Trans RINA, Vol 152, Part B2, Intl J Small Craft Tech, 2010 Jul-Dec 4.2 DYNAMIC SINKAGE
The dynamic sinkage of models A, C, D, C1 and C2 is presented in figures 11 to 16, respectively. The influence of L/∇1/3 on dynamic sinkage is shown in Figure 30 and illustrates that the non-dimensional sinkage increases with L/∇1/3. Results for model B are omitted since valid data were not recorded due to a faulty sensor.
Figure 34 shows that there is no significant influence of transverse steps on the dynamic sinkage. Figure 38 indicates that as load coefficient increases the non- dimensional
sinkage (ZV/∇1/3) increases by a small
amount. 4.3 DYNAMIC TRIM
The dynamic trim of models A,B,C,D,C1 and C2 is presented in figures 17 to 22, respectively. The influence of model, or L/∇1/3, on dynamic trim is shown in Figure 31. This shows that the dynamic trim angle increases with reducing L/∇1/3. This is to be expected given the smaller wetted surface area as L/∇1/3 reduces.
The influence of transverse steps and load coefficient on dynamic trim are shown
in Figures 35 and 39,
respectively. These figures indicate that there is little influence of transverse steps on the dynamic trim angle and that a higher load coefficient increases the dynamic trim angle in a speed range approximately 3.5< Fr∇ <5.5.
4.4 WETTED SURFACE AREA AND SCALING
One of the most difficult parameters to determine experimentally for planing craft is the dynamic wetted surface area. There is no universal, or recommended, method that may be applied [16], yet its determination is critical if scaling from model to full scale is to be achieved and power predicted accurately. Methods to determine dynamic wetted surface area vary from visual observations of the points where the flow separates from the hull (transom immersion, spray root line crossing chine edge and keel) to underwater video use.
The dynamic wetted surface area (aft of the spray root line) was determined from photographs of the model taken during each run. Wetted surface areas for models A,B,C,D,C1 and C2 are presented in figures 23 to 28, respectively. Figure 32 shows that non-dimensional wetted surface area reduces with reducing L/∇1/3.
Scaling of resistance data from model to full scale may also be undertaken by different methods and again there is no universal or recommended procedure [16]. These methods, although all based on Froude scaling, differ in the manner in which they include whisker spray in the dynamic wetted surface area and the flow direction – hence shear stress on the hull – in the different regions of the wetted surface area. The behaviour of spray is also affected by the surface tension of the water, which leads
B-58
to different behaviour of spray at model and full scale. In general the spray at model scale forms a more continuous body of water, whereas at full scale it tends to break into smaller droplets of
water. As described, in this
investigation the dynamic wetted surface area was determined from photographs of the model taken during each run. The wetted surface area was divided into a ‘whisker spray region’ and a ‘pressure wetted area’ in the manner of Savitsky [18]. However, whereas Savitsky defines the front of the whisker spray region relative to the spray root line, in the present work it is determined directly from the photographs. A representative pair of photographs is shown in figure 4. The image on the left is used to identify the locations where the spray root line and the whisker spray cross the chine edge. The image on the right is used to identify the location where the water contacts the keel. Similar images were used for all runs. The onset flow is assumed to be reflected about the spray root line, to give the flow direction in the whisker spray region. Determination of the spray drag according to [18] allows a spray drag coefficient to be calculated.
ITTC resistance coefficients for model C are presented in figure
41. Individual
determined using the method of Savitsky [18]. The frictional resistance coefficient
ITTC 1957 skin friction line, using the Reynolds’ number based on the mean dynamic wetted length.
In line with recommended ITTC procedures [16] the air resistance of the model is calculated. The air resistance is calculated assuming a drag coefficient of 0.7 and the model frontal area, as suggested in [18]. CD is the horizontal component of the lift vector calculated using Savitsky’s method [18]. Figure 41 illustrates that spray drag becomes significant above a speed of Fr∇=5.0. Explicit inclusion of the spray drag term improves agreement between a summation of resistance components and the measured total resistance, although a discrepancy still remains.
5 SCALING EXAMPLES
An example of how to scale the data presented in this paper to full scale is included below. This example uses a geometrically similar full-scale vessel of model C2 with a scale factor λ=7.5 and hence a length of 15m. The vessel design speed is 64 knots.
5.1 CONVENTIONAL FROUDE SCALING WITH AIR RESISTANCE
In scaling model data for planing craft, the ‘residuary’ resistance may be determined through subtraction of the frictional and air resistance components from the total resistance of the model. A form factor is not generally applied, nor recommended, due to the difficulties in determining a suitable value with separated flow regimes [16].
resistance components are is
obtained from the
©2010: The Royal Institution of Naval Architects
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