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:
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. ....
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
In particular, Fann notes that:
In MPI error for range, the major contributors to the accuracy results are
the muzzle velocity and the range wind.
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.