# On the hydro dynamics of flat bottomed kayaks

Discussion in 'Hydrodynamics and Aerodynamics' started by Christian Nally, Oct 4, 2022.

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### Christian NallyJunior Member

I’m contemplating a collection of four kayaks you can attach to make one long boat.

Imagine two kayaks, of extremely simple construction. Zero rocker, diamond-shaped when viewed from above, and absolutely flat-bottomed.

In this case, connecting the two would involve attaching the bow-tip of one boat to the midships side of the front boat. The very vertical sidewall panel of each boat would be attached to each other, face to face. The new overall length would be 50% longer than before. Adding a third and fourth boat in a similar way with make the full length 200% of a single hull, the beam 200%, and the matched faces would form an X when viewed from above.

My question revolves around how much of a sacrifice a purely flat bottom is. The side panels of each hull would meet the flat (diamond-shaped) bottom at 90 degrees.

I’ve read the following quote describing kayak hulls and I’m hoping for some perspective from the esteemed knowledge base gathered here.

<quote>
Flat bottom kayaks will be very stable but slower. Kayaks with a V-shaped hull will be faster than a flat bottom but are generally not as stable. These V-shaped hulls are considered a bit more advanced. There is also a combination or partial V-hull. These kayaks are a good blend of the two and are considered to be average at both speed and stability.
</quote>

How much slower?

I’ve not seen many serious boats with 90 degree bottom outside joins and purely flat bottoms (even though it seems that would simplify construction).

Can anyone estimate how much of a penalty that kind of design would cause compared to a curved or v cross-section when viewed from aft?

Is there a reference that would show how it would effect a propulsion force vs. speed curve?

Bonus question: how would the combined quad row or sail compared to a single hull?

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### gonzoSenior Member

There are several variables, which makes the answer rather complex. The interaction between the hulls will affect how much drag there will be generated. This will change at different speeds. A flat bottom kayak should have some rocker. What is the goal of attaching four kayaks? It would be more expensive than building a larger boat; like an umiak.

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### Christian NallyJunior Member

Hi Gonzo,

To simplify the discussion, let's consider a single hull intended for rowing.

Let's say you had a certain amount of wood, and you were choosing between two designs:

1) a pure flat-bottomed boat (flat vertical sides that are 100% flat and vertical, also 100% flat horizontal bottom)

and

2) a boat with curves that balance all sorts of desireables, like maneuverability, initial and secondary stability, etc. and comes out like a middle of the road kayak and/or rowboat.

How much of a penalty would you suffer by choosing option 1) ?

I'm not concerned about maneuverability at all, only propulsive efficiency in relatively flat water.

Does that help narrow down what I'm asking?

Why? (Or rather, what penalty would you pay by having a strictly flat bottom with no curve in any direction?)

Thanks again!

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### Alan CattelliotSenior Member

Hi,

Man... I find this subject very interessant, although I've got a very very very little experience in such hulls. I did very small researches, and quick calculations using my drag formulas for hull's shape (multihull).

I compared also my results with those given in the attached publication I found on the internet. Theoritical calculations are made using the common breakdown of the hydrodynamic drag into the sum of a friction drag and a wave drag. The authors compare calculations and with measurements made on "two male expert kayakers who used their own kayaks". In the introduction, orders of magnitude are calculated : "one deduces for an athlete and boat mass of 90 kg at V = 4.8 m/s, a drag force FD ≈ 75 N, which means a dissipated power PD = FD · V ≈ 360 W. In this example, the wave drag [...] accounts for 22% of the total drag."

I build a model of two single kayaks, diamond shaped in top view, pure flat bottom. The model called "Rec" has rectangular sections. The model called "Tri" has triangular section. Both models have the same displacement, the same length, and the same beam. As a consequence, the only dimension that is different between the two kayaks is the draft. The model that I've build are pure mathematical models, so I can prove that, given the hypotheses :

- the draft of "Tri" is always twice the draft of "Rec"
- the wetted surface area of "Tri" is always greater than the wetted surface area of Tri"

I set the displacement and the length of the kayaks as the numbers found in the article. I arbitrary set the beam@waterline equal to 700mm (0.7m), as no direct indications are given in the study of the beam they used for the calculations. In the table below, dimensions and location are in meters, surface are in m2, volumes in m3, and mass in kg.

When I use my hydrodynamic model to compare the kayaks "Tri" and "Rec", I have this results : Vertical, Power in kW. Horizontal, Speed in m.s--, "Tri" drag curve in red, "Rec" drag curve in blue. The curves are very similar. Below 8kts, there is no noticeable difference in drag between "Tri" and "Rec".

The breakdown between friction and wave drag @ speed equal to 4.80m.s-1 is given downbelow, for the rec kayak : Rf : Friction drag, Rrh0 : Wave drag, DRrhphi0 : induced drag. My hydrodynamic models gives approximatively the same breakdown as the one given in the study. Since we use approximatively the same formulas, there is no surprise there.

If we can assume that my theorical hydrodynamic model is correct, and with the given hypothetis, then the drag difference between the kayak "Tri" and "Rec" is around 10% ( 334 Watts for "Rec" and 311 Watts for "Tri", as calculated). It should be noted that these theoritical drag are about three times the ones measured in the study (fig.13), although being on agreement with the numerical approximation of the study (introduction).

In on hand, flat bottom hulls do not fit well in my model. In the other hand, the hull shape that are measured in the paper are very optimized. As a consequence, my calculated drag seems to increase too much with the speed. So in conclusion, the 10% difference is only theoritical, and the question of what could happen in reality should be study with more precise calculations are to be done.

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### Christian NallyJunior Member

Thank you Alan. This is the very sort of thing I'm looking for.

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Christian, a flat bottom with no rocker will make a miserable handling boat. You need to get at least the front end of the bow curved upward to just below or even a little above the water surface. If the bow is immersed the boat will be too much influenced by the direction of any chop on the water surface. The boat will be a bear to try to steer or to make any sort of a turn.

There is more. Without some bottom rocker you will, more than likely, have some undesirable section area distributions. The result will be that the boat will require more effort to paddle. If you mean to paddle short didtances....say 100 yards then the extra effort is not important. If you figure to paddle any distance, maybe a mile or two, the extra effort required will punish you unnecessarily.

Imagine that you have sawn the boat into bread slices. The individual slice will let you see what the sections look like. in this hypothetical case the intersection of the bottom and the sides will have a 90 degree turn. We can call the intersection the chine. That sharp corner will generate some turbulence in the water. That will cost you some more paddling effort. If you can round that intersection, even a small amount, the result will be worth the trouble of doing so.

I am guessing that you want to use flat panels and rectangular sections to avoid bending any of the lumber. Bending the lumber is not a problem for a shape like a kayak. Plywood will bend easily, and you can make some nice curves with very little difficulty.

Can you post a drawing of the kayak that you have in mind? A rough sketch will do, especially if you include some proposed dimensions.

Explore the internet to see if you can find the plans, or at least a description of, the "The Six Hour Canoe". It is a flat bottomed, double ended, kayak like, boat that has been built many times over the years. Sure enough, it is possible to build in six hours. But that is only for a craftsman with a bit of experience. For a rank amateur it might take a couple of days. It has the appropriate curves and it will move pretty nicely in flat water. Two sheets of ply is all you need to make a boat of about 15 feet 6 inches in length.

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### rwatsonSenior Member

Can you do this study with curved corners ?
Somewhere in the back of my mind I remember significant increased friction in a towed body with sharp chines at non planing speeds.

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### Alan CattelliotSenior Member

Yes, you're absolutely right. The comment from MESSABOUT about the hard-chine is also very true, regarding the way the turbulence tends to develop near the sharp edge. Even with the analytical model that I use, which only gives approximative results based on the bulk parameters listed down below, we should notice some difference between kayaks with pure rectangular section, rounded rectangular section and pure triangular section.

Again, the rounded rectangular section has been made "mathematically", with a variable radius maximum at the master beam and linearly decreasing to the bow and the transom. The kayak with rounded rectangular section is named "Rec_smooth" in the following results, and is double-ended, flat bottomed, like the two others models of kayak, named "Tri" and "Rec". I arbitrary choosed a radius of 75mm @max Beam.

"Rec" is in blue, with squared dots. "Tri" is in red, with triangular dots. "Rec_smooth" is in green, with round dots.
I slightly modify my hydrodynamic model, trying to improve it, in comparison with the numbers that are given in the study I attached to my last post. Unfortunately, I couldn't do much, since analytical formulas are not very accurate. Still, the relative difference between the calculated drag may give us an order of magnitude and a ranking.

"Rec_smooth" drag is really comparable to "Tri" drag above 4.80m.s-1. The drag gradient vs speed is the highest for "Tri", which may indicate that "Rec_smooth" may be a good compromise between pure triangular and pure rectangular sections. The turbulence has not been explicitely taken into account here, but even with this analytical model, it has been observed that bigger radius tend to lower the wetted surface area, compared with "Rec".

Again, one should be carefull with the interpretation of these results. Also, it would be interessant to put the rocker in play. Mathematical formulas are getting bigger and bigger... I made a try with a simple a elliptical rockers, but the draft seems too high to me. I guess that the standard rocker of a kayak is way more stretched... They may have very flat sections in the middle, and be only rocketted at the very end...@rwatson, @messabout, @Christian Nally, @gonzo, what is your experience ?

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Among the several important measures of a kayak, or other boat design, is the area distribution curve. Refer back to the previously mentioned bread slices, or section views of the boat. We know how deeply each section will be immersed. That kind'a depends on the rocker of the bottom, the depth of immersion, and the width of the wet section. We can calculate the areas of any or all of the parts of the sections that are under water. ( problem here is that we needed to know the actual draft of the boat before we can calculate section areas.... more about that later).

Use the areas of the individual sections to construct a simple x- y graph which we can call the curve of areas. If we believe in the most widely accepted postulates of Isaac Newton, then we can use his second law for argument. This: F=ma The "a" factor is for acceleration. If the "a" factor is high, then the Force required (F) is higher. Simple math here. So let us fiddle with the area curve such that we manage to minimize the acceleration of a mass of water at any of the progressive sections..... Let me back up a pace or two. When a floating object moves from one location to another, some water has to be moved out of the way. It seems like a good idea to move the floating object in such a way as to minimize the velocity of movement of any and all those little molecules of water. Refer now to the area curve.

Some curves will look somewhat similar to a bell curve. In that case you can see that parts of the curve have a noticeably different tangent slope. The places where the slope is larger than in other locations, is clear evidence of increased acceleration of water particles. Back to the drawing board.....Rearrange the rocker curve in conjunction with the plan view of the waterline. Or in other words try to make your area curve look more like a smooth curve that has no inward curves. A sine curve stretched way out in the x direction. What we are doing is trying to reduce or eliminate the change of acceleration rate of the water mass as the boat moves through the water.

I do hope that I have not gotten too far out on a crackpot limb here by invoking Newtons laws. But physics is pretty reliable.

If anyone cares, I will explain a simple cocktail napkin method for determining the draft of a kayak or other small boat. Or you can tell me to buzz off and I will go to my room.

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### Christian NallyJunior Member

Thank you Messabout for the detailed response.

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### gonzoSenior Member

An 200 lb competitive rower can generate about 270 watts for a short time. Is the chart for a kayak with a motor?

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### Alan CattelliotSenior Member

The hydrodynamic model may be inaccurate to an extend I cannot define well, since it has only been correlated with catamaran and trimaran hulls whose lenght is greater than 15m. There should be some adjustments to be made in the parameters influencing the wave and frictionnal drag. Still, It seems in good agreement with the experimental study given in a previous post, section 4.4. An Algebraic Approximate Solution for the Mean Velocity :

" Using the values obtained for Athlete A1 (Fm = 89.6 N, Me = 77.3 kg, K = 1.25, SCD = 5.85 × 10−3 m2) we have τ = 4.2 s and Vmax = 4.95 m/s. The same evaluation for Athlete A2 (Fm = 112 N, Me = 86.8 kg, K = 1.1, SCD = 6.38 × 10−3 m2) leads to τ = 4.4 s and Vmax = 5.6 m/s."

Which give for Athlete A1 Mean Max Power = 89.6 x 4.95 = 428 W, and for Athlete A2 Mean Max Power = 112 x 5.6 = 627 W. One can compare these numbers with those given in https://www.researchgate.net/public...and_power_output_of_elite_flat-water_kayakers

" The mean maximal power output was 610 ± 65 and 359 ± 33 W for the male and female athletes, respectively. "

Does someone have some other references ?

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### gonzoSenior Member

Is that maximum power for a few seconds? No other source shows values so high for any reasonable sustained period.

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### Alan CattelliotSenior Member

Indeed. The article "On the Physics of Kayaking" precise that these power calculations are averaged on a 8 to 10 seconds periods. I don't have this information for the second reference I gave.

270W for a short period is very different from 300W in average. So, the calculations I've made would be too high. If there are correct, is it the "pure flat bottomed" shape with no rocker that is the cause ? If they are not correct, could the friction drag calculation be the cause of this ? The hull lines of a kayak are "pinched" in the aft direction, unlike the hulls shape that are normally used in the hydrodynamic model. At this point, I lack some informations to understand the gap that you've highlighted, Gonzo.

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### sailhandSenior Member

Just a thought bubble here, do any of these models account for a degree of hydrodynamic lift from the different hullshapes. I imagine more lift from the flatter hullshape than the v shape keel. Would this have any effect on the accuracy of the modelling at both lower and higher speeds. Would the hull achieve a crossover point where the lift was substantial enough at increased speeds to sufficiently reduce wetted surface area below that of the v shaped keel, possibly planing. I imagine your average paddler would never achieve such speeds however it would be interesting to consider the effect of the hullshape on draft, wetted surface area, Resistance etc. in these models or is this too complex for such a simple model. Cheers

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