Chapter V: Part 5

The most usual type of heteropolar alternator has an internal rotating field-magnet system, and an external stationary armature, as in fig. 10. The coils of the armature, which must for high voltages be heavily insulated, are then not subjected to the additional stresses due to centrifugal force; and further, the collecting rings which must be attached to the rotating portion need only transmit the exciting current at a low voltage.

The homopolar machine possesses the advantages that only a single exciting coil is required, whatever the number of polar projections, and that both the armature and field-magnet coils may be stationary. From fig. 8 it will be seen that it is not essential that the exciting coil should revolve with the internal magnet, but it may be supported from the external stationary armature while still embracing the central part of the rotor. The E.M.F. is set up in the armature coils through the periodic variation of the flux through them as the iron projections sweep past, and these latter may be likened to a number of "keepers," which complete the magnetic circuit. From the action of the rotating iron masses they may also be considered as the inducing elements or "inductors," and the homopolar machine is thence also known as the "inductor alternator." If the end of the rotor marked S in fig. 8 is split up into a number of S polar projections similar to the N poles, a second set of armature coils may be arranged opposite to them, and we obtain an inductor alternator with double armature. Or the polar projections at the two ends may be staggered, and a single armature winding be passed straight through the armature, as in fig. 36, which shows at the side the appearance of the revolving inductor with its crown of polar projections in one ring opposite to the gaps between the polar projections of the other ring. But in spite of its advantage of the single stationary exciting coil, the inductor alternator has such a high degree of leakage, and the effect of armature reaction is so detrimental in it, that the type has been gradually abandoned, and a return has been almost universally made to the heteropolar alternator with internal poles radiating outwards from a circular yoke-ring. The construction of a typical machine of this class is illustrated in fig. 37.

Since the field-magnet coils rotate, they must be carefully designed to withstand centrifugal force, and are best composed of flat copper strip wound on edge with thin insulation between adjacent layers. The coil is secured by the edges of the pole-shoes which overhang the pole and tightly compress the coil against the yoke-ring; the only effect from centrifugal force is then to compress still further the flat turns of copper against the pole-shoes without deformation. The poles are either of cast steel of circular or oblong section, bolted to the rim of the yoke-ring, or are built up of thin laminations of sheet steel. When the peripheral speed is very high, the yoke-ring will be of cast steel or may itself be built up of sheet steel laminations, this material being reliable and easily tested to ensure its sound mechanical strength. If the armature slots are open, the pole-pieces will in any case be laminated to reduce the eddy currents set up by the variation of the flux-density.

Owing to the great number of poles[20] of the alternator when driven by a reciprocating steam-engine, the diameter of its rotor is usually larger and its length less than in the continuous-current dynamo of corresponding output. The support of the armature core when of large diameter is therefore a more difficult problem, since, apart from any magnetic strains to which it may be subjected, its own weight tends to deform it. The segmental core-disks are usually secured to the internal circumference of a circular cast iron frame; the latter has a box section of considerable radial depth to give stiffness to it, and the disks are tightly clamped between internal flanges, one being a fixed part of the frame and the other loose, with transverse bolts passing right through from side to side (fig. 37). In order to lessen the weight of the structure and its expense in material, the cast iron frame has in some cases been entirely dispensed with, and braced tie-rods have been used to render the effective iron of the armature core-disks self-supporting.

Owing to the high speed of the turbo-alternator, its rotor calls for the utmost care in its design to withstand the effect of centrifugal force without any shifting of the exciting coils, and to secure a perfect balance.

The appearance of the armature of a typical three-phase alternator is illustrated in fig. 38, which shows a portion of the lower half after removal of the field-magnet.

With open slots the coils, after being wound on formers to the required shape, are thoroughly impregnated with insulating compound, dried, and after a further wrapping with several layers of insulating material, finally pressed into the slots together with a sheet of leatheroid or flexible micanite. The end-connexions of each group of coils of one phase project straight out from the slots or are bent upwards alternately with those of the other phases, so that they may clear one another (fig. 37). A wooden wedge driven into a groove at the top of each slot is often used to lock the coil in place. With slots nearly closed at the top, the coils are formed by hand by threading the wire through tubes of micanite or specially prepared paper lining the slots; or with single-turn loops, stout bars of copper of [U]-shape can be driven through the slots and closed by soldered connexions at the other end.

Shape of E.M.F. curve.

The first experimental determination of the shape of the E.M.F. curve
of an alternator was made by J. Joubert in 1880. A revolving
contact-maker charged a condenser with the E.M.F. produced by the
armature at a particular instant during each period. The condenser was
discharged through a ballistic galvanometer, and from the measured
throw the instantaneous E.M.F. could be deduced. The contact-maker was
then shifted through a small angle, and the instantaneous E.M.F. at
the new position corresponding to a different moment in the period was
measured; this process was repeated until the E.M.F. curve for a
complete period could be traced. Various modifications of the same
principle have since been used, and a form of "oscillograph" (q.v.)
has been perfected which is well adapted for the purpose of tracing
the curves both of E.M.F. and of current. The machine on which Joubert
carried out his experiments was a Siemens disk alternator having no
iron in its armature, and it was found that the curve of E.M.F. was
practically identical with a sine curve. The same law has also been
found to hold true for a smooth-core ring or drum armature, but the
presence of the iron core enables the armature current to produce
greater distorting effect, so that the curves under load may vary
considerably from their shape at no load. In toothed armatures, the
broken surface of the core, and the still greater reaction from the
armature current, may produce wide variations from the sine law, the
general tendency being to give the E.M.F. curve a more peaked form.
The great convenience of the assumption that the E.M.F. obeys the sine
law has led to its being very commonly used as the basis for the
mathematical analysis of alternator problems; but any deductions made
from this premiss require to be applied with caution if they are
likely to be modified by a different shape of the curve. Further, the
same alternator will give widely different curves even of E.M.F., and
still more so of current, according to the nature of the external
circuit to which it is connected. As will be explained later, the
phase of the current relatively to the E.M.F. depends not only on the
inductance of the alternator itself, but also upon the inductance and
capacity of the external circuit, so that the same current will
produce different effects according to the amount by which it lags or
leads. The question as to the relative advantages of differently
shaped E.M.F. curves has led to much discussion, but can only be
answered by reference to the nature of the work that the alternator
has to do--i.e. whether it be arc lighting, motor driving, or
incandescent lighting through transformers. The shape of the E.M.F.
curve is, however, of great importance in one respect, since upon it
depends the ratio of the maximum instantaneous E.M.F. to the effective
value, and the insulation of the entire circuit, both external and
internal, must be capable of withstanding the maximum E.M.F. While the
maximum value of the sine curve is [root]2 or 1.414 times the
effective value, the maximum value of a [Lambda] curve is 1.732 times
the effective value, so that for the same effective E.M.F. the
armature wires must not only be more heavily insulated than in the
continuous-current dynamo, but also the more peaked the curve the
better must be the insulation.

Excitation.

Since an alternating current cannot be used for exciting the
field-magnet, recourse must be had to some source of a direct current.
This is usually obtained from a small auxiliary continuous-current
dynamo, called an _exciter_, which may be an entirely separate
machine, separately driven and used for exciting several alternators,
or may be driven from the alternator itself; in the latter case the
armature of the exciter is often coupled directly to the rotating
shaft of the alternator, while its field-magnet is attached to the
bed-plate. Although separate excitation is the more usual method, the
alternator can also be made self-exciting if a part or the whole of
the alternating current is "rectified," and thus converted into a
direct current.

Quarter-phase alternators.

The general idea of the polyphase alternator giving two or more
E.M.F.'s of the same frequency, but displaced in phase, has been
already described. The several phases may be entirely independent, and
such was the case with the early polyphase machines of Gramme, who
used four independent circuits, and also in the large two-phase
alternators designed by J.E.H. Gordon in 1883. If the phases are thus
entirely separate, each requires two collector rings and two wires to
its external circuit, i.e. four in all for two-phase and six for
three-phase machines. The only advantage of the polyphase machine as
thus used is that the whole of the surface of the armature core may be
efficiently covered with winding, and the output of the alternator for
a given size be thereby increased. It is, however, also possible so to
interlink the several circuits of the armature that the necessary
number of transmitting lines to the external circuits may be reduced,
and also the weight of copper in them for a given loss in the
transmission.[21] The condition which obviously must be fulfilled,
for such interlinking of the phases to be possible, is that in the
lines which are to meet at any common junction the algebraic sum of
the instantaneous currents, reckoned as positive if away from such
junction and as negative if towards it, must be zero. Thus if the
phases be diagrammatically represented by the relative angular
position of the coils in fig. 39, the current in the coils A and B
differs in phase from the current in the coils C and D by a quarter of
a period or 90 deg.; hence if the two wires b and d be replaced by the
single wire bd, this third wire will serve as a common path for the
currents of the two phases either outwards or on their return. At any
instant the value of the current in the third wire must be the vector
sum of the two currents in the other wires, and if the shape of the
curves of instantaneous E.M.F. and current are identical, and are
assumed to be sinusoidal, the effective value of the current in the
third wire will be the vector sum of the effective values of the
currents in the other wires; in other words, if the system is
balanced, the effective current in the third wire is [root]2, or 1.414
times the current in either of the two outer wires. Since the currents
of the two phases do not reach their maximum values at the same time,
the sectional area of the third wire need not be twice that of the
others; in order to secure maximum efficiency by employing the same
current density in all three wires, it need only be 40% greater than
that of either of the outer wires. The effective voltage between the
external leads may in the same way be calculated by a vector diagram,
and with the above _star connexion_ the voltage between the outer pair
of wires a and c is [root]2, or 1.414 times the voltage between either
of the outer wires and the common wire bd. Next, if the four coils are
joined up into a continuous helix, just as in the winding of a
continuous-current machine, four wires may be attached to equidistant
points at the opposite ends of two diameters at right angles to each
other (fig. 40). Such a method is known as the _mesh connexion_, and
gives a perfectly symmetrical four-phase system of distribution. Four
collecting rings are necessary if the armature rotates, and there is
no saving in copper in the transmitting lines; but the importance of
the arrangement lies in its use in connexion with rotary converters,
in which it is necessary that the winding of the armature should form
a closed circuit. If e = the effective voltage of one phase A, the
voltage between any pair of adjacent lines in the diagram is e, and
between m and o or n and p is e [root]2. The current in any line is
the resultant of the currents in the two phases connected to it, and
its effective value is c [root]2, where c is the current of one phase.

Three-phase alternators.

When we pass to machines giving three phases differing by 120 deg., the
same methods of star and mesh connexion find their analogies. If the
current in coil A (fig. 41) is flowing away from the centre, and has
its maximum value, the currents in coils B and C are flowing towards
the centre, and are each of half the magnitude of the current in A;
the algebraic sum of the currents is therefore zero, and this will
also be the case for all other instants. Hence the three coils can be
united together at the centre, and three external wires are alone
required. In this star or "Y" connexion, if e be the effective voltage
of each phase, or the voltage between any one of the three collecting
rings and the common connexion, the volts between any pair of
transmitting lines will be E = e [root]3 (fig. 41); if the load be
balanced, the effective current C in each of the three lines will be
equal, and the total output in watts will be W = 3Ce = 3CE/[root]3 =
1.732 EC, or 1.732 times the product of the effective voltage between
the lines and the current in any single line. Next, if the three coils
are closed upon themselves in a mesh or _delta_ fashion (fig. 42), the
three transmitting wires may be connected to the junctions of the
coils (by means of collecting rings if the armature rotates). The
voltage E between any pair of wires is evidently that generated by
one phase, and the current in a line wire is the resultant of that in
two adjacent phases; or in a balanced system, if c be the current in
each phase, the current in the line wire beyond a collecting ring is C
= c [root]3, hence the watts are W = 3cE = 3CE/[root]3 = 1.732 EC, as
before. Thus any three-phase winding may be changed over from the star
to the delta connexion, and will then give 1.732 times as much
current, but only 1/1.732 times the voltage, so that the output
remains the same.

Armature reaction in alternators

The "armature reaction" of the alternator, when the term is used in
its widest sense to cover all the effects of the alternating current
in the armature as linked with a magnetic circuit or circuits, may be
divided into three items which are different in their origin and
consequences. In the first place the armature current produces a
self-induced flux in local circuits independent of the main magnetic
circuit, as e.g. linked with the ends of the coils as they project
outwards from the armature core; such lines may be called "secondary
leakage," of which the characteristic feature is that its amount is
independent of the position of the coils relatively to the poles. The
alternations of this flux give rise to an inductive voltage lagging
90 deg. behind the phase of the current, and this leakage or reactance
voltage must be directly counterbalanced electrically by an equal
component in the opposite sense in the voltage from the main field.
The second and third elements are more immediately magnetic and are
entirely dependent upon the position of the coils in relation to the
poles and in relation to the phase of the current which they then
carry. When the side of a drum coil is immediately under the centre of
a pole, its ampere-turns are cross-magnetizing, i.e. produce a
distortion of the main flux, displacing its maximum density to one or
other edge of the pole. When the coil-side is midway between the poles
and the axes of coil and pole coincide, the coil stands exactly
opposite to the pole and embraces the same magnetic circuit as the
field-magnet coils; its turns are therefore directly magnetizing,
either weakening or strengthening the main flux according to the
direction of the current. In intermediate positions the ampere-turns
of the coil gradually pass from cross to direct and vice versa. When
the instantaneous values of either the cross or direct magnetizing
effect are integrated over a period and averaged, due account being
taken of the number of slots per coil-side and of the different phases
of the currents in the polyphase machine, expressions are obtained for
the equivalent cross and direct ampere-turns of the armature as acting
upon a pair of poles. For a given winding and current, the determining
factor in either the one or the other is found to be the relative
phase angle between the axis of a coil in its position when carrying
the maximum current and the centre of a pole, the transverse reaction
being proportional to the cosine of this angle, and the direct
reaction to its sine. If the external circuit is inductive, the
maximum value of the current lags behind the E.M.F. and so behind the
centre of the pole; such a negative angle of lag causes the direct
magnetizing turns to become back turns, directly weakening the main
field and lowering the terminal voltage. Thus, just as in the
continuous-current dynamo, for a given voltage under load the
excitation between the pole-pieces X_p must not only supply the net
excitation required over the air-gaps, armature core and teeth, but
must also balance the back ampere-turns X_b of the armature.

Evidently therefore the characteristic curve connecting armature
current and terminal volts will with a constant exciting current
depend on the nature of the load, whether inductive or non-inductive,
and upon the amount of inductance already possessed by the armature
itself. With an inductive load it will fall more rapidly from its
initial maximum value, or, conversely, if the initial voltage is to be
maintained under an increasing load, the exciting current will have to
be increased more than if the load were non-inductive. In practical
working many disadvantages result from a rapid drop of the terminal
E.M.F. under increasing load, so that between no load and full load
the variation in terminal voltage with constant excitation should not
exceed 15%. Thus the output of an alternator is limited either by its
heating or by its armature reaction, just as is the output of a
continuous-current dynamo; in the case of the alternator, however, the
limit set by armature reaction is not due to any sparking at the
brushes, but to the drop in terminal voltage as the current is
increased, and the consequent difficulty in maintaining a constant
potential on the external circuit.

The coupling of alternators.

The joint operation of several alternators so that their outputs may
be delivered into the same external circuit is sharply distinguished
from the corresponding problem in continuous-current dynamos by the
necessary condition that they must be in synchronism, i.e. not only
must they be so driven that their frequency is the same, but their
E.M.F.'s must be in phase or, as it is also expressed, the machines
must be in step. Although in practice it is impossible to run two
alternators in series unless they are rigidly coupled together--which
virtually reduces them to one machine--two or more machines can be run
in parallel, as was first described by H. Wilde in 1868 and
subsequently redemonstrated by J. Hopkinson and W.G. Adams in 1884.
Their E.M.F.'s should be as nearly as possible in synchronism, but,
as contrasted with series connexion, parallel coupling gives them a
certain power of recovery if they fall out of step, or are not in
exact synchronism when thrown into parallel. In such circumstances a
synchronizing current passes between the two machines, due to the
difference in their instantaneous pressures; and as this current
agrees in phase more nearly with the leading than with the lagging
machine, the former machine does work as a generator on the latter as
a motor. Hence the lagging machine is accelerated and the leading
machine is retarded, until their frequencies and phase are again the
same.

Uses of alternators.

The chief use of the alternator has already been alluded to. Since it can be employed to produce very high pressures either directly or through the medium of transformers, it is specially adapted to the electrical transmission of energy over long distances.[22] In the early days of electric lighting, the alternate-current system was adopted for a great number of central stations; the machines, designed to give a pressure of 2000 volts, supplied transformers which were situated at considerable distances and spread over large areas, without an undue amount of copper in the transmitting lines. While there was later a tendency to return to the continuous current for central stations, owing to the introduction of better means for economizing the weight of copper in the mains, the alternating current again came into favour, as rendering it possible to place the central station in some convenient site far away from the district which it was to serve. The pioneer central station in this direction was the Deptford station of the London Electric Supply Corporation, which furnished current to the heart of London from a distance of 7 m. In this case, however, the alternators were single-phase and gave the high pressure of 10,000 volts immediately, while more recently the tendency has been to employ step-up transformers and a polyphase system. The advantage of the latter is that the current, after reaching the distant sub-stations, can be dealt with by rotary converters, through which it is transformed into a continuous current. The alternator is also used for welding, smelting in electric furnaces, and other metallurgical processes where heating effects are alone required; the large currents needed therein can be produced without the disadvantage of the commutator, and, if necessary, transformers can be interposed to lower the voltage and still further increase the current. The alternating system can thus meet very various needs, and its great recommendation may be said to lie in the flexibility with which it can supply electrical energy through transformers at any potential, or through rotary converters in continuous-current form.

AUTHORITIES.--For the further study of the dynamo, the following may
be consulted, in addition to the references already given:--

_General_: S.P. Thompson, _Dynamo-Electric
Machinery--Continuous-Current Machines_ (1904), _Alternating-Current
Machinery_ (1905, London); G. Kapp, _Dynamos, Alternators and
Transformers_ (London, 1893); _Id., Electric Transmission of Energy_
(London, 1894); Id., _Dynamo Construction; Electrical and Mechanical_
(London, 1899); H.F. Parshall and H.M. Hobart, _Electric Generators_
(London, 1900); C.C. Hawkins and F. Wallis, _The Dynamo_ (London,
1903); E. Arnold, _Konstruktionstafeln fuer den Dynamobau_ (Stuttgart,
1902); C.P. Steinmetz, _Elements of Electrical Engineering_ (New York,
1901).

_Continuous-Current Dynamos_: J. Fischer-Hinnen, _Continuous-Current
Dynamos_ (London, 1899); E. Arnold, _Die Gleichstrommaschine_ (Berlin,
1902); F. Niethammer, _Berechnung und Konstruktion der
Gleichstrommaschinen und Gleichstrommotoren_ (Stuttgart, 1904).

_Alternators_: D.C. Jackson and J.P. Jackson, _Alternating Currents
and Alternating Current Machinery_ (New York, 1903); J.A. Fleming,
_The Alternate Current Transformer_ (London, 1899); C.P. Steinmetz,
_Alternating Current Phenomena_ (New York, 1900); E. Arnold, _Die
Wechselstromtechnik_ (Berlin, 1904); S.P. Thompson, _Polyphase
Electric Currents_ (London, 1900); A. Stewart, _Modern Polyphase
Machinery_ (London, 1906); M. Oudin, _Standard Polyphase Apparatus and
Systems_ (New York, 1904). (C. C. H.)

FOOTNOTES:

[1] _Experimental Researches in Electricity_, series ii. Sec. 6, pars.
256, 259-260, and series xxviii. Sec. 34.

[2] _Ibid._ series i. Sec. 4, pars. 84-90.

[3] "On the Physical Lines of Magnetic Force," _Phil. Mag._, June
1852.

[4] Faraday, _Exp. Res._ series xxviii. Sec. 34, pars. 3104, 3114-3115.

[5] _Id._, ib. series i. Sec. 4, pars. 114-119.

[6] _Id._, ib. series ii. Sec. 6, pars. 211, 213; series xxviii. Sec. 34,
par. 3152.

[7] Invented by Nikola Tesla (_Elec. Eng._ vol. xiii. p. 83. Cf.
Brit. Pat. Spec. Nos. 2801 and 2812, 1894). Several early inventors,
e.g. Salvatore dal Negro in 1832 (_Phil. Mag._ third series, vol. i.
p. 45), adopted reciprocating or oscillatory motion, and this was
again tried by Edison in 1878.

[8] The advantage to be obtained by making the poles closely embrace
the armature core was first realized by Dr Werner von Siemens in his
"shuttle-wound" armature (Brit. Pat. No. 2107, 1856).

[9] _Nuovo Cimento_ (1865), 19, 378.

[10] Brit. Pat. No. 1668 (1870); _Comptes rendus_ (1871), 73, 175.

[11] _Ann. Chim. Phys._ l. 322.

[12] Ibid. li. 76. Since in H. Pixii's machine the armature was
stationary, while both magnet and commutator rotated, four brushes
were used, and the arrangement was not so simple as the split-ring
described above, although the result was the same. J. Saxton's
machine (1833) and E.M. Clarke's machine (1835, see Sturgeon's
_Annals of Electricity_, i. 145) were similar to one another in that
a unidirected current was obtained by utilizing every alternate
half-wave of E.M.F., but the former still employed mercury collecting
cups, while the latter employed metal brushes. W. Sturgeon in 1835
followed Pixii in utilizing the entire wave of E.M.F., and abandoned
the mercury cups in favour of metal brushes pressing on four
semicircular disks (_Scientific Researches_, p. 252). The simple
split-ring is described by Sir C. Wheatstone and Sir W.F. Cooke in
their Patent No. 8345 (1840).

[13] By the "leading" side of the tooth or of an armature coil or
sector is to be understood that side which first enters under a pole
after passing through the interpolar gap, and the edge of the pole
under which it enters is here termed the "leading" edge as opposed to
the "trailing" edge or corner from under which a tooth or coil
emerges into the gap between the poles; cf. fig. 30, where the
leading and trailing pole-corners are marked ll and tt.

[14] Such was the arrangement of Wheatstone's machine (Brit. Pat. No.
9022) of 1841, which was the first to give a more nearly "continuous"
current, the number of sections and split-rings being five.

[15] Its development from the split-ring was due to Pacinotti and
Gramme (Brit. Pat. No. 1668, 1870) in connexion with their ring
armatures.

[16] And extended by G. Kapp, "On Modern Continuous-Current
Dynamo-Electric Machines," _Proc. Inst. C.E._ vol. lxxxiii. p. 136.

[17] Drs J. and E. Hopkinson, "Dynamo-Electric Machinery," Phil.
Trans., May 6, 1886; this was further expanded in a second paper on
"Dynamo-Electric Machinery," _Proc. Roy. Soc._, Feb. 15, 1892, and
both are reprinted in _Original Papers on Dynamo-Machinery and Allied
Subjects_.

[18] _Exp. Res._, series i. Sec. 4, par. 111. In 1845 Wheatstone and
Cooke patented the use of "voltaic" magnets in place of permanent
magnets (No. 10,655).

[19] Between Moutiers and Lyons, a distance of 115 m., energy is
transmitted on the Thury direct-current system at a maximum pressure
of 60,000 volts. Four groups of machines in series are employed, each
group consisting of four machines in series; the rated output of each
component machine is 75 amperes at 3900 volts or 400 h.p. A water
turbine drives two pairs of such machines through an insulating
coupling, and the sub-base of each pair of machines is separately
insulated from earth, the foundation being also of special insulating
materials.

[20] For experiments on high-frequency currents, Nikola Tesla
constructed an alternator having 384 poles and giving a frequency of
about 10,000 (_Journ. Inst. Elec. Eng._ 1892, 21, p. 82). The
opposite extreme is found in alternators directly coupled to the
Parsons steam-turbine, in which, with a speed of 3000 revs. per min.,
only two poles are required to give a frequency of 50. By a
combination of a Parsons steam-turbine running at 12,000 revs. per
min. with an alternator of 140 poles a frequency of 14,000 has been
obtained (_Engineering_, 25th of August 1899). For description of an
experimental machine for 10,000 cycles per second when running at
3000 revs. per min., see _Trans. Amer. Inst. Elect. Eng._ vol. xxiii.
p. 417.

[21] As in the historical transmission of energy from Lauffen to
Frankfort (1891).

[22] In the pioneer three-phase transmission between Laufen and
Frankfort (_Electrician_, vol. xxvi. p. 637, and xxvii. p. 548), the
three-phase current was transformed up from about 55 to 8500 volts,
the distance being 110 m. A large number of installations driven by
water power are now at work, in which energy is transmitted on the
alternating-current system over distances of about 100 m. at
pressures ranging from 20,000 to 67,000 volts.

DYNAMOMETER (Gr. [Greek: dynamis], strength, and [Greek: metron], a measure), an instrument for measuring force exerted by men, animals and machines. The name has been applied generally to all kinds of instruments used in the measurement of a force, as for example electric dynamometers, but the term specially denotes apparatus used in connexion with the measurement of work, or in the measurement of the horse-power of engines and motors. If P represent the average value of the component of a force in the direction of the displacement, s, of its point of application, the product Ps measures the work done during the displacement. When the force acts on a body free to turn about a fixed axis only, it is convenient to express the work done by the transformed product T[theta], where T is the average turning moment or torque acting to produce the displacement [theta] radians. The apparatus used to measure P or T is the dynamometer. The factors s or [theta] are observed independently. Apparatus is added to some dynamometers by means of which a curve showing the variations of P on a distance base is drawn automatically, the area of the diagram representing the work done; with others, integrating apparatus is combined, from which the work done during a given interval may be read off directly. It is convenient to distinguish between absorption and transmission dynamometers. In the first kind the work done is converted into heat; in the second it is transmitted, after measurement, for use.

_Absorption Dynamometers._--Baron Prony's dynamometer (_Ann. Chim.
Phys._ 1821, vol. 19), which has been modified in various ways,
consists in its original form of two symmetrically shaped timber beams
clamped to the engine-shaft. When these are held from turning, their
frictional resistance may be adjusted by means of nuts on the screwed
bolts which hold them together until the shaft revolves at a given
speed. To promote smoothness of action, the rubbing surfaces are
lubricated. A weight is moved along the arm of one of the beams until
it just keeps the brake steady midway between the stops which must be
provided to hold it when the weight fails to do so. The general theory
of this kind of brake is as follows:-Let F be the whole frictional
resistance, r the common radius of the rubbing surfaces, W the force
which holds the brake from turning and whose line of action is at a
perpendicular distance R from the axis of the shaft, N the revolutions
of the shaft per minute, [omega] its angular velocity in radians per
second; then, assuming that the adjustments are made so that the
engine runs steadily at a uniform speed, and that the brake is held
still, clear of the stops and without oscillation, by W, the torque T
exerted by the engine is equal to the frictional torque Fr acting at
the brake surfaces, and this is measured by the statical moment of the
weight W about the axis of revolution; that is--

T = Fr = WR. (1)

Hence WR measures the torque T.

If more than one force be applied to hold the brake from turning, Fr,
and therefore T, are measured by the algebraical sum of their
individual moments with respect to the axis. If the brake is not
balanced, its moment about the axis must be included. Therefore, quite
generally,

T = [Sigma]WR. (2)

The factor [theta] of the product T[theta] is found by means of a
revolution counter. The power of a motor is measured by the rate at
which it works, and this is expressed by T[omega] = T2[pi]N/60 in
foot-pounds per second, or T2[pi]N/33,000 in horse-power units. The
latter is commonly referred to as the "brake horse-power." The
maintenance of the conditions of steadiness implied in equation (1)
depends upon the constancy of F, and therefore of the coefficient of
friction mu between the rubbing surfaces. The heating at the surfaces,
the variations in their smoothness, and the variations of the
lubrication make [mu] continuously variable, and necessitate frequent
adjustment of W or of the nuts. J.V. Poncelet (1788-1867) invented a
form of Prony brake which automatically adjusted its grip as [mu]
changed, thereby maintaining F constant.

The principle of the compensating brake devised by J.G. Appold
(1800-1865) is shown in fig. 1. A flexible steel band, lined with wood
blocks, is gripped on the motor fly-wheel or pulley by a screw A,
which, together with W, is adjusted to hold the brake steady.
Compensation is effected by the lever L inserted at B. This has a
slotted end, engaged by a pin P fixed to the framing, and it will be
seen that its action is to slacken the band if the load tends to rise
and to tighten it in the contrary case. The external forces holding
the brake from turning are W, distant R from the axis, and the
reaction, W1 say, of the lever against the fixed pin P, distant R1
from the axis. The moment of W1 may be positive or negative. The
torque T at any instant of steady running is therefore {WR +- W1R1}.

Lord Kelvin patented a brake in 1858 (fig. 2) consisting of a rope or
cord wrapped round the circumference of a rotating wheel, to one end
of which is applied a regulated force, the other end being fixed to a
spring balance. The ropes are spaced laterally by the blocks B, B, B,
B, which also serve to prevent them from slipping sideways. When the
wheel is turning in the direction indicated, the forces holding the
band still are W, and p, the observed pull on the spring balance. Both
these forces usually act at the same radius R, the distance from the
axis to the centre line of the rope, in which case the torque T is (W
- p)R, and consequently the brake horse-power is

(W - p)R x 2[pi]N
-----------------.
33,000

When mu changes the weight W rises or falls against the action of the
spring balance until a stable condition of running is obtained. The
ratio {W/p} is given by e^{ mu[theta]}, where e = 2.718; mu is the
coefficient of friction and [theta] the angle, measured in radians,
subtended by the arc of contact between the rope and the wheel. In
fig. 2 [theta] = 2[pi]. The ratio W/p increases very rapidly as
[theta] is increased, and therefore, by making [theta] sufficiently
large, p may conveniently be made a small fraction of W, thereby
rendering errors of observation of the spring balance negligible. Thus
this kind of brake, though cheap to make, is, when [theta] is large
enough, an exceedingly accurate measuring instrument, readily applied
and easily controlled. It has come into very general use in recent
years, and has practically superseded the older forms of block brakes.

It is sometimes necessary to use water to keep the brake wheel cool.
Engines specially designed for testing are usually provided with a
brake wheel having a trough-shaped rim. Water trickles continuously
into the trough, and the centrifugal action holds it as an inside
lining against the rim, where it slowly evaporates.

Fig. 3 shows a band-brake invented by Professor James Thomson,
suitable for testing motors exerting a constant torque (see
_Engineering_, 22nd October 1880). To maintain e^{ mu[theta]} constant,
compensation for variation of [mu] is made by inversely varying
[theta]. A and B are fast and loose pulleys, and the brake band is
placed partly over the one and partly over the other. Weights W and w
are adjusted to the torque. The band turns with the fast pulley if
[mu] increase, thereby slightly turning the loose pulley, otherwise at
rest, until [theta] is adjusted to the new value of [mu]. This form of
brake was also invented independently by J.A.M.L. Carpentier, and the
principle has been used in the Raffard brake. A self-compensating
brake of another kind, by Marcel Deprez, was described with
Carpentier's in 1880 (_Bulletin de la societe d'encouragement_,
Paris). W.E. Ayrton and J. Perry used a band or rope brake in which
compensation is effected by the pulley drawing in or letting out a
part of the band or rope which has been roughened or in which a knot
has been tied.

In an effective water-brake invented by W. Froude (see _Proc. Inst. M.
E._ 1877), two similar castings, A and B, each consisting of a boss
and circumferential annular channel, are placed face to face on a
shaft, to which B is keyed, A being free (fig. 4). A ring tube of
elliptical section is thus formed. Each channel is divided into a
series of pockets by equally spaced vanes inclined at 45 deg.. When A is
held still, and B rotated, centrifugal action sets up vortex currents
in the water in the pockets; thus a continuous circulation is caused
between B and A, and the consequent changes of momentum give rise to
oblique reactions. The moments of the components of these actions and
reactions in a plane to which the axis of rotation is at right angles
are the two aspects of the torque acting, and therefore the torque
acting on B through the shaft is measured by the torque required to
hold A still. Froude constructed a brake to take up 2000 H.P. at 90
revs. per min. by duplicating this apparatus. This replaced the
propeller of the ship whose engines were to be tested, and the outer
casing was held from turning by a suitable arrangement of levers
carried to weighing apparatus conveniently disposed on the wharf. The
torque corresponding to 2000 H.P. at 90 revs. per min. is 116,772
foot-pounds, and a brake 5 ft. in diameter gave this resistance. Thin
metal sluices were arranged to slide between the wheel and casing, and
by their means the range of action could be varied from 300 H.P. at
120 revs. per min. to the maximum.

Professor Osborne Reynolds in 1887 patented a water-brake (see _Proc.
Inst. C.E._ 99, p. 167), using Froude's turbine to obtain the highly
resisting spiral vortices, and arranging passages in the casing for
the entry of water at the hub of the wheel and its exit at the
circumference. Water enters at E (fig. 5), and finds its way into the
interior of the wheel, A, driving the air in front of it through the
air-passages K, K. Then following into the pocketed chambers V1, V2,
it is caught into the vortex, and finally escapes at the
circumference, flowing away at F. The air-ways k, k, in the fixed
vanes establish communication between the cores of the vortices and
the atmosphere. From {1/5} to 30 H.P. may be measured at 100 revs. per
min. by a brake-wheel of this kind 18 in. in diameter. For other
speeds the power varies as the cube of the speed. The casing is held
from turning by weights hanging on an attached arm. The cocks
regulating the water are connected to the casing, so that any tilting
automatically regulates the flow, and therefore the thickness of the
film in the vortex. In this way the brake may be arranged to maintain
a constant torque, not withstanding variation of the speed. In G.I.
Alden's brake (see _Trans. Amer. Soc. Eng._ vol. xi.) the resistance
is obtained by turning a cast iron disk against the frictional
resistance of two thin copper plates, which are held in a casing free
to turn upon the shaft, and are so arranged that the pressure between
the rubbing surfaces is controlled, and the heat developed by friction
carried away, by the regulated flow of water through the casing. The
torque required to hold the casing still against the action of the
disk measures the torque exerted by the shaft to which the disk is
keyed.

_Transmission Dynamometers._--The essential part of many transmission
dynamometers is a spring whose deformation indirectly measures the
magnitude of the force transmitted through it. For many kinds of
spring the change of form is practically proportional to the force,
but the relation should always be determined experimentally. General
A.J. Morin (see _Notice sur divers appareils dynamometriques_, Paris,
1841), in his classical experiments on traction, arranged his
apparatus so that the change in form of the spring was continuously
recorded on a sheet of paper drawn under a style. For longer
experiments he used a "Compteur" or mechanical integrator, suggested
by J.V. Poncelet, from which the work done during a given displacement
could be read off directly. This device consists of a roller of radius
r, pressed into contact with a disk. The two are carried on a common
frame, so arranged that a change in form of the spring causes a
relative displacement of the disk and roller, the point of contact
moving radially from or towards the centre of the disk. The radial
distance x is at any instant proportional to the force acting through
the spring. The angular displacement, [theta], of the disk is made
proportional to the displacement, s, of the point of application of
the force by suitable driving gear. If d[phi] is the angular
displacement of the roller corresponding to displacements, d[theta] of
the disk, and ds of the point of application of P, a, and C constants,
then

xd[theta] a
d[phi] = --------- = -- P ds = C.P ds,
r r
_
/s2
and therefore [phi] = C | P ds;
_/s1

that is, the angular displacement of the roller measures the work done
during the displacement from s1 to s2. The shaft carrying the roller
is connected to a counter so that [phi] may be observed. The angular
velocity of the shaft is proportional to the rate of working. Morin's
dynamometer is shown in fig. 6. The transmitting spring is made up of
two flat bars linked at their ends. Their centres s1, s2, are held
respectively by the pieces A, B, which together form a sliding pair.
The block A carries the disk D, B carries the roller R and counting
gear. The pulley E is driven from an axle of the carriage. In a
dynamometer used by F.W. Webb to measure the tractive resistance of
trains on the London & North-Western railway, a tractive pull or push
compresses two spiral springs by a definite amount, which is recorded
to scale by a pencil on a sheet of paper, drawn continuously from a
storage drum at the rate of 3 in. per mile, by a roller driven from
one of the carriage axles. Thus the diagram shows the tractive force
at any instant. A second pencil electrically connected to a clock
traces a time line on the diagram with a kick at every thirty seconds.
A third pencil traces an observation line in which a kick can be made
at will by pressing any one of the electrical pushes placed about the
car, and a fourth draws a datum line. The spring of the dynamometer
car used by W. Dean on the Great Western railway is made up of thirty
flat plates, 7 ft. 6 in. long, 5 in. x 5/8 in. at the centre, spaced
by distance pieces nibbed into the plates at the centre and by rollers
at the ends. The draw-bar is connected to the buckle, which is carried
on rollers, the ends of the spring resting on plates fixed to the
under-frame. The gear operating the paper roll is driven from the axle
of an independent wheel which is let down into contact with the rail
when required. This wheel serves also to measure the distance
travelled. A Morin disk and roller integrator is connected with the
apparatus, so that the work done during a journey may be read off.
Five lines are traced on the diagram.

In spring dynamometers designed to measure a transmitted torque, the
mechanical problem of ascertaining the change of form of the spring is
complicated by the fact that the spring and the whole apparatus are
rotating together. In the Ayrton and Perry transmission dynamometer or
spring coupling of this type, the relative angular displacement is
proportional to the radius of the circle described by the end of a
light lever operated by mechanism between the spring-connected parts.
By a device used by W.E. Dalby (_Proc. Inst. C.E._ 1897-1898, p. 132)
the change in form of the spring is shown on a fixed indicator, which
may be placed in any convenient position. Two equal sprocket wheels
Q1, Q2, are fastened, the one to the spring pulley, the other to the
shaft. An endless band is placed over them to form two loops, which
during rotation remain at the same distance apart, unless relative
angular displacement occurs between Q1 and Q2 (fig. 7) due to a change
in form of the spring. The change in the distance d is proportional to
the change in the torque transmitted from the shaft to the pulley. To
measure this, guide pulleys are placed in the loops guided by a
geometric slide, the one pulley carrying a scale, and the other an
index. A recording drum or integrating apparatus may be arranged on
the pulley frames. A quick variation, or a periodic variation of the
magnitude of the force or torque transmitted through the springs,
tends to set up oscillations, and this tendency increases the nearer
the periodic time of the force variation approaches a periodic time of
the spring. Such vibrations may be damped out to a considerable extent
by the use of a dash-pot, or may be practically prevented by using a
relatively stiff spring.

Every part of a machine transmitting force suffers elastic
deformation, and the force may be measured indirectly by measuring the
deformation. The relation between the two should in all cases be found
experimentally. G.A. Hirn (see _Les Pandynamometres_, Paris, 1876)
employed this principle to measure the torque transmitted by a shaft.
Signor Rosio used a telephonic method to effect the same end, and
mechanical, optical and telephonic devices have been utilized by the
Rev. F.J. Jervis-Smith. (See _Phil. Mag._ February 1898.)

H. Frahm,[1] during an important investigation on the torsional
vibration of propeller shafts, measured the relative angular
displacement of two flanges on a propeller shaft, selected as far
apart as possible, by means of an electrical device (_Engineering_,
6th of February 1903). These measurements were utilized in combination
with appropriate elastic coefficients of the material to find the
horse-power transmitted from the engines along the shaft to the
propeller. In this way the effective horse-power and also the
mechanical efficiency of a number of large marine engines, each of
several thousand horse-power, have been determined.

When a belt, in which the maximum and minimum tensions are
respectively P and p lb., drives a pulley, the torque exerted is (P -
p)r lb. ft., r being the radius of the pulley plus half the thickness
of the belt. P and p may be measured directly by leading the belt
round two freely hanging guide pulleys, one in the tight, the other in
the slack part of the belt, and adjusting loads on them until a stable
condition of running is obtained. In W. Froude's belt dynamometer (see
_Proc. Inst. M.E._, 1858) (fig. 8) the guide pulleys G1, G2 are
carried upon an arm free to turn about the axis O. H is a pulley to
guide the approaching and receding parts of the belt to and from the
beam in parallel directions. Neglecting friction, the unbalanced
torque acting on the beam is 4r{P - p} lb. ft. If a force Q acting at
R maintains equilibrium, QR/4 = (P - p)r = T. Q is supplied by a
spring, the extensions of which are recorded on a drum driven
proportionally to the angular displacement of the driving pulley; thus
a work diagram is obtained. In the Farcot form the guide pulleys are
attached to separate weighing levers placed horizontally below the
apparatus. In a belt dynamometer built for the Franklin Institute from
the designs of Tatham, the weighing levers are separate and arranged
horizontally at the top of the apparatus. The weighing beam in the
Hefner-Alteneck dynamometer is placed transversely to the belt (see
_Electrotechnischen Zeitschrift_, 1881, 7). The force Q, usually
measured by a spring, required to maintain the beam in its central
position is proportional to (P - p). If the angle [theta]1 = [theta]2
= 120 deg., Q = (P - p) neglecting friction.

When a shaft is driven by means of gearing the driving torque is
measured by the product of the resultant pressure P acting between the
wheel teeth and the radius of the pitch circle of the wheel fixed to
the shaft. Fig. 9, which has been reproduced from J. White's _A New
Century of Inventions_ (Manchester, 1822), illustrates possibly the
earliest application of this principle to dynamometry. The wheel D,
keyed to the shaft overcoming the resistance to be measured, is driven
from wheel N by two bevel wheels L, L, carried in a loose pulley K.
The two shafts, though in a line, are independent. A torque applied to
the shaft A can be transmitted to D, neglecting friction, without
change only if the central pulley K is held from turning; the torque
required to do this is twice the torque transmitted.

The torque acting on the armature of an electric motor is necessarily
accompanied by an equal and opposite torque acting on the frame. If,
therefore, the motor is mounted on a cradle free to turn about
knife-edges, the reacting torque is the only torque tending to turn
the cradle when it is in a vertical position, and may therefore be
measured by adjusting weights to hold the cradle in a vertical
position. The rate at which the motor is transmitting work is then
T2[pi]n/550 H.P., where n is the revolutions per second of the
armature.

See James Dredge, _Electric Illumination_, vol. ii. (London, 1885);
W.W. Beaumont, "Dynamometers and Friction Brakes," _Proc. Inst. C.E._
vol. xcv. (London, 1889); E. Brauer, "Ueber Bremsdynamometer and
verwandte Kraftmesser," _Zeitschrift des Vereins deutscher Ingenieure_
(Berlin, 1888); J.J. Flather, _Dynamometers and the Measurement of
Power_ (New York, 1893). (W. E. D.)

FOOTNOTE:

[1] H. Frahm, "Neue Untersuchungen ueber die dynamischen Vorgaenge in
den Wellenleitungen von Schiffsmaschinen mit besonderer
Beruecksichtigung der Resonanzschwingungen," _Zeitschrift des Vereins
deutscher Ingenieure_, 31st May 1902.

DYNASTY (Gr. [Greek: dynasteia], sovereignty, the position of a [Greek: dynastes], lord, ruler, from [Greek: dynasthai], to be able, [Greek: dynamis], power), a family or line of rulers, a succession of sovereigns of a country belonging to a single family or tracing their descent to a common ancestor. The term is particularly used in the history of ancient Egypt as a convenient means of arranging the chronology.