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This page 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. -DHP

Boat Dimensions = LOA, LWL, B, Disp, etc.

Rig Dimensions = I, J, P, E, etc.

Size of Sails = LP, Area

**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

LWL/BWL = Waterline Length/Waterline Beam Ratio

WPA = Waterplane Area

WPL = Waterplane Loading

CWP = Coefficient of the Waterline Plane

itWP = Moment of Intertia of the Waterline Plane

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

LBS/IN = Pounds per inch immersion

**SOURCES:**

**Books** ( Click here for more 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

- Johnson, Peter (1971)
*Yachtsman's Guide to the Rating Rule*, Nautical Publishing Co.

- 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

- Calder, Nigel, (2001)
*Beam and Draft*, Ocean Navigator, 114: 84-88

- Calder, Nigel, (2001)
*True Displacement*, Ocean Navigator, 116: 92-100

- Calder, Nigel, (2001)
*Assesing Stability*, Ocean Navigator, 118: 74-80

- Calder, Nigel, (2004)
*Crunching the Numbers*, Sail, April 2004, Vol 35 #4:57-61

- Empacher, Dieter (1997)
*By the numbers: The significance of design ratios in describing vessel performance*, Ocean Navigator, 85: 64-66

- Gerr David (2004)
*Stable by Design*, Sail, September 2004, Vol 35 #9:68-73

- Marshall, Roger (2000)
*Shaping an Offshore Hull*, Ocean Navigator, 107: 56-63

- US Navy Web-based Naval Architecture

- Michael Kasten's Essential Design Data page

- John Holtrop's Boat Design Page

- Ted Brewer Presents A Primer on Yacht Design

- Brewer by the numbers (Good Old Boat Magazine)

- 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

- Modern Keel Design by Charles Mason

- Comparing the Ratios by Jay E. Paris

- Stability and the GZ Curve by Peter Nielsen

- In search of vanishing stability, Sail Magazine, July 1999

- Graham Radford Yacht Design, STABILITY DISCUSSION

- US Sailing Keelboat Course and Info

- NSC - Keel Boat Metrics Calculator

**Boat Dimensions ** (top)

**LOA = Length Overall**. length from stem to stern not counting projections of pulpits or spars.

**LWL = Waterline Length**. Length at Waterline when the boat is at rest.

**B = Overall Beam**. Widest part of boat

**BWL = Beam Waterline**. Widest part of boat at the waterline.

**D = Draft**. Deepest extent of hull, typically bottom distance from waterline to bottom of keel.

**Disp = Displacement**. (weight of boat), the weight of the water displced by the boat.

**Ballast**. weight of ballast

**SA = Sail Area**. Area of main and the foretriangle based on I, J, P, E dimensions.

**Rig Dimensions ** (top)

For the basic sloop there are four figures to describe the size of the rig: I, J, P and E.

**I = Foretriangle Height**. This is the distance up from the shear line (gunwale) to the top of the hoist for the highest headsail. From the IOR rule it is the highest of the following: the intersection of the headstay (or an extension of it) and the front edge of the mast (or an extension of it), the center of the eye for the spinnaker or jib halyard block. This is a little confusing (and why shouldn't it be?) and you may have hard time finding a sailmaker who can actually tell you what this dimension represents.

**J = Foretriangle Base**. This the distance from the front of the mast to the point where the headstay intersects the shear.

**P = Mainsail Hoist**. This is the distance beween the black bands on the mast.

**E = Mainsail Foot**. This is the distance beween the black bands on the boom.

Mizzen sails (on yawl or ketch) are measured as mainsails with the dimensions called PY and EY.

**Size of Sails** (top)

**LP = Luff Perpendicular**. This is a perpendicular from the luff of a sail running through the clew. This dimension is used to determine the rated percent size of a sail. The percent size of a sail is the ratio of LP/J. If the LP is 15 feet and the J is 10 feet the sail is a 150%. This does not reflect the sail size as compared to the 100% foretriangle. It does not account for luff length. Two headsails with the same LP will have the same percent size regardless of the luff lengths. One could have a luff that was half the length of the other and therefore be half the area of the other but still be the same percent size.

If the lengths of the sides of the sail are known the LP can be found from the following perimiter formula:

LP=leech*sin(2*acos(sqrt(P2*(P2-foot)/luff*leech)))

where: P2 = 1/2 perimeter = 1/2 * (luff + leech + foot)

**Area** of sails is calculated using basic triangle shapes without accounting for roach or leech hollow.

**Mainsail** area is 1/2 foot * luff or 1/2 luff * foot.

**Headsail** area is 1/2 luff * LP.

If the LP is not known the sail area can be found from the following formula that uses the perimiter:

SA=sqrt(P2*(P2-Luff)*(P2-leech)*(P2-foot)

where: P2 = 1/2 perimeter = 1/2 * (luff + leech + foot)

**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 waterline 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 sensitive to loading. 2000 lbs of gear will have a larger effect on performance for a 10,000 lb boat than 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.

**LWL/BWL = Waterline Length/Waterline Beam Ratio** (top)

LWL/B = LWL / Beam

This is the waterline length divided by the waterline beam. Waterline beam is not a commonly reported figure. A rough estimate can be made by taking 90% of the overall beam but this ratio varies with hull form.

**WPA = Waterplane Area **(top)

WPA = LWL x BWL x hull fineness factor

This formula gives an approximation. BWL can be approximated as Beam x .90 and the hull fineness factor (my term) is about 68% for fine ended sailboats and 71% for full ended sailboats (Gerr). Or, if you know the LBS/IN immersion you can work backwards to get the WPA by the formula:

LBS/IN * 12 / 64 = WPA.

**WPL = Waterplane Loading **(top)

WPL = Displacement / Waterplane Area

WPL = DISP / WPA

Waterplane Loading is the displacement divided by the waterplane area. According to David Gerr, waterplane loading is a good indicator of comfort in a seaway (See "The Nature of Boats" by David Gerr, Ch 14). The lower the waterplane loading the faster the heave acceleration for a given displacement. That means the boat will bob up and down faster and be more uncomfortable than a boat with the same displacement but a higher WPL. Consider a plank of wood on edge vs flat on the water and how it would behave in waves. The only difference between the two in the different orientations is the WPL.

**CWP = Coefficient of the Waterline Plane**(top)

CWP = WPA / LWL x BWL

The Coefficient of the Waterline Plane is the ratio of the water plane area to the rectangular area defined by the waterline length times the waterline It is basically the percentage of that area actually taken up by the hull.

**itWP = Moment of Intertia of the Waterline Plane**(top)

itWP = (CWP^{2} / 11.7) * LWL * BWL^{3}

The Moment of Intertia of the Waterline Plane is a measure of stability. It is the resistance of the boat to being rolled. The greater the Moment of Intertia and the lower the center of gravity the greater the stability (Gerr - Sail 9/04). The stability increases with the cube of the BWL so small increases in beam create large increases in stability.

**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). Any two boats will have the same CSF value if their displacement and beam are the same. One could have a light hull with 50% ballast in a bulb at the bottom of an eight foot fin, the other could have a heavy hull with 20% ballast in a 2 foot deep full length keel. The stability characteristics of the two boats will be drastically different despite the identical CSF value.

**MCR = Motion Comfort Ratio** (top)

MCR = DISP / (.65*BEAM^{4/3}(.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)

Also known as **AVS**, the angle of vanishing stability.

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. The LPS by itself is an incomplete picture of stability. The relative size of the positive to negative areas of the stability curve (a plot of righting moment vs roll angle from 0-180 degrees) should also be examined. The effects of dynamics on stability will also influence the actual performance of the boat. A heavy rig can help prevent capsizing by resisting the roll until the wave energy has passed. But it will also have a negative effect on LPS. In the 30th anniversary edition of Adlard Coles' "Heavy Weather Sailing" (Peter Bruce Ed.) they compared two 28.5 foot boats of the same class, one with a conventional rig, the other with roller furling jib and in-mast roller furling main. The LPS was 127 deg for the conventional and 96 deg for the roller equipped. The in mast roller main was likely the major component of the reduction but I would not under-estimate the effects of some of the older heavy roller furling headsail systems.

Calculating the AVS for the Pearson 10M

**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 fore 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".

**LBS/IN = Pounds per inch immersion ** (top)

This is the amount of weight added or subtracted to the boat to change the immersion by one inch. If the LBS/IN is 1000 adding 1000 lbs of gear or cheese (or feathers) will make the boat sit one inch lower in the water. If you know the waterplane area (WPA) you can find the LBS/IN by the formula:

LBS/IN = WPA * 64 / 12

Pearson Model Data Table . . .

Here are some Hewlett Packard HP-41 calculator programs I wrote for some of the design ratios and some other boat related values. These will run on any of the HP-41 series and on the HP-42. With a little modification they will run on any of the HP RPN machines. If you have a TI or some other algebraic machine you should dump it and get an HP RPN machine, they are simply the best.

SA/D and D/L

CSF

MCR

Sail area, LP and J

True wind from apparent, boat speed and heading

VMG on new heading

More HP-41 stuff...

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