Ingalls James Monroe. Handbook of Problems in direct fire

Handbook. — New York: John Wiley & Sons, 1890. — 400 s.This book was prepared while the Author was engaged in teaching ballistics to student officers at the Artillery School, Fort Monroe; and most of the examples were selected from those which had been given out from time to time to the classes under his instruction, as exercises in the practical applications of the ballistic formulae which the more advanced students were required to deduce. It was suggested to the Author, by officers of high rank, that a collection of these and similar examples, in book form, would be of permanent value, not only to the Artillery, but also to the other branches of the service, both regular and militia.Definitions. Notation. General Formulae of direct fire. Formulae relating to the horizontal range. Auxiliary formulae. Ballistic coefficient. Coefficient of reduction. Density of the air. Ballistic tables. Auxiliary tables.Given the muzzle velocity and data for the ballistic coefficient, to calculate the velocity at a given distance from the gun. Comparison of computed with measured velocities. Striking energy of a projectile. Formulae for striking energy in terms of metric units. Penetration of projectiles. Eleven examples.Given the ballistic coefficient and the remaining velocity at a given distance from the gun, to determine the muzzle velocity. Three examples.To compute the distance from the gun at which the muzzle velocity will be reduced a given amount. Five examples.To compute the coefficient of reduction when the muzzle velocity and final velocity are both measured. One example.To compute the time of flight when the muzzle velocity and distance passed over by the shot, are given. Three examples.To compute the remaining velocity after a given time, taking into account the effect of the wind. One example.To compute the remaining velocity at a given distance from the gun, taking into account the effect of the wind. Two methods. Three examples.To compute the effect of a wind upon the range. Application to the 3.2-in. B. L. steel gun. Remarks upon Problems VI, VII and VIII. Two examples.Given the ballistic coefficient, the muzzle velocity, and angle of departure, to compute the remaining elements. Two methods. Nine examples.Given the range and angle of departure, to compute the muzzle velocity. Two methods. Six examples.Given the range and striking velocity, to compute the remaining elements of the trajectory. Three examples.Given the muzzle velocity and range, to compute the remaining elements of the trajectory. Two methods. Three examples.Given the muzzle velocity and angle of departure, to compute the elements of the trajectory at the summit. Effect of altitude upon the flight of a projectile. Table of altitude factors. Penetration of armor. Five examples.Given the muzzle velocity, to determine the angle of departure which will cause a projectile to hit an object situated above or below the level of the gun. Two methods. Horizontal range. Rigidity of the trajectory. Seven examples.The computation of coordinates for plotting a given trajectory. Two methods. Approximate expression for y. Five examples.Given the elements of a trajectory and any ordinate, to compute the corresponding abscissa. Practical applications. Danger-space. Application of the principle of the rigidity of the trajectory. Approximate method for computing the danger-space. Sladen’s method of computing danger-spaces. Danger-range. Point-blank firing. Effect of error in estimating distances. Fourteen examples.Given the range, the final velocity, and the maximum ordinate, to compute the initial velocity and the ballistic coefficient, for small angles of departure. Relation between weight and calibre of bullet. Inverse problem. Relation between velocity, weight of projectile, and powder charge. Three examples.To calculate the volumes and weights of oblong projectiles and their ballistic coefficients. Relative weights of oblong projectiles. Ballistic coefficients of different oblong projectiles. Similar oblong projectiles. Length of ogival head. Eighteen examples.Given the muzzle velocity, the angle of departure, and the range, to compute the ballistic coefficient and coefficient of reduction. Best method of computing the coefficient of reduction. Two examples.To calculate the drift of an oblong projectile. General explanation of drift. Mayevski’s formula for drift. Baills’ formula for drift. Effect of wind upon drift. Didion’s method of computing the deviating effect of wind. Maitland’s formula for wind deviation. Formula for computing the area of transverse section of oblong projectile. Twist of rifling. Rotation of a projectile about its axis. Revolutions per second. Surface velocity of rotation. Angular velocity of projectile’s rotation. Moment of inertia of an ogival head. Radius of gyration of an ogival head. Moment of inertia of the cylindrical part of a projectile. Radius of gyration of body of projectile. Radius of gyration of a cored shot or shell. Weight of cored shot. Centre of gravity of an'ogival head. Total muzzle energy of an oblong projectile. Twelve examples.To determine the probability of fire and the precision of fire-arms. Preliminary considerations. Centre of impact. The sum of the squares of the vertical (or horizontal) deviations with reference to the centre of impact, is a minimum. Absolute deviations. Centre of impact on a horizontal target. Law of the deviation of projectiles. Mean quadratic deviations. Mean deviations. Relation between the mean quadratic and mean deviations. Expression for it in term of the mean quadratic and mean deviations. General probability table. Probable deviation. Fifty-per-cent zones. Twenty-five-per-cent rectangle. Probable rectangle. Table for computing sides of rectangles having a given probability. Enveloping rectangle. Comparison of experiment with theory. Table for computing the width of a zone of given probability. Probability of hitting any plane figure. Curves of equal probability. Relations between the semi-axes of ellipses of equal probability and the deviations. Probability of a projectile falling within an ellipse of equal probability. Table for computing the semi-axes for a given probability. Area of probable ellipse. Equation of probable ellipse. Table for computing the probability of a given ellipse. Probability of hitting a given object. Supply of ammunition. Probability that at least one shot will hit the object. Criterion for rejecting abnormal shots. Probability of the arithmetical mean. Twenty-one examples.To compute a range table. General considerations. Range column. Angles of departure. Angles of elevation. Variations of the angles of departure or of elevation. Variations of the muzzle velocity. Time of flight. Drift. Angle of fall. Striking velocity and penetration of armor. Range table for 8-inch B. L. naval gun. Variation of the angle of departure due to a variation of the range. Variation of the range due to a variation of the muzzle velocity.