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## An Overview of a Few Common Misconceptions Regarding

## Beam, Ballast & Displacement

## As They Relate to Seakeeping

Copyright 2000 - 2012 Michael Kasten

## INTRODUCTION

This article was originally prepared as a response to questions posed on the Trawler World mailing list on the subject of Beam vs. Ballast as these two factors affect a vessel's Stability and Rolling Behavior. There are many opinions among boaters regarding the quantity of

ballastas it relates to stability and on the amount ofbeamas it relates to comfort.Most of what we read in the common literature relating to stability presents an incomplete picture at best. In fact, applying actual science to the question rather than hearsay, we find many popular notions to be entirely incorrect.

However, on occasion a few truthful bits do emerge. Here is an overview that should shed some light on our stability questions...

## ON ROLL MOTION...

BEAMIncreased beam definitely does

notprovide increased comfort. Increased beam also doesnotprovide increased safety, or what we would call "seakeeping" ability... Consider the following...A relatively light weight vessel with a wide waterplane will naturally have a very active roll behavior on the water. In other words, such a vessel will react to the shape of the water's surface very readily. This describes the majority of semi-displacement vessels and virtually

allplaning vessels. Adding ballast or making the water plane wider will only result in a more "harsh" roll motion.While fairly wide beam is generally beneficial to a true planing vessel, with displacement or semi-displacement types adding beam or ballast will only serve to degrade performance due to increased displacement and wavemaking.

Roll accelerations are well documented as being the primary culprit inducing seasickness. In general we observe that while greater beam will provide less roll

angle, greater beam will also provide much more harsh, rapid, aggressive rollaccelerations. Other factors being equal, stiffness (initial stability) varies as thecubeof the beam. in other words, small changes in beam have a dramatic effect.We conclude from this that widening the water plane (increasing beam) will increase stiffness, but will at the same time reduce comfort and degrade seakindliness.

BALLASTWe are often barraged with obsolete notions about ballast. One such notion is the commonly held belief that a certain

'ballast ratio'must be achieved on sail boats. This is a myth pure and simple - an out-dated rule of thumb that must be given the "deep six...!" Similarly, among power boaters there is the popular but incorrect perception that power boats need a certain amount of ballast in order to have adequate stability.Why are these notions false...?

First, we can observe the

disadvantagesof increasing the amount of ballast. Heavier displacement means more volume that must be pushed through the water, thus more ballast equals greater resistance which will only slow the boat down. Conversely, in order to sustain a given speed, the added ballast will cost more in terms of fuel, engine power, and / or sail area.Second, we can observe that adding ballast will not provide an improvement in comfort.

Why is this you ask...?

As with added beam, if we add ballast the roll motion will become more aggressive due to the added righting force. Even though the added ballast may reduce the typical roll

angle, there will be a less gentle "return" at the end of the roll, i.e. there will be a shorter rollperiod, rollaccelerationswill be greater, the roll motion will beless comfortable, and the incidence ofseasicknesswill increase.The same applies whether aboard a displacement power vessel or a sailing vessel.

Can you have too much ballast...??

As it turns out, yes...!

With a very light structure such as GRP or aluminum, there can be an over-concentration of ballast. This is neither necessary nor desired, since it will tend to produce an

overly harsh rolling motion, i.e. a short roll period with high accelerations. If instead the vessel's mass is well-distributed, the rolling motions will be vastly more "seakindly" to those on board, and will be more gentle on the rig. In other words, with a distributed mass, there will be a longer roll period with greatly reduced accelerations.This is due to having increased the vessel's "Roll Moment of Inertia" which is explained below...

STABILITYThe essential task is to achieve an optimum Vertical Center of Gravity which, combined with the right proportion of beam, freeboard and structural weights, will provide good sailing performance, a seakindly motion, and will yield a large range of positive stability. These are our actual goals... not some mythic "percentage" of ballast!

DISPLACEMENTOther factors being equal, greater displacement ordinarily equates to greater comfort, i.e. the quality of '

seakindliness' we all seek. The reasons for this may not be so readily apparent.Displacement vessels (sail or power) will usually have a less aggressive roll motion, a longer roll period, and a more gentle "return" at the end of the roll than semi-displacement or planing types. This is primarily due to displacement types having a proportionately less wide waterplane and greater displacement. We find that comfort and seakindliness are enhanced by keeping beam to the

least amount necessaryfor initial stability and / or for sail carrying ability.Conversely we observe that adding ballast will be counter-productive in terms of comfort.

How then can displacement benefit comfort...??

ROLL MOMENT OF INERTIAWhile the

amountof displacement per water plane area will have a very real effect on a vessel's reaction to the sea surface, it is thedistributionof a vessel's massthat has the greatest effect ondynamic rollmotions. A vessel's "Mass Moment of Inerita" also called "Roll Moment of Inertia" is a way of expressing resistance to being put into motion by a force.We can improve

comfort, and we can improvesafetyby increasing the "Roll Moment of Inertia" of the vessel. This is accomplished by spreading out the various weights aboard rather than having them highly concentrated. This is very much counter to the often assumed requirement for a specific 'ballast ratio' on sail boats, or that there must be a certain amount of ballast present for the safety of a power boat.For the most basic understanding of this, we can observe that an object with its mass distributed toward its perimeter will have a much higher resistance to changes in motion. It is therefore evident that it will be more

dynamicallystable. This can be intuitively thought of as the "gyroscope" effect.On boats, it has been well proven that distributing weights away from the roll axis, say into the structure and the rig, is extremely favorable to a vessel's

dynamic stability. By direct observation, we have learned that boats that have been dismasted are much more likely to be rolled over.Why, you might ask...? Don't they have a much lower CG as a result of the dismasting...?

A dismasted sailboat is more likely to capsize due to the greatly reduced "Roll Moment of Inertia" and the consequent relative ease with which a heavy roll can be suddenly induced. This cannot be demonstrated by any kind of

staticanalysisas one would normally expect. Said differently, while the dismasted boat obviously has 'more' static stability without its mast, in the ocean wheredynamicforcesare at work, the effect is the opposite...!More explicitly, Roll or Mass Moment of Inertia is a way of expressing resistance to being put into

motionby a force. This is quite different fromstaticTorque or "Righting Moment" which is calculated as a quantity of mass times its distance from an axis. Instead, Roll Moment of Inertia is calculated as a quantity of mass times thefourth powerof its distance from an axis.It is helpful to perform a few basic calculations... For example, assume we have 2,000 pounds of ballast located 5 feet from the roll axis. This will provide a Righting Moment (Torque) of 10,000 lb-ft and will yield a Roll Moment of Inertia of 5^4 * 10,000 = 3,125,000 lb-ft^4. By contrast, a 200 pound mast located 25 feet from the roll axis will introduce a Heeling Moment of 5,000 lb-ft, but will have a Roll Moment of Inertia of 25^4 * 200 = 78,125,000 lb-ft^4.

In this example, the mast exerts exactly

halfthestaticmoment (torque) as compared to the ballast, but the mast is some25 timesmore effective at resisting being put into motion...!! It is by this simple example that we can observe the extraordinary benefits conferred by well-distributed masses.Many years ago during the Fastnet Race, rigorous analyses done after the loss of many vessels revealed that the boats which had concentrated ballast, light structure, and very light rigging suffered excessively due to their harsh rolling motions which caused many dismastings, consequent capsizes, and widespread seasickness.

By comparison, boats with heavier structure, lesser "ballast ratios" and heavier rigs resisted being "thrown" into severe rolling, had a much more seakindly roll motion, were easier on their rigs, did not lose their rigs, did not capsize, and did not experience nearly the degree of sea sickness among their crews. This is counter-intuitive because undoubtedly the heavier vessels had a higher center of gravity and therefore less "

static" stability. However due to their distributed masses they had much greater "dynamic" stability, which enhanced both seakindliness and seakeeping ability.With regard to structure, as compared to a fiberglass vessel a steel vessel will inherently have its mass distributed farther from its roll center, therefore a steel vessel will have a higher roll or mass moment of inertia and will be less active 'dynamically' in terms of roll, pitch, and yaw.

ROLL ATTENUATIONOn power vessels, the most effective strategy for roll attenuation (certainly the most effective strategy per dollar spent) will be the use of properly designed paravanes. These will degrade performance somewhat, particularly at higher speeds, but for those times when performance is imperative, the paravanes can be retrieved...

On power vessels, if cost is less of a consideration and convenience of use is a paramount concern, then active stabies will possibly be the best choice, even though they are only effective under way.

On sailing vessels, the weight of the rig and the wind in the sails do an excellent job of reducing roll motions. It is rare that a sailing vessel would resort to the extremes used by power boaters...!

The above are among the various factors that affect a vessel's perceived "comfort" which is the usual consideration with regard to roll motions. Of course the comfort of the crew is a safety factor, and it should not be overlooked...! For further discussion of these phenomena, please see my web page that describes other possible Roll Attenuation Strategies.

## ON STABILITY...

Several of the above factors primarily affect a vessel'sinitial,or"perceived"stability. In a completely separate category is a vessel'sultimatestability.

BALLAST RATIOUltimate stability, i.e. the ability to resist or to recover from a large angle roll, ordinarily is enhanced by the addition of ballast. However, whether adding ballast will provide an improvement in ultimate safety for any given vessel is a question that only a detailed analysis can answer.

On the one hand, in a '

static' sense, more ballast lowers the center of gravity, and should therefore be beneficial. For example it is obvious that for sail carrying, more ballast is beneficial. For comfort though, it is not, because for resistance to being rolled in actualdynamicconditions, added ballast will only increase the harshness of the roll. Without question, a balance must be struck.A light weight vessel having a large concentration of ballast will have greater stiffness (initial stability), but will have a much lesser Roll Moment of Inertia, will be much more easily put in motion, and will be more likely to experience large roll angles due to wave action. In other words, the light weight vessel with a high ballast ratio is more likely to be capsized...!

While the 'ballast ratio' may have some utility as a measure of seakindliness (i.e. more equals less), it is in fact quite meaningless as a measure of either stability or seakeeping ability.

Why?

We know nothing about a vessel's true stability picture without considering the distribution of weights, the vessel's center of gravity, and the shape of the boat. In other words,

dynamicstability andlarge anglestability must be considered as equal partners with the vessel'sstaticstability.

A/B RATIOPopularized by Beebe in Voyaging Under Power, the A/B ratio was originally promoted as a quick way to judge a power boat's seakeeping ability. It simply compares the Above water area to the Below water area. Small numbers are viewed favorably, large numbers not.

We are so frequently taunted with questions about the A/B ratio of power boats that we should be clear about one thing: The A/B ratio is very misleading, therefore obsolete and nearly useless. As a criterion of stability or sea keeping ability it is a gross oversimplification of the factors that should be considered. We have much better tools at our disposal for the analysis of stability and we should make use of them.

The range of positive stability of a sail or power vessel (static stability) depends entirely on three factors. The third though equally important is often ignored:

To the above we would ordinarily add a fourth factor: Movable Weights. For the moment we'll simplify the question by assuming all weights to be fixed and therefore that the CG remains in one place.

- Shape
- Center of Gravity
- Prevention of Flooding
After numerous stability analyses on a variety of craft, we quickly observe that increasing the volume of enclosed space above the waterline increases large angle stability. We achieve this by increasing freeboard and the volume enclosed by the vessel's superstructure. More enclosed space equals more buoyancy and a greater righting force.

This must not ignore the center of gravity. Therefore the weight of superstructures must be kept within limits. Those limits however are not determined by some arbitrary A/B ratio, but instead by a thorough study of a vessel's weights, combined with a rigorous analysis of a vessel's large angle stability.

As an interesting and somewhat contrary example, we observe that the large angle stability of power boats will nearly always be greater than that of a typical sail boat in the same size range. This may come as a surprise, but it is proven time and again by rigorous analyses of different vessel types.

Why is this so...? After all, don't sail boats have a higher ballast ratio and a smaller A/B ratio than power boats...?

This is due to the relatively much larger enclosed volume of the superstructures. In fact we can say that the relatively greater large angle stability of power vessels is

becauseof their relatively higher A/B ratio...!Where Captain Beebe’s original A / B ratio concept is shown to have good validity is when considering the

windageof the superstructure of a power boat. This is actually rigorously modeled in the IMO extended weather criteria where a wind-force is imposed, as well as a rolling moment to leeward resulting in a certain amount of heeling energy. In this analysis, there must be excess reserve righting energy in order to pass this criterion.It is extremely difficult to pass this criterion if the vessel has excessive windage combined with insufficient volume below the water. In other words, if there is a larger profile below the water, it is more likely that the boat will have sufficient displacement to “handle” its windage profile above the water.

Beebe probably did not need a crystal ball to know this…! He was after all a highly seasoned voyager, as well as quite an intuitive designer, thus Beebe was prescient with regard to the IMO wind and weather criteria.

FLOODINGIn any analysis of stability, we must also make rational assumptions with regard to flooding... The primary key to prevention of flooding is to have a strong superstructure and adequately strong openings that are actually capable of keeping the water out in the event of a capsize. In terms of ultimate stability, a vessel's potential 'downflooding' points are also a primary consideration.

On power vessels for example, the location of engine room ventilation openings are possibly the most common violations of common sense and of good practice in terms of downflooding, and therefore of ultimate stability. Sliding glass doors and picture windows come to mind as being a close second...

Sailing vessels are ordinarily well fortified against downflooding. Still, dorades, hatches and companionways are possible sites for downflooding.

A strategy aimed at "keeping the water out" and assuring that all the various possible openings can be quickly covered will provide the most benefit in terms of ultimate or large angle stability for any vessel.

Whether they are displacement types, semi-displacement types, or planing types, if given sufficiently strong superstructure with robust windows, hatches and doors having adequate WT seals, most power boats will have an enormous range of positive stability. A large portion of those power boats will actually be fully self righting, which is much more than can be said for the majority of sail boats. The key is to keep the water out...

WINDAGEA thorough stability analysis must also account for the windage of a vessel's freeboard, superstructure, sails and rigging. Windage is a 'shape' related factor, and an important one.

Most of the various stability criteria that are in use around the world consider windage. In fact on close scrutiny we observe that windage is quite an important limiting factor. If there is any validity to the use of the A/B ratio as a measure of anything, it is possibly useful as a relative comparison of windage. It is important to note however that there is

notany given value here that means anything at all. It can only be a relative comparison, which even then is not of much use in an absolute sense, except to note that one boat has more and another less.The real story lies in actually calculating a vessel's wind resistance and its heeling due to wind pressure, then comparing that to the vessel's righting curve. This is of course not simple, because in order to even have a righting curve we must first have calculated the vessel's CG and its shape, and we must then have done a large angle stability analysis.

Nevertheless this is the only way to derive a true comparison from one vessel to another. Actual calculation of windage and its effects on the stability of the boat in question is the only method internationally recognized as having any credibility among the various criteria of survivability.

MOVABLE WEIGHTSThe shape of tanks... In terms of movable weights, the shape of tanks is a primary consideration.

Why...? Free surface effect.

When you step into a partially filled skiff, you'll immediately discover the dramatic effect of free surface.... Numerically speaking, the motion of liquids in tanks degrades stability in proportion to the cube of the width of the tank. Suffice it to say that the liquids should be kept from sloshing, and that tall narrow tanks are generally better than wide shallow tanks.

## WHAT CRITERIA TO APPLY...

PREVIOUSLYWe have looked at a few of the commonly used, but over-simplified and now outmoded / obsolete ways of judging stability, seakindliness and seaworthiness such as the 'A/B ratio' for power boats promoted by Beebe and the commonly quoted 'ballast ratio' for sail boats.

There is yet another commonly used but highly misleading criterion we may encounter. It is the

metacentricheightoriginally introduced by Frederik Henrik Af Chapman in the 1600's. While quite useful as a gauge of initial stability and therefore as a preliminary gauge of sail carrying ability and of seakindliness, a vessel's metacentric height is not of much use as a gauge of ultimate, or large angle stability. In other words, it is a useful piece of data re: initial stability and roll period, but it is not in any way definitive re: seaworthiness or survivability.These various criteria have all had their place in the history of boat design, however we must look beyond the overly simplistic view they offer. More accurate comparisons are more subtle, and will therefore require more than a cursory inquiry.

PRESENTLYWe now have much better stability analysis tools available, and we should insist on using them to their best advantage. Computer analysis has made possible a much more detailed picture of the various elements of stability and seakeeping ability than had been practical even as recently as two decades ago.

In the case of seakeeping, stability and roll motion, we have observed that waterplane area, beam, VCG, displacement, and roll moment of inertia are all important factors. Also important are the shape of the underbody, the configuration of appendages, and the volume and watertight integrity of deck structures.

In terms of

ultimate stability, there are many different standards being used throughout the world. Among the most familiar are the ISO (European Union), IMO (International) and US Coast Guard (US only), and others that are applied locally in various regions. Each of them have rigorous criteria that apply to commercial power or sailing vessels. Within the EU, quite rigorous criteria have also been formalized for recreational craft.For any new design, after a thorough weight analysis is done in order to determine the VCG, a large angle stability analysis can then be done. With the results of these analyses in hand, we can then determine the vessel's compliance with the ISO, IMO, USCG or other applicable stability criteria.

In terms of

comfort, internationally recognized criteria for seakindliness are still under development, however Maxsurf seakeeping software can easily perform the analysis of dynamic vessel motions.

## SUMMARY

If there is one absolute truth in all of this, it is this: With regard to seakindliness and seaworthiness there are no absolutes, only tendencies...! Due to the complexities involved, we may attempt to apply generalities to the problem, however such generalities are necessarily prone to oversimplification, therefore they will nearly always be misleading if applied too broadly.... or too blindly...Michael Kasten

Port Townsend, 2002 - 2012

Please see our AVAILABLE BOAT PLANS web page.

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