ARTICLE
Analytical formulae for 2D ballistic limit curves over a range of material thicknesses based on Recht-Ipson model and symbolic regression
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1
Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering, AGH University, Krakow, Poland
 
2
French-German Research Institute of Saint-Louis (ISL), Saint-Louis, France
 
These authors had equal contribution to this work
 
 
Submission date: 2026-03-26
 
 
Final revision date: 2026-06-12
 
 
Acceptance date: 2026-07-04
 
 
Publication date: 2026-08-17
 
 
Corresponding author
Teresa FRAS   

PCe, INSTITUT FRANCO – ALLEMAND DE RECHERCHES DE SAINT - LOUIS, France
 
 
 
KEYWORDS
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ABSTRACT
The study discusses an application of the physics-aware symbolic regression (PASR) paradigm, with the embedded Recht–Ipson (R-I) model, to describe the relationship between the 7.62mm AP P80 projectile’s initial impact and the residual velocities of the S355 steel plates of varying thicknesses. The present approach results in a straightforward analytical “SR R-I” formula, which can be easily applied in engineering practice to determine ballistic limit curves and velocities (BLCs and BLVs). The proposed approach has demonstrated statistical effectiveness that outperforms other machine learning (ML) algorithms in both fitting accuracy and the predictive capability of these terminal ballistic features.
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