Put strain gauges on the paddle to measure its bending. Test the paddle beforehand in a lab to ensure you know its modulus of elasticity. (i.e. to calibrate your strain gauge setup with known loads).

Trying to measure force indirectly will always introduce additional error. If you try to use the boats acceleration to measure the paddle force you'll need an accurate model of the boat dynamics including drag and inertia terms. Trying to do this type of modeling outside of a pool setting will be very difficult, with waves and wind etc... too many uncontrolled parameters.

If you are wanting to investigate the effectiveness of the paddle strokes (the efficiency of the stroke in generating forward momentum), then you should measure the force directly via a strain-gauged paddle, and simultaneously measure the boat's acceleration. Then the best stroke technique will generate the highest change in forward momentum, while requiring the least power input from the paddler. I think you should do this in a pool to eliminate uncontrollable variables. Maybe once you get that measurement configuration all setup, you can try taking into realistic settings.

True an inefficient stroke could still make a big splash. So what would be better a) attaching a boat to a strain gauge in a pool and measuring pull on the gauge or b) measuring change in speed of water flow if someone was sitting beside a circular tank or had a flow meter mounted on a boat? Even a bad stroke style could result in amazing strain in a pool but in reality it would not work out as well over a race. I'm not interested in least power from the paddler because I believe that is a fallacy. Physiological efficiency of stroke cannot be measured by looking at stroke power.

Merlin sell the Excalibur paddle complete with sensors and related software www.youtube.com/watch?v=mzPO9u501TA. It is rather expensive and I think you could use small sensors like those available from X2 Biosystems to analyse paddle acceleration and angles. If you then also add a pressure sensor where the paddler grips the paddle and also measure boat acceleration (just put your smartphone in a plastic bag and tape it to the boat) you may be able to create a mathematical model of the relationship between pulling force, blade angle and velocity, and boat boat velocity. You may also want to include video analysis so you get a fuller picture of stroke length.

Here's  a paper that is relevant to what you want to do " A KAYAK TRAINING SYSTEM FOR FORCE MEASUREMENT ON-WATER" https://ojs.ub.uni-konstanz.de/cpa/article/viewFile/4566/4253. They also measure foot force which is of course very important when you are propelling a boat forward.

Some of the answer depends on the goal. Do you want to develop a better paddle, or do you want to improve the athlete's skill in using the paddle. Of course the end result is the combination of the two. At a guess the force from the main stroke is the applied force less the drag as water gets sucked behind the void at the back of the paddle.

It is possible (especially for beginners) to waste some power as the paddle enters and leaves the water.

In the lab an inexpensive approach might be to use a wind tunnel. They are relatively inexpensive and easy to build. It would give you numbers to play with. While water and air are both fluids, I am not sure how easily the results can be converted. You could look to the engineering department and see if there is someone working in fluid mechanics. Of course that will rapidly involve a bunch of long mathematical equations, and that could be good or bad depending on your sense of fun.

In a controlled environment you have a few more options. 

Rather than a "real" paddler, set up a 4 bar linkage to mimic the paddling action. You can then use a model hull and measure the pulling force on the hull. If you then also measure the power input to the mechanism,  you can measure stroke efficiency and observe the effect of changing angles, stroke rate, stroke length etc.

If you have enough money, maybe use a scara robot

Some more thoughts ....

To measure power, a simple approach would be to put an accelerometer on an OC1 and also measure time to cover a set distance. From the accelerometer data you can determine power at different phases of the stroke. Here is an example of the kind of information you can derive for a dragon boat https://backsixpush.wordpress.com/2012/11/15/boat-speed-and-individual-strokes-surprising-results/

If you also put a camera on the outrigger, you can use software like Kinovea to analyse angles, rate of paddle movement etc.

I belong to Dragon Boat crew and we had the same dilemma.  The composite sum of the entire crew's output can be measured by the boat's acceleration and speed.  This can be easily done using a smartphone app using the phone's accelerometer.  However, individual paddler performance is not so easy to measure.

We ended up attaching a strain gauge to the paddle to measure individual paddler output by proxy.  Measuring the bend of the paddle at its fulcrum point will be able to determine the proportional work output thats being exerted by a paddler.  The force of the water against the blade during a paddler's stroke will cause the shaft to bend (albeit slight), but the strain gauge will be able to measure these bending forces quite easily.  

An earlier post indicated that the modulus of elasticity of the paddle material used needs to be accounted for during calibration.   While this may be desirable, its not absolutely necessary to be able to record an accurate pressure/force value.  The idea is that you want to measure individual paddler output, but only in comparison to other paddlers.  If you calibrate the strain gauge to a full range of bend of the paddle and assign it an arbitrary numerical range - e.g. 0-10 or 0-100, by comparing the results of a paddling session between different paddlers using the same strain-gauge fitted paddle.  The paddler with the highest numbers are your strongest paddlers.  The ones with the lowest numbers are your weakest paddlers.  While it might be desirable to know that Tom exerted 98.35 lbs per square inch on the paddle, knowing instead that he recorded a value of 50 in relation to Phil who exerted only a 30 may be enough.

We analyzed several broken paddles that were broken by strong paddlers who pulled so hard during their stroke, that the shaft snapped in two pieces.  All the paddles were shown to have broken right around the area of the shaft that meets the blade - the neck.  Since this point is the area that receives the most force (subject to the most bend), we attached the strain gauge there.

Although you didn't ask about this, some other practical info about our application using a strain gauge. The strain gauge is wired to a small 2.4GHz wireless transmitter (also mounted to the paddle shaft along with two AA batteries) . All components can be water-proofed with either a polyurethane-based sealant or an equivalent epoxy resin.  The wireless transmitter sends up to 200 samples per second to a remote USB base station attached to a laptop.  This allows us to not only record the results to a logfile for later analysis, but we can also visualize the results on a chart in real-time (while on the boat).  The base station allows up to 24 simultaneous transmitters to be received so the entire crew of 20 paddlers can be simultaneously captured and compositely analyzed to see the output of the entire crew.

Ben has developed a great system. He is correct that you only need to know proportional work done to differentiate between paddlers. It would also be interesting to look at the correlation between the cumulative force and boat acceleration (just stick a smartphone to a seat and use the accelerometer).

It may be worth to do some calibration as I expect that even paddles of the same make have some difference in defelction. But you can easily check that by clamping the paddle horizontally and putting a reference weight on the tip, or use a luggage scale and record at what force you get the same strain gauge reading.

One problem with the system is that it measures force on the paddle which doe not necessarily equates to propulsive force. For example two paddlers that apply equal force, but one has a good reach so the paddle is mainly at a positive angle while the other pulls further back and pulls mainly at a negative angle. The latter provides much less propulsive power. To get around this problem you need to do some video analysis (I find Kinovea is great for this) so you can relate force to paddle angle. You can then apply a correction factor for each paddler. A lot of work, but excellent feedback for the paddlers.

Here is YouTube video of the sensor-based paddle that i prototyped that demonstrates the use of the paddle in my swimming pool.  

https://www.youtube.com/watch?v=A72K37yGxVw&feature=youtu.be

I've found that take a minimum of at least 100 samples per second (10ms intervals between samples) is necessary to re-construct the details of the paddle/stroke.

Jacob brought up some excellent points about how measuring force via strain gauge does not necessarily equate to propulsive force.  It provides at best a first-order measure of raw force being output by the paddler.  In dragon boat paddling technique, conventional wisdom dictates that the paddler end their stroke (i.e. pull the paddle out of the water) when the paddle reaches mid-thigh.  When the paddle goes beyond this imaginary line of mid-thigh, the paddle will begin to pull water upward, driving the boat downward into the water, causing drag, and slowing the boat.  This negative blade angle is most easily measured using an 3-axis accelerometer, which i have yet to attach to the paddle.  Its only with this additional component of information correlated with the force/output data that you will be able to measure effective (positive) work output.   In the YouTube video, you see the wave-form that rises / falls with each stroke.  The area under the wave-form represents raw force/output being produced by the paddler.  The portion of this area that results from negative paddle angle must be subtracted by the portion of the area from positive paddle angle.  A good paddler will minimize the amount of negative angle by insuring that the paddle exits before the mid-thigh vertical line is reached.  But the accelerometer should be able to identify those paddlers who exit late and accumulate excess negative work that reduces effective output.

I am planning to include the use of a 6-axis accelerometer (+gyro) in my solution by using the new Intel Curie processor recently announced at CES.  In addition to being able to be powered by a +3v Lithium coin battery, the processor has an on-board 6-axis accelerometer, an on-board Bluetooth LE module for wireless transmission of data, 12-bit ADC to interface to the analog strain gauge, and the size of the processor is smaller than an eraser head at the tip of a pencil.  The small form factor, low-power requirements, and rich set of features make it conducive for use as an athletic performance measurement / enhancement tool.  Its $10 price tag is also attractive.

https://www.youtube.com/watch?v=A72K37yGxVw&feature=youtu.be

That's very exciting Ben (and thank you Deon for posing the question that triggered Ben's response)

I think there's a great market for a such a device that can be retrofitted to a paddle. Especially if it can be made so that you only need to fit the strain gauge and "plug-in" the processor and WiFi bits when needed. The ability to get a picture of performance of the whole boat is of particular value to any team.

The low cost is of course also attractive. Even paddling poolside is far better than using an erg to compare individual paddler performance or observe the effect of a change in technique.

I recommend that you also have a 6-axis accelerometer fitted to the boat so you can correlate power to acceleration. It would create a fantastic research and performance measurement tool.

I have a background in product development and international marketing. Just email me at [email protected] if you like me to give you a hand with this.

Some more comments about Ben's message.

It's not quite correct to say that once the paddle is past mid thigh it slows the boat down. While some component of the force will be vertical (down), there is still propulsive force. But at some point it becomes more effective to pull the paddle out and start a new stroke. The data that your system will be able to collect will make it possible to determine where this point is. You should be able to get data like that in the attached image from Sara Ho's "Biodynamics of Dragon Boat Paddling"

After taking out the sensor-rigged paddle this weekend for its maiden voyage with the ASU dragon boat crew at Tempe Town Lake, we were able to obtain some incredibly useful data and at the same time, learn a number of valuable lessons.

1) Even though a full-bridge strain gauge design is being used for the sensor, it is not immune to temperature drops.

I did another YouTube video that experienced a big shift in the zero calibration point from the time i started the video to when it ended 2 minutes later (see YouTube link) and noticed a big change in its zero calibration point.

It wasn't until i ran a test later on did i figure out what was going on.  I did an experiment where i dipped the paddle (which had been sitting in the warm house at 78 degrees F prior) into the pool, which was close to 45-50 degrees F. I turned on the sensor, and with the paddle at rest, i watched the reading slowly drop from its original zero point, completely on its own without any pressure on the paddle. It took almost 3-4 minutes before the reading finally stabililized.  But it DID finally stabilize and remain constant.  It confirmed my suspicions that temperature does affect a full-bridge strain gauge.

Nonetheless, after waiting for it to settle, I was able to calibrate its zero point, and use the paddle in the pool without experience wide fluctuating zero points.

I am slightly confused at this because all of the reading i've done on wheatstone bridges is that while quarter bridge circuits are subject to temperature variations, full-bridge circuits are not. I must have missed something in my research, because this full-bridge strain gauge is definitely not immune to temperature variations.

2) While acclimating the sensor to the water (or environment) it will be tested under before calibration helps, it does not completely solve the problem.

Before taking the boat out, i spent a few minutes holding the paddle under water allowing the paddle sensor to settle. I watched the readings slowly increase before seeing it bottom out at about -2.2mv, at which point i calibrated that as the zero point.

During the session, we passed the paddle around to each crew member asking them to do the same stroke routine as everyone else ( 10 strokes each at 70% max, 80% max, 90%, then 100%). After recording each paddler and looking at the results later at home, i noticed that almost every paddler saw a jump in their zero values at some point in their 40 stroke data recording session, which lasts approx 1 minute.  

If you take a look at some of the raw data shown in the attached image links, you'll see that some paddlers were negatively impacted as their zero point went below the zero line. Others were incorrectly "rewarded" as their zero point went above the zero line. The total effective work output for each paddler is calculated by summing up the area under each "stroke curve" across all strokes captured, so those whose data is artificially lowered are incorrectly penalized and those whose data are artificially elevated are incorrectly rewarded.

This was simple enough to correct using an offset adjustment algorithm to bring the data back to zero.  I ran a script as a post-processing step to normalize the data before doing the final compilations to rank each paddler based on max stroke and overall effective work output.

Other than these issues, the paddle performs very similar to the much higher priced Merlin paddle that essentially does the same thing. We put this paddle together for about $400, but we are now working on something that will be less than $20-$30 to allow an entire crew to outfit their paddles rather than have a single expensive test paddle.  I think we've learned everything we've needed to from this initial prototype.  On to bigger and better things (actually, smaller, cheaper, faster).

I attached a summary of some of the more interesting observations from the data that was collected across 14 different paddlers.  Please view the attached Google Doc for those findings.

https://www.youtube.com/watch?v=5tgdw09XL6E

Thx guys - let me know when you have a cheap gauge that my club (Lanikai Canoe Club) can buy. We only train in the ocean which introduces other variables and makes steering more important. The ocean temperatures vary depending on how deep the water is and how far off coast. If we stay close to coast in same depth water we might get less movement. I was hoping One Giant Step from New Zealand was going to make an outrigger paddle with their 12-strain gauge kayak paddle setup (which was promised a few years ago) but they are 2k a pop and never deliver or answer questions with any accuracy. We are constantly refining our stroke and the skeptical young guys really need to see some hard data before they will change what they are doing. I'm not researching this anymore because I changed jobs out of university environment, but I'm happy to be a part of your research and be a guinea pig... Send me the gear and ?Ill send you the data :)

I came across this instrument which is a clip-on, so easy to use with existing gear. https://www.motionizeme.com/

It doesn't measure force, but if you integrate the data (and video) with good real-time speed measurement (so you get the change of velocity during the stroke), the 'skeptical young guys' will be able to observe the impact of changes to the stroke.

Very cool but speed is variable in ocean with waves and this method is best suited to more limited stable environments like lakes and rivers. It would still be hard to separate elite paddlers who are close in performance. Maybe useful over long distances?

That's exactly why you want real-time speed measurement (i.e at say 0.1s intervals) so you can calculate acceleration as well and correlate it with paddle angles, stroke rate, etc. Of course stable environments are better and measuring paddle force is good too.

Because you are looking at small differences between elite paddlers, I reckon the best way is to make them go head-to-head in single canoes. That will eliminate differences due to environmental variables. But you can still compare paddle angles and stroke rate.

Regarding your previous comment Jacob -  "While some component of the force will be vertical (down), there is still propulsive force." The reason we dont want to go past neutral is that the upward force generated after neutral will pull the canoe down into the water and that will slow it down regardless of propulsive force.