Stability Chapter 2 Worksheet Terms and Definitions
Stability – The tendency of a vessel to return to an erect position after being inclined by an
external force. Also known as positive stability.
Transverse stability – Stability of rolling motion or stability.
Positive Stability – Exist when G coincides below M. The vessel will have the means to
return to its original position by itself. An example of positive stability is a cone resting on
its base. When disturbed by an outside force, it will have the means to return to its original
position by itself.
Neutral Stability – Exist when G coincides with M. The vessel does not tend to return to an
upright position if inclined, nor continue its inclination if the inclining force is removed. An
example of neutral stability is a cone resting on its side or a ball on a perfectly level
tabletop. When something has neutral stability, an outside force can influence it, but it will
not have the ability to respond in a positive or negative way by itself. On a level surface a
neutrally stable object such as a cone on its side or a ball will just stay where you put it.
Negative Stability – Exist when G coincides above M. The vessel will list to either side and
will not remain upright. A list due to a negative initial stability is known as an “angle of
loll.” Negative Stability can be characterized by a cone balanced on its pointed end. If it is
disturbed, it will fall and not return to its original position on its own. When it is disturbed,
a system with negative stability will continue to move until positive or neutral stability is
achieved.
Longitudinal Axis –
Transverse Axis –
Vertical Axis –
Roll – Motion about the vessel’s longitudinal axis, transverse stability.
Pitch – Motion about the vessel’s transverse axis, longitudinal stability.
Yaw – Motion about the vessel’s vertical axis, directional stability.
Heave – The vertical bodily motion of the vessel, positional motion stability.
Sway – lateral, side to side, bodily motion, lateral motion stability.
Surge – longitudinal bodily motion, lateral motion stability.
G – Symbol for center of gravity of a component of weight on a vessel.
B – Symbol for center of buoyancy or buoyant force.
KG – Height of center of gravity of the vessel above the keel or baseline.
KB – Linear, distance from the keel to the center of buoyancy. (When vessel is upright)
Couple – A moment created by two equal forces exerted in opposite directions and along
parallels lines. In transverse stability, a couple is created by the forces G and B acting
parallel to each other in opposite directions.
Moment – The product of two numbers. For example, the product of a force weight moved
multiplied by a distance is weight moment. The product of an area multiplied by a distance
is an area moment. The product of a volume multiplied by a distance is a volumetric
moment.
Righting Moment – The product of the weight of a vessel (displacement or ∆) and the
righting arm (GZ), so = ∆GZ
GZ – Symbol for writing arm; horizontal distance measured between the vertical lines of
forces between G and B. GZ is measured horizontally from G to a point of intersection of
the upward line of force from B at a point labeled Z.
Transverse Metacenter (M) – The highest point to which G may rise and still permit the
vessel to have positive stability. Found at the intersection of a line of action of B when the
ship is erect with the line of action of B when the ship is given small inclination. The height
of the transverse metacenter above the keel, KM, KMt, or TKM.
GM – Metacentric height; distance from the center of gravity (G) to the transverse
metacenter (M)
BM – Symbol for transverse metacentric radius; distance between center of buoyancy (B)
and transverse metacenter (M).
Formulas:
Righting Moment = (∆)(GZ) = product of the vessel (displacement) x righting arm (GZ)
Sin(Theta) = GZ/GM = righting arm x metacentric height