# How do bullets fly?

Author: Ruprecht Nennstiel, Pfingstbornstr.33, D 65207 Wiesbaden, Germany

## Abstract

This document attempts to explain the basics of the complicated subject of bullet motion through the atmosphere without using neither formulas nor mathematical derivations, but expecting familiarity with the way of physical thinking. It also includes new experimental observations of bullets fired from small arms, both at close and long ranges. Numerous illustrations are included and can be viewed via links to promote further understanding. This article is also thought as an introduction for all types of readers (hunters, sportsmen, ballisticians, forensic scientists), interested in the "mysteries" of the exterior ballistics of bullets, fired from small arms.

This document (including all graphs) can also be downloaded and be read offline (some ziping software is required).

Readers, interested in an exterior ballistics software including special features for forensic ballistics are requested to link to another web page of this author.

## Contents

- Introduction
- Flying bullets on a microscopic scale
- Forces and moments affecting flying bullets
- Bullet stability
- Bullets at short ranges
- Bullets at long ranges
- Anomalies of bullet flight
- Summary, Acknowledgments, References
- Download this document

## Figures

### Shadowgraphs

Shadowgraph photography - experimental set-up
Shadowgraph of a .308 Win. bullet at supersonic flight
Shadowgraph of a 9mm Luger FMJ bullet at supersonic flight
Shadowgraph of a .32 ACP bullet at subsonic flight

### Basics

The wind force
Adding two forces to the wind force
The overturning moment
The gyroscopic effect
The Magnus effect
The Magnus force
The Magnus moment
Static stability factor (example)
Over-stabilized bullet on a high-angle trajectory
The yaw of repose
The yaw of repose for a 7.62x51 Nato FMJ bullet fired at 32°
Long range Doppler radar velocity measurement of a 7.62 x 51 Nato bullet
Coning motion of destabilized Nato bullet
Doppler radar velocity measurement of coning bullet

### Yawing motion of handgun bullets

Two arms model of yawing motion
Yawing motion in general
Experimental set-up to investigate yawing motion
Yawing motion of M193 bullet cal. 5.56 x 45
Yawing motion of an armor-piercing bullet, cal. 5.56 x 45
Yawing motion of M74 bullet, cal. 5.45 x 39
Yawing motion of an armor-piercing bullet, cal. 7.62 x 51 Nato
Yawing motion of M80 bullet, cal. 7.62 x 51 Nato
Yawing motion of KTW bullet, cal. .357 magnum
Yawing motion of 9mm Luger FMJ RN bullet
Yawing motion of a wadcutter bullet, cal. .38 special
Yawing motion of .32 ACP FMJ RN bullet

## Formulas

The drag force
The lift force
The Magnus force
The overturning moment
The Magnus moment
The gyroscopic stability condition
The dynamic stability condition
The tractability condition
The yaw of repose

This web page is supported by Columbia International Forensics Laboratory

Thanks for all previous comments! New comments are welcome!
Send eMail to: Ruprecht Nennstiel, Wiesbaden, Germany

Last Update: 29.08.1998