HISTORICAL NOTES CURRENT SCIENCE, VOL. 86, NO. 7, 10 APRIL 2004 1033 Robins–Magnus effect: A continuing saga Tapan K. Sengupta and Srikanth B. Talla The experimental observation by Robins, that a projectile spinning about its axis of travel experiences a transverse force (lift) due to a cross-flow was refuted by Euler purely as a contradiction to expected symmetry of fluid flow. This undoubtedly had taken away the precedence of finding this effect by Robins and subsequently the same was credited to Magnus—a testimony of intuition overtaking physical observation. In the last century, Prandtl looked at this problem once again and came up with a maximum lift value that a section of a spinning projectile (cylinder) experiences due to cross-flow. This proto-typical model is extensively used to explain the aerodynamic phenomenon of lift generation. However, in recent times experimental and numerical investigations have identified a new temporal instability for this flow at high rotation rates that sets the lift generation process for spinning axi-symmetric bodies exceeding the above maximum limit. In this note, we trace the origin of this particular effect to its present day status with respect to flow past a rotating cylinder. The beginning Benjamin Robins’ contribution 1 to fluid mechanics and aerodynamics has recei- ved less recognition than it deserves due to various reasons. One of the major rea- sons is that he propounded too many new ideas in a short span of time and he was also busy defending Newton’s contribu- tion to calculus. He was largely a self- taught person with a desire to take up teaching profession. Upon proving New- ton’s ‘Treatise of quadratures’, he was elected Fellow of the Royal Society, London at the early age of twenty. How- ever, he switched his attention to engi- neering by constructing bridges, mills, harbours, making rivers navigable and draining fens. That he had multifaceted talent is evident, when one notes that he is now acknowledged as the father of sci- ence of ballistics 2,3 (introducing the con- cept of rifling the bore of guns, holding the importance of air-resistance in decid- ing the range of artillery shots and im- proving the accuracy of projectiles by spinning them), credited for fundamental contributions to aerodynamics 4 (the com- plex relationship between drag, shape of the body, its angle of attack and air– velocity could not be explained by the then simple theory propounded by New- ton and he suggested that ground testing of vehicle is a prerequisite for a success- ful design), experimental fluid mechan- ics 1,4 (developing the whirling arm, the predecessor of present day wind tunnels, the only experimental device at that time and ballistic pendulum for the measure- ment of velocity of projectiles) and his many contributions to mathematics. He also noted the drag rise at transonic flight regime almost 200 years ago, before its importance was re-discovered around the Second World War 4 . Additionally, he dabbled in contemporary politics and also got involved in controversies related to writing the accounts of Lord Anson’s voyage around the world. To this, one must add the fact that he left the centre- stage of England, when he was appointed the engineer-general of the East India Company to improve the fortifications at St. David, Madras, where he died of fe- ver at an early age of forty-four. In writ- ing the book on ballistics 2 , he recorded the experimental observation (with bal- listic–pendulum and whirling arms) that a spinning projectile experiences a nor- mal force due to cross-wind. It is clear that in the absence of cross-flow, a proje- ctile at zero incidence will not experience any side-force or lift. It was, however, not clear why a lift force will be experi- enced due to cross-flow. Existence of such a lift force due to cross-flow was not supported by Euler, the leading hy- drodynamicist of the time, and this effect was rediscovered by Magnus 5 , almost a century later. In this note, we will dis- cuss this particular effect with respect to flow past a rotating cylinder starting with Robins’ work to its present day status. It is incorrectly stated in some refer- ences 6 that Robins was responsible for finding the lift force acting on a rotating sphere. Undoubtedly, he experimented on spherical shots used for artillery pur- poses, but he was also first to suggest that a teardrop or egg-like shape of pro- jectile with a centre of gravity near the front of it. The observation of Robins’ for spinning projectiles was made using the whirling arm – not a very satisfactory experimental device by the present day standard. A whirling arm was used to measure aerodynamic forces at low speed, where the tested body was used to be hung at the end of a long arm that was free to rotate. This arm was rotated by a falling weight via a shaft with cable– pulley arrangement. The rotation of the arm produces the relative motion in air, the same principle that is even used today in wind tunnels to measure forces for steady flight. However, sustained rota- tion of whirling arm will impart angular momentum to the surrounding air, thereby making the accuracy of such measure- ments a point of concern. It is with this equipment that he reported his findings 2 in 1742. It is noted 4 that, Euler was so excited about Robins’ book that he per- sonally translated it into German in 1745 adding some commentary . . . . Euler’s interest in Robins’ work was both a hin- drance and a help. The hindrance con- cerned Robins’ observation of the side force exerted on a spinning projectile moving through the air. Euler considered that to be a spurious finding, due to manu- facturing irregularities in the projectile. Recognized as the dominant hydrody- namicist of the eighteenth century, Euler far overshadowed Robins, and thus Rob- ins’ finding was not taken seriously for another century, until Gustav Magnus (1802–1870) verified the phenomenon as a real aerodynamic effect. This book 2 was also translated into French in 1751, the year of Robins’ death. It is to be noted that Napoleon read the latter translation from Euler’s German translation of the original book 5 , while he was a young ar- tillerist at Auxonne, France. It must be pointed out that both Euler and Robins had mutual admiration for each other’s work. For example, Robins published in 1739 Remarks on M. Euler’s