A review of dual-spin projectile stability

This paper gives a succinct review of dual-spinprojectile stability and some technologies relating to them. It describes how the traditional stability factors from linear projectile theory are modified to better describe a controlled dual-spin projectile. Finally, it reviews works which have investigated how different aspects of a controlled dual-spin design can affect flight stability, primarily airframe structure and canard properties. A conclusion is given, highlighting important guidelines from the enclosed discussion

A novel dual-spin actuation mechanism for small calibre, spin stabilised, guided projectiles

© Cranfield University 2022. All rights reserved. No part of this publication may be reproduced without the written permission of the author and copyright holderSmall calibre projectiles are spin-stabilised to increase ballistic stability, often at high frequencies. Due to hardware limitations, conventional actuators and meth ods are unable to provide satisfactory control at such high frequencies. With the reduced volume for control hardware and increased financial cost, incorporating traditional guid ance methods into small-calibre projectiles is inherently difficult. This work presents a novel method of projectile control which addresses these issues and conducts a systems level analysis of the underlying actuation mechanism. The design is shown to be a viable alternative to traditional control methods, Firstly, a 7 Degree-of-Freedom (DoF) dynamic model is created for dual-spin pro jectiles, including aerodynamic coefficients. The stability of dual-spin projectiles, gov erned by the gyroscopic and dynamic stability factors is given, discussed and unified across available literature. The model is implemented in a Matlab/Simulink simulation environ ment, which is in turn validated against a range of academic literature and experimental test data. The novel design and fundamental operating principle are presented. The actuation mechanism (AM) is then mathematically formulated from both a velocity change (∆V ) and a lateral acceleration (a˜) perspective. A set of axioms are declared and verified using the 7-DoF model, showing that the inherently discrete system behaviour can be controlled continuously via these control variables, ∆V or a˜. Control state switching is simplified to be instantaneous, then expanded to be generically characterised by an arbitrarily complex mathematical function. A detailed investigation, parametric analysis and sensitivity study is undertaken to understand the system behaviour. A Monte Carlo procedure is described, which is used to compare the correction cap abilities of different guidance laws (GLs). A bespoke Zero-Effort-Miss (ZEM) based GLis synthesised from the mathematical formulation of the AM, with innately more know ledge of the system behaviour, which allows superior error correction. This bespoke GL is discussed in detail, a parametric study is undertaken, and both the GL parameters and PID controller gains are optimised using a genetic algorithm. Artificial Intelligence (AI) Reinforcement learning methods are used to emulate a GL, as well as controlling the AM and operating as a GL, simultaneously. The novel GLs are compared against a traditional proportional navigation GL in a nominal system and all GLs were able to control the AMs, reducing the miss distance to a satisfactory margin. The ZEM-based GL provided superior correction to the AI GL, which in turn provided superior correction over proportional navigation. Example CAD models are shown, and the stability analysis is conducted on the geometry. The CAD model is then used in CFD simulations to determine aerodynamic coefficients for use in the 7-DoF dynamic model. The novel control method was able to reduce the 95% dispersion diameter of a traditional ballistic 7.62mm projectile from 70mm to 33mm. Statistical data analysis showed there was no significant correlation or bias present in either the nominal or 7-DoF dispersion patterns. This project is co-sponsored by BAE Systems and ESPRC (ref. 1700064). The con tents of this thesis are covered by patent applications GB2011850.1, GB 2106035.5 and EP 20275128.5. Two papers are currently published (DOI: 10.1016/j.dt.2019.06.003, the second DOI is pending) and one is undergoing peer review..PH

Modelling the external ballistics of tranquilliser darts

Thesis (MEng)--Stellenbosch University, 2021.ENGLISH ABSTRACT: To facilitate the design of tranquilliser darts, several ballistic models are investigated, derived, implemented and verified. Sensitivity analysis showed the required model fidelity and parameter accuracies are significantly less stringent for subsonic, flat trajectories. This agrees with doppler radar measurements suggesting drag stabilised darts have a near constant drag coefficient. This is further corroborated by computational fluid dynamics (CFD) analysis: aerodynamic coefficients are independent of velocity but sensitive to angle of attack. The tailpiece however ensures there is little to no pitching and/or yawing, eliminating non-linearities due to instability (the angle of attack). Consequently, a single CFD analysis at an average velocity can sufficiently estimate the aerodynamic forces and moments. For the same reasons, Point-mass and Modified point-mass approximations are qualitatively on par with Rigid-body approximations (in most cases). Due to drag stabilisation by the tailpiece, the drag coefficients measured and simulated are high (CD >= 0.9). Future designs' aerodynamic efficiency can be improved by rather using spin stabilisation. Point-mass and Modified pointmass approximations are however unable to account for instabilities. If considered, Rigid-body approximations are recommended to confirm initial stability.AFRIKAANSE OPSOMMING: Om die ontwerp van verdowingspyle te vergemaklik, is verskeie ballistiese modelle ondersoek, geïmplementeer en geverifieer. Sensitiwiteitsanalise toon modelgetrouheid asook dat parameterakkuraatheid minder streng is vir kort en plat trajekte. Dit stem ooreen met doppler radar metings waar die verdowingspyl se sleur koëffisiënt konstant is. Berekenings vloeimeganika (BVM) toon dat die verskeie koëffisiënte onafhanklik is van snelheid maar sensitief vir invalshoek. Die stert verseker 'n klein invalshoek en bevorder sodoende die konstante geaardheid van die koëffisiënte. Gevolglik sal 'n eenmalige BVM simulasie, by 'n gemiddelde snelheid voldoende wees om die aerodinamise kragte en momente te bepaal. Vir soortgelyke redes is Puntmassa en Gemodifiseerdepuntmassa analises kwalitatief gelykstaande aan Rigiede-liggaam analises. As gevolg van die stert, is die sleur koëffisiënt hoog (CD >= 0.9). Aerodinamies kan verdowingspyle vebeter word deur eerder gebruik te maak van spin stabilisasie. Puntmassa en Gemodifiseerde-puntmassa neem aan die verdowingspyl is stabiel, wat nie noodwendig die geval is nie. Indien spin stabilisasie oorweeg word, stel ons Rigiede-liggaam simulasie voor as 'n grondslag om stabiliteit te bevestig.Master

Influence of air rifle pellet geometryon aerodynamic drag

Air rifles and air pistols find widespread use in formal and recreational sports events. Despite their widespread use in sport, they have rarely been studied scientifically. The influence of air rifle pellet geometry on aerodynamic drag was investigated experimentally and theoretically at Mach number of 0.58 (approximately 200 m/s) and Reynolds number of 54,000 using a low-turbulence open wind tunnel. Measurements were made of surface pressure and aerodynamic drag distribution for five pellets having different geometries. Pellet overall drag was also measured with a load cell system. Theoretical analysis based on 2-D potential flow theory was used to study the relationship between nose shape and drag. Results indicate that the overall drag of non-spherical pellets was dominated by the drag on their front face, with the face contributing approximately 65 % of the overall pellet drag, while base drag contributed almost all of the remaining 35 %. The net drag contribution of the pellet side-slopes was close to zero. The geometry of the front face had a weak influence on the drag acting on the pellet base. This influence was exercised through the behaviour of the free shear layer separating from the pellet head rim. It was apparent that the presence of the tail in a dome-head pellet enabled flow reattachment and a rise in base pressure, which reduced the base drag. In contrast, at Re ~ 54,000, flow reattachment on the rear surface of the spherical pellet was not possible. For this reason, its base drag was higher than that for the dome-head pellet. Flat-, cone-, and cavity-head pellets had higher overall drag coefficient 2 values than a spherical pellet. The higher overall coefficients were due to the higher face drag than the spherical pellet, which was not compensated sufficiently by their lower base drag

The Response of a Structural Target to an Explosive Charge Incorporating Foreign Objects: A Numerical Study

This dissertation reports on the results of a numerical investigation into the effect of incorporating foreign objects into explosive and its subsequent influence on the response of a target structure. The explosive, the container and the ball bearings were simplified representation of the key components of an improvised explosive device (IED). The numerical study was aimed at studying the ball bearing interaction with blast when incorporated into charge, and was based on previous experiments. In the experiments, 22g of plastic explosive charge (26mm in diameter with a length-to-diameter ratio of 1) was detonated inside a fully confined cylindrical mild steel container of 9.3mm wall thickness and 273mm outer diameter. Different experiments were carried out using charges with varying numbers of ball bearings arranged in different configurations. The ball bearings were either packed around the cylindrical charge in row(s), or were randomly embedded into the charge. In the numerical simulations, i) a quarter symmetry model in the radial plane and ii) a half symmetry model in the axial plane were developed in ANSYS AUTODYN using Euler and Lagrangian meshes, based on the previous experiments. The cylindrical target and the ball bearings were modelled using Lagrangian elements, while the air and the PE4 plastic explosive were modelled using Eulerian elements. Ball bearings of fixed diameter 5mm, were placed at positions relative to the charge corresponding to the experimental conditions. The predicted crater depth created in the cylindrical target by ball bearing impact were compared to the experimental results. A comparative numerical study was then conducted to investigate how different factors influenced the ball bearing behaviour and the target response. The parameters tested included the total number and size of ball bearings incorporated in the explosive charge, the manner in which the ball bearings were distributed inside or outside the charge, and the length-to-diameter ratio of explosive used. The numerical models provided insights into how the ball bearing interacted with the blast when incorporated into charge. 2D numerical simulation techniques were used to simulate the velocity distribution of a cased cylindrical explosive charge. The results of the numerical simulations were verified against previously reported equations for fragments and pre-formed fragments, which are based on experimental data which indicated a non-uniform velocity distribution along the cylinder axis. Overall, there was a good agreement between the 2D model and the experimental measurements, including the distribution of the lower velocity values near the cylinder edges. The ball bearing velocity - crater depth correlation was also compared to the projectile velocity equations from literature. A good correlation was shown in all radial simulations. In the axial plane simulations, a good correlation was observed only when the projection angle of the ball bearing was nearly perpendicular to the charge surface. The effect of the ball bearing presence on the overall pressure observed in the confined space is also studied. The inclusion of ball bearings in the charge resulted in an overall decrease in peak pressure, and the percentage decrease was proportional to the total number of ball bearings. Charge covered in rows of ball bearings acted similar to encased charges, especially to charges with pre-fragmented casings. It was observed that an increase in length-to-diameter ratio of the charge led to an overall increase in blast magnitude

Aeronautical engineering: A special bibliography, supplement 45, June 1974

This special bibliography lists 430 reports, articles, and other documents introduced into the NASA scientific and technical information system in May 1974

The Viability of Image Registration as a Method for the Quantification of Displacement in Penetrating Impact Experiments

Experimental characterisation of tissue deformations associated with penetrating impact of fragments from explosive devices is challenging. Whereas experiments involving ballistic gelatine tissue simulants enable direct visualisation of deformation patterns, quantification of these deformations remains difficult. This thesis investigates the use of image registration for this purpose. Image registration methods optimise alignment of corresponding structures in image pairs, and in the process estimate the deformation fields that best achieve this. In the current context, it is hypothesised that registration of consecutive images from videos of gelatine penetration events can enable the corresponding gelatine deformation fields to be estimated. Three main activities were undertaken towards validation of this hypothesis: the proposed registration approach was tested on a series of synthetic images emulating the types of deformations expected in penetration events; the approach was then tested on images derived from a carefully controlled indentation experiment, in which a block of gelatine was deformed quasi-statically with a rigid indenter while the resulting deformation was filmed; and finally it was tested on video footage from projectile penetration experiments, in which metal projectiles were fired into blocks of gelatine and filmed with a high speed video camera. A series of complementary studies was also undertaken in support of these experiments. Firstly, to better understand the parameters of real penetration scenarios, the fragment generation and flight behaviour of a typical explosive device were analysed. Secondly, to improve understanding of the material behaviour of the test gelatine, mechanical characterisation tests were undertaken, and a visco-hyperelastic constitutive model was proposed. The individual registration operations themselves appeared to perform well, in the sense that initially disparate consecutive image pairs were brought into good alignment. However, composition of the corresponding transformation fields, necessary for tracking accumulated deformations over the course of a video sequence, was found to yield artefacts and unphysical deformation estimates in some cases. These were judged to result both from deficiencies in the methods themselves, and flaws in the experimental arrangements. Therefore, while the proposed registration approach appears to show promise, further work is needed to establish its validity conclusively. The thesis closes with a discussion of possible approaches to the latter

A cumulative index to Aeronautical Engineering: A special bibliography, January 1975

A cumulative index to the abstracts contained in NASA SP-7307 (41) through NASA SP-7037 (52) is presented. Subject, personal author, corporate source, contract, and report number indexes are included

Electron Thermal Runaway in Atmospheric Electrified Gases: a microscopic approach

Thesis elaborated from 2018 to 2023 at the Instituto de Astrofísica de Andalucía under the supervision of Alejandro Luque (Granada, Spain) and Nikolai Lehtinen (Bergen, Norway). This thesis presents a new database of atmospheric electron-molecule collision cross sections which was published separately under the DOI : With this new database and a new super-electron management algorithm which significantly enhances high-energy electron statistics at previously unresolved ratios, the thesis explores general facets of the electron thermal runaway process relevant to atmospheric discharges under various conditions of the temperature and gas composition as can be encountered in the wake and formation of discharge channels