Methodology for Estimating the Preparation Time of the Return Stage of a Space Rocket for Re-Launch Using the Example of the FALCON 9 FT Launch Vehicle

The purpose of the research is to propose a methodology for estimating the preparation time of the return stage of a space rocket for re-launch based on the Student's t-distribution using the Euler gamma function.

Methods. Statistical analysis of the dynamics of repeated launches of the first stage of the Falcon 9 launch vehicle (PH) showed that the first re-launch of the return stage was at 1046.2 was carried out on August 7, 2018, 88 days after her landing on the OCISLY offshore platform. In total, 3 re-launches of this stage took place in the period from 2018 to 2020. The average time interval required to prepare this stage for subsequent launch was 205 days. The 1058 stage, which was first launched in May 2020, was re-launched 6 times (the last time was in March 2021). The average time interval required to prepare this stage for subsequent launch was 50 days. Analysis of the available data shows that from the moment of the first re-launch of the stage in August 2018 to the present, the average preparation time of the returned stages for the next launch has decreased fourfold - from 205 days to 45-50 days.

Results. The application of the proposed methodology to the sampling of the time intervals of preparation for the relaunch of stages B1056, B1058, B1059, B1060 in the period from 2019 to 2021, allows us to obtain the following values of the time of preparation of the returned stage of a space rocket for re-launch: t = 55 ± 10 days, i.e. t (45; 65) days, which is confirmed by the analysis of the presented statistical data. The discrepancy between the calculation results and real data is within the statistical error.

Conclusion. The presented methodology makes it possible to estimate the average time required to prepare the return stages of the launch vehicle for subsequent launches, and, consequently, to predict the capabilities of participants in space activities who have reusable space systems at their disposal to increase their orbital groupings. Therefore, the proposed methodology can be used in the development of algorithms, models, methods for estimating the preparation time of the returned stages for re-launches of the PH, as well as for evaluating the effectiveness of the use of reusable (partially salvageable) PH of various classes for their intended purpose.

1. Ganiev T. A., Karyakin V. V. Kosmicheskaya politika mirovykh i regional'nykh derzhav [Space policy of world and regional powers]. Moscow, Archon Publ., 2020. 175 p.

2. Karbovskaya V. V. [Prospects for the development of the international space market of heavy class launch vehicles]. Tsiolkovskii. Problemy i budushchee rossiiskoi nauki i tekhniki. Materialy LII nauchnykh chtenii pamyati K. E. Tsiolkovskogo [Tsiolkovsky. Problems and the future of Russian science and technology. Materials of the LII scientific readings in memory of K. E. Tsiolkovsky]. Kaluga, Eidos Publ., 2017, pp. 477-478. (In Russ.)

3. Medvedev A. A. Predlozheniya po povysheniyu konkurentnosposobnosti raket- nositelei srednego i tyazhelogo klassov za schet primeneniya mnogorazovykh elementov v otechestvennykh sredstvakh vyvedeniya [Proposals to increase the competitiveness of medium- and heavy-class launch vehicles through the use of reusable elements in domestic launch vehicles]. Kosmonavtika i raketostroenie = Cosmonautics and Rocket Science, 2018, no. 3

4. (102), pp. 111-121.

5. Koroteev A. S., Nesterov V. M., Eliseev I. O., Balashova A. V. Effektivnost' ispol'zovaniya i problemy spaseniya pervykh stupenei raket nositelei [Efficiency of use and problems of rescue of the first stages of launch vehicles]. Polet. Obshcherossiiskii nauchno-tekhnicheskii zhurnal = Flight. All-Russian Scientific and Technical Journal, 2018, no. 2, pp. 3-11.

6. Gorevich B. N. Analiz novykh napravlenii razvitiya PRO SShA v svete prinyatoi amerikanskoi strategii PRO [Analysis of new directions in the development of US missile defense in the light of the adopted American missile defense strategy]. Vestnik vozdushno-kosmicheskoi oborony= Bulletin of Aerospace Defense, 2019, no. 2 (22), pp. 117-126.

7. SpaceX. Available at: http://spacex.com. (accessed 25.05.2021)

8. Blue Origin. Available at: http://blueorigin.com. (accessed 25.05.2021)

9. Rocket Lab. Available at: http://rocketlabusa.com. (accessed 25.05.2021)

10. Krasnoslobodtsev V. P., Kuzmin Yu. N., Raskin A. V., Tarasov I. V., Baykin V. A. Kompaniya "Space-X" i programma kommercheskikh pilotiruemykh poletov SShA [Space-X Company and the US Commercial Manned Flight Progra]. Dvoinye tekhnologii = Dual Technologies, 2020, no. 3 (92), pp. 16-19.

11. Kuznetsov I. I., Kuznetsov Yu. L., Mukhamedzhanov M. Zh., Ukraintsev D. S., Shokhov G. V. Otsenka energeticheskikh poter' rakety-nositelya tipa "folkon" pri razlichnykh variantakh realizatsii raketodinamicheskoi sistemy spaseniya pervoi stupeni [Estimation of energy losses of a Falcon-type launch vehicle in various variants of the implementation of the rocket-dynamic rescue system of the first stage]. Kosmonavtika i raketostroenie = Cosmonautics and Rocket Engineering, 2016, no. 3 (88), pp. 83-92.

12. Danilkin V. A., Mogilenko V. I., Panov Yu. P. Sposob upravleniya poletom mnogo- stupenchatoi rakety-nositelya i mnogostupenchataya raketa nositel' [The method of flight control of a multi-stage launch vehicle and a multi-stage launch vehicle]. Patent RF, no. 2006135022/02, 2008.

13. List of Falcon 9 and Falcon Heavy launches. Available at: http://nasa.fandom.com. (accessed 25.05.2021)

14. Rahman R. M., Bogatova O. A., Korolev D. A. Sravnenie effektivnosti raketonositelei [Comparison of the effectiveness of launch vehicles]. Novaya nauka: Teoreticheskii i prakticheskii vzglyad. = New Science: Theoretical and Practical View, 2016, no. 6-2 (87), pp. 122-126.

15. Savelyeva M. V., Goridko N. P. Rossiya na mirovom rynke kosmicheskikh puskovykh uslug: konkurentnosposobnost' i ekonomicheskaya bezopasnost' [Russia on the world market of space launch services: competitiveness and economic security]. Drukerovskii vestnik = Drukerovsky Bulletin, 2018, no. 3 (23), pp. 163-175.

16. Seliverstov A. I., Shevchenko I. V. Metodicheskie podkhody k sozdaniyu dinamicheskoi modeli rakety-nositelya tyazhelogo klassa [Methodological approaches to the creation of a dynamic model of a heavy-class launch vehicle]. Tekhnologiya mashinostroeniya = Technology of Machine-Building, 2014, no. 4, pp. 44-47.

17. Tyapkin S. A., Mukhin I. E., Koptev D. S. Metod sovmestnogo primeneniya pokazatelya struktury vibrosignala i izvestnykh rezul'tatov identifikatsionnykh izmerenii v zadachakh preventivnogo obnaruzheniya neispravnostei aviatsionnykh dvigatelei [Method of joint application of the vibration signal structure indicator and known results of identification measurements in the tasks of preventive detection of aircraft engine malfunctions]. Izvestiya Yugo-Zapadnogo gosudarstvennogo universiteta. Seriya: Upravlenie, vychislitel'naya tekhnika, informatika = Proceedings of the Southwest State University. Series: Management, Computer Engineering, Computer Science. Medical Instrumentation, 2020, vol. 10, no. 2, pp. 57-67.

18. Kretov A. S., Chizhukhin V. N., Kovalevsky M. M., Mekhonoshin Yu. G. K obosnovaniyu vybora sposoba spaseniya blokov raket nositelei [To substantiate the choice of the method of rescue of carrier rocket blocks]. Izvestiya vysshikh uchebnykh zavedenii. Aviatsionnaya tekhnika = Proceedings of Higher Educational Institutions. Aviation Equipment, 2021, no. 1, pp. 3-11.

19. Kuznetsov Yu. L., Ukraintsev D. S. Analiz vliyaniya skhemy poleta stupeni s raketno- dinamicheskoi sistemoi spaseniya na energeticheskie kharakteristiki dvukhstupenchatoi rakety-nositelya srednego klassa [Analysis of the effect of the flight scheme of a stage with a rocket-dynamic rescue system on the energy characteristics of a two-stage medium-class launch vehicle]. Vestnik Samarskogo gosudarstvennogo aerokosmicheskogo universiteta imeni akademika S. P. Koroleva (natsional'nogo issledovatel'skogo universiteta = Bulletin of Samara State Aerospace University named after Academician S. P. Korolev (National Research University), 2016, vol. 15, no. 1, pp. 73-80.

20. Pirogov S. Yu., Prokopenko E. A. Metodika energomassovogo analiza dvukhstupenchatoi rakety-nositelya, oborudovannoi sistemoi spaseniya stupenei [Methodology of energy-mass analysis of a two-stage launch vehicle equipped with a stage rescue system]. Trudy Voenno-kosmicheskoi akademii imeni A. F. Mozhaiskogo = Proceedings of the Military Space Academy named after A. F. Mozhaisky, 2018, no. 665, pp. 231-236.

21. Wentzel E. S. Teoriya veroyatnostei [Probability Theory]. Moscow, KNORUS Publ., 2010. 664 p