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.
LeewayWhen 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.
Downwash from the keelNow 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 theoryHoerner (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.
Flow around a hullMarchaj 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.
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.
Keuning experimentsMarchaj’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.
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.
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
shows a graph of Keuning’s results, and there are a couple of points that are
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.
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.
Estimating “minimum drag” weather helmThe 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.
Rudder separationDownwash 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.
Keel downwash using Keuning dataEquation 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:
SkegThe 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.
ClassesWe consider four different classes and their typical aspect ratios and rudder separations, as shown in Table 1.
Estimating leewayTo 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.
Estimating weather helmUsing 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.
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
ConclusionsNaturally, you may be rather sceptical by this point. Five degrees of weather helm gives minimum rudder drag? Seriously?
ReferencesA. 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 (www.hiswasymposium.com/assets/files/pdf/2006/Keuning@hiswasymposium-2006.pdf)
AcknowedgementsGraham Bantock gave valuable comments on an earlier draft. The errors are all mine.
©2023 Lester Gilbert