Firing Tables Research Articles

Study on the Firing Table Compiling of a New Type of the Very Low Altitude Interception Device

The Firing Tables Compiling of a new type of the very low altitude interception device is studied in this paper. Based on the analysis of drag coefficient identification during the date processing of the Firing Tables experiment, and the theoretical trajectory correction, then according to the defects of the traditional methods for the Compilation of Firing Tables, a new method of determining the correction data is developed which replaces the simple data with the correction function. This method will reduce the error to an obvious degree.

Simulating and Testing on Trajectory for Bomb with Parachute under Low Altitude Condition

With the development of precision guidance ammunitions, more and more parachutes are used for controlling speed and adjusting posture. At the same time, this will increase the complexity of movement for bomb with parachute. This paper created a simulating model of trajectory for bomb with parachute under low altitude condition. By the comparative study on theoretical trajectory and testing, it can determine the parameters and firing table, and it’s very useful for aircraft ammunition on research and development.

Development of Mortar Simulator with Shell‐In‐Shell System – Problem of External Ballistics

The shell‐in‐shell system used in the mortar simulator raises a number of non‐standard technical and computational problems starting from the requirement to distribute the propelling blast energy between the warhead and the ballistic barrel, finishing with the requirement that the length of warhead′s flight path must be scaled to combat shell firing tables. The design problem of the simulator is split into two parts – the problem of external ballistics where the initial velocities of the warhead must be determined, and the problem of internal ballistics – where the design of the cartridge and the ballistic barrel must be performed.

Improbable Warriors: Mathematicians Grace Hopper and Mina Rees in World War II

June 2003 · Historically Speaking39 Improbable Warriors: Mathematicians Grace Hopperand Mina Rees in World War Il Kathleen Broome Williams Between 1943 and 1945 mathematicians Grace Murray Hopper (1906-1992) and Mina Spiegel Rees (1902-1997) each held positions from which they influenced the nation's ability to wage a modern, math-dependent war.They knew of each other duringthewarand afterward theirUves intersected frequently since they moved in the same professional circles. These improbable warriors were among the few women whose war service proved profoundly beneficial to their later careers. In 1983 Grace Hopper, then seventy-six years old, was made an admiral by special appointment ofthe president ofthe United States. In 1987 the U. S. Navynameditsnew computer center in San Diego for Hopper, and in 1996, four years after her death, it launched the U.S.S. Hopper, an Arleigh Burke-class guided missile destroyer. The recipient ofnumerous medals, awards, and honorary degrees, Grace Hopper was esteemed as a pioneer in the field of computing . Admiral Hopper never went to sea, but her computer expertise and managerial skills made her a pivotal figure in the navy's march to the computer age. Even when she retired in 1986—the oldestserving officer in the navy—Grace Hopper continued working as a consultant for Digital Equipment Corporation. She died in 1992 andwas buried with full military honors in Arlington National Cemetery. Atthe heartofall these accomplishments was Hopper's brilliance in mathematics. Had it not been for World War ?, however, she might never have left the genteel campus in New Yorkwhere she was teaching. Hopper majored in mathematics at VassarCollege . AfterearningaMasters degreein 1930 and fouryears later a Ph.D. fromYak— a rare accomplishment for women in those days—she returned to Vassar to teach. But one year after Pearl Harbor Hopper joined theWAVES—navywomen—andupon graduating from midshipmen's school her mathematical skills landed herin the navy's Computation Project at Harvard University. The rapidlyexpanding data management needs ofWorld War ? accelerated the development ofmodern digital computers, especially in Britain and the United States. One American electro-mechanical device begun before the war was the brainchild ofHoward Aiken, professorofphysics and applied mathematics at Harvard. Aiken's Mark I, built by IBM, was the first functional, large-scale, automatically sequenced, general-purpose, digital computerto be produced inAmerica. When it was completed in 1944, the MarkI was installed at Harvard andwas immediately leased for the duration ofthe war by the U.S. Navy, desperate for gunnery and ballistics calculations. Aiken, a naval reserve officer, was given command of the navy's Harvard Computation Project. Aiken's computingmachine was in many ways unique. Itwas fifty feetlong, eight feet tall, and eight feet deep, filling an entire room. It had more than 750,000 parts, used 530 miles ofwire, and weighed about five tons. Most impressive were its speed and its automatic functioning. When programmed instructions were fed into the machine on punched paper tape it performed a series of arithmetic operations without human intervention . Aiken estimated that the Mark I was nearly one hundred times more productive than a manuallyoperated calculator. The original wartime staffof the Computation Labwas small—fewer than a dozen. Initially, Hopperwas one ofonlythreemathematicians writing programs for the Mark I and thus was one ofthe first-ever computer programmers. Throughoutthewarthis team, which grewto almostfortybyJanuary 1946, ran the Mark I around the clock, churning out essential data for all sorts of ordnance projects. Hopper's first task at the lab was to write a program for computing rocket trajectories. Her program accommodated inputvariables includingtargetbearing, elevation andrange, the ship's angle ofpitch and roll, drift angle, and time offlight. Until the Mark I became operational, the navy had to rely on what Hopper called "acres of girls down at Aberdeen [Proving Ground] using handdriven calculators" to create such firing tables,' and they could not keep up with the wartime demand. Anotherproblem Hopper tackled was to discern the best way for a minesweeperto locate magnetic mines. Further , she wrote a 561-page Manualthat gave a full and detailed description ofthe MarkI: all its parts and all its circuits, as well as how to programit. Years later,whenshewas asked how she learned to program the Mark I, Hopper's...

Iterative learning identification of aerodynamic drag curve from tracking radar measurements

The aerodynamic drag coefficient curve of spin-stabilized projectiles is very important to the fast generation of accurate firing tables. To identify it from Doppler tracking radar measured velocity data in flight tests, an iterative learning concept (ILC) is applied. High-order ILC algorithms are proposed. Convergence conditions are given in a general problem setting. A 3-DOF point mass trajectory prediction model is proposed. The learning gains, which vary with respect to both time and iteration number, have been used for a faster convergence compared to the constant learning parameter choices. Furthermore, in this paper, a bi-linear ILC scheme is proposed to produce even faster learning convergence. The flight testing data reduction results of an actual firing practice demonstrate that the iterative learning method is very effective in curve identification.

Before the ENIAC [weapons firing table calculations

During World War II, the Ballistic Research Laboratory of the US Army was charged with the responsibility of preparing firing tables for the various new weapons under development. The computations required for the preparation of these firing tables were so time-consuming that they overwhelmed the facilities available at the laboratory. In spite of the extensive arrangements the laboratory made with the University of Pennsylvania for assistance, the backlog continued to grow. At one point, more than 100 female students were engaged to carry out firing table calculations. It was to relieve this bottleneck that John W. Mauchly and J. Presper Eckert, two members of the faculty of the Moore School of Engineering, the University of Pennsylvania, proposed the construction of the ENIAC (Electronic Numerical Integrator And Computer), which was funded by the US Army. In this article, I describe the nature of the computations required in the preparation of firing tables and explain the reasons why these calculations were so burdensome.

NNERVE: neural network extraction of repetitive vectors for electromyography--Part I: Algorithm.

Artificial neural network (ANN) based signal processing methods have been shown to have significant robustness in processing complex, degraded, noisy, and unstable signals. A novel approach to automated electromyogram (EMG) signal decomposition, using an ANN processing architecture, is presented in this paper. Due to the lack of a priori knowledge of motor unit action potential (MUAP) morphology, the EMG decomposition must be performed in an unsupervised manner. An ANN classifier, consisting of a multilayer perceptron neural network and employing a novel unsupervised training strategy, is proposed. The ANN learns repetitive appearances of MUAP waveforms from their suspected occurrences in a filtered EMG signal in an autoassociative learning task. The same training waveforms are fed into the trained ANN and the output of the ANN is fed back to its input, giving rise to a dynamic retrieval net classifier. For each waveform in the data, the network discovers a feature vector associated with that waveform. For each waveform, classification is achieved by comparing its feature vector with those of the other waveforms. Firing information of each MUAP is further used to refine the classification results of the ANN classifier. Then, individual MUAP waveform shapes are derived and their firing tables are created.

John von Neumann and the Origins of Modern Computing by William Aspray

174 Book Reviews TECHNOLOGY AND CULTURE John von Neumann and the Origins of Modem Computing. By William Aspray. Cambridge, Mass.: MIT Press, 1990. Pp. xvii+ 376; illus­ trations, notes, bibliography, index. $35.00. In 1943, the Hungarian-born mathematical physicist John von Neumann visited London on behalf of his adopted country, the United States. He was studying aspects of mine warfare for the U.S. Navy. While in England, von Neumann developed what he jokingly called “an obscene interest in computational techniques.” This volume shows how von Neumann’s interest in computing and computing machines shaped the description, design, and use of the first elec­ tronic computers. William Aspray begins with a brief account of von Neumann’s family, education, research, and migration to the Institute for Ad­ vanced Study (IAS) at Princeton. He then describes wartime work on the Manhattan Project and several other government-funded pro­ grams that prompted von Neumann’s interest in computation. Dur­ ing this time, von Neumann was closely associated with those building the pioneering ENIAC computer at the University of Pennsylvania. In the closing months of the war, he wrote a draft description of the next computer they hoped to build, the EDVAC. This work, the first account of a stored-program electronic computer, would have enor­ mous influence in the following years. The ENIAC and other wartime computers were used to carry out large numbers of relatively routine calculations, such as those needed in the preparation of firing tables. By early 1945, von Neumann wanted to build a computer devoted to scientific research. Finding funds for the project, hiring staff, and securing a place to build the machine all offered challenges. The core of Aspray’s book is his account of how von Neumann and his associates came to build a computer at the IAS; what von Neumann contributed to the logical design and engineering of the IAS computer; and how the instru­ ment was used in studies of numerical analysis, meteorology, and diverse other areas. Aspray concludes with an account of von Neu­ mann’s contributions to the theory of information and of his postwar work as a consultant to government and industry. Three aspects of this book deserve special mention. The first is Aspray’s skillful use of a wide range of publications, government documents, manuscripts, and oral histories. Some of these materials have only become available recently, and this volume suggests how they can and should be incorporated into the history of computing. Second, Aspray examines the electronic computer as a mathematical tool. As its name suggests, the computer was originally designed to do computations. Von Neumann and others who pioneered in comput­ ing worked out the logical design of such instruments and mathemat­ ical procedures for using them efficiently. They often used computers to solve problems of mathematics and mathematical physics. To those TECHNOLOGY AND CULTURE Book Reviews 175 familiar with the history of early computing, these statements will come as no surprise. For those preoccupied with later computer technology and its applications, Aspray’s account may be a useful reminder. Finally, Aspray’s book bears powerful witness to the role of military considerations not only in the history of computing but in postwar American science. Von Neumann built a computer to solve “scientific” problems. Some of this work, such as Martin Schwarzschild’s astrophysical research, was notjustified by its possible military importance. However, von Neumann persuaded military agencies that they should contribute funds to build the IAS computer not only because copies of it could then be built at military installations, but because the work he and his associates planned to do was of direct military significance. The first large problem run on the IAS computer related to the design of the hydrogen bomb. Computations for weather forecasting, which took the largest amount of the computer’s time, were important to the U.S. Navy. During the same period, von Neumann made theoretical studies of linear programming that proved of great use in solving logistics problems of the U.S. Air Force. Computer develop­ ment in the 1950s was often described in terms of “business” and “scientific” applications. Scientific applications included not only projects like the IAS...

Vannevar Bush and the Differential Analyzer: The Text and Context of an Early Computer

One day in 1942, the Rockefeller Differential Analyzer was dedicated to winning the war. For the next several years this large mathematical machine, the centerpiece of MIT's Center of Analysis, labored over the calculation of firing tables and the profiles of radar antennas.' Weighing almost a hundred tons and comprising some two thousand vacuum tubes, several thousand relays, a hundred and fifty motors, and automated input units, the analyzer was the most important computer in existence in the United States at the end of the war.2 (See fig. 1.) Wartime security prohibited its public announcement until

Modelling the firing tables of field artillery (cannon 105 mm howitzer)

In some areas the procedure for firing heavy field artillery requires the look-up of sets of firing tables. This paper proposes to model the firing tables by a family of functions which can be utilized by microcomputers. In so doing, the manual calculation of firing procedure will be substituted by a computerized one which has the advantages of speed and accuracy. Besides, utilizing this proposed model in microcomputers is more advantageous than storing the whole firing tables in the computer memory since the latter method requires large memory size that may impede the mobility and flexibility of the firing control system.

A series of base functions for global analytical approach to firing table

A series of base functions has been proposed for global analytical approach to the firing table on cannons and guns. Numerical tests on the firing table of a gun of specific model prove that it is satisfactory, showing that these functions should also be useful to approach to the firing table of firearms of other models.

An Appraisal of the Errors Involved in Estimating the Size Distribution of a Given Aggregate Income

IN ALMOST any science, quantitative problems arise for which approximation methods provide the most expedient solution. Refined methods often do not justify the labor they entail, either because the problem in hand does not require great precision, or because errors in the basic data limit the precision attainable. In exterior ballistics, for example, the gravitational attraction of the moon, which affects the motion of a projectile, is not taken into account in the calculation of firing tables because the effects of this attraction are small in comparison with the random errors resulting from unavoidable variations in the most carefully standardized ammunition and the most skillfully manufactured gun barrels. Some time ago in this REVIEW an approximation method for estimating the size distribution of incomes was discussed.' For most years little information is available on the distribution of incomes, but for I935-36 the National Resources Committee has compiled excellent data. Could the N.R.C. distribution be used as the basis for estimating the distribution for other years? If the aggregate income for some other year, say I946, can be determined (or predicted for some future year), and if the inequality of the distribution can be assumed to remain unchanged, the distribution for this other year can be estimated quite readily. This assumption of the same degree of inequality naturally suggests the Lorenz curve as a tool of analysis; however, the real key to the problem is the cumulative frequency curve. In a later article, graphical interpolation with the cumulative frequency curve was proposed as the most direct approach.2 It had the advantage of being simple, easy, and quick. Its accuracy, though not great, appeared adequate. Great precision was almost impossible, regardless of method, because the basic data and the underlying assumptions were approximations themselves. Moreover, most of the problems involving income distributions such as estimates of consumer expenditures or tax receipts do not require great precision. As an example, a problem originally proposed by Ames was discussed: to estimate an income distribution having the same inequality as the N.R.C. distribution, but an average income of $2000 instead of the $I502 for the N.R.C. distribution. cumulative frequency curve was drawn for families (including single persons) from the N.R.C. data -and also the corresponding curve for incomes received and the required distributions of both families and incomes received were read directly from these curves.3 In this example, the curves were drawn on semi-logarithmic paper, and the class intervals chosen were those of the N.R.C. distribution; however, it was stated that many other graphical devices would suffice, and it should have been obvious that any other set of class intervals could have been chosen. Furthermore, the fundamentals of the method are perfectly adaptable to numerical interpolation. In commenting upon this example, Eugene Clark and Leo Fishman might have criticized the arbitrary assumption of an unchanging inequality of income, or pointed out some of the fundamental weaknesses of the underlying data that make precise calculations difficult.4 Instead, they made a major issue out of a very minor point: namely, that the average income in any class interval depends upon the slope of the distribution curve, and that a change in the slope will inevitably affect the average income. 1 Edward Ames, A Method for Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, XXIV (I942), Pp. I84-89. 2David Durand, A Simple Method for Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, XXV ( 943), Pp. 227-30. 3 Ibid., Table I. 4 Eugene Clark and Leo Fishman, Appraisal of Methods for Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, XXIX (I947), PP. 43-46.