Trans RINA, Vol 153, Part A4, Intl J Maritime Eng, Oct-Dec 2011
The influence of the relaxation of the beam constraint is of greatest significance for ships at the bottom end of the new Mini-Cape class where it overlaps with the Panamax sector at a deadweight of around 85,000 tonnes. This is effectively the unconstrained version of the traditional Panamax12 class of ship whereby increase in displacement is achieved predominantly by increasing beam with only a modest change in length, up to only 236.0m in the longest flexibility in terms of
case with potentially more block coefficient selection.
Analysis of this sector enables the effects of the relaxation of the constraint on hull form and performance to be isolated from the additional effects of increased deadweight with larger Mini-Capesize ships. In the analysis below these unconstrained vessels are referred to as “U-Panamax”.
Figure 13, summarises the dimensional ratios observed in a sample of 223 recent (built since 2000) bulk carriers between 80,000 and 90,000 deadweight, divided into traditional Panamax (155 vessels) and U-Panamax (68 vessels). Analysis of the implications of these changes is presented in Section 7.2
7.2 IMPLICATIONS OF THE CHANGES IN RATIOS
It is of interest to give a broad appreciation of the
influence of these changes in dimensional ratios with respect to ship cost, performance and operation; the principal interest being resistance and propulsion given that most other performance criteria, such as stability and strength, are likely to be equally met by both designs.
7.2(a) Influence on first cost
The observed values of L/B and B/T all fall within generally accepted values, such as those given by Watson [19]. It is worth noting the influence that length has on the first cost, however. relationship
Fisher [20] between a 1% change
estimates the in
principal
dimensions and block coefficient with the percentage change in capital cost. The order of the influence of length, beam, depth (draught) and block coefficient is the same as that noted by Watson. Namely that as a means to increase deadweight and displacement, increasing beam is a cost effective course where draught and fullness cannot be increased further.
The depth in the U-Panamax designs remains largely unchanged. The L/D ratio is increased slightly in the case of the largest beam designs due to the increase in length. As the design bending moment will be slightly increased due to the length and displacement increase in these designs there is a slight increase in the steel mass and lightships that results in a marginal reduction in
12 Panamax in this context referring to a specific size class of bulk carrier, rather than the limiting dimensions of the Canal.
©2011: The Royal Institution of Naval Architects
deadweight displacement ratio, Kd, from 0.87 to 0.86 from the data collected; especially as the increase in beam also provides a less structurally efficient value of B/D. This has attendant implications for first cost.
7.2(b) Influence on stability
From a stability perspective if the draught is restricted then the beam is normally larger than would otherwise be required so bulk carriers tend to have higher stability than required due to other design considerations.
worth noting that for an increase in beam for the same depth then there will be a reduction in the angle at which deck
edge immersion occurs with a corresponding
reduction in the angle of maximum righting lever, GZ, but that the increase in beam will have the benefit of increasing the transverse metacentre, KMT, and initial stability even if the range of stability is reduced.
The modest increase in length will result in an increase in the required rule freeboard but U-Panamax ships, relative to Panamax vessels of similar size, exhibit a reduction in depth in order to meet this freeboard requirement as the design draught is reduced from around 14.5 to under 14.0 and as low as 12.8 m for the largest beam designs explaining the reduction in T/D previously observed.
7.2(c) Influence on resistance and propulsion
Resistance is influenced by principal dimensions, form parameters such as CB and LCB, as well as more detailed issues regarding section shape and features such as bulbous bows. The discussion here is limited to trying to assess the influence of the noted changes to principal dimensions and form characteristics.
The value of circular M, or length to displacement ratio, L/Δ1/3 for both classes of ship is 5.0 which is consistent with the general guideline that there is no advantage to increase this quantity above 5.2 for CB over 0.75. The increase in beam results in reduced values of L/B consistent with benefitting resistance at Froude numbers, Fn, around 0.15,
predominates, about 65%
where frictional resistance of total resistance, and
residuary resistance accounts for the remaining smaller proportion of the total still water resistance, namely about 35% of total resistance. Therefore the reduction of wetted surface area afforded by a lower L/B and a deep ship is of benefit. This is partly mitigated by an increase in B/T that has generally a detrimental effect on resistance although the influence of changing B/T in this range for fuller slower ships is less than for faster finer ships. For an average B/T value of 2.4, an increase to around 3.0 would increase resistance in the order of around 3% for a full bodied ship with Froude number around 0.14 and CB approaching 0.85, so the increase in beam and reduction in draught observed is not beneficial. For lower L/B ratios there would be expected to be a reduction in CB to compensate and if some of the data for U-Panamax vessels is studied then it does appear that the
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