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#18: How to calculate gyradius for ship motion
Ship motion prediction programs require a ship's radius of gyration (or
gyradius) around the longitudinal, transverse, and vertical axes passing
through its center of gravity. The gyradius is defined as the square
root of the ratio of total rotational inertia to mass for each axis:
Gyradius = SQRT ( I / M )
Hull inertia can be estimated by various standard methods, but the inertia
contributed by tank loads is a particular problem for ship motion programs,
because that requires modeling and configuration for every tank on the
vessel, a potentially very time-consuming task.
Fortunately, GHS can calculate tank inertia and total gyradius directly,
thereby sparing users of ship motion programs this burden. These values
can either be reported for manual entry into other programs, or they can
be written from system variables into text files for automatic reading
into ship motion programs that support this feature.
Inertia Input
The minimum input needed is to specify Light Ship hull gyradius in each of
three axes using the command:
WEIGHT weight, lcg, tcg, vcg /GYRADIUS: longitudinal, transverse, vertical
Note that the initial weight and center parameters can be replaced by a
single asterisk to use the current values:
WEIGHT * /GYRADIUS: longitudinal, transverse, vertical
Another approach is to estimate hull inertia as if the Light Ship weight
were evenly distributed over a box with specified dimensions, using the
command:
WEIGHT * /BOX: length, width, height
In the examples above, the lightship weight is given as a point weight.
If the lightship weight is instead given as a longitudinal distribution,
the /GYRADIUS and the /BOX parameters only include the potential inertial
contributions of the longitudinal weight distribution in directions where
an asterisk is given instead of a value, such as:
WEIGHT d1 @ l1, ..., dn @ ln, tcg, vcg /BOX: *, width, height
Rotational inertia can also be assigned to each individual fixed weight
using the corresponding /GYRADIUS or /BOX parameter for the ADD command.
If neither /GYRADIUS or /BOX is included for a point weight, then it
will have zero inertia about its own center of gravity.
Keep in mind that in addition to the moment of inertia about it's own
center of gravity, every weight item (including the Light Ship) also
contributes inertia according to the product of its weight times the
square of the distance from its own center to the relavant axis of rotation
through the overall vessel center of gravity.
It is possible to ignore all inertia effects for particular fixed
weights by including the /GYRADIUS:OFF parameter on their ADD commands.
Specifying only the overall vessel inertia without considering the
inertia of individual fixed weights can be done by first combining all
added weights with the Light Ship using the command:
WEIGHT *
Gyradius Output
Once the Light Ship inertia has been assigned, the gyradius for the entire
vessel around each center axis can be reported using the STATUS INERTIA
command. Since gyradius includes the inertia contributions of every tank
load at the current waterplane, STATUS INERTIA requires every tank to be
INTACT in order for gyradius to be shown.
To skip the full detailed list of all weight and tank inertia values,
just the total inertia and gyradius around each axis can be shown using
the command:
STATUS INERTIA: TOTAL
Each gyradius value can then be copied to the clipboard (for later pasting
into a ship motion program) by selecting it with the mouse and keying in
Ctrl-C (or right-clicking and picking Copy).
Gyradius values may also be retrieved using the GYRADL, GYRADT, and
GYRADV system variables. For example, these values can be displayed
on the screen using the command:
MESSAGE {GYRADL} {GYRADT} {GYRADV}
The total rotational inertia of the current intact tank selection around
its own center axes can be retrieved using the TINERTL, TINERTT, and
TINERTV system variables. For example, the own inertia for all HOLD
tanks can be seen using the commands:
TANK HOLD*
MESSAGE {TINERTL} {TINERTT} {TINERTV}
The tank system variables make it possible to make calculations and prepare
custom reports on tank inertia contributions. For example, the total
longitudinal inertia for the current tank selection can be calculated as
follows:
VARIABLE TankInertiaL, DistanceT, DistanceV
SET DistanceT = {TTCG} MINUS {TCG}, DistanceV = {TVCG} MINUS {VCG}
SET TankInertiaL = {DistanceT} TIMES {DistanceT}
SET TankInertiaL = {DistanceV} TIMES {DistanceV} PLUS {TankInertiaL}
SET TankInertiaL = {TWEIGHT} TIMES {TankInertiaL} PLUS {TINERTL}
GHS version 13.40 or later is required to access these features.
For help updating your GHS version, please contact support@ghsport.com.
Copyright (C) 2012
Creative Systems, Inc.