# Balance, Part II

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 sailing

We 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.

Figure 1. CE and CLR positions.

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.

Figure 2. Aligned CE and CLR positions in heeled equilibrium.

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.

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).

The guess we might make about the position of the CLR is just that, a guess. If we do not have access to powerful Computational Fluid Dynamics (CFD) and Velocity Prediction Program (VPP) software and a super-computer, we are left with the modeler’s state of the art, cutting out the profile view of the underwater hull shape and balancing it on a pin. Can we turn our guess into an estimate, using software to simulate the pressure distribution around a hull, keel, and rudder assembly, towing tank tests to calibrate our simulations, and further fudge-factor calculations to correct for wave drag? Claughton, et al (2013) say we can, and we’ll look at their claims shortly, but currently no one can calculate the actual lead that properly trims a design until it is on the water and sailed.

## In a gust

This 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.

Figure 3. Further heeling in a gust moves the CE abeam and effectively aft.

## In a lull

In 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.

Figure 4. Reduced heel in a lull moves the CE inboard and effectively forward.

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?

## Quiz

Take 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.

Figure 5. Canoe body heeled at 15 degrees with internal ballast.

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 experiment

Pierre 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.

Figure 6. Pierre Raynaud’s IOM in the swimming pool.

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.)

Figure 7. Heeled canoe body luffing paths for various angles of heel.

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 moment

It 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.

Figure 8. Luffing (pitch) moment generated by a heeled hull which otherwise shows no lift component.

## Conclusions

A 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.

Figure 9. Heeled, rigged, and helmed—it is all about moments.

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.

Following on from the 1903 flights at Kittyhawk, the theory of flight was sewn up by the mid-1920s. The only new theories appeared with supersonic flight in the late 1940s. Today any airplane can be designed, and it’ll fly to within 1 percent of its predicted performance. But we still can’t determine, from the drawing board, the balanced mast position to within 10 percent LWL, though an experienced designer with a history of practical experience with a family of past hull lines for a particular class should be able to do better, within 2 percent, say.

Perhaps those using CFD to look at the forces and moments on a heeled, yawed, and moving hull, appendages, and rigs are able to make more exact calculations, and we might finally be able to position a rig on a hull with some confidence about the resulting balance.

## References

Claughton, 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)

Garrett, R (1996). The Symmetry of Sailing: The Physics of Sailing for Yachtsmen. Sheridan House.

#### Acknowedgements

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