76
150 REFERENCES Abramowitz,M., Stegun, I.A., edit., Handbook of Mathematical Functions, National Bureau of Standards, App ie t ematics eries Achenbach, Ed s "Influence of Surface Roughness on the Crossflow around a Circular Cylinder," Journal of Fluid Mechanics, Vol. 46, March, 1971, pp. 321-335. Ang, A.H.S,, and Tang, W.H., Probabilit Conce ts in En ineerin Plan- 99 1 .9 1 9 .1919. A diber t, J.M.E9 e Lai, N.WO e and Bea, R.G., "DeSign Of Pipelines tO Resist Seafloor instabilities and Hydrodynamic Forces," ~pre rint. Energy Technology Conference, Houston, Texas, Nov. 1978. Beattie, J,FO e Brown, L.P., and Webb, B., "Lift and Drag Forces on a Submerged Circular Cylinder," Pre rint, Third Annual Offshore Technology Conference, Houston, exas, April 1971, Vol. 1, pp. 319-328. Blumberg, R., "Design for Environmental Extremes," Vol. 25, No. 4, Oct. 1966, pp. 31-34. Blumberg, RE e "Introduction-Offshore Risks," American Society for Oceanography Public pp. 294-303. 966, Blumberg, Ro s and Rigg, A.MO e "HydrOdynamiC Orag at Super '.ritiCal Reynolds Numbers," paper presented at A.S.M.E. meet.; Pet. Session!, Los Angeles, June 14, 1961. Bowie, G.L., "Forces Exerted by Waves on a Pipeline at or near the Ocean Bottom," U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belddoir, Virginia, Technical ~pa er No. 77-11, October, 1977. Byrd, P,F. and Friedman, M.D., Handbook of Elli tic Inte rais for En ineers and Ph sicists, pringer- er ag, Carnahan, 8., Luther, H.A., and Wilkes, J.O., A lied Numerical Methods, John Wiley ImSons, N.Y., 1969. Carpenter, L.H., "On the Notion of Two Cylinders in an Ideal Fluid," Journal of Research of the National Bureau of Standards, Vol. 61, No. 2, Augu~st, 9SB, pp. 83 37. Chakrabarti, S.K., Tarn, W.A., 8 Wolbert, A.L., "Wave Forces on a Ran- 9 1 ." ~di 19 Odd I ~9 Conference, Paper No. 2190, pp, 723-740.

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Page 1: Abramowitz, M., Stegun, I.A., edit., Handbook of

150

REFERENCES

Abramowitz, M., Stegun, I.A., edit., Handbook of Mathematical Functions,National Bureau of Standards, App ie t ematics eries

Achenbach, Ed s "Influence of Surface Roughness on the Crossflow arounda Circular Cylinder," Journal of Fluid Mechanics, Vol. 46, March,1971, pp. 321-335.

Ang, A.H.S,, and Tang, W.H., Probabilit Conce ts in En ineerin Plan-99 1 .9 1 9 .1919.

A diber t, J.M.E9 e Lai, N.WO e and Bea, R.G., "DeSign Of Pipelines tOResist Seafloor instabilities and Hydrodynamic Forces," ~pre rint.Energy Technology Conference, Houston, Texas, Nov. 1978.

Beattie, J,FO e Brown, L.P., and Webb, B., "Lift and Drag Forces on aSubmerged Circular Cylinder," Pre rint, Third Annual OffshoreTechnology Conference, Houston, exas, April 1971, Vol. 1,pp. 319-328.

Blumberg, R., "Design for Environmental Extremes,"Vol. 25, No. 4, Oct. 1966, pp. 31-34.

Blumberg, RE e "Introduction-Offshore Risks,"American Society for Oceanography Publicpp. 294-303.

966,

Blumberg, Ro s and Rigg, A.MO e "HydrOdynamiC Orag at Super '.ritiCalReynolds Numbers," paper presented at A.S.M.E. meet.; Pet.Session!, Los Angeles, June 14, 1961.

Bowie, G.L., "Forces Exerted by Waves on a Pipeline at or near theOcean Bottom," U.S. Army, Corps of Engineers, Coastal EngineeringResearch Center, Fort Belddoir, Virginia, Technical ~pa er No.77-11, October, 1977.

Byrd, P,F. and Friedman, M.D., Handbook of Elli tic Inte rais forEn ineers and Ph sicists, pringer- er ag,

Carnahan, 8., Luther, H.A., and Wilkes, J.O., A lied Numerical Methods,John Wiley Im Sons, N.Y., 1969.

Carpenter, L.H., "On the Notion of Two Cylinders in an Ideal Fluid,"Journal of Research of the National Bureau of Standards, Vol. 61,No. 2, Augu~st, 9SB, pp. 83 37.

Chakrabarti, S.K., Tarn, W.A., 8 Wolbert, A.L., "Wave Forces on a Ran-9 1 ." ~di 19 Odd I ~9

Conference, Paper No. 2190, pp, 723-740.

Page 2: Abramowitz, M., Stegun, I.A., edit., Handbook of

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Chung, T.J., Finite Element Anal sis in Fluid 0 namics, NcGraw Hil]Book Co , , p ~

Dalton, C., and Helfinstine, R.A., "Potential Flow Past a Group ofCircular Cylinders," Journal of Basic Engineering, A.S.M,E. Trans-actions, December, 1971, pp. 636-642.

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Denson, K.H., and Priest, M.SRA "Effects of Angle of Incidence on WaveForces on Submerged Pi peli nes," A.S.C.E. National Meeting onWater Resources Engineering, P t 2120, 1974, pp. 1-11,

Garrison, C.JNA "Added Mass Of a Circular Cylinder in Contact with aRIPEN 6 d ." J I f ed ti . P I. 6, 6 . I. J1972, pp. 59-60.

Garrison, C.J., "Drag and Inertia Coefficients in Oscillatory FlowAbout Cylinders," A.S.C.E. National Water Resources and OceanEngineering Convention, ~pre rint 2693, San Oiego, California,April, 1976, pp. 1-23.

Goda, Y., "Wave Forces on a Vertical Circular Cylinder: Experimentsand a Proposed Method of Mave Force Computation," Port and HarbourTechnical Research Institute, Vokusuka, Japan, ~Re ort Ro. R.August, 1964.

Grace, R.A. & Nicinski, S.ANA "Wave Force Coefficients from PipelineResearch in the Ocean," Proceedin s of the 1976 Offshore Techno-~lo Conference, Paper No., pp. F8~9~

Grace, R.R., "Near Bottom Mater Notion Under Ocean Waves," ProceediFifteenth Conference on Coastal Engineering, Honolulu, Hawaii,July, 1976, pp. 2371-2386.

Grace, R.A. & Zee, G.T., "Further Tests on Ocean Wave Forces on aSphere," A.S.C.E. Journal of the Waterwa s, Harbors and Coastal~E' 6 . IT,T6 P.,P.RTNE

Grace, R.A., "Hawaii Ocean Test Pipe Project: Experimental Setup,"Proc d , Civil Engineering in the Ocean IV, San Francisco,

Grace, R.Ade Castiel, J., Shak, A.T., and Zee, G.T.Yda "Hawaii Oceant«PIP I: t «I I ."u~.tEngineering in the Ocean IV, San Francisco, Sept. 1979.

Grace, R.A., "A Slanted Look at Ocean slave Forces on Pipes," A~Re ortto the American Gas Association, Aug. 1979.

Grice, C.F., "Finding Underwater Objects; Part 3 � Case Histories,

Feb. 1968, pp. 34-39.

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Guven, 05 9 Patel, U.C., and Farell, C., "SurfaCe ROughneSS Effects Onthe Mean F1ow Past Circular Cylinders," Iowa Institute ofHydraulic Research, University of Iowa, Iowa City, Iowa, May 197~,

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5 « I 51, ~V. 9. 91. pp. 98- 5.

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Isaacson, M. de St. 0., Private Comtunication, January-February, 1979.

Iversen, H.W., and Balent, R., "A Correlating Modulus for Fluid Resis-tance in Accelerated Motion," Journal of ~AIied ~PN sics,Vol. 22, No. 3, March, 1951, pp. 324-328.

Jones, G.W., Jr., "Unsteady Lift Forces Generated by Vortex Sheddingabout a Large, Stationary, and Oscillating Cylinder at HighReynolds Numbers," A.S.M.E., Symposium on Unsteady Flow,

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Jones, W.T., "Forces on Submarine Pipelines from Steady Currents,"A.S.M.EAe Pa er 71-UnT-3 presented at the Petroleum MechanicalEngineering wit Underwater Technology Conference, Sept. 19-23,1971, Houston, Texas.

Kennard, E.M., "Irrotational Flow of Frictionless Fluids, Mostly ofInvariable Density." U,S. Navy. David ~Ta lor Mode1 Basin,washington, D.cpe February, 1967, Report; 2299.

Keulegan, G.H,, and Carpenter, L.Hps "Forces on Cylinders and Platesin an Oscillating Fluid," Journal of Research of the NationalBureau of Standards, Vol. 60, No. 5, MMays 9 8, pp. 4%2-II'10.

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Kulin, G., "Solitary Wave Forces on Submerged Cylinders and Plates,"Nationa l Bureau of Standards Re ort No. 5876, Apr. 22, 1958.

Laird, A.D.K.. "Eddy Forces on Rigid Cylinders,"and Harbors Division, A.S,C.E., Nov. 1961, p

L b,ll..~l" i .61 diNew York, New York.

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and Water

Milne-Thomson, L.M., Theoretical H drod namics, 5th edit., 1968,McMillan, N.Y.

Nath, B., Fundamentals of Finite Elements for En ineers, The AthlonePress, Lon on, Eng an , , ppen ix

Patton, K.T., "Tables of Hydrodynamic Mass Factors for TranslationalMotion," A.S.M.E.. Pa er No. 65-HA/UNT-2.

Rance, P.Jre "The Influence of Reynolds Number on Have Forces,"~td mpNetherlands, July, .1969, Vol. IV, Paper 13,

Roshko, A., "Experiments on the Flow Past a Circular Cylinder at VeryHigh Reynolds Numbers," Journal of Fluid Mechanics, Vol. 10,1961, pp. 345-356.

Sarpkaya, T., and Garrison, C.J., "Vor tex Formation and Resistance inUnsteady Flow," Journal of A lied Mechanics, Vol. 30, Series E,No. 1, March 196, pp.

Sarpkaya, Tr e "Forces on Cylinders and Spheres in a SinusoidallyOscillating Fluid," A.S.M.E., Journal of Fluid Mechanics, Vol, 98,Serves 1, No. 3, September, 19T5, pp, 499-505,

Sarpkaya, T., "In-line and Transverse Forces on Cylinders in Oscilla-tory Flow at High Reynolds Numbers," Proceedin s Eighth AnnualTechnology Conference, Houston, Texas, 19 6, Paper No. OTC 2533.

Sarpkaya, T., "Forces on Cylinders near a Plane Boundary in a Sinu-soidally Oscillating Fluid," A.S.M.E., Journal of Fluids

i 9

Sarpkaya, T., "In Line and Transverse Forces on Cylinders near a 'Wallin Oscillating Flow at High Reynolds Number," Proceedin s of the

71«~cf.p..pp,Ã:ler

Sarpkaya, T., "Hydroelastic Response of Flexibly-Mounted Cylinders inHarmonic Flow," Proceedin s of the 1977 Offshore TechnoloConference, Paper No.

Page 5: Abramowitz, M., Stegun, I.A., edit., Handbook of

Sarpkaya, T., Collins, N.J. and Evans, S,R., "Wave Forces on Rough-Walled Cylinders at High Reynolds Numbers," Proceedin s, NinthAnnual Offshore Technology Conference, Houston, exas, May l 977,Paper No. OTC 2901.

Shapiro, A.H., ~Sha e and Flow - the Fluid ~gnanics of ~Bra, 196I,Doubleday Co., Garden City, New York.

Shore Protection Manual, Vols. l-3, U.S. Arrqy Coastal EngineeringResearch Center, 973.

Snodgrass, F.Eie et al., "Propagation of Ocean Swell Across thePacific,u Phil. Trans. of the ~Ro al ~Societ of London, Yol. A259,1966. pp. 59T-497.

Stelson, T.E. and Mavis, F.T., "Yirtual Mass and Acceleration inFluids," A.S.C.E., Transactions, Yol. 122, l957, pp. 518-530.

Tong, P., and Rossettos, J .N., Finite Elements Method: Basic Tech-s d I 1 mentatio , The MIT Press, Cambridge, Mass.,

En ineerin , Prentice-Hall Inc.,sey, 9

Wiegel, R.L.,Englewood

Worthington, H.Wia and Herbich, J.B., "Computer Prediction of WaveHeights in Coastal Areas," ~Pre rints, Third Annual OffshoreTechnology Conference, Houston, Texas, April 1971, Paper No.OTC 1427.

Yamamoto, Ta 9 Nath, J.H., and Slotta, L., "Wave Forces on Cylindersnear Plane Boundaries," A.S.C.E., Journal of the Haterwa s,tl 1 dC» 1~El 1 0 .Il9l.ll1974, pp. 745-559.

Yamamoto, T. and Nath, J.H., "High Reynolds Number Oscillating Flow by

Chapter l36, l976, pp. 232l-2340.

Schlichting, H., ~Boundar ~La er ~Theor, 4th edition, 1950, Mcgraw Hill,New York, New York.

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8 I BL I OGRAPH Y

Achenbach, E,, "Distribution of Local Pressure and Skin Friction Arounda Circular Cylinder in Cross-Flow up to Re - 5 x 106, Journal ofFluid Mechanics, Vol. 34, 1968, pp. 625-639.

Beckman, Hde and Thibodeaux, M,H., "Wave Force Coefficients for Off-shore Pipeline," A.S.C.E., Journal of the Waterwa s and HarborsDivision, Vol. 188, No. WW2, May, 1962, pp, 125-12

Blumberg, RR 9 "Hurricane Winds, Waves and Currents Test PipelineDesign," Parts 1-4, Pi eline Industr , June, July, August,Sept., 1964.

Brodetsky, Sd a "Discontinuance Fluid Motion Past Circular and Elliptic1 11 d ." ~di . 4Vol. 102, No. 718, 1923, pp. 542-553.

Bushnell, M.JRe "Forces on Cylinder Arrays in Oscillating Flow,"~Pre rint, 9th Annual Offshore Technology Conference, Houston,Texas, 1977, Paper No. OTC 2903.

Chiu, W.S. and Lienhard, J.H., "On Real Fluid Flow over Yawed Circu'larCylinders," American Society of Mechanical Engineers, Transactions,4 1 11 1 ~ii, 1 .'11.11, .4~4T99, pp. Stiiy.

Collins, W,M., and Dennis, S.C.RR a "Flow Past an Impulsively StartedCircular Cylinder," Journal of Fluid Mechanics, Vol . 60, 1973,pp. 105-127.

Dalrymple, R.Ada "Waves and Wave Forces in the Presence of Currents,"Proceedin s, Civil Engineering in the Oceans III, University ofDe aware, Newark, Delaware, June, 1975, pp. 999-1018.

Dalton, C. and Hamann, F., "The Forces on a Cylinder Oscillating Sinu-soidally in Water," A.S.M.E. Pa er No. 71-Pet-2, 1971.

Dean, R.G,, HEvaluation and Development of Wave Theories for EngineeringApplication," U.S. Army, Corps of Engineers, Coastal EngineeringResearch Center, Fort Belvoir, Virginia, S ecial Re ort No. 1,Nov. 1974.

Dean, R.Gde and Aagaard, P.M., "Wave Forces: Data Analysis and Engi-neering Calculation Method," Journal of Petroleum TechnoloVol. 22, No. 3, 1970, pp. 368-375.

Dennis, S.C.Rde and Chang,G. Z., "Numerical Solutions for Steady FlowPast a Circular Cylinder at Reynolds Numbers up to 100," Journalof fluid Mechanics, Vol. 42, Part 3, 9 July l970, pp. 471-4449.

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156

Dwyer, H.A., and McCroskey, W.Jn e "Oscillating Flow over a Cylinder atLarge Reynolds Number," Journal of Fluid Mechanics, Vol. 61,1973, pp. 753-767.

Fage, A., and Warsap, J., "The Effects of Turbulence and Surface Rough-ness an the Drag of a Circular Cylinder," Aeronautical ResearchCouncil, R. and M., No. 1283, 1929.

Garrison, C.Jne and V.S. Rao, "Interaction of Waves with SubmergedObjects," A.S.C.E., Journal of the ~waterwa s, Harbors and Coastal

1971. pp. 5 . 7

Garrison, C.J., "Hydrodynamics of Large Objects in the Sea. Part I-A

January, 1974, pp. 5-12.

Garrison, C.J., Field, J,B., and May, M.D., "Drag and Inertia Forces ona Cylinder in Periodic Flow," A.S.C.E., Journal of the Waterwa s,Port Coastal and Ocean Division, Vol. 103, No. WW , May 19pp

Grace, R.Ai e and Casciano, F.M., "An Experimental, Pilot Study of OceanWave-Induced Forces on a Bottom-Mounted Sphere," University ofHawaii, Center for Engineering Research, ~Re ort No. PAC 6829,June, 1968.

Grace, R.Aae "The Effects of Clearance and Orientation on Wave-InducedForces on Pipelines: Results of Laboratory Experiments,"University of Hawaii, J.K.K. Look Laboratory of OceanographicEngineering, ~Re ort No. 16, April, 1971.

Grace, R.A., "Available Data for the Design on Unburied, SubmarinePipelines to Withstand Wave Action," Institution of Engineers,Australia, National Conference Publication No. 7311, 1973,pp. 59-66.

Grace, R.A., "Wave Forces on Submerged Objects," University of Hawaii,J.K.K. Look Laboratory of Oceanographic Engineering, Miscellaneous~Re ort No. 10, July, 1974.

Grace, R.A., "Near Bottom Water Motion Under Ocean Waves," P oc d'Fifteenth Conference on Coastal Engineering, Honolulu, Hawaii,July, 1976, pp. 2371-2386.

Gran, S., "Wave Forces on Submerged Cylinders," Pre rints, Annual Off-shore Technology Conference, Houston, Texas, 19 3, Paper No.OTC 1817.

Heltinstine, R.Aie and Shupe, J.Wae "Lift and Drag on a Model OffshorePipe1ine," Pre rint, Fourth Annual Offshore Technology Conference,Houston, Texas, 2, Paper No. OTC 1568, pp. 563-572,

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Hol!and, S.Md P "Screw Anchors Hold Wandering Submarine Line,"Pi eline Industr, Vol. 17, No. 6, Dec. 1962, p. 54.

Hudspeth, R.Tde Dalrymple, R.Ade and Dean, R.Gde mComparison of WaveForces Computed by Linear and Stream Function Methods," ~pre rint,Sixth Annual Offshore Technology Conference, Houston, Texas,1974, Paper No. OTC 2037.

Jones, W.T., "On-Bottom Pipeline Stability in Steady Water Currents,"~Pdi . dtgl Id t dfd t gt «Houston, Texas, May 1976, Vol. 2, pp. 763-778.

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JOrdan, S.Kd e and J.E. FrOmn, "OSCillatOry Drag, Lift and TOrque On aCircular Cylinder in a Uniform Flow," ~ph sics of Fluids, Uol . 15,No. 3, March, 1972, pp. 371-376.

"t I g ttttt ttg t gt tt .u~gdiNinth Annual Offshore Technology Conference, Houston, Texas,May, 1977, Vol. 4, pp. 71-78.

Kim, Y.T., and Hibbard, H.Cde "Analysis of Simultaneous Have Force andWater Particle Velocity Measurement," Pre rint,. Seventh OffshoreTechnology Conference, Houston, Texas, 9 , Paper No. OTC 2192.

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Mo. MYS, May, 1972, pp. 89K-999.

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Lundgren, Hde B. MathieSSen, and H. GraVeSen, "Wave l OadS On PipelineSg

the Behavior of Off-Shore Structures BOSS 1976!, August, 1976,University of Trondheim, Norway, Vol. 1, pp. 236-247.

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Stansby, P.K., "An Inviscid Model of Vortex Shedding from a CircularCylinder in Steady and Oscillatory Far Flows," Proceedin s,Institution of Civil Engineers, Vol. 63, Part 2, , pp. 865-880.

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. I . 1999.. T89-991.

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Van Dyke, M., Perturbation Methods in Fluid Mechanics, Academic Press,999 .

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Wieget, R.L,, Beebe, K.E. and Noon, J., "Ocean Wave Forces on Circular91 ' 1 " .! ..J 1 I I e Ti 91

Paper 1199, Vol. 83, '1957, pp.~

Wilson, B.WIP and Reid, R.OJP Discussion Of "Wave Force COeffiCientsfor Offshore Pipelines," by H. Beckmann and M.H. Thibodeaux,Journal of the Waterwa s and Harbors Division, A.S.C.E., Vol. 89,~o. WW, T9E3, pp.

Wilson, J.FJ 9 and Caldwell, H.N., "Force and Stability Measurements onNodels of Submerged Pipelines," Second Annual Offshore TechnologyConference, Houston, Texas, April, 1970, Paper 1224.

Yamamoto, T., "Hydrodynamic Forces on Multiple Circular Cylinders,"Jou at of H d 1' D' ' ' , A.S.C.E., Vol. l02, No. HY9,

Yamamoto, TJ e Hath, J., and Slotta, L., "Yet Another Report on CylinderDrag or Wave Forces on Horizontal Submerged Cylinders," Oregon StateUniversity, Engineering Experiment Station, Bulletin No, 47,April, 1973.

Yamamoto, T, and Nath, J.HI 9 "Forces on Many Cylinders near a PlaneBoundary," A.S.C.E. National Water Resources and Ocean EConvention, 1976, preprint 7633, pp. 1-19.

Page 11: Abramowitz, M., Stegun, I.A., edit., Handbook of

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Page 19: Abramowitz, M., Stegun, I.A., edit., Handbook of

6~ rN CQ

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Page 20: Abramowitz, M., Stegun, I.A., edit., Handbook of

169

CQ

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Page 21: Abramowitz, M., Stegun, I.A., edit., Handbook of

170

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Page 22: Abramowitz, M., Stegun, I.A., edit., Handbook of

ChCh CO

Ch CV IhP! CV CCICV bk hl

0 0 0

OCa AJ CVCIJ CV CV

e

e � O 0

CO Ch C4P! CO

P0 J � O

Ca IhPl

~ g Ih Pl

0 0 0

0 IhLA CFl 0

4 4 OJ

r 0 0

Page 23: Abramowitz, M., Stegun, I.A., edit., Handbook of

172

TABLE I3 MEAN AND EXTREME C' VALUESi'd x

5215 a~ 35' a

ex-

treme

ex

tremen mean mean

8.98 8.98

3.92 3.92

1.88

2.01

2.01

2.25

l.. 93

l.. 88

2. 06

1. 3l.

1.70

1.59

1.60

2.01

l. 84

1.78

1.74

1.631.64

1.31

1. 70

1. 38

l. 32

1.61

1.53

1.33

1.44

0.90

l.. 32

1.61

1.28

1.18

1.25

0.90

0.50 0.50

1.22 1.22

1.05 1.05

200243211

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4 i

4.64.8

5.0

5.2

5.4

5.6

5.8

6.0

6.2

6.4

6.6

6.8

7.07.2

7.4

7.6

7.8

8.0

8.2

8 ~ 4

8.6

8.8

0 0 3 312 6

9

lo

l.o

13

10

1,3

14 9 98 8 88 710 6 5

0

0 6 1 34 4 24 1 1

2 0 0 0 10 0

6.97

5.91

3.82

4.02

3. 71

3. 31

3. 27

3. 38

2.95

2.84

2.90

2.73

2.48

2.20

2.37

2.46

2.41

2.42

2.12

2.23

2. 12

2.06

6.97

6.57

5.06

5.68

5.29

4.40

4 ' 42

4.09

3.65

3.40

3.47

3. 85

3. 39

2. 73

2. 90

3. 092.87

3.00

2. 72

3. 10

2. 85

2.29

1

0 3 58 9 5 7

13 818

16

10

ll

18

12 84

l.3

Il 911 3

6 6 6

4 4 4 0 1 1 22 2 I0 1

0 0 0 0

4.72

3.65

3.37

3.20

3.05

2.75

2.85

2.49

2.26

2.33

2.19

2. 10

2.05

1.831.'77

2.10

1.85

l.. 60

1.57

1.63

1.56

1.59

1.50

1.52

1.39

l. 34

1.28

5. 14

4,62

4.25

4.78

3.99

3.80

4.36

3.29

2.74

3.45

3.62

2.71

2.81

2.26

2.16

2.50

2.80

2.19

2.08

2.001.66

1.89

2.13

1.79

1.96

1.54

1.70

0 1

0 7 2 710 910

ll

14 8 7ll

8 9 38

13

10 6 7 54 7

4 5 2 51

0 1

0 0 0 0 0-0

0 0 0

2.39

3.35

1.99

2.32

2.071. 9'7

1.75

1.60

1.76

1.52

1 ~ 29

1.43

l.. 29

1.27

1.17

1.I4

1.01

1.07

1.08

1.13

1.03

1.01

1. l.3

0.86

0.65

0.90

0.78

3,18

9

3.08

2.48

2.65

2. 78

2. 4l.

2. 79

2.13

1.93

2.06

F 00

1. 78

1.62

1.391.39

1.35

1.81

1.76

1.25

1.32

1.82

1 14

0 ~ 75

l. 32

0.78

Page 24: Abramowitz, M., Stegun, I.A., edit., Handbook of

173

TABLE 14 MEAN ANO EXTREME K' VALUESMX

a 35I 15 0~52

OX

Meae

12.41 12.41

9.32

7 79

6.09

5.86

4.89

4.63

5.414. 65

4.46

3.63

4.09

3.78

3.11

2.62

2.93

2.67

2.272.83

2.41

2.57

2.64

1.89

1.58

1.47

1.59

1.87

1.46

1.57

le 631.29

1.29

1.20

1. 38

1.87

I. 44

l.51

1.25

l. 35

l. 14

1.29

1.29

1.07

1.04

l.27

0.840.81

0.99

0. 84

0.98

0.84

0.81

0.99

0.50 0.50

0.71 0.71

0.75 0.75

l.04 1.04

0.58 0.58

200218209

0.4

0 ' 60.8

I.O

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3 8

4.0

4.2

4,.4

4.6

4.8

5 0

5.2

5.4

5.6

5.8

F 0

6.2

6.4

6.6

6.8

7.0

7.2

7.4

7.6

F 8

8.0

8.2

8.4

8.6

8.8

0

0 1 3 312 6 9 810

14 912

14 9 9 78 8 9 710 5 6

0 0 7 1 34 1 24 I 1 20 0 00 10

9.32

7.13

3.69

4.50

F 80

3.69

3.583.50

3.18

2.81

2.95

2.77

2.33

2.00

2.11

2.16

1.982.l2

1.79

l.97

1.94

1.58

1

0 35

e

9 5 910 716

15

11

ll

14

lo-

8 8 5ll 7

8 4 4 5 4 4 4 10 3 21 1 10 l 00 1 0 l

7 ~ 53

4.18

4.22

3.47

4.06

2.87

2.54

2.43

F 10

2.13

2.02

1.96

},.77

1.711.35

1.56

1.86

1.35

l.19

1.28

1. 26

1.21

l. 18

1. 06

0.92

1.06

1.10

4.93

6.62

S.BG

5 ' 62

5 ' 44

5.14

4.15

3.33

3.63

3.22

3.23

2.68

2.68

2.39

1.862.30

3.04

2.20

1.77

1.60

1. 66l. 35

2.06

L.19

1.21L . 3' ~

1 . 10

0 I1 74 7

Il 910

10

14

6

jo 78 3510 9 5 7 6 3

7 4 5 2 5 I 0 1 0 0 0 0 0 0 0 0 0 0

1.97

3.14

2.71

2.33

1.541. 44

1.60

1.32

I.79

1.3$

1.52

1.21

0.95

1.17

0.94

1.22

0.80

1.03

0.03

0.98

0.73

0.75

0.81

0.66

0.87

0.65

0.57

0.76

0.40

1.97

3.14

3.64

4.02

3.23

4.39

F 24

3.15

2 ' 522.60

3.07

1. 98

1.26

2.28

1.58

1.60

1.16

1.72

1.251.12

1.13

1.01

1.11

0.99

1.49

0.85

0.66

1.31

0.40

Page 25: Abramowitz, M., Stegun, I.A., edit., Handbook of

174

Page 26: Abramowitz, M., Stegun, I.A., edit., Handbook of

CJl

AJ

ChP

O Q

Page 27: Abramowitz, M., Stegun, I.A., edit., Handbook of

O

I'Ill

m I COLA O

O O

CO

O

Q3 LA OC4

I I O

LAPJ Ch

0 0 0 0 0LA LO CV

LA

EA

CV

fT$CJ

QJ

O OO OO O

Page 28: Abramowitz, M., Stegun, I.A., edit., Handbook of

177

O

Or Al

O OO Q

C0

O OCV CV

O O

O O

OQ P

0 0I

CII

r O

O OO

C4

Q QI

LD caO r

O OI

Ca OCV

O OI

O Q

O

00

O

ChQID

I

CCI

O O

AJOQI

CV

O O

a CI

O

CD

Page 29: Abramowitz, M., Stegun, I.A., edit., Handbook of

17F

~ s VllA

IjjCL

Ch

0 0Ch CJl Ch Ch0 0 0 0

O 0 O 0

CUCh Ch0 0

0 0

e

O 0 O

o 0 a

O CCj OID �

0 O 0

O

Itj IIj

LA

Cjl CJl rQl LCj

4Ch

cv 0

VlCJ

cd

o Cj

4Jt4

Cf!

CQ

N N

vl VlIjI - CLj

UI

X X

X X� C

1 IX X

IX X X

-I -8 -N -N -I

Q IjjC 0 O

CjI

CIj-O djI�

O N ClX Ca Ch < LO 0 Ljj

I 0 0 0 0 0 0 0

O 0 0 O 0 0 0

O C4 h Ch ~ 0 Lhd 0! ct O CV Ljl Ch 0

5l ~ r P! CV hl

Page 30: Abramowitz, M., Stegun, I.A., edit., Handbook of

179

OPI-

'P

Vl Vl I III IllVl Vl ~ ul Vl

CL II CL CL

0 w 0g Ch C0 Ch

0 0 0 8

0 0 0 Q 0

a0 CD Ch

a 0

O 0 Q

00 Ch0 0

a 0

LA CJl ~ 4' I Ch i!i IAX H W CV fl ~ h FjI 0 0 0 0 ~ O 0 ~ O

e 0 O 0 O 0 O O e O e

iO I I ~IO

4 4II- II- 4

0I I IA C5 ~

Ch IIt' C7l ~ r Ch

OD LACh

CQ K CP h h N 0 y LA' ~CV 0 Ch h Ct IC7 IA>C I cj I p

II-

O 0 0 N cCI cCI

Eh t/l0 4

k. 4I

0C X

K I! CLo

9

O

40vlICPC't70 0C9

V IlS-O CJ

I�

0

I

I�

4J

CV CI

ID P! Ch & Ch 'Cl N ~ Chcf 4 4 4 4 CV 8 4 4 Cll

CV CV OJ hJ ~ r

Page 31: Abramowitz, M., Stegun, I.A., edit., Handbook of

O

Vl Vl Vl

n$Cl. G. CL

0 0 0Cjl

0

0O Ch 0r

0 0 0

00CFl

0 O

0 0

C!

CD

0 0

0 0

0CV

Vl rVltljO.

Vl ~ l/l VlVl ~ Vl

Cl ill lCIa w o. o.l/j

I�

laJI�

CY

0'

I LO

CjlCO

Lh O

CD CO

llO

O

QlN

Vl Vl-dJ -QJ4 l t

X X

0 CC:

I

C!

8

O

VlQJ

O 0CQ

QlS-O Ql

I�

4 0 QPC O

C9

Rj

l-O Ql

I

Ch > W 'LO P! C0 M Ca

I Eco 0 0 0 0 0 0 0 0

0

Cjl r R Cl ~ Cjl

O cf lD O H LQ LD O~ ~ 4CV P! W LA lD

I OJ

X X X X X

Page 32: Abramowitz, M., Stegun, I.A., edit., Handbook of

vl

CD

CL0

/!

Ul

4 4 W 0

PJCV

0

LOCU

0

0

04

O

O

CP

Page 33: Abramowitz, M., Stegun, I.A., edit., Handbook of

LA

CDCV

CDCh

CD

CD

CD

CD

CDCD

CDCl CD

Co

CD

cC

ChCD

X:CO

Ch

CCI

l-

I gID 3NQ ID

or4

182

Page 34: Abramowitz, M., Stegun, I.A., edit., Handbook of

CVCh

CD

CD

CD CD

CVLA

CD

COLD

CDCD

CD

O

I

EflI�

LL

CD

zI3

III

CFlC re

4JCIC

~ r0tv 3CIPCO CX

0I

I

CiS-O Cl

CLI

CFl

rt5

I

183

Page 35: Abramowitz, M., Stegun, I.A., edit., Handbook of

l84

3,2

5.0

2 6

OP

O 2.2

2.0

1,8

1,6

1,e

I � ! 2

1 0 0.0 0.2O.l

Relative Clearance

Fig.l Variation of Ci with ~ andD

Page 36: Abramowitz, M., Stegun, I.A., edit., Handbook of

185

Page 37: Abramowitz, M., Stegun, I.A., edit., Handbook of

F 19 ~ 3 go0thern weS fl Approach Dfrectjon

Page 38: Abramowitz, M., Stegun, I.A., edit., Handbook of

187

Fig. 4 Wave Dir ection Indicator

Page 39: Abramowitz, M., Stegun, I.A., edit., Handbook of

188

CJ

<V

Page 40: Abramowitz, M., Stegun, I.A., edit., Handbook of

~~9- 6 Moorina gyrate~

Page 41: Abramowitz, M., Stegun, I.A., edit., Handbook of

F'lg 7 p art of Frame f p ipe ease

Page 42: Abramowitz, M., Stegun, I.A., edit., Handbook of

Fiq. 8 System for Changing Pipe Base Orientation

Page 43: Abramowitz, M., Stegun, I.A., edit., Handbook of

192

Page 44: Abramowitz, M., Stegun, I.A., edit., Handbook of

193

O Q'P

t4

O

3 O

O C C0 4l63

U'.

O 5

Page 45: Abramowitz, M., Stegun, I.A., edit., Handbook of

Fiq. 11 Detail of Strain Gage Rod

Page 46: Abramowitz, M., Stegun, I.A., edit., Handbook of

Leading to Bridge circuit on boat

via underwater connector� 3

Junction Box

strain gagewire conductor

cross sectional viewof measurement rod

Fio. 12 Strain Gage Circuit

Actual color code

I: black2: white3: red

Page 47: Abramowitz, M., Stegun, I.A., edit., Handbook of

196

O O O O 5tg I4

I Qll4

o ~e

O

OO O

SNOIS IAIC LHVHD

Page 48: Abramowitz, M., Stegun, I.A., edit., Handbook of

197

CD

Page 49: Abramowitz, M., Stegun, I.A., edit., Handbook of

198

Swe I I

Fig. 15 Ducted Current Meter and Base

Page 50: Abramowitz, M., Stegun, I.A., edit., Handbook of

199

Page 51: Abramowitz, M., Stegun, I.A., edit., Handbook of

200

Page 52: Abramowitz, M., Stegun, I.A., edit., Handbook of

201

~ 0.563/47 ~~o.- eeteCSLOIIPP

"xeLx1 f26ll

gZ I.a 35'

v2

4V~ ! cc.l >{>pi!Z Sec.'.

.04

7.41 . 41,38

C 1.07.3251.42

C 1.77.312.08 1. 82

37 .335P 237

'2.74 1.60.378

to .08 1.40

1.254 .04

I .IO 11.10/! S. I 4pg 6.67z! 7. IB

IC 7.55rp 784

1530,86

,Sl1.35

.37

291.94

29 28.13 7.08.26

lp 8,38 7,25.24.228- 2.44.22!.i 8.84

!!. 9. 05.21 .22

2 IS239.289. 53

212. 68

.20 .219.7 3

!a 9.94

I Q 16

2,6821

2,6822 .211,68

.21 .21510.37 2,56

23 .2310.60

!e 10.862,34

.267. 08

.31 ,39I I .17

! R 11.49

I I . 94

.34

ab'i m j

Fig. 18 Samp1e of Data Reduction Sheet 1

Page 53: Abramowitz, M., Stegun, I.A., edit., Handbook of

202

Fig. 19 Sample of Data Reduction Sheet 2

Page 54: Abramowitz, M., Stegun, I.A., edit., Handbook of

203

EJ

O dJ

O

CO

W ! A H � 0 � cv < H 0 � cvI I >+ I a I

Page 55: Abramowitz, M., Stegun, I.A., edit., Handbook of

204

l.2

C'H I.Q

0.8

0.6

0.4

0.2

0.0 0 IO 20 30 40 SO 60~ '!

Fig. 2i Variation of CH with a

Page 56: Abramowitz, M., Stegun, I.A., edit., Handbook of

205

160

I50

110

130

120

110

100

90

e 80

70

60

O 50E

4. ia

30

20 20 30 40 50 60 70 60 90 100 110 IZQ 130 110 150 160maX EstImated ib!

Fig. 22 Measured versus Estimated F ', a = 15max'

Page 57: Abramowitz, M., Stegun, I.A., edit., Handbook of

206

120

I I 0

100

90

80

70

60

50

07 40

2 0 I 0 20 30 40 SQ 60 70 80 90 100 110 120F',�Estimated Ib!

Fig. 23 Measured versus Estimated F ', e = 35max

Page 58: Abramowitz, M., Stegun, I.A., edit., Handbook of

207

I20

I I 0

IOO

90

80

7Q

60

Pn 50Q

4O

!c 300

E ao IO 20 30 40 50 60 70 80 90 IOO I lO l20F~~�Estimated ib!

Fig. 24 Measured versus Estimated F', m = 52max '

Page 59: Abramowitz, M., Stegun, I.A., edit., Handbook of

20B

OLA

ij

x- E

Page 60: Abramowitz, M., Stegun, I.A., edit., Handbook of

209

Page 61: Abramowitz, M., Stegun, I.A., edit., Handbook of

210

O CIlIU

h- x lP

E

Page 62: Abramowitz, M., Stegun, I.A., edit., Handbook of

21$

4J

.6

Page 63: Abramowitz, M., Stegun, I.A., edit., Handbook of

212

0

CD

E

Page 64: Abramowitz, M., Stegun, I.A., edit., Handbook of

213

Page 65: Abramowitz, M., Stegun, I.A., edit., Handbook of

214

Page 66: Abramowitz, M., Stegun, I.A., edit., Handbook of

215

O I 5 tljm

I4

X gy0.E

Page 67: Abramowitz, M., Stegun, I.A., edit., Handbook of

B6

OP

4P

o

l&

Page 68: Abramowitz, M., Stegun, I.A., edit., Handbook of

217

Page 69: Abramowitz, M., Stegun, I.A., edit., Handbook of

218

a

Fig. 35 Ve1ocity Profi1es with the same maximum Yeloci tyand Accel era tion

Page 70: Abramowitz, M., Stegun, I.A., edit., Handbook of

O

O

hf5-

I

4JR

lL

I

hl

U'IONCP

L.Igj

I

ClV O IN

tJVl

219

Page 71: Abramowitz, M., Stegun, I.A., edit., Handbook of

220

Page 72: Abramowitz, M., Stegun, I.A., edit., Handbook of

221

Page 73: Abramowitz, M., Stegun, I.A., edit., Handbook of

222

3 C0 P

fO

B

C/l

tJ'P $CU

E S-0

cv ~ 0

Page 74: Abramowitz, M., Stegun, I.A., edit., Handbook of

223

Page 75: Abramowitz, M., Stegun, I.A., edit., Handbook of

224

REC

R lANGLE

Fig. 4I General Flow Scheme of Subroutines

Page 76: Abramowitz, M., Stegun, I.A., edit., Handbook of

225

Fig. 42 General Flow Scheme of Triangular Integration