3.2.1 During the ramp phase of a free-fall launch,
the forces acting on the lifeboat are the weight of the boat, the
normal force between the launch rail and the launch ramp, and the
frictional force between the launch rail and the launch ramp. These
forces are shown in figure 3.2 After the boat is released, it accelerates
down the ramp under the influence of these forces. The equations of
motion that govern the behavior of the lifeboat as it slides along
the launch ramp are:
Figure 3.2 Forces Acting on the Lifeboat During the Ramp Phase
Equations 3.1, 3.2, and 3.3 represent the acceleration in
the X direction, the Z direction, and the rotational acceleration,
respectively. The term θ is the launch angle, μ is the coefficient
of friction between the launch ramp' and the launch rail, and g is
gravitational acceleration.
From Equations 3.1 and 3.2 it can be seen that the acceleration
of the lifeboat along the ramp is constant, and from Equation 3.3
it can be seen that the lifeboat does not rotate. The motion of the
lifeboat is independent of its mass (all of the forces acting on the
lifeboat and its acceleration are a function of its mass which appears
on both sides of the equations and, as such, cancels). The only parameters
affecting the motion of the boat as it slides along the ramp are the
coefficient of friction, the angle of the launch ramp, and gravity.
The location of the CG only affects the duration of the ramp phase,
i.e., the time during which the lifeboat accelerates along the ramp.
As previously stated, the ramp phase ends when the CG is directly
over the end of the launch ramp.
3.2.2 The angle at which the lifeboat enters the
water and its behavior after water entry are affected, in part, by
the velocity of the lifeboat at the beginning of the rotation phase.
This velocity is dependent upon the duration of the ramp phase which
in turn is dependent upon the distance from the CG to the launch ramp.
From the equations of motion, the velocity of the lifeboat along the
ramp at the end of the ramp phase can be found to be:
3.2.3 From examination of Equation 3.4 it is evident
that the magnitude of the coefficient of friction cannot exceed tanθ
if the lifeboat is to move along the ramp. Also from examination of
Equation 3.4 it is apparent that the velocity increases as the length
of the ramp increases and as the angle of the launch ramp increases.
3.2.4 Friction does not have a significant affect
on the velocity along the ramp. Shown in figure 3.3 is Vr as
a function of ramp length for three values of the coefficient of friction.
These data were computed with a launch angle of 35°. The coefficient
of friction in most free-fall lifeboats ranges from 0.02 to about
0.05 (the middle curve in figure 3.3). The difference between the
top and middle curve or between the middle and bottom curve is slightly
less than four per cent. This ratio does not change with ramp length.
Figure 3.3 Variation of Velocity With Ramp Length for Three Coefficients of
Friction
3.2.5 The two significant parameters affecting
the velocity of the lifeboat at the beginning of the rotation phase
are the length of the launch ramp in front of the CG at the time the
boat is released and the angle of the launch ramp. The distance between
the CG and the front of the launch ramp is the distance L shown on
figure 3.1. Presented in figure 3.4 is the velocity of the lifeboat
along the ramp at the beginning of rotation as a function of the length
L. Data have been presented for a launch angle of 35° and a coefficient
of friction of 0.05. The launch angles of 25° and 45° represent
a trim of ±10° as required by SOLAS (IMO, 1986, 1990).
Most free-fall lifeboats currently produced are launched at an angle
of about 30°-35° measured from the horizontal.
Figure 3.4 Variation of Velocity for Three Launch Angles
3.2.6 Presented in figure 3.5 is rate at which
the velocity at rotation changes are as a function of the distance
from the CG to the end of the ramp. As can be seen from figures 3.4
and 3.5, the most significant increases in velocity occur during the
first two to three meters that the lifeboat slides along the ramp.
After that the rate of change becomes more linear and is in the order
of 0.5 to 0.6 meters per second per meter of length.
Figure 3.5 Rate of Change of Velocity with Respect to Ramp Length