Lego 27feb14
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Predictions of the Resistance and Squat of 12 “Lego” Series Model Hulls L. Lazauskas, Cyberiad, [email protected] February 27, 2014 Summary Predictions of the resistance and squat of Doctors’ “Lego” Series model hulls are compared to measured val- ues. All predictions were made using Flotilla version 6.1. Consult the Monohull Manual for an explanation of the notation used. 1 NOTES The performance of Doctors’ Lego series has been reported in several papers by Doctors and his co-workers [1],[2],[3],[4],[5],[6], and the thesis by Robards [7]. 2 GEOMETRY The Lego series is based on the standard Wigley parabolic hull. In the Lego series, hulls are created from the front half of the Wigley hull with varying amounts of parallel middle body and varying transom stern sizes. Body plans of the hulls are shown in Fig. 1. Principal geometric particulars are summarised in Table 1. 3 RESULTS All results were calculated with Flotilla 6.1. Hulls were represented with 41 waterlines but a different number of stations was used for each hull, varying from 41 stations for Lego 1 to 151 stations for Lego 12. 512 θ-intervals were used in the calculation of hydrodynamic integrals. A different turbulent eddy viscosity was used for each hull, varying from ν t =0.0000095m 2 s -1 for the L=0.75 m Lego 1 hull to ν t =0.0000689m 2 s -1 for the L=2.813 m Lego 12. Consult the Monohull Manual for a description of the method for scaling the turbulent eddy viscosity. 3.1 Resistance Fig. 2 shows the specific resistance components of the vessels. Specific resistance is defined as R/Δ where R is the resistance component and Δ is the weight of the vessel in Newtons. Predictions for Froude numbers greater than 1 are poor for models 1 to 3, the shortest, stubbiest hulls in the set. These hulls are difficult cases for Flotilla and, indeed, for most codes, because they possess very large transom sterns. Another difficulty is that the lengths of the hulls are very short, well below the recommended minimum of about 1.5 m for towing tank models. As expected, predictions tend to become better as the hull length increases. The form drag and splash drag are very small for these hulls. It is possible that the discrepancies between experiments and predictions are due to neglect of splash drag and wave-breaking at very high Froude numbers. In that case, Flotilla’s splash drag model is inadequate. This is not unexpected because the mathematical model was derived from the behaviour of the planing splash of surface effect ships. 1
Transcript of Lego 27feb14
Predictions of the Resistance and Squatof 12 “Lego” Series Model Hulls
L. Lazauskas, Cyberiad, [email protected] 27, 2014
Summary
Predictions of the resistance and squat of Doctors’ “Lego” Series model hulls are compared to measured val-ues. All predictions were made using Flotilla version 6.1. Consult the Monohull Manual for an explanationof the notation used.
1 NOTES
The performance of Doctors’ Lego series has been reported in several papers by Doctors and his co-workers[1],[2],[3],[4],[5],[6], and the thesis by Robards [7].
2 GEOMETRY
The Lego series is based on the standard Wigley parabolic hull. In the Lego series, hulls are created fromthe front half of the Wigley hull with varying amounts of parallel middle body and varying transom sternsizes. Body plans of the hulls are shown in Fig. 1. Principal geometric particulars are summarised inTable 1.
3 RESULTS
All results were calculated with Flotilla 6.1.Hulls were represented with 41 waterlines but a different number of stations was used for each hull,
varying from 41 stations for Lego 1 to 151 stations for Lego 12.512 θ-intervals were used in the calculation of hydrodynamic integrals.A different turbulent eddy viscosity was used for each hull, varying from νt = 0.0000095m2s−1 for the
L=0.75 m Lego 1 hull to νt = 0.0000689m2s−1 for the L=2.813 m Lego 12. Consult the Monohull Manualfor a description of the method for scaling the turbulent eddy viscosity.
3.1 Resistance
Fig. 2 shows the specific resistance components of the vessels. Specific resistance is defined as R/∆ whereR is the resistance component and ∆ is the weight of the vessel in Newtons.
Predictions for Froude numbers greater than 1 are poor for models 1 to 3, the shortest, stubbiest hullsin the set. These hulls are difficult cases for Flotilla and, indeed, for most codes, because they possessvery large transom sterns. Another difficulty is that the lengths of the hulls are very short, well below therecommended minimum of about 1.5 m for towing tank models. As expected, predictions tend to becomebetter as the hull length increases.
The form drag and splash drag are very small for these hulls. It is possible that the discrepanciesbetween experiments and predictions are due to neglect of splash drag and wave-breaking at very highFroude numbers. In that case, Flotilla’s splash drag model is inadequate. This is not unexpected becausethe mathematical model was derived from the behaviour of the planing splash of surface effect ships.
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Robards’ [7] predictions for models 1, 4, 6, 8, 10 and 12 in Fig. 2 were made with the Hydros programof Doctors. It seems that the program was unable to capture all of the features of the resistance curvesdespite the use of two form factors, one applied to the skin-friction and the other to the wave resistance.
3.2 Squat
Fig. 3 shows the change in positions of the bow and stern relative to their static (i.e. at rest) values. Spikesin the curves at higher Froude numbers are due to the hulls running at close to the critical depth-basedFroude number.
The experimental values of the Lego 9 hull were deemed to be atypical and have been omitted. It ispossible that the locations of the forward and aft towing posts were recorded incorrectly.
There is a tendency for Flotilla to under-predict the stern position at high Froude numbers.
Acknowledgements
This research was partly funded by the the Australian Institute of Sport, Rowing Australia, and CSIRO.Thanks to Prof. L.J. Doctors for providing towing tank data.
References
[1] Doctors, L.J., “Prediction of resistance for ships with a transom stern”, The Australian Naval Architect,Vol. 2, No. 2, July 1998.
[2] Doctors, L.J., “Progress in the prediction of squat for ships with a transom stern”, The Australian
Naval Architect, Vol. 3, No. 4, Nov. 1999.
[3] Doctors, L.J., “The squat of a vessel with a transom stern”, 15th Int. Workshop on Water Waves and
Floating Bodies, Cambridge, Israel, 27 Feb. – 1 Mar. 2000.
[4] Doctors, L.J. and Day, A.H., “Steady-state hydrodynamics of high-speed vessels with a transom stern”,24th Symposium on Naval Hydrodynamics, Val de Reuil, France, Sept. 17–22 2000.
[5] Doctors, L.J. and Day, A.H., “Nonlinear effects on the squat of a vessel with a transom stern”, 17thInt. Workshop on Water Waves and Floating Bodies, Cambridge, U.K., 14–17 April 2002.
[6] Doctors, L.J. and Day, A.H., “Nonlinear free-surface effects on the resistance and squat of high-speedvessels with a transom stern”, 24th Symposium on Naval Hydrodynamics, Fukuoka, Japan, July 2002.
[7] Robards, Simon William, “The hydrodynamics of high-speed transom-stern vessels”, M. Engineering
thesis, The University of New South Wales, Nov. 2008.
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Hull L (m) L/B B/T C∇ CB CM CP CVP CWP S/L2
Lego 1 0.750 5.00 1.600 4.48 0.444 0.500 0.667 0.667 0.667 0.297Lego 2 0.938 6.25 1.600 5.05 0.486 0.573 0.729 0.667 0.729 0.243Lego 3 1.120 7.50 1.600 5.65 0.500 0.625 0.750 0.667 0.750 0.204Lego 4 1.313 8.75 1.600 6.32 0.486 0.656 0.729 0.667 0.729 0.173Lego 5 1.500 10.00 1.600 6.60 0.556 0.667 0.833 0.667 0.833 0.158Lego 6 1.688 11.20 1.600 7.10 0.566 0.667 0.850 0.667 0.850 0.141Lego 7 1.875 12.50 1.600 7.61 0.567 0.667 0.850 0.667 0.850 0.127Lego 8 2.063 13.80 1.600 8.18 0.552 0.667 0.828 0.667 0.828 0.114Lego 9 2.250 15.00 1.600 8.47 0.593 0.667 0.889 0.667 0.889 0.107Lego 10 2.438 16.20 1.600 8.91 0.597 0.667 0.896 0.667 0.896 0.099Lego 11 2.625 17.50 1.600 9.37 0.595 0.667 0.893 0.667 0.893 0.092Lego 12 2.813 18.80 1.600 9.88 0.582 0.667 0.874 0.667 0.874 0.085
Table 1: Principal particulars of Doctors’ Lego series model hulls.
Lego 1Lego 1 Lego 2Lego 2 Lego 3Lego 3
Lego 4Lego 4 Lego 5Lego 5 Lego 6Lego 6
Lego 7Lego 7 Lego 8Lego 8 Lego 9Lego 9
Lego 10Lego 10 Lego 11Lego 11 Lego 12Lego 12
Figure 1: Body plans of Doctors’ Lego series hulls.
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0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
R/∆
F
Lego 1 Exp. Robards Wave Hollow Friction Form Splash Total
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
R/∆
F
Lego 2 Exp. Wave Hollow Friction Form Splash Total
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
R/∆
F
Lego 3 Exp. Wave Hollow Friction Form Splash Total
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
R/∆
F
Lego 4 Exp. Robards Wave Hollow Friction Form Splash Total
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
R/∆
F
Lego 5 Exp. Wave Hollow Friction Form Splash Total
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
R/∆
F
Lego 6 Exp. Robards Wave Hollow Friction Form Splash Total
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
R/∆
F
Lego 7 Exp. Wave Hollow Friction Form Splash Total
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
R/∆
F
Lego 8 Exp. Robards Wave Hollow Friction Form Splash Total
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
R/∆
F
Lego 9 Exp. Wave Hollow Friction Form Splash Total
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
R/∆
F
Lego 10 Exp. Robards Wave Hollow Friction Form Splash Total
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
R/∆
F
Lego 11 Exp. Wave Hollow Friction Form Splash Total
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
R/∆
F
Lego 12 Exp. Robards Wave Hollow Friction Form Splash Total
Figure 2: Specific resistance components of Doctors’ Lego series model hulls.
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-0.040
-0.020
0.000
0.020
0.040
0.060
0.080
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
z/L
F
Lego 1 Exp. Bow Exp. Stern Pred. Bow Pred. Stern
-0.040
-0.030
-0.020
-0.010
0.000
0.010
0.020
0.030
0.040
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
z/L
F
Lego 2 Exp. Bow Exp. Stern Pred. Bow Pred. Stern
-0.030
-0.020
-0.010
0.000
0.010
0.020
0.030
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
z/L
F
Lego 3 Exp. Bow Exp. Stern Pred. Bow Pred. Stern
-0.030
-0.020
-0.010
0.000
0.010
0.020
0.030
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
z/L
F
Lego 4 Exp. Bow Exp. Stern Pred. Bow Pred. Stern
-0.020
-0.010
0.000
0.010
0.020
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
z/L
F
Lego 5 Exp. Bow Exp. Stern Pred. Bow Pred. Stern
-0.020
-0.010
0.000
0.010
0.020
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
z/L
F
Lego 6 Exp. Bow Exp. Stern Pred. Bow Pred. Stern
-0.010
0.000
0.010
0.020
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
z/L
F
Lego 7 Exp. Bow Exp. Stern Pred. Bow Pred. Stern
-0.010
0.000
0.010
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
z/L
F
Lego 8 Exp. Bow Exp. Stern Pred. Bow Pred. Stern
-0.010
-0.005
0.000
0.005
0.010
0.015
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
z/L
F
Lego 9 Pred. Bow Pred. Stern
-0.010
-0.005
0.000
0.005
0.010
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
z/L
F
Lego 10 Exp. Bow Exp. Stern Pred. Bow Pred. Stern
-0.010
-0.005
0.000
0.005
0.010
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
z/L
F
Lego 11 Exp. Bow Exp. Stern Pred. Bow Pred. Stern
-0.010
-0.005
0.000
0.005
0.010
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
z/L
F
Lego 12 Exp. Bow Exp. Stern Pred. Bow Pred. Stern
Figure 3: Location of bow and stern of Doctors’ Lego series model hulls.
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