Methods Of Determining The Weight Distribution Of Ships

Methods of Determining theLongitudinal Weight Distributionof a ShipDavid Laurence Hansch, Naval ArchitectNorthrop Grumman Newport NewsFor Presentation at a Joint Meeting between theHampton Roads Section of theSociety of Naval Architects andMarine EngineersHampton Roads Chapter of theSociety of Allied WeightEngineersPresented January 24th 2008

AbstractApproximation methods for weight distribution of ships are surveyed. Groupingmethods such as the “Bucket” and station method are also explored. Detailbased methods are explained. Finally, an improved method of distribution basedon details is proposed. Guidance for the requirements of a weight database forthis method is given and an alternative summary method is suggested toovercome difficulties caused by failure to meet certain database requirements ofthe detail method. Extensive appendices provide necessary figures andequations for using these methods.ContentsAbstract.2Introduction .3The Weight Distribution Problem .3Approximation Methods .4Grouping Methods .5Direct Distribution Methods.6General Philosophy of Distribution .6Mechanics of Distribution .6An Improved Direct Distribution Method.7Validating the Distribution .8Database Requirements for Direct Distribution Methods.8Summary Methods.9Accuracy of Weight Distributions .9Conclusion .10References .10Appendix A: Survey of Approximate Methods of Weight Distribution.12Appendix B: Equations for the Direct Calculation of Weight Distributions.192

IntroductionDetermination of the longitudinal weight distribution is vital to the propercalculation of the longitudinal strength of a ship. The longitudinal weightdistribution also affects speed loss in a seaway [1]. Weight distributions of allthree principal axes can also be used to calculate the ship’s gyradii [2] whichhave a profound effect on the seakeeping performance of a vessel. Before theadvent of computers, determination of a ship’s weight distribution was a “ratherlaborious process” [3]. Due to the amount of labor involved, approximationmethods were developed over the years. With the advent of computers,methods of collecting all of the weights with centers between given locationsbecame less labor intensive giving rise to grouping methods.For longitudinal strength calculations, various levels of detail are acceptable.However, the standard is a “Twenty Station Weight Distribution” which actuallyconsists of 22 weight segments divided by 21 stations, (Stations 0 through 20).The Weight Distribution ProblemWeight distributions are needed for numerous uses however weight data isstored in databases as large numbers of discrete details. These details areessentially lumped masses and can represent items which extend for largeportions of the length of esign.References1. Swaan, W. A. and H. Rijken, "Speed Loss at Sea as A Function ofLongitudinal Weight Distribution". International Shipbuilding Progress, Vol11. No 115. March 1964.2. Hansch, David L. “Weight Distribution Method of Determining Gyradii ofShips”. Paper No. 3399. Presented at the Chesapeake Bay RegionalConference of the Society of Allied Weight Engineers. Nov 2, 2006.3. Munro-Smith, R. Applied Naval Architecture. American ElsevierPublishing Company, Inc. New York 1967.4. Comstock, John P. Introduction to Naval Architecture. SimmonsBoardman Publishing Corporation. New York, New York. 1944.5. Hughes, Owen. Ship Structural Design: A Rationally-Based, ComputerAided Optimization Approach. Society of Naval Architects and MarineEngineers. Jersey City, New Jersey. 1988.6. Principles of Naval Architecture Volume I. Edited by Rossell, Henry E. andLawrence B. Chapman. The Society of Naval Architects and MarineEngineers. New York. New York. 1941.7. Marine Vehicle Weight Engineering. Edited by Cimino, Dominick andDavid Tellet. Society of Allied Weight Engineers, Inc. USA. 2007.10

8. Filiopoulos, Christos and Debasish Ray, “Total Ship Weight ManagementComputer Program – For Today’s and Tomorrow’s Applications”.Presented at the 58th Annual Conference, Society of Allied WeightEngineers, Inc. 1999.9. ShipWeight User’s Guide Version 7.0. BAS Engineering. November 2005.11

Appendix A: Survey of Approximate Methods of WeightDistributionApproximation per Comstock [4]This sort of representation is typically used to approximate the hull weight, “thesteel, woodwork, fittings and outfit except anchors and cables, hull engineeringexcept windlass and steering gear, any spread-out items of deadweight, such aspassengers and crew, and designer’s margin.” Comstock goes on to note that,“The diagram must be proportioned that not only will the area be correct but alsothe LCG.” The cargo should be, “distributed over the length of the cargo holds astrapezoids, and so on until the diagram includes all the weights in the loadedship.”12

Approximation per Biles from Munro-Smith [3]This approximation is appropriate for passenger and cargo vessels. WH is theweight of the hull in tons and L is the length of the ship in feet. The centroid ofthe diagram (LCG) is given is 0.0056L abaft midships. The centroid can beshifted by increasing the ordinate at one end of the ship and decreasing theother. The amount to add and subtract (x) is defined as:x 54 WH Shift of Centroid**LL713

Approximation according to Prohaska from Munro-Smith [3]The Table below gives the ordinates for the plot based on Prohaska’s work. Amethod to move the LCG from midships is not provided.14

Parabolic Approximation by Cole from Munro-Smith [3] and PNA [6]This distribution is intended for vessels which don’t have parallel middle body.The centroid of the distribution can be shifted by “swinging the parabola”. Thismethod is better depicted in the following figure from PNA [6].As PNA states, “Through the centroid of the parabola draw a line parallel to thebase and in length equal to twice the shift desired (forward or aft). Through thepoint thus determined draw a line to the base of the parabola at its mid-length.The intersection of this line with the horizontal drawn from the intersection of themidship ordinate with the original parabolic contour determines the location of onpoint on the corrected curve. Parallel lines drawn at other ordinates, as indicatedin Fig 4, determine the new curve.”15

Trapezoidal Approximation from PNA [6]This approximation is useful for ships with parallel midbody.Approximate Hull Weight Curve based on Buoyancy Curve from Hughes [5]16

20 Station Distributions by ship type From Marine Vehicle WeightEngineering [7]17

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Appendix B: Equations for the Direct Calculation ofWeight DistributionsNote: This Appendix is largely reprinted from Reference [2].This appendix is included in order to enable the reader to create a spreadsheet to calculatethe weight distribution of a ship based on details or summaries. The format andfunctionality of the various tabs required to perform the calculations are explained andthe equations are given. Reproducing the code of the Excel spreadsheet used by theauthor is not practical, but this presentation is intended to enable the reader to create asimilar tool based on the same trapezoid and compound shape reasoning.Nomenclature:CGCG MAXCG MINWeightTRAPTHRHWZWALZLASZHRHCWeight ZWeight AZ slopeZ interceptBreak PointA slopeA interceptCompoundLDISTCenter of GravityMaximum Center of Gravity in any detail in a groupMinimum Center of Gravity in any detail in a groupWeight of groupTrapezoid style representationHeight of Triangle part of a trapezoid in TRAP representationHeight of rectangular part of trapezoid in TRAPrepresentationWeight of the trapezoidal part of a compound distributionWeight of the triangular part of a compound distributionLength of the trapezoidal part of a compound distributionLength of the triangular part of a compound distributionHeight of the Triangle part of a compound distributionHeight of triangular part of a trapezoid in a compoundHeight of the rectangular part of a trapezoid in a compoundWeight of the Trapezoid part of a compound (internal check)Weight of the Triangle part of a compound (internal check)Slope of Trapezoid part of compoundY intercept for trapezoid part of compoundPoint where triangle part of compound ends and trapezoidpart beginsSlope of triangular part of compoundY intercept of triangular part of compoundCompound Style RepresentationLongitudinal distance between CG min and CG max19

Entry sheet AGAHAIAJAKALHeadingGroupDescriptionWeightCGMAX CGMIN CGLDISTFA (0 if LCG is in fwd half 1 if aft)Virtual Center (Local Center)Representation TypeTHRHweight checkHTRAP SlopeTRAP InterceptCenter CheckVirtual Center %Compound MethodWZWAVirtual CZLocal CZLZLASZHRHCWeight ZWeight AZ slopeZ interceptBreak PointA slopeA intercept20

Equations:TH WT RH WTCenter LdistLdist 2LDist322Ldist TH42weight check LDist 2 RH TH2H TH RHTRAP Slope If FA 1:H RHMAX CG MINCGElse:H RHMINCG MAXCGTRAP Intercept If FA 1:H TRAP slope MAXCGElse:RH TRAP slope MAXCGCenter Check If FA 12TH LDist RH LDist23Weight check2 MINCGElse:TH LDist2 RH LDist6Weight check22 MINCGVirtual Center % Virtual Center / LDist21

Virtual CZ If FA 1:2 LA WAVirtual Center weight 3WZElse:1 LA WAVirtual Center weight 3WZLocal CZ If FA 1Virtual CZ – LAElseVirtual CZLZ LDist – LAWA Weight – WZS 2 WALAZH If FA 1WZ Local CZ LZLZ23 LZ224ElseWZ Local CZ LZLZ 2RHC WZLZWeight Z 2 LZ6 ZH242LZ RCH ZH2Weight A S LALZ22

Z slope If FA 1ZHLZElse ZHLZZ intercept If FA 1RHC Z slope ( MINCG LA)ElseRHC Z slope ( MINCG LZ )Break Point If FA 1MINCG LAElseMINCG LZA Slope If FA 1SLAElse SLAA interceptIf FA 1S A slope ( LFWD LA)ElseS A slope ( LAFT LA)Compound Shape Calculations:Compound Method12Center Locations Covered66 - 73 %73 - 79 %WZ0.8 x Wt0.93 x WtLALDist / 2LDist / 2379 - 84 %0.89 x Wt2 x LDist / 3484 - 87.5 %0.9 x Wt3 x LDist / 4587.5 - 91.25 %0.99 x Wt3 x LDist / 423

Calculation Tool:The equations presented in this appendix enable creation of a spreadsheet that takesweight, extent and center inputs and calculates a representative weight distribution foreach group. If the center of the group falls in the middle third of the group’s length, therepresentation is a trapezoid. If the center is outside the middle third, a compoundconsisting of a triangle and a trapezoid represents the weight distribution. This calculatorincorporates five compound combinations to represent shapes where the center isbetween 66 and 91.25 % of the length of the group from either extent. (The fivecompound shapes, applicable range, trapezoidal shape weight and the relative length ofthe triangular part of the compound appear in a table in the Equations section of thisappendix.) The weight and length parameters were chosen to provide the greatestcoverage.A Compound Weight DistributionAfter the distribution is calculated, the equation of the line along the top of the shape iscalculated.The inputs and calculations described above all take place on a sheet labeled “Entry”.Sheets labeled “A”, “Z”, “TRAP” calculate the weight per foot from the three equationsof the lines: the “Sort” sheet selects the correct weight for each location. This “Sort”sheet sums the total weight per foot at each location and then transfers this data to a sheetthat stores the weight distribution. The weight is then calculated by Simpson’s Rule andthe center is calculated directly by summing the moments in order to verify the weightdistribution.Segmenting and integrating the ship’s weight in this manner is accurate; however, the useof Simpson’s Rule introduces slight integration errors. The difference in total shipweight is generally on the order of less than a half of a percent; this can be improved byincreasing the number of samples taken along the axis.24

Figure 4: An Example of a Compound Weight Distribution As with the trapezoidal direct distribution method, the weight per foot of each weight record is summed for each location to determine the weight per foot curve for the entire ship. This is