Trajectory estimation model for a solid body with an irregular shape undergoing extremely high aerodynamic forces

Elvedin Kljuno, Alan Catovic


A generalized (6DOF) model for evaluating fragment trajectory elements is defined, which incorporates a novel model for estimating the projected surface of the body and novel model for estimating aerodynamic force and moment. This 6DOF model is developed on the basis of differential equations of the center of mass motion and movement around the center of mass (currently no known model incorporates movement of the body around its center of mass), and can model the parameters that play an essential role in movement of the bodies with irregular shape through the atmosphere. In our model the basic parameters (i.e. body dimensions) can be arbitrarily changed in the initial part of the analysis, and based on their values and values of initial kinematic parameters (initial velocity, position, orientation), trajectories can be determined (as well as other parameters: velocities, orientation) in a relatively short amount of time.
The calculation of the complete trajectory of the fragments can be used in a number of applications: the analysis of the effects of the fragments (i.e. the safety analysis of the location of the ammunition depots, due to the potential explosion of the projectile) or in the estimation of a danger zones when demining larger quantities of the munition. Also, from the point of view of the parameters of the lethal zone of HE projectiles, it is generally important to estimate the trajectory of the fragments in the range up to 50m, so this model can be used to model such a scenario also. This model could also be potentially used wherever there is a need to calculate flight mechanics parameters of irregularly shaped bodies. Generalized (6DOF) model for estimation of an irregularly shaped body trajectory is implemented in a computer program, written in MatLab. Based on the model, the trajectory calculations were performed for the complete trajectory and for shorter distances to the center of the explosion, with varied geometric-inertial parameters and initial kinematic conditions for the given fragment.


aerodynamic force, irregular shape, fragment, solid body, trajectory

Full Text:



L.A. Twisdale and P.J. Wickery, "Comparison of debris trajectory models for explosive safety hazard analysis," 25th DoD Explosive Safety Seminar, Anaheim, California, 1992.

J. Hokanson, "Fragment and debris hazards from accidental explosions," Naval Surface Weapons Center, Dahlgren VA, 1981.

E.W. Baker, P.S. Westine, J.J. Kulesz, J.S. Wilbeck and P.A. Cox, "Manual for the prediction of blast and fragment loadings on structures," USDOE Albuquerque Operations Office, 1980.

F. McCleskey, "Quantity Distance Fragmenf Hazard Computer Program," Naval Surface Warfare Center, 1988.

L.A. Twisdale, W.L. Dunn and R.A. Frank, "Probabilistic methodology for turbine missile risk analysis," Nuclear Engineering and Design, 1984.

J.G. Connor, Jr., "Accidental Torpedo Detonation in Submarine Tender Workshops," Nineteenth Explosives Safety Seminar, Los Angeles, CA, 1980.

M.M. Swisdak, Jr., "Determination of Safe Handling Arcs Around Nuclear Attack Submarines," Nineteenth Explosives Safety Seminar, Los Angeles, CA, 1980.

M. Crull and M.M. Swisdak, Jr., "Methodologies for calculating primary fragment characteristics," Department of Defense Explosives Safety Board, Alexandria, VA, 2005.

H.L. Schreyer and L.E. Romesberg, "Analytical Model for High Explosive Munitions Storages," Mechanics Research Inc., Albuquerque, NM, 1970.

W.E. Baker W. E., J.J. Kulesz, R.E. Ricker, P.S. Westine, V.B. Parr, L.M. Vargas and P.K. Moseley, "Workbook for Estimating Effects of Accidental Explosions in Propellant Ground Handling and Transport Systems," NASA Contractor Report 3023, 1978.

S. Murman, "Characterization of space shuttle ascent debris aerodynamics using CFD methods," 43rd AIAA Sciences Meeting, 2005.

J.F. Moxnes, Ø. Frøyland, J. Ivar, I.J. Øye, T.I. Brate, E. Friis, G. Ødegårdstuen, T.H. Risdal, "Projected area and drag coefficient of high velocity irregular fragments that rotate or tumble," Defence Technology, 2017.

TNO Report, "General description of the missile systems damage assessment code (MISDAC)," Prins Maurits Laboratorium TNO, 1994.

E. Kljuno and A. Catovic, "Estimation of projected surface area of irregularly shaped fragments," Defence Technology Journal, 2019a.

E. Kljuno and A. Catovic, "A generalized model for estimation of aerodynamic forces and moments for an arbitrary shaped body," Defence Technology Journal, 2019b.

B. Zecevic, J. Terzic, A. Catovic and S. Serdarevic-Kadic, "Influencing parameters on HE projectiles with natural fragmentation," New Trends in Research of Energetic Materials, Pardubice, 2006.

A. Catovic and E. Kljuno, "Prediction of aerodynamic coefficients for irregularly shaped body using numerical simulations," International Journal of Advanced and Applied Sciences, 5(7), Pages: 71-85, 2018.



  • There are currently no refbacks.

Copyright (c) 2021 Elvedin Kljuno, Alan Catovic

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN: 2303-4521

Digital Object Identifier DOI: 10.21533/pen

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License