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February 10th, 2021

How Do Bullets Fly — Great Online Resource Explains Key Factors

Bullet External Ballistics
“The overturning moment MW tends to rotate the bullet about an axis, which goes through the CG (center of gravity) and which is perpendicular to the plane of drag….

Ruprecht Nennstiel, a forensic ballistics expert from Wiesbaden, Germany, has authored a great resource about bullet behavior in flight. Nennstiel’s comprehensive article, How Do Bullets Fly, explains all the forces which affect bullet flight including gravity, wind, gyroscopic effects, aerodynamic drag, and lift. Nennstiel even explains the rather arcane Magnus Force and Coriolis Effect which come into play at long ranges. Nennstiel’s remarkable resource contains many useful illustrations plus new experimental observations of bullets fired from small arms, both at short and at long ranges.

Shadowgraph of .308 Winchester Bullet

Bullet External Ballistics

A convenient index is provided so you can study each particular force in sequence. Writing with clear, precise prose, Nennstiel explains each key factor that affects external ballistics. For starters, we all know that bullets spin when launched from a rifled barrel. But Nennstiel explains in greater detail how this spinning creates gyroscopic stability:

“The overturning moment MW tends to rotate the bullet about an axis, which goes through the CG (center of gravity) and which is perpendicular to the plane of drag, the plane, formed by the velocity vector ‘v’ and the longitudinal axis of the bullet. In the absence of spin, the yaw angle ‘δ’ would grow and the bullet would tumble.

If the bullet has sufficient spin, saying if it rotates fast enough about its axis of form, the gyroscopic effect takes place: the bullet’s longitudinal axis moves into the direction of the overturning moment, perpendicular to the plane of drag. This axis shift however alters the plane of drag, which then rotates about the velocity vector. This movement is called precession or slow mode oscillation.”

Raise Your Ballistic IQ
Though comprehensible to the average reader with some grounding in basic physics, Nennstiel’s work is really the equivalent of a Ph.D thesis in external ballistics. You could easily spend hours reading (and re-reading) all the primary material as well as the detailed FAQ section. But we think it’s worth plowing into How Do Bullets Fly from start to finish. We suggest you bookmark the page for future reference. You can also download the complete article for future reference and offline reading.

CLICK HERE for “How Do Bullets Fly” complete text.

(1.2 MB .zip file)

Photo and diagram © 2005-2009 Ruprecht Nennstiel, All Rights Reserved.

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December 25th, 2015

Shooting Science: The Coriolis Effect Explained

Whittington Coriolis Effect
The Coriolis Effect comes into play with extreme long-range shots like this. The rotation of the earth actually moves the target a small distance (in space) during the course of the bullet’s flight. Photo by Dustin Ellermann at Whittington Center Range.

Coriolis Effect Bryan Litz Applied BallisticsWhen you’re out at the range, the Earth seems very stable. But it is actually a big sphere zooming through space while spinning around its axis, one complete turn every 24 hours. The rotation of the earth can create problems for extreme long-range shooters. During extended bullet flight times, the rotation of the planet causes an apparent deflection of the bullet path over very long distances. This is the ballistics manifestation of the Coriolis Effect.

Bryan Litz of Applied Ballistics has produced a short video that explains the Coriolis Effect. Bryan notes that Coriolis is “a very subtle effect. People like to make more of it than it is because it seems mysterious.” In most common shooting situations inside 1K, Coriolis is not important. At 1000 yards, the Effect represents less than one click (for most cartridge types). Even well past 1000 yards, in windy conditions, the Coriolis Effect may well be “lost in the noise”. But in very calm conditions, when shooting at extreme ranges, Bryan says you can benefit from adjusting your ballistics solution for Coriolis.

Bryan explains: “The Coriolis Effect… has to do with the spin of the earth. You are basically shooting from one point to another on a rotating sphere, in an inertial reference frame. The consequence of that is that, if the flight time of the bullet gets significantly long, the bullet can have an apparent drift from its intended target. The amount [of apparent drift] is very small — it depends on your latitude and azimuth of fire on the planet.”

Coriolis Effect Bryan Litz Applied Ballistics

Coriolis is a very subtle effect. With typical bullet BCs and velocities, you must get to at least 1000 yards before Coriolis amounts to even one click. Accordingly, Bryan advises: “Coriolis Effect is NOT something to think about on moving targets, it is NOT something to think about in high, uncertain wind environments because there are variables that are dominating your uncertainty picture, and the Coriolis will distract you more than the correction is worth.”

“Where you could think about Coriolis, and have it be a major impact on your hit percentage, is if you are shooting at extended range, at relatively small targets, in low-wind conditions. Where you know your muzzle velocity and BC very well, [and there are] pristine conditions, that’s where you’re going to see Coriolis creep in. You’ll receive more refinement and accuracy in your ballistics solutions if you account for Coriolis on those types of shots. But in most practical long-range shooting situations, Coriolis is NOT important. What IS important is to understand is when you should think about it and when you shouldn’t, i.e. when applying it will matter and when it won’t.”

The Coriolis Effect — General Physics
The Coriolis Effect is the apparent deflection of moving objects when the motion is described relative to a rotating reference frame. The Coriolis force acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object’s speed in the rotating frame.

A commonly encountered rotating reference frame is the Earth. The Coriolis effect is caused by the rotation of the Earth and the inertia of the mass experiencing the effect. Because the Earth completes only one rotation per day, the Coriolis force is quite small, and its effects generally become noticeable only for motions occurring over large distances and long periods of time. This force causes moving objects on the surface of the Earth to be deflected to the right (with respect to the direction of travel) in the Northern Hemisphere and to the left in the Southern Hemisphere. The horizontal deflection effect is greater near the poles and smallest at the equator, since the rate of change in the diameter of the circles of latitude when travelling north or south, increases the closer the object is to the poles. (Source: Wikipedia)

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September 22nd, 2012

New Litz Book: Accuracy and Precision for Long Range Shooting

Litz Accuracy Precision Shooting BookLitz Accuracy Precision Shooting BookBryan Litz, chief Ballistician for Berger Bullets (and a trained rocket scientist) has authored an impressive new book: Accuracy and Precision for Long Range Shooting. Bryan’s new book is a companion to his successful treatise, Applied Ballistics for Long-Range Shooting. Now in its Second Edition, Litz’s Applied Ballistics book has become the “go-to” Ballistics book for precision shooters worldwide.

While Bryan’s first book covers the science of ballistics and trajectory calculation, his new book examines practical issues involved in long-range accuracy. Bryan explains: “In a nutshell, this book focuses on the uncertainties of practical shooting which affect hit percentage on various size targets. In other words, classic ballistics teaches you how to calculate windage and elevation corrections. This book will help you understand what your chances are of hitting a target under certain conditions, and how to improve those chances through training and design.

Practical Examples
Does a low ES/SD really make a difference at long range? Absolutely. In Chapter 6, you can see that reducing muzzle velocity variation from 20 fps Standard Deviation (SD) to 10 fps SD improves hit percentage on a 5″ circle at 500 yards from 83% to 93%.

Ever wonder how much spin drift, Coriolis affect, or using G1 vs. G7 BC’s affect your chances of hitting a target? In Chapter 10 for example, you’ll learn that ignoring spin drift in ballistic calculations reduces hit percentage on a 10″ target from 21% to 15% at 900 yards for a specified environment and cartridge.

The new book is divided into three main sections.
Litz Accuracy Precision Shooting Book
Part 1 focuses on Precision, which explores how hit percentage is related group size. Litz explains the variable that affect group size: muzzle velocity variation, range estimation error, wind estimation error, and inherent rifle precision

Part 2 focuses on Accuracy, which is how well the group is centered around the aim-point. Topics include: leveling your sights, trajectory modeling and secondary effects, calibrating ballistic solutions, and live fire verification.

Part 3 focuses on Weapon Employment Zone (WEZ) analysis. WEZ evaluates firearm effectiveness in terms of hit percentage. The author applies WEZ in the contexts of score shooting, varmint and big game hunting, and tactical shooting. WEZ is also used to compare hit percentage for the 300 Win Mag vs. .338 Lapua Mag.

Litz Accuracy Precision Shooting Book

Book is 300-page, Hard-Cover Format
Accuracy and Precision for Long Range Shooting is a 6″x9″ hardcover book with 300 pages, and retails for $34.95. The book is currently at the printers, and should begin shipping by October 15, 2012. In the mean time, you can pre-order and save $5 off the regular $34.95 retail price.

CLICK HERE to Pre-Order Litz Book or Get More INFO.
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