by Lester Gilbert
We touched on balance in the “Weather Helm” article of Model Yachting Issue 182 and thought that the topic deserved an article all by itself. In fact, it’ll run to two articles—Part I here, and Part II in the next Issue—because there is a lot to talk about.
To start, we need to improve the definition of
balance that we used. Most radio
sailors think a balanced boat is one that sails her course
hands off, but that is really a
definition of trim and not balance.
We make this distinction now, because we saw that a well-trimmed boat could (and
probably should) have some amount of weather helm, and so it must always be
sailed hands on, and we reserve the idea of balance for a boat that continues to
sail her course with minimal heading change when a gust or a lull comes by. The
idea of the boat behaving herself when in equilibrium we’ll call
balance is when the boat behaves
herself during a dynamic change of wind speed.
In- and out-wedgesWe take the sections of the upright hull, strike a heeled waterline, and compare the areas of the in-wedges with the out-wedges at each section. A section lines plan of a narrow-transom hull is illustrated in Figure 1, with an upright waterline and an estimated waterline for 15 degrees of heel defining the wedges.
The lines of the hull in Figure
1 show sections that are based on
circular arcs and that would be appropriate for a class such as the IOM, where
both the stem and the transom just touch the water. (I have a spreadsheet
that allows you to draw circular arc sections in a variety of ways and that
provides some of the graphs and calculations mentioned in this article.)
We can see in Figure 2
that the midsections immerse more volume on heeling (the shaded midsection
in-wedge is larger in area than the crosshatched, midsection out-wedge), while
both fore and aft sections immerse less volume (shaded in-wedges larger in area
than crosshatched out-wedges). Let’s take essentially the same lines, but now
have a wide-transom hull. The comparison of the in- and out-wedges is shown in
In this case, we see a somewhat different outcome in Figure
3, such that the fore and midsections
immerse more volume on heeling (the shaded in-wedges are larger in area than the
crosshatched out-wedges), while the aft sections immerse less volume.
Curve of wedge area changesWe can now draw a graph of the changes in immersion, section by section, and the results are illustrated in Figure 4 and Figure 5 for the narrow- and wide-transom hulls, respectively.
The COWAC (curve of wedge area changes) graphs of Figure
4 and Figure
5 are used to suggest which boats are
likely to be better balanced, and which boats are likely to be badly balanced.
As is customary in these articles, before proceeding, let’s have a quick
quiz—which hull would the COWAC graph say is better balanced?
Better balanced, please, not
better trimmed. Don’t carry on
reading! Pause and reflect…
The first issue, of course, is that the water surface does
not remain perfectly flat when the boat is heeled; if nothing else, the boat
must be moving in a reasonable breeze to heel at 30 degrees, and so the hull
will sit in its self-generated Froude wave, such that each section will have its
own unique waterline depending upon the local wave amplitude.
The second issue is that, while the hull as a whole might
rise a little on heeling, we would not expect it to continue sailing without any
pitch change. We would probably expect the hull to pitch bow-down, while
remembering there are some hulls that are known to pitch stern-down and lift
their bow when heeled, and again each section will have its own waterline.
The third issue is that, while a narrow-transom hull would
show less yaw in the same way as a heeling cylinder, a wide-transom hull will
yaw in the same way as a heeling cone. We can call this
slew, and it is illustrated in Figure
3 where, imagining the hull is sailing
towards you with the wind on her starboard side, you can see the bow-, mid-, and
aft-sections are offset. The angle of slew of our wide-transom design is
estimated at around 2.5 degrees at 30 degrees heel, and so, again, each section
will have its own waterline.
We are going to ignore these complications for this analysis and have our hull sailing upon a flat surface with no pitch change. We will include slew, but because our lines are arcs of circles, slew has no effect upon the calculations. If you wish to get serious, your naval architecture software will generate the right waterlines and COWAC graphs for you.
Conclusions so farThere are anecdotal claims of correlation between a COWAC graph for a hull and its balance in practice when sailing, but there is no rigorous evidence. The COWAC graph illustrates static characteristics of the hull, but balance is a dynamic matter. It is not surprising that there cannot be any rigorous demonstration of cause and effect.
We know that, in practice, a boat is trimmed by moving the
position of the mast. Part II of this article will start by looking at theories
of how the centers of lateral hull resistance (CLR) and aerodynamic effort (CE)
should be arranged. By way of a spoiler alert, we’ll find out how these theories
are just as inadequate as the theories of balance we’ve looked at here.
Fortunately, Part II will explain why all current theories of balance are
ReferencesBoebert, E, (2007). “That Peculiar Property:” Model Yachting and the Analysis of Balance in Sailing Hulls. 18th Chesapeake Sailing Yacht Symposium, downloaded from (www.sname.org/HigherLogic/System/DownloadDocumentFile.ashx?DocumentFileKey=9818a2eb-c8e9-45ee-bd9d-5029f13d432c) on 20 October 2016.
Charles Satterthwaite (1960). Sailing Theory. AYRS. Downloaded from (www.ayrs.org/repository/AYRS031.pdf) on 20 October 2016.
AcknowedgementsGraham Bantock gave valuable comments on an earlier draft. The errors are all mine.
©2023 Lester Gilbert