(J) (D
2(D
A STUDY ON STERN WEDGES AND ADVANCED SPRAY RAIL
SYSTEM ON CALM WATER RESISTANCE
OF HIGH-SPEED
DISPLACEMENT HULL FORMS
Q)-
Predrag Bojovic Prasanta K Sahoo Marcos SalasABS Americas Department of Maritime Engineering Faculty of Engineering Sciences
O
[6885 Northchase Drive Australian Maritime College, PO Box 986 University Austral of Chile
°
ouston, TX 77060, USA Launceston, TAS 7250, Australia Casilla 567, Valdivia, ChilePbojovic@eagle.org P. Sahoo@mte.amc.edu.au msalas@uach.cl
ABSTRACT
The first part of the research presented was published in the proceedings ofSea Australia
2000 (Bojovic and Sahoo 2000), which presented the results of the tests of model #13 with stern wedges, with and without spray rails. The wedges were faired into the hull surface at the bilges and had O 4 70 and 100 angles relative to the hull surface. Two pairs of spray
rails were fitted based on the Advanced Spray Rails System, described by Muller-Graf (1991).
The research presented in this paper was performed with spray rails and included additional wedge angle tests on model #13, together with a set of tests with increased wedge length (3%
instead of 2% Lpp). In addition, models #05 and #09 were tested with spray rails and
wedge length of 2%
over the range of wedge angles and speeds. The test results
demonstrated very valuable benefits available from stern wedge fitting to this type of vessel. They are presented together with the results of the analysis. The effect of wedge angle variation is discussed and a mathematical model was developed and implemented as the
performance prediction sojh.vare. The effect of wedge length variation is also discussed.
1 INTRODUCTION
1.1 BACKGROUND
The systematic series of high-speed displacement hull forms is obtained from two parent hulls by systematic variation of three hull form parameters - LIB, B/T and CB. The series' parameter space with the fourteen models built to date is presented in Figure 1.
1.2 TESTING OUTLINE
The results of earlier work regarding the application of spray rails and stern wedges have
been described Bojovic and Sahoo (2000). That work contains the literature review, reasons
leading to stem wedge tests rather than trim tabs ones, descriptions of testing procedure,stern wedge configuration, spray rails geometry and test results. Table 1 presents the test matrix for the set of tests carried out with model #13.
These tests clearly demonstrated significant benefits available from the installation ofstem wedges, as the CR reduction was in excess of 10% for Fn above 0.4. A larger decrease of
residuary resistance was achieved at higher wedge angles, indicating that the optimum wedge angle was greater than 10°. Another look at the literature, Muller-Graf (1991), found that tests in the Berlin Model Basin also didn't reach the optimum wedge angle with wedge angles
up to 10°, as can be seen from Figure 2.
Table 1: Test matrix for model #13 tests
j
pw
ua
Figure 1: AME CRC Systematic Series Parameter Space
10 -o p30
30
40-I I:--
-10---1--t-- I I ¿ -20- Wd9e L*nQth LW - 0.02133 LWL t I I IT T T
l I 1T r
6« Weg inçUnation I I l.pnd 6,() I IT1t
wthSR2---.2]
1 4 vIthASR$i-.-
(SRisR2) -f- - -- LWL/BWL 6.251 Hufi without pendcg
t 1
-I I I I I
:-t
.-i
rT-\ I
I I I J I I
0.9
Fri -
1.0 1.2Figure 2: Change of Residual Resistance due to the ASRS (MuIler-Graf, 1991) The early test results were found very valuable and provided the motivation to extend the
research work to greater wedge angles. Also, it was decided to test two other series' models, with different L/B ratios, since the literature, Millward (1976), suggests that the LIB ratio
influences benefits from stern wedge installation. For that purpose it was decided to test rebuilt models #05 and #09. From Figure 1 it can be seen that the three models tested (#05,
#13 and #09) lay on the "diagonal" of the systematic series parameter space. Their body
plans are presented in Figure 3 and their particulars in Table 2.
Wedge angle Without Spray Rails With Spray Rails 0° V V 4° V
/
70 V V 100 V V 0.8 0.2 0.3 0.4 0.5 06 0.7Rfer*ncs HuH: without Spray Ra
The earlier tests didn't find explicit benefits from spray rail installation. However, it was
decided to continue performing tests with them, as ITTC (1984) suggests that
semi-displacement round-bilge hulls should be tested with spray rails, in order to avoid substantial increase of the wetted surface area, which could reach 50 to 60% of the wetted surfacearea at rest.
In addition, it was decided to perform an investigation into the effect of stern wedge length,
by conducting tests on model #13 with a wedge length of 3% The test matrix was
defined and is presented in Table 3.
Figure 3: Body plans - models #05, #13 and #09 Table 2: Model particulars
Table 3: Test matrix (all tests)
Models L (m) B (m) T (m) (kg) WSA (m2) L/B BIT CB L/V'
#05 1.6 0.4 0.1 25.347 0.6087 4 4 0.4 5.447 #13 1.6 0.267 0.082 15.777 0.4384 6 3.25 0.45 6.379 #09 1.6 0.2 0.08 12.806 0.3747 8 2.5 0.5 6.839 Wedge angle (deg) #05 (wedge length 2%
L)
#09 (wedge length 2% Lp) #13 (wedge length 2%L)
#13 (wedge length 3%L)
O (bare hull) 4 1 7/
Vf Vf IO/
/
13 1/
/
16/
22/
"
The initial test data analysis performed during and immediately after the testing, concluded that the research outcomes would significantly benefit from an additional set of data for a wedge angle of 22°. Therefore, an extra set of test for 22° wedges (on all three models) was
organised and performed, at the test speeds listed in Table 4.
Table 4: Tested speeds
2 RESULTS
2.1 TEST DATA
Test results were analysed according to the standard procedure, by subtracting the frictional resistance, calculated according to the ITTC 1957 ship-model correlation line, from the total resistance. The residuary resistance was made non-dimensional using the standard formula,
Equation 1:
RI?
CR
2
All tests were performed at the standard displacement, outlined in Table 2, and analysed
using the wetted surface area for the bare hull, as it was assumed that the presence of the stern wedge did not significantly change the wetted surface area.
As expected, the test results of increasing wedge angles followed the trend of resistance decrease up to a certain wedge angle, above which an increase of resistance occurred. In
order to define the influence of the wedge angle variation on the model's performance at the particular tested speed, quadratic parabolas were fitted to the test data. This was performed
using the standard least-squares technique, Kreyszig (1988).
2.2 EFFECT OF WEDGE ANGLE
As mentioned above, the stern wedge installation benefits occur only above Fn 0.4. Below this speed a performance decrease occurs. This performance decrease may be a result of stern
flaps scaling effects. It is known that the flow conditions around the model stern flap are
somewhat different from those on the ship. Actual performance of full-scale prototype stern
flaps during trials have exceeded their model test predictions, exhibiting no negative effects at lower speeds caused by increased transom immersion due to stern wedge presence. At Fn of around 0.40, the residuary resistance of the hull with the wedge is level with the bare hull residuary resistance. Consequently, above this speed performance improvement occurs. It can be seen that a significant decrease of residuary resistance could be achieved with stern wedge installation and the existence of an optimum wedge angle can be seen from these plots.
The results are summarised in Figures 4 and 5. When the installation of a stern wedge (of a given length) is considered for a particular design, there are usually two questions that need to be answered: "what is the optimum wedge (angle)?" and "what are the benefits from the optimum wedge?" Figures 4 and 5 answer those questions. From Figure 4 it can be seen that
(1)
Speed(m/s) 0.6 0.9 1.2 1.3 1.4 1.7 1.9 2 2.1 2.4 2.7 3 3.3 Fn 0.15 0.23 0.3 0.33 0.35 0.43 0.48 0.5 0.53 0.61 0.68 0.76 0.83
I
a relative consistency of trends exists, with a slight optimum wedge angle decrease with speed. Figure 5 quantifies the benefits achievable with stern wedge installation. It also confirms some literature statements, that beamier hulls obtain greater benefits from stern
wedge installation, as model #05 demonstrated the highest residuary resistance reduction.
Figure 5 also illustrates an interesting fact, that the shorter wedge on model #13 is more
efficient than the longer one, at speeds up to approximately Fn 0.73.
Another practical question regarding wedge sizing could be 'how sensitive are wedge
benefits to the deviation from the optimum angle?" Figure 6 illustrates the effect of a wedge angle (±) 2° different from the optimum angle. It can be seen that this variation causes less than 0.5% change in residuary résistance. Figure 7 illustrates the wedge angle limits, which would ensure residuary resistance benefits within 0.5% of the optimal.
0) a) C 0.95 E 0.9 Q. o 0.85
I
0.7 18 l6E6
E4
Q.02
o 0.8+#05
W-#13w2 o O.75----#13w3 L.o
.#05
*#13w2
A--#13 w3Figure 5: C relative to Bare Hull at the optimum Wedge Angle against Fn.
0.4 0.5 0.6 0.7
Fn 0.8 0.9 11
Figure 4: Optimum Wedge angle against Fn.
04 0.5 0.6 0.7
2.4 EFFECT OF SPRAY RAILS
The spray rails used in the tests presented here are described in Bojovic and Sahoo (2000). They are based on Advanced Spray Rail System, described in Muller-Graf (1991). That paper
reports that this spray rail system when combined with the optimum stern wedge leads to remarkable power savings which are larger than the sum of the savings obtained by each
component solely, with improved seakeeping qualities and reduced apparent loss of
metacentric height at high speeds.
Figure 2 presents the results obtained in Berlin Model Basin. They show some benefits
available from spray rail installation only, for Fn between 0.40 and 0.90. Figure 8 presents the test results obtained for three tested models, with and without the spray rails.
The spray rail installation benefits are the most prominent for model #05. It has the lowest LIB and L/V"3 ratios. The spray rails system contributed mostly through the rising of fore-body due to significant lift developed by the spray rails. However, the benefits from spray
rails installation only are not the focus of the research presented here, as spray rails are
recommended for testing of this type of hull.
E o w w w Cs w C, = w w C) w w C, = C, nu C., E E C-e w 0.008 0.00 7 0.006 0.005 0.0 04 0.003 0.00 2 0.001 D -.-- #05 ---#13 w2 -*-#13 w3 )(-- #09 -....-#09 #05 #13w3 A #05 e A #13w3 04 0.5 0.6 0.7 0.8 0.9 Fn
Figure 7: Wedge angle limits for CR within ±0.5% from optimal
0 4 0.5 0.6 0.7 0.8 0.9
Fn
2.5 EFFECT OF WEDGE LENGTH
The sizing of the stern wedge involves selection of the wedge length and the wedge angle.
While the effect of the wedge angle was tested on the three models, the effect of wedge
length variation was tested on model #13 only, with wedge lengths of 2% and 3% Lpp.
In order to visualise the results better, it was decided to use a combination of two overlapping
3D surface plots, as presented in Figure 9. The vertical values represent the CR values
relative to the bare hull condition, as a function of Fn and wedge angle. The intersection of
the two surfaces can be clearly seen on the left side of the figure. On the right side, the
intersection curves and the "optimum-angle" curves for both surfaces are plotted as vertically extruded surfaces. The "height" of these surfaces corresponds to 2% (or 0.02) on the plot's vertical axis. Additionally, the optimum-angle curves are presented in Figures 4 and 5.
o o o Q - - .. #05 without SR #05 with SR --G--#l3withoutSR #l3withSR - - o- - -#09 without SR #09 with SR 01 0.3 0.5 0.7 0.9 Fn
Figure 8: Test results with and without spray rails
Figure 10 presents the same surface plots, but with contour curves on them, in order to better visualise trends of change. These contour curves are presented in a contour plot in Figure 11. It can be seen that "the best" shorter wedge performance (at the optimum angle) provides a
better performance than "the best" longer wedge performance for Fn up to 0.7. The longer wedge is more efficient above this speed. An explanation of this could be speculated on the
basis of trade-of between wedge's induced
drag and hull drag reduction due to
morebeneficial vessel's trim. It is also possible that the wedge angle change is more efficient than
wedge length change in changing the vessel's trim. This deserves a further investigation, perhaps through some additional testing ofone or more models.
3 CONCLUDING REMARKS
The first part of the research identified clear benefits available from the installation ofstern
wedges on one of the series' models. This provoked further research into this area and the subsequent towing tank tests explored wedge angles above 100 and the effect of wedge length change. Also, two additional series' hulls were tested with 2% Lpp wedge over the range of
wedge angles and speeds. The test matrix is outlined in Table 3. The current research
2% Lfr E
2% L - crrvw
0.6 67 0.1 0.9 LO
FN
Figure 11: CR relative to the bare hull- contour plot
Figure 9: CR relative to the bare hull- 2% and 3% Lpp wedge lengths
The test
results confirmed there are significant benefits available from stern wedge
installation on this type of vessel. While the results present a very reliable source of data,
some additional tests would make the picture more complete. It would be beneficial to test
some additional models to identify the correlation between the wedge effects and the hull
parameters. After considerable thought, the wedge effect was linked to L/V"3, while arguably
it could have been linked to L/B or some combination of the series'
parameters. Theinvestigation of wedge length variation provided interesting results arid additional tests with one or more models would provide better understanding of interrelating parameters - wedge length and wedge angle, leading to highly practical outcomes.
While the main focus of this report was in quantifying and optimising stern wedge benefits, which at model scale occur only at Fn >0.4, care was taken to enable reliable estimates of the performance penalty below this speed. As mentioned in section 2.2 full-scale performancesat
low speed might be better than the corresponding one at model scale.
On the other hand, if something could be improved, then it was not perfect in the first
instance. While the test results presented here indicate that stern wedge should be
incorporated into the design of this type of vessel, they could also be interpreted as an indication that the hull should be altered. Maybe "classic" straight aft buttocks should be
made slightly "hooked" to incorporate the wedge in a more natural way and to enable lift
generation along a greater length. A similar approach, for hard-chine, planing vessels, was
examined in Blount (1995). Both convex and concave aft buttocks shapes were explored.
4 ACKNOWLEDGMENTS
The authors would also like to thank the authorities of the Australian Maritime College and
the University of Austral of Chile for their continued support during the course of this research work.
5 NOTATION AND ABBREVIATIONS
AMECRC Australian Maritime Engineering CRC Ltd
ASRS Advanced Spray Rail System
B Model beam
B/T Beam-draft ratio
CB Block coefficient (V / L x B x T)
CG Centre of Gravity
CR Coefficient of residuary resistance
Fn Froude number based on length
ITTC International Towing Tank Conference
L Model length
LIB Length-beam ratio
LCG Longitudinal centre of gravity
Length between perpendiculars
L/V"3, L/voV'(l/3) Length-volume ratio (slenderness) ratio
T Model draught
6 REFERENCES
Bojovic, P. and Sahoo, P. (2000): "Effect of Stern Wedges and Advanced Spray Rail System on Calm Water Resistance of High-Speed Displacement Hull Forms", Proc. Of Sea Australia 2000, Sydney, Australia.
Blount, D.L. (1995): "Factors influencing the Selection of a hard Chine or Round Bilge Hull for High Froude Numbers", Proc. of Fast Sea Transportation 1995, pp 3-20
Miliward, A. (1976): "Effect of Wedges on the Performance Characteristics of Two Planing Hulls". Journal of Ship Research, Vol. 20, No. 4, pp. 224-232.
ITTC (1984): "A survey of Available Knowledge on the Drag Scaling of Model
Appendages", 17th IT[7'C, pp. 368-376.
Kreyszig, E. (1988): "Advanced Engineering Mathematics", Sixth Edition, John Wiley &
Sons, Section 19.5, pp. 1029-1031
Muller-Graf, B. (1991): "The Effect of an Advanced Spray Rail System on Resistance and Development of Spray of Semi-Displacement Round Bilge Hulls", Proc. of Fast Sea
