US. ee ere a) TP 79-1 Relation Between Immersed Weight and Volume Rates of Longshore Transport by [ a : ‘IT Cyril J. Galvin Ae Ci aby / TECHNICAL PAPER NO. 79-1 _ MAY 1979 Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING RESEARCH CENTER GB Kingman Building USB Fort Belvoir, Va. 22060 VG no Mo! TP 79-1 Relation Between Immersed Weight and Volume Rates of Longshore Transport by Cyril J. Galvin 0 TECHNICAL PAPER NO. 79-1 MAY 1979 Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING a) a) | 6B 1) ee e/a, aad RESEARCH CENTER Kingman Building Fort Belvoir, Va. 22060 Reprint or republication of any of this material shall give appropriate credit to the U.S. Army Coastal Engineering Research Center. Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copies are available from: National Technical Information Service ATTN: Operations Division 5285 Port Royal Road Springfield, Virginia 22161 The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. NN A OY 0 0301 0089554 4 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) REPORT DOCUMENTATION PAGE READ UNSTRUCTIONS BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER IW? 79a . TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED RELATION BETWEEN IMMERSED WEIGHT AND VOLUME Technical Paper RATES OF LONGSHORE TRANSPORT 6. PERFORMING ORG. REPORT NUMBER - AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s) Cyril J. Galvin - PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS Department of the Army Coastal Engineering Research Center (CERRE-CP) D31196 Kingman Building, Fort Belvoir, Virginia 22060 - CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Coastal Engineering Research Center 13. NUMBER OF PAGES Kingman Building, Fort Belvoir, Virginia 22060 - MONITORING AGENCY NAME & AODRESS(if different from Controlling Office) 15. SECURITY CLASS. (of thia report) UNCLASSIFIED 1Sa. DECL ASSIFICATION/ DOWNGRADING SCHEDULE - DISTRIBUTION STATEMENT (of this Report) Approved for public release; distribution unlimited. - DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) » SUPPLEMENTARY NOTES - KEY WORDS (Continue on reverse side if necessary and identify by block number) Energy flux methods Longshore transport Littoral material Sand 20. ABSTRACT (Continue em reverse side if necessary and identify by block number) As presently used, the immersed weight rate, I»), is the volume rate, Q, of longshore transport, multiplied by a constant. For use in engineering prob- lems, Ip, must be converted back to the equivalent Q. The Ig formulation ma be important where the unit weight of sand differs significantly from the unit weight of sand at the open-coast sites contributing data to the design curve. Increase in void ratio may result in a 10- to 20-percent increase in actual (as compared to predicted) shoaling volumes where sand accumulates in protected water. Void ratio should be measured in field studies of longshore transport. DD , 0%, 1473 cvrnion oF 1 nov 65 1s OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (Wren Data Entered) 4 a see ULE eta ets Syl 8 rts? th tun, eo e ; dbase ”y es gid wt ¥ ie ; ay pirat? pew ay i pine +o lest: alge . a a, iy 1 "dante es in i ee Re ew eh ai ee ae uy, sh ot a yore ay ae re mene LK be robe rhe to ty hops : once ye SWlw jae “a e? es a itis / ‘i ae Hea Pye 54 ee: a We fl a ee iw Wi a a Oe ae Comey 4 a we i ou paiilaaers ae a Prikl yi Sy ae eT pee Sieh d ee if Py) me ie ee ree rd a a mn | a ae eT : Kee, AE So AW, Gi Ab imgh > Daal ¢ hry Meo 4 ae me 4 (et ae F ; i@ , ved " 4 aT (rut \ PS een vad, me ; afaial eh oS a aie 4 a A ou ‘ | me. “ » Aes Py = ie 7 1 7 ‘ , } u f N ‘ "a i: 7 : * = 4 pied © yi r 2604 Ra: a ary nab Pan yen wa 7 f w i 4 we. en ‘ i )* “ ; A o a uv ’ i © Wi : - / OT ay Sieh a ; wer ey ye > oy, : % i ~ ae ay wrt | , rye pli { i ¥ { yess bid Ly }. SEPT Ue SD UP Raia! eae oti my nD billy ré Be ee | > e aa iW MN tl my bey ae seni ruven iP i r Catt : , f i a, “haan ) Page eld Die tO 54 ‘i ae) i ite @ iy me add bala i aa A ee yearn i's — UNOS Ee aT ai Ly aah fils ; f weet. ral led diy, ache tia ain ie re Son ve ‘ si “a pits — ¥ wae © ete, 5 te inde" ak 1 ae: e ae \ = fe er — ae us all i 7 1h oe i ‘ dl ion iy PREFACE This report is published to show the relation between two versions of the energy flux method of predicting longshore transport: The volume rate prediction recommended in the Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977), and the immersed weight rate prediction proposed in other publications. The need for this explanation was indicated by inquiries from field engineers to the staff at CERC. The report was prepared by Dr. Cyril Galvin, formerly Chief, Coastal Processes Branch, CERC, under the general supervision of Mr. R.P. Savage, Chief, Research Division. Comments on this publication are invited. Approved for publication in accordance with Public Law 166, 79th Congress, approved 21 July 1945, as supplemented by Public Law 172, 88th Congress, approved 7 November 1963. ED E. BISHOP Colonel, Corps of Engineers Commander and Director CONTENTS CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI). SYMBOLS AND DEFINITIONS. I TUNATROIUIGIIION 6g 9 6 oo ooo 1. Volume and Immersed Weight Rates of Longshore Transport. Zo PURTOSO II UNIT WEIGHT OF SAND. III PRESENT USE OF IMMERSED WEIGHT CALCULATION . IV RESULTS. V CONCLUSIONS. LITERATURE CITED . TABLE Ranges of volume concentration, a', and unit weights of SAT Gee Sar Wace er icant. Ms 5 FIGURES 1 Two sets of longshore transport data from protected waters related to SPM design curve . Z WSS OF In Ain RESEMS RACELES®. Page 12 15 11 13 CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) UNITS OF MEASUREMENT U.S. customary units of measurement used in this report can be converted to metric (SI) units as follows: sss _-________ nnn Multiply inches square inches cubic inches feet Square feet cCublemteet yards square yards cubic yards miles Syuare miles knots acres foot-pounds millibars ounces pounds ton, long ton, short degrees (angle) by To obtain ooo eee eee oe 25.4 millimeters 2.54 centimeters 6.452 Square centimeters 16.39 cubic centimeters 30.48 centimeters 0.3048 meters 0.0929 square meters 0.0283 cubic meters 0.9144 meters 0.8% square meters 0. 7646 cubic meters 1.6093 kilometers 259.0 hectares 1.852 kilometers per hour 0.4047 hectares 1.3558 newton meters 1.0197, <1 Ome kilograms per square centimeter 28.35 grams 453.6 grams 0.4536 kilograms 1.0160 metric tons 0.9072 metric tons 0.01745 radians 5/9 Celsius degrees or Kelvins! Fahrenheit degrees ooo eee 1To 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. SYMBOLS AND DEFINITIONS a' volume concentration, ratio of volume of solids to total volume in a sand deposit (defined by eq. 8), dimensionless e void ratio, ratio of volume of voids to volume of solids in a sand deposit (defined by eq. 7), dimensionless G specific gravity (defined by eq. 6), dimensionless I, immersed weight rate of longshore transport (defined by eq. 5), pounds of sand (weighed under water) per year K constant of proportionality in energy flux method (defined by eq. 1), cubic yards-seconds per pound-year Py, the energy flux factor, foot-pounds per second per foot Q volume rate of longshore transport, cubic yards per year Y unit weight of sand (defined by eq. 10), pounds per cubic foot Ys umit weight of solids in sand, pounds per cubic foot Ve submerged unit weight of solids (defined by eq. 4), pounds per cubic foot Y, unit weight of distilled water, pounds per cubic foot Y unit weight of water in which sand is immersed, pounds per cubic foot NOTE.--The dimensionless immersed weight coefficient (Longuet and Higgins, 1972, p. 211), using the definitions above, equals the term in parenthesis in equation (5), multiplied by 2 to account for the use of significant height in Pp,, and divided by 31.536 x 10°, the number of seconds in a year. RELATION BETWEEN IMMERSED WEIGHT AND VOLUME RATES OF LONGSHORE TRANSPORT by Cyrtl J. Galvin I. INTRODUCTION 1. Volume and Immersed Weight Rates of Longshore Transport. Two general formulas are presently (1978) in use for predicting longshore transport rates from incident wave conditions. They are usually identified as the energy flux method and the immersed weight rate. The energy flux method empirically relates longshore transport rate, Q, to a computed variable called the energy flux factor, Po,, by an equation of the form:. Q=K Pos . (1) The equation of this form recommended for design in the Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977) is Q 5 7,500 Po. (2) where Q is in cubic yards per year and Py, is in power per unit length of shore line (foot-pounds per second per foot). The proportion- ality constant, K, has units to balance the equation (cubic yards- seconds per pound-year). A number of investigators recommend using the immersed weight rate of transport, Ip, rather than Q (Bagnold, 1963; Komar and Inman, 1970; Longuet-Higgins, 1972). The immersed weight rate leads to a dimension- ally homogeneous equation with a dimensionless coefficient, instead of the peculiar units that K has in equation (1). The immersed weight is related to the volume rate by ln 8 27 ev Ne Q. (3) where 27 converts cubic feet to cubic yards, a' is volume solids/volume sand in place, and Nes is the difference We Site (4) between specific weight of sand grain, y,, and water, y,; i.e., the immersed specific weight of the sand grain. From equation (1), the immersed weight longshore transport rate is ig & (7 a y2 1) Bo. o (5) Thus, the immersed rate is equal to flux rate multiplied by a term which is assumed to be constant. 2. Purpose. There is some confusion concerning the relative validity of equations (2) and (5) as predictors of longshore transport. Authoritative publica- tions have urged the use of I in equation (5), and this has created the impression that the SPM equation (2) is distinct from, and inferior to, the immersed weight rate of computing longshore transport. This report shows that, based on present knowledge, there is at this time (1978) no practical difference between equations (2) and (5). How- ever, an immersed weight prediction could be important if significant variations in a' or y{ exist on the shore. This possibility suggests that measurements of a' and y{ should be included in field programs to measure longshore transport rate. II. UNIT WEIGHT OF SAND The applicability of an immersed weight transport prediction depends on a knowledge of the unit weight of sand. The discussion in this sec- tion concerns the unit weight of dry sand, but it is easily extended to cover sand immersed in seawater. The unit weight of sand, y, is dependent on two variables. The first variable is the specific gravity of the sand grains, given by G = Y8/ Vy (6) where y, is the weight density of the material making up the sand grain, and y,, is the weight density of distilled water. Most sand grains are quartz with a specific gravity of 2.65. However, on some beaches sand grains may be composed of calcium carbonate with a specific gravity, when a pure solid, from 2 to 11 percent higher than quartz (G of 2.71 for pure calcite to 2.94 for pure aragonite). (Carbonate sands may also be effec- tively lighter than quartz when grains are made of porous shell material.) The second variable is the amount of space taken up by voids in the sand deposit. This can be described by several terms. The usual soil mechanics parameter is the void ratio, e, defined as e = Volume of voids/volume of solids . (7) The usual parameter in coastal research (see eq. 3) is "volume concen- tration" defined as a' = Volume of solids/total volume . (8) The void ratio is related to the volume concentration by ea Gl = atjfal . (9) In terms of the volume concentration, the unit weight of sand is Yel Gye (10) The few times that the unit weight of sand has been considered in longshore transport predictions, it has been assumed that the sand is all quartz (G = 2.65) and that a' = 0.60. This value of a' is appar- ently derived from Chamberlain (1960) where a' = 0.60 is reported for fine sand collected from the beach face, after compaction. However, a'. can vary significantly. For example, Chamberlain reported data equivalent to a' = 0.53 for sand at the head of a submarine canyon and as low as 0.27 for micaceous sand lower in the canyon (taken from Shepherd, 1963). Theoretically, for sands consisting of perfect spheres of the same size, a' ranges from 0.52 to 0.74, going from loosest to most dense (42 percent increase). The following Table shows the actual data (when converted to a! values) reported in Sowers and Sowers (1970, p. 30). Table. Ranges of volume concentration, a', and unit weights of sand, y (from Sowers and Sowers, 1970). Sand a! mas al min Ymas Ymin (1b/ft3) (1b/ft >) Uniform 0.67 0.54 110 89 subangular Well-graded 0.74 0.59 122 97 suban gular Since G and a' have been assumed to be 2.65 and 0.60 when calculated, this is equivalent to saying that all sand is assumed to have a unit weight, from equation (10), of 99.2 pounds per cubic foot. Using the "relative density" as defined by Sowers and Sowers (1970, p- 31) and the Table, a sand having the assumed a' = 0.60 would be 9 "loose" sand in the case of uniform well-rounded sand grains, slightly loose for uniform subangular sand, and the loosest possible for well- graded subangular sand. However, it is probable that sand along the shoreline should be more on the dense side, rather than on the loose side because of the compact- ing effects of water soaking and wave action. Moreover, it is evident that the weight density will vary with the grain-size distribution and grain shape (Sowers and Sowers, 1970). Thus, the constant a' = 0.60 is an assumption not likely to be generally true. Unit volume is equal to the reciprocal of the unit weight. Since uniform sands may vary 24 percent in unit weight (Table), the same variation may occur in unit volume. Since most independent, local field estimates of longshore transport are based on surveys of sand volumes, it is possible that the energy flux prediction can be significantly affected by variation in unit volume of the sand. For example, Caldwell's (1956) and Komar's (1969) data are from surveys of the nearshore zone subject to wave action, and these data are 19 of the 23 data points used to establish the SPM longshore transport curve (Figure 4-37 in SPM). If the sand settled out in quieter waters, the same number of sand grains might be expected to yield larger surveyed volumes. This possibility is consistent with the data from Channel Islands Harbor (Bruno and Gable, 1977) and Santa Barbara (Galvin and Vitale, 1977), California, which do plot above the SPM curve (Fig. 1). (However, even a 24-percent decrease in unit volume would only bring these California data points about 20 percent closer to the SPM curve on that log-log plot.) III. PRESENT USE OF IMMERSED WEIGHT CALCULATION The immersed weight formulation has been strongly recommended by some for longshore transport prediction. As shown by equation (3), the immersed weight rate equals the volume rate multiplied by two sand- related parameters, a' (eq. 8) and Nie (eq. 4). However, the present use of Ip with the SPM design curve (eq. 2) implies a constant unit weight which probably was lacking in the under- lying data. The existing design curve in SPM is based on three sets of field data for which a' and even Yg are not available. One set meas- ures short-term volume changes in the high tide surf zone (Komar, 1969); the second set measures longer term variations in the littoral zone (Caldwell, 1956); and the third set measures pumping rates of probable carbonate sand (Watts, 1953). Thus, there is a good deal of uncertainty in a' and yj, for all three sets, and a' in particular is likely to be different in each set of data. Therefore, it is probable that all three sets of data involve slightly different unit weights of sand. Those studies that use Ig have assumed a yj for quartz sand and a' = 0.6 to compute I,. This is permissible when other data are lacking. 10 Santa Barbara 106 Channel Islands Longshore transport rate (yd°/yr) 103 = : 10 10 10 10° 10% Energy flux factor (ft—Ib/s/ft) Figure 1. Two sets of longshore transport data from protected waters related to SPM design curve. However, to apply the result to typical engineering problems, the same assumptions must be made about yj and a' to get back to a value of Q, since Q is the quantity needed in design. The steps involved for the present immersed weight procedure are shown in Figure 2. Although immersed weight rates are not presently practical in field- work, immersed weight rates of longshore transport are routinely measured in some laboratory experiments (Savage, 1959). IV. RESULTS The results of this analysis are summarized as follows: In practical application, the immersed weight formulation does not presently improve the engineering prediction. The required engineering quantity is a volume rate of sand in place, Q, and all the existing data were originally measured in terms of Q, or in Q equivalents. Therefore, to develop the immersed weight formulation from existing data, it is necessary to estimate values of a!' and y! and convert Q values to I, by equation (3). Then, to use the immersed weight formulation to solve a problem, the procedure must be reversed and con- verted back to the required Q. Available data have led the investigators who have worked with I to assume that both a' and y! are constants. To the extent that this is a fact, I, is directly proportional to Q, independent of any other variables, and the use of I, is equivalent to Q, after two added calculations. However, in the three sets of data on which the SPM design curve is based, it is probable that neither a' or Yg were constant. The available soil mechanics information indicates the need for more data on void ratio and sand grain specific gravity. The Table and re- lated information suggest that a' may vary significantly, although the upper limit of variation is probably less than the theoretical 42-percent increase in a' possible in going from loosest to most dense packing of spherical sand grains. Most sand beaches are quartz, but calcium carbo- nate sands of the tropics could have a yg (for pure aragonite) as much as 18 percent higher than quartz sands, or even less than quartz sands when the carbonate grains are derived from porous shell material. V. CONCLUSIONS 1. Volume rate, Q, is the longshore transport parameter needed for design. 2. As presently used, the immersed weight rate equation is equal to the volume rate equation recommended by SPM, multiplied by a constant (eq. 3). Thus, the volume rate prediction (eq. 2) arrives more directly at Q. 12 Start . Design problem requires Q 4 —_— _— —_ ah Available data — in terms of Q : ecause To solve problem, Theory requires I, convert Dae to Q, Ree ; using a'=0. if a and Y, vary yee 165 yy Construct Ip curve using a’ =0.6 7,7 '.89 7, (quar tz) Figure 2. Use of I, in present practice. 3. Longshore transport which produces shoaling in protected waters could produce more shoaling than predicted merely because of looser packing of sand grains. The magnitude of this increase is expected to be on the order of 10 to 20 percent and should not be greater than 42 percent. 4, Field studies of longshore transport should include measurements to determine the void ratio (eq. 7), or equivalently a' (eq. 8), in the littoral zone and in protected waters. LITERATURE CITED BAGNOLD, R.A., "Mechanics of Marine Sedimentation,'' The Sea, Vol. 3, John Wiley §& Sons, New York, 1963, pp. 507-528. BRUNO, R.O., and GABLE, C.G., ''Longshore Transport at a Total Littoral Barrier," Proceedings of the 15th Coastal Engineering Conference, American Society of Civil Engineers, Vol. 2, 1977, p. 1203. CALDWELL, J.M., "Wave Action and Sand Movement Near Anaheim Bay, California," TM-68, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., Feb. 1956. CHAMBERLIN, T.K., "Mechanics of Mass Sediment Transport in Scripps Submarine Canyon, California," unpublished Ph.D. Thesis, University of California, Scripps Institution of Oceanography, La Jolla, Calif., 1960. GALVIN, C., and VITALE, P., "Longshore Transport Prediction - SPM 1973 Equation,'' Proceedings of the 15th Coastal Engineering Conference, American Society of Civil Engineers, Vol. 2, 1977, pp. 1133-1148. KOMAR, P.D., ''The Longshore Transport of Sand on Beaches," unpublished Ph.D. Thesis, University of California, San Diego, Calif., 1969. KOMAR, P.D., and INMAN, D.L., ‘Longshore Sand Transport on Beaches," Journal of Geophystcal Research, Vol. 75, No. 30, Oct. 1970, pp. 5914- S927 6 LONGUET-HIGGINS, M.S., ''Recent Progress in the Study of Longshore Currents," Waves on Beaches and Resulting Sediment Transport, Academic Press, New York, 1972, pp. 203-248. SAVAGE, R.P., ''Laboratory Study of Effect of Groins on Rate of Littoral Transport: Equipment Development and Initial Tests," TM-114, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington D.C., June 1959. SHEPARD, F.P., Submarine Geology, 2d ed., Harper and Row, New York, 1963. SOWERS, G.B., and SOWERS, G.F., Introductory Soil Mechanics and Founda- tton, 3d ed., The MacMillan Co., New York, 1970. U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protectton Manual, 3d ed., Vols. I, II, and III, Stock No. 008- 00113-1, U.S. Government Printing Office, Washington D.C., 1977, 1,262 pp. WATTS, G.M. "A Study of Sand Movement at South Lake Worth Inlet, Florida," TM-42, U.S. Army, Corps of Engineers, Beach Erosion Board Washington, D.C., Oct. 1953. ee hank Per eek Rea OR ae, eter ere tis B: tna tol On iy oe ae Pi ; ; are RP Pe on Ane " eye Y. “Wi witmuata | bea AM iy wi EL CRD cet OCR Tan E i ) Oe ) ) ehitenda Sitice PIBG Si oC iieteol 4G HEMET exis ea) epee aaa to’ ae Bes th tis Ue) R re Uf oo » HART ser, BAP: — ji heir: ; gel ‘Cal > patel iden: ON EERROA . O1Gu ; ‘ a : : ihre tes.) i ! H 179 = 6 Ou BaTesn* €02OL *T-62 dL ‘iteded Teoptuyoey *‘Jeque) yoieesey BuTAssuTSuq TeqseoD *S'M :SeTIeS ‘II ‘eTITL ‘I ‘pues *¢ ‘saaem Aq Jaodsueiq pues *Z ‘310dsuezq Te1079TT ‘T *9AIND usTSep ey} OF BJep But InqTaquos SoqfFsS yseoo-uedo oyuj qe pues jJo 4YZTeM ATuN 9yQ wory ATJUPDTJTUSTS S1aJJTP pues jo AYSTEM 4Tun 9yj e1eYyAM Quezzodwt |q Aew uot zeTnwi0j PY] ayz ‘0 JUeTeaTNbe ay} 07 yOeqG paezteAuoD oq ysnw 4] ‘smaetqoid 3utaseu -T3ue uf eSsn Jog ‘*JueJSuOD e Aq pattdtztnm ‘j10dsueisq sioyssuoT jo ‘bh ‘aqez ountoa 3yi st ‘*] ‘aqea QYU3TeEM pesaoumMT |Yy, pesn AT Uasead sy “ct ‘d : Aydeasottqtg (1-62 dL * 103uUe9 yoreesey SuTiseuTsuq Te3seoD *s'n — Jeded TeoTuyoey) “TTF : ‘d CT "6161 ‘20TAIaS UoTJeEWAOFUT TeoOTUYyDeT TeuCTIeN WOIF eTgeTTeae : ‘eA ‘pTety3utadg { 1z9quaD YyoAeesey BuTiseUu -T3uq Te3seoD *S'n : ‘eA SAFOATEg ‘34a — ‘UEATeED *f TEAAD Aq / Jaod -Suei} a10YyS3u0T JO sajei ouMTOA pue AYZTeM pesioMMIT UBeMjeq UOTIETOY ‘f TPaAkD SuTATed £29 Loos “Oss BATSSn* €02OL "T-6/ dL ‘aeded Teotuysey *Zeque) yoieesey BuTAseuTZuq Teqseog *S'M :seTAzeS “II ‘eTITL “I ‘pues °¢ ‘Seaem Aq Aaodsuezq pues *z ‘jAodsueiq TeI0IITI ‘T *‘@AIND UZTSep ay OF eJep But AnqTajuos SoqTs yseod-uedo ay 3e pues fo AYy3TeM 4WTuUN 9yq wWorAF ATJUeOTJTUZTS SIOJJIp pues Fo WYStTem 4Tun oy A ezeyM Auejiodwt aq Aew uot IeTNWI0Z FT ayuL *O JueTeATnbe ay 07 yoeq pezreauod aq ysnu %] ‘smatqoid 3utTazseu =-T3ue UT esn Joq ‘jueqsuoD e Aq paettdtzqtnm ‘310dsueiq etoyssuoT jo ‘h ‘93e1 owntoa 0y3 St ‘7 ‘a3ea AY3TeM pastemMT ay} pesn ATjuUesead sy “ct ‘d : Aydeaz0tTqT¢ (1-62 dL * 12qua9 yoreesey SupieeuTsuq Teqseop *s*n — azeded TeoTuyoel) “TTF : *d CT “6L61T ‘29TAIVS uoTIeWAOFUT TedTUYyeT, TeBuOTIEN WOIF SeTqeTTeae : ‘eA ‘SpTetTysutads { taquseD Yyoieesey ZuTiseUu -T3ug [Te3SeOD *S'N : ‘BA SATOATEG *3q — SUTATeD ‘¢ TEIAD Aq / Jaod -SUPI} eTOYSSUOT JO Saqjei sUNTOA pue 4Y3TeM pesisMMT UseMJeq UOTIeTOY "Pf Tpakp Surated £29 D6 20u BIT8sn* €072OL ‘T-62 dL ‘aeded ~Teotuyoey ‘loqueD) YyoTeesey BuTAeeuT3uq TeqseoD *S*n :SeTIeS “II ‘“eTITL ‘I ‘pues ‘¢ ‘saaem hq aodsueij pues *z ‘ja0dsuezq [e107ITT ‘T ‘aAind u3TSep ay} 07 eJep B3uTynqTazquoD SoqTs yseoo-uedo ayq je pues Jo WY3TeM ATuUN 9YyA wWorZ ATIUPOTITUSTS SIOJJTp pues Fo 4YStem 4tun oy eA0yM Juejizodwt oq Aew uot IeTNWI0F FT eyuL °d JUeTeATNbe 9yQ 072 yDeq paqateauoD aq ysnuw Fy ‘swetqoad SutsseUu -T3ue UT asn Jog ‘*juejJSuOD e Aq pet{Tdt3ztnm ‘jz10dsue1z} sioys3uoT jo ‘h ‘aqe1 ountoa ayj st ‘%7 ‘93ea 3Y3TEM pesieumMT By} pesn AT UeSeAd sy “ct ‘d : Aydeas0tTqtg (1-62 dl $ 1equep yoiresey B3uTiseutsugq Teqseoy *s*n — aeded Teotuydey) ‘TTT : ‘d ct "6461 ‘®0TAIeS UOTJeWAOFUT TeoTuUYoeT TeuoTIeN wWOIZ eTqeTTeae : ‘eA SpTeTy3utads £ azsequag yoAeessy BuTisveu -F3ug TeqIseOD "S'n : “eA SATOATEG *3q — SUFATeD *¢ TEAAD Aq / aod -SUeI] eTOYSZUOT Jo Saje1 sUNTOA pue YSTeM pasieuMT useMjzeq UOoTIEeTEY *f Tako SufaTeo Le9 ESE Ow eIT8sn* €072OL ‘T-62 dL ‘aeded ~eotuyosy *‘ZequeD yoAeesey BuTIseuT3uyq TeqseoD *S‘p :SeTaeS “II ‘“eTITL ‘I ‘pues ‘¢ ‘seaaem fq Qaodsueiq pues *z ‘*}iodsuei1q [e1073TT ‘T ‘aAanod usTsep ayq 07 eIep But InqTrQUOD saqts 4seoo-uedo oy} Je pues jo Y3TeM ATUN 9YyQ WoIFZ ATJUeDTJTUSTS SI9jjIp pues Jo 3Yy3TemM TUN |9YyQ sreyM Juejiodut eq Aew uoTjeTNWI0FZ by aut ‘0 JueTeatnba ay 03 yoeq pazreauod aq ysnu %] ‘smatqoad 3utTazeeu -—T3ue UT esn 10g ‘JuUeQsUOD e Aq pettdrjtnu ‘j10dsueiz3z s10ys3u0T jo ‘h *9]e1 aUNTOA 3yj ST “By *aqe1 WYyZTOM pesiemMT 9yQ pesn ATJUssSeid sy "ct ‘d : AydeaZ0rtqtg (T-6L dL $ 103uU99 yoreesey SupiseutTsug Teqseog *s‘nq — rzeded Teotuyoey) “TTT : *d CT "6161 ‘e0TAIeS UuoTJeMAOJUT TeoTUYdeT TeuoTIeN woz eTqeTTeae : ‘eA ‘ppTetTs3utads { aequepg yoieesey BuTsseu -T3uq TeISeOD *S'n : "eA SATOATEG ‘3G — SUTATeED *f THAAD 4q / aod -SsueI} sOYS3UOT JO Ssajei ouNTOA pue 4YSTeM pesioMMT UsEeM}eq UOTIETOY If THaIAQ SupatTeg Le9 [= 6)/ eo eBITEsn* €0ZOL "T-6L dL ‘aeded Teotuysey ‘aque yoeesoy BuT~reeuTsuq TeqseoD *S'M :Setazeg “II ‘eTIFL ‘I ‘pues *¢ ‘Saaem fq Aiodsuezq pues *Z ‘3 AaOdSueI} Te107ITT ‘T *9AIND uUsTSep ey} OF eJep Bur 3nqytAquUoOD saqTs yseoo-uedo 9043 4e pues Jo 3Yy3TeM ATuN 9Yy} Worx ATJURDTFTUSTS SlejJjJTp pues jo WYyZTeM ATUN |YyZ ereYyM Juejaodwyt oq Aew uoFjeTNWI0FZ by eayL ‘dO JUeTeATNbe 9y} 0F YOeq pazazeAuoD eq 4Ssnu %y ‘swetqoad Sutaeeu -[T3ue uf esn Jog ‘queqsuod e Aq pet{Tdzazqtnw ‘j10dsueaj ezoys3ZuoT jo ‘OH ‘aqe1 omntoa ay st ‘*] ‘a3ea aySTeM pesieumy oy pesn ATJUesead sy “ct ‘d : Aydeaso0tTqta (T-6Z dL $ 193uU99 yoreesey BuTrAseuT3ugq TeqIseoD ‘S'n — aeded TeoTuyoel) “TTF : *d CT "6161 ‘90TAIeS UCTJeMAOFUT TeOTUYys TEUOTIEN WoOAF oTQGeTTeAe : ‘eA ‘pTeTy3utadg { toqueD yO1resey BuT1seU -T3uq TeqIseoD *S'n : “eA SATOATEgG “3a — ‘UFATeED *¢ TEAAD Aq / qaod -SUPI} BTOYSZUOT FO SazeI SUMTOA pue IYSTEeM pesroMMT UPeM}eq UOTIeTOY ‘f TEAkD SupaTed £09 UG, POE eITesn* €0cOL "T-62 dL ‘i1eded Teotuyoey ‘zequeg yo1eessey BuTrtseuTsuq TeqseoD *S°N :SeTIeS ‘II ‘“eTIFL ‘I ‘pues ‘¢ ‘seaem Aq qtodsuerz pues *Z ‘3A0dsue1z TP10I4TT ‘T ‘aAand usTSep ayq OF eIep But ynqTaquoD SsejTs yseod-uedo oy} 4e pues Jo 4Y3TeM 4ATuN syq worZ ATJUeDTFTUSTS SA2JITP pues Jo YZTem yTuN 9y3 e19YyM quejzodumy oq Aew uoTIeTNWAOZ FT eyuL *O JueTeatnba |yj 07 YDeq peaqaeaAuodD eq Jsnu ty] ‘swetqoid 3upasseu -T3ue UL asn Jog ‘jueqzsuos e fq pet tdzatnm ‘310dsue1z aroys3u0T Fo ‘ ‘a3e2 euntoa oy st ‘57 ‘a3e1 QYU3TeM pasrouMT 9YyR pesn ATJUesead sy “ct ‘d : Aydeasorrqta (1-62 dL { 103uU99 yoreasey Sutiseut3ug Teqseog *s*n — aeded Teofuyoey) “TTF : *d GT "6L6L ‘20TAIeS UOTIeWAOFJUT TedTUYos] TeUOTIEN WOAF OTQGeTTeAe : ‘eA ‘pTeTyZuTads § zequep Yyoteesoy SuTie0u -T3uq Teq3seoD “Stn : “eA SATOATOG ‘34a — SuTATeED *f TEAAD Aq / jaod -sueij atoyssuo,T jo Sajei ewnTOA pue 4YSsTeM pesiemMT useMzZeq UOTIeTOY "fp TRIAD SupatTed 179 = 6)/a Ou e3Tssn* €072OL *T-6Z dL ‘iteded Teotuysey ‘Zaque) Yoreesey SuTisveuT3uq TeqseoD *S'n :SeTteg “II ‘eTIFL ‘I ‘pues ‘¢ ‘seaem Aq Aaodsuez} pues *Z ‘J aodsueiz} [P109IFT ‘T "aAIND usTSep ay} 0} e}ep BuUTInqTajUOD seqts yseoo-uedo ayq qe pues Jo 4YS3TeM JTUN |Yy A wWoryT ATJUeOTFTUBTS SI2}JIp pues Jo 4YZTem 4TuN 9yz ez0YyM JuejzodwE aq Aew uoTIeETNWAOZ FY] ayz *d JueTeatnbe ey 03 yoeqG peqaeauod oq ysnu *%] ‘swetqoad 3uyzaaeu =-—3ue u~t osn 10g ‘*jueqRSuOD e Aq poettdzatnm ‘j320dsueiq eioyssuot jo ‘dO S931 OWNTOA eYyq ST ‘by ‘a3ea1 QU3TeM pesaoumT oYyQ pesn ATJUesead sy “ct ‘d : Aydeasottqtg (1-62 dL * 103uU89 yoressoy Bup~ieeuTsuq Teqseog *s‘n — tzeded [Teotuyoey) “TTT : *d CT "6161 ‘20TAIeS UOTJeWIOFUT TeoTuYyoe] TeuoTIeN woAF oTGeTTeae : ‘eA ‘pTeTyZutidg { tejqueD yoreesey B3utiseU =-—T3ug TeIseoD *S'N : “BA SATOATEG *3q — ‘uTATeD *¢ TT4A4D Aq / Ja0d -SUPI} eLOYSZUOT JO SajeI BWNTOA pue Y3TEeM pesiouMT UseM}eq UOTIeTOY "Cf TFaAD ‘uzateg Le9 as POU PITssn* €072OL "T-6/ dL ‘aeded Teopfuyoey *Joque9) yoIeesey BUTIeeUT3Uq TeqseoD *S'N :SeTIeS “II ‘“eTITL ‘I ‘pues ‘¢ ‘soaem fq jtodsueiq pueg *Z ‘J10dsuez} Te10IIFT “T *asAInd ustTsep xyj OJ eJep But ynqTaqUOD saqqts yseoo-uedo ey3 qe pues Jo 4YyZTeM 4TUN |YyQ worz ATJUeOTFTUZTS S1IejJj—Tp pues Jo 4YZTeM TUN |yQ ereYyM JuejiodmT aq Ae UOTJeTNUIOZ ty eyL °d0 queTeatnbe ay 07 yYOeq peqzAeAUOD 9q JsnuU 7 “‘swetqoad 3utazseu -T3ue UT 9sn Jog ‘queqsuoo e Aq pettdtarnu ‘jxo0dsue1q eizoys3uoT jo ‘OH *9]e1 oUNMTOA 9yq ST