Stability Calculation

(At preliminary stage of cargo ships design)

Introduction

Calculation of the stability is one of the basic and primary tasks that are to be done at the initial ship design stage, where it is not absolutely necessary to be quite exact, but where a quick calculation is very advisable, even if being approximate, allowing to analyze many alternative dimensionings in a short time. In this blog post I enclose a form where main cargo ship dimensions are to be input by the user and from them the program makes an approximate calculation and stability results are displayed for transverse metacentric height GM and righting levers GZ at several heeling angles.

Definitions

I recollect here some of the basic concepts relating to ship stability, that can be calculated in intact hull condition and in damaged condition after a flooding. In this study only intact condition is considered and refering only to general or bulk cargo ships (cargo, bulkcarrier, tanker). No other ship types are contemplated, as for containers, fishing, passenger, yacht, war, dredging, special cargo etc. This program allows a ship's length bet. 70 and 300 meters. Ship stability is here defined by her transverse metacentric height GM in upright condition and by her righting lever GZ at diferent heeling angles. Several maritime authorities issue regulations for minimum values of GM and GZs and in this programa I use IMO rules (see Ref.1) to check if stability is acceptable. First a table with calculated GM and GZs values is shown and then another table comparing calculated and required values.

Only 5 ship particulars are required from the user together with ship type: bulkcarrier, tanker or cargo ship

• Length between perpendiculars
• Breadth
• Depth to Upper deck
• Draft at design condition (Td)
• Block coefficient

The user can also define following further particulars, but if he doesn't the programa will do, by estimating average, normal values for this type and size of ship (Ref.2). These optional data are shown with an * and in gray color cells. But one must take into account that these program estimated data are not fully reliable and therefore, if possible, values based in own experience or calculations, should be used instead.

• Load line coefficiente at Td draft
• An additional draft, lower than Td
• Light ship weight
• Light ship c.of gravity height
• Cargo spaces c.of gravity height
• Total Consumables weight
• Consumables in D.Bottom tanks in % of total
• Superestrutures length in % of Lpp

The program calculates stability assuming that all cargo spaces are full (homogeneous cargo), whatever the draft be, with no deck cargo.

The values of metacentric height GM and righting levers GZs are calculated by formulae shown in the book at Ref.2, Cap. 3.9. Levers are valid, although approximate, within following ranges: Block coefficient bet. 0,52 and 0,80, Breadth / Draft bet. 2 and 4,50, Depth / Draft bet. 1,30 and 2,20.

In tankers metacentric height is corrected for free surface effect in all cargo tanks, assuming double hull and one longitudinal bulkhead (L.B.) if deadweight is less than 50.000 Tm and two L.B. if bigger. No correction is applied to GZs as tanks are assumed to be full. In all ship types a free surface correction is estimated in consumables tanks.

Results

In the first table results are displayed for both design and actual draft, for metacentric height and righting levers at heel angles of 5, 10, 15, 30, 45 y 60 degrees. In the second table a comparison is made between calculated values for actual draft and IMO required ones, that are these:

1. Metacentric height GM (m) > 0.15
2. Righting lever GZ(m) at 30º o bigger > 0.20
3. Dynamic stability (meter*radian) at 30º > 0.055
4. Dynamic stability (meter*radian) at 40º > 0.090
5. Dynamic stability (meter*radian) bet. 30º and 40º > 0.030

References

1. Ref.1 IMO International Code on Intact Stability, 2008 (2008 IS CODE)
2. Ref.2 El Proyecto Básico del Buque Mercante.(Basic design of merchant ships) R. Alvariño, J.J. Azpiroz, M.Meizoso FEIN 2007

Stability Calculation

Cargo ships

Bulkcarrier Tanker General cargo

Length Lpp (m)
Breadth B (m)
Depth to Uper deck(m)
Draft design(m)
Block Coefficient @ design T.
Load line Coefficient @ design T.*
Draft @ actual condition(m) *
Light ship weight(t) *
Light ship KGl(m) *
Cargo spaces KGc(m) *
Consumables weight(t) *
% of Consumables in D.Bottom *
Superstructures length as %Lpp *

Results @ draft >>>	Design	Actual
Draft (m)
GM (Metacentric height) (m)
GZ(m) at   5º
GZ(m) at 10º
GZ(m) at 15º
GZ(m) at 30º
GZ(m) at 45º
GZ(m) at 60º

Stability IMO criteria

Criteria	Actual	s/IMO	Fulfil?
GM (Metacentric height) (m)
GZ(m) at 30º o mayor
Dynamic stab.(m*rad) at 30º
Dynamic stab.(m*rad) at 40º
Dynamic stab.(m*rad) bet. 30º & 40º