Login| Sign Up| Help| Contact|

Patent Searching and Data


Title:
METHOD FOR DETERMINATION OF THE DISPLACEMENT OF DEFLECTED SHIPS
Document Type and Number:
WIPO Patent Application WO/2003/043880
Kind Code:
A1
Abstract:
On the ships fitted with traditional draft marks at three positions: at aft perpendicular, amidships and at forward perpendicular, doa,dom, dof, it is possible to define the value of the equivalent draft for hydrostatic calculations, usrign the data for the ship's hull ans a rigid body on an even keel, employing the observed saggin or hogging amidships wm and the draft correction facvtor Cd or the draft correction coefficient cd=1/Cd as follows (Formula I). The procedure for determination of the displacement of longitudinally deflected ships is based on the expression for the draft correction factor Cd employing actual flotating waterline characteristics, such as the waterline length, Lwl, water-plane area Awl, longitudinal moment of inertia IL of the waterline about a transverse axis through the center of flotation, moment to change trim one unit MT1 and tons per unit of immersion TP1, as follows : (Formula II), or by using the general parabolic approximation for the waterline shape depending only on water-plane coefficient (formula III). The values of the corrections factors, as presented, can be calculated once for all drafts, already in the design phase and are valid in the entire ship's service lifetime. The displacement of a longitudinally deflected ship can be also determined using the water-plane area Awl, the correction factor as defined by the first requested, and the observed displacment &Dgr o, as &Dgr = &Dgr o + wm&Upsi seaAwlCd, or the standard displacement&Dgr s, when it is &Dgr =&Dgr s-wm&gammad seaAwl (1-Cd). Besides, the same accuracy can be accomplished y only two draft readings doea,doef at positions aft and forward (Formulare IV) centred with respect to the water-plane centre of flotation, what provides simultaneous corrections due to longitudinal deflection and trim. The position correction factor Cx is defined as (Formula V). The equivalent draft for determination of the displacement of longitudinally deflected ships is obtained as (Formula VI).

Inventors:
Ziha, Kalman (Ljudevita Posavskog 15, Zagreb, 10000, HR)
Application Number:
PCT/HR2002/000046
Publication Date:
May 30, 2003
Filing Date:
October 10, 2002
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
Ziha, Kalman (Ljudevita Posavskog 15, Zagreb, 10000, HR)
International Classes:
B63B9/00; B63B39/12; (IPC1-7): B63B39/12; B63B9/00; B63B9/08
Download PDF:
Claims:
PATENT CLAIMS
1. The method for determination of the displacement of the longitudinally deflected ships, characterized by that the displacement of the longitudinally deflected ship's hull is determined on the basis of the draft readings at aft perpendicular, amidships and at forward perpendicular, at only one side, or averaging readings at both ship's sides, dao,dmo,dfo, using the <BR> <BR> <BR> <BR> a m f<BR> <BR> ship's hull sagging or hogging wm = 2 , employing the equivalent draft<BR> <BR> 1 dao + 2dmo(cd 1) + dfo, where the draft correction factor Cd or dme = dmo + wmCd = dmo + wm = cd 2cd its reciprocal value cd=1/Cd, can be calculated for waterplane length Lwl, area Awl, moment of inertia of the waterline about a transverse axis through the centre of flotation IL, moment to change trim one <BR> <BR> <BR> <BR> unit MT1 and tons per unit of immersion Tupi, as follows: Cd = ###### # ### ### or in an<BR> <BR> <BR> (Lwl/2)2 TP1 (Lwl/2)2 approximate form based only on waterplane coefficient CWP, as follows Cd = ### ####.
2. 3(32CWP).
3. The method for determination of the displacement of the longitudinally deflected ships, characterized by, that the displacement of the longitudinally deflected ship's hull is determined on the basis of waterplane area A,,,, draft correction factor Cd, from the first request and observed displacement A, as follows: A = A° + wmγseaAwlCd or using the standard displacement s, as follows # = #s wmγseaAwl(1Cd).
4. The method for determination of the displacement of the longitudinally deflected ships by adequate placement of draft marks characterized by, that the displacement of the longitudinally <BR> <BR> <BR> <BR> doe +doe<BR> <BR> deflected and trimmed ship's hull is determined on the basis of the equivalent draft dmse = ## ###,<BR> <BR> ion 2 employing draft readings da°e, dfe at suggested lengthwise aft and forward positions Cx, centred with respect to the centre of flotation, where the position factor is defined by the draft correction factor from the first request.
Description:
METHOD FOR DETERMINATION OF THE DISPLACEMENT OF DEFLECTED SHIPS DESCRIPTION OF THE INVENTION Field of application This invention applies to more accurate determination of the displacement of merchant ships built from elastic materials, which suffers from significant temporary or permanent longitudinal deflections in ship's service due to hull bending, such as hull sagging or hogging, what provokes changes of the immersed hull form, leading to inaccuracies in determination of the ship's displacement, particularly important for modern large merchant ships.

According to International Classification, this invention can be classified as: B-63 (Ships and floating objects) 9/08 (Properties) Technical problem The problem tackled by this invention is the more accurate determination of ship's displacement whose hull under longitudinal loadings caused by bending, changes the immersed hull form. Absolutely accurate determination of ship's displacement is very complex and in most cases impossible, due to a number of imperceptible and immeasurable circumstances, such as, temporary or permanent, longitudinal or transverse, local or global, residual or thermal deformations, as well as corrosion, ageing, damages, reparations or hull fouling, what cannot be accounted for in realistic conditions of the ship's service. The ship's displacement is the most important property for determination of the ship's operational efficiency and every improvement in practices and accuracy of its determinations is useful either for the ship's crew or for the ship-owner.

State of art The shipping practice applies simplified approximate method for the determination of the change of the displacement due to small longitudinal deflection of the immersed hull based on the assumption of a parabolic deflection line. The methods currently in use do not account for the shape of the immersed ship hull and therefore are less accurate. Since the draft and deadweight survey methods based on draft readings aft, amidships and forward, has been established earlier when the ships were smaller and of different shape, the inaccuracies of traditional methods are particularly significant for large modern merchant ships with full hull form.

The ship's displacement, as well as the other hydrostatic particulars of hulls, traditionally are calculated for all anticipated drafts, using lcnown methods from the theory for ships considered as rigid bodies on a hypothetically even keel, and represented by diagrams and/or tables, once for the entire ship's service lifetime, usually already in the design phase. During the deadweight survey procedure, the displacement, the trim and the deflection are determined on the basis of draft readings or results of automatic draft measurements using adequate devices, aft, forward and amidships, sometimes both on portside and starboard sides, employing the permanent ship's hydrostatic data, for each load case.

The basic geometrical relations of a longitudinally deflected ship hull in a sagging condition, as well as the notation used in the text, are presented on Fig. 1.

The average or the mean draft of ship in service is traditionally obtained on the basis of draft readings da, d d'observed on aft perpendicular, on portside and on starboard sides amidships and on forward perpendicular, and represents the standard draft, see Fig. 1., for hydrostatic calculations and determination of displacement, as follows: 1 In order to simplify the procedure and save time and expenses of survey, it is usual to take draft readings on only one, usually the most accessible side.

The hull sagging or hogging are defined traditionally amidships, regardless of the actual position of the extreme value, on the basis of observed drafts, as follows: <BR> <BR> <BR> <BR> do<BR> dao + dfo ms - dmo = -dmo From the term (2), it is obvious that the deflection amidships is positive for sagging condition and negative for hogging condition, Fig. 1.

The traditional, simplified draft and displacement survey method for longitudinally deflected ships due to bending is based on the equivalent draft for hydrostatic calculations defined by using observed drafts, as follows: <BR> <BR> <BR> <BR> wv4 da +6d, ° +df<BR> <BR> '"'8 Substituting (1) and (2) into (3), the equivalent draft can be rewritten on the basis of 1/4 of the amidships deflection, as follows: <BR> <BR> <BR> <BR> dmw114 = dmo + 1/4 dao + dfo - dmo = dmo+ 1/4#(dmm - dmo) = dmo + 1/4#wm<BR> <BR> <BR> 24 The equivalent draft defined by the term (4) is denoted in shipping sometimes as the"quarter mean draft" or the"mean of mean draft". Put succinctly, the equivalent draft for hydrostatic calculations of a longitudinally deflected ship hull, according to (4), is obtained as the observed draft amidships corrected for 1/4 of the hull deflection amidships according to (2).

To the observed draft amidships d',, from the hydrostatic data (displacement curve, hydrostatic tables), the observed displacement denoted as A°, can be assigned, and to the standard draft amidships d, Sn according to (1), from the hydrostatic data (displacement curve, hydrostatic tables), the standard displacement denoted as AS, can be assigned by considering the hull on even keel as a rigid body, Fig. 2.

It is traditionally accepted that the displacement of a longitudinally deflected hull A can be assessed for a ship hypothetically considered on even keel as a rigid body, by the displacement pertinent to the corrected amidships draft d, ''4, according to (4), Fig. 2. Of course, for large amounts of sagging or hogging and/or large trim, it is more appropriate to use traditional lengthwise integration for displaced and inclined sectional areas, so called Bonjean's curves.

Invention essence The amount of ! 4 of the amidships sagging or hogging in (4) is appropriate for draft corrections in only some particular cases and in general does not account for the shape of the ship hull. For more accurate displacement assessments of a longitudinally deflected ship, a variable draft correction factor denoted Cd as well as its reciprocal value'd are introduced in the following manner : @ Cd<BR> <BR> <BR> <BR> <BR> <BR> <BR> dme = dmo + Cd.wm = dmo + 1/c@#wm (5)<BR> <BR> Cj The essence of the invention is in the rational, but still simple and practical method for determination of the variable draft correction factor Cd in (5), employing the true data of the hull form presented by the sole water-plane characteristics on different anticipated drafts, Fig. 1. The invention employs the practically adopted assumption of relatively small, for this purpose parabolic hull deflection line, considering ship's sides as parallel in the range of the hull deflection.

The invention is extended by a suggestion for a new placement of ship's draft marks, instead on perpendiculars aft and forward and amidships, at only two positions alongside the hull, where the observed drafts coincides with equivalent drafts of a ship hypothetically considered on an even keel as a rigid body, Fig. 1. By the draft marks placed as it is presented in this text, both the more accurate correction due to longitudinal deflection and the correction due to the trim are simultaneously accounted for the displacement survey. The suggested positions of draft marks aft and forward are determined on the basis of the draft correction factor Cd defined in (5) and are generally valid for usually adopted practical assumption of small deflections and small trim in ship service.

Description of the invention The ship's hull deflection line by longitudinal bending is assumed on the basis of many experimental and numerical evidences that the prove how the deviations are of limited order of significance and usually appropriate for technical calculations, in the form of a second order parabola with the extreme value in the centre of flotation, as it is shown: <BR> <BR> <BR> <BR> <BR> .. 2<BR> <BR> <BR> <BR> w(x) = wm<BR> <BR> <BR> <BR> (L, l 2 The parabolic defection line (6) after rectification represents the equivalent floating line, which defines the same displacement of a deflected ship as it is of the hypothetically rigid hull on even keel, Fig. 1.

It is obvious that the deflection line of a ship's hull in service is neither symmetric nor parabolic, moreover, that the actual shape and the true position of the extreme value are practically immeasurable.

Therefore, the more practical assumption for modern large ships about the position of extreme value of the deflection line in the centre of flotation, instead in the mid between the perpendiculars, i. e. Wm t WL X is introduced, Fig. 1. On the other hand, it is not practical to determine the hull deflection shape and the position of the extreme value on board more precisely. Moreover, in most cases it is imperceptible, and therefore, for ships with traditionally placed draft marks, the deflection amidships has to be considered as the extreme of the deflection line.

The changes in hydrostatic properties due to hull deflection are mostly dependent on the floating water- plane geometric characteristics. The longitudinal change in buoyancy due to relatively small deflection w (x) of o a hull with hypothetically parallel ship's sides, with respect to the actual water-plane of length Lwl, and breadth b (x), at any position'x'along the ship, is defined as follows: qb (x) = rsea w (x) b (x) The displacement of the deflected ship part in the area of the floating line in the water of specific gravity y sean supposing a parabolic floating line (6), can be obtained by longitudinal integration of (7), as it is shown: The correction of draft amidships relative to the observed amidships draft, due to the displacement of the deflected hull part, can be determined as a parallel immersion or emersion employing area of a water- plane Awl and moment of inertia IL of the waterline with respect to the transverse axis through the centre of flotation CF, as follows: <BR> <BR> dmd = #d = wm # IL/Awl = wm#Cd (9)<BR> <BR> γsea#Awl (Lwl/2)²

The dimensionless draft correction factor Cd due to deflection is derived only by basic water-plane geometric characteristics employing (9), and can be easily calculated from commonly available ship's permanent hydrostatic particulars, as shown: <BR> <BR> <BR> <BR> <BR> (10)<BR> <BR> wl Alternatively, in some practical cases, the correction of draft amidships may be approximated by substitution of the moment to change trim one unit MTI and tons per unit of immersion TPI in (10) and can be expressed in consistent units (for inconsistent units, additional units conversion is required), as follows: <BR> <BR> <BR> <BR> MT1 Lpp<BR> <BR> <BR> Cd # # (10a)<BR> TP1 (Lwl/2)2 For simplicity, the true water-plane shape of beam BWI and water-plane area coefficient C-p = Awl/(LwlBwl), can be approximated by a symmetric general parabola of order k, in the following form: <BR> <BR> <BR> <BR> (Lwl/2)k - xk<BR> b(x) = Bwl (11)<BR> <BR> (Lwl/2)k The substitution of (11) in (7) and the repeated integreation as in (8), having in mind that k=CWP/(1- Cwp) :, may lead to satisfactory assessments of water-plane area characteristics as follows: k , z BwlLwl# # # = BwlLwlCWP (12) 1(14)<BR> Cd # 3(3 - 2CWP) It is easily recognizable from (14), that Cd significantly differs from 1/4 and that it is an increasing function of CWP. Specifically, Cd=1/4 only for a unique value of Cwp is amounting to CWP=0. 834. The maximum value of Cd=1/3 is attained for Cwp=l, i. e. for rectangular waterline shape. The minimum value of Cd=1/6 is attained for Cep=112, i. e. for triangular waterline shape.

The invention takes a step further. When the deflection is not too great, a second order symmetric parabola (6), shifted vertically relatively to the observed waterline, for amount of parallel immersion defined as a fraction of the maximal deflection supposed at the position of to the centre of flotation in amount ouf weld in (6), Fig. 1., can be used as an approximation denoted equivalent waterline of the hull, as shown: <BR> <BR> [Cd(Lwl/2)2 - x2]<BR> w(x) = wm (15)<BR> <BR> <BR> (Lwl/2)2

In order to find the true displacement of a deflected hull, it is imagined that the equivalent waterline is rectified back to a plane waterline by vertical translation of hull sections at some position"x", amounting to the value w (x) defined by the equivalent waterline (15), Fig. 1.

The positions along the ship's hull with respect to longitudinal centre of flotation LCF, where the observed drafts are equal to the equivalent draft can be obtained in intersections between the equivalent waterline line and the observed waterline by employing the square root of the draft correction factor Cd (10), (lOa) or (14), Fig. 1., from the condition w (x) =0 in (15), as: The position factor denoted Cx in (16), is defined as shown: As the consequence of above assumptions, for trimmed deflected ships, is the equivalent waterline passing through the longitudinal centre of flotation, what is intrinsic to the suggested method because of the fact that the corrections due to deflection and due to trim are accounted for all at once. The draft marks placed on the specified positions are closer to the amidships, therefore making easier their fitting on ship's sides, slightly reducing the accuracy of draft readings at perpendiculars, but increasing the accuracy in obtaining of the equivalent draft, in general simplify and accelerate draft survey, which are due to less intense motion even more accurate, and finally, improve the accuracy of deadweight survey.

Application procedure This invention is easily applicable to existing ships with traditionally placed draft marks by determining either once for the ship's all possible and anticipated drafts in the entire service lifetime or in each particular situation the value of draft correction factor accurately, according to 10) i (lOa) and approximately according to (14).

Commonly, the observed amidships draft is corrected to the equivalent amidships draft din using deflections amidships wm (2) and the draft correction factor (10, 10a or 14) instead of constant 1/4 in (4), as shown: <BR> <BR> <BR> +1/cd#wm = ### # ####### # ## # ### = ### # ##### # ## # ###<BR> <BR> <BR> <BR> <BR> <BR> d d The equivalent draft (18) is identical to the term (5) and represent a more rational basis for comprehensive and accurate displacement assessment of deflected ship hull of the commonly used equivalent"mean of mean"draft (3), since the draft correction factor Cd (10, 10a or 14) accounts appropriately for the hull form via the water-plane geometrical characteristics. The substitution f = 2 cd in (18), simplifies the procedure.

Alternatively, the standard mean draft amidships (1) can be corrected to the equivalent amidships draft using deflections amidships (2) and the draft correction factor (10, 10a or 14), as follows: dna = dms - (wm - dmd) = dms - dm(1 - Cd) To obtain the actual displacement A of the deflected hull from the permanent hydrostatic particulars for a rigid hull on an even keel, the equivalent mean draft can d,, e, be used, as clarified on Fig. 2.

Hence, the actual displacement of a deflected ship hull on a hypothetically even keel can be defined relative either to the standard displacement or to the observed displacement, employing the amidships deflection wu (2) and the draft correction factor Cd (10, 10a or 14), as follows: A=A°+AA°+C, (20) # = #s - (wmγseaAwl - #dd) = #s - wmγseaAwl(1-Cd) The expressions γseaAwlCd in (20) and γseaAwl(1 - Cd) in (21) represent the displacement correction per unit of longitudinal deflection of the ship hull amidships, relatively to the observed displacement or standard displacement, respectively. For small deflections and hypothetically parallel ship's sides, the unit of displacement increment may be viewed as constant amounting to the slope of the displacement curve, i. e. , its first derivative Ysea Awl, Figure 2.

If there is a trim encountered on board, displacement of a hypothetically rigid hull on an even keel position (20,21), have to be additionally corrected for changes due to the trim. When the trim is not too great, the axis of rotation for change of trim without change of displacement may be assumed to pass through the centre of flotation LCF of the even-keel waterline. In order to find the true displacement for a trimmed waterline the ship is imagined as rotate back to a waterline parallel to the base. Then the solution may be reached algebraically. For very large trims and deflections, it is best to make use of Bonjean's curves for direct lengthwise integration of curves of areas of inclined and deflected sections. Water density correction is normally included during a deadweight survey.

The suggested procedure based on traditional draft marks placement at ends and amidships, but applying the more accurate draft correction factor, as it is explained above, accounts for the true shape of the ship hull, and therefore represents a rational improvement with respect to traditional methods of draft and displacement survey, since they do not consider the hull form and its changes by drafts.

The aim of the considerations in the sequel is to prove that an alternative placement of draft marks, quite different of current practice, on only two positions alongside the ship's hull, provide easier, faster, more simple and more accurate equivalent draft and consequently, more accurate displacement of a deflected, and moreover, of a trimmed ship, all at once.

The two drafts observed on ship sides aft and forward, on lengthways positions xd in (16) from the centre of flotation CF, are denoted as follows: daoe,dfoe.

The distance defined by (16) can be interpreted as the lengthways position of draft observations which provide directly immediate values for equivalent draft calculation. Following the assumption about the position of the maximal deflection close to the centre of flotation LCF, the standard equivalent draft is defined by only two draft reading, Fig. 1., compared to the conventional term (3) which requires three draft readings, as it is shown: <BR> <BR> <BR> <BR> <BR> <BR> daoe + dfoe<BR> dLCFse = (22)<BR> 2<BR> <BR> <BR> <BR> <BR> Since the standard equivalent draft (22) virtually coincides with the position of the longitudinal centre of flotation, both corrections for deflection and trim are accounted for all at once. It is obvious from (22), that the determination of the standard equivalent draft (22) does not requires readings of mean draft, as it is normally the case, for example in expression (3). The positions of the draft marks alongside, centred with respect to the longitudinal centre of flotation that define the standard equivalent draft which is pertinent to the same displacement of the trimmed and deflected hull as it is of the hypothetically rigid hull on the even keel.

In order to get additional ship service information, if required, there are some additional calculations available in the procedure, related to the ship's trim and drafts at traditional positions.

The trim with respect to draft marks at new positions is defined as: trinzcm = doe-doe (23) The angle of trim in general is obtained on the basis of the trim itself, and of the distance between the draft marks amounting 2xd, as follows: tCM = trimCM/2xd (24) The trim with respect to the perpendiculars is obtained by employing the length between the perpendiculars, as follows: tramp. =tcM Lpp (25) Note the positive trim is by bow, negative otherwise.

The aft draft da and the forward draft df at the perpendiculars, accounting only for the hull trim and neglecting the hull deflection, are assessed as follows: da = daoe-tCM#(Lpp/2-xd + LCF) (26) df = dfoe + tCM#(Lpp/2 - xd - LCF) The mean draft is: da + df dm = (28)<BR> 2<BR> <BR> <BR> <BR> <BR> Note that for the displacement and trim determinations is sufficient to employ only the two draft readings at specified positions. The draft observation at the position of the longitudinal centre of flotation denoted

as d LCF, is required only if the hull deflection at this position is of interest. Otherwise, the draft marks at the positions of the longitudinal centre of flotation are not needed.

The relative hull hogging or sagging wcM with respect to the observed draft marks is defined by employing the observed draft do and the equivalent draft dLCF, both at the position LCF, as follows: wCM = dLCFse - dLCFo The overall sagging or hogging at the position of LCF, can be assessed by employing wcM and the draft correction factor Cd, as follows wLCF = wCM/Cd.

Note WCM and WLCF are considered positive for hogging and negative for sagging condition.

Normally, the amidships deflection wm does not differ significantly of the deflection wLCF at LCF, moreover, the difference even cannot be practically measured.

The aft draft da and the forward draft df at the perpendiculars, accounting for the hull trim and deflection, are calculated as follows: da = daoe - tCM#(Lpp/2 - xd + LCF) + wLCF(1 - Cd) d f = dfoe + tCM#(Lpp/2 - xd - LCF) + 2LCF(1 - Cd) For constant draft correction factor Cd=1/4, it follows from (17) that the position factor is CX=1/4 From (16), it follows that for Xa=+Lpp/4, is dnZse (22) close to d,, w'14 (4), that is, if the draft marks are placed at aLpp/4 from amidships, the equivalent mean draft d, ri is very close to the'quarter mean draft'd » W, 4.

For ships with traditionally placed draft marks at aft perpendicular, amidships and on forward perpendicular, drafts are observed on three places aft amidships and forward. This invention employs the observed drafts on board, the average or mean draft calculated according to (1), hull hogging or sagging according (2), as well as the equivalent draft amidships according (18) or (19) in order to determination deflected ship's displacement from hydrostatic data tables or from the displacement curve.. Besides, the ships observed or mean displacements can be determined and then corrected for the difference of the deflected hull according to (20) or (21).

This invention provides a simplified method for determination of the displacement of deflected ships employing only two draft marks placed lengthwise centred with respect to the centre of flotation, at the distance defined by (16), or (17), instead of traditionally placement of draft marks at aft perpendicular, amidships and on forward perpendicular. Technically, the draft observations on the new positions of draft marks, is performed analogously to the observations at aft perpendicular, amidships and on forward perpendicular, moreover, the draft measurements can be arranged by adequate automatic devices. The two draft readings at new positions define the standard equivalent draft (22) in order to determine the

displacement of the deflected and trimmed ship's hull, all at once. Although is not necessary, for some practical situations may be useful to put draft marks at the positions of longitudinal centres of flotation, Fig. 3. in order to obtain the hull deflection at this position. For the traditional freeboard control is retained the Pllimsol's mark. The procedure is applicable on digital computers In addition, the new draft placement eliminates the problem of encountering hogging on one side and sagging on the other side for excessively transversely inclined ship hull fitted with traditional draft marks at perpendiculars and amidships. The alternative placement of draft marks in positions of greater hull breadth in the area of the parallel midbody adds sense for averaging both port and starboard draft marks, even for ships with significant heeling angle. The loaded conditions with sensible trim and small deflections are of utmost interest for deadweight survey, much more than the ballast conditions, and therefore the new placement of draft marks nearby the load line in combination with traditional draft marks at stern which impacts on propeller immersion and rudder effectiveness and at bow, which affects maneuverability and lamming, appears practical and useful 1 Nomenclature A,,, ==area of the water-plane; Blvrbeam of the water-plane; Ca-correction factor for draft of a deflected hull; Cwp ; ==waterline coefficient; d=draft in general; IL=moment of inertia of the waterline about a transverse axis through the centre of flotation; LCF = centre of flotation of the water-plane; L", rlength of the water-plane; MTI=moment to change trim one unit; 7P7=tons per unit of immersion ; x, rpositions of equal equivalent and observed drafts; hull deflection in general; Greek symbols γsea=specific gravity of sea water; A=displacement in general; Subscripts a, m, frelated to aft, mean and forward; Superscripts e, s, o=related to equivalent, standard and observed; related to deflected hull

EXAMPLE The innovation is applied to a bulk-carrier built recently in Croatian shipyards with following main particulars: Loa=187.63 m, Lpp=179.3 m, B=30.8 m, D=15.45 m, d=10.8 m, DWT=41600 t, Lightship weight=8400 t, service speed = 14.5 knots, The results are presented in Table 1 and on Fig. 1.

Table 1. Example: Hydrostatic data and correction factors according the suggested innovation for a bulk-carrier built in a Croatian shipyard d LWL Cwp LCF Awl # IL TP1 MT1 Cd 1/Cd Cd Cx Xd AWLCd Cd in m in m2 t 103m4 t/m tm/m e.10 e. 10a e. 17 e. l6, rr : m'e. 14 Ship particulars, Hydrostatic data Tl : e true waterline shape Parabolic 0 167. 38 0. 608 4.000 3136 0 4202 3214 23921 0. 191 5. 227 0. 191 0.219 36.604 600 0. 187 1 174.95 0. 760 4.520 4048 3816 6827 4149 38873 0. 220 4. 537 0. 220 0.235 41.066 892 0. 225 2 177. 20 0.785 4.961 4283 8136 7696 4398 43998 0.229 4. 369 0. 229 0.239 42.390 983 0. 233 3 178. 42 0. 803 5.031 4407 12605 8225 4527 47011 0.234 4. 264 0. 234 0. 242 43.200 1038 0.239 4 178.27 0.818 5.007 4485 17175 8539 4636 49372 0.240 4.173 0. 240 0.245 43.633 1082 0.244 5 177. 99 0. 829 4.734 454221811 8781 466450471 0.244 4. 097 0.245 0.247 43.969 1114 0.248 6 178. 10 0. 838 4.174 4596 26503 9042 4719 51686 0.248 4. 031 0. 248 0. 249 44.354 1145 0. 252 7 178. 46 0. 847 3.353 46556 31252 9354 4781 53470 0. 252 3.963 0.252 0.250 44.822 1181 0.255 8 180. 92 0. 852 2.223 4725 36068 9761 4853 55630 0.252 3. 961 0.251 0.251 45.451 1209 0.257 9 184. 40 0.849 0.754 4817 40963 10301 4944 58889 0.252 3.975 0.251 0.251 46.244 1212 0.256 10 183. 20 0.873-0. 977 4918 45956 10933 5047 62496 0.265 3. 774 0.265 0.257 47.149 1318 0.266 11 183.60 0. 886-1. 929 5010 51051 11518 5141 65897 0.273 3.666 0.273 0.261 47.947 1362 0.271 12 184. 00 0.898-2. 620 5088 56204 11983 5215 68450 0.278 3. 594 0.278 0. 264 48.531 1416 0.277 13 184. 42 0.908-2. 840 5155 61408 12409 5284 70812 0.283 3.532 0.283 0.266 49.064 1459 0.282 14 184. 85 0. 916-3. 060 5213 66714 12782 5343 72945 0.287 3.484 0.287 0.268 49. 518 1496 0. 285

Figure 1. Example: The draft correction factor and the position factor for a bulk-carrier

An example of positioning of draft marks according the innovation presented in this patent claims for a bulk-carrier built recently in Croatian shipyards.

Figure 2. Example: The suggested alternative placement of draft marks on ship's side for a bulk-carrier