Out of popular demand, we give some aerodynamic
background for the sail shapes described in "The
Quest for the Perfect Shape". This
is by no means a complete treatise of sail aerodynamics
- we are merely scratching the surface - but should
shed some light on why sails look the way they do.
The light air case
In light air, a sailboat will almost always go
faster if sail lift can be increased. As long
as there is no significant flow separation, drag
increases as the square of the lift. As lift continues
to increase, drag rises even more rapidly until
we reach maximum lift and the sails start to stall.
Until near maximum lift, sail drive will increase
and the boat speed ditto, in spite of the quickly
rising drag and the related heeling force. This
is because in light air the heeling force (or
moment) is not an issue, at least up to very high
values of the side force, when the induced drag
of the underwater hull gets excessive.
So, in light air we need to look for shapes that
- round headsail entry to allow for large angle
- maximum overlap to allow bringing the boom
to the centerline and over, inducing lots of
camber into the sailplan looked as a whole
- maximum fullness of both sails separately
- possibly a rounded leech of mainsail to increase
- twist as needed to prevent stalling
The headsail enjoys a beneficial lift from the
mainsail behind it - after all, it is sailing
in the "safe leeward position". To prevent
flow separation on the leeward side, we want a
round, full entry. For best performance in light
airs, boats need to sail low and fast, at large
apparent wind angles.
Overlap helps to maximize lift in two ways. Firstly,
the genoa benefits as its leech is in the high
speed airflow on the leeward side of the main.
The highly accelerated airflow on the leeward
side of the headsail, creating most of the suction
that drives the boat, does not need to decelerate
to apparent wind speed at the leech of the genoa.
Instead, deceleration will happen gradually over
the leech of the main.
Ironically, the overlapping genoa leech benefits
the main at the same time: it prevents the airflow
from accelerating too much over the forward part
of the mainsail. Consequently, the airflow does
not have to slow down as much as it approaches
the mainsail leech, and is not as prone to separate.
Separation is caused by the deceleration of the
flow, and the flow has to decelerate close to
apparent wind speed at the leech of the mainsail
(the trailing edge of the wing as one), unless
it separates already earlier.
Camber (fullness) will increase lift, but up
to a limit: as the airflow on the leeward side
accelerates to more than twice the apparent wind
speed, it will stop to a halt at the windward
side, or even start to flow against the wind,
and lift will be decreased. This happens in practice
at around 20% depth.
Rear loading, achieved by curving the mainsail
leech, may increase the lift a touch more by adding
to the positive pressure on the windward side
of the sail. Care must be taken that separation
will not be increased too much on the leeward
side - leech tell tails are a good indicator.
Twist is used to regulate the size of the flow
separation areas. Maximum lift (and drive) is
achieved with significant areas of separated flow,
but there is a limit to it. The flow separation
is controlled by the amount of twist. Due to their
triangular shape, sails are "tip stallers":
separation always starts at the head spreading
down along the leech.
Here's the reason: as the angle of attack is
increased (the boat bears off or you sheet in),
the narrower top part of the sail is progressively
more and more loaded (per unit area) than the
lower, wider part of the sail. This is nature's
attempt to minimize the harmful lift induced drag,
by spreading the loading more evenly over the
By virtue of their triangular planform, sails
twist the airflow in front of and over them as
much as 30-40 degrees (!) up along the luff. In
the lower part, the sail is headed (effective
wind angle is decreased), while towards the head
the effective angle increases rapidly (see sketch).
The end result is flow separation starting at
the top, while the actual mechanism of this massive
bending of the airflow lies in the trailing edge
vortices and the strong tip vortice shed at the
leech of the sail, at high lift connected with
large apparent wind angles (see illustration of
the airplane on the right).
This is why in light airs we want sails that
are flatter down low (less loading per unit area)
and get fuller towards the head (more loading
per unit area). A more even vertical distribution
of loading means less induced drag and more drive
- the famous elliptical loading being ideal but
not achievable with triangular sails. The deeper
profile fits better for the twisted flow, but
you also want to move the maximum camber forward
towards the top, further increasing the entry
angle, to ensure a smooth flow without separation
bubbles at the luff.
Wind is slowed down close to the sea surface
because of friction: windspeed is usually several
knots more at the mast top than at the deck level.
When this wind speed gradient is combined to the
boatspeed, we also experience a twist in the apparent
wind in the order of 5 degrees or so (close hauled
- downwind the twist can be double as much).
The increase in the apparent wind speed and the
wind angle both contribute to loading more the
upper part of the sail plan, rendering the triangular
sailplan more efficient than it would be in uniform
The case for heavy air
When we reach the design wind and more,
maximum lift and the associated flow separation
ceases to be an issue. Instead, the heeling moment
starts to dominate the performance of the sailboat.
We saw in the Quest
for the Perfect Shape that drag not only
reduces the driving force of the sails, but also
increases the heeling force. Therefore, minimizing
drag and maximizing the lift to drag ratio become
Flattening and twisting the top part of the sails
helps keeping heeling moment under control. So
does the (often undervalued) triangular shape
of the sails: As the helmsman starts to pinch
to prevent excessive heeling, the sails are set
at a narrower at angle to the wind. The opposite
of what was discussed in the light wind case occurs.
The upper part of the sails is unloaded, and the
effective angle of attack is more even from foot
to head. With the reduced lift coefficient the
leech vortices are less powerful than in light
air, and the sails do not twist the wind nearly
as much as before.
This is a property of the triangular planform
(side view) of the bermudan sails, something that
the hip elliptical leech sails do not enjoy. The
sails automatically adjust their loading when
the apparent wind angle changes so that the sailboat
can cope with a larger wind range more easily.
To avoid backwinding, we want to flatten especially
the mainsail in its front part. The feathered
top of the sail needs to be even flatter, moving
the point of maximum draft towards the leech.
In extreme conditions, it is advantageous to
allow the top "reverse" completely a
part of the time, providing a negative heeling
force (lift to windward), supporting the boat
with a large lever. This allows to produce much
more lift down low and you end up with more drive
for a given heeling moment. However, before the
sail starts to backwind you want to flatten it
as much as possible. Backwinding not only pushes
the boat back but also tends to increase weather
helm, usually a problem in heavy air.
Separation starts at the top of the sails
spreading down the leech. The orange areas
represent separation on the leeward side,
while the greenish areas mark luffing.
Simulation run on MacSail.(mouseClick
to animate in new window)
The shot of an
airplane performing agricultural spraying
illustrates neatly the strength of the
tip vortex spinning behind the wing. Like
the airplane flying close to the ground,
sails operate at high lift, giving rise
to strong trailing edge vortices. If only
air was not invisible! The vortices influence
the flow over the sails, inducing a "header"
in the lower part and a "lift"
at the head. Producing & keeping up
the vortices consumes energy, giving rise
to the induced drag (sometimes called
vortex drag). Induced drag is easily 75%
of the total air drag of a sailboat -
shaping the sails for minimum induced
drag is most important for good performance
Sails bend the airflow in front of them
remarkably much. In the sketch above,
the sails are nicely sheeted at an apparent
wind angle of 18 degrees, yet the entry
angle of the jib is about 40 degrees in
the lower part, and up to 75 degrees towards
the head (referred to the boat centerline).
The mainsail is slightly headed in its
lower part due to the genoa, but towards
its head the flow is bent considerably,
too.As you can see, the entry angle should
not be constant but increase towards the
head. This is a property of the triangular
sail planform. The upwash of the flow
also depends on the angle of attack: the
larger the angle, the more the flow is
bent. In addition, at smaller angles,
the difference in the upwash between the
foot and the head is proportionally less
than at large angles. Sail aerodynamics
are complicated.(mouseClick for enlarged
view in new window)