The wind's law
of the 2nd power
Why can't we do away with one
best shape of sails? The principal reason for
this lies in the nature of wind power itself:
The pressure that the wind exerts onto the sails
& the rig of a sailing boat depends on the 2nd
power of the [apparent] wind speed. Double the
wind speed from say 5 knots to 10 knots, and the
pressure (force) on the sails is quadrupled. Increase
the wind from 5 to 15 knots and the pressure is
nine times bigger - to 20 knots, and a force 16
times as big will be heeling your boat over. In
the Southern Ocean, the Whitbread sixties frequently
sail in winds of 60 knots - the pressure on the
rig then is 144 times more than in the light airs
of the doldrums. No wonder you have to do something
with your sails, to cope from 5 to 20 or 30 knots
Meanwhile, the controls we have
on the sails only work in a linear manner: Flatten
your sails to half, from say 12% depth to 6% (flatter
than this is hard to get) and the force is halved.
The same goes for the angle angle of attack: Narrow
the apparent wind angle the boat is sailing from
32 degrees in light winds to 16 degrees in a stiff
breeze, and the heeling force is again halved.
In the mean time, the wind pressure follows its
merciless square law.
Luckily, the heeling moment is
more important a factor in the sailboat equation
than the sail force per se. The heeling moment
of the sails is opposed to the righting moment
of the boat, provided by the keel and/or the crew
weight. To keep heeling moment under control,
we can pull some special tricks. Twisting off
the sails in their upper part (often called feathering),
where they influence the heeling moment most,
is very efficient and helps to keep things under
control. Finally, when nothing else works, we
resort to changing the headsail and even reefing.
The design wind
Most boats are designed so that
they get powered up in 10 to 12 knots of true
wind. This wind force, where the boat is sailing
at its optimum heel and nearly maximum upwind
speed is often called the design wind. Below and
up to the design wind we want the sails to be
powerful, to provide as much forward drive as
possible, and we are not concerned with the heeling
moment. Once the design wind is attained, the
heeling moment to drive ratio becomes more and
more important, and we try to maximize drive,
with the heeling moment constrained to its maximum
value. This calls for a very different sail shape
in the lightest zephyrs from those of a stiff
To understand sail shape it is
useful to visualize the mainsail and the jib as
a single "wing" (airfoil) with a slot
in the middle. The slot between the main and the
headsail makes it possible to adjust the power
of the rig, to cope with the huge variation in
sail force described earlier. In light winds,
a narrow slot ÓgluesÓ the airflow onto the leeward
side of the mainsail, preventing flow separation.
This is enhanced by the overlap of the headsail.
You can sheet the mainsail closer to the boat
centerline and even over it, effectively increasing
the camber of the main + jib combination.
In a breeze, opening the slot
allows to spill the wind and to depower the rig.
As the slot widens up, more air flows through
it and less is bent to the lee of the headsail,
or goes over the mainsail. The slot works like
a safety valve. With an open slot the mainsail
can be sheeted further outboard, effectively reducing
the camber of the ÓwingÓ, and at the same time
also diminishing its angle of attack. Thus the
two-sail rig with a separate mainsail & headsail
allows for much better power control than a single
While looking at mainsail-foresail
together as a wing, you can distinguish three
areas, looking up from the deck:
The part of the foresail
below the boom level. This part does not enjoy
the beneficial "lift" from the mainsail.
The part up from the boom
level to the hounds (where the forestay attaches
to the mast). In this part the jib benefits
of the main behind it, while the main is being
backwinded. However, the presence of the jib
is not all detrimental to the main, as it
helps prevent flow separation on its leeward
The part of the mainsail
above the hounds (on a fractional rig). The
main is no longer under the influence of the
jib while at the same time it starts to get
narrow. There is also a pronounced "dent"
in the profile where the forestay turns into
the top of the mast.
The airflow is different in these
three parts and this influences the sail shape
The perfect shape - the mainsail
While it s important to remember
that the main and the jib are just two different
parts of one and the same airfoil, itÕs easier
to describe them in detail by to looking at them
separately. The two sails perform a very different
task so itÕs only natural that they should be
quite different in shape too. The mainsail is
closer to us so itÕs shape is more familiar:l
The correct cross section of
the mainsail resembles the arc of a circle which
is more or less flattened in its rear part. The
maximum depth is close to the middle of the sail.
Vertically, the relative depth increases from
the boom up, especially in lighter winds.
In light winds, we want a full
main and the fullness can be further forward behind
the mast. The fullness allows to sheet the boom
close to the boat's centerline and gives power.
Looking vertically up the sail, the foot is fairly
full, the mid part is deeper and the top is deepest.
The lower and more triangular the sailplan, the
more pronounced the difference in fullness between
the lower and the upper part should be. The leech
of the sail is fairly straight with little twist,
exept in lightest zephyrs.
As the breeze builds up and the
boat starts to attain its design wind, you want
to start to flatten the sail as a whole and especially
in the upper part, to keep heeling moment under
control. The top gets flatter than the mid-part,
and the entry gets finer as the maximum flow moves
towards the middle and even aft of it. The flatter
main can be sheeted further outboard without excessive
backwinding. In the overlap area, the want to
flatten the front of the main as much as possible
to minimize backwind. At the same time, twist
is gradually increasing.
The same applies for the top
of the sail above the hounds: The most efficient
way to control heeling moment is to let the sail
twist off. Simultaneously, you want to flatten
the top as much as possible - you end up in a
partly inverted shape with the maximum depth well
aft of the middle. In strong winds, the whole
front part of the mainsail can be inverted (backwinding),
so that only the roach( the batten area) is filled
all the time. By the time even the roach starts
flapping it's time to change into a smaller headsail
The shape of the headsail will
vary much less than that of the mainsail in different
winds, if we ignore changing it entirely into
another sail. One reason is that attached to the
forestay, the headsail cannot be nearly as readily
trimmed as the mainsail supported by a bendy mast
and the boom. Another reason is the role of the
headsail as the "leading edge" of the sailplan
forming one airfoil: the foresail stays put while
the main acts like a flap or aileron behind it,
regulating the power.
This does not mean we would not
want a different jib for light and heavy air.
The basic shape of the jib is very different from
that of the main. Looking at the cross section,
the entry is much rounder. Maximum flow is further
forward, about 40% from the luff (or even closer),
and from mid-chord back a jib or a genoa should
be perfectly flat with a clean exit, especially
in its lower part with overlap.
The headsail needs to be much
more twisted than the main, for the leech to follow
up the surface of the sail behind it. The more
overlap, the more twist is required. When the
distance from the leech of the genoa to the mainsail
is even all the way from the boom to the hounds,
the slot is said to be even. This is a good setting
for medium winds. When the distance from the leech
of the genoa to the mainsail is getting smaller
as we approach the hounds, the slot is closing.
This brings power in light winds. When the slot
gets wider towards the top, it is said to be open
and allows to spill power in heavy air.
In light winds, you want a headsail
with a round entry with lots of fullness to allow
sailing at wide angles to the apparent wind. The
top of the sail should be very full, up to 20%.
As the breeze builds up, ideally you want to flatten
the sail in front & in the upper part. This
can be done to some extent by tightening the forestay
by different means, but often the opposite is
true: the forestay sags more, an the headsail
gets fuller. In small boats and one-designs, you
move the jib lead back. This tightens the foot
to keep the lower part flat and opens the upper
leech to depower & allow sheeting the main
further outboard. On a big boat, you switch to
initially a genoa with less overlap and finally
to a jib.
The big picture
In the animated drawings on the
right, we are looking separately at cross sections
of both the main and the jib at different heights.
However, even more important to the performance
of the sailboat than the sails' cross sections
is the shape of their leech, the twist. One might
go as far as to say that cross section is only
a means to "place" the leech into a desired location
in space. What lies in between the luff and the
leech, wrinkles, creases or inverted curves, is
of little consequence as long as the leech of
the sail (the twist) is correct. Severe wrinkles
in front of the battens may be detrimental, in
the extent that they affect the shape of the leech
(which may be falling off or hooking in).
This is especially true for the
mainsail, whose airflow is more or less spilled
by the mast in front of it. We would want the
front part of the genoa or a jib to be as smooth
as possible, as there may be a possibility for
some laminar flow on either side of it. However,
shape is more important than smoothness, so in
light air it pays to ease the halyard to wrinkle
or scallop the luff, making the sail fuller. Even
for the headsail, wrinkles in the leech area or
a small hook are of little consequence.
To get the big picture, consider
the sail to start at the luff of the genoa and
to end in the leech of the mainsail.
Appendix: Every picture tells a story
picture can tell more than a thousand words -
the appendix consists of a picture
gallery of sails with comments (will open
in a new window).
friendly version. Will print out nicer than
this 2-column display-version.
cursor over the buttons to pick a wind speed.
See how dramatically the heeling force goes
up as wind increases.
forces & moments
heeling moment is caused on one hand by
the sail heeling force acting in the center
of pressure of the sails, and on the other
hand the side force developed by the keel,
the rudder and the underwater hull. This
couple trying to overturn the boat is balanced
by another couple, the righting moment,
caused by the buoyancy of the boat and the
weight of the keel and the hiking crew (these
forces are not shown).
the heeling force grows in a quadratic manner
with wind speed, the heeling is best controlled
by feathering the sails (twisting the head
off) and flattening them especially in the
upper part. This lowers the aerodynamic
center of effort, making it possible to
keep the boat upright.
get a feel about the actual forces &
moments, see SailPowerCalc.
mainsail and the jib can be seen as
a single ÓwingÓ (airfoil) with a slot
in the middle. This "wing"
can be divided in three areas with
different flow characteristics:
part of the foresail below the boom
part up from the boom level to the
hounds (where the forestay attaches
to the mast)
part of the mainsail above the hounds
(only on a fractional rig).
at a cross section, the profile starts
at the jib luff and ends at the mainsail
leech. The chord is the straight line
between these two, and the twist of
the airfoil as a whole is referred
to this line. The camber is between
the fictive curve and the chord line,
and can be adjusted by letting the
mainsail traveler out (less camber)
or pulling it in (more camber).
are "discontinuities" in
the sailplan at the junctions of the
three areas: a discontinuity in the
chord and the twist where the mainsail
starts (I & II), and also discontinuities
in the "quarter chord line"
(gray dashed line). The quarter chord
line is an important aerodynamic factor,
as it determines the sweep within
the hounds, there is a discontinuity
(dent) in the leading edge : increasing
rake and bending the topmast back
smoothes out this discontinuity. Sails,
looked as a wing, are complex creature:
Very highly cambered, much twisted,
with discontinuities, a sharp leading
edge and a slot in the middle - much
more complicated than a 747 wing with
all its flaps and ailerons.
shape of a sail section is defined with
sufficient accuracy by two percentages and
three angles: the camber, expressed in percentage
of the local sail chord (width, 12%), the
position of the max. camber, similarly expressed
in percentage of the local sail chord (47%),
the twist expressed in degrees relative
to the sail foot chord (10 degrees), the
entry angle (32 degrees) and the exit angle
(17 degrees), as defined in the illustration.
define the geometry of a complete sail,
we usually take three sections, at 25% -
50% - 75% heights, and the foot section
plus the headboard. We also need to know
the sheeting angle between the centerline
of the boat and the foot chord of the sail,
and the mast bend or forestay sag, to be
able to fully describe one setting of the
cursor over the buttons to simulate sail
shape for a wind range (helicopter view
from the lee).
figures are indicative, but show you the
trend upwind from light to heavy air. The
real "best" shape varies from
boat to boat: Light, modern, fast and big
boats in general tend to have flatter sails
than old, heavy, and small boats.
see how the sheeting of the main & jib
influence sail forces & airflow, take
a look at SailTrimSim (will open in a new window).