Weather helm (AMYA MY #182)

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Weather Helm

by Lester Gilbert


On the pond, we know that the helm (the rudder angle we use) of a sailing boat can be adjusted by either moving the sail plan forward to reduce weather helm, or moving the sail plan back to increase weather helm. For many years, I thought I understood weather helm, and I thought I understood why most sailors want a little weather helm while sailing their boats. Let’s take a quick run through this conventional wisdom on balance and weather helm.


To begin with, we imagine an ideally “balanced” boat is one that sails her course “hands off” without any particular helm input, either weather or lee. We have probably heard other sailors telling us that the rudder is a device for creating drag, and that the boat makes her best speed if the rudder remains neutral. If we sail competitively, we have also heard the advice that a little weather helm is a good thing, however, because it allows the boat to positively react to a change of wind direction, and so we need to put up with this necessary evil in order to have a more responsive boat. Finally, we will have carefully changed our mast rake (or moved the mast) as the wind built or died during the day at an event in order to keep the boat “balanced,” probably with only some small weather helm.


You might have guessed by now that I’m going to tell you this is only a little bit right and all mostly wrong… Let’s see why.



When beating against the wind, we know that the boat resists the force of the wind, which is trying to push her sideways and off course. Old-time sailors might talk about the “grip” of the boat in the water. What is happening is that the boat, mainly the keel, pushes against the water and in doing so makes leeway. The result of the push, or the leeway, is a lifting force that keeps the boat more or less going where she is aimed. Not exactly where she is aimed, of course, because the leeway is the difference between the boat’s heading and her actual course. Generally the stronger the wind, the more the leeway, which is really just another way of saying that more lifting force is being generated by the boat to resist the stronger wind.


Leeway is like the angle of attack of a wing, and much as with a wing, the leeway of a keel is what generates the lift needed by the boat.


Downwash from the keel

Now this is the science bit. Whenever a keel (or any other device) generates lift, it also generates what is known as downwash, and anything behind it, such as a rudder, experiences this downwash as a change in the angle of the oncoming water. When the boat makes leeway, the keel is generating lift, and there is downwash behind the keel. This is one of the reasons it is not smart to sail close behind and to leeward of another boat. Your rig will be in the downwash of the rig of the other boat and your keel will be in the downwash of its keel.


Keel downwash in theory

Hoerner (1965) provides a theoretical formula for downwash behind a wing, given the coefficient of lift being generated by the wing and the wing’s aspect ratio, simplified and shown as Equation 1:



This classic result can be derived from the “momentum theory of lift,” explained in Momentum theory of lift.


A common choice when designing an appropriate fin for the keel of a boat is to require the fin to provide a coefficient of lift of 0.3 when the boat is heeled at 30 degrees. In this case, Eq. 1 suggests the resulting downwash behind a keel of aspect ratio 1 is approximately 5 degrees (if the constant is 18.2). What is interesting about this formula is the simple linear relationship between downwash and lift coefficient.


To connect the theory of Equation 1 with some of the experimental data that we will look at shortly, it is useful to know the connection between leeway and lift coefficient. A rough rule of thumb from basic aerodynamics tells us that the lift coefficient, for small angles of attack before stall, is approximately one-tenth the angle of attack. Airfoils develop about 0.1 lift coefficient per degree of attack, counting from the angle of zero lift. Using this rough estimate, if our keel has Cl = 0.3, say, then the boat is probably sailing with around 3 degrees of leeway.


Flow around a hull

Marchaj has a picture of keel downwash in his book, Aero-hydrodynamics, illustrated in Figure 1. The hull is heeled at around 30 degrees, as though it were beating on port, and is making leeway against the flow of water.



Figure 1.Underwater view, looking “up,” of flow around a heeled hull with leeway (based upon Photo 4.3 in Marchaj, 2000).


The flow indicators in Figure 1 are not as clear as they could be, but we can see that the rudder is more or less in alignment with the downwash at the stern of the hull. The rudder is not “neutral” in this situation, and we can see that it is showing what we’d call weather helm. If the rudder were “neutral,” it would not be aligned with the local flow of water. Instead, the local water flow would be acting to generate rudder lift so as to turn the hull into the wind, i.e., giving lee helm.


Figure 1 is our first suggestion that “neutral” helm is not the same as “no weather or lee helm” and is not the same as “minimum drag.” On the contrary, if we set up the boat to be “balanced” and have “neutral” helm, we have actually given it lee helm, and we have not set it up with the lowest possible rudder drag.


Keuning experiments

Marchaj’s picture of keel downwash is pretty clear that when we set “neutral” helm we actually give the boat lee helm, but we now need data to calculate downwash. Keuning and collaborators tested a model with different keels in a towing tank in 2006, looking at the downwash experienced by the rudder when the model was towed with some leeway. It is worth looking at their experiments in some detail. Figure 2 shows the profile outline of the model they used.



Figure2. Hull model (based upon Keuning et al, 2006).


Figure 3 shows the three keels that were attached to the hull for the tests. Keel “A” is the kind of high aspect ratio keel we might see on an International One Metre, while keel “C” is the kind of low aspect ratio keel we might see on an International A Class or a 36R.



Figure 3. Test keels and their geometric aspect ratio (based upon Keuning et al, 2006).


While Keuning towed the model upright and at 15 degrees heel, we’re going to look at the heeled data only. It turns out the upright data is pretty similar. The key point here is that Keuning measured downwash by moving the rudder until it gave zero lift, which is the point at which it gave minimum drag. The angle of the rudder was therefore the angle of downwash as experienced by the rudder. Figure 4 shows a graph of Keuning’s results, and there are a couple of points that are worth making.



Figure 4. Downwash experienced by the rudder for different keels at three angles of leeway, hull heeled at 15 degrees (based upon Keuning et al, 2006).


First, it is clear that high aspect ratio keels have less downwash. Second, the amount of downwash increases with leeway. But the relationship between leeway and downwash is a not a straight line; instead, they are approximately exponential curves, and an exponent of 0.5 (a square root) is a pretty good approximation.

The Keuning data suggests a quite simple formula for the downwash experienced by the rudder in their experiment:



Equation 2 paints a rather different picture about the relationship between downwash and lift. It suggests that, in practice, this relationship is not the theoretical linear relationship of Equation 1 but is a reducing exponential one, a square root.


The factor “1.34” in Equation 2 is merely an adjusting constant that matches the experimental results from the leeway and keel aspect ratios to the particular hull used, and we’ll improve this later on in the article.


Implications of downwash for “balance”

If we are sailing a boat that looks anything like Figure 2, then we can read off some of these numbers. For example, an A Class might make around 5 or 6 degrees of leeway in a blow, and with a keel aspect ratio (AR) not too different from 0.7, the expected weather helm is around 3 to 3.5 degrees.


In this example, a perfectly “balanced” boat sails with minimum drag at around 3 degrees of “weather helm.” That is usually considered to be a lot of weather helm, and if I felt I had to push that amount of rudder on the transmitter I’d be moving the rig forward very smartly! But wait! If you give your boat neutral helm and set it up so that it sails “hands off,” you in fact effectively give it lee helm (and you add drag) because the rudder is no longer aligned with the perfectly normal downwash from the keel. If you move the rig and position it to give your boat a little weather helm, just a touch like everyone tells you to do of around 1 degree, nevertheless you have still effectively given the boat lee helm and added drag.


Estimating “minimum drag” weather helm

The problem with our current radio control systems is that we cannot know and cannot feel what the rudder “wants to do.” When sailing full size, with a good breeze and good heel, you can feel the pressure on the tiller, and it tells you where there is least pressure—i.e., least lift (which is when there is least drag on the rudder)—and that is usually when it is some degrees off neutral or centered.

[Ed.  This is a vitally important point that can and should be experienced in practice.  Go and crew a full-size keel boat and helm it on the beat, well-heeled in a good breeze.  Heck, go and chat to keel boat owners and helms at your local sailing club.  This is your question: "On the beat, how far off the centre-line do you hold the helm to keep the boat balanced when well heeled and making best VMG?"]

Our task now is to estimate the correct amount of helm to expect for our radio-controlled model for minimum drag, and this is the same as estimating the downwash in the vicinity of the rudder.


The first part of this task is to estimate a general value for the amount of downwash the keel generates, and we can do that using leeway and the keel aspect ratio in Eq. 2.


The next part of the task is to estimate how much of the keel downwash is experienced by the rudder. Compare the relative distance between rudder and keel shown in Figure 1, and the relatively large separation between the rudder and the keel shown in Figure 2. In boats with the rudder closer to the keel we would expect the rudder to experience higher downwash than otherwise. We’ll estimate the adjustment to the downwash for rudder separation in a following section.


Then we may need to make an adjustment for any skeg in front of the rudder. Modern radio-controlled boats have all-moving rudders, but older boats and free sailing boats may have rudders hung at the end of a skeg.


Finally, we need some way of estimating leeway in order to calculate expected weather helm. Leeway is very difficult to determine just by looking at the boat sailing because common leeway angles for modern designs are so small. For an IOM it might be 1.5 degrees in a moderate breeze. But in the last section we’ll propose a solution based on heel, which is much easier to see.


Rudder separation

Downwash is due to lift, and is the manifestation of the circulation discussed in Circulation theory of lift. The circulation around a keel generating lift is considered to be centered on the keel quarter chord and has a given strength. As we move away from the center of lift, although the circulation has a constant strength, the actual downwash experienced naturally diminishes with increasing distance.


If downwash of, say, 7 degrees is seen 1 m. away from the keel, then we would expect to see downwash of 3.5 degrees 2 m. away, and so on. In this case, we could say that the strength of the circulation was “7,” and a rudder 0.5 m. away from the keel would experience 14 degrees downwash.


We can estimate the keel-to-rudder separation in the Keuning experiment as follows. Figure 2 shows Keuning’s “keel 1” fitted, and Keuning tells us this keel has a mean chord of 0.23 m. Some measuring with a ruler tells us that the center of lift of the rudder is thus approximately 1.09 m. away from the center of lift of the keel.


Keel downwash using Keuning data

Equation 2 estimates downwash for a rudder 1.09 m. away from the keel. We can adjust the formula so that it gives a “standard” downwash for a rudder at a “standard” separation of 1 m. Then, knowing the actual separation for a particular boat, we can estimate the actual downwash by dividing by the actual separation. This gives us the formula we will now use to estimate weather helm for a variety of classes as Equation 3:




The effect of the skeg needs some careful analysis, and what follows is a simple start, which is undoubtedly not completely accurate.


First we note that a skeg is used by free-sailing boats to improve directional stability.


Also, the effect of the skeg is to reduce (dampen) the effectiveness of the rudder. For example, an all-moving (no skeg) rudder angle of 3 degrees has very roughly the same effect as a skeg-mounted rudder angle of 6 degrees if the skeg has the same chord as the rudder.


For our purposes here (estimating the minimum drag rudder angle, which is aligned with the downwash experienced by the rudder) to a first approximation, we can ignore any skeg.



We consider four different classes and their typical aspect ratios and rudder separations, as shown in Table 1.



Table 1. Aspect ratio and rudder separation parameters for different classes.


Estimating leeway

To use Eq. 3 we need to know rudder separation, keel aspect ratio, and leeway. The first two are straightforward to measure, are strongly associated with a particular class of boat, and are shown in Table 1. The tricky part in using Eq. 3 is estimating the leeway a boat might make.


About the only easily observed visual indicator we have about a boat sailing, and about the lift being generated by its keel, is the amount of heel it shows. In general terms, the stronger the wind the greater the heel, and the stronger the wind the more lift needed from the fin and hence the more the leeway. So leeway and heel angle are closely connected. The problem we have is that if one boat has a wider beam than another it will show less heel; if one boat has a smaller fin that another, it will show more leeway; and so on for draft, ballast, and a number of other factors that get in the way of any simple relationship between leeway and heel. Our solution is to use a fudge factor.


In general, boats within most classes are broadly similar with regard to displacement, beam, and so on. What most distinguishes one class from another is the class rule restriction on draft, and where draft is restricted, boats will likely have lower aspect ratio, less efficient fins. And we know that less efficient fins need more leeway to generate the lift their boats need. Another way of saying this is that less efficient keels make more leeway, all other things being equal. So the fudge factor is to decrease estimated leeway in proportion to increasing AR for a given angle of heel. We’ll use the square root of the AR as our decrementing factor.


Modest angles of heel (up to, say, 30 degrees) are a function of the sail force, as is the required lift coefficient to resist it. Another way of saying this is that the lift coefficient, the angle of leeway, and the heel angle, are in linear proportion.


To give a starting point, we’ll say (pretty arbitrarily!) that a boat with keel AR = 1.0 gives 5 degrees of downwash when heeled at 30 degrees. (We mentioned this as a ball-park figure earlier, given by Eq. 1, where we considered that the keel was giving a lift coefficient of 0.3.) We’ll scale this by the square root of the AR of the class we are interested in, and then use Eq. 3 to estimate weather helm. The result is Figure 5.



Figure 5. Estimating leeway from heel for four different classes.


Estimating weather helm

Using heel angle as a proxy for leeway, and using our “square root of AR” as a fudge factor to convert heel angle to an estimate of leeway for different classes as shown in Figure 5, Figure 6 uses Eq. 3 to give us the estimated weather helm we are seeking.



Figure 6. Estimated “minimum drag” weather helm (downwash) depending upon heel for four different classes.


We can useFigure 6 to estimate the kind of weather helm we should deliberately set when adjusting our mast position for a given wind. For example, suppose we are sailing an IOM and go for a test sail. Imagine we find we are heeling at 18 or 20 degrees. From the graph, we can see that we should adjust mast rake (rig position) to give us around 1.5 degrees weather helm at the transmitter. More dramatically, suppose we are sailing an A Class and find she heels at 30 degrees—so we would set the rig to give 5 degrees weather helm at the transmitter. Of course, to do any of this scientifically, we will first have calibrated our transmitter so we know many clicks on the trim button correlate to one (or 5) degrees of rudder movement.



Naturally, you may be rather sceptical by this point. Five degrees of weather helm gives minimum rudder drag? Seriously?


The first conclusion is, well, yes, seriously: there is downwash off your keel that affects your rudder, and setting “neutral” helm in fact sets lee helm. That’s pretty clear.


But 5 degrees? Ah, OK, well, the second conclusion is that you’ll have to make up your own fudge factor to suit your boat and your preferred sailing style. You will have noticed that not even the experts can agree on the exact relationship between leeway and downwash at the rudder. Some think it a linear relationship; others think it an exponential. Have fun with that!


And what about the business of adjusting mast rake as the wind builds or dies, because we find our boat sails with increasing weather helm in the first instance or, worse, gains lee helm in the second? Well, this analysis suggests that you may need to adjust mast rake, but not for the reasons you thought, and not by the amount you’ve done previously. So our third and final conclusion is that the purpose of adjusting rake is to actually dial in a particular amount of weather helm needed by the boat and our sailing style according to the conditions. In many situations, it might mean leaving the mast where it is, because increasing weather helm with increasing wind is what the boat requires and does not need to be dialed out. What is therefore needed is a much more skilled, anticipatory, and sensitive thumb on the rudder stick. But I guess you knew that already!



A. Marchaj (2000). Aero-hydrodynamics. Adlard Coles.

S.F. Hoerner (1965). Fluid Dynamic Drag, Author.

J. A. Keuning, M. Katgert, and K. J. Vermeulen (2006). Keel—Rudder Interaction on a Sailing Yacht. In 19th International HISWA Symposium on Yacht Design and Yacht Construction, Amsterdam. Downloaded from (



Graham Bantock gave valuable comments on an earlier draft. The errors are all mine.


©2024 Lester Gilbert