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.

This commentary on Robin's Principles of gunnery is one of the major sources: This wired article is another, which mentions Magnus observing cannonballs. Nothing I have found so far gives any evidence of the Magnus effect being observed in a real battle situation. I can't even find any evidence of Magnus actually having observed the effect in cannonballs in or out of the arena of battle.

To clarify. I'm not looking for examples of where the Magnus effect has been exploited in the battlefield, but rather of examples in which it (or some deviation which was later recognised as the Magnus effect) was observed.

  • 5
    "I've read a lot about the Magnus effect altering the trajectories of cannonballs and musketballs." Where did you read about this? Please let us know where you have looked already so that people trying to answer don't waste time looking in places you've already checked. Aug 16 '19 at 9:12
  • 4
    @TomLancaster Please don't answer in comments. Just edit the requested information into your question. Aug 16 '19 at 10:06
  • 1
    "Overall, the effect of the Magnus force on a bullet's flight path itself is usually insignificant compared to other forces such as aerodynamic drag." -- en.wikipedia.org/wiki/Magnus_effect#In_external_ballistics Aug 16 '19 at 10:48
  • 4
    The magnus effect has certainly been experienced in the battefield, because that was what prompted Magnus to study the phenomenon, but I doubt that any artillery commander ever saw a cannonball going astray and thought "Oh, what a nice example of the Magnus effect!! I'm going to document it". At best you'll find some reports complaining of the general accuracy of a weapon.
    – Rekesoft
    Aug 16 '19 at 11:12
  • Clarification: Are you looking for references where others merely observed and commented on witnessing the effect, or are you looking for attempts to deliberately exploit the effect? [Like some artillery officer trying to use it to drop shot behind some cover, or extend range, to hit a target that they would have otherwise missed? - An effect sometimes used in modern paintball.] Aug 16 '19 at 21:47

Making use of the Magnus effect in the era of round cannonballs fired from unrifled cannon was impractical. The rotation of the ball is caused by minor irregularities on the surface of the ball, and in the barrel of the gun. That means that the rotation is on a random axis, and at a random speed, or certainly should be. If it isn't, the cannon has a constriction or a bulge in its barrel, and is liable to burst. A randomly rotating ball won't behave predictably enough to make use of the effect.

Once artillery had switched to elongated projectiles in rifled guns, the Magnus effect become noticeable for long-range gunnery, and was incorporated into fire-control systems. The US Navy's Mk38 Gunfire Control system, used in the Iowa-class battleships late in WWII, incorporated Magnus effect corrections in its Mark 8 Rangekeeper, an electro-mechanical analogue computer.

  • Despite it being a baseball analogy, I believe your first paragraph is far more accurately expressed as "smooth bore guns fire knuckle-balls; rifled barrels fire sliders (high velocity) and curve-balls (low velocity)". Aug 17 '19 at 13:01
  • 1
    @PieterGeerkens: The OP tagged it "physics", so I've given a physical explanation. I don't know enough about baseball to evaluate your analogy. Aug 17 '19 at 13:08
  • Here is a link that explains the Magnus Effect on cricket bowling, if that helps. Your statement of "the rotation is on a random axis" I believe to be inaccurate - it is the very absence of spin that introduces the observed instability of trajectory - a la a kunckleball. Wasn't wobblie or something similar the traditional cricket terminology for a ball bowled with no spin? Aug 17 '19 at 13:12
  • If you can handle the physics here is a 2006 Phd thesis that analyzes NATO state of the art in artillery ballistics calculations. I am working on an answer from it right now. Aug 17 '19 at 13:16
  • @PieterGeerkens: No, cannonballs almost always had some rotation in flight. It wasn't designed into them or the gun, but it happened. It would very rarely be about an axis along the trajectory, so it wouldn't stabilise the trajectory as rifling does. It was also slower than rifling-induced rotation. If cannonballs did not rotate, how could Magnus have observed his effect on them? Aug 17 '19 at 13:24

For firearms the main Magnus effect is on range, in particular the range at which the bullet drops from supersonic to subsonic. (The direction of crosswind relative to orientation of barrel rifling either increases or decreases range - similar to a topspin/backspin effect.) Thus it is usually only necessary to account for in extreme long-range sniping. This effect was known and well understood before such became commonplace in the late 20th century. Prior to then the Magnus Effect's would have affected battles only as a reduced (below theoretical) range for accurate sniping.

For artillery fire the Magnus Effect is more pronounced, mainly because the time of flight is increased. However it remains only comparable to the Coriolis Effect in magnitude (though non-hemispheric).

A 2006 PhD Thesis - Development of an Artillery Accuracy Model - by Chee Meng Fann at Naval Postgraduate School at Monterey, California, compares several trajectory models in use at that time. After defining the various ballistics phases and noting the physical forces acting on an artillery projectile, Fann notes:

The trajectory of a projectile can be modeled using different methodologies. The common methodologies are the Zero Drag Model, the Point Mass Model, and the Modified Point Mass Model.


The point mass model, which is used in this thesis, takes into consideration the drag and environmental effects and is able to provide relatively accurate results with limited computing capacity. The trajectory prediction can be further improved with increasing degree of freedom (DOF) in the point mass model. The simplest point mass model is the two degree of freedom (2 DOF) model which has the drag and the gravity components. The 2 DOF can be enhanced by the inclusion of the deflection motion. On the other hand, the modified point mass model is complex. It has five degree of freedom but is capable of predicting the trajectory with good accuracies. However a modified point mass model requires more computing resources.


2. Modified Point Mass Model
The modified point mass model is a compromise between a simple point mass model and a computationally intensive 6 DOF point mass model. In the modified point mass model, the effects due to the spin rate of a projectile are included.

Fann next provides significant description of the various trajectory models, with a comparison of their accuracy, finally concluding:

  1. A 3 DOF model is sufficient to show the general behavior of the trajectory of an artillery-fired projectile. However, it cannot predict the drift as accurately as the modified point mass model. ....

  2. A 3 DOF trajectory model is easy to implement and the computation is less intensive that the NABK model, which is a 5 DOF model. The simplicity of the 3 DOF model enables greater insight into the mechanics of the trajectory, which the 5 DOF does not, while still producing accurate results.

In particular, Fann notes that:

  1. In MPI error for range, the major contributors to the accuracy results are the muzzle velocity and the range wind.

  2. ....

  3. .... For instance, if the muzzle velocity can be better controlled, the accuracy error will reduce. This is similar for meteorological conditions. The error budgets for wind, density, and temperature will reduce if the staleness hour is small.

Thus as recently as 2006 the computational resources required for an artillery trajectory model accounting for Magnus and Coriolis Force were of uncertain value, with variations in muzzle velocity and accuracy in meteorological conditions resulting in significantly greater error by comparison. Also, as the Magnus effect increases with wind speed, staleness of meteorological data simultaneously effects both the Magnus Effect and the much greater wind drift, accuracy is improved by the simple expedient of improving meteorological data, regardless of whether Magnus is explicitly accounted for - while attempting to account for Magnus with stale wind data is meaningless.

Thus while Magnus was able to observe the eponymous effect in 1852 - on a clear range, with white powder, of single shots - the errors introduced by shot-to-shot variations in crosswind, muzzle velocity, barrel windage and temperature would remain far more significant right past World War One. For example, Byng and Currie in 1917 at Vimy Ridge greatly increased effectiveness of the Canadian walking barrage (in particular, by preventing it from walking backward after a few dozen shots) through a simple expedient: calibrating thermal adjustments for every gun individually instead of by date of manufacture, thus accounting for individual variations in barrel wear.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.