Summary

1. Introduction

1.1 Mathematical Model

1.2 Wave Resistance

1.3 Viscous Resistance

R_v=1/2*rho*U²*S*C_v

where rho is the water density (herein 1025.9 kg/m³) and S the wetted surface area of the hull. When skin friction dominates, the drag coefficient C_v approximately equals C_f, where C_f is a skin friction coefficient which can be estimated using the ITTC 1957 ship correlation line (Proc. 8th ITTC).

C_f = 0.075/(log₁₀ (R)-2)²

where R = UL/nu is the Reynolds number. Here L is the length of the waterline, and nu is the kinematic viscosity (herein, 1.18838x10^-6m²s^-1).

1.4 Form Effects

In fact, there is still considerable controversy over the very use of form factors, let alone the method to be employed. At a recent conference (FAST97, 1997) there were at least four papers that used form factors in their resistance predictions, and each used or recommended a different method! Obviously, the blithe inclusion of a form factor that seems to improve the fit of a model to some given set of data can be used to mask poor testing procedures, or to blur inadequacies of a mathematical model, or, sadly, both. Small wonder that two recent ITTC Committee meetings recommended that no additional corrections be made in routine resistance predictions of high speed craft (Insel and Molland, 1991).

In their examination of eight-oared rowing shells, Scragg and Nelson (1993) found a simple empirical formula for the form factor of these hulls. Their form factor was based only on the sum of the entrance and exit angles in the waterplane. They also found a good correlation for single and double shells. At first glance then this might seem to be an appropriate factor to use in the estimation of form effects of sea kayaks, given that the waterplane angles are roughly similar. However, sea kayaks can have hollows at the bow and stern, whereas these are explicitly prohibited for competition rowing shells. Hollow bows can lead to a slight reduction in wave drag, but sometimes there is an attendant increase in visous drag due to flow separation. This would not be accounted for in Scragg and Nelson's method. Furthermore, because stability is an important consideration for kayaks, they have smaller length-to-beam ratios than rowing shells. Consequently, three-dimensional effects are likely to be greater for kayaks than for thinner hulls.

In the present study we use Holtrop's (1984) empirical method which is based on a regression analysis of random model and full scale test data of a wide variety of hull forms. For the sake of comparison, we also show results for the case with no additional form drag component.

1.5 Experiments

2. Results

2.1 Chinook

Chinook: Body Plan

Chinook: Total resistance

2.2 Puffin

Puffin: Body Plan

5

Puffin: Total resistance

2.3 Sea Runner

Sea Runner: Body Plan

Sea Runner: Total resistance

2.4 Wind Dancer

Wind Dancer: Body Plan

Wind Dancer: Total resistance

2.5 Comparisons

In the following figure, the total resistance coefficient is defined by
C_t = R_t/(1/2*rho*U²*D^2/3)
where
R_t is the total resistance in Newtons,
U is the speed of the boat in ms^-1,
rho is the density of water in kg m^-3, and
D is the displacement of the boat in m³.

The volumetric Froude number is given by
F_nv = Ug^-1/2D^-1/6
where g is gravitational acceleration.

Comparison: Total resistance coefficients (including form effects)

In general, there is a pronounced hollow in the graphs of C_t at about F_nv = 0.9. These hollows correspond to hollows in the wave resistance curve.

The graph shows that the Puffin hull is superior at the highest speeds considered in the present report. At lower speeds, there is very little difference between the Chinook, Sea Runner and Puffin hulls. This is consistent with the experimental results.

3. Conclusion

Of course, it would be a fairly simple matter to deduct the estimated wave resistance and skin friction from the experimentally derived total drag, and thence to derive a simple form factor specific to the sea kayaks examined in the present note. But then again, the cooking time and the mess in the kitchen doesn't always justify the fudge!

The monetary rewards of sea kayak and canoe design have never been sufficient to justify tank testing or any other objective and methodical method of hull form development. Designers have, therefore, relied upon subjective evaluations of boats to determine performance values. This is neither reliable nor consistent. Test paddlers carry with them an extraordinary amount of baggage including personal and aesthetic bias, moods swings, the inability to duplicate test protocols and the more obvious inability to quantify or even sense performance variations in any reliable manner. This and the absence of formal design training for most designers results in a wide range of hull forms and little consensus on what is good or bad. Almost every shape has its proponents and detractors.

Existing performance prediction methods based upon empirical data (Savitsky, Holtrop, Winters) have not proven satisfactory because there isn't enough data to span the range of hull forms and dimensions that constitute the genre. The fit between the predicted values and test values in this series is encouraging and computer programs such as Michlet (Lazauskas and Tuck, 1997) and GODZILLA (Lazauskas, 1997) may provide designers in this field with economical and reliable tools in developing hull forms.

4. References

Proc. Fourth Int. Conf. on Fast Sea Transportation, FAST'97, Sydney, Australia, 21-23 July, 1997.

Proceedings of the 8th ITTC, Madrid, Spain 1957, published by Canal de Experiencias Hidrodinamicas, El Pardo, Madrid.

Insel, M. and Molland, A. F., "An Investigation into the Resistance Components of High Speed Displacement Catamarans"", RINA 1991, pp. 1-20.

Jackson, P. S., Performance Prediction for Olympic Kayaks, J. Sports Sciences, 1995, vol. 13, pp. 239-245.

Lazauskas L. User's Guide for GODZILLA, The University of Adelaide, Applied Mathematics Report, 1997, in preparation.

Lazauskas L. and Tuck, E. O., User's Guide for Michlet, The University of Adelaide, Applied Mathematics Report, 1997, in preparation.

Michell J.H., The wave resistance of a ship, Phil. Mag. (5) vol 45, pp. 106-123, 1898.

Noble, Peter, Wadden, Michael, Bourke, Timothy, Williams, David and Nordbo, Knut, An Introduction to Ethnotechnology for Naval Architects: Sea Kayak Design of Yesterday and Tomorrow, Marine Tech., Vol. 31, No. 4, Oct. 1994, pp. 305-314.

Sea Kayaker Magazine, Winter 1986, pp. 35-40.

Scragg, Carl A. and Nelson, Bruce D. "The Design of an Eight-Oared Rowing Shell", Marine Technology, Vol. 30, No. 2, April 1993, pp. 84-99.

Tuck, E. O., Wave Resistance of Thin Ships and Catamarans, Report T8701, Applied Mathematics Department, Uni. of Adelaide, 1987, pp. 21.