Kayak Speed

[leong]

I just read the following statement in the fitness paddling website http://race.fit2paddle.com/C1159474119/E20...5945/index.html

A bit of science here, for the same boat, to double the speed, requires 4 times the horse power, or to get your kayak from 4 mph to 8 mph requires you to put out a 400% increase in effort.

Of course, the obvious mistake here is that a 300% increase in power corresponds to 4 times the power (not 400% as stated). But this is not the interesting mistake. According to the data at http://www.unold.dk/paddling/articles/kayakvelocity.html the force required to propel a CD Gulfstream (for example) at 3 knots is 0.87 pounds and at 6 knots it is 6.24 pounds. Thus, the force alone goes up by a factor of 7.17. However, the power goes up by a factor of 14.34 (much more than the stated factor of 4).

This will be quite trivial to some of you, but I believe many of the kayakers reading this will not see how I arrived at the 14.34 factor.

As kayakers this is an important concept. It will help you understand why it's hard for a fast paddler to catch up when a slower paddler is given a headstart. Or it will help you understand why you sweat a lot more from a small increase in speed.

[subaruguru]

In a frictionless environment energy and force requirements are related linearly to mass but to the square of speed, so it's easy to see that you have to work 4x as hard to double speed. From another perspective that's why it takes 4x as far to stop a vehicle going twice as fast.

From what I remember about early writings of Winters et al, as well seeing data in kayak reviews, the relationship with kayak-dimensioned craft displacing a mass in a fluid of known density is not at all simply quadratic once that "hull speed" kink is approached, above which the speed/force curves show increasingly diminished returns despite great effort exerted.

I'm sure the fluid dynamics engineers and physicists onboard can explain all this....

I have a curiosity about the effect of the increased buoyancy of salt water (4% saline is it?).

Is there a standard factor or incremental reference used to convert kayak-like vessel speeds for fresh vs sea water? Is it about the 4% one might predict crudely from the difference in fluid density?

[leong]

In a frictionless environment energy and force requirements are related linearly to mass but to the square of speed, so it's easy to see that you have to work 4x as hard to double speed. From another perspective that's why it takes 4x as far to stop a vehicle going twice as fast.

From what I remember about early writings of Winters et al, as well seeing data in kayak reviews, the relationship with kayak-dimensioned craft displacing a mass in a fluid of known density is not at all simply quadratic once that "hull speed" kink is approached, above which the speed/force curves show increasingly diminished returns despite great effort exerted.

I'm sure the fluid dynamics engineers and physicists onboard can explain all this....

I have a curiosity about the effect of the increased buoyancy of salt water (4% saline is it?).

Is there a standard factor or incremental reference used to convert kayak-like vessel speeds for fresh vs sea water? Is it about the 4% one might predict crudely from the difference in fluid density?

Ern, we can discuss your question another time.

But you missed the point of my question. No, it doesn't take 4 times the power to double the speed from 3 to 6 knots. Why is the effort (power) required about 14 times greater for a doubling of speed in the kayak example? No, there's nothing unusual about the Gulfstream. You'll also get about 14 for both of my boats (Falcon 18 and Seda Impulse) and almost all other kayaks (even yours) going from 3 to 6 knots!

[ccarlson]

Power = Force X velocity

So, power at 3kts is 2.61, at 6kts is 37.44 which is 14.34 times the power expended at 3kts

I just read the following statement in the fitness paddling website http://race.fit2paddle.com/C1159474119/E20...5945/index.html

A bit of science here, for the same boat, to double the speed, requires 4 times the horse power, or to get your kayak from 4 mph to 8 mph requires you to put out a 400% increase in effort.

Of course, the obvious mistake here is that a 300% increase in power corresponds to 4 times the power (not 400% as stated). But this is not the interesting mistake. According to the data at http://www.unold.dk/paddling/articles/kayakvelocity.html the force required to propel a CD Gulfstream (for example) at 3 knots is 0.87 pounds and at 6 knots it is 6.24 pounds. Thus, the force alone goes up by a factor of 7.17. However, the power goes up by a factor of 14.34 (much more than the stated factor of 4).

This will be quite trivial to some of you, but I believe many of the kayakers reading this will not see how I arrived at the 14.34 factor.

As kayakers this is an important concept. It will help you understand why it's hard for a fast paddler to catch up when a slower paddler is given a headstart. Or it will help you understand why you sweat a lot more from a small increase in speed.

[leong]

Power = Force X velocity

So, power at 3kts is 2.61, at 6kts is 37.44 which is 14.34 times the power expended at 3kts

Yup, and even seakayakermagazine doesn't seem to get it since they publish force vs. speed.

[EEL]

Yup, and even seakayakermagazine doesn't seem to get it since they publish force vs. speed.

I believe they indicate that an average paddler cannot paddle above a certain resistance point for a sustained period of time which is an indirect way of talking about power limitations.

Well, if its theory time; then these and included references should be an entertaining read.

http://www.keelhauler.org/khcc/seakayak.htm

and for a good many charts showing many factors of a great variety of traditional designs and some modern ones

http://personal.inet.fi/koti/tonivee/KOG/index.html

I suspect anyone who has tried to push a typical sea 18' "expedition" kayak (A/K/A barge) over 5Kts for a prolonged time gets the idea rather quickly.

Ed Lawson

It only takes over 4Kts for me. Bzzt

Ok, 3 Kts

[JohnHuth]

Power is the rate of energy expenditure per unit time. Joules/second = Watts

(kilogram*meters^2/seconds^3)

In the case of an object that is overcoming friction etc and takes a constant force to maintain a constant velocity, indeed the formula is Force*velocity (same units of kilogram*meters^2/seconds^3)

I would guess that, as a paddler, you're most interested in how hard you're paddling, as opposed to the instantaneous force.

Part of the issue on the drag forces is that they go up very rapidly - typical frictional forces in a turbulent regime go like the square of the velocity. With bow/stern wave effects, things can get a bit more complicated as the bow and stern waves can interfere with each other - so it's not going to quite go like the square of the velocity, particularly as you approach the limit of hydroplaning, where the force goes up faster than the square of the velocity and then drops off significantly in planing. Direct measurements for a given hull shape are usually the best way to go.

This discussion has this vague sense of deja vu about it. I remember someone telling me to not bring up Froude numbers.

[Phil Allen]

Yup, and even seakayakermagazine doesn't seem to get it since they publish force vs. speed.

True, but speed is velocity without directionality. So if the test is a boat moving in a straight line the approximation should be fine.

[Brian Nystrom]

Part of the issue on the drag forces is that they go up very rapidly - typical frictional forces in a turbulent regime go like the square of the velocity. With bow/stern wave effects, things can get a bit more complicated as the bow and stern waves can interfere with each other - so it's not going to quite go like the square of the velocity, particularly as you approach the limit of hydroplaning, where the force goes up faster than the square of the velocity and then drops off significantly in planing. Direct measurements for a given hull shape are usually the best way to go.

John is right. If you compare speed increases that are well below the theoretical hull speed (1-2, 1.5-3, 2-4 knots), you should get numbers that are much more in line with the standard predictions. Once you get to the point that wavemaking drag is the dominant factor, the predictions break down.

[EEL]

Direct measurements for a given hull shape are usually the best way to go.

I seem to recall that once upon a time SeaKayaker Magazine tested quite a few sea kayaks in a tow tank to obtain objective data and discovered the differences at normal paddling speeds among them were quite small and above those speeds the results were a bit confounding. I believe as part of that process they concluded the methods used for calculating resistances they publish to be relatively accurate all things considered.

Is anyone with an interest in this stuff using Freeship to model and calculate resistance and stability figures for various commercial kayaks? It seems the only people who do this (or at least publish it) for their designs are some of the sellers of plans or kits for strip and S&G boats. For example if you want to know the design displacement for a Night heron or its resistance numbers, no problem. Want the same numbers for say an Avocet or Tempest and you will not get far. Not sure it matters, but something to do while in front of the fire during the winter.

Ed Lawson

[leong]

Power is the rate of energy expenditure per unit time. Joules/second = Watts

(kilogram*meters^2/seconds^3)

In the case of an object that is overcoming friction etc and takes a constant force to maintain a constant velocity, indeed the formula is Force*velocity (same units of kilogram*meters^2/seconds^3)

I would guess that, as a paddler, you're most interested in how hard you're paddling, as opposed to the instantaneous force.

Part of the issue on the drag forces is that they go up very rapidly - typical frictional forces in a turbulent regime go like the square of the velocity. With bow/stern wave effects, things can get a bit more complicated as the bow and stern waves can interfere with each other - so it's not going to quite go like the square of the velocity, particularly as you approach the limit of hydroplaning, where the force goes up faster than the square of the velocity and then drops off significantly in planing. Direct measurements for a given hull shape are usually the best way to go.

Everything you said John is correct and well said. But correctness doesn't imply relevance. All I said is that the author was mistaken when he said that it requires a four-fold increase in power to increase from 4 MPH to 8 MPH. Such a kayak would be worth $millions. Then I gave the example that it requires more than a 14-fold increase in power to take a Gulfstream from 3 to 6 Knots.

[leong]

True, but speed is velocity without directionality. So if the test is a boat moving in a straight line the approximation should be fine.

No No No. A Kayak moving at a constant speed of 3 Knots in a straight line (i.e. moving at a constant velocity of 3 Knots in some direction) needs approximately a 14-fold increase in power to move at 6 Knots.

[leong]

John is right. If you compare speed increases that are well below the theoretical hull speed (1-2, 1.5-3, 2-4 knots), you should get numbers that are much more in line with the standard predictions. Once you get to the point that wavemaking drag is the dominant factor, the predictions break down.

I don't know what standard predictions you are talking about? For some boats, increasing the speed from 1.5 Knots to 3 Knots requires about a 6-fold power increase. For the Gulfstream, increasing the speed from 2 to 4 knots requires a 7.8-fold increase in power.

[JohnHuth]

Everything you said John is correct and well said. But correctness doesn't imply relevance. All I said is that the author was mistaken when he said that it requires a four-fold increase in power to increase from 4 MPH to 8 MPH. Such a kayak would be worth $millions. Then I gave the example that it requires more than a 14-fold increase in power to take a Gulfstream from 3 to 6 Knots.

I was simply pointing out that the likely origin of the 4 fold increase statement likely came from the way the simplest form of how the drag force scales with velocity, the relationship to power (as one person had previously posted) and also the additional factor of the bow wave. I was just trying to be helpful

[EEL]

I was just trying to be helpful

No good deed goes unpunished.

Ed Lawson

[Phil Allen]

No No No. A Kayak moving at a constant speed of 3 Knots in a straight line (i.e. moving at a constant velocity of 3 Knots in some direction) needs approximately a 14-fold increase in power to move at 6 Knots.

Sorry if my wording confused you. I wasn't arguing against your major point, just that the terms velocity and speed were effectively interchangeable here.

Phil

[leong]

I was simply pointing out that the likely origin of the 4 fold increase statement likely came from the way the simplest form of how the drag force scales with velocity, the relationship to power (as one person had previously posted) and also the additional factor of the bow wave. I was just trying to be helpful

John, you were helpful and I my response was not intended as a put down in any way. Sorry if you took it as an insult.

I look at the subject this way: Yes, the force of air drag on a body moving through the air is roughly proportional to the speed. However, I'd say the total drag on a kayak moving through the water at moderate speeds (say less then 4.5 knots) is roughly proportional to the square of the speed; hence, the power would be roughly proportional to the cube of the speed.

For example, the proportionality constant for the Gulfstream is 0.1 (for speed in knots and force in pounds); i.e. Total drag force = 0.1 * speed squared. Using this formula for the Gulfstream I get speed vs. force of (the seakaykers published values of force are in parentheses):

2 ---> 0.4 (0.42)

3 ---> 0.9 (0.87)

4 ---> 1.6 (1.63)

4.5 -> 2.03 (2.25)

So for kayaks at moderate speeds why not these rules of thumb:

1. Force to propel is proportional to the square of speed.

2. Power to propel is proportional to the cube of speed.

For most purpose you are not interested in absolute estimates of force or power (so you don't need the specific proportionality constant for your boat) . You just want to know the percent increase of force or power needed to get some percent increase in speed.

Feel free to chew me out directly at leon dot g at verizon dot net.

[Nick Schade]

Yup, and even seakayakermagazine doesn't seem to get it since they publish force vs. speed.

It should be noted that Sea Kayaker doesn't claim to predict power requirements, but instead publish drag predictions. "Drag" is a force, so the units of pounds is appropriate. And if subject of the original post had said "drag increases as a square of velocity", this discussion would not have gone very far.

I'm agnostic as to whether it would be better for Sea Kayaker to publish drag or power predictions as I am unable to gauge either in any meaningful way while I'm paddling. Of course since power is the force * speed, publishing the drag is actually the same as publishing power, all you need to do is a simple multiplication. The benefit of the data for the average kayaker is not in the actual numbers, but in comparing one boat with another. If boat X has a drag of 4.47# at 4.5 knots and another is 4.01 at the same speed, you can assume with some confidence that the one with the lower number will be easier to paddle at at 4.5 knots.

Because the absolute value of the numbers is less interesting than the relative value in comparison to other boats, it is not even all that critical how accurate the model it is so long as it fairly precise in predicting differences. I think the models are fairly good at differentiating gross differences (between a Romany and an Epic 18) but less useful predicting minor differences (Epic 18 vs a QCC 700).

[leong]

It should be noted that Sea Kayaker doesn't claim to predict power requirements, but instead publish drag predictions. "Drag" is a force, so the units of pounds is appropriate. And if subject of the original post had said "drag increases as a square of velocity", this discussion would not have gone very far.

I'm agnostic as to whether it would be better for Sea Kayaker to publish drag or power predictions as I am unable to gauge either in any meaningful way while I'm paddling. Of course since power is the force * speed, publishing the drag is actually the same as publishing power, all you need to do is a simple multiplication. The benefit of the data for the average kayaker is not in the actual numbers, but in comparing one boat with another. If boat X has a drag of 4.47# at 4.5 knots and another is 4.01 at the same speed, you can assume with some confidence that the one with the lower number will be easier to paddle at at 4.5 knots.

Because the absolute value of the numbers is less interesting than the relative value in comparison to other boats, it is not even all that critical how accurate the model it is so long as it fairly precise in predicting differences. I think the models are fairly good at differentiating gross differences (between a Romany and an Epic 18) but less useful predicting minor differences (Epic 18 vs a QCC 700).

Nick, of course you are quite correct. But several of my motives for posting were the following:

1. The referenced article was wrong (whether a typo or a misconception). But I've seen this same type of error so many times in the non-technical literature that I believe it was a misconception.

2. Yes, there is nothing wrong with publishing drag as a function of speed. However, many paddlers might equate paddling effort with drag; it is much more meaningful to equate effort to power. Example: A man can push the ground with a force of 150 pounds (his weight) for hours at a time by just standing still or walking on a flat surface. But he can't climb a steep hill at 4 MPH for very long.

3. Once you look at paddling power as a function of speed (for a given boat) you realize how much more effort = power is required to increase your speed.

4. Based on several of the posts in this thread it appears that there are misconceptions within the paddling community regarding the definitions of work, power and force.

5. Although too technical to discuss here, an understanding of how power increases with speed has some practical applications for me related to racing and/or pursuing paddlers ahead of me.

[leong]

John, you were helpful and I my response was not intended as a put down in any way. Sorry if you took it as an insult.

I look at the subject this way: Yes, the force of air drag on a body moving through the air is roughly proportional to the speed. However, I'd say the total drag on a kayak moving through the water at moderate speeds (say less then 4.5 knots) is roughly proportional to the square of the speed; hence, the power would be roughly proportional to the cube of the speed.

For example, the proportionality constant for the Gulfstream is 0.1 (for speed in knots and force in pounds); i.e. Total drag force = 0.1 * speed squared. Using this formula for the Gulfstream I get speed vs. force of (the seakaykers published values of force are in parentheses):

2 ---> 0.4 (0.42)

3 ---> 0.9 (0.87)

4 ---> 1.6 (1.63)

4.5 -> 2.03 (2.25)

So for kayaks at moderate speeds why not these rules of thumb:

1. Force to propel is proportional to the square of speed.

2. Power to propel is proportional to the cube of speed.

For most purpose you are not interested in absolute estimates of force or power (so you don't need the specific proportionality constant for your boat) . You just want to know the percent increase of force or power needed to get some percent increase in speed.

Feel free to chew me out directly at leon dot g at verizon dot net.

Oops, I was talking about slow speed air drag. I meant to say:

Yes, the force of air drag on a body moving slowly through the air is roughly proportional to the speed.

[JohnHuth]

No worries. It's a good discussion.

I guess part of what I was trying to do is to explain some of the basics for folks who aren't up on the arcane lore of physics.

To add - there are roughly three regimes you can consider.

1.) Laminar - when the velocities are quite slow, the flow of particles of water (or whatever fluid you're in) will follow well-defined lines that flow around the craft. This is when the drag force is roughly linear with velocity.

2.) Turbulent - when the velocities are higher, the flow of particles form little eddies and vortices, and that increases the drag and it scales roughly with the square of velocity. The lines of flow become confused with all the little eddies that form, so you can't say that the lines of flow are distinct and predicable, like in laminar. Think "chaotic".

3.) Bow-wave dominated - when the force associated with the bow wave becomes large, the force is a higher power of velocity than squared. If you want to get real technical, vessels produce both a bow wave and a stern wave, and the wavelength varies with speed (using "velocity" and "speed" interchangeably here, since I'm assuming that you're moving straight ahead). The way the bow and stern wave interact can produced little bumps in the drag force, where it can increase with speed, then actually decrease a bit, until you hit a "brick wall" dominated by the bow force.

Since these forces depend a lot on hull shape, that's why I believe that ultimately one must resort to hull measurements - or computer models, as has been suggested. It's a real labor of love to make a computer model of a kayak hull, and, e.g. use the Delft Ship model - but it's pretty cool, because you can get a lot of insight from such an exercise.