Changes

The righting moment is a force generated by the righting arm (GZ). The righting arm is the transverse distance between the centre of gravity (CG) and the centre of buoyancy (CB) [28]. Hopefully this will become clearer as you read on.

The centre of gravity 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.

The centre of buoyancy 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.

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.

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.

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.

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.

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 [http://www.sname.org/ Society of Naval Architects & Marine Engineers]. It is very sensitive to the distance items are from the CG.

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 (G force) you experience during a roll. High rates of acceleration are very uncomfortable, stress the body, and make it impossible to sleep. Marchaj <ref> Marchaj, Seaworthiness, The Forgotten Factor, chapter 4, "Boat Motions in a Seaway"</ref> has proposed four physiological states: Imperceptible, Tolerable, Threshold of Malaise, and Intolerable. Malaise starts at 0.1 G, Intolerable starts at 0.18 G.

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 (SLR) 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 S/L between 1.1 and 1.2. SLR is closely related to the Prismatic Coefficient.

Prismatic Coefficient (Pc) 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.<ref> FPB 83 – Wind Horse, http://www.setsail.com/dashew/FPB83_Intro.html</ref>

Bulb designs for large ships often incorporate a bow thruster or sonar dome. Putting the bow thruster forward as much as possible increases the steering leverage. A watertight hatch gives access to the interior of the bulb. With a bulb, you will need a bowsprit for the anchor, or hawseholes port and starboard, to avoid scraping the bulb with the anchor chain.

== 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: