On Oct 3, 6:58*pm, Ronald Raygun wrote:

please don't dismiss me as a "dennis". *I'm genuinely trying to
understand why I can get the energy budget to add up using your result.

My apologies. Perhaps I read too much into your explaining
confidently that JB's analysis was wrong (rather than suggesting that
maybe it was wrong, or asking for clarification). I've been through
this thing a whole bunch of times, and that's almost always a dead
giveaway.

If there's a mistake in my maths or my arithmetic, please help me find it..

Fair enough. The mistake is not in your math, but in your assumptions
(or perhaps a simple miscommunication). In your above post you say
"Looks like your analysis also requires an infinite propeller". Yes -
that's right. JB starts with a lossless prop (as he states). I'd
have to go back and look at his analysis, but I suspect he shows that
there's lots of excess power available with that assumption. This
lets us distinguish the difference between an engineering problem and
a problem of violating physical law. If we have excess power in the
no-losses situation, we know it's just down to an engineering problem.

And yes, as you suggest (and as we also have suggested) a lossless
prop will always be of infinite diameter and will have zero delta-
velocity across the disk. An 85% efficient prop however can be
significantly smaller than that (and will have a non-zero delta-V).

One thing to keep in mind is that prop efficiency is typically defined
relative to "V-infinity". This is the free-stream velocity. In the
case of an airplane, it's the plane's airspeed. For this definition
eff = power_out / power_in

power_out = thrust * V_infinity
power_in = torque * rotational_rate

Relative to the aircraft this is the definition that makes sense. The
pilot really doesn't care how much breeze the prop makes. He just
cares how much force it creates at a given airspeed. If you're
designing house fans you wouldn't use that definition for efficiency.
In this case you DO care how much breeze your prop creates.

Of course choosing different definitions for efficiency cannot change
the outcome of an experiment, but it can lead you to an incorrect
result if you use a different definition than what is assumed by the
person that did the analysis.

Does this make sense?