Exterior ballistics
Spin drift
A spin-stabilised bullet walks sideways, in the direction of the rifling, for the whole of its flight. For small-arms trajectories that is typically 8–9 inches at 1000 yards and about 2 inches at 500. It is a bias, not scatter: the same rifle puts it in the same place every shot.
The short answer
A right-hand twist barrel drifts the bullet right. A left-hand twist drifts it left, by the same amount. Bryan Litz of Applied Ballistics publishes 8–9 inches at 1000 yards as typical for small arms, and no more than 10–12 inches for flat fire — under 10 degrees — across a wide range of small-arms calibres.
Nine inches at 1000 yards is 0.86 MOA, or 0.25 mrad — a minute of angle is a sixtieth of a degree and subtends 1.047 inches per 100 yards; a milliradian subtends 3.6 inches per 100 yards. Smaller than most wind call errors, which is why it gets ignored. But a wind error is as likely left as right, and spin drift is the same direction on every shot that barrel will ever fire. It moves the centre of the group, not its size.
Source: Bryan Litz, Gyroscopic (spin) Drift and Coriolis Effect, Applied Ballistics, 2021.
What causes it
A rifle bullet is statically unstable — its centre of pressure, where the air load acts, sits ahead of its centre of gravity, so any angle between the bullet's axis and its direction of travel produces a moment that tries to increase that angle. Left alone it would tumble. Spin is what stops it.
Now add gravity. Gravity does not only pull the bullet down, it continuously rotates the bullet's velocity vector — the direction it is actually travelling — downwards, at g cos θ / V radians per second, where θ is the trajectory angle and V the speed. The axis has to follow, or the angle between axis and flight path grows without limit.
Here is the part that surprises people. A spinning body does not move in the direction of the torque applied to it; it moves 90 degrees away, in the direction of spin. That is gyroscopic precession. So when the air tries to lever the nose up relative to the descending flight path, a right-hand-spinning bullet answers by moving its nose to the right. It settles at the angle where the precession it produces exactly matches the rate at which the flight path is turning down — the yaw of repose. At that angle the bullet flies slightly nose-right, and the lift the air generates on a yawed bullet pushes it sideways, to the right. Integrated over the flight, that is spin drift.
The yaw of repose
Setting the precession rate equal to the rate the trajectory is turning gives the steady-state angle:
Ix — moment of inertia about the spin axis, kg·m²
p — axial spin rate, radians per second
g — 9.80665 m/s², standard gravity (3rd CGPM, 1901)
θ — trajectory angle to the horizontal
ρ — air density, kg/m³ (1.225 at ICAO sea level)
S — frontal area, πd²/4 · d — calibre, m · V — speed, m/s
CMα — overturning moment coefficient slope, per radian
This is the standard result, derived in R. L. McCoy, Modern Exterior Ballistics, 2nd ed., section 10.6, as the particular solution of the linearised yawing motion; McCoy writes it compactly as PG/M, and the line above is that expression with his definitions substituted.
Read the exponents and you have the behaviour. The repose angle goes as 1/V³. The sideways force it produces goes as ½ρV²S CLα αR, so the velocity terms partly cancel, the air density cancels altogether, and the sideways acceleration ends up proportional to p/V. Spin decays slowly, because the spin damping moment is small, while speed falls by half or more over a long shot — so the sideways push is largest at the far end and the drift piles up late. The same ratio explains why stability improves downrange: Sg depends on p²/V², and in flat fire a bullet that leaves the muzzle gyroscopically stable stays that way.
Spin rate and stability factor
Spin rate comes straight from velocity and twist, with no aerodynamics in it. At 2600 ft/s the bullet covers 31,200 inches a second; in a 1-turn-in-11.25-inch barrel that is 2,773 turns per second — 166,400 rpm, or p = 17,400 rad/s.
The gyroscopic stability factor Sg compares the stabilising gyroscopic action with the destabilising aerodynamic moment; above 1 the bullet is stable. Computing it properly needs CMα, which needs spark-range or wind-tunnel data, so shooters use Don Miller's empirical rule instead:
l — bullet length in calibres · t — twist in calibres per turn
V — muzzle velocity, ft/s · T — air temperature, °F · P — station pressure, inHg
The constant 30 gives the stability factor at 2800 ft/s in the ICAO standard atmosphere — 59 °F and 29.92 inHg. The velocity term corrects for speed and the last term for air density; use the pressure where you are standing, not a sea-level-corrected one. The rule is for solid and lead-core bullets; plastic-tipped bullets need the Courtney–Miller modification. Sources: Don Miller, A New Rule for Estimating Rifling Twist, Precision Shooting, March 2005, pp. 43–48; the standard conditions as stated in Courtney and Miller, A Stability Formula for Plastic-Tipped Bullets, Part 1, Precision Shooting, 2012; the corrections as given in Litz's Applied Ballistics for Long Range Shooting, appendix B.
Litz recommends an Sg of 1.5 or more. Below that a bullet can group well and still fly with a measurably depressed ballistic coefficient; Berger's twist calculator, built on his testing, used to treat 1.4 as the line; the updated version also reports when stability is costing BC, which that testing found can happen anywhere between 1.2 and 1.5, by as much as 10 %.
How much, at what range
Litz publishes a closed-form fit. He built it mostly on six-degree-of-freedom simulations of representative bullets, with some spark-range and radar data, and checked it with limited live fire. It is a curve fit, not a derivation, and should be read as one — what it is good for is showing which input matters.
Bryan Litz, Applied Ballistics for Long Range Shooting, 3rd ed., 2015, equation 6.1.
It needs a real time of flight. Federal publishes the velocity of its Gold Medal 308 Win 175 gr Sierra MatchKing load (GM308M2) as 2600 ft/s at the muzzle, then 2427, 2262, 2102, 1949 and 1803 ft/s at 100-yard steps to 500. Time of flight is the integral of dx/v across that table; by trapezoid on the six published points, 0.694 seconds to 500 yards. Hold that fixed and vary only the stability factor:
| Sg = 1.4 | 1.7 inches of drift at 500 yards |
|---|---|
| Sg = 1.7 | 1.9 inches |
| Sg = 2.0 | 2.0 inches |
| Sg = 2.5 | 2.4 inches |
Across the whole practical stability range the answer moves seven tenths of an inch. Time of flight is the variable that matters, and it enters at the power 1.83. Doubling the range takes the time of flight to about 1.71 seconds — that is Federal's published G1 0.505 carried past the end of its table in Army Standard Metro air, the combination that reproduces the table to within 2 ft/s — a factor of 2.47, which multiplies the drift by 2.471.83 = 5.2. This bullet, 1.242 inches long, from a 1-in-11.25 barrel in that same air has a Miller Sg of 1.91, and the formula returns 10.4 inches at 1000 yards: above the 8–9 inches Litz calls typical, inside the 10–12 he gives as the ceiling.
What spin drift is not
It is not Coriolis. Spin drift depends on the rifling direction and on the air, and nothing on the Earth's rotation. Coriolis deflection depends on latitude and firing azimuth, and nothing on the barrel. They are independent and they add: Litz gives roughly 9 inches of spin drift plus 2.5 inches of Coriolis at 1000 yards for a right-twist barrel in the northern hemisphere, 11.5 inches right in a dead calm. The same load through a left-twist barrel gives 6.5 inches left — 9 left and 2.5 right — because the spin drift changed sides and the Coriolis did not. (The Applied Ballistics article prints this as 6.5 inches to the right; the arithmetic says left.)
It does not reverse south of the equator. Coriolis does. Spin drift follows the barrel.
It is not the bullet “following the rifling”. The bullet leaves the muzzle straight down the bore line with nothing yet pushing it sideways. The drift is generated by gravity bending the flight path; a bullet fired straight up would have none.
It changes with air density. Density cancels out of the sideways force itself — it is in the denominator of the repose angle and the numerator of the lift — but not out of the drift: thinner air raises Sg and shortens the time of flight, and both terms of the formula move. A solver holding spin drift as a fixed table against range is wrong the moment the air changes.
A check that can fail
Spin drift is hard to measure directly because everything else pushes the bullet sideways too. The old answer is drift firing, and it is what Litz used to test his formula: fire the same ammunition, in the same conditions, from two barrels of identical specification but opposite twist direction. Every lateral influence that does not depend on twist — wind, cant, Coriolis, the shooter — is common to both, so the separation between the two group centres is twice the spin drift.
From a pair of 1-in-10 barrels his 175-grain .308 bullets landed 22.8 inches apart at 1000 yards: 11.4 inches of drift each, against 10.4 from the formula. A longer 185-grain bullet measured 6.7 inches against 8.8 predicted. That is a test with a number that can come out wrong — and for the second bullet the formula did, by 2.1 inches. Looking at one group and calling it close is not a test.
Litz, Applied Ballistics for Long Range Shooting, 3rd ed., chapter 6.
Work it out
The Miller rule for Sg, then Litz's fit for the drift. Time of flight has to come from a ballistic solver or a published table. The defaults are Federal's GM308M2 from a 1-in-11.25 barrel at 1000 yards, in the Army Standard Metro air (59 °F, 29.53 inHg) that Federal's table matches.
In the solver
Range Walkout Coming soon is our long-range ballistic solver for Android. It works from points marked on a range map — range, incline, bearing and latitude come off the targets you place — and computes spin drift the way this page does, Miller stability and then Litz's fit, adding it and Coriolis into the windage it gives you rather than leaving them to be added by hand. It assumes a right-hand twist. Muzzle velocity can be back-computed from a known-range shot. Details on the products page →
Related: the Coriolis effect on a rifle bullet · truing muzzle velocity from a known-range shot
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