Method for determining the penetrating ability of small arms bullets into protective equipment

Authors

DOI:

https://doi.org/10.32347/2410-2547.2026.116.160-171

Keywords:

method, model, coefficient, frontal resistance, bullet, protective environment

Abstract

Adoption of foreign and new domestic types of weapons and ammunition requires conducting a large amount of experimental research. However, the short-term nature of the processes that occur with ammunition on the trajectory complicates direct measurements of the quantities that characterize them, forcing the use of complex measuring and recording equipment. In this context, mathematical modeling of the processes of external ballistics and aerodynamics of ammunition movement comes to the fore.

The mathematical modeling method allows to significantly reduce the time and reduce the total cost of ammunition for their testing. Modeling methods, based on mathematical calculations and formulas, allow you to determine the future trajectory of ammunition based on a minimum set of parameters and in a short time. This method makes it possible to accelerate the compilation of temporary firing tables for the use of ammunition and accelerates their arrival to units that directly perform tasks in the combat zone.

Mathematical modeling methods allow us to obtain dependencies for determining the level of protection of military personnel when performing assigned tasks by units, taking into account the fact that the effectiveness of measures to ensure the protection of personnel depends on the type of protective barriers, effect of small arms bullets depends on their mass, shape, and bullet speed at the moment of encountering a protective obstacle.

The development of a scientific and methodological apparatus for conducting research to determine the parameters of new weapons and increase the ballistic protection of personnel from small arms remains an urgent scientific task.

The paper examines the process of interaction of a bullet with various types of protective environments. A method for determining the penetration ability of small arms bullets into protective equipment and models for determining the depth of bullet penetration into various types of obstacles are proposed. The results of calculations of the penetration depth of a bullet from an AK-74 assault rifle into various types of protective environments are presented. Further improvement of armor protection designs can be achieved by developing new technical solutions using the proposed method for determining the penetration ability of small arms bullets into protective equipment.

References

Vaskivskyy M.I. (2024) Metodychnyy pidkhid do provedennya analizu inozemnoho ozbroyennya ta viyskovoyi tekhniky v interesakh uzahalnennya dosvidu yoho boyovoho zastosuvannya ta ekspluatatsiyi. (Methodical approach to analyzing foreign weapons and military equipment in the interests of generalizing the experience of its combat use and operation) Perspektyvy rozvytku ozbroyennya ta viyskovoyi tekhniky Sukhoputnykh viysk: Zbirnyk tez dopovidey Mizhnarodnoyi naukovo-tekhnichnoyi konferentsiyi (Lviv, 15-16 travnya 2024 r. 490 s). – Lviv: NASV, s. 7 – 9.

DSTU V 8821-:2018. Standartyzatsiya u sferi ozbroyennya ta viyskovoyi tekhniky. Chastyna 1. Osnovni terminy ta vyznachennya ponyat (Standardization in the field of armaments and military equipment. Part 1. Basic terms and definitions)[Chynnyy vid 01.09.2019]. Vyd. ofits. (DSTU V 8821:2018. . – Kyiv: DP UkrNDNTS. – 44 s.

DSTU V 15.003:2021. Systema rozroblennya i postavlennya na vyrobnytstvo ozbroyennya ta viyskovoyi tekhniky. Protsesy zhyttyevoho tsyklu ozbroyennya ta viyskovoyi tekhniky (System for the development and production of weapons and military equipment. Life cycle processes of weapons and military equipment) [Chynnyy vid 01.09.2022]. Vyd. ofits. (DSTU V 15.003:2021. . – Kyiv: DP UkrNDNTS, – 100 s.

Chyzhyk H.V., Rohal L., Korneva A., Shyrokov A.V., Berezovskyy O.M., Bisyk S.P., Slyvinskyy O.A. (2025) Osoblyvosti deformuvannya ta ruynuvannya staley riznykh klasiv mitsnosti v umovakh udarnoho stysku. (Features of deformation and fracture of steels of different strength classes under impact compression conditions). – Kyiv: Problemy mitsnosti, №1, s. 87 – 100.

Slydenko V. Rozrobka dyskretno-bezperervnoyi matematychnoyi modeli udarnoho prystroyu z parametramy vplyvu na kharakterystyky udarnoho impulsu/V. Slydenko, O. Slydenko, L. Marchuk ta insh. (2023) (Development of a discrete-continuous mathematical model of an impact device with parameters influencing the characteristics of the impact pulse) Eastern-European Journal of Enterprise Technologies, №5(7). – s.70 – 79.

Shuhaylo O.P., Khalchenkov O.V. (2025) Empirychni ta chyselni pidkhody do modelyuvannya navantazhen vid zasobiv povitryanoho urazhennya. Povidomlennya 1. Ohlyad i porivnyannya empirychnykh metodiv". (Empirical and numerical approaches to modeling loads from air weapons. Message 1. "Review and comparison of empirical methods"). – Kyiv: Problemy mitsnosti, № 2. – s.45 – 58.

Shuhaylo O.P., Khalchenkov O.V. (2025) Empirychni ta chyselni pidkhody do modelyuvannya navantazhen vid zasobiv povitryanoho urazhennya. Povidomlennya 2. Chyselne modelyuvannya vybukhu. (Empirical and numerical approaches to modeling loads from air weapons. Message 2. Numerical modeling of explosion). – Kyiv: Problemy mitsnosti, № 3. – s. 34 – 45.

Ivanchenko H.M., Hetun H.V., Bezklubenko I.S., Solomin A.V., Hetun S.YU. (2024) Matematychna model napruzheno-deformovanoho stanu bahatosharovykh konstruktsiy z riznymy pruzhnymy vlastyvostyamy. (Mathematical model of the stress-strain state of multilayer structures with different elastic properties). – Kyiv: Opir materialiv i teoriya sporud / Strength of Materials and Theory of Structures, № 113. – s.131 – 138.

Ivanchenko H.M., Hetun H.V., Bezklubenko I.S., Solomin A.V., Posternak O.M.( 2023) Vplyv vybukhovykh navantazhen na budivli ta sporudy tsyvilnoho zakhystu naselennya. (The impact of explosive loads on buildings and civil defense structures). – Kyiv: Opir materialiv i teoriya sporud / Strength of Materials and Theory of Structures, № 111. – s. 39 – 43.

Kotsyuruba V.I., Bilyk A.S., Veretnov A.O., Haydarly H.S., Borta R.M., Tertyshnyy B.I. (2022) Metodyka rozrakhunkiv ta obgruntuvannya vymoh do inzhenernoho zakhystu obyektiv krytychnoyi infrastruktury vid BPLA typu barazhuyuchyy boyeprypasy. (Calculation methodology and justification of requirements for engineering protection of critical nfrastructure facilities from loitering munitions-type UAVs). – Kyiv: Opir materialiv i teoriya sporud / Strength of Materials and Theory of Structures, № 109. – s. 164 – 183.

Malyuk V. H., Kalyta O. M., Zyuban M. I. (2011) Kompyuterna model dlya analizuvannya faktoriv, shcho vplyvayut na polit kuli striletskoyi zbroyi. (Computer model for analyzing factors affecting the flight of a small arms bullet). – Kharkiv: Zbirnyk naukovykh prats Akademiyi vnutrishnikh viysk MVS Ukrayiny. Vyp. 1 (17). – s. 65 – 71.

Hrabchak V.I., Bondarenko S.V. (2013) Analiz isnuyuchykh ta perspektyvnykh metodiv vyznachennya syly oporu povitrya rukhu snaryadiv. (Analysis of existing and promising methods for determining the air resistance of projectiles). – Lviv: Viyskovo-tekhnichnyy zbirnyk Akademiyi sukhoputnykh viysk imeni hetmana Petra Sahaydachnoho, Lviv, 2(9). – s. 20 – 24.

Hayda P. I., Trofymenko P. YE., Lyapa M. M. (2011) Osnovy teoriyi polotu i konstruktsiyi raket : navchalnyy posibnyk. (Fundamentals of flight theory and rocket design). – Sumy: Sumskyy derzhavnyy universytet. – 248 s.

Kubota T., Isikava KH., Takada S. (2025) Vyazkyy opir pry rukhu eliptychnoho intrudera v dvomirnomu hranulyarnomu seredovyshchi. (Viscous drag during the motion of an elliptical intruder in a two-dimensional granular medium). – Kyiv: Problemy mitsnosti, №4. – s. 125 – 135.

Nikolayev S.V. (2021) Striletska zbroya ta vohneva pidhotovka: konspekt lektsiy. (Small arms and firearms training). – Odesa: Odeskyy derzhavnyy ekolohichnyy universytet. – 125 s.

Turskyy O.YU., Semenov M.V. (2024) Inzhenerne zabezpechennya boyu: navch. posib. (Engineering support of the battle). – Kyiv : KI NHU. – 256 s.

Skyba O.V., Shabanova O.V., Rybachok D.V., Ozeran H.P. (2025) Pohlyady shchodo konstruktsiyi vohnevykh sporud z urakhuvannyam suchasnykh zahroz ta rezultativ vyprobuvan. (Views on the design of fire structures taking into account modern threats and test results). –Dnipro: Zbirnyk naukovykh prats DNDI VS OVT, Vyp. 3(25). – s.67 – 76.

Vayda T.S., Kuznyetsov O.S. (2020) Indyvidualni zasoby bronezakhystu pravookhorontsiv: deyaki aspekty klasyfikatsiyi ta katehoruvannya. Sluzhbovo-boyova pidhotovka yak osnova profesiynoyi diyalnosti politseyskykh: materialy kruhloho stolu (m. Odesa, 27 lystopada 2020 roku). (Individual means of body armor protection for law enforcement officers: some aspects of classification and categorization). – Odesa: ODUVS. – 194 s.

Biryukov I. YU., Biryukov O. I. (2020) Formalizatsiya zalezhnosti vplyvu zminy pochatkovoyi shvydkosti kul korotkostvolnoyi zbroyi na yikh vrazhayuchi vlastyvosti. (Formalization of the dependence of the influence of changes in the initial velocity of short-barreled weapon bullets on their striking properties). Intehrovani tekhnolohiyi ta enerhozberezhennya № 2. – s.37 – 48.

Petruchenko O. S. (2018) Obgruntuvannya parametriv bahatosharovoyi zakhysnoyi konstruktsiyi boyovykh mashyn na osnovi neliniynykh matematychnykh modeley. – Rukopys. Dysertatsiya na zdobuttya naukovoho stupenya doktora filosofiyi (kandydata tekhnichnykh nauk) za spetsialnistyu 05.02.09 – dynamika ta mitsnist mashyn/ O.S. Petruchenko. (Justification of the parameters of the multilayer protective structure of combat vehicles based on nonlinear mathematical models). – Lviv. – 160 s.

Velychko L. D., Petruchenko O.S., Kondrat V.F. (2015) Dynamika zakhysnoyi konstruktsiyi pry udari kuli abo oskolka snaryada. (Dynamics of a protective structure when hit by a bullet or shell fragment). – Lviv: Viyskovo-tekhnichnyy zbirnyk Akademiya sukhoputnykh viysk, № 13, Lviv: ASV. – s.13 – 19.

Kharchenko V. V. (1999) Modeli protsesiv vysokoshvydkisnoho deformuvannya materialiv z urakhuvannyam vyazkoplastychnykh efektiv. (Models of high-speed deformation processes of materials taking into account viscoplastic effects). – Kyiv: NANU, IPM. – 280 s.

Tannachart Wantang, Manop Pipathattakul, Fasai Wiwatwongwana (2023) Experimental investigation of Ballistic capabilities in Carbon-Kevlar composites: Effects of weight and layer variations against 9 mm projectiles. Results in Materials. Vol. 20, рр.1–11.

Kristoffersen M., Costas M., Koenis T., Brоtan V., Paulsen C., Bоrvik T. (2020) On the ballistic perforation resistance of additive manufactured AlSi10Mg aluminium plates. International Journal of Impact Engineering, Vol. 137. рр.1–16.

Kovtun A. Modeli vzayemodiyi vysokoshvydkisnoho udarnyka z zakhysnymy pereshkodamy / Kovtun A., Tabunenko V., Nesterenko S. // (Models of interaction of a high-speed impactor with protective obstacles). – Kyiv: Opir materialiv i teoriya sporud/ Strength of Materials and the Theory of Structures. – 2019. – № 102. – s. 207-219.

Published

2026-05-28

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