# Why does a stiff boat rudder produce forward thrust when pumped left to right?

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• Jurgen M

#### Jurgen M

In small sailing boat like optimist is well know technique when there is no wind, rudder pumping which push boat forward.You just need push-pull rudder left to right with fast movement.

1) Rudder is stiff(not flexibile like flippers for diving),so why rudder produce forward thrust if high and low pressure around rudder switch each time when rudder passes center line position so thrust component of resultant force change direction from forward to backward all the time. From looking pressure distribution it seems boat must stay on place, thrust= zero.. Can you explain forward thrust with pressure distribution around rudder?
Please don't explain rudder thrust with Newton 3 law, rudder push water back-boat goes foward becuase, action-reaction is too simple and don't explain how pressures/net resultant force around rudder produce thrust.

2) If rudder is flexibile like flippers for diving, will it produce more thrust because and why? I think it will, because in every position of pumping reslutant force will point more forward..
Also what is ideal "pump angle"(angle from left to right swing) of rudder movement to produce max thrust?

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Please don't explain rudder thrust with Newton 3 law, rudder push water back-boat goes foward becuase, action-reaction is too simple and don't explain how pressures/net resultant force around rudder produce thrust.
Just because it is simple doesn’t mean that it is wrong, and in fact Newton’s third law is the answer: If water is pushed backwards the boat will be pushed forward.

Your diagram is confusing you because you’ve placed the pivot point in the center of the rudder. With that design we can see from symmetry that there will be no net movement of the water and hence no net force (note below). However that’s not how real boats (at least those that can be propelled by thrashing the rudder) are designed; with the rudder post off-center both the left and right strokes will displace water in the same direction to produce a net force.

(Note - the symmetry is not perfect unless the rudder post is also in the center of a symmetrical hull. I’m ignoring these hull effects because you’re not considering them either, and because they complicate the analysis without providing any additional insight into the physics involved)

bob012345, russ_watters and pbuk
Just because it is simple doesn’t mean that it is wrong, and in fact Newton’s third law is the answer: If water is pushed backwards the boat will be pushed forward.
When rudder rotate when resultant froce point slightly forward(produce thrust), must be different pressure compare to part where resultant force point backward.Othervise boat will stay at place.
I can't find this pressure imbalance...that is point of question

Your diagram is confusing you because you’ve placed the pivot point in the center of the rudder. With that design we can see from symmetry that there will be no net movement of the water and hence no net force (note below).
You are mixing hiking stik with rudder

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When rudder rotate from 1 to 2 is pressure field at him 100% identical compare when rudder rotate from 2 to 3?
If yes, why boat move forward?

(For my logic from 1 to 2 rudder produce thrust, in position 2 thrust is zero, from 2 to 3 rudder produce force in backward direction/drag)

In position 2 thrust is zero, becuase pressure act prependicular to surface,so rudder here produce side force...

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When the rudder is far left or right, the water is trapped inside the angle between the rudder and the stern. Maybe this creates a jet of water in the direction shown:

If this is true, then clearly the X-component of the reaction force will push the boat forward.

The question remains, "what about the force on the rudder?". Well, if the water is indeed trapped then it also exerts pressure on the stern, just as gas trapped in a rocket's combustion chamber. But pressure acting near the vertex of the angle is NOT balanced since it's opposite side is open.

When the rudder is far left or right, the water is trapped inside the angle between the rudder and the stern. Maybe this creates a jet of water in the direction shown:
View attachment 305400
If this is true, then clearly the X-component of the reaction force will push the boat forward.

The question remains, "what about the force on the rudder?". Well, if the water is indeed trapped then it also exerts pressure on the stern, just as gas trapped in a rocket's combustion chamber. But pressure acting near the vertex of the angle is NOT balanced since it's opposite side is open.
Stern don't look like this in reality so there is no water trapped between stern and rudder.
Even if you move ruder 2m from stern (with some beams) to exclude affects of " trapped water", boat will still move forward..

The correct answer was given in #2. It is nothing to do with "trapped water" (this is not a thing) and forget about pressure: the boat goes forwards because water is propelled backwards.

the boat goes forwards because water is propelled backwards.

This is true, but must be some pressure imbalance to achieve that.
Action-reaction don't comes from nowhere, must be surfaces where this "force" act, boat is in fluid so we are talking about static pressures at rudder sides to explain net force which obviusly point slighlty forward and produce thrust that move boat forward.

Also what is ideal "pump angle"(angle from left to right swing) of rudder movement to produce max thrust?
With a rigid rudder, perfect timing and unlimited torque the optimum angle would be 180°, however in practice things are not perfect so this must be found by trial and error according to the particular boat and wind and sea conditions. In practice you can also achieve more thrust by heeling the boat from side to side which changes the optimum angle.

2) If rudder is flexibile like flippers for diving, will it produce more thrust because and why?
Yes in theory this would produce more thrust for the same reason that flippers for diving are flexible. If you want to ask this, start another thread.

If I may, let me make another attempt

Let's think about how it would work if there was no water flow away from the boat, and then that may help figure out why there is such a flow.

If we try to imagine no net rearward water flow, we have to imagine the water being pushed clockwise and anticlockwise in an arc along with the rudder. But that would require some centripetal force, and there is none (at least neglecting viscosity). So maybe we can loosely say that centrifugal force drives the water away from the boat, whether the rudder moves clockwise or anticlockwise.

Edit: This doesn't quite explain the original question, because it doesn't tell us how the reactive force is actually tranfserred back to the boat. But it could be a good point to start thinking.

This doesn't quite explain the original question, because it doesn't tell us how the reactive force is actually tranfserred back to the boat.
Yes this is point of my question.

This is true, but must be some pressure imbalance to achieve that.
Action-reaction don't comes from nowhere, must be surfaces where this "force" act, boat is in fluid so we are talking about static pressures at rudder sides..
Don't shout.

View attachment 305399

When rudder rotate from 1 to 2 is pressure field at him 100% identical compare when rudder rotate from 2 to 3?
If yes, why boat move forward?

(For my logic from 1 to 2 rudder produce thrust, in position 2 thrust is zero, from 2 to 3 rudder produce force in backward direction/drag)

In position 2 thrust is zero, becuase pressure act prependicular to surface,so rudder here produce side force...

It seems you understand why water is pushed backwards in the movement between 1 and 2 so there is no need to confuse yourself any longer about this. Your question is actually "why is less water propelled forwards in the movement between 2 and 3". The answer to this is that the movement between 2 and 3 is slower, maintaining laminar flow over the rudder so that it "cuts through" the water rather than pushing it forwards.

If I may, let me make another attempt
With respect, I think it is probably best not to.

This is true, but must be some pressure imbalance to achieve that.
Centrifugal force would be rearward only.

Centrifugal force would be rearward only.
Yes centrifugal force push water reward all the time.

Rudder when moving from 2 to 3, where is high pressure side and where is net force pointing?

Do you agree with my pressures fields and resultant force?
(red arrow is resultant force)

Yes centrifugal force push water reward all the time.
Then you have an explanation for the forward thrust. Now the challenge is to apply that understanding in the inertial frame.

One thing to consider is the momentum of the water that you are deflecting. At the end of a stroke from 2 to 3 (as the rudder moves from center to the right and comes to a stop). You have this slug of water that is moving rightward. As you bring the rudder to a stop and then reverse, this slug of water is deflected rearward.

The key is that the water is not just a viscous medium that resists the rudder with a coefficient of drag. It has mass. You cannot just look at rudder velocity. You have to look at acceleration. Which is 90 degrees out of phase with velocity.

Rudder when moving from 2 to 3, where is high pressure side and where is net force pointing?
When moving from 2 to 3 the high pressure side is at the front of the rudder and there is a component of force that is slowing the boat down. However because the flow is (more) laminar than it is when moving from 3 to 2 the pressure differential is less and so this slowing down force when moving from 2 to 3 is less than the speeding up force when moving back quickly from 3 to 2.

Then you have an explanation for the forward thrust. Now the challenge is to apply that understanding in the inertial frame.

One thing to consider is the momentum of the water that you are deflecting. At the end of a stroke from 2 to 3 (as the rudder moves from center to the right and comes to a stop). You have this slug of water that is moving rightward. As you bring the rudder to a stop and then reverse, this slug of water is deflected rearward.

The key is that the water is not just a viscous medium that resists the rudder with a coefficient of drag. It has mass. You cannot just look at rudder velocity. You have to look at acceleration.
Look at my post 18, I can't understand how rudder produce thrust when moving from 2 to 3 because pressure fileds don't allow that..
Please talk with pressures not action-reaction.

Action reaction is explantion for kids, don't tell nothing.

Look at my post 18, I can't understand how rudder produce thrust when moving from 2 to 3 because pressure fileds don't allow that..
It doesn't produce (rearward) thrust, look at my post #20.

It doesn't produce (rearward) thrust, look at my post #20.
So we all agree that rudder produce drag(even if push water backward) from 2 to 3 ?

Yes of course it produces drag, and it doesn't push water backward from 2 to 3 (water is allowed to flow backward in this stage).

Yes of course it produces drag, and it doesn't push water backward from 2 to 3 (water is allowed to flow backward in this stage).
I think rudder push water back, becuase of centrigfugal force...

I think rudder push water back, becuase of centrigfugal force...
I don't think that, and I don't think that thinking about (presumably a reactive) centrifugal force is helpful here.

Look at my post 18, I can't understand how rudder produce thrust when moving from 2 to 3 because pressure fileds don't allow that..
It works. So pressure fields must allow that.

Please talk with pressures not action-reaction.

Action reaction is explantion for kids, don't tell nothing.
Then translate action reaction to pressure fields. And see if the explanation becomes richer as a result. And do not forget the momentum field.

I don't think that, and I don't think that thinking about (presumably a reactive) centrifugal force is helpful here.
No, dammit, It is not a reactive centrifugal force. It is a centrifugal force that is responsible (in the rotating frame) for the net rearward motion of the water. Since the motion is rearward and is real, there must be a reaction force somewhere. One just has to chase it down -- if one cares.

If the name is important, that is a "centripetal reaction force".

Oh, I find that way of looking at it rather confusing because water is also moving backwards due to the forward motion of the boat.

For me it is simple (and perhaps helped by the fact that I was doing this less than 18 hours ago, after the end of the race of course) - pull back hard towards the centreline to push water backwards and create forward thrust, then ease the rudder away from the centreline without stalling to set up for the next thrust whilst creating as little drag as possible.

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... At the end of a stroke from 2 to 3 (as the rudder moves from center to the right and comes to a stop). You have this slug of water that is moving rightward. As you bring the rudder to a stop and then reverse, this slug of water is deflected rearward...
Here is a simplified situation that (I hope) contains the essential features of the rudder case, capturing what jbriggs444 says. We have a tube immersed in water and "wagged" around an axis near one end.

In jbriggs' view, when the tube changes direction (either from CW to CCW or from CCW to CW) the water in the tube exerts a reactive force on the wall, which has a "boatward" component during both changes of direction.

This makes sense to me as one possible contributing factor -- but is it the only source of an average push driving the water along the tube?

If we rotate the tube uniformly in one direction, say CW, the above mechanism would be out of action. But I'm guessing that centrifugal action would still propel the water through the tube.

But even as I was composing this post (hoping to prove that centrifugal effects also contribute to propulsion), I realized that the centrifugal ejection of water would not result in an opposite backward reaction, because that is just the water "refusing" to be accelerated along a circle and "insisting" on moving along a tangential straight line -- so this can't contribute any propulsion to the boat!

jbriggs444, pbuk and Lnewqban
I really don't want to enter this discussion. But I just want to point out that the physics of this topic are the same as the sculling method of propulsion.

bob012345
Consider that when the rudder is deflected, the pivot point moves sideways, which makes the hull of the boat deflect some in opposite direction to the rudder.
That creates areas of higher and lower pressure on both sides of the boat, which eventually start moving water from high to low pressure zones.
Not the natural and fluid movement of a fish, but not as effective neither.

https://thefishingwire.com/the-physics-of-fish-movement/

Delta2, pbuk and anorlunda
For me it is simple (and perhaps helped by the fact that I was doing this less than 18 hours ago, after the end of the race of course) - pull back hard towards the centreline to push water backwards and create forward thrust, then ease the rudder away from the centreline without stalling to set up for the next thrust whilst creating as little drag as possible.
I agree. I have done the same thing. There is a technique that involves non uniform movement of the tiller. You push harder when the tiller is to one side and pushing forward. It's not just waving a piece of wood under water.

It also works much better with a simple rudder hung on the transom and not with a nearly balanced rudder.

Since the motion is rearward and is real, there must be a reaction force somewhere.
But where is this reaction force,I can't find it?

I agree. I have done the same thing. There is a technique that involves non uniform movement of the tiller. You push harder when the tiller is to one side and pushing forward. It's not just waving a piece of wood under water.

It also works much better with a simple rudder hung on the transom and not with a nearly balanced rudder.
What do you say, is rudder produce thrust or drag when move from position 2 to 3?