1. The meplat is the front surface of a bullet or shell; the term derives from the French méplat, meaning “plane,” inappropriately enough. (Planes are flat, whereas the front surfaces of bullets are curved.) One exception to the aerodynamic instability of bullets might be the early Minié ball: it was short and had a conical hollow at the back to help the soft metal expand into rifling grooves, as you may recall from chapter 4. This geometry may have been enough to bring the CG in front of the CP.
2. Wolfgang Haack was a German mathematician who discovered the minimum drag shapes in 1941. His work was kept secret until after World War II. See Boos-Bavnbek and Høyrup (2003) for details.
3. Target shooters favor these handloads because they help achieve consistency (by minimizing irregularities that ruin accuracy), are more aerodynamic, and are economical.
4. The definitive work on the physics of gyroscopes, the monumental About the Theory of the Gyroscope, was written between 1898 and 1914 by two German mathematical physicists, Felix Klein and Arnold Sommerfeld. Less eminent physics students, struggling with the mathematics of gyros (which involve vector cross products and the right-hand rule), have been seen putting down their pens during examinations and manipulating their right hands in front of their eyes, in a manner that must appear bizarre to observers unfamiliar with vector dynamics. Readers who are seriously interested in the mathematics and physics of gyroscopes would be better advised to turn to a modern physics textbook on the subject, such as Kibble and Berkshire (1996).
5. It is usually not the case; a bullet emerges pointing in a slightly different direction than that in which it moves, for several reasons. The violence of the muzzle blast can throw a bullet a little to one side or cause it to tilt. Imperfections in manufacture, exacerbated by rapid spinning, may induce secondary rotations, and so forth.
6. An overstabilized bullet has too much twist, with the result that the direction of angular momentum does not change throughout the trajectory. In a high-angle shot such a bullet may land base first. This is not good: a lot of speed is lost in the final stages of such a trajectory because of the larger bullet cross section presented to the air, and the penetrating power of the bullet is reduced. Handgun bullets are usually overstabilized, but it doesn’t matter because handgun ranges are so short. A bullet which tips over as its velocity vector tips over, so that its nose lies on the line of flight, is said to have a tractable flight—and this is the ideal case. In practice, the precession is not always circular as with the gyroscope, but describes a more complicated revolution.
7. Of course, a crosswind will also push the bullet to one side, but that is an additional and quite separate consideration.
8. I have here provided a “momentum transfer” explanation of the Magnus force. Some explanations make use of Bernoulli’s law, which says that higher speeds generate lower pressures, pulling the bullet to the left. This explanation is wrong. In fact, the air pressure may be reduced on the left side of the bullet, but this is what causes higher air speeds (instead of higher speeds causing lower pressures). Much of the confusion that exists in popular literature is due to misapplication of Bernoulli’s law. For a fuller explanation of the Magnus effect, and of the popular misconceptions concerning aerodynamic forces in general, see the appendix to my book of the physics of sailing (Denny 2009). For detailed explanations of the aerodynamic forces that act upon projectiles, see Canada DND (1992). A full mathematical treatment is provided in the appendix to the U.S. Department of Defense handbook on fire control systems (1996).
9. If you want to know more about these forces and torques, consult the appendix to U.S. Department of Defense (1996). See also Nennstiel (1996) for a detailed account specifically of the external ballistics of handguns and rifles. Nennstiel quotes experimental confirmation of the theoretical developments and concludes that while short- and medium-range trajectories are pretty well understood, there is as yet no fully reliable theory of long-range trajectories. Farrar, Leeming, and Moss (1999) is a good textbook account of all the details. Both these references are heavy on math.
10. A history of the Paris Gun and its deployment is provided by Marshall (1987).
11. In fact, there were several guns. The wear and tear on the barrels was considerable, and they needed to be rebored after 65 shots.
12. See Maitland-Addison (1918).