The Shape of the Canoe
Part 3: Applying the Theory

by John Winters

For centuries, boats and ships were built by eye, the product of accumulated skills and knowledge handed down to and built upon by succeeding generations. Improvements came slowly. Only within the past 100 years has science played a major role in boat design. Even today, canoes are rarely "designed"; they're more often adaptations or modifications of earlier shapes. Given the apparent success of this method, many would question the need for a more scientific approach. The value, of course, lies in the plodding nature of trial and error and the preponderance of failure over success. The designer, by applying hydrodynamic principles developed through experimentation (and, of course, trial and error), is able to improve the breed more rapidly while minimizing mistakes and risks. The process used is rarely inspirational (advertising hype not withstanding), and begins with a set of parameters for the proposed new canoe that might look something like this.

If you need reminder as to the meanings of any terms, see the Glossary for quick reference.

Design Criteria for "New Canoe"

1. Primary purpose is tandem wilderness tripping of up to two weeks in duration, but most extensive use on weekends.

2. Some whitewater capability, but not a priority.

3. Intended for canoeists of intermediate to advanced capabilities.

These rather simple criteria are remarkably enlightening. First, we can ascertain displacement by adding the expected weights of the paddlers, the desired weight of the canoe, the expected gear weight and 1/2 the food weight for the longest trip. (Half the food weight is to compenstae for the diminishing of supplies as the trip progresses and for lightly loaded weekend trips.) For a design example, let us say that these are 320 lbs., 60 lbs., 58 lbs. and 28 lbs. respectively, totalling 466 lbs. The criteria also suggests some things about the hull shape. Since the target market is skilled, extreme beam for stability is not needed, nor must there be a straight keel with the attendant increase in wetted surface, for directional stability. (The occassional whitewater use also mandates some rocker.) We also know that length must be moderate to fit a variety of uses such as bushwacking and puddlehopping as well a s charging across vast areas of flatwater.

Cruising Speed

Before the first line is put on paper, the arbitrary decision concerning the anticipated cruising speed is made which can make or break the design. There is an ideal range of lengths and shapes for every speed, and to vary widely from this range will result in substandard performance. For this case, we will set the cruising speed at 4 mph, from which we can determine the length. Figure 1 (gif, 36k) shows a plot of frictional, residual and total resistance for a canoe tested by the author and extrapolated for waterline lengths from 13' to 19' at a speed of 4 mph. Two things are immediately apparent. As the length increases, there is a gradual increase in frictional resistance and a more rapid decrease in residual resistance. When the two are combined for total resistance, we discover that length is not an unmitigated blessing and the ideal length at 4 mph is 15.5'. This is not to say that we should use 15.5'. There are times when we might overload the canoe or wish to paddle much faster, and so, we should choose 16.5' for its increased capacity, potential for higher speeds and negligible increase in frictional resistance.

Given length and speed, the Speed/Length ratio is determined and from that and the ideal Longitudinal Co-efficient. In this case the S/L is 0.85 and the "best" Cl is 0.51. From this we calculate the area of the largest section by the formula;

          Cl = Disp (cu. ft.)/vol of Vp = 7.48/x = 0.51, 
          therefore x = 14.67 
          and the area of the largest section 
          = 12.47/16.5 = 0.89 sq ft.

The shape of the midship section is important, not because of its effect on resistance, but because it influences the shape of all other sections; i.e. A full midships section generally results in full sections towards the ends. The two characteristics of the maximum that do affect performance are waterline beam and, to a lesser degree, the midships co-efficient (Cx). Studies show that the least wetted surface for hulls having Cl's below 0.56 is obtained when Cx is 0.94. Most canoes fall somewhat below this figure which represents a rather full section. The trade off is in seaworthiness as the finer section has a more forgiving motion in waves. By far the greatest influence on resistance at the section is the Beam/Draft ratio and both increased beam which should never be more than necessary for stability. How much stability is "necessary"? Only the paddler really knows and the designer can only hope that his guess is right. The ultimate stability of a canoe, unlike other types of boats, lies with the passenger and a successful design will take this into account.

On this hypothetical canoe, an elliptical section of 32" waterline and 5.1" draft fits our parameters. (This means, of course, a 32" waterline at a draft of 5.1 inches.) The Cx of 0.79 is not too far out of line and the beam is sufficiently narrow for good performance. Do not confuse "beam" as used here with the "beam" seen most in canoe literature, which is taken at the 3" or 4" waterline -- or at the widest point of the hull! While this number may give vague indications of hull shape, if you know where it's taken, it has no significance unless it happens to be the waterline beam or is dictated by rule, as with some racing canoes.

Section Shape and Function

The shape of the maximum section has a profound effect on stability. A wide, flat section produces greater intitial stability and a quicker, more pronounced motion in waves, while a rounder section has less initial stability but a more predictable motion. However, since the entire waterplane contributes to stability, it would be erroneous to consider the midships section in isolation from the remainder of the hull. The trend toward longer and finer ends in modern canoes carries with it a loss in stability which is not always warranted in recreational canoes. By the same token, the very full ends used to increase stability and please the mass market are an equally great sin. The designer, unless pressured by some special consideration, will compromise. Slightly concave waterlines forward and a long entry are known to reduce resistance and improve the canoe's action in a seaway, while fuller lines aft are acceptable. Should the stern be filled out too much, directional stability will suffer or, if it is too fine, there will be a loss of control in following waves. There is a subtle balancing act here, and few firm rules, due to the complicated nature of turbulent flow near the stern and compromises made for maneuverability and seaworthiness.

Profile and Function

The profile is determined next. In this case, rocker is incorporated to improve maneuverability (remember the whitewater). A fringe benefit is that rocker reduces the hull's tendency to "hog" and so, is to structural benefit. The degree of rocker is usually arbitrarily set based on past experience. Unfortunately, too much for one may not be enough for another, and the debate will enliven campfires for years to come without resolution. The designer makes his choice and hopes for the best while proclaiming to all who will listen that he alone is following the path of true enlightenment.

Where rocker ends and deadwood begins is arguable and the term "deadwood" is used here more as a convenience than in a technical sense. For our purposes, a workable definition is: "that portion of the profile lying below a fair curve drawn from the waterline to a point 2' from the bow or stern". (" The Shape of the Canoe, Part 1") At the bow, the deadwood can be cut away severely. Contrary to popular opinion, it is not a major contributor to directional stability and, in fact, can make steering more difficult. Boats turn with their bows describing a smaller arc than the stern and, as the turn is initiated, pressure builds on the outside of the bow, holding it in place and accelerating the swing of the stern. By cutting away the forward deadwood, the bow is free to slide slightly through a larger arc. This is particularly important in heavy waves where a deeply immersed bow or stern experiences the greatest effects of water particle movement and can cause a broach. The stern, however, utilizes lateral resistance to resist swinging and, because of the turbulent flow and lower Cf, the added area is less detrimental. Once again we have the subtle balancing act of pros and cons for which there is no perfect answer. For whitewater, both ends should be cut away severely since the bow is not always the bow nor the stern always the stern relative to the water flow.

Fairing and Function

Now a process of trial and error begins as each section is drawn to provide the proper displacement. Some designers will draw a curve of areas first, which shows the area of each section graphically and then draw each section to fit the curve. Figure 2 (gif, 12k) is typical; each section on the curve represents a percentage of the area of the maximum section. More often, he simply draws a few sections with the shape he wants, fairs the lines to suit and calculates the volume. There will be some adjustments to achieve the desired displacement but, with practice, they become quite small as the designer develops a "feel" for drawing. Much is made of sectional shapes in advertising that attributes or implies some mystical importance to a particular shape or combination of shapes. In fact, subjective evaluations of these features are all we have, and their reliability is highly suspect. Indeed, to determine the best sections would involve testing an infinite variety of shapes, which is simply not possible. In a way, this is a blessing, as the designer can be as artsy as he pleases without doing much damage.

The topsides are generally drawn at the same time as the underbody, and offer the same freedom of expression. The benefits of one configuration over another are specific, and are exercises in compromise and occasional gratuitous variations. High ends and freeboard will keep out waves but offer greater wind resistance. Tumblehome can make paddling easier in the area where beam is reduced but allows more slop to come in and reduces ultimate stability. Flared ends will turn waves away but encourage pitching, which slows the canoe, while the increased beam caused by flare forces the paddler to reach further out with each stroke. As yet, no universally perfect shape has evolved, although there are "perfect" shapes for very specific purposes.

For the most part, the design is finished. The center of bouyancy is usually ignored, as are stability calculations, although the mathematically inclined can derive great enjoyment and their computers exercise in developing the tables of numbers. All that remains is the evaluation of the prototype, but that is another topic. For the time being, let's leave our designer under the delusion that he has made a breakthrough in canoe design. Being more pragmatic and less emotionally involved, we know the truth: breakthroughs are few and far between.

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