ABSTRACT

Title of Thesis: THE EFFECT OF CONFINED AREAS
ON HELICOPTER PERFORMANCE

Dylan Black
Master of Science, 2023

Thesis Directed by: Dr. John Tritschler
Department of Aerospace Engineering

Flight test performance of an OH-58C helicopter hovering in confined areas is discussed

using a combination of pilot-recorded data cards and instrumentation data time histories. The test

includes an investigation of the effects of wall height and blade loading on hover performance

in close proximity to a three-walled structure forming a confined space. Hover performance

for a range of altitudes far from the confined area, at the edge of the confined area, and at the

center of the confined area are discussed. Significant performance penalties (i.e., up to 20%

greater than the power required to hover out of ground effect) were observed at various positions

within the confined space. Additionally, the pilots reported uncommanded vehicle excursions at

some positions within the confined area, necessitating increased control inceptor activity. These

observations are indicative of unique aerodynamic interactions that affect helicopter performance

and handling qualities within confined areas.



THE EFFECT OF CONFINED AREAS ON HELICOPTER PERFORMANCE

by

Dylan Black

Thesis submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment

of the requirements for the degree of
Master of Science

2023

Advisory Committee:
Dr. John Tritschler, Chair/Advisor
Associate Professor Joseph Milluzzo, Co-Advisor (Special Member)
Associate Professor Anubhav Datta
Assistant Professor Umberto Saetti



This publication is a work of the U.S. Government as defined in Title 17, United
States Code, Section 101. Copyright protection is not available for this work in

the United States.
2023



Acknowledgments

This work was made possible by the support and encouragement of countless individuals.

First, I’d like to thank my advisor, Dr. John Tritschler, for the opportunity to work on such a

unique project. He has ensured that I leave every meeting with a renewed zeal as well plenty of

new and exciting questions to investigate.

I would like to thank my co-advisor, Dr. Joseph Milluzzo, for his counsel over the last three

years and for encouraging me to consider graduate school in the first place. Thanks are also due

to Professor Anubhav Datta and Professor Umberto Saetti for challenging me in class as well as

taking the time to serve on my thesis committee and review the manuscript.

This work would not have been possible without the pilots who flew the test. Thank you,

John Holder, Chad Berman, Camille Lampert, and Jason Wyatt for venturing into lesser-known,

potentially hazardous flight conditions to create this unique data set.

I would like to extend my sincere thanks to numerous professors and staff at the United

States Naval Academy. Thank you, Dr. Gabriel Karpouzian, for laying the foundation required

for graduate-level engineering. Thank you, Dr. Ondrej Juhasz and Col. Scott Davids, along with

Dr. Milluzzo, for your stewardship of the undergraduate rotorcraft program. Thank you, Dan

Rodgerson, Steve Galindo, and Nick Hlavaty, for your tireless work in the lab.

I cannot begin to express my thanks to Cole Shenk, for agreeing to do this program with

me. I know the hours spent troubleshooting control laws and drafting slides in the wee hours of

ii



the morning likely conflicted with some of your other plans in life – sleep, namely – but despite

all of this, I am daily challenged to keep pace with your immutable optimism. Thanks also to

Jack Prewitt, Sridatta Satuluri, Vivek Uppoor, Logan Swaisgood, and Batin Bugday for sharing

your valuable time and talents.

I am extremely grateful for my family. To my parents, Tom and Janis, as well as my sister,

Bridget; you have never hesitated to support me throughout all of life’s endeavors. Thank you for

instilling in me a sense of duty and responsibility. I treasure your phone calls, visits, and loving

prayers.

I would not be where I am today without the support of my wife, Sophie. Thank you for

your love, encouragement, and patience. This year has been the best year of my life, and we’re

only just getting started. I would be remiss if I did not thank Dr. Tritschler and Dr. Milluzzo for

letting me take a month off for the wedding and honeymoon.

All thanks be to God for His design and for placing these people along my path.

iii



Table of Contents

Acknowledgements ii

Table of Contents iv

List of Tables vi

List of Figures vii

List of Abbreviations ix

Chapter 1: Introduction 1
1.1 Rotor Wake in Ground Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Classical Ground Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Adverse Ground Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3.1 Laboratory Investigations of Adverse Ground Effect . . . . . . . . . . . . 7
1.3.2 Flight Test Investigations of Adverse Ground Effect . . . . . . . . . . . . 10

1.4 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Chapter 2: Methodology 15
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.1 Description of the Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Description of the Confined Area . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Test Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.2 Experimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.3 Development of Data Extraction Method . . . . . . . . . . . . . . . . . . 23

Chapter 3: Results 30
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Analysis of Handwritten Data Cards . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2.1 Hover Performance on the Basis of Handwritten Data Cards . . . . . . . 31
3.3 Analysis of Instrumentation Data . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3.1 Hover Performance on the Basis of Instrumentation Data Histories . . . . 39
3.3.2 Collective Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.4 Comparison to Model Rotor Hover Performance in Confined Areas . . . . . . . . 48

iv



Chapter 4: Conclusions 51
4.1 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 52

Appendix 55

Bibliography 74

v



List of Tables

2.1 Bell OH-58C Kiowa characteristics. . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Tabular representation of the test matrix. Bold-faced table entries indicate an

example hover ladder. A hover ladder was completed for each combination of
confined area location, wall height, and rotor speed. . . . . . . . . . . . . . . . . 21

2.3 Winds and confined area wall height for each test day. . . . . . . . . . . . . . . . 23
2.4 Extraction method properties. Method 2 was used to extract the time-histories

which were used in the analysis of instrumentation data (see Section 3.3). . . . . 27

3.1 Comparison of full-scale rotor to model rotor. . . . . . . . . . . . . . . . . . . . 48

vi



List of Figures

1.1 Comparison between the OGE and IGE wake of a hovering rotor (from Ref. 7). . 2
1.2 Flow recirculation at deck edge (from Ref. 12). . . . . . . . . . . . . . . . . . . 3
1.3 Cheeseman and Hayden thrust models over a range of hub heights for HIGE as

compared to flight data for various helicopters from Lewis (data from Refs. 4–6). 6
1.4 Helicopter landing and encountering brownout conditions (from Ref. 17). . . . . 7
1.5 PIV flowfield measurements indicative of flow recirculation for different rotor

positions relative to a single-walled obstacle (from Ref. 24). . . . . . . . . . . . . 8
1.6 PTV visualization of flow recirculation due to obstacle (right), compared with a

mirrored proprotor wake in obstacle-free ground effect (left) (from Ref. 12). . . . 9
1.7 Snapshot of a rotor flowfield in the corner of water tank with tip clearance of

1/32R (from Ref. 28). Top view (a) shows bunching up of vortices. Side view
(b) shows upstream excursion of vortex filament at wall. . . . . . . . . . . . . . . 11

1.8 Effect of wall spacing on the power ratio of the rotor between parallel walls (data
from Ref. 29). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.9 Power ratios for a UH-72 hovering over level ground and sloped terrain as a
function of hub height and blade loading (Ref. 30). . . . . . . . . . . . . . . . . 13

1.10 V-22 EFP flight test (Ref. 31). . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1 Simulated LPD-17 flight deck. . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Preparation for CAL testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 The Elevated Fixed Platform (EFP). . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 OH-58C during CAL testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 Top view of the confined area structure. . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Schematic representation of the test matrix for hover ladders at each confined area

station: Free, Edge, and Center. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 Representative aircraft orientation (a) inside and (b) outside of the confined area. 22
2.8 Aircraft orientation, wind direction, wind speed, and wall height during each test

day. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.9 Time history of rotor torque for the first sortie, for hw = 2.04R. . . . . . . . . . . 25
2.10 Time history of radar altitude for the first sortie, for hw = 2.04. Each radar

altitude peak corresponds with the top of each hover ladder. . . . . . . . . . . . . 26
2.11 Radar altitude output test points from Method 1 (i.e., the least permissive criteria). 29
2.12 Radar altitude output test points from Method 2 (i.e., the most permissive criteria). 29

vii



3.1 Example hover ladder: Free, NR = 96%. . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Power ratios for each hover ladder with a fixed rotor speed, NR = 98%. The

power required out-of-ground-effect, CPOGE
, for all three locations was determined

through a visual fit of Equation 1.1 to the power ratios for obstacle-free ground
effect (Figure 3.2a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3 Power ratios computed from a selection of handwritten data cards for hw = 2.04R. 35
3.4 Power ratios computed from a selection of handwritten data cards for hw = 1.56R. 36
3.5 Power ratios computed from a selection of handwritten data cards for hw = 1.08R. 37
3.6 Power ratios computed from a selection of handwritten data cards for hw = 0.60R. 38
3.7 Comparison of power ratios computed from handwritten data cards and instrumentation

data histories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.8 Collective pitch inputs for a selection of data cards, for hw = 2.04R. . . . . . . . 44
3.9 Collective pitch inputs for a selection of data cards, for hw = 1.56R. . . . . . . . 45
3.10 Collective pitch inputs for a selection of data cards, for hw = 1.08R. . . . . . . . 46
3.11 Collective pitch inputs for a selection of data cards, for hw = 0.60R. . . . . . . . 47
3.12 Hover performance of an OH-58 (from time histories and data cards) and an

isolated rotor (Shenk, Ref. 34) at the center of a U-shaped confined area. . . . . . 50

viii



List of Abbreviations

A Rotor disk area, πR2

c Blade chord
CT Thrust coefficient, T/ρA(ΩR)2

CT/σ Blade loading coefficient
CP Power coefficient, P/ρA(ΩR)3

hw Wall height
Nb Number of blades
lfw Front wall length
lsw Side wall length
r Yaw rate
R Rotor radius
t Time
tmin Minimum on-condition duration
tmax Maximum off-condition duration
T/TOGE Thrust ratio (equivalent to CT/CTOGE

)
P/POGE Power ratio (equivalent to CP/CPOGE

)
w Vertical speed
xw Longitudinal distance from hub to wall
yw Lateral distance from hub to wall
z Hub height above the ground

NR Rotor speed, %
TQ Engine torque, %

δr Yaw rate tolerance
δw Vertical speed tolerance
σ Rotor solidity, NbcR/A

AGL Above ground level
EFP Elevated fixed platform
GARTEUR Group for Aeronautical Research and Technology in Europe
HIGE Hover-in-ground-effect
HOGE Hover-out-of-ground effect
IGE In-ground-effect
OGE Out-of-ground-effect
NACA National Advisory Committee for Aeronautics
USNTPS United States Naval Test Pilot School

ix



Chapter 1: Introduction

The fundamental value of all rotorcraft, when compared to their fixed wing counterparts,

is derived from their ability to hover. Because of this unique ability, helicopters can takeoff and

land in a variety of operational environments, from rugged mountains to urban centers. When

operating any rotorcraft, it is important to remember that any mechanism which affects the rotor

flowfield can also affect rotorcraft performance and handling qualities. An understanding of

hover in ground effect (HIGE) and hover out of ground effect (HOGE) performance in a variety

of operational environments is therefore essential to rotorcraft safety.

Chapter 1 is organized as follows. Section 1.1 provides an introduction to the fundamental

flow structures responsible for ground effect. Section 1.2 presents a survey of classical ground

effect models. Section 1.3 discusses various non-ideal flight conditions in which adverse ground

effect is possible. Section 1.4 outlines the organization of the thesis.

1.1 Rotor Wake in Ground Effect

Rotors generally experience a performance benefit when hovering within one rotor diameter

of the ground, since the induced power required for a given thrust condition is reduced for

decreased inflow through the rotor disk. This performance benefit has been well documented

(Refs. 1– 6).

1



Figure 1.1: Comparison between the OGE and IGE wake of a hovering rotor (from Ref. 7).

Though the underlying flow structures are complex, ground interference effects are most

pronounced in hover and at low forward speeds. Ground effect is generally considered negligible

for advance ratios greater than 0.10 (Ref. 8. In addition to operational factors such as rotor

hub height above the ground, numerous design parameters can affect the rotor wake in ground

effect, including the number and position of rotors, blade loading, blade geometry, and number

of blades.

During hover, and in the absence of obstacles, the ground affects a rotor flowfield by turning

the wake radially outward into a wall jet and decreasing the magnitude of the induced velocity

through the rotor disk. Figure 1.1 shows a schematic of a characteristic rotor wake in and out of

ground effect. Fradenburgh (Ref. 9) employed early flow visualization methods to investigate the

underlying ground-wake interaction, noting that the thickness of the jet boundary is a function of

rotor height above the ground and disk loading.

2



Figure 1.2: Flow recirculation at deck edge (from Ref. 12).

Any obstacle to the flowfield may have additional effects on the rotor inflow and resulting

IGE performance. During shipboard operations, water entrained in the flow field can yield

visualization of flow recirculation. Figure 1.2 shows an example of flow recirculation from a

ship’s deck. Timm (Ref. 11) employed flow visualization techniques to show that flow recirculation

is possible when a rotor in ground effect operates in close proximity to ground obstacles. The

primary requirement for flow recirculation was that the obstacle height exceeded the height of

the radial wall jet induced by ground effect. Contrary to the reduction of inflow associated with

obstacle-free ground effect, the presence of ground obstacles was shown to increase the inflow

through the rotor disk and increase the resulting power required.

Transition to forward flight may also cause recirculation in the form of a ground vortex.

Horn (Ref. 10) investigated recirculation induced by obstacles and transition to forward flight

using Navier-Stokes computational fluid dynamics coupled with a helicopter flight dynamics

model.

3



1.2 Classical Ground Effect

The literature includes many classical ground effect models which predict the performance

of rotors parallel to a flat, infinite ground plane with no obstacles affecting the rotor outwash.

Hover performance OGE is often considered as a worst-case reference flight condition. Performance

benefits IGE are conceptualized as a power ratio, i.e., P/POGE , less than one for fixed thrust, or

a thrust ratio, i.e., T/TOGE , greater than one for fixed power.

Betz (Ref. 1) proposed a combination of a simple momentum theory approach for heights

less than one-quarter radius and an image sink potential flow method for heights exceeding one-

quarter radius. To validate the theory, a rotor was moved closer to the ground and rotational speed

was reduced to match TOGE at each test point.

Knight and Hefner (Ref. 2) modeled the effect of the ground on rotor inflow as a cylindrical

vortex sheet. The effect was reported as torque ratios for fixed thrust, which is equivalent to power

ratios for fixed thrust and rotational speed. The Knight and Hefner model predicted a decrease in

torque as the rotor approached the ground. The predictions were in agreement with experimental

results for heights above one-half radius.

Zbrozek (Ref. 3) introduced an empirical model for rotor ground effect, which characterized

the increase in rotor thrust for a given power as a function of height above the ground. Empirical

methods were introduced for isolated rotors and the benefits of ground effect were documented

from experiments without thorough treatment of the underlying inflow effects.

Hayden (Ref. 4) developed an empirical method for predicting HIGE power requirements

for full-scale helicopters on the basis of a series of tethered and free hover flight tests reported by

Lewis (Ref. 5). Hover performance IGE was empirically predicted for a variety of single main

4



rotor helicopters. Figure 1.3 demonstrates that for fixed power in hover, as a helicopter moves

closer towards the ground, i.e., z/R decreases, the thrust ratio, TIGE/TOGE , increases.

Cheeseman and Bennett (Ref. 6) developed an analytical method for predicting the HIGE

thrust benefit for an isolated rotor over an ideal ground plane using a potential flow method of

images, with an image source instead of the image sink used by Betz (Ref. 1). The effect of

the ground in hover was conceptualized as a thrust ratio relating IGE to OGE rotor thrust as a

function of hub height alone, expressed by the equation

[
TIGE

TOGE

]
P=constant

=
1

1− 1

16( z
R)

2

, (1.1)

where z is the hub height above the ground. In another model, HIGE effects were also predicted

as a function of hub height and blade loading, expressed by the equation

[
TIGE

TOGE

]
P=constant

=
1

1− σClαλi

CT

1

16( z
R)

2

. (1.2)

Cheeseman and Bennett’s theoretical predictions were in good agreement with all existing

empirical models for hub heights above one-half rotor radius, but were presented in the form

of a simple, closed-form, analytical solution as opposed to the prior existing empirical curve-

fit methods. Hub heights below one-half rotor radius are not operationally relevant, as most

helicopter rotors are positioned more than one-half rotor radius above skids or landing gear.

5



Figure 1.3: Cheeseman and Hayden thrust models over a range of hub heights for HIGE as
compared to flight data for various helicopters from Lewis (data from Refs. 4–6).

1.3 Adverse Ground Effect

In contrast to classical ground effect performance models, operational experiences indicate

that the presence of the ground is not always beneficial. As a helicopter transitions from hover

to a low forward speed at a low height above the ground, the induced velocity increases, leading

to an increase in power required as opposed to the typical decrease in power required associated

with transition to forward flight far above the ground (Ref. 13). Heyson (Ref. 14) predicted the

effect of the ground in forward flight by modeling the rotor as a directional source, concluding

that the positive effect of the ground decreases more rapidly with increasing hub heights at low

forward speeds when compared to hover. Increases in power required were discovered which

were caused by the onset of ground-induced vortex ring state and premature blade stall for rotors

6



Figure 1.4: Helicopter landing and encountering brownout conditions (from Ref. 17).

with a rearward tilt in low-speed forward flight. In addition to the possibility of developing a

ground vortex in transition to forward flight, shuddering on approach and loss of yaw control

are possible due to ground-wake-rotor interactions (Refs. 15, 16). At high speeds, ground effect

provides a smaller performance benefit compared to hover.

Low altitude operations over sand or snow can introduce unique issues due to human

factors. Brownout is a potential threat due to aerodynamic interaction with ground sediment

which can lead to pilot disorientation and loss of visual awareness (Ref. 7,17). Figure 1.4 shows a

helicopter encountering brownout conditions during landing. Recent accidents involving vehicles

during the takeoff and landing phases of flight (Ref. 18) have prompted research investigations to

understand the fundamental causes and effects of obstacle induced flow recirculation.

1.3.1 Laboratory Investigations of Adverse Ground Effect

The complex turbulent flow structures which are inherent to recirculating flow have necessitated

increased understanding of rotor wake flows out of ground effect. The structure and strength of

7



Figure 1.5: PIV flowfield measurements indicative of flow recirculation for different rotor
positions relative to a single-walled obstacle (from Ref. 24).

the wake is known to be affected by parameters such as disk loading, number of rotor blades,

number and placement of rotors, blade geometry, fuselage shape, and rotor height (Ref. 19).

Particle image velocimetry (PIV) flowfield measurements for a hovering rotor in classical, obstacle-

free ground effect characterized the aerodynamic interaction between blade tip vortices and the

ground and showed a correlation between rotor height and the resulting wall jet height (Ref. 20).

A GARTEUR Action Group was formed to investigate rotor-obstacle interactions (Refs. 21–

24). Recent PIV flowfield measurements for a hovering rotor in close proximity to a cube

structure indicates pronounced flow recirculation when the rotor plane is aligned with and just

below the top of the obstacle (Refs. 23, 24). Figure 1.5 shows the flowfield at three rotor hub

heights and fixed spacing from the obstacle. Locations where flow recirculation occurred were

associated with significant thrust reduction as well as pitching and rolling moments due to asymmetric

rotor inflow.

Negative effects of the ground can occur in a variety of operationally relevant circumstances.

Performance penalties can exist for rotors hovering over inclined and moving surfaces (Refs. 25, 26)

which depend on the rotor-ground angle, the rate and direction of heaving motions, and rotor

blade loading. Additionally, the nature of non-ideal ground effect is often non-monotonic with

8



Figure 1.6: PTV visualization of flow recirculation due to obstacle (right), compared with a
mirrored proprotor wake in obstacle-free ground effect (left) (from Ref. 12).

respect to hub height, but low test matrix resolution can lead to misleading, monotonic results

(Ref. 27).

Vehicles with higher disk loading and induced inflow may be more susceptible to non-

ideal recirculation effects. The combination of high disk loading, rotor-on-rotor interactions,

complicated proprotor geometry, and shipboard environmental concerns including ship-wake

interactions and partial ground effect approaches make tiltrotors particularly susceptible to non-

intuitive performance effects. A recent laboratory-scale study investigated tiltrotor-obstacle interactions

in zero-wind conditions through an extensive set of hover performance measurements and particle

tracking velocimetry (PTV) flowfield measurements which specifically targeted test cases with

flow recirculation (Ref. 12). Figure 1.6 shows a case of recirculation which was associated with

a rotor torque increase of 7% above OGE torque for a fixed thrust.

9



Another case that results in performance penalties which may be due to flow recirculation

is hover in confined spaces, where there is more than one obstacle interacting with the wake

flowfield. Konuş (Ref. 28) investigated the confined area flowfield for a rotor in a water tank.

Flow visualization and PIV measurements were conducted for wake interactions with a pair of

walls forming a corner. With a small tip clearance of 1/32R, Konuş noted a bunching up of vortex

filaments at the walls not unlike vortex ring state and a periodic excursion of vortex filaments

upstream of the rotor disk (i.e., flow recirculation). Iboshi (Ref. 29) investigated confined area

performance effects for a teetering rotor confined between a set of parallel walls. The confined

area geometry was altered by varying wall spacing and wall height to achieve a comprehensive

set of performance data in two-walled confined spaces. Figure 1.8 shows the results for varying

hub heights and wall spacing. For a large wall-spacing, the performance effects closely matched

what is expected of classical, obstacle-free ground effect. As wall spacing was decreased, a

distinct performance penalty became apparent. For a wall spacing of 2.5 – 3.0R, the change in

power ratio with hub height became non-monotonic. A 10% increase in power required above

POGE was recorded for a wall spacing of 2.5 – 3.0R just below the top of the walls. The power

at z = 2.2R approached POGE for most cases aside from a wall spacing equal to 5.0R, which

induced a 5% power penalty at z = 2.2R.

1.3.2 Flight Test Investigations of Adverse Ground Effect

Adverse ground effect studies have also been investigated at full-scale. Flight testing of

a UH-72A Lakota examined hover performance over sloped terrain, which was compared to

laboratory analysis of a rotor over an inclined platform (Ref. 30). Figure 1.9 shows power

10



Figure 1.7: Snapshot of a rotor flowfield in the corner of water tank with tip clearance of 1/32R
(from Ref. 28). Top view (a) shows bunching up of vortices. Side view (b) shows upstream
excursion of vortex filament at wall.

Figure 1.8: Effect of wall spacing on the power ratio of the rotor between parallel walls (data
from Ref. 29).

11



ratios for hover over sloped and level terrain at various rotor hub heights and thrust conditions.

Hovering over sloped terrain resulted in performance effects which were significant enough to

avoid being masked by the typical variation seen in flight test data. For some conditions (i.e.,

certain combinations of hub height and blade loading), the effect of sloped terrain was observed

to increase power requirements above those associated with OGE hover power requirements.

A series of flight tests of a V-22 and three single-main-rotor helicopters (Ref. 31) investigated

hover performance in close proximity to an Elevated Fixed Platform (EFP). The V-22 tests

included a series of approaches and hover test points and the helicopters were tested in hover.

Figure 1.10 shows a photograph taken during the test. While these flight tests bridge the gap

between full-scale and laboratory tests for inclined surfaces and flows around obstacles, there

have been no such full-scale studies to investigate the effects of confined areas on helicopter

performance. As such, the present study includes flight test data collected at the United States

Naval Test Pilot School (USNTPS) that will be useful to continue the characterization of confined

area rotor performance. The results will provide a data set for investigating the scalability

of laboratory experiments and validating computational models of single main rotor helicopter

performance in confined areas.

1.4 Thesis Organization

The current chapter provided an introduction into the effects of the ground on hover performance.

The fundamental flow mechanics were discussed, and a survey of existing theoretical and experimental

models for classical ground effect was conducted. Additionally, a literature review of various

non-ideal ground effect experiments has shown that adverse performance effects are possible in

12



Figure 1.9: Power ratios for a UH-72 hovering over level ground and sloped terrain as a function
of hub height and blade loading (Ref. 30).

Figure 1.10: V-22 EFP flight test (Ref. 31).

13



a variety of flight conditions including transition to forward flight, hover over sloped terrain or

a moving ground plane, and hover near various flowfield obstacles. These experiments included

both laboratory and full-scale flight tests with performance and flowfield measurements.

Chapter 2 presents the methodology of the current work, including the equipment used and

test techniques. Processing methods for extracting useful records from instrumentation data time

histories are also discussed.

Chapter 3 presents the resulting hover performance inside of a confined area, including the

analysis and comparison of handwritten data with instrumentation data. The effect of confined

areas on variation of collective blade pitch is also investigated.

Chapter 4 presents the conclusions as well as recommendations for future work.

14



Chapter 2: Methodology

2.1 Introduction

A Bell OH-58C Kiowa helicopter was tested through a series of flights to collect hover

performance data in close proximity to a three-walled structure. This chapter provides a comprehensive

description of the experiment, including details of the aircraft and the confined area, as well as

test techniques and challenges.

2.2 Equipment

2.2.1 Description of the Aircraft

The OH-58C has a teetering rotor with a NACA 0012 airfoil section throughout. Additionally,

the blades are untwisted and rectangular. The combination of a simple rotor design and the ability

to vary thrust coefficient through a wide range via fuel burn alone makes the aircraft well suited

for academic studies. Table 2.1 shows relevant aircraft characteristics.

15



Table 2.1: Bell OH-58C Kiowa characteristics.

Parameter Units Value

Vehicle Characteristics

Minimum gross weight lb 2,500
Maximum gross weight lb 3,200
Minimum CT/σ — 0.066
Maximum CT/σ — 0.083
Main Rotor Characteristics

Airfoil — NACA 0012
Rotor radius, R ft 17.65
Chord, c in 13
Number of blades, Nb — 2
Rotor solidity, σ — 0.039
Nominal angular speed, ω RPM 354
Nominal tip speed, Vtip ft/s 655

Tail Rotor Characteristics

Airfoil — NACA 0012
Rotor radius, R ft 2.71
Chord, c in 5.3
Number of blades, Nb — 2
Rotor solidity, σ — 0.104
Nominal angular speed, ω RPM 2626
Nominal tip speed, Vtip ft/s 745

Engine Characteristics

Maximum continuous torque % 85
Maximum intermittent torque (5 min) % 100
Maximum rated power hp 420

16



The flight control system of the OH-58C consists of dual conventional mechanical controls,

with no stability augmentation system. The helicopter was instrumented for flying qualities and

performance testing, and data were recorded via instrumentation as well as with hand-recorded

data cards. The instrumentation consisted of a boom to measure airspeed and vehicle attitude

as well as an interface with the production aircraft data to record engine parameters, fuel burn,

rotor speed, and flight control positions. A radar altimeter was used to measure fuselage height

above ground level (AGL). Two cockpit displays allowed for real time monitoring of a subset of

the recorded parameters, and analog tapes of all parameters were digitized at 1.67Hz for analysis

purposes.

2.2.2 Description of the Confined Area

The EFP was originally constructed from shipping containers to simulate the flight deck of

an LPD-17 class ship (Ref. 31). The EFP was a four-walled cube with a flat top and was used

for a series of hover and approach tests. After these tests, the EFP was partially deconstructed to

create a three-walled structure suited for Confined Area Landing (CAL) tests. Figure 2.3 shows

the EFP from the original test and its deconstruction. Figure 2.4 shows the OH-58C operating

inside of the confined area resulting from the partial deconstruction of the EFP.

The confined area consisted of a front wall of length, lfw = 4.73R, and two side walls of

length, lsw = 4.50R, where R= 17.65ft. The position of the helicopter within the confined area

was defined by the longitudinal distance between the hub and the front wall, xw, and the lateral

distance between the hub and each side wall, yw.

Two longitudinal stations within the confined area were tested as well as a level ground

17



Figure 2.1: Simulated LPD-17 flight deck. Figure 2.2: Preparation for CAL testing.

Figure 2.3: The Elevated Fixed Platform (EFP).

position far from any obstacles. Performance measurements were collected for multiple target

hub heights at the entrance (xw,e = 4.50R) and the center (xw,c = 2.25R) of the structure, where

yw,e = yw,c = ±2.36R. Performance measurements were also obtained at an additional position

far from the structure (xw,f = yw,f = ±∞), so that the performance effects of hovering in the

confined area could be compared to classic, obstacle-free ground effect. For the present work, the

stations far from the structure, at the entrance of the structure, and at the center of the structure are

referred to as Free, Edge, and Center, respectively. Figure 2.5 shows a top view of the confined

area with depictions of the Edge and Center stations.

2.3 Test Techniques

2.3.1 Safety

Safety considerations in the test flights included the definition of “knock-it-off” torque

limits as well as a “build-up” philosophy to the sequencing of test points. Test-specific risks

such as loss of yaw control inside of the confined area were identified and mitigated. Weather

18



Figure 2.4: OH-58C during CAL testing.

requirements also contributed to flight safety and provided conditions suitable for data quality.

2.3.2 Experimentation

Test points were completed for a range of target hub heights, aircraft locations, and thrust

settings. Target hub heights, z, were achieved using the radar altimeter and visual references

when operating inside of the confined space and using the radar altimeter when operating outside

of the confined space. Figures 2.6 and 2.2 show schematic and tabular representations of the

hover ladder test matrix. Pilots held each hover test point for approximately 30 seconds. Pilots

flew a series of test points (i.e., a hover ladder) at each location (Free, followed by Edge, followed

19



Figure 2.5: Top view of the confined area structure.

20



Figure 2.6: Schematic representation of the test matrix for hover ladders at each confined area
station: Free, Edge, and Center.

Table 2.2: Tabular representation of the test matrix. Bold-faced table entries indicate an example
hover ladder. A hover ladder was completed for each combination of confined area location, wall
height, and rotor speed.

Confined Area Location Wall Height (R) Rotor Speed (%) Rotor Hub Height

Free 2.04 96 0.74
Edge 1.56 97 1.02

Center 1.08 98 1.53
0.60 99 2.04

100 2.89
3.17

by Center) and repeated the sequence to achieve a spread of thrust settings. A separate sortie was

flown for each container wall height (i.e., four, three, two, and one container high).

The test matrix was designed to define a hover power polar representative of each combination

of hub height and longitudinal position relative to the confined space. During each test flight, the

pilots employed the free-air, ground-referenced hover test technique, in which the rotor speed,

NR, and gross weight, W , varied to achieve the widest possible spread in thrust coefficient, CT .

Rotor speeds were reduced for the earlier, heavier test points (to maximize CT ) and increased for

the later, lighter test points (to minimize CT ). Five sorties were completed for a total of 9.3 hours

of OH-58 flight test data.

21



(a) Aircraft nose oriented into the wind
for Free test points.

(b) Aircraft nose oriented into the confined area for
Edge and Center test points.

Figure 2.7: Representative aircraft orientation (a) inside and (b) outside of the confined area.

During each flight, the aircraft was oriented with its nose into the confined area for the Edge

and Center test points and into the wind for the Free test points. It is noteworthy that the pilots

reported the test points executed at the Edge and Center were less stable than Free test points.

Figure 2.7 shows the difference in heading among test points inside and outside of the confined

area for a representative case. The heading of the aircraft with its nose into the confined area

was 307°, and the direction of the wind varied for each test day. It was important to consider the

possible effects of the wind when analyzing the effects of the confined area. Maximum sustained

winds for each test day were 6–10 kts with few gusts. These winds were higher than desired for

hover testing, however, a limited test window drove the team to accept more permissive wind

limits for the test.

The relative wind direction differed greatly between test points inside and outside of the

confined area due to the difference in aircraft heading. The true wind direction also fluctuated

within ±20° of the mean true wind direction during each sortie. Figure 2.8 shows the mean true

winds and aircraft orientation inside of the confined area, while Table 2.3 lists the magnitude and

22



direction of the winds as well as the wall height for each test day. During the third test day, winds

were near zero at the start of the test and increased to 10 kts by the end of the test; the wind speed

was negligible for the first three hover ladders only, and was greater than 5 kts for the remainder

of the test. During each of the other test days, the wind speed fluctuated within ±1 kt of the mean

wind speed listed in Table 2.3.

Table 2.3: Winds and confined area wall height for each test day.

Day Wind Direction (°) Wind Speed (kts) Wall Height (R)

True Relative Range Average

1 050 103 6 – 8 7 2.04
2 000 053 7 – 9 8 1.56
3 170 223 0 – 10 7 1.08
4 130 183 5 – 7 6 0.60

2.3.3 Development of Data Extraction Method

While it is conventional in hover performance flight testing to execute a trimmed hover

test point with minimal control inputs for a set duration, this was not achievable for all test

points within the confined area (i.e., at Edge and Center locations). For these test points, pilots

commented that (i) hover maintenance required more continuous control inputs than is typical in

standard hover testing, (ii) uncommanded vehicle excursions occurred (particularly in the pitch

and heave axes), and (iii) the mean trimmed control positions appeared to be different than they

were for the Free hover points taken immediately before and after the points in the confined

area. The pilots further commented that these observations exhibited some dependency on the

hover height for test points within the confined area. Such comments are consistent with the

indication of complicated aerodynamic interactions for test points executed within the confined

23



(a) Free, Day 1;
(050° T, 6–8 kts)

(b) Edge, hw = 2.04R
Day 1; (050° T, 6–8 kts)

(c) Center, hw = 2.04R
Day 1; (050° T, 6–8 kts)

(d) Free, Day 2;
(000° T, 7–9 kts)

(e) Edge, hw = 1.56R
Day 2; (000° T, 7–9 kts)

(f) Center, hw = 1.56R
Day 2; (000° T, 7–9 kts)

(g) Free, Day 3;
(170° T, 0–10 kts)

(h) Edge, hw = 1.08R
Day 3; (170° T, 0–10 kts)

(i) Center, hw = 1.08R
Day 3; (170° T, 0–10 kts)

(j) Free, Day 4;
(130° T, 5–7 kts)

(k) Edge, hw = 0.60R
Day 4; (130° T, 5–7 kts)

(l) Center, hw = 0.60R
Day 4; (130° T, 5–7 kts)

Figure 2.8: Aircraft orientation, wind direction, wind speed, and wall height during each test day.

24



0 1000 2000 3000 4000 5000 6000

Time (s)

0

20

40

60

80

100

120

140

T
o
rq

u
e
 (

%
)

Figure 2.9: Time history of rotor torque for the first sortie, for hw = 2.04R.

area. Because of the subjective variation in the test point stability that was observed by the pilots,

a method was devised to automatically extract test point data records from the full instrumentation

time history.

The extraction method took aircraft instrumentation data consisting of a time vector and

individual vectors for each recorded vehicle state, and it extracted portions of the full time-history

into individual data records on the basis of (i) user-specified tolerances on each data parameter,

(ii) a minimum on-condition duration to count as a data run, and (iii) a maximum off-condition

duration to end a data run. Many vehicle states were initially considered as possible extraction

parameters, including engine torque, translational speeds, angular rates, and control inputs. On

25



0 1000 2000 3000 4000 5000 6000

Time (s)

10

20

30

40

50

60

70
R

a
d
a
r 

a
lt
it
u
d
e
 (

ft
)

Hover Ladders

Figure 2.10: Time history of radar altitude for the first sortie, for hw = 2.04. Each radar altitude
peak corresponds with the top of each hover ladder.

the basis of manual selection and adjustment, extracting periods of near-zero vertical speed, w,

and yaw rate, r, was determined to give the best results. Vertical speed was computed from the

rate of change (first-order finite difference) of radar altitude and yaw rate was directly measured.

Figure 2.10 shows the radar altitude for the duration of the flight, where each peak shown in

Figure 2.10 represents a distinct hover ladder. Extracting on the basis of vertical speed allowed

for elimination of transition time between test points, such as when the aircraft was climbing

between target altitudes or maneuvering between stations. Similarly, extracting on the basis of

yaw rate identified periods of near-zero yaw moment. Extracting on the basis of yaw rate limited

26



Table 2.4: Extraction method properties. Method 2 was used to extract the time-histories which
were used in the analysis of instrumentation data (see Section 3.3).

Condition On Off

No. δw (ft/s) δr (deg/s) tmin (s) tmax (s)

Restrictive 1 ±0.35 ±8 6 2
Permissive 2 ±0.35 ±8 2 3

the influence of transient tail rotor inflow on the torque measurements.

The tolerances for vertical speed, δw, and yaw rate, δr, were defined manually, as shown

in Table 2.4. On-condition test points were defined as individual test points which were within

both of the defined tolerances. Off-condition test points were defined as individual test points

which were outside of one or both of the defined tolerances. To extract periods of on-condition

test points (i.e., data runs) as opposed to isolated individual test points, additional extraction

properties were introduced, where tmin was the minimum on-condition duration to count as a

complete data run and tmax was the maximum off-condition duration before an individual run

was considered to have ended.

The permissiveness of the extraction method was adjusted by altering its properties, where

increasing δw, δr, and tmax would make the extraction method more permissive and increasing

tmin would make the extraction method less permissive. The extraction function selected time

periods from the sorties, and parameters of interest, were analyzed for the extracted periods,

including altitude and performance coefficients. Extraction function properties were manually

adjusted to determine criteria that yielded results for all hub heights and confined area stations.

Table 2.4 shows the properties of two distinct sets of parameters, where Method 1 was the least

permissive, and Method 2 was the most permissive.

27



For the purposes of extraction method development, δw and δr were fixed such that approximately

50% of the total sortie time history was on-condition. The permissiveness of each method was

entirely controlled by changes to tmin and tmax. Figure 2.11 shows the output radar altitude time

history from Method 1. This method was too fine to capture target altitudes in the middle of each

hover ladder (hub heights near the top of the walls) which necessitated a coarser method for that

region. Method 1 rejected target altitudes near the top of the walls on the basis of vertical speed,

which was indicative of increased vertical motion when the rotor height was near the wall height.

Altitudes close to the ground and far above the ground were permitted by Method 1. Figure 2.12

shows the output radar altitude time history from Method 2, which captures performance over

the entire range of target altitudes. Hover performance was extracted by applying Method 2 over

the duration of the test flight. Although Method 2 may be excessively permissive for deep IGE

and OGE conditions, it was desirable to apply a single set of criteria to all test points in order to

facilitate meaningful comparative analyses across different conditions.

28



0 1000 2000 3000 4000 5000 6000

Time (s)

10

20

30

40

50

60

70

R
a
d
a
r 

a
lt
it
u
d
e
 (

ft
)

Figure 2.11: Radar altitude output test points from Method 1 (i.e., the least permissive criteria).

0 1000 2000 3000 4000 5000 6000

Time (s)

10

20

30

40

50

60

70

R
a
d
a
r 

a
lt
it
u
d
e
 (

ft
)

Figure 2.12: Radar altitude output test points from Method 2 (i.e., the most permissive criteria).

29



Chapter 3: Results

3.1 Introduction

The following analysis of confined area helicopter performance was computed from helicopter

instrumentation data as well as hand-recorded data cards. For both sets of data, the power

coefficient was determined using the equation,

CP =
KQ TQ NR× 550

ρ A V 3
tip

, (3.1)

where KQ is the engine torque coefficient, TQ is the engine torque, NR is the rotor speed, ρ

is the air density, A is the rotor disk area, and Vtip is the blade tip speed. The factor of 550

converts power from engine shaft horsepower to ft-lb-s−1. Density was computed from the

mean barometric pressure and temperature for each test day. Mean recorded torque, TQ, and

rotor speed, NR, were used to calculate the power required from the handwritten data cards.

Instantaneous values of these parameters were used from the time history for the first test flight,

which was conducted for a wall height of four shipping containers. Instrumentation data from the

subsequent three flights (i.e., those with wall heights of three, two, and one shipping container)

were not usable for performance analysis. The present work includes a comparison between the

hand recorded data and instrumentation data for the first test flight (i.e., a wall height of four

30



shipping containers) in order to assess the feasibility of using solely the handwritten data for

performance analyses.

3.2 Analysis of Handwritten Data Cards

The following analysis was computed from the handwritten data cards which were recorded

by the pilots during the flights. Figure 3.1 shows an example data card for a single hover ladder far

from the confined area. A similar data card was produced for the hover ladder at each combination

of rotor speed and hover location relative to the confined area (i.e., Free, Edge, and Center), for

a total of 12–15 hover ladders per sortie. At each hover height (defined by a target radar altitude

value), pilots recorded total fuel burn and rotor torque from cockpit instruments. Fuel burn was

recorded in tenths of a gallon and rotor torque was recorded as a percent (i.e., the units of the

gauges). In some instances, the pilots noted fluctuations in the torque gauge by recording a

torque range on the data card instead of a discrete value (e.g., Run 5 shown in Figure 3.1). The

data cards show increased fluctuations inside the confined space, especially for hover heights

with the rotor hub near the top of the walls, for 1R < z < 2R. Fluctuations were also apparent in

the instrumentation data, which will be discussed in Section 3.3. For the purposes of processing

the data cards, the median of each torque range was used in the calculation of power required.

3.2.1 Hover Performance on the Basis of Handwritten Data Cards

The pilots recorded 12–15 data cards for each sortie, corresponding to a hover ladder for 4–

5 rotor speeds at each station with respect to the confined area: Free, Edge, and Center. Figure 3.2

shows the power ratio, CP/CPOGE
, at each target hub height for a rotor speed of NR= 98%. The

31



Figure 3.1: Example hover ladder: Free, NR = 96%.

32



0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(a) Free, CT /σ = 0.075

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(b) Edge, CT /σ = 0.072

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(c) Center, CT /σ = 0.072

Figure 3.2: Power ratios for each hover ladder with a fixed rotor speed, NR = 98%. The power
required out-of-ground-effect, CPOGE

, for all three locations was determined through a visual fit
of Equation 1.1 to the power ratios for obstacle-free ground effect (Figure 3.2a).

OGE power condition, CPOGE
, for each rotor speed was visually approximated from the Free

hover ladder (i.e., the classical ground effect results) and applied to calculate power ratios for

the following two hover ladders at the Edge and Center of the confined space. This process was

repeated independently for each rotor speed on each test day.

Figure 3.3 shows power ratios, CP/CPOGE
, for a selection of three rotor speeds during

the first sortie, for a wall height of hw = 2.04R. Notice that CP/CPOGE
> 1 is indicative of a

performance penalty, when power required exceeds power required OGE. Appendix A includes

power ratios for all tested rotor speeds.

Figure 3.3 shows that power required was dependent on hub height and confined area

effects. A distinct power penalty was seen at many hub heights at the Edge and Center of the

confined area (see Figures 3.3b, 3.3c, 3.3e, 3.3f, 3.3h, 3.3i). The power penalty was greater at

the Center than the Edge location, with a peak power penalty of 23% at the Center location for a

hub height of z = 1.53R (see Figure 3.3c). The magnitude of the confined area power penalty at

most other hub heights was similar for each thrust condition tested, for CT/σ = 0.066− 0.077.

Figure 3.4 shows similar power penalties for decreased wall heights (i.e., hw = 1.56R). For

each thrust condition, the maximum power required was for the rotor at (or just above) the top of

33



the confined area, though a power penalty was present for hub heights both above and below the

top of the walls. Power required in the Center of the confined area (see Figures 3.4c, 3.4f, 3.4i)

was generally greater than power required at the Edge location (see Figures 3.4b, 3.4e, 3.4h).

Confined area effects were less pronounced for each of the two lower wall heights. On

the third and fourth test days, the confined area walls were two containers tall (hw = 1.08R),

and one container tall (hw = 0.60R). Figures 3.5 and 3.6 show the hover ladder power ratios for

hw = 1.08R and hw = 0.60R, respectively.

The effect of the confined area on hover power required was diminished at test points

with higher blade loading for hw = 1.08R (see Figures 3.5a – 3.5c) and hw = 0.60R (see

Figures 3.6a – 3.6c). The diminished effects correspond with the highest thrust conditions tested

(CT/σ = 0.081 − 0.083). It is important to note that such high thrust conditions were not

reached for the test with increased wall heights. The test day with hw = 1.08R also presented

winds which were calm for test points with CT/σ = 0.083 and increased to 10 knots during the

remainder of the test. As such, it is difficult to isolate the effect of wall height, blade loading, and

wind fluctuations on hover performance in confined areas.

Figure 3.6 also shows that the maximum power condition for the 1-container-high confined

area was at a rotor height far above the wall height, (i.e., maximum power at z ≈ 2.0R, even when

hw = 0.60R). In fact, the maximum power condition was most often at z ≈ 2.0R, regardless of

the wall height. This is noteworthy, since 2.0R is often used as the de facto limit for obstacle-

free ground effect (Ref. 8). This can have consequences on any rotorcraft flight where flowfield

obstacles may be present.

34



0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(a) Free, CT /σ = 0.077

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(b) Edge, CT /σ = 0.077

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(c) Center, CT /σ = 0.074

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(d) Free, CT /σ = 0.075

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(e) Edge, CT /σ = 0.072

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4
H

u
b
 H

e
ig

h
t,
 z

/R

(f) Center, CT /σ = 0.072

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(g) Free, CT /σ = 0.066

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(h) Edge, CT /σ = 0.066

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(i) Edge, CT /σ = 0.066

Figure 3.3: Power ratios computed from a selection of handwritten data cards for hw = 2.04R.

35



0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(a) Free, CT /σ = 0.080

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(b) Edge, CT /σ = 0.079

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(c) Center, CT /σ = 0.078

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(d) Free, CT /σ = 0.072

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(e) Edge, CT /σ = 0.073

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4
H

u
b
 H

e
ig

h
t,
 z

/R

(f) Center, CT /σ = 0.073

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(g) Free, CT /σ = 0.068

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(h) Edge, CT /σ = 0.068

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(i) Center, CT /σ = 0.068

Figure 3.4: Power ratios computed from a selection of handwritten data cards for hw = 1.56R.

36



0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(a) Free, CT /σ = 0.081

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(b) Edge, CT /σ = 0.081

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(c) Center, CT /σ = 0.081

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(d) Free, CT /σ = 0.075

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(e) Edge, CT /σ = 0.076

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4
H

u
b
 H

e
ig

h
t,
 z

/R

(f) Center, CT /σ = 0.075

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(g) Free, CT /σ = 0.070

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(h) Edge, CT /σ = 0.070

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(i) Center, CT /σ = 0.070

Figure 3.5: Power ratios computed from a selection of handwritten data cards for hw = 1.08R.

37



0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(a) Free, CT /σ = 0.083

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(b) Edge, CT /σ = 0.083

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(c) Center, CT /σ = 0.083

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(d) Free, CT /σ = 0.076

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(e) Edge, CT /σ = 0.077

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4
H

u
b
 H

e
ig

h
t,
 z

/R

(f) Center, CT /σ = 0.077

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(g) Free, CT /σ = 0.071

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(h) Edge, CT /σ = 0.071

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(i) Center, CT /σ = 0.071

Figure 3.6: Power ratios computed from a selection of handwritten data cards for hw = 0.60R.

38



3.3 Analysis of Instrumentation Data

The following analysis was computed from aircraft instrumentation data. Figures 2.9 and

2.10 show rotor torque and radar altitude time histories for the duration of the first test flight. For

this flight, the structure was four containers high, which corresponds to hw = 2.04R. Figure 2.9

shows that the torque time history is incomplete, indicating dropouts in the torque data at the

beginning of the flight that were resolved around t = 1000s. The torque data for subsequent

sorties have similar issues intermittently over the duration of each flight. As such, the torque time

history from the first test flight was compared against handwritten data cards in order to analyze

the accuracy of the handwritten data and assess the validity of drawing conclusions for the other

three wall heights on the basis of handwritten data, since the torque time histories from those

flights were unusable.

3.3.1 Hover Performance on the Basis of Instrumentation Data Histories

Time histories of the thrust and power coefficients were calculated from the fuel flow, rotor

speed, and torque time histories. Hover power coefficients were extracted using the time periods

output by Method 2 (see Section 2.3.3, Figure 2.12) and then sorted by location (i.e., Free, Edge,

or Center). Figure 3.7 shows power ratios, CP/CPOGE
, computed from data cards and time

histories for a selection of rotor speeds. As discussed in Section 3.2, the OGE power condition

for each rotor speed was visually approximated from the obstacle-free ground effect results and

applied to power ratios for the following two hover ladders at the Edge and Center of the confined

space.

For each confined area station, the handwritten data cards are in close agreement with

39



the instrumentation data histories. A distinct performance penalty was associated with hover

at the Edge and Center of the confined area. This performance penalty was non-monotonic

in nature (see Figures 3.7b, 3.7c, 3.7e, 3.7f, 3.7h, 3.7i), as opposed to the typical monotonic

variation that was seen for hover over unobstructed terrain (see Figures 3.7a, 3.7d, 3.7g). Power

penalties experienced at the Center of the confined area were greater than power penalties at

the Edge location. Additionally, the power penalty was present for hub heights within one rotor

radius above and below the top of the walls. The overall maximum power penalty according to

handwritten data cards was approximately 20% at the Center for NR = 99% at z ≈ hw = 2.04R,

though the power penalty varied from 8% – 28% under the same conditions according to the

instrumentation data (see Figure 3.7f). Power penalties resulting from the analysis of handwritten

data cards are in accordance with the mean power penalties predicted by the instrumentation data

histories.

Analysis of the instrumentation data histories provided additional insights into the variance

of rotor hub height and power required which were not gained through the analysis of the

handwritten data cards. Figures 3.7a – 3.7c show that the hover power exhibited greater fluctuations

for locations within the confined area (Figures 3.7b and 3.7c) compared to locations free from the

confined area (Figure 3.7a), as shown by the variation of power required at each hub height. Since

the same extraction method was applied to the data from each station, the increased variance

inside the confined area may be indicative of aerodynamic interactions in confined hover. At the

Center of the confined area, for 1.5R < z < 3R , there was also significant variation of hub height

(see Figures 3.7c, 3.7f, 3.7i). Figure 3.7i shows that few test points satisfied near-zero vertical

speed at the Center for NR = 100% and z < 3R. The use of the same extraction criteria for

all conditions highlights the greater variation of the data from the Center of the confined area.

40



Figure 3.7 quantitatively confirms pilot observations of vehicle excursions during the conduct of

the test.

3.3.2 Collective Pitch

Analysis of the performance data histories for a wall height of hw = 2.04R has shown

that fluctuations of aircraft position and power required may occur during hover in confined

areas. Although the performance data for wall heights below hw = 2.04R were unusable, control

inceptor time-histories were available for analysis. Variation of collective and power required

are related, since an increase to collective pitch causes an increase in both induced power and

profile power. Figures 3.8 – 3.11 show that the fluctuations of rotor torque from the first flight

(hw = 2.04R) are seen in the collective pitch time-histories for all flights (hw = 0.60R – 2.04R).

Figure 3.8 shows the collective pitch for a selection of data cards with a wall height of

hw = 2.04R. Figures 3.8a and 3.8b show that the collective pitch time histories for some data-

cards were incomplete, but the majority of collective pitch time histories for each wall height

were available for analysis. Figures 3.8d, 3.8e, and 3.8f show the collective pitch for NR = 98%

for each position with respect to the confined area (i.e., Free, Edge, and Center, respectively).

The fluctuations of collective and hub height are much greater inside of the confined area (see

Figures 3.8e and 3.8f) when compared to the relatively small fluctuations during hover in classical

ground effect (see Figure 3.8d). There was a smaller difference in hub height variation between

each confined area position for a rotor speed of NR = 100% and wall height of hw = 2.04R,

but the collective pitch variation remained larger at the Center and Edge compared to positions

outside of the confined area for those conditions (see Figures 3.8g –3.9i). Of note, the highest

41



0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(a) Free, CT /σ = 0.075

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(b) Edge, CT /σ = 0.072

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(c) Center, CT /σ = 0.072

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(d) Free, CT /σ = 0.069

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(e) Edge, CT /σ = 0.68

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(f) Center, CT /σ = 0.068

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(g) Free, CT /σ = 0.066

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(h) Edge, CT /σ = 0.066

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(i) Center, CT /σ = 0.066

Figure 3.7: Comparison of power ratios computed from handwritten data cards and
instrumentation data histories.

42



rotor speed, NR = 100%, corresponded with the lowest loading conditions, CT/σ = 0.069.

Figure 3.9 shows that the variation of hub height and collective pitch for each rotor speed

is similar for hw = 1.56R and hw = 2.04R. Fluctuations of collective pitch were similar for all

thrust conditions inside of the confined area, whereas vertical fluctuations were greatest for the

highest loading conditions (see Figures 3.9a –3.9c, CT/σ ≈ 0.08).

Figures 3.10 and 3.11 show the collective pitch inputs for a wall height of hw = 1.08R

and hw = 0.60R, respectively. The tendency of the confined area to increase the variation of hub

height and collective pitch was less apparent for lower wall heights. For a wall height of hw =

2.04R, Figure 3.8c shows that hub height variation at the Center of the confined area was greatest

for CT/σ = 0.074. For a wall height of hw = 1.08R, at similar loading conditions, vertical

fluctuations were minimal (see Figure 3.10f). Variation of collective pitch was still present above

the confined area, though the effects were less pronounced for lower walls (see Figures 3.11a –

3.11c). Appendix B includes collective pitch variation with hub height for all tested rotor speeds.

43



20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(a) Free, CT /σ = 0.077

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(b) Edge, CT /σ = 0.077

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(c) Center, CT /σ = 0.074

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(d) Free, CT /σ = 0.075

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(e) Edge, CT /σ = 0.072

20 30 40 50

Collective Position, 
collective

0

1

2

3

4
H

u
b

 H
e

ig
h

t,
 z

/R

(f) Center, CT /σ = 0.072

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(g) Free, CT /σ = 0.066

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(h) Edge, CT /σ = 0.066

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(i) Center, CT /σ = 0.066

Figure 3.8: Collective pitch inputs for a selection of data cards, for hw = 2.04R.

44



20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(a) Free, CT /σ = 0.080

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(b) Edge, CT /σ = 0.079

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(c) Center, CT /σ = 0.078

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(d) Free, CT /σ = 0.072

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(e) Edge, CT /σ = 0.073

20 30 40 50

Collective Position, 
collective

0

1

2

3

4
H

u
b

 H
e

ig
h

t,
 z

/R

(f) Center, CT /σ = 0.073

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(g) Free, CT /σ = 0.068

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(h) Edge, CT /σ = 0.068

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(i) Center, CT /σ = 0.068

Figure 3.9: Collective pitch inputs for a selection of data cards, for hw = 1.56R.

45



20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(a) Free, CT /σ = 0.081

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(b) Edge, CT /σ = 0.081

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(c) Center, CT /σ = 0.081

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(d) Free, CT /σ = 0.075

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(e) Edge, CT /σ = 0.076

20 30 40 50

Collective Position, 
collective

0

1

2

3

4
H

u
b

 H
e

ig
h

t,
 z

/R

(f) Center, CT /σ = 0.075

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(g) Free, CT /σ = 0.070

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(h) Edge, CT /σ = 0.070

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(i) Center, CT /σ = 0.070

Figure 3.10: Collective pitch inputs for a selection of data cards, for hw = 1.08R.

46



20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(a) Free, CT /σ = 0.083

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(b) Edge, CT /σ = 0.083

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(c) Center, CT /σ = 0.083

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(d) Free, CT /σ = 0.076

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(e) Edge, CT /σ = 0.077

20 30 40 50

Collective Position, 
collective

0

1

2

3

4
H

u
b

 H
e

ig
h

t,
 z

/R

(f) Center, CT /σ = 0.077

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(g) Free, CT /σ = 0.071

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(h) Edge, CT /σ = 0.071

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(i) Center, CT /σ = 0.071

Figure 3.11: Collective pitch inputs for a selection of data cards, for hw = 0.60R.

47



Table 3.1: Comparison of full-scale rotor to model rotor.

Parameter Units OH-58C rotor Model rotor

Airfoil — NACA 0012 NACA 0012
Rotor radius, R ft 17.65 1.33
Chord, c in 13 0.98
Number of blades, Nb — 2 2
Rotor solidity, σ — 0.039 0.039
Nominal tip speed, Vtip ft/s 655 419
Nominal tip Reynolds No., Retip — 4,500,000 218,000
Nominal tip Mach No., Mtip — 0.58 0.37

3.4 Comparison to Model Rotor Hover Performance in Confined Areas

Shenk (Ref. 34) investigated the hover performance of an isolated model rotor in a U-

shaped confined area that matched the dimensions of the CAL test setup at 1:13 scale. There were

many differences between the experimental conditions of the flight test and the model rotor test.

Table 3.1 shows the properties of each rotor. The full-scale rotor tip speed was 56% higher than

the model rotor tip speed. While the current work investigated the performance of a helicopter

in unconstrained hover, the lab test investigated the performance of an isolated rotor fixed to a

beam. Additionally, the helicopter encountered various non-zero wind conditions which were not

present during the lab test. The lab test also provided a much finer test matrix resolution. Flight

test ladders were typically comprised of six target hub heights for each set of test conditions,

whereas comparable lab test ladders were comprised of 45 hub heights.

Figure 3.12 shows a comparison of the hover performance of an OH-58 and an isolated

rotor at the center of the confined area. Similar winds and loading conditions were chosen to

compare hover performance resulting from each test for each wall height. Figures 3.12a and 3.12d

show remarkably good agreement considering the differences in the experiments. These results

48



suggest that generalization between lab-scale and full-scale performance in confined areas may

be possible.

The agreement between helicopter and isolated rotor performance suggests that the performance

penalties for this confined area configuration are attributable to the main rotor flow field effects,

though perhaps with some secondary effects due to the presence of the fuselage, tail rotor, or

winds. Figures 3.12a, 3.12b, and 3.12c show hover performance at the center of the confined

area with various wall heights. During each of the corresponding flight test periods, the wind

speed was 8 kts, and the wind direction for each day suggests that wind-obstacle interactions

may have affected main rotor inflow. Presumably, the wind might provide a net increase to rotor

inflow when the rotor is below the walls, and a decrease in the net inflow when the rotor is above

the walls, though such claims amount to no more than speculation without further investigation.

Figure 3.12d shows hover performance at the center of the confined area with a wall height of

hw = 0.60R and a blade loading of CT/σ = 0.071. For these conditions, there was strong

agreement between the hover performance of the helicopter and isolated rotor. During this flight

test period, the wind speed was 5 kts, which is relatively low when compared to the average

winds during the test, which were discussed in Section 2.3.2. Additionally, the wind direction

was 130°T, (or 180°R), so the wind approached the aircraft from the open side of the confined

area and wind-obstacle interactions affecting hover performance were perhaps minimized. The

direction of the wind could be just as important as the magnitude of the wind when considering

how wind-obstacle interactions may contribute to differences in hover performance.

49



0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

Time History

Data Card

Shenk

(a) hw = 2.04R, CT /σ = 0.072,
Flight Test Winds: 050° T, 8 kts

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(b) hw = 1.56R, CT /σ = 0.073,
Flight Test Winds: 000° T, 8 kts

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(c) hw = 1.08R, CT /σ = 0.073,
Flight Test Winds: 170° T, 8 kts

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(d) hw = 0.60R, CT /σ = 0.071,
Flight Test Winds: 130° T, 5 kts

Figure 3.12: Hover performance of an OH-58 (from time histories and data cards) and an isolated
rotor (Shenk, Ref. 34) at the center of a U-shaped confined area.

50



Chapter 4: Conclusions

The present work was an investigation of helicopter operations in confined areas. The

experiment included tests of an OH-58C helicopter operating far from, at the entrance of, and

at the center of a U-shaped set of shipping containers with fixed spacing and four unique wall

heights. The study built upon previous research into the effects of wall height and extended it to

confined areas. The results may serve as a useful set of full-scale helicopter performance data for

investigations into the scalability of laboratory studies and validation of computational models for

rotorcraft in confined spaces. From this study, the following key conclusions have been drawn:

1. A distinct performance penalty was observed for rotorcraft operation while in confined

spaces. The maximum penalty observed was as high as 20% above OGE power.

2. For a U-shaped wall configuration with the tested wall spacing, operating in the Center of

the confined area results in greater performance penalties than operating at the Edge of the

confined area.

3. The performance penalty associated with confined spaces is sensitive to variation in both

the hub height and blade loading.

4. Maximum performance penalties for a given blade loading typically occur when the hub

height of the rotorcraft is at or near the top of the confined area.

51



5. For the purpose of understanding the effects of confined spaces, the handwritten data cards

and instrumentation data were observed to be in close agreement. This result suggests that

it is reasonable to consider mean performance effects of the confined area on the basis of

hand-recorded data alone.

6. The hover performance of an isolated rotor in a model-scale confined area was similar to

the computed performance for the full-scale flight test. Differences between the computed

hover performance from each test could be attributed to the presence of a fuselage and tail

rotor as well as wind effects. These differences warrant further investigation.

The possibility of power penalties has important implications for missions that require

confined area helicopter operations.

4.1 Recommendations for Future Work

The current work investigated the effect of confined areas on single-main-rotor helicopter

performance. Significant power penalties were documented which warrant further study. In

addition to power penalties, uncommanded vertical excursions were noted by the pilots and

confirmed by altitude time histories inside of the confined area. Further analysis of the instrumentation

data to include the effect of confined areas on handling qualities is warranted.

There is a large body of recorded data from the CAL test which were not included in

this investigation. Two additional helicopters were tested and pressure data from anemometers

mounted inside of the confined area exists for each of the three tests. Investigation of this data

may allow for the generalization of confined area effects on the performance of conventional

helicopters. This could inform the development of improved operational tactics, techniques, and

52



procedures.

The complex aerodynamic interactions which contribute to adverse ground effect are still

not fully understood and require further study through flowfield measurements and computational

models. The present data set provides a baseline for launching into such investigations. A number

of computational studies of varying fidelity could be valuable to an increased understanding of

the problem, including dynamic inflow models, free-wake models, and RANS CFD.

Future experimental investigations might consider using flowfield PIV or pressure transducers

along the blade to study confined area inflow. Parametric studies might evaluate the effect

of various rotor design parameters including blade loading, twist, taper, and solidity to assess

whether certain rotor designs might be more vulnerable to adverse confined area effects. Future

experiments might also consider testing the effect of varied wall spacing. Alternatively, experimental

studies might focus on the effects of the permeability of flowfield obstacles or the viscosity of

the operating fluid. Small-scale, free-flight vehicles might be useful to assess handling qualities

and wind tunnel testing over confined areas could be used to investigate the impact of the wind

on confined area performance.

The inclusion of a fuselage or tail rotor in laboratory studies could bridge the gap between

laboratory and full-scale studies by simulating more of the aerodynamic interactions inherent

to helicopter operations. The impact of various compound helicopter configurations including

additional rotors or a wing may introduce additional confined area effects. The issue of rotor-

on-rotor interactions within confined areas is especially pertinent to a growing field of vehicles

designed for urban air mobility. Recent initiatives by industry to design vehicles capable of

emissions-free vertical flight have led to an unprecedented number of novel multirotor designs.

The V-22 has been the focus of a number of wake-obstacle interaction studies due to its high

53



disk loading and potential for rotor-on-rotor interactions, and it will become similarly important

for eVTOL designers to consider this issue. A thorough understanding of possible confined

area effects is necessary for these specialized vehicles to safely navigate urban environments,

though increased understanding of confined area rotorcraft behavior will be beneficial to the

entire industry.

Confined area effects have been shown to cause a significant increase in hover power

required. Knowledge of the possibility for dangerous confined area effect is equally important for

rotorcraft designers, operators, and mission planners. Designers should conduct confined areas

tests to develop design-specific guidelines for operations near obstacles, including minimum tip

clearances and increased power margins. Pilots should be aware of the possibility of aerodynamic

recirculation to overtorque the engine. Training materials and performance references should

reflect that confined landing zones can cause adverse performance effects.

54



Appendix

Appendix A, Hover power ratio tables on the basis of handwritten data cards

Appendix B, Hover power ratio plots on the basis of handwritten data cards

Appendix C, Collective pitch plots on the basis of instrumentation data histories

55



Power ratios for hw = 2.04R, nominal CT/σ = 0.077.

Location CT/σ z/R CP/CPOGE

Free 0.077 0.74 0.94
1.02 0.92
1.53 0.98
2.04 1.00
2.89 0.98
3.17 0.99

Edge 0.077 0.74 0.99
1.02 1.04
1.53 1.09
2.04 1.11
2.89 1.03
3.17 1.03

Center 0.074 0.74 1.00
1.02 1.05
1.53 1.23
2.04 1.13
2.89 0.95
3.17 1.03

56



Power ratios for hw = 2.04R, nominal CT/σ = 0.075.

Location CT/σ z/R CP/CPOGE

Free 0.075 0.74 0.88
1.02 0.96
1.53 0.99
2.04 0.98
2.89 0.94
3.17 1.00

Edge 0.072 0.74 0.94
1.02 0.98
1.53 1.02
2.04 1.06
2.89 1.00
3.17 0.96

Center 0.072 0.74 0.93
1.02 1.01
1.53 1.07
2.04 1.08
2.89 1.01
3.17 0.97

Power ratios for hw = 2.04R, nominal CT/σ = 0.069.

Location CT/σ z/R CP/CPOGE

Free 0.069 0.74 0.92
1.02 0.99
1.53 0.96
2.04 0.96
2.89 0.95
3.17 0.95

Edge 0.068 0.74 0.97
1.02 1.07
1.53 1.04
1.92 1.03
2.89 1.03
3.17 1.03

Center 0.068 0.74 0.97
1.02 1.04
1.53 1.14
1.92 1.21
2.89 1.13
3.17 1.03

57



Power ratios for hw = 2.04R, nominal CT/σ = 0.066.

Location CT/σ z/R CP/CPOGE

Free 0.066 0.74 0.91
1.02 0.96
1.53 1.02
2.04 0.98
2.89 0.96

Edge 0.066 0.74 0.98
1.02 1.02
1.53 1.05
2.04 1.07
2.89 1.03
3.17 1.03

Center 0.066 0.74 1.03
1.02 1.04
1.53 1.11
2.04 1.12
2.89 1.01
3.17 1.03

Power ratios for hw = 1.56R, nominal CT/σ = 0.080.

Location CT/σ z/R CP/CPOGE

Free 0.080 0.74 0.91
1.02 0.97
1.53 0.97
2.04 0.99
2.89 0.97
3.17 0.95

Edge 0.079 0.74 0.97
1.02 1.06
1.53 1.15
2.04 1.10
2.89 1.04
3.17 1.02

Center 0.078 0.74 1.02
1.02 1.10
1.53 1.14
2.04 1.17
2.89 0.97
3.17 0.97

58



Power ratios for hw = 1.56R, nominal CT/σ = 0.075.

Location CT/σ z/R CP/CPOGE

Free 0.075 0.74 0.89
1.53 0.96
2.04 0.96
2.89 1.02

Edge 0.075 0.74 0.90
1.02 0.93
1.53 1.06
2.04 1.07
2.89 0.98
3.17 0.98

Center 0.075 0.74 1.02
1.02 1.06
1.53 1.11
2.04 1.04
2.89 0.93

Power ratios for hw = 1.56R, nominal CT/σ = 0.072.

Location CT/σ z/R CP/CPOGE

Free 0.072 0.74 0.92
1.53 1.03
2.04 0.97
2.89 0.97

Edge 0.073 0.74 1.04
1.02 1.07
1.53 1.13
2.04 1.13
2.89 1.06
3.17 1.06

Center 0.073 0.74 1.06
1.02 1.09
1.53 1.13
2.04 1.18
2.89 1.05

59



Power ratios for hw = 1.56R, nominal CT/σ = 0.070.

Location CT/σ z/R CP/CPOGE

Free 0.070 0.74 0.91
1.02 0.95
1.53 0.94
2.04 0.99

Edge 0.070 0.74 0.95
1.02 1.05
1.53 1.10
2.04 1.12
2.89 0.94
3.17 1.01

Center 0.070 0.74 1.04
1.02 1.06
1.53 1.11
2.04 1.00
2.89 1.01
3.17 0.99

Power ratios for hw = 1.56R, nominal CT/σ = 0.068.

Location CT/σ z/R CP/CPOGE

Free 0.068 0.74 0.95
1.02 0.97
1.53 0.98
2.04 1.00
2.89 0.95

Edge 0.068 0.74 1.03
1.02 1.10
1.53 1.10
2.04 1.12
2.89 1.04
3.17 1.10

Center 0.068 0.74 1.01
1.02 1.09
1.53 1.13
2.04 1.10
2.89 1.03
3.17 0.98

60



Power ratios for hw = 1.08R, nominal CT/σ = 0.081.

Location CT/σ z/R CP/CPOGE

Free 0.081 0.74 0.89
1.02 0.94
1.53 0.96
2.04 1.00
2.89 1.01
3.17 1.01

Edge 0.081 0.74 0.90
1.02 0.96
1.53 1.01
2.04 1.03
2.89 1.01
3.17 0.99

Center 0.081 0.74 0.95
1.02 1.01
1.53 1.02
1.53 1.02
2.04 0.99
2.89 0.97

Power ratios for hw = 1.08R, nominal CT/σ = 0.078.

Location CT/σ z/R CP/CPOGE

Free 0.078 0.74 0.92
1.02 0.95
1.53 0.99
2.04 0.99
2.89 0.99
3.17 0.95

Edge 0.078 0.74 0.96
0.96 1.03
1.64 1.05
2.04 1.05
2.83 1.03
3.34 0.98

Center 0.078 0.79 0.98
1.08 1.04
1.53 1.08
2.09 1.07
2.83 1.02
3.23 0.98

61



Power ratios for hw = 1.08R, nominal CT/σ = 0.075.

Location CT/σ z/R CP/CPOGE

Free 0.075 0.74 0.93
0.96 0.97
1.53 0.99
2.21 0.99
2.89 0.99
3.45 1.00

Edge 0.076 0.74 1.04
1.02 1.08
1.53 1.04
2.04 1.06
2.89 1.06
3.17 1.03

Center 0.075 0.74 1.01
1.02 1.04
1.53 1.08
2.04 1.04
2.89 0.99
3.17 1.01

Power ratios for hw = 1.08R, nominal CT/σ = 0.072.

Location CT/σ z/R CP/CPOGE

Free 0.072 0.74 0.94
1.02 0.98
1.53 1.01
2.04 1.01
2.89 0.98
3.17 0.92

Edge 0.073 0.74 0.99
1.08 1.01
1.75 0.98
2.04 0.98
2.83 0.97
3.28 1.04

Center 0.073 0.74 0.99
1.02 1.05
1.53 1.02
2.21 1.04
2.83 0.98
3.17 0.94

62



Power ratios for hw = 1.08R, nominal CT/σ = 0.070.

Location CT/σ z/R CP/CPOGE

Free 0.070 0.74 0.96
1.02 0.99
1.53 0.98

Edge 0.070 0.74 1.05
1.02 1.04
1.53 1.04
2.04 1.05
2.89 1.02
3.17 0.96

Center 0.070 0.74 1.04
1.02 1.05
1.53 1.02
2.04 1.02
2.89 1.04
3.17 1.01

Power ratios for hw = 1.08R, nominal CT/σ = 0.083.

Location CT/σ z/R CP/CPOGE

Free 0.083 0.74 0.87
1.02 0.89
1.53 0.96
2.04 1.00
2.89 1.01
3.17 1.00

Edge 0.083 0.74 0.90
1.02 0.96
1.53 1.01
2.04 1.02
2.89 1.01
3.17 1.00

Center 0.083 0.74 0.89
1.02 0.96
1.53 0.96
2.04 1.01
2.89 0.99
3.17 1.00

63



Power ratios for hw = 1.08R, nominal CT/σ = 0.079.

Location CT/σ z/R CP/CPOGE

Free 0.079 0.74 0.88
1.02 0.95
1.53 1.00
2.04 0.99
2.89 0.99
3.17 0.99

Edge 0.080 0.74 0.95
1.02 1.01
1.53 1.02
2.04 1.06
2.89 1.02
3.17 1.07

Center 0.079 0.74 0.97
1.02 1.03
1.53 1.08
2.04 1.11
2.89 1.03
3.17 1.08

Power ratios for hw = 1.08R, nominal CT/σ = 0.076.

Location CT/σ z/R CP/CPOGE

Free 0.076 0.74 0.89
1.02 0.93
1.53 0.97
2.04 1.00
2.89 1.01
3.17 0.97

Edge 0.077 0.74 0.95
1.02 0.99
1.53 1.01
2.04 1.04
2.89 0.96
3.17 0.96

Center 0.077 0.74 0.98
1.02 1.05
1.53 1.05
2.04 1.08
2.89 0.98
3.17 0.96

64



Power ratios for hw = 1.08R, nominal CT/σ = 0.073.

Location CT/σ z/R CP/CPOGE

Free 0.073 0.74 0.89
1.02 0.95
1.53 0.98
2.04 1.00
2.89 0.97
3.17 0.97

Edge 0.074 0.74 0.95
1.02 0.97
1.53 0.98
2.04 1.03
2.89 0.94
3.17 0.97

Center 0.074 0.74 0.97
1.02 1.03
1.53 1.04
2.04 1.00
2.89 0.96
3.17 0.96

Power ratios for hw = 1.08R, nominal CT/σ = 0.071.

Location CT/σ z/R CP/CPOGE

Free 0.071 0.74 0.92
1.02 0.96
1.53 0.99
2.04 1.00
2.89 0.97

Edge 0.071 0.74 0.97
1.02 0.99
1.53 1.04
2.04 1.05
2.89 1.03
3.17 1.03

Center 0.071 0.74 1.00
1.02 1.03
1.53 1.04
2.04 1.04
2.89 1.03
3.17 1.00

65



0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(a) Free, CT /σ = 0.077

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(b) Edge, CT /σ = 0.077

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(c) Center, CT /σ = 0.074

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(d) Free, CT /σ = 0.075

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(e) Edge, CT /σ = 0.072

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(f) Center, CT /σ = 0.072

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(g) Free, CT /σ = 0.069

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(h) Edge, CT /σ = 0.068

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4
H

u
b
 H

e
ig

h
t,
 z

/R

(i) Center, CT /σ = 0.068

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(j) Free, CT /σ = 0.066

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(k) Edge, CT /σ = 0.066

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(l) Edge, CT /σ = 0.066

Power ratios for all hover ladders for hw = 2.04R.

66



0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4
H

u
b
 H

e
ig

h
t,
 z

/R

(a) Free, CT /σ = 0.080

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(b) Edge, CT /σ = 0.079

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(c) Center, CT /σ = 0.078

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(d) Free, CT /σ = 0.075

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(e) Edge, CT /σ = 0.075

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(f) Center, CT /σ = 0.075

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(g) Free, CT /σ = 0.072

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(h) Edge, CT /σ = 0.073

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(i) Center, CT /σ = 0.073

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(j) Free, CT /σ = 0.070

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(k) Edge, CT /σ = 0.070

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(l) Center, CT /σ = 0.070

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(m) Free, CT /σ = 0.068

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(n) Edge, CT /σ = 0.068

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(o) Center, CT /σ = 0.068

Power ratios for all hover ladders for hw = 1.56R.

67



0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4
H

u
b
 H

e
ig

h
t,
 z

/R

(a) Free, CT /σ = 0.081

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(b) Edge, CT /σ = 0.081

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(c) Center, CT /σ = 0.081

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(d) Free, CT /σ = 0.078

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(e) Edge, CT /σ = 0.078

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(f) Center, CT /σ = 0.078

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(g) Free, CT /σ = 0.075

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(h) Edge, CT /σ = 0.076

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(i) Center, CT /σ = 0.075

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(j) Free, CT /σ = 0.072

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(k) Edge, CT /σ = 0.073

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(l) Center, CT /σ = 0.073

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(m) Free, CT /σ = 0.070

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(n) Edge, CT /σ = 0.070

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(o) Center, CT /σ = 0.070

Power ratios for all hover ladders for hw = 1.08R.

68



0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4
H

u
b
 H

e
ig

h
t,
 z

/R

(a) Free, CT /σ = 0.083

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(b) Edge, CT /σ = 0.083

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(c) Center, CT /σ = 0.083

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(d) Free, CT /σ = 0.079

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(e) Edge, CT /σ = 0.080

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(f) Center, CT /σ = 0.079

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(g) Free, CT /σ = 0.076

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(h) Edge, CT /σ = 0.077

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(i) Center, CT /σ = 0.077

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(j) Free, CT /σ = 0.073

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(k) Edge, CT /σ = 0.074

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(l) Center, CT /σ = 0.074

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(m) Free, CT /σ = 0.071

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(n) Edge, CT /σ = 0.071

0.7 0.8 0.9 1 1.1 1.2 1.3

Power Ratio, C
P

/C
P,OGE

0

2

4

H
u
b
 H

e
ig

h
t,
 z

/R

(o) Center, CT /σ = 0.071

Power ratios for all hover ladders for hw = 0.60R.

69



20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(a) Free, CT /σ = 0.077

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(b) Edge, CT /σ = 0.077

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(c) Center, CT /σ = 0.074

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(d) Free, CT /σ = 0.075

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(e) Edge, CT /σ = 0.072

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(f) Center, CT /σ = 0.072

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(g) Free, CT /σ = 0.069

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(h) Edge, CT /σ = 0.068

20 30 40 50

Collective Position, 
collective

0

1

2

3

4
H

u
b

 H
e

ig
h

t,
 z

/R

(i) Center, CT /σ = 0.068

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(j) Free, CT /σ = 0.066

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(k) Edge, CT /σ = 0.066

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(l) Center, CT /σ = 0.066

Collective pitch for all hover ladders for hw = 2.04R.

70



20 30 40 50

Collective Position, 
collective

0

1

2

3

4
H

u
b

 H
e

ig
h

t,
 z

/R

(a) Free, CT /σ = 0.080

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(b) Edge, CT /σ = 0.079

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(c) Center, CT /σ = 0.078

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(d) Free, CT /σ = 0.075

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(e) Edge, CT /σ = 0.075

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(f) Center, CT /σ = 0.075

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(g) Free, CT /σ = 0.072

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(h) Edge, CT /σ = 0.073

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(i) Center, CT /σ = 0.073

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(j) Free, CT /σ = 0.070

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(k) Edge, CT /σ = 0.070

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(l) Center, CT /σ = 0.070

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(m) Free, CT /σ = 0.068

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(n) Edge, CT /σ = 0.068

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(o) Center, CT /σ = 0.068

Collective pitch for all hover ladders for hw = 1.56R.

71



20 30 40 50

Collective Position, 
collective

0

1

2

3

4
H

u
b

 H
e

ig
h

t,
 z

/R

(a) Free, CT /σ = 0.081

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(b) Edge, CT /σ = 0.081

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(c) Center, CT /σ = 0.081

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(d) Free, CT /σ = 0.078

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(e) Edge, CT /σ = 0.078

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(f) Center, CT /σ = 0.078

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(g) Free, CT /σ = 0.075

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(h) Edge, CT /σ = 0.076

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(i) Center, CT /σ = 0.075

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(j) Free, CT /σ = 0.072

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(k) Edge, CT /σ = 0.073

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(l) Center, CT /σ = 0.073

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(m) Free, CT /σ = 0.070

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(n) Edge, CT /σ = 0.070

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(o) Center, CT /σ = 0.070

Collective pitch for all hover ladders for hw = 1.08R.

72



20 30 40 50

Collective Position, 
collective

0

1

2

3

4
H

u
b

 H
e

ig
h

t,
 z

/R

(a) Free, CT /σ = 0.083

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(b) Edge, CT /σ = 0.083

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(c) Center, CT /σ = 0.083

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(d) Free, CT /σ = 0.079

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(e) Edge, CT /σ = 0.080

20 30 40 50

Collective Position, 
collective

0

1

2

3

4

H
u

b
 H

e
ig

h
t,

 z
/R

(f) Cent