SAILING AGAINST THE WIND
Now that we know something about the parallelogram of forces we may return to the problem of sailing across and against the wind. In Fig. 60 we are looking down on the deck of a ship and the wind is represented by the arrow. The dotted line A B represents the direction in which the boat is traveling and the line C D represents the plane of a sail. If the line E F represents the magnitude and direction of the force of the wind at the center of the sail, then we can tell how much pressure is being exerted directly against the sail, by drawing the line g F perpendicular to the sail and completing the parallelogram by drawing from E a line parallel to the sail intersecting g F at G and another line parallel to g F intersecting the plane of the sail at H. Then the length of the line G F represents the pressure against the sail. If the line G F is half as long as the line E F, then only half of the force of the wind is exerted in the direction G F. In other words, a wind pressure of one pound per square foot blowing in the direction of G F will do as much work as two pounds in the direction E F. The force of the wind has been broken up into two “components,” one (G F) at right angles to the sail, and the other (H F) edgewise to the plane, and of course the latter has no effect upon the propulsion of the boat.
FIG. 60.—FORCES THAT MOVE A SAILBOAT
If there were nothing to prevent it, the boat would sail in the direction G F; but the keel of the boat offers resistance to motion in this direction, and we must construct another parallelogram around the force G F to find the magnitude of the force exerted in the direction A B. The line K F is drawn at right angles to A B, and then the parallelogram is completed by drawing a line from G to K parallel to the line A B and another from G to M parallel to K F. We have then resolved to force G F into two components M F and K F. The former tends to push the boat along its course while the latter tends to make it drift to leeward. The length of the line M F is little more than a quarter of the length of the wind force E F and the leeward acting force K F is actually considerably greater than the forward acting force M F. Even with a deep keel there will be some drift to leeward. This is corrected by means of the rudder of the ship which is turned to head the ship further into the wind so that although the boat does not actually travel in the direction of its axis it may be made to travel along the course A B. Of course the boat cannot sail directly against the wind, but it can accomplish the same result by tacking alternately to port and starboard so that eventually it can reach a port that lies in the direction from which the wind comes.