Aim of the Course:

Purpose of the course is to gain knowledge in external ballistics of spin stabilized projectiles with base-bleed and rocket motor. The lectures cover physics of base-burn projectiles, modeling of base-burn effects, calculation of trajectories, and estimation of influence of base-bleed parameters on the dispersion. Numerical examples are run to illustrate the influence of base-bleed system on range and dispersion. It is assumed that attendees of course have basic knowledge in general external ballistics (see course “External Ballistics of Projectiles and Rockets”), mathematics, gas-dynamics and computer skills. The attendees will obtain copy of the Matlab program TwoDoFSim which will be extensively used throughout the course for educational purposes. Besides, one example, showing the influence of base-bleed parameters and the motion of projectile around the center of mass will be run by the professional program ProMoS-6DoF (see ProSTools section).

Who should attend?

The course is designed for graduated students, engineers - researchers in the research institutions. It is advanced course, and it is assumed that attendees of course have good knowledge in general projectile aerodynamics (for basic knowledge see course “Classical Aerodynamics of Projectiles and Rockets”) and external ballistics (for basic knowledge see course “External Ballistics of Projectiles and Rockets”)


Duration is two weeks (twelve working days); 54 lectures (one lecture duration 45min) , but other arrangement is possible.

Course Outline

1. Review of Aerodynamics Spin Stabilized Projectiles
Aerodynamic forces and moments acting on projectile in flight. Aerodynamic drag and its compo-nents. Nature of base drag and influencing parameters. Influence of Mach number. Influence of Reynolds number. Influence of meplat and hemispherical nose rounding. Means of drag reduction. Minimum drag projectile shape.
2. Review of External Ballistics
Forces acting on projectile in flight. Atmosphere and its characteristics. Models for trajectory calculation - 2DoF, 3DoF and 6DoF model. Methods for solving the complete system of equations.
3. Physics of Base-Burn Projectiles
Gas generator. Aerodynamics of base injection. Injection parameter. Thrust due to base-bleed. Effect of flame temperature. Effect of spin to mass flow rate. Effect of ambient pressure to mass flow rate. Influence of Mach number.
4. Modeling of Base-bleed Process for Trajectory Calculation
Modeling the base-burn projectile drag. Drag reduction. Mass flow rate. Complete system of equations of base-bleed process.
5. Modeling of Power-On Base Drag for Rocket Motors
Difference between rocket motor jet characteristics and base-bleed jet. Modeling of base pressure. Influence of Mach number.
6. Trajectory Calculation by 2DoF Model
Point mass and modified point mass model. Calculation examples. Examination of the influence of the base-bleed parameters on the range.
7. Trajectory Calculation by 6DoF Model
Calculation of trajectory by program ProMoS-6DoF - example. Examination of the influence of base-bleed parameters on the dispersion of trajectories.
8. Basis of Base-bleed Unit Design
Determination of projectile after-body shape. Determination of optimal burning time. Determination of mass flow rate and mass of base-bleed grain.

Lecturer: Dr Miodrag Curcin