Foil for current-driven propulsion?

No, vectors are not independent of the inertial reference frame. The relative velocity between bodies remains the same though. Polar diagrams assume there is no current, so the bottom and the water are static with respect to each other. However, if I were to use a polar diagram for navigation and there was current, it would skew the diagram.

 

Polars don't assume anything about the current. The speeds they use are boat speed and wind speed (both with respect to the water) There's no involvement at all of the bottom.

 

In the case of wind, Vwind and current , Vcurrent relative to bottom (undescored for vectors !):
- first you determine the wind speed with respect to the water, Wich is[/SIZE] W= Vwind-Vcurrent (vectors addition !),
- then determine the velocity of the boat VB with respect to water using the polars with this wind speed w[/COLOR]
- then add (vector addition again!) Vcurrent to get the velocity of the boat relative to the bottom, VB+Vcurrent

 

No, vectors are not independent of the inertial reference frame. The relative velocity between bodies remains the same though. Polar diagrams assume there is no current, so the bottom and the water are static with respect to each other. However, if I were to use a polar diagram for navigation and there was current, it would skew the diagram.

For navigation, the Polar diagram has a relative motion with respect to ground, and a such gets skewed.

 

I'm not sure anyone would recommend the use of Polars for navigation.

 

To calculate ETA. It is pretty standard.