HULL SHAPE AND CANOE PERFORMANCE
(First published in CANOE magazine, October 1993 )
Selecting a canoe can be an intimidating experience when a new buyer is first confronted with the wide variety of available styles. CANOE magazine, for example, lists 11 different tandem canoes in their 1990 BUYERS GUIDE. Seven of these, Cruising, Touring, Down River, Casual Recreation, Weekender, Sportsman, and Day Tripper, sound like fairly similar designs. The differences are real, however, and largely due to small details in the underbody shape. How does a buyer sort out some of the subtle factors that go into making a canoe feel just right? Maybe your trying to decide between two similar designs, and you notice that one has one inch more draft, and a slightly more vee'd midships section than the other. What difference will this make? Is the difference important? Are there some "rules" we can learn to help make the our selection, or do we have to rely on antidotal evidence from friends, salesmen, or other "experts".
Naval architects have developed design rules based on calculations that predict speed potential, drag, stability, and displacement. These rules are validated by experiments conducted in towing basins, and other carefully controlled tests. Canoe design, on the other hand, has always been more art then "science", and has followed an experimental approach in its evolution. A canoe designer has a new idea, builds a prototype, and tests it in the water (or marketplace). This approach results in a slow, steady, improvement of the technology, but new, or unusual, designs are difficult to evaluate analytically, since little quantified data exists. Using some of the basic processes developed by naval architects can help evaluate canoe designs, at least in a general sense.
For example, I designed a 15 foot tandem canoe for a customer interested in flat water, family day trips and camping. My design had several inches of rocker, and asymmetrical waterlines. The customer was concerned that the boat would not track well enough, and float out of trim. He wasn't sure why, It just "looked different"! Using the analytical approach described later in this article, I was able to convince him that the boat would be suitable for his intended use, not do anything too "strange", and would still have reasonable performance.
One reason that a more analytical approach to canoe design is now possible is due to the revolutionary change in Computer Aided Design (CAD) capability in the last few years. As an aerospace engineer (my 8  5 life), I have used CAD tools for many years to synthesize and evaluate designs. Just five years ago, this capability required main frame computers, and dozens of engineering specialists to write the software. Now, personal computers have developed, along with engineering software, to the point where it is practical to use them in canoe design. The first CAD programs were used by canoe builders to produce "fair" hull shapes and extremely accurate building templates. Now, more advanced programs are available that can model hydrodynamic variables such as drag, stability, and even structural properties (stress and strain). These new tools are now available to help us evaluate canoe designs, and gain additional insight as to what features effect basic performance.
A computer program can generate a great deal of information in a short period of time. The trick is in asking them the right questions, and then interpreting the answers, using lots of good judgement, and common sense. One approach is to compare, using simple calculations, features that seem to have an impact on performance. Only three variables control what a canoe's underwater shape looks like; the amount of bottom rocker (profile view), the crosssection shape (section view), and the waterplane shape (plan view). Unfortunately, these variables can be combined into an infinite variety of hull shapes, all with different performance characteristics. I decided to hold as many of these variables constant as possible, and then make small changes to the remaining variables, and see if the results make any sense.
To keep the study simple, I focused on looking at the effect of rocker on a standard, two place, 16 foot, touring canoe. "Rocker" is used to describe the side view of the keel. A canoe with a flat bottom has no rocker. The rest of the basic dimensions were fixed at 400 pounds total weight (the canoe, two riders, and gear), a waterline length of 14.5 feet, a deck beam of 34.5 inches, and waterline beam of 32 inches. Four canoes were designed to these basic values, using the PROLINES yacht design program, and an IBM 386 computer. To minimize the number of variables, all four designs were symmetrical, started with the same basic lines, and were then modified (as little as possible) into the following configurations:
1. flat sections, flat bottom, no rise at ends
2. flat sections, flat bottom, raised ends, 1 inch more draft than #1
3. slightly arched sections, slight rocker along entire bottom, 1.11 inch more draft than #1
4. deep vee sections, more midships rocker, 3.8 inch more draft than #1, and finer sections than 1,2, or 3
Modifications began by "pulling" down the center line profile view to the desired rocker. Next, each sectional view was "adjusted" to fair smoothly into the new centerline, and the plan and profile views checked for distortion. The hydrodynamics were calculated, and more changes made to the underbody sections until the desired displacement and waterline length were reached. This typically required between 6 to 10 iterations on the computer for each design. A typical iteration requires the computer to "think" for about 5 minutes. Before these computer tools were available, this amount of work would have required hundreds of hours of detailed, manual drafting and calculation labor!
In addition to satisfying the computer, the final configurations were all reasonably good looking boats. Figure 1 shows the section and profile lines for the four basic canoes. The first two are very conventional. Number 3 begins to have noticeable rocker, and number 4 is fairly radical, with a large amount of rocker and finer ends. Weight varied from 394.8 to 402.0 pounds., waterline lengths were between 14.8 and 14.9 feet, and Waterline beam dimensions were within 1.2 inches of each other.
After calculating "smooth" lines for each design, the PROLINES program next did a series of detailed hydrodynamic calculations. These calculations included the midships cross sectional area, the moment required to trim the bow 1 inch, the weight required to settle the boat one inch, the righting moment at various degrees of heel, the underwater lateral area, total wetted surface area, and hydrodynamic drag (caused by both waves and surface friction). The stability calculations assumed that the 400 pound weight was concentrated 12 inches above the waterline, and the drag calculations were computed for a boat speed of 4.13 knots. Effects of tumble home and flare were not considered in the stability calculation.
My investigation of "rocker" took a slightly different approach. Rocker is usually associated with highly maneuverable boats, like those designed for white water. To quantify the effect that "rocker" has on the turn resistance of a canoe, it is necessary to determine the torque needed to make the canoe push aside the water while turning. During a turn, the lateral underbody of the canoe pushes against the water, which resists this motion. The water pushed by the ends of the canoe contribute more to this resistance than water near the center, since the ends have a longer "lever arm" to act upon. In addition, the ends of the canoe also swing through more distance than the center areas, which pushes the water at the ends faster, again increasing the force on the ends. The bottom line is that turn resistance is influenced by both the size of the lateral area, and how this area is distributed from the center of the canoe.
A basic relationship common in engineering, called the "moment of inertia", takes into account these factors, and is a good approximation for quantifying the turn resistance of a canoe. Canoes with a small moment of inertia will turn very quickly, and since the ends of the canoe count heavily in the calculation, it is more complicated than just measuring rocker or draft. To include this factor, each canoe's lateral area was imputed into another CAD program (naturally), where the moment of inertia of the underbody lateral area was calculated (the units of "area moments of inertia" are area times distance squared, or distance to the 4th. power).
The results from these programs are summarized in table 1.
CANOE DESIGN
#1, flat, no rocker 
#2, flat, raised ends 
#3, slight rocker 
#4, max rocker 

STABILITY 

maximum beam (in.) 
34.5 
34.5 
34.4 
34.7 
waterline beam (in.) 
32.2 
32.2 
31.0 
31.8 
max. righting moment (ft.lbs./deg.) 
77/20 
82/20 
65/20 
13/10 
midships sectional area (sq. in.) 
99 
102 
110 
141 
moment to trim bow 1 in. (ft.lbs.) 
95 
95 
93 
62 
maximum draft (in.) 
3.6 
3.7 
4.7 
6.4 
MANEUVERABILITY 

lateral area (sq. ft.) 
5.3 
3.9 
4.1 
5.1 
moment of inertia (ft^4) 
72 
63 
56 
49 
PERFORMANCE 

weight to increase draft 1 in. (lbs) 
144 
145 
140 
115 
wetted surface area (sq. ft.) 
32 
29 
28 
24 
total drag force, at 4.1 knots (lbs) 
7.7 
7.5 
6.9 
6.5 
TABLE 1
The results from a study like this never yield absolute answers. They can identify trends, however, and allow for informed comparisons between similar canoes (don't try to predict kayak performance with this data). My conclusions are:
STABILITY: Designs 1&2 are very stable, with #2 having a slight edge (I have no idea why). #3 has 20% less stability, and would require some attention and a higher skill level. #4 is close to unstable, and would be a real handful to control. Stability reduces with increased rocker, as the underbody begins to take the shape of a "ball". Trim is effected in much the same way. The first three are all similar with respect to trim moments and weights, and should not be too sensitive to load changes. #4 is far more sensitive, since its flotation is concentrated in the center of the canoe. It appears that some rocker can be tolerated, but anything extreme would have poor stability and load carrying characteristics.
MANEUVERABILITY: Raising the ends of a flat, no rocker design (#2) reduces the moment of inertia (turn resistance) by 9%. Adding a slight rocker (#3) reduced it by 23%, which should not be a problem for an experienced paddler. As expected, #4 has the lowest turn resistance, and would be difficult to keep in a straight line. As a second thought, I added a 4"x8" skeg to the back of #4, and it brought the moment of inertia back up to 63. No real surprises here, except that a slight amount of rocker seems to help turn performance a lot more than raised ends. Moving water with the ends of the canoe takes a lot of effort!
PERFORMANCE: As the amount of rocker increases, the cross sectional area increases, but wave drag is reduced. This sounds backwards. Pushing a larger area through the water should result in more drag (paddles work that way, right?). Wrong. Wave drag on a canoe hull is more sensitive to how "sharp" the waterlines are than it is to cross sectional area. Even though the midships cross sectional area of #4 is 42% more than #1, its predicted drag is 16 % LESS. Canoes #1&2 push the water apart quickly, and pay a drag penalty. Rocker takes volume out of the ends of the boat, which tends to sharpen the waterlines. Sharp, fine ends are common in racing designs, but it's interesting that even a slight amount, like #3, results in 11% less drag than #1, and 9% less than #2. This amount of reduced drag would be very noticeable after a few hours of hard paddling.
Like I mentioned earlier, canoe design is more art then science. No one has a "perfect" design, or knows all the answers. You can use the general conclusions from this article to help your judgement, but always try the canoe out on the water, configured the way your most likely to use it. Don't be reluctant to try one that's a "little" different! My next canoe will be similar to #3, but just a tad asymmetric. Not because the computer says its good, I just like the way it looks!