in., what horse power is absorbed by the brake if ẞ is 30°, and n is

300 revolutions per minute?

The application of the ordinary railway car is

167. Friction of Brake Shoes. brake shoe to the wheel of an

shown in Fig. 196, where F' is the axle friction, F the brake-shoe friction, N the normal pressure of the brake

high speeds of modern

trains require a system of perfectly working brakes, capable of stopping the car when running at its maximum speed in a very short distance.

The coefficient of friction between the shoes and wheel for cast-iron wheels at a speed of 40 mi. per hour is about , while at a point 15 ft. from stopping the coefficient of friction is increased 7 per cent, or it is about .27. The coefficient for steel-tired wheels at a speed of 65 mi. per hour is .15, and at a point 15 ft. from stopping it is .10. (See Proc. M. C. B. Assoc., Vol. 39, 1905, p. 431.)

The brake shoes act most efficiently when the force of friction F is as large as it can be made without causing a

slipping of the wheel on the rail (skidding). The normal pressure N, corresponding to the values of the coefficient of friction given above, varies in brake-shoe tests from 2800 lb. to 6800 lb., sometimes being as high as 10,000 lb.

Problem 263. A 20-ton car moving on a level track with a velocity of a mile a minute is subjected to a normal brake-shoe pressure of 6000 lb. on each of the 8 wheels. If the coefficient of brake friction is .15, how far will the car move before coming to rest?

Problem 264. In the above problem the kinetic energy of rotation of the wheels, the axle friction, and the rolling friction have been neglected. The coefficient of friction for the journals is .002, that for rolling friction is .02. Each pair of wheels and axle has a mass of 45 and a moment of inertia with respect to the axis of rotation of 37. The diameter of the wheels is 32 in. and the radius of the axles is 2 in. Compute the distance the car in the preceding problem will go before coming to rest. Compare the results.

Problem 265. A 30-ton car is running at the rate of 70 mi. per hour on a level track when the power is turned off and brakes applied so that the wheels are just about to slip on the rails. If the coefficient of friction of sliding between wheels and rails is .20, how far will the car go before coming to rest?

Problem 266. A 75-ton locomotive going at the rate of 50 mi. per hour is to be stopped by brake friction within 2000 ft. If the coefficient of friction is .25, what must be the normal brake-shoe pressure?

Problem 267. A 75-ton locomotive has its entire weight carried by five pairs of drivers (radius 3 ft.). The mass of one pair of drivers is 271 and the moment of inertia is 1830. If, when moving with a velocity of 50 mi. per hour, brakes are applied so that slipping on the rails is impending, how far will it go before being stopped? The coefficient of friction between the wheels and rails is .20.

168. Train Resistance. The resistance offered by a train depends upon a number of conditions, such as velocity, acceleration, the condition of track, number of cars, curves, resistance of the air, and grades. No law of resistance can be worked out from a theoretical consideration, because of the uncertainty of the influence of the various factors involved. Formulæ have been developed from the results of tests; the most important of these are given

below.

Let R represent the resistance in pounds and v the velocity in miles per hour. W. F. M. Goss has found that the resistance may be expressed as

R = .0003 (L+ 347) v2,

where L is the length of the train in feet (see Engineering Record, May 25, 1907).

The Baldwin Locomotive Works have derived the formula

as the relation between the resistance and velocity. When all factors are considered, this becomes

ย

R = 3 + 2/2 + .3788 (t) + .5682 (c) + .01265 (a)3,

6

where t = grade in feet per mile, e the degree of curvature of the track, and a the rate of increase of speed in miles hour in a run of one mile.

per

To get the total resistance it is necessary to include, in addition to the above factors, the friction of the locomo

tive and tender. This is given by Holmes (see Kent's "Hand Book") as

where W is the weight of the engine and tender in pounds and R1 the resistance in pounds due to friction.

Other formulæ derived as the result of experiments are

shown graphically in Fig. 197.

The formula themselves are as follows (see Engineering,

It is evident that these formulæ do not agree as closely as one would wish. The difference must be due chiefly to the different conditions under which the tests were made. These conditions should be taken into account in any application of the formulæ to special cases.