(1) DISP / LENGTH RATIO = disp./2240/(.01*lwl)^3 Dimensionless, if you ignore the constant "2240" that converts displacement from pounds to long tons. ".01" is another constant that scales the result. Probably the most used and best understood evaluation factor. Low numbers (resulting from light weight and long waterlines ) are associated with high performance. Depending on who you ask, cruising designs begin around 200 and can go up to the high 300's. Many racing designs are below 100. The general trend for new designs is towards lower ratios that favor higher performance. The trade off is that a light boat will have more violent motion in storms. This requires constant attention to steering and sail trim, resulting in crew fatigue.
(2) SAIL AREA / DISP RATIO = sail area/(disp/64)^.666 Dimensionless. "64" converts displacement. to cubic feet . This is basically a ratio of power to weight, calculated using a 100% jib. Most monohull designs range between 16 and 18. Racers can be much higher, motor sailors lower. The ratio is independent of boat length.
(3) VELOCITY RATIO = 1.88*lwl^.5*sail area^.333/disp^.25 / (HULL SPEED) Sort of dimensionless (knots/knots). The numerator of the equation calculates potential maximum speed, using an empirical relationship. Boats with a generous sailplan and light displacement will have a velocity ratio greater than 1. Under powered or extra heavy boats will be less than 1. Where HULL SPEED = 1.34*lwl^.5 and has dimensions of velocity (knots). Derived from the speed of a wave under gravity forces, but generally regarded as the highest practical velocity for a displacement boat assuming a reasonable power input (2-3 hp per ton).
(4) LOA / BEAM RATIO = loa/beam Dimensionless. This ratio measures the fineness of the hull. Fine hulls, having ratios of 3.5 - 4.0 and higher, are long and slender which promotes easy motion, high speed (due to low drag), and good balance when heeled. Many newer designs favor wider hulls which have a larger interior volume, sail flatter, and have high reaching and down wind speed potential.
(5) CAPSIZE RISK = beam/(disp/(.9*64))^.333 Dimensionless. An empirical factor derived by the USYRU after an analysis of the 1979 FASTNET Race. The study concluded that boats with values greater than 2 should not compete in ocean races, due to their high inverted stability. The formula penalizes boats with a wide beam (the most important factor in inverted stability), and light weight boats because of their violent response (low roll moment of inertia) to large waves. It does not indicate anything about static stability
(6) COMFORT FACTOR = disp/(.65*(.7*lwl+.3*loa)*beam^1.33) Dimensions of "Length" to the 2/3 power. An empirical term developed by yacht designer Ted Brewer. Large numbers indicate a smoother, more comfortable motion in a sea way. The equation favors heavy boats with some overhang and a narrow beam. These are all factors that slow down the boat's response in violent waves. Racing designs can be less than 20, and a full keel, Colin Archer design, could be as high as 60.
(7) ROLL ACCELERATION = (6.28/T)^2*RADIUS*(ROLL ANGLE*3.14/180)/32.2 Units of G's, where "T" is the ROLL PERIOD. From Marchaj's book, SEAWORTHINESS, THE FORGOTTEN FACTOR, chapter 4, "Boat Motions in a Seaway". The author presents a graph of roll acceleration Vs four physiological states; Imperceptible, Tolerable, Threshold of Malaise, and Intolerable. Malaise starts at .1 G, Intolerable begins at .18 G. Spending much time under these levels of acceleration reduces physical effectiveness and decision making ability through sleep deprivation. The radius term assumes an off center berth located 1.5 feet inboard from the maximum beam. The roll angle is 10 degrees. G levels above .06 are considered undesirable for offshore cruising conditions. Several light weight, large beam designs have G levels above .4, definitely "intolerable" for any length of time. The ROLL PERIOD is calculated from the equation: T = 6.28*( I /(82.43*LWL*(.82*beam)^3))^.5 , and has dimensions of seconds. The roll period is based on the moment of inertia, I, waterline length, and beam. The term (.82*beam) has been substituted for the waterline beam due to lack of data. The general rule of thumb is that boats with periods less than 4 seconds are stiff and periods greater than 8 seconds are tender. The MOMENT OF INERTIA is calculated from the equation: I = (disp^1.744 )/35.5 , and has dimensions of lb.ft.^2. An empirical term used by SNAME for analysis of the 1987 Fastnet race. The moment of inertia is very sensitive to the distance items are from the center of gravity. A heavy rig can greatly increase I, with little impact on displacement.
