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Interior Ballistics

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Interior Ballistics Interior Ballistics JAMES M INGALLS Colonel United States Army, retired Formerly Instructor of Ballistics at the U. S. Artillery School ; Author of Treatises on Exterior and Interior Ballistics, Ballistic Machines, Ballistic Tables, Etc. THIRD EDITION NEW Y O R K J O H N W I L E Y & S O N S LONDON: CHAPMAN & HALL, L im it e d 1912 C o p y r i g h t i q u By JAMES M. INGALLS PREFACE TO THE EDITION OF 1894 ( SECOND EDITION) W h e n , in the summer of 1889, it was decided by the Staff of the Artillery School to add to the curriculum a course of interior ballistics, the instructor of ballistics, knowing of no text-book on the subject in the English language entirely suited to the needs of the school, employed the time at his disposal before the arrival of the next class of student officers in studying up and arranging a course of instruction upon this subject, so important to the artillery officer. The text-book then planned was partially completed and printed on the Artillery School press, and has been tested by two classes of student officers. In the summer of 1893 the author again had leisure to work on the unfinished text-book, but in the meantime he had found so much of it which admitted of improvement that, with the encouragement of Lieutenant-Colonel Frank, Second Artillery, the Commandant of the School, it Was decided to rewrite nearly the entire work as well as to complete it according to the original plan by the addition of the last two chapters. With the exception of portions of Chapters IV and V, the author claims no originality. He has simply culled from various sources what seemed to him desirable in an elementary text­ book, arranged it all systematically from the same point of view and with a uniform notation. A rtillery School, February 15, 1894. iii PREFACE TO THE THIRD EDITION The second edition of this work was used as a text-book at the Artillery School until the School suspended operations at the outbreak of war with Spain, in April, 1898. This edition, having become exhausted, the author has been induced by the request of officers for whose wishes he has great respect, to prepare a new edition embodying the results of some investiga­ tions which were published in Volumes 24, 25 and 26 of the Journal of the United States Artillery, and which have been favorably received by Artillery Officers, both at home and abroad. The Journal articles have been rewritten, and many improve­ ments attempted, suggested by friendly criticisms for which the author wishes to express his thanks. As most of the formulas of interior ballistics in the present state of our knowledge of the subject are more or less empirical in their nature, many applications of the formulas deduced in Chapter IV are given in the following chapter to show their agreement with the results of actual firing with guns of widely different calibers. In this connection it is gratifying to be able to quote from an article published in the Journal of the Royal Artillery, vol. 36, No. 9, by Captain J. H. Hardcastle, R.A., who states, with reference to the formulas of Chapter IV as applied to firing-practice with English guns loaded with cordite, that “ After many dozens of calculations I can find no serious disagreement between the results of calculation and experiment.” VI PREFACE In this paper Captain Hardcastle has very ingeniously adapted the formulas of Chapter IV to slide-rule operations, thereby lessening the labor of calculation somewhat, though at the expense of accuracy in some cases. For the benefit of those who are accustomed to use the slide rule in making logarithmic com­ putations a supplemental table of the X functions has been added to Table I, omitting the function X S9 which is not used in Captain Hardcastle’s method. This work was prepared primarily for the officers of our Coast Artillery Corps; but it is hoped that gun-designers and powder-manufacturers may find in it something useful to them. The author desires to express his indebtedness to Lieut.- Colonel Ormand M. Lissak and Major Edward P. O’Hem of the Ordnance Department for valuable suggestions and for data employed in the “ applications.” Also to Captains Ennis and Bryant, for assistance in computing Table I. Providence, R. I., September 20, 1911. TABLE OF CONTENTS C H A P T E R I PAGE Definition and object.— Early history of gunpowder. Robins' experi­ ments and deductions. Hutton's experiments. D ’Arcy’s method. Rumford's experiments with fired gunpowder. Rodman’s inventions and experiments. Modern explosives. Density of powder. Inflam­ mation and combustion of a grain of powder. Inflammation and combustion of a charge of powder...................................................i to 14 CHAPTER II Properties of perfect gases.— Marriotte’s law. Specific volume. Specific weight. Law of Gay-Lussac. Characteristic equation of the gaseous state. Thermal units. Mechanical equivalent of heat. Specific heat. Specific heat of a gas under constant pressure. Specific heat under constant volume. Numerical value of R for atmospheric air. Law of Dulong and Petit. Determination of specific heats. Ratio of specific heats. Relations between heat and work in the expansion of a per­ fect gas. Isothermal expansion. Adiabatic expansion. Law of tem­ peratures. Law of pressures and volumes. Examples. Theoretical work of an adiabatic expansion in the bore of a gun. Noble and AbePs researches on fired gunpowder in close vessels. Description of apparatus employed. Summary of results. Pressure in close ves­ sels deduced from theoretical considerations. Value of the ratio of the non-gaseous products to the volume of the charge. Determina­ tion of the force of the powder, and its interpretation. Theoretical determination of the temperature of explosion of gunpowder. Mean specific heat of the products of combustion. Pressure in the bore of a gun derived from theoretical considerations. Table of pressures. Theoretical work effected by gunpowder. Factor of effect. Actual work realized as expressed by muzzle energy..........................15 to 54 CHAPTER III Combustion of a grain of powder under constant atmospheric pressure.— Notation. Definition of the vanishing surface. General expression for the burning surface of a grain of powder. Expression for the VII viii TABLE OF CONTENTS PAGE volume consumed in terms of the thickness burned. Definition of the form characteristics. Fraction of grain burned. Applications. Spheres. Cubes. Strips. Solid cylinders. Piereed cylinders. Multiperforated grains. General expression for surface of combus­ tion of multiperforated grains. Maximum surface of combustion. Slivers. Expression for volume of slivers. Proposed ratio of dimen­ sions of multiperforated grains to web thickness. Expression for weight of charge burned at any instant. Expressions for initial volume and surface of combustion of a charge of powder.. Expression for specific gravity of grain. Initial surface of unit weight of powder. Volume of charge. Gravimetric density. Density of loading. Reduced length of initial air space. Working formulas for English and metric units. Examples.............................................. 55 to 78 CHAPTER IV Combustion and work of a charge of powder in a gun.—'Introductory remarks. Sarrau’s law of burning under a variable pressure and reason for adopting it. Expression connecting the velocity of burning of grain with velocity of projectile in bore. Expression for fraction of charge burned in terms of volumes of expansion of the gases generated. Expression for velocity of projectile while powder is burning. Velocity of projectile after powder is all burned. Pres­ sure on base of projectile while powder is burning. Pressure after powder is burned. Expression for the initial pressure upon the sup­ position that the powder was all burned before the projectile had moved from its seat, and the relation of this pressure to the force of the powder. Method of computing the X functions. Special formulas. Expressions for maximum pressure. Formula for velocity of combustion under atmospheric pressure. Working formulas. Eng­ lish units. Metric units. Characteristics of a powder. Expressions for constants in terms of the characteristics for English and metric units. Expressions for force of powder when weights of charge and projectile vary........................................................................79 to 97 CHAPTER V Applications.— Formulas which apply only while powder is burning. For­ mulas which apply only after powder is all burned. Formulas which apply at instant of complete combustion. Discontinuity of pressure curve for certain forms of grain. Monomial formulas for velocity and pressure. Typical pressure and velocity curves. Example of TABLE OF CONTENTS IX PAGE monomial formulas, as applied to the 8-inch B. L. R. Comparison of computed velocities and maximum pressures with observed values. Determination of travel of projectile at point of maximum pressure, and also when powder is all burned. Expression for fraction of charge burned for any travel of projectile. Examples. Greatest efficiency when charge is all consumed at muzzle. Application to hypothetical 7-inch gun. Binomial formulas for velocity and pressure. Forms of grain for which binomial formulas must be employed. Methods for determining the constants from experimental firing. Applications to Sir Andrew Noble’s experiments with a 6-inch gun. Description of the experiments. Discussion of the data for cordite, 0.4", 0.35", and 0.3" diameter. Remarks on the so-called “ force of the powder” as deduced from the calculations. Examples. Applica­ tion to the Hotchkiss 57-mm. rapid-firing gun. Data obtained by D ’Arcy’s method. New method for determining the form char­ acteristics of the grains. Application to the magazine rifle, model of 1903. Powder characteristics. Formulas for designing guns for cordite, with application to a hypothetical 7-inch gun.
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