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
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, feet
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)
Area Available from 30 deg. to Limiting Angle, foot·degrees
Area Required from 30 deg. to Limiting Angle, foot·degrees
Angle at Maximum Righting
Arm, degrees
Summary of Calculated Results
Minimum Angle for Maximum Righting Arm, degrees
Metacentric Height Available,
feet
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
The effectiveness of this value meeting the requirements
is checked next:
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, foot·degrees
Area Required to Limiting
Angle, foot·degrees
Filename of the calculations that are contained here.
Vessel Draft, feet. 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, feet, 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, Long Tons.
Keel to Metacenter for the Transverse Direction, feet,
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
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).
Vertical Center of Gravity, feet, above the Baseline
is positive. This value should already include the
free surface correction.
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.
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:
This is the initialization
value, feet.
Longitudinal Center of Gravity, feet, 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 English units of feet·degrees
Minimum Moment Area Required between 30 degrees and
crtical angle, in English units of foot·degrees
Metacentric Height Calculations
Available Metacentric Height, feet
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.