First up, apologies if this isn't quite the place for this; Aerospace is still in Area 51 so there doesn't seem to be a better place for it. If it helps, feel free to give theoretical answers and I'll go crunch the numbers myself.
I'm working on a model aircraft which will act as a testbed for various configurations of wing. The overall length is about a metre; the wingspan will be between one and two metres depending on the configuration being tested. We're looking at two types of propulsion, both driven by electric motor: free propeller, and ducted fan. Either way, it'll be rear-mounted to keep airflow over the wings clean.
My knowledge of aerodynamics is not what it once was, and "what it once was" was a little shaky. Here's what I know:
- All else being equal (airspeed, RPM, thrust) a free propeller is less efficient than a ducted fan of the same diameter.
- Ducted fan efficiency increases with RPM, so they're built to run fast, which gives more thrust per unit disc area, so ducted fans tend to be smaller and spin faster.
- Efficiency increases as the momentum change per unit mass of air decreases, yielding best efficiency at zero-thrust cruise (sadly).
- Ducted fans become less attractive at high speeds because the duct itself adds drag.
Given a rough estimate of required thrust and cruising airspeed, how do I determine which of the two systems is more efficient?
- about 1m long
- wingspan around 1.5m (give or take 30-50cm)
- fuselage diameter roughly 15-20cm
- roughly 5-7kg operating mass
- airspeed 30m/s (very roughly)
- Propeller would be rear-mounted ("pusher"), anything up to about 30cm in diameter, 2-4 blades. Probably folding if that matters.
- Ducted fan would be any size that fits inside the fuselage (including duct clearance), so 15-18cm(ish). Duct would be integrated in a manner similar to jet fighter intakes; overall from intake to nozzle around 30-50cm. Fuselage shape is affected as little as possible.
I've tried to work out some of the finer details, but things like Reynolds number calculations have given me very varying results so I don't really trust them. Any help here would also be appreciated.