Someone asked for the theory of paddles, and I had happened so save some theorectical equations from the thread that was much debated last year and I have post it below for the benefit of all. And much of the recent speculation of the uninformed is incorrect, fluid mechanics is very complex and NOT intuitively obvious. You can not compare "pushing" against a fluid with pushing against a solid object. By definision fluids only generate thrust when you create motion in the fluid, and the best thrust DOES NOT occur with the paddle blade with the highest drag (in fact such a paddle would have the worst efficiency). It works out that for low speed, long distance curising, a thinner and smoother blade (on both surfaces), with the higher the aspect ratio of the paddle, the better the efficiency. This is why the high aspect ratio native style paddles are superior for long distance sea kayaking. And the total area of the blade and the speed you pull the paddle through the water is irrelevant to efficiency. For maxium thrust however, maximum blade area is desirable, as in WW kayaking or surf kayaking where short bursts of sudden acceleration are necessary, but this is not efficient for long distance low speed cruising. For those so enclinded, below is the "proof" that the higher the aspect ratio for a smooth blade, the more effiecnt the paddle design. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Paddle Aspect Ratio 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 out. 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 more out then you put into it, but that does not happen in this universe [nor in the Brozian Universe either]. 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 composed of 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 known 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) over a hundred years ago 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 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 vigorous theoretical 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 below. 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 wrote 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 increases directly. The base drag Cdo is going to be 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. 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 "Simplified Aircraft Performance and Design" by Donald Crawford, and my class notes and 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/ ***************************************************************************
As usual, Peter posts a bunch of meaningless* equations when we get to this subject. For those of you who might be awed by such, don't be - Peter understands equations but not physics, and his gobbledy-gook is not accepted by anybody here with a real clue about physics or fluid dynamics. (* physical meaningless because they don't apply to the physical conditions he's talking about) I'll just point out for starters this: >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 > Note that the velocity cancels because he says it does - because he uses the same velocity in both places. But of course the paddle handle does not move at the same velocity as the paddle blade, so this is complete nonsense. This is the very briefest sample of the kind of physics mistakes permeating Peter's work, and I have no intention of going through all his work and pointing out all his mistakes. Peter Chopelas wrote: >Someone asked for the theory of paddles, and I had happened so save some >theorectical equations from the thread that was much debated last year and I >have post it below for the benefit of all. > >And much of the recent speculation of the uninformed is incorrect, fluid >mechanics is very complex and NOT intuitively obvious. You can not compare >"pushing" against a fluid with pushing against a solid object. By >definision fluids only generate thrust when you create motion in the fluid, >and the best thrust DOES NOT occur with the paddle blade with the highest >drag (in fact such a paddle would have the worst efficiency). > >It works out that for low speed, long distance curising, a thinner and >smoother blade (on both surfaces), with the higher the aspect ratio of the >paddle, the better the efficiency. This is why the high aspect ratio native >style paddles are superior for long distance sea kayaking. And the total >area of the blade and the speed you pull the paddle through the water is >irrelevant to efficiency. For maxium thrust however, maximum blade area is >desirable, as in WW kayaking or surf kayaking where short bursts of sudden >acceleration are necessary, but this is not efficient for long distance low >speed cruising. > >For those so enclinded, below is the "proof" that the higher the aspect >ratio for a smooth blade, the more effiecnt the paddle design. > > >+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ > >Paddle Aspect Ratio > >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 out. >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 more out then you put into it, but that >does not happen in this universe [nor in the Brozian Universe either]. > >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 >composed of 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 >known 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) over a hundred years ago >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 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 >vigorous theoretical 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 below. > >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 wrote 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 > >increases directly. The base drag Cdo is going to be 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. > >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 >"Simplified Aircraft Performance and Design" by Donald Crawford, and my >class notes and 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/ >*************************************************************************** > > *************************************************************************** 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/ ***************************************************************************
Here are some observations drawn from airplane wings I have seen or flown and paddles I have built and/or used: -A paddle is used like a wing used at high angle of attack, making it susceptible to stall (cavitation in water world). Stalling a wing results in a dramatic reduction of lift. In our case that is a dramatic reduction in propulsive force -Putting camber on a wing helps it to achieve higher angles of attack without stalling. That's putting a curve into the blade. A simple symmetrical blade has some advantages, but delayed stall is not one. Thus, those who use Greenland paddles must incorporate motion into their stroke that reduces or eliminates cavitation by reducing the angle of attack. There is an article that addresses this in Sea Kayaker which I am too lazy to look up at the moment. -A "wing" paddle has a huge camber, just like the wing of an airplane used for low speed work, or like the wings of an airliner with leading and train edge flaps deployed for landing. -Higher aspect ratio wings have a higher lift-to-drag ratio. That implies greater efficiency when paddling a high aspect ratio paddle. On the other hand, Greenland paddles are symmetrical which reduces wing efficiency. Also, lift-to-drag theory applies to a wing that is designed to move parallel to the wing surface, not perpendicular to it. This is confusing to translate into paddling, but the velocity of the paddle through the water parallel to the blade surface creates drag which is not related to the velocity of the boat through the water. That may disconnect the lift-to-drag ratio from having a positive bearing on paddling efficiency. -Lower aspect ratio wings have more gentle transitions into stall (cavitation). That's why trainer airplanes have wings like a Hershey bar. Lower aspect ratio paddles should not break into cavitation as abruptly and my observation from lousy paddles I have built is that they do not. Conversely, my Greenland paddle required careful technique to prevent cavitation. My opinion (neither smart enough nor fast enough to make a conclusion): Racers use wing paddles because they are indeed faster and more efficient at propelling a boat through the water. On the other hand, it's not all about speed and efficiency. It's about fun. When I paddled with a Greenland paddle I was pain free (although slower) for more miles. Paddling with a high aspect ratio paddle is arguably better for your body, especially when paddling long distances. When I'm older and wiser I'll stop paddling in all situations with my WW paddle and start using something with a higher aspect ratio. Steve Brown AR=b^2/s AR=b/c Cdi= Ct^2/(pi)AR Cd(total drag)=Cdo+Cdi ........... 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/ ***************************************************************************
Let me preface this by saying I'm a fixed wing pilot and a helicopter crew chief with several thousand hours flight time. I also spent several years supporting wind tunnel operations testing aircraft and spacecraft in another lifetime. That said, I'm having a terrible time trying to relate the operation of an aircraft wing or helicopter blade to the functionality of any kind of paddle. In my mind, wings generate lift by orienting them to present the least planform to the medium it's moving through, in most cases. Paddles must present the maximum planform to generate the most resultant force to the kayak and paddler. Can anyone point me to a very basic source of information or theory, preferably web based, that can get me somewhere in the neighborhood of what you people are talking about? Looking at the movies that someone provided a link for earlier did nothing to alleviate my confusion. Thanks in advance, Dave G. *************************************************************************** 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/ ***************************************************************************
On 10 Jun 2003 at 10:43, Dave Gorjup wrote: > That said, I'm having a terrible time trying to relate the operation > of an aircraft wing or helicopter blade to the functionality of any > kind of paddle. In my mind, wings generate lift by orienting them to > present the least planform to the medium it's moving through, in most > cases. Paddles must present the maximum planform to generate the most > resultant force to the kayak and paddler. The paddles that most match a wing or propellor model are the wing paddles. These are shaped like a wing section (cambered, with a blunt, rounded leading edge, fine trailing edge etc). The section is open underneath in most cases, so are a little more like a wing with flaps down and leading edge devices deployed, rather than a traditional NACA foil with a closed cross section (I can't help but think they'd be a tad more efficient if they were closed like the Schleicher from Nimbus, but I digress.) The motion of the paddle (as demonstrated to me by Greg Barton last year an the East Coast Canoe & Kayak Festival) is to plant ahead and sweep the paddle out (primarily) and back - relative to the paddler. The paddle is planted initially with the shaft as vertical as possible. Hence the motion of the blade is a curved path out and up toward the surface and the leading edge is outward through the entire stroke. Hence the wing paddle generates lift like a wing and the direction of the lift is nominally forward (i.e. direction of kayak motion). Conventional paddles use a mix of drag and lift, though the proportions are more open to debate than established (on these fora) in fact. Many discount the idea that it is overwhelmingly drag that produces the force and there are compelling reasons to think this way. We know that avoiding flutter necessitates the use of a slightly canted paddle blade, but whether this results in a nice, unstalled flow is subject to debate. The cant in the Greenland paddles (GP) (as some paddles use them) is sufficient to suggest that it does not stall and therefore some form of lift is imagined to dominate. However, Nick Schade has presented convincing reasons for believing that the lift on a GP doesn't actually contribute to the forward motion as such (this discussion is achived in QajaqUSA's web site) or at least not in the way that wing paddles do. Peter's analysis (aside from its problems) is a scalar, not vector analysis and we've not had much luck in getting him to identify the meaning of the results in terms of what actually happens to the paddle generating forces that move the kayak. My feeling, looking at his work but without doing any detailed analysis, is that his results (if corrected) would represent an efficiency that does not result in a meaninful contribution to forward motion (i.e his efficiency is in the generation of both useful and useless forces). By analogy, the results that Nick talked about in a recent post on "work = change of energy" were correct but confused a couple of people because it didn't take into account the work done in moving the kayak forward versus the work done in moving water around without moving the kayak (i.e the work wasted). Such is the problem with working with scalars instead of vectors. Hopefully this presents a precis of the multiple discussions pertaining to the mythical lift characteristics held on Paddlewise, Baidarka and QajaqUSA so far. Mike *************************************************************************** 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/ ***************************************************************************
Thanks all, for the enlightenment I've received both on P'Wise and back channel. It's given me an initial understanding and a lot to think about. About the only thing I can say right now is that I'm not particularly comfortable with the analogy to aircraft wings or propellers, or helicopter blades. I think, so far, that I would feel better if I relate wing paddles to a mainsail on a sailboat where a rudder, keel, and sail interact more like a the components of powering a kayak but acting on different mediums (water vrs. air). Like I said, I'm just beginning to munch on this so I may toss out that analogy also. Thanks again, Dave G. *************************************************************************** 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/ ***************************************************************************
[Moderator's Note: Content unaltered. Excessive quoting (i.e. headers/footers/sig lines/extraneous text from previous posts, etc.) have been removed. Please edit quoted material in addition to removing header/trailers when replying to posts.] The analogy works better for the propeller of an airplane or helicopter where the propulsive force is more obvious, especially when compared to a Greenland paddle. Greenland paddles require a significant and obvious slicing motion to prevent cavitation (flow separation?). An even better example is a bird wing during vertical or near vertical takeoff. Fast birds with relatively high aspect ratio low camber wings, such as doves, don't do that well on takeoff where there is a need to generate high lift at low speeds (high angle of attack). Slow birds such as quail with low aspect ratio high camber wings do extremely well in that flight regime. Any bird hunter knows that shooting a dove during takeoff is not even good sport, but hitting a quail in the same circumstance is quite challenging. Steve Brown -----Original Message----- From: Dave Gorjup Subject: RE: [Paddlewise] PaddleWise [wing theory] Let me preface this by saying I'm a fixed wing pilot and a helicopter crew chief with several thousand hours flight time. I also spent several years supporting wind tunnel operations testing aircraft and spacecraft in another lifetime. That said, I'm having a terrible time trying to relate the operation of an aircraft wing or helicopter blade to the functionality of any kind of paddle. In my mind, wings generate lift by orienting them to present the least planform to the medium it's moving through, in most cases. Paddles must present the maximum planform to generate the most resultant force to the kayak and paddler. Can anyone point me to a very basic source of information or theory, preferably web based, that can get me somewhere in the neighborhood of what you people are talking about? Looking at the movies that someone provided a link for earlier did nothing to alleviate my confusion. *************************************************************************** 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/ ***************************************************************************
On 10 Jun 2003 at 7:04, Steve Brown wrote: Lots of interestng and useful comparisons, Steve. > -A paddle is used like a wing used at high angle of attack, making it > susceptible to stall (cavitation in water world). Stalling a wing > results in a dramatic reduction of lift. In our case that is a > dramatic reduction in propulsive force Nit to pick - cavitation is not possible for us weaklings. True cavitation results from a pressure drop across the paddle on the order of one atmosphere. Even over a small area, that would translate into a big force. The correct term is "ventilation" - it's basically air drawn down by the paddle from the surface of the water. If deep enough, the blade will stall without any venilation. Mike *************************************************************************** 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/ ***************************************************************************
Steve brown wrote: > Here are some observations drawn from airplane wings I have seen or flown > and paddles I have built and/or used: > > -A paddle is used like a wing used at high angle of attack, making it > susceptible to stall (cavitation in water world). Stalling a wing results in > a dramatic reduction of lift. In our case that is a dramatic reduction in > propulsive force You mean ventilation (cavitation is when the water is vaporized, which I do not think the pressure gradients are quite large enough to occur in a paddle). but a high AR shape, whether wing or paddle, will be more susceptible to stall, and therefore not desirable for the rough water conditions of WW or surf kayaking. More thrust can be developed for short burst of power with less risk of stalling the paddle with a large area, low AR paddle, which is why they work best for WW and surf kayaking. But they are not as efficient for LOW POWER, LOW SPEED, LONG DISTANCE CRUISING, assuming the shape is the same. > > -Putting camber on a wing helps it to achieve higher angles of attack > without stalling. That's putting a curve into the blade. A simple > symmetrical blade has some advantages, but delayed stall is not one. Thus, > those who use Greenland paddles must incorporate motion into their stroke > that reduces or eliminates cavitation by reducing the angle of attack. There > is an article that addresses this in Sea Kayaker which I am too lazy to look > up at the moment. > Actually for the short burst of power when necessary, the cant of the Greenland stick, it traps a strong vortex on the low pressure side of the blade which prevents stalling, allowing very high angles of attack and thrust. It is costly in terms of drag, but effective for short burst of thrust. During low power, low speed, long distance cruising, the blade is sliced through the water with little vortex formation (except at the tip), which is where the high AR blade has its advantage. > -A "wing" paddle has a huge camber, just like the wing of an airplane used > for low speed work, or like the wings of an airliner with leading and train > edge flaps deployed for landing. > wing paddles are an outgrowth of developing paddles for racing, which is an attempt to maximize SPEED (i.e. min time over a distance) requiring MAX thrust (right at the stall), not efficiency at low speed (i.e. min energy output over a given distance). If you where to have two identical wing shapes except for AR, and use them both at low speeds to measure energy consumption over the same distance, the high AR will be superior. > -Higher aspect ratio wings have a higher lift-to-drag ratio. That implies > greater efficiency when paddling a high aspect ratio paddle. On the other > hand, Greenland paddles are symmetrical which reduces wing efficiency. Irrelevant, we do a lot more with a paddle than just go forward, any paddle design in a compromise between its various functions. If you were to optimize the profile and blade shape for simply moving forward AT LOW SPEED, you would end up with a shape that would be good for little else. I like a fully symmetrical paddle in both profile and planform so no matter HOW I am holding the paddle, I always will have it in the CORRECT position, especially for emergency maneuvers. This compromises its efficiency for cruising, but makes it more suitable for all the other functions a paddle must perform. Also, > lift-to-drag theory applies to a wing that is designed to move parallel to > the wing surface, not perpendicular to it. This is confusing to translate > into paddling, but the velocity of the paddle through the water parallel to > the blade surface creates drag which is not related to the velocity of the > boat through the water. That may disconnect the lift-to-drag ratio from > having a positive bearing on paddling efficiency. You are confusing yourself. You need to go back and carefully reread the posting. There is no useful drag on the paddle, the thrust, (or "lift") is the USEFUL force coming off the blade for propelling yourself forward, the drag is defined as the force FELT at the handle of the blade. Minimum force at the handle, and maximum thrust at the blade is HOW the efficiency is measured, efficiency reduces to simply Thrust/Drag(at the handle). So 100 percent would be where you get the same amount of trust as the force at the handle you put into it (it is that simple!). The drag of the hull is unrelated to anything to do with the efficiency of the stroke. > > -Lower aspect ratio wings have more gentle transitions into stall > (cavitation). That's why trainer airplanes have wings like a Hershey bar. > Lower aspect ratio paddles should not break into cavitation as abruptly and > my observation from lousy paddles I have built is that they do not. > Conversely, my Greenland paddle required careful technique to prevent > cavitation. Low AR are not just more gentle, but also more stall resistant (i.e. they can go to much high angles of attack relative to the flow direction before stall). And yes, the high AR paddles DO take more skill and experience to use properly, and not a good choice for newbies, though I think they should transition into them real soon if they intent to keep paddling over long distances. > > My opinion (neither smart enough nor fast enough to make a conclusion): > Racers use wing paddles because they are indeed faster and more efficient at > propelling a boat through the water. How are you measuring efficiency? If you mean least time over a given distance, YES. If you mean least expended energy over a given distance (ignoring the amount of time it takes), NO. This is like comparing a fuel economy of a Honda Civic with an Unlimited drag racer. Both do the job they were designed for very well, but what they were optimizing is very different! On the other hand, it's not all about > speed and efficiency. It's about fun. When I paddled with a Greenland paddle > I was pain free (although slower) for more miles. Paddling with a high > aspect ratio paddle is arguably better for your body, especially when > paddling long distances. When I'm older and wiser I'll stop paddling in all > situations with my WW paddle and start using something with a higher aspect > ratio. I also enjoy the feel of a symmetrical high aspect ratio paddle. But if someone thinks it is more fun to paddle around using a tennis racket, who an I to criticize. There are some people that go jogging with weights around the arms and legs to get a better workout, who am I to tell them they do not know what they are doing? It is not efficient, but that is clearly not their goal. 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. 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Bob said it well. This analysis doesn't pass even the most casual sanity check. Measurements of conventional "euro" paddles show an efficiency of about 74% and for wing paddles of 89%. If a high aspect ratio paddle is twice as efficient this would mean a Greenland style paddle is 148% to 178% efficient. In other words the high AR paddle would actually be generating energy. Cool! As Bob pointed out, the velocities aren't the same thus shouldn't cancel. And the final equation is a ratio of forces, essentially force in and force out as best as I can follow. The idea that the drag force at the paddle blade is different in anything but sign from the force being applied by the paddler's hands is self evident nonsense. For forces to balance this would require that there be some other force acting on the paddle besides the hands and the water, the analysis gives no indication of where the extra force goes. If this mystery force is the wind, I would expect to see some factor for the wind included in the calculation. There are obviously some faulty assumptions in the analysis. The equations do not agree with available empirical data nor are they physically logical. I don't know what the faulty assumptions are, but the canceling of the velocity is a good place to start. On Monday, June 9, 2003, at 07:30 PM, Peter Chopelas wrote: > > Cd(total drag)=Cdo+Cdi > > Ct=SQRT[3(pi)AR(Cdo)] > > Thrust=S(Ct(rho)V^2)/2 > > Total drag=S(Cd(rho)V^2)/2 > > efficency=P-out/P-in = TxV/DxV = T/D since the velocity cancels > > Efficency= [S(Ct(rho)V^2)/2]/[S(Cd(rho)V^2)/2] > > Eff. = Ct/(Cdo+Cdi) > > = Ct/(Cdo+Ct^2/(pi)AR) > > 1/Eff. = Cdo/Ct + Ct2/(pi)AR(Ct) = Cdo/Ct + Ct/(pi) AR > > 1/Eff. = K1 + K2/AR > > 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 > > > 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 Nick Schade Guillemot Kayaks 824 Thompson St Glastonbury, CT 06033 USA Ph/Fx: (860) 659-8847 http://www.guillemot-kayaks.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/ ***************************************************************************
In a message dated 6/10/2003 1:46:34 PM Central Daylight Time, michaeldaly_at_rogers.com writes: > . However, Nick Schade has presented > convincing reasons for believing that the lift on a GP doesn't > actually contribute to the forward motion as such (this discussion is > achived in QajaqUSA's web site) or at least not in the way that wing > paddles do. > Then I have a question: When one slices the paddle verically down a few inches into the water, absolutley perpendicular to the boat, then flatten the blade so that the entire width of the blade is popped upwards, one will get forward motion. Is that not lift generating forward motion? We did that scenario at the recent greenland symposium here on the west coast. we sliced the blade down just a few inches, flattened it and popped it back up. No rotation, no sweeping, nothing. We did it many times on each side, achieving about a knot, maybe more of speed. Now, as soon as the E=MC Sqared formulas start into the thread my eyes glaze over. I'll need some explanation in addition to that. I'm just curious if we were practicing some other form of motion than lift or lift does generate forward motion. Rob G *************************************************************************** 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/ ***************************************************************************
On Wednesday, June 11, 2003, at 10:57 AM, Rcgibbert_at_aol.com wrote: > In a message dated 6/10/2003 1:46:34 PM Central Daylight Time, > michaeldaly_at_rogers.com writes: > > >> . However, Nick Schade has presented >> convincing reasons for believing that the lift on a GP doesn't >> actually contribute to the forward motion as such (this discussion is >> achived in QajaqUSA's web site) or at least not in the way that wing >> paddles do. >> > > Then I have a question: When one slices the paddle verically down a few > inches into the water, absolutley perpendicular to the boat, then > flatten the blade > so that the entire width of the blade is popped upwards, one will get > forward > motion. Is that not lift generating forward motion? > > We did that scenario at the recent greenland symposium here on the west > coast. we sliced the blade down just a few inches, flattened it and > popped it back > up. No rotation, no sweeping, nothing. We did it many times on each > side, > achieving about a knot, maybe more of speed. I have done that too and I agree that what you are doing uses lift almost exclusively. It is kind of an entertaining way to move. However it helps demonstrate why I don't think lift is a big constituent in most paddle strokes. Your really need to move your paddle fast to go only 1 knot using this pure lift stroke. Cruising along at 3 or 4 knots requires significantly more power yet most people are quite able to make their boat move at those speeds with a much more relaxed cadence. It seems obvious to me that if you can go significantly faster with a conventional stroke than you can with a pure lift stroke, most of the power in the conventional stroke must come from something other than lift. I also just don't see a lot of transverse (side-to-side) or vertical (up-or-down) motion in most peoples stroke including the various forms of Greenland strokes out there. The Wing paddle stroke does include a fair amount of transverse motion, but even with the wing paddle which was invented on the theory of incorporating lift, there is some question as to whether lift is a significant portion of its power. Nick Schade Guillemot Kayaks 824 Thompson St Glastonbury, CT 06033 USA Ph/Fx: (860) 659-8847 http://www.guillemot-kayaks.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/ ***************************************************************************
On 11 Jun 2003 at 10:57, Rcgibbert_at_aol.com wrote: > Then I have a question: When one slices the paddle verically down a > few inches into the water, absolutley perpendicular to the boat, then > flatten the blade so that the entire width of the blade is popped > upwards, one will get forward motion. Is that not lift generating > forward motion? If I understand your description, yes, that is correct. However, you're considering a special case, as it were, and not an entire Greenland stroke. Nick was considering the entire stroke, where, for a considerable portion of the stroke, the blade is oriented in such a way as to prevent the lift vector from pointing forward (as it would in a wing paddle). The lift on the blade does exist and generates a force, but it _indirectly_ contributes to the forward motion. With a wing paddle, the lift force is directed forward and thus contributes directly to forward motion. Mike *************************************************************************** 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/ ***************************************************************************
Since we don't move with the speed of light, we should leave that formula out (e=mc ^2). Also our paddles don't go into fusion or fission mode.... Heike *************************************************************************** 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/ ***************************************************************************
In a message dated 6/11/2003 1:50:24 PM Eastern Standard Time, nick_at_guillemot-kayaks.com writes: > ... The Wing paddle stroke does include a fair amount of transverse motion, > but even with the wing paddle, which was invented on the theory of > incorporating lift, there is some question as to whether lift is a significant portion > of its power. ... And another correspondent pointed out the preponderance of theory and formulae, and the lack of data and observation ... I once had the opportunity to watch a wing paddle technique training video. Playing it in slow motion revealed clearly (and caused some open mouthed staring at the screen) that both the paddle and the boat were moving forward in relation to the water (the paddle less so, of course), i.e., the paddle moved in the direction of travel of the hull between the catch and the finish (of the stroke). On the basis of that observation one might perhaps be forgiven for suspecting that the "theory of incorporating lift" resulted at least in a smidgeon of practical results. :-) Best regards, Ralph Ralph C. Hoehn Folding Boat Center P.O. Box 700 Enfield NH 03748 info_at_FoldingBoatCenter.com www.FoldingBoatCenter.com phone: +1-802-649-2555 -- Ralph phone: +1-603-632-9500 -- Alv (yup, they rhyme) *************************************************************************** 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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