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Methodology for measuring the wind drag coefficient on coastal dune vegetation

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Methodology for measuring the wind drag coefficient on coastal dune vegetation
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UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 92/017
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Burger, Tracy A.
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Gainesville, FL
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Coastal and Oceanographic Engineering Department, University of Florida
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Subjects / Keywords:
Aerodynamic drag
Sea oats
Coastal plants

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This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.

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UFL/COEL-92/017

A METHODOLOGY FOR MEASURING THE WIND DRAG COEFFICIENT ON COASTAL DUNE VEGETATION: A STUDY ON SEAOATS (UNIOLA PANICULATA)
by
Tracy A. Burger
Thesis

December 1992




A METHODOLOGY FOR MEASURING
THE WIND DRAG COEFFICIENT ON COASTAL DUNE
VEGETATION: A STUDY ON SEA-OATS (UNIOLA PANICULATA)
By
TRACY A. BURGER

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA

1992




ACKNOWLEDGEMENTS

Several people have contributed to this thesis, making its completion possible. J.B. Miller, District 7 Park Manager, and John Fillyaw, John D. MacArthur Beach State Park Ranger, were extremely helpful in my quest for quality sea-oats specimens. Special thanks go to Paden Woodruff for all his help and encouragement. Dr. D. Max Sheppard was invaluable for his patience in the designing and building phase of this project and as a friend. Without the aid of the coastal lab personnel, namely, Vernon Sparkman, Chuck Broward, Jim Joiner and Sidney Schofield, this project would not have been possible. I must also thank Dr. Robert Dean and Alan Niedoroda for the time they took out of their busy schedules to sit as supervisory committee members. Their comments were important. Lastly, I cannot ignore the sacrifices and support of my husband, Bryce, in the last three years and the eternal patience of my biggest fan, Romeo. I wouldn't have made it through without them. Iguana lives.




TABLE OF CONTENTS

ACKNOWLEDGEMENTS..............

LIST OF TABLES........................................

LIST OF FIGURES...................
KEY TO SYMBOLS AND ABBREVIATIONS ABSTRACT........................

CHAPTER
1.1
1.2 1.3
1.4
CHAPTER
2.1

1 INTRODUCTION..........
Background................
Statement of the Problem....... Study Purpose and Approach .. Definition of Key Terms........
2 PRINCIPLES AND THEORY. Forces on a Plant Leaf.........

2..2 The Drag Coefficient Equation.........
2.3 Other Methods of Obtaining the Canopy Cd

2.4 Reynolds Number Dependence of the Drag(

CHAPTER 3 METHODOLOGY........................
CHAPTER 4 EXPERIMENTAL PROCEDURES.............
4.1 Instrument Calibration.......................
4. 1.1 Force Transducer.....................
4.1.2 Pressure Transducers and Pitot-Static Tubes..
4.1.3 Temperature Thermistor................
4.1.4 Fifth Wheel........................
4.2 Leaf Area Density Measurements................
4.3 Testing Procedures.........................
CHAPTER 5 DATA ANALYSIS.......................
5.1 Signal Readings...........................

.v

...........
...........
...........
...........
oefficient ....




5.1.1 Fifth W heel .............................. 23
5.1.2 Pitot-Static Tube ................................ 28
5.1.3 Differential Pitot-Static Tube ...................... 28
5.1.4 Force Transducers ............................. 28
5.1.5 Thermistor ................................... 31
5.2 Other Analysis Techniques .............................. 31
CHAPTER 6 RESULTS AND CONCLUSIONS ........................ 34
6. 1 Results ............................................ 34
6.2 Conclusions ........................................ 36
6.3 Comments ......................................... 37
APPENDIX A LEAF AREA MEASUREMENTS AND CALCULATIONS . 39
APPENDIX B INSTRUMENTATION .......................... 54
B. 1 Predicted Strain and Deflection Calculations ................. 54
B.2 Pitot-Static Tube Theory ........................... 58
REFERENCE LIST ...................................... 62
BIOGRAPHICAL SKETCH ................................. 64




LIST OF TABLES
A. 1 GENERAL CHARACTERISTICS MEASUREMENTS
OF SEA-OATS .. ...................................
A.2 LEAF, STALK, AND SEEDHEAD AREA MEASUREMENTS AND LAI
CALCULATIONS FOR PLANT 1 ........................
A.3 LEAF, STALK. AND SEEDHEAD AREA MEASUREMENTS AND LAI
CALCULATIONS FOR PLANT 2 ........................
A.4 LEAF, STALK, AND SEEDHEAD AREA MEASUREMENTS AND LAI
CALCULATIONS FOR PLANT 3 ........................
A.5 LEAF, STALK, AND SEEDHEAD AREA MEASUREMENTS AND LAI
CALCULATIONS FOR PLANT 3 ........................

B.1 CALCULATED FORCE, STRAIN
DIFFERENT WIND SPEEDS. .

AND DEFLECTION QUANTITIES AT . . . . . . . . . . . . 58




LIST OF FIGURES

2.1 LEAF ANGLE OF INCIDENCE ........................ 7
2.2 DRAG COEFFICIENT FOR CYLINDERS AS A FUNCTION OF
REYNOLDS NUMBER ............................... 10
3.1 VEHICLE APPARATUS FOR MEASURING THE DRAG COEFFICIENT
OF DUNE PLANTS ................................. 14
4.1 CALIBRATION CURVE FOR STRAIN GAGE 1 .............. 18
4.2 CALIBRATION CURVE FOR STRAIN GAGE 2 ............... 18
4.3 CALIBRATION CURVE FOR THE PRESSURE TRANSDUCER .... 19 4.4 CALIBRATION CURVE FOR THE FIFTH WHEEL ............ 21
5.1 UNFILTERED OUTPUT SIGNALS FROM CYLINDER TEST AT A
VEHICLE SPEED OF APPROXIMATELY 15 MPH ............. 24
5.2 UNFILTERED OUTPUT SIGNALS FOR CYLINDER TEST AT A
VEHICLE SPEED OF APPROXIMATELY 50 MPH ............. 25
5.3 POWER DENSITY SPECTRA OF SIGNALS IN FIGURE 5.1 ....... 26 5.4 POWER DENSITY SPECTRA OF SIGNALS IN FIGURE 5.2 ....... 27 5.5 FILTERED AND UNFILTERED PRESSURE SIGNALS ........... 29
5.6 CALCULATED VELOCITIES FROM FIFTH WHEEL AND
PRESSURE SIGNALS ................................ 30
5.7 POWER DENSITY SPECTRA FOR FORCE TRANSDUCER 1 AT
TWO DIFFERENT VEHICLE SPEEDS .................... 32
6.1 LEAF AREA DENSITY PROFILE FOR SEA-OATS ............. 34




6.2 PLOT OF THE MEASURED DRAG COEFFICIENT VS. REYNOLDS
NUMBER FOR THE CYLINDER ......................... 35
6.3 PLOT OF THE MEASURED DRAG COEFFICIENT VS. REYNOLDS
NUMBER FOR SEA-OATS ............................. 35
A. 1 SEA-OATS HEIGHT HISTOGRAM ........................ 42
A.2 SEA-OATS UPPERMOST FOLIAGE HEIGHT HISTOGRAM ........ 42 A.3 SEA-OATS BASAL STEM CIRCUMFERENCE HISTOGRAM ...... 43 A.4 SEA-OATS NUMBER OF LEAVES HISTOGRAM ................ 43
B. 1 PLANTERBOX DETAILS .............................. 55
B.2 DETAIL OF FORCE TRANSDUCER ....................... 56
B.3 DETAIL OF PITOT-STATIC TUBE SUPPORT ................. 59
B.4 DETAIL OF PITOT-STATIC TUBE ........................ 60
B.5 DETAIL OF FIFTH WHEEL ............................ 61




KEY TO SYMBOLS AND ABBREVIATIONS

A two-sided leaf area per unit plant volume
A, one-sided leaf area per unit plant volume
b planterbox leg width
Cd drag coefficient
D characteristic plant length
d cylinder diameter
E modulus of elasticity
F force
Fd drag force
F, force on instrumented planterbox leg
F, force on non-instrumented planterbox leg
F" force per unit volume
FDNR Florida Department of Natural Resources
H total plant height
h planterbox leg thickness
I moment of inertia; bh2/12
L average plant spacing
I cylinder length




LAD leaf area density; leaf area per unit plant volume
LAI leaf area index; one-sided leaf area per ground area
M moment
m unit mass
p pressure
Re Reynolds number; ULp/g
S section modulus; bh2/6
T temperature
U time mean velocity
u air velocity
u free-stream velocity
v distance from strain gage to top of pin joint
z height
5 planterbox leg deflection
5, turbulent eddy transfer coefficient
Strain
dynamic (absolute) viscosity
kinematic viscosity p air density
CT axial stress
7 shear stress
6 leaf angle of incidence




Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science A METHODOLOGY FOR MEASURING THE WIND DRAG COEFFICIENT ON SMALL COASTAL DUNE
VEGETATION: A STUDY ON SEA-OATS (UNIOLA PANICULATA) By
TRACY A. BURGER
DECEMBER 1992
Chairperson: Dr. D. Max Sheppard
Major Department: Department of Coastal and Oceanographic Engineering
Current plant canopy wind flow models require three aerodynamic parameters to predict the effects of wind on sand transport--the plant drag coefficient, Cd, the leaf area density profile, LAD, and the turbulent eddy transfer coefficient, 6. The LAD and Cd characterize the plant canopy and its effects on air flow and, prior to this study, data on these parameters for dune vegetation did not exist. The purpose of this study was to design and test a methodology for measuring the wind drag coefficient of coastal dune plants. The objectives were 1) to measure and record the parameters needed to calculate Cd, namely, the force, relative velocity and air temperature; 2) to measure the leaf area density of sea-oats; 3) to validate the method by measuring the quantities needed to compute the drag coefficient for a right circular cylinder where




data exists; and 4) to explore the Reynolds number dependence of the canopy drag coefficient.
In order to generate a controlled relative velocity between the air and the plant, either the air must be moved around the plant or the plant must be moved through the air. Because wind tunnels large enough to accommodate most dune plants are rare and expensive to use, the decision was made to move the plants through the air. The apparatus and instrumentation required to measure the necessary parameters was mounted on an automotive vehicle. The instrumentation included a force transducer, three pitot tubes connected to sensitive pressure transducers to measure the relative velocity and relative velocity gradients with height, a fifth wheel attached to the vehicle to accurately measure the vehicle velocity, and a thermistor to measure the air temperature. The first tests were conducted with a right circular cylinder. Sea-oats plants were used in the second series of tests. A range of vehicle speeds were covered in both series.
Results indicate a good agreement between Cd values obtained in these tests an d those obtained by a number of other investigators. Thus, it is believed that the Cd values obtained for the sea-oats are equally vaiid.




CHAPTER 1
INTRODUCTION
1. 1 Background
The study of vegetation and its influence on the atmosphere has been an active field of research in a variety of disciplines for many decades. In agriculture, scientists study the extent to which weather and climate limit crop yield. In ecology, the concern is how micro-climatic change affects an ecosystem's equilibrium. Hydrologists attempt to relate land use and vegetative cover to the soil water evaporation. And, more recently, meteorologists have been looking for ways to more realistically characterize surface conditions for modeling the planetary boundary layer. Thus, the development of an air flow model through vegetation, or canopy flow model, within the earth's surface boundary layer is of great interest in many fields of research.
Research into the development of a canopy flow model has, necessarily, initiated an increased number of studies on the aerodynamic properties of plants, including momentum source and sink distributions, turbulence intensity distributions, wind velocity profiles, canopy drag forces, sheltering effects of plant canopies, canopy density distributions, and plant flexibility.




Measurements of such properties, however, often require sophisticated,
expensive or unavailable equipment, thus making it difficult or impossible to obtain the necessary data. Most data that is available in the literature is based on experiments on agricultural plants.
1.2 Statement of the Problem
One application of canopy flow model research is the prediction of aeolian sand transport through coastal dune vegetation. Coastal engineers have studied the trapping of wind-blown sand by vegetation and the benefits of such a sand reserve for shore protection against storms for a number of years. Yet, the physical details of the plant-wind interaction in coastal areas has not, until recently, been examined in detail.
The development of a canopy flow model for use in the prediction of aeolian sand transport has been investigated most recently by Sheppard and Niedoroda (1992) in a research effort supported by the Florida Department of Natural Resources (1TDN'R), Division of Beaches and Shores. In their research, three aerodynamic parameters, which vary with the type of canopy, were required for the application of their one and two dimensional models--the plant drag coefficient, Cd, the vertical leaf area density profile, LAD, and the turbulent eddy transfer coefficient, 61. The Cd and LAD characterize the plant canopy and its effects on air flow and is usually obtained empirically. The 61 scales the turbulent transfer of the Reynolds stresses and is obtained by calibrating the model with experimental mean wind velocity and LAD profile data. If the Cd and LAD are known, then 6, is computed.




3
Currently, data for these parameters for coastal dune plants do not exist in the literature. In Sheppard and Niedoroda (1992) the parameters had to be estimated based on similar non-coastal vegetation. The accuracy of these aeolian sand transport models are dependent on the accuracy of the data for these input parameters. There is thus a critical need for a methodology for measuring these quantities and actual values of these parameters for common dune plants.
1.3 Study Purpose and Approach
The purpose of this study was to develop and test a methodology for
determining the wind drag coefficient of coastal dune plants. The drag coefficient is known to depend on the Reynolds number, i.e., to depend on the relative velocity between the incident surface (plant parts) and the fluid (air), the characteristic length of the plant, and the kinematic viscosity of the fluid. To obtain a nearly uniform velocity over the height of the plant the decision was made to move the plant through still air. The plant support was instrumented so that the total force exerted on the plant by the wind could be measured. The relative velocity and air temperature were also measured, and the vertical distribution of leaf area (LAD) was obtained prior to the experiment. Experiments were conducted over a range of velocities so that the Reynolds number dependence of the drag coefficient could be determined. To validate this approach, tests were conducted on a cylinder where the drag coefficients are known.




1.4 Definition of Key Terms
Researchers with a variety of backgrounds, e.g., meteorology, agronomy,
agricultural engineering, aeronautical engineering, etc., have studied and reported on canopy flow problems. This has resulted in different definitions being used for many of the same terms. To avoid such confusion here, precise definitions for the salient parameters and terms used in this thesis are presented below.
Drag Coefficient. C,: This indicates the effectiveness of a particular body in absorbing momentum from the airflow (Thom, 1975). It is also called the momentum transfer coefficient. This study deals only with the effectiveness of the entire body of the plant to absorb momentum rather than that of individual leaf elements. Precisely, it is the constant of proportionality in the following equation: Fd -p. ., A U2 = CdP, A U2 (1. 1)
where Fd is the drag force, Cd is the drag coefficient, pj, is the mass density of air, A is the leaf surface area. and U is the time mean air velocity.
Leaf Area Density. LAD: This is the vertical leaf area density profile or the leaf area per vertical unit of plant volume. In this study, A, is the one-sided leaf area per unit plant volume and A is the two-sided leaf area per unit plant volume.
Reynolds Number. Re: The Reynolds number is defined as:
Re=- UD p (1.2)
11
where U is the time mean velocity, D is the characteristic plant length (defined below), p is the mass density of air, and pt is the dynamic viscosity of air.




5
Plant Characteristic Length, D: The plant characteristic length used in
computing the Reynolds number should be a meaningful length that characterizes the plant. If the plant were a simple cylinder whose axis was normal to the flow, the characteristic length would be the diameter of the cylinder. In the case of a complex plant, no such obvious length exists. A discussion of possible plant characteristic lengths is presented in Chapter 2 of this study.




CHAPTER 2
PRINCIPLES ANT) THEORY
2.1 Forces on a Plant Leaf
Whenever wind blows on a plant, the plant parts (i.e., the leaves, stems, stalks, etc.) experience a net force due to the movement of the air around the individual plant surfaces. The portion of the net force that acts parallel to the direction of the wind is called the drag force, Fd, and, as stated in Chapter 1, can be expressed as
Fd = CdpA U2. (2.1)
In fluid mechanics the drag force is defined as Fd -= .pA UCd, (2.2)
where the 1/2 is included to form the dynamic, pressure, /pU', and A is usually the area of the body projected on a surface normal to the flow. The drag force, as defined here, can be separated into two components. One is the result of normal stresses and is called the bluff-body or pressure force, and the other is due to shear or tangential stresses acting on the body and is called the tangential or skin friction force. Both take the form of Equation 2.1.
In general, for a plant leaf, Cd is expected to be a function of U and the leaf angle of incidence, 0 (see Figure 2. 1). Based on experimental data, Thom (1968)




INCIDENT
WIND
Figure 2.1: LEAF ANGLE OF INCIDENCE.
concluded that Cd becomes less dependent on wind speed as increases, thereby confirming that the bluff-body force is proportional to U2 at maximum 0 (see Equation 2.1). Baldocchi (1989) theorized that Cd decreases as U increases and increases as the leaf width decreases.
2.2 The Drag Coefficient Equation
In Sheppard and Niedoroda's (1992) analysis the force per unit mass (of air) is defined as
force F = Cd AU2' (2.3)
unit mass m
where A, is the one-sided leaf area per unit volume. This can also be expressed as a force per volume of air,
F I AIU2 = CdpAU2. (2.4)
unit volume unit volume)
Since A, varies with height, z, F* = CdPAl(z) U2. (2.5)




8
dF = F*.dV, (2.6)
and
dV = dxdydz = L2.dz (2.7)
where L is the average spacing between the plants, then dF = CdPAl(Z) U2L2.d, (2.8)
and
F = CdPU2L2f nAl(z).dz, (2.9)
where H is the total plant height. Therefore, Cd = F
p U2L2foAi(z)dz (2.10)
Using Equation 2.10, the C, can be calculated provided F. L, and A,(z) are knoWn for a particular plant.
For a cylinder, the drag coefficient equation is
Cd 2F (2.11)
pIU2d
where d and 1 are the diameter and length of the cylinder, respectively.
2.3 Other Methods of Obtaining the Canopy Cd
Other methods of obtaining the canopy drag coefficient include forcemomentum measurements in a wind tunnel on single plant elements and anemometer wind velocity profile measurements in the field. The drag coefficient can be expressed as a function of friction velocity, u., and the free stream velocity, u,,, as
Cd= 2( u.', (2.12)
(see Cowan, 1968) where Pr (2.13)




and 70 is the shear stress on the leaf surface. The friction velocity can be estimated from wind velocity profile measurements. Foliage elements can be suspended in a wind tunnel on a momentum balance, the drag force measured and the drag coefficient calculated using Equation 2.1. In this manner, Thorn (1968) measured the total drag force on an artificial bean leaf and estimated the leaf drag coefficient, which he designated C,(u). Later, in Thom (1971), he compared this data to drag coefficient estimations calculated from wind profile measurements taken through a bean field. He concluded that in calculating the total drag coefficient for an entire plant. C, the drag coefficient measured for an individual leaf element must be divided by a constant shelter factor, Pd, to compensate for the drag reduction caused by aerodynamic interference that neighboring foliage elements have on the individual leaf element. The need for a shelter factor actually results from a lack of knowledge of the velocity field throughout the canopy.
2.4 Reynolds Number Dependence of the Drag Coefficient
As mentioned in Chapter 1, the drag coefficient is known to be dependent on the Reynolds number. This dependence has been studied for cylinders and is shown in Figure 2.2.
However, to obtain this relationship for a plant, a characteristic plant length, D, must be defined. Difficulty in specifying this length for a plant stems from the change in the orientation of the whole plant and individual leaf elements as the wind velocity changes. This in turn is dependent on the size of the leaf elements, the angle




Fig~u DRAG COEFFICIENT FOR CYLINDERS AS A FUNCTION OF REYNOLDS NUMBER (SCHLICHTING, 1955).
uf leaf cientaion. : .e --ering effect of neighboring plant elements, and the
:exibilit of the plan: and the plant parts.
Very little has been said about the Reynolds number dependence of canopy Cd.
Cowan comments.
With leaves. such as those of corn, with a breadth of 5 cm or more, Reynolds
numbers will :end to be large throughout the crop under normal day-time
conditions (200 at a windspeed of 6 cm see2) and the drag coefficient of the :eaves may oossiblv be constant. This applies to the leaves with large angles of attack which will absorb most of the drag in the stand. The coefficients of
:hose oriented more nearly parallel to the wind, due to the lower values of
Reynolds number and greater streamlining, may be expected to increase with
decreasing windspeed and thus with proximity to the ground surface. With
small leaves such as clover, grasses. etc., Reynolds number at the same
windspeed \wili be about five-fold smaller and changes of the drag coefficients
with windspeed can be expected to be more marked. (Cowan 1968, 542)
What constitutes a meaningful length scale will depend somewhat on the
physical structure of the plant. Therefore, what is appropriate for a grass-like plant
will most likely not be meaningful for a shrub or tree, etc. This is obviously a
subject that needs further investigation. In the absence of an accepted length scale for




11
the sea oats plants, the decision was made to use the average leaf width as the length scale for purposes of presenting the data obtained in this work.




CHAPTER 3
METHODOLOGY
The objective of this study was to develop and test a methodology for
measuring the quantities needed to compute the drag coefficient for dune plants. These quantities are indicated in Equation (2.10), Cd = F
P u2L2 fH'A(z).dz
The leaf area distribution with height, A1(z), was measured using techniques described in Pearcy et al. (1989). As stated earlier, a number of approaches for measuring the other quantities were considered, including mounting plants in a large wind tunnel and measuring the forces exerted on an instrumented plant. The method chosen consisted of moving plants through relatively still air and monitoring the required quantities. Plants of similar size and shape were mounted on either side of the instrumented plant in an apparatus designed to be mounted on a vehicle (see Figure 3. 1).
A series of experiments were performed on a right circular cylinder as part of this study to demonstrate the ability of the method to produce drag coefficient data. In the sea-oats experiments, the spacing between the plants was fixed based on data obtained from measuring the leaf area density profiles as detailed in Chapter 4. This spacing should be made adjustable for future tests so that plants of different average




13
spacing can be tested and so that the effects of spacing on the drag coefficient can be examined. A schematic diagram of the apparatus and instrumentation is presented in Figure 3.1. A brief desrcription of the apparatus and instrumentation is given below. Detailed information on the instruments developed during this study is presented in Appendix B. The procedures used in calibrating the instruments and performing the experiments are described in Chapter 4.
In order to generate a controlled relative velocity between the air and the plant, either the air must be moved around the plant or the plant must be moved through the air. Because wind tunnels large enough to accommodate most dune plants are rare and expensive to use, the decision was made to move the plants through the air. This approach has the added advantage of providing a uniform flow around the plant.
The apparatus and instrumentation required to measure the necessary
parameters was mounted on an automotive vehicle. In separate tests, the plants and the cylinder were secured in the planterbox and the truck driven at a series of speeds while data was recorded on an IBM compatible personal computer.
The apparatus consisted of a force transducer instrumented planterbox mounted on a frame and attached to a motor vehicle. A pickup truck was used for the experiments performed as part of this study. A streamlined cowling mounted up- and downstream of the planterbox provided a smooth transition for the flow around the planterbox. Plants similar in size and shape were placed in uninstrumented boxes on




pitot tubes

planterbox

cowling

cowling

fifth wheel
Figure 3.1: VEHICLE APPARATUS FOR MEASURING THE DRAG COEFFICIENT IN DUNE PLANTS.




either side of the instrumented plant to more closely similate the wind effects on a plant in the field. This situation attempts to recreate the forces on a sea-oats plant located at the forefront of a vegetated dune system. Wind speeds within a stand of vegetation are extremely different from those on the leading plant due to canopy sheltering at that location. Plants interior to a canopy will experience a reduced and more turbulent flow, but the coefficients determined using the methods presented here can be used provided the correct Reynolds number is used.
In addition to the force transducer on the planterbox, wind speed
measurements were made at three elevations throughout the plant height using pitotstatic tubes connected to sensitive pressure transducers. The vehicle speed was accurately measured using a fifth wheel device mounted behind the vehicle. The air temperature was monitored with a shielded thermistor placed inside the cowling.
Two of the pitot-static tubes were used in the differential mode to discern if a velocity gradient over the plant height existed. The middle tube measured the relative velocity between the plant and the air. If the air was perfectly still, the fifth wheel and center pitot tube reading should, of course, be the same.




CHAPTER 4
EXPERIMENTAL PROCEDURES
4.1 Instrument Calibration
Before actual testing could begin, the vehicle apparatus and instrumentation had to be designed, constructed and calibrated. Detailed information on each measuring device is presented in Appendix B. A brief description of each instrument is given below with the calibration procedure and curves.
4. 1. 1 Force Transducer
The strain gage force transducer was designed to measure the total wind force on an individual plant. This total force and the corresponding deflection of the transducer box legs must be estimated to ensure that the transducer components can record the proper range of strains without damage. This range, and thus the ultimate transducer design, will vary with the wind velocity and size and type of plant. The strain and the total leg deflection were estimated based on the expected wind force on the sea-oats plant and are detailed in Appendix B.
Once designed and constructed, the transducer and its output signal were calibrated for the expected range of forces involved. This was done by placing a cylindrical rod in the transducer and creating a horizontal load on it such that the




17
previously estimated forces were similated. This was accomplished by using a simple weight and pulley system. Weights were hung on a tray and the corresponding strain gage output voltage recorded. Plots of force vs. voltage were created for each strain gage leg and a third order polynomial was used to obtain a fit to the data. These are shown in Figures 4.1 and 4.2.
-4. 1.2 Pressure Transducers and Pitot-Static Tubes
Three Microswitch 160PC Low Pressure Sensor pressure transducers were
connected in series to three twenty-five centimeter stainless steel pitot-static tubes and used to measure the air velocity at the plant height and to discern any gradients in the wind velocity profile. Pitot-static tubes measure the difference between the stagnation pressure and the static pressure. Using this difference in pressure in Bernoulli's equation allows the computation of the free stream velocity U= 2Ap (4.1)
The pitot-static tubes were placed at heights of 40, 80 and 120 cm from the base of the plant.
The pitot-static tube and pressure transducer were calibrated using a small wind tunnel and liquid manometer. The pitot-static tube was placed in the wind tunnel where the air speed was controlled manually. The pressure transducer output voltage and manometer reading were recorded at air speeds from 10 mph to 60 mph. These values were plotted and a linear regression calibration curve calculated. This is shown in Figure 4.3.




20.0 15.0 -

.. .. . ... i .1 .. ... ,
1.0 2.0 3.
volts

0 4.0 5.0 6.0

Figure 4.1:
20.0
15.0
2
) 10.0
0
5.0

0.0 i
-1.0c

Figure 4.2:

CALIBRATION CURVE FOR STRAIN GAGE 1; F = 0.0273V2 + 2.7166V + 0.1981.
0.0 1.0 2.0 3.0 4.0 5.0 6.0
volts
CALIBRATION CURVE FOR STRAIN GAGE 2; F = 0.0602V2 + 2.6625V + 0.4599.

S

2
O 1
0
4
0

0.0
5.0 -

u.U

-LO
.- 1.0

I

n..............




2.5 19
02.0 ,) 1.5
C.)
1.0
Q.)
Q) 0.5
0.0 2.0 4.0 6.0 .0 10.0
volts
Figure 4.3: CALIBRATION CURVE FOR THE PRESSURE TRANSDUCER; P = 0.2536V + 0.02894.
4.1.3 Temperature Thermistor
A temperature sensor was placed underneath the planterbox cowling and
shielded from the wind. The device was known to be accurately calibrated by the manufacturer and gave a 1 millivolt per degree Kelvin change.
4.1.4 Fifth Wheel
A fifth wheel was constructed and secured to the vehicle to more accurately measure and record the actual vehicle velocity. The fifth wheel apparatus was constructed using the front wheel and fork from a 26 inch bicycle. The circumference of the wheel was measured by rolling the wheel one full revolution and




measuring the distance covered. A common digital bicycle speed indicator and electronic counter was used to record the frequency of wheel revolutions. The digital signal was then sent to a D to A (digital to analog) converter and then to the data acquisition board in the computer.
This device was calibrated by recording the wheel frequency output and
voltage output at a range of vehicle velocities. The results were plotted and a linear regression curve fitted to velocity vs. l/voltage. This plot is shown in Figure 4.4.
4.2 Leaf Area Density Measurements
Leaf area measurements were made at John D. MacArthur Beach State Park in Palm Beach County, Florida. Primary plant characteristics--plant height and spacing, stem basal diameter, and number of leaves and stalks--were obtained manually from 58 different plants and statistical profiles--means, standard deviations, ranges and histograms--computed (see Appendix A). From these data more detailed measurements were made on those plants that most closely represented the population. The average plant spacing, L, was determined from the spacing of the 58 plants located in this dune system. For purposes of computing the LAI and LAD, it was assumed that the plants grow in straight rows (although this would never occur naturally), the average spacing being L.
It was discerned that four to five plants representing the population would be analyzed for specific leaf area measurements. The stratified clip method was used to measure the leaf areas in ten equal horizontal layers on four sea-oats plants. A




25.0
20.0
S15.0
ol
0 10.0
0
5.0
0.0 0.5 1.0 1.5 2.0 2.5
1/volts
Figure 4.4: CALIBRATION CURVE FOR THE FIFTH WHEEL; U = 9.6923/V + 0.4297.
traversing system was designed to measure the ten level layers. This consisted of clamping two horizontal rectangular bars to vertical bars around the plant. Beginning at the top layer, the horizontal bars were leveled at each layer and all plant matter above this layer cut and identifiably bagged for further measurements. Later, leaf, stalk and seedhead dimensions were measured and recorded for each plant at each layer (see Appendix A).
4.3 Testing Procedures
The vehicle was equipped with the above described testing apparatus and transported to the testing location--a smooth, lightly travelled, paved road. The




22
vehicle was driven at speeds from 15 mph to 55 mph, for 20 second periods, first conveying the cylinder, then the sea-oats. All data were recorded on the hard drive of an IBMI compatible computer using a GLOBAL LAB data acquisition system.




CHAPTER 5
DATA ANALYSIS
5.1 Signal. Readings
The analog signals from the load cells, thermistor, pitot tubes, and fifth wheel were viewed and recorded using a Data Translation DT2801 board and GLOBAL LAB data acquisition software. Figures 5.1 and 5.2. show sample raw output signals for tests with a right circular cylinder at two different velocities. Figures 5.3 and 5.4 show power density spectra of the signals presented in Figures 5.1 and 5.2 after the signal mean was removed. The power spectra were used to determine the level and frequency of the noise in the various signals. This frequency was then used in filtering the noise out of the signal.
51. 1 Fifth Wheel
Channel CR00 was the output signal of the fifth wheel. This signal was expected to be reasonably constant with gradual increases or decreases in vehicle velocity. Periodically, the digital counter reset, causing violent spikes in the recorded signal. Rough terrain or dips in the roadway that were encountered during the testing also resulted in noise, the frequency of which increased with vehicle speed.




CHOO--fifth wheel S1600 4
E _________________

1400

4
0 2 4 6 8 10 124 6 18 20
[sec]
CH01--pressure

7 -4500
E
-4750
0 2 4 6 8 10 12 14 16 18 20
[sec]
CHO2--differential pressure
0 2 4 6 8 10 12 14 16 18 20
(sec]
CHO3--force transducer 1
2 o
-2
0 2 4 6 8 10 12 14 16 18 20
[sec]

CHO4--force transducer 2

0 2 4 6 8 10 12 14 16 18 20
[sec]

Figure 5.1: UNFILTERED OUTPUT SIGNALS FROM CYLINDER TEST AT A
VEHICLE SPEED OF APPROXIMATELY 15 MPH.




CHOO--fifth wheel

II

0 2 4 6 8 10 12 14 6 18 20
[sec]

6 8 10 12 i 6 8 20
[sec]

O
o
-5

0 2 4 5 8 10 12 14 16 18 20
[sec)

0 2 4 6 8 10 12 14 16 18 20
[sec]
CHO4--force transducer 2
0 2 4 6 8 10 12 14 16 18 20
[sec]
Figure 5.2: UNFILTERED OUTPUT SIGNALS FOR CYLINDER TEST AT A
VEHICLE SPEED OF APPROXIMATELY 50 MPH.

o "




cower density spectrum of pressure signalet
0

[Hz]

Power density soectrum of force

transducer 1

C~~ .001
E C~Cc5-

P~ ~

[Hz]

power density spectrum of force transducer 2

CN .Q

0 2 4 6 8
[Hz]
Figure 5.3: POWER DENSITY SPECTRA OF SIGNALS IN FIGURE 5.1.

J

---- w




zower density spectrum of pressure
c :
:
S.( 0

signal

C 2 4 6 8 1
[Hz]
ocwer density spectrum of force transducer 1

0 2 4 6 8
[Hz]
ower density soectrum of force transducer 2

I~ '
I.
/
- ~ \~A Vk~A

[Hz]
Figure 5.4: POWER DENSITY SPECTRA OF SIGNALS IN FIGURE 5.2.

Jl C1
S.C002
0




5.1.2 Pitot-Static Tube
Channel CHO 1 was the output signal from the central pitot-static tube/pressure transducer. The purpose of this instrument was to measure the relative velocity between the air and the plants at mid height of the plants. Because of the noise introduced by the stiff vehicle suspension and vortex shedding of the pitot-static tube mount, this reading required filtering. This was done using a lowpass, sixth-order Butterworth filter with a cutoff frequency of 1 hertz. Sample raw and filtered pressure signals are shown in Figure 5.5.
The velocities calulated from the pressure transducer and fifth wheel were expected to be close in magnitude, with the fifth wheel velocity steadier than the pressure velocity. This was the case as shown in Figure 5.6. The velocities computed from the pitot-static tube signals were used in the computation of the drag coefficients.
5.1.3 Differential Pitot-Static Tube
Channel CH02 was the output signal for the differential pitot-static tubes. The purpose of this instrument was to detect any velocity gradients with height that might exist. This signal remained small throughout the tests, confirming that the velocity over the cylinder and the plants was uniform with height.
5.1.4 Force Transducers
Channels CH03 and CH04 were the output signals for the strain gage force




unfil tered

-4000
-4200

-4400

0 2.5 5 7.5 10 12.5
[seci CHO1

filtered pressure

15 17.5 20

signal

-4400

0 2.5 5 7.5 10 12.5 15 17.5
[sec]
fch01

Figure 5.5: FILTERED AND UNFILTERED PRESSURE SIGNALS.

-3800
-4000
-4200 -

signal

pressure




0 2.5 7.5 10 12.5 15 17.5

[sec]
---- fifthwheel ------

pressure

9
E
7 6

0 2.5 5 7.5 10 12.5 15 17.5

[sec]
------- fiffthwheell ------

pressure 1

Figure 5.6: CALCULATED VELOCITIES FROM FIFTH WHEEL AND PRESSURE SIGNALS.




31
:nsducers. These signals were expected to be noisy at lower speeds because of the Clow czg force magnr.:udes expected compared to the mechanical noise due to the stiff zruck suspension system. The total force was obtained by averaging the forces from "e two transducers. The power density spectra for one of the transducer signals at two different vehicle speeds are shown in Figure 5.7. Note that the frequency of the vehicle induced noise" increased with speed as expected. The wind induced load should be approximately constant throughout the test except for wind gusts.
A lowpass. sixth-order Butterworth filter with a cutoff frequency of 2 hertz
was used for all force transducer signals. The phase shift introduced by such a filter did not present a problem since the signal is of such low frequency.
5.1.5 Thermistor
Channel CH05 was the output signal of the temperature sensor. This signal was expected to be. and was. approximately constant throughout each test. Small variations--on the order of two degrees--were noticed from test to test.
5.2 Other Analysis Techniques
The air density and dynamic vicosity were found by averaging the temperature over each test and consulting a standard table of properties of air (e.g., Handbook of Tables for Applied Engineering Science (1970)).
The filtered signal data files were converted to ASCII files for further analysis in spreadsheet format. The filtered digital data were converted to volts and the




power density

0.002 I

o 0.0015
< V 0.001
0
0.0005 -

:jN~ AAK

[Hz] pc7chO3

0.0005 0.0004 K0.0003
N
0.0002
0.0001

02 4 6 8
[Hz]
pc17ch03

Figure 5.7: POWER DENSITY SPECTRA FOR FORCE TRANSDUCER 1 AT
TWO DIFFERENT VEHICLE SPEEDS.

I I

at 25 mph

s pectru m




33
appropriate calibration equation applied. From this data, the drag coefficients and Renolds numbers were calculated from 20 second averages using Equations 1.2,
2.10. and 2.11.




CHAPTER 6
RESULTS AND CONCLUSIONS
6. 1 Results
The avera-e one-sided leaf area index (LAI) calculated for the plants surveyed in this study is 1.69. Note that this is the value for a plant spacing of one foot and must be adjusted if the spacing is different. The vertical leaf area density profile is shown in Figure 6. 1.
1.0 0.8
0.2
0.0
0.0 1.0 12.0 3.0
LAD (m') Figure 6. 1: LEAF AREA DENSITY PROFILE FOR SEA-OATS.
The Cd vs. Re relationships for the cylinder and the sea-oats plant are shown in Figures 6.2 and 6.3 respectively.




I1 i ....

10000

Figure 6.2: PLOT OF
2-

S

06666

3000660
Re

46600

THE MEASURED DRAG COEFFICIENT NUMBER FOR THE CYLINDER.

66o50000

VS. REYNOLDS

40000 60000 80000 100000 120000 140000 Re

Figure 6.3: PLOT OF THE MEASURED DRAG COEFFICIENT VS. REYNOLDS NUMBER FOR SEA-OATS.




6.2 Conclusions
The objectives of this study were to develop and test a methodology for
measuring the parameters needed to calculate the wind drag coefficient for coastal dune plants and to determine the dependence of this coefficient on the Reynolds number.
The methodology described in this study can be used to measure the drag
coefficient of any plant that can be mounted in the apparatus. Since many dune plants are .,.,a:,,eiv small in size and weight, they would fit into this category. Even plants that would be too large when mature can be tested as young plants, as long as the proper scaling laws are applied.
For the range of Reynolds numbers covered in this study, the values of the canopy drag coefficient. C,, are relatively constant. The range of velocities covered in these experiments is important because it is over this range that aeolian sand transport is initiated. This range is also that which has a high frequency of occurrence along Florida's coastline.
The apparatus used in these experiments was designed for plants of the approximate size, spacing and LAD as sea-oats. It will have to be modified to accomodate plants that differ significantly in one or more of these quantities. Some relatively simple modifications to the instrumented planterbox support will change the range of the force transducers. Changing the plant spacing will require more extensive modifications to the apparatus.




The vehicle used during these tests was the only one available for use in this capacity at the time of these tests. It was a pick-up truck whose suspension was not suited for the purposes of this experiment. A vehicle with a softly sprung suspension system is desired to reduce the amount of road induced vibration of the apparatus and instrumentation.
At lower relative velocities, the signal to noise ratio was very small. At
higher velocities, the ratio was much larger and the data of higher quality. Additional work is needed to increase the signal to noise ratio at lower velocities. Using a vehicle with a suspension system that dampens the road vibration, stiffening the pitot tube support, taking steps to reduce the vortex shedding vibration, etc. will improve the quality of the data obtained using this methodology.
6.3 Comments
The prediction of aeolian sand transport through dune vegetation is important in the understanding of the dynamic forces involved in dune movement and shoreline stability. Current canopy flow models require measured values for certain plant characteristics. The drag, coefficient and leaf area density profile are two such characteristics. Values for these quantities for dune vegetation do not exist in the literature. The methodology developed and tested as part of this study will provide this information. Because of the success in obtaining cylinder drag coefficients very near previously measured values, the method described herein for measuring the drag coefficient in coastal dune plants is considered to be sound and effective.




38
It is recommended that the methods developed in this study be refined and
applied to other species of dune vegetation. It is hoped that the data presented in this studv will serve as a catalyst for further research in this area.




APPENDIX A
LEAF AREA MEASUREMENTS AND CALCULATIONS
The following pages provide recorded measurements and statistical data used in the development of the leaf area density profile for sea-oats.




Table A. 1: GENERAL CHARACTERISTICS OF SEA-OATS.

MEASUREMENTS

UPPERMOST STEM
PLANT PLANT FOLIAGE BASAL NO. OF NO. OF NO. OF
SPACING NO. HEIGHT HEIGHT CIRCUM. LEAVES SEEDHEADS STALKS
;-,6 1 172 115 12.0 26 1 1
35 2 162 108 8.0 21 1 1
22 3 143 104 6.0 17 1 1
22 4 173 103 6.5 12 1 1
40 5 142 84 6.0 8 1 1
38 6 153 102 14.0 24 1 2
29 209 92 14.0 22 1 1
is 147 98 24.0 57 1 4
19 9 154 91 23.0 64 1 5
11 10 206 98 8.0 12 1 1
13 11 179 93 5.0 13 1 1
5s 12 150 104 7.0 12 1 1
14 13 209 96 16.0 27 1 2
15 14 1S8 94 9.0 11 1 1
42 15 1S6 105 8.5 16 1 1
43 16 169 87 9.0 16 1 1
16 17 165 101 9.0 25 1 1
14 1s 178 91 7.0 18 1 1
18 19 142 83 12.0 25 1 1
30 20 138 96 8.0 11 1 1
44 21 142 89 6.0 12 1 1
86 22 170 83 20.0 49 1 1
13 23 153 89 14.0 22 1 1
25 24 127 80 6.0 15 1 1
41 25 140 93 12.5 28 1 1
27 26 132 90 7.5 14 1 1
35 27 157 97 12.0 26 2 2
48 28 178 102 10.0 23 1 1
36 29 167 93 14.0 21 1 1
30 131 103 6.0 12 1 1
31 147 96 14.0 27 1 2
32 130 91 8.0 12 1 1
33 162 98 8.0 15 1 1
34 162 93 7.0 12 1 1
35 140 93 19.0 33 2 2
36 143 92 9.0 17 1 1
37 124 89 15.0 29 1 1
38 157 94 13.0 22 1 1
39 152 97 11.0 22 1 1
40 128 91 11.0 13 1 1
41 153 97 9.0 23 1 1
42 174 86 12.0 20 1 1
43 151 100 9.0 11 1 1
44 143 87 9.0 19 1 1
45 174 95 13.0 27 1 1
46 150 92 16.0 28 1 1
47 138 94 12.5 44 1 1
48 155 98 10.0 21 1 1
49 170 91 9.0 17 1 1
50 176 100 10.0 15 1 1
51 158 88 14.0 32 1 1
52 154 95 11.0 19 1 1
53 152 97 15.0 42 1 1




Table A. 1--continued

UPPERMOST STEM
PLANT PLANT FOLIAGE BASAL NO. OF NO. OF NO. OF
SPACING NO. HEIGHT HEIGHT CIRCUM. LEAVES SEEDHEADS STALKS
54 157 97 12.0 30 1 1
55 153 105 11.5 15 1 1
11 56 135 78 12.0 27 1 1
11 57 175 100 31.0 93 2 2
11 58 138 87 7.0 15 1 1
MEANS: 1.1 4.6 ti 11.j 43.4 1
SL. imV 7.0 I 4.9 19.7 TO 14.5

NOTES:
DATE: 4-16-1992 TIME: 1:20 PM
PLACE: John D. MacArthur Beach State Park, Palm Beach County, Florida WEATHER CONDITIONS: windy, mostly cloudy, near 80 degrees F PLANT AGE: 3 4 years
PHENOLOGICAL STAGE: seedhead just formed and visible OTHER SPECIES PRESENT: beach bean, beach elder, palmetto. sea-grape All measurements in centimeters.




I..

4 1.4 174i4 194 204 HEIGHT (em)

Figure A. 1: SEA-OATS HEIGHT HISTOGRAM.

U O 93 98 10
UPPERMOST FOLIAGE HEIGHT (,.m)

Figure A.2: SEA-OATS UPPERMOST FOLIAGE HEIGHT HISTOGRAM.

124 1 4 144




5 1 14 1 29
BASAL STEM CIRCUMFERENCE (cm)
Figure A.3: SEA-OATS BASAL STEM CIRCUMFERENCE HISTOGRAM.
6
5.______t
Al_____

-diT

II

9 14 21) 26 32

33 44 50 56 62 64 74 6.92 NUMBER OF LEAVES

Figure A.4: SEA-OATS NUMBER OF LEAVES HISTOGRAM.




Table A.2: LEAF, STALK, AND SEEDHEAD AREA MEASUREMENTS
AND LAI CALCULATIONS FOR PLANT 1.

STALK SliliDi EAD) 1
LAYER CUTTING LEAF LEAF LEAF STALK STAI.K AREA SEEDIIHEAD SIIHE)IIAD AREA PLANT PLANT
NO. NO. WIDTII LENGTH AREA CIRCIUM. LENGTH (projected) CIRCUM. IiiNGTII (projected) AREA LAD) HEIGIr'HT
IA 1 0.4 47.4 18.96 4.0 14.9 18.98
LAYER IA TOT ALS: 18.96 ] t 0.00 18.98 37.94 1 0.3 I 0.1
IB 1 .1 14.h 16.28 I 4.) 13.2 18.92I II
L.AYER I HI 0AI..S: Ii IL 0.0 1!==~ 189) =Ti' [ WNX
2 1.4 10.21 14.281 1 1 1 11
LAYER ICTOTALS: I11_5.9 I 344 _I_20.06 I2 49.481 0004 I 0.3
I1 1 1 1 1.2 1 7.415 20.52 2.8 14.50 1025
2 0.4 32.9 3.6[ F.0I
LAY IR IFT)AI ALS: 4392 II.i.93 11 0.003 0.4
G I. Z. .2o1 13.5 13.54
2 1.3 7.4 9.62
L A Y E R I- -rArS : -I 2 z I ]z a1-r 3 6 6 =
3 0.3 29.8 8.94
4 0.1 2.8 0.28
5 1.3 7.3 9.49
A : !!_45.91 U I__13,53 0.00 1 0.8 I4 0.027.5
i1 i 0.1 10.3 1.03 31.0 11.9' 15.4
2 1.3 35.7 46.41
1G3 1.1 28.7 3 1.2 3 57
4 0.4 17.4 6.96
5 1.3 29.9 38.87
6 0.7 29.3 20.51
7 0.7 36.5 25.55
8 1.1 48.9 53.79
4.9 0.5 12.8 6.405
10 0.7 36.8 25.76
W11 0.7 21.2 14.84
12 0.7 18.0 12.60




11'61 L C1 8
,L'_ Z'Z L"I L
01,111, 07 1 Z'I 9 ZZ'L I C71 1,11 L*1, [ 6"I1 C1 1
_0' L51 60 Zt'j 1,'9Z V
6161 L171 13 O',9 0"19 II z
I~~( VC C9*1~ CO~ -VE C*91_
6'0 A [o CV ) r1,1, MAr KI .1 677 I....I L7'*1t II :"V.0T, 11 WRAV7
801'! 8*8 9"_ 1,z
01'Z 09 t'0 Z
6L5 C'61 t:o zz 91' 81 L'O Iz
P,8L5 Z,817 V" Oz91*'Z *11 L'I 61 ZO"L 1Z 0 81
90,91 9'171 I' LI 06"0Z 0"61 V'T 91
_OZ'91 Z'91 01 51 Z/.'9 8"91 1,0 171
___________ _______ ______ _____IVII V91 C0 Et____01,51 l1 01 ZI
19". 8"17 81 11
ZI'sZ L51 9,1 O 0}6"LZ (01 6"0 6
_81 1'61 LO 8
(00"0 am (), !I0 I L
06"81 6841 01 9
_W81 Z'9Z Lo _;
_ _I'1 9"I V 1'71, Z'LZ O t,
V1' 161 00 i1,zi 91 '0 WV c
_,0Z 191 vo owoii V I 8'o Z
...... ~ ~~ Z 9t 90 175)11, '{ lI
. .. 11 ~ (I rO S:'o1 I:o II w!y
__~---Z' __ __ T 2L -L fLT.OL

1.1101,11 1 .INV 1.1
/,

(IV I

VI)IV .INV 1.1

(t1) oid)
V IV'
(1 Villit(_1_( !!!, '

II I.')N~I I IV 111(1 i; Is

VI)IV
- IIV1.

ILI.f)NII W1IDII: ) Vv)IV 1 IV.IS IX IV.I.S IVAf I

I)N1 I .lV;,I'

I L.1l I A
:IVI.

'ON ON
ONLI.LI.3 Ig HAV'I

,,

(IVAI I(VIAN




Table A.2--continucd

STALK SIIEDHEAD z/
LAYER CUTTING LEAF LEAF LEAF STALK STALK AREA SIEDlIEAD SFEFDIllAD AREA PLANT PLANT
NO. NO. WIDTIH I.ENGTII AREA CIRCUM. LENGTH (projected) CIRCUM. LEN(iTl'lI (projected) ARHA LAI) IHEIGI'
1I 9 0.5 26.5 13.25
10 1.2 17.3 20.76
11 1.1 18.2 20.02
12 1.6 17.0 27.20
13 0.7 9.5 6.65
14 1.2 11.2 13.44
15 0.9 16.4 14.76
16 1.0 15.7 15.70
17 0.4 19.8 7.92
18 0.3 31.3 9.39
19 0.8 9.7 7.76
20 1.6 12.3 19.68
LAYER 1. TOTALS: I 400.31 1 27.11 0.00 427.42 0.034 [ 1.0
0.9 OTALU S I 1548.6 0.122_

NOTES:

All lengths in centimeters. Layer height: 13.7
Plant height: 137
Ground area: 929.03
LAI: 1.666

cm cm
sq cm




Table A.3: LEAF, STALK, AND SIEID)I IlEAI) AREA MIEASLJRIIMiNT'S
AND LAI CALCULATIONS FOR PLANT 2.

IFAF STALK Sllil)E 111AI) 1 /
LAYER CUTTING LEAF LEAF LEAF STALK STALK AREA SEIi)illEAI) SEII)IIEAI) AREA PLANT PLANT
NO. NO. WIDTI I LENGTli I AREA CIRCIJM. iENGTIl (projected) CIRCJM. I.INT(il'l (piojcccd) AREA IAl) III(GilT
2A 1 0.3 23.0 6.90 0.6 6.0 1.15
LAYR2ATOTAS: 6.901 f 11 1 1.15 8.o5 01001 0. I
2 I 1 18.1 1.1 3i 18.4 1 .58
2AYI( 21O0.2 142AIS: 6
IAYILI 10 1Al: Z1.0.
A I 0.6 I 12.4 1o 3.0 I.4 16. 10
2 1.3 12.0 15.601
LAYE '1'0 A LS: )I II 1.,79 I 8 11o[o4I
2D 10 1 1.21 16.8 0.1 16.8 11.7
42 00.41 31.0 12.40
LA .k .. 1': 3.161.2 0.0 44.56 0.03.
SAY (, l 20.4 18.361 J 2.9 I .1 15.9
2 1.4 15.5 21.70
LAYEK4 0IALS: 40.06.
Zh 09 0.MA .0 2.91 17.4 16.07
11 1.4 13.8 19.32
LAY5 521 Ju ALS: 32 1 2.00 21.2 0.0h 1.
21__ 4 0.6 458:9 2748 0.7 20.8 4.64__ ___S1 2 1.2 20.7 6.21 3.3 17.2 18.082
2 1.5 15.0 22.50
______ 0.4 84.4 33.76 _____ ____ ______ _______2 1.2 49.0.6 58.8066
3 1.0 31.5 31.50
4 0.9 22.445.8 20.1648
5 1.1 45.5 50.0528
2 0.8 57.3 4520.76 3.3 17.2 18.08
3 1.1 17.4 19.14
4 0.4 84.4 33.76
5 1.2 49.0 58.80
6 1.0 31.5 31.50
7 1 0.9 22.41 20.161
81 1.1 45.5 1 50.051
91 0.81 57.31 45.841




Table A.3--continucd

LEAF STALK SII'Di IA/)
LAYER CUTTING LEAF LEAF LEAF STALK STALK AREA SI'Ii)I IlAI) SIFDIIlAI)AD AREA I'IANT PANT
NO. NO. WIDTI I LENGTI I AREA CIRCIUM. IiNGTII (projected) CIRCUIJM. IiENGII (projected) AREA LAD 11lIGHT
21 10 0.7 18.7 13.09
11 0.9 22.9 20.61
12 0.6 21.2 12.72
13 1.6 17.5 28.00
14 0.2 7.7 1.54
15 0.3 31.1 9.33
16 0.5 22.2 11.10
17 0.7 9.3 6.51
18 0.2 20.5 4.10
19 1.1 20.8 22.88
20 1.7 7.8 13.26
21 1.7 5.6 9.52
LAY__K 11 48_.__ 11 o
2J 1 1.7 9.4 15.98 2.0 8.6 5.48
2 1.8 6.5 11.70 3.7 16.2 19.09
3 1.4 19.6 27.44 1.2 0.5 0.19
4 1.1 19.7 21.67 2.2 7.5 5.25
5 0.7 58.1 40.67 1.5 2.7 1.29
6 0.7 62.4 43.68 1.6 6.5 3.31
7 0.2 22.9 4.58 2.4 16.6 12.69
8 0.6 96.9 58.14
9 0.6 53.2 31.92
10 0.8 80.2 64.16
11 0.5 57.0 28.50
12 0.7 9.9 6.93
S 13 1.0 15.7 15.70
14 0.5 46.7 23.35
15 1.6 20.9 33.44
16 0.5 53.1 26.55
17 0.4 63.5 25.40
18 0.5 53.7 26.85
19 0.9 16.8 15.12
20 1.7 8.6 14.62
21 0.4 5.0 2.00
22 0.3 59.8 17.94
23 1.1 19.5 21.45




LAYER NO.

I.hAF CIJI'TfIN(G
NO.

LEAF I.EAF WIDTi I I.F'NG i I

LEAF AREA

STALK CIRCM JM

STAI .K
ILEN(lll

AREA
(pIOjce(ld)

SI ll, )1 A CIRCI M.

S I,,)1 IiAl) I E. 'N( iTl I

ARA
(Ir-cld)

I1 ANT AIIA

1/
I' ANT IIIlTI II

21 24 0.7 7.6 5.32 ..
25 1.2 12.8 15.36
26 0.2 22.9 4.58
27 0.4 3.8 1.52
28 1.2 7.0 8.40
29 1.2 9.5 11.40
30 1.3 7.0 9.10
LA Y ER 2.1 TOTA 'S: 6.47 47.30 1 0.00 I 680.7 | .4 I
N TOTAl: I708.77 0.108 j

NOTES:
All lengths in centimeters. Layer height: 17 cm
Plant height: 170 cm
Ground area: 929.03 sq cm
LAI: 1.839

able A.3--contined




T'Fable A.4: LEAF, STALK, AND SEED IEAD AREA MEASUREMENTS
AND LAI CALCULATIONS FOR PLANT 3.

STALK SlllliAD /
LAYER CLt'ING LEAF LEAF LEAF STALK STALK AREA SFlIiI)IIEAD SEFl)IIAI)AD AREA PIANT PIANT I NO. NO. WIDTH LENGTH AREA CIRCUM. LENGTH (projected) CIRCUM. LENGTH (projected) AREA LAD) HilIGII
3A 1 0.2 18.2 3.64 2.7 16.1 13.84
ILAYER 3A TOTAL.S: 64.I .. 0.00 ...........
311 1 1' 0.11 Z0.7 14.421 1 1/ '3. 21.8I 25.)9 .II "I ..
LA Y A 3411 IIAooN:)111748 ].o0II 0.2
'l l 0.5 3 16.70 3.2 0
3 I~2 U.82 41 33. 0 28 1. 12
2 1.2 20.81 2496 1 __ 1 11
LAYER 3CTOTALS: I8 117_1I_.21IIII 21.50 63.16 0.004 0.3
3D 1 0. 41. 2. 3.0 18.8 13.1
I2 1.4 19. 241.00 I I
LAYR 3L1TOTALS: 1 1 1.. 0.0031 0.4
3G 1 1.3 18.9 24.57 3.0 18.0 1.20
2 1.3 18.1 23.53 1z11_=
1AYER 31-4 FOAI.S: 4854]1 ]1TT1IJ7l)0U[ 5
3 0.2 14.6 2.92 2 1. 1
4 0.9 30.2 27.18
L 2 1.4 19.0 26.60
3 1.1 44.3 48.73 4 0.4 12.5 5.00 5 1.5 9.6 14.40
G6 1.5 5.0 7.5 03 1
LAYER 3H TOTALS: ji18.05 19.95 0.00I I 138.00 0 .008 | 0.8
31 1 1.0 21.6 23. 532.1 3.3 2.21
2 1.2 57.8 69.36 3.4 17.8 19.27
3 1.3 41.6 54.0892
4 02 27.18
4 1.6 17.7 28.32 5 0.6 10.0 6.00
46 0.8 17.0 13.60
4 0.4 12.5 5.00
_____5_5 1. 9.6 14.40 _ _ _ _ _ _ _ _ _ _ _
2 1.2 57.8 69.36 3.4 17.8 19.27 _ _ ___ ___I __3 13 416 5408 I_ _ __ _ __ _I_
4 1.6 177 28.232____ 1I ___ __I5 0.6 10.0 600)_________ ___I __61 0.81 17.01 13.601_ _ _ _ ___ __ _ _




'I'Table A.4--continued

STALK SIiEDI lEAD z/
LAYER CUTTING LEAF LEAF LEAFI STALK STALK AREA SliFI)IlliAD SIHiI)IIiAD AREA I'LANT I'LANTI
NO. NO. WIDTH LIENGTII AREA CIRCUM. LENGTH (projected) CIRCIJM. I.IIN(G'iI (projected) AREA LAI) IIIGIT
31 7 0.5 3.6 1.80
8 0.5 11.2 5.60
9 1.6 15.4 24.64
10 1.6 11.5 18.40
11 0.2 5.2 1.04 J H
LAYERTT 3'1' rrt: = 244.441 48 0.0 265.92 II0 .0 0.9
. I 0.8 19. 15.76 1.8 14.8 8.48
2 0.6 46.8 28.08 1.0 4.3 1.37
3 1.6 3.8 6.08 2.1 13.5 9.03
4 1.3 45.1 58.63 2.1 17.2 11.50
5 0.9 7.0 6.30 2.2 12.2 8.55
6 1.6 4.4 7.04 1.3 8.1 3.35
7 0.2 9.0 1.80 3.6 18.3 20.98
8 1.6 1.0 1.60
9 0.7 9.4 6.58
10 0.9 10.7 9.63
11 0.7 4.0 2.80
LAYER 31ALS: 14430 =0 : 20.5 0.013
0.9 TOA. _o8.9I oo1I

NOTES:
All lengths in centimeters. LAYER HEIGHT:. 17.7 cm
PLANT HEIGHT: 177 cm
GROUND AREA: 929.03 sq cm
LAI: 1.085




Table A.5: LEAFI, STALK, AND SilIDI liAD ARli.A MiLASUJRIMiN'TS
AND LAI CALCULATIONS FOR PLANT 4.

LEAF
CUTTING LEAF LFAFI NO. WIDT IL.ENGTI

IEAF AREA

STAIL.K STAI.K (CIRCUM. LIN(iTIl I

STALK
AREA (projected)

S-FI)II"AI) SIT I ll IA) ClRCUM. I ,I-N(iTI I

AReA (projcced)

PL ANT AREiA

I.A)

I'P ANT 1 IGHTl 1

4A 1 0.3 32.9 t9.87 2.2 13.6 9.53 I t
LAR4A TOTALS: 9. 9. 19.4 "o )l T0.1
4 B 1 1.1 13 1 3.43To
4C" 1 0.7 57.'1 1.. 39.97 2.2 7.31 V.o1.6 4.8 .12I .
2 1.5 1C 11.0 16.50
LAYHR 4CTOTAl: 5.47 0.9 0.004 .
2 1.5 11.3 16.95
I-AYI.I( 41) lTTALs: 04.15 I jI lI 0.0 81. 1
4E' 111 [ 1.77 10.9 10.35) io3.2/ I 05[ 171 I I
I AYl2R4T 10T IAL : 9II T7"3 I I 1 7 II 1_ 215 II 1"1_I
4Vl[3 1 0.7 6 6.511 3 )2 846.27 34 19.4I 21.01
2 0.9 26.5 23.85
______ I ___4_TOTAI__,______ .40 If 2Tf.0 l FI II I0.______ ___.41 '__.11 II '' .
3 1.6 18.3 29.2818 1_/L
i 10 1 ALS: !I *-~ Ij___________ L ~1.0 1 ]~T II7I
2 0.8 20.9 16.723 1.7 14.2 24.14
lYJ 6OTALS: I.319.76 TT.II) l71. .0. .7
_ f_1 15.9 22.26 3.4 20.2
2 1.7 16.5 28.05
3 1.4 28.7 40.18
4 1.7 20.5 34.85 II
5 1.3 41.1 53.43
' Y 4tTO-TALS:. 178.77 21.87 .. .....l.x 00 .6 1J '1.
S1 1.9 15.8 30. 2.3 6.5 4./ ..
2 1.3 75.9 98.67 3.9 20.5 25.46
3 1.2 84.9 101.88 1.9 2.5 1.51
4 0.7 45.8 32.06 5 1.4 34.6 48.44 6 0.9 33.4 30.06 7 0.8 30.9 24.72 S8 0.4 40.6 16.24 9 0.3 21.9 6.57

IAYER NO.




iTable A.5--(co(lintinal(I

LAY5ift NO. I

C 11'lN( I
NO.

L I I I. i':A I WIDTHI IFNOVil I

Il.lAl AIWhA

NTIAIl.K .FAl K (55((J1M.

STALK :NOTi I

(FA I(i ) (prespeeod)

S.I il) Il!A ) (CII(I I M.

5 .I I ) III AI ) I5I NT I

SI', l WAD (noI IM C A ) (pieiocl~)

1'1 A NT
AltifA

/
11 ANT Ill5' I 5'T

41 10 0.8 I.._ 14.04
11 0.6 53.5 32.101
12 0.6 31.4 18.84
13 0.9 39.2 35.28
14 1.8 18.5 33.30
15 1.8 21.1 37.98
16 0.8 14.3 11.44
4 T1 I 1.1 18. I 9.21 1.3. 1.1 6A I 7
2 1.9 15.7 29.83 2.4 10.8 8.25
3 2.0 7.9 15.80 3.0 17.7 16.91
4 1.0 103.0 103.00 4.0 17.2 21.91
5 0.5 24.2 12.10 0.8 30.2 7.69
6 0.2 15.4 3.08 2.4 13.2 10.09
7 1.8 4.3 7.74 2.1 6.9 4.61
8 0.9 36.3 32.67 1.9 22.4 13.55
9 0.8 12.7 10.16
10 1.9 14.0 26.601
11 0.5 16.1 8.05
12 1.5 17.7 26.55
13 0.5 9.9 4.95
14 1.2 20.3 24.36
15 1.1 24.0 26.40
16 1.3 17.5 22.75
-1.1TA-iA:-14.283.48 .I 05 1.1 ''(TOIAi^S:- 18915.12 0I.105

NOTES:

All lengths in centimeters.
LAYER HEIGHT: 19.5
PLANT HEIGHT: 195
GROUND AREA: 929.03
LAI: 2.041

cm cm
sq cm




APPENDIX B
INSTRUMENTATION
The following pages provide descriptions and detailed drawings of the instrumentation used in this study.
B. 1 Predicted Strain and Deflection Calculations
To design the planterbox. the strain and deflection in the box legs were
estima-d based on the expected wind force on the sea-oats plant. With the two back legs having pin joints at both ends and the two front legs pinned at the top and fixed at the bottom, the total horizontal force, F, will be supported by the front legs (see Figure B.2). From basic mechanics of materials, the shear force, F,, on each of the front legs is
F1 3EI6 (B. 1)
y3
where E is the modulus of elasticity, 6 is the deflection of the leg, y is the distance from the pin connection point of the leg to the center of the strain gage, and I is the moment of inertia represented by I bh3 (B.2)
12
where b and h are the leg width and thickness, respectively. In terms of the total force. F.




force transducer
-rc nt View
o
11I

II

I''.

N':KKK

I Z

_lan View

- planterbox

Back View

Side View

Figure B. 1: PLANTERBOX DETAILS.

iI




bail JDint
O

- 3.2 cm

14.6 cm

7.3 cm

rigid support

FRONT VIEW

Figure B.2: DETAIL OF FORCE TRANSDUCER.

1
F, = 1F,
2

where F is given by.

F = CdpAIL2HU2,

and F, is
FI= 1CpA 1L2HU2, (B.5)
2
where Ca is the drag coefficient. p is the mass density of air, A, is the one-sided leaf area per plant volume. L is the plant spacing, H is the plant height, and U is the mean air velocity.
The strain. e. is given by

e O
E

(B.6)

where a is the axial stress.

strain gage

", t33 n-

SIDE VIEW

(B.3)

(B.4)




o M (B.7)
S
E is t*e n.~,culus of elasticity. S is the section modulus.
S = bh2 (.8)
6
-:d M is :e moment at the strain gage, given by M = Fx y. (B.9)
Subszitu'zg equations B.7. B.8 and B.9 into equation B.6 results in S 3CdpA1L2HU2y (B. 10)
Ebh2
..e estimated strain and deflection were calculated using the quantities below :or les made of 04-T4 aluminum and a previously measured drag coefficient for
p = 1.177 kg/m3,
A = 1.076 m-1, L = 0.305 m,
H = 1.571 m,
E = 7.3(10a>) N/m2, b = 0.032 m,
h = 0.00163 m,
Cd = 0.18 and

y = 0.067 m.




Table B. shows the cala:ed values of the forces, deflections and strains on the
st:e es a 1 ve.c mes ranging from 15 to 55 mph.
Because the eld stress.
o = 3.24 x (108) Pa,
,corresx cs to a stra ,n or
S= 4434 p e,
the calculated wind 1,oading will not cause permanent deformation in any of the planterbox legs.
Tabie B. 1: CALCULATED FORCE. STRAIN AND DEFLECTION QUANTITIES AT DIFFERENT WIND SPEEDS.
TOTAL LEG
VELOCITY 1ELOCITY FORCE FORCE STRAIN DEFLECTION
I moh) (Mnrs) (N) (N) (m)
5 .7 1 1.4948 0.7474 0.000048 0.0001
20 S.94 2.6574 1.3287 0.000086 0.0002
2 11.1S 4.1521 2.0761 0.000134 0.0002
30 13.41 5.9791 2.9895 0.000194 0.0004
35 15.65 f S.1382 4.0691 0.000264 0.0005
40 -.SS 10.6295 5.3147 0.000344 0.0006
45 20.12 13.4529 6.7265 0.000436 0.0008
50 .25 1 16.6085 8.3043 0.000538 0.0010
B.2 Pitot-Static Tube Theory
When the pitot-static tube is used to measure the velocity in an incompressible
fluid, the difference between stagnation pressure, p, and the static pressure, Po,




is re-a: : -e ee-s~ ve ocx,,y through Bernoulli's equation, p po = p.

tub :i "

36"

to pressure transducers

Figure B.3: DETAIL OF PITOT-STATIC TUBE SUPPORT.

(B.11)




60
- holes ree-stream velocity.
static pressure
stagnation pressure
Figure B.4: DETAIL OF PITOT-STATIC TUBE.




bolted to trailer hitch

Figure B.5: DETAIL OF FIFTH WHEEL.




REFERENCE LIST

Baldocchi. Dennis. 19S9. Canopy-atmosphere water vapour exchange: Can we
scale from a leaf to a canopy? In Estimation of areal evapotranspiration: Proceedings of an international workshop held during the XIXth General
Assembly of the International Union of Geodesy and Geophysics at
Vancouver, British Columbia, Canada, 9-22 August, 1987, by the International
Association of Hydrological Sciences. IHAS publication no. 177. 21-41.
Boliz. Ray E. and George L. Tuve. eds. 1970. Handbook of Tables for Applied
Engineerin, Science. Cleveland: The Chemical Rubber Company.
Cowan. I.R. 1968. Mass. heat and momentum exchange between stands of plants
and their atmospheric environment. Quart. J. Roy. Met. Soc. 94 (October):
523-544.
Fox. Robert W.. and Alan T. McDonald. 1985. Introduction to Fluid Mechanics.
3rd ed. New York: John Wiley & Sons.
Pearcv. R.W.. J. Ehleringer. H.A. Mooney, and P.W. Rundel, eds. 1989. Plant
phyvsiological ecoiog : Field methods and instrumentation. New York:
Chapman and Hail.
Schlichting. Hermann. 1955. Boundary Layer Theory. Translated by J. Kestin.
New York: McGraw-Hill Book Co. Inc.
Sheppard. D.M. and A.W. Niedoroda. 1992. Physical effects of vegetation on windblown sand in the coastal environments of Florida. Gainesville: University of
Florida. Department of Coastal and Oceanographic Engineering. TR/085.
Thom. A.S. 1968. The exchange of momentum, mass, and heat between an artificial
leaf and the airflow in a wind-tunnel. Quart. J. Roy. Met. Soc. 94 (October):
44-55.
. 1971. Momentum absorption by vegetation. Quart. J. Roy. Met. Soc. 97:
414-428.




63
S1975. Momentum. mass and heat exchange of plant communities. In Vegetation and the Atmosphere, ed. J.L. Monteith. 57-109. New York: Academic Press.




BIOGRAPHICAL SKETCH

The author was born and raised in Waterloo, Iowa. After graduating from high school in 1984, she pursued a Bachelor of Landscape Architecture degree at Iowa State University. Ames. Coursework in the natural sciences, namely geology, sparked a great interest in coastal dynamic systems and the processes of shoreline erosion. So inspired, the author entered the University of Florida, Gainesville, as a postbaccalaureate student with future plans of obtaining a Master of Science degree in coastal engineering.