by Lester Gilbert
We started our consideration of Balance in the “Part I”
article of Issue 187 and found that changes of in- and out-wedge areas for a
heeled hull had anecdotal support for predicting balance in practice, but there
was no rigorous evidence. In this final article we’ll look at the “standard”
theory of how the centers of lateral hull resistance (CLR) and aerodynamic
effort (CE) should be arranged, and we’ll finally review an experiment that
shows why these theories are inadequate.
Theory of sailingWe know that the sails are like airplane wings, giving lift that drives the boat forward and heels it over. The aerodynamic sail force is considered to act through the CE (center of effort) of the sail plan, roughly one third of mast height above deck and (depending on the ratio of foresail to mainsail area) somewhat forward of the mast.
We know that the keel, the rudder, and to some extent the
hull are like wings that, using the boat’s leeway, resist the side force of the
rig moving the boat sideways. The hydrodynamic hull force is considered to act
through the CLR (center of lateral resistance), which (very roughly) for an IOM
is 40 percent of draft and some distance aft of the fin quarter chord.
Our discussion of balance and helm is focused on yaw and
hence only on the forces acting in the horizontal plane—in plan view—and will
ignore the forces acting in the vertical plane, involved with the righting
moment and heel lever. When the boat is sailing in equilibrium, the aerodynamic
and hydrodynamic forces are in balance. In order to be in balance, the
aerodynamic force acting through the CE must align, in plan view, exactly with
the hydrodynamic force acting through the CLR, as illustrated in Figure
2 for a boat which is sailing nicely
heeled at, say, 25degrees. It is clear from Figure
1 that, in the vertical plane, the
aerodynamic and hydrodynamic are completely offset and form a heeling couple,
opposed by the righting moment of the hull and ballast.
Although we may not know it, when we trim the boat to sail
the course we want, sailing theory tells us that we are arranging the position
of the CE (raking the mast, twisting the sails, setting the sheeting angles) and
the CLR (setting the rudder angle) so that the forces acting through them “line
up and are equal.”
The estimate we might make about the position of the CE is
usually quite a good one (but it’s still an estimate), because we have very good
theories of flight, which give good results for aerodynamic forces. It remains
an estimate because we cannot calculate, exactly, how much the CE moves, given a
change in the foresail twist measured at the upper batten from, say, 5 to 10
degrees. We would have a good chance of calculating it if the foresail was a
hard wing sail, but it is soft, thin, and takes up shape in different ways
depending on (for example) wind speed, construction, and age.
Mast-to-fin “lead”In practice, everyone knows that the mast must be positioned forward of the keel. This is called “lead” [think "lead the dog towards the rabbit", not "cast the bulb in lead"]. This ensures that the CE aligns with the CLR (Figure 2), because the CE is somewhat aft of the mast. For a Bermuda rig, builders and sailors know the mast must be stepped somewhere between 3 and 10 percent LWL forward of the fin leading edge (and as low as 1.5 percent for an IOM).
In a gustThis theory of sailing tells us that, when the boat luffs up in a gust and bears away in a lull, it must be because the CLR has moved so that the hydrodynamic force no longer lines up with and is equal to the aerodynamic force. You will probably be familiar with the various intricate vector diagrams that illustrate the forces and moments of a heeled sailing boat and the effects of movement of the CLR.
Figure 3 shows the
standard theory of forces when a gust hits. The boat heels to, say, 45 degrees
and the additional heel moves the CE further abeam and thus aft of the line
where it balances the CLR. The forces are now offset, resulting in a yaw moment
to weather. Correcting this requires weather helm, and it is said that the helm
moves the CLR aft so that the hydrodynamic force acting through it, again, lines
up with the aerodynamic force acting through the new CE.
In a lullIn a lull, the reduced heel of, say, 5 degrees moves the CE inboard and thus forward of the line where it balances the CLR. The forces are now offset, resulting in a yaw moment to lee. Correcting this requires lee helm, and it is said that the helm moves the CLR forward so that the hydrodynamic force acting through it, again, lines up with the aerodynamic force acting through the new CE.
But theorists eventually admit their apparently rigorous
analysis completely fails to predict balance characteristics in practice. The
theory of sailing, probably best outlined in Garrett (1996) for the emphasis
placed on the balance between aero and hydro forces, is descriptive but not
predictive. What’s wrong?
QuizTake your yacht. Take away the sails, remove the mast, and all rigging. Take away the keel and the rudder but place the ballast inside the hull so it doesn’t tip over. You are left with the canoe body.
Impart some forward motion to the canoe body, so she moves
straight ahead without leeway. What is her heading and course? Now, move the
ballast to one side so the canoe body heels over at, say, 15 degrees
(illustrated in Figure 5), and push her
off again. How has her heading and course changed, if at all?
Pierre Raynaud’s experimentPierre answered the quiz with an experiment. To give his IOM hull some drive, he mounted an electric flight motor and aero propeller low on a stub mast, and an offset container with some ballast at the top of the mast. The arrangement is shown in Figure 6, where the de-rigged boat is heeled to port.
The hull was heeled at 10, 20, and 30 degrees and driven
along at about 1 m/s, similar to the speed that might be seen in an IOM
close-hauled in a 4 m/s breeze. The boat luffed up, that is, she turned away
from her direction of heel just as she would if she were carrying sail and were
caught in a gust. This is illustrated in Figure
7, where we see that the luff trajectory was increasingly tight
(decreasing radius) with increased heel. (Note that the fin and rudder were in
place, but this was for convenience; we have towed a hull in a towing tank
without fin and rudder and have reproduced these findings.)
Did you guess that when you answered the quiz? It turns out
that almost anything that could be considered a hull will, when heeled, turn up
towards her weather side. Experienced
dinghy sailors know this, as do most canoeists, kayakers, and motorized
small-craft sailors. This inherent behavior of a heeled hull shape is
unaccounted for, however, in the current “standard” theory of sailing when the
hull heels due to the action of the wind while sailing. In particular, there
seems little prospect of calculating the magnitude of the luffing moment from
the shape of the hull or the hull sections. We need to look elsewhere.
Airfoil pitching momentIt is known that a heeled hull provides some contribution to hydrodynamic lift in proportion to its leeway. We can see that the heeled waterplane has an airfoil section, and in some sense the hull is a very short–span, blunt wing. As well as generating lift, a wing has a pitching moment. What is interesting is that, as long as the wing is moving through a fluid, at zero lift, the wing still has a substantial pitching moment. This is illustrated in Figure 8, where the high pressure at the bow, coupled with the low pressure to weather, shows how the luffing (pitching) moment occurs. The heeled hull follows its camber line curve, and perhaps this is the luffing moment we saw in Pierre’s experiment.
ConclusionsA heeled hull when underway luffs strongly to weather. When rigged, [mast] lead is required so the offset aerodynamic force can provide an opposing torque and keep the boat on course. Helm doesn’t move the CLR; it provides the adjusting moments needed to hold course. This is illustrated in Figure 9.
No one knows how to calculate the hull’s luffing moment from
the lines plan or any other drawing board element. Well, perhaps this
conclusion might not be true; perhaps
those who know might not be telling us.
ReferencesClaughton, A, Pemberton, R, & Prince, M (2013). Hull-Sailplan balance, “lead” for the 21st Century. (www.hiswasymposium.com/assets/files/pdf/2012/Claughton%20HISWA%202013.pdf)
AcknowedgementsGraham Bantock gave valuable comments on an earlier draft. The remaining errors are all mine.
©2023 Lester Gilbert