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**Wind Tunnel Testing from FIT conducted by graduate student Eric Roehl
under direction from Professor Lee Harris. **

*prepared by*

*Eric Roehl, Ocean Engineering Graduate Student, and Lee Harris, P.E.,
Associate Professor of Ocean Engineering Division of Marine and Environmental
Systems Florida Institute of Technology Melbourne, Florida 32901 *

**prepared for **

**Reef Ball Development Group LTD. 7085 Chappell Circle Doraville, GA 30360
**

**April 1996 **

**Table of Contents **

**1.0 INTRODUCTION 3
2.0 METHODOLOGY 4
2.1 THEORY 4
2.2 WIND TUNNEL MODEL TESTS 5
2.3 WAVE TANK MODEL TESTS 7
3.0 RESULTS 11
3.1 WIND TUNNEL TEST RESULTS 11
3.2 WAVE TANK TEST RESULTS 12
3.3 WAVE TANK STABILITY ANALYSIS CORRELATION 12
4.0 CONCLUSIONS AND RECOMMENDATIONS 15
5.0 TECHNICAL REFERENCES16
APPENDIX STABILITY ANALYSIS GRAPHS 17 **

**Creating an artificial reef has become a popular method of disposing of
unwanted items which would take up valuable space in landfills. Recently,
there has been a movement to design artificial reef modules rather than just
dumping waste products into the ocean. These modules come in a wide variety
of sizes and shapes, many using items such as old concrete pipes and excess
concrete from construction sites. Each is designed around the idea of creating
habitat for fish as well as promoting coral growth. Manufactured artificial
reefs are being used both to replace damaged or destroyed natural reefs and
to create new reefs. **

**With artificial reefs becoming more common and being used in a wider range
of environments, the stability of the individual reef modules is becoming
a concern. During periods of high wave action, wave forces can cause movement
and even the destruction of the modules. Of concern is the damage caused
to natural reefs and established artificial reefs by moving modules or broken
module fragments. **

**The Reef Ball Development Group, LTD. produces the Reef Ball, Pallet Ball
and Bay Ballartificial reef modules. **

**Table 1 shows the general characteristics of the three Reef Ball modules.
**

Module Type |
Width |
Height |
Weight |
---|---|---|---|

Bay Ball |
3 feet |
2 feet |
350 to 750 lbs |

Pallet Ball |
4 feet |
3 feet |
1500 to 2200 lbs |

Reef Ball |
6 feet |
4 feet |
3000 to 6000 lbs |

**This report documents the stability analyses performed for the above three
type of artificial reef units. Wind tunnel tests were performed to determine
drag coefficients of the units. Wave tank tests were performed to evaluate
the stability of the units during wave attack, using a scale model Reef Ball
unit deployed at various depths, and under varying wave conditions. Analytical
analyses were performed based on the results of the wave tank tests, and
the results are presented in numerous graphs in the Appendix. These graphs
can be utilized to determine the required sizes and weights of Reef Ball
units needed for stability for different design depth and wave conditions.
**

{NOTE: THE REEF BALL DEVELOPMENT GROUP, LTD WILL INTERPRET THESE GRAPHS AS A SERVICE TO OUR CLIENTS}

**2.0 METHODOLOGY 2.1 THEORY Linear wave theory was used though out the
stability analysis. This was done for the ease of use for the calculations.
**

**The basic equation for the stability of submerged objects is a balance
between the lateral wave forces and the resisting forces. **

**Fwave = Fdrag + Finertia = Resistance Force = *(Weight - Buoyancy - Flift)
EQN 1. **

**Fdrag and Finertia are lateral wave forces, and * is the coefficient of
static friction of an object resting on sand (* = 0.6 used in this analysis).
Weight is the dry weight of the module and Flift is the wave induced lift
force. The lift force is assumed to be one-half of the drag force. This is
a conservative estimate and contributes to the safety factor in the analysis.
**

**A set of wave periods were selected for the analysis (8, 10, 11, 12, 14,
16, 20, 24 seconds). Next, using the U.S. Army Corps of Engineer's Automated
Coastal Engineering System (ACES) computer software analysis program, wave
lengths were calculated for waves with the above periods at depths from 10
feet to 120 feet. Finally, a range of wave heights were selected to represent
normal and storm conditions (3', 5', 7', 10', 15', 20', 25'). **

**Since the analysis includes shallow water depths, it is necessary to determine
if any of the design waves have broken. For example, a 25 foot high wave
can not exist in 10 feet of water. Two checks are performed to test for breaking
waves. If the wave has broken, the largest wave which can exist at a given
depth is used in the calculations, otherwise the given design wave height
is used. **

**Based on the wave period, wave height, and wave length at a given depth,
the horizontal water particle velocity can be calculated using the following
equation: **

** EQN 2. **

**Where U is the maximum horizontal particle velocity, H is the wave height,
T is the wave period, k is the wave number (k = 2*/L), d is the water depth,
and z is the depth at which the particle velocity was calculated. For all
the calculations, the depth analyzed was 6 feet above the sea floor, so that
(z + d) = 6 feet. **

**The drag force is calculated using the classic drag equation: **

** EQN 3. **

**Where CD is the coefficient of drag, * is the density of sea water, and
Area is the projected cross sectional area of the module. See Section 2.2,
Wind Tunnel Model Tests, for further details on the determination of values
for CD. **

**By adding in a safety factor (SF = 2) into Equation 1 and solving for
the weight, the final equation for the required module weight is obtained:
**

** EQN 4. **

**Equation 4 does not include the inertia force which is shown in Equation
1. This is done because as a wave passes, the maximum drag and inertia forces
occur at different points in the wave cycle, thus the effects are not cumulative.
Also, the inertia force is negligable when compared to the drag force, allowing
the ineriia force to be dropped from the calculations. **

** In the early stages of the analysis, it was determined that the coefficient
of drag (CD) would be very crucial in the calculations. In order to get a
better idea as to what this number would be, a series of wind tunnel tests
was conducted at the Florida Tech wind tunnel using one of the reef ball
scale models. The model used was approximately five inches high, with a six-inch
diameter base. The following photograph shows the test section of the Florida
Tech wind tunnel. **

** PHOTOGRAPH 1. WIND TUNNEL TEST INSTRUMENTATION **

**Instrumentation consists of strain gages connected to the vertical rod
supporting the Reef Ball unit, which are connected to the computer for analysis
and recording. The video camera mounted on the tripod is used to document
the flow around the unit, as smoke is injected into the tunnel, as shown
in Figure 2 below (which does have considerable reflection from the front
glass). **

** PHOTOGRAPH 2. SMOKE FLOWING AROUND REEF BALL UNIT IN WIND TUNNEL TESTS
**

{Omitted to save download time.)

** PHOTOGRAPH 3. REEF BALL UNIT IN WIND TUNNEL **

**(Light refection off the front glass of the test section creates distortion
in the picture.) The wind tunnel tests were used to determine the drag
coefficient (CD) for the Reef Ball(TM) scale model units. To confirm the
accuracy of the wind tunnel data, a smooth, metal cylinder was also tested.
The results of the tests for the Reef Ball (TM) and the cylinder are presented
and discussed in Section 3 of this report. For visualization of the fluid
flow around the Reef Ball(TM) unit, smoke was injected into the wind flow,
as shown previously in Photograph 2 and in Photograph 4 below. **

** PHOTOGRAPH 4. SMOKE FLOWING AROUND THE REEF BALL UNIT **

**Wave tank model tests were performed using the Reef Ball(TM) scale model.
The Florida Tech wave tank is a free standing, steel beam frame structure
with glass sides and open top .**

**The internal dimensions of the wave tank are thirty feet long by twenty-two
and one-half inches wide by three feet deep (30' x 221/2" x 3'). An eight-foot
(8') long, smooth plastic section comprises the bottom where the test units
are located. A second eight foot (8'), smooth plastic section is used as
a variable slope beach and wave absorber on the lee side of the units. The
wave absorbing angle is changed for each water depth or wave height. Wave
energy is thus more efficiently absorbed, and reflection off the back vertical
glass wall of the tank is reduced. Changing the angle of the wave absorber
also reduces reflection off the absorbing plastic sheet itself. **

**Water depths for testing are adjusted by filling or draining the tank.
A pivoting, flap type, paddle wavemaker generates waves through a rotary
motor. Wave period is regulated by the speed of the motor, while stroke length
is regulated by the position of the connecting rod on the radius of the plate
attached to the motor. **

**The size and characteristics of the Florida Tech wave tank caused some
limitations in wave generation. The motor power and allowable radius of the
plate limited the maximum wave height to approximately nine inches (9"),
depending on water depth, and a period of approximately 1.5 to 4.0 seconds.
Larger waves at shallower water depths were unattainable due to the
characteristics of the paddle type wavemaker. Larger waves and shorter periods
were therefore obtained by manually operating the paddle. While this method
produced less consistent waves, it allowed for larger wave heights and longer
periods. However, waves large enough to cause unit movement and structural
instability could not be generated for some of the water depths in the wave
tank tests. **

**A second limitation attributable to the size of the wave tank is wave
reflection. Reflection from the paddle occurs due to its proximity to the
structure and the first two wave gages. The adjustable angle of the absorbing
beach is limited, so as waves become larger, water that overtops the beach
can result in some reflection from the back vertical wall of the tank. As
water depth increases, the absorbing beach requires a steeper angle which
may increase reflection off the beach itself. Therefore the wavetank test
results should be used primarily for comparison purposes between the different
types of units tested. Due to the height of the foreshore slope and the wave
heights generated, the maximum allowable depth for testing is approximately
twenty-two inches (22"). **

**For stability tests, one wave gage was located directly adjacent to the
individual Reef Ball (tm) model test unit to record wave height. The gage
was connected to an IOmega Tech Daq Book data acquisition system and Gateway
laptop computer. SnapMaster software from HEM was used to run the
instrumentation. Wave records of voltage were transformed into wave height
records by calibration of the gages at each water level. The tests were
videotaped using a tripod mounted camcorder, making it possible to correlate
visual and wave height records. Video shot during testing was used to help
determine points of unit instability as well as wave interaction characteristics.
Some photographs from video frames shot during the tests are shown in the
photographs on the following pages. **

**PHOTOGRAPH 5. WAVE TANK TESTS OF REEF BALL MODEL **

** (a) 12" water depth on smooth bottom **

** (c) 15" water depth on smooth bottom **

** (e) 18" water depth on smooth bottom **

** (b) 12" water depth on sand bottom **

** (d) 15" water depth on sand bottom **

** (f) 18" water depth on sand bottom **

**3.0 RESULTS 3.1 WIND TUNNEL TEST RESULTS The results of the wind tunnel
tests are shown below in Figure 3. The results show that values for CD range
from 0.8 to 1.0 for most Reynolds Number values. The Reynolds Number is defined
as an index of flow rate and turbulence, the higher the value the greater
the flow rate and turbulence. The Reynolds Number also allows the test results
to be used for any fluid, both gases and liquids, and provides the mechanism
for converting the values according to the density and viscosity of the fluids.
FIGURE 3. WIND TUNNEL TEST RESULTS From these results, two different values
for the drag coefficient (CD) were used for the stability analysis. In shallow
water (10 to 30 feet) where the water velocities are large, CD was set to
1.2. For deeper water, the CD was set to 1.0. The increase in drag coefficient
for Reynolds Number greater than 200,000 warrants further investigation,
and could be further examined by using a larger scale model in the wind tunnel.
3.2 WAVE TANK TEST RESULTS Wave stability tests were conducted by generating
increasingly larger wave heights until movement of an individual unit was
observed. Various water depths were tested. The video camera record indicated
the exact moments of initiation of unit movement. The point of unit movement
was then correlated with the appropriate wave height through the wave record.
Individual units were tested on both (1) a smooth bottom and (2) a sand bottom,
to evaluate the stability of the units on both hard and soft bottoms. **

**The test results for the largest waves for which the model unit remained
stable are shown in Table 2 below. For the 18-inch water depth, the Reef
Ball model unit remained stable for the largest wave height able to be generated
in the wave tank, 9.19 inches. Therefore, a wave height greater than 9.19
inches would be necessary for movement of the Reef Ball. The test results
in Tables 2 & 3 can be applied to full-scale reef units by appropriate
scale factors, as further discussed in the following section of this report.
**

**TABLE 2. WAVE TANK STABILITY TEST RESULTS (HARD BOTTOM) UNIT TYPE STRUCTURE
HEIGHT WATER DEPTH WAVE HEIGHT PERIOD **

**TABLE 3. WAVE TANK STABILITY TEST RESULTS (SAND BOTTOM) UNIT TYPE STRUCTURE
HEIGHT WATER DEPTH WAVE HEIGHT PERIOD **

**3.3 WAVE TANK STABILITY ANALYSIS CORRELATION The stability analysis was
corroborated using the results of the wave tank testing. Using the procedure
presented in the Methodology Section for the stability analysis, the predicted
required weight should be greater than the actual weight of the model used
in the wave tank tests. The actual weight of the Reef Ball model was 4.34
pounds. Table 3 is a summary of the three wave conditions from the wave tank
tests used to verify the results of the stability analysis and the predicted
required weight. **

**TABLE 4. PREDICTED REQUIRED WEIGHT FOR UNIT STABILITY (HARD BOTTOM) **

**Predicted Required Weight **

**Wave Height Wave Period Water Depth Linear Cnoidal **

**0.50 feet 2.6 sec 1.00 feet 3.23 lbs 8.60 lbs **

**0.55 feet 1.7 sec 1.25 feet 2.62 lbs 6.13 lbs **

**0.61 feet 1.8 sec 1.50 feet 2.49 lbs 6.13 lbs **

**TABLE 5. PREDICTED REQUIRED WEIGHT FOR UNIT STABILITY (SAND BOTTOM) **

**Predicted Required Weight **

**Wave Height Wave Period Water Depth Linear Cnoidal **

**0.52 feet 1.7 sec 1.00 foot 3.31 lbs 7.66 lbs **

**0.59 feet 1.9 sec 1.25 feet 3.14 lbs 7.59 lbs **

**0.77 feet 1.8 sec 1.50 feet 3.92 lbs 10.64 lbs **

**Using the information in Tables 4 & 5 it is possible to scale the
results, using Froude model law scaling to transform the wave tank waves
into real waves. Tables 6 & 7 shows the results of this Froude scaling,
for linear wave theory only, as applied to all three reef ball types. **

**TABLE 6. RESULTS OF FROUDE SCALING (HARD BOTTOM) Wave Height Wave Period
Water Depth Required Weight **

**Bay Ball (Scale Factor = 4.8) **

**2.40 feet 5.7 sec 4.8 feet 357 lbs **

**2.64 feet 3.7 sec 6.0 feet 290 lbs **

**2.93 feet 3.9 sec 7.2 feet 275 lbs **

**Pallet Ball (Scale Factor = 7.2) **

**3.60 feet 7.0 sec 7.2 feet 1206 lbs **

**3.96 feet 4.6 sec 9.0 feet 978 lbs **

**4.39 feet 4.8 sec 10.2 feet 929 lbs **

**Reef Ball (Scale Factor = 9.6) **

**4.8 feet 8.1 sec 9.6 feet 2858 lbs **

**5.28 feet 5.3 sec 12.0 feet 2318 lbs **

**5.86 feet 5.6 sec 14.4 feet 2203 lbs **

**TABLE 7. RESULTS OF FROUDE SCALING (SAND BOTTOM) Wave Height Wave Period
Water Depth Required Weight **

**Bay Ball (Scale Factor = 4.8) **

**2.50 feet 3.7 sec 4.8 feet 366 lbs **

**2.83 feet 4.2 sec 6.0 feet 347 lbs **

**3.70 feet 3.9 sec 7.2 feet 434 lbs **

**Pallet Ball (Scale Factor = 7.2) **

**3.74 feet 4.6 sec 7.2 feet 1235 lbs **

**4.25 feet 5.1 sec 9.0 feet 1172 lbs **

**5.54 feet 4.8 sec 10.2 feet 1463 lbs **

**Reef Ball (Scale Factor = 9.6) **

**4.99 feet 5.3 sec 9.6 feet 2928 lbs **

**5.66 feet 5.9 sec 12.0 feet 2778 lbs **

**7.39 feet 5.6 sec 14.4 feet 3468 lbs **

**From all of the analyses performed for this study, stability curves for
all three Reef Ball artificial reef unit types were prepared, and are included
in the Appendix. The results are broken down by module type and wave period.
Each graph contains stability curves for seven different wave heights, and
presents the minimum required unit weight for stability, as shown in one
of the graphs reproduced below: FIGURE 4. MINIMUM REQUIRED WEIGHT FOR REEF
BALL UNIT STABILITY for various water depths and wave heights with wave period
of 10 seconds. **

**4.0 CONCLUSIONS AND RECOMMENDATIONS Design data for Reef Ball, Pallet
Ball and Bay Ball artificial reef units resulted from the combination
of wind tunnel, wave tank, and analytical analyses. The results of this study
present the minimum required individual unit weights required for structural
stability. The only structural instability noted in the wave tank tests was
sliding, which occurred for much higher wave heights for units on a sand
bottom as compared with those on a smooth bottom. No overtopping of the units
was ever observed. **

**Due to the increase in drag coefficient at the highest values of Reynolds
Number tested in the wind tunnel, it is recommended that the wind tunnel
analysis be continued to further examine the characteristics of the reef
ball at higher Reynolds Numbers. This would require further wind tunnel tests
using a larger scale model. If it is determined that the coefficient of drag
increases substantially, the stability analysis should be modified to reflect
these increases. **

**5.0 TECHNICAL REFERENCES Dean, Robert and Dalrymple, Robert, 1991. Water
Wave Mechanics for Engineers and Scientists. World Scientific, New Jersey..
**

**Roberson, John and Crowe, Clayton, 1990. Engineering Fluid Mechanics.
Houghton Mifflin Company, Boston, MA. **

**U.S. Army Corps of Engineers, 1994. Automated Coastal Engineering System
(ACES). Coastal Engineering Research Center, Waterways Experiment Station,
Vicksburg, Mississippi. Version 1.07e. **

**U.S. Army Corps of Engineers, 1984. Shore Protection Manual. Coastal
Engineering Research Center, Waterways Experiment Station, Washington, D.C.:
U.S. Government Printing Office. 2 Vols. **

**APPENDIX STABILITY ANALYSIS RESULTS FOR THREE DIFFERENT REEF BALL UNITS
FOR DIFFERENT WAVE PERIODS **

**A. BAY BALLS Figure A-1 Bay Ball stability curves for waves with periods
of 8 seconds 18 Figure A-2 Bay Ball stability curves for waves with periods
of 10 seconds 18 Figure A-3 Bay Ball stability curves for waves with periods
of 11 seconds 19 Figure A-4 Bay Ball stability curves for waves with periods
of 12 seconds 19 Figure A-5 Bay Ball stability curves for waves with periods
of 14 seconds 20 Figure A-6 Bay Ball stability curves for waves with periods
of 16 seconds 20 Figure A-7 Bay Ball stability curves for waves with periods
of 20 seconds 21 Figure A-8 Bay Ball stability curves for waves with periods
of 24 seconds 21 **

**B. PALLET BALLS Figure B-1 Pallet Ball stability curves for waves with
periods of 8 seconds 22 Figure B-2 Pallet Ball stability curves for waves
with periods of 10 seconds 22 Figure B-3 Pallet Ball stability curves for
waves with periods of 11 seconds 23 Figure B-4 Pallet Ball stability curves
for waves with periods of 12 seconds 23 Figure B-5 Pallet Ball stability
curves for waves with periods of 14 seconds 24 Figure B-6 Pallet Ball stability
curves for waves with periods of 16 seconds 24 Figure B-7 Pallet Ball stability
curves for waves with periods of 20 seconds 25 Figure B-8 Pallet Ball stability
curves for waves with periods of 24 seconds 25 **

**C. REEF BALLS **

**Figure C-1 Reef Ball stability curves for waves with periods of 8 seconds
26
Figure C-2 Reef Ball stability curves for waves with periods of 10 seconds
26
Figure C-3 Reef Ball stability curves for waves with periods of 11 seconds
27
Figure C-4 Reef Ball stability curves for waves with periods of 12 seconds
27
Figure C-5 Reef Ball stability curves for waves with periods of 14 seconds
28
Figure C-6 Reef Ball stability curves for waves with periods of 16 seconds
28
Figure C-7 Reef Ball stability curves for waves with periods of 20 seconds
29
Figure C-8 Reef Ball stability curves for waves with periods of 24 seconds
29 **

** Figure A-1 Bay Ball stability curves for waves with periods of 8 seconds
Figure A-2 Bay Ball stability curves for waves with periods of 10 seconds
**

** Figure A-3 Bay Ball stability curves for waves with periods of 11 seconds
Figure A-4 Bay Ball stability curves for waves with periods of 12 seconds
**

** Figure A-5 Bay Ball stability curves for waves with periods of 14 seconds
Figure A-6 Bay Ball stability curves for waves with periods of 16 seconds
**

** Figure A-7 Bay Ball stability curves for waves with periods of 20 seconds
Figure A-8 Bay Ball stability curves for waves with periods of 24 seconds
**

** Figure B-1 Pallet Ball stability curves for waves with periods of 8 seconds
Figure B-2 Pallet Ball stability curves for waves with periods of 10 seconds
**

** Figure B-3 Pallet Ball stability curves for waves with periods of 11
seconds Figure B-4 Pallet Ball stability curves for waves with periods of
12 seconds **

** Figure B-5 Pallet Ball stability curves for waves with periods of 14
seconds Figure B-6 Pallet Ball stability curves for waves with periods of
16 seconds **

** Figure B-7 Pallet Ball stability curves for waves with periods of 20
seconds Figure B-8 Pallet Ball stability curves for waves with periods of
24 seconds **

** Figure C-1 Reef Ball stability curves for waves with periods of 8 seconds
Figure C-2 Reef Ball stability curves for waves with periods of 10 seconds
**

** Figure C-3 Reef Ball stability curves for waves with periods of 11 seconds
Figure C-4 Reef Ball stability curves for waves with periods of 12 seconds
**

** Figure C-5 Reef Ball stability curves for waves with periods of 14 seconds
Figure C-6 Reef Ball stability curves for waves with periods of 16 seconds
**

** Figure C-7 Reef Ball stability curves for waves with periods of 20 seconds
Figure C-8 Reef Ball stability curves for waves with periods of 24 seconds
**

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