The greater the angle between the two lifting forces the less weight can they lift. If two men are carrying a ten-pound satchel, each will be lifting five pounds, if the pull is directly upward; but this is a rather inconvenient way of carrying the bag and usually they pull at a slight angle from the vertical, and so each must carry more than half the weight. If they move so far apart that the angle between them is more than 120 degrees, each will be carrying more than the full weight of the bag.
FIGS. 58 AND 59.—PARALLELOGRAMS OF FORCES
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.
THE SPEEDY CLIPPER
Before the advent of the steamship, sailing vessels were developed to a high degree of efficiency. The speedy clippers of 1816 to 1845 used to cross the Atlantic at an average speed of 6 to 9 miles per hour and sometimes even better, which compares favorably with a common steam freighter of to-day. The largest sailing vessel ever built was the Thomas W. Lawson, a seven-masted schooner. She was launched in 1902, but foundered in 1907 off the Scilly Islands. This great ship was a steel vessel 395 feet long, with a displacement of 10,000 tons and a cargo capacity of 7,500 tons. She had a sail spread of 40,617 feet.