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Hidrostatics of a Deflected Ship Hull

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Hidrostatics of a Deflected Ship Hull Displacement of a Deflected Ship Hull Kalman Ziha1 (M) Alternative position of draft marks nearby the load line Plimsoll mark LL LCF 0.6m 0.6m Traditional position of draft marks This note summarizes relevant approximations based on permanent waterplane characteristics for a more accurate assessment of the effects of longitudinal deflections of an elastic ship's hull on drafts and displacement during marine surveys of merchant ships. The possibility of a different practice for placement of draft marks alongside a ship, ensuring the same precision in displacement assessment of a deflected and trimmed hull by only two draft observations, is investigated by employing the waterplane properties. Correction factors for conventional ships, based on waterline coefficient for changes of hydrostatic load, arising due to hull deflections, are also summarized. The results are demonstrated on a bulk-carrier built in Croatia as an example. Nomenclature __________________________ Awl=area of the waterlplane; MT1=moment to change trim one unit; d Bwl=beam of the waterlplane; M =change of the bending moment; d Cd=correction factor for draft of a deflected hull; Q =change of the shear force; CM=correction factor for bending moments; TP1=tons per unit of immersion; CQ=correction factors for the shear force; xd=positions of equal equivalent and observed drafts; CWP=waterline coefficient; w=hull deflection in general; d=draft in general; Greek symbols IL=moment of inertia of the waterline about a γsea=specific gravity of sea water; transverse axis through the center of flotation; ∆=displacement in general; LCF = center of flotation of the waterlplane; Subscripts Lwl=length of the waterlplane; a, m, f=related to aft, mean and forward; Superscripts __________ 1 e, s, o=related to equivalent, standard and observed; Associate professor, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Croatia d=related to deflected hull Introduction In practice of a draft survey, the means of the drafts A ship's displacement plays the most important role in measured on draft marks placed on ship’s port and the validation of ship's operational efficiency. starboard sides, not necessarily exactly on the aft and Nevertheless, the determination of displacement is not forward perpendiculars and in the midship section, are always accurate. Numerous related conditions on-board recalculated to drafts on positions in virtual coincidence are practically imperceptible and immeasurable. Some with respective perpendiculars and midship section, Fig. uncertainties come from different global, local, thermal, 1., and are designated as observed drafts aft, amidships longitudinal or transverse, as well as permanent or and forward, as shown: o o o temporary deformations of an immersed ship hull. dda ,,m df . Additionally, a hull is subjected to fouling, corrosion, Reading and averaging both port and starboard draft damages, reparations and aging. Normally in the end, marks is useful but rarely done in service due to the hull deformations cannot even be considered in practical expense. The standard mean draft amidships used for determination of the displacement on-board during draft conventional hydrostatic calculations during the and deadeight surveys in the ship's service. Hence, it is deadweight survey of a hypothetically rigid ship hull on nearly impossible to accurately determine the ship's an assumed even keel position, Fig. 1., is obtained as the displacement. Although ships operate under different mean of the observed drafts aft and forward as follows: loading conditions and with widely varying amounts of o o trim and hull deflections, the commonly used hydrostatic d a + d f d s = (1) particulars are traditionally defined for the ship floating at m 2 successive plane waterlines parallel to each other and The effect of a small trim on displacement can be usually parallel to the base. In most cases when the trim assessed on the basis of the known position of the is not too great and the deflection is small, however, it is longitudinal center of flotation LCF, and superimposed entirely satisfactory, to make use of approximate practical during a deadweight survey to the displacement of a ship calculations based on hydrostatic particulars and ordinary hypothetically on an even keel (Comstock, 1967) and displacement curves, otherwise numerical lengthwise floating on a standard mean draft (1). integration over inclined and deflected sections using The ship hull deflection is usually considered as hog or Bonjean’s curves is more appropriate (Comstock, 1967). sag only amidships, defined as the deviation of the This note tries to add impetus to a more accurate and observed draft amidships from the standard mean draft practical assessment of a ship's displacement provided amidships (1) and can be presented as: primarily for deadweight survey of loaded merchant ship s o (Durham, 1982). A comprehensive procedure applicable wm = d m − d m (2) during marine surveys on-board for relatively small It follows from (2), that the deflection amidships is longitudinal deflection effects of an elastic ship's hull on positive for hogging condition and negative for sagging drafts and displacement is suggested. The displacement condition, Fig. 1. assessment is based on standard hydrostatic particulars A commonly adopted method of marine surveys for derived for a ship's hull as a rigid body, as well as direct assessment of the effects of the hull longitudinal observations during a draft survey. The idea presented in deflection on the ship displacement is to perform standard the note makes use of a parabolic approximation of the hydrostatic calculations with an equivalent value of draft deflection line, as do most methods. The method amidships (Comstock, 1967), denoted as "quarter mean suggested here takes the approach further by considering draft" or "mean of mean draft", as shown: the actual ship's hull form via the waterplane properties o o o w1/ 4 d a + 6 ⋅ d m + d f (Ziha, 1997). The note also demonstrates how a different d m = (3) placement of draft marks alongside a ship hull, nearby the 8 load line, may be appropriate during a draft survey. By substitution of (1) and (2) into (3), the following Suggested placement of draft marks at once provides an equivalent term explains the meaning of (3), as follows: equivalent input draft accounting simultaneously for o o o w1 / 4 o 1 d a + d f d m deflection and trim corrections for displacement d m = d m + − = assessments using only two draft readings, aft and 4 2 4 (4) forward at specified positions. The proposed placement o 1 s o o 1 of draft marks provides at least an additional accuracy = d m + ⋅ (d m − d m ) = d m + ⋅ wm checking during a deadweight survey. Finally, the 4 4 methods are illustrated by a bulk-carrier example. 1. Assessment of the drafts and longitudinal deflections Lwlaft Lwlfor Longitudinal center of flotation LCF xd xd wmCd Equivalent hull wm deflection line wm(1-Cd) x Waterplane characteristics WL A , C , I W(x) WL WP L CF e e e dm dm dm Equivalent draft Equivalent draft equal to equal to observed draft o observed draft oe dm oe da df d se m d o d o f a s dm Base line A.P. wm wmCd F.P wm(1-Cd) Lpp /2 Lpp /2 Fig.1 Notation used relating to a deflected ship hull Put succinctly, the equivalent “quarter mean” draft (3) for assessment of a displacement of a deflected hull is A second order symmetric parabola is often used to obtained by modification of the mean of draft readings on present the deflection line of the ship's hull: port and starboard sides amidships for one quarter of the x 2 wx()= w (6) deflection observed amidships (2) during a draft survey. m 2 The term (4) will be subjected to further critical (/Lwl 2) investigation, especially with respect to the constant draft correction factor due to deflection amounting to 1/4. Let The parabolic deflection line after rectification us assume a more general case of an equivalent draft (3) represents the equivalent waterline defining the actual and (4), when instead of a constant 1/4, a variable draft displacement of a ship as a rigid body, Fig. 1. It is correction factor Cd and its inverse denoted as draft obvious that the deflection line of a ship’s hull is neither symmetrical nor parabolic, but the deviations of the correction coefficient cd = 1/ Cd are introduced: parabolic form are usually of limited order of significance o o o e da + 2dm (cd −1) + d f o (Ziha, 1997). Experimentally and numerically dm = = dm +Cd ⋅wm (5) determined hull deflection (Mackney and Ross, 1999) 2cd show that it can be satisfactorily fitted by parabola. On Note that for Cd=1/4 (cd=4) the equivalent draft (3) the other hand, it is not practical to determine the hull appears as a special case of the more general term for deflection shape on board more precisely; moreover, in equivalent draft (5). In the sequel, a rational and more most cases it is impossible. accurate method for assessments of the draft correction A further assumption about the position of the maximal factor Cd based on an assumption of parallel ship's sides deflection close to the center of flotation LCF, since the for small parabolic deflections for true waterplane exact position is practically indeterminable, may lead to geometric characteristics, will be investigated. simplification of draft survey procedure without 2. Assessment of the hull deflection effects significant effect on displacement calculation accuracy. The hydrostatic characteristics considering small the moment to change trim one unit MT1 and tons per unit longitudinal deflections of the ship hull depend mostly on of immersion TP1 in (8) and can be expressed in waterplane geometrical properties, Fig.
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