Changes in Propeller Performance Due to Ground and Partial

CHANGES IN PROPELLER PERFORMANCE DUE TO GROUND AND PARTIAL

GROUND PROXIMITY

Thesis

Submitted to

The School of Engineering of the

UNIVERSITY OF DAYTON

In Partial Fulfillment of the Requirements for

The Degree of

Master of Science in Aerospace Engineering

Jielong Cai

University of Dayton

Dayton, Ohio

May 2020

CHANGES IN PROPELLER PERFORMANCE DUE TO GROUND AND PARTIAL

GROUND PROXIMITY

Name: Cai, Jielong

APPROVED BY:

Sidaard Gunasekaran, Ph.D. Aaron Altman, Ph.D. Advisory Committee Chairman Committee Member Assistant Professor Tech Advisor Mechanical and Aerospace Engineering Air Force Research Laboratory

Markus Rumpfkeil, Ph.D. Committee Member Associate Professor, Director, Aerospace Program Mechanical and Aerospace Engineering

Robert J. Wilkens, Ph.D., P.E. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean for Research and Innovation Dean, School of Engineering Professor School of Engineering

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Jielong Cai

2020

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ABSTRACT

CHANGES IN PROPELLER PERFORMANCE DUE TO GROUND AND PARTIAL

GROUND PROXIMITY

Name: Cai, Jielong University of Dayton

Advisor: Dr. Sidaard Gunasekaran

With the increased usage of propeller-driven unmanned-aerial-vehicles (UAV) in closed spaces such as caves, buildings, pipelines, etc. for photography, surveillance, and inspection, understanding the influence of the ground and ceiling on a remote-controlled (R/C) propeller is of the utmost importance. The flying characteristics of drones changes when an object or a ground plane is in its close proximity due to changes in its propeller performance. The changes in performance are due to the changes in the flow field around the propeller that occur due to ground proximity, which is also known as ground effect.

Ground effect on lifting rotor performance has been studied theoretically and experimentally for decades. Historically, most investigations focus on helicopter rotors, which have high aspect ratio, lower pitch and rarely have spanwise twist. This research focuses on smaller size rotors, in particular, the thin-electric propeller which is used widely on small UAVs. The research considers parameter variations not broadly available in the literature such as propeller pitch, diameter, solidity, and blockage. In particular, extreme ground effect is considered, where the ratio of ground plane stand-off distance to propeller diameter is 0.1 or less. Moreover, the propeller is reversed, to examine the ceiling effect.

Typically, the ground effect investigation is done with a ground plane that is big enough to be considered an infinite plane. In this research, both infinite plane and circular plates of similar diameter (or less) of the propeller are used as ground planes. Various circular plates with different diameter to propeller diameter ratios are used in the research representing different ‘blockage

iv5 ratios’. The investigation gives insight into changes in propeller performance in proximity to fuselages of a given diameter in propeller-driven airplanes under pusher and puller configurations.

All experiments were conducted on a thrust-stand built in-house at the University of

Dayton Low-Speed Wind Tunnel (UD-LSWT) Laboratory. All propellers used in the experiment are from the “thin electric” APC series, with diameter ranging from 11 inches to 17 inches and pitch from 4.5 inches to 14 inches. The propeller peak Reynolds number varies from 90,000 to

190,000 in the experiment. Circular plates with diameter ratio from 0.5 to 1.0 are used in the blockage effect experiment. Force, torque and RPM propeller data are taken during the experiment from a propeller diameter normalized ground distance of -1.5 to 1.5.

Results from the infinite ground experiment are separated into three major sections: thrust coefficient and power coefficient, power required at constant thrust, and effective thrust. A significant increment in the thrust coefficient and decrement in the power coefficient is found in ground proximity among the propellers with a pitch-to-diameter ratio less than 0.7. This results in a decrement of power required at constant thrust in ground effect. Almost identical changes in the power required at constant thrust in the ceiling effect is also found in most of the low pitch to diameter ratio propellers.

For the blockage experiment, a less significant reduction in the power required in constant thrust for all propellers is found at lower blockage ratios as expected. Similar trends in the effect on? thrust for different propellers at the same blockage ratio are found. Results for the positive h/D region (the puller configuration), overlap regardless of the propeller pitch to diameter ratio or solidity.

A phenomenological expression (an algebraic equation) for power required at constant thrust as a function of propeller parameter is established during the research to predict the changes in the propeller performance in ground effect which will benefit the operation of small UAVs in both open and confined areas.

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ACKNOWLEDGMENTS

It has been a journey of two years for me to complete this thesis topic, and I definitely could not have finished this thesis without help from my family, friends, professor and the community of the University of Dayton.

I would like to thank my parents and my grandfather for supporting my master's degree and always encouraging me to try different things and be brave. My wife, Naihui, who always helps me regain confidence whenever I have a hard time. Dr. Sidaard Gunasekaran, as my advisor and a friend, who brought me into the field of aerospace engineering, and guided me through the thesis and projects that I have been involved in during the past three years.

I would also like to thank Dr. Michael OL and Dr. Anwar Ahmed for their advice, both technical and personal and unconditional help throughout the thesis. I would also like to thank

Michael Mongin for taking pictures and videos of the experiment as well as Neal Novotny, Thomas

Campbell and Scott Chriss for helping me with data acquisition for a few cases. I also give my special thanks to Kevin Pierson, the manager of Makerspace at UD for helping me make some of the parts used in the experiment and all the professors in the Mechanical and Aerospace

Engineering department at the University of Dayton for educating and guiding me through my master's degree.

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TABLE OF CONTENTS

ABSTRACT……………………………………………………………………………………….iv

ACKNOWLEDGMENTS……………………………………………………………………...... vi

LIST OF FIGURES………..………………………………………..………………………...…...x

LIST OF TABLES..……………………………………………………………………………...xiii

NOMENCLATURE……………………………..………………………………………….…...xiv

CHAPTER I INTRODUCTION AND MOTIVATION………………………………………..1

1.1 Motivation ...... 1

1.2 Ground Effect on Large Rotor ...... 2

1.3 Ground Effect and Ceiling Effect on Propeller Driven Drones ...... 5

1.4 Partial Ground Effect and Blockage Effect on Propellers ...... 7

1.5 Overarching Research Objectives ...... 9

CHAPTER II THEORETICAL BACKGROUND……………………………………………..11

2.1 The Conservation Laws for Rotor in Fixed Location ...... 11

2.2 Blade Element Theory ...... 13

2.3 Betz Ground Effect Theoretical Model ...... 15

2.4 Cheeseman and Bennett’s Ground Effect Theoretical Model ...... 17

2.5 Hayden’s Experimental Ground Effect Model ...... 19

2.6 He and Leang’s Ground Effect Model ...... 20

2.7 Drawbacks in the Existing Models ...... 21

CHAPTER III EXPERIMENTAL TEST SETUP………………………………………………24

3.1 Propeller Ground Effect Experiment Setup ...... 24

3.2 Propeller Partial Ground Effect Experimental Setup...... 27

3.3 Post Processing of Data Collected ...... 29

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3.4 Flow Visualization ...... 31

3.5 Unsteady Pressure Transducer Measurement ...... 32

CHAPTER IV RESULTS: INFINITE GROUND EFFECT ON PROPELLER

PERFORMANCE………………………………………………………………………..33

4.1 Comparison of the Propeller Thrust and Torque Result in OGE Condition ...... 33

4.2 Changes in Propeller Thrust and Power Coefficient in Traditional Ground Effect ...... 35

4.3 Calculation of Power Required at Constant Thrust ...... 38

4.4 Propeller Parameter Study in Traditional Ground Effect ...... 40

4.4.1 Effect of Propeller Pitch ...... 40

4.4.2 Effect of Propeller Diameter ...... 43

4.4.3 Effect of Propeller Pitch to Diameter Ratio ...... 45

4.4.4 Effect of Propeller Solidity...... 46

4.5 Flow Visualization ...... 48

4.5.1 Surface Tuft Flow Visualization...... 49

4.5.2 Smoke Flow Visualization ...... 52

CHAPTER V RESULTS: PARTIAL GROUND EFFECT ON PROPELLER

PERFORMANCE………………………………………………………………………..54

5.1 Power Required at Constant Thrust ...... 54

5.2 Propeller Effective Thrust at Different Blockage...... 57

5.3 Partial Ground Effect Flow Visualization ...... 60

5.4 Unsteady Pressure Transducer Measurement ...... 62

CHAPTER VI PREDICTION OF PROPELLER GROUND AND PARTIAL GROUND

EFFECT………………………………………………………………………………….64

6.1 Phenomenological Expression and Prediction for Traditional Ground Effect ...... 64

6.2 Phenomenological Expression and Prediction for Partial Ground Effect ...... 70

CHAPTER VII CONCLUSIONS AND FUTURE WORK……………………………………...73

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7.1 Conclusions ...... 73

7.2 Future Work ...... 75

REFERENCES ...... 76

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LIST OF FIGURES

Figure 1. Propeller driven UAVs for pesticide spray (left) and cave inspections (right)...... 1

Figure 2. Propeller wake out of ground effect (left) and in ground effect (right) ……………...….2

Figure 3. Ratio of in-ground-effect (IGE) to out-of-ground- effect (OGE) power-required at

constant thrust, vs. h/D from literature…………………………………………………....3

Figure 4. Ratio of in-ground-effect (IGE) to out-of-ground- effect (OGE) thrust at constant

RPM, vs. h/D from literature……………………………………………………….……..4

Figure 5. Knight and Heffner [5] data for normalized power ratio vs. h/D for various blade pitch

angles…………………………………………………………………………………..….5

Figure 6. Example of helicopter blade (left) and propeller blade (right)………………………..…6

Figure 7. Example for a drone in ceiling effect……………………………………………………7

Figure 8. Reduction in power and thrust coefficient v.s blockage ratio………………………..….8

Figure 9. Example of Propeller Flow Field…………………………………………………...….11

Figure 10. Example of a blade element…………………………………………………………...14

Figure 11. Example of the propeller at small distance to the ground………………………….…15

Figure 12. Normalized power required at constant thrust for Betz’s model………………….…..17

Figure 13. Example of image source propeller…………………………………………………...18

Figure 14. Comparison of Cheeseman and Bennett model with Knight’s experimental result…..19

Figure 15. APC 11x7 propeller (upper) and APC 11x7C propeller (lower)……………………...24

Figure 16. Schematic of the experimental setup for the preliminary study……………………....25

Figure 17. Schematic (side view) of thrust stand and ground-plane……………………………...26

Figure 18. Photographs of thrust-stand (left) and propeller/motor/fairing (right)………………..27

Figure 19. Schematic (side view) of thrust stand and circular ground-plane…………………….28

Figure 20. Photograph (side view) of thrust stand and circular ground-plane…………………....28

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Figure 21. FFT Plot for APC 17x7 propeller thrust data under 5,700 RPM…………………...…29

Figure 22. Propeller thrust (left) and torque (right) before and after filtration…………………...30

Figure 23. Averaged force measurement of 1 kg check load in 10 minutes……………………...31

Figure 24. Placement of the Kulite pressure transducer on ground plate……………………..….32

Figure 25. Comparison of Thrust Coefficient for APC 17x7 Propeller…………………………..34

Figure 26. Ratio of IGE to OGE thrust coefficient for 11x5.5 propeller, at various test-RPM…..35

Figure 27. Ratio of IGE to OGE power coefficient for 11x5.5 propeller, at various test-RPM….36

Figure 28. Example of calculating power required at constant thrust (T=6N)…………………...39

Figure 29. Power required at constant thrust for APC 14x6 propeller…………………………...39

Figure 30. Normalized power required at constant thrust, for a selection of propellers………….41

Figure 31. Ratio of IGE to OGE thrust coefficient for the cases of Figure 30…………………...41

Figure 32. Ratio of IGE to OGE power coefficient for the cases of Figure 30…………………..42

Figure 33. Normalized power required for constant thrust, for propellers with same pitch….…..43

Figure 34. The ratio of IGE to OGE thrust coefficient for the cases of Figure 33……………….44

Figure 35. Normalized Power Required for Constant Thrust, for various propeller pitch to

diameter ratios……………………………………………………………………………45

Figure 36. Normalized Power Required for Constant Thrust, with respect to propeller pitch to

diameter ratio, at several different h/D values………………………...………………....46

Figure 37. Normalized Power Required for Constant Thrust, for higher and lower solidity…….47

Figure 38. Normalized thrust coefficient, for higher and lower solidity………………………....47

Figure 39. Surface tuft flow visualization for APC 17x7 at h/D = 0.3 for the traditional ground effect experiment...... ……………………………………………………...…………49

Figure 40. Side view sketch for propeller flowfield in ground effect………………………….…50

Figure 41. Normalized stagnation streamline diameter v.s h/D……………………………….….50

Figure 42. Tuft flow visualization for APC 17x7 (upper) and 17x12 (lower) at each h/D……….51

Figure 43. Smoke flow visualization on 17x7 (upper) and 17x12 (lower) propellers……………52

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Figure 44. Example of different blockage ratios………………………………………………….54

Figure 45a. Normalized power required at constant thrust in partial ground effect 17x7……..…55

Figure 46a: Normalized thrust coefficient for APC 17x7 in partial ground effect……..………...57

Figure 47: Normalized plate drag for different blockage ratio…………………………………..58

Figure 48. Normalized Effective Thrust at Different Blockage…………………………………..59

Figure 49. Tuft flow visualization of near-surface flowfield on the ground……………………...61

Figure 50. Ratio of diameter of stagnation streamline, to propeller diameter……………………62

Figure 51. Pressure data vs. propeller radial station, B = 1.0, for 17x12 and 17x7 propeller…...63

Figure 52. 푷풅풆풇풔 corrected by solidity difference…………………………………....…………...65

Figure 53. Power required at constant thrust in ground effect for all propellers tested…………..65

Figure 54a. Correction of normalized power required at constant thrust……………………..….66

Figure 55a. Comparison of predicted changes in 푷푰푮푬/푷푶푮푬 and experimental result…...……..68

Figure 56. Comparison of the prediction for APC 17x7 propeller……………………………….69

Figure 57. Power required deficit v.s blockage ratio at different h/D for APC 17x7…………….70

Figure 58a. Comparison of predicted changes in 푷푩 푰푮푬/푷푶푮푬 and experimental result………..72

13xii

LIST OF TABLES

Table 1. Propeller properties………...…………………………………………………..………..23

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NOMENCLATURE

퐴 = Propeller Disk area (푚2)

퐵 = Propeller Blockage Ratio

푇 퐶 = Propeller Thrust Coefficient; 퐶 = 푇 푇 휌푛2퐷4

푃 퐶 = Propeller Power Coefficient; 퐶 = 2휋 퐶 = 푃 푃 푄 휌푛3퐷5

푄 퐶 = Propeller Torque Coefficient; 퐶 = 푄 푄 휌푛2퐷5

퐷 = Propeller Diameter, (푚)

푑푝 = Ground-plate Diameter, (푚)

퐹퐷 푝 = Drag on Ground-Plate, (푁) h = Distance to the ground-plate, (푚) n = Propeller RPS

P = Power, (푊)

푃푑푒푓 = Power required deficit p = Pressure, (푃푎)

훾 = Propeller Pitch, (𝑖푛)

Q = Torque (푁푚)

S = Propeller Blade Projected Area (푚2)

T = Thrust, (푁)

Teff = Effective Thrust, (푁)

V = Velocity, (푚/푠)

휌 = Air Density, (푘𝑔/푚3)

푆 휎 = Propeller Solidity; 휎 = 0.25휋퐷2

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CHAPTER I

INTRODUCTION AND MOTIVATION

1.1 Motivation

Nowadays, the use of propeller-driven unmanned-aerial-vehicles (UAV) in open space and proximity to ground such as agricultural drones for pesticide spray, building inspections, and closed spaces such as pipeline, sewer, and cave inspections are very common (Figure 1). In these situations, the UAV is in close proximity to the ground and/or the ceiling of the closed spaces. Therefore, understanding the influence of the ground and ceiling on a remote-controlled R/C propeller, which most of these drones use is of utmost importance. The flying characteristics of the drone changes when an object is in close proximity to the ground due to changes in its propeller performance and the flowfield around the propeller. The changes in the propeller flowfield will also affect the operation of the drone, for example, the pesticide spray (shown in Figure 1) will have a very different drift characteristic which could cause some unexpected issues.

Figure 1. Propeller driven UAVs for pesticide spray (left) and cave inspections (right) [1]

One solution for the UAV safe operation in a closed area is to add a metal cage around the

UAV (shown in Figure 1). This will prevent the UAV from crashing into any surface including the ground, partial ground (such as rocks that stick out) and ceiling during operation. However, the cage is an inconvenience as it adds weight to the UAV, adds blockage to the propeller and interferes with the camera’s field of view.

Understanding the changes in the performance in the ground and partial ground proximity and constructing a control algorithm based on the physics of propeller operation in ground effect will provide a safer operation for the UAV in both open and closed space operations. Also, understanding the blockage effect on the propeller will provide a better design guideline for the propeller placement on the UAV which will increase the overall performance of the UAV.

1.2 Ground Effect on Large Rotors

Ground effect on lifting rotor performance has been studied theoretically and experimentally for decades. Placing the propulsor adjacent and parallel to a ground-plane will change the flow field of the propeller wake significantly. This can be seen in Figure 2 below in the flow visualization of a rotor disk out of ground effect (OGE) and in ground effect (IGE) done by

Fradenburgh [2]. In the OGE case, the tip-vortex of the rotor blade travels along with the propeller wake downward while in the IGE case, the tip-vortex and the propeller wake are deflected outward radially due to the proximity of the ground. Also, the core-flow region of the propeller wake is expanded due to the existence of the ground.

Tip-vortex h

Core-flow

Figure 2: Propeller wake out of ground effect (left) and in ground effect (right)

In general, the ground proximity offers two benefits to the propeller performance: an increase in thrust-produced, and a decrease in power-required, both for a given rotational speed.

One way of presenting the ground effect results which includes both changes in the thrust-produced and power-required is the normalized power required ratio 푃퐼퐺퐸/푃푂퐺퐸 vs. h/D, at constant thrust. h/D is the ratio of the distance from the propeller reference-point above the ground, h (shown in

Figure 2 above), to the propeller diameter, D.

Experimental results from the literature (Zbrozek [3], Gilad, Chopra, and Rand [4], Knight and Heffner [5], and Tanner and Overmeyer [6]) indicates that the IGE thrust at any given RPM will be higher than OGE in the experiment. Correspondingly, the power-required will also be lower.

This phenomenon results in a reduction of the power required at constant thrust in ground effect.

For example, when approaching the ground for landing, the throttle setting has to be reduced for a rotorcraft, to keep thrust constant for a safe landing.

Experimental results from the literature are plotted in Figure 3 along with the theoretical model of Betz [7] and Cheeseman and Bennet [8]. The experimental model developed by Hayden

[9] is also shown below. At each h/D distance, the corresponding IGE value of power required in constant thrust (푃퐼퐺퐸), is normalized by the OGE power required in constant thrust (푃푂퐺퐸). Zbrozek studied rotor blades with no twist and constant pitch at 150 RPM. Gilad studied a rotor of 54 inches diameter with no twist at 70 RPM. Fradenburgh studied a rotor of 24 inches diameter with no twist at 5700 RPM. Tanner and Overmeyer tested a rotor of 133 inches diameter at 1150 RPM.

1.00

0.90

푃퐼퐺퐸 0.80 Betz 1937 푃 Tanner and Overmeyer 2015 푂퐺퐸 Knight 1941 (6 Deg Pitch) 0.70 Knight 1941 (10 Deg Pitch) Knight 1941 (14 Deg Pitch) Zbrozek 1947 0.60 Gilad 2011 Cheeseman & Bennett Hayden 1976 0.50 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 h/D

Figure 3: Ratio of in-ground-effect (IGE) to out-of-ground- effect (OGE) power-required at constant thrust, vs. h/D from literature All experimental results in Figure 3 appear to follow a general trend: reduction of

푃퐼퐺퐸/푃푂퐺퐸 with the decrement of h/D. Results from Zbrozek, Gilad, and Knight (6-degree pitch

3 blade) nearly overlap. All experimental results have a smoother drop-off of IGE power-required vs. h/D when compared to Betz’s theory, where the 푃퐼퐺퐸/푃푂퐺퐸 drops precipitously when h/D is less than 0.3. Cheeseman and Bennet slightly underpredicted the ground effect but predicts better than

Betz’s model. On the other hand, Hayden’s model, the model developed from experimental investigations seems to agree very well with the other experimental results.

An alternative presentation of the ground effect is to plot the ratio of IGE to OGE thrust, for a given RPM, vs. h/D. Experimental data from Fradenburgh [2] (Sikorsky S-60, 22m rotor, 5 blades, relatively “high” solidity), Hayden [9] (OH-6A, 8 m rotor, 4 blades, relatively “medium” solidity) and Law [10] (Bell-47 J-2, 11.3m rotor, 2 blades, relatively “low” solidity) are shown below in Figure 4.

1.6

High Solidity 1.5 Fradenburgh (S-60)

1.4 Hayden (OH-6A)

푇퐼퐺퐸 1.3 푇푂퐺퐸 Harold Law (Bell 47) 1.2

1.1 Low Solidity

1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 h/D

Figure 4: Ratio of in-ground-effect (IGE) to out-of-ground- effect (OGE) thrust at constant RPM, vs. h/D from literature

All rotors have an increment in thrust with the reduction of the value of h/D. Despite the difference between the fuselage layout and engine size and placement in helicopters, the difference between the thrust increment is considerable and suggests that a geometric or aerodynamic variable besides h/D is material, and are most likely are related to the solidity of the rotor.

In the experimental data of Knight and Hefner [5] (60 inch rotor, no twist and various pitch angles from 4 degrees to 14 degrees at 900 RPM) shown below in Figure 5, IGE power is seen to be affected by blade pitch angle. The pitch here is the geometric pitch angle of the blade, which is different from the pitch in the thin-electric propeller where the linear displacement per revolution is defined as pitch. The 4-degree and 6-degree cases have a reduction of 40% in power at constant thrust at lower h/D values. But the 8 and 10-degree cases have a reduction of 27% in power at constant thrust, and the 12 and 14-degree cases only have a 16% reduction in power at lower h/D value. The result suggests that the pitch of the rotor blade has a significant effect on the rotor in ground effect.

1.00

0.95

0.90

0.85

0.80 푃퐼퐺퐸 푃푂퐺퐸 0.75

0.70 4deg 6deg 8deg 0.65 10deg 12deg 14deg 0.60

0.55 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 h/D

Figure 5: Knight and Heffner [5] data for normalized power ratio vs. h/D for various blade pitch angles.

1.3 Ground Effect and Ceiling Effect on Propeller Driven Drones

Most of the literature mentioned in the last section focuses on the large rotor with low pitch and very low twist on the blade, which is very similar to helicopter blades (shown in Figure 6).

This is because the majority of the helicopters have a mechanism called collective pitch, which will change blade pitch angle from a small angle, which is usually used in the hovering or

5 takeoff/landing process, to a high angle in forward flight. However, R/C propellers do not have collective pitch mechanisms but are usually designed to have higher pitch and twist distribution

(shown in Figure 6) for better performance. The difference in the pitch and twist between the helicopter blade and propeller blade results in significantly different performance characteristics when in ground proximity.

Figure 6: Example of helicopter blade (left) and propeller blade (right) [11]

Moreover, the aspect ratio of helicopter blades is comparatively larger, leading to a higher blade diameter under same chord length, which makes the normalized distance between placement of the rotor blades and ground, h/D, relatively small. Most of the propeller-driven vertical takeoff and landing (VTOL) aircraft, like the V-22 Osprey, have a relatively smaller blade diameter and are placed far above the ground which results in a relatively high h/D. However, in multi-rotor drones (in Figure 1), large R/C propellers are used which results in a smaller h/D value when compared to helicopters. Therefore, ground proximity becomes a significant issue for modern drones, especially the ones operating near a ground plane. The thesis aims to investigate and quantify ground effect on R/C propellers religiously used on modern drones.

Another aspect that the small-scale drones face which the helicopters usually don’t, is the ceiling effect. As drones operate in enclosed spaces, like tunnels and caves, in close proximity to the ceiling is unavoidable. For ground effect, the pressure side of the propeller disk is in close proximity to the ground, while for the ceiling effect, the suction side of the propeller is in close proximity to the ground. This results in a very different propeller flowfield between the propeller

6 disk and ceiling. At the time this thesis is written, to the best of the author’s knowledge, there has been no reported investigation on the ceiling effect.

Figure 7 below shows an example for drones in ceiling effect, with the close proximity to the ceiling, the propeller performance changes drastically. The sudden gain in thrust at low h/D results in the uncontrollable crash of the drones into the ceiling. This type of phenomenon is not related to helicopter operation but will potentially interfere with day-to-day operations of the drone and may even result in catastrophic failure. Therefore, understanding the ceiling effect will benefit the operation of drones in closed spaces, and fill the knowledge gap of the rotor disk in the ceiling effect.

Figure 7: Example for a drone in ceiling effect

1.4 Partial Ground Effect and Blockage Effect on Propellers

Different from the ground effect study which uses an ‘infinite’ ground-plate, where the diameter ratio of the ground-plane to the propeller was large, the partial ground effect study primarily focuses on the “finite” ground effect by using circular plates of different diameters and two different types of blockages: core flow blockage and radial flow blockage. This type of ground effect occurs when there is an uneven or corrugated ground plane such as caves, buildings, etc.

Such operational conditions are very rare for helicopters.

Moreover, this “blockage” type study gives insight into changes in the overall propeller performance, especially thrust production, with proximity to fuselages for propeller-driven drones in pusher and puller configurations. Modern drones usually place the propeller very close to the

7 drone body or motor support arm, which affects the performance of the propeller. This study hopes to provide better design guidelines for propeller placement on drones leading to higher propeller performance.

Studies on the propeller-fuselage blockage effect have been done on both large-scale propellers and R/C size propellers at different advance ratios. The experiment done by Weick

[12,13] on a large-scale propeller suggests that the maximum propeller efficiency increases by 1% with a 3% reduction of blockage ratio in the range from 0.35 to 0.42. A decrement of 4% in the maximum efficiency was found with a smaller propeller-fuselage distance for a 10’5’’ propeller.

Verstraete and MacNeill’s [14] experimental result for an R/C-sized propeller indicates that with an increase in blockage ratio (퐵 = 푑푃/퐷 , where 푑푝 is the plate diameter and 퐷 is the propeller diameter), the thrust and power coefficient decreases when compared to OGE conditions, as shown in Figure 8.

45%

40% Thrust Coefficient 35% Power Coefficient 30%

25%

20%

15%

Reduction Coefficient Reduction in 10%

0% 0.45 0.50 0.55 0.60 0.65 0.70 Blockage Ratio

Figure 8: Reduction in power and thrust coefficient vs. blockage ratio [14]

The majority of the literature primarily discusses the effect of different blockage size, while the placement and the configuration of the propeller are rarely investigated. These are also very

8 important parameters that will affect the propeller performance in blockage and these parameters were investigated in this research.

1.5 Accomplished Research Objectives

The overarching research objectives are to investigate and predict the changes in the propeller performance, specifically, the power required at constant thrust and the thrust generated at constant power by the propeller, in proximity to an ‘infinite’ ground plate and in proximity to a finite ground plate with different blockage ratios. Force and torque based experiments were relied upon as the primary method of investigation, in conjunction with different methods of flow visualization to better understand the flow physics occurring between the propeller and the infinite and finite ground plane.

The performance changes in R/C propellers in proximity to the ground were investigated as a function of the propeller geometry. Flow visualization results indicate strong relationships between ground effect and the propeller flowfield. The comparison of the infinite ground and partial ground clarifies the boundary between the partial ground and infinite ground, as to what point the finite ground plate can be considered to approach ‘infinite’ behavior. The effective thrust of the propeller was also determined for the cases with finite ground plate under different blockage ratios in an effort to inform the effects of fuselage blockage on propeller performance.

With the analysis of the changes in the propeller performance in ground proximity, an algebraic equation for power required at constant thrust as a function of propeller geometry (pitch, diameter, solidity) was developed to predict the propeller performance in proximity to the ground.

Different blockage ratios are then involved in the algebraic equation to account for the changes in partial ground effect. This will benefit the operation and design of UAVs using R/C propellers, with a closed-loop, feed-forward control system developed based on the algebraic equation. The power output of the propeller will change accordingly when approaching the ground and ceiling in closed spaces thereby avoiding an unexpected crash of the UAV.

The publications and presentations involved in author’s thesis work are listed below:

Publications:

1.Cai, J., Gunasekaran, S., Ahmed, A., and OL, M., V., "Changes in Propeller Performance Due to

Ground Proximity", AIAA SciTech 2019 Forum, AIAA 2019-1097.

2. Cai, J., Gunasekaran, S., Ahmed, A., and OL, M., V., "Propeller Partial Ground Effect", AIAA

SciTech 2020 Forum, AIAA 2020-1028.

Journal Draft in Review:

1.Cai, J., Gunasekaran, S., Ahmed, A., and OL, M., V., "Changes in Propeller Performance Due to

Ground Proximity", Journal of Aircraft.

Presentations:

1. “Changes in Propeller Performance due to Ground Proximity”, 2018 Annual Dayton Engineering

Sciences Symposium, October, 2018, Dayton, Ohio.

2. “Changes in Propeller Performance due to Ground Proximity”, 2019 AIAA Aerospace Science

Symposium (SciTech), January 2019, San Diego, California.

3. “Changes in Propeller Performance due to Ground Proximity”, 2019 AIAA Dayton-Cincinnati

Aerospace Sciences Symposium, March 2019, Dayton, Ohio.

4. “Propeller Partial Ground Effect”, 2019 Annual Dayton Engineering Sciences Symposium,

October, 2019, Dayton, Ohio.

5. “Propeller Partial Ground Effect”, 2020 AIAA Aerospace Science Symposium (SciTech),

January 2020, Orlando, Florida.

6. “Propeller Partial Ground Effect”, 2020 AIAA Dayton-Cincinnati Aerospace Sciences

Symposium, March 2020, Dayton, Ohio.

CHAPTER II

THEORETICAL BACKGROUND

In this chapter, the governing equations for rotors and three different models for ground effect will be introduced. This includes two theoretical models and one experimental model for large rotorcraft, and one combination theoretical and experimental model for non-twisted propellers.

2.1 The Conservation Laws for Rotor in Fixed Location

Let’s consider a simplified 2D propeller flowfield shown in Figure 9 below. The propeller is fixed at a certain location, which is similar to a helicopter in its hovering condition. The dashed lines represent the control volume. The incoming flow from an infinitely long distance has a velocity of zero, which results in an infinite area of the control volume boundary. The propeller is driving the flow from left to right which results in the thrust of the propeller aiming toward left. 퐴 stands for the propeller disk area, 푉 is the local velocity of the flow while 푑푆 is the unit normal area vector which always points outward from the control volume. 휌 is the density of the fluid.

−∞ 푑푆 V +∞ _ 퐴 Flow

+∞ Thrust y

−∞ x Figure 9: Example of Propeller Flow Field

Starting with the governing equation for fluid flow, assuming the flow is 1D, incompressible, inviscid and quasi-steady, the simplified conservation of mass equation can be written as:

∬ 휌푉⃗ . 푑푆 = 0 ( 2.1 )

While the simplified conservation of x-momentum equation can be written as:

∬ 푝 푑푆 + ∬(휌푉⃗ 푑푆 ). 푉⃗ = 퐹 ( 2.2 )

퐹 is then the net force acting on the fluid. Also, the simplified conservation of energy equation can be written as:

1 2 ∬( 휌푉⃗ . 푑푆 )|푉⃗ | = 푃 ( 2.3 ) 2

Where P is the work done on the fluid. Now, assuming the flow velocity coming into the control volume is negligible, and the ambient pressure holds constant, based on Equation 2.2, the thrust generated by the propeller can be written as:

⃗⃗⃗⃗ 푇 = ∬(휌푉⃗ 푑푆) . 푉⃗ = 푚̇ 푉푝푟표푝 ( 2.4a )

Where 푚̇ is the mass flow rate of the fluid and 푉푝푟표푝 is the local fluid velocity at the propeller. One thing to notice is that, assuming the pressure holds constant can only be applied to the OGE condition. For IGE condition, due to the presence of the ground plane, the assumption does not hold anymore. Next, from Equation 2.3 and 2.4a, the power required to generate the thrust can be written as:

1 2 1 푃 = 푇푉 = ∬( 휌푉⃗ . 푑푆 )|푉⃗ | = 푚̇ 푉2 ( 2.4b ) 푝푟표푝 2 2 ∞

Where 푉∞ is the fluid flow velocity of the far wake. Equation 2.4 is the foundation of the Betz’s ground effect model. Moreover, based on Equation 2.4 a and b, it is easy to see that the relation between the 푉푝푟표푝 and 푉∞ can be written as:

1 푉 = 푉 ( 2.5a ) 푝푟표푝 2 ∞

Based on the conservation of mass in Equation 2.1, the far wake disk area can be calculated as:

1 퐴 = 퐴 ( 2.5b ) ∞ 2 푝푟표푝

This indicates that the far wake disk area is the half of the propeller disk area, while the propeller

1 wake area between the propeller disk and far wake will fall between: 퐴 < 퐴 < 퐴 . 2 푝푟표푝 푤푎푘푒 푝푟표푝

This implies that a ground plate with 푑푝 ≤ 퐷 could be sufficient as an ‘infinite’ ground for propeller ground effect. This hypothesis is tested and discussed in this thesis.

For the non-dimensional coefficient, based on the Buckingham Π theorem and dimensional analysis [15]. The thrust, torque and power coefficients can be written as:

푇 푇 푇 퐶푇 = = 2 2 = 2 4 ( 2.6a ) 휌퐴푉푡𝑖푝 휌퐴휔 푅 휌푛 퐷

푄 푄 퐶 = = ( 2.6b ) 푄 휌퐴휔2푅3 휌푛2퐷5

푃 푃 퐶 = = = 2휋 퐶 ( 2.6c ) 푃 휌퐴휔3푅3 휌푛3퐷5 푄

Equation 2.6 will be used to calculate the thrust, torque and power coefficient in the later sections.

2.2 Blade Element Theory

The blade element theory (BET) is another method to analyze the rotor performance. In general this involves breaking a rotor blade into multiple small sections, or elements which is similar to Prandtl’s lifting line theory. Let’s assume a 2 bladed rotor with a symmetric airfoil, fixed pitch angle, no taper ratio and geometric twist and very high aspect ratio. Let’s take a 2D blade

푦 element, away from the root of the rotor with R being the radius of the rotor disk. This blade 푅 element sketch is shown below in Figure 10. The rotation of the blade element is towards the negative X-axis and the thrust is towards the positive Y-axis.

There are two major flow velocity components for a blade element, the out of plane flow component 푈푃, which is normal to the rotor disk, and the tangential flow component 푈푇. The blade geometry pitch at the element is equal to 휃, due to the velocity component 푈푃, an induced angle of attack 휙 occurs. Thus, the actual angle of attack 훼 is smaller than 휃, resulting in the lift force L and

13 drag force D, off the X and Z axis with an angle of 휙. The thrust generated by this element is then denoted 퐹푧 and the drag which contributes to the torque of the blade is denoted by 퐹푥.

Figure 10: Example of a blade element

The force acting on the X and Z axis can be calculated as:

퐹푧 = 퐿 푐표푠휙 − 퐷 푠𝑖푛휙 and 퐹푥 = 퐿 푠𝑖푛휙 + 퐷 푐표푠휙 ( 2.7 )

Using small-angle approximation, Equation 2.7 is simplified and the thrust and power of the rotor are described as:

푑푇 = 2 ∗ 푑퐿 and 푑푃 = 2 ∗ 휔(휙 푑퐿 + 푑퐷) 푦 ( 2.8 ) where 휔 is the angular velocity of the rotor. Assume the local lift coefficient of the blade element is 퐶퐿, using equation 2.6, the thrust coefficient of the blade can be rewritten as:

2 푑퐿 푦2 푦 푑퐶 = = 0.5 휎 퐶 푑 ( ) ( 2.9 ) 푇 휌퐴(휔푅)2 퐿 푅 푅

The lift coefficient of the blade element can also be written as:

퐶퐿 = 퐶퐿훼 푂(휃 − 휙 − 훼0) ( 2.10 ) where 퐶퐿훼 is the lift curve slope for the airfoil, which can be assumed as 2휋 from thin airfoil theory

[15], and 훼0 is the zero-lift angle of attack of the airfoil, which is equal to zero for the symmetric airfoil. Based on Equation 2.9, the thrust coefficient can be calculated as:

1 1 푦 2 푦 1 1 푦 2 푦 퐶푇 = 휎 ∫ 퐶퐿 ( ) 푑 ( ) = 휎퐶퐿훼 ∫ (휃 − 휙) ( ) 푑 ( ) ( 2.11 ) 2 0 푅 푅 2 0 푅 푅

Since the inflow velocity ratio 휆 can be written as:

푉 푉 푦 푦 휆 = 𝑖푛푑푢푐푒푑 = 𝑖푛푑푢푐푒푑 ( ) = 휙 ( ) ( 2.12 ) 휔푅 푉푇 푅 푅

Equation 2.11 can be written as:

1 1 푦 푦 2 푦 1 휃 휆 퐶푇 = 휎퐶퐿훼 ∫ (휃 − 휙/( )) ( ) 푑 ( ) = 휎퐶퐿훼 [ − ] ( 2.13 ) 2 0 푅 푅 푅 2 3 2

It is clear that the thrust coefficient based on BET is highly dependent on the rotor blade pitch and solidity based on the functional dependence of variable 휃 and 휎. Equation 2.13 is the foundation of the ground effect prediction model using BET in Section 2.4 and 2.6.

2.3 Betz Ground Effect Theoretical Model

Betz [7] developed the typical ground effect model in 1937. In Betz’s model, there are two different portions for the ground effect distance, the small distance, and the large distance.

Let’s consider the small distance first. Figure 11 below shows the 2D propeller flowfield at small distance to the ground. Again, assuming the flow is incompressible, inviscid and quasi- steady. D is the diameter of the propeller disk and h is the distance to the ground. The propeller slipstream boundary (the control volume) is marked blue. The average radial flow velocity underneath the propeller is noted as 푉표푢푡. At an infinite distance, the thickness of the outward radial flow is noted as ℎ𝑖푛푓 while the velocity of the radial flow is noted as 푉𝑖푛푓.

Figure 11: Example of the propeller at small distance to the ground

At very small distance to the ground, Betz assumes that a pressure is ‘built up’ between the propeller and the ground plane. Thus, the pressure acting on the ground is the same as the pressure

15 acting radially outward (toward the red dashed line in Figure 11). Now, the thrust of the propeller based on the pressure in this region can be calculated as:

1 퐷2 푇 = 휌푣푉2 휋 ( 2.14 ) 2 표푢표푡 4

According to the conservation of momentum, the radial flow velocity in Equation 2.14 can be written as:

2푇 푉 = √ ( 2.15 ) 표푢푡 휌퐴

The radial flow volume pre-unit time can then be calculated as:

1 ℎ 2푇 푉 ℎ ∗ 휋푑 = 2퐴√ ( 2.16 ) 2 표푢푡 푑 휌퐴

The power required to move the flow through the pressure built up region can be then calculated as:

푇 ℎ 2푇 ℎ 2푇 푃 = ∗ 2퐴√ = 2푇√ ( 2.17 ) 퐼퐺퐸 퐴 푑 휌퐴 푑 휌퐴

Compared to the power required to generate the same thrust out of ground effect below:

푇 푃 = 푇√ ( 2.18 ) 푂퐺퐸 2휌퐴

The normalized power required at constant thrust in ground effect at small distance can be written as:

푃 ℎ 퐼퐺퐸 = 4 ( 2.19 ) 푃푂퐺퐸 푑

While at large distance, Betz introduced an image propeller sink disk, 2h away from the propeller.

The induced velocity 푣𝑖 of the propeller due to the sink disk can be calculated as:

푇 푣 = 퐴√ /4휋(2ℎ)2 ( 2.20 ) 𝑖 2휌퐴

Thus, the total axial velocity of the propeller then becomes:

푇 퐴 푉 = √ (1 + ) ( 2.21 ) 푎푥𝑖푎푙 2휌퐴 16휋ℎ2

Due to the induced velocity, the power required at constant thrust will increase with the reduction of h/D distance. In equation, the normalized power required at constant thrust for large distance in ground effect can be written as:

−2 푃퐼퐺퐸 퐴 1 ℎ = 1 + 2 = 1 + ( ) ( 2.22 ) 푃푂퐺퐸 16휋ℎ 64 푑

With equation 2.19 and 2.22, the Betz ground effect theoretical model is plotted in Figure 12. The cross point of the curves in Figure 12 is called the Betz threshold, where the power required for the propeller to generate constant thrust reduces significantly.

1.40

1.20

1.00

0.80 푃퐼퐺퐸 푃푂퐺퐸 0.60

0.40 Small Distance 0.20 Large Distance Betz Threshold 0.00 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 h/D

Figure 12: Normalized power required at constant thrust for Betz’s model

2.4 Cheeseman and Bennett’s Ground Effect Theoretical Model

Cheeseman and Bennett [8] modified Betz’s model based on the experimental result. As seen in Figure 3 previously, Betz’s model does not agree with the experimental results found in the literature. The major difference is that most experimental results experience a smooth reduction in

푃퐼퐺퐸/푃푂퐺퐸 and the reduction occurs at a much higher h/D distance than 0.3. Also, no significant increment in 푃퐼퐺퐸/푃푂퐺퐸 in ground effect has been seen in any experimental result.

Cheeseman and Bennett believed that the image sink flow that Betz introduced should be modified into a source flow, where the ground is removed and replaced by another propeller moving the same amount of fluid towards the original propeller disk, the same distance from the original ground plane, like a ‘mirrored’ propeller. This concept is illustrated below in Figure 13.

Figure 13: Example of image source propeller

In this case, the induced velocity of the propeller due to the source flow is the same as shown in

Equation 2.22. However, the total axial flow velocity of the propeller becomes:

푇 퐴 푉 = √ (1 − ) ( 2.23 ) 푎푥𝑖푎푙 2휌퐴 16휋ℎ2

Thus, the normalized power required at constant thrust in ground effect becomes:

−2 푃퐼퐺퐸 퐴 1 ℎ = 1 + 2 = 1 − ( ) ( 2.24 ) 푃푂퐺퐸 16휋ℎ 64 푑

Equation 2.24 is plotted in Figure 3 in Section 1.2. As mentioned previously, this model does a better job predicting the rotor ground effect than Betz’s model.

Moreover, based on the blade element theory in Equation 2.13, Cheeseman and Bennett modified Equation 2.24 to account for the effect of the blade solidity and pitch, which affect the thrust coefficient for the blade. This is shown below in Equation 2.25.

푃 퐶 휆 1 ℎ −2 퐼퐺퐸 = 1 − 휎 퐿훼 𝑖 ∗ ( ) ( 2.25 ) 푃푂퐺퐸 4퐶푇 64 푑

Where:

푣 퐶 휆 = 𝑖 = √ 푇 ( 2.26 ) 𝑖 휔푅 2

Using this prediction model and comparing with the ground effect experimental result from

Knight [5], this is shown below in Figure 14a.

1.00 0.95 0.90 0.85

푃퐼퐺퐸 0.80 푃푂퐺퐸 0.75 0.70 Knight 6 Deg 0.65 Knight 8 Deg 0.60 0.55 Knight 12 Deg 0.50 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 h/D

Figure 14a. Comparison of Cheeseman’s model with Knight’s experimental result

The prediction model underpredicts the ground effect when compared to the experimental result from Knight. Moreover, the model is only validated when h/D is greater than 0.25 due to the occurrence of a singularity at h/D = 0.25. Thus, the extreme ground effect at small ℎ/퐷 is not predictable with this model. Also, the actual value of 휆 is very hard to obtain from the experiment, which limits the application of the prediction model.

2.5 Hayden’s Experimental Ground Effect Model

Hayden developed his ground effect model based on the experimental result from multiple helicopter flight tests. With a second order curve fit, the power required at constant thrust can be written as:

푃 1 퐼퐺퐸 = ( 2.27 ) 푃 ℎ 2 푂퐺퐸 퐴 + 퐵 ( ) 퐷

Where A = 0.9926 and B = 0.0379. Again, Equation 2.18 is plotted in Figure 3 in Section

1.2. The model has a pretty good prediction for the large rotor in ground effect and can be applied

ℎ to any value. However, it does not take parameters like pitch or solidity into account when 퐷 compared to Cheeseman and Bennett's model.

2.6 He and Leang’s Ground Effect Model

He and Leang [22] developed their ground effect prediction model based on BET and experimental results. According to the momentum theory [15], 휆 = √퐶푇∞/2 for the rotor in OGE hovering condition. Apply this to Equation 2.13 and written in terms of propeller pitch angle 휃 and solidity 휎, the OGE thrust coefficient can be written as:

퐶퐿훼 휎 64휃 + 3퐶퐿훼 휎 퐶푇 푂퐺퐸 = (32휃 + 3퐶퐿훼 휎 − 6퐶퐿훼 휎√ ( 2.28) 192 12퐶퐿훼 휎

For maximum possible ground effect, the induced velocity 푣𝑖 at the propeller disk should be equal to zero. Thus, the inflow ratio 휆 = 0. According to Equation 2.13, the maximum 퐶푇 퐼퐺퐸 can be written as:

1 휃 퐶 = 휎퐶 [ ] ( 2.29 ) 푇 퐼퐺퐸 푀푎푥 2 퐿훼 3

A coefficient 퐶푎 is then defined as:

2 퐶푇 퐼퐺퐸 푀푎푥 √192퐶퐿훼 휎휃 + 9퐶퐿훼 휎 − 3퐶퐿훼 휎 퐶푎 = − 1 = ( 2.30 ) 퐶 2 푇 푂퐺퐸 32휃 + 3퐶퐿훼 휎 − √192퐶퐿훼 휎휃 + 9퐶퐿훼 휎

Obviously, the coefficient 퐶푎 is related to the maximum ground effect thrust ratio, as a function of rotor disk pitch angle and solidity. To account for the change between maximum ground effect and

OGE, another coefficient 퐶푏 is introduced as a function of 휎. This coefficient represents the curvature of the 푃퐼퐺퐸/푃푂퐺퐸 and is obtained through the experimental data.

퐶푏 = 0.93휎 + 1.23 ( 2.31 )

Using Equation 2.21 and 2.22, the normalized power required at constant thrust can be calculated as:

푃퐼퐺퐸 1 = −퐶 ∗2ℎ/퐷 ( 2.32 ) 푃푂퐺퐸 퐶푎푒 푏 + 1

Again, comparing Equation 2.23 with the ground effect experimental result from Knight

[5] is plotted below in Figure 14b. Although the model is able to predict ground effect at small h/D, the model overpredicts the ground effect when compared to Knight’s result. Also, the model can only be applied to rotor blades with no twist, while the R/C propeller has a geometric twist along the span of the blade. It is safe to say that model that can be applied to the R/C propeller is in demand.

1.00 0.95 0.90 0.85 0.80 푃퐼퐺퐸 0.75 푃푂퐺퐸 0.70 Knight 6 Deg 0.65 Knight 8 Deg Knight 12 Deg 0.60 6 Deg Prediction He et al 0.55 8 Deg Prediction He et al 12 Deg Prediction He et al 0.50 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 h/D

Figure 14b. Comparison of He et al. model with Knight’s experimental result

2.7 Drawbacks in the Existing Models

As seen above, there are three major drawbacks for the existing models to be applied to

R/C propellers. First, most of the models are developed for larger rotors with almost no twist on the blade, while R/C propellers have a noticeable twist distribution along the span of the blade. To apply the same model on the R/C propeller is not quite appropriate. Second, some of the models have a singularity which limits the ability of the model to predict the IGE performance at small

ℎ/퐷. Third, none of the existing models have the ability to predict ceiling effect. The end goal of this thesis is to develop a ground effect and ceiling effect prediction model which can be applied to

R/C propellers in extreme ground effect.

CHAPTER III

EXPERIMENTAL TEST SETUP

All experiments were conducted on a thrust-stand at the University of Dayton Low-Speed

Wind Tunnel laboratory. Two different experimental setups have been used for different purposes: propeller ground effect study and propeller partial ground effect study (blockage effect). All propellers used in the experiment are from the “thin electric series” made by Advanced Precision

Composites (APC). The selection of the propeller is based on the evidence in the literature for their relatively high efficiency and good geometric repeatability across a broad range of diameters [16],

[17]. All propellers were driven by an E-Flite Power 60-400kV brushless out-runner electric motor and powered by a PSW 30-108 constant-voltage power supply.

The parameters of all propellers tested in the experiment are shown in Table 1. The propeller is named by its diameter and pitch. For example, 17x12 indicates the diameter of the propeller is 17 inches and the pitch of the propeller is 12 inches. The blade Reynolds number is calculated at 70% blade-span, for the peak RPM achieved for each given propeller.

Table 1. Propeller properties

Propeller Pitch (훾)/ Solidity (휎) Peak Rotational Peak Reynolds Diameter (D) Tip Speed (m/s) Number (x1000) 17x12 0.705 0.0718 124.6 145 17x10 0.588 0.0753 132.1 160 17x7 0.412 0.0846 142.0 190 14x7C 0.500 0.1080 119.9 185 14x14 1 0.0659 110.6 105 14x8.5 0.607 0.0744 117.9 108 14x7 0.500 0.0772 122.3 110 14x6 0.429 0.0808 122.9 109 11x7C 0.636 0.1359 96.3 155 11x12 1.091 0.0793 94.3 91 11x10 0.901 0.0798 97.8 94 11x7 0.636 0.0749 100.1 91 11x5.5 0.500 0.0896 102.1 92 11x4.5P 0.409 0.0967 101.8 89

The cases in Table 1 allow various parameter-combinations to elucidate trends. For 7” pitch, the three diameters (11”, 14” and 17”) comprise a study of the pitch of the propeller. While at least

3 different pitch propellers are studied for the same diameter, providing a study of the diameter of the propeller as well as the pitch to diameter ratio.

Variation in solidity beyond what is available from the APC catalog was achieved by machining a larger propeller down to a smaller diameter while preserving the pitch. This provides a higher solidity of the blades when compared to a standard APC propeller. The resulting “cut” cases are labeled “C” in Table 1. All derive from cutting what was initially the 17x7” propeller. A comparison of the APC 11x7 and APC 11x7C propeller is shown below in Figure 15.

Figure 15: APC 11x7 propeller (upper) and APC 11x7C propeller (lower)

The Pitch-to-diameter ratio of the propeller varies from 0.4 to 1.1, the solidity of the propeller varies from 0.07 to 0.14. The RPM-range of the propeller, with the lower bound restricted due to signal-to-noise considerations, and the upper bound limited by the power supply’s capacity, was 3000-6000, depending on propeller diameter. This results in the propeller blade Reynolds number variation from 90,000 to 190,000.

3.1 Propeller Ground Effect Experiment Setup

Prior to the final experimental setup, another experimental setup was used for preliminary study. This is shown in Figure 16 below. The propeller and motor are mounted vertically on an interface and then connected to the ATI Mini-40 F/T sensor at the bottom. The sensor is then mounted on a metal rod which can be translated along the vertical axis. Two 4x4 feet foam boards are used to simulate the ground, the foam boards are glued together with a cutout for the metal rod

24 in the center of the connection line. A laser pointer is mounted above the propeller disk, and the photodiode is placed underneath the foam board plate for the RPM measurement.

Figure 16. Schematic of the experimental setup for the preliminary study

Several issues were discovered during the preliminary study. Due to the diameter difference between the sensor and metal rod, a larger cutout in the foam board is required for the study of higher h/D values, though this will result in an air gap between the sensor/sensor interface and the foam board at small h/D. A significant amount of flow will go through the air gap and result in an imperfect ground condition. Also, a small hole cutout is required for the laser to go through the foam board which will also introduce errors in the force and torque measurement. Therefore, this setup was soon jettisoned and a more robust setup was put together as discussed below.

The schematic of the final propeller ground effect experimental setup is shown in Figure

17 below. The propeller and motor are attached horizontally to an ATI Industrial Automation Mini-

40 six-component force balance (www.ati-ia.com [18]). A vertical wall is then used as the ground plane, which will have no cutouts through it. Thrust is thus the axial-force along the balance axis of the sensor, and torque is a rotational moment about the balance axis of the Mini-40. The balance bolts to an aluminum-extrusion frame on the aluminum rail which is secured to the lab floor. The

25 force/torque balance has a maximum of 120 N force and resolution of 0.02 N on its Z-axis and maximum torque of 2 Nm and resolution of 1/4000 Nm about its Z-axis. The encountered peak thrust and torque were 40 N and 1.2 Nm, respectively. A laser pointer and photodiode are used to measure the propeller RPM once again.

F/T Transducer Mini-40

Figure 17. Schematic (side view) of thrust stand and ground-plane

The data sampling rate was 100 Hz, for a 15-second duration at each data-point, with two runs to improve data repeatability for each data point (value of RPM, propeller diameter /pitch

/type, and h/D value).

Photographs of the experimental setup are shown below in Figure 18. With the thrust-line oriented horizontally, a vertical wall acts as the ground, and different h/D is achieved by sliding the thrust-stand’s frame towards the wall. To attenuate the effect from the aluminum frame, the propeller-disk is more than one diameter behind any transverse members of the aluminum frame.

The 3D-printed plastic streamline-cowling covering the sensor is <3.3% of the propeller disk-area, for the case of the smallest propeller, to minimize the effect of sensor and fixture mount on the propeller performance.

Figure 18. Photographs of thrust-stand (left) and propeller/motor/fairing (right).

To achieve negative h/D to investigate the ceiling effect, the propeller is attached to the motor in a reverse sense on the motor shaft. The motor rotation direction is also reversed, achieved by exchanging two of the three wires between the motor and its electronic speed controller. The propeller orientation shown in Figure 18 is the experimental setup for the ceiling effect, where the airflow (pressure-side of the propeller) is away from the ground plane.

The dimensionless ground-offset distance in the ground effect investigation is from -1 h/D to +1 h/D, with larger h/D deemed to be sufficiently close to infinity. For very small h/D, there is an ambiguity in prescribing the distance between the ground and the propeller plane because of the curved geometry of the propeller. For propellers with high blade twist and taper, at small nominal value of h/D, the actual h/D will vary considerably along the blade span. To be consistent across all the cases, the midpoint of the propeller hub is used as a reference to measure the distance to the wall. For APC “thin electric” propellers, the hub is thicker (deeper), for larger values of blade pitch. This partially attenuates what would have been large proportional disparities in h/D between low-pitch and high-pitch propellers of the same diameter, for small h/D.

3.2 Propeller Partial Ground Effect Experimental Setup.

The schematic of the propeller partial ground effect experiment is shown in Figure 19 below, with a photograph of the experimental setup following. Similar to the ground effect

27 experiment, the motor and propeller are attached to an ATI Industrial Automation Mini-40 six- component force balance (inside the plastic shroud shown in the left half of Figure 20; www.ati- ia.com [19]). The balance bolts to an aluminum-extrusion frame on the aluminum rail which is secured to the lab floor. The data sampling rate was 100 Hz, for a 15-second duration at each data- point, with two runs to improve data repeatability for each data point.

F/T Transducer Mini-40

Figure 19. Schematic (side view) of thrust stand and circular ground-plane

Figure 20. Photograph (side view) of thrust stand and circular ground-plane

To consider partial ground-effect, a circular disk is mounted a distance h away from the plane of the propeller. The disk is attached to an ATI Industrial Automation Gamma six-component force balance www.ati-ia.com [19], the drag force of the disk is the axial-force along the sensor’s z-axis. The balance has a maximum of 200 N force and resolution of 0.025 N on its Z-axis. Three

17 inch propellers, APC 17x7, 17x10 and 17x12, were tested with three different disks with the blockage ratio 퐵 = 푑푃/퐷 of 0.5, 0.75 and 1.0.

3.3 Post Processing of Data Collected

Due to significant vibration generated by the motor, noise is found in both force and torque data. Using the experimental data for the APC 11x7 propeller in the OGE condition, which is discussed in the previous section. Applying a fast Fourier transform (FFT) on the thrust data, the dominant frequencies can be observed. The FFT of the thrust data for a propeller running at 5,700

RPM (95 RPS) is shown below in Figure 21.

RPM: 6,000 12,000 18,000 24,000 30,000

Peak Frequency

Figure 21: FFT Plot for APC 17x7 propeller thrust data under 5,700 RPM/95 RPS

A strong peak occurs at the frequency of the 95 and 190 Hz, which is corresponding to the propeller operation RPM and 2 times of the propeller RPM as the propeller has two blades.

Significant peaks also occur at 3 times, 4 times and 5 times of the propeller frequency, indicating

29 the presence of harmonics. Thus, all the signal frequencies greater than 2 times the propeller RPS and frequency less than half of the propeller RPS are removed to reduce the noise in the force data.

A bandpass filter is used to filter out the higher frequency data. The histogram of thrust data before and after the filtration is plotted below in Figure 22.

It is clear that after data filtration a comparatively normal distribution resulted while maintaining the same mean value. This filter is applied to the torque data as well, the torque data seems to have less deviation than the force data due to a balanced propeller and relatively shorter moment arm (propeller diameter), the filtration also improves the distribution of the data, while the mean value of the data does not change after filtration.

Figure 22: Propeller thrust (left) and torque (right) before and after filtration

Transducer drift occurs for most F/T transducers. A check load of 1 kg is placed on the Z- axis of the ATI Mini-40 F/T transducer for 5 minutes at a 10 Hz sampling rate. The force data is averaged every second, and plotted vs. time below in Figure 23.

It is clear that transducer drift occurs only after 2 minutes below which the readings are approximately constant. To minimize the error in force and torque measurement and avoid drift issues, the transducer is biased in between each run, and the data was taken within 2 minutes after biasing. Tare values are also taken before and after each test, and then the average of the two tares is subtracted from the respective force and torque readings.

Sensor Drift

Figure 23. Averaged force measurement of 1 kg check load in 5 minutes

3.4 Flow Visualization

Two different flow visualization methods were used to study the flowfield between the propeller and ground in ground effect: surface tuft flow visualization and smoke flow visualization.

The surface tuft flow visualization is performed using a micro poly tuft-array. The average length of the tuft is one inch. Three different ground conditions are tested: the infinite ground (with a ground plane of 72 inches x 60 inches), the 17 inch blockage plate and 8.5 inch blockage plate.

A 30 inches x 24 inches tuft-array is used on the ‘infinite’ ground plane for a visualization of the ground effect study. The tuft-array used for the partial ground effect study is the same size as the blockage plate. Nine different propellers are tested in the experiment, under RPM approximately

5,000 between h/D = 0.1 and 0.5 with an increment of 0.1 h/D for all experiments.

Smoke flow visualization was performed on the APC 17x7 and APC 17x12 propellers to visualize the flowfield in between the ground plate and the propeller disk. Both propellers are running at approximately 1000 RPM between h/D = 0.1 and 0.5 with an increment of 0.1 h/D for all experiments. A smoke-wand with 1/8-inch diameter is used for the injection of smoke to the propeller flow field and placed about 2 inches behind the propeller disk.

3.5 Unsteady Pressure Transducer Measurement

Unsteady pressure transducer measurement was performed to support the result from the flow visualization. Seven Kulite XTEL-10L-190 pressure transducers (www.kulite.com) [20] were placed flush on the 17 inch ground plate at normalized radial locations 푟/퐷 of 0.23, 0.35, 0.41,

0.47, 0.53, 0.58 and 0.7 to measure the pressure distribution on the ground plate. The sketch and photo of the pressure transducer placement are shown in Figure 24 below. All transducers have a pressure measurement range of +/- 170 Kpa gage pressure and are calibrated from -30 Kpa to 100

Kpa gage pressure. 5 seconds of data were taken for each h/D value at 5,000 Hz sampling rate.

Pressure data were taken in the h/D range from 0.1 to 0.5, in 0.1 h/D increments. Two propellers, the APC 17x7 (low 훾/퐷) and 17x12 (high 훾/퐷) are used for the pressure measurement. The 17x7 propeller has an RPM of 6,100 and the 17x12 propeller has an RPM of 5,400, such that both produce around 34.5N thrust in OGE condition.

Figure 24: Placement of the Kulite pressure transducer on ground plate

CHAPTER IV

RESULTS: INFINITE GROUND EFFECT ON PROPELLER PERFORMANCE

The experimental results for all force-based testing for the traditional ground effect will be presented and analyzed in this chapter. The experimental result in the OGE case will be compared with results from other studies. The data processing method will be discussed. Normalized power required at constant thrust is the prime variable for ground effect and partial ground effect comparison between different propeller parameters. Flow visualization results will be presented and the unsteady pressure transducer measurements further complements the findings in the flow visualization.

4.1 Comparison of the Propeller Thrust and Torque Result in OGE Condition

Before proceeding to the ground effect results, the baseline propeller thrust and torque measurement obtained from testing are compared with results in the literature to ensure the confidence of the force and torque measurement in the experiment. The experimental results for the APC 11x7 propeller are compared with similar results found in the UIUC database [17], and the earlier experiment by Gunasekaran et al. [21], also conducted at the University of Dayton

LSWT laboratory, but with a different experimental setup.

The results from the current experiment are shown for both out of ground effect (OGE) and out of ceiling effect (OCE). In the OCE measurement, the propeller is reversed from the OGE configuration to examine the additional interference effects caused by elements of the experimental setup such as the aluminum frame. The comparison is shown below in Figure 25. The error bars represent the 95% confidence interval after noise filtration. For both thrust coefficient and power coefficient, current data for both OGE and OCE fall around the result from the UIUC database, with a difference of 2% between the OGE and OCE results. The difference between the current experimental setup and Gunasekaran et al. is around 10%. Using different F/T transducers (Mini-

40 v.s Mini-45), electric motor (E-Flite Power 60 v.s OMA-3810) and different experimental setups could be responsible for the difference in the experimental data.

0.115

0.110

0.105 퐶푇

0.100

UIUC Database 0.095 Gunasekaran et. al Current Experiment (OGE) Current Experiment (OCE) 0.090 3,000 3,500 4,000 4,500 5,000 5,500 6,000 6,500 7,000 RPM

Figure 25.a: Comparison of Thrust Coefficient for APC 17x7 Propeller

0.046

0.044

0.042 퐶푃

0.040

UIUC Database 0.038 Gunasekaran et. al Current Experiment (OGE) Current Experiment (OCE) 0.036 3,000 3,500 4,000 4,500 5,000 5,500 6,000 6,500 7,000 RPM

Figure 25.b: Comparison of Power Coefficient for APC 17x7 Propeller

All three data sets have the same slope with respect to RPM: slightly positive for thrust, and essentially zero for power. The comparison of the thrust and power coefficient gives confidence in the current test setup.

4.2 Changes in Propeller Thrust and Power Coefficient in Traditional Ground Effect

Before the propeller parameter study in ground effect, a typical trend of the changes in propeller thrust coefficient and power coefficient in ground effect is presented using the data from the APC 14x6 propeller. The h/D distance is from -2 to +3.5 to confirm any change in the propeller performance at large h/D values. Both thrust coefficient and power coefficient are normalized by the OGE result at the same RPM. The thrust coefficient at different RPMs is shown below in Figure

26. Here, the positive h/D distance stands for the result of the ground effect, while the negative h/D distance is the result of the ceiling effect.

Ceiling Effect Ground Effect 1.35

1.30

1.25 Area of Interest 1.20 퐶푇퐼퐺퐸 1.15 퐶푇 푂퐺퐸 1.10 4500 5000

1.05 5500 6000

1.00

0.95

0.90 -2.00 -1.00 0.00 1.00 2.00 3.00 h/D

Figure 26. Ratio of IGE to OGE thrust coefficient for 11x5.5 propeller, at various test-RPM

A significant increment in the thrust is found at h/D values between -1.0 and 1.0. The increment of thrust coefficient at positive h/D value seems smoother than the negative h/D, where a sudden increment in the thrust coefficient occurs at the smallest h/D value. The change in the thrust coefficient data is negligible at h/D values greater than +/- 1.5 which agrees with most of the literature [2-10]. However, the value of the normalized thrust coefficient at large h/D values is less than 1, which indicates some effect of the ground on the propeller thrust generation. The cause of this phenomena remains unknown and requires further investigation. Nevertheless, the research

35 focus on small h/D values between -1.5 and 1.5 where significant changes in the propeller performance occurs due to ground proximity.

There is a drift towards higher 퐶푇 with increasing RPM of a magnitude comparable to the error-bars for the data. The direction and magnitude of the drift in the thrust coefficient are consistent with the thrust results. This could be due to the increment of the Reynolds number on the propeller blade which results in a slight increment of the thrust coefficient, which agrees with the result in Figure 25. The scatter of the thrust coefficient at each h/D distance is less than 5%.

The power coefficient result is shown below in Figure 27.

Ceiling Effect Ground Effect

1.05

1.00

0.95

퐶푃퐼퐺퐸 0.90 퐶푃 푂퐺퐸 0.85

0.80 4500 5000 0.75 Area of Interest 5500 6000 0.70 -2.00 -1.00 0.00 1.00 2.00 3.00 h/D

Figure 27. Ratio of IGE to OGE power coefficient for 11x5.5 propeller, at various test-RPM.

Different from the thrust coefficient result, a significant decrement in the power coefficient occurs between h/D value of -0.5 and 0.3. Almost no changes in the power coefficient at positive h/D value until a sudden drop at h/D of 0.3, which is the Betz threshold, this makes the 퐶푃 curve less symmetric when compared to the 퐶푇 curve in Figure 26. While the changes in the power coefficient at negative h/D value are smoother than the positive regime, no significant change in the power coefficient is found in the negative h/D region. Moreover, the peak increment of the

36 thrust coefficient occurs at slightly negative ℎ/퐷 value while the peak increment of the power coefficient occurs at slightly positive ℎ/퐷 value.

A scatter in power coefficient also occurs at different RPM setting of the propeller, which is also caused by the 퐶푃 drop at higher Reynolds number as seen in Figure 25. The overall difference in power coefficient at different RPM is less than 3%. Nevertheless, all RPM-curves follow the same trend, for both thrust and power coefficient. Thus, in the following sections, the data is averaged across the measured RPM range or interpolated as need be.

Looking at higher h/D values, a small drop in the thrust coefficient is found at h/D distances greater than +/- 0.5, where the normalized value is less than 1. For power coefficient, the result at h/D ranges greater than 1 fall around 1, while across negative h/D ranges the value is slightly less than one. This could be due to the drop in the thrust coefficient at the same h/D range seen in Figure

26.

One thing to be noticed is that the normalized thrust coefficient between 0.5 and 3.0 h/D is less than 1, which indicates a loss in the thrust of the propeller. This phenomenon occurs in most of the propellers tested. The return flow or recirculated flow due to the presence of the ground could possibly increases the induced angle of attack of the propeller, which in turn reduces the thrust coefficient of the propeller. This phenomenon required further investigation as ℎ/퐷 > 3.5 was not investigated elsewhere in the literature.

For the power coefficient, the result stays around 1 at h/D > 0.5 which differs from the thrust coefficient result. A small drop of 퐶푝 occurs at a higher negative h/D range. This agrees with the drop of the 퐶푇 occurring in the same h/D range. The changes in the 퐶푇 and 퐶푃 at the same RPM when compared with OGE condition could be caused by the orientation of the propeller as the pressure side of the propeller is flipped for the h/D < 0 cases.

4.3 Calculation of Power Required at Constant Thrust

One manifestation of both changes in thrust and torque data in ground effect is “normalized power”, (푃퐼퐺퐸/푃푂퐺퐸), at constant thrust. To calculate this, the available thrust and torque data points across the RPM range at each h/D distance is interpolated with a second-order curve fit for thrust vs. RPM, and a third-order curve fit for power vs. RPM. Several thrust levels are selected for each propeller for the OGE result, with the RPM for each thrust found, the power required for OGE is then calculated accordingly. An example of the process using the APC 14x6 propeller data can be seen in Figure 28.

For every h/D, the previous process is repeated, with the selected OGE thrust value, the

IGE RPM at which thrust for each h/D equals the aforementioned OGE thrust is then found. At the resulting RPM, the IGE power 푃퐼퐺퐸 is calculated. The result for each propeller at different thrust levels is then averaged for the propeller parameter study. The calculated 푃퐼퐺퐸/푃푂퐺퐸 result for the

APC 14x6 propeller is shown in Figure 29.

It is obvious that the power required at constant thrust starts to reduce at +0.5 h/D for the ground effect cases, which agrees with results found in the literature. The ceiling effect, where the h/D value is negative, has a very similar change of 푃퐼퐺퐸/푃푂퐺퐸 when compared to the ground effect.

The result between -1.0 and +1.0 h/D is approximately symmetric, with a smaller 푃퐼퐺퐸/푃푂퐺퐸 value at very small negative h/D due to the sudden increment in thrust as shown in Figure 26 previously.

Looking at higher h/D ranges for ground effect, the value of 푃퐼퐺퐸/푃푂퐺퐸 is greater than 1 between 0.5 and 3.5 h/D, with an average value of 1.04. This indicates a slightly lower performance of the propeller when compared to OGE. This is due to the loss of thrust in that h/D range as discussed previously. Surprisingly, this agrees with Betz’s ground effect theory as mentioned previously, where a slight increment of 푃퐼퐺퐸/푃푂퐺퐸 occurs at h/D > 0.3 caused by the induced flow velocity. However, instead of an increment of 푃퐼퐺퐸/푃푂퐺퐸 up to 17%, the increment in the experimental result is less than 5%.

Figure 28: Example of calculating power required at constant thrust (T=10N). Ceiling Effect Ground Effect

1.00

0.90 푃 퐼퐺퐸 0.80 푃푂퐺퐸 0.70

0.60 9N 12N 0.50 Area of Interest 15N 18N 0.40 -2.00 -1.00 0.00 1.00 2.00 3.00 h/D

Figure 29: Power required at constant thrust for APC 14x6 propeller

The 푃퐼퐺퐸/푃푂퐺퐸 value drops back to approximately 1.0 at a dimensionless distance greater than 3.5, which is also seen repeatedly in the APC 17x7 propeller result. Thus, h/D = 4.0 is considered as OGE from here on out, which is different from most literature where h/D = 1.5 is usually considered OGE. Again, h/D values between -1.0 and 1.0 will be discussed in detail in the following sections.

For the ceiling effect, the value of 푃퐼퐺퐸/푃푂퐺퐸 returns to 1.0 at h/D = -1.0 and remains the same at a higher negative h/D range. This indicates that for the ceiling effect, h/D greater than -1.0 can be considered as the out of ceiling effect (OCE). Again, this is seen in other propeller results.

4.4 Propeller Parameter Study in Traditional Ground Effect

In this section, the effect of different propeller parameters including the pitch, diameter and solidity will be investigated.

4.4.1 Effect of Propeller Pitch

To study the effect of propeller pitch, the set of propellers chosen has 3 different diameters,

11 inches, 14 inches, and 17 inches, and each propeller diameter has two different pitches. The experimental result for the 푃퐼퐺퐸/푃푂퐺퐸 is shown in Figure 30 below. For all plots in this section, the propeller with the same diameter will have the same symbol while different color stands for different propeller pitch. The symbol for each propeller will be consistent throughout the paper.

For the 17x7 propeller, normalized power at the most extreme ground-separation is half of the OGE value. The trend of 푃퐼퐺퐸/푃푂퐺퐸 vs. h/D is approximately symmetric, for small positive or negative h/D, but there is a slight asymmetry between h/D = + 1 and h/D = -1.

For the 17x10 propeller, IGE power-reduction is much less dramatic and is also asymmetric.

For h/D ~ -0.2, there is an odd reversal in 푃퐼퐺퐸/푃푂퐺퐸. The two 11-inch propellers are intermediate cases, with the 11x5.5 (lower pitch) resembling more the 17x7, and the 11x7 (higher pitch) resembling more the 17x10. For the 14-inch propellers, the 14x7 propeller follows the overall trend as the 17-inch and 11-inch propeller, while the 14x14 propeller with the highest pitch among all propellers shows almost negligible changes in 푃퐼퐺퐸/푃푂퐺퐸. 40

Ceiling Effect Ground Effect 1.10

1.00

0.90

0.80 푃퐼퐺퐸 푃푂퐺퐸 0.70

0.60 11x5.5 11X7 14x7 14x14 0.50 17x7 17x10

0.40 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 h/D

Figure 30. Normalized power required at constant thrust, for a selection of propellers.

푃퐼퐺퐸/푃푂퐺퐸 is a succinct presentation-format of IGE results, but it potentially masks the extent to which thrust is increasing, or power-required is decreasing, as discussed previously for the 14x6 propeller. A reversion to the more direct presentation of thrust coefficients is given in

Figure 31 below. Ceiling Effect Ground Effect

1.30 11x5.5 11x7 1.25 14x7 14x14

1.20 17x7 17x10

1.15 퐶푇 퐼퐺퐸 1.10 퐶푇 푂퐺퐸 1.05

1.00

0.95

0.90 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 h/D

Figure 31. Ratio of IGE to OGE thrust coefficient for the cases of Figure 30

The trends of Figure 30 repeat in Figure 31, with a higher increment of thrust coefficient for the lower pitch propeller with the same diameter. For all propellers, peak thrust-increase appears to be at slightly negative h/D, and then drop significantly at higher negative h/D. Moreover, the positive-negative h/D symmetry for the 17x7 case is not as evident as in Figure 30. The power coefficient for the same set of propellers is plotted below in Figure 32.

The difference in the reduction of the power coefficient seems less significant when compared to the increment in the thrust coefficient, except for the 14x14 propeller, which has been an outlier in this study. The peak power-reduction for the 17x7, 14x7 and 11x5.5 cases is at commensurately slightly positive h/D. For the same diameter propeller, the lower pitch propeller will have a higher reduction in the power coefficient when compared to the higher pitch propeller.

The 17x10 case meanwhile still contains a curious reversal in both thrust and power at h/D ~ -0.2.

For all propellers in Figure 32, reduction in power coefficient for the positive h/D range does appear to start near 0.3 h/D, again, this is the Betz threshold mentioned previously.

Ceiling Effect Ground Effect 1.05

1.00

0.95

0.90 퐶푃 퐼퐺퐸 퐶푃 푂퐺퐸 0.85

0.80 11x5.5 11x7

0.75 14x7 14x14

0.70 17x7 17x10

0.65 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 h/D

Figure 32. Ratio of IGE to OGE power coefficient for the cases of Figure 30

Based on the changes in the thrust and power coefficient, and the combined positive/negative trends in thrust and power result, it is obvious that the symmetry for the 17x7

42 case in Figure 30 is the result of a higher increment in thrust at negative h/D and higher reduction in power at positive h/D.

Overall, for the same propeller diameter, a lower pitch propeller will have a higher reduction in the power required at constant thrust, thus elicit better performance in ground effect.

4.4.2 Effect of Propeller Diameter

The next sets of propellers have the same pitch (7 inches) but different diameter, to investigate the effect of diameter on the propeller ground effect. The normalized power required of constant thrust for each propeller is shown below in Figure 33. Ceiling Effect Ground Effect 1.10

1.00

0.90

푃퐼퐺퐸 0.80 푃푂퐺퐸 0.70

0.60

0.50 11X7 14x7 17x7

0.40 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 h/D

Figure 33. Normalized power required for constant thrust, for propellers with same pitch.

It is obvious that the result for the 14x7 propeller falls in between the 17x7 and 11x7 propeller. Moreover, the result is more symmetric than the 11x7 propeller. The thrust and power coefficient plot is shown below in Figure 34. The overall trend of the thrust and power coefficient for all propellers remains the same as the previous case. Again, a significant increment in the thrust coefficient is found for the higher radius propeller, the 17x7 case, while the 11x7 case shows a lot less increment in the thrust.

Ceiling Effect Ground Effect 1.35

1.30 11x7 14x7 17x7 1.25 1.20 퐶 푇 퐼퐺퐸 1.15 퐶푇 푂퐺퐸 1.10 1.05 1.00 0.95 0.90 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 h/D

Figure 34a. The ratio of IGE to OGE thrust coefficient for the cases of Figure 33

On the other hand, the power coefficient result gives very minimum difference among the propellers, the results almost overlap on each other for the 14x7 and 17x7 case surprisingly. Again, the reduction of power coefficient in ground effect occurs around h/D = 0.3, which is the Betz threshold, while the change in power coefficient is smoother for the ceiling effect. Ceiling Effect Ground Effect 1.05

1.00

0.95

0.90 퐶푃 퐼퐺퐸 0.85 퐶푃 푂퐺퐸 0.80

0.75

0.70 11x7 14x7 17x7

0.65 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 h/D Figure 34b. The ratio of IGE to OGE thrust coefficient for the cases of Figure 33

4.4.3 Effect of Propeller Pitch to Diameter Ratio

The variations in the previous two sections motivate the search for pitch-to-diameter ratio, or some other parameter, to arrive at a better collapse of the data for ground effect prediction. Figure

35 replots the 푃퐼퐺퐸/푃푂퐺퐸 for the select propellers. Among propellers with the same pitch (7 inches), the trend is towards larger savings in IGE power, and better positive/negative h/D symmetry, with increasing diameter, as mentioned previously. This indicates that, with a decreasing ratio of pitch to diameter, propeller performance in ground effect is improved.

The 11x5.5 and 14x7 have the same pitch-to-diameter (훾/퐷) ratio (= 0.5), and indeed, their

푃퐼퐺퐸/푃푂퐺퐸 curves nearly overlap, the variation between the two is just short of being fully covered by their respective error-bars. However, the 11x7 has a higher pitch to diameter ratio than the

17x10, and yet it is the 17x10 which has the more anomalous 푃퐼퐺퐸/푃푂퐺퐸 curve.

The 14x14 propeller, which has the highest 훾/퐷 ratio among all propellers, shows a minimal change in the power required at constant thrust, which differs from all other cases.

To reiterate, except for the 14x14 case, ground-proximity reduces 푃퐼퐺퐸/푃푂퐺퐸, as expected; but the extent to which this happens, evidently depends on the pitch to diameter ratio. Ceiling Effect Ground Effect

1.10

1.00

0.90

푃퐼퐺퐸 0.80 푃푂퐺퐸 0.70

0.60

0.50

0.40 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 h/D 14x14 11X7 17x10 14x7 11x5.5 17x7 훾/퐷 = 1.00 0.64 0.59 0.50 0.50 0.41 Figure 35. Normalized Power Required for Constant Thrust, for various propeller pitch to diameter ratios.

Figure 36 below replots the some of the results of Figure 35, along with the result of other propellers tested, to emphasize the effect of pitch to diameter ratio, 훾/퐷, on 푃퐼퐺퐸/푝푂퐺퐸. Different from the previous plot, the X-axis represents the 훾/퐷 of the propeller and each legend group represent the same ℎ/퐷 value. For each h/D, 푃퐼퐺퐸/푃푂퐺퐸 is seen to decline, as γ/D gets smaller.

1.00

0.90

0.80 푃퐼퐺퐸 푃푂퐺퐸 0.70

0.1 h/D 0.60 0.2 h/D 0.3 h/D 0.50 0.40 0.50 0.60 0.70 0.80 0.90 1.00 훾/퐷

Figure 36. Normalized Power Required for Constant Thrust, with respect to propeller pitch to diameter ratio, at several different h/D values.

4.4.4 Effect of Propeller Solidity.

The next parameter study is the propeller solidity, 휎. The propeller solidity can be calculated using the following equation:

4푆푝푟표푝 휎 = ( 4.1 ) 휋퐷2

Where the 푆푝푟표푝 is the projected area of the propeller on the rotor disk. Figure 37 below shows PIGE/POGE vs. h/D, for 7”-pitch propellers: off-of-the-shelf APC 11x7 and 14x7, and cut- diameter versions of the 17” propeller (14” and 11” diameter). The 11x7 and 11x7C share 훾/퐷

(square symbols), as do the 14x7 and 14x7C (triangular symbols). It is obvious that for each such pair, the case with higher solidity, the cut version of the propeller, has a higher reduction of

PIGE/POGE through positive h/D values, which indicate a greater ground effect. This trend is also applicable to the ceiling effect where the h/D value is negative.

Ceiling Effect Ground Effect 1.00

0.90

0.80

푃퐼퐺퐸 0.70 푃푂퐺퐸

0.60

11X7 11x7C 0.50 APC 11x7 APC 11x7C 14x7 14x7C 0.40 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 h/D

Figure 37. Normalized Power Required for Constant Thrust, for higher and lower solidity

Results of the higher and lower pitch propellers are replotted in Figure 38a and Figure

38b below, in terms of the thrust and power coefficients vs. h/D.

Ceiling Effect Ground Effect 1.35 14x7 14x7C 1.30

1.25 11x7 11x7C

1.20 퐶푇퐼퐺퐸 퐶푇푂퐺퐸 1.15

1.10

1.05

1.00

0.95 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 h/D

Figure 38a. Normalized thrust coefficient, for higher and lower solidity

Ceiling Effect Ground Effect

1.00

0.95

0.90

퐶푃퐼퐺퐸 0.85 퐶푃푂퐺퐸

0.80 14x7 14x7C

0.75 11x7 11x7C

0.70 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 h/D

Figure 38b. Normalized power coefficient, for higher and lower solidity

Results in Figure 38 reveal how the usage of PIGE/POGE is succinct, but can mask constituent trends. The two cut propellers (solid green symbols) clearly have a larger IGE increase in thrust, for both positive and negative h/D cases. However, it does not evince commensurate savings in the power-coefficient. On the contrary, the result for the higher solidity propeller at negative h/D values shows a decrement in the savings in the power coefficient surprisingly.

For all cases and both coefficients, scatter is higher for negative h/D than for positive. Just as with pitch to diameter ratio, solidity is seen to matter, with a higher solidity leads to a greater ground effect, this agrees with the Cheeseman’s prediction model [8].

4.5 Flow Visualization

Multiple flow visualization methods were used to visualize and understand the flowfield on the ground plane and in between the ground plane and propeller disk in an attempt to explain the trends observed in the force-based testing. The tuft flow visualization and smoke flow visualization are discussed in this chapter for a better representation of the flowfield on the ground and in-between the propeller and the ground.

4.5.1 Surface Tuft Flow Visualization.

Six different propellers, 17x7, 17x10, 17x12, 14x6, 14x8.5 and 14x14 are selected from the traditional ground effect experiment and tested in the surface tuft flow visualization, with 0.1 ≤

ℎ/퐷 ≤ 0.5 at RPM ~6,000. The result for the APC 17x7 propeller at h/D = 0.3 is chosen to be presented first below in Figure 39.

Figure 39. Surface tuft flow visualization for APC 17x7 at h/D = 0.3 for the traditional ground effect experiment.

Two different flow fields are found on the ground plate, separated by a projected

“stagnation streamline”, approximately circular, of diameter on the order of half of the propeller diameter. Exterior to this circular “stagnation streamline”, the projected streamlines appear to be radially outward. Interior to the circular “stagnation streamline”, the projected flow can be described as being swirling, without a discernible radial component, or in other words, tangential.

Surprisingly, this type of flow has not been discussed in the existing literature, to the best of author’s knowledge.

A side view sketch of the propeller flowfield in the ground effect is shown below in Figure

40. Again, the stagnation streamline separates the flow into the inboard tangential flow and the outboard radial flow

Stagnation Streamline

Figure 40. Side view sketch for propeller flowfield in ground effect

The diameter of the stagnation streamline 퐷푑𝑖푣 is measured for all six propellers tested in the surface tuft flow visualization. The value of 퐷푑𝑖푣 is then normalized by the diameter of the propeller and plotted with respect to h/D below in Figure 41.

0.50 0.45 0.40 0.35

퐷퐷𝑖푣 0.30 퐷푝푟표푝 0.25 0.20 Stagnation Streamline Vanishes 0.15 APC 17x7 APC 17x10 APC 17x12 0.10 APC 14x6 APC 14x8.5 APC 14x14 0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 h/D

Figure 41. Normalized stagnation streamline diameter v.s h/D

It is clear that the lower γ/D propeller (17x7 and 14x6) has a larger “stagnation streamline” when compared to the higher γ/D propeller(17x12, 14x14) at the same h/D. Recall from the traditional ground effect force-based experimental result in the last section, the lower γ/D propeller

50 does have a greater ground effect. This indicates that the circular “stagnation streamlines” and their respective size on the ground plane is conjectured to correlate with ground effect in some fundamental way.

Moreover, with the increment of the h/D distance, the stagnation streamline diameter reduces for all propellers and then vanishes at a threshold h/D. The stagnation streamline still occurs at 0.5 h/D for the 14x6 propeller while the stagnation streamline vanishes at h/D = 0.3 for most of the higher γ/D propellers. The image of the tuft flow visualization for APC 17x7 (low γ/D) and

APC 17x12 (high γ/D) at each h/D in ground effect is shown below in Figure 42. It is clear that with the increment of h/D, the stagnation streamline size reduces and then vanishes.

Figure 42. Tuft flow visualization for APC 17x7 (upper) and 17x12 (lower) at each h/D

Recall from the power coefficient data in Figure 32 in the previous section, the normalized power coefficient for all propellers in the positive h/D range (ground effect) drops around 0.3 h/D, with the lower low γ/D ratio propellers. This drop happens at a slightly higher h/D, around 0.4.

This agrees with the flow visualization very well and indicates that the stagnation streamline is strongly connected to the changes in the propeller power coefficient. The existence of the stagnation

51 streamline could be a boundary between the ‘large distance’ and ‘small distance’ to the ground in

Betz’s ground effect theory.

4.5.2 Smoke Flow Visualization

Promising surface tuft visualization results motivate the smoke visualization experiment performed on both APC 17x12 and APC 17x7 propeller at ℎ/퐷 = 0.3. Images for smoke flow visualization are shown below in Figure 43.

Figure 43. Smoke flow visualization on 17x7 (upper) and 17x12 (lower) propellers

The smoke-wand is first placed close to the root of the propeller blade. Smoke emanating from the wand is concentrated towards the center of the propeller wake and stays within the stagnation streamline. By moving the smoke wand towards the tip of the blade, the stagnation streamline can be observed, where the direction of the smoke switches from center-seeking to radially outboard. For the highest pitch propeller, this deviation happens around 38% of the

52 propeller radius, while for the low pitch propeller case, this happens at around 50% of the propeller radius. The smoke-wand is then moved towards the tip of the propeller and a very uniform radial flow occurs until the tip vortex of the propeller blade is observed around the edge of the propeller disk.

The existence of two different types of flowfield on the ground plane indicates a connection between the associated flow physics and the propeller performance. Therefore, the following questions needed to be asked:

1. Which type of flowfield is highly influential in changing the propeller performance? Is it the radial or the tangential flow?

2. What if the ground plane is limited to the size of the stagnation circle diameter? Will there be any ground effect?

3. How would the effective thrust change as a function of the ground plane diameter?

In an effort to answer these questions, partial ground effect on the propeller performance was investigated which is discussed in the next chapter.

CHAPTER V

RESULTS: PARTIAL GROUND EFFECT ON PROPELLER PERFORMANCE

In this chapter, the results from the partial ground effect experiments are discussed. Three

17’’ propellers with different pitches: 17 x 7, 17x10 and 17 x 12 with a normalized stagnation streamline diameter of 0.48, 0.41 and 0.38, accordingly, were used for the study. Three different blockage ratios: 퐵 = 푑푝/퐷 of 0.5, 0.75 and 1.0 were used, all greater than the normalized stagnation streamline diameter of the propeller tested. The proximity of the 0.48 normalized diameter blockage to the value of the 0.5 normalized diameter plate is, however noted. This is illustrated below in Figure 44.

Figure 44. Example of different blockage ratio

5.1 Power Required at Constant Thrust

The normalized power required at constant thrust, for each propeller at different blockage in the partial ground effect, along with the ‘infinite’ ground effect result, is shown in three different plots of Figure 45 below. The results for the same propeller will have the symbol while the different color represents different blockage ratio B.

Classical ground-effect was found to be strongest for the lower pitch-to-diameter ratio propeller, APC 17x7, from the infinite ground effect experiment. This trend holds for all values of blockage ratio B, as the normalized power required at constant thrust for the APC 17x7 propeller at different blockage ratios is lower than the other two propellers tested.

Ceiling Effect Ground Effect 1.05

0.95

0.85

푃퐼퐺퐸 0.75 푃푂퐺퐸 APC 17x7 Ground 0.65 APC 17x7 0.5 Blockage 0.55 APC 17x7 0.75 Blockage APC 17x7 1.0Blockage 0.45 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 h/D

Figure 45a. Normalized power required at constant thrust in partial ground effect 17x7 Ceiling Effect Ground Effect 1.10

1.05

1.00

푃퐼퐺퐸 0.95 푃푂퐺퐸 0.90 APC 17x10 Ground 0.85 APC 17x10 0.5 Blockage APC 17x10 0.75 Blockage 0.80 APC 17x10 1.0 Blockage 0.75 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 h/D

Figure 45b. Normalized power required at constant thrust in partial ground effect 17x10 Ceiling Effect Ground Effect

1.05

1.00

0.95 푃퐼퐺퐸 0.90 푃푂퐺퐸 APC 17x12 ground 0.85 APC 17x12 0.5 Blockage 0.80 APC 17x12 0.75 Blockage APC 17x12 1.0 Blockage 0.75 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 h/D

Figure 45c. Normalized power required at constant thrust in partial ground effect 17x12

It is clear that the performance of all propellers in the B = 1.0 case, where the plate diameter is equal to the propeller diameter, closely follows that of the infinite ground plane-case, at both positive and negative h/d distance. Evidently, B = 1.0 can be defined as “infinite ground”. Recall from Equation 2.5 where the final propeller wake disk area is half of the propeller disk area, this also supports that B = 1.0 sufficient enough as “infinite ground”.

B = 0.5 case is the opposite from the B = 1.0 case. For the 17x7 propeller, the change in

PIGE/POGE is only 30% from the infinite-ground case. Surprisingly, for the 17x10 propeller, B =

0.5 shows a negligible ground effect, where normalized power at small h/D lies around 1.0. For the

17x12 propeller, the changes in PIGE/POGE for the B = 0.5 case is about 50% when compared to the infinite ground plate, but it should be noted that all cases for 17x12 evince a reduced ground effect, and barely follows the overall trend discussed in the previous section.

The B = 0.75 case lies between the B = 1.0 and B = 0.5 cases, as expected. Around 70% in power required difference is found for B = 0.75 case when compared to power required reduction

B = 1.0 for 17x7 and 17x10 propeller, while the 17x12 propeller has very small difference between the B = 0.75 case and the B = 1.0 case.

The aforementioned trends were examined in more detail in Figure 46.a and Figure 46.b for the 17x7 propeller, which evinces the strongest ground effect, by plotting the individual thrust and power coefficients, normalized by their OGE reference values.

For B = 1.0, the IGE increment in thrust and decrement in power required overlap the infinite-plate result, which again indicates that B = 1.0 can as act as a surrogate for “infinite” ground.

For B = 0.5, changes in power required and thrust-produced are less than 6%. Recall from the flow visualization result in last chapter, the normalized stagnation streamline diameter for the 17x7 propeller is 0.48, slightly smaller than the B = 0.5 case. As the B = 0.5 case eliminates the majority of the radial flow region, the increment in thrust and decrement in power required becomes negligible. This indicates that majority of the contribution to the ground effect is due to the outboard radial flow on the ground when compared to the inboard tangential flow.

Ceiling Effect Ground Effect

1.30 17x7 Ground 1.25 17x7 0.5 Blockage 17X7 0.75 Blockage 1.20 17x7 1.0 Blockage 퐶푇퐼퐺퐸 1.15 퐶 푇푂퐺퐸 1.10

1.05

1.00

0.95 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 h/D

Figure 46a: Normalized thrust coefficient for APC 17x7 in partial ground effect

Ceiling Effect Ground Effect

1.00

0.95

0.90

퐶푃퐼퐺퐸 0.85 퐶푃푂퐺퐸 0.80 17x7 Ground

0.75 17x7 0.5 Blockage 17x7 0.75 Blockage 0.70 17x7 1.0 Blockage 0.65 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 h/D

Figure 46b. Normalized power coefficient for APC 17x7 in partial ground effect

5.2 Propeller Effective Thrust at Different Blockage.

To study the overall effect of the placement of the propeller on the air-vehicle, an alternative presentation of the partial ground effect study is introduced: effective thrust Teff, which can be written as:

Teff = 푇 − 퐹퐷푝 ( 4.2 )

Where T is the thrust of the propeller, and 퐹퐷푝 is the drag force on the ground disk. This represents the net thrust generated by the propeller when placed on a fuselage or support arm with a blockage ratio of B and at a distance of h/D.

First, the measured drag force of the plate is investigated. The measured 퐹퐷푝 at each h/D placement is normalized by the OGE thrust and then normalized by the square of blockage ratio,

B2. This is also the ratio of the blockage plate area. The result is plotted in Figure 47 below.

APC 17x7 0.5 Plate 1.60 APC 17x7 0.75 Plate APC 17x7 1.0 Plate 1.40 APC 17x10 0.5 Plate APC 17x10 0.75 Plate 1.20 APC 17x10 1.0 Plate APC 17x12 0.5 Plate 퐷푃푙푎푡푒 1.00 APC 17x12 0.75 Plate 푇 ∗ 퐵2 푂퐺퐸 0.80

0.60

0.40

0.20

0.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 h/D

Figure 47: Normalized plate drag for different blockage ratio

Using this normalization, the nine curves, which are the combinations of three γ/D ratio and three blockage values do not quite collapse to one curve at positive h/D region. It is clear that some residual variation across difference blockage, but very little difference across different γ/D ratio as the curve for the same blockage ratio falls close to each other.

With the propeller oriented in the ceiling effect where h/D < 0, the curve seems to collapse better for different γ/D ratios at the same blockage ratio. Moreover, the drag force on the plate relaxes to zero by h/D = -1. This indicates that the propeller no longer has an effect on the blockage plate. This is not true for the ground effect where the plate is placed on the pressure side of the propeller. Even for h/D = 1.5, there is drag on the plate. This is not surprising since the simple

58 propeller momentum theory [15] claims that the propwash has an infinite downstream extent. In reality, it takes a very long distance for the propeller wake to dissipate, it would be almost impossible to determine at what h/D value the propeller will not affect the blockage plate.

For both positive and negative h/D, maximum plate drag occurs at a very small distance around h/D ~ 0, which is to say, extreme ceiling-effect and extreme ground-effect result in a plate drag over twice as large as that of the far-wake case where h/D is greater than 1.5.

Here, the positive h/D distance models a puller configuration where the propeller is placed in front of the fuselage, while the negative h/D distance represents the pusher configuration. The direct experimental data for the propeller thrust is subtracted by the blockage plate drag respectively to calculate the effective thrust. The effective thrust is then normalized by the thrust measurement in the OGE condition. The normalized effective thrust is given below in Figure 48. Pusher Configuration Puller Configuration 1.00

0.90

0.80

0.70

0.60 APC 17x7 0.5 Blockage 푇푒푓푓 APC 17x7 0.75 Blockage 0.50 푇∞ APC 17x7 1.0 Blockage 0.40 APC 17x12 0.5 Blockage APC 17x12 0.75 Blockage 0.30 APC 17x12 1.0 Blockage 0.20 APC 17x10 0.5 Blockage APC 17x10 0.75 Blockage 0.10 APC 17x10 1.0 Blockage 0.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 h/D

Figure 48. Normalized Effective Thrust at Different Blockage

At positive h/D, 푇퐸푓푓/푇푂퐺퐸 varies similarly for all three propellers, despite the difference in propeller γ/D ratio. 푇퐸푓푓/푇푂퐺퐸 never reaches 1.0 at positive h/D, even at h/D = 1.5. Surprisingly,

59 the difference between h/D = 1.0 and 1.5 is negligible. At higher positive h/D, the propeller effective thrust is about 80% of the thrust in OGE for B = 0.5, 70% for B = 0.75 and 50% for B =

1.0. This essentially means that the pressure-field in the wake of the propeller has not yet relaxed to free-stream as mentioned previously. The B = 0.5 has a minor effect on the propeller effective thrust as expected since the ground effect benefits of the B = 0.5 case is also negligible. While for

B = 1.0, effective thrust goes to zero as h/D goes to zero, and the result for B = 0.75 lies in between.

The result is simply a restatement of the pressure due to the propeller thrust, matching the pressure at the ground-plate. Or in other words, that B = 1.0 is already a sufficiently large plate, as to capture all of the propeller thrust force.

At negative h/D, scatter in the data for small h/D is larger than higher h/D, but the trend is similar despite the difference in the propeller parameter. For -h/D at 1.0 and above, the effective thrust has relaxed to its OGE value, for all plate B-values, which indicate that the effect of the plate on the propeller performance is negligible. When compared to positive h/D value, the recovery of

푇푒푓푓 at negative h/D range is much faster, where the 푇푒푓푓/푇푂퐺퐸 arrives at the same value as h/D =

1.5 at h/D = -0.2.

Overall, the study for effective thrust suggests, in the absence of other complicating factors, better performance for the pusher configuration where the propeller is placed behind the fuselage, than the tractor configuration. For a tractor configuration, the normalized effective thrust is a function of h/D distance and blockage ratio B, which is the placement of the propeller on the air- vehicle and the area behind the propeller pressure side which blocks the propeller flow. Surprisingly, the pitch to diameter ratio, which has been proven to affect the propeller performance greatly in ground effect, is found to be relatively irrelevant for the propeller effective thrust.

5.3 Partial Ground Effect Flow Visualization

The surface tuft flow visualization is repeated for the partial ground effect condition. The experimental result for APC 17x12 (high γ/D) and APC 17x7 (low γ/D), at h/D = 0.3. Two

60 blockage ratios, B = 1.0 and 0.5 are investigated, along with the surface tuft flow visualization result for the traditional ground effect are shown in Figure 49 below.

Similar to the ground effect result, two different flow fields are found on the ground plate, the radial outward flow region and tangential inward flow region, separated by the stagnation streamline. For different propeller under different ground conditions, the size of the stagnation streamline is different. The general trends, where the lower γ/D leads to a larger stagnation streamline, still holds. Besides, the traditional ground plane has the largest stagnation streamline size, following with the B = 1.0 blockage plate which has a very similar stagnation streamline size while the B = 0.5 blockage plate has the smallest stagnation streamline size.

Figure 49. Tuft flow visualization of near-surface flowfield on the ground

Figure 50 below plots the diameter of these “stagnation streamlines” vs. h/D under different ground conditions. The result is normalized by the propeller diameter.

0.50 0.45 0.40 0.35

푅퐶𝑖푟푐 0.30 푅푝푟표푝 0.25 0.20

0.15 APC 17x7 Ground APC 17x12 Ground 0.10 APC 17x7 1.0 Plate APC 17x12 1.0 Plate 0.05 APC 17x7 0.5 Plate APC 17x12 0.5 Plate 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 h/D

Figure 50. Ratio of diameter of stagnation streamline, to propeller diameter

The overall trend agrees with the traditional ground effect result, where the stagnation streamline diameter reduces slightly for both propellers with the increment of h/D, then vanishes at higher h/D. For h/D = 0.1, B = ∞ and B = 1.0 cases nearly overlap, but diverge slightly for larger h/D. B = 0.5 consistently evinces the smallest stagnation-streamline diameter, though not by much

– perhaps surprising, given that the streamline comes so close to the B = 0.5 plate’s edge. Moreover, the stagnation streamline for higher γ/D propeller disappears at smaller h/D distance than lower

γ/D propeller, this also agrees with the traditional ground effect result.

Recall from the force-based experiment for partial ground effect earlier in this chapter, with a smaller blockage ratio B, the ground effect reduces accordingly, where the smaller stagnation streamline size also occurs at the smallest blockage ratio case. Again, this indicates that there is some connection between the stagnation streamline size and the strength of the ground effect.

5.4 Unsteady Pressure Transducer Measurement

Seven Kulite XTEL-10L-190 pressure transducers are placed on the 1.0 blockage plate to study the pressure distribution. The 17x7 propeller has an RPM of 6,100 and the 17x12 propeller has an RPM of 5,400, such that both produce around 34.5N thrust in OGE condition.

Variation of pressure with respect to the disk radius is shown in Figure 51 below. The magnitude of the pressure 푃(푟) is normalized by the ratio drag force experienced by the ground plate and the area of the ground plate. This provides an average pressure acting on the blockage plate. The normalized pressure thus becomes a relative distribution.

For each h/D value, 푝(푟) attains its maximum value in the vicinity of r/R ~ 0.5, this indicates that the ‘stagnation streamline’ occurring in the flow visualization is indeed the stagnation point of the propeller wake. For the 17x7 propeller, the peak pressure occurs at the 0.5 r/R location while the peak for 17x12 propeller occurs at the 0.4 r/R location. Both agree with the flow visualization result. It remains to explain on physical grounds how the size of the projected stagnation streamline relates to relative IGE thrust-benefit for smaller γ/D propellers.

푝(푟)

푝푃푙푎푡푒

Figure 51. Pressure data vs. propeller radial station, B = 1.0, for 17x12 and 17x7 propeller

CHAPTER VI

PREDICTION OF PROPELLER GROUND AND PARTIAL GROUND EFFECT

Based on the force-based experimental result, a phenomenological expression is developed to predict the changes in propeller performance in ground proximity based on the propeller parameter including the pitch to diameter ratio (훾/퐷) and propeller solidity (휎). The algebraic model was also extended to include the blockage ratio for partial ground effect prediction.

6.1 Phenomenological Expression and Prediction for Traditional Ground Effect

As discussed in Chapter IV, two propeller physical parameters, 훾/퐷, and 휎 have a significant impact on the propeller performance in ground effect. The effect of the propeller solidity on the propeller ground effect is studied using the experimental result from the 14x7, 11x7 (both low solidity) and 14x7C and 11x7C (both high solidity).

Here, a new variable is introduced, normalized power required deficit, with the following expression:

푃퐼퐺퐸 푃푑푒푓 = 1 − ( 6.1 ) 푃푂퐺퐸

This is just the reduction of the normalized power required at constant thrust in ground effect. Now, with the idea of the power required deficit, applying the following equation to calculate the corrected deficit for the solidity difference.

푃푑푒푓 푃 = ( 6.2 ) 푑푒푓푠 휎 ∗ 100

The equation is applied to the result in Figure 37 in Chapter IV. The result is shown below in Figure 52. Using the APC 14x7 and 14x7C propeller as an example, since the 훾/퐷 ratio for both propellers is the same, while the only difference is the solidity, applying Equation 6.2 collapses the curve, reducing the difference from 25% to less than 8%.

0.000 -0.005 -0.010 -0.015 -0.020

−푃푑푒푓푠-0.025 -0.030

-0.035 11X7 11x7C 14x7 14x7C -0.040 -0.045 -0.050 -1.00 -0.50 0.00 0.50 1.00 h/D

Figure 52. 푷풅풆풇풔 corrected by solidity difference

The next parameter to account for is the 훾/퐷 ratio, Figure 53 below is the 푃퐼퐺퐸/푃푂퐺퐸 experimental result for all propellers tested in the ground effect study. The scatter in the experimental result suggests that the prediction model for the larger rotor does not apply to propellers. Taking the 훾/퐷 ratio into account for the ground effect prediction is essential.

1.05

0.95

0.85 푃퐼퐺퐸 푃푂퐺퐸 0.75

0.65 11x4.5P 11x5.5 11X7 11x7C 11x12 14x6 14x7 14x7C 14x8.5 0.55 14x14 17x7 17x10 17x12 0.45 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 h/D

Figure 53. Power required at constant thrust in ground effect for all propellers tested

Now, based on the modification of Equation 6.2, the final prediction equation is derived below for the propeller ‘classical’ ground and ceiling effect.

2 푃푑푒푓 훾 ℎ 1 − ( ) (0 ≤ ≤ 0.5) 푃푐 휎 ∗ 100 퐷 퐷 = { 1 ( 6.3 ) 푃 푃푑푒푓 훾 ℎ 푂퐺퐸 1 − ( ) (−0.5 ≤ ≤ 0) 휎 ∗ 100 퐷 퐷

Figure 54 below shows the power required at constant thrust results in Figure 53, ‘corrected’ by Equation 6.3. Most of the propeller results evince reasonable collapse to one curve, which indicates a very good correction (or prediction) of the model. The correction of the medium-high

훾/퐷 ratio propellers, including 17x10 and 14x8.5, is partially successful, as the ground effect (h/D >

0) curves collapses while the ceiling effect (h/D < 0) curves do not. This is mainly due to the unusual increment of 푃퐼퐺퐸/푃푂퐺퐸 at small negative h/D case.

1.010

1.005

1.000

0.995 푃푐 푃푂퐺퐸0.990

0.985 11x4.5 11x5.5 11X7 0.980 11x7C 11x12 14x6 14x7 14x7C 14x8.5 0.975 14x14 17X7 17x10 17X12 0.970 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 h/D

Figure 54a. Correction of normalized power required at constant thrust

Several high 훾/퐷 ratio propellers do not follow the overall trend, which are 11x10, 11x12,

14x14 17x12. The poor IGE results of higher 훾/퐷 ratio propellers, and failure of these cases to collapse to one curve in Figure 54, are probably related to the blade stall as the propeller approaches

66 the ground. It is possible that at closer proximity to the ground, the induced angle of attack of the blade decreases, which in turn will increase the effective angle of attack along the propeller blade.

Since the high pitch propeller already has a higher geometric pitch along the blade span, the ground proximity may exacerbate a tendency towards a stall angle of attack. However, this hypothesis has not been proven in this paper due to the time constraint of the thesis. Thus, the 훾/퐷 ratio of the propeller that is applicable to Equation 6.3 is:

훾 ℎ 훾 ℎ 0 < < 0.588 ( < 0 ) 푎푛푑 0 < < 0.636 ( > 0 ) ( 6.4 ) 퐷 퐷 퐷 퐷

훾 Figure 54b below replots the propeller with 0 < < 0.636. It is clear that all curves 퐷 collapse on each other very well, except for some small deviation in the propeller with 0.588 <

훾 < 0.636 at small negative ℎ/퐷 value. 퐷

1.000

0.995

0.990 푃푐 푃푂퐺퐸 0.985

0.980 11x4.5 11x5.5 11X7 11x7C

14x6 14x7 14x7C 14x8.5 0.975 17X7 17x10 0.970 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 h/D

Figure 54b. Correction of normalized power required for the selected propellers

A second-order polynomial fit is done on the remaining propeller data for a ‘baseline’ ground effect curve, between h/D of -0.5 to +0.5. This is shown below in Equation 6.5.

2 ℎ ℎ ℎ −0.0513 ( ) + 0.0508 ( ) + 0.9873 (0 ≤ ≤ 0.5) 푃푐 퐷 퐷 퐷 = 2 (6.5 ) 푃 푂퐺퐸 ℎ ℎ ℎ −0.1449 ( ) − 0.1277 ( ) + 0.9707 (−0.5 ≤ ≤ 0) { 퐷 퐷 퐷

Using this ‘baseline’ curve, input the propeller 훾/퐷 and 휎 parameter to Equation 6.3, we will then calculate the predicted ground effect performance for the selected propeller with a different value of 훾/퐷 and 휎 within the applicable range: 17x7, 14x7, and 11x7. The following equation is derived from Equation 6.4:

2 푃푐 훾 ℎ 1 − (1 − ) ∗ 휎 ∗ 100/ ( ) (0 ≤ ≤ 0.5) 푃푃 퐼퐺퐸 푃푂퐺퐸 퐷 퐷 = 1 ( 6.6 ) 푃 푂퐺퐸 푃푐 훾 ℎ 1 − (1 − ) ∗ 휎 ∗ 100/ ( ) (−0.5 ≤ ≤ 0) { 푃푂퐺퐸 퐷 퐷

The predicted ground effect curve is then plotted below in Figure 55a with the force- based experimental result. It is clear that Equation 6.3, along with the baseline curve in Equation

6.5, predicts the ceiling effect (h/D < 0) well for all propellers selected. While the model slightly underpredicted the performance at very small h/D values for both the 14x7 and 11x7 propeller, which have a slightly high 훾/퐷 than 17x7 propeller.

1.05

0.95

0.85

0.75 푃퐼퐺퐸 푃푂퐺퐸 17x7 Experiment 0.65 14x7 Experiment 11x7 Experiment 17x7 Predicted 0.55 14x7 Predicted 11x7 Predicted 0.45 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 h/D

Figure 55a. Comparison of predicted changes in 푷푰푮푬/푷푶푮푬 and experimental result

The overall error in the prediction is less than 6%. This can be seen in Figure 55b, as positive error represents the overprediction of the ground effect while negative error represents underprediction.

7.00

5.00

3.00

1.00

-1.00 % % Error

-3.00

-5.00 17x7 14x7 11x7

-7.00 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 h/D

Figure 55b. Error in the traditional ground effect prediction model

The prediction model is also compared with other prediction models discussed in Chapter

II for the APC 17x7 and APC 14x7 propeller. The result is shown in Figure 56 below.

1.05

0.95

0.85

푃퐼퐺퐸 0.75 푃푂퐺퐸 17x7 Experiment 0.65 17x7 Predicted Cheeseman 17x7 Predicted He et al 14x7 Experiment 0.55 14x7 Predicted Cheeseman 14x7 Predicted He et al Hayden Large Rotor Prediction 0.45 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 h/D

Figure 56. Comparison of the prediction for APC 17x7 propeller

He et al. model [22], over predict the ground effect for the 14x7 propeller and underpredict the ground effect for 17x7 propeller. Hayden’s model [9], which is developed based on larger rotors, over predicted the ground effect. While the Cheeseman model [8] slightly underpredict the ground effect at ℎ/퐷 > 0.25. Also, his model is not valid for smaller ℎ/퐷 value due to the occurrence of the singularity. The model developed in this research does a better job predicting than the other prediction models.

6.2 Phenomenological Expression and Prediction for Partial Ground Effect

Three different propellers are studied for partial ground effect. Based on the analysis in the last section, the 17x12 propeller does not follow the overall trend of ground effect, while the 17x10 propeller has an unusual performance at h/D < 0. Thus, for the partial ground effect prediction, the result of the 17x7 propeller will be focused on, as it is a very good representative of the propellers that Equation 6.3 can be applied to for ground effect prediction.

To better understand the partial ground effect, the power required deficit, 푃푑푒푓, shown in

Equation 6.1 is plotted vs. the blockage ratio, at each positive h/D distance below in Figure 57.

0.50

h/D = 0.058 0.40 h/D = 0.118 h/D = 0.176 0.30 h/D = 0.235 h/D = 0.294 푃푑푒푓 h/D = 0.353 0.20

0.10

0.00

-0.10 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Blockage Ratio (B)

Figure 57. Power required deficit v.s blockage ratio at different h/D for APC 17x7

It is clear that with the decrement of the blockage ratio, the power required deficit reduces as mentioned in the previous analysis. A second-order polynomial fit is done for the data point at

2 the same h/D values, with the 푅 value for each curve > 0.98. It is clear that the 푃푑푒푓 drops to zero around the B = 0.4 which indicates the possibility that there would be no ground effect on a blockage plate with B < 0.4. Recall that the normalized diameter of the stagnation streamline for all propellers are between 0.4 and 0.5, the radial flow region could be eliminated when B < 0.4.

This would result in zero ground effect benefit. Although no experiment is done to validate this, both sets of evidence indicate the likelihood of this hypothesis being true.

Thus, the ground plate area within the B = 0.4 (r/R = 0.4) is limited, a new variable, the effective blockage, is introduced as written below:

2 2 2 퐵푒푓푓 = √(퐵 − 0.4 )/(1 − 0.4 ) ( 6.6 )

Based on the ‘baseline’ curve (Equation 6.3), the predicted ground effect 푃푃 퐼퐺퐸/푃푂퐺퐸

(Equation 6.5) and effective blockage ratio 퐵푒푓푓 (Equation 6.5). Equation 6.7 below is developed for partial ground effect prediction:

푃 ℎ 1 − (1 − 푃 퐼퐺퐸) ∗ 퐵1 (0 ≤ ≤ 0.5) 푃 푃 푒푓푓 퐷 퐵 퐼퐺퐸 = 푂퐺퐸 ( 6.7 ) 푃 푂퐺퐸 푃푃 퐼퐺퐸 √2 ℎ 1 − (1 − ) ∗ 퐵푒푓푓 (−0.5 ≤ ≤ 0) { 푃푂퐺퐸 퐷

The predicted partial ground effect curve (푃퐵 퐼퐺퐸/푃푂퐺퐸), along with the experimental result from the force-based experiment, is plotted below in Figure 58. It is clear that the scatter for the predicted and experimental result for the ceiling effect (h/D <0) is very small, except for the B =

0.5 case at a small h/D value, where the equation overpredicts the ceiling effect. This indicates that

Equation 6.7 predicts the ceiling effect well.

On the other hand, Equation 6.7 also over predicted the ground effect for the B = 0.5 case in ground effect. This is due to the minor difference for the B = 0.5 case between 0 < h/D < 0.2.

For other blockage ratios, Equation 6.7 predicts well at small h/D distances. However, between h/D

= 0.25 and h/D = 0.4, Equation 6.7 slightly under predicts the ground effect as the scatter in the experimental data for different blockages is small. The overall error in the prediction is less than

6% and is shown below in Figure 58b. Again, the positive error represents the overprediction of the ground effect while negative error represents underprediction.

1.05

0.95

0.85

0.75 푃퐼퐺퐸 푃푂퐺퐸 APC 17x7 0.5 0.65 Blockage APC 17x7 0.625 Blockage 0.55 APC 17x7 0.75 Blockage APC 17x7 1.0Blockage 0.45 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 h/D

Figure 58a. Comparison of predicted changes in 푷푩 푰푮푬/푷푶푮푬 and experimental result 8.00 APC 17x7 0.5 Blockage 6.00 APC 17x7 0.625 Blockage APC 17x7 0.75 Blockage 4.00 APC 17x7 1.0 Blockage

2.00

0.00 % % Error -2.00

-4.00

-6.00

-8.00 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 h/D

Figure 58b. Error in the partial ground effect prediction model

CHAPTER VII

CONCLUSIONS AND FUTURE WORK

7.1 Conclusions

Changes in R/C propeller performance due to ground proximity were found, not surprisingly, to increase thrust produced, and to decrease power-required, for a given propeller rotational speed. Higher solidity, and especially lower pitch-to-diameter ratio, led to a stronger ground effect. For the highest ratio of pitch to diameter ratio, there are anomalous results in extreme ground effect, possibly due to blade stall caused by the reduction of induced flow velocity. Flow visualization done by high-density surface tuft-array on the ground plane shows a circular stagnation streamline, separating the inward tangential flow and outward radial flow. Smoke flow visualization and static pressure measurements on the ground plate confirms the projected streamline as the stagnation streamline.

The existence of the stagnation streamline strongly relates to the ground effect. The lower pitch to diameter ratio propellers which encounter greater ground effect have a bigger stagnation streamline diameter. The reduction of the propeller power coefficient in the ground effect occurs at the same time as the stagnation streamline is projected on the ground plane, around h/D = 0.3 which is the Betz’s threshold where a significant drop in the power coefficient occurs in Betz’s ground effect theory.

The ceiling effect is investigated, which has not been discussed widely for larger rotors due to the rare occasion for larger rotorcraft to encounter the ceiling effect. The overall trend for the ground effect is similar to what is observed in the ceiling effect, where higher solidity and lower pitch-to-diameter ratio leads to a stronger ceiling effect. Highly symmetric ground and ceiling effect results are found for the small pitch to diameter ratio propeller, while the physics behind the ground and ceiling effect is very different.

An algebraic equation was developed for the prediction of the traditional ground and ceiling effect. Utilizing combinations of the propeller pitch to diameter ratio and solidity, instead of rotor geometry pitch angle, the algebraic equation leads to a collapse of the different cases in the normalized power required at constant thrust, vs. the ratio of ground distance to propeller diameter.

This collapsed curve is used as a ‘baseline’ ground effect to predict ground and ceiling effect using the algebraic equation. The uniqueness of the prediction model is that it can be applied to R/C propellers with a pitch to diameter ratio less than 0.636, in extreme ground and ceiling effect. While most of the existing models in the literature are only applicable for rotors with no blade twist.

Besides traditional ground and ceiling effect, partial ground and ceiling effect, which becomes very common for drones operated in complicated environments, was studied using different circular plates with blockage ratios ranging from 0.5 to 1.0. For the blockage ratio of 0.5, ground effect benefits: increment in thrust and reduction in power required, are very small. This is also reflected in the surface tuft flow visualization, with a smaller stagnation streamline occurs on the circular ground plate. While for the blockage ratio of 1.0, where the diameter of the circular plate is equal to the propeller disk, the ground effect benefits followed those of traditional ‘infinite’ ground. This relation holds for the ceiling effect as well, suggesting that any further increase in the circular ground plate diameter will have a minor effect on the propeller performance in ground proximity.

Further development of the ground effect prediction model was done based on the experimental result in partial ground effect to include the effect of different blockage ratios. The prediction model takes the blockage ratio into account and has a pretty good agreement with the experimental result. To the best of the author’s knowledge, none of the existing models in the literature has the ability to predict the partial ground effect.

Last but not least, the propeller effective thrust is studied, which provides a design guideline for R/C propeller placement on drones and propeller driven aircraft. The force on the circular blockage plate is subtracted from the propeller thrust to calculate the effective thrust. With

74 a higher blockage ratio, the propeller effect on thrust at constant power reduces, for both pusher and puller configuration, as expected. For the pusher configuration, the effective thrust becomes independent of the propeller pitch to diameter ratio. The changes in effective thrust are negligible when placing the propeller one diameter away from the blockage, although the normalized effective thrust never becomes close to 1.0. While for pusher configurations, the effect of the blockage is negligible since the normalized effective thrust for all blockage and propeller goes back to 1.0.

In general, placing the propeller one diameter away from any blockage will minimize the penalty of thrust reduction due to any type of blockage. In situations that the propeller is installed close to any type of blockage (like the cowl of a radial engine), the blockage should remain within the size of the propeller projected stagnation streamline, approximately 40% of the propeller diameter, to minimize the effect of the blockage.

To sum up, the ground effect on propellers is similar to larger rotors to some extent, while using the model developed for the larger rotor to predict propeller ground effect is not entirely accurate. Accounting for basic propeller parameters, especially solidity and pitch to diameter ratio, for the prediction of changes in propeller performance due to ground proximity is more suitable for

R/C propellers.

7.2 Future Work

Another type of partial ground effect has been proposed by the author during the current work, the annulus blockage, where a circular opening is located at the center of the ground plate, as an ‘opposite’ to the partial ground effect blockage plate discussed in the current work. A comparison of these two types of partial ground effect might provide a better prediction of the partial ground effect as a function of the blockage area.

Moreover, the loss of thrust coefficient in ground effect between h/D = 0.5 and 3.0 remains unknown. Further investigation is required to understand the effect of advance ratio on ground effect and ceiling effect. This brings the ground effect study in forward flight which also provides practical application to the modern drone operation.

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