Trans RINA, Vol 153, Part A4, Intl J Maritime Eng, Oct-Dec 2011


block coefficient drops, reducing from an average value of 0.82 or more for existing Panamax ships to around 0.79 for the larger ships. This reduction in CB is likely to be of particular benefit in reducing the relative fullness of the aft lines so help to minimise regions of high curvature and so reduce separation resistance and potentially improve flow to the propeller disc as well as benefitting shipbuilding cost.


In combination with these influences on resistance it is interesting to also consider the corresponding influences on propulsive efficiency. Given that the influences on propulsive efficiency are complex and include the main characteristics of the propeller and blade section as well as the influence of aft body hull shape and local features on propeller–hull interaction [21] the discussion here will be again simply limited to the potential influence of the noted changes in main particulars.


Propulsive Efficiency, ηD or QPC, is the product of Open Water Efficiency, ηO, Hull Efficiency, ηH, and Relative Rotational Efficiency, ηR. Open Water Efficiency depends on propeller diameter, pitch ratio (P/D) and propeller revolutions. Generally the larger the diameter with accompanying


values of P/D and


Water Efficiency, ηO, so may not provide benefit to the overall Propulsive Efficiency.


Similarly, a comparison of typical relationships for


estimating w show a dependence on CB with conversely beneficial values achieved as fullness, V1/3 and B/T increases. If again the formulae proposed by Holtrop and Mennen are considered, although these relationships are too complex to generalise, it is apparent that there is a further dependence


on length and breadth with a


reduction in L/B being potentially beneficial. This is also suggested by Schneekluth and Bertram [23] where a reduction of propeller diameter in proportion to the draught is also beneficial. The complexity of the Holtrop and Mennen relationships reflect the influence of the detailed form of the ship, particularly the aft body lines and propeller clearance, have on the propulsion fractions which are therefore obviously not adequately represented by arguments simply based on simple main parameters. Hence it is difficult to suggest the overall influence of the parameter changes observed but it is likely that with form optimisation values of w around 3 are likely to be achievable.


propeller


revolutions, the greater the value of ηO, Propeller diameter is limited by draught and suitable propeller tip clearances. Where the draught is increased there is obvious benefit but, as has been noted, this is not always the case.


It is of interest to see the potential influence on the latter two terms, namely ηH and ηR, as these are influenced by dimensions and form although there is uncertainty in their estimation.


Hull efficiency accounts for the interaction between the hull and propeller. ηH is defined as (1-t)/(1-w). Therefore to achieve beneficial values the Thrust Deduction, t, value should


Fraction, w, maximised.


With respect to t as a consequence of the propeller’s influence on the aft body, this is generally benefited by larger L/B ratios and finer forms with the longitudinal centre of buoyancy, LCB, forward to improve the flow of water into the propeller. However, these requirements are difficult to meet with fuller ships but, with the reduction in CB suggested, such an approach might be available again in reducing the fullness of the aft body through moving LCB forward. The influence of CB is apparent as this is the parameter that most empirical estimates of t are based upon, with reduction in fullness being beneficial. The estimation of t proposed by Holtrop and Mennen [22] also includes the product of beam and draught and more beneficial values of t are achieved by reductions in both. A reduction in propeller diameter is also beneficial and in the case of the larger ships with a reduced draught this will be the case but such a reduction will likely be outweighed with respect to loss in Open


Relative Rotational Efficiency takes into account the difference between the


propeller in the open water


condition and when behind the ship. Relative Rotational Efficiency is benefitted by increased propeller diameter relative to length and with respect to increasing CB, both of which may not be the case in the ships discussed. ηR also increases with L/Δ1/3 and B/T so some overall benefit is possible.


8. IMPLICATIONS FOR FUEL CONSUMPTION AND CO2 PRODUCTION


It follows from the above analysis that the relaxation of the Panamax beam


constraint be minimised and the Taylor Wake will provide the


opportunity to reduce fuel consumption and therefore make a contribution to the reduction of CO2 production by shipping.


This opportunity stems from two effects:


firstly by virtue of the more efficient new hull forms (without the beam constraint) that are possible for the existing Panamax parcel size (around 80,000 to 85,000 tonnes) and, secondly, by virtue of the larger vessel sizes that may in future constitute the Panamax class of ship (section 5.3 above). These two effects are considered separately below. In making these estimates the methodology and consensus factors proposed in IMO’s “Second Greenhouse Gas Study” have been used [24].


8.1 REDUCTION DUE TO IMPROVED HULL FORMS


As a simple key performance indicator, Table 11 shows the average total installed power per knot of service speed per deadweight for recent, built 2007 to 2010, Panamax and U-Panamax vessels in the 70,000 to 90,000 deadweight range.


A-226


©2011: The Royal Institution of Naval Architects


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