# Friction Coefficient

Discussion in 'Hydrodynamics and Aerodynamics' started by jesdreamer, Sep 30, 2015.

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### JoakimSenior Member

Certainly there can be trim change and squat of a displacement vessel, but not much the way you described it. It is much more related to the wave pattern thus totally different from airfoil and not creating induced drag.

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### DCockeySenior Member

What do you mean by "Bernouli forces"? Are you referring to pressure?

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### jesdreamerJunior Member

Bernouli Forces

By the term Bernouli forces I realize the Bernouli effect at increased flow velocity is a decrease in pressure normal to flow direction -- this causes what people refer to as a "suction" on aft portion of the hull and it is the related ambient forces which cause an increase in trim angle, etc, etc --

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### JoakimSenior Member

Changes in trim are not related to low pressure according to Bernoulli equation. They are related to the wave pattern created by the vessel. The stern starts to sink due to own bow wave.

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### DCockeySenior Member

What do you mean by this? Pressure does not have a direction associated with it.

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### jesdreamerJunior Member

Posts 34 &35 both make good points -- As to Pressures due to Bernouli effect, I agree pressure has no direction but as with the spoon in faucet flow if an adjacent surface is not restrained, It will be forced into the flow by an inbalance in pressures (which end up with a net force perpendicular to direction of flow).

Now as to the trim situation, I do agree that wave action is a major effect and in fact is probably the main effect leading to swamping a displacement boat by moving too fast -- I can visualize no drag effect related other than the need to now climb up the angle. If there is in fact any Bernouli effect of flow along a curved hull, it seems to me that related net force causing some degree of tilt is perpendicular to hull at point in question and thus has a component toward rear which I would consider to be an induced drag (I realize this is not a single point question and integration would be involved).

And I really would like to see a similar series of drawings and data to describe wave induced trim effect as stern area is widened or has more buoyancy.

I visualize the wave effect on trim as something separate and additive to any Bernouli effect.

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### JoakimSenior Member

To get considerably lower pressure under the hull the water would need to have rather high speed. A streamlined body like a kayak will not change the velocities in the water that much and thus will not change static pressure that much (except due to waves).

Squat is important factor only for swallow waters and even then probably only for rather flat bottom hulls like typical ships. Then there is only limited space for water to make room for the hull leading to rather high velocities under the hull. https://en.wikipedia.org/wiki/Squat_effect

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### JoakimSenior Member

You can find several formulas for squat. For ship 150 m LOA, 25 m beam, 9 m draft and Cb of 0.7 doing 10 knots in 10 m water depth (only 1 m clearance!) the squat is about 0.7 m. If the water depth is increased to 20 m (or draft to 4 m), squat is 0.3 m.

A kayak may have a Cb of 0.4. Changing the ship above to that reduces squat to 0.4 m. Changing the dimensions to more typical Kayak dimensions reduces the squat to 0.00 m in 10 m water depth and 0.02 m in 2 m. The formula is probably not accurate for a kayak, but it shows the order of magnitude.

10 knots is about the K1 500 m world record speed. 5 knots would be a more typical speed. The squat at 5 knots is 1/4 of 10 knots.

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### jesdreamerJunior Member

How Hull & water react to speed

First off, I believe I have been using the word "squat" incorrectly -- I have been using the word to describe hull attitude or trim, such as in the way a speedboat transom sinks if full throttle quickly applied from rest. I see it is really related to increased draft when traveling under certain conditions in shallow water. I will stick to using "trim" to describe attitude when trying to climb out of the "hole" -- I have no interest in shallow water effects --

Please check out some of the "You Tube" videos on canoe and kayak racing, particularly the Sprints where effort is max -- I think I see some increase in draft while at speed in kayak races when using 2-ended paddles. Am I correct?? Then in the canoe races with paddler kneeling & a single ended paddle, it looks to me as though bow might rise at begin of stroke and aft certainly seems to sink during force segment of each stroke --

I would like to understand just what is happening to hull-water interface in these videos. In the kayak races, might the hull overall length simulate a reduced area per Bernoulli, and increased velocity all along hull interface be yielding reduced pressure, lower buoyancy, and thus, increased draft??

In the kneeling canoe races, I don't understand why the bow rises with each stroke -- I visualize zero downward force from paddle which would be inefficient, I only visualize paddle force toward rear, and I feel front hook on paddle face as well as stroke "configuration or path" support this belief. In addition it appears that paddlers might lean forward at stroke, this moving CG forward and encouraging bow sink, Likewise I see stern draft dramatically increase during each stroke -- and doubt paddle can provide any causative force while in feathered aspect.

I would expect to hear that "bow rise in kayak is hull climbing up the bow wave during high force of the stroke", but sharp bow cleaves the water and bow wave really only shows up to sides of the hull (I visualize zero bow wave under hull since water is incompressible). But I do visualize increase in "flow velocity" as water travels under hull and thus reduced pressure and less resultant buoyancy -- so I can see how the aft end might develop more draft. I visualize hull trying to climb out of the resultant hole (low buoyancy area) into the high buoyancy area up toward bow. To me, this seems to present a problem different than climbing a bow wave and somewhat different than the situation when 2nd wave moves to behind stern at higher speed -- does this make sense to anyone?? Might it affect the way we look at friction and hull design??

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### DCockeySenior Member

Bow rising with each stroke for solo paddler, kneeling with single blade paddle - my thought is this occurs because of the vertical offset between the line of action of the force of the water on the blade and the center of mass of the canoe and paddler. The offset results in a bow up moment on the canoe which causes the bow to pitch up.

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### jesdreamerJunior Member

If the paddler leans forward during each stroke this shift in CG doesn't sound like it would contribute to bow rise. Have you looked at the stroke path?? Do you think a coach, paddle blade designer, or paddler would allow a stroke which caused a compliment of force in any direction other than toward rear??

As long as we are in fantasyland, perhaps the sudden surge in velocity yields reduction in buoyancy due to Bernouli, allowing aft to sink and thus bow to pivot up against the related increase in pressure along front 1/3 of hull??

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### DCockeySenior Member

Nothing "fantasyland" about my suggestion. A reasonable assumption is the force of the paddle on the water is parallel with the surface, and the line of action is below the surface of the water and goes though the center of the submerged part of the paddle. Another reasonable assumption is the CG of the combined canoe and paddler is somewhere around the waist of the paddler. That offset between the line of action of the force and the CG of the mass being propelled will cause the bow to rise with the stroke of the paddle. Simple dynamics, no fluid mechanics needed.

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### jesdreamerJunior Member

I do admit that with paddle center of force at some significant distance below hull, we end up with a moment tending to lift the bow -- We all know that each stoke tends to turn the canoe/kayak unless paddler shifts weight or adjusts paddle angle or stroke -- so a bow rise moment appears to be there as well. interesting analysis. Also if CG is at waist of the paddler then when he leans forward at start of stroke it might have very little or near zero effect on bow draft. Now who can explain what all is taking place and how these detrimental factors might be dealt with??

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### Leo LazauskasSenior Member

There are dozens of papers available that you could find in a Google search.
Here are some...

Mathew Ben Brown, "Biomechanical Analysis of Flatwater Sprint Kayaking ",
PhD thesis, 2009
http://eprints.chi.ac.uk/819/1/507155.pdf

http://paginas.fe.up.pt/clme/icem15/ICEM15_CD/data/papers/3816.pdf
https://ojs.ub.uni-konstanz.de/cpa/article/viewFile/4822/4462
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3588614/
http://www.sersc.org/journals/IJBSBT/vol4_no4/4.pdf
https://isbweb.org/images/conferences/isb-congresses/2013/oral/sb-performance.06.pdf

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### philSweetSenior Member

Yes.

The added velocity perturbation can be computed. The longer and slimmer, the less the effect. Shallow boats also have a relaxed attitude due to the surface sucking down and reducing the apparent area of the hull. Averages are easier than instantaneous point values. And when you have the velocity field, you can take a stab at how much the pressure on the hull is reduced. Doing this for a boat being towed on flat water is really hard - a symmetrical boat with no side forces, no propulsion, no maneuvering, clean hull, no waves, no wind. You're talking a college degree in hydro.

To get propulsion, maneuvering, and sideforces figured in, you have to go digital. There is no analysis. You need an advanced degree just to operate the software. And your own powerplant to run the computers. Because of the cost, engineers have been avoiding this sort of direct attack for two centuries, and will probably continue to avoid it for a good while longer. Collectively, we have a thousand years of experience building many millions of kayaks. Collecting that knowledge is still cheaper than trying to reproduce it in a computer.

What we can do is collect tables of trade-offs. Comparing boats to one another and charting the variances. With kayaks, you mostly give an Olympic medal winner a bunch of boats and get him to tell you what he thinks. Its a cost thing. Trained humans are really good at this. You can build a kayak and test it cheaper than you can model it. But there are crappy models that still help with deciding what direction to push the envelope. Again, this takes some math.

This is what pushing the envelope looked like around 1950. This is mostly a collection of techniques that've been available for about 250 years, but nicely organized. Its an aero paper, but the same idea.

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930092099.pdf

So you have a bit of catching up to do.

You have to understand, this type of problem has attracted the world's best mathematicians since Galileo drew pictures of the flow in mill races. Many millions of hours of thought and development have ensued. It's a billion dollar a year industry related to performance and fuel economy. Testing tanks are national treasures. When one big ship can burn 300 tons of fuel per day, hull pressures really are an item of interest. There's about 500 of them this size. Imagine a 1% fuel savings. That's a quarter billion dollars annual savings just in the 500 biggest ships. Airliners consume about 600,000 tons of jetfuel per day worldwide. Turbomachinery is another segment interested in pressure predictions - almost all the electricity generated in the world comes from fluid interfaces.

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