Canoe with square bottom hull vs rounded hull

Hopefully someone can answer this question for me and save me from modeling up two hulls and running the kaper numbers. Scenario are two canoes:

• They are of equal length
• They are of equal beam
• They have an identical top view
• They have an identical profile view (both have flat bottom with no rocker).
• The only difference is one has a square bottom and the other has your typical rounded bottom.

Q: All things equal (paddler strength, water test conditions) which is mathematically faster?

I would suspect the rounded hull with less surface area would be faster, as that is what I've always read. It also matches up with my previous designs and first hand experience paddling rounded hull canoes. Yet, the architect who designed a boat I've been asked to review insists the square hull is faster. Your thoughts?

Thanks for your input in advance!

 

Rounded. Really a hydrodynamics engineering 101 question. Was this guy a building architect?

 

You nailed it.

 

Interestingly, in the early days of the Moth there was a question just like yours. Ian Ward, a pioneer of Moth design, told me that the faster hull for sailing was a narrow square hull because it produced less wavemaking resistance.

 

Sailing speeds are higher and I can see a benefit of a flat hull to get up on plane and hold an edge. However, canoes travel slower and are submerged typically about 20-40% (varies based on loading). The resistance also varies depending on the shape of the hull at different drafts. For this case though the sides of the boat are perpendicular to the deck so you have a single chine/square channel passing through the water. There is extra surface area to be sure.

 

If one has a rounded bottom and the other "square" (I assume that means flat), then the waterline beams are going to be very different. In that case the plan view of the sheer is irrelevant. You would have to also indicate the displacement to be able to calculated the submerged shape.

 

This isn't just a matter of the flat-bottom planing better.

The flat hull can be made narrower for the same displacement, so it can have less wavemaking drag at all speeds. And it's wetted area wouldn't be much different than the round hull, so it wouldn't have a big penalty in skin friction.

So the flat hull can often be better than the round hull.

 

Hi Gonzo, yes square = flat hull. To clarify the loading/weight added to each boat would be identical. Every round hull boat I've raced typically has a narrower waterline beam. Thus, it is faster than a flat/square shaped hull. I suppose there's a reason Olympic hulls are round! It comes down to less drag at the end of the day.

 

The hard chines (square bottom) will generate more eddys than rounded chines. Eddy making implies that some work has been done and according to Newton you will have had to invest some energy in order to generate those eddys. Rounded chines of....say 10% of the overall waterline beam will reduce the wetted surface somewhere in the neighborhood of 8 to 10 percent. That is a big neighborhood and these numbers are merely ball park or SWAG estimates.

The canoe,if not mechanically powered, will not go very fast. Therefore it is desirable to do whatever reduces the effort to propel it at those lower speeds. That suggests rounded chines, lightest overall weight, and superbly finished wetted surfaces. No wax or other surface coatings allowed.

Not to complicate things but there is another section configuration that is easier to build and almost as effective as the round chine option. That would be the so called "trapeze bottom". That configuration has flat beveled chines and has some structural advantages that the round chine type does not have.

 

Hi Doug H., in this case the beam for both boats is the same. In fact, the top view is identical for both. I don't want to modify the beam of the square hull to be narrower. I know this might help even things out. Assuming both boats met the criteria above (identical top & side profiles) and were equally and loaded (e.g. two paddlers) a rounded hull should be faster. Doug Lord's sketch above is a closer comparison to what I'm talking about (round vs. square hull).

If you or anybody has numbers to prove otherwise do show your calculations. Perhaps there is a reference to this in a hydrodynamic book some place.

 

If you can't make the flat-bottomed one narrower, then I'm sure it will have more drag than the round one.

I've done more detailed calculations of this some time ago, but don't have time to look for (or repeat) them at the moment.

For what it's worth, I opted for semicircular sections in designing my trimaran.

 

Perhaps you would care to enlighten us as to how two boats can have the same waterline shape, same immersed side profile, and same displacement but one has round vs rectangular sections.

Because skin friction, form drag and wave drag all scale differently, there is no simple mathematical solution to the original question. The resistance depends on the details of specific configurations and the operating conditions. Programs like Michlet can answer questions like this. Tuck and Lazauskas looked at similar issues using Michlet. In this paper, they consider boats that have the same displacement, but are allowed to vary in length in order to minimize the resistance for different speeds. Lazauskas estimated the resistance of hull forms of the same displacement and length with different cross section shapes in his Master's thesis. Of course, at 76 m long and 1200 tons of displacement, the ships he was considering were not exactly canoes. But you can find papers on the web that used Michlet to optimize the design of kayaks and other small craft.

It turns out the resistance of a canoe or rowboat depends on the unsteady motion of the boat and is different from what you'd predict based on the average speed, as shown by these tests.

 

There are many variables and maybe 10% would be the difference taking into account same displacement and modifications for hull depth, rocker, bwl, and lwl.

Taking this into consideration, something which weighs heavily upon my decision making process is overall costs for construction.

For a cruiser it is said hull build is 25% of overall costs, for what you describe more likely approaching 90%. With this in mind, George Buehler in his book had a performance comparison of round bottom vs single chine V bottom with very similar qualities however, with savings in material and labor a much longer hull is possible which will totally outperform the former otherthan wetted surface area.

Now you take it one step further and you have the dory/sharpie hull, with another step you get to the Bolger box, for your purposes they have been found to be good performers and worthwhile projects

 

Hi Goodwilltoall, thanks for the references. To clarify a comparison to a single chine flat bottom canoe (e.g. square bottom) is that I'm looking for. The sides are basically perpendicular to the deck. I am going to model it up in the coming weeks when I get some time and will run the performance numbers. For now I just wanted some high level feedback on square vs. round.

 

Hi Tom, thanks for the additional resources. I agree there is a lot more analysis that could be considered. For this example assume a typical canoe of 16ft operating in identical conditions (smooth pond, no wind). For resistance on canoes the Kaper method is used the most. As I recall it is focused on resistance in the 5-8mph range (typical canoe paddling speed).