HomeMy WebLinkAboutEIR 86-05; BATIQUITOS LAGOON; Tidal Circulation; 1985-07-01<Vr'
ALTERNATIVES FOR MAINTAINING TIDAL CIRCULATION
IN THE BATIQUITOS LAGOON, CALIFORNIA
JULY 1985
BY
Scott A. Jenkins, Ph.D.
and
David W. Skelly, MS.
CENTER FOR COASTAL STUDIES
SCRJPPS INSTITUTION OF OCEANOGRAPHY
LA JOLLA, CALIFORNIA
Alternatives for Maintaining Tidal Circulation
in the Batiquitos Lagoon, California
by
Scott A. Jenkins, Ph.D.
and
David W. Skelly, MS.
Center for Coastal Studies
Scripps Institution of Oceanography
La Jolla, California
I. Sea Level and Tidal History
Batiquitos Lagoon is a feature of the most recent period of the
Pleistocene Epoch. In fact it did not exist as a lagoon structure as
recently as 18,000 years before present. Figure 1 shows the sea level
variations for Southern California over the last 40,000 years of the
Pleistocene Epoch. We note that sea level was about 120 meters below
its present level at the end of the Mid-Wisconsin Regression. Thus
Batiquitos Lagoon was "high and dry" 18,000 years ago. It Was not in
fact a lagoon then, but rather a stream valley cut in the Linda Vista
Terrace. Following the melting of glacial ice at the end of the
Mid-Wisconsin Regression, sea level gradually rose to nearly its present
level some 6,000 years before present. This sea level rise drowned the
seaward end of the San Marcos river valley, thus forming the Batiquitos
Lagoon system. During this sea level rise, fluvial material filled the
floor of the San Marcos River valley with sand and gravel deposits up to
10 meters thick (Inman, 1983; Inman and Jenkins, 1983).
During the last 6,000 years, the rise in sea level has been very
slight, about 15 cm per century. However the fluvial deposits of sediments
on the lagoon floor has continued, steadily reducing the mean depths and
tidal prism of the lagoon. Whatever species utilize the lagoon as a
MSL 0
50
3
£.
too
J I 35 30i i i i i i 25i
Thousondi ol Yeori Before Present
1520i i i
150-J Mid-Wisconsin Tronsgression Mid-Wisconsin Regression Flondrlon Tronsgression
-IOO
Modern
-< L|50
Figure 1. Late Quaternary fluctuations in sea level. Solid line is the "generalized"
sea level curve (from Curray, 1965); dashed line is detailed curve for northwestern
Gulf of Mexico (from Curray, 1960; 1961).
-3-
shallow water breeding ground must be relative newcomers to the lagoon,
sometime during the last 6,000 years. In fact, prehistoric La Jolla and
Del Mar Man have had a presence around the lagoon and neighboring river
valleys even before this time (Masters, 1983).
In modern times, sedimentation in the lagoon has taken a rapid up-
turn due to Man's development of the San Marcos River valley and the
construction of the road beds for the railroad, Highway 101 and the
Interstate-5 Freeway which directly encroach on the lagoon.
These developments are summarized in Table #2 together with
recorded rainfall and the sources for these records. Periods of heavy
rainfall concurrent with some of these man made developments resulted in
higher erosion rates and episodes of high sedimentation in the Jagoon.
The corresponding reduction in tidal prism (the volume of water exchanged
between the lagoon and the sea in one tide cycle) has been dramatic. Table
1 gives a listing of tidal prism estimates for Batiquitos Lagoon as a whole
with separate estimates for the west basin (west of 1-5) and east basin
(east of 1-5), from 1887 to 1978, based on work by Gayman, 1978; and
Inman and Frautschy, 1965.
Table 1: Loss of Tidal Prism at Batiquitos Lagoon 1887-1978
Year
1887
1888
1960
1965
1978
Tidal Prism
West Basin
(meters) 3
g2.15 x 10b
c1.85 x 10°
g1.63 x 10°
g1.34 x 10°
Tidal Prism
East Basin
(meters)^
2.17 x
1.86 x
1.66 x
1.43 x
g10b
g10b
g10b
g10b
Tidal Prism
for Total Lagoon
(meters) 3
g
4.32 x 10°
g3.71 x 10°
g3.29 x 10°
g2.77 x 10°
9.43 x 103
GRAPHIC RECORD OF HISTORIC EVENTS . CLIMATIC RECORD AND OTHER OCCURRENCES
PERTINENT TO THE TIDAL HISTORY OF BATIQUIJOS LAGOON
I05O I860 '1870 1080 IQ90 1900 1910 1920 I93O 1940 I95O I960 7970 BED
HISTORIC MOSIGNIFICANTEVENTS
MAPS
c(OH h'.AP
M.-.JOR FLOODS
DHXSEtSiNG CRKR0? MAGNITUDE
A\".:1JAL RilMFALLCITY OFSAN OI£CO
CSY ANDV.'ilT PERIODS
CONSTRUCTIONANDDEV£XOr:/£NT
LAND USE
1 1 1 1 1 1 1
'"'fu'ssgEG0 I-LAMO CnAI.'lS
iB'fhrK^ZRCLST
jcj^ffL^rca,
1 1 1 1 1 1 1 1 1
Tninn •'. '-'.ExiCAM pn HANOO ,1,
115 REY I-?GU\'
'"Cw^If
IOO YR AVER
\\tT
tltAZlNG (CATTLE *f;D SMECP)I
1.1 i ii i i i i
°r
.CtMITOS..c/v;>>.:..'iA eccav.ES
l-VflCELER I-UJC6GS1 SUrtvET
1 10 7 S 56 6
KO • 10 15 J7JOI8 15
iOE • 100" _
1 11
AKOliKE
1 1 1 ' 1 1 1 1 1 1
' 1 STATE »flGHV;AY 101JiNCf&OCO HIOr.VAY O 1 'CHAWING5l» hOAO .-MTRAIS i \.j AFRIAIMTaicT Q<M-I:« 1 P,OIOSH.*H
SiN WtRCOSCftEEK fLOOO,
• O HOO • O ODD X^
9 K 2 11 II 4 18 . 12(7 16
12 7 6079 28 6 866
J \ } t
1 1 1 1 1 1
H88WP I-Z6UIB*
o
15
6 I
*1
JUvra-Lnj-^-n-
r
111! HIGHWAY lOt l-RilL^CiO Rt-AtlEK'UENT ^-^-{nenioGC t-moK-.vif o< OC^STB (vc-vsyssE) VsyviGt.
. (i'i v 1 K?v.' '-LAND FILL LfiGrvSr'^ CJS-H.1RG£[-»"AS V-HrSAl'/iY IOI ItrtioSt j-l-5 FKEEV/AY
BRiDGt ^ |_ gj^ gjp-j-j rjiCEK
Table 2. From G.G. Kuhn (in prep)
<*.OL\V.V ' ' -•:• •: ••.-.V" •• '.:. '.•••.v". '\, *-•-•- ••• . •„., • .'• ...
M•:* '••• ;;v^Me'*-o;o '•-!:^^i^y-.uc-;t< -: ••-.
A/r-v\'mi*^ •• /^- •• v. •*• •^4W^-;/:^^^^,:'. :•'< -!>\4v>$w$<ti;$<f* .•*&*'< s .-J^1'-" "-' v
,-v, .-»..».,•.. ,v» • ..."^MrtvV'^A • ic-4* -v • v .•••'•• >: '••; j• '.•''. ,•••''•>;.'••»• v -v. ; !i'«.f.V .v\x\!,rk'>' >..\. 'si^-1 ; • .'•• v* ' -W ,,v.h-i >''-v ..:;•. ... •.'(• 'VA."-N\ '• .»/?.•»" ;•i>.,"U V / ,."'•»"• .;.;•... --^^^vuSv :• i.^,*'-1* •• •-'• •' •••/ '^UV:r:^M-«:;';M--v:::.,.'v •' -.
SCALE: I'11 = 2000'» .
...... • .' >• '••\. >
' V- "•'. '.
.•.M.;,V:
'.;:'•••••;» \-...;-':, '.I''.'.••, '/.JVt.A-i.V:'.;;.,.. .}•••• >' ;- ...',. ., i ;. \?•:>«..•!»>••('•\ T • i • , 1 -i*> v) • •:• >• V- • i. '. ,-\ i • U. .'t.ip y-i \,a^\^^v*i|a:M^u%-ir
-:A*A1':.- '"'''
Figure 2 California Southern Railroad Map, 1881. Three parallel lines indicate proposed railroad
route. Note 3000 ft. long south tidal channel and 1100 ft. north channel. Lagoon Entrance
channel is about 6-700 ft. south of present highway bridge.
-6-BEST
QMGINAL
:.<-tv.C*rv - v .A •' :vi . - • .:-.v- ••;-__> •--.• j. '• ^ -:^^-r .-.--r-vv. • -..^-^^=L-C-> ^
SCALE: 1" = 2000'
Figure 3. U.S. Coast & Geodetic Survey 1887-8 Map (#1899) of northern half of Batiquitos
Lagoon. No entrance channel is shown. Reduced copy is not too clear, but suggests road
may run across beach between lagoon and ocean. Note 3300 ft. road (or wagon track) across
northern lagoon embayment.
O
SCALE: 1:62,500
Figure 4. U.S. Geological Surgey Map, Oceanside 15' Sheet 1898 clearly shows no channel connecting
lagoon with sea. Road without bridge runs between lagoon and the ocean.
V
Figure 5. Lagoon area map showing the total acreage and the bridges at Carlsbad Blvd., the Santa Fe
Railroad and Interstate 5.
-9-
We find that Batiquitos Lagoon maintained an excess of 3 x 10
meters of tidal prism up until the mid-1960's. Historical photos and
surveys indicate a natural open inlet throughout most of this period.
A detailed analysis of the inlet configuration shown in historical survey
data is contained in the University of San Diego Report, 1978.
The inlet channel was permanently stabilized at the northern side of
the lagoon by the construction the Highway 1 bridge in the late 1920's.
Before bridge construction the inlet channel would naturally move back
and forth between the adjacent headlands. The movement of the inlet
channel was caused by wave climate changes and the consequent changes in
longshore transport rate and direction. Figure 2 shows the inlet channel
near the southern headland. Figures 3 and 4 not only show no inlet
channel but show a road across the lagoon entrance. With rapid
development of the drainage basin from the mid 1960's on, combined with
record rainfall and flooding during the winters of 1977-78, 1979-80 and
1982-83, the tidal prism of the lagoon has suffered a drastic reduction.
The records of the aerial photo bank indicate that the inlet to the sea
under the Highway 101 and railroad bridges was open only sporadically at
the reduced tidal prisms during the 1970-80 period.
The inlet sill depth plays a critical role in determining the
magnitude of the tidal prism. Only that portion of the tidal excursion
laying above the inlet sill depth will force an exchange of water between
the lagoon and the sea. Batiquitos Lagoon has two such critical sill
depths, one beneath the Highway 101 bridge and the other beneath the 1-5
bridges. The road bed of these two bridges constrain natural adjustments
to the sill depths, see Figure 5.
10 15
9 - 14
UJ
6
1
• 0
1
13
ho} 12
10
*
BATIQUITOS LAGOON
TIDES
1 1 1 1 I I I 1 1 1 1 1 1 1 1
0
15 BRIDGE
RR BRIDGE
PIER
• / •\ \ i ;
\ \ //1*'
, •. /\ \ ,
1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 ' I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I
024 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24
P.4FEB80 25FEB80 26FEB80
(NOAA Tide Stations #9410339, #9410342 and #9410230.)
i
o
Figure 6. Spring Tides over three day period when lagoon was open to tidal action in 1980.
-n-
The resultant effects on tidal range inside the lagoon is clearly
shown by tide gauge measurements taken in 1980 and plotted in Figure 6.
The tidal variation measured in the west basin beneath the railroad bridge
follows the tidal variation in the open sea as measured at Scripps Pier,
with about a one-foot attenuation in tidal amplitude due to frictional
losses through the inlet. However, the tidal variations at the 1-5 bridge
are flat over the low tide portions of the records with no change below
-1.0 ft MSL. Thus the sill depth in front of or beneath the 1-5 bridge
must be about -1.0 ft MSL with the effect of greatly diminishing the tidal
prism in the east basin. Since the lagoon was receiving flood runoff during
this period, these tidal variations are more representative of a "best case"
from the standpoint of tidal exchange in the lagoon during the recent past.
During the summer months no exchange at all occurs beneath the railroad
bridge. Figure 7 is a photograph of the lagoon in late July, 1975 showing
the inlet channel clogged with sand and mud flats beneath the railroad
bridge. Figure 8 shows the inlet channel when there is some exchange of
lagoon and ocean water during high tides with wave overwash. Figures 9 and
10 show the lagoon when it is open to tidal action with the sill at about
MSL.
Besides inlet(s) sill depth, tidal extremes will also periodically
alter the tidal prism of the lagoon. Figure 11 gives plots for the extreme
high tides for several locations on the California coast from 1983 until
the year 2000 (Cayan and Flick, 1985). From the standpoint of maintaining
tidal circulation and an adequate tidal prism, the times of greatest
concern are the minimums, e.g., 1987, 1991, 1995, 1996 and 2000. At these
times the amount of tidal range above the inlet sill depths will be
the smallest, and the tidal prism and tidal circulation will be minimal.
This is of particular concern to the inlet(s) themselves. If high waves
Figure 7. Aerial photograph taken July 31, 1975 showing the lagoon entrance channel
plugged with sand. (Aerial Photobank, Sorrento Valley, CA.)
/3
c>$*«T
. "* f J ^
Figure 9. January 27, 1979. (Aerial Photobank, Sorrento
Valley, CA.)
Figure 10. January 1, 1985, (Aerial Photobank, Sorrento
Valley, CA.)
'
PREDICTED EXTREME HIGH TIDES
fl
9.0 r
8.0'-
7.0
6.0 L-
7.0
6.0 L
HUMBOLDT
crii
LOS ANGELES
1983 1984 1985 1986 1987 1988 1989 1990 199! 1992 1993 1994 1995 1996 1997 1998 1999 2000
Figure 11. Plots of predicted extreme high tides 1980-2000.
-17-
happen to occur at these same periods when tidal flow and scour through
the inlets is smallest, than the inlets may permanently close.
II. Inlet Processes
A natural inlet maintains a precise equilibrium with the tidal
prism which is dependent upon the amount of wave power that is directed
along shore. A natural inlet maintains its stability through a steady
state balance between tidal scour and wave induced sand transport. This
balance may be expressed in terms of the energy fluxes associated with
these two competing processes. If the energy delivered longshore by
wave action during the flood phase of the tide cycle is less than the
energy available in the ebb flow of the same tidal cycle, than the inlet
will remain open. The wave energy varies as the breaker height H. , and
breaker angle,oC» whereas the ebb flow energy is dependent upon the tidal
prism V and the tidal range above the sill depth, ~r. Thus there is a
minimum tidal prism V . , that will maintain an open inlet under attack
by waves of a given height and direction. Following the work by O'Brien
1980, the minimum tidal prism is given by
2T.-W Hr; Cn sine*. cosoC
V - F b (1)vPmin - u;
where TF is the duration of flood tide, C is the group speed of the
breaking waves and W is the constrained channel width as determined by the
available span beneath the bridges = 43.8 meters.
There is no possible unique answer for a minimum tidal prism from
equation (1) since the wave climate and tidal ranges will vary in time as
independent random variables. Instead we calculate a minimum tidal prism
for a set of recurrence intervals of closure based on wave and tide statistics
-18-
(thati.s the time between inlet closure if the tidal prism were a particular
value). To do this, deep water wave statistics published as occurrence
tables in DNOD (1977) and Marine Advisors (1960) were shoaled to Batiquitos
Lagoon inlet on a digital computer using a linear ray shoaling trans-
formation adapted from Dobsen (1967). The resulting shoaled breaker
heights, directions, and group speeds after accounting for directional
island shadowing effects from San Clemente, Santa Catalina, San Nicolas
and Santa Barbara using a data adaptive technique from Pawka, et al., 1982,
are tabulated in Appendix Tables Al through A12. Fortunately the largest
waves and lowest tides seldom occur simultaneously. For this reason the
minimum tidal prism for a given closure recurrence interval is less than
the sum of the individual components (waves and tides) for the same
recurrence interval. Instead, the recurrence interval of closure for a
given minimum tidal prism must be calculated from the individual probability
distribution using a double convolution integration given in Papoulis (1965),
The results are found in Table 3,
Table 3: Recurrence Interval of Inlet Closure for a Minimum
Tidal Prism at Batiquitos
Tidal Prism Vpml-n (meters)
3.12 x 106
3.05 x 106
2.72 x 106
1.89 x 106
8.24 x 105
3.26 x 104
Recurrence Interval of Closure, years
30
20
10
5
1
0.2
-19-
Th us the pre-1960 values of tidal prism for the combined east and
west basins of the lagoon are all above the critical minimum necessary to
maintain the inlet open to the sea against attack by the largest waves and
minimum tides recurring every 30 years. Comparing Table L-and Table 3,
we find the present small tidal prism will result in inlet closures about
five times each year. It should be remembered that such statistical
manipulation is better suited for identifying trends rather than absolute
values. The figures in Table 3 do however support the available survey
and photo evidence.
Having identified the approximate size of minimum tidal prisms which
will maintain an open inlet against wave attack, we can now specify the
required inlet cross sectional area. The relation between tidal prism and
inlet cross section has been understood for some time. O'Brien (1931)
was one of the first to show this relation plotted in Figure 12 but
with limited data. Inman and Frautschy extended this to values
0 (106m3) and below, and Inman and Harris (1966) found additional
supporting data. Reading Figure 12 for the value of a 30-year recurrence
closure, V = 3.12 x 106 m3, we find that an inlet cross-section of
2215 m would be required.
III. Methods to Maintain Tidal Circulation
Two basic approaches are offered to maintain tidal circulation in
the west basin of the Batiquitos Lagoon. These are equilibrium and
non-equilibrium methods. Equilibrium methods basically involve restoring
sufficient tidal prism to maintain the lagoon entrance by natural tidal
scour. Non-equilibrium methods involve power augmented systems to maintain
an open lagoon in spite of a non-equilibrium configuration. The primary
motivation for non-equilibrium methods is to avoid excavation of large
volumes of material.
I05
San Francisco Bay
Columbia R. ..
Willapa Bay .
no4 -
LJ
22
<
I
O
UJ
O ABSECON INLET
Gray's Harbor .
San Diego Bay •jHumbolt Bay
Coos Bay .oQui Nhon
Umpqua R . /
xjillamook
Chu Lai '/
Absecon Channel ^ X, »H.ue
I0
2
UJ
O
Main Channel-
Coquille
Newport Bay »v
>i»Yaquina Bay
,AJ\lehalem R.
Mission Bay (Mar. 1954)
ro
oi
UJtr
I02
'Gamp Pendleton (Feb. 1956)
• DIURNAL RANGE
A MEAN RANGE
a TROPIC RANGE
J L 1 '
1 ' ' 1—L.• • i 1 L.
10 =I06 I07 I0e
TIDAL PRISM , M3
10s 1010
Figure 12. Tidal prism versus inlet area (Inman and Frautschy, 1965;
Inman and Harris, 1966).
-21-
A) Equilibrium Method
According to Table 2, excavation of the 'lagoon to create a tidal
fi ^prism of 3.12 x 10 m will essentially restore a self-maintaining inlet.
Considering the existing tidal prism, this would require excavation of
fi "34.07 x 10 yd from the lagoon system. If both the west and east basins
are included together in this excavation, it appears feasible to remove this
large volume of material without endangering California Least Tern nesting
sites. One possible scheme would not disturb the existing perimeter region
of the lagoon above the +3.5 feet MSL contour. Below the +3.5 feet MSL
contour, the bank would be graded downward at an average slope of -3% until
-5.0 feet MSL is reached, where 0 feet MSL corresponds to +2.88 feet MLLW.
Along the existing stream bed and flood channel the bottom will be maintained at
-5.0 feet MSL to form a flood channel of at least 144 feet in width. In
certain bottleneck sections of the lagoon there will have to be local
bank slopes steeper than -3% in order to maintain a flood channel of
sufficient width at -5.0 feet MSL depths. The resultant excavated volumes
by this scheme are about 1.0 million cubic yards removed from the west
basin and 3.0 million cubic yards from the east basin. In the process a
wetlands belt whose average width is about 180 feet is created between
the MLLW and MHHW shore contours inside the lagoon. On the other hand
a sufficient deep water cross section is maintained in the tidal channel
to permit tidal flux without extreme bottom friction losses.
The borings conducted in the east and west basins by Woodward and
Clyde, 1985, indicate three-dimensional sedimentary deposits in the portion
of the upper two feet of this proposed excavation containing significant
fractions of fine silts and clays. This material totaling about 581,000
cubic yards will have to be dispersed in landfill sites. The remaining
fi }sediments in the proposed excavation, totaling about 3.488 x 10 yds ,
are suitable sand sized material (0.16 to 0.25 mm) for beach nourishment.
-22-
Thus the high costs of excavating such a large volume of material could
be offset by selling that material to neighboring communities who are
suffering extreme beach erosion. If these communities are not capable of
accepting part or all of the suitable sand fractions at the time of
excavation, then that material could be stored as a vegetated beach dune
behind the berm crest of the beaches in the immediate neighborhood.
The excavation should take place during the summer months when the
lagoon is dry. A dry lagoon would enable large earth moving equipment to
remove a considerable amount of material at one-fifth the cost of dredging.
The earth moving equipment will be effective only down to the water table
and then clam shell or dredging will be required. The dredging would
proceed systematically from west to east utilizing the ocean as a water
source. Because the lagoon is partitioned into three sections by the
bridges there will most likely be three dredge mobilization costs
($200K-$300K each). Even though there is no reason to expect the dredge
spoils to be contaminated they will need to be analyzed for EPA priority
pollutants (organics and trace metals). There are EPA certified labs
in the area who will know the required number of samples and analysis
procedures. The top few feet of the lagoon sediments are silty clays
which can be used for fill in the adjacent developments. The sand beneath
this silty clay can be sold for beach nourishment.
B) Non-Equilibrium Methods
Bull-dozer and Pilot Channel: This is the most common stop-gap method
in use on both coasts today. For one reason or another, the minimum tidal
prism cannot be restored and the inlet closes on a regular basis.
Evacuation of only 1.065 x 10 yds will result in an inlet closure about
once every year. However, a pilot channel dug by a bull-dozer at low tide
-23-
5 3will release a prism of 8.3 x 10 meters that will scour open a channel
Pwith 72 meters cross section. This channel should remain open for another
year under statistically normaly seasons of waves and tides. The bull-dozer
must remain on standby since the time of the next closure is uncertain.
The required dredged project depth for this method would be -5.04 feet MSL
for the 131.2 acres comprising the west basin. The channel depth that
would maintain the required cross section and yet fit between the 144 foot
span of the Carlsbad Blvd. bridge would be at -5.38 feet MSL. Because of
the bridge clearance a smaller piece of earth moving equipment such as a
"bobcat" will be required to work beneath the bridge. The smaller equipment
will feed the bulldozer which will in turn push the material to the
downdrift beach.
C) Fluidizer System with Jetties
This approach has the same dredging requirements as the bull-dozer
pilot channel method. It would use a permanent fluidizer/eductor system
to maintain the channel against periodic closure (Jenkins et al., 1980).
It requires two 400 foot long jetties which span the beach berm and protect
the system from ingesting cobbles. The entrance will be artificially
narrowed by placing the jetties at 106 feet apart, yielding maximum flood
currents of 89 cm/sec. Thus the jetties are also required to prevent bank
erosion. However the high flow speeds prevent shoaling of longshore
transport in the channel. Instead a shoal will result inside the lagoon as
the flow diverges and the suspended load is deposited. The fluidizer system
is placed on this shoal where it is protected from direct attack by waves.
The fluidizer system is shown schematically in Figure 13. It
consists of a pipe with high pressure jets injecting water into the shoal,
causing it to form a slurry which moves readily down shallow gravity slopes.
At the base of the shoal an eductor pump collects the slurry and pumps the
CRATER-
SINK
WATER LEVEL-
INJECTION WATER
FLUIDIZING PIPE
'\
,SAND FLOW
BUNDER PIPE
•WATER LEVEL
INITIAL SURFACE
',f|fi*W SURFACE \ S / ,'
.'' ' l|f l' I i i ' \>—^f t ' t D I D C l!'1 l *" ' ' i i ' * ''
. i '' , ' t V' '. '* IV t, i J' , i' f»\ .^
''l':jv !';;OUCT' 'FLOW •.',•;.," .•; (^'^:^''
1,., v , >' ' ,\i, *'',') '* A" %
Figure 13. Schematic diagram of duct-flow fluidization: (A) angled water jets from bottom nozzles
in the fluidizing pipe suspend sand and move it along the oval duct formed beneath the pipe;
and (li) sand feeds down the natural angle of repose (about 30°) perpendicular to the
fluidized duct. As the sand enters the duct it is carried along axially and finally dis- •
. charged into deeper water or into a crater-sink, (from Bailard and Ionian, 1975).
rv>-c»i
-25-
sand back to the downdrift beach which will normally be that portion south
of the jetties. The nominal longshore transport of sand which the fluidizer
must bypass across the inlet in this manner is 215,000 yds . The pumping
system required to bypass this amount of 0.2 mm size sand would have a
2,000 gpm flow rate and operate a 158 hp at a todal head of 244 feet.
The fluidizer pipe required would be 6" diameter and 400 feet long, having
1,920 jets, each with a diameter of 0.064 inches. Figure 14 shows the water
jets and fluidizer pipe used to open the Los Penasquitos Lagoon in May
1977 (Figure 15).
D) Drag Bucket and Pier
With this method a very small design tidal prism is chosen while
3"brute force" is employed to maintain the inlet. As little as 30,000 yds
could be excavated from the west basin. Closures of the inlet could be
expected about five times annually, perhaps more. A 400-foot long pier is
built from the Highway 101 bridge out across the surf zone. A mobile crane
is operated from the deck of the pier which drags a bucket from the lagoon,
seaward. The material dug from the inlet channel is deposited in the surf
zone where longshore transport by waves moves the material away from the
inlet. Since no hydraulic equilibrium is involved, any arbitrary channel
depth and width which permits tidal circulation may be chosen.
E) Syphon
This method abandons an open channel inlet to the lagoon altogether.
Instead a 6.0 foot diameter syphon pipe is buried at -2.0 feet MSL between
the lagoon and the 025 feet MSL contour on the ocean side of the inlet.
Tidal variations in the ocean side will circulate water in and out of the
lagoon. The concept requires as little as 30,000 yds of excavation to the
present lagoon. However, it has a practical limitation due to biofouling.
A killing agent of some sort is required. Back flushing with hot water
;-26-
f£-~" •"•'• 'K-VvV vvrt*-- '.-.&*. _>*-. \_ •- ""-^^M^E»»u.i.-i -• -tliSiuft*,:- ,k 7-^.'.'--.>tj<s:
Figure 14.
Figure 15.
-28-
is commonly done by coastal power plants. Anti-fouling paints are not
environmentally acceptable. Two pipes with one being reamed while the
other functions as a syphon was used successfully by Scripps Aquarium.
The long term maintenance costs of reaming are a serious detraction to
this approach.
VI. Effects of Salt Water Flux from the East Basin.
A plan for restoration of the east basin of Batiquitos Lagoon has
been advanced that will impact the west basin alternatives for maintaining
tidal circulation to the extent that relatively small quantities of
high salinity water will be introduced. According to the recent version
of the east basin plan, the two basins will be partitioned by a weir
situated near the 1-5 bridge as shown in Figure 5. Because of this weir
only that portion of tidal prism held by the west basin will be free to
circulate with ambient sea water through the inlet under the Highway 101
bridge. Ground water of about 34 /oo salinity will be pumped into the
east basin at a rate of 4,000 gallons per minute. This flow rate is
roughly three times the evaporation rate over the acreage of the east basin.
Because evaporative losses are replaced by 34 /oo salinity ground water,
the salinity in the east basin will exceed the ground water salinity. To
stabilize both the water level and the salinity in the east basin during
the dry summer months, approximately 2,666 gpm must be passed continuously
over the weir from the east basin to the west basin. This action will
stabilize the salinity in the east basin near 50 /oo. In the winter months,
the salinity in the east basin will be considerably less than this due to
the infusion of fresh water runoff from Pacific storms. The pumping of
ground water and the bypassing of water from the east to the west basin
can be greatly reduced, cutoff altogether, or regulated according to
the design water level.
-29-
Thus, the greatest potential adverse effect from the east basin
restoration plan appears to be the flux of 2,666 gpm of 50°/oo salinity
water introduced over the weir into the west basin during summer months.
This will have the greatest effect on salinity elevations during the flood
tide interval when the west basin is holding water. The longest durations
.of flood tide occur near the railroad bridge and have been observed for
as long as eight hours. The west basin could therefore receive and hold
as much as 6,338 cubic yards of high salinity water, before releasing it
into the sea with the insuring ebb tide. The amount by which salinities
are elevated in the west basin during this time depends upon which of
the alternatives outlined in the previous section are implemented.
If the equilibrium methods are adopted in the west basin, then 4.081
x 106 yds3 of 32°/oo ambient sea water will mix with 6,338 yds3 of 50°/oo
bypass water during the flood tide phase. As a result, the salinity in
the west basin will be elevated to 32.028 /oo by the time ebb tide insues.
This is a negligible amount of salinity elevation, only 28 ppm, and is
barely measurable with a standard Beckman analytical salinometer.
If non-equilibrium methods are implemented, then somewhat higher
salinities result in the west basin near the end of the flood tide phase,
For either the bull dozer or fluidizer plan, 1.077 x 10 yds of 32 °/oo
sea water will mix with the high salinity water released from the east
basin. This will elevate salinities in the west basin to 32.105 /oo, or
an increase of 105 ppm above ambient sea level. If the Pier and Drag
4 3line or the Syphon method is implemented, then as little as 4.23 x 10 yds
of 32°/oo sea water will mix with the high salinity discharge from the
east basin. The resulting salinities will rise by the end of flood tide
in the west basin to 34.34°/oo, an increase of 2.34°/oo. This much
salinity elevation during the insuing ebb flow may have measurable effects
on the local marine communities.
-30-
In conclusion, the large tidal prisms afforded by the equilibrium
methods serve as a dilution basin to buffer the beach ecology from the
effects of high salinity discharges from the proposed east basin plan.
The non-equilibrium methods have much less dilution capacity. Some
damage to organisms populating the neighboring beach seems possible for the
small tidal prisms associated with the Pier/Drag line method or the Syphon
method. This damage could be mitigated by increasing the project dredge
volumes above projected minimum values of 3 x 10 yds . How much
additional dredge volume would be needed cannot be determined until
lethal salinity levels for the beach ecology are established.
-31-
PRELIMINARY COST ESTIMATES
1. - Equilibrium Method
6 3Remove 4.07 x 10 yd (Can remove about 581,000 by earth moving,
can dredge about 3.488 x 105).
a. Remove 581,000 yd by earth moving equipment
@ .70/yd3 $ 406,700
b. Dredge 3.488 x 106 yd3
@ $4/yd3 • 13,952,000
c. Total Excavation Estimate Cost 14,358,000
d. Value of removed sediments
3.488 x 106 @ $2.50/yd3 8,720,000
e. Net cost $ 5,638,000
.2. Bulldozer and Pilot Channel Method
Remove 1.065 x 10 yd
3a. Remove approximately 300,000 yd by earth moving equipment
@ $ .70/yd3 210,000
b. Dredge 765,000 yd3 @ $4/yd3 3,060,000
c. Sell removed sands 765,000 yd3 @ $2.50/yd3 1,912.500
d. Net cost to remove 1.065 x 106 yd3 $ 1,357,500
e. Bull doze opening channel 5' x 40' x 100'
Approximately $2,000.00 per opening
3. Fluidizer Method- ~~~ fi "3Remove 1.065 x 10 yd
•a. Remove approximately 300,000 yd by earth moving equipment
@ $ .70/yd3 210,000
b. Dredge 765,000 yd3 <? $4/yd3 ' 3,060,000
c. Sell removed sands 765,000 yd3 @ $2.50/yd3 1,912.500
d. Net cost to remove 1.065 x 106 yd3 $ 1,357,500
e. Fluidizer to maintain channel
(1) System cost $ 14,300
(2) 4 man days labor per opening and
minor energy costs
Preliminary Cost Est.
Page Two
-32-
f. Jetty Construction 2 & 400'
(1) Materials 12,000 tons of 5-ton rock $ 240,000
(2) Mobilization, design installation $ 100.000
$ 340,000or $375.00/ft.
4. Pier and Drag Line Method
43'Remove 3 x 10 yd and build pier
a. Dredge 3 x 104 yd @ $4/yd
b. Pier construction
c. Dragline system
d. Maintenance
50 Syphon Method
4 3Remove 3 x 10 yd and syphon
a. Dredge @ $4/yd
b. Syphon system
c. Maintenance
$ 120,000
515,187
30,000
approx 8,000/yr.
$ 120,000
3,000,000
10,000/yr or more
REFERENCES
Bailard, J. A. and D. L. Inman, 1965, "Analytical model of duct-flow
' fluidization," Proc. Symp. on Modleing Techniques, ASCE, San
Francisco, CA, p. 1402-1421.
Bailard, J. A. and D. L. Inman, 1978, "Opening tidal inlets using sand
fluidization," NOAA Sea" Grant annual report, Scripps Institution of
Oceanography.
Benton Engineering, Inc. , 1964, "Soils Investigation, La Costa Beach Inn,
West of Highway 101, North of Leucadia, California" prepared for Tracy
Price Associates, Planning, Engineering, Architects, 21 pp.
Bruun, P. 1966 Tidal Inlets and Literal Drift, Norway.
Cayan, D. R. and R. E. Flick, 1985, "Extreme Sea Levels in San Diego,
California, Winter 1982-1983," Scripps Institution of Oceanography,
University of California, SIO Reference No. 85-3, 58 pp.
COE LAD, 1971, "Flood Plain Information San Marcos Creek, San Diego County
California," U. S. Army Corps of Engineers, Los Angeles District,
April 1971, 30 pp. with plates and appendices.
Costa, S. L. and 0. D. Isaacs, 1975, "Anisotropic sand transport in tidal
inlets" Proc. of the Symposium on Modeling Techniques, ASCE/San Fran-
cisco, CA Sept. 3-5, 1975 p. 254-273.
Curray, J. R., 1961, "Late Quaternary Sea Level:! a discussion", Geoldgical
Soc. Amer.. Bull., v. 72, n. 11, p. 1707-12.
Curray, J. R., 1965, "Late Quaternary history, continental shelves of the
United States", p. 723-735 in H. E. Wright, Jr. and D. G. Frey (eds)
The Quaternary of the United States, Princeton Univ. Press, 922 pp.
DNOD, 1977, "Deep water wave statistics for the California Coast, Station 5."
Department of Navigation and Ocean Development, Sacramento, California,
37 pp.
Dobson, R. S., 1967, "Some applications of digital computer to hydraulic
engineering problems", Tech. Rep. No. 8£, Dept. of Civil Engineering,
Stanford University.
Gayman, W., 1978, "Estimation of Present and Past Tidal Prisms in
Batiquitos Lagoon," June 3, 1978, 17 pp.
Harris, R. W., D. L. Inman, J. A. Bailard, and R. L. Oda, 1976, "Study
and Evaluation of Remedial Sand Bypassing Procedures," U. S. Army
Engineers Waterways Experiment Station Contract Report H-76-1.
Hagyard, T., I. A. Gilmour, and W. D. Mottram, 1969, "A Proposal to Remove
Sand Bars by Fluidization," New Zealand Journal of Science, , v. 12,
p. 851-864.
Inman, D. L., 1983, "Application of coastal dynamics to the reconstruction
of paleocoastlines in the vicinity of La Jolla, Calif.," p. 1-49 in
P. M. Masters and N. C. Flemming (eds) Quaternary Coastlines and Marine
Archaeology, Academic Press, London, 641 pp.
Inman, D. L. and J. D. Frautschy, 1965, "Littoral Processes and the
Development of Shorelines," Coastal Engineering. (Santa Barbara
Specialty Conference), Amer. Soc. Civ. Engrs.. p. 511-536.
Inman, D. L. and R. W. Harris, 1966, "Investigation of sedimentation and
dredging requirements, various locations, Republic of Vietnam," prepared
for U.S. Navy, OICC Republic of Vietnam, under contract by 78944 with
Daniel, Mann, Johnson and Mendenhall, Saigon, 237 pp.
Inman, D. L. and S. A. Jenkins, 1984, "Oceanographic Report for Oceanside
Beach Facilities," prepared for the City of Oceanside, 266 pp.
Jenkins, S. A., D. L. Inman and J. A. Bailard, 1980, "Opening and
Maintaining Tidal Lagoons and Estuaries," Proc. 17th Conf. on
Coastal Engineering, Sydney, ASCE, p. 1528-1547.
Kuelegan, G. H., 1951, "Water Level Fluctuations of Basins in Communication
with Seas," Third Progress Report on Tidal Flow in Entrances, U.S.
Beach Erosion Board.
Kuhn, G. G. and F. P. Shepard, 1984, Sea Cliffs, Beaches and Coastal
Valleys of San Diego County: Some Amazing Histories and Some
Horrifying Implications.University of California Press, Berkeley
and Los Angeles, California, 193 pp.
Marine Advisors, 1961, "A Statistical Survey of Ocean Wave Characteristics
in Southern California Waters," prepared for the U.S. Army Corps of
Engineers, L. A. District, Technical Report. EN 14714, 30 pp.
Masters, P. M., 1985, "Coastal Evolution and Marine Archaeology in
Southern California," Oceanus, v. 28, n. 1, p. 27-34.
Murray, W. A. and A. G. Collins, 1978, "Fluidization Applied to Sediment
Transport - II," Lehigh University, Fritz Engineering Lab Report 710.2.
Newitt, D. M., et al., 1955, "Hydraulic Conveying of Solids in Horizontal
Pipes," Trans. Inst. Chem. Engin., v. 33, p. 93-110.
George S. Nolte and Associates, 1983, "The Batiquitos Lagoon plan:
a feasible solution to the restoration and enhancement of an important
natural resource", prepared for Hunt Properties, Inc., Dallas, Texas,
13 pp.
O'Brien, M. P., 1931, "Tidal prisms related to entrance areas," Civil
Eng., v. 1, n. 8, pp. 738-739.
O'Brien, M. P., 1980, "Comments on tidal entrances on sandy coasts,"
Proceedings, ASCE Coastal Engineering Conference, v. 3, p. 2504-2516.
Papoulis, A.,, 1965, "Probability, Random Variables, and Stochastic
Processes," Geological Soc. Amer..Bull., v. 72, n. 11, p. 1707-1712.
Pawka, S., 1983, "Island shadows in wave directional spectra," Jour.
Geophysical Res., v. 88, n. C4, p. 2579-2591.
Richardson, T. W. and E. C. McNair, Jr., 1981, A Guide to the Planning
and Hydraulic Design of Jet Pump Remedial Sand Bypassing Systems,
U. S. Army Engineer Waterway Experiment Station, Instruction Report
HL-81-1.
Salazar, M. H., S. C. U'ren, and S. A. Steinert, 1980, "Sediment Bioassays
for NAUSTA San Diego Dredging Project," Naval Ocean Systems Center.
Technical Report #570, April 1980, 46 pp.
University of San Diego, Environmental Studies Laboratory,1978, "Tidal As-
pects of Batiquitos Lagoon 1850 to Present" prepared for County of San
Diego.
Weisman, R. N., A. G. Collins and J. M. Parks, 1980, "Stabilization of
Tidal Inlet Channels by Fluidization," Proc. Conf. on World Dredging,
WODCON IX, Vancouver, B. C.
Woodward-Clyde Consultants, 1985, "Soil Test Boring Logs Grain Size
Distribution Data Batiquitos Lagoon, Carlsbad, California," prepared
for Sammis Properties, San Diego, CA.
APPENDIX TABLES A 1 - A 13
NORTH SWELL SHOALED BREAKER HEIGHTS, ANGLES AND GROUP SPEED
(From DNOD data, station # 5)
Hoo = deep water wave height (meters)
K = breaker height (feet)
"^b = breaker angle (degrees)
Cn = group speed (feet/sec)
Table A-l INTRA-ISLAND DEEP WATER DIRECTION =245°
Hb=ft. , °*> =deg. , Cn=ft./sec.
T HQQ
Hb
9.4
sec °<b
Cn
Hb
12.2 °U
sec Cn
Hb
17.0 o<b
sec Cn
O.lm
0.57
+1.95°
4.62
0.99
+2.02°
6.13
1.45
+3.51°
6.96
0.5m
2.58
+1.31°
9.65
2.94
1.30°
10.58
3.18
+2.81°
11.14
1.0m
4.70
+1.01°
12.98
5.13
+1.55°
14.05
5.34
+2.10°
14.39
1.5m
6.64
+0.68°
15.33
7.26
+1.65°
15.95
5.21
+3.51°
13.89
2.0m
8.55
+0.38°
17.15
9.14
1.51°
18.16
9.01
+2.65
18.42
2.5m
.10.22
+0.001°
19.62
10.94
+1.18°
20.09
10.57
+3.07
20.08
3.0m
12 ,09
0.09°
20.55
12.74
+0.62°
21.59
12.00
3.33°
21.74
TABLE A-2 ZNTRA-ISIAND DEEP WATER DIRECTION =267°
rn TT ^^
Hb
9.4 ^
sec
Cn
Hb
12.2 o<b
sec
Cn
Hb
17.0 <*b
sec
Cn
O.lm
0.94
3.33°
6.01
1.77
3.73°
8.25
0.70
3.77°
5.26
0.5m
3.31
3.57°
11.46
3.26
2.44°
10.94
3.01
0.34°
10.42
1.0m
5.82
4.7°
14.53
5.64
4.21°
14.50
5.89
0.37°
14.44
1.5m
8.10
5.92
16.86
6.94
2.91°
16.26
7.87
1.06°
17.15
2.0m
10.10
7.5°
19.50
8.88
2.99°
17.68
9.79
1.44°
19.02
2.5m
11.23
5.8°
19.81
10.38
2.98°
20.26
10.64
0.29°
20.16
3.0m
13.03
7.04°
21.58
12.15
2.94°
21.23
12.64
0.54°
21.35
TABLE A-3: INTRA-ISLAND DEEP WATER DIRECTION =277°
rn TT
Hb
9.4 °^b
sec
Cn
Hb
12.2 <*b
sec
Cn
Hb
17.0 <Xb
sec
Cn
O.lm
0.99
2.22°
5.96
0.78
5.8°
5.31
0.81
4.76°
5.74
0.5m
3.23
2.02°
11.28
3.06
4.63°
10.74
3.86
4.71°
11.86
1.0m
5.17
5.47°
14.09
5.22
4.28°
14.40
7.07
2.12°
16.08
1.5m
7.18
6.49°
15.94
7.43
6.31°
16.76
9.75
2.57°
18.71
2.0m
8.87
7.92°
18.33
10.09
4.53°
19.67
11.79
2.84°
21.74
2.5m
9.14
8.19°
18.73
12.19
5.42°
21.14
13.96
2.85°
23.34
3.0m
12.57
8.76°
20.63
14.31
6,03°
22.13
15.95
2.75°
24.65
TABLE A-4 INTRA ISLAND DEEP WATER DIRECTION =287°
O.lm 0.5m 1.0m 1.5m 2.0m 2.5m 3.0m
Hb 0.64 3.98 6.84 9.60 12.00 14.33 16.22
9.4 <*,. 5.92° 7.43° 11.32° 13.25° 15.27° 16.58° 18.21°
sec
Cn 4.94 11.98 16.34 18.51 20.76 22.44 24.50
SOUTH SWELL SHOALED BREAKER HEIGHTS, ANGLES AND GROUP SPEED
(from Marine Advisors data, station C)
= deep water wave height
Hb = breaker height (feet)
°<-b = breaker angle (degrees)
Cn = group speed (feet/sec)
TABLE A-5 INTRA ISLAND ITOP WATER DIRECTION
T
13
sec
15
sec
17
sec
19
sec
HOO
Hb
*b
Cn
Hb
*b
Cn
Hb
*b
Cn
Hb
^
Cn
0.5ft.
0.94
-10.50°
5.87
1.19
-10.78°
6.76
1.49
-9.66°
7.38
2.77
-11.97°
10.40
1.5ft.
3.13
-12.91°
11.02
3.23
-11.19°
11.21
3.34
-7.19°
11.34
3.13
-8.22°
10.81
2.5ft.
4.83
-15.62°
13.43
4.02
-17.29°
12.66
5.07
-9.86°
13.93
4.49
-11.79°
12.99
3.5ft.
6.28
-15.14°
15.45
5.33
18.33°
13.86
6.74
-10.96°
15.62
5.73
-14.58°
15.05
TABLE A-6 INTHA ISLAND DEEP WATER DIFECTICN =202o
T HOO
Hb
13 <*b
sec
Cn
Hb
15 ^b
sec
Cn
Hb
17 ^
sec
Cn
Hb
19 tffe
sec
Cn
0.5ft.
1.06
-8.4°
6.24
0.88
-7.74
5.69
0.89
-7.82°
5.79
1.03
-6.99°
5.99
1.5ft.
3.51
-11.42°
11.52
3.56
-10.40°
• 11.40
3.29
-6.80°
11.35
3.75
-7.96°
11.67
2.5ft,
5.36
-12.98°
13.86
4.42
-8.42°
12.61
5.40
-3.55°
14.58
5.41
-8.49°
14.23
3.5ft.
6.99
-14.56°
16.19
5.79
-9.43°
14.70
7.04
-3.77°
16.77
6.97
-8.73°
16.05
TABLE A-7 INTRA ISLAND DEEP WATER DIRECTION =225°
T Hoo
Hb
13 C*b
sec
Cn
Hb
15 ^b
sec
Cn
Hb
17 %,sec
Cn
Hb
19 «k
sec
Cn
- 0.5ft.
0.92
-0.39°
6.01
1.07
-0.84°
6.35
1.01
+1.63°
6.09
1.36
+4.06°
6.94
1.5ft.
3.06
-5.41°
11.54
3.08
-3.74°
10.78
3.10
-5.86°
10.58
3.11
-1.28°
10.48
2.5ft.
4.09
-6.63°
12.12
3.73
-4.05°
11.57
4.53
-5.67°
12.86
4.57
-3.98°
12.75
3.5ft.
5.37
-6.41°
14.08
5.83
-6.06°
15.11
5.93
-5.61°
14.50
5.89
-5.53°
14.73
TABLE A-8 H7TRA ISLAND DEEP WATER DIRECTION =240°
m TT
Hb
9.5 <**
sec
Cn
Hb
12.2 <*b
sec
Cn
Hb
17.0 °^
Cn
0.5m
2.72
+2.06°
10.20
5.56
+0.23°
14.93
3.22
+0.80°
11.11
1.0m
4.73
+3.46°
13.55
9.54
+0.62°
18.56
5.69
+0.85°
14.31
1.5m
6.59
+3.63°
15.76
12.53
+0.63°
. 21.98
7.77
+0.45°
17.20
2.0m
8.33
+3.67°
17.55
15.07
+0.56°
23.91 '
9.86
+0.33°
18.90
2.5m
10.14
+3.80°
18.54
16.90
+0.75°
25.36
11.64
+0.25°
21.11
3.0m
11.04
+4.32°
19.93
18.46
+0.65°
26.40
13.35
+0.34°
23.00
SHOALING WAVES DUE TO LOCAL WIND GENERATION
(from Marine Advisors data, station C)
TABLE A-9 DEEP WRIER DIRECTION BAND; 304-326°
T Hoo 0.5ft. 1.5ft. 2.5ft. 3.5ft.
Hb 2.74
9
sec
3 b 19.61°
sec
Cn 9.31
Hb
5 4.01 4.57
Sec ^V>
21.07° 23.41°
Cn 11.52 12.96
Hb 4.31
7 ^ 16.52°
sec C* 12.13
TABIE A-10 DEEP WATER DIRECTICN BAND; 282-303'
T
3
sec
5
sec
7
sec
Hoo
Hb
Cn
Hb
Cn
Hb
«b
Cn
0.5ft. 1.5ft. 2.5ft. 3.5ft.
3.06
23.59°
10.74
3.86 6.89
12.86° 19.13°
11.86° 15.77
7.32
18.38°
16.34
TABLE A-ll DEEP WATER DIRECTION BAND 259-28Oc
T HOO
Hb
3 sec *i
Cn
Hb
5 sec °^i>
Cn
Hb
7 sec <*v,
Cn
Hb
9 sec o^
Cn
1.5ft.
1.74
15.40
7.71
1.88
17.84°
8.47
2.48
10.82°
9.87
2.5ft.
2.83
13.96
10.32
4.16
20.68°
12.09
4.47
18.12°
12.5
3.5ft.
6.94
19.67°
14.88
5.43
20.66°
13.97
5.82
19.23°
14.60
TABLE A-12 DEEP WATER DIFECTICN BAND 237-258°
T
3 sec
5 sec
7 sec
9 sec
H.»
Hb
<*b
Cn
Hb
Cn
Hb
Cn
Hb
Cn
1.5ft. 2.5ft. 3.5ft.
1.76
9.21°
8.24
1.80 3.53
11.61° 7.79°
8.34 11.40
2.25 4.99
11.49° 11.84°
9.17 13.45
6.19
7.01°
15.13
TABLE A-13 HFFP WATER DIRECTICN BAND 180°-225e
rn TJ
Hb
3 b
sec
Cn
Hb
c oa't,•J "0
sec
Cn
Hb
7 C^uo
sec
Cn
Hb
9 ^sec
Cn
1.5ft. 2.5ft. 3.5ft. 4.5ft.
1.93
14.38
' 8.26
2.02 3.0 6.28 7.04
19.74 19.47 16.73 18.33
8.08 10.22 15.45 16.17
3.01 5.45 6.99
18.86 19.27 14.56
10.28 13.9 16.19
2.63
17.36
10.21