Main dimensions and main ratios 33
1.7 The design equation
The design equation describes the displacement:
1 D L B T CB KAppendages
D density, L B T CB D r.
The design equation can be applied to determine the main dimensions. The initial values for the design equation can be derived from `similar ships', formulae and diagrams and are frequently (within limits) varied arbitrarily. The desired design characteristics are greatly influenced by the ratios L=B, B=T and CB. L=B and CB affect the resistance, B=T the stability. The design equation is expressed in terms of these ratios. The result is an equation to determine B:
B D |
1 B=T |
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1=3 |
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CB L=B KAppendages |
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B is therefore the only unknown directly obtainable from the design equation. Using this, the ship's length and draught are then determined from the given ratios L=B and B=T.
Usually the resistance increases with decreasing L=B. This tendency is amplified by increasing speed. The minimum resistance for virtually all block coefficients and customary corresponding speeds is obtained for 8 < L=B < 9. Ships with CB higher than recommended for the Froude number should be increased in width and draught to allow a more favourable CB.
A similar equation can be formulated for the volume up to the horizontal main deck tangent line rD (`Hull volume depth') using the relationship B=D. The value B=D also provides information on the stability, as an inclination of
the height of the centre of gravity above the keel .KG/.
rD D L B D CBD ! B D
rD B=D
CBD L=B
CBD is the block coefficient based on the depth, or more precisely, the waterplane which is tangent to the uppermost continuous deck at its lowest point. CBD will often be used in the subsequent course of the design. CBD can be derived approximately from CB based on the construction waterline, see Section 3.4.
1.8 References
ABICHT, W., ARNDT, B. and BOIE, C. (1974). Freibord. Special issue 75 Jahre Schiffbautechn. Gesellschaft, p. 187
ALMAN, P., CLEARY, W. A. and DYER, M. G. et al. (1992). The international load line convention: Crossroad to the future. Marine Technology 29/4, p. 233
BOIE, C. (1965). Kentersicherheit von Schleppern, Hansa, p. 2097
JENSEN, G. (1994). Moderne Schiffslinien. Handbuch der Werften Vol. XXII, Hansa, p. 93 KRAPPINGER, O. (1964). Freibord und Freibordvorschrift, Jahrbuch Schiffbautechn. Gesellschaft,
p. 232
. and ¨ . (1996). Zur direkten Berechnung des Freibordes fur¨ den Schiffsent-
MEIER, H OSTERGAARD, C
wurf. Jahrbuch Schiffbautechn. Gesellschaft, p. 254
¨ . (1974). Entwerfen von Schiffen, Handbuch der Werften Vol. XII, Hansa, p. 17
VOLKER, H