Hans Albert Einstein (His Life as a Pioneering Engineer) || Epilogue

293

Epilogue

In their readable 1938 book The Evolution of Physics, Albert Einstein and Leopold Infeld devote a chapter to what they call “The Rise of the Mechanical View,” the application of classical physics, often simply called mechanics, to explain and formulate the motion of bodies from sediment particles to planets. This mechanical view, at the heart of contemporary scientific and engineering thinking, guided Hans Albert Einstein’s approach to understanding and formulating sediment transport by flowing water in rivers. It enabled him to make substantial technical contributions over about three decades and become recognized as the world’s foremost expert on sedi-ment problems in rivers, extensively advising engineers coping with river-sediment problems in the United States and abroad.1

Hans Albert’s contributions were important because rivers, large and small, play vital roles in the economy of many regions. Moreover, his contributions were made during an especially active period of major engineering projects that altered the water flow and bed-sediment transport behavior of several large rivers, when engineers were rapidly awakening to the potential problems that sediment transport posed for their projects. The problems commonly revolved around two central questions: How much bed sediment can a river flow transport? And how

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does flow depth vary with flow rate? Answering these questions is compli-cated by the ability of flowing water to erode, transport, and deposit sedi-ment, actions that enable river channels to move up, down, and sideways and to adjust their roughness.

In 1931, when Hans Albert began as a student in Professor Meyer-Peter’s hydraulics laboratory, engineers could not reliably answer the two questions. However, by capitalizing on momentous advances in fluid mechanics and laboratories, Hans Albert achieved remarkable progress toward addressing them. The detailed insight into bed-particle movement he gained while in Meyer-Peter’s laboratory led to his major work, the now-classic U.S. Department of Agriculture Bulletin 1026, “The Bed-Load Function for Sediment Transportation in Open Channel Flows.” When Bulletin 1026 appeared in 1950, it was the most comprehensive method, the “Einstein method,” for estimating how much bed sediment a river flow may transport as bed load and suspended load; their sum yields an estimate of total load of bed sediment transported. Moreover, Bulletin 1026 intro-duced a new method for estimating flow depth in channels subject to chang-ing bed roughness (caused by changing dune or bar size) as sediment load varied. The Einstein–Barbarossa method for estimating bed roughness and commensurate flow depth appeared in a 1952 landmark paper, “River Channel Roughness.”

Subsequent methods for predicting bed sediment load have built on the Einstein method, improving it or modifying it for more convenient use. And other methods have been developed since Bulletin 1026, most taking simpler approaches and some remaining doggedly empirical, their develop-ers judging flow and sediment transport in river channels to be too complex for mechanically based formulation.2 But none have the overall mechanical heft of Bulletin 1026.

Hans Albert’s contributions were important and widely recognized, but they did not receive universal acclaim from his contemporaries. Some thought rivers far too complex for the two questions to be dependably answered by means of mechanical formulation. In their opinion, the mechanical view was useful for explaining component physical processes—such as why flowing water can entrain and transport sediment particles, or why dunes form on a river’s sandy bed—but they did not see it leading to practical methods that enable engineers to address the two questions reliably.

A fundamental part of the complexity, as the noted river geomor-phologist Luna Leopold points out in his slim book A View of the River, is that the considerable variability in space and time of parameters defining water flow and bed sediment complicates predicting channel adjustments


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epilogue 295

in depth, width, and alignment (1994). To Leopold and most fellow river geomorphologists and to engineer adherents of the regime theory of river analysis, the best that can be done is to define average values based on observations laboriously acquired by measurement of river and canal chan-nels. The variability at times has seemed so overwhelming that even experts on river behavior have occasionally characterized the typical river channel in almost metaphysical terms—as “carpenter of its own edifice” (Leopold 1994) and “both art and artist” (Kennedy 1983).

Other contemporaries, however, thought that Hans Albert had not taken the mechanical view far enough and that he had too sketchily patched formulations together and resorted to empirical compromise to come up with methods for engineers to use. The distinguished hydraulics engineer Hunter Rouse, in his book Hydraulics in the United States, 1776–1976, described the Einstein method as “empirical” and sniped that Hans Albert (in Bulletin 1026) “was able—at least to his own satisfaction—to convert his empirical transport formula into an analytical one.” Rouse then added, “At best a very complex function, the Einstein bed-load formula was prob-ably fully understood only by its creator…. As a consultant his advice was practical, sound and widely sought. But his intuitive grasp of a sediment problem was not easy to inculcate in others” (Rouse 1976).

Hans Albert was aware of the complications that rivers pose for purely mechanical formulation, but he persevered with the mechanical view and laboratory experiments, further investigating these complications or seeking ways to best work around them. He shared his father’s tenacity for pursuing viewpoints intuitively and dearly held and for seeming to be little concerned by criticisms of his work.

In this effort, his story personifies the mix of success, difficulty, and inevitable criticism experienced by engineers and scientists who use the mechanical view to describe the complicated behavior of alluvial rivers, or other analogous complex systems. The effort begins with enthusiasm and with apparent good promise of success, based on innovative new insights into component processes. Formulation seems within reach, and significant progress is indeed made, but soon, simplifying assumptions and curve- fitting empiricism are invoked as approximations for working around bar-riers blocking pure, mechanics-based formulation.

In the 1970s, the decade of Hans Albert’s death in 1973, a further major development opened up the way for remarkable advances with the mechanical view. Computer-based numerical simulation created new pos-sibilities for applying the mechanical view to model complex channels and dynamic flow conditions. At first, such models were one-dimensional approximations, representing only longitudinal profiles of channel bed,


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water surface, and sediment transport. Over the next several decades, engi-neers developed two-dimensional and three-dimensional models that can handle greatly increased levels of complexity and enable engineers to simu-late water and sediment movement in complicated channels like the crooked Mississippi River. Today, computer-based methods are commonly used to address the two questions stated earlier, those regarding rates of sediment movement and flow depth variations in rivers. In 1975, two years after Hans Albert died, and after a 10-year writing effort, a task force appointed by the American Society of Civil Engineers (ASCE) published the now-classic book Sedimentation Engineering (ASCE Manual of Practice 54), which for decades has been regarded as the primary resource for informa-tion addressing sediment engineering problems in watersheds, streams, and rivers (Vanoni 1975). Although the book extensively cites Hans Albert’s work, he neither served on the task force nor contributed chapters or sec-tions to the book. His absence here is a minor mystery because he was well acquainted with people who were closely involved with the book, which was conceived shortly after the First Sedimentation Conference in 1947 by his Soil Conservation Service (SCS) colleague Carl Brown and completed by former SCS colleague Vito Vanoni, who chaired the task force and wrote a sizable portion of the book. Hans Albert’s friend Don Bondurant also served on the task force and contributed a section. A little more than 30 years later, in 2008, ASCE published a goliath, 1,100-page update and expansion of Sedimentation Engineering summarizing new knowledge and methods (Garcia 2008).

With the passing years, even Hans Albert’s regime theory nemesis, Thomas Blench, more openly acknowledged the importance of the mechan-ics view for advancing river science and engineering. His last book, Mechan-ics of Plains Rivers: A Regime Theory Treatment of Canals and Rivers (Blench 1986), at least included the word “mechanics” in its title.

In 1988, ASCE established the Hans Albert Einstein Award “to honor Hans Albert Einstein for his outstanding contributions to the engineering profession and his advancements in the areas of erosion control, sedimenta-tion, and alluvial waterways.” The award’s first recipient was Vito Vanoni. The award recognizes Hans Albert’s milestone contributions. He and SCS colleagues were the first to formally distinguish between the two main types of sediment load conveyed by rivers: bed-sediment load and wash load (Einstein et al. 1940). The Einstein method (Einstein 1950) was the first comprehensive procedure for calculating the total rate of bed-sediment transport, taking into account different sizes of sediment particles and the host of complexities associated with bed-sediment movement and relating the bed load and suspended load components of bed-sediment transport.


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The Einstein–Barbarossa method (Einstein and Barbarossa 1952) was the first for estimating the relationship between flow depth and flow rate in alluvial channels that took into account bed-sediment transport and chang-ing bed-form dimensions. The notion of dividing flow resistance into two parts, particle roughness drag and bed-form drag, was also new for alluvial river mechanics.

Hans Albert’s contributions involved many incremental advances, such as how flowing water lifts particles from a channel bed and how moving particles form dunes whose changing shape affects flow depth. Hans Albert’s student, Hsieh Wen Shen, outlined these advances in a paper pre-pared two years after Hans Albert’s passing (1975). He listed 13 significant contributions associated with Hans Albert’s work with flow and sediment transport in channels.3 He also mentioned contributions in other areas, such as sediment transport in pipes, erosion, and transport of clay.

Hans Albert’s highly competent graduate students, who amplified and expanded his work, became an especially important part of his legacy. Two of them, Hsieh Wen Shen and Ray Krone, immediately followed Vanoni in receiving the Einstein Sedimentation Award; a third student, Alfred Har-rison, received it about 10 years later. Hans Albert’s student Ning Chien returned to China in 1955, became China’s top expert on river sediment processes and problems, and made important contributions to projects on the Yellow and Yangtze Rivers.4 Chien’s book Mechanics of Sediment Transport with coauthor Zhaohui Wan (1983) and his other publications were the leading Chinese texts addressing river sediment concerns; in 1999, ASCE published an English version of Mechanics of Sediment Transport (Chien and Wan 1999). Hans Albert passed away just before he planned to travel to China to visit river projects with Chien.

Another student, Walter Graf, wrote the books Hydraulics of Sedi-ment Transport (1971) and Fluvial Hydraulics (1998), which became widely used. Hsieh Wen Shen organized, wrote, or coordinated the publication of other widely referenced books on rivers and sediment—River Mechanics (1971, 1973); Sedimentation (1972); and, with Hideo Kikkawa, Applica-tion of Stochastic Processes in Sediment Transport (1980).

The path leading Hans Albert to become a leading expert and an intellectual predecessor of a subsequent generation of successful engineers led from Europe to the United States and was influenced by his father, Albert. As a student in Meyer-Peter’s lab, Hans Albert benefited from Euro-pean advances in fluid mechanics and laboratory experimentation. At key moments, Albert directed his son to become a student at Meyer-Peter’s lab and then to move to the United States. However, Albert’s influence extended in subtle ways beyond prompting Hans Albert’s career moves.


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Although Hans Albert’s prominence in the field of engineering could not be equated with Albert’s worldwide recognition both for scientific achievement and humanitarian effort, father and son shared many similari-ties. The similarities ranged from the parallel tracks of their lives to their shared love of music and sailing, their temperaments, and their professional approaches. Both men were professional successes, internationally respected and recognized for their activities. Both loved their work with a passion, and both immersed themselves totally in their work, dedicating their lives to scientific endeavors as the core of life’s meaning. Both father and son were direct in their approach to scientific problems, zeroing in rapidly on the question at hand and addressing it in simple and straightforward terms. Thinking in an organized and clear manner, each was able to pick up gen-eralizations and trends rapidly and identify the fundamental aspects of complicated phenomena. They were remarkably perceptive and intuitive thinkers.

A shared tenacity and stubbornness additionally united father and son. These traits combined with the lack of conventionality to feed the intellectual independence for which both Albert and Hans Albert became renowned. Each made major contributions in his field because he could discard conventional wisdom and forge ahead into intellectually uncharted territory. Each was able to focus for years on a single approach or theory, even when his efforts appeared fruitless, producing as a result the theories of both relativity and of sediment transport for which each became famous.

Toward the ends of their lives, both were respected for what they had discovered in earlier years, but they also became alienated from the schol-arly community’s current direction. Hans Albert, for example, continued his unidirectional efforts to improve and augment his method for calculat-ing bed-sediment transport, combining his search with an inability to deviate from his assumptions, even when data were provided to support counterproposals. Perhaps by his later years, his apparent tunnel vision mattered little. Hans Albert had stood at the center of historic developments in understanding rivers. His leading role in significantly evolving this under-standing from its former status—that of a largely empirical art—to one more soundly based on mechanics principles and expressed in mathematical formulations places Hans Albert prominently in engineering history. He became the iconic expert on how rivers transport sediment. The traits and experiences he shared with his famous father and his father’s influence may have helped guide him onto the path toward eminence, but he attained eminence in his own right.

Hans Albert Einstein’s formulations of bed-sediment transport (espe-cially bed-load transport) and of flow depth were innovative and insightful.


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epilogue 299

They capitalized on emerging concepts of turbulence and probability and on the emergence of labs in which one could see the concepts at play. Though the many complexities associated with rivers inevitably compli-cated formulation and prompted the need for simplifying approximations to yield practical methods for engineers and scientists, Hans Albert’s con-tributions became major milestones in river engineering, and his name is forever connected to river engineering and science.

References Cited

Bishop, A. A., Simons, D. B., and Richardson, E. V. (1965). “Total bed-material transport.” J. Hydraul. Div., 91(2), 175–191.

Blench, T. (1986). Mechanics of plains rivers: A regime treatment of canals and rivers for engineers and environmentalists, University of Alberta, Edmonton.

Brownlie, W. R. (1981). “Prediction of flow depth and sediment discharge in open channels.” Report No. KH-R-43A, W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, CA.

Burkham, D. E., and Dawdy, D. R. (1980). “General study of the modified Einstein method of computing total sediment discharge.” U.S. Geological Survey, Water-Supply Paper 2066.

Chien, N., and Wan, Z. (1983). Mechanics of sediment transport, China Science Press, Chinese Academy of Sciences, Beijing, China.

Chien, N., and Wan, Z. (1999). Mechanics of sediment transport, Trans. J. S. McNown. ASCE Books, Reston, VA.

Colby, B. R., and Hembree, C. H. (1955). “Computations of total sediment discharge, Niobrara River near Cody, Nebraska.” Water-Supply Paper 1357, U.S. Geological Survey, Washington DC.

Colby, B. R., and Hubbell, D. W. (1961). “Simplified methods for computing total sediment discharge with the modified Einstein procedure.” Water-Supply Paper 1595, U.S. Geological Survey, Washington DC.

Einstein, A., and Infeld, L. (1938). The evolution of physics, Princeton University Press, Princeton, NJ.

Einstein, H. A. (1944). “Bed-load transportation in Mountain Creek.” Soil Conservation Service Report SCS-TP-55, U.S. Department of Agriculture, Washington, DC.

Einstein, H. A. (1950). “The bed-load function for sediment transportation in open channel flows.” U.S. Department of Agriculture, Soil Conservation Service, Tech. Bulletin No. 1026, Washington, DC.

Einstein, H. A. (1973). “The Rhein study.” Chapter 4. Environmental impact of rivers, H. W. Shen, ed., Pub. by H. W. Shen, Fort Collins, CO, 4-1–4-17.


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Einstein, H. A., Anderson, A., and Johnson, J. (1940). “A distinction between bed load and suspended load.” Trans. Amer. Geophysical Union, 628–633.

Einstein, H. A., and Barbarossa, N. L. (1952). “River channel roughness.” Trans. ASCE, 117(1), 1121–1132.

Garcia, M., ed. (2008). Sedimentation engineering: Processes, measurements, mod-eling, and practice, Manual of Practice 110, ASCE Books, Reston, VA.

Graf, H. W. (1971). Hydraulics of sediment transport, McGraw-Hill Book Company, New York.

Graf, H. W. (1998). Fluvial hydraulics: Flow and transport processes in channels of simple geometry, J. Wiley and Sons, New York.

Guo, J., and Julien, P. Y. (2004). “Efficient algorithm for computing Einstein inte-grals.” J. Hydraul. Eng., 130(12), 1198–1201.

Heimann, D. C., Sprague, L. A., and Blevins, D. W. (2011). “Trends in suspended sediment loads and concentrations in the Mississippi River Basin, 1950–2009.” USGS Scientific Investigations Report 2011-5200, U.S. Geological Survey, Reston, VA.

Kennedy, J. F. (1983). “Reflections on rivers, research, and Rouse.” J. Hydraul. Eng., 109(10), 1253–1271.

Leopold, L. (1994). A view of the river, Harvard University Press, Cambridge, MA.

Meyer-Peter, E., Favre, H., and Einstein, H. A. (1934). “Neuere versuchsresultate über den geschiebetrieb.” Schweizerische Bauzeitung, 103(13), 147–150.

Meyer-Peter, E., and Müller, R. (1948). “Formulas for bed-load transport.” Proc. Intl. Assoc. for Hydraulic Research, Second Meeting, Stockholm, Sweden, IAHR, Stockholm, 39–64.

Nakato, T. (1984). “Numerical integration of Einstein’s integrals, I1 and I2.” J. Hydraul. Eng., 110(12), 1863–1868.

Rouse, H. (1976). Hydraulics in the United States, 1776–1976. Iowa Institute of Hydraulic Research, University of Iowa, Iowa City, IA.

Shen, H. W., ed. (1971). River mechanics I and II. 2 Vols., Pub. by H. W. Shen, Fort Collins, CO.

Shen, H. W., ed. (1972). Sedimentation (Einstein), Proceedings of Symposium to Honor Professor H. A. Einstein, June 17–19, 1971, Pub. by H. W. Shen, Fort Collins, CO.

Shen, H. W., ed. (1973). River mechanics III: Environmental impact on rivers, Pub. by H. W. Shen, Fort Collins. CO.

Shen, H. W. (1975). “Hans A. Einstein’s contributions in sedimentation.” J. Hydraul. Div., 101(5), 469–488.

Shen, H. W., and Kikkawa, H. (1980). Application of stochastic processes in sedi-ment transport, Water Resources Publications, Littleton, CO.

Shen, X. (2004). “Ning Chien: His life and recent book.” Journal of Sediment Research, 5, 77–83.

Vanoni, V. A., ed. (1975). Sedimentation engineering. Manual of Practice 54, American Society of Civil Engineering, New York.


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epilogue 301

Endnotes

1 Table E-1 lists some of the rivers and streams that engaged Hans Albert Einstein’s expertise. It summarizes approximate values of water flow rate and sediment transport rate associated with these rivers, doing so to indicate the range of channel sizes with which he worked and to give the reader a feel for the magni-tudes of water and sediment conveyed by a range of rivers and streams. Annual values of flow and sediment transport can vary markedly for any river and stream; accurate measurements of sediment transport are commonly rather difficult to obtain. A particularly useful reference is Heimann et al. (2011), which indicates the long-term variation of suspended-sediment load in the extensive watershed of the Mississippi River. As various engineering works throughout the basin were completed, many parts of the Mississippi River watershed experienced substantial reductions in suspended sediment load.

2 For example, Colby and Hembree (1955), Colby and Hubbell (1961), Bishop et al. (1965), Burkham and Dawdy (1980), Nakato (1984), and Guo and Julien (2004) further developed the Einstein method. Brownlie (1981), how-ever, developed a purely empirical method very scantily clad in mechanical concepts.

One of the other methods resulted from Meyer-Peter’s project concerning the Alpine Rhine. When Hans Albert left for the United States in 1938, Meyer-Peter still needed a method for predicting the sediment transport capacity of a narrowed Alpine Rhine. Hans Albert and Meyer-Peter had begun developing a simple method (Meyer-Peter et. al. 1934), but Hans Albert’s doctoral research had diverted him toward the mechanics of bed-sediment movement and left this method unfinished. A subsequent student, Robert Müller, worked further on the method and presented it as the Meyer-Peter and Müller bed-load method (Meyer-Peter and Müller 1948). Their essentially empirical method is simpler than the Einstein method but only gives an estimate of bed load, not total load.

3 Shen (1975) lists the following 13 prominent contributions: “This paper examines some of Einstein’s major contributions to the field of sedimentation. Einstein was the first (together with his colleagues) to: (1) Establish the separation of washload and bed material load; (2) separate alluvial bed roughness into form resistance and grain resistance; (3) determine the variation of form resistance with flow; (4) establish experimentally the continuous exchange of bed load particles in motion and the particles on bed layer; (5) apply stochastic analysis to sediment transport analysis; (6) formulate a stochastic model for sediment bed load trans-port; (7) introduce the importance of instantaneous lift force on particles and conduct experiments to determine its values; (8) relate the probability of particle motion to flow parameter; (9) relate the probability of particle motion to sediment transport rate; (10) introduce hiding factors for lift force correction in sediment mixture (nonuniform sizes); (11) recommend a comprehensive procedure to calculate sediment transport rate; (12) relate bed load rate to the integration of


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Table E-1. Approximate annual quantities of water flow and sediment transport by rivers (large and small) studied by Hans Albert Einstein

River or Stream

Average Annual Rate of Water Flow(m3/s)

Total Suspended Sediment Load(Bed-Sediment and Wash Load)(million metric tons/year)

Estimated or Measured Bed Load(metric tons/year)

Data Source

Alpine Rhine (at Diepoldsau, Switzerland)

230 5.0 0.1 million Einstein (1973)

Enoree River near Pelham, SC, 1994–2012

4 0.1 — USGS Site 02160326

Mountain Creek (South Carolina)

0.5 0.013 3,900 Einstein (1944)

Rio Grande (at Albuquerque, NM, 1970–1990)

42 1.4 5 to 8% of total load

USGS Site 08330000

Salinas River(at Spreckels, CA)

10 1.9 — USGS Site 11152500

Missouri River (at Culbertson, MT)

260 5.6 — USGS Site 06185500

Missouri River (at Hermann, MO, before 1953)

2,800 284 5 to 8% of total load

Heimann et al. (2011)

Arkansas River (at Little Rock, AR, before 1962)



Mississippi River (at Tarbert Landing, MS, before 1953)



Atchafalaya River (at Simmesport, LA, before 1953)



Notes: These estimates are approximate and are meant to indicate approximate relative magnitudes of flows and sediment transport. Some sites show high variability of water flow rates and sediment loads (especially the Salinas River).Measurements of bed load are not common at most sites. The percentage of bed load to total load is usually lower for larger rivers (e.g., Heimann et al. 2011). The suspended load for Mountain Creek is estimated based on the creek’s flow relative to flow in the Enoree River, which is in a similar watershed. Typically, wash-load scales only loosely with flow rate in a channel. The United States Geological Survey (USGS) gives water flow and sediment transport data for river and stream gage sites across the United States. The sites can be accessed via the web interface <http://waterdata .usgs.gov/usa/nwis/rt>.


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epilogue 303

suspended load; (13) present a graphical solution and integrate the total sus-pended load. Although not covered in this paper, Einstein also made significant contributions on secondary currents, erosion and deposition of cohesive material, flow fluctuations in viscous sublayer, transport of bed particles due to oscillating flow motion, vorticity, deposition of suspended particles in a gravel bed, sediment transport in pipes, and many others. His influence in sedimentation cannot be overstated.”

4 A useful paper on Ning Chien’s career is Shen (2004).


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Hans Albert Einstein (His Life as a Pioneering Engineer) || Epilogue