The Shape of the Canoe
Part 1: Frictional Resistance

by John Winters

The past century has brought a quiet revolution in the field of naval architecture. Today, largely through the use of the towing tank, where models are tested under controlled circumstances, we have access to an extensive body of knowledge about the motion of ships and the factors affecting that motion. Military and large scale commercial interests prompted most of this research, although in recent years the same methods have been used to design the expensive water toys for the obscenely rich. Eventually, what is learned in less savoury pursuits filters down for more prosaic use. The surprising thing (or perhaps, not so surprising) is that the application of this knowledge to canoes has been largely superficial, despite great strides in materials use. Certainly, to the layman, the connection may not be apparent between large naval ships, racing sailboats and the canoe, and it could be that the canoe industry has just been slow to recognize the connection as well.

To nature, of course, they are all but moving, floating objects; she treats them all equally and consistently, if not simply. If we know the principles that apply to one, we can, with some modification, apply them to the other. In doing so, a number of unfamiliar terms and symbols will be used. Naval architecture, like other sciences, has developed a language uniquely its own for precision and convenience. Don't be concerned. The terms quickly become familiar, and if you get stumped, the Glossary can be used for quick reference.

So, if you'll be patient with a bit of hydrodynamic arcanum (and recognize that, even though the basic principles are unchallanged, there will always be debate over the details), we will explore the theory behind the motion of canoes and how dimensions and shapes affect that motion.

Modern naval architecture began some 100 years ago when the physicist William Froude put forth the elegantly simple proposition that the resistance of a floating body in motion was the sum of two parts - frictional resistance (Rf) and residual resistance (Rr), and that the two could be analysed separately. We know now that this is not 100% true, that variations in speed cause incalcuable changes in wetted surface and turbulence. Fortunately, these errors are small, and from a practical standpoint, can be ignored. Frictional resistance is that which occurs between the hull and the water while the residual resistance is the sum of all other resistances of which wave-making, form, and yaw are the most important. Other forces come into play under special circumstances (air resistance due to headwinds and energy losses due to pitching are the most obvious), but as they can be avoided by the skilled or prudent canoist, they are rarely serious design considerations. We will deal first with friction.

Frictional Resistance

The combined effects of wetted surface, surface condition, surface length and speed comprise the resistance due to friction and can be calculated with the formula:

            Rf = 0.97 x Cf x Sw x V^2 where:

               Rf = Resistance in pounds
               Cf = Coefficient of friction
               Sw = Wetted surface
                V = Velocity in ft/sec
             0.97 = Constant for fresh water

As the water passes, friction slows the water molecules next to the hull, creating a layer of water that is carried along with the hull. This layer, called the boundary layer, is initially quite thin and the flow within it is laminar. As it progresses along the surface, variable pressures cause turbulence. The layer gradually increases in thickness: near the stern, it breaks away into eddies. It is within this layer that friction is generated between the water molecules and not as might be supposed, between the water and the surface. Where the flow is laminar, the coefficient of friction is quite small; it is theoretically possible for canoes to maintain laminar flow for the full length of the hull. Practically, however, this is not possible. Turbulent flow sets in near the bow with an attendant increase in friction. The major factors affecting the frictional coefficient are the smoothness of the hull, velocity and length of the hull.

Since the builder and the paddler are responsible for the velocity and surface condition, the designer's influence is restricted to surface area and length. U.S. Navy studies have shown that, for conventional shapes (i.e. those that are not extreme in dimensions or configuration), wetted surface varies with length, amount of deadwood, Beam/Draft ratio and hull shape, in that order of importance.

Effect of Length

Surface area varies roughly by the square root of length and the first power of beam, and the merits of increasing either must be balanced against the deleterious effects of additional area. Figure 1 (gif, 29k) shows a typical Curve of Resistance for both friction and wavemaking. It can be seen that wavemaking resistance does not become important until the Speed/Length ratio begins to exceed 0.7. Nevertheless, the greatest emphasis in canoe design has centered upon wavemaking. Some years back, a famous paddler entered a very long canoe in a marathon race. He was the odds-on favourite, but despite a superhuman effort, he lost. Since the winning speed was well below the onset of wavemaking resistance for his canoe, it is a safe guess that the excessive wetted surface caused by length did him in. This balance between speed and length is a critical part of design that we will explore in more detail later, but, for the time being, we can say that added length is not an unqualified blessing.

Effects of Deadwood

At the bow and stern there may be vertical sections of hull that, because they lie below the waterline, do not affect residual resistance. A convenient, although not accurate, term for these areas is "deadwood". There has been a modern trend towards straighter keels and more deadwood to provide directional stability, but there is a price to pay in the form of additional wetted surface. The rather minor change in profile A to B in Figure 2 (gif, 23k) results in a 1.5% reduction in the surface area of a typical 16 foot canoe without affecting wavemaking resistance. Whether the reduced friction is worth the loss in directional stability is a moot point determined subjectively by the paddler.

It is worth noting that cutting away the bow may improve both the steering and directional stability - canoes turn with the stern describing a greater arc than the bow. Once the turn begins, pressure builds up on the outside of the bow, effectively locking the bow in place and accellerating the turn. The unpleasant aspect of this phenomenon is particularly noticeable in broaching conditions, when the amount of hull buried in a wave trough becomes critical. Removing forward deadwood minimizes the hull's influence and increases the effect of forward control strokes. Deadwood at the stern, however, can be desirable. It acts like a skeg and resists the lateral movement of the stern. An analogy can be drawn between the canoe and an arrow: the feathers of the arrow are on the back ot the shaft to provide stability; not on the front, where they would cause erratic flight.

Effect of Shape

Ask almost anyone what hull section provides the least wetted surface and they will answer "Round". While this is true, its importance has been greatly exaggerated. Figure 3 (gif, 83k) shows six sections of equal area. A, B, C and D have identical waterline beams and remarkably similar girths despite radically differing shapes. Only the elliptical section fares badly, but when the beam is reduced and draft inreased appropriately, as in E, it has the least girth of all. Finally, there is the flat bottomed section F that is the equal of any when given the proper beam. Of course, the other shapes could be equally reduced in beam, but the point to be made is that shape alone does not determine wetted surface. In fact, for usual shapes, Beam /Draft Ratio has the greatest impact, and the waterline should be as narrow as possible within the confines of maintaining acceptable stability.

Another factor affecting girth, and consequently wetted surface, is the fullness of the maximum section (area; not shape). This can be represented by dividing the section area by the area of a rectangular section having the same beam and draft to give the Section Coefficient (Cx). The best Cx lies between 0.94 for fine-ended hulls and 0.88 for full-ended hull. The difference between ideal and typical values is about 4 percent. Aesthetic and handling considerations generally prevent designers from ever achieving the ideal.

The great disappointment for the designer is that, after reducing friction to a minimum, the paddler is unlikely to notice the effect. A 5 percent decrease in wetted surface is worth bragging about, but a single year's scratching and banging can easily double Cf from 0.004 on a new fiberglass canoe to 0.008. This more than offsets the designer's efforts. The cavalier attitudes of most canoeists towards their boats is evidence that a 50 percent resistance increase is not often noticed if only because the onset of its effect is so gradual.

In our next article, we will examine the more glamorous field of residual resistance.

Go to Part 2: Residual Resistance.

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