Principles of Stability

References

• INE: Ch 22 (389-400) • INE: Ch 23 (401-402, 409) • PNE: Ch 3 (1-10) • HW: LG #24

Principles of Stability

• Gravity – Force exerted on a body drawing towards the center of the earth. Acts through center of gravity (G) • Buoyancy – An object floating in liquid displaces a volume of liquid equal to the submerged volume of the object. This exerts a pressure on all surfaces of the object resulting in a force opposing gravity through the center of buoyancy (B)

Principles of Stability

• Archimedes Principle – object submerged in fluid is buoyed up by a force equal to the weight it displaces • Displacement – Weight of ship equal to weight of water displaced by volume of underwater body of ship – W = V x 1/35 – Displacement depends on density of water (salt vs fresh)

Displacement Curve: Plots draft vs displacement for a particular ship Archimedes’ Principle – An object floating or submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced

Vocabulary

• Draft: how far your boat is in the water, measured in ft or yds • Freeboard: what is left above water (rough measure of reserve buoyancy) • Depth of hull: gunwale to keel • Reserve buoyancy: volume of the watertight portion of ship above waterline

WATERLINE RESERVE BUOYANCY

Reference Points

• Keel (K): bottom line of ship, base line • Center of buoyancy (B): single force that acts vertically upward. Located at geometric center of underwater body. Moves as ship heels • Center of gravity (G): single force that acts vertically downward. Located at geometric center of ship. Does not move as ship heels

Reference Points (con’t)

• When at rest, B and G lie on same vertical line.

• Metacenter (M): intersection of two lines of action of B as ship heels

Terms

• Metacentric Height - GM – measure of stability • Righting Arm (GZ) – Perpendicular distance between the lines of action between the two forces – GZ = GM (sin (Φ)) G Ф M Z B

Terms

• Couple – Two forces of equal magnitude acting in opposite and parallel directions produce a rotation motion – Created when ship heels and Buoyant force and Gravity are no longer in line with each other – When inclining a ship, this couple produces either a

righting moment

or an upsetting moment depending on the relative location of B and G – RM = W x GZ

Linear Measurements

• KG: height of center of gravity above keel • GM: Metacentric height (measure of initial stability to 7 degrees, after that we use stability curve)

States of Stability

• Positive: M above G • Neutral: M and G same position • Negative: M below G • GM used as a measure of stability up to 7º, after that values of GZ are plotted at successive angles to create the stability curve

Stability Curve (Cont)

• Effects of draft on righting arm: – Righting arms (GZ) decrease – Displacement (W) increases – Righting moment overall may increase or decrease. Function of hull shape, magnitude of displacement change

Effect Of Draft On Righting Arm

Definitions

• Roll: Back/forth motion transversely • Pitch: Back/forth motion longitudinally • Yaw: Side to Side • List: Difference between Port and Stbd draft • Trim: Difference between fwd/aft draft • Center of Flotation: Point at which ship trims about

Effects of Weight Shifts

• Weight shifts effect Center of Gravity (G) • Shift of G will be in same direction of weight shift (vertical, horizontal, fore/aft) • GG 1 = (w) (s) / W – GG 1 : Distance of shift of Center of Gravity – w: Shifted component weight – s: Distance component is shifted – W: Weight of entire system

Effects of Weight Shifts (con’t)

• Vertical Shifts: – As G shifts up, for a given angle of heel, righting arm decreases (ship less stable) • Horizontal Shifts: – G will shift in the direction of weight shift, causing the ship to heel to one side – Righting arm is decreased since G is moved from centerline toward B

Free Surface Effect

• Occurs when a compartment or tank is only partially flooded / filled • As the ship rocks, water wants to maintain a level condition causing “sloshing” of water • As water shifts in direction of heel, Center of Gravity shifts thus decreasing the righting arm • This effect reduced by pocketing

Summary