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Towline Pull Static Requirements (English Units)

Description: This template computes the static (metacentric height) towline pull requirements for vessels that are equipped to tow.  It is based on 46CFR173.095(b) of Subchapter S - Subdivision and Stability.  Several drafts, over the vessel's range of operation, are evaluated in this template. 

These calculations apply specifically to vessels equipped with Z-Drives.  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 (Voith-Schneider) tugs, or with paddle wheels.

Note there are also dynamic (moment area) requirements contained within 46CFR173.095(a).  A tow vessel may alternatively comply with these dynamic requirements.  These dynamic requirements are covered in another template.  The dynamic criterion is often less stringent than the static requirements contained in this template.

Electronic Document Type:  Microsoft Excel spreadsheet           Cost: Free

Number of Pages: single sheet                        


  • The following inputs are required for each draft:

    • T, Draft, feet (over operational range of tug)

    • D, Displacement, long tons

    • KMT, Height from Keel to Metacenter, feet

  • Characteristics of Vessel inputs, irrespective of draft:

    • B, Moulded Beam, feet

    • d, Depth to top of Freeboard Deck, feet

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

    • D, propeller diameter, feet

    • HP, shaft power per shaft, at the engine, horsepower

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

    • N, Number of Propellers, non dimensional value

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

    • Name of Vessel

    • Length of Vessel, feet

    • Name of Firm Operating Vessel

  • Characteristics required irrespective of vessel:

    • K, Formula Constant for English Units, 38, non dimensional value


  • f, Minimum Freeboard present, feet, for each draft specified

  • s, Modified Factor that applies specifically to Z-Drive Tugs, non dimensional value

  • P, shaft power per shaft, at the propeller, horsepower

  • GMr, Required Metacentric Height, feet, for each draft specified

  • KG, Maximum Allowable VCG (Vertical Center of Gravity), feet, for each draft specified

Suggested Reading:

  • Subchapter S - Subdivision and Stability, Title 46 Shipping, USCG

  • Procedure H1-04, MSC Guidelines for Review of Stability for Uninspected Tugboats (C), dated 3/21/00, USCG, Washington D. 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.

  • 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..  

  • NAVIC 12-83, Intact Stability of Towing and Fishing Vessels, Research Results, dated 15 Nov. 1983, United States Coast Guard, Washington, D. C.

  • Principles of Naval Architecture, by SNAME, Jersey City, N. J.

  • MSC Marine Technical Note - MTN 01-01 Towline Pull Criteria for Vessels Equipped with Z Drives, dated September 17, 2001

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Minimum System Requirements: Windows 95/98/NT/2000/XP/Vista/Windows7

Sample: A sample document is shown below.