Why flapping rudder produce net thrust if one half-stroke produce thrust and second half-stroke drag? In small sailing boat like optimist is well know technique when there is no wind, rudder pupming which push boat forward.You just need push-pull rudder stick left to right with fast movement.
Rudder works complety under the hull, so there is no pressure interaction between stern and rudder.
Forward half-stroke is when rudder rotate from centerline to left or right
(from 2 to 1 or from 2 to 3).
Why stiff rudder(not felxibile like flippers) produce net thrust if forward half-stroke produce drag?
(Or maybe forward half stroke produce thrust as well? I dont think so..)
Please explain your answer with pressures at rudder sides for two condition;

*

*boat speed zero


*boat is moving
Avoid Newton 3 law.


 A: I suspect it has nothing to do with regions of higher or lower pressure (if those even exist). When you pump the rudder you are pushing water backward and by Newton's Third Law that water exerts an equal and opposite force on the boat, pushing it forward.
A: Below the horizontal line is my original answer, submitted 5 hours ago, but there is a better explanation that I overlooked.
In a comment to another answer Gordon McDonald points out that since the rudder hinges right at the stern the rear edge of the rudder sweeps out a sector of a circle. That alone will tend to result in pushing water rearward. Most likely that effect is the main factor.



When the stiff rudder is moved side-to-side it creates vortices in the water. It could be that an overall effect of the side-to-side motion is to create pairs of vortices that are constantly being shed of the rudder edge.
Hypothesis:
The side-to-side motion of the (stiff) rudder tends to continuously create vortex pairs that detach from the rudder. The vortex pair extending from the rudder will tend to lag behind when the rudder is swung the other way, making the vortex pair act somewhat like a very short flipper. That would make the side-to-side motion of the rudder act as a very inefficient flipper.
A: I guess that during the forward thrust portion of the stroke the skipper pushes harder and faster creating more turbulence and drag and thus more thrust. During the reverse thrust part they slow down for more laminar flow and thus less drag and less thrust. So over one cycle the net impulse is forward.
But I also guess that the actual situation is more complex and involves more fluid dynamics.
A: The key point may be that stern of the boat moves laterally. During the first half of the stroke, the force exerted on the rudder by the water is forward and to the side. The sideways component causes the boat to rotate, so that, if you were to release the tiller and allow to rudder to align itself with the flow (which means, in the inviscid approximation, no net force on the rudder) the rudder would naturally continue past center, allowing it to reach the starting position for the return stroke without generating a backward force. The rotation of the boat eventually stops—let’s say a skeg provides some lateral resistance—and now you’re ready for the return stroke having produced some forward thrust and no backward force.
Of course, you wouldn’t actually let go of the tiller for the second half of the stroke, but by mimicking the motion you’d get if you did, it seems logical that net thrust could be generated.
