ASTM F1321-14(2021)

Standard Guide for Conducting a Stability Test (Lightweight Survey and Inclining Experiment) to Determine the Light Ship Displacement and Centers of Gravity of a Vessel

SIGNIFICANCE AND USE
4.1 From the light ship characteristics one is able to calculate the stability characteristics of the vessel for all conditions of loading and thereby determine whether the vessel satisfies the applicable stability criteria. Accurate results from a stability test may in some cases determine the future survival of the vessel and its crew, so the accuracy with which the test is conducted cannot be overemphasized. The condition of the vessel and the environment during the test is rarely ideal and consequently, the stability test is infrequently conducted exactly as planned. If the vessel is not 100 % complete and the weather is not perfect, there ends up being water or shipyard trash in a tank that was supposed to be clean and dry and so forth, then the person in charge must make immediate decisions as to the acceptability of variances from the plan. A complete understanding of the principles behind the stability test and a knowledge of the factors that affect the results is necessary.
SCOPE
1.1 This guide covers the determination of a vessel’s light ship characteristics. In this standard, a vessel is a traditional hull-formed vessel. The stability test can be considered to be two separate tasks; the lightweight survey and the inclining experiment. The stability test is required for most vessels upon their completion and after major conversions. It is normally conducted inshore in calm weather conditions and usually requires the vessel be taken out of service to prepare for and conduct the stability test. The three light ship characteristics determined from the stability test for conventional (symmetrical) ships are displacement (“displ”), longitudinal center of gravity (“LCG”), and the vertical center of gravity (“KG”). The transverse center of gravity (“TCG”) may also be determined for mobile offshore drilling units (MODUs) and other vessels which are asymmetrical about the centerline or whose internal arrangement or outfitting is such that an inherent list may develop from off-center weight. Because of their nature, other special considerations not specifically addressed in this guide may be necessary for some MODUs. This standard is not applicable to vessels such as a tension-leg platforms, semi-submersibles, rigid hull inflatable boats, and so on.  
1.2 The limitations of 1 % trim or 4 % heel and so on apply if one is using the traditional pre-defined hydrostatic characteristics. This is due to the drastic change of waterplane area. If one is calculating hydrostatic characteristics at each move, such as utilizing a computer program, then the limitations are not applicable.  
1.3 The values stated in inch-pound units are to be regarded as standard. No other units of measurement are included in this standard.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Historical
• Publication Date: 14-Jan-2021
• ICS: 47.020.01 - General standards related to shipbuilding and marine structures
• Technical Committee: F25 - Ships and Marine Technology
• Drafting Committee: F25.01 - Structures

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: F1321 − 14 (Reapproved 2021) An American National Standard
Standard Guide for
Conducting a Stability Test (Lightweight Survey and
Inclining Experiment) to Determine the Light Ship
Displacement and Centers of Gravity of a Vessel
This standard is issued under the fixed designation F1321; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
INTRODUCTION
This guide provides the marine industry with a basic understanding of the various aspects of a
stability test. It contains procedures for conducting a stability test to ensure that valid results are
obtained with maximum precision at a minimal cost to owners, shipyards, and the government. This
guide is not intended to instruct a person in the actual calculation of the light ship displacement and
centersofgravity,butrathertobeaguidetothenecessaryprocedurestobefollowedtogatheraccurate
dataforuseinthecalculationofthelightshipcharacteristics.Acompleteunderstandingofthecorrect
procedures used to perform a stability test is imperative to ensure that the test is conducted properly
and so that results can be examined for accuracy as the inclining experiment is conducted. It is
recommended that these procedures be used on all vessels and marine craft.
1. Scope applicable to vessels such as a tension-leg platforms, semi-
submersibles, rigid hull inflatable boats, and so on.
1.1 This guide covers the determination of a vessel’s light
1.2 The limitations of 1 % trim or 4 % heel and so on apply
ship characteristics. In this standard, a vessel is a traditional
hull-formed vessel. The stability test can be considered to be if one is using the traditional pre-defined hydrostatic charac-
teristics.Thisisduetothedrasticchangeofwaterplanearea.If
two separate tasks; the lightweight survey and the inclining
experiment.The stability test is required for most vessels upon one is calculating hydrostatic characteristics at each move,
such as utilizing a computer program, then the limitations are
their completion and after major conversions. It is normally
conducted inshore in calm weather conditions and usually not applicable.
requires the vessel be taken out of service to prepare for and
1.3 The values stated in inch-pound units are to be regarded
conduct the stability test. The three light ship characteristics
asstandard.Nootherunitsofmeasurementareincludedinthis
determined from the stability test for conventional (symmetri-
standard.
cal) ships are displacement (“displ”), longitudinal center of
1.4 This standard does not purport to address all of the
gravity(“LCG”),andtheverticalcenterofgravity(“KG”).The
safety concerns, if any, associated with its use. It is the
transverse center of gravity (“TCG”) may also be determined
responsibility of the user of this standard to establish appro-
for mobile offshore drilling units (MODUs) and other vessels
priate safety, health, and environmental practices and deter-
which are asymmetrical about the centerline or whose internal
mine the applicability of regulatory limitations prior to use.
arrangement or outfitting is such that an inherent list may
1.5 This international standard was developed in accor-
develop from off-center weight. Because of their nature, other
dance with internationally recognized principles on standard-
special considerations not specifically addressed in this guide
ization established in the Decision on Principles for the
may be necessary for some MODUs. This standard is not
Development of International Standards, Guides and Recom-
mendations issued by the World Trade Organization Technical
This guide is under the jurisdiction of ASTM Committee F25 on Ships and
Barriers to Trade (TBT) Committee.
Marine Technology and is the direct responsibility of Subcommittee F25.01 on
Structures.
2. Referenced Documents
Current edition approved Jan. 15, 2021. Published February 2021. Originally
2.1 ASTM Standards:
approved in 1990. Last previous edition approved in 2014 as F1321–14. DOI:
10.1520/F1321-14R21. E100Specification for ASTM Hydrometers
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F1321 − 14 (2021)
3. Terminology
3.1 Definitions:
3.1.1 inclining experiment, n—involves moving a series of
weights, in the transverse direction, and then measuring the
resultingchangeintheequilibriumheelangleofthevessel.By
using this information and applying basic naval architecture
principles, the vessel’s vertical center of gravity KG is deter-
mined.
3.1.2 Condition 1, n—vessel in Condition 1 is a vessel
complete in all respects, but without consumables, stores,
cargo, crew and effects, and without any liquids on board
FIG. 1 Movement of the Center of Buoyancy
except machinery fluids, such as lubricants and hydraulics, are
at operating levels. Condition 1 is sometimes referred to as
“operational light ship.”
3.1.3 Condition 0, n—vessel in Condition 0 is a vessel as
inclined.
3.1.4 lightweight survey, n—this task involves taking an
audit of all items which must be added, deducted, or relocated
onthevesselatthetimeofthestabilitytestsothattheobserved
condition of the vessel can be adjusted to the light ship
condition. The weight, longitudinal, transverse, and vertical
location of each item must be accurately determined and
recorded. Using this information, the static waterline of the
ship at the time of the stability test as determined from
measuring the freeboard or verified draft marks of the vessel,
thevessel’shydrostaticdata,andtheseawaterdensity;thelight
FIG. 2 Metacentric Height
ship displacement and longitudinal center of gravity can be
obtained. The transverse center of gravity may also be
calculated, if necessary.
around which the vessel’s center of buoyancy (“B”) swings for
3.1.5 relative density, n—(formerly known as specific
small angles of inclination (0° to 4° unless there are abrupt
gravity)—ratio of the mass of a given volume of material at a
changes in the shape of the hull).The location of B is fixed for
stated temperature to the mass of an equal volume gas free
any draft, trim, and heel, but it shifts appreciably as heel
distilled water at the same or different temperatures. Both
increases. The location of B shifts off the centerline for small
referenced temperatures shall be explicitly stated.
anglesofinclination(“θ”),butitsheightabovethemoldedkeel
(“K”) will stay essentially the same. The location of M, on the
4. Significance and Use
other hand, is essentially fixed over a range of heeling angles
up to about 4°, as the ship is inclined at constant displacement
4.1 From the light ship characteristics one is able to calcu-
and trim. The height of M above K, known as “KM”, is often
late the stability characteristics of the vessel for all conditions
plotted versus draft as one of the vessel’s curves of form.As a
of loading and thereby determine whether the vessel satisfies
general “rule of thumb,” if the difference from the design trim
theapplicablestabilitycriteria.Accurateresultsfromastability
ofthevesselislessthan1%ofitslength,the KMcanbetaken
test may in some cases determine the future survival of the
directly from either the vessel’s curves of form or hydrostatic
vessel and its crew, so the accuracy with which the test is
tables. Because KM varies with trim, the KM must be com-
conducted cannot be overemphasized. The condition of the
puted using the trim of the ship at the time of the stability test
vessel and the environment during the test is rarely ideal and
whenthedifferencefromthedesigntrimofthevesselisgreater
consequently, the stability test is infrequently conducted ex-
than 1% of its length. Caution should be exercised when
actly as planned. If the vessel is not 100% complete and the
applying the “rule of thumb” to ensure that excessive error, as
weather is not perfect, there ends up being water or shipyard
would result from a significant change in the waterplane area
trash in a tank that was supposed to be clean and dry and so
during heeling, is not introduced into the stability calculations.
forth, then the person in charge must make immediate deci-
sions as to the acceptability of variances from the plan. A
5.2 Metacentric Height—The vertical distance between the
complete understanding of the principles behind the stability
center of gravity (“G”) and M is called the metacentric height
test and a knowledge of the factors that affect the results is
(“GM”). At small angles of heel, GM is equal to the initial
necessary.
slope of the righting arm (“GZ”) curve and is calculated using
the relationship, GZ = GM sin θ. GM is a measure of vessel
5. Theory
stability that can be calculated during an inclining experiment.
5.1 The Metacenter—(See Fig. 1). The transverse metacen- As shown in Fig. 1 and Fig. 2, moving a weight (“W”) across
ter (“M”) is based on the hull form of a vessel and is the point the deck a distance (“x”) will cause a shift in the overall center
F1321 − 14 (2021)
FIG. 4 Relationship betweenGM,KM, andKG
FIG. 3 A Typical Incline Plot
of gravity (G–G') of the vessel equal to (W)(x)/displ and
parallel to the movement of W. The vessel will heel over to a
new equilibrium heel angle where the new center of buoyancy, FIG. 5 Measuring the Angle of Inclination
B', will once again be directly under the new center of gravity
(G'). Because the angle of inclination during the inclining
angle, θ, accurately, pendulums or other precise instruments
experiment is small, the shift in G can be approximated by
areusedonthevessel.Whenpendulumsareused,thetwosides
GMtan θ and then equated to (W)(x)/displ. Rearranging this
of the triangle defined by the pendulum are measured. (“Y”) is
equation slightly results in the following equation:
the length of the pendulum wire from the pivot point to the
W x batten and (“Z”) is the distance the wire deflects from the
~ !~ !
GM 5 (1)
~displ!~ tan θ! reference position at the point along the pendulum length
where transverse deflections are measured. Tangent θ is then
SinceGManddisplremainconstantthroughouttheinclining
calculated:
experiment the ratio (W)(x)/tan θ will be a constant. By
tan θ 5Z/Y (2)
carefully planning a series of weight movements, a plot of
tangents is made at the corresponding moments. The ratio is
After each weight movement, plotting all of the readings for
measured as the slope of the best represented straight line
each of the pendulums during the inclining experiment aids in
drawn through the plotted points as shown in Fig. 3, where
the discovery of bad readings. Since (W)(x)/tan θ should be
three angle indicating devices have been used. This line does
constant, the plotted line should be straight. Deviations from a
not necessarily pass through the origin or any other particular
straight line are an indication that there were other moments
point, for no single point is more significant than any other
acting on the vessel during the inclining.These other moments
point. A linear regression analysis is often used to fit the
must be identified, the cause corrected, and the weight move-
straight line.
ments repeated until a straight line is achieved. Figs. 6-9
5.3 Calculating the Height of the Center of Gravity Above illustrate examples of how to detect some of these other
the Keel—KM is known for the draft and trim of the vessel moments during the inclining and a recommended solution for
during the stability test. The metacentric height, GM,as each case. For simplicity, only the average of the readings is
calculated above, is determined from the inclining experiment. shown on the inclining plots.
The difference between the height KM and the distance GM is
5.5 Free Surface—During the stability test, the inclining of
the height of the center of gravity above the keel, KG. See Fig.
thevesselshouldresultsolelyfromthemovingoftheinclining
4.
weights. It should not be inhibited or exaggerated by unknown
5.4 Measuring the Angle of Inclination—(See Fig. 5.) Each moments or the shifting of liquids on board. However, some
time an inclining weight, W, is shifted a distance, x, the vessel liquids will be aboard the vessel in slack tanks so a discussion
will settle to some equilibrium heel angle, θ. To measure this of “free surface” is appropriate.
F1321 − 14 (2021)
FIG. 8 Steady Wind From Port Side Came Up After Initial Zero
Point Taken (Plot Acceptable)
NOTE 1—Recheck all tanks and voids and pump out as necessary; redo
all weight movements and recheck freeboard and draft readings.
FIG. 6 Excessive Free Liquids
NOTE 1—Redo Weight Movements 1 and 5.
FIG. 9 Gusty Wind From Port Side
NOTE 1—Take water soundings and check lines; redo Weight Move-
This shift of liquids will exaggerate the heel of the vessel.
ments 2 and 3.
Unless the exact weight and distance of liquid shifted can be
FIG. 7 Vessel Touching Bottom or Restrained by Mooring Lines
precisely calculated, the GM from Eq 1 will be in error. Free
surfaceshouldbeminimizedbyemptyingthetankscompletely
5.5.1 Standing Water on Deck—Decks should be free of and making sure all bilges are dry or by completely filling the
water.Watertrappedondeckmayshiftandpocketinafashion tanks so that no shift of liquid is possible. The latter method is
similar to liquids in a tank. not the optimum because air pockets are difficult to remove
5.5.2 Tankage During the Inclining—If there are liquids on frombetweenstructuralmembersofatank,andtheweightand
board the vessel when it is inclined, whether in the bilges or in centeroftheliquidinafulltankmustbeaccuratelydetermined
the tanks, it will shift to the low side when the vessel heels. toadjustthelightshipvaluesaccordingly.Whentanksmustbe
F1321 − 14 (2021)
left slack, it is desirable that the sides of the tanks be parallel (4)Lube oil tanks,
vertical planes and the tanks be regular in shape (that is, (5)Sanitary tanks, or
rectangular, trapezoidal, and so forth) when viewed from (6)Potable water tanks.
above, so that the free surface moment of the liquid can be 6.2.1.2 To avoid pocketing, slack tanks should normally be
accurately determined. The free surface moment of the liquid of regular (that is, rectangular, trapezoidal, and so forth) cross
in a tank with parallel vertical sides can be readily calculated section and be 20 to 80% full if they are deep tanks and 40 to
by the equation: 60% full if they are double-bottom tanks.
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: F1321 − 14 F1321 − 14 (Reapproved 2021) An American National Standard
Standard Guide for
Conducting a Stability Test (Lightweight Survey and
Inclining Experiment) to Determine the Light Ship
Displacement and Centers of Gravity of a Vessel
This standard is issued under the fixed designation F1321; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
INTRODUCTION
This guide provides the marine industry with a basic understanding of the various aspects of a
stability test. It contains procedures for conducting a stability test to ensure that valid results are
obtained with maximum precision at a minimal cost to owners, shipyards, and the government. This
guide is not intended to instruct a person in the actual calculation of the light ship displacement and
centers of gravity, but rather to be a guide to the necessary procedures to be followed to gather accurate
data for use in the calculation of the light ship characteristics. A complete understanding of the correct
procedures used to perform a stability test is imperative to ensure that the test is conducted properly
and so that results can be examined for accuracy as the inclining experiment is conducted. It is
recommended that these procedures be used on all vessels and marine craft.
1. Scope
1.1 This guide covers the determination of a vessel’svessel’s light ship characteristics. In this standard, a vessel is a traditional
hull-formed vessel. The stability test can be considered to be two separate tasks; the lightweight survey and the inclining
experiment. The stability test is required for most vessels upon their completion and after major conversions. It is normally
conducted inshore in calm weather conditions and usually requires the vessel be taken out of service to prepare for and conduct
the stability test. The three light ship characteristics determined from the stability test for conventional (symmetrical) ships are
displacement (“displ”), longitudinal center of gravity (“LCG”), and the vertical center of gravity (“KG”). The transverse center of
gravity (“TCG”) may also be determined for mobile offshore drilling units (MODUs) and other vessels which are asymmetrical
about the centerline or whose internal arrangement or outfitting is such that an inherent list may develop from off-center weight.
Because of their nature, other special considerations not specifically addressed in this guide may be necessary for some MODUs.
This standard is not applicable to vessels such as a tension-leg platforms, semi-submersibles, rigid hull inflatable boats, and so on.
1.2 The limitations of 1 % trim or 4 % heel and so on apply if one is using the traditional pre-defined hydrostatic characteristics.
This is due to the drastic change of waterplane area. If one is calculating hydrostatic characteristics at each move, such as utilizing
a computer program, then the limitations are not applicable.
1.3 The values stated in inch-pound units are to be regarded as standard. No other units of measurement are included in this
standard.
This guide is under the jurisdiction of ASTM Committee F25 on Ships and Marine Technology and is the direct responsibility of Subcommittee F25.01 on Structures.
Current edition approved May 1, 2014Jan. 15, 2021. Published May 2014February 2021. Originally approved in 1990. Last previous edition approved in 20132014 as
ε1
F1321 – 13F1321 – 14. . DOI: 10.1520/F1321-14.10.1520/F1321-14R21.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F1321 − 14 (2021)
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
E100 Specification for ASTM Hydrometers
F1321 − 14 (2021)
3. Terminology
3.1 Definitions:
3.1.1 inclining experiment—experiment, n—involves moving a series of weights, in the transverse direction, and then measuring
the resulting change in the equilibrium heel angle of the vessel. By using this information and applying basic naval architecture
principles, the vessel’svessel’s vertical center of gravity KG is determined.
3.1.2 Condition 1—1, n—vessel in Condition 1 is a vessel complete in all respects, but without consumables, stores, cargo, crew
and effects, and without any liquids on board except machinery fluids, such as lubricants and hydraulics, are at operating levels.
Condition 1 is sometimes referred to as “operational light ship.”
3.1.3 Condition 0—0, n—vessel in Condition 0 is a vessel as inclined.
3.1.4 lightweight survey—survey, n—this task involves taking an audit of all items which must be added, deducted, or relocated
on the vessel at the time of the stability test so that the observed condition of the vessel can be adjusted to the light ship condition.
The weight, longitudinal, transverse, and vertical location of each item must be accurately determined and recorded. Using this
information, the static waterline of the ship at the time of the stability test as determined from measuring the freeboard or verified
draft marks of the vessel, the vessel’svessel’s hydrostatic data, and the seawater density; the light ship displacement and
longitudinal center of gravity can be obtained. The transverse center of gravity may also be calculated, if necessary.
3.1.5 relative density—density, n—(formerly known as specific gravity)—ratio of the mass of a given volume of material at a stated
temperature to the mass of an equal volume gas free distilled water at the same or different temperatures. Both referenced
temperatures shall be explicitly stated.
4. Significance and Use
4.1 From the light ship characteristics one is able to calculate the stability characteristics of the vessel for all conditions of loading
and thereby determine whether the vessel satisfies the applicable stability criteria. Accurate results from a stability test may in some
cases determine the future survival of the vessel and its crew, so the accuracy with which the test is conducted cannot be
overemphasized. The condition of the vessel and the environment during the test is rarely ideal and consequently, the stability test
is infrequently conducted exactly as planned. If the vessel is not 100 % complete and the weather is not perfect, there ends up being
water or shipyard trash in a tank that was supposed to be clean and dry and so forth, then the person in charge must make immediate
decisions as to the acceptability of variances from the plan. A complete understanding of the principles behind the stability test
and a knowledge of the factors that affect the results is necessary.
5. Theory
5.1 The Metacenter—(See Fig. 1). The transverse metacenter (“M”) is based on the hull form of a vessel and is the point around
which the vessel’svessel’s center of buoyancy (“B”) swings for small angles of inclination (0° to 4° unless there are abrupt changes
in the shape of the hull). The location of B is fixed for any draft, trim, and heel, but it shifts appreciably as heel increases. The
location of B shifts off the centerline for small angles of inclination (“θ”), but its height above the molded keel (“K”) will stay
essentially the same. The location of M, on the other hand, is essentially fixed over a range of heeling angles up to about 4°, as
the ship is inclined at constant displacement and trim. The height of M above K, known as “KM”, is often plotted versus draft as
one of the vessel’svessel’s curves of form. As a general “rule of thumb,” if the difference from the design trim of the vessel is less
FIG. 1 Movement of the Center of Buoyancy
F1321 − 14 (2021)
than 1 % of its length, the KM can be taken directly from either the vessel’svessel’s curves of form or hydrostatic tables. Because
KM varies with trim, the KM must be computed using the trim of the ship at the time of the stability test when the difference from
the design trim of the vessel is greater than 1 % of its length. Caution should be exercised when applying the “rule of thumb” to
ensure that excessive error, as would result from a significant change in the waterplane area during heeling, is not introduced into
the stability calculations.
5.2 Metacentric Height—The vertical distance between the center of gravity (“G”) and M is called the metacentric height (“GM”).
At small angles of heel, GM is equal to the initial slope of the righting arm (“GZ”) curve and is calculated using the relationship,
GZ = GM sin θ. GM is a measure of vessel stability that can be calculated during an inclining experiment. As shown in Fig. 1 and
Fig. 2, moving a weight (“W”) across the deck a distance (“x”) will cause a shift in the overall center of gravity (G–G') of the vessel
equal to (W)(x)/displ and parallel to the movement of W. The vessel will heel over to a new equilibrium heel angle where the new
center of buoyancy, B', will once again be directly under the new center of gravity (G'). Because the angle of inclination during
the inclining experiment is small, the shift in G can be approximated by GMtan θ and then equated to (W)(x)/displ. Rearranging
this equation slightly results in the following equation:
~W!~x!
GM 5 (1)
displ tan θ
~ !~ !
Since GM and displ remain constant throughout the inclining experiment the ratio (W)(x)/tan θ will be a constant. By carefully
planning a series of weight movements, a plot of tangents is made at the corresponding moments. The ratio is measured as the slope
of the best represented straight line drawn through the plotted points as shown in Fig. 3, where three angle indicating devices have
been used. This line does not necessarily pass through the origin or any other particular point, for no single point is more significant
than any other point. A linear regression analysis is often used to fit the straight line.
5.3 Calculating the Height of the Center of Gravity Above the Keel—KM is known for the draft and trim of the vessel during the
stability test. The metacentric height, GM, as calculated above, is determined from the inclining experiment. The difference
between the height KM and the distance GM is the height of the center of gravity above the keel, KG. See Fig. 4.
5.4 Measuring the Angle of Inclination—(See Fig. 5.) Each time an inclining weight, W, is shifted a distance, x, the vessel will
settle to some equilibrium heel angle, θ. To measure this angle, θ, accurately, pendulums or other precise instruments are used on
the vessel. When pendulums are used, the two sides of the triangle defined by the pendulum are measured. (“Y”) is the length of
the pendulum wire from the pivot point to the batten and (“Z”) is the distance the wire deflects from the reference position at the
point along the pendulum length where transverse deflections are measured. Tangent θ is then calculated:
tan θ5 Z/Y (2)
After each weight movement, plotting all of the readings for each of the pendulums during the inclining experiment aids in the
discovery of bad readings. Since (W)(x)/tan θ should be constant, the plotted line should be straight. Deviations from a straight
line are an indication that there were other moments acting on the vessel during the inclining. These other moments must be
identified, the cause corrected, and the weight movements repeated until a straight line is achieved. Figs. 6-9 illustrate examples
of how to detect some of these other moments during the inclining and a recommended solution for each case. For simplicity, only
the average of the readings is shown on the inclining plots.
5.5 Free Surface—During the stability test, the inclining of the vessel should result solely from the moving of the inclining
FIG. 2 Metacentric Height
F1321 − 14 (2021)
FIG. 3 A Typical Incline Plot
FIG. 4 Relationship between GM,KM, and KG
FIG. 5 Measuring the Angle of Inclination
weights. It should not be inhibited or exaggerated by unknown moments or the shifting of liquids on board. However, some liquids
will be aboard the vessel in slack tanks so a discussion of “free surface” is appropriate.
F1321 − 14 (2021)
NOTE 1—Recheck all tanks and voids and pump out as necessary; redo all weight movements and recheck freeboard and draft readings.
FIG. 6 Excessive Free Liquids
NOTE 1—Take water soundings and check lines; redo Weight Movements 2 and 3.
FIG. 7 Vessel Touching Bottom or Restrained by Mooring Lines
5.5.1 Standing Water on Deck—Decks should be free of water. Water trapped on deck may shift and pocket in a fashion similar
to liquids in a tank.
5.5.2 Tankage During the Inclining—If there are liquids on board the vessel when it is inclined, whether in the bilges or in the
tanks, it will shift to the low side when the vessel heels. This shift of liquids will exaggerate the heel of the vessel. Unless the exact
weight and distance of liquid shifted can be precisely calculated, the GM from Eq 1 will be in error. Free surface should be
minimized by emptying the tanks completely and making sure all bilges are dry or by completely filling the tanks so that no shift
F1321 − 14 (2021)
FIG. 8 Steady Wind From Port Side Came Up After Initial Zero Point Taken (Plot Acceptable)
NOTE 1—Redo Weight Movements 1 and 5.
FIG. 9 Gusty Wind From Port Side
of liquid is possible. The latter method is not the optimum because air pockets are difficult to remove from between structural
members of a tank, and the weight and center of the liquid
...