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

Guidance Law Design for a Class of Dual-Spin Mortars

To minimize the cost and maximize the ease of use, a class of dual-spin mortars is designed which only rely on GPS receiver and geomagnetic measurements. However, there are some problems to be solved when the range is small, such as low correction authority and trajectory bending. Guidance law design for this mortar is detailed. Different guidance laws were designed for the ascending and descending segments, respectively. By taking variable parameter guidance law in the vertical plane and using compensation in the lateral plane, the problems mentioned above were resolved. Roll angle resolving algorithms with geomagnetic measurements were demonstrated and the experiment results proved to be effective. In order to verify the effectiveness, Seven-Degrees-of-Freedom (7-DOF) rigid ballistic model were established and hardware in the loop simulation was introduced. After the transform function of the actuator was obtained, the control model of the shell was improved. The results of the Monte Carlo simulation demonstrate that the guidance law is suitable and the mortar can be effectively controlled

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

Method to Develop a Control System for a Stable and Guidable Hybrid Projectile

A Hybrid Projectile (HP) is a munition that transforms into an unmanned aerial vehicle (UAV) after being launched from a tube. In many situations it is desirable for this type of projectile to change its point of impact and depart from its current ballistic trajectory similar to a UAV following a path. A method was created to utilize deflectable control surfaces in conjunction with a guidance system to ensure the HP was statically and dynamically stable and to maneuver the HP to a desired point of impact. Methods were devised to control heading and pitch using vertical and horizontal tail surfaces. Testing and tuning these control methods were done using the Six Degree of Freedom (6DoF) system in Simulink. A cruciform tail section was utilized so that the HP could be statically and dynamically stable. The simulation showed that the method devised was able to guide a 40 mm HP up to 6250 projectile diameters off of the line of fire and increase range by 25.8% while landing within 125 projectile diameters of the desired impact point

Projectile linear theory for aerodynamically asymmetric projectiles

Currently, there are few analytical tools within the ballistics community to aid in the design and performance evaluation of aerodynamically asymmetric projectiles. The scope of this thesis is to (1) create analytical tools that are capable of quantifying aerodynamically asymmetric projectile performance, (2) demonstrate the ability of these models to accurately account for aerodynamic asymmetries, and (3) gain insight into the flight mechanics of several aerodynamically asymmetric projectiles. First, a six-degree-of-freedom (6 DOF) flight dynamic model, which uses a point-force lifting-surface aerodynamic model, was developed to replicate flight characteristics observed from measured results of common projectiles. A quasi-linear flight dynamic model was then created using the machinery of Projectile Linear Theory (PLT). From this, flight dynamic stability models were developed for linear time-invariant (LTI) and linear time-periodic (LTP) systems. Dynamic simulation and stability trade studies were then conducted on asymmetric variants of 4-finned, 3-finned, 2-finned, and hybrid projectile configurations. First, stability of symmetric projectiles are validated and show that the classical and extended PLT model yielded identical results. Results show that aerodynamic asymmetries can sometimes cause instabilities and other times cause significant increase in dynamic mode damping and increase/decrease in mode frequency. Partially asymmetric (single plane) configurations were shown to cause epicyclic instabilities as the asymmetries became severe, while fully asymmetric (two plane) can grow unstable in either the epicyclic modes or the roll/yaw mode. Another significant result showed that the LTP stability model is able to capture aerodynamic lifting-surface periodic affects to evaluate dynamic stability requirements for asymmetric projectiles.MSCommittee Co-Chair: Dr. Ari Glezer; Committee Co-Chair: Dr. Mark Costello; Committee Member: Dr. Wayne Whitema

Aerodynamic fuze characteristics for trajectory control

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1998.Includes bibliographical references (p. 131-135).by Alexander Michael Budge.M.S

TRAJECTORY OPTIMIZATION AND AERODYNAMIC MODELING OF LONG RANGE MORPHING PROJECTILES

The use of pattern search and gradient-based optimization methods to determine optimal geometries of morphing guided unpowered projectiles are examined. An investigation of continuously varying geometries vs. discrete-point morphing concepts is performed. A detailed aerodynamic analysis, applicable to a wide flight envelope, is coupled with a trajectory simulation program for use within the optimization schemes. Optimal projectile geometries that give maximum range subject to the constraints of static stability and trimmed conditions were then determined. Deployment of a single optimum geometry set of wings and canards at apogee provided a 98.6% increase in range over the baseline projectile configuration. Dual geometry and continuous morphing schemes increased the range over the baseline geometry by an additional 3.4% and 12.1% respectively. The trade off between range and morphing complexity showed that deployment of a single optimized geometry was the most beneficial for unguided unpowered 155mm projectiles

Small-Caliber Exterior Ballistics : Aerodynamic Coefficients Determination by CFD

The models used to calculate small-caliber projectile trajectories are often only drag-based, given the presumed short ranges and the assumed small variation of the aerodynamic parameters in flight. Depending on the type of application, "field" calibrations are then performed to compensate for the observed deviations. However, with the new small-caliber applications and the inherent increased challenges, these simplified methods do not yield satisfactory results anymore in terms of accuracy and attitude upon impact. In the first part, next to reviewing existing trajectography models, we discuss their implementation in our own trajectory program \textit{VTraj}, developed in LabVIEW. The six degrees of freedom (6 DoF) model allows to compute the flight of any symmetrical or asymmetrical projectile (spin- or fin- stabilized). Its parameters include a complete set of static and dynamic contributions, including Magnus and pitch damping forces \& moments. This model allows the analysis of all translation and angular motions of the projectile's body. The models give good agreement with published results on standard reference projectiles for the trajectory parameters. In part two, we focus on the methodology to capture the static and dynamic coefficients by steady and unsteady RANS methods for subsonic, transonic and supersonic flight conditions. Accurate resolution of the flow in the boundary layer and in the wake of the projectile proved to be of utmost importance for the correct determination of the coefficients. The coefficient extraction methods are assessed with published results for canonical shapes and good agreement is achieved. The results highlight the strong dependency of the pitch damping coefficient on the reduced pitch frequency which varies along the flight path. Rigid Body Dynamics (RBD) as well as Computational Fluid Dynamics (CFD) are finally combined in order to evaluate the behavior of specific small-caliber applications: non-lethal projectiles operating in the low subsonic domain, long-range projectiles with focus on transonic domain crossing, and asymmetric configuration are studied. The resolution of the dynamic flow around the projectile and the prediction of stability upon impact are confronted with experimental results and the match is very promising. The research also gives new insight into the diverse phenomena at hand in the transonic domain, or for projectiles with mass unbalance, and the change they impart on static and dynamic stability characteristics

Guidance, navigation, and control for munitions

The United States Army is currently looking for new methods of guiding munitions, which would allow the military to employ guided munitions in place of traditional munitions. This will give the US Army an edge on the battle eld and also allow the use of munitions in areas where traditional mortars and artillery cannot be used, including dense urban environments where collateral damage is not acceptable.In this thesis, an innovative approach to Guidance, Navigation, and Control (GN&C) is developed for a spinning projectile that utilizes a single axis canard actuation system. Utilizing the projectiles spin, the controller can provide a full range of aerodynamic forces, over the 360o of rotation, that provides maneuverability using only one actuator. This technique minimizes the need for multiple actuators and maintains the inherent aerodynamic stability provided by the spin.The GN&C system design described in this thesis consists of a tracking regulator for sinusoidally oscillating the canard system, a nonlinear state estimator for attitude measurement, and a guidance law to guide the projectile to a target. By combining the three components, we can demonstrate a closed-loop guidance system that will hit a target accurately at distances normally not achieved by an unguided projectile.Ph.D., Mechanical Engineering -- Drexel University, 200