On Oct 9, 9:18*am, Ronald Raygun wrote:

....about heroes and plebs. Sorry for the shamefully delayed reply.

Let's change the skater analogy to match your Cessna. *Suppose our hero
has a rope tied around his waist which is tied to a stake in the ground
behind him. *This time the plebs are coming towards him at 1 m/s from the
front, and he pushes back on one of them for a second at the same 60 N as
before, accelerating him to 2 m/s. *During the second of contact the pleb
travels 1.5 m, so our hero does 90 J of work. *The 60 kg pleb's kinetic
energy increases from 30 J to 120 J.

Okey dokey.

The hero's arm may conceivably have been 100% efficient at converting 90 J
of chemical energy into a 90 J kinetic energy increase for the pleb. *In
the same way, the Cessna's prop could conceivably be 100% efficient at
converting engine power into kinetic air power. *We don't care what happens
to the accelerated pleb after he's left the grasp of the hero's arm, in
terms of how that pleb might vaporize when it collides with another pleb.
Likewise we shouldn't need to care whether the accelerated air gets hot
as it slows down a few tens of yards downstream.

Well, yes and no (have I got that one covered?). You're right that
the prop might have been 100% efficient in converting its power to
kinetic energy of the air. But several things should be said about
that...

1) The prop *will be* 100% efficient in transferring its energy to the
air - there's no other choice.
2) This is why the efficiency for an airplane propeller is measured
differently than that of a house fan - they have two different jobs.
3) The above statement is more true than you might guess. You might
say - "but no - they both have the job of accelerating air". But this
isn't the case. The airplane prop has the job of pulling the plane
forward through an airmass while the house fan has the job of
accelerating air. For a given thrust and airspeed a given propeller
can not be more efficient than some amount that's easily calculated -
because it's only able to develop its thrust by moving an amount of
air that can be encountered by a prop of its specific diameter. So
it's less an issue of not caring what happened to the air afterwards,
and more an issue of considering that you have a prop that can *only*
generate the desired thrust by accelerating the air in an inefficient
manner (namely accelerating a small amount of air by a relatively
large delta-V).

The above is not intended to be argumentative. It's intended to help
you understand another perspective. The measure of efficiency of an
airplane prop is not as arbitrary as it might first seem (imo).


I was thinking about the prop's efficiency as how its kinetic output power
relates to the mechanical input power. *I think you're considering prop
efficiency in terms of what the plane gets out of the deal.

That's right. But keep in mind, its output power *must* equal it's
input power. So if you don't like the definition given, you have to
think of another somewhat arbitrary definition. For example, you
could say that only the velocity added along the axis of the prop
counts as being approved output energy - while the swirl velocity is
wasted energy. But then we could have this same debate about how much
energy the prop "really" added to the air. The point being - without
some sort of "arbitrary" definition of prop efficiency, the prop will
always be 100% efficient.

In your Cessna
with the brakes on, I presume you are considering the prop as running at 0%
efficiency because its thrust is doing no work *on the plane*.

Correct. But it's not "my" definition.

If I cut the skater's rope so that he can accelerate too (corresponding to
your Cessna releasing the brakes), he will travel forward 0.5 m during the
second, and so he will have done 120 J of work. *90 J of that is still going
into the pleb, and the remaining 30 J will have accelerated himself.

O.K.

*In my sense his arm is still 100% efficient, in another sense he could be thought
of as 25% efficient because, out of 120 J expended, 30 J have gone into
useful KE, and 90 J into useless KE.

Agreed. I think you'll find that in your sense everything is always
100% efficient. That's why efficiency formulas are always somewhat
arbitrary.

*But in your sense I think he's being
50% efficient because 30 J/s (30 W) is 50% of the best he could get by
exerting 60 N at 1 m/s (60 W). *Am I right?

I don't really have a particular sense. In the sense of the airplane
propeller his efficiency would be the energy he gained divided by the
energy he expended. Yes - it's arbitrary - but only sort of. First
because efficiency relates to the desired result, and second because
any "non arbitrary" definition of efficiency will always be 100%
(because mass/energy isn't created nor destroyed).