How does the earth's rotation affect the path of a bullet?
I recently read an article about a Navy SEAL sniper. The author lists possible variables that go into determining a shot, one of which is the rotation of the earth. How exactly does this affect a bullet in flight? Also, for my nonsniper purposes, does it affect my gas mileage?
Took a while to get to the bottom of this. But of course we did.
The article I'm guessing you saw, entitled “The Way of the Sniper,” appeared in Men’s Journal, November 30, 2009. Written by Rick Telander, it tells the story of navy sniper Scott Tyler. Telander writes:
“Each rifle a sniper uses has unique characteristics that are compounded by the ammunition and many, many exterior factors. There is wind. There is humidity. There is the spin of the Earth. There is even the fact that as a rifle is fired, its barrel heats up, the metal contracts, and the bullets are propelled faster.”
Reading this, your columnist didn’t doubt the rotation of the earth affects a bullet in flight. That’s because of the Coriolis effect, discussed here in the past: any object moving horizontally on or near the earth’s surface is deflected slightly off course due to the spinning of the planet beneath it. The Coriolis effect has a big effect on phenomena like hurricanes and other weather systems, a small effect on small objects. But if the small object is a precisely aimed rifle bullet, and that bullet travels far enough, it’s not something you can completely ignore.
The question in my mind was: how, if at all, did a shooter account for the Coriolis effect when aiming? Your wind, your humidity, and for that matter your temperature and barometric pressure — these are all dynamic conditions that, to varying degrees, a marksman will want to factor into each shot. However, it’s hard to imagine a sniper on the field of battle drawing a bead and thinking: Damn, I better get the latest data on the rotation of the earth.
Una agreed this was unlikely and began inquiring about what shooters actually did. She couldn’t reach Telander or a military sniper but did talk things over with a couple of hard-core target shooters at her local rifle range and online. Based on that plus her own calculations she determined as follows:
1. Range is obviously critical. At 100 yards, typical of what a police sharpshooter might encounter, most environmental factors, including the Coriolis effect, are negligible. But military snipers generally are much farther away, typically 400 yards and up — the world record for a confirmed kill in combat as of May 2010 is 8,120 feet, or 1.54 miles.
2. At 1,000 yards the Coriolis deflection is small but not necessarily trivial. Una computed that at the latitude of Sacramento, a bullet traveling 1,000 yards would be deflected about three inches to the right. In addition, you'd have to aim higher or lower depending on the degree to which you were facing east or west. If you were firing due east, you'd have to aim six inches lower, since the earth rotates from west to east and your target would have dropped away from you slightly by the time the bullet arrived. If you were firing due west, you'd have to aim six inches higher.
3. Amateur long-range shooters can improve their aim using laser rangefinders and scopes with bullet-drop compensators; they'll also consult “cheat sheets” of bullet and rifle performance and their own log of prior results, called a DOPE ("data on personal equipment") book. Military snipers may not always have access to such stuff in combat. But let’s take it as given that, one way or another, you can adjust for obvious environmental factors in the field — no doubt the best shooters do it instinctively.
4. Horizontal deflection caused by the Coriolis effect is more esoteric but in theory easy to adjust for, since it’s a function of your distance from the equator. When possible, any shooter, whether professional or amateur, makes a few test shots on arriving at a new location and tweaks his or her sights accordingly. Mostly this is to correct for maladjustments due to jostling in transit and such, but it also compensates for the Coriolis effect.
5. As we've seen, vertical deflection depends on, and can vary considerably according to, what direction you’re shooting. Nonetheless, none of the amateur shooters we heard from worried much about it, and my guess is military snipers don’t either. More important things can go wrong, and besides, assuming your target is standing, what's a couple inches up or down?
Turning now to your wimpy civilian concerns, don’t sweat the Coriolis effect on your gas mileage. In Sacramento, the rotation of the earth causes your car to drift about 16 feet to the right per mile. That may be an issue if you’re barreling down a narrow two-lane, but correcting for it costs you less than a hundredth of a mile per gallon.
The print version of this column contained an error introduced by Cecil's hapless assistant Little Ed, who had the earth turning in the wrong direction. Our apologies to disappointed readers hoping to see the sun rise in the west.