One Shot, One Kill: The Coriolis Effect – Lin Sen

In the now-classic Call of Duty 4 Modern Warfare, the only time you get to lay your hands on the sleek .50 Barrett M82 is during this scene – One shot, One Kill. Now, if you are familiar with the plot, there is this guy called Imran Zakhaev whom you are supposed to put a hole through from a mile away. If you do not know what I am talking about, watch this video:

One of the clichés in contemporary FPS cinematic is to cite the Coriolis Effect. For the movies, we have the 2007 film Shooter. But what indeed is this “Coriolis Effect”? And does it really affect the shot in the above situation? (Oh btw, you were scripted to fail. Zakhaev’s arm gets blown off even if you shoot his head)

The Coriolis force that we are concerned with presently is the fictitious force which is seen when the observer is in a rotating frame. The following diagram may help illustrate this point. Given that there is a stationary planar disc, on which I put a particle. The particle is now going to move with constant speed from the center to the circumference.

Now imagine that you rotate your vision at a constant angular velocity. The disc seems fine – you can’t tell if it’s moving or not. But the particle seems to follow a curved path, because relative to the disc, it is not moving tangentially.  As it moves out in the radial direction, the apparent tangential velocity increases, and we need some force to account for this tangential acceleration.

This is the fictitious Coriolis force. It is not really there. We just added it because you are rotating your head, and the particle appears to move in such a way. Quantitatively, it is given by:

Up to this point, all you need to remember is that the Coriolis Effect is the changes in trajectory of a particle when one goes into a rotating frame. We can now go on to analyze a rather simplistic view of our initial problem. How significant is it in shooting Zakhaev?

Prypiat, Ukraine is located at approximated 51.405556 deg North. Assuming Earth is a sphere of radius 6370km, spinning at 7.27×10-5 rad/s. Also assume that the shot is directed in the NS direction. Since angle shot upwards is small, we can assume shot was fired horizontally. (Bad assumption, but I lazy) Horizontal distance is around 1.5km.

Muzzle Velocity of .50 Caliber Barrett M82 is 853m/s. Time in flight =1.8s.

Looking from the above the North Pole, projected values are:

Velocity of Earth’s rotation at point of shot: 
Velocity of Earth’s rotation at Zakhaev’s head:
Difference in velocity = 1.487573 x 10-3 m/s

Note that we have to account for initial velocity because when the bullet is shot out, the gun was co-rotating with Earth at the original latitude.

Finally, the deflection in the bullet’s final impact point is….. 2.68 mm. Even if the previous bad assumption about a horizontal shot wasn’t made, it’s still around the same order of magnitude. Unless you are near the equator, this is likely to be the least of your problems.

The Coriolis Effect is often one of the last few effects that a sniper’s calculations account for, together with the Eötvös effect (Go read up). In reality, numerous other factors compound and more complicated situations may result. Together, a whole list of phenomena forms the study of External Ballistics, which you may check out at Wikipedia.

And oh, if by the end of this issue, you are thinking COD4 is a bad game, I need to defend it. It’s a damn good shooting game, together with MW2. (Don’t like BlackOps so much) Go play.

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