165. Application. _Windla.s.s, Cogwheels._ In the old-fashioned windla.s.s used in farming districts, the large wheel is replaced by a handle which, when turned, describes a circle. Such an arrangement is equivalent to wheel and axle (Fig. 112); the capstan used on shipboard for raising the anchor has the same principle. The kitchen coffee grinder and the meat chopper are other familiar ill.u.s.trations.

Cogwheels are modifications of the wheel and axle. Teeth cut in _A_ fit into similar teeth cut in _B_, and hence rotation of _A_ causes rotation of _B_. Several revolutions of the smaller wheel, however, are necessary in order to turn the larger wheel through one complete revolution; if the radius of _A_ is one half that of _B_, two revolutions of _A_ will correspond to one of _B_; if the radius of _A_ is one third that of _B_, three revolutions of _A_ will correspond to one of _B_.

[Ill.u.s.tration: FIG. 113.--Cogwheels.]

Experiment demonstrates that a weight _W_ attached to a cogwheel of radius 3 can be raised by a force _P_, equal to one third of _W_ applied to a cogwheel of radius 1. There is thus a great increase in force. But the speed with which _W_ is raised is only one third the speed with which the small wheel rotates, or increase in power has been at the decrease of speed.

This is a very common method for raising heavy weights by small force.

Cogwheels can be made to give speed at the decrease of force. A heavy weight _W_ attached to _B_ will in its slow fall cause rapid rotation of _A_, and hence rapid rise of _P_. It is true that _P_, the load raised, will be less than _W_, the force exerted, but if speed is our aim, this machine serves our purpose admirably.

An extremely important form of wheel and axle is that in which the two wheels are connected by belts as in Figure 114. Rotation of _W_ induces rotation of _w_, and a small force at _W_ is able to overcome a large force at _w_. An advantage of the belt connection is that power at one place can be transmitted over a considerable distance and utilized in another place.

[Ill.u.s.tration: FIG. 114.--By means of a belt, motion can be transferred from place to place.]

166. Compound Machines. Out of the few simple machines mentioned in the preceding Sections has developed the complex machinery of to-day.

By a combination of screw and lever, for example, we obtain the advantage due to each device, and some compound machines have been made which combine all the various kinds of simple machines, and in this way multiply their mechanical advantage many fold.

A relatively simple complex machine called the crane (Fig. 116) maybe seen almost any day on the street, or wherever heavy weights are being lifted. It is clear that a force applied to turn wheel 1 causes a slower rotation of wheel 3, and a still slower rotation of wheel 4, but as 4 rotates it winds up a chain and slowly raises _Q_. A very complex machine is that seen in Figure 117.

[Ill.u.s.tration: FIG. 115.--A simple derrick for raising weights.]

[Ill.u.s.tration: FIG. 116.--A traveling crane.]

167. Measurement of Work. In Section 150, we learned that the amount of work done depends upon the force exerted, and the distance covered, or that _W_ = force distance. A man who raises 5 pounds a height of 5 feet does far more work than a man who raises 5 ounces a height of 5 inches, but the product of force by distance is 25 in each case. There is difficulty because we have not selected an arbitrary unit of work. The unit of work chosen and in use in practical affairs is the foot pound, and is defined as the work done when a force of 1 pound acts through a distance of 1 foot. A man who moves 8 pounds through 6 feet does 48 foot pounds of work, while a man who moves 8 ounces (1/2 pound) through 6 inches (1/2 foot) does only one fourth of a foot pound of work.

[Ill.u.s.tration: FIG. 117.--A farm engine putting in a crop.]

168. The Power or the Speed with which Work is Done. A man can load a wagon more quickly than a growing boy. The work done by the one is equal to the work done by the other, but the man is more powerful, because the time required for a given task is very important. An engine which hoists a 50-pound weight in 1 second is much more powerful than a man who requires 50 seconds for the same task; hence in estimating the value of a working agent, whether animal or mechanical, we must consider not only the work done, but the speed with which it is done.

The rate at which a machine is able to accomplish a unit of work is called _power_, and the unit of power customarily used is the horse power. Any power which can do 550 foot pounds of work per second is said to be one horse power (H.P.). This unit was chosen by James Watt, the inventor of a steam engine, when he was in need of a unit with which to compare the new source of power, the engine, with his old source of power, the horse. Although called a horse power it is greater than the power of an average horse.

An ordinary man can do one sixth of a horse power. The average locomotive of a railroad has more than 500 H.P., while the engines of an ocean liner may have as high as 70,000 H.P.

169. Waste Work and Efficient Work. In our study of machines we omitted a factor which in practical cases cannot be ignored, namely, friction. No surface can be made perfectly smooth, and when a barrel rolls over an incline, or a rope pa.s.ses over a pulley, or a cogwheel turns its neighbor, there is rubbing and slipping and sliding. Motion is thus hindered, and the effective value of the acting force is lessened. In order to secure the desired result it is necessary to apply a force in excess of that calculated. This extra force, which must be supplied if friction is to be counteracted, is in reality waste work.

If the force required by a machine is 150 pounds, while that calculated as necessary is 100 pounds, the loss due to friction is 50 pounds, and the machine, instead of being thoroughly efficient, is only two thirds efficient.

Machinists make every effort to eliminate from a machine the waste due to friction, leveling and grinding to the most perfect smoothness and adjustment every part of the machine. When the machine is in use, friction may be further reduced by the use of lubricating oil.

Friction can never be totally eliminated, however, and machines of even the finest construction lose by friction some of their efficiency, while poorly constructed ones lose by friction as much as one half of their efficiency.

170. Man's Strength not Sufficient for Machines. A machine, an inert ma.s.s of metal and wood, cannot of itself do any work, but can only distribute the energy which is brought to it. Fortunately it is not necessary that this energy should be contributed by man alone, because the store of energy possessed by him is very small in comparison with the energy required to run locomotives, automobiles, sawmills, etc.

Perhaps the greatest value of machines lies in the fact that they enable man to perform work by the use of energy other than his own.

[Ill.u.s.tration: FIG. 118.--Man's strength is not sufficient for heavy work.]

Figure 118 shows one way in which a horse's energy can be utilized in lifting heavy loads. Even the fleeting wind has been harnessed by man, and, as in the windmill, made to work for him (Fig. 119). One sees dotted over the country windmills large and small, and in Holland, the country of windmills, the landowner who does not possess a windmill is poor indeed.

For generations running water from rivers, streams, and falls has served man by carrying his logs downstream, by turning the wheels of his mill, etc.; and in our own day running water is used as an indirect source of electric lights for street and house, the energy of the falling water serving to rotate the armature of a dynamo (Section 310).

[Ill.u.s.tration: FIG. 119.--The windmill pumps water into the troughs where cattle drink.]

A more constant source of energy is that available from the burning of fuel, such as coal and oil. The former is the source of energy in locomotives, the latter in most automobiles.

In the following Chapter will be given an account of water, wind, and fuel as machine feeders.

CHAPTER XVII

THE POWER BEHIND THE ENGINE

171. Small boys soon learn the power of running water; swimming or rowing downstream is easy, while swimming or rowing against the current is difficult, and the swifter the water, the easier the one and the more difficult the other; the river a.s.sists or opposes us as we go with it or against it. The water of a quiet pool or of a gentle stream cannot do work, but water which is plunging over a precipice or dam, or is flowing down steep slopes, may be made to saw wood, grind our corn, light our streets, run our electric cars, etc. A waterfall, or a rapid stream, is a great a.s.set to any community, and for this reason should be carefully guarded. Water power is as great a source of wealth as a coal bed or a gold mine.

The most tremendous waterfall in our country is Niagara Falls, which every minute hurls millions of gallons of water down a 163-foot precipice. The energy possessed by such an enormous quant.i.ty of water flowing at such a tremendous speed is almost beyond everyday comprehension, and would suffice to run the engines of many cities far and near. Numerous attempts to buy from the United States the right to utilize some of this apparently wasted energy have been made by various commercial companies. It is fortunate that these negotiations have been largely fruitless, because much deviation of the water for commercial uses and the installation of machinery in the vicinity of the famous falls would greatly detract from the beauty of this world-known scene, and would rob our country of a natural beauty unequaled elsewhere.

[Ill.u.s.tration: FIG. 120.--A mountain stream turns the wheels of the mill.]

172. Water Wheels. In Figure 120 the water of a small but rapid mountain stream is made to rotate a large wheel, which in turn communicates its motion through belts to a distant sawmill or grinder.

In more level regions huge dams are built which hold back the water and keep it at a higher level than the wheel; from the dam the water is conveyed in pipes (flumes) to the paddle wheel which it turns.

Cogwheels or belts connect the paddle wheel with the factory machinery, so that motion of the paddle wheel insures the running of the machinery.

[Ill.u.s.tration: FIG. 121.--The Pelton water wheel.]

One of the most efficient forms of water wheels is that shown in Figure 121, and called the Pelton wheel. Water issues in a narrow jet similar to that of the ordinary garden hose and strikes with great force against the lower part of the wheel, thereby causing rotation of the wheel. Belts transfer this motion to the machinery of factory or mill.

173. Turbines. The most efficient form of water motor is the turbine, a strong metal wheel shaped somewhat like a pin wheel, inclosed in a heavy metal case.

[Ill.u.s.tration: FIG. 122--A turbine at Niagara Falls.]

Water is conveyed from a reservoir or dam through a pipe (penstock) to the turbine case, in which is placed the heavy metal turbine wheel (Fig. 122). The force of the water causes rotation of the turbine and of the shaft which is rigidly fastened to it. The water which flows into the turbine case causes rotation of the wheel, escapes from the case through openings, and flows into the tail water.

The power which a turbine can furnish depends upon the quant.i.ty of water and the height of the fall, and also upon the turbine wheel itself. One of the largest turbines known has a horse power of about 20,000; that is, it is equivalent, approximately, to 20,000 horses.

174. How much is a Stream Worth? The work which a stream can perform may be easily calculated. Suppose, for example, that 50,000 pounds of water fall over a 22-foot dam every second; the power of such a stream would be 1,100,000 foot pounds per second or 2000 H.P. Naturally, a part of this power would be lost to use by friction within the machinery and by leakage, so that the power of a turbine run by a 2000 H.P. stream would be less than that value.

Of course, the horse power to be obtained from a stream determines the size of the paddle wheel or turbine which can be run by it. It would be possible to construct a turbine so large that the stream would not suffice to turn the wheel; for this reason, the power of a stream is carefully determined before machine construction is begun, and the size of the machinery depends upon the estimates of the water power furnished by expert engineers.

A rough estimate of the volume of a stream may be made by the method described below:--

Suppose we allow a stream of water to flow through a rectangular trough; the speed with which the water flows through the trough can be determined by noting the time required for a chip to float the length of the trough; if the trough is 10 feet long and the time required is 5 seconds, the water has a velocity of 2 feet per second.

[Ill.u.s.tration: FIG. 123.--Estimating the quant.i.ty of water which flows through the trough each second.]

The quant.i.ty of water which flows through the trough each second depends upon the dimensions of the trough and the velocity of the water. Suppose the trough is 5 feet wide and 3 feet high, or has a cross section of 15 square feet. If the velocity of the water were 1 foot per second, then 15 cubic feet of water would pa.s.s any given point each second, but since the velocity of the water is 2 feet per second, 30 cubic feet will represent the amount of water which will flow by a given point in one second.