Matt wrote: >>I still can't figure out why the paddler made almost the same distance per stroke without also using more energy to go faster (when using a higher stroke rate with the narrower blade). It just doesn't compute. It takes a given amount of energy to move a given kayak at a given speed though the water. If you move it faster that takes more energy. Matt, It is simple, there was more net thrust available from one of the paddles than the other, with presumably the same apparent effort from the paddler. As far as reaching any general conclusions there are a couple of complicating factors: assuming the total power output was the same (which is not related to the stroke rate--lower force x higher stroke rate, or higher force x lower stroke rate could make the same power output), then faster speed would occur with the more efficient paddle, if you had the same power output. OTOH, if the higher stroke rate allowed for a more efficient use of the paddler's available energy because of better suited bio-mechanics of the body/muscle "machine" at the higher stroke rate, than more power would actually be available to create more thrust. So he may have put out more power, even though the effort felt the same. In either case, it is likely that he paddled at the rate he felt comfortable with each paddle at the same apparent effort level. The results was there was more net thrust with the higher aspect ratio blade and higher stroke rate than there was with the other, so he could maintain a higher speed (with the higher drag). Of course the difficulty is that this would vary for one person to the next, and the blade shapes and profiles are probably not the same, nor the weight of each paddle. And the higher speed may have favored that particular blade shape. It is entirely possible that a different weight, size and strength paddler would get different results. So without carefully controlled tests there are no general conclusions to be drawn here except that the higher aspect ratio paddle worked better for him on that day in those conditions. IF all other factors were the same, it can be proven [both theoretically and probably experimentally] that a higher aspect ratio blade will convert more of the available power into thrust than will the lower aspect ratio blade. The problem is there many other complicating factors, the least of which is the variation in human factors from one person to the next, which could nullify any meaningful gain with changes in aspect ratio. One thing for sure, more tests done under controlled conditions with different paddlers, and paddles would be very interesting. Peter *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
>Peter wrote: >IF all other factors were the same, it can be proven [both theoretically and experimentally] that a higher aspect ratio blade will convert more of the available power into thrust than will the lower aspect ratio blade. John Winters wrote: >Peter, Do you have the tests to prove your statement? Sure do John, this has been rather well known for almost a centry and is described in many text books, but you will have to look them for yourself in the following books: "Theory of Flight" by Richard Von Mises [1945], Chapter VII; "Theory of Wing Sections" by Abbott and Von Doehnoff [1949], Chapter One; "Aerodynamics" by Theodore Von Karman [1954]. The relationship was first described by F.W. Lanchester in "Areodyanmics" [1907], you might also look up "Applied Hydro- and Aeromechanics" by Prandtl and Tietjens (1934). And there are many others, go find them. And I can prove it using the following equations that I put together some time ago with you in mind. Some time ago I was clearing out my garage to make room to build another kayak and ran across a very old box of my engineering textbooks and the rather lengthy thread about high aspect ratio paddles came to mind. I spent a few evenings thumbing through them and I put together a few equations for you all. Therefore just for grins I have listed a mathematical proof that you technical types might find interesting. If the rest of you just read my text you should be able to follow the idea of the math without having to do it, at the very least if you may find the conclusion very interesting. The aspect ratio (AR) of a surface is the span squared divided by the area of the surface: AR=b^2/s where b=span s=surface area This form of the AR equation is used to accommodate all shapes, notice that for rectangular surfaces the AR simply becomes the length divided by the width (or chord length c) or AR=b/c Lets define some terms so everyone can follow. As you move a paddle blade (technically a "foil") through the water what you feel at the handle end is the drag which you are pulling against to push your kayak forward, the blade OTOH must generate "thrust" so you have something to push against at the handle end. The total "drag" you feel at the handle is directly related to the "thrust" the blade experiences in the water. I think this relationship was confusing everyone, keep this strait and the rest will make sense. Consider it this way, in an ideal world, if the amount of drag you push against at the shaft is exactly equal to the amount of forward thrust you get out of it, you would have 100 percent hydrodynamic paddle efficiency. This is ignoring the efficiency of the human "machine" of course because we just want to compare energy input at the handle, to the forward thrust output. This also ignores the energy it takes to raise and lower the paddle since we want to compare the hydrodynamic efficiency, not the mechanical efficiency. A paddle that weighs the same, with the same inertia and stiffness, will have the same mechanical efficiency [and a paddle with zero weight, and infinite stiffness, is 100 percent mechanically efficient]. Also consider that you can never get more thrust out than the drag you put in. It would be nice if you could get more out then you put into it, but that does not happen in this universe [nor in the Brozian Universe either i suspect]. The drag is composed of two parts, parasitic drag and induced drag. The parasitic drag is what you would feel if you just slide the blade through the water sideways without producing any hydrodynamic thrust, it is the skin friction drag, the interference drag of the sharp edges and irregularities, the drag of the volume of the blade displacing water as you pull it through it. To minimize this you would want very smooth foil shapes, very thin, and shapes that would not cause turbulence. This is also know as the "base" drag on any surface when it moves through a fluid even when it is not generating any thrust or lift. For automobiles for example all the aerodynamic drag on it can be considered parasitic since lift is not desired nor necessary (though most car shapes do generate lift, but it is undesirable since it reduces the traction of the tires, and causes induced drag on the body). The induced drag is the drag caused by the lift or thrust you are generating, IOW it is the "cost" of creating the thrust. This has been experimentally determined (and verified many times) for a hundred years now to act according to the following equation: Coefficient of induced drag is: Cdi= Ct^2/(pi)AR Where Ct is the Coefficient of "thrust", pi is the mathematical constant 3.1415927. Coefficients are constants that are always used to normalize the factors from the variables that affect lift, drag, thrust, etc. for different flow conditions, more on this below. Notice that as the AR gets larger, the coefficient of induced drag gets smaller. With finite shapes there is no way around induced drag, if you generate lift or thrust in a fluid, you must overcome this extra drag to get it (actually indirectly related to Newton's laws of action/reaction; when you get thrust, there is a drag reaction). And like many things in physics, it was this relationship between these variables that was first experimentally observed, and then later with much theoretical vigorous mathematics "proven" to be valid (even though the experimentalists had already proven it). So this relationship between the induced drag and the AR is just a natural phenomenon that is both observed and mathematically valid as well. It is just a fact of nature that this relationship occurs and I can not "prove" it with mere words, you will have to go and prove it for yourself, or study the textbooks I have listed above. So the total drag on any surface creating thrust (or lift) like a paddle in the water is a combination of the base parasitic drag, and the induced drag expressed like this: Cd(total drag)=Cdo+Cdi Also the expression for induced drag could be rearranged to express the relationship to the coefficient of thrust: Ct=SQRT[3(pi)AR(Cdo)] Again as the AR goes up, the Thrust goes up too. The total thrust force on the blade will be dependant on this coefficient of thrust, times the kinetic energy of the mass flow RATE, and the size of the paddle, or surface area=s. Kinetic energy is half of the mass times the velocity squared. So thrust is expressed as follows: Thrust=S(Ct(rho)V^2)/2 the Greek letter rho is the mass density of the fluid, for sea water it is about 64 LBS/cubic foot divided by one G or 32.2 Feet/sec^2 The total drag is expressed similarly: Total drag=S(Cd(rho)V^2)/2 Since the efficiency we are looking for is the power-out (i.e. thrust) divided by the power-in (resistance at the paddle handle) we have to convert these forces (in lbs. for example) to units of power by multiplying them by the velocity of the paddle blade through the water. So the equation will reduce to the following: efficency=P-out/P-in = TxV/DxV = T/D since the velocity cancels substituting the above relationships in we get the following: Efficency= [S(Ct(rho)V^2)/2]/[S(Cd(rho)V^2)/2] This reduces to: Eff.=Ct/Cd since everything else cancels. Notice that the density cancels, so the temperature of the water does not matter, the loss in thrust is exactly balanced by the lost in drag. And also notice the area of the blade cancels, this is why I had posted earlier that the area is irrelevant to the efficiency (more on this later). Clearly the size of the blade is not part of the efficiency equation, nor is the velocity you pull the paddle through the water. Substituting these to determine the relationship between AR and Efficiency we get: Eff. = Ct/(Cdo+Cdi) = Ct/(Cdo+Ct^2/(pi)AR) to clarify this relationship further take the inverse so we can break the equation up: 1/Eff. = Cdo/Ct + Ct2/(pi)AR(Ct) = Cdo/Ct + Ct/(pi) AR To simplify further lets call the roughly constant ratios of Cdo/Ct and Ct/(pi) as constants K1 and K2 we get: 1/Eff. = K1 + K2/AR >From this you can see that as the Aspect ratio increases, the efficiency increases directly. The base drag Cdo is going to be about the same for similar designed blades of the same surface area even if the AR is different. And the Coefficient of thrust is the same since we are producing the same thrust with each different AR to push the kayak at the same speed (even if the effort at the handle is different). Notice too that even at infinite aspect ratio [where K2/AR=zero], the best efficiency you can get would be 1/K1. Which means the higher Ct/Cdo, the better. Which in turn means, the more thrust, and least drag you can get out of the paddle, the better the paddle's efficiency. You can see from this relationship that there is no component of the drag that is useful, any drag on the blade reduces its efficiency. Intuitively this is easy to grasp if you just imagine putting a large drag device on the end of a paddle shaft instead of a blade, say something like a giant pine cone, it would not work as good as a smooth foil shape. Although you can use it go forward, the equation above, and common sense, tells you that it would be a lot of effort for the amount of forward progress you would make. You can see clearly from this relationship that if you want to increase efficiency you want maximum thrust at the paddle blade, with minimum effort (or drag) at the handle end where you are holding it. Aha! Now that makes sense, max thrust for the least effort! And that is what we want to consider when we discus the efficiency of the paddle. Also keep in mind this is about efficiency and not total available thrust. Making the paddle as big as possible would provide the max thrust, this is from the momentum theory and Newton's laws of motion, the more and faster you accelerate a mass of water, the bigger the thrust reaction. So for racing, rapid accelerations, or rapid control movements like you need in WW or surf kayaking, the biggest blade you can handle would be best, and aspect ratio is not as important. But for low speed cruising to minimize energy expenditure over long periods of time, the high AR paddle is king. Plugging in a few numbers for a typical kayak at 5 knots (about 5 LB of drag, therefore 5 Lbs. of thrust at five knots need to be generated) I came up with the following for different paddle AR but with the same blade area: for typical Euro touring blade it has a blade approx. 6"x18" and AR= 3:1 a typical native style blade 3"x36" an AR=12:1 hypothetical very high AR paddle of 2"x54"...AR=27 the following sustained power at the handle would be required from the paddler to maintain the same thrust output: AR=3:1 P=0.4 hp AR=12:1 P=0.22 hp AR=27: P=0.15 hp Wow! This makes me want to make one of those really long, very high AR paddles just to try it out. It would have to be 10.5 feet long! There may be a practical limit to AR, just like an aircraft wing or a propeller, but it would be worth a try. Something else I just worked out is that the power requirements for a typical paddle/paddler might be something like this: Power in at the handle: 824 ft-lb/min or about 0.025 hp (typical sustainable output for human arms in reasonably good condition) Though you could measure this indirectly with an actual person paddling by measuring oxygen uptake with a portable device (you would have to assume a oxygen uptake rate to power output ratio but that could also be experimentally determined on a human dynamometer). Though O-2 uptake would give you a simple way to compare one paddle to another. Useful Power-out: 5 lb drag at 5 knots = 5 LB x 5 x 1.688 feet/sec/knot = 42.2 foot-lb/min = 0.001279 hp efficiency of converting power-in to forward movement: 0.001279/0.025 = 0.051 or about 5 percent which is about what I suspected. The rest of your input goes to other things like heating water, lifting the weight of the paddle, etc. how much a new paddle design could help this is unknown, but the equations indicate a good design could as much as double the efficiency. One thing for sure, even with these assumed numbers (which are within reasonable range based on my experience doing testing on Olympic athletes), there is lots of room for improvement in paddle design. And certainly there are many other aspects that affect efficiency than just AR of the paddle: the foil shape, the stroke mechanics, the surface finish, perhaps shaft/blade stiffness, etc. The lightest, stiffest, highest AR, and smoothest blade [both surfaces] would be the most effient for converting your effort into thrust for low power, long-distance cruising. Needless to say, it appears that the design of the hull (which everyone always focuses on) is only one part of the total picture, and perhaps I suspect not even the majority part. It is the paddles!!! Also unknown by me from this analysis is the effect of the surface wake that the paddle creates as it is moved through the water. Though I suspect the surface wake does not produce any thrust but just drag. This means the most efficient way to paddle would be to try to minimize the surface wake of the paddle as much as possible. That would be from a fairly thin smooth blade, slicing downward through the water as you pull it back; it would make the least surface wake. Note that there is a native technique which I have found comfortable. You start with the paddle at almost level and about a 45 deg angle across the front of your hull, reaching horizontally out, and then slicing downward as you pull it back, ending with the paddle nearly vertical at the end of the power stroke by your side, but ready to move it back across in front of you to start the next stroke. Also there is a racing stroke where the racers push the blade out sideways from the gunwale in the water as they pull back. Both of these strokes would keep a surface wake from the paddle minimum since you are moving the blade through the water with the small dimension of the blade, not in the direction of the full width of it. Pulling a fat Euro paddle strait back through the water, making lots of vortexes and a large surface wake, would be the least efficient way to paddle (though you will accelerate just fine in a short burst, it just will not be efficient). But regardless of the effects of a surface wake, you can not escape the importance of the AR. >From this you can see that smooth foil shaped, high aspect ratio blades are best for conserving energy over long hauls. It will not work well for maximum accelerations, nor for quick manuvering strokes, and likely very poorly for a C-C type roll. In fact for all of these needs you have to use very different techniques with a high AR paddle. Most of this I have pulled from "Theory of Flight" by Von Mises, and from a few other books if you are so inclined to verify the equations. There will be a quiz next week. Peter Chopelas *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
At 11:38 PM 7/26/02 -0700, Peter Chopelas wrote: > >Lets define some terms so everyone can follow. As you move a paddle blade >(technically a "foil") through the water what you feel at the handle end is Way over my head, as usual -- but one observation: is a paddle technically a foil? The angle of attack is such that it would be operating in a stalled condition. -- Wes --------------------------------------------------------------------------- Wes Boyd's Kayak Place http://www2.dmci.net/wesboyd/kayak.htm Kayaks for Big Guys (And Gals) | Trip Reports | Places To Go | Boats & Gear --------------------------------------------------------------------------- *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
At 11:38 PM -0700 7/26/02, Peter Chopelas wrote: ><snip> >Consider it this way, in an ideal world, if the amount of drag you push >against at the shaft is exactly equal to the amount of forward thrust you >get out of it, you would have 100 percent hydrodynamic paddle efficiency. >This is ignoring the efficiency of the human "machine" of course because we >just want to compare energy input at the handle, to the forward thrust >output. This also ignores the energy it takes to raise and lower the paddle >since we want to compare the hydrodynamic efficiency, not the mechanical >efficiency. A paddle that weighs the same, with the same inertia and >stiffness, will have the same mechanical efficiency [and a paddle with zero >weight, and infinite stiffness, is 100 percent mechanically efficient]. ><snip> >Since the efficiency we are looking for is the power-out (i.e. thrust) >divided by the power-in (resistance at the paddle handle) we have to convert >these forces (in lbs. for example) to units of power by multiplying them by >the velocity of the paddle blade through the water. So the equation will >reduce to the following: > > efficency=P-out/P-in = TxV/DxV = T/D since the velocity cancels > >substituting the above relationships in we get the following: > > Efficency= [S(Ct(rho)V^2)/2]/[S(Cd(rho)V^2)/2] Thrust and drag are both forces. They are not power. The amount of force you apply to the paddle is exactly matched by the amount of force generated by the water on the paddle. It is impossible to push with 1 pound of force and have what you are pushing against push back at with 1/2 or 2 pounds of force. The forces must be equal and opposite. If they aren't equal there must be something wrong with your analysis. In the above equation for efficiency you incorporate the velocity. This presumably converts the force to power. However, you drop it immediately, saying the velocities cancel. This leaves an equation where efficiency is the ratio of two opposing forces "T" and "D". That ratio is always going to be 1. If it is not, there would have to be some outside force acting on the paddle, not just the paddler and the water. While drag through the air would work, in your analysis there is no third force, only the force applied by the paddler (Thrust), and the force caused by the water (Drag). Your equation depends on two opposing forces being different. That is a physical impossibility. I must assume that it is incorrect to cancel out the velocities. Since the power applied by the paddler is near the center of the paddle and the power applied by the water is near the end of the blades, I don't know why the velocities involved would be the same. -- Nick Schade Guillemot Kayaks 824 Thompson St Glastonbury, CT 06033 (860) 659-8847 *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
----- Original Message ----- From: "Peter Chopelas" <pac_at_premier1.net> > >Peter wrote: > > >IF all other factors were the same, it can be proven [both theoretically > and experimentally] that a > higher aspect ratio blade will convert more of the available power into > thrust > than will the lower aspect ratio blade. > > John Winters wrote: > > >Peter, Do you have the tests to prove your statement? > SNIPPED: A LONG ENGINEERING EXPLANATION OF WHY A LOW ASPECT RATIO PADDLE, NAMELY A EUROPEAN PADDLE, CREATES VARIOUS DRAGS THAT MAKE THEM INEFFICIENT VIS-A-VIS HIGH ASPECT RATIO PADDLES SUCH AS GREENLAND ONES Don't give up on your European paddle quite yet. There is a simple way of reducing the drag of a European paddle caused by it being a low Aspect Ratio paddle: Drill several strategically placed holes in the blade surface. This will have two beneficial effects. One, it will allow some water to pass thru and this will significantly reduce the build up of drag. Two, the surfaces removed by the holes will help raise the Aspect Ratio (span squared divided by surface area) of the European paddle above the critical Aspect Ratio of 6:1 known as the half dozen factor. You can make further gains if you take care in the shape andd placement of the holes themselves. Avoid drilling round holes. A perfectly round hole will create a strong reversing vortex that might actually increase drag not reduce it. The best hole shape would be one with jagged or saw tooth edge that will break up the water jetting through the hole. Placement of the holes? They should be drilled in a star pattern, the Star of David pattern being the best because of its intersection of two inversed triangles, a mystical pattern that should also bring you good luck. Of course, the easiest way to do all this is to just have your European paddle manufactured in Greenland. :-) ralph diaz *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
Ralph Diaz said: > Of course, the easiest way to do all this is to just have your European > paddle manufactured in Greenland. :-) I use a Hutchinson designed Toksook Paddle--an Inuit design manufactured in England. ;-) Steve Holtzman *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
----- Original Message ----- From: "Steve Holtzman" <sh_at_actglobal.net> To: "ralph diaz" <rdiaz_at_ix.netcom.com>; "Peter Chopelas" <pac_at_premier1.net>; <PaddleWise_at_paddlewise.net> Sent: Saturday, July 27, 2002 10:01 AM Subject: Re: [Paddlewise] [PaddleWise] Paddles > Ralph Diaz said: > > Of course, the easiest way to do all this is to just have your European > > paddle manufactured in Greenland. :-) > > I use a Hutchinson designed Toksook Paddle--an Inuit design manufactured in > England. > > ;-) > > Steve Holtzman Actually that is OK. England has never been a part of Europe anyway, or certainly at most a reluctant part of it. Derek Hutchinson is certainly not European! :-) ralph diaz *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
----- Original Message ----- From: "ralph diaz" <rdiaz_at_ix.netcom.com> > Actually that is OK. England has never been a part of Europe anyway, or > certainly at most a reluctant part of it. Derek Hutchinson is certainly not > European! :-) Touché ;-) Steve Holtzman *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
Thank you, Peter for the detailed and patient explanation. You must have been saving it up for when this topic resurfaced on Paddlewise. I had the same question Wes did though. Are you using the paddle as a foil when comparing AR efficiency or does this still all somehow apply with a stalled foil as well? There seem to be several practical limits to using high aspect ratio paddles. You must either reduce the blade area or make the blades very long to get a high AR and maintain the blade area. Reducing the blade area reduces the thrust. Making the blades longer (2"x54") has several problems I can imagine. Since you are pivoting the paddle during the stroke the pressure at different points along the blade will vary (higher at the tip and less and less as you measure going towards your hand. The pressure could become negative (meaning that nearer the hand the blade might be moving forward under water rather than backward. If that were the case, that part of the blade would be using power to thrust in the wrong direction and be working against you. Not only would a 54" long blade be ungainly to get in and out of the water (and lift the extra blade weight--that also has more leverage being so far away). It will also be a much harder paddle to control during the stroke because another characteristic of high AR is a that it stalls at a shallower angle of attack so blade placement angle will become very critical and the flutter rate of the blade will become uncontrollably fast under higher loads). I suspect that since the foil penetrates the surface at full width you will also likely have an efficiency loss due to ventilation (air getting behind the blade and destroying the lift). The long blade needs to be sliced down into the water--while remaining closer to horizontal than vertical (because it is so long) and the direction (and the angle of attack) needs to change abruptly at some point while the blade is underwater so it can return to the surface and generate lift again on its upward path to the surface. There will be a loss of efficiency from stopping the momentum in one direction and them accelerating again once you have reversed blade direction. A wing paddle stroke starts close to the kayak and moves outward until the blade reaches the surface without any abrupt direction changes (energy robbing stops and starts). I suggest you get the high aspect ratio by using two very small foils, say 24"x1.5", (on each end of the paddle-four foils in all) for your paddle blades. They would lie next to each other separated by half an inch or so. That way you will get two narrow lifting foils on each end of the paddle (so the high AR paddle doesn't have to be so long to get the same blade area) and as long as they are used like a wing to generate "lift" you will also benefit from the "slot effect" between the blades increasing the "lift". I'm hereby trademarking the names "Bye-paddle", "bi-paddle", "slot-paddle", "forked stick", and the slogan "four blades are better than two". You could get rid of the ventilation problem by keeping the blades entirely under water and maybe centered directly below the kayak (perhaps spinning around on a shaft that could be spun continuously in the same direction and powered by your strong legs and feet on pedals while leaving your weaker arms and hands free to perform tasks requiring greater dexterity. Of course, we'd have trouble calling it a kayak anymore. It would be way more efficient that way as it could also take more advantage of the high AR efficiency gains with out the high AR paddles problems. A few weeks ago I saw an ultralight airplane that had two 9.5 HP engines that turned two about 18" long by 1" wide "slot effect" dual propellers. As hard as it was to believe, dat thing could fly, I seen it wit mine own eyes. Matt Broze http://www.marinerkayaks.com *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
John Winters wrote: >Did I read Peter Chopelas correctly that the ratio of thrust to paddle area was unimportant or, at least the wrong issue? Not exactly. What I was saying is we should be concerned with the direct measure of thrust output vs. work input. At best thrust per unit area is an indirect measure. >Suppose we had two paddles one 120 sq. inches and one 80 square inches. both produce the same thrust at the same velocity and the same power input. Does this mean that both paddles are equally efficient or that the difference is unimportant? That depends on what you are trying to measure. If your measure is thrust out vs. power in, then yes they are exactly the same. There are other measures you might want to consider, there are a lot more things we do with a kayak paddle than just move it forward. >Can anyone think of any reasons why a smaller paddle that produces as much thrust as a larger paddle might prove advantageous? sure, but that was not the question. And measuring thrust per unit area does not tell you which paddle would be best in terms in thrust per unit power input. >Also what is one to make of C.A. Marchaj's use of the Driving Force Coefficient ( Equivalent to the Thrust Coefficient or thrust per unit area)? Marchaj is measuring something different because the source of power is different. On a sail, the power input comes from the wind; the bigger the sail area the higher the power input. When deriving the sail efficiency equation the sail area simply falls out because the power input is directly related to the size of the sail (if you go review how Marcharj derived his equation you will see this). Measuring thrust per unit area on a sail IS a direct measurement of efficiency, you do not need to determine what the power input is since that is directly related to the size of the sail.. On a paddle, the power input is fixed by what is available from the paddler, and presuming steady state paddling conditions, either the heart rate or the O2 uptake would be directly related to the power output of the paddler. Unlike the sail area, the thrust per unit area of the paddle blade tell you nothing of the power input it takes to generate a given thrust. Peter *************************************************************************** PaddleWise Paddling Mailing List - Any opinions or suggestions expressed here are solely those of the writer(s). You must assume the entire responsibility for reliance upon them. All postings copyright the author. Submissions: PaddleWise_at_PaddleWise.net Subscriptions: PaddleWise-request_at_PaddleWise.net Website: http://www.paddlewise.net/ ***************************************************************************
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