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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 )
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 .........................
Sv
: : : : :
...........
. . . .
Coefficient ..
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
1 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/I
S section modulus; bh2/6
T temperature
U time mean velocity
u air velocity
U, free-stream velocity
y distance from strain gage to top of pin joint
z height
5 planterbox leg deflection
5, turbulent eddy transfer coefficient
e strain
j dynamic (absolute) viscosity
0 kinematic viscosity
p air density
Ca axial stress
r 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
and those obtained by a number of other investigators. Thus, it is believed that the
Cd values obtained for the sea-oats are equally valid.
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
(FDNR), 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, i1. 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, CA: 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 Pair, AU2 = CdP, AU2 (1.1)
where Fd is the drag force, Cd is the drag coefficient, p, 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, At 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 UDp (1.2)
where U is the time mean velocity, D is the characteristic plant length (defined
below), p is the mass density of air, and t 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 AND 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 = CdpAU2 (2.1)
In fluid mechanics the drag force is defined as
(2.2)
Fd = -pAU2C,
where the 1/2 is included to form the dynamic pressure, /2pU2, 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, Ca 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 K\
7I
Figure 2.1: LEAF ANGLE OF INCIDENCE.
concluded that Cd becomes less dependent on wind speed as 6 increases, thereby
confirming that the bluff-body force is proportional to U2 at maximum 4 (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 AU (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 =F = Cd AIU = CdpAU2 (2.4)
unit volume unit volume )d vu
Since A, varies with height, z,
F' = CdPA(z)U2. (2.5)
8
dF = F'*dV, (2.6)
and
dV = dxdydz = L2dz (2.7)
where L is the average spacing between the plants, then
dF = CdAl() U2L2.dz, (2.8)
and
F = CdPUL f Al(z).dz, (2.9)
where H is the total plant height. Therefore,
F
Cd = (2.10)
p U2L2foAi(z)'dz (2.10)
pU l Af(z)-dz
Using Equation 2.10, the Cd can be calculated provided F. L, and A,(z) are known
for a particular plant.
For a cylinder, the drag coefficient equation is
2F
Cd (2.11)
plU2d
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 force-
momentum 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( (2.12)
(see Cowan, 1968) where
uo (2.13)
SPair
i
and t, 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 Ca(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
2:
J- !:02: z .-i'022 '( 1Oi 2 4 5J 1*: 4 5 6 10' i 6 13i
Figure >.. : DRAG COEFFICIENT FOR CYLINDERS AS A FUNCTION OF
REYNOLDS NUMBER (SCHLICHTING, 1955).
oi leaif c'en:aon. :he heltering effect of neighboring plant elements, and the
fexi bilit of :he 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 sec2) and the drag coefficient of the
:eaves may possible 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
those 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 \iil 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
pU2L2f H A(z) dz
The leaf area distribution with height, Ai(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 description 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
I
pitot
tubes
planterbox
cowling
cowling
S\ 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 pitot-
static 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 = 2A. (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.. ........3 .
1.0 2.0 3.
volts
n .......l........ n .. ll,|,
0 4.0 fi.0 6.0
Figure 4.1:
20.0
15.0
2
Q) 10.0
0
5.0
5.0
0.0 in
-1.c
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
0
<4-
.0.0
5.0
-^
u.U
-1.0
.- 1.0
I
n ......... .
I
2.5 19
,) 1.5
1.0
.) 0.5
0 .0 ....... ........
0.0 2.0 4.0 6.0 8.0 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. 1/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
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 IBM 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.
5.1.1 Fifth Wheel
Channel CHOO 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.
I
CHOO--fifth wheel
" 1600 4
E_ _
1400
4
0 2 4 6 8 10 12 i4 6 18 20
[sec]
CH01 --pressure
7 -4500
-4750
0 2 4 6 8 10 12 14 16 18 20
[sec]
CHO2--differential pressure
-1
0 2 4 6 8 10 12 14 16 18 20
[sec]
CHO3--force transducer 1
2
-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
i 1
0 2 4 6 8 10 12 14 '6 18 20
[sec]
5 8 10 12 14 '6 18 20
[sec]
0
C
-5
0 2 4 6 8 10 12 14 '6 18 20
[sec)
0 2 4 6 8 10 12 14 16 18 20
[sec]
CH04--force transducer 2
2>1 I
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.
s 0-'
nower density spectrum of pressure signal
= 0.303005 -
1,!
>72u'~
[Hz]
Power density spectrum of force
transducer 1
E\ C.001 -
>
P~ 1
[Hz]
power density spectrum of force transducer 2
CN
0 2 4 6 8
[Hz]
Figure 5.3: POWER DENSITY SPECTRA OF SIGNALS IN FIGURE 5.1.
-- J
-- -
L
--~-
I j
j
zower density spectrum of pressure
. -
c
C2
signal
C 2 4 6 8
[Hz]
ocwer censity spectrum of force transducer 1
0 2 4 6 8
[Hz]
oower density spectrum of force transducer 2
-II.
[Hz]
Figure 5.4: POWER DENSITY SPECTRA OF SIGNALS IN FIGURE 5.2.
.1
.C002
.C
,?
s
~ c.~ao2
5.1.2 Pitot-Static Tube
Channel CHO1 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
[sec]
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 -0
signal
pressure
0 2.5 5 7.5 10 12.5 15 17.5
[sec]
------ fifthwheel ------
pressure
9
v) 8
E
7
6
0 2.5 5 7.5 10 12.5 15 17.5
[sec]
------ fifthwheell ------
pressure
Figure 5.6: CALCULATED VELOCITIES FROM FIFTH WHEEL AND
PRESSURE SIGNALS.
31
: ansducers. These signals were expected to be noisy at lower speeds because of the
low cmig force magn,:udes expected compared to the mechanical noise due to the stiff
truck suspension sys:em. The total force was obtained by averaging the forces from
"te two transducers. The power density spectra for one of the transducer signals at
:wo 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 approxima:ely constant throughout the test except for wind gusts.
A lowpass. sixth-order Butterworth filter with a cutoff frequency of 2 hertz
vas 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 -
N-
< 0.001
.4-
0
0.0005 -
'5-
:jN~ AA
[Hz]
pc7ch03
0.0005
0.0004
K 0.0003
S0.0002
0.0001
0 2 4 6 8
[Hz]
pc17ch03
Figure 5.7: POWER DENSITY SPECTRA FOR FORCE TRANSDUCER 1 AT
TWO DIFFERENT VEHICLE SPEEDS.
I I
I
at 25 mph
spectru m
33
appropriate calibration equation applied. From this data, the drag coefficients and
Reynolds 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 average 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 -
S0.6
0.4
0.2
0.0 I
0.0 1.0 2.0 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
20000
30000
Re
40000
THE MEASURED DRAG COEFFICIENT
NUMBER FOR THE CYLINDER.
50000
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
a-e .relaivel 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. Cj, 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
accommodate 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
study 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 7 209 92 14.0 22 1 1
1S 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
58 12 150 104 7.0 12 1 1
14 13 209 96 16.0 27 1 2
15 14 158 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 18 178 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
S 56 135 78 12.0 27 1 1
S 57 175 100 31.0 93 2 2
S 58 138 87 7.0 15 1 1
MEANS: 1 _57.1 _4.6 i 11. 423.4 1__
S D V.: 1.7 i 7.0 I 4.9 1. T 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..
164 174 14 194 204
HEIGHT (em)
Figure A.1: SEA-OATS HEIGHT HISTOGRAM.
UPP 9E 98 10H
UPPERMOST FOLIAGE HEIGHT (em)
Figure A.2: SEA-OATS UPPERMOST FOLIAGE HEIGHT HISTOGRAM.
124 134 144
<;' --------I- I---- -------------------I--
5 11 14 7 20 2 26 29
BASAL STEM CIRCUMFERENCE (cm)
Figure A.3: SEA-OATS BASAL STEM CIRCUMFERENCE HISTOGRAM.
6
_- _______--
7- ---------------------------------------
-dir
II
8 14 3) 26 32
3M 44 50 56 62 64 74 0 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 SliliDH EAID 1
LAYER CUTTING LEAF LEAF LEAF STALK STALK AREA SEEDIEAD SIl)DIIEAD AREA PIANT PLANT
NO. NO. WIDTI LENGTH AREA CIRCUM. LENGTH (projected) CIRCUM. LENGTH (projected) AREA LAD HEIGHT
IA 1 0.4 47.4 18.96 4.0 14.9 18.98
LAYR IA TOTALS: 18.96 0. 00 18.98 37.94[ 0.003 0.1
2 1.4 10.2 14.28 II
LAYER IC TOTALS: I_ __ 25.98 i| 3.44 25.9 81201.06 I4.4981 0.004 0.3
2 0.4 32.9 13.16[ F9_
LAYER IDTOIALS: 150 43.93 11 0.0031 0.4j[
2 1.3 7.4 9.62 2. 13.54 -
LAYER IETOTALS: -- 2T II 12.04 36.,6 6= 0.5
2 1.1 36.2 39.82
3 1 0.8 34.9 27.92
LAYER IFTOTALS: 90.49 12.47 0.00 102.96 0.008 0.6
1G 1 1.6 13.3 21.28 3.1 13.7 13.53
2 0.2 29.6 5.92
3 0.3 29.8 8.94
4 0.1 2.8 0.28
5 1.3 7.3 9.49
1H i 0.1 10.3 1.03 3.' 13.9 15.49
2 1.3 35.7 46.41
_3 1.1 28.7 31.57
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
9 0.5 12.8 6.40
10 0.7 36.8 25.76
11 0.7 21.2 14.84_____ _
_12 0.7 18.0 12.60 ____________
LAYER CI 'ITIN(O
NO. NO.
IEAF
WlD'Il
1E1AIF
1. ,N(i'l I
L.VIAIF STALK STALK
AREA :CIICIIM. I 1.N(VI1 I
:ilAI.K
AI(REA
(ploj-crda)
SIRI)l IM.AI
C(ll<( M.
SIl('.I I II'.A l)
I .1 :NOl 1
I INuI ii
(pIoj1 tAd)
'I.ANT
ARVIIA
IAl )
Il
PLANT
I IlI il Tl
111 13 0.3 20.5- 6.1
14 0.2 246 4.92
AYrR IITOTASI': 29536 -- 5 --. 10R5 00 24 --
f11 1 .9 6 .7 R..2 0.6 ,16.2 .. .
2 0.8 13.5 10.80 0.4 16.1 2.05
3 0.8 15.6 12.48 0.5 19.1 33.04
4 0.2 27.2 5.44 3.4 13.6 14.73
5 0.7 26.2 18.34
6 1.0 18.9 18.90
7 1.0 10.0 10.00
8 0.7 19.4 13.58
9 0.9 31.0 27.90
10 1.6 15.7 25.12
11 1.8 4.8 8.64
12 1.0 15.1 15.10
13 0.7 16.3 11.41
14 0.4 16.8 6.72
15 1.0 16.2 16.20
16 1.1 19.0 20.901
17 1.1 14.6 16.06
18 0.3 23.4 7.02
19 1.7 14.8 25.16
20 1.2 48.2 57.84
21 0.7 18.8 13.16
22 0.3 19.3 5.79
23 0.4 6.0 2.40
24 1.6 8.8 14.08
LAYt1 ItTOTALS: 1421.27 ]1 22.91 "0." 41 0 0.9
IJ 1 63.42 -0.7 15.3 -3.41
2 1.1 51.0 56.10 4.1 14.7 19.19
3 1.3 26.4 34.32 0.9 15.7 4.50
4 1.3 11.9 15.47
5 1.4 12.3 17.22
6 1.2 12.0 14.40
7 1.7 2.2 3.74
8 1.3 14.7 19.11
--
"
Table A.2--con(lit(,(d
Table A.2--continued
STALK SEEDHEAD z/
LAYER CUTTING LEAF LEAF LEAF STALK STALK AREA SEEDIIEAD SFFDDHI AD AREA PIANT PLANT
NO. NO. WIDTI I.ENGTIH AREA CIRCUM. LENGTH (projected) CIRCUM. LEN(iTI (projected) AREA LAI) HEIGHT
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: | 400.31 27.11 0.00 427.42 0.034 1.0
0.9 TOTALS: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
T'ablc A.3: LEAI:, STALK, AND SIHEDII IlAI) AREIA MIASLJRIIMliN'Il
AND LAI CALCULATIONS FOR PLANT 2.
LFAF STAIK SEEl)11 AI) /
LAYER CUTrING LEAF LEAF LEAF STAIK STALK AREA SEIi)IIEAI) SEI)I1EAI) AREA P1ANT PLANT
NO. NO. WIDTII LENGTHi AREA CIRCUM. iLENGTIl projectede) (CIRCM. Il(ilG (piojccctl) AREA IAl) IllEGilT
2A 1 0.3 23.0 6.90 0.6 6.0 1.15
LAYER 2ATOTALS: 6.901 | 1.15 85 0o.ool I
211 I. 1.0 8' 1 1.16 3 18i.4 17.58
A2 20.2 14.8 2.960
IAYK Li r0 1 Al: 21.06 0. 7 .. .5t i 38 0.
S1 0.6.2. 1.3 3.01 l7.4 0616.2- ---- I ----06
2 1.3 12.0 15.60_ _
LAYER 2C iTOTALS: 2 7.90 1 .7 I || [1( I (.( I (.
2D 1 1.2 16.84 2 60 2.2. 16.8 11.7 6. ....
S2 0.4 31.0 12.40
LAY1YER 21 10 1AL:: 32.56 3.-5_ 11.707 0.00- 44.33 )0.003 0.4
LAYER 2EITOTUIALS: 40.06 15.79 0.00 55.5 0.5
2F 13 0.9 4 2.91 17.4 16.07 -
lAYJ' 10 JuALS: 1 .5532 1.07 0.00 13r | -th -
2 1 .3 20.73.0 16.672 .2.." 17. 1
2 1.5 15.0 22.50_
IAY (,6'0O AI .: 28.71 JI Al____ 16._472_ 4_
211 i .6 43.8 26.28 3.2 17".0 1732 _.. '
2 1.1 50.6 55.66
3 1.0 34.5 34.50
4 0.6 45.8 27.48
2 1.2 17.3 20.76 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_ 0.9 22.4 20.16
8 1.1 45.5 50.05
9 0.8 57.3 45.84
Table A.3--continucd
LEAF STALK SlilDillAI) 7/
LAYER CUTTING LEAF LEAF LEAF STAI.K STALK AREA SIFiDIl)AI) SlilDIlliAD AREA I'ANT IPANT
NO. NO. WIDTII LENGTII AREA CIRCIM. IENGTHI (projected) CIRCUM. ILiNGTII (projected) AREA LAD ItliIGHT
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
LAYEK21 TOTAl 1.: 1- 1 486.55J 1I1 22.71 0.0| |t 509.26 .02 =1 0.9
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
S7 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
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
S 22 0.3 59.8 17.94
S 23 1.1 19.5 21.45
LAYER
NO.
I.JAFI
CIJI'ING
NO.
.EAF LEAF
WIDTi II .lNG iI
lIEAF
AREA
STA .K
CIRCI M.
STAI.K
I I:N(ll
ARlEA
(plojccleId)
Sill IDAI ) M
CIRC M.,
SI:1; )1 Ii Al)
L.N(iTil I
(AKliA
(" i oiHi l)-
PI ANT
ARI'A
1/
I' ANT
III I ITI
21 24 0.7 7.6 5. 3__ 2
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
LAYER 1 TALS 47.30 0.00 I' 680.77 I .4
_. *7TOTAls: 4708.771 0.108 t[
NOTES:
All lengths in centimeters.
Layer height: 17 cm
Plant height: 170 cm
Ground area: 929.03 sq cm
LAI: 1.839
" -------
a'blec A.3--contiitiiued
Table A.4: LEAF, STALK, AND SEEDI IEAD AREA MEASUREMENTS
AND LAI CALCULATIONS FOR PLANT 3.
STALK SlEl'EDillAD //
LAYER CUTTING LEAF LEAF LEAF STALK STALK AREA SEI)IllEAD SEFl)IIEAD AREA PIANT PIANT
NO. NO. WIDTH LENGTH AREA CIRCUM. LENGTH (projected) CIRCUM. LENGTl (projected) AREA LAD HEIGlIT
3A 1 0.2 18.2 3.64 2.7 16.1 13.84
LAYER 3A TOTALS: 3.64 .0.00 17.4 1 0.1
3I 1 0.7 7 2. 25.69 I .1/. 2I 0.3
AYE 3 2 1OTAIS: 9.0 14.42 .60 0.00 25.69 40.11 .2
3C'l 1 0.5 3.41 1 1 T 21.11 6.5.70 3. 12.3 .-- -
2 1.3 11.8 15.34
3D ~ 1 .0 214. 21.30 T. 18.8| 13.17
2 1.4 17.2 24.08
3 0.7 36.5 25.55
2_____ 1.4 19.0 26.60
LAYER 3CTOTALS: 0.4 21.50 .1 004 1
5 1.5 9.6 14.40
LAYER 3H TOTALS: 33,.90 5II 13.17 II 9 0.00 47.07 0.003 | 0.4
21 1. 13.6 24.085 55. _______ 1=1_ =
2 1.2 57.8 60.36 3.4 17.8 14 19..27
.AYER 31 TOTALS: 152.47 It 15.16 | 0.00 67.63 0.004 0.6
3G 1.3 41.6 54.57 3.0 18.0 17.20
2 1.3 18.1 23.53
3 0.2 14.6 2.9200
4 0.9 30.2 27.183
3r -- -1.4 11.3 15.82 3.5 17.9 19.95
______2 1.419.0 26.60 ________ _____ _______
_____ ______3 1.1 44.3 48.73____________________
______85 1.5 9.6 14.40_______ ____ ____
LA^R3 I6r 1.5 5.0 7.50 ______ ________ ____
LAYER 3H TOTALS: 18.05 19.95 | I- 138.00 .H .0.8.
31 1 1.0 21.6 LIM)r -- .1 3.37 2.21
______ 93 1.341.6 54.08 _____________________ ________ _____ ____ _____
___________4 1.6 17.7 28.32 __________
S5 0.6 10.0 600 ________ _______________ ______
6 0.8 17.0 13.60 ________ _______ _____ ____ ______
'Table A.4--continued
STALK SIiEDI lEAD z/
LAYER CUTTING LEAF LEAF LEAF STALK STALK AREA SEliI)IlliAD SIHDI)1EAD AREA I'ANT I'LANT
NO. NO. WIDTH LENGTH AREA CIRCUM. LENGTH (projected) CIRCIM. I.ING(TH (projected) AREA LAD IIEIGlHT
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___
LAYER 31' TTrALS: 244.44 2148 X 1 0.00 265.92 II0 .00 0.9
3. I 0-.8 19.7 1.76 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 3r'AL: 14430 63.27 0.00 207.57 0.013 1. r0
0.9 TOTALS: 1oo8.o9 _I o.061 II
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: LEAI', STALK, AND SlilI liAD ARIiA MiLASU RIMiN'TS
AND LAI CALCULATIONS FOR PLANT 4.
LEAF
CUTTING LEAF L.FAI
NO. WIDTH ILENGTiH
I.EAF
AREA
STAI.K STAI.K
CIRCUM. LN(i'TM I
STAI.K
AREAI
(projected)
S IH CIIJ.AI) SI l)ll IA )
CIKCUM. I ,I-N(iTIl I
ARAH
(projected)
PLANT
ARiA
I.AI)
I'.ANT
4A 1 0.3 32.9 -9.87 2.2 1.6 9.53
LAYR 4A TOTALS: 9.7 9.7 14 oolI 0.1
LAYIlR 411 TOT1AIljS: Ul 0.4 I2 .
4C| 1 0.7 57.1 39.97 2.2.1 0.o 1. 9T V
2 1.5 1 11.01 16.50
LAYHR 4CTOTAlS: i 56.47 5.3 9. I .9 0.004
2 1.5 11.3 16.95_
LIAYI:RI 41) TOTA LS: I 64.15 I I 1.1 .. .... 1 0.0 1 > i .11 O1
41E '| 1| 1.5 | 10.9 16.35) .2| 2i.T"/ I97.17 I II Ii
1,2YlTR'10 T i| T/..11 ii T1
2 0.9 26.5 23.85____________________ __
3 1.6 18.3 29.28
AI I('4 T0 TALS: !I .40 __ 21.0I .0 12.4 'I).17 I[ 'I L .6
4--TJ~ 1" 1.3 20T1.4 253 18.8 19 ---,-
2 0.8 20.9 16.72
3 1.7 14.2 24.14
Y1 LTOTALS: I 67.3 19.76 \ (.I) 87TT.1 .0 1.7
-4-- 1 1.4 15.9 22.26' 3.4 20.2 2 -
2 1.7 16.5 28.05
3 1.4 28.7 40.18
4 1.7 20.5 34.85
5 1.3 41.1 53.43
AYKR, 41 -TO'TlA LS: 178.77 21.87 ........... l.)MF 200.,4 '1T11 11.8
S1 1.9 15.8 30. 2.3 6.5 4./7 ..
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
8 0.4 40.6 16.24
S9 0.3 21.9 6.57
I.AYER
NO.
Table A.5--co(linulc
L.AYIl<(
NO. I
(:f11 IN(.
NO.
I'.Al I .N il' I
WIDTH iL'.NdTiIl
AIWIA5
AlIt5A
S'TAl1.K
( fI( '1M
STALL .K
.1 :NOTl I
ALI .K
(|ls ,)- I( ,l)
Sil')DI lA)1
(CI( II M.
Sl' I IIIIIA I )
I .I ,N 1 > I I
A II'.A
(|nl(>c)( rl)
1I' AN I
ARi'VA
I/
41 10 0.8 I.3" 14.04
S11 0.6 53.5 32.10
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
I"AVR I TOTAl-S: n ^2.-2 31+I MTN[ "_ _._ "_-._ T -6.61 -- -
4 -1 I 1.1 18. 19.K0 1.3 1.1 -Tr -
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 26.60
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
-OTA : A 373.4 .I I s7.32z 0. 1.
1.1 -..'...- 'I I Ai^"i q'l- 5.72'no 1.0
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 pianterbox. the strain and deflection in the box legs were
estimated 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, Fi, on each of the
front legs is
F, = 3EI, (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
= bh' (B.2)
12
where b and h are the leg width and thickness, respectively. In terms of the total
force. F.
force transducer
-r nt View
----------- o ----1-----
II
I''
: X,:: :.. :.,,
\\\\\\-,\\-~
^^:^:<^
12"
Plan View
-- planterbox
Back View
Side View
Figure B.1: PLANTERBOX DETAILS.
iI
i F
bail jicnt
- 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 = CdpAL2HU2,
and F, is
FI= 1CpA L2HU2, (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
E
(B.6)
where a is the axial stress.
strain gage
S2.:t3 cm
SIDE VIEW
(B.3)
(B.4)
a M (B.7)
S
E is he .ociulus of elasticity. S is the section modulus.
S =bh2 (B.8)
6
-zd M is :he moment at the strain gage, given by
M = Fxy. (B.9)
Subszitung equations B.7. B.8 and B.9 into equation B.6 results in
S 3C pA,2HU2y (B. 10)
Ebh2
..e esnrma:e strain and deflection were calculated using the quantities below
:oCr ies made of 2024-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(10'>) N/m2,
b = 0.032 m,
h = 0.00163 m,
Cd = 0.18 and
y = 0.067 m.
Table B.: show s the cal:.a:ed values of the forces, deflections and strains on the
instr-en ie ls a velocities ranging from 15 to 55 mph.
Because the ield s-ress.
o = 3.24 x(108) Pa,
correso-c.ds to a strain of
E = 4434 Ipe,
the calculated wind loading will not cause permanent deformation in any of the
planterbox legs.
Table B.1: CALCL-ATED FORCE. STRAIN AND DEFLECTION QUANTITIES
AT DIFFERENT WIND SPEEDS.
TOTAL LEG
VELOCITY \-ELOCIT FORCE FORCE STRAIN DEFLECTION
I moh (m-rs (N) (N) (m)
5 7o.1 1.4948 0.7474 0.000048 0.0001
20 S.94 2.6574 1.3287 0.000086 0.0002
25 11.1S 4.1521 2.0761 0.000134 0.0002
0 113.41 5.9791 2.9895 0.000194 0.0004
3515.65 f S.13S2 4.0691 0.000264 0.0005
40 V-.SS 10.6295 5.3147 0.000344 0.0006
45 20.12 13.4529 6.7265 0.000436 0.0008
50 ."225 I 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-ia:e- :Co -.e ee-se-S vel- ocxy through Bernoulli's equation,
p Po = pU1.
tub:ri -----)-.c "
36"
I~~
to pressure transducers
Figure B.3: DETAIL OF PITOT-STATIC TUBE SUPPORT.
(B.11)
60
holes
ee-stream ---
velocity %i"
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.
Bolz. Ray E. and George L. Tuve. eds. 1970. Handbook of Tables for Applied
Engineering 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
physiological ecology: 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 wind-
blown 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.
I
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.
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