# Efficiency estimation for small-scale (~15cm) propellers

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?

Some details:

• Aircraft: