Method for determining the initial conditions for the use of uncontrolled reactive ballistic bodies from mobile carrier

DOI: 10.34759/trd-2023-131-16

Аuthors

Ispulov A. A.^*, Kalmykov A. V.^**

Air force academy named after professor N.E. Zhukovskii and Y.A. Gagarin, Voronezh, Russia

*e-mail: ispulovy@yandex.ru
**e-mail: kalmykov_an@bk.ru

Abstract

The problem of ballistics is the process of calculating the trajectory of an uncontrolled reactive ballistic body after it has been separated from the carrier. At present, the basis for calculating the trajectory is the canonical model of motion, which describes the change in velocity, nutation angle, angular velocity of nutation, trajectory inclination angle, and rocket coordinates. However, this model is adequate only in conditions of uniform rectilinear flight; when the carrier is maneuvering, additional corrections are made depending on the angles of attack and slip of the carrier. The accuracy of the use of unguided reactive ballistic bodies depends on the initial launch conditions, which are determined by the parameters of the carrier and target motion. Development of a methodology for determining the initial conditions for launching an unguided reactive ballistic body with a vertical maneuver of a movable carrier. A technique has been developed for determining the initial conditions for launching an uncontrolled reactive ballistic body with a vertical maneuver of a movable carrier, for which analytical expressions have been obtained to determine the initial values of velocity, nutation angle, angular velocity of the nutation angle, and trajectory inclination angle. The results obtained make it possible to obtain the dependences of the resulting initial velocity, the initial nutation angle, the initial nutation angular velocity, and the initial trajectory inclination angle on various conditions for launching an uncontrolled reactive ballistic body during a vertical maneuver of a movable carrier. The obtained experimental dependences can be used in the development of a ballistic algorithm to obtain the exact initial conditions necessary for integrating the differential equations of a complete ballistic motion model, which in turn will improve the aiming accuracy.

Keywords:

external ballistics, trajectory, uncontrolled reactive ballistic body, moving carrier, initial launch conditions

References

1. Ganulich A.K. Aviatsionnye pritsel’nye sistemy, ikh issledovanie i ispytanie (Aviation sighting systems, their studyand test), Moscow, VVIA im. N.E .Zhukovskogo, 1984, 210 p.
2. Mubarakshin R.V. Pritsel’nye sistemy strel’by (Sighting firing systems), Moscow, VVIA im. N.E. Zhukovskogo, 1973, 332 p.
3. Krasnov A.M. Aviatsionnye pritsel’no-navigatsionnye sistemy (Aviation sighting and navigation systems), Moscow, VVIA im. N.E. Zhukovskogo, 2005, 623 p.
4. Postnikov A.G. Vneshnyaya ballistika aviatsionnykh neupravlyaemykh sredstv porazheniya (External ballistics of aviation unguided weapons), Moscow, VVIA im. N.E. Zhukovskogo, 2003, 396 p.
5. Dmitrievskii A.A., Lysenko L.N. Vneshnyaya ballistika (External ballistics), Moscow, Mashinostroenie, 2005, 608 p.
6. Vytrishko V.M., Gul’tyaev N.N. Trudy MAI, 2013, no. 71. URL: https://trudymai.ru/eng/published.php?ID=46808
7. Bel’skii A.B., Postnikov A.G. Izvestiya Rossiiskoi akademii raketnykh i artilleriiskikh nauk, 2014, no. 3, pp. 60-69.
8. Krasnov A.M. Trudy MAI, 2012, no. 61. URL: https://trudymai.ru/eng/published.php?ID=35640
9. Krasnov A.M. Trudy MAI, 2013, no. 49. URL: https://trudymai.ru/eng/published.php?ID=27946
10. Bel’skii A.B. Izvestiya Tul’skogo gosudarstvennogo universiteta. Tekhnicheskie nauki. 2018, no. 11, pp. 175-189.
11. Lebedev V.V., Moiseev S.N., Filippov A.V. II Vserossiiskaya nauchno-prakticheskaya konferentsiya «Kalibr»: sbornik nauchnykh statei. Voronezh, VUNTs VVS «VVA», 2018, pp. 242-248.
12. Ilyukhin S.N., Kazakovtsev V.P., Koryanov V.V. Molodezhnyi nauchno-tekhnicheskii vestnik, 2015, no. 11, pp. 193-203.
13. Arnol’d V.I. Obyknovennye differentsial’nye uravneniya (Ordinary differential equations), Moscow, Nauka, 2000, 368 p.
14. Bogoslovskii S.V., Dorofeev A.D. Dinamika poleta letatel’nykh apparatov (Aircraft Flight Dynamics: A Study Guide), Saint Petersburg, SPbGUAP, 2002, 64 p.
15. Korolev S.A., Zorina E.K. IV Vserossiiskaya nauchno-tekhnicheskaya konferentsiya «Molodye uchenye — uskoreniyu nauchno-tekhnicheskogo progressa v XXI veke»: sbornik trudov. Izhevsk, Izd-vo INNOVA, pp. 50-56.
16. Korolev S.A., Rusyak I.G., Sufiyanov V.G. Intellektual’nye sistemy v proizvodstve, 2016, no. 4 (31), pp. 13-18.
17. Rusyak I.G., Korolev S.A., Tenenev V.A., Vagin A.V., Beloborodov M.N. Izvestiya Tul’skogo gosudarstvennogo universiteta. Tekhnicheskie nauki. Problemy spetsial’nogo mashinostroeniya, 2018, no. 12-3, pp. 231-239.
18. Korolev S.A., Rusyak I.G., Tenenev V.A. Intellektual’nye sistemy v proizvodstve, 2018, vol. 21, no. 3, pp. 103-109.
19. Korolev S.A., Rusyak I.G., Sufiyanov V.G Izvestiya Tul’skogo gosudarstvennogo universiteta. Tekhnicheskie nauki, 2017, no. 11-3, pp. 23-33.
20. Vygodskii M.Ya. Spravochnik po vysshei matematike (Handbook of higher mathematics), Moscow, AST: Astrel’, 2006, 991 p.

Download