PropeJ1y 01 tte Uniled States Government USCEC MR 81-4 

Movable-Bed Laboratory Experiments 

Comparing Radiation Stress and 

Energy Flux Factor as Predictors 

of Longshore Transport Ra te 

by 

Philip Vitale 

MISCELLANEOUS REPORT NO. 81-4 

APRil 1981 

Approved for public release; 

distribution unlimited . 

U.S. ARMY, CORPS OF ENGINEERS 

COASTAL ENGINEERING 

RESEARCH C ENTER 

Kingman Building 

Fort Belvoir, Va . 22060 
Rep r ln t ~. repuhl1ca c!on of dnl' of t il!' material 

s!lall glv ~ appr" prlate "redit to lhe u.s. ~rwy C"".t 1 

Engln~~rlng s~acch Ce nle r . 

Ltcll t l:d free o i strlbu ej'Ja wlchtn the Unit e.d Sta ~§ 

of ~l !\le " op!"" DC t hLs pub ticn [ ion !lAs b"~n Ill.: de by 

this (;erlte r . Mtll,1oMl c"pies are a"a ll ~bl , frum : 

1atiomZ 7J'8~~H i.ca:L !r .. t"O·f"riGtiort S~~'ui 

A TrW.' Ore 'U i ona lli Iti. d;:;>! 

S28~ P,-r>/: Royal flood 

Sp,.i1l{!fi(!! , '1i,.gint a .?.?261 

Contents of chis re porl are nl.lt to b\~ u5t'd Lo r 

FtdVt:![llslng. pub l i c.;J tlon, o r promo[iona t' u r-POEh.:S .. 

CLt -ilt lon of trade nltlOC:,G rlo -s 1Ior t;;.on!H:i[u t e an oft irial 

e.ndorsemcn[ or .... pp i'"I') ' ... .,I l 01 ~ lise ot s l.:c.n C: ')\Dmereh,l 

produc t " . . 

The f1ndings in rh1& re port are not to b cn n e,tt'ue.d 

B " an o f f lc:.iill Depart ment of the: Army pOSithll'l unless 

so ~es gnate J by othe r d uc:ha r j -zed doc.l1.fiW o t .:; . 
lINCLASS IF lED 

S (C: U I'IJ'T Y CLASSlFICATlON Of' HHS PAG ~ '" "''''0 E (W7'1 D l! rJ) 

REPORT DOCU MENTATION PAGE READ fNSTRUCTIONS 

BEFORE COMPLETrNG FOR.\1" , RE'PORT NUMBER r- GaVT ACCESS!ON NO. , A£CIPIENT'" CATALOG NUI,40eR 

HH 81-4 

4 . T IT L.1t l_d JII'''lI rl.,) , TYPE: OF fH::PQfH a. PERIOD COV~R~O 

MOil ALf.:- hEIl I..,\M 'lRATORY EXP EfW IEN'fS CO>I PAR INC !-liscc-llu!leous \{CfJ ort 

R ... .J) lAtl OO·j TR ~ AHU El;£ RGY FW;< FACTOR .~S 

PREIJICTORS OF LONCSH ~l': TIl/\N$PORT RAn: , Pf:RFOR'-4ING ORG. I'I£PQRT NU"4E1£R 

, AU T a;A.7;j-- ,. CONTRACT OR GR"'NT NVMer:R(8) 

Phllip Vitale 

, PEFlF" O" .... ING ~(,j. .. ""t ! ATIO.' NAME ANa AODRESS >0. PRO(jhAM E:.L.E.ME:.NT. PROJECT, TASK 

l)e pa r tI, ~ 11 t Q[ the Army ARt:A & ..... ORK UNIT NiJM6ERS 

Coasc ,l i .ngineerlng Reserch CenC l--' L" (C ~R RE -CS) 031193 

Ki ngman Bulldin , Fort Belvoir, Vir g inia n060 

... CON T HQ LlIl'IG CF FICE ,..AME AND AOtlRESS " REPORT OAT!:: 

i)epar t of tile Army ,\priL 1981 

COl,) stal b lgJ ne€!.r lng Rescd rch Center " NUMBER or PAGES 

I( i ngt;'lil n lkl i.l <! 1ng, Fort I\!t voLr, Virginia Z2t,bO 94 , 6.lONliORING AG II'II CV NAMe:" AOORJ:; S"$(JI dlll"T""" I'om Co"tTol/lnA O(flcto) ". SECURITY CLASS. (0/ l"lft 'cporl) 

Ui'~U.'\SS {FLEl> 

Iii .... D';C'.l ASSJ r:-I C. A 'rI0«,' P O .. ~ G 'lAOI N G-

$CH tr.QU'.... f 

... DISTRISUTION STATEMENT (0/ Ihh. R .. porl) 

Approved for publ ic reLease, dl~[ribution unLimited. 

". GI$TRIBUTIO,... ';T.!ITE!>IENT r,,1 ,,, .. Ir"'" ~nlr,~d In {Jloc'" 20. II dllfrrrl!' ir<lrn Rr-porl) 

" SUP~LEMENTARY NOTES 

" KEy WORDS ICon''"'''''' on r"'· .. r.~" ~Id" If n~c "1fuy '>l,d Id~,,(lly by Moc), n:Jmb ... r) 

Ene rgy fLux Movable-bed experif1~ents 

Longsho re transport rate Rad ia[ ion stress 

20 AeSTRACT (Conl/nuo "n ,""ou. ~JdfJ If n. 1:"'t1 ... ,uy IJInd Jd""lIfy by block nu",b.r) 

The results of tllree-dimensionaL mova bie -bed Labora[ory t(:8tS are used 

to er.1pirically rel.Jte the longshore sediment [ ransport rate to the rtldi.ati.on s [ress dnd the longshorE' enerGY flux factor. Both corn:>la[e equally \.,'p. Il 

with the longshore transrort ra [e 1 produc ing correi<.lt ion cOE'fficienc squared va tup.! s of apprOXLrnate{y 0.70. The surf simiLarity pa rame t e r alt;o shows d 

ti [ron ~ influence on [he longshore tralltipOrl ra [e. 

DO 1473 EO!T!OI't Of" , HO\l 6~ IS oaSOLETE U;,CLASSIFlED 
PREFACE 

This r epo rt 1s published t o pr ovide coastal engineers ins i ght into the 

importa nt coast al process of l ongsho re transport along sandy beaches by prese nting the results of th ree -d imensional movable-bed laboriJtory tests. It is 

ho pe d that future s tudie s !,Jill expand on the analys es of the da ta in this 

r-e po rt. The repo rt was prepared und e r the nearshore sediment transport 

r "6eo r c h prog r am of the U.S. Army Coastal Engineering Reaearch Center (CERC). 

The repo r t was written by Philip Vi t ale , 

general sup.ervision of Or. R.M. So rensen, 

Struct ures Branch, Research Division. 

Hydra ul ic Engineer, under the 

Chief, Coastal Processes and 

The aut hor 8cknowledge s C. Calvin. R.P. Savage . and R.P. Stafford for their 

ass ist ance and advice in the design and operation of the experiment, and M.S. 

Ba rtolome i, S.L. Douglas, B. Keely, H. Koenig, ~' .W. le ffler, J. C. Tingler, J. 

Sull ivan , K. P. Zirkle, and, in particular, L.O. Tornese fo r their help in 

collecting and analyzing the data. 

Comments on this publication a r e invited. 

Approved fo r public ation 

approved 3 1 July 1945. as 

approved 7 November 1963 . 

in accordance with Public I.1.W l 66 , 

supplemented by Public Law 172. 

~w Colonel, Corps of Engineers 

Commander and Director 

3 

Cong ress, 

Cong ress, 
I 

II 

III 

IV 

V 

VI 

VII 

APPENDIX 

A 

8 

C 

D 

E 

F 

CONTENTS 

CONVERS ION FACTORS, u. s. CUSTOMARY TO I1ETRIC (S 1) •• 

Page 

7 

SYMBOLS AND DEFINITIONS.......................................................................... 8 

INTRODUCTION •••••••••••••• 

EI1P IRICAL RELAT IONS. 

Homentum Flux. 

Energy Flux ••• 

...................... 

1. 

2. 

3. 

4. 

Longshore Transport Rate............................. .............. .. ............ .. 

Empi rical Rela t ions.. .. .. .. .. .. .. .. .. ........................................ .. 

5. Surf Similarity Parameter... ............ .. .............. .. 

EXPERIMENTAL SETUP •• 

1. Basin Layout ••• 

2. 

3. 

4. 

Generators ......... 

Sand-Moving 

Instruments. 

Sys tern ••• 

5. Dye Inject.ion ............... .. 

6. Sand Size ................................................................................. .. 

EXPERIMENTAL 

1. 

PROCEDURE .......................... .. 

Hourly 

Daily 

Cycle ..................................... .. 

2. Cycle ............................. .. 

3. Test Cycle ................. .. 

4. Range of Variables •• 

OAT A ........................................... .. 

1. Hourly and Daily Data in Appendix A •• 

2. Summary Da ta Ta ble ... 

3. 

4. 

DATA 

1. 

2. 

3. 

Survey Data ..•.•.. 

Overhead Photos ••• 

ANAL'iSlS ........... . 

Calcula tion of Sxy' 

Calculation of P£b. 

Calculation of ( ••• 

4. Special Tests .•.•.....••••••....•.•...•••.•..••..•. 

5. Dally Cycle Graphs ............................................ . 

6. Test Cycle Graphs......... . .•.••.. 

7. Surf Similarity Relation. 

8. Comparison to Past Data. 

SUMHAR'i AND CONCLUSIONS •••••• 

LITERATURE CITED ................. . 

HOUR L'i AND DAILY DATA. 

8EACH SURVE'i DATA ••••• 

PLOTTED BEACH PROFILES •• 

SELECTED BREAKER BAR AND WATERLINE 

HOURLY CYCLE CALCULAT IONS •• 

DAIL'i C'iCLE CALCULATIONS ••• 

4 

. ................................. . 

PHOTOS ••• 

11 

11 

11 

13 

14 

15 

15 

15 

17 

20 

21 

21 

25 

25 

26 

26 

28 

28 

32 

33 

33 

33 

35 

35 

35 

35 

36 

36 

37 

38 

41 

42 

42 

45 

46 

47 

62 

67 

76 

88 

93 
2 

) 

4 

S 

6 

7 

8 

2 

) 

4 

S 

6 

7 

8 

9 

11 

[2 

CONTENTS--Cont inued 

TABLES 

Page 

Locations of overhead cameras mounted on the catwalk.................. 24 

Locations of dye i nject i on by test num ber ••••••••...••.••••.•.•••••••. 2S 

test cycle var i ables and da t a .......•..•.•....•....•.•...........•.... n 

Example of hourly and daily data tables in Appendix A ••••••••••••••••• )4 

Test cycle calculations .•....•......•. ...•.•. o •••••••••••••••••••••••• )6 

Compa risons of tests I and 2 ............... . .... . ............. . )8 

Daily cycle statistics ..•....•.•....•.••. •.• .........•.•.......... ~ ... )8 

Test cycle statisticS .......................................... ........ . 41 

FIGURES 

Coordinate system for momentum flux derivation........................ 11 

Diag ram of test basin setup •••••.•••.••.•••.••.•.••••••.•••••••..•...• 

Photo of test basin setup ........... 0 •••••••••••• 0 ..................... . 

Photo of sand trap .................... o. 0" o. 0" 0 .... 00 . . ............. 0 •• 

Diagram of 

length of 

diffraction analysis used to determine the alongshore 

the test beach ............................................. . 

Shore-normal profile of the test beach, sand trap, concrete aprons, 

and adjacent rubble ..........•..•.•.•.•....•.•..•...•....•.•..•.. •. .. 

Coordinate system used for test beach with locations of wave gages .... 

Diagram of educ tor. 0 ••••••••••••••••••• 

Photo of weighing station .............................................. . 

Diagram of sand feeder ..........•.........•.................. ..... ..• . 

Photo of sand feeder ................................................... . 

Dtagram of complete sand-moving system ......•.•....•............. .•.•. 

Size distribution of sand used for all tests ..•............... . . . .. . •. 

16 

17 

18 

19 

19 

20 

22 

22 

2) 

,) 

24 

2S 

14 Schematic diagram of the int errelationship of the three 

experimental cycles............................................. . ..... 26 

15 Example of overhead photo ................................... .. ... .... .. 27 

5 
CONTENTS 

F1GURES--Continued 

Page 

16 Example of breaking wave •••.•.•.•.••.•.•.•••••.•••••.•.••••••.••••.••• 27 

17 Example of strip-chart wave record.......................................................... 27 

18 Example of surf zone photos ••.•.••.•.•.•.•.•.•••..•.•.•...•.•..•••.•.• 29 

19 Example series of drainage photos .•.•.•....•...•.•...•....•.•.•....... 30 

20 E.xample of bed-form photo.................................................................................. 32 

21 Determination of beach slope used to calculate the surf 

similarity parameter............ ....... .................. ...... ...... 37 

22 Relation between longshore transport rate, 19..' and radiation 

stress, Sxy' using daily cycle data ••••.•.•••.•.•.•••..•.•...•.•••..• 39 

23 Relation between longshore transport rate, 19.' and lonGshore 

energy flux factor, P'p"b' using daily cycle data ....•.....•.•.•.•.•..• 40 

24 Relation between longshore transport rate, 11.' and radiation 

25 

26 

27 

28 

stress, Sxy' using test cycle data .....•............••...........••.• 41 

Relation between longshore transport rate, 

energy fl~x factor, Ptb , using test cycle 

l'p'" and longshore 

da t a •••.•.•.••••••••••••••• 

Relation between Kc; and the surf similarity parameter, E., 

using test c.ycle data ••••••••••••••••••••••••••••••••.••••••••••••••• 

Relation between ~ and the surf similarity parameter, (, 

using test cycle gata •.•••••••••••••••••••••••.•••••••.••••••.••••••• 

Comparison of data in this report to past reports, using SPl'l 

Figure 4-36 .......................................................... . 

b 

42 

43 

43 

44 
CONVERS10N FACTORS, U.S. CUSTOMARY TO METR1C (5r) UNLTS OF flEA5UREMENT 

u.s. customary units of measurement used in this report can be converted to 

metric (51) units as follo~s: 

Mul tiply 

inches 

square inches 

cubic inches 

feet 

square feet 

cubic feet 

yards 

square yards 

cubic yards 

miles 

square miles 

knots 

acres 

foot-pounds 

millibars 

ounces 

pounds 

ton, long 

ton, short 

degrees (angle) 

Fahrenheit degrees 

by 

25.4 

2.54 

6.452 

16.39 

30.48 

0.3048 

0.0929 

0.0283 

0.9144 

0.836 

0.7646 

1.6093 

259.0 

1. 852 

0.4047 

1.3558 

1.0197 

28.35 

453.6 

0.4536 

1.0160 

0.9072 

0.01745 

5/9 

x 10- 3 

millimeters 

centimeters 

To obtain 

square centimeters 

cubic centimeters 

centimeters 

meters 

square meters 

cubic meters 

meters 

sq ua re me. te rs 

cubic meters 

kilometers 

hectares 

kilometers per hour 

hectares 

newton me te rs 

kilograms per square centimeter 

grams 

grams 

kilograms 

metric tons 

met ric tons 

radians 

Celsius degrees or Kelvins 1 

lTo obtain Celsius (C) temperature readings from Fahrenheit (F) readings, 

use formula: C = (5/9) (F -32). 

To obtain Kelvin (K) readings, use formula: K = (5/9) (F -32) + 273.15. 

7 
SYMBOLS ~~ DEFINITIONS 

a l ratio of sand volume to total volume of a sand deposit 

b subsc ript for breaker 

C wave phase velocity 

g 

H 

H 

i 

n 

o 

R 

wave group velocity 

water depth 

median sand size 

energy density 

flux of wave energy per alongshore distance 

acceleration of gravity 

wave height 

average wave height 

root-mean-square wave height 

significant wave height 

longshore transport rate in immersed weight per unit time 

subscript for any pOint seaward of breaker zone 

empirical coefficient relating l~ to P~b 

empirical coefficient relation l~ t o Sxy 

wave number = 2n/L 

wavelength 

ratio of Cg to C 

subscript for deepwater condition 

energy flux term 

longshore energy flux factor as used in this report 

longshore energy flux factor as used in the SPM 

longshore transport rate in volume per unit time 

range of coordinate system defined in Figure 7 

8 
SD1BOLS AND DEFINITIONS--Continued 

r correlation coefficient 

S station of coordinate system defined in Figure 7 

Sxy radiation stress component (flux of y-mornentum in x-direction) 

T ~ave period 

t time 

u onshore component of water particle velocity 

v alongshore component of water particle velocity 

x coordinate in onshore direction 

y coordinate in alongshore direction 

z coordinate in vertical direction 

a angle between wave crest and shoreline 

0g angle between wave generator and shoreline 

B angle of beach slope with horizontal 

n water surface elevation 

8 wave phase 

~ surf similarity parameter as used in this report 

~b surf similarity parameter as used in Kamphuis and Readshaw (1978) 

p mass density of water 

Ds mass density of sand 

w angular frequency of wave 2n/T 

9 
MOVABLE- BED LABORATORY EXPERL'1ENTS COMP AR ING 

RADLATION STRESS AND ENERGY FLUX FACTOR AS PREDICTORS 

OF LONGSHORE TRru~SPORT RATE 

by 

Philip Vitale 

I. INTRODUCTION 

Three-dimensional movable-bed laboratory tests were c.onduc.ted to c.ompare 

radiation stress and energy flux fac.tor as predictors of the longshore sediment transport rate. The tests were performed in the U.S. Army Coastal Engineering Research Center's (CERC) Shore Processes Test Basin (SPTB). This 

report presents derivations 'of the radiation stress and the energy flux 

factor, documents the experimental setup and procedure, tabulates most of the 

data, and performs the data analyses. Many photos were taken during the 

tests; however, only a few were used 1n the report. The complete set of test 

photos is available from CERC's Coastal Engineering Information and Analysis 

Center (CELAC). 

II. EMPIRICAL RELATIONS 

The longshore transport data are related empirically to the two expressions representing wave conditions. One, radiation stress, is based on momentum flux) the other on energy flux. An important concept which is also used 

in the data analyses is the surf similarity parameter. 

1. Momentum Flux. 

The dependent variable studied here is the longshore transport rate caused 

by waves approaching the beach; therefore, the consequential mOmentum term is 

the onshore flux of alongshore momentum. The derivation of the term follows 

Longuet-Higgins (1970) which applies the concept of wave momentum flux to the 

generation of longshore currents. 

The coordinate system used is shown in Figure 1. The y-axis is along the 

shoreline, the x-axis is norlD8.1 to the shoreline and positive shoreward, and 

the z-axis originates at the stillwater level and is positive upward. USing 

this system, the onshore flux of alongshore momentum is the flux of y-momentum 

in the x-direction, Sxy' This term is One component of what is commonly 

called the radiation stress tensor. 

Shore'in~7 

Figure 1. Coordinate systen for momentum 

flux derivation. 

11 
According to 

particle velocity 

angle, a, to the 

small-amplitude 

in the x- and 

shoreline (Fig. 

wave theory, the components of the 

y-directions for a wave traveling 

1) are, respectively, 

= ~~ cosh ik(z + d)] cose u 2 L cosh kd cosa 

H gT cosh ik(z + d) 1 v =::. -2 -L cos8 sina cosh kd 

where 

H = wave height 

g acceleration of gravity 

T wave period 

L wavelength 

d water depth 

k wave number 

6 wave phase. 

The last two terms are defined as 

and 

2. 

L 

6 kx - wt 

where t is time, and w the wave angular frequency 

w 

water 

at an 

(1) 

( 2) 

The y-momentum (alongshore momentum) per unit volume is pv where p is 

the water mass density. The flux of this momentum in the x-direction 

(onshore) per unit alongshore distance and unit water depth is pvu. Integrating over the water column and averaging over time produce the mean alongshore momentum flux in the x-direction per unit alongshore distance 

n 

s = J pvu dz 

xy -d 

where the overbar denotes the mean with respect 

surface elevation. Substituting equations (1) and 

terms of higher than second order produce 

s 

xy 

- sina 

(ECg cosa) C 

12 

(3) 

to time and n the water 

(2) into (3) and dropping 

(4) 
where C is the wave phase velocity, Cg the wave group velocity, and E 

the wave ene rgy density 

H2 

pg rmS 

8 (5) 

where H

rms 

is the root-Olean-square 

theses in equation (4) is the flux 

Fx' assuming straight and parallel 

energy dissipation is assumed, 

(nns) "'ave height. The term in pa renof wave energy per alongshore distance, 

bathymetric contours. When zero wave 

F :::: EC cOSa x g constant (6 ) 

d iss i pa t ion is assumed to be ze ro up to the breake r zone; 

is constant from deep water to the breaker zone. Since the 

to C is constant due to Snell's law, equation (4) r which 

alongshore wave momentum entering the surf zone, is constant 

breaker zone. 

In this report, 

therefore, Fx 

ratio of sino 

represents the 

seaward of the 

Equation (4) can be revised for application of monochromatic waves, as in 

this report. For such wave conditions, the average wave height, H, measured 

during the tests (and discussed later in Section IV) is equal to H"ms. By 

re"'riting equation (4), 

Sxy is now defined 

that equation (4) is 

for conditions where 

2. Energy Flux. 

s - ( pgti2 

C ) sina 

xy - 8 g cosa --C-- (7) 

for use with laboratory monochromatic wave data. Note 

valid for any ",ave condition; equation (7) is valid only 

H equals Hrms . 

In literature, the longshore transport rate has been empirically related 

most frequently to a term found by multiplying both sides of equation (4) by 

the wave phase velocity, C, to yield 

P, = (EC cosa) sina (8) L g 

Unlike Sxy' Pi is not constant seaward of the breaker line; therefore, 

specifying ",here Pi is being calculated is ne cessa ry. This report, following convention, determines Pi at the breaker line, 

representing the value of Pi at the 

transport is occurring. The subscript 

(9 ) 

pOint closest to where the longshore 

b denotes breaker values. The term 
in parentheses in equation (9) has been shown to be constant (see eq. 6) 

seaward of the breaker line; therefore, subscript b may be replaced by i 

which represents any point seaward of the breaker line. Making this change, 

using equation (5), and letting Hrms equal H for monochromatic waves, 

equation (9) becomes 

(10) 

The Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal 

Engineering Research Center, 1977) provides a term Similar to Ptb except 

that the wave height used is the significant height, Hs. The term, called 

the longshore energy flux factor, is defined as 

is derived in Galvin and 

and Hs has been showTl in 

cosa 

Sch\oleppe (1980). The relationship 

Longuet-Higgins (1952) to be 

( 11) 

between 

(12) 

assuming a Rayleigh distribution of wave heights as well as a number of other 

conditions. Therefore, 

Since Pn 

te rminol ogy 

and P£,s are 

and refers to 

essentially the same terms, this report uses 

Ptb as the longshore energy flux factor. 

3. Longshore Transport Rate. 

( 13) 

the SPM 

The longshore transport rate, Q, given in the SPM in units of volume per 

unit time, is also commonly shown as I£, with units of immersed weight per 

unit time. The relationship between the two is 

(ps - p) ga' Q (14) 

where Ds is the mass denSity of sand and a' the ratio of sand volume to 

total volume of a sand deposit, which takes into account the sand porosity. 

For discussions of equation (14), see Komar and Inman (1970) and Galvin 

(1979). Since the laboratory tests described here measured It directly, 

this term is used in most of the data analysis. 

14 
4. Empirical Relations. 

The expressions derived in the preceding parag raphs are used to set up the 

following empirical relations 

(15) 

and 

( l6) 

where ~ and Ks are coefficients to be determined from the test data in 

this report. 

Equation (15) is based on the concept that the work done in moving the 

sand alongshore is proportional t o the energy which approaches the beach. The 

units are consistent and ~ is dimensionless. 

Equation (16) is based on the concept that the sand transported alongshore 

depends on the alongshore force ex.erted by the wave motion On the bed inside 

the surf zone. By the equation of motion, this force is related to the change 

of momentum inside the surf zone. The alongshore momentum, Sxy ' enters the 

surf 'Zone through the breaker line but cannot exit through the shore line 

boundary. Therefore, the change in alongshore momentum is Sxy and equation 

( l6) results. Kg has dimensions of length over time. 

5. Su rf Similarity Parameter. 

Kamphuis and Readshaw ([978) showed that l), and Ks are dependent upon 

the surf similarity parameter, 

tan 8 (17) 

in which tan 8 is the beach s lope, Hb the breaker height, and Lo the 

deepwater (d/L > l/2) wavelength. ~b reflects variations in beach shape, 

breaker type, and rate of energy dissipation. Using the results of laboratory 

tests, the following relationships were found by Kamphuis and Readshaw 

Kp " 0.7~b for 0 .4 < ~b < l .4 ( l 8) 

Ks " 0.08~b for 0.4 < ~b < l.25 ( 19) 

For values of ~b higher than the upper limits, I), and Ks become independent of ~b · 

The surf Similarity parameter is evaluated in this report to determine its 

effect on the longshore transport rate. 

rr I. EXPER L'lENTAL SETUP 

This sec tio n discusses the setup in the SPTB (Fi gs. 2 and 3) and describes 

the wave gene rators, wave gages, and cameras and their positions. Also diScussed are the sand-moving system, the method for measuring the longshore 

current velocity, and the size distribution of t he sand used in the experiment. The design of the setup was based in l a r ge part on r'airchild (l970). 

l5 
Backbeach Rubble I f.s--weiqhinq Station 

Rubble 

Sand Feeder 1 ------------ SWL ~ 

g 

Updrift 

Dawndrift ~ 

Can crete ... E -

Supplementory Conc re t e I- Apron .D on ... .D 

- U => "': 

Deposition .D Apron c Test Beoch '\ - .D " a:: - Areo => U) J a:: 

~\ ~4S7m-=:J ~7.62m .1. 4.S7m-l 

0.91 m ~oo A Walls 

0° 

10° 

~ 

Rubble 

Figure 2. Diagram of test basin setup_ 
Figure 3. Photo of test basin setup. 

1. Basin Layout. 

A diagram of the basin setup is shown in Figure 2. The basin is 45.72 

meters long, 30.48 meters wide, and 1.22 meters deep. The alongshore and the 

shore-normal directions of the sand beach were 7.62 and 11.45 meters, respectively. The backbeach was 3.05 meters in the shore-normal direction, but it 

was not part of the test beach. 

Immediately downdrift of the beach was the sand trap, 0.91 meter wide and 

l2.7 centimeters deep (fig. 4), used to catch the longshore transport. 

Concrete aprons, 4.57 meters in the alongshore direction, were located on 

the downdrift side of the sand trap and on the updrift side of the beach. The 

updrift apron provided enough distance for the longshore current to develop 

between the updrift training wall and the beach. This phenome.non is discussed 

in Galvin and Eagleson (1965). The downdrHt apron served two purposes--one 

as a platform for depOsiting the longshore transport that escaped the trap, 

the other as a surface on which the waves traveled to diminish diffraction 

effects since no downdrift training walls were used. 

The major limitation in the experimental planning was the size of the 

SPTB, which permitted three wave generators, each 6.10 meters long, to be 

linked together and leave enough room to be rotated through various angles to 

the beach. The other limitation waS the decision not to use downdrift training walls due to the wave reflection problem. When downdrift training walls 

are used, the wave energy, which is reflected off the beach at an angle in the 

downdrift direction, strikes the downdrift wall and is reflected back toward 

the updrift direction. The energy is then reflected by the updrHt wall and 

the process repeats. The reflected wave energy is being trapped within the 

l7 
Figure 4. Photo of sand trap. 

two walls; this produces some complicated wave variability problems (eag. t 

see Fairchild, 1970). With no downdrift training walls, the reflected wave 

energy moves away from the beach area into the outer parts of the test basin 

where most of it is eventually dissipated by the rubble slope along the edge 

of the basin (Fig. 2). ThiS, however, creates a problem with wave diffraction. The energy of the wave leaving the generator spreads laterally into 

still water and gradually decreases the wave height toward the updrift end of 

the wave crest. 

To minimize the decrease in wave height over the test beach, it was 

designed using the diffraction diagram for a wave traveling past a semiinfinite breakwater from Figure 2-33 of the SPM. The period and angle used in 

the diffraction analysis were 3 seconds and lO°, respectively. since these 

values produced the maximum diffraction closest to the beach. The spreading 

of wave energy into the shadow of a breakwater is analogous to the spreading 

of wave energy into the area of the test basin downdrift of the generators. 

The diagram (Fig. 5) indicated that the alongshore length of the beach should 

be 7.62 meters. Most of the diffraction-caused decrease in wave height occurs 

over the downdrift concrete apron. 

Rubble, ranging in size from 7.62 to 15.24 centimeters , was placed at 

several locations in the basin to absorb wave energy and provide gradual 

slopes between the concrete aprons and the basin floor. The beach) sand 

traps, concrete aprons, and adjacent rubble were all built to the same shorenormal profile (Fig. 6). This profile was based on Olesnutt's (1978) longterm two-dimensional tests in which waves were run onto a sand beach to 

determine profile response. After superposing several of Olesnutt's (1978) 

18 
-0.4 

-0.3 

-0.2 

_-0. 1 

E 

Ol /lrac!ion 

Coefficient 

Wow e U'$t! Q for Analysi s 

T = 3.00 $ 

L = 7.S0m 

0.7 0. 9 

06 0$ 10 

'l 

, 

oq: 10 0 

=-

T t 8eo{.h 

Tr oi ninQ Wall 

WOv e Gellero tor 

Figure 5. Diagram o f di f f raction analysis used t o de t ermine 

t he alongs ho re lengt h of the test beach. 

~----,:( 0.00 , 0. 3051 

I 

I 

I 

I 

I 

I 

o ____ _ __ I .1. ____ _ 

I 

• 0 . 1 o 

.. 

<II 0 .2 .. 

u 

g 0 .3 

o 0. 4 

0 .5 

0 .6 

Ba Ckb&oCh 

I 

I 

Test Beach 

111 .46,0.7101 

0.76--L __ ~~ __ ~~ __ ~~ __ -L __ L--L __ L--L __ ~~~ 

- 3 -2 -I 0 2 3 4 5 6 7 8 9 10 II 12 

Stolion {m} 

Figu re 6. Sho re-no rma 1 pro f ile of the te s t be ac h , s and t rap . 

co nc rete a prons, and adjacent rubbl e . 

19 
profiles run for 80 hours or more with wave periods similar to those used in 

this experiment, the shore-nonnal profile in Figure 6 waS drawn as a compromise or average through the superposed profiles. This profile was used t o 

l essen the onshore-of fshore adjustment of the beach. 

Figure 7 shows the coordinate system 

is a t the updrift , sho r eward corner of 

along the alongshore axis , and stations 

axis. Any point on the beach, or in the 

station pair. 

used for the t est beach . The o rigi n 

the beach . Ranges (in meters) are 

( in meters) along the shore-normal 

basin, can be described by a rangeRonQ~ tm) 

" 12 10 a 6 • 2 o -2 -. -6 , , I I , 

Rubble Boc<beoch Rubble 

-

test Beoch lJpdr i ft 

Concrete -.+: __ ~W! ____________ Apron 

80 60 ' 0 20 0 

Wot~r Depth (em) 

DownlJrifl 

Concrete 

Apron 

'" Q 

;: 

" C 

Q 

'" 

I Go,. 'B 

'R 3.80, S Breo~er Lin,) 

ruts 12-1~ 

• 

Goqt 4 A 

'.380,56.001 

ru!'~-!! 

• 

GOQ t 3 

I R 3.80,59.001 

Tt~ls 5-1~ 

• 

G09t 2 

tR 3.80, 5 12 ~0) 

All Tt", 

• 

G0 9' 1 

(AO OO, SI ~O) 

AU Tu" 

Figure 7. Coo r dina t e system used for test beach with locations 

of wave gages (R ;:: range, S;:: station) . 

2. Genera tors. 

-

-

-

-

-

-

-• 

-2 

o 

2 

E 

• c 

o 

6 

8 

10 

12 

The th ree piston-type 6.10 meter-long generators used in this experiment 

produced only monoch romatic waves and are discussed in Stafford and Chesnutt 

(1977). The generCl tors were set at four different angles--O°, 10°, 20° , and 

30 0 --to the beach during the experiment . fo r each setti ng, an updrift training wall was built from the generator t o the i - foot depth. This allowed 

circulation pa st the wall to feed the longshore cu rrent. Figure 2 shows the 

setup of the fou r generators and training wall. 

For t he 100 and 20° tests, the training wall was curved to a llow for wave 

r efrac t ion. Howe ver, since the wall s t opped a t the I-foot depth, the curves 

20 
were small and considered not worth the construction effort. Therefore, the 

curve for the 30° tests was deleted and a straight training wall was used. 

3. Sand-Moving System. 

As the waves approached the beach at an angle, the sand moved in the 

downdrift direction. Most of it deposited in the sand trap. The sand which 

escaped the trap deposited either on the downdrift concrete apron or beyond 

the apron and rubble (covered to keep sand from being lost within it) onto the 

basin floor. This area is shown in Figure 2 as the supplementary deposi tion 

area. Although separate measurements of the sand deposited in each area were 

not taken, it is estimated that 80 to 95 percent of the longshore transport 

fell into the trap. The greater the transport rate and the suspended sediment, the greater was the amount of sand escaping the sand trap. 

The trap was cleaned continually during a test using an eductor attached 

to a small centrifugal pump. Water was pumped through the eductor at high 

speed, creating a suction to pick up the sand (Fig. 8). The sand was pumped 

to the I<Ielghing station (Fig. 9), deposited in one of tl<lO bins, and I<Ieighed 

submerged.. When divided by the appropriate time period, the value became the 

immersed weight longshore transport rate. 

After the 

sand feeder. 

which sand is 

I<Ieighing, 

The sand 

introduced 

bot tom. A diagram and a 

The primary advantage of 

amount of sand introduced 

and its development. 

the sand was pumped, using another eductor, into a 

feeder is a vertical cylinder open at both ends in 

through the top and removed by waves through the 

photo of the feeder are given in Figures 10 and 11. 

the feeder is that it permits waves to control the 

onto the beach. Savage (1961) discusses the feeder 

In summary) the complete sand-moving system (Fig. 12) included the 

follol<ling: 

(a) A sand trap, a downdrift concrete apron, and a downdrift 

deposition area which trapped the sand; 

(b) a downdrift eductor-pump combination which moved the trapped 

sand to the weighing station; 

(c) a I<Ieighing station I<Ihich I<Ieighed the amount of sand moved; 

(d) an updrift eductor-pump combination which moved the sand from 

the weighing station to the sand feeder; and 

(e) a sand feeder which redeposited the sand onto the beach. 

4. Instruments. 

Wave heights were measured using parallel-wire wave gages (see Fig. 7). 

Gages 1 and 2, located seaward of the toe of the beach, were used for all 15 

tests. Gage J, located over the beach, was used for tests 5 to 15. Gage 4A, 

located close to the breaker line, was used for tests 5 to 11. Beginning with 

test 12 for the remainder of the tests, gage 4A was adjusted to measure the 

breaker he ight and then renamed gage 4 B. 

21 
@o UTPUT : Sa nd and Water Mixture to 

Weighinq Station or Sand 

Feeder 

! \ 

® High-Speed Jet 

Creates Vacuum 

\J 

® Sand ond Water Mixture (rom 

Sand Trap or Weiqhinq S totion 

Pulled in by Vacuum 

./ 

CD INPUT: Clear 

Cenlrl 

-----T-- ------ ( 

I ..... -- I 

.. I ----~ .... ----: A--- \ --_ ---

Water from 

lugol Pump 

----- Figure 8. Diagram of eductor. 

Fig ure 9 . Phot o of weighing s tati on. 

22 
Overllo ... --

Area 

I 

Ove: tklw Re!Urtl to WtiQhinq 

Sto1 ion ( Mow-Iy ~ole, ) 

Sand, 

S::JI[tS 

0.1 

Sand ,\!ovtd 

Qu1 ond 

On to &oach 

by S"osh 

Sor.1 and Wofer 

11'111 0" IrQm 

1 j";' "". 

leQs (xle"r1 ThrollQh Beach 

'0 Bosin flGOr 

Figure 10. Diagram of sand feeder . Figure 11. Photo of sand feeder. 
Contrete 

Apron 

Q) 

Softd D'tPosih 

In Sand Trap 

® Send is Noved to WeiQl'linQ Stolion 

Sand Beath 

• 

Concrete 

Apron 

~====i=;i!)® f,-,-.,-V'fY'","",,yyyyyyvvv!(J) 

® Waus Breck Dnd 

Tronsporl Sand 

Alon95hofe 

Feeder Redeposl1s 

Sand Onlo Beoel'! 

o wovt Generators Drive Waves 01 An9't to Beocl'l 

Sandi5 ® W.iqh.d 

Sand is 

Moved 10 

Sand Feeder 

Figure 12. Diagram of complete sand-rnoving system. 

Two cameras were mounted over the 

was a view camera with an adapter for 

white photos, and the other a standard 

the cameras are given in Table 1. 

beach on the catwalk of the SPTB. One 

taking 4- by 5-inch Polaro id black-and3S-millimeter camera. The locations of 

Other instruments used in the tests include standard hydraulic scales for 

weighing the sand, and a standard level and rod for surveying the beach after 

each test. 

Table 1. Locations of overhead cgmeras 

mounted on the catwalk. 

Location) I Camera 

View 35-mm 

(m) (m) 

Range 3.9 3. 9 

Statio n 4.9 4.7 

Elevation above SIlL 8.5 8.5 

lAccurate onl y to ± 0.1 meter. 

24 
5. Dye Injection. 

Longshor:e cur rent velocities f o r tests 5 to 15 were measur:ed by inje cting 

dye 1nto the surf zone through a hose which ran from the sand feeder to a 

s malL stake 1n the surf zone. Dye was poured by hand into the top of the 

hose . Table 2 gives the locations o f the dye injection by test numbers. The 

change in l oca tion of the stake in te sts 7 t o 10 was a procedural error and 

not planned for a spec ial purpose. The dye injection procedure is discussed 

in detail in the next section. 

Table 2. Locations of dye injection by test number. 

Test Nos. Dye inje c ted Dye timed Dye timed Timed dis tanee 

at range frow range to range trave led 

(m) (m) (m) (m ) 

5 and 6 3.00 3.60 7. 60 4.00 

7 to 10 3.82 3.82 7.73 3.78 

11 to 15 3.00 3.73 7.73 4.00 

6. Sand Size. 

Figure 13 s hows the s ize distribution of the sand used for all 15 tests. 

The median diameter was 0 . 22 millimeter . The geome tr ic standard deviation is 

defined as 

" g 

d 1/ 2 _ 16_ 

dS4 

(20) 

where diG and dS4 are the sand 

tive t y , of the samp le is coar:ser. 

1.22. Figur e 13 indicates that the 

s izes a t which 16 and 84 percent, respecThe value of O'g f o r the sand used was 

sand was well so rted . 

.. 

,. 

'. 1 0. 

• 0 :0. 

~ 0 

~O . 

O ~ 

.. 

o. 

0 

0 

1\ 

0 \ 

• • 

, 

• 

, 

• 

l 

l 

.. • 

~Ol O.O,o.lQ.,l 0' I • 

"-;-..... 

---r-- 6~Ef02l ..... 

I-Hilr-I--1\ 

\ 10 10)0 40 ~ .0 70'0 to " "" ,u " ., p" Cauu, 

figure 13. Size distribution of sand used for all tests. 

25 
IV. EXPERL'lENTAL PROCEDURE 

Each test was composed of three major data collec tion cycles: an hourly 

cycle, a daily cycle, and a test cycle. For example, wave heights were 

measured every hour (hourly cycle), water temperature was measured twice a day 

(daily cycle), and beach surveys were taken at the end of each test (test 

cycle). The typical test schedule was 4 hourly cycles daily for 6 days for a 

total of 24 run-hours per test. Tests 1 and 2, as discussed later, were 

exceptions to this schedule. Figure 14 is a schematic diagram of the interre 1a t ions hi p of the three eye les. Si nee waves we re run eve ry ot he r day, a 

complete test took about J weeks. 

Nell lnl Variobln SrI. 

WoUr Orplh Corrected 

100.11111. 

f---4~ 

Bo~if\ Oroine~. 

" OroinoQt ol'ld 6td-Fo,1ft 

4 HOUR DAilY CYCLE ..... BtoCh Sulvty,d. 

>--1 ----il >--1 ----il I I 

:" / """'-All RttnCllning Sor·d Pitted U~ , '" Slirt lone Photos ond weighed. 

I , 

I " 

I '. J HOuR CYCLE ' 

\!ioler Tflllp,rotllrt ond 

Drplh RftOrded. 

BlOCh PhoIO --'t 

BrtOktr ·Pllolo 

Figure 14. Schematic diagram of the interrelationship 

of the three experimental cycles. 

1. Hourly Cycle. 

The various types of data collected in a typical hourly cycle are shown in 

Figure 14, along with an indication of time of collection. Before a new hour 

of run-time was started, photos of the beach were taken from overhead with 

both the 35-millimeter camera (Fig. 15) and the view camera. A reference rope 

in the alongshore direction at station 5 and painted arrows on the concrete at 

each station bordering the beach can be seen in Figure 15. Photos, such as 

shown in figure 15, provide a record of the change in \.o,'aterline and breaker 

bar throughout the tests. 'The waves were then turned on and usually, within 5 

minutes of the start, an overhead photo of the breaking wave was taken with 

the view camera. The angle between the breaking wave and the reference rope 

was later measured from the photo to determine the breaking angle of the \.o,'ave 

(see Fig. 16). Note that this procedure assumes the alongshore direction 

rema ined cons ta n t th roug hou t the tes t. In ac t ual i t y, howe ve r, the alongs hore 

contours are changing, as evidenced in Figure 15. 

After i:l. run-time of 30 minutes, wave data were collected for 2 minutes. A 

sample strip-chart record is shown in figure 17. The wave height was determined from this record. For a given length of wave record, a horizontal line 

was drawn along what appeared to be the average wave-crest elevation. A 

horizontal line was also drawn for the wave troughs. The distance between the 

two lines was measured to determine the average wave height, H. This procedure assumes that a nearly uniform distribution of wave heights is produced by 

the monochromatic wave generators. 

26 
'" ~ 

0 

c 

if, 

c 

C 

+ 

Figure I~ . Example or overhead photo. 

figure 16 . Example of photo of breaking wave. 

27 

line established 

~ by eye 

wave reco rd. 

6 50 
Immediately after the wave data were collected, dye was injected into the 

surf zone~ as discussed in Section III, and the leading edge of the dye was 

timed over a distance of approximately 4 meters (see Table 2) to determine the 

longshore current velocity. Also recorded were the station at which the dye 

left the downdrift edge of the beach and the station at which the waves were 

breaking. Therefore, the determination of whether the dye moved offshore, 

along the breaker line, or onshore could be made. Most of the dye injections 

traveled along the breaker line. 

During the hourly cycle, sand was continually picked up from the trap area 

and weighed when a bin was full. A complete record of the amount of sand 

moved in a given time period existed only at the end of the day after the 

waves had been stopped and all the remaining sand had been picked up and 

weighed. Therefore, the longshore transport rate can be given for a daily 

cycle or a test cycle only. 

2. Daily Cycle. 

At the start of every test day (see Fig. 14). the wa ter temperature was 

recorded, the water level was corrected to 0.710 meter, the wave gages were 

calibrated, and a check of all equipment was made. The hourly cycles were 

then s ta r ted. Four hour ly cycles were us ua lly completed each day. 

Shortly before the waves were turned off at the end of the day J photos of 

the surf zone were taken from the side (see Fig. 18 for examples). After the 

waves were stopped, all the sand in the sand trap, on the downdrift concrete 

apron, and in the downdrift deposition area was moved to the weighing station 

and weighed. The day's longshore transport movement was then determined after 

the final weighing. This quantity, divided by the total number of run-hours, 

provided the immersed weight longshore transport rate for the day. 

3. Test CYCle. 

At the beginning of each test, new test values for the wave period, T, 

the generator angle, Qg' and the generator eccentricity, Ecc, were 

selected and set (Fig. 14). Ecc is half the distance the generator bulkhead 

moves. The combination of period and eccentricity produced a predicted wave 

height, using the calibration curve of the generators (see Fig. 2 in 

Fairchild. 1970). This guided the selection of T and Ecc but was not used 

for wave height determination. 

The beach was regraded to the shore-normal profile (see Fig. 6) before 

each new test. This included raking the beach to remove all traces of ripples 

from the prior test. The basin was usually flooded to cover the entire beach 

and left over a weekend to allow the new beach to stabilize before the new 

test cycle began. 

After the test was completed, the basin was drained in 10-centimeter 

increments, producing depth contours of 0, 10, 20, 30, 40, 50, and 60 

centimeters. An overhead photo of the waterline was taken at each 

increment. M example series is shown in Figure 19. Surveys of the beach 

were then taken, USing a standard level and rod, along ranges 1.5, 2, 3, 4, 5, 

6, 7, and 7.6 meters. The elevation on each range was read at all major 

breaks in slope. 

28 
Figure \8. Example of surf zone photos. 

29 
w 

o 

Figure 19. E~G P e series of drainage photos. 
Figu re 19 . Exampl e series of drainage photos.--Continued 
Finally t photos of the beach were taken at close range to document important bed forms, such as ripples and bars (Fig. 20) . 

Figu r e LU . Example ot bed-forn photo. 

4 . Range of Variables. 

Table 3 gives the test variables fo r all is tests. Note that the 0 . 710-

meter water depth and the sand were the same for all tests. The wave heights 

listed are the average of all the hourly measurement6 of gages 1 and 2 f o r 

each test. 

Tab Ie 3 Test cycle variables and data 

Test Total Period Cenerator \lat.er Wove Break.er Longshore it ·10" 

No . run- t.ime .::Ingle teeper , t.ure height angle current 

( hr) ( A) (degree. ) ( · C. ) ( eal ( dfl&Te • • ) (em!6) (N/.) 

1 25 2.)5 10 22 . S 8. 2 I _I 6,117 

2 50 2.)5 10 22.8 8 . 0 7 -- b.890 

J 2' 1.50 10 ZO . 7 l2.8 7 -- 8.J9b 

, 2' 1. 90 \0 15.9 11. 5 7 -- 6,IBB 

5 l' ) . 00 \0 12 . b 7.2 ) J 7 , 544 

b 2' 2. )5 20 12.) 7.7 9 17 9 . 9bb 

7 2' 1.90 20 1 J. 7 10.2 11 )0 7.281 

8 2' 1. 90 20 D . 8 10 . 0 II 20 ) ."b 

9 24 I. 50 20 14.7 10. ) IS 27 5.227 

10 2' J. 90 20 IS . 8 Ib.5 15 19 10,605 

11 14 2. )5 00 10.7 7.4 -5 0 892 

12 24 2 . )5 lO 23.1 8.1 20 28 lb.328 

II 24 l.OO JO 23.1 b.9 IS 7 1l,941 

14 2' l . OO 30 19.4 15 . b )0 2) 32.9l8 

15 24 I. 90 )0 1 b. I 15. I 19 40 25.502 

I • t.ot. available. 

32 
V. DATA 

The data collected during the experiments are provided in Appendixes A to 

D. Appendix A contains the hourly and daily data for each test. Appendix B 

lists the beach survey data, which are plotted in Appendix C, taken after each 

test. Appendix D provides 35--millimeter photos of the beach taken during a 

test with the waves stopped. 

I. Hourly and Daily Data in Appendix A. 

Table 4 is an example of how the daily and hourly data are tabulated in 

Appendix A. Column 1 lists the run-time over which the data were collected. 

Run-time is defined as the cumulative time of wave operation from the beginning of the test. A run-time of 05 10 means that up to that pOint, waves had 

been run at the beach for a cumulative total of 5 hours and 10 minutes. This 

would be the case even if the first wave had been run 2 days before. 

Column 2 lists the length of time (in minutes) waves were stopped to take 

overhead photos of the beach. The letters CFD or TC indicate that the testing 

was completed for the day or the test was completed. Between any tv.'O entries 

1n column 2, the waves were run continuously. For example, from the beginning 

of the test at run-time 00 00 to run-time 01 00 (see Table 4), the waves were 

continuously run. At that point the waves were stopped Eor 5 minutes to take 

overhead photos of the beach. The waves were then re::;tarted and run continuously until run-time 02 00. 

Columns J and 4 list the water temperature and the water depth, 

tively. These measurements were taken in the morning before the 

started and in the afternoon after the testing stopped. 

re s pectest ing 

Column 5 lists the immersed weight of sand moved during testing from the 

previous entry in the column. A value is always listed with a CfD or Te entry 

since it was only at the end of the day that the balance of sand not weighed 

during the time the wave s were running could be picked up and weighed. In 

Table 4, the value of 4,227 immersed pounds of sand is the quantity of sand 

transported from run-hour 04 00 to 08 00. This column is not a cumulative 

listing of sand transported. 

Columns 6, 7, 8 , and 9 list the wave heights measured by gages I, 2 , 3, 

and 4A or 48, respectively. Section 111 discusses the locations of these 

gages, which are shown in Figure 7. Column 10 lists the breaker angles measured froUl the Polaroid 4- by 5-inch photos of the breaking waves (see Fig. 

16) . Column II lists the longshore current velocity measured by dye injections, as discussed in Section 111. Column 12 lists the breaker type, using 

the following code: sg, s urging; p, plunging; c, collapsing; and sp, spilling. A double entry indicates both types of breakers were evident with the 

first type predominant. 

2. Summary Data Table. 

For a comparison of test conditions, Table J provides the average values 

of water temperature, wa ve height, wave breaker angle, longshore current 

velocit y, and average longshore transport rate in iramersed pounds per second 

for each test. Also included are the wave period and generator angle. 

33 
Table 4 . Exam121e of hourl y and da ily data tables in AeEendix A. 

'"' "'1 10\ 0 0 , ~ .tCO' os " 1.1'-, .. ~ 'l ~ " Oi t .. " , 

,", II·, '<l~ ... l l' -! I Ie 41 't- I .... ' .. ~t o .. '" "(IC .. I &"1, .... , It \O"'~~CI/I l!~l."([1f 

.,{'P"I O '\-. (l t P , .. ~ll (' '' ' ,. .... 'Ll '\lI/~ 1 " ,, ~t 

.. . ,tluJvl , . ,,, !; I,C l , 1.41'.( I G, C; ( j GI C.I ft/., O"IIIU ("/5 

U.1 " ,1 , 0 .. , " •• 0 '.0 '. , ,., , " • .. , • " .. ' ' .. '.' 0._ 

, " • " , j 

.. o. , ' . 0 , .. '. , " " • j ,. 

" •• 1 , .' .. , , .. " • '" Ud ',> ,. ~l )11 

0 1</. , '1. <' 

• • " " , .1 , .. '.' I I ,. " • , • • " " • .. .. , '.' .. , \ 1 ., " • • " " " .. ' ' .. .. ' J \ ,' " • • " " , .. '.' .. ' '.' 11 , 1 " • • " , 11.1 ' 1,0 ~ll' 

• • I) •• I t • ., 

• , .. • " .. , '. , ' .. \I . , " • • • I " .. • " • • 1 , .. , .. II. , .> 

" • '" H.' '. ,- J .I 

" • 'I. , 'L ,0 

" I .. " " .. ' .. ' •• I 10 • • " " • " " • , . " " , .1 .. ,•• • '. , .. " • " " • \. 

" " '.' ' .. .. ' ' .. " " " , " " " " .. '.' '.' '.' II, : " " ,0 • JJ.\ '1, 6 H." , . l l . , , I," , . • t · " " '. , .. ' '.' '.1 .- .. • .. " , " " " .. ' .. ' ... . .. .. • " " " • " " .. ' .. .. , '.' ••• " " • " " • " " " • • I '. , .. ' 10 " " " • ,. , ll •• '1, 0 ,.11 

" • H.e ", ll 

" , " " " ••• , .. ' . , .. ' .-

" • " " • " " " .. ,'.' ••• ••• .. • " ., I " • ,. " " .. ' , .' , ., , .. " " • " " • " " .. , .. '. I '. I II " , Hoi t L. ~ '.' " p,~ 

II '\ ." " • " " " ,. , , .' ••• ' .. .. • " .. • .. " " • • I 

.. ' .. '.' '.' " " " .. ., lId ' 1 • ~ IUO 

ICFD tes ting completed for day ; TC = testing completed. 

34 
3. Survey Data. 

After each test, the SPTB was drained and the beach was surveyed. The 

distance and elevation pairs are listed in Appendix B and plotted in Appendix 

C. The elevation datum is the stillwater level (SWL), which corresponded to a 

0.710-meter water depth. 

4. Overhead Photos. 

Every hour during testing, the waves were stopped to take an overhead 35-

millimeter photo of the beach (see Fig. 15). The photos show the waterline, 

the longshore bar, and the swash zone. They are useful for a qualitative 

description of how the beach responded to the waves. Appendix D contains a 

series of photos for run-times 01 00, 08 00, 16 00, and 24 00. 

VI. DATA fu~ALYSIS 

This section includes the data analysis to determine the relations between 

I~ and Sxy and 1£ and P£b' The empirical coefficients found from these 

relations are then, in turn, related to the surf similarity parameter, ~, 

which is adapted to the data collected. Also included is an explanation of 

the calculations of Sx ' Ptb , ~, and l~, along with plots of the various relationships. The wave fi"eight used in the calculations is that measured at the 

toe of the beach (average of gages 1 and 2 wave heights). The breaker wave 

height, which would have been a better value, was not used for the following 

reasons. The wave height at the toe of the beach was measured for all 15 

tests; the breaker height was not. fUSO) only one gage was used to measure 

breaker height, while two were used at the beach toe. The significant difference in height between waves lUeasured at the two beach toe gages (see App. A) 

indicates that some wave height variability existed along the wave crest. 

Therefore, the average of the measurements at the two beach toe gages is 

probably a more reliable estimate of the entire wave passing the toe than the 

one gage measurement at the breaker is of the entire breaker wave. A comparison of the data in this report with past studies ls shown in a Q versus 

P~b graph, 

[. Calculation of Sxy' 

Equation (7) 

( 

pgli2 C ) sina S == cosa -- xy 8 g C 

was used to calculate Sxy. Rearranging the equation, 

s 

xy 

pg -2 16 H n sin 2a (21 ) 

where n is the ra.tio Cg/C and a function of the water depth and wave 

period or length. Sx was calculated at the toe of the beach by using the 

average of the wave ~eights measured at that location (see Fig. 7), and by 

using the generator angle for Cl. This was calculated for each set of wave 

data. Thus, for the standard 24-hour test, 24 values of Sxv were calculated 

(see App, E). The average of Sxy for each test is listed 1n Table 5. 

35 
Table 5. Test cycle calculations. 

Test Total Sxy P~b l~ 

I 

Ks 1), [, 

run time 

(hr) ( N/m) ( J /m/s) (N/s) (m/ s) 

1 25 J. 179 2. 201 0 . 611 6 0 . 5190 0 . 2779 0 . 6604 

2 30 I. 137 2.043 0.6889 0.6058 0.3373 0.6686 

3 24 2.280 3.232 0.8396 0.3682 0.2598 0.3374 

4 24 2.158 

I 

3.615 0.6188 0.2868 0.1712 0.4508 

5 24 0.987 0.789 0.7544 0.7640 0.9557 0.8997 

6 24 1.977 2.144 0.9966 0.5042 0.4648 0.6815 

7 24 3.161 4.158 0.7281 0.2303 0.1751 0.4787 

8 24 3.018 3.918 0.3446 0.1142 0.0880 0.4835 

9 24 2.808 4.286 0.5227 0.1862 0.1220 0.3761 

10 24 8.250 14.761 1.0605 0.1285 0.0718 0.3764 

12 24 2.942 4.839 1. 6328 0.5550 0.3374 0.6644 

J3 24 2.241 2.948 1.1941 0.5328 0.4051 0.9190 

14 24 11.578 28.802 3.2938 0.2845 0.1144 0.6112 

15 24 9.253 13.536 2.5502 0.2756 0.1884 0.3934 

2. Calculation of P~b' 

Equation (10) 

'Nas used to calculate Ptb - The term in the parentheses, like Sx) 'Nas 

calculated at the toe of the beach. HoW'ever, the sine term used the breaker 

angle as measured from the photos of the breaking 'Naves. The breaker angle 

used in the calculation 'Nas the average of the breaker angles collected 30 

minutes before and after the wave data were collected (see Fig. 14). P~b was 

calculated for each set of 'Nave data, 24 values of Ptb W'ere calculated for 

the standard 24-hour test (see App. E). The average of P~b for each test is 

lis ted in Ta ble 5. 

3. Calculation of [,. 

The surf simila ri ty parame ter of Kamphuis and Readshaw (1978) was 

presented in equation (17) as 

For the data in this report, a different surf similarity parameter is needed 

since H will be substituted for Hb, as discussed at the beginning of this 

section. Therefore, the surf similarity parameter in the following analysis is 

(22) 

36 
The same beach slope was 

Figure 21. A value 0 f 

H for the entire test. 

used for all 15 tests and was detemined as shown in 

~ was calculated for each test using the average 

These values are listed in Table 5. 

E 

..J 

~ 

U) 

.. 

0 

CD "

" v 

c 

0 

-'" 0 

-0.4 

-0.31=----........ 

-0.2 

-0.1 

I 

I 

I 

I 

I 

I 

I 

0 ________ 1 ______ _ 1~~Y3~~ ______________ 3!~ __ 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

Backbeach 

I 

I 

I 

:--.., Slope Usea in Surf Similorit), Paramefer 

"~ 0.Z5J-0.OOO " Ion 0 ,0.0644 ..... 6.56 -2.65 ..... 

" 

Test Beach 

0.7c--L_~~_~~_~~-~~-~~~~~~~~ 

-3 -2 -I 0 2 3 . 4 5 6 7 8 9 10 II 12 

Station Iml 

Figure 21. Deter~ination of beach slope used to calculate 

the surf similarity parameter. 

4. Special Tests. 

Three tests were performed under special circumstances. Test 2 was a 

repeat of test 1; test 8 was a repeat of test 7, except the sand feeder was 

moved shoreward; and test 11 was done with a generator angle of zero. 

Tests 1 and 2 were both run with a period of 2.35 seconds, a generator 

angle of 10°, and a generator eccentricity of 5.97 centimeters. Test 1 ran 

for 25 hours, test 2 for 50 hours. A twofold comparison of the two tests was 

originally planned. The first 25 hours of test 2 data was to be compared to 

the test 1 data, and then, both sets of data were to be compared to the last 

25 hours of test 2. Unfortunately, due to an experimental error, only the 

first 30 hours of the test 2 longshore transport data was collected accurately. Therefore, the only comparison made was test 1 to the first 30 hours 

of test 2. Reference to test 2 in the remainder of the report refers to the 

first 30 hours only. Appendix A contains all 50 hours of test 2 data. 

Table 6 compares the results of the two tests. The differences listed 

give an indication of the repeatability of the data collection. The longshore 

transport rate changed by L2 .. 6 percent, which is a significant variation. This 

is an inherent problem of longshore transport tests, indicating that some 

important unknown factors are at work. 

37 
Table 6. Comparison of tests 1 a~d 2. 

Test Avg It Sxy Ptb 

run-time IT 

I Total 

, (hr) (em) 

Avg I 

(d ~eeS) ( 11/ S ) (N/m) (J/m/o) 

1 2, 

2 30 

Pc t difference l 

lpct difference -

8.17 H 

8.03 7 

-1.7 -1 2. 5 

(r~. t 1 - Te ot 2) 100 

Tes t 1 

0.612 1 .18 2.20 

0.689 1. 14 2.04 

+12.6 -3.4 -1 , 3 

Tests 7 and 8 were both run with a period of 1.90 seconds, a generator 

allgle of 20°, and a generator eccentricity of 5.97 centimeters. The 0111y 

difference was that the sand feeder, which was located at the SWL for all 

other tests, was moved shoreward 1.4 meters for test 8. The feeder was moved 

because the shorelille at the elld of test 7 sigrlificantly allgled shoreward 

toward the downdrift side of the beach. 111i5 call be seen in the test 7 photos 

in Appendix D. The feeder was moved shoreward to see if a straight shoreline 

resulted. It did, as the photos in Appendix 0 for test 8 show. Another major 

effect was the change in It froID O. 728 ~ewtOn per second for test 7 to 0.345 

newton per second for test 8, a decrease of 53 percent.. Test 8 is excluded 

from the remaining data analyses. 

Test 11 was run with a period of 2.35 seconds, a generator angle of 0°, 

and a generator eccentricity of 5.97 centimeters. 1lle test was meant as a 

control to determine the amount of sand moved by the diffusion caused by 

breaking ;:aves. This value of it for test 11 was 0.089 newton per seco~d. 

A comparable quantity of sand, 0.059 newton per second, also moved updrift. 

Test 11 is also excluded from the remaining data analyses. 

5. Daily Cycle Graphs. 

As discussed previously, longshore transport could be measured only on a 

daily cycle or test cycle basis. For the typical 24-hour test, six values of 

longshore transport rate were calculated. Each rate covered a period of 4 

rUIl-hours. During this time period, four values of Sxy and Ptb were 

calculated, averaged, and related to the corresponding value of 1£. These 

values are listed in Appendix F and plotted in Figures 22 and 23. Table 7 

lists the important statistical parameters. 

Table 7. Daily cycle statistics. 

Relation Figure r2 i l..i!a!;l 6q\Jor~s lines 

No. Standard j Y-interc.ept TIl rough or is! n 

slope slope 

It versus Sxy 22 0.74 0.21 0 .36 0.28 

It versus Ptb 23 0.73 0.09 O.~8 0.13 I 

The square of the correlation coefficients, r2, represents the fraction 

of the variation of It about its mean which is explained by the abscissa 

term. r2 for Sxy a~d P9_

b are 0.74 and 0.73, respectively. These numbers 

show that It correlates well with both terms to approximately equal 

degrees. The least squares lines listed in Table 7 are in Figures 22 and 23, 

which also include the least squares lines calculated with the limitation that 

th~ lines pass through the origin. The slopes of these lines are 0.28 for 

the It versus Sxy graph and 0.13 for the 12 versus P1b graph. 

38 
L 4 

o 

" G 

5 

H 

o 

R 3 

E 

T 

R 

A 

" 5 2 

P 

o 

R 

T 

R 

A 1 

T 

E 

c 

, 

,. 

,. 

,. 

o ,."0 

,. 

,. 

,. 

,. 

,. 

,. 

c , 

,. 

,. , 

8 

13" 

,. 

,. 

,.' 0 

,. 

o 

,. 

,. 

,. 

RADIATION STRESS N~~ 

,. ,.ro 

,. 

,. 

Pigure 22. Relation between longshore transport rate, lt~ 

and radiation stress, Sxy' using dally cycle 

data (tests 8 and 11 excluded). 

39 
L 5 

o 

" G 

S 

H 

o 04 

R 

E 

T 

: 3 

" 5 

p 

o 

R 2 

T 

R 

A 

I 1 

e 

, 

, 

, 

, 

, 

, 

, , , 

, 

q, 

o 

o 

c 

o 

, , , , 

, 

, , , , 

Q' 

, 

, 

" c 

, " 0 

, , , 

LONGSHORE ENERGV FLUX FACTOR J/PI/S 

, 

Figure 23. Relation between longshore transport rate, l~, 

and longshore energy flux factor, P£b' using 

daily cycle data (tests 8 and II excluded). 

40 

, 

" 

, 

, , , 
6. Test Cycle Graphs. 

The average longshore transport rate for each test was calculated and 

compared with the test average of Sxy and P£b- These values are listed in 

Table 5 and plotted in Figures 24 and 25. Statistical values are in Table 

8. rZ for 1£ versus Sxy and 1£ versus P£b are 0.72 and 0.74, respectively. As with the daily cycle calculations, Ix. is shown to correlate well 

with both terms to approximately equal degrees. Figures 24 and 25 include 

both the standard least squares line and the least squares line forced through 

the ori&in. The slopes of the latter lines are 0.26 for the it versus Sxy 

graph and 0.13 for the It versus P£b graph. 

l~ 

1£ 

Ks 

Kp 

Relation 

versus Sxy 

ve rsus P£b 

versus ~ 

versus ~ 

L 4 

0 

" Q 

5 

H 

0 

R 3 

E 

T 

iii 

R 

" 5 2 

p 

0 

R 

T 

R 

A 1 T 

E 

" I " S 8 

Table 8. Text cycle statistics. 

I 

Figure 

No. 

24 

25 

26 

27 

2 

, rZ least squares 

Standard i Y-intercept 

slope I 

0 . 72 0 . 2 1 

0.74 0.09 

0.70 0.82 

0.56 0.89 

4 6 8 

RADIATION STRESS 

0 . 4 0 

0.58 

-0.07 

-0.22 

18 

IV" 

lines 

Through origin 

slope 

0 . 16 

0.13 

Figure 24. Relation between longshore transport rate, 1.2, J 

and radiation stress, SXY' using test cycle 

data (tests 8 and 11 excluded). 

41 
L S 

0 

" G ,-

5 

H 

0" 

$I 

E 

T 

R 3 A 

" 5 

P 

0 

R 2 

T 

R 

A 

~ 1 

" , B 

5 

e 

c 

5 

, , o ,-

, , , , ., 

, 

o 

15 

,'-

, , 

28 

, , , , 

, 

,'-

25 

LONGSHORE ENERGV FLUX FACTOR 

, 

, , , , 

, , , , 

38 

J'rvs 

,'-

, , 

3S 

Figure 25. Relation between longshore transport rate, 1£) 

and longshore energy flux factor, P£b' uSing 

test cycle data (tests 8 and 11 excluded). 

7. Surf Similarity Relation. 

Figures 26 and 27 were drawn to test the dependence of Ks and ~ on 1;. 

Test numbers are indicated in the figures. Table 8 lists the statistics. 

The K terms were calculated using equations (I5) and (16). These graphs 

show that K is far from being constant, as is commonly assumed, and that it 

is strongly related to (. 

8. Comparison to Past Data. 

The units of 1£ and F£b were converted to those used in the SPM and 

plotted in Figure 28, which is taken from Figure 4-36 of the SPM. The SP~j 

figure was modified by shifting the x-axis to convert from P£s to P£b' 

Equation (13) shows the relation between P£b and P£s' Test numbers for the 

data points of this report are noted in Figure 28. 

1\.ro major observations are immediately apparent. The first is that the 

laboratory data in this report, as in laboratory data from past reports, have 

considerable scatter. Since the surf similarity parameter, ~, in this 

report varies by a significant amount for the different tests, as shown in 

Figures 26 and 27, some scatter is expected. The surf similarity parameter, 

of course, does not explain all of the scatter in the laboratory data. There 

are still some laboratory and scale effects which are not yet understood. 

42 
0.75 

:to.50 

0,15 

KS ' 0.82 [ - 0.07 

,2 , 0.70 

'"' 

" • 

.9 

• '0 

.2 

'2. 

to 6 

• 

·4 

/ • 14 

·7 

. , 

. " 

°0~-L~0~.I~~Of.~1~~0~.J~~~0~ .• ~L-~0~,5~~~0.~6~--Df.~7~~D~.8~~~D~.9~--I~,0 

Figure 26. Relat ion between 

parameter, t:. 

(tests 8 and 11 

C 

Ks and the surf similarity 

using test cycle data 

eKcluded) • 

43 

I. 00 r--r--,.-r--r----r-r--r----r-r--r-,-.,--,--.,c--r---,--r--r----r--, 

0.75 

~O.50 

0,15 . , 

9 

0.1 0.2 O,J 

Kp'0.89C-O.22 

,2 , 0.56 

.15 01 • 4 

• '0 

.6 

12- 2 

• I 

., . 

0,' 0,5 0,6 0.7 

C 

. , 

. " 

0,8 0.9 

Figure 27. Relation between Kp and the surf similarity 

parameter, f" using test cycle data 

(tetits 8 and 11 eKcluded). 

43 

1.0 
~ 

>. 

"-

.... 

SPM Design Curve 

* 

/* * ~. ** 

* *. • 

914 

~ 10 4 * 

• 12 A-

. 

0 

'" 

0 

0:: 

~ 

0 

0-

"' co 

0 

~ 

fOJ 

~ 

0 

"" "' 0-

co 

0 

--' 

10 3 

10 2 

10' 

13 ~. 6e e 3 • 

5e 2~ e e7 

•• I qee 9 

• 

•• . • • • .. . ~ 

.. .t..~ :- I ~ • . ~. . ......... . ... ... ~. ._.y". e. .~ \ .. . . ,. --.... 

• • • •• 

•• • • 

• 

• 

elO 

e Presenl Lab Dala (Test No. Included) 

* Post Field Data 

• Past Lab Data 

100 L-__________ L-__________ L-__________ L-________ ~ __________ _ 

10- 3 10- 2 10-' 100 10' 10 2 

Longshore Energy Flux Foetor, P.l b (It-Ib/s/lt ) 

Figure 28 . Compar ison of data in this report to past reports, 

using SPt1 Figure 4-36 (tests 8 and 11 excluded). 

44 
The second observation is that most of the data fall beneath the SPH curve 

data, 

field 

connoting low values of ~. Since the SPH curve is based 

mostly from Komar and Inman (1970), a possible explanation is 

data were collected under conditions of higher values of E. 

the laboratory data. Karnphuis and Readshaw (1978) suggest 

Inman's data were indeed collected under conditions of high 

reasonable to assume that the ~ values were also high. 

VIi. SUMMARY fu~D CONCLUSIONS 

on field 

tha t the 

than 

tha t 

~b' 

those for 

Kama rand 

It seems 

An analysis of the radiation stress, SXY' and the energy flux factor, 

Ptb , shows that both predict longshore transport rate, It, to comparable 

degrees. Approximately 70 percent of the variance of It about its mean is 

explained by each term. There appears to be no major advantage in choosing 

one over the other to predict the longshore transport rate. However, S y x 

has the advantage of being constant seaward of the breaker zone while P£b 

is not. This makes the calculation of SKY more convenient than P£b' 

which must be determined at the breaker line. Q1 the other hand, P~b has 

the advantage of having the same units as It. which means that Kp is 

dimensionless. 

The empirical coefficients, Ks and ~, are far from constant although 

K is commonly assumed to be so in practice. Part of the variation of the 

cgefficients can be related to the variation of the surf similarity parameter, 

~, as shown in Figures 26 and 27. These figures show that Ks and "p will 

increase with E,.. The considerable scatter eVident in Figure 28 can be partly 

explained by the relation between the empirical coefficients and ~. The data 

in this report and past laboratory and field data are compared in Figure 28. 

The laboratory data generally predict lower values of l~ for a given P£b 

compared to the field data. Part of this trend can be explained by the differences in the surf similarity parameters, assuming the field data ~ere 

collected under conditions of high~. Also, laboratory and scale effects 

probably contribute to the lower laboratory transport rates. The relative 

importance of these factors is suggested as a subject of future research. 

45 
LITERATURE CLTED 

nlESNUTT, 

V Ill, ~iR 

C. B., "Analysis of Results from 10 "lovable-Bed Experiments," Vol. 

n-7, Lanorator,! E:ffects i.n Beach Studies, U.S. Army, Corps of 

Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., June 

1978. 

FAIRCHILD, J.C., "Laboratory Tests of longshore Transport," Proceedings of the 

12th Conft;~Y'ene.e on Coastal En.gineerinq, American Society of Civil Engineers, 

Vol. ll, 1970, pp. 867-889. 

GALVIN, C.J., "Relation Between Immersed i~leight and Volume Rates of Longshore 

Transport," TP 79-1, U.S. Army, Corps of Engineers, Coastal Engineering 

Research C.enter, Fort Belvoir, Va.) Hay 1979. 

GALVIN, G.J. Jr., and Et\GLESON, P.S., 

Currents on a Plane Beach," TH-IO, U.S. 

Engineering Research Center, Washington, 

"Experimental Study of Longshore 

Army, Corps of Engineers, Coastal 

D.C., Jan. 1965. 

GALVIN, C. and SCH\,,'EPPE, C.R' I "The SPN EnerGY 

Longshore Transport Rate," TP 80-4, U.S. Army, 

Engineeri.ng Kesearch Center, Fort Belvoir, Va.., 

Flux ~k=thod for Predicting 

Corps of Engineers, Coastal 

June 1980. 

K..A~1PHUIS, J.W., and READS!-iA~\ J.S., 

Transport Ra.te," ProceedJngs of the 

American Society of Civil Engineers, 

"A flodel Study of 

] 6th ConI erence on 

Vol. Il, 1978, pp. 

Alongshore Sediment 

Coasto.l- Engineering, 

1656-1674. 

KO~1AR, P.O" and li'-."MAX, D.L., "Longshore Sand Transport on Beaches," JOllrrnal. 

of r,eophysicaL ReseaMh, Vol. 75, No. 30, Oct. 1970, pp. 5914-5927. 

LONGUET-HIGGINS, M.S., "On the Statistical Distribution of the Height of Sea 

Waves, 1," JOIll'YIO..Z of ,11a-r-l.ne ReHearcn, Vol. 11, 1952, pp. 245-266. 

LONGUET-l1IGGINS, M.S., 

Waves," dournal. of' 

pp. 6778-6801. 

"longshore Currents Generated by Obliquely Incident Sea 

G'eophys7:caZ FfeBearch, Vol. 75, No. JJ, Nov. 1970, 

SAVAGE, R.P., "A Sand feeder for Use in l.3.boratory Littoral 

Studies," The Anrw.ar BulZetin of the ReaC!h Erosion Board, Vol. 

Army, Corps of Engineers, Washington, D.C., July 1961. 

Transport 

15, U.S. 

STAffORD, R. P" and CHESNUTT, G. B., "Procedures Used in 10 Movable-lled 

Experiments I" Vol. I, MR 77-7, Laboratory Effects in Peach Studies, U. S. 

Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, 

Va.) June 1977. 

U. S. ARMY, CORPS Of ENGl NEERS, COASTAL WG INEERING RESEARCH CENTER, .%ore 

Protection ,"lanuac, 3d ed., Vols, I, 11, and lII, Stock No. 008-022-00113-1, 

U.S. Government Printing Office, Washington, D.C., 1977, 1,262 pp. 

46 
APPENDIX A 

HOU RLY fu~ DAILY DATA 

The data in this appendix are available on computer cards from CEIAC. 

47 
111' .. .1" )00 I,U 11(0" 0, "'~IUI ' u.,~( " on'", 

' U' T, .. , v,,,,, ,,, ",f. 1 ".'" P'''' ''lI!l • ... 't liE all 1 "II.t. . ~O '~. , .".-,. 1' 0 '·10' ri. ... Oi."" ·,1'''' ,. "" LI , ....... , .. ., "~ 'I ttl ' ' " ... elea , ",,.(it r 'IH ) ,." " ' .6 OU_'" ,.,. , , 'I, ., 

, • " " , , ,,, \~ ,~ -, . , , II, ~ '-' , 'I ,~ 

, " " ~, "j 

r · "., ," ., , , , 'l ~ , • • " I ~,~ ., , , , 0, 

" " 10.1 ", " , 

" .." , ' ... , • " , JHt 

• • " " ' .. • · "

" , , , " " , • , . , 

, 

" , ' " .1 " . , 

" ,0, ' .. " , Lelo) , 11 ... 'I. ~ • , , " '.' '. , " , 

" " '.0 , ., " , 

" " I t ,I " . " I " " • " " L ~ · "" , 

" , 

" " I (I ,' · " " , ,0 , & , , .. H,~ 'I ~ 

" " " , • , r " , " " " . · " " • " " ',- ' .. " , 

" " 11 , 0 -.' " , " " " , . , 10 , 0 " , 

" " 10.' ' , 0 

" ,,, )IU 

" , 11.8 'I . " " , 

" " " , I I' . , ',' 

" , " H, " . J, iI 

" <. 

" , 

" " 10 ,1 " . " , " " , 

" I I 1 O , " ,. , ,. 10 ) 0 , , · ",. " " ., l' ~ 

TU' .. 1(111 0 0 I.n UtQ"OI 'I~HI"'D' '''Dll " Onl(tI 

, lL' '1. 11 

" , " lo,a ), . , , , Il , " I Q." , .. , , , , r " , , 10," -, . , " 10,0 · " , 

, 

" ,0. It " , 

° CF!J te s t ing comple ted for day; Te = testing comple ted. 

48 
nl' .. to'" 

' v, '1-' -, .. fU .. 

". _U,. '.08( •••• •••• "fI~"'f 

."'f ••• • r..'· 

•• l .'.u.1t • , 0"10' " .. , "". ., 'P' c. U., . 'U .. ,It, '''t .. -, cr", Ivl ,. ,,, '.'f I ~'if I •• U I i lil . .,., .... U l ,-,I 

" 10,~ 

- " . • C>O lHl 

• 

.1, 0 

• " " , '" • " I G, 0 ., . , , • • I " 10 .' 0 '.' C-' I .~~ 

, I) 

• • , I •• '

• " ',I ',I 

" , 

" " I, • , .1 

" • " " · ", " 

" • " " · .' " . " I 

" .. · .' · .~ " , ,-, 19.~ 

I' 0 1I. , 'L ~ 

" • I' " " • 

-" , ,-

" .. 

1

0

• 0 , ,0 

.. , 

" " " ' ., 0 

" • " • " " " · .' ., . .. , 

" .. 1 o · ,. .. • I ' " '.' · " " • ," H~40 

" • 

'1, 0 

" • " .. 

- ,I · "" • .. 

Il " 

, .1 , ,I 

" .. " " · "-" II , II 

.. • .. '.1 ,. , " I 

" I .. " .. · .' " . " • '" la .. ~ 

" , H.o 'I .' " .. • " , ,. • ,I " " to IO.l 

II · " • " • " .. <I, ~ . " , .. 0 

" • " " .. I Q ,I • •• .. .. " • -. , • ,I .. .. " '. ' · "" ", l"w 

.. 1).0 'I. ~ 

" , .. .. " , " I " , 

" " " to -,' '.' " • " " • " .. -, , ',I U • " " " .., " , , . ). I 

)' " ) . • .. • •• '.1 

" I 

c' 0 

" • U.' 

.".(\ 

" " " " I ,I " . " • " , , " .. _ ,I 

" > I' 0 

" , , • " ' 

.. .,. " , 

" " " ..') 

49 
l( .t " (0'" 

'" T IR! "1"\,11 •• " It_ ·&11_ 1"",1110 . n. lOll 'PI' "U~I' lO~C''' .' ......... 1)0"(01 "I" til'!>' ·tlll'" t· ."'~, (\IIU .. , 

•• tt~, lUI t· '''' ,,, '''1 , ""f 1 Glel I "III til,., Ole'''' (",I 

" I .~ I, • 

" .. " " I ~ , '1 " , ., t t " .. , 11.' 'I ,oJ ., 

.. " " ., , 

',' ',' ., I ., " ,. " . ',' • , .. " . ", . " , , 

" 10 

.. " .. I " , " . .. " , .. " " , , " 

" , c·. " I I' " 'I , (I 

" , " " .. " . " . , .. " " . ., , .. 0 

" ., • .. " , '" " , .. , .. " " , .. " ' • " " ,.. " " I " ' " , 't 

lit' .. '11 1111 I. " nco"OI 111"1'''0_ ""'Ll " OU· ... 

, II, • 'I., • 0 " " 

I ), ~ I I, J , 

, , 

• , " 11. I \1.' , • 2 I 

• " \1, , 

I I, .. 

.. , 

.. I} . " 

". ) , C" 11, 0 '0. '\I ,"J 0 11 ,6 11,' 

I 

.. 11.\ I ... . 

I 

, 

I . 

11.1 

, I. , 

• , I 

• " 1', e I)

. ) 

• 

C·, II • ~ 'e. J , H,Q J I . r , 

.. , II •• I' •• C·. ll. e> " .A 1'~J , 

" 

}I.a J! .~ 

.. , 11.0 I) 

• • 

, , I, " . 

I'. ) 10 • '10 

" , 

" .. l' " I I, ~ 

II , II , II .. II. ) \o.Q 

" c·, II. ~ 

J ( •• )0 I e 

" 

l Q ... '1. 0) 

" • " " ii,' 

I' .(1 

" 0 11 , 11 .. 

1 ,.1 I J ,I 

" 

, '" 

" 

, 

" " I' ." l'l.' " • " • " " " I I.' I ~.) 

.. , c· , l' .1 '0 .• i~I Q 

.. I \'\1 ., J I ~ 

.. • " " 11.oJ 11,1 " • " • " " I I. I 11 .1 

50 
ru' OJ 'I,.., au .. 'I'" .. twfi . -.1 ••

.• r, _ 1-·.·'1.0 

. ... f ... i,.' ... ,,

'" ,-0_" "0' • ........ .... 'lO' 11- OC ' , .. -, It'"~ (' i "LI e",,..[., t", M' -, (CUI'" (. <0' .. ,( , ~,u I .... I •••• IIA'" 0 ........ e·/· 

.. , .. '" , .. " ",- 11.1 

" , , . , 

" " " .... II ,_ 

.. , C'' "" '1, 0) 1010 

It , 

\ ' ~ 

' 1.>1 It • " II " . I', • \ J.I , • " • " " " I'" II.) 

" , '" " • " " t I. \\ \ I ,8 

.. , .. • " " I),l .',0 I' , IC " 0>1 

rUT .. 'tll,Oo 1,'0 t.eQ"O' it~UUO. 'WeiLl " OU.u. 

",0 , 

'. , \\ 

" , • o. J I .' 

, 

It I ~ ,.I 

1 1.1 , "' , 

" 11 .1 

I ) .' 

• • " 11. 0 \1, _ 

• ,-, 

11. t " . ~ Ih~ 

• • 

I II, ~ 

' 1.0 

• " \I " 1',1 ., 

, 

" I' 

. 0 10/0, ~ 

• • '" 

• " 

10.' 1 J,' , 

, • " 10, 1 11,_ t cOO I' " ' 0.' 1 10" 

• 

\ ', , '1. 0 

" • " I' .' II. ~ 

• • ,• • ,., 11,1 11.1 

" • "' " ,.." I ~. o Il. ' 

" • " , 

" " 10. >1 II.' 

" • C', I'. , " .0 1'1' .. , " .1 '1.1 

" • .. " 10.1 II, I 

.. , .. , , .. " I' .1 II •• 

.. • ... " 

, , . .. • o' 11.0 

.. , .. , .. " '0 , II.' .. • C-' I' .• " ." I I ", 

" , I t,~ 

, : , I" 

.. • .. " • o· II.) 

.. , .. • 

" " '0 • t 

i.' .. • '" " .. • " • o' I I " 

.. • I' ,

" " '0' I.~ 

10 • C'O ... 1 

't ,1t , "to' 

" , It ,~ 

' \ .0 

.. • " " '0

,' I),' 

" • " • • " " '0.' "," 11 • '" " • " " '0 , ' 1 ,1 .. , 

51 
'I tI " (0'" 

'0- 1 J-. -'"'''''' ·"tll .,t,_ 1 .... rq." .... , .. ,. .... , •• •• ~1· ... O"',1oI0U ....... ,to"'" ,, .. , Ot"" ."C'" ,. ''''ll CU'.,,,, t," •• •• lCU'to, ,. , .. "'1 , .'111 • "01 ) "'C. U, •• OUUI' C·" 

" .. • .. ., , II,' .. .. " 0 'c I"~ 'I, I: 1110 

lUf .. '(1f'00 1,00 .ltOIi't W, .. ,..'O_ '''Ii~1 " O(lIIfrtl 

0 Il,~ f\ ,~ 

.. • · " , • ,I • ,I I I ,I 

• .. , , " " , , " I ~". I, 

I 

.. 

• · " , " , " I, • 

I 

.. -, . , ,- ., I II," , C" II,' " ,0 lUI , . I.' ",1) 

I 

10 I, _ 

, , " · ,. ''.~ 

I 

" -,' -" .. ' ' .' • • • '" 10' ' . , ' .. " . , 1.0 , 

.. • .., , .' .,. It. P , ,., II.'!> 11. ' HI-

- II.~ " .~ I I 10 I •• I.- ,0. ~ • Q. ~ 

I 

, • lO -,- · .- '. - Ie ,I 

" , " " • " " -,- ' .. I, , le,l 

" - " • " 10 · .' .,- '.- Ie. " " , C'' 16.'" " • I J. 0 'I, ~ 

" , 

" .. -" " • '. , " . 1,0 

" I 

" " I,' " , I, ' ',I 

" , I, 

" I , . " " , · " '.' I, • 

" C 

" , 

" .. ." ',' .. , I, , 

" • C" ,lot' '",' lUC 

" - ,. ,t ': ." 

" , " 10 " I " ' , ,I 0,1 I '-3(; ,. • " • " " , ,. , .. • ,I , " .. ,,, 

" • '" " • " .. · " 

0, , ' .. , " '~I(. 

" - " , I • " I,' " , I Q.O10 , C" ,- ,0 'c,o lH~ 

10 • ,- .0 " ,~ " " " .. • ,I , " ',' . ,- " " " • " .. , ,I • ,0 ',' ... II • " II " , .. " " • ,0 " ° ••• 0, ) " " • " " .. .,' 0,_ ',' 1,0 " " I, 

t· 0 'C \ J •• 'OJ, ' ilo" 

I( af .. .,11100 t.n "to"o, '~"["'O· ."C\I .. 0"'''1 

", e , " .. 1001 " ' " ' !D.c " • 

• 

-

" " , , ,0 '.' I,' " • 

S2 
ttlT .. (0"" 

'"' q"f ","\1111 _ IJ(II -llfA ,I<"'(lItO _ ....... l<t ""'T .11"'11( _ .... ItU .. O •• ..( .... ,TO"'UI J T("', 01,,11 ltl"" C' ."'ll (uut .. , tt'l 

•• ., Ctl~I~' . ' CO' .. , . • !.'r GI't J .. ,t .. ,. . O"~ln (-I' 

f 0 

f • '" 10 

• 10 10.' , " . " · ,." " ... , , \I 

10 , " " . " . . " " ..... 0 ." , 0.' '\ .0 U·' • II.' ," ,0 \I 

" '" · " , " ',. " • • • I 

10 · ,.',0 , " .,. " " , .11 1 

" ." .,' -,' · " .' , 

• , " ',1 " ' . ,.',' " • , .. II.' ,e.' 10.0 

U.O ",0 , 

10 ',I · ,." - '" " , • , • " · " " . -,. ", " " , " " I " " .. ." .,' " . ',' " " • " \I 10 - ',' '" .,1 ,,' " - " , .. , II •• T L, ~ ,'.0 

" • 11,0 Tl,o. 

\I I , 

" .. ',I ',' " , ',' " " 0 

" • , 

" " .,' .,- , " '" " - " , . , ." • I' " ',I • ,0 

, ,. ." " " 0 

" I 

" " ',' ',' . ,.., . I' 0 " '" II,' '0, • " .. " • I' ,0 '1,0 

" • \I 

" " ',I " . , ,0 

-" " " , 

" • " \0 ',' , ,I , " "l " " 0 110 

I' I II 

" " , " " - .,- " , " " 0 • I' I 

" " ',I · " , " .,. .. • " - '" I J ,I J 1,0 n,. 

" 0 I',. '1,0 .. .. • " .,- '" , " · " " " • " • \I 

" 10 

-" " , ." 10,lO 

lJ • 'I " lJ • " .. ',' ',1 .,. " . I' n 

.. • .. • " .,1 • ,I '01 · ,.a " ., .. • 'C II ,. '" . u,· lUI 

'f'100 I. '0 1t(!)IOO' " it,,'"IT!). ""<ILl .. [llGlltu 

• " , ",a 

• \I 

.. L I ,- I J ,0 11,0. 11,1 IO • .. II 0 

• " 11,1 I L.l 11,8 

, 

0 to I~II " - " '0 I I.- 10.1 J I.) •• 0 

I 

10 11.1 II ... I I._ " 0 

0 ," ',. " ,a 110' .' " ,0 " ,<I • 10 ',I ,0, I II. , " " • 

- • • I " , 10 • ,I '" II. , 1/ • , .. 1111 

53 
.. • 

, • ., 

, 

, 

.. • 

• • 

" · " , " 10 ). ' " , " , II ' 0 " , " 0 11 • ,

uU 

. . II • 

11 h 

. ' , ,. . I~ 10 " . " I' 1

. 0 .. , .. , .. . It I e " , " , ,,, 10 

II • " It I, . 

" . " " . , I' l ¢ " , 10 • 

.. . iO 10 II , 

It " )0 . II , 

II • 

U 10 .. .. . lJ )0 

It 'I .. . 

, 

• 

.. • 

, . 1 J' 

• • • , .. • I • 

J I 

I " 

• " • 

.. • 

, 

· " • I 

.. 

, 

• " 

• • , " " , " 10 I. t 

"~II\,1T" "'''lO' 

'00 

" 

.. 

'" 

" 

, 00 

'" 

10. 

" 

'" 

.. 

r'o I , 

'.II tl ,,~, 

ttl\. lUI 

II,' 

II,' 

l' .1 

" .1 I ' .1 I\ I,. '.' 

11.1 

, I.' 

",' 

" II 

H, c '1, 0 

" • B 

~II'~ "' JD ", '''-J .. 

IU' 

10,1 

'lOti 

hU I 

'.' 

'.' 

• •• 

.. , 

'. , 

'. , '.1 

10 ,0 

'.> 

I,. 

· .,

',' 

• •• 

.,. 

' .. 10. 0 

" . 

.. ' 

lUI .. 

.", ,. "." .. , ,uri . ... U. 1 1 ,r I' .1 

',' 

· .'

II. r 

. ,. I I. (I 

11,' I' o' 

10. ' p, 1 ".-

· .' 

I) . , 11, 0 

11 .' 1'

, 1 

10, 1 

I' .. 

., . 

".' 

,. II 

I I.' 

10,1 11,_ 

u.' 

UII '.11' 

",' " ot 

I I •• 

'!~IOD I," IUO"I)I Gt""'III ,,' ..... LI 10 OUIIU' 

",' ". ~ 

Ut_ 

" . 

10 .' 

" . 

, .1 

.,. ." 

• •• 

• .> 

., . 

• ,> 

II.' >, 1 

• .1 

',I 

• .> 

> •• 

II.' 

II,' 

10.' 

I'.' 

••• 

" .t 

II.' 

I J.I n.' 

I I It 

11 01 

, ... I I.' 

". J ., .1 

,II, a_I" ..... coLI DUII,,_ 

" 

" 

• 

11 

11 

" 

" 

.. 

" 

" 

" 

1\ 

II 

II 

1\ 

1\ 

1\ 

IS 

II 

11 

II 

" 

II 

11 

II 

" 

~g "I'IG: 1 'II ...... ' C-/. 

" 

" 

.> 

" 

" 

" 

" 

.. 

.. 

.. 

II 

" 

.. 

II 

II 

II 

II 

II 

.> 

" 

.. 

.. 

II 

.. 

.. 

.. 

" 

.. 

" 

• 

• 

• 

•••• 

• 

• 
" . II " h . " . " " . , /I H 

" 

I " J'0 " . I. " 1. 0 " " . , I' 'e 

" 

,. " , ,. I, " , " I' 10 . ... 

.. , IS" I, ,

" . , , " 1. .. . " . " , lG J. 

II " . • It 10 .. , .. , lila 

... 

.. , 1114 

U ". " . 

• " • • " , 

.. 

, • 

.. 

• • , 

" • J 

, " • • 

· • " • , • .. • 

• 

, • 

, " • 

• , " " . " , I Q IQ " " . , \ 1 10 

.1l " . • 

II " I. " . " II IQ . .. . " J ,~ 10 " . " I' 10 . .. . " . 

", 

.. 

," 

, .. 

." 

" 

.. 

• •• 

• 

'" 

'" 

.. 

,,, 

.. 

'" 

'. u'" "' thilUI 

II,. 

It.O 

I J,o 

",0 .1.' 

, •• 1 

" .1 

, '.0 

\'" 

,. " 

" ,0 

" .. '1, 0 

h •• 

111I'[lIIlla 

-t alf' ,01 

lUI 

n. 

.to 

h' 

',' 

.,. 

.,' 

I,' 

" , .,. 

.,' ',' 

" , 

" . 

. " 

.,. 

',' 

ttiT Q' 

.". "'IG'" C. 

lhra, ~.;r 1 

I' ,I 

1',- II.' 

I r.t 

11.1 I r. I 

II II 

Il, t 11,1 

1101 ", , 

It. , 

II.' 

, 1,0 

II.' 

",0 

.1.0 

II,' I' 01 

i." 11'" 

1t,1 

,. I' 

"t' 

" " 

n., 

,. ,1 

u •• 

It,' 

u •• 

"'100 1,'0 nCaltOI GfltlUIOtl '''tL. U OtillU. 

" .~ , 1,0 

r" • " ,0 

".0 " .0 

'-,' 

" ,a 

IUO 

I tJO 

tU-

',' 

II.' 

",0 

". , 

I' .1 

11,1 

10 II 1 1 .0 

',1 

\0,' 

II, • 

II.r 

11.0 II ,I 1\ ,I 

" . 10,1 1001 

" . , , ,I " 01 

10 . , 

11 ,0 11,0 

',' 

1

1 .0 11.1 

" . 1101 

I I It 

" . 11,' I' .• 

. "II, • 

. ,. 11.1 lI.t 

'" 11.' 

" , 11,' II" 

',' If,t 

" , II,. II,· 

',' Il,t I J.I 

" . II,' 11.' 

',' 

55 

• e( .tllll 

'~'~I O""IU 

" 

.. 

II 

" 

.. 

• 

.. 

to 

" 

" 

to 

II 

.. 

" 

" 

" 

" 

" 

" 

.. 

" 

.. 

.. 

.. 

" 

" 

" 

" 

" 

" 

LO tu .. " __ (. .. O-r • 

tW/' 

" 

" 

, . 

" 

" 

" 

" 

" 

" 

" 

.. 

" 

" 

" 

" 

" 

so 

.. 

.. 

" 

to 

" 

II 

" 

.. 

" 

.. 

" 

, 

• 

, 

• 

'1'_1' 

.1'.1' 

.,., 

., .... 

"., 

"., 

".I' 

"., 

.. 

.. 

.. 

.. 

.. 

.. 
. , ". 

" . " In " . " l'le . 

" " 

, 

, " It ,0 " . • ,. ' 0 " . " " . , U )0 " . " II J. . " . " II . • II ~ " " . , .J h Uti 

.. 0 

• 

". " 

• o 

" • • .. 

• • .. 

• • ,

, . " . , . , .. 

• • 

.. 

• , 

" • • o 

• o " • , 

, " " . " ,e JO . " . It " .0 . " . " . " Uu 0 

" " . , 1110 " . " 0 

" )C 

" " . 

. ' )0 " " . " ,,)0 . " . " . .' 10 " , " . " U 

" " . , " ~ 

" " 0 " , 1 0 '0 " . " ) 

"1.11'.' 'jl'l "0""'0' IV'~ 

,0, 

" , 

" 

' 0 

,0, 

'" 

, 

'" 

t 

,. , 

.. 

'" 

, 

," 

'" 

flU 'V, 

1 ,., 

1 '.' 

1 ,., 

,I., 

",,1 

", . II, I 

' ....... '0 •• '1 __ ' ." 

,." 

to· 

to' 

IIGr I 

I' ,. 

, , " 

, , fl 

, ,.' 

, , ,I 

",I 

II.' 

'I'I 11 

...... , f.'" ,. ltiU. IIIC;I • 

II,' 

It ,0 II. , 

11,1 

' .. , I.' 

•• t 110' 

o •• " ", • • t 

10 •• II. , 

n,l 

'1. I 

II.' 

11.0 

11,0 

, 0.\ 

10 ,I 

10 " 

"t1 l00 1.'0 .ICO-OI ""lIllO •• ".LI ' 0 O,.'tll 

. , ,0 

" .. ". e 

" ,6 ",0 

'0,' " ,. '0,' ", I) 

'D,' 

" ,0 

"I' 

JUI 

, 1.1 

", J 

,I. , 

l' ,I 

II, , 

t I,' 

1',0 " , , 

,. " 

I' .t 

" I) I I.' 

I' ,G 18, , 11,' 

I' .1 It.J 

11,1 I e ,I " .' 

" ,0 

,I. J 11.1 

P.' 

u •• 

II, , 

\ ', I ", , 

'I, I I' ,-

11,1 

I',' 1'.0 It •• 

1\ , 0 1701 

", . ". , 

1',,1 

".' If._ 

\',1 , '. 1 

I ' .' 

, . ,I .... ", , ,I,' , ,,, 

, I,' "" 

56 

,,(.,., _ u 

p,U_U I 

" 

" 

" 

" 

" 

" 

" 

" 

" 

\I 

" 

" 

" 

" 

" 

" 

" 

.. 

" 

II 

" 

" 

" 

" 

" 

" 

" 

" 

" 

" 

" 

l'''''''''·. ,"""1.' ,.,1 

" 

.. 

" 

" 

" 

.. 

.. 

" 

.. 

.. 

.. 

" 

,. 

" 

.. 

.. 

It 

.. 

.. 

.. 

" 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.. 

.'-f,,·,. 

hI" 

" 

" 

" 

.. 00 00 

to 

" 

o 
TflT I' to"" 

,," ... 

" III /I • 

/I • 

" J. 

.. " . " It u .. .. . 

• • • · 1 .. • 

.. • 

• • It 

" • , 

•• • • • \l 

• .' .. · , > • 

· , " . ,

" 

• 

· " , • 

· " " " 

10 10 . " . I " I 10 . " " . , I. " 1t . I J ., " , " II 1~ . I' , " , I- Je " . " , I' 10 

16 t " , " II> H . 

I' " . • I' 10 

I' • I' • 

I' H 

,. 

" . 0 

I ~ 10 

10 

,. . .. 1 

H 10 " , I " J 11 . II • " II }. . /I , 

II , 

11 10 

.. "" . 

• 

· " · " · " 

"l!"uH' 'II I .. 

"O~.(OI U rI' 

.. 

•• 

.. 

" 

I" 

" 

," 

" 

I" 

• 

I" 1 00 

" 

'" 

tlll ' 

I I •• 

Uri 

II. T 

~ I. ~ 1I.' 

10.0 I' " 

,I, • 

n •• 

1

1 "'

111' 110' 

1r1J "'! ." . ." ""',,' ~"I I " '''I 1 

I" .0 

II •• 

TUT II 

",1 

I 'P,' 

tt" 

'(11,00 I,n IItO"O. ~r"f"JOIl ''''ll gO 0''''(1' 

'I,D 

'1,0 

'0.' 'I,.e 

'0.' 

" .0 

" .0 '1,0 

... 

... 

" 

." 

". 

... 

10 ,. 

" J 

" . 

· " 

" , 

" . 

IO,J 

',' 

· ,.

',1 

· " 

• ,> 

., . 

" , 

· ,.

" . 

" . 

',' 

" . 

• ,I 

· " 

',> 

· " 

',1 

H., If 

" , · ,. 

" . J " \1,' 

• ,I " . I J.' 

" J 10,0 

',' ',' Il.' 

" . " , II,' 

" . · " 

II,. 

" , " J II •• 

. "" . " , ',' il.' 

t,> · " I I 01 

" . " . J, t 10,0 11,1 

t ,t .,. II,' 

· " 

',1 I J.' 

• ,I ., . ',' " , J', I 

· " ',' 11.' 

',1 " . \ I. t 

" t " . • ,I ',' 11.' 

t, • " . ',1 · " II •• 

I,t ',' II,' 

'rJl,I)~ I.n .lto .. O. Q(~('UTOII '''OLI 10 OUII((, 

" ,0 

57 

,IIIU[1I 

'Io'LI 

0("((' 

" 

" 

" 

.J 

.t 

•• 

., 

•• 

., 

•• 

•• 

.. 

., 

.. 

.. 

.. 

.. 

., 

.. 

.. 

.. 

., 

·1 

.. 

.. 

.. 

.1 

.. 

" 

lO",."O" 

tlllllllt .. , 

t"" 

" 

II 

•• 

.. 

.J 

, 

o 

o 

o 

o 

o 

o 

o 

o 

, 
....... 

.. 

• I 

.. 

• • 

· J , " , ,10 , • 

I 

.. 

• 

.. • 

, 

• .. , 

.. • 

, 

• 

.. • • • • .. • J. , " 

, ~ 11 . " . " " ,. 

. " . " . " 11)0 . Jl , Jl • 

IJ lo 

I' , 

" I L. )c " , " , " H 

" 0 " , " I ,. '0 " , " I 

" It' " . " . " 10 I ' • 

L' L' , .. 10 

.. . .. " . . U 't; " . I

" I 

1

. 0 .. , " I llU 

II • 

.. , U I. ,J II 

... 

• 

.. 

• 

.. , 

.. 

• 

.. • 

• • • 10 · I , • · .. 

• 

.. 

" 

f' , 

.. 

flO 

" 

'" 

" 

eoo 

" 

" 

'1 

eO, 

" 

" 

" 

" 

" 

" 

-.11- 'I·' ChUv' 

" ",. " 

.... 

'S .e 

",1 

,) .t 

,S .' , ... 

".J 

u" ". , 

'c " " ,0 

'C, ' ",0 

1Il1>0,.1110 

-t I g"1 

'" 

"., 

"" 

,u. 

•••• 

t',1 

,u, 

.40Cl 

" , ' , 1 

10.1 

• ,I 

' 0. 1 

· " 

II , 0 

10 •• 

II .1 

· " 

" . 

" I 

" . 

',' 

., , 

',1 

" , 

" I 

'''' 11 

.. ,VI ",I'''' 

,." I " hU J 

., J " I 

I, • ., , 

'. I .. ' 

" , " , 

',!! 

. " 

I, • I.' 

I, , I. , 

" , I, , 

" . • ,I 

1.1 I, , 

'.J I,' 

'.' " I '.' ., . I, J ., . · " " . • ,I ... ., . I, I 

'.' ., J 

" . " , 

1,1 , .' 

I.' " I 

1,1 ',1 

un U,I, 

· " 

· " 

" . 

t,l 

II.' 

t •• 

'.1 

'.J 

' .. 

',e 

" I 

I" 

I, • 

'.1 

1.1 

I.' 

1.1 

., I 

-,' 

10,1 

\1,0 

' .. ,(IIIDIl '.00 nco"o. il",ru1C1' ''''~l '0 Cl I''-UI 

•• 1 , ,I ',1 ' .. ., , · " 

" , · " 

I, I , .1 " . ." 

1,1 , " '. J -, . , " , ,. I.' " .' 

I, , I,' '.1 l I.' 58 

.11 .... 1 

'''IoLl 1,1",11'" 

" 

II 

" 

" 

" 

.. 

" 

" 

" 

" 

II 

II 

" 

" 

" 

.. 

II 

" 

" 

" 

.. 

" 

" .. 

" 

" 

" 

" 

" I -

LO",,"I,II, 

C II"'" , , .. ,I 

.. 

II 

II 

" 

II 

" 

.. 

II 

.. 

n 

.. 

.. 

n 

" 

I' 

" 

.. 

" 

" 

.. 

" 

" 

" 

" 

I 

• 

• 

• 

.. 

" 

" 

" 

" 

" 
..... 

-

• • • · .. 

• , .. • • • • • • · .. • • • 

· " .. .. . 

. .. . I' II .. . .. . II It " . " II U . .. . .. . II I , " \ . . \ ' . II 1 0 " \ . . I I' j, It • 

It I ,. I, 

\' 

\. . . " I. .. 0 

,. \ . . I 

..l' " . .. , .." . U . .. . U II " ' I . , Jl I, 

II • " .. . " II II • 

II I UJI 

.., ., ,. . 

• • · .. · " I • 

, 

.. 

• .. 

• I 

.. 

• • • · .. • • • I · .. • • 

.. , 

• o " 

, . 

, • 

•. • 

• .. " . " . 10 " \I • 

-lw TtI U'" 

1""10 I n-. 

10 

10 

coo 

It 

'" 

10 

.. 

" 

,0, 

" 

.. 

" 

lO, 

" 

.. 

.. 

'" 

" 

10 

' 0 

.. 

." 

10 

10 

.. 

coo 

" 

It 

.. 

ClLllu, 

n,l 

II,. 

n, • II. , 

, .. , II,' 

", , ",' 

'1.1 

It •• 

" .. n .• 

'1,0 

'\ ,Q 

'1.0 ' 1 , 0 

",0 

'1,0 

'1. 0 'L, Q 

1""''''(0 

.( U'" 

<II 

'"' 

Ihl O 

n •• 

ItIJ 

.nt "'IIII,n 

C' 

" lit I '" I 

0'''1 ' 

., . " ' .,' 

, ,\ ',1 ',' 

• ,J , ,I · " 

.,1 , " , ,. 

., . ',' ',' 

• ,I ',' ',1 

· , \ ',' " . , " · ,. .,. 0, \ ',' ., . ., . ' ,1 ., . " . " , · " 

· " " . · " ., . · " 

., \ 

'" , ,\ ., , 

.,' " . " , 

· ,.• ,I 0,' 

., , , " . ,. 

.,' · " " , 

'I" I' 

un "'" 

L I " 

L I 01 

H,r 

L' ,I 

',' 

',. 

· ,\ 

',' 

',' 

I, • 

10

, ' 

,,' 

.,1 

· ,.

.,. 

., . 

· ,.

'~'IOQ J,O ~ IIoCO"O. 10( ..... 1.1 0 • • .\.I ' 0 OIIi'UI 

'I, e 

YO, • 'I.' I tal' 

L I,' . ' . 0 I',' 

L , •• L' 0' I ', a .', , I I . , 

1

1 .-

1', I 

It,' I' , I 

\' . , ",, 

... , I ••• 

II,' 

I' . 0 \' .' II,' 

" , 0 r I •• 

L 1.1 .... 

1t.1 ,I ,' l ' .1 " ,t \' .. \1 .' L ••• 

59 

'1111[1 11 (_ ''''\.1 OI~· U 

.. 

\I 

It 

It 

" 

" 

It 

It 

It 

It 

It 

.. 

It 

" 

\. 

.. 

\I 

.. 

1\ 

" 

.. 

" 

II 

.. 

.. 

.. 

" 

" 

.. 

.. 

.. a";:, OOOI, CUfo " IIT ,,,,, , 

" 

II 

" 

" 

.. 

.. 

.. 

.. 

.. \ ' 

" 

.. 

" 

" 

" 

" 

" 

.. 

" 

" 

" 

" 

" 

" 

" 

" 

" 

" 

" 

.. 

• 
.. ~ . ., 

" , It 10 

.. 0 

It, 0 

.. I 

t' 10 

" 0 " 11 JO . ,. 

,. . I~ 1 41 ,I ., .. 0 " . " SO II 0 ,. 0 

II • 

" 10 

,. " . 0 

., 10 " , " , \' )0 " . " , I' 10 " .. . 0 .. , 10 J~ 

" I " , I I 10 II to I I '0 .. " 

U 10 

II • II • 

1111 

uti 

.. . 

• • • • , Jo . , . , ,. I - . -.. , -.. . , . , Jo 

• • 

.. • 

• " 

• · .. • , 

,. 

o 

o 

, 

.. 

.. .. 

• · , · .. 

". " 10 

I t 

" " \I 

1

. 0 

" I " . " I II 10 " . " , \1 ) 0 " , ,. , ,. I~ 

"1"""(1 ·,U' "IOI ft'" 

1-' 

.. 

" 

.. 

" 

'" 

.. 

" 

" 

'" 

" I, 

, 

I, 

I, 

• 

"' 

'" 

.. 

" . 

" 

to 

... 

U~II "" 

., .' 

\' .1 I ' .I \,., \' .. , '" 

ltot 

It,. I' ., 

'I),' ".0 

11.' 

,,,,,,' .. 0 

·Uc .. , Lt. 

IIUI 

I 0 I YO 

II 'U 

.nt "( It" , ,- '"'' . "fo" "" I 

11,_ 

I I, I 

",I 

I' " " 

, 41 

",' ,. ,-

, 1.' Il,' 

" .. \' " 

,I. , \', , , , " 

It .' 

\, .. I',' 

\ ' .1 

,. " 

1 •• 0 It

.- II.' 

lUI 11 

Il.' 

" .t 

Uol 

IT .1 

", ' ,. " 

I'.' 

't'10D 1,'0 nCD"OI '.""UO. '''",t ' 0 0lC.". 

'1,' 

" " ,. " 

, I.~ 

., ,e 

, ... 

.... " 1' 

tI.' 

11.1 

I' " ,,. ' 

Il, , 

II,' 

II " 

II,' 

II,' 

60 

It ,0 1 I,' ".0 

\ ... ". ) 

1'.1 II , J 

,1, 1 

U.I I I.' ",1 

t r , 0 

t' •• ",' 

tI, , 

.... 11 .' II,' 

" ,0 ",- ",' 

tJ ,I "" 

II,' 

I', , " ,I 

It " 

I ' ,I iI •• 

" ,. 

I'. ' \. ,t 

".' 

'-'.'1' ''''It 

0(11"" 

.. 

" 

.. 

" 

II 

.. 

.. 

" 

" 

" 

" 

.. 

" II 

,. 

" 

" 

.. 

II 

II 

" 

" 

" 

" 

" 

.. 

" 

" 

.. 

\tlo,,'''OI, ( yUI., 

'''I' 

II 

.. 

II 

, . 

,. 

.. 

II 

II 

II 

.. 

II 

II 

II 

.. 

.. 

" 

.. 

.. 

II 

II 

.. 

.. 

" 

.. 

.. 

.. 

.. 

.. 

"., 

'~I' 

'.1' 

, .. ' 

',,, 

'.1' 

"" 

'.1. 

"1' 

. ... 

'.1' 

,.,, 
lUI " CO'" I U" , :.t '"''IW't' ·"r' -"f- ,,. ..... to "'1 lO t " lOy .-u.t_ ~I).U" ·I ••••••• '''''101 ~ .. , 01' POI lOt I~'" , . ... ,'-, CU'., .t 11"1 .. .. UUl u, ,. ", v aOl , i,1;I • "n, il" I"', DI'.(U C-', 

.. < • .. , .. .. .. I' of ,. , I II.' " 'lOt' .. , ... It" '0,' . ... .. • \'.' " ,0 .. , .. .. " t r.' \ I,' \', . \',' ., ' .. 1' 

" • .. " 

, .. " " I',' 'I,' 10, r ", , ., ,." .. • .. .. , .. .. .. I J,' 11.0 I ' .t 10.' ., ,,,1' , , • , .. .. , .. " " ".1 ,J, ) I' ,J 1O . ' " •• t' 

" • ... II • • " " . ... " • I J ,0 '1. 0 

" , .. " .. ,J.I It,' ' 0. I ,. 

" , .. " , .. " .. 11, 0 It,' '0,' .. " , .. " • .. " " 11,- . '.1 10 , • .. • " • .. " , " " " 11.1 It, • II .' ., " " I, 

0' , " , .. , ".t ,,,0 

6 l 
APPENDIX B 

BEACH SURVEY DATA 

62 
6.,> . ". •• I? ,I ~ 

L ." oL I , 

I ." l .' " I . ' ••• ( I, 1. 11 ~ • • 1I1 

J . 01 '. ". J . tt _ •••• 

' .U •. n, 1.' • .. " , ' .11 1 ... ,~ 

• •• ~ •• ,. e '.H .".) "., . ,1', '. 1, ~ I., . " U J I.'. 0, •• ~ ' .1) .,H, to.,. _,'" , I .1' _ " ', 11,'\ _ . U , 

, . ' l .,-, 

I, , . • J\ , l,!'lo .1" 

l . eI ' I." I' ~ I.') JI ~ ,,1, "", ' . " . ,, 1 ) 1. '1 •• n, 'o ti '.110 

t o I' " " , 

10 ." • • n " II." • • 1' , 11 . 1, . . ... 

?~ .l", .,. ~ I. " .1 ,. 

•• " ,n, I." ~" )." •• 0 1 , 

J, II " " , 

).10 • • ', ~ 1 ,'I ~1 , 

' . " 0 II ~ ' .1, .. , '" •. " .. u , I.IJ • ," . '", .. , .. , 

.. . .. • • .00 

_" 10 ' '.' 1- . HI ~ 

,-, (., 

I.'" . r l.. I ~ . , 1, ' . " . , lt l ~ •• 1 ,) _ . , . , 

1.10 ' .1 ' ,' I." .. u . I , J , ""~ 1, 1f 01 ~ _.10 •. tI ~ 

t. II " " , 

'." _.l ~ ' .9, •. 1.0 •• " 0 • • It, '.1' .. ,1, , . 10 •• n, t." .. tl, IG .U •• " 0 

II," "" 1I I I ," • • " 0 

I .U . / 11 , • •• 0111 

•• It ol ' 

1, 1 I . ". 1 ,4 " • • I '.11 '.f" J •• I .... g I.· .. '~' •••• ' .1" '." ..... ,.I , -. 1 11 

•. ,. ·.H' '. 11 '.U' , ....... , ',n ..• U ~.h . . ... 

'.10 ,"," 

" II • • ", If . U - •• 11 II . ·) •• ',t 

'" "a 1 ,0 

u O I.'. oil' I . I . 01 h 

J.H " e U \ .• , • • : 1' 101, ' .H' 1.1' to 

t. II " I" ,.1' • ,UI , . ,. .. Itt 

, •• , •• "t t ..... .. 0 I." .. 1,. 16.'. · . UI 

\1 . '1 ' . ' ft 

t.to • ,t. 1 ." .11 1 

I. LI , , ' 0 I.', ·.,n I . U ,o •• • • " ·.109 

) , r. " '" I." •. ~ •• t ..... IL ' ~ •• ,n, ' .0' _.". '.n -.)\. II, IJ • • 1" \I. " •. , .. 

• • h . 1 11 

, . I e • I o 

I ." ' . OJO lor ... \01 

t. ») _ •• " 

.. .. ' oIU 

I. ' I • • 1" .... . . ,n I,.' .. , .. r. u "'" '." .. lO t It ." •. tI' I I." " 'I G 

o. ~ I . " 0 

I . " . , " ' \, " .·It I. " . 1'1 

I ." . 11\ ' . · O .. HI 10 " .. 0 ' 0 t." .. 11 1 ) •• , • . ~ 

.... ... ".~l .. n , 1,41 .. 1 )1 ' .1' •• u , ' . " _. Itl I." •. '" • • U ..... , I." .... 1. ' . .... 110 

"." •. U' 11 •• , " ft' 

, l • H' I .tt I' 

I . U _ .H' 

1.1' .. I' , 1.II .. P ' 

1 , 0. • • • ) : 

I,ll .. ' " • • 1I . , I U 

• • ,. ... If 

.. ",.". • .I, ...•• ' ." ... n It.t, .. II, II . 11 '" " ' 

.... : , 1 . 1 

I . ot .JIO ,.t. . I " 1. ,. ."0 I. II • I~ ' I.J, ••• 01 

\ '" .... 0 

' .It .. \10 

I •• , ... I 

... , .. "0 . . ... ,'11 ',u ..... 11. 8 • •• '" 

' .', • II , , . ,. • \I ~ 

I." . J' ;' I. ?) ~~ 

, . " " Ht '. I .. ,.: I •• , _ . 11 1 ' .H .. ot, • • \I • • " , 

'. I .. 1,. ' .P -.,., ... ,.. ,,' '.J' . . ~. o 

.~ ' _.~ ) 

I •• ' • • 1" 

' .1 ' .. " 1I , . ... _ . 411 11. " .. " 0 

(~ .11, 1.11 li lt 

I v •• DI 

.e ~ . 11 ) I. ' ... , .. I . .. .. : • • 

I ." •• f"" I." ' . 0 " I . ,. • • 1\ 1 

' '." .. ' .

.. . ," " . . . .... 110 , .1' _. U, · . I l • • •• , 

•••• ·,tI, .1 . , •••• 11 ".U •. '" 

,~ o • ,., I." ., .; I." .,n '. u .)0 ' I.,. _. ,,: 1.11 .. II ~ 

J •• , .. , ., ......... , I . .... 1" • • ,. ·.UI 

' . 61 "" i ·.u .. ,,. 19 ,1) • •• n II." .. ' .• 

.. . l " . ) 

.,. IH' 

' °1 C' I 0,.. .1', .~. "., , •• , ,1 ~ 

•• ~~ , I" .,. .'" I . n . , {. )1 

I ... .. 0 1 0 '.1 ' .. ~ I . U • • n o t •• , ' '' " ' , •• o 

,." ·.n, ',I' .. It. 1101 ' -.'U 

0 •• , .11 ' ' .• ' .1\, ' .1' •. a , ',' 0 .. 0 1 , 

1.11 • • 10 ' 

J. t · .. ~~ . ' ... .. \') I." •. 1" ' ,11 · . h o ,." .. ,., • • •••• 10' '.to _.U • '.n ..••• '." .,.n I I ." •• 101 

Tf:$' 1 

..... " 0 ... ~ . ," .. ., ". ~ I." 

Iol ~ _ 

"'.. 1" 0 

I . U • • 11' 

•• ,. _ 01 ' 0 

"" -"., .,

'- .. ", .... . " .. .. ,... ' 

' . " _ ,Ito 

' ." .,U' 11"0 • ,II' II . U _,'" 

•• 1) .1' ) 

I •• ' • I \ 

1.0 ' • ,, (0 l . 11 •• 11, 

,. ... -... ' ), ~ .,n ~ 

1 .11 'oI U •. " .LI ~ 

1 . 1' "" 0 1 .<1 .. .. ' 

l.tI - • • " •.•• _.U, 1f . 1! • • n' II ." .. !I, 

~o .IIC 

1. ' 0 . 11 0 

10 1, 0I19 

I .U - . GI O 

). 11 ~oI " 

I • • , • •• '0 '.H ~ .•• , ' ," •• ,10 '." .,If' '.f' .. u • ... , .... . '." .... . '." ."" Il.tt "'1, 

".'1 •. 11' 

I . J; ., , 

.. " .1" ,. t . • ~ 

" • • 1. )l~ 

I .: ' • • ,, ' I.~ ' • • , ). I." " •. • , • .r. o 

' •• J '. ' " .... "" ~ t. " .,." ...... " , ,; ,' 0 _,'" ". _, o,ne 

rc:;j I i .ifot 1'\ ~ ... ", 

63 

I ' .) 

' " H .... 

''''' I " ) 

... , .. ., " f .1 1, I . U , '0 ' I . n ~ 

.... • I, a ,.,. ... , ,," "'0' '.tI .... , ,,, 0 • • •• , 

10)' ••• h 

J.n "" 0 ioU ' 01 1 0 

' .1 ' • • 110 

. ... "'" 

~.~ ~ ,I" 1 ." ., U 

.~ , .0" I . u . 010 , ... ~n 

I . I ' - , "' lo ll • • 11 ' , ... .... , . " •• ,\ ' 0 

I . Ie "' ' I." •. u, , ... "'" t. " .. 1 " •. ., •. ,10 ' .U ' . IU 

•. 9' " •• I , U • • U' • • II ".! t 

.... '.'" II ." '.'" 

tI . f l l. 

I ' , ' '' ' 

'.00 .u, . ' 0 .1;' 

I . ' , . I H ,. 11 . ,., 

I . " • • 00' '.'0 .. ~1 ' , •• , •• I n 

10 ' 0 .,1" 1,'1 _.0" .. "... " ' ,,, .. ,., t • •• " JI' • • t • ••• t. \ .... " '" 11 , 1, ,, . 

. , , ~I ' 

I >" I 

J.t' .I'Q I." .1 " , . 'I .0" 

I," " ' . I. .0'" 1 , 01 " . too ).' ~ •• 0 " 

I ••••• 1 1. 

I . -I •••• ~ 

• • " • • 110 ,." ... ,. ,." _,n, '," .... , I," ' . "1 •••• _. JO. 

. . n < • • n ' .'t ·,U. 11 ," " It, 

, , . h h 

( '" • ~I 

~, ; . IIg 

I . U "I) 1.1, .ta t .1O ' .1 " , • • ~ _ 0\ 40 

J.1t ' . 11t 

1.1' .. \.0 

•. " ·.1" .. , •• ,U' 

•. " ' 0'" ' ,' 1 .. U' ....... ".I ~ •• 11) 

II." • • I l, II." .,'" 

•• ," '.? 

) " " ,,, . • "J 

, •• ) 01 " I. ,. _.H' 10 ) '1 • • ; 

I ..... ~ 

10 ' 1 .. ~~ 

~ • • • 0 I~ 

, .•• _ .J.' . , " . 01 1( 

' oJ ) "' I~ .... ·.tI, I'''' "" .t " .• \ ~.u , 

I ,~" ' .1 

".'0 .1 ' . . " 01': I ." IO~ 

I.1l .J\) I • • , •• ~ • 1.-' .. t ft 10 " ., •• , 

I . n ' 01 . 0 1 .11 • • \00 

. ... .. n' t.,. "'" '., •• ,U' • •• I ' " ' . 

If.'1 "'-' 11. 1, "'" 

; . H .J" I . " . \ 1, 

1 .1\ . U' I .' ~ u 

'.1, "'" I " J ••• " ..1, .. I I . 

t . u •. , 60 

I." .... , t , " . , .. . 

l.I' • •• " •• ), .,10' ",1 ,,'0' II ." _,1ft 

' .0' .", •• I ... ) 

o\ ~ oI' ~ 1." .1" I.u ... , . 

' • • ~ .. 0 ", 

, .1' •. 0' . ' ,J' " . If' • •• t _.11' "'" - , ' 00 ', • • ·,.t u .,.1 _,U, 

',11 .011. 

, ." .. Ito •••• "'It 1" ,0 •. U' I ' ,U ••• ,. II." ·.'1' 

1 . ,;. "'~ 

' .'. .\'0 I." .. 4~ ' . ,1 ' . ,, 11 ' .. ) .. ;., ~ ' 01 1' •• " .. I ll • • 11 • • H , 

' • • ' , , ' 00 I t • • ' .. u, I' ., •• ,1\0 

~.~ H r. I 

0 .11 . D o '.r· .I'~ I ," . 1 1' I ,ll . 01 , 

I. " • , 0" I . U .... , 

1 .\1 .,. 01 

J .U 0"" _." ·.U' '" ... ,,~ ' .,' · . Ht '.,. .... , .. . " • • I f, II ," • • fI. 

O.t) '),0 

, • • r .IU 

.... ,' 0' ~ ~.o u 1.1' .II ~ J." •• 1" '01' .... . .. ,..... , ', .... ,., '." •. It. ... . to .... , 

II ... f. '" 
..... ~r I.' 

'1. Hr~ 

1"1 ('C 

,,'~ .r" I. I' . "" 

I,U, ."" I." .n, ',II .11 . 1.1, •• e .. ),1' " tlo 

'. "., H ""'" .. ,\" 

'." . II , '," ..... ~:: : ::::; ,..n •. U, II." •. 11. 11.' ••. 11, 

"0~~1 1,' 

D.~C .11,. 

." ~ ,'. .It, 1.11 .1' , I. ~ 1 • ,1'1 

I.') • •• It I." .... , •••• , .. I t , 

",~J •. U 1 ,.,It •. "0 •• ') -.U·o '.1' . ")c. " h ••• ,~ 

11." •• '4, 

II.h' ... ", 

~."e .1" I,,~ ot I, I.f, ,I" i.'e ,'" )" 0 .. , ~ I, 

1.1., •• ~" 

1.'0 .,0'" ','Q -0\1, '.'e "P), '.·e •. ,.~ ','O •• H." I.l~ •• U, 1.'~ _.JI, '.OD •• 11~ 

•. '0 •. 1'" '.'e •. ,Ie ','0 . ,'I, 10, 10 ""~ 10.'0 .... '0 

Ii ,'0 •••• , '11,10 •• '" 

". I Lt. I~C I", 

e.( e ,I', I .,} "(~ 

J,el o\l~ 

1,)~ ,0'", 

1.'1 "( 10 ','0 .. ~.~ 

I." .. 10, 

'.11 •. ~" ..... ",~ 

-.' I " ,,~ '.1' "\" "~' .,'1, '.-' ,," "'" •• 10~ 

•• 0, •• 1" 

1,00 •• I't 

10.00 .. ,'" I I ,co •••• , .',,, •• 11, 

t.u .IU 

I." , In I." ., 

, ." .. " 1.11 . t n 1,1' . 1'" ,.'t ..• n ,. o •••• ,~ ,.,1 ., 01 , 

'.11 ",I', '1" I, I 0' "I, -,)1, •. " .,~It '.17 •. }n l.U _,.,. '.1, .,~o. 

.... " -",.. u. " •.• ,. Il.U •• !o' 11." •• 71' 

III ILl' 

/ .. , I"' 

I,O~ .iJt 

.',' • I" 1." .1l~ 

'." '" c ~, ',o~ •• B' 

',1' •. "0' '.'I .. .I\Q 

t.11 •• 1I~ 1," .oIe, '", .,,,. ••••••• n II ,I' •. In 11._1 •• 111 

.... H I.: 

,.~~ .,~) 

• It! .il' 

I.I ~ oI'Q 

I.~ I .11' 

I,' t .\H '.' ~ .0., "/4 "'" ~. ' 0 •• ,00 ,. I, .. c" .... ~ .. t_D ,,0' ",oi~' 

•• '~ _.ll'l J. " ... 0. ' .n -oJ" '. " -.)1'1 ', 1. ·,.~I 

'.') ."" '.10 .,'n \ •• 10 •••• , 

11,10 '"" II.'~ .,711 

,.~c- olU ! .,~ ,\ I 0 

J. ~ ~ • 11 a 1.'1 '.':1'1 10 IA •• O_l I." 'oO~~ J ." •• 12'1 •• J' •• o~, 

...... '" •. 9, .,,~~ 

, jl, • ,.I., •• '1 .... ,. 

'." ."10 '." •• ,10 

'.DO .,'" 

11,0& "'" 11,00 "," ,,," .,'a 

',eo .U' •• 7 .11' 

I,ll • ". \ ,.1 ~'t 

I,U .\0' 

'." .. u \ , .. ' ..... ·.11 .. .: 1' ,.71 .. I" 

•. ,' .,U. •• 10 • • U , 

•• '0 • ,I" '.,) ..... . ,," •. 'l' ...•.. '" 10.1 ••• '" II." •• 711 

,,, nH 

r"\ ("J 

~. t, .lle 

• 08 • I" 

\ ,11\ .1" 1." _.~o, 

Q.1I ..... 0 

.,'" .. I'e 1.11 ..... 

•• '~ .. 110 

, •• ~ •• 11' 1.11 .. lI' I •• ) .. 'IIr 

11.)0 ..... , 

II." •• '1. 

a~ .0' 

I.U , ,t .. , 

I.I .! .H, ,,/» .110 

, .'0 .Ol~ I." •. ,,' '.J, .. 1'0 0." .. I"' '.'t .. 11'1 

.... • ,.1" '.11 _.1" 1. :1 •• Il' I,ll .. 10' ,0." •. U, 11.1 •• ,t" 

( ,~~ ,I Q\ 

I .'J . (~~ 

" ~l • ~., 

,.~9 .,oH 1,lI .. ~7~ 

•• 1 I .. lie 

'.61 ~ol~' 

'.U .. Bo I." .,IJO 

T ,," •• J!' '.80 •• 1', I," .... , '.H •. '" I •• e ••• ,10 

JI.C' .... 0 

lI.n •. II' 

Ifo rc.1~ 

1"1 1''1 0... .~n 

1". 01" I." .le'S I.tl .I~'S 

J •• 1 .''''0 ".11 •. oe\ 1 •• \ _ • ••• I." •••• , ).1' .,I n 

I.u, "~ " ) . ., ... ..,. 

".'~ •• )T. 

1.'0." .. 

'." .-1 11 I •• ' •• I 't '.4" .,H~ ' . IS •• llt 

. ... """ •• 11 •• ", 

1.\1 .,l~' 

J.'I '.10, '.It _.I n • .•• · •• a '.~G o "H 

•.•• ,'4' 

10." • • '"t II.Ii •• ' " 

~.,t ,I'e ,'8 • I ' • 1.11 .\'0 

1, " .1" i.·o •• OU 1,1'1 .,,~, 

• of' • • 11: ' •• 1 •• 1" 

~.I' •• 100 I •• l •• 110 

'.11 •• J I 0 _.'0 .. 11' • •• 1 ,,'n II •• , •• '0' 

II.ty " 'I I 

e.~~ .l'! 

I.H .1" 

I. It ,,~o 

1.'0 ,ce, J.I~ •• 0., ".~e '01'~ 

.... ·.18' 

'. It ',l~' '.10 ~.)Ol '.11 •.• ~, '.10 _.Il, '.'0 .. n. 1°." •••• , II." " '0' 

c.n .1'0 

1.1'; 01\0 

I, l' ,a~~ 

J, I) • dl' 

lol' •• 0"' l,l} """' 1,111 •• O" 

J .)' • ,d" 

I.', " Jl' • •• 0 ',"0 ~." •• 1'0 

','0 _.lfr 

',1' •• 191 I,.' .,i'~ 

1 •• \ _.10' 

'.,. '.110 '.U .,'" '.1' _.'II" p", .,1" II.CO ••• ,! 

Il •• ' "'" 

.... ,!, " ~ 

'" Ill· l~ I I") 

C,~G .1" ....... .,.,. 01 ' " •• n .t" 

"') ••• H .,1, .... ' 1" . .. . ll. ' •. , 11 " .. .. I·{ •. " ·ot" '.H •. "0 .., ••• l1C ,," _,"0 ' ... -.II~ •.. , ...... ""1 _,'" '," o. ,U t , •• 10 _,.,,, 

J! .11 ••• J" II.'. '.H' 

ID'T S 

64 

.... .~., .1 1 .I'e l.u ,Ill ,. , .. .. on I • • ,. .,Il, • • I' • • 110 . .,. " ,~, 

... , ..•.. , 

•• • , .. U& 

" •••• )10 '." ••••••• ."" TO II." .,." II." •• UI 

e.! .j" I ,I. ".~ I." ~ . I 0' "'0 •. 0(' ]'00.,1 1 0 I." ... tT, 1.1'1 •• 1" 

.,.e " I'~ ,,10 ... 11' a,)O •• ,.! 1.1~ •• I'~ 

'.11 ."" ', ••• ,n, ... "0 ••• ,. I •• ,o •. ,e, 

·":.r "~ 

I', 11.'" I'", r~ I 

O.H .r" I, I) ,,~: 

1.1) '"'" 1.&1 ·.ll' 1,~ I • • 0" 

I. \' •• 01 ~ 

1.1e •• IH 

I.~l .01~~ 

",'1 -, PO "1 e " lJr ,., ••• H' ",1 " no '.t •. ,~' 0 '.'0 ... J" I .... ,0" '.n .. ,n II." .,.11 11,,0 ""0 II • ., •• '11 

'~""'I •• 0 

IT, Hl. (OOC (~I 

•• 10 .IH 

Ioh . 14 1 

l,n . 1" I." .... '.1' •. '1' '.'1 •. 1" \oIl oI~' I. " _. 110 1 h' I ••• H 

:::t :: :: ',',' .. u. "." .. ,1-1 '.1' •. 1 ~I , •• ; •• IU 

'." ·.H I 

••• t •• '" t," _.In 

'." •• 'll la." '.Il, 

I'''H I.~ 

f.t. .~'O ,I' .It, ! .1. .,,, • •• 1 ••• , I I.' ... Of .l ' .U .,HI 1 ,10 •• 1' , '." .... , •.• ~ •• u. ' ....... Itt 

I.n ... '" 

',11 •• '" 10.1-1 .,,-, 

110" ••••• 

11,11 • • ". 

l.ltoU .,~ 

~.n ,") 1 ,I' • 18C 

I.H ,)1'1 

r.n •• tl'l 

I. ~ 0 '. C10 },.O .,1" 1 ,., " If I 

'.1' •• 1'1 '.1' • ,In ',10 •• iU 

'.10 •• 1" I.', " JlI ','0 .,In 

'," -,'" 10.'0 ••• " 11." ",10' 

'.H .~.~ 

.q\ .In ," .1:0 [.11 ,0" 

1.11 •• ':H 1". ',1';0 

I ••• 'ol" 

l.CO •• 11' 

J,), " I H '.H •. H' 

'. '. " '" ',10 •• l"' •• Ie •• lIe I,'C .,101 

'.}} ,.H} 8.1 I •• tl' 

A ...... '" 

'.~J ','" IC.'O ""~ .1. ~o .," 1 ,'.11 •. '" 

0.00 .1" 

I." dn I." ,t" 1.1 , .U' I . H ..... 

I." •••• , '010 'oin 1.1 ...... ) 

I, , • •• 1" 

_.1' 'Il" 

• • 1 \ _. ~ 

',11 •• 'il ., ~ .,~H 

•• 1'1 •• ~II ,.n ..... ... ' .. " ... ,H ' .. ' ... . '1 •• " •••• 0 ',_' ••• '1' ' ..... '" 10.1. _.1" ,a." ." " II.'. _. H _t 

t .co .11) .'1 .", 1.1' .In 1.'11 •• tll 1.:4 r.I'1 t I." " ." • ~ . .. ... 1. ' 

'ol l ••••• 

..,. .. ,11 1 '.1, •.•• , '.41' .,))0 "." .... 10 ID," .,.It II." .,rn 

.'~.f I.~ 

~.H .iI. Ide ,160 

I," • II~ 

1 ... 1 •• 0\0 

)01 1 •• 0

1,.' '.\I~ " Jo., •. 0" 

"'0 _.In ,. I (I- ... 111 

'.1, .. UI 

.. " .. ", '.10 •• , .. 

','o."n 

I~. I ••••• , 

11,""PC' 

',".r ',t 

". Ill> I~} \') 

~.~~ ,II~ 

.~. ,110 

" •• ,H I " ... :~~ 

~oT' 'd8~ 

l.~~ •• ~.~ 

1,01 " "' '.8) " l/~ 

~." ·.10~ ,.1) .. rn 

' ..... • 111 

•• 1 ••• 1" loll •• IeQ 

to}' •• 1)'1 

.. ,! •• ,'00 

!O,~O •• II~ 

11.00 .... , 

Il," .,1n .,," .. II' 

...... ( T •• 

'.f! .)Co I'" .1" t .:. 01 ,,, 

I,U t .... ,." .• 1'1 1,H •• 1' I,.' •• 1"" 1,,1 _",. -.'j •. ,,, , .'1 .. ,,, '.If .,~,. 

.t ~ •• ttl 

'''' ."1, '." .. ", 11."' ""II 

O, ti ,i'~ 

I,t·: .1 'p 1,,1 .In 

I. CI .OH '.11 •.• ), 1.\, • ,0'\ 

J.'~ .,'0' '.'0 _'.'0 ", ... Ill '011 "U' ••••• ,1" '.11 .. ,., •• 1' •• 1" If.,.i •••• t II." •. ,,, 

..B .n~ 

I"~ oj.J I." .. ~~ I.n .. o,~ 

'.I~ '01" J.'~ •. 0'0 

".H .01" '.ot •. /l' '.'0 •• 1 1 0 

7.10 •• U' 

I." '.110 

','0 ""0 1'.10 .... n II.', "'0' 

Q.H .I'~ 

.~~ ./H 

,If "H 

\.1\ '.0 " I.n •• t·'t },~, ·,17' 1.0' •• 011 

100' •• ,n 1, .. ~ .,,00 

I." •• H~ '.1' .,n~ ',II .,~n '.n •. 111 •• U •• llo ',.' ·.11' ',h ,,"0 '.eo ... ., 10_00 _.110 

)1.00 •• 1" 

II ,"0 .,'" 1'.11 •• 11t 
'I '~ ~ \ ,t 

• 11 l~t, 

, \., 

"C, .1., ,I •• 'H ,1., .1 I , .. '.... 

I." '~ I ,'l •• " t I." ~ 

1.1. -" " 1. ' 1 _. ,111 I ," ~.I' t I." .,1'. \ . '4 ·.1' 

'," '.11. 1, 1 ' .... 1' 

1,1 . .... , 

I.l • • ,'" 

f._, •.• l, I"" .,11. I'.' • . , .. , " ." ·,n. 

··-";.r ' .' 

~,IO .'" 

1.1' " '"' 1.U dl. 

" ... n . I," .", .... , •. u~ 

I." ' .C " 1.11 •• t •• '," .. ," •• f' ' .1': '." 'oI" '." t." •'''', .•• , ' •• 1 •• ". ... . , ••• ~t 

'.'_ •. n_ 

I.', •• U • . ." .. '" 

'.11 .... . II . .. .. u, II," •• ,1, • • •• .llt I . t. oIh I ." 011, I." .,(1. c .u •• ct, •••• "."t 1.'1 '0\" 

'.1' '''', • •••••• 1. '." ..... t . .. " U' ' .-, •. 1'. ... ., •• )1 , 

'." • • It, '.1' _.41, .... -"" '.t, _ .••• It.', ... ,., II. IS . .. . . . II." .. .. " 1 10 HI. I ' ) I ' , 

I. ~; .t' , 

1.'0 oI lr 1," I " '0 •. " , 1. 11 •• : " 

I," '.llt J." _.~'. - ." '.I'~ '." '.1'. '." . "'0 1,1, .", ~ ' .• ' ··.·C '." .. t., II.'C •• AI, 

II ," •• ' 10 

•• .. ~f ,~ . . ... U .I .'-1 .~ .. ." . "' ." ,I" '.11 ',U' 1. 11 • ••• , , ••• '.1 ~ ,.' 1 ,01\' 

, .... -01" 

. ..... . 11"\ 

.. " "'" '.1 1 ... - . 

'." • • 11 \ 

~: : ::;;: '. 11 • • UI 

'," ' .'1' 

'. U •• 11, ,I ' .. n, I ........ . 

".' •• ,fI' 

t . .. " .~ 

t." ., •• 

,.\ . oIn , . ., .1)' • ... . u. ,," -",' '.11 •. ,., , ... . "" ,." .,," I . It -,I.' • •• • • • 1" • • " · .11t •.•• .. . n, •• 't •. • • • , . .. . . u . 

t. 1I "' " 

....... 1,. tt . .. . .. n II." •• IJ, 

II. HI' I · J I ~I 

'.11 . 1" 

. " 01 " , I ., I, " .1 . 0\ ' I . " •• 0\1 " .. , ."

,. I .... " \01 

_.1 1 " \ ', 

t, U •• ll t t." .,It. I." .. n, • • I I " J OI •. " ·.H.' 

r, .. . 01" 

. '," .. '" ," ..... I • • • •••••• I'," .. ,.. II." • ••• 0 

t. el ," .;0 

I. " 01/9 

I .'G "') 

I. " ,"0 I,ll .,on , ..... ,.. t • ., """ '." -ot" .,U •• , .. I ,ll •• l •• 

1,', ",)f' T." •. H. ......... 

'." ','lI It." ..... II." ..••• 

11,11 "'1' 

10 "9 ' I. ' 

IS. 1t ,r., .. , .,., ._, .11' ,.n ..• 1 1 

,.-... '': 

,.1, •. 0" ,,II • •• ,. 

Jo " •• 1" I . l • •• 1'. 1" 1 .. 1', 

:::: ::!!l 

t .I.' • • 1\ ' '.1 .... .I', •• '1 .... u. '., .... '" II. U ••••• If." .... , H." •. , .. 

'.01 .'" 1.1t .111 

•• " .0" .~' ~" ., ..... ~ 

•• n .. 4'0 

1,11 •• " 0 

"II • • ' It 

',0' •• I'e .,,, .. '11 

'," .. 'f l •• " • • I &t 

'." .. ,II' I,ll .. IH '." .. u. .. " .. ". II." •. '" 

~.H .. It. ,.J) .1 i, ,. U ,. n 1 O! , ..... ).ce •• '" I •• , •. 11' ,,'1 .. I" '.'0 •. '~ ,.J, .. 1" ,.tt _.,.. I.~l .. '" 1." •• 19' '." .... , ',II ••••• '0 ." _.II~ I' ." ..... 

r ,,'0 .'(101 

1. 1' \'~ I.fl .u, 1.1) .. . ... I." •. '0, -1,"0 • • '~ 

1,0' ... 1" l.n •• 110 • ...... 0'0 I .? ... Iot .", ... ,' •. ,. _. 'I' e: ~ ::::: '." _.U. . ..... '"

','" .. . 110 11.11 ••• r, 11. 1 , •• '" 

e.e' ,1'1 ". ,," . " .OT, 

I. " •• , " 

1 •• ' .. 110 1 .• ' -,,1, '.U .. 1\ 14 '.t! .. lfl 

'." .. '1' ..... ·.H' ' " •• ,11, '.11 .. It, ". 11 •. ,,. ••• 1 •• 11' \ ........ . II •• ' •••• , H." •. '0' 

.,I~ ,h, 

1,,1 "" '.~l .0" '.11 ,I,. l,eI " ' n I.U .,." I •• , •• 0., 

I, I' •• 11. 

, .. ,.. ". 

.'.It •.• " ... . ".. '.f ••. 11' ' ,U ..... '. 1' .,.,. I', ..... .. I I ," .. ?II 

Ih~1 ' .' 

o. tt .u. • 1, .11' ... .11' 10" •• '\1 '.11 •. 11, ,. , • •• 11' ! . . ... 1'1 • ••• .. . . II , .. , .... . •• 1 1 • •• '. '.n . ... , I , ll •• n. '.u .... " If •• ' •• • •• II." ... .. "," .... . 

-.~ , .. ~ 

..e o • , ., I,U ,I" Iol~ 01 .' 

.. " ~ ... l.n ••• , 1.1' , . .. I". '01 " .,10 •• t., ... , "'" 'ole •• " .. •• 1 I •• \ " ••••••••• '. 14 . , " . 

'.10 •• ~ 

If • • ' ..... 

II." '."11 

"'" " 

.~~ 

.. ,. , .. , I." I . ,. 

'. " '. " ' .. ' '.1' '.u 

• ,'I 

'. " 

I ', " II • • ) 

.JO O .\1 , .1 " ,~ ~ 

.. _,0 , ., '. 

·.1\ 0 . ,,,, -.u. 

•. 'n 

... " ..... 

', "0 

"'" 

..... I ' .0 

C." O .I U .') oI l~ 

I ... '· U • . 1, ,; ,. '.1' " "0 I •• ' •• ,',1 I ,,. .oI ' I. " •. 1" '.\ .. ",.) .,., "" ~ •• 11 .. HI I., •• 01' ~ .... . , .. , t . .. '." 0 '0 ," "'11 \1." •. ," II. " •. ,,0 

65 

"" r I. I 

•. ,11 ,I.' 

1.: _ .1 1 ~ 10" .,n 1,,, .f~' 

I.,. l~ I." .. o ' .11 -. " , • • " .. . 16~ • ••• · . I t O .... "'" ' •• , "01" . . .... 11 0 

t,1t •• "0 1' . 1' "'" II , U ••• " II." .... , 

~d' ,JIO , " .l H 

,.~ ~ .". 1 ,~, ,01' 

I •• , " ~ I, I. ~I _. 1)\ J." .. 1 " 

,,~t • 01'( ','. '. "e ., •• ·.,eo ••• , " 1'0 '." .. , .. I . " •••• 0 

1.1, •• ." 

1,,1' "" 0 11. 1' ••••• 

II." .,". 

c. '1) .U, .-' .fn .11 ,,,t 

1. " "'" 1 .11 •••• , I." •. tI' I., • •• 1" ,, " ..... '01' •. r •• " , • • , 111 

.. " ..... ', 11 'oJ" t, II •• "1 10.)) •• tt. I' .' •.. '" 

0.'" 1 • • 1 '.11 1." 

).1' 

I. II · ... " II 

"n • • U I , It 

.... ' ,,, 10 , tI 

II ... 

,JH .oto .4" ,H' 

.,0" 

• • )h '. "t " II, 

• .1" .. '" "'" 0, '" ••• n ..... " '"~ 

til UI~ 1- , I I 1 . H 

, ." r ," 

I, \I 

1, r. · ,., , .11 

· , ." ,l ' , ,10 '., . 10 •• , 

II." 

• 1;9 

,II ' 

· .~o, 

" ~ r~ 

.. ,;'0 

_.It '" , . ' 

" '" .... '. '" , · .,,. 

· ,," ... " 

:J ,I " ,I, ./ H 

I . J I .1' 0 

I .~, • .)1 ' 

lol l "( " 1. 1 ) • ,1 '0 

1,11. ,. n 

I, U .01 " .,., • ,I" 

'."' •• 1

1• .,'I •. ln I." .,U' '." .. '" '." " If' 

I) ." •• 1" 

11.,v .,.n II ." •• 10, 

I., "t , 

... . ,,, ." .,"' t . t • •••• , 1 01 . '. 1" • • u ... t, '.e ...... . ' ,J •• ,10' 

"') •• f" ....... " '.t! . " " "" 0 • ••• 

"" ••• n , .. , ..... . 11." •• '" 11.'1 ••••• 0 ,0: 

1.11 

1. 1' J .H 

I • •• 

I. I I 

' •• 0 

.... 

'.1' '.11 

., Of 

',u '.1 • '.J! 

II. '. 

.. ', . ! oQ ..q •. e n 

" "".\ ~ 

.. 'II 

.,IOt 

.. , .. ., 1' ( •• U O •• )11 

•• 11. .,." 

.. n, 

.. ~" " ~ 

e •• ; "., 1 ,t. .111 

1,0' ,I' . 

I. n •• Q. I." .". ~ I,., •. 1" .. " .. ,., .,., .,1" 1 ••••• JJ ~ 

'." • • IU ... , ..... 10.1\ •••• 0 1\ • • , •••• , 

II. !u. { - I I" 

~ 01 '" ... & ,'0') .' t .11; I.r., •• , • t .H • • , ., I." .. II~ 1. \ •• .,,, 

"" 0 • .,'1 ',10 0011' 

• 0)' '. 1 '0 

&." ·.f O~ "" •. '1, . ," .,I·l ..... ,1" I,"~ ..... '." ••• t. 10 •• 0 • •• ' 0 

II." •. '1, 11." •• U, 

II . ht • ,,,, ,-} 

"f • •• , 

••• .11 • 

.... .t" 

I .f' •• 6,1 I .U ... '1' l •• a .ot" • ... .. ) 1' t .U •• 111 ' . " •• 1" '.11 •. U' '.11 •. ' 11 '.' ... \'. ".11 .... , lI.t, •••• , ' ,10 .1'0 , ,'I ,llg '. tt ,." I ,.' .,Ill '.1 ••. on '.n ' . IU I • • , ... ft '.11 ..•• , • •• , •• 1' 0 ' .,' '.l'~ I. U .. U, . . .... UI f,,. ••••• II.U _.'" 

... 00 

I • •• 

t ,~. 1 01 ' 

I, ' ) 

.... 

'. II , ,.1 

' .. ' '." '.11 ' ... ·.It 

, 0, " 11.91 

.,.~ 

.J" ,H' 

.~O\ 

• • ltl .,p, .,1·. 

..... , .,1" 

• .I" . . .. 0 ... ,.,. '" .. ," ... " 

"~H I • • 

o. u .Ut 

," . BI 

1.0 1 01 " 

1,1) .11' I : I: 

'01 ' '.HO ','- . ,.'0 I" • •• (" 0 

1 • • t 'diC 

'.1/',111 t " , " I " ' ,Il . ,110 

"- ~ .. /., '.t. " Ut '.," "," . . , • .• ,'04 It." .. ,., 

110 01 •• a,o II . It " 'DO 
,,, ' .. 

t " 

'AI '·1 

o .0 : .I'~ 

. ' c ... , \ •• , .1 1, 

~ .10 • • \ 

1.11 • • " 

I . 'I " \1 ~ I ." -d'~ I.', ,,"3 ' .•••. ,1, ....... H, 

1,11 _"" ~ I.', Ad', ' .. ' ... ~ 

".11 -.U C I.', .. n, 10." .... 1' Ie . " 0 '.'e ".,. •. 1', II.', •. ,'!> 

II.') • • ,, ~ 

'.'¢ .I ~. 

),~o d' ~ 

'.I) d~1 

) 01", 

I.'. 01 " I," ~ : t • • .' , I.'" .. ~ .", ... ,. l.tI • • 11 .' " ,," • • '~ 

I, J I .. . It ' 1." _"1 ~ '.1, •. ,' ~ •. 1, " IJ ~ 

',.' '" '0 

'. 1 ••• 110 ',f, .,.J, '.u .. tt, "," •• 1 1 , II." ."" It." _." . 

~. ~r. .,., .' ~ .,., .,. .11 .., ~ . ",. I,h ~. I." . "'. 1.1) '. ,I, I . " I _ . 1 •• 

'." • • 'f

l • ·"1 .. \~ 

'.I ~ . . 1', , .• , '.H ~ 

•• 11 " u~ 

'.n ,''"' '," '" ' e ','0 o,nt< U , •••••• , 

11.1' •••• , II." •. " e 

~ ~h 

t·'! "', 

" .... , 11 10 • I I ,. ,. I ~ .,,~ 

I . It • I. 

'.' \ •• 0 J- t. ' ( •• t " 

l,n • . r " 

'.1: '. 1 \ , " .. : ··" t I . r, • • II ~ 

r," '01', '. ' \ ' . It, 

10,0' ' . I' ~ II," '.11, II." "'" 

..... , 1. 0 

If' I' f " " ) 

1.'1) . 1'0 

.'~ .U' .... 01 11 

• ," ·1 " ,." 0 .100 I.H • • ( " 

I." • ,r PI 

,. J@ ' 01 11 

I ,! ' .. ' H 

• ,'e .. "" • ," - . 11 0 .," ·.lI' '.U .,J" ','I .,J'I ." ••. 'tI '.11 "'" ". " • • tte ,'.1, "'" II.n .,.,. 

It, ll • • ,.. 

,. ~ 

. ., 

.u 

1.1C 

· I." II 

,,': I, " , .. ' ,. " }, 11 

J ,'1 I •• , 

'.'" '." I," ·.t \ '.4, 

• .J~ 1.1, I." I'. " 11. t l 

I • • '1 

.,., ,11 1 

• 1" .,1 ' • II' 

• I·' , 

· ' •• 0" ; .. ~ · ./H 

• .11' 

• ,11\ 

• ,I O~ 

• ,ItO 

•• 1'0 

" He 

• ,)11 

· .·10 ..... ·.'n · ., .. · .... .. '" 

.... " ,, : 

e ,ee • '" ~ 

.1' .,,) ~. . .. , • " . '.1 ~ 

,. II .. { It 

, •• I '. '~ ' 01 ' 0 0\" I." ~,IH ,.\. 0,,0. •• ,. .,1.; • • '1 '.n, •.• , ' ,l't '." .. "~ r.l , •• ,H ' , 11 'dt, '." ..... •••• '. h' H.'I I.IH 11.1' .... , 11,'" •. 1,. 

.... :;, t • • 

'. "<1 ,II, 

. " 0\ " .~, .11' , .' ~ " ,: " 1 . 0 , • • •• , I . " ' . 1 1( 

l.'1 - ./lI ~ . ,,~, 

• • , " H I 

I. " •• HI 

'. " • • e~ 

'.'0 -, ." II." -.,., II. It '.11 0 II." " ,'1 

e .00 1 , . 1 I." ,.\e 

}olO I." I." ... , ,.~I 

, ,'1 

. " . ,. " '." I." 

'.11 Ie . 0. ,e, " 1 1 , '1 

.H' .111 

• 1' 0 ,Cit 

.. ( II '" e', .. III 

. ,,", ... 1" •• 111 

•• 111 

•• H' 

.. I" .. ',. t." • ... u, 

-.'" 

.. '" 

Iq I H" 

'" I ( ', 

Q ~. .) I ~ 

... ,1'( 

1 .,1 .10) , ~. .~I : t." _. '" t ."' •• I" 1,', _.111 

"'1 .. I' ~ I." .. " 0 

','I • • H e 

• • 'J .. ,., 

',', _ .)1= T." .. ". ...... 110 

".11 •• 110 U . l ' •• " t II. It • • ••• II." •. ' 1. 

'. 00 ' •. t, .t.e .'J . ., I. n ... ,r, ,.l, •. 11., ,.,. .. ',e J." .. "~ ) . '1 .. ~' O 

.. " .. '" 

• • " t •• f" I." .. n

,) '.tI ..•• , .... , " n ; 

•.•• I."" 

I e ... ... "0 

I"" •• ' Ie lI . t, .,'1' 

~~ I 1. 0 

• ,. . ,., I ~I 

c .~e ." e , _. .11 ' .0' . 1" I, " toU' 

1.1 ... , " 

1.' 1 .. ' " 

'." . ,11 ' 1 •• ' •• 1" "" .. ,I, '.ll .. H' ,.1' •. 10 ' •• I~ •• I I( '.r, .. " e ' . ' 0 •.•• , ' ,"' •.• n 

10. " ..... 

II.') _ ,'" 

~.n .110 

,." .IH I." . ,., l.~ • • : " 

I. I I .C'C 

I.tI ,on 1,., ., ou LI' ... ~,~ 

I, ~ ••• 1 )1 

• • 10 .. 1' 0 

, ••• ,.UI 

'.1' • • II, •• ,. _olH 

, .• , •• 'to I." •• 11 0 

'.10 .... 00 10." .,," Ie •• ' ',"0 11 ,10 • • •• , 

t.n . .110 

1.,1 .1 00 

' ,0 I • 

l l, 

I. ' 0 , 110 

1.1( ... , h ) 0)' • ••• , ,," '.1" •. ', ·.1'. '.11 •. ,1, ,," "'" I . " •• )10 

.. 1.'" -.'" ,. ..... ",0 .. ,1, ",," ••• 00 1 1.0 ' ,,"1 . .. " .. '" 

=< " 

t." 

... 

... 

• .~ I I • • • I. ,. 

I.U 

1,'0 

• .11 

· •"• • . 1 

'." 

'." '.0' , ... .... I. I' 

to. ,. 

tI • • ' II ," 

• lie .Io, 

.11' " .. : .C" .. 'I t 0, ,., 

"'" 

"'''0 .. ", .. 1., ... 110 _ .UI .

·.

.

H' .. , 

... " ·"'0 

• •• 0. 

• " '0 

• • rll 

'.~ a ,)81 

C~ I!~ 

•• " .0' 0 Itl' _, :; ~ 

I." ' • • 1 ~ 

1 ., 1 ' '''0 ),~e .. 1 .. 0 

I •• ) .dl e 

I, . I •• )1" 

',ll.,l,t 

•• " - ,It I l •• ' .,," '.11 _., ,, '." .. ,,, 10." ."'0 

"' .1' •• 710 I\ •• ~ -.'11 

. 00 .~ "' ) ... ~ •• , " 11 

1 , I I .. ~ I ," . 0 I' I.to • • CI, 

I.' ~ ... " I." ,)~ , 

I". '. lI t 

1.'0 ·.lIt 

"." ·.I/~ 

".~~ '.II~ 

•• '1 •• 1\0 '.R' -.lIo 

• .J' "'U .'.t) .. '" II.el -," 0 II •• ) o. I •• 

66 

. ... \. I ".f: 

t,H .11\ 

.1' .JII ,I, .1" 

) ." .I'f ,.,. .e·" , •••• ,111 

). t •• 11 . ) . 11 ·," 0 • • , •• 011( 

•• tt - 01' ( 

,. ,. •• 1'1 

t.l1 _,I " t •• , " II, r." •. II ~ 

'd\ _". ~ t ,,, ,,'1' • • It •• '" 10. " • , •• , 11 ." ·,t" II. " . , 1 10 

II. nh 

t .. ) ( '" 1 . '0 . 11 0 . 11 . ,.: 

.~ . 0\1( 

I oI~ •• Ol~ 

, ,J' '. o~ ~ '.1 I .... " 1 .)1 ... I' 

10') ~,IO~ 

I. l ."., 

" 'I •• 1" '.Jl .,J'o , •• , •• JI~ 

I .1~ • d, e 

1.1' •• 11' I.U •• " 0 

.,'~ • •• H .0.' I .... " 1 •• It ... ' 1' 

110" •• 'H 

I • • nt • 

(' I c' ' 

1010 • H' .H . let 

•• ~ oll ~ 

.. " ... : I. ' ) • ) " 1 , 1 1 • &1 ' 

loJ1 •• I, 

1 • • 1 ' .' l ') 

I. U •• t I . t, •• 11, - ..... lIt •. J' • ,1" "'0 •. "0 ,.1. "'" t." .. 1" I." .... a • ••• '.J It 

11.0 ' • ••• t II "1 _ ,It, 

(. 00 , .. , 

',1' tin ••• e .1" I . I , .eo. I.n ... 0" I .U •• ,ro 

1.11 . "" '.11 •. ,H "ot .,H' I.H .,n. ,.1 ) ., 1( 1 

'.U .,111 , ", .01" . . .... . · 1 

• ·.U 0.11 "'" .,'01 

10." -•• " 

" , ...... ' 0 

II,' ••• 10' 

It. HIl" ( '" I ' ) 

O.H 

. " I ,I • I." , .~I I." '." 1 . 0' I.,. ... ,'.1 ) I , " .. " , ." 

',11 ".n 

1

0 ." 11, t1 1 • • _. 

• I II 

.l t 

.4H 

..1) 

.~ 10 

• .e

1 o • . oot • • 1'0 •• IH 

o ,IIC 

• , 110 

,,)" -.'" 

• .J" ..... 

• .1" • .tll .,.'. 

" "' 

I" Hh [., c·, 0 . 0. .1 : 1 . 11 .Bt oi l .110 1 . 11 .~ " 

I ,~l • ,'H) 

l.\~ •• JIO 

1.'1 _.IH 

J. U • ,l'~ ' .J) •• liO _ . " •• 1 1 , 

t. , •• oJ .. 

o. U ,." 0 '.Ot _.UI 

,." •• J" 

.. " ." .. _.'0 •. '0' 

IC. " • • '" II. " ..... 

I' .'1 '. TO' ( , 1( ., •• .t. .1 I. '.n 01 / 1 '.H .tl, L •• t . "te I . II _.on J." .. '" 1." .,11' 1.'0 • •• '~ 

_.10 ..... , 1 , ' 0 • ,. " t." .. 11' ' •••• , U\ 

II. '." II 

.

••• . '" 0. 

......... , II.') • • JO, 

... "" .... t .. ) 

~,H ... ,.,1 

, ." 

l, G' 

1. \ , 

I ... 

I ... , 

, ,eo 

\,u 

, ... ,,!o 

J.lI '. 01 • ,'0 t." 10," 10 ." 11.1 0 

l' .11 

~ • t ~ 

... I." 

, .1. l.·i 

J ,' l · ," ' .01 1." .... 1.11 

.. " ..... 10.J' 

11. )1 

,I,ll 

•• 11 , Ito 

• L' O U~ 

· ., ~ _ . 1') 

· .\., • .11' •• 11, 

"'

•• Ih " · .,., .,Uo "' U' ••••• •• u • 

• •••• · ,.,. · .,t, . .... .J!' .1 1; 

.1 1) 

,0" 

•• OI~ 

.. ,., • ,JI, 

" rt' " ,,, • ,,.0 • • J " • •• re ..... 

.... , ... ", .. ,JO, 

• •• e oJO I e. t ( .1)' .'j "" \ ,I, .•.• '''' .... . , ,,'1 •. ,tt J •• , .... 1, , .• , . .. fI ' , ...... n •• So .oJ" .." " I" '.t t • • '1' • ••• , , "0 

'." ••• t • 

II . .. ... .. 

11.

4

, "'" 

O.~o ••• , 

.~, "" ,.I, "I • 1._. .I~ ' 

1.' 0 •• " J,I O .. o 

)01· _.0" I.u •• 0" 

I.A I •• 1 I. "~' ... n _.n . 0110 

~ _.110 

. ,. , '," 0 t ....... , . '.tI ", I I ' 

10011 •• • • • 

.1 .IO ••• t O 

11, 11 . ,'" 

o .Ot .i'O 

.It .1 " 

1 01 0 .111 ,.1\ . ,0' ,.,. .~ , r. , ••• ;'0 1 .1 1 •• 0" ) . 1' ·01 0 0 

),11 " I " 

•. J' •. ," '," .,,,. 1.1' •••• 0 

',., •• 1'0 •. t, •. J,' '.If ·."e • •• S .,U. " .. .... . '.1' ••••• '.11 ••••• 11. 11 ."0. ,0 ."" ~ .. .. ..... .... . II." .. , .. 

'.ot; .111 •• t ,U' I.', . t •• t." _ .-FO, 1.1' ••••• 

" •• •• 11 ~ 

~. H •• 11 ) 

"." •• '10 0.'. ,''" '.It •. ,.~ '' ." . 1) "'" •• \1, 

II.', "." "'" ••••• II." •. 10' 

.... . f " 

C,te dc' . 11 ,n, • ,. ,III 

•• ,~ oil . ',0_ .11. 

S, U • • 0" loll .... , 

.~ I ,"'0 •••• -.llt 

•• eo _d " '," .. ) .. I,' i ' , "0 '." " "" '." ',," 0 

16 •• ' •••• 0 II,.' "'" II ," ••••• 

or . 'H. I~. tOOl 

c .0' . Joo I • • e die • • " 01' , 1.1' 01 " '.I. .0., I." •. 10 ' J .1: •• I; I ,n .. In I,", 1. IID 

-." ·. 110 - . ' : " I ' 0 1.' 1 • ,I., ' • ., -.uo 1,," "" 0 ',tI .,.,. 

11.0' "'" 

11.1' "'" 
APPENDIX C 

PLOTTED BEACH PROFILES 

67 
TEST 1 

Range 

----------------------------- ~ 

'" 

G' " 00 

% 

C .. ~ 

.... 

'" > 

"' -' 

"' ____ ___ Il.O 

c _____ _ _ 1,6 

o 3 12 

St~tion (me tec!) 

,,- SHORELINE POSrTION 

VERTICRL ORT UM 18 ~L 

HORll0NTAL OATUM IS 

STATION 0 

OATE 

1 SJU177 

19JU177 

19 JUL77 

19JUL77 

19JUL 77 

ISJUL77 

ISJUL77 

IS JUL77 

16 

• 

., 

'" 

o " '" .... 

<r 

> 

"' -' 

"' 

-, a 

TEST 2 (1 of 2: 

Range 

--------------------------- ~ 

_""-" __ -- __ ___ • 2JJ 

DRTE 

JRU(}77 

t6RU(}71 

JAUan 

t6AU(}71 

JRUa77 

16RU(}7 7 

4,0 t6AU(}71 

JAUa77 

8 9 12 \6 

Station ( meters ) 
TEST 2 (~ of ,,~ 

Range 

------------------------------ !ill 

~ 

" ---------.- &D 0-

'"' 2 

0 '" -----.-. 6P ~ -

'" > 

w 7,0 .J ------ W 

18 

Q 

o 6 9 12 

Station (~tcr8) 

,,- SHOR'Ll~' POSITION 

VfR1IeAL OATUM IS SWL 

HaRIlo~TAL OATUM IS 

!1ATION 0 

OATf 

3AU077 

ISAU077 "" 

16AUO" r 

SAU077 ,. 

0 

-'" ~ 

> '" 

I SAU077 w 

.J 

w 

3AUG77 

3AUG77 

ISAU077 0 

16 D 

R4n£e 

----------------------------- ~ 

_____ ZO 

--~~-,,-------------------

______ 3D 

DATE 

70en7 

7Den7 

7Den7 

4,0 70en7 

70en7 

70en7 

7Den7 

70en7 

3 12 
TEST 4 

Range 

1.5 

.. 

____ ___ s.o 

___ • ___ GJl 

_ ••• _. __ • _____ _ ___ • • _________ • 1.0 

o 9 12 

"'- SHORELINE POSITION 

VERTICAL OATUM IS SWl 

HORIZONTAL OATUn [3 

sTATION 0 

OATE 

lB~OY'7'7 

113~OV77 

tswovn 

laNOv" 

laNav11 

t6PJOVi7 

16 

'" 

c 

-, 

o 

TEST 5 

1 a 9 

Station (:letHa) 

Range 

1$ 

2.0 

ao 

••••• _ GO 

•••• ___ 1.0 

_ _ ____ 1$ 

t2 

OAlE 

290EC11 

290EC11 

290EC11 

290EC11 

290EC11 

290EC11 

290EC11 

290fC11 
.. 

,. 

c ... 

.... 

« 

,. 

"' .... 

"' 

c 

TEST 6 

Q 3 

Station (meters) 

Range 

I~ 

'\.- 'HORfUNf POSITION 

VfRT(CAL OATun (3 S~L 

»OR(10NTAL OATUn (3 

HAHON 0 

OAlf 

3ffe1e 

3ife1e '" 

3Ff818 " 

3F£818 ,. 

c ... ~ 

.... 

« 

,. 3F£818 "' - "' 

lFf618 

3Ff818 

3Ff818 c 

16 Q 

TEST 7 

Range ORlf 

----- --~----- ------- ----- L6 13nAR1e 

t3nAR18 

1.0 IlnAR1a 

'0 tlnRR1e 

t3nRR18 

----------------------- ------- I!.O 13rtRR;18 

1.0 t3nAR18 

t3nRR1e 
" 

TEST 8 

Range 

---------------------------------- ~ 

., 

" N " Z 

" N 

r 

'" > 

'" -' _______ 6~ 

'" _______ aD 

~ ______ 1,0 

" _______ 'J.6 

a 9 

Station (octer,) 

,,- SHORELI~f POStT 10~ Vf~TICAL OATUM IS SWL 

HORI10~TAL OATUM IS 

STAT[O~ a 

OATE 

2lAPR1S 

HAPRle 

2lAPR 18 

,LAPR1S 

C!lAPR16 

2 L APR1S 

?LAPR7a 

,1APR7a 

16 

• 

z '" .. r 

.. 

> 

'" --' '" 

c 

Q 

'I'EST 9 

Range ___ ____ ______________ - _____ L6 

2.0 

3 6 9 

Statton (~etcra) 

OATE 

19MAnS 

19MAns 

19MAne 

19MAns 

19MAne 

19MAna 

19MAne 

16 
r 

w ""Z 

0 

~ 

'" ,. 

W 

~ 

'" 

N 

c 

-• 

o 

TEST 10 

,,- SHORELI NE pas I T ION 

VERTICAL OATU" IS S~ L 

HORI10NTAL OATU" IS 

STATION 0 

Range DATE 

-~--=-c:c--- ---------- -~ ------------- 23JUN78 lS 

------.---.-------------- _ __ 2.0 23JUN78 '" 

23JUN78 r 

'Jl 23JUN78 '" 0 N 

~ 

'" ,. _ _____ b.O 23JUN78 W 

..J 

W 

_______ BP 23JUN78 

23JUN78 

23JUNn c 

3 12 16 o 

Station (cetera) 

TEST 11 

Station (uuera) 

Range 

U; 

'1.0 

12 

DATE 

20JUL78 

20JUL 76 

20JUL78 

20JUL78 

20JUL18 

21JUL 78 

21JUL78 

21JUL18 

15 
lEST l2 

• 

______________ ___________ _ ____ L5 mll~ 

__ <.,;:_ _ _ _ _ _ 3D 

~:---.. _ _ _ _ _ _ _ ao 

o 

-; 

o 1 9 12 

Station (meters) 

~- 3HORELI~E POSITION 

VERTICAL OATUM 13 SWL 

HORI,ONTAL OATUM IS 

8TAT ION 0 

DATE 

23AUG7S 

23AUG7S 

23AUG78 

23AUG78 

23AUG78 

23AUG78 

23AUG78 

23AU078 

16 

• 

'" 

I: 

2 

C N ~ 

.... 

'" > 

W 

-' W 

o 

-; 

o 

reST I J 

9 

Station (~eter8) 

Range 

L5 

______ _ 7,S 

IZ 

DATE 

183EP78 

18SEP78 

183EP7S 

18SEP78 

ISSEP78 

18SEP7S 

IBSfP78 

16 
en " " 

'" ON 

~ 

'" > 

w 

-' "' 

0 

-, 

TEST 14 

-------------------------

o 9 

Station (meters) 

Range 

1.6 

------- 3.0 

----~ 6.0 

6jl 

- - --- 7,0 

------ 7,6 

12 

"'-- 8HOftELlWE r03(HOW 

VEftTIORL OATUM (3 S~L 

HOftI2 0MT RL OATon (S 

STRT(OW 0 

OATE 

lBOc:17t!1 

lSDCne ~ 

1600178 <: 

(60On8 '" ., N 

-

~ 

'" > 

1600178 w 

-' w 

180e178 

160078 

1600178 co 

1fi o 

TIST 15 

Range 

i.> 

16NOY7S 

1BIrJOV1£1 

1 SWOV78 

16WOV78 

------ 6jl 18WOn8 

------ 7,0 16WOn8 

16WOn8 

9 12 16 

Station (meters) 
APPENDIX 0 

SELECTED BREAKER UM AND WATERLlNE PHOTOS 

The following photos from 35-lIlillimeter slides were taken 

run-hours 01, 08, 16, and 24. Figure 15 provides an 

features. The coclplete set of slides is available from CEIAC. 

76 

at. approxima t.e 

explanat.ion of 
Figure D-la. Figure D-l b. 

Figure D-lc. Figure D-ld. 
I'1gu re I)-- 2a. f"igure 1)--2b. 

Figure 1)-- 2c . Fig u r e I)-- 2d . 
. --

Figure D-3a. fig ure D- 3b. 

-. 

Figure D- 3.::. Figure D-3d. 
o '" 

figu re D- 4a. 

figure l}-4c. 

figure D-4b . 

figure D-4d . 
Figure D-5a. Figure D-5b. 

Figure D-Sc. Figure D-5d. 
()O 

N 

figur e 1>-6a . 

Figure D-6c . 

Figure D-6b. 

~ .... --. 

Figure D-6d . 
00 

w 

Figure D-7a. 

Figure lJ-le. 

Figure D-7b. 

-

Figure D-7d. 
Fi gur e [}--8a . Figure 1)--8b . 

Figur e [}--8c . Figure 1)--8d. 
Figure D-9a . Figure D--9b. 

Pigure D- 9 0. Fi gure D--9d . 
-

figure [}-lOa. figure [}-lOb. 

figure [}-lOc. Figure [}-lOd. 
Figure D-lla. Figure D-llb. 

Figure D-Ilc. Fi gure D-lld. 
APPENDIX E 

HOURLY CYCLE CALCULATIONS 

A listing of the program which calculates the values in this appendix, 

usi ng rhe dara in Appendix A, is available from CEIAC. 

88 
",OUR, , C'I'CLf CALCLtL"lr)JrrilI5 

He. r ·'IIE DAT A "', .... t. ~[lG,.T e.Rf.lI(F~ OX , ". HIT ,,' .... £ DAr ... 

·.v! ~[1r."'T 

"'E ".(iII' . ., PeR 

.11 10 TI .. r G .. r:E \ thOU A "CL' ~ AII ~ TP'" 

" H. t I GAlirl 6h

11::t,. f ;S 

.' "- ,. '" Of Gllrr! "I" J I"/S ." -. ,- ,-

OIUlt' "" JI"I~ 

" , 0. I) ,." , , I. 1 1'I'j 2, I.i" \ , " 11.c 17. \ , • 2. c e.e 1. 'Q1 

, " , .0 .. , , • I • 1 I) 0 2.2<'1:> , I " , 1 .. ' \ , • & , • 2. ! ?EI 1 .':. <;q 

, " 10).0 •• 2 B • I. ,5e. 2.21 :3 , , " i2 .. 7 17, /J , , c.,Ql 3. QO 1 

, " 10",2 .. , , • I .2"" 2. UO 2 , \ " 12:." I ~. , , • 2.e.1B u.Q.,Q 

" , .' , .' , I, I • I ;:> 8 t'.tllIEI , , " \ 3. I I 11.0 0 • 2.D'I'0 1I.1"\~ 

, " '. , ••• 10 , .Qe.5 2.0

0 ., \ 5 " 11.2 I ... 7 , ~ 2." ') .... 5(11 

• " '.2 ,. , , I I • 1 213 2.17 !o , • " \ 2. /j 11. , , 1 2.l1D 3.7;:>1 

, " 10. 2 t.. ~ , I.?! 4 2.1 QQ , , 2' Il:.to I;:>. Q , ) 2.11114 1.1)1': 7 

, J, , , '.' 1 , I • 1 no ?171.! I , " , J. 0 1 1. Q , , 2.lb2 2.01 Q 

· , " , .0 ,. , • 1. I ')0 2.17? , , " '. , 15. , 2 • 2. I PoD 1 .82,1i 

,0 " '.' '. , , , I .?1 1/ (!."Qo , J ' " 11. 13 !Q.t. • , 2.1QII Z.7"\fI. 

; , " 11'\ .. 2 ,., , , I • 11"10 2 .Ht,li , J' " 11.1 1 Q • f1 , , 2.212 2.11,li 

;, " 10. 0 • • 2 

, I. J "io 2.211 , , 2 , , I 1.1 15.1"1 , , 2.1.! I Z 2.'Jn 

; , 3, IO .. e. •• 2 , • 1 .21.110 I.Q"l I i' " 1].2 11. ? , " 2,1131 2.?Q? 

i ' J, , .2 ,., • • I • lOU I. eQI , , ' " 11 .. 11 to.e , , l.e.ee 1.5

Q2 

j' 30 '.' '. , • , 1 .27" 2. \ ~ 1 , i' " 12. , \ 1.1 • 5 , , Z.5 Q4 1.1307 

, . " '.' '. " • • 1.27t1 ?I.I"\Q , I' " 1Z.0 \;:>.2 , 1 Z.01.l3 1,1117 

, , " 11. 0 .. , , • l,lOQ Z .517 , , , " 12 .. 1 II.to 1 1 1,41)Q 2.e6Q 

i' " 10.0 .. ' • • 1.211Q 2.I.I0Z , " " 12 .. ~ I?~ • 2. \11 2 • e 72 

J' " 10 .. 0 .. , ~ 1 ,21 u 2,0'51 J j' " 12.e 1, .,Ii • I, 2.111 1.'" 

" " 10. , , .. • ! 1.072 llto,lill I " " 11.1 11.Z )0 , , 2.1112 -S .l" 

, 1 " '.' '.' , 1 1,I2e 1, Q07 \ 1 ' lo IZ.1 1 \ • , 11 • 1 • Q I 0 1.l !II! 

;2 " 10 .. 2 ••• , 1 1.21111 7.103 1 ,2 I, 12.4 \ I. e , ; ,z.12e 2ol24 

" " 10 .. 0 '.' , , I. I 00 I.QQ2 \ ,J lO 1l~2 ll.to , • 1.15015 1.'!7b 

'" " >0 10 _ to •• 0 , • 1.21 Q ,z.0,!] 

'" " 0 • 11.'5 , , I .7 Q 1 1.7

QO 

, 0 " 10.u '.' I. I 'i0 I.Q'j'j , " 1n:1.! 11. ;:> , • Z.21.!1 1. e.1'I ~ 

2 , Jo 10. , '.' 1.\'Jtl I.Q"I) 2 " I I. J 11.,Ii • ZII.!

Q7 1. u .. I 

2 , " 1"I.w ., , • I ,? II Ii ?Z"2 , " I 1 .0 10;,,>1 • , 2.eOto II. '.)! I) 

2 , " 11"1.0 .. , , • I. \ fl5 ?21'\Q " 11 :Q Ib.flO , • 1.11Q 5.10Q 

, • " 10. , " , , • 1011"1 I.! 21~n~ 

, " 1 1.0 I u ,2 • ~ 2.'5'57 tI. I n Q 

, , '0 10. 11 ,. " • , 1.2~w 2. In"\ • " 10. , \1.fI. , 2.u17 u. I Qu 

, • " '.' ',0 , 

• Gl e.'5 1.7u,li 1 " 1 ("I .. /. I? ~ , • 2.\10 1.I7Q 

, , Jo I 0 <. 0 , ., , , 1 • I) 1.0 I) C • Ctt fI. • " I I.e 1;:>.'5 • , 2.1

7 ! II.OQ? 

, , '0 l("l,,~ e..? , 1 1 .21 u 2 ... SQ , " 11,,2 11. Z , , 2,lQ7 1o.1QQ 

2 , " '.' ,. , 1 1.0"''.) 1 • 7t) 7 " 

10 " 111.0 \7.7 , ? 0 7 'J 3, ') 7 I 

2 1 ' " '. ' , . , , I., '5e. I. Q.p; , J' " 10.0 1",7 , 2.Ze.2 1. e Q 1 

, J' 30 0 .' ••• 0 I.I~O 1 .6 \ e. , ! 2 " 10 .. 1 17,1 , , i,,,'57 J • 7 7 I.! 

, ,2 " , 

· • · ., • , I., ?B ? 0" J • , , '0 10. I 17. ~ , • 2.0'57 II,ClOP2 " " , , ••• 0 • 1.126 ?Olll " i ' '0 , , 1211"1 , , I,euu 3. l~ I.! 

2 

" " 0 :' .. , • • I 01 I " 1.6\ tl 

" " Q:~ 17.,Ii , • 2.002 10 to 7'5 

2 i' " 10

a O .. , • 7 1.\28 1.17Z J.~ " '.' 1\.) , ~ 2,1 &7 1.Q77 

, , . " '.' .. , , I 01 , I.! l.fI}l~ 1 30 '. ' 11.11 , 7 I .I! 10 1. \I !I 

, , , " '. ' .. , • \ • I 00 I.QQZ 

" " '.' I , •. ~ 1 1 1,704 2.7&1to 

2 , . ], I 0" () '. , , 1.128 2.011) ;, " '.' \ 2" . ~ , .. 1.810 2.ll'" 

, 

" " ::~ .. , , I • 1 1 ~ 1.l!l'Iti ,0 " I 0." n. ? • • l.ll' !.V1 

, ,0 " " " 1 I .012 I • e \ 1 • , ' '0 10.~ 12.' • , i.O') !.1e.. 

2 /' " '.J .. , • I .0 1.I'j I • eQ., " J, ,.5 1111 , • I.I! HI 2Ie~,. 

, " J, o. 0 .. " • I • I 7 1 ?12rd • ,\ '0 '.1 1 I • c , • 1.~6J 2.~ 1\ 

, " " , 

· 

, ." , , , 1.1 11 2 2.1.174 , " '0 0 .' ., , 10 , I ol 7 I 2. e. ~ I , " " '.' .. " , 0 .QOI 1 I QI:j to , " " 10.2 ••• , , 1.2 11 11 2.to4q 

, " " , .' • .1 

, • I. J \11 2. Q 1 e 

2 " 10 10 .. 1 .. , , • I 01 71 ,z, 120 , ;' , ',7 .. ' • > 1.,z0~ 1 ,Ito I 
"OUP, .., C'Cll CjlCULiTYOHI 

HIT • ,,,,£ O ... t ... • ...... f. I'I(IGHT IIJ;I~ UFR .. , .,. UIT ...... \lE 0&1' ... .... \If MliGMT IIR!UfR ... Ol. 

II~ TJ~1 IO H;ll , ~ ... (jrl II.!CLr!l: J;lu H TI"l G"'GEI ~ ... Orz ... H(iI,.[ 5 

.' "' c· C" Inc-lIl'F! 't" J,""s ," "" C • C" OlGRlFS HI' J,~" 

, 10 '. ' ,.' " Z .71'1", • ~QI , , " 11.1,1 Ih O " " I,I.';O~ b.O II 

, , " '.' '" , , I .0 71i .1, 1.10 , I " 1('.1 11.1 " I, 1.1. I 0 II 5,2"8 

, , \, '.' ,. , , , ,'Q7 7 ."Q l • , " ". • 11'1,1) , , , , ",001 OJ,, ,,, 

, \ \, '.' ,. , , .'311 .1 }b 1 , " 111111 1 1 • b " " 

},QOQ II.Q~I 

, " " '. , , .' , 

,8 H • I, i' ~ , " " 

'.' In,S 10 " 2.Q01 !.. "'" 

, , " '. ' '.' I , • , '2 .2Q 1 1 , '. '. ' '., 1\ " 2.b ll b " '''~S , , ,. '. , , .' , I ,00 I ,bi'l 1 , .. '.' , 1. 1 " , , } , I ~ 0 ., ,l} I 

, , " '.' ,. " , , .011 ."01 1 1 \. , . 

I I. tI 10 , 2.o

Ql 10111 

• S , " ',' , .' I , 1 ,1 HI ,u(Jl 1 , " '.' '.' , , , 2 • .,b2 '5, I i'b 

, • 

\ , " • '. , , ~ .07' ,IIQI 1 , 

'. ' 

.. ' .. " " ldQ/:I 1. ~H 

S 1 ' " '.' A.' , , .0'50 d .... fI 1 , ' " '.' '1.1 " I' } .lOb 1I,2i'l 

, , , " '. " '. , , .011 .';,~e , 

I ' " '. , '.' I. 'I ,,10] h2Qe 

, ;1 \, '.' '.' " 1.0011. , 11 1" 1 , , " 0:& 10 .(1 1\ , ? 1, OS6 II. I 2 1 

, , " ,. '.' , .' , 

1 ,012 1 • I bb , i' >, 10.0 \n.4 " I, 3,1"'Q 1I, 21'q 

, j" " '.' ,., " , .Qll ,111) , I" I, , ." 11.2 1\ I, 1. 2! I 

" . I 02 

, , . " '.' , . , , I 1.0

'

(1 ,b

1 S I' \0 '.' , ." 1\ " 1,11'52 ~ ,ill 

, i' " '.' 1. , \ 1,111 1 ." 0 2 " \, , .' I I." " 0 l.n7 11,012 

, 

" " '." , . , • • 1.01" I .11 ~l " , ,. '.0 1\." , " 5.21 " l,8

0tl 

, 

" 

,. '.' ,., , , I,ObO .Q]2 . , Jo '.' 11'1.7 1\ " 1.1 eo lI,lllS I, S ,I " '.' ,.' I I, , Qll 1.'S0'5 J 10 '.' '.' " I? 2.';,00 l.ol)';, 

, " " '. ' 1. , \0 , 1,01t 1.'5lZ , /' " '.\ I 1'1. I " 

I.' 2.fllle l.l:IO I 

, " " ,.1 ,., , I t.Ol1 ,b }9 1 /' \, 10,.0 11.o!! 1\ , J 1.'5

Qb II.':IOu 

" " , , 1 n ." 1\ 

" 

}" eo II.

Obl 

" " ~:8 In.l 

" " 2. 7l~ l.et)l 

-.0 , " 10.1 ,. , " • J. 

. 001 2,b~" 

0 , , " '.' ~." , " 1.°tlU 2,1M I 1 .1 , J •• ' • l,n, 

, " \(1.2 <., 10 I J 2.l)u\ 7. ,bi'l • " 

1

0 ." , , , , " '.' '. , , '? 

2

1 blS ll2bl , , " ',' ,., II I, I.Q}Q 2.tll'lb , , " 10.b '" " , J 1.13 11 1,°"0 

• • " , " , .. 1\ I, J. I 1 1} 2.7 

QO • I ,. '.' '" II " i ,11l l.t"~b , , " '.' ,. , " , I • Q I 1 2.itl~ , " " '.' '., Il I ) 2,b'" 1 ,e},,: , , , , ',' 11.8 , , I.Q1Q 2,llb , , I , '. ' '. , " '? 2.0"0 ) ,6111. , , " '. , .. , , , 1.110 \ I. "i'1 , , " '.' I I • S , , 

" 

l.'n ].13;00 

• • " '.1 , ., , • 1 • QfoU ! le!'!tI , , " , .' 10.0 1\ • 2,l'~ ?,b<lQ , , I, '. , , ., , 10 1,111 ct I • QQO , , I. , .' 11,2 , I , 2, I)"~ ] • I o. 

• I' 30 '. ' ,., I. I.~b.\ 1,01.11') , , " '.' In . " " " 2.1 n] 3. U ~] 

• " 

,. " , .. , , , I I QOo I, Q') I , ,. 

.1, 0," 12.b , . , i l,otl1 .. ,IIOQ 

• l' " 

' .1 ,., , , I • Q 1 1 2.11'1 0 , I' " ".' 12." 1\ " l."oo ".21'e , I ' " '.' ••• , , I • Q)Q 1 • Ill:! , , , ). ~,J 11 J.8f1n ". " 11,0 ,. " , , " " ',' ,., , • I.eee 1. 7 18 ; I " ,,:2 1.3 p II ./j 'lO • Ii'. " 10 .. , i ' " ',' ,." , , i 1 ." 3 I , Q0 2 , I" " '.' Ii' .l " " .\.(\~1 ..... J o'Oj , I • " 0.' ,., " , ~ ,Ob 1 2.52 0 2,QQl , > " , , >.' , ~.} I 0 'o~ 

, I' " '.' II." " , 1.8i'/l , ,., " , 

" " a.- I I .1 • .. 2. q 31 h(l"b , , , 30 ,.' " , (',J.OO 2.(120; , , ' Jo ~:l 11.1 to " 2.~' Q 11.0-''' 

• i' " ":1 , .. , ! 2,0 11 1 I • bi! e , i' " ',' II," " " 2.Q17 11.1121 , Z' " '.' .. , , II I,Q]O 2. t lb A i' 10 ',' I) . (1 1\ " 1. II Q " • 3 .. 1 

• , , 10 '.' .. , \I T 1.1'0 1 .01 J. A Z, " '.' li'.'" " .. 2.Q 17 3."?n 

• " 10 '.' , .1 T J ."" I ,bba , , , J, , . , ,,, .b 10 " 1.180 ".Ob 3 , " '. '.' , ., • 1. "fit t,Oelf! • ~2 " a., 17. a Il .. l .2 t I " .1 02 

• " lo '. , I I ,1 10 " 

1. uO 1 .. . I (1 0 
WOUI?I'I' C'I'CLr. CALCUL"'tO HI 

HI' _A ... r o A"" If ..... f ~flC~' .!II? f AI( f I? 'I! PLB HIP .. A ... l D A"'" ·" ... l "'[IOHT !lR[

U (. ." PL, 

'U" TIM! C" rot.! r;;ACf(l ,,="'CLf! -[I'" TlN[ C .. r;E I C.l,OIl .. .. c.; Lf~ 

N' " '" C· D~Cl?fr! HI" J, .. ,...!I " "' C· C' tI[la

r ,. OJ" JIIIIIIB 

, 0 " '.' 12, c IS I, loll '5 II.Ql0 Il 0 " • • 

, 'oJ II " 1.511 41,n, 

• I '0 11.' • 0' IS " i.Q I e 'I,30e " , '0 " ' ,. , " " 

1,.''1' IIIU, , , '0 1.:'.0 '0' " , , 3.002 •• 121 I> I " 10.1 -.' n " I ••• • , , 1. '" '0 1(1.1 In, ~ " , , 1.31.11 ... 'hi! " , " Ic.e ,., " " ~ I 1.&bQ , , " I 1.2 '0' " " 2 , eO Q 1.i.2Q! I> , '0 10. 1 11:'1 ... .. ., •• 'I'JS '.e,' , , Jo I!.' '0' " " i'. Ql'II Ii .Joao " , 10 10.1 10.1 >t h 1; ,111J e."Ji 

• • " , 1.1 '0 , , , I, 2.bU 3.tHI " , " ,.S '0' " " 1.1.0021'1 b.'I'Qe 

• , " IO"b '0' " , " 21b'l''::> 1.Qufl " , " \ o. j lad , , >i "'." ]'i l'.IOi'Q 

, • '0 10. e , o' '" " 02.l.Ib7 1. b ~? \l , '0 '.' ,. , >t ,. 2.b12 1.1 • jo!. 

, , '0 1 1.0 '0 I , , " "'.64.18 II.Ol.lb " , '0 It .0 '0 , , , " 2.'I''iQ 1o.0Qo 

, ,0 '0 ',8 '. b 'S , , I. QII., J. n l? " , ° '0 11).'::> , 0' " " Z .b~b l.I.lbl 

, i I " 10.2 '., , " , , 2.31'1' 1. u Jo " i ' '0 11'1.1 ,., " '> 2.b~1 I.I.Q~3 

, 1 ' 

10 1 1.2 '. , , , , , c,5

Qe lobQ8 " , , '0 11.1 'oJ " " ".71 b 10 .2bO 

• l' " II .. ~ ,. , " " 2. Q~b ".11.1 Q " i' " 10.1 ,. , " " 2.5 t I ].SH 

, " " I 1.7 '.0 " " 2.for'lQ II, 11"\0 " , ' " " " ". , " " Z,Qb5 .... !:!Ab 

• j' In 10 .. ~ ',' " " 2.!;InQ "0 I ~ b " ! ' " 9:9 ,. , " " 2. S' e II .o"iil. 

, j. " , 1.2 I , , ? 1\ " 1." ,1.4 J.. b,l.':l " I' " '.' " " 21 " Z.7'i0 1.1,405 

• , , '0 1 ) • j \1'1.1'1 " I , i.1I71.1 ". bQ 'I' " , ' '0 '.' ,. , " " 2."'11 II dO'::> 

• i' " ! 1.1.1 11'1. \ 10 " LOICI "l.c"il " I • 10 , .b S., " , , i. ':l'l'S ~ • I '17 

• , . " '2. \ , ,0 " " 2,Ql8 II,QI'I& " , . '0 " , ,.0 " , I 2, B2 I II. !:!'I' j 

, ,0 '0 1 I • Ii '. , " " to 1.1 ~ 2 ],t'o'ib " ,0 " '.7 ,., 2' '0 2.Q2'8 1.I.91lf!: , , I 10 ". , A. ?r. " " 2.Ij·a 11.011'1 " , , " '.' ,. , " , , 2.01 C ... 098 

• i' '0 11.1 '. , " " 2.~t;1 II ,'"I?2 " " '0 '.' " .' " " 2,1<)b ~. cQo 

, " '0 12.2 In. ? " I, ].2AQ ,::>.1",1 " " 10 '-' ,.0 " '0 2.]lIb 1.7'1' 1.1 

"" 

\0 0 10 , 1.1." le.l " I, 1.0·. I ! • l'lS 11 ° '0 '.' , .. " " 

i.ltOo J.III 

\0 I 10 lOS.} I ~. r'I '" , " !.lQ2 11. 'jQ I tl , 10 " ' '.0 IS " i! ,'5" l,UI 

10 , '0 '11.1 1".1 " , , ?IIbl 1i!.Ollil 11 , "' ',I 7., " , , ,.0219 J.il'l 

10 , 10 I Cj.l I A I? " " 8.1.191 1".71 S " , '0 '.' , o' " " 2.139 }. S! t. 

" , '0 ,".7 I ~. 0 " " B. 0 Qe \",912 " , '0 '.' , • 0 

" " 2. ~ 0 b 1. Q 1 t. \0 S ,. \].e 1'1' ... 10 I, 1 do? 11.'SQ~ " , 30 b. ' ,.' , . I , 02. \l'/,[ 2.

Qtl '5 

\0 b '0 1 ':l.l I '1'.7 , b " 8.~l,jl I '::>. b'l' 0 " , " '. " .. ' Il , , '.21 Q Z.!til 

\0 , '0 , ..... e:. p.Q " , . 8 ... Ql 1 bol 116 II , '0 , ,I ,., II " i!dO~ 1.7 • 

10 • '0 Ii,;. 7 IFI. ~ " " e 011.1\ I II. ~.?1 " , '0 '. I '. , , S " 2.20'1' l.I"!iS 

\0 , '0 \4.1 .. " I Pod " " !I,04.l1 ·11. oa15 " • 10 ',' ~ • (I " '0 i! • 0 7~ 1012S 

\0 1 ° 10 11.11 lA.~ " , ,. 'I'.7Q" ll.~"ll II 1 ° 10 '.' .. , " " i. 079 j,OJo 

\0 , I 10 14.1 ... '1' 17. Q .. " 

e,oLll 11oI.1F1Q " " 

'0 '.' .. , , " I, 2.2'19 c.B9! 

\0 l' '0 1'1.1 1'1', 1 " " e. (j.l I '5 .~Qc " " 10 , .' b. , ,. I b " oI'I'/,[ c.~Qb 

" I , 10 I ..... 1 A 0 1'1 " , , '.9 ..... \., .'54Q " i' 10 '.' ,.b " " 2.20'1' 1. (Ie b 

\0 i' '0 1 .... 0 C 1.1'1 jb " "J 8 17.'>"7 II 

" 

'0 '.' '.' " I, 2,lO':l 1. lb 9 

" , , '0 I ~ .. 'I' \ Q. "i " , , '. I , 1",Io'il " i' " '.' b.' 10 I, i! .co 'I' ? • Q u ~ 

,0 i' '0 \ 1.1 ... 1 IQ.? " , " r..1

Q i HIoObb " ,b 10 ',5 b.7 " " C. [)'I'Q c.IJ(le 

\0 I' '0 I". , \1'1. ~ " I b ~.}"I 11.1 • .11"11 \l l' '0 , .' '0 , " I, I. Q",::> 2 .1.1 0 1 

10 ; , , . 1 ".' IQ.8 10 , . e.bQjI lb. 0 4.1 ~ " I' ,. '," , 0 0 " " C .(1'1'2 ..s.HI 

, ° i' 10 11.'1' 21'1.'1' 10 I, e,QCjS Ie."?') " .,' '0 6. 5 , 0 I 18 " e,itl'l' 1.01.11 

10 ,0 )0 ll ... ':l 19."\ jb " 8.2q 1~.lO'l' " 2° 10 '.' ,. , " " 2.el Q c. ':ll 8 

to , , 10 I" .1 I Q.? " " 

~.II4l lb. I 1111 " 2' 10 '," '" " " c.l1 0 c. '>1 0 

jO ;' lo , } .. 'I' LI'I .... " , , ',8 .. b II..Q I q " " '0 ',7 , .' 11 I, C. \ ! 0 c., ~iI 

10 " Jo \ .. _ b lA.n 10 " b.O ~ 1 I" .1AQ II " Jo , _I , .. II ,j ~.ll'c ii'.lb5 
WOUII'I , OCll CAltUlATtO"14 

HIT 11""( OAT .. III 

AvE ... f [Ct(7 

8

R[,I((" 'If PL' 

All '" 1[ ... ( /; .r;t I 

th/;O ,"ClfS .' •• ,. " OtCRfl! .,. J,-,! 

, . D In , ~,,1 11. Q " 2. 1100'l l,.7'JO 

, ' , In 15 .. 0 I to. 8 " " ,l.

o b5 l8. JIB 

, " 2 I, n .. b 11.1. , ,. " 

, 0.0;1511 Zl.'l7. 

, " I lD ,o;.b Ib.2 , .1 " ,2.ob') 1')o~68 

, " " " 11.1" I I b ,II. " I' I 1 • }lfl 2701 76 

" 

, " '". " 1'.n " " II.HII.I 

1 8. ')1? 

, . , I, '''>,,0 til. .r Z' li 

I J.IH }l.U) 

, " , lO I')"b , 1 • , " , , , }.?} 0 } 101 o~ 1 

, , • " 11.1 • 0 , .... ,1 " " ,1.11 1.18 } I .t 1\ 

, ' , 'n 1001:1 10.1'1 " J, II .",JQ lQ ,'''''' 

" , , In , ". , ," .r " 

1, ' Z ,0 III H.c,,? , , i' In \(,0,,1.1 '1'1,8 " " , I, D III 2 Q,o{l l) 

, " J Z In , ~.:. 1 16" \I ,~ 10,IUl Z 8

, 0, Q 

, , , I 'n " .' l'i.n 10 l> ,0.

e '5 '" C$'. 0 1 1 

'" ; " J, \ u" b \<;,(1 12 " 

, 0.It,lll Z ?f.o" 

, " , \ In '~.' 1<;," " 'n HI, 0 1:>'/ co,ZSo 

, " i' " \ \ .. e 10,8 '" '0 I I 01 'z 

? 7,O?0 

, " , , ., 1').6 1\.0 " " I' .0 80 50

.b12 

'" is , D 1 iJ.1 I ',7 lZ , , 

, Z,O h'5 l" ,~n Q 

, " , ' In lu:.!. Ib,~ " , I 1 I 

, ,)1.10 1 \ ,">" 

, " ;' " \ 1 .. 2 III ,1.1 " " Q.OSQ ? II .11 \ II 

, " ,I 'n ,') .. € , ,." 12 " ".1:>80 ., I • 

bO I:> 

'" ,2 on , 1.1 I. 3 10. r " 

'.' 

11,0

0 0 '. 5;>~ , , ;' 'n IS _ 0 I<',n " , , \ o. n~ 27 .I:>QQ 

'" N 

" In 11 .. 6 11'1,0 

" " 10.111 1 ~. \" 

" , lD \ 1. 8 I '. fJ 

" " 10,o'D Il.fJVO 

, , 2 " 12.6. I 7 • b " 2n Q, 

10 Q tloibO 

" I 'n 11.' Ib.Z " .. 9" 1 I:> 13.15

0 0 

" " ~~:~ l"i. e " , . 

" .00;15 I 

Z. I? 1 

" , " , , • n " " Q ,liZ 1 , .. ,Z"'o 

" , " ".~ I 1:>

. " , , " ~ ,0 ')'5 ''', 1:1\ 'i 

" , " Iii , b 1 b • '" , ' " 10.01)1 \ ~ • Q 11.8 

, , , " \1 .. 2 I , • r-

" " o.Z~o I J. 6f)1.I 

" , " \ 3 ..... Ib,'" " " o • b \ 0 IOj.P' 

" l' " l\.tI 10,11 , ' 'n o,Zoo I u ,11 "5 

" , , " \ 1~" I (I • 

r. " " Q.ZOO 1/ •• 2 '') 

" jl In 

I r .. & 1 '.n , , , , o. o"'S 11. <j1'l0 

" ) , 

.'. I l .. Z 1 S, 0 

" 

2n 

6 ,1:>\u 1 3 , 1 QO 

" I' 

' n 1(, .11 11 1 , 

.1, >0 " , 0 • "') 1 1" , Q~6 

" " .. 1' .. < \11. \ " " , 

O. I 1 , Iii .1 , 1 

" i. ,. IZ .. '> '0." ,. " a. ,or; 3 Ir.HI1 

" ; , 

., 1.l.0 lb.'" " " 

e , /:I , j I Ii • 1 3 u 

" i' " IJ. , Ior;,r " " e 

, }rli l\oI~O 

" 

i ' ,. 13 .. 1 I '. '\ ,. , , O. II~ ~ 12 .01f) 

" " ,n 1 \ .. 1 \'i." " " 1:1

. 51 $' 1 1 , 'r 1 

" " In 

1<.0 lb.~ , . 2, e, ~2 I 2 ,01'1 " 

" ,2 1. 

Il ." I". \ ,n 

, j O,tlfI(: 15.tl

l o 

" " In 

\ L(: Ior;.b I' " !I.u')' 1 J 

, b 1<,1 
APPE~DlX F 

DAlLY CYCLE CALCULATlONS 

t\ listing of th~ program whIcb calculates the v.Jlues in this appendix, 

using t he da t a in Appendix A, is availab l e from CElAC. 

93 
O"TL" CTC\,..[ CH CII\,..'1 IO"'-e 

TnT "II"'" fI "( ~);" .. 'I H IL " " TnT RII~ fI W( !Ii x Y pee 11 " ., ~l?r'I'" 10 ,111'1" , n 

"' HO ",,,, J I"'S , " "IS "' ". " ,,, J '''/5 .; ,5 "IS 

t • 1 B'i '. u 'lo \ , JIo 1.1 B • ..,7'l~ ,1,nO , " 1. n \ r'I ~ • b 7"> .71 I 7 • ;l16 u • \ 0' r 

, , '\ • 1 01"1 7, ;l'i'" .'lr'l~1"I .ub?7 .::> 2 'il:! , ::>.t>'i ' ,."",n • ~ 781 • 1 1,1 23 .IOb7 

? , ; • \ 71'1 ;l. 'lo" 1 • S",b 7 ,u fl1 0 • :? U n r) 

, , " \.12 ' ~. ~) 'i , 1) ~II .\ ('1(;0 ./I t. .. 

, , ; • \ I) 2 ) , \ 1,1 0 .51<,.0\ • OJ I) 7 U .) IJ" I , I? " 1. \ "'2 1.1 • (11 7 .;.<) 7 ~ • II 7 \ 1.1 

. 1'<' 1'5 

, , " '" \ 1i1 ),? P, 7 ,1'11

0 8 • It, 

2

1 8 .2 T! D , , , ,n ::>. Q,":< 'lo 'lo. 0'" \ .1 II S, .no~8 • II U ob 

, " " 7.26 0 ).::>..16 .1:>72", ." 3 I) 1 .) OQO; , ,n " t, \ p.i! <., r'I':)O .(:17) • II 7 lI'i .",)~5 

, ,n " ; • I S) 1.

0 ,,1'\ , ~"'lo ~ .,1'1

7 1 , t 'lo <; (j , 0 " ,.n9b (j."'7' ,bl<,.lr'l .) I 1')'1 ., 1,I.::!.IiI 

, n , ~ .21 '5 ),127 .b .. 

0 1 .OJ'l12 • ~ 1 f,j~ 

, , ;>.1] I') u , I )':i .1,1,,0,,> • t bOS .11 \8 

, , • " • n O'l 2.1"170; .1'17

7 1 ,"'l~" ,,,,"1 , , " ::>,1">1,1 t. '5 3~ • '5 Ob~ .)"12 • 1 o~o 

, , , , '\ , 1 2 ~ , .0)'5 .7) 7,":< ,ft" 7 0 • '77 Q 

, 1 , " ) , 700 u. I OJ 7 ." ,,1,1 0 .lbb'i .1118 

, I ' " ; • 1 ! b I .... o'i ,1'177<; ."UbO · 'b 11 

, , ' '0 t .0':> 1 u • ~I< OJ • L ,":<b"> ,\110" ./101 ... 

, ,0 " \ • 1?0 '.?;> ' • 7" 21'\ .,,).71 • , I " /I. • ,n " ::>.100, 3.

0 17 • UOo 7 • , 00 ~ .I2o il 

, ;' In i . , .: ~ ?~ 1\ ,bAOS .nO"S • ~2 lib , ,? " t. n7b 1.1,01,11 , ,,00 7 • \ b 1 " .' 0 no, 

0 , ::>,1 (l ~ CII. (I 'JI.I .A"211 .11]7 .?l ) 7 " 0 " .iii, 0 11 1 (; • \ l~ I • Ol'l(;~ ,1<:'/,;') ./1 7 1 (l 

, )."'Sii ~ , I ,,? .... 0;01 • t PA .; 0 (; 7 l 0 I' " '" • 0,1 (; 10; • 7\ 11 I ,o).lilq~ • \ 277 .1':10 011 

" ;l'::>U? 2.? u t .0,2) .lilo; ... .1,1 I 1'10 10 I' ?n .... 'lOb 1,,;l7' 1 • C'o eo .121'B .1171 0 

1 , '6 ;.;lOl )."'S" • T~ 1 "> • 12 7'\ .;l<:l2b I 0 ,0 ,,, .... 1'l" 1 <;., bt> ) • I "I II • I ~ ~ 1.1 • 'I 7 ob 

i' 20 ::>.11'::>" 1. \ 72 ,I'q\ , \ ~Il 0 , ;l"" 7 I' 0 ::>,'l;l/l. ". r'l20 I , 1 ",01 • u""S .?e 77 

" ~ !J ). ;l.!.0 L?IQ • a, U '1 .P;l,,> .;l~ol " , /_ ."SO 7 • 1'1 ~ (j I .b1'~1l .HI'.I.I .11

0 '1' 

vo , ~ • 13 "> 1.1', , .1;l Q (\ 011 ?1 .IQbl> " , " ::>, '" 7 ? (; ,u 26 1 .I':I .. ~ .62(;i/ • '5 170 <c- , , ::>.'::>71'1 u, I (j A .b"'!(; .?,::>Qs • jt:II 2 t? 1 , " ).1'1"2 u. \ 'lo ~ 1 .7, ., 110 

'"~''''' • II n 1 n 

, " ?, ;l7~ 1.

o AO ,,":«1)0, .;l ':- 0 1 ,\" 8 \ " , , " ;>.6q{) (; • 'i 7 i' I • 1. ~ I .6'i72 • Vib1 

1 , I, , • Q 0 n 1 • ? 1 (l • ':>0. ... 7 ,)O(jl .'<;71'\ " ,0 2a ?" II (j. 1I;l7 \ .7'" J,I!i .7 10" .u020 

i' " t • $\ 7 U 1. , ~ 'i .01\'1'0 .12101.1 .I

0 3Q " , , ?, :sq{) 1. ~ 0, 1 .5,,0 II ,~u 11', • , M;' 

,0 '" 7 .... 0} ;l,OOO • ') tIl .~f\l)b .1 77 2 " , ::>. ?~ 1 1.1"10/1. ! ,1 r'I" 7 • 5 7 211 • ill II, 

, 0 " .0" 1 ."1'\0 .';:~5Q .'5°H .00ll2 II 10 ::>.1 11 1 ;l,"'Or; I .1 II 0 1 ..... 1"'''> • ,"'tt'5 

, , .... Q1 .IIA2 • II<J 11.1 ,Q (j '2 [0 1 .71>1'1,) " 1 , " ::>. \ 1'1t, ~. II (; n 1.\ "I 5 ."-(.1:>" • HZ" 

, , " , , n1i1 • U ~, ,.IiI)l'Ill • 

1 0 ~ 5 \ ,0 I 1a " , 'I' , • t U iI ;l. " lib lol;l22 ,'i 2' (J • II ('t;lS 

, J' " ,0$\1'\ ,onb .7121 ,7 <J I ~ ."'080 " i' " ~. 21:>(; ;l .... '::>' I • \ 1 (I iI ."10 0 ,(,;j 03 

, 1 ' '0 t • oS 2 I • I ~ 1 .~"I? .1foJ o 1 ,1..,7\ " " " ::>.?UI ;l.;l2.1i1 I. \ .. \<.1 ." I 112 .S2 \ 2 

, ,n " .0" 1 \ .22 OJ .b",QQ ,700~ ,'i 7! 2 ! " , I ; • "OU 2 " ,01 , j.)oHO .::>71'11'1 • 1 21 U 

, 0 , ::>.001 2 .... \ \ \ .011 I (J • ~~, 0 0 ,1Q88 , " " , 1~,l1\L 

1

n .bS 7 1. I "ll 'I .;lOjr'l1 .11)\ I 

, " " 'I ,072 ".;>(J~ • 0, (1) • 11 71'1) .11 ! 1'1(J , " , " I ~ ... flU ) I) "'" 2 l.ZlIb O .,0Ql • \ 0110 

, , " '\ • Q 0 ~ 1 .02 (; .Onb .111:\1.11 .1,,800 , " l ' " 1 ~ , 7 c? 1 21'.~0' 1.1u}u .11 \ 0 • \ 22 Q 

, 1 ? " t • q I 1 1,OQJ I • C'i' 01'1 • OJ 3111 ,~ 1 20 I" I' " It.O

Q2 10,05'1' lolullI .)1'11\7 ,1015 

, ;. '0 ".IS'5 ;l. , I', 7 1.0,110(1 • ~ 0'5 1 .ij">bb " ,0 '" 1 Ii • 00 1 

2

7

• 77 1 :5. OQ2 'i • n81 .IHo 

, ,0 " ! • qo 8 ! ,I'o'i 1,1')/1')1 .~2bQ .')'51:>0 

" 

0 , l!l.bO~ , J .1.1 1 0 ;'.2Q1~ .11bo • \ 7\ I 

1 0 , u ol 0 1 ~.tl ll \ .215 I .?oo 1 ,;l2b5 

" 

" , Q,loo 11."ij,!> 2.1 )OIJ • .?2 b 1 , I 010 

, " t,Q5\ 

'.' • • ~q~1I , ?S ) Il .I

Q t>fI " • " 0.377 \ij,,"1:! oi!.lo,JQ2 .?e \ 2 .1 no 

, i.777 

• • b .'I'lq~ • P 52 1 • 1 121'1 ' , l' I. ').lIe~ 

1 10 .001 2.

b fo H .2'" 1 jj • 1 ~o 2 

1 , , 1..r;iIQ .u .! ?1 .,.~ 12 , ;l 10 l c? .I7H I' I· " .... eol 11.0ei1! "J. 'lt

lOIi .HII!I .UB 

, , " ';.h2 , .t!lqtl .eqOI .2~le • 

1 07 /.1 " ,0 '" .IiI.

1 .,1i 11. OJ i' I l.lIl1eO ,3Z"Q .11

0 0 

, l' to ;l,07S 1. ;1~ .1'1 ?n ,20'il1 • 1 '5'" 7 , I' '0 ,.0 q 5 1.' 5;l .e3"'e .? 0 bl.l .162S , ,0 '" 't. oe~ II • ~tI~ , ~'5bO • I "'00 ,110'" 
Lt.h. W.t llp 

J't1vab l. d 1.bor . t.1 ry "l[I" "r ~n fl C:GClllpAr l o& .. d i "tLo,;.n IIln., •• ruJ 

, rw r,.¥ t l ux ,.u:lor •• jl rr..d5CCo rl'l ot 10 aMr. t r ... flll fo')Cl r .. u:' t by 

jl'I;;LlIp 1tlll l~. -'o rt Idval :- , t,'oJ . : U. :;. /.,ra y c.o. ..... l (.n,ln.uu.o k •• lll rc:h Cen ,-1' i Sp rl a:lt, h ll:ld , '0' • • : A ... a ll.M_t" 1,.- t. r l!'! , 19",. 1 f'I . ; 11 1. i n ,: •. -·(.!U .. c11 _n",.,. r.:: port U.::.. W .,/ w ollH.d 

l_a1no .. rl"! K<!' I!j.n:: " u: nte r ; .. tI . 8t-' .. ) 

• ·•· .. r ti d • . 

- "prLL fl} J.-

IU'DL101nphy: ., . ,-" . 

n"clI-d.'..,n" lol'tlll ptO ..... b~~-:. a ~""t. or or f c •• , f •• " l t l HU ..,. .. d 

tQ ... pi ·d e. ll ... · r'C l at 'M LoM,.""'!" ."JI nL tOIl'rort r e ec Tn 1.1\ .. 

carll., II a LCc ll •• nd Lbr 10('1,&,1.0["": ,.nor,)' flu" III(tvr. ~)ln c.(:rtorl .. t.c tlq ..... 1)1 _ .1 ..,ll h l ' 10 ,.hor. 1'r.lnlllJO rl t " C'I; h~ • ..,r! 

lite , a nty f\l' Ct , .e . 1<1: 0 .I~ .. U ~tr" "1 I nf lul ne. on thlt h '.,. 

t . 1114f ullc ...z .. J.. l . " w_ blt tw4t. . j. ~.11I": nL u.nlllN ft. 

... '.i.Ivtt' lotfW'r",y . I. r(dlf. I I. ~' lu: HJ.Jo..: .. Ua,MlU",' r" po rt 

( .ut f. \ J1 c o:rt pt .·,I!'*c4 r .. " Cont.::r ( I.). » ; no. 111 - 4 . 

TC 0 ) . \'idle t no. 81-4 t 1 

Vlt l h:. "'111 , H.,y .. blrbc ~ ·J.tWlr.;Jtory cxr"rl_nt. -r~. nl f'IIIIJlat l t'n Ir ~ •• 4 d 

.. nor f L/ l ux I ClO t ... Qrddi c l ut. ul I" " ,.. •• h'lrc t f4f11'11"" 1 t 'f tc I tly 

nt H t Jl 'J 1t .I/:. - -tflrl Ivo 1' , .. . . : U.S. M." .ltAl J(I"I" rt' h..~ 

a.. ilrCIi ee."l. r ; Sp t l n,f !<l1 4 . 1.'". : .nI.La.le I e"" .!(t IS, iJIJ. I. 

: p. ; H t. ; !1 .-(M.l.e.t. IIIInttDu " rQ \"t I U. ". v ... C .... .. (. l llta ln\:.: r111~ J:.i. ... 1t. ~1t.ll r; rlCI- It-C.) 

to·.·,: r r tc:l c. 

"p rtl ")6 .~ 

tJbl .~hy : p. H . 

nu •• -d'''nli l otU l w.>~ bl lk J I ~o tOI"Y , l r .. . uL L:' H ...... I! 

t.o ; .• , li e. h· .. ,ut .. t~ 10 .. , .. "' .... UJI nt tr ... _!fU ll r.lll ll to -rh., 

u d U l lt>n . tr ..... tp; _M t'. h."".lIot. ,·raol r"., I~ x t t Ot . &loci. cc rr*I.\c ~':a ud J.y 1 wlt" t tl!; l.o n".h ;:. tf,n_port r. t .. ; t l_ •• .lCC 

_i_ U ar B y ... r.m .. t .. r " Iall._ •• LC" "" If.fJucm Cc on t r.. r ftt . 

i. lIy"' nuH c oOde J" , . "')"'1I0J. 13. · ) . ~Ih nt .III. tt. 

.. . vc 0: '1:1' I. H tlc . n . rfr. : ~'Ctill ""I'OU. refil'l rt 

(CQJI \.oi l SU,;. l o l:t:'rl ." 1l.c: . I:.arch l.o~1'\ 'Itt (U.S.» ; no . 31-.. . 

t (,) .u>t\ I CIT nQ. 5 1- 62 ? 

\'1("'11 . ~ul lp 

l"~v.bln d l .. tJor .. locy .xr<! r i.t" ... c.. " 1n,, uJi, Ion at n .... n.! 

.nu r~ I L~ ( u: t o c •• , pc.a llet " r ,. 01 l on,."ou U llOa-po rt r.a:tl: I tt, 

rk H r .'j' . t". --fon lvu.l . 'lot. : .!I. Ar-.v lo.a.t .1 t.n,1.r;. (l rl rt, 

"uhrch (;cft«" ; ~y llllil .. ld, \ • • : .110 U .oJ" Itc. ,," , 19~1. 

I1 J p. : 111. ~ U ~ • . --( K"(.1).IWlu"" . .. ( IrL U. '1. -'1".'11 u l 

r. ql! leoJo.:t : .}I k ~.' h \4ale r ; !';,:) . tH"" l 

:;;" t ~Lllo: • 

- '!'prU 1951.w 

klbJt o.;r ... ph~' : p ... 6. 

t .. "-.t"",,,1un,1! Malo ,bl.'-bed '.t.ur" t~ J t..:}o f ( e.-lilt " ar .. deoJ 

t o I'JIpl rl ... ll, r_ t ilL" ( hi! J ... ~ •• t ... r _-,JIM ... ( t r .. ".i .... n , .. t .. t ( ' ... 

01~ "'1 " .(1." 4Ad d)L 1'"'1£" ,, ;,o r l. "",,f.), tiu" t "c tor. bo ttt c.:J rrt'l t'L~ "' ...... 1 y WlI11 w t!l ( hi ) oln,.httCol tUf"!1'f,rt ; t " • !,If 

, .. 1 1. r tty l a r_IIt.r .1'0 ,.r wa. 01 tn ..... tnl OI n ... on t .. ,. '.Cr, . \. lIy<Jra ltil le ~.l .. . 2. ~.~ .. dc . J • .x..d\.wrIt lr"".j fl. 

l" . 'Oil n: l:ner y. 1. It 1. I~ . Ih'l : "-. Ir.dlllr.Qw l,l f " p'lrL 

, lIa l £nau>e. rL n i.: I .. . rCII ~·nt.:r VJ • • ~J ; no. 1:" -4. 

1 0,j . l J 1..r 11.:1. 1I 1-1, 627 

,,·t al!,'! , f'hllt)'l 

.. ..,. ... 1:-t..1 l. b..Iratr.ll ~ IIlC.p. r l 'rn. ("~'ItT n.:- r ,uU.lh,u\ IIlfll.' .~.:. 

.n.r..:f ! hut ,. ' tl.)r ~. rr-"G.o.: JI . (oj \anlll..ttUCIIII n ""'lI 'O tt : •• te I by 

"',ll ip '/l l.Jlr. - -I"' rl &o LJ{J lr . \'11 . : l .$ . , ... " ""' ... .r.. '" I inil1 •• ' lrl f'lii 

Auo.tc h c..'it.r ; Sf" l"lll,f .:La , '4i . : .1'0' ,: 1 .. ,11 ll. ;-rl~ , 1'9lk . 

19 "1 , . : I~ . i . 1 c. ... -( '!o\I.~ ~ I.II. ~' ~~ rt \..'. :s. ,U II'I -.lott4 ~ 

r,,~t1t(, 1 r h" fU,t('_U d L CC ~ ; >lQ . ,,1 -,,1 

to .... r 1 t ic . 

Apr , L UI .-

11IIt " Cr.\7 hy: p. lob. 

r .. ·~I_h.I"". l .n .·.hl..-'t>o: ' , ,,D..tr-a t Qry t.:1'[ r .... ~ . .. , ., •• J 

to c.l' tcle ... l1 y re l a, " ' ht Ol" &6n~l • •• a f SE"n1 [ f a"" Cl r oltv c ... t l. 

h .tatiu" H .... and trw: lCh,.htoro! l'_ f a.:.' (1 1.1111 I.(:.I.QI . !»t h (o r-

,,-.1_(. I q ..... Jl' 11 ",u P'! t llll: I v1\.e lio (u Lr.ao"pgrt r a t, ej Iftot: . u r ( 

~' llu 1t)' ' .... r ... t<'l r .L~ .ho....... Ir-.)I\j£ tnt \,I ..I· on ~ht r.-tu . 

I. Uyduu"r . ._ fu ..... ,il.l .. • l ... d... J. dt nt I. rlllll_FO rt. 

l, . •• '~ I1U', y. 1. ~. U . ""' , C". ; ,"lIc lll .n~I. "'~ trpv rt 

( CoAl/ t oil [liiClnrt'ftl~ "coif(;tt (,;en.l.rt <U.S. )I ; no-. li l....:.. . 

y ..... U) . U\ o lr.r 00. ~.- 4 621