A 5 Section 3: Reference Information

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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Immediately a quantity of liquid is withdrawn from the tank the situation changes completely and the stability of the ship is adversely affected by what is known as the "free surface effects".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 (m⁴) 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 heel¹.

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	0.02-0.2
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

HA₁ = GZ₁ / Cos^1..3 Θ_f

Where:

HA₁= 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

HA₂ = The mean wind heeling arm at any angle Θdegrees (= 0.5 x HA₁ 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 ( HA₁) is derived from:

HA₁ = GZ_f / Cos^1..3Θ_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 

HA₂ = GZ₂₀ / Cos^1..3 20

The ratio HA₂ / HA₁ 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 ( V₂) 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
• HA₁: 1.362 degrees
• GZ ₂₀: 0.464 metres
• HA₂: 0.503 metres
• Hence V₂: 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. 

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