Aim of the Course:

Purpose of the course is to gain knowledge in external ballistics and making firing tables of spin stabilized projectiles with base-bleed and rocket assistance. The lectures cover explanation of the equations of rocket motion based on three degree and six degree of freedom model, stability analysis, calculation of trajectories, and method for the calculation of the firing tables. Numerical examples will be run to illustrate the influence of parameters on range and dispersion. It is assumed that attendees of course have basic knowledge in general external ballistics, mathematics, gas-dynamics and computer skills. For the calculation several Matlab programs will be used. Examples will be run by the professional programs LinPAC for aerodynamic calculation ProMoS-6DoF for trajectory (see section ProSTools).

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 four weeks (twenty working days); 100 lectures (one lecture duration 45min), but other arrangement is possible.

Course Outline

1. Firing Tables (FT) - An Introduction
Role and importance of FT. Limitations. FT vs. ballistic computer - advantages and disadvantages.
2. Review of Projectiles with Base-Bleed and Rocket Motor
Review of spin stabilized projectiles with base-bleed and rocket assistance in service. Advantages and disadvantages of using base-bleed and rocket assistance.
3. Review of Aerodynamics of Spin Stabilized Projectiles
Aerodynamic forces and moments acting on projectile in flight. Aerodynamic drag and its components. Influence of Mach number and Reynolds number. Methods of determination of AC. Calculation of AC by program LinPAC. Experimental methods.
4. Review of External Ballistics of Spin Stabilized Projectiles
Forces acting on projectile in flight. Earth and Atmosphere and its characteristics. Models for trajectory calculation - 2DoF, 3DoF, 6DoF model and modified 3DoF model. Methods for solving the complete system of equations.
5. Review of Equations of Base-bleed Process
Burning of fuel. Equations for mass flow rate. Equations of drag reduction.
6. Review of Equations of Process in Rocket Motor
Burning of propellant. Equations for mass flow rate and thrust.
7. Methods of Calculation of the Dispersion
Method of differential coefficients, Monte-Carlo method. Influence of rocket motor – examination of the various parameters on the dispersion.
8. Methods of Producing Firing Tables (FT)
Firing problem. System of equation defining firing problem. Method of solving the equations. Differential coefficients and Corrections.
9. Firing Tables Formats
Contents of the FT for artillery projectiles. Standard and practice for FT formats. General methods of determination of FT data.
10. Trajectory Calculation and FT data Calculation by 6DoF Model
Calculation of trajectory by program ProMoS-6DoF, Examples.
11. Methods of FT data Verification
Standards, External Ballistic Testing, Procedure for FT calibration.

Lecturer: Dr Miodrag Curcin