Search

A feasibility study was recently completed on a hopping transporter concept for locomotion on the moon. Termed a Lunar Pogo because it would operate similarly to a conventional pogo stick, this vehicle would accelerate up an inclined leg, pick up the leg, and then enter ballistic flight over the moon's surface. Upon recontacting the lunar surface, the Lunar Pogo would decelerate down the leg. Propulsion would be provided by expansion of gas against a piston. Operation would be partially conservative because much of the energy expended by the gas during takeoff would be recovered by compressing the gas during landing. Two models of the ballistics and propulsion have been set up to estimate performance. The simplified first-order model illuminates the thermodynamics of ideal operation. The second-order model, which includes realistic effects such as sliding, provides a better approximation to actual performance. In a one-man Lunar Pogo, an astronaut would typically make 15-m (50-ft) leaps at an average speed of 5-8 km (3-5 miles) per hour.

This ballistics apparatus, assembled at practically no cost, eliminates the need of a spring gun and the nuisance of requiring sufficient space (as in the ballistic pendulum) to project a steel ball horizontally from the laboratory table. It also illustrates the behavior of a loaded spring in the gravitational field.

Analytical studies show that the effect of low-level wind on rocket trajectory dispersion is reduced by judicious shaping of the rocket's thrust-time curve. The dispersion is reduced by a periodic thrust which is initially large and oscillates for a few cycles. When the horizontal wind is constant, the phase of the oscillations depends only on the rocket aerodynamic pitching frequency and not wind magnitude or direction (provided linear aerodynamics is not violated). A series of six-degree-of-freedom trajectory simulations of the ARC AS® sounding rocket confirms that the predicted dispersion reduction does occur. The reduction for singlestage, solid-propellant rockets, however, seems to be limited by the state-of-the-art of internal ballistics. The possibility of winds being highly variable suggests that a single initial high-low thrust variation may be a reasonable design goal. For larger vehicles with strap-on boosters, the duration of the high-thrust boost should not exceed the time required to execute about one-quarter of the first pitching oscillation.

A systematic development of the dynamics of motion appropriate in the supersonic velocity region where satellite orbits can exist, or escape from a gravitational field may arise, is presented.A more realistic treatment of the falling body problem is offered which leads to vertical flight relations that clearly indicate transition from bound to free states of motion.The results of celestial mechanics are adapted and extended toward a broader appreciation of high energy ballistics.In particular, an idealized gunnery table is constructed giving the optimal firing angle and range as well as the time of flight for firing velocities approaching the satellite region.Some elementary features of the satellite orbit are delineated.

The individual wind profile may differ considerably from the mean monthly profile. In cognizance, the correlation method was developed. This method yields some improvement, but requires elaborate mathematical treatment. The computational effort is probably not in accord with the results obtained due to the limitations of the linear correlation concept. The author has developed a new method, called characteristics method. The individual wind profile is represented by mathematically describing the profile with a few characteristic coefficients. This method seems superior to the correlation method.

Small metallic pellets have been fired at velocities up to 6 km/sec by means of modified shaped charges. Previous work in this field has been confined largely to observations of meteors and conventional shaped charges. Data obtained on ballistic phenomena verify the conventional drag force determinations extrapolated to large Mach numbers. Steel pellets at velocities of 2.5 km/sec lose little mass in flight. Pellets composed of lighter metals, such as aluminum at a velocity of 5 km/sec, burn vigorously with the emission of much light and heat. It has been found that the motion of both nonburning and burning pellets can be represented within experimental error by the empirical equation v=v0e−αs, where v0 is the initial velocity of the pellet, v is its velocity after it has traveled a distance s through the air, and α is a constant.

A model of the working recurve bow amenable to analytic solution is developed. The equations of motion of the bow and arrow system are obtained and numerically integrated by computer. It is shown that subject to the approximations, the system is 100% efficient. Variations of the transfer of energy between bow and arrow are discussed in terms of bow parameters and the effects on the archer. A discussion of first-order exterior ballistics and arrow penetration indicates the equipment characteristics most desirable for both the target archer and hunter, subject to the archer's own capabilities.

1. Introduction .—The first part of this paper, written by Love, contains a theoretical solution of the problem of rational hydrodynamics which has been named by writers on ballistics, “Lagrange’s problem”; the second part, written by Pidduck, gives the application to ballistics. In the problem it is supposed that a given mass of gas, which is initially in a uniform state, is contained in a segment of a tube of uniform section. At one end the segment of the tube is bounded by a fixed transverse section, and at the other end the tube is closed by a piston of given mass, which is initially at rest and is free to move along the tube without resistance. It is required to find the subsequent states of the gas and the motion of the piston.

This is the first part of a two part article by Mr. Drake, the purpose of which is to give a factual account of shotgun ballistics for use as a work of reference by forensic experts. The second part of the article, to be published in Volume 3, No. 1, in September of this year, will deal mainly with pattern, penetration and gun bursts.

Millimeter wavelength radars are used to study plasma effects associated with ionized flow fields of projectiles launched at hypersonic speeds into a free-flight ballistic range. Two CW Doppler radars, at frequencies of 35 and 70 Gc/s, measure the nose-on backscattering radar cross sections during flight. The design and performance of the two radars are described in detail. A signal simulator provides absolute calibration. The purpose is to measure changes that occur in the radar cross sections of hypersonic projectiles caused by highly ionized flow fields. Under certain conditions the nose-on backscattering radar cross section of a blunt-nosed metal projectile decreases drastically when a thin, shock-produced layer of ionized gas covers the projectile. A theoretical analysis of this effect is given. Comparisons between theoretical predictions and experimental data show good correlation.

Of the criteria that are used in the design of servomechanisms, the so‐called ``minimum mean‐square'' error criterion is used quite widely in cases where the undesirability of the error increases with its magnitude. There is, however, an important class of applications, particularly in the field of ballistics, where a more appropriate criterion can be defined as the probability that the error be less than some prescribed tolerance. The problem of maximization of this probability is shown to reduce to a number of implicit equations whose solution in practice must be carried out by cut and trial. It is further shown that under certain conditions the maximization of probability yields the same values for the design constants as the minimization of mean‐square error. These conditions are discussed for the general case as well as for certain specific cases which are important in practice.

INSTANTANEOUS photography by means of an -electric spark provides the investigator of highspeed phenomena with a most valuable source of data. Such photographs are of the shadow variety, the bullet shadow being projected upon a photographic plate by a spark of great intensity and short duration. If the bullet is moving with a speed equal to or greater than that of sound, it propagates from both its nose and base a compressional wave. Light from the photographing spark in passing through the denser atmosphere of the compressional wave is refracted as by a lens, so that the wave front is also projected upon the photographic plate with the bullet. The method lends itself readily to the investigation of a projectile's stability at various points along its trajectory and to many allied problems of exterior ballistics. Instructive photographs of the recoil and shell ejection of automatic rifles, pistols, and machine guns may also be obtained in this manner.

High loading densities and flexible thrust-time histories can be obtained in solid-propellant rocket motors by incorporating circumferential slots into a cylindrically perforated grain (slotted-tube motors). However, the head-end pressure of such motors can depart markedly from predictions by conventional methods. The departures are characterized by abnormally high head-end pressures at ignition; propellant fracture and case rupture have occurred. Analysis of test data and water table investigations have indicated that these effects are caused by aerodynamic interactions between the axial port flow and radial slot flows coupled with propellant deformation near the slots. An analytical model of the aerodynamic interaction region was constructed, and a graphical technique was developed to account for coupling effects so that the motor operating point could be denned. Design modifications based on the analysis and test results that minimize slot effects are discussed. Peak head-end pressures during ignition of the Castor II motor were predicted to be somewhat higher than test results.

A new type, ultra high speed, motion picture camera is being developed in the Optics Section of the National Research Laboratories for the purpose of assisting research in the recently important fields of high speed aerodynamics, ballistics, and other high rate phenomena. It is expected that the camera will enable pictures having good resolving power to be taken at rates as high as 200,000 per sec. This report describes the principle of the camera and also describes a small experimental model that has been made. Pictures taken at the rate of 64,000 per sec. with the model are included.

n/a

The calculus of perturbations, as commonly used in exterior ballistics, is modified for application to rocket missiles, that is, to projectiles which experience thrust and lift forces. In this form, the calculus can be used as in conventional ballistics, to investigate the effect of disturbing factors upon a trajectory. In addition to this, it is of considerable value in establishing analytically certain principles of guidance and control. Two examples are given of this: the theory of range control of the German V-2 missile, and a theoretical system of free flight guidance by radio.

Summary Horizontal spore discharge has been studied in the genera Daldinia, Sordaria, Pleurage and Ascobolus. The average distance of discharge for the full spore-complement of the ascus increases with the size of the projectile. In Pleurage taenioides a consideration of the form of the ascus jet, as caught on a rapidly rotating disk, suggests that as the four spores are shot from the ascus the vigour of discharge tends to fall with the escape of successive spores.

This paper deals with the scope of the borderline field between aerodynamics and physics, which has become known as aerophysics. It emphasizes the desirability of utilization of ballistics ranges for aerophysics investigation. In this connection, it reviews in outline form the history of ballistics: the age of speculative ballistics, the age of geometrical ballistics, the age of physical ballistics. Examples of aerophysical research are cited from aeroballistics (high speed gas flows) investigations conducted at the Naval Ordnance Laboratory, White Oak, Maryland.

Very few quantitative data are available on the response of human bones to projectile impacts. Steel spheres of various diameters were projected at embalmed human femurs. Electronic monitoring and high-speed photography were used to determine the amount of energy lost by the projectiles in fracturing the femurs. The extent of damage produced by the projectiles was studied quantitatively, and the effects of projectiles of different diameters were determined.

Summary The ballistics of horizontal spore discharge in fifteen species and two varieties of Ascomycetes have been studied. An apparatus for measuring horizontal discharge is described and formulae derived for the volumes of irregularly shaped spores. The average and maximum distances of discharge for the selected fungi are recorded and include maximum ranges of more than 50 cm for Podospora fimiseda and the 64-spore variety of P. decipiens. An analysis of the relationship between the average distance of horizontal discharge and projectile size shows that the formula d=Kr2 does not hold true for comparisons between a large number of unrelated species. If, however, only closely related species, such as those of the genera Podospora and Sordaria, are considered then considerable agreement with the formula is observed. If, in a single species, the relationship between size and distance of discharge of various sizes of spore-projectiles is analysed, the results are in accordance with the formula d = Kr2 only if there is relatively high separation of the full spore complement into projectiles of different sizes. It is suggested that deviation from the formula occurs because the initial velocity of discharge is not constant for all projectiles.

The paper provides a short survey of the actual state of the theoretical exterior ballistics. In particular the fundammental equations defining the motion of a rotating projectile are given in a form suitable for numerical calculation. Then, using the argument that a projectile possesses full rotational and also mirror summetry, the explicit development of the force and moment components is given in terms of the linear and angular velocities. Finally this development is compared with the experimentally known aerodynamic coefficients and stability derivatives.

Two ballistics problems that may arise in future transportation have been formulated and solved in detail. The first problem is that of a vehicle moving along a great circle of the earth; the second problem is that of a rocket moving radially away from the earth. In both cases the magnitude of the resultant acceleration applied to the body has been set equal to a constant. The value of this acceleration will be determined ultimately by the maximum acceleration that human beings or material objects can withstand.

For ballistics work where pressures of several thousand psi are encountered, it is essential that the gages used to measure transient pressures be checked against a “standard gage” of known behavior. Such a standard gage and the method of calibrating it are described in the paper.

T-burner experiments have provided the most fruitful technique for obtaining the acoustic admittance of burning solid propellants The objections to the findings of these experiments are: 1) the admittance values are questioned on the grounds that acoustic losses in the appaiatus are not well enough understood for adequate corrections to be made, and 2) relative acoustic losses are great enough that some operational propellants, known to produce oscillations in motors, burn stably in the T-burner The first objection is largely removed by demonstrating that three different methods for operating the burner and analyzing the data give results in close agreement Besides confirming the results of the other two, one method described here also provides a means to study more stable propellants, thus removing the second objection to the T-burner technique

This, the final lecture of a series on Electron Ballistics, is not a summary of the material which has been previously presented but rather it is an attempt to show how the ballistic approach can be extended to the analysis of high-frequency devices. Much that might otherwise be said about ultrahigh frequencies cannot be said because of secrecy requirements. However, there is considerable material which can be presented, within the limits of the necessary security regulations, which may be of interest to those who are not already well acquainted with the subject. I will, perforce, not be able to say anything specific about actual devices utilizing the principles to be discussed.