- 1 Design for Stability
- 1.1 Summary
- 1.2 Hull Form
- 1.3 Length on Water Line
- 1.4 Reserve Buoyancy
- 1.5 Roll Stability
- 1.6 Roll Period
- 1.7 Roll Acceleration
- 1.8 Roll Moment of Inertia
- 1.9 Roll Damping Systems
- 1.10 Maximum Hull Speed
- 1.11 Speed/Length Ratio
- 1.12 Prismatic Coefficient
- 1.13 Midsection Coefficient
- 1.14 WP Area
- 1.15 A/B Ratio
- 1.16 Ballast to Displacement Ratio
- 1.17 Displacement to Length Ratio
- 1.18 Capsize Risk
- 1.19 Length to Beam Ratio
- 1.20 Motion Comfort Ratio
- 1.21 References
Design for Stability
AAmpere (amp), SI unit of electrical current good hull combines performance and stability in every sense from its shape to the quality of its construction and the durability of its materials.
A well designed hull has a stable self-righting form. A large range of positive stability is achieved with an optimum vertical centre of gravity combined with the right proportion of beam, freeboard and wide weight distribution. In most yachts stability increases until 45-60 degrees of heel and then slowly diminishes until it vanishes at 90-120 degrees.
The hull can incorporate passive stabilizers like radius chines and bilge keels. A flared bow optimizes performance underway. A double hull, if affordable, offers extra security against penetration by floating objects. A bulbous bow reduces the horsepower and fuel required for a given speed, and slightly increases the top speed in displacement boats of more than 45 ftFoot, while providing a mount for a bow thruster and forward-looking sonar. Active stabilizers are effective but expensive and work better on a round bilge.
Hulls can be rounded (round bilge) or designed with a hard chine. A chine is the line of intersection between the sides and bottom of a flat-bottomed boat. A radius chine has a VVolt-bottom, rising to a second chine that starts the sides, yielding a shape closer to a rounded bilge. A rounded hull looks nicer than a slab side, and intuitively should sit better in the water.
The arguments for round bilges versus chines run like this: A round-bilge, like a submarine hull, offers little resistance to the water when it rolls. This is bad. A hard chine, or radius chine, offers resistance along the edge or edges. This is good. A chine also yields more interior space than does a round bilge. (A shoe box shape has the greatest interior volume but has infinite wave resistance at its ends.) Incidentally, a radius chine is easier to weld up in steel plate than a round bilge. And curves are more expensive to fabricate than straight lines.
But because round-bilge hulls roll more, they are paradoxically better suited to roll correction by active stabilizers.
The truth is there are good and bad designs of both types, from a stability perspective. Either type of hull can be designed to be self-righting in a knockdown from a beam-on wave. Breaking waves at the bow or stern are a different story for either design, depending on the waterline length.
Other features to look for are a fine bow section with substantial flare, and a deep bulbous forefoot. (See #Bulbous Bow, below.) A fine bow with a deep forefoot slips efficiently through the water, providing fuel economy and a comfortable ride. A flare provides good reserve buoyancy, reduces pitching and keeps spray off the foredeck. A flared bow reduces pitching because as the bow submerges, the flare increases the resistance to the water. Also, as speed increases you want the bow to rise, not dig in.
Past the bow, the hull should shift from a gentle to a rapid increase in beam. If this is done right, the boat will sail in a pool of calm water. The bow generates a positive pressure wave, which is cancelled out by the negative wave caused by the rapid increase in hull form. Such a boat will have a low Prismatic Coefficient (also see below).
Length on Water Line
A boat’sSecond length on the water line (LWLLength on the water line) affects its resistance to capsizing, and the maximum speed of a displacement hull. (A bulbous bow can increase maximum speed.) If the height of a beam abaft wave breaking at the bow or stern exceeds the boat’s length, it won’t be able to motor up it to the top. It is likely to pitchpole, i.e., tumble end over end. Also in general, in heavy weather and high waves or offshore, a longer boat performs better, and has better directional stability. (See #Length to Beam Ratio.)
The significant height of an ocean wave on a normal day runs three to five ft, with storm thresholds around 10 ft. Severe storm areas usually run up to 35 ft;  although 25 ft appears to have been the norm historically. It is possible winter weather in the North Atlantic is becoming more severe with waves 40-50 ft. Between 1975 and 1999 the largest storm waves off the coast of Washington USA increased by 50%percent to 12 mMetre, SI unit of length; although this might have been due to El Nino.
Studies of non-displacement sailing boats show that most boats can survive a breaking wave with a height of 55% LOALength over all. No comparable data exists for displacement boats but we should expect similar results. The same studies show that a wide-beamed boat hit by a wave with a height of 35% LOA can easily capsize. (The storm threshold is the wave height separating calm from storm. It varies with location, e.ggram., 13 ft in southern California.)
The table shows values of significant wave height for different boat lengths. Taking a 13-ft storm-threshold wave off Southern California as our benchmark, and assuming we accidentally get beam-on, we can surmise that the minimum length for an offshore boat is 40 ft. On the other hand, if we get stuck in an extreme storm with 35-ft waves beam abaft, then we better have a 70-ft one. This alone doesn’t guarantee survival, but for a small boat bigger is better when it comes to riding tall waves.
Thirty-five foot waves are not to be sneered at in any size of boat. On November 9, 1913, a storm on the Great Lakes with 35-ft wave height sank 12 freighters in a single night. The Queen Mary II took a severe pounding from 30-35-ft waves on her maiden voyage in 2004. On March 3, 2005, the 72-ft sailing yacht, Team Save the Children, competing in the Global Challenge 2004-2005, became airborne when hit by an exceptionally large wave in the south Pacific. Today, worldwide, about two large ships sink every month; although most are heavily laden freighters and some are poorly maintained.Rogue, or freak, waves are another matter. They can arise anywhere in any sea condition, in heights from 50 to 100 ft or more, endangering even the largest ships.  Until recently they were thought to be rare but most common in the Agulhas Current off the Cape of the same name on the southeast coast of South Africa, between Durban and Port St. Johns. In early 2016, researchers at MIT said they may have developed a method that would allow ships to have 2-3 minutes of warning before a rogue wave appears. In December 2016 the World Meteorological Organization officially measured the highest recorded rogue wave.
|Waterline Length vs.|
Significant Wave Height (ft)
|Boat LOA||LOA Breaking Wave
@ 55% LOA
|Beam On Wave|
@ 35% LOA
But research in 2004 by the European Space Agency indicated freak waves are very common, and not always associated with currents like the Agulhas or the Gulf Stream. During a three-week period, its MaxWave project using satellite-borne Synthetic Aperture Radar detected 10 massive waves, some nearly 100 ft (30 m). The next phase of the project, WaveAtlas, will analyse two years worth of data to map the location and frequency of freak waves. 
In 2005, the Naval Research Laboratory in Mississippi reported that Hurricane Ivan created waves of 30-40 m. Such rogue waves will become more common as hurricanes increase in frequency due to global warming. (Warmer water superheats hurricane cells.)Even coastal waves can become rogues. Waves have been observed on the Alabama coast as high as 32 m; while coastal 30-ft waves are frequent in Maine. Rogues have also been observed on the Ottawa River.
Freeboard, the distance from the waterline to the edge of the highest watertight deck amidships, is a rough measure of reserve buoyancy. Typically buoyancy is lost when the edge of the freeboard meets the water.Freeboard plus draft is the total height of the hull. A generous freeboard gives lots of headroom inside, and makes it easier to recover from a knockdown. Too much freeboard makes a boat tippy. The combination of extremely wide beam and low freeboard is dangerous.
There are several kinds of roll or heeling stability: ballast, form, static and dynamic. These are important in determining a boat’s resistance to capsizing from a beam-on wave, and the type of rolling motion. The rolling motion dictates your comfort.
Dynamic stability and large angle stability must be considered as equal partners with the boat's static stability.
Inherent in the design of every boat is a restoring force from rolling called the righting moment (RMRighting moment), and a point of instability. A boat capsizes when the force of a wave causes it to heel over to its point of instability, called the Angle of Vanishing Stability. Beyond this point, the boat capsizes and may stay inverted. The wider the beam, the more difficult it will be to revert. The upside down boat sits on the water like a flat-bottomed boat. The deeper the keel, the greater the counterbalancing force to the superstructure and the easier it is to revert.
Many displacement boats will self-right from 65-70 degrees before they turn turtle. Unlike sail boats very few have positive stability to 130 degrees.
A boats’s stability can be divided into two performance categories: initial stability and ultimate stability.
Initial stability defines the angles of heel that are normal to a vessel's operation. This is also the static stability. This is usually between zero and 15 degrees of heel. A wide-beamed boat heels less (has greater stiffness), and is more comfortable. But a narrower-beamed boat has more ultimate stability. Ultimate stability is the angle of vanishing stability.
The righting moment is a force generated by the righting arm (GZRighting arm). The righting arm is the transverse distance between the centre of gravity (CGCentre of gravity) and the centre of buoyancy (CBCentre of buoyancy). Hopefully this will become clearer as you read on.
Ballast is weight added to a boat below the waterline to counteract the effects of weight above the waterline.  Without the ballast a vessel witll be very tippy and happier upside down.
On a sail boat, ballast must counteract the lateral forces on the sails. Without this a sailboat will lay down in the water and capsize.
Ballast is usually placed in the keel, which acts as a lever, so you don't need as much weight below as above. The keel is filled with a high density material, such as concrete, iron, or lead. By placing the weight as low as possible in a sailboat (often in a large bulb at the bottom of the keel) the maximum righting moment can be extracted. However, this will increase the #Roll Moment of Inertia, which can be avoided by distributing weight instead of concentrating it. Also, removing weight from high up is more effective than adding it lower down.
Adding excessive ballast will make the roll motion more aggressive and less comfortable. Extra ballast will reduce the roll angle but the return will be snappier with a higher roll acceleration and more conducive to seasickness.  Ballast really plays a role at higher angles of heel. Once the heel angle starts to reach or exceed 45 degrees ballast comes into its own.
A ballast tank, found on larger vessels and some yachts, holds water to balance the boat. Water can be pumped from side to side to counteract rolling. On large cargo ships travelling empty water can be pumped in to lower the centre of gravity and keep the propeller and rudder submerged.
Static stability determines the angle of heel under constant wind or wave conditions. Factors that increase static stability are heavy displacement, low centre of gravity, and a centre of buoyancy that shifts outboard quickly when the boat heels. Boats with wider beams exhibit more static stability (stiffness) and less dynamic stability.
Dynamic stability determines the roll in response to a transient wind gust or violent wave that is shifting the performance into the zone of ultimate stability, i.e., instability. Heavy displacement and a narrow beam improve dynamic stability somewhat. A wider beam catches the wave early, giving it more leverage and time to act on the hull. Once a boat is inverted, the increased static stability associated with a wider beam becomes a liability since it keeps the boat inverted for a longer period of time.
From this, we can see that a lower CG is better. The lower the CG, the longer is the initial righting arm (GZ), giving the boat a quick roll and snappy response. The higher the CG, the lower is the righting moment (RM) and the slower the roll. Carrying ballast and other weighty items as low as possible lowers the centre of gravity. Keeping superstructure weight to a minimum and not storing heavy items on deck will also help. Adding ballast to the flybridge to slow the roll, as some people have advocated, is a very bad idea.
A good amount of freeboard will improve both the maximum righting moment and the limit of positive stability. Too much freeboard will make the boat tippy by raising the CG. Adding ballast to make the boat stiffer reduces the freeboard and reduces the zone of positive stability. Adding ballast to the flybridge, as recommended by one magazine, is absolutely crazy.
What Affects Static and Dynamic Stability
Centre of Gravity
The centre of gravity (CG) is the point inside the hull where the downward force of gravity equals the weight of the boat, i.e., its displacement. It is the midpoint of the mass. Keeping weight low in the hull lowers the CG. A low CG increases stiffness, i.e., resistance to heeling and capsizing. That’s why engines are mounted low, ballast is put in the keel; and heavy superstructures or loads on deck are bad. Makes you wonder about dinghies on the boat deck.
Centre of Buoyancy
The centre of buoyancy (CB) is a counteracting force to gravity. It is the midpoint of the underwater volume of the boat, i.e., it is the centre point of the geometric shape of the hull. It is on the centre line of the hull, usually amidships with a vertical height just a bit more than half the draft.
The upward thrust of the CB counteracts the downward thrust of gravity. To illustrate this, float a bowl in some water. Put your finger in the centre and push down. The bowl will resist sinking and push back. Your finger is gravity. The resistance you feel is the buoyancy.
Plenty of hull area beneath the waterline lowers the CB. As a boat is more heavily loaded, increasing the draft, the CB moves lower, reducing the righting arm, and the freeboard and ultimate stability are reduced.
When a boat is upright, the CB is above the CG, on the centreline. As a boat heels, the CB moves to the side in the direction of the heel. The horizontal distance between CG and CB is the righting arm (GZ). Heeling changes the underwater shape of the boat, and begins to move it toward a tipping point. As the edge of the freeboard meets the water, the outboard shift of the CB reduces and eventually changes direction as the boat heels further. This is caused by the change in the underwater hull shape. Obviously as the CB changes direction, the GZ is reduced.
Righting Moment = GZ*DDisplacement, Depth of ship
The righting moment (restoring force) is GZ multiplied by displacement (D). The longer the righting arm and/or the heavier the displacement, the greater the restoring forces.
As the boat exceeds its range of initial stability, and enters the zone of ultimate stability, the restoring force begins to decrease. This happens due to the changing shape of the immersed hull. As it continues to heel, the CB shifts inboard and the righting moment becomes less and less just when the boat needs more and more to restore it to upright. The boat becomes increasingly unstable. When the CB moves to the opposite side of the CG, the righting moment becomes an upsetting moment. When the boat reaches its Angle of Vanishing Stability it capsizes.
The roll period of a boat is an excellent indication of its stability. The lower the roll period, in seconds (s), the more stable the boat. The boat will be more uncomfortable but will have greater resistance to capsizing. The roll period is based on the moment of inertia, waterline length, and beam. The moment of inertia, (D^1.744/35.5), was developed by the Society of Naval Architects & Marine Engineers. It is very sensitive to the distance items are from the CG.
The formula for roll period is not too difficult but is too lengthy to describe here. Generally, boats with periods less than 4 s are stiff and periods greater than 8 s are tender. Stiff boats resist rolling and capsizing, and recover quickly. Tender boats roll more, recover slowly and are less resistant to capsizing. As a rule of thumb, for comfort the minimum natural roll period should be equal to a vessels maximum waterline beam in yards. For example, a boat with a beam of 17 ft 9 in should have a minimum roll period of 5.9 s. For safety the roll period should be less.
Waves also have periods. A wave period is the time between two crests or troughs passing the same point. Typical ocean wave periods are 5 to 20 s. If the natural roll period of a boat is equal to or an even interval of the wave period, then the wave periods will synchronise and harmonically amplify the roll in what is called a standing wave. At the least this will make the motion uncomfortable; at worst it will capsize the boat very suddenly. Many deep-water service boats are being designed with roll periods greater than 20 s, but generally this is not advisable.
Waves are made by wind from weather action. Long slow periods indicate the waves have travelled a long distance, so the disturbance is far away. Short periods mean it is close by.
Roll acceleration is the force of gravity (GForce of gravity force) you experience during a roll. High rates of acceleration are very uncomfortable, stress the body, and make it impossible to sleep. Marchaj  has proposed four physiological states: Imperceptible, Tolerable, Threshold of Malaise, and Intolerable. Malaise starts at 0.1 G, Intolerable starts at 0.18 G.
Roll Moment of InertiaThe roll moment of inertia defines the amount of torque (think wave pressure) required to rotate a mass (think roll the boat). Increasing inertia (reducing rolling) is accomplished by spreading out weight aboard rather than having it highly concentrated. Because of the leverage or gyroscopic effect, weight at the perimeter of the boat will have a much higher resistance to changes in motion, increasing dynamic stability.
Roll Damping Systems
Roll damping systems, as the name implies, are designed to reduce the roll of a vessel. Reducing roll increases comfort. Roll-damping systems are passive or active, and can be internal or external. The main types are:
- Bilge Keels
- Active Stabilizers
- Ballast Stabilizers
- Flopper Stoppers
Bilge keels are a type of fin attached to the chines of the hull. They serve as passive roll stabilizers, by offering resistance to the water when the boat rolls. They should be located as far aft as possible, to reduce roll and improve stability. Long low-aspect keels can reduce rolling by 35-55%. (Aspect ratio is the ratio of width to height, e.g., 4:3 is 4 units wide by 3 units high.)
Bilge keels can be tied into the structure and made strong enough to support the hull and keep the boat upright when it is accidentally or deliberately grounded. To support grounding, both the keel and bilge keels are engineered three to four times stronger than ABC requires. Failing to engineer the keels adequately can cause bilge plates to crack. Such keels will offer some protection to accessories attached to the main keel. Bilge keels can also be designed as short angled fins.
The downside of bilge keels is that they increase drag slightly. Hopefully the extra drag will be offset by the performance of a bulbous bow.
Active StabilizersActive stabilizers are another type of roll-damping fin. They have electric or hydraulic motors so that their angle of attack in the water can be adjusted dynamically, a little bit like wing flaps on an airplane. Electro-mechanical sensors and a control system make automatic adjustments to the fins. Actuators can be electric or hydraulic. The plates on the hull must be strengthened where the stabilizers are attached. They should be located close to the pivot point of the hull, typically just aft of the maximum beam. As mentioned before, active stabilizers are more effective on a round bilge hull than on a hard chine hull. Although they can dampen rolling motions more than 80%, they do not increase stability. Unfortunately, they are not considered workable at speeds below 8 knots.
Ballast stabilizers were once common only on large cruise ships but have begun appearing in European yachts and a few large trawlers like Cape Horn. A ballast stabilizer consists of two interconnected water tanks, one on either side of the centreline. As the boat heels a pump transfers water rapidly between tanks to counterbalance the rolling motion. A variation on this theme is to use sliding weights.
Obviously the pumping systems should have excellent redundancy. You wouldn’t want water ballast on the wrong side of the boat at the wrong time.
Paravanes & Flopper Stoppers
A discussion of roll damping would be incomplete without mentioning paravanes and flopper stoppers. Paravanes are long poles extended horizontally from the sides of a trawler, with winged paravanes that reduce the boat’s rolling inertia when underway.
Flopper stoppers are similar, but with flotation devices on the ends for use at rest. For either, the supporting mast structure raises the centre of gravity, which decreases ultimate stability.
Paravanes work the same way a high-wire performer uses a balance pole, or you use your arms when play walking down a beam or curb. They originated on fishing trawlers, which anyway have booms to set and raise nets. They can be very effective.
At other times, the booms can bounce, or even smack the boat, so people weigh them down with chain. They’re also cumbersome to set and raise. If a boom is lost in bad weather, the boat can capsize from the imbalance. You might want to consider them only if you’re converting a fishing boat that was designed for them.
Maximum Hull Speed
Hull Speed = 1.34 * LWL^1/2
Maximum hull speed of a displacement boat in knots is 1.34 times the square root of the length of the hull at the water line. Maximum speed is attained when the length of the bow wave is the same as the waterline length. Maximum hull speed is really the maximum efficient hull speed. You can drive a boat faster than its hull speed but it will take increasing gobs of power to do so.
The Speed/Length Ratio (SLRSpeed/Length Ratio) is the boat’s maximum velocity in knots divided by the square root of the LWL in feet. For example, with an LWL of 54 ft 04 in and a maximum speed of 9 knots, a boat's SLR is 1.22. Typically a boat is at its most fuel efficient at an SWetted surface/Llitre between 1.1 and 1.2. SLR is closely related to the Prismatic Coefficient.
Prismatic Coefficient (PcPrismatic Coefficient) is a dimensionless coefficient of form (glad you understood that!), allowing comparisons with other boats even of different size. It is the ratio of the under body volume to the volume of a prism having a length LWL, and a section equal to the boat’s maximum midsection. It indicates the fineness of the ends compared to the midsection. In general, it is a reasonable measure of the wave resistance of a boat, and thus related to the amount of power required to drive it forward. In aircraft design it has been found that the Sears-Haack body shape is least susceptible to wave drag. This is a canoe shape ill-suited to a small live-aboard. Larger boats like the 83-ft Wind Horse are exploring semi-canoe shapes.
Pc is relative to the Speed/Length Ratio (SLR). For every SLR, there is an ideal Pc. A low Pc for a given SLR indicates extremely fine ends and a large midbody. A high Pc means more displacement is distributed toward the ends. Some suggested values are given in Table 3-2. Opinion varies because of the complexity of hull design and hydrodynamics in different wave conditions. With an SLR of 1.22 (previous example), a boat’s Pc should be between 0.58 and 0.62. Block Coefficient Block coefficient is the volume of a hull as a proportion of the volume of a rectangular block having the same length, width and depth. The higher the coefficient, the lower is the propeller efficiency.
Midsection Coefficient is the area of the midsection, divided by the beam on the waterline multiplied by the (draft plus the freeboard).
WPWetted areA Area
The wetted area (WP) of the boat’s hull is an indicator of friction through the water. WP is very important in a submarine but less so in a surface ship, where wave resistance is more important.
A/BMeasure of stability Ratio
A/B, the ratio of the area above the water to the area below the water, is a deprecated measure of stability that is not used by marine architects. It is a gross rule of thumb that is easily misused. Stability can be better predicted using computer programs that consider many factors. For argument's sake, a lower ratio, say below 2.5, is inherently more stable than a top-heavy boat with a high A/B ratio of say 3.0 or more.
Ballast to Displacement Ratio
[Based on sail boats]
Ballast/Displacement Ratio = BtBallast/D * 100
Ballast displacement ratio is the boat’s ballast divided by the boat's displacement converted to a percentage. This ratio indicates the resistance to heeling (stiffness). An average ratio is approximately 35%. A higher ratio indicates greater stiffness.
Displacement to Length Ratio
Displacement/Length Ratio = D/(0.01 * LWL)^3
Displacement to length ratio indicates if the boat is a heavy (results greater than 300), medium (200-300) or light (75-200) cruiser. Displacement is in long tons (2240 lbPound weight). Note that ranges for sail boats are different (325-400, 275-325 and 200-275 respectively). A D/L of 280-350 indicates a boat is a heavy cruiser suited for serious offshore work.
[Based on sail boats]
Capsize Risk = BBeam/(D/[0.9*64])^0.333
The Capsize Risk is a seaworthiness factor derived from the USYRU analysis of the disastrous 1979 FASTNET Race, funded by the [www.sname.org/ Society of Naval Architects and Marine Engineers]. Values less than two are good for sail boats. No comparable data exists for displacement boats.
Length to Beam Ratio
Length/Beam Ratio = LOA/B
A lower Length to Beam (L/B) number indicates a beamier boat. Boats with a wider beam have better initial stability, and more interior room. They have worse ultimate stability, and high inverted stability, meaning it is hard to turn them upright. A beamier hull (L/B ratio below 2.7) has more room inside, but is less efficient and pounds much more going into head seas. A beamier boat has less roll angle but more roll acceleration, which is the primary culprit of seasickness. Even small changes in beam have a dramatic effect. 
A narrow hull has better directional control and steers better. For boats from 30 to 50 feet in length a hull with an L/B ratio above 3.0 is more efficient and pounds less into head seas.
Motion Comfort Ratio
Comfort factor = D/(0.65*(0.7*LWL+0.3*LOA)*B^1.33)
This Comfort Factor, developed by Ted Brewer, predicts the overall comfort of a sail boat when it is underway. The formula predicts the speed of the upward and downward motion of the boat as it encounters waves and swells. Faster motion makes passengers more uncomfortable.
The higher the number, the more resistant a boat is to movement, and the more comfortable it is. Obviously bigger boats give a better ride in calm conditions; however, the formula rightly favours a narrow beam. Less beam means less roll acceleration: the main cause of seasickness. Use with caution analysing power boats.
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