Transport Publication TP 13313 E
 Table of Contents
 Introduction
 Definitions
 Application
 Construction and Structural Strength
 Stability
 Freeboard and Freeboard Marking
 Watertight &Watertight Integrity
 Water Freeing Arrangements
 Bilge Systems
 Fluid Systems
 Machinery
 Electrical Systems
 Steering Gear
 Fire Safety
 Life Saving and Emergency Equipment
 Communication Equipment
 Navigation Equipment
 Anchors and Cables
 Miscellaneous Marine Equipment
 Accommodation
 Protection of Personnel
 Appendix A: Sample Stability Information Booklet
 Section 1: Operational Information
 Section 2: Technical Data and Loading Conditions
 Section 3: Reference Information
A 5.1 Notes on the Use of Free Surface Moments
Provided a tank is completely filled with liquid no movement of the liquid is possible and the effect on the ship's stability is precisely the same as if the tank contained solid material.
Immediately a quantity of liquid is withdrawn from the tank the situation changes completely and the stability of the ship is adversely affected by what is known as the "free surface effects". This adverse effect on the stability is referred to as a "loss in GM " or as a "virtual rise in VCG " and is calculated as follows:
Loss in GM due to Free Surface Effects:
=( Free Surface Interia (m^{4}) x Density of Liquid in Tank (Tonnes/m³) ) / Displacement of Vessel (Tonnes)
= Free Surface Moment (Tonne.m) / Displacement of Vessel (Tonnes)
The free surface moments listed in the Tank Capacities Table refer to isolated tanks. If tanks are cross coupled the free surface moments will be considerably greater. Cross connection valves should therefore remain closed when the vessel is at sea.
A 5.2 Hydrostatic Plot
[Click on the image to enlarge]
Figure 12  Hydrostatic Curves
A 5.3 Cross Curve Plot
Figure 13  Cross Curves
A 5.4 Notes on the use of KN Cross Curves
KN curves for displacements of 25 to 75 tonnes are presented for angles of heel at intervals between 10 and 140 degrees. The hull, main deck and enclosed deckhouses (see Figure 4 below) are assurned watertight at all angles of heel^{1}.
To obtain righting arm ( GZ ) curves at a given displacement, the following equation should be used:
GZ
=
KN

KG.sin
(heel angle)
(See Figure 15 below)
This enables the value of GZ to be calculated at each of the heel angles presented, and subsequently plotted as in the loading conditions presented herein.
A 5.5 Inclining Experiment Report
Weight  Shifts  Weight  Distance  Deflections  1  Deflections  2 

No.  Direction  Tonnes  Metres  mm  mm 
1  > Stbd  0.3050  4.8600  33.00  31.00 
2  > Stbd  0.3050  4.8600  36.00  32.00 
3  > Port  0.3050  4.8600  35.00  32.00 
4  > Port  0.3050  4.8600  39.00  35.00 
5  > Port  0.3050  4.8600  33.00  29.00 
6  > Port  0.3050  4.8600  36.00  32.00 
7  > Stbd  0.3050  4.8600  34.00  32.00 
8  > Stbd  0.3050  4.8600  36.00  31.00 
Pendula Lengths in Metres^{*}: 
1) 2.115 2) 1.960
Draught Readings forward to Midships, above keel line:
Position (metres): 8.800
Draught (metres): 3.240
Position (metres): 28.800
Draught (metres) 2.040
S.G. of Water 1.0210
As inclined Condition
*One pendulum acceptable for vessels less than 24 m
Items to be removed to calculate Lightship
Item name  Weight  LCG  VCG  FSM 

Tonnes  Metres  Metres  Tonne.Metres  
Fuel (Port)  0.92  2.400  2.030  0.00 
Fuel (Port)  0.92  2.400  2.030  0.00 
F.W. (Fwd)  1.12  0.020  1.030  0.00 
Electrician's Tools  0.07  4.000  1.600  0.00 
Inclining Weights  1.22  0.800  3.750  0.00 
Personnel  0.23  0.000  3.000  0.00 
Items to be added to calculate Lightship
Item name  Weight  LCG  VCG  FSM 

Tonne  Metres  Metres  Tonne.Metres  
Anchor & Chain  3.800 0.00  9.000  0.30  0.00 
Liferafts  0.15  5.900  3.900  0.00 
Lightship Condition
A 5.6 Beaufort Scale of Wind Speeds and Corresponding Pressures
Table 6: Windspeed and Pressure Chart
Beauford Number
metre 
General Description  Limits of Speed in knots  Pressure kg. per sq. 

1  Light Air  1 to 3  0.020.2 
2  Light Breeze  4 to 6  0.3  0.6 
3  Gentle Breeze  7 to 10  0.8  1.7 
4  Moderate Breeze  11 to 16  2.0  4.2 
5  Fresh Breeze  17 to 21  4.8  7.3 
6  Strong Breeze  22 to 27  8  12 
7  Near Gale  28 to 33  13  18 
8  Gale  34 to 40  19  26 
9  Strong Gale  41 to 47  27  37 
10  Storm  48 to 55  38  50 
11  Violent Storm  56 to 63  52  66 
12  Hurricane  64 and over  68 and over 
A 5.7 Metric/Imperial Conversion Chart
Multiply By  To Convert  To Obtain  From 

0.039370  millimetres  inches  25.400 
0.39370  centimetres  inches  2.5400 
3.2808  metres  feet  0.30480 
2.2046  kilogrammes  pounds  0.45359 
0.00098421  kilogramme  tons (2240 lbs )  1016.0 
0.98421  metric tonnes of 1000 kilos  tons (2240 lbs )  1.0160 
2.4999  tonne per centimetre  tons per inch  0.40002 
8.2017 (M.C.T.C)  tonnes metric units (M.C.T.I)  foot ton units  0.12193 
18798  metre radians  foot degrees  0.0053198 
To Obtain  To Convert From  Multiply By 
 10 mm cubed = 1 cubic centimetre
 1 cubic centimetre F.W. S.G. 1.0 = 1 gramme
 1000 cubic centimetres F.W. S.G. 1.0 = 1 kilogramme
 1 cubic metre F.W. S.G. 1.0 = 1 tonne (1000 kilos)
 1 cubic metre S.W. S.G. 1.025 = 1.025 tonnes
 1 tonne S.W. S.G. 1.025 = 0.975 cubic metres
 1 cubic metre = 35.315 cubic feet
 1 cubic foot = 0.0283 cubic metres
A 5.8 Notes for Consultants on the Derivation of the Maximum Steady Heel Angle to Prevent Downflooding in Gusts
Figure 16: Stability Curves
HA_{1} = GZ_{1} / Cos^{1..3} Θ_{f}
Where:
HA_{1} = The magnitude of the actual wind heeling lever at 0 degrees which would cause the ship to heel to the downflooding angle (Θ_{f}) or 60 degrees
whichever is least.
GZ _{1} = The lever of the ship's GZ curve at the downflooding angle or 60 degrees
whichever is least
HA_{2} = The mean wind heeling arm at any angle Θdegrees (= 0.5 x HA_{1} x COS^{1. 3Θ})
5.9 Notes for Consultants on the Derivation of Curves of Maximum Steady Heel Angle to Prevent Downfloowing in Squalls
The wind heeling moment is proportional to the wind pressure, and to the apparent wind speed squared. It is also dependent upon the area, height, shape and camber of the sails, the apparent wind direction and the prevailing wind gradient. As a sailing vessel heels the wind heeling moment decreases and at any heel angle (Θ ) between 0 (upright) and 90 degrees it is related to the upright value by the function: HMO = HMΘ cos ^{1..3} Θ where HMO is the heeling moment when upright.
The heel angle of a sailing vessel corresponds to the intersection of the heeling arm ( HA ) curve with the righting arm ( GZ ) curve, where HA = HM/Displacement.
When subjected to a gust or squall the vessel heels to a greater angle where the heeling arm curve corresponding to the gust wind speed intersects the GZ curve.
Figure 13: Stability Curves
Thus for a given heel angle a heeling arrn curve may be deduced and for a given change in wind speed the resulting change in heel angle can be predicted.
The vessel will suffer downflooding when the heeling arm curve intersects the GZ curve at the downflooding angle. This situation is illustrated in the diagram where the 'heeling arm in squall' curve intersects the GZ curve at 52 degrees. If we assume a scenario where sufficient sail is set to heel the vessel to the downflooding angle (60 degrees should be used if the downflooding angle exceeds that value) in a squall of, say 45 knots, then we can predict the wind speed which would result in any lesser heel angle in these circumstances. The upright heeling arm in the squall ( HA_{1} ) is derived from:
HA_{1} = GZ_{f} / Cos^{1..3}Θ_{f}
If we consider a steady heel angle prior to the squall of 20 degrees we can derive similarly the corresponding value of the upright heeling arm HA2
HA_{2} = GZ_{20} / Cos^{1..3} 20
The ratio HA_{2} / HA_{1} corresponds to the ratio of wind pressures prior to the squall and in the squall thus for a squall speed ( V_{l} ) of 45 knots resulting in downflooding, the wind speed prior to the squall ( V_{2} ) which would result in a heel angle of 20 degrees would be:
In this example, which is illustrated in the diagram,
 Θ_{f}: 52 degrees
 GZ _{f}: 0.725 degrees
 HA_{1} : 1.362 degrees
 GZ _{20}: 0.464 metres
 HA_{2} : 0.503 metres
 Hence V_{2} : 27.4 knots
Thus when sailing with an apparent wind speed of 27.4 knots at a mean heel angle of 20 degrees, an increase in the apparent wind speed to 45 knots from the same apparent wind angle would result in downflooding if steps could not be taken to reduce the heeling moment.
These values correspond to a point on the 45 knot squall curve on page lo. which was derived from a series of such calculations using different steady heel angles. Similarly the curves for other squall speeds were derived using different values for V_{l} .
These calculations should be performed for both loading conditions and the results corresponding to the worst case ( i.e. the lowest maximum steady heel angles) presented in the booklet.