Provided there is no ambient wind (i.e. a perfectly calm day), will a wind turbine attached to the deck of a coal burning megayacht that is traveling in some fixed direction at 20 knots generate electric power as if the wind speed was 20 knots (due to the motion of the ship)?
Do you see any practical applications, or do they already exist (if so what are some of them), of wind turbines being attached to ships?
Yes, the wind turbine will generate electricity as if it were a 20 knot wind. It will also create more drag, forcing the ship to burn more fuel to maintain its 20 knot speed. What you end up doing is inefficiently converting coal power into electricity.
I can’t see any practical benefit of doing this on a ship, but there are some practical applications of this sort of thing. Airplanes for example have what is called a “ram air turbine” or RAT which is generally only used in emergencies, but it takes the wind speed of the aircraft and converts some of that energy into electricity (again, sacrificing drag to do so). Under normal operation, things like hydraulics get their power from the plane’s engines. If the engines fail, you would lose hydraulics (and some other things) which would make the plane very difficult to control. To prevent this from happening, if the engines fail the RAT goes into use and provides emergency power to the hydraulics and other necessary systems.
Here is the wikipedia page for the ram air turbine:
It seems like it would make more sense to have the coal used to power a fan to blow on the turbine. You could then take the electricity that the turbine produced and use it power a flashlight pointed at a solar panel.