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/ ***************************************************************************Received on Wed Jun 11 2003 - 06:29:23 PDT
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