Editing Coriolis force (section)

===Ballistic trajectories===
The Coriolis force is important in [[External ballistics#Coriolis drift|external ballistics]] for calculating the trajectories of very long-range [[artillery]] shells. The most famous historical example was the [[Paris gun]], used by the Germans during [[World War I]] to bombard [[Paris]] from a range of about {{convert|120|km|sp=us|abbr=on}}. The Coriolis force minutely changes the trajectory of a bullet, affecting accuracy at extremely long distances. It is adjusted for by accurate long-distance shooters, such as snipers. At the latitude of [[Sacramento]], California, a {{convert|1000|yd|abbr=on}} northward shot would be deflected {{convert|2.8|in|abbr=on}} to the right. There is also a vertical component, explained in the Eötvös effect section above, which causes westward shots to hit low, and eastward shots to hit high.<ref name=Taylor0>The claim is made that in the Falklands in WW I, the British failed to correct their sights for the southern hemisphere, and so missed their targets. {{Cite book|title=A Mathematician's Miscellany |author=John Edensor Littlewood |page=[https://archive.org/details/mathematiciansmi033496mbp/page/n62 51] |url=https://archive.org/details/mathematiciansmi033496mbp |year=1953 |publisher=Methuen And Company Limited}} {{Cite book|title=Classical Mechanics |author=John Robert Taylor |page=364; Problem 9.28 |url=https://books.google.com/books?id=P1kCtNr-pJsC&pg=PA364 |isbn=978-1-891389-22-1 |year=2005 |publisher=University Science Books}} For set up of the calculations, see Carlucci & Jacobson (2007), p. 225</ref><ref>{{cite news |title=Do Snipers Compensate for the Earth's Rotation? |url=https://www.washingtoncitypaper.com/columns/straight-dope/article/13039128/do-snipers-compensate-for-the-earthrsquos-rotation-what-the-coriolis |access-date=16 July 2018 |work=Washington City Paper |date=25 June 2010 |language=en}}</ref>

The effects of the Coriolis force on ballistic trajectories should not be confused with the curvature of the paths of missiles, satellites, and similar objects when the paths are plotted on two-dimensional (flat) maps, such as the [[Mercator projection]]. The projections of the three-dimensional curved surface of the Earth to a two-dimensional surface (the map) necessarily results in distorted features. The apparent curvature of the path is a consequence of the sphericity of the Earth and would occur even in a non-rotating frame.<ref>{{cite book |first1=Barry A. |last1=Klinger |first2=Thomas W. N. |last2=Haine |date=2019 |chapter-url=https://books.google.com/books?id=Kr2GDwAAQBAJ&pg=PA291 |title=Ocean Circulation in Three Dimensions |chapter=Deep Meridional Overturning |department=Thermohaline Overturning |isbn=978-0521768436 |publisher=Cambridge University Press |access-date=2019-08-19 }}</ref>

[[File:Trajectory-groundtrack-drift.png|thumb|Trajectory, ground track, and drift of a typical projectile. The axes are not to scale.]]

The Coriolis force on a moving [[projectile]] depends on velocity components in all three directions, [[latitude]], and [[azimuth]]. The directions are typically downrange (the direction that the gun is initially pointing), vertical, and cross-range.<ref>{{Citation |last=McCoy|first= Robert L.|year= 1999|title=Modern Exterior Ballistics   |publisher=Schiffer Military History  |isbn=0-7643-0720-7 }}</ref>{{rp|178}}

<math display="block"> A_\mathrm{X} = -2 \omega ( V_\mathrm{Y} \cos \theta_\mathrm{lat} \sin \phi_\mathrm{az} + V_\mathrm{Z}  \sin \theta_\mathrm{lat} )  </math>
<math display="block"> A_\mathrm{Y} = 2 \omega ( V_\mathrm{X} \cos \theta_\mathrm{lat} \sin \phi_\mathrm{az} + V_\mathrm{Z}  \cos \theta_\mathrm{lat} \cos \phi_\mathrm{az})  </math>
<math display="block"> A_\mathrm{Z} = 2 \omega ( V_\mathrm{X} \sin \theta_\mathrm{lat}  - V_\mathrm{Y}  \cos \theta_\mathrm{lat} \cos \phi_\mathrm{az})  </math>
where
* <math> A_\mathrm{X} </math>, down-range acceleration.
* <math> A_\mathrm{Y} </math>, vertical acceleration with positive indicating acceleration upward.
* <math> A_\mathrm{Z} </math>, cross-range acceleration with positive indicating acceleration to the right.
* <math> V_\mathrm{X} </math>, down-range velocity.
* <math> V_\mathrm{Y} </math>, vertical velocity with positive indicating upward.
* <math> V_\mathrm{Z} </math>, cross-range velocity with positive indicating velocity to the right.
* <math> \omega </math> = 0.00007292&nbsp;rad/sec, angular velocity of the earth (based on a [[sidereal day]]).
* <math> \theta_\mathrm{lat} </math>, latitude with positive indicating Northern hemisphere.
* <math> \phi_\mathrm{az} </math>, [[azimuth]] measured clockwise from due North.