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Measurement model and accuracy analysis of parabolic ballistic projectile flight parameters based on random matrix

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Abstract

The existing six light screen array measuring methodology of uniform linear trajectory is unable to determine the impact coordinate and flight speed of the terminal parabolic trajectory projectile. With the parabola trajectory in the terminal trajectory test as the objective, a method is presented to test the flight characteristics of a projectile with a variable speed parabola trajectory. By accounting for the effects of air resistance and gravity on the projectile's trajectory, the space motion equation for the projectile is determined. The impact position and flight speed of the terminal parabolic trajectory projectile cannot be determined by the current six light screen array measurement approach of uniform linear trajectory. A technique is described to evaluate the flight properties of a projectile with a variable speed parabola trajectory, with the goal being the parabola trajectory in the terminal trajectory test. The space motion equation for the projectile is calculated by taking into consideration the effects of gravity and air resistance on its trajectory. The precision of the measurement algorithm is assessed. The results show that the measurement error of the impact coordinates in the detection target plane is not larger than 3.5 mm. The developed measurement model expands the use of the six light curtain rays in the field of terminal trajectory measurement.

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References

  1. Li X, Mu L, Zang Y, Qin Q (2020) Study on performance degradation and failure analysis of machine gun barrel. Defence Technol 16(2):362–373

    Article  Google Scholar 

  2. Li HS, Zhang XQ, Zhang XW, Guo QM (2022) A line laser detection screen design and projectile echo power calculation in the detection screen area. Defence Technol 18(8):1405–1415

    Article  Google Scholar 

  3. Chen D, Mu D, Chen D, Ni J (2022) Analysis on the speed properties of the shock wave in the light curtain. Open Phys 20(1):9–22

    Article  ADS  Google Scholar 

  4. Bertin D (2017) 3-D ballistic transport of ellipsoidal volcanic projectiles considering horizontal wind field and variable shape-dependent drag coefficients. J Geophys Res 122(2):1126–1151

    Article  Google Scholar 

  5. Kong X, Yang W, Li B (2021) Application of stabilized numerical integration method in acceleration sensor data processing. IEEE Sens J 21(6):8194–8203

    Article  ADS  Google Scholar 

  6. Chen YW, Lee YL, Chen YB (2017) The study applies fuzzy weighted input estimation for the prediction of target trajectory in a fire control system. Trans Can Soc Mech Eng 41(1):1–21

    Article  CAS  Google Scholar 

  7. Li H, Zhang X, Miao W (2019) Multiple target information fusion matching algorithm based on a line laser and a single plane array camera. Appl Opt 58(15):4025–4035

    Article  ADS  PubMed  Google Scholar 

  8. Sun Y, Xu J, Wu H, Lin G, Mumtaz S (2021) Deep learning based semi-supervised control for vertical security of maglev vehicle with guaranteed bounded airgap. IEEE Trans Intell Transp Syst 22(7):4431–4442

    Article  Google Scholar 

  9. Lee JY, Jo BU, Moon GH, Tahk MJ, Ahn J (2020) Intercept point prediction of ballistic missile defence using neural network learning. Int J Aeronaut Space Sci 21(4):1092–1104

    Article  Google Scholar 

  10. Kelfoun K, Harris A, Bontemps M, Labazuy P, Chausse F, Ripepe M, Donnadieu F (2020) A method for 3D reconstruction of volcanic bomb trajectories. Bull Volcanol 82(4):1–15

    Article  Google Scholar 

  11. Li H, Ni J, Yang X, Dong Q (2022) Test influence of screen thickness on double-N six-light-screen sky screen target. Open Phys 20(1):1–8

    Article  ADS  Google Scholar 

  12. Nobahari H, Kermani MA (2017) Integrated optimization of guidance and control parameters in a dual spin flying vehicle. Sci Iran 24(5):2473–2489

    Google Scholar 

  13. Russo M, Cesqui B, La Scaleia B, Ceccarelli F, Maselli A, Moscatelli A, Zago M, Lacquaniti F, d’Avella A (2017) Intercepting virtual balls approaching under different gravity conditions: evidence for spatial prediction. J Neurophysiol 118(4):2421–2434

    Article  PubMed  PubMed Central  Google Scholar 

  14. Hestroffer D, Sánchez P, Staron L, Bagatin AC, Eggl S, Losert W, Murdoch N, Opsomer E, Radjai F, Richardson DC, Salazar M, Yano H (2019) Small so-lar system bodies as granular media. Astron Astrophys Rev 27(1):1–64

    Article  ADS  Google Scholar 

  15. Yang Y, Zhang Y, Dai L, Li J, Mumtaz S, Rodriguez J (2016) Transmission capacity analysis of relay-assisted device-to-device overlay/underlay communication. IEEE Trans Industr Inf 13(1):380–389

    Article  Google Scholar 

  16. Maurel C, Michel P, Biele J, Ballouz RL, Thuillet F (2018) Numerical simulations of the contact between the lander MASCOT and a regolith-covered surface. Adv Space Res 62(8):2099–2124

    Article  ADS  Google Scholar 

  17. Çelik O, Tsuda Y, Yoshikawa K, Kawakatsu Y (2021) Reduced-gravity experiments of nonspherical rigid-body impact on hard surfaces. Adv Space Res 67(1):436–476

    Article  ADS  Google Scholar 

  18. Trache D, Tarchoun AF (2019) Analytical methods for stability assessment of nitrate esters-based propellants. Crit Rev Anal Chem 49(5):415–438

    Article  CAS  PubMed  Google Scholar 

  19. Giulietti F, Pollini L, Avanzini G (2016) Visual aids for safe operation of remotely piloted vehicles in the controlled air space. Proc Inst Mech Eng G 230(9):1641–1654

    Article  Google Scholar 

  20. Aubin D (2017) Ballistics, fluid mechanics, and air resistance at Gâvre, 1829–1915. Arch Hist Exact Sci 71(6):509–542

    Article  MathSciNet  Google Scholar 

  21. Modanli M, Faraj BM, Ahmed FW (2020) Using matrix stability for variable telegraph partial differential equation. Int J Optim Control 10(2):237–243

    MathSciNet  Google Scholar 

  22. Ahmad S, Bashir S, Rafique MS, Yousaf D (2017) Growth of surface structures correlated with structural and mechanical modifications of brass by laser-induced Si plasma ions implantation. Appl Phys A 123(4):1–12

    Article  Google Scholar 

  23. Jiang K, Du CR (2022) Dynamics in binary complex (dusty) plasmas. Rev Mod Plasma Phys 6(1):1–45

    Article  Google Scholar 

  24. Anthony N, Emami MR (2018) Asteroid engineering: the state-of-the-art of Near-Earth Asteroids science and technology. Prog Aerosp Sci 100:1–17

    Article  Google Scholar 

  25. Gerstenberg T, Tenenbaum JB (2017) Intuitive Theories. Oxford Handbook of Causal Reasoning. Oxford University Press, Oxford, pp 515–548

    Google Scholar 

  26. Shukla S, Behera BK (2022) Auxetic fibrous structures and their composites: a review. Compos Struct 290:115530

    Article  Google Scholar 

  27. Zhou J, Sun J, Zhang W, Lin Z (2023) Multi-view underwater image enhancement method via embedded fusion mechanism. Eng Appl Artif Intell 121:105946

    Article  Google Scholar 

  28. Zhou J, Pang L, Zhang W (2023) Underwater image enhancement method by multi-interval histogram equalization. IEEE J Ocean Eng 48(2):474–488

    Article  Google Scholar 

  29. Faraj BM, Taha D (2021) Comparison between steepest descent method and conjugate gradient method by using matlab. Salih, DTM, & Faraj, BM (2021). Comparison between steepest descent method and conjugate gradient method by using matlab. J Stud Sci Eng 1(1):20–31

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Authors and Affiliations

  1. College of Optoelectronic Engineering, Xi’an Technological University, Xi’an, 710032, Shaanxi, China

    Rongli Cai

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  1. Rongli Cai
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RC is responsible for designing the framework, analyzing the performance, validating the results, and writing the article. SA is responsible for collecting the information required for the framework, provision of software, critical review, and administering the process.

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Correspondence to Rongli Cai.

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Cai, R. Measurement model and accuracy analysis of parabolic ballistic projectile flight parameters based on random matrix. J Eng Math 144, 12 (2024). https://doi.org/10.1007/s10665-023-10320-4

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