Sailing directly into the wind - designing the best rotor

The diagram above shows a section through the blades of two different wind turbines, or rotary sails, used to propel at boat or land vehicle
directly into the wind that powers it. 3a is a large area blade set at about 45 degrees. 3b is a small area high-speed blade set at an angle of
about 70 degrees. The vector lines show the magnitude of forces and in what direction. "Lift" is always at 90 degrees to the plane of the aerofoil
surface. Because of the angle of the blades in relation to the the rotation axis, the lift produced has two components.

A portion of the lift drives the turbine round (the driving force).
 Whilst the other portion opposes the movement of the craft against the wind. (The retarding force).

Obviously, to get the best performance going directly into the wind - you need to maximise the driving force and minimise the
retarding force.

Comparing the two kinds of setup shown in the diagram.

As can be seen, although the blade in fig3a produces less lift than that in 3b (because of the lower speed) the driving force is
greater than in 3b. Also, the retarding force in fig 3a is less than the retarding force in fig3b. Therefore, the forces shown
in fig3a result in a driving force greater than the retarding force (which is what you want for going directly into the wind). Whereas in
fig3b the driving force is less than the retarding force (which results in being unable to go directly into the wind).

To summarise:
 The rotor giving the most power is not necessarily the best for driving into the wind, because if the angle of the blades is more than
45 degrees to the oncoming wind, the lift produced overcomes the drive produced, and results in a force pulling the craft back.

See also: Why a turbine rotor blade set at 45 degrees cannot go faster than the wind.
And: Why producing a vertical autogiro and trying to penetrate the wind does not work very well.