Unfortunately, the one I have in mind is not listed there. I recorded it on my DVR and then recorded that on my iPhone so the video here is not... um .. of pristine quality. But that's not necessary to make my point. The episode is called "Power My Party Boat" and involves attaching two paddle wheels to a pontoon boat, anchoring the boat in the Tennessee River, and having the passing current generate electricity by turning the paddle wheels.

They utilized automobile alternators (one, with which they had problems, from a salvage yard and the other new) to actually generate the electricity, ran the current (the electrical current, not the river current) through a voltage regulator into a set of batteries. The electrical current was thus used to charge the batteries. They then used a pair of inverters to supply energy to a "kegerator" (a refrigerator with a keg of beer inside and a tap). a flat screen television, a laptop computer, and a string of lights.

Here's a video clip:

- A "kegerator": 100 watts
- A flat panel television (I'll assume 32", Energy Star qualified): 77 watts
- Laptop computer: 20 watts
- Light string (20 lights, incandescent, at 0.4 watts per light): 8 watts

The total is 205 watts and I've been VERY generous.

In order to determine the plausibility, we need to know the size of the paddles and the speed of the river. While I can't find definitive data for the speed at the location the Rednecks utilized, this paper mentions "there are some sites with velocities in excess of 5 fps (feet per second)." The show mentioned 3 fps, I'll average the two and go with 4 fps or 1.2 meters/second.

As to the size of the intercepted stream, I'm estimating that each paddle wheel intercepts about 2 square feet (again, generous) or 0.19 meters^2. I'll round to 0.2 meters^2 and multiply by two for two wheels. Thus, the intercepted stream is 0.4 meters^2.

The basic equation for determining the power in a stream of moving water is P=(rho*A*V^3)/2 with A the area, V the speed (assuming the area is perpendicular to the velocity of the stream flow), and rho the density of the water. Here we have rho=1000 kg/m^3; V=1.2 m/s; A=0.4 m^2. Thus, the total power in the stream intercepted by the paddles is about 690 watts.

Now, a paddle wheel is not the most efficient way to extract energy from passing water. The best sources I found were here and here. The Rednecks seemed to have built an "undershot" water wheel, whose efficiency seems to top out at 25%. Considering the slapdash nature of the construction, I'm going with the 20% listed in the second article. This means that, before the alternators, the voltage regulator, the batteries, and the inverter, the system could deliver about 0.2*690 or 138 watts.

Now, a paddle wheel is not the most efficient way to extract energy from passing water. The best sources I found were here and here. The Rednecks seemed to have built an "undershot" water wheel, whose efficiency seems to top out at 25%. Considering the slapdash nature of the construction, I'm going with the 20% listed in the second article. This means that, before the alternators, the voltage regulator, the batteries, and the inverter, the system could deliver about 0.2*690 or 138 watts.

And yet the lights were on, the beer was cold, the television and computer were working. What gives? I suspect that the batteries were supplying the power at the rate of 205 watts (or likely more), and the paddle wheel system was simply slowing the rate of discharge. I'll concede that, if I were on the boat, I'd be able to live with intermittent operation of most of those appliances, so it's possible that the river could supply my energy needs in such a circumstance. And the wheels could certainly have been built much bigger - available power scales directly with area. But I'm disappointed because the show, as presented, was quite misleading.