Open AccessA graphical method of drawing trajectories for high-angle fire
Publication year - 1917
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1917.0022
Subject(s) - trajectory , point (geometry) , position (finance) , range (aeronautics) , constant (computer programming) , altitude (triangle) , function (biology) , mathematics , motion (physics) , geometry , magnitude (astronomy) , mathematical analysis , observation point , physics , computer science , classical mechanics , geology , engineering , finance , astronomy , evolutionary biology , economics , biology , programming language , seismology , aerospace engineering
In May, 1915, I described a graphical method for finding the time of flight, the range, the angle of elevation, in fact, the elements of a trajectory, having given the curve of resistance as a function of the velocity and assuming that the density of the air was constant at all points along the trajectory. The method is therefore only applicable to trajectories of low altitude. In this paper I describe a graphical method for obtaining a series of points on a trajectory of high altitude, taking into account the variation of the density of the air with height. Let A, fig. 1, be a point on a trajectory where the velocity is given and equal in direction toϕ A and in magnitude to VA , and whose position is given by the co-ordinates X and Y. The problem is to find the co-ordinatesx ,y , with reference to the point A, of a second point B, on the trajectory, taking into consideration the actual resistance of the air to the motion of the shell, it being assumed that the variation of the density of the air is known as the shell rises or falls in height; and to find the angleϕ B defining the direction of motion and the magnitude of the velocity at the point B in the trajectory.