Ronald Raygun wrote:

ThinAirDesigns wrote:

@Ronald Raygun:

What The Natural Philosopher tells you above is the simple truth. Do
the math.

Momentum = MV
Energy = 1/2 MV^2

I figured this out a few hours before reading this.

Oops, pressed wrong button and the message went out before I'd written
the rest.

The thrust you get is equal to the rate of change of impulse, and this
corresponds to the air speed difference (output air speed minus input air
speed) multiplied by the rate at which mass is put through the prop.

This means that to get a particular thrust value, you can either put
through one particular quantity of air per second at one particular speed
difference, or alternatively you can put through k times that quantity
at 1/k times the air speed difference, for any real positive k.

This impinges on the power requirement, which is equal to the difference
in the input and output airs' kinetic power.

Power = 1/2 (mass throughput rate) * (v2^2-v1^2)

In the special case where v1=0, we get

Power = 1/2 Thrust * v2 [because Thrust = (mass rate)*(v2-v1)]

I concede that this shows that in principle the power needed to produce
a given amount of thrust can be made as small as we want by making the
output air speed as small as we like. Unfortunately the mass throughput
required per unit of time is now equal to thrust/v2, which means that if
we wanted to reduce the power to zero, we'd need to put through an
infinite amount of mass each second.

This is clearly unachievable, and so I must reject your analogy with the
two-by-four plank leaning against the wall, until such time as you can
produce a 2X4 of infinite length and zero density. :-)

You have tried to to show that my force/energy analysis is wrong
because those calcs show that in a perfect world 0hp is required at
exactly windspeed. Well, the analysis and equations are correct and
would be wrong if they *didn't* show this.

Depends what you mean by perfect. You merely stipulated that the components
(propeller, motor, generator) should initially be 100% efficient. A
propeller is 100% efficient if the mechanical power you put into it from the
motor matches the power which comes out, which is represented by the
difference between the before and after kinetic energies of the air being
put through per unit of time. I did not expect it would necessarily have
to have infinite size. If input and output power are zero, its efficiency
is 0/0 which is undefined. How can you say it's 100%? Hardly a perfect
world!

Anyway, let's leave the silly static special case and return to the one
in which I originally took exception to one aspect of your analysis. The
case with the car travelling at 55ft/s in a 27.5ft/s wind, and 10lb of
thrust.

If you're wanting to get 10lb thrust in those circumstances using only
1/2hp, then (if my calculations are right) this is possible only if you play
the same silly game as you've done with the static case, i.e. you would end
up with prop air output speed the same as air input speed, i.e. zero speed
difference and hence a need for infinite air throughput.

I had thought that the purpose of your discussion which included the
analysis was to try to persuade unbelievers (who no doubt think the whole
DDWFTTW idea is impossible, and that your documented demonstrations of it
nevertheless actually working must therefore be elaborate hoaxes). I would
comment that an analysis which only works with infinitely large propellers
is hardly going to be terribly persuasive.