30. The action of the wind upon the sails of a vessel affords a very
instructive and useful example of the decomposition of forces. By the
parallelogram of forces we are able to explain how it is that a vessel
is able even to sail against the wind. A force is that which tends to
produce motion, and motion generally takes place in the line of the
force. In the case of the action of wind on a vessel through the medium
of the sails, we have motion produced which is not necessarily in the
direction of the wind, and which may be to a certain extent opposed to
it. This apparent paradox requires some elucidation.
[Illustration: FIG. 13.]
31. Let us first suppose the wind to be blowing in a direction shown by
the arrows of Fig. 13, perpendicular to the line AB in which the ship’s
course lies.
In what direction must the sail be set? It is clear that the sail must
not be placed along the line AB, for then the only effect of the wind
would be to blow the vessel sideways; nor could the sail be placed
with its edge to the wind, that is, along the line O W, for then the
wind would merely glide along the sail without producing a propelling
force. Let, then, the sail be placed between the two positions, as in
the direction P Q. The line O W represents the magnitude of the force
of the wind pressing on the sail.
We shall suppose for simplicity that the sail extends on both sides
of O. Through O draw O R perpendicular to P Q, and from W let fall
the perpendicular W X on P Q, and W R on O R. By the principle of the
parallelogram of forces, the force O W may be decomposed into the two
forces O X and O R, since these are the sides of the parallelogram of
which O W, the force of the wind, is the diagonal. We may then leave
O W out of consideration, and imagine the force of the wind to be
replaced by the pair of forces O X and O R; but the force O X cannot
produce an effect, it merely represents a force which glides along the
surface of the sail, not one which pushes against it; so far as this
component goes, the sail has its edge towards it, and therefore the
force produces no effect. On the other hand, the sail is perpendicular
to the force O R, and this is therefore the efficient component.
The force of the wind is thus measured by O R, both in magnitude and
direction: this force represents the actual pressure on the mast
produced by the sail, and from the mast communicated to the ship. Still
O R is not in the direction in which the ship is sailing: we must again
decompose the force in order to find its useful effect. This is done
by drawing through R the lines R L and R M parallel to O A and O W,
thus forming the parallelogram O M R L. Hence, by the parallelogram of
forces, the force O R is equivalent to the two forces O L and O M.
The effect of O L upon the vessel is to propel it in a direction
perpendicular to that in which it is sailing. We must, therefore,
endeavour to counteract this force as far as possible. This is
accomplished by the keel, and the form of the ship is so designed as
to present the greatest possible resistance to being pushed sideways
through the water: the deeper the keel the more completely is the
effect of O L annulled. Still O L would in all cases produce some
leeway were it not for the rudder, which, by turning the head of
the vessel a little towards the wind, makes her sail in a direction
sufficiently to windward to counteract the small effect of O L in
driving her to leeward.
Thus O L is disposed of, and the only force remaining is O M, which
acts directly to push the vessel in the required direction. Here, then,
we see how the wind, aided by the resistance of the water, is able to
make the vessel move in a direction perpendicular to that in which the
wind blows. We have seen that the sail must be set somewhere between
the direction of the wind and that of the ship’s motion. It can be
proved that when the direction of the sail supposed to be flat and
vertical, is such as to bisect the angle W O B, the magnitude of the
force O M is greater than when the sail has any other position.
32. The same principles show how a vessel is able to sail against the
wind: she cannot, of course, sail straight against it, but she can sail
within half a right angle of it, or perhaps even less. This can be seen
from Fig. 14.
The small arrows represent the wind, as before. Let O W be the line
parallel to them, which measures the force of the wind, and let the
sail be placed along the line P Q; O W is decomposed into O X and O
Y, O X merely glides along the sail, and O Y is the effective force.
This is decomposed into O L and O M; O L is counteracted, as already
explained, and O M is the force that propels the vessel onwards. Hence
we see that there is a force acting to push the vessel onwards, even
though the movement be partly against the wind.
[Illustration: FIG. 14.]
It will be noticed in this case that the force O L acting to leewards
exceeds O M pushing onwards. Hence it is that vessels with a very deep
keel, and therefore opposing very great resistance to moving leewards,
can sail more closely to the wind than others not so constructed; a
vessel should be formed so that she shall move as freely as possible
in the direction of her length, for which reason she is sharpened at
the bow, and otherwise shaped for gliding through the water easily;
this is in order that O M may have to overcome as little resistance as
possible. If the sail were flat and vertical it should bisect the angle
A OW for the wind to act in the most efficient manner. Since, then, a
vessel can sail towards the wind, it follows that, by taking a zigzag
course, she can proceed from one port to another, even though the wind
be blowing from the place to which she would go towards the place from
which she comes. This well known manœuvre is called “tacking.” You will
understand that in a sailing-vessel the rudder has a more important
part to play than in a steamer: in the latter it is only useful for
changing the direction of the vessel’s motion, while in the former it
is not only necessary for changing the direction, but must also be used
to keep the vessel to her course by counteracting the effect of leeway.