Hydrodynamic Drag of Some Small Sprint Kayaks

Leo Lazauskas - The University of Adelaide, Australia
and
John Winters - Redwing Designs, Canada

Dept. Applied Mathematics Technical Report LW9701
30 October 1997

Summary

Some popular small (0.098 m3 displacement volume) sprint kayaks are compared on the basis of their upright, calm-water, total (wave plus viscous) resistance. Comparisons are also made with the drag of some simple mathematical hullforms, and with a kayak optimised for minimum total resistance under constraints intended to give adequate intact stability.

Introduction

The purpose of the present note is to compare the total resistance of some sprint popular kayaks. We are also interested to see how these extant boats compare with a hull optimised for minimum total resistance.

The offsets for the kayaks were provided to the authors from a variety of sources. In light of this, we cannot guarantee that the offsets correspond to exact model names. We also stress that we are only looking at the total calm-water drag. If we say that one hull is superior to another, we only mean that within a very limited context. There are many factors that we have not taken into account that affect the overall performance of kayaks under real racing conditions. For example, and among many others, we do not include the effects of the change of speed during a paddle stroke, nor the effect of changes of trim and sinkage.

The mathematical hulls in the present note have parabolic waterlines and elliptical cross-sections. PEP hulls have parabolic sideviews, PEE hulls have elliptical sideviews, and PER hulls have rectangular sideviews. Hull lines for these and the other hulls are shown in the Appendix.

Mathematical Model

Wave resistance was predicted using Michell's integral, see Tuck (1987). The hulls were represented by 21 equally spaced stations and 21 waterlines; 320 intervals of theta were used in the calculation of the integrals. The standard ITTC correlation line was used for the viscous resistance. No allowance was made for form drag effects. The computer program Michlet (Lazauskas, 1997) was used for all calculations.

Results for the boats will be given in the form of two graphs. The first graph shows the volumetric resistance coefficient as a function of boat speed (in knots). The second shows the surface area-based total resistance coefficient.

The total (volumetric) resistance coefficient, is defined by
Ctv = Rt/(1/2*rho*U2*D2/3)
where
Rt is the total resistance in Newtons,
U is the speed of the boat in ms-1,
rho is the density of water (herein 1021.8) in kg m-3, and
D is the displacement of the boat in m3.
The kinematic viscosity is 0.000001054 sq. m per sec.

The total (area-based) resistance coefficient, is defined by
Cts = Rt/(1/2*rho*U2*S)
where
S is the wetted surface area in m2.

In the tables showing the principal dimensions of the boats, Cp is the prismatic coefficient based on the (submerged) mid-section area.

John Winters' Sprint Kayak

This boat was designed by the second author.

The principal dimensions of the boats are given in the following table. In all cases, the length on the waterline of each boat is 5.138 metres, and the waterline beam is 0.3596 metres.

Quantity JW PEP PEE PER
Draft (metres) 0.111 0.127 0.115 0.102
Wetted Area (sq. m.) 1.777 1.703 1.739 1.818
Cp 0.635 0.534 0.590 0.667

Table 1: Principal dimensions of Winters' kayak and equivalents

Figure 1(a): Total (volumetric) resistance coefficients

Clearly, at racing speeds, say between 6 knots and 13 knots, the PER hull has the lowest total resistance. In this range, the drag of the PEE hull and the Winters' hull are quite similar.

Figure 1(b): Total (area-based) resistance coefficients

'Eagle-like' Kayak

The offsets for this boat are similar to those of the Eagle kayak, an American boat popular with top level paddlers for a number of years.

The principal dimensions of the boats are given in the following table. In all cases, the length on the waterline of each boat is 5.144 metres, and the waterline beam is 0.3713 metres.

Quantity Eagle PEP PEE PER
Draft (metres) 0.117 0.123 0.111 0.098
Wetted Area (sq. m.) 1.757 1.717 1.752 1.828
Cp 0.624 0.534 0.590 0.667

Table 2: Principal dimensions of 'Eagle-like' kayak and equivalents

Figure 2(a): Total (volumetric) resistance coefficients

For the range 5.0 knots to 11.5 knots, the PER hull has the lowest drag. Above 11.5 knots, the Eagle-like hull is best.

Figure 2(b): Total (area-based) resistance coefficients

Winters' 'Stealth' Kayak

This boat was designed by Winters in 1992.

The principal dimensions of the boats are given in the following table. In all cases, the length on the waterline of each boat is 5.199 metres, and the waterline beam is 0.3632 metres.

Quantity Stealth PEP PEE PER
Draft (metres) 0.113 0.124 0.112 0.099
Wetted Area (sq. m.) 1.810 1.719 1.755 1.833
Cp 0.626 0.534 0.590 0.667

Table 3: Principal dimensions of Winters' 'Stealth' kayak and equivalents

Figure 3(a): Total (volumetric) resistance coefficients

The PER hull has the lowest drag for speeds from 5.0 knots to 13.0 knots. As with Winters' other kayak considered here, the performance is quite similar to that of the PEE 'equivalent' hullform for intermediate speeds.

Figure 3(b): Total (area-based) resistance coefficients

'Struer-like' Kayak

This boat is similar to a popular European kayak designed by Struer.

The principal dimensions of the boats are given in the following table. In all cases, the length on the waterline of each boat is 5.1405 metres, and the waterline beam is 0.3472 metres.

Quantity Struer PEP PEE PER
Draft (metres) 0.134 0.131 0.119 0.105
Wetted Area (sq. m.) 1.759 1.691 1.730 1.812
Cp 0.597 0.534 0.590 0.667

Table 4: Principal dimensions of 'Struer-like' kayak and equivalents

Figure 4(a): Total (volumetric) resistance coefficients

The PER hull is best for speeds greater than about 5.0 knots. The PEE hull is better than the Struer-like hull by a small constant amount over the entire range of speeds considered here.

Figure 4(b): Total (area-based) resistance coefficients

Comparisons

Having assessed the kayaks, it is natural to ask whether we can do much better. GODZILLA (Lazauskas, 1997) was set the task of finding the optimum kayak for a design speed of 10.0 knots, and with a maximum waterline length of 5.2m and a minimum waterline beam of 0.3713m. The same hullform family as described in Lazauskas and Tuck (1996) was used. It was presumed that the beam constraint would ensure adequate intact stability, at least comparable to the Eagle-like hull which has the greatest waterline beam of all the hulls considered herein. GODZILLA found that the optimum hullform had a waterline length of 5.2m, a draft of 0.0994m, and a waterline beam of 0.3713m. The prismatic coeficient for this hull is 0.656 and the surface area is 1.826 m2. The hullform has parabolic waterlines and cross-sections that are slightly fuller than elliptical.

Figure 5(a): Comparison of total (volumetric) resistance coefficients

Figure 5(a) shows that, of the extant hulls, the Struer-like boat is superior for speeds below about 5 knots, the Stealth is best in the range 5.0 to 8.5 knots, and the Eagle-like boat is best for speeds greater than about 8.5 knots. The hullform found by GODZILLA, was superior to all the extant hulls in the range 5.0 knots to 12.5 knots.

Figure 5(b): Comparison of total (area-based) resistance coefficients

Conclusion

We have assessed a number of small kayaks on the basis of their total calm-water resistance. Of course, there are many other factors affecting the overall performance of kayaks, so that outside of the hydrodynamic drag, we cannot say with confidence that any one hull is superior to others under real race conditions.

The temptation to rush right out and build one of GODZILLA's PER hulls might be strong but the caveats in the introduction of this paper should be heeded. This study is confined to level, straight ahead, calm water drag. In real life racing, yaw, pitch, surge, waves and even tactics play major roles.

For instance, each stroke introduces a yaw component that varies with stroke mechanics. Paddlers using a wide sweeping stroke introduce more yaw than those with a more upright stroke. Consequently wide stroke paddlers seem to prefer boats with more directional stability and the boat that suits one paddler may not suit the other. Since the racing is straight line from start to finish one might think directional stability is all important but top level paddlers do a considerable amount of wake riding that requires good control characteristics. Moreover, the detrimental wake effects are significant on such light boats particularly since the paddler must devote most of his efforts and concentration to just going as fast as possible. Directional stability is achieved in sprint kayaks through low block coefficients, high L/B ratios and greater lateral area aft than forward all of which is augmented by the rudder. The desired maneuverability is usually achieved by introducing fore and aft rocker most of which is forward where it appears desirable to reduce turning moments.

Would a straight keeled boat like the PER and GODZILLA boats handle as well? Boats with straight keel lines have been tried without success but the lack of success may be due to other factors than the underwater profile. Certainly a PER type boat is worth building just to answer that question. Even if we assume that boats with more rocker are advantageous we can still learn important lessons from the Godzilla boat. Higher prismatic coefficients in the 0.65 or 0.66 range are worth examining (Most are below 0.64 now). Designers should also take another look at length. It has been common practice to rake the bow aft to reduce weed build-up (plumb bows pick-up a remarkable amount of weed on some courses) and also because raked stems are perceived by paddlers to be "faster". Always lurking in the background is the ICF rule that requires a minimum beam. Ergonomics dictates that the boat be as narrow as possible at the paddling position so boats have adopted the unique diamond plan form with the widest point well aft of the paddler. This forces the designer to do some clever manipulation in the stern to retain a suitable shape while maintaining the minimum beam. One wonders if designers would have arrived at a shape similar to GODZILLA's if they were not influenced by the paddler's subjective opinions. Many paddlers who, if they do not like the elusive "feel" of a boat will not paddle it. Often, in experimental design, trying to attain an objective results in a boat that may be slower. We simply don't know how to balance the requirements of handling with lower resistance yet.

Appendix: Lines Drawings

References

Lazauskas and Tuck, E.O., Low Drag Racing Kayaks, 1996.

Lazauskas, L., User's Manual for Michlet and GODZILLA.

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