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True mean draught (TMD) When a ship trims due to shifting a weight, i.e. no change of displacement, the only draught which does not change is the draught at the longitudinal centre of flotation. It is this draught which will give the appropriate displacement on the hydrostatic tables, and it is called the true mean draught. The position of the LCF is therefore critical to a draught survey. The difference between the true mean draught and the arithmetic mean draught is known as the layer correction. ^ Some stability information books tabulate trim factors, forward and aft, but no position for the longitudinal centre of flotation (LCF) forward of the aft perpendicular(AP). The LCF can be found from the trim factors by the following formula: ^ Trimmed hydrostatics Some ships are supplied with 'trimmed hydrostatics'. These normally consist of several sets of hydrostatic data each one calculated for a particular trim. They may be in 20 cm steps covering the range of trims over which the vessel is expected to operate. Each set of hydrostatic data consists of displacements tabulated against draught for a particular density. The densities may be in increments of 0.005 from 1.000 to 1.025 and the draughts in 5 cm steps. Such tables avoid the need for both the 1st and 2nd trim corrections and also the density correction which are described within the chapter Assessment of underwater volume on pages 16 to 37. Trimmed hydrostatic tables need to be interpolated for draught, density and trim in order to find the correct displacement. This interpolation is fairly difficult and needs careful thought in order to achieve an accurate result. Check the use of trimmed hydrostatics in the introduction to the stability information book. ^ The displacement, deadweight, tonnes per centimetre immersion (TPC) and moment to change trim per centimetre (MCTC) for salt water are shown against the true mean draught (TMD) in the deadweight or displacement scale. It may also show the same for fresh water. If only salt water values are givert then the scale should be entered with the TMD in actual observed density. Calculations should be carried out: with these figures as the density correction will take care of the adjustments at a later stage. The scale will also show summer load draught and the lightship draught. It will relate the final TMD to the final displacement. Study it carefully to make certain of the weight to volume relationship. ^ The capacity plan shows all the cargo compartments, ballast spaces and bunker tanks on the ship. Capacity tables list every space in the ship which may be used for cargo, ballast, stores, fuel, lubricating oil and fresh water. The position of each space is indicated by the number of the ship's frames at each extremity of the space. The volume of each space, in cubic metres, is listed for: Grain space  the gross volume measured to the ship's side plating. Bale space  the nett volume measured to the inside of the frames or spar ceiling (cargo battens). Spaces for liquid only are tabulated in either cubic metres or the number of tonnes of the liquid which the tank normally holds, specifying the density used to calculate those tonnes. If the tables give cubic metres then these must be multiplied by the observed density to find tonnes. If the tables give tonnes then they must be divided by the density of the table and multiplied by the observed density. ^ Sounding tables are separate tables, often found in the care of the chief officer and/or the chief engineer. The tables may be calibrated with either soundings or ullages. The calibrations may use cubic metres (i.e. tonnes of fresh water) or the average density of the liquid which is normally carried in the tank and give tonnes of that liquid. For accurate assessment of the quantity of liquid in any tank, the actual density of the liquid should be determined and the quantity recalculated. ^ Sounding correction tables The sounding tables will have been calculated for the ship on an even keel. Correction tables should accompany any sounding table of a tank for which the sounding pipe is not at the longitudinal centre of the tank. The table should give the correction for any sounding and for each metre of trim of the ship over the normal operating range of trims and require interpolation for the actual trim. In the absence of such tables, calculations will have to be made from the original plans. ^ The stability information book may include a table to apply the corrections for trim. Investigate carefully whether this includes both the 1st. and 2nd. trim corrections. See pages 30 to 33. Position of marks The stability information book may provide a correction to apply to the appropriate draught readings to correct the reading, to the value it would have had, at the correct position. See pages 21 to 26. Hull deflection The stability information book may provide a special means of calculating the vessel's hull distortion correction when calculating an accurate underwater volume. See pages 26 to 30. ^ British Standards Institute (BSI), International Standards Organisation (ISO) or the Zeal certificate of conformity, provides the appropriate correction to apply to the hydrometer By kind permission of G H Zeal Ltd. Hydrometer and certificates ^ General arrangement plan The general arrangement plan shows the layout of the ship and indicates all the spaces within it. It gives the position of all the spaces, their use and capacity. Other plans More detailed plans of ballast tanks and bunker tanks may be necessary. If the vessel is trimmed it may be important to know the horizontal surface area of liquid in the tank and the relative position of the sounding pipe in order to assess the quantity of liquid in the tank accurately. LIGHTSHIP The lightship weight is that which has been determined during an inclining experiment. It includes: the ship and its full equipment, engine room spares, water in the boilers to working level and lubricating oil in the engines. It does not include: personnel, cargo, fuel, stores and water. ^ The inclining experiment may have been performed a considerable time ago, but, over a period of years, the lightship weight will increase. This is due to the changes in the equipment, the build up of paint over the ship, the storage of old equipment, mud in the ballast tanks, the accumulation of dunnage etc. This phenomenon is known as the growth of lightship and is thought to amount to about 0.2% of the light displacement per annum. This growth is accounted for in the lightship constant. ^ Vessels which regularly assess their lightship weight find that the weight from their calculations differs from the tabulated value in the stability information book. This difference is named the lightship constant at that particular draught survey. A record should be kept of the lightship constant at each draught survey. It may not be a constant value since it is the result of inaccuracies of calibrations, accumulations of sludge, unsymmetrical hull distortion and many other factors. It can only be used for a guide to the consistency of results and the variations experienced on previous surveys. When carrying out a deadweight survey the value of the lightship constant may become more significant and a record of previous values is then important. ^ The underwater volume of the ship, and ultimately its displacement, is normally found by carefully reading and analysing the draught marks and by carefully establishing the density of water in which the vessel is floating. The corrected mean draught is used to enter the hydrostatic tables in the stability information book and to find the appropriate displacement equivalent to this draught and density. This value must then be corrected to determine the precise weight of the ship in its present circumstances. ^ The draught survey is based upon the accurate reading of the draught marks, therefore no effort should be spared to achieve accuracy. Draughts should be measured to two decimal places, that is to the nearest centimetre. Before cargo operations commence, the water density and all six draught marks should be read, recorded and comments made on the prevailing conditions. During the time that the readings are being made, no transfer or discharge of liquid of any sort, or movement of any weight within the ship, should be allowed. The draughts and density should be taken again on the completion of the loading or discharging operation. ^ In turbulent conditions there may be waves, swell, pitching and rolling to take into account. In these conditions, the wave pattern should be studied to establish the wave cycle. During a series of average waves the mean of the highest and lowest draught readings should be recorded. A total of 12 mean readings should be obtained. The highest and lowest means should be rejected and then the average of the remaining ten will give the most accurate reading possible under the circumstances. The forward, aft and midships draught measurements should all be found in a similar fashion. QUESTION 1: The following are mean draught readings (in metres) over an observed cycle of waves. Calculate the appropriate draught. 11.25 9.80 11.40 9.70 11.35 9.75 11.30 9.60 11.00 9.90 11.25 9.70 ANSWER: Reject 11.40 and 9.60 m. Add remainder = 105. Estimated draught reading = 105/10 = 10.50 m. ^ A measuring device may be used to improve the accuracy of the draught measurement. Such devices are based on the principle that the turbulence on the surface of the water does not extend down to any great depth. They use a long, flexible, open ended, weighted hose projecting downwards to below the turbulence. The device is held directly in front of the draught marks and, after allowing a few seconds for the tubes to fill with water, the mean water level is indicated by the float. The float may have a small rise and fall, but this will be minimal compared with the wave motion. The device is difficult to use at the bow and the stern. It should be held close enough to the draught marks under the overhang of the bow and the stern to avoid parallax. The device may be attached to the hull by a strong magnet. A statement describing the prevailing sea conditions should be included in the survey report to avoid a dispute later. ^ Every attempt should be made to read the draughts on the offshore side of the vessel although, in some situations, this may prove to be impractical or even dangerous. In such an event, the onshore marks should be read and the other side calculated with the help of a manometer. The manometer should comprise of a short length of clear, rigid, plastic tube fitted to each end of a hose, to facilitate the measuring of the water levels. If possible the hose should stretch the full beam of the vessel and the measurements should be taken at the extreme breadth. The outboard reading is found by adding or subtracting the manometer reading (2d) to the inboard draught. When this proves impossible, then the mean draught at the centreline, may be calculated using similar triangles. The levels must be measured from the same base line, and taken at equal distances from the centreline on both sides of the vessel. All air must be excluded from the hose and the water levels in both tubes kept at a height which is higher than the deck at the centreline. The heights of water levels, on both sides of the ship, are measured above the deckline (h) or some other fixed level. The difference between the two heights is then halved and the result (d) is added to, or subtracted from, the one draught reading to obtain the mean draught at the centreline. QUESTION 2: The port draught midships = 8.00 m. The starboard side is to be found by manometer, where the readings are taken at 8.50 m on either side of the centre line. The vessel's full beam = 20.85 m. Calculate the midships mean draught (ie. centreline draught) if there is a difference of 25 cm between the two readings of the manometer and the starboard reading is the higher. ANSWER: Effective beam =8.50х2 = 17.00m. By similar triangles 0.25 /17 = d / 20.85 d = 20.85 x 0.25 /17 = 0.307 m full beam difference. Half beam difference =0.307/2 = 0.153m. Centreline draught = 0.153 + 8.00 = 8.153 m. Note: It may be more practical in some situations to measure the midships freeboard and from this calculate the midships draught. ^ Draught gauges may be very helpful as a check, but should never replace the reading of draughts using the fixed draught marks on the ship's hull. SQUAT While measuring the draught, when there is a strong current running and there is water depths of less than twice the draught of the vessel, the draught readings may be misleading, due to the effects of squat. The survey report should include reference to possible squat effects, even if a suitable correction to the draught readings cannot be determined. ^ Firstly, correct observed draughts, forward, aft and midships, for the effect of any list or heel by calculating the mean of port and starboard in each case. Note; see notes on page 26, as there may also be a list correction (in tonnes) to apply to the displacement. Secondly, when the vessel is trimmed and the vessel's draught marks are not sited at the correct position on the perpendiculars; corrections to the observed draughts must be applied. This incorrect positioning of the draught marks may be termed misplacement of marks, it is shown in the photographs on pages 22 and 23. АР aft perpendicular FP forward perpendicular LBP length between perpendiculars D AP draught at aft perpendicular Da draught at aft draught marks D M draught at midships Dm draught at midships draught marks D FP draught at forward perpendicular Df draught at forward draught marks Misplacement of marks forward Misplacement of marks midships Misplacement of marks aft Forward correction = (apparent trim x distance D FP to Df)/(distance Da to Df) Aft correction = (apparent trim x distance D AP to Da)/(distance Da to Df) Midships correction = (apparent trim x distance D M to Dm)/(distance Da to Df) Where: apparent trim = the difference between Da and Df Sign convention: If the direction of misplacement of the draught mark from the perpendicular (or midships position) is the same as the direction of the trim, then the correction is negative () when applied to the observed draught. Note; even keel would not require the above corrections to be applied. QUESTION 3: With reference to the following particulars, calculate the correct draughts, forward, aft, and midships, if the observed draughts are: forward 6.35 m aft 7.88 m midships 7.12 m Position of draught marks: Forward: 0.15 m aft of line of stem at summer load line (SLL). Rake of stem = 22°. summer load draught = 10.471 m. Aft: 6.00 m forward of AP. LBP = 170 m. ANSWER: Apparent trim =7.886.35 = 1.53m Arithmetical mean draught = 7.115 m Midships draught =7.12 Vessel not suffering from hog or sag Distance from SLL 10.471  6.350 = 4.12Г m By simple trigonometry Tan 22° x 4.121 = 1.665 m Distance from FP 1.665 + 0.15 = 1.815 m Length between marks = 170  (6.0 +1.815) = 162.185 m Correction to draught = 1.815 x 1.53 / 162.185 = 0.017 m Draught forward = 6.350  0.017 = 6.333 m Correction aft. = 6.00 x 1.53 / 162.185 = +0.057 m Draught aft. = 7.88 + 0.057 = 7.937 m ^ The corrections to the perpendiculars and midships assume that the keel of the vessel is straight. When the vessel is hogged or sagged, these corrections may no longer be correct. The tabulated corrections in the stability information book, or the formulae on the previous page, must be corrected to the particular circumstances. The easiest method to find these corrections would be to use the trim between the midships mark and the particular end draught then calculate using this half length trim, the half length and the distance of the misplacement. Repeat this procedure at the other end draught mark with the similarly modified trim, the half length and the distance of misplacement. EXAMPLE: Observed draughts forward 6.00 m midships 6.40 m aft 7.40 m. Distance of forward mark from FP = 2.0 m aft Distance of aft mark from AP = 5.0 m forward. LBP =100m Total trim = 1.40 m AMD = 6.70 m. Therefore the vessel is hogged. Trim forward to midships = 0.40 m Forward correction = 2 x 0.4 / (50  2) =  0.017 m Forward draught = 5.983 m Trim aft to midships = 1.0 m Aft correction = 5.0 x 1.0 / (50  5) = +0.111 m Aft draught = 7.511 m ^ When a vessel lists, it often rises in the water. This means that the mean of the side draughts is a centreline draught which is less than the actual draught that would have been observed, had the vessel been upright. This may be ignored for small angles of list, however, if the draught survey is to be carried out on a vessel which has suffered a cargo shift or is lying at a large angle of list, then it should be calculated. The correction, in tonnes, to be applied to the displacement, is by the formula: Correction for list = 6 (TPC_{2}  TPC_{1}) x (d_{2}  d_{1}) tonnes Where: d_{2} and d_{1} = midship draughts on each side. TPC_{1} = the TPC equivalent to the draughts d_{1} TPC_{2} = the TPC equivalent to the draughts d_{2} Sign convention: Always positive (+). QUESTION 4: Vessel is listed 5°. The draughts midships are: Port 6.00 m (equivalent TPC 32) Starboard 8.00 m (equivalent TPC 34) ANSWER: Correction = 6(34  32)(8.00  6.00) = 24 tonnes positive (+). Note; it will normally be a small correction. ^ When the observed draughts have been corrected for list and displacement of marksman arithmetical mean of the forward and aft draughts must be calculated, ie. the arithmetical mean draught (AMD). Compare the AMD with the corrected midships draught to establish whether the hull is distorted. The AMD should equal the draught midships if the ship is neither hogged or sagged. If the actual draught is less than AMD then the vessel is hogged. If the actual draught is greater than AMD then the vessel is sagged. 
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