Aim of the Course:

Purpose of the course is detail calculation and analysis of the performance of the anti-armor unguided shoulder launch projectiles (Light Anti-armour Weapons - LAW) and possible means of increasing effective range and precision. The program ProMoS-6DoF based on six degree of freedom model of projectile motion will be used for trajectory and the dispersion calculation and data for determination of sighting system. As the example one LAW rocket will be considered.

Who should attend?

The course is intended for students, engineers - researchers in the research institutions and engineers in the productions factories. It is advanced course, and it is assumed that attendees of course have good knowledge in general projectile aerodynamics and external ballistics.


Duration is two weeks (twelve working days); 50 lectures (one lecture duration 45 min), but other arrangement is possible.

Course Outline

1. Introduction. Propulsion methods and types of launchers for LAWs.
Basic characteristics of the unguided anti-armour projectiles, also called LAW - Light Anti-armour Weapons. Review of the LAWs in service. Rocket propulsion. Recoilless propulsion. Phases of Flight. Methods of imposing spin.
2. Analytical Solution of the Eqs. of Motion of Unpowered Trajectory
Euler model of the differential equations of projectile motion. Analytical solution of the equations of motion. Effective (point-blank) range of anti-tank projectile and influencing parameters. Possible ways to increase the effective range. Initial firing elements.
3. Characteristics of Impulse and Sustainer Rocket Motors and Inertial Characteristics
Thrust as a function of time. Thrust misalignment. Calculation of burned mass of propellant. Influence of the propellant temperature on thrust and mass flow rate characteristics. Simulation of mass, centre of mass and moment of inertia. Inertial characteristics of the rocket with buster and sustainer motor. Mass static and dynamic unbalance.
4. Motion of a rocket in the launching tube
Equation of motion of the projectile in the launching tube powered by rocket motor. The role of lock. Relation between initial velocity and total impulse. Constrain on the burning time. Numerical example by program ProMoS-6DoF.
5. Aerodynamic Forces and Moments Acting on Projectile
Important derivatives of aerodynamic coefficients. Calculation of aerodynamic derivatives of the rocket in function of Mach number by the program LinPAC.
6. Stability of Flight
Static stability. Gyroscopic stability. Dynamic stability. Magnus instability. Practical and theoretical stability. Relation between natural frequency and spin rate.
7. Six DoF Model of Motion for Trajectory Simulation
Recapitulation of governing equations for six degree of freedom model of projectile motion. Initial conditions. Preparation of the equations for simulation. Solving of flight equations by numerical method and determination of the characteristic points of anti-tank projectiles. Calculation of the range for given initial and atmospheric conditions of the LAW rockets by program ProMoS-6DoF. Simulation of trajectories - example.
8. Simulation of the Trajectory Dispersion and Calculation of Differential Coefficients
Differential coefficients by finite difference method. Standard deviation calculation based on differential coefficients. Basis of Monte Carlo statistical method. Simulation of random variables. Simulation of random functions. Calculation of probable errors (CEP) along trajectory - example.
9. Analysis of the Influence of Separate Disturbances on the Probable Errors and Discussion on the Method for Reducing the Dispersion for LAWs
Influence of initial velocity, initial angles, initial angular rate. Influence of atmospheric temperature and pressure. Influence of longitudinal and lateral wind. Influence of total impulse burning time and ignition time. Influence of rocket motor misalignment. Influence of aerodynamic and mass asymmetries. Influence of the spin. The condition for minimal dispersion of the LAW with rocket assistance on trajectory.
10. Firing Elements and Data for Sighting System Calculation Based on Six DoF Model
Efficient numerical algorithms for the determining firing elements for specified effective range. Calculation of the quadrant elevation vs. range for the LAW rockets by ProMoS-6DoF. Influence of lateral and longitudinal wind. Influence of the motion of target. Determination of data for sighting system. Example for a rocket by ProMoS-6DoF.
11. First Round Hit and Kill Probabilities
Hit probability on the stationary and moving target. Influence of lateral wind. Possibility to increase hit probability by sighting device and simple fire control computer. First round kill probability. Examples.

Lecturer: Dr Miodrag Curcin