Heeling Moments

The following sections explain the calculation methods used in determining the heeling moments for evaluating wind and other heeling moment criteria.

NES 109 Wind Heeling

The wind velocity at a height of 10m (or as given by you) is taken as the nominal wind speed, which depends on the vessel type, as follows:

For intact conditions:

For damaged conditions, the nominal velocity, Vn, depends on the intact displacement, disp, and is calculated as follows:

• if disp > 5000.0, Vn = 22.5 + 0.15*sqrt(disp),

• else if disp < 1000, Vn = 20.0 + 0.005*disp,

• else Vn = 5.06*log(disp) - 10.0.

• he local velocity, V, at height Z is given by:

• V = Vn(Z/10)**power

where the value of power can be input by you, the default being 1/7 = 0.1428.

The wind pressure, p0, for a 100 knot wind can also be input by you. The default value is assumed to be 195.3 kg/m2. The pressure at other speeds, V, is obtained from the expression:

pressure = p0*(V/100)**2

Using these expressions, Calc determines the wind force on the exposed wind profile of the ship, together with its centre of pressure. With the underwater centre of pressure assumed to be at half the draft, the upright wind moment can be calculated. To determine the wind moment at other angles of heel, a cosine or cosine squared factor is applied, depending on the criterion. A straight line option is also available, that means, the heeling moment does not vary with heel angle.

A rollback angle of 25 degrees, is used in connection with the area criteria. This is applicable to ships of conventional hull form with bilge keels.

NES109 Turning

The heeling lever due to high speed turning is given by the expression:

heeling lever (m) = V**2 cos(theta)/(Rg)

where:

• V = speed in the turn (65% of approach speed) in m/s

• h = vertical separation of the CG and ½ draft point (ship upright) in meters.

• R = radius of steady turn.

• g = acceleration of gravity (m/s2)

• V (in knots) and R are must be given by you.

NES109 Crowding

The effects of crowding of personnel are calculated as follows:

1. Curves of righting levers are to be calculated assuming all passengers standing on the upper deck, with the crew at their stations.

2. Heeling lever = w.a.cos(theta)/disp

   where:

   w = weight of personnel (75 kg each - more if carrying equipment)

   a = distance of CG of personnel from centreline, assuming all move as far as possible and each occupies 0.2 sq.m.

   disp = displacement (tonnes)

   theta = angle of heel.

   w and a must be given by you.

3. If the number of passengers is not defined, assume 2.5 per square meter of available deck space.

NES109 Tugs

Tugs must have sufficient stability to withstand the maximum possible bollard pull acting athwartships. The heeling lever is given by:

heeling lever = (T/disp).AB cos(theta)

where:

• T = bollard pull in tonnes

• AB = vertical distance from the centre of the propeller to the attachment point for the tow line.

• disp = displacement (tonnes)

• theta = angle of heel.

T and AB must be given by you.

Australian DOD Tugs

Tugs must have sufficient stability to withstand the maximum possible bollard pull acting athwartships. The heeling lever is given by:

where:

• nprop = number of propellers

• shp = shaft horse power

• dia = propeller diameter,

• h = vertical lever (m)

• a = h/0.3048;

• s = factor = 0.55 to 1.0;

• h = vertical distance from the centre of the propeller to the attachment point for the tow line.

• disp = displacement (tonnes)

A749 Wind Heeling

The steady state wind heeling lever is given by the expression:

lw1 = P.A.Z.sf/(1000g.disp)

where:

• lw1 = steady state heeling lever in meters.

• P = wind pressure in N/m2,( default = 504 N/m2)

• A = projected lateral area of the portion of the ship and deck cargo above the waterline;

• Z = vertical distance from the centre of A to a point at one half the draft (m).

• disp = displacement in tonnes

• g = acceleration of gravity (m/s2) (9.8065 m/s2).

• sf = steady wind multiplication factor (default = 1.0)

lw2 = gf*lw1

where:

• lw2 = gusting wind heeling moment;

• gf = gusting wind multiplication factor (default = 1.5)

sf, gf and P must be given by you, but default values are provided.

When considering area criteria, a rollback angle must be assumed. This is calculated according to Res. A749, section 3.2.2.3. The area of bilge keels, is an input to this calculation and must be given by you.

The rolling period is also used in determining the rollback angle, and is estimated using the formula:

T = 2.C.B/sqrt(GM)

where:

• T = rolling period in seconds;

• C = 0.373 + 0.023(B/d) - 0.043(L/100);

• L = waterline length of the ship in meters

• B = moulded beam of the ship in meters;

• d = mean moulded draft of the ship in meters;

• GM = metacentric height corrected for free surface effect in meters.

If GM is less than zero, then the rolling period is taken to be greater than 20, that means, the highest value in the table for factor 's'.

A749 Turning

The heeling lever due to high speed turning is given by:

h = 0.02*Vo*Vo*(KG - d/2)/L

where:

• h = heeling lever in meters;

• Vo = speed of the vessel in the turn in meters/sec

• KG = height of the centre of gravity above the keel (meters);

• L = waterline length of the vessel;

• d = mean draft in meters.

The turning speed in m/s must be given by you.

A749 Passenger Crowding

The procedure for estimating the weight and location of passengers, is described in IMO res. A.749, section 3.5.2. In essence, the weight of each passenger should be assumed to be 75 kg, unless a lower weight can be justified, and the location should be the most unfavorable having regard to stability.

The heeling lever is given by:

h = wt*lev/disp

where:

• h = heeling lever due to passenger crowding (meters);

• wt = total weight of passengers (tonnes);

• lev = displacement from centreline of passengers (meters).

wt and lev must be given by you.