Ship & Boat International May/June 2007

Keel Ventilation Lenght in Full Scale

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

15

Dss=0.125m Dss=0.250m Dss=0.375m

Resistance of planing catamaran with 0.25m step and interceptor

100000 120000

20000 40000 60000 80000

0 20 25 30 35 Speed, Vs [kn]

Fig 3. Ventilation length in model scale for the stepped hulls.

Fi 3. Ventilation length in model scale for the stepped hulls.

resistance however, do not necessarily become lower, because the resistance due to the step (the base drag of the step) increases with increasing step height. Fig 4 shows the trim angle as function of

speed. For the stepped hulls, the trim is given both in terms of the local trim angle (Local DSS), which is the running trim of the bottom of each hull, and the total trim angle (Total DSS), which is the trim of the vessel itself. The total trim angle will be smaller than local trim angle, the difference increasing with increasing step height. It is seen that increasing the step height decreases the running trim at higher speeds. It is believed that this is due to the high pressure in the stagnation zone at the end of the ventilated area. When the ventilation length increases

(Fig 3), this high pressure zone moves aft, thus reducing the running trim. However, analyses of the residual resistance coefficient of the different alternatives suggests that the reduction in resistance due to the step is not due to a beneficial change in trim, since the residual resistance coefficient is not reduced by the trim, but due to a reduction in wetted area due to the ventilated area of the rear hull.

Interceptor blade at the step edge In order to see how the stepped hull could be further improved, an interceptor blade was mounted on the step edge. Step height of Dss Dis

=16.7mm and Dis =25mm was

tested. The results are shown in Fig 5. For the highest speeds (above 32knots) the

interceptor reduces the resistance both relative to the stepped hull without interceptor and the smooth hull. Around and above 40knots the reduction relative to the smooth hull is about 20%. This is due to several effects. The interceptor creates a region of high pressure on the aft part of the fore planing surface. In this region the pressure is rather low on conventional planing surfaces.

Trim angle stepped hulls

0.00 0.50 1.00 1.50 2.00 2.50

15 Keel Ventilation Length in Full Scale 10.00

Smooth hull Local Dss=0.125 m Local Dss=0.250 m Local Dss=0.375 m Total Dss=0.125 m Total Dss=0.250 m Total Dss=0.375 m

20 25 30 35 Speed, Vs [kn]

Fig 4. Trim angle for the hulls with step compared to the smooth hull.

SHIP & BOAT INTERNATIONAL MAY/JUNE 2007 40 45 50

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

15

Dss=0.250m Dis=0mm Dss=0.250m Dis=16.7mm Dss=0.250m Dis=8.3mm Dss=0.250m Dis=25mm

40 45 50 15 20 25 30 35 Speed, Vs [kn]

Fig 5. Total resistance for smooth hull, hull with 0.25m step height, and hull with 0.25m step and interceptor at step edge.

The lift therefore increases and the wetted

surface of the fore planing surface is reduced. Another effect is that the interceptor deflects the flow from the step edge and directs it downwards compared to the case without interceptor. This increases the ventilation length, resulting in reduced wetted surface of the aft planing surface, see Fig 6. For the lowest speeds the interceptor only

creates increased resistance. As we see from Fig 6, the ventilation length is not increased due to the interceptor for a speed of 25knots. Then we have only the increased resistance due to the interceptor, and no reduction in resistance due to reduced wetted surface. The interceptor resistance increases with interceptor depth, as is seen in Fig 5 for the 25knots speed. However, for the 40knots speed, the variation

in interceptor depth has another effect. We see that among the interceptor depths that are tested, the depth of 16.7mm is the most optimal. Both when the interceptor depth goes down to 8.3mm and when it goes up to 25mm, the resistance increases. This suggests that the ideal interceptor depth

=0.250m was chosen. Interceptor depths of =8.3mm, Dis

lies somewhere between 8.3mm and 25mm, maybe somewhere around 16.7mm. Fig 6 shows that the ventilation length increases with increasing interceptor depth for the highest speeds. When this although do not result in reduced resistance when the interceptor depth goes from 16.7mm to 25mm, it is because the interceptor resistance increases more than the frictional resistance decreases. Fig 7 shows the trim angle for the hull

with step and different interceptor heights, compared to the smooth hull. It is seen that the use of interceptor increases the running trim significantly at the highest speeds, since the interceptor creates significant lift located just in front of the step. Again, when comparing the trim and resistance of smooth and stepped hulls it can be concluded that the reduction in resistance is not primarily due to more beneficial trim, but probably due to reduced

40 45 50

Smooth hull Dss=0.25m Dis=0mm Dss=0.25m Dis=16.7mm Dss=0.25m Dis=8.3mm Dss=0.25m Dis=25.0mm

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

15

Trim angle 0,250m Step and interceptor

Smooth hull Local Dss=0.250m Dis=0mm Local Dss=0.250m Dis=16.7mm Total Dss=0.250m Dis=0mm Total Dss=0.250m Dis=16.7mm Local Dss=0.250m Dis=8.3mm Local Dss=0.250m Dis=25mm

20

25

30

35 Speed, Vs [kn] Fig 5. Total resistance for smooth hull, hull with 0.25m step height, and hull with 0.25m step and

Fig 7. Running trim angle for smooth hull, hull with 0.25m s Fig 7. Running trim angle for smooth hull, hull

with 0.25m step height, and hull with 0.25m step and interceptor at step edge.

wetted surface. Fig 8 shows the dynamic (running) wetted

surface. The smooth hull is compared to the hull with step and with step and interceptor. It is clearly seen how the step decreases the running wetted surface at high speeds, and how the interceptor decreases the wetted surface even more. The similarity with the plot in Fig 6 showing ventilation length is obvious. The running wetted surface was determined from observations of ventilation length, and intersection between the water and the keel at the bow, and between the water and the chine both at the bow and aft of the step. Fig 9 shows the total and residual resistance

coefficients for the smooth hull compared to the hull with step and interceptor. The alternative hull configurations are the same as in Fig 5. The resistance coefficients are calculated as C = R/(1/ N and S0

2rV 2 S0 ), where R is resistance in is the wetted surface at zero speed

(excluding the wetted area of the transom). Dynamic (running) wetted surface is only used to calculate the frictional resistance in model and full scale.

interceptor at step edge. Dynamic wetted surface

100.0 120.0 140.0

20.0 40.0 60.0 80.0

0.0 20

40

45

50

Dss=0.250m Dis=16.7mm Dss=0.250m Dis=25mm Dss=0.250m Dis=8.3mm Smooth hull Dss=0.250m Dis=0

25 30 35 Speed, Vs [kn]

Fig 8. Dynamic wetted surface for smooth hull, hull with 0.2 Fig 8. Dynamic wetted surface for smooth hull,

hull with 0.25m step height, and hull with 0.25m step and interceptor at step edge.

step and interceptor at step edge. Total resistance coefficient and residual resistance coefficient

0.00E+00 1.00E-03 2.00E-03 3.00E-03 4.00E-03 5.00E-03 6.00E-03 7.00E-03 8.00E-03

0.60 0.80 1.00 1.20

Smooth hull Dss=0.250m Dis=0mm Dss=0.250m Dis=16.7mm Dss=0.250m Dis=8.3mm Dss=0.250m Dis=25mm Smooth hull Dss=0.250m Dis=0mm Dss=0.250m Dis=16.7mm Dss=0.250m Dis=8.3mm Dss=0.250m Dis=25mm

40 45 50

1.40 Froude number based on Lpp, Fn [-] 20 Fig 4. Trim angle for the hulls with step compared to the smooth hull. 25 30 Fig 6. Ventilation length. Fig 6. Ventilation length. 35 Speed, Vs [kn] 40 45 50

Fig 9. Total resistance coefficient in full scale Cts and residual resistance coefficient Cr for smooth hull, hull with 0.25m step height, and hull with 0.25m step and interceptor at step edge.

63 Fig 9. Total resistance coefficient in full scale Cts and residu

1.60

Trim angle [degrees]

Ventilation length [m]

Ventilation length [m]

Rts [N]

Cr [-]

Cts [-]

Dynamic wetted surface [m2]

Trim angle [degrees]

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 | Page 67 | Page 68 | Page 69 | Page 70 | Page 71 | Page 72