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Engineering

An Anthropomorphic Model

B

Henry Petroski

eing able to feel the forces in an unusual structure, even if only by proxy through a model, is a great advantage for engineers, students and laypersons alike. If we can actually be part of the model, and feel the forces directly, all the better. Probably the most famous anthropomorphic model of a major engineering work is that of the Forth Bridge, located near Edinburgh, Scotland. This structure had its origins in the need for fixed crossings of the firths (or estuaries) of the Forth and Tay rivers on the country’s east coast. Without such crossings, rail traffic was interrupted by the need to transfer rolling stock to and from ferries at each river’s shores. The railway engineer Thomas Bouch was commissioned to design the two bridges, and construction of the one across the shallower Firth of Tay was completed in 1878. It was not a particularly daring design, and the bridge was remarkable only for its length of almost two miles across the wide estuary. Unfortunately, the longest and highest girders of the bridge collapsed during a storm in December 1879, killing 75 people who were on the train making the crossing at the time. A court of inquiry found that the structure was “badly designed, badly constructed and badly maintained,” and its engineer was discredited. Construction was halted on the suspension bridge that Bouch had designed to cross the deeper Firth of Forth, and subsequently an entirely new design was commissioned from the firm of the distinguished engineer Sir John Fowler and his young partner Benjamin Baker, who would be knighted on the completion of the project. Baker would be the lead designer of the bridge, and he would also confess to the enormity of the task: “If I were to pretend that the designing and building of the Forth Bridge was not a source of present and future anxiety to all concerned, no engineer of expewww.americanscientist.org

If seeing is believing, feeling may be understanding rience would believe me. Where no precedent exists, the successful engineer is he who makes the fewest mistakes.” Fortunately for engineers, it is precisely where no precedent exists that they tend to be the most careful and hence successful. The Cantilever Comes to Britain

Baker’s design for the bridge was quite unusual for its time. It was based on the cantilever principle, which had roots in corbeled arches and vaults. Galileo was the first to provide a rational analysis of a cantilever structure, understanding that if he could successfully determine a relationship between the geometry, material strength and load carried at the end of a generic cantilever beam, then he could predict the behavior of beams of more complex design and thereby shed light on the hitherto inexplicable spontaneous failure of massive structures like obelisks and ships. Galileo’s analysis of the cantilever beam was correct in methodology but flawed in detail; still, it provided the basis for a rational method of structural analysis that is taught to engineering students to this day. The classic illustration for what has come to be known as Galileo’s Problem has been widely reproduced and, although not strictly speaking an anthropomorphic model, provides a feel for the gross forces involved. A true anthropomorphic version of the cantilever is readily produced by stretching one’s arm out horizontally and holding a briefcase, backpack or similar load in one’s hand. Even without such a load at its extremity, the outstretched arm

represents a cantilever beam whose self-weight must be supported at the shoulder alone. Railroad bridges employing the cantilever principle had been built in North America during the 1880s, but the form was new to Britain, so Baker prepared a public lecture to explain the nature of a cantilever bridge, tracing its roots to centuries-old Oriental examples but not mentioning any contemporary American examples. His 1887 lecture is an exemplar of the form, and its highlight was an anthropomorphic model—variously referred to also as a living model and a human cantilever—of one full span of the structure that was being built across the Firth of Forth. The apparatus for the model consisted of a pair of chairs, four wooden struts, two pallets of bricks, a swinglike seat and rope to connect some of the components to each other. Three men were required to complete the tableau of the model. Two of the men sat upright in the chairs, and each of these men grasped the tops of a pair of struts, the bottoms of which were notched to bear against the edge of the chair seat. The triangular arrangement so formed on either side of each man represented the portions of the bridge structure cantilevered out from the bridge towers, which were represented by the torsos of the seated men and their chairs. To the tops of the inside struts were attached the sides of the swing seat, which represented the suspended central portion of the bridge span across which the railroad trains would run. Each outside cantilever, consisting of a man’s arm and associated strut, was tied by rope to a pallet of bricks, which proHenry Petroski is Aleksandar S. Vesic Professor of Civil Engineering and a professor of history at Duke University. Address: Box 90287, Durham, NC 27708-0287

Copyright © 2013 by Henry Petroski. Requests for permission to reprint or reproduce this article should be directed to the author at [email protected].

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When engineer Benjamin Baker was faced with the need to convince a skeptical public that a new type of bridge, the cantilever, was the right choice for spanning the Firth of Forth, near Edinburgh, Scotland, he prepared a model for a lecture presented at the Royal Institution in London. Using three men, chairs, sticks, rope and bricks for counterweights, he demonstrated the principles that would make the record-length span possible. The model was likely photographed at the construction site and shown by use of a photographic lantern slide. (Photograph by Evelyn George Carey from Mackay, The Forth Bridge: A Picture History.)

vided a counterweight to balance half the weight of the suspended central span plus half the weight of the third man, who occupied the suspended seat. In Baker’s lecture demonstration, a large drawing of the bridge span was displayed behind the human model, thereby making it self-evident—if it was not already—what parts of the model corresponded to what parts of the bridge. In Baker’s own words: Two men sitting on chairs extended their arms and supported the same by grasping sticks butting against the chairs. This represented the two double cantilevers. The central girder was represented by a short stick slung from one arm of each man and the anchorages by ropes extending from the other arms to a couple of piles of brick. When stresses are brought on this system by a load on the central girder, the men’s arms and the anchorage ropes come into tension and the sticks and chair 104

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legs into compression. In the Forth Bridge you have to imagine the chairs placed a third of a mile apart and the men’s heads to be 300 ft. above the ground. Their arms are represented by huge steel lattice members, and the sticks or props by steel tubes 12 ft. in diameter and 1¼ in. thick. Baker’s lecture incorporating the human model was prompted by several factors. One was that the Tay Bridge that collapsed (and was rebuilt, reopening in 1887, the year of the lecture) was on the same rail line that the new-style bridge would carry over the Forth. There was thus public anxiety about the safety of the line generally. The other factor prompting the lecture was the unfamiliarity of the bridge form that was being erected over the Forth. Although steel cantilever rail bridges were not absolutely new, this one under construction near Edinburgh was novel to Britain and was to have the longest spans of any in the

world. The North British Railway, no doubt at least in part to allay fears that might have kept paying passengers from booking travel across the soon-tobe-completed bridge, surely would not have discouraged Baker from giving his lecture, in which he would emphasize that, in spite of the public’s confusion of the two, the Tay and Forth bridges were quite distinct. The lecture was delivered on May 20, 1887, at a weekly evening meeting of the Royal Institution in London. In addition to clarifying the location of the Forth Bridge, which is about 35 miles south of the Tay, Baker gave a sense of its enormity and thereby the difficulty of the task of erecting it. His challenge in preparing his lecture, he admitted, was that he “had to consider how best to make a general audience appreciate the true nature and direction of the stresses on the Forth Bridge, and after consultation with some engineers on the spot, a living model was arranged.” Although Baker did not claim that the idea was wholly his, the

Copyright © 2013 by Henry Petroski. Requests for permission to reprint or reproduce this article should be directed to the author at [email protected].

model has been closely associated with him ever since. Anthropomorphic Evolution

Baker may have consulted with some engineers on the spot, but as with most things designed, the details of the model that was to become so famous involved fine-tuning, some of which was captured in photographs, a collection of which now reside in the National Archives of Scotland. The photos were taken by Evelyn George Carey, an assistant engineer on the project who also became its official photographer. The bridge under construction was also documented by Philip Phillips, son of the resident engineer, Joseph Phillips. The younger Phillips published contemporary with the project several books capturing its progress in sketches and photographs. One of the books was subtitled The Giant’s Anatomy, reinforcing the tendency to speak of the bridge in anthropomorphic terms. Still another example was provided by reference to the bridge towers as having a “Holbein straddle,” an allusion to the characteristic spread-legged stance in which the Northern Renaissance artist Hans Holbein painted his male subjects. To give the Forth Bridge stability in the wind— and not incidentally distinguish it from the Tay that collapsed—the structure narrowed from about 120 feet wide at the base to only 33 feet wide at the top. Many of Carey’s striking images of the bridge under construction have become very familiar, but photos he took of early efforts at a human cantilever have remained relatively obscure, no doubt because their inferior composition and execution makes them pale in comparison to the one that has become iconic. In one of the alternative models, the chair seats are so high that the feet of the men sitting in them do not touch the ground and so make these men appear suspended like the one on the swing seat. And, by an unfortunate positioning of the swing seat before what appears to be a stone pillar or fence post, the elevated seat appears not to be supported by the cantilevers but by a pier beneath it. In addition, the struts employed are longer than they need to be, thus confusing the geometry of the structure. And, finally, the lines of the bridge in the drawing hung above the human model do not show up clearly. It is no wonder that this version of the model had to be improved. Another reason for emending it might www.americanscientist.org

Like the engineering project itself, Baker’s model underwent considerable modification and evolution before reaching the finished state shown on the opposite page. In the second version (above) the bridge drawing has appropriately weighted lines, but other elements, such as the size of the counterweight support lines and the slope of the ground (requiring shims for the left chair) are less than ideal. (Photograph from Gray & Maggin, Evelyn George Carey: Forth Bridge.)

be seen in the precariousness of the central figure. It was later suggested that if someone stumbled over an anchorage, the gentleman in the swing seat would have “an ignominious tumble.” Had that happened, it might have but further demonstrated the effectiveness of the model in simulating the behavior of the real structure. In a subsequent version of the model, the background drawing of the bridge is much improved and looks more like the one in the iconic image. It differs from that in having all members of the cantilever—diagonals and chords alike—drawn with the same weight line, thus failing to emphasize the upper and lower chords to which the model’s struts and arms holding them correspond. The suspended nature of the swing seat is more clearly visible, but the struts remain longer than necessary. Also, the cords supporting the swing seat and those connected to the piles of bricks remain lightweight and do not show up well against the background. Furthermore, the model was photographed before a building with a distracting off-center window, destroying the symmetry that could be better emphasized. Finally, the ground on which the building is erected appears to slope slightly down to the left, which seems to have necessitated placing the left chair on some boards to make it level with the right,

but the effect is to make the ground look cluttered. It is easy to see why this version of the model also was not used in Baker’s lecture. The third of Carey’s photographs is the well-known one, and its composition and that of the human model itself correct the faults found in the previous two representations. The ground and background are simple and uncluttered; the size of the drawing is no larger than it has to be; the struts are of an appropriate size; the ropes are heavier; and the photo itself clearly shows what the model is intended to demonstrate. Once again, we have a dramatic illustration of how humanmade things evolve by improving on their predecessors through elimination of their faults. Varying the Anthropomorphology

Different combinations of people appear in each of the three versions of the human cantilever. The three in the first do not reappear as a group in the later two, but the men occupying the chairs in the second version appear to be the same ones who occupy them in the iconic version. (Even though they bear no resemblance to the famous engineers, the anonymous chair sitters have been incorrectly identified as Fowler and Baker on occasion, including in a 2007 BBC news story about the issuance by the Bank of Scotland of a

Copyright © 2013 by Henry Petroski. Requests for permission to reprint or reproduce this article should be directed to the author at [email protected].

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A re-creation of the anthropomorphic model was on display at the Forth Bridges Visitor Centre for many years. In 2012, the Forth Bridges Visitor Centre Trust, members of which are shown here, donated it to the town of South Queensferry. (Photograph courtesy of Roland Paxton.)

new ₤20 note featuring an image of the bridge and the living model of it.) The person in the suspended seat does change from the second to the last version of the model, and his identity is known because of the special circumstances that caused him to be in Scotland at the time. Engineering has always been an activity of wideranging geographical interest, with practitioners from far-away lands visiting the sites of innovative construction projects to learn firsthand how something new was being done. This was true in ancient Rome, when the likes of Vitruvius and Frontinus traveled around the empire to study temples and aqueducts and talk to their engineers about successful practices and failed efforts. In the 19th century, when the nascent railroad was presenting

new challenges in bridge building, the greatest projects became magnets for visitors from afar. The construction at midcentury of the Britannia Tubular Bridge across the Menai Strait in northwest Wales was one such project, and the construction of the bridge across the Firth of Forth was another. At 1,710 feet long, each of its two spans was to be the longest in the world when the bridge was completed. Among those who traveled to Britain in the latter third of the 19th century, when the railroad was being introduced in Japan, was the young engineer Kaichi Watanabe. He came to Scotland with a degree from the University of Tokyo and continued his studies at Glasgow University. He became Baker’s assistant and a construction foreman on the Forth Bridge project. Watanabe is said

to have been invited to participate in the famous model “to remind audiences of the debt the designers owed to the Far East.” His relatively slight stature may also have made him a likely choice to occupy the suspended seat. An illustration of the iconic version of the model appeared in the engineering press first in the United States, in the issue of Engineering News dated June 11, 1887, which was only about three weeks after the model’s debut at the Royal Institution in London, and a full seven weeks before it appeared in the British Engineering. The American “journal of civil engineering and construction” called the model “novel” and “ingenious,” captioning the engraving of it “A Japanese Illustration of the Cantilever Principle,” and referring to it as “a Japanese idea, as may be suspected from the central figure,” perhaps inferring too much from Watanabe’s position in the model. Whoever or whatever culture should be credited, the Engineering News article reported that during Baker’s lecture the human cantilever was “received with loud and general applause.” It does not seem likely that the model was demonstrated live at the lecture but rather that it was projected from a lantern slide, for the Royal Institution, where the lecture was given, has occupied a formal becolumned stone building on Albemarle Street since shortly after its founding in 1799. The setting of the demonstration must have been the construction site of the bridge, where Baker conferred with colleagues, probably including Watanabe, and the model was created “on the spot,” with its various stages captured by on-site photographer Carey. The photograph of the final demonstration, at least, was converted into one of the lantern slides with which the lecture was illustrated. Engineering News acknowledged the American bridge engineer Thomas C. Clarke, who visited the construction site in 1887, for the use of the photograph from which the journal made the engraving appearing in its pages, attesting the speed with which engineering news, knowledge and documents traveled across the Atlantic in the late 19th century. An Enduring Model

The replica model has certain details that make it less than true to the physical principles demonstrated in the original. (Photograph by Catherine Petroski.) 106

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However much misinformation and anonymity remains associated with the original human cantilever model, it has become an unforgettable image

Copyright © 2013 by Henry Petroski. Requests for permission to reprint or reproduce this article should be directed to the author at [email protected].

that has often been reproduced and recreated. When I was at the bridge site in 2003, there was on the grounds of the Visitor Centre a pair of chairs and all the rest of the apparatus needed for a trio of visitors to participate in animating the model while looking out at the real bridge. Today, that apparatus has been relocated across the Forth to South Queensferry, where it sits in the back court of the Orocco Pier Restaurant. According to Roland Paxton, engineer, scholar of British engineering, bibliophile and lover of bridges, “the replica model is on loan to the restaurant from the town’s Forth Bridge Memorial Committee to whom it was donated by the Forth Bridges Visitor Centre Trust in 2012.” The final meeting of the trust was commemorated in a photograph of the trustees posing with a re-creation of the human cantilever model, with Chairman Paxton sitting in the catbird seat, albeit not nearly as high off the ground as Watanabe in the original model. There are some other interesting differences in the two demonstrations posed 125 years apart. In the 1887 Baker-lecture tableau, the human participants representing the towers are grasping the struts with their palms facing the camera, suggesting that their arms are indeed in tension, as they would be expected to be to hold the struts at the angle necessary to support the swing seat as high above the ground as it is. In the 2012 re-creation, however, the gentlemen in the chairs are grasping the struts with their palms facing away from the camera, a less natural and efficient way to hold up the struts, which are less steeply inclined. Furthermore, in contrast to the original living model, in which the chair occupants grasp the struts as close to their far end as possible, thereby exerting minimum force to form isoscelestriangle cantilevers, the trust members are holding the struts at about midpoint, which does not give the model the verisimilitude it should have. In addition, the way they are holding the struts suggests that rather than supporting them, they are leaning on them, thus putting their arms not in tension but in compression. This is especially evident in the open right hand of the gentleman in the left chair: He does not even have his fingers wrapped around the strut and appears to be pushing down on it with the heel of his hand. As for the gentleman in the right chair, www.americanscientist.org

his arms appear to be crooked a bit, further suggesting that they are not being fully extended in tension. The men are posing with the model apparatus, but those in the chairs may not have been experiencing the forces involved to the extent that the original model was designed to demonstrate. In the original model, Watanabe holds his hands close to his side, grasping the swing seat, perhaps to secure his balance. In the 2012 re-creation, however, Paxton is resting his hands on the struts, perhaps because the other gentlemen have left room for him to do so, but the potential effect is to introduce confusion among observers of this human model reenactment about how the real structure works. In fact, given that the gentlemen in the chairs do not appear to be holding the struts in place with any tension in their arms, the actual structural action of the model appears to be more of an arch than a cantilever. What holds the swing seat and its living load in place is the chairs and their occupants serving as abutments rather than towers. The same was not the case in the living model used in Baker’s lecture, for the second version photographed by Carey shows especially clearly that the suspended seat was hung by ropes from the struts. Finally, in the Baker demonstration the notched lower end of each strut rests on the edge of a chair. However, in the Visitor Centre Trust model this does not seem to be the case. Extrapolating the visible portion of any one of the struts suggests that its lower end does not rest on the edge of the chair seat but rather intersects the chair structure just under the seat. Closer inspection of the juncture of the upper end of a strut with the suspended seat shows it to look like a welded joint. This indicates that the struts are metal tubes and suggests that such connections may have been employed at least in part to keep the apparatus complete and so always at the ready to be used. In fact, this is the case. The nature of the apparatus without people partially obscuring some of its parts is shown in a 2003 photograph taken when it was still located at the Visitors’ Centre. The struts are indeed made of steel tubing and are not entirely straight and separate like simple lengths of “loose sticks,” as Engineering News described their counterparts. Rather, the steel struts contain an elbow, so when the short part is fixed to or fitted over a fix-

ture under the chair seat, the long part representing the lower chord of the cantilever assumes the proper angle. The effect can be seen in the in-place anchorage struts, which clearly do not need any human arm to hold them at a proper angle. The angle of the bend in the tube and the length of rope are such that the rope is kept taught even when the model is not in use. With the steel chairs so bolted to the concrete slab, not only is the distance between them fixed, but they are also capable of resisting sideways forces. When the middle two steel struts are properly installed beneath the steel chairs, the middle seat is locked in place by an arch-like action, and the mechanism is effectively a rigid structure. When the chairs are occupied, the men on them can steady—but need not hold up—the struts supporting the middle seat, which explains why the members of the Trust did not need to pull up with their arms to make the model work in the same way the human participants did in the original enactment. Regardless of these quibbles about the false structural action of this reconstruction of the living cantilever apparatus, the anthropomorphic model of the Forth Bridge remains a brilliant concept and one that deserves to be re-created, photographed and reflected upon. It just cannot always be relied on to give the participants sitting on it a true feel for the forces involved in the real structure. Bibliography Baker, B. 1887. Bridging the Firth of Forth. Engineering, July 29, pp. 114, 116. Baker, Benjamin. 1887. Bridging the Firth of Forth. Proceedings of the Royal Institution, 12 (No. 81): 142–149. Engineering News. 1887. A novel illustration of the cantilever principle. June 11, p. 385. Gray, Michael, and Angelo Maggi. 2009. Forth Bridge: Evelyn George Carey. Milan: Federico Motta Editore. Mackay, Sheila. 1993. The Forth Bridge: A Picture History. Edinburgh: HMSO. Paxton, Roland, ed. 1990. 100 Years of the Forth Bridge. London: Thomas Telford. Phillips, Philip. 1888. Sketches of the Forth Bridge; or, The Giant’s Anatomy, from Various Points of View. Edinburgh: R. Grant & Son. Phillips, Philip. 1890. The Forth Railway Bridge; Being the Expanded Edition of The Giant’s Anatomy. Edinburgh: R. Grant & Son. Westhofen, W. 1890. The Forth Bridge. Engineering, Feb. 28, pp. 213–283. Wills, Elspeth. 2009. The Briggers: The Story of the Men Who Built the Forth Bridge. Edinburgh: Birlinn.

Copyright © 2013 by Henry Petroski. Requests for permission to reprint or reproduce this article should be directed to the author at [email protected].

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