Towline Pull Dynamic Requirements (Metric)
Description:
This template computes the
dynamic (moment area) towline pull
requirements for vessels that are equipped to tow. It is based on 46 CFR 173.095(b)
through 46 CFR 173.095(f) of Subchapter S 
Subdivision and Stability. According to 46 CFR 173.095(a)
evaluation is required for several conditions or drafts,
over the vessel's range of operation. 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
operating conditions.
As a free bonus this package also includes the static (metacentric height) towline pull
requirements for vessels that are equipped to tow. This free bonus is based on 46 CFR 173.090(b) of Subchapter S 
Subdivision and Stability. Several
conditions or drafts,
over the vessel's range of operation, are evaluated with this bonus template.
It is included because the static requirements must be computed first,
to obtain input terms like s and P which are needed to compute the dynamic requirements.
According to
46 CFR 173.095(a) a vessel may comply with either the static or dynamic
requirements. Therefore if a vessel meets the normally more
stringent static requirements, the dynamic requirements need not be
computed. However, a vessel will often not meet the static
requirements. So when this occurs, the dynamic requirements will
require computation. Fortunately vessels will often meet the less
stringent dynamic requirements.
These calculations apply specifically to vessels equipped
with ZDrives. This includes tractor
tugs, OSVs, workboats and fish boats. They do not apply to tugs,
offshore supply vessels, workboats, fish boats or
tractor tugs that are conventionally shafted, or with vertical axis
propulsion (VoithSchneider) tugs, or with paddle wheels.
There are several advantages and benefits of this
calculative method. The first is clear and neat documentation. For each
condition or draft evaluated all the inputs and outputs are identified in
one document. Second, once you get used to it, this approach is
fast. With some quick data inputting the template automatically and
quickly generates the vessels "Curves of Statical Stability," determines
the angle of the maximum righting arm, determines the vessel's limiting
heel angle, computes the residual moment area available between the
intercept angle and limiting angle, and then checks all these things to
see if they meet the United States Coast Guard requirements. Third,
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
MathCAD
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
MathCAD
document. So, this template clearly documents, saves time and it is
economical.
Cost:
$40.00
Electronic
Document Types:

Mathsoft
MathCAD Version 6
or later (for dynamic template only)

Microsoft
Internet Explorer
or compatible web browser (for instruction of dynamic template only)

Microsoft Excel
or compatible spreadsheet (for
static template only)

zip file extraction utility (comes standard with
Windows XP), required to unzip file that contains the dynamic and static
templates.
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, BM_{T}, or KM_{T }
(where KM_{T} = VCB + BM_{T}),
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
displacement.

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.
Number of
Pages: three sheets when printed (for
dynamic template)
Inputs:

Stars * are
present next to variables, on this dynamic template, that quickly identify
inputs that are required.

The following inputs are required for each operating
condition or draft (required for dynamic templates only):

filename,
name of file for these computations, one file per condition
or draft evaluated.
(example: TBLF1B.mcd)

VCG, Vertical
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
normally based
on "Curves of Form" and "Cross Curves of Stability"
data.

VCG_{0},
Vertical Center of Gravity used in making the "Cross Curves of
Stability" calculations, meters
above Baseline.

When Type = 1, with
output from a hydrostatics program for a specific
condition, normally set VCG_{0} equal to zero. If the
assumed VCG_{0} 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."

q_{f},
Downflooding Angle, degrees, based on the condition or draft being
evaluated and the vessel's geometry. This input is to be as per
Part 46 CFR 173.095 (e) which requires using the location, that causes
the smallest heel angle, to where the hull does not close automatically.
This is usually at a coaming top at the bottom of a watertight door
opening. This value is further discussed in References D and E.

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,
input data
(heel angles with corresponding righting arm values)
is from a hydrostatics
program output for the specific vessel condition being evaluated.

INPUT =
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.

q_{i},
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
analysis template.

GZ_{i}", Righting Arms, meters,
hydrostatic program output
or "Cross Curves of Stability" data corresponding to the input heel angles (q_{i}).
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 (required for both static and dynamic templates):

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."

D, Displacement,
metric tons

KM_{T}, Height from Keel to Metacenter,
feet, compute this value if required where KM_{T} = VCB + BM_{T}
= verical center of buoyancy + metacentric radius.

Characteristics of Vessel inputs, irrespective of draft
(for both static and dynamic templates):

h, Maximum vertical distance from center of
propeller shaft to towing bitts, meters

D, propeller diameter, meters

N, Number of Propellers, non dimensional value

Name of Vessel

Type of Vessel
(i. e. ZDrive Tug, Vertical Axis Tug, Conventionally Propped Tug,
etc.)

Length x Beam x Depth of Vessel, meters

Name of Firm Operating Vessel

Characteristics of Vessel inputs, irrespective of draft
(for static template only):

B, Moulded Beam, feet

d, Depth to top of Freeboard Deck, meters

HP, shaft power per shaft, at the engine, metric
hp

h, efficiency
of ZDrive between engine and propeller, in range of 0.95 to 0.98
according to McGowen & Meyer paper listed in references below

q, Angle between
lines shown in Figure F1A (plan view), degrees. First line is
drawn between vertical axes of ZDrives. Second line is drawn
along the closest slipstream edge of the ZDrive unit behind the unit
facing directly athwartships (transverse).

Characteristics required irrespective of vessel (for
static and dynamic criteria):

K, Formula Constant for metric, 13.930, non
dimensional value

A_{R}, Residual Moment Area required for
metric units is equal to
0.61 meterdegrees.

Outputs
from Static Analysis:

f, Minimum Freeboard present, meters, for each
draft specified

s, Modified Factor that applies specifically to
ZDrive Tugs, non
dimensional value

P, shaft power per shaft, at the propeller, KW
(Kilowatts)

GM_{r}, Required Metacentric Height
to meet static requirements, meters, for conditions or drafts specified

KG, Maximum Allowable VCG (Vertical Center
of Gravity) for static requirements, meters, for conditions or drafts specified

Outputs
from Static Analysis Required as Inputs for Dynamic Analysis:

s, Modified Factor that applies specifically
applicable to ZDrive Tugs, non dimensional value

P, shaft power per shaft, at the propeller, KW
(Kilowatts)

Outputs
from Dynamic Analysis:

GM_{a}, 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 VCG_{0} when a nonzero value is present.

Heeling Arm
Curve with plot.

q_{m},
Angle of Maximum Righting Arm, degrees.

q_{L},
Limiting Angle, the lesser of the downflooding angle, 40 degrees or the
angle or maximum righting arm, degrees.

q_{j},
Intercept Angle (or Equilibrium Angle) between lines heeling arm and
righting arm curves, degrees.

A_{2}, Residual Moment Area Available,
degreesmeters, This is the area between the righting arm and
heeling arm curves, in the region between the intercept angle to the
limiting angle.

check, equal to one only if all of the dynamic
criteria are met. (i. e. the intercept angle must be less than the
limiting angle (the lesser of 40 degrees, angle of maximum righting arm,
or downflooding angle), and the residual moment area available must be
more than 0.61 meterdegrees)

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 the criterion's requirements.

Suggested
Reading:
Reference A)
Subchapter S  Subdivision and Stability, Title 46 Shipping, USCG,
Washington, D. C.
Reference B) Procedure H104, 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,
D. C.
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,
N. J..
Reference E) NAVIC 1283, 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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