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#5: Powerful RASR limit type
The LIMIT command now includes a new RASR type, which limits the ratio between
the absolute righting arm and a sine function.
This type of limit is particularly useful when the righting arm curve is
complex and not well characterized by traditional measures of area, range,
maximum arm, etc. The RASR limit simultaneously checks range, area and
maximum RA while guaranteeing that the righting arm curve does not
dip below expected values leading to undesirable stability characteristics.
RASR limit checks the ratio of absolute righting arm to the function:
v * sin ((h-eq0) * 180 / range)
v = limit value
h = heel angle
eq0 = equilibrium without heeling moment
range = angle beyond equ0 at which sine curve goes to zero
The ratio is checked at every angle for which the righting arm is calculated
between two given angles. For example,
LIMIT RASR from 5 to 60 range 90 > 0.5
checks the ratio in the interval 5 degrees to 60 degrees. The sine
function has a range between zeroes of 90 degrees. In this example, the
limit is considered to be satisfied when the ratio of the absolute righting
arm to the sine function is at least 0.5 at every angle in that range.
Note that a sine curve with a range of 180 degrees with an amplitude
of 1.4 ft (0.43 m) has the following characteristics:
Area to 30 = 10.74 ft-deg (0.057 m-rad)
Area to 40 = 18.75 ft-deg (0.10 m-rad)
Arm at 30 degrees = 0.7 ft (0.21 m)
These values are roughly equivalent to the limits in the traditional
energy criterion. The exception is the GM, which is 1.4 ft (0.43 m) for
the sine curve and 0.5 ft (0.152 m) in the energy criterion. The RASR
limit provides for a starting angle at which the ratios are to be checked
which may be set several degrees beyond equilibrium, thus allowing the initial
slope of the RA curve (GM) to be less than would be required if the
ratio checking began at equilibrium.
You need GHS version 9.86 or later to access this feature.
If you need help updating your GHS version, contact firstname.lastname@example.org.
Copyright (C) 2011
Creative Systems, Inc.