On Oct 6, 3:02*am, Ronald Raygun wrote:

I'm sure that's what it was meant to do... But at first it doesn't

That's exactly what it does. *At first* it considers a 100% efficient
device - as you suggest. He then looks at the excess energy available
and answers the engineering question - "is this enough energy to make
it work in the real world?"

You're getting stuck on the notion that a 100% efficient propeller
would have to be infinite in size. Why? 100% efficient ball bearings
and zero rolling resistance tires can no more easily exist in the real
world than a prop of infinite diameter. Exactly how large a prop
would you allow in the first part of the proof when he is simply
trying to see if a DDWFTTW cart would violate the laws of physics?

because his analysis made the explicit assumption
of a loosless propeller, and hence the implicit assumption of an infinite
propeller. *Yes, he slipped in a rider at the end allowing for 85%
efficiency

In other words, he did precisely what you suggest. He starts with
lossless components, determines that no laws of physics would be
violated, and then addresses the real-world questions. In the very
beginning of the analysis he explains that he's starting with lossless
components, but that losses will be dealt with later. There's nothing
hidden or tricky about this.

the implication of this gets in the way of
promoting understanding, given that most readers (here) would be unaware
that 100% efficiency implies infinite size.

100% efficient components don't exist in the real world. I think he
assumes that everyone but Dennis would recognize that.



When we got to discussing the static case and when I said: ...
His reply was: ...

Yes, and his reply is correct.

That's a good approach, but the prop efficiency stuff ought to have gone
into the engineering part, whereas he seems to have it initially in the
physics part.

The imperfect prop is introduced in the engineering part. The perfect
prop is assumed in the physics part. There's no other way to follow
the very approach you suggest.

*It seems to me that the physics analysis would be more
illuminating if it allowed us to work with finite values of air throughput.