rpm

0.3

(lbf) y = -6.58E-05x2 + 8.40E-03x + 8.35E-02

D R² = 9.99E-01 (7x10 6000rpm) 0.2

y = -1.91E-04x2 + 1.09E-02x + 6.11E-02 R² = 9.99E-01 (7x10 5000rpm) 0.1

y = -2.48E-05x2 + 4.77E-03x + 6.07E-02 R² = 9.99E-01 (3x4 5000rpm) 0 0 5 10 15 20 25 q (psf) Figure 110. Dynamic tare for spinner-nacelle configurations in loads and coefficient forms and corresponding trend line equations.

138

0.024

y = 1.57E-02x2 + 3.34E-03x - 1.31E-03 R² = 1.00E+00 (3x4 nsnn 5000rpm) 3x4 nsnn 5000 rpm

0.018 7x10 nsnn 6000 rpm

D 0.012 C y = 1.97E-02x2 - 3.40E-03x - 2.91E-04 R² = 9.99E-01 (7x10 nsnn 6000rpm)

0.006

0 0 0.4 0.8 1.2 1.6 2 J

0.5

y = -3.96E-04x2 + 4.07E-02x - 1.36E-02 R² = 1.00E+00 (3x4 nsnn 5000rpm) 3x4 nsnn 5000 rpm 0.4 7x10 nsnn 6000 rpm

0.3 (lbf) D 0.2 y = 1.84E-04x2 + 3.15E-02x - 2.05E-02 R² = 9.98E-01 (7x10 nsnn 6000rpm)

0.1

0 0 5 10 15 20 25 q (psf)

Figure 111. Dynamic tare for no-spinner no-nacelle (nsnn) configurations in loads and coefficient forms, and corresponding trend line equations.

139

0.3 1

0.24 0.8

CT Vortex 0.18 CP Vortex 0.6

P CT D CT D nsnn ,C η

T CP

C CP nsnn 0.12 eta D 0.4 eta D nsnn eta Vortex

23°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2

J Figure 112. Dynamic tare results (“D”) for configurations with and without spinner-nacelle for PD1 β0.75 = 23° at 3×4 LSWT compared with vortex theory analysis results.

0.3 1

0.24 0.8

CT Vortex CP Vortex CT D 0.18 CT D nsnn 0.6 P CP

,C CP nsnn η T eta D C eta D nsnn 0.12 eta Vortex 0.4

28°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2

Figure 113. Dynamic tare results (“D”) for configurations with and without spinner-nacelle for PD1 β0.75 = 28° at 3×4 LSWT compared with vortex theory analysis results.

140

0.3 1

0.24 0.8

0.18 0.6 P ,C η T C 0.12 0.4 CT Vortex CP Vortex CT D 33°@0.75R CT D nsnn 0.06 CP 0.2 CP nsnn eta D eta D nsnn eta Vortex 0 0 0 0.4 0.8 1.2 1.6 2

J Figure 114. Dynamic tare results (“D”) for configurations with and without spinner-nacelle for PD1 β0.75 = 33° at 3×4 LSWT compared with vortex theory analysis results.

0.3 1

CT Vortex CP Vortex CT D 0.24 CT D nsnn 0.8 CP CP nsnn eta D 0.18 eta D nsnn 0.6

P eta Vortex ,C η T C 0.12 0.4

15°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2 J

Figure 115. Dynamic tare results (“D”) for configurations with and without spinner-nacelle for COMP β0.75 = 15° at 7×10 NIAR compared with vortex theory analysis results.

141

0.3 1

CT Vortex CP Vortex CT D 0.24 CT D nsnn 0.8 CP CP nsnn eta D eta D nsnn 0.18 eta Vortex 0.6 P ,C η T C 0.12 0.4

20°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2 J Figure 116. Dynamic tared results (“D”) for configurations with and without spinner-nacelle for COMP β0.75 = 20° at 7×10 NIAR compared with vortex theory analysis results.

0.3 1 CT Vortex CP Vortex CT D 0.24 CT D nsnn 0.8 CP CP nsnn eta D eta D nsnn 0.18 eta Vortex 0.6 P η ,C T C 0.12 0.4

25°@0.75R 0.06 0.2

0 0 0 0.4 0.8 1.2 1.6 2 J

Figure 117. Dynamic tared results (“D”) for configurations with and without spinner nacelle for COMP β0.75 = 25° at 7×10 NIAR compared with vortex theory analysis results.

142

0.3 1

0.24 0.8

CT Vortex 0.18 CP Vortex 0.6

P CT D ,C

CT D nsnn η T CP C CP nsnn 0.12 eta D 0.4 eta D nsnn eta Vortex

0.06 0.2 30°@0.75R

0 0 0 0.4 0.8 1.2 1.6 2 J

Figure 118. Dynamic tared results (“D”) for configurations with and without spinner-nacelle for COMP β0.75 = 30° at 7×10 NIAR compared with vortex theory analysis results.

143

CHAPTER 6

CONCLUSIONS

This study provides details of propeller and all other geometric descriptions, corresponding experimental data and boundary conditions that are necessary for the validation of small propeller analysis. Errors and uncertainties in instrumentation and model fabrications have been identified and introduced. Traditional test results, such as thrust and power coefficients along with efficiency curves as a function of advance ratio for two different propellers, at different pitch angles are presented. Two separate wind tunnel results were compared in order to study any bias in facility or individual data acquisition system. Sensitivity study of the performance to a range of rpm at certain pitch settings for both propellers was presented. Nacelle surface pressures at eight azimuth angles and eight axial locations were measured. A propeller wake survey at a certain test conditions for both propellers were conducted at three different azimuth angles and three axial locations. The nacelle-spinner effect was also demonstrated. Finally, spinner/hub drag effect was excluded from the data by applying the dynamic tare, to measure the propeller isolated performance, and plotted against the vortex theory predictions.

Comparison results between the two tunnels showed about 5% discrepancy in PD1 data with higher thrust and power coefficients at the 7×10 NIAR. Overall, data for the COMP matched well for both tunnels. Overall nacelle surface pressure distribution was consistent and coherent between tunnels. Wake survey results for PD1 at the vicinity of the propeller indicated a possible flow separation at the root to mid-section of the blade. The propeller with both spinner and nacelle performed 10 ~ 15% better than without covering configurations, mainly because of the hub drag.

Finally, dynamic tared results are compared to show the propeller performance excluding the spinner/hub and nacelle effect. These results matched well and also with the vortex theory analysis

144

for the PD1 propeller. However, dynamic tared results for the COMP had better efficiency when with spinner-nacelle configurations than no-spinner no-nacelle ones. Possibly, the spinner and the nacelle had positive interactions on the COMP propeller performance. Remarkably, vortex theory results agreed especially well for efficiency curves with no-spinner no-nacelle dynamic tared results which also supports this argument.

Propeller profile coordinates along with blade, spinner, and nacelle geometry information are available in Appendix A. Complete data tables of the 7×10 NIAR results are also presented numerically in Appendix B. Additional data or supplemental geometry descriptions (CAD file, etc.) are also available upon request via email at [email protected] or [email protected].

RECOMMENDATIONS

Additional tests would be advantageous for a sweep of yaw and nose pitch or system angles of attack. However, system structural and aeroelastic analyses need to be performed to assure the safety of the test. Also, flow visualization would be a plus but not necessary for validation purposes. Although particle image velocimetry can be a great addition to the database, extensive time and tunnel capabilities are required which was not the priority of this project.

145

REFERENCES

146

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151

APPENDIXES

152

APPENDIX A

E387 Profile Coordinates for PD1 (.scad file copy) polygon([ [ 95.0000 , 0.7842 ], [ 94.5693 , 0.8547 ], [ 38.9610 , 8.2060 ], [ 93.4048 , 1.0452 ], [ 37.8352 , 8.2297 ], [ 0.0473 , -0.1812 ], [ 92.2342 , 1.2361 ], [ 36.7106 , 8.2434 ], [ 0.0948 , -0.2926 ], [ 46.1675 , -0.3590 ], [ 91.0609 , 1.4271 ], [ 35.5873 , 8.2471 ], [ 0.1690 , -0.3909 ], [ 47.3528 , -0.3193 ], [ 89.8871 , 1.6178 ], [ 34.4658 , 8.2405 ], [ 0.2722 , -0.4783 ], [ 48.5380 , -0.2805 ], [ 88.7134 , 1.8082 ], [ 33.3463 , 8.2235 ], [ 0.4085 , -0.5579 ], [ 49.7231 , -0.2425 ], [ 87.5394 , 1.9984 ], [ 32.2286 , 8.1958 ], [ 0.5850 , -0.6340 ], [ 50.9081 , -0.2054 ], [ 86.3648 , 2.1886 ], [ 31.1120 , 8.1573 ], [ 0.8096 , -0.7141 ], [ 52.0928 , -0.1691 ], [ 85.1898 , 2.3789 ], [ 29.9955 , 8.1078 ], [ 1.0906 , -0.8060 ], [ 53.2773 , -0.1339 ], [ 84.0147 , 2.5693 ], [ 28.8781 , 8.0474 ], [ 1.4368 , -0.9069 ], [ 54.4616 , -0.0996 ], [ 82.8398 , 2.7597 ], [ 27.7594 , 7.9763 ], [ 1.8345 , -1.0048 ], [ 55.6456 , -0.0663 ], [ 81.6652 , 2.9498 ], [ 26.6402 , 7.8947 ], [ 2.2781 , -1.0926 ], [ 56.8296 , -0.0341 ], [ 80.4911 , 3.1396 ], [ 25.5215 , 7.8029 ], [ 2.7998 , -1.1731 ], [ 58.0135 , -0.0030 ], [ 79.3175 , 3.3290 ], [ 24.4047 , 7.7008 ], [ 3.4615 , -1.2513 ], [ 59.1973 , 0.0270 ], [ 78.1443 , 3.5179 ], [ 23.2906 , 7.5884 ], [ 4.3372 , -1.3314 ], [ 60.3812 , 0.0559 ], [ 76.9717 , 3.7062 ], [ 22.1795 , 7.4654 ], [ 5.3511 , -1.4003 ], [ 61.5649 , 0.0837 ], [ 75.7996 , 3.8938 ], [ 21.0713 , 7.3316 ], [ 6.3653 , -1.4480 ], [ 62.7483 , 0.1103 ], [ 74.6281 , 4.0806 ], [ 19.9662 , 7.1869 ], [ 7.3940 , -1.4796 ], [ 63.9313 , 0.1357 ], [ 73.4573 , 4.2664 ], [ 18.8651 , 7.0310 ], [ 8.4742 , -1.4988 ], [ 65.1139 , 0.1599 ], [ 72.2875 , 4.4510 ], [ 17.7690 , 6.8639 ], [ 9.6045 , -1.5082 ], [ 66.2963 , 0.1827 ], [ 71.1187 , 4.6343 ], [ 16.6792 , 6.6851 ], [ 10.7544 , -1.5085 ], [ 67.4784 , 0.2042 ], [ 69.9509 , 4.8161 ], [ 15.5964 , 6.4943 ], [ 11.9034 , -1.5010 ], [ 68.6605 , 0.2242 ], [ 68.7838 , 4.9962 ], [ 14.5211 , 6.2909 ], [ 13.0513 , -1.4872 ], [ 69.8427 , 0.2429 ], [ 67.6172 , 5.1746 ], [ 13.4541 , 6.0743 ], [ 14.2049 , -1.4678 ], [ 71.0247 , 0.2601 ], [ 66.4506 , 5.3512 ], [ 12.3971 , 5.8441 ], [ 15.3672 , -1.4438 ], [ 72.2066 , 0.2759 ], [ 65.2841 , 5.5259 ], [ 11.3529 , 5.6001 ], [ 16.5372 , -1.4159 ], [ 73.3880 , 0.2902 ], [ 64.1181 , 5.6986 ], [ 10.3244 , 5.3420 ], [ 17.7113 , -1.3847 ], [ 74.5687 , 0.3029 ], [ 62.9532 , 5.8691 ], [ 9.3121 , 5.0688 ], [ 18.8872 , -1.3507 ], [ 75.7490 , 0.3140 ], [ 61.7900 , 6.0369 ], [ 8.3147 , 4.7788 ], [ 20.0640 , -1.3144 ], [ 76.9289 , 0.3234 ], [ 60.6291 , 6.2016 ], [ 7.3362 , 4.4714 ], [ 21.2422 , -1.2759 ], [ 78.1088 , 0.3310 ], [ 59.4705 , 6.3627 ], [ 6.3923 , 4.1501 ], [ 22.4224 , -1.2358 ], [ 79.2887 , 0.3368 ], [ 58.3144 , 6.5199 ], [ 5.5013 , 3.8202 ], [ 23.6049 , -1.1941 ], [ 80.4685 , 0.3407 ], [ 57.1606 , 6.6728 ], [ 4.6622 , 3.4805 ], [ 24.7894 , -1.1514 ], [ 81.6478 , 0.3429 ], [ 56.0092 , 6.8208 ], [ 3.8577 , 3.1222 ], [ 25.9755 , -1.1078 ], [ 82.8260 , 0.3431 ], [ 54.8601 , 6.9636 ], [ 3.1065 , 2.7525 ], [ 27.1628 , -1.0634 ], [ 84.0029 , 0.3413 ], [ 53.7134 , 7.1007 ], [ 2.4773 , 2.4111 ], [ 28.3509 , -1.0185 ], [ 85.1787 , 0.3371 ], [ 52.5691 , 7.2317 ], [ 1.9828 , 2.1137 ], [ 29.5395 , -0.9733 ], [ 86.3541 , 0.3305 ], [ 51.4272 , 7.3561 ], [ 1.5811 , 1.8426 ], [ 30.7284 , -0.9279 ], [ 87.5294 , 0.3214 ], [ 50.2875 , 7.4736 ], [ 1.2376 , 1.5807 ], [ 31.9176 , -0.8824 ], [ 88.7044 , 0.3097 ], [ 49.1496 , 7.5838 ], [ 0.9376 , 1.3256 ], [ 33.1068 , -0.8369 ], [ 89.8776 , 0.2954 ], [ 48.0130 , 7.6864 ], [ 0.6884 , 1.0958 ], [ 34.2959 , -0.7915 ], [ 91.0477 , 0.2783 ], [ 46.8775 , 7.7812 ], [ 0.4907 , 0.9029 ], [ 35.4849 , -0.7463 ], [ 92.2151 , 0.2578 ], [ 45.7429 , 7.8679 ], [ 0.3368 , 0.7413 ], [ 36.6735 , -0.7013 ], [ 93.3812 , 0.2337 ], [ 44.6093 , 7.9464 ], [ 0.2205 , 0.5979 ], [ 37.8618 , -0.6567 ], [ 94.5451 , 0.2062 ], [ 43.4768 , 8.0164 ], [ 0.1347 , 0.4635 ], [ 39.0497 , -0.6125 ], [ 95.0000 , 0.1941 ]]); [ 42.3458 , 8.0776 ], [ 0.0744 , 0.3326 ], [ 40.2370 , -0.5687 ], [ 41.2162 , 8.1297 ], [ 0.0367 , 0.2014 ], [ 41.4239 , -0.5255 ], [ 40.0880 , 8.1726 ], [ 0.0198 , 0.0695 ], [ 42.6103 , -0.4828 ], [ 0.0232 , -0.0593 ], [ 43.7963 , -0.4408 ], [ 44.9820 , -0.3995 ],

153

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154

PD1 Blade Geometry (.scad file copy) union(){ translate([0,0,25.4]) rotate ([0,0,-62.364]) linear_extrude(height=127, twist=-44.707, $fn=150)

translate([-10.17,-0.75,0]) scale(0.254) include;

translate([0,0,-25.4]) rotate ([0,180,62.364]) linear_extrude(height=127, twist=-44.707, $fn=150)

translate([-10.17,-0.75,0]) scale(0.254) include;

translate([0,0,34.925]) sphere(5.08, $fn=36); translate([0,0,-34.925]) sphere(5.08, $fn=36); cylinder(h=69.85,r=5.08,center=true,$fn=36); }

COMP Blade Geometry (.scad file copy)

R=152.4; //propeller radius (mm) d=R/30; //step size

module p(t){

translate([0,0,t]) rotate([0,0,-1714.5/t]) resize([-0.0033*pow(t,2)+0.6*t-4.5,0,0],auto=true) translate([-40.0569,-2.9581,0]) linear_extrude(height=0.1) include; }

for(t=[7*d:d:R])

translate(){p(t);p(t+d);}

Spinner Geometry (.scad file copy)

$fn=100;

translate([0,0,-3.755]) parabo (100);

module parabo (y) {

rotate_extrude(convexity=10) difference(){

projection(cut=true, center=true) translate([0,-97.5,0.24*y])

155

rotate([81,0,0]) cylinder(h=2*y, r1=0.445*y, r2=0, center=true); mirror([0,1,0]) square([2*y,2*y]); } } translate([0,0,-3.81]) cylinder(h = 2.54, r1=43.69, r2=44.27, center=false);

Nacelle Geometry (.scad file copy)

$fn=100; // Number of fragments

L=647.7; // Nacelle length (mm) D=88.9; // Diameter at Z=0 (mm) d=1; // Step size (mm) d=0.1 for max accuracy

module p(t){

translate([0,0,t]) resize([-0.000848*pow(t,2)+0.549*t+88.9,-0.000848*pow(t,2)+0.549*t+88.9,1]) linear_extrude(height=d) circle (d = D); }

for(t=[1:d:L])

translate(){p(t-1);p(t+d-1);}

Assembly Geometry (.scad file copy)

translate([0,0,-16.51]) rotate([90,180,0]) include;

include ; include;

$fn=100;

156

APPENDIX B

This appendix contains numerical data obtained at the 7x10 NIAR wind tunnel which includes boundary conditions, propeller performance results, pressure coefficients and wall pressure gradients. Tunnel total and static pressure readings presented here are the differential to the tunnel absolute barometric pressure gauge. Corrected tunnel dynamic pressure, qcor, was implemented to obtain the propeller performance coefficients. Tared dynamic pressure, qtare, was used for nacelle pressure coefficients and wall pressure gradients. Additional nomenclature and subscriptions are:

Pt Total pressure

Ps Static pressure en Test section entrance ex Test section exit abs Absolute (i.e., tunnel absolute barometric pressure) ind Indicated (i.e., raw measured tunnel dynamic pressure) tare Tared dynamic pressure accounted for the C-mount cor Corrected tunnel values for both the C-mount and propeller tunnel blockage

157

PD1 Propeller

Run β0.75 (deg) Ptabs (inHg) Temp (F) qind (psf) qtare (psf) Pten (psfd) Psen (psfd) qen (psf) Ptex (psfd) Psex (psfd) qex (psf) 18 23 28.5832 75.67 0.0496 0.0492 0.4277 0.3865 0.0412 0.4290 0.3960 0.0330 18 23 28.5820 76.19 1.0150 1.0067 1.4270 0.4126 1.0145 1.4236 0.4051 1.0185 18 23 28.5850 76.30 1.6130 1.5998 2.0362 0.4177 1.6184 2.0320 0.3912 1.6407 18 23 28.5835 76.30 2.6172 2.5958 3.0406 0.4235 2.6171 3.0374 0.3673 2.6700 18 23 28.5831 76.30 3.6028 3.5734 4.0304 0.4209 3.6095 4.0202 0.3322 3.6880 18 23 28.5840 76.26 5.1826 5.1403 5.6236 0.4065 5.2171 5.6136 0.2703 5.3433 18 23 28.5818 76.20 7.8136 7.7498 8.2243 0.3684 7.8559 8.2100 0.1469 8.0631 18 23 28.5830 76.10 10.3969 10.3120 10.8405 0.3577 10.4828 10.8084 0.0442 10.7641 18 23 28.5835 76.06 13.0008 12.8946 13.3698 0.2635 13.1063 13.3443 -0.1436 13.4879 18 23 28.5790 76.00 15.5884 15.4610 15.8783 0.1365 15.7418 15.8462 -0.3660 16.2122 26 23 28.8230 70.80 0.0350 0.0347 0.4690 0.4441 0.0249 0.4700 0.4454 0.0246 26 23 28.8236 71.60 1.0186 1.0103 1.5008 0.4846 1.0162 1.4988 0.4697 1.0290 26 23 28.8240 71.80 1.6202 1.6070 2.0982 0.4802 1.6180 2.0929 0.4478 1.6451 26 23 28.8239 71.90 2.6080 2.5867 3.1067 0.4910 2.6156 3.0986 0.4268 2.6718 26 23 28.8222 72.00 3.5944 3.5650 4.1047 0.4869 3.6179 4.0981 0.3927 3.7054 26 23 28.8224 72.04 5.2050 5.1625 5.6942 0.4726 5.2216 5.6784 0.3318 5.3466 26 23 28.8226 72.10 7.7924 7.7287 8.2656 0.4242 7.8414 8.2427 0.2025 8.0402 26 23 28.8189 72.10 10.3948 10.3099 10.8786 0.4085 10.4701 10.8605 0.0972 10.7633 26 23 28.8232 72.20 12.9860 12.8799 13.4140 0.3207 13.0933 13.3838 -0.0832 13.4670 26 23 28.8231 72.30 15.6002 15.4728 15.9185 0.1715 15.7470 15.8769 -0.3226 16.1994 23 28 28.8010 70.30 0.0419 0.0416 0.4412 0.4042 0.0370 0.4352 0.4146 0.0206 23 28 28.8020 70.50 0.9830 0.9750 1.4397 0.4416 0.9981 1.4371 0.4147 1.0224 23 28 28.8060 70.60 2.1165 2.0992 2.5834 0.4490 2.1344 2.5753 0.4130 2.1623 23 28 28.8032 70.60 4.2067 4.1723 4.6894 0.4589 4.2304 4.6732 0.3620 4.3112 23 28 28.8060 70.60 6.1858 6.1353 6.6521 0.4232 6.2289 6.6368 0.2642 6.3726 23 28 28.8060 70.70 8.8014 8.7295 9.2377 0.3662 8.8716 9.2189 0.1223 9.0966 23 28 28.8056 70.77 11.3907 11.2976 11.8107 0.3273 11.4834 11.7903 -0.0062 11.7965 23 28 28.8039 70.90 14.5894 14.4702 14.9190 0.1914 14.7276 14.8794 -0.2511 15.1305 23 28 28.8087 71.00 18.1919 18.0433 18.3810 -0.0085 18.3895 18.3272 -0.5828 18.9099 23 28 28.8078 71.32 23.3866 23.1955 23.3325 -0.3142 23.6467 23.2697 -1.0728 24.3425

157

cpr @ x/L where Φ = 0°

Run qcor (fps) T (lbs) Q (in.lbs) rpm Ucor (fps) J η CT CP Re0.75 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 18 0.049 1.461 3.317 3956.3 6.572 0.100 0.084 0.153 0.182 74,416 10.897 -7.6319 -9.5930 -9.8565 -8.2173 -7.3977 -7.7782 -7.1050 18 1.007 2.133 4.771 5025.0 30.127 0.360 0.307 0.138 0.162 95,535 1.1468 0.0440 -0.4109 -0.6241 -0.5969 -0.5182 -0.5726 -0.5053 18 1.600 2.051 4.587 5017.5 38.022 0.450 0.388 0.133 0.156 96,040 0.7195 0.0687 -0.2526 -0.4120 -0.4021 -0.3454 -0.3544 -0.2949 18 2.596 1.972 4.413 5025.0 48.475 0.580 0.494 0.128 0.150 97,250 0.4396 0.0546 -0.1751 -0.3093 -0.3132 -0.2533 -0.2322 -0.1596 18 3.573 1.907 4.244 5051.3 56.901 0.680 0.580 0.122 0.142 98,765 0.3200 0.0444 -0.1374 -0.2538 -0.2599 -0.2099 -0.1881 -0.1148 18 5.140 1.849 4.071 5085.0 68.274 0.810 0.699 0.117 0.135 101,002 0.2251 0.0335 -0.1088 -0.2105 -0.2141 -0.1721 -0.1371 -0.0665 18 7.750 1.694 3.888 5111.3 83.863 0.980 0.819 0.106 0.127 104,110 0.1565 0.0044 -0.1053 -0.1948 -0.1967 -0.1541 -0.1142 -0.0456 18 10.312 1.400 3.624 5156.3 96.761 1.130 0.831 0.086 0.117 107,403 0.1233 -0.0126 -0.1024 -0.1877 -0.1873 -0.1471 -0.1068 -0.0392 18 12.895 1.138 3.289 5242.5 108.218 1.240 0.818 0.068 0.102 111,308 0.0924 -0.0283 -0.1037 -0.1800 -0.1783 -0.1395 -0.0989 -0.0343 18 15.461 0.889 2.917 5370.0 118.511 1.320 0.771 0.050 0.087 115,765 0.1029 -0.0288 -0.1055 -0.1820 -0.1757 -0.1389 -0.0999 -0.0344 26 0.035 2.166 4.861 4803.8 5.430 0.068 0.058 0.151 0.177 92,565 24.922 -15.979 -17.472 -17.804 -15.066 -11.997 -13.822 -10.835 26 1.010 2.049 4.586 4916.3 29.923 0.365 0.312 0.136 0.160 95,831 1.0756 0.0180 -0.3683 -0.5693 -0.5408 -0.4353 -0.5094 -0.3826 26 1.607 2.016 4.503 4946.3 37.778 0.458 0.392 0.132 0.155 97,064 0.6990 0.0260 -0.2509 -0.4014 -0.3915 -0.3100 -0.3306 -0.2168 26 2.587 1.950 4.378 5006.3 47.972 0.575 0.489 0.125 0.147 99,265 0.4302 0.0338 -0.1705 -0.3002 -0.2991 -0.2384 -0.2284 -0.1232 26 3.565 1.903 4.247 5051.3 56.343 0.669 0.573 0.120 0.140 101,151 0.3132 0.0293 -0.1339 -0.2511 -0.2495 -0.1990 -0.1852 -0.0883 26 5.162 1.851 4.078 5092.5 67.829 0.799 0.693 0.115 0.132 103,586 0.2111 0.0147 -0.1136 -0.2098 -0.2135 -0.1663 -0.1420 -0.0506 26 7.729 1.709 3.941 5118.8 83.023 0.973 0.806 0.105 0.127 106,681 0.1483 -0.0061 -0.1106 -0.1952 -0.1937 -0.1475 -0.1179 -0.0316 26 10.310 1.444 3.742 5205.0 95.912 1.106 0.815 0.086 0.116 110,751 0.1127 -0.0232 -0.1089 -0.1918 -0.1887 -0.1446 -0.1144 -0.0341 26 12.880 1.164 3.392 5298.8 107.219 1.214 0.796 0.067 0.102 114,818 0.0915 -0.0325 -0.1081 -0.1844 -0.1805 -0.1407 -0.1098 -0.0302 26 15.473 0.924 3.046 5418.8 117.528 1.301 0.754 0.051 0.087 119,237 0.0798 -0.0387 -0.1082 -0.1837 -0.1757 -0.1380 -0.1072 -0.0302 23 0.042 2.303 6.382 4878.8 5.953 0.073 0.050 0.156 0.226 93,919 16.825 -20.737 -21.153 -18.138 -14.188 -11.346 -14.188 -11.035 23 0.975 2.224 6.221 4950.0 29.402 0.356 0.243 0.146 0.214 96,335 -0.0297 -0.1095 -0.1302 -0.1730 -0.2040 -0.1302 -0.1184 -0.0327 23 2.099 2.130 5.994 5006.3 43.218 0.518 0.352 0.137 0.202 98,636 0.5874 0.0462 -0.2172 -0.3517 -0.3496 -0.2756 -0.2913 -0.2042 23 4.172 2.029 5.746 5092.5 60.992 0.719 0.484 0.126 0.187 102,452 0.3153 0.0302 -0.1351 -0.2411 -0.2459 -0.1934 -0.1762 -0.0961 23 6.135 1.970 5.560 5152.5 73.990 0.862 0.583 0.119 0.176 105,571 0.2224 0.0218 -0.1104 -0.2040 -0.2090 -0.1634 -0.1339 -0.0595 23 8.729 1.972 5.335 5216.3 88.279 1.015 0.717 0.117 0.165 109,301 0.1643 0.0121 -0.0991 -0.1833 -0.1861 -0.1427 -0.1103 -0.0371 23 11.298 1.891 5.313 5235.0 100.446 1.151 0.782 0.111 0.163 112,118 0.1369 -0.0014 -0.0990 -0.1780 -0.1787 -0.1399 -0.1009 -0.0307 23 14.470 1.657 5.166 5280.0 113.696 1.292 0.792 0.096 0.156 115,873 0.1153 -0.0137 -0.1017 -0.1761 -0.1769 -0.1373 -0.0975 -0.0306 23 18.043 1.389 4.851 5388.8 126.975 1.414 0.773 0.077 0.141 120,925 0.0974 -0.0224 -0.1059 -0.1749 -0.1729 -0.1353 -0.0953 -0.0293 23 23.196 1.071 4.368 5606.3 143.981 1.541 0.721 0.055 0.117 128,895 0.0847 -0.0288 -0.1078 -0.1727 -0.1712 -0.1324 -0.0928 -0.0289

158

cpr @ x/L where Φ = 45° cpr @ x/L where Φ = 90° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 18 10.136 -8.5100 -9.8858 -8.2173 -8.7734 -6.8708 -6.8708 -6.3439 9.4334 -8.2466 -9.8858 -9.3296 -7.6904 -7.4270 -7.1342 -6.7830 18 1.1110 -0.0390 -0.4238 -0.4910 -0.5940 -0.4910 -0.5311 -0.4510 1.1182 0.0111 -0.4381 -0.5225 -0.4782 -0.5296 -0.5168 -0.4381 18 0.6970 0.0219 -0.2607 -0.3273 -0.4003 -0.3273 -0.3445 -0.2445 0.7105 0.0453 -0.2688 -0.3481 -0.3282 -0.3526 -0.3273 -0.2517 18 0.4207 0.0246 -0.1751 -0.2466 -0.3066 -0.2466 -0.2261 -0.1290 0.4340 0.0440 -0.1856 -0.2566 -0.2577 -0.2616 -0.2211 -0.1324 18 0.3031 0.0226 -0.1378 -0.2002 -0.2546 -0.2043 -0.1857 -0.0926 0.3200 0.0440 -0.1450 -0.2131 -0.2127 -0.2224 -0.1857 -0.0951 18 0.2114 0.0187 -0.1119 -0.1674 -0.2099 -0.1651 -0.1419 -0.0514 0.2276 0.0335 -0.1167 -0.1758 -0.1763 -0.1775 -0.1394 -0.0528 18 0.1439 -0.0057 -0.1110 -0.1603 -0.1930 -0.1506 -0.1214 -0.0356 0.1530 0.0077 -0.1177 -0.1657 -0.1653 -0.1636 -0.1198 -0.0367 18 0.1124 -0.0214 -0.1124 -0.1560 -0.1815 -0.1451 -0.1141 -0.0327 0.1232 -0.0088 -0.1197 -0.1610 -0.1589 -0.1546 -0.1130 -0.0339 18 0.0779 -0.0357 -0.1132 -0.1510 -0.1762 -0.1384 -0.1085 -0.0278 0.0866 -0.0266 -0.1219 -0.1561 -0.1538 -0.1489 -0.1076 -0.0315 18 0.0967 -0.0349 -0.1154 -0.1512 -0.1761 -0.1400 -0.1081 -0.0262 0.0881 -0.0265 -0.1242 -0.1566 -0.1539 -0.1511 -0.1049 -0.0289 26 22.018 -16.103 -19.090 -15.813 -15.025 -11.997 -12.412 -11.997 24.009 -15.357 -19.049 -17.265 -12.785 - -13.158 -11.582 26 1.0186 0.0123 -0.3940 -0.4225 -0.5265 -0.4496 -0.4353 -0.3697 1.1026 0.0507 -0.3683 -0.4766 -0.4496 - -0.4624 -0.3669 26 0.6694 0.0296 -0.2500 -0.3091 -0.3826 -0.3181 -0.2930 -0.2025 0.7232 0.0619 -0.2419 -0.3369 -0.3181 - -0.3091 -0.1980 26 0.4168 0.0344 -0.1755 -0.2323 -0.2924 -0.2373 -0.2067 -0.1093 0.4608 0.0594 -0.1649 -0.2518 -0.2484 - -0.2167 -0.1109 26 0.3072 0.0333 -0.1380 -0.1933 -0.2442 -0.2014 -0.1675 -0.0782 0.3354 0.0551 -0.1303 -0.2014 -0.2054 - -0.1788 -0.0834 26 0.2050 0.0181 -0.1139 -0.1644 -0.2068 -0.1674 -0.1312 -0.0464 0.2317 0.0356 -0.1111 -0.1747 -0.1730 - -0.1390 -0.0525 26 0.1394 -0.0057 -0.1149 -0.1572 -0.1902 -0.1492 -0.1131 -0.0287 0.1621 0.0094 -0.1125 -0.1641 -0.1621 - -0.1183 -0.0331 26 0.1011 -0.0242 -0.1163 -0.1574 -0.1817 -0.1465 -0.1091 -0.0289 0.1268 -0.0103 -0.1172 -0.1624 -0.1589 - -0.1144 -0.0339 26 0.0818 -0.0337 -0.1153 -0.1522 -0.1775 -0.1407 -0.1055 -0.0258 0.1082 -0.0198 -0.1188 -0.1584 -0.1550 - -0.1109 -0.0315 26 0.0704 -0.0410 -0.1180 -0.1529 -0.1762 -0.1401 -0.1047 -0.0263 0.0938 -0.0276 -0.1217 -0.1584 -0.1557 - -0.1101 -0.0316 23 14.156 -21.257 -20.598 -17.376 -15.401 -12.629 -11.000 -11.000 14.364 -21.534 -22.816 -18.866 -14.257 -11.312 -12.629 -11.728 23 -0.0740 -0.0903 -0.1553 -0.1641 -0.1922 -0.1479 -0.1080 -0.0416 -0.0297 -0.0903 -0.1435 -0.1907 -0.1878 -0.1641 -0.1479 -0.0504 23 0.5449 0.0180 -0.2172 -0.2920 -0.3352 -0.2804 -0.2611 -0.1850 0.5737 0.0427 -0.2303 -0.3057 -0.2810 -0.2989 -0.2611 -0.1713 23 0.2980 0.0185 -0.1386 -0.2007 -0.2407 -0.1952 -0.1696 -0.0868 0.3174 0.0340 -0.1482 -0.2107 -0.2055 -0.2104 -0.1727 -0.0827 23 0.2046 0.0121 -0.1132 -0.1695 -0.2005 -0.1616 -0.1334 -0.0510 0.2215 0.0227 -0.1172 -0.1721 -0.1754 -0.1738 -0.1379 -0.0505 23 0.1458 0.0045 -0.1029 -0.1554 -0.1796 -0.1424 -0.1133 -0.0295 0.1605 0.0149 -0.1070 -0.1565 -0.1554 -0.1537 -0.1120 -0.0307 23 0.1178 -0.0075 -0.1047 -0.1523 -0.1755 -0.1390 -0.1060 -0.0246 0.1339 0.0017 -0.1101 -0.1556 -0.1529 -0.1487 -0.1061 -0.0260 23 0.0961 -0.0197 -0.1074 -0.1517 -0.1749 -0.1378 -0.1057 -0.0255 0.1112 -0.0117 -0.1151 -0.1559 -0.1518 -0.1480 -0.1058 -0.0282 23 0.0804 -0.0299 -0.1093 -0.1504 -0.1729 -0.1350 -0.1034 -0.0249 0.0964 -0.0199 -0.1176 -0.1547 -0.1501 -0.1451 -0.1042 -0.0263 23 0.0676 -0.0369 -0.1109 -0.1489 -0.1721 -0.1350 -0.1022 -0.0245 0.0825 -0.0279 -0.1205 -0.1540 -0.1499 -0.1442 -0.1031 -0.0266

159

cpr @ x/L where Φ = 135° cpr @ x/L where Φ = 180° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 0.020 0.137 0.255 0.373 0.490 0.608 18 10.224 -7.7197 -9.0369 -8.5100 -7.9246 -6.7830 -7.1635 -7.6904 9.5797 -7.6904 -10.149 -9.3589 -9.0662 -7.0757 18 1.2026 0.0554 -0.3437 -0.4510 -0.5211 -0.4524 -0.4910 -0.4638 1.1497 0.1083 -0.3694 -0.5225 -0.5883 -0.4925 18 0.7807 0.0723 -0.2103 -0.3111 -0.3390 -0.2949 -0.3192 -0.2778 0.7564 0.0912 -0.2265 -0.3580 -0.3985 -0.3472 18 0.4717 0.0701 -0.1385 -0.2367 -0.2616 -0.2289 -0.2211 -0.1496 0.4889 0.0884 -0.1485 -0.2633 -0.3027 -0.2605 18 0.3474 0.0629 -0.1072 -0.1894 -0.2208 -0.1926 -0.1781 -0.1112 0.3833 0.0766 -0.1184 -0.2103 -0.2458 -0.2119 18 0.2573 0.0467 -0.0875 -0.1573 -0.1811 -0.1559 -0.1363 -0.0668 0.2663 0.0587 -0.0931 -0.1718 -0.2004 -0.1662 18 0.1831 0.0183 -0.0874 -0.1521 -0.1709 -0.1447 -0.1192 -0.0475 0.1965 0.0322 -0.0951 -0.1657 -0.1826 -0.1514 18 0.1406 0.0007 -0.0902 -0.1500 -0.1635 -0.1395 -0.1123 -0.0416 0.1574 0.0155 -0.0990 -0.1617 -0.1743 -0.1444 18 0.1023 -0.0176 -0.0938 -0.1474 -0.1580 -0.1354 -0.1079 -0.0381 0.1151 -0.0029 -0.1024 -0.1584 -0.1660 -0.1381 18 0.0899 -0.0222 -0.0954 -0.1484 -0.1600 -0.1362 -0.1041 -0.0400 0.1177 -0.0038 -0.1047 -0.1608 -0.1649 -0.1402 26 25.047 -13.490 -15.896 -18.509 -12.785 -10.379 -12.412 -12.412 26 1.1867 0.1434 -0.2885 -0.5009 -0.4353 -0.3797 -0.4496 -0.4097 26 0.7689 0.1192 -0.1836 -0.3423 -0.3109 -0.2670 -0.2930 -0.2428 26 0.4942 0.0945 -0.1182 -0.2373 -0.2512 -0.2134 -0.2117 -0.1399 26 0.3710 0.0842 -0.0887 -0.1860 -0.2095 -0.1812 -0.1784 -0.1040 26 0.2616 0.0582 -0.0743 -0.1465 -0.1747 -0.1524 -0.1387 -0.0667 26 0.1944 0.0298 -0.0806 -0.1283 -0.1637 -0.1412 -0.1213 -0.0475 26 0.1511 0.0066 -0.0851 -0.1230 -0.1622 -0.1395 -0.1176 -0.0469 26 0.1317 -0.0039 -0.0866 -0.1167 -0.1582 -0.1365 -0.1142 -0.0435 26 0.1195 -0.0133 -0.0910 -0.1157 -0.1581 -0.1371 -0.1119 -0.0427 23 15.023 -20.737 -20.425 -17.410 -13.460 -11.069 -11.624 -12.282 23 -0.0194 -0.0563 -0.1169 -0.1760 -0.1627 -0.1065 -0.1361 -0.0534 23 0.6272 0.0812 -0.1596 -0.2673 -0.2920 -0.2509 -0.2605 -0.1980 23 0.3450 0.0561 -0.0992 -0.1852 -0.2104 -0.1796 -0.1693 -0.0961 23 0.2494 0.0422 -0.0815 -0.1592 -0.1787 -0.1526 -0.1350 -0.0639 23 0.1894 0.0286 -0.0757 -0.1452 -0.1595 -0.1361 -0.1113 -0.0416 23 0.1586 0.0148 -0.0783 -0.1435 -0.1565 -0.1345 -0.1078 -0.0376 23 0.1331 -0.0002 -0.0854 -0.1458 -0.1556 -0.1333 -0.1069 -0.0384 23 0.1192 -0.0097 -0.0882 -0.1472 -0.1559 -0.1322 -0.1048 -0.0361 23 0.1059 -0.0185 -0.0914 -0.1472 -0.1541 -0.1318 -0.1037 -0.0344

160

cpr @ x/L where Φ = 225° cpr @ x/L where Φ = 270° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 18 8.1162 -7.3391 -10.179 -9.5930 -8.4807 -8.1880 -6.2268 -7.0464 10.663 -9.0369 -10.1785 -6.5195 - -9.5930 -7.6319 -7.1050 18 1.1039 0.0640 -0.4095 -0.5454 -0.5497 -0.6040 -0.5211 -0.4796 1.2140 -0.0347 -0.3408 -0.3423 - -0.6827 -0.5783 -0.4782 18 0.7006 0.0912 -0.2427 -0.3454 -0.3742 -0.3913 -0.3210 -0.2778 0.7708 0.0183 -0.2166 -0.2436 - -0.4831 -0.3661 -0.3120 18 0.4335 0.0740 -0.1640 -0.2638 -0.2833 -0.2982 -0.2233 -0.1535 0.4762 0.0329 -0.1374 -0.1912 - -0.3493 -0.2616 -0.1801 18 0.3232 0.0702 -0.1225 -0.2099 -0.2325 -0.2510 -0.1849 -0.1265 0.3547 0.0327 -0.1031 -0.1571 - -0.2873 -0.2051 -0.1301 18 0.2248 0.0593 -0.0962 -0.1724 -0.1917 -0.2018 -0.1422 -0.0744 0.2545 0.0279 -0.0772 -0.1360 - -0.2346 -0.1564 -0.0772 18 0.1474 0.0287 -0.0926 -0.1581 -0.1779 -0.1805 -0.1250 -0.0529 0.1779 0.0118 -0.0780 -0.1382 - -0.2013 -0.1328 -0.0546 18 0.1205 0.0095 -0.0965 -0.1567 -0.1716 -0.1679 -0.1193 -0.0462 0.1434 -0.0025 -0.0757 -0.1369 - -0.1896 -0.1254 -0.0486 18 0.0889 -0.0076 -0.0977 -0.1515 -0.1645 -0.1612 -0.1127 -0.0425 0.1093 -0.0176 -0.0778 -0.1372 - -0.1770 -0.1156 -0.0430 18 0.0824 -0.0100 -0.0987 -0.1525 -0.1653 -0.1587 -0.1174 -0.0417 0.1290 -0.0134 -0.0765 -0.1391 - -0.1758 -0.1156 -0.0411

161

cpr @ x/L where Φ = 315° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 18 9.3163 -7.9246 -11.6128 -8.4807 -8.2173 -7.1342 -7.6611 -7.9246 18 1.0638 -0.0090 -0.5354 -0.5640 -0.6040 -0.5583 -0.5583 -0.5468 18 0.6763 0.0264 -0.3472 -0.3661 -0.4174 -0.3877 -0.3706 -0.3544 18 0.4185 0.0396 -0.2289 -0.2833 -0.3199 -0.2944 -0.2527 -0.2012 18 0.3047 0.0412 -0.1732 -0.2289 -0.2591 -0.2506 -0.2051 -0.1531 18 0.2198 0.0313 -0.1368 -0.1892 -0.2153 -0.2057 -0.1584 -0.0903 18 0.1530 0.0099 -0.1320 -0.1800 -0.1986 -0.1850 -0.1291 -0.0633 18 0.1208 -0.0057 -0.1261 -0.1719 -0.1881 -0.1753 -0.1228 -0.0539 18 0.0899 -0.0218 -0.1247 -0.1681 -0.1774 -0.1660 -0.1135 -0.0472 18 0.0933 -0.0198 -0.1274 -0.1656 -0.1776 -0.1669 -0.1135 -0.0462

23 14.399 -20.771 -24.514 -17.514 -16.752 -13.287 -13.945 -13.668 23 -0.1169 -0.1080 -0.3074 -0.2055 -0.3074 -0.2011 -0.2705 -0.2675 23 0.5353 0.0270 -0.3243 -0.3455 -0.3970 -0.3647 -0.3517 -0.3147 23 0.2932 0.0240 -0.1862 -0.2307 -0.2763 -0.2542 -0.2121 -0.1582 23 0.1891 -0.0005 -0.1505 -0.1947 -0.2275 -0.2090 -0.1648 -0.1017 23 0.0794 -0.0483 -0.1186 -0.1724 -0.1966 -0.1729 -0.1263 -0.0714 23 0.0278 -0.0517 -0.1024 -0.1603 -0.1762 -0.1416 -0.1103 -0.0597 23 0.0242 -0.0465 -0.0948 -0.1566 -0.1716 -0.1384 -0.1029 -0.0533 23 0.0225 -0.0433 -0.0899 -0.1552 -0.1653 -0.1285 -0.0984 -0.0492 23 0.0319 -0.0385 -0.0868 -0.1500 -0.1550 -0.1100 -0.0970 -0.0439

162

South Side Wall cpr @ l' Run 0.051 0.139 0.228 0.316 0.360 0.404 0.448 0.492 0.536 0.580 0.624 0.668 0.714 0.809 0.905 1.000 18 -1.6898 -0.9872 -1.3970 -2.2166 -1.9532 -1.0165 -1.6898 -2.2752 - -1.3678 -0.8409 -1.8947 -1.4556 -1.6605 -1.6898 -1.4849 18 -0.1048 -0.0576 -0.0776 -0.1177 -0.1048 -0.0719 -0.0648 -0.1062 - -0.0633 -0.0505 -0.0762 -0.1077 -0.0776 -0.1191 -0.1077 18 -0.0600 -0.0303 -0.0429 -0.0681 -0.0681 -0.0474 -0.0429 -0.0609 - -0.0591 -0.0339 -0.0411 -0.0699 -0.0510 -0.0852 -0.0951 18 -0.0353 -0.0120 -0.0253 -0.0508 -0.0564 -0.0331 -0.0458 -0.0464 - -0.0403 -0.0297 -0.0292 -0.0569 -0.0558 -0.0614 -0.0880 18 -0.0249 -0.0076 -0.0137 -0.0362 -0.0362 -0.0270 -0.0362 -0.0403 - -0.0318 -0.0209 -0.0278 -0.0443 -0.0471 -0.0548 -0.0741 18 -0.0119 0.0052 -0.0066 -0.0251 -0.0276 -0.0189 -0.0276 -0.0253 - -0.0248 -0.0169 -0.0166 -0.0382 -0.0379 -0.0433 -0.0668 18 -0.0077 0.0036 -0.0059 -0.0198 -0.0232 -0.0211 -0.0284 -0.0250 - -0.0248 -0.0179 -0.0178 -0.0337 -0.0423 -0.0458 -0.0646 18 -0.0053 0.0084 -0.0014 -0.0144 -0.0197 -0.0182 -0.0275 -0.0211 - -0.0210 -0.0170 -0.0169 -0.0314 -0.0418 -0.0430 -0.0610 18 -0.0050 0.0079 -0.0019 -0.0176 -0.0217 -0.0196 -0.0290 -0.0206 - -0.0248 -0.0186 -0.0174 -0.0341 -0.0425 -0.0435 -0.0628 18 -0.0056 0.0068 -0.0030 -0.0177 -0.0211 -0.0222 -0.0290 -0.0211 - -0.0248 -0.0186 -0.0186 -0.0331 -0.0455 -0.0454 -0.0623 26 -1.2115 -1.3774 -0.4233 -1.2115 -0.0500 0.1574 -0.4648 -0.1329 - -0.0085 -0.0085 -0.3403 -0.5063 0.3648 -0.8381 0.5723 26 -0.0519 -0.0177 0.0023 -0.0248 -0.0120 0.0222 -0.0248 -0.0148 - 0.0037 -0.0106 -0.0091 -0.0148 0.0151 -0.0391 -0.0163 26 -0.0259 -0.0044 -0.0098 -0.0259 -0.0179 0.0036 -0.0179 -0.0197 - -0.0080 -0.0170 -0.0161 -0.0277 -0.0179 -0.0349 -0.0456 26 -0.0202 -0.0124 -0.0102 -0.0258 -0.0202 -0.0180 -0.0308 -0.0263 - -0.0247 -0.0202 -0.0191 -0.0469 -0.0308 -0.0414 -0.0525 26 -0.0099 -0.0043 -0.0063 -0.0140 -0.0212 -0.0043 -0.0212 -0.0144 - -0.0208 -0.0172 -0.0132 -0.0334 -0.0326 -0.0439 -0.0483 26 -0.0095 -0.0003 -0.0017 -0.0121 -0.0174 -0.0109 -0.0277 -0.0204 - -0.0249 -0.0171 -0.0115 -0.0358 -0.0327 -0.0433 -0.0539 26 -0.0059 0.0002 -0.0024 -0.0147 -0.0180 -0.0123 -0.0249 -0.0166 - -0.0231 -0.0162 -0.0143 -0.0356 -0.0370 -0.0423 -0.0579 26 -0.0120 -0.0036 -0.0108 -0.0237 -0.0263 -0.0247 -0.0341 -0.0237 - -0.0353 -0.0250 -0.0223 -0.0483 -0.0497 -0.0510 -0.0662 26 -0.0082 0.0005 -0.0051 -0.0186 -0.0207 -0.0218 -0.0321 -0.0218 - -0.0280 -0.0228 -0.0185 -0.0403 -0.0467 -0.0466 -0.0649 26 -0.0065 0.0023 -0.0057 -0.0178 -0.0212 -0.0224 -0.0325 -0.0229 - -0.0274 -0.0230 -0.0197 -0.0384 -0.0473 -0.0464 -0.0640 23 -0.3968 -1.1938 -0.3968 -1.9907 -0.7087 -0.8819 -0.7087 -1.7135 - -0.6740 -0.3622 -1.2977 -1.0898 -1.0205 -1.3670 -1.1245 23 0.0456 0.0264 0.0737 0.0042 0.0308 0.0397 0.0308 0.0013 - 0.0471 0.0323 0.0205 0.0279 0.0175 -0.0105 -0.0135 23 0.0194 0.0228 0.0448 0.0126 0.0064 0.0290 0.0126 0.0050 - 0.0139 0.0263 0.0139 0.0112 0.0002 -0.0067 -0.0211 23 0.0129 0.0150 0.0226 0.0002 -0.0064 0.0050 0.0002 -0.0005 - 0.0005 0.0036 0.0040 -0.0071 -0.0157 -0.0223 -0.0357 23 0.0126 0.0161 0.0168 -0.0029 -0.0029 -0.0020 -0.0029 -0.0031 - -0.0027 -0.0005 -0.0024 -0.0139 -0.0224 -0.0289 -0.0423 23 0.0074 0.0129 0.0121 -0.0064 -0.0094 -0.0091 -0.0155 -0.0096 - -0.0109 -0.0063 -0.0061 -0.0233 -0.0294 -0.0340 -0.0491 23 0.0003 0.0068 0.0039 -0.0140 -0.0164 -0.0163 -0.0247 -0.0164 - -0.0234 -0.0151 -0.0127 -0.0340 -0.0401 -0.0435 -0.0610 23 0.0031 0.0090 0.0040 -0.0118 -0.0154 -0.0155 -0.0238 -0.0163 - -0.0192 -0.0155 -0.0127 -0.0320 -0.0414 -0.0413 -0.0566 23 0.0015 0.0090 0.0038 -0.0111 -0.0156 -0.0174 -0.0259 -0.0162 - -0.0194 -0.0164 -0.0135 -0.0295 -0.0409 -0.0415 -0.0580 23 0.0011 0.0107 0.0034 -0.0122 -0.0163 -0.0197 -0.0272 -0.0166 - -0.0193 -0.0158 -0.0148 -0.0304 -0.0429 -0.0422 -0.0577

163

Run β0.75 (deg) Ptabs (inHg) Temp (F) qind (psf) qtare (psf) Pten (psfd) Psen (psfd) qen (psf) Ptex (psfd) Psex (psfd) qex (psf) 22 28 28.5289 75.96 0.0387 0.0384 0.3793 0.3603 0.0190 0.3777 0.3727 0.0050 22 28 28.5296 76.10 1.0150 1.0067 1.4076 0.4062 1.0014 1.4072 0.4010 1.0061 22 28 28.5278 76.20 2.1169 2.0996 2.5554 0.4307 2.1247 2.5530 0.3972 2.1558 22 28 28.5287 76.30 4.1930 4.1587 4.6466 0.4296 4.2170 4.6365 0.3285 4.3080 22 28 28.5270 76.35 6.2043 6.1536 6.6351 0.3987 6.2364 6.6244 0.2324 6.3920 22 28 28.5279 76.50 8.8072 8.7352 9.2311 0.3617 8.8694 9.2076 0.1133 9.0943 22 28 28.5276 76.65 11.4054 11.3122 11.8162 0.3303 11.4859 11.7837 -0.0068 11.7904 22 28 28.5298 76.80 14.6245 14.5050 14.9102 0.1708 14.7394 14.8684 -0.2853 15.1537 22 28 28.5288 77.00 18.2092 18.0604 18.3632 -0.0207 18.3839 18.3247 -0.6021 18.9268 22 28 28.5283 77.20 23.3993 23.2081 23.3626 -0.2968 23.6593 23.3169 -1.0699 24.3868 24 33 28.8093 70.55 0.0233 0.0231 0.3974 0.4386 -0.0412 0.3934 0.4391 -0.0456 24 33 28.8098 70.80 1.0210 1.0127 1.4669 0.5089 0.9580 1.4635 0.4984 0.9651 24 33 28.8117 70.90 1.6104 1.5972 2.0356 0.4987 1.5369 2.0333 0.4706 1.5627 24 33 28.8091 71.06 2.6113 2.5900 3.0509 0.5073 2.5436 3.0442 0.4506 2.5936 24 33 28.8089 71.10 3.5873 3.5580 4.0471 0.5100 3.5371 4.0386 0.4236 3.6150 24 33 28.8103 71.20 5.2007 5.1582 5.6480 0.4920 5.1559 5.6254 0.3557 5.2697 24 33 28.8073 71.30 7.8175 7.7536 8.2361 0.4445 7.7916 8.2129 0.2267 7.9862 24 33 28.8046 71.34 10.3980 10.3131 10.8350 0.4215 10.4135 10.8140 0.1152 10.6988 24 33 28.8042 71.40 13.0077 12.9014 13.3891 0.3298 13.0594 13.3584 -0.0654 13.4238 24 33 28.8039 71.50 15.6048 15.4773 15.8672 0.1778 15.6894 15.8416 -0.3096 16.1512 25 33 28.8172 71.10 0.0500 0.0496 0.4118 0.4465 -0.0347 0.4069 0.4490 -0.0420 25 33 28.8178 71.40 2.1371 2.1196 2.5752 0.5031 2.0720 2.5720 0.4625 2.1095 25 33 28.8150 71.50 6.2141 6.1633 6.6541 0.4725 6.1816 6.6398 0.3028 6.3370 25 33 28.8185 71.58 12.4966 12.3945 12.8781 0.3456 12.5325 12.8405 -0.0262 12.8667 25 33 28.8187 71.73 17.7013 17.5567 17.8739 0.0638 17.8101 17.8455 -0.4825 18.3280 25 33 28.8164 71.80 19.7867 19.6250 19.8724 -0.0665 19.9390 19.8425 -0.6886 20.5311 25 33 28.8182 72.00 21.7840 21.6060 21.7816 -0.1803 21.9619 21.7378 -0.8721 22.6099 25 33 28.8190 72.16 23.3922 23.2011 23.3137 -0.2860 23.5997 23.2524 -1.0387 24.2911 25 33 28.8178 72.30 25.9802 25.7679 25.7957 -0.4431 26.2388 25.7514 -1.2758 27.0272 25 33 28.8152 72.50 28.6056 28.3719 28.3117 -0.5816 28.8933 28.2721 -1.5048 29.7769

164

cpr @ x/L where Φ = 0°

Run qcor (fps) T (lbs) Q (in.lbs) rpm Ucor (fps) J η CT CP Re0.75 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 22 0.038 2.310 6.468 4878.8 5.770 0.071 0.048 0.159 0.233 91,471 20.734 -19.671 -16.107 -12.843 -8.9414 -4.8147 -9.4666 -3.7642 22 1.007 2.211 6.247 4920.0 30.167 0.368 0.249 0.150 0.222 93,326 1.2412 0.0940 -0.2064 -0.3938 -0.4038 -0.2479 -0.4467 -0.2064 22 2.100 2.108 5.972 5025.0 43.638 0.521 0.351 0.137 0.203 96,454 0.6662 0.1106 -0.0807 -0.2344 -0.2515 -0.1582 -0.2392 -0.0999 22 4.159 1.996 5.670 5107.5 61.479 0.722 0.486 0.126 0.187 100,121 0.3695 0.0699 -0.0630 -0.1756 -0.1839 -0.1184 -0.1254 -0.0204 22 6.154 1.923 5.485 5175.0 74.815 0.867 0.581 0.118 0.176 103,353 0.2595 0.0456 -0.0637 -0.1594 -0.1685 -0.1144 -0.1034 -0.0087 22 8.735 1.910 5.266 5216.3 89.160 1.026 0.710 0.115 0.166 106,622 0.1894 0.0277 -0.0663 -0.1533 -0.1594 -0.1113 -0.0890 -0.0041 22 11.312 1.811 5.230 5261.3 101.480 1.157 0.765 0.107 0.162 109,857 0.1573 0.0130 -0.0724 -0.1538 -0.1567 -0.1120 -0.0834 -0.0029 22 14.505 1.579 5.090 5283.8 114.930 1.305 0.773 0.093 0.157 113,201 0.1291 -0.0045 -0.0808 -0.1569 -0.1597 -0.1164 -0.0845 -0.0108 22 18.060 1.298 4.749 5430.0 128.259 1.417 0.740 0.072 0.138 118,754 0.1086 -0.0173 -0.0886 -0.1613 -0.1615 -0.1209 -0.0865 -0.0150 22 23.208 0.946 4.210 5606.3 145.409 1.556 0.668 0.049 0.115 125,913 0.0942 -0.0253 -0.0960 -0.1621 -0.1612 -0.1200 -0.0855 -0.0160 24 0.023 2.297 8.090 4860.0 4.403 0.054 0.029 0.157 0.289 93,537 -1.4821 -64.666 -59.120 -47.780 -37.748 -33.261 -31.454 -31.516 24 1.013 2.320 8.171 4871.3 29.964 0.369 0.200 0.157 0.290 94,879 0.6691 -0.3079 -0.8240 -0.9819 -0.9378 -0.8368 -0.8184 -0.7572 24 1.597 2.286 8.037 4886.3 37.673 0.463 0.251 0.154 0.284 95,821 0.4899 -0.1457 -0.5162 -0.6415 -0.6136 -0.5505 -0.5352 -0.4901 24 2.590 2.217 7.796 4965.0 48.018 0.580 0.315 0.145 0.266 98,397 0.3512 -0.0514 -0.3066 -0.4356 -0.4128 -0.3744 -0.3527 -0.2855 24 3.558 2.140 7.548 5010.0 56.308 0.674 0.365 0.137 0.253 100,279 0.2718 -0.0321 -0.2333 -0.3462 -0.3328 -0.2944 -0.2660 -0.2029 24 5.158 2.064 7.306 5062.5 67.829 0.804 0.434 0.130 0.240 102,933 0.1979 -0.0251 -0.1848 -0.2806 -0.2736 -0.2323 -0.1980 -0.1245 24 7.754 1.997 7.070 5137.5 83.192 0.972 0.524 0.122 0.226 106,937 0.1460 -0.0256 -0.1508 -0.2349 -0.2297 -0.1927 -0.1530 -0.0772 24 10.313 1.998 6.922 5175.0 95.962 1.113 0.613 0.120 0.218 110,127 0.1167 -0.0217 -0.1300 -0.2127 -0.2083 -0.1683 -0.1335 -0.0564 24 12.901 2.073 6.838 5208.8 107.341 1.236 0.716 0.123 0.212 113,195 0.0955 -0.0227 -0.1196 -0.2001 -0.1962 -0.1596 -0.1242 -0.0502 24 15.477 2.116 6.819 5208.8 117.578 1.354 0.803 0.125 0.212 115,611 0.0877 -0.0261 -0.1178 -0.1951 -0.1897 -0.1529 -0.1167 -0.0416 25 0.050 2.326 8.091 4867.5 6.515 0.080 0.044 0.158 0.288 93,712 5.3213 -24.645 -22.351 -18.141 -13.204 -10.591 -10.765 -8.6746 25 2.120 2.255 7.883 4946.3 43.424 0.527 0.288 0.148 0.272 97,531 0.5113 -0.0064 -0.2598 -0.3862 -0.3773 -0.3176 -0.3237 -0.2408 25 6.163 2.045 7.252 5088.8 74.157 0.874 0.471 0.127 0.236 104,449 0.2149 0.0013 -0.1321 -0.2206 -0.2146 -0.1674 -0.1433 -0.0573 25 12.395 1.986 6.863 5223.8 105.211 1.209 0.668 0.117 0.212 112,970 0.1148 -0.0105 -0.1026 -0.1864 -0.1823 -0.1420 -0.1118 -0.0314 25 17.557 1.951 6.835 5216.3 125.237 1.441 0.785 0.115 0.212 117,649 0.0906 -0.0216 -0.1060 -0.1801 -0.1757 -0.1369 -0.1060 -0.0272 25 19.625 1.846 6.790 5253.8 132.416 1.512 0.785 0.108 0.207 120,127 0.0860 -0.0250 -0.1065 -0.1787 -0.1738 -0.1348 -0.1041 -0.0256 25 21.606 1.733 6.684 5283.8 138.945 1.578 0.782 0.100 0.202 122,363 0.0791 -0.0296 -0.1101 -0.1793 -0.1741 -0.1353 -0.1047 -0.0266 25 23.201 1.645 6.574 5310.0 143.987 1.627 0.778 0.094 0.196 124,169 0.0748 -0.0318 -0.1108 -0.1780 -0.1735 -0.1330 -0.1034 -0.0254 25 25.768 1.516 6.397 5388.8 151.749 1.690 0.765 0.084 0.186 127,596 0.0711 -0.0351 -0.1138 -0.1778 -0.1730 -0.1333 -0.1035 -0.0259 25 28.372 1.392 6.209 5452.5 159.237 1.752 0.751 0.075 0.176 130,750 0.0680 -0.0363 -0.1143 -0.1774 -0.1729 -0.1325 -0.1022 -0.0258

165

cpr @ x/L where Φ = 45° cpr @ x/L where Φ = 90° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 22 16.607 -17.533 -17.307 -9.2415 -8.1536 -5.8276 -4.1019 -3.7267 20.621 -15.844 -15.807 -12.580 -7.9285 -7.1782 -6.5404 -3.0514 22 1.0824 0.1298 -0.2750 -0.2579 -0.4009 -0.2994 -0.2722 -0.2321 1.2469 0.2070 -0.2479 -0.3909 -0.2994 -0.3508 -0.3523 -0.1663 22 0.5839 0.1230 -0.1198 -0.1562 -0.2371 -0.1884 -0.1507 -0.0807 0.6593 0.1655 -0.1068 -0.2083 -0.1829 -0.2131 -0.2014 -0.0608 22 0.3321 0.0755 -0.0796 -0.1226 -0.1756 -0.1295 -0.0977 -0.0114 0.3750 0.1001 -0.0727 -0.1486 -0.1368 -0.1482 -0.1170 -0.0069 22 0.2300 0.0501 -0.0754 -0.1184 -0.1580 -0.1212 -0.0866 -0.0023 0.2609 0.0688 -0.0725 -0.1364 -0.1285 -0.1357 -0.1020 0.0052 22 0.1597 0.0298 -0.0762 -0.1179 -0.1528 -0.1171 -0.0820 0.0003 0.1902 0.0460 -0.0773 -0.1331 -0.1271 -0.1284 -0.0914 0.0054 22 0.1306 0.0132 -0.0829 -0.1234 -0.1524 -0.1171 -0.0806 0.0006 0.1590 0.0270 -0.0858 -0.1350 -0.1299 -0.1281 -0.0903 0.0020 22 0.1051 -0.0054 -0.0913 -0.1290 -0.1566 -0.1207 -0.0857 -0.0066 0.1324 0.0071 -0.0961 -0.1397 -0.1327 -0.1307 -0.0924 -0.0055 22 0.0869 -0.0193 -0.0988 -0.1352 -0.1606 -0.1244 -0.0898 -0.0113 0.1150 -0.0064 -0.1047 -0.1434 -0.1380 -0.1344 -0.0958 -0.0112 22 0.0743 -0.0291 -0.1020 -0.1365 -0.1616 -0.1249 -0.0910 -0.0127 0.0993 -0.0174 -0.1098 -0.1451 -0.1393 -0.1353 -0.0959 -0.0141 24 -2.2299 -64.292 -56.503 -45.723 -38.121 -33.137 -33.137 -29.086 -1.7314 -65.352 -59.183 -47.655 -38.433 - -29.086 -29.896 24 0.6804 -0.4060 -0.7984 -0.8582 -0.9207 -0.7814 -0.8070 -0.7273 0.7032 -0.3420 -0.8112 -0.8596 -0.8212 - -0.7416 -0.7473 24 0.5242 -0.1862 -0.4919 -0.5541 -0.5856 -0.5225 -0.5469 -0.4549 0.5350 -0.1619 -0.4910 -0.5388 -0.5234 - -0.4973 -0.4675 24 0.3779 -0.0786 -0.2966 -0.3716 -0.4055 -0.3516 -0.3466 -0.2693 0.3867 -0.0486 -0.2960 -0.3527 -0.3472 - -0.3260 -0.2816 24 0.2941 -0.0487 -0.2300 -0.2952 -0.3308 -0.2810 -0.2584 -0.1835 0.3050 -0.0268 -0.2296 -0.2871 -0.2855 - -0.2474 -0.1920 24 0.2124 -0.0388 -0.1804 -0.2373 -0.2641 -0.2200 -0.1940 -0.1114 0.2205 -0.0238 -0.1798 -0.2340 -0.2312 - -0.1890 -0.1220 24 0.1518 -0.0336 -0.1480 -0.1983 -0.2224 -0.1836 -0.1528 -0.0703 0.1642 -0.0185 -0.1491 -0.1957 -0.1948 - -0.1511 -0.0739 24 0.1173 -0.0285 -0.1308 -0.1796 -0.2025 -0.1662 -0.1325 -0.0511 0.1340 -0.0159 -0.1342 -0.1783 -0.1761 - -0.1314 -0.0567 24 0.0953 -0.0284 -0.1226 -0.1689 -0.1930 -0.1563 -0.1233 -0.0437 0.1106 -0.0164 -0.1262 -0.1678 -0.1676 - -0.1214 -0.0485 24 0.0836 -0.0321 -0.1207 -0.1651 -0.1883 -0.1496 -0.1162 -0.0360 0.0994 -0.0180 -0.1252 -0.1645 -0.1628 - -0.1154 -0.0414 25 3.6081 -24.790 -22.496 -16.370 -12.595 -9.4586 -9.4586 -8.9069 4.3921 -24.239 -22.380 -18.112 -11.898 - -9.1973 -8.4423 25 0.4922 -0.0125 -0.2605 -0.3142 -0.3631 -0.3087 -0.2904 -0.2204 0.5561 0.0242 -0.2476 -0.3291 -0.2972 - -0.2843 -0.2224 25 0.2060 0.0016 -0.1284 -0.1776 -0.2062 -0.1653 -0.1307 -0.0508 0.2354 0.0205 -0.1255 -0.1830 -0.1769 - -0.1375 -0.0527 25 0.1085 -0.0142 -0.1090 -0.1529 -0.1781 -0.1408 -0.1064 -0.0248 0.1305 0.0004 -0.1105 -0.1558 -0.1515 - -0.1110 -0.0295 25 0.0823 -0.0251 -0.1103 -0.1510 -0.1742 -0.1368 -0.1011 -0.0220 0.1004 -0.0111 -0.1140 -0.1536 -0.1500 - -0.1044 -0.0273 25 0.0769 -0.0286 -0.1098 -0.1496 -0.1728 -0.1349 -0.0997 -0.0214 0.0969 -0.0134 -0.1144 -0.1526 -0.1490 - -0.1033 -0.0252 25 0.0693 -0.0338 -0.1127 -0.1508 -0.1741 -0.1364 -0.1013 -0.0227 0.0897 -0.0194 -0.1174 -0.1541 -0.1499 - -0.1045 -0.0258 25 0.0676 -0.0352 -0.1127 -0.1500 -0.1733 -0.1350 -0.1006 -0.0222 0.0870 -0.0212 -0.1176 -0.1541 -0.1493 - -0.1037 -0.0272 25 0.0614 -0.0389 -0.1132 -0.1503 -0.1736 -0.1353 -0.1001 -0.0233 0.0822 -0.0238 -0.1195 -0.1535 -0.1504 - -0.1040 -0.0272 25 0.0598 -0.0404 -0.1133 -0.1493 -0.1726 -0.1353 -0.1006 -0.0228 0.0781 -0.0267 -0.1204 -0.1539 -0.1502 - -0.1032 -0.0272

166

cpr @ x/L where Φ = 135° cpr @ x/L where Φ = 180° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 0.020 0.137 0.255 0.373 0.490 0.608 22 20.959 -12.318 -12.881 -9.6167 -5.2273 -3.0514 -5.4524 -3.7267 19.045 -17.383 -18.395 -12.355 -15.619 -13.894 22 1.2998 0.3400 -0.1134 -0.2450 -0.2922 -0.1391 -0.2979 -0.2321 1.1997 0.1269 -0.3437 -0.4095 -0.6183 -0.6083 22 0.6998 0.2409 -0.0355 -0.1438 -0.1740 -0.1075 -0.1623 -0.0931 0.6806 0.1367 -0.1329 -0.2104 -0.3564 -0.3256 22 0.3930 0.1440 -0.0239 -0.1101 -0.1350 -0.0904 -0.1035 -0.0270 0.4110 0.0925 -0.0796 -0.1472 -0.2223 -0.2040 22 0.2930 0.0985 -0.0304 -0.1081 -0.1271 -0.0922 -0.0948 -0.0152 0.3009 0.0676 -0.0730 -0.1339 -0.1874 -0.1664 22 0.2222 0.0686 -0.0412 -0.1108 -0.1263 -0.0950 -0.0861 -0.0102 0.2346 0.0527 -0.0699 -0.1284 -0.1713 -0.1519 22 0.1827 0.0467 -0.0506 -0.1169 -0.1310 -0.1016 -0.0837 -0.0111 0.2060 0.0351 -0.0744 -0.1295 -0.1637 -0.1417 22 0.1536 0.0247 -0.0627 -0.1249 -0.1355 -0.1075 -0.0897 -0.0177 0.1651 0.0190 -0.0845 -0.1372 -0.1630 -0.1395 22 0.1402 0.0081 -0.0731 -0.1315 -0.1399 -0.1148 -0.0934 -0.0217 0.1488 0.0076 -0.0911 -0.1404 -0.1620 -0.1373 22 0.1270 -0.0047 -0.0791 -0.1349 -0.1423 -0.1182 -0.0943 -0.0244 0.1387 -0.0017 -0.0955 -0.1423 -0.1591 -0.1349 24 1.3219 -65.289 -55.382 -51.518 -38.433 -31.703 -29.647 -29.647 24 0.7672 -0.3207 -0.7288 -0.9250 -0.8311 -0.7600 -0.7401 -0.7800 24 0.5611 -0.1421 -0.4396 -0.5802 -0.5469 -0.5198 -0.4964 -0.4883 24 0.4201 -0.0419 -0.2543 -0.3616 -0.3577 -0.3411 -0.3305 -0.2999 24 0.3415 -0.0151 -0.1912 -0.2806 -0.2907 -0.2741 -0.2543 -0.2061 24 0.2563 -0.0081 -0.1480 -0.2172 -0.2393 -0.2167 -0.1935 -0.1371 24 0.1917 -0.0046 -0.1171 -0.1714 -0.2007 -0.1799 -0.1539 -0.0891 24 0.1576 -0.0041 -0.1035 -0.1516 -0.1835 -0.1648 -0.1359 -0.0718 24 0.1324 -0.0037 -0.0962 -0.1406 -0.1718 -0.1555 -0.1267 -0.0602 24 0.1220 -0.0056 -0.0938 -0.1348 -0.1670 -0.1486 -0.1198 -0.0541 25 5.2632 -23.716 -21.451 -19.360 -11.578 -8.9940 -7.8325 -8.1229 25 0.5772 0.0629 -0.1960 -0.3277 -0.3087 -0.2686 -0.2829 -0.2523 25 0.2593 0.0420 -0.0879 -0.1543 -0.1805 -0.1522 -0.1368 -0.0702 25 0.1543 0.0176 -0.0782 -0.1256 -0.1556 -0.1354 -0.1134 -0.0451 25 0.1263 0.0051 -0.0808 -0.1213 -0.1533 -0.1329 -0.1080 -0.0396 25 0.1235 0.0019 -0.0817 -0.1198 -0.1515 -0.1318 -0.1064 -0.0392 25 0.1156 -0.0042 -0.0857 -0.1213 -0.1543 -0.1337 -0.1079 -0.0401 25 0.1129 -0.0063 -0.0857 -0.1215 -0.1531 -0.1331 -0.1072 -0.0395 25 0.1097 -0.0107 -0.0874 -0.1220 -0.1537 -0.1339 -0.1081 -0.0406 25 0.1049 -0.0134 -0.0888 -0.1214 -0.1540 -0.1340 -0.1073 -0.0395

167

South Side Wall cpr @ l' Run 0.051 0.139 0.228 0.316 0.360 0.404 0.448 0.492 0.536 0.580 0.624 0.668 0.714 0.809 0.905 1.000 22 3.5889 6.5526 4.3017 3.5889 3.5889 4.4142 4.3017 4.2642 - - 6.0649 4.7143 4.6018 5.3521 3.9265 4.5643 22 0.1527 0.2814 0.1798 0.1398 0.1527 0.1984 0.1927 0.1641 - - 0.2342 0.1827 0.1770 0.1798 0.1398 0.1369 22 0.0729 0.1470 0.0983 0.0537 0.0729 0.0948 0.0852 0.0784 - - 0.1182 0.0928 0.0715 0.0729 0.0537 0.0393 22 0.0440 0.0783 0.0537 0.0374 0.0343 0.0450 0.0343 0.0370 - - 0.0506 0.0412 0.0274 0.0246 0.0149 -0.0017 22 0.0328 0.0604 0.0393 0.0218 0.0197 0.0269 0.0176 0.0239 - - 0.0351 0.0288 0.0129 0.0066 0.0045 -0.0152 22 0.0219 0.0443 0.0265 0.0112 0.0081 0.0130 0.0034 0.0110 - - 0.0189 0.0160 -0.0012 -0.0102 -0.0149 -0.0315 22 0.0184 0.0393 0.0220 0.0078 0.0042 0.0067 -0.0017 0.0042 - - 0.0114 0.0090 -0.0064 -0.0148 -0.0171 -0.0334 22 0.0135 0.0314 0.0172 0.0033 -0.0013 0.0004 -0.0096 -0.0012 - - 0.0033 0.0015 -0.0131 -0.0235 -0.0244 -0.0414 22 0.0091 0.0263 0.0121 0.0002 -0.0065 -0.0061 -0.0154 -0.0048 - - -0.0028 -0.0029 -0.0189 -0.0311 -0.0295 -0.0460 22 0.0070 0.0231 0.0093 -0.0046 -0.0103 -0.0109 -0.0207 -0.0096 - - -0.0070 -0.0060 -0.0222 -0.0347 -0.0334 -0.0512 24 -10.019 -9.7073 -8.8349 -10.580 -8.8349 -7.9626 -9.4580 -8.9595 - -10.517 -8.8349 -8.7103 -10.704 -8.8349 -9.4580 -9.5827 24 -0.1728 -0.1927 -0.1728 -0.1600 -0.1472 -0.1386 -0.1742 -0.1756 - -0.1443 -0.1585 -0.1571 -0.1500 -0.1728 -0.1870 -0.1785 24 -0.1123 -0.0988 -0.0871 -0.1123 -0.1042 -0.0907 -0.1123 -0.1222 - -0.1024 -0.1033 -0.1015 -0.1222 -0.1033 -0.1295 -0.1313 24 -0.0625 -0.0542 -0.0575 -0.0681 -0.0631 -0.0597 -0.0731 -0.0692 - -0.0669 -0.0625 -0.0614 -0.0792 -0.0781 -0.0886 -0.1003 24 -0.0556 -0.0422 -0.0483 -0.0596 -0.0596 -0.0463 -0.0596 -0.0564 - -0.0588 -0.0556 -0.0511 -0.0714 -0.0706 -0.0782 -0.0867 24 -0.0335 -0.0240 -0.0257 -0.0360 -0.0413 -0.0349 -0.0492 -0.0444 - -0.0436 -0.0439 -0.0433 -0.0522 -0.0595 -0.0648 -0.0779 24 -0.0202 -0.0141 -0.0185 -0.0306 -0.0339 -0.0299 -0.0427 -0.0343 - -0.0356 -0.0356 -0.0302 -0.0481 -0.0512 -0.0547 -0.0720 24 -0.0148 -0.0063 -0.0109 -0.0239 -0.0278 -0.0261 -0.0356 -0.0279 - -0.0328 -0.0264 -0.0263 -0.0447 -0.0486 -0.0538 -0.0679 24 -0.0127 -0.0038 -0.0085 -0.0230 -0.0272 -0.0261 -0.0376 -0.0262 - -0.0313 -0.0272 -0.0251 -0.0427 -0.0501 -0.0499 -0.0674 24 -0.0154 -0.0066 -0.0146 -0.0258 -0.0309 -0.0312 -0.0404 -0.0300 - -0.0371 -0.0301 -0.0276 -0.0515 -0.0561 -0.0551 -0.0736 25 0.7915 0.6754 0.7915 1.0529 1.3432 1.4594 1.0529 0.7334 -1.8799 1.1109 1.0819 0.8496 0.9948 1.8949 0.7915 1.7788 25 0.0065 0.0228 0.0255 0.0065 0.0065 0.0289 0.0126 0.0174 -0.0567 0.0072 0.0133 0.0079 -0.0078 0.0126 -0.0132 -0.0146 25 0.0037 0.0135 0.0102 -0.0008 -0.0050 -0.0043 -0.0160 -0.0055 -0.0267 -0.0113 -0.0071 -0.0024 -0.0227 -0.0225 -0.0291 -0.0466 25 -0.0043 0.0070 -0.0011 -0.0162 -0.0184 -0.0162 -0.0259 -0.0151 -0.0237 -0.0259 -0.0184 -0.0172 -0.0408 -0.0421 -0.0421 -0.0622 25 -0.0025 0.0083 -0.0009 -0.0139 -0.0169 -0.0196 -0.0276 -0.0176 -0.0178 -0.0239 -0.0178 -0.0148 -0.0357 -0.0422 -0.0429 -0.0590 25 -0.0006 0.0096 0.0015 -0.0109 -0.0156 -0.0167 -0.0265 -0.0148 -0.0137 -0.0206 -0.0164 -0.0131 -0.0324 -0.0409 -0.0408 -0.0572 25 -0.0014 0.0090 -0.0002 -0.0126 -0.0163 -0.0187 -0.0286 -0.0167 -0.0133 -0.0214 -0.0170 -0.0152 -0.0333 -0.0430 -0.0429 -0.0583 25 -0.0013 0.0101 0.0004 -0.0117 -0.0157 -0.0180 -0.0284 -0.0166 -0.0112 -0.0217 -0.0163 -0.0142 -0.0315 -0.0417 -0.0410 -0.0582 25 -0.0020 0.0097 -0.0004 -0.0134 -0.0181 -0.0209 -0.0306 -0.0184 -0.0115 -0.0214 -0.0182 -0.0152 -0.0333 -0.0431 -0.0435 -0.0599 25 -0.0017 0.0108 0.0007 -0.0130 -0.0167 -0.0203 -0.0295 -0.0174 -0.0098 -0.0198 -0.0164 -0.0147 -0.0305 -0.0432 -0.0417 -0.0579

168

COMP Propeller

Run β0.75 (deg) Ptabs (inHg) Temp (F) qind (psf) qtare (psf) Pten (psfd) Psen (psfd) qen (psf) Ptex (psfd) Psex (psfd) qex (psf) 27 15 28.8198 70.90 0.0148 0.0147 0.4853 0.4608 0.0245 0.4791 0.4591 0.0200 27 15 28.8209 71.51 1.0283 1.0199 1.5271 0.5080 1.0191 1.5225 0.4872 1.0354 27 15 28.8254 71.90 1.6072 1.5941 2.0928 0.4908 1.6020 2.0871 0.4509 1.6363 27 15 28.8210 72.20 2.6009 2.5797 3.1003 0.5007 2.5996 3.0923 0.4290 2.6633 27 15 28.8218 72.40 3.5999 3.5705 4.1147 0.5033 3.6114 4.1027 0.3992 3.7035 27 15 28.8212 72.50 5.1953 5.1529 5.7108 0.4762 5.2345 5.6956 0.3184 5.3772 27 15 28.8178 72.60 7.7927 7.7290 8.2675 0.4340 7.8335 8.2400 0.1853 8.0546 27 15 28.8250 72.70 10.4003 10.3153 10.8874 0.4121 10.4753 10.8657 0.0744 10.7912 27 15 28.8209 72.70 12.9947 12.8885 13.4362 0.3270 13.1092 13.4050 -0.1045 13.5095 27 15 28.8208 72.80 13.0036 12.8974 13.4464 0.3312 13.1152 13.4166 -0.0985 13.5151 28 15 28.8259 72.60 0.0272 0.0270 0.4336 0.4209 0.0127 0.4291 0.4179 0.0112 28 15 28.8231 72.70 0.4629 0.4591 0.8891 0.4391 0.4500 0.8770 0.4340 0.4429 28 15 28.8250 72.70 1.0256 1.0172 1.4728 0.4562 1.0166 1.4675 0.4359 1.0316 28 15 28.8246 72.70 2.1197 2.1024 2.5885 0.4679 2.1207 2.5808 0.4126 2.1682 28 15 28.8243 72.70 3.1050 3.0796 3.6042 0.4918 3.1124 3.5987 0.4056 3.1931 28 15 28.8233 72.80 3.6031 3.5737 4.1030 0.4860 3.6170 4.0864 0.3776 3.7089 28 15 28.8255 72.80 4.2111 4.1767 4.7091 0.4886 4.2205 4.7000 0.3640 4.3360 28 15 28.8274 72.80 4.7073 4.6688 5.2104 0.4841 4.7262 5.1952 0.3421 4.8531 28 15 28.8243 72.80 5.7153 5.6686 6.2178 0.4765 5.7413 6.2073 0.3007 5.9066 28 15 28.8257 72.81 6.8005 6.7449 7.2852 0.4532 6.8321 7.2681 0.2428 7.0253 31 20 28.7930 73.50 0.0245 0.0243 0.4526 0.4267 0.0259 0.4494 0.4258 0.0236 31 20 28.7917 73.60 1.0314 1.0230 1.4832 0.4722 1.0110 1.4751 0.4565 1.0187 31 20 28.7909 73.70 1.6070 1.5939 2.0776 0.4676 1.6101 2.0710 0.4349 1.6361 31 20 28.7907 73.80 2.5953 2.5741 3.0773 0.4815 2.5957 3.0671 0.4176 2.6495 31 20 28.7880 73.80 3.5892 3.5599 4.0929 0.4860 3.6069 4.0810 0.3895 3.6914 31 20 28.7859 73.90 5.2031 5.1606 5.7040 0.4703 5.2337 5.6892 0.3217 5.3675 31 20 28.7905 73.90 7.8060 7.7422 8.2760 0.4291 7.8468 8.2558 0.1902 8.0656 31 20 28.7902 73.99 10.3948 10.3099 10.8727 0.4013 10.4714 10.8469 0.0768 10.7702 31 20 28.7888 74.00 12.9775 12.8715 13.4074 0.3120 13.0954 13.3786 -0.1070 13.4856 31 20 28.7876 74.10 15.5670 15.4398 15.8888 0.1704 15.7185 15.8617 -0.3407 16.2024

169

cpr @ x/L where Φ = 0°

Run qcor (fps) T (lbs) Q (in.lbs) rpm Ucor (fps) J η CT CP Re0.75 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 27 0.015 2.083 1.759 5925.0 3.489 0.035 0.080 0.096 0.042 93,872 71.957 5.8387 -14.566 -23.885 -24.964 -23.787 -25.945 -41.347 27 1.020 1.662 1.734 5898.8 30.114 0.306 0.561 0.077 0.042 94,236 0.7967 0.1401 -0.2609 -0.4613 -0.4628 -0.3809 -0.3639 -0.5277 27 1.594 1.481 1.679 5906.3 37.689 0.383 0.645 0.068 0.041 94,796 0.4657 0.0538 -0.2109 -0.3473 -0.3636 -0.3130 -0.2949 -0.3554 27 2.580 1.198 1.550 5958.8 47.989 0.483 0.713 0.054 0.037 96,365 0.2467 0.0078 -0.1708 -0.2702 -0.2802 -0.2339 -0.1999 -0.2233 27 3.570 0.940 1.388 6000.0 56.486 0.565 0.731 0.042 0.033 97,746 0.1525 -0.0209 -0.1491 -0.2322 -0.2387 -0.1911 -0.1572 -0.1608 27 5.153 0.573 1.081 6168.8 67.888 0.660 0.669 0.024 0.024 101,489 0.0844 -0.0441 -0.1377 -0.2104 -0.2093 -0.1693 -0.1324 -0.1165 27 7.729 0.009 0.547 6435.0 83.175 0.776 0.024 0.000 0.011 107,319 0.0284 -0.0650 -0.1352 -0.1973 -0.1908 -0.1529 -0.1181 -0.0914 27 10.315 -0.371 -0.026 6633.8 96.102 0.869 23.271 -0.014 -0.001 112,009 0.0004 -0.0728 -0.1300 -0.1867 -0.1773 -0.1406 -0.1071 -0.0761 27 12.889 -0.378 -0.505 6907.5 107.419 0.933 1.335 -0.013 -0.009 117,690 -0.0196 -0.0775 -0.1269 -0.1793 -0.1694 -0.1333 -0.1001 -0.0638 27 12.897 -0.378 -0.505 6907.5 107.456 0.933 1.336 -0.013 -0.009 117,696 -0.0197 -0.0796 -0.1290 -0.1824 -0.1724 -0.1354 -0.1032 -0.0669 28 0.027 2.144 1.785 5943.8 4.781 0.048 0.111 0.098 0.043 93,865 39.130 3.1532 -9.4438 -14.515 -14.621 -14.461 -15.048 -23.535 28 0.459 1.901 1.781 5928.8 20.171 0.204 0.416 0.087 0.043 93,962 1.9524 0.3152 -0.5474 -0.8453 -0.7920 -0.7230 -0.7450 -1.2844 28 1.017 1.693 1.753 5928.8 30.101 0.305 0.562 0.078 0.042 94,392 0.7989 0.1421 -0.3010 -0.4879 -0.4893 -0.4214 -0.3874 -0.5672 28 2.102 1.366 1.643 5970.0 43.346 0.436 0.692 0.062 0.039 95,862 0.3275 0.0282 -0.1848 -0.3074 -0.3197 -0.2691 -0.2465 -0.2821 28 3.080 1.100 1.503 5988.8 52.496 0.526 0.735 0.050 0.035 96,887 0.1893 -0.0113 -0.1651 -0.2567 -0.2605 -0.2221 -0.1838 -0.1960 28 3.574 0.967 1.415 6052.5 56.563 0.561 0.732 0.043 0.033 98,235 0.1447 -0.0245 -0.1607 -0.2433 -0.2462 -0.2063 -0.1684 -0.1720 28 4.177 0.816 1.299 6086.3 61.162 0.603 0.724 0.036 0.030 99,195 0.1194 -0.0319 -0.1481 -0.2254 -0.2243 -0.1871 -0.1471 -0.1447 28 4.669 0.697 1.194 6135.0 64.674 0.633 0.705 0.030 0.027 100,297 0.1013 -0.0371 -0.1466 -0.2213 -0.2200 -0.1756 -0.1392 -0.1321 28 5.669 0.474 0.994 6240.0 71.278 0.685 0.625 0.020 0.022 102,607 0.0672 -0.0474 -0.1396 -0.2079 -0.2067 -0.1658 -0.1292 -0.1109 28 6.745 0.234 0.765 6333.8 77.764 0.737 0.430 0.009 0.016 104,777 0.0441 -0.0566 -0.1376 -0.1986 -0.1954 -0.1576 -0.1213 -0.0972 31 0.024 2.459 2.913 5992.5 4.526 0.045 0.073 0.111 0.069 94,253 43.447 -3.9010 -19.427 -23.338 -20.612 -19.427 -20.375 -22.746 31 1.023 2.283 2.733 6041.3 30.204 0.300 0.479 0.101 0.063 95,775 1.0081 0.2226 -0.2996 -0.5389 -0.5389 -0.4855 -0.4714 -0.4052 31 1.594 2.164 2.685 6041.3 37.744 0.375 0.577 0.096 0.062 96,203 0.6112 0.1414 -0.2109 -0.3979 -0.3979 -0.3555 -0.3356 -0.2534 31 2.574 1.976 2.630 6037.5 48.013 0.477 0.685 0.088 0.061 96,877 0.3637 0.0723 -0.1610 -0.2919 -0.2964 -0.2505 -0.2153 -0.1398 31 3.560 1.772 2.569 6052.5 56.495 0.560 0.738 0.078 0.059 97,837 0.2563 0.0298 -0.1458 -0.2518 -0.2582 -0.2146 -0.1721 -0.0964 31 5.161 1.455 2.388 6116.3 68.057 0.668 0.777 0.063 0.054 99,974 0.1607 -0.0065 -0.1401 -0.2258 -0.2272 -0.1848 -0.1496 -0.0718 31 7.742 1.002 2.000 6273.8 83.396 0.798 0.763 0.041 0.043 104,161 0.0987 -0.0347 -0.1317 -0.2039 -0.2024 -0.1632 -0.1291 -0.0546 31 10.310 0.591 1.536 6472.5 96.258 0.892 0.656 0.023 0.031 108,840 0.0690 -0.0446 -0.1261 -0.1919 -0.1877 -0.1499 -0.1190 -0.0447 31 12.871 0.218 1.078 6675.0 107.569 0.967 0.374 0.008 0.021 113,463 0.0429 -0.0527 -0.1239 -0.1868 -0.1798 -0.1419 -0.1136 -0.0407 31 15.440 -0.384 0.109 6543.8 117.831 1.080 -7.243 -0.015 0.002 113,204 0.0104 -0.0637 -0.1224 -0.1823 -0.1719 -0.1365 -0.1081 -0.0371

170

cpr @ x/L where Φ = 45° cpr @ x/L where Φ = 90° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 27 67.641 4.6615 -17.116 -20.550 -26.043 -23.983 -25.847 -23.199 67.347 4.6615 -16.332 -21.237 -23.002 -25.945 -25.847 -25.259 27 0.7868 0.1302 -0.2707 -0.3992 -0.4642 -0.3837 -0.3456 -0.1917 0.7882 0.1543 -0.2594 -0.4006 -0.4091 -0.4119 -0.3442 -0.2114 27 0.4639 0.0502 -0.2172 -0.2976 -0.3554 -0.3058 -0.2714 -0.1477 0.4621 0.0737 -0.2100 -0.3012 -0.3220 -0.3220 -0.2714 -0.1712 27 0.2389 -0.0028 -0.1703 -0.2339 -0.2747 -0.2339 -0.1926 -0.0899 0.2462 0.0123 -0.1708 -0.2339 -0.2495 -0.2440 -0.1976 -0.1044 27 0.1493 -0.0265 -0.1491 -0.2052 -0.2342 -0.1943 -0.1568 -0.0644 0.1602 -0.0156 -0.1532 -0.2040 -0.2096 -0.2088 -0.1608 -0.0749 27 0.0769 -0.0508 -0.1433 -0.1805 -0.2079 -0.1654 -0.1344 -0.0469 0.0909 -0.0383 -0.1431 -0.1852 -0.1841 -0.1805 -0.1347 -0.0575 27 0.0175 -0.0721 -0.1378 -0.1714 -0.1908 -0.1548 -0.1203 -0.0413 0.0285 -0.0620 -0.1408 -0.1744 -0.1729 -0.1663 -0.1222 -0.0488 27 -0.0108 -0.0799 -0.1349 -0.1628 -0.1783 -0.1441 -0.1106 -0.0344 0.0038 -0.0686 -0.1382 -0.1660 -0.1631 -0.1564 -0.1132 -0.0418 27 -0.0303 -0.0835 -0.1312 -0.1587 -0.1717 -0.1378 -0.1036 -0.0302 -0.0139 -0.0734 -0.1368 -0.1613 -0.1572 -0.1494 -0.1079 -0.0378 27 -0.0324 -0.0856 -0.1332 -0.1597 -0.1738 -0.1398 -0.1057 -0.0334 -0.0180 -0.0765 -0.1398 -0.1634 -0.1593 -0.1514 -0.1110 -0.0399 28 37.688 1.5519 -10.351 -13.127 -14.675 -14.568 -15.048 -14.141 36.621 2.0323 -10.405 -13.714 -14.034 -15.102 -15.048 -14.301 28 1.9210 0.2681 -0.5976 -0.7356 -0.7983 -0.7042 -0.7606 -0.5913 1.8708 0.2932 -0.5442 -0.7011 -0.6979 -0.7638 -0.7324 -0.6477 28 0.7904 0.1067 -0.3110 -0.4242 -0.4907 -0.4242 -0.3846 -0.2288 0.7791 0.1180 -0.2996 -0.4143 -0.4355 -0.4511 -0.3577 -0.2529 28 0.3282 0.0138 -0.1971 -0.2691 -0.3129 -0.2691 -0.2375 -0.1245 0.3193 0.0262 -0.1910 -0.2684 -0.2821 -0.2821 -0.2307 -0.1362 28 0.1921 -0.0234 -0.1646 -0.2259 -0.2638 -0.2175 -0.1829 -0.0842 0.1936 -0.0108 -0.1693 -0.2231 -0.2348 -0.2301 -0.1829 -0.0964 28 0.1447 -0.0342 -0.1607 -0.2163 -0.2454 -0.2018 -0.1684 -0.0757 0.1524 -0.0197 -0.1607 -0.2115 -0.2172 -0.2163 -0.1684 -0.0866 28 0.1204 -0.0392 -0.1481 -0.1985 -0.2264 -0.1830 -0.1478 -0.0592 0.1267 -0.0299 -0.1481 -0.1957 -0.2026 -0.1954 -0.1512 -0.0716 28 0.0946 -0.0486 -0.1469 -0.1914 -0.2188 -0.1775 -0.1405 -0.0581 0.0995 -0.0375 -0.1466 -0.1929 -0.1923 -0.1914 -0.1432 -0.0637 28 0.0631 -0.0578 -0.1424 -0.1830 -0.2028 -0.1670 -0.1317 -0.0474 0.0730 -0.0464 -0.1444 -0.1807 -0.1840 -0.1782 -0.1317 -0.0570 28 0.0364 -0.0639 -0.1380 -0.1753 -0.1920 -0.1583 -0.1245 -0.0419 0.0478 -0.0543 -0.1416 -0.1753 -0.1766 -0.1694 -0.1248 -0.0524 31 42.796 -5.7973 -18.775 -20.079 -22.272 -18.953 -21.679 -19.546 40.603 -5.7973 -19.960 -20.968 -19.486 -20.612 -20.020 -21.027 31 1.0419 0.1804 -0.2968 -0.4615 -0.5404 -0.4615 -0.4615 -0.3193 1.0179 0.2043 -0.2982 -0.4390 -0.4601 -0.5009 -0.4221 -0.3461 31 0.6356 0.1143 -0.2173 -0.3311 -0.3979 -0.3392 -0.3311 -0.2064 0.6185 0.1378 -0.2191 -0.3184 -0.3473 -0.3564 -0.3058 -0.2145 31 0.3660 0.0572 -0.1599 -0.2500 -0.2958 -0.2449 -0.2136 -0.1062 0.3637 0.0717 -0.1605 -0.2399 -0.2556 -0.2606 -0.2035 -0.1213 31 0.2514 0.0168 -0.1454 -0.2170 -0.2534 -0.2097 -0.1725 -0.0722 0.2567 0.0346 -0.1458 -0.2121 -0.2214 -0.2206 -0.1725 -0.0867 31 0.1543 -0.0185 -0.1404 -0.1959 -0.2255 -0.1837 -0.1474 -0.0575 0.1643 -0.0009 -0.1401 -0.1931 -0.1970 -0.1959 -0.1474 -0.0681 31 0.0840 -0.0419 -0.1323 -0.1781 -0.2024 -0.1632 -0.1271 -0.0414 0.0913 -0.0285 -0.1353 -0.1795 -0.1812 -0.1728 -0.1290 -0.0507 31 0.0467 -0.0522 -0.1296 -0.1680 -0.1873 -0.1507 -0.1158 -0.0345 0.0588 -0.0411 -0.1344 -0.1689 -0.1683 -0.1616 -0.1172 -0.0419 31 0.0235 -0.0593 -0.1280 -0.1629 -0.1811 -0.1450 -0.1109 -0.0323 0.0353 -0.0483 -0.1326 -0.1647 -0.1636 -0.1557 -0.1132 -0.0388 31 -0.0049 -0.0707 -0.1288 -0.1594 -0.1759 -0.1413 -0.1068 -0.0307 0.0051 -0.0598 -0.1350 -0.1629 -0.1595 -0.1525 -0.1095 -0.0377

171

cpr @ x/L where Φ = 135° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 27 70.290 6.5254 -14.664 -20.452 -23.199 -20.550 -24.082 -26.730 27 0.8673 0.1924 -0.2227 -0.3724 -0.4006 -0.3611 -0.3470 -0.2538 27 0.5109 0.0989 -0.1775 -0.2805 -0.3193 -0.2850 -0.2642 -0.1974 27 0.2908 0.0329 -0.1396 -0.2183 -0.2451 -0.2177 -0.1976 -0.1256 27 0.2034 0.0033 -0.1229 -0.1903 -0.2117 -0.1842 -0.1608 -0.0935 27 0.1227 -0.0220 -0.1112 -0.1732 -0.1878 -0.1629 -0.1369 -0.0723 27 0.0557 -0.0505 -0.1175 -0.1667 -0.1758 -0.1516 -0.1252 -0.0635 27 0.0250 -0.0584 -0.1125 -0.1607 -0.1671 -0.1431 -0.1153 -0.0575 27 0.0087 -0.0648 -0.1118 -0.1561 -0.1599 -0.1383 -0.1093 -0.0518 27 0.0044 -0.0669 -0.1139 -0.1581 -0.1619 -0.1404 -0.1125 -0.0551 28 37.208 1.6587 -9.0168 -13.607 -13.714 -13.234 -15.102 -15.582 28 2.0183 0.3810 -0.5191 -0.7042 -0.7356 -0.6477 -0.7073 -0.6760 28 0.8442 0.1576 -0.2628 -0.3973 -0.4426 -0.3888 -0.3591 -0.2925 28 0.3686 0.0515 -0.1601 -0.2567 -0.2821 -0.2554 -0.2314 -0.1615 28 0.2310 0.0070 -0.1389 -0.2128 -0.2324 -0.2095 -0.1871 -0.1179 28 0.1918 -0.0080 -0.1341 -0.2055 -0.2232 -0.1954 -0.1684 -0.1051 28 0.1566 -0.0133 -0.1188 -0.1861 -0.2023 -0.1816 -0.1543 -0.0906 28 0.1260 -0.0226 -0.1176 -0.1830 -0.1988 -0.1741 -0.1460 -0.0834 28 0.1066 -0.0337 -0.1132 -0.1739 -0.1856 -0.1652 -0.1337 -0.0730 28 0.0774 -0.0434 -0.1171 -0.1679 -0.1792 -0.1578 -0.1262 -0.0654 31 42.973 -5.0862 -17.768 -20.612 -20.375 -19.249 -21.146 -22.272 31 1.1291 0.2296 -0.2490 -0.4221 -0.4812 -0.4404 -0.4362 -0.3700 31 0.6898 0.1532 -0.1775 -0.3058 -0.3546 -0.3284 -0.3067 -0.2308 31 0.4174 0.0868 -0.1297 -0.2293 -0.2567 -0.2399 -0.2142 -0.1414 31 0.2992 0.0496 -0.1154 -0.2061 -0.2279 -0.2040 -0.1798 -0.0977 31 0.2037 0.0120 -0.1164 -0.1834 -0.2037 -0.1814 -0.1549 -0.0804 31 0.1326 -0.0177 -0.1070 -0.1717 -0.1829 -0.1622 -0.1319 -0.0635 31 0.0867 -0.0300 -0.1061 -0.1633 -0.1728 -0.1514 -0.1230 -0.0538 31 0.0614 -0.0391 -0.1055 -0.1604 -0.1677 -0.1482 -0.1176 -0.0488 31 0.0382 -0.0508 -0.1096 -0.1591 -0.1635 -0.1434 -0.1139 -0.0489

172

South Side Wall cpr @ l' Run 0.051 0.139 0.228 0.316 0.360 0.404 0.448 0.492 0.536 0.580 0.624 0.668 0.714 0.809 0.905 1.000 27 -11.231 -12.506 -10.250 -12.113 -9.3666 -8.8761 -10.348 -10.446 - -9.2685 -9.2685 -10.053 -11.427 -8.3857 -10.3476 -8.7781 27 -0.1606 -0.1394 -0.1338 -0.1479 -0.1479 -0.1126 -0.1606 -0.1493 - -0.1324 -0.1324 -0.1310 -0.1507 -0.1338 -0.1479 -0.1253 27 -0.1115 -0.0989 -0.1034 -0.1034 -0.1034 -0.0908 -0.1124 -0.1133 - -0.1025 -0.1025 -0.1097 -0.1386 -0.1115 -0.1287 -0.1395 27 -0.0676 -0.0597 -0.0575 -0.0676 -0.0731 -0.0597 -0.0782 -0.0737 - -0.0720 -0.0726 -0.0664 -0.0944 -0.0832 -0.0888 -0.1055 27 -0.0443 -0.0346 -0.0370 -0.0483 -0.0519 -0.0499 -0.0556 -0.0527 - -0.0552 -0.0515 -0.0511 -0.0749 -0.0705 -0.0709 -0.0862 27 -0.0282 -0.0215 -0.0254 -0.0360 -0.0385 -0.0321 -0.0489 -0.0388 - -0.0433 -0.0436 -0.0405 -0.0595 -0.0617 -0.0670 -0.0805 27 -0.0322 -0.0262 -0.0288 -0.0443 -0.0462 -0.0423 -0.0514 -0.0445 - -0.0564 -0.0460 -0.0425 -0.0704 -0.0704 -0.0704 -0.0892 27 -0.0200 -0.0129 -0.0187 -0.0342 -0.0342 -0.0341 -0.0447 -0.0356 - -0.0420 -0.0355 -0.0316 -0.0563 -0.0602 -0.0602 -0.0755 27 -0.0135 -0.0079 -0.0125 -0.0270 -0.0292 -0.0313 -0.0406 -0.0323 - -0.0385 -0.0323 -0.0302 -0.0508 -0.0552 -0.0561 -0.0734 27 -0.0157 -0.0080 -0.0157 -0.0292 -0.0323 -0.0323 -0.0427 -0.0334 - -0.0386 -0.0334 -0.0313 -0.0498 -0.0573 -0.0572 -0.0745 28 -7.5756 -7.8425 -7.0952 -8.1094 -7.6290 -6.3479 -7.6290 -7.6824 - -8.0560 -7.0952 -8.0026 -8.6965 -6.6148 -8.1094 -6.7749 28 -0.5850 -0.6007 -0.5254 -0.5850 -0.4972 -0.5129 -0.5254 -0.5003 - -0.5505 -0.4940 -0.4909 -0.6760 -0.5536 -0.5254 -0.5317 28 -0.2515 -0.2586 -0.2515 -0.2515 -0.2260 -0.2189 -0.2515 -0.2274 - -0.2628 -0.2246 -0.2232 -0.3067 -0.2642 -0.2784 -0.2812 28 -0.1095 -0.1067 -0.1095 -0.1163 -0.1101 -0.0937 -0.1225 -0.1047 - -0.1218 -0.1095 -0.1019 -0.1492 -0.1225 -0.1417 -0.1492 28 -0.0697 -0.0716 -0.0655 -0.0739 -0.0786 -0.0674 -0.0870 -0.0749 - -0.0865 -0.0739 -0.0688 -0.1052 -0.0912 -0.1001 -0.1141 28 -0.0560 -0.0576 -0.0560 -0.0709 -0.0673 -0.0576 -0.0745 -0.0713 - -0.0777 -0.0745 -0.0664 -0.0975 -0.0930 -0.0971 -0.1124 28 -0.0388 -0.0437 -0.0388 -0.0485 -0.0519 -0.0437 -0.0616 -0.0554 - -0.0578 -0.0582 -0.0478 -0.0747 -0.0740 -0.0775 -0.0875 28 -0.0257 -0.0328 -0.0288 -0.0344 -0.0375 -0.0359 -0.0489 -0.0436 - -0.0427 -0.0399 -0.0396 -0.0523 -0.0630 -0.0661 -0.0779 28 -0.0210 -0.0265 -0.0184 -0.0352 -0.0352 -0.0316 -0.0423 -0.0425 - -0.0372 -0.0372 -0.0347 -0.0497 -0.0586 -0.0588 -0.0756 28 -0.0137 -0.0206 -0.0157 -0.0236 -0.0315 -0.0268 -0.0396 -0.0319 - -0.0334 -0.0334 -0.0312 -0.0458 -0.0534 -0.0573 -0.0695 31 -10.657 -11.546 -10.657 -10.123 -8.9973 -9.2936 -10.123 -10.183 - -9.4714 -8.9973 -9.4714 -11.309 -9.5307 -9.5899 -9.7084 31 -0.1730 -0.1786 -0.1462 -0.1730 -0.1730 -0.1392 -0.1730 -0.1884 - -0.1448 -0.1448 -0.1701 -0.1490 -0.1462 -0.1856 -0.1504 31 -0.1206 -0.1161 -0.1034 -0.1206 -0.1287 -0.0989 -0.1377 -0.1224 - -0.1197 -0.1197 -0.1269 -0.1396 -0.1115 -0.1459 -0.1396 31 -0.0682 -0.0754 -0.0631 -0.0732 -0.0788 -0.0654 -0.0838 -0.0793 - -0.0726 -0.0732 -0.0721 -0.0900 -0.0782 -0.0945 -0.1056 31 -0.0560 -0.0386 -0.0447 -0.0483 -0.0560 -0.0503 -0.0633 -0.0564 - -0.0592 -0.0556 -0.0511 -0.0714 -0.0633 -0.0786 -0.0867 31 -0.0282 -0.0319 -0.0307 -0.0413 -0.0439 -0.0374 -0.0542 -0.0441 - -0.0486 -0.0411 -0.0408 -0.0598 -0.0592 -0.0673 -0.0857 31 -0.0218 -0.0157 -0.0185 -0.0322 -0.0358 -0.0335 -0.0443 -0.0360 - -0.0391 -0.0374 -0.0337 -0.0549 -0.0564 -0.0616 -0.0754 31 -0.0239 -0.0155 -0.0226 -0.0369 -0.0381 -0.0353 -0.0459 -0.0370 - -0.0473 -0.0381 -0.0342 -0.0641 -0.0616 -0.0628 -0.0807 31 -0.0177 -0.0090 -0.0177 -0.0301 -0.0333 -0.0323 -0.0437 -0.0353 - -0.0395 -0.0343 -0.0301 -0.0529 -0.0593 -0.0582 -0.0744 31 -0.0153 -0.0055 -0.0144 -0.0257 -0.0309 -0.0320 -0.0412 -0.0308 - -0.0370 -0.0327 -0.0284 -0.0497 -0.0569 -0.0568 -0.0711

173

Run β0.75 (deg) Ptabs (inHg) Temp (F) qind (psf) qtare (psf) Pten (psfd) Psen (psfd) qen (psf) Ptex (psfd) Psex (psfd) qex (psf) 36 20 28.4617 72.70 0.0324 0.0321 0.4473 0.3541 0.0932 0.4317 0.3495 0.0822 36 20 28.4657 72.47 1.0204 1.0121 1.4816 0.4033 1.0783 1.4649 0.3833 1.0816 36 20 28.4658 72.10 1.6054 1.5923 2.0765 0.4101 1.6664 2.0575 0.3715 1.6860 36 20 28.4649 72.00 2.6105 2.5892 3.0914 0.4186 2.6728 3.0734 0.3491 2.7243 36 20 28.4651 71.90 3.6026 3.5732 4.1183 0.4303 3.6880 4.0959 0.3285 3.7675 36 20 28.4663 71.80 5.2096 5.1670 5.7028 0.4085 5.2943 5.6801 0.2572 5.4229 36 20 28.4647 71.90 7.8040 7.7402 8.2855 0.3777 7.9078 8.2482 0.1428 8.1053 36 20 28.4647 72.10 10.4076 10.3226 10.9130 0.3550 10.5581 10.8780 0.0269 10.8511 36 20 28.4642 72.40 12.9934 12.8872 13.4335 0.2638 13.1697 13.3860 -0.1544 13.5403 36 20 28.4660 72.70 15.5945 15.4671 15.9372 0.1380 15.7992 15.8972 -0.3842 16.2814 32 25 28.7614 72.50 0.0194 0.0192 0.4290 0.4599 -0.0310 0.4589 0.4620 -0.0030 32 25 28.7593 73.26 1.0269 1.0185 1.4848 0.5219 0.9629 1.5205 0.5105 1.0100 32 25 28.7627 73.60 1.6189 1.6057 2.0291 0.4836 1.5456 2.0619 0.4575 1.6044 32 25 28.7617 73.80 2.5942 2.5730 3.0102 0.4811 2.5291 3.0521 0.4248 2.6273 32 25 28.7608 74.03 3.5836 3.5543 4.0180 0.4821 3.5359 4.0598 0.3954 3.6644 32 25 28.7615 74.20 5.2019 5.1594 5.6254 0.4617 5.1637 5.6648 0.3236 5.3412 32 25 28.7612 74.30 7.7914 7.7277 8.2057 0.4216 7.7841 8.2400 0.1981 8.0418 32 25 28.7641 74.40 10.3987 10.3137 10.8170 0.3948 10.4221 10.8311 0.0804 10.7508 32 25 28.7591 74.50 12.9848 12.8787 13.3740 0.3010 13.0730 13.3708 -0.1041 13.4749 32 25 28.7616 74.50 15.5807 15.4534 15.8859 0.1784 15.7075 15.8357 -0.3263 16.1620 33 25 28.7589 74.10 0.0303 0.0301 0.4121 0.4487 -0.0366 0.3987 0.4509 -0.0521 33 25 28.7550 74.34 1.0324 1.0240 1.4499 0.4931 0.9569 1.4473 0.4812 0.9661 33 25 28.7560 74.50 2.1294 2.1120 2.5587 0.4923 2.0664 2.5547 0.4533 2.1014 33 25 28.7553 74.50 4.1954 4.1611 4.6345 0.4837 4.1508 4.6283 0.3793 4.2490 33 25 28.7560 74.60 6.2106 6.1599 6.6429 0.4643 6.1786 6.6312 0.2920 6.3392 33 25 28.7539 74.60 8.8181 8.7461 9.2164 0.4124 8.8040 9.1996 0.1531 9.0465 33 25 28.7546 74.70 11.4016 11.3085 11.7959 0.3793 11.4166 11.7775 0.0312 11.7462 33 25 28.7538 74.80 14.6011 14.4818 14.9098 0.2278 14.6820 14.8668 -0.2402 15.1070 33 25 28.7562 74.90 18.1586 18.0102 18.3090 0.0282 18.2808 18.2664 -0.5669 18.8333 33 25 28.7553 75.10 23.3912 23.2001 23.3160 -0.2748 23.5908 23.2462 -1.0647 24.3109

174

cpr @ x/L where Φ = 0°

Run qcor (fps) T (lbs) Q (in.lbs) rpm Ucor (fps) J η CT CP Re0.75 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 36 0.032 2.385 2.825 5958.8 5.256 0.053 0.085 0.110 0.068 92,931 38.756 2.1011 -7.8917 -10.849 -10.446 -8.7431 -10.536 -11.252 36 1.012 2.214 2.678 5970.0 30.194 0.304 0.479 0.102 0.064 93,856 1.2073 0.3721 -0.1003 -0.3550 -0.3678 -0.2739 -0.2852 -0.1942 36 1.592 2.121 2.643 5977.5 37.916 0.381 0.583 0.097 0.063 94,413 0.7313 0.2348 -0.0827 -0.2617 -0.2780 -0.2192 -0.2228 -0.1342 36 2.589 1.965 2.610 5992.5 48.396 0.485 0.697 0.089 0.062 95,395 0.4136 0.1238 -0.0920 -0.2171 -0.2371 -0.1810 -0.1509 -0.0714 36 3.573 1.777 2.561 6045.0 56.884 0.565 0.748 0.080 0.060 96,926 0.2854 0.0674 -0.0959 -0.2015 -0.2156 -0.1644 -0.1257 -0.0467 36 5.167 1.470 2.384 6112.5 68.440 0.672 0.791 0.064 0.055 99,108 0.1763 0.0197 -0.1032 -0.1938 -0.1952 -0.1531 -0.1152 -0.0375 36 7.740 1.013 1.979 6262.5 83.803 0.803 0.785 0.042 0.043 103,160 0.1023 -0.0170 -0.1070 -0.1811 -0.1831 -0.1403 -0.1033 -0.0300 36 10.323 0.599 1.498 6412.5 96.800 0.906 0.691 0.024 0.031 107,116 0.0637 -0.0340 -0.1062 -0.1772 -0.1743 -0.1326 -0.0984 -0.0274 36 12.887 0.241 1.044 6618.8 108.174 0.981 0.432 0.009 0.020 111,778 0.0429 -0.0442 -0.1058 -0.1749 -0.1701 -0.1311 -0.0970 -0.0269 36 15.467 -0.101 0.606 6810.0 118.518 1.044 -0.334 -0.004 0.011 116,138 0.0272 -0.0511 -0.1062 -0.1740 -0.1653 -0.1282 -0.0942 -0.0274 32 0.019 2.622 4.675 5906.3 4.005 0.041 0.044 0.122 0.114 93,073 45.004 -23.622 -39.264 -39.189 -34.249 -31.555 -30.882 -31.555 32 1.019 2.581 4.169 6060.0 30.120 0.298 0.353 0.114 0.096 96,249 1.1329 0.1291 -0.4336 -0.6994 -0.6853 -0.5934 -0.5976 -0.5538 32 1.606 2.559 3.937 6131.3 37.862 0.371 0.460 0.110 0.089 97,798 0.7669 0.1481 -0.2438 -0.4456 -0.4447 -0.3873 -0.3864 -0.3030 32 2.573 2.488 3.817 6180.0 47.974 0.466 0.580 0.105 0.085 99,264 0.4540 0.0941 -0.1661 -0.3127 -0.3172 -0.2764 -0.2495 -0.1711 32 3.554 2.403 3.752 6195.0 56.416 0.546 0.669 0.101 0.083 100,207 0.3184 0.0579 -0.1459 -0.2671 -0.2659 -0.2185 -0.1828 -0.1038 32 5.159 2.244 3.723 6195.0 68.007 0.659 0.758 0.095 0.082 101,359 0.2138 0.0259 -0.1320 -0.2336 -0.2348 -0.1901 -0.1521 -0.0665 32 7.728 1.877 3.536 6240.0 83.270 0.801 0.812 0.078 0.077 103,846 0.1413 -0.0095 -0.1265 -0.2113 -0.2113 -0.1705 -0.1310 -0.0510 32 10.314 1.513 3.213 6360.0 96.226 0.908 0.817 0.061 0.067 107,394 0.1008 -0.0271 -0.1222 -0.2011 -0.1981 -0.1578 -0.1205 -0.0447 32 12.879 1.191 2.846 6468.8 107.546 0.998 0.798 0.046 0.058 110,684 0.0788 -0.0378 -0.1187 -0.1941 -0.1881 -0.1502 -0.1137 -0.0397 32 15.453 0.882 2.413 6592.5 117.820 1.072 0.748 0.033 0.047 114,125 0.0642 -0.0448 -0.1162 -0.1892 -0.1812 -0.1442 -0.1089 -0.0363 33 0.030 2.625 4.638 5917.5 5.048 0.051 0.055 0.122 0.112 92,949 30.569 -14.760 -23.385 -24.247 -18.402 -17.060 -17.922 -17.060 33 1.024 2.592 4.162 6067.5 30.229 0.299 0.356 0.114 0.096 96,052 1.2067 0.1942 -0.3514 -0.6158 -0.5891 -0.4977 -0.5244 -0.4443 33 2.112 2.531 3.843 6146.3 43.489 0.425 0.534 0.109 0.086 98,081 0.6033 0.1458 -0.1453 -0.3185 -0.3240 -0.2742 -0.2606 -0.1712 33 4.161 2.355 3.739 6198.8 61.113 0.592 0.711 0.099 0.083 100,373 0.2907 0.0612 -0.1156 -0.2288 -0.2309 -0.1810 -0.1464 -0.0602 33 6.160 2.110 3.663 6210.0 74.395 0.719 0.791 0.089 0.081 101,965 0.1949 0.0240 -0.1148 -0.2081 -0.2067 -0.1632 -0.1275 -0.0421 33 8.746 1.714 3.417 6296.3 88.682 0.845 0.810 0.070 0.073 105,049 0.1376 -0.0083 -0.1130 -0.1954 -0.1937 -0.1519 -0.1170 -0.0371 33 11.308 1.355 3.063 6382.5 100.862 0.948 0.801 0.054 0.064 108,045 0.0995 -0.0257 -0.1123 -0.1888 -0.1823 -0.1435 -0.1095 -0.0320 33 14.482 0.972 2.594 6562.5 114.159 1.044 0.747 0.037 0.051 112,718 0.0757 -0.0366 -0.1092 -0.1826 -0.1762 -0.1383 -0.1051 -0.0287 33 18.010 0.566 2.003 6750.0 127.324 1.132 0.611 0.020 0.037 117,596 0.0605 -0.0431 -0.1084 -0.1783 -0.1704 -0.1333 -0.1000 -0.0271 33 23.200 0.068 1.299 7057.5 144.524 1.229 0.124 0.002 0.022 124,992 0.0419 -0.0502 -0.1108 -0.1775 -0.1691 -0.1307 -0.0998 -0.0266

175

cpr @ x/L where Φ = 45° cpr @ x/L where Φ = 90° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 36 35.216 0.8016 -8.6982 -8.7879 -10.491 -9.1912 -10.849 -8.8327 36.247 1.5634 -9.1464 -10.401 -8.7879 - -10.043 -9.5496 36 1.1333 0.3337 -0.1245 -0.2639 -0.3692 -0.2767 -0.2767 -0.1202 1.1931 0.3977 -0.1259 -0.2966 -0.2753 - -0.2497 -0.1330 36 0.7014 0.2176 -0.0899 -0.2029 -0.2780 -0.2201 -0.2029 -0.0790 0.7394 0.2583 -0.0908 -0.2174 -0.2192 - -0.1948 -0.0872 36 0.3930 0.1144 -0.0964 -0.1754 -0.2260 -0.1810 -0.1498 -0.0375 0.4297 0.1444 -0.0920 -0.1815 -0.1910 - -0.1448 -0.0469 36 0.2753 0.0621 -0.0959 -0.1668 -0.2067 -0.1636 -0.1261 -0.0225 0.3124 0.0875 -0.0959 -0.1741 -0.1753 - -0.1301 -0.0330 36 0.1833 0.0158 -0.1060 -0.1615 -0.1938 -0.1517 -0.1183 -0.0258 0.2162 0.0356 -0.1057 -0.1668 -0.1679 - -0.1208 -0.0310 36 0.1036 -0.0207 -0.1111 -0.1552 -0.1813 -0.1422 -0.1059 -0.0201 0.1244 -0.0040 -0.1143 -0.1602 -0.1567 - -0.1096 -0.0278 36 0.0598 -0.0377 -0.1124 -0.1507 -0.1725 -0.1359 -0.1011 -0.0186 0.0860 -0.0239 -0.1170 -0.1569 -0.1523 - -0.1038 -0.0260 36 0.0361 -0.0486 -0.1141 -0.1500 -0.1702 -0.1343 -0.0991 -0.0185 0.0612 -0.0346 -0.1208 -0.1551 -0.1507 - -0.1023 -0.0260 36 0.0204 -0.0549 -0.1161 -0.1493 -0.1683 -0.1313 -0.0977 -0.0200 0.0438 -0.0424 -0.1233 -0.1538 -0.1494 - -0.1013 -0.0261 32 42.984 -26.841 -40.087 -34.998 -34.923 -30.807 -31.555 -29.460 39.691 -26.167 -39.264 -35.896 -33.576 -32.229 -32.229 -30.807 32 1.1315 0.0909 -0.4449 -0.5821 -0.6853 -0.5679 -0.5807 -0.4775 1.0990 0.1277 -0.4605 -0.5920 -0.5948 -0.6075 -0.5679 -0.4972 32 0.7723 0.1292 -0.2420 -0.3622 -0.4438 -0.3703 -0.3703 -0.2555 0.7445 0.1445 -0.2429 -0.3613 -0.3793 -0.4035 -0.3541 -0.2752 32 0.4686 0.0824 -0.1599 -0.2551 -0.3161 -0.2607 -0.2450 -0.1420 0.4669 0.1020 -0.1655 -0.2506 -0.2708 -0.2808 -0.2344 -0.1532 32 0.3261 0.0498 -0.1415 -0.2172 -0.2610 -0.2099 -0.1836 -0.0831 0.3313 0.0676 -0.1419 -0.2160 -0.2253 -0.2282 -0.1800 -0.0941 32 0.2152 0.0167 -0.1298 -0.1935 -0.2309 -0.1862 -0.1499 -0.0522 0.2233 0.0340 -0.1323 -0.1957 -0.1996 -0.2010 -0.1474 -0.0626 32 0.1363 -0.0167 -0.1272 -0.1783 -0.2077 -0.1669 -0.1325 -0.0430 0.1409 -0.0016 -0.1302 -0.1798 -0.1850 -0.1783 -0.1326 -0.0525 32 0.0866 -0.0337 -0.1269 -0.1719 -0.1949 -0.1572 -0.1223 -0.0384 0.0944 -0.0198 -0.1317 -0.1729 -0.1748 -0.1692 -0.1237 -0.0460 32 0.0604 -0.0433 -0.1249 -0.1660 -0.1881 -0.1502 -0.1161 -0.0334 0.0751 -0.0314 -0.1306 -0.1680 -0.1678 -0.1609 -0.1174 -0.0421 32 0.0398 -0.0497 -0.1243 -0.1610 -0.1834 -0.1455 -0.1110 -0.0307 0.0529 -0.0380 -0.1305 -0.1646 -0.1638 -0.1575 -0.1137 -0.0376 33 28.892 -16.245 -23.002 -20.606 -19.695 -16.197 -17.539 -16.197 27.167 -15.383 -23.864 -21.277 -17.970 -18.402 -17.970 -17.970 33 1.1955 0.1591 -0.3627 -0.4977 -0.5877 -0.4850 -0.5103 -0.3950 1.1871 0.1956 -0.3514 -0.4963 -0.5103 -0.5244 -0.4977 -0.4021 33 0.5965 0.1376 -0.1508 -0.2551 -0.3233 -0.2674 -0.2483 -0.1419 0.6060 0.1615 -0.1453 -0.2612 -0.2674 -0.2865 -0.2422 -0.1494 33 0.2855 0.0550 -0.1156 -0.1859 -0.2232 -0.1769 -0.1447 -0.0461 0.3017 0.0733 -0.1156 -0.1866 -0.1931 -0.1924 -0.1447 -0.0554 33 0.1940 0.0173 -0.1151 -0.1719 -0.2009 -0.1616 -0.1249 -0.0323 0.2029 0.0338 -0.1148 -0.1733 -0.1775 -0.1740 -0.1293 -0.0412 33 0.1216 -0.0139 -0.1153 -0.1629 -0.1875 -0.1484 -0.1134 -0.0282 0.1328 0.0024 -0.1178 -0.1639 -0.1675 -0.1629 -0.1196 -0.0368 33 0.0791 -0.0287 -0.1168 -0.1584 -0.1816 -0.1450 -0.1098 -0.0273 0.0973 -0.0160 -0.1208 -0.1626 -0.1625 -0.1573 -0.1135 -0.0331 33 0.0521 -0.0406 -0.1178 -0.1565 -0.1777 -0.1408 -0.1049 -0.0247 0.0690 -0.0281 -0.1227 -0.1587 -0.1584 -0.1518 -0.1087 -0.0300 33 0.0321 -0.0482 -0.1171 -0.1522 -0.1733 -0.1369 -0.1006 -0.0228 0.0475 -0.0360 -0.1238 -0.1572 -0.1549 -0.1485 -0.1053 -0.0278 33 0.0184 -0.0562 -0.1192 -0.1525 -0.1724 -0.1351 -0.1012 -0.0235 0.0318 -0.0439 -0.1270 -0.1569 -0.1541 -0.1473 -0.1049 -0.0294

176

cpr @ x/L where Φ = 135° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 36 38.039 2.1459 -7.4884 -10.043 -9.0567 -7.8020 -9.6393 -10.446 36 1.3041 0.4233 -0.0476 -0.2767 -0.2838 -0.2426 -0.2639 -0.1714 36 0.8181 0.2818 -0.0411 -0.1948 -0.2174 -0.1912 -0.2029 -0.1116 36 0.4881 0.1639 -0.0558 -0.1654 -0.1871 -0.1654 -0.1548 -0.0675 36 0.3547 0.1020 -0.0660 -0.1523 -0.1777 -0.1539 -0.1374 -0.0519 36 0.2454 0.0487 -0.0820 -0.1439 -0.1693 -0.1470 -0.1255 -0.0461 36 0.1678 0.0068 -0.0840 -0.1368 -0.1600 -0.1394 -0.1141 -0.0406 36 0.1103 -0.0129 -0.0888 -0.1357 -0.1566 -0.1354 -0.1096 -0.0391 36 0.0855 -0.0245 -0.0927 -0.1340 -0.1548 -0.1342 -0.1078 -0.0391 36 0.0716 -0.0319 -0.0952 -0.1327 -0.1534 -0.1325 -0.1065 -0.0382 32 43.058 -24.221 -35.746 -37.019 -32.977 -28.637 -30.807 -31.555 32 1.1739 0.1531 -0.3686 -0.5552 -0.6061 -0.5510 -0.5694 -0.5298 32 0.7767 0.1678 -0.1855 -0.3371 -0.3873 -0.3524 -0.3541 -0.3039 32 0.5128 0.1266 -0.1247 -0.2400 -0.2724 -0.2506 -0.2400 -0.1672 32 0.3763 0.0891 -0.1042 -0.2022 -0.2318 -0.2079 -0.1836 -0.1127 32 0.2562 0.0466 -0.1008 -0.1834 -0.2063 -0.1840 -0.1549 -0.0776 32 0.1767 0.0105 -0.1036 -0.1701 -0.1869 -0.1660 -0.1371 -0.0669 32 0.1351 -0.0092 -0.1010 -0.1659 -0.1780 -0.1568 -0.1296 -0.0589 32 0.1012 -0.0204 -0.1025 -0.1624 -0.1720 -0.1525 -0.1217 -0.0530 32 0.0803 -0.0270 -0.1025 -0.1599 -0.1679 -0.1477 -0.1181 -0.0497 33 29.802 -14.137 -21.085 -20.175 -17.539 -16.581 -17.060 -17.539 33 1.2489 0.2462 -0.2867 -0.4724 -0.5103 -0.4555 -0.4850 -0.4457 33 0.6558 0.1915 -0.0949 -0.2299 -0.2749 -0.2415 -0.2483 -0.1794 33 0.3398 0.0917 -0.0769 -0.1734 -0.1931 -0.1689 -0.1478 -0.0713 33 0.2349 0.0507 -0.0840 -0.1616 -0.1824 -0.1564 -0.1310 -0.0557 33 0.1735 0.0147 -0.0911 -0.1573 -0.1717 -0.1499 -0.1206 -0.0480 33 0.1298 -0.0039 -0.0904 -0.1554 -0.1648 -0.1453 -0.1163 -0.0461 33 0.0956 -0.0157 -0.0938 -0.1533 -0.1612 -0.1399 -0.1116 -0.0432 33 0.0767 -0.0248 -0.0951 -0.1521 -0.1576 -0.1370 -0.1088 -0.0399 33 0.0685 -0.0336 -0.0991 -0.1531 -0.1571 -0.1371 -0.1079 -0.0403

177

South Side Wall cpr @ l' Run 0.051 0.139 0.228 0.316 0.360 0.404 0.448 0.492 0.536 0.580 0.624 0.668 0.714 0.809 0.905 1.000 36 -0.8564 -0.2291 -0.0498 -1.3045 0.3983 -0.2739 -0.4531 -0.9460 -2.9177 0.0398 0.8464 -0.3635 -0.0946 0.3983 -0.4531 -1.3941 36 -0.0106 0.0235 0.0022 -0.0249 0.0022 -0.0049 -0.0106 -0.0135 -0.1031 0.0306 0.0292 0.0050 -0.0135 -0.0106 -0.0249 -0.0547 36 -0.0013 0.0123 -0.0013 -0.0176 0.0069 -0.0049 -0.0176 -0.0275 -0.0845 0.0005 0.0078 -0.0076 -0.0194 -0.0176 -0.0347 -0.0619 36 -0.0052 0.0087 0.0004 -0.0208 -0.0152 -0.0074 -0.0152 -0.0163 -0.0614 -0.0147 0.0004 -0.0091 -0.0269 -0.0308 -0.0314 -0.0681 36 -0.0028 0.0109 0.0049 -0.0141 -0.0064 -0.0120 -0.0213 -0.0145 -0.0435 -0.0096 0.0013 -0.0056 -0.0294 -0.0290 -0.0326 -0.0632 36 -0.0174 -0.0057 -0.0121 -0.0302 -0.0277 -0.0269 -0.0355 -0.0280 -0.0483 -0.0380 -0.0224 -0.0221 -0.0564 -0.0536 -0.0589 -0.0846 36 -0.0041 0.0018 -0.0041 -0.0181 -0.0164 -0.0211 -0.0302 -0.0235 -0.0283 -0.0267 -0.0162 -0.0160 -0.0373 -0.0440 -0.0475 -0.0696 36 -0.0002 0.0057 0.0011 -0.0146 -0.0158 -0.0168 -0.0275 -0.0185 -0.0222 -0.0222 -0.0171 -0.0144 -0.0327 -0.0418 -0.0430 -0.0621 36 0.0002 0.0058 0.0002 -0.0123 -0.0164 -0.0206 -0.0278 -0.0196 -0.0184 -0.0227 -0.0174 -0.0153 -0.0308 -0.0423 -0.0423 -0.0658 36 -0.0003 0.0069 -0.0011 -0.0124 -0.0168 -0.0213 -0.0279 -0.0201 -0.0176 -0.0220 -0.0185 -0.0177 -0.0321 -0.0445 -0.0444 -0.0646 32 -12.023 -10.226 -12.023 -12.771 -11.349 -9.6277 -10.675 -10.750 - -11.948 -9.9270 -10.526 -12.172 -9.9270 -11.349 -10.152 32 -0.2131 -0.1650 -0.1862 -0.2131 -0.2003 -0.1523 -0.2003 -0.2159 - -0.1848 -0.1862 -0.1834 -0.2428 -0.1735 -0.2399 -0.2046 32 -0.1873 -0.1326 -0.1622 -0.2035 -0.1703 -0.1416 -0.1703 -0.1721 - -0.2026 -0.1533 -0.1524 -0.2465 -0.1873 -0.2044 -0.2223 32 -0.1045 -0.0967 -0.1096 -0.1252 -0.1146 -0.0967 -0.1252 -0.1157 - -0.1297 -0.0939 -0.0878 -0.1571 -0.1303 -0.1460 -0.1622 32 -0.0746 -0.0613 -0.0706 -0.0823 -0.0819 -0.0690 -0.0896 -0.0827 - -0.0929 -0.0783 -0.0661 -0.1164 -0.1010 -0.1087 -0.1241 32 -0.0436 -0.0372 -0.0436 -0.0592 -0.0567 -0.0506 -0.0592 -0.0570 - -0.0642 -0.0514 -0.0433 -0.0776 -0.0723 -0.0826 -0.1011 32 -0.0253 -0.0210 -0.0270 -0.0426 -0.0393 -0.0369 -0.0479 -0.0411 - -0.0424 -0.0374 -0.0337 -0.0566 -0.0616 -0.0652 -0.0806 32 -0.0201 -0.0129 -0.0187 -0.0331 -0.0331 -0.0328 -0.0447 -0.0345 - -0.0395 -0.0330 -0.0303 -0.0500 -0.0564 -0.0577 -0.0757 32 -0.0157 -0.0080 -0.0157 -0.0271 -0.0313 -0.0313 -0.0407 -0.0324 - -0.0365 -0.0313 -0.0281 -0.0468 -0.0532 -0.0552 -0.0745 32 -0.0110 -0.0028 -0.0092 -0.0196 -0.0248 -0.0267 -0.0378 -0.0274 - -0.0292 -0.0257 -0.0240 -0.0368 -0.0491 -0.0507 -0.0659 33 -3.6913 -3.8830 -3.6913 -3.6913 -3.2601 -2.5892 -3.7392 -4.2184 - -2.7330 -3.2121 -3.1642 -3.3559 -2.3496 -3.7392 -2.0621 33 -0.0927 -0.0716 -0.0786 -0.0927 -0.0927 -0.0716 -0.1053 -0.0955 - -0.0899 -0.0392 -0.0631 -0.1081 -0.0392 -0.1194 -0.0842 33 -0.0649 -0.0417 -0.0458 -0.0519 -0.0581 -0.0356 -0.0587 -0.0533 - -0.0574 -0.0512 -0.0444 -0.0724 -0.0519 -0.0778 -0.0792 33 -0.0256 -0.0173 -0.0194 -0.0291 -0.0353 -0.0243 -0.0388 -0.0329 - -0.0350 -0.0353 -0.0284 -0.0519 -0.0419 -0.0516 -0.0682 33 -0.0164 -0.0087 -0.0122 -0.0230 -0.0274 -0.0244 -0.0339 -0.0297 - -0.0314 -0.0251 -0.0248 -0.0449 -0.0426 -0.0512 -0.0667 33 -0.0189 -0.0090 -0.0174 -0.0310 -0.0342 -0.0278 -0.0403 -0.0312 - -0.0434 -0.0279 -0.0263 -0.0585 -0.0541 -0.0571 -0.0752 33 -0.0154 -0.0053 -0.0141 -0.0261 -0.0284 -0.0271 -0.0391 -0.0284 - -0.0367 -0.0284 -0.0236 -0.0484 -0.0521 -0.0544 -0.0707 33 -0.0091 -0.0005 -0.0091 -0.0211 -0.0239 -0.0269 -0.0359 -0.0257 - -0.0305 -0.0249 -0.0212 -0.0431 -0.0490 -0.0507 -0.0687 33 -0.0067 0.0023 -0.0045 -0.0178 -0.0223 -0.0242 -0.0334 -0.0229 - -0.0284 -0.0216 -0.0187 -0.0376 -0.0468 -0.0483 -0.0647 33 -0.0066 0.0043 -0.0066 -0.0181 -0.0227 -0.0256 -0.0359 -0.0237 - -0.0281 -0.0234 -0.0201 -0.0391 -0.0494 -0.0503 -0.0670

178

Run β0.75 (deg) Ptabs (inHg) Temp (F) qind (psf) qtare (psf) Pten (psfd) Psen (psfd) qen (psf) Ptex (psfd) Psex (psfd) qex (psf) 34 30 28.7490 73.42 0.0377 0.0374 0.4209 0.4006 0.0203 0.4170 0.4046 0.0124 34 30 28.7471 73.90 1.0240 1.0156 1.4674 0.4539 1.0135 1.4612 0.4448 1.0164 34 30 28.7489 74.20 1.6112 1.5980 2.0382 0.4392 1.5990 2.0327 0.4166 1.6161 34 30 28.7464 74.40 2.6074 2.5861 3.0470 0.4497 2.5973 3.0400 0.3963 2.6437 34 30 28.7451 74.50 3.5639 3.5348 4.0258 0.4483 3.5775 4.0140 0.3658 3.6482 34 30 28.7483 74.60 5.1985 5.1560 5.6503 0.4287 5.2216 5.6303 0.2987 5.3316 34 30 28.7459 74.70 7.8028 7.7391 8.2318 0.3836 7.8481 8.2176 0.1669 8.0508 34 30 28.7485 74.80 10.4128 10.3277 10.8348 0.3574 10.4774 10.8101 0.0553 10.7548 34 30 28.7483 74.90 12.9910 12.8849 13.3734 0.2742 13.0992 13.3345 -0.1191 13.4536 34 30 28.7450 75.00 15.6074 15.4799 15.8746 0.1295 15.7451 15.8393 -0.3663 16.2056 35 30 28.7481 74.50 0.0279 0.0277 0.3995 0.3879 0.0115 0.3954 0.3911 0.0043 35 30 28.7461 74.60 2.1213 2.1040 2.5796 0.4576 2.1220 2.5740 0.4188 2.1552 35 30 28.7481 74.71 6.1909 6.1403 6.6214 0.3999 6.2215 6.6041 0.2339 6.3703 35 30 28.7486 74.90 12.4848 12.3828 12.8622 0.2750 12.5872 12.8130 -0.0956 12.9086 35 30 28.7466 75.00 17.6811 17.5367 17.8520 0.0024 17.8495 17.8144 -0.5653 18.3797 35 30 28.7500 75.10 19.7782 19.6166 19.8685 -0.1289 19.9974 19.8167 -0.7681 20.5848 35 30 28.7471 75.20 21.7844 21.6064 21.7866 -0.2478 22.0344 21.7302 -0.9590 22.6892 35 30 28.7485 75.33 23.3917 23.2006 23.2982 -0.3460 23.6442 23.2376 -1.1065 24.3441 35 30 28.7505 75.60 26.0346 25.8219 25.9138 -0.4262 26.3400 25.8564 -1.2888 27.1452 35 30 28.7505 75.73 28.5688 28.3354 28.3654 -0.5600 28.9254 28.2951 -1.5088 29.8040

179

cpr @ x/L where Φ = 0°

Run qcor (fps) T (lbs) Q (in.lbs) rpm Ucor (fps) J η CT CP Re0.75 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 34 0.037 2.687 6.074 5842.5 5.648 0.058 0.049 0.128 0.151 91,746 19.436 -19.652 -22.772 -20.923 -17.958 -15.185 -14.992 -14.068 34 1.016 2.629 5.867 5883.8 30.109 0.307 0.263 0.123 0.144 93,152 1.0966 -0.0094 -0.5283 -0.7920 -0.7367 -0.6077 -0.6375 -0.5538 34 1.598 2.594 5.722 5925.0 37.812 0.383 0.332 0.120 0.138 94,240 0.7465 0.0616 -0.2943 -0.4971 -0.4863 -0.4223 -0.4205 -0.3367 34 2.586 2.549 5.521 5962.5 48.148 0.485 0.427 0.116 0.132 95,568 0.4832 0.0661 -0.1811 -0.3370 -0.3409 -0.2858 -0.2736 -0.1861 34 3.535 2.546 5.238 6041.3 56.318 0.559 0.519 0.113 0.122 97,482 0.3783 0.0617 -0.1465 -0.2756 -0.2703 -0.2230 -0.2092 -0.1196 34 5.156 2.548 4.924 6123.8 68.051 0.667 0.659 0.110 0.112 99,917 0.2667 0.0441 -0.1139 -0.2231 -0.2218 -0.1746 -0.1480 -0.0614 34 7.739 2.447 4.875 6191.3 83.407 0.808 0.775 0.104 0.108 102,762 0.1832 0.0189 -0.1070 -0.1986 -0.1969 -0.1526 -0.1167 -0.0335 34 10.328 2.233 4.830 6183.8 96.379 0.935 0.826 0.095 0.107 104,449 0.1455 -0.0058 -0.1076 -0.1915 -0.1911 -0.1483 -0.1146 -0.0315 34 12.885 1.967 4.621 6225.0 107.671 1.038 0.844 0.082 0.101 106,789 0.1179 -0.0184 -0.1059 -0.1876 -0.1826 -0.1428 -0.1091 -0.0292 34 15.480 1.739 4.394 6356.3 118.031 1.114 0.842 0.070 0.092 110,382 0.0991 -0.0280 -0.1064 -0.1854 -0.1792 -0.1406 -0.1074 -0.0284 35 0.028 2.730 6.087 5827.5 4.840 0.050 0.043 0.131 0.152 91,200 29.768 -24.091 -27.265 -25.704 -18.835 -14.048 -15.765 -15.036 35 2.104 2.598 5.660 5970.0 43.452 0.437 0.383 0.118 0.135 95,007 0.6387 0.1123 -0.1587 -0.3319 -0.3366 -0.2750 -0.2792 -0.1779 35 6.140 2.503 4.890 6210.0 74.347 0.718 0.702 0.105 0.108 101,588 0.2403 0.0489 -0.0904 -0.1908 -0.1915 -0.1434 -0.1174 -0.0240 35 12.383 1.965 4.672 6262.5 105.649 1.012 0.813 0.081 0.101 106,652 0.1326 -0.0093 -0.0981 -0.1788 -0.1770 -0.1343 -0.1038 -0.0182 35 17.537 1.449 4.135 6416.3 125.757 1.176 0.787 0.057 0.085 112,205 0.0939 -0.0279 -0.1007 -0.1764 -0.1705 -0.1316 -0.0997 -0.0210 35 19.617 1.274 3.911 6510.0 133.014 1.226 0.763 0.049 0.079 114,824 0.0868 -0.0314 -0.1017 -0.1753 -0.1685 -0.1293 -0.0978 -0.0194 35 21.606 1.093 3.639 6603.8 139.604 1.268 0.728 0.041 0.071 117,348 0.0791 -0.0347 -0.1026 -0.1749 -0.1685 -0.1277 -0.0977 -0.0204 35 23.201 0.958 3.425 6648.8 144.667 1.306 0.697 0.035 0.066 118,933 0.0735 -0.0366 -0.1032 -0.1745 -0.1672 -0.1272 -0.0975 -0.0202 35 25.822 0.740 3.050 6783.8 152.627 1.350 0.626 0.026 0.056 122,329 0.0645 -0.0404 -0.1058 -0.1744 -0.1676 -0.1263 -0.0969 -0.0202 35 28.335 0.555 2.740 6915.0 159.888 1.387 0.537 0.019 0.049 125,557 0.0576 -0.0426 -0.1077 -0.1748 -0.1674 -0.1268 -0.0972 -0.0210

180

cpr @ x/L where Φ = 45° cpr @ x/L where Φ = 90° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 34 17.896 -19.575 -23.965 -19.383 -17.573 -15.146 -13.722 -12.643 17.973 -19.229 -23.888 -18.998 -15.878 -16.186 -15.146 -13.375 34 1.0569 -0.0306 -0.5410 -0.6445 -0.7339 -0.6063 -0.6190 -0.5141 1.0810 0.0204 -0.5283 -0.6389 -0.6204 -0.6573 -0.5935 -0.5141 34 0.7257 0.0526 -0.3033 -0.4033 -0.4763 -0.4115 -0.3871 -0.2952 0.7600 0.0851 -0.3033 -0.4079 -0.4124 -0.4358 -0.3952 -0.2943 34 0.4737 0.0533 -0.1861 -0.2685 -0.3287 -0.2791 -0.2641 -0.1561 0.4954 0.0828 -0.1811 -0.2730 -0.2797 -0.3042 -0.2591 -0.1700 34 0.3730 0.0515 -0.1424 -0.2210 -0.2650 -0.2218 -0.1990 -0.1012 0.3864 0.0768 -0.1424 -0.2218 -0.2259 -0.2397 -0.1990 -0.1029 34 0.2606 0.0402 -0.1142 -0.1776 -0.2201 -0.1757 -0.1419 -0.0466 0.2723 0.0601 -0.1114 -0.1776 -0.1840 -0.1880 -0.1422 -0.0525 34 0.1762 0.0158 -0.1076 -0.1623 -0.1934 -0.1526 -0.1147 -0.0237 0.1838 0.0323 -0.1089 -0.1655 -0.1671 -0.1640 -0.1184 -0.0311 34 0.1237 -0.0080 -0.1109 -0.1599 -0.1854 -0.1490 -0.1116 -0.0252 0.1392 0.0070 -0.1157 -0.1635 -0.1641 -0.1599 -0.1169 -0.0326 34 0.0912 -0.0219 -0.1132 -0.1575 -0.1816 -0.1438 -0.1076 -0.0249 0.1121 -0.0068 -0.1178 -0.1605 -0.1592 -0.1553 -0.1109 -0.0282 34 0.0719 -0.0310 -0.1145 -0.1564 -0.1787 -0.1427 -0.1065 -0.0246 0.0979 -0.0168 -0.1207 -0.1592 -0.1583 -0.1537 -0.1110 -0.0298 35 27.323 -25.236 -28.410 -19.772 -18.783 -17.899 -15.973 -14.048 28.311 -23.831 -28.775 -22.218 -18.419 -18.835 -15.973 -16.077 35 0.6154 0.1103 -0.1580 -0.2538 -0.3346 -0.2798 -0.2545 -0.1532 0.6599 0.1466 -0.1587 -0.2641 -0.2737 -0.2983 -0.2545 -0.1512 35 0.2314 0.0482 -0.0930 -0.1500 -0.1854 -0.1441 -0.1071 -0.0142 0.2494 0.0670 -0.0904 -0.1558 -0.1556 -0.1587 -0.1160 -0.0186 35 0.1036 -0.0099 -0.1045 -0.1498 -0.1739 -0.1377 -0.1000 -0.0150 0.1275 0.0058 -0.1082 -0.1536 -0.1515 -0.1486 -0.1056 -0.0206 35 0.0653 -0.0310 -0.1096 -0.1496 -0.1721 -0.1353 -0.0966 -0.0159 0.0916 -0.0162 -0.1157 -0.1537 -0.1508 -0.1466 -0.1037 -0.0217 35 0.0577 -0.0346 -0.1098 -0.1483 -0.1702 -0.1330 -0.0970 -0.0166 0.0802 -0.0200 -0.1165 -0.1527 -0.1497 -0.1442 -0.1019 -0.0223 35 0.0508 -0.0386 -0.1108 -0.1483 -0.1704 -0.1327 -0.0963 -0.0171 0.0708 -0.0242 -0.1174 -0.1528 -0.1492 -0.1445 -0.1027 -0.0226 35 0.0460 -0.0408 -0.1110 -0.1477 -0.1699 -0.1327 -0.0965 -0.0176 0.0637 -0.0274 -0.1182 -0.1523 -0.1493 -0.1443 -0.1019 -0.0230 35 0.0391 -0.0455 -0.1129 -0.1485 -0.1703 -0.1330 -0.0959 -0.0182 0.0564 -0.0319 -0.1209 -0.1532 -0.1502 -0.1444 -0.1023 -0.0245 35 0.0327 -0.0488 -0.1148 -0.1490 -0.1705 -0.1327 -0.0965 -0.0186 0.0499 -0.0355 -0.1229 -0.1540 -0.1503 -0.1448 -0.1024 -0.0242

181

cpr @ x/L where Φ = 135° Run 0.020 0.137 0.255 0.373 0.490 0.608 0.725 0.843 34 19.976 -17.110 -20.923 -17.996 -17.110 -13.375 -13.722 -13.375 34 1.1660 0.0871 -0.4347 -0.6063 -0.6247 -0.5552 -0.5793 -0.5666 34 0.8240 0.1337 -0.2276 -0.3700 -0.4169 -0.3637 -0.3943 -0.3448 34 0.5361 0.1179 -0.1288 -0.2485 -0.2891 -0.2613 -0.2585 -0.1967 34 0.4206 0.1021 -0.0968 -0.2027 -0.2336 -0.2055 -0.1949 -0.1273 34 0.3117 0.0824 -0.0746 -0.1651 -0.1882 -0.1631 -0.1469 -0.0748 34 0.2255 0.0491 -0.0754 -0.1541 -0.1707 -0.1463 -0.1228 -0.0477 34 0.1757 0.0235 -0.0837 -0.1539 -0.1673 -0.1461 -0.1201 -0.0471 34 0.1464 0.0077 -0.0856 -0.1529 -0.1635 -0.1418 -0.1153 -0.0445 34 0.1220 -0.0036 -0.0894 -0.1535 -0.1616 -0.1415 -0.1145 -0.0436 35 29.040 -20.448 -26.225 -22.218 -17.638 -13.579 -16.441 -15.505 35 0.7037 0.1958 -0.0950 -0.2292 -0.2709 -0.2306 -0.2477 -0.1847 35 0.2825 0.0899 -0.0529 -0.1418 -0.1580 -0.1322 -0.1176 -0.0376 35 0.1623 0.0219 -0.0749 -0.1449 -0.1545 -0.1309 -0.1080 -0.0354 35 0.1203 -0.0021 -0.0840 -0.1471 -0.1541 -0.1323 -0.1073 -0.0358 35 0.1167 -0.0065 -0.0852 -0.1476 -0.1530 -0.1318 -0.1058 -0.0344 35 0.1081 -0.0106 -0.0863 -0.1483 -0.1525 -0.1311 -0.1060 -0.0346 35 0.1012 -0.0140 -0.0886 -0.1490 -0.1531 -0.1319 -0.1055 -0.0350 35 0.0926 -0.0188 -0.0905 -0.1502 -0.1533 -0.1325 -0.1064 -0.0360 35 0.0865 -0.0229 -0.0922 -0.1511 -0.1530 -0.1335 -0.1074 -0.0362

182

South Side Wall cpr @ l' Run 0.051 0.139 0.228 0.316 0.360 0.404 0.448 0.492 0.536 0.580 0.624 0.668 0.714 0.809 0.905 1.000 34 -4.4018 -4.2478 -5.1336 -4.7870 -4.4018 -3.1695 -4.7870 -4.8255 - -5.0950 -3.6701 -3.2465 -5.9038 -4.0553 -5.1336 -4.4789 34 -0.1455 -0.1114 -0.1455 -0.1582 -0.1455 -0.0987 -0.1455 -0.1611 - -0.1568 -0.0916 -0.0902 -0.2008 -0.1185 -0.1596 -0.1497 34 -0.0853 -0.0726 -0.0853 -0.0853 -0.0853 -0.0645 -0.0943 -0.0871 - -0.1015 -0.0681 -0.0582 -0.1366 -0.0771 -0.1195 -0.1213 34 -0.0519 -0.0386 -0.0469 -0.0625 -0.0569 -0.0441 -0.0625 -0.0581 - -0.0614 -0.0414 -0.0352 -0.0787 -0.0569 -0.0781 -0.0892 34 -0.0328 -0.0267 -0.0365 -0.0442 -0.0479 -0.0344 -0.0515 -0.0446 - -0.0511 -0.0287 -0.0279 -0.0633 -0.0552 -0.0629 -0.0788 34 -0.0073 -0.0056 -0.0098 -0.0151 -0.0229 -0.0162 -0.0307 -0.0257 - -0.0173 -0.0173 -0.0145 -0.0257 -0.0332 -0.0436 -0.0517 34 -0.0026 0.0037 -0.0008 -0.0112 -0.0164 -0.0105 -0.0216 -0.0166 - -0.0162 -0.0146 -0.0108 -0.0235 -0.0285 -0.0373 -0.0546 34 -0.0043 0.0042 -0.0018 -0.0147 -0.0186 -0.0170 -0.0277 -0.0200 - -0.0197 -0.0172 -0.0146 -0.0316 -0.0368 -0.0407 -0.0586 34 -0.0031 0.0058 -0.0020 -0.0145 -0.0187 -0.0164 -0.0280 -0.0198 - -0.0228 -0.0176 -0.0144 -0.0321 -0.0384 -0.0415 -0.0589 34 -0.0049 0.0049 -0.0040 -0.0153 -0.0204 -0.0198 -0.0300 -0.0204 - -0.0240 -0.0196 -0.0179 -0.0350 -0.0430 -0.0438 -0.0598 35 -0.4658 -0.2576 -0.9862 -0.5178 0.0026 1.1995 -0.5178 -0.1015 -5.3053 0.0546 0.9913 0.1067 -1.5586 1.4596 -0.9862 0.8352 35 -0.0321 -0.0095 -0.0321 -0.0451 -0.0382 -0.0225 -0.0451 -0.0328 -0.1081 -0.0567 -0.0191 -0.0054 -0.0903 -0.0444 -0.0642 -0.0779 35 -0.0093 0.0006 -0.0093 -0.0158 -0.0179 -0.0130 -0.0245 -0.0182 -0.0376 -0.0266 -0.0156 -0.0090 -0.0442 -0.0355 -0.0463 -0.0616 35 -0.0020 0.0082 -0.0020 -0.0128 -0.0160 -0.0150 -0.0258 -0.0172 -0.0225 -0.0225 -0.0150 -0.0128 -0.0332 -0.0377 -0.0399 -0.0578 35 -0.0024 0.0084 -0.0009 -0.0123 -0.0176 -0.0188 -0.0276 -0.0176 -0.0170 -0.0231 -0.0170 -0.0148 -0.0350 -0.0422 -0.0428 -0.0606 35 -0.0006 0.0103 0.0015 -0.0115 -0.0163 -0.0181 -0.0285 -0.0168 -0.0144 -0.0212 -0.0164 -0.0144 -0.0324 -0.0409 -0.0422 -0.0593 35 -0.0008 0.0103 0.0005 -0.0113 -0.0162 -0.0186 -0.0292 -0.0179 -0.0126 -0.0214 -0.0170 -0.0140 -0.0320 -0.0411 -0.0428 -0.0595 35 -0.0007 0.0113 0.0004 -0.0117 -0.0163 -0.0186 -0.0278 -0.0166 -0.0118 -0.0205 -0.0158 -0.0137 -0.0315 -0.0406 -0.0416 -0.0593 35 0.0015 0.0128 0.0026 -0.0094 -0.0145 -0.0177 -0.0280 -0.0159 -0.0074 -0.0173 -0.0146 -0.0132 -0.0271 -0.0395 -0.0404 -0.0568 35 0.0012 0.0124 0.0012 -0.0115 -0.0158 -0.0193 -0.0294 -0.0169 -0.0084 -0.0188 -0.0154 -0.0141 -0.0291 -0.0413 -0.0417 -0.0589

183