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Page 1: Draft Survey Manual

DRAFT SURVEY

by Dirk Rombaut

DECEMBER 2003 All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, including photocopying and recording, or by any information storage and retrieval system, without prior written permission of the Société Générale de Surveillance S.A.

Page 2: Draft Survey Manual

Preface It is internationally accepted in bulk trading that cargo measurement by draft survey is the most convenient and economical way of establishing the weight of cargo loaded on board a vessel. However, many operators in the industry consider draft measurement as a doubtful practice in which the cunning of the surveyor is more important than his professional expertise and experience. As it often happens, this conviction is both right and wrong at the same time. In fact, in many parts of the world, including some "industrialized" countries, this technique is still surprisingly empirical and based on local habits. In such cases, cargo measurement by draft survey ends up in a fish-market type of negotiation between the surveyor on one side and the ship's officers on the other. Yet, increasing value of raw materials commands a more professional approach. Following this trend SGS recognizes the need of experienced and competent draft surveyors. Experience has shown that draft surveys can be carried out by non-seafaring people provided they have been properly instructed in both theory and practice. To support this instruction, a need developed within SGS for an adequate training manual. It should be evident that if cargo is measured by SGS affiliates at both loading port and discharge port, it is of the utmost importance that the draft survey procedures used are the same. In an attempt to standardize procedures within SGS, the first comprehensive draft survey manual was written in 1967 by SMES (Rotterdam). However, this was designed for ex-captains of seagoing vessels and somewhat difficult for non-specialists to understand. Today, the Draft Survey Manual, prepared by SGS Belgium, is a modern, readily understandable document. This manual, when properly digested and applied, will contribute to enhance the professionalism of our Marine Services and to change some of the unfavourable opinions which are still delaying proper application of cargo measurement by draft survey. No attempt should be made to read the manual from beginning to end. This would be a rather discouraging task. Each section should be read and fully understood before moving on to the next. For the benefit of those studying the subject for the first time, the manual explains the basic principles of draft survey procedures. For those who have no seafaring experience, certain aspects are explained in greater detail than might otherwise be necessary. Furthermore - bearing in mind that the manual may be used by SGS representatives whose first language is not English - it has been written in a clear and uncomplicated way. It includes an explanation of technical terms with translations from English into French, German and Spanish. Draft survey will involve the surveyor in the measurement of a variety of vessels of different types and nationalities - each with its own characteristics. The high level of accuracy required depends on careful attention to detail and the proper handling of unusual circumstances which may arise from time to time. Here, there is no substitute for proper practical training and experience - the mere study of this manual is not enough. It seems probable that in the years to come various additional corrections and new forms of measurement apparatus may be developed and this manual will therefore need to be revised from time to time in order to keep abreast of modern practice. Suggestions for improving this manual are welcome and can be sent to the author, Dirk Rombaut, at SGS Belgium, Antwerp.

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Page 3: Draft Survey Manual

Table of Contents 1 GLOSSARY OF TERMS - ENGLISH 2 GLOSSARY OF TERMS - FRENCH 3 GLOSSARY OF TERMS - GERMAN 4 GLOSSARY OF TERMS - SPANISH 5 INTRODUCTION TO DRAFT SURVEY 6 READING OR MEASURING THE DRAFT 6.1 Introduction 6.2 Reading the draft 6.3 Measuring the draft 6.4 Calculation of the mean drafts fwd, aft and midships 6.5 Exercise m/v Mindiv 7 PERPENDICULAR CORRECTION 7.1 Introduction 7.2 Position of the draft marks 7.3 Principle of perpendicular correction 7.4 Formula 7.5 Exercise m/v Mindiv 8 CORRECTION FOR HULL DEFLECTION 8.1 Introduction 8.2 Types of deformation 8.3 Factors which can influence the deflection 8.4 Formula 8.5 Exercise m/v Mindiv 9 CALCULATION OF THE CORRESPONDING DISPLACEMENT 9.1 Introduction 9.2 Definitions 9.3 Hydrostatic particulars 9.4 Exercise m/v Mindiv 10 CORRECTING THE DISPLACEMENT FOR TRIM AND LIST 10.1 Introduction 10.2 Definitions 10.3 Principle of trim correction 10.4 First Trim Correction (FTC) 10.5 Second Trim Correction (STC) 10.6 Total Trim Correction (TTC)

10.7 Displacement corrected for trim 10.8 List correction 10.9 Exercise m/v Mindiv

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Page 4: Draft Survey Manual

Table of Contents 11 CORRECTING THE DISPLACEMENT FOR DENSITY 11.1 Introduction 11.2 Definitions 11.3 Sampling of the surrounding water 11.4 Measuring the density 11.5 Displacement corrected for density 11.6 Exercise m/v Mindiv 12 DETERMINATION OF THE DEDUCTIBLE LIQUIDS 12.1 Introduction 12.2 Definitions 12.3 Ballast water 12.4 Fresh water 12.5 Bunkers 12.6 Net displacement 12.7 Other items 12.8 Exercise m/v Mindiv 13 THE CARGO WEIGHT AND CONSTANT 13.1 The cargo weight 13.2 The constant 13.3 Exercise m/v Mindiv

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Page 5: Draft Survey Manual

Section 1: Glossary - English

SECTION 1

GLOSSARY OF TERMS - ENGLISH

Term or abbreviation Definition and explanation aft At or towards the rear part of the vessel. aft draft Draft, measured at the aft part of the vessel. aft perpendicular An imaginary vertical line, at right angles to the keel,

passing through the first frame and therefore located on or nearby the ship's rudder post.

AP Aft perpendicular. after peak tank A compartment situated at the extreme rear of the vessel

often used to contain fresh water or ballast water. ballast Water pumped into or out of the vessel in order to maintain

stability. ballast tanks Tanks aboard the vessel especially designed to receive

ballast water or, in the case of tank vessels, cargo tanks used to contain ballast.

breadth Maximum width of the ship. boiler feed water tanks Tanks provided aboard the vessel to contain water used

for the production of steam. bilges Spaces at the bottom of the engine room or pump rooms

where water is allowed to accumulate. As the bilges usually also contain waste oil, they may not be discharged within the port limits. For draft survey purposes, the quantity of liquid in the bilges should be controlled before and after loading or discharge, so that any change in quantity can be detected.

bunker tanks Tanks intended to contain fuel oil either for steam raising

purposes or for the provision of power to the main engines and auxiliaries.

calibration tables See tank sounding tables centre of flotation The point around which a ship tips often called the "tipping

centre".

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Page 6: Draft Survey Manual

Section 1: Glossary - English

cofferdams fwd and aft These terms apply more particularly to ocean tankers,

coastal tankers and tank barges. They are empty spaces provided in order to separate the cargo tanks from the machinery space aft, from the forward peak, and other forward parts of the ship. Cofferdams frequently contain water, either intentionally or accidentally, and should therefore always be sounded both before and after cargo is measured by draft survey.

constant The difference between the light ship weight according to

ship's documents and the net empty survey displacement after deducting all measurable weights.

deadweight This is the weight of a vessel's cargo, fuel, water and

stores. deck line A line clearly marked on the port and starboard sides of the

vessel, amidships as required by International Load line Regulations.

deep tanks Tanks situated near to the bottom of the vessel. density (true) The mass of a volume unit of a liquid. It may be expressed

in terms of grams per millilitre, kilograms per cubic meter, pounds per cubic foots, etc.

density (apparent) Density, as defined above, but without allowing for the

buoyancy effect of the atmosphere. The apparent density of seawater, fresh water, ballast water, etc. is measured by the SGS draft survey hydrometer. This gives weights comparable to those that would be obtained by weighing a carefully calibrated container on an accurate weighbridge to obtain commercial weights.

diesel oil Fuel oil used to feed diesel engines. There are various

grades of diesel oil including light diesel oil for auxiliary engines and heavier diesel oil for main engines.

displacement The total weight of water displaced by the vessel.

Displacement includes the light ship weight and all other weights on board including cargo, ballast bunkers, etc.

displacement table/scale A table, especially prepared for each vessel, giving the

displacement corresponding to various drafts. double bottom tanks Tanks situated in the vessel's double bottom and used

either for bunkers or ballast water.

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Page 7: Draft Survey Manual

Section 1: Glossary - English

draft (draught) Depth of water from the water surface down to the bottom

of the ship's keel. draft marks A series of figures painted or welded on the vessel's hull,

usually forward, midships and aft, on both port and starboard sides and indicating the draft of the vessel at the points where the draft marks are situated.

draft survey A system of cargo measurement based on measuring the

draft of the vessel before and after loading or discharge, taking into account any changes in weight other than cargo, which may have taken place during cargo handling operation, i.e. changes in the weight of water ballast, bunkers, stores, etc.

drinkable water Fresh water for human consumption. engine water Water used for the cooling of diesel engines. even keel When the forward and aft drafts of a vessel are identical,

the ship is said to be on an 'even keel'. fore (forward) At or towards the front part of the vessel. forward draft Draft, measured at the forward part of the vessel. forepeak tank A compartment situated at the extreme forward part of the

vessel often used to contain ballast water. forward perpendicular An imaginary vertical line, at right angles to the keel and

passing through the point where the summer load line intersects the vessel's stem.

FP Forward perpendicular. free board Distance between the upper part of the deck line and the

water level. freeboard (assigned or statutory) The distance from the upper part of the deck line to the

summer load line as 'assigned' or stated in the Freeboard Certificate relating to the vessel concerned.

fresh water Not salt water (sea water). This is the water on board a

vessel for drinking, washing, etc. fuel oil (heavy) High density fuel oil used either as boiler fuel or as fuel for

main diesel engines suitably adapted for the purpose.

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Page 8: Draft Survey Manual

Section 1: Glossary - English

hogging The deflection of a vessel loaded in such manner that the

draft amidships is less than the mean of the forward and aft drafts.

hydrostatic curves A document especially prepared for each vessel indicating,

among other things, the centre of flotation or 'tipping centre' at various drafts.

keel The part of a ship extending along the bottom from stem to

stern. LCF Longitudinal centre of flotation. length between Distance between the forward and aft perpendiculars perpendiculars (LBP) measured parallel to the keel. list Inclination of the vessel from the vertical position

measured at the longitudinal midships axis. It is usually measured by means of an inclinometer giving results in degrees of angle. List can also be calculated, if necessary, from the difference between the port and starboard midships drafts.

light ship weight The weight of the vessel after completion of construction

but without fuel bunkers, stores, etc. The light ship weight is usually mentioned on the vessel's displacement scales and represents the difference between the displacement scale and the deadweight scale.

lubricants Oils for lubricating the main engine, auxiliary engines and

other moving equipment aboard the vessel. mean aft draft Average of the aft drafts on port and starboard sides. mean forward draft Average of the midships drafts on port and starboard

sides. mean midships draft Average of the midships drafts on port and starboard

sides. midships Longitudinal centre of the vessel as indicated on the hull

by the Port and Starboard load line marks.

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Page 9: Draft Survey Manual

Section 1: Glossary - English

moment The moment of a force is a measure of the rotating effect

of the force about a given point. The rotating effect will depend upon the magnitude of the force and the length of the lever upon which the force acts, i.e., the perpendicular distance between the line of action of the force and the point around which the moment is being exerted.

Moment to change The force required to change the trim of a vessel by trim 1 cm (MTC) 1 cm. This is defined as the weight - in metric tons,

multiplied the distance it is moved from the centre of flotation - in meters.

Moment to change The force required to change the trim of a vessel by trim 1 inch (MTI) 1 inch. This is defined as the weight - in long tons,

multiplied the distance it is moved from the centre of flotation - in feet.

Plimsoll line Another name for summer load mark. port side The left-hand side of the vessel as seen by an observer

facing forward. rudder post The vertical axis around which the rudder turns. sagging The deflection of a vessel loaded in such manner that the

draft amidships is greater than the mean of the forward and aft drafts.

scale drawings Vessel's plans prepared so that each centimetre of

distance on the scale corresponds to a known distance on the vessel. For example, a scale marked 1/100 means that 1 cm on the drawing corresponds to 1 m on the ship itself.

sounding Distance between the bottom of a tank and the surface of

the liquid which it contains. sounding pipe A fixed pipe through which soundings are taken. sounding tables Calibration tables giving volumes corresponding to liquid

heights. specific gravity Ratio between the mass or weight in air of a given volume

of liquid and the mass or weight in air of the same volume of distilled water. Both the temperature of the liquid and the temperature of the water must be defined. There are thus various forms of specific gravity which can lead to considerable confusion. It is for this reason that the term apparent density is preferred, as this corresponds to weights obtained by weighing on a weighbridge.

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Page 10: Draft Survey Manual

Section 1: Glossary - English

starboard side The right-hand side of the vessel as seen by an observer

facing forward. stem correction Correction applied to the mean forward draft when the

forward draft marks are not situated at the forward perpendicular.

stern correction Correction applied to the mean aft draft when the aft draft

marks are not situated at the aft perpendicular. summer load line An imaginary line, parallel to the keel passing through the

upper edge of the summer mark which corresponds to the maximum draft permitted in the summer zone in sea water.

summer mark The line, surrounded by a circle, permanently marked by

centre punch, or by welding, on the port and starboard sides of the vessel amidships as prescribed by the ship's load line certificate.

t per cm immersion The number of metric tons required to change the (TPC) mean draft of the vessel by 1 cm. t per inch immersion The number of long tons required to change the mean (TPI) draft of the vessel by 1 inch. trim Difference between the mean draft forward and the mean

draft aft, both measurements having been corrected to the forward and aft perpendiculars where necessary.

trim corrections Corrections applied to the displacement of the vessel when

the vessel is not floating on an even keel. ullage Distance between the surface of the liquid in a tank and

the top of the tank or corresponding sounding pipe.

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Page 11: Draft Survey Manual

Section 2: Glossary - French

SECTION 2

GLOSSARY OF TERMS - FRENCH Terme anglais/français aft/arrière aft draft/enfoncement arrière aft perpendicular/ perpendiculaire arrière AP after peak tank/ compartiment de poupe ballast/ ballast, lest ballast tanks/ compartiments à ballast breadth/largeur boiler feed water tanks/ compartiments pour l'eau des chaudières bilges/ fonds de cale

Définition et explication A ou vers l'arrière du navire. Enfoncement mesuré à l'arrière du navire. Ligne verticale imaginaire, perpendiculaire à la quille, passant par la première membrure et passant par conséquent sur ou proche de l'axe du gouvernail. Aft perpendicular. Compartiment situé à l'extrémité arrière du navire souvent utilisé pour recevoir de l'eau douce ou du ballast. Eau de rivière ou de mer, pompée ou refoulée par le navire de façon à ajuster l'assiette et/ou l'enfoncement du navire. Compartiments prévus spécialement pour recevoir le ballast ou, dans le cas de navires citerne, compartiments prévus pour contenir la marchandise, mais aussi utilisés pour le ballast. Largeur maximale du navire. Réservoirs du navire qui contiennent l'eau utilisée pour la production de vapeur. Emplacements au fond de la salle des machines ou des pompes où l'eau peut s'accumuler. Du fait que les fonds de cale contiennent également de l'huile usagée, ils ne doivent pas être vidés dans l'enceinte portuaire. En matière de jaugeage, les fonds de cale doivent être contrôlés avant et après chargement afin de prendre en compte tout changement quantitatif.

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Page 12: Draft Survey Manual

Section 2: Glossary - French bunker tanks/ compartiments pour hydrocarbures de soute bow/proue calibration tables/ tables d'épalement centre de flottaison cofferdams fore and aft/ batardeaux avant et arrière constant/ constante deadweight/ poids lourd deck line/ ligne de pont deep tanks/ compartiments de cale density (true)/ densité (vraie)

Compartiments conçus pour recevoir le combustible lourd (fuel-oil) pour la production de vapeur et pour la propulsion des moteurs principaux et auxiliaires. Voir stem. Tables donnant pour chaque compartiment ou réservoir le volume correspondant à la hauteur de liquide (sounding) ou à la hauteur libre (ullage). Point autour duquel le navire oscille, souvent appelé "point de bascule". Ce terme s'applique plus particulièrement aux navires citerne de haute mer, côtiers et aux péniches citerne. Ce sont des caissons creux conçus pour séparer la citerne contenant la marchandise, d'une part de la chambre des machines et, d'autre part, du compartiment avant ou de la partie avant de l'embarcation à l'avant. Différence entre le poids à vide du navire indiqué sur les documents du navire et le déplacement net à vide après déduction de tous les poids mesurables. Différence entre le poids à vide du navire et celui du navire en charge. Cela inclut le poids du chargement, des combustibles, de l'eau et de la constante. Une ligne clairement marquée sur les côtés babord et tribord au milieu du navire, au niveau de pont, comme requis par l'International Loadline Regulation. Compartiments situés près du fond du navire. Masse (dans le vide) d'une unité de volume d'un liquide. On peut l'exprimer en grammes par millilitre, kilogrammes par mètre cube, livres par pied cube, etc.

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Page 13: Draft Survey Manual

Section 2: Glossary - French density (apparent)/ densité apparente diesel oil/ diesel displacement/ déplacement displacement table/ table de déplacement double bottom tanks/ compartiments de double fond draft (draught)/ enfoncement draft marks/ marques d'enfoncement

Densité, comme définie ci-dessus, mais exprimée en termes de masse apparente dans l'air, c'est-à-dire sans correction pour la poussée exercée par l'air sur l'eau et sur les poids normalement employés dans le commerce. La densité apparente de l'eau de mer, de l'eau douce, du ballast, etc. est mesurée par le densimètre SGS et permet d'obtenir des poids comparables à ceux que l'on obtiendrait en pesant un conteneur soigneusement calibré sur un pont à bascule précis, de façon à obtenir des poids commerciaux. Combustible pour les moteurs diesel. Il y a plusieurs types de diesel, depuis le diesel léger pour les moteurs auxiliaires jusqu'au diesel lourd utilisé pour les moteurs principaux. Poids total du volume d'eau déplacé par la coque du navire; sont inclus le poids à vide du navire et tous les autres poids à bord, y compris le chargement, le ballast, les hydrocarbures de soute, etc. Une table spécialement préparée pour chaque navire donnant le déplacement correspondant aux divers enfoncements. Compartiments situés dans le double fond du navire, utilisés pour contenir soit du ballast, soit des hydrocarbures. Hauteur d'eau entre la surface de l'eau et le bas de la quille du navire. Série de chiffres peints ou soudés sur la coque, (à l'avant, au milieu et à l'arrière du navire, à babord et à tribord), qui indiquent l'enfoncement du navire aux endroits où ces marques sont situées.

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Page 14: Draft Survey Manual

Section 2: Glossary - French draft survey/ jaugeage drinkable water/eau potable engine water/eau pour le moteur even keel/ quille "horizontale" fore (forward)/avant forward draft/ enfoncement avant fore peak tank/ compartiment de proue forward perpendicular/ perpendiculaire avant FP freeboard/ hauteur libre freeboard (assigned or statutory)/ hauteur libre officielle fresh water/ eau douce fuel oil (heavy)/ combustible lourd

Système de détermination du poids d'une cargaison basé sur la mesure de l'enfoncement d'un navire avant et après chargement ou déchargement, prenant en considération toutes les variations du poids autres que celles dues à la marchandise, qui peuvent survenir pendant la manutention de la marchandise, c'est-à-dire les variations du poids du ballast, des hydrocarbures de soute, de la constante, etc. Eau potable pour l'équipage. Eau de refroidissement des moteurs diesel. Lorsque les enfoncements avant et arrière sont identiques, on dit que le navire a sa quille "horizontale". A ou vers l'avant du navire. Enfoncement mesuré à l'avant du navire. Compartiment situé à l'extrémité avant du navire, souvent utilisé pour recevoir le ballast. Ligne imaginaire verticale, perpendiculaire à la quille qui passe par le point d'intersection entre la ligne d'été et la ligne de proue. Forward perpendicular. Distance variable entre le haut de la ligne de pont et la ligne de flottaison. Distance fixe entre le haut de la ligne de pont et la ligne d'été officielle figurant sur le "certificat de hauteur libre" du navire concerné. Pour la mesure des liquides déductibles d'un jaugeage, c'est la somme de l'eau potable et de l'eau (douce) non potable qui est prise en compte. Combustible lourd utilisé pour les chaudières ou le moteur principal et spécialement adapté à cet usage.

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Page 15: Draft Survey Manual

Section 2: Glossary - French hogging/ cambrure hydrostatic curves/ coubres hydrostatiques keel/quille LCF length between perpendiculars (LBP)/ longueur entre les perpendiculaires list/ bande, gite, assiette latérale light ship weight/ poids à vide du navire lubricants/ lubrifiants mean aft draft/ enfoncement arrière moyen mean forward draft/ enfoncement avant moyen mean midships draft/ enfoncement moyen au milieu du navire

Déformation du fond d'un navire telle que l'enfoncement au milieu du navire est plus petit que la moyenne des enfoncements avant et arrière. Document propre à chaque navire qui indique entre autres, la position du centre de flottaison en fonction de l'enfoncement. Partie inférieure axiale de la coque du navire. Le centre longitudinal de flottaison. Distance entre les perpendiculaires avant et arrière parallèlement à la quille. Inclinaison du navire par rapport à la position verticale mesurée au niveau de l'axe longitudinal au milieu du navire. La bande est normalement mesurée à l'aide d'un inclinomètre donnant des résultats en degrés d'angle. La bande peut aussi être calculée, si nécessaire, par la différence entre les enfoncements babord et tribord au milieu du navire. Poids du navire après construction mais sans combustible, approvisionnements de bord, etc. Le poids à vide du navire est normalement indiqué sur les tables de déplacement du navire et représente la différence (pour un enfoncement donné) entre les échelles de déplacement et de "poids lourd". Huiles pour lubrifier le moteur principal, les moteurs auxiliaires et autres équipements mobiles du navire. Moyenne des enfoncements arrière, babord et tribord. Moyenne des enfoncements avant, babord et tribord. Moyenne des enfoncements babord et tribord mesurés au milieu du navire.

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Page 16: Draft Survey Manual

Section 2: Glossary - French midships/ milieu du navire moment/ moment moment to change trim 1 cm/ moment pour changer l'assiette de 1 cm. MTC Plimsoll line/ligne Plimsoll port side/ babord rudder post/axe du gouvernail sagging/ flexion scale drawing/ plan à échelle sounding/ hauteur de liquide sounding pipe/ tuyau de sonde sounding tables/ tables de sonde

Centre longitudinal du navire indiqué sur la coque par les marques d'été babord et tribord. Le moment d'une force est la mesure de l'effet de rotation de cette force autour d'un point donné. Cet effet dépend de la grandeur de la force et de la longueur du levier sur lequel la force s'exerce, c'est-à-dire la distance perpendiculaire entre la ligne d'action de la force et le point autour duquel le moment s'exerce. Force en tonnes métriques multipliée par la distance en mètres nécessaire pour changer l'assiette du navire de 1 cm. Moment to change trim 1 cm. Autre nom pour la ligne d'été. Partie gauche du navire pour un observateur placé sur le navire et regardant l'avant. Axe vertical autour duquel pivote le gouvernail. Déformation du fond d'un navire telle que l'enfoncement au milieu du navire est plus grand que la moyenne des enfoncements avant et arrière. Plan du navire préparé de telle sorte que toute dimension en cm sur le plan corresponde à une dimension connue sur le navire. Par exemple, une échelle de 1/100 signifie que 1 cm sur le plan correspond à 1 m sur le navire lui-même. Hauteur entre le fond d'un réservoir et la surface du liquide qu'il contient. Tuyau fixe au travers duquel on mesure la hauteur de liquide dans un réservoir. Voir calibrations tables.

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Section 2: Glossary - French specific gravity/ poids spécifique starboard side/ tribord stem correction/ correction avant stern correction/ correction arrière summer load line or summer line/ ligne d'été summer mark/ marque d'été t per cm(TPC)/ t par cm trim/ assiette longitudinale trim corrections/ corrections d'assiette ullage/ hauteur libre

Rapport entre le poids dans l'air d'un volume donné de liquide et le poids du même volume d'eau distillée. Les températures du liquide et de l'eau doivent être définies. Il y a donc plusieurs formes de poids spécifiques, ce qui peut entraîner d'importantes confusions. Pour cette raison, on préfère utiliser le terme "densité apparente" qui correspond à des poids obtenus par pesage sur pont bascule. Partie droite d'un navire pour un observateur placé sur le navire et regardant vers l'avant. Correction appliquée à l'enfoncement moyen avant lorsque les échelles d'enfoncement avant babord et tribord ne sont pas situées sur la perpendiculaire avant. Correction appliquée à l'enfoncement moyen arrière lorsque les échelles d'enfoncement arrière babord et tribord ne sont pas situées sur la perpendiculaire arrière. Ligne imaginaire, parallèle à la quille, passant par le bord supérieur de la marque d'été, qui correspond à l'enfoncement maximum autorisé dans la zone "été" en eau de mer. Ligne entourée d'un cercle, marquée de façon permanente par poinçonnage ou soudure, sur les côtés babord et tribord au milieu du navire, conformément aux prescriptions du "Loadline Certificate" du navire. Nombre de tonnes métrique nécessaires pour changer l'enfoncement moyen du navire d'un centimètre. Différence entre les enfoncements moyens avant et arrière, après corrections avant et arrière éventuelles. Corrections appliquées au déplacement lorsque le bateau n'a pas sa quille horizontale. Hauteur entre la surface du liquide et le haut du réservoir ou du tuyau de sonde correspondant.

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Section 3: Glossary - German

SECTION 3

GLOSSARY OF TERMS - GERMAN Term or abbreviation Definition and explanation aft Hinten oder in Richtung des hinteren Teiles des Schiffes. aft draft Tiefgang, gemessen bzw, abgelesen am Hinterschiff. aft perpendicular Eine imaginäre Linie, die im rechten Winkel zum Kiel durch

die Mitte order entland des hinteren Endes des Ruderpfostens verläuft.

AP Hinteres Lot. after peak Eine Abteilung im hinteren Ende des Schiffes, welche

meistens zur Aufnahme von Ballastwasser oder auch Frischwasser benutzt wird.

ballast Wasser, Hafen-/Fluss- oder Seewasser, welches in das

Schiff eingelassen oder ausgepumpt wird, um den Tiefgang oder den Trimm des Schiffes zu verändern.

ballast tanks Tanks speziell dafür ausgelegt, um Ballastwasser

aufzunehmen oder im Falle von Tankschiffen und Ladungstanks, die auch zur Augnahme von Ballastwasser dienen.

breadth Grösste Breite des Schiffes. breadth moulded Breite des Schiffes auf Spanten, also die Breite ohne

Aussenhaut. boiler feed water tanks Tanks an Bord des Schiffes vorgesehen für die Aufnahme

von Wasser für die Damferzeugung.

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Section 3: Glossary - German bilges Abteilungen am Boden des Maschinenraumes oder

Pumpraumes, in denen sich Wasser und/oder Öl sammeln kann; da die Bilgen allgemein auch Schmutzöl beinhalten, dürfen sie nicht innerhalb der Hafengrenzen ausgepumpt werden; für Draft Survey-Zwecke sollte die Flüssigkeitsmenge vor und nach Beladung oder Entleerung des Schiffes kontrolliert werden, so dass jede Änderung der Menge festgestellt werden kann.

bunker tanks Tanks, die entweder Öl für die Dampferzeugung oder den

Antrieb der Hauptmaschinen und Hilfsmaschinen aufnehmen.

calibration tables Siehe Tank-Peil-Tafeln: tank sounding tables. centre of flotation Der Auftriebzentrum ist der Schwerpunkt vom

unbeladenen Schiff und wird auch Kippmoment gennannt. cofferdams fwd and aft Diese Bezeichnungen beziehen sich im besonderen auf

Tankschiffe, Küstentanker und Tankleichter; es sind Leerräume, die dazu dienen, hinten-Ladungstanks vom Maschinenraum und vorne-Vorpiek und andere Teile zu trennen; Kofferdämme enthalten manchmal Wasser, beabsichtigt oder unbeabsichtigt, und sollten deshalb immer gepeilt werden bei Anfangs- und Endeiche.

constant Ist die Differenz zwischen dem Leerschiffgewicht gemäss

Schiffsunterlagen und der bereinigten/Netto-Verdrängung laut Schiffseiche nach Abzung aller feststellbaren Gewichte.

deadweight Ist die Differenz zwischen dem Gewicht des leeren

Schiffes (Leerschiffe-Gewicht) und dem Gewicht des Schiffes im abgeladenen Zustand; die Tragfähigkeit beinhaltet das Gewicht der Ladung, des Treibstoffes, des Wassers und der Ausrüstung.

deck line Ein Strich deutlich markiert an der Backbord und

Steuerbordseite in der Mitte des Schiffes gemäss "International Loadline Regulations".

deep tanks Tanks, welche sich in der Nähe des Schiffbodens

befinden. density (true) Die Masse einer Volumeeinheit einer Flüssigkeit; sie kann

in Bezeichnungen von Gramm per Milliliter, Kilogram per Kubikmeter, engl. pounds per Kubifuss, etc. ausgedrückt werden.

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Section 3: Glossary - German density (apparent) Dichte, wie oben definiert, jedoch ausgedrückt in der

Bezeichnung "Masse in Luft", d.h. ohne Berücksichtigung des Luftauftriebes; die scheinbare Dichte des Seewassers, Frischwassers, Ballastwassers, usw. wird durch des SGS Draft Survey Hydrometer gemessen und gibt das Gewicht des Wassers an, welches vergleichbar ist mit dem Gewicht, was man erhält, wenn man einen volumenmässig sorgfältig vermessenen gefüllten Behälter auf einer genauen Waage wiegt, so wie man handelsübliche Gewichte feststellt.

diesel oil Brennstoff zum Antrieb von Dieselmotoren; es gibt

verschiedene Sorten von Dieselöl; einschliesslich leichtem Dieselöl für die Hilfsdiesel und schwerem Dieselöl für die Hauptmaschinen.

displacement Das Gewicht des Wassers, welches durch das Gewicht

des Schiffes verdrängt wird; die Verdrängung beinhaltet das Gewicht des leeren Schiffes (leerschiffgewicht) plus aller anderen Gewichte an Bord, einschliesslich Ladung, Ballast, Bunker, usw.

displacement table Eine Tabelle speziell für jedes Schiffe erstellt, woraus die

jeweilige Verdrängung zu dem entsprechenden Tiefgang zu entnehmen ist.

double bottom tanks Tanks, welche sich im Doppleboden des Schiffes befinden

und für die Aufnahmen von Ballastwasser oder Brennstoff bestimmet sind.

draft (draught) Tiefe des Wassers von der Wasseroberfläche hinunter bis

zum boden des Kieles. draft marks Eine Zahlenreihe auf dem Schiffsrumpf, aufgemalt oder

aufgeschweisst, normalerweise vorne, mittschiffes und hinten auf beiden Seiten des Schiffes; sie gibt jeweils den Tiefgang des Schiffes dort an, wo sich diese Marken befinden.

draft survey Eine Methode der Ladungs-Gewichts-Bestimmung,

basierend auf der Ermittlung des Schiffstief-ganges vor und nach des Be- oder Entladung under Berücksichtigung aller Gewichtsveränderungen, die während der Ladungsarbeiten stattgefunden haben können, ausser den Veränderungen der Ladung, d.h. Gewichtsveränderungen beim Ballast-wasser, Brennstoff, Ausrüstung, usw.

drinkable water Frischwasser für den menschlichen Verbrauch.

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Section 3: Glossary - German engine water Wasser zu Kühlungszwecken der Dieselmotoren. even keel Wenn die Tiefgänge vorn und hinten identisch sind, sagt

man, das Schiff ist auf ebenen Kiel. fore (forward) Am oder in Richtung des vorderen Endes des Schiffes. forward draft Tiefgang am vorderen Teil des Schiffes

gemessen/abgelesen. forepeak tank Eine Abteilung im äusseren vorderen Ende des Schiffes,

meistens benutzt zur Aufnahme von Frischwasser oder Ballastwasser.

forward perpendicular Eine gedachte senkrechte Linie im rechten Winkel zum

Kiel, die durch den Punkt führt, wo die Sommer-Seewasser-Tiefgangslinie den Vorsteven schneidet.

FP Forward perpendicular - vorderes Lot. freeboard Distanz zwischen der Oberkante des Deckstriches und der

Wasseroberfläche. freeboard (assigned or staturory) Die Distanz zwischen der Oberkante des Deckstriches und

der Sommer-Seewasser-Ladelinie ist der "assigned" oder angegebene Freibord, welcher für dieses Schiff im Freibordzeugnis festgelegt ist.

fresh water Für den Zweck des Draft Survey kann Frischwasser bei

den deductable liquids als Gesamtmenge bestehend aus Trinkwasser und Waschwasser angesetzt werden.

fuel oil (heavy) Schwer Öl, benutzt entweder als Brennstoff für Kessel

oder Hauptmaschinen mit entsprechender Aufbereitung für diesen Zweck.

hogging Die Verformung eines Schiffes, welches in der Weise

beladen würde, dass der Tiefgang mittschiffs geringer ist als das Mittel aus dem vorderen plus hinteren Tiefgängen.

hydrostatic curves Ein Dokument (Formkurvenblatt) für jedes Schiff erstellt, in

dem sich u.a. eine Kurve befindet, von der das centre of flotation oder tipping centre (Wasserlinienschwerpunkt, Auftriebzentrum) mittels entsprechendem Tiefgang herausgenommen werden kann.

keel Teil des Schiffes, der sich am Schiffsboden vom Vor- zum

Hintersteven erstreckt.

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Section 3: Glossary - German LCF Länge zwischen Auftriebzentrum und Mittschiff. length between perpendicular Abstand zwischen vorderem und hinterem Lot parallel zum (LBP) Kiel gemessen. list Neigung des Schiffes gegenüber der aufrechten Position

gemessen an der Längsschiffs-Mittel-achse; sie wird gewöhnlich mittels eines Inklinometers (Neigungsmesser) gemessen, welches die Winkelgrade anzeigt; die Schlagseite kann auch aus der Tiefgangsdifferenz der Backbord- un Steuerbord-Mittschiffstiefgänge errechnet werden.

light ship weight Das Gewicht des Schiffes nach Fertigstellung, aber ohne

Brennstoffe, Ausrüstung, usw.; das Leer-Schiff-Gewicht wird gewöhnlich in der Verdrängungskala angegeben und ist die Gewichts-differenz aus den Angaben der Verdrängungskala und Tragfähigkeitskala.

lubricants Oele zur Schmierung der Hauptmaschine, Hilfsmaschinen

oder anderer beweglicher Teile an Bord des Schiffes. mean aft draft Das Mittel aus den Tiefgängen gemessen bzw. abgelesen

auf Backbord- und Steuerbordseite des Hinterschiffes. mean forward draft Das Mittel aus den Tiefgängen gemessen bzw. abgelesen

auf Backbord- und Steuerbordseite des Vorschiffes. mean midships draft Das Mittel aus den Tiefgängen gemessen bzw. abgelesen

auf Backbord- und Steuerbordseite mittschiffs. midships Mitte der Längsschiffachse; wird am Schiff angezeigt durch

die Backbord- und Steuerbord- lademarken. moment Das Moment einer Kraft ist das Mass für die Drehwirkung

der Kraft um einen gegebenen Punkt; die Drehkraft hangt ab von der Grösse der Kraft und der Länge des Hebelarmes, auf den die Kraft einwirkt, d.h. die senkrechte oder waagerechte Entfernung zwischen dem Angriffspunkt der Kraft und dem Punkt, an dem sich das Moment auswirkt.

moment to change trim 1 cm Die Kraft in metrischen Tonnen multipliziert mit der

Entfernung in Metern, die benötigt wird, um den Trim des Schiffes um 1 cm zu ändern.

MTC Trimmoment für 1 cm Trimmänderung.

Einheitstrimmoment - ETM.

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Section 3: Glossary - German Plimsoll line Andere Bezeichnung für Seewasser-Sommer-Marke. port side Linke Seite des Schiffes bei Blickrichtung zum Vorderteil

des Schiffes. rudder post Die vertikale Achse, um die sich das Ruder dreht. sagging Die Verformung eines Schiffes, welches in der Weise

beladen wurde, dass der Mittschiffs-Tiefgang grösser ist als das Mittel aus vorderem plus hinteren Tiefgang.

scale drawings Schiffspläne derart gezeichnet, dass jeder Zentimeter des

Masstabes einer bestimmten Entfernung auf dem Schiff entspricht, z.B. ein Massstab 1/100 heisst 1 cm im Plan bedeutet 1 m auf dem Schiff.

sounding Entfernung zwischen dem Boden des Tanks und der

Oberfläche der Flüssigkeit, die sich im Tank befindet. sounding pipe Ein festinstalliertes Rohr, durch das Peilungen

vorgenommen werden. sounding tables Masstabellen, die die Volumen der entsprechenden

Flüssigkeitshöhen der einzelnen Tanks angeben. specific gravity Verhältnis zwischen der Masse oder dem Gewicht in Luft

eines gegebenen Volumens einer Flüssigkeit und der Masse oder dem Gewicht in Luft desselben Volumens destillierten Wassers; beide Temperaturen für Flüssigkeit und destilliertes Wasser müssen dazu angegeben werden; es gibt deswegen die verschiedensten Angaben von "specific gravities", welche zu erheblichen Verwirrungen führen können; aus diesem Grunde wird die Bezeichnung "apparent density" vorgezogen, weil nur durch sie Gewichte ermittelt werden, die man auch bei der Gewichtsermittlung auf einer Waage erhält.

starboard side Die rechte Siete des Schiffes bei Blickrichtung zum

Vorderteil des Schiffes. stem correction Berichtigung des gemittelten vorderen Tiefganges, wenn

die vorderen Tiefgänge (Backbord und Steuerbord) sich nicht am vorderen Lot befinden.

stern correction Berichtigung des gemittelten hinteren Tiefganges, wenn

die hinteren Tiefgänge (Backbord und Steuerbord) sich nicht am hinteren Lot befinden.

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Section 3: Glossary - German summer load line Eine angenommene Linie parallel zum Keil, welche durch

die Oberkante der Sommer-Marke verlaüft und welche dem Maximum-Tiefgang in Seewasser innerhalb der Sommerzone entspricht.

summer mark Die Linie, die mit einem Kreis eingefasst ist und mittels

Körnung oder Schweissnaht dauerhaft fixiert ist auf der halben Schiffslänge an Backbord- und Steuerbordseite des Schiffes, wie im Freibord-Zeugnis vorgeschrieben.

t per cm (TPC) Die Anzahl der metrischen Tonnen, die die Veränderung

des Mitteltiefganges um einen Zentimeter hervorruft. trim Differenz zwischen gemitteltem vorderen gemitteltem

hinteren Tiefgang, nachdem, wenn notwendig, beide Tiefgänge auf die Lote korrigiert wurden.

trim corrections Berichtigungen zur Verdrängung des Schiffes, wenn das

Schiffe nicht auf ebenem Kiel schwimmt. ullage Entfernung zwischen Oberfläche des Flüssigkeit in einem

Tank und der Oberkante des Tanks bzw. des Peilrohres.

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Section 4: Glossary - Spanish

SECTION 4

GLOSSARY OF TERMS - SPANISH Término inglès/español aft/ popa aft draft/ calado de popa aft perpendicular/ perpendicular de popa AP/ PP after peak tank/ tanque "peak" de popa ballast/ lastre ballast tanks/ tanques de lastre

Definición y explicación En o hacia la parte posterior del barco. Calado, medido en la parte de popa del barco. Una línea vertical imaginaria, en ángulo recto a la quilla pasando por el centro o lado de popa del poste del timón del barco. Perpendicular de popa. Un compartimento situado en el extremo posterior del barco utilizado frecuentemente para contener agua potable o agua de lastre. Agua, agua de rio o de mar, bombeada dentro o fuera del barco para ajustar el asiento o calado del barco. Tanques diseñados especialmente en la parte interior del barco para recibir agua de lastre o, en el caso de los tanques del barco, tanques de carga utilizados para contener lastre.

breadth / manga Anchura máxima del barco.

boiler feed water tanks/ tanque de alimentación de calderas

Tanques de abordo para contener agua utilizada para producir vapor.

bilges/ sentinas

Espacios en el fondo de la sala de máquinas o de bombas donde se puede acumular el agua. Dado que las sentinas normalmente también contienen aceites de desecho, no pueden ser descargadas dentro de los límites del puerto. A efectos de control por calados, la cantidad de líquido de las sentinas debe ser controlada antes y después de la carga o descarga para que no se produzca ningún cambio en la cantidad.

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Section 4: Glossary - Spanish bunker tanks/ tanques de combustibles

Tanques para contener fuel oil, ya sea para la subida del vapor o para proveer de fuerza a las máquinas principales y auxiliares.

calibration tables/ tablas de calibración

Ver tablas de sondeo de tanques.

centre of flotation/ centro de flotación

El punto sobre el cual un barco se equilibra, a menudo llamado el "centro de equilibrio".

cofferdams fwd and aft/ ataguias proa y popa

Estos términos se aplican especialmente a los buque-tanques oceánicos, tanques costeros y tanques lancha. Son espacios vacios para separar los tanques de carga del lugar de máquinas de popa y del peak de proa y otras partes del barco. Los ataguias contienen frecuentemente agua, ya sea intencionada o accidentalmente, y por lo tanto deben ser siempre sondeados antes y después de que la carga esté siendo medida por control de calados.

constant/ constante

Diferencia entre el peso del barco en vacio de acuerdo a los documentos del mismo y el desplazamiento neto en vacio inspeccionado después de deducir todos los pesos medibles.

deadweight/ peso muerto

Diferencia entre el peso del barco en vacio y el barco cargado. Esto incluye la carga, el fuel, el agua y las provisiones.

deck line/ línea de cubierta

Línea claramente marcada a los lados de babor y estribor del barco, centrada como requieren las Regulaciones Internationales de Carga.

deep tanks/ tanques de profundidad

Tanques situados cerca del fondo de las sentias del barco.

density (true)/ densidad (real)

La masa de unidad de volumen de un liquido. Se puede expresar en términos de gramos por milímetro, kilogramos por metro cúbico, libras por pie cúbico, etc.

density (apparent)/ densidad (aparente)

Densidad como la arriba definida, pero expresada en términos de masa en aire, p.e. sin permitir el efecto de flotación de la atmósfera. La densidad aparente del agua de mar, agua potable, agua de lastre, etc. se mide con el hidrómetro de control por calados SGS, y dá pesos comparables a aquellos que se obtendrían pesando un contendor cuidadosamente calibrado en una báscula-puente fiable, para obtener pesos comerciales.

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Section 4: Glossary - Spanish diesel oil

Fuel oil utilizado para abastecer las máquinas diesel. Existen varios grados de diesel oil, incluyendo diesel oil ligero para máquinas auxiliares y diesel oil más pesado utilizado para las máquinas principales.

displacement/ desplazamiento

Peso total del agua desplazada por el barco. El desplazamiento incluye el peso del barco en vacio además de los otros pesos a bordo, incluyendo la carga, lastre, tanques, etc.

displacement table/ tabla de desplazamiento

Una tabla específicamente preparada para cada barco, que da el desplazamiento correspondiente a varios calados.

double bottom tanks/ tanques de doble fondo

Tanques situados en el doble fondo del barco y utilizados tanto para combustible como para agua de lastre.

draft (draught)/ calado

Profundidad del agua desde la superficie de esta hasta el fondo de la quilla del barco.

draft marks/ marcas de calado

Una serie de signos pintados o soldados en el casco del barco, normalmente en proa, centro y popa, en los lados babor y estribor, que indican el calado del barco en los puntos donde están situadas las marcas de calado.

draft survey/ supervisión del calado

Sistema de medida de la carga, basado en la medida del calado del barco antes y después de la carga o descarga, teniendo en cuenta cualquier cambio en el peso a parte de la carga, que pueda haber tenido lugar durante las operaciones de manipulación de la carga, p.e. cambios en el peso del agua de lastre, combustible, provisiones, etc.

drinkable water/ agua potable

Agua destinada al consumo humano.

engine water/ agua de máquina

Agua utilizada para los sistemas de refrigeración de las máquinas diesel.

even keel/ equilibrio de asientos

Cuando los calados de proa y popa de un barco son idénticos, se dice que el barco está en "equilibrio de asientos".

fore (forward)/ proa

En o hacía la parte frontal del barco.

forward draft/ calado de proa

Calado medido en la parte de proa del barco.

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Section 4: Glossary - Spanish forepeak tank/ tanque "peak" de proa

Un compartimento situado en el extremo de la parte de proa del barco utilizado a menudo para contener agua potable o agua de lastre.

forward perpendicular/ perpendicular de proa

Una línea vertical imaginaria, en ángulo recto a la quilla pasando a través del punto donde la línea de carga de verano intersecciona el mastil del barco.

FP / PF

Perpendicular de proa.

freeboard/ altura borda

Distancia entre la parte superior de la línea de cubierta y la superficie del agua.

freeboard (assigned or statutory)/ altura borda (asignada o estatutoria)

La distancia desde la parte superior de la línea de cubierta a la línea de carga de verano como "asignada" o establecida en el Certificado de Altura Borda del barco concerniente.

fresh water/ agua potable

Para el propósito de control de medida de calado de los "líquidos deducibles", el agua potable se puede definir como el total de agua para beber y lavarse que hay a bordo del barco.

fuel oil (heavy)/ fuel oil (pesado)

Fuel oil de alta densidad utilizado ya sea como calentador o como fuel para las principales máquinas diesel, adecuadamente adaptado para el propósito.

hogging/ quebranto

Encorvadura de un barco cargado de tal manera que el calado de centro es menor que la media de los calados de popa y proa.

hydrostatic curves/ curvas hidrostáticas

Un documento especialmente preparado para cada barco, indicando, entre otras cosas, el centro de flotación o "centro de equilibrio" en varios calados.

keel/ quilla

Parte de un barco a lo largo del fondo desde proa a popa.

LCF

Distancia entre el centro de flotación y el centro del barco.

length between perpendiculars (LBP)/ longitud entre perpendiculares (LEP)

Distancia entre las perpendiculares de popa y proa medidas paralelamente a la quilla.

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Section 4: Glossary - Spanish list/ bandeo

Inclinación del barco desde la posición vertical medida en el eje longitudinal del centro. Se mide normalmente por medio de un inclinómetro que da los resultados en grados de ángulo. El bandeo se puede también calcular, si es necesario, por la diferencia entre los calados de centro de babor y estribor.

light ship weight/ peso del barco en vacío

El peso del barco después de terminada su construcción pero sin tanques de fuel, despensas, etc. El peso del barco en vacío se menciona normalmente en las gráficas de desplazamiento y representa la diferencia entre la gráfica de desplazamiento y la gráfica de peso muerto.

lubricants/ lubricantes

Aceites para lubricar la máquina principal, máquinas auxiliares y otros equipos de cinética en el exterior del barco.

mean aft draft/ calado medio de popa

Promedio de los calados medidos en los lados babor y estribor de popa del barco.

mean forward draft/ calado medio de proa

Promedio de los calados medidos en los lados babor y estribor de proa del barco.

mean midships draft/ calado medio de centro

Promedio de los calados medidos en los lados babor y estribor del centro del barco.

midships/ medio

Centro longitudinal del barco como se indica en el casco por las marcas de línea de carga de babor y estribor.

moment/ momento

El momento de una fuerza es la medida del efecto de rotación de dicha fuerza en un punto dado. El efecto de rotación dependerá de la magnitud de la fuerza y de la longitud del brazo sobre el que actúa, es decir la distancia perpendicular entre la línea de acción de la fuerza y el punto alrededor del cual se ejerce el momento.

moment to change trim 1cm/ momento de cambio del trimado 1 cm

Es la fuerza en toneladas métricas multiplicada por la distancia en metros requerida para cambiar el trimado del barco de 1 cm.

MTC

Momento para cambiar el trimado de 1 cm.

Plimsoll line/ línea Plimsoll

Otra manera de denominar a la línea de verano.

port side/ lado babor

Lado izquierdo del barco visto por un observador de cara a la proa.

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Section 4: Glossary - Spanish rudder post/ poste de timón

Eje vertical alrededor del cual gira el timón.

sagging/ arrufo

Encorvadura de un barco cargado de tal manera que los calados de centro son mayores que la media de los calados de popa y proa.

scale drawings/ planos

Son los planos del barco preparados de tal manera que cada centímetro de distancia en la escala corresponde a una distancia conocida en el barco, p.e. en la escala marcada como 1/100 significa que 1 cm de plano corresponde a 1 m de la estructura del barco.

sounding/ sondeo

Distancia entre el fondo de un tanque y la superficie del líquido que contiene.

sounding pipe/ sonda

Tubo fijo a través del cual se hace el sondeo.

sounding tables/ tablas de sondeo

Son tablas de calibración que dan los volumenes correspondientes a los pesos de los líquidos contenidos.

specific gravity/ gravedad específica

Es la relación entre la masa o peso en aire de un volumen dado de líquido y la masa o peso en aire del mismo volumen de agua destilada. La temperatura del líquido y la del agua deben ser definidas. Hay varias formas de gravedad específica que pueden conducir a considerable confusión. Es por esta razón que el término "densidad aparente" es preferible, ya que se corresponde con el peso obtenido pesando sobre una báscula puente.

starboard side/ lado estribor

El lado derecho del barco tal y como un observador lo vería de cara a proa.

stem correction/ corrección por stem

Es la corrección aplicada al promedio del calado de proa cuando los calados delanteros de babor y estribor no están situados en la perpendicular correspondiente.

stern correction/ corrección por stern

Es la corrección aplicada al promedio del calado de popa cuando los calados de popa lados babor y estribor no están situados en la perpendicular correspondiente.

summer load line/ línea de carga de verano

Línea imaginaria, paralela a la quilla del barco que pasa por el eje superior de la marca de verano y que corresponde al calado máximo transportado en una zona de verano en agua de mar.

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Section 4: Glossary - Spanish summer mark/ marca de verano

Línea rodeada por un círculo prominentemente marcada en el centro por grabado o soldado a la plancha en los lados babor y estribor del barco tal y como prescribe el Certificado de Carga Máxima del barco.

t per cm (TPC)/ toneladas por cm

El número de toneladas métricas requeridas para cambiar el promedio del calado de un barco en 1 cm.

trim/ trimado

Es la diferencia existente entre el promedio del calado de proa y el promedio del calado de popa habiendo sido corregidas ambas medidas a la perpendicular de proa y popa cuando fuese necesario.

trim correction/ corrección por trimado

Son las correcciones aplicadas al desplazamiento de un barco cuando este no está flotando con la quilla plana, es decir, en equilibrio de calados.

ullage/ vacios

Distancia existente entre la superficie del líquido en un tanque y el tope de ese tanque o la correspondiente sonda.

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Section 5: Introduction

SECTION 5

INTRODUCTION TO DRAFT SURVEY 5.1 General principles The first question we need to answer is “What is a draft survey?” Draft survey is an indirect weighing method which assesses the weight of a cargo loaded on board or discharged from a vessel. The method is based upon the principle of Archimedes which states the following: ‘A vessel, freely floating in water, will displace a weight of water equal to its own weight.’ and it is exactly the weight of this displaced water which is calculated by draft survey. In the following sections of this manual, details will be given regarding the procedures to be followed but before going any further, it is essential that you understand the following three points: Point 1: The weight of water displaced by a vessel does not simply equal cargo weight but consists of:

• The weight of the cargo, if any on board. • The weight of the vessel itself, also called the light ship. • The weight of the liquids on board, also called deductible liquids, such as:

o Ballast water required for stability. o Fresh water such as drinking water and cooling water. o Bunkers such as heavy fuel, diesel oil and lubricating oil.

• The constant which is the total of all unknown weights on board. Point 2: Since seawater (density 1025 kg/m³) is heavier than fresh water (density 1000 kg/m³) the volume of water displaced by an object floating in salt water is smaller than the volume of water displaced in fresh water. Or, when a ship is moved from fresh water into seawater, it will rise slightly out of the water because of the smaller volume of seawater displaced for the same weight. Point 3: The data, represented in the vessel’s documents and required for draft survey calculation, are based upon a vessel:

• Floating in water of a well defined density, usually 1025 kg/m³. • Being on even keel (= without trim) that is with equal drafts forward and aft. • Being upright (= without list) that is with equal drafts on port and starboard side.

Unfortunately, these conditions are rarely encountered in practice and corrections will have to be applied. These will be explained in the following sections of the manual.

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Section 5: Introduction 5.2 Introduction to the m/v "MINDIV" The m/v MINDIV is a hypothetical vessel with clearly specified dimensions as given below. This vessel will be used in the subsequent sections of the manual to illustrate the various techniques and calculations involved with a draft survey. General Particulars: Type of ship : Single deck bulk carrier Dead weight : 26000 t Light ship : 5000 t Constant as per Chief Officer : 200 t Length overall : 180.000 m Length between perpendiculars : 170.000 m Breadth moulded : 20.000 m Summer freeboard : 3.000 m Summer load draft : 10.000 m The general holds and tanks arrangement of the m/v Mindiv is presented in figure 1. 5.3 Abbreviations and conversion factors

P : portside (left side from steering position) S : starboard side (right side from steering position) Fwd : forward Aft : after (abaft) Mid : midships Stem : the front side of a vessel (bow) Stern : the backside of a vessel 1 Foot = 1’ = 1 Ft = 12 inches 1 Inch = 1” MT = Metric Tonnes = Tonnes = To = Tn = t (the International Standard abbreviation) LT = Long Tons = Tons = Ts 1 Ft = 0.3048 m. 1 LT = 1.016047 MT.

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Section 5: Introduction

FIGURE 1

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Section 6: Drafts

SECTION 6

READING OR MEASURING THE DRAFT 6.1 Introduction In this section of the manual, we are going to consider the procedures for reading and measuring a vessel's draft - that is the depth of its keel in the water. These procedures rely upon marks which appear on every vessel and which are of known height above the keel. Draft reading : direct reading of the draft from the draft marks marked on the

hull of the vessel. Draft measuring : determining the draft by measuring the distance between a

reference point on the hull of the vessel and the waterline. During draft reading or measuring it is important to halt all operations on board which can change the position of the draft marks to the water such as: - Ballast operations (ballasting, deballasting or transfer of ballast water) - Bunker operations (bunkering or transfer of fuel, diesel etc.) - Gear operations (opening or closing of hatch covers; movement of booms, deck cranes etc.) - Loading or discharging operations of cargo or eventually other essential items. Note also the position of the anchors. Whenever possible, draft readings or measurements should be effected jointly with the Chief Officer or his representative. 6.2 Reading the DraftSeagoing vessels usually have six scales of draft marks painted or welded on the vessel's hull. These scales are positioned on port and starboard side of the vessel, forward, midships and aft. The value of each draft mark in these scales represents the distance from its position to the underside of the keel plate (extreme drafts - keel included). The scales can be calibrated either in meters (metric system) or in feet (imperial system). In some cases, both systems will be used. Taking a draft reading is simply a matter of noting the water level on the scale. Often this is not as easy as it sounds. The draft marks can be difficult to read, due to rust or poor painting, or the sea could be choppy or there could be a swell. Where the vessel is in a state of excessive trim, the stern or bow scales could even be clear of the water. To ensure the highest level of accuracy readings should be taken close to the water line, from a launch, if possible, to reduce the parallax error. Examples of metric and imperial draft scales are given in the following pages.

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Section 6: Drafts

METRIC SYSTEM

FIGURE 2

FIGURE 3

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Section 6: Drafts

METRIC SYSTEM

FIGURE 4

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Section 6: Drafts

IMPERIAL SYSTEM - ROMAN FIGURES

FIGURE 5

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Section 6: Drafts

IMPERIAL SYSTEM - ROMAN FIGURES

FIGURE 6

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Section 6: Drafts

IMPERIAL SYSTEM - ARABIC FIGURES

FIGURE 7

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Section 6: Drafts

IMPERIAL SYSTEM - ARABIC FIGURES

FIGURE 8

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Section 6: Drafts 6.3 Measuring the Draft 6.3.1 Principle When the midships draft scale is not marked or cannot be clearly read, the draft must be measured indirectly. This is done by measuring the distance between the surface of the water and any point on the vessel's hull that is of known height above the keel. The measured distance is then subtracted from the height of the reference point above the keel. To illustrate this, let's consider a rectangular box 5.00 meters high (Figure 9). To determine its draft, the distance between the top of the box and the water is measured and this distance subtracted from the total height of the box.

FIGURE 9

Total height of the box 5.00 m Distance between the top of the box and the water line - 3.00 m Draft 2.00 m As you can see, this gives the same result as measuring the distance from the bottom of the box to the surface of the water. In the following sections of the manual, we will show that a vessel is merely a more complicated shape of box and that the same principles apply, provided that corrections are made to account for the profile of the vessel's hull. 6.3.2 Deck line and Load lines These compulsory lines (Figure 10) are marked in the midships position on the hull of every vessel on port and starboard side. Their primary function is to indicate the maximum permissible loading of the vessel in different zones and water types. However, because the lines are of known height above the keel, they can also be used to determine the vessel's draft. The deck line simply indicates the position of the deck.

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Section 6: Drafts The summer load line or summer draft indicates the maximum permissible draft in seawater to which a vessel located in a summer zone can be loaded. This is often referred to as the Plimsoll line, after Mr. Plimsoll, who became concerned about the large number of vessels being lost due to overloading. The distance between the top of the deck line and the top of the summer load line is known as the summer freeboard. This distance will be specified in the vessel's International Load line Certificate which must be in the possession of the vessel's master. The summer freeboard should not be confused with the vessel's freeboard, which is simply the distance between the deck line and the water line.

FIGURE 10

The other marks on the loading scale indicate the maximum draft to which the vessel can be loaded in different zones in fresh water (left side) and salt water (right side). The letters denote the zone and water type. For example, the fresh water line F indicates the level to which the vessel can be loaded in a summer zone in fresh water (and still be on the salt water line when it reaches the sea). The WNA or Winter North Atlantic zone is only applicable for vessels up to 100 m length. The locations of the different zones are presented in figure 11. And a practical example of a hydrostatic document with the positions of the summer load line and the deck line of the m/v Emerald is shown in figure 12.

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FIGURE 11

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Section 6: Drafts

FIGURE 12

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Section 6: Drafts The load lines can only be certified by certain classification bodies. To ensure their accuracy, they must be checked at approximately twelve monthly intervals. The date of the last survey will be indicated on the International Load line Certificate. COUNTRY CLASSIFICATION BODY ABBREVIATIONBritain Lloyds Register of Shipping LR France Bureau Veritas BV Germany Germanischer Lloyds GL Norway Den Norske Veritas NV Italy Registro Italiano Navale RI United States American Bureau of Shipping ABS Russia Register of Shipping of the USSR PC Japan Nippon Kaizi Ngokai NK 6.3.3 Measuring the draft on the m/v Mindiv The figure below shows the load line arrangement of the m/v Mindiv.

FIGURE 13

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Section 6: Drafts Because the heights of the marks above the keel are given in the vessel's general particulars, the midships draft is easily determined. This can be done in two ways. The first method is to measure the distance between the top of the summer load line and the surface of the water and to subtract this from the known height of the summer load line above the keel.

FIGURE 14

Height of the summer load line above the keel : 10.00 m Measured distance between the summer load line and the water : - 4.00 m Draft : 6.00 m Alternatively, the draft could be found by measuring the distance between the top of the deck line and the surface of the water and subtracting this from the known height of the deck line above the keel.

FIGURE 15

Height of the deck line above the keel : 13.00 m Measured distance between the deck line and the water : - 7.00 m Draft : 6.00 m

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Section 6: Drafts As you can see, both methods give the same result. In fact, any mark on a vessel's hull of known height above the keel can be used to determine the draft. For example, where draft marks are illegible or corroded or when the vessel is close to the quay and the marks cannot be read, the draft could be obtained by measuring the distance from a legible draft mark to the water line. A practical example of measuring the draft from the top of the deck line is presented below.

FIGURE 16

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Section 6: Drafts

FIGURE 17

FIGURE 18

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Section 6: Drafts 6.4 Calculation of the mean drafts fwd, aft and midships The objective is to calculate out of the six drafts, obtained by reading or measuring, one representative draft (quarter mean). This will have to be done in different steps. The first step will be the calculation of the mean drafts fwd, aft and mid. These mean drafts are simply the means of the port and starboard side drafts on fwd, aft and midships e.g.: Observed draft fwd P : 1.630 m Observed draft fwd S : 1.630 m Observed mean draft fwd : 1.630 m Observed draft aft P : 4.230 m Observed draft aft S : 4.190 m Observed mean draft aft : 4.210 m Observed midships P : 2.740 m Observed midships S : 3.010 m Observed mean draft mid : 2.875 m The next step will be the correction of these three mean drafts to the perpendiculars (see next section). 6.5 Exercise m/v Mindiv Observed draft fwd P : 7.620 m Observed draft fwd S : 7.660 m Observed draft aft P : 10.260 m Observed draft aft S : 10.380 m Observed midships P : 8.860 m Observed midships S : 9.140 m Calculate the mean drafts fwd, aft and mid.

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Section 7: Perpendiculars

SECTION 7

PERPENDICULAR CORRECTION 7.1 Introduction Perpendiculars are imaginary vertical lines, dividing the length of the vessel into two equal parts, in order to simplify various calculations such as trim, stability, etc. Ships documents are always based on draft readings at the perpendiculars. When a draft mark is not situated at its perpendicular then the observed draft reading needs to be corrected to the perpendicular.

FIGURE 19

FP or fwd perpendicular : An imaginary vertical line at right angle to the keel

situated at the point where the summer load line intersects the vessel's stem.

AP or aft perpendicular : An imaginary vertical line at right angle to the keel

passing through the first frame (zero frame) and therefore located on or nearby the ship's rudderpost.

MP or midships perpendicular : An imaginary vertical line at right angle to the keel

situated midway between the FP and the AP LBP or Length Between Perpendiculars : Distance between the FP and the AP. Observed draft : Draft read on the vessel Corrected draft : Draft corrected to its perpendicular

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Section 7: Perpendiculars Observed Trim : Difference between the observed mean drafts fwd and aft. Corrected Trim : Difference between the corrected mean drafts fwd and aft. Trim F : Trim Fwd / by the head / by bow / by the stem / draft aft < draft fwd Trim A : Trim Aft / by the stern / draft aft > draft fwd It is useful to know that the numbering of the frames usually starts from aft and that the AP is at the position of the first frame usually marked 0 (zero) on the plans, although on USA built vessels and some other ones frame numbering starts from fwd. 7.2 Position of the draft marks The following figure illustrates how draft marks can be situated on or away from their perpendiculars.

FIGURE 20

The fwd draft mark scale is situated 2.0 m aft of the FP. The midships draft mark scale is located 0.5 m aft of the MP. The aft draft mark scale consists of two sections. The section from 8 m up to 12 m is located on the AP, the section below 8 m is located 7.0 m fwd of the AP. When correcting a draft reading to its perpendicular, the first step is to find the distance between the observed draft mark and the perpendicular. This distance is sometimes directly presented in the vessel's documents. If not, it may be estimated by aligning the position of the observed draft mark and its perpendicular to the quay and then measuring the distance between those markings. Also a ship's plan, on scale, might help to determine this distance. The distance between the midships drafts and the MP, which passes through the middle of the Plimsoll circle, can sometimes be measured directly on the hull. Be attentive when the fwd draft marks follow the profile of the vessel's hull (Figure 3 & 19). In this case the distance between the draft marks and the FP will vary depending on the draft of the vessel. The following pictures show some practical examples of draft mark positions.

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Section 7: Perpendiculars

FIGURE 21

FIGURE 22

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FIGURE 23

FIGURE 24

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FIGURE 25

7.3 Principle of perpendicular correction 7.3.1 Even keel condition Consider a vessel floating on even keel that is without trim or with equal drafts fwd and aft.

FIGURE 26

O denotes observed draft and C corrected draft.

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Section 7: Perpendiculars Both fwd and midships drafts are not observed at their perpendiculars but at a position aft of them. However, since the vessel is on even keel, these observed draft readings equal the required readings on their perpendiculars and no correction has to be applied (O=C). The aft draft is observed on the perpendicular (AP) and requires no correction. In other words, a perpendicular correction is not required when the vessel is on an even keel or when the draft mark is situated on the perpendicular. 7.3.2 Trim by the stern

FIGURE 27

Both fwd and midships observed draft readings do not equal anymore the required readings on their perpendiculars (O≠C) and corrections will have to be applied. It is also clear from this figure that readings on the perpendiculars would turn out lower than the observed draft readings (C<O). The corrections therefore will have to be subtracted from the observed drafts. The aft draft is observed on the perpendicular (AP) and requires no correction.

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Section 7: Perpendiculars 7.3.3 Trim by the head

FIGURE 28

None of the observed draft readings equal the required readings on their perpendiculars (O≠C) and corrections will have to be applied. A reading on the perpendiculars for fwd and midships would turn out higher than the observed draft readings (C>O). The corrections will have to be added from the observed drafts. A reading on the aft perpendicular (AP) would turn out lower than the observed draft reading (C<O). The correction will have to be subtracted to the observed draft. 7.4 Formula The perpendicular correction [m] can be calculated by following formula: Perp. Corr. [m] = Observed Trim [m] x Distance (Observed draft mark - Perpendicular) [m]

LBM [m] LBM : Length Between the observed fwd and aft draft Marks.

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Section 7: Perpendiculars 7.5 Exercise m/v Mindiv

FIGURE 29

Correct the observed mean drafts fwd, aft and mid to their perpendiculars and calculate the corrected trim.

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Section 8: Deflection

SECTION 8

CORRECTION FOR HULL DEFLECTION 8.1 Introduction When a vessel is subjected to an uneven distribution of weight, hull deformation can occur. This will lead to different draft readings fwd, midships and aft, even when the vessel is upright and on even keel. This is at the same time the reason why all of the three mean drafts must be taken into calculation to obtain one representative draft, called quarter mean or mean of means corrected. 8.2 Types of deformation 8.2.1 Hogging Hogging is best illustrated by a beam supported at its midpoint and carrying a weight at each end. The result is that the beam bends in a concave manner.

FIGURE 31

The same deformation occurs when a vessel is loaded either side of midships.

FIGURE 32

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Section 8: Deflection 8.2.2 Sagging Sagging can be illustrated by a beam, supported at its ends and carrying a weight at the centre. The result is that the beam is deformed in a convex manner.

FIGURE 33

The same deformation occurs when a vessel is loaded with a weight at midships.

FIGURE 34

8.3 Factors which can influence the deflection Deflection is mainly influenced by the cargo whether or not loaded on board and its eventual distribution over the vessel. In general, a vessel tends to hog in empty (also called light) condition and to sag when loaded. Of course, this is not a universal rule and does not apply to all vessels or conditions of loading. Besides the cargo, deflection can also be influenced by the position of the vessel's castle and engines, ballast condition, position of the hatch covers, solar bending etc.

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Section 8: Deflection 8.4 Formula 8.4.1 Quarter mean Due to the deflection all of the three mean drafts must be taken into calculation. Considering the shape of a vessel however, being much wider at the midships drafts than at the fwd and aft drafts (Figure 35), the formula will not be a simple add up and divide by three. It is obvious that more value must be attached to the midships draft. In fact, for bulk carriers in general, the best result is obtained by attaching 75% of the value to the midships draft and 25% to the fwd and aft drafts together (3/4 rule) by following formula: Quarter mean [m] = 6 Mid + Fwd + Aft 8 The quarter mean, also called mean of means corrected, can be considered as one draft in which the original six drafts of the vessel are condensed in the right proportions. This quarter mean will, as next step, be used to enter the hydrostatic documents of the vessel in order to find the corresponding displacement (see next section). 8.4.2 Deflection Value [m] = Difference between Fwd + Aft and Mid. 2 Hogging [m] = Fwd + Aft > Mid 2 Sagging [m] = Fwd + Aft < Mid 2

FIGURE 35

8.5 Exercise m/v Mindiv Calculate the quarter mean and determine the value and type of the deflection.

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Section 9: Displacement

SECTION 9

CALCULATION OF THE CORRESPONDING DISPLACEMENT 9.1 Introduction In this section will be explained how the corresponding displacement for the quarter mean can be obtained. This is done at hand of specific documents available on board of the vessel, the hydrostatic particulars. These hydrostatic particulars present, amongst other data, a list of drafts, the quarter means, together with a corresponding list of displacements. These displacements indicate how many tons of water of a well defined density, usually 1.025 kg/l, is displaced by the vessel at a certain draft. Since draft survey uses the vessel in itself as a balance and the hydrostatic particulars can be considered as the display of that balance. The hydrostatic particulars, in metric or imperial system, can be presented as tables, scales or curves and this in a wide variety of models, depending on the country or shipyard of origin. 9.2 Definitions Displacement = the total weight of water displaced by a floating vessel. Deadweight = the displacement minus the light ship weight. Keel = plate with a thickness of about 2 to 3 cm welded on the underside of the vessel. Shell = plate welded on the sides of a vessel Extreme drafts = drafts referring to the underside of the keel (keel included). Moulded drafts = drafts referring to the upper side of the keel (keel not included). Extreme displacement = displacement of a vessel with keel, shell and appendages. Moulded displacement = displacement of a vessel without keel, shell and appendages. Displacement SW = displacement of the vessel in salt water (density usually 1.025 kg/l). Displacement FW = displacement of the vessel in fresh water with a density of 1.000 kg/l.

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Section 9: Displacement Since the draft marks on the hull of a vessel always refer to the underside of the keel, extreme drafts and extreme displacements should be used at any time. When the hydrostatic particulars mention only moulded drafts the keel thickness is to be added in order to obtain the extreme drafts. Only displacement and never deadweight should be used in order to avoid an erroneous density correction later on. If the hydrostatic particulars mention only deadweight the weight of the light ship is to be added in order to obtain the displacement. And since the additional listed data in the hydrostatic particulars, required for future corrections, refer to salt water, displacement SW should be used at any time. 9.3 Hydrostatic particulars Examples of a hydrostatic table, scale and curves of the m/v Waterdale are presented on next pages.

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Section 9: Displacement 9.3.1 Hydrostatic table

FIGURE 36

The corresponding displacement can be read directly from the table for a listed draft. For a draft in between an interpolation will be required. Example. How much is the corresponding displacement at a quarter mean of 2.185 m? 2.000 m = 533.880 t /1.025 2.500 m = 697.080 t /1.025 0.500 m = 163.200 t /1.025 0.010 m = 3.264 t /1.025 0.185 m = 60.384 t /1.025 2.185 m = 594.264 t /1.025

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Section 9: Displacement 9.3.2 Hydrostatic scale

FIGURE 37

The corresponding displacement for a listed draft can be obtained from the scale by alignment. For a draft in between it is suggested to align with a nearby listed draft above and below the required draft and determine then the corresponding displacement by interpolation. Example. How much is the corresponding displacement at a quarter mean of 2.185 m? 2.100 m = 568.000 t /1.025 2.200 m = 599.000 t /1.025 0.100 m = 31.000 t /1.025 0.010 m = 3.100 t /1.025 0.085 m = 26.350 t /1.025 2.185 m = 594.350 t /1.025

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Section 9: Displacement 9.3.3 Hydrostatic curves

FIGURE 38

The corresponding displacement for a listed draft can be obtained from the curve by alignment. For a draft in between it is again suggested to align with a nearby listed draft above and below the required draft and determine then the corresponding displacement by interpolation. Example. How much is the corresponding displacement at a quarter mean of 2.185 m? 2.000 m = 10.7 cm x 50 = 535.000 t /1.025 2.500 m = 14.0 cm x 50 = 700.000 t /1.025 0.500 m = 165.000 t /1.025 0.010 m = 3.300 t /1.025 0.185 m = 61.05 t /1.025 2.185 m = 596.050 t /1.025

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Section 9: Displacement 9.3.4 Conclusions The table is the most accurate and convenient form to use. Scales and curves are in general less practical and less accurate because of the estimation errors which occur inevitable during reading. Large hydrostatic curves can give accurate readings as long as extreme care is taken in aligning and reading. Small alignment errors can result in large mistakes! Scales are sometimes available as part of the general arrangement plan. Often they are small and difficult to read which reduces, together with possible alignment errors, their accuracy. 9.4 Exercise m/v Mindiv

Hydrostatic Table m/v Mindiv - Sea water 1.025 Draft [m] Displ [t] Deadw [t] TPC [m] LCF [t] MTC [txm] 8.900 27212 22212 33.73 1.85 A 367 9.000 27550 22550 33.87 1.97 A 372 Calculate the corresponding displacement.

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Section 10: Trim and List

SECTION 10

CORRECTING THE DISPLACEMENT FOR TRIM AND LIST 10.1 Introduction In the previous sections of the manual, we have seen how a vessel's quarter mean is calculated and how the vessel's documents are used to determine the corresponding displacement. We have also seen that the hydrostatic data in these documents, including the corresponding displacement, are only correct for a vessel being on even keel (no trim) and upright (no list). Such condition however is very rarely met in practice and corrections will have to be applied. This section of the manual will now explain why and when these corrections will be necessary and how they are calculated. 10.2 Definitions Trim : Difference between the corrected mean drafts fwd and aft. List : Difference between the P and S midships drafts. Trim denotes corrected trim, draft denotes quarter mean draft. List is in practice usually measured with an inclinometer, indicating how many degrees the vessel is inclined. LCF = Longitudinal Centre of Flotation or tipping centre. The LCF is a point located somewhere on the vessels' water plane area through which:

• The transversal axis passes around which the vessel trims (fwd/aft rotation). This axis divides at the same time the immersed part of the vessel in two equal fwd and aft volumes.

• The longitudinal axis passes around which the vessel lists (P/S rotation).

This longitudinal axis divides at the same time the immersed part of the vessel in two equal P and S volumes.

TPC = Tonnes Per Centimetre immersion or the number of metric tonnes required to change

the quarter mean draft of the vessel with 1 cm.

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10.3 Principle of trim correction Consider a rectangular box, floating on even keel. FIGURE 39 MP

0 is a point midway the box on the same level as the water surface (water plane area). The transversal axis, which divides the underwater part of the box into two equal fwd and aft volumes passes, due to its symmetrical shape, precisely midway the box. Conclusion: LCF is at the same position as O. Consider now a simplified model of a vessel featuring a smaller hull structure at the fwd. FIGURE 40 MP

0 is a point at midships on the same level as the water surface (water plane area). Here there is, due to the asymmetry, a difference (a) between the immersed fwd and aft volumes. The fwd immersed volume is smaller and the transversal axis has moved proportional to the aft in order to have again two equal under water volumes. Conclusion: LCF is now located aft of midships.

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Section 10: Trim and List Consider next the same vessel, still on even keel but at a higher draft. FIGURE 41 MP

Increasing the draft increases also the difference (b) between the immersed fwd and aft volumes and the transversal axis moves more backwards in order to have again two equal under water volumes. Conclusion: LCF moves to the aft by increasing draft. And finally the same vessel in trimmed condition... FIGURE 42

Since the vessel rotates around the LCF (transversal axis) and not around the midships (O) a draft (D) below O (the even keel position) is now read. Therefore a correction, equal to O-D, will have to be applied. This correction will be needless for a vessel on even keel or when LCF is located at midships.

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Section 10: Trim and List 10.4 First Trim Correction (FTC) 10.4.1 Formula We have seen that LCF varies by draft. This will lead to the first trim correction: FTC [t] = Corrected trim (F or A) [m] x LCF (F or A) [m] x TPC [t/cm) x 100

LBP [m] LCF [m] : the position of LCF from midships. If LCF is presented otherwise e.g. as a distance from the AP, it must be recalculated as a distance to the midships. The values of the corresponding LCF and TPC at the quarter mean can be obtained from the hydrostatic particulars (see figure 36 and 38). Take care not to confuse LCF with LCB (longitudinal centre of bouncy). 10.4.2 Sign of the correction Taking a closer look to the hydrostatic table or curves of the m/v Waterdale confirms that the LCF indeed moves to the aft by increasing drafts but reveals also that LCF can be located forward of the midships. It is very important to establish where LCF is located, fwd or aft of midships, as this will determine the sign of the FTC. In case of doubt rely on the fact that the LCF moves to the aft by increasing drafts. If the absolute value of the LCF increases with increasing drafts then LCF is aft of midships. If the absolute value of the LCF decreases with increasing drafts then LCF is fwd of midships. In general LCF tends to be fwd of midships at the lowest draft and aft of midships at the highest draft though for some vessels LCF will remain all the way on the same side of midships. This sign of the FTC depends on the nature of the trim (F or A) in combination with the position of the LCF (F or A) against midships at can be determined as follows: AA or FF (equal letters) : positive sign + AF or FA (opposite letters) : negative sign - Example : trim by the stern or aft (A) with LCF fwd of midships (F) equals an opposite letter

combination (AF) hence a negative sign. 10.4.3 Formula for the imperial system. FTC [LT] = Corrected trim (F or A) [Ft] x LCF (F or A) [Ft] x TPC [LT/inch) x 100

LBP [Ft]

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Section 10: Trim and List 10.5 Second Trim Correction (STC) 10.5.1 Introduction The positions of LCF, as listed in the hydrostatic data, are based on the even keel condition. Inducing a trim however increases the difference between the immersed fwd and aft volumes and LCF (the transversal axis) will move towards the increased immersed volume in order to have again two equal under water volumes. This means that the position of LCF does not vary only by draft but also by trim. This additional variation of LCF by trim will lead to the STC. 10.5.2 Formula STC [t] = Trim² [m] x 50 x dm/dz [txm] LBP [m] 50 : a constant (metric system) MTC [txm] : moment to change the trim by 1 cm. The MTC indicates how many tonnes on

board of a vessel must be moved 1 meter fwd or aft from the trimming axis (LCF) to change the trim of the vessel by 1 cm. MTC can be obtained from the hydrostatic particulars (figure 36, 37 and 38). The MTC must be divided by 100 if it represents a change of trim by 1 meter.

dm/dz : the variation of MTC over a draft interval of 1 meter obtained at the drafts 0.5 m

above and 0.5 m below the quarter mean. Or, in practice, the difference between the MTC at the draft equal to the quarter mean + 0.5 m and the MTC at the draft equal to the quarter mean + 0.5 m. (See figure 35 for a quarter mean of 6.000 m.)

FIGURE 43

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Section 10: Trim and List 10.5.3 Sign of the correction Always positive. 10.4.3 Formula for the imperial system. STC [LT] = Trim² [Ft] x 6 x dm/dz [LTxFt] LBP [Ft] 10.6 Total Trim Correction (TTC) TTC [t] = FTC [t] + STC [t] Remark: the position of LCF, indicated in figure 42, is actually a combination of the movement by draft and the movement by trim. The distance O-D equals therefore the TTC. 10.7 Displacement corrected for trim Finally, the TTC has to be applied on the corresponding displacement which was calculated in the previous section, to obtain the displacement corrected for trim. 10.8 List correction 10.8.1Principle The water plane area of a vessel increases always by list forcing the vessel to lift slightly out of the water. The correction for list will therefore always be positive or to be added to the displacement.

FIGURE 44

Apart from the fact that the formula for list correction is only an approximation to begin with, it is far more important to realize that carrying out a draft survey by list will strongly reduce the accuracy of the complete survey for many other reasons such as ballast determination.

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Section 10: Trim and List A much better solution is to reduce the list of the vessel down to 0.5° or less by altering e.g. the ballast or eventually by shifting the cargo or turning the deck cranes if available. An eventual list correction will then become negligible and must not be applied. 10.8.2 Formula When desired, the list correction can be estimated by following formula: List correction [t] : 6 x List [m] x ∆TPC [t] (metric system) List correction [LT] : 0.72 x List [Ft] x ∆TPI [LT] (imperial system) List : difference between the midships drafts ∆TPC : difference between the TPC's or TPI's of the midships drafts. 10.9 Exercise m/v Mindiv

Hydrostatic Table m/v Mindiv - Sea water 1.025 Draft [m] Displ [t] Deadw [t] TPC [m] LCF [t] MTC [txm] 8.300 25215 20215 32.82 1.13 A 333 8.400 25544 20544 32.97 1.27 A 338 8.500 25874 20874 33.12 1.39 A 347 8.600 26206 21206 33.27 1.52 A 352 8.700 26540 24540 33.43 1.62 A 357 8.800 26875 21875 33.58 1.74 A 362 8.900 27212 22212 33.73 1.85 A 367 9.000 27550 22550 33.87 1.97 A 372 9.100 27889 22889 34.01 2.07 A 376 9.200 28230 23230 34.15 2.17 A 380 9.300 28572 23572 34.28 2.26 A 384 9.400 28925 23925 34.40 2.34 A 389 9.500 29260 24260 34.52 2.43 A 392 9.600 29606 24606 34.64 2.50 A 396 Calculate the displacement corrected for trim and list.

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Section 11: Density

SECTION 11

CORRECTING THE DISPLACEMENT FOR DENSITY 11.1 Introduction The displacement corrected for trim as calculated in previous section refers to a vessel floating in salt water of a well defined density usually 1.025 kg/l (see section 9). If in practice the vessel floats in water of a different density a correction will have to be applied. 11.2 Definitions True density [kg/l in vacuum] Density measured in vacuum True density [kg/l in air] x volume [l] = Mass [kg in vacuum] - scientific purposes Apparent density [kg/l in air] Density measured in air Apparent density [kg/l in air] x volume [l] = Weight [kg in air] - commercial weight 11.3 Sampling of the surrounding water 11.3.1 Sampling method First of all a representative sample of the surrounding water must be taken. Care must be taken since the density of the surrounding water may differ for various reasons from surface down to lower levels. The surface level may have a different density due to e.g. contamination with cargo spilled during handling or recent abundant rainfall. The water below may be stratified in different density layers e.g. at tidal locations and estuaries or at locations nearby e.g. locks or power plants. Therefore a sample has to be taken with the adequate equipment such as a sampling can (figure 47) which is heavy enough to sink when empty and closed and not e.g. a bucket which scratches off only the surface layer of the water. An average sample can be obtained by lowering down this can at such a rate that it will be full at time it reaches the underside of the keel (running sample). The filling time can eventually be adjusted by fitting a plug with a hole on the can. Next the sampling can is drawn up and the density can be measured. Taking a sample from a certain level can be done by closing the sampling can first with a plug to which a rope is attached. When the can is lowered to the required depth the plug can be removed by jerking the rope allowing the can to fill with water (local sample) Different local samples, obtained at different depths, can eventually be combined to obtain an average sample.

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Section 11: Density 11.3.2 Sampling positions FIGURE 45

This depends largely on the local circumstances and the draft of the vessel. In normal circumstances it is usually sufficient to draw one running sample at the waterside of the vessel at midships. For large ships it might be advisable, especially when the density can be expected to differ from stem to stern, to draw three running samples, one at the MP, one halfway the AP and MP and one halfway the AP and MP. The average of the three density measurements will be used for further calculation. Instead of the running sample a combination of three local samples can always be taken, one close to the surface of the water, one close to the keel and one in between.

11.3.3 Precautions Take care not to draw samples nearby a local disturbance such as a shore draining pipe or the water ballast outlet of the vessel, especially when the vessel has recently discharged ballast water. Sample the water just before or after reading the draft since density may change in time, especially in tidal waters. Always take samples at the water side of the vessel as there could be stagnant water of different density trapped between ship and quay. Once the sample has been taken the density must be measured immediately to prevent the outside conditions (sun, wind, temperature etc.) to alter the temperature hence the density of the sample.

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Section 11: Density 11.4 Measuring the density 11.4.1 The hydrometer

The density of the sample can be measured at hand of a hydrometer. This is a graduated device made of glass from which the density can be directly when floating. Since the complete draft survey procedure must render at the end a commercial weight or weight in air the hydrometer must be graduated equivalent in apparent density or density in air. As the instrument is to be used in water or seawater, liquids of medium surface tension, it has to be graduated likewise. A hydrometer designed for oil measurements is not suitable for use in water.

FIGURE 46 11.4.2 Reading the hydrometer The surface tension of the water causes a small quantity of liquid to rise up against the stem of the hydrometer to form a meniscus (figure 48) . Do not read at the top of the meniscus but read the hydrometer where the level of the liquid surface, imaginary continued, meets the scale. Shield against draught or wind during reading. Do not read the hydrometer directly but allow sufficient time for the hydrometer to adapt to the temperature of the liquid. 11.4.3 Temperature correction Do not apply! A hydrometer is usually calibrated and therefore most correct at 15°C. If immersed in water at a temperature higher or lower than 15°C the instrument will expand or contract and a small correction would be applicable. Therefore a temperature correction table is sometimes supplied with the better hydrometers. At the same time however, also the ship itself will expand or contract in about the same extend to that water temperature. The corrections however for the hydrometer and the vessel are of opposite sign and therefore tend to compensate for each other. Since temperature corrections are not applied for the vessel equally no temperature corrections should be applied for the hydrometer. The temperature of the surrounding water must not be recorded.

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Section 11: Density

FIGURE 47

FIGURE 48 FIGURE 49

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Section 11: Density 11.4.4 Testing the hydrometer. Check first the scale alignment indicator (figure 49). Take a sample of pure water, measure the temperature and read the density. This reading should match the apparent density figure mentioned in the table of figure 50 at the recorded temperature.

FIGURE 50

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Section 11: Density 11.4.5 Certificate of conformity The hydrometer should be accompanied with a certificate of conformity at time of purchase. An example of such a certificate is presented in the figure below.

FIGURE 51

11.5 Displacement corrected for density The displacement corrected for density can be calculated by following formula: Displ corr for density [t] = Displ corr for trim [t] x density of the surrounding water [kg/l] Density indicated in the hydrostatic particulars [kg/l] This correction is only to be applied on displacement and never on deadweight. Calculating the density correction on deadweight would be erroneous as the light ship, which is a part of the total displacement, would not have been taken into account. If the hydrostatic particulars mention only deadweight the weight of the light ship is to be added in order to obtain the displacement. The displacement corrected for density equals the weight of the vessel inclusive everything there is on board. Or, more specific: - Deductible liquids - Light ship - Constant - Cargo

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Section 11: Density 11.6 Exercise m/v Mindiv

FIGURE 52

The apparent density was read on the hydrometer as in figure 52 Calculate the displacement corrected for density. FIGURE 52

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Section 12: Deductible liquids

SECTION 12

DETERMINATION OF THE DEDUCTABLE LIQUIDS 12.1 Introduction Since the final draft survey figure will be result of the difference between the survey prior to and after loading the only unknown variable on board has to be the cargo weight. This means that all other items on board which can change in weight between the initial and final survey must be determined so that eventual changes can be taken into account. These items are mainly liquids, such as ballast water, bunkers and fresh water, also called the deductible liquids. 12.2 Definitions Sounding : Distance between the bottom of the tank and the liquid surface Ullage : Distance between the liquid surface and the top of the tank Overflow : Pumping a liquid into a tank until it overflows through the air pipe(s) 12.3 Ballast water A vessel in loaded condition will have ballast on board, mainly for stability reasons. Vessels in light condition, i.e. without cargo on board, usually have a minimum of ballast on board in order to carry as much as possible cargo. This means that, during discharging ballast water will be taken and, in case of loading, ballast will be discharged as much as possible. Therefore all ballast tanks must be measured at initial and final survey including the tanks which Even the tanks, considered by the Chief Officer to be empty or full, are not always complete empty or full and must be measured too. Since vessels can carry large quantities of ballast all tanks should be carefully measured. 12.3.1 Sounding Sounding is a common system for measuring ballast tanks. It is done with a metal tape, a sounding tape, on which water finding paste is applied in the area where the sounding level is expected. This water finding paste provides accurate readings as it changes colour in contact with water (figure 53). The sounding tape should be lowered down carefully in the sounding pipe until the bottom of the tank is gently touched in order to avoid an inaccurate reading due to tape bending or splashing of the liquid. It is advisable to read during sounding at the same time the height of the sounding pipes. By this blocked pipes can be detected and, in case of discharging, at final survey, tanks can be measured by ullaging and a sounding pipe extension can be applied. Some vessels are equipped with remote ballast gauges. Do not rely on these as they may not be reliable. A zero sounding most often does not mean that a ballast tank is complete empty. Some water, called the inpumpables, might be left. This is at the same time the reason why in ballast calibration tables eventual corresponding volumes to the zero sounding should be taken into account.

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Section 12: Deductible liquids

FIGURE 53

FIGURE 54

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Section 12: Deductible liquids 12.3.2 Ullage Remark: this system may only be applied when the height of the sounding pipes were measured by tape. Never rely on information of heights of sounding pipes sometimes mentioned in the vessels' documents! Ullage is a practical system to measure ballast tanks which are close to full. Water finding paste is applied on the lower part of the tape. Then the tape is lowered into the sounding pipe until a small section is immersed in the water and reading is reading is effected at the upper edge of the sounding pipe. This reading minus the immersed part will then equal the ullage. Sometimes it is possible to ascertain by eye when the bottom end of the sounding weight touches the water. Then the ullage can be read directly. 12.3.3 Overflow Obviously this system can be used for full ballast tanks only. Overflow (figure 54) tends to be reliable for double bottom and peak tanks but NOT for topside tanks (airlocks)! Topside tanks should therefore always be checked by sounding or ullaging, and in case of overflowing sounding pipes, by applying a sounding pipe extension in order to detect and calculate eventual airlocks. Airlocks occur when the air pipes are not situated at the highest point of the tank at time of overflow due to trim or list in combination with their mounted position. Accepting topside tanks to be full by overflow is a very common error committed in draft survey which can result in very large errors, especially when long tanks are concerned. 12.3.4 Ballast hold On most large bulk carriers one of the holds, usually hold 4, might be used as ballast tank. Because of the large volume of such a hold a small error in measurement can produce a significant deviation. Therefore it is advisable to ask the Chief Officer, in case of discharging, to fill the ballast hold after the final survey. In case this is impossible, request to overflow the hold or, if not allowed, to fill the hold at least above the deck level. Since the hatch coaming has a much smaller water surface area than the hold the effect of an error in measurement will be reduced. The quantity of water in the hold can then be calculated by subtracting the volume of the empty space above the water level from the total capacity or grain capacity of that hold. The volume of this empty space can be calculated from the distance(s) measured between the top of the hatch coaming and the water level. Effects of trim and list can hereby eliminated directly by measuring these distances at the positions presented in figure 53.

FIGURE 55

It is not advisable to take soundings of the ballast hold through the bilge pipe(s). Dirt is often accumulated in the bilges which renders an eventual sounding unreliable.

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Section 12: Deductible liquids 12.3.5 Corresponding volume of ballast Consider next three conditions of trim. Even keel

FIGURE 56

Trim by the stern

FIGURE 57

Trim by the head

FIGURE 58

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Section 12: Deductible liquids The soundings, obtained by trim, for the same quantity of ballast, will be higher (trim by the stern) or lower (trim by the head) compared to the sounding at even keel and a correction for trim will have to be applied. Dimension and sign of these ballast trim corrections depend on the condition of trim and the position of the sounding pipe on the tank. The same effect applies also to list. Most large vessels carry ballast calibration tables, also called sounding tables, for each ballast tank presenting a list of soundings with a corresponding list of volumes. These are used to calculate the volume of water in each ballast tank. These tables may be available for even keel together with different trim conditions. From the table as presented in figure 57 the corresponding volume to a particular sounding at a certain trim can be obtained by interpolation.

FIGURE 59

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Section 12: Deductible liquids 12.3.6 Trim and list corrections In some cases only sounding tables for even keel are available. Moreover, some vessels, especially the smaller ones, do not carry sounding tables at all and provide only the maximum capacities of each tank. In this case ballast trim corrections, and eventually volume determination, has to be calculated by formula. There are two different sounding corrections possible. Which one to be applied depends on the condition whether (slack condition - figure 58) or not (wedge condition - figure 59) the water level in the tank reaches the opposite side of the tank. Imaginary sounding The sounding at which the water level reaches the opposite corner of the ballast tank (figure 58) determines which correction will have to be applied and must therefore be calculated first.

FIGURE 60

I [m] = Trim [m] x L [m] LBP [m]

I [m] : Imaginary sounding. This is the sounding at which the water level intersects the

corner of the tank at the opposite side of the sounding pipe. L [m] : Length of the tank H [m] : Height of the tank A comparison of the obtained sounding (S) with the imaginary sounding (I) will determine which condition occurs hence which formula will have to be applied.

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Section 12: Deductible liquids Slack condition (S > I)

FIGURE 61

Correction C [m] = Trim [m] x Distance (sounding pipe - mid of the tank) [m] LBP [m]

If the sounding pipe is located completely aft of the tank (common in practice) or completely fwd then Distance (sounding pipe - mid of the tank) = L /2 and the formula can be simplified into:

Correction C [m] = Trim [m] x L [m] 2 x LBP [m]

and since (Trim x L)/LBP = I

Correction C [m] = I [m] 2 The sign of the correction depends on the location of the sounding pipe in combination with the nature of the trim. Here the correction will be negative. In case the sounding pipe would have been located at the fwd end of the ballast tank the correction would have been positive. This correction (C) is finally to be applied on the obtained sounding (S) to obtain the sounding corrected for trim (Sc).

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Section 12: Deductible liquids Wedge condition (S < I)

FIGURE 62

Sounding corrected for trim Sc [m] = S² [m] x LBP [m] 2 x Trim [m] x L [m]

Reminder: the slack correction is to be applied on the obtained sounding, the wedge correction equals directly the corrected sounding. List corrections The same formulae can be applied to correct the soundings for list by replacing - Trim by List. - LBP by the breadth of the vessel. 12.3.6 Corresponding weight of ballast In order to calculate the weight of ballast on board the apparent density of the ballast water must be determined. Samples can be drawn e.g. from the eventual overflow, through manholes or even through sounding pipes. The density of ballast water, taken at the place of survey, equals of course the density of the surrounding water. The density must then be measured with the same type of hydrometer as described in section 11 and the result should be compared with the density of the water normally to be expected at the location of ballasting. Be aware that ballasting can be effected at different places. Different ballast tanks can therefore contain different ballast water densities. Multiplying the ballast volumes by their density will finally result in the ballast weight.

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Section 12: Deductible liquids 12.3.7 Ballast and accuracy of a draft survey Ballast determination can generate considerable errors and deviations reducing substantially the accuracy of a draft survey. Therefore it is advised, as a general rule, to have as less as possible ballast changes between initial and final survey. No change in ballast is the best of all. In this case eventual anomalies, generated at the initial survey remain constant and will be cancelled out at final survey. 12.4 Fresh water The same procedures apply for determining the fresh water on board as for ballast. However, direct reading is sometimes effected at hand of transparent plastic gauges. The difference between the quantity of fresh water on board at initial and final survey can be counterchecked at hand of the daily consumption together with the quantity of fresh water eventually received. For practical purposes the density of fresh is assumed to be 1.000 kg/l. 12.5 Bunkers Bunkers usually consist of heavy fuel, diesel oil and lubricating oil. Since the consumption of bunkers in port is relatively very small compared to the cargo weight and since any further change on board, due to bunkering or delivery on shore, can be controlled at hand of receipts, a bunker survey is not carried out as part of a draft survey. Instead of the bunker figures, as presented by the Chief Engineer, are accepted. At final survey the presented bunker figures can be counterchecked by taking into account the daily consumption together with eventual deliveries. Bunker contents are sometimes presented as volumes. The corresponding weights are then to be found by multiplying these volumes with their respective densities. These densities can differ considerably. Correct figures should be obtained from the Chief Engineer. In case of absence, following densities can be used as a guideline: Heavy fuel : 0.900 kg/l Diesel oil : 0.850 kg/l Lub oil : 0.900 kg/l 12.6 Net displacement The total weight of ballast, fresh water and bunkers is then subtracted from the displacement corrected for density resulting in the so-called net loaded displacement. 12.7 Other items Also all other items, apart from the deductible liquids, which will cause a change in weight between initial and final survey must be determined. For instance, anchors can be lowered down or pontoons may be placed on the quay. As it is very often impossible to assess an accurate weight of these items it is advised to have them in the same position at time of both surveys.

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Section 12: Deductible liquids 12.8 Exercise m/v Mindiv Obtained soundings in ballast tanks: Topwingtank 4 P 0.970 m Topwingtank 4 S 0.550 m Ballast water density 1.025 kg/l Apply the ballast table of figure 59 to calculate the ballast. Fresh water 225 m³ Heavy fuel 286.500 t Diesel oil 56.400 t Lub oil 24500 l Calculate the net loaded displacement.

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Section 13: Cargo and Constant

SECTION 13

THE CARGO WEIGHT AND CONSTANT 13.1 The cargo weight The net loaded displacement, as calculated in previous section, equals the weight of: - Cargo - Light ship - Constant. Light ship : The weight of a ready to sail vessel, determined at the completion of its

construction without ballast, fresh water, bunkers or stores on board. Constant : The total weight of all items which came on board or which were eventually

removed after the determination of the light ship such as spare parts, provisions, paint, ropes, accumulation of sediments in the ballast tanks, "black" fuel etc.

To calculate the cargo, light ship and constant must be determined. The light ship is usually presented in the vessels' documents. The constant however, consisting of a number of unascertainable weights, can not be calculated directly as such but can be obtained by carrying out a draft survey without the cargo on board. This survey, also called the light survey, will result in the net light displacement equal to: - Light ship - Constant The weight of cargo loaded or discharged on board, can now be calculated as follows: Cargo weight = Net loaded displacement - Net light displacement Cargo weight = Net loaded displacement - Light ship - Constant This means that the weight of the cargo can be established without a separate determination of light ship and constant. 13.2 The constant 13.2.1 Principle The constant is an important reference point in draft survey. Its value should be evaluated and compared with the constant usually experienced on the vessel. Unacceptable values or substantial differences with the declared experience constant require further investigation. Verify e.g. if the correct light ship's figure is applied, are eventual bulkheads included in the light ship, are former draft survey reports available which confirm the declared constant etc.). If no acceptable reason can be found then an error in draft survey measurement and/or calculation must be considered.

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Section 13: Cargo and Constant Due to its nature the constant does not remain constant but tends to increase gradually in time due to e.g. building up layers of paint, gathering an increasing amount of spare parts on board, accumulation of sediments in the ballast tanks etc. The constant can also sometimes change abruptly, especially after dry-docking, due to e.g. repairs, cleaning of the ballast tanks, remnants of previous cargo, water in the hold(s) and/or bilges etc. This is at the same time the reason why a light survey always has to be carried out even when a same vessel is surveyed in short intervals. 13.2.2 Negative constant In some occasions the obtained constant may be very small or even negative. This does not necessarily mean that the draft survey is erroneous. A negative constant is perfectly acceptable on condition that an acceptable cause can be provided such as the removal of equipment e.g. deck cranes or tweendeck without adjustment of the light ship figure in the documents. Or the light ship figure was already incorrect from the beginning. This can happen when, for saving costs, the same light ship figure was applied on a number of "identical" sister ships. 13.3 Exercise m/v Mindiv The final survey after discharging or light survey resulted in a net light displacement of 5191.820 t. Calculate the cargo weight discharged. Calculate and evaluate also the constant.

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SGS - DECEMBER 2003