GZ Curves (Part 1: Interpretation)

Q. What is a GZ Curve?
Ans. GZ Curve is a curve indicating the transverse distance between the centre of gravity (G) and centre of buoyancy (B) in a condition when the vessel is heeled to a certain angle. The shipyard provides the information to calculate GZ for various angles of heel and for various displacements. Ship’s trim generally is zero for making the hydrostatic tables. All particulars are for static sea conditions. This is the reason the curve is also called the curve of statical stability.

Q. What is the implication in wave (dynamic) conditions?
Ans. The shipyard cannot provide GZ values for infinite conditions of waves and hence the GZ values are provided only for calm conditions.

A mariner must understand that in a particular wave condition the righting lever may actually be larger or smaller than the GZ value given in the Stability Manual. It is for this reason that the Master must closely observe the ship’s behaviour in the varying sea conditions and act diligently.

Q. What is the purpose of providing GZ curve information on a ship?
Ans. The purpose of GZ curve information is:

  1. To demonstrate the compliance to intact stability criteria in any service condition.
  2. To demonstrate the compliance to damage stability criteria in a condition of hull breach.
  3. To find the effect of; transverse, vertical shift of a weight; effect of free surface; effect of grounding on GZ curve.

Q. In, which other situations does the GZ curve is very handy?
Ans. The GZ curve:

  1. Provides quick and accurate status of stability at one glance.
  2. Helps in calculating quantity of moved bulk cargo such as grain in a listed ship.
  3. Helps in estimating the list of ship during the heavy lift operations.
  4. Helps in assessing the effect of internal flooding in intact condition on stability.
  5. To pre-calculate resultant list or angle of loll that may be cause because of a certain cargo operation.

Q. What is the significance of area under GZ curve?
Ans. The area under GZ curve is a measure of the dynamic stability of a ship. Dynamic Stability at an angle can be understood as the energy required or work done by an external agency to heel the ship to that angle. Mathematically, this is equal to the product of displacement of the vessel and area under the curve in meter – radians.

The area under the curve is normally found by Simpson’s rules. GZ curve indicates the stability potential and thus the capability of the ship to resist heeling in rough sea conditions.

Q. What is the significance of various minimum criteria listed in the ‘Intact Stability Criteria’? OR Why is the GM alone not the adequate information for making an accurate assessment of the ship’s stability?
Ans. The ship must have the required righting capability and resistance to heel at most desired angles of inclination. She should also have the required minimum, initial GM. The GM0 alone may be considered as single most important stability parameter to ensure a good overall stability.  She should have adequate range of positive stability so that she is able to return to the upright equilibrium in moderate sea conditions instead of capsizing to the extreme angle of equilibrium. The minimum safety standard is maintained by ensuring that the vessel at least complies with the Intact Stability Criteria’.

Q. What information is available from a GZ curve?
Ans. The following information is available from a GZ curve:

The initial GM: The slope of GZ curve at the origin is indicative of ‘Initial stability’ (GM0).

Maximum righting arm: Is the maximum vertical distance or separation of the GZ curve from the baseline.

The maximum righting moment: Can be found by multiplying the maximum GZ with displacement.

The angles of Equilibrium: The heel angles at which the GZ curve touches the x-axis or the base line are the angles at which the ship can be at equilibrium.

The range of positive stability: Is the range in degrees between the upright equilibrium angle and angle of vanishing stability.

Angle of deck edge immersion: The point at which the concavity changes to convexity is called point of contra flexure. This occurs approx. at the deck edge immersion.

Angle of maximum list that the vessel can sustain: Is based on the principle that if the listing moment caused is more than the maximum righting moment the ship will capsize.

Angle of dangerous list: Some say that the angle half the maximum permitted list angle is the limiting danger angle of list.

Angle of loll for the condition of negative upright GM0: The GZ curve loops in negative direction and then again rises upwards intersecting x-axis at angle of loll.

The angle of list due to G being off centre: This is found by the intersection of cosine curve (GG1 cos θ) with original GZ curve.

Dynamic stability: Dynamic stability at any angle of heel is found by multiplying the area under the curve till that angle by the displacement of the vessel.

Q. What are the special cautions a Master must observe in respect of stability?

  • He must use the loading and stability manual closely, particularly in respect of

i. using ready reckoner tables,

ii. complying with stability related precautions in bad weather, and

iii. studying the intact and damage stability details for the voyage (presently loaded condition).

  • He must remember that the stability data, the ship is provided with, is for static conditions and the data will be different in wave conditions.
  • He must use professional knowledge of stability blended with the knowledge of seamanship and lessons learnt from incidents involving similar ships / weather.

Q. How is the GZ information of a ship derived?
Ans. KN tables are normally provided in loading and stability manual for salt water. The table is entered with the displacements and Heel angles as arguments. GZ value for a given displacement and angle of heel is found by KN – KG sin θ.

Q. Can these tables be used in fresh water or dock water?
Ans. Yes, the value of KN for a given heel is purely dependent on the underwater volume and hence position of COB. Since, KN tables are prepared for under water volume in saltwater, if the vessel is floating in any other density water say, dock-water then the argument value of displacement figure will have to be modified by multiplying it with saltwater density and dividing by dock-water density.

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