Donald Pack's wartime papers

Donald Pack worked for the Branch for Theoretical Research, Armament Research Department, Ministry of Supply, Fort Halstead, from 1942 to 1946. During this time he collaborated with a number of colleagues on important wartime research which was published with permission from the Chief Scientific Officer, Ministry of Supply, after the war ended. Below we give some details of some of this work:

(with R Hill and N F Mott) Theoretical research report 2/44, U.K. Armament Research Department, 1944 (unpublished) Penetration by Munroe Jets.
(with R Hill and N F Mott) Theoretical research report 13/44, U.K. Armament Research Department, 1944 (unpublished).
(with R Hill) An investigation, by the method of characteristics, of the lateral expansion of the gases behind a detonating slab of explosive.

Originally a Ministry of Supply report of January 1944, it was published by the Royal Society of London in 1947.

Abstract: The phenomena occurring when an uncased explosive charge is detonated in a fluid medium are examined by hydrodynamical methods. Attention is focused chiefly on the pressure and velocity distributions in the gaseous products of the explosion, which expand laterally behind the detonation wave as it travels down the charge, the results being shown in graphical form. To simplify the problem, the charge, and the gas and fluid fields, were treated as two-dimensional. The hydrodynamical equations were solved numerically using the method of characteristics. This dates back to Monge, but it is only recently that it has been applied to the numerical solution of hyperbolic equations. The methods of numerical integration used in this paper are similar to those developed early in the war by the Research Section of the External Ballistics Department, Ordnance Board, for determining the velocity distributions around projectiles moving at supersonic speeds. The nature of the boundary conditions made it necessary to find explicit theoretical formulae for the gas field near the charge, and the analysis involved is given at length. For the problem in which the surrounding medium is air, the shape and position of the shock waves set up by the explosion are calculated. The shock waves are found to be straight to the nominal accuracy of the calculations (1 in 5000) for six charge widths from their intersections with the block of explosive.
On the formation of shock-waves in supersonic gas jets (Two-dimensional flow)

An abbreviated account was given before the Sixth International Congress of Applied Mechanics in Paris, September 1946. Although Pack was working for the Branch for Theoretical Research, Armament Research Department, Ministry of Supply, when he carried out the work, he was on the staff of University College, Dundee when it was published in 1948.

Abstract: When a jet of gas issues from an orifice as a parallel stream with a given supersonic velocity and flows in a steady state through an outer medium at rest, its behaviour is governed by the ratio between the exit pressure of the jet and the pressure of the outer medium. If this ratio is only a little greater than unity, the jet has a periodic structure to a first approximation. This state has been examined by earlier workers; it is discussed here from the point of view of the 'characteristics' of the hyperbolic second-order partial differential equation of potential flow. The periodic structure ceases to give an adequate representation of the jet as the pressure ratio is increased, and shock-waves occur on account of the compressive effect of the outer medium. A method is given for computing the conditions in a steady two-dimensional supersonic jet. It is shown how the point of origin of a shockwave and the shape of the shock-wave formation may be obtained by theoretical means. The results of two calculations, given graphically, are discussed and compared, as far as possible, with experimental work. An expression is obtained for the minimum pressure in a jet. From the general behaviour of a jet with increasing chamber pressure it is found possible to infer the initial direction of the shock-wave arising at or near the muzzle of a gun after firing.

Introduction: There are many physical problems which depend for their proper resolution upon a knowledge of the behaviour of a jet issuing from an orifice with a velocity greater than the local velocity of sound, two of the most important arising in connexion with the gas stream from a gun and from the exhaust of a rocket motor. These problems are at best rotationally symmetrical, and involve, in their theoretical solution, a great amount of labour in computation, since analytical solutions proper to the initial conditions are not known at present, and numerical (or graphical) methods must be employed. The same difficulty arises when two-dimensional (plane) jets are considered, but the numerical work is shorter; we shall limit ourselves in the present paper to a study of properties of such jets, and in particular to those properties which are the most interesting features of the natural problems - namely, the formation and the form of the shock-waves which occur.
(with W M Evans and H J James) The propagation of shock waves in steel and lead.

The work of this paper was also carried out while Pack was working for the Ministry of Supply and published by the Physical Society of London in 1948.

Abstract: An investigation is made of the stress system set up by an explosive detonating in contact with a metal surface. An extrapolation from data on the compressibility of steel and lead leads to the conclusion that the shock wave set up by the detonation has an initial velocity in steel which is less, and an initial velocity in lead which is greater, than the velocity of plane elastic waves. The time taken by the fastest pulse to penetrate various lengths of steel and of lead has been measured experimentally, and the results confirm that the plane elastic waves move more quickly for steel; while for lead the shock wave before damping has a velocity well in excess of that of the elastic waves.

Review: Using a type of electric-pin method (developed by G I Taylor in 1944) and a Baird-type microsecond chronometer to follow the propagation of shock waves through various lengths of steel and lea, they first observe a two-wave structure indicating an elastic-plastic response. They measure the velocity of the plastic wave - a stress wave that results in the irreversible repositioning of atoms relative to their neighbours, and a type of shock wave - and find that its velocity in steel is less than (and in lead greater than)the velocity of planar elastic waves.
(with W M Evans) Penetration by High-Velocity ('Munroe') Jets: I.

The work of this paper was also carried out at the Armament Research Establishment, Fort Halstead, Kent. It was communicated to the Royal Society by N F Mott in 1950.

Abstract. By means of certain simplifying assumptions a formula is developed for the penetration into a ductile target by a high-velocity Munroe ') Jet. The action of the jet is divided into two stages, each making its contribution to the total penetration In the first stage a hole is formed by the lateral compression of the target as the jet penetrates it; the second stage begins when the last particle of the jet has ceased to act, the hole continuing to deepen until the residual energy in the target has been spent. At the high pressures set up by a Munroe jet the strength of the target plays only a subsidiary part In the phenomenon.

Introduction: Experiments were carried out by Munroe (1888) in which gelatinous cartridges, each with a conical indentation in the end, were placed against a steel target and exploded. It was observed that these cartridges produced indentations in the target which were similar in form to those in the original cartridge. The discovery was not entirely new ; at the end of the eighteenth century it had been known that the existence of a hollow in the forward end of a blasting charge led to an enhancement of the explosive effect along the axis. The 'hollow charge' was used to some extent in mining in Europe during the early part of the nineteenth century, but it appears to have fallen into disuse, and Munroe's later work led to little research of interest until recent years.
(with W M Evans) Penetration by High-Velocity ('Munroe') Jets: II.

The work of this paper was also carried out at the Armament Research Establishment, Fort Halstead, Kent. It was communicated to the Royal Society by N F Mott in 1950.

Abstract: Work is described in which the two stages of penetration by a high-velocity ('Munroe') jet were separated experimentally. The large penetrations measured in lead targets are shown to result from the flow which takes place in the metal after the jet itself has been consumed For a given Jet at a given stand-off it is possible to predict the penetration into a combination of targets from the results of a very small number of standard experiments. The method depends upon the calculation of a certain quantity which is constant for a given jet at a given stand-off, and examples are given of the determination of this quantity from experimental data.

Introduction: In a previous paper (Pack and Evans 1951, to be referred to as I) is given a theory of penetration by Munroe jets in which the penetration observed in a ductile target is divided into two parts : (i) the primary penetration, which depends chiefly upon the density of the target, and (ii) the secondary penetration, which takes place after the jet has ceased to act, and which represents the expenditure of the energy left in the target at the time the last particle of the jet has been consumed. In the present paper work is described in which the factors involved have been separated experimentally, and an analysis of the results provides reasonable confirmation of the proposed theory, making it possible to predict the penetration of a high-velocity jet into any combination of ductile targets, using the results obtained from a very small number of standard experiments. It is known that when a conical metal lining is used for a hollow charge, the metal divides into two parts, the high-velocity Munroe jet in front and a slower, much wider (and often solid) piece of metal, usually called the 'plug', behind. The plug is capable of increasing the penetration, acting after the jet has been consumed, and our experiments have thrown some light upon its behaviour.

Last Updated May 2017