# Does a boat's glide (deceleration) give a reasonable measure of resistance?

Discussion in 'Hydrodynamics and Aerodynamics' started by Paddlelite, Mar 5, 2013.

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I’ve been playing around with an easy, on-water means of comparing the efficiency of human-powered craft (canoes, kayaks, and paddleboards) which operate in a narrow speed range. With about 10 seconds of high-definition video taken with a still camera as the craft decelerates on a glide, you can dig out position data and compute speed accurately to the nearest 10th of a mph over fraction-of-a-second intervals, such as every sixth or eighth of a second. As long as the boat carries the same weight passenger, and displays a “ruler” made for this purpose, capturing the data is fairly simple. The analysis is the tedious part.

The picture shows some early results comparing three paddleboards (done before the latest refinements in video analysis.) For purposes of comparing boats, I display their deceleration curves so that they meet at some common low speed. Naturally, the curve with the least slope (slowest deceleration) represents the “fastest” boat, which may be a different boat for different segments of the whole speed range.

I realize that this only shows speed over time, and that resistance would be better represented by plotting deceleration, i.e., the first derivative or slope of the speed curves. That data wasn’t really smooth enough to be meaningful though.

So I’m wondering if there’s any inherent flaw or limitation that anyone can think of with using deceleration on a glide as a means of resistance comparison. Also, when I fit a curve to the raw data, what order of polynomial best represents theoretical declining speed? (I'm displaying mostly 4th order curves now.)

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### gonzoSenior Member

I think it could be used, but the math will be staggering. You need to include a lot of variables like displacement to skin friction to wave making to trim angle changes all at different speeds.

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### DMacPhersonSenior Member

Actually, the math may be easier than you think - but it requires a bit of computing. The late Martin Abkowitz, professor of ocean engineering at MIT, was a big proponent of a "systems identification" approach to predicting hydrodynamic coefficients using trial data. His efforts were largely in maneuvering, but he also described ways to determine total drag from ship deceleration. It is based on a fairly clean F=ma, where "m" is the weight plus added mass (typically some 5% for most hulls) and "a" is acceleration (a negative value). The process is to record position versus time, from which you derive velocity and acceleration (deceleration). Then you can calculate "F" at each time step, which will be a negative number whose magnitude is equal to the total drag... or something along those lines. See if you can find a copy of the 1980 SNAME Transactions, and read the paper by Abkowitz.

Don MacPherson
HydroComp

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### PetrosSenior Member

I actually used to perform this kind of test when I worked for a company that built race cars. It is called a coast-down test. Your procedure does not seem like it would give reliable results, it was not that complicated.

You need to know the total mass, and we used to do the tests in a series of short segments. For example, we would time with a stop watch the deceleration time over say a 10 mph segment, say from 80 to 70 mph, and assume that would be the approximate average drag at 75 mph. Than from 70 to 60, than 60 to 50, and so fourth. The average deceleration was taken for each of these points and plotted for 55, 65, 75, etc.

In a land vehicle you also had to know the rotating inertia of all the turning parts when coasting (wheels, axles, differential, up through the trans main shaft and gear cluster), and convert it to equivalent vehicle mass. With the equivalent mass, and the deceleration at each steed, we could calculate drag pretty accurately. At lower speed most of the drag was mechanical friction (which is generally lineal with speed), and the aero drag was exponential. We could than separate the two.

In your case you would also have the mass of the fluid stuck in the boundary layer of the hull, if you were only trying to get a comparison however you can just ignore it. But if there is a large difference in length there could be some error in the comparisons. More moving mass means more momentum, and unless you convert the deceleration into pounds of drag (or newtons), you will not know which one has the lowest drag. IOW, the fastest deceleration is not necessarily the lowest drag if that one has the least mass. That is why you need to reduce your data to lbs drag, not just deceleration.

You can do this if you had an accurate speed measurement and a stop watch. Take multiple runs to get a good deceleration time. You would want to use fairly tight numbers, from say 7 mph to 5 mph, 6 mph to 4 mph, etc. Or you can just straddle the assumed cruise speed you are trying to measure.

The math is not that difficult and the means you are using seems like there is a lot of risk of systematic error.

There was a thread on this topic where they were trying to determine least drag between two hulls, towed by another boat, with a balance beam, one hull tied off to each end of the balance beam. boat with the least drag would tow ahead of the the other.

5. ### Submarine TomPrevious Member

If you've got the hull(s) in the water, why not just tow them off a pole in clean water and measure the drag with a small scale?

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### DCockeySenior Member

I never ran a coast down test but was familar with them when I was involved in automotive aerodynamics research. Aero drag is much closer to being quadratic with speed rather than exponential with speed. Excellent point about the need to add in the effects of rotating mass.

The added mass of a boat is not due only to "the mass of the fluid stuck in the boundary layer of the hull" but also to the entire flow field around the hull. Added mass depends on the the direction of the acceleration/decceleration, and the displacement and shape of the hull. Fore/aft added mass for a typical boat will be considerably less than for side to side or up/down motion. A reasonable approximation for Paddlelite's purpose of comparing relative similar hulls of approximately equal displacement would to assume the differences of added mass between the hulls is small.

Last edited: Mar 5, 2013
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### PetrosSenior Member

We actually built a torsional pendulum, an accurate low friction turntable with a torsional spring. Each rotating part was put on it, and a pick-up on the edge of the turntable would record the period. Knowing the spring rate, and the period, I could calculate the rotating inertia of each part, and than added it all up. It worked out that rotating inertia of the race car was about 10 percent of total weight, which would be a little less for a typical street car. So adding about 10 percent of the weight to mass of a typical car will get you pretty close.

As for the added mass of the moving fluid around a hull, it would be any body's guess. This fluid also has a lot of internal friction, i.e. viscosity, so there are other factors at play here. But as pointed out, for similar size hulls it can be ignored since it should be similar.

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It would be nice to have a towing rig, but this is a simple one-person test with no investment in equipment. I set up the camera and tripod on shore filiming a planned field of view, then jump in a boat, paddle up to speed, and glide through the field of view, typically between the ends of two docks. Conditions must be flat and the water sufficiently deep.

The deceleration is too rapid to measure with stopwatch or gps. I examine every nth frame of video, tracking position, on a pixel by pixel basis, of two points on the boat. Those two points are 1 foot markers on a "ruler" carried on board. This not only provides redundancy by tracking two points, but the pixel distance between them is the unit of measure (one foot) used to measure the movement of the points from frame to frame in the video. That creates an auto-correcting method for perspective error and even camera lens distortion which might cause a one foot object to appear larger or smaller as it moves accross the field of view. As long as the "ruler" by which you measure movement changes size along with everything else, measurement is preserved.

As I said, it's rather tedious, but produces decent accurancy. With a field of view about 30 feet wide, I can get instantaneous speed to the nearest 10th of a mph. I didn't aspire to measure resistance in any absolute sense, only have a basis of comparison between boats. As suggested earlier, I should make sure to equalize the mass between boats.

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### DCockeySenior Member

Test in the calmest conditions possible to minimize the effects of wind. Also, test the exact same configuration multiple times over several days to determine repeatability.

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### PetrosSenior Member

you might run it in both directions several times, than average. that should cancel effects of slight air or water movement.

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### DCockeySenior Member

Running both ways doesn't cancel the effect of the wind. In the rare situation that the wind stays the same speed and is from dead ahead in one direction and dead astern in the other, and the wind speed is considerably less than the speed of the boat then it will come close to canceling. But otherwise it doesn't cancel.

Consider the situation with the wind on the beam. Then depending on the shape of the boat the aerodyanmic drag may be increased or decreased. And the change in aerodynamic drag will be the same for with the boat traveling in oppostie direction.

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### PetrosSenior Member

of course, that is why I said it will cancel any SLIGHT air movements. and slight water movements too. It just makes a better approximation to average it from both directions. If there was any noticeable air or water movement, there is no point in doing the test that day at all. results will be meaningless.

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### Luc VernetSenior N.A.

Since all the factors like skin friction, wave making are present, and of course the mass well known, this does not seem stupid at all (for full displacement vessels that is). The test described here, however, has a few flaws: parallax error when filming unless from a distance (and always same angle), great influence of wind and current (as noted), specially on such light object, hence also short distance/time on which the deceleration can be measured (filmed), resulting in multiple aberrations and a whole "cloud" of points, variations of the body position (on board weights), etc.
However, with a more massive boat, meaning longer measuring time, and perfect , identical conditions, that would give a meaningful comparison result, without actually any "math" but just curves, and just very simple equipment: no tow boat, singe person, etc.... it could then be interesting for basic analysis. Am I wrong?
Of course, a towing system with a mean of measuring the needed force is better. Ultimately, its called a towing tank.

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### JoakimSenior Member

Since the boat slows down very rapidly compared to its length, I think that using this method to measure anything else that the starting speed resistance is vastly inaccurate. The flow and wave pattern around the boat will just not be the same in such a rapid transient as it would be at constant speed. During the whole test the boat moves just a few hull lengths and speed drops to less than half.

I would paddle the first half of the recording region at constant speed (in order to measure accurately the starting speed) and the stop paddling. Measuring the dV/dt at rather small speed change would probably be the most accurate.

There seems to be quite much scatter in your data, which makes measuring the short interval too inaccurate. There are rather cheap 10 Hz GPS units and accelerometers, which could be more accurate.

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### gonzoSenior Member

The really cheap way to test models is to make a yoke (stick) balanced at the center and tie a model to each end. The one that pulls the most is the one with more resistance. You can test them at various speeds to compare. Francis Herreshoff produced some very sophisticated hull shapes with that method.

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