How Does A Rudder Help In Turning A Ship?

Have you ever wondered why all ships have their rudders placed at the aft of their propellers? Why isn’t a rudder placed at the bow (forward) of the ship? Or for that matter, why is it always placed behind the propeller? Just imagine a ship with a rudder at its bow. Wouldn’t it look ugly? Well, we naval architects are least bothered about that, when it comes to ship design practices.

The first priority of any ship design, is the achievement of function-ability of the designed product, and then comes its aesthetic value. Rudders are placed at aft, instead of at the bow, not because of aesthetics, but because of its hydrodynamic efficiency when placed at aft. Not quite versed with that term? Read on..

rudder

To understand this, we need to delve into the mystery of the role of a rudder in a ship. Did you know that a rudder does not turn a ship? Yes, you read it right. So how does a ship turn, then? And if not the rudder, then what is it that turn’s the ship? Let’s for the entire article henceforth, assume a starboard turn. Which means, the rudder is moved to the starboard side. When the helmsman changed the rudder angle from zero to some angle towards the starboard, at that very moment, a lift force acts on the rudder. The direction of the lift force is towards the port side, as illustrated in Figure 1.

ship rudder
Figure 1: Rudder force on a ship with rudder to starboard

This rudder force, as you can see, is directed along a transverse direction to the ship. In other words, this force will cause the ship to attain a sway velocity towards the port side, because the rudder force is nothing but a sway force towards the port side. It is because of this, a ship will sway slightly to the port when the rudder is turned over to hard starboard. But this sway is so negligible in comparison to the turning moment towards starboard, that the sway is hardly felt. But yes, the sway does occur.

Other than this, the rudder force has another effect on the ship. It creates a moment about the centre of gravity of the ship, in the direction as shown in Figure 2. (To understand why is the moment directed in the direction shown, apply simple law of translation of a force into a moment about a point, or look at it like this- the centre of gravity of the ship is forward of the rudder, and given the direction of the rudder force, the moment it will create about the C.G will be along the direction shown).

Rudder moment when rudder is moved to starboard
Figure 2: Rudder moment when rudder is moved to starboard

Imagine the size of a rudder in comparison to the size of the ship. The rudder is incomparably smaller to the size of the hull that is to be turned by it. So, how does the rudder turn the ship? Well, as we saw before, the rudder doesn’t turn a ship. In fact, the rudder moment created by the rudder, is negligibly small to turn the ship by the required heading angle. If that’s the case, then what is it that turns the ship?

When the rudder moment acts about the ship’s centre of gravity, it slightly changes the ship’s orientation by giving it a drift angle (illustrated in Figure 3). This moment is not large enough to turn the ship to the required heading angle, but all a designer has to do, is make sure that the rudder moment is enough to introduce a slight drift angle into the ship’s movement. The ship, with that drift angle, is now moving along the initial direction. But this isn’t pure surge anymore. Follow Figure 3, and you’ll see you can make components of the ship’s velocity along the surge (longitudinal) direction and sway (transverse) direction. Thus, it’s evident, that by introducing a drift angle, the rudder has introduced a small surge velocity to the ship. Notice the direction of this surge velocity in the figure below. Doesn’t it reinforce the reason behind why there is a small sway towards the port side during a starboard turn?

rudder of vessel
Figure 3: Drift angle due to the rudder moment.

What happens after this, is what makes the ship turn. To understand the mystery behind the turning of a ship, let’s not focus on the surge velocity here. The prime focus should be on the sway component. Because, that sway velocity component, is what changes the hydrodynamics around the ship’s hull to cause it to turn. Follow Figure 4 as you read further. This figure focuses on the effect of the sway velocity and how it turns the ship.


With a sway velocity towards the port side, the hull sways towards port. When it does so, it exerts a force on the water particles that are in its port side. The water particles in turn, exert an opposite force on the ship’s hull, due to the inherent inertia of the water particles. The direction of this inertia force is always opposite to the sway velocity, since inertia force always opposes motion. So, the ship’s hull experiences an inertia force on its hull in the starboard direction. Now, this force can be categorised into two.

One, the part of it that acts on the stern of the ship (Inertia force at stern) and the other half acting at the bow (inertia force at bow). Follow the figure below, and you’ll visualize that the inertia forces at stern will create an anticlockwise (towards port) moment about the centre of gravity, whereas the bow inertia forces will create a clockwise (towards starboard) moment about the centre of gravity. Now, the hull is designed such that the sway inertia forces at the bow is more than that at the stern, therefore the resultant moment is towards the starboard direction as shown in Figure 4.

ship and rudder
Figure 4: Hydrodynamic moment due to sway velocity

What’s important to know here is that when the hull exerts force on the water around it, during its sway velocity to the port, the inertia force exerted by the water on the hull tries to achieve an equilibrium, which means, the magnitude of the inertia force is in the order of the ship’s displacement. It is that large, a force. So, when the resultant hydrodynamic moment acts on the ship, its magnitude is in the order of the ship’s displacement. This moment (unlike the moment cause by the rudder force alone) is sufficient enough to turn the ship. But as you can see, this hydrodynamic moment wouldn’t have come to play, had the ship not attained a drift angle or a sway velocity component, which was mainly due to the action of the rudder. This, is enough to justify, that the rudder does not turn the ship. It only initiates a drift angle in the ship, which results in a hydrodynamic moment, which is actually the driving force behind the turning action.

The hydrodynamic moment, is in the same direction of the rudder moment (both trying to turn the ship to starboard). The rudder angle keeps the rudder moment intact, which in turn, keeps the hydrodynamic moment intact. Once the rudder is again brought back to midships, first the rudder force vanishes, which results in the diminishing of the rudder moment. It is only after that, the drift angle is reduced to zero, and the hydrodynamic moment becomes zero, therefore thwarting the turning action. It is due to this indirect linking of the rudder to the turning action, that ships are sluggish when it comes to manoeuvring with rudder action.

The resultant moment diagram for a ship performing a starboard turn is as shown in Figure 5 below.

ship rudder
Figure 5: Moments acting on a ship during starboard turn.

Coming to what does this entire theory have to do in relation to the positioning of the rudder behind the ship. Well, if you didn’t know of the above, it was impossible for you to even imagine like a designer, i.e. why a rudder is placed behind the ship. Now that you are aware of the real physics behind a ship’s turning, here is why a rudder is always placed at the aft:

  • The rudder, when turned to starboard, creates a force towards the port (which we named, the rudder force). Note the direction of rudder moment that was created about the CG by the rudder force. The direction of the rudder moment was towards the starboard (so as to create a drift angle towards the starboard). Now imagine placing the rudder at the ship’s bow. Given a starboard angle to the rudder, the rudder force would still be in the port direction. But what about the moment about CG? Visualise this – The rudder moment would be towards the port, causing a drift angle towards the port, and the net hydrodynamic moment would cause the ship to turn to port. Whereas, you turned the rudder starboard for a starboard turn. See the problem?
  • There’s another reason why rudders are never placed at the bow. It is to protect the rudder from collision damages. But this however, isn’t a primary reason. The primary one, is what you just read above.
  • Lastly, why is a rudder always placed behind a propeller? Well, the propeller does nothing but increases the velocity of the water that flows out of its slipstream. And the lift generated (rudder force) is proportional to the velocity of water falling on it. So if a rudder is placed at the aft of the propeller, the increased velocity of the propeller outflow results in a greater lift force. It is only for this reason that a rudder is placed aft of the propeller. However, if a rudder is placed just forward of the propeller, it will have the same turning effect with respect to direction, but the magnitude won’t be the same, given the fact that the flow on the rudder is not as much as it would have been, had it been placed behind the propeller slipstream.

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15 Comments

  1. <<>>

    If the above is correct, by designing the hull such that the sway inertia forces at the bow is less than that at the stern, you should be able to turn a ship to port side by turning the rudder starboard! Shouldn’t you? But what ever the hull design is, when a ship in motion turns its rudder to starboard, she always takes a turn to starboard only!

  2. One, the part of it that acts on the stern of the ship (Inertia force at stern) and the other half acting at the bow (inertia force at bow). Follow the figure below, and you’ll visualize that the inertia forces at stern will create an anticlockwise (towards port) moment about the centre of gravity, whereas the bow inertia forces will create a clockwise (towards starboard) moment about the centre of gravity. Now, the hull is designed such that the sway inertia forces at the bow is more than that at the stern, therefore the resultant moment is towards the starboard direction. If this is correct, by designing the hull such that the sway inertia forces at the bow is less than that at the stern, you should be able to turn a ship to port side by turning the rudder starboard! Shouldn’t you? But what ever the hull design is, when a ship in motion turns its rudder to starboard, she always takes a turn to starboard only!

  3. Well, ships use to move in a specific media:water and usually in a specific direction:advancing front and this is the reason for the rudder location
    There is a possibility of locating them aft but with a screw propeller in aft the productivity will decay

  4. as per the above explanation it seems that if the ship is at rest i.e. zero velocity and hence zero inertia then it would be difficult to turn a ship when it is just starting to move because in that case the net hydrodynamic moment would be very less.

    just want to confirm my understanding is right or wrong ?

  5. For Hemant, I present the following: a ship just beginning to move, under power, will actually turn surprisingly fast, in relation to forward travel, for her screw has had to impart velocity to the column of water in reaction to which, the ship’s inertia must be overcome in order for movement to commence. In that the ship’s momentum at bare steerage is an inverse squre of that at higher speed, its radial inertia is less, so that the lateral component of force from the deflected water column is proportionally stronger in its effect. Likewise, the dynamic pressure of the water, passing the hull on either side, is less. At the same time, the steering factor we did not mention, namely the curvature of the waterline at the bow, has a pronounced hydrodynamic effect: as the rudder moment offsets the bow to the side of its original track, the lateral component of force from the water ahead, becomes slightly greater on the one side than the other, and the relative path of water particles on that side becomes longer. Pressure builds and the ship’s bow continues to fall off course. As momentum instntaneously follows the new course, the offset commences anew, and water pressure, bow offset, and momentum force the turn, as the hull seeks linear equilibrium. Furthermore, ship’s mass and momentum, versus water pressure, cause the ship to heel outboard, wetting more surface on one side than the other, drifting the ship in the direction of the turn, each instant that it aligned on a new track. So even at low speed, although her turn seems slow, for her length of travel, it is quite fast.

  6. This was so informative for a female like me, who didn’t understand the function of the rudder properly. Thank you.

  7. After reviewing this article, I have to applaud the author for tackling the very complicated subject of ship maneuvering. But I believe the presentation misses some of the finer points of rudder design. I am a professional naval architect, with a Master’s in Engineering. My studies included ship maneuvering, and I would add the following explanation to enhance this article.

    There are two questions posed in this article: what causes a ship to turn, and why place the rudder at the stern? First, I will address what causes a ship to turn.

    To consider ship turning, there are a whole list of forces that act on a ship which you have to consider. For steering, these forces help a ship to turn
    1. Rudder
    2. Hydrodynamic inertia

    The rudder and hydrodynamic inertia help turn the ship. This is largely what is described in the article. But don’t discount the rudder. It produces a very big turning moment. When you consider moments, you have to think of the force and its distance to the center of gravity on the ship (which is usually close to midships). It is true, the hydrodynamic inertia is quite large. But that inertia acts on the ship very close to the center of gravity. It has a small moment arm. The rudder is all the way at the stern. It has almost half the ship length for its moment arm. Take an example of a typical 300 m long ship. The hydrodynamic inertia will have a moment arm of 5-10 m. But the rudder has a moment arm of almost. 150 m. That is a 15x larger length to work with. This makes the rudder more important than hydrodynamic inertia. Small forces can produce big moments if you give them a large moment arm.

    This is why the rudder is the important player. It has to be. Because that hydrodynamic inertia is not as reliable as you think. It’s exact location changes, depending on several conditions. A vessel with aft trim will push the hydrodynamic inertia farther aft. The speed of your vessel changes its location. And hull shape has a major effect on hydrodynamic inertia. For example, there are double ended ferries which are completely symmetric longitudinally. Their hydrodynamic inertia is practically centered right on the center of gravity. It does little good. But the ship still turns, because of the rudder. That is the point of the rudder: We designed it to create a strong force that will not change location depending on vessel conditions.

    So why place the rudder in the stern? That is because the rudder has two jobs:
    1. Make the ship turn.
    2. Keep the ship going in a straight line when not turning.
    The second job is why we put the rudder at the stern. This is what we call course keeping. The fancier term is directional stability. Consider this: a ship is traveling along and gets its bow pushed to starboard. Say a wind pushed it. In a ship with good directional stability, that wind will cause the ship to turn slightly, and it will continue in a straight line. On a new heading, but still in a straight line. All without the helm ever changing the rudder. If the ship has bad directional stability, it will continue to keep turning, spiraling out of control. We don’t see this in reality because no captain wants to let their ship spiral out of control. A halfway decent helm control (autopilot or sailor) can compensate for bad directional stability. But they should not need to. A ship with good directional stability will almost steer itself.

    So how does a stern rudder make for good directional stability? It all comes down to relative water velocities. Imagine a ship with forward velocity. Something pushes on its bow and starts it turning to starboard, with the rudder locked dead center. Now think about the water velocities back at the rudder. The rudder sees the forward velocity of the ship. But it also see a sideways water velocity going from port to starboard. When it sees that water moving from port to starboard, the rudder generates lift in the starboard direction. This creates a turning moment to port. That turning moment fights against our initial starboard turn, until the ship finally stops turning. No turn means no sideways velocity at the rudder, and the rudder stops turning. Placing a rudder at the stern means the ship is always directionally stable. Towed barges are an excellent example of this. Towed barges have skegs on their stern. The skeg acts like a rudder locked dead center. It keeps the barge towing in a straight line and makes for an easy tow. If the barge has no skeg, or too small a skeg, the tow will wander back and forth.

    There are several other reasons to put the rudder at the stern. Here are all the reasons I can think of:
    1. Directional stability
    2. Generates lift from the propeller stream at low ship speeds. This gives you some control at low speeds.
    3. Puts all the big machinery at one end of the ship, with the engine room. This saves on maintenance spaces and makes it easier to arrange the cargo holds in the rest of the ship. There are plenty of exceptions to this rule. But it is still a good rule of thumb. Rudders take hydraulic lines or power lines. They can be pretty big. As a designer, I would rather not make space to drag those lines all the way across the ship.

    You can actually test these ideas with a few simple experiments yourself. You will need:
    1. Styrofoam block
    2. Thin strip of wood (balsa works best) for a rudder
    3. Electric hobby motor
    4. Hobby propeller
    5. Battery pack
    6. Sand paper
    7. Glue
    8. Wooden dowel

    Use the Styrofoam block and sand paper to make a simple ship hull. It doesn’t need to be perfect. Just give it a pointy bow and a raked stern. Sand the surfaces and round all the edges to make it smooth like a ship. Next cut the wood into the shape of a rudder. A simple rectangle shape works. Just keep it roughly to scale with the rest of your ship. (Don’t put it in the ship yet.) Cut out a space for the motor and battery pack. Test your ship in the water and make sure it floats with the weight of the motor and battery pack. Now it is time to do some tests.

    Test 1: Don’t put the rudder in. Leave the battery pack and motor out. Use the wooden dowel to push sideways on the ship. Did the ship rotate? Which direction? Try pushing at different longitudinal points on the ship model. See if you can find a position where the ship only moves sideways and does not rotate. That is the center of hydrodynamic inertia. Mark that spot. Now try moving adding battery pack to the ship. Push on the same spot and you will notice the ship turns again. That was because the battery pack moved the ship’s center of gravity. (The battery is much heavier than the Styrofoam.)

    Test 2: Add the rudder on the back of the ship. Push it up into the Styrofoam with some glue and allow the glue to dry. Leave the battery pack and motor out. Drill a vertical hole in the center of the ship at the same longitudinal position that you marked. Drill vertically down from the main deck. (Don’t drill through the ship.) Now set your ship floating and put the dowel in the vertical hole. Anchor the dowel to something. This will allow the ship to rotate, but not move sideways in sway. No sway means no hydrodynamic inertia. Now take your hobby motor and propeller. Use them to blow water at a 45 deg angle across the rudder. Be careful to hit the rudder only, and not the rest of the ship hull. You should see the ship start to rotate. But there is no hydrodynamic inertia, because the dowel stops the ship from moving in sway. So from this experiment, we see that the rudder is the major player in making a ship turn.

    Test 3: Take the dowel out. Put the motor and battery pack in your ship. Find a nice calm pool of water. A swimming pool works best, with no one in it. Turn on the motor and let the ship go. Did it spiral off to one side? Go in a straight line? Try taking out the rudder. Then how did the ship perform? Experiment with different rudder sizes and locations. Maybe you can make the ship go in a straight line. This will be hard with a model because it is not an exact science. Another trick to try: put two rudders on the ship and give them both a slight initial angle. This way, they oppose each other and always create a stabilizing force.

  8. In shallow water, the TC is larger: Is it bcz of less water flow due to less ukc and as a result the rudder force is lesser which results smaller drift angle ?

  9. Thank you Nicholas Barczak for your extensive reply. Thanks also Soumya Chakraborty for the original post. There are a few other questions in my mind that I want to answer:

    1. I’m told by a captain friend that the pivot center of a ship moves forward with ship’s velocity. He says it starts out at the center of mass at 0 velocity but moves forward, and quite substantially, as forward velocity picks up. He also says that the pivot center moves aft with astern velocity. Why this happens and how far it moves is still a puzzle to me. Must have to do with the transverse pressure distribution on the ship set up by turning the rudder and thus the sideways velocity.

    2. If the rudder is turned, the ship starts to turn in a circle. When the ship is turning around in a circle, orbiting a point at a fixed rate, there has to be a centripetal force pointing exactly at the center of the turning circle. It’d be interesting to consider where on the hull and how that steady sideways force is generated. Is the ship’s longitudinal axis tangent to the turning circle, so that it cleanly slicing around in a circle? Or is the ship always skidding a bit? I suspect it is the latter, in order to set up the athwart pressure distribution on the hull that makes the ship turn.

    3. When airplanes were invented, the first inventors assumed that turning the plane would be done by a rudder, just as it was on a ship. But it turns out that rolling the airplane is what causes it to turn. Same is true with a bicycle: you don’t turn it by turning the handlebars, except at low speeds. You roll into the turns. It wasn’t by chance that bicycle mechanics (the Wright brothers) figured out how to turn an airplane. On a plane, the rudder is just a secondary control that keeps the tail behind the plane and prevents the plane from skidding or slipping. It would be really interesting to compare the turning mechanics of a ship and a plane. Also throw in there a car, because a car isn’t rigidly connected to the ground; the tires deflect, so that the forward motion of the car is somewhere between the longitudinal axis of the car and the angle into which the front wheels are pointed. Anyway, it’d be real nice to write a technical paper to compare just turning of different kinds of vehicles.

    4. My captain friend, mentioned above, told me how he gets to know a particular kind of ship, gets to know how the pivot center moves with velocity, and he uses this knowledge or feel when manoeuvering a vessel next to a dock. He said he even has developed this feel for the dinghy he uses to go back and forth to his sailboat. He’s always docking it, and he’s developed the feel for its motion forward and aft, so that he can bring it alongside a dock. It would be nice also to write some type of manoeuvering guide for vessels based on the discussion here. It’d contain information like this, for example: “For vessels of this particular type, to manoeuver them alongside a dock, you need to do such and such. You go forward a bit, then aft, and thus you can make the stern of the vessel approach the dock in this fashion and be attached to the dock with a stern line. Then you do such and such to get the bow to come in…” It would be cool to have a dynamic model of some or several common vessels where this could all be proved out. We could try this out in a bridge simulator, supposing that the models have been verified for this manoeuver for the real ship.

    5. My captain friend also tells me that when you come out of a turn, you actually have to put in counter-rudder to get the ship to quit turning. If you just put the ship’s rudder to center, you keep turning. This must be because of the hydraulic inertia mentioned above. He also says that the turning radius for a ship in shallow water is greater than that in deep water. This must be because the ship moving through the water is not just the ship. It imparts velocity to a mass of water around it. It is this continuing movement of the surrounding water that the ship continues to turn even after the rudder is centered. And it must be the friction of this surrounding moving mass with the bottom that makes turning harder in shallow water. It’d be cool to have an explanation of that.

    Anyway, quite amazing that a simple, longitudinal floating object with a hinged flap could set up something so complicated.

  10. The first reason listed for not having a rudder on the bow makes zero sense. Obviously, you would need a rudder at the bow to simply rotate the opposite way of a rudder at the stern to achieve the same turn.

    As you said, the third reason isn’t really a driving design consideration.

    So, left with only the second reason (loss of propeller slip stream), can we consider the possibility that a rudder placed at the extreme forward end of the vessel might provide a better turning moment per angle of rudder turn than a rudder at the stern? With this more efficient Turning Moment/Rudder Angle ratio, might we compensate for the loss of the propeller slipstream?

  11. Hello,

    In your diagram you show the ship rotating around the C of G about Midship. Surely a ship rotates around her pivot point which, when going ahead is about 1.3 distance from the bow?
    I would also like to know your comments regarding the effect on the ability to turn when you introduce a 1.5 knots current acting mid-ship along the starboard side andthe ship suddenly looses power during the turn

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