SYMBOLS COMMON IN NAVAL ARCHI TECTURE USED IN THIS BOOK. Area of load water plane. Sail area in square feet. Centre of effort of sail plan. Distance of centre of effort forward of centre of im mersed lateral plane. Coefficient of fineness of load water line = A LXB a b. Bilge diagonal coefficient. Bm Moulded breadth of ship. Coefficient of midship section area = ХА Bxd Centre of gravity of displacement (centre of buoyancy). Centre of gravity of displacement from aft perpendicular. Centre of gravity of ship above base. Centre of gravity of ship and engines. Moulded depth to upper deck. Displacement in tons of salt water (gross). Displacement in cubic feet (volume). Displacement in tons at load draught. Displacement in tons at light. Displacement of fore body. Displacement of after body. Coefficient of fineness of displacement (block coefficient). Freeboard from statutory deck line. Freeboard to top of rail amidship. G Coefficient of centre of gravity = H After perpendicular (after side of rudder post). Forward perpendicular (fore side of stem at upper deck). Indicates the half-length between perpendiculars and is the sign of the mid-section or "dead flat." XA. M.C. G.Z. G.M. B.M. L.M.C. G Mid-section area. Height of transverse metacentre above base. Height of transverse metacentre above centre of gravity. Longitudinal metacentre above base. Centre of gravity below L. W.L. Centre of gravity above L.W.L. Prismatic coefficient. I.H.P. Indicated horse power. . E.H.P.. Effective horse power. N.P. B.P. Length of ship between perpendiculars. W.L. Length of ship on load water line. Placed before dimensions indicates that these are the registered or tonnage dimensions. Moment of inertia of load water plane. Metacentre and moment. Moment to alter trim one inch at load line. On drawings locates the intersection of projected water line with the elevation. Centre of gravity, or moment about centre. Centre of gravity of water line. Centre of gravity of mid-section area. Centre of gravity of sail plan, or centre of effort. Common interval or abscissa between ordinates. Resistance. G, or U, Half-girth of midship section (Lloyd's). Draught of water moulded (mean). Draught of water forward Mean draught Power. Speed in knots per hour. Admiralty constant = to bottom of keel. I.H.P. Per inch; also tons per inch of immersion at L. W.L. Square inch. Algebraical Signs. :: Multiplied by. Ratio. Is to. f Functions. : So is. As (ratio). Divided by.9 Gravity. Perpendicular to. Not parallel. ... Because. ... Therefore. Angle. L Right angle. Δ Triangle. Parallelogram. Square. Circumference. Circle. k Coefficient. n Any number. A Finite difference. THE NAVAL CONSTRUCTOR CHAPTER I. DISPLACEMENT (D). THE displacement of any floating body whether it be a ship, a barrel, a log of lumber or, as in the case of the great Philosopher who first discovered its law, the human person, is simply the amount of water forced or squeezed aside by the body immersed. The Archimedian law on which it is based may be stated as : — All floating bodies on being immersed in a liquid push aside a volume of the liquid equal in weight to the weight of the body immersed. From which it will be evident that the depth to which the body will be immersed in the fluid will depend entirely on the density of the same, as for example in mercury the immersion would be very little indeed compared with salt water, and slightly less in salt water than in fresh. It is from this principle that we are enabled to arrive at the exact weight of a ship, because it is obvious that if we can determine the number of cubic feet, or volume as it is called, in the immersed body of a ship, then, knowing as we do that there are 35 cubic feet of salt water in one ton, this volume divided by 35 will equal the weight or displacement in tons of the vessel. If the vessel were of box form, this would be a simple enough matter, being merely the length by breadth by draught divided by 35, but as the immersed body is of curvilinear form, the problem resolves itself into one requiring the application of one of a number of ingenious methods of calculation, the principal ones in use being (1) The Trapezoidal Rule, (2) Simpson's Rules, and (3) Tchibyscheff's method. Simpson's First Rule. The calculation of a curvilinear area by this rule is usually defined as dividing the base into a suitable even number of equal parts, erecting perpendicular ordinates from the base to the curve, and after measuring off the lengths of these ordinates, to the sum |