On 14 Oct, 19:38, Andy Champ wrote:

Same speed *relative to the the surface it is on*.

Yes, so you accept it has spare energy left over after it has overcome
the drag of the windmill. So the windmill on the foredeck of our power
boat has enough energy to push against the wind pushing back on it. It
also has enough energy left over after this to move it forwards.

Which means you can gear that spare energy to the engine and save some
petrol.

Yet you and I both accept you can't do that.

So there's a paradox.

In other words there is some spare energy left over to drive the cart
forwards after the energy required to hold the windmill in equilibrium
with the wind is expended. In my example above that spare energy is
used to drive the cart forwards but in your example of the windmill on
the foredeck that surplus energy can be used to save petrol.

Now we both accept that idea is laughable so you have to explain why
it's not laughable when the wind blowing is caused by nature.

...but most importantly, why oh why oh why doesn't someone just post
the mathmatical proof, the last time this came up I said I'd leave the
thread 'till proof turned up and none did. Odd that.

Lets take this step by step.

Or to put it another way "Lets take this step by step so I can keep
talking rather than posting the maths that I claim is simple to prove
my case."

Do you accept that it is possible for the cart to move directly upwind?

It is essential that we assume that to be the case so you can explain
the paradox exposed by the windmill on powerboat example.

If in a headwind the windmill pushes back harder than it is pushed
then it must do that no matter how that headwind comes about. Which
leaves us with a power boat with a windmill on it's foredeck getting a
net gain in energy from wind that it is creating.