Do these measurements of drag for my canoes make sense?

Looking for some advice from you who have been at this a while.
I have a short, fat, lightweight solo canoe (10.5 ft, 29" beam, 16 lbm) that is perfect for pond hopping but I'm looking for something more efficient for longer trips, and have tried a few. They do "feel faster", but I'd like to quantify the difference.
So I paddled what I have about as fast as I could, then coasted to a stop logging the speed decay with a GPS app on my phone. Did a curve fit. Differentiated the curve fit for acceleration. Used the mass to get drag. Plotted drag vs speed. Some figures attached. I did it multiple times for both my two man canoe and my solo canoe. The data (to me at least) are remarkably repeatable and generally make sense?
I realize paddling at one speed and decelerating through the same speed are not the same forces (hydraulic mass, trim, yaw, angular acceleration, who knows what else) but I'm willing to believe these are second order effects and this is largely valid for a fair comparison.
But I have questions, too. For example, the solo boat at 5 mph has a speed ratio of almost
exactly the magic 1.34, but I see no sharp increase in drag even though it feels like maybe there is. In fact, it looks linear or flatter like it's all low Re skin friction? Pointy bow? I'm really not sure.
Any comments on what I'm missing are welcome before I go out and try a bunch of others. I've seen this idea kicked around, but no results or rebuttal. Thanks.

 

Here's a thread with discussions of canoe drag: Canoe with square bottom hull vs rounded hull | Page 2 | Boat Design Net

Scrolling down to post #29 on page 2, there's an attachment from @Dolfiman that might be of particular interest to you.

 

Data looks reasonable at first look. Nothing sudden like a step increase in drag happens at SLR of 1.34 (or any other value). Given the uncertainties in the speed data, the approximation of the curve fit and then differentiating the fitted curve the data looks about as good as I would expect. Staring at the data I see a bit of a step in speed around 44 seconds and another around 52 seconds. I wonder if those could be due to the wake overtaking the boat as it deaccelerates.

 

A short fat canoe hull has a high gradient of curvature which will slow you down or needs more power.

 

Hi,

I tried to reproduce your post-processing of datas, using the "Fig.1 Portion of raw data as recorded on an iPhone by the PhyPhox application", for time > 34s. It seems that, at least three mistakes are done in the summary you present.

(1) You didn't made the estimation on the error of measurement. Error calculations is very important for the interpretation of the results.
(2) You've used a third order polynomial fit, but you should have used an inverse function as interpolant.
(3) You may have used only the mass of the canoes to obtain the drag from the acceleration.

(1)
In the graph, down below, I compare the results of the 'speed' column with a speed calculated from the 'distance' column and the 'time' column, nammed speed2 in the graph downbelow. As you can see, there is a gap between the two, and the gap is not constant in time. You've got here a source of non-constant error.
For the purpose of comparison between series, and with external data sources, the heading of the boat should also be taken into account. I also see that, in the figure "Fig 5. Summary of data from two man canoe (two trial runs, calm winds, both in same direction) and one man canoe (six trial runs, three heading west and three headed east, very slight westerly wind).", you have done your measurements on the one man canoe in two opposite directions. Which is excellent. Why haven't you done the same for the two man canoe ?

(2)
As defined, the drag you seek is .5 * density_H2O * Wetted_Surface * square_of_boat_speed * Drag_coefficient. A basic integration will show you that the deceleration of the boat subject only to frictional forces should be proportionnal to the inverse of the time. In the attached pdf, you will find the correct formulation and its demonstration, together with theoritical details. The experiment has been made when paddling, but part of the methodology may be applicable for your 'non-paddling' protocole. You may also note that, by using the inverse function for regression, you may have a greater difficulty to fit the data points, but in return, you will be able to complete the error calculation, putting error bars in your graphs.

(3)
If I do the calculations of the drag, from the raw data you gave, using this conversion :
["Acceleration(lbf)"] = ["Speed(m/s)"].diff()*(-1)*(16lbm)*(2.2369mph/m*s), where
Speed(m/s)"].diff() is the speed derivative with respect with the time. The multiplication by (-1) is done to take into account the decelerated nature of the movement (after you stop paddling ).

As you can see, I found numbers in the same magnitude as yours, so I deduce that you use the (16lbm) value to do your calculations. Which is wrong.
If you didn't jumped into the water after stop paddling, or, if you stayed on board after t = 34s (with reference with your Fig.1 in the document 'Summary of canoe drag data maughan 8oct22-1.pdf', then you must add to the (16lbm) your own mass to obtain the inertial mass. If I assume a skipper mass of 75kg = 165,347lbm, then the total is around 200lbm, which is more than 10 times the values you calculated for the drag.
@4.86mph = 1.79 m/s, the corrected drag should be around 10 times 4.5lbf, the value you calculated, resulting in a corrected drag around 45lbf, approximatively 200N. If you consider the study hereby attached Fig13, you will find that it is more than 2 times the awaited drag value at 4.8m/s = 8.95mph, which may be around 75N.

In conclusion, I would say that there is quite a few more insights and calculations to be made, in order to exploit the raw data you present. The order of magnitude of the drag you calculated is not correct, it lacks also an error estimation. The comparison "2 men wenonah" and "1 man horbeck" should be re-established, using a more rigourous protocole.





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I reproduce the procedure given in applsci-12-08925 (On the Physics of Kayaking) 3. Pure Deceleration: The Zero Propulsion Limit, Fm(T) = 0 (page 5), with the datas given in Summary of canoe drag data maughan 8oct22-1 Fig1. Portion of raw data as recorded on an iPhone by the PhyPhox application.

Please note that I skip the application of the Added Mass equation, given in 3.2 of applsci-12-08925 (On the Physics of Kayaking), since I did not take into account the mass distribution of the kayak and its skippers. Judging by the numbers given in the study, I introduce an uncertainty around 5% in the following calculations.

Steps to apply the procedure

1. Select a portion of raw data where the "Pure Deceleration" hypothetis is correct, Note V0, "V zero"

2. Compute Vo/V(t) for each data point in the exploited interval. Determine the slope value of a linear interpolation that start at the Y-axis value = 1

3. Compute the drag in Newton by squaring the speed V(t) in the exploited interval, multiplied by the inverse of the slope value, times the speed Vo : Drag = ['Speed(m/s)']^2 * (1/slope ) * Vo

These numbers are far better in order of magnitude than those found in Summary of canoe drag data maughan 8oct22-1. I compared this results with a theoritical calculation of the hull drag of a kayak, made in good agreement with the study applsci-12-08925 (On the Physics of Kayaking). See also On the hydro dynamics of flat bottomed kayaks https://www.boatdesign.net/threads/on-the-hydro-dynamics-of-flat-bottomed-kayaks.67431/
The given "orange" points are all under the computed drag curve, which is not surprising, since they represent only the hull drag, neglecting the windage. Is it possible that the windage be half of the computed drag ? I don't know. Still, comparing this graphs with the data exploited in Summary of canoe drag data maughan 8oct22-1 confirm that more efforts than those made in this summary result in a closer order of magnitude of the drag estimation.

I hope that my procedure proposal will help everyone with this kind of consideration.

 

Wow! Thanks everyone for your responses to my original post. That's a lot of effort. Very helpful. Let me try to answer some of the questions, mostly I guess from Alan.

1) Speed uncertainty. This is a great catch. Maybe you get what you pay for (free) but the velocity I used is the one PhyPhox reports as calculated velocity. Thanks for noticing that it's different from velocity as calculated manually from reported distance and time. I also calculated velocity from change in latitude and longitude (111,1139 m/deg lat, 80,390 m/deg long) and that's different too! So I guess I don't know what to believe. The recorded one seems the smoothest, like maybe there's more there than we see and I'll use that one for now. Hopefully the same across each test. (At high speeds, it does agree with my GaiaGPS and my Toyota, by which I mean it's about 2 mph faster than the speedometer. At lower speeds, who knows. It doesn't want to do anything until the distance has moved at least a few meters.)



3) ["Acceleration(lbf)"] = ["Speed(m/s)"].diff()*(-1)*(16lbm)*(2.2369mph/m*s). Not sure what to make of this equation with all the different units, but I didn't give you enough information to duplicate my calculation. I did of course use the full system mass in my calculation. The data example was for my two man canoe with 391 lbm total mass, including two paddlers, paddles, clothing, canoe, and gear, or about 178kg. No hydraulic mass or windage in the calc. The initial deceleration is about 0.12 m/s^2 so that's ~22 N or 5 lbf, roughly what you have there, though I'm not sure I understand what you've done.

I tried it with the two man canoe as a simple test when we were out on the water, mostly to see if the velocity curves would be reasonably smooth and repeatable. When it looked like they might be, I went out special with my solo canoe for multiple tests in each direction. That's my main interest. Very repeatable.

The reference you added is very helpful. I've been looking for a physics-based explanation of what's going on in paddling, or at least one I can understand. Equation 5 and this method essentially simplify the problem to a constant Cd and first order velocity decay, but it gives roughly the same results as the instantaneous velocity change readings like I've done here (if they can be trusted). As I understand it:

where m = 391 lbm or 177.7 kg
Vo = 2.29 m/s
and tau for my data from this test set is 0.0694:


So the drag curves are


or when compared to my original graph in lbf and mph:


Pretty close, really, and I'll bet if I limited the analysis to a small segment where Vo/V is even closer to linear they would be nearly the same.

This is really helpful. There's a lot of knowledge here. Probably accurate enough to compare varies design, at least roughly.

Thanks again.

 

From a different perspective, what’s your paddling style?

Where in your stroke do you apply the most power?

What is the shape of your stroke?

Are you a lefty or a righty? Is your stroke different left to right? More power? Less? Shape different?

Weight longitudinally during stroke? Recovery? Do you rock forward and back? Keep your weight still?

Long stroke, glide?

Short stroke, little glide?

Where do you like to sit longitudinally?

Do you keep the canoe level side to side during a stroke? Or do you lean?

Do you lean during your glide? Or are you upright?

All these factors require a different hull shape. Or perhaps a different hull shape during different times of your stroke. (For example, lower prismatic tends to accelerate quicker, but speed tops out quicker, glides at a lower speed & etc & etc)

How did you come by your stroke?

How much have previous hulls / local conditions / type & Length of blade produced your stroke? Do you want to change your technique?

And then there’s maneuvering, whether you launch off a dock, or shore (Rocky, sand, mud, etc.?). Windy, er, venues?

Canoes can be very personal beasties. Or demanding beasts.

 

I can't believe I missed this thread since I design and build canoe/kayaks. From my experience kayaking, the water depth affects the drag on the kayak. The deeper the water, the less effect water depth has on drag. To ensure fairness in competition, the International Canoe Federation requires race courses to have a minimum depth of 2 meters. Hull lengths are 5.2 meters (singles), 6.5 meters (doubles), and 11 meters (fours). Do you remember the water depth when running your experiment?

 

Indeed. Good thing you are with us.

 

I’m trying to understand the idea of water depth minimum to insure competition fairness - is the idea that -2 meters irons out differences in depth over the course? Coming from competitive swimming, although everyone knew that shallow water was slower, everyone was swimming (usually) in a pool with the same bottom contour under them ( except for L shaped pools with the diving area to the side, the swimming part shallow, and there were a lot of tactical/political crapshoots going on to get the lane next to the deep water, although you would tend to drift towards it, and scrape against lane floats which favored some types of strokes, as well as sprinting vs distance.). Some swimmers would change their stroke depending on bottom depth and contour. Do lighter paddlers benefit from shallow water? Do lighter paddlers exploit hull design for shallower water? Do canoe designs/ paddling strategies exploit undulating underwater racecourse bottom contours? Do better paddlers/coaches pay attention to bottom contours? Fascinating stuff.