Skip to main content
SpringerLink
Log in

A Mathematical Model of the Motion of a Spinning Projectile

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

A semiempirical mathematical model of motion of the center of mass of a spinning projectile in the atmosphere is proposed. This model takes into account the effects of the derivation and change in the frontal resistance due to variation in the angle of attack. These effects are accounted for without a detailed description of spinning in our model, which allows using a large integration step and provides the capability of real-time computation of ballistic corrections. The selection procedure of the model parameters for real weapon systems is described in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.

Similar content being viewed by others

REFERENCES

  1. R. L. McCoy, Modern Exterior Ballistics: The Launch and Flight Dynamics of Symmetric Projectiles, 2nd ed. rev. (Schiffer, Atglen, PA, 2012).

    Google Scholar 

  2. P. N. Melnikov and M. A. Terpigorev, “Calculations of the trajectory of an artillery projectile,” Izv. Tul’sk. Gos. Univ., Tekh. Nauki, Issue 12 (2), 89–94 (2014),

    Google Scholar 

  3. GOST (State Standard) V 24288-80. Unguided rocket-propelled and rocket-assisted artillery projectiles. The method of calculating the flight trajectory (Izd. Standartov, Moscow, 1980) [in Russian].

  4. https://www.hornady.com/.

  5. A. A. Konovalov and Yu. V. Nikolaev, External Ballistics (TsNII Informatsii, Moscow, 1979) [in Russian].

  6. B. N. Okunev, Rotation Motion of an Artillery Projectile (Gos. Izd. Tekh.-Teor. Lit., Moscow − Leningrad, 1943) [in Russian].

  7. Ya. M. Shapiro, External Ballistics (Oborongiz, Moscow, 1946) [in Russian].

    Google Scholar 

  8. I. A. Kozlitin and A. S. Omelianov, “A method for constructing a smooth approximation of drag laws,” Mat. Model. 28 (10), 23–32 (2016).

    MathSciNet  Google Scholar 

  9. V. L. Khaikov, “Review of mathematical formulas for the air resistance law of the 1943 year. Part 1,” Elektron. Inf. Sist., No. 4 (15), 74–90 (2017).

  10. V. L. Khaikov, “Review of mathematical formulas for the air resistance law of the 1943 year. Part 2,” Elektron. Inf. Sist., No. 1 (16), 85−97 (2018).

  11. A. I. Kobzar, Applied Mathematical Statistics. For Engineers and Scientists (Fizmatlit, Moscow, 2006) [in Russian].

    Google Scholar 

  12. Manual on 30-mm Automatic Grenade Launcher (AGS-17), 2nd ed., reprint (Voen. Izd., Moscow, 1982) [in Russian].

  13. Manual on 12.7-mm Machine Gun “Utyos” (NSV-12.7) (Voen. Izd., Moscow, 1986) [in Russian].

  14. A. K. Efremov, “Approximation for the air resistance law of the 1943 year,” Nauka Obraz. Elektron. Nauchno-Tekh. Zh. (Mosk. Gos. Tekh. Univ. im. N. E. Baumana), Issue 10, 269−284 (2013).

  15. V. V. Burlov, et al., Ballistics of Barrel Systems, Ed. by L. N. Lysenko and A. M. Lipanov (Mashinostroenie, Moscow, 2006) [in Russian].

    Google Scholar 

  16. A. A. Dmitrievskii and L. N. Lysenko, External Ballistics, 4th ed. rev. (Mashinostroenie, Moscow, 2005) [in Russian].

    Google Scholar 

  17. GOST (State Standard) 4401-81. Standard Atmosphere. Parameters (IPK Izd. Standartov, Moscow, 2004) [in Russian].

    Google Scholar 

  18. N. N. Kalitkin and P. V. Koryakin, Numerical Methods, Book 2: Methods of Mathematical Physics (Akademiya, Moscow, 2013) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    I. A. Kozlitin

Authors
  1. I. A. Kozlitin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. A. Kozlitin.

Additional information

Translated by E. Oborin

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kozlitin, I.A. A Mathematical Model of the Motion of a Spinning Projectile. Math Models Comput Simul 13, 80–90 (2021). https://doi.org/10.1134/S2070048221010117

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048221010117

Keywords:

Search

Navigation