Cranz C., Becker K. Exterior ballistics

Translated from the second german edition. — London: His Majesty’s Stationery Office, 1921. — 494 p. (Handbook of Ballistics. Vol. I)Exterior ballistics being a theoretical examination of the motion of the projectile from the muzzle to the target.The motion of a projectile in a vacuum
The parabolic trajectory
Family of trajectories with constant initial velocity
Family of trajectories with constant angle of departure
Fire over sloping ground
Examples
Trajectory in a vacuum, taking into account the decrease of gravity with the altitude, and the convergence of vertical lines owing to the curvature of the earth
FormulaeThe resistance of the airAir-resistance to an elongated shell on the assumption that its axis lies in the direction of motion of the centre of gravity
General considerations
Theoretical considerations of the law of air-resistance
Empirical laws of air-resistance
Experimental methods
On the influence of the skew position of the shell on the direction of motion of the centre of gravity.
General equations
Calculations relating to the shape of the shell head.
The coefficient of form-value
The most suitable shape of head
The density of the air
Calculation of the density
Critical remarksProblems relating to the trajectory
The general equations and their integrability
An inversion problem
General properties of the trajectoryFirst group of calculations in the approximate solution of the ballistic problem. Approximate solution of the differential equations
The integrability of the equations
Method of Euler-Otto
Method of Bashforth
Method of development in seriesSecond group of numerical methods of approximation. Exact solution of an approximate equation
General considerations
Solution of J. Didion
Bernoulli-Didion method
Method of Siacci
The Krupp-Gross method
Siacci’s other methods
Vallier’s method
Charbonnier’s solution
The secondary ballistic functions
Graphical methods of solutionInvestigation of modern methods of calculation
The accuracy of various methods
Practical applications
The effects of the law of air-resistanceThe high angle trajectory, and the method of swinging the trajectoryCalculation of a high angle trajectory
Motion of a shell in a vertical line
Shooting nearly vertical
Calculation of high angle trajectoriesOn the tilting of the trajectory
The ordinary procedure of tilting the trajectory
The method of Burgsdorff and Gouin
Percin’s methodSolution of various trajectories. Employment of experimental results for the construction of range tables
Solution of problems by means of Table 12, Vol. IV
The use of other tables
Practical applications of the calculation of range tablesLateral deviations of a shell
General considerations
The effects of small changes in the initial velocity, etc.
Deviations due to various causes
Deviations due to the wind
Deviation due to rotation of the earth
Deviation of bullets with bayonet fixed to the rifleLateral deviations due to rotation of the shell
Deviations of spherical shells
Deviation of a rotating elongated shell
The flight of a rotating shell
Explanations of the drift
Precession and nutation
Curvilinear motion of the centre of gravity
The drift of a rotating shell
Experimental demonstrationsAccidental deviations
Application of the Theory of Probability to Ballistics
The propositions of Bernoulli-Laplace, Poisson and Bayes
Theory of the scattering of projectiles
True and apparent deviations
Successive differences
Recapitulation of results
Calculation of the arithmetic mean in grouped observations
Axes of symmetry of target-diagram
The axes of the target-diagram
The probability of hitting a given area
Probability of hitting a given circular area
Probability of hitting a given elliptical target
Gauss’s method of least squaresOn the explosive effects of shells
Penetration of projectile into a rigid body
Depth of penetration
Effects of shell bursts
Penetration of shells into water
Deflection from the normal trajectory
Gauss’s method of least squaresNotes and appendix
General indexPhotographic records