sailboat righting moment

Righting moment = W X GZ.
Where: W = displacement in tons (2,240 pounds).
GZ = righting arm in feet.

There are certain factors which may cause either W or GZ to vary. It is the purpose of this discussion to consider some of these variations, and to develop a method of describing a ship's total stability characteristics.

If the angle of heel is small, the metacenter may be regarded as being fixed. In this case a triangle is formed, whose sides are GM, GZ, and the line of action of the buoyant force (triangle GZM in fig. 4-1), in which the apex angle (GMZ) is the angle of heel. The angle

For convenience, designate the angle of heel (GMZ) by the Greek letter θ. Then the relation between metacentric height and righting arm for small angles may be expressed as:

GZ = GM X sin θ.
But, righting moment = W X GZ.
Therefore, righting moment = W X GM X sin θ.

In other words, righting moment equals displacement times metacentric height times the sine of the angle of heel. As the ship rolls, W remains constant. If it does not roll more than about 10° from the upright, GM remains practically constant. Initial stability consists of these two constants (GM and W) times a ratio called the sine of an angle. Consulting a table of sines will reveal that as the angle gets larger, the sine increases. Consequently, as the ship heels farther the righting moment gets larger.

In view of the fact that stability varies with the angle of inclination, it is necessary to express stability at greater angles of heel in terms of a series of righting moments for successive angles of heel. With displacement (W) remaining constant as the ship rolls, the righting may be used instead of moments, bearing in mind that the moment can always be readily obtained if one multiplies the arm by displacement.

Using graphic means, it is possible for a design activity to determine the distance GZ for any given angle of heel. A series of values of GZ for successive

Figure 4-2 is a typical curve of stability in which a series of righting arms is plotted vertically against corresponding angles of heel which are plotted horizontally. This curve indicates that initial stability increases with angle of heel at almost a constant rate, but at larger angles the increase in GZ begins to level off. Then GZ gradually diminishes, finally becoming zero when the ship is almost on her beam ends.

When weight is added to a ship, displacement and draft are increased at the expense of reserve buoyancy and freeboard. One result of this is a reduction in righting as shown in figure 4-4. Another result is a change in righting moments due to increasing W in the expression: righting moment = W X GZ. Although both of these variations always occur simultaneously, they are due to independent causes, and must be considered separately. The gain in W does not necessarily compensate for the loss in GZ when weight is increased.

1. Increased due to gain in .
2. Decreased due to loss of .

There is a third factor to be considered later, which usually follows a change in displacement; namely, a shift in the center of gravity.

. The design activity inclines the line drawing of the ship at a given angle, and then draws on it a series of waterlines. These waterlines are chosen at evenly spaced drafts throughout the probable range of displacements. With each waterline inclined at the given angle, the center of buoyancy for this waterline can be located by graphic means, as well as the line of action of the buoyant force. The center of gravity of the ship is assumed at a fixed point called the , and the righting arm is now the perpendicular distance from the axis to the buoyant force.

Figure 4-5 depicts the midship section of a ship inclined at a fixed angle, with the axis assumed at point A. The lines of buoyant force are sketched in for successive drafts. It is evident that the righting arm successively decreases as freeboard is lost, ranging from AZ at the 10-foot waterline down to AZ at the 24-foot waterline. The actual determination of AZ in the drafting room involves complicated graphic

Plotting all the cross-curves to the same scale on one sheet facilitates their use in obtaining stability curves, as described in Article 4-6. The entire set of cross-curves is based upon the assumption that the ship's center of gravity lies in the centerline plane and is located at point A. The axis A is chosen at a round number of feet above the keel, and for reasons to be demonstrated later, is usually chosen below any actual location of G for the conditions of loading in which the ship is to operate.

It is noteworthy that the Z end of AZ is accurately and correctly determined in the cross-curves, but that

The cross curves are used for the purpose of finding a curve of stability for the ship at any required displacement. This is done by drawing a vertical line on the cross-curve sheet at the given displacement. At the intersection of this line with the 10° cross-curve, read the value of the righting arm (on the scale at the left in fig. 4-6). Plot this righting arm at 10° on the grid of the proposed stability curve. Repeat the process for 20°, 30°, etc., until a series of 9 points is plotted on the grid. Now fair a smooth line through these points from 0° to 90°, forming the required curve of stability.

For example, suppose that a stability curve for 11,500 tons displacement is to be taken from the cross-curves of U.S.S. MIDDLETOWN, and plotted on the grid in figure 4-7. First, draw a vertical line, MN in figure 4-6, at 11,500 tons. At point (a) on this line the righting arm is found to be 1.4 feet, as read on the scale at the left. Plot 1.4 at 10°, establishing point ( ) on figure 4-7. Now find the righting arm at point ( ) in figure 4-6, as 2.8, and plot this value at 20° to establish point ( ) in figure 4-7. In this manner points ( ) through ( ) are obtained in figure 4-7, and they correspond to points ( ) through ( )

Any stability curve that is taken from the cross-curves in the above manner is said to be "uncorrected;" that is, not corrected for the actual height of the ship's center of gravity above the keel. It does, however, embody the effect on righting arm of the freeboard for a given position of the center of gravity. The method of correction for KG, the actual height of G above the base line, is presented in Article 6-4.

A comparison of cross-curves and stability curves is effected in the three-dimensional representation of a surface obtained by plotting displacements in one dimension, angles of heel in a second, and righting arms in the third dimension as shown in figure 4-8.

The two types of curves may be compared as follows:

1. :

Vertical values are righting arms.
Horizontal values are displacements.
Successive curves are for different angles of heel.

2. :

Vertical values are righting arms.
Horizontal values are angles of heel.
Successive curves are for different displacements.

A more simple method than re-plotting can be used to convert any curve of righting arms to a curve of righting moments. Merely multiply each figure in the scale at the left by the proper value of displacement.

WARNING: if two or more GZ curves for different displacements are plotted on the same grid, they can NOT be converted to a group of righting-moment curves by changing the scale at the left. In such a case, it is necessary to choose a new scale of foot tons and replot all the curves, multiplying each of them by its own proper displacement.

A curve of static stability is either a curve of righting

To find the righting moment (or arm) at a given angle of heel on the stability curve, enter the horizontal scale at the required angle, proceed vertically upward to the curve, and then proceed horizontally and read the righting moment

Three important properties of any curve of stability are now evident (see fig. 4-11):

2. The angle at which the maximum righting moment (or arm) occurs, A.

3. The range of stability, 0C.

The curves of stability thus far presented apply only to the intact ship; their properties affect the ship's rolling characteristics, but do apply to a vessel which has taken on a permanent list. The latter case is to be dealt with later.

is defined as the amount of work done in inclining a ship to a given angle. This work is done against the righting moment, and is done by some type of inclining moment. From physics we know that work is equal to moment times the angle through which the moment acts. Inspection of a righting-moment curve shows that any area on it represents work, since an area on the graph is a moment (measured vertically) times an angle (measured horizontally). Furthermore, the area under the curve up to any angle of heel represents the work done in inclining the ship to that angle of

When the rolling ship passes through a specified angle of heel, (such as 25° in the example) the dynamic stability represented by the shaded area also represents the amount of energy that was stored in the vessel in process of inclining it from an even keel to the given angle, and this energy will be available to return the ship to an even keel after the cause of the inclination is removed.

The total dynamic stability is the total amount of work that would have to be done on a ship to capsize it, and is therefore represented by the area under the righting-moment curve for the entire range of stability, as indicated by the shaded area shown in figure 4-13.

If the scale of degrees were converted to angles in

Since any stability curve can he converted to a righting-moment curve by multiplying every ordinate by the displacement for which it was plotted, it is also possible to regard areas under the righting-arm curve as indicative of dynamic stability, in a similar manner to that described above for righting-moment curves.

The direction in which the curve starts out from the origin depends on GM. If GM is large the curve is steep; if GM is small the curve starts out flat. To determine GM from a righting-arm curve, draw a tangent to the curve at the origin, and a vertical line at 57.3° angle of heel. The height of the intersection of these two lines is the value of GM and may be read on the righting-arm scale.

To find the GM of the curve in figure 4-14:

1. Draw a tangent to the curve at the origin (OD).
2. Erect a vertical line at 57.3° (AD).
3. Read GM (4.1 feet) on righting-arm scale (E).

In using this method of finding GM on a curve of righting moments, it is necessary to convert the scale at the left to righting arms.

The term embraces all factors which define the ship's transverse stability. The factors which constitute the stability characteristics can be found on that curve of stability which applies to the condition in which the ship is operating. These factors are:

1. Metacentric height (GM).
2. Maximum righting arm (moment).

All the properties of the stability curve are interrelated. It is difficult to alter one of the above factors without affecting all the others, yet no one of them in itself serves as a complete criterion of stability. Rather, it is necessary to have a composite of the five factors listed above as a general index of the ship's ability to resist capsizing.

There are certain properties of a ship, and of the loading within the ship, which if altered, produce a change in stability characteristics. These properties are:

1. Draft (displacement, freeboard).
2. Vertical height of ship's center of gravity.
3. Athwartship location of the center of gravity.
4. Free surface effect.
5. Free communication effect.
6. Trim.

The effects of draft, (displacement or freeboard) have been discussed in this Chapter. The effect of the vertical height and athwartship location of the center of gravity will be analyzed in Chapters VI and VII. Chapter VIII will be concerned with free surface and free communication effects of liquids within the ship. In Chapter X, the influence of trim on transverse stability will he discussed briefly. Finally, specific cases summarizing all seven characteristics will be analyzed under the subject of "Impaired Stability" in Chapter XIII.

both when the ship is in the design phase, and after it is completed. The designer must forecast the position of G in order to provide the ship with adequate stability.

The designer uses calculations to

Using the best available data, the vertical position of G is calculated by totaling the weight and vertical moments of the various items concerned. The sum of the moments divided by the total weight of the ship gives the vertical position of G.

Since it is necessary to estimate many of the weights and their locations, the value obtained is only approximate. Moreover, as the ship progresses through the different stages of design and construction, alterations of various magnitudes further reduce the accuracy of the calculation. Nevertheless, this approximate determination of G is necessary; limitations to its use are realized by the designers.

Although the position of the center of gravity as estimated by calculation is sufficient for design purposes, an accurate determination thereof is requisite to computation of the ship's stability. Therefore, an inclining experiment is performed to obtain a precise measurement of KG, the vertical height of G above the keel (base line).

The inclining experiment actually measures meta-centric height (GM) accurately. But if the ship's draft is known, KM can be found on one of the curves of form prepared from the ship's lines: the KM curve. The KG = KM - GM (see fig. 5-2A).

. An inclining experiment consists of moving one or more large weights across the ship and measuring the angle

GM = ( X d) / ((W + ) X tan θ),

Where:

= inclining weight in tons.
= distance weight moved athwartship in feet.
W = displacement of ship in tons.
θ = angle of list.

Tangent θ = /L.

Certain preparations must be made in anticipation of the experiment. The Navy yard or building yard at which it is to be carried out issues a memorandum to the Commanding Officer of the ship outlining the necessary work to be done by ship's force and the yard in order to prepare the ship for inclining. The more important items are listed below:

1. Ship to have no list.
2. Ship to be brought to a condition of minimum trim.
3. Bilges to be dry.
4. Liquid in fuel-oil and water tanks to be in accordance with instructions of the memorandum.
5. Inventory of all consumables to be made by ship's force and inclining party.

Except for necessary watches, the ship's force is put ashore during the performance of the experiment. The inclining party does the actual work involved, and collects data for the calculations. If the ship has excessive trim during the inclining experiment, a correction for this factor is made before KG is computed.

. The KG obtained from the inclining experiment is accurate for the particular condition of loading that obtained when the ship was inclined. This is known as Condition I, or the . The ship may have been in any condition of loading at the time of the experiment, and this may not have been an operating condition. In order to convert the data thus obtained to practical use, KG must be determined for operating conditions. The method employed in calculating KG for other conditions of loading is set forth in Chapter IX.

The accuracy of data obtained in the inclining experiment depends, of course, upon complete and careful cooperation by members of the ship's force and the inclining party. Any indifference or lack of cooperation usually will give rise to undependable results.

A check, or unofficial inclining experiment, may subsequently be performed. The method for doing this is outlined in Appendix A. Such an experiment may also prove useful after damage that has resulted in flooding, or in cases involving heavy emergency topside loading.

Information obtained guides BuShips in decisions about proposed alterations, and in making recommendations as to loading and ballasting. It also provides data on the stability of a given vessel.

If one weight in a system of weights is moved, the center of gravity of the whole system moves along a path . Moreover, the distance that the center of gravity of the system moves may be calculated from the formula:

GG = / W.

Where:

= component weight (tons).
= distance component weight is moved (feet).
W = weight of entire system (tons).
GG = shift in center of gravity of system (feet).

Weight movements in a ship can take place in three possible directions - athwartship, fore-and-aft, and vertically (perpendicular to the decks). The most general type of movement is, of course, inclined with respect to all three of these. Such a diagonal movement can be divided into components in each of the three directions; and one component can be studied at a time without reference to the others. For example, if a weight is to be moved from the hold on the starboard bow to the main deck on the port quarter, this movement may be regarded as taking place in three steps:

Throughout this text, reference to locations, directions, and movements are always made with respect to the ship, not with respect to space. Further, directions and measurements are based on even-keel conditions. For example, a "vertical" distance of seven feet means that the seven-foot distance is measured perpendicular to the base line. If it is stated that the depth of water in a compartment is four feet, the meaning is that if the ship were upright, with no list and no trim, the average depth of water in that compartment would measure four feet from surface to deck.

) due to relocation of .

Fore-and-aft weight shifts are discussed in Chapter X. It is now proposed to study how vertical and athwartship relocations of weight influence the of the ship.

. Assume that a weight of iv tons is moved straight up from the second

GG = /W.

GG = vertical rise of G (feet).
= weight moved up (tons).
= vertical shift of w (feet).
W = displacement of ship (tons).

:

The U.S.S. MIDDLETOWN is operating with a displacement of 11,500 tons. Her ammunition totals 670 tons. Find the rise in G if all ammunition is moved from the magazines to the main deck, a distance of 36 feet.

:

GG = (670 X 36)/ 11,500 = 2.1 feet.

Moving a weight which is already aboard the ship will cause no change in displacement. Consequently, there can be no change in M, the metacenter. If M remains fixed, then the upward movement of the center of gravity results in a loss of metacentric height. Expressed mathematically:

G M = GM - GG
G M = new metacentric height (feet).

The terms "new" and "old" are used to indicate before the weight movement and after the weight movement respectively. With the weight now on the main deck, moving it to the second platform would reverse the positions of G and G . The shift in G would be found from the same formula as before, the only difference being that GG now becomes a in metacentric height, instead of a loss.

If the U.S.S. MIDDLETOWN's GM was 3.7 feet before the weight was moved in problem 1, what is her GM afterward?

G M = 3.7 - 2.1 = 1.6 feet.

A vertical shift in the ship's center of gravity changes every righting arm throughout the entire range of stability. If the ship is at any angle of heel, such as θ in Figure 6-2, then the righting arm is GZ with the center of gravity at G. But if the center of gravity shifts to G , the righting arm becomes G Z . And G Z is smaller than GZ by an amount GR. In the right-triangle GRG , the angle of heel is at G , so that by trigonometry the loss of righting arm may be found from:

GR = GG X sin θ.

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• Measurements

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Stability measurements give important hydrostatic and stability data necessary for determining elements of both performance and safety. The results of a stability test gives a boat's righting moment, vertical centre of gravity (VCG) and limit of positive stability (LPS), which with the Stability Index (SI) can help determine a boat's eligibility to enter races categorized according to the WS Offshore Special Regulations.

Freeboard measurements give a boat's waterline in measurement trim from which displacement, wetted surface and overhangs are calculated from the hull shape defined in the offset filet. Freeboards are measured at freeboard points identified in the hull offset file together with specific gravity of the water that equalize displacement calculation for boats measured in fresh water with those measured at the sea.

Inclining test

An inclining test is performed on a boat in measurement trim while floating in calm water and not affected on any side by lying to a mooring, and with no one aboard.   

• Two poles are simultaneously positioned on port and starboard sides, at defined position (approximately at the longitudinal centre of flotation)
• The poles are suspended outboard to provide arms for supporting weights and arranged to be perpendicular to the boat’s centreline and as horizontal as possible but still allowing sufficient clearance to prevent the weights from touching the water.
• Either a manometer or an ORC-approved electronic inclinometer is placed on the deck and positioned athwart the boat where it can be read by the measurer.
• Weights, depending on the size of the boat, are suspended on one the pole on port side and resulting heel angle is recorded.
• Half of total weight is suspended at the same time on the port in starboard sides so that the total distance between weights can be measured.
• All weights are then suspended on starboard side and resulting heel angle is recorded again.

Alternatively to the procedure defined above and particularly on boats that would require heavier weights to be suspended, a boat’s boom may be used to suspend weights as follows:           

• The boom is placed outboard and fixed to the shrouds.
• Heel angle without weights is be recorded either with a manometer or an ORC-approved electronic inclinometer
• Weights are suspended on the end of the boom and resulting angle recorded again either with a manometer or an ORC-approved electronic inclinometer.
• Same procedure is repeated on port and starboard sides, averaging the results
• Longitudinal position of the weight and distance from the boat’s centerline is measured on both sides.

From the resulting heel angle, the amount of weight and the distance between weights it is possible to calculate the position of the vertical centre of gravity and the complete set of hydrostatic and stability data for the boat. A stability curve can then be calculated showing the righting arm against heel angle. The important point on that curve is the angle when the righting arm is equal to 0, called LPS (limit of positive stability) or AVS (angle of vanishing stability). This means that if the boat is heeled at that angle from an upright position it will still return to being upright, while beyond this angle the boat will capsize.

For boats with a canting keel, an inclining test is performed with the keel on centerline. After the keel is fully-canted the resulting heel is recorded so that the effect of the canting keel on the boat's stability can be calculated.

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• Prismatic Coefficient

Understanding the Prismatic Coefficient in Yacht Design

So, what exactly is the Prismatic Coefficient (or Block Coefficient as it's also known) and why do sailboat designers get so involved with it?

Well, hull drag and wave-making resistance isn't only a function of length and surface area; the shapes of the immersed fore and aft hull sections have an influence upon it too.

What is actually crucial is the rate of change of the cross-sectional areas of the hull.

A boat whose hull changes slowly will slip through the water easier and generate less wavemaking resistance than a hull with a rapid rate of change.

This is where the prismatic coefficient comes in; it's a measure of how quickly the cross-sectional area changes, or in sailing parlance, of how full or fine the ends are.

The coefficient is defined as  'the ratio of the immersed volume to the volume of a prism with its length equal to the waterline length and cross-sectional area equal to the maximum cross-sectional area'  and is quantified as:~

Prismatic Coefficient (Cp) = V/(AxL)

V is the immersed volume of the hull in cubic feet

A is the maximum cross-sectional area in square feet.

L is the waterline length in feet.

The Cp thus indicates the longitudinal distribution of the underwater volume of a yacht's hull.

• A low (fine) Cp indicates a hull with fine ends.
• A large (full) Cp indicates a hull with relatively full ends.

But it doesn't end there...

The American Admiral David W Taylor discovered while working on warship design during the 1st World War that, for every speed/length ratio, there's an optimum Cp, as follows:

So for a displacement boat sailing at its maximum Speed/Length Ratio of 1.34, the optimum Cp is 0.63. But in light conditions most boats won't achieve anything like their hull speed, and so would be punished in these conditions by a Cp optimized for hull speed.

And herein lays the designer's dilemma, as his creation will sometimes be nudging along gently in light airs and at others blasting along at hull speed or beyond. Knowledge of the predominating conditions in the area that the boat is to be sailed will help him select the Cp.

It's something of a black art, based on technical knowledge and empirical guesswork - and having made his decision, he's likely to keep it very close to his chest.

For more on Cp and other design ratios, take a look at General Hull Form Equations...

Any Questions?

Why is the prismatic coefficient important for yacht hull design?

The prismatic coefficient affects the resistance and performance of the yacht at different speeds. A low Cp indicates a hull with fine ends that has less wavemaking resistance at low speeds, but also less buoyancy and power potential at high speeds. A high Cp indicates a hull with full ends that has more wavemaking resistance at low speeds, but also more buoyancy and power potential at high speeds.

What is the optimum prismatic coefficient for a yacht hull?

There is no single optimum prismatic coefficient for a yacht hull, as it depends on the intended speed range, displacement, length, and seakeeping characteristics of the yacht. However, there are some general guidelines based on empirical data and naval architecture theory. For example, for displacement yachts sailing at their maximum speed/length ratio of 1.34, the optimum Cp is around 0.63. For semi-displacement yachts sailing at speed/length ratios between 0.6 and 1.1, the optimum Cp ranges from 0.63 to 0.68. For planing yachts sailing at speed/length ratios above 1.1, the optimum Cp ranges from 0.68 to 0.76.

How does the prismatic coefficient affect the stability of a yacht?

The prismatic coefficient affects the initial stability of a yacht, which is the resistance to heeling or rolling due to external forces such as wind or waves. A high Cp means a wider beam and a larger transom area, which increase the initial stability but also increase the tendency to broach in a following sea. A low Cp means a narrower beam and a smaller transom area, which decreases the initial stability but also decrease the tendency to broach in a following sea.

How does the prismatic coefficient affect the comfort of a yacht?

The prismatic coefficient affects the dynamic stability of a yacht, which is the ability to return to an upright position after heeling or rolling due to external forces such as wind or waves. A low Cp means less dynamic stability, which means more motion and less comfort in certain sea conditions. A high Cp means more dynamic stability, which means less motion and more comfort in certain sea conditions.

How does the prismatic coefficient affect the volume of a yacht?

The prismatic coefficient affects the volume distribution of a yacht, which determines how much space is available for accommodation, storage, machinery, and other functions. A low Cp means more volume in the midship section and less volume in the fore and aft sections, which may limit the layout options and engine room size. A high Cp means more volume in the fore and aft sections and less volume in the midship section, which may increase the layout options and engine room size.

How does the prismatic coefficient affect the displacement of a yacht?

The prismatic coefficient affects the weight distribution of a yacht, which influences its performance and stability. A low Cp means more weight in the midship section and less weight in the fore and aft sections, which may reduce frictional resistance but also reduce hydrodynamic lift. A high Cp means more weight in the fore and aft sections and less weight in the midship section, which may increase frictional resistance but also increase hydrodynamic lift.

How does the prismatic coefficient affect the fuel consumption of a yacht?

The prismatic coefficient affects the fuel consumption of a yacht by affecting its resistance and power requirements at different speeds. A low Cp means less resistance and power requirements at low speeds, but also less potential for higher speeds. A high Cp means more resistance and power requirements at low speeds, but also more potential for higher speeds. Therefore, depending on the cruising speed and range of the yacht, different values of Cp may result in different fuel consumption rates.

How can I change or optimize the prismatic coefficient of my yacht?

Changing or optimizing the prismatic coefficient of a yacht requires modifying its hull shape, which may involve adding or removing material, changing its curvature or deadrise angle, altering its length or beam, or changing its displacement or trim. This is not an easy task and should only be done by a qualified naval architect or boat builder who can assess the impact of such changes on the overall performance, stability, comfort, and safety of the yacht.

How can I measure or estimate the prismatic coefficient of my yacht?

Measuring or estimating the prismatic coefficient of a yacht requires knowing its immersed volume, maximum cross-sectional area, and waterline length. These can be obtained from the yacht's plans, specifications, or hydrostatics, or by using various methods such as displacement measurement, waterline tracing, or sectional area curve. Alternatively, there are some online calculators or software tools that can estimate the prismatic coefficient based on some basic dimensions and parameters of the yacht.

The above answers were drafted by sailboat-cruising.com using GPT-4 (OpenAI’s large-scale language-generation model) as a research assistant to develop source material; to the best of our knowledge,  we believe them to be accurate.

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Intact, Damage, and Dynamic Stability of Floating Structures

• Reference work entry
• First Online: 01 January 2022
• Cite this reference work entry

• Shuqing Wang 4 &
• Liwei Yu 4  

40 Accesses

The stability is the capability of the floating structure to maintain to its upright floating position both in still water and in waves, whether intact or damaged, and it relates to the interaction among the center of gravity (COG), center of buoyancy (COB), and metacenter of intact or damaged hull under various scenarios.

Scientific Fundamentals

Introduction.

The stability is one of the most essential performances for offshore structures. The stability calculation, also referred as stability check, during the design, construction, and operation stage of the offshore structure is fundamental for the safety of the offshore structure and required by the administrations (e.g. Classification Society, Maritime Office). The relation of the COG, COB, and metacenter of offshore structure can be found in Fig. 1 , and the nomenclature adopted in this entry is listed in Table 1 .

COG, COB, and metacenter of offshore...

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ABS (2012) Rules for building and classing mobile offshore drilling units. American Bureau of Shipping, Houston, USA

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Wang, S., Yu, L. (2022). Intact, Damage, and Dynamic Stability of Floating Structures. In: Cui, W., Fu, S., Hu, Z. (eds) Encyclopedia of Ocean Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-6946-8_24

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RM CALCULATOR

Static righting moment the boat creates at 30 degrees heel. 

Please fill in the values to calculate an estimated righting moment.

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• Righting Moment Augmentation in Modern Sailing Yachts

In the last year, two major events in the Pacific Northwest crowned champions that sailed vessels utilizing a system of enhanced or assisted ballast— Team Angry Beaver won Race to Alaska aboard a canting-keel Schock 40; and the water-ballasted Riptide 41, Blue , topped the fleet of the biggest, fastest boats in a variety of conditions throughout the Van Isle 360. To help us better understand these systems, we are honored to have the help of world-renowned Pacific Northwest designer and the mind behind Blue , Paul Bieker.

Ultralight Displacement Boats (ULDBs) started making inroads into the sailing scene in the 1970s.   This was partially driven by the new cored composite structures and improved engineering methods that allowed yacht structures to be significantly lighter than they had previously been.

The first modern ULDBs that I am aware of were designed by John Spencer in New Zealand–the classic example being Infidel (renamed Ragtime ).   Incidentally, she was the first ULDB that I watched glide by us as I trimmed the blooper on a death-rolling two tonner back in the late 70s.   The Santa Cruz scene followed the Kiwi lead, with designers like Bill Lee creating boats that excelled in the California downwind classic races such as TransPac. These boats were exceedingly fast downwind but pretty slow upwind in most conditions.   As time went on, Bill Lee, George Olsen, and Carl Schumacher produced smaller ULDBs for the wider sailing public.   These boats continued the pattern of downwind strength and upwind weakness established by their predecessors (with Carl Schumacher using more powerful hull shapes to improve the situation somewhat).

Once sailors got a feel for the excitement of sailing a ULDB downwind it was a hard thing to walk away from.   The answer to making a ULDB get around a windward leeward race course in reasonable form is to design the boats with a bit more hull form stability (more beam) than early ULDBs and to sail the boats with extra crew members that are only there as moveable ballast.   Nowadays, most of the performance keelboats on the race course are sailed with a significant proportion of their crew acting as self-propelled units of ballast.

The Alternatives

Sailboats that want to go fast on an upwind/downwind course are between a rock and a hard place.   Downwind, minimum weight is the most important factor for achieving high performance and upwind righting moment (the resistance of the boat to tipping) is the most important factor.   The problem is that righting moment in a monohull keelboat comes to a large degree from ballast weight, so improving upwind performance comes with a loss downwind and vice-versa.   One solution is using additional crew as moveable ballast; the other is to use some other system for increasing righting moment without increasing the downwind weight of the boat.

There are three methods that are currently being used to increase the righting moment of ultralight boats without compromising their downwind performance: water ballast, canting keels, and side foils (hydrofoils that extend off the leeward side of the boat to provide lift and righting moment).

Water Ballast

Water ballast systems are the lowest tech solution to increasing righting moment and they are what I have the most experience with (most of the boats that I have designed since 1995 have had water ballast systems).   A water ballasted yacht has port and starboard tanks that can be filled as needed to provide righting moment when required for upwind sailing and reaching.   The tanks are always empty for downwind sailing unless the boat is being forced up onto a tighter than normal reach.   Some high performance offshore yachts also have aft centerline ballast tanks to help keep the stern down (and bow up) in heavy air downwind sailing.   Water ballast systems usually require a pump (or pumps) to fill the tanks, however the other functions (transfer from one side of the boat to the other and draining) are achieved with the help of gravity alone.   The extra power achieved with a water ballast system is significant, for instance our Riptide 41 design ( Blue ) carries 850kg (the weight of 10 people) of water ballast per side.   This increases the upwind righting moment of the boat by almost 40% without giving up any downwind performance.   Careful design allows us to do this while still passing all of the stability requirements for Category A offshore racing.   The downside of sailing a water ballast boat is that the ballast is a bit slower to move around the boat than a typical crew.   For instance, filling a tank typically takes on the order of 5 minutes and transferring water from one side of the boat takes around 20 seconds.   This puts a premium on planning ahead on the racecourse and it makes tacking a bit more cumbersome and slow than on a conventional yacht.   The upside is that you can sail with approximately half the crew as you would on a conventional ULDB designed for racing and you are significantly lighter downwind.

Water ballast also has significant advantages when cruising.   Boats are typically cruised with much fewer people than when racing.   Typical modern racer/cruisers are quite tender when shorthanded, so cruising can be a bit frustrating on windy days.   In contrast, a water ballasted boat has almost as much righting moment cruising as it does racing so sailing performance is relatively unaffected.   Another advantage is that a water ballasted boat is significantly lighter than a conventional boat when unballasted­—so speed and efficiency under power is better.

Canting Keel

The primary alternative to water ballast for giving ULDBs the power necessary to sail well upwind and reaching is canting keel systems.   The first operational canting keel yacht that I am aware of was Fiery Cross , designed and built by Jim Young after being inspired by the imaginings of L. Francis Herreshoff.   The first canting keel boat I was aware of was Red Herring , designed by David Hubbard of wing sailed catamaran fame.   The first production canting keel yacht was the Schock 40—designed and built in Southern California around 2000.   The system has become fairly common in offshore racing boats which are focused on outright speed.

Canting keel boats rely on a keel fin that is hinged at the bottom of the boat to increase the righting moment of the boat.   The keel fin extends into the hull of the boat and is attached to a device (usually a hydraulic ram) which cants it relative to the hull.   The maximum cant angle is usually on the order of 45 degrees each side of centerline.

The final alternative for providing righting moment on ULDBs is the use of foils projecting from the side of the boat and configured to provide a combination of side force and lift.   The lift reduces the effective displacement of the boat as well as providing righting moment.   The current IMOCA solo offshore racing yachts have pushed this to the point where they are effectively flying on many points of sail.   The problem with this sort of arrangement for most boats is that the lift is proportional to the square of the boat speed and most boats just don’t go fast enough to get the foil into a range of operating speeds where they are effective.   Even in large high performance yachts they are not effective at providing righting moment upwind (i.e. their effect on righting moment does not compensate for their added drag).

With the understandable challenges that come with side foils, we are typically left with two realistic options for making ULDBs perform well on reaches and upwind: water ballast and canting keels.   Of the two options, canting keels hold the most potential, especially power reaching.   On the other hand, water ballast offers relative simplicity and has the advantage that the boat is operating at a lighter weight downwind and in light air.   This makes it a reasonable choice for light air and windward/leeward sailing, which is why I have gravitated towards that solution for the boats I have designed for the Pacific Northwest.

From the February 2020 issue of 48° North

Paul Bieker

Paul Bieker is the founder and owner of Bieker Boats, which recently relocated from Seattle to Anacortes. He has designed everything from the fastest International 14s in the world to the hulls of the most recent America’s Cup multihulls, and many things in between.

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More Righting Moment Means Less Heel

• By Jeremy McGeary
• Updated: June 12, 2006

Wind force on the sails causes a sailboat to heel. Resistance to heeling, called righting moment (RM), results from the lateral movement of the boat’s center of buoyancy away from the center of gravity (CG).

To compare the heeling behavior of a catamaran versus a monohull, consider a 45-foot mono as having similar accommodations to those of a 40-foot cruising cat. The mono displaces 30,000 pounds, and the cat displaces 18,500 pounds. Each has about 950 square feet of sail area.

The moment of force required to heel the monohull 1 degree is about 1,900 pounds-feet. The force to heel the cat the same amount is 9,200 pounds-feet, almost five times greater, because the newly immersed part of the catamaran is much farther from the CG than that part of a monohull.

In general, the righting moment of a monohull increases close to linearly up to about 25 degrees of heel. The maximum RM for this boat would be about 80,000 pounds-feet at about 65 degrees of heel.

For the catamaran, the RM increases linearly for the small angles of heel illustrated here.

Its maximum, 142,000 pounds-feet, occurs at the point the windward hull flies, in this case at about 16 degrees of heel.

The top illustration shows the two boats at rest. The middle one shows the catamaran at 1 degree of heel and the monohull subjected to the same force at 5 degrees of heel.

In the bottom panel, the monohull is heeling 15 degrees–the limit of comfort for some sailor–while the cat, under a similar load, heels only 3 degrees.

These numbers are approximations based on data from several boats.

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Measuring Performance

What do the numbers tell us about seaworthiness, stability and speed.

All sailors are performance oriented. It’s only when we delve into the details that differences arise. One-design racers know that their place in the fleet hinges on tactics as well as boat speed. Those racing to Bermuda, Hawaii or even more distant landfalls, discover that a timely finish depends upon boat speed in the fog, in the middle-of-the-night and during light air interludes—not just when everyone is rolling along at hull speed.

A cruiser faces a different quest. Their perspective on performance is shaped by a smaller crew members, more reliance on self-steering gear and a propensity to enjoy the ride rather than shave seconds off each mile. So, when it comes to defining your performance perspective, make sure you and your crew agree on the traffic lane in which you prefer to sail and make sure your boat aids and abets that effort.

Race boat designers are innovators, and when it comes to an empirical approach to yacht design, they and their computers juggle a wide range of variables. Speed under sail isn’t the only frame of reference. At the same time they also have to contend with rating rules meant to penalize what makes a sailboat go fast. The goal is to come up with a design that favors boat speed, safety, sail-handling efficiency and creates a sailboat that’s minimally penalized by the rating rule. At times this “shaped to a rule” approach can lead to some unwanted attributes. In this overview, we will ignore the trend to design to a rating rule and look at the features that make some sailboats much better performers than others.

Our version of performance is more than a singular focus on polar diagrams and boat speed. We agree that good performance needs to be realized in a wide range of wind and sea states. But we also place considerable emphasis on seaworthiness, seakindliness, ease of boat handling and crew comfort. These can be contradictory elements, and which gets most emphasis helps to define the differences among the sailboats being built today.

Boat speed-related features are fairly easy to recognize. For example, most sailors have caught on to the idea that tall rigs, large sail plans and light displacement are more than a subtle promise of speed. Shorter rigs, sprouting from heavy displacement hulls are fine in windy parts of the world. But they don’t deliver much drive in light air. When a yacht broker mentions that, “you don’t need to tuck in a reef until it’s blowing over 25 knots,” take a close look at the rig and the vessels displacement. Then ask yourself if it’s not more likely that delayed sail shortening is really due to a shortfall in sail area? You can also answer the question by working out the sail-area to-displacement ratio following the details below or go online to www.tomdove.com/sailcalc/sailcalc.html . The answer gives you a good idea of the boat’s potential power under sail.

Decades ago, in the heyday of the cruiser/racer, a single design stereotype defined most of the fleet. In those days, the majority of sailboats on Long Island Sound, Tampa Bay or berthed in Marina del Rey slips were white hulled sloops sporting blue mainsail covers. This was an egalitarian era when cruisers raced and racers cruised. The net result was better seamanship. Cruisers could set spinnakers and racers knew how to anchor.  Today, sailboats have become more differentiated.  The fast, agile, nicely fitted out cruiser/race is still around by much less common. The result is even fewer racers are going cruising. Modern race boat deck layouts make anchoring  a gymnastic event and there’s little likelihood that there’s even a properly sized anchor on board. Cruisers are missing out on the seamanship development linked to racing and how it benefits sail handling while cruising.

Yacht design guru Bill Lee, coined the apt phrase “Fast is Fun.” He also recognizes that too fast can be trouble and what defines the latter is often determined by the skill set of the crew. Knowing when and how to shorten sail is a talent every sailor should cultivate. Some put that lesson on hold, and that’s OK as long as they master the art of avoiding challenging situations. This is hard to do and can lead to a lot of anxiety. Plus, it also takes much of the fun out of sailing. It’s better to prepare your boat and her crew to cope with the unexpected. This begins with developing an awareness of the boundary between being reasonably powered up versus being on the edge, about to lose control.  It’s not a situation enumerated by a specific boat speed, wind velocity or angle of heel.  But as one crusty old Maine coast cruiser put it, ”I can’t say exactly where trouble lies, but you’ll know when you get there.” The best solution is knowing how to depower in a hurry and safely cope with reductions in sail area.

Singlehanders, along with most shorthanded crews, really value the uptick in performance they get from the right gear. It improves efficiency in reefing, setting and dousing sails.  Cruisers with an aversion to performance sailing have usually been through too many fire drills.  Their version of how much sail area to set is often based upon bad experiences with less than adequate gear. Today’s sailing hardware and furling systems are rugged and reliable, but they still need to be carefully maintained. The crew must also know how to operate the gear in all kinds of conditions—from a midday thunderstorm to a midnight gale.

What to look for

The next time you go to a local boat show, do a little DIY performance profiling. At most shows, you’re likely to run into a full spectrum of sailboat designs. Start with the speedsters and tally up the go fast features. Sail area leads the list and with it comes lower windage, lighter weight rigging and spars—all have benefitted from better engineering and higher modulus materials.

A GZ curve illustrates righting lever. The high peak represents a boat’s maximum righting arm, which is only a part of the overall stability picture.

An offshore sailboat should have a limit of positive stability (LPS) (also known as the angle of vanishing stability- AVS) of 120 degrees or more. It is this ability to recover from a deep capsize that’s like money in the bank to every offshore passagemaker.  

• The area under the positive portion of the GZ curve should be compared with the area under the negative portion. The higher the ratio between the two, the more seaworthy and less likely a monohull is to capsize and the more likely it will recover from a deep knock down.
• Lowering ballast lowers the CG and increases a vessel’s limit of positive stability. In these examples, three identical 30 footers with the same amount of ballast, but differing keel stub depths, alter their draft and GZ curves. Boat 1 (5’ draft), Boat 2 (6’ draft) and Boat 3 (4’ draft). Note that Boat 3, the shoal draft option, has the lowest LPS and Boat 2, has the deepest draft, highest LPS and will sail to windward better than the other two boats.

A growing concern among many offshore cruisers has been a trend toward increased beam, diminished draft and a reduction in ballast. Sailing a reach makes these design changes less noticeable, but as soon as you harden up, a performance shortfall comes into play. With less ballast and no one perched on the rail, excessive heel necessitates a reef. In many cases, the shallow draft keel is almost completely hidden as the leeward portion of the hull submerges. This causes the sailboat to slide sideways and every beat to windward becomes a lesson in leeway.

The preference for deep draft is one thing that hasn’t changed too much among race boat designers.  Centerboards, dagger boards, drop keels and can’ting keels are also in the mix.  And it’s clear that there’s been a downward trend in displacement that fits into the performance-enhancing puzzle. Today, the “less is more” rule prevails. In the 1980s, a race-winning, IMS 40-footer weighed around 18,000 pounds. Now many 40 footers tip the scale at around 10,000 pounds and carry more sail area than their predecessor. The trend flips, however, when it comes to the price tags and sticker shock. It gets quite expensive to shave weight and add speed due to the need for more esoteric materials and aerospace construction skills. The bottom line is how much is it worth to you to add a few tenths of a knot?

Multihull aficionados continue to assail the logic of lead.  Monohull designers are using less but locating it more strategically at the tip of a high aspect ratio foil. This lowers the CG, increasing the righting moment but greatly adds to the stress focused at the keel to hull junction. Keel failures have become enough of an issue that the ISAF Technical Committee has been looking into the problem and they are favoring recommendations that builders increase the hull laminate thickness in the area around the keel attachment. This is a good example of how performance-enhancing features must be considered in the greater context of overall vessel design and construction. Good performance is desirable, staying afloat is essential.

Stability Examined

Righting moment and buoyancy are forces that work together to resist the heel induced by wind pressure on the sail plan. The more sail area, the greater the heeling moment. Multihulls have very high initial stability that’s derived from their wide beam. Monohulls have less initial stability, so when sailing to windward they soon begin to heel over. However, their “ace in the hole” is a highly appreciated attribute called secondary righting moment. It’s derived from ballast and keel geometry.

Multihulls might have been a side show a few decades ago, but they now hold a mainstream role in the sailboat marketplace. Like cruising monohulls, they range from comfortable houseboat like cruisers to absolute speedsters. The latter features more sail area, lighter displacement and much more clearance between the sea surface and the underside of the bridge deck.

Fixed wing masts, C and T foils and all carbon construction can help to juice up the ride. However, the downside to state-of-the-art, aircraft quality carbon fiber construction, seen aboard $7.8 million Fast Forward Composites Eagle 53, can result in serious sticker shock. But the ride says it all, acceleration with the fixed-wing spar is near instantaneous. Time will tell if it’s all just too radical or a full-scale glimpse of what lies ahead.

Displacement/length ratio

I prefer to preview a sail in a new boat by tallying up the numbers.  For example, the J/99 is a 32’ J/Boats, Inc racer/cruiser with enough Spartan accommodations below to do some fast passage making. She looked like a double-hander’s delight and with an ISO Cat A rating and the following vital signs, the performance potential is clear:

8,900 lbs. displacement

6.5 ft. draft

11.2 ft. beam

137 limit of positive stability

37 percent ballast ratio

170 D/L ratio

24.1 SA/D ratio

The data indicated an excellent performer in a wide range of wind speeds and the boat lived up to expectations.

For decades, naval architects and yacht designers have been putting complex as well as simple equations to good use. We’ll take a look at a few of the latter and see how they can help to put a more definitive label on specific sailboats.

Displacement length ratio is a comparative tool that allows us to group sailboats into five different performance categories.  The ratio itself is a non-dimensional number that defines the relationship between weight and length of a vessel. Most sailboats fall between 100 and 400 on this rating scale. At the low end reside light weight speedsters and at the high end are heavy vessels that need a lot more sail area to attain the performance of vessels toward the lower end of the scale. The D/L ratio is a handy way to empirically make boat-to-boat comparisons.

The equation used in this calculation is based on a vessel weight expressed in long tons (2,240 pounds) and the load waterline length (LWL) measured in feet. Don’t let the math bother you. It can be followed like a recipe and a calculator will insure the accuracy of your arithmetic. D/L = DLT ÷ (0.01 X LWL)3

So, let’s assume we are calculating the D/L ratio of a sailboat with a 32’LWL and 18,000 pounds of displacement:

• Convert displacement (D) in pounds to D in long tons (18,000 ÷ 2,240 = 8.0357)
• Multiply the constant 0.01 times the 32’ LWL (0.01 x 32 = .32)
•  Cube the result (.323 = .0328)
•  Divide displacement (in long tons) by the modified LWL (8.0357 ÷ .0328 = 245)
• The displacement length ratio is 245 , it lies in the upper half of the moderate category, a highly populated portion of the scale and a region representative of many offshore cruising boats. (Ultralight <90, Light 90 – 180, Moderate 180 – 270, Heavy 270 – 360, Ultraheavy > 360)

When looking at D/L ratios, it’s important to know the trim state of the vessel when it was measured. The weight of fuel, water and a cruising payload will affect the trim. Brochures often provide “light trim” statistics, but “half trim” status is used by most designers and presents a more realistic profile.

Whatever the case, make sure that the boats you compare are all in the same state of trim. The lighter the vessel, the more of an impact a sizeable payload will have. Also recognize that sailboats with no overhang and those with long overhangs skew the ratios in opposite directions. Plumb bowed, long LWL vessels earn lower ratios while long overhangs contribute to higher ratios.

Sail Area/displacement ratio

Sail-area/displacement ratio is a performance-linked statistic that defines potential power under sail.  The comparative metrics are vessel displacement and sail area—a sailor’s rendition of an automotive horsepower-to-weight ratio. In this case, sail area is measured in square feet or meters. No attention is given to how efficient or inefficient the hull shape happens to be. In other words, it doesn’t matter if the hull shape looks like the city dock or the underbody of the first to finish in the Newport-to-Bermuda Race. As long as their displacements and working sail area are the same, so will their SA/D ratios. The value of this metric lies in its ability to depict potential power for a given displacement—another useful tool in boat-to-boat evaluations. Solving the equation does involve changing vessel weight into the volume of water it displaces.

Headsail area in the formulae below refers to the working sail area or more specifically (J x I) ÷ 2 = SA (headsail). The mainsail area has become the actual square footage because the large roach (race boats) or the hollow leech (associated with in-mast furling systems) cause simple triangle area calculations to be too inaccurate.

In the following calculation we look at a sailboat that displaces 18,000 pounds and has a working sail area of 750 square feet.

• Convert water volume to weight one cubic foot of salt water = 64 pounds (18,000 ÷ 64 = 281.25)
• Calculate the sail-area displacement using (SA/D = SA sq.ft. ÷ (D cu.ft. ÷ 64)2/3) ( 750 ÷ (281.25)2/3 = 17.44)
• So our SA/D is 17.44, which puts it near the top of good performance. ( <15 under-canvased, 15-18 good performance, 18-20 excellent performance, 20< a handful)

Ballast ratio

Ballast Ratio—is a quick and easy calculation that doesn’t involve long tons or a weight-to-water volume conversion. It’s a simple comparison of weight of ballast to weight of the entire boat calculation, expressed as a percentage. B ratio = (Bwt ÷ Disp) x 100.

Assume an 18,000 pound sailboat has 7,200 pounds of ballast.

B#ratio = (8200 ÷ 18000) x 100 = .40

A 40 percent ballast ratio contributes to a sailboat’s secondary righting moment. How much it contributes,depends on how deep the ballast is placed. The big plus behind a substantial secondary righting moment is that it results in a very small negative portion to the boat’s stability curve. This means that the vessel is much less likely to capsize and quite able to quickly recover from a deep knock down.

Many naval architects consider a 120°-130° limit of positive (LPS) a minimum for smaller to mid-sized offshore  cruising sailboats. This can be accomplished with a high ballast ratio and less draft or a lower ballast ratio and deeper draft. The latter often entails a fin and bulb or anvil shape at the very tip of the keel.

These numbers aren’t SAT scores and higher isn’t better. They should be thought of as a sequel to a compass heading rather than a patient’s vital signs. For those targeting a specific type of sailing—a high latitude ocean crossing, for example—it makes sense to favor a mid-range D/L ratio and the “good performance” range of the SA/D ratio. It’s also important to take a close look at the ballast ratio in conjunction with the boat’s LPS.

Those cruising summer weekends, exploring anchorages close to home, don’t need to lug along as much lead or iron and can look favorably at ballast ratios around 30 percent. However, if it’s a light to ultra-light displacement, a beamy boat with a high SA/D ratio and a shoal-draft keel, beware of a low ballast ratio. This combination means you’ll need lots of friends on the rail when it starts to blow and if you heel beyond the initial righting moment’s sweet spot (around 40-60 degrees) there’s very little secondary righting moment to prevent a knock down.

Multihull sailors put all their eggs in one basket, but it’s a big basket. Extreme beam delivers immense initial stability that peaks around 10-15 degrees of heel. With this powerful heel stopping ability there’s an assumption the secondary righting moment will never be needed. Sailed appropriately, and never caught over canvassed, the initial stability does its job.

However, no multihull designer or builder offers a “can’t be capsized” warranty. Avoiding that outcome is the job of the skipper and crew who must keep careful track of the sail area set, the sea state being encountered and the potential for major fluctuations in wind velocity. Wave face geometry and a changing water plane also affect capsize avoidance. It’s no surprise that the SA/D and D/L ratios of the multihulls in the charter trade are very different than the same ratios calculated for the multihulls that race to Bermuda.

Sailboats, like automobiles, are designed to excel at specific jobs. Just as a Ford F-150 and a Ferrari 488 Spider have decidedly different missions, so does an Island Packet 42 Motor Sailor and a Farr 400. In between these two specialty boats lies a wide range of other sailboats that target a compromise between the two. Sailors, like the boats available, range significantly in how they prefer to spend time on the water.

Hopefully, those seeking to make fast passages end up aboard a boat that can perform up to those standards. And likewise, those out to savor slower meandering and enjoy a comfortable life aboard won’t step below into a cabin lacking head room, festooned with pipe berths, and accessorized with a  two burner camping stove and an unenclosed head. The same goes for performance upgrades and making decisions as to whether to invest in light wind sails or add another fuel tank to bump up range under power. Perhaps both.

Contributing Editor Ralph Naranjo is the author of The Art of Seamanship . He is an adjunct lecturer at the Annapolis School of Seamanship.

RELATED ARTICLES MORE FROM AUTHOR

Thanks Ralph a well put together article with very little bias. Very impressive.

Likewise to above. I’ve tried many times to lay this information out for relatively new sailboat buyers and I wish I could do it half as well as Ralph did in this article. Bravo, Matey

Ralph – recheck your math and formula for SA/D…

Not clear if you multiply the entire formula by 2/3 or juts the denominator – either way it does not seem to come out as you show.

Last year, due to delamination and lots of water intrusion, I replaced the ‘barn door’ rudder on my ‘83 Cal 35 with a slightly shorter and more elliptically shaped rudder. There was a noticeable difference in performance and I moved up more than several places in the one race I enter every year.

D/L is not a dimensionless number (it’s dimensions are are long ton / ft3), neither is SA/D (ft2/ton). Nevertheless, the numbers can be useful at least when comparing boats with similar hull shapes.

Some more discussion of the impact of hull shape (i.e. impact of hard chines, impact of location of max beam, amount of buoyancy in bow & stern, etc.) would be meaningful, as (esp the french) modern cruisers and races have dramatically different shapes than 1970s or 80s cruisers and behave quite differently when compared at similar ratios.

Very nice article. I think the confusion about the 2/3 factor is that the denominator is taken to the 2/3 power. So the equation for denominator is (D in pounds / 64)**2/3. I believe the ** or ^ symbol is missing. Again, good overview with excellent examples. Jim

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How to know if a design's righting moment is enough?

Discussion in ' Stability ' started by PhilippeCE , Apr 16, 2022 .

• righting moment

PhilippeCE Junior Member

Hello all! When designing a monohull sailboat, how do you know the design has a sufficient righting moment? lets say we have a sail of 100 square feet, and the horizontal center of effort of that sail is 10 feet from the center of gravity of that boat. at 25 mph, the wind will exert 2.5 pound of force per square feet of sail so 250 lb for the whole sail. if you multiply by the lever the mast create, 10 ft, you get 2500 lb-ft of torque. should the boat have a righting moment of 2500 lb-ft to be able to withstand this sort of wind on a beam reach? as the boat heels, the force on the sail will decrease, but is there a general rule to how much righting moment a sailboat needs?  

AlanX Senior Member

There was (in 2005) a couple of formulas for the minimum righting moment in one of the Australian Standards (that I no longer have). It was: Mr=1.5*B*(225*n+Dwt) (Nm) where: B was the overall beam (m) n was the maximum number of persons on board Dwt was the displacement weight (kg). And: As<Mr/128 where: As was the sail area (m^2) Also sail area is typically estimated using: As=k*Dvol^0.667 (m^2) where: k is between 15 and 22 Dvol is the displacement volume (m^3) You can estimate the Displace volume using: Dvol=Pc*LWL*BWL*DWL (m^3) where Pc (the Prismatic coefficient varies between 0.5 to 0.8, but for a sailboat the optimum is 0.63. Anyway, hope this helps AlanX  

@AlanX and MR is minimm righting moment? im surprised its not dependant on the sail area.  

The first equation based on displacement and beam (plus people hanging on the beam). The second is based on sail areas (which is just a factor). The above are simple rules or checks from the Australian Standards (circa 2005). If you want to calculate the actual moment then you need wind speed, sail area, keel and sail centroids. (If you want to get carried away, the drag coefficient of the sail would be even better.) If you want to calculate the actual righting moment then you need to map the righting moment verses heel. (Yeah, I did that too.) This is how I used them (to check the mast Z) way back then: Regards Alan  

I found another one for estimating the righting moment that looks like something I did: Form Righting Moment = 90%*9.81*BWL*Dwt/6 Form Righting Moment = DEGREES(ATAN(2*DWL/BWL))/90%​ It was obviously based on centre of buoyancy for the mid-section of a flat bottom unballasted sharpie. Here are my calcs for a sharpie based on maximum heel moment (done to 5 degree heel increments) and 16.4m^2 sail area with a 12.5kt/hr wind speed (way too low!). Clearly I had problems with freeboard and did not meet the required righting moment from the standards: Yeah, I build the boat and capsized on the first outing. Had to add ballast. Regards AlanX  

Ad Hoc Naval Architect

PhilippeCE said: ↑ ...When designing a monohull sailboat, how do you know the design has a sufficient righting moment?.. Click to expand...

TANSL Senior Member

It is not the same to speak of the righting moment, which depends to a great extent on the shapes of the boat, than of the heeling moment, which depends on the external forces applied to the boat. It would be useful to clarify what the various formulas mean. PhilippeCE said: ↑ @AlanX and MR is minimm righting moment? im surprised its not dependant on the sail area. Click to expand...

@AlanX thanks a lot! I was confused about what Mr and As stood for in your first post. As I understand it, the first formula is the righting moment that come from the hull shape the displacement + the number of people who can use their weight to try to right the ship. I still find it a big weird to use that formula instead of taking the maximum righting moment you get by calculating the righting moment for different heel angle, as I'm trying to calculate this for a keeled sailboat where the form stability is half the story. What I find more interesting is "required righting moment" = sail area ( in m^2 ?) * 128. which is dependent on the sail area which makes a lot of sense, although not as precise as I'd imagine something like that to be since it doesn't take into account the length of the mast(s), and maybe a couple other things that I think should matter. for the design I'm looking for it would be about 10*128, and since its a really small boat that is in the ballpark of the righting moment it would already have. @Ad Hoc Hi! What I meant by sufficient is what a naval engineer would consider sufficient. if you know the conditions in which the boat should perform well, how do you go about finding a 'sufficient' value for the righting moment. I looked at your post and well It definitely underline that it's not a simple matter. On the other hand it's true that a boat wouldn't necessarily sail well at the heel angle it has its maximum righting moment and it's something that I would like to take into account. But my question remains... I guess MR=AS*128 is simplistic, but what would be a more precise formula, if you know what conditions the boat should perform well in? I'd imagine it would take the sail area into account, the beam, the draft, the maximum wave height and possibly other things... is there such a formula or it's just impossible to approximate the necessary righting moment in a single equation?  

PhilippeCE said: ↑ ...... is there such a formula or it's just impossible to approximate the necessary righting moment in a single equation? Click to expand...

gonzo Senior Member

As the boat heels, the heeling force is reduced. The calculation at zero heel only takes into consideration initial stability. The maximum stability for a keel boat is usually close to 90 degrees of heel, at which angle the force on the sails is negligible. Flooding angle is often the driving constraint, since floating is the most important safety aspect of any boat.  

@Ad Hoc if you had to figure it out for a design, how would you do it?  

DCockey Senior Member

PhilippeCE said: ↑ ets say we have a sail of 100 square feet, and the horizontal center of effort of that sail is 10 feet from the center of gravity of that boat. at 25 mph, the wind will exert 2.5 pound of force per square feet of sail so 250 lb for the whole sail. if you multiply by the lever the mast create, 10 ft, you get 2500 lb-ft of torque. Click to expand...

@DCockey Alright I guess I agree that you would need a bit more info to determine how you would do it. What I'm looking for is for a general keeled sailboat, not a light dinghy.  

PhilippeCE said: ↑ @Ad Hoc if you had to figure it out for a design, how would you do it? Click to expand...

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NSRI’s 6th Offshore Rescue Craft arrives at Gqeberha

The National Sea Rescue Institute’s (NSRI) sixth Offshore Rescue Craft (ORC) Rescue 6 has completed her maiden voyage from Cape Town to her home station in Gqeberha’s port of Port Elizabeth and arrived at 15h30 on 25 September 2024.

Built by Two Oceans Marine in Cape Town, the ORC is designed for high performance in harsh maritime conditions. It is self-righting and purpose-built for rescue operations in extreme conditions. At 14.8m long and 4.8m wide, it can be deployed as far as 50 nautical miles from land and has an expected lifespan of at least 40 years.

Rescue 6’s delivery crew, made up of NSRI Training Manager Graeme Harding as delivery coxswain, outgoing NSRI CEO Dr Cleeve Robertson, NSRI Executive Director Mark Hughes, and three Gqeberha volunteer crew members, sailed Rescue 6 from Cape Town to Mossel Bay on September 24 th and 25th, 2024.

After a crew swap and refuelling at Mossel Bay on Tuesday night, she arrived at her new home in Gqeberha’s port of Port Elizabeth late on Wednesday afternoon.

“The crew at Station 6 is very excited about the arrival of our new rescue boat, said Justin Erasmus, NSRI’s Gqeberha station Commander. “She is going to make a huge difference to our crew safety and the type of operations that we can safely do.”

“We are still looking for a naming sponsor, so at the moment, we use her call sign Rescue 6 as her name,” said Justin.

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This world-class search and rescue vessel can carry up to 23 survivors and accommodate six volunteer rescue crew in shock-mitigating seats, allowing for high-speed operation in difficult sea conditions.

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