Ship Geometry Primer
The ship geometry primer is meant to be a review of naval architecture terminology as well as definitions. The coverage of the primer will include:
- Coordinate systems and nomenclature
- Hull definitions and explanations
- Curves of form and equations
Coordinate systems
We will begin the coordinate system definitions by first using the right-hand rule. We define the postive x-direction as towards the bow, the positive y-direction as port, and the positive z-direction as upwards.
Coordinate System
We can also number the axes along with terms of motion:
- Longitudinal translation is surge
- Transverse translation is sway
- Vertical translation is heave (it is improperly called sinkage occasionally)
- Rotation about the x-axis is heel or roll
- Rotation about the y-axis is trim or pitch
- Rotation about the z-axis is yaw
Drawings of ships are called lines plans showing the three-dimensional ship displayed in two-dimensional cuts. The sheer plan shows the buttock lines of a ship in the x-z, or longitudinal plane as well as the sheer and draft lines on amidships.
Lines Plan
The body plan shows the sections of a ship in the x-y, or transverse, plane. Transverse sections are called stations and are numbered bow to stern, from 0 to 10, respectively. Station 5 is the length-wise middle of the hull, or amidships. By convention, the starboard side of the body plan shows stations 0 to 5. The port side of the body plan shows stations 5 to 10. The table of offsets is generated mostly from the body plan.
The half-breadth plan shows the waterlines in the y-z, or horizontal, plane.
Hull definitions
Main Dimensions
Loa (Length Overall): The total length of a boat. Normally, this excludes any sprits, but I choose to define Loa by including all fittings. To exclude these, the Lod term is used instead.
Lod (Length on Deck): The length of a boat eliminating rails, sprits, or other features which are not integral to the volume of the hull.
Lwl (Length Waterline): The longitudinal distance between the fore and aft intersections of the hull and the waterplane.
Lbp, Lpp (Length between perpendiculars): The longitudinal distance between the forward-perpendicular and the aft-perpendicular. This distance is almost always the same as LWL
Fp (Forward Perpendicular): The vertical line through the fore intersection of the stem with the waterplane
Ap (Aft Perpendicular): Commonly is the vertical line through the aft intersection of the hull with the waterplane. For a ship, this may be defined as through the rudder post.
B, Bmax (Beam): The greatest width of the hull.
Bwl (Beam Waterline): The greatest width of the hull intersecting the waterplane
T, Tmax (Draft): The maximum vertical distance between the waterplane and the deepest portion of the entire boat.
Tc (Canoe Draft): The maximum vertical distance between the waterplane and the canoe draft line.
D, Dmax (Depth) : The maximum vertical distance between the lowest point of the keel and the sheer line.
Dc (Canoe Depth) : The maximum vertical distance between the draft line and the sheer line.
Curves of Form
A sectional area curve is one of the principal methods of describing the distribution of the submerged volume of a hull. Mathematically, its symbol as a function of longitudinal position is "A(x)".
The block coefficient is a ratio between the displaced volume, V, and a rectangular prism with orthogonal distances of length, breadth, and draft. For a sail craft, I choose to use canoe volume, Lwl, Bwl, and Tc. This may be redesignated as the canoe block coefficient. The canoe block coefficient is near 0.4 for a typical yacht.
The midships coefficient, Cm, is a ratio of the midships sectional area and a rectangle of maximum breadth and draft. Again, for a sail craft, I utilize Bwl and Tc. For newer fin-keeled yachts, this value is near 0.75. However, it is much more difficult to separate the canoe body from the rest of the keel for a full-keeled yacht.
The prismatic coefficient, Cp, describes the fineness of a hull and is the ratio between block and midships coefficients. For a sailboat, this number will be as low as 0.48 for a boat designed for light winds, to 0.62 for a downwind sled.
The waterplane coefficient is the ratio between the waterplane area, Awp, and a rectangle of maximum waterline beam and length.
The vertical prismatic coefficient is the vertical equivalent to the prismatic coefficient.
The volumetric coefficient is a nondimensional form of the displacement to length ratio. It describes the fullness of a hull for a given length.
The displacement/length ratio is more commonly used for sailboats. Instead of volume (with units of cubic length), it uses displacement with units of long tons (long ton = 2240 pounds). Generally, a hull with a lower D/L ratio will have less wavemaking resistance. A D/L ratio of 100 is considered a very light hull. Typical sailboats have D/L ratios near 240. A heavy boat has a ratio over 350.
