|
STANDARD
First edition
19924 2-l 5
Refrigerated light hydrocarbon fluids -
Calibration of spherical tanks in ships -
Part 2:
Triangulation measurement
- Jaugeage des reservoirs spheriques
Hydrocarbures legers refrigeres
ZI bord des navires -
Partie 2: Methode par trianguiation
Reference number
ISO 909 l-2: 1992( E)
---------------------- Page: 1 ----------------------
ISO 909%2:1992(E)
Contents
Page
. . . . . . . . . . . . . . . . . . . . . . . .*. 1
1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2 Normative references ~.,,,,.,,.,.,,.,.,.,.~.
3 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
4 Precautions during measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
5 Equipment . . 2
6 Preparation . . 3
7 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .*. 5
8 Coordinate System . 8
9 Calculation . 8
13
IO Data processing .
11 Calculation procedure . 13
12 Calibration table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Annexes
15
A Safety precautions .
16
B Calibration uncertainty .
............................. 18
C Example of main gauge table at - 160 “C
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
D Example of trim correction table
E Example of Iist correction table . . 20
F Example of correction table for tank Shell expansion or
contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
0 ISO 1992
All rights reserved. No part of this publication may be reproduced or utilized in any form
or by any means, electronie or mechanical, including photocopying and microfiim, without
Permission in writing from the publisher.
International Organization for Standardization
Case Postale 56 l CH-1211 Geneve 20 l Switzerland
Printed in Switzerland
ii
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ISO 9091=2:1992(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide
federation of national Standards bodies (ISO member bodies). The work
of preparing International Standards is normally carried out through ISO
technical committees. Esch member body interested in a subject for
which a technical committee has been established has the right to be
represented on that committee. International organizations, govern-
mental and non-governmental, in liaison with ISO, also take patt in the
work. ISO collaborates closely with the International Electrotechnical
Commission (IEC) on all matters of electrotechnical standardization.
Draft International Standards adopted by the technical committees are
circulated to the member bodies for voting. Publication as an Inter-
national Standard requires approval by at least 75 % of the member
bodies casting a vote.
International Standard ISO 9091-2 was prepared by Technical Committee
ISO/TC 28, Petroleum products and lubricants, Sub-Committee SC 5,
Measurement of light hydrocarbon fluids.
ISO 9091 consists of the following Parts, under the general title Re-
frigerated light hydrocarbon fluids - Calibration of spherical tanks in
ships:
- Part 1: Stereo-photogrammetry
-
Part 2: Triangulation measurement
Annexes A, B, C, D, E and F of this part of ISO 9091 are for information
only.
. . .
Ill
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ISO 9091=2:1992(E)
Introduction
Large quantities of light hydrocarbons consisting of compounds having
one to four carbon atoms are stored and transported by sea as re-
frigerated liquids at pressures close to atmospheric. These liquids tan
be divided into two main groups: liquefied natura1 gas (LNG) and
liquefied Petroleum gas (LPG). Bulk transportation of these liquids by
sea requires special technology in ship design and construction to en-
able such transportation to be safe and economical.
Measurement of cargo quantities in ships’ tanks for custody transfer
purposes has to be of a high Order of accuracy. The two Parts of this
International Standard, together with other Standards in the series,
specify methods of internal measurement of ships’ tanks from which
tank calibration tables tan be derived.
For internal measurement, methods of liquid calibration, physical
measurement, Optical measurement and stereo-photogrammetry, etc.
are in general use. Liquid calibration cannot be used for large spherical
tanks designed to operate at near atmospheric pressure with refriger-
ated light hydrocarbons because the hydrostatic pressure exerted by the
calibrating liquid may exceed the design pressure when filled higher
than a certain level. This patt of ISO 9091 covers a calibration technique
with a central
applicable to spherical tanks equipped
pipe/instrumentation column.
iv
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INTERNATIONAL STANDARD ISO 9091=2:1992(E)
Refrigerated light hydrocarbon fluids - Calibration of
spherical tanks in ships -
Part 2:
Triangulation measurement
3.1 base Point: Centre Point of the theodolite set
1 Scope
above the traverse Point.
1.1 This part of ISO 9091 specifies a triangulation
3.2 basic Pentagon: Pentagon connecting base
method for the internal measurement of spherical
Points.
tanks in liquefied gas carriers.
1.2 This part of ISO 9091 also sets out the calcu- 3.3 basic target: Portable target mounted on a
lation procedures for compiling the calibration ta- tripod with a tribrach.
bles to be used for the measurement of cargo
quantities.
3.4 benchmark: Point on which a staff is erected to
determine the height of the theodolite above the
South pole.
2 Normative references
The following Standards contain provisions which,
3.5 calibration: Process of determining the total
through reference in this text, constitute provisions
capacity or partial capacities of a tank correspond-
of this patt of ISO 9091. At the time of publication,
ing to different levels.
the editions indicated were valid. All Standards are
subject to revision, and Parties to agreements based
3.6 calibration table; main gauge table: Table, often
on this patt of ISO 9091 are encouraged to investi-
referred to as a tank table or a tank capacity table,
gate the possibility of applying the most recent edi-
showing the capacities of or volumes in a tank cor-
tions of the Standards indicated below. Members of
responding to various liquid levels measured from
IEC and ISO maintain registers of currently valid
the gauge reference Point, with the ship on an even
International Standards.
keel and upright.
Petroleum and liquid petroleum
ISO 75074 :-‘1,
Calibra tion of vertical cylindrical tank 3.7 datum Point: Position used as the datum in the
produc ts -
-
Part Ir Strapping method. preparation of a calibration table.
This Position may differ from the gauge refer-
NOTE 1
ISO 8311:1989, Refrigerated lighf hydrocarbon fluids
ence Point.
-
Calibration of membrane tank and independenf
prismatic tank in ships - Physical measurement.
3.8 deadwood: Any tank fitting which affects the
capacity of a tank.
3 Definitions
3.8.1 positive deadwood: Fitting whose capacity
For the purposes of this patt of ISO 9091, the follow-
adds to the effective capacity of the tank.
ing definitions apply.
1) To be published.
---------------------- Page: 5 ----------------------
ISO 909%2:1992(E)
3.8.2 negative deadwood: Fitting whose volume 4.2 If any unusual distortions are found in the tank
Shell, additional measurements shall be taken by
displaces liquid and reduces the effective capacity.
the calibrator to obtain sufficient data for correct
calculation in the calibration table, and the
3.9 equator: L argest horizontal circumference of a
calibrator’s notes should be provided in connection
spherical tank.
with such extra measurements.
3.10 gauge reference Point: Point from which the
liquid depth is measured.
4.3 Duplicate measurements of angles shall be
taken to check whether they agree within 16 s, and
if they do not agree, measurement shall be con-
3.11 latitude: Horizontal circumferences on the
tinued until two consecutive readings agree. The
surface of the sphere parallel to the equator.
average of the two shall be recorded.
3.12 longitude: Vertical circumferences on the sur-
lf consecutive measurements do not agree, the rea-
face of the sphere passing through the north and
son for the disagreement shall be clarified and, if
South poles.
necessary, the entire calibration procedure shall be
repeated.
3.13 list: Transverse inclination of a ship.
If the measurement has been interrupted, the last
angle measurement taken should be repeated. If the
3.14 north pole: Zenith, or highest Point, of a
new angle values do not agree, within the required
spherical tank Shell, an imaginary Point in most
tolerante of 16 s, with the earlier measurements,
spherical tanks due to the pipe tower or other
then the earlier set should be rejected.
appurtenances.
3.15 pipe tower: Large-diameter pipe coaxial with
4.4 Measurement shall be carried out when the
the tank’s north-South axis, containing pipes for
temperature fluctuation of the wall is limited to the
loading and discbarging, measuring instrumen-
minimum.
tation, ladder, wiring and other in-tank facilities.
NOTE 2 Temperature fluctuations should be checked
during measurement procedures.
port: Left-hand side of a ship facing forward.
3.16
South pole: Nadir, or lowest Point, of a spheri-
3.17
4.5 Measurements shall not be carried out when
cal tank.
there is any motion of the ship, or Vibration of the
tank.
3.18 starboard: Right-hand side of a ship facing
If calibration is carried out before installation of the
forward.
tank in the hull of the ship, the distance between
predetermined Points on the interior of the tank shall
3.19 target: Position distinctively marked on the in-
be measured after installation to ensure that no
side surface of the tank for the triangulation method
distortion of the tank has occurred. If distortion has
(see 6.1).
occurred, the calibration shall be repeated.
3.20 traverse Point: Position on the inside surface
4.6 The paint used to mark the targets shall be
of the tank above which a theodolite is set for de-
manufactured from materials which are resistant to
termining the coordinates of a target.
liquids at cryogenic temperatures.
3.21 trim: Longitudinal inclination of a ship.
5 Equipment
4 Precautions during measurement
5.1 Basic target
A target mounted on a tribrach indicating a base
4.1 Utmost care and attention shall be exercised
Point.
in taking measurements and anything unusual oc-
curring during the measurement which might affect
5.2 End-to-end rule
the results shall be recorded. The calibration
method described in this part of ISO 9091 may be
A rule graduated in centimetres and millimetres, to
applied to ships whether afloat or in dry-dock. How-
be used to measure deadwood, etc. The rule should
ever, its use in dry-dock may be preferable, because
bear the identification of a recognized standardizing
trim or Iist, if any, will remain the Same throughout
authority or certificate of identification.
the measurement.
2
---------------------- Page: 6 ----------------------
ISO 909%2:1992(E)
shall be stencilled on the inside surface of the tank
5.3 Measuring tape
Shell at each intersection of latitude and longitude
A tape bearing the identification of a recognized at 20’ intervals. The marking error shall be less than
standardizing authority or a certificate of identifi- 10 mm in both vertical and horizontal directions.
cation.
Dimensions in millimetres
5.4 Optical level
Stamped 1 rSproyed
An Optical level having an erect image, a magni-
fication of x 20 or greater, capable of being focussed
to 1,5 m or less and with a spirit-level sensitivity of
40 s per 2 mm or less.
5.5 Staff
A scale graduated in millimetres to be erected on a
benchmark.
5.6 Steel rule
A rule, to be used to measure clearances, etc.,
Figure 1 - Example of marking
graduated in millimetres. The rule should bear the
identification of a recognized standardizing authority
or certificate of identification.
5.7 Subtense bar
6.2 Basic Pentagon
A subtense bar having a length greater than 5 % of
the distance between the base Points with a length 6.2.1 Determination of traverse Points
uncertainty of less than 0,Ol % of its length.
Mark five traverse Points so that each target tan be
measured from at least four traverse Points without
5.8 Surface thermometer
being obstructed by the pipe tower.
A thermometer used to measure the temperature of
the surface of the tank with an accuracy of + 0,5 “C
in Order to convert the coordinates of the targets at
6.3 Marking of benchmark
the temperature at the time of measurement to
those at the certified reference temperature.
Mark the benchma rk at an ar *bitrary p osition near
the South pole of th e tank (see figure 2).
5.9 Theodolite
A theodolite, recommended to have an erect image
6.4 Set-up of measuring instruments (see
with a minimum circular reading of 1 s and a spirit
figure 2)
plate level sensitivity of 20 s per 2 mm or less.
6.4.1 Set staffs upright on the benchmark and on
5.10 Tribrach
the South pole of the tank.
A levelling platform, mounted on the tripod, with
three levelling screws and a clamping device to
6.4.2 Set up a level (for the basic target) using a
fasten the theodolite.
tripod and tribrach, on an arbitrary Point at which
the siaff on the South pole tan be observed through
6 Preparation
the opening of the pipe tower (see figure3).
6.1 Marking of targets
6.4.3 Set up a levelled tribrach (for the base Point)
on a tripod at each of five traverse Points (see
During construction of the tank and Prior to the in-
figure 4).
stallation of the pipe tower, targets (see figure 1)
---------------------- Page: 7 ----------------------
ISO 9091=2:1992(E)
Base polnt Openlng
/- /-
- South pole
Tra
Arbl trary poln t
Figure 2 - Set-up of instruments for determining the height of the base Point
South pole
Benchmark
and target
Figure 3 - Location of benchmarks
---------------------- Page: 8 ----------------------
ISO 909%2:1992(E)
Dimensions in millimetres
Platf orm f or
-J
Traverse Point
k- Shoe
Figure 4 - Example of shoe arrangement for platform
where
7 Measurement
a is the level rea ding on the
7.1 Elevation of base Point from South pole
South pole staff;
b is the level rea ding on the
7.1.1 With the level, read the scale of the staffs set
bench mark staff.
up on the South pole and on the benchmark re-
spectively, as shown in figure 2.
7.1.2 With the theodolite mounted on the tripod of
the traverse Point (A) as shown in figure2, read the
scale of the staff set up on the benchmark.
7.2 Horizontal distance of base Points
7.1.3 Elevation ZY of the base Point is determined
as follows:
Horizontal distances tan be obtained using the sub-
ZI = C + (a - b)
tense bar method. This patt of ISO 9091 describes
the subtense bar method, but an alternative method
where
is acceptable if it gives an accuracy equivalent to
the subtense bar method.
is the elevation of the theodolite from
the South pole;
c is the reading of the theodolite on the
benchmark staff;
7.2.1 Set a subtense bar on the tribrach of Point B,
(a - b) is the elevation of the benchmark from
as shown in figure5.
the South pole,
5
---------------------- Page: 9 ----------------------
ISO 9091=2:1992(E)
Subtense bar
it
Setting of subtense bar
Figure 5 -
Repeat the measurement procedures given in 7.3.3
7.2.2 Measure the horizontal angle 2a subtended
and 7.3.4.
at Point A between the end-marks of the subtense
bar. This measurement shall be taken at least twice
(see 4.3).
7.3.6 Repeat the Same procedure of measurement
at Points C, D and E.
7.2.3 Calculate the mean horizontal angle at each
traverse Point from the average of two consecutive
readings.
7.2.4 The horizontal distance L tan be calculated
from equation (1):
L=‘+-& . . .
(1)
where 2 is one-half the length of the subtense bar.
7.3 Vertical height and horizontal angle of
base Point
7.3.1 Repeat the Same procedure as described in
E
7.1.
Measurements with the theodolite on
Figure 6 -
Point A
7.3.2 Set up a basic target on each of the tripods
at Points B, C, D and E.
7.3.3 With the theodolite at Point A, collimate the
basic target at Point B and adjust the scale of the 7.4 Horizontal and vertical angles of target
horizontal angle to O”OO’OO”.
7.4,l Set up the theodolite on the tripod at base
Point A and the basic target on the tripod at base
7.3.4 Measure the horizontal angles of LBAC,
Point B.
LBAD and LBAE as shown in figure6.
7.4.2 Collimating the basic target with the
7.35 Remove the theodolite from Point A and reset
theodolite, adjust the horizontal scale to an angle
it on the tripod at Point B. Set up a basic target on
of 0”00’00”.
Point A.
---------------------- Page: 10 ----------------------
ISO 9091=2:1992(E)
7.4.3 Measure and record the horizontal and verti-
7.7 Location of level gauge
cal angles to each target (see figure7). If the line of
sight to a target is obstructed by the pipe tower, then
For trim and list corrections, measure the horizontal
record this fact in the calibrator’s notes.
distance of the level gauge on the tank bottom from
the vertical axis connecting the South and north
7.4.4 Shift the theodolite and the basic target onto poles.
the other base Points and measure the angles in the
manner described in 7.4.2 and 7.4.3.
7.8 Vertical diameter
7.5 Temperature
If the tank has a dome with a built-in north pole,
Take the average temperature of the inside surface
measure the distance between the north and South
of the tank with a surface thermometer.
poles with a steel tape.
In the case of a dome that lacks the north pole and
Height of gauge reference Point
7.6
has only the grating top floor of the pipe tower, set
If the gauge reference Point and the datum Point an Optical level by standing a theodolite in the mid-
differ, measure the height of the gauge reference dle of the above-mentioned floor, above the imagin-
Point from the datum Point (South pole) of the tank at-y north pole, and measure with a steel tape the
by means of an Optical level or any other levelling distance H between the above-mentioned Optical
device. level and the South pole.
.
\
\
- Base Point
Basic
Pentagon
Measured horizontal angles: al, a2, a3, a4, a5
Measured vertical angles: pl, &, P3, P41 P5
Measurement of the target
Figure 7 -
---------------------- Page: 11 ----------------------
ISO 9091=2:1992(E)
Then measure the height h of the Optical level from As the subtense bar is set horizontally, the projected
the bottom edge of the dome along the coaming of length of the subtense bar on the horizontal plane
the dome and calculate the imaginary height Ah of is 21. Therefore, the horizontal distance (h,,) is given
the north pole from the above-mentioned edge by in equation (2):
means of the curvature of the tank, which is obtain-
1
. . .
able from the design value of the vertical diameter. h
AB = - (2)
tan a
The vertical diameter between the north and South
With the Point A as the origin of the coordinates, the
poies is given by the formula
coordinates of the Point B tan be given as in
equations (3) to (5):
Diameter = H - h + Ah
(3)
As an alternative, measure the vertical inside height
at a convenient distance from the centre-line. From
. . .
YB = 08
the vertical inside height, the vertical diameter tan (4)
later be calculated.
V . . .
zB= AB (5)
where VAe is the vertical distance from A to B.
7.9 Deadwood
9.2 Determination of coordinates of base
7.9.1 The volume of deadwood such as ladders,
Points (C, D, E) on the basic Pentagon
submerged Pumps and any other structures in the
tank shall be calculated from their dimensions, or
Measure the horizontal angle and the relative height
any other suitable means of assessing their vol-
between every pair of base Points on the basic
umes.
Pentagon, and obtain the data as shown in
figure IO.
7.9.2 The volume of internal piping containing
cargo fluid shall be calculated as the differente be-
Calculate the lengths a2 and q as shown in figure 11
tween the internal and extemal volumes of the pip-
from equations (10) and (ll), using the length a, and
ing, i.e. the volume of the metal.
angles al, a2 and a3.
By using equations (10) and (11) and the horizontal
7.9.3 The volume of the deadwood shall be calcu-
distance (hAB) given in equation (2), calculate the
lated at the respective heights where pipes and
horizontal distance between Points (B, C) from
other fittings are present.
equation (6) and Iikewise, obtain other distances in
the Order shown in figure 12.
8 Coordinate System
sin agAc
h h . . .
BC = AB (6)
Sin(a,CB - aDCA)
The
The coordinate System i s shown in figure 8.
of the base line
x-axi s is taken on the e xtension
Obtain the relative heights for each base Point di-
(AB) on the horizontal plane, the y-axis perpendicu-
rectly from the data measured on the staff.
lar to the x-axis on the Same horizontal plane and
the z-axis on the vertical plane.
Obtain the coordinates of the base Point C (xc, y,,
zc) from equations (7) to (9) using the horizontal
distance hAB in equation (6) and horizontal angle 8,
9 Calculation
as shown in figure 13 and Iikewise, obtain the coor-
dinates of other base Points.
9.1 Calculation of coordinates of base Points
. . .
= XB + h,, cos 8,
(7)
Xe
(A, B) on the basic Pentagon
. . .
JIc =yB -t h,, sin OB
(8)
Calculate the distance between A and B using the
. . .
= ZB + I/BC
(9)
ZC
data measured with the subtense bar (see figure9).
---------------------- Page: 12 ----------------------
ISO 9091-2:1992(E)
Base
Slde vlew Hortzontal vlew
Coordinate System for calculation
Figure 8 -
Subtense bar
Y
X
Known values:
length of the subtense bar = 21
horizontal angle = 2a
Figure 9 - Data for calculation of the coordinates of base Points (A, B)
---------------------- Page: 13 ----------------------
ISO 909192:1992(E)
[ \i---
’ ‘. i
’ . .
\
1’
\ \
\
\
1’
‘*
//,
\
\
\
N, :
\
\
h
\
I =\
\
\
-JyfL
%A /$y
-m-w ,*---ir--
A
-
Vertlcal helqht to be measured
HorlzontaL angles to be measured
(The dotted llnes Indlcate projec-
tlon onto the horizontal plane)
Figure 10 - Data measured for coordinate determination
The following equations are valid for the triangle shown:
sin a2
. . .
= a, -
(IO)
a2
sin ai
sin a3
. . .
= a, -
(11)
%
sin al
Data for calculation of relative lengths
Figure 11 -
10
---------------------- Page: 14 ----------------------
ISO 909+2:1992(E)
,T Known dlstance
Figure 12 - Calculation Order
i
\
\
\
\
=
e
A n
8
= acBA + 8, - n
B
0
= aDcB + 8, - ft
C
0
= aEDc + 8, - n
D
8
= aAED + 8, - n
E
Figure 13 - Horizontal angles for determining base Point coordinates
11
---------------------- Page: 15 ----------------------
ISO 9091-2:1992(E)
Target 7
Figure 14 - Coordinates of a target
. . . (17)
y’i= hBi sin@ - ac&) or & sin agci
93 . Calculation of coordinates of targets
. . .
z’i = VBi or Vci + VBC
Determine the coordinates of the targets using the
Transform the coordinates shown in equations (16)
triangle which is formed by a target and two arbi-
to (18) to the basic coordinate System (x, y, z) as
trary base Points out of the five (A, B, C, D, E).
shown in equations (19) to (21) using the rotation
angle 0 and distance (XB, YB, +) between both coor-
Figure 14 is an example of calculation given when
dinate Systems (see figure 15).
the base Points B and C are selected as a base line
of a triangle. Apply the Same procedure to other at=
bitrary Points selected.
Obtain the horizontal and the vertical distances be-
tween the target (0 and the base Points (B or C)
\
\
shown in figure 12 using equations (12) to (15). 8
\
bi = h,, sin(n sin aBci >
. . .
Y’
(12)
- aBCi - ‘CBi
. . .
VBi = &f tan ßBi
. . .
)
(14)
. . .
VCi = I&i tan ßci
(15)
X’
Obtain the coordinates of Point (I!) (x’i, y’i, z’I!) as in-
Figure 15 - Transformation from local coordinate
dicated in equations (16) to (18) against the local
(x’, y’, z’) System to basic coordinate (x, y, z)
coordinate System (x’, y’, z’) where the x’-axis is
taken in the projection of line BC onto the horizontal
plane, the y’-axis perpendicular to the x’-axis on the
Same plane, the z’-axis vertically, and the origin is
. . .
Xi = xß + x’i cos 8 - y’i sin 0
Point B. (19)
X’i = hBi COS(7T - a(--i) Or . . .
yi=yB +x’isin ß +y’icos 0
(20)
h . . . . . .
zB + z’i
i ‘Os ‘BCi - BC (16) zi = (2’)
h,
12
---------------------- Page: 16 ----------------------
ISO 9091=2:1992(E)
level. Then the volumes at one-centimetre intervals,
where
starting from the South pole, the volume of
deadwood being deducted, are obtained also by
6=tan-’ XB-*c,
-
computation to compile a main gauge table.
The probability combination to select two arbitrary
11.2 Calculation of liquid head
base Points out of the five is
5!
Calculate the volume of the tank in the loaded con-
= 10
2! (5 - 2)!
dition with the contents at the density at which the
calibration table is certified, then compare the above
This indicates that theoretically, the maximum num-
volume with that in the empty condition. The differ-
ber of triangles to determine the location of the tar- ence in volume is treated as deadwood.
get (0 is 10. Furthermore, as shown in equations (16)
to (18), two kinds of coordinates for one target tan
11.3 Trim correction
be obtained from one triangle. Therefore, the coor-
dinates of one target tan be given in a maximum of
Trim corrections shall be given as an addition to or
20 different ways. Determine the mean value of them
subtraction from the apparent liquid level measured
to obtain the coordinates to be used.
by the tank gauge. Trim corrections are calculated
by comparison of the liquid levels given by the Same
9.4 Correction for trim or list
volume of liquid in the tank with the ship upright and
on even keel and with the ship in trimmed condition
If the tank was measured in tilted condition, all the
and upright for the condition of trim under consider-
data obtained shall be corrected to those in upright
ation.
condition.
11.4 List correction
10 Data processing
List corrections shall be given as an addition to or
Calculate the radius of each level using the coordi-
subtraction from the apparent liquid level measured
nates of the targets set on each level, and obtain the
by the tank gauge. List corrections are calculated
average radius of the best-fit circle of each level by
by comparison of the liquid levels given by the Same
least-Square adjustment or other suitable math-
volume of liquid in the tank with the ship on even
ematical solution. The average radii obtained as
keel and upright and with the ship listed and on even
above and their level heights are converted to those
keel for the condition of Iist under consideration.
at the reference temperature at which calibration
tables are certified, using the certified coefficient of
11.5 Combined trim and list corrections
linear expansion of the tank material.
The trim and list corrections compiled in accordance
11 Calculation procedure
with 11.3 and 11.4 may be combined in one table.
11.1 Calculation of tank volume
11.6 Correction for tank Shell expansion or
contraction
Compute the fractional volume of the space en-
circled by a spherical band between the two adjoin-
Corrections for the tank Shell expansion or con-
ing levels comprising the targets marked on the tank
traction, due to the temperature in the loaded con-
surface at each level by using the radii of the re-
dition deviating from the reference temperature at
spective levels, and obtain the total volume of the
which the tank table was certified, shall be made by
spherical tank at the certified reference temperature
multiplying the coefficient of expansion of the ma-
of the calibration table by adding the above frac-
terial of the tank Shell.
tional volumes.
NOTE 3 The coefficient of expansion is not constant, but
The fractional volumes for the remainder of the tank,
varies with temperature.
below the lowest targets and above the highest tar-
gets, are calculated from the data of the appropriate
12 Calibration table
sub-divided level. Calculate fractional volume below
the lowest level using the coordinate of the South
shall consist of the following re-
Calibration tables
pole and designated curvature of
...