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Tow Vessel Dynamic Weather Requirements

Description: 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 174.145 (a) through 46 CFR 174.145 (f) of Subchapter S - Subdivision and Stability.  According to 46 CFR 174.145 (a) 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 operating conditions.

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 one document. 

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. 

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. 

In summary this template neatly organizes your work, saves you time and it is economical to use.

Cost: $30.00

Electronic Document Types

  • Mathsoft MathCAD Version 6 or later

  • Microsoft Internet Explorer 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 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, 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 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                       


  • 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):

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

    • 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.

    • VCG0, 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 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."

    • qf, 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 been closed.

    • 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. 

    • qi, 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.

    • 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."

    • D, Displacement, metric tons

    • 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, etc.)

    • 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.

  • Outputs 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.

    • qm Angle of Maximum Righting Arm, degrees.

    • qL 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 limiting angle.

    • A2 Moment Area Available, meterdegrees,  The area under the righting arm curve, in the region between thirty degrees and the limiting angle.

    • 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.

  • Suggested Reading:

    • Reference A) 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, 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 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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Minimum System Requirements: Windows 95/98/NT/2000/XP/Vista/Windows7

Sample: A sample document my be seen by clicking here.