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["WILLIAM JONES" <billj AT harborside.com>]

Don Bowen wrote:
> Look into a Pelton Wheel.
Thanks, Don, jackpot.  You might recall that a few years ago I posted on how 
the optimal speed for a flat sail or underhanded waterwheel is one-third the 
speed of the water or wind, regardless of whether this is achieved by a high 
gear ratio or high opposing torque.  Well, they derive a similar formula in 
your article, except that because the force on a flat sail is proportional to 
the square of the wind speed, and the force induced by suddenly stopping the 
water is simply a linear function of the water speed, in the latter case the 
power is maximized if the vane speed equals _one-half_ the speed of the 
water.  It's just a slightly different formula.
When I was in the sixth grade we went on a field trip to Scripps.  They had 
this great waterwheel that drove some unseen load.  I observed that there 
were two distinct components providing torque, the sudden halting of the 
water, and the force of gravity as the water rode downward.  But I'd not yet 
taken algebra, let alone calculus.  Anyway, when I said to ignore the force 
of momentum, it's not that I really plan to do that, it was just for the 
purpose of analyzing that particular type of waterwheel, the "Ferris" wheel.  
In real life we would want to add together the contributions of both, in both 
the mathematical model and the device itself.
One useful formula that I don't have to derive now, but can simply quote from 
your paper, is the terminal velocity formula.  As the water falls 2 feet, it 
attains a speed of Sqrt(128) ~ 12 feet/sec, since 2gh = 2 * 32 * 2 = 128.  
This represents about a half a cubic foot per second, when you multiply 12 
feet by the cross-sectional area of the 3" hose, about 30 pounds of water per 
second.  So now, our goal is to find the power output, finally given by 
taking the product of 30 and 4, the vertical drop in feet, giving 120 fp/s, 
which is around 150 watts, not counting the contribution of forward momentum.
So tomorrow I will attempt to derive a formula that takes both into account.