Hey Rp,
Thanks for your comments. Yes and no. The difference is this. An over shot wheel is only 63 percent efficient because its weight is not applied at all times 90 deg to the axis. This means that there is a loss while one container is waiting to arrive at the 3 o'clock or the 9 o'clock position. The same is with an internal combustion engine. When the piston is top dead center and the combustion phase takes place it is timed so that the maximum torque is taking place as close to 90 deg on the cam, but the losses are exactly proportional to the slow burn of the gasoline (leaded unleaded....or octane) 90 deg is the sweetspot anything less or more has a degree of loss of efficiency. The only way around it that I can see is to apply a system where the force is always applied at 90 degrees to the axis. I am sure there are other arrangements other than what I have written about but to me it is the simplest. For instance if you have a wheel with 12 pockets able to hold 10 pounds each, such as an overshot wheel. and you add up all the weights, the weights at 12 and 6 do not apply force, the weights at 1 and 5 are only applying a very small force etc. etc... if you divide the cubic inches of one pocket by 231 and multiply by 8.33 and multiply by the number times the number of pockets to give you the actual weight on the wheel, then find the torque that the wheel is putting out, the difference is right at 63 percents. The chain and containers/bucket is closer to 100 percent - frictional losses that apply to any system. That difference in efficiency can mean $100s or $1000s of dollars of savings, by simple changing designs. I will make an excel sheet soon of the efficiency of an overshot wheel in comparison to this design.
Jon
Attached is a screen shot of the difference between the two systems as show by an engineering program (which is free by the way). The paddle wheel number is higher (but still 20 % less than the other shown) because the place that I measured it from is not at the center of gravity of the weights attached to the paddle wheel. The actual difference is closer to 63% or 37% inefficient.
If your not concerned about money, there is nothing like sitting on a grassy slope watching a water wheel.