Aim of the Course:

Purpose of the course is to gain knowledge in external ballistics and making firing tables of rockets with cluster/cargo submunitions. The lectures cover explanation of the equations of rocket motion based on six degree of freedom model, stability analysis, physics of dispensing of submunitions, calculation of tra-jectories, equation of motion of bomlets with ribbon streamer and parachute and the dispersion the rock-ets and submunition. Numerical examples will be run to illustrate the influence of parameters on range and dispersion, method for the calculation of the firing tables. 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 the 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”).


Course is designed for 72 lectures (one lecture duration 45min) in three weeks (18 working days), but other arrangement is possible.

Course Outline

1. Review of MLRS and Rocket Projectiles with Cluster Warheads
Review of rockets with CW in development and production. Multi Launch Rocket System 122-mm GRAD.
2. Review of Aerodynamics of Fin 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.
3. Review of External Ballistics of Rocket Projectiles
Forces acting on projectile in flight. Earth and Atmosphere and its characteristics. Models for trajectory calculation - 2DoF, 3DoF and 6DoF model. Methods for solving the complete system of equations.
4. Aerodynamics of Bomblets
Aerodynamics of bomblets with ribbon streamer. Aerodynamics of bomblets with parachute.
5. Dynamics of Bomlets Dispensing
Determination of initial conditions of bomblets flight dynamics. Influence of rocket spin.
6. Methods of Calculation of the Dispersion
Method of differential coefficients, Monte-Carlo method, Dispersion of the rockets at point of warhead opening, Dispersion of bomblets – examination of the various parameters on the dispersion.
7. Determination of Optimal Height and Corresponding flight time
Influence of angle of elevation, rocket velocity and height at warhead opening to the dispersion of bomblets, determination of optimal height.
8. Methods of Producing Firing Tables (FT)
Firing problem. System of equation defining firing problem for rocket and for rocket and submunitions. Method of solving the equations. Differential coefficients and Corrections.
9. Firing Tables Formats for Rockets and Rockets with cluster warheads
Contents of the FT for artillery rockets, Additional necessary data for FT of rockets with bomblets, 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, Example – bomblets with ribbon stabilizer.
11. Methods of FT data Verification
Standards, External Ballistic Testing, Procedure for FT calibration.

Lecturer: Dr Miodrag Curcin