Cricket Dynamics
1 General Comments
The general equations of motion that model the
trajectory are represented by the following vector equations,
S F = dP/dt, (2-1)
and S MG =
dHG/dt, (2-2)
where, F is the vector of external forces
(gravitational and dynamic), P is the linear momentum vector, MG is the vector
of external (aerodynamic) moments about the center of mass, G, of the ball and HG
is the angular momentum vector referenced to the center of mass of the ball.
These equations can be expanded to show more
qualitatively how the forces, moments and velocities play a role in the trajectory
dynamics. First, equation 2-1 is simplified by exploiting the definition of linear
momentum. Linear momentum is defined as the product of the mass, m, with the translational
velocity of the center of mass, V, and noting that the mass of the ball remains constant
when pitched transforms equation 2-1 into,
S F = m dV/dt (2-3)
This equation is expanded further by noting that
the only forces acting on the ball are the gravitational force, FG, and the
aerodynamic force, FA. Substituting these forces for the summation in equation
2-3 results in,
FG + FA = m dV/dt (2-4)
Equation 2-2 also s expanded by exploiting the
definition of angular momentum and assuming that the inertia matrix, IG, is
diagonal (i.e. the ball is spherical and the mass uniformly distributed) and constant. In
this case equation 2-2 can be written as
S MG = IG
dw /dt
In the following sections these forces and
moments will be examined in more detail and the final set of equations of motion is
presented.
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2 Gravitational Force
The gravitational force FG is
calculated by,
FG = mg
Where, g is the gravitational field strength or
acceleration due to gravity.
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3 Aerodynamic Forces
The Force is applied to the cricket:
Vf2-Vi2
= 2ad
Speed range is 15<U<30 m/s (i.e.
54<U<108Km/hr)
Force = m x a
Mass of cricket = 150g = 0.15kg
In the sport pitching machine, the main project specification is
designed or produced a low cost non-powered system to propel the ball automatically at
different suitable adjustable speed, rotation and angular direction. The design will be
done by CAD and some hand drawing. Beside the above, it is also more concerned about the
accuracy, repeatability, precision, safety and quiet. Moreover, the machine should be
enhanced safety features, lightweight, compact, set up fast and easily, portable,
affordable, easy to operate, elevation and angular adjustment, long life cycle, warranty,
quiet and height adjustment and ball capacity or feeder and drive system. The British
Standard (BS 7000) is the guideline or checklists for managing the design. It includes the
specification, conceptual design, and feasibility design to provide a good quality to
achieve the project specification.
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