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Predictive Physics-Based Model for Projectile Trajectory Instability



OBJECTIVE: Develop a physics-based model to predict trajectory instability of a long rod penetrating semi-infinite targets.

DESCRIPTION: There is an urgent need to develop a physics-based model to predict this trajectory instability. In the transition zone near the point of maximum penetration depth and the onset of the semi-hydrodynamic regime, projectiles were observed to bend and yaw violently without significant mass loss. While prior works exist to model the impact response in the transition zone [Ref 1], these studies typically focused purely on the penetration depth via semi-empirical methods.The penetration depth of cylindrical projectiles into targets across a broad range of impact velocities typically exhibits three distinct regimes. At lower impact velocities, the projectile undergoes nearly rigid body penetration within the target. Towards the high end of the velocities in this regime, the maximum penetration depth is achieved. With further increasing striking velocities, the projectile begins to experience erosion and the penetration depth starts to saturate. This regime is known as the semi-hydrodynamic regime. At even higher velocities, the impact phenomenon becomes hydrodynamic where the projectile strength becomes practically negligible.This phenomenon has been observed experimentally across a range of different target materials, including metals [Ref 2], geomaterials [Ref 3], and fluids [Ref 4], and across several different types of projectiles and shapes. This yawing and bending instability causes severe deviation from the desired trajectory, and severely limits projectile penetrating performance [Ref 2]. Stability and vibration dynamics models have long been established for slender rods moving axially in fluid [Ref 5]. Depth of penetration models focused most on solid targets.The proposed model aims to identify critical conditions and parameters resulting in this instability across different targets in order to optimize the penetrative capabilities of projectiles. The parameters of interest may include, but not be limited to, projectile aspect ratio, nose shape, velocity, and strength of materials that are interacting under conditions of different soil types or hardened materials, e.g., reinforced concrete.The Phase II effort will likely require secure access, and SSP will process the DD254 to support the contractor for personnel and facility certification for secure access. The Phase I effort will not require access to classified information. If need be, data of the same level of complexity as secured data will be provided to support Phase I work.Work produced in Phase II may become classified. Note: The prospective contractor(s) must be U.S. owned and operated with no foreign influence as defined by DoD 5220.22-M, National Industrial Security Program Operating Manual, unless acceptable mitigating procedures can and have been implemented and approved by the Defense Counterintelligence and Security Agency (DCSA). The selected contractor and/or subcontractor must be able to acquire and maintain a secret level facility and Personnel Security Clearances, in order to perform on advanced phases of this project as set forth by DCSA and SSP in order to gain access to classified information pertaining to the national defense of the United States and its allies; this will be an inherent requirement. The selected company will be required to safeguard classified material IAW DoD 5220.22-M during the advanced phases of this contract.

PHASE I: Develop a physics-based model for long rod penetration. Identify critical conditions and parameters that affect long rod penetration into different soil types or hardened materials, e.g., reinforced concrete. Assess the viability of the model for long rod penetration to include mechanisms not inherent just in fluid flow or solid cavity expansion, such that the stability of the trajectory can be predicted, together with dominating parameters dictating the onset of instability. Compare the model prediction with typical penetration cases in this and subsequent phases to assess the feasibility of the model. The Phase I Option, if exercised, will include the initial design specifications and capabilities description to build a prototype solution in Phase II. Develop a Phase II plan.

PHASE II: Model validation and critical condition determination. Design and conduct penetration experiments with flash X-ray sequence imaging for global trajectory response and Synchrotron X-ray high-speed imaging for local projectile-target interactions to validate the model. Simultaneously, document existing experimental data in literature and conduct numerical simulations on different semi-infinite target media to fine-tune the model and identify parameter critical ranges. Validate the model within the scope of the physical and numerical experiments and literature data, and that it is ready to be further developed into a design tool.It is probable that the work under this effort will be classified under Phase II (see Description section for details).

PHASE III: Develop the model into a predictive tool, together with the resulting stability criteria and critical parameters, for applications involving long-rod penetration into semi-infinite targets. Perform systematic penetration experiments to expand the model application range over a variety of projectile/target combinations. Ensure that the final product is an efficient, low-cost method of design projectiles and predicting their capabilities in penetrating various semi-infinite targets.Applications of the final product are not limited to defense applications, as the developed model may be extended to other fields such as pile-driving in civil engineering fields.

KEYWORDS: Trajectory of Cylindrical Projectiles, Instability of Cylindrical Projectiles, Penetration of Hardened Targets, Physics-based Model, Semi-hydrodynamic Regime


1. Chen, X. & Li, Q. “Transition from nondeformable projectile penetration to semihydrodynamic penetration.” J. Eng. Mech., 2003, pp. 123-127. 2. Piekutowski, A. J., Forrestal, M. J., Poormon, K. L. & Warren, T. L. “Penetration of 6061-T6511 aluminum targets by ogive-nose steel projectiles with striking velocities between 0.5 and 3.0 km/s.” Int. J. Impact Eng., 23, 1999, pp. 723-734. 3. Bivin, Y. K. & Simonov, I. V. “Mechanics of dynamic penetration into soil medium.” Mech. Solids, 45, 2010, pp. 892–920. 4. Roecker, E. T. & Ricchiazzi, A. J. “Stability of penetrators in dense fluids.” Int. J. Eng. Sci. 16, 1978, pp. 917-920. 5. Gosselin, F., Païdoussis, M. P. & Misra, A. K. “Stability of a deploying/extruding beam in dense fluid.” J. Sound Vib. 299, 2007, pp. 123-142.

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