Foil for current-driven propulsion?

Why can use this data ? air is at rest relative to the land frame, so his relative velocity relative to the reference frame fixed with water is equal and
opposite to the velocity of the current.
Vair/land=0=Vair/water+Vwater/land , so Vair/water=-Vwater/land= -Vcurrent
this a pure result of Galilean transform
Am I missing something

 

The air is not at all at zero energy state relative to the water, it flows from downstream at Vw= -Vcurrent !
PS : Energy is dependant on reference frame, in the reference frame associated with the water, flow energy is zero (as V current =0 / water) but flow energy of the air comes from the relative motion of the air / water equal to -Vcurrent . So relative motion of the foiler in this frame is the same as in open sea with true wind = -Vcurrent

 

Let's assume you are correct. Since in this scenario you are moving directly into the wind how do you extract energy from the air flowing over the boat? In english; I'm not a mathematician.

 

That is really confusing. You are not taking energy from the water using the air. There are two fluids with a relative velocity. That creates a potential that can be used to sail. The only difference from sailing with a wind and static water is the frame of reference.

 

Energy is not dependent on the frame of reference. Potential difference is what allows energy to be removed or introduced into a system.

 

English is not my native language ! I admit it is astounding, but it is the results of very low drag of foilers and high performance of their wing sails. If you look at the performance
of F50 foilers , they are able to sail downwind courses at velocities well above 2 time the real wind velocity, in fact they sail with very low apparent wind angle and are trimmed as in upwind
conditions. You can observe this on youtube movies, and they tack downwind on their apparent wind as if they were upwind. So they are able to sustain downwind VMG superior to
the real wind velocity. You can extract energy (forward thrust) from the sail as long as you have enough apparent wind angle which is determined by aerodynamic performance of the boat. This angle is very low on F50 foilers.
Obviously you can't sail directly downwind wind in a sustained course, you have to broad reach and tack downwind (yes, tack, not jibe, the apparent wind stay always foward !) During the tack the thrust is briefly interupted and the boat turns thanks to his inertia and low aero/hydro drag. These performances results are now well established, and can be applied directly to the Amazon river case.
But you have to admit the Galilean principle of relativity, wich is at the base of the classical Physics !!!!
" Per se muove"

 

Agree, I was only referring to Kinetic energy flow !

 

There is no such thing as kinetic energy flow. Fluids flow though and may have kinetic energy.

 

Everybody makes this much more complicated than necessary.

Imagine you're in a boat aimed upriver, but floating along with the current. Add a sail to the scenario and it will feel like you're on a dead run. The boat will move through the water but not fast enough to make progress upriver (with respect to the ground).

Now, if your boat is fast enough that you would normally "tack" downwind, you can head up to a broad reach and your VMG will be larger, and if your boat is really fast (like the foilers) you'll be making progress over the ground (not just through the water).

Isn't that simple?

 

Sorry for butting in, but I think I can help
Wikipedia (a dangerous source, but useful) :"in physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors."
PE = Mgh - h, height is relative to the FoR
KE = 1/2 mv^2 V, velocity is relative to the For

Definitely, energy is dependent on the FoR.

 

Not correct. Potential is the difference of energy levels and it may be dependent on the frame of reference; it is an extrinsic quality. Energy is not dependent on a frame of reference; it is an intrinsic quality.

 

Yes, you are right, it is what I expained with the most simple physical arguments !

 

Obviously I was talking of Kinetic energy flux , which is well defined

So, in a frame fixed with the water, it has kinetic energy with no relative velocity ?

 

You have your own definition of Energy, not the energy defined in Physics !
The only intrisic energy of a particle at rest ,is its energy at rest, E0=m0*c2,
for any other observer,
E²=m0*c^4+c²*p² which depends on the reference frame !

 

OK, I have understood you refer to thermodynamic defition of internal energy (thermal) . but here we don't deal with themodynamics as we are in incompressible flow, we deal only about momentum and kinetic energy fluxes available for a partircular observator, wich depends on her reference frame. Am I missing something ?