Estimating Main Dimensions and Coefficients in
Preliminary Ship Design
Volker Bertram, TU Hambuig-Harburg^ 1. Introduction
The main dimensions decide many of the ship's characteristics, e.g. stability, hold capacity, power requirements, and even economic efficiency. Therefore determining the main dimensions and ratios forms a particularly important phase in the overall design. In modern practice, this involves modification of existing designs taken from databases. Computer-aided design systems then allow quickly and accurately to explore various alternatives. However, in academia simple estimation formulae are still popular despite their inherent inaccuracies. These formulae are commonly used in formal optimization procedures and more recently knowledge-based systems. This is especially questionable as many of the used formulae are based on ships built at least two decades ago and must be considered as outdated by now. I will introduce here a few alternatives based on more modern hull forms. Schneekluth and Bertram (1998) discuss the issue in far more detail and covers also the topic of formal optimization of the main dimensions. The nomenclature follows the usual standards unless stated specifically otherwise.
Generally, main dimensions are often restricted by the size of locks, canals, bridges, etc. The most common restriction is water depth. Main dimensions determined by the following formulae and diagrams should be always checked for these restrictions.
2. Ship's length
The desired technical characteristics can be achieved with ships of greatly differing lengths. Increasing the length of a conventional ship (while retaining volume and fullness) increases the hull steel weight and decreases the required power. Usually, the length is determined from similar ships or from formulae and diagrams (derived from a data base of similar ships). The resulting length then provides the basis for finding the other main dimensions.
Based on the statistics of optimization results according to economic criteria, the 'length involving the lowest production costs' can be roughly approximated by Schneekluth's formula:
r _ A O . 3 1^0.3 O 9 + 0-5
^ ' " - ^ ^ (0.145/F„)-F0.5
Lpp [m] = length between perpendiculars
A [t] — displacement
V [kn] = speed
Fn = V/y/g • L = Proude number
The formula is applicable for ships with A > lOOOt and 0.16 < Fn < 0.32. Unfortunately, the optimization was based on cost structures prevailing more than 20 years ago in Germany. Still, the formula may serve as a reasonable first estimate especially for ships with small CB-Despite its tendency to recommend longer ships than usually built, the formula appears to be a better alternative than older formulae of Ayre, Posdunine or Volker.
The length should be checked for suitable interference of bow and stern wave systems ac-cording to Proude number. Unfavorable Pioude numbers with mutual reinforcement between bow and stern wave systems should be avoided. Wave breaking complicates this simplified con-sideration. At R'oude numbers around 0.25 usually considerable wave breaking starts, making this Pi-oude number in reality often unfavorable despite theoretically favorable interference. The regions 0.25 < F„ < 0.27 and 0.37 < Fn < 0.5 should be avoided, Jensen (1994).
^Lammeisieth 90, D-22305 Hamburg, Germany, bertrain@ifspc228.schiflbau.uni-hamburg.de
It is difficult to alter an unfavorable Roude number to a favorable one. One way of minimiz-ing, though not totally avoidminimiz-ing, unfavorable interferences is to alter the lines of the hull form design while maintaining the specified main dimensions. With slow ships, wave reinforcement can be decreased if a prominent forward shoulder is designed one wavelength from the stem. The shoulder can be placed at the end of the bow wave, if Cg is sufficiently small. Computa-tional fluid dynamics (CFD) can help in this procedure.
3. Ship's width and stability
Where the width can be chosen arbitrarily, the width will be made just as large as the stability demands. For slender cargo ships, e.g. containerships, the resulting B / T ratios usually exceed 2.4. For ships with restricted dimensions (particularly draught), the width required for stability is often exceeded.
A preliminary calculation of lever arm curves usually has to be omitted in the first design stage, since the conventional calculation is particularly time consuming, and also because a fairly precise lines plan would have to be prepared for computer calculation of the cross-curves of stability. Firstly, therefore, a nominal value, dependent on the ship type and freeboard, is specified for GM. This value is expected to give an acceptable lever arm curve. The metacentric height is usually expressed as sum of three terms: GM = KB + BM - KG.
Based on a recent evaluation of Japanese ships, we estimate:
KB = T ( o . 7 S - 0.285-^^ (1)
The accuracy of this formula is usually better than 1% T. For BM, Murray's formula is still used:
{3CwP - 1)^2
BM = ^ ' (2)
If unknown, CWP is estimated as a function of CB using approximate formulae as given below. 4. 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 center of buoyancy determine the length of entrance, parallel middle body and run of the section area curve.
Recommendations for the choice of CB are usually based on the form CB = Ki - 7^2 i^n (Alexander formula), where Ki and K2 are constants. This is in reality too simplified and cannot be recommended even as a simple estimate any longer. Even if only JP„ is taken as a parameter, real ships show a distinct S-curve shape and not a linear correlation, Jensen
(1994) recommends for modern ship hulls CB according to Fig. 1. Similarly a recent analysis
of Japanese ships gives (Mark Wobig of TU Hamburg-Harburg in personal communication) gives for 0.15 < F„ < 0.32:
CB = -4.22 + 27.8 • y/F\, - 39.1 • F„ + 46.6 • (3)
Schneekluth and Bertram (1998) give further formulae for estimating CB including as an
ad-ditional parameter L/B. These formulae are based on optimization calculations for 'lowest production costs' for specified deadweight and speed.
5. Midship section area coefficient and midship section design
The midship section area coefficient CM is rarely known in advance by the designer. The choice is aided by criteria of resistance, production, container stowage, and roll damping. Fig. 1 shows recommended values for modern hull forms. For vertical side walls and flat bottom, the bilge radius is:
R = - CM) • 2.33 -BT (4)
Due to the smaller rolling resistance of the ship's body and the smaller radius of the path swept out by the bilge keel, ships with small CM tend to experience greater rolling motions in heavy seas than those with large CM- The simplest way to provide roll-damping is to give the bilge keel a high profile. Schneekluth and Bertram (1998) give recommendations for the size of the bilge keel.
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 Fig. 1: Recommended CB and C M , Jensen (1994)
6. Waterplane area coefficient
In the early design stages, Cwp is uncertain. Many approximate formulae for the stability contain CWP- If these formulae are not to be disregarded, Cwp has to be estimated. The value of Cwp is largely a function of CB and the sectional shape. The following are some approximate formulae for CWP of ships with cruiser sterns and 'cut-away cruiser sterns'. As these formulae are not applicable to modern vessels with submerged transom sterns, they should be tested on a 'similar ship' and the most appropriate ones adopted.
U section form, no projecting stern form: Cwp = 0.95Cp -t- 0.17v^l - Cp Average section: Cwp = (1 + 2CB)/3
V section form, possibly as projecting stern form: Cwp = VCB - 0.025
CWP = Cp^^
CWP = (1 + 2 C B / V ^ ) / 3
Tanker, bulker Cwp = ^0/(0.471 + 0.551 • CB)
References
JENSEN, G. (1994), Moderne Schiffslinien, Handbuch der Werften Vol. XXII, Hansa-Verlag
SCHNEEKLUTH, H.; BERTRAM, V. (1998), Ship design for efficiency and economy, Butterworth-Heinemann
