Contributions from
The Museum of History and Technology:
Paper 19
Elevator Systems
of the Eiffel Tower, 1889
Robert M. Vogel
ELEVATOR SYSTEMS of the EIFFEL TOWER, 1889
By Robert M. Vogel
This article traces the evolution of the powered passenger elevator from its initial development in the mid-19th century to the installation of the three separate elevator systems in the Eiffel Tower in 1889. The design of the Tower’s elevators involved problems of capacity, length of rise, and safety far greater than any previously encountered in the field; and the equipment that resulted was the first capable of meeting the conditions of vertical transportation found in the just emerging skyscraper.
The Author: Robert M. Vogel is associate curator of mechanical and civil engineering, United States National Museum, Smithsonian Institution.
The 1,000-foot tower that formed the focal point and central feature of the Universal Exposition of 1889 at Paris has become one of the best known of man’s works. It was among the most outstanding technological achievements of an age which was itself remarkable for such achievements.
Second to the interest shown in the tower’s structural aspects was the interest in its mechanical organs. Of these, the most exceptional were the three separate elevator systems by which the upper levels were made accessible to the Exposition visitors. The design of these systems involved problems far greater than had been encountered in previous elevator work anywhere in the world. The basis of these difficulties was the amplification of the two conditions that were the normal determinants in elevator design—passenger capacity and height of rise. In addition, there was the problem, totally new, of fitting elevator shafts to the curvature of the Tower’s legs. The study of the various solutions to these problems presents a concise view of the capabilities of the elevator art just prior to the beginning of the most recent phase of its development, marked by the entry of electricity into the field.
The great confidence of the Tower’s builder in his own engineering ability can be fully appreciated, however, only when notice is taken of one exceptional way in which the project differed from works of earlier periods as well as from contemporary ones. In almost every case, these other works had evolved, in a natural and progressive way, from a fundamental concept firmly based upon precedent. This was true of such notable structures of the time as the Brooklyn Bridge and, to a lesser extent, the Forth Bridge. For the design of his tower, there was virtually no experience in structural history from which Eiffel could draw other than a series of high piers that his own firm had designed earlier for railway bridges. It was these designs that led Eiffel to consider the practicality of iron structures of extreme height.
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Figure 1.—The Eiffel Tower at the time of the
Universal Exposition of 1889 at Paris.
(From La Nature, June 29, 1889, vol. 17, p. 73.)
Figure 2.—Gustave Eiffel (1832-1923).
(From Gustave Eiffel, La Tour de Trois Cents Mètres,
Paris, 1900, frontispiece.)
There was, it is true, some inspiration to be found in the paper projects of several earlier designers—themselves inspired by that compulsion which throughout history seems to have driven men to attempt the erection of magnificently high structures.
One such inspiration was a proposal made in 1832 by the celebrated but eccentric Welsh engineer Richard Trevithick to erect a 1,000-foot, conical, cast-iron tower (fig. 3) to celebrate the passing of the Reform Bill. Of particular interest in light of the present discussion was Trevithick’s plan to raise visitors to the summit on a piston, driven upward within the structure’s hollow central tube by compressed air. It probably is fortunate for Trevithick’s reputation that his plan died shortly after this and the project was forgotten.
One project of genuine promise was a tower proposed by the eminent American engineering firm of Clarke, Reeves & Company to be erected at the Centennial Exhibition at Philadelphia in 1876. At the time, this firm was perhaps the leading designer and erector of iron structures in the United States, having executed such works as the Girard Avenue Bridge over the Schuylkill at Fairmount Park, and most of New York’s early elevated railway system. The company’s proposal (fig. 4) for a 1,000-foot shaft of wrought-iron columns braced by a continuous web of diagonals was based upon sound theoretical knowledge and practical experience. Nevertheless, the natural hesitation that the fair’s sponsors apparently felt in the face of so heroic a scheme could not be overcome, and this project also remained a vision.
Preparatory Work for the Tower
In the year 1885, the Eiffel firm, which also had an extensive background of experience in structural engineering, undertook a series of
Preliminary studies for a 300-meter tower were made with the 1889 fair immediately in mind. With an assurance born of positive knowledge, Eiffel in June of 1886 approached the Exposition commissioners with the project. There can be no doubt that only the singular respect with which Eiffel was regarded not only by his profession but by the entire nation motivated the Commission to approve a plan which, in the hands of a figure of less stature, would have been considered grossly impractical.
Between this time and commencement of the Tower’s construction at the end of January 1887, there arose one of the most persistently annoying of the numerous difficulties, both structural and social, which confronted Eiffel as the project advanced. In the wake of the initial enthusiasm—on the part of the fair’s Commission inspired by the desire to create a monument to French technological achievement, and on the part of the majority of Frenchmen by the stirring of their imagination at the magnitude of the structure—there grew a rising movement of disfavor. The nucleus was, not surprisingly, formed mainly of the intelligentsia, but objections were made by prominent Frenchmen in all walks of life. The most interesting point to be noted in a retrospection of this often violent opposition was that, although the Tower’s every aspect was attacked, there was remarkably little criticism of its structural feasibility, either by the engineering profession or, as seems traditionally to be the case with bold and unprecedented undertakings, by large numbers of the technically uninformed laity. True, there was an undercurrent of what might be characterized as unease by many property owners in the structure’s shadow, but the most obstinate element of resistance was that which deplored the Tower as a mechanistic intrusion upon the architectural and natural beauties of Paris. This resistance voiced its fury in a flood of special newspaper editions, petitions, and manifestos signed by such lights of the fine and literary arts as De Maupassant, Gounod, Dumas fils, and others. The eloquence of one article, which appeared in several Paris papers in February 1887, was typical:
We protest in the name of French taste and the national art culture against the erection of a staggering Tower, like a gigantic kitchen chimney dominating Paris, eclipsing by its barbarous mass Notre Dame, the Sainte-Chapelle, the tower of St. Jacques, the Dôme des Invalides, the Arc de Triomphe, humiliating these monuments by an act of madness.[1]
Further, a prediction was made that the entire city would become dishonored by the odious shadow of the odious column of bolted sheet iron.
It is impossible to determine what influence these outcries might have had on the project had they been organized sooner. But inasmuch as the Commission had, in November 1886, provided 1,500,000 francs for its commencement, the work had been fairly launched by the time the protestations became loud enough to threaten and they were ineffectual.
Upon completion, many of the most vigorous protestants became as vigorous in their praise of the Tower, but a hard core of critics continued for several years to circulate petitions advocating its demolition by the government. One of these critics, it was said—probably apocryphally—took an office on the first platform, that being the only place in Paris from which the Tower could not be seen.
Figure 3.—Trevithick’s proposed cast-iron tower (1832)
would have been 1,000 feet high, 100 feet in diameter at the base,
12 feet at the top, and surmounted by a colossal statue.
(From F. Dye, Popular Engineering, London, 1895, p. 205.)
The Tower’s Structural Rationale
During the previously mentioned studies of high piers undertaken by the Eiffel firm, it was established that as the base width of these piers increased in proportion to their height, the diagonal bracing connecting the vertical members, necessary for rigidity, became so long as to be subject to high flexural stresses from wind and columnar loading. To resist these stresses, the bracing required extremely large sections which greatly increased the surface of the structure exposed to the wind, and was, moreover, decidedly uneconomical. To overcome this difficulty, the principle which became the basic design concept of the Tower was developed.
The material which would otherwise have been used for the continuous lattice of diagonal bracing was concentrated in the four corner columns of the Tower, and these verticals were connected only at two widely separated points by the deep bands of trussing which formed the first and second platforms. A slight curvature inward was given to the main piers to further widen the base and increase the stability of the structure. At a point slightly above the second platform, the four members converged to the extent that conventional bracing became more economical, and they were joined.
Figure 4.—The proposed 1,000-foot iron tower designed by
Clarke, Reeves & Co. for the Centennial Exhibition of 1876 at Philadelphia.
(From Scientific American, Jan. 24, 1874, vol. 30, p. 47.)
That this theory was successful not only practically, but visually, is evident from the resulting work. The curve of the legs and the openings beneath the two lower platforms are primarily responsible for the Tower’s graceful beauty as well as for its structural soundness.
The design of the Tower was not actually the work of Eiffel himself but of two of his chief engineers, Emile Nouguier (1840-?) and Maurice Kœchlin (1856-1946)—the men who had conducted the high pier studies—and the architect Stéphen Sauvestre (1847-?).
In the planning of the foundations, extreme care was used to ensure adequate footing, but in spite of the Tower’s light weight in proportion to its bulk, and the low earth pressure it exerted, uneven pier settlement with resultant leaning of the Tower was considered a dangerous possibility.[2] To compensate for this eventuality, a device was used whose ingenious directness justifies a brief description. In the base of each of the 16 columns forming the four main legs was incorporated an opening into which an 800-ton hydraulic press could be placed, capable of raising the member slightly. A thin steel shim could then be inserted to make the necessary
In order to appreciate fully the problem which confronted the Tower’s designers and sponsors when they turned to the problem of making its observation areas accessible to the fair’s visitors, it is first necessary to investigate briefly the contemporary state of elevator art.
Elevator Development before the Tower
While power-driven hoists and elevators in many forms had been used since the early years of the 19th century, the ever-present possibility of breakage of the hoisting rope restricted their use almost entirely to the handling of goods in mills and warehouses.[3] Not until the invention of a device which would positively prevent this was there much basis for work on other elements of the system. The first workable mechanism to prevent the car from dropping to the bottom of the hoistway in event of rope failure was the product of Elisha G. Otis (1811-1861), a mechanic of Yonkers, New York. The invention was made more or less as a matter of course along with the other machinery for a new mattress factory of which Otis was master mechanic.
Figure 5.—Correcting erection discrepancies by raising pier member—with hydraulic press and hand pump—and inserting shims.
(From La Nature, Feb. 18, 1888, vol. 16, p. 184.)
Figure 6.—The promenade beneath the Eiffel Tower, 1889. (From La Nature, Nov. 30, 1889, vol. 17, p. 425.)
Figure 7.—Teagle elevator in an English mill about 1845. Power was taken from the line shafting.
(From Pictorial Gallery of Arts, Volume of Useful Arts, London, n.d. [ca. 1845].)
The importance of this invention soon became evident to Otis, and he introduced his device to the public three years later during the second season of the New York Crystal Palace Exhibition, in 1854. Here he would demonstrate dramatically the perfect safety of his elevator by cutting the hoisting rope of a suspended platform on which he himself stood, uttering the immortal words which have come to be inseparably associated with the history of the elevator—“All safe, gentlemen!”[4]
The invention achieved popularity slowly, but did find increasing favor in manufactories throughout the eastern United States. The significance of Otis’ early work in this field lay strictly in the safety features of his elevators rather than in the hoisting equipment. His earliest systems were operated by machinery similar to that of the teagle elevator in which the hoisting drum was driven from the mill shafting by simple fast and loose pulleys with crossed and straight belts to raise, lower, and stop. This scheme, already common at the time, was itself a direct improvement on the ancient hand-powered drum hoist.
The first complete elevator machine in the United States, constructed in 1855, was a complex and inefficient contrivance built around an oscillating-cylinder steam engine. The advantages of an elevator system independent of the mill drive quickly became apparent, and by 1860 improved steam elevator machines were being produced in some quantity, but almost exclusively for freight service. It is not clear when the first elevator was installed explicitly for passenger service, but it was probably in 1857, when Otis placed one in a store on Broadway at Broome Street in New York.
In the decade following the Civil War, tall buildings had just begun to emerge; and, although the skylines of the world’s great cities were still dominated by church spires, there was increasing activity in the development of elevator apparatus adapted to the transportation of people as well as of merchandise. Operators of hotels and stores gradually became aware of the commercial advantages to be gained by elevating their patrons even one or two floors above the ground, by machinery. The steam engine formed the foundation of the early elevator industry, but as building heights increased it was gradually replaced by hydraulic, and ultimately by electrical, systems.
THE STEAM ELEVATOR
The progression from an elevator machine powered by the line shafting of a mill to one in which the power source was independent would appear a simple and direct one. Nevertheless, it was about 40 years after the introduction of the powered elevator before it became common to couple elevator machines directly to separate engines. The multiple belt and pulley transmission system was at first retained, but it soon became evident that a more satisfactory service resulted from stopping and reversing the engine itself, using a single fixed belt to connect the engine and winding mechanism. Interestingly, the same pattern was followed 40 years later when the first attempts were made to apply the electric motor to elevator drive.
Figure 8.—In the typical steam elevator machine two vertical cylinders
were situated either above or below the crankshaft, and a small pulley
was keyed to the crankshaft. In a light-duty machine, the power was
transmitted by flatbelt from the small pulley to a larger one mounted
directly on the drum. In heavy-duty machines, spur gearing was
interposed between the large secondary pulley and the winding drum.
(Photo courtesy of Otis Elevator Company.)
Figure 9.—Several manufacturers built steam machines in which a gear
on the drum shaft meshed directly with a worm on the crankshaft. This
arrangement eliminated the belt, and, since the drum could not drive the
engine through the worm gearing, no brake was necessary for holding the load.
(Courtesy of Otis Elevator Company.)
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Figure 10.—Components of the
steam passenger elevator at the time of its peak
development and use (1876).
(From The First One Hundred Years,
Otis Elevator Company, 1953.)
By 1870 the steam elevator machine had attained its ultimate form, which, except for a number of minor refinements, was to remain unchanged until the type became completely obsolete toward
By the last quarter of the century, a continuous series of improvements in the valving, control systems, and safety features of the steam machine had made possible an elevator able to compete with the subsequently appearing hydraulic systems for freight and low-rise passenger service insofar as smoothness, control, and lifting power were concerned. However, steam machinery began to fail in this competition as the increasing height of buildings rapidly extended the demands of speed and length of rise.
The limitation in rise constituted the most serious shortcoming of the steam elevator (figs. 8-10), an inherent defect that did not exist in the various hydraulic systems.
Since the only practical way in which the power of a steam engine could be applied to the haulage of elevator cables was through a rotational system, the cables invariably were wound on a drum. The travel or rise of the car was therefore limited by the cable capacity of the winding drum. As building heights increased, drums became necessarily longer and larger until they grew so cumbersome as to impose a serious limitation upon further upward growth. A drum machine rarely could be used for a lift of more than 150 feet.[5]
Another organic difficulty existing in drum machines was the dangerous possibility of the car—or the counterweight, whose cables often wound on the drum—being drawn past the normal top limit and into the upper supporting works. Only safety stops could prevent such an occurrence if the operator failed to stop the car at the top or bottom of the shaft, and even these were not always effective. Hydraulic machines were not susceptible to this danger, the piston or plunger being arrested by the ends of the cylinder at the extremes of travel.
THE HYDRAULIC ELEVATOR
The rope-geared hydraulic elevator, which was eventually to become known as the “standard of the industry,” is generally thought to have evolved directly from an invention of the English engineer Sir William Armstrong (1810-1900) of ordnance fame. In 1846 he developed a water-powered crane, utilizing the hydraulic head available from a reservoir on a hill 200 feet above.
The system was not basically different from the simple hydraulic press so well known at the time. Water, admitted to a horizontal cylinder, displaced a piston and rod to which a sheave was attached. Around the sheave passed a loop of chain, one end of which was fixed, the other running over guide sheaves and terminating at the crane arm with a lifting hook. As the piston was pressed into the cylinder, the free end of the chain was drawn up at triple the piston speed, raising the load. The effect was simply that of a 3-to-1 tackle, with the effort and load elements reversed. Simple valves controlled admission and exhaust of the water. (See fig. 11.)
Figure 11.—Armstrong’s hydraulic crane. The main cylinder was inclined, permitting gravity to assist in overhauling the hook.
The small cylinder rotated the crane. (From John H. Jallings, Elevators, Chicago, 1916, p. 82.)
The success of this system initiated a sizable industry in England, and the hydraulic crane, with many modifications, was in common use there for many years. Such cranes were introduced in the United States in about 1867 but never became popular; they did, however, have a profound influence on the elevator art, forming the basis of the third generic type to achieve widespread use in this country.
The ease of translation from the Armstrong crane to an elevator system could hardly have been more evident, only two alterations of consequence being necessary in the passage. A guided platform or car was substituted for the hook; and the control valves were connected to a stationary endless rope that was accessible to an operator on the car.
The rope-geared hydraulic system (fig. 13) appeared in mature form in about 1876. However, before it had become the “standard elevator” through a process of refinement, another system was introduced which merits notice if for no other reason than that its popularity for some years seems remarkable in view of its preposterously unsafe design. Patented by Cyrus W. Baldwin of Boston in January 1870, this system was termed the Hydro-Atmospheric Elevator, but more commonly known as the water-balance elevator (fig. 12). It employed water not under pressure but simply as mass under the influence of gravity. The elevator car’s supporting cables ran over sheaves at the top of the shaft to a large iron bucket, which traveled in a closed tube or well adjacent to and the same length as the shaft. To raise the car, the operator caused a valve to open, filling the bucket with water from a roof tank. When the weight of water was sufficient to overbalance the loaded car, the bucket descended, raising the car. On its ascent the car was stopped at intermediate floors by a strong brake that gripped the guides. Upon reaching the top, the operator was able to open a valve in the bucket, now at the bottom of its travel, and discharge its contents into a basement tank, to be pumped back to the roof. No longer counterbalanced, the car could descend, its speed controlled solely by the brake.
The great popularity of this novel system apparently was due to its smooth operation, high speed, simplicity, and economy of operation. Managed by a skillful operator, it was capable of speeds far greater than other systems could then achieve—up to a frightening 1,800 feet per minute.[6]
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Figure 12.—Final development of the
Baldwin-Hale water balance elevator, 1873.
The brake, kept applied by powerful springs,
was released only by steady pressure on a lever.
There were two additional controls—the
continuous rope that opened the cistern valve to fill
the bucket, and a second lever to open the
valve of the bucket to empty it. (From
United States Railroad and Mining Register,
Apr. 12, 1873, vol. 17, p. 3.)
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Figure 13.—Vertical cylinder,
rope-geared hydraulic elevator with 2:1
gear ratio and rope control (about 1880).
For higher rises and speeds, ratios of
up to 10:1 were used, and the endless
was replaced by a lever.
(Courtesy of Otis Elevator Company.)
In addition to the element of potential danger from careless operation or failure of the brake, the Baldwin system was extremely expensive to install as a result of the second shaft, which of course was required to be more or less watertight.
Much of the water-balance elevator’s development and refinement was done by William E. Hale of Chicago, who also made most of the installations. The system has, therefore, come to bear his name more commonly than Baldwin’s.
The popularity of the water-balance system waned after only a few years, being eclipsed by more rational systems. Hale eventually abandoned it and became the western agent for Otis—by this time prominent in the field—and subsequently was influential in development of the hydraulic elevator.
The rope-geared system of hydraulic elevator operation was so basically simple that by 1880 it had been embraced by virtually all manufacturers. However, for years most builders continued to maintain a line of steam and belt driven machines for freight service. Inspired by the rapid increase of taller and taller buildings, there was a concentrated effort, heightened by severe competition, to refine the basic system.
By the late 1880’s a vast number of improvements in detail had appeared, and this form of elevator was considered to be almost without defect. It was safe. Absence of a drum enabled the car to be carried by a number of cables rather than by one or two, and rendered overtravel impossible. It was fast. Control devices had received probably the most attention by engineers and were as perfect and sensitive as was possible with mechanical means. Cars with lever control could be run at the high speeds required for high buildings, yet they could be stopped with a smoothness and precision unattainable earlier with systems in which the valves were controlled by an endless rope, worked by the operator. It was almost completely silent, and when the cylinder was placed vertically in a well near the shaft, practically no valuable floor space was occupied. But most important, the length of rise was unlimited because no drum was used. As greater rises were required, the multiplication of the ropes and sheaves was simply increased, raising the piston-car travel ratio and permitting the cylinder to remain of manageable length. The ratio was often as high as 10 or 12 to 1, the car moving 10 or 12 feet to the piston’s 1.
In addition to its principal advantages, the hydraulic elevator could be operated directly from municipal water mains in the many cities where there was sufficient pressure, thus eliminating a large investment in tanks, pumps and boilers (fig. 14).
By far the greatest development in this specialized branch of mechanical engineering occurred in the United States. The comparative position of American practice, which will be demonstrated farther on, is indicated by the fact that Otis Brothers and other large elevator concerns in the United States were able to establish offices in many of the major cities of Europe and compete very successfully with local firms in spite of the higher costs due to shipment. This also demonstrates the extent of error in the oft-heard statement that the skyscraper was the direct result of the elevator’s invention. There is no question that continued elevator improvement was an essential factor in the rapid increase of building heights. However, consideration of the situation in European cities, where buildings of over 10 stories were (and still are) rare in spite of the availability of similar elevator techniques, points to the fundamental matter of tradition. The European city simply did not develop with the lack of judicial restraint which characterized metropolitan growth in the United States. The American tendency to confine mercantile activity to the smallest possible area resulted in excessive land values, which drove buildings skyward. The elevator followed, or, at most, kept pace with, the development of higher buildings.
Figure 14.—In the various hydraulic systems, a pump was required if
pressure from water mains was insufficient to operate the elevator directly.
There was either a gravity tank on the roof or a pressure tank in the basement.
(From Thomas E. Brown, Jr., “The American Passenger Elevator,”
Engineering Magazine (New York), June 1893, vol. 5, p. 340.)
European elevator development—notwithstanding the number of American rope-geared hydraulic machines sold in Europe in the 10 years or so preceding the Paris fair of 1889—was confined mainly to variations on the direct plunger type, which was first used in English factories in the 1830’s. The plunger elevator (fig. 16), an even closer derivative of the hydraulic press than Armstrong’s crane, was nothing more than a platform on the upper end of a vertical plunger that rose from a cylinder as water was forced in.
There were two reasons for this European practice. The first and most apparent was the rarity of tall buildings. The drilling of a well to receive the cylinder was thus a matter of little difficulty. This well had to be equivalent in depth to the elevator rise. The second reason was an innate European distrust of cable-hung elevator systems in any form, an attitude that will be discussed more fully farther on.
THE ELECTRIC ELEVATOR
At the time the Eiffel Tower elevators were under consideration, water under pressure was, from a practical standpoint, the only agent capable of fulfilling the power and control requirements of this particularly severe service. Steam, as previously mentioned, had already been found wanting in several respects. Electricity, on the other hand, seemed to hold promise for almost every field of human endeavor. By 1888 the electric motor had behind it a 10- or 15-year history of active development. Frank J. Sprague had already placed in successful operation a sizable electric trolley-car system, and was manufacturing motors of up to 20 horsepower in commercial quantity. Lighting generators were being produced in sizes far greater. There were, nevertheless, many obstacles preventing the translation of this progress into machinery capable of hauling large groups of people a vertical distance of 1,000 feet with unquestionable dependability.
The first application of electricity to elevator propulsion was an experiment of the distinguished German electrician Werner von Siemens, who, in 1880, constructed a car that successfully climbed a rack by means of a motor and worm gearing beneath its deck (figs. 17, 18)—again, the characteristic European distrust of cable suspension. However, the effect of this success on subsequent development was negligible. Significant use of electricity in this field occurred somewhat later, and in a manner parallel to that by which steam was first applied to the elevator—the driving of mechanical (belt driven) elevator machines by individual motors. Slightly later came another application of the
In both of these cases the operational demands on the motor were of course identical to those on the prime movers which they replaced; no reversal of direction was necessary, the speed was constant, and the load was nearly constant. Furthermore, the load could be applied to the motor gradually through automatic relief valves on the pump and in the mechanical machines by slippage as the belt was shifted from the loose to the fast pulleys. The ultimate simplicity in control resulted from permitting the motor to run continuously, drawing current only in proportion to its loading. The direct-current motor of the 1880’s was easily capable of such service, and it was widely used in this way.
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Figure 15.—Rope-geared hydraulic freight elevator
using a horizontal cylinder (about 1883).
(From a Lane & Bodley illustrated catalog of hydraulic elevators, Cincinnati, n.d.)
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Figure 16.—English direct plunger
hydraulic elevator (about 1895).
(From F. Dye, Popular Engineering,
London, 1895, p. 280.) Adaptation of the motor to the direct drive of an elevator machine was quite another matter, the difficulties being largely those of control. At this time the only practical means of starting a motor under load was by introducing resistance into the circuit and cutting it out in a series of steps as the speed picked up; precisely the method used to start traction motors. In the early attempts to couple the motor directly to the winding drum through worm gearing, this “notching up” was transmitted to the car as a jerking motion, disagreeable to passengers and hard on machinery. Furthermore, the controller contacts had a short life because of the arcing which resulted from heavy starting currents. In all, such systems were unsatisfactory and generally unreliable, and were held in disfavor by both elevator experts and owners.
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Figure 17.—Siemens’ electric
rack-climbing elevator of 1880.
(From Werner von Siemens,
Gesammelte Abhandlungen und Vorträge,
Berlin, 1881, pl. 5.)