Computational Prediction of Complicated Atmospheric Motion for Spinning or non- Spinning Projectiles
A full six degrees of freedom (6-DOF) flight dynamics
model is proposed for the accurate prediction of short and long-range
trajectories of high spin and fin-stabilized projectiles via atmospheric
flight to final impact point. The projectiles is assumed to be both rigid
(non-flexible), and rotationally symmetric about its spin axis launched
at low and high pitch angles. The mathematical model is based on the
full equations of motion set up in the no-roll body reference frame and
is integrated numerically from given initial conditions at the firing
site. The projectiles maneuvering motion depends on the most
significant force and moment variations, in addition to wind and
gravity. The computational flight analysis takes into consideration the
Mach number and total angle of attack effects by means of the
variable aerodynamic coefficients. For the purposes of the present
work, linear interpolation has been applied from the tabulated database
of McCoy-s book. The developed computational method gives
satisfactory agreement with published data of verified experiments and
computational codes on atmospheric projectile trajectory analysis for
various initial firing flight conditions.
[1] McCoy, R., Modern Exterior Ballistics, Schiffer, Attlen, PA, 1999.
[2] Fowler, R., Gallop, E., Lock, C., and Richmond H., "The Aerodynamics
of Spinning Shell," Philosophical Transactions of the Royal Society of
London, Series A: Mathematical and Physical Sciences, Vol. 221, 1920.
[3] Cooper, G., "Influence of Yaw Cards on the Yaw Growth of Spin
Stabilized Projectiles," Journal of Aircraft, Vol.38, No. 2, 2001.
[4] Guidos, B., and Cooper, G., "Closed Form Solution of Finned Projectile
Motion Subjected to a Simple In-Flight Lateral Impulse," AIAA Paper,
2000.
[5] Costello, M., and Peterson, A., "Linear Theory of a Dual-Spin Projectile
in Atmospheric Flight," Journal of Guidance, Control, and Dynamics,
Vol.23, No. 5, 2000.
[6] Burchett, B., Peterson, A., and Costello, M., "Prediction of Swerving
Motion of a Dual-Spin Projectile with Lateral Pulse Jets in Atmospheric
Flight," Mathematical and Computer Modeling, Vol. 35, No. 1-2, 2002.
[7] Cooper, G., "Extending the Jump Analysis for Aerodynamic Asymmetry,"
Army Research Laboratory, ARL-TR-3265, 2004.
[8] Cooper, G., " Projectile Aerodynamic Jump Due to Lateral Impulsives,"
Army Research Laboratory, ARL-TR-3087, 2003.
[9] Murphy, C., "Instability of Controlled Projectiles in Ascending or
Descending Flight," Journal of Guidance, Control, and Dynamics, Vol.4,
No. 1, 1981.
[10] Hainz, L., and Costello, M., "Modified Projectile Linear Theory for Rapid
Trajectory Prediction," Journal of Guidance, Control, and Dynamics,
Vol.28, No. 5, 2005.
[11] Etkin, B., Dynamics of Atmospheric Flight, John Wiley and Sons, New
York, 1972.
[12] Joseph K., Costello, M., and Jubaraj S., "Generating an Aerodynamic
Model for Projectile Flight Simulation Using Unsteady Time Accurate
Computational Fluid Dynamic Results," Army Research Laboratory,
ARL-CR-577, 2006.
[13] Amoruso, M. J., "Euler Angles and Quaternions in Six Degree of
Freedom Simulations of Projectiles," Technical Note, 1996.
[14] Costello, M., and Anderson, D., "Effect of Internal Mass Unbalance on
the Terminal Accuracy and Stability of a projectile," AIAA Paper, 1996.
[1] McCoy, R., Modern Exterior Ballistics, Schiffer, Attlen, PA, 1999.
[2] Fowler, R., Gallop, E., Lock, C., and Richmond H., "The Aerodynamics
of Spinning Shell," Philosophical Transactions of the Royal Society of
London, Series A: Mathematical and Physical Sciences, Vol. 221, 1920.
[3] Cooper, G., "Influence of Yaw Cards on the Yaw Growth of Spin
Stabilized Projectiles," Journal of Aircraft, Vol.38, No. 2, 2001.
[4] Guidos, B., and Cooper, G., "Closed Form Solution of Finned Projectile
Motion Subjected to a Simple In-Flight Lateral Impulse," AIAA Paper,
2000.
[5] Costello, M., and Peterson, A., "Linear Theory of a Dual-Spin Projectile
in Atmospheric Flight," Journal of Guidance, Control, and Dynamics,
Vol.23, No. 5, 2000.
[6] Burchett, B., Peterson, A., and Costello, M., "Prediction of Swerving
Motion of a Dual-Spin Projectile with Lateral Pulse Jets in Atmospheric
Flight," Mathematical and Computer Modeling, Vol. 35, No. 1-2, 2002.
[7] Cooper, G., "Extending the Jump Analysis for Aerodynamic Asymmetry,"
Army Research Laboratory, ARL-TR-3265, 2004.
[8] Cooper, G., " Projectile Aerodynamic Jump Due to Lateral Impulsives,"
Army Research Laboratory, ARL-TR-3087, 2003.
[9] Murphy, C., "Instability of Controlled Projectiles in Ascending or
Descending Flight," Journal of Guidance, Control, and Dynamics, Vol.4,
No. 1, 1981.
[10] Hainz, L., and Costello, M., "Modified Projectile Linear Theory for Rapid
Trajectory Prediction," Journal of Guidance, Control, and Dynamics,
Vol.28, No. 5, 2005.
[11] Etkin, B., Dynamics of Atmospheric Flight, John Wiley and Sons, New
York, 1972.
[12] Joseph K., Costello, M., and Jubaraj S., "Generating an Aerodynamic
Model for Projectile Flight Simulation Using Unsteady Time Accurate
Computational Fluid Dynamic Results," Army Research Laboratory,
ARL-CR-577, 2006.
[13] Amoruso, M. J., "Euler Angles and Quaternions in Six Degree of
Freedom Simulations of Projectiles," Technical Note, 1996.
[14] Costello, M., and Anderson, D., "Effect of Internal Mass Unbalance on
the Terminal Accuracy and Stability of a projectile," AIAA Paper, 1996.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:51995", author = "Dimitrios N. Gkritzapis and Elias E. Panagiotopoulos and Dionissios P. Margaris and Dimitrios G. Papanikas", title = "Computational Prediction of Complicated Atmospheric Motion for Spinning or non- Spinning Projectiles", abstract = "A full six degrees of freedom (6-DOF) flight dynamics
model is proposed for the accurate prediction of short and long-range
trajectories of high spin and fin-stabilized projectiles via atmospheric
flight to final impact point. The projectiles is assumed to be both rigid
(non-flexible), and rotationally symmetric about its spin axis launched
at low and high pitch angles. The mathematical model is based on the
full equations of motion set up in the no-roll body reference frame and
is integrated numerically from given initial conditions at the firing
site. The projectiles maneuvering motion depends on the most
significant force and moment variations, in addition to wind and
gravity. The computational flight analysis takes into consideration the
Mach number and total angle of attack effects by means of the
variable aerodynamic coefficients. For the purposes of the present
work, linear interpolation has been applied from the tabulated database
of McCoy-s book. The developed computational method gives
satisfactory agreement with published data of verified experiments and
computational codes on atmospheric projectile trajectory analysis for
various initial firing flight conditions.", keywords = "Constant-Variable aerodynamic coefficients, low and high pitch angles, wind.", volume = "1", number = "7", pages = "327-5", }