
2D Flow simulation around sail sections
by Lester Gilbert Terminology
Sail sections are described in terms of their chord, amount
of maximum draft as a % of chord, and the position of that maximum draft, again
as a % of chord. Airfoil sections
are generally similarly described in terms of their chord “c”, thickness “t” as
a fraction of chord, and position “p” of maximum thickness as a fraction of
chord. Although more properly used
for wings and sails, the forward part of a sail section or airfoil section is
the luff or leading edge and the aft part is the leech or trailing edge.
Note that, because wings are “thick” and sails are “thin”, a symmetric
wing with t = 0.1, that is, 10% thickness would yield a sail with 5% draft if
its upper surface were turned into a sail.
Also note that, for the same reason, the visual shape of a wing section
is usually dominated by its thickness distribution while the shape of a sail
section is completely dominated by its camber distribution.
Section curves
The easiest sail block to make (see
Sail blocks analysis for some details
of sail making with blocks) would have a circular arc profile, and in order to
position maximum draft somewhere other than at 50% of chord it would have a flat
aft run, so the short list of plausible section curves begins with “Circular
arc” and “Arc with aft run”. An
alternative approach is a “Biarc” curve which has a smaller radius arc from
luff to position of maximum draft and a larger radius arc aft.
Deriving a sail section from an
equation
Turning an interesting equation into a plausible candidate
for a sail section involves a trial and error process.
I constructed an Excel spreadsheet to calculate a section using 30 (x, y)
data points, and arranged the 4 luff data points to be more closely spaced than
the remaining 26 points.
Figure
1.
Raw plot of the NACA thickness equation.
Figure
2.
Plot of the NACA thickness equation from Figure
1
after translation, rotation, and scaling (exaggerated ordinate). Sail section candidates
In addition to Circular arc, Arc with aft run, Biarc, NACA
thickness, and NACA camber, other candidate curves for a sail section are
Logarithmic Spiral, Archimedean Spiral, Catenary, Parabola, Sine, and Tangent.
For all equations, it is the trial and error first step which selects a
promising part of the curve for translation, rotation, and scaling to turn it
into a section.
Figure
3.
Section curves of 8% maximum camber at 40% of chord plotted with
exaggerated ordinate.
Figure
4.
Luff entry for section curves (plotted with exaggerated
ordinate). Generating a simulation model
“Solidworks” is a popular application for 3D design for
engineering which has a module for the simulation of structures (finite element
analysis, FEA) and flows (computational fluid dynamics, CFD).
The simulation module relies on the construction of a mesh of cells which
overlay the model under investigation.
The behaviour of the fluid or material in a small cell can be relatively
easily computed, yielding an overall flow or structural simulation with
successive iterations through adjoining cells.
This is one way of explaining the essence of FEA and CFD – the quality of
its output depends on the quality, coverage, and resolution of the mesh, as does
the time taken to run the simulation in silicon.
Running the CFD flow simulations
The CFD simulations were 2D and not 3D.
The focus was on the sail section and not on the sail; and since the
simulations did not include the effect of a mast, the results are applicable
mainly to foresail sections. The
global mesh envelope for the virtual wind tunnel comprised a rectangle
approximately 3 chord lengths long and 2 chord lengths high, with the section
placed in the middle. A higher
quality mesh placed a second envelope on the section approximately 2 chord
lengths long and one chord length high and generated 4, 8, or 16 subcells for
every global cell present, while the highest quality mesh placed additional
subsubcells around the fluidbody boundary.
Figure
5.
Streamlines across a NACA thickness section (8% draft at 40%
chord) set at 10° AoA with apparent wind of 5 m/s illustrating a
leech bubble (cropped image).
Different sections
Although there were 11 candidate sections in my list, their
shapes tended to fall into three groups:
like a circular arc, like a parabola, or like the NACA thickness
polynomial. Performance did not
differ markedly for sections within a group, and so most of the simulations
involved sections built from a circular arc, from a parabola, or from the NACA
thickness equation.
Figure
6.
CL for section curves plotted at various AoA.
Different camber position vs AoA
Figure 7
illustrates CL for the NACA 8xx8 section run at various AoA in a 5 m/s apparent
wind, with the xx position of maximum camber set at 35%, 40%, 45%, and 50%.
Figure
7.
CL for NACA 8xx8 section curve plotted at various AoA. Different camber position vs apparent wind speed
Figure 8
illustrates CL for a parabola section of various positions of maximum draft run
at 11° AoA in a range of apparent winds.
Figure
8.
CL for parabola section curve with various positions of maximum
draft plotted at various wind speeds.
Calibration
A key component of any successful simulation is its
validation against previous, physical wind tunnel findings.
There is very little published hard data freely available for sails, and
so the absolute values in these 2D results, eg a CL of 1.8 for the NACA 8458 at
11° AoA in a 5 m/s wind could be quite wide of the mark.
Within a set of runs, however, the relative performance seems plausible.
Simulating a flying shape
During some discussion of these simulations with Graham
Bantock, he wondered what would change if the sail was simulated in “soft” Mylar
and hence subject to deformation when flying.
An interesting question, since the 2D simulations assume complete
rigidity of the section shape.
Figure 9
shows the simulated result using FEA of deforming a 3D sail strip of parabolic
profile under a constant load along its length equal to the expected lift force
from a 5 m/s wind at an angle of attack of 10°.
The result is indistinguishable from a circular arc profile.
Figure
9.
Deformed Mylar sail strip (exaggerated; shaded resultant force
contours) from original parabolic shape (light grey) of 8% draft
at 40% chord.
Incident wind from left to right in the image. Conclusions
CFD simulations of different sail sections do show
performance differences, but these are subject to a number of caveats.
The differences are relatively small;
they are highly dependent on the CFD meshing;
and they are not calibrated or validated by physical wind tunnel data.
On the other hand, within a family of simulations runs, they do show
relative differences which can be taken to be indicative.
Acknowedgements
Graham Bantock reviewed an earlier draft and provided
comments and corrections. Any
remaining errors are exclusively mine.

©2023 Lester Gilbert 