Motions of Small Boats Moored in Standing WavesA study was conducted to determine the dynamic characteristics of small boats moored with non-linear-elastic lines in an asymmetrical manner. The motions being considered are surge motions where the moored boat is allowed to move either in the direction of the bow or the stern, but not in other coordinate directions. An analytical model is proposed where the small boat is simulated by a block-body which is moored asymmetrically to a fixed dock. A method is developed from which the nonlinear restoring forces and the dynamic response of the boat in surge can be obtained. (Author Modified Abstract). |
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24 foot-8 inch 25 foot Moored 33 foot a₁ approximately asymmetrical restoring forces block body boat displacement boat in surge boat motions bow lines breaking strength determined dimensions displaced weight Division 1 ATTN elastic characteristics Engineering Division Engrg feet foot Moored Boat foot-5 inch Moored forcing function free oscillation free travel ft/sec Harbor Boat important wave periods inch Moored Boat Inches Slack length Library Linear Springs MANILA ROPE Marina del Rey max ft MAXIMUM MOTION moored body mooring lines mooring system MOTION FROM AT-REST-POSITION MOTION TOWARD BOW MOTION TOWARD STERN negative x-direction nylon obtained particle acceleration period of oscillation periods of free pontoon Predicted Restoring Force presented in Fig Raichlen range of wave Response Curve Section shown in Fig small boat moored small craft harbor standing wave stern lines STERN MOTION surge motions taut lines Tollycraft U. S. Army Univ variation vessel
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Page 157 - Navig. Congr., London, July 1957, pp. 205-227. = 6. O'Brien, JT and Kuchenreuther, DI; "Forces Induced on a Large Vessel by Surge," Proc. ASCE, v. 84 (WW 2), Mar. 1957, 29 pp. 7. O'Brien, JT and Kuchenreuther, DI; "Forces Induced by Waves on the Moored USS Norton Sound (AVM-1)", Tech. Memo. M-129, US Nav.
Page 157 - ... Study of the Movement of Moored Ships Subjected to Wave Action": Proceedings of the Institution of Civil Engineers, Vol. 12. Wendel, K. (1956). "Hydrodynamic Masses and Hydrodynamic Moments of Inertia": The David Taylor Model Basin, Translation 260. Wiegel, RL , Dilley, RA, and Williams, JB (1959). "Model Study of Mooring Forces of Docked Ships": Journal of Waterways and Harbors Division, ASCE, Vol. 85, WW2~!
Page 157 - Ship Response to Range Action in Harbor Basins,* Trans. ASCE, v. 116, 1951, pp. 1129-1157. 3. Abramson, HN and Wilson, BW; "A Further Analysis of the Longitudinal Response of Moored Vessels to Sea Oscillations,
Page 5 - ... mooring systems used by a number of large vessels. In general those systems consisted of a large number of lines extending from the bow, the stern, and the midship of the vessel to the dock which restrict motion both in the fore and aft direction as well as in the direction perpendicular to the dock. Even though the elastic characteristics of the individual mooring lines may be quite different from one another, on the average the restoring force for motion in the fore and aft direction for similar...
Page 82 - ... Some of the complexities of the problem can be seen from Fig. 2 which compares the maximum motion (in one direction only) of the boat as a function of wave period and the forcing function £ for taut mooring lines and for 8 in. slack. C is a rather complicated function, and Raichlen describes it as the maximum with respect to time of the water particle velocity averaged over the displaced volume of the moored body. All other things being equal, C i» directly proportional to the standing wave...
Page 11 - ... For a more complete development of the basic equation of motion the interested reader is referred to Wilson (1958), Kilner (I960), and Raichlen (1965). The block body is a rectangular parallelepiped of length 2L, beam B, and draft D moored in a way such that the only allowable motions are in surge. The standing wave is formed in water of a constant depth d by a progressive wave which is reflected from a perfectly reflecting surface located a distance b from the center of the moored body. The...
Page 7 - ... evident that the restoring force for motion in one direction may be quite different from the restoring force for similar displacements in the opposite direction. This asymmetry can have a significant effect upon the motion of the boat and potential boat damage. For instance, if a boat is moored in the slip with little clearance between the bow of the boat and the front of the slip, impact damage to the bow may be possible due to the asymmetrical restoring forces. This type of damage possibly...
Page 9 - ... perhaps be neglected for large vessels. THEORETICAL CONSIDERATIONS An analysis is presented in this section which describes the motions of a moored body in surge when exposed to a standing wave system. The mooring system used in the analytical model can result in non-linear asymmetrical restoring forces which resist the wave-induced motions. Only surge motions (boat displacements either toward the bow or toward the stern) are considered, and the boat is treated as a block body with no attempt...
Page 84 - backbone" curves, £ = 0, correspond to the case of free oscillation and are the same as those shown in Fig. 9. These examples demonstrate that simple changes in the mooring system can have a profound effect upon the dynamics of the moored boat. For instance, the motions induced by storm waves (8 sec. to 12 sec. periods) for the boats moored with 8 in. of slack in the lines are approximately five to six times greater than those for the boat moored with taut lines. Where one mooring arrangement may...
Page 41 - The method of approach used in determining the variation of the restoring force with the displacement of the boat in the direction of either the bow or the stern follows directly from Eqs. 17 and 18. For a given displacement the component tensions, T* , computed from Eq. 18 and the corresponding repeating this procedure until the restoring force vs.