Air to Ground Rocket Dispersion Minimization

Dispersion of the impact points of the unguided rockets is a consequence of disturbances, such as thrust misalignments, rocket asymmety, manufactoring inacuracy, etc. Infuence of some disturbances are most significant in the initial phase of flight when the rocket leaves the launcher due to the small velocity. This influence is minimized by rotation of the rockets in the launcher tube which in practice is realized by the guide pin connected to the rocket and groove in the launcher tube or by canted nozzles. Also the rotation of the rocket in the launching tube and in flight can be realized by canted fins foled in the nozzle when the rocket is in the launcher tube. These fins are deployed when the rocket leaves the tube and creates rocket rotation in free flight. The rolling moments of the rocket in the launcher tube and during free flight are calculated by CFD simulation. The CFD simulation is also used for calculation of the fin hinge moment generated by exaust gases from rocket motor which is required for deployement of the fins when the rocket leaves the launcher tube. The roll rate required for minimization of the rocket dispersions and roll rate in the launcher tube for various cant angle of the fins are calculated by 6DOF numerical simulation. The results of simulation are used to select the best value of the fins cant angle


Introduction
ISPERSION of the impact points of the unguided rockets is a consequence of disturbances, such as manufacturing inaccuracies, thrust misalignments, rocket asymmetry, atmospheric condition, firing platform motion and aiming errors. Influence of some disturbances, such as thrust misalignments and asymmetric aerodynamic can be minimized by spinning of the rocket. Spinning of the rocket during the flight is realized by cant angle of the stabilizing fins. Still, influence of these disturbances is most dominant in the initial phase of flight when the rocket leaves the launcher. Influence of the disturbances in this phase of flight can be minimized by rotation of the rocket in the launcher tube [1,2,3].
Rotation of the rocket in the launcher tube can be achieved by the groove in the inner side of the launcher tube which forces the rotation of the rocket. The level of the rocket rotation is dictated by cant angle of the groove. The general problem of this solution is the weight of the launcher related to the thickness of the launcher tube and the difficulty related to the manufacturing.
Morse analyzed the effects of wake unsteady flow and velocity gradients of the rotor wake free stream boundary on rocket trajectory [4]. The force and moments, both steady and unsteady, were destabilizing while the rocket is in the rotor wake. By reducing static directional stability, the flight should be more repeatable and experience much less perturbation. D Most attention was recently paid to computational fluid dynamics (CFD) methods to simulate the missile launch procedure and missile exhaust plume [5].
Lee presented CFD models to simulate the missile launch from a canister in general or from a helicopter with the focus on the missile movement [6].
The purpose of the paper is to analyze the possibility to use the stabilizing fins for both the rotation of the rocket in free flight and rotation in the launcher tube by folding them in the divergent part of the nozzle and launcher tube. The rotation of the rocket in the launcher tube is generated by the fins exposed to the exhaust gas of the burning propellant in the divergent part of the nozzle and launcher tube. These fins are deployed immediately after the rockets leaves the launcher tube by the moment over hinge axis of the fins generated by the exhaust gas of the burning propellant.

Aerodynamic characteristics of the rocket
Basic dimensions of the air to ground rocket analyzed in the paper are given in Fig.1. The rolling moment of the rocket is obtained by cant angle of the fins δ .  The aerodynamic characteristics of the rocket are determined by the semiempirical software DMAC [7] and by CFD calculation with FLUENT software [8]. Diagrams of the axial force coefficients are given in Fig.3. There are satisfactory agreement in the supersonic, while the difference in the subsonic region of Мach numbers is 20%.

Dispersion of the air to ground rockets
Since the trajectories of the air to ground rockets are almost straight line the sketch of the impact points on the plane normal to the line of sight are illustrated in Fig.7.
The circular probable errors (CEP) are not convinient for analysis of the dispersion of the air to ground rockets because CEP depends on distance between the launcher and the plane normal to the line of sight ( ) T D . The angular value of CEP ( CEP ε ) is more convinient for analysis because this angular value of CEP is invariant to distance T D .
where CEPn R is CEP in the plane normal to the line of sight. Impact point dispersions of the air to ground rockets due to rocket parameters are analyzed by numerical simulation rockets trajectories in free flight by six degree of freedom (6DOF) simulation [9].
Influence of the cant angle of the stabilizing fins δ and static margin / to the angular dispersion CEP ε is given in Fig.8. There is a decrease of the angular dispersion with an increase of the cant angle of the stabilizing fins δ and increase of the static margin / cp x D Δ .   Dispersion of the impact points of the air to ground rockets can be minimized by increase the roll rate of the rockets during the free flight in the atmosphere, the initial velocity and the initial roll rate of the rockets at the moment when the rocket leaves the launcher.

Rocket rotation in the launcher tube
The picture of the rear part of rocket 3D model with folded fins inside the divergent part of the rocket motor nozzle is presented in Fig.11. Cut dispay of the mesh of the nozzle, launcher tube and six fins inside divergent part of the nozzle and launcher tube is given in Fig.12. Surface mesh of the two opposite fins exposed to the propellant combustion products flow in the divergent part of the nozzle and launcher tube is given in Fig.13. Simulation of the exhaust gas flow of the burning propellant in the nozzle and launcher tube with folded fins was done by FLUENT software package [8]. The 3D density based second order explicit solver with k-ε realizable viscous model was used for numerical calculation of the flow in computational domain.
Working fluid is modeled as an ideal gas with parameters calculated for frozen expansion of propellants combustion products: specific heat 1770 J/(kg K), thermal conductivity 0.2 W/(m K), viscosity 7.7·10 -5 kg/(m s) and molecular weight 23 kg/kmol.
Inlet of the nozzle was set as the mass-flow inlet boundary of the domain with next parameters: mass flow rate 5.3 kg/s; turbulent intensity 2 %, turbulent viscosity ratio 5, and total temperature 2300 K. Outlet of the launching tube was set as the pressure outlet boundary with sea-level conditions: total temperature 300 K, pressure 101325 Pa and default turbulence parameters. All solid surfaces were set as no-slip, adiabatic wall boundary conditions.
Convergence of the numerical calculation of the flow was determined by tracking the change of the residuals. The numerical calculation of the forces and moments on the fins exposed the flow of the burning propellant was stopped when the forces and moments were changed less than 1% through 50 previous iterations.
Dislpay of the vertical cut of the dynamic pressure field in the control volume and dynamic pressure on the fins in front of the cut is given in Fig.14. Dynamic pressure distribution on the inner surface of the nozzle and the part of the fins exposed to the exhaust gas of the burning propellant are given in Fig.15. The calculated component of the forces and moments for the one fin in the axis system fixed to the hinge axis (Fig.16) are given in Table 1. The positive sign of the calculated rolling moment of the rocket generated by six fins folded in the nozzle 21.5 Nm L = is illustrated in Fig.6.

Numerical simulation
Aerodynamic derivatives of the rolling moment coefficient in function of Mach number are given in Fig.17. Six degree of freedom software for trajectory calculation of the unguided rockets is used for calculation of the roll rate of the rocket in the launcher tube and during free flight after the rocket leaves the launcher tube [9].
Roll rates of the rocket in function of time of flight are given in Fig.18   The roll rates of the rocket in the launcher tube and vicinity of the launcher tube are illustrated in Fig.19. Having in mind the decrease of the dispersion with increase of the roll rate of the rocket at the muzzle of the launcher tube (Fig.10) and achieved roll rate with different cant angle (Fig.19), it can be concluded that satisfactory roll rate of the rocket in the launcher tube can be achieved with cant angle of the fins 2 δ = .

Conclusion
Numerical simulations by 6DOF software are used for analysis of the rocket impact point dispersions due to rocket rotation during free flight, initial velocity, and rocket rotation in the launcher tube.
Since the initial velocity of the air to ground rockets launched from hovering helicopter is zero, the impact point dispersions can decraese by an increase of the rocket rotation in the launcher tube.
Influence of the manufacturing inaccuracies to rocket dispersion can be minimized by rotation of the rocket during the free flight in the air. This rotation can be generated by the cant angle of the fins.
The same fins folded in the divergent part of the nozzle can be used to generate the rotation of the rocket in the launcher tube.
CFD calculations are used to determine the forces and moments on the fins exposed to the exhaust gas of the burning propellant during movement of the rocket in the launcher tube. The forces and moments acting on the each fin are given in the axis system aligned with hinge axis of the fin. The most dominant moment is over fin hinge axis in the direction to open the fins.
The forces generated on the fins by the exhaust gas of the burning propellant create the rolling moment and rotation of the rocket in the launcher tube.
Six degree of freedom software for trajectory calculation of the unguided rockets is used for calculation of the roll rate of the rocket in the launcher tube and during free flight after the rocket leaves the launcher tube.

Minimisation de la dispersion chez les fusées air sol
La dispersion des points de l'impact de la fusée non guidée est la conséquence des perturbations telles que l'excentricité de la force de poussée, l'assymétrie de fusée, l'imperfection de fabrication etc.L'influence de certaines perturbations est la plus signifiante dans la phase initiale du vol lorsque la fusée quitte le lanceur à la vitesse relativement petite. Cette influence se minimise avec la rotation de la fusée dans le tube de lancement qui est réalisée en pratique par le contact de la goupille de guidage de fusée et la rainure dans le tube ou au moyen des gicleurs inclinés. La rotation de fusée dans le tube se réalise aussi dans le vol par les stabilisateurs inclinés qui sont fermés dans le gisleur lorsque la fusée est dans le tube de lancement. Les stabilisateurs s'ouvrent quand la fusée quitte le tube de lancement et produisent la rotation de fusée en vol. Le mouvement du roulement de fusée dans le tube de lancement et pendant le vol libre a été calculé par la simulation CFD. Cette simulation a été utilisée aussi pour le calcul du moment des gonds de stabilisateur formé par les gaz d'échappement du moteur de fusée et qui est nécessaire pour l'ouverture des stabilisateurs après la sortie du tube de lancement. Par la simulation numérique 6DOF on a calculé la vitesse d'angle nécessaire pour la minimisation de la dispersion de fusée et la vitesse d'angle indispensable dans le tube de lancement pour les différentes valeurs des angles d'inclinaison des stabilisateurs par rapport à l'axe longitudinal. Les résultats de la simulation ont été employés pour choisir les meilleures valeurs de l'angle d'inclinaison sous l'aspect de la dispersion minimale.