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This article attempts to provide explanations for the basic sailboat design ratios used to compare boats with one another. Some of it is my interpretation of what I have read in the books, articles, and web pages I refer to below. I do not claim to know anything about these subjects so, as with anything you read on the internet, it's up to you to evaluate it's worth. I suggest you look at the sources I refer to, as well as additional sources, and draw your own conclusions. Email me at dan@pfeiffer.net

RATIOS:
HSPD = Hull Speed
SA/D = Sail Area Displacement Ratio
D/L = Displacement Length
BR = Ballast Ratio
L/B = Length/Beam Ratio = LOA/Beam
LWL/B = Waterline Length/Beam Ratio
OR = Overhang Ratio
CSF = Capsize Screening Formula
MCR = Motion Comfort Ratio
M/F = Main/Foretriangle Ratio
LPS = Limit of Positive Stability
Cp = Prismatic Coefficient
MT1 = Trimming Moment

Books

• Brewer, Ted (1994) Understanding Boat Design 4th Ed, International Marine
  
• Bruce, Peter (1999) Adlard Coles' Heavy Weather Sailing 30th Anniversary Ed, International Marine
  
• Chapelle, Howard I. (1967) The Search for Speed under Sail 1700-1855, WW Norton and Company
  
• Gerr David (1992) The Nature of Boats, International Marine
  
• Garrett, Ross (1996) The Symmetry of Sailing: The Physics of Sailing for Yachtsmen, Sheridan House
  
• Larsson, Lars and Rolf Eliasson (1994) Principles of Yacht Design, McGraw Hill
  
• Marchaj, C.A. (1964) Sailing Theory and Practice, Dodd, Mead & Company
  
• Marchaj, C.A. (1996) Seaworthiness: The Forgotten Factor, Adlard Coles Nautical / Tiller
  
• Marshall, Roger (1986) A Sailors Guide to Production Sailboats, Hearst Marine Books
  
• Technical Committee of the Cruising Club of America, John Rousmaniere Ed (1987) Desirable and Undesirable Characteristics of Offshore Yachts, W.W. Norton & Company
  

Articles

• Calder, Nigel, (2001) Beam and Draft, Ocean Navigator, 114: 84-88
  
• Calder, Nigel, (2001) True Displacement, Ocean Navigator, 116: 92-100
  
• Empacher, Dieter (1997) By the numbers: The significance of design ratios in describing vessel performance, Ocean Navigator, 85: 64-66
  
• Marshall, Roger (2000) Shaping an Offshore Hull, Ocean Navigator, 107: 56-63
  

Web Sites

• John Holtrop's Boat Design Page
  
• Ted Brewer Presents A Primer on Yacht Design
• Performance Cruising Parameters by Rodney S. Johnstone (J/Boat Designer)
• Explanation of D/L and SA/D by Joel White, N.A. June 1997
  
• Doug Axtell's Bristol Yachts Page
  
• Carl's Sailing Calculator
  

HSPD = Hull Speed (top)
HSPD = SQRT(LWL)*1.34
This is the theoretical hull speed for a displacement hull (like most sail boats). It is a function of the length of the wave created by the boat as it moves through the water. Wave speed is a function of wavelength, longer wavelength is faster. Longer boats make longer waves. Since longer waves are faster boats that make longer waves are faster [Garrett]. The hull speed may not be as precise a figure as the formula leads you to believe (1.34 sounds pretty precise doesn't it?). LWL is not static. As the boat heels it can increase. Older racing boats with long overhangs used this to get some extra un-measured LWL to beat the rating rules of the day. As the boat goes faster the bow and stern are immersed deeper in the wave made by the boat. This also increases waterline. In the 19th century sailing ship speeds were often expressed with a hull speed factor. A ship might have a speed factor of 1.17, meaning it can make a speed of 1.17 x sqrt(lwl) [Chapelle]. There are conditions where you can exceed the theoretical hull speed. Surfing down a wave for example. I have had my boat (LWL=21.6 feet, HSPD=6.25) surfing at 10 knots on waves. When surfing or planing the hull is not in a displacement mode. So hull speed may be a bit of a moving target.

SA/D = Sail Area Displacement Ratio (top)
SA/D = SA / (Disp/64)2/3 [ HP-41 Program ]
This ratio is an indicator of how much sail area a boat has relative to it's displacement. A boat with a higher value will accelerate faster and get to hull speed with less wind. All else being equal, the boat with the higher SA/D will be a better light air performer. This is basically a power to weight measure.

D/L = Displacement Length (top)
D/L = (Disp/2240)/(0.01*LWL)3 [ HP-41 Program ]
The displacement length ratio is a measure of a boat's speed potential. For displacement boats (most sailboats), speed potential is a function of waterline length (unless your planing or surfing down a wave). Longer water line boats can go faster. Lighter boats accelerate faster and reach hull speed with less wind. All else being equal, the boat with the lower D/L will be a better light air performer. Lower displacement will also make a boat more sensative to loading. 2000 lbs of gear will have a larger effect on performance for a 10,000 lb boat then for a 20,000 lb boat.

These two ratios together (SA/D & D/L) can give a good comparison of two boats speed potential relative to one another (all other things being equal of course). If boat A has a SA/D of 19 and a DL of 230, and boat B has a SA/D of 16 and a DL of 230, boat A will probably be a better light air boat. As the wind pipes up boat A will probably be shortening sail before boat B and the effective SA/D may then be the same. Boat A's advantage will then disappear. However, speed potential is not all there is to performance.

BR = ballast ratio (top)
BR = Ballast/Disp
The ballast ratio is a measure of the percentage of a boats displacement taken up by ballast. It can give some indication of how stiff or tender a boat may be. Note that it takes no account of the location of the ballast or of the hull shape of the boat. Two boats can have the same ballast ratios with very different righting moments. If the hulls are the same, boat A with all it's ballast in a bulb at the bottom of the keel will be stiffer then boat B with a long shoal draft keel even though they may have the same BR. Racing boats tend to have higher BR's then cruising boats.

L/B = Length/Beam Ratio (top)
L/B = LOA/Beam
This is simply the length overall divided by the beam.

LWL/B = Waterline Length/Beam Ratio (top)
LWL/B = LWL/Beam
This is the waterline length divided by the overall beam. All other factors being equal (of course they never are) the longer boat will be faster (in displacement mode, not planing/surfing). Waterline beam might be interesting to know but it is not a commonly reported figure.

OR = Overhang Ratio = (Overall Length - Waterline Length) / Waterline Length (top)
OR = (LOA-LWL)/LOA
This is the overall length minus the waterline length divided by the overall length. A larger value indicates longer overhangs. A value of 0 would mean no overhangs. Boats with longer overhangs have more reserve buoyancy. Also, as a boat moves faster the bow and stern waves move to the ends of the boat. Longer overhangs let the waves get longer. The overhang ratio has been influenced by rating rules. Under rules that penalize LWL more then LOA longer overhangs developed. The IMS rule has lead to shorter overhangs. Moderate overhangs are considered by some to be good for ocean voyaging boats. The reserve buoyancy helps keep the bow from submerging in waves and helps reduce pitching.

CSF = Capsize Screening Formula (top)
CSF = Beam/(Disp/64.2)1/3 [ HP-41 Program ]
The capsize screening formula is a somewhat controversial figure. It came into being after the 1979 Fastnet race in England where a storm shredded the race fleet. The Cruising Club of America (CCA) put together a technical committee that analyzed race boat data. They came up with this formula to compare boats based on readily available data. A lower value is supposed to indicate a boat is less likely to capsize. a value of 2 is taken as a cut off for acceptable to certain race committees. However this is an arbitrary cutoff based on the performance of boats in the '79 Fastnet. The CSF takes no account of hull shape or ballast location. The CCA characterizes the formula as "rough". They go on to say that "While the capsize screening formula places a limit on excess beam, which is important for good stability range, it does not control for another main determinant, ballasting. With only simple data, this is as far as we can go." Naval Architect Robert Perry calls it,"...far too simplistic to be always accurate, but it is one of the currently popular ways of looking at a boat's offshore suitability." (Sailing Magazine, Nov. 2001, p.44).

MCR = Motion Comfort Ratio (top)
MCR = DISP / (.65*BEAM4/3(.7*LWL+.3*LOA)) [ HP-41 Program ]
This ratio was invented by Ted Brewer who say's he dreamed it up "tongue in cheek" as a measure of the motion comfort of a boat. A boat that has a more corky motion is considered less comfortable then one less affected by wave action. A higher value is better (if you like comfort). Smaller and beamier boats tend to have a lower ratio. This is best used to compare boats of similar size. A 26 footer should probably not be compared to a 40 footer using this ratio. The ratio is a factor of LOA and LWL and it may assume that boats with long overhangs tend to have wineglass shaped cross sections which provide more gradual buoyancy as they are immersed. However, a boat like a Valiant 42 has a long LWL for it's LOA and possesses this more wineglass shaped cross section. The ratio also favors displacement (higher gives larger result) and there is no accounting for distribution of weight. It also takes no account of waterline beam, a value that can be quite informative but is rarely available on stat sheets.

M/F = Main/Foretriangle Ratio (top)
M/F = mainsail area / 100% foretriangle area
I made this up to compare the size of the main to the foretriange. This doesn't really tell you anything about the performance characteristics of a boat but it might tell you about relative ease of sail handling for similar sized boats. A higher value means the main is larger in proportion to the standard sail area. This has changed back and forth over the years. The Pearson Triton (mid 60's) had a large mainsail, the P30 (mid 70's) had a small one. These days a lot of boats are going back to large main sails (e.g. J/32). My P26 has a little main sail and I sometimes think of it as a trim tab for the big genoa.

LPS = Limit of Positive Stability (top)
The limit of Positive stability (LPS) is the roll angle at which a boat will no longer right itself and become inverted (capsized). If a boat with an LPS of 120 degrees rolls past this point it will continue to roll and become inverted. The LPS is a static measure of stability and is calculated from the geometric relationship between the center of gravity (CG), the center of buoyancy (which moves as the boat rolls) and the metecentric height (GM). It is a complicated calculation made by naval architects. Typical sailboats produced from the early 70's on have LPS's in the 100-120 degree range. Designs typical of the 30's and 40's (e.g. many Alden designs) have LPS in the 160 degree range. The Offshore Racing Council (ORC) measures LPS for IMS ratings and requires a minimum of 120 degrees for participation in offshore races.

Cp = Prismatic Coefficient (top)
Cp = (displacement / 64) / (midship area x LWL)
The Prismatic Coefficient is the ratio between the actual underwater volume of the boat and an imaginary prism made from the midship section area x the LWL. That's the volume the boat would have if it didn't taper for and aft of the largest cross section area. Displacement hulls require a Cp between .51 and .56 for best efficiency with .54 as the optimum(Gerr). The Cp is a measure of the fineness of the ends of the boat. A block of wood would have a Cp of 1. High speed planing boats have Cp in the 0.72 to 0.78 range because they carry the max midship area all the way aft to provide a large planing surface.

MT1 = Trimming Moment (top)
The trimming moment is the moment in foot*lbs required to change the vessel trim by 1". If the value is 1000 ft*lbs it takes 100lbs at 10 feet from the CG to change the trim by 1".