Re: sailing upwind?

[brian whatcott <inet@INTELLISYS.NET>]

At 11:20 12/30/99 -0800, John M wrote:

> .... perhaps a better illustration of
> the power of momentum conservation as an analysis tool.
>
> John Mallinckrodt      mailto:ajm@csupomona.edu
> Cal Poly Pomona          http://www.csupomona.edu/~ajm

John is begging us to consider the momentum balance and the
energy budget and the power budget, I dare say.

I earlier advanced that:
"...Leigh's windmill propulsion seems to demand only that the
superstructure and air prop drag due to the wind is less than the
 water prop thrust due to power from the air prop.
Some positive net force will provide
headway even into the teeth of the wind."

For Leigh's position to be tenable, we have that the momentum loss
in the wind is balanced by the momentum gain in the water,
while the force exerted by the wind on the boat is less than the force
exerted by the boat on the water, and the power generated by the air prop
is greater or equal to the water prop power dissipation.

It is attractive to suppose that the power generated in the air prop is
a function not only of air density, air speed squared, frontal area,
but also an efficiency factor related to coefficient of lift of the
air prop section.

 In that case, the drag force exerted by the wind could be in large part
related to density, speed and area factors already mentioned but also the
coefficient of drag of the air prop section.

This would be attractive because the coefficient of lift of wing and
prop shapes can be made many times greater than their coefficient of
drag: (ignorance of which relation led professors of an earlier era
 to opine on the impossibility of heavier than air flight)

Without placing a defining relation in the note, I can at least say
that this is a question of momentum conservation and energy dissipation
turning on the difference between a deltaV and a deltaVsquared.

When I consider concrete cases (a regrettable tendency to which engineers
in particular are wont) I can pluck out of the air the four meter prop
supplying  240 kW at 120 kt wind speed, 60kW at 60 kt windspeed and 15kW
at 30 kt wind. I can visualize exit air from the 30 kt gale at 15 kt.

 I can visualize the water prop being scaled proportionate to the air/water
density ratio, and I finally see that I am trying to minimise generation
and transmission losses so as to arrive at a system that effectively uses
an air prop to drive an air prop in hopes of gaining propulsion thereby.

Most interesting!
 I used an intuitive 'reductio' argument - but what I wanted to
demonstrate was a momentum balance argument. Any offers?


brian whatcott <inet@intellisys.net>
Altus OK