14 Block coefficient and prismatic coefficient
The block coefficient CB and the prismatic coefficient CP can be determined using largely the same criteria. CB, midship section area coefficient CM
and longitudinal position of the centre of buoyancy determine the length of entrance, parallel middle body and run of the section area curve (Fig. 1.15). The shoulders become more pronounced as the parallel middle body increases. The intermediate parts (not named here) are often added to the run and the entrance.
CB considerably affects resistance. Figure 1.16 shows the resistance curve for a cargo ship with constant displacement and speed, as CB is varied. This curve may also have humps and hollows. The usual values for CB are far greater than the value of optimum resistance. The form factor (1 C k)—representing the viscous resistance including the viscous pressure resistance—generally increases with increasing CB. Typical values for (1 C k) lie around 1.13 for CB < 0.7 and 1.25 for CB = 0.83. In between one may interpolate linearly.
Shipowner requirements can be met using a wide variety of CB values. The 'optimum' choice is treated in Chapter 3.
If CB is decreased, B must be increased to maintain stability. These changes have opposite effects on resistance in waves, with that of CB dominating. With lower CB, power reduction in heavy seas becomes less necessary.
Recommendations for the choice of CB normally draw on the statistics of built ships and are usually based on the form CB = K1 — K2 (Alexander
26 Ship Design for Efficiency and Economy formula); one due to Ayre is Cb = C  1.68F„
C = 1.08 for singlescrew and C = 1.09 for twinscrew ships. Today, often C = 1.06 is used.
The results of optimization calculations provided the basis for our formulae below. These optimizations aim at 'lowest production costs' for specified deadweight and speed. The results scatter is largely dependant on other boundary conditions. In particular, dimensional restrictions and holds designed for bulky cargo increase CB. A small ratio L/B decreases CB:
The formulae are valid for 0.48 < CB < 0.85 and 0.14 < Fn < 0.32. However, for actual Fn > 0.3 only Fn = 0.30 should be inserted in the formulae.
These formulae show that in relation to the resistance, CB and L/B mutually influence each other. A ship with relatively large CB can still be considered to be fine for a large L/B ratio (Table 1.6). The Schneekluth formulae (lower two lines of Table 1.6) yield smaller CB than Ayre's formulae (upper two lines), particularly for high Froude numbers. For ships with trapezoidal midship section forms, CB should relate to the mean midship section width.
Jensen (1994) recommends for modern ship hulls CB according to Fig. 1.17. Similarly an analysis of modern Japanese hulls gives:
CB = 4.22 + 27.8 • ^f¥~n  39.1 • Fn + 46.6 • F\ for 0.15 < Fn < 0.32
Formula 
Froude number Fn  
0.14 
0.17 
0.20 
0.25 
0.30 
0.32  
Cb 
= 1.08  1.68Fn 
0.85 
0.79 
0.74 
0.66 
0.58 
0.54 
Cb 
= 1.06  1.68Fn 
0.83 
0.77 
0.72 
0.64 
0.56 
0.52 
Cb 
= 0.23F2/3 
0.85 
0.75 
0.68 
0.58 
0.51 
0.51 
Cb 
= 0.14/Fn 
0.85 
0.82 
0.72 
0.56 
0.48 
0.48 
Figure 1.17 Recommended block coefficient CB (Jensen, 1994), based on statistics
Figure 1.17 Recommended block coefficient CB (Jensen, 1994), based on statistics
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