Formulas Computed in Yacht Design

Formulas Computed in Yacht Design

NOTE: You do NOT have to be a Naval Architect to use Yacht Design. The formulas are plotted on bar graphs making comparisons between boats easy.

Sail Area Displacement:
The Sail Area/Displacement Ratio relates sail area in square feet at 100 percent foretriangle to displacement in cubic feet raised to the two-thirds power,or SA(square feet)/((D(cubic feet)/64)^2/3). To determine displacement in cubic feet, divide the boat's displacement in pounds by 64--the weight of a cubic foot of sea water. The SA/Disp ratio provides a measure of how powerful a given sail plan is in relation to the displacement of a vessel and its associated wave making resistance. In terms of a conventional displacement boat, an SA/D figure of 12 would be considered quite low, while anything over 20 would be considered generous.

Displacement Length:
This ratio is equal to the displacement in long tons (2240 pounds) divided by 0.01 times LWL cubed. The lower the Disp/Length, the shallower the waves generated by the hull as it moves through the water and the lower the hull's wave making resistance.Disadvantages of lighter boats include reduced load-carrying ability and a less dampened motion at sea: disadvantages of heavier boats include poorer light air performance and reduced agility under sail. COMPARISON: Ultralight < 100, Light 140 to 175, Moderate 200 to 285, Heavy 300 to 350.

Hull Speed:
A basic hydrodynamic law states that the speed of a wave in knots is equal to 1.34 times the square root of the wave length in feet. Because wave speed equals boat speed, a longer waterline, which generates longer transverse waves, confers greater speed.

Motion Comfort:
The Motion Comfort ratio, created by Naval Architect Ted Brewer is computed as: displacement/(2/3 * ((7/10 * LWL) + (1/3 * LOA)) * BEAM^4/3). This relates displacement, length and size to comfort, the higher values represent greater comfort.The Length Over All is not the deciding factor, some smaller boats can have a Motion Comfort Ratio equal to their larger sisters.

Ballast Displacement:
The Ballast Displacement is a simple ratio of a boats ballast divided by its displacement expressed as a percentage.This ratio is an indication of a boats stiffness, or its ability to resist healing. A ratio of 33% is average while 40% or more is quite stiff.

Screen Number:
The Screen Number is computed by dividing the maximum beam by the cube root of displacement (lbs.) divided by 64 (weight cubic ft sea water) or beam/((weight/64))^1/3. The Screen Number was devised by The United States Yacht Racing Union and The Society of Naval Architects & Marine Engineers Joint Committee on Safety From Capsizing, June 1985.It is an indicator of a vessels ability to resist capsizing. Less then 2.0 is good coefficient for cruising yachts.