Why You Can't Shoot Straight: The Basic Science of Shooting
By John Cramer
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About this ebook
This is a book about the science of shooting guns but it also applies to archery. Beginning with the most basic science, that gravity means you can never shoot straight, it carefully and clearly explains the physical science behind all aspects of shooting. Projectile motion, the effects of air resistance and rotational motion on projectiles, the importance of projectile shapes and materials, the science behind zeroing and many other topics are explained in the basic science section. We then move on to advanced and applied science topics such as the optics of scope sights and laser sights, the impact of moving air and atmospheric disturbances on aiming. Sabot bullets, shooting up and down hill, recoil control, the science behind shooting at moving targets and other subjects are thoroughly covered. Along the way, the author includes historical asides on such topics as Custer's last stand, the Battle of Cowpens and the development of the rifle.
John Cramer
Dr. John A. Cramer is an emeritus Professor of Physics at Oglethorpe University in Atlanta, Georgia having earned his PhD. Degree from Texas A&M University. He has some forty years of experience teaching undergraduate physics and physical sciences and has authored numerous popular science articles. An avid outdoorsman and shell collector, his science interests extend well beyond physics.Dr. Cramer’s books include: A Brief History of Physical Science, How Alien Would Aliens Be? Why You Can't Shoot Straight: the basic Science of Shooting and Science Activities for K-5. All these are available in ebook formats. A Brief History of Physical Science, and How Alien Would Aliens Be?, are also available in print at most online retailers.
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Why You Can't Shoot Straight - John Cramer
This is a book about the science of shooting guns but it also applies to archery. Beginning with the most basic science, that gravity means you can never shoot straight, it carefully and clearly explains the physical science behind all aspects of shooting. Projectile motion, the effects of air resistance and rotational motion on projectiles, the importance of projectile shapes and materials, the science behind zeroing and many other topics are explained in the basic science section. We then move on to advanced and applied science topics such as the optics of scope sights and laser sights, the impact of moving air and atmospheric disturbances on aiming. Sabot bullets, shooting up and down hill, recoil control, the science behind shooting at moving targets and other subjects are thoroughly covered. Along the way, the author includes historical asides on such topics as Custer's last stand, the Battle of Cowpens and the development of the rifle. It was fun to write and I hope you will enjoy, and learn by, reading it. - John Cramer
WHY YOU CAN’T SHOOT STRAIGHT
The Basic Science of Shooting
by
John A. Cramer
Copyright 2020 by John A. Cramer
ISBN 9978-1-466-14544-3
Smashwords Edition
Smashwords Edition, License Notes
This ebook is licensed for your personal enjoyment only. This ebook may not be re-sold or given away to other people. If you would like to share this book with another person, please purchase an additional copy for each recipient. If you’re reading this book and did not purchase it, or it was not purchased for your use only, then please return to Smashwords.com and purchase your own copy. Thank you.
TABLE OF CONTENTS
INTRODUCTION
Chapter 1. BASIC SHOOTING SCIENCE
PROJECTILE MOTION
MUZZLE VELOCITY AND RECOIL
ROTATION AND STABILITY
AIR RESISTANCE
ZEROING IN
COLLISIONS WITH OBSTRUCTIONS AND TARGETS
MOVING TARGETS
Target Tracking and Depth Perception
Leading the Target
The Shot String
Shot Patterns
Choke
THE CHEMISTRY OF SHOOTING
Propulsion
Fouling
Chapter 2. ADVANCED SHOOTING SCIENCE
UP HILL AND DOWN
CROSS-PATH FORCES
THE GYROSCOPIC EFFECT
DEFORMED BULLETS AND INSTABILITY OF ROTATION
THE CORIOLIS EFFECT
SABOT BULLETS
AERODYNAMIC CHARACTERISTICS OF PROJECTILES
RECOIL CONTROL
CUSTER’S LAST STAND, OBTURATION AND SWAGING
DEFORMATION ON IMPACT AND ENERGY DELIVERY
Chapter 3. APPLIED SHOOTING SCIENCE
OPTICS AND AIMING AIDS
Iron Sights
Telescopic Sights
Red Dot Sights
Laser Sights
Bore Sights
LONG RANGE AND WINDAGE
What is Long Range?
Finding the Distance
Corrections for Distance
Corrections for Wind
Corrections for Air Resistance
Mirage effects
APPENDIX 1: FORMULAS OF PROJECTILE MOTION
Parabolic Motion – No Air Resistance.
Motion with Air Resistance.
APPENDIX 2: MUZZLE VELOCITY, INITIAL VELOCITY, AND RECOIL VELOCITY
APPENDIX 3: PROJECTILES WITH AIR RESISTANCE
Horizontal motion
Upward vertical motion
Downward vertical motion
APPENDIX 4: OVERSHOOT ERROR SHOOTING ON AN INCLINE
About the Author
INTRODUCTION
This is a book about the science of shooting guns, that is, rifles, shotguns and pistols. What I will say about guns often applies to archery shooting but I will not try to address archery directly. Although ballistics will occasionally come up, this is not a book on ballistics nor will I discuss how good this or that cartridge or load or bullet is for this or that situation. For that you must read shooting magazines and the shooting sections of hunting magazine. There are quite a few good shooting editors out there writing such stuff; go get your hands on their writings and read it carefully. They get most of it right most of the time. Trust them particularly when they tell you about things they have actually tried and tested.
Although this book is very much about accurate shooting, it is not a book to train you to shoot well or accurately. Only much practice can do that. I am a physics professor with more than 40 years experience teaching college physics. I am not an expert marksman or a professional shooter. I am not even a magazine shooting editor. What I am is a science teacher and what I do well is teach science. This book is, as the subtitle says, about the science, particularly the physics, of shooting. You can shoot (perhaps not well) without knowing any of the science of shooting but, the more of the science you understand, the greater will be your capacity for improving your shooting. I hope to help you make your shooting more deliberate and well thought out and, hence, more accurate and rewarding.
The science of shooting is mostly the science of motion. That is to say, most of this book is about basic physics. There will be a bit of chemistry and some optics (which is also physics) but physics of motion covers most of it. The basic science is also the easiest but it is, for all that, also definitely the most important. Thus, I will begin with the basic science and then progress to some advanced topics where the motions or details are somewhat more complicate, as, for example, the odd spiral motion of the tip of a bullet in flight which very few shooters are even aware of. This is stuff that most of us never need think about in our shooting but which is important for people like military or police snipers, anyone doing very long range shooting or for people doing very specialized shooting. You can skip it if you like or dip into it later when curiosity gets the better of you. Then, in the applied science section I will tackle the science of important devices, like telescopic sights, that shooters commonly use to assist them in the task of shooting accurately and effectively even at long distances.
As a physics professor, I confess I am sometimes overcome with the desire to write equations as explanations. Although I have been unable to completely suppress this ingrained impulse, I have placed all such stuff in the appendices where only readers as nerdy as myself will likely venture. The rest of you are safe as anyone can be who undertakes to learn a little applied physics.
Along the way you will find quite a few historical asides about how the science of shooting has developed. I put this stuff in because I enjoy it too much to leave it out. I hope you enjoy it too but you can skip it if you just have to get right to the science.
Enjoy the read but be sure to get out and use the new found knowledge in the field or at the range. There is no substitute for practice.
Chapter 1. Basic Shooting Science
With a title like Why You Can’t Shoot Straight, I had better explain right from the start that it is meant simply to catch your attention and not to insult you. Guns never shoot where you point them but it’s not your fault; no, it’s all gravity’s fault. The light that defines a straight path to an object doesn’t behave like the bullet or the shot the gun sends to the object. Light travels so very fast that gravity has no time to act on it effectively. A bullet, on the other hand, is very much affected by gravity. It is a projectile and the light is not. Thus, light travels in straight lines and bullets and shot do not and you can’t shoot straight whether you want to or not.
Projectile motion
It follows, then, that the most important thing for a shooter to know about bullets and shot is that, while in flight, they are all projectiles. Projectile motion is one of the most familiar types of motion. Thrown rocks and sticks, balls hit or shot, a thrown javelin, and a stream of water are all projectiles.
Projectiles have been studied since the time of Aristotle but a useful understanding of their motion had to wait until the Renaissance when cannon balls became important. As everyone knows, the Renaissance was a time of renewed learning but it was also a time of political unrest and warfare. The newly discovered cannon was busy making tall castles obsolete and the defense industry of the day was into designing better, and lower, fortifications. The offense industry of the day was of course busy trying to understand the path of a cannon ball so they could take castles apart more quickly and efficiently.
A fellow by the name of Nicolo Fontana spent many hours observing and drawing the paths of cannon balls. Fontana was a mathematics professor best known now for being the first to discover the general solution for cubic equations. As a lad of twelve he had been given an horrific saber cut in the face when the French invaded his home town near Venice. The cut left him with a speech impediment, a serious handicap for a professor (and also for his students), but Fontana was widely known by his nickname, Tartaglia, Italian for the stammerer.
He was so closely associated, in fact, with his nickname that for a long time his real name remained unknown. Many sources still refer to him as Nicolo Tartaglia or just Tartaglia.
It seems obvious now but no one at the time realized that cannon balls, and all projectiles generally, follow smoothly curved paths. Aristotle had mislead everyone, himself included, into thinking that projectiles travel upward and outward in a straight line until they run out of gas
and then fall pretty much straight down. Seemingly, Tartaglia was the first to realize the path is a smooth curve.
The most important feature of projectile motion was then discovered by another Venetian, Galileo Galilei. It occurred to him that a projectile is doing two things at the same time. It is traveling horizontally, parallel to the ground, and it is moving vertically, first up and then down. The two motions are independent of each other but they happen simultaneously. This simple idea is the key to predicting the motion of a projectile. In fact, predicting that motion is exactly where Galileo went next.
Since the two motions are independent, they can be studied separately; so Galileo first investigated the vertical motion and showed that it was just a case of free fall, that is, constant acceleration under gravity. He measured that acceleration. We now give it in meters or feet (neither unit was available to Galileo) as 32.2 ft/s² or 9.8 m/s². Use whichever unit makes you happier. Happily, when Galileo then studied the horizontal motion he found it is even simpler; it’s just motion at constant speed. With both motions well understood, Galileo then was easily able to prove that Tartaglia’s smooth curve was a parabola.
Parabolas are familiar to most of us as the curves generated by plotting quadratic equations in high school algebra. The parabolas that describe projectile paths are the upside-down ones, cups that will not hold water, with the highest point in the middle of the flight. To see the relevant equation, check out Appendix 1. What part of this infinite curve a particular object follows depends on starting and ending conditions. A cannon ball shot uphill will end at a higher point than it started from and the