Page 364 - Practical Ship Design

Freeboard and Subdivision 32 1

The calculation of the factorp, is a complex one and with a need to calculate this
for many different cases, it will generally be done by computer. To give a feel for
the realities behind the complex figuring, Fig. 1 1.4 presents a manual calculation
for a simplistic ship of 100 m. This ship has no longitudinal bulkheads or
watertight decks below the bulkhead deck. The first column gives all the formulae,
and the second the conditions attached to their use.
Reverting to Fig. 11.3, it will be seen that there are four different formulae forp, of
so-called “single” compartments, which may be made up of one, two, three, four,
five or six (max. in this case) actual compartments, depending on whether these:
- extend to both AT and FT,
- extend to AT,
- extend to FT’,
- extend to neither AT nor FT.
From these 15 “single” compartment pi values, the pi values for the 5 two-compart-
ment cases, the 4 three, the 3 four, the 2 five can be calculated using the method
shown in Fig. 11.3. In each case the calculation starts with the pi figure for the
group as a single compartment, from this is subtracted the two pi values for groups
of one less compartment starting from the same end points and finally the bit that
this procedure deducts twice is added back.
Some of the symbols used in MSC 19(58) tend to obscure the physical meaning
of parts of the calculation, which becomes clearer if it is realised that J is the
compartment length non-dimensionalised by expressing it as a proportion of the
ship’s length and y is therefore the ratio of actual damage to the assumed maximum
damage J,,,.
A plot of Jnlax against length is given in Fig. 11.5(a). Figure 1 1 S(b) shows a plot
of F, and F2 against y. These factors figure in the formulae for p and q as shown in
Fig. 11.5, whilst p and q feature in the formulae for pi. At the top of Fig 11.5(b)
there is an approximate indication of which y values apply to single, two, three,
four, etc. compartments.
Figure 11 S(C) shows a plot of a and F against E, which is a non-dimensional
representation of (2x) the distance of the centre of a compartment from amidships
with a negative value indicating an aft compartment and a positive value a forward
one.
S is a non-dimensional representation of (2x) the distance from amidships to the
nearest bulkhead of the compartment. The choice of S as the symbol for this seems
unnecessarily confusing with J and J,,, representing quite different features.
Figure 1 1.4 presents a spreadsheet illustrating the use of all these formulae. For
this purpose, the figure has been set out to cover the six single compartments of the
ship, although three separate sheets should be used in practice - one covering 1 to
N compartments, each of which includes the A.T., a second covering 1 to (N - 1 )
compartments, each of which includes the F.T. and a third for the (N - 2)