The Coriolis Effect and Long-Range Shooting
Following the long-range shooting series? Here’s the next installment of external ballistics theory: the Coriolis Effect.
The Coriolis Effect is a variable that affects the bullet flight both on the horizontal and the vertical plane of the trajectory.
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What is the Coriolis Effect and How Does it Affect Shooting?
When talking about ballistics, the Coriolis Effect refers to the deflection on the trajectory of the bullet generated by the spinning motion of the Earth. Its effect is negligible at medium distances, but becomes important around 1000yds and beyond, especially because it can add to other minimal errors and keep you off target.
Coriolis effect affects everything not firmly attached to the Earth’s surface. It affects fluids, like air and water, as well as floating and flying objects like ships, airplanes, and… bullets.
Despite being associated with Coriolis, the phenomenon that actually affects the vertical component of the trajectory is called Eötvös Effect. The rotation of the Earth generates a centrifugal force, the same that pushes you to the side when you make a sharp turn in your car. This force acts perpendicular to the Earth rotatory axis, adding or subtracting to the gravity force.
When an object flies eastward, in the same direction of Earth’s rotation, centrifugal force acts opposite of gravity, pushing it away from the Earth’s surface. If the object flies westward, in the opposite direction of the Earth rotation, centrifugal force pushes the object toward the ground concurrently to gravity force. Thus, bullets fired to the east always fly a little higher, and, conversely, bullets fired to the west always travel somewhat low.
The amount of drop change is a function of:
Latitude – The linear velocity of a point on the Earth’s surface, and thus the amount of centrifugal force, is maximum at the equator and decreases going toward the poles, where it is null.
Shooting direction, or azimuth – The amount of drop change is highest when shooting east or west, and as the trajectory angles north or south, the amount of drop change decreases, becoming null, as the angle points toward either pole.
Muzzle velocity – The amount of centrifugal force is determined by the speed of the flying object.
How Does The Eötvös Effect Alter Tragrectory?
Before, I mentioned that the vertical element associated with the Coriolis effect is actually called the Eötvös effect.
To give you an idea of how the Eötvös effect alters a trajectory, here’s an example.
Let’s say you’re firing a .308 175gr bullet, with a muzzle velocity of 2700fps, from a latitude of 45°. The drop at 1000yds will be 392 inches, shooting either to the north or south (without error). Shooting with an azimuth of 90°, or eastward, the drop will be 388in. Shooting with an azimuth of 270°, or westward, the drop will be 396in. In either case, there is a total change in a drop of 4in. An easy assumption is to predict that when shooting with an intermediate azimuth, the drop change will be linear. This is incorrect. Instead of a 2in change for an azimuth of 45°, the error is a function of the sine of the azimuth angle.
For those of you who don’t have a fondness for trigonometry, this essentially means that you have half the error at 30° rather than at 45°. Changes in latitude have a minimal effect since, at the equator, where the effect is greatest, the error would be 5in, only one inch more than the error we calculated at 45° latitude.
What Is Most Affected by the Coriolis Effect?
The horizontal component of the bullet trajectory. Because of the Coriolis effect, every moving object not connected to the ground is always deflected to right in the Northern Hemisphere, and always toward left in the Southern Hemisphere. The deflection is not east or west, but specifically to the right or left with reference to the shooting direction.
It doesn’t matter in which direction you shoot; it is a function of latitude and average bullet speed. Its effect is maximum at the poles and decreases as one moves toward the Equator, where it is minimal. The explanation of this phenomenon is more difficult than the explanation of the Eötvös Effect, so I won’t go into detail.
Coriolis Effect Examples
Here’s an example of error due to the Coriolis effect: firing the same .308 175gr bullet at 2700fps muzzle velocity, from a latitude of 45° in the Northern Hemisphere, the deflection at 1000yds will be of 3in to right. At the North Pole, where the effect is maximum, the deflection will be a little more than four inches. The deflection will be the same in the Southern Hemisphere, but it will be to the left, instead.
As you can see, these errors are subtle, even when shooting at long range. However, especially when combined with other potential error factors in your long-range shooting equation, it could make the difference between hitting and missing your target. If you have portable ballistic software, you can use it to calculate Coriolis for you at every distance. But, if you’re doing the math on your own, I wouldn’t start to take Coriolis into consideration unless shooting at 1,000 yards, or more.
The Coriolis effect is more complicated than movies like Shooter make it seem, isn’t it?
The Coriolis effect isn’t an issue that comes up for most AR-15 shooters given the shorter range that ARs are usually used for. But why be ordinary? If you choose to build your own AR-15, you can easily create something that can reach out to the kind of distances where the Coriolis effect becomes an issue. Consider an alternative caliber like .224 Valkyrie, which is specifically designed for long-range shooting.
Besides the right caliber, long-range shooting requires the use of a good long-range optic. One often-heard rule of thumb is to spend as much on your scope as you spent on your rifle. It’s really up to you, but generally speaking, when it comes to accuracy, you get what you pay for. Look for a scope maker with a solid reputation like Leupold, Swarovski, Zeiss, or Bushnell. Consider a maximum magnification level of 18x to 25x. No matter how much you spend, the equipment will never compensate for skill. Enjoy learning how to time your shots with your breathing and heart rate. Have fun!
Such a load. One of the FE experiments to disprove the Coriolis Effect was to shoot a cannon straight up and the ball would fall near the cannon. This page was referenced as proof but this experiment shoots all that in the ass.
The first assumption, not based on the actual “true” heliocentric model fails to notice that the earth is moving rather rapidly, 804 MPH at my latitude. To travel 24,000 miles around the circumference in 24 hours boils down to simple distance over time Newtonian math. The ball must have a surface speed to cover that distance, simple as.
The problem would need to take into consideration the actual speed in feet per second to properly calculate how far the dropped object should move away.
There are 5280 feet in a mile multiplied by 804 MPH to get feet/hour (at my latitude) then FPS would entail dividing this total by 60 minutes/hour x 60 seconds/minute to get feet/second and then finally multiplying by the 10 second travel time.
So, in 10 seconds the ball would travel (5280×804/60×60) x10 = 4,187,232 feet/hour/3600 seconds/hour = 1163.12 feet/second x 10 seconds travel time = 11,631.2 feet traveled, a little over 2.2 miles, and double that if a cannon were used as it is considered equal time to travel up as down so, 10 seconds to ascend with a short pause at the top then 10 seconds down.
Four miles plus seems as if it would be noticeable, especially if you were in the counterclockwise path downstream.
If calculated for the equator where the surface speed is a little over 1000 MPH the fall distance would be 14,666.67 feet or 2.78 miles away and 5.56 miles away for the cannon shot. This is not the way the world works.
All the military references are bull feces.
Most guys making flight path with use a conic projection. Rather than a flat cylindrical one like the Mercator. That way they get their great circle route and can draw straight lines..
Einstein never cited a single source. So I’d trust the more modern studies on the topic. As they are proper academics. Lots of people were studying Relativity. and Einstein basically just said he did everything without citing and supporting works.
Justin_0318 There was no such thing as “Einstiens theory of relative motion”. The Theory of Relativity is also not applicable, because standing on earth is not a static frame of reference.
It is trivial to “prove the earths rotation” without even using a device – simply watch the wheel and turn of the stars as they spin about the north/south pole axis.
Likewise no flight model worth its salt will disregard the curvature of the earth at the very least your geographical location is in spherical co-ordinates to begin with, and even at moderate altitudes and speeds flying at a set altitude is a long way off of a straight line.
How could any of this be possible if there is relative motion? Einstiens theory of relative motion was proposed to account for why the Michelson-Morely experiment failed, which was conducted to prove earths rotation. He stated that all bodies moved relative to one another and that no optical experiment could be conducted to prove earths rotation. Therefore, somebody is incorrect. You can’t have relative motion and coriolis, theu contradict each other. Also, you are incorrect about airplanes being affected by coriolis. Linear aircraft models operate under the “flat, non-rotation earth assumption” because of what NASA claims is relative motion.
Stillearning I’m sorry, I didn’t edit my initial response soon enough.
No. Look at the bluest diagram. There’s one set of arrows that
depicts exactly what you’ve asked. Actually they should hit each other
(all other things being equal). The earth rotates on it’s axis once a
day and is about 25,000 miles in circumference. Therefore, the
rotational speed at the equator is about 1,000 mph. At the poles, the
rotational speed is 0 mph. So if your off the equator either direction,
you’re going slower than 1,000 mph. If one shooter is off the equator
to the North the same amount as another shooter is off the equator to
the South, then they’re going less than 1,000 mph by the same amount.
If they’re firing at the equator from those positions their bullet
starts at the something less than 1,000 mph but is going into an area
that IS traveling at 1,000 mph. So, the bullet appears to turn left from the Southern hemisphere and to the right from the Northern hemisphere… but both to the West.
Not
let me confuse you further. If you were in a helicopter hovering
directly over a spot above the equator, your rotational speed is
something greater than 1,000 mph. If you drop a bomb, the bomb is
dropping at a rotational speed of > 1,000 mph to an area going 1,000
mph. In that case, it will hit East of the spot. That is not really
shown on either diagram.
It’s weird, but that’s the way it is.
DougMH Stillearning Yeah, agreed. It is always nice to be able to explain an effect though, and articles like this aid with understanding. For practical purposes, like the vast majority of the hunting, it is most often easier just to walk closer 🙂
TimU Rifles mate, rifles.
In Vietnam, I was a technician on the AN/TPQ-10 Radar Course Directing Central (ground control bombing system). Coriolis effect was certainly a part of the radar’s analog computer. The diagrams below show the effects of earth’s rotation and trade winds.
Firing north to south is going to have the greatest effect on any bullet firing because of the earth’s rotational speed. East to west is more on the trade winds.
The bottom line is whether north, south, east or west, a 1,200 yard shot is going to be minimally affected and you should be much more concerned about surface winds and other stuff than the Coriolis effect.
Besides, if you’re shooting in any kind of match, the effect will be exactly the same on every shot and you will compensate for it with your sights or scope without thinking about it. If there is no wind and your first shot (after fouling the barrel) is to the right, you’ll move to the left. The rest of the rounds will be fine.
If you’re a long-range hunter and you zero your rifle at 1,200 yds shooting N-S (hitting dead center every time), then you go hunting and take a 1,200 yd shot E-W, technically, you will not hit dead center (all other factors such as wind being taken out of the equation). But at 1,200 yds, the effects are negligible and a perfect wast of your time to consider.
Things I consider FAR more important than worrying about the Coriolis Effect.
Bullet (brand and weight)
Powder and powder measurement
Neck Tension (bullet seating)
Case weight (volume)
Flash hole consistency (consistent burn rate)
Load development (ladder testing or a good barrel tuner (I chose the latter))
SURFACE WIND, WIND, WIND
Just my two cents!
Are you saying??….. So, if you have two shooters, one in southern hemisphere and one in northern hemisphere 2000 yrds apart both set perfectly for a 1000 yrd shot at the equator with one target. Are you telling me that those bullets will miss each other by 6 inches, one right and one left? Considering they havent calculated for errors, wind being equal, and weapons shooting exact. Am I right to assume that is what you are saying??
Interesting article. I do artillery in the military and we take the rotation of the earth into consideration when shooting. It is very similar to small arms, except we are shooting in tens of kilometers and make adjustments in multiple meters rather than inches. Of course it helps that our rounds explode, so we only have to hit close to the target, not on it.
jshjr I agree with you when you say that practice is essential, especially because wind reading (maybe the greater challenge of long range shooting) requires a lot of field practice to be mastered.
However, formulas are essential. Everyone with good marksmanship can shoot tight groups at every distance. The real challenge is to hit the target at the first shot, not after 10 shots of adjustments, and you simply can’t do that without formulas (unless you are using a ballistic software). The theory of external ballistic is not really essential, if you know the formulas and how to compensate for variables, you don’t really need to know “Why”. Nevertheless, I believe that knowing the theory behind what we do is always helpful, specially in those particular situation where standard approaches doesn’t work and you have to use your head to work things out 😉
Te group of 10″ at 1600yd is impressive BTW!
jshjr I agree with you when you say that practice is essential, especially because wind reading (maybe the greater challenge of long range shooting) requires a lot of field practice to be mastered.
However, formulas are essential. Everyone with good marksmanship can shoot tight groups at every distance. The real challenge is to hit the target at the first shot, not after 10 shots of adjustments, and you simply can’t do that without formulas (unless you are using a ballistic software). The theory of external ballistic is not really essential, if you know the formulas and how to compensate for variables, you don’t really need to know “Why”. Nevertheless, I believe that knowing the theory behind what we do is always helpful, specially in those particular situation where standard approaches doesn’t work and you have to use your head to work things out 😉
Te group of 10″ at 1600yd is impressive BTW!
Shooter was a good movie, and while it had several excessively noticeable flaws in the guns of the movie (the scope image in the finale, gunshot noise on video tape at the same time of impact despite the long distance, blowing up a gas tank with a single sho), overall they did much better than most Hollywood movies with their guns.
And if I remember the quote correctly, he only references that the Coriolis effect is a factor, not how hard of a factor it is compared to say, wind speed and direction.
Shooter was a good movie, and while it had several excessively noticeable flaws in the guns of the movie (the scope image in the finale, gunshot noise on video tape at the same time of impact despite the long distance, blowing up a gas tank with a single sho), overall they did much better than most Hollywood movies with their guns.
And if I remember the quote correctly, he only references that the Coriolis effect is a factor, not how hard of a factor it is compared to say, wind speed and direction.
I have read all of your articles. They are very good and informative. Now for a true story…
About 10 yrs ago or so, I was issued 1 ea 338 Lapua Dakota Arms Long Bow, 400 rnds of match grade ammo (250 grn Seneca??) and two “How To” text books on long range shooting. Long and short, I found that it took 5 minutes or so to calculate the shoot at range…and I am pretty good at math.
After moving to Texas, I had the opportunity to take a course from a retired British Royal Marine who was a scout sniper. My thought process was such that the Brits had used the 338 Lapua for their snipers for many years, so why not learn from the guys that more or less introduced the 338 Lapua to the battle field. I brought the books, rifle and ammo. He looked at the books and looked at the rifle. Then looked me in the eye and asked if I wanted to learn how to shoot the rifle or learn how to read books. After a few choice comments about stupid yanks, the books were tossed and 300 rnds later I was shooting 5-1/2″ groups at 1000 yds and 10″ groups at 1600 yrds (Bullets cost more than the course).
Moral to the story…yes; a very good understanding of Ballistics (practical and theory) is required, but sooner or later, you have to hit the range and send the bullets down range and ‘plot’ the bullet at the various ranges. The rest is practice in varying wind conditions, angles etc., and altitudes (one would be surprised what differing altitudes will do to your plots). Just knowing the formula’s do not make you a shooter.
Nice job an a veryyyyyy difficult topic to wrap your head around.
Holy Cow–I thought an ICBM was headed our way 😉 Very interesting article indeed.
Nice job. Well written.
The USMC could use that as an opening statement in class instead of the head spinning mumbo jumbo they fed us.
Wow! That is a head full. I am still digesting the easy parts 🙂