CHAPTER 40 SHIP WAVES IN NAVIGATION CHANNELS. J. W. Johnson Department of Engineering University of California Berkeley, California INTRODUCTION

Transcription

1 CHAPTER 40 SHIP WAVES IN NAVIGATION CHANNELS J. W. Jhnsn Department f Engineering University f Califrnia Berkeley, Califrnia INTRODUCTION Ships mving thrugh water generate surface waves which in many navigatin channels cause severe wavewash damage t the bank* In sme waterways, rather extensive prtectin wrks have been cnstructed t reduce this destructive actin t levee faces (Hertzberg, 1954). This actin, termed "freshre ersin", has been described by Lewis (1956) fr the lwer Mississippi River as fllws: "The attack, interestingly enugh, takes place at lwwater. It is due largely t the waves created by passing ceanging ships and is augmented by shallw draft traffic. It may be asked at this pint why this attack is new, in view f the fact that ship and barge traffic has lng existed n the river in very substantial vlume? The answer is that the recent technlgical advances in ceanging and river transprtatin have greatly increased maximum and average speeds, and accrdingly, the wave making ptentials." Despite the imprtance f this prblem, very little quantitative data are available n the characteristics f ship waves at a given distance frm the sailing line in terms f type f ship, displacement, speed, and water depth. Naval architects have lng been interested in the waves generated by ships, but primarily frm the standpint as t hw the waves affect the resistance f the ship (Havelck, 1908, 1934, and 1951; Lunde, 1951; Birkhff, et al, 1954). The pineer wrk in the field f ship resistance was dne by Rankine (1868) and Frude (1877); hwever, as discussed belw under the sectin n thery, Lrd Kelvin (1887a, 1887b) was perhaps the first t present a thery f< such waves by calling attentin t the similarity f actual ship waves t the waves generated by a pressure pint mving acrss the water surface. Standard text bks n naval architecture (Taylr, 1943; Rbb, summarize Lrd Kelvin's thery which prvides a methd f pltting the wave patterns as well as the relative wave heights thrughut the pattern. What was apparently the first cmprehensive set f measure ments f actual ship waves were the bservatins f Hvgaard (1909) the waves generated by several different types f ships. He cmpared the actual angles f the diverging waves with the theretical values f 666

2 SHIP WAVES IN NAVIGATION CHANNELS Lrd Kelvin fr deep water cnditins. Fr restricted waterways numerus investigatins have been made t determine the frm f canal crss sectin and system f bank prtectin t be adpted with a view t resisting the destructive wash f passing tws and mtr bats. These studies cnsisted f mdel tests (Krey, 1913 and 1929) as well as tests and bservatins with bats in actual canals (De Bruyn and Maris, 1935; RSik, 1935; Schijf, 1949; Sum, 1935; Vanderlinden, 1912; Van Ln, 1912; Wrtman, 1894). As discussed belw there is very little infrmatin in any f these varius studies n the actual wave heights that ccurred during the tests. THEORY As riginally discussed by Frude (1877), the main features f the entire disturbance behind a ship, which is cnfined between tw straight lines, is that there are tw distinct systems f waves. These are the transverse and the diverging waves (Figure 1). Curves f equal phase in the tw systems meet n the straight line bundaries f the disturbed regin in cusps. These lines ften are designated as the "cusp lcus". Wave heights are greatest and the crests the sharpest at the cusps, as well as at the pint f the dis turbance, s that breaking water will be fund at these pints, if anywhere. There is a striking similarity between the waves generated by an actual ship mving acrss the water surface and the theretical wave pattern resulting frm a single mving pint as develped by Lrd Kelvin (1887a). His slutin shws that fr deep water the whle pattern f waves is cmprised between tw straight lines drawn frm the bw f the ship and inclined t the wake n its tw Sides at equal angles f a = 19 28'. Figure 2 shws a plt f a Kelvin wave grup caused by a travelling disturbance, and Figure 3 shws a single crest f Kelvin's wave grup with relative heights at varius pints. The height in this instance is the elevatin f the wave crest abve the undisturbed water level. The difference between the Kelvin wave grups and actual waves is that a Kelvin grup is an ideal system resulting frm frces applied at a single mving pint; whereas an actual wave grup is due t frces spread ver a ship's hull. Actually, the applicatin f the Kelvin thery perhaps is valid nly at a distance f several ship lengths frm the stern. An essential parameter which determines the wave pattern created by a ship n a straight curse is accrding t the Kelvin thery A = C_ (1) C 667

3 COASTAL ENGINEERING in which C is the ship speed and C 0 is the velcity f a wave in shall water; that is, C 0 = %&> where g = acceleratin f gravity, and d water depth. The wave amplitudes, and hence the wavemaking resistance f the ship apparently depends n the character f the ship's hull. Hwever, the general shapes f the curves frmed by the wav< crests and trughs and their spacing depend upn X and the speed f the ship and nt upn the shape f the hull. Fr X = 0, 1.e. infinite depth, the character f the wave pattern given by the Kelvin thery is as shwn in Figures 2 and 3. Relatinships fr wave patterns fr a travelling disturbance water f any depth have been develped by Havelck (1908). A simp] fied methd f pltting such wave patterns has been presented by Rl (1952). Fr a finite water depth d, the angle a between the ship's curse and the cusp lcus increases as X increases and appraches i theretical value f 90 as X increases frm zer t the critical valu f 1.0. The value f the angle a increases, hwever, vary slwly with X until X is smewhat greater than 0.7 (Figure 12). Fr finite depth, the spacing f the waves cntinues t be prprtinal t the speed, but the cnstant f prprtinality depends n the value f X. The spacing increases fr a given speed with diminishing depth, but this increase is small fr X values less than 0.7. At X = 1, r = 90, and the wave pattern cnsists essentially f a single wave with its crest at right angles t the ship. When the critical value X = 1 has been passed, the character f the wave pattern behind the ship chanj cmpletely, and there are n lnger distinct systems f waves as th transverse system disappears, the disturbed regin lies between tw straight lines with the angle a being expressed in terms f X. The angle a theretically appraches zer at high speeds (r lw depths and the straight line bundary is nw a phase curve f the wave system and nt a cusp lcus f such curves as in the case where X < 1.0. DEEPWATER CONDITIONS OBSERVED SHIP WAVE CHARACTERISTICS Observatins n waves generated by actual ships have been made by naval architects in cnnectin with studies n ship resistai Mst f these investigatins have been with mdels, and nly a few systematic bservatins with full size ships appear t have been mi The mst extensive bservatins were thse f Hvgaard (1909) wh< made measurements n bth wave height and wave pattern fr varii sized ships and mdels perating in deep water. A typical example 668

4 SHIP WAVES IN NAVIGATION CHANNELS Fig. 1. Frude's sketch f the characteristics f ship waves, Trans. Inst. Naval Arch., Fig. 2. Crest f a Kelvin wave grup in deep water caused by a travelling disturbance at 0 (Taylr, 1943). MW^C Fig. 3. Single crest f Kelvin wave grup in deep water with relative heights at varius pints given by numbers (Taylr, 1943) 669

5 COASTAL ENGINEERING t X UJ I Ui I I.V VELOCITY, 8 10 KilmetersHur Fig. 5. Relatin between velcitj travel and wave height at shre f canal under the influence f a sin^ tugbat (Franzius, 1936). 12 Fig. 4. Typical wave pattern as bserved by Hvgaard (Trans. Inst. Naval Arch., 1909). TABLE I Summary f Hvgaard's Observatins n Diverging Ship Waves a L V V Cusp Ship r Displacement Length Speed nr Lcus Height f Mdel r Tnnage «t) (Knts) (degrees) Bw Breaker SS United 10,000 tns ft States " 10,000 tns " Danish Patrl 47 tns Inches Bat " " "i " n " " " " " Olfert 11 Fisher 3,450 tns ft " " ft S S Drnnmg 1,760 tns ft.maud SS Kng Haakn 1,760 tns Danish Mine 107 tns inches Vessel Destryer Mdel 505 lbs " " " " " " " Battleship 2,620 lbs Mdel 11 " " " " " " Merchant Vessel 2,422 lbb Mdel " " " 670

6 SHIP WAVES IN NAVIGATION CHANNELS f Hvgaard's bservatins is shwn in Figure 4 and a summary f sme f his bservatins are presented in Table 1. The Kelvin thery predicts that the diverging wave system is the same fr all hull frms and speeds; hwever, Hvgaard's measurements lead him t state that: "The bservatins here recrded shw that this is nt the case, the bliquity f the waves being greatly influenced by speed and frm f the ship, and being nt ever the same fr all waves in the same ship at a given speed." SHALLOWWATER CONDITIONS As a ship mves thrugh relatively shallw water the flw cnditins arund the hull, as well as the surface waves which are generated, will be different frm deepwater cnditins, and the ship resistance is increased. The change in flw cnditins arund the hull prbably increases the skin frictin resistance slightly, but the majr increase in resistance apparently is due t the increased wave heights ccurring with shalwater cnditins. Perhaps the best summary f the prblem f ship resistance in shallw water is that by Taylr (1943), wherein previus investigatins are reviewed and a tentative attempt is made t define the cnditin at which depth effects cause the resistance t begin t increase. Since the effect f the waves prbably is the principal cause f increased resistance, the relatinship presented by Taylr is f imprtance in evaluating the effect f depth n the wave characteristics. Fr mderate and slw speed vessels, that is, vessels capable f deepwater speeds in knts f 0.9 L r less, Taylr shws that the relative minimum depth fr n increase f resistance is given by the expressin, d min = 10 D _V_ (2) vl dmin = ininimum depth fr n increase f resistance ft. D draft ft, V = speed in knts L = length f vessel ft. This relatinship gives the critical pint at which ship resistance starts t increase, but unfrtunately n infrmatin is available 'rm the data n the actual change in the characteristics f the waves hems elves. 671

7 COASTAL ENGINEERING Fr a high speed vessel in water f depth less than the ship's length, Taylr (1943) states that "at a definite speed in a given depth the vessel will begin t experience appreciably increased resistance as cmpared with the resistance in deep water. The excess f resistance abve the nrmal increases with speed until it reaches a maximum. This maximum appears t be at abut a speed such that a trchidal wave, travelling at this speed in water f the same depth, is abut 114 times as lng as the vessel." Frm bservatins n the peratin f canal bats in restricted waterways Rsik (1935) made sme measurement f wave heights. He stated that: "The wave frm the bw usually narrws suddenly abut half the length f a vessel, whereas behind the stern it is suddenly thrust ut. Accrding t the speed at which the craft is travelling, the first wave behind it reaches a height f 2 meters measured frm crest t hllw. This wave is fllwed by several thers f an elngated frm and tw r three gruped waves having 1 2 t 23 the height f the first ne. The effect f the wave is all the greater n the banks when a vessel runs clse alngside them. On the Danube this distance des nt drp belw 15 t 20 meters. At a distance f 50 meters frm the banks the effect is nly half, and at a distance f 250 meters it scarcely makes itself felt. The influence f the waves makes itself felt if the ship speed craft exceeds 8 km an hur." N mentin is given by Rsik as t the type r displacement f the vessel r the water depth t cause such wave cnditins. Other wave data f limited extent are given by Franzius (193i in Figure 5. Infrmatin is lacking n the size, shape, and displacement f the tugbat and the depth and width f the canal under which these bservatins by Franzius were made. As mentined previusly, bservatins n the mvement f tw bats in restricted waterways have been made bth by mdel tes and with actual canal bats. Mst f these latter studies were cncerned primarily with the maximum speeds that were allwed in varius canals. This maximum speed was nt based n scientific stuc but prvisinal speeds were adpted and the extent f bank ersin c served. The maximum speeds usually were expressed as a functir f the rati f the midship crss sectinal area f the bat t the c 672

8 SHIP WAVES IN NAVIGATION CHANNELS sectinal area f the canal. Fr example, Vanderlinden (1912) states that where the canal crsssectinal area is eight times that f the bat a maximum speed f 10 t 12 km per hur is pssible. Allwable speeds in varius canals als have been given by Wrtman (1894) and Van Ln (1912). In a discussin f the effect f ship waves n the banks and beds f canals Sum (1935) bserves that the greatest damage ccurs abut ne meter abve and belw nrmal water level. In narrw canals he recmmends a maximum speed f 5 km per hur. Where a river's width is meters Sum (1935) states that the waves are frm 30 t 80 cm in height. N mentin is made, hwever, f the size r type f bat that prduced such waves. Perhaps the mst cmprehensive investigatin n bats perating in cmparatively narrw waterways was that f Schijf (1949) wh used bth mdels and actual pwer bats in his studies. His tests shw that in a canal with erdible bed and banks the maximum velcity is dependent n the rati f the midship crsssectin f the bat t the crsssectin f the canal, the shape f the hull, and the methd f prpulsin. MODEL STUDIES SHIP WAVE MEASUREMENTS Equipment and Prcedure As evidenced by the abve discussin, relatively few data are available n the wave heights t be expected at a given distance frm the sailing line f a ship with a given hull shape and displacement mving thrugh shallw water at a given speed. T btain such data and better define the imprtance f the variables invlved, a series f mdel experiments were made at the University f Califrnia mdel basin. In these studies ship mdels were twed at varius speeds in water f varius cnstant depths, and the wave characteristics measured at varius distances alng a perpendicular t the sailing line. The general arrangement f the test facilities is shwn in Figure 6, and the characteristics f the mdels tested are shwn in Figure 7 and Table H. In additin t the gemetric characteristics f the varius mdels, Table II als shws values f the "blck cefficient" and the "displacementlength rati." These cefficients cmmnly used by naval architects are defined as fllws: 673

9 COASTAL ENGINEERING Blck Cefficient = b = JL'X 1) x B where v = vlume f displacement L = waterline length B = waterline beam at midship D = draft at midship DisplacementLength Cefficient = TPI 3 TOO" where A = displacement in tns L = waterline length in feet TABLE II Mdel Characteristics and Test Cnditins (Fresh Water Tests) Mdel Displacement Water Line Dimensins» Wa LB D 3 dej lbs. Length Beam Draft b L \ d (ft) (ft) (ft) J 00 (ft) A L A H \ 1. L 1. B C D 51.5 E F

10 SHIP WAVES IN NAVIGATION CHANNELS Falling weight drive Sheave Sheave Drive line Wave gage Tw line Elevatin Fig. 6. Equipment used fr investigating ship waves by mdels, 675

11 COASTAL ENGINEERING Mdel A Mdel C ^fl V \ Mdel B Fig. 7. Phtgraphs f Mdels A, B, and C used in ship wave studies. MODEL DIMENSIONS, in Inches Mdel L B D e f h Mdel A L Run 8a June 6, 1956 Fig. 8. Typical chart recrd f ship waves shwing the varius terms determined in the tests. D E F PLAN 676 ELEVATION Fig. 9. Idealized mdels used in determining scale effects in ship wave studies.

12 SHIP WAVES IN NAVIGATION CHANNELS The twing system shwn in Figure 6 was driven by falling weights with the mdel being attached fre and aft by strings t a taut line which passed ver sheaves at tw ends f the mdel basin. Craft speeds were varied by varying the weights n the driving system. All tests were made with fresh water in the mdel basin. Wave characteristics were measured in a lcality where the mdel had attained a cnstant speed. These measurements were made at five psitins by parallelwire resistance elements (Wiegel, 1956), lcated as shwn in Figure 6, and recrding n a six channel Brush recrder. The sixth channel f the recrder was used t determine the speed f the craft frm timing marks made n the recrder chart by a cntact actuated during each revlutin f ne f the sheaves n the drive system. Measurement f the waves was made at varius cnstant speeds frm the lwest speed that waves culd be recrded accurately t the highest speed that the driving system culd be perated. Fr a mdel with "gd" lines (Mdel A^, Figure 7) the resistance t mtin was small enugh that sufficient weights culd be placed n the driving mechanism t attain a craft speed well beynd the critical speed where the wave height was a maximum. A typical example f a wave height recrd is shwn in Figure 8. Such chart recrds were analyzed fr the maximum crest elevatin abve stillwater level and fr the maximum wave height. This maximum wave height usually was the vertical distance f the maximum crest height abve the preceding trugh (Figure 8). The angle between the cusp lcus and the sailing line was cmputed fr each test frm the time lag between maximum wave height ccurrence at tw wave gages, the distance between gages, and the mdel speed. T give a measure f the effect f scale n the results frm mdel tests a series f runs were made with an idealized ship frm cnstructed t three different sizes as shwn in Figure 9. These three mdels were tested under cnditins in which certain variables were held cnstant t determine the effect f abslute size f the craft n the wave characteristics. Test Results A typical example f the type f wave height data btained frm the tests n a particular mdel is shwn in Figure 10, where fr Mdel AT the values f maximum wave height, H, and maximum crest elevatin, S, as determined at varius distances x frm the sailing line, are pltted as a functin f ship speed. The water depth was held cnstant during the tests. Als indicated in Figure 10 are scales shwing values f V^L, and X (as defined by equatin 1). In the term, V^L > which is cmmnly used by naval architects in cmparing the perfrmance f ships, V is the ship speed in knts, and L is the waterline length in feet. It is f imprtance t nte in Figure 10 hw rapidly the wave height increases'with speed up t a critical pint. 677

13 COASTAL ENGINEERING Beynd this critical speed the wave heights decrease and apprach a cn stant value fr relatively high speeds. The rapid increase in wave height with ship speed fr speeds belw the critical speed cnfirms the bservatin f Lewis (1956) as quted in the Intrductinnamely, that increased ship speeds has resulted in greatly increased wave heights and cnsequently serius wavewash ersin prblems. An item f interest in cnnectin with Figure 10, and similar plts fr ther mdels is that the maximum wave height, H, is apprximately twice the value i S, the maximum crest elevatin abve the stillwater level. In additin t the data n wave heights as measured frm the recrder charts the time between the ccurrence f the maximum crest height and the preceding trugh (see Figure 8) was determined and has been termed the "halfperid." Figure 11 shws such data pltted again X. These data were btained frm the same series f tests fr which th height data in Figure 10b is presented. Within the accuracy f measure ment the halfperid was independent f the distance, x, frm the sailing curse. Fr the tests frm which the wave height data shwn in Figure 10 were btained the angle, a,between the cusp lcus, r pint f maximum wave height, and the sailing line was cmputed and is pltted against X in Figure 12. Als shwn n this plt is the theretical curve f Lrd Kelvin. There is fair agreement between thery and experiment. Wave height data similar t that shwn in Figure 10 were btained fr the ther mdels and test cnditins listed in Table II. T permit a cmparisn f the wave generating capacity f the varius hull frms represented by the mdels, dimensinless plts were prepared using the fllwing parameters: where H, f ( V d x ) (5) D" TIT' D H = maximum wave height, ft. D = ship draft at midsectin, ft. L = ship length at water line, ft. V = ship speed in knts* d = water depth, ft. x = perpendicular distance frm sailing line t pint f wave measurement. 678

14 SHIP WAVES IN NAVIGATION CHANNELS 1 ' ' ' ' ' ' ' ' ' ' ' ' ' 20 ' ' ' 3' 0 VL 1,1 I ' '" 2 CC X= 1 5' *\ r t LI r * «: e 0»s» \ t r Js f a. 0_ I I..., x = 3 0' ^.^ i ^ : 0 r*c^ *% 5 "» _* s b i T' ^T^ 0 ]_ > ',2* ia ta Xr **..,4^ * ^ et ft n, H _. X = 5' C 1 rk ^ 1 1.v^ * ^^^^^^ * 1 1 e x = ll' LI*! e. 0 I C, in FeetSecnd Fig.10. Typical data n wave height as a functin f ship speed and distance f wave recrder frm sailing curse. Mdel A^ with a water depth f 0.52 ft. used in tests. 679

15 COASTAL ENGINEERING < MODEL 4=396 ) <*L r 0 ^ Tr I. x 1 \ X \ X " In \, Mdel AL d = 0 52 ft Runs #713 June 6, 1956 <elvm thery "» X 1^ x! _ 1 i I > X Fig. 11. Relatinship between pe Fig. 12. Relatinship between an rid fr maximum wave and X. e, between the cusp lcus and Mdel AL with a water depth f 0.52 sailing line and X fr Mdel AT. ft. used in tests. IV del B \, M del A Mdel 1 TEST CONDITIONS A del H ' MODEL A L D d f g punds feet feet feet AL AH " C " V ' a vr Fig. 13. Relatinship between the wave heightship draft rati and the relative ship speed, VH L,. 680

16 SHIP WAVES IN NAVIGATION CHANNELS Figure 13 shws a plt f HD as a functin f V V L fr a cnstant water depth and psitin f wave measurement fr mdels AT, AJJ, B, and C. Due t the slight differences in the length, L, and draft, D, fr the varius mdels, there is a slight difference in the values f xl and dd between mdels. The curve fr mdel A^ in Figure 13 was derived frm the basic data presented in Figure 10. This mdel was the nly ne in which the resistance t mtin was lw enugh that the mdel culd be twed at speeds in excess f the critical cnditin fr maximum wave height. Cmparisn f the curves fr mdels A^ and AJJ gives an indicatin f the effect f varying the displacement with a particular hull shape. The actual wave heights were greater fr mdel AJJ than fr mdel AT at a particular speed; hwever, because the draft is less fr mdel AL than fr AJJ, the HD versus speed curve fr the lighter mdel (A^) plts abve the curve fr the heavier mdel (AJJ). Cmparisn f the curves fr mdels AJJ, B and C in Figure 13, where the displacement was a cnstant, shws the general effect f hull frm n the relative wave making capacity f the varius mdels; that is, the better the ship lines the lwer are the wave heights fr a particular speed. T prvide infrmatin n the variatin f wave height with distance frm the sailing curse Figure 14 has been prepared fr ne f the mdels (Mdel AJJ). This figure shws the rati HD pltted against the rati xl fr a cnstant speed, VV L, with dd as a parameter. The curves shwn are crss plts frm such curves as shwn in Figure 13. The curves in Figure 14 shw that when the water depth is relatively small cmpared with the draft the wave height decreases rapidly with distance frm the sailing line; whereas, fr the larger water depth, the rate f decrease in wave height with distance, is cnsiderably less. Further infrmatin n the effect f water depth n the height f ship waves is shwn in Figure 15 which is a crss plt frm Figure 14. In this figure the wave heightdraft rati, HD, is pltted against the depthdraft rati, dd, fr a cnstant speed f VA L~ = 1.1 at a cnstant distance frm the sailing line f xl = 1. In additin t the three values f dd shwn in Figure 15 (namely, 2.26, 4.35, and 7.95) sme data were btained in a relatively narrw twing tank with a dd value f These data were rather limited; hence the pint n the curve in Figure 15 at the dd value f 22.5 is nt accurately defined; cnsequently the curve beynd a value f d D = 7.95 is shwn as a dtted line. Als shwn in Figure 15 is the limit fr n increase in ship resistance as cmputed frm equatin 2. This plt indicates that when the rati f depth t draft (dd) is less than abut 8, the wave heights increase rapidly with a decrease in depth, that is, when the depth is greater than abut 8 t 10 times the draft the waves are essentially thse fr deepwater cnditins. 681

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18 SHIP WAVES IN NAVIGATION CHANNELS Scale Effects As mentined abve, a series f tests were made with the idealized ship frm shwn in Figure 9. The three gemetricallysimilar mdels were twed at varius speeds in water f varius depths such that a cnstant value f depthdraft rati f 5.3 existed in the tests. The wave heights were measured at the distances frm the sailing line as shwn in Figure 6. The wave height data fr each mdel were pltted n diagrams similar t Figure 10. Frm these basic data the dimensinless parameters presented in equatin 5 were cmputed and pltted as shwn in Figure 16, which is similar t Figure 14 fr Mdel Ajj. Figure 16 shws fr each mdel the rati HD pltted as a functin f xl fr a cnstant speed rati, VV L, f 1.0 and a cnstant depthdraft rati f 5.3. Inspectin f this graph shws that the scaling law fr the larger mdels (mdels D and E) agree almst exactly, but the curve fr the smallest mdel (mdel F) plts cnsiderably belw the ther curves, thus indicating that there is an effect f abslute size f mdel. In ther wrds, if mdels are t Small in abslute size the predictin f prttype values frm mdel data is f questinable value. Obviusly mre experimental data are required t better define the limit f mdel size fr reliable prttype predictins. POWER BOAT STUDIES A limited number f bservatins were made n the waves generated by a 42 ft. pwer bat f 241 cu. ft. displacement perating at varius speeds in water abut 7 ft. deep. Measurements were made f wave heights in the tests. In a few instances vertical aerial phtgraphs were made t determine wave patterns. Phtgraphs f wave patterns fr valuesf X frm 0.70 t 1.32 are shwn in Figures 17 and 18. A summary f the pertinent data fr each f the tests shwn in the phtgraphs is presented in Table III. The angle r shwn in this table is the angle between the sailing line and a line drawn frm the bw thrugh what appears t be the pint f maximum wave height. 683

19 COASTAL ENGINEERING m 3 t i i H U ; a ti > ri t tjb fl H > s +> cfl O, 5 U 3 O? ft =J. rt CM ^3 "* t t~ cs c. 1 H S m W> O T3 ih h 0) 1H Q) fe *» <.3 M +J i i s 03 d) u Ul U <x> H +J ni ft <U > rt Is l> tuo t rl fe bu ii fn 684

20 SHIP WAVES IN NAVIGATION CHANNELS \ m CO»H 3 O rh fcu H H & fa > +> a CJ).3 > a +J a 42 b. <u 0) H? 5 < =>.? (M 3 <* J3 l 03 CO * fi A.3» CM <D fa (> )!H 03 0 M 0) H> H rt a QJ > cd CO it nl CO.H W) H M ih fa fa 685

21 COASTAL ENGINEERING 1.0 Seal s f X I.I I 1 i 1 ' x \ < ^,6,0 ^^ ^ , ' X5^. J: = 6 0 O6.0 =3.3 =3.7 < ' 6.0 Numbers by pints indicate 0.2 values f n l V Fig. 19. Relatinship between the rati f wave height and draft and relative speed fr a 42 ft. pwer bat with relative distanc xl and depthdraft rati as parameters. 686

22 SHIP WAVES IN NAVIGATION CHANNELS TABLE III Summary f Ship Wave Patterns Bat length = 42 ft. Bat displacement = 241 cu. ft. Bat draft (midship) = 1.9 ft. Blck cefficient = 0.37 Displacementlength cefficient = 101 C d C a d igure ftsec ft. D ftsec X degrees 17a Q ' 17b c ' 18a b c Examinatin f the phtgraphs in Figures 17 and 18, and in particular Figure 18a, indicates a discrepancy between the character f the actual ship waves and thse expected by thery near the critical value f X = 1, The mdel test data summarized in Figure 12 indicates that the angle a apprximates that expected by the Kelvin thery. In Figure 18a, hwever, where X has a value clse t 1.0, the value f the angle a is nly 15 (Table III) instead f abut 90 as wuld be expected by thery. It is pssible that the shrt steep waves which appear t frm the cusp lcus are in reality lwer in height than are the lng lw steepness waves which are utside f what has been assumed t be the cusp lcus. The measurement f wave height during the tests were made by waterlevel recrders installed at tw distances, x, frm the sailing line. Frm the waterlevel recrder charts the maximum wave height (distance frm maximum crest elevatin t preceding trugh) was determined. The rati f wave height t draft was then cmputed and pltted as a functin f the relative speed f the craft, V~L, as shwn in Figure 19 with the rati, xl, as a parameter. A scale f X is als shwn in this figure. All runs were made with a value f the "ati t depth, dd, equal t 3.3 except in ne run where dd equaled 3.7. Althugh the data are limited and sme scatter ccurs, examina,in f Figure 19 shws results similar t thse determined frm the ndel studiesnamely, that fr a particular rati f depth t draft here is a certain speed at which the wave height is a maximum. In "elatively shallw water this pint ccurs in the vicinity f X =

23 COASTAL ENGINEERING Fr values f X > 1 the wave heights reduce with increase in speed and appear t apprach a cnstant value at high speeds. As t be expected the wave heights decrease with increasing relative distances, 2., frm the sailing line. CONCLUSION The data frm a series f mdel tests define the variables invlved and their relative imprtance in determining the characteristic! f waves generated by passing ships. It appears that with mdels f sufficient size reliable prttype predictin can be made f the waves generated by a particular hull shape; hwever, additinal mdel studie and prttype bservatins are required t permit such predictins t be made with cnfidence. ACKNOWLEDGEMENTS The tests described were cnducted with research funds prvic by the University f Califrnia. Mr. A. L. Arnld assisted in cnducting the tests and analyzing the data, and Miss Margaret Lincln p pared the illustratins. REFERENCES Birkhff, G., B. V. Krvin Krukvsky, and J. Ktik (1954). Thery f Wave Resistance f Ships., Sciety f Naval Archite and Marine Engrs., Vl. 62, pp DeBruyn, H. C. P. and A. G. Maris (1935). Frm f Crss Sectin and System f Bank Prtectin t be Adpted n Canals and Rivers. 16th Internatinal Cngress f Navigatin, Brussels, 1st Sectin, 1st Cmmunicatin, Paper 39, pp Franzius, O. (1936). Waterways Engineering. The Technlgy Pres Mass. Inst. f Tech., Cambridge, p Frude, William (1877). Experiments upn the Effect Prduced n tl Wavemaking Resistance f Ships by Length f Parallel Middl Bdy. Trans., Inst. f Naval Architects, Vl. 18, pp

24 SHIP WAVES IN NAVIGATION CHANNELS Havelck, T. H. (1908). The Prpagatin f Grups f Waves in Dispersive Media, with Applicatin t Waves n Water Prduced by a Travelling Disturbance. Prc. Ryal Sciety f Lndn, Series A., pp Havelck, T. H. (1934). Wave Patterns and Wave Resistance. Trans., Inst. f Naval Architects, Vl. 76, pp Havelck, T. H. (1951). Wave Resistance Thery and its Applicatin t Ship Prblems. Trans., Sciety f Naval Architects and Marine Engrs., Vl. 59, pp Hertaberg, R. (1954). WaveWash Cntrl n Mississippi River Levees. Trans. Amer. Sc. Civil Engrs., Vl. 119, pp Hvgaard, William (1909). Diverging Waves. Trans., Inst. f Naval Architects, Vl. 51, pp Lrd Kelvin (Sir William Thmsn) (1887a). On the Waves Prduced by a Single Impulse in Water f any Depth. Prc. Ryal Sc. Lndn, Vl. 42, pp. 80T83. Lrd Kelvin (Sir William Thmsn) (1887b). On Ship Waves. Prc. Inst. f Mech. Engrs., pp Krey, H. (1913). Fahrt der Schiffe auf beschranktem Wasser. Schiffbau, Berlin. Krey, H. and R. Winkel (1929). Experiments n Mdels f Canals. Hydraulic Labratry Practice, Amer. Sc. f Mech. Engrs., pp Lewis, William H. (1956). The Freshre Ersin Prblem in the Lwer Reaches f the Mississippi River. Shre and Beach, VL.24, N. 1, pp Lunde, J. K. (1951). On the Linearized Thery f Wave Resistance fr Displacement f Ships in Steady and Accelerated Mtin. Trans., Sciety f Naval Architects and Marine Engrs., Vl. 59, pp Rankine, W. J. M. (1868). On Waves which Travel alng with Ships. Trans., Inst. f Naval Architects, Vl. 9, pp Rbb, A. M. (1952). Thery f Naval Architecture. Charles Griffin & C., Ltd., Lndn, 689

25 COASTAL ENGINEERING Rsik, J. (1935). Frm f Crsssectin and System f Bank Prtec tin t be Adpted n Canals and Rivers. 16th Internatinal Cngress f Navigatin, Brussels, 1st Sectin, 1st Cmmunic tin, Paper 40, p. 4. Schijf, J. B. (1949). Prtectin f Embankments and Bed in Inland and Maritime Waters, and in Overflw r Weirs. XVII Inter natinal Navigatin Cngress, Lisbn, Sectin I, pp Sum, J. (1935). A Study f the Effect upn Navigatin and upn the Upkeep f the Banks and Bed f Canals and Canalized Rivers. 16th Internatinal Cngress f Navigatin, Brussels, Sectin 1, 1st Questin, Paper 7, p. 16. Taylr, D. W. (1943). The Speed and Pwer f Ships, U.S. Gvt. Printing Office. Vanderlinden, M. (1912). Dimensins t be Assigned, in any Given Cuntry, t Canals f Heavy Traffic. Reprt f Prceedings f the 12th Cngress, Permanent Int. Assc. f Navigatin Cngresses, p Van Ln, A. R. (1912). Prtectin f the Banks f Navigable High ways. 12th Cngress, Permanent Int. Assc. f Navigatin Cngresses, Sectin 1, 2nd Cmmunicatin, Paper 43, p. 3. Wiegel, R. L. (1956). Parallel Wire Resistance Wave Meter. Prc First Cnference n Castal Engineering Instruments. Cuncil n Wave Research, Berkeley, Calif., pp Wrtman, H. (1894). Cnstructin f Navigatin Canals Affrding Operatin at High Speed, 6th Internatinal Cngress f Navigatin, 1st Questin, Paper 2, p