Have you performed any tests that lead you to believe the speed can be
greater than by putting the fan at the stern?
That is, will the fan in the front blowing over the sails increase
speed more than when it is at the rear and not blowing over the sails?
Bob Clark
Here's another way to look at the scenario. Suppose you had your giant
fan on a raft with no sail or keel. This raft is connected to the
sailboat by a rope. Suppose this rope initially is slack. You turn on
the fan directed towards the sailboat. The wind produced by the fan
allows the sailboat to move forwards by tacking into the wind. The raft
and fan also move forwards separately due to the momentum thrust of the
fan. The instant the rope is about to become taut you turn off the fan.
When the rope tightens, the sailboat will get a higher speed because of
the forward momentum of the raft. The raft will also be pulled backward
but it won't affect the forward speed of the boat as long as it does
not contact the boat. You make the rope long enough so this doesn't
happen. Once the rope is slack again. You turn on the fan again. The
process repeats.
You see the result will be that the sailboat will wind up having a
speed due to *both* the wind produced by the fan acting on the sails
and from the momentum thrust produced by the fan.