DESIGN BASICS
The following ratios and factors are commonly used by naval architects and boat designers to help them predict how a specific design will perform. The selected values represent those found on a typical offshore cruising boat, where safety and comfort are of primary importance.
In addition to the definitions below, plots showing how these factors relate to the database boats can be found at the Data Base Plots page.
DISP / LENGTH RATIO = disp/2240/(.01*lwl)^3 Probably the most used and best understood boat evaluation factor. Low numbers (resulting from light weight and long waterlines ) are associated with high performance and quick response. Cruising designs begin around 200 and can go up to the high 300's. Many racing boats are below 100. My approach is to start with a minimum of 230, optimal of 280 - 320, and maximum of 370. This will give us boats with a nice blend of weight (for good load carrying capability and seaworthiness) and reasonable performance. My numbers may seem high to some, but they are in agreement with the experience of many blue water sailors.
SAIL AREA / DISP RATIO = sail area/(disp/64)^.666 This is a ratio of power to weight, calculated using a 100% jib. Most monohull designs range between 16 - 18. Racers can be much higher, motor sailors lower. We want a cruiser with enough power to sail well but not so much that the crew is fatigued by constant sail changes or worried about having a fragile oversize rig. I selected 14 as the minimum, 15 - 17 optimal, and 18 maximum.
VELOCITY RATIO = 1.88*lwl^.5*sail area^.33/disp^.25 / (1.34*lwl^.5) The numerator of this equation is an empirical formula that relates high speeds to a long lwl, large sail area, and small displacement. The denominator is the traditional Hull Speed term. Their ratio is a measure of how well our ideal cruising boat will perform under sail. A well designed boat (adequate sail area and light weight hull) will have values are between 1 and 1.1. All out racing machines will be as high as 1.8. I selected 1.0 as the minimum, 1.04 - 1.08 as optimal, and 1.14 maximum. One should never under estimate the pleasure, and sometimes safety, of owning a fast boat.
CAPSIZE RISK = beam/(disp/(.9*64))^.333 A seaworthiness factor derived from the USYRU analysis of the 1979 FASTNET Race, funded by the Society of Navel Architects and Marine Engineers. Values less than 2 are good. The formula penalizes wide boats for their high inverted stability and light weight boats because of their violent response to large waves. All multi hulls, some modern coastal cruisers and many racing designs have problems meeting this criteria. Since safety is a very important feature in a cruising boat, I selected values less than 1.8 for full credit Anything over 2 scores zero.
COMFORT FACTOR = disp/(.65*(.7*lwl+.3*loa)*beam^1.33) This is 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 lots of overhang and a narrow beam. These are all factors that slow down a boats response in violent conditions, which is a major factor in reducing crew fatigue. This design philosophy is contrary to many modern racer / cruisers. A value of 30 - 40 is recommended for a cruising boat. Racing designs are typically less than 30, and a full keel, Colin Archer design, could be as high as 55. Ted’s recommendations were used for the optimal values, with a minimum of 25 and a maximum of 50.
LENGTH TO BEAM RATIO = loa / beam This ratio appears to be lower now than in older designs. Wide boats are popular today since they provide form stability and large interior volume. On the downside, excess beam contributes to poor balance, distorted heeled waterlines, and high inverted stability. Since stability and volume are not so difficult to achieve in larger boats, the L/B ratio increases with LOA. (plot of L/B Vs LOA)
ROLL PERIOD (T) = 2*PI*((disp^1.744/35.5)/(82.43*LWL*(.82*beam)^3))^.5
The roll period is based on the moment of inertia, waterline length, and beam. The moment of inertia, (disp^1.744/35.5), was developed by SNAME. Large values resist rolling forces. The moment of inertia is very sensitive to the distance items are from the CG. A heavy rig can greatly increase I, with little impact on displacement. This equation was developed to support the 1987 Fastnet race investigation. The term (.82*beam) has been substituted for the waterline beam due to lack of data. Using (.82) results in a close match for the few boats with measured periods. Simply stated, a sailboat’s roll period, in seconds, is inversely proportional to its stability. Tender boats have long periods, stiff boats have short periods. The roll period is very easy to determine, you simply grab a shroud and push / pull until the boat is rocking over a few degrees. Then measure the time it takes for ten full cycles , and divide by 10. 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 roll period is related to LOA and strongly related to COMFORT FACTOR.
ROLL ACCELERATION = (2*PI/T)^2*RADIUS*(ROLL ANGLE*PI/180)/32.2 ( units of G's)
In Marchaj's book, SEAWORTHINESS, THE FORGOTTEN FACTOR, chapter 4, "Boat Motions in a Seaway". The author presents a graph of roll acceleration ( in G's ) 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, beamy designs have G levels above .4, definitely "intolerable" for any length of time.