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Basic Stability – Guide 2… Calculations Home Page Home Page Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll Guide 2 – Stability Calculations This guide will cover the following… • Loadline, Fresh Water Allowance • Dock Water Allowance • Draft, Mean Draft, Trim • Displacement and Block Coefficient • Hydrostatic Tables, TPC • Movement of G in the transverse plane • Movement of G in the longitudinal plane • Free Surface and Loll Guide 3 (the third and final guide in this series) The next guide will cover stability calculations using MV Twosuch , an excerpt from a ship’s stability booklet that will be used for examination purposes. by Stevehdc 1 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll Loadlines Loadlines from a Ship Stability perspective often involve calculations to determine how much to sink the summer loadline in dock water so that the vessel will be on her Top of F summer marks when entering salt water. Fresh Water Allowance (FWA) Top of S Assume a vessel loaded in Fresh Water of RD 1.0 so that the water level is at the TOP of the F load line. If the vessel was then placed into Salt Water of RD 1.025 the vessel would float with the water level at the TOP of the S loadline due to the density of the water changing. FWA Fresh Water Allowance can be found in the ship’s stability manual. 2 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll Dock Water Allowance ( DWA ) Calculation The number of millimetres by which the Summer Load Line can be submerged in Dock Water so that the vessel will be at its Summer Load Line when the vessel To determine the DWA enters Salt Water (density 1025 kg/m³) (ퟏퟎퟐퟓ − 풅풐풄풌 풘풂풕풆풓 풅풆풏풔풊풕풚) Dock Water Allowance ( DWA ) - Calculation 푫푾푨 = 푭푾푨 × A calculation is required to determine how much you can (ퟏퟎퟐퟓ − ퟏퟎퟎퟎ) sink your Summer load line below the water at a river berth, so you can be on your Summer Load Line when entering the (ퟏퟎퟐퟓ − 풅풐풄풌 풘풂풕풆풓 풅풆풏풔풊풕풚) 푫푾푨 = 푭푾푨 × ocean (ퟐퟓ) FWA units millimetres DWA units millimetres Orals Question A common Orals question is Calculation of DWA The following examples will assist you in becoming competent with this important calculation 3 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll Dock Water Allowance - Calculation A vessel is loading cargo in Dock Water density 1012kg/m³, if the vessel has a FWA of 160 mm, how much can the Summer Load Dock Water Allowance - Calculation Line be submerged in Dock Water, so that the vessel will float at her Summer Marks on entering Salt Water? (density 1025 kg/m³) (ퟏퟎퟐퟓ − 풅풐풄풌 풘풂풕풆풓 풅풆풏풔풊풕풚) 푫푾푨 = 푭푾푨 × Try the following examples to check your ability to carry out (ퟏퟎퟐퟓ − ퟏퟎퟎퟎ) this important calculation. (ퟏퟎퟐퟓ − ퟏퟎퟏퟐ) 푫푾푨 = ퟏퟔퟎ × Question FWA Density (ퟐퟓ) mm kg/m³ 푫푾푨 = ퟖퟑ. ퟐ 풎풎 1 150 1016 2 120 1006 3 110 1018 4 110 1012 Answers shown on next page … 4 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll Dock Water Allowance - Calculation Dock Water Allowance - Calculation (ퟏퟎퟐퟓ − ퟏퟎퟏퟔ) 푫푾푨 = ퟏퟓퟎ × (ퟐퟓ) 1 Question FWA Density 푫푾푨 = ퟓퟒ 풎풎 mm kg/m³ (ퟏퟎퟐퟓ − ퟏퟎퟎퟔ) 푫푾푨 = ퟏퟐퟎ × 1 150 1016 (ퟐퟓ) 2 2 120 1006 푫푾푨 = ퟗퟏ. ퟐ 풎풎 3 110 1018 (ퟏퟎퟐퟓ − ퟏퟎퟏퟖ) 푫푾푨 = ퟏퟏퟎ × 4 110 1012 3 (ퟐퟓ) 푫푾푨 = ퟑퟎ. ퟖ 풎풎 (ퟏퟎퟐퟓ − ퟏퟎퟏퟐ) 푫푾푨 = ퟏퟏퟎ × 4 (ퟐퟓ) 푫푾푨 = ퟓퟕ. ퟐ풎풎 5 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll Displacement The total weight of the vessel and everything on board that Draft Marks … how to read vessel. (Often abbreviated to 'W‘.) (assume the blue lines represent Q. How can we determine the displacement of a vessel? the water level) A. By observing the draft. 1.30 metres Draft Sometimes written as "Draught" The measurement of "how deep 1.20 metres the vessel sits in the water" This is measured at specific points of the vessel...eg. the forward draft or after draft. Mean Draft 10cm The mean draft is the arithmetical mean of the fore and aft drafts. 2 That is the fore and aft drafts added together and divided by 2. 1.10 metres 10cm Trim The difference in draft readings between the forward draft 1M 10cm marks and the after draft marks. 1 metre 6 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll Trim (by head or stern) Mean Draft and Trim If the forward reading is larger, the vessel is considered to be trimmed by the head. Consider a vessel with the following drafts: If the after reading is larger, the vessel is considered to Fwd draft = 3.60m be trimmed by the stern. Aft draft = 3.80m Find mean draft and the trim of the vessel Calculations for mean draft and trim are commonplace on board ship 푓푤푑 푑푟푎푓푡 + 푎푓푡 푑푟푎푓푡 푚푒푎푛 푑푟푎푓푡 = 2 Hydrostatic Table 3.60 + 3.80 This table is found in the Stability manual on 푚푒푎푛 푑푟푎푓푡 = 2 board the vessel. The table lists variables used in the calculation 풎풆풂풏 풅풓풂풇풕 = ퟑ. ퟕퟎ풎 of stability. On smaller vessels, the mean draft is calculated 푇푟푖푚 = 푎푓푡 푑푟푎푓푡 ~푓푤푑 푑푟푎푓푡 and used to enter the hydrostatic table. 푇푟푖푚 = 3.80~3.60 Displacement and other variables can then be 푻풓풊풎 = ퟎ. ퟐퟎ풎 풃풚 풕풉풆 풔풕풆풓풏 determined by inspection. On larger vessels a further calculation to convert mean draft to draft at the LCF is required. 7 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll Hydrostatic Table (extract from stability booklet M.V. Twosuch) Hydrostatic Displacement TPC MCT 1 cm LCF KM Draft (m) (tonnes) (t-m) (m aft 0) (m) 2.60 156.5 1.168 1.438 -1.072 3.94 2.65 162.5 1.172 1.465 -1.065 3.91 2.70 168.0 1.180 1.480 -1.060 3.89 2.75 174.0 1.185 1.500 -1.050 3.87 If the table is entered with a mean draft of 2.60m the values associated with this draft can be viewed … our Displacement would be 156.5 tonnes and all the other values in the table in this row would be valid for this draft. If the vessel had a draft of 2.75m the Displacement would be 174.0 tonnes. If the vessel had a displacement of 168 tonnes, the mean draft would be 2.70 metres. 8 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll TPC Tonnes per centimetre immersion, the amount of weight in Calculation using TPC tonnes required to change the draft of the vessel by 1 cm Vessel can submerge the Summer If a vessel is box shaped, it would have the same TPC value Load Line by 83.2 mm or 8.3cm. irrespective of its draft. How much cargo can be loaded if the vessel has a TPC value of 8? Ships vary in shape as their draft changes and consequently the TPC will vary as the draft changes. Look at how the Hydrostatic table shows change of TPC value with change in draft. 퐴푚표푢푛푡 푡표 푙표푎푑 = 푠푖푛푘푎푔푒 × 푇푃퐶 퐴푚표푢푛푡 푡표 푙표푎푑 = 8.3 × 8 Up to now we have determined the change in draft measured in mm or cm. By using TPC we can convert a change in draft to an amount 푨풎풐풖풏풕 풕풐 풍풐풂풅 = ퟔퟔ. ퟒ 풕풐풏풏풆풔 of weight in tonnes. 9 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll KG Height of the centre of gravity of the ship above the baseline, weight referred to as KG. (from the keel ‘K’ to the centre of gravity ‘G’) Vessel with Movement of G – Load and discharge weight on The height of G will change as weights are loaded or deck discharged. It is important for the person in charge of G monitoring the stability of the vessel, to know how G will move in all cases. The basic principles of movement of G are as follows: G moves towards the loaded weight Weight is discharged G moves away from the discharged weight G G moves away from the discharged weight 10 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll Movement of G - a weight already on board Assume the weight is already on board and is shifted on deck weight Vessel with weight on deck The height of G will not change as the weight height will not change G Movement of G in this case: weight G moves parallel to the shifted weight Weight is shifted G G moves parallel to the shifted weight 11 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll Movement of G - Lifting a Weight When a weight is lifted by a crane or derrick, the The weight is weight is considered to act at the head of the crane or considered to derrick. Subsequent lifting or lowering of the hoist act at the head wire will not change the position of the vertical centre of gravity of the weight. of the crane weight This is an important consideration as the centre of gravity of the vessel, “G “ will now rise a considerable amount as the weight is initially lifted and remain at that height until the crane or G moves G2 derrick head is lowered. towards the head of the crane when G1 the weight is lifted clear of the deck 12 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll G moves towards the loaded weight Calculation – Vertical Shift of G In order to calculate the shift of G from its original A weight of 10 tonnes is loaded on the position to its new position the following formula is used: centre line.
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