A METHOD FOR PRELIMINARY ESTIMATION OF THE LENGTH OF MIDSHIP BODY BLOCK TO BE INSERTED DURING SHIP S CONVERSION

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1 POLIH MARITIME REEARCH (9) 07 Vol. 4; pp /pomr A METHOD FOR PRELIMINARY ETIMATION OF THE LENGTH OF MIDHIP BODY BLOCK TO BE INERTED DURING HIP CONVERION Jan P. Mchalsk, Prof. Gdańsk Unversty of Technology, Poland ABTRACT The paper presents a method for prelmnary estmaton of the length of the mdshp body block, whch nserted n the orgnal hull, ncreases the deadweght of the shp n lne wth a requred quantty. The method may be useful for establshng the scope of converson to better adjust the shp for transportaton tasks. The problem s formulated by usng a mathematcal model so selected that ts soluton, under set of assumptons, s obtaned n a closed analytcal form. The presented method can be useful for applcaton to pre-nvestment analyss of the shp converson costs and functonal profts. Keywords: shp desgn, shp converson, ncrease of shp deadweght, lengthenng of shps FORMULATION OF THE PROBLEM, AUMPTION AND AIM OF THE WORK Proftablty of the martme transport depends on adjustng functonal features of the shp to ts operaton n gven sea navgaton and market condtons. The functonal adjustment of the shp conssts n the approprate selectng of both ts functonal type and techncal parameters, that can be made ether by commssonng the buldng of a new shp of requred features or purchasng of an exstng shp whch satsfes the gven requrements or by the commssonng of an approprate converson of owned shp. In many cases such converson s capable of satsfyng gven requrements to an acceptable degree and t usually represents the cheapest soluton. Decson on purposefulness of shp s converson may result e.g. from necessty of ncreasng the followng shp parameters: shp deadweght; shp speed; capacty of shp holds or cargo tanks; number of shpped contaners; length of cargo trals; under-deck space volume. To satsfy the requrements t s usually enough to perform converson of the shp, whch conssts n ts lengthenng by nsertng a hull block nto mdshp zone. In the avalable subject-matter lterature any descrpton of a parametrc method for a smple assessment of an extent of lengthenng the shp n order to reach a requred ncrease n deadweght of the shp after ts converson, s stll lackng. In shpyard s realcondtons [], [] the ssue n queston s solved by teratve ncreasng the block length, determnng ts structure and weght n order to obtan a proper length of the hull block, whch s rather very labour and - tme consumng. The assumed cogntve am of ths work conssts n elaboratng an orgnal parametrc method sutable for prelmnary estmaton of length of hull block to be nserted wthn mdshp zone n order to ncrease deadweght of the shp and (optonally) ts speed (by replacng the exstng propulson engne wth a new one of a greater output and mass) by a quantty requred by shp owner, as well as prelmnary estmaton of mass of the block n queston. The utltaran am conssts n provdng a soluton useful for applcaton n real shpbuldng condtons. The consdered range of converson concerns the case when shp draught, breadth and depth would not be changed after converson. The soluton of the ssue s presented analytcally n the form of a relaton whch explcte expresses dependence of the cylndrcal block length ΔL on the requred deadweght ncrease ΔPn and (optonally) the requred speed ncrease Δv as well as the shp parameters before converson. Also, 4 POLIH MARITIME REEARCH, No /07 Download Date /6/8 5:8 AM

2 s presented evaluaton of the method s error n case of lnearzaton of the ssue, as well as a determned relaton whch ntroduces correcton nto lnear expresson and sgnfcantly mproves accuracy of the method. Usefulness of the presented method may deal wth ts applcaton for analyzng relatons between profts and expendtures dependng on the assumed parameters of shp converson,.e. the method useful for pre-nvestment consderatons n shp owner offces, consultng offces and also n shp desgn offces. The ssue n queston may be consdered mportant n the lght of the opnon expressed by the consultng agency Clarkson s, statng that the world market of shp converson oders s estmated to be worth about mld Euro [] of nvestment per year, n whch the lengthenng of shps by nsertng cylndrcal block for ncreasng shp deadweght, takes a sgnfcant share. MATHEMATICAL MODEL OF THE IUE Parametrc descrpton of the shp before converson s defned by a vector of ts sgnfcant techncal parameters, x, of known numercal values: n x x, x,... x LB,T,,,, H, P n, vne, () where the followng notaton s used : L shp length between perpendculars; B shp breadth; H shp hull depth; T shp constructonal draught; shp hull block coeffcent; mdshp secton coeffcent; Pn shp deadweght; V shp speed; Ne man engne output. Changeablty of shp mass components can be expressed n an approxmate way by usng approxmate module functons such e.g. as gven n [4], [5], whch determne dependence of shp mass components on ts man dmensons and speed: M xc L B H M xc L B H / () / / / D x v Mxc Ne c CA M x const 4 gdze: M hull mass; M outft mass; M power plant mass; M 4 superstructure mass; CA factor stands for proportonalty coeffcent, and D shp dsplacement. Proportonalty coeffcents of the module functons are determned on the bass of shp parameters before ts converson: c M M M c H LBH Ne LB c / / D / v CA () Ne As shp hull longtudnal bendng moment ncreases along wth square of shp length, therefore, n case of lengthenng the shp, ts hull secton modulus W n bendng should be so ncreased, wthn the range of the nserted block, as not to mpar overall hull strength. In accordance wth the relaton for the requred value of the hull secton modulus W n bendng, gven e.g. n [6]: Cw W O L B 0, 7 (4) k the unt mass of the nserted block structure s adjusted by the factor b whch ncreases hull secton area wthn the range of the nserted block : L L L (5) wth not takng nto account a rather low nfluence of change of the block coeffcent resultng from nsertng the block nto shp hull. hp length extenson affects value of conventon freeboard. Its prelmnary, smplfed estmaton wth takng nto account the followng [7]: change of table value of freeboard; correcton whch covers change of the coeffcent ; correcton connected wth the requred bow heght; leads to the relaton whch expresses change of the mnmum value of the summer freeboard MFB: 5 50 MFB L [mm] L 5.6 (6) L where L, ΔL are gven n[m]. As the estmaton provdes a negatve value t s not necessary to account for any ncrease of MFB. The ssue n queston has two nterestng utltaran aspects consstng n determnaton of: the length, ΔL, of the cylndrcal nserton block, whch corresponds wth the assumed ncrease of the shp deadweght ΔPn and (optonally) of the shp speed Δv; the deadweght ncrease DPn resultng from the nserton of the ΔL long block, e.g. an addtonal hold of the requred length ΔL. The nserton of the cylndrcal block of the length ΔL s assocated wth the change of: the ntal hull block coeffcent by the value of Δ; the ntal shp dsplacement by the value ΔD; the ntal shp mass by the value of ΔM. POLIH MARITIME REEARCH, No /07 4 Download Date /6/8 5:8 AM

3 Moreover, t was used to ncrease the nserton block mass ΔM by addng the technologcal margn of mass R proportonal to mass of the block. Buoyancy equaton expressed by balance of dsplacement and mass components after converson of the shp can be wrtten as follows: DxDx Pn Pn MxMxRx (7) where: Pn, D and M stand for deadweght, dsplacement and mass of the shp before converson, respectvely, and ΔPn, ΔD and ΔM are values of the same parameters of the shp after ts converson; R M M s the technologcal margn of shp mass. Value of the mass margn s usually contaned wthn the range, 0, 0, and depends on appled shpyard s standards. oluton of the ssue n queston s presented n the form of the closed formula whch expresses the cylndrcal nserton length dependng on a requred shp deadweght ncrease and speed, together wth the formula for estmatng the nserton block mass. NON-LINEAR MODEL If the shp converson has to concern both the shp deadweght change ΔPn > 0 and ts speed Δv > 0 whch leads to replacement of exstng man engne by other one of a greater output and smlar rated rotatonal speed, then, under taken assumptons, the buoyancy equaton of the shp after ts converson (7) can be expressed as follows: L D Pn Pn c L L BH L / c L LB H / c D v v / M CA 4 By substtutng the factor β whch adjusts the hull secton modulus n vertcal bendng t s possble to express the buoyancy equaton as follows: L D L L L M L Pn Pn L L / / / D v v c M L LB H c 4 CA The nserton block length ΔL can be determned by solvng the above gven non-lnear equaton wth the use of numercal methods, that s rather not very convenent n practce. It s much more useful to have a formula for determnng ΔL value explcte. To obtan such relaton the non-lnear segments of the buoyancy equaton (9) was lnearzed provdng ths way the formula for determnng ΔL value. Applcablty merts of the determned formula was verfed by evaluatng value (8) (9) of the error resultng from the lnearzaton; the error value was then assessed wth takng nto account the aspect of applcatons n engneerng. LINEARIZED MODEL By takng nto account only the lnear parts of the ncreases of the shp mass M (x) and shp dsplacement D(x), whch result from the changes Δx n shp parameters, the balance of mass ncreases after converson can be expressed by the general lnear relatons as follows : Dx P n M x (0) 4 D 4 4 x Mj x x Pn x () x j x On substtuton, nto Eq. (), of the lnear mass ncreases resultng from the modular formulae as well as the dsplacement ncrease, the buoyancy equaton of shp after converson takes the followng form: M L L L v D L L v L Pn M M () On determnaton the value ΔL from Eq. (), the searched formula s reached as follows: v Pn M L v D M M L VERIFICATION OF THE METHOD () On the bass of the set of the data dealng wth bult shps (of known values of x and M ) was conducted a seres of calculatons consstng n comparson of the results obtaned from the lnear formula () wth the results of solvng the non-lnear equaton (9). From the performed nvestgatons can be concluded that lnearzaton error value depends on values of the relatve ncreases : ΔPn/Pn and Δv/v. In the range of the ncreases from 5 % up to 0% the relatve percentage error of the ΔL s contaned n the nterval from about % to about 7%, that s llustrated by the results gven n Tab.. Tab. The mean relatve percentage error ΔPn[%] Δv[%] POLIH MARITIME REEARCH, No /07 Download Date /6/8 5:8 AM

4 The mean relatve percentage error ΔPn[%] Δv[%] It was concluded that n the consdered ssue the accuracy of the results obtaned from Eq. () does not satsfy demands of engneerng applcatons especally n case of greater values of the relatve ncreases ΔPn and Δv. To mprove the accuracy of the formula, the functon Fc(x) for correctng Eq. was formed; the ΔL values corrected ths way more better approxmate the results from the nonlnear model. The functon Fc(x) was determned from the condton of mnmzng value of the lnearzaton error. The correctng functon n queston was obtaned by applyng the method of least squares of devatons. As a result t reached the followng form : Fc x Pn Pn v v The corrected formula () took fnally the form as follows: v Pn M Lc Fcx v L D M M (4) (5) Eq. (5), on nverson, may serve to estmate value of shp deadweght ncrease after nsertng the block of the requred length ΔLc, e.g. one-hold block : CONCLUDING PART EXAMPLE OF APPLICATION OF THE METHOD The presented queston conssts n prelmnary estmaton of nserton block length and mass as well as power plant mass (n advance of desgnng the block structure) n case when the requred ncrease of shp deadweght s equal to 500 t, and the man engne should be replaced wth other one of a greater output so selected as to ncrease shp speed by.50 knots. The parameters of the consdered shp before converson are gven n Tab.. Tab.. Deadweght 450 t peed 6.80 knots Length 4. m Breadth 0.0 m Draught (max) 8.9 m Depth.80 m Man Engne Power output 5740 kw Mass of teel Hull 97 t Mass of uperstructure 08 t Mass of Outft 54 t Mass of Machnery 774 t Block Coeffcent Mdshp ecton Coeffcent 0.98 Length of the nserton block: The length of the block s obtaned by substtutng the values of shp parameters nto Eq. (5): Lc D M M v Pn M Fc x L v (6) The calculatons analogous to those ncluded n Tab., performed by means of the corrected formula, show much lower values of error of the method (see Tab. ). Tab.. The mean relatve percentage error after correcton ΔPn [%] Δv [%] L 4.6 m Mass of the nserton block together wth ts technologcal margn: L / L M B L M c L LB H M L L / t Mass of the shp s power plant: M M / / / / D v v ,50 c t CA Mass of the empty shp after converson: M M + M M +M +M +M +M = =6505 t 4 POLIH MARITIME REEARCH, No /07 45 Download Date /6/8 5:8 AM

5 Dsplacement of the shp after converson: D D LBT t Deadweght of the shp after converson: Pn Pn M t CONTACT WITH THE AUTHOR Jan Mchalsk e-mal: janm@pg.gda.pl Poltechnka Gdańska Narutowcza /, 80- Gdańsk Polska The requred shp deadweght after converson s equal to 5950 t, hence n the consdered case the total error n estmatng shp mass s equal to 9 t and results from lnearzaton of the ssue (n ths example the assumed technologcal mass margn amounts to about 9.7 t). BIBLIOGRAPHY. Lloyd Werft Wns Ferry Lengthenng Contract. hpreparng & Converson Technology. nd quarter 06.. BCTQ Helps transform Red Falcon. hpreparng & Converson Technology. 4 th quarter 04.. Dscusson on shpbuldng ndustry n Poland ( n Polsh). A conference presentaton gven by J. Czuczman, Gdańsk Watson D.G.M.: Practcal shp desgn. Elsever Nogd L.M.: Theory of shp desgn (n Polsh). Wydawnctwo Morske, Gdyna Polsk Rejestr tatków : Rules for the classfcaton and constructon of sea-gong shps, Part Hull ( n Polsh). Gdańsk Polsk Rejestr tatków :: Regulatons for freeboard of seagong shps ( n Polsh ) Gdańsk POLIH MARITIME REEARCH, No /07 Download Date /6/8 5:8 AM