I've read a lot about the Magnus effect altering the trajectories of cannonballs and musketballs. Robins noticed it with Musket balls and Magnus with canonballs, but presumably they weren't the first to notice. Does anyone know of any examples of where the Magnus effect was noticed in the theatre of war itself, and if so, any effects it had on the battle?


I am afraid nobody noticed it, because nobody could have noticed it. A deviation is only a deviation when one has something that it is a deviation from. To "notice" the Magnus effect one has to operate from a theory that predicts a parabolic trajectory, and be able to separate the subtle deviations caused by spin from other deviations. Hall even wrote that the smoothbore "gun itself was so inconsistent in its behavior that great accuracy in preliminary work, even in the lay of the gun itself, was labour in vain". So it is not something that can be simply "observed" without theoretical analysis, and the prerequisites for that were not in place prior to Newton. If then, since it requires fluid mechanics. Even after that, separating the Magnus effect from everything else required careful experimental setups impossible in real battles. Robins (1747), Magnus (1852), Lafay (1912) all staged controlled experiments to "observe" the effect, or rather to confirm theoretical predictions that took it into account.

Tartaglia, for example, depicted trajectories of cannonballs as straight line segments connected by a circular turn to vertical descent. Even Galileo in Two New Sciences (1638) treated "these violent shots" as a special case, mentioned that the “beginning of the parabola” may be flatter, listed a number of complicating factors, and admitted his inability to calculate their effects. As Brugh summarizes in Ballistics in Renaissance Science:

"The Magnus effect (1852) and Bernoulli’s principle (1738) have helped to explain the inaccuracy of smoothbore ballistics in retrospect, but the operators of early modern firearms were more interested in developing battlefield tactics for overcoming these shortfalls than explaining them. Since smoothbore weapons fired rounded shot from unrifled gun barrels, slight imperfections in the shot or the barrel could send the shot spinning on an axis, giving it unpredictable angular momentum... Thanks to the inaccuracy and unreliability of early modern firearms, tacticians and commanders of the sixteenth and seventeenth (even eighteenth) centuries took a stochastic approach to gunpowder weapons for both the infantry and artillery. Infantry and heavy cavalry units, especially in the late 1500s, developed tactics and drills like the countermarch, the caraçol, and weapons drill that sought to sustain high rates of fire on the battlefield in order to increase the chances of hitting targets."

Newton mentioned the effect in connection with tennis balls rather than warfare in a 1671 letter to Oldenburg, but he more speculated than observed it:

"I remembered that I had often seen a tennis ball struck with an oblique racket describe such a curved line. For a circular as well as progressive motion being communicated to it by that stroke, its parts on that side where the motions conspire must press and beat the contiguous air more violently, and there excite a reluctancy and reaction of the air proportionately greater."

So it is not surprising that no real "observations" are known before Robins "who was in gunnery what the immortal Newton was in philosophy, the founder of a new system deduced from experiment and nature, the service of artillery was a mere matter of chance, founded on no principles, or at best, but erroneous ones", as an artillery officer wrote in 1789. In particular, Robins was first to account for various effects of the air-resistance on high-speed projectiles, and to separate the effects of the spin. His best known work is New Principles of Gunnery (1742), but the "Magnus" effect is predicted and illustrated experimentally in Of the Nature and Advantage of Rifled Barrel Pieces presented to the Royal Society in 1747. Here is from Steele's Muskets and Pendulums: Benjamin Robins, Leonhard Euler, and the Ballistics Revolution:

"In one of his experiments, he bent a fixed musket barrel a few degrees to the left. The bullet he shot had a trajectory that completely coincided with his theory. The bullet holes in the tissue-paper curtains showed that the bullet first began moving toward the left, in the direction of the musket's deflection. Eventually the bullet reversed its lateral direction of motion and crossed to the right side of the musket. Robins explained this apparent paradox by noting that the deflected musket forced the bullet to rotate from the left to the right. This would cause the air flow to be greater on the right-hand side; hence, the friction or "pressure" force pushed the projectile to the right, which its trajectory demonstrated. This phenomenon is now called the Magnus effect, named after a 19th-century German physicist who investigated it with full knowledge of Robins's work."

While Robins's explanation is very similar to Newton's, he was first to back it up by theoretical calculations and a convincing experiment.

  • $\begingroup$ Firstly, thanks for such a detailed answer @Conifold. You positted that "To "notice" the Magnus effect one has to operate from a theory that predicts a parabolic trajectory, and be able to separate the subtle deviations caused by spin from other deviations. " Forgetting about the vertical motion (so no need for understaanding parabolas) wouldn't Newton's First law have suggested the shot should not have deflected horizontally? If people were aiming at long distances an misssing by a long way wouldn't they have thought something amiss, even if they couldn't explain it? $\endgroup$ Aug 16 '19 at 9:18
  • $\begingroup$ Is what you are saying that no-one noticed because in the heat of battle they never saw precisely where their shots landed, and even if they did they couldn't distinguish the magnus effect from other defectsin the weaponry? I suppose when firing of a cannonball, for example, as long as it hits the ship somewhere it doesn't really matter where? $\endgroup$ Aug 16 '19 at 9:22
  • $\begingroup$ @TomLancaster It is not really about the heat of battle. As Brugh says, everybody noted low accuracy and scatter, but they had no way of pinpointing the cause(s) with the low quality of weapons and very rudimentary understanding of aerodynamics, as Galileo admitted. The horizontal deflection could be (and often was) caused by a slight asymmetry in the weapon itself, or in the gunpowder discharge, etc. Even expecting the spin effect, one needed to control for confounding factors. Robins was very clever having the musket bend work against the spin to convince people of its existence. $\endgroup$
    – Conifold
    Aug 16 '19 at 10:16

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