Calculate Area between Limiting Angles

Check if this condition meets minimum area requirements

Check Maximum Righting Arm Locations, per 46 CFR 174.145(d)

The Maximum Righting Arm shall occur at an angle of
heel of at least 25 degrees

Sheet 2 of 3

Check Angle of Vanishing Stability, as per 46 CFR 174.145(e)

The Angle of Vanishing Stability is first calculated
and then checked to see that it is greater than 60
degrees.

Iteration Fineness, fractions of a degree

Initial Angle of Range needed for iterations below,
degrees.

Iteration Values, first value of range important because of multiple intercepts
possible for some cases, degrees.

Tolerance Allowed on GZ Difference, meters

The Maximum Available Righting Arm in this region is:

Angle Corresponding to this Maximum Righting Arm, degrees

Determine Limiting Angle, as per 46 CFR 174.145(b)

Limiting Angle, the least of 40 degrees, Angle of Maximum
Righting Arm and Downflooding Angle.

Check Area from Zero Degrees to Limiting Angle, as per
46 CFR 174.145(b)

Calculate Area up to Limiting Angle

Check if this condition meets minimum area requirements

Check Area from 30 Degrees to Limiting Angle, as per
46 CFR 174.145(c)

Displacement, metric tons

Area Available from 30 deg. to Limiting Angle, metersˇdeg.

Keel to Metacenter, meters

Area Required from 30 deg. to Limiting Angle, metersˇdeg.

KG value evaluated, meters

Angle at Maximum Righting
Arm, deg.

Summary of Calculated Results

Minimum Angle for Maximum Righting Arm, deg.

Metacentric Height Available,
meters

Intercept Angle, End of Positive Stability Range, degrees

Results of this analysis, satisfactory only if equal
to one.

Min. Intercept Angle for Positive Stability Range, degrees

Sheet 3 of 3

Intercept Angle

The effectiveness of this value meeting the requirements
is checked next:

Summary of Results

This value is one if vessel meets the requirements of
proposed 46 CFR 174.145

Graph of Righting Arm Curve

Curve of
Statical Stability

Summary of Criterion Requirements

Summary of Important Inputs

Area Available to Limiting Angle, metersˇdeg.

Draft, meters

Area Required to Limiting Angle, metersˇdeg.

*

26.5m x 9.5m
x 4.3m

*

Filename of the calculations that are contained here.

*

TBL_F2A.MCD

Vessel Draft, meters. When INPUT =1 put in the mean
draft for the condition under evaluation. When INPUT=2
it usually means the level draft is being evaluated.
Otherwise it is the LCF draft.

Vertical Center of Gravity, meters, above Baseline.
The is the same VCG (or KG) value that was used for
constructing the "Cross Curves of Stability."
This value facilitates fast cross checking with the
other vessel data.

*

*

Downflooding Angle, based on the above draft and the
vessel's geometry. Requires the lowest location where
the hull begins to flood after all WT openings have
been closed for bad weather.

*

Condition Inputs from Hydrostatics Program or Curves
of Form & Cross Curves of Stability

Input Righting Arms are below. No free surface effects are included
in this data
.

*

Vessel Displacement, Metric Tons.

Keel to Metacenter for the Transverse Direction, meters,
this value obtained at the same time as the above displacement
for the level trim case. Where KMT = VCB + BMT.

Tow Vessel, Dynamic Weather Criterion, VCG Check, as per 46 CFR 174.145

Table
F2A

*

Date: 12
July 2004

This analysis is based on the dynamic weather requirements
contained in
CFR Title 46 Stability, Subpart E -Special Rules Pertaining
to Tugboats and Towboats, 174.140 and 174.145
. This analysis was prepared in a Windows 95 operating
system (or later version) with MathCAD version 6 (or
later version).

*

*

Units: Metric

Vertical Center of Gravity, meters, above the Baseline
is positive. This value should already include the
free surface correction.

Vessel Inputs

*

*

Tug Company
Name

Client

*

M/T Tugboat
Name

Vessel Name

TYPE =1 when a specific VCG is being checked. TYPE=2
when seeking the maximum allowable value for this criterion.
In a TYPE 2 analysis this VCG value is ITERATED to
obtain the highest possible value that meets all this
criterion's requirements.

*

Z-Drive Tug

Vessel Type

Vessel Particulars,

LBP x Beam
x Depth

This last column of table below shows Corrected Righting
Arms for VCG value.

The formula for representing GZ as a function of theda
is derived as follows:

A cubic spline is used to represent the end conditions.

The above function is redefined below in terms of a
cubic interpolation function.

This function is graphed on the last page of this

analysis.

Determine Angle of Maximum Righting Arm,
as per 46 CFR 174.145(b)(2)

Determining Maximum Righting Arm & its Corresponding
Angle, Range from Zero to 90 Degrees

The Angle corresponding to maximum righting arm is obtained
from the following iterative process.

This is the initialization
value, meters.

*

Longitudinal Center of Gravity, meters, aft of Midships
is positive. For the level trim case this equals the
LCB value and it is obtained at the same time as the
displacement above.

*

If Input = 1 data for this condition is directly from
a hydrostatics program, if Input =2 data are from the
"Curves of Form" and the "Cross Curves
of Stability."

*

Vessel Inputs for Tow Vessel as
Defined by 46 CFR 174.145

Minimum Moment Area Required from zero degrees to critical
angle, in metric units of meterˇdegrees

Minimum Moment Area Required between 30 degrees and
crtical angle, in metric units of meterˇdegrees

*

*

Metacentric Height Calculations

Available Metacentric Height, meters

Sheet 1 of 3

Calculations for Righting Arm Curve

In this formula
a correction
VCG
0
is made to the Righting Arm Curve.

The procedures, techniques and presentation
contained on these pages are copyrighted. Only purchasers of the template may utilize them,
any other use is strictly prohibited.