Trans RINA, Vol 152, Part B2, Intl J Small Craft Tech, 2010 Jul-Dec
a) Total resistance of model C2 from table 9: RTM=83.55 N
b) Determine the total resistance coefficient for the model: CTM= 0.0032
c) Determine the frictional resistance coefficient for the model using the ITTC 1957 formula and the mean wetted length, Lm, from table 9: CFM=0.0030
d) Determine the air resistance coefficient for the model: RAAM=5.14 N CAAM=0.0001967
e) Determine the residuary resistance for the ship: CR= 7.15 x 10-6
f) Determine the frictional resistance coefficient for the ship using the ITTC 1957 formula: CFS=0.0019
g) Determine the air resistance coefficient for the ship (assuming same drag coefficient and non-dimensional frontal area at full scale as model. If actual frontal area and drag coefficient are known they should be used here): RAAS=2169 N CAAS=0.000192
h) Determine the total resistance coefficient for the ship: CTS=0.0021
i) Determine the total resistance for the ship: RTS=23761 N
The example has been included to illustrate the difficulties associated with implementing the standard ITTC high speed marine vehicles scaling procedure. This procedure results in a residuary resistance coefficient CR that is very small. The whisker spray resistance calculated using Savitsky’s method [18] gives a values CSM=0.00033. If this is included in the calculation, the resulting value of CR is negative. Since this is unrealistic, one of the resistance components may be too large. That is, either the frictional or air resistance coefficient may be too large. The former depends on the calculation of Reynolds’ number using the mean wetted length and is relatively insensitive to small changes in this length. The suitability of the ITTC 1957 skin friction correlation line may be questioned for such high speed vessels, given its derivation
for conventional merchant ship scaling
(although it is recommended in [16] for high speed craft). Using the Schoenherr method to determine skin friction resistance does reduce the skin friction coefficient but only by a very small amount.
The air resistance coefficient is based on an assumed air drag coefficient of 0.7 (as suggested in [16]). This could
be a source of error, but it is again unlikely to make
sufficient difference to the results given the size of the air resistance component.
Alternatively, the total resistance coefficient as
calculated from the measured total resistance may be too small. This depends on the dynamic wetted surface area – which is the measured quantity with the greatest uncertainty (tables 4 to 10). However, if the maximum calculated uncertainty is applied to the wetted surface area in this example (~10%), the change in total resistance coefficient, together with the attendant changes in air and spray drag coefficients, does not result in a significantly greater residuary resistance coefficient. The explicit inclusion of spray drag still results in a negative value of this coefficient. Further study of the components of resistance of planing craft at both model and full scale is thus required.
It should also be noted that the principal particulars of this standard series, including the highest test speeds, lie outside the range of parameters used by Savitsky in deriving the whisker spray drag formulation [18]. It is unclear what effects this may have had on the calculation of spray drag coefficient for this series – although as observed in section 4.4 the inclusion of spray drag appears to improve the calculation of total resistance from its constituent components.
6 CONCLUSIONS
A new series of hard chine planing hulls has been developed to investigate the performance of modern high speed vessels in calm water and waves. The influence of length-displacement ratio on the resistance, sinkage, trim angle and wetted surface area are investigated for a wider range of speeds than previous studies. Furthermore, the influence of altering static trim and load coefficient are included for some models in the series. The influence of transverse steps on the performance characteristics of the parent model is presented and shown to result
in a
significant reduction in resistance, for either a single or double step. An uncertainty analysis is included with the data.
Dynamic wetted surface areas determined by visual observation are presented for all conditions and shown to decrease with speed for all length-displacement ratios and to decrease with length-displacement ratio. The inclusion of a whisker spray drag term, as initially presented by Savitsky [18], is shown in an investigation of the components of resistance for the parent hull. This spray drag term is significant at speeds higher than Fr∇=5.0. Summation of individual resistance compared to total resistance
components of is
greatly
improved through inclusion of the spray drag term, although there is still a discrepancy.
In order to demonstrate the application of the data presented, examples are given for scaling from model to
©2010: The Royal Institution of Naval Architects
B-59
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66