How to build a cardboard paddlewheel

Here's an idea for a paddlewheel.

 

Paddle design is only as good as the weakest point from the input force supplied by the occupant to the output resistance of the water. The smaller the paddle area the smaller the resistance and so the less force required but the less propulsion per revolution. The number of paddles also needs consideration.

Weak points:

1. Input force - Handle for turning the axel: Handle breaks rather than turn the axle
2. Output resistance - axel spins and spokes snap.
3. The axle could crumple, snap or tear under torsion. 
4. The paddles themselves collapse

As well as the paddle wheel failing, it also has the potential to destabilise the boat. Corrugated cardboard has a natural boyancy. If the paddle wheel sits too low in the water with the axel below the waterline it will not function well. If it sits too high then the paddle blades will just skim the surface.
The above design sits in the water just up to the top of the paddle and the radius of the paddle wheel is designed so that the axel just rests on the side of the boat. 
The paddlewheel is not fixed to the boat for several reasons. Firstly, it means that as the wheel  gets wetter and heavier it doesn't drag the boat over. Second, since the occupant will be sitting and not kneeling there needs to be space under the axel for the occupant's legs. Third, It allows the direction of the wheel to be manipulated to help steer the boat  a little.
Power is designed to transfer to the boat via the oarlock (this too needs to be strong enough not to snap, crumple or tear the boat). In practice, a lot of the power was transferred to the boat through the straight arm of the person holding the tube surrounding the axle.

Six blades seemed to be about the right compromise for a smooth rotation without having too many cuts in the disks. The disks were made hexagonal rather than circular so that taping and designing the paddles to match was easier. Each blade area is 20x20cm. Again this seemed a reasonable size. In practice the resistance seemed about right. Not too had to turn but provided good propulsion.

The axle was built from 3mm thick tubing of between 5 and 6.5cm diam. It was thickened by slitting extra 5cm tubing and wrapping three pieces around the 5cm diam axel until the 7cm tube fitted snugly over the top. These thickend tubes were drilled with a 30mm core cutter to allow 30mm diam. tube to be inserted. The 30mm tube is crucial to the design. Two pieces lock the wheel to the axle and two pieces connect the crank handle to the axle.

Care should be taken to tape all edges. If water gets inside the corrugations the glue will soften and the cardboard will soon lose its stiffness and collapse.