Trans RINA, Vol 157, Part A3, Intl J Maritime Eng, Jul-Sep 2015
Table 3: Minimum achieved non-dimensional drag and corresponding slenderness ratio. Slenderness ranges where normalised drag was within 5% of minimum value
Fr = 0.29
Lowest non- dimensional drag
LIGHT HEAVY
Corresp. Slendern.
Slendern. w/i 5% of lowest achieved drag
0.137 11.5 10 – 14
MEDIUM 0.147 13.0 11 – 14 0.164 13.2 11 – 13
Lowest non- dimensional drag
Fr = 0.37
Corresp. Slendern.
Slendern. w/i 5% of lowest achieved drag
0.117 11.5 10.5 – 14 0.122 11.9 10.5 – 13 0.129 12.2 10 – 13
Lowest non- dimensional drag
Fr = 0.45
Corresp. Slendern.
Slendern. w/i 5% of lowest achieved drag
0.132 12.7 12 – 15 0.134 13.0 11.5 – 14.5 0.138 13.2 11 – 13.5
3.3 (a) Non-dimensional Analysis
around L/1/3 = 13 observed for all three cases. The difference for the varying displacements is indistinguishable and the drag solely depends on the slenderness ratio with the effect of transom immersion becoming negligible. At this particular Froude number the biggest impact of the slenderness on the resistance can be seen and drag savings of up to 25% can be
Figure 12 c) indicates that at Fr = 0.45 an increasing slenderness leads to a reduction in drag with a minimum
achieved if a slender hull is used with L/1/3= 13 instead of 9.
The most appropriate slenderness for the three Froude numbers presented varied from 11.5 to 13.2 whereas the difference between the minimum values for the light and heavy displacement varied by 20%, 10% and 5% for Fr = 0.29, 0.37 and 0.45 respectively. The slenderness ratio may be varied up to +/- 2 to be within 5% of the lowest achieved value. See Table 3 for the values of lowest drag, corresponding slenderness ratio and the range of slenderness ratio to remain within 5% of the lowest achieved value. Furthermore, for most cases it was observed that
the optimum values of slenderness
featuring minimal resistance with respect to buoyancy exist and exceeding the optimum slenderness can lead to an increase in resistance at a similar rate than the decrease at slenderness ratios below the optimum value.
3.3 (b) Transport Efficiency
The performance of a ferry in operation should not only be assessed by its drag with respect to its displacement, but
also the drag with respect
TE dwt g V = Pinstalled
If we assume that ©2015: The Royal Institution of Naval Architects A-169 to its payload or
deadweight which can be defined as transport efficiency. In earlier work [19], transport efficiency was defined as:
and P=R V, ET
Transport efficiency can be expressed as Propulsion
TE = η RT
It was assumed that ηpropulsion = 0.5 and is constant for all speed, hulls and displacements. Therefore, transport efficiency is inversely proportional to the total drag over deadweight.
Figure 13 (a-c) shows the transport efficiency over the speed range from 20 – 35 kn for each displacement. It decreases with increasing values at
higher displacements. For
speed and reaches higher the light
displacement case the transport efficiency of the different length ships ranged from 10.5 at 20 kn to 3.5 at 35 kn. The highest transport efficiency was achieved for the 150 m hull throughout the speed range, with other hulls being capable of reaching within 5% or 10% of the highest value depending on the speed range, only the 190 m hull did not reach within 10% of the highest transport efficiency at any speed. Most appropriate speed ranges for each hull are summarised in Table 4 and Figure 14.
Secondly, for the medium displacement case the transport efficiency varied from 15.5 to 6 over the entire speed range. Again the 150 m hull demonstrated the best performance throughout the speed range and the shortcomings of the 110 m hull and 130 m hulls were noted.
Finally, for the heavy displacement case the transport efficiency ranged from 20 to 8.5 over the speeds under consideration. The 170 m and the 190 m hulls show most beneficial transport efficiencies throughout the all speeds, with major drawbacks for the 110 m and 130 m hull.
dwt g
P=P η inst E Propulsion /
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