Waterwheel

Design

Mechanic

• The materials are chosen arbitrarily. Whatever you have available. The heavier the material the more problematic the bearings and middle axis longevity may be.
• Sheet thickness depends on the material chosen. In the images 4mm thickness for plexiglas is shown. For steel 2mm may suffice. Stress analysis will clarify. Of course the thicker the better for minizing losses of energy into vibration but the bearings and holder suffers more then too. So there must be a compromise.
• The design is following the building blocks principle.
• The axle's bearings may be ball or slide.
• It's uncertain if the cheapest metal candidate (steel) needs to be zinc-coated, rust-protection-painted or similar. Or if stainless steel should be chosen to achieve an optimum.
• Environment depends but a pitch-back or counter-stream configuration or (best) both is recommended.
• Prefer overflow over underflow waterwheel. Power efficiency c_p will rise significantly if you surrect an aquaduct/penstock and divert some water of the stream. The water height energy will be captured by the buckets, it's not optimal design but often simplicity wins (consider the energy lost in vibrations if a sophisticated pelton system is integrated, though that might be interesting to evaluate). The underflow is purely kinetic, while overflow (pitch-back) uses the kinetic energy twice - and the height of the water too.

Stress analysis

A stress analysis for common materials: wood, plexiglas, cheap plastic, metal (steel), aluminium.

Why a waterwheel design?

Initially a turbine was planned. Turns out there is neither enough water flow (high-throughput turbine, Kaplan, Francis), nor enough height difference (for a pressure/impulse turbine).

An archimedian screw does work. Its construction so far has failed.

A cross-flow (universal turbine, often used as wind turbines, exist as drag and/or lift variants) was the turbine of choice until it turned out that power harvest was low despite the water hitting the turbine blades twice.

While the theoretical maximum is 58% (Betz-Limit), it turns out the efficiency will be no higher than 30%. And that's already quite optimistic, it'll rather be <20% if custom-built. There also is just not enough water in the stream to drive it efficiently (cross-flow need flow!).

They do extract some of the direct height energy of water too (overshot cross-flow), but it's not significant.

A helix might have improved the overall sitation. It's just not possible to manufacture it (so far).

Therefore the last hope lay in a waterwheel. Turns out it does have a chance to extract up to 80% of the energy of the water if the design is lucky.