Trajectory modification of a transonic spherical projectile under hop-up mechanism

Document Type : Article


Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, P.O. Box 91775-1111, Iran.


Improvement of shooting accuracy of air gun pellets is important in sport competitions which is questioned by shooting enthusiasts. Hence, the performance of a transonic spherical projectile as an air gun pellet with 4.5 mm-caliber under a mechanism known as Hop-up is numerically examined in the present study. Hop-up mechanism is resulted in a rotational motion of spherical projectile, so a Magnus Force is generated which prevents the altitude loss of the projectile caused by its weight. The motion of the projectile is assumed in four degrees of freedom including three translational motions and one transverse rotational motion. The projectile confronts the continuous variations of velocity due to the influence of the aerodynamic forces so experiences an unsteady flow. In order to numerical analysis of the problem, the 3-D compressible turbulent Navier-Stokes equations based on “Roe” scheme and dynamic equations of the projectile motion are solved in a coupled form as a fluid-structure interaction and in a moving computational grid. The results obtained from these studies show that the proper rotation of the projectile for a certain distance, can neutralize the altitude loss. It is also demonstrated that the momentum of the projectile is decreased by increasing its angular velocity.


Main Subjects

  1. Nietubicz, C.J. and Gibeling, H.J. Navier-Stokes computations for a reacting M864 base bleed projectile", Army Research Lab Aberdeen proving Ground MD, pp. 1-38 (1995). 2. Chakraverty, S., Stiharu, I., and Bhat, R.B. Inuence of aerodynamic loads on ight trajectory of spinning spherical projectile", AIAA Journal, 39(1), pp. 122- 125 (2001). 3. Pechier, M., Guillen, Ph., and Cayzac, R. Magnus e_ect over _nned projectiles", Journal of Spacecraft and Rockets, 38(4), pp. 542-549 (2001). 4. Silton, S.I. Navier-Stokes computations for a spinning projectile from subsonic to supersonic speeds", Journal of Spacecraft and Rockets, 42(2), pp. 223-230 (2005). 5. DeSpirito, J., Silton, S.I., and Weinacht, P. Navierstokes predictions of dynamic stability derivatives: evaluation of steady states methods", Journal of Spacecraft and Rockets, 46(6), pp. 1142-1154 (2009). 6. Yu, W. and Zhang, X. Aerodynamic analysis of projectile in gun system _ring process", Journal of Applied Mechanics, 77, pp. 1-8 (2010). 7. Kim, J., Park, H., Choi, H., and Yoo. J.Y. Inverse Magnus e_ect on a rotating sphere", International Symposium on Turbulence and Shear Flow Phenomena, Poitiers, France (August 28-30, 2013). 8. Pier, B. Periodic and quasiperiodic vortex shedding in the wake of a rotating sphere", Journal of Fluids and Structures, 41, pp. 43-50 (2013). 9. Robinson, G. and Robinson, I. Comment on 'The motion of an arbitrarily rotating spherical projectile and its application to ball games", Journal of Physica Scripta, 88(1), pp. 018101-018117 (2013). 10. Jensen, J.H. The motion of an arbitrarily rotating spherical projectile and its application to ball games", Journal of Physica Scripta, 89(6), pp. 067001-067003 (2014). 11. Poon, E.K.W., Oon, A.S.H., Giacobello, M., Iaccarino, G., and Chung, D. Flow past a transversely rotating sphere at Reynolds numbers above the laminar regime", Journal of Fluid Mechanics, 759, pp. 751-781 (2014). 12. Rafeie, M. and Teymourtash, A.R. The aerodynamic and dynamic analysis of three common 4.5 mm caliber S.E. Salimipour et al./Scientia Iranica, Transactions B: Mechanical Engineering 26 (2019) 796{807 807 pellets in a transonic ow", Scientia Iranica, Transactions B: Mechanical Engineering, 23(4), pp. 1767-1776 (2016). 13. Salimipour, S.E. and Teymourtash, A.R. Numerical simulation and operation comparison of two sizes of air gun pellets with 4.5 and 5.5 mm calibers", Fluid Mech. and Aerodynamics, 3(3), pp. 35-47 (2015) (In Persian). 14. Teymourtash, A.R. and Salimipour, S.E. Compressibility e_ects on the ow past a rotating cylinder", Physics of Fluids, 29, p. 016101 (2017). 15. Mirsajedi, S.M. and Hosseini Zarj, M.H. Improvement in moving mesh algorithm around an oscillational airfoil", Aerospace Sciences and Researches, 2, pp. 71- 82 (2009). (In Persian) 16. Karimian, S.M.H. and Ardakani, M. Immersed boundary method for the solution of 2D inviscid compressible ow using _nite volume approach on moving cartesian grid", Journal of Applied Fluid Mechanics, 4(2), Special Issue, pp. 27-36 (2011). 17. Bloom_eld, K., How to Win an Airsoft War: Secret Tactics for Success Revealed, Ed., 1st, Airsoftezone. com (2011). 18. Blazek, J., Computational Fluid Dynamics: Principles and Applications, Ed., 1st, Elsevier Science Ltd, pp. 212-215, 414-415, 238-241 (2001). 19. Walters, D.K. and Cokljat, D. Three-equation eddyviscosity model for Reynolds-averaged Navier-stokes simulations of transitional ow", Journal of Fluids Engineering, 130, pp. 121401-14 (2008). 20. Furst, J. Numerical simulation of transitional ows with laminar kinetic energy", Journal of Engineering Mechanics, 20(5), pp. 379-388 (2013). 21. Jameson, A., Schmidt, W., and Turkel, E. Numerical solutions of the Euler equations by _nite volume methods using Runge-Kutta time-stepping schemes", AIAA Paper, 81-1259 (1981). 22. Carlson, D.J. and Hoglund, R.F. Particle drag and heat transferrin rocket nozzles", AIAA Journal, 2(11), pp. 1980-1984 (1964). 23. Crowe, C.T. Drag coe_cient of particles in a rocket nozzle", AIAA Journal, 5, pp. 1021-1022 (1967). 24. Korkan, K.D., Petrie, S.L., and Bodonyi, R.J. Particle concentrations in high Mach number, two-phase ows", TR 74-0102, Aerospace Research Laboratories, Wright-Patterson AFB (1974). 25. Henderson, C.B. Drag coe_cients of spheres in continuum and rare_ed ows", AIAA Journal, 14(6), pp. 707-708 (1976). 26. Mittal, R., Dong, H., Bozkurttas, M., Najjar, F.M., and Vargas, A. A versatile sharp interface immersed boundary method for incompressible ows with complex boundaries", Journal of Computational Physics, 227, pp. 4825-4852 (2008).