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


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.


Fin-stabilized Flat trajectory Aerodynamical coefficients CFD Stability Pitch damping 



Computational fluid dynamics


Rigid body dynamics


Reynolds averaged Navier-Stokes


Point-mass model


Three degrees of freedom


Drag force (N)


Drag coefficient


Zero-yaw drag coefficient

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

Yaw-induced drag coefficient


Lift force (N)


Lift coefficient

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

Yaw-induced lift coefficient


Pitch moment (N m)


Pitch coefficient

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

Yaw-induced pitch coefficient


Pitch damping moment (N m)


Pitch damping coefficient


Total transverse angular velocity (rad/s)


Velocity (m/s)


Air density (kg/m3)


Mach number

AoA / α

Angle of attack / yaw angle (deg.)


Caliber of the projectile (m)


Transverse surface of the caliber (m2)


Muzzle velocity (m/s)


Quadrant elevation (deg.)


First max pitch angle (deg.)


Time of flight (s)



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.


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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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