To be efficient on a relatively slow boat paddles need to be of a pretty large diameter, as you've already worked out. The other problem with them is controlling depth of immersion, as this is critical to getting good efficiency. Other than that, you can get surprisingly good efficiency with large diameter, slow turning, paddle wheels, easily up around 60%, which compares well with off-the-shelf propellers, although this falls short of the efficiency that can be achieved with a well-matched propeller set up.
Power for a given hull displacement sort of works for big boats, but starts to fall over for small boats with low power requirements. If you can determine the power that your hull needs to propel it at the speed you want to cruise at, either by practical measurement (a crude tow test with a spring balance will give you a rough idea of hull resistance with speed) or by modelling the hull in one of the free programmes, like Michlet or Freeship, then you will have a much better idea of the power needed.
For example, my solar powered river boat is 18ft overall and displaces about 600lbs with two people on board. The hull resistance data shows that at 2kts it needs about 7N of thrust, which is about 7 watts of power (at the output of the prop, not the motor input, power being simply speed (in m/S) x thrust (in N)). Increasing the speed to 4kts increases the thrust to 26.3N and the power required to about 56 watts. At the fastest practical displacement speed of 5kts the resistance increases to 46.4N and the power increases to about 119 watts.
If the propulsion system has an overall efficiency of 50% (allowing for propeller efficiency, motor efficiency, drive train losses and electrical losses) then the power from the battery/solar panels to do 5kts will be around 238 watts. To this has to be added a margin to allow for wind, manoeuvring etc. Doubling the cruise power requirement for sizing the system maximum capability is probably a good idea to give a big enough buffer of power in reserve for a low power boat, so making the total power capability required around 500 watts. This doesn't match the "1000 watts per ton rule" very well, in fact it is around 2000 watts per ton, so illustrates why it is useful to use a pretty good estimate of hull resistance as a starting point.
There is some interesting analysis of paddle wheel efficiency on a thread on pedal powered boats over on the Boat Design forum. I could probable find the point in the thread and post a link if you're interested. The conclusions were "make the paddles very large in diameter", that much I remember!
Jeremy
--- In electricboats@yahoogroups.com, "cptrdbrd" <cptrdbrd@...> wrote:
>
> Hi all
>
> I noticed a post earler that referd to a rule of thum "1000W per ton" does this aply to pattel wheelers to? I am thinking about building a SMALL 1 or 2 person side wheeler with 2 eletric wheel chair moters (500W each) and the gear boxes that are atached. Then reduce down with a 3-1 belt reduction.this will give me about 4-5 knots with a 5-6' wheel. I have the speed controll and the joy stick to controll it. Any input?
> Paul
>
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