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THE EXTERNAL AND INTERNAL
BALLISTICS OF SIXTEENTH
Many of the most commonly held misconceptions concerning warfare at sea in the sixteenth century are rooted in the seemingly obvious but mistaken belief that the range of sixteenth-century cannon was proportionate to the length of the barrel. In the text, the main thrust of our argument was to point out that the essential inaccuracy of smooth-bore weapons firing a spherical projectile combined with the terminal ballistics of an inert cannonball to make the whole question of maximum range essentially irrelevant. But while tactically valid, this argument is inadequate from the scientific and technical point of view. Military and naval historians have attached sufficient importance to the supposed range advantage of long cannon to make it necessary to lay this misconception to rest once and for all.
The idea that long guns meant long range in the sixteenth century stems from two main sources: the commonly held sixteenth-century belief that this was true (at least in theory) and the fact that for modern artillery pieces using smokeless propellants it is true.
The first of these is essentially a matter of external ballistics, the behavior of the projectile after leaving the gun. Our most useful evidence of the external ballistics of sixteenth-century cannon should be the range data contained in most published sixteenth- and early seventeenth-century works on artillery. Ballistic analysis of this range data has shown, however, that such figures must be regarded with extreme caution if they can be used at all. This is true both of range figures in absolute terms and of the relative value of ranges given for various types of cannon.
There is no valid ballistic explanation, as we will show, for the supposed range advantage of the culverins over the cannons which the range tables in such works invariably show. If culverins did, in fact, fire at greater ranges and there is no solid evidence that they did it was not because of any intrinsic ballistic advantage, but for the structural reason that they could safely withstand a larger powder charge. Even this seems unlikely since all sixteenth-century cannon (except perhaps for the pedreros) appear to have been overcharged to the point that a further increase in charge would have resulted in an actual reduction in muzzle velocity and range. For reasons which we discuss in Appendix 3, culverins were rightly considered in the sixteenth century to be stronger and safer than members of the cannon class. As such, they were probably assigned to better gunners and used for long shots more often than their shorter and less safe competitors; but their actual range capabilities safety aside were no greater than those of the shorter cannons. The unreliability of sixteenth-century range data was demonstrated by an analysis of the values given by Collado and by Diego Prado y Tovar, Encyclopedia de Fundición de Artilleria y su Platica Manual (1603), undertaken by Mr J. W. Kochenderfer and his co-workers in the Firing Tables Branch, U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland, under the direction of Mr Charles H. Lebegern, Jr., Chief, Firing Tables Branch, in the spring of 1970, using orthodox external ballistic theory as stated by Robert F. Lieske and Mary L. Reiter, Ballistic Research Laboratories Report No. 1314, Equations of Motion for a Modified Point Mass Trajectory (Aberdeen Proving Ground, March 1966), and the accepted drag coefficients for spherical projectiles. They determined that the maximum ranges given by Collado, fol. 27, and all of the ranges given by Prado y Tovar which were subjected to analysis would have been attainable only with muzzle velocities in the neighborhood of 6,000 feet per second, nearly five times the speed of sound and almost three times the muzzle velocities of modern small arms. The general relationships involved are shown graphically in Fig. 15.
Experimentally derived mid-nineteenth-century data, most authoritatively given in the published work of Captain Thomas Jefferson Rodman, makes it plain that any muzzle velocity for black powder artillery in excess of 2,000 feet per second must be held suspect, particularly for the larger pieces. It would be premature to state categorically that all range data given by early sources is totally untrustworthy that given by John Smith, A Sea-mans Grammar (London, 1627), for example, and, significantly, most range references by sixteenth-century Venetian naval sources1 are at least within reason but it seems clear that to the sixteenth-century gunner, long ranges in general and maximum range in particular were a highly theoretical proposition. We should not therefore expect too much accuracy in what he tells us about them.
This is largely a matter of perception: maximum range means something quite different to the modern gunner than it did to his sixteenth-century predecessor. Rather than a tactically significant figure which he actually used in battle and strove to determine beforehand through careful measurement, maximum range seems to have represented something of a philosophical ideal to the sixteenth-century gunner. Inasmuch as he could achieve nothing at maximum range except by blind luck, why should it have been otherwise? Most of the so-called range figures which he left us are therefore little more than educated guesses which reflect his prejudices concerning the types of gun which he felt should have been able to shoot farthest and which he himself preferred to use when long-range fire was called for.
Our second major point, that long black powder cannon the culverins had no intrinsic ballistically based range advantage over the shorter cannons, is a matter of internal ballistics, the behavior of the propellant charge and the projectile within the cannon barrel. Most modern authors, without realizing it, have made the a priori assumption that the internal ballistics of black powder cannon are the same as those of modern cannon burning nitrocellulose-based propellants. This assumption is demonstrably false.
While the burning rate of nitrocellulose propellants increases as a direct function of increased pressure and temperature, that of black powder remains essentially constant.2 The reasons for this phenomenon, bound up in the incredibly complex chemistry of black powder, are not fully understood and are beyond the scope of the present study. The ballistic effects of this difference in burning characteristics, however, are abundantly clear and have been experimentally demonstrated on numerous occasions. These are illustrated in Fig. 16.
Artillery projectiles cannonballs and modern artillery shells alike are driven by the pressure on their bases exerted by the gas evolved through explosive decomposition of the propellant charge. The muzzle velocity attained by an artillery projectile is proportionate to the average pressure exerted on the projectiles base multiplied by the time over which it is exerted. In more precise terms, the projectiles muzzle velocity is a function of the area under the time/pressure curve (minus friction losses which are generally negligible insofar as our analysis is concerned). But as the projectile accelerates down the barrel driven by the pressure of the evolving propellant gases, the volume of gas behind the projectile expands with increasing rapidity. If the projectile is to continue to accelerate, then the burning propellant must continue to evolve gases at a rate sufficient to keep the constantly expanding volume behind the projectile pressurized.
With nitrocellulose-based propellants, the increase in temperature and pressure within the chamber acts to increase the burning rate and hence the rate of evolution of propellant gases as the projectile moves down the barrel. In addition the propellant is generally shaped into grains whose geometry is carefully tailored to produce an increase in the burning surface with time, and hence an increase in the rate of gas evolution as well.
With black powder, however, none of these considerations apply. For reasons connected with the means of propagation of the decomposition reaction in black powder (apparently through a fine spray of molten salts)3 the burning rate is essentially independent of temperature and, above a quickly reached threshold of about 350 psi., of pressure.4 Thus the rate of evolution of propellant gases within a black powder cannon is essentially constant. As the cannonball accelerates down the barrel, a point is reached where the projectile is expanding the volume behind it faster than the decomposition of the black powder can keep it pressurized. Extending the length of the barrel beyond this point will result in an actual reduction in the muzzle velocity and range of the cannon.
The point at which this occurs was determined by numerous nineteenth-century experiments and, according to one source, at least roughly by sixteenth-century experimenters as well.5 Data presented by Captain J. G. Benton, A Course of Instruction in Ordnance and Gunnery ... (New York, 1862), Fig. 31, shows that for a twelve-pound field gun an absolute velocity threshold was reached at a barrel length of about 25 calibers (25 times the bore diameter). Bentons data indicates, moreover, that extending the barrel length beyond 16 calibers resulted in a gain in muzzle velocity of only about 5½ per cent while extending it beyond 12 calibers yielded only about a 12 per cent gain. Due to the effects of aerodynamic drag, which increases as a function of the velocity squared, these increases in muzzle velocity would have resulted in even smaller increases in range. All of these considerations are shown graphically in Figs. 15 and 16.
This data is, of course, not precisely applicable to all sizes and classes of sixteenth-century artillery. The powder charges used in Collados day were on the whole nearly three times as large as those used in Bentons experiment, a factor which was partly compensated for by greater windage a greater difference in size between the bore and the ball in the sixteenth century. The time/pressure curve in sixteenth-century cannon would thus have had a slightly different shape and the greater quantity of powder would have physically filled several calibers of the bores length.6 T. J. Rodman, Reports of Experiments on the Properties of Metals for Cannon and the Qualities of Metals for Cannon and the Qualities of Cannon Powder ... (Boston, 1861), gives data which indicates that the optimum barrel length for very large black powder cannon was shorter than Benton suggests, apparently because a large mass of powder decomposes more efficiently than a small one. Probably for the same reason, proportionately much longer barrels do yield higher muzzle velocities in small arms. This probably applies to some extent to very small artillery pieces as well. Sixteenth-century cannon powder was more coarsely grained than that used in Bentons experiment (though not in Rodmans) and would thus have burned somewhat more slowly. Nevertheless, it is clear that the muzzle velocities of sixteenth-century cannon were not a direct function of barrel length. Indeed, many sixteenth-century cannon including all of the culverins except perhaps Venetian ones had barrels considerably longer than the length which would have produced the greatest muzzle velocity. Even if greater muzzle velocities could have been attained, the rapid rise in the coefficient of drag of spherical projectiles which doubles between Mach 0.5 (one half the speed of sound, or about 550 feet per second on a standard day) and Mach 1.5 (about 1,700 feet per second on a standard day), would have acted to level out differences in range.
Instead, as we show in Appendix 3, cannon were cast with long barrels not for ballistic reasons, but for structural ones to give them added strength and safety.
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1Olesa Muñido, La Organización Naval, vol. I (Madrid, 1968), p. 319. Of equal significance, the Venetian values seem to have been maximum effective ranges rather than maximum ranges, a far more useful concept which no one else seems to have even attempted to quantify.
2See J. D. Blackwood and F. P. Bowden, The Initiation, Burning and Thermal Decomposition of Gunpowder, Proceedings of`the Royal Society, Series A, CCXIII, No. 1114, 304ff. This article is virtually the only sound, experimentally based, published source of information on the chemistry of black powder. For a general explanation of black powder internal ballistics in relatively non-technical terms see E. D. Lowery, Internal Ballistics: How a Gun Converts Chemical Energy into Projectile Motion (New York, 1968).
3Blackwood and Bowden, The Initiation, Burning and Thermal Decomposition of Gunpowder, pp. 298-301.
4This was determined experimentally in a series of tests conducted under a grant from the Department of History, Princeton University, at the H. P. White Laboratory, Bel Aire, Maryland, on 1 July 1970, by the author and personnel of the H. P. White Laboratory under the direction of Mr. William Dickinson, Director, and Mr. L. S. Martin, Assistant Director. While the value of this threshold pressure was only approximately determined, there can be no doubt as to its existence, particularly where dry-compounded serpentine powder is concerned.
5Benton, A Course of Instruction ..., p. 127, states that a large culverin 58 calibers long was cast for Charles V. On test firing it was found to have a relatively short maximum range. In a series of experiments it was cut down progressively to 43 calibers, gaining about 1,500 yards range in the process. The range is probably exaggerated; but otherwise the story rings true.
6The larger sixteenth-century powder charges certainly did not result in any significant increase in muzzle velocity. A French experiment with a 36 pound cannon 16 calibers long, cited by Benton, A Course of Instruction ..., p. 130, Shows this clearly. When the powder charge was increased from the weight of the ball (the most common sixteenth-century charge) to one and one-sixth times the weight of the ball the muzzle velocity dropped from 1,320 feet per second to 1,170 feet per second.