Gyroscopic (spin) Drift and Coriolis Effect

Gyroscopic (spin) Drift and Coriolis Effect
By: Bryan Litz
Most long range shooters are aware of the effects of gravity, air resistance (drag)
and wind on their bullets trajectory. There are many commercial ballistics programs on
the market that do a fine job of predicting trajectories which only account for gravity,
drag and wind. Gravity drag and wind are the major forces acting on a bullet in flight,
but they’re not the only forces. In this article, I’ll explain some of the more subtle forces
that influence the path that bullets take.
Gyroscopic drift and Coriolis acceleration is the subject of this article. These
effects are commonly misunderstood by many long range shooters for a couple
reasons. The first reason is because their effects are small in comparison to other
factors. Secondly, the theory behind them can be difficult to understand. Big or small,
understood or not, these influences affect every trajectory in a predictable way. I’ll try to
explain where these forces come from, what practical consequence they have on your
trajectories, and what you can do to predict and correct for them.
Gyroscopic (spin) Drift
First, a quick fact about spinning objects…
Picture a spinning object like a bullet or a top. The spinning thing has a ‘spin
axis’, about which it’s spinning. If you try to disturb the spin axis by applying a force, or
a torque to that axis, the spinning object reacts in a strange way. Rather than simply
moving in the direction that you pushed it, the spin axis reacts by moving 90 degrees
from the applied force, in the direction of rotation. In other words, if you have a top
spinning clockwise on the table in front of you, and you push the top of it’s stem straight
away from you, the stems first reaction is to jump to the right. After the initial reaction, it
will precess into its new equilibrium. Now, on to bullets.
Consider a bullet fired at some angle on a long range trajectory. The bullet starts
out with its spin axis aligned with its velocity vector. As the trajectory progresses, gravity
accelerates the bullet down, introducing a component of velocity toward the ground. The
bullet reacts like a spiraling football on a long pass, by 'weather-vaning' it's nose to
follow the velocity vector, which is a nose-down torque. The price you pay for torqueing
the axis of rotation is that the nose points slightly to the right as it 'traces' to follow the
velocity vector. This slight nose right flight results in a lateral drift known as ‘gyroscopic
drift’.
Having a left or right twist will change the direction of gyroscopic drift. Bullets
fired from right twist barrels drift to the right, and vise versa by the same amount,
typically 8-9 inches at1000 yards for small arms trajectories. Gyroscopic drift is an
interaction of the bullets mass and aerodynamics with the atmosphere that it’s flying
in. Gyroscopic drift depends on the properties (density) of the atmosphere, but has
nothing to do with the earth’s rotation.
Coriolis Acceleration
Accelerations due to the Coriolis Effect are caused by the fact that the earth is
spinning, and are dependant on where you are on the planet, and which direction you're
firing. It breaks down like this:
There are horizontal and vertical components to Coriolis acceleration.
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The Horizontal component depends on your latitude, which is how far you are
above or below the equator. Maximum horizontal effect is at the poles, zero at the
equator. The horizontal component doesn't depend on which direction you shoot.
Typical horizontal Coriolis drift for a small arms trajectory fired near 45 degrees North
Latitude is about 2.5-3.0 inches to the right at 1000 yards.
The Vertical component of the Coriolis effect depends on what direction you
shoot, as well as where you are on the planet. Firing due North or South results in zero
vertical deflection, firing East causes you to hit high, West causes you to hit low. The
vertical component is at a maximum at the equator, and goes to zero at the poles.
Typical vertical deflection at 45 degrees North (or South) latitude for a 1000 yard
trajectory is the same as for the horizontal component: +2.5 to 3.0 inches (shooting
east), or -2.5 to 3.0 inches when shooting west.
What are the consequences?
So those are the facts. But what does all this mean, practically, to long range
target shooters? The answer lies in understanding the following: The effects of
gyroscopic drift and Coriolis drift are independent, and cumulative. In other words, they
add, and you can make them add up in more or less favorable ways.
For example (typical 1000 yard small arms trajectory), if you always shoot in the
northern hemisphere where the horizontal drift is always to the right, and you have a
right twist barrel as most of us do, then your bullet will drift to the right approximately 9"
due to gyroscopic drift, and an additional 2.5" due to Coriolis, resulting in 11.5" right
drift, even in zero crosswind. However, if you had a left twist barrel in the northern
hemisphere, gyro drift and Coriolis drift would partially offset each other, resulting in
only 6.5" drift to the right. What's that mean practically, to competitive target shooters? I
can think of only one answer:
Long range prone shooters (perhaps some BR shooters as well) like to set a
"zero wind" value on their sights as a reference point. If this zero wind setting is
determined for a 100 yard zero, then it will be wrong for longer ranges. The difference
between the left and right twist barrel means that the long range, no wind zero will be off
by either 1/2 or 1 MOA due to the combined effects of gyroscopic and Coriolis drift.
Considering this, it would be more beneficial to have a left twist barrel. Having said that,
I wouldn't order a special made barrel for that reason. It might cost more, and I'm more
comfortable letting the barrel makers do what they're more comfortable with. I'd do the
math and adjust my long range zero wind setting before I'd special order a left twist
barrel.
Furthermore...
As the most precise shooters on the planet, BR shooters are allowed sighters,
before they begin their record shots. Allowing sighters gives BR shooters the luxury of
'dialing out' all these small components of deflection that are different on different
ranges, etc. So BR shooters don’t really have to understand, or care about the effects.
However, long range hunters and snipers are people who have more of an interest in
having the very first shot hit the point of aim (they require precision AND accuracy).
Therefore, I think that those people may be more interested in understanding and
correcting for such effects as gyroscopic drift and Coreolis drift. Of course, it may not
be worth it to carry around the flushing toilet that’s required to measure the strength of
the Coriolis effect that day.
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Regardless of how the effects add or subtract from each other, these effects are
‘knowable’, and therefore correctable by anyone who understands and accounts for
them. To my knowledge, there are no commercial ballistics programs (affordable to the
average shooter) that calculate gyroscopic drift. It depends on a number of aerodynamic
coefficients that are not easy to calculate. However, the good news is that gyroscopic
drift is relatively constant for a wide range of small arms calibers and flat fire (less than
10 degrees) trajectories. You can count on no more than 10 to 12 inches at 1000 yards.
As for Coriolis acceleration, you can look that up in physics books, or ballistics
books like Modern Exterior Ballistics.
I have an idea for how one might alleviate some of the hassle caused by
gyroscopic and Coriolis drift. Since most of us live in the Northern Hemisphere, and
most of us use right twist barrels, we suffer the unfortunate consequence that the
gyroscopic drift, and the lateral component of the Coriolis drift compound each
other. Most of us probably have at least 1 MOA of drift to deal with on our sights
between short and long range wind zeros. I haven’t done the math on this yet, but it
seems that you ought to be able to figure out the correct degree of ‘cant’ at which to
mount your scope, that will counteract the effects of drift. The angle should be very
small, as to be indiscernible by the shooter. I doubt you would get it to work out
perfectly for all ranges, but you might be able to get it ‘good enough’. This practice can
also be applied to iron sights by mounting your level at a small angle to level. Some
day I’ll have to do the math on that one.
If you’re interested in actually calculating Coriolis drift, check out my book: “Applied
Ballistics for Long Range Shooting” which has worked examples of these calculations.
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