Approximate Closed-Form Solution for projectile Trajectory and its Applications to lead Angle Computations

M.S. Ganagi; V.P. Singh

doi:10.14429/dsj.49.3827

M.S. Ganagi Centre for Aeronautical Systems Studies & Analyses. Bangalore .
V.P. Singh Centre for Aeronautical Systems Studies & Analyses. Bangalore .

DOI: https://doi.org/10.14429/dsj.49.3827

Keywords: Algorithm, Ballistic projectiles, Closed form solution

Abstract

In this paper, an approximate closed-form solution for trajectories of ballistic projectiles is derived. The assumption made in this derivation is to neglect the variation of the elevation angle along the trajectory in a small interval of time. The closed-form solution has been used to develop the 3-logarithm for a lead angle computation as well as faster computation of trajectories. The fact that one of the analytical expressions although complex, is invertible and is made use of in the algorithm.

Author Biographies

M.S. Ganagi, Centre for Aeronautical Systems Studies & Analyses. Bangalore .

Dr MS Ganagi obtained his MSc in Mathematics From Karnataka University in 1982,and PhD in Relativistic Fluid Dynamics from Indian Institute of Science, Bangalore,in 1989.He Joined DRDO at the Advenced Numerical Research & analysis Group(ANURAG) , Hyderabad,in 1988and worked there for seven years. In 1995, he was transferred to the Centre for Aeronauutical System Studies & Analyses (CASSA) Bangalore. He has Published 10 Paper in national/international jouernals. His areas of Research are aeronautical systems simulation and parallel processing.

V.P. Singh, Centre for Aeronautical Systems Studies & Analyses. Bangalore .

Dr Vp Singh obtained his PhD in Shock Waves from University of Dehli in 1971. He Joined DRDO at the Defence Science Laboratory (now DScc),Dehli. He worked at various DRDO establishments. At present, he is Associate Director at CASSA and is heading Weapon Evalution System Group . He is a member of the Aeronautical Society of India , Operational Research Society of India and Computer Society of India . His areas of research are shock waves and systems analysis . he has published more than 45 papers in national/international jouernals and authored three books .

References

Bliss, G .A. 'Mathematics for exterior ballistics. John Wiley.and Sons, London, 1944.

Jain, M.K.; Iyengar, S.R.K. & Jain, R.K. Numerical methods. Wiley Eastern Limited 1994.

Singh, V.P. & Ganagi, M.S. Approximate blosed-form solution tor two-dimensional trajectories of projectiles. Centre for Aeroriautical Systems Studies & Analyses, Bangalore, Report No. CASSA-S-97-4.