Stability and Trim for the Ship's Officer

By William E. George

Stability and Trim for the Ship’s Officer has been completely updated after twenty-two years. Aboard today’s vessels, technology and computers abound as ship’s gear. The once long and tedious calculations for stability, trim, and hull strength are now done in minutes. But no matter how much change the industry has undergone, the laws of physics are constant. The only way to verify that the computer is coming up with accurate figures is to read the ship’s drafts. Two new chapters have been included, “Prerequisites for Stability, Trim, and Hull Strength Calculations,” and “U.S. Coast Guard Questions on Stability, Trim, and Longitudinal Hull Strength.” The appendix has also been updated to include the Stability Data Reference Book—August 1989 Edition, which is the same supplied in the United States Coast Guard license examination room.

• Language: English
• Publisher: Open Road Integrated Media
• Release date: Jun 30, 2009
• ISBN: 9781507300770

Book preview

CHAPTER 1

Prerequisites for Stability, Trim, and Hull Strength Calculations

The true mastery of the subjects of stability, trim, and hull strength should be the responsibility of all deck and engine officers aboard every vessel. An awareness of the effect of changes to the vessel’s cargo weights, as well as the use of ballast and bunker tanks, should be a safety concern to all of the ship’s officers, not just the vessel’s master and chief officer. As you will read in a later chapter, a valve left open can cause uncontrolled shifts of weight that can result in the loss of a vessel. It should also be noted that smaller vessels are less forgiving than larger ones. Deck and engine officers on these smaller displacement vessels, such as commercial fishing industry vessels, supply vessels, and towing vessels, need to pay very close attention to what they are doing when moving weights on their vessel and how the vessel is responding to these changes.

In keeping the idea of economical and safe operation of the vessel in mind, the ship’s officer should be able to, with the knowledge in this book, intuitively predict how a change made to the vessel’s loaded condition will reflect in the vessel’s trim, list, and hull strength both prior to the change and before any calculations are made on the vessel’s loading computer or done manually. This method provides a good double check on the information obtained from the vessel’s approved loading computer.

The principles that are covered in this book apply to all vessels, unless the vessel is aground. The unique condition of a grounded vessel will be covered as a special case in chapter 12, The Ship in the Damaged Condition, Effect of Grounding on Stability. While the laws of physics have not changed, vessels will continue to change to meet their intended designed mission for transportation, service, and national defense. This first chapter will be referred back to constantly in the chapters that follow. This book is focused on the ship’s officer being able to understand the subjects of stability, trim, and hull strength with the same proficiently as the deck officers understand navigation and the engine officers understand the operating principles of their vessel’s fuel system. It is the goal of this book for ship’s officers to be able to predict what will happen in the future rather than dwell on documenting what has happened in the past.

THE PARADIGM OF ACTUAL VS. ASSUMED LOADING CONDITIONS

A paradigm is a generally accepted viewpoint of something at a given time. It is very important that the ship’s officer realize from the outset that the paradigm of the actual loaded condition is the vessel itself. The vessel should be considered a full scale experiment such that it displays its actual condition as long as it is not aground, because it is in an equilibrium condition. On the other hand, the paradigm of a vessel’s loading computer, loading manual, or trim and stability booklet represents only an assumed loading condition based on the data used to calculate this assumed condition.

While these are great tools for planning a final loaded condition prior to the cargo operations, they seem to be of little help to the vessel’s officer when decisions need to be made as to where the last 2,000 tons of bulk cargo are to be loaded. It has been the author’s experience to observe vessel officers using the ship’s loading computer or trim and stability booklet’s calculation forms as trial and error calculating devices rather than tools that confirm where and how much to load to achieve the desired stability, trim, and hull strength.

The major point is that if an officer needs to know the actual condition of a vessel, he or she should read the vessel’s actual drafts! In the following chapters, this book will demonstrate professional protocols for the ship’s officer to practice that will ensure the true condition of the vessel is known.

THE STUDY OF STABILITY, TRIM, AND HULL STRENGTH VS. NAVIGATION—(AN ANALOGY)

The subjects of stability, trim, and hull strength are each related but different; however, they are no more difficult to master than navigation and are not just for deck officers. In navigation, the positions of departure and destination are known. Along the way, the position of the vessel is determined to monitor the progress of the voyage and make sure hazards are avoided along the way. In navigation, the vessel’s actual position is constantly monitored to a planned position in time. This allows adjustment to the course, speed, or estimated time of arrival (ETA) to the destination.

The problem in the past was that the subjects of stability, trim, and hull strength have been approached as complete stand-alone calculations with no reference to checking the vessel’s condition until all of the loading was more or less completed. The same was done with the arrival condition at the next port. The vessel’s arrival condition was calculated with the hope that it would be accurate when the vessel arrived at the next port with no means of checking for an actual worst-case condition prior to arrival.

While trim (the difference between the forward and after draft) can easily be checked by observing the vessel’s drafts, initial stability (GM) is not as directly observable. Hull strength can be somewhat observed by checking the vessel’s hull deflection. This book will strive to facilitate the ship’s officer’s understanding that the vessel’s actual condition is observable and can be used to confirm the progress of cargo operation as well as a starting point to generate new calculations based on the observed actual condition.

READING THE VESSEL’S DRAFT MARKS—THEY ARE NOT JUST FOR NAVIGATION

Reading the vessel’s draft marks, routinely and accurately, is the key to determining the vessel’s actual condition. This is no different from getting a fix when you are navigating on the bridge, or gauging a fuel oil tank in the engine room. The proper observation of the vessel’s drafts can result in determining the displacement, the weight of the vessel, within less than one half a percent! In addition, the application of the vessel’s trim to fuel tank soundings can increase the accuracy of bunker calculations greatly. The draft readings will also result in determining the vessel’s trim and list, which can be used to calculate the actual longitudinal and transverse center of gravity of the vessel as observed. While the stability, a tendency, cannot be directly observed from the vessel’s draft marks, the actual mean draft (the average draft) obtained will aid in determining hydrostatic data needed to calculate the vessel’s stability. Regular draft readings will also aid to prevent the vessel from exceeding the limits imposed on it due to its loading manual or its load line.

The Location of the Draft Marks

Think of the ship’s hull as a highly calibrated vessel. The draft marks are how it is calibrated. Merchant vessels have six sets of draft marks. (See figures 1-1 and 1-2.) The draft marks are located on the port and starboard sides at the bow usually aft of the forward perpendicular, at amidships, and at the stern forward of the after perpendicular. The actual draft marks are located such that they can be read for the range of the drafts the vessel will experience. As shown in figure 1-2, the draft marks cannot be located at the vessel’s forward and after perpendiculars due to the curvature of the hull. The draft of a vessel is the vertical distance from the lowest point of the hull to the waterline. On merchant vessels this lowest point is the vessel’s baseline. One caution—the vessel could always have some sort of appendage extending below its baseline. The vessel’s officer should consult the vessel’s plans for such appendages.

Fig. 1-1. Think of the ship’s hull as a highly calibrated vessel. Merchant vessels have six sets of draft marks. Photo: Captain Milton L. Fox.

Fig. 1-2. Typical locations of draft marks, as shown in a ship’s stability booklet.

APPARENT DRAFT VS. TRUE DRAFT

The drafts obtained from reading the draft at the draft marks are known as apparent draft. The true draft is where the waterline intersects the forward and after perpendiculars. The forward perpendicular is located at the intersection of the design waterline and the stem of the vessel. The after perpendicular is located at the intersection of the rudder post and the design waterline. When trim is equal to zero, the apparent drafts equal the true drafts! When there is trim, the drafts at the perpendiculars, the true drafts, do not equal the drafts at the draft marks, the apparent drafts. The conversion from apparent draft to true draft due to trim will be covered shortly.

READING DRAFT MARKS

Draft marks can be displayed in English units of feet and inches and Metric units meters and centimeters. (See figure 1-3.) The reader will soon discover it is much easier working with drafts meters and centimeters than feet and inches. Drafts in feet and inches are read to the closest inch and calculated to the closest tenth of an inch. Drafts in meters are read to the closest centimeter and calculated to the closest tenth of a centimeter. Please note this section covers how draft marks are read. The method of how to actually observe them will be left up to the seamanship and resourcefulness of the reader. Always remember, safety first. Drafts can also be obtained by measuring freeboards from a known point on deck to the waterline.

In the English system, used on most U.S. flag vessels, each draft mark in Arabic numbers or Roman numerals is 6 inches high. The bottom of each Arabic number or Roman numeral draft mark rests at the beginning of the reading in whole feet. The top of the number or numeral is at the reading in whole feet plus six inches. The vertical distance between the numbers or numeral is also six inches. Odd and even numbers or numerals are shown. Draft marks in the English system of feet and inches can be displayed as seen in figures 1-4 and 1-5.

In the Metric system, each numeral in Arabic numbers is 10 centimeters high and 10 centimeters apart. The first number that starts a draft in whole meters is usually designated with a capital M following it, such as 4M. If the waterline was observed to just touch the bottom of the 4M, the apparent draft would read 4.00 meters. If the waterline was observed to just touch the top of the 4M, the apparent draft would read 4.10 meters. If the waterline was observed to just touch the middle of the 4M, the draft would read 4.05 meters. Between drafts in whole meters only the even numbers are shown for the distance between the drafts in whole meters such as 2, 4, 6, and 8. Each represents respectively 20, 40, 60, or 80 centimeters. Please refer to and study figure 1-3. With a little practice it is very possible to read the drafts within one centimeter. They can be displayed as and read as seen in figures 1-6 and 1-7.

Fig. 1-3. Examples of how draft marks in English and Metric units are displayed. Note: In this illustration all draft marks are shown hand drawn on a grid so that corresponding drafts in different systems can be read. One meter equals 3.2808 feet. One inch equal 2.54 centimeters. Courtesy Captain S. Fraser Sammis, past president, National Cargo Bureau, Inc.

Fig. 1-4. Photo of draft marks in feet and inches using Arabic numbers. This draft mark reads 22 feet and 8 inches.

Fig. 1-5. Photo of draft marks in feet and inches using Arabic numbers. This draft mark reads 19 feet and 4 inches.

A little bit more about metric draft marks. The drafts can also be displayed in decimeters, which are units of 10 centimeters. Refer back to figure 1-3 for examples of variations of this. A reading of 50 decimeters would be equal to 5.00 meters. Drafts in whole meters can also be shown as described before as 4M, but the intermediate drafts between whole meters can be shown in decimeters in even units of 20, 40, 60, and 80. They are read in the same manner to the closest centimeter.

DRAFT READINGS AND WATER DENSITY

From the outset, a good rule to keep in mind is that if it’s important enough to read your vessel’s drafts, it’s also important enough to obtain a good water density using a hydrometer. It is necessary to understand that almost all vessels’ computers and approved stability booklets assume full saltwater for all calculations (density = 1.025). In reality, the actual condition will normally vary, due to the brackish water in harbors. Following the paradigm of actual vs. assumed loading conditions, the assumed condition is not as accurate as the actual observed condition when the proper water density is taken into consideration. On a vessel with a 70,000 ton displacement, the difference between a density of an assumed density of 1.025 and an actual density of 1.020 will be 350 tons less. This represents an increase of roughly 2.12 inches or 5.38 centimeters of actual draft that would be more than the assumed draft condition.

Fig. 1-6. Photo of draft marks in meters and centimeters taken at the starboard bow. This draft mark reads 10.20 meters. In the real world, not all draft marks are freshly painted.

Fig. 1-7. Photo of draft marks in meters and centimeters taken at the starboard stern. This draft mark reads 10.56 meters.

Brass Load Line Hydrometers vs. Glass Draft Survey Hydrometers

Hydrometers made for use with the ship’s loadline marks are usually made of brass and are graduated in specific gravity 60°F/60°F in vacuo. Hydrometers used in draft surveying to determine the weight of the vessel’s cargo are graduated in density kg/liter in air (density in air is sometime termed apparent density). For example, the reading on a specific gravity hydrometer indicates a ratio not a weight. The reading on a draft survey hydrometer indicates a weight. Thus, a reading of 1.012 on a specific gravity hydrometer means the sample of water in which it is immersed weighs 1.012 times as much as an equal volume of pure freshwater weight in a vacuum. A reading on a draft survey hydrometer means that one liter of the sample water in which it is immersed weighs 1.012 kilograms weighed in air. Consider the significance of in vacuum as opposed to in air. If you had a beam balance inside of a bell jar from which all air had been extracted and you placed one pound of lead on one pan and piled a light product, such as balsa wood, on the other pan until the scales balanced, you could claim to have provided one pound of balsa wood. However, when you removed the bell jar to retrieve your pound of balsa wood, the scale would tip. This is because both the balsa wood and the lead are now being floated by the surrounding air. And, obviously, the balsa wood displaces more air than does the lead and, therefore, experiences more buoyancy from the air. So now it appears that you do not have a pound of balsa wood. You have been short changed because of the in air/in vaccum differences. See figure 1-8.

Actually, in the case of draft surveys (determining cargo weight by Archimedes’ principle), the discrepancy is in the other direction, that is, the in air/in vacuum difference causes an over-indication instead of a shortage. This is because the instrument reading is related to the reference standard and not the sample. A volume of pure water that weighs one pound in a vacuum weighs 0.998 pounds in air for the identical volume. One of these values must be the reference to apply to the total immersed volume of the ship’s hull, as indicated by its draft marks, in order to obtain the actual weight of the ship and everything that is in it. Since cargoes are weighed in air, the 0.998 reference is the logical one to use and this is the one used by a draft survey hydrometer. A specific gravity hydrometer may be used for commerce if it is corrected for the in air/in vacuum difference. Thus, a reading on a specific gravity hydrometer minus 0.002 is equal to the reading of a draft survey hydrometer.

To illustrate the effect of this difference consider the same draft survey as worked up for each of these instruments:

Fig. 1-8. Consider the significance of in vacuum as opposed to in air. Courtesy Captain Joseph Downs, National Cargo Bureau, Inc.

In this example, the use of the specific gravity hydrometer indicates that 150.25 long tons more cargo was discharged than actually discharged. Although this is an error of less than 0.2 percent and well within the 0.5 percent error that is generally attributed to the draft survey method, it is an error, which can be eliminated by the use of a draft survey hydrometer.

This slight difference leads directly to the question of why the specific gravity hydrometer, which has been universally used for draft surveys a great many years, is now to be rejected in favor of the draft survey hydrometer. The reason is that, due to the greatly increased deadweight of today’s ships, the slight difference has become a significant number. This, in turn, has pressured commercial interests to require greater precision.

Another question that is sometimes asked If the draft survey hydrometer is correct, why isn’t it used for load line calculations? First of all, the draft survey hydrometer is not correct as opposed to the specific gravity hydrometer being incorrect. Both are correct for their intended purpose. The load line regulations are not concerned with the weight of cargo. Instead, they are concerned with the freeboard (the reserve buoyancy) of the ship. For calculations pertaining to load line matters, Article 12(2) of the International Convention on Load Lines, 1966, refers to … fresh water of unit density. Therefore, the reference standard is 1.000 and the specific gravity hydrometer is the correct instrument to use. A draft survey hydrometer may be used in lieu of a brass specific gravity load line hydrometer if a +0.002 correction is applied.

Finally, there is a question: If the draft survey hydrometer reads weight in kilograms per liter, how do our calculations result in metric tons? This is due to the advantage of the Metric system regarding interchangeability of units. Thus, a draft survey hydrometer reading is in kilograms per liter. If you multiply this by 1,000/1,000, a metric tons per cubic meter results.

Calculating the Correction to Displacement for Density

The formula used to correct displacement for density as illustrated previously is the same for English and Metric units as follows:

Correction to displacement for density

= (1.025 – observed density)(displacement)/1.025

where observed density is determined with a hydrometer.

Displacement is taken from the hydrostatic tables for the observed draft for saltwater displacement. If the displacement is in long tons, the correction is in long tons. If the displacement is in metric tons, the correction is in metric tons.

Unless the observed density is greater than 1.025, the correction is always negative.

If your ship’s hydrostatics are based on 1.026, substitute this for 1.025 in the formula above.

Note: In the preceding example calculation, there are four density correction calculations where the above formula has been used.

See appendix F for more information on draft survey hydrometers.

DETERMINING THE MEAN DRAFT

The word mean simply means the mathematical average of two or more observations, such that (A + B)/2. For example the mean of 4 and 6 is equal to (4 + 6)/2 = 5.)

The forward mean draft is the average of the drafts read at the bow on the port and starboard side. It is an apparent draft reading. The after mean draft is the average of the drafts at the stern on the port and starboard side. It too is an apparent draft reading. The midship mean draft is the average of the drafts at the midship marks on the port and starboard side. If the midship marks are actually located at amidships, half way between the forward and after perpendiculars, then it is a true draft reading. If not, it is apparent and must be corrected to amidships to be a true reading.

Why are mean drafts used? Mean drafts are used to average out any list or distortion, or twist in the hull. By using the port and starboard drafts to calculate the mean draft, the draft is actually calculated on the vessel’s centerline. By using the forward and after mean draft, the equivalent draft is calculated at midships. When you compare the midship mean draft with the forward and after mean draft, the hull deflection can be determined. Remember, you cannot read drafts on the centerline, only calculate them.

SOME BASIC CALCULATIONS WITH THE FORWARD AND AFTER DRAFT READINGS

EXAMPLE 1. Determine the mean draft on the centerline of the vessel at the bow if the port forward draft mark reads 36 feet 3 inches and the starboard forward draft mark reads 36 feet 9 inches. Note this is also known as the forward mean draft.

SOLUTION. 36 feet 6 inches. This is the average of the port and starboard forward draft mark readings. (The term mean simply is the average of two numbers, such that (A + B)/2. For example, the mean of 4 and 6 is equal to (4 + 6)/2 = 5.)

EXAMPLE 2. Determine the mean draft on the centerline of the vessel at the stern if the port after draft mark reads 39 feet 4 inches and the starboard after draft mark reads 39 feet 10 inches. Note this is also known as the after mean draft.

SOLUTION. 39 feet 7 inches. This is the average of the port and starboard after draft mark readings.

EXAMPLE 3. The vessel’s trim is the difference between the forward and after drafts. The forward draft mark reads 9.38 meters, and the after draft mark reads 10.56 meters. What is the apparent trim?

SOLUTION. Apparent trim = 1.18 meters by stern.

EXAMPLE 4. The forward draft mark reads 24 feet 4 inches and the after draft mark reads 22 feet 8 inches. What is the apparent trim?

SOLUTION. Apparent trim = 1 foot 8 inches by bow.

EXAMPLE 5. The average or mean port and starboard forward draft marks are 9.38 meters, and the after mean draft marks read 10.56 meters. What are the drafts at the forward and after perpendiculars if the forward marks are 6 meters aft of the forward perpendicular and the after marks are 15 meters forward of the after perpendicular? The distance between the draft marks is 195 meters. What is the true trim?

SOLUTION.

EXAMPLE 6. The forward draft mark reads 24 feet 4 inches, and the after draft mark reads 22 feet 8 inches. What are the drafts at the forward and after perpendiculars if the forward marks are 26 feet aft of the forward perpendicular and the after marks are 45 feet forward of the after perpendicular? The distance between the draft marks is 680 feet. What is the true trim?

SOLUTION.

USING THE MIDSHIP DRAFT MARKS

The vessel’s maximum draft and corresponding freeboard are determined for a merchant vessel at amidships when consulting the vessel’s seasonal load line. (For some smaller commercial fishing industry vessels and supply vessels, the maximum draft midships with a minimum freeboard is determined at the stern. Consult the vessel’s loading manual, stability letter, or load line certificate for exact requirements.) By observing the port and starboard midship draft marks, the mean midship draft can be determined. When you compare the mean midship draft with the mean forward and after draft, it is possible to calculate the vessel’s hull deflection in terms of hog or sag. Hog is when the vessel’s mean amidships draft is less than the mean forward and after draft and can load more cargo than indicated by the fore and aft mean draft. Sag is when the vessel’s mean amidships draft is greater than the mean forward and after draft and can load less cargo than indicated by the fore and aft mean draft. Also consider, when comparing mean fore and aft and mean amidships drafts, the drafts read at the draft marks must be corrected to the perpendiculars so that the mean fore and aft draft is located at amidships. Refer back to figure 1-2 for location of the draft marks and perpendiculars.

EXAMPLE 7. The forward mean draft reads 9.38 meters, and the after mean draft reads 10.56 meters. What are the drafts at the forward and after perpendiculars if the forward marks are 6 meters aft of the forward perpendicular and the after marks are 15 meters forward of the after perpendicular? The distance between the draft marks is 195 meters. What is the true forward and aft mean draft? If the midship port draft is 10.15 meters and the midship starboard draft is 9.90 meters, calculate the hull deflection.

SOLUTION.

EXAMPLE 8. The forward draft mark reads 24 feet 4 inches, and the after draft mark reads 22 feet 8 inches. What are the drafts at the forward and after perpendiculars if the forward marks are 26 feet aft of the forward perpendicular and the after marks are 45 feet forward of the after perpendicular? The distance between the draft marks is 680 feet. What is the forward and aft mean draft? If the midship port draft is 22 feet 2 inches and the midship starboard draft is 23 feet 10 inches, calculate the hull deflection.

SOLUTION.

DETERMINING THE QUARTER MEAN DRAFT CORRECTED FOR DEFLECTION

Keeping in mind that a merchant vessel, not a barge, is finer at the ends than in its parallel mid-body, all drafts do not contribute equally to the one mean draft that represents the vessel floating with trim and hull deflection. This one mean draft is known as the mean draft corrected for deflection, or the quarter mean draft, or the mean of mean of means draft. The abbreviation for this is M/M/M. Simply stated the quarter mean draft is equal to the mean port and starboard forward draft plus the mean port and starboard after draft plus six times the mean port and starboard midship draft divided by eight. This is because six eights of the vessel is in the middle and only one eight is considered to be each at the bow and stern sections that are finer. The quarter mean draft is significant because it is the equivalent draft that can be used to enter the vessel’s hydrostatic data to extract a very exact displacement in metric tons or long tons for saltwater (density = 1.025). The accuracy of this displacement is within + or – 0.5% or 99.5% accurate. This will be a significant number when doing calculations in the future. As you will see, it is much easier and quicker to read the drafts and calculate total displacement than do a detailed inventory of the vessel.

EXAMPLE 9. The true mean forward draft is 9.90 meters. The true mean after draft is 10.10 meters. The midship mean draft is 9.90 meters. Calculate the hull deflection in terms of hog or sag. What is the vessel’s quarter mean draft? If the Hydrostatic Table shows the following draft and displacement relationships, what is the vessel’s saltwater displacement without any correction to displacement for trim applied?

SOLUTION. Calculate the hull deflection in terms of hog or sag.

What is the vessel’s quarter mean draft?

M/M/M = (F + A + 6M)/8(990 + 10.10 + 6(990))/8 = 933 meters

If the Hydrostatic Table shows the following draft and displacement relationships, what is the vessel’s displacement? By interpolation

54,500 + 0.3(500) = 54,650 MT

EXAMPLE 10. The forward draft mark is 8 meters aft of the forward perpendicular. The after draft marks are 15 meters forward or the after perpendicular. The length between perpendiculars (LBP) is 165 meters. The amidships draft marks are at amidships. Using the drafts recorded in figure 1-9, calculate the hull deflection in terms of hog or sag. What is the vessel’s quarter mean draft? If the Hydrostatic Table shows the following draft and displacement relationships, what is the vessel’s saltwater displacement without any correction to displacement for trim applied?

SOLUTION. Calculate the hull deflection in terms of hog or sag.

Calculate the apparent forward mean draft:

Fore port and starboard mean = (8.65 + 8.70)/2 = 8.675 meters

Calculate the apparent after mean draft:

After port and starboard mean = (9.35 + 9.42)/2 = 9.385 meters

Calculate the apparent trim:

Apparent aft mean draft – apparent forward mean draft

= 9.385 – 8.675 = 0.71 meters aft

Fig. 1-9. Typical way the drafts are written in a notepad when observed. Note the observed water density is also recorded. When a vessel has a list, it is possible for the amidships draft to be actually greater than the after draft due to the vessel’s beam at the location of the draft marks.

Calculate the trim per meter of length:

Calculate correction to forward and after draft marks to perpendiculars:

Calculate the drafts at the forward and after perpendiculars:

Calculate the apparent after mean draft:

Calculate the forward and aft mean draft:

Forward and aft mean = (8.635 + 9.460)/2 = 9.048 meters

Calculate the midship mean draft (marks are at midship, no correction required):

Midship port and starboard mean = (8.52 + 9.54)/2 = 9.030 meters

Calculate hull deflection:

What is the vessel’s quarter mean draft?

Using the Hydrostatic Table in example 10 showing the draft and displacement relationships, what is the vessel’s saltwater displacement without any correction to displacement for trim applied?

By interpolation

45,000 + 0.034/0.1(500) = 45,170.00 MT

CALCULATING AIR DRAFTS

An air draft is the vertical distance from the vessel’s actual waterline upward to a point on the vessel such as an Inmarsat-C Antenna, the top of Hatch Cover No. 4, the top of Hatch Cover No. 1, or the top of the Whip Antenna on the foremast. The air draft calculation requires the ability to calculate your vessel’s true drafts and trim. Figure 1-10 illustrates a calculation of how the height of specific points on the ship can be calculated knowing the vessel’s true draft at the perpendiculars and the true trim. This is a useful calculation to determine the height of eye on the bridge for the specific draft and trim of the vessel as well as the minimum clearance a vessel requires to pass under a bridge. The general formula for air draft is as follows:

Air draft = (A) – (dA – ((h)/(LBP)T))

where

EXAMPLE 11. The height of the bridge is 30 meters above the keel. Your vessel’s true after draft is 8.5 meters and true trim is 4.0 meters. If the length between perpendiculars is 185 meters, calculate the height of the air draft of the bridge at the starboard gyro repeater if it is located 33 meters forward of the after perpendicular.

Fig. 1-10. An illustration of the calculation of air draft at various points on a vessel.

where

THE VESSEL AS ITS OWN BEST LOADING COMPUTER

To determine or define the vessel’s true condition at any point in time, you need to establish the vessel’s total weight in tons (displacement) and the vessel’s coordinates for its center of gravity, G. The vessel’s coordinates for its center of gravity are known as the longitudinal center of gravity, the vertical center of gravity, and the transverse center of gravity. In following chapters, these will be discussed at length. Remember the vessel must be afloat to use this method. It should also be noted that a standard clause in vessel’s charter parties requires a safe berth, one that has adequate depth of water to prevent grounding as the vessel works cargo and pumps ballast.

An Example of Determining Actual vs. Assumed Displacement

Because the vessel has six sets of draft marks, either in meters or feet and inches, you can read all six marks and get a very good average draft that corresponds to tables provided to get the total weight of the vessel known as the displacement. So to find the actual weight of the vessel, you can read all six drafts and make some small corrections for trim and water density, which will be covered in chapter 9. The actual calculation takes no more time than reading the drafts. Or, you can calculate an assumed displacement by making a complete inventory of the vessel by adding up all the weight you can attempt to identify. To do this, you need to sound all tanks (ballast, fuel, freshwater, lube oil) and void spaces. Once you obtain all the tank sounds, they must be corrected for trim so you still need to read the drafts. This could, in reality, take hours! If you leave any weights out or if the weights you use are over- or understated, your calculated answer’s error will increase. The sum of all these known weights should add up to the total displacement. As you can see, it is much faster and more accurate to read the drafts than to do all the data input or bookkeeping required to calculate an assumed displacement. This is a simple example of using the vessel as its own loading computer to determine its total displacement.

In like fashion, the coordinates of the vessel’s actual center of gravity can be determined. The details of these methods will be covered in chapters 3 and 9.

Again the paradigm of the actual condition is very powerful when you want to know the truth about a vessel’s condition. Remember, as long as the vessel is not aground, the vessel knows its true condition, and all you need to do is observe it.

Protocols in Dealing with Actual Loading Conditions

When you visit a doctor’s office for any reason, the doctor or his staff usually observes your weight, blood pressure, heart rate, and temperature. These are your vital signs. By recording your vital signs at every visit, the doctor can quickly observe if your condition is stable, improving, or getting worse.

In like manner, you as a ship’s officer can take the actual observations of drafts, list, and rolling period of your vessel so you can routinely determine its actual displacement as well as the coordinates for the center of gravity. Like all observations, there are proper ways to obtain them. The work expended in the beginning to learn to read and calculate drafts accurately and calculate trim will pay off greatly for the confidence and accuracy you will gain. It will also give you the ability to quickly confirm if the data in your vessel’s loading computer is complete and accurate. The medical professionals always examine their patients prior to any treatment, in like manner the ship’s officer should examine the vessel to determine its displacement and coordinates for its center of gravity. The ship’s officer also needs to have an understanding of the assumptions the shipbuilder used to prepare the information that he worked with as found in the vessel’s loading computer, loading manual, or stability booklet. Could you imagine trying to learn how to navigate without a knowledge of latitude and longitude or where the equator or the north or south poles are located? It is very hard to comprehend the subjects of stability, trim, and hull strength without a knowledge of the basic assumptions the designer made. If you know the basic assumptions made by the shipbuilders to generate the documents that are provided for you on the ship to do your job, you will be able to readily understand the corrections that need to be made to observed conditions to calculate accurate results using this information. Likewise, you will also be able to determine by verification of the vessel’s actual condition if the vessel’s loading computer is providing you with good information. The Capacity Plan is one plan that helps to establish the assumed conditions the shipbuilder used. The following study of the Capacity Plan found on merchant vessels will help to reveal these assumed conditions the ship’s officer needs to know.

The Capacity Plan

One universal plan that is posted on virtually all well-managed vessels is the Capacity Plan. This plan usually contains a to-scale profile view of the vessel and a midship section of the vessel as well as the capacities of all cargo spaces and tanks, and a deadweight scale. The unusual thing about the Capacity Plan is that it is made by the shipyard to the specifications of the vessel owner’s requirements. This plan is a compilation of approved information from other approved sources such as the vessel’s Trim and Stability Booklet, Load Line Document, and General Arrangement Plan. What makes the Capacity Plan so interesting is that while it is posted on almost all vessels, there is no regulation requiring it to be posted! Keep in mind that the Capacity Plan is optional. Because it is posted on almost all vessels, it must be considered a very useful plan to have as your reference. In most cases, the Capacity Plan reveals some assumptions that the naval architect or the shipbuilder made when the calculations were prepared for the vessel. For example by close examination, there are waterlines drawn showing no list or no trim. The vessel is also drawn so that no hog or sag of the hull is indicated. While this may seem trivial, these basic assumptions that must be understood just as a student of navigation must be taught the assumed conditions of the grid for latitude and longitude, such as all meridians are great circles running through the north and south poles and that the equator is a great circle located 90° from each pole.

Fig. 1-11. The Capacity Plan. This plan has a wealth of information. It is usually posted in the ship’s office or passageway near the ship’s office. The plan can easily measure eight-feet wide and four-feet high.

Throughout this book reference will be made to the vessel’s Capacity Plan. Distances can be scaled longitudinally, vertically, and transversely. Tank capacities are calculated for the no trim and no list conditions. Usually water densities are assumed at 1.025. As you proceed with your study of the subject, the Capacity Plan will be a tool you will learn to reference. Study your vessel’s Capacity Plan closely. Notice the small details, then stand back and notice the overall presentation. On one document, the vessel’s hydrostatics (by use of the deadweight scale)