Developing a Set of Lines In Ship Geometry

The development of a set of lines presupposes a tentative (or final) selection of suitable hull dimensions, coefficients, LCB, sectional area curve and design waterline. This selection is based on considerations of displacement, capacity, trim, stability, resistance and propulsion, as well as in the chapter on Mission Analysis and Basic Design, Ship Design and Construction (Taggart, 1980). Fig. below is a generalized plot whereby the offsets of a sectional area curve may be drawn to fit prescribed hull features (prismatic coefficients and LCB.) In order to use Fig. above, one enters Fig.(a) with LCB and total
C_p to get C_{PA} and C_{PF}; these are then used in Fig.(b) to find the sectional area curve offsets.

Given the desired hull characteristics, the process of drawing and fairing a preliminary small-scale set of lines generally begins with fixing the profile of the vessel in the centerplane, the design waterline and deck line in the half-breadth plan, and the midship body plan section. Intermediate sections may next be sketched in to satisfy the pre-determined sectional area curve, often by reference to previous designs and typical hull forms (SNAME Hydrodynamics Committee, 1966). A few additional waterlines, between the deck and the DWL, and between the DWL and the baseline, are then drawn in the half-breadth view using halfbreadths at the stations and making as small and as few changes as possible in these. The sections in the body plan are then changed to achieve consistency with the waterline half-breadths, and section areas checked. A few buttocks are then drawn in and checked and the process repeated. Alternatively, diagonals, rather than waterlines, are preferred by some designers as a fairing medium, and are used to check the consistency of section shape variation from station to station before buttocks and intermediate waterlines are drawn. Liberal use of the eraser is required, the drawing frequently being made on the back of transparent cross-section paper, chosen so that the grid of the paper matches the grid of waterlines, buttocks and stations desired. Because of the flatness of angle of intersection of buttocks and waterlines on narrow, finelined ships at the quarter length, it is sometimes the practice to foreshorten station spacing in the profile and half breadth plan to assist in fairing.

As the ship design progresses, one or more larger scale lines drawings must be prepared and faired with increasing precision. In the fairing process, some general guides should be remembered. For example, the general shape of buttock endings, particularly for buttocks near the ship's centerline, must reflect the shape of body plan stations, if a gradual and progressive hange of waterline slope is to be achieved.


Nine of the often conflicting considerations involved in developing a set of lines, other than those of resistance and propulsion, may be noted here:

  • (a) Generous clearances around the propeller tend to reduce vibration excitation forces, but a large diameter propeller tends to improve populsive efficiency and hence to reduce required shaft horsepower, assuming the propeller design is not restricted in RPM.
  • (b) A large amount of "fin" area aft, both fixed and movable, tends to promote directional stability. Generous movable area (rudder area) tends to improve the ability to initiate and recover from turns.
  • (c) A small bilge radius, together with a bilge keel right at the turn of the bilge, tends to increase roll damping. However, wetted surface, and hence frictional resistance, tend to be increased by a small bilge radius.
  • (d) V-sections are generally favorable to stability and seakeeping performance, but are often objectionable from the viewpoint of resistance and/or propulsion.
  • (e) Ships which must operate in heavy weather may experience slamming on the flat of bottom forward unless large deadrise angles are used and the extent of flatness is minimized. However, a long straight flat keel is desirable from drydocking considerations.
  • (/) Generous flare forward, sometimes with a gently sloped longitudinal knuckle well above the waterline, may be used instead of an increase in freeboard forward in achieving dry decks when in a seaway.
  • (g) Ships with bulbous bows may experience damage to the bulb from anchor handling unless the bow in way of the hawsepipe is flared out sufficiently to allow an unobstructed drop from the pipe extremity, taking into account the possibility of the ship's rolling to the opposite side.
  • (h) Hull surfaces composed of portions of cylinders and cones-i.e., developable surfaces are more easily fabricated than surfaces of compound curvature, but may incur added resistance.
  • (i) Excessive waterline angles forward of the propeller should be avoided, as well as blunt waterline endings, since they may promote separation in the flow, especially in the case of very full, slow-speed vessels. Such separation tends to cause propellerexcited vibration, as well as greater resistance and less efficient propulsion.
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