UNIVERSITY OF CALIFORNIA LOS ANGELES DYNAMOMETERS AND THE MEASUREMENT OF POWER: A TREATISE ON THE CONSTRUCTION AND APPLICATION OF DYNAMOMETERS; WITH A DESCRIPTION OF THE METHODS AND APPARATUS EMPLOYED IN MEASURING WATER-POWER. BY JOHN J. FLATHER, Pn.B., M.M.E., PROFESSOR OP MECHANICAL ENGINEERING, PURDUE UNIVERSITY; AUTHOR OP AMERICAN EDITION WILSON'S " STEAM-BOILERS." SECOND THOUSAND. NEW YORK: JOHN WILEY & SONS, 53 EAST TENTH STREET. 1893. COPYRIGHT, 1892, BY J. J. FLATHER. ROBERT DRUMMOND, Electrotyper, m and 448 Pearl St, New York. FERRIS BROS., Printers, 326 Pearl Street, New York. TT *?$' PREFACE. THE aim in the following pages has been to present in convenient form, for the use of Technical Students and Engineers, a description of the construction and principles of action of the various types of Dynamom- eter employed in the measurement of power. A chronological presentation of the subject has not been attempted, as many of the forms once used have entirely disappeared ; with very few exceptions the various types discussed are those now in use. In the measurement of the mechanical horse-power of a hydraulic motor the effective power may be as- <4\ certained by means of a friction-brake, or other dyna- v^) mometer, under any given conditions ; but as these Y^may be such that the maximum power of the wheel is 1 not developed, it remains for the Engineer to determine " those conditions best suited to the wheel under con- sideration. In Chapter VI is given a discussion of the methods and apparatus in use for ascertaining the effi- ciency of a given wheel, including the determination of flow in rivers and streams. The work here presented has been used as the basis of a course of lectures to Engineering students, and is 379424 iv PREFACE. the outgrowth of a series of articles published in the A merican Machinist. In its preparation free use has been made of numer, ous publications relating to the subject, and references for further information are given in foot-notes through- out the text. Special mention is due Professor Andrew Jamieson, of Glasgow, for use of matter and figures from his " Steam and Steam-engines " (London : Chas. Griffin & Co.;. The writer is also under obligations to Professors Jas. E. Denton, J. Burkitt Webb, Dr. Mansfield Merriman, and others. J. J. FLATHER. LAFAYETTE, IND., August i, 1892. CONTENTS. CHAPTER I. PAGE tjf TERMINATION OF DRIVING POWER I Horse-power from number of men employed Friction of shafting in mills and machine-shops Horse-power from width of belt. CHAPTER II. FRICTION-BRAKES 19 Prony brakes Proportions of small brakes Regulators- Water-cooled brakes Determination of brake-power Belt brakes Compensating brakes Rope brakes Rappard's band-brake Brake for vertical shafts Materials for brake- blocks Lubrication Width and velocity of rubbing surface. CHAPTER III. ABSORPTION-DYNAMOMETERS 54 Richards dynamometer Alden dynamometer Alden brake used to test locomotive Froude water-brake. CHAPTER IV. TRANSMISSION-DYNAMOMETERS 72 Morin dynamometer Webber balance-dynamometer Briggs belt dynamometer Tatham dynamometers Other belt dynamometers Brackett cradle-dynamometer Webb floating dynamometer Hartig dynamometer Emerson power-scale Van Winkle power-meter Flather hydraulic dynamometer Indicator-cards from dynamometer. VI CONTENTS. CHAPTER V. PAGE POWER REQUIRED TO DRIVE LATHES 151 Friction in lathes Table of horse-power for small lathes Formula for horse-power running light Weight of metal removed per hour per horse-power General deductions. CHAPTER VI. MEASUREMENT OF WATER-POWER 165 Efficiency of motors Determination of weight of water Tank-measurement Current-meters Float-measurements Mid-depth velocity Water-meters Weir-measurements Coefficient of discharge Hook-gauges Flow of water in pipes Loss of head Pressure-head. DYNAMOMETERS AND THE MEASUREMENT OF POWER. CHAPTER I. DETERMINATION OF DRIVING POWER. IN designing a modern machine-shop or manufac- tory, and in estimating the cost of power for its working plant, an accurate knowledge of the amount of power absorbed by the different machines is not only desirable, but essential to economy and efficiency. If the power required is not known, the engine or motor provided may prove incapable of driving the work ; or, on the other hand, the motive power may be largely in excess of that required : in either case there is an unnecessary expense in the first case, in remedying the evil, and, in the second, in the daily ex- penditure of fuel for excess of power. So also in fitting up a factory: if a more accurate knowledge of the power required to drive machine- tools were known, there would be a greater economy in running them. The writer has in mind a case 2 DYNAMOMETERS that came under his notice a few years ago, in which a certain wood-planer had its countershaft changed three times different diameters of pulley, and differ- ent widths of belt, and finally a heavier counter- shaft being used before it would work satisfactorily Machines are largely belted by guesswork. If the. pulleys guessed at are nearly large enough to do the work, the workman stretches his belt to its utmost, and manages to run the machine by taking light cuts ; if, however, the belt has a velocity and width barely sufficient to run the machine, and an ordinary cut will throw off the belt, then, if split pulleys, are not in use, a length of shafting is taken down and a larger pulley put in the place of the one which has shown itself to be insufficient to drive. Sometimes both a greater width of belt and a larger pulley have to be resorted to. Another case was where a 6-inch belt running over a 36-inch pulley at 120 revolutions per minute had been put in, and had been running for more than a year driving a roomful of high-velocity machines used for covering magnet-wire. Evenness of motion is specially desirable in this class of machinery; and yet, when all the machines were on, the shaft would vary from 80 revolutions per minute to its normal speed. Rosin or belt-oil was in order every few days, and when the slip became too great the engine had to be shut down and the belt relaced. The relacing was done by the use of clamps, and the belt finally be- came so taut that the increased friction on the beat- ings near the driving-pulley kept the boxes and shaft constantly hot. This belt was a continual source of annoyance and expense ; but, because it had been AND THE MEASUREMENT OF POWER. 3 deemed large enough to furnish power for the forty or more machines in the room, no change had ever been made, and it had run for over a year in this same manner. A Q-inch belt was put on, and no trouble was afterwards experienced, though it has now been run- ning for several years. It is easy enough to remedy a defect like this ; but prevention would have been better, and would have considerably reduced the expense account. The knowledge of the power re- quired to drive the machinery was wanting. The question arises : How can this power be estimated ? In the discussion of an inquiry as to the power required to drive machine-tools, Mr. G. H. Babcock stated at a meeting of the American Society of Me- chanical Engineers* that for a general rule in ordi- nary machine-work we may take roughly one horse- power as sufficient to drive machine-tools necessary to keep ten men at work ; but this, he adds, does not necessarily include shafting, engine, etc., nor blowers for foundry work. Expressed algebraically, this rule of thumb would be where N equals the number of men employed ; or, if we let 10 = C, a constant, we have -- H.P. * Trans. A. S. M. E vol. vm. 4 D YNA MOME TERS The above as it stands is of little or no value ; in the first place, C is too large, as will be shown by the following data, obtained from a large nurrber of rep- re'sentative machine-shops ; and, in the second place, the power required to drive the machinery varies between such wide limits, even in the same class of work, that separate values of C cannot be determined which may be relied upon as giving even a rough ap- proximation. Such a formula is of value only when C has been determined for two or more similar plants, and applied to another equipment working under similar condi- tions and this indeed is rarely met with. By a reference to the above table it will be noticed that two firms on exactly the same line of work that of manufacturing machine-screws require a total horse-power such that the number of men employed per horse-power is in the one case 2, and in the other 0.62 ; or as 3 to I. The small value of C in both cases is evidently due to the nature of the machinery, which is largely automatic, one man being able to feed several machines. A comparison of the values of C (obtained for total power used) of two well-known firms, the Pratt & Whitney Manufacturing Co. and the Brown & Sharpe Manufacturing Co., shows that the latter employ only 3.91 men per horse-power, while Pratt & Whitney employ 6.04 ; and yet these shops may be considered to belong to the same class. Another comparison of two firms running about the same class of machinery is that of the Bald- win Locomotive Works and William Sellers & Co. The Baldwin Locomotive Works give a value of AND THE MEASUREMENT OF POWER. !.,. d H I>X -WJ J 3AUQ O "JJ J3J 3AUQ oj bay s|J Jt : S u 6 D YNA MOME TEKS 1.64 for C per total horse-power, and Sellers & Co. give 2.93. If we deduct the power required to run the shafting in each works, the values become, respec- tively, C, 8.20, C, = 4-87. A closer result obtains between the Pond Machine- Tool Works and William Sellers & Co. throughout all the data given. The percentage of power required to drive shafting is in one case 41 per cent., and in the other 40 per cent. The values of C and C, are as fol- lows : C. Ci. Pond Machine-Tool Works 2.4 4.1 1 William Sellers & Co 2.93 4.87 Average ................ 2.66 4.49 These values are sufficiently close to enable one to deduce an approximate value for C and C l which would apply to either case, but when used in connec- tion with other and similar shops the results could not be depended upon, even roughly. Thus the average value of C, as shown above, is 2.66 per total horse-power. Applied to Wm. Sellers & Co. this gives = 2.66 X 102.45, = 273 men employed. AND THE MEASUREMENT OF POWER. 7 Applied to Pond Tool Works : N= 2.66 x 1 80, = 478 men employed. In the former case N should equal 300, and in the latter 432. These results are only rough estimates, but are correct to within 10 per cent of the actual number employed. If we apply the formula to the Pratt & Whitney Co., manufacturers of machine-tools, we obtain : N = 2.66 X 120, = 319 men; whereas we find from the table that 725 are employed. Looked at from its most favorable standpoint by comparing those values for similar grades which most nearly agree, it will be seen that the formula is really of no practical value, and much less can it have any weight when looked at from an engineering stand- point. A look at some of the results obtained from the data given may prove to be interesting. It has been stated that ten is too large a value for the number of men employed per horse-power when applied to machine-tools, even neglecting the power required to drive the shafting, etc. The average value of C 1 obtained from table is 5.13, or say 5.0 ; while the minimum value is 0.833, the maximum being 10.25. It would be out of the ques- 8 D YNA MOME TERS tion to apply the formula with the average value of T,, viz., 5.0, to either of these cases ; nor is it practicable to apply any other value of C l either to determine the horse-power from the number of men employed, or, vice versa, to obtain the number of men employed from the horse-power furnished. It will be noticed in the sixth column, headed " Per cent of power required to drive shafting," that very wide differences occur. The maximum is that used by the Baldwin Locomotive Works, viz., 80 per cent an extremely large factor; while the minimum given by J. A. Fay & Co. is only 15 per cent; the average, 38.6 per cent, corresponds to that quoted by William Sellers & Co. within less than if per cent. Mr. J. T. Henthorn, in a paper read before the American Society of Mechanical Engineers, states that the friction of the shafting and engine in a print-mill should not exceed 19 per cent of the full power. Out of fifty-five examples of a miscellaneous character which he has tabulated, seven cases are below 20 per cent, twenty vary from 20 per cent to 25 per cent, fifteen from 25 per cent to 30 per cent, eleven from 30 per cent to 35 per cent, and two above 35 per cent, while the average of the total number is 25.9 per cent. Mr. Barrus, speaking of this subject, quotes eight cases, the data of which were obtained from tests made by himself in various New England cotton-mills, in which the minimum percentage was 18, and the maxi- mum 25.7, the total average being 22 per cent. Mr. Samuel Webber states that 16 per cent of the total power of a mill is sufficient to overcome the friction of shafting and engine 10 per cent for the AND THE MEASUREMENT OF POWER. 9 shafting alone. But in this estimate Mr. Webber does not include the loss due to the belts running upon loose pulleys, which he does not consider to be part of the shafting, as they are not so running while the machinery is in operation : and when it is not, they may be thrown off as well as not, except for conven- ience. He further estimates, both from his own ex- perience and the observations of others, that the power consumed by the machine-belts on the loose pulleys in a large cotton-mill is about 8 per cent of the whole. This 8 per cent added to the 16 per cent loss due to shafting and engine will give 24 per cent of the total power a result which agrees closely with the average values given above. The writer believes that for shops using heavy ma- chinery the percentage of power required to drive the shafting will average from 40 to 50 per cent of the total power expended. This presupposes that under the head of shafting are included elevators, fans, and blowers. In shops using lighter machinery and with foundry connected the power percentage will be about the same as above ; but, if the foundry work is done out- side, the power required to drive the shafting will not average so high, the range being about 10 per cent less, or from 30 to 40 per cent of the total. In machine-shops with a line of main shafting run- ning down the centre of a room, connected by short belts with innumerable countershafts on either side, often by more than one belt, and, as frequently happens, also connected to one or more auxiliary 1 D YNA MO ME TEKS shafts which drive other countershafts, we can see why the power required to drive this shafting in machine-shops should be greater than that found in cotton and print mills, the machinery of which is in general driven from the main lines of shafting. Nor can we neglect the loss due to belts upon loose pulleys, as with the numerous clutches and countershafts in use the conditions more nearly approach those which exist when the machinery is in operation. There is no doubt, however, that a large percentage of the power now spent in overcoming the friction of shafting in or- dinary practice could be made available for useful work if wider and looser belts were employed, or, what would have the same effect, if the belts were slackened and their speed increased ; and also if more attention were paid to lubrication. As the power required to drive the machinery in a modern plant cannot be even approximately ascer- tained from its relation to the number of men employed, the question still remains open : How can this power be measured ? One method frequently used is that by which the power required is ascertained from the velocity and width of driving-belt. Different rules have been given in our text-books and engineering journals in order to estimate the driving power of a belt from its width and velocity. A rule which the writer has used in his prac- tice when the difference in diameters of pulleys is not very great is : Every inch in width of a single laced belt, having a velocity of 800 feet per minute, will transmit one horse-power up to a velocity of about 5000 feet per minute ; beyond 5000 the centrifugal force of the belt AND THE MEASUREMENT OF POWER. II largely diminishes its power. Expressed as a formula we have in which b equals breadth of belt in inches, and V equals velocity of belt in feet per minute. To illustrate this, let us look at an example. Suppose the main shaft of a factory runs at 125 revolutions per minute, and a 12- inch pulley on this shaft drives a lo-inch pulley on the counter of a i6-inch lathe through a 3 inch belt ; the lathe is driven by a 2^-inch belt running from a lo-inch step to an 8-inch. What power does the lathe absorb when the belt is taxed to its limit ? The speed of the belt is 392 feet per minute ; if we disregard slip, which is about two per cent of the total velocity, this would give Now, as shown, the belt will transmit according to our formula 1.22 H. P., and by calculating H. P. for the different machines in the factory a measure of the driving power may be obtained, to which a certain per cent should be added for power required to drive the shafting. This process might give an approximation somewhat nearer the truth than the method previously discussed, but as the formula is based on a certain permissible stress in the belt-fibres, which stress is well within the limit of safety, we do not know how much more power 1 2 D YNAMOME TERS the belt is exerting, nor do we know that it is exerting as much as the formula calls for. Although we can calculate what the width of a belt ought to be to trans- mit a given horse-power, x, at a given velocity, the stress in the belt may be greater or less than that on which our formula is based, and the resulting horse- power transmitted may be x y. In order to measure the amount of driving power from the velocity and width of belting, the tension on the tight and slack sides of a belt, the arc of contact a between belt and pulley, and the coefficient of fric- tion are all necessary. The width of a belt of thickness / must be such that its cross-section multiplied by its permissible working stress /is capable of resisting the maximum tension 7", in the driving side of the belt, or 7", = btf. We have the general equation PV H.P. = > 33000 Now if we let P = 1 . where m is a function of the m arc of contact a, and coefficient of friction 0, we obtain //./> = bf f V 33 ooo; ' If bt = one square inch, the horse-power transmitted per looo feet per minute is expressed by //, = -^ . AND THE MEASUREMENT OF POWER. 13 This Reuleaux calls the specific duty of a belt, the value of which he gives for leather belting, as varying from 5.3 to 9.8 ; hence = 5-3 to 9.8. As f varies in different belts, and ;// varies with a and 0, it is seen that any general formula, whether rational or empirical, is not trustworthy when the total amount of power absorbed is desired however satis- factory such a formula may be when used to calculate the width of belt to transmit safely a given horse- power. The only reliable method of determining this transmission of power is by the use of some form of dynamometer. Where power is rented from one firm to another, t4ie necessity of obtaining correct estimates of the amount consumed is apparent. A case in point is that of the Lowell Hosiery Co., which rented an estimated total of 13^ horse-power, for which $125 per horse-power per annum was paid. A dynamometer test being made, it was ascertained that 28^ H. P. was being used more than double the amount paid for. Another case is that of the North- ampton Tape Co., whose lease called for 30 H. P.; a dynamometer being applied to the shaft it was found that ii H. P. was the maximum transmitted. Still another case is that of a company in Worcester, which hired rooms and power, the basis of rent being esti- mated at 13 H. P. Forty horse-power was actually 1 4 D YNA MO ME TERS used, as shown by a dynamometer test, and the rent was increased accordingly. Many such instances could be cited to show that very wide differences exist between the amount of estimated power and the amount actually developed as deter- mined by an accurate dynamometer. Such wild es- timates are at first sight difficult to account for, since there are several good rules in use for ascertaining the width of belt to transmit a given horse-power; however, as already shown, as these rules do not take into count the individual differences in belt-tension, there will result, with variations of velocity and tension, cor- responding variations of power transmitted. Mr. Henry R. Towne's experiments with leather belting show that the ultimate strength of a laced belt ^" thick is about 200 pounds per inch of width ; as- suming a factor of safety of 3, this gives 66 pounds as the allowable strain per inch of width in single belting (Morin assumes 55 pounds). For a spliced or riveted belt the permissible strain may be 125 pounds per inch of width. The following table, compiled by Mr. Nagle, gives a list of belts in use, and the actual horse-power trans- mitted by them, compared with which are calculated widths by the formulae of Webber and Nagle. The widths in the ninth and tenth columns have been calcu- lated by the writer and added to Mr. Nagle's table ; the handy rule referred to in the last column being the one previously mentioned, namely, _ 800 H.P. b- _ AND THE MEASUREMENT OF POWER. TABLE II. WIDTH AND VELOCITY OF BELTING. 1 ^s A Width of Belt. if -S 1 c |.= v * . ( - ! jl ll fi jj. ic i JrtJ J II fl ll 32 Q s H e ^ Z. o 33 375 5,600 60 98 Double 24 22 34 3*i 27 250 3,080 84 58 4-p'y 48 50 28 28 23 22O 2,451 42 135 Single 22 9 8 31 84 70 175 3-179 72 93 Double I9i 25 26 22 175 3,629 "Si 55 29 15 22 23 20 130 2,117 70 18 18 22 29 24i "5 3,490 84 82 Mi 8 17 17 go 2,860 60 87 12 10 15 15 "i 77 2,268 60 77 Mi 12 12 16 I3i 45 2,000 48 37 Si gle 20 21 15 21 18 49 2,111 72 24 M 21 18 21 18^ 43 1, 800 60 44 18 20 M 23 19 4 1 I.Sog 60 42 1 74 12 16 21 18 40 2,OOO 72 37 ' 8 14 13 19 16 18 850 22 116 Double 6 19 8 IO 8* 8 942 30 40 Single 7 12 8 8 7 In the formula used by Mr. Nagle, the coefficient of friction deduced from the experiments of Mr. Towne is assumed at 42 per cent. As this coefficient was obtained while the belt was at rest or had no apparent velocity, the friction between the surface of the pulley and the belt will be somewhat different when in motion, although the experiments made by Wm. Sellers & Co., with belting running at an average velocity of 800 feet per minute, give coefficients varying from 25 per cent to 100 per cent. Rankine assumes 15 per cent as the coefficient of friction, but the results of all other inves- tigators show this value to be too low. Morin gives 1 6 D YNA MO ME TERS 28 per cent as an average value for dry belts on smooth cast-iron pulleys, and 12 per cent for very greasy shop belts on cast-iron pulleys the mean of these being 20 per cent. Recent investigations at the Massachusetts Institute of Technology show that this mean value is a little low, but probably nearer the truth than either Towne's or Rankine's coefficient. According to these later experiments* the value 27 per cent was chosen as being the best under the average conditions to which an ordinary belt is subjected in practice allow- ing 2^ per cent for slip and this value has been used in calculating the widths given in column 9, the formula used being 1000 H.P- Reuleaux' formula, in which = 0.28, instead of 0.27 as here used, is 1 100 H.P. V being in feet per minute. The average arc of con- tact, a, on the smaller pulley being equal to .95^, or a little less than 180. Upon consideration it will be seen that the rule 800 H.P. ~F' * Trans. A. S. M. E., vol. VH. AND THE MEASUREMENT OF POWER. I/ commonly used in the machine-shops, differs somewhat from _ looo H.P. i. 06 F~' which takes into account the arc of contact and the coefficient of friction, the average values a .95 ?r and = .27 being used. Reduced to an equivalent form this equation becomes 943^. O = T+ , which will give a width of belt a little greater than that obtained by using the shop rule referred to. As the arc of contact on smaller pulley decreases, the width of belt will have to increase ; thus for an arc of contact of 120 the width of belt should be 25 per sent greater than that found from the above rule. As these formulas are based on a given thickness of belt, t, if we increase this thickness the power trans- mitted ought to increase in proportion, and for double belts we should have half the width required for a single belt under the same conditions. With large pulleys and moderate velocities of belt it is probable that this holds good, and this value has been used in those cases in the table where double belts are em- ployed. With small pulleys, however, when a double belt is used there is not such perfect contact between the pulley-face and the belt due to the rigidity of the latter and more work is necessary to bend the belt- 1 8 D YNA MO ME TERS fibres than when a thinner and more pliable belt is used. The centrifugal force tending to throw the belt from the pulley also increases with the thickness, and for these reasons the width of a double belt required to transmit a given horse-power when used with small pulleys is generally assumed not less than seven-tenths the width of a single belt to transmit the same power. An inspection of the fourth column shows that the actual stress or belt-pull for single belting varies from 24 to 135 pounds per inch of width. Considering these varying tensions and comparing the calculated width with those found in actual practice, we arrive at the same conclusion previously reached, viz., that the driving power of a belt is not directly determinable by the use of a formula unless the belt-pull or stress is known for each particular case. AND THE MEASUREMENT OF POWER. 19 CHAPTER II. FRICTION-BRAKES. WE have already stated that the only satisfactory method of ascertaining the amount of power is by the use of some form of dynamometer by which we mean an instrument or machine for measuring the power exerted by a prime mover, or the amount of power consumed in driving a machine or machinery plant. Although the engine-indicator is an instrument for measuring power, and is thus a dynamometer, as it neither transmits nor absorbs the power, its discussion will not be entered into in these pages. The use of the engine-indicator in connection with a new form of transmission-dynamometer designed by the writer will be shown farther on. Among the many machines and devices for measur- ing power one of the simplest is the Prony friction- brake ; and but for certain disadvantages attendant on its use it would possess a superiority to all other contri- vances. Primarily this consists of a lever L, Fig. I, connected to a revolving shaft or pulley in such a manner that the friction induced between the surfaces in contact will tend to rotate the arm in the direction in which the shaft revolves. This rotation is balanced by weights P, hung in the scale-pan at the end of the 20 D YNAMOME TERS lever. A counterpoise attached to the brake-arm is often used in order to balance it before adding weights in the scale-pan. If not balanced, the weight of the lever-arm must be ascertained and its moment added to the total moment of the weight in order to obtain an accurate measure of the friction. In order to measure the power for a given number of revolutions of pulley, we add weights to the scale-pan and screw up on bolts b b, until the friction induced balances the weights and the lever is maintained in its horizontal position, while the revolutions of shaft per minute re- main constant. That this measure of the friction is equivalent to a measure of the work of the shaft will be seen when we consider that the entire driving power of the shaft is expended in producing this fric- tion at the required number of revolutions per minute and this driving power is equal to the mechanical effect of the shaft when running at the same speed in the performance of useful work. With the ordinary form of lever-brake, in order to maintain a stable equilibrium of the lever the weight should be supported on a knife-edge and act below the centre of the shaft. In this case, when the weight THE MEASUREMENT OF POWER. 21 falls or rises, through any irregularity of the brake, the lever-arm is decreased or increased, and the slight irregularity is overcome by a corresponding change of moment; whereas, if the weight act above the axis, any increase or decrease in weight will cause it to act through a longer or shorter arm, as the case may be, and the lever cannot of itself come back to its hori- zontal position. This does not apply to that form of brake where the force is measured on a platform scale, as it is evident the lever-arm is practically constant. Although the construction of the lever is of great im- portance, Mr. Heinrichs has shown that the propor- tions of the brake for different horse-powers are even more important in order to obtain uniformity of test. From a number of experiments made with a Prony brake of the design shown in Fig. 2, Mr. Heinrichs gives the following dimensions as being most suitable for the horse-powers designated : * Mechanics, 1884. 22 D YNA MOME 7 ~JfS TABLE III. DIMENSIONS FOR PRONY BRAKE. Number of Revolu- Size of Brake. Diameter Brake-pulley. Length. Width. pulley. . in. in. From 2 to 5 / 1200 tO I8OO 24 ii 4 horse-power. | 7OO tO I2OO 24 J 6 From 5 to 8 ) 1200 tO I60O 24 N 6 horse-power, j 8OO tO I20O 24 4 6 A regulator or dash-pot attached to the end of the lever-arm or scale-beam may be used with the Prony brake and other various forms of dynamometer in which the pressure is weighed in order to maintain a more even balance and to prevent vibrations and sudden shocks due to momentary slip of the belt or inefficient lubrication of the brake. This dash-pot is generally in the form of a cylinder from 4 to 6 inches in diameter, partly filled with oil or water in which a piston about j 1 ^ inch less in diameter is submerged. This piston will allow the oil to pass freely around it as it rises or falls with a slow motion, but will oppose a resistance to any sudden movement. An adjustable piston by which the motion of the oil can be regulated as desired is sometimes an advantage. This can be readily made by turning two disks to fit the bore of the cylin- der and drilling several holes through both disks by clamping together. FIG. 3. AND THE MEASUREMENT OF POWER. 2$ By connecting these disks to a stem with a shoulder and nut, any desired area of opening between the disks can be obtained by turning one upon the other and tightening the nut. The piston should be attached to the scale-beam by an eye and pin so as to move freely, and the beam should be balanced and adjusted with the piston in place in the liquid before beginning to weigh. A dash-pot, Fig. 3, used in the Lowell hydraulic tests, was made with a thin disk of iron turned to fit loosely in its cylinder ; six -f-inch holes were drilled and tapped in it and fitted with brass thumb-screws, any or all of which could be removed if desired to allow a freer pas- sage Of the water contained in the cylinder ; the screw being left on the plate in order to maintain the original balance. Instead of hanging weights in a scale-pan, as in Fig. I, the friction may be weighed on a platform-scale; in this case the direction of rotation being the same, the lever-arm will be on the opposite side of the shaft. A modification of this brake, in which the lever acts on a platform-scale, is that in use in the Sibley College Engineering Laboratory, and is shown in Fig. 4. The brake-wheel is keyed to the shaft, and its rim is pro- vided with inner flanges about two inches deep, which form an annular trough for the retention of water to keep the pulley from heating. A small stream of water constantly discharges into the trough and revolves with the pulley the centrifugal force of the particles of water overcoming the action of gravity ; a waste-pipe /, with its end flattened, is so placed in the trough that it acts as a scoop, and removes all surplus water. 2 4 D YNAMOMETERS The brake consists of a flexible metal strap to which are fitted blocks of wood forming the rubbing surface ; the ends of the strap are connected by an adjustable FIG. 4. bolt-clamp, by means of which any desired tension may be obtained. The horse-power or work of the shaft is determined from the following : Let W=\vork of shaft in foot-pounds per minute, equals power absorbed per minute ; P= unbalanced pressure or weight in pounds, acting on lever-arm at distance L ; L length of lever-arm in feet from centre of shaft ; V ' = velocity of a point in feet per minute at distance L, if arm were allowed to ro- tate ; N = number of revolutions per minute. ; H.P. = horse-power. AND THE MEASUREMENT OF POWER. 2$ Then will W= PV = 2nLNP. PV Since H.P. , we have 33000 If L = , we obtain 271 NP = 63.024 inches, practically 5 feet 3 inches a value often used in practice for the length of arm. It will be noticed that neither the diameter of the pulley nor the pressure and weight of the friction- blocks on the same, nor the coefficient of friction enter into the formula for obtaining the horse-power. As previously noted, the friction induced between the brake-blocks and the rim of the pulley tends to rotate the brake in the direction in which the shaft revolves ; this rotation is counterbalanced by the weight acting upon the arm of the brake, and when the system is in equilibrium the moments are equal; that is, if F = friction between blocks and pulley acting at radius = Ri , and P = counterbalance acting at distance L from centre of shaft, we shall have FR. = PL. Multiplying each member of the equation by 2nN, where N = number of revolutions of shaft per minute, we obtain 27tN X FR, = 2icNPL = W. 26 D YNAMOME TERS That is, the work absorbed per minute by friction equals the work in foot-pounds per minute at the end of the lever-arm. And since we have the means of obtaining this work Wwhen the weight P and arm L are known, it will readily be seen that the friction and radius of brake-pulley do not have to be considered in obtaining the measure of the power of a rotating shaft. If, however, the coefficient of friction, 0, between the rubbing surfaces be known, we may obtain from the above equation an expression for the pressure exerted on the pulley-rim by the brake : PL Let F = p- represent the force of friction between F the surfaces in contact at the pulley-rim, then ~r will equal the pressure exerted upon the pulley necessary to produce the force F. The coefficient of friction varies from .06 to .50, de- pending upon the different materials in contact and upon the lubrication of the surfaces. Within certain limits, the more perfect the lubrication the smaller the coefficient between any two materials. A brake-dynamometer similar to the one shown in Fig. 4 is used by the Westinghouse Machine Co., in testing their engines before being sent out of the fac- tory. For engines above 125 horse-power and under 250 a brake-wheel is used which is 48 inches in diameter and 24 inches face, with internal flanges about 3^ inches deep, carrying a stream of water about 2 inches deep, fed by a -inch pipe, the overflow being removed as shown in figure by means of the scoop-pipe. The rubbing surface is composed of 28 hard-wood AND THE MEASUREMENT OF POWER. 2/ blocks, oak or hickory, which are each 3^ inches wide, spaced if inches apart. These blocks are lubricated with fat pork or suet, which is packed in against the flat face of the wheel between the blocks. The lever- arm is 63^ inches long. For smaller engines a brake-wheel 48 inches in diameter by 13 inches face is used, the details being the same as in the larger wheel except the brake-arm, which in this case is shorter, being 27! inches long. Even with the sizes given a brake-rim occasionally catches fire, the cooling water not being sufficient to carry off the heat quickly enough. The following reports of tests made with these brakes were furnished to the writer through the courtesy of the Westinghouse Machine Co., both tests being on their Automatic Compound Engines : Size of engine i6&2? X 16 8 & 13 X 8 Initial steam-pressure 93 96 Terminal steam-pressure 13 14 High-pressure M. E. P 45-37 49-8? Low-pressure M. E. P 19-75 22.12 Indicated horse-power 205.5 4!'73 Brake horse-power 183.48 38.25 Loss or friction , 22.02 3.48 Percentage of loss 10.7 8.3 Gross indicated water-rate 23.95 24.77 Gross brake water-rate 26.83 27.03 Revolutions per minute 249 378 Brake-load (pounds) 785 241 Dead weight on scales 50 n Radius of brake (inches) 63^ 27! Duration of test (minutes) 8 15 The arm of the brake is often omitted, in which case the friction is induced either by the use of a flexible 28 DYNAMOMETERS brake-strap supplied with wooden blocks, or simply by the use of a band or ropes thrown over the pulley. For small powers ordinary leather belting from two to four inches wide is generally used, but care should be taken that the belt is not sticky : a well-worn flexi- ble belt free to slip on the pulley-face will give the most uniform results. The belt should be narrower than the pulley-face, and, in order to provide against its slipping off the rim sideways, it should be tacked to three or four light strips of wood FIG. 5 . placed across the face of the pulley : these strips being cut out to receive the pulley-rim and leaving a projection of about inch on each side of the rim, as shown in cross-section in Fig. 5. In Fig. 6 is seen the general arrangement of this method, the belt being carried over the pulley on the motor to be tested and one end secured to the floor by any convenient means. The other end is provided with a scale-pan or flat wooden box to carry the weights. A wire or stout cord attached to the bottom of the box and secured to the floor will prevent the accidental pulling of the box over the shaft while making the test. This wire must necessarily remain slack when the weights are in the box. With this form of brake the power is measured as with the lever-brake ; that is, the work, W, of shaft in foot-pounds per minute equals the product of the weight. P, in the scale-box multiplied by the velocity, V, in feet per minute of the lever-arm of the weight (see page 24), which in this case is equal to the radius of the pulley plus half the thickness of the belt. If we AND THE MEASUREMENT OF POWER. 29 neglect the belt-thickness, the velocity V will equal the circumferential velocity of the pulley, hence or the horse-power 27tRNP = "33000 = - 0001 where R is radius of arm in feet, and N = number of FIG. 6. revolutions per minute. If we take radius of arm, r, in inches we shall obtain H - p - = = ao0001 3O DYNAMOMETERS In working with this belt brake, in order to obtain accurate results the weights should be so adjusted that there shall be no tension in the end of the belt which is secured to the floor. A common error is to over- load the scale-box and create a pull on the end b which will cause an indication of power in excess of its true value. A spring-scale or balance interposed between the end b and the floor, as shown in Fig. 7, will give I FIG. 7 . the amount of the pull, if any exists, which pull should be deducted from the weight in the scale-box. It is evident that the weight of the spring-scale should be added to the pull which it indicates in order to obtain the total tension in the end b. Another method is to scrape the belt, thus causing a greater adhesion to the pulley-face ; this will pull the belt around in the direc- AND THE MEASUREMENT OF POWER. 3 1 tion of the arrow, tending to life the weight in the scale-box, thus producing a slackness at the end secured to the floor. With care in the weighting, if sufficiently small weights are provided there need be little or no tension at b. A 3-inch belt over a 24-inch pulley run- ning at .200 revolutions per minute, with a w r eight of 50 pounds in the scale-box, will measure about 2 horse- power 32 D YNAMOME TERS For larger powers the brake-strap is lined with wooden blocks and encircles the pulley, the friction being measured either by attaching weights to a hook or scale-pan and screwing up on an adjusting bolt which brings the two ends of the strap together ; or a spring balance is used in connection with the adjusting screw, as shown in Fig. 8. In the Brauer compensating brake, the band which encircles the pulley is of thin rolled iron when the pulley-rim is flat ; wire ropes are used for a grooved pulley. For small forces Mr. Gisbert Kapp has advanta- geously employed the arrangement represented in Fig. 9. The brake-cord, which embraces half the pulley FIG. 9. circumference, is attached at E on a level with the knife-edge of the scale-beam, and at D in a point somewhat below, so that the lever-arm of D is in- AND THE MEASUREMENT OF POWER. 33 creased while that of E is diminished, thus forming a compensating device. The spring S and nut N allow an adjustment of the tension in the cord after the scale-pan is weighted. The brake recommended by the Royal Agricultural Society,* designed by Mr. C. E. Amos and Mr. Appold, is somewhat similar to those already described, but, as will be noticed, Fig. 10, this brake is provided with a self- acting system of levers which are arranged to adjust the tension in order to compensate for the variations in the moment of friction. * Proc. British Inst. C. E., vol. xcv, 1888-89. 34 D YNA MOME '2 'ERS In this brake the strap is made in two parts to which blocks of wood are secured, and at a convenient point the two portions are joined by a right-and-left-hand adjusting screw. The other ends of the strap are jointed to a double swinging lever in such a manner that the radii of the two ends of the strap from the centre of oscillation of the lever are unequal. If, through deficiency of lubrication or other causes, the wheel should tend to carry the strap around with it in the direction of the arrow, the greater radius of the end nearer the weight would effect a loosening of the strap and a diminution of the friction ; whereas if the friction is momentarily insufficient to sustain the weight, it will in falling tighten the strap, and thus maintain automatically a fairly constant moment. This form of brake, like that of Appold, can only be used for measuring small horse-powers, unless we take into account the reaction at the point of suspension of the lever. So long as the friction between the wooden blocks and wheel is such that the weight of the brake-strap and suspended weight is sufficient, at the required speed, to carry the load without tightening the adjust- ing screw to any extent, the lever does not affect the results the conditions being similar to those which would obtain if the brake were without compensating lever, and the strap so slack that the bottom-blocks barely touch the wheel. That the resultant of the ten- sions in the brake-band resolved along the lever affects the measure of the power can be shown by means of the following figure (u). AND THE MEASUREMENT OF POWER. 35 Let the lever-ECD be in the position shown, and the system in equilibrium. The tensions of the brake- blocks on the lever towards the right at C, and left at D, are represented in the figure by T l and T y On the other hand, the reactions of the lever on the brake- blocks are T l towards the left at C, and T y towards the right at D\ then, since there is equilibrium in the sys- FlG. IT tern, the algebraic sum of the moments taken about the centre of shaft must equal zero. The resultant of the forces T l and T t , which we may call Q, must pass through the point of suspension, , of the lever. Resolving this force Q into its vertical and horizontal components acting at the point E, which is 36 D YNAMOME TEKS directly under the centre of the shaft or centre of moments, we have the moment of the vertical compo- nent equal to zero. Calling the horizontal component h, and the vertical component v, we have the sum of the moments about the centre of rotation : PR FR, - hr - vo = o, in which P is the weight acting on brake at radius R ; F is the friction between brake-blocks and rim of pulley acting at radius R l ; and // is that component of the reaction at the point of support of the lever which tends to produce a rotation about the centre of shaft ; its lever-arm = r. Since FR l PR hr, we have 2?rNFR l = 27tN(PR - hr) ; that is, the work absorbed by friction equals the work of the shaft in foot-pounds per minute (when R t , R, and r are in feet, and N = revolutions per minute), or, as previously found, W= 2nN(PR-hr\ and horse-power = --- (PR hr). The amount of the force h is best obtained by the use of a spring-balance. With a high coefficient of AND THE MEASUREMENT OF POWER. 37 friction the force h may be small, and might be disre- garded in approximate measurements, but in every case where accuracy is desired its moment must be con- sidered. Ropes used as brake-straps have given very satisfac- tory results. Prof. Andrew Jamieson, of the Glasgow College of Science and Arts, states that he prefers a rope brake to any one of the numerous forms which he has tried, and believes that it could be adopted for large powers and for long continuous runs, for the following reasons : " It could be constructed on^very short notice from materials always at hand in every factory, and at very .'J79424 38 D YNA MO ME TERS little expense. It is so self-adjusting that no accurate fitting is required. It can be put on and taken off in a moment ; is very light and of small bulk. It needs little or no attention for lubrication. The back-pull registered by the spring-balance is steady, and might be made a minimum by properly adjusting the weight. For larger powers only more, or larger, or flatter ropes, or a larger brake-wheel, would be required." Fig. 12 represents a rope-brake used by Prof. Jamie- son to indicate a gas-engine of fifteen brake horse- power. In this test the diameter of ropes was 0.6 inch, working over a 5-foot fly-wheel. The following are some of the conditions under which the test was made : * Mean revolutions of brake-wheel per minute 205 Weight, P, in Ibs 157 Mean back-pull on balance, in Ibs 4 Mean brake H. P. during two hours' run 1 5.23 Gas-consumption per brake H. P. in cu. ft. per hr. 24.3 " indie. " " " 18.9 More recently Prof. Jamieson has used the forms of rope-brake shown in Fig. 13. These are of the same kind employed in the trials of gas-engines under the auspices of the Society of Arts, London, and give much more satisfactory results than any other form of brake hitherto devised for light work. The substitution of the spring-balance in the right-hand figure for the weight shown at the left of the figure is a decided ad- *Sce paper by W. W. Beaumont in Proc. British Tnst. C. E., 1888-9; also Jamieson's Steam and Steam-engines (London, 1890). AND THE MEASUREMENT Of POWER. 39 FIG. 13. Two FORMS OF ROPEB-RAKB USED BY PROF. JAMIESON. 40 D YNA MOME TERS vantage, since by the use of two spring-balances of different periods of oscillation the " hunting" action of the brake is effectually minimized, enabling observa- tions to be taken with great precision. To obtain the brake-load it is only necessary to add the weight of the hanging part of the lower balance to its own reading, and subtract from this sum the back-pull as registered by the reading of the upper scale. This form of brake deserves to be better known ; for with it no lubrication whatever is required, and con- tinuous runs of any desired length of time may be carried out without any fear of overheating or requir- ing to stop for adjustment. With this brake Prof. Jamieson conducted a five- hour continuous test of Brown's Rotary Engine,* and obtained for speeds varying from 560 to 600 revolu- tions per minnte an average brake horse-power of 20.78. As the brake-wheel used was 4 feet in diame- ter it will be seen that the average surface velocity was nearly 7300 feet per minute a very unsatisfactory speed for friction-brakes. An interesting form of brake-dynamometer invented by M. Rappard, modified in order to adapt its use to large forces and high-speed machinery, is thus described in a recent issue of La Lumiere Electrique : f " One of these improvements consists in the substitu- tion, for the rubbing surfaces, of linen bands secured to metallic straps, instead of the ordinary belts usually employed. In this way a composition belt is obtained * Trans. Inst. Engineers and Shipbuilders in Scotland, Nov. 1891. f August i, 1891. AND THE MEASUREMENT OF POWER. 4! which is entirely inextensible, very strong and perfectly free to allow water to pass to cool the surfaces. "A strip of brass .08 inch thick covered with bands of linen .04 inch thick constitutes a very desirable form of belt for this work. " It is by the use of this new form of inextensible strap that M. Rappard has been able to construct the machines represented by Figs. 14 to 16. The apparatus represented by Fig. 14 consists " ist. Of a brake shaft connected by a universal joint to the motor to be tested. " 2d. Of a drum mounted mid-length of the brake- shaft, and of two loose pulleys placed on each side of the drum, upon the hubs of which the arms of a forked balance-yoke are supported. " 3d. Of three metallic straps, two for the loose pulleys and the other for the drum : this last, which produces the friction, is covered with a band of linen ; from the forked yoke to which it is attached this strap passes over the drum and descends vertically to the lower cross-bar of the frame. " The two other straps, also attached to the forked yoke, envelop the lower surface of the loose pulleys, from which they rise vertically and are attached to the upper cross-bar of the frame. " This vertical frame of wood (it would be better to construct it in part of wrought-iron pipe) carries at top and bottom two strong cross-bars, through which pass the bolts which receive the ends of the straps. " These bolts are for regulating the tension of the straps so as to produce the necessary friction to balance the load of the brake. DYNAMOMETERS " The whole apparatus is suspended by a chain which, after passing over a pulley rigidly supported above the frame, descends vertically and is attached to the lower bar of the frame, as shown. AND THE MEASUREMENT OF POWER. 43 "This arrangement is used to insure an equal rolling and unrolling of the belts on the pulleys and drum, in order to maintain a constant load on the brake not- withstanding the vertical movement. The weight of the frame and the brake-load are carried upon a rod situated in the centre of the vertical portion of the chain. " There will often be an advantage in placing the apparatus horizontally; in this case the plane of the bands is placed tangentially to the upper part of the drum, the horizontal motion being obtained by means of small friction rollers placed under the frame. At each end of the frame there is a chain which, after being stretched horizontally, passes under the pulley at an angle and descends vertically to the floor. The chains should be long enough so that they do not leave the floor whatever the. motion of the frame. " The brake-load is placed upon that one of the two chains which is connected to the cross-bar of the frame to which are attached the bands from the loose pulleys. " Fig. 15 is another arrangement of the Rappard bal- ance-dynamometer which permits placing the brake- shaft nearer the floor. The centre strap, covered with canvas, and which forms the rubbing surface, passes downwards and under a guide-pulley, thence upwards to the rod which receives the weights. " The two other bands, after passing under the loose pulleys, ascend, and are carried over guide-pulleys, thence downwards, and are attached to the extremities of a short beam, the centre of which receives the eye of the rod which carries the load. " Tension in the straps is obtained by means of two 44 D YNAMOME TERS screws and nuts which allow the shaft of the guide-pul- leys to be raised or lowered. " The water necessary for cooling the straps of the FIG. 15. brake instead of falling upon the exterior surface, is delivered to the interior of the drum by two small pipes passing between the drum and the two loose pulleys. The water is retained in the interior of the drum by AND THE MEASUREMENT OF POWER. 45 two narrow flanges, and is distributed over all the sur- face centrifugally; perforations across the face of the drum allow the water to lubricate the strap. " These automatic-balance-brakes permit very accu- rate results, for there is only the friction of the brake- shaft bearings to be deducted from the total measure of the work ; however, this friction is very small, since, on an average, it does not rise above one fourth per cent of the total work in an apparatus measuring 50 horse- power. " Still this cause of error can readily be overcome if desired, by mounting on friction rollers. In this case the brake-shaft bearings are replaced by the lengthened hubs of the loose pulleys, which are supported by four pairs of rollers as shown in Fig. 16; as will be noticed, the hubs of the loose pulleys do not revolve, and only follow the angular displacement of the forked yoke caused by the variations of friction." If we wish to determine the horse-power of a verti- cal shaft for instance that of a turbine by means of a friction-brake, we can no longer suspend the weight directly from the bar or lever, but must insert a bent lever, so that the vertical direction of the weight may be converted into a horizontal force. 46 D YNAMOME TERS Fig. 17 represents a friction-brake for a vertical shaft which w#s used by Francis in his Lowell hydraulic experiments in testing a i5O-horse-power turbine. The brake-wheel rim A is of cast-iron 5^ feet in diameter and 24 inches width of face. This rim is 3 inches thick, and is cast with internal lugs which permit it to be bolted to a spider keyed to the turbine shaft D, provision being made for a slight expansion between the end of the arms and the brake-rim, which is flanged to receive the brake-shoes. The brakes, E and F, are of maple, and are tightened by two 2-inch square bolts ; one of the brake-arms, F, is connected to the swinging lever, K, by means of the rod KL, as shown. From one end of this lever the scale-pan is hung, and to the other AND THE MEASUREMENT OF POWER. 4? end is connected a hydraulic regulator, N (see Fig. 3), which consists of an iron plate, half an inch thick, turned -jig- inch less than diameter of cylinder, free to move up and down in a cylinder filled with water, so that it acts, as previously noted, as a moderator in con- trolling any sudden vibrations of the lever-arm. The brake is cooled by means of a forked pipe, R, which throws jets of water against the wheel, the quantity of cooling water being about .17 cubic feet per minute. When running slow the lubrication was with linseed and resin oil ; water, however, was preferred for the faster speeds about 60 revolutions per minute. Mr. Samuel Webber, in 1884, had occasion to test a large turbine at Augusta, Ga., and for this pur- pose had a brake made similar in appearance to the one shown in Fig. 4, page 24, but arranged hori- zontally with a bent lever like the one just shown. In this brake the friction-pulley was 7 feet in diameter and 24 inches face. The brake-lever was of oak, 16 inches square, reaching 15.91 feet from the centre of shaft to the point of connection with the bent-lever scale-beam, which latter had a leverage of two to one to reduce the amount of weights to be handled. Lubrication was supplied by strong soap-suds fed from three large cans placed at intervals around the brake. Besides this a thin jet of water was thrown upon the brake through a flattened nozzle. The apparatus worked perfectly, and a steady test was obtained of 475 H. P. at 76 revolutions of the wheel per minute. This is probably the heaviest test of a single motor ever made with a brake. 48 DYNAMOMETERS The strap of the brake was made of boiler-iron lined with blocks of soft wood, and the pulley had deep flanges, so that the brake set into it like a saddle. The iron clamp was in two pieces hinged together at a point opposite the adjusting bolt. In connection with this brake Mr. Webber used a hydraulic regulator for the scale-beam, the cylinder of which was 18 inches diameter and the piston i/| inches. In using any form of friction-brake, if the surface in contact with the pulley be too large, it will be found that a considerable weight may be added to the scale- pan without materially altering the position of the lever-arm ; but if, on the other hand, this rubbing surface be too small, the resulting friction will show great irregularity probably on account of insufficient lubrication the jaws being allowed to seize the pulley, thus producing shocks and sudden vibrations of the lever-arm. The material in contact with brake-pulley, no doubt, enters largely into the question of smooth running, especially if the lubrication be not of the best. Soft woods, such as bass, plane-tree, beech, poplar, or maple, are generally to be preferred to the harder woods for brake-blocks. Old leather belting, secured to wooden blocks, forms a good rubbing surface, provided the leather is not sticky or gummy, and maintains a very regular motion of the brake if properly lubricated. For high speeds and small powers the writer has found strong soap-suds very efficient for this purpose. A convenient method of supplying the lubricant to small brakes is to place a large can, provided with a pet-cock, directly above the brake, allowing the soapy water to trickle down two or more wires which lead to AND THE MEASUREMENT OF POWER. 49 the pulley-surface. A trough and shield can be suit- ably arranged to catch the excess of water thrown from the pulley. For light tests Mr. Webber has found that cork gives a very good rubbing surface. Babbitt metal has also been used for this purpose the pulley being grooved and the Babbitt shoes cast to fit it. There is no doubt that this material would give excellent results as a brake-rubbing surface if properly lubricated. $O D YNAMOME TERS Self-cooling brakes, Fig. 18, where both the rim of the pulley and the brake-strap were hollow, with a stream of cold water flowing through them, were used by Mr. Emerson at Lowell in 1869, oil being used on the metallic rubbing surfaces as the lubri- cant. In this brake the wheel B is made of cast-iron, and the friction-band of composition or gun-bronze, the hollow band being supplied with water from the out- side, while the rim of pulley is kept cool by means of water which enters the hub and is delivered through the hollow arms to the rim. Mr. W. W. Beaumont, in his excellent paper on " The Friction-brake Dynamometer," previously re- ferred to, has given a formula by means of which the relative capacities of brakes can be compared, judging from the amount of horse-power ascertained by their use: If W= width of rubbing surface on brake-wheel in inches ; V= velocity of point on circumference of wheel in feet per minute ; K= coefficient, then " ~H.P: The average of three brakes cited by Mr. Beaumont gives the value of K as 860. In Table IV is given a number of tests and the size of brake used, from which the value of A" has been cal- culated, as shown in the last column. These figures AND THE MEASUREMENT OF POWER. have been collected from various sources and represent varied practice. TABLE IV. CAPACITY OF FRICTION-BRAKES. R.P.M. Brake- pulley. Length of Horse- power. Brake- puliey. Face ir inches. Dia in feet. arm in inches. Design of Brake. Value of K. 21 150 7 5 33 Royal Ag. Soc., com- pensating 785 19 148.5 7 5 33-38 McLaren, compensating 8 5 8 20 146 7 5 32.1 9 McLaren, water-cooled and compensating. . . 802 40 180 10.5 5 32 Gatrett, water-cooled and compensating. . . 741 33 IKO 10.5 5 32 Garrett, water-cooled and compensating. 749 150 150 10 9 Schoenheyder, water- cooled 282 24 142 12 6 38.31 Balk, compensating. . . . 1385 180 100 24 5 I26.I Gately & Kletsch, water- cooled 209 475 76.2 24 7 15. gift. Webber, water-cooled. . 84.7 125) 2CQ ( 290) 2CO C 24 4 63 Westinghouse, water- cooled 465 *y i 40 i I2C C *D ) 3 22 ) 2QO f '3 4 *7l VVestinghouse, water- cooled 847 A *D J ^yw j By referring to the table it will be seen that the above calculations for eleven brakes give values of K varying from 84.7 to 1385 for actual horse-powers tested, the average being K = 655. By a comparison of the sizes and speeds given by Mr. Heinrichs (see Table II), K is found to average 895 for small horse- powers varying from 2 to 8. From the nature of the device, these latter brakes are not water-cooled. 52 D YNA MO ME TERS In the Gately & Kletsch water-cooled brake (for de- scription of which see article by Prof. R. H. Thurston in Jour. Franklin Inst., April 1886) the wheel was designed to measure 540 horse-power, but it does not appear to have been used to indicate more than 180 horse-power. For this number K = 209. In the Schoenheyder water-cooled brake K = 282 ; in the large Westing- house brake K varied from 288 to 709 for actual horse- powers tested, averaging 465. For the smaller Westinghouse brake, K averaged 847, which seems to be the only case in which the value of the coefficient for non-compensating brake ex- ceeds that ascertained for compensating brakes. The average value of K for the several water-cooled non- compensating brakes is 377, and for the compensating brakes ^=853. Neglecting the extreme value as given for the Balk brake, K will equal 762. From these deductions it would appear that when the brake-strap is provided with some form of compen- sating device (as, for instance, that shown in Fig. 10) by which a self-acting adjustment of the tension of the strap is supposed to maintain a nearly constant moment of friction, the rubbing surface is generally greater than when such device is not employed. Instead, therefore, of assuming an average coefficient of 860, the writer would propose the following : K 400 for water-cooled brake non-compensating ; K = 750 for water-cooled brake compensating ; ^=900 for non-cooled brake with or without com- pensating device. AND THE MEASUREMENT OF POWER. 53 For metal brake-shoes the value of K could prob- ably be much less, as the radiation of heat from the metallic surfaces would be greater. From the above values of K the width of brake- wheel can be obtained for the different types : _ V V in which, as before, W '= width of bearing surface in inches on pulley, and V = velocity of a point on cir- cumference of pulley in feet per minute. In the different forms of Prony and friction brake, it is evident that as the work of the shaft is all spent in overcoming the resistance due to friction, no useful work is done. The friction-brake is thus an absorbing dynamometer. 54 D YNAMOME TERS CHAPTER III. ABSORPTION-DYNAMOMETERS. ANOTHER form of absorbing dynamometer is that de- signed by Prof. C. B. Richards, of the Sheffield Scien- tific School of Yale University. It consists of a tank, AB (Fig. 19), within which two paddle-wheels revolve Oil Supply FIG. , 9 . in oil, thus producing a resistance and a tendency to rotate the whole tank, which is mounted on friction- rollers. This tendency to rotate is measured by the lever-arm acting on a platform-scale. By means of the valve v the oil in the tank can be allowed to circulate with greater or less freedom ; by closing the valve a AND THE MEASUREMENT OF POWER. 55 pressure is brought to bear on the oil in the tank, so that the resistance to the rotation of the inner wheels thus becomes a drag on the driving power ; when the maximum resistance is obtained without decreasing the number of revolutions per minute of the shaft, the force of resistance, measured on the scale-beam, will enable us to calculate the horse-power consumed. In order to prevent any change of temperature in the oil, a constant stream of water is discharged onto the tank through a perforated pipe, P, above it. Beneath the tank proper a metal receiver, R, catches the water, which is then carried off by the waste-pipe W, shown at the bottom of the receiver. Part of the tank AB, and also of the outside receiver R, is torn away in the figure, in order to show more clearly the circulation of oil and position of the paddle- wheels. One of these latter is mounted on the pulley- shaft, and has the same direction of rotation as the belt-pulley ; the other is driven by a gear (not shown), and revolves in the opposite direction. A casing at each end of the tank fits close to the paddle-wheels, the blades of which roll on each other. In this re- spect the internal arrangement is similar to that of various rotary engines and blowers. In order that there should be a minimum amount of vibration of the scale-beam while weighing the pressures, a rod and dash-pot were used the latter being supported by an arm attached to the side of the scales. The size of this dynamometer was 30 X 14 X 18 inches, and would measure from ^ to 14 horse-power. With this apparatus, as with the Prony brake, it will be seen that an absorbing dynamometer cannot be 56 D YNAMOME TERS used to determine the power which is actually trans- mitted to a machine ; it can only measure the power which is produced in circumstances as similar as pos- sible to those under which the machine is operated ; and this power is assumed equivalent to that con- sumed by the machine. About the year 1873, Prof. Richards used this principle of measuring the tendency of the belt to rotate a body about its axis, and de- signed a stand or cradle upon which the machine itself was suspended on trunnions. When the machine to be tested was put in motion, its tendency to rotate thus became a measure of the resistance. This same principle was introduced by Prof. Brack- ett, of Princeton, a number of years later, in his cradle-dynamometer, which is now very generally and successfully used in testing dynamos and electric mo- tors. A little consideration will show that the cradle- dynamometer measures the actual power transmitted to the machine or developed by the motor, and is thus a transmitting dynamometer. As such it will be con- sidered subsequently. An absorption-dynamometer, by which also any desired load can be maintained on the engine, is the invention of Prof. Alden, of Worcester. This dyna- mometer is essentially a friction-brake in which the' pressure causing the friction is distributed over a com- paratively large area, thus giving a low intensity of pressure between the rubbing surfaces. This friction is produced by the pressure of water from the city pipes acting upon two copper plates in contact with a smooth cast-iron disk keyed to the shaft AND THE MEASUREMENT OF POWER. which revolves in a bath of oil between the plates. These latter are secured by a water-tight joint to a casing which does not revolve, and to which is bolted a lever-arm carrying weights as in an ordinary Prony brake. The shell or casing is so constructed that it permits an equal pressure of water upon both sides of the disk a sufficient quantity of the water being al- lowed to pass through the machine to carry off the heat due to the energy absorbed. An ingenious form of valve operated by the slight angular motion of the dynamometer varies the supply of water, and con- sequently the pressure between the frictional surfaces, thus securing auto- matic regulation. Referring to Figs. 20 to 24, A (Fig. 20) is an iron disk keyed to the crank-shaft B. The sides of this disk are finished smooth, and each side has one or more shallow radial grooves, as shown at X (Fig. 21). The outer shell consists of two pieces of cast-iron, C C, bolted together, but held at a fixed distance apart by the iron ring D whose thickness is the same as that of the disk A and by the edges of the copper plates E E. Each of these plates at its inner edge makes with the cast-iron shell a water-tight joint by being " spun " out into a cavity in the iron and held by driven rings F F. Thus between each copper plate and its cast-iron shell there is a water-tight compartment, WW, into which water from the city pipes is admitted at G, and passing 5 > YNAMOME TERS to the opposite compartment through passages, as shown at O, is discharged through a small outlet at H- The chamber MNN is filled with oil, which finds its way from TV to M along the grooves in the disk A. The shaft is free to revolve in the bearings of the cast-iron shell CC. The shell has an arm carrying weights, as shown in Fig. 21. The arm has its angular motion limited by stops at P and Q. FIG. 21. An automatic valve at V (Fig. 22 and shown in sections, Figs. 23 and 24) regulates the supply of water to the machine. The valve consists of two brass tubes fitted one in- side the other, but free to revolve relatively to one another. The inside tube has one end closed. Each tube has slots parallel, or nearly parallel, to its axis. One tube connects with the supply-pipe S, the other with a pipe rigidly fixed to the brake and com- municating with one of the compartments W. A flex- AND THE MEASUREMENT OF POWER. 59 ible tube, R, encloses the whole. The valve is so adjusted that a slight angular motion of the brake varies the free water passage through the slots (see Fig. 23) ; and the aperture at H, through which the water is discharged, being small and constant, the press- ure of the water in the chambers W W is thus auto- matically varied. The dynamometer is operated as follows : The chamber NNM being filled with oil, weights are sus- pended from the arm to give the desired load. The engine is started, and when up to speed a valve is suit- ably opened in the water-pipe leading to the automatic valve (V], which latter being open, allows water to pass to the compartments W W. The pressure of this 60 D YNAMOME TERS water forces the copper plates against the sides of the revolving disk A with which they were already in contact causing sufficient friction to balance the weights upon the arm, which then rises. This motion operates the automatic valve, checking the flow of water to the brake and regulating the moment of the friction on the disk to the moment of the weights ap- plied to the arm of the brake. The first trial of the machine gave remarkable results, the arm standing midway between the stops, with only a slight and slow vibration, and this without the use of a dash-pot. The water seems a little sluggish in its action in response to the motion of the regulating valve, so that there is no sudden vibration of the arm, and the load is practically constant.* In experimenting with a 5O-horse-power Alden brake, Prof. Goss, of Purdue University, has found that the operation of the brake is very materially improved by cutting spiral grooves on each face of the revolving plate and connecting the inner com- partment between the copper disks with two pipes the one near the hub, and the other at the outer cir- cumference of the shell. This admits of a better dis- tribution and circulation of the oil, which is fed from the pipe connected to the chamber near the hub. From this chamber the oil is carried to the circumfer- ence, both by the radial grooves and by the spiral groove which crosses the former, thus ensuring a very even and uniform distribution of the oil, which then passes out at the circumference into a strainer situated * Trans. A. S. M. E., vol. VI. AND THE MEASUREMENT OF POWER. 6 1 above the oil feed-pipe, whence it is again carried to the central chamber at the hub, and the process repeated as long as the machine is in operation. An interesting application of the Alden brake has been made in the Experimental Laboratory of Purdue University by which the power of an eight-wheeled passenger locomotive is absorbed. In this arrange- ment, Fig. 25,* the locomotive, weighing 43 tons, is ' mounted .with its drivers, which are 63 inches in diameter, upon heavy supporting wheels, of the same diameter, free to revolve by contact with the drivers in either direction : the prolonged axles of the support- ing wheels are each provided with a large flat cast iron disk keyed to the shaft, which is allowed to rotate in a closed case between plates of copper, about three- sixteenths inch thick, which can be forced against the rotating disk by hydraulic pressure as in the Alden dynamometer. Each brake was designed for a load of 200 H. P. under a moment of 10500 foot-pounds, with a maximum water pressure of 40 pounds per square inch. The shaft to which the disk is keyed is 7$ inches in diameter. The disk is 56 inches in diameter and 2f inches thick ; it is provided with thirty-two radial oil- grooves on each face, besides which a spiral groove of about 4 inches pitch is cut across the face intersecting the radial grooves, thus thoroughly distributing and circulating the oil as in the smaller brake previously alluded to. The locomotive is free to move forward or backward only through a very small distance (about a quarter of an inch), its tendency to motion in either * From Am, Machinist, April 28, 1892. 62 DYNAMOMETERS AND THE MEASUREMENT OF POWER. 63 direction being measured by a system of levers and weights connected to the draw-bar by which the trac- tion of the engine can readily be weighed. Any desired load and speed can be maintained by means of the powerful 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. The smoke is exhausted through the roof of the building by a Sturtevant blower which is placed above the smoke-stack, but not in connection with it. An absorption-dynamometer, designed by Mr. Wm. Froude* to measure the power of large marine engines is essentially another form of water-brake. In this arrangement, the engine in delivering its power may be assumed to be winding up a weight out of indefinite depth, but the weight instead of being constant and assigned (as in the case of the suspended weight on a friction-brake) will vary with the speed of rotation much in the same way as the resistance of the propeller itself does; and thus the work performed by the engine under trial will more closely resemble its natural work, though the same circumstance renders necessary an automatic method of recording the varia- tions of the resistance which occurs during the trial. The reaction, as will be shown, instead of arising from the friction of two solid surfaces, will consist of a series of fluid jets which are maintained in a condition of in- tensified speed by a sort of turbine revolving within a casing filled with water, both turbine and casing being mounted on the end of the screw shaft in place of the Proc. Brit. Inst. M. E., vol. for 1877. 64 D YNA MO ME TEKS screw ; the turbine revolving while the casing is dy- namometrically held stationary. The jets are alter- nately dashed forward from projections in the turbine against counter-projections in the interior of the casing, tending to impress forward rotation upon the casing, and are in turn dashed back from the projections in the casing against those in the turbine, tending to re- sist the turbine's rotation. The important point is that the speed of jets is intensified by the reactions to which they are alternately subjected ; and thus, in virtue of this circumstance, a total reaction of very great magnitude is maintained within a casing of com- paratively very limited dimensions. The nature of this arrangement will be understood by referring to the following figures, which represent the dynamometer as designed to measure 2000 H. P. In Fig. 26, A represents the screw end of the screw- shaft ; BB shows in section what has been termed " the turbine " ; it is a disk or circular plate 5 feet in diameter, with central hub keyed to the shaft in place of the screw, and revolving with the shaft. The disk is not flat throughout its entire zone, being shaped into a semi-oval section which sweeps around the whole circumference concentric with the axis. In Fig. 27 Fig. 26 is repeated and the "casing" is added, CC representing the front and DD the back. The face is shaped into a channel the counterpart of that in the turbine disk, so that the two semi-oval chan- nels in effect form one complete channel. The back of the casing encloses the turbine entirely, but without touch- ing it. The casing is also provided with a hub, which is an easy fit over that of the turbine, so that the latter AND THE MEASUREMENT OF POWER. 6$ is free to revolve within the casing, which is stationary. Both casing and turbine are provided with a series of twelve fixed diaphragms, one of which is showgi in Fig. 28. These diaphragms cut the channel obliquely, being semicircular in outline, so that when set at an angle, as shown in side-view (Fig. 29), their circular edges fit the FIG. 27. FIG. FIG. 29. PROUDE'S M DYNAMOMETER. oval bottom of the channel, while their diameters span the major axis of the oval. Thus is formed by casing and turbine, when the diaphragms are opposite to each other, a series of cells ; and as the function of the tur- bine is to rotate while the casing remains at rest, one half of each cell is moving past the other half in such a manner that the moving half, if viewed from its sta- 66 D YA'AMOME TEK$ tionary counterpart, would appear to be advancing antagonistically towards it. The effectiveness of this combination to resist rotation will be seen to depend essentially on this assumed antagonistic motion. The channel and casing is filled with water, and the turbine is made to rotate as described. When the tur- bine is thus put in motion, the water contained in its half-cells is urged outward by centrifugal force, and in obeying this impulse it forces inward the water con- tained in the half-cells of the stationary casing, and thus a continuous current is established outward in the turbine's half-cells, and inward in those of the casing. The current, though in fact originated solely by cen- trifugal force, possesses, when once called into exist- ence, a vitality and power of growth quite independent of centrifugal force and dependent on, what has been called, the virtually antagonistic attitude or motion of the two sets of diaphragms and the cells of which they are the boundaries.* It can be shown that, with a dynamometer of given dimensions, the reactions which tend to stop rotation of the turbine and to give rotation to the casing will be as the square of the speed of rotation of the shaft to which it is attached; and that by comparing two similar, but differently-dimensioned turbines, their re- spective moments of reaction for the same speed of ro- tation should be as the fifth powers of their respective diameters. Mr. Froude constructed an experimental pair of dy- namometers in which the turbine diameters were re- * For discussion of principles involved, see Appendix in vol. for 1877 Proc. Brit. Inst. M. E. AND THE MEASUREMENT OF POWER. spectively 12 inches and 9.1 inches. /I2V Now(- ; ) =4. and therefore the ratio of moments of the two instru- The , but ments at a given speed should also have been 4. ratio determined by experiment was in fact 3.8 the small difference is referable to the circumstance FIG. 31. FROUDE'S MARINE-ENGINE DYNAMOMETER. that in the larger of the two instruments the internal surface was rougher and the friction of the water greater. The data thus obtained not only verify the scale of comparison based on the fifth power of the re- spective diameters, but also furnish a starting-point by which to proportion the dimensions of an instrument required to deal with any given horse-power delivered at a given speed. It thus appears that an instrument similar to that shown in Figs. 30 and 31 will measure 2000 H. P. at 90 revolutions per minute; the turbine being 5 feet in di- 68 D \ 'NAMOME TERS amcter, and formed with two faces, with a double-sided casing to match. This double arrangement, it may be added, while it supplies a double circumferential reac- tion with a given diameter, has the advantage of oblit- erating all mutual thrust on working parts. In order to adapt this dynamometer to measure varying horse- powers that is, to produce readily a greater or less reaction with a given number of revolutions two sliding shutters, E E, of thin metal, fitted between the turbine and casing, are arranged so that each shutter may be carried forward by a screw-motion governed from the outside. By this means the internal water-ways or passages through the cells are contracted and the reactions greatly reduced. The experiments with the models showed that, with any given speed of turbine, the reaction could be re- duced with a perfectly graduated progression in any required ratio down to one-fourteenth. The intensity of reaction is thus easily brought un- der the control of the operator within a wide range. The brake represented in the figures, and designed, as stated, for an engine of 2000 H. P. at 90 revolutions per minute, is also capable of dealing with one of 340 H. P. making 120 revolutions per minute. The mechanical reaction due to friction in the working parts of the instrument, while of relatively small amount, is in effect wholly incorporated with the hydrodynamical reaction, and is thus taken account of. In applying this dynamometer to measure the power of a ship's engines the instrument is mounted upon the screw shaft in place of the screw, as shown in Fig. 32. AND THE MEASUREMENT OF POWER. The casing is provided with proper apertures, capa- ble of being closed at will, to permit the egress of air and ingress of water. If the moment to be measured and recorded be re- garded as the product of two factors, force and lever- age, of which the one varies inversely as the other, it is plainly a question to be settled by considerations of FIG. 32. MARINE-ENGINE DYNAMOMETER. MODE OF APPLICATION. convenience, whether the record shall involve a large force delivered at short leverage, or vice versa. In the present case it will be seen that a large leverage is desirable ; for, if we assume the force to be acting at the circumference of the casing, say 3 feet from centre 2OOO ^X* ^ 3 OOO of shaft, there will be required ^^ .i 4 X3X9Q = 389 4 Ibs. a force which will bear large reduction. In the arrangement shown (Fig. 32) the leverage has been in- creased in the ratio of 10 to I. The lever here shown consists of a rod F and wire rope , connected to the casing C at one end and unit- 70 D YNA MO ME TERS ing in H at the other. As the force at H acts down- wards, it will be seen that F is in compression and G in tension. A suitable weighing apparatus, consisting of a sys- tem of flat springs and levers, is provided for ascertain- ing the load, to which is attached a recording device connected to the screw-shaft through the rod L, which takes its motion by bevel gears directly from the shaft. More recently, Prof. Osborne Reynolds,* of Owens College, Manchester, has constructed several of these water-brakes for experimental purposes ; and as the ^result of his experience he finds that air is drawn from 'the water and accumulates in the centre of the cells, -^occupying water space and diminishing resistance, besides producing an irregular motion. This would be prevented if passages could be provided through the outside to the axis of vortex within, carrying a supply of water at or above atmospheric pressure, so as to pre- vent the pressure at this point falling below that of the atmosrJliere. This was accomplished by Prof. Reynolds by perforating the vanes of the turbine and supplying water through the perforations. It also appeared that by having similar perforations in the casing open to the atmosphere the pressure at centre of vortex could be rendered constant, whatever the supply of water and speed of wheel, so that it would then be possible to run the brake partially full and regular; resistance from nothing to maximum, without sluices. These conclusions being verified on a small model (4-inch turbine), three larger brakes with i8-inch wheels * See Proc. Brit. Inst. C. E-, vol. xcix, also Van Nostrand's Science Series, No. 99. AND THE MEASUREMENT OF POWER. 71 were constructed. These brakes proved everything desirable except when running under a constant load with varying speeds. This matter was considered dur- ing their construction, and an arrangement was devised by which the supply and exit of water to and from the brake was automatically controlled ; the lifting of the lever opening the exit and closing the supply so as to diminish the quantity of water in the brake, and vice versa. During the twelve months these brakes have been in use they have received no attention whatever. The casing is provided with a lever 4 feet long from centre of shaft to the weight. When the speed of engines reaches about 20 revolutions per minute the levers rise (whatever load they have on), and though always in slight motion, they do not vary half an inch until the engines stop ; during the run, the load on the brakes may be altered at will without any other adjust- ment. The engines to which the brakes were connected were each designed to work with any steam-pressure up to 200 pounds per square inch, at any piston-speed up to 1000 feet per minute, and to have expansion-gear to cut off from o up to two-thirds stroke. Each engine was furnished with a fly-wheel weigh- ing 1 200 pounds. The dimensions of engines were as follows : High-pressure . . 5 inches diameter, 10 inches stroke Intermediate... 8 " " 10 " " Low-pressure... 12 " " 15 " " All the cylinders were steam-jacketed, but arranged so that any or all of the jackets could be cut out. 72 D YNAMOME TERS CHAPTER IV. TRANSMITTING-DYNAMOMETERS. Half a century ago, Morin gave as the requirements of a dynamometer the following, viz.: First. The sensibility of the instrument should be proportioned to the intensity of efforts to be measured, and should not be liable to alterations by use. Second. The indications of flexures should be ob- tained by methods independent of the attendance, fancies, or prepossessions of the observer, and should consequently be furnished by the instrument itself, by means of tracings, or material results, remaining after the experiments. Third. We should be able to ascertain the effort exerted at each point of the path described by the point of application of the effort, or, in certain cases, at each instant in the period of observations. Fourth. If the experiment from its nature must be continued a long time, the apparatus should be such as can easily determine the total quantity of work ex- pended by the motor. To meet these conditions, Morin made the spring- dynamometer, in order to obtain the magnitude of a force, as, for instance, the traction of a horse on a loaded wagon or canal-boat. In this dynamometer a force was measured by the flexure produced by it on two springs connected at AND THE MEASUREMENT OF POWER. 73 their ends and loaded in the middle. When a steel bar of rectangular cross-section is placed freely upon two supports, and subjected in the middle to a force P perpendicular to its length, its flexure, s, so long as it does not exceed the limits of elasticity, will be : First. Proportional to the effort P. Second. Proportional to the cube of the arm of the lever / of this effort. Third. In an inverse ratio of the width of the bar b, in a direction perpendicular to the plane of flexure. Fourth. In an inverse ratio of the cube of the thick- ness of the bar /i, at its middle point. Fifth. In an inverse ratio of the modulus of elas- ticity, E, for the material of the bar. The deflection for the force P will be, therefore, PI* i s = - X -g = equation of elastic curve, or, since W = --- = moment of flexure for rectan- gular strip, we have for deflection i pr Since we have to take into account the deflection of two springs, = 1 ^_ ~ 2 Eb/f Now, if the longitudinal profile of the bar is para- bolic, the flexure will be double that of a spring of 74 # YNA MOMETERS uniform thickness, while the strength remains the same. Hence we have where n is a number to be determined by experiment. If in the construction of a spring-dynamometer, known weights be applied, and the deflection s ob- served, the number;/ can be calculated and used in the construction of a scale. Morin found that with good steel the deflection may reach one tenth of the length of the spring before the relation between it and the force changes. In order to meet the second, third, and fourth requirements above mentioned, a self-registering apparatus was used, by which the work performed was traced upon a continuous roll of paper, set in motion by suitable wheel-work. When required to determine the force of rotation of a shaft or pulley the above dynamometer requires modification ; the essential features, however, remain the same. The following description illustrates the application of the foregoing principles to the rotation-dynamom- eter. Upon a shaft resting on two cast-iron supports are three pulleys of the same diameter, Figs. 33 and 34. A is fixed, C is loose, and B is movable around the shaft between the limits which we shall indicate. This apparatus being placed between the driving-shaft and a machine whose resistance is to be measured, the loose pulley C receives the power from the driving-shaft by AND THE MEASUREMENT* OF POWER. 75 means of a belt, which, when transferred to A, sets the shaft 5 in motion. The pulle'y B is free on the shaft, and is connected to it by means of two parabolic springs which are fastened to the shaft, and at the end G to the rim of B. These springs turning with the shaft deflect more or less, according to the resistance encountered, and when the resistance to flexure overcomes the resistance of FIG. , 3 . FIG. 34. LMJ MORIN'S TRANSMI M-DYNAMOMETER. the machine, motion is transmitted through the springs to B. Upon the shaft is a worm, K, having a stop,/, so that by means of a sliding bar, mn, it may be prevented from revolving with the shaft during the experiment. By a suitably arranged train of gearing a series of drums is set in motion, by means of which a roll of paper is caused to pass under a pencil, P, attached to one of the arms of pulley B, thus recording the resist- ances, and giving a measure of the work performed. Using the same notation previously given, and sub- 76 D YNA MCME TERS stituting R radius of path in feet for L, we have the work done W= 27tRNP; where P= resistance overcome in the machine driven by the dynamometer. P can be readily ascertained when deflection of spring is known. One of the prin- cipal objections to the use of this instrument is that the centrifugal force of the rotating pieces enters as a factor into the final result ; for accurate work this will necessitate corrections for different speeds, and in this respect Morin's dynamometer does not fulfil his third requirement of a good instrument, viz.: " We should be able to ascertain the effort exerted at each point of the path described by the point of application of the effort, or, in certain cases, at each instant in the period of observations." Another form of transmitting-dynamometer, some- times called the differential dynamometer, was intro- duced into this country by Mr. Samuel Batchelder, of Saco, Maine, in 1836. The principle of this machine is, that to hold a weight by the radius of a circle in a horizontal position takes as much power as to lift the same weight through the distance which would be traversed by it in any given number of revolutions if rotated in the circle and in the time required for such number of revolutions. We have already seen that this is the governing principle of the Prony brake where the lever is maintained in a horizontal position, the work being estimated as though the weight suspended at the end of the lever rotated in a circle whose radius was equal to the length of arm L. Though alike in princi- ple, the methods by which these two dynamometers AND THE MEASUREMENT OF POWER. JJ operate are radically different. The Batchelder in- strument, improved and modified, is now made by the FIG. 35.-WEBBER B Lawrence Machine Co., and known as the Webber bal- ance-dynamometer. The following description of this machine (see Fig. 78 DYNAMOMETERS 35) is taken from a paper by S. S. and W. O. Webber, read before the Society of Mechanical Engineers.* " On the receiving-shaft are fixed a pair of fast- and-loose pulleys at one end, and a spur-gear at the other. This spur-gear drives a corresponding gear of the same size and number of teeth, which is fixed on the end of a sleeve or collar, having on its other end a bevel-gear which forms one side of what is known as a ' box' or 'compound ' gear. A corresponding gear on the opposite side of the ' box ' is fixed on the delivering- shaft which passes through the sleeve above mentioned, and also through the fulcrum of the scale-beam. The two remaining sides of the box are composed of a pair of equal and similar gears, which revolve freely around the scale-beam on either side of the fulcrum. " One would really be sufficient for the purpose, but a pair is used in order to preserve a balance. When motion is given to the shafts by means of a belt to the receiving-pulley, the intermediate gears revolve about the scale-beam without effect ; but when a belt is car- ried from the delivering-pulley to the machine to be tested, the resistance causes the intermediates to act with the effect of levers on the scale-beam, and would put the latter in revolution about its axis or fulcrum if it were not restrained by the weights, which are to be added, and adjusted until a balance has been obtained. It will be readily seen that the real motion of the scale-beam, were it free to move, would only be one half that of the shafts, and the weights in actual use are therefore double their apparent value or .in other * Trans. A. S. M. E., vol. iv. AA'D THE MEASURED EXT OF POWER. 79 words, the weight marked 1000 pounds is in reality two pounds instead of one." The circumference of the circle through which the weight would travel, were it free to move, is ten feet, therefore we can readily calculate the horse-power from the following : HP - Pv - p ~ 33 ooo ~~ 33 ooo since 2nR = 10, we have 33000' in which, as in our former notation, P pounds weight, N = revolutions "per minute, and v = velocity in feet per minute. The weights are marked for N = 100. Another form is that known as the belt transmission- dynamometer, used by Dr. Hopkinson in his tests with the Siemens dynamo-electric machines. The principle involved is the weighing of the result- ing stress from a deflected belt, and by this means as- certaining the direct stress upon the belt itself. As previously intimated, the power exerted by a belt is the difference of strain on the two sides of the belt, multiplied by the velocity of a point on the belt. A belt connecting two shafts, when at rest, has the same tension in all its parts, but as soon as work is performed by the belt this uniform tension ceases, the driving- shaft exerts a pull on the driven proportional to the resistance overcome, and as the adhesion of the belt is 8o D YNA MOME TERS brought into play, one side that on which the pull is exerted is tightened, while the other is correspond- ingly slackened.* To obtain a measure of this difference in belt-strain, the dynamometer shown in Fig. 36 was designed by Mr. Robert Briggs. FIG. 36. BRIGGS BELT-DYNAMOMETER. In this arrangement it is evident that when at rest, or running with no resistance, the system will come into equilibrium with equal but opposite angles for both the lower and upper belt provided the weight of the car- rier-pulleys, the frame supporting same, and the weight * In a series of experiments on leather belting made by Wm. Sellers & Co. in 1885 it was shown that the sum of the belt-tensions is not constant, but increases with the load. This is contrary to the generally accepted theory that the sum is constant, but subsequent experiments have shown that the total tension actually increases as the difference increases, whether the belt be horizontal or vertical. \ND THE MEASUREMENT OF POWER. Si of the belt are balanced. It can be shown that the resultant of strain from the deflected belt varies as the cosine of the angle which the belt makes with the ver- FIG. 37. tical, or W= 2P cos a, (Fig. 37) ; therefore, if we make the angle 75 31', the cosine will equal 0.250, or cos- 1 =75 31'. Let cos a .25 ; tension on tight side of belt = 7", ; tension on slack side of belt = T^ ; weight = W ' force transmitted = P\ then will 7 1 , T, = P. Now, since W= 2P cos a, and cos a = 0.25, we have W 2P X , hence If, therefore, a weight w be applied on the scale- beam so that it exerts a force W, acting downwards, there will be transmitted by the belt a force P= 2 W, in order to maintain the system in its central position; and this force is a measure of the driving power of the belt! 82 D Y A' A MO ME 7ERS Accepting these relations of angles and force, the following diagram, Fig. 38, will show the relative posi- tions of the arrangement employed. An allowance of y 1 ^ inch has been made for half the thickness of belt when the radii of the line of the belt on the two pulleys become as shown, 8.1 and 12.1 for the 16- and 24-inch pulleys respectively. Diam. 8 D YNAMOME TERS stability is reduced, to the small amount required, by raising some of the ballast to the top of the caisson or to a (removable) shelf t Q, over the machine. See Fig. 46. For dynamometers of large size the use of heavy ballast can be avoided by the stability-trough K. This is a trough of triangular section running entirely round the inside of the caisson and partly filled with the same liquid as is in the tank ; by putting more liquid in the trough the stability is decreased. The machine should be put on in the first place at about the right height ; the higher it is the less the stability. The right height can be determined by a simple calculation of the centre of gravity of the float, but this is not necessary, for the machine may be at once mounted and blocked up until the float shows signs of insta- bility, when the final adjustment can be made with the ballast. The countershaft should then be blocked up to about the same height. Instead of setting a light machine high on the caisson to secure small stability, loose ballast can be put at once on the shelf Q until the proper stability is obtained. By a suitable arrangement of mechanism upon the caisson power may be transmitted from one machine to another, both standing upon the floor, and the ma- chine becomes a transmitting-dynamometer. A very high degree of precision can be attained with this dynamometer. In fact, as there is practically no friction in the liquid to interfere with the action of the caisson, almost any degree of precision may be reached. Experience has shown that in close comparative tests of machines, or in measuring their friction or air-resist- ance, there is no other dynamometer with which the AA r l) THE MEASUREMENT OF POWER. 10Q (almost unavoidable) accidental errors may not cover up or reverse the results ; this is the natural result of the simplicity of principle and construction of this dynamometer. The particular machine illustrated in the figures as mounted for the purpose of being tested will serve as an illustration of this fact. In attempting to measure the friction of gearing it has been cus- tomary to measure the power supplied to the gears and that received from them, and to take the difference of these two quantities as the amount lost in friction ; but the unavoidable error in measuring these two quanti- ties by ordinary means is such as to introduce much uncertainty into the value obtained for the friction, and in many cases to render it entirely valueless. In explanation of the particular method illustrated for measuring the friction of gears, it may be further explained that the lower shaft has two gears fast to it, while on the upper shaft the forward gear is free to turn on the shaft. The upper gears are connected by an adjustable spring, N, by means of which the loose wheel is powerfully rotated so as to bring the teeth of the upper and lower wheels in contact, with a known and adjustable pressure. By this arrangement it must be evident, upon examination, that the horse-power or energy transmitted by the gears is carried around in a circuit only through the gears themselves, and does not at all embarrass the direct measurement of the loss due to friction. The gear at the back, or counter- shaft side, on the lower shaft drives the gear above it, communicating to it a certain horse-power, dependent upon the velocity of the teeth and the pressure between them. This gear drives the one in front of it on the 1 1 D VNA MO ME TERS upper shaft, by means of the spring N, and then this gear drives the gear beneath it, thus returning the horse-power to the lower shaft, less the loss by friction. The upper shaft is adjustable on the standards M. The dynamometer, therefore, is called upon to meas- ure the friction only, and no such reliable determina- tion of frictional losses can be made by a measurement of gross and net horse-powers, where the small quan- tity lost must be obtained as the difference between the relatively large gross and net quantities. This differential method of measuring friction was first pub- lished by Professor Webb in the Transactions of the American Society of Mechanical Engineers.* In measuring the friction and internal air-resistance of any machine no special precautions are needed ; the machine is simply run for that purpose and the measurement made in the same way as any other measurements of the power absorbed by the machine. It is, however, to be noted that, in attempting to do this with a dynamo, the residual magnetism will cause a waste of power in Foucault currents, which will be included in -and may invalidate the measured result. This residual magnetism, however, may be nearly eliminated by means of a current from a battery, or from another machine, which is passed through the field and successively reversed and reduced by means of a rheostat. There is no way of separating the in- ternal air-resistance from the friction, except to get rid of it by running the machine in vacuo. If it be the external air-resistance or " fanning" that *Vol. ix. p. 213. AND THE MEASUREMENT OF POWER. Ill is in question, the machine is to be run as a motor, the belt having been removed, and the measurement is to be made in the same way as before, but with a degree of care suited to the small quantity to be determined. A dynamometer for measuring 40 to 50 H. P. occu- pies, without the countershaft, a floor-space of about ninety inches square, and may, if desired, be built beneath the floor, so as to have the general appearance and convenience of platform-scales. A patent has been applied for upon the Floating Dynamometer. In the experiments of Hartig a dynamometer was used in which, by means of a series of gears, the rotat- ing force is made to act upon a pair of springs, one of which* is furnished with a pencil which describes a curve as a roll of paper is caused to move before it. The principle of action will be understood from the follow- ing, which is abstracted from Weisbach's Mechanics.* To the interior of the wheel CA, Fig. 48, upon which the rotating force P acts at A, is bolted an annular gear which engages at D and D^ with two equal gears, DE and D^E, both of which act upon a third gear, EE. This last gear revolves freely upon the shaft C of the wheel DD t , and is firmly attached to the drum BC upon which the resistance Q acts, while the other two gears, DE and D^E, have their axes supported by a lever, FCF l , which revolves freely about C. On the hub of this lever is a band, one end of which is fast- ened to the dynamon>eter-springs H H, which latter are bolted at M to the floor. We see that here the rotat- * Dubois* translation, vol. n. part I. 115 D YNA MOME TJtS ing force P is held in equilibrium by two forces, R and R, that out of these last arises a couple, R,R, which holds the force of resistance Q in equilibrium, and that therefore the forces 2.R and 2R act at F and /'", and stretch the springs H H with a certain force Z. FIG. 48. ARRANGEMENT USED BY HARTIG. Let a = lever-arm CA of the force P\ b = lever-arm CB of the resistance Q ; r = radius CD of large annular gear ; r l = radius CE of centre gear-wheel, and hence radius FD of intermediate gear, c = lever-arm of the force Z CL. Then we shall have Pa - Rr = Rr, or Pa = 2Rr ; AND THE MEASUREMENT OF POWER. 113 also, Qb = 2Rr, , and Zc Qb = Pa. Substituting above values for Qb and Pa, we have hence and Pa _ 2Rr P _ b_ r_ ~~ ~~ * Pa 2Rr P c ^ -, or = - X Zc 2K(r+r t y Z r-j-r, Among other forms of dynamometer not already discussed is the Emerson Power-scale an instrument which is connected directly to the revolving shaft with- out the interposition of belts, except that used to drive the shaft itself. The machine in principle is a rotary scale, and its construction closely resembles the well- known Fairbanks platform- scales. This dynamometer is largely used in cotton-mills to determine the power consumed by the individual machines, and when used with care forms an excellent instrument for the purpose, being self-contained and readily applied. In this machine, the pulley which receives the power is loose on the shaft, and is connected with the latter by means of a spider which is keyed to the shaft, the hub of the spider forming one of the guides to the position of the pulley (not shown in the figure); to connect this spider with the loose pulley, a lever is pivoted into lugs on the rim of the wheel on opposite sides, the long arm of which connects with an annular slotted collar on the shaft by means of short links. 114 D YNAMOME TERS The short arms of the crank-levers connect on the inside of the fixed wheel with two radial links, one parallel to the outer arm of the bell-crank, and the other at right angles to it, receiving at its upper end a pivot passing through a swivel hung to the arm of the spider-wheel, and having its extreme end pivoted to a stud fixed on the inner side of the rim of the receiving pulley. The strain of the power received through the belt on the pulley will necessarily react on the levers, and, through them, on the spider, which may be considered as a support to these levers in sustaining them in position to connect the loose receiving pulley with the shaft. The levers are connected by pivots with the sliding collar, in the annular groove of which is seated a strap with which is connected a forked lever. Attached to the end of the long arm of this lever is a rod carrying movable weights ; connected with this rod is a chain which runs over the cylindrical head of a pendulum-weight having a pointer which traverses a fixed quadrant: this quadrant being divided by a scale to denote the relative pressure exerted through the medium of the receiving pulley on the shaft. A dash- pot filled with oil is connected to the long lever and chain-rod to prevent unnecessary oscillations of the pendulum. These instruments are made in halves, so that they may be readily applied without disarranging pulleys or line-shafting. The cotton-mill scale shown in Fig. 49 is fitted with special clutch and split bushings to fit shafts varying from f inch to i^ inches, being secured in position by nut B. In this form of scale two sets of prime levers, K K, are used, so as to operate without change when AND THE MEASUREMENT OF POWER. 115 running in either direction. Two studs, one of which is shown at C, are used to connect the loose driving pulley with the spider which is keyed to the shaft. These FIG. 49. EMERSON POWER-SCALE. Oc studs are screwed into a plate with projecting lug which drives the spider by means of the pin G in the rim. When the slide H is pushed in as shown in thr 1 16 D YNAMOME TERS figure, the stop G is thrown out of gear with the loose plate, and this latter is free to revolve on the hub of the spider, being driven by the loose pulley. These scales are constructed so that the pivots in the ends of the levers at L describe a circle whose circumference is two feet, and the quadrants are gradu- ated to read pounds ; if the graduations are insufficient, weights may be added at J, the leverage of the scales being such that an actual weight of one pound placed at J has the effect of fifty pounds on the quadrant. In the larger power-scales the centre of pivots of the prime levers (K) is always taken at such a distance from the centre that the distance passed through in one revolution is equal to a given number of feet. Thus in the scale designed to weigh 65 horse-power, the greatest diameter of the machine is 38 inches and the space passed through by pivot L in one revolution is 9 feet. To ascertain the number of horse-power by means of an Emerson power-scale it is first necessary to find the centrifugal force of the unbalanced moving parts of the scale. This is obtained by running the belt on the tight pulley, the loose plate being disconnected from the spider, then note the reading as shown by the position of the pendulum on the quadrant. This amount will be small for slow speeds, and below a certain minimum speed will be zero ; but as it varies with the square of the number of revolutions, it should in every case be determined at the same velocity at which the total force is determined. In a test by Mr. Channing Whitaker to determine the effect of a cotton- mill scale it was found that at a speed of 416 revolu- AND THE MEASUREMENT OF POWER. ll'J tions per minute the reading was one-half pound, but at the speed of 1000 revolutions per minute it amounted to thirty-six pounds. Having ascertained the amount to be deducted for a given speed, which is in fact equivalent to balancing the scale, we can find the horse-power developed from PV our general formula --- = H.P. If f = total pounds indicated on the quadrant, _/"= pounds necessary to balance at given speed, N '= number of revolutions per minute, C = path in feet of end of lever (X), then F f=P, and N X C = V, which substituted in above formula will give net horse- power. The observed data of a test with a cotton-mill scale was as follows : The gross indicated force = 83 pounds; the tare or balancing force = 23 pounds; revolutions per minute = 791. The path of end of lever being 2 feet, we obtain (83-23)791 X 2 = 2 ' 8 7 horse-power. Another form of shaft-dynamometer is the Power- meter which has recently been patented by Mr. Franklin Van Winkle. This is a rotary transmitting- dynamometer which is especially adapted for adjust- ment to any shaft or pulley for measuring power transmitted by a shaft to a pulley, or vice -versa, in this respect resembling the Emerson power-scale. n8 D YNAMOME TERS Helical pull-springs are employed for weighing the amount of force transmitted from the driving to the driven portion of the dynamometer. Figs. 50-58 will illustrate the construction and ap- plication of this dynamometer. Figs. 50-55 are illustrative more particularly of the "light portable " style. The construction and opera- FIG. 50. tion of all other styles will, however, be understood from this description, as it embraces the features of the others. Similar letters refer to similar parts throughout the I several views. To facilitate the application of the dynamometer to a shaft, the main framework and all parts which sur- round the shaft are made in halves, in order that the dynamometer may be mounted on the shaft in the manner of a split or separable pulley. AND THE MEASUREMENT OF POWER. I ig Split bushings are used for reducing the bore on any shaft smaller than the hole in the hub. For bushing machines employing four springs it is immaterial whether or not the machine is concentric with the shaft ; hence rough wood-bushings may be employed. The main hubs of all machines are chambered in the middle of their length, in order to leave room for cord to be tied around the outside of wood bushings or lag- ging of any kind that is convenient for building up the size of the shaft. Thin manila drawing-paper wrapped around the shaft answers the purpose admir- ably. The main framework consists in an elliptical plate I2O D YNAMOME TERS B, the outline of which is best shown in Fig. 51. This plate has a central hub C, prolonged on one side, with the grooved collar e near its end ; this hub projects a short distance to the other side of the plate, with a spherical exterior surface D (see Figs. 52 and 53) terminating in the plain collar E, the plate and hubs being made in halves and held together by bolts passing through the projecting lugs FIG. 52. G G. The central hollow hub of this main framework is recessed along a portion of its prolonged end and bored out in the remaining portions of its length to re- ceive the shaft upon which it may be placed, as shown in Fig. 53. A is a circular plate the middle portion of which is dished or crowning. This plate is made in halves coming together along the line HH, Fig. 51, and held together by bolts passing through projecting lugs //, Fig. 50, the plate being provided with a short central hollow hub which is bored out to fit loosely around AND THE MEASUREMENT OF POWER. 121 the spherical portion D of the central hub of the main framework. AT is a rock-shaft the ends of which have counter- sunk recesses, by means of which it is mounted on conically-pointed screws L L, which pass through lugs projecting from B and are held firmly in place by lock-nuts MM. N is an arm on AT projecting toward the plate A, and o and o are parallel arms projecting from K at right angles to N, one over each side of the hub C. P P are links connecting by pivotal screws the ends of the parallel arms o o to the grooved collar Q, which, being made in halves, encircles the reduced por- tion of hub C, being free to slide along C, and provided with feathers which project into the slots S, Fig. 52. T is a connecting-rod having spherical socket-ends with detachable caps. U and U' are spherical or ball-ended stud-bolts set in the end of the arm N, and in the curved slot x in the plate A, respectively, and connected by the con- necting-rod T (see Fig. 51). When the plate A, rock- shaft K, and collar Q are mounted on the framework of the dynamometer and connected as described, then any change of relative angular position between the plates A and B around the axis of hub C will cause Q to move along the hub, the direction and degree of travel being dependent upon the relative direction and degree of motion between the two plates A and B. V V are bosses on one side of the plate A, project- ing toward B. X is a similar boss on the plate B, projecting toward the plate A. IV, Fig. 51, is a helical pull-spring connecting the 122 DYNAMOMETERS plates A and B. The material of the helix forming W is turned up in eyes at both ends, through which the suspending pins Kand Y' pass, the pins being held in place by set-screws, as shown in Fig. 53. If the plate A be rotated on its axis in the direction indicated by FIG. 53. the arrow Z, Fig. 51, any resistance offered to such rotation by B will be transmitted through W to A, causing W to elongate, and thereby permitting A to advance in its relative angular position with respect to B in direction of the arrow Z until the resistance offered by B is overcome by W. Then B follows along in the rotation primarily imparted to A. The direc- tion of arrow c in Figs. 52 and 54 is the same with respect to B as arrow Z in Fig. 51. Consequently, AND THE MEASUREMENT OF POWER. 12$ when A advances in rotation with respect to B in the manner described and the ball-stud U' is fixed in the slot x of the plate A, then U', T, and U and the end of the arm TV are carried in direction of arrow/, im- parting a partial revolution of the shaft K on its axis, resulting finally in movement of the parallel arms o, links P, and collar Q in direction of arrow d. If, dur- ing such rotation of A, the resistance offered by B lessens, then the spring, by reason of transmitting a lesser strain, resiles to such length as may cor- respond to the reduced resistance and carries B for- ward in the direction of rotation toward its original position with respect to A. Each particular degree of resistance transmitted by the spring from one plate to the other produces its particular position of the sliding collar Q on the hub, and will be indicated upon the scale by the pointer , as follows : In Fig. 50 / and g are rings made in halves, the in- terior surfaces of which are suitably bevelled for fitting loosely around the grooves in the sliding collar Q and fixed collar e. These rings are each provided with two bosses for the purpose of receiving the guide-rods / /', one end of each being screwed into g, while /"is free to slide over the remaining portion of the rods. The ring f has a projection /, see Figs. 54 and 55, to which is pivoted the link k, and the ring g has projecting from it the scale-plate /, the lower portion of which is made in form of a segmental arc, on which is laid off a scale. In Fig. 54 is a pointer-hand pivoted at/ and con- nected by the link k to the ring/", its free end being carried over the scale in accordance with the motion of the ring f, in the sliding collar Q along the hub- 124 DYNAMOMETERS When the hub is in rotation, the scale-rings f and g may be prevented from rotating with the hub, and caused to remain stationary by holding the downward, extending portion of the scale-plate in the hand, or by securing the lower portion of the scale-plate by twine or otherwise to a stationary object. The position as- sumed by the pointer-hand on the scale may be noted while the hub is in rotation. If the plate B receives the primary rotation instead of A, but in a direction opposite to that indicated by the arrow Z, Fig. 51, and such rotation be resisted by the plate A, then the spring JFwill be similarly elon- gated, and n will be carried over the scale in the same manner. The periphery of the plate B has cut out of it a gap or notch bounded by projecting lugs q and r, through which pass the set-screws s and /. u is the stop-bracket projecting from the plate A through the gap in B. When the spring in its normal length and without any strain upon it connects A and , as previously described, then A is to be turned past B sufficiently to take up any lost motion between the suspending pins and the plates A and B or between the suspending pins and the eyes of the spring. The screw s is then to be set down and secured in con- tact with n. With u and s thus in contact the dyna- mometer may be driven backward without injury to or derangement of its parts. When driven in the direc- tion which tends to elongate the spring, the maxi- mum relative motion between the two plates and consequently the maximum elongation of the spring are both limited by u coming in contact with the AND THE MEASUREMENT OF POWER. 12$ end of the screw /. If, however, it be desired to measure resistance transmitted between the plates when the relative directions of rotation are opposite to those described, then in order that such resistance may be transmitted in a manner tending to elongate W it is necessary for W to be connected from the pro- jecting hub X of the plate B to the projecting hub V of the plate A by means of the suspending pins Fand Y" When the spring is connected without strain, as shown in Fig. 51, the proportions of the dynamometer are such that the distance from X to V is greater than the distance from X to V by such an amount that in order to connect W without strain from X to V it is first necessary to rotate A around B in the direction of arrow Z a sufficient distance to bring the side of the stop-bracket u against the end of /. t is then in posi- tion to operate as a backward stop, while s becomes the forward stop. When W is thus changed about, the partial rotation of A past B, which is incidental there- to, results in carrying the pointer-hand to a point to the left of the zero of the scale that is to say, in di- rection of the arrow d. The pointer-hand may be re- turned to zero by loosening the ball-stud V ' in the slot x of the plate A and moving it along the slot to such position that n again indicates zero, in which position U' may be again secured to A. When thus adjusted, any resistance to rotation between the plates A and B, causing the spring to elongate, will cause n to assume a position to the right of the zero of the scale. Successive positions which the end of the pointer- hand n will assume on the arc of the scale-plate for 126 D YNA MO ME TERS different numbers of horse-powers or foot-pounds per minute transmitted from A to B or B to A, employ- ing a given spring, may be determined for a given speed of rotation of the dynamometer, inasmuch as the degree of elongation of the spring is ascertainable for any degree of resistance to rotation which the plate A may offer to the plate B, or vice versa. Thus if the distance from centre of shaft to centre of the suspend- ing pins of the spring W be 5 inches, and the elonga- tion of the spring be I inch under a pull of 200 pounds, the horse-power transmitted at 100 revolutions per minute for an elongation of half an inch will be jr D 2lRNP 27T X 5 X 100 X 100 fl.r. = = = = Q. 15 2. 33000 33000 For a given extension of the spring, which represents a corresponding force P, the pointer-hand will assume a definite position, and if the lever-arms of the instru- ment be suitably proportioned, the arc may be so graduated that for a given spring the successive divi- sions will represent horse-powers and decimals for a fixed number of revolutions per minute. Fig. 50 illus- trates the appearance of a divided and figured scale laid off on / in the manner described for a stated speed of rotation of the dynamometer as, for instance, one hundred revolutions per minute using always the same spring. In dynamometers heretofore made this has been the only type of scale provided, and when such a scale is used at any other speed of rotation, or when any change is made in the spring employed dif- ferent from those for which the scale is especially con- AND THE MEASUREMENT OF POWER. 12? structed, then, in order to arrive at the true number of horse-powers, the operator must make calculations for every reading. To obviate this the Van Winkle dynamometer is provided with a "differential" scale-plate by which the horse-power for varying speeds is indicated directly FIG. 54 DIFFERENTIAL SCALE-PLATE. by the pointer, within the limits of the spring used. This consists of a flat spade-shaped plate d' of form shown in Fig. 54, the narrow upper portion of which has parallel slotted openings e' . The differen- tial plate when used is to be laid upon the face of / under the pointer-hand, as shown, and may be secured in different positions of vertical adjustment by means of screws f'f, which pass through the slots into the 128 D YNAMOME TERS upper part of /. When using always the same spring or equal springs, arbitrarily-spaced lines, each repre- sentative of a speed of rotation, are made upon the face of the upper portion of / in form of a scale g', and so laid off that the upper edge of d' may be brought opposite to any division on g' . As shown in Fig. 54, the face of d' is laid off with a central zero- line, to the right and left of which are curved lines marked "1,2, 3, 4," etc. These " differential curves " are of such form that when the upper edge of d' is set opposite to that division of g' corresponding to any given speed of rotation made by the dynamometer, then the end of the pointer-hand will be on the curve marked " I " when one horse-power is being trans- mitted, on curve " 2 " for two horse-powers, " 3 " for three horse-powers, etc., to the right or left of the zero- line, according to the direction of resistance for which the spring and pointer-hand may have been adjusted. When the dynamometer is always to be used at a constant speed of rotation and for the purpose of greater or less sensitiveness of action, different strengths of springs are employed at different times. Then in a similar manner the differential scale-plate may be laid off in curves to be used for indicating different horse-powers, the divisions of the scale g' be- ing then taken as representative of different strengths of springs instead of different speeds of rotation. For springs offering different degrees of resistance to elongation, each of which may be used in the dyna- mometer at different speeds of rotation of the latter, the same general form of differential scale-plate is employed in conjunction with the compounding scale- AND THE MEASUREMENT OF POWER. I2 9 plate y, Fig. 55. The scale-divisions g' are then dis- carded, excepting a single division-line k', which, for greater explicitness of location, is marked with an arrow-head. By means of the binding-screw k! ', which passes through the slotted projecting portion of the FIG. 55 COMPOUNDING SCALE-PLATE. back of /', the latter may besecured in different vertical adjustments with reference to /, so that any one of the division-lines drawn on the face of j' may be opposite to h' . Beginning at a certain division on j', as, for exam- ple, that marked " loo," and proceeding upward, lines are drawn each of which is representative of the num- ber of pounds required to elongate different springs I 30 D YNAMOME TERS I inch, as one hundred, two hundred, three hundred, etc.; and similarly beginning at " 100" on/' and pro- ceeding downward, lines are drawn representative of different speeds of rotation of the dynamometer, as, for instance, one hundred, two hundred, three hundred, etc., revolutions per minute. The spacings of the divisions of the compounding scale-plate j' and the curves on the differential scale- plate, when used in conjunction with the compounding scale, are such that the pointer-hand will indicate the correct number of horse-powers on the differential scale-plate provided j' is so adjusted that the division representing the strength of spring employed is oppo- site the division-line //' marked with an arrow-head, and the upper edge of d' is fixed opposite to that divi- sion on/' representing the speed of rotation. In order to apply the dynamometer, as, for instance, for the purpose of measuring the horse-power taken by a pulley /', Fig. 53, from line-shaft c', the pulley is first loosened from the shaft by removing set-screws, keys, or other means of fastening, making of it a loose pulley. A short distance one side or the other of the pulley the plate B is mounted on the shaft, the halves being secured together by the bolts through lugs G. Then the rock-shaft K and its connections, the scale- ring and scale employed, and finally the plate A are all mounted on B. The weighing spring W is then connected according to the direction of motion, and the ball-stud U' is set in the slot x, so as to bring the pointer n to indicate zero when the stop-bracket u is against the end of the screw s or t for a back-stop. The dynamometer is then moved along the shaft until AND THE MEASUREMENT OF POWER. 131 the periphery of the plate A comes against the arms of the pulley. The periphery of A has a projecting surfacejj/', which is perforated all around by holes, as shown in Fig. 51. The plate A is secured to the pul-* ley by means of bolts and straps which pass over the arms. The plate B is then secured to the shaft by the set-screw S' (shown in Figs. 51 and 52). When the shaft is set in motion, any power taken from it by the pulley for driving other machinery by means of a belt will be transmitted from the plate R to the pulley through the spring W, resulting in a greater or less elongation of W, and consequent movement of the pointer-hand to a position on the scale-plate employed, and the latter, as previously noted, may be held sta- tionary or secured to a stationary object to prevent its turning with the dynamometer. It will be noticed that the performance of the weigh- ing springs is transmitted by positive mechanism to the pointer-hand on the dial ; no wrapping connectors of any kind being employed. The Light Portable style weighs, complete, 62^ Ibs., and, as intimated in the description, it is supplied with springs of different degrees of sensitiveness, up to a capacity of 20 horse-power at 100 revolutions per minute. Another form of the Van Winkle dynamometer has two or more springs similarly connected in a series. The pins for suspending the weighing springs are the same distance apart and at a uniform distance from the axis of the dynamometer. One of the springs operates the same as the single spring employed in the Light Portable style, taking up the load from the beginning. 132 D YNAMOME TERS This is called the initial weighing spring. The remain- ing springs have looped eyes at one end, the loops being of such different lengths that after the initial spring has been loaded to a portion of its capacity the FIG. 56 VAN WINKLE Dv looped springs assist the initial, drawing on their sus- pending pins, one after another. This system of suspending the weighing springs greatly facilitates accuracy in construction, application, and use of the dynamometer. The holes for the suspending pins being equally spaced, the springs are interchangeable in location ; and A.VD THE MEASUREMENT OF POWER. 133 the amplitude of swing, or change of relative angular position between the plates, being dependent upon the resistance of only one, or as many springs as may be necessary for transmitting any load, the divisions of the zero end of the scale are coarser than if all springs started to pull at the beginning, and admit of smaller fractional sub-division. Still another form is shown in Figs. 56, 57, and 58, in which A is the pulley-plate and B the plate which is FIG. 57. secured to the shaft. It differs from the Light Port- able style in requiring the connecting-rod, which oper- ates the rock-shaft, to be changed to the other side of the machine, in order to use the dynamometer in a reverse direction : and the weighing springs being sus- pended from stud-bolts, the springs, together with their stud-bolts, must be removed from the plates A and By and the studs inserted each in the opposite plate in holes provided for the purpose. Fig. 57 illustrates the parts of the " Standard Port- able" dynamometer, and Fig. 58 illustrates it applied to a shaft and pulley. 134 D YNAMOME TERS It is claimed by the manufacturer that these dyna- mometers are only about one-half the weight of other types for equal capacities. The dynamometers have been tested after several years' use and the weighing springs have been found to retain their original strength. No allowance for centrifugal, frictional, or other FIG. 58 VAN WINKLE DYNAMOMETER APPLIED TO SHAFT. error is made in using this instrument. The weighing springs are so proportioned that, as has been proven in tests of the dynamometer, the indications of the scale are unaffected by centrifugal disturbance beyond the highest speeds of shaft in practice. The transmitting mechanism is so proportioned and balanced that any tendency to centrifugal disturbance is avoided. The only sources of frictional disturbance are in the AND THE MEASUREMENT OF POWER. 135 pivotal joints of the rock-shaft motion and the friction due to the weight of the scale. When, however, the dynamometer is employed for measuring the amount of power which a pulley receives from a shaft, then this small amount of friction is not thrown on the weighing springs. There is no friction between the pulley and the shaft, nor between that portion of the dynamometer which is secured to the pulley and the rest of the instrument. This, at first sight, may not appear to be the case ; tests of the dynamometer show, however, that no fric- tion exists in cases where the pulley when loosened from the shaft is loose enough to be turned on the shaft by hand. The explanation furnished for the absence of friction is, that the belt drawing the pulley always in the same direction, accompanied by rotation of both shaft and pulley, any change of load permits of the pulley assuming an appropriate angular position with respect to the shaft by rolling on the shaft ; con- sequently, in the standardizing and operation of these dynamometers centrifugal force and friction are neg- lected because they can exert no appreciable influence; the actual resistance which the springs offer for various degrees of elongation being the one thing which is taken into account in calibrating any scale. Different sizes of these dynamometers have been employed in the measurement of power required by mills, tenants, and machines, requiring from a fraction of a horse-power up to several hundred horse-powers, and under the widest range of circumstances. The facility with which they may be applied, and their precision in indication of the lighest to the heavi- 136 DYNAMOMETERS est loads, have earned for them a prominent place among dynamometers manufactured for general use. Two Van Winkle dynamometers furnished to a firm in Antofagasta, Chili, respectively of 450 and of 600 horse-power capacity, at 120 revolutions per minute transmit the power of two 9-inch shafts. They are believed to be the most powerful rotary transmitting-dynamometers, of any type, ever con- structed. While investigating the subject of power transmis- sion as applied to milling-machines, the writer con- structed an apparatus shown in Fig. 59 by which he FIG. 59. proposed to measure the magnitude of the force exerted by the teeth of the cutter, but the results were not wholly satisfactory when applied to a milling-machine. Used on a planer, however, a measure of the useful AND THE MEASUREMENT OF POWER. \tf work was readily obtained from the card taken from the indicator attached. Prof. L. P. Breckenridge, of the Michigan Agricul- tural College, had previously made some interesting ex- periments with a similar apparatus for determining the pressure exerted by a drill working under similar con- ditions, and more recently has successfully applied the apparatus to planer tools. (See American Machinist, August 14, 1890.) The action will be understood by an inspection of the figure. The thrust of the tool acts upon the planger of the cylinder, thereby forcing the contained oil into the pressure-gauge and into the cylinder of the indicator. By a suitable arrangement of cords, the drum of the indicator is made to revolve synchronously with the stroke of the tool or with the work; and as the pencil is forced upwards by the pressure exerted at the point of the tool, it will be seen that a measure of the work performed can be ob- tained from the card. The gauge is simply a check on the indicator. It is evident that the total work per- formed cannot be obtained by this means, as the force required to drive the machine itself is disregarded. To obtain the total work, and at the same time the useful effect, the writer next designed the hydraulic dynamometer shown in Figs. 60 to 62. The plan of mounting the cylinder upon a rotating pulley was ob- tained from an article which appeared in Industries* but the details and arrangement of the present dyna- mometer are in many respects very different from the one there illustrated. To maintain the lever-arm con- * See also Sc. American Sup., Feb. g, 1889. 138 DYNAMOMETERS FIG. 6o.-FLATHER HYDRAULIC DYNAMOMETER. AND THE MEASUREMENT OF POWER. 139 slant, the cylinder through which the transmitting force acts should not be bolted rigidly to the pulley- arm, as in the case with the machine just referred to, but should be pivoted in such a manner as to obtain a constant lever-arm. The action of the Flather dyna- mometer is this: The pulley L, which receives the power, is loose on the shaft and free to turn within certain limits. F, secured to the shaft, is belted to the machine to be tested, and carries a cylinder, C, which is supported on trunnions by means of the brackets b ; this cylinder is partially filled with oil, and connected to centre of shaft by a small flexible tube. The end of the shaft is bored out and is provided with a hollow steel tube free to revolve in the spindle and fitted with gland and stuff- ing-box nut to prevent leakage of oil. Connected with this steel tube is the stand S, carrying a pressure- gauge and an indicator. When motion is given to the pulley L it revolves through a small arc until a steel pin in its arm comes in contact with the plunger in cylinder C. If there is no resistance to be over- come, the indicator-pencil and gauge finger remain at zero ; but as soon as resistance occurs the plunger is forced inwards. When the power overcomes the resistance, motion is communicated to the pulley F, and the machine is driven through the force trans- mitted by the oil. As the plunger is forced inwards, the indicator- pencil and gauge-finger will in consequence rise, and the amount of rise will determine the pressure per square inch acting on the plunger. If the distance of the lever-arm acting on the plunger is known, the 140 D YNAMOME TEKS U LJ FIG. 61. AND THE MEASUREMENT OF POWER. 141 1 42 D YNAMOME TERS. power can be readily ascertained from the formula P X 2nrN H.P.= 12 X 33000 in which r equals radius in inches of path traversed, and .A^ equals number of revolutions per minute. If the construction of the machine be such that r is con- stant, as in the present case, and equal to C, the formula becomes : o.o oo i H.P. = - ~-~ - = o.oo ooi 586/>AT. When r is variable its exact determination would be a difficult matter, but if this variation of arm be neg- lected the final result will be vitiated. In the experimental machine constructed by the writer the pulleys were each 12 inches in diameter and 3^ inches face ; the cylinders were 1.954 inches in diam- eter, presenting an area of 3 square inches. The plungers were of hard bronze and were kept tight by leather cup-washers secured to the end ; grooves in the plunger, as for water-packing, and cast-iron piston- rings were successively used, but abandoned after a short trial as not being trustworthy. A 5-lb. spring was used in the indicator (a Tabor), as with stronger springs the card obtained was not sufficiently large to show the delicate changes which it was desired to bring out. Instead of a piston having an area of 3 square inches, the results of experiments show that an area of 2 or even I inch would have been more satisfactory for the work in hand. 1 44 D YNA MOME TERS It would seem that the centrifugal force of the plunger would materially affect the true value of the force transmitted, but a careful examination of this force with varying lever-arms, corresponding to different positions of the plunger, shows that the actual effect is very small. As the lever-arm of the driving force is constant, the centre of gravity of the plunger will have a vary- ing arm dependent upon its position relative to the cylinder. This is shown in Fig. 63, in which G, G', and G" are three positions of the centre of the plunger, the lever-arms of which are 3.67 inches, 3.87 inches, and 3.50 inches respectively the radius of the driving force being constant and equal to 3.6 inches. The centrifugal force,/, of the plunger can be calcu- lated from the formula W being the weight in pounds, r the radius in inches, and N the number of revolutions per minute. In the case before us IV= 1.75 pounds. If we assume A^to equal 100, 150, 200, 250, we obtain for/ the values shown in the following diagrams, Figs. 64, 65, 66. As the centrifugal force acts along the radial line through the centre of gravity of the plunger, it will be seen that only the horizontal component can be con- sidered as a force acting in the direction of motion. If we assume the average radius of the centre of gravity of the plunger (3.67 inches), and the average number of revolutions per minute to be 175 we find from Fig. 64 that the corresponding value of / is 5.7 pounds, as AND THE MEASUREMENT OF POWER. 145 c I igfcsss^^NSsss \ **%: ^s^S^ww ^ I :! G is center of gravity for mean position,. G " " " " " inner , \\ G"" " " " " outer '* \ \J FIG. 6 3 . i 4 6 DYNAMOMETERS shown by dotted coordinates. If \ve decompose this force into its two components (see Fig. 63), we find the horizontal component is 1.37 pounds, the vertical being 5 pounds ; now the vertical component produces a cer- tain amount of friction against the walls of the cylinder which retards the motion of the plunger ; if we take the coefficient of friction in this case to equal seven FIG. 6 4 . ?.-,o ^ <- ^~ 3 ro - - *r s_ / / -. 10 { t* / \ / 1 1 2 6*. FIG. 65. ,x ^ c X ^^ c ,x" / 1 /I / / 1234 5 J 10 ri 12 w per cent, we obtain 0.35 pound for the friction which acts in the opposite direction to that of motion, hence 1.37 .35 = i. 02 pounds equals the effective compo- nent of the centrifugal force. As this acts on an area of 3 square inches, the effective component at the given speed is only 0.34 pound per square inch, which, if AND THE MEASUREMENT OF POWER. 147 there were no friction in the machine, would have to be deducted from the actual force as indicated on the pressure-gauge or card. Experiments to ascertain the friction of the machine showed that 0.425 foot-pound, only, was necessary to overcome the friction when the machine was at rest with belts thrown off. With the sensitive spring used in the indicator very small changes in the forces were determinable. At the ordinary speeds at which the machine was run there was no appreciable difference in pressure, as shown by the zero line, whether tlu machine was stopped or running with the transmitting belt thrown off ; with both belts on, however, a resist- ance at the plunger as small as three-fourths pound could readily be determined, as will be shown subse- quently. From this it was concluded that for ordinary speeds the effect of the centrifugal force of the plunger was neutralized by the friction in the dynamometer; in any case it could be neglected by obtaining the zero line when running free at a given speed. The small coiled spring outside of the cylinder, Fig. 61, connecting the arms of the loose pulley L with the bracket b, keeps the pin/ in contact with the plunger; the action of this spring is to force the plunger into the cylinder, and thus raise the pressure on the gauge ; this force is, however, counteracted by another spring inside the cylinder, which resists the inward motion of the plunger, yet acts with an equal force to keep the plunger in contact with the pin. When resistance is applied to the pulley jpthe plunger is forced into the cylinder until this resistance is overcome; the inner spring is thereby compressed and presents a resistance I 48 D YNAMOME TERS to the motion of the piston. As the spring is very light, and the compression seldom exceeds half an inch, it will be seen that this force of resistance is hardly appreciable. An examination of an indicator-card, Fig. 67, from SCAUE,..5 Ft.P.M,..ZaA36 Dyn.l4Hg 1 1 1 Cut- V' ^/ \ METAL ( Wrought Iran. F S E D._ .48 per inch. ! * ,T j= \ roO(. r ..O;amoii(J point. f!ov,r feed H./ht ^ btsufi-, f ( 9*. t.ty.ir.s i/i. this dynamometer shows that the power required to drive a i6-inch Flather lathe with back gears in, well lubricated, and running light at 36 revolutions per minute, is PV o.i i X (5 X 3 G") X 211 X 3.6" X 140 -- =.o' 3 = 434-3 foot-pounds, where o.u equals the height of card in inches; 5 pounds equals the spring used ; area of cylinder-piston equals 3 inches ; radius of arm equals 3.6 inches ; the revolutions of dynamometer being 140 per minute. With the screw feed in, still running light, the power AND THE MEASUREMENT OF POWER. 149 was found to be 0.020 H. P., or 710.6 foot-pounds; with the load on, which was a light cut T *g- inch deep on a round bar of wrought-iron with diamond-pointed tool, the maximum power registered was 0.102 H. P., or 3474 foot-pounds. SOALE....5/6* MACHWEj R.P.M^ Lathe 36 DynJjD METAL,, 210 " FEEOj.... 4^per twci TOOL,, Work of Machine. FIG. 68. FRICTION-CARD FOR i6-iNCH LATHE. A peculiar result, shown in Fig. 68, was obtained on several cards, this being a greater amount of power used to drive the lathe running free without back- gears than under the same conditions with the back- gears thrown in. A somewhat similar occurrence, repeatedly con- firmed, was noticed by Mr. Wilfred Lewis in the course of some experiments with a 48-inch lathe. The probable reason for this is that the work of friction in the spindle-brasses and other bearings is much less at the lower velocity. With the belt on any given step of a four-stepped cone-pulley the reduction of velocity in the main spindle-journals, when back-gears are thrown in, will be about nine to one, which reduces the work of friction very 1 50 D YXA MOMK TERS materially ; the superior lubrication of the cone-pul- ley due to the revolving spindle also reduces its fric- tion below that required to drive the spindle at the greater velocity without the back-gears, and, with the ratio of speeds as great as that ordinarily employed, this reduction in journal-friction more than compen- sates for the work spent in overcoming the resistance due to the gearing. AND THE MEASUREMENT OF POWER. CHAPTER V. POWER REQUIRED TO DRIVE LATHES. It has been stated that the power required to run a small lathe while taking a light cut in wrought-iron was one-tenth horse-power. By a comparison of data on the subject it will be seen that the actual power consumed is quite variable, and that the power required to turn off metal may be much less than that required to file or polish the same in the lathe, or even to run the lathe empty. It is evident that the power required to do useful work varies with the depth and breadth of chip, with the shape of tool, and with the nature and density of metal operated upon ; and while it would also appear that the power required to run a machine empty should be constant for a given speed, a little investigation will show that this latter is often a variable quantity. In the case of a lathe, for instance, when the ma- chine is new, the working parts have not become worn or fitted to each other as they will be after running a few months; and at first, the length of time depending on the frequency of its use, the lathe will run hard, in which condition the power required will be greater than will be the case after the running parts have be- come worn. i$2 DYNAMOMETERS Another cause of variation in this portion of the power absorbed will be found in the driving belt : a tight belt will increase the friction very considerably. Hence to obtain the greatest efficiency of a machine, that is, the ratio of useful work to total power ab- sorbed, we should use wide belts, and run them just tight enough to prevent slip. The belts should also be soft and pliable, otherwise power is consumed in bending them to the curvature of the pulleys. Another point in this connection, sometimes over- looked, is the relative diameter of cone-pulleys. A belt may be wide enough and loose enough to run well on the larger steps of the driven shaft, but on the higher speeds may be altogether too tight. The writer has in mind a small lathe in which it was necessary to let out the belt three quarters of an inch when chang- ing from the largest to the smallest step on the cone- pulley. A third cause is the variation of journal-friction, due to slacking up or tightening the cap-screws, and also the end-thrust bearing screw. When one man runs a lathe so that a pull on the belt will revolve the spindle half a dozen times, and another man screws down the boxes of the same lathe so that he can only move the spindle by a series of- tugs with both hands on the belt, no dynamometer is needed to show that the power absorbed will be different in the two cases. The power necessary to drive the lathe over and above that required to turn off metal or do useful work is often increased by setting up the tail-stock centre too hard, or by letting the centre run dry. In one of the writer's experiments it was noticed that AND THE MEASUREMENT OF POWER. 153 the power absorbed constantly increased, and with no perceptible change in thickness of chip or condition of tool. The cut was smooth and clean, yet the dyna- mometer showed nearly three times the power ordi- narily required. The tool was withdrawn from cut with very little change in the pressure ; a drop of oil on the dead-centre, however, instantly caused the line to fall, but the normal pressure was reached only when the centre was eased a little. Subsequent trials showed conclusively that the ordinary running power could be more than doubled by carelessness at this point. Hartig's* investigations show that it requires less total power to turn off a given weight of metal in a given time than it does to plane off the same amount ; and also that the power is less for large than for small diameters. This latter fact is readily understood when we consider that the faster we run a lathe-spindle the more power it requires, provided we do not consider the intervention of intermediate gear-shafts ; when back gears are used, the power will be less with the belt running upon a given step of the cone-pulley than if the gears were thrown out, although such power may be greater than that required to produce a greater number of revolutions of the spindle when running without back gears. This is clearly shown in Table V, which gives the actual (measured) horse-power required to drive a lathe empty at varying numbers of revolutions of main spindle. * Versuche tiber Leistung und Arbeiis-Verbrauch der Werkzeug- maschinen. '54 DYNAMOMETERS TABLE V. HORSE-POWER FOR SMALL LATHES. Without Back Gears. With Back Gears. Revolutions of Spindle per minute. Horse-power required to drive empty. Revolutions of Spindle per minute. Horse-power required to drive empty. Remarks. 47.0 80.5 O.IOI .118 29.0 49-7 O.II3 .128 12" lathe built by Zim- mermann, of Chem- 138.0 M7 85.3 177 nitz, Germany. 47-4 80.4 125.0 188.0 159 .202 259 339 4-84 8.18 12.8 19.2 .132 .150 .187 230 Small lathe (i3i") built by Zimmermann. New machine. 54-6 82.2 122.0 183.0 .206 .260 339 455 6.61 9-95 14.8 22. I 157 177 .206 249 \1\" lathe built by Zimmermann. New machine. 81.11 .126 8-34 *.I33 132.72 219.08 MS .197 14.6 24-33 '14? 20" Fitchburg lathe. 365.00 .310 38.42 274 iS.8 .086 2.31 035 33-5 137 4.12 .047 26" lathe built by Zim- 54-6 .210 6.72 063 mermann. 82.2 .326 | 10.8 .087 * Horse-power greater than should be the case, on account of belt rubbing on back-gear hollow shaft. The only exception is the series of values given for the 12-inch lathe, which show a larger horse-power when the back gears are thrown in. It will be noticed that the relative speeds of the spindle in this lathe are not properly proportioned, there being, practically, only four variations of speed, whereas there should be six. AXD THE- MEASUREMENT OF POWER. 155 The ratio of the smallest number of turns of the cone to the smallest number of turns of the spindle is ||, or 1.62 to i, instead of 8 or 9 to i as in the other cases, from which fact we are led to conclude that if the ratio be small between the speed of the cone (which revolves freely on the spindle when back gears are used) and the speed of the spindle, the work spent in driving the spindle through the back gears will be greater than the work saved by reduced friction in the bearings. From this it is apparent that there will be a certain ratio of reduction for which the power required to run the lathe with or without back gears will be the same : with a greater ratio it will take less power with the back gears in, and with a lesser ratio more power will be required. Assuming the lathe to be in good condition, the brasses a good running fit, and the belt not too tight, we see from these results that, in order to estimate the total horse-power required to do a certain amount of work, we must know something about the speed at which the lathe will be run, which speed is. of course, dependent upon the diameter and nature of work. If we plot the curve of horse-power and revolutions from the above table, we shall obtain straight lines, or approximately straight lines, as shown in Fig. 69, which is drawn for four different lathes varying in size from 12 to 20 inches swing the power necessary to drive with back gears in not being considered in this diagram. Here the number of revolutions of spindle per minute is given on the extreme left, and the horse- power on the lower line. All the lines emanate near ISO D YNA MOME TERS. the point A, and diverge with different degrees of rapidity. The lines for the 12-and 2O-inch lathes are parallel for a portion of their length, and show the least increase in horse-power for a given increase in speed. The line for the i/^-inch lathe falls away very .05 - 4 .10.15 AM .25 .30 .35 .40 .45 .5 FIG. 69. HORSE-POWER REQUIRED TO DRIVE SMALL LATHES. quickly, which shows a rapid increase in power for a given increase in number of revolutions. The average for the four lathes represented is given in the line AB, which strikes the base-line for horse-power at the point about .095, corresponding to which the revolutions per minute = o. If we wish to find the horse-power for any given speed, say 80 revolutions per minute, we have simply AND THE ^MEASUREMENT OF POWER. 157 to draw a line parallel to the base line from the point Soon the revolution scale, until it cuts the line AB; the distance cut off, DC, or what is the same thing, oE, will give the horse-power direct. In the assumed case it is .19 +. As AB was chosen as the mean of all the lines represented, the horse power measured upon it can only approximate the actual, which, in the extreme cases, 12- and 17^-inch lathes, will vary more and more as the speed increases. If we let //./*. = horse-power necessary to drive lathe empty, and N =. number of revolutions per minute, then the equation for the line AB will be ' H.P. t = O.O95 -f O.OOI2.W. In the same way we can plot similar curves for the power necessary to drive the lathes empty when the back gears are in ; from this we can assume an average and find the equation of the line as before. With the same notation previously given, this equation for lathes under 20 inches swing is H. P., = 0.10 -\-o.oo6N. The larger lathes vary so much in construction and detail that no general rule can be obtained which will give, even approximately, the power required to run them, and although the formulas just obtained show that at least 0.095 horse-power is needed to start the small lathes, for which the line AB has been drawn, Fig. 69, there are unquestionably many American lathes under 20 inches swing working on a consumption of less than .05 horse-power. The amount of power required to remove metal in a 158 D YNAMOME TERS machine is also variable, but determinable within more accurate limits. The shape and condition of tool, the hardness of material to be cut, the rate of feed and depth of cut, all affect the final result. Every machinist has some special form of lathe-tool, ground to some particular angle, and with a given amount of rake not measured, but ground so it will look right which will give the cleanest cut, and turn off the metal quicker than any other tool in the shop. One man uses a round-nose tool with no top-rake for cast-iron, and with a coarse feed and square chip (depth of chip equal to the breadth) turns out con- siderable work during the day. Another uses a diamond point, or some other form, which he grinds and sets a little differently from every one else, and he, too, turns out a large quantity of work. For wrought- iron, steel, or brass, it is the same ; every man has his own form of tool which he considers will do the best and quickest work. Without entering into the question of which is the better form of tool to use in a given case, we shall assume ordinary conditions, and try to ascertain how much power is absorbed by a lathe in removing metal ; the power required to run the lathe will not be in- cluded in this discussion. As a means of convenient comparison, the work done has been reduced to the weight of metal removed, or that would be removed, in one hour, provided all conditions remained the same. Referring again to Dr. Hartig's researches, we find, in connection with a 13^-inch lathe, that the greatest amount of work done per hour was 11.55 pounds of wrought-iron removed under the following conditions : AND THE MEASUREMENT OF POWER. 159 Cutting speed = 24.6 feet per minute ; breadth of cut = .017 inch; depth of cut = .08 inch; horse-power (//./I,) required to turn off the metal = .230. As a result of twenty-three experiments on this lathe, we find that H.I\ = CW, where C is a constant, and W the weight of chips removed per hour ; C = .032 for wrought-iron, and C= .025 for cast-iron. The greatest amount of wrought-iron removed per hour on a i/^-inch lathe was 25 pounds; the cutting speed was 15.88 feet per minute; breadth of cut was .04 inch, and thickness of chip .20 inch ; horse- power required = .66. The following is the result of forty-one experiments on this lathe : H.P., = CW, where, as before, IV = weight of chips per hour ; C= .045 for steel, = .027 for wrought-iron, = .03 for cast-iron. On a 26-inch lathe the weight of chips removed per hour = 10.93 pounds ; the cutting speed 32 feet per minute ; breadth of cut = .024 inch, and thickness of cut .08 inch ; horse-power required = .413. From ten measurements the constant C was found to be .04 for cast-iron ; as this is 25 per cent higher than ordi- 1 6O D YNAMOME TERS narily obtained, we infer that the iron was much harder, or the tool in poor condition, or perhaps both affect the result. For a heavy turning and facing lathe 50 inches swing, treble geared, as a result of twenty experiments, C was found to be .027 for cast-iron. For another heavy lathe, 56 inches diameter of face- plate, C was found to be .031 for cast-iron, as a result of twenty-four experiments. A small lathe of 1 2 inches swing, turning wrought-iron at the rate of 4.88 pounds per hour, at a velocity of 23.4 feet per minute, breadth of cut = .018 inch, thickness of chip = .062 inch, required .21 horse-power. For this lathe C = .045 for wrought-iron, = .028 for cast-iron. From these and other data we find that the horse- power required to turn off metal can be obtained, if we know the amount of chips removed per hour, by using the formula H.P., = CIV, in which suitable values of C obtained from the fore- going are .030 for cast-iron, .032 for wrought-iron, .047 for steel. As we should infer, the size of lathe, and therefore the diameter of work, has no apparent effect on the cutting power, as shown by the constant C. If the lathe be heavy the cut can be increased, and conse- quently the weight of chips increased, but the value of A. YD THE MEASUREMENT OF POWER. 161 C appears to be about the same for a given metal through several varying sizes of lathes. Mr. J. F. Hobart, working on this line a few years ago, published some interesting results in the American Machinist* from which the writer has computed the average weight of metal removed per hour, and the corresponding useful horse-power the horse-power required to run lathe empty being neglected, from which the values of C, in the subjoined Table No. VI, have been obtained. All the experiments were conducted on a 2O-inch Fitchburg lathe (previously mentioned in Table V), and the metal cut throughout was cast-iron. TABLE VI. HORSE-POWKR REQUIRED TO REMOVE METAL IN A 2O-INCH LATHE. t 3 1 - if JQ u S3 o 1 g .2 to! JZ *0 'g._j J^ c .2 .gs c o ^ ^ w a 1 g H Tool used. 5 u& 3 u ii K'> 5s 3 1 2 || *- !! &| 11 "s I 1 I 5 Is 4> 3 _3 J 22 Side tool 37 90 I3-3O .025 2 T e Diamond 30 50 12" . 01 5 .218 10. 70 .O2O 3 1 3 17 Round-nose 42.61 125 .015 352 14.95 .023 4 2 Left - hand round- nose ... . 26 29 . I2S .015 237 9.22 .026 5 4 Square - faced tool * j/ ^" broad 25 82 OT5 I2 5 2 55 9.06 .028 6 I Square - faced tool ^" broad 25.27 .048 .048 .200 10.89 .Ol8 7 I Square - faced tool i" broad 25.64 .125 .015 .246 8.99 .027 See American Machinist, Sept. n and 18, 1886. 1 62 D YNAMOME TERS An examination of the above table shows that an average of .26 horse-power is required to turn off 10 pounds of cast-iron per hour, from which we obtain the average value of the constant C = .024. As will be noticed, most of the cuts were taken so that the metal would be reduced \" in diameter; with a broad surface cut and a coarse feed, as in No. 5, the power required per pound of chips removed in a given time was a maximum ; the least power per unit of weight removed being required when the chip was square, as in No. 6. The work of R. H. Smith,* who conducted similar ex- periments in England on a 29-inch lathe (i4^-inch cen- tre), has also been cast into the same form with the average results shown in Table VII. TABLE VII. HORSE-POWER REQUIRED TO REMOVE METAL IN A 2g-iNCH LATHE. 1 Cd i, .a i IP "I u CO u SJ U jj . "o Metal. in o If u C ^ ti III "o IS z. s u 1 >o ^.2 1" |3 4 Cast-iron 12.7 .05 .046 .105 5-49 .019 A Cast-iron . . II . I .135 .046 .217 I 2 06 .017 2 Cist-iron . . 12. 85 .04 .038 ooS i - . yu 3.66 .027 4 Wrought-iron 9.6 03 .046 . tiyo 059 2.49 023 4 Wrought-iron 9.1 .06 .046 .138 4.72 .029 4 Wrought-iron 7-9 .14 .046 .186 .019 2 Wrought-iron 9-35 .045 .038 .092 2-99 .031 Steel 6 .02 .046 I .03 . O42 4 Steel 5.8 .04 .046 .085 2 .O .042 Steel 5T * .06 .108 2.64 .O4O 41 *See Cutting Tools, by R. H. Smith, Cassell & Co., London, 1884. AND THE MEASUREMENT OF POWER. 163 Besides the general results which we here obtain, the relative cutting speeds and amount of metal turned off per hour is quite significant. With the American lathe the cutting speeds on cast-iron were about 30 feet per minute; the German experiments on the same metal averaged 19 feet, while the English speeds on cast-iron were always much less, varying from 14 to 2 feet per minute. The small values of C, .017 and .019, obtained for cast-iron, are probably due to two reasons : the iron was soft and of fine quality, known as pulley-metal, requiring less power to cut ; and, as Prof. Smith re- marks, a lower cutting speed also takes less horse-power. In summing up the results here presented, if we omit for the present the power necessary to over- come the internal friction of the lathe, there would seem to be no good reason why an average of the cases cited should not be taken as representing average practice. Hardness of metals and forms of tools vary, otherwise the amount of chips turned out per hour per horse-power would be practically constant, the higher cutting speeds decreasing but slightly the visible work done. Taking into account these variations, we find that the weight of metal removed per hour, multiplied by a certain constant, is equal to the power necessary to do the work. This constant we have deduced as follows : Cast-iron. Wrought-iron. Steel. Hartig 0.030 0.032 0.047 Smith 023 .028 .042 Hobart 024 Average 026 .030 .044 . 1 64 D YNA MOME TEKS For a cut under ordinary conditions which would remove 6 pounds of cast-iron, 5 pounds of wrought-iron, or 3^ pounds of steel chips per hour, the horse-power necessary would be practically the same. CxW=. 026x6 =. CxlV. 030x5 =.i$H.P. C X W= .044 X 3i = .15 H.P. As previously shown, the power necessary to run the lathe empty will vary from about .05 to .3 H.P., which should be ascertained and added to the useful horse-power, to obtain the total power expended. AND 7^HE MEASUREMENT OF POWER. 10$ CHAPTER VI. MEASUREMENT OF WATER-POWER. IN testing a hydraulic motor a friction-brake or other absorbing dynamometer applied to pulley on the driv- ing-shaft, as already described, will give the power de- veloped by the motor under the given conditions, but this power maybe less than that which it is possible to attain, or which might be developed by the wheel when running at a greater or even a lesser speed : for if the velocity of the wheel be reduced to zero, there will be no power developed ; and if, on the other hand, the speed be excessive, the water will flow through the motor, giving up but little of its energy to the wheel. In making a test of a hydraulic motor, therefore, it will be necessary to find the available energy of the water which passes through the wheel in a unit of time, and also the power developed by the motor in the same time while running at different velocities and with dif- ferent quantities of water. A wheel may be working under conditions which will develop a maximum power, but the efficiency of the motor may not be so great as when developing a lesser power. The problem then presents itself to de termine the speed of wheel and quantity of water which will give the maximum amount of power; and 1 66 D YNA MO ME TER S secondly, to determine that speed and quantity of water which will give the maximum efficiency. The efficiency of the motor in any case will be the ratio of the useful work performed, as determined by a dynamometer, to the theoretical or available work due to the energy of the water ; that is, where V = efficiency; P= effective work of the wheel in foot-pounds per unit time ; W = weight of water passing the wheel per unit time ; h = available head of water above the motor in feet. If h is the total height of fall from upper level in head-race to lower level in tail-race, or if it is the dif- ference in levels between reservoir and the discharge- pipe of the motor when the latter is supplied by a P system of pipes, we shall obtain in ij = -7777 an expres- sion for the efficiency of the fall ; but if h is only the height from the level of head-race to the motor, in the one case, and the effective pressure-head, as determined by a gauge in the supply-pipe at a point near the motor, in the other, then this expression will give the efficiency of the motor. It will be apparent that to obtain the greatest ef- ficiency of the fall, the wheel should be placed as near as possible to the level of the water in the tail-race ; and that in the case of motors supplied by systems of AND THE MEASUREMENT OF POWER. 167 piping, the latter should be arranged to reduce the available head as little as possible. In determining the available energy of a fall of water, the most important and at the same time most difficult measurement to be made is that of the quan- tity of water delivered to the motor in a given time. If the volume be small, the most reliable method of measurement is to weigh the water discharged into a tank or barrel placed upon platform-scales, as shown in Fig. 70, which represents an arrangement used at the Lehigh University for testing a small hydraulic motor. For larger quantities the water discharged may be collected into a receiving-tank of known capacity, and its weight determined from its volume. Sometimes two tanks are employed, with an automatic arrange- ment by which each tank is filled and emptied alter- nately. A counter attached to the apparatus gives the number of times each tank has been filled. In ordi- nary tests the weight of a cubic foot of water may be assumed with sufficient accuracy at 62.5 pounds. With the arrangement shown in Fig. 70 the quantity of water passing the wheel per minute was 428 pounds or 51 gallons under a pressure at the gauge of 65 pounds per square inch, the diameter of nozzle being f inch. The head corresponding to this pressure j<; 150 feet (see page 203) ; and since the weight of water passing the wheel per minute is known, the theoretical horse- power may be obtained from _. = _ = 33000 33000 1 68 D YNAMOAIE TERS AND THE MEASUREMENT OF POWER. 169 With the motor running at 526 revolutions per min- ute and an unbalanced pressure of 6^ pounds on the scales, the lever-arm of the brake being 1 5 inches, the brake horse-power is B.H.P. = 0.0001 904 PRN = o.oooi 904 x 6.25 x ~l X 5 26 = 0.78 ; therefore the efficiency under the given condition was 0.78 ri = = 40 per cent. 1-94 By lowering the pressure to 30 pounds per square inch (equals 69 feet head), the quantity of water pass- ing the wheel per minute, with the same nozzle, was decreased to 295 pounds, corresponding to which the theoretical horse-power is 0.62. The speed of wheel also being decreased to 354 revolutions per minute, the brake horse-power was only 0.40, but the efficiency has bee'n increased to 40 6 2 = 6 4 per cent. From this it will be seen, as previously noted, that a wheel may develop a maximum horse-power under given conditions, but the efficiency may be much less than that obtained under different conditions when the horse-power is not so great. The effect of varying the size of nozzle with varying head and load may be seen from the following tabulated results from tests made 170 D YNA MOME TERS on a small motor by Mr. J. C. Escobar, the pressure ranging from 30 to 75 pounds per square inch. TABLE VIII. TEST OF A SMALL HYDRAULIC MOTOR. Diameter of Nozzle. Gauge Press- ure in Ibs. per sq. inch. Head of Water on Wheel in feet. Weight on Scales in Ibs. 4|l sa^a f||| "o 11. Ill & Theoretic Horse-power of Water. Effective or Brake Horse- power. Efficiency of Wheel, per cent. f 65 150 0-5 428 668 1.94 .OS 4 65 150 6.25 428 526 I 94 . 7 S 40 J 55 127 6.0 391 404 1.50 57 38 *l 45 104 6.0 346 341 1.09 .48 44 35 81 5-o 3 io 341 78 41 52 30 | 69 4-75 295 354 0.62 .40 64 75 173 0-5 276 697 1-45 .08 6 75 173 6.25 276 544 i-45 .Si 56 65 150 6.0 255 468 1.25 .67 60 1 55 127 4-5 238 571 0.91 .61 66 45 104 4.0 220 521 0.69 49 7i 35 81 3-5 198 375 0.48 3i 63 I 30 69 3-o 172 412 0.36 .22 61 r 75 173 0-5 119 812 0.62 .09 15 75 173 3-5 119 428 0.62 35 57 H 65 150 3-5 112 380 0.41 3i 75 55 127 3-0 104 400 0.40 .28 7i I 45 104 2-75 *> 334 0-33 .22 65 The following results will show very clearly the effect of varying the load for the same head and diameter of nozzle. It will be noticed that as the load increases the speed decreases, and that the power developed increases with the load up to a given poin*-; beyond this, how- ever, the power, and hence the efficiency, decreases as the load is increased. AND THE MEASUREMENT OF POWER. I/I TABLE IX. EFFECT OF INCREASING LOAD FOR A GIVEN NOZZLE. Weight on Scales in Ibs. Revolutions of Wheel per minute. Theoretic Horse-power of Water. Effective or Brake Horse- power. Efficiency of Wheel, per cent. 0-5 651 O.QI2 0.07 8 I.O 637 15 16 i-5 624 .22 24 2.0 618 29 32 2.5 612 36 39 3-o 600 42 46 3-5 594 49 53 4.0 588 36 61 4-5 571 .61 66 5-o 544 65 70 5-5 517 .68 73 5-75 433 .66 72 Gauge pressure = 55 pounds, corresponding to a head of 127 feet ; diameter of nozzle = f inch. For larger wheels the following methods for deter- mining the quantity of water are employed : determi- nation of the velocity of flow in a conduit of known cross-section by means of floats or current-meters ; direct measurement by various forms of water-meter; measurement over weirs and through orifices. When current-meters are used it is customary to divide a section of the stream (taken at right angles to the general direction of flow) into a number of parts, preferably of equal area, and to observe the velocity, as indicated by the current-meter, in each of these parts. From the mean of the observed velocities at different depths in each subdivision of the section the average velocity of the whole section is obtained ; by multiply- 1 72 D YNA MOME TERK ing the area of cross-section by the velocity per second the quantity of water passing through the section per second will be obtained. If A area of channel at the given section in square feet ; V m = average velocity of current in feet per second ; Q = cubic feet of water passing through the channel per second, then A V w = Q. A closer determination may be made by ascertaining the discharge of each subdivision from its area and mean velocity; the discharge of the stream will then be the sum of the discharges thus found. .It is evident that the mean velocity of each sub- division, and hence of the entire section, will be more closely determined the greater the number of vertical stations across the stream. A very accurate method of obtaining the area at the given section in narrow streams or small navigable rivers is to run a cord or wire across the channel at right angles to the stream, and to take a number of soundings at equal intervals measured along the wire. The lead for the soundings should be of sufficient weight to insure a vertical measurement in every case; its weight varies from five pounds for shallow, still water to twenty pounds for deep and swift currents. A long cylindrical shape, similar to a sash-weight, AND THE MEASUREMENT OF POWER. 1/3 offering little resistance to the water, is suitable for the purpose.* It is essential that the cord attached to the lead should be thoroughly stretched before being graduated. The graduations are placed one foot apart and indicated by a small strip of cotton attached to the line, every five feet being denoted by a leather strip. Sounding-poles are preferable for shallow channels, and should be graduated to feet and tenths. When float-measurements are used to ascertain the velocity of the current, it is advisable to take sound- ings in two sections, in order to determine accurately the discharge of the stream. If a sufficient number of soundings be made, and the results plotted on section paper, the free-hand curve joining the lower ends of the vertical ordinates will represent very closely the contour of the bed of the channel, from which the area of the section may be obtained, either by the use of a planimeter or by one of the approximate methods. For subsequent use in determining the height of the water, a permanent bench-mark, as for instance a spike driven into a tree-stump, should be established in the immediate vicinity and a water-gauge located near by. For this purpose a white-painted board, graduated to feet and tenths plainly marked in black, is fastened to a stake or post firmly set at the edge of the water; the zero-point of the scale is located with reference to the bench-mark previously set, which also provides a * Johnson's Surveying. Wiley & Sons, 1890. 1 74 D YNA MO ME TERS means of resetting the gauge in case of disturbance or renewal. The current-meter used at the present time is gen- erally some modification of Woltmann's Mill or Tachom- eter shown in Fig. 71, which consists of a small wheel with inclined floats or vanes, /% held in the current, FIG. 71. WOLTMANN'S MILL. which causes it to revolve at a speed nearly propor- tional to the velocity of the water passing it. By a suitable arrangement of gearing connection is made with an indicator which records the number of revolu- tions. Sometimes a rudder is attached to cause the AND THE MEASUREMENT OF POWER. 175 wheel to face the current. The apparatus is either held at the extremity of a pole, D, or, by being adjust- able along a vertical rod fixed in the bed, it may be set at any desired depth below the surface. That the exact number of revolutions in a given time may be obtained, the instrument is arranged with a cord and spring so that the recording device may be thrown in or out of gear at any instant. In some of the more recent instruments electrical connection is made with the rotating shaft by a " make- and-break contact," and the number of revolutions are shown on a registering apparatus on shore or at the surface of the water in a boat, as the case may be. FIG. 72. CURRENT-METER. The form of current-meter shown in Fig. 72 * was used upon the gauging of the Connecticut River, and was designed particularly to avoid the catching of float- ing substances, such as leaves and grass, upon either the vanes or the axis, and to render the record of the instrument independent of the position of its axis with respect to the line of the current : also to get less friction upon the axis, so as to measure low velocities accurately. * Made by Buff & Berger, Boston. 1 76 D YNA MOME TERS This current-meter is also adapted to be used with an electric register for showing the number of revolu- tions of the wheel. It is constructed upon the principle of Robinson's anemometer, turning by the difference of pressure upon opposite vanes of the wheel. The vanes of this meter, however, instead of being hemi- spherical cups with a straight stem, are made conical at the ends, and are hollow and taper to the central hub, so as to offer no obstruction to the slipping off of straws, leaves, or grass as the wheel revolves. The central hub is made tapering, so that any object can slide off easily, and it extends over the joints at the ends of the axis, so as to enclose and protect them from floating substances. The axis runs in agates, through which a fine plati- num wire connects with the metal of the frame. The forward end of the frame which carries the wheel can be turned and secured in any position so that the wheel can be horizontal, vertical, or at any desired angle. The electrical connection is made by carrying an in- sulated wire from near the centre of the instrument, where the insulated wire from the battery is attached to it when in use, out to the end of one arm of the wheel-frame, where it ends in a fine platinum wire resting upon a ring in the hub of the wheel. This ring is made of alternate interchangeable sections of silver and hard rubber, secured in place by screws, so that their position can be changed to register whole or part revolutions as desired. There is also a socket and set-screw in the body of the frame near the centre, for the return-current, which AND THE MEASUREMENT OF POWER. 177 can be carried most conveniently through a plain wire slightly twisted around the in- sulated wire so as to form one cord. If the instrument is run upon a wire, or has a metallic connection with the surface, the return-current can be made through that. This meter can be used in connection with any apparatus for registering the revolutions of the wheel by the breaks in the electric circuit. The Price current-meter,* which is used to a considerable extent by the U. S. Coast and Geodetic Survey, is shown in Fig- 73- Made by W. & L. E. Gurley, Troy, N. Y. D YNAMOAIE TERS The wheel of this meter carries five conical buckets, very strongly and compactly formed so as to be able to resist injury from floating driftwood, while at the same time it is so designed as not to be liable to ob- struction from leaves or grass. A hollow trunnion fitting freely upon the rod sup- ports the frame by a pivot on each side, and thus by the rod and pivots the meter is free to move both horizontally and vertically, and so adjust itself to the direction of the current. The rod is of brass, f inch in diameter and 2 feet long, its upper end having an eye of brass screwed firmly on and pinned, and its lower end screwed into a brass socket in the weight B, and secured by a nut. The weight B is of lead and weighs ELECTRIC REGISTER about sixty pounds ; it has a rudder of wood, which can be set at any angle with the weight, or turned up parallel with the rod when not in use. This weight is only used for deep-water and harbor surveying where the cur- rents are very strong. For shal- FIG. 74 . lower waters the meter is used upon a rod of wood or metal. The electric register used with this instrument is shown in Fig. 74. Before using a current-meter it will be necessary to calibrate it in order to ascertain the number of revolu- tions of the wheel with known velocities of current. The calibration of the instrument is most readily ob- tained by causing it to pass through a measured dis- AND THE MEASUREMENT OF POWER. 1/9 tance at a uniform velocity in still water not less than 5 feet deep. To secure a good rating there should be no wind and the meter should be immersed to a depth of about 2 feet below the surface. The usual method of obtaining the velocities for rating the meter is to attach the instrument to a vertical rod which projects 2 or 3 feet in front of the bow of a small boat, and to either row or pull the boat, by means of cords, at as uniform a rate as possible, over a measured course of about 200 feet, observers on shore noting the exact time of passing the range-lines. By varying the speed of the boat for successive passages, which should be at a uniform rate, a table of constants may be computed from which the velocity of any current can be deter- mined from the number of revolutions per minute as shown on the dial. Frequent ratings of a meter while in use will insure reliability in its readings. In the method of measurement by surface-floats the velocity is obtained by observing the time of transit of a light floating body, such as a flat disk, or ball of wood, over a known distance. By placing several floats across a stream and noting their velocities, the average surface-velocity may be approximately computed, but this method is apt to be very inaccurate when there are any local disturbances due to wind or eddies in the current. The use of double floats presents a much more reliable means of obtaining the velocity. As in the method with current-meters the velocity of the filaments should be ascertained in several verti- cals across the stream and at various depths below the surface. For this purpose a body slightly heavier than 1 8O D YNA MO ME TERS the water is suspended at the desired depth from an- other body floating at or just beneath the surface, and of such a form and size as to offer less resistance to the stream than the first, so that without sensible error the velocity with which the floats are carried along by the current is that of the submerged body and of the stream at the particular depth below the surface at which it is placed. For the surface-float a block or ball of wood is often used, but hollow floats, such as glass or metallic balls, are preferred by many engineers, as they may be par- tially filled with water and sunk just below the surface, where they are less affected by the wind. A small flag or other suitable indication will locate the position of the float. For the sub-surface-floats metallic balls have been used from 6 to 8 inches in diameter. Humphreys and Abbot, in their work on the Mississippi, used small kegs without top or bottom, ballasted with strips of lead so as to sink and remain upright ; these kegs were 9 inches high and 6 inches in diameter, but for depths greater than 5 feet below the surface a larger size, 12 inches high and 8 inches in diameter, was used. A very convenient form of float is made by joining two sheets of galvanized iron at right angles, intersect- ing in their centre lines, and weighting the lower edges with lead. This maintains the float in an upright position and gives the required tension on the connect- ing cord. The vanes should be from 8 to 20 inches high, depending upon the depth of stream in which they are to be used. Cylindrical air-cavities are pro- vided along the upper edges of the vanes. AND THE MEASUREMENT OF POWER. l8l By connecting the upper and lower floats with a fine wire, chain, or, preferably, a braided silk cord, and varying its length, we shall obtain the several veloci- ties at varying depths. The mean of all these observed velocities may be assumed to be the average velocity of the current. To obtain the mean velocity in a perpendicular by a single measurement, a floating rod is employed. This rod may be either of wood or tin in sections screwed together for convenience ; the lower section being fitted with a hollow metal cap which is filled with enough shot or gravel to cause it to sink to the re- quired depth and to maintain a nearly vertical position. The immersion of the rod should be at least nine tenths of the depth of the water, which should not be more than 20 to 25 feet. If the channel were of uniform depth, and the rod reached to the bottom without actually touching, then the velocity of the rod would be very nearly the mean velocity of all the filaments in the vertical plane through which the rod passes. As the rod does not reach the bottom, its velocity can only record the mean velocity of the filaments in a vertical plane to a depth equal to its immersion. In general the rod-float will give for small channels more reliable results than those obtained by the use of the double ball-float. To obtain the velocity or rate of motion of floats, two parallel range lines are laid off on shore, from 100 to 200 feet apart, and the float placed in the current at some distance above the first range-lines. Two tran- sits are usually employed for timing the floats, one 1 82 D YNA MOME TERS being set on each range. In addition two time-keepers will be required to take the exact time on stop-watches when signalled by the observer at the transit. If the stream is not too wide, the passage of the float across the fixed ranges may be noted by a single ob- server using only a stop-watch and, if occasion require it, a field-glass. The watch is started when the float crosses the first line, then the observer walks to the lower station and stops the watch the instant the float passes the range-line. The total distance, s, divided by the number of seconds,/, will give the mean observed velocity, v, of the float, or s v = -. t On account of the uncertainty of float-measurements, due to action of the wind, local currents, eddies, and other causes, several observations should be taken to obtain a fair average value of the velocity. Approximate determinations of the mean velocity of a stream in any vertical may be made from a single measurement by obtaining either the mid-depth ve- locity or the surface-velocity, and multiplying such velocity by a coefficient. It has been shown that the curve plotted for the velocity of the filaments in a vertical will, in general, be represented by a parabola whose axis is parallel to and beneath the surface, except when the wind is down-stream with a rate equal to or greater than the velocity of the current. According to Humphreys and Abbot the axis of the parabola, or filament of maxi- mum velocity, will approach the surface or recede from AND THE MEASUREMENT OF POWER. 183 it, depending upon the direction and intensity of the wind. This is shown in Fig. 75, which is taken from the report of Humphreys and Abbot.* When the air is calm the axis will be found to lie about 0.3 of the entire depth of stream beneath the surface. A down-stream wind brings the axis nearly Telocifies'in feet per second. 7.5 7.8 8.1 The scale of wind forces varies from (calm) to 10 (hurricane). KIG. 75. VELOCITY OF CURRENT AT VARYING DEPTHS. to the surface, while with the wind up-stream it is found below the mean depth. It will be noticed that these curves intersect at about mid-depth, from which it is inferred that the velocity of the mid-depth fila- ment is not affected by the wind.f * Physics and Hydraulics of the Mississippi River. f For an exhaustive discussion of velocity of currents, see Hering & Trautwine's translation of Ganguillet & Kutter's General Formula for Flow of Water in Rivers. 1 84 D YNAMOME TERS This mid-depth velocity will represent very closely the mean velocity of the vertical, being from one to six per cent greater, according to the velocity of stream, depth, and roughness of bed. Hence by taking the different station or division mid-depth velocities and applying a coefficient of from 0.96 to 0.98, the mean velocity of the sub-section will be ob- tained. The other method that of measurement from sur- face velocity alone has been employed to a consider- able extent, but it must be remembered that the results are only approximate, and for this reason should be used only for rough estimates. From many experi- ments to determine the mean velocity in a vertical from its measured surface velocity, it has been found that if the observation be taken when there is no sensible wind, the mean velocity of the current may vary from O.8 to 0.9 of the surface velocity. If a mean value of 0.85 be used for the coefficient, the discharge calculated from the average of all the surface velocities thus ob- tained may be assumed to approximate the actual discharge within a limit of from ten to twenty per cent. For obtaining the surface velocity a current- meter should be used. The method of measurement by water-meters is often employed to ascertain the quantity of water used by a motor when the latter is supplied through a small pipe. The water-meter consists essentially of a case, divided into two parts, supplied with plungers or other suitable mechanism by which the volume of water which passes through the meter in a given time (stroke or AND THE MEASUREMENT OF POWER. 185 revolution) may be measured. A convenient register is attached, similar in appearance to that used in the more familiar gas-meter, by which the quantity of water passing through the meter may be read directly in cubic feet. The accuracy of water-meters depends upon their construction, and in all cases where such meters are used for tests the readings of the instrument should be carefully compared with the actual flow as measured by the use of a tank of known capacity. Any error thus ascertained will furnish a constant for correction when the meter is in use. A recent form of water-meter has been experimented upon by Mr. Clemens Herschel, in which a compound tube provided with piezometers is used to determine the discharge. This apparatus is constructed upon the results of experiments by Venturi which show that when water flows through a pipe of which the section is contracted and subsequently gradually increased, the pressure in the smallest section is much less than in the largest on either side of the contraction, and may with suitable proportions sink below the atmos- pheric pressure, so that it can be measured by a vacuum-gauge. The velocity in the smallest section is theoretically that due to the effective head correspond- ing to the difference between the pressure in the largest section before the contraction and that in the smallest section, plus the influence of the velocity in the largest section, generally very slight. To obtain the actual velocity, the theoretical quantity has to be multiplied by a coefficient to be determined by experi- ment. 1 86 /)} \VA MOVE TERS When the latter is known, and also the area of section of the smallest part of the pipe, the true velocity cf flow can be determined from the observed difference of pressures.* The method of measuring the flow of water over weirs is that usually employed in testing the larger hydraulic motors, for the reason that it is generally the most convenient and practicable. The stream to be measured is dammed by a weir and all the water compelled to flow through a rectangular open- ing at the top. Occasionally the weir is suppressed or drowned and the water is allowed to fall over the whole length of the weir, in Which case the sides of the conduit or head-race should be parallel and vertical for some distance up-stream above the weir. If h denote the height in feet of the water-level above the edge of weir, measured a few feet back from the sill before the sheet of water begins to curve downwards, L the length of the weir-opening in feet, then the theoretical quantity of water discharged per second can be shown to be Q = \Lh V^gh. The results of experiments, however, show that the actual quantity is less than this, therefore a coeffi- cient must be used to determine the correct amount. It has been found that the coefficient varies with th following dimensions and conditions : Length of weir ; Height of water over weir ; * Bodmer : Hydraulic Motors. See also "The Venturi Water- meter," Trans. A. S. C. E., Nov. 1887. AND THE MEASUREMENT OF POWER. 187 Width of canal of approach or head-race ; Nature and thickness of edges of weir; Distance from bottom of weir to bottom of conduit. When the length of opening in weir is less than the width of head-race, so that the opening has thin edges at the ends, it is said to have end-contractions, since the thin ends cause the stream of water to contract in flowing through. The formula deduced by Francis* from experiments on weirs from ten to twenty feet wide and from seven to nineteen inches depth of water over crest, is Q = 0.623 X \Lh V~2gk', or, as it is generally written, when there are no end-contractions, and when end-contraction occurs and n (usually 2) is the number of end-contractions. To secure accurate results, the up-stream edge of the crest of the weir is made straight, sharp, and smooth usually by constructing it with an iron edge, bevelled sharply, and fitting similar apertures at the sides. The depth of the water below the crest of the weir should be not less than one-third of the length of the weir ; otherwise the velocity of approach must be * Lowell Hydraulic Experiments. i88 D YNA MOME TERS considered, as this tends to increase the volume of water carried over. Air should have free access to the space under the sheet as it flows over the crest. A more exact determination may be obtained by the use of the following coefficient tables computed by Mr. Hamilton Smith, Jr.,* from the experiments of Poncelet, Lesbros, Francis, Fteley & Stearns, and others, in which a separate coefficient is given for varying lengths of weir and under different heights above crest of weir. TABLE X. COEFFICIENTS FOR DISCHARGE OVER WEIRS: Twa END-CONTRACTIONS. Coefficient = c in formula Q - c X Effective L = Length of Weir in Feet. Head in Feet. .66 2 3 4 5 7 10 '5 19 .1 .632 639 .646 .652 653 653 .654 .655 655 656 15 .619 .625 634 .638 .639 .640 .640 .641 .6 4 a .642 .2 .611 .618 .626 .630 .631 .631 632 .633 634 634 25 .605 .612 .621 .624 .625- .626 .627 .628 .628 .629 3 .601 .608 .6l6 .619 .621 .621 .623 .624 .624 .625 4 595 .601 .609 .613 .614 .615 .617 .618 .619 .620 5 .590 596 .605 .608 .6lO .611 .613 .615 .616 .617 .6 .587 593 .601 .605 .607: .608 .611 .613 .614 7 .585 590 598 .604 .606 .609 .612 613 ;6?4 .8 595 .600J .602 .604 .607 .611 .612 .613 9 592 .598 .600 .603 .606 .609 .611 .612 .0 .590 595 598 .601 .604 .608 .610 .611 .1 587 593 .596 599 .603 .606 .609 .610 .2 585 591 594 597 .601 .605 .608 .610 3 .582 .589 .592 .596 599 .604 .607 .609 4 .580 587 .590 594 598 .602 .606 .609 -5 585 589 592 596 .601 .605 .608 .6 .582 .587 .591 595 .600 .604 .607 7 594 599 .603 .607 Smith's Hydraulics. Wiloy & Sons, 1886. AND THE MEASUREMENT OF POWER. 189 The heads in the first column are the effective heads, and in such cases when the water approaches the weir with a sensible velocity the head ti due to that velocity \k' = J must be used in connection with the head h over the weir, in which case the effec- tive head may be considered equal to h -j- 1.4/1'; hence As an example of the application of the table, the following is taken from Merriman's " Hydraulics." Let it be required to find the discharge per second over a weir 4 feet long when the head h is 0.457 foot, there being no velocity of approach. From the table the coefficient of discharge is 0.614 for k = 0.4, and 0.610 for h = 0.5, which gives about 0.612 for Ji = 0.457. Then the discharge per second is Q .612 X | X 8.02 X 4 X V'OiTT) 1 = 4-4 CLlbic feet If the width of the feeding-canal be 7 feet and its depth below the crest be 1.5 feet, the velocity-head will be h' = -^ = 0.015557;'; but the velocity v = quantity of water discharged, divided by the area of the stream ; hence Q* (4-04) 3 (7 X (i-5 + -457))" ' 1 9O D YNA MO ME TERS the velocity-head then becomes h' = - OI 55s = o- 001 34 foot. The effective head now becomes h-\- 1.4/1' = 0.459 foot, and the discharge per second is Q = .612 X 1 X 8.02 X 4 X V / (459)' = 4-O7 cu bic feet. As this result depends upon the degree of accuracy with which the quantities used are ascertained, and also upon a possible slight error in obtaining the coeffi- cient, it may be assumed that a probable error of at least one per cent exists in the final result. It will be evident that as the velocity-head //' is small compared with the head over weir, the latter may be used as the effective head, with no appreciable error, in selecting a coefficient from the table for the first approximation. The method of measurement over weirs is often em- ployed in testing-flumes by constructing the tail-race with a rectangular opening, through which the dis- charge which flows from the motor is measured in the manner just described. The determination of the height of water over weirs requires considerable care for accurate tests, on ac- count of the small height generally involved. For this purpose some form of the Boyden hook-gauge is usually employed. The instrument,* shown in Fig. 76, consists of a * Made by W. & L. E. Gurley, Troy, N. Y. AND THE MEASUREMENT OF POWER. 19 l wooden frame 3 feet long and 4 inches wide, in a rect- angular groove of which another piece is made to slide carrying a metallic scale divided to feet and hun- dredths, and figured from O to 2^ feet, as shown. Connected with the scale is a brass screw passing through a socket, fastened to another shorter sliding piece, shown above, which can be clamped at any point on the frame, and the scale with hook moved in either direction by the milled-head nut. There is also a vernier attached to the frame, and movable under the screw-heads which secure it, in order to adjust its zero to correspond with the point of the hook when setting the gauge. The vernier reads to thousandths of a foot. The form of hook-gauge designed by Emer- son and used in the Holyoke testing-flume is shown in Fig. 77. In this gauge a small gear operated by a worm engages a finely cut rack on the back of the scale-rod which permits a very close adjustment of the hook, the vernier being arranged to read to ten-thou- sandths of a foot. When in use the hook is raised from below the level of the water until its point barely pricks the surface, when it will be noticed that a slight swell and distortion of the reflected light is caused just above the point of the hook ; by carefully lowering the hook until this distortion disappears, the point may be assumed to be at the level of the water, which 192 DYNAMOMETERS can then be read from the vernier. The instrument is supposed to have been previously set with its vernier at zero, when the point of the hook was exactly on a level with the sill of the weir. The hook-gauge is generally enclosed in a wooden case or box open at the top, and provided with a small inlet at the bottom, in order to prevent any dis- turbance of the water in the vicinity of the hook. As previously stated, the measurement of the head over the weir must be taken several feet back of the crest, where the water is level. To allow the observations to be taken more readily, the water may be led by a hose or other pipe from the bottom of the race-way above the weir (up- stream) into the hook-gauge box, which may be placed at any convenient point near by. Very accurate results may be obtained by the use of a good levelling-rod with a hook secured to the foot ; the slide may be operated by a small gear and rack which can be attached to the rod to allow a fine adjustment of the hook. The total head or fall can be obtained very precisely by the use of a hook, at the level of the water in the tail-race, secured to a graduated rod placed beside FIG. 77. AND THE MEASUREMENT OF POWER. 193 a fixed cylinder with glass tube attached, which is con- nected by means of a rubber hose with the upper water- level. By this arrangement the reading on the scale at the water-level in the glass tube will give the total height between the two levels the graduations on the rod being a measure of the distance from the point of the hook.* Another method of obtaining the total head is to run a line of levels from one to the other. Permanent bench-marks being established, gauges can then be set in the head and tail races, and graduated so that their zero-points will be at some datum below the tail-race level. The difference in readings will give the required total head.f Simpler methods will suggest themselves and may be used where less accuracy is required, as in rough estimates of water-power. As water in most cases where available for power has a commercial value, the most advantageous and profitable use of it should be considered. In this relation not only the efficiency of the motor employed, but the pipes which supply the motive power have an important bearing upon the result. When water is delivered to a hydraulic motor through a pipe or nozzle, as in the numerous class of small motors fed from a city main, the diameter and length of pipe, as well as the size and shape of nozzle, largely affects the work done on the motor. The head is not that due to difference in levels * R. H. Thurston. Trans. A. S. M. E., vol. vui. f Merriman's Hydraulics, p. 288. 1 94 D YNA MOME TERS between the reservoir and the motor, but is much less on account of losses in transmission due to friction in the pipes, loss at entrance, loss due to bends and angles in the pipe, changes in cross-section, and other causes. As any loss of head is a direct loss of power, such loss should be prevented as much as the circumstances in the case will justify. Where both the water-supply and head are limited, such pipe should be put down as will avoid, as far as possible, serious loss in the head or supply ; where, on the other hand, water is abundant and a very considerable head can be obtained, a loss in this way may be justified to a larger extent to save cost of pipe. The greatest loss in long pipes is that due to friction, which loss may be deduced approximately from the following formula : in which h l = height of resistance of friction,* /a co- efficient obtained by experiment for different condi- tions, / the length of pipe in feet, d its diameter in feet, and v the velocity of water in feet per second. The coefficient of friction,/, is not constant, but varies with the velocity and with the diameter and internal condition of the pipe. From this it will be seen that the loss due to friction is independent of the pressure of the water ; that it is proportional to the length of pipe ; that it increases nearly with the square of the velocity ; that it is in- * Weisbach. AND THE MEASUREMENT OF POWER. 195 versely proportional to diameter of pipe ; and that it decreases with the smoothness of the pipes and joints. The coefficient, f, varies, according to Merriman, from o.oi to 0.05 and is often assumed in approximate calculations at 0.02. The following table of coefficients for smooth clean iron pipes obtained from deductions of Fanning, Smith, and others has been compiled by Prof. Merriman, and will give the value to use in any particular case, from which the probable loss due to friction may be obtained. TABLE XI. FRICTION FACTORS FOR_SMOOTH, CLEAN IRON PIPES. Coefficient = /in formula hi =/ . d zg D meter i Feet. Velocity in Feet per Second. 3 4 6 10 IS 05 0.047 0.041 0.037 0.034 0.031 O.O29 O.O28 .038 .032 .O3O .02& .026 .024 .023 25 .032 .028 .026 025 .024 .022 .O2I .5 .028 .026 .025 .023 .022 .O2O .Oig 75 .026 .025 .024 .022 .021 .Oig .018 025 .024 .023 .022 .020 .018 .017 25 .024 .023 .022 .O2I .Oig .017 .Ol6 5 -023 .022 .O2I .O2O. .Ol8 .016 015 75 .022 .021 .020 .018 .017 015 .014 2. .021 .O2O .Oig .017 .Ol6 .014 .013 2-5 .020 .Oig .018 .Ol6 015 -013 .012 3- .Oig .018 .016 .015 .014 013 .012 3-5 .Ol8 .017 .Ol6 .014 .013 .012 4- .017 .Ol6 .015 013 .012 .Oil .016 ' 015 .OI4 .013 .OI2 6'. .015 .014 .013 .012 .Oil 1 96 D YNA MOME TERS The loss of head due to resistance as the water en- ters a pipe will vary with the form of mouthpiece em- ployed, and may be taken as for average cases, although with a perfect bell-shaped mouthpiece this loss will be zero. For long pipes the loss due to entrance is very slight, as compared with the loss due to friction. The other losses which occur, such as those due to change of cross-section, angular connections, curvature of bends, and resistance of valves, are not so readily obtainable. Where the radius of curvature is great as compared to the diameter of pipe, and few bends occur in the pipe, the loss will be small ; also where conical reduc- ers are used when changing from one diameter to another, the loss for each change will be barely ap- preciable and may be neglected. Moreover, as the actual conditions are generally unknown, these latter losses will have to be neglected in ordinary computations, and the formula for the velocity will then be that obtained for pipes compara- tively straight, smooth, and of essentially the same diameter. Assuming the general formula *=. 2g we can obtain the velocity of flow corresponding to a given hydrostatic head from V '= VUgh' if no losses AND THE MEASUREMENT OF POWER. 1$? occur in the pipe ; but if the velocity-head of the issu- ed ing stream equal the losses in the pipe will then be equal to the hydrostatic head minus the velocity-head, v* hence equal to //' -- This loss must be equal to the sum of the losses due to friction, and to entrance (provided the lesser resist- ances due to curvature and other causes be neglected) ; therefore By substituting the values previously found for h^ and //, there is obtained or which is a convenient formula to use in obtaining the velocity of flow in straight pipes of uniform diameter, from which the head corresponding to this velocity may be obtained by substitution in the general formula V h = The head, h! ', necessary to overcome the re- D YNA MOME TERS sistances in a given length and diameter of pipe and to maintain the velocity, v, may be calculated from If a given supply of water, Q, be required per second, the theoretical area of pipe will be A = \nd* ; therefore the velocity in the pipe will be v = ^ = r 2 ; hence /i Ttu the theoretical head required to maintain the flow will be osr *(*+/$ provided the inner surface of the pipe be reasonably smooth. If an iron pipe be unprotected by any surface coating it will in time become coated with scale or lime deposits and more or less tuberculated. These depos- its affect the discharge in a twofold manner : first by reducing the area of pipe, and secondly by increasing the roughness. Therefore to reduce the loss as much as possible it will be an advantage to cover the inner sur- face with coal-tar varnish or some other suitable coat- ing. In any case the velocity-head of the issuing jet will equal v 1 ; hence if the discharge, Q, and also the area, a, of jet < be known, the velocity, v, can be determined from * For a discussion of the loss due to bends, curvature, reduction in area, resistances in valves and cocks, see Weisbach, Coxe's transla- tion, pages 874 et seq. AND THE MEASUREMENT OF POWER. 199 Q V* Q* v = -, therefore = - 5, and the velocity-head will then be h Q * - W In the determination of the value of the area, a, of issuing stream the general method employed is to caliper the jet at its least cross-section. By carefully ascertaining the diameter of jet for a given orifice or tube and comparing the area of latter with the area of jet there is obtained a value, C', which may be used as a coefficient in obtaining actual contraction for a given opening. Thus if a equals the area of jet, and' A equals area of circular orifice in a thin plate, there is obtained _ ~ A ~ where d = diameter of jet and D diameter of orifice. The average value of C' thus found = 0.62. If the orifice have rounded or curved edges, the con- traction will be very much diminished and the coeffi- cient will be found to vary from 0.62 to i.o. If the actual quantity of w r ater which flows through an orifice in a given time be measured, there will be found, as in the case of flow over weirs, that this quan- tity is much less than the theoretical discharge calcu- lated for the area of opening under the given head ; therefore the theoretical discharge must be multiplied by a coefficient C in order to determine the actual dis- charge. 20O D YNA MOME TERS This coefficient of discharge varies from about 0.59 to 0.64 for circular orifices in a thin plate, depending upon the size of orifice and the head. For ordinary cases the coefficient of discharge, C, = 0.61 may be as- sumed. It can be shown further that the velocity of flow through an orifice in a thin plate is diminished about two per cent by friction, and that the theoretical veloc- ity must be multiplied by a coefficient to obtain the actual velocity. This coefficient of velocity C t will vary slightly, increasing with the head, but 0.98 may be assumed to meet most conditions. It will be noticed that the coefficient of velocity is equal to the ratio coefficient of discharge _ C _ coefficient of contraction C 1 From these considerations it will be seen that the circular orifice in a thin plate offers another method of ascertaining the discharge. If the area of reservoir or supply-tank be large compared to area of orifice, and if the head, /*, at centre of orifice in a vertical plane is large compared with the diameter of opening, the theo- retical discharge may be assumed equal to therefore the actual discharge will be CQ! Q, hence 0.61 nd* . - AND THE MEASUREMENT OF POWER. 2OI As it is impracticable to place the buckets or vanes of a water-motor sufficiently near an orifice to utilize the energy of the jet, short tubes, nozzles, or tips are used for this purpose, and for these separate coefficients will have to be determined. When the discharge takes place through a short cylindrical tube whose length is about three times its diameter, it will be found that under ordinary condi- tions there is no contraction of the jet, but the velocity of the stream is diminished about 18 per cent; hence the coefficient of velocity C, may be assumed to be 0.82 for such short pipe when the inner corners are not rounded. When there is no contraction, that is when C I, the coefficient of discharge C will equal 7 the coefficient of velocity, since -~-, = C^ ; hence the coefficient of discharge in this case will equal 0.82. It has been found that if a conical converging tube be used, the coefficient of velocity and of discharge are both very much higher than for a straight tube, and for this reason such tubes or mouthpieces are used, with certain modifications, when it is desired to utilize the energy of flow to the best advantage. From ex- periments by D'Aubuisson and Castel * on conical tubes with varying angles of convergence and with square corners at entrance, the coefficient of discharge attained its maximum value of 0.946 for a tube whose sides converge at an angle of 13^ ; but the coefficient of velocity increased continually as the angle increased ; for a tube whose angle was 48 50' the coefficient of velocity was 0.984. In these experiments the tube * Weisbach. 202 DYNAMOMETERS was inch diameter at small end, and its length 2.6 times its diameter. The results of Castel's experiments also show that under varied heads the coefficients of discharge and of velocity were practically constant for the same mouth- piece. Some experiments by Lespinasse on the canal of Languedoc * show the great advantage in using converging mouthpieces to effect an increase in the discharge ; the mouthpieces employed were truncated rectangular pyramids 9.59 feet long, the dimensions at one end 2.4 by 3.2 feet, at the other .44 by .62 foot ; their opposite faces were inclined at angles of 11 38' and 15 18', and the head employed was 9.59 feet. The experiments resulted in determining a coefficient of discharge varying from 0.976 to 0.987. If the motor to be tested be supplied with several conical or curved mouth-pieces, it is advisable to cali- brate each one in order to obtain its coefficient of discharge, C. By inserting a gauge near the discharge, in the sup- ply-pipe, which should be large relatively to the nozzle, the hydrostatic head may be obtained, by multiplying the gauge-pressure by 2.304 as shown hereafter. By this means the actual discharge may be obtained by noting the pressure and calculating the theoretical discharge for the given mouth-piece from then Q'XC will equal the actual discharge. * Jackon's Hydraulic Manual. AND THE MEASUREMENT OF POWER. 2OJ If we assume the weight of a cubic foot of water to be 62.5 pounds, and the height of a column of water to be h feet, the total pressure, P, per square foot will be P =62.5/1, and h .oi6P. As the pressure is ordinarily given in pounds per square inch, the above will become and /* = 2.3O4/. This will give the available hydrostatic head corre- sponding to a given pressure, p, in the pipe as ascer- tained by the reading of a pressure-gauge inserted near the nozzle (see Fig. 70, page 168), the reading of the gauge to be taken when the water in the pipe has no velocity. In obtaining the pressure from a gauge in order to determine the effective head available at the motor, the pipe to which the gauge is connected should be inserted in the supply-pipe near the entrance to the nozzle, at right angles to the axis of the supply-pipe, and, preferably, the latter should be tapped on one side rather than on top. If the gauge-tube be inclined toward the stream in the pipe when the water is flow- ing through, the tendency will be to increase the press- ure-head; and if it be inclined in the opposite direction, the reverse will be the case. If the reading of gauge be taken when the motor is running, there will be a certain diminution of head, as 204 & YNA MOME TERS indicated by the gauge, due to the velocity of the water in the pipe. When the diameter of supply-pipe is large compared to that of the nozzle at discharge which is usually the case, as the velocity and energy of the water is best utilized by such arrangement the reduction of pressure-head is barely appreciable and may be neglected, as the error from this cause is well within the limits of the degree of accuracy attained in determining other quantities involved. When, however, the supply-pipe and nozzle do not greatly differ in size, the velocity in the pipe approaches more nearly to the velocity at the nozzle, .and the pressure-head may in such cases differ materially from the effective head. If h equals the known pressure-head, and h t equals the head due to the velocity, V, in the pipe, then the effective head will be F* h' = h + ; 2* the velocity v at the end of the nozzle will then be but since the same quantity of water which discharges from the nozzle must pass through the pipe, the respective velocities will be inversely proportional to the sectional areas, and hence to the squares of their respective diameters ; that is, v _A _ D^ V~ a~ d*' AND THE MEASUREMENT OF POWER. 20$ or in which V, A, and D represent the velocity of flow, area of cross-section, and diameter of pipe ; and v, a, and d are the corresponding values at the outlet of nozzle. Substituting this value of V \r\ the expression for v, above, there is obtained from which the effective head, //'(== ),rnay be calcu- V 2gl lated. When the diameter of pipe is large compared to the diameter of nozzle at discharge, the ratio will be very small, in which case v = C^ V2gh will approach v=C l \ l 2gh' ; if the ratio of sectional areas, or is less than one to ten, the error in using // for h' will be less than one-half of one per cent, and when the ratio is less than one to twenty, h may be assumed to equal h' within a limit of .025 of one per cent, a greater 200 D YNA MOME TERS degree of accuracy than can be obtained from the other factors involved. As an example, a motor is supplied by a pipe two inches in diameter having a nozzle whose diameter at discharge equals half an inch, the gauge-pressure in the pipe near the entrance to the motor equals 43 pounds, and the coefficient of velocity = 0.98. According to the exact formula, Q-9 6 X = 4/64.4 X 95-49 = 78.41 feet per second. From the approximate formula ^ = C, we find, by assuming the effective head, h', equal to the pressure-head, //, v t = .98 1/64.4 X 99.07 = 1/64.4 X 95.1 f= 78.26; that is, the gain in using the exact formula will only be v 78.41 - = ' -*-- = 1.0019, v l 78.26 or about two tenths of one per cent, which can readily be neglected without sensibly affecting the result. INDEX. Absorption-dynamometer, Richards', 54 " Alden's, 56 " " Fronde's, 63 Adjustment of cradle-dynamometer, 103 Air-resistance, measurement of, no Alden's absorption-dynamometer, 56 Allowable strain in belting, 14 Amos & Appold's brake, 33 Approximations for driving power, 3, n Arc of contact, influence of, 12, 16, 17 Area of channel, measurement of, 172 B Babcock, G. H., rule for estimating horse-power, 3 Band-brakes, 28, 40 Barrus, friction of shafting, 8 Belt brake, 28 " transmission-dynamometer, Briggs, So " " Hopkinson, 79 ' " " other forms, 94, q6 " velocity of, used to determine horse-power, 10 Belting, coefficient of friction, 15 strength of, 14 Belts, double, 17 " in actual use, Table of, 15 . . " slip in, 16 207 2O8 INDEX. Belts, specific duty of, 13 " wider, should be used, 10 Bench-marks, 173, 193 Boyden hook-gauge, 190 Bracket! cradle-dynamometer. q8 Brake-blocks, 48 Brake-tests on engines, 27 Brakes, band, 31, 40 belt, 28 rope, 37 " water, 56, 63 Buff & Berger's current-meter, 175 Calibration of current-meters, 178 " Emerson power-scale, 116 " Tatham dynamometer, 03 Capacity of friction-brakes, 51 Centrifugal force, effect of, in power-scale, u6 Coefficient of contraction, 200 " discharge, 199 " friction for belting, 15 " flow in pipes, 195 " " velocity, 200 Coefficients for discharge over weirs, 188 Compensating brakes, 133 Compound scale-plate, 129 Cradle-dynamometer, 98 Current-meters, 171 " Buff & Berger's, 175 calibration of, 178 " Price's, 177 " Woltmann's Mill, 174 Dash-pots, 22, 47, 48, 54 Determination of brake-power, 24 " mechanical equivalent of heat, 93 INDEX. 209 Differential scale-plate, 127 Discharge through orifices, 199 Dimensions for Prony brake, 22 Double belts, 17 Driving power from velocity of belt, 10 Dynamometer, Alden, 56 Balance, 77 " Belt, 94, 96 " Brackett, 98 " Briggs, So Cradle, 98 " Differential, 76 " Emerson, 113 " Flather, 137 " Floating, 103 " Froude, 63 " Hartig, in " Hopkinson, 70 " Hydraulic, 137 " Marine, 63 " Morin, 72 " Reynolds, 70 " Richards, 54 " Tatham, 82, 87 Van Winkle 117 " Webb, 103 Webber, 77 Dynamos, friction in, no Effect of increasing load on water-wheel, 171 Efficiency of water-wheels, 16 Electric register for current-meters, 175, 178 Emerson power-scale, 113 Estimated power, variance of, 14 Experiments on lathes, 158, 161 " " water-wheels, 167, 170 ' with leather belting, 14 2 IO INDEX. Flather hydraulic dynamometer, 137 Float measurements, 173, 179 Floating dynamometer, 103 Flow of water over weirs, 186 Formula for brake-power, 25, 29 " " measurement over weirs, 187 " " power required to drive lathes, \yi " width of belt, n, 16 " " width of rubbing surface, 153 Friction and air-resistance, no Friction, coefficient of, in belting, 15 " factors for iron pipes, 195 " in lathes, 149, 151 " of shafting in machine-shops, 9 " mills, 8 " " toothed gears, measurement ol, 100 " " water in pipes, 194 " work of, in Prony brake, 25 Friction-brake, Alden's, 56 " capacity of, 51 " " for vertical shaft, 46 " " Prony, 19, 21 " used to test locomotive, Ol Froude's absorption-dynamometer, 63 Gas-engine test, 38 II Hartig's experiments on lathes, 158 " transmission-dynamometer, in Heinrich's proportions for small brakes, 21 Henthorn, J. T., friction of shafting, 8 Herschel, C., Venturi water-meter, 185 Hobart, J. A., experiments on lathes, 161 INDEX. 211 Hollow brake-strap, 50 Hook-gauge, 190 Hopkinson belt-dynamometer, 79 Horse-power determined from velocity of belt, n, 18 " " required to drive machinery, 5 " " " shafting, 5 " " transmitted by belts in use, 15 Hydraulic dynamometer, 137 Hydrostatic head, 203 I Improved Alden brake, 60 Indicator-cards from dynamometer, 148 Indicator, use of, with dynamometer, 136 J Jamieson, rope brake, 39 " gas-engine test, 38 Kapp's compensating brake, 32 L Lathes, Hartig's experiments on, 158 " power required to drive, 148, 151 " table of horse-power, 155 Leads for sounding, 172 Locomotive, brakes for, 61 " method of mounting, 61 Loss of head in pipes, 194 Lubrication of Alden brake, 60 " " brakes, 27, 48 M Machinery, power required to drive, 3, 5 Machines, belting of, 2 Machine tools, power required to drive, 136 Marine-engine dynamometer, 63 212 INDEX. Materials for brake-blocks, 49 Mean velocity, 181, 184 Measurement of friction in toothed gears, 109 " power from belt used, 10 " rented power, advantage of, 13 " velocity by surface-floats, 179 " water over weirs, 186 " water-power, 165 Metal, power required to remove, 159 Meters, current, 171 " power, 117 water, 184 Method of mounting locomotive, 161 Mid-depth velocity, 182 Moderators, 22, 47, 48 Morin transmission-dynamometer, 72 Nagle, table of belting, 15 Number of men employed per horse-power, 3, 5 Power, rented, measurement of, 13 required to drive machinery, 5 " " machine tools, 136 " shafting, 5 " " remove metal, 159 " scale, Emerson, 113 Power-meter, Van Winkle, 117 Pressure due to head, 203 Price, current-meter, 177 Prony friction-brake, 19, 21 R Rappard band-brake, 40 Rating current-meter, 178 Registering belt dynamometer, 97 Regulators, 22, 47, 48 INDEX. 213 Resistance of air in dynamos, no Reynolds' water-brake, 70 Richards' absorption-dynamometer, 54 Rod floats, 181 Rope brakes, 37 . Royal Agricultural Society's brake, 33 Rubbing surface, 48 Rule for estimating horse-power from belt used, II " " " " " from men employed, 3 Shaft-dynamometer, 113, 117 Shafting, friction of, 8, 9 Shafting, power required to drive (Table), 5 Sibley College brake, 23 Slip in belt, 16 Sounding-poles, 173 Specific duty of a belt, 13 Spring dynamometers, 72, 117, 131 Strength of belting, 14 Surface-velocity, measurement of, 179 " " of pulley with rope brake, 40 Table of capacity of friction-brakes, 51 " " coefficients for discharge over weirs, 188 " " dimensions for Prony brake, 22 " " friction factors for iron pipe, 195 " " horse-power required to drive machinery, 5 " " " " " " " small lathes, 155 " " " " " " remove metal, 161, 162 " " test of hydraulic motor, 170 " " widths and velocities of belting, 15 " showing effect of increased load on water-wheels, 171 Tatham's transmission-dynamometers, 82, 87 Tension in belts, 12, 18, 81 Test of small water-wheel, 167, 170 Tests on engines, 27, 38 2H INDEX. Towne, H. R., experiments on belting, 14 Transmission-dynamometers, 72 Balance, 77 Belt, 94, 96 Briggs, 80 Brackett, 98 Cradle, 98 Differential, 76 Emerson, 113 " " Flather, 139, 142 Floating, 103 " Hartig, in Hopkinson, 79 Hydraulic, 137 Morin, 72 " " Tatham, 82, 87 Van Winkle, 137 Webb, 103 Webber, 77 Turbine brake, 63, 70 Van Winkle power-meter, 117 Velocity-head, 198 Velocity of belt, power measured by, 10 " " belting, 15 " " current at a varying depth, 183 Vertical friction-brake, 46 W Water-brake, 60, 63, 70 " cooled brakes, 23, 33, 50 " gauge, 173 " meters, 184 " power, measurement of, 165 " wheels, efficiency of, 166 " measurement of, 165 " " test of, 167, 170 INDEX, 21 S Webb floating dynamometer, 103 Webber balance-dynamometer, 77 Webber, S., friction of shafting, 8 " " large friction-brake, 47 Weirs, measurement of water over, 186 Westinghouse, engine-tests, 27 friction-brakes, 26 Width of rubbing surface, 50 Widths of belt in actual use, 15 Woltmann's Mill, 174 Work absorbed by friction, 26 " done on brake, 25, 29 UNIVERSITY OF CALIFORNIA, LOS ANGELES THE UNIVERSITY LIBRARY This book is DUE on the last date stamped below OCT 2 9 1954 REtTD COL LIB. College Jjbwy JUN? JUNUii 23m-10,'4(2ll UC SOUTHERN REGIONAL LIBRARY FACILITY ! Ill II II Illl I AA 000700691 TJ 1053 F61d 1893 3 1158 00734 0887