^LZ77^AA,V^ - ttu-ir.tdl.org

SOLAR CONCENTRATOR WIND LOADINGS

by

GEOFFREY L. WAGNER, B.S.M.E.

A THESIS

IN

MECHANICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial FulfiUment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

MECHANICAL ENGINEERING

Approved

Chajêrson of the Committee

<r ^LZ77ÂA,V^

^

Accepted

^^^f/^^JÛ. Dean of the Gr

December, 1996

ACKNOWLEDGMENTS

Q. ' ^ I would like to extend my special thanks to Dr. Jerry Dunn for all his

help and insight. Without his guidance and assistance this work would not

have been possible. I would also Uke to extend my thanks to Dr. Ertas and

Dr. Oler for their time and expertise as members of my thesis committee.

Your assistance and encouragement helped me to get through my thesis. My

special thanks goes Cummins Power Generation for the support of the project

and for the assistance and direction given throughout the project.

I also would like to extend a warm thank you to my family and friends

that always encouraged me throughout this ordeal. My family has always

been behind me whether it be moral or financial support so I could not have

made it through without them. Thanks also goes to RocheUe Pritchard for

the help on the project, from the beginning to the end. I could not have

finished the project without you. In addition, Uoyd Lacy was a large

contributor to the project through his assistance in the machining and

materials advice.

Most importantly, I would like to thank the Lord for His grace and

mercy. His guidance carried me through the project and without Him, I am

nothing.

11

TABLE OF CONTENTS

ACKNOWLEDGMENTS ii

ABSTRACT iv

LIST OF TABLES v

LIST OF FIGURES vi

NOMENCLATURE viii

CHAPTER

I. INTRODUCTION 1

Concentrating Solar Energy Systems 3 Dish/Stirhng Technology 4 Wind Engineering 5 Modeling 8 Previous Studies 9 Objective 11

n. EXPERIMENTAL PROCEDURE 13

Tow Tank 13 Load Cell 15 Data Acquisition System 16 Calibration of Load Cell 19 Model 26 Measurement of Forces and Moments 26

m . EXPERIMENTAL RESULTS AND DISCUSSION 32

IV. CONCLUSIONS AND RECOMMENDATIONS 41

REFERENCES 43

APPENDICES

A. CALIBRATION DATA 44 B. SUPPORT PIPE DATA 48 C. MODEL LOAD DATA 56

111

ABSTRACT

The objective of this project was to determine the maximum wind

loadings on a notched parabohc solar concentrator. To accomplish this

objective, a test program was conducted using the Texas Tech tow tank. The

results from testing a one-tenth scale model were put into nondimensional

force and moment coefficients. The maximum coefficients are as follows: hft,

-0.92; drag, 1.42; side force, 1.05; yaw moment, -0.23; roU moment, 0.72; and

pitch moment, 1.28. These results shovdd be used as a starting estimate for

the beginning stages of the structural design of the solar concentrator

support structure.

IV

LIST OF TABLES

2.1. Maximum Load Estimates for the Load

CeU CaHbration 21

2.2. Calibration Maximum Percent Error Results 25

4.1. Maximum Nondimensional Coefficient Results 41

A.I. Six Component Load Cell Calibration 45

B.l. Support Pipe Force/Moment Data Evaluation, Yaw -45 deg 49

B.2. Support Pipe Force/Moment Data Evaluation, Yaw -30 deg 50



B.5. Support Pipe Force/Moment Data Evaluation, Yaw 15 deg 53



C.l. Concentrator Force/Moment Data Evaluation, Yaw -45 deg 57

C.2. Concentrator Force/Moment Data Evaluation, Yaw -30 deg 58

C.3. Concentrator Force/Moment Data Evaluation, Yaw -15 deg 59

C.4. Concentrator Force/Moment Data Evaluation, Yaw 0 deg 60




\

LIST OF FIGURES

1.1. Cummins Power Generation 25 kW Solar Concentrating System 2

1.2. Direction of Forces and Angles Relative to the Wind Direction 7

1.3. One-tenth Scale Model of Cummins Power

Generation 25 kW Solar Concentrator 12

2.1. Texas Tech's Tow Tank Facility 14

2.2. Load CeU Illustration 15

2.3. Wheatstone Bridge Configuration 16

2.4. Data Acquisition System 17

2.5. Measurements Group Model 2100 Strain

Gage Amplifier 17

2.6. Controls to Balance Bridges and Setting the Gain 18

2.7. Calibration Setup 20

2.8. Lift Calibration Curve 22

2.9. Drag Calibration Curve 22

2.10. Side Force Calibration Curve 23

2.11. Yaw Moment Calibration Curve 23

2.12. Roll Moment Calibration Curve 24

2.13. Pitch Moment Calibration Curve 24

2.14. One-tenth Scale Model of Solar Concentrator 27

M

2.15. Load CeU, Support Pipe, and Model Setup with Direction of Positive Forces and Moments 28

2.16. Yaw Angles and Direction of Positive Forces

and Moments 29

3.1. Lift Coefficients for Varying Yaw Angles 33

3.2. Drag Coefficients for Varying Yaw Angles 33

3.3. Side Force Coefficients for Varying Yaw Angles 34

3.4. Yaw Coefficients for Varjdng Yaw Angles 34

3.5. RoU Coefficients for Varying Yaw Angles 35

3.6. Pitch Coefficients for Varying Yaw Angles 35

vu

NOMENCLATURE

A

aij

^

ap

ar

CD

CF

CL

CM

CpM

CRM

CsF

CYM

d

D

F

f

FD ,Di

FL,Li

FsF, SFi

t-Tnodel

t-prototype

t^ratio

MpM , Pi

MRM,Ri

MYM , Yi

Characteristic area

Calibration coefficients

Acceleration of model

Acceleration of prototype

Acceleration ratio

Drag coefficient

Force coefficient

Lift coefficient

Moment coefficient

Pitching moment coefficient

Rolling moment coefficient

Side coefficient

Yawing moment coefficient

Characteristic diameter

Aperture diameter

Force

Focal length

Drag force

Lift force

Side force

Length of model

Length of prototype

Length ratio

Pitching moment

Rolling moment

Yawing moment

Vlll

q

Qm

Qp

Qr

P

Re

Rem

Rcp

Tn,

Tp

T.

V

Voi

Vu

Vn,

Vp

Vpi

V.

VRI

VsFi

Vvi

Dynamic pressure

Volumetric flow rate of model

Volumetric flow rate of prototype *

Volumetric flow rate ratio

Fluid density

Reynolds number

Reynolds number of model

Reynolds number of prototype

Time of model

Time of prototype

Time ratio

Wind velocity

Vohage due to drag force

Voltage due to lift force

Velocity of model

Velocity of prototype

Voltage due to pitching moment

Velocity ratio

Voltage due to rolling moment

Voltage due to side force

Voltage due to yawing moment

IX

CHAPTER I

INTRODUCTION

For the past twenty years, efficient energy management and effective

conservation procedures have been very important considerations for our

society. An oU embargo in the 1970s and early 1980s combined with various

circumstances such as the loss of tax credits and new efficiency standards

imposed by the government brought about a new awareness concerning

energy. The Clean Air Act of 1991 and the Persian Gulf War have spurred a

revival in the need for reUable and environmentaUy friendly energy sources.

One possibility for a renewable energy source is that of solar energy

coUectors.

A United States Joint Venture Program (USJVP) is making an effort

to increase the feasibility of solar coUecting systems. Numerous companies

have been concentrating their efforts in dish/Stirling concentrator

technology. There has already been developed a 7.5-kW free-piston engine

dish/Stirling system and through the efforts of the joint venture program the

development and testing of a 25-kW kinematic-piston Stirling engine, shown

in Figure 1.1, for terrestrial power generation. Some of the controlling

factors in determining the size and power generation of solar concentrators

are the engines and the wind loads on the support structures. With regard to

wind loading, the wind loads affect the accuracy of the reflector as a

paraboloid, pointing accuracy, loads on the drive system, safety in extreme

winds, and freedom from osciUations (Wyatt, 1964). In an effort to determine

the mean wind loads of a 25-kW concentrator, testing of a scale model

concentrator was carried out by Texas Tech University Department of

Mechanical Engineering.

Figure 1.1. Cummins Power Generation 25 kW Solar Concentrating System

Concentrating Solar Energy Systems

Most of the solar energy research done in the past few years has been

focused on intermediate to high temperature technologies, which includes

solar energy concentrating systems. Solar coUectors are essentiaUy heat

exchangers which can vary widely in design and types. Two main

classifications are concentrating and nonconcentrating systems. Their

general design geometry can be cylindrical or paraboloidal, and can be

continuous or faceted. Concentrating coUectors are classffied by their

tracking requirements which can be one-axis tracking, two-axis-tracking or

non-tracking systems. Because concentrating coUectors focus solar radiation,

they provide energy at temperatures higher than that provided by flat-plate

coUectors. The focused solar radiation passes through an aperture onto an

absorber which usuadly requires tracking of the sun. In most concentrating

systems, the concentrated Ught is used to heat a fluid as a source for a

generator. The working fluid is usuaUy a Hquid (plain water), oU, gas (air) or

black Uquids (water and Indian ink mixture) which can use a transparent

glass tube instead of a black-coated copper tube as the receiver (Imadojemu,

1995). Other concentrators use dish-mounted Rankine, Brayton, or StirUng

cycle engines to produce electric power.

One factor that determines the effectiveness of concentrators is the

concentration ratio. Concentration ratios can vary from values sHghtly

greater than unity to high values of the order of 10 . The concentration ratio

is defined as the ratio of the coUector aperture area to the absorber area. As

the ratio increases, the operating temperature increases which emphasizes

the importance of precision in optical quaUty and positioning of the optical

system.

Solar energy usage has enormous potential for a conservation minded

friture. Electricity can be generated through heat coUection/conversion or

from photo conversion. Other uses for solar energy include the production of

fuels and chemical processes, space heating, wood or vegetable drying, and

solar cooking (Imadojemu, 1995).

Dish/Stirling Technology

Solar concentrators and StirUng engines are a perfect match because

concentrators provide the high temperatures needed for power production

from the Stirling engine. A Scottish minister. Rev. Robert StirUng, patented

the Stirling engine in 1816 and the first solar appUcation was by the famous

British/American inventor John Ericsson in 1872. The StirUng engine is the

most efficient device for converting heat into mechanical work (Stine, 1993).

A high efficiency StirUng engine results in more output for a given size

concentrator. To the consumer, this means lower cost electricity. StirUng

engine efficiency increases with operating temperature; and therefore, these

devices are operated up to the thermal limits of the materials used in their

construction. Engine conversion efficiencies are around 30 to 40% for a

temperature range of 650° to 800°C (1200° to 1470°F) (Stine and Diver,

1994). The engines typicaUy operate at high pressure, 5 to 20 MPa (725 to

2900 psi), to maximize the power output (Stine and Diver, 1994).

In order to obtain the high temperatures that are required for StirUng

concentrators, tracking the sun is necessary. Tracking mechanisms are very

expensive and are very sensitive because variations in tracking accuracy can

result in a large increase in temperature, conversely, inaccuracy in the

tracking system could cause lower efficiencies. In addition, inaccuracies

could result in faUure of the receiver because temperatures could be greater

than the thermal Umits of materials not designed to be operated at high

levels of solar heat flux. The largesT mechanical loads on the tracking

mechanisms are those caused by the wind. Therefore, knowing the mean

wind loads is critical in designing the tracking systems for Stirling

concentrators.

Wind Engineering

Wind is caused by atmospheric pressure differences that arise from

unequal heating of the Earth's surface. Some of the important factors that

influence the wind include the Earth's rotation, precipitation, cloud cover,

non-uniform surface temperature and roughness, and topographic reUef

(Roschke, 1984). It is because of the variabUity and randomness of these

factors that makes it very chaUenging to characterize wind mathematicaUy.

The need for wind engineering comes from the fact that moderate to strong

wind conditions can cause extensive damage to structures.

One of the purposes of wind engineering is to determine the resultant

wind forces and moments. By applying BernouUi's principle and dimensional

analysis, the wind force and moment can be expressed in the form of

equations 1.1 and 1.2

F = lpVÂCp (1.1)

M = ipVÂdC^ (1.2)

where p is the mass density of the airstream, V is the wind velocity, A is a

characteristic area of the body, d is a characteristic dimension of the body,

and CF and CM are the dimensionless force and moment coefficients. The

dimensionless coefficients depend on the geometric properties of the body and

on Reynolds number. The term V2pV2 is the dynamic pressure of the

undisturbed flow and is designated as q.

In aerodynamics, the force is usuaUy separated into the three

orthogonal forces of drag, Uft, and side force. Their corresponding coefficients

are CD, CL, and CSF. The moment may also be broken into three orthogonal

moments of yaw, roU, and pitching moments with corresponding coefficients

of CYM, CRM, and CPM. These aerodynamic forces and moments are expressed

in equation form in equations 1.3 through 1.8.

Lift: FL= CL-qA (1.3)

Drag: FD = CoqA (1.4)

Side Force: FSF = CsF-qA (1.5)

Yawing Moment: MYM = CYMdqA (1.6)

RoUingMoment: MRM= CRM-dqA (1.7)

Pitching Moment: MpM=CpMdqA (1.8)

It is important to note that the positive direction of the forces is fixed

relative to the wind direction. Figure 1.2 shows the direction of the forces

relative to the wind direction as weU as the yaw, roU, and pitch angles. Drag

is in the horizontal direction paraUel to the wind and the positive direction is

the same as the wind direction. lift direction is in the vertical direction

normal to the wind. The side force is in the horizontal direction normal to

the wind and Uft directions. The yaw, roU, and pitch angles are measured

from the wind direction to the center of the model or prototype.

Top

Wind

D i r e c t i o n

View

Drag 1

Side F o r c e

J Yaw Monent

Side View

Wind

D i r e c t i o n

D r a g

L i f t

O Pi tch ing Monent

F r o n t View

L , f t

Wind D i r ec t , c ^ inô C o n c e n t r o t o r

Figure 1.2. Direction of Forces and Angles Relative to the Wind Direction

Modeling

Sometimes it is necessary to determine the performance of a structure

through experimental testing of another structure. This is caUed model

testing where the structure being tested is the model and the structure whose

performance is being predicted is the prototype. It is possible for the model

to be smaUer than, the same size as, or even larger than the prototype.

Model experiments of structures have resulted in savings that more than

justified the expenditures of funds for the design, construction, and testing of

the model.

In order for the model and prototype to have similar results, it is

necessary to have geometric, kinematic, and d5niamic simdarity. When the

ratios of aU the corresponding dimensions of the model and the prototype are

equal, it is caUed geometric similarity. These ratios are written in equations

1.9 through 1.11:

Length: 'model

'prototype ~ ^r«tio (1.9)

Area:

Volume:

LJ model

l-< prototype

T 3 LJ model

1-1 prototype

— T 2 . 1^ ntio

T 3 i~) ratio

(1.10)

(1.11)

Kinematic simUarity exists between model and prototype when their

streamlines are geometricaUy sinular. The kinematic ratios from this

condition are shown in equations 1.12 to 1.14.

8

Acceleration: a =?^ = hiL^ (1.12) a„ L T"

p p p

Velocity: V = ^ = 1IHIE_ (1.13) ' V„ L T-'

p p p

O L T ' Volume flow rate: Q =-^= " " (1.14)

' Q„ L' T ' ^ p p p

Dynamic simdarity exists between model and prototype having

geometric and kinematic simdarity when the ratios of aU forces are the same.

For dynamic simUarity, the Reynolds numbers must be equal as shown in

equations 1.15 and 1.16.

pLV Reynolds number Re = (115)

Re„=Rep (1.16)

Previous Studies

Several previous studies have been conducted on wind loadings on

solar concentrators. There is general agreement that wind loads influence

the design, performance, cost, safety, and maintenance and replacement costs

of solar concentrators. Wind loads are functions of wind conditions and the

design and configuration of the concentrator. As shown above, the force and

moments are functions of the square of the mean wind velocity as weU as the

concentrator diameter. Drag force increases as the pitching angle increases

to a maximum of 90°. In addition to drag force, the wind forces and moments

can vary considerably with wind angle of attack and can be either positive or

negative.

E.J. Roshke (1984) has made several general conclusions about wind

loadings on solar concentrators. Roshke stresses that the annual energy

production is related to the wind conditions, which are therefore important to

the design of the concentrator. Roshke points out that there are several

methods to reduce wind loads including introducing or increasing the

porosity of the concentrator, the use of spoUers and fairings, and shifting the

point of rotation forward of the dish vertex. Roshke also notes that to avoid

scale effects, Reynolds numbers must be greater than 10 and preferably 10

(Roshke, 1984).

L.M. Murphy (1981) has made several observations about how solar

coUectors are affected by wind loadings. Murphy has noted that wind forces

are difficult to model because the coUector moves to track the sun. Murphy

(1981) also points out that the pointing accuracy and survival are crucial

design factors, but the slew-to-stow condition is the major design motivator.

Murphy Usts the criteria for the design of solar dishes as the maximum

survival wind speed of 100 mph, design wind speed for normal operation of

36 mph, maximum wind speed during which the coUector must track of 36

mph, and a 100 j ^ mean recurrence interval. Murphy notes that Colorado

State University states that there is a diminishing effect of Reynolds

numbers for Re > 15,000. Murphy also Usts the maximum force and moment

coefficients for a dish coUector with a 75° rim angle and a dish

depth/diameter ratio of 0.2. The results were a maximum drag coefficient of

10

1.5, maximum Uft coefficient of 0.25-0.30, and a maximum pitching moment

coefficient of-0.05 at a pitch angle of 40° (Murphy, 1981).

Objective

The primary objective of this study is to obtain aerodynamic data to

determine mean wind forces and moments acting on the 25 kW USJVP

concentrator. The previous modeUng techniques were used to test a one-

tenth scale model, shown in Figure 1.3, in the Hydrod5niamic Tow Tank of

the Department of Mechanical Engineering. The model was bmlt by

Cummins Power Generation, located in AbUene, Texas. The model has an

aperture diameter of 3.5 ft and a {/D ratio of approximately 0.656. The model

is mounted to a support pipe with the capabUity to vary the pitch and yaw

angles in order to test the model under properly simulated conditions. This

study did not include studies on the effects of a ground plane or the engine

receiver on wind forces and moments.

11

Figure 1.3. One-tenth Scale Model of Cummins Power Generation 25 kW Solar Concentrator

12

CHAPTER II

EXPERIMENTAL PROCEDURE

In order to complete the objectives of this project, the experiment was

divided into sections where each section must be accompUshed prior to

beginning the next. The first step in the experiment was to become familiar

with the tow tank facUity and measuring equipment. This equipment

included the load ceU and the data acquisition system. The next major step

in the experiment was to caUbrate the load ceU in order to accurately

measure the wind loads appUed to the model. The last step was to perform

the testing of the model in the tow tank.

Tow Tank

The tow tank faciUty at Texas Tech is used to measure aerodynamic

loading and characteristics of large models. The tow tank has the advantage

of being able to test the model at a slower velocity to obtain the same

Reynolds number as in air. Another advantage is that larger models can be

tested in the tow tank than in the Texas Tech wind tunnel. The tow tank is

15 ft wide, 10 ft deep, and 80 ft long and is shown in Figure 2.1. RaUs are

attached to the waUs of the tow tank along the 80 ft span. The raUs support

a moving bridge which spans the tow tank and houses the bridge motor,

computer, strain gage amplifier, bridge control panel, video equipment, and

load ceU. The bridge is able to push or puU models through the water at a

velocity of 0 to 5 feet per second, depending on the model size and the

capabUity of the load ceU. The temperature of the water is approximately 67"=

F year around. The facUity has the capabiUty of providing flow visualization

13

Figure 2.1. Texas Tech's Tow Tank FaciUty

14

using a dye system that injects food dye into the water which can be recorded

using special video cameras that can be located at any depth in the water

Load CeU

The load ceU is the instrument that is used to measure loads on the

models. The load ceU was buUt by Casey Osborne under the supervision of

Dr. J.W. Oler. An Ulustration of the load ceU is shown in Figure 2.2. The

load ceU uses strain gages to provide a voltage output proportional to the

appUed loads. Strain gages are used because their resistance changes as the

appUed strain changes. Since strain gages are sensitive to temperatures, the

readings are compensated by connecting four gages into a Wheatstone bridge

circuit (Figure 2.3). In this configuration, the temperature effects are

canceUed. The load ceU is designed to measure aU six components of force

and moments and has 24 strain gages in 6 Wheatstone bridge circuits, one

for each force and moment.

Lift Gages

Yaw Monent Gages

Drag Gages P i tch Monent Gages

Side Fo rce Gages

J r-f\^—Roll Monent Gages

Figure 2.2. Load CeU lUustration

15

Figure 2.3. Wheatstone Bridge Configuration

Data Acquisition System

The data acquisition system used for this project includes the load ceU,

strain gage amplifier, DASH-16 A-D board, and computer. Figure 2.4

Ulustrates the configuration of the data acquisition system. The output

voltages from the load ceU are sent to the strain gage amplifier for

amplification. The amplifier is a Measurements Group model 2100 system,

shown in Figure 2.5, with three conditioner modules for a combination of six

ampUfier channels and a digital display. The output from the amplifier is in

the range of 0 to 4096 mUUvolts. Prior to any measurements, the strain gage

amplifier must be turned on for at least one hour to aUow time to warm-up.

16

Computer

1

DASH-16

Data Acquisition Board

Strain Gage AmpUfier

1

Load CeU

Figure 2.4. Data Acquisition System

2120A Output

o o Balonce

Output

o o Bolonce

Citcrt* Z#ro

G G C>c.<> Col C.c.-t* Col

B B

2120A Output

o o Balance

Output

o o Bolonce

GoinGb "' ^ G o i n

Cxcilv 7»ro

G G C>c.t< Col

e B

Br->dgr Anp

G G [•c,1» Col

2120A Output

o o Bolonce

Output

o o Bolonce

^ \ .goo /

E»c.1» Z»ro

G G t»c.-t» Col

B A

0

Br,dO» Anp

G G Cxc.lr Col

B B

2131 IhQi1«< Sisp<*v

o o Chonnel 3 /

o Ex-ternol

6 6 o

•«»« Power

5 0

2nOA

Chonnel

•D: O

Externa l Power

o o 0

Figure 2.5. Measurements Group Model 2100 Strain Gage AmpUfier

17

The output is sent to the DASH-16 data acquisition board inside the

computer. A program written by Dr. Oler is used to read the signal from the

board to determine the resultant loads.

There are two important steps in the procedure that are performed

with the strain gage amplifier. The first is balancing the bridges on the

ampUfier. This is necessary prior to each data coUection. Balancing the

bridges involves turning the balance control (Figure 2.6) to adjust the output

lamps so they wUl dim off indicating that the bridge is balanced. The next

ai20A Output

o o Balance

DutpuJ;

6 Balance

GainG^ "" -feCo in

Br.dge Anp

Exci-t* Zero

G G Exci-tff Col

on A

g B

Bridge ^r*P

E)'Ci*e Z e r o

G G E«citp Col

on A 0 s

OUTPUT L a n p s

BALANCE C o n t r o l

GAIN Mu l t i p l i e r Sw i t ch

GAIN P o t e n t i o n e t e r Sw i t ch

Figure 2.6. Controls to Balance Bridges and Setting the Gain

step in the procedure is to set the gain of the amplifier. The purpose of this is

to find the aUowable maximum amplification of the load ceU signals. The

output of the amplifier must be in the range of 0-4096 mV. For a safety

factor, a range of 600-3400 mV is recommended. For maximum

amplification, the gain multipUer switch is set at 200X. The bridges are then

balanced to prepare for the maximum expected loading on the load ceU. Once

18

the loads are appUed, adjust the gain potentiometer control untU the outputs

on the digital display of the amplifier are within the desired range.

CaUbration of Load CeU

Before any testing could begin in the tow tank, the load ceU had to be

caUbrated. This was necessary to relate the yoltage or output from the load

ceU to the specific appUed loads. Load ceU caUbration was performed by

placing the load ceU with the support pipe onto a mounting stand which was

on the waU out of the water. A combination of weights from a precision

weight set were added to simulate yarious combinations of lift, drag, and side

force and yaw, roU, and pitch moments. Figure 2.7 shows a schematic of the

mounting stand and the loading arrangement. Prior to the caUbration, the

gain and zeroes of each channel of the strain gage ampUfier must be set.

This was done by applying the maximum expected loads for the caUbration

and setting the gain to maximize the output without reaching the maximum

or minimum capacity of the ampUfier and the A/D board of the computer.

Once the gains and zeroes of each channel are set, the caUbration

procedure can begin. It is important to note that at each caUbration reading,

1000 samples are taken at 100 Hz. Before the loads are appUed, zeroes are

taken to account for any weights that are not part of the precision weight set

such as the weight of buckets and hooks used during the caUbration. Now

the loads can be appUed. An ayerage of the no-load yoltages are subtracted

from the loaded yoltages to obtain the net yoltage difference deyeloped by

each load combination. This is repeated for each load configuration

throughout the caUbration. These yoltage differences are used to solye for

the caUbration coefficients, the aij terms in equation 2.1. The caUbration

coefficients were solyed using a least squares optimization algorithm.

19

Yaw Monent

Support Pole

Drag

L i f t and Roil Monent

L i f t and P i t ch Monent

T

Figure 2.7. CaUbration Setup

20

11

•21

31

Ul

'51

'61

'12

'22

'32

'42

a 13

a 32

'62

'23

'33

'43

53

•63

•14

•24

•34

'44

54

•64

•15

'25

a,.

'45

'55

'65

16

26

36

46

56

66 _

[V..] VD,

V

VR,

[\\

* =

[Li] Di

SF,

Yi

Ri

L P i j

(2.1)

Diagonal dominance is desired for the coefficients because this would

minimize the effect of one channel on the other. Howeyer, drag is expected to

haye a large effect on the pitch and the side force on the roU. This is because

of the configuration of the strain gages on the load ceU.

The results of the caUbration are an important part of the experiment.

A summary of the maximum load estimates used in the caUbration is shown

in Table 2.1. These maximum load estimates were used LQ determining the

Table 2.1. Maximum Load Estimates for the Load CeU CaUbration

Force/Moment

Liftabf) Drag abf)

Side Force Qbf) Yaw Moment (ft-lbf) RoU Moment (ft-lbf)

Pitch Moment (ft-lbf)

Maximum Load

55 90 20 20 20 55

gain as weU as in the caUbration loading sequence. This loading

arrangement sequence was performed by starting the caUbration at

minimum loads and graduaUy increasing to the maximums. The caUbration

curyes resulting from the caUbration are shown in Figures 2.8 to Figure 2.13.

21

20 30 40 Lift Measured (Ibf)

Figure 2.8. Lift CaUbration Curye

50 60

100

80

- 6 0 s

< M)40

20 -

: 1 1 1 1 ,.• 1 ! 1 • /

1 1 i j

t

i i

i i . /

\ X :

; : P ^ r 1

.^ ^ ^.. .1 . i 1 . 1 1 1 1 .__1 ^ ^ 1 . ^ . ^ 1 ^ 1 1

20 40 60 Drag Measured (Ibf)

Figure 2.9. Drag CaUbration Curye

80 100

22

25

20

Xfl

5 -

o JD H H |

^ ^ M ^

08 S '*« w

^ 4> O o

b « •o

15

10

-I 1 I I ' ' u

5 10 15 20 Side Force Measured (Ibf)

Figure 2.10. Side Force CaUbration Curye

25

£ v l

2^20 "T £

Act

ual

Mom

ent

o

> 5

n

—

—

_... J — _

: -

— 1 — A 1 ! 1 1 1

\ 1

i i E

: 1

i i t

]•::

.,,•

• t

• i

i , . > , i .

; • y

i>'^

- - • -

. . ! .

5 10 15 20 Yaw Moment Measured (ft-lbf)

Figure 2.11. Yaw Moment CaUbration Curye

25

23

1^20 A

ctua

l O

l

Rol

l M

omen

t

-

• ^ 1 L.

,/''"

:

- -:• ^ X :

i i

i

1 1 1 1 1 i

. •

i

1

j

i 1 1 J i ]

•

> i . , .

5 10 15 20 Roll Moment Measured (ft-lbf)

Figure 2.12. RoU Moment CaUbration Curye

25

10 20 30 40 50 Pitch Moment Measured (ft-lbf)

60

Figure 2.13. Pitch Moment CaUbration Curye

24

The resulting maximum errors for the caUbration are shown in Table 2.2.

Table 2.2. CaUbration Maximum Percent Error Results

Component

Lift

Drag

Side Force

Yaw Moment

RoU Moment

Pitch Moment

Maximum Percent Error

0.572

1.165

0.439

0.514

7.060

11.208

Maximum Percent Error

ofTop75%ofLoads

0.137

0.122

0.438

0.141

2.318

1.653

The maximum errors occurred at the lower range of the caUbration where

error is not as sigmficant because the objectiye is to determine the maximum

wind loadings. The caUbration coefficient matrix is shown in equation 2.2.

^ i j =

-0.068623

-0.000043

0.000567

0.000065

-0.001578

-0.001385

0.002713

-0.097639

-0.003474

-0.003210

0.000540

0.772837

-0.000941

0.004481

-0.098628

-0.003098

0.768802

-0.048991

-0.003027 0.000901

-0.001394

0.145119

-0.002156

-0.014981

-0.000064 -0.001540

-0.001236

-0.003456

-0.517809

0.016475

0.001724 0.003156

0.002542

0.004262

-0.020676

-0.602642

(2.2)

As can be seen in equation 2.2, the coefficients for Uft, drag, side force, and

yaw moment channels are diagonaUy dominant but the coefficients for roU

and pitch moment are not. A reyiew of the bridge configuration for the load

25

ceU indicated that a significant degree of cross-coupling could be expected for

side force on roU and drag on pitch. This result can be seen in yalues for asa,

ass and a62, ase.

Model

For this experiment, a one tenth scale model was buUt by Cummins

Power Generation to be tested in the tow tank. The model is shown in Figure

2.14. This figure also includes the support pipe and elbow that connects the

model to the load ceU. A fiberglass surface was used to simulate the

paraboUc reflecting surface of the concentrator. A steel rod space frame

backed the fiberglass surface for rigidity and repUcates the actual

concentrator support structure. The concentrator model was attached to a

support pole at a connection which aUows for pitch adjustments up to 360

degrees at increments of 15 degrees. The purpose of the support pole was to

connect the model to the load ceU which would place the center point of the

model at a depth of 5 feet. It is important to note that the model was

attached to the support pole upside down for ease of pitch adjustments. The

flange where the support pole attaches to the load ceU aUows for yaw

adjustments of up to 360 degrees. Figures 2.15 and 2.16 show a schematic of

the model, load ceU, support pole, and the direction of positiye forces and

moments.

Measurement of Forces and Moments

A combination of the aboye systems and setups is necessary for the

measurement the simulated wind forces and moments induced on the

concentrator model. The model and support pole are connected to the load

26

Figure 2.14. One-tenth Scale Model of Solar Concentrator

27

Side Force

Mount ing B r a c k e t

L i f t

i >Yaw

Pole-

I n v e r t e d C o n c e n t r a t o r ( no t ch up")

Drag

Roil

Pi tch

Load Ceil

78.5

Point o f C a l i b r a t i o n

No te : All dimensions a r e in inches, N o t t o sca le ,

Figure 2.15. Load CeU, Support Pipe, and Model Setup with Direction of Positiye Forces and

Moments (Drawn by RocheUe Pritchard)

28

Yaw Angle - 4 5 Yaw Angle 45

P i t ch O Yaw

Figure 2.16. Yaw Angles and Direction of Positiye Forces and Moments

29

ceU which is attached to the front center of the bridge. After the cables are

connected to the data acquisition system, testing can begin. A program

written by Dr. Oler is used to control the data acquisition and measurement

of the forces and moments. The program sayes the model type, date of run,

yelocity, pitch and yaw angles, forces and moments, and yoltage differences.

Before data is taken, the bridges of each channel of the strain gage ampUfier

must be balanced because the initial output is caused by the static weight of

the model and support pole. After the bridges are balanced, the program

begins the data acquisition process with the recording of the zeroes of each

channel. Zeroes are taken at 100 Hz for ten seconds. The program then

requires that the desired run speed be entered. The run begins by

accelerating up to the desired speed in a two second time span. To insure

that the data is taken at the desired speed, once on speed, the bridge trayels

an additional 20 feet (5.72 model diameters) before beginning data

acquisition. Data is now recorded for the desired run speed and

configuration. Two data sampling frequencies were used to eyaluate the

effect of fluid induced oscUlations on the model. Frequencies of 100 Hz for

1000 data points and 150 Hz for 900 data points were used and resulted in

no sigmficant differences between the two frequencies. Zero load yoltages

are subtracted from the ayerage of the data points resulting in the net

yoltage differences caused by the simulated wind loadings on the model. The

net yoltage differences were multipUed by the coefficient matrix to calculate

the resulting loads. Ten runs were made for each configuration and then

ayeraged. It is important to note that these ayeraged loads include the loads

due to both the model and support pole. To obtain the load due to the

support pole solely, the process was repeated at each configuration of the

support pole alone. The ayeraged data of the support pole alone were

30

subtracted from the ayeraged data due to the support pole and model to

result in the net load caused by just the model. This data was used in the

calculations of the coefficients.

The speed of the tests were Umited by the capacity of the load ceU. It

was determined that the maximum safe test yelocity was 2.5 ft/s. This

resulted in a Re5molds number of approximately 808,000. This Re5niolds

number is greater than the Reynolds number that recommended by Roschke.

31

CHAPTER III

EXPERIMENTAL RESULTS AND DISCUSSION

The objectiye of the test program was to determine the maximum wind

loadings on the solar concentrator. To accompUsh this objectiye, a test

program was conducted using the Texas Tech tow tank. It was decided that

the tests should be done at pitch angles of 0, 30, 60, and 90 degrees and yaw

angles of 0, ±15, ±30, and ±45 degrees. Testing of the support pole with the

model was done first to confirm the maximum load estimates that were

assumed in the caUbration. The results showed that the loads measured

whUe testing feU within the caUbration range that was used. To find the

load that was induced by only the model, runs were made of only the support

pole. The model loads were found by subtracting the loads of the support

pole from the measured loads of the support pole and the model. The net

loads for the model were then conyerted into their nondimensional

counterparts. The nondimensional coefficients were plotted to eyaluate the

load characteristics as a function of pitch and yaw angles. Figures 3.1

through 3.6 show these results.

As can be seen from Figure 3.1, the Uft coefficients are symmetrical for

positiye and negatiye yaw angles. For pitching angles of 0 and 90 degrees,

the lift coefficient is relatiyely smaU. The minimum lift occurs at a 90degree

pitch angle which corresponds to a position with a minimum lift area

(maximum drag area). Lift is also smaU for a 0 degree pitch angle because

this position is the stow position or position of minimum loads. Lift increases

at a 30 and 60 degree pitch angles because as the pitch angle increases in the

30 to 60 degree range the area aboye and below the center of pressure

becomes unequal. This causes a pressure (force) difference causing a

32

I -0.3 S-0.4

U-0.5

'T 0 deg. Pitch 30 deg. Pitch 60 deg. Pitch 90 deg. Pitch

h -f—

-15 0 15 Yaw Angle (deg)

Figure 3.1. Lift Coefficients for Varying Yaw Angles

45


Figure 3.2. Drag Coefficients for Varying Yaw Angles

33


Figure 3.3. Side Force Coefficients for Varying Yaw Angles


Figure 3.4. Yaw Coefficients for Varying Yaw Angles

34

I 0.4 £ ^ 0.2 ••* c E 0 o

-0.4

-0.6

- K ^

\ \

^— 0 deg. Pitch -•— 30 deg. Pitch ^— 60 deg. Pitch ^— 90 deg. Pitch

' I I I I I I

-45 -30 -15 15 30 45

Yaw Angle (deg)

Figure 3.5. RoU Coefficients for Varying Yaw Angles

s .Si 'S €

• * *

e B o 0 deg. Pitch

*— 30 deg. Pitch 60 deg. Pitch

A— 90 deg. Pitch

_L. I I i

-45 -30 •15 0 15

Yaw Angle (deg)

30 45

Figure 3.6. Pitch Coefficients for Varying Yaw Angles

35

negatiye Uft coefficient. The maximum Uft coefficient of -0.92 occurs at a yaw

angle of 0 degrees and 30 degrees pitch. Maximum lift coefficients at each

pitch angle occurred at a yaw angle of 0 degrees. This is apparently due to

the notch in the model which is shown in Figure 2.16. The yariances shown

in the figure shows that data runs were repeatable.

The drag coefficient results are shown in Figure 3.2. The figure shows

that the drag steadUy increases as the pitching angle increases and as the

yaw angle approaches 0 degrees. The trend results from the fact that the

frontal area increases as the pitching angle increases and the yaw angle

approaches 0 degrees, as shown in Figure 2.16. It is logical then that the

point of maximum drag should occur at a 0 degree yaw angle and 90 degrees

of pitch and a minimum drag occurs at a pitch angle of 0 degrees. As the

figure shows, the corresponding maximum drag coefficient of 1.42 occurs at

this point. In addition, the figure shows that whUe the yariation in drag

coefficient data is smaU at 0 and 30 degree pitching angles, the yariance

increases for 60 and 90 degree pitching angles. But since the trends and

symmetry are in agreement with theory and the yariances are relatiyely

smaU, the drag results should be suitable to proyide an estimate for wind

loadings with a low uncertainty.

Side force coefficient results for yarying yaw angles are shown in

Figure 3.3. These results show that the side force loads are symmetrical for

both positiye and negatiye yaw angles. As explained aboye, the opposite

signs for the side force are a result of the center of pressure rotating from one

side of the caUbration point to the other. The side force yariances in the data

are also smaU showing that the data was consistent for multiple runs. A

minimum side force occurs at a yaw angle of 0 degrees for aU the pitch angles

because the center of pressure occurs along the axis of the caUbration point

36

resulting in equal frontal areas to the left and right of the caUbration point.

As seen in Figure 3.3, the absolute yalue of side force coefficient increases

with increasing pitching angle because as the pitching angle increases the

frontal area increases. In addition, the trend in side force coefficients

indicates that at yaw angles of -45 degrees the coefficient is at a maximum

and then decreases. At a yaw angle of 0 degrees, the side force coefficient is

approximately 0. The coefficient then decreases to a negatiye maximum

yalue to a 45 degree yaw angle. The maximum side force coefficient of

approximately 1.05 occurred at yaw angles of ±45 degrees and a 90 degree

pitching angle. This result occurred at these yaw positions because they

corresponded to the position of maximum frontal area occurring on one side

of the point of caUbration.

Yaw moment coefficient results are shown in Figure 3.4. The

S5rmmetry is not as weU defined as in the side force coefficient results, but the

trends are similar to that found in the side force coefficients. Maximum yaw

coefficients for each pitch angle occurs at ±45 yaw angle positions. At a 0

degree yaw angle, the yaw coefficient is approximately 0 simUar to that of the

side force coefficients. The figure also shows that the yariance is larger than

for the preyious results but the yaw moment coefficients are so smaU that

they are not yery significant and the scale is also smaUer than those of the

other coefficients. Minimum yaw coefficient occurs at a 0 degree pitch angle

because the frontal area is a minimum at this position. Side force coefficient

increases as the pitch angle increases because the frontal area increases.

Although this trend is true, the maximum yaw moment coefficient of

approximately 0.22 occurs at a pitching angle of 60 degrees and yaw angles

of ±45 degrees. This result was not expected because the frontal area is

37

maximum at 90 degrees pitch. The effect of the notch and/or the indicated

data yariation may contribute to this result.

Figure 3.5 shows the results of the roU moment coefficients for yarying

yaw angles. Although the figure appears to be symmetrical, the numbers do

not coincide for both positiye and negatiye yaw angles. The trends are

consistent with expectations from -45 to 15 degree yaw angles. Howeyer, at

30 degree yaw angle, the absolute yalue of the 60 and 90 degree pitch angle

roU coefficient data are lower than the 30 degree pitch angle roU coefficients.

If the data was extrapolated from the 15 degree yaw angle to the 45 degree

yaw angle, it appears that the data would correspond to their negatiye yaw

angle positions. The difference of the positiye and negatiye yaw angle roU

coefficients could be caused by seyeral factors including caUbration errors

and the effects of the support pole on the model. Howeyer, the yariances in

the roU coefficients indicate that the runs were repeatable for at least 10 runs

for each point and that this result might be inherent in the solar concentrator

model. The maximum roU moment coefficient occurred at a yaw angle of -45

degrees and a pitch angle of 90 degrees. This maximum yalue was

approximately 0.72.

The pitch moment coefficients are shown in Figure 3.6. As can be

seen, the figure does not appear symmetrical. The expected trend is similar

to that found in the drag coefficients in Figure 3.2. The minimums should

occur at the ±45 yaw angles and the coefficients should increase to a

maximum at a 0 degree yaw angle. Also, the pitch coefficients should

increase as the pitch angle increases. Signs of these trends are eyident in

Figure 3.6. The pitch coefficient does increase as the pitch angle increases

and is a maximum at a 0 degree yaw angle. Howeyer, the yalues at positiye

and corresponding negatiye yaw angles are not equal. Part of this problem

38

could be accounted for as part of a continual problem found in the caUbration

of the pitch moment. The errors in the caUbration could not be reduced in

the pitch moment. The errors are beUeyed to be caused from caUbrating

about a point which is approximately 6.5 ft below the load ceU. The total

pitch moment, as seen from the load ceU, is the appUed moment from the

caUbration and a contributing moment caused by the drag force being appUed

with a 6.5 ft moment arm. Eyen though the trends do not correspond with

expected trends, the maximum pitch moment coefficient seen in Figure 3.6 is

approximately 1.3 at a 90 degree pitch and 0 degree yaw angle. Variances in

the pitch coefficients are significant for the 90 degree pitch angle position.

This position corresponds to the location of the maximum pitch coefficient.

In an effort to find other possible solutions in the errors of sjnnmetry

found in the roU and pitch results, fiirther testing of the load ceU was done.

There could be seyeral possible reasons for this phenomena, such as, there

could be a problem in the caUbration, the model was not buUt symmetricaUy,

or a problem in the design of the load ceU. To rule out the design of the load

ceU, further tests were done. These tests were done with the load ceU in the

caUbration position. Known weights were appUed to determine how, for

example, the roU output yaries as the drag is increased. Initial results haye

shown that the Uft, drag, side force, and the yaw appear to be reasonably

accurate except at loads under 10 pounds. The roU and pitch results showed

that the load ceU was measuring loads which were larger than appUed.

Again this could be from the results of a bad caUbration or from a problem

with the design of the load ceU. The requirement in this test program to

caUbrate at 6.5 ft below the load ceU tended to increase the uncertainty in the

calculated and measured loads. One of the other efforts that was performed

on the load ceU was rotating the load ceU and applying a load. This effort

39

was performed to confirm that the load ceU was aUgned correctly. The

results of this testing showed that the load ceU was aUgned symmetricaUy.

In summary, the trends of affects of yaw and pitch angles were

generaUy consistent with physical expectations. Most components exhibit

symmetrical load characteristics. The Uft, drag, side force, and yaw figures

show that the coefficients are symmetrical with only minor discrepancies.

Howeyer, for the roU and pitch components, the discrepancies became

significant. One significant trend in the symmetry of the Uft, drag, and pitch

moment coefficients is that the coefficients are approximately the same for

both positiye and negatiye yaw angles. This is due to the geometry of the

model and the direction of the forces and moments which can be seen in

Figure 2.16. In the same manner, the side force, yaw moment, and roU

moment coefficients are opposite in sign for positiye and negatiye yaw angles.

40

CHAPTER IV

CONCLUSIONS AND RECOMMENDATIONS

The objectiye of this research project was to determine the wind

loadings on a notched paraboUc solar concentrator. The results from Texas

Tech's tow tank testing of the one tenth scale model were put into

nondimensional force and moment coefficients. Since the nondimensional

coefficients are yaUd for both the model and the actual solar concentrator

prototype, they are the major results of the project. The maximum

coefficients are shown in Table 4.1.

Table 4.1. Maximum Nondimensional Coefficient Results

Component

Lift

Drag

Side Force

Yaw Moment

RoU Moment

Pitch Moment

Coefficient

-0.92

1.42

1.05

-0.23

0.72

1.28

Based on the aboye resiUts, the structural design of the solar concentrator

support structure should use these results for maximum load estimates.

Howeyer, as seen preyiously, the roU and pitch moment coefficients haye

errors in the figures because S5anmetry is not present from negatiye to

positiye yaw angles. These yalues could be only used as a starting estimate

for the beginning stages of the structural design.

41

There are stUl seyeral things that could be done in the future which

would make the work more conclusiye. Some of the things that could be done

include:

• Determine the problem with the roU and pitch measuring false loads.

• If the problem is with the design of the load ceU, then the load ceU must

be redesigned or purchase a new load ceU.

• Retesting of the model in the tow tank for the configurations tested for

this project and for different configurations such as the model being

rotated on one side (the y-notch on one side).

• Flow yisualization can also be performed on the model.

• Computational fluid dynamics program inyestigation of the model.

42

REFERENCES

Imadojemu, H. E., "Literature Suryey of Concentrating Solar CoUectors," Solar Enedneering. Vol. 1, pp. 719-730, 1995.

Murphy, L.M., "Wind Loading on Tracking and Field Mounted Solar CoUectors," Proc. ASME Solar Energy Diyision. Solar Engineering -1981. edited by Reid, R.L., Murphy, L.M., and Ward, D.S., pp. 719-727, April 1981.

Roschke, E. J., Wind Loading on Solar Concentrators: Some General Considerations. U.S. Dept. of Energy DOE/JPL-1060-66, May 1, 1984.

Stine, W. B., "An International Suryey of paraboUc Dish/StirUng Engine Electrical Power Generation Technology," Solar Engineering 1993. pp. 421-427, 1993.

Stine, W. B. and R. B. Diyer, A Compendium of Solar Dish/StirUng Technology. SAND93-7026 UC-236, Albuquerque, NM: Sandia National Laboratories, January 1994.

Wyatt, T. A., "The Aerodynamics of ShaUow Paraboloid Antennas," Annals. New York Academy of Sciences. Vol. 116, pp. 223-238, 1964.

43

APPENDIX A

CALIBRATION DATA

44

Table A. 1. Six Component Load CeU CaUbration CaUbntkm Fac: cal6-29.dat Coefficient File: cof6-29.dat

Calibration CoefBcients -0.068623 -0.000043 0.000567 0.000065 -0.001578 -0.001385

0.002713 -0.097639 -0.003474 -0.00321 0.00054 0.772837

-0.000941 0.004481 -0.098628 -0.003098 0.768802 •0.048991

-0.003027 0.000901 -0.001394 0.145119 -0.002156 -0.014981

-0.000064 -0.00154 -0.001236 -0.003456 •0.517809 0.016475

0.001724 0.003156 0.002542 0.004262 -0.020676 -0.602642

Compontent

Channel 1 Channel 2 Channel3 Channet4 Channel 5 Channel 6

>iamea

Lift Drag

Side Force Yaw Ron Pitch

Max% Error 0.572 1.165 0.439 0.514 7.060 11.208

Gains

4x200 5x200

4.9 X 200 5x200

0.9 x 200 0.84 X 200

Lift Voltage -75.504 -150.963 -380.906 -530.739 -757.657 -5.472 -14.425 -29.239 -61.434 -83.464

1.149 0.173 5.307 1.842 -1.026 -2.964 •4.462 -6.422 0.093 0.123 0.063 -0.1

-1.135 -0.979 -2.204 -3.245 -2.815

Drag Voltage 0.243 -0.338 1.624 -0.284 0.017

-136.025 •413.783 -556.502 -835.205 -973.549

-1.576 -3.517 •1.207 •5.733 0.15 1.141 0.428 1.367 0.014 0.25 0.583 0.509 •0.183 •1.503 -2.866 •3.845 •1.912

Side Force Voltage •0.086 •1.264 •1.842

•3 •4.463 •1.326 •1.755 •1.673 1.031 2.961

-51.508 •103.823 •154.648 •207.303 •0.482 •1.326 -1.794 •1.899 •0.268 0.523 0.916 •0.041 -0.43 -0.91 •1.476 •2.222 -2.097

Yaw Voltage

0.06 0.074 -0.044 -0.001 0.101 1.327 5.57 8.295 14.316 17.424 -3.321 -6.222 -7.405 •12.816 35.762 72.155 107.629 143.371 -0.283 •0.617 •0.773 -0.749 0.151 0.91 1.812 1.758 3.254

RoU Voltage -0.635 -1.003 -2.229 -3.03 -4.035 5.129 17.447 26.093 43.679 53.135 -76.908 -154.537 -229.982 -307.357 -0.639 -1.926 -3.101 -3.469 -9.75

-19.629 -29.513 -39.665

0.17 0.302 0.249 0.312 0.358

Pitch Vohage 0.143 0.445 1.399 1.647 2.155

-177.057 -534.221 -714.736 -1069.771 -1244.739

0.471 0.762 2.796 2.556 -0.567 -1.024 -1.393 -1.936 0.043 -0.127 •0.199 -0.36

-13.455 -27.266 -67.963 -81.265 -93.902

Load No. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Lift Meas. 5.182 10.360 26.148 36.426 52.001 -0.302 -1.070 -0.761 0.058 0.881 -0.019 0.106 -0.180 0.116 -0.038 -0.012 •0.019 0.009 •0.005 •0.005 0.000 0.012 0.054 0.014 0.022 0.069 0.018

Lift Actual 5.21 10.42

26.036 36.456 52.072

0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001

Percent Error 0.534 0.572 0.429 0.082 0.137 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

45

Table A. 1. Continued Calibration File: cal6-29.dat CoefiBcient Ffle: cof6-29.dat

Calibration CoefiBcients •0.068623 -O.000043 0.000567 0.000065 •0.001578 -0.001385

0.002713 •0.097639 -0.003474 -0.00321 0.00054

0.772837

-0.000941 0.004481 -0.098628 -0.003098 0.768802 -0.048991

-0.003027 0.000901 -0.001394 0.145119 -0.002156 -0.014981

-0.000064 -0.00154

-0.001236 -0.003456 -0.517809 0.016475

0.001724 0.003156 0.002542 0.004262 -0.020676 -0.602642

Compontent

Channel 1 Channel 2 Channel 3 Channel 4 Channel 5 Channel 6

Names

Lift Drag

Side Force Yaw Ron Pitch

Max% Enor 0.572 1.165 0.439 0.514 7.060 11.208

Gains

4 x 2 0 0 5 x 2 0 0

4.9 X 200 5 x 2 0 0

0.9 X 200 0.84 X 200

Drag Meas. -0.019 0.037 -0.143 0.047 0.024 12.710 38.686 52.042 78.125 91.079 0.040 0.113 -0.219 0.101 0.015 -0.052 0.048 -0.013 0.012 0.007 -0.009 0.009 -0.027 0.057 0.060 0.110 -0.117

Drag Actual

0.000001 0.000001 0.000001 0.000001 0.000001

12.86 38.896 52.072 78.108 90.968

0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001

Percent Error 0.000 0.000 0.000 0.000 0.000 1.165 0.539 0.058 0.022 0.122 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Load No.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Side Force Meas. -0.034 0.043 •0.034 0.004 0.021 0.142 0.215 0.221 -0.028 -0.211 5.187 10.454 15.562 20.871 -0.004 0.024 0.023 -0.022 0.039 -0.028 -0.055 0.051 0.008 0.023 -0.021 0.021 •0.032

Side Force Actual

0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001

5.21 10.42 15.63 20.84

0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001

Percent Error 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.439 0.324 0.438 0.149 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Load No.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Yaw Meas. 0.006 0.011 -0.017 -0.007 0.002 •0.139 -0.196 •0.143 0.041 0.150 •0.049 -O.033 0.215 -0.126 5.190 10.474 15.628 20.811 -0.006 -0.025 -0.016 0.025 -0.034 0.022 -0.014 -0.073 0.083

Yaw Actual

0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001

5.21 10.42 15.63 20.84

0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001

Percent Error 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.375 0.514 0.015 0.141 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

46

Table A. 1. Continued Calibration File: cal6-29.dat Coefficient File: cof6-29.dat

Calibration Coefficients -0.068623 -0.000043 0.000567 0.000065 -0.001578 -0.001385

0.002713 -0.097639 •0.003474 •0.00321 0.00054

0.772837

•0.000941 0.004481 •0.098628 •0.003098 0.768802 -0.048991

•0.003027 0.000901 -0.001394 0.145119 -0.002156 •0.014981

-0.000064 -0.00154

-0.001236 -0.003456 -0.517809 0.016475

0.001724 0.003156 0.002542 0.004262 -0.020676 -0.602642

Compontent

Channel 1 Channel 2 Channel 3 Channel 4 Channel 5 Channel 6

Names

Lift Drag

Side Force Yaw

Ron Pitch

Max% Error 0.572 1.165 0.439 0.514 7.060 11.208

Gains

4 x 2 0 0 5 x 2 0 0

4 .9x200 5 x 2 0 0

0.9 x 200 0.84 X 200

RoU Meas. 0.379 -0.224 0.311 0.066 -0.191 -0.082 0.449 -0.292 -0.091 0.067 0.219 0.197 0.142 -0.254 -0.103 -0.151 0.031 0.078 4.842 10.570 15.992 20.517 •0.139 •0.293 0.140 •0.190 0.140

RoU Actual

0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001

5.21 10.42 15.63 20.84

0.000001 0.000001 0.000001 0.000001 0.000001

Percent Error 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 7.060 1.440 2.318 1.551 0.000 0.000 0.000 0.000 0.000

Load No. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Pitch Meas. 0.199 •0.276 0.994 •0.380 -0.086 1.714 2.467 1.073 -0.249 -1.678 -0.197 -0.544 1.273 -0.689 -0.064 0.455 -0.399 0.120 -0.158 -0.070 0.051 -0.030 7.990 15.307 38.795 46.094 55.175

Pitch Actual

0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001 0.000001

7.185 15.63

39.054 46.869 54.684

Percent Error 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 11.208 2.064 0.664 1.653 0.899

47

APPENDIX B

SUPPORT PIPE DATA

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55

APPENDIX C

MODEL LOAD DATA

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63

PERMISSION TO COPY

In presenting this thesis in partial fulfillment of the requirements for a

master's degree at Texas Tech University OP Texas Tech University Health Sciences

Center, I agree that the Library and my major department shall make it freely

available for research purposes. Permission to copy this thesis for scholarly

purposes may be granted by the Director of the Library or my major professor.

It is understood that any copying or publication of this thesis for financial gain

shall not be allowed without my further written permission and that any user

may be liable for copyright infringement.

Agree (Permission is granted.)

student's Signature ^ Date

Disagree (Permission is not granted.)

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