Tow Vessel Dynamic Weather Requirements (Metric)
This template checks for compliance to
the dynamic (moment area) weather criterion for vessels that are equipped
to tow. It is based on 46 CFR
through 46 CFR 174.145 (f) of Subchapter S -
Subdivision and Stability. According to 46 CFR
evaluation is required for each loading and operating condition. Recommend using separate
copies of this template for each condition or draft considered.
Minimum conditions to evaluate should include departure, arrival and light
ship. Refer to Reference D for additional details regarding these
There are several advantages and benefits of this
calculative approach. The first advantage is clear and neat documentation. For each
condition or draft evaluated all the inputs and outputs are easily identifiable in
Second, once you get used to it, this approach is
very fast. With some quick data inputting this template automatically generates the vessel's "Curve of Statical Stability," determines
the angle of the maximum righting arm, determines the vessel's limiting
heel angle, computes the moment area available between zero
degrees and the limiting angle as well as between thirty degrees and the limiting angle,
it checks to make sure that the angle of heel for the maximum righting arm is
equal to or greater than 25 degrees, and that the vessel has range of
positive stability up to at least 60 degrees. It simultaneously checks
all these things to
see if the vessel's condition meets the United States Coast Guard requirements.
this approach is cost effective. One could use
Hullform, SHCP (Ship
Hull Characteristics Program) or some other inexpensive hydrostatics
program to generate input data required for this
document. But this template can also be readily used in conjunction
with the more expensive hydrostatics programs. Alternatively and
more economically a person, with the appropriate computational skill set,
could easily use the "Curves of Form" and "Cross Curves of Stability" to
generate the input for this
In summary this template neatly organizes your work, saves you time and it is
economical to use.
MathCAD Version 6
or compatible web browser (for instruction of dynamic template only)
zip file extraction utility (comes standard with
Windows XP), required to unzip file that contains the dynamic and static
Vessel Input Data Required:
Hydrostatic Input Information required:
Option One: A computer model of the hull envelope and a
simple hydrostatics program are utilized. With the following hydrostatic program
inputs: Displacement, LCG & VCG (recommend setting VCG = 0). The
hydrostatic program should be able to output: VCB, BMT, or KMT
(where KMT = VCB + BMT),
Forward Draft, Mean (T) Draft, Aft Draft and Righting Arms in ten degree increments starting from zero
and ending at 70. This corresponds to INPUT = 1 in this template.
Option Two: Involves usage of Curves of Form, Cross Curves of Stability and
the Lines Drawing. In the template this corresponds to INPUT=2.
This option usually means a draft with zero trim (level trim) is the
selected condition under evaluation. Otherwise it means the "Curves of
Form" values correspond to a LCF draft based on the condition's input
General Arrangement Drawing, or some method of getting
scaled configuration information (especially with respect to down flooding
locations) about the vessel.
Lines Drawing, or some method of getting scaled hull
envelope information about the vessel.
Pages: three sheets when printed
Stars * are
present next to certain variables. These stars quickly identify
the inputs that are required.
The following inputs are required for each operating
condition or draft (required for dynamic templates only):
name of file for these computations, one file per condition
or draft evaluated.
Center of Gravity, meters
(this value depends on TYPE defined next).
This VCG value should already include a correction for free surface
effects. Sometimes this is referred to as the "virtual vcg" for
the condition or draft being evaluated.
TYPE, Type of Analysis.
TYPE = 1 when a specific VCG is being checked.
This type is usually selected when output from a hydrostatic program is available for a
specific vessel condition.
TYPE = 2 when the maximum allowable VCG is being
sought. In a TYPE 2 analysis the VCG value is iterated upward until
the vessel no longer satisfies the requirements, then it is changed
back to it's last criterion compliant value. This type of
analysis usually applies to a specific operating draft, and is
on "Curves of Form" and "Cross Curves of Stability"
Vertical Center of Gravity used in making the "Cross Curves of
Stability" calculations, meters
When Type = 1, with
output from a hydrostatics program for a specific
condition, normally set VCG0 equal to zero. If the
assumed VCG0 is not equal to zero, set it equal to the
actual value it was assumed for in the hydrostatics program.
When Type = 2, set equal to VCG value assumed when
making the "Cross Curves of Stability."
Downflooding Angle, degrees, based on the condition or draft being
evaluated and the vessel's geometry. This input is per
Part 46 CFR 170.055 (a) which requires the location, that causes the
smallest heel angle, to an opening that cannot be closed watertight.
According to Reference D this downflooding angle is based on foul
weather conditions, in which all non-essential openings have already
LCG, Longitudinal Center of Gravity, feet,
where distances aft of amidships are defined as positive.
For INPUT= 1,
this is the LCG value that was used as input for
the hydrostatics program generating output
for the specific vessel condition.
For INPUT= 2, this is usually the level trim case where this
value is equal to the LCB value. Otherwise it is the value
obtained from the Weights and Moments analysis for the vessel in the
specific vessel condition.
INPUT, Input source for "Curves of Statical
Stability" data. This data is not corrected for free surface.
In this analysis the free surface effects are already compensated for through
the use of virtual VCG values.
INPUT = 1,
(heel angles with corresponding righting arm values)
is from a hydrostatics
program output for the specific vessel condition being evaluated.
2, input data (heel angles with
corresponding righting arm values) are from the vessel's "Cross Curves
of Stability" for the specific displacement under evaluation.
Heel Angles, degrees, based on the condition or draft being evaluated
and the vessel's geometry. Usually input in equal increments.
Example values would be increments of 10, starting with zero, then 10,
20, 30, 40, 50, 60 and 70. Eight values are input to the
hydrostatics program or "Cross Curves of Stability." These eight values are
also input into a table at the bottom of the first page of this dynamic
GZi", Righting Arms, meters,
hydrostatic program output
or "Cross Curves of Stability" data corresponding to the input heel angles (qi).
Eight values are to be entered into the table at the bottom of the
first page of this dynamic analysis template.
The following inputs are required for each operating
condition or draft:
T, Draft, meters
When Type = 1, with hydrostatics program output for a specific
condition, set equal to the program output's mean draft.
When Type = 2, this usually means a level draft is being
evaluated. Otherwise it is the draft at the LCF. This option indicates usage of "Curves of
Form" and "Cross Curves of Stability."
KMT, Height from Keel to Metacenter,
feet, compute this value if required where KMT = VCB + BMT
= verical center of buoyancy + metacentric radius.
Characteristics of Vessel inputs, irrespective of draft:
Name of Vessel
Type of Vessel
(i. e. Z-Drive Tug, Vertical Axis Tug, Conventionally Propped Tug,
Length x Beam x Depth of Vessel, meters
Name of Firm Operating Vessel
Characteristics required irrespective of vessel:
Ab Minimum Moment Area required
between zero degrees and the critical angle, for
metric units this is equal to 5.15 meterdegrees.
Ac Minimum Moment Area required
between thirty degrees and the critical angle, for
metric units this is equal to 1.72 meterdegrees.
from Dynamic Analysis:
GMa, Available Metacentric Height
(corresponding to input VCG)
to meet dynamic requirements,
meters, for condition or draft specified
Curve of Statical Stability (Corrected
Righting Arm Curve) with plot
for the condition or draft under evaluation.
Corrected for VCG0 when a non-zero value is present.
Angle of Maximum Righting Arm, degrees.
Limiting Angle, the lesser of the downflooding angle, 40 degrees or the
angle or maximum righting arm, degrees.
A1 Moment Area Available, meterdegrees, The area under the righting arm curve, in the region between
zero degrees and the
A2 Moment Area Available, meterdegrees, The area
under the righting arm curve, in the region between thirty degrees and the
check, equal to one only if all of the dynamic
U. S. C. G. criteria are met.
KG, Maximum Allowable VCG (Vertical Center
of Gravity) for dynamic requirements, meters, for condition or draft specified.
This applies if the TYPE=2 option is selected, otherwise (for the
TYPE=1 option) you will know if the VCG
input passes or fails this criterion's requirements.
Subchapter S - Subdivision and Stability, Title 46 Shipping, USCG,
Washington, D. C.
Reference B) Procedure H1-04, MSC Guidelines for Review of
Stability for Uninspected Tugboats (C), dated 3/21/00, USCG,
Washington D. C.
Reference C) COMDTINST M16000.9, Marine Safety Manual, Volume IV,
Sections 6.C.1, 6.E.1b. & 6.E.2, United States Coast Guard, Washington,
Reference D) McGowen,
John F., & Meyer, Richard B., Has Stability Delayed the Delivery of
Your Tug?, Marine Technology, January 1980, 6 pages,
SNAME, Jersey City,
Reference E) NAVIC 12-83, Intact Stability of Towing and Fishing
Vessels, Research Results, dated 15 Nov. 1983, United States Coast
Guard, Washington, D. C.
Reference F) Principles of
Naval Architecture, by SNAME,
Jersey City, N. J.
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