Motion analysis during sabot opening process

For FSAPDS projectile, the trajectory and stability are dependent on different forces in different phases of the motion. During the first phase gravity, aerodynamic drag along with propellant gas force affect the motion. The motion is influenced by shock wave and mechanical force in sabot opening phase and the effect of time lag during opening of sabots also forms part of this work.

I_xx,I_yy,I_zz

Moment of inertia about the X, Y, and Z-axis, respectively

m

Mass of projectile

r

Position vector

V

Velocity of projectile

C

Mass centre of the projectile body

Ω

Angular velocity

C_i

Mass centre of the i^th sabot component

S

Projectile reference area

O-XYZ

Inertial coordinate system

P

Pressure in gas flow

ρ_s

Density of the gas in the vicinity of sabot

ρ

Air density

l

Projectile characteristics length

p

Axial spin of the projectile

x, y, z

Range, altitude, and drift, respectively

C_La/C_Na

Lift/Normal coefficient

F/M₁

Propellant gas force/moment

C_D/C_X

Drag/axial coefficient

F₂/M₂

Aerodynamic force/moment

C_Mα

Overturning moment

F₃/M₃

Gravity force/moment coefficient

C_Npα

Magnus force coefficient

C_MPα

Magnus moment coefficient

C_tp

Spin damping moment coefficient

C_Mqt

Pitch damping moment coefficient

C_Nqt

Pitch damping force coefficient

C_v

Specific heat of gases around projectile

u,v,w

Velocity components in projectile frame

L_c

Length between the centre and tip of sabot

L_s

Length of the sabot

Ф

Angle of side slip

θ

Angle of attack

ω₁,ω₂,ω₃

Angular velocity components of projectile

δ₁,δ₂

Angles made by projectile axis in velocity frame

η₁, η₂

Angles made by the propellant gas direction in projectile frame

ε₁, ε₂

Angles made by propellant gas direction in inertial frame

1

for the projectile coordinate systems

2

for the velocity coordinate systems

3

for the sabot component-fixed coordinate systems

s

for the sabot

p

for the projectile

X

Vector cross product