LONGITUDINAL STABILITY AND TRIM

A ship floating at equal draught all along is said to be on an even keel, or to have zero trim. If the fraughts are not the same from bow to stern, the ship is floting with a trim. Deeper draughts aft than forward result in trim by the stern. If the draught forward exceeds the draught aft, the condition is called trim by the head or bu the bow. The measure of the amount of trim is simply the difference between the after and forward draughts.

Figure 10.1.

Two waterlines (or waterplanes) are shown on the ship in Figure 10.1; a trimmed waterline (W1L1) and the even keel waterline (WL) corresponding to the same displacement. They are shown intersecting at the centre of flotation of the even keel waterplane. The quantities shown in the figure are defined as follows

Centre of Flotation (F): Geometric center of the ship's waterline plane. The ship trims about this point. May be forward or aft of the midships depending on the ship's hull shape at the waterline.

Longitudinal Centre of Flotation (LCF) : Distance from the centre of flotation (F) to the midships. Used to distribute changes of trim between the fwd and aft draughts.

Trim (t) : The difference between the forward and after draughts

Parallel Rise/Sinkage (PR/PS): When weight is removed/added from/to a ship at LCF, the forward and aft drafts will change by the same amount.

Change in Trim (CT): The sum total of the absolute values of the change in forward and after drafts.

Trimming Arm (TA): The distance from the center of gravity of the weight to the LCF. If the weight is shifted, TA is the distance shifted.

Trimming Moment (TM): Moment about the LCF produced by weight additions, removals, or shifts (wd), where w is the amount of weight added, removed, or shifted.

Moment to Trim One cm (MT1cm): The moment necessary to produce a change in trim (CT) of one cm. Found using the hydrostatic curves.

Tons Per cm Immersion (TPcm): The number of tons added or removed necessary to produce a change in mean draft of one cm.

TF : Draught forward

TA : Draught aft

TM : Mean draught at amidships. It is the average of TF and TA.

TO : Draught at centre of flottion, also called the corresponding even keel draught.

tF : Forward difference in draughts

tA : Aft difference in draughts

Trim angle ([pic]) :

Trim could be specified by stating the angle of trim, the way heel is characterizaed by its angle. But the practical consequences or trim are associated with the draughts at the ends of the ship rather than with the angle of trim, so trim is defined as the difference in the draughts aft and forward.

[pic]

The angle of trim may be expressed as follows

[pic]

LONGITUDINAL WEIGHT SHIFTS

When a weight is shifted longitudinally (fore 'n' aft) the net effect on a ship is similar to a see-saw, one end goes up and the other goes down. The pivot of the "see-saw" is located at the Longitudinal Center of Flotation (LCF).

To calculate the effect of shifting a weight longitudinally on the ship’s drafts, follow these steps:

1. Calculate the Trimming Moment (TM):

2. Calculate the Change in Trim (CT):

3. Calculate the change in forward draft (DdFWD):

The + or - sign depends on the location of LCF. If LCF is aft of MP use "+" and if LCF is forward of MP use "-".

4. Calculate the change in aft draft (DdAFT):

NOTE: If the weight was shifted forward, DdFWD will be positive and DdAFT will be negative. If the weight was shifted aft, DdAFT will be positive and DdFWD will be negative.

Example Problem

The FOWK just completed a transfer of 6500 gallons of diesel fuel (diesel = 322 Gallons/LT). The fuel is now located 135 FT forward of it’s original position. Prior to transfer, the ship’s...