## Keels and Rudders: How they work and why they stop working

The keel and rudder of a sailing boat are there to resist sideways forces when the boat is sailing on anything other than a run and to steer the boat. They do this by generating sideways forces from the water flowing over them, the sideways force is usually called “lift” because it’s generated in the same way that an aircraft wing makes lift, even though in a boat the keel and rudder are vertical so the lift goes sideways…

In this article we’ll look at how this lift force is generated, how it changes depending on the way the boat is sailed and how this affects a boat’s performance. We’ll use this knowledge to look at some practical situations where the boat doesn’t do what you want it to and see how to change the way the boat is sailed to make it behave.

There are lots of different designs of keel, centre board, centre plate, dagger board and rudder. We’ll use the word “foil” as a general term to refer to any of these (technically they are all hydrofoils, foils working in water, but it’s common to shorten this to just “foil”. An aircraft wing is an aerofoil, a foil working in air). We’ll call the foil who’s primary purpose is to stop the boat going sideways the keel and we’ll look at a single keel, all of the other options (centre board, wing keel, dagger board, bilge keels etc.) work in the same basic way. Fortunately the different sorts of rudder design are all called rudders.

## Generating Lift

A foil generates lift using energy from the fluid that it’s moving through (or that’s flowing over it). Both an aircraft wing and a boat’s foils move through a fluid (air or water) but for a description of how they work it’s easier to think about the foil being stationary and the fluid flowing over it, they’re just different points of view.

Although aircraft wings are generally shaped to be more curved on top (the direction that you normally want the lift to be in) a wing with a symmetrical section will also fly and a normal aircraft wing will fly upside down (generating lift in the opposite direction to normal). This works because as well as the wing’s shape, its angle of attack determines how it generates lift. This is important for us because boat foils generally have a symmetrical cross section, we want them to generate lift equally well to port or to starboard depending on the situation. So a foil with a symmetrical cross section generates lift by being set up to have an angle of attack to the fluid flow.

As well as generating lift a foil generates drag. This is a force dragging it backwards (in the same direction as the fluid is flowing over it).

We won’t go into the details of generating lift here (NASA have lots of information about how wings work, also the late Jef Raskin’s article Coanda Effect: Understanding Why Wings Work is thoroughly recommended, as well as being an interesting discussion of how the received wisdom can be wrong). For our purposes the important points are that for a given foil:

- The amount of lift is proportional to the angle of attack (up to a point). So within reason if you double the angle of attack you double the lift.
- There is a limit to how much lift you can generate at a given speed. If you increase the angle of attack too far the foil stalls and the lift it generates decreases dramatically.
- The amount of lift is proportional to the square of the speed. So if you double the speed you get four times the lift.
- Drag also increases in line with the angle of attack (up to the stall point). This is in addition to the basic drag on the foils and hull from moving through the water.
- When a foil is stalled is produces a lot more drag then when it’s not stalled.

### Getting an Angle of Attack

We’ve seen that a foil generates lift from its angle of attack. For a rudder it’s easy to see where this comes from, if we want to turn to port we need the rudder to push to starboard and we do this by moving the tiller to starboard (or the wheel to port) so that the rudder is at an angle to the water flowing over it. We can control how strong the rudder pushes by how far we move it away from amidships.

What about the keel? In some boats we can move it up and down but we can’t angle it from side to side so how does it get an angle of attack? The answer is leeway.

When a boat is sailing on anything other than a dead run the force that the rig is generating can be resolved into a driving component in line with the boat and a sideways component at 90 degrees to the boat. This sideways force it what the keel is there to resist. The sideways force makes the boat slip to leeward as well as going forwards, to the boat actually travels at a small angle downwind of its heading (we’ll call this the leeway angle).

To make things clearer lets twist the picture around so that the direction through the water (in other words the direction that the water is flowing to the keel) is horizontal.

Now we can see that relative to the water flow the boat’s leeway has given the keel an angle of attack. The angle of attack is exactly the same as the leeway angle, so if we’re making 5 degrees leeway then our keel has a 5 degree angle of attack to the water flow.

### How much leeway?

When the boat is sailing at a steady speed all of the forces in it are in balance (this is Newton’s first law, if all the forces are in balance they add up to zero so the boat carries on at a steady speed).

The sideways force from the rig is balanced by the lift from the keel. If the keel is generating less lift than the sideways force from the rig the boat will slip across track more quickly (the force from the rig accelerates the boat sideways). The increasing sideways speed increases the leeway, which increases the angle of attack and so increases the lift from the keel. Eventually the leeway builds up to the point where the lift from the keel balances the sideways force from the rig and the forces on the boat are back in balance.

If the lift from the keel increases (for example if the boat speed increases) then the boat is accelerated back the other way, decreasing the leeway and lift until everything is back in balance again.

So we can see that the leeway angle is determined by the sideways force from the rig balancing against the lift from the keel. For a given boat speed the boat will settle on a leeway angle that gives just the right amount of lift to balance the sideways force from the rig.

The boat’s speed through the water is determined in much the same way. The driving force from the rig accelerates the boat forwards and as the boat speed increases the drag caused by moving through the waters goes up. When the speed gets to the point where the drag balances the driving force the boat stops accelerating and settles at that speed. Of course a change in the driving force puts the forces out of balance and so changes the boat speed. In the same way a change in the drag changes the boat speed.

## Heeling Effects

The lift that a foil generates is perpendicular to its surface, if our boat is upright any lift generated by the keel or rudder acts horizontally. When we’re sailing it’s unusual for the boat to be absolutely upright, as the boat heels the lift forces from the foils move away from the horizontal.

We’re interested in generating a horizontal force from the keel and rudder, to look at how this changes with heel angle we use the fact that a force at an angle can be represented as the combined effect of a horizontal force and a vertical force.

From the diagram we can see that the angle between the lift force and the horizontal is the same as the angle of heel. The forces make a right angled triangle and the horizontal force turns out to be equal to the lift force multiplied by the cosine of the angle of heel. As the angle of heel increases the horizontal force decreases by the cosine of the heel angle (assuming that the lift force stays the same of course).

Here’s a table showing how the horizontal force from a foil depends on the angle of heel. The table shows the horizontal force as a percentage of the lift force:

Angle of Heel | Horizontal Force |

0 | 100% |

5 | 100% |

10 | 98% |

15 | 97% |

20 | 94% |

25 | 91% |

30 | 87% |

35 | 82% |

40 | 77% |

45 | 71% |

50 | 64% |

55 | 57% |

60 | 50% |

We can see that for heel angles up to 20 degrees or so the horizontal force is much the same as the lift force, but as the boat heels to 25 degrees and beyond the horizontal component of the lift force starts to fall off more rapidly. By the time the boat is over at 60 degrees only half of the lift force is going in the direction that we need (though by this point most skippers will be doing their best to de-power the boat!).

Looking at this the another way: If we need a foil to produce a certain sideways force then the more the boat heels the more lift the foil has to create to generate that sideways force. At small angles of heel (20 or 25 degrees) the difference is not significant but at larger angles it can be substantial.

### The Effect of Heeling on the Rudder

The lift from the rudder is used to turn the boat, and also to stop the boat from turning. This second point is important to remember when we’re sailing to windward with some weather helm. The person on the helm will be steering to leeward to keep the boat running straight. The more weather helm the boat has the more force is required from the rudder to keep it on track, and the force from the rudder depends on the boat’s speed and the angle of the tiller.

As the boat heels over the horizontal component of the rudder’s lift is reduced. If the weather helm and boat speed are constant then we need to increase the rudder angle to generate more lift so that the horizontal component stays the same. At 25 degrees of heel the rudder has to generate about 10% more lift than it did when vertical to produce the same tuning force, if we push the boat to 40 degrees we’re asking the rudder for 30% more lift.

Increasing the angle of heel also has the effect of increasing the weather helm. This needs more turning force from the rudder to counteract it just as the effective turning force it produces is being reduced. The result is that as the boat heels we find ourselves winding on more and more rudder to keep her running true. The rudder angle that we need increases more quickly than the table of horizontal force for heel angle would suggest.

Increasing the lift generated by the rudder also increases the rudder’s drag. So as we heel the boat we get more drag from the rudder for a given tuning force. Drag slows the boat down, and slowing the boat down increases leeway. Slowing the boat down also means that we need a bigger rudder angle to generate the lift that we need.

As the boat heals we’ve got three effects adding up to make life hard for the rudder; the increasing heal reduces the horizontal component of the rudder’s lift, it increases weather helm which the rudder needs to produce more lift to counteract and the increased rudder angle increases drag, slowing the boat and requiring a bigger rudder angle to produce the same amount of lift.

If we sail with a lot of weather helm then we’ll need a big rudder angle to keep the boat running true. As well as being tiring for the helmswoman this slows the boat down. Taking steps to reduce weather helm, sorting out the sail trim or putting a reef in, will make the boat much more pleasant to sail and will often make it sail faster, a double win!

### Twin Rudders

Modern racing boats like open 60s have wide, flat sterns. This style is beginning to appear in some cruiser-racer designs, particularly in smaller boats. When a boat like this heels over the middle section of the stern (looking from behind) can start to lift out of the water. With a single rudder this means that at large heeling angles some of the rudder is out of the water where it’s not doing any good at all, so the force available from the rudder is reduced even more. Many boats of this design get around this problem by having twin rudders canted outwards a little. As the boat heels the windward rudder lifts out of the water but the leeward one is nicely submerged .At the same time the heeling of the boat has brought the rudder into a more vertical alignment so its lift is closer to horizontal, this helps to allow for some of the loss of lift from the airborne parts of the windward rudder.

### Heeling and Leeway

Now lets have a look at how heeling affects leeway.

As a boat heels over, the horizontal component of the keel’s lift is reduced. The keel is balancing the sideways force on the rig and if this isn’t changed by the increase in heel then the keel will have to produce more lift to balance this force. Moving the keel away from vertical also changes the way that it meets the water and has the effect of reducing the angle of attack for a given leeway angle, so to produce the same amount of lift the angle of attack must increase. These two effects add up so that at a constant speed increasing heel will increase leeway. The effect is small at small angle of heel but starts to increase above 20 degrees or so.

We can change the angle of heel in steady conditions by the way that we trim the sails. If we over sheet when sailing to windward then we’ll increase the angle of heel and so make more leeway. In fact with the sails over sheeted there will be less drive from the rig so the boat will slow down and the leeway will increase even further. With increased leeway and less boat speed our progress to windward will be much worse.

An increase in wind speed will also make the boat heel more as a result of the increased sideways force. The boat will make more leeway both because of the increased heel and because of the greater sideways force. At the same time the increased force on the rig will generate a greater driving force, speeding the boat up. An increase in boat speed increases the lift from the keel, reducing leeway.

The two effects work against each other, which one wins depends on how far the boat is heeling, the shape of its stability curve, the efficiency of its rig and how close it is to displacement hull speed. These parameters vary from boat to boat and from day to day so it’s difficult to make predictions but in general:

- At large angles of heel a boat will be sailing quite inefficiently so further heeling is likely to increase leeway.
- At small angles of heel a properly trimmed boat will be sailing efficiently so the speed increase from a gust will normally win and progress to windward will be better.

## Stalling

Back at the start of this article we said that the lift produced by a foil increases in proportion with its angle of attack up to a point. That point is the stall angle, beyond which the angle of attack is so large that fluid can’t bend quickly enough to follow the top surface of the foil so it breaks away into turbulent flow. When a foil is stalled the amount of lift it produces is much less than it was just before the stall angle and the turbulent flow over its top surface produces a lot of drag. A stalled foil produces little lift but lots of drag.

The stall angle depends on the design of the foil. Also some foils go from generating lift to being stalled quite suddenly while others stall more gradually.

Once a foil is stalled it is necessary to reduce its angle of attack to get it generating lift properly again.

### Rounding Up

Sailing to windward with the boat well healed can generate a lot of weather helm. We’ve already seen that to counteract this and keep the boat running true it’s necessary to use a lot of rudder angle.

As the weather helm increases we need to increase the rudder angle further and further and eventually we get to the rudder’s stall angle. When the rudder stalls most of the sideways force it was generating disappears, leaving little to counteract the weather helm, so the boat will turn to windward. If there was a lot of weather helm and the rudder stalled suddenly this can be quite a sudden course change. Even with a more gentle stall the boat will turn uncontrollably to windward.

Once the boat has turned itself into the wind the power from the rig is reduced and the boat will settle back to more or less upright. The weather helm is dramatically reduced and we can get the boat back under control and sailing again. If it was not just a one of gust that caused the boat to round up it’s sensible to reduce sail before getting under way, otherwise we’re likely to find ourselves rounding up uncontrollably again.

In a close quarters situation an uncontrolled rounding up can be just what you don’t want, potentially leading to a collision or grounding, so it pays to be careful not to push the boat too hard and not to put potential hazards close to windward on a gusty day.

The boat rounds up because the rudder has stalled and the weather helm turns it to windward. If the crew act quickly it’s usually possible to recover by de-powering the main sail, either travelling it down or letting the main sheet fly, then re-powering the sail once the boat is back on course. On a gusty day this can be an exhilarating way to sail, playing the main traveller in the gusts. On the other hand on a long beat this rapidly becomes tiring and reducing weather helm by de-powering the boat is the better option. Often the boat will sail faster anyway with reduced heel, so consider putting a reef in if it starts to get over powered.

### Stalling out of a Tack

Sometimes, especially on a light wind day, we go through a tack then find that the boat gets stuck with very little boat speed not answering the helm. The boat seems to have turned more than enough to have made it through the tack but with the tiller hard down (wheel hard to windward) it refuses to come back up to close hauled. What’s happened is that we’ve stalled the keel.

Going through a tack the boat will naturally lose some speed because there’s no power to drive it while it is going through the wind. If the helmsperson straightens up as the boat gets to close hauled on the new tack the boat may not be going quickly enough for the keel to generate the force required to counteract the sideways force from the rig. We know that in this situation the leeway angle increases, but if the boat is going too slowly the leeway angle increases all the way up to the stall angle without the keel generating sufficient lift so the keel stalls. The ends up making a lot of leeway, sufficient for the drag from the slalled keel to balance the force from the rig, so it its track through the water is significantly downwind of its heading.

The boat will settle with its heading some way downwind of close hauled so the natural reaction of the helmsperson is to try to turn hard to windward. Because of the large leeway angle this actually puts the rudder more or less in line with the water flow so it has little effect and the boat carries on slipping sideways.

For many boats this stalled keel position is quite stable. If the boat turns further downwind the water flow starts to meet the rudder on its windward side, turning the boat back towards the wind. If the boat turns upwind the water flow starts to come from the leeward side of the rudder, turning the boat back downwind. So the boat settles into the stalled position, making a lot of leeway and not much progress.

Stalling the keel normally happens on light wind days when the boat is going slowly. This is because at a given angle of attack the lift that the keel generates is proportional to the square of the speed. If the yacht is making 3 knots close hauled but drops to 1 knot following a tack then the lift from the keel for a given leeway angle is reduced by a factor of 9 (from 3 squared to 1 squared). If we were making 5 degrees leeway at 3 knots we would need 45 degrees leeway at 1 knot to generate the same sideways force, that is well beyond the stall angle of a yacht’s keel. On a windy day the boat will be travelling faster and although it will lose speed through a tack it will normally still come out with sufficient speed to keep the keel working properly.

### Recovering from a Stalled Keel

To recover move the rudder back to amidships. The water flow now meets the rudder at an angle from the downwind side, creating lift to windward and so turning the boat downwind. This turns the boat more into line with the water flow, reducing the angle of attack of the keel and bringing it out of the stall. With normal water flow re-established over the keel there is much less drag on the boat so its speed can build up, at the same time the turn downwind gives more driving power from the rig which also helps to re-build the boat speed. As the boat speeds up it can be gently brought back onto the wind. With good boat speed the keel is now able to generate the lift required at a reasonable leeway angle and the boat will sail close hauled.

### Avoiding Stalling the Keel

A better solution is not to stall the keel in the first place, here’s how to tack a boat on a light wind day:

Start by carving the boat through the tack in a steady turn to carry as much way as possible, if you slam the rudder hard over to tack quickly the large rudder angle will generate lots of extra drag and slow the boat down which is exactly what we want to avoid. Once through the tack let the boat come through past close hauled and onto a close reach before straightening up. On a close reach the keel will not need to generate as much lift as it does when close hauled so it is less likely to stall, also the close reach will generate more drive from the rig to help to get the boat back up to speed. As the boat’s speed builds up gently bring the heading back up to close hauled and you’re off again.

## The Problem with Pinching

All sailors should know that pinching (sailing above the best close hauled course) when sailing to windward is bad. Let’s use our knowledge of how keels work to put some numbers on a typical example to see why pinching is bad.

In a typical cruising yacht we could be making 5 knots close hauled with our heading at 40 degrees to the true wind. On this course lets say that we’re making 5 degrees of leeway, so our ground track is at 45 degrees to the true wind. This gives us a velocity made good (VMG) to windward of 3.5 knots.

Now we’ll pinch up by 5 degrees so our heading is 35 degrees to the true wind. The sails are not driving properly because we’re sailing above close hauled so our speed through the water will fall, lets assume we lose a knot so our boat speed is now 4 knots. With less boat speed there is less lift from the keel so the boat needs to settle on a larger leeway angle to maintain the same amount of lift. Remembering that lift is proportional to the square of speed the leeway needs to increase by the ratio of the old speed squared to the new speed squared, which is 5^2/4^2 or a factor of 1.6 in this case. This gives us a new leeway angle of 8 degrees (5 * 1.6) and a ground track that is 43 degrees to the true wind.

With a ground track at 43 degrees to the true wind and a water speed of 4 knots our VMG to windward is 2.9 knots. In this example pinching has cut 17% off our VMG.

Our example used quite a small leeway angle, in other words assumed a boat with an efficient deep keel. In a more conservative boat with a less efficient keel we may be making something like 7 or 8 degrees leeway close hauled. For a boat making a heading of 40 degrees to the true wind 7 degrees leeway gives us a ground track that is 47 degrees, pinching up by 5 degrees and dropping speed from 5 to 4 knots increases the leeway to 11 degrees so our new ground track becomes 47 degrees, only one degree better for a 20% loss of boat speed.

The amount that the leeway increases depends on the ratio of old speed to new speed, or in other words the percentage of speed that we lose by pinching. Losing a knot from 4 knots boat speed is worse than losing a knot from 5 knots boat speed. On a light wind day it is tempting to pinch a little to try to point a little nearer to the destination, in fact if the boat speed is already low any loss from pinching is going to have a greater effect so in these conditions it is even more important than ever to keep a good boat speed.

## Reducing Drag Improves Pointing

As a boat moves through the water a drag force is generated that tries to slow it down. The force depends on how quickly the boat is going and on how “slippery” the boat is. For a given driving force from the rig the boat will go faster if it generates less drag (because the boat settles at the speed at which the power from the rig is balanced by drag on the boat).

We saw that pinching decreases boat speed and increases leeway, giving a double loss in progress to windward, if we can reduce drag then the boat speed increases and the leeway reduces, giving a double gain in progress to windward.

How much drag a boat generates at a particular speed (how slippery it is) depends on the size and shape of the hull and fins, the smoothness of the surface finish and the drag of any other components, particularly the propeller if the boat has an inboard engine (if your boat is driven by an outboard engine then I hope you’re lifting or stowing it when you’re sailing). We can’t do anything about the shape of the boat (except possibly lifting the keel/centre board up off the wind in some boats), but we can do something about the other items.

On any boat that’s kept in the water the most significant effect on surface finish is marine fouling, that is all of the algae, barnacles and so on that grow on the hull. Fouling spoils the surface finish of the hull, breaking up water flow and increasing drag. On the foils fouling has an even worse effect, as well as increasing drag the disrupted water flow reduces the amount of lift that the foil generates. This means that a boat with heavy fouling will suffer more, going to windward, than we would expect from just the loss in speed. With the keel working less well and the boat going slower than normal leeway will be particularly bad. The moral is, if you want to keep a boat sailing well make sure that you keep the level of fouling down.

The other significant contribution to drag when sailing is the propeller. A folding or feathering propeller will have significantly less drag when sailing than a fixed prop (well the extra expense has to be for something!). The makers of these props claim speed improvements of anything up to a knot, which can make a significant difference to the boat’s performance, especially to windward. Here’s an example:

A boat with a fixed propeller is making 4 knots boat speed with a heading 40 degrees off the true wind and is making 5 degrees of leeway. This gives it a ground track that is 45 degrees to the true wind and a VMG to windward of 2.8 knots. If we take a more conservative claim of half a knot speed improvement with a feathering/folding prop fitted the boat should make at least 4.5 knots in these conditions, which will reduce the leeway angle to 4 degrees. At 4.5 knots this gives a VMG to windward of 3.2 knots, the combination of improved speed and slightly higher pointing has given a 14% improvement in velocity made good to windward.

As is often the case out of site shouldn’t be out of mind when it comes to the underside of a boat. Taking care to chose the right anti-fouling, maybe a mid-season scrub or fitting a lower drag propeller will all improve the boat’s performance. Even if you never race, keeping the boat in a state that lets it sail close to it’s potential makes every voyage that little bit more rewarding.

Geweldige zeilcursus van Jim, hij kent de kneepjes van het vak en weet dit goed over te brengen!

**Matthijs**Cursist