# 2.0  Introduction

2.0  Introduction

This Introduction is an open letter to all readers. It will introduce the subject matter which we are attempting to present in this Fourth Edition of the Sierra Reloading Manual.

In the previous editions we began this reference section, as we do now, with a definition:  Exterior ballistics is the study of the motion of a projectile from the instant it leaves the gun muzzle to the instant it strikes the target. We pointed out that this subject seems simple, but it is really technically complex. It is worth the time and effort it takes to study exterior ballistics, because shooters who understand can improve their shooting skills. They will know what happens to the trajectories of their bullets if they change altitudes, if the weather changes, if they must shoot in windy conditions, if they shoot uphill or downhill, and so on.

In the previous editions we took as our goal to explain exterior ballistics in enough technical depth to be of interest to those shooters already knowledgeable about the subject, but without using extensive technical detail and mathematics that would overwhelm a person just beginning to study the subject. Consequently, we used a style of presentation in which we described the physics of trajectories qualitatively in words, and we presented quantitative examples for specific shooting situations which we considered typical for most shooters. The mathematical formulations of exterior ballistics were included in the Third Edition only.

Your letters and calls to us have communicated a clear message. Some have been complimentary and some have offered constructive criticisms, and we are grateful for both. Almost without exception, though, every letter and call has requested additional technical information. It is clear that our original objective satisfied the needs of some of you, but fell short of the needs of others. There are many of you who need the mathematical laws of ballistics to support your own computations. In this edition of the Sierra Reloading Manual we are trying to satisfy your needs also.

We have included more technical depth in this reference section, including the necessary mathematics. In Section 6.0 , the differential equations of bullet motion are derived. The analytical model for aerodynamic drag is presented. Siacci’s approach to solving the differential equations is described. Mayevski’s analytical expression of the drag model is described. Finally, this section presents closed form solutions to the differential equations of motion, originally found by Siacci’s team.

At the same time we have not forgotten our original goal. We have remembered those of you who are interested in exterior ballistics but do not care to delve into the calculus. Sections 3.0 through5.0 retain most of the information from the previous editions. This information has been extensively revised and updated. These sections present the essentials of ballistics without a great deal of mathematics.

Section 3.0 is a historical overview of the development of ballistics. The history of ballistics is important and interesting. It teaches us that, as necessity is the mother of invention, the need for increased weapon accuracy has motivated the development of physical sciences, mathematics, and instrumentation related to ballistics.

Section 4.0 is devoted to the ballistic coefficient. This important characteristic of a bullet is defined. Then, its effects on bullet trajectory are described. The techniques we use to measure ballistic coefficient are described. Important lessons we have learned from 25 years of test experience are presented. Finally, a new subsection has been added in this fourth edition of the Sierra Manual which describes the effects of gyroscopic precession (or coning) motion of the traveling bullet on the measurement of ballistic coefficient.

Section 5.0 discusses a number of important topics in exterior ballistics. The first is the effects of altitude and atmospheric conditions on bullet trajectories. The second topic is shooting uphill or downhill. Then, the effects of winds on a bullet trajectory are described. Wind effects are followed by a discussion of relationships among bullet trajectory, sight height, line of sight, and zero range for sighting in a rifle. The concept of point blank range is introduced, and a method for maximizing point blank range of any gun for any size of game animal is described. The last subsection describes the effects of cartridge temperature (actually propellant temperature) on muzzle velocity.

Section 6.0 then presents the mathematics of bullet trajectories.