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Aerodynamical CFD Study of a Non-Lethal 12-Gauge Fin-Stabilized Projectile

  • V. de BrieyEmail author
  • I. Ndindabahizi
  • B. G. Marinus
  • M. Pirlot
Original Paper

Abstract

Nowadays, the trajectory model for a subsonic fin-stabilized projectile at a low angle of attack is typically a point-mass model (PMM), taking only gravity and a constant zero-yaw drag into account. This choice can be qualitatively justified for non-lethal projectiles given the short ranges. The disadvantage of this approach is the lack of prediction on the precision and the attitude of the projectile when hitting the target, because of a possible instability in flight. However, the use of non-lethal projectiles requires that the impact conditions are met, otherwise more serious injuries may occur. Therefore, the consideration of other forces and moments acting on the projectile in flight is mandatory to predict static and dynamic stabilities, already in the body shape design as well as in the controller design process in the field of non-lethal ammunitions. Starting from a geometry in caliber 12-gauge, static coefficients (drag, lift, and pitch) for different angles of attack using steady RANS simulations with a low-order turbulence model were found. Different trajectories were then analyzed using those coefficients and the difference between the PMM and a 3-DOF accounting for drag, lift, and pitch in function of the angle of attack is indeed negligible in height and in range as long as the launch conditions are completely undisturbed. The slightest destabilization makes the PMM completely inappropriate. Knowledge of the pitch damping coefficient then becomes a necessity to optimize stabilization following minor disturbances.

Keywords

Fin-stabilized Flat trajectory Aerodynamical coefficients CFD Stability Pitch damping 

Nomenclature

CFD

Computational fluid dynamics

RBD

Rigid body dynamics

RANS

Reynolds averaged Navier-Stokes

PMM

Point-mass model

3-DOF

Three degrees of freedom

D

Drag force (N)

CD

Drag coefficient

CD0

Zero-yaw drag coefficient

\( {C}_{{\mathrm{D}}_{\upalpha^2}} \)

Yaw-induced drag coefficient

L

Lift force (N)

CL

Lift coefficient

\( {C}_{{\mathrm{L}}_{\upalpha^2}} \)

Yaw-induced lift coefficient

M

Pitch moment (N m)

CM

Pitch coefficient

\( {C}_{{\mathrm{M}}_{\upalpha^2}} \)

Yaw-induced pitch coefficient

H

Pitch damping moment (N m)

CH

Pitch damping coefficient

qt

Total transverse angular velocity (rad/s)

V

Velocity (m/s)

ρ

Air density (kg/m3)

Ma

Mach number

AoA / α

Angle of attack / yaw angle (deg.)

d

Caliber of the projectile (m)

S

Transverse surface of the caliber (m2)

MV

Muzzle velocity (m/s)

QE

Quadrant elevation (deg.)

Pitch_i

First max pitch angle (deg.)

TOF

Time of flight (s)

Notes

Acknowledgments

I would like to thank Cyril Robbe for his encouragement in the experiments as well as Gabriel Kempeneers, Pascal Delhaye, and Jules Deberlanger for their collaboration in the Ballistic Laboratory.

References

  1. 1.
    Morrison AM, Ingram CW (1976) Stability coefficients of a missile at angles of attack. J Spacecr Rocket 13(5):318–319.  https://doi.org/10.2514/3.27910 CrossRefGoogle Scholar
  2. 2.
    Silton S, Howell B (2011) Predicting the dynamic stability of small-caliber ammunition. 25th International Symposium on BallisticsGoogle Scholar
  3. 3.
    Weinacht P (2004) Projectile performance, stability, and free-flight motion prediction using computational fluid dynamics. J Spacecr Rocket 41(2):257–263.  https://doi.org/10.2514/1.1037 CrossRefGoogle Scholar
  4. 4.
    Cayzac R, Carette E, Champigny P, Thépot R, Donneaud O (2004) Analysis of static and dynamic stability of spinning projectiles. 21st International Symposium on Ballistics, pp 66–73Google Scholar
  5. 5.
    DeSpirito J, Silton S, Weinacht P (2009) Navier-Stokes predictions of dynamic stability derivatives: evaluation of steady-state methods. J Spacecr Rocket.  https://doi.org/10.2514/1.38666 CrossRefGoogle Scholar
  6. 6.
    Silton S (2005) Navier-Stokes computations for a spinning projectile from subsonic to supersonic speeds. J Spacecr Rocket 42(2):223–231.  https://doi.org/10.2514/1.4175 CrossRefGoogle Scholar
  7. 7.
    Silton S (2011) Navier-stokes predictions of aerodynamic coefficients and dynamic derivatives of a 0.50-cal projectile. 29th AIAA Applied Aerodynamics Conference, American Institute of Aeronautics and Astronautics, Honolulu, Hawaii.  https://doi.org/10.2514/6.2011-3030
  8. 8.
    Bhagwandin VA, Sahu J (2013) Numerical prediction of pitch damping stability derivatives for finned projectiles. Report Weapons and Materials Research Directorate, ARL  https://doi.org/10.2514/1.A32734 CrossRefGoogle Scholar
  9. 9.
    Sturek WB, Nietubicz CJ, Sahu J, Weinacht P (1994) Applications of computational fluid dynamics to the aerodynamics of army projectiles. J Spacecr Rocket 31(2):186–199.  https://doi.org/10.2514/3.26422 CrossRefGoogle Scholar
  10. 10.
    Sahu J (2006) Time-accurate numerical prediction of free flight aerodynamic of a finned projectile.  https://doi.org/10.1109/HPCMP-UGC.2006.72
  11. 11.
    Cayzac R, Carette E, Thépot R, Champigny P (2005) Recent computations and validations of projectile unsteady aerodynamics. 22nd International Symposium on Ballistics, pp 2–9Google Scholar
  12. 12.
    Weinacht P (2007) Virtual wind tunnel experiments for small caliber ammunition aerodynamic characterization. doi:MD21005–5066Google Scholar
  13. 13.
    Sahu J (2006) Numerical computations of unsteady aerodynamics of projectiles using an unstructured technique. Theor Comput Fluid Dyn:886, 21005–893, 25066Google Scholar
  14. 14.
    Lesage F (1997) Navier-Stokes prediction of pitch damping coefficients for projectiles. Centre de Recherche pour la Défense ValcartierGoogle Scholar
  15. 15.
    Despirito J, Heavey K (2006) CFD Computation of Magnus moment and roll damping moment of a spinning projectile. AIAA Atmospheric Flight Mechanics Conference and Exhibit.  https://doi.org/10.2514/6.2004-4713
  16. 16.
    Oktay E, Akay H (2002) CFD predictions of dynamic derivatives for missiles. 40th AIAA Aerospace Sciences Meeting & Exhibit.  https://doi.org/10.2514/6.2002-276
  17. 17.
    Park SH, Kim Y, Kwon JH (2003) Prediction of damping coefficients using the unsteady Euler equations. J Spacecr Rocket 40(3):356–362.  https://doi.org/10.2514/2.3970 CrossRefGoogle Scholar
  18. 18.
    Kokes J, Costello M, Sahu J (2007) Generating an aerodynamic model for projectile flight simulation using unsteady time accurate computational fluid dynamic results. WIT Trans Model Simul.  https://doi.org/10.2495/CBAL070041
  19. 19.
    Sahu J (2008) Numerical computations of dynamic pitch-damping derivatives using time–accurate CFD techniques. International Symposium on BallisticsGoogle Scholar
  20. 20.
    Sahu J (2005) Advanced time-accurate CFD/RBD Simulations of projectiles in free flight. DODUGC, Vol. 1, pp 86–91.  https://doi.org/10.1109/DODUGC.2005.7
  21. 21.
    Mc Coy RL (1999) Modern exterior ballistics. Schiffer Publishing Ltd, AtglenGoogle Scholar
  22. 22.
    User guide for the AOP-53 AeroFI (2011) NATO technical shareable software (NTSS) for the determination of aerodynamic coefficients (Release 1.2), Version 1.3Google Scholar
  23. 23.
    STANAG 4655 LMC - EDITION 1 (2010) An engineering model to estimate aerodynamic coefficientsGoogle Scholar
  24. 24.
    Spalart PR, Allmaras SR (1991) A one-equatlon turbulence model for aerodynamic flows. AlAA-92 G439, Boeing Commercial Airplane Group Seattle, WA 98214–2207, 30th Aerospace Sciences Meeting and ExhlbH. Reno, NVGoogle Scholar
  25. 25.
    Silton SI (2017) Quasi-steady simulations for the efficient generation of static aerodynamic coefficients at subsonic velocities. 35th AIAA Applied Aerodynamics Conference, No. June, pp. 1–16.  https://doi.org/10.2514/6.2017-3398

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • V. de Briey
    • 1
    Email author
  • I. Ndindabahizi
    • 1
  • B. G. Marinus
    • 2
  • M. Pirlot
    • 1
  1. 1.Department of Weapon Systems and BallisticsRoyal Military AcademyBrusselsBelgium
  2. 2.Department of MechanicsRoyal Military AcademyBrusselsBelgium

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