Classics in physical geography revisited
Haim Tsoar
Progress in Physical Geography 18, 1 (1994) pp. 91-96
Bagnold, R.A. 1941: The physics of blown sand and desert dunes. London: Methuen.

Links and pictures were added by Hezi Yizhaq.

"sense-impression - the hot varnish smell of a car standing in the sun, a cloudless sunset, the finding of sand grains in the pocket of an old coat. Out comes the map again; and the eye hovers over some blank space still further away which nobody has ever reached. Happy calculations follow about petrol and distances - dreams of just one more desert trip."
RA Bagnold, Libyan Sands, 1935
The modern study of geomorphology has its foundations in nineteenth-century Europe and it is natural and obvious that little attention was paid by the European landform scientists to aeolian processes of desert. Relatively little interest and inquisitiveness therefore, were shown in aeolian processes during the first half of the twentieth century. The several books and articles that were published on aeolian sand dunes during that period were merely descriptive and made no reference to the fundamental processes of aeolian sand transport and dynamics, and formation of aeolian bedforms.
As a soldier, engineer and explorer, Bagnold possessed an inquisitive mind, and was the first to change the study of aeolian sand transport and sand dunes from descriptive to processes orientated. By being neither a scientist according to formal standards, nor a professional geomorphologist, Bagnold had the advantage of studying the processes of blown sand and desert dunes with an open mind, uninhibited by any traditional ideas. The result is a book that combines unique field observations in remote desert areas, with wind tunnel simulation experiments and physical process analysis of airflow. The book is a landmark in geomorphology, by being an early precursor of a new attitude to research based on dynamic processes.
Maps of expditions
Ralph A. Bagnold Biography
Bagnold number
Important people in LRDG History
Searching for Zerzura
In Retrospect: the physics of sand dunes
For three decades after the book was published, very little interest was shown in aeolian transport of sediments by researchers in geomorphology and sedimentology, so that, for 40 years, Bagnold's book was the only authority and reference in the field of physics of blown sand and desert dunes, and a second textbook on aeolian processes was published only 44 years after 1941. After the second world war, Bagnold himself lost interest in blown sand and desert dunes, and turned his curiosity to the problems of sediment transport by water. Bagnold's work was rediscovered at the end of the 1970s by a group of scholars in Denmark, USA and UK, as a consequence of a significant international increase in interest in aeolian studies, as well as the result of development of boundary-layer wind tunnels, improved high-precision instruments and application of modem mathematical and statistical techniques.
The Lybian Desert Home page
Desert Eco Tours
Holland, Shaw (standing), Newbold, Dwyer, Bagnold.
The book has three parts: the first deals with the physics of sand transport; the second with grain-size analysis and ripple formation; and the third with sand dunes. The first part, which comprises about 40% of the book, is the only portion based on experiments and physical principles of fluid dynamics. Bagnold did his simu1ation work at a time when the velocity pattern of turbulent fluid flow in the boundary layer became known through the pioneering work of Prandtl (1935) and von Karman (1934; 1935). Bagnold's book is the first textbook in dynamic geomorphology to deal with the processes of fluid (wind) action on a sediment as a problem of fluid dynamics. The physics and mathematics he uses for calculations are simple, clear and easy to understand by scholars as well as students with a limited background in these subjects. This talent and ability of Bagnold's to present simple quantative explanations of aeolian processes can be found all over the book.

In the first chapter, Bagnold commences with a classification of wind-blown particles.
Where most sedimentologists before Bagnold used arbitrary limits of grain sizes to distinguish between sand and dust or sand and pebbles, Bagnold found a quantitative dynamic way to define these limits. According to him, the limit between sand and pebbles is when grains are not movable, either by direct shear stress of the wind or by the impact of other moving grains. The distinction between sand and dust is according to the grains' terminal velocity of fall. However, Bagnold realized that these limits are not practical, as they are changed, not only by the grain size, but according to the shape and density of the grain as well. Therefore, he uses representative values of these limits calculated for quartz spheres, and refers to them as typical values, that have been used by sedimentolog1sts and geomorphologists ever since.
Bagnold's perception of the process of saltation - as a steady cloud of sand moving by bounds along the surface and gaining energy from the wind's pressure to make up for the impact energy losses - is the basis for all new advanced models of aeolian sand transport made in the last few years (McEwan and Willetts, 1991; Werner, 1990; Ungar and Haff, 1987; Anderson and Haff, 1988; 1991; Sørensen, 1991). However, empirical estimations by the above mentioned researchers have indicated that the equilibrium value at which the grains transfer all momentum from the wind to the bed, is not as assumed by Bagnold, because the cloud of grains transported in equilibrium with the wind consists of grains that are splashed up by impact to much lower elevation and much shorter jump length than ordinary saltating grains. These grains gain very little momentum from the wind, hence their impact speed is so low that they can, in most cases, neither rebound nor eject other grains.
Camp 9. in the Great Sand Sea
In his wind-tunnell observation, Bagnold has indeed distinguished between ejected slow speed grains that rise almost vertically, and grains that have clearly ricocheted off the surface and continued forward at a flat angle without losing much speed. However, Bagnold has pointed out that no exact distinction exists between the motion of the surface grain (surface creep) and those grains in saltation whose paths through the air are very low. This differentiation has recently been sharpened by Mitha et al. (1986), Ungar and Haff (1987) and others who dubbed this short trajectory, low-energy ejecta by the, term 'reptation'. The perception of reptation, which has only recently been recognized, provides a new insight into understanding models of sand transport and impact ripples (Anderson, 1987; 1990).
Extricating a light car with rope ladders.(1930)
The proportion of surface creep sand of the total sand transport as measured by Bagnold who used surface creep traps in the wind tunnel and the field, is 20% to 25%. Anderson et al. (1991) hold the opinion that this proportion is exaggerated, as Bagnold's creep traps, by their very construction, catch mainly reptating and saltating grains. Chapter 4 of the book gives the reader a background in the nature of surface airflow and fluid mechanics. It would be better to have this chapter at the beginning of the book to make the processes described in chapters one to three clearer.
Mathematical models of dunes (Hans Hermann website)
An article on dunes formation by Haim Tsoar (in Hebrew, published in 1982)
Bagnold was aware to the problematics of the wind-tunnel results and decided to verify them against the reality of the natural conditions in the desert. In 1938 he conducted wind profiles and sand flow measurements over an open dune surface in the Egyptian-Libyan desert. The results of these measurements, given in Chapter 6, were found by Bagnold to agree well with those achieved in the wind-tunnel experiments. In his open field measurements, however, Bagnold did not realize the importance of bursts (eruptions) and sweep sequences in the boundary layer, that generate a large Reynolds stress and play an important role in the initiation of saltation. The structure of bursts and sweeps in space, time and scale are different from the relatively orderly flow pattern found in the wind tunnels. The values of U*t found in the wind tunnel cannot, therefore, reconcile field results (Anderson et at., 1991).
Boustead, Sandford, Bagnold, Paterson, Prendergast, Craig, Shaw, Harding-Newman.
In the second part of the book Bagnold deals with the distinctive size distribution of aeolian sand deposits. Several years before the book was published, Krumbein (1934) introduced a simple and rational f scale of grain sizes in which the log-normal distribution of sand deposits turns into normal distribution by taking -log2d (d is the grain diameter in mm). The f scale became the standard conventional method in which grain-size distribution is analysed. Bagnold introduced a different grain-size distribution in which both the grain-size and grain-frequency scales are transformed logarithmically (Bagnold used log10) and achieved a hyperbola-shaped curve for-which he found four parameters characterizing hyperbolic curve. This method of plotting and analysing grain-size distribution was completely ignored by sedimentologists, mostly because it is more intricate statistically. In the late 1970s when interest was revived, statisticians found that many natural distributions more closely approximate a log-hyperbolic distribution than lognormal distribution (Barndorff-Nielsen1, 1977).
Extricating a stuck lorry with the help of steel channels. Craig on left, Prendergast facing, Bagnold on right.
The fact that most aeolian sand is far from being log-normally distributed, while being very well described. by the log-hyperbolic distribution, has recently made the later distribution a more powerful method for dynamical interpretation or sand dunes as was shown by Bagnold in 1941 (Bagnold and Barndorff-Nielsen, 1980; Barndorff-Nielsen and Christiansen, 1988; Haitmann and Christiansen, 1988).
Gilf Kebir
The recent, new, conceptual model of aeolian saltation, that emphasizes the effect of the low-energy ejecta of reptation, suggests a new theoretical model for aeolian ripples (Anderson, 1987; 1990). This new model indicates that, while ripple wavelengths are affected by grain trajectory lengths, they do not correspond with (characteristic path length in saltation. Anderson claims that ripple spacing is influenced by the probability distribution of the total trajectory population, in which low-energy reptated grains outnumber higher saltating grains by about nine to one. According to this model, the ripple wavelength should be approximately six times the mean reptation path length [more accurate this is the fastest growing wavelength at the initial-linear stage, and the final wavelength may differ due to a coarsening process, Hezi Yizhaq].
Mathematical model of aeolian sand ripples
While the first and second parts of the book reflect Bagnold's brilliant scientific side, the third part also shows Bagnold the explorer and adventurer. Because of the difficulties in conducting experimental simulation on sand dunes in the wind tunnel, no knowledge of physical background on flow over hillocks and no data are available about long-term wind regime in deserts, this third part is based, therefore on observations and inferences.

Based on rate of sand transport, Bagnold first gives explanations to the basic phenomenon of sand accretion and the self-accumulation of aeolian sand into dunes, which have not been disputed since. Bagnold does not find the description of sand dunes landscapes enough and gives some brilliantly simple theoretical models for the relation between rate of sand removal; rate of dune advance and surface slope, or the rate of slip face advance, that was later tested in the field by several investigators, and found to be correct.
The classification of sand dunes, as given in the book, cannot be applied to all world sand fields, being based entirely on the observation made in the Libyan Desert. However, by excluding dune types related to vegetation we find Bagnold's classification very similar to modern classifications (pye and Tsoar, 1990: 162).

Lack of knowledge of flow pattern around obstacles prevents Bagnold from better understanding sand accumulation related to obstructions. For example, windward accretion of sand (echo dune) is interpreted by Bagnold as sand grains which strike the obstacle, ricochet off it, and come to rest in the relatively stagnant air in front~ and not by the reverse flow eddy formed in front of the obstacle (Tsoar, 1983a). He was not aware also of the importance of the lee-side eddies of sand dunes in determining processes of sand transport and deposition. In his model of sand advance, all the sand coming over the crest falls in the lee-side like snow flakes, because of the still air inside the wind shadow. This lack of awareness to lee-side eddies, led Bagnold to introduce an improper model for the transition from barchan to seif dune by bi-directional wind (Tsoar, 1984).

Many of the world's desert coastal dunes are widely covered by transverse dunes (e.g., Inman et al., 1966; Tsoar, 1990), while in the book, this dune types virtually ignored on the ground of the instability of long transverse dune. The description of this instability with the resulting blowout is similar to that of the formation of blow outs and parabolic dunes in vegetated sandy areas, which is not covered thoroughly in the book., An attic analysis of barchan dune, which gives the foundation to many recent models (e.g., Howard et al., 1978) is followed by a description of seif dunes, that ignores the dynamical implication, of its devious shape (Tsoar, 1983b). Bagnold uses the term 'longitudinal' as synonymous with 'seif'. For many years, the term 'longitudinal' has been too closely used by many scholars and has been applied to linear dunes different in origin, morphologic details, and dynamics (Tsoar, 1989). Bagnold's vague description of the longitudinal dune is probably one factor in that confusion.
Jebel Uweinat
Bagnold gives simple models of the internal structure of sand deposits, based on some observations, together with the dynamical processes of sand erosion and deposition on sand dunes. The two processes, mentioned in the book, that bring about accretion (by grain fall) and encroachment deposits (by grainflow) are most important in understanding the internal sedimentary structure of aeolhin bedforms. A third process responsible for tractional deposits has been recognized by Hunter (1977) to be formed by aeolian climbing ripples. Bagnold's book was written at a time of little interest in and concern for the environment in general, and ecological changes in particular. The aim of his work was to study the free interplay of wind and sand, uncomplicated by the effects of moisture, vegetation, or fauna (p. xxi). Since vegetation for Bagnold is but a special kind of surface roughness' (p. 183), he does not thresh over the effect of vegetation on the morphology and dynamics of desert sand dunes. It is impossible therefore, to use Bagnold's work for understanding the morphology and dynamics of desert vegetated dunes such as the dune types found in the deserts of South Africa, Australia, Asia, California, Sinai and more.
Southern Gilf Kebir
Finally, I would like to make a personal observation. When, as a graduate student, I became interested in dynamics of aeolian sand and sand dunes, I had very little knowledge and background on the subject. This was due mostly to the fact that no one had offered us a course in aeolian processes or in fluid dynamics. Bagnold's book gave me the setting that two or even three courses of the subject would not have been able to provide.

Haim Tsoar
Department of Geography
Ben-Gurion University of the Negev
e-mail: or

Bagnold at Algodones sand dunes (Southern California) on February 1978 (photograped by Haim Tsoar)

Anderson R.S. 1987: A theoretical model for aeolian impact ripples. Sedimemology 34, 943-56.
- 1990: Eolian ripples as examples of self organization in geomorphological systems. Earth Science Reviews 29, 77-96.
Anderson, R.S. and Haff, P.K.1988: Simulation of eolian saltation. Science 241,820-23.
- 1991: Wind modification and bed response during.
saltation of sand in air. Acta Mechanica (Supplementum) 1,21-52.

Anderson, R.S, Sorensen, M. and Willetts, B.B.
1991: A review of recent progress in our understanding of aeolian sediment transport. Acta Mechanica (Supplememum) 1, 1-19.

Bagnold, R.A. and Barndorff-Nielsen, a. 1980:
The pattern of natural grain. size distributions. Sedimentology 27, 199-207.

Barndorff-Nielsen, O.E. 1977: Exponentially decreasing distributions for the logarithm of particle size. Proceedings of the Royal Society of London (Ser. A) 353,401-19.

Barndorff-Nielsen, O.E. and Christiansen, C.
1986: Erosion, deposition and size distributions of sand. Proceeditlgs of tire Royal Society of London (Ser. A) 417, 335-52.
Bagnold at Algodones sand dunes (Southern California) on February 1978 (photograped by Haim Tsoar)
Hartman, D. and Christiansen, C. 1988: Settling velocity distributions and sorting processes on a longitudinal dune: a case study. Earth Surface Processes and Land Forms 13, 649-56.

Howard, A.D., Morton, J.B., Gad-el-Hak, M. and Pierce, D.B. 1978: Sand transport model of barchan dune equilibrium. Sedimentology 25, 307-38.

Hunter, R.E. 1977: Basic types of stratification in small eolian dunes. Sedimentology 24,361-87.

Inman, D.L., Ewing, G.C. and Corliss, J.B. 1966:
Coastal sand dunes of Guerro Negro, Baja California, Mexico. Bulletin of the Geological Society of America 77, 787-802.

Karman, T. von 1934: Turbulence and skin friction. Journal of the Aeronautical Sciences 1, 1-20.
- 1935: Some aspects of the turbulence problem.
Proceedings of the 4th International Congress 011 Applied Mechanics, Cambridge 54-91.

Krumbcin, W.E. 1934: Size frequency distributions of sediments. Journal of Sedimentary Petrology 4, 65-77.

McEwan, I.K. and Willetts,. B.B. 1991: Numerical model of the saltation cloud. Acta Mechanica (Supplemelltum) 1, 53-66.

Mitha, S., Trail, M.Q., Werner, B.T. and Haff, P .K. 1986: The grain-bed impact process in aeolian saltation. Acta Mechanica 63, 267-78.

Prandtl, L. 1935: The mechanics of viscous fluids. In Durand, W.F., editor, Aerodynamic theory, Volume III. Berlin: Julius Springer, 34-208.

Pye, K. and Tsoar, H. 1990: Aeolian sand and sand dunes. London: Unwin Hyman.

Sharp, R.P. 1963: Wind ripples. Journal of Geology 71, 617-36.

Sørensen, M. 1991: An analythic model of windblown sand transport. Acta Mechanica (Supplemelltum) 1,67-81.

Tsoar, H. 1983a: Wind tunnel modeling of echo and climbing dunes. 111 Brookfield, M.E. and Ahlbrandt, T.S., editors, Eolian sediments and processes, Amsterdam: Elsevier, 247-59.
- 1983b: Dynamic processes acting on a longitudinal. (seif) sand dune. Sedimentology 30, 567-78.
- 1984: The formation of seif dunes from barchans a discussion. Zeitschrift fur Geomorphologie 28, 99-103.
- 1989: Linear dunes - forms and formation. Progress in Physical Geography 13, 507-28.
- 1990: Trends in the development of sand dunes along the southeastern Mediterranean coast. Catena (Supplement) 18, 51-60.

Ungar, J.E. and Haff, P.K. 1987: Steady state saltation in air. Sedimentology 34, 289-99.

Walker, J .D. 1981: An experimental study of wind ripples. Unpublished M.Sc. thesis, Massachusetts Institute of Technology.

Werner, B.T. 1990: A steady-state model of windblown sand transport. Journal of Geology 98, 1-17.
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