The horse power or work of the shaft is determined from the following: Let W =work of shaft in foot-pounds per minute, equals work absorbed per minute; P =unbalanced pressure or weight in pounds, acting on lever-arm at distance L; length of lever-arm in feet from centre of shaft; V = velocity of point in feet per minute at distance L, if arm were allowed to rotate; N = number of revolutions per minute; H. horse power. Then will W=PV=2 L N P; therefore since N P.' H. P. H. P. will equal 33,000 ,000 If L=33 then H. P. will equal It will be evident that leather belts and ropes may be used as friction brakes to absorb the power of a shaft or mo tor. In such cases it be comes necessary to ascer tain the back tension in the belt or rope and sub tract this from the total weight or pull on the other side.
A disc absorption-dy namometer,•by which any desired constant load can be maintained on the en gine, or motor, is the in vention of Mr. George Alden, of Worcester, Mass. This dynamome ter is essentially a fric tion brake in which the pressure causing the fric tion is distributed over a comparatively large area, thus giving a low intensity 3f pressure between the rubbing surfaces.
This friction is produced by the pressure of water acting upon two copper plates in con Act with a smooth cast-iron disc, keyed to the ;haft which revolves in a bath of oil )etween the plates. These latter are .ecured by a water-tight joint to a cas rig which does not revolve, and to which s bolted a lever-arm carrying weights Ls in an ordinary Prony brake. The hell or casing is so constructed that it oermits an equal pressure upon both ides of the disc — a sufficient quantity if the water being allowed to pass hrough the machine to carry off the heat lue to the energy absorbed.
An interesting application of the Al len brake has been made in the Experi mental Laboratory of Purdue University by which the power of a locomotive is absorbed. In this arrangement, Fig. 5, the locomotive is mounted with its drivers upon heavy supporting wheels free to revolve in either direction by contact with the drivers: the prolonged axles of the supporting wheels are each provided with a large flat cast-iron disc keyed to the shaft and allowed to rotate in a closed case between plates of copper, which can be forced against the rotating disc by hydraulic pressure as in the Alden dynamometer. The locomotive is free to move forward or backward only through a very small dis tance (about a quarter of an inch), its tendency to motion in either direction be ing measured by a system of levers and weights connected to the draw-bar by which the traction of the engine can readily be weighed. Any desired load and speed can be maintained by means of the friction brakes which are bolted securely to stone foundations —in this respect differing from the Alden dynamometer, which is free to rotate through a small arc. A modification of this mounting has been constructed for use in the railway laboratory of the University of Illinois. In this case there are eight supporting wheels arranged on four shafts each provided with a brake at both ends of the shaft. These brakes contain
three cast-iron discs which run between copper plates arranged as in the Alden brake. Each of the eight brakes is capable of absorbing 450 horsepower.
Another form of absorption dynamometer is that of Froude originally designed to measure the power of large marine engines. The re sistance in this dynamometer is obtained by the reaction of a series of fluid jets maintained at a high velocity by a modified form of turbine which revolves in a casing filled with water, both turbine and casing being mounted on the end of the screw shaft in place of the propeller —the turbine revolving while the casing is dynamometrically held stationary. In a dyna mometer of this type the reactions which tend to' stop rotation of the turbine and give motion to the casing vary as the square of the speed of rotation of the shaft to which they are attached; and, further, by comparing two similar but differently-dimensioned turbines, the respective moments or reaction for the same speed of rota tion will be found to vary as the fifth power of their respective diameters.
An earlier form of hydraulic brake was an ordinary centrifugal pump, the resistance to ro tation being regulated by a valve placed in the outlet pipe. This apparatus was rather cumber some, particularly at low speeds, and the range ana metnon of regulation were not very satis factory.
The present type of Fronde dynamometer which is almost universally used in England for factory purposes, consists of a rotor revolving in water contained in a casing, suitably mounted on friction rollers, and connected to a water supply. The rotor is fixed on the shaft, which projects on either side of the casing, so that the engine or motor to be tested may be readily coupled to it. Motors running in either direc tion can thus be tested by coupling to either end of the brake shaft. Each face of the rotor is formed with a semi-elliptical annular channel divided into a number of compartments by means of oblique vanes. The corresponding faces of the casing are also formed with similar channels divided in the same way. When in action the water in each annular channel is ro tated continuously by the centrifugal force im parted to it by the rotor, and passes consecu tively from one compartment into the next. An extremely high speed of rotation of the water may thus be obtained and the power put into the dynamometer is by this means converted into heat which passes away in the water leaving the machine. Incidentally it is interesting to note that Osborne Reynolds used one of these dynamometers to check the mechanical equiva lent of heat and found it to equal 778 foot pounds — the value now in use. The motion of the water causes the rotor to react on the casing, which tends to turn on the friction rollers. This is prevented by means of an ex tension arm, working between stops, at the end of which are the balance weights.