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Coriolis and Eötvös: When the Earth's Rotation Moves Your Impact

How far the Earth's rotation moves a 6.5 Creedmoor and a .308 at 1,000 yards by latitude and shot direction, why shooting east lands high, and the distance where it finally reaches one click.

At 45° north, a 6.5 Creedmoor fired 1,000 yards drifts 2.5 inches right from the Earth’s rotation. Its spin drift is 7.4 inches, and one 0.1 mil click is 3.6 inches. Coriolis is real, it’s always the same direction in a given hemisphere, and for this rifle at mid latitudes it stays under one click out to 1,000 yards.

Two effects from one rotation

The Earth turns once a day under the bullet’s flight. Seen from the ground, a bullet in flight seems to feel two small sideways forces.

Horizontal (Coriolis). In the Northern Hemisphere every shot drifts right, in the Southern Hemisphere left. It’s zero at the equator and largest at the poles, growing with the sine of latitude. Direction of fire hardly matters: at any latitude in this article, shooting north, east or west changes the horizontal drift at 1,000 yd by no more than 0.03 in.

Vertical (Eötvös). Shooting east, the bullet lands high. Shooting west, it lands low. North and south there’s no vertical effect. It’s largest at the equator and shrinks toward the poles with the cosine of latitude.

By latitude at 1,000 yards

Coriolis effect at 1,000 yd, Northern Hemisphere. Horizontal shown shooting north; shooting west the vertical is the same amount low.
Latitude6.5: right, in6.5: right, MIL6.5: high shooting east, in.308: right, in.308: high shooting east, in
0°0.00.0013.50.04.0
15°0.90.0263.41.13.9
30°1.80.0503.12.03.5
45°2.50.0702.52.92.8
60°3.10.0851.83.52.0
75°3.40.0950.93.91.0

Between 30° and 60° the horizontal part at 1,000 yd is 1.8 to 3.1 in for the 6.5 and 2.0 to 3.5 in for the .308. At 45° the horizontal and vertical parts are equal for an east or west shot. Near the equator the vertical part is the only one. In the Southern Hemisphere the horizontal drift is the same size to the left: 2.5 in at 45° S.

By direction of fire

6.5 Creedmoor at 1,000 yd and 45° N by direction of fire.
Shooting towardRight, inVertical, in (+ high)Total, MIL
North (0°)2.50.00.070
Northeast (45°)2.5+1.80.085
East (90°)2.5+2.50.098
Southeast (135°)2.5+1.80.085
South (180°)2.50.00.069
Southwest (225°)2.5-1.80.085
West (270°)2.5-2.50.098
Northwest (315°)2.5-1.80.085

Here the total stays under a tenth of a mil at 1,000 yd, whichever way you face. The largest totals are east and west, where the vertical part adds to the horizontal one.

Where Coriolis passes a click

Coriolis and spin drift for the 6.5 CreedmoorHorizontal Coriolis drift at 45 and 60 degrees north and spin drift, in MIL, from 0 to 1,500 yards for the 6.5 Creedmoor. 0.0 0.1 0.2 0.3 0.4 0 250 500 750 1,000 1,250 1,500 Range, yd Drift to the right, MIL Spin drift Coriolis, 60° N Coriolis, 45° N One 0.1 mil click
The horizontal part of Coriolis grows steadily with range and stays under spin drift all the way to 1,500 yd. At 45° N it reaches 0.1 mil at about 1,350 yd for the 6.5.

At 45° N the horizontal drift reaches half a 0.1 mil click at about 800 yd for the 6.5 and 700 yd for the .308. It reaches a full click at about 1,350 yd and 1,200 yd. At 60° N, a full click comes at about 1,150 yd for the 6.5. Coriolis needs more distance than spin drift to matter, and it never catches up with it in this range span.

Put it in wind terms: at 1,000 yd and 45° N, Coriolis moves the 6.5 as much as a 0.37 mph full-value crosswind. That’s finer than any wind call. What makes Coriolis worth including at long range is the same thing that makes spin drift worth including: it’s a bias, not scatter. In the Northern Hemisphere, with right-hand twist, the two add. Leave both out and every long shot starts 9.9 in right at 1,000 yd before the wind does anything.

The textbook shortcut overstates it

A common way to estimate the horizontal part multiplies Earth’s rotation rate (7.29 × 10−5 radians per second), the range, the time of flight and the sine of latitude. For the 6.5 at 1,000 yd and 45° N that gives 2.8 in. The full solution gives 2.5 in, about 9% less. The shortcut is exact only for a bullet that never slows down. A real bullet slows, and the air resists its sideways motion just as it resists its forward motion, so less of the Coriolis push turns into drift. The .308, which slows down more, shows a bigger gap: 3.3 in from the shortcut against 2.9 in solved, 14% less. The error is small in inches, and it grows with the bullet’s loss of speed.

When to ignore it

In the app

Ballista has a “Coriolis” switch in the Air sheet. When it’s on, the solver needs your latitude and the shot direction in degrees true. “Use my location” reads the latitude on your device and rounds it to about 7 miles; the app never saves your location. You can also type the latitude, and you type the shot direction. With the switch off, the sheet notes “Coriolis matters past about 800 yards.” That’s close to the half-click distances above.

Sources

  • Robert L. McCoy, Modern Exterior Ballistics, Schiffer Publishing, 1999. Coriolis and Eötvös effects on the trajectory.
  • Bryan Litz, Applied Ballistics for Long-Range Shooting, 3rd ed., Applied Ballistics LLC, 2015. Coriolis effect for long-range shooting.
  • Every number in this article: Ballista engine (BallistaCore point-mass solver), inputs in the box above. See how we compute.