Abstract
We develop a comprehensive six degrees of freedom (6-DOF) model to examine the flight behaviour of a guided projectile. A 120-mm mortar is used as a representative projectile system in the work. The analysis is carried out using the developed code for varying muzzle velocities and launch angles in order to predict the path behaviour such as maximum range and altitude. In the 6-DOF model, the projectile is assumed as a rigid body of finite length with distributed mass. In order to estimate the precise location of the projectile, every DOF is tied to a coordinate which defines its position at every instance.
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Abbreviations
- \({\vec{\Lambda }}\):
-
Coriolis acceleration due to earth rotation (rad/s)
- Cd:
-
Coefficient of drag
- \(\sum {\vec{F}}\):
-
Vector sum of all aerodynamic forces (N)
- \(\vec{g}\):
-
Acceleration due to gravity (m/s)
- \(\vec{H}\):
-
Total vector angular momentum of the projectile (kg m2/s)
- \(\dot{I}_{y}\):
-
Rate of change of the rocket projectile’s transverse moment of inertia (kg m3)
- m:
-
Mass of projectile (kg)
- \(\dot{m}\):
-
Rate of change of the rocket projectile’s mass (kg/s)
- \(\sum {\vec{M}}\):
-
Vector sum of all aerodynamic moments (Nm)
- rt:
-
Distance from projectile centre of mass to the throat of the rocket nozzle (positive if throat is aft of the centre of mass) (m)
- S:
-
Impact area of the projectile (m2)
- t:
-
Time (s)
- T:
-
Rocket thrust force (N)
- \(T_{s}\):
-
Rolling moment due to rocket spin torque (Nm)
- \(\vec{V}\):
-
Velocity vector with respect to the ground fixed coordinate axes (m/s)
- \(\overrightarrow {{V_{0} }}\):
-
Muzzle velocity vector (m/s)
- \(V_{0}\):
-
\(\sqrt {V_{{1_{0} }}^{2} + V_{{2_{0} }}^{2} + V_{{3_{0} }}^{2} }\) (M/s)
- \(\overrightarrow {{v_{0} }}\):
-
Initial velocity vector with respect to air \(\left[ {v_{0} = \vec{V}_{0} - \vec{W}_{0} } \right]\) (m/s)
- VM:
-
Muzzle velocity (m/s)
- \(\phi_{0}\):
-
Vertical angle of departure, positive upward (°)
- \(\theta_{0}\):
-
Horizontal angle of departure relative to the 1–2 plane, positive to the right when looking downrange (°)
- \(\alpha_{0}\):
-
Initial pitch angle at the gun muzzle (°)
- \(\beta_{0}\):
-
Initial yaw angle at the gun muzzle (°)
- ρ:
-
Density of air (kg/m3)
References
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Acknowledgements
The authors would like to acknowledge Department of Science and Technology, Government of India, for their financial support through Grant File no. CRG/2020/002034 dt 11-03-2021.
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Khambra, S., Kumar, C., Chatterjee, D., Mondal, B. (2024). Predicting the Flight Behaviour of a Guided Projectile Through a Six Degrees of Freedom Trajectory Model. In: Singh, K.M., Dutta, S., Subudhi, S., Singh, N.K. (eds) Fluid Mechanics and Fluid Power, Volume 6. FMFP 2022. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-99-5755-2_49
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DOI: https://doi.org/10.1007/978-981-99-5755-2_49
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