Intact Stability GM Quick Check: Metacentric Height, Free Surface Correction and a Worked Example

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Every loading condition on a ship or workboat starts with one question: is the vessel stable enough to sail? The fastest first answer is the transverse metacentric height, GM. This post sets out the hydrostatic fundamentals behind it, shows how free surface in slack tanks erodes it, explains how the inclining experiment fixes the lightship KG, and works through a loading condition for a small cargo vessel. It ends with the first checks against the IMO 2008 Intact Stability Code. It is a screening method, not a substitute for a full stability booklet. It also sits alongside our wider overview of marine engineering and naval architecture . Fundamentals: KB, BM, KM, KG and GM A floating vessel is in equilibrium when weight equals buoyancy and both act along the same vertical line. Buoyancy is the resultant of hydrostatic pressure on the hull, a topic we cover in pressure and fluid statics . When the vessel heels through a small angle, the underwater shape changes, and the centre of buo...
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Angles & Directions

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Angles & Directions

Angles are also called bearings. Bearings are the acute angles between lines and meridians. They are divided into following types.

Related Terms :

  • Meridian : Imaginary line joining North and South poles.
  • Declination : Difference between magnetic and true meridians.
  • Azimuth : Clockwise angle taken from Geodatic North.
* If area is greater ➤ use Geodatic North
* If area is smaller ➤ use Magnetic North
  • Magnetic Declination maybe towards East or West.
  • For east    ➤     Magnetic bearing=true bearing - Declination
  • For west   ➤     Magnetic bearing=true bearing + Declination

  • Forward Bearing : Bearing taken in the direction of traverse.
  • Backward Bearing : Bearing taken in opposite direction of traverse.
  • Forward bearing - Backward bearing=180
  • For anti-clockwise :  FB of line = BB of previous line + angle
Example: In an anti-clockwise traverse <A=102'30',<B=110', <C=98'30', <D=112'30', <E=116'30'. Observed bearing of AB=40'30'(assume forward bearing). Calculate all the other bearings of traverse.

  • For clockwise : FB of line = BB of previous line - angle
  • Traverse : A series of lines of known lengths and directions.
  • Contour lines : lines of same elevations.
  • Zenith : an imaginary point just above an observer.
  • Nadir : an imaginary point directly below an observer.
  • Local Attraction : 
The magnetic needle does not point to the magnetic North when it is under the influence of the external attractive forces. The magnetic needle is deflected from its normal position if placed in the vicinity of metal piece such disturbing influence is khown as local attraction. 
Correction = calculated bearing - observed bearing
Example: Following bearings were observed in running a compass traverse. Apply correction for local attraction. Calculate corrected bearings. 
  • Conversion from WCB to Quadrental Bearing : 
Interior angle=BB of previous line - FB of next line

Types of Error w.r.t Traversing :

  • Systematic Errors which follow some Mathematical rule. 
  • Commutative Errors increase with the number of measurements. 
  • Random Error follows theory of change and do not follow any Mathematical rule. 
  • Compensating rule states that neither errors magnitude nor their signs are fixed. 

Axis of Co-ordinates :

In a survey work, the points are plotted w.r.t two√ lines which are parallel and perpendicular to the meridian and these lines are called Axis of coordinates and their interaction is called Origin. 
  • Latitude: distance measured parallel to meridian (N or S).
  • Departure: distance measured parallel to a line perpendicular to the meridian.
  • If latitude and departure are known, then:
L = √ (lat) ^2 + (dep)^2
𝝷 = tan^-1 (Dep/lat) ➤ (for Quadrental bearing) 

Closing Error :

The distance by which the end point of a traverse shortens to coincide with the starting point is called Closing Error. 

Precision :

Precision is the ratio between closing error and perimeter of sides.
Precision= closing error/Perimeter
Perimeter = 1 : n

Bow-Ditch or Compass Rule :

Bowditch rule is the Mathematical procedure to bring coordinates together. It is also used when both the linear and angular measurements are compatible to each other, i.e.,they are of equal precision. 
This rule is preferable when chances of error are greater in linear measurements. 
Question: Find the consecutive, independent coordinates, area by using independent coordinates and precision for the following data. 
Length(m) and bearing of line are given below:
AB = 285.10m, 26'10'NE
BC = 610.45m, 75'25'SE
CD = 720.48m, 15'30'SW
DE = 203.00m, 1'42'NW
EA = 647.02m, 53'06'NW
Question: Find the area of traverse and unknown bearings with the help of area. The data is given below in blue ink.
Note: Interested fellows can contact me by sharing his or her email address in the comment below and I will send you more question and related theory. 

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