A11101 11171*1

NBS

PUBLICATIONS SEP f 7 1979

NBSIR 79-1751

Custody Transfer Systems for

LNG Ships: Tank Survey

Techniques and Sounding

Tables

Richard H F. Jackson*

Richard S Collier**

Seymour Haber*

Peter V Tryon*

‘Center for Applied Mathematics

“Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

U S. Department of Commerce

Boulder. Colorado 80303

July 1, 1978

Issued May 1 979

Prepared for The Maritime Administration

Department of Commerce

Washington, D.C.

QG

NBSIR 79-1751

CUSTODY TRANSFER SYSTEMS FOR

LNG SHIPS: TANK SURVEY

TECHNIQUES AND SOUNDING

TABLES

Richard H. F. Jackson*

Richard S. Collier**

Seymour Haber*

Peter V. Tryon*

*Center for Applied Mathematics

**Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

U S. Department of Commerce

Boulder, Colorado 80303

July 1, 1978

Issued May 1 979

Prepared for The Maritime Administration

Department of Commerce

Washington, D.C.

U S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

ABSTRACT

Static measurements of liquefied natural gas (LNG) for custody transfer

purposes require an accurate and precise knowledge of the container volume and

the volume-height relationship. The extremely low temperatures of LNG (less

than 150° K) preclude in situ surveys; however, the increasing value of the

cargo requires more precise and accurate measurements than previously used for

bulk marine cargoes.

A description and assessment of the application of photogrammetric techniques to the ambient temperature survey of a 35-meter diameter spherical

aluminum container are presented. Sample sounding tables (height-volume) are calculated, and an estimate of error is given.

Key words: accuracy; statistical analysis; cryogenic; error estimation; liquefied

natural gas; LNG; marine; mathematical modeling; measurement; photogrammetric;

precision; ship cargo; strapping; survey.
ACKNOWLEDGMENTS

The authors gratefully acknowledge the assistance, advice, and encouragement of James D. Siegwarth, Patricia J. Giarratano, Dwain E. Diller, and

Douglas B. Mann of the NBS Thermophysical Properties Division, Robert J. Hocken,

NBS Dimensional Technology Division, and Christoph Witzgall of the NBS Operations Research Division. Additionally, without the patience and cooperation of

Don Shaaf and personnel in the General Dynamics Quincy Shipbuilding Division

much of this work would not have been possible. Discussions with photogrammetric consultants John Kenefick, Duane Brown, and John Strahle were also most

helpful.
LIST OF TABLES AND FIGURES

Page

Table 1. Summary of target residuals by horizontal row 21

Table 2. Rod end-point coordinates 34

Table 3. Gauge rod data 33

Table 4. Mean radial target residuals 43

Table 5. Volume error as a function of height 45

Table 6. Percentage standard deviation of the error in the volume

of the tank below the plane at height h 47

Figure 1. Tank schematic

Figure 2. Distribution and numbering scheme for targets on inner plate

and equatorial ring 4 Figure 3. Tank residuals displayed as a function of height 3 2

Figure 4. Residuals in equatorial ring region, displayed as function

of height . 3-4 Figure 5. Residual plots of target rows as noted

Figure 6. Residual plots of target rows as noted 16

Figure 7. Residual plots of target rows as noted 3-7 Figure 8. Residual plots of target rows as noted 18

Figure 9. Residual plots of target rows as noted 19

Figure 10. Residual plot of top polar plate 20

Figure 11. Target residuals grouped by plate and displayed by strake.... 22

Figure 12. Plot of x coordinate vs. the standard error of 26

Figure 13. Plot of z coordinate vs. the standard error of x 27

Figure 14. Plot of x coordinate vs. the standard error of the radius.... 28

Figure 15. Plot of y coordinate vs. the standard error of the radius.... 29

Figure 16. Plot of z coordinate vs. the standard error of the radius.... 30

Figure 17. "Wrap-around" display of traget residuals, from it to 0 32

Figure 18. "Wrap-around" display of target residuals, from 0 to it 33

Figure 19. Volumes of tank internals.. 41

Figure 20. Piecewise linear plot of mean radial residuals 49
TABLE OF CONTENTS

Page

1. INTRODUCTION 1

2. THE SURVEY METHOD 2 Photo gramme trie Surveying 2

The Tank Model

Tank Model Modifications 6

3. ANALYSIS OF AQUARIUS TANK NUMBER 4

6

Tank Description 2 Sources of Error

Exploratory Statistical Analysis

Calculation of Best-fitting Sphere

The Best-fitting Sphere

Analysis of Residuals 33

)

t Target Measurement Errors

Random Errors: Analysis of Residuals

Random Errors: Internal Estimates of Target Coordinate Error

31 Systematic Error

37 Calculation of Sounding Tables

Tank Model 1 ^

Tank Model 2 38

Tank Model 3

^

Comparison of NBS ' and Consultants’ Results 44

Sounding Table Error: Target Coordinate Error Contribution 44

Sounding Table Error: Model Error Contribution 48

Sounding Table Error: Plate Curvature Error Contribution 50

REFERENCES 52

APPENDIX A: NBS SOUNDING TABLES . 53

APPENDIX B: PORTIONS OF PHOTOGRAMMETRIC CONSULTANTS' SOUNDING TABLES... 60
1. INTRODUCTION

The Liquefied Natural Gas (LNG) Program of the National Bureau of Standards

(NBS) is designed primarily to supply property data for the materials and fluids

of interest and to aid in the establishment of measurement methods and instrumentation for custody transfer of this fluid in commerce. This report concerns

work, supported in part by the Maritime Administration of the Department of

Commerce, in the area of custody transfer: specifically, static measurements of

the quantity of fluid contained in a storage tank before and after delivery,

either into or out of the tank.

The analysis reported herein was performed on spherical LNG tanks con- structed by General Dynamics/Quincy Shipbuilding Division for use in the LNG

ship Aquarius. Previous methods for calibrating such tanks and calculating

"list and trim" tables relied heavily on measurements taken with tapes, referred

to as "strapping" [5]. Ship owners and therefore ship builders have a specific

interest in these measurements and the resulting tables of volume vs. height,

since they are used by a ship’s captain to determine the amount of cargo at any

particular time. The resultant estimates of volume added or removed are then

mathematically combined with fluid density measurements to determine mass transferred. Gas sampling and analysis provide average BTU content, and the combination of mass transferred and BTU content yields total heating value of the cargo.

One objective of the Maritime Administration is to promote the development

of the LNG shipbuilding industry in the United States. The Mar Ad was therefore

interested in establishing accurate and precise tank-calibration technology for use with the first LNG ships constructed in U.S. shipyards. Since strapping

measurements are typically made at the shipyard during construction, the analysis

of tank strapping accuracies reported here was undertaken.

In essence, strapping is a geometric survey of the inside of the ship tank,

relating measured points on planes and surfaces to fixed reference points. The

balance of the work concerns the mathematical treatment of the measured data to

construct an accurate model of the tank geometry. (Error estimates can be made

by relating the model to the measured and reference points.) The volume-height

relationships are then derived from the mathematical model.

This report contains three sections, a list of references, and two appendices. Following this introductory section, section 2 presents the photogrammatric technique for calibrating large tanks. The analysis of sounding table

accuracies that can be expected from the survey technique is presented in

section 3. Also included is a discussion of similarities and differences
between the analysis performed by the photogrammetric consultants and that

performed by NBS. Appendix A contains samples of the sounding tables computed

by NBS, and appendix B contains portions of the sounding tables computed by the

photogrammetric consultants.

It should be pointed out that NBS had no specific contract authority to

gather and analyze data. Only the extensive cooperation of the Maritime Administration, the ship builder, the ship owner, and the photogrammetric con- tractors made it possible to complete and publish this work.

2 . THE SURVEY METHOD

Rectangular and spherical tanks are usually dimensioned by conventional

strapping techniques; sufficient lengths and circumferences are measured by

taping so that the shape of the tank can be determined and used to calculate the

volume as a function of height. Since the spherical tanks on the General

Dynamics ships do not lend themselves well to conventional taping, a photogrammetric technique to measure tank volume has been developed (by a commercial

firm)

Photogrammetric Surveying

The wide-angle analytic photogrammetric technique used to determine the

dimensions of the General Dynamics tanks offers potentially higher accuracy than

strapping. The claimed precision for this technique approaches 1 part in

100,000, or approximately ±0.4 mm for a 35 m diameter tank.

The photogrammetric method, described in detail in [1], consists of determining the x-, y-, and z-coordinate values for targets on the inner tank sur- faces by photographing the targets from nine different positions within a tank.

Targets are required on the tank so that points on the surface can be identifiable from photograph to photograph (see figs. 1 and 2 for tank target distributions). The 408 targets used in these tanks are 7/8" diameter white spots

surrounded by a black background and are spray-painted on during construction of

the tank. Special photographic plates consisting of thin emulsions of uniform

thickness on very flat glass plates are used for the photography.

The two-dimensional positions of the target images on the plates are measured to within 3 ym with a monocomparator. These values are related to the
Figure 1. Tank schematic.

3
Figure 2. Distribution and numbering scheme for targets on

inner plate and equatorial ring.

4
x-, v-, and z- coordinates through a large set of mathematical equations that are solved by computer. The unknowns calculated are the x-, y-, and z- coordinates,

the directions of the principal axis of the camera, the coefficients of the lens

distortion correction equation, and the uncertainties for the coordinate values.

Details of the technique, however, are proprietary. The resulting coordinates

have an arbitrary scale; hence, calibration lengths must be known to correct to

coordinates in real space. This information is provided by targets placed at

known spacings on calibration tapes visible in the photographs. The targets

should be photographed when the tank is isothermal, either after dark or after

the tank has been insulated.

The Tank Model

Construction of a mathematical model of the tank is essential to the calculation of tank capacity tables. The model is a mathematical description of the

tank surface fitted to the target coordinates; its accuracy depends not only on

the accuracy of the target coordinates but also on the density of targets on the

tank surface and the regularity of the tank surface between target locations.

It is clearly desirable to have as many targets as possible to reduce the

uncertainty in interpolating between targets. However, there is a practical

limit to the number of targets that can be measured because of the time and cost

in reducing the data. With one exception (discussed in the next section), NBS

had no control over the number or placement of targets painted on the tank

surface.

Model construction usually begins with the calculation of some regular

solid, e.g., a perfect sphere, prism, etc., which best fits the target coordinate data developed from the survey. Differences between actual target coordinates and the coordinates of the closest point on the surface of the model solid

are then calculated. These "residuals" are then studied for patterns that would

iicicate systematic distortions (bulges, bends, or twists) in the shape of the

tank.

On the basis of patterns discovered during this exploratory residual

analysis, a special-purpose technique is developed to integrate numerically the

composite tank model, which specifies a regular solid along with a table of

deviations or residuals.

5
The final step in this analysis is the calculation of sounding tables

giving tank volumes at regular intervals of liquid height in the tank. Error

bounds on these tank table values are developed in this report.

Tank Table Modifications

There are a number of modifications to the sounding tables that must be

made before their construction is complete. List, trim, thermal contraction,

and stress effects must be accounted for. List and trim corrections, however, are not addressed in this report since NBS did not have access to the data or

the procedures used in making these corrections.

It is standard practice to correct tank tables for thermal contraction by

applying contraction coefficients as if the tank were mechanically unconstrained.

The dimensions of the tank are decreased uniformly according to the thermal

contraction of the material. Actually, tank mounting constraints and variations

in the thermal expansions of the structural material can introduce strains in

the tank that might affect cargo capacity. These thermal stress effects cannot

presently be analyzed, because data on constraint effects and anisotropic thermal coefficients are lacking.

Another effect is the cargo load, which stresses both the tank and the ship

hull. The tank strains supposedly have been measured during hydrostatic tests,

but this information has not been made available. Data on capacity effects from

hull strains are also unavailable. An analysis of the effects of these strains on the tank tables is therefore beyond the scope of this work. Furthermore, the

photogrammetric contractors do not include such corrections in their report.

3. ANALYSIS OF AQUARIUS TANK NUMBER 4

As part of the Maritime Administration Custody Transfer program mentioned

earlier, NBS was asked to evaluate the methodology used to calibrate the LNG

tanks constructed by General Dynamics at its Charleston facility. In addition,

NBS was asked to comment on the accuracy of the sounding tables subsequently

constructed. In this section, we present our analysis and describe how it

differs from the analysis performed by the photogrammetric consultants. Included also is a discussion of the accuracy of the sounding tables constructed

and an assessment of the limitations, additional co those implicit in the last

paragraph, to the applicability of those tables

6
Tank Description

Each tank calibrated is spherical, with a diameter of approximately 36.5

meters and a capacity (volume) of 25,000 cubic meters. The tanks are constructed

of four bands ("strakes") of aluminum plates in the shape of spherical trapezoids

(see fig. 1), with special cap plates at the top and bottom. The only internal

structure is a cylindrical tower extending from cap to cap containing piping,

wiring, depth gauges, etc.

The first step in constructing a tank is to weld together the equatorial

ring by which the tank is supported. The ring is set up on jigs, and the tank

plates making up the central strakes (previously welded into pairs) are welded

in place above and below the equatorial ring. The top and bottom strakes are then welded in place. The bottom and top circular plates are welded in after

-he rest of the welding is completed, and the internal staging is removed.

After a tank is completed, it is loaded on a crawler, supported from

beneath, and moved to the hydrostatic test stand. After the test, the tank is

moved to the insulation building and insulated. Then, it is moved to a barge

for transporting to the shipyard at Quincy where it is lifted into place on the

ship

Sources of Error

The procedure for constructing sounding tables was discussed in section 2. Basically, that procedure consists of:

a. photogrammetrically surveying target coordinates on the inside

surface of the tank;

b. constructing a mathematical model of the tank geometry;

c. developing a mathematical technique for computing volumes below

specified heights in the tank; and

d. determining effects on tank shape (and therefore tank volume) of

tank loading, cooling, liquid loading, sagging, sloshing, etc.

Each stage of calculation has associated with it an error bound on the accuracy

of the result. These error bounds can be calculated using the appropriate

statistical analysis; this can always be done and is straightforward.

Difficulties arise only in regard to the "tightness" of those bounds, i.e.,

7
their balance between realism and conservatism. These error bounds will be

discussed later in this section. First, we present our analysis and the resulting sounding tables.

Exploratory Statistical Analysis

Here we present the results of an exploratory statistical analysis of the

target coordinate data for Aquarius Tank Number 4 obtained from the photogrammetric consultants. A best-fitting sphere is obtained by using linear least

squares to minimize the sum of the squares of the radial residuals. Analysis of

these residuals then provides information on how the tank wall deviates from a true sphere, information of value to the numerical integration procedure described later.

In fitting a sphere, if the usual concept of a distance measure

(d=/x2 + y

2”

+ z

2

) is used, the distance between a point and the surface of a sphere is a nonlinear function of the unknown parameters of the spheres This

complexity results in a nonlinear least squares problem for finding the bestfitting sphere. Witzgall [7] has developed a technique that avoids this com- plexity and reduces the problem to a linear one, allowing the use of linear

least squares.

Below, we summarize the approach suggested by Witzgall and show how to

remove its bias. The formulation is for an arbitrary n-dimensional space

and thus applies equally well to circles in 2-=space, spheres in 3-space, and

hyperspheres in n-space (Rn

)

Calculation of the Best-fit ting Sphere

Here we present a summary of the mathematics used in calculating the bestfitting sphere. Although condensed, it remains technical, thereby necessitating

a warning: the reader who is uninterested in the mathematical foundations for

subsequent results can skip over this section without loss of information.

A sphere consists of all points xeR

U satisfying

x’x - 2a ’x - y

“ Qj

8
where x and a are nxl vectors, y is a scalar, and x* is the transpose of x. The

vector a represents the coordinates of the center. This equation can be written

(x-a)’ (x-a) = a'a + y.

from which it is seen that the radius of the sphere is

r = v

/aTa + y.

where we restrict y to satisfy y >_ -a ‘a. The Euclidean distance between a point yeR

n and the surface of the sphere

S(a, r) having center a and radius r is the modulus of the difference of the

radius and the distance, p, between y and a, i.e..

Aeucl (y > S) ’ l r - P

where p

z = (y-a) ' (y-a)

The technique proposed by Witzgall for avoiding the nonlinearity is to use a different distance measure (or metric) instead of the usual Euclidean measure.

He calls this a "square" metric and defines it as follows:

A

square

(y,s)

Using this metric we have

r

2 - p

2 = 2y’a + y - y

! y

or

y‘y = y + 2a‘y -f p

z - r2

.

This equation is suitable for the applications of linear least squares where

9
y'y is the dependent variable;

2y^» 2 y2

» ...» 2y

n are the independent variables;

y, a^, a

2

» ...» are the unknown parameters; and

p2 „ r 2 t he residual.

Thus, any linear least squares computer program can be used to find the sphere

which minimizes

m o l (p

2 - r*) . i-1

where m is the number of observations and where p is now indexed by i over the

set of data points.

Furthermore, we note that

P± 2 ~ r

2 = (p i + r)(p

i

- r),

so that we can transform A to A and conversely. In particular,

square eucl m 2 m 2 2 l (p

2 - r

2

) = l (p + r) (p - r) ; i-1 i-1

so that the least squares formulation using square distance is equivalent to

weighted least squares in Euclidean distance with weights p^+r. Thus, using

"square distance," points outside the sphere receive more weight than points

inside, and the sphere will be larger than the "Euclidean distance" sphere.

This bias can be reduced by first using unweighted linear least squares and then

A A recomputing using weights l/(p.; +r), where r is the estimate of r obtained

from the previous unweighted analysis. This could be iterated in an obvious

manner; the convergence of this numerical process has not been checked. In

the present example, with r=18 meters and p -r -.03 meters, the recomputation

“6

^ reduces the radius by 6x10 meters, which is negligible. However, if the

residuals were large relative to the radius, the correction and its iterative

properties could be important.

The Best-fitting Sphere

Using the technique described above, the radius of the best-fitting sphere

for Aquarius Tank Number 4 was determined to be:

10
r = 18.2682 meters.

with a standard error of

SE - .0071 meters.

With respect to the coordinate system defined by the consultants, the coor- dinates of the center are:

a

l = x

= .0003 meters. SE = .0013 meters;

a

2 = y

= -.0009 meters, SE = .0013 meters;

a

3 = z = -.0137 meters. SE = .0011 meters

The standard errors given above are computed using the usual least squares

theory that assumes the radial residuals from a perfect sphere are random. As

shown below, this assumption is incorrect. The purpose of the best-fitting

sphere, however, is only to serve as a reference surface for further analysis.

Analysis of Residuals

With the calculation of the best-fitting sphere, we are now in a position

to perform the exploratory analysis of residuals that provides specific information on tank shape. A thorough residual analysis, such as was performed here,

typically includes many types of graphical displays; in the interest of brevity, we present here only a selected few examples. Nevertheless, the discussion

includes all important highlights.

The targets are arranged in 21 rows around the sphere: 1 row on each of

the top and bottom polar plates; 3 rows on the equatorial ring; and 4 rows on each of the four strakes. On each plate there are 4 targets arranged and numbered as indicated in figure 2.

Figure 3 shows the residuals (in Euclidean distance) plotted versus their

height along the vertical axis in the tank. (In that graph and subsequent

ones, a dot indicates one value while a number as plot symbol indicates the

frequency of the data value.) This clearly shows the general nature of the

tank distortion. The bottom polar plate and the bottom edge of the #1 strake are flattened (as if the tank were free-standing on a flat surface) and lie

internal to the sphere by as much as 6 cm. The //I strake must have a "sharp"

11
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Figure

3.

Tank

residuals

displayed

asa

function

of

height,

(Note:

plot

symbols

other

than

dot

indicate

frequency

of

data

value.)
bend near the second row of targets, because the residuals for the upper

three rows of targets on the #1 strake and all points on the // 2 strake

average 0.8 cm outside the sphere. Figure 4 is an enlargement showing the

residuals from the equatorial ring and the adjacent rows on the strakes.

As is clearly shown, the equatorial ring is curved inward.

Figures 5-10 show plots of the amplitude of each of the 21 horizontal

rows of residuals versus angle around the tank. Table 1 summarizes the

residuals by row. The most interesting fact is that in some regions the

residuals are following some major distortion of the tank and are thus not

undom. In other areas (at joints between strakes), the residuals appear

random but have standard deviations similar to those in the nonrandom regions,

in particular, the regions of randomness are adjacent to the seams where 42

Les are joined. Howe. . ^.n only one case (bottom polar plate) do the

"nonrandom" residuals appear to be such that they could be approximated by

a. simple surface or polynomial. In fact the first strake, row 1 residuals

can be fitted well by a sine v_urve, though not nearly as well as those for

the bottom polar plate.

13
o

CD

CNJ

00

•^f C\i

f o

co

(ujuj) sjenpssay gejpey

14

Height

in

tank

(m)

Rgure

4.

Residuals

in

equatorial

ring

region,

displayed

as

function

of

height.
Figure

5.

Residual

plots

of

target

rows

as

noted.

(Vertical

axis:

Residua!

values

in

meters.)

(Horizontal

axis:

Horizontal

angle

in

radians.)
•• I I I

csi5o©

jt: «S

k.

Cfi X3coo©

CO

16

Figure

6.

Residual

plots

of

target

rows

as

noted.

(Vertical

axis:

Residual

values

in

meters.)

(Horizontal

axis:

Horizontal

angle

in

radians )
52

dacc

«s co

to3 « iS"

CM§2c

<0 3 o 1 CO3 so ry ^ l2 i

17

Figure

7.

Residual

plots

of

target

rows

as

noted.

(Vertical

axis:

Residual

values

in

meters.)

(Horizontal

axis:

Horizontal

angle

in

radians.)
18

Figure

8.

Residua!

plots

of

target

rows

as

noted.

(Vertical

axis:

Residual

values

in

meters.)

(Horizontal

axis:

Horizontal

angle

in

radians.)
I I I

c\j£oL_

a>~

CO

k_

•—> c3o

LL 5P

0)CO

Ifl

.c; tf£ i i i

19

Figure

9.

Residual

plots

of

target

rows

as

noted.

(Vertical

axis:

Residual

values

in

meters.)

(Horizontal

axis:

Horizontal

angle

in

radians.
(ui) ©npsA senpssay

20

Horizontal

angle

(raoians)

Figure

10.

Residua!

plot

of

top

poiar

plate.
Table 1. Summary of target residuals by horizontal row.

Standard Degrees of

Row // Average (cm) Deviation (cm) Freedom * Random

1 Bottom plate -5.75 .70 7 No

2 -2.67 .76 15 No

3 First .72 .31 17 No

4 Strake .54 .33 17 No

5 . 66 .53 17 Yes

6 i .81 .84 25 Yes

7

|

Second .97 .38 23 No

8

1 Strake .72 .70 23 No

9 ] 1.11 . 66 26 No

10 .14 1.05 8 No

11 Equatorial -1.45 .90 26 No

12 Ring

.06 .82 8 No

13 \ 1.03 .73 27 No

14 1 Third .30 .49 23 No

15 ( Strake .33 .38 23 Yes

16 .28 1.20 23 Yes

17 \ -.62 .89 21 Yes

18 f Fourth -.94 .70 17 Yes

19 1 Strake .32 .42 17 No

20 -.43 .69 17 No

21 Top Plate -1.98 .77 7 No

Pooled Standard Deviation .71 387

Figure 11 shows the set of four residuals for each plate. The zero lines

for the 18 plates on the #1 and #4 strakes are indicated in the left margin

tor che 24 plates on the #2 and #3 strakes in the right margin. A 1-cra amplitude mark is given in the lower right corner. The plates are adjacent vertically and may also be matched from one set (column) to the next. The plot is

intended to show patterns in the curvature*' of the plates. If the curvature of

a plate were perfect, the line connecting the four points would be flat. Note,

-xample, that the first residual from all plates in the //I strake is large

k

degrees of freedom is equal to one less than the number of targets in a row.

21
1 - 2 - 3- 4 - 5- 6 - 7 - 89 -

10 -

11 -

12 -

13 -

14-

15-

16-

17 -

18

22
and negative, indicating a sharp curvature. Furthermore, the second, third, and

fourth residuals for each plate in the //4 strake form a concave pattern, indicating a sharp degree of curvature.

Target Measurement Errors

Errors in the volume tables result in part from random and systematic

errors in the target coordinate measurements. We next analyze the experimental

evidence available so as to place bounds on the measurement errrors. Later, the

effects of the errors on the volume tables are considered.

We are concerned with two types of error: random and systematic (sometimes

called bias). Systematic errors, e.g., scaling error, are the types that result

in non-zero values for certain average errors: specifically, average error in

target location and average error in length of a gauge rod. Random errors,

e.g., photographic plate resolution error, cause errors in individual target

coordinates that vary about the average error. Systematic error thus refers to an average error for a given survey.

Causes of systematic error may be the same for many surveys; for example, errors

in photo equipment, computer programs, or survey techniques. On the other hand,

the value of the systematic error in each survey may vary randomly from one survey to the next due, for example, to errors in setting the scale. Since we have only one survey, we cannot study this possibility; the limits to be set on systematic error apply to this survey alone and cannot be extended to other

surveys.

The lack of a second Independent survey also limits our analysis of random

error, but we have two approaches. First, the residual standard deviation from

a fitted model provides an upper bound to the measurement error standard deviation. However, it may not be a "sharp" bound because it includes the effects of

model error (in this case, actual deviations in the tank surface from the circular cross section assumed by the model) . The second approach involves usirig the

internal estimates of the standard error of the estimated coordinates derived

from the estimation algorithm. There may, however, be sources of random error

that are not included in these internal estimates.

No definitive analysis is possible without two or more independent

surveys. Random fluctuations due to model error will be common to all surveys

23
and could perhaps be separated from the measurement random error by variancecomponent analysis methods.

Random Errors: Analysis of Residuals

An upper bound to the standard deviation of the random errors of the photogrammetric survey in the ra dial direction can be obtained from table 1. The

standard deviation given for each horizontal row of targets is computed from the

deviations of individual residuals from the average for that row. It is thus

the standard deviation from the best-fitting circle at each height on the sphere.

Each standard deviation includes both the target measurement error and the local

deviations of the sphere from a circle at each level. These two error components cannot be separated without analyzing repeated independent surveys.

The standard deviations for each row appear to be reasonably consistent

from top to bottom of the tank. The pooled value (rms weighted by the number of

degrees of freedom*) is 7.1 ram. We will use 7 mm as the upper bound to the

standard deviation of the target coordinates in the radial direction.

Random Errors: Internal Estimates of Target Coordinate Error

The standard errors of the x-, y-, and z-coordinate values for each target were provided by the contractor. These standard errors were plotted against the

x, y, and z coordinates, and several patterns emerged. First, all plots showed

two ranges of values: a sparse distribution of high values and a more dense

distribution of low values. These distributions are illustrated in figures 12

and 13. As will be seen later, the upper group probably comes from groups of

targets masked by the central tower, and which therefore appear on one fewer

photograph than the others. The standard errors of the estimated coordinate

values are proportional to l//m, where m is the number of measurements.

The second pattern to emerge results from studying the plots of the

standard error of x (s ) vs. x and the standard error of y (s ) vs. y (For x y brevity, we have included in figure 12 only the first of these plots.) Both

plots show U-shaped patterns with the standard errors being highest at coor- dinate values ±18 meters. This shows that the precision of measurement is

poorest in the radial direction (parallel to the plane containing the cameras)

^Pooling" is a well-known technique; see p. 297 of [2] for an explanation.

24
and best in the tangential direction (perpendicular to the camera plane). It

appears that there is a factor of about 3 relating the radial and tangential

errors. This is significant since errors in the radial direction have the

most effect on the volume of the tank.

Figure 13 shows the third important pattern observed: standard errors

increase with increasing values of z. (The same pattern appears in plots of vs. z and s^ vs. z; but, again for brevity, we include only one as an illustration.) This demonstrates that precision grows poorer with increasing distance from the cameras to the targets.

The standard error of the radius determined for each target can be determined from the standard errors of the three coordinate values using standard

propagation of error techniques (see [6]).

The standard error of the radius is:

r 2 2

X sX + y

2 2 2l s + z s y z

2 2 , 2 X + y + z

if the x-, y- , and z-coordinate estimates are independent. If the coordinate

estimates are correlated (which is likely since they are derived from the same

data), then

s =

2 2 2 2 2 2 xs+ys+zs + 02xys

x y z

J s p + 2xzs s p + 2yzs s p x y xy x z xz y z y z 2 2 2 x + y + z

1/2

where p is the correlation coefficient of x and y, etc.

xy

There is potential for a significant increase in s^ if the correlation

coefficients are large and the signs are such that the contribution is positive.

We may place an upper bound on by assuming all the correlation coefficients

are ±1 with the sign chosen so that the contribution is positive.

Figures 14, 15, and 16 show the upper bounds for s vs. x, y, and z respectively. All the plots show the clustering of higher values, and figure 16 shows

the increase in s^ with the z coordinate noted earlier. If independence is

assumed, the appearance of the plots remains similar; but the maximum value

becomes 1.5 mm instead of 2.0 mm. The effect of correlation among the coordinate estimates on the radial standard deviation is thus not more than +30%.

(A reduction in this estimate is possible if the sign of the correlation is

favorable.

25
•32

OS&>3

<5>

0) «5C

O

o

O

(uuiu) 9^uipjooo x |o jojjQ pxepueis

26

Figure

12.

Plot

of

x

coordinate

vs.

the

standard

error

of

x
.. 00

. . in

CN*

o

- CD

co

o

•

' CO

- CD

05

. CM

in

CO

(0©

_2©

>

©*—

COE

Xj

u-o

o

o

N

cd m CO CM 05 00 cd m CO CM

(ujuj) eieujpjooo x jo jojje piepueis

27

Figure

13.

Plot

of

z

coordinate

vs.

the

standard

error

of

x.
m

..

<D

€*3 O

00 • CD • • CT>

.. ir>

oo

0)3

“5©

©3£

T5Ooo

28

Figure

14.

Plot

ofx

coordinate

vs.

standard

error

of

the

radius.
GO

in

CM

a>

CD

co

o

coI

CD

I

CD

I

CM

m

oo

E

&

3

05>

0>COE

X)

tn, o

o

o

>%

(ujuj) smpej eg) |0 joija pjepue^s

29

Figure

15.

Plot

of

y

coordinate

vs.

the

standard

error

of

the

radius.
4*

€M ^ ® fJ>

1

to

CM

nnw • • *ns T

a>

CO

® ® ^ ® *

• 9

es» • x • w

© e^i

« &) tfi o w •<?

• c$ <S^fi 9 U)(A^

tf> «* « •

W CM ^ (*)

^ w o «

- CO

o

• to

- CO

o>

m

CD3

CO>

0)

*-» COc

T3

i_O

o

o

N

0 e

9*3 5S* K • «

* u> J& ^ *

.. CM

L to

I I I <

• to • • to n ..00

• o> f——

4——4—I—

« w ^ OS5 ffl n cc in 'tr o w

•*** «j=*=» 'f1* y«"

(lulu) smpej am jo jojjs pjspuejg

30

Figure

16

Plot

of

z

coordinate

vs

the

standard

error

of

the

radios
These results are consistent with the residual standard deviation. The

upper bound to the total radial-direction, random-error, standard deviation is

7 mm while the internal estimate is on the order of 1 mm. The peak value is

2 mm. The difference may be due to other sources of random error, random

fluctuations in the tank surface, or a combination of the two. Regardless, the

question cannot be resolved until a second independent survey is available.

Another informative method of displaying the internal estimates of random

error is to plot the target z coordinate on the vertical axis against

0 (= tan ^"(y/x), where -ir < 0 <_ tt), the angle in the horizontal plane. The plot

is thus a projection of the target coordinates on a plane surface. Different

plotting symbols are then used to display the desired characteristics.

Figures 17 and 18 use the symbols A and B to indicate whether the s^ value

for each target is in the lower or upper group respectively (see fig. 16). It can be seen that the B's are arranged in nine narrow vertical groups. Presumably, these targets are masked by the central column from one camera position

and thus appear on one less photographic plate, as mentioned earlier.

In an effort to determine more precisely the factor relating the magnitude

of errors in the radial and tangential directions, s^ vs. x and s^ vs. y were

also plotted separately for narrow ranges of z, and also for the two groups of

high- and low-error targets.

The ratio could not be determined from the low-error group because the

standard errors provided by the consultants contained only one significant

digit. For the high standard-error group, the only z range for which there was

an adequate number and distribution of targets was the group that was on, and

adjacent to, the equatorial ring. The factor of three holds there. We are not

able to determine if the factor changes with height.

Systematic Error

As a check for systematic error in the survey, seven gauge rods with targets at each end were placed in the tank during the survey. The rods were constructed from two-inch square 5093 aluminum tubing in tx^o pieces joined by a flange in the center.

Rods 1-5 were placed around the bottom of the tank while rods 6 and 7 were placed near the top. The x, y, and z coordinates locating the ends of each rod are given in table 2.

31
(m) (anjeA a+eujpjooo 2) >juei us )i)8|9H

32

Angle

in

horizontal

plane

(C

, in

radians

Figure

17.

“Wrap

around”

display

of

target

residuals,

from

- n

to

0.
(uu) (a^uipjooo z) >fu@i u| lyS^H

o

00

S'- 04

cvi

T“

c\i

cq

T“

8X5 T”

04

T~

05

CO

00

o

33

Angle

in

horizontal

plane

(0),

in

radians

Figure

18.

“Wrap-around”

display

of

target

residuals,

from

0

to

n.
Table 2. Rod end-point coordinates (m)

Rod X y z

1 2.1885 -8.9500 -15.7102

1.3089 -5.1156 -17.4291

2 4.6285 -6.3103 -16.4456

7.1239 -2.8493 -16.5168

3 7.5256 .7120 -16.5691

5.8784 4.6593 -16.5997

4 3.0506 7 . 0377 -16.5191

-1.1255 7.3089 -16.6504

5 -4.0084 5.7746 -16.8055

-6.6706 2.4913 -16.7619

6 .9479 -2.4609 17.8288

-2.6246 - .1752 17.8466

7 2.6472 .0806 17.8384

- .8601 2,4881 17.8441

All rods were placed with the targets against the tank surface so that

length is in the tangential direction. The exact rod orientations can be

determined from the above coordinates.

The first six rods were measured by the NBS Dimensional Technology Division. Each rod was broken down, reassembled, and measured three times. The

average length for each rod, corrected to 68° F, is given in table 3. The pooled

standard deviation from the reassemblies of the rods was 0.024 mm (12 degrees of

freedom), and a 95% tolerance interval for 95% of future reassembled lengths is

0.074 mm. It follows that the random error in the rod lengths (due to reassembly, primarily) is a negligible component of the standard deviation of the

differences between NBS measurements and the photo survey (s = 0.85 mm). The

limit to systematic error in the NBS measurements is ±0.001 mm, which is a negligible fraction of the systematic difference observed.

34
Table 3. Gauge rod data.

Consultants' Consultant

Rod

Number

NBS Measurement

at 68°F (m.)

Measurement

Converted to

68°F (m.)

NBS

Difference

(mm.

Average Temp.

During

Measurement

1 4.2927 4.2937 1.0 34.6

2 4.2664 4.2680 1.6 35.0

3 4.2783 4.2779 - .4 33.5

4 4.1881 4. 1876 - .5 34.2

5 4.2278 4.2277 - .1 36.0

6 4.2405 4.2416 1.1 38.0

7 4.2534 4.2545 1.1 37.8

Rod 7 is a special case since it was measured only in Boulder. The Boulder

group also measured all 6 other rods. A bias between Boulder and Washington

(due in part to the measurement of the halves separately?) of 0.452 mm

(S.E. = 0.086 mm) was observed. The length given for rod 7 is the Boulder

length minus the estimated bias.

The lengths obtained by the photo survey and their differences from the NBS

values are also given in table 3. The photo survey lengths have been adjusted

from those supplied by the contractors. The contractors originally corrected

the lengths to 68 °F assuming a common starting temperature, but NBS temperature

measurements showed that the rods were actually at different temperatures (shown

in table 3) when measured. The differences between the NBS and photo survey

results originally showed a systematic error* which was removed by correcting

the lengths for the actual temperature at measurement.

The length differences range from -0.5 mm to +1.6 mm with an average of

0.54 mm (S.E. = 0.32 mm). A 99% confidence interval for bias in the rod lengths

is thus 0.54 ±1.19 mm, or the inter /al (-0.65, 1.73) mm. This bound, however, applies only to the tangential direction. We assume

that the appropriate factor for degrading this to the radial direction is the same factor 3 observed for between-measurement standard error in the radial and

tangential directions. This leads to bounds on the bias of (-2.0, 5.2) mm in

the radial direction.

35
While every effort has been made in the above analysis to make the bound on possible bias a conservative one, there are several factors which could cause it

to be an underestimate.

1. Most of the rods were at the bottom of the tank where measurement errors

(and perhaps bias) are smallest.

2. The rods were very short. Targets close together may have highly corre- lated measurement errors which cancel in the length computation. In

addition, there may be additional errors that accumulate in length measurement when the targets involved span several photographic plates.

3. The factors that resulted in a bias of 0.54 mm on this survey could vary

randomly between independent surveys and have a standard deviation much

larger than the standard deviation of the errors within a single survey.

> The above bound on the bias applies uniquely to this survey and does not

apply to the surveys of any other tanks . These points suggest several concepts to consider in any future efforts to

evaluate the precision and accuracy of photo surveys.

1. An additional survey, independent of the first, is essential.

2. Gauge rods should be distributed more uniformly throughout the tank.

3. Some longer rods should be used.

4. Some rods should be placed perpendicularly to the tank surface so that

measurement errors in the radial direction can be evaluated directly.

The covariances of the coordinate estimates are a necessary part of the

analysis and should be supplied by the contractor.

36
Calculation of Sounding Tables

The sounding tables constructed here are tables of volume versus elevation

for the unloaded tank. The use of the term "elevation" requires comment. The

term is intended to represent the depth of the LNG in the tank at a particular

moment. That is, assuming that the tank is in its standard position (it has

the same orientation with respect to the true vertical direction as it had while

being measured), and assuming that the liquid surface is a horizontal plane, the

elevation should be the distance from that horizontal plane to the (inside)

bottom of the tank. However, that last point is apparently not accessible to

measurement. It_ has been assumed that what is, in fact, measured is the dis3

tance from the liquid surface plane to the pedestal probe point (P ), and the

elevation is then determined by adding to that measured distance the known

3 vertical distance of the P~ above the bottom of the tank.

3 The elevation of the P , however, is not obtained through direct measurement. The photo gramme trie consultants estimated the location of the tank

bottom by using a mathematical model. After determining a "sphere of best fit,"

they determined a second, concentric sphere that best fit the bottom-most ring

of targets on the bottom cap of the tank. They then took the bottom of this

second sphere as the bottom of the tank.

3

In the present analysis, the elevation of the P was also determined from a mathematical model of the bottom region of the tank. However, the model used

here is more complicated, and felt to be more reasonable. It is described below

in the description of Model 3.

Three different sounding tables were constructed, based on two different

mathematical models and one system of volume corrections applied to the second

model. The three tables are based on increasingly sophisticated analyses, but

the final results differ only slightly.

Tank Model 1

The first model developed was a simple mathematical sphere. The sphere

that best fit the target location measurements (at ambient temperature) was found earlier in this section to have center (.005, -.0009, -.0137) and radius

37
18.2682. We assumed that an isotropic contraction occurs and converted this

to the average temperature of LNG, -160°C, by use of the following linear

thermal expansion coefficient obtained from the 1967 edition of the Alcoa

Aluminum Handbook:

L (0 to -320°F) = L (1 + C ( 1 1 . 74t - .00125t

2 - . 0000248t

3

) 10

6

),

L (0 to 1000°F) = L (1 + C ( 1 2 . 19t + . 003115t

2

) 10“ 6

)

where

= length at 0°F,

L

t = length at t°F within range indicated,

C = alloy constant (1.020 for 5083 Aluminum).

This resulted in a sphere with the same center but a radius of 18.20485 m.

) However, it was felt that for the purposes of building tank models a modification to this "contracted" best-fitting sphere was necessary. The first

modification considered was one that resulted in a sphere which would best fit

the data if the points on the top and bottom caps of the tank, and those on

the equatorial ring, were excluded. This resulted in a sphere with the same center but with a radius of 18.2113.

3

In this model the height of the P above the bottom of the tank is 0.2352

meters. However, it has been assumed that elevation is determined by the users

3

of the sounding tables by measuring liquid level height above the P , and adding

3

to that number the "known" height of the P above the tank bottom. It has

furthermore been assumed that this known height will be taken to be 0.1705 m, as given in the report from the photogrammetric consultants. So in the sounding

table for Model 1, elevation is defined as: (recorded depth - 0.2352 m +

0,1705 m), which makes the tables reported here directly comparable to those

produced by the photogrammetric consultants.

The table for Model 1 is given by the column headed VOLUME 1 in appendix A.

Tank Model 2

In this case. Model 1 is modified by replacing the top and bottom regions

of the nominal sphere with segments (caps) of other, flatter spheres. (The

38
nominal sphere is now the sphere of Model 1.) Each such flatter (higher radius)

sphere was taken to have its center on the polar axis of the nominal sphere, but

not to be concentric with the latter. (If they were concentric and touched

somewhere—which they must for the model not to be discontinuous—they would

coincide.

Since Model 2 is still a surface of revolution about the polar axis of the

nominal sphere, we can describe it via its (x,z)-plane cross section. Using the

coordinates of the center of the best-fitting sphere, the nominal sphere becomes

the circle

x

2 + (z+. 0137)2 = r2 (r =18. 2113m.),

o o

and each of the model caps is given by the equation:

x

2 + (z+. 0137-a)

2 = (r +b)2

. o

.he fact that the x coordinate of the center of the nominal sphere is actually

.0005 rather than 0 is irrelevant to the calculation of the sounding tables and

has been ignored.)

Using this model, the parameters for the bottom model cap are

a = 2.37m., b = 2.30m.,

and for the top model cap

a = -2.37m. b = 2.30m.

This bottom model cap locates the bottom of the tank at z=-18.1550; the consultants' model described above located it at -18.1603.

Each model cap extends for a vertical distance of 0.537 m and a horizontal

distance of 4.389 m before meeting the nominal sphere. Comparing the VOLUME 1 figures with the VOLUME 2 figures in appendix A, we see that the model caps

together subtract 2.41 cubic meters from the volume of the tank. The difference

between the consultants' model tank bottom and this one, while possibly of

interest in connection with the location of the bottom of the tank, is much

39
smaller than the difference between Model 2 and Model 3. It is not significant

for the sounding table.

The calculation of the first two sounding tables involved another topic:

accounting for the volume displaced by the tower structure inside the tank.

This was called "tank internals" by the consultants, and the calculation was based on blueprint specifications rather than on direct measurement. This seems valid; the total volume of the tower structure is about 7.6 cubic meters, so that high accuracy is not needed.

However, in their tank internals figures the consultants also included an estimate of the inward bulge of the equatorial ring relative to their own sphere

of best fit. The graph in figure 19 represents the consultants' tank internals

figures for tank number 4; the near-vertical part in the middle is the equatorial ring contribution. In the NBS analysis, that part was eliminated and the

tank internals were represented by the formula*

0.7345a, 0 < a £ 2.316,

V (a) = {

0.7345x2. 316+0. 1744 (a-2. 316), 2.316 £ a .

This represents the volume of the tower, as a function of altitude, a (in meters),

above the bottom of the tank, to an accuracy of ±0.3 cubic meters.

Tank Model 3

In this case the table is constructed by a numerical integration of the discrepancy between the actual measurements and Model 2. The procedure is as follows.

1. For each horizontal ring of targets, a mean z-coordinate value is

established and the mean radial residual is determined. (This is the same as integrating the radial residuals around each ring of targets

by the trapezoid rule, which is the best rule for integrating around a circle.) These radial residuals are displayed in table 4.

2. By linear interpolation between adjacent targets on a horizontal ring,

a piecewise-linear function of z is constructed, approximating the

mean radial residual at all values of z; at the top and bottom of the

model tank, the radial residuals are taken to be zero for this purpose.

*The coefficients in this formula were obtained from table V-l of the consultant's

final report.

40
9

8

7

6

5

4

3

2

1

0

Elevation (m)

Figure 19. Volumes of tank internals.

41
3 . Calling the piecewise-linear function e(z), the volume corrections are calculated from the formula:

2-rrr

1 / e(t)dt,

-18.155

z < -17.61815;

VCORR^ V

CORR ( " 17 - 61815) + 2lvro

V (17.59875) + 2nr / e(t)dt, C0RR 1 16. 59075

/ e(t)dt, -17.61815 ^ z < 17.59075;

-17.61815

z

z < 17.59075;

where r^ = 18.2113 and r^ = 20.5113. All units are meters. (The

three parts are for the bottom model cap, the nominal sphere, and

the top model cap.) The constants are derived as the vertical limits

of the top and bottom caps from tank model 2. V is added to the

CORK

values in VOLUME 2 to give values for VOLUME 3, as listed in the

appendix.

It should be noted that the above expression for V is not

LURK

for the change in volume resulting from radial distortion of model

with function e(t). It is an approximation of sufficient accuracy

purpose

an exact formula

2 in accordance

for the present

42
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

Table 4. Mean radial target residuals in meters.

Mean z e(z)

Coordinate, z(i)

-18.1550 0

-18.0329 -.0099

-17.9533 +.0106

-16.9947 +.0008

-14.9747 -.0010

-12.5078 +.0002

-11.7968 +0017

- 8.6966 +.0033

- 4.6732 -.0003

- .9500 +.0047

- .2469 -.0050

- .0189 -.0209

.2099 -.0058

.9187 +.0039

4.6301 -.0034

8.6699 -.0031

11.7571 -.0036

12.4686 -.0126

14.6601 -.0158

16.5733 -.0032

17.6457 -.0035

17.8109 +.0025

17.9894 -.0117

18.1276 0

43
Comparison of NBS' and Consultants* Results

The data from the VOLUME 3 table will be regarded as the "NBS results."

These figures are higher than the consultants' by 0.05% to 0.07%, which is

probably due to the different methods used for the last numerical integration:

where we fitted the data with a piecewise-linear function, the consultants used

a polynomial of high degree. The other obvious difference, locating the bottom

of the tank, does not account for more than a small fraction of the final differences in the sounding tables.

Sounding Table Error: Target Coordinate Error Contribution

Errors in the sounding tables may arise in four different ways: photo

survey systematic error or bias, photo survey random coordinate error, approximation error in the numerical integration procedure, and tank model failure.

The first two sources are statistical in nature and can be analyzed directly.

It has been established that an upper bound to the survey bias in the

radial direction is 5 mm. We are now concerned with the volume of a spherical

segment below a plane at height h above the bottom of the sphere:

V = tt h

2 (3r - h) . h 3

It follows that

dV, = tt h^ dr.

h

and that the percentage error in volume is

100 dV

AV = -5—

h

= 300 Ar

3r - h

For Ar = 0.005 m and r = 18.2 meters, we obtain the results shown in table 5.

44
Table 5. Volume error as a function of meters of height.

h AV.h

2 0.029% (0.064 m

3

)

14

10

6 0.031%

0.034%

0.037%

18 0.041%

22 0.046%

34

26

30

0.052%

0.061%

0.073%

36 0.092% (20.7 m

3

)

Recall that the bound to possible bias used applies to this tank survey

uniquely and need not apply to photo-surveying any other tanks. While the

analysis is intentionally conservative, there are several unknown factors that

could cause the bias to be underestimated.

Analysis of the coordinate random errors established an upper bound of 7 mm

for the standard error of the radius to a target. It is believed that this is

predominantly real tank surface fluctuations and that the random errors of

measurement are smaller, perhaps as small as a 1-2 mm standard deviation. This

implies that the appropriate method for computing volume tables is to integrate

through each target as if it were without error rather than to use a fitted

surface (Model 3 as opposed to Model 1 or 2). The effects of random error can be approximated as follows.

First, assume that the 408 targets are uniformly distributed over the

surface of the sphere and that the effect of one target error on the integration

is to displace a neighborhood of the target, equal in area to 1/408^ of the

surface, in or out. The differential effect on the volume is then

45
It follows that if we let V. be the volume error associated with the i

1

target, then

sd(V

i

) 4

408

2

tt r sd (r . )

l

We have sufficient information to let sdCr^) vary with the z coordinate and

with the number of plates involved. However, to obtain an upper bound, we will

use the worst-case value, sd(r^) = 7 mm. Let be the volume below the plane at height h. The error in V^, AV^, is

the sum

K

-

i=l V

where the sum is over the K targets below h. It follows that

sd(AV

h

)

9 /K 4 tt r 408

sd (r)

If the targets are uniformly distributed on the surface, K can be determined

from

K

408

2 tt rh

, 2

4 it r

or

K =

204 h

r

The standard deviation of AV as a percentage of V is thus

100 sd(AV

h

) ^ lop [204 (h/r) ] ^ 4 tt r

2 sd (r)

V

h 408 (1/3) tt h

2

(3r - h)

42.008 r 3/2

sd (r)

h

3/2

(3r - h)

If we take the values sd(r) - 0.007 m and r — 18.2 m, we obtain the results

shown in table 6.

46
Table 6. Percentage standard deviation

of the tank below the plane

of the error

at height h.

in the volume

h sd(AV

h

) % 3sd (AV )%

n

1 0.42 1.26

2 0.15 0.45

6 0.032 0.096

10 0.016 0.048

14 0.011 0.033

18 0.0082 0.025

22 0.0068 0.020

26 0.0060 0.018

30 0.0056 0.017

34 0.0056 0.017

36 0.0057 0.017

Note that the percentage error for shallow depths is very large because of

the large tank-bottom surface involved with a small volume.

In actual use (custody transfer of the contents between the 95% and 5%

levels), the top and bottom surfaces are not involved. The following computations apply.

Between the 31.4-meter and 5-meter heights, the surface area is 72.5% of

the total, thus

sd (AV ) s

v'K* 4 tt r^ sd(r)

408 9

where AV is the error in the volume sold and K* = 0.725 x 408 = 295.8. Then

S

3 sd (AV ) is 1.2 m . As a percentage of the volume sold, this is 0.0053%. The

2 ±3a uncertainty in the volume sold is then ±3.6 m or ±0.016%. This result is

conservative, being based on an upper bound to the actual random error. However,

it is small compared to the possible error due to bias in the radius of the

tank.

47
Sounding Table Error; Model Error Contribution

Earlier in this section, it was pointed out that, since there are no replicate measurements of the target coordinates, it is not possible to provide

conclusive statements about target coordinate accuracy. That problem plagues us again in this discussion. We are not in a position to provide definitive,

mathematically sound error bounds on model error contribution to sounding table

error. We can, however, provide judgments that are sure to be conservative

upper bounds. In this section, we offer such judgments.

The accuracy of the final volume corrections (difference between VOLUME 2 and VOLUME 3 values) is the first item of interest. These values are derived

from the table of mean radial residuals, which are obtained by integrating

(averaging) the individual radial residuals that appear in table 1. It is clear

from figures 5 through 10 that the individual residuals varied widely on many

rings of targets. How accurately does the mean radial residual represent the

integral of the radial residuals for the given "latitude"? The representation

is probably not within 10%,

Still more serious is the question of how well the tabulated mean radial

residuals—tabulated for just those z-coordinate values that are the mean z values for the several rings of targets-—indicate what occurs at intermediate

values of z. Not well, we suppose, since the tabulated values of e vary

considerably. A graph of the piecewise-linearized e is given in figure 20.

Even if the erratic behavior of e at the top, bottom, and equator is removed,

the remaining nontabular e values could easily be off by 50% or more. This last leads to the conclusion that one should not fit a high-degree

polynomial to such data. For integration purposes, a piecewise-linear fit is

best; it has the effect of localizing the variations of e at the top, bottom,

and equator to where they occur. A high-order fit, if used with the unmodified

e's, distributes these effects throughout the table. The photogrammetric

consultants apparently did remove the equatorial-ring variations before doing

their integration. In the piecewise-linear integration, the total effect of

these variations is limited to approximately 0.75 cubic meters. The consultants

estimate the (negative) volume contribution of the equatorial ring at 1.4 cubic

3

meters. The difference (-0.65 m ) is less than 0.01% of the volume of the

half -full tank and is insignificant. (In a comment on an earlier version of

this report, the consultants stated that the sharp fluctuations of the e values in the cap region were also eliminated from the polynomial fit.)

48
20

Mean Radial Residual Value (m)

Figure 20. Piecewise linear p at of mean radial residuals.

49

Vertical

Distance

from

Center

of

Tank

(m)
Sounding Table Error: Plate Curvature Error Contribution

Another question about accuracy which must be addressed is: To what

degree is the behavior (i.e., the size and variation of the radial residuals)

of the target points typical of the tank as a whole? One way of looking at

this is to consider the question of bowing out (or bowing in = flattening)

of the individual tank plates relative to the nominal sphere.

In an attempt to gain a clearer picture of this, a sphere was fit to

each plate that had four target points, and a "local radius of curvature"

was for that plate. The difference, r-r , where r is the radius of the

LUL

sphere of best global fit, indicates the bowing or flattening of the plate.

To summarize the results: for the lowest ring of plates (just above the

bottom cap of the tank), the difference ranges from +35 cm to +66 cm,

averaging +48 cm; for the next ring, r-r ranges from -34 to +15 cm,

JLUL averaging -2 cm; for the next ring (just above the equatorial ring) , the

range is from -50 to +17, averaging -7 cm; for the topmost ring of plates,

the range is from -10 to +48, averaging +17 cm. A positive value for r-r^Qr

indicates bowing, a negative value flattening.

From these facts we concluded that the average flattenings of the two

middle rows of plates were too small to matter, and probably valueless as averages, considering what the ranges were. For comparison, the flattening of

the caps in Model 2 had r-r = -230 cm, and each produced a volume difference

LUly

of only about 2 cubic meters. As for the top and bottom rings of plates, the

larger positive average values of r-rT _ _ are probably due to the rapid change in

LOO

curvature where those rings connect to the top and bottom caps of the tank (the

"sharp bend" noticed in the exploratory statistical analysis) . That volume

effect is taken into account in Model 2. So the bowings seem to have no significant effect on the corrected volume calculation.

The final volume corrections, obtained by integrating in the manner described above, ranged from approximately +3 to -7 cubic meters. Figuring

that e did not fluctuate between the "tabular" values of z more than twice

the amount of fluctuation displayed in those values, and that in any case,

these fluctuations are not likely to be in the same direction, we concluded,

conservatively, that these final corrections are not off by more than 200%.

Since the correction amounts to no more than 0.03% of the volume, we conclude that the VOLUME 3 values are accurate to ±0.06% or ±2 cubic meters,

whichever is the larger for each elevation. Since the consultants' figures

50
are lower than ours, the worst possible case would be that in which our own figures are low by the full amount of our upper estimate. That would make

the consultants' figures low by as much as 0.12%.

It should be stressed that these figures are intended as conservative

upper bounds on the magnitude of the errors; the actual errors are probably

much smaller. (For example, another possibility consistent with our estimate

is as follows. The largest inaccuracy in our own table could be only 0.03%,

in the direction of overestimation; and the consultants' largest error would

then be also about 0.03%, in the opposite direction.)

One further question remains, however: could the target points be

atypical? Notice on figure 2 that the points are all near edges (welding seams)

of plates, not in the centers. Could it be that the welding seams are "close

to" the nominal sphere but the interior of a plate is much farther away (bowed

in or bowed out)? This would mean total plate curvature is not that calculated

on the basis of the locations of the four target points. We have not been able

to discover any reasons why this would be the case. In fact, there is some support for it not being so. The plates are given their curvature in a hot press and then checked by

template and welded into place, with seams that fit well to the design specifications judging from the nearby target points. It would be surprising for

this to be the result of a coincidence in which the edges of all the plates

possessed the correct curvature while the interiors of the plates had a different one. (It is not unreasonable that the caps came out with a different

curvature from the plates because their geometry is different.) The other

fairly large deviation from the design—-the "sharp bend" referred to above—is

presumably the effect, in the completed sphere, of the difference between the

caps and the plates, as worked out through the internal stresses of the tank.

More quantitatively, we calculated the effect on the volume of the most

extreme flattening, in which the plates would be quite straight in the side-toside direction and curved only in the z direction (so that a cross section of

the tank by a horizontal plane would be a polygon) . That would reduce the

volume of the tank by about 400 cubic meters. Such bowing would be obvious

to the eye. However, visual inspection of the tank, including following the

motion of light reflections in its surface, did not reveal any. We conclude,

therefore, that there is little or no systematic bowing, and that the volume

effect of whatever bowing exists is probably no greater than the errors previously discussed.

51
REFERENCES

[1] Brown, D. C., Close-range camera calibration, Photogrammetric Engineering,

J37, 855-866 (1971).

[2] Brownlee, K. A., Statistical Theory and Methodology in Science and

Engineering, John Wiley and Sons, New York (1965).

[3] Collier, R. S., Ellerbruch, D., Cruz, J. E. , Stokes, R. W. , Luft, P. E.,

Peterson, R. G., Hiester, A. E., Mass quantity gauging by rf mode analysis,

NBS Report NBSIR 73-318, National Bureau of Standards, Boulder, Colo.

(1973).

[4] Collier, R. S., Ellerbruch, D., RF total mass gauging in large storage

containers: Empty tank modes, NBS Report NBSIR 73-346, National Bureau of

Standards, Boulder, Colo. (1973).

[5] Jelffs, P. A., Calibration of containers and gauges, J. Inst. Pet., 53 , No. 561, 117-125 (1972).

[6] Ku, H. H. , Precision measurement and calibration: Statistical concepts and

procedures, NBS Special Publication 300, _1_, 331-363 (1969).

[7] Witzgall, C., Best approximating sphere in R

n

, unpublished working

paper. Center for Applied Mathematics, National Bureau of Standards,

Washington, D.C.

52
APPENDIX A NBS SOUNDING TABLES

ELEVATION VOLUME 1 VOLUME 2 VOLUME 3

PEDESTAL

.1715 '7.978 56 1 .63252 • 1 . 5 3 8 3

- . 2 3 • 7 9 8 P 1

• - 2 . ? 9 5 9 9 2.2 1 ? 8 R 7

. 3 7 • 2 9 0 9 8 5.35 3 \) 7 5 . 8 0 ' 5

. M 11.9 0 S

9 068880 • ' 9,9 8 9 1 8

• s 17.68 .115.2797 1 5 . 5 9 9

'”.6 " ' 8 .88/ ?

' 2 2 « S 0 7 7 r

' , 9 6 7 7

. 7 3 2 . 4 2 6 0 3 0 . 3 r l 6 3 ‘ . 8 7 6

• 8 “8 1 .9659 3 7 « U 9 i 5 3 . 5 7 3 7

. 9 5 1 .5958 69.2718 8 ,78° 7 r. cr 6 2. a 0 98 -

6 0 . 8 3 -1 9 6>V. 9 97 6

i . i 7 5. 10 3

72.7258 7 ?• .3111

1

.

83.8622 '8 6

0/8 7 7 8 6 * 6 8 8 7

l . 3 102.889 100.518 101.120

1 • 1 1 8 . 37 H 1 1 A >

:.:L- 116.6! 2

53
ELEVATION VOLUME 1 VOLUME 2. VOLUME 3

I . 3 134.912 132.937 1 3 3 . 1 5 6

1 .

' 192.479 190.121 ! 5 0 , 7 0 5

5 .

? 17 1.119 168.74

4

1 6 9 ,37?

i . 8 1 9.4. 77 4 1 °fi . 4 1 I P? . 0 3 1

! . 9 2 1 i . 4 9 8 20 9 . i 8

3

7 0 4 ,717

2.'C 233.162 2 3 0.76 3 231 .423

2. J 299.981 2 5 3 . 5 n 7 2 5 4 .14 2 2 . ?: "

2 7 ? . 6 0 3 2 7 7 , 23 « 277.84

8

2 . 3 3 tl 4 .344 30 1 .96 3 3 c; ? « 5

0 5

2 . 4 " 3 3 J ,149 347.73

)

3 ? 8 . 3 6 1 2 .

3

3 9 6 .915 394.9 0

2

3 5 5 . 1 9 7 2*6 3 9 4 .469 ~ 39?', ?5 5" “'3 8 ? . 87 5

2 .

7

413. 3 9

8

4 1 .7 f; 5 4 1 1 . 5

0 9

'2.8 4 4 3 . C 99

' 4 4 0 . 6 9 5

' ” 4

,J

! , 2

0 3 2 .

9

473. 7 6

4

4 7 1 , ?

5

4 7 1 . 94 9 "3.0 " ~ 9 0 5 . 3 8 7 5 0 2.97 3

' 5 0 3 . 5 6 3 3 • 1 937.941 535.947 534.128

3.2 ~

9 7 1 . 9 BT

' 569.067 569.634

3 . 3 6 0 5 . 9 4 0 6 !; 3 . 5 2 6 6 0 4 „ 0 8 4 3. u 44i. 33

2

6 3 8 . 9 18 ~ 4 39 , 4 4 6

3.3 6 7 7 . 6 9 6 7 5 » 7’ 3 6 675.774

3 .

6

7 1 4 . 9 .8 9 7 f? . 4 75

' 7 13 » 0 0 3 3 .

7

753.341 7 5 0 .628 751.147

3 .

8

7 4-?. 1 [' 2 789.68 4” “ 7 9 0 .109

3 . 9 832. C 4

4

829.650 8 3 0 . 1 c

3 4.0 8 7 2 . 9 2

1'“' 8 7 0 . 5 0

7

8 7 1 . 0

r 3

4 . ! 9 1 '1*666 912.753 912.74?

. q - ? 9 9 -/ . 7 0 9

~9"5 4 rQ 8 j

‘ ' 9 5 5 O' 3 6 4

4 .

3

1 0 0 : . P 0 998.384 «?98. 8 4 3

S © 4 ! 34 9 . 17 To 4 2 . 7 4 I 0 4 3 . 2 3

4 .

3

S 0 9 0 - 4 1 1 08 8 , 00 ! D 5 8 .

i! 7 4 .

6

1 1 3 6. 5

i

1 1 34 , C 9 5134.56

4 . 7 1 1 « 3 . 4 6 118 1. ;j 4 1181.5

4 • 8 8-

”

i 23 1 .29 1 ? ? 8 . 3 3 ”1229.7

9

4.90 s 2 7 9.8

8

1 2 7 7 . 4 6 1 ’77,9?

s .'c:> ! 3 2 9 .~ 3 4 1326.93 1327.39

3.10 1379.6

3

1377.2

2

1377.47

5 . 70 t 4 3 3.74 * 1428.32' ~ 1*4 2 8.7 3

3.30 1482.46 ! 4 8 3 . 2 5 14«0.70

3.40 1535.39 1532.97 1533.43

3.90 i S88 . 92 1586.5 t 5 0 6 . 9 6 3.6 0 1643.24 ‘ 6 80 . 8

3

1641 .29

3.70 1698.36 1695.9

4

1696.4

3 .80 1734.25 “ TM1 7 5 1 . 8«~ 175 2.3

‘

5 . 9Q 1810.9? 1808.51 1808.96

6 . 00 1-8 6 8 . 34 1 4 6 5. 95'" ”1846.43

<S • 1 i_f 1926.57 1924.15 1924.44

4.20 * 19 80 .53 1983.

n

1 4 8 3.62

6*30 2045.24 2 G 4 2.8 2 ’ 0 4 3 . 3 5

4.40 2105 .69 2 1 0 3.28 7103.9?

4.90 2166.89 2164. 4

7

2165.03

4.60 2 2 29,83 02 226 .*4 0"' 2226.9a

6 . 7 0 2 2 9 1 . 46 2289.05 2249.45

4.8 0 2354.43 2357.4? 7353.04

4 . 9 fj 2418.91 2416.5 2 4 17. ! 5

' " 7 . 00 ”

? 4 8 3 , ? 2 4 8 1 . ? 0 "2441 .06

7.10 2549 . 19 2546.78 2547.47

7.20 2615.38 2612.96 2613.43

54
ELEVATION VOLUME 1 VOLUME 2 VOLUME 3 7 . 3 0 ? 6 8 ? . 2 S 2 6 7 9 - 8 3 > 6 8 0 . ' 9 7 . M 0 7 7 49.8 * 2 747.3 9 ? 7 “ 8 . t 6 7 .SO 2818.03 2815.6? 2 3 ! 6 . u 1 7 » 6 Cf 2886.93 7884.51 2885.3 3

7.70 2956.49 2 9 5 4 . j 7 2954.8? 7 . « C 3026.7 3 0 2 4.29 3 0 2 5, 17

7.90 3097.57 3095.1 6 3 0 8 6 .

f: 6 8 • CO ' ' ' 3169.08 3 1 66 . 6 7 7 1 6 7 v / 0 8 . 1 0 3241.23 3238.61 3 2 .7 8 . 7 8 8 . 2 0 3354.01 3311.59 ' 33 12. r 9 8.00 3387.41 3 3 8 5. 0 0 3 386.0?

8.90 3461.43 3459.0? 3460. 0 7 8 . SC 3536.07 3533.66 3 0 3 4.7 4 8*60 3611.31 “'3608.90 3 6 1 ( , 0;| 8 . 70 3687.15 3684.74 3 6 5 5 . ' 9 8 . 80 3763.59 3761.27 3762.36 8 . 90 3840.61 3838.19 3 8 9 9.41

9.00 3918.21 3915.80 3 '517.05 9 . t C 3996.39 3993 . 97 3995.76 9 . 20 4 3 7 5 1 3 ~ 4 0 7 2 . 7

2'

A 0 7 4 c r 4 9 00 4154.44 4152. 0 3 4 1 r 3.39

.9 .40 4 2 3 4 .3 1 4 2 3 1.89 4 2 3 3.99

9. SC 4314.72 4312.31

u 3 1 3 . 9 A 9 . 60 4395.68 4393.26 4 3 9 4.7 3 9.70 4477.17 4474.76 4476.2 6

9.8 0

*- 4 5 5 9 19 ~ ~ 4556.78 4558.37 9 . 90 4641.74 4639.33 4 6 4 , j * 0 l ' ~ 10.00 4724.81 4722.40 ' 4774 . C 1

10.10 4808 . 39 4805.98

A 8 0 7 . A 7 10.20 4892.47 ' 4 8 9 0 ." 06 4991.73

10.30 4977.06 4974.64 4976.3 5

'10.40 5062.13 ' 5059 • 72 506 1 . as l 0.£D 5147.70 5 1 4S . 28 5147.04 l C .6 0 5233.74 5 2 3 1. 3 3 5233 . < !

10.70 5320.26 5317.85 5319.66 i c . e o 5407.25 5404.83 5 4 0 6 . 6 7 10.90 5494.69 5492.28 A A 9 4 c 14 I l .00 5582.60 5 5 8 C • 1 8 5 5 8 2.0 6

11.10 5670.95 > 5668.53 5670 . 4 a 11.20 5759.74 5757.33 5759.75

11.30 5846.97 5846.56 5848.0

11.40 5938.64 ‘ 5936.22 5938.18 1 1 .SO 6028.7? 6026 . 3 1

6023.79

11.60— 611 9; 2 2 6 116,01 6119.8

11.70 6210.14 6207.72 6209.73

11. 80 6 30 1 .96 6 ? 9 9 . 0 4

6301 .07

11.90 6393 . 1 7 6390.76 6 3 9 2 . 8 C. 12.00 64 85 . ?9 6482,87 6484 . c ? 1 ? . 1 0 6577.78 6575.37 6 5 7 7 . a 3 12.20 6 6 70.66 6668.25 667Cs

12.30 6763.91 6761,50 6 7 6 3 . a 8 | 2 . - — 6857 • 53 ; 6 8 55 .1 1 6857.7 1 2 .SO 695 1 .5 1

6949.09 6951.19

12.60 7045.89 7 0 4 3 .4 3 7 0 4 5 . r 3

12.70 7140.52 7 1 3 8 . II 7140.22

12.80

— • 7735.54 7 73 3 . | 3 7 2 3 5 . ? 4 12.90 7330.91 7328.49 7 3 3 0 . 4 ! 1 3. CO' ~ 7426.59 7 4 24 T1 8 7 4 76'. 7 0
ELEVATION VOLUME 1 VOLUME 2 VOLUME 3

I 3 „ 0 7 5 2 2 , 6 ! 7 20. !

9

/ 5 ? 2.31

i > « 2 0 7 6 | 8 •> r- 4 7 6 16. 4 ? 7 6 ! 8 . 6 4

\ 0 . ? u 7715. 5

8

7 7 I 3 . I 7 7 7 i 5 . 7 3

13 . 'i 0 7 8 1 2 * 5 2 7810. i

r

7 B 1 2 i ?3

i ?

.

r o 7 9 0 <5.7/ 7927.36 7 9 ; ; 9 ,

11 7 13.60 8 0 0 7.3 8 0 0 4 . p.9 ”'P 0 i • 7 . ,) 13.70 8 1 G 5.53 8 ! 0 7.71 3 1 9 4 7 ?

l 3 .80 " 8? 03'. 7 3 8700.31 ‘ 8 3 0 7.8?

13.90 8 3 0 5 . 6 8799. 19 8 301 . 3

r

1 M . 00 0'4'Ch: . 7 4

' 8 39 7 . 8.3 3 .3 V V . 8 q 14.10 3 4 9 9. ; 4 ?> 4 9 6.73 8 4 9 8 , 8 r.

1 4 , 7 0 8598 . 31 5 5 9 5 .'! 8

'

• 5 9 8,(1

M.30 869 7 .

7

6 6 9 5.29 8 697.4?

1 4 . 4 0

' 8797. 3

5

3 7 9 4 . 9 3 8 7 9 7 . 0 A

1 4 . SO 8897.23 8 894.81 8 8 9 6.97

-e > o 1

8997.34 8 9 ? 4 * 9 ? 8 9 7 7.29

14.70 9 G 9 V . 6 7 9 ; J 9 5.3

6

9 r- 9 7 . q q 14 . 40 9198.7? 9 5 9 5. 8 1 9 19 8^;

14.90 9298.98 9296.57 9?98.7

3

15.00 9399.94 9397.53 9399.7

6

15.10 9 5 0! * 1 9498.69 9 5 0 0 * ° 5

15.20 9 6 0 2.46 '9 6 0 o7 e 4 9602.3?

15.30 9 7 0 3.9-9 9 70 1 . 5

8

9 7 0 3 . p 8

15.4 0

' 9 8 Li 5 . 7 1 9 3 0 3 .30' 9 8 0 5.4?

15.50 9 9 0 7.60 9 8 05, 18 9 9 0 7.54

1 5.60 1 G J09 .'7

' if.oG7 .

2

... , q j> 0 9 .

6

15.70 \ 1 0 1 i i . 9 1 0 10 9.5 1 0 ! i i . 9

1 5.80 10214.2 10211.8 1 C ? 5 4,3

15.90 50316.

8

10314.

3

i C 3 1 6 . e 16.00 10419.4 ~7C4 \1 .0" 104(9.5

16.10 1 0 5 2 2.2 i 5 i 9 , p 10522.3

1 6 ; 2 o '1062571' 1 0 6 2 2.

7

106 25.

3

1 6 . 30 1 0 7 2 8 . 2 10725.3 10728.4

1 6 . 4 0 10831.3 I 0 8 2 8 . 9 108 31 .6

16.50 10934.6 10932.2 10934.9

16.60 I 1038.0 1 1035.6 1 10 3 8.3

16.70 ! H 4 1 . 4 1 S 13 9.0 1114J.8

16.80 1 1 245.0 1 12 4 9.6 11 245 .

4

16.90 S 1348.6 11346.2 11349.1

17.00' 1 14 5 2.4 1 14 5 1. 0 1 1452.9

17.10 1 1 556 . 2 1 1553.8 1 1 5 5 6.7

17.20 1 16 6 0.0 1 1657.6 1 16 6 0.7

17.30 11764.0 1 1761 .3 1 1 7 6 4.6

1 7 .'4 0 I 1 8 6 7.9 i 18 6 5.9 1 1 °68 . 6'

1 7 . 50 11971.9 l 19 6 8.5 1 19 7 2.7

“T 7 .60 1 2076.0 12073.6 12076.7

17.70 13180.1 17177.7 17180.8

1 7 . ft 0 12284.2 1 7 7 8 1 . 8 12 7 8 4

.

9

1 7 . ° 0 12388.4 1 7 386.0 1 7 3 P, 9 . 0

i fi • co

' 12492.5 '

1 7 490. 1 17493.1

18.10 1 7596 . 7 17594.3 12 5 9 7 . 1 "10.20 ~~~ ~

5 2 7 0 0 . 9 17693.5 12 70 1 . 0

18.30 1 2805.0 1 7 8 l, 7 . 6 1 7 p 0 5 . 1 18.40 17909.2 1 2906.3 12909.1

18.50 13013.4 13)1 f . 9 13 013.

7

18.60 1 3 1 1 7 .5" 13 11 5 . 1

-

' 13 117.3

1 0 . 7 0 » 32 7 1 .6 13713.2 t 3 ?? 1 , 4 “•“! 8 . 80 — ' ' 13325.6 13323.7 1 3 3 7 5.4

56

'SI

IV
ELEVATION VOLUME 1 VOLUME 2 18.90 1 3929.6 \ 3 9 2 7 . ? 19.00 1 3 5 ? ? . A 1 3 S 3 ‘ ? ! 9 . 1 0 13 6.37, 0 i 3 6 3 r' i 19.20 5 3 7 8! .8 .1 37 3 9 , 19.30 1 3 8 9 5 . 7 1 8 j. ? .

>; 19.30' 13998.9 1 3 9 9 A , 5

19.50 1 9 V 02.0 1 9 i. 5 1.1

19.60 ' 19 1 5 A . » 1 5 j 0 8 . 7

19.70 < 9 ? 5 7, I 19.80 *19362.9 I 9 3 A . 5

19.90 19966.2 (99 6 3 . 8 2 0.0 0 19569.3 ) 9 0 6 •!. ... 9

20. ! 0 19672.9 1 9 6 7 .. r- 20. 20 

19775. 3 ! 9 7 1 ? . 9

20.30 ) 11 6 7 8 . 1 1 9 87' . 7 20.80 “'19980.7 1 “ 7 7 8 . 3 20 .50 1 5 C P 3 . 2 l 0 0 8 ; , 8 ‘ 2 C . A O' 1 0 1 9 5. A 15183,2

20. 70 1 528 7 . 815285,9

"20.80 15389.8 1 5 3 8 7.9

2G. 90 15991.7 15989.3 " 2 1 .00" 18593,9 155 9 1 .0' 2 l . 1 C 15699.9 15697,5

'21.20 1 0 7 9 A . 3 1 0 7 9 3 » 9 2 1.30 1 5897 . 9 1 5 8 5 5 . 0

21.80 15998.9 ~ 1 5 9 9 6 , 0 2 1.50 16099.1 16096,7 2 1.60 16199.7 16197.7 2 1.70 1 A 3 0 0 . G 56297. A

“21.80 16926. 1 l A 3 9 7 ,7 2 1.90 16999.9 16997.5 2 2 . C D 16058.6 16897,?

22.10 1 6 6 9 9 . o 16696.5

22 , 20 16 7 98 . 1 167 95.7

22.30 1 6 B 8 7 . 0 i 6 8 9 9 . A 22 . 90 i 6 9 9 5 . 6

16993.2

22 , 50 17099.Q 17 0 9! . 2 2 . A 0 "* 1719 2.0“ T 7 1 89 . A

22. 7Q 17289.8 17207.4

"22.80 ”17387 , 9“ 1 7 38 9 . 9 22.90 17989,6 17982. ? 2 3.00 17 5 8 1 . 5 *1 7 5 7 9 ,5

23.10 17678.1 17675.7

23.20 ’ 1 7779 .'9 17772.0

23.30 17870.9 17869.0 2 3.80 1 7966.1 ~ 1 7 9 6 3". 7

23.50 1 906 1 . 9 1

'*?

C 5 9 . O

23.60 ~ 1 8 15 61 <T

r T8 1 5 9 . 0

23 . 7C 18251.1 18298.7 2 3.80 18395.9 "18 3 9 3 .7

23.90 18939.9 18936.9

— 29. 00 18532,9 1 8 0 30 . 5

29.10 18626.2 18623.8

'* 29 . 20 18 7 19. rr- 18716.6 2 8.30 18 8 1 1.5 1 8 « 0 9 . 1 29.90 ' 18 9 2 3.6 — j , . 2

29 . 50 18995.3 1899?.?

29.60 19086,6 1 9UR9T1

57

VOLUME 3 1 •" 2 v . 0 ! 3 o 3 3 . “ ! 3 A 3 7 . 9 I 3 7 'I l . 3 1 3 8 9 0 . ! I 3 7 '< f. . 9 i 9 o o ? . b » * : c; 6 , ? 1 9 2 0 9 . 7 l 3 7. 3 . I ) « 6 6 . 3 l 9 0 A

tJ . 5 I

11 7 7 7 t 9 1 9 / / 5 • 5 t 4 0 7 3 . 3 > 'I 9 8 1.0 1 0 0 9 3. 0

15 18 5 9 l 5 7 3 a . ! I 0 3 9 0 c ) [ 0 9 9 V . n 13593.7 l 0 A 9 0.?

15796.6

10897.7

10 9 9 8. 7 I 6 L 9 9.9

>8197. c>” 18 3 0 0 . 2 l AM o *" 3 ! ( 0 0 J > 7 1 A 0 9 9 • 8 ! A A 9 9 . I 1 A 7 9 8.7 1 6 « 9 7 . 1 1A ° 9 0.7 1 7 0 9 9. 0 r 7 1 <> 2 , r 17789.8

17 387 .3 1 7 8 8 9 . 5

17 0 8 1 .9 I 7 A 7 8 . 0 1 7 7 7*;,? J 7870.? 1 7 .9 A 0 . 8 1 3 0 A l . I 13108.1

19730.7 1 8 38 5'. 0

18838.9

19337.4 1 3 A ? 0 . A " 18713.8 I R 8 10.9 I 3 9 Q ? . 9 1 R 9 9 8 . A 1 9 0 8 0.8
ELEVATION VOLUME 1 VOLUME 2 VOLUME 3 2 3 , 7 0 1 9 l 7 7 3 19 17 5 . ' 1 5 i 7 6 0 7

.? 3 . 8 0 19267 . V \ 9 9 6 5 , 3 : 9 ? 6 7 . 5 ? ‘i . 9 0 19 3 5 8 . •:;> i f> 3 S l‘- .6 ,935/. 

?s . no 1 9 S S 7 . 6 1 9 h 3 5 . ? i 9 6 6 6 . 7

25.10

J 9 5 3 6 . 6 l 9 5 3 8. 8 i 9 5 3b, 9

25. 20 19625.6 19 5? 3 , ? 19673.6 2 5. "50 19713.9 19711.5 13712,9 2 5 . 3 0 1 9 8 :• 1 . A 1 9 7 9 0 . 5 ! 9 5 or,'. A 2 5.50 19669.2 1 9 A 6. / .

P. 1 ? 8 A

A . 1 2 5.60 1997 6 . 1

19 9 7 5. /• ! 9 9 7 3.0 2 5 . 7 0 2 0 6 6 7 . 6

2f 7 6 ' . ^ 2 00 6 l . 5 2 5 . a 0 2 0? AS. 6 2 v 136. ?

>•• •• 18 7. 5

25 . 90 20? 3 3 . 2 2 0 2 3! .a 2 0 7 3 3, 0 2 6.03 ' 2C3 i 9 . 2 ' 2 f‘ 3 16. 8 2 0 3 5 8 . G 2 6.10 ? 0 M 0 3 . 6 2 0 8 t- 5 ,3 7G«0 2 , 5 2 6.20 208 R 7 . 8

20885. 8 2 0 3 P '0 , 5

26.30 7057 i . S

.705 6 3 . 9 2 0 5 7-.'. • 26 . on " 2 0658 . M ' 2 0 65? . C

20653 . 0

26 . 50 20736.9 2 0 7 3 8.5 7 0 7 3 5 = 5 2 6.60 2C.8 ! 8 * 9 2 0.8 i 6 .5 20817.3 2 6.70 20900 . S

20 697 . 9 0 r> 0 c<

q 26 . SO 2093 1.3 2 09 7 3 . 9 7 0 0 7 9 t 7 26 . 90 2 1 0 6 i .6 2 f <3 5 9 . ,7 7 l 0 6 J , 1 " 27 . 30 " 21181.5 2. 1139. 1 '2 1 13 9.9 2 7.10 21220.7 21218.3 21719.1 2 7.20 21299.5 21297.0 21297.8

27 . 30 21377.6 21375.2 2 1 3 75 . 9 2 7. SO 2 1 S 55 .2 2 1 657 , 7 2 18 5 3. 3

27 . 50 21 532 , 1 21529.7 2 1 5 3 0 , 3

27 . 60 2 1 608 . 5 2 ! 6 0 6 . 1 2 l 6 0 6.7 2 7.70 2 1 6 8 S . 3 21681.9 ? 1 A 8 2 . 5 2 7.60 21759.5 2 17 5 7 , 1 21757.6

27.93 2 1 8 3 S , 1 21831.7 21832.2 2 8 . 03 21938.1 2 1 90S . 7 7 1 9 0 6 . 1 28 . 1 0 21931.5 21979.1 2 1 0 7 9 . 5

28.20 ” 22053.2 27051 i 8 ' 2 2 1 5 2 . 2 2 8.30 22126,3 22123.9 22128.? 2 8. HO 22 19 7. '8 2 ? 19 5

.6' " 2? 1 9577

28 . 50 22268.6 77266,2 7 ? 9 6 6 . 3

"'2 8 . 60 2 2 3 3

8'. 8 '2.7 3 36 ,8 ’ 2 3 3 6 . 6

28 . 70 22803.3 22305,9 2 2 3 0 6. 1 2 8.83 2 2 3 7 7 . 1 22878.7 22378.9 2 8.90 22535.3 2 75 M 9 e Q ? ? 5 3 3. 0

29.00 22612.3 22610. 8 2 2 6 1 ,.j . 5

29.10 22679.7 2 ? 6 7 . ? 22677.3

29.20 22735. 3

22783.

R 2 2 7 8 3. 3 ? 9 . 3 0 2 2 8 1 1.2 27803.3 22808.8 2 9 . SO 2 2 8 7 6. 0

27873.6 2 2 R 7 3 , 5

29.50 22980.0 22937.6 ’2937.5 2 9.60 230C3.3 '2 3 003 . 9 2 3 ( . 0 0 * 7 29.70 23565.9 23063,5 7 7 0 6 3.3

29.60 ' ' 23127.8 23125.3 7 3 1 2 5 . ! 29 . 90 2 3 l 8 9 . T 23186.5 2 3 ! P A . 2 3 0.00 2 3 2 8 9. 3 2 3 2 3 6.9 9 3 9 3 6 . 6 3 3. t 0 7 3 3*. 9 . C 2 3 306 . 6 7 3 7 0 6 . 2

30. 2 0 23367.9 2 3 365 . 5 7 3 7 6 5. 1? 3 u . 3 0 7 3 3 2 6 . 1 23823.7 ? 3 8 . 1 3 0 . *1 0 23863.5 23801,1 7 7 3 p 0 . 3

58
ELEVATION VOLUME 1 VOLUME 2 VOLUME 3 3 0 . - 3 7 3 r> 4 0 . 1 7 3 5 3 7 „ 7 7 3 5 3 6 .

'/ ' 3 0. G 9 7 c. 5 . ° ,v 3 1 9 8.5 9 3 5 7 7 . 6 3 G . 7 ».J 7 3 6 5 1 . • 7 3 6 4 8 „ A

'» 3 6 4 7 , 5 3 O . 5 0 2 3 7 05. 3

73732.8 7 3701.6 3 0 . 9 0 23758.7 7 3 7 5 4 . .3 ? 3 7 5 5 . C 3 1 ii G 23811.4 7 3 8 0 9. f, 2 8 8 0 7. 8 3 1.10 7 3 9 A 3 . 3 ? 3 8 6 . 9 7 3 8 5 9, 7 3 1 . 2C ? 3 « i 4 . 3 739)1.9 7 3 9 10. 1 3 1 . 3 f;

23969.6 7 3963.1 7 3 9 6 0,7 3 ! .

*! 0 2 fU?i4. » 2 9 •: ! < . 4 7 4 0 (j ? , 4 3 } .GO 2 4 V. 4 2.5 2 9 6 . 1 7 4 5 7 . H 3 I .AO 7 9 1 ! l . 3 ? 4 1 O

"> „ 9 7 4 1 0 5 , 4 3 l . 70 7 4 { 5 7 . 2 2 8 ! 5 9 . 8 7 4 ! 5 7 . 1 3 I . 8 j 7 4 2:' 3 . ? 29 7-.;.r > 4 i ° * : a 0 3 1.90 3 4 7 9 S . 4 2 9 7 '• 6 •; 

7 u 7 4 3 . 0 3 2.00 74792.7 2979 .3 7 4 7 6 7.7 3 2. 10 743 36, 1 74333.7 7 4 3 3 0 . 5 3 2.20 24378.7 24 376 .3 7 -I 3 7 7,9 3 ? < 30 74927. 4 7 4 9 S P . 0 7 4 4 1 4 . 4 3 2 . 4 0 2 4 4/ 1 • 7 7 4 4 55 . 8 ‘ 7 9 4 5 5) . 5

3? . GO 7 4 5 0 1.1 2 4 4 9 8.7 7 9 4 9 4.7

32. 60 24540.1 24537. 7

74533. 6 3 2.70 2 9 5 7 8 .? 2 4 5 7 5 . 3 7 4 5 7 1.5

32 .'30 “ 24615.4 29617. 9 7 4 6 0 8.8

32.90 2 4 6 5 1 .6 2 4 6 4 9.7 7 *! 6 4 4.5 3 3 . <_< 0 2 4 6 8 6 . 9

2468 9 . 5 " 7467

V , 7 3 3. 10 24721.3 247)8.9 74713,9 3 3. ?0 7 4 7 5 4". 8 ? 4 7 5 ° . 4 747 4 7 . ? 33.30 24787.3 24784.9 2 4 7 7 9 . 6 3 3 .'«D“ 2 4 R 1 8 . 8 7 9 8 1 5 0 5 ' 7 9 4 ! 1 . 0

33.5 0

24847.5 2 4 8 4 7 . 1 7 4 8 9 ) . 5 3 3*60 24 8 7 9'. I* '24876.7 7 4 7 1 . 0

33.70 2 4 9 0 7 . S 24905. 4 ? 9899.5

33^80' 2 4 9 3 5 .5 2 9 9 3 3 . O' 7 4 927 . i 33.90 24962.7 2 4 9 6 9 . 7

74953.7 3 4.00 24 987 . 9" 24935.5 7 4 9 7 9 ,'3 34.10 7501 2.6 250 1 0 . 2 7 5 0 0 4.0 ’ 34.20 ~2 5 0 3 6 • 3 2 5 0 3 3 • $ 7 5 C 2 7.6

34.30 75L59.0 2 5 5 5 6.6 ? 5 0 5 fi . 7 3 4.9 0 7 5 0 8 C . 7 25078.3 2507 1 .8

34 . GO 25151 .4 25099.0 25092.5

"34.60 ~

25131.0 25 3 16.6 "25112.0

34.70 25139.6 2513/.2 7 5 13 0 . 6

34.80 ~ 25 157.2 25 154.8 25148.1

34.90 25173.7 25171.3 7 8 16 4.6

3S . 00 “ 2 5 1 8 Q .7 ’ 25 3 8 6 . 8 2 5 I 8 0 . ! 3 5.10 25203.6 25201.2 75194,4 ' 3 5 . 2 0 "75216.9 25214.5 2 5 7 07.7

35. 30 25229.2 25726.8 7 5 7 7 0 . 0 3 5.40 25240.4 25738.fi 2 5 7 3 1.1

35 . 50 25750.5 2 5 7 4 8 . 1 25741 . ? 3 5.60 ~ "75259.5 2 5 2 5 7 . 1 7 5 ? 5 ,J . 7 35.70 75767.5 2 5 2 6 5. 1 25758.1

35. OC "25774.3 25 7 7 1 . 9 7 5 v 6 4 . R 35 . 90 25280,0 25277.4 75970.4 3 6.00 "" " ' 75289.6 " 25 7 8 1 . 7 2 5 9 7 4 . 7

36 . i 0 25288 . i2528 4 . 8 7 5 7 7 7.7

36.20 ' ? 5 2 9 0 . 9 2 5 7 8 6 . 5 ' 90979.3

59
APPENDIX B: PORTIONS OF PHOTOGRAMMETRIC

CONSULTANTS' SOUNDING TABLES

S8UNDING table AT -160 DEGREES C, Tan < Mi - 4

ELL V » ( M

)

VOL. (S) DIFF. ELEV. (M) VOL t (S) DIFF .

BUI T 0 M *50 15*344 • 582

• 0000 . 000 •51 15*929 .585

* 52 16*5 2

4

.595

PEDESTAL .53 17*130 * 6 06

* 1705 2*213 m a* «=> •* 54 17*748 • 6 1 £

* 55 18*378 .6 30

.18 2*438 .225 .56 19.019 *641

.IS 2*66? .22 4 57 19*671 . 652

• HO 2.897 .225 • 5 8 2 0 * 3 3 3 .664

• 21 3*144 .247 • 59 21*010 .675

.22 3.403 .259 6 0 21*697 .687

• 23 3.673 .270 •61 22*395 .698

• 84 3.955 .282 .62 23. 1C4 .709

.25 4 • 248 .293 * 63 23.885 .721

• 8 6 4.553 » 305 • 64 24«557 • 732

27 4. £70 .317 .65 25*301 .744

» 2’8 5. 198 • 328 *66 26*055 . 754

.29 5.538 .340 .67 26*822 . 767

.30 5*890 *352 *68 27*599 .777

*31 6 * 253 * 36

3

. 69 28**88 .789

* 32 f- « 628 .375 .70 29. 188 .800

. 33 7.014 .386 .71 30*000 .812

.34 > 7.412 .398 *72 30*823 .823

. 35 7.821 4C9 .73 • 31*657 • 8 3

. 36 . 8 * 242 .421 *74 32*502 .8 45

.37 8*674 *4 32 .75 33.359 .857

. 38 9. US .44 4 *76 3 4*227 * 8 6 8

.39 .9.574 * 456 *77 35UC7 *880

.40 10*041 *467 *78 35*998 .891

* 4 i 10*519 .478 .79 36. SCO .902

.42 11*009 » 49C * 8 0 37.813 .913

*43 11*513 .502 *81 38*741 .928

44 12*024 .513 *82 33*683 . 94 2

.45 12.549 .525 *83 40*637 >954

.46 13.085 .536 * 8 4 41*602 .365

.47 13.632 • 547 *85 42*578 .9 76

.48 14 . 191 .559 .86 43*566 • 988

. 4 9 14.762 .571 •87 44*564 .998

.88 45*574 1-010

.89 46*596 1*022

*90 47*628 1*032

.91 48*672 1*044

-92 49.726 1 • C 5 4

93 50*792 1 .066

* 94 51 * 869 1.077

.95 52.958 1 .089

.96 54*057 U099

.97 55*168 1*111

.98 56*290 1.122

• 9 q 57*423 1.133

60
SOUNDING TABLE at -160 DEGREES Cjt tank no* a ELE V » (M) V0L. (S) DIFF. ELEV. ( M

)

V0L* (S) DIFF.

2 *00 22s. 718 2.221 2*50 352.397 2.722

2 • 01 230.950 2.232 2*51 355.129 2*732

2 *0? 233. 186 2.236 ? « 5? 357.871 2*74?

C .03 235.431 2.245 2*53 360*62? 2*751

2 .04 237.686 • 2.255 2*54 363.383 2*761

2 .05 239.951 2.265 c * 5'5 366*154 2.771

2 .06 242*227 2.276 ? * 56 368*935 2*781

2 .07 244.512 2.285 2*57 371.725 2*790

2 .08 246.807 2.295 ? *58 374.526 2*801

2 .09 249. 113 2.3C6 2 « 5 9 377*336 2*810

2 . 10 251*428 2.315 2*60 380*155 2*819

2 .11 253.754 2*326 2 » 6 3 382*985 2*830

2 • 12 256. C90 2*336 2*62 385*824 2*839

2 • 13 258 .435 2.345 2*63 388*673 2*849

2 .14 260*791 2.356 2*64 391*532 2*859

2 • 15 263.157 2.366 2*65 394. 4C0 2*868

2 .16 265.533 2.376 2*66 397*278 2*878

2 • 17 267*918 2.385 2 * 67 400*166 2*888

2 .18 270*314 2*396 2*68 403*063 2*897

2 .19 272.720 2.406 2*69 405*970 2*907

2 .20 275. 136 2.416 2*70 408.887 2*917

2 .21 277.56? 2*426 2 * 7 i 411.813 2*926

2 .22 279.997 2.435 2*72 414*750 2*937

2 • 23 282*443 2.446 2*73 417*695 2*945

2 .24 284*899 2*456 2*74 420*651 2*956

2 .25 287.365 2*466 2*75 423.616 2*965

2 • 26 289.840 2*475 2*76 426 * 59

1

2*975

2 .27 292*326 2*486 2*77 429*575 2*984

2 .28 294.821 2*495 2*78 432*569 2*994

2 .29 297.327 2 • 5C6 2*79 435*573 3*00 4 2 .30 " 299.842 2 • 5 1

5

2»8o 438*586 3*013

2 302*367 2 * 525 2*85 4 4 1

• 6 09 3.023

2 •32 304* 906 2*539 2 * 82 444*641 3*032

2 .33 ' 3Q7.461 2*555 2*83 447* 683 3*042

2 .34 310*025 2*564 2*84 450=735 3*052

2 .35 312*600 2*575 2*85 453 * ^96 3*061

2 .36 3

1

5 • 1

8

4 2*584 2*86 456.867 3 07

1

2 • 37 317*778 2*594 2*87 459.943 3*081

2 .38 320*382 2*604 2*88 463*038 3 • 09q

2 .39' 322*996 2*614 " 2*89 466* 137 3*099

2 .40 325.619 2*623 2 *90 469*246 3*109

2 .41 328*253 2*634 2 • 9 i 472*365 3*119

2 • 42 330*896 2*643 2*92 475*493 3*128

2 .43 333.549 2*653 2*93 478*631 3*138

2 .44 336*213 2*664 2*94 481*778 3*147

2 .45

' 338*885 2*672 2*95 484*935 3*157

2 .46 341.568 2.683 2*96 488*101 3*166

2 .47 344.261 2.693 2*97 491*277 3*176

2 .48 346*963 2*702 2*98 494*462 3*185

2 .49 349*675 2.712 2*99 497*657 3*195

- - .... .

61
SOUNDING TABLE AT -j,6o DEGREES C/ TANK N6, 4

ELEVt (M) VOL. (S) D IFF • ELEV, (M) VOL « (S) DIFF.

4 , 00 868*218 4*123 4*50 1085*605 4*561

A. 01 872.351 4*133 4*51 1090* 174 4*565

A. 02 876*492 4*141 4 * 52 1 094 * 75? 4*578

A. 03 880.643 4.151 4*53 3 099,338. 4 • 5 S 6

4 • OA 884 * 80? 4.159 4*54 1 103*933 4*595

4,05 888.970 4.168 4*55 1108*537 4«6Q4

4*06 893. 146 4.176 A * 56 1113*149 4*612

4.07 897.332 4.186 4 « 57 1117*770 4-621

4*08 901*527 4.195 A . 58 1 122*399 4*629

4.09 905.730 4.203 A * 59 1 1 27 5 036 4*637

4,10 909*942 4.212 A . 60 1 .1 31.68 3 4-647

4 « 1 i 914. 163 4.221 A * 6 1 1136*337 4 » 6 b 4

4.12 918*393 4.230 A *62 1141*001 4*664

4.13 922*63? 4.239 A * 63 1 145*672 4-671

4.14 926.879 4.247 A • 6 A 1150*353 4*681

4.15 ' 931.135 4.256 A * 65 1155*042 4-689

4.16 935*400 4.265 A ® 66 1 1 5 9 <• 7 3 5 4 •• 697

4.17 '939.674 4*274 A » 67 1164*445 4 * / 0 6

4 . 18 943.957 4.283 A * 68 1169* 1.59 4 * 7 1

4

4.19 948*248 4.291 A *69 1173*882 4*723

4.20 952*549 4.301 A * 70 1178*613 4*731

4.21 956*858 4.309 4*71 1 183-352 4*739

4.22 961.175 4.317 4*72 1188*101 4*749

4.23 965.50? 4.327 4*73 1192*857 4*756

4,24 969*837 4.335 A * 74 1197*622 4*765

4.25 974.181 4.344 4*75 1202*396 4*774

4.26 978.534 4,353 4 » 76 1 207*178 4*782

4.27 982*895 4*361 A * 77 1211*968 4*790

4.28 987*265 4.370 4*78 1216*767 4*799

4.29 991*644 4.379 4*79 1221*574 4*807

4.30 996*032 4.388 4 * 80 1226*389 4*815

4,31 1000*428 4.396 4.81 1231*213 4,824

4.32 1004.833 4 » 4Q5 4*82 1236*046 4*833

4.33 1009.247 ~4 » 4 14 4*83 1240*887 4*841

4.34 1013.670 4,423 4*84 1245 * 736 p 8 ^ S

4.35 1018*101 4,431 4*85 1250*593 4*857

4.36 1022.540 4.439 4*86 1255*459 4 *866

4.37 1026*989 4*449 4*87 1260*334 4,875

4.38 1031.446 4.457 4*88 1265*216 4*382

4.39 1035.912 4.466 4*89 1270*107 4*891

4 .40 1040*386 4.474 4*90 1275-007 4*900

4,41 1044*869 4.483 4*91 1279*914 4*907

4.42 1049.361 4.492 4*92 1284*330 4*916

4.43 1053.861 4.500 4*93 1289*755 4*925

4.44 1058.370 4.509 4*94 1294*687 4*93?

4 . 45 1062.888 4.518 4*95 1299*628 4*941

4.46 1067.414 4.526 4*96 1304*578 4-950

4.47 1071.949 4.535 4*97 1 309*535 4*957

4.48 1076*492 4.543 4*98 1314*501 4*966

4.49 1081*044 4.552 4*99 1319,475 4*974

-v+

62
SOUNDING TABLE at -160 DEGREES Z, TANK NO. 4

ELEV* (M) VOL. 
 DlFF.

6 00 1863.497 5.780

6*01 1869*285 5.788

6 • 02 1875*080 5.795

6.03 188 Q .883 5.803

6 * 04 1886.693 5.810

6 • 05 1892*513 5*819

6*06 1898.337 5*825

6.07 1904.171 5.834

6.08 1910 .

C

12 5.841

6.09 1915.860 5.848

6.10 1921.717 5.857

6.11 1927.580 5*863

6.12 1933.452 5*872

6.13 1939.331 5.879

6.14 1945*217 5.886

6.15 1951.111 5.894

6.16 1957.013 5.902

6*17 1962.922 5 . 9 C 9

6*18 1968.839 5.917

6.19 1974.763 5*924

6.20 1980*695 5.932

6.21 19 S 6. 635 5.940

6*22 1992*582 5*947

6.23 1998.536 5.954

6.24 2004.498 5.962

6.25 2010*468 5.970

6.26 • 2016.444 5.976

6.27 2022*429 5.985

6.28 2028*421 5.992

6.29 ' 2034.420 5.999

6 . J 0

* 204 C * 427 6*007

6.31 2046.442 6*015

6.32 2052.463 6.021

6.33 2058*493 6.030

6.34 2064.529 6*036

6.35 207 Q .574 6*045

6.36 2076*625 6 • 05

1

6.37 2082*684 6*059

6.38 2088.751 6.067

6.39 2094 • 825 6.074

6.40 2100*906 6 . o 8

1

6.41 2106*995 6*089

6.42 2113.091 6*096

6.43 2119*194 6.103

6.44 2125.305 6«111

6*45 2131*423 6*118

6*46 2137.549 6*126

6*47 2143*682 6.133

6 * 4 6 2149.822 6*140

6.49 2155*970 6.148

ELEV. (M) vol. (s) DlFF*

6»5o 2162* 125 6*155

6 • 5

1

2168*288 6*163

6 *52 2174*457 6*169

6*53 2180*634 6*177

6*54 2186*819 6*185

6*55 2193*010 6*191

6 * 56 2199*209 6*199

6*57 2205*416 6*207

' 6*58 2211*629 6*213

6*59 2217*850 6*221

6*60 2224*078 6*228

6*61 2230*314 6*236

6*62 2236*557 6 *243

6*63 2242*807 6 * 250

6*64 2249*064 6*257

6*65 2255*328 6*264

6*66 ?261*6CC 6*272

6*67 2267*879 6*275

6 » 68 2274*165 6*226

6*69 2280*459 6*29 4 6 * 70 2286*759 6*300

6*71 2293*067 6*303

6*72 2299*382 6*31

5

6*73 2305*704 6*322

6*74 2312*034 6*330

6*75 2318*371 6*337

6.76 2324*714 6*343

6*77 2331*065 6*351

6*7 8 2337*424 6*359

6*79 2343*789 6*365

6*80 2350*161 6*3/2

6 * 8

1

2356*541 6*380

6®82 2362*928 6*387

6*83 2369*322 6*394

6*84 2375*723 6*401

6*85 2382*131 6 * 4 0 8

6*86 2388*546 6*415

6*87 2394*969 6*423

6*88 2401*398 6*429

6*89 2407*835 6*43/

6*9o 2414*279 6*444

6 • 9

1

2420*729 6*450

6*9? 2427*187 6*458

6*93 2433*652 6*465

6*94 2440*124 6*472

6*95 2446*603 6*479

6 « 96 2453*089 6*486

6*97 2459*582 6*493

6*98 2466*083 6.501

6*99 2472*590 6*507
SOUNDING table at -160 DEGREES C, TANK NO. A

ELEV.(M) VOL - ($) iff. FLF V • (M) VfiL * ( 3 5 D I

f- F .

8.00 3164.S11 7.184 8*50 3532*129 7*495

8.01 3172.10? 7,191 8*55 3539 ,631 7*502

8.02 3179.299 7.197 8*52 3547* 138 7*507

8.03 3186.503 7,204 8*53 3554 ,65? 7*514

8.04 3193*713 ' 7.210 8*54 3562*171 7-519

8*05 3200*929 7 *216 8*55 3569 • 697 7*526

8.06 3208.152 7*223 8*56 3577*229 7*532

8.07 3215,381 7*229 8 * 57 3584*766 7*537

8 « 08 3222*616 7*235 8*58 3592*310 7*544

8 * C9 3229.857 7,241 8*59 3599*859 7*549

8 « 1

0

3237 « 1 05 7,248 8 * 6 0 3607,415 7*556

8.11 3244.360 7,255 8*61 3614,977 7*562

8.12 3251*620 7*260 8*62 3622,544 7*567

8.13 3258.887 7.267 8*63 3630*118 7*574

8.14 3266*160 7,273 8*64 3637*697 7*579

' 8.15 3273*440 7,280 8 ® 6 5 364 5*28-3 7*586

8.16 3280.725 7*285 8 * 66 3652*874 7*591

8.17 3288*017 7,?92 8*6 7 3660 * 472 7*598

8*18 3295.315 7 ,298 8*68 3668*075 7*603

8.19 3302*620 7 « 305 8*69 3675*684 7*609

8.20 3309.931 7.311 8 * 7C 3683*300 7*616

8.21 3317.248 7*317 8 * 7

1

3690*921 7*621

8*22 3324*571 7,323. 8.7? 3698*548 7*627

8.23 3331 » 900 7*329 8.73 3706*181 7*633

8 • 24 3339*836 7*336 8*74 3713*820 7*639

8.25 3346,578 7,342 8*75 3721*464 7 » 644

8.26 3353*926 7*348 8*76 3729,115 7.651

8,27 3361.281 7 * 355 8 * 77 3736*772 7*657

8.28 3368.641 7.360 8»78 3744,434 7*66?

8.29 3376 * 00? 7.367 8*79 3752*103 7*669

8.30 3383*381 7.373 8»8o 3759*777 7*674

8.31 3390*760 7.379 8*81 3767*457 7*680

8 * 32 3398* 145 7.385 8*8? 3775*143 7*686

8,33 3405*537 7*392 8*83 3782*834 7*691

8 » 34 3412*934 7*397 8.84 3790*53? 7*698

8 ® 35 3420*338 7.4Q4 8*85 3798*235 7*703

8.36 3427*748 7*410 8*86 3805*945 7*710

8.37 3435* 164 7,416 8*87 3813*660 7*715

8*38 3442*586 7.422 8*88 3821*381 7*721

8.39 3450* 015 7.429 8*89 3829*107 7*726

8,40 3457*449 7.434 8*9o 3836*840 7*733

8 « ‘i 1 3464.890 7,441 8 * 9 1 3844*578 7*738

8.42 3472.336 7.446 8*9? 3852*322 7,744

8.43 3479.789 7.453 8*93 3860*07? 7*750

8.44 3487*248 7.459 8*94 3867*828 7 * 756

8,45 3494*713 7.465 8*95 3875*589 7*761

8.46 3502*184 7.471 8*96 3883*357 7*768

8.47 3509*661 7,477 8*97 3891*130 7*773

8.48 3517*145 ' 7.484 8«98 3898*908 7*778

8.49 3524*634 7.489 8*99 3906*693 7*785

64
S0UNDINU TABLE AT DEG^FES Ct TANK NO. 4

el tv . ( M

)

V£?L • (S) D!FF. ELEV. <M> V 9 1- » (S) DIFF.

10 00 4721 • 386 8.332 10*50 5144*340 8*579

1C 01 4729.723 8.337 10*51 5152*924 8.584

10 0? 4738 » C65 8.342 10*52 5161.512 8*588

10 03 4746.412 8.347 10*53 5170* 1C5 8*593

1C 04 4754 . 764 8.352 10*54 5178.703 g • 5 9 8

10 05 4763.121 8.357 10*55 5187*3C6 8 *603

10 06 4771 .484 8.363 10*56 5195.913 8.607

10 07 4779.851 8.367 10 « 57 5204*525 8.612

10 08 4788.223 8.372 10*58 5213*142 8*617

10 09 4796.601 8.378 5 0*59 5221 » 764 8*62?

10 10 4804.983 8.382 10*60 5230*390 8 » 6 2 6

10 11 4813.371 8.388 50*61 5239*021 8*631

10 12 4821.763 8.392 10*62 5247.657 8.636

10 13 4830* 161 8.398 10*63 5256.297 8*640

10 14 4838.563 8.402 10*64 5264.942 8*645

10 15 4846.971 8.408 10*65 5273*59? 8.650

1C 16 4855.384 8.413 10*66 5282*246 8 « 6 5 4

1C 17 4863» 801 8.417 10*67 5290*905 8.659

10 18 4872.224 8.423 10*68 5299.569 8*664

10 19 4880*651 8.427 10*69 5308*238 8*669

1C 20 4889*084 8.433 10*70 5316*911 8*673

10 21 4897.521 8.437 10*71 5325*589 2*678

10 22 4905.964 8.443 10*72 5334*271 8*682

1C 23 4914.411 8.447 10*73 5342.958 £.687

10 24 4922.863 8.452 10*74 5351 *650 8* 692

10 25 4931.321 8.458 10*75 5360*346 £.696

1C 26 4939.783 8.462 10*76 5369. 047 £.701

1C 27 4948.250 8.467 10*77 5377 * 753 8*706

10 28 4956.722 8.472 10*78 5386*463 8.710

1C 29 4965.199 8.477 10*79 5395*178 8*715

10 30 4973.681 8.482 10*80 5403.897 8*719

10 31 4982. 168 8.487 10*81 5412*621 8.724

10 32 4990*659 8.491 10*82 5421*350 8*729

1C 33 4999. 156 8.497 10*83 5430*083 8.733

10 34 5007.657 8.5C1 10*84 5438*821 8.738

10 35 5016* 164 8.5Q7 10*85 5447*563 8*742

10 36 . 5024.675 8.511 10*86 5456 » 3 1

0

£.747

10 37 5033*191 8.516 10*87 5465*061 £ « 751

1C 38 5041.712 8.521 10*88 5473.817 8*756

10 39 5050*238 8.526 10*89 5482.577 8*760

10 40 5058.769 8.531 10 *90 5491*342 8*765

10 41 5067.304 8.535 10*91 5500.112 8.770

10 42 5075.844 8.540 10*92 5508*886 8*774

1C 43 5084.389 8.545 10*93 5517*665 8.779

1C 4 4 5092.939 8.550 10*94 5526.448 8.783

1C 45 5101*494 8.555 10*95 5535*235 8.787

10 46 5110*054 8*560 10*96 5544.027 8.79?

1C 47 5118.618 8.564 10*97 5552*824 8*797

10 48 5127.187 8.569 10*98 5561 *625 8.801

10 4 9 5135.761 8.574 10*99 5570*430 8.805

65
SOUNDING TABLF o

•«— v0 <

t— < DEGREES Ct TANK NO. 4

ELEV* <n VOL. (s> iff* ELF. V • { M ) VqL* (s) DjFF.

12.00 6481.737 9*226 12*50 6947*772 9*410

12*01 6490*966 9.229 12*51 6957*185 9*413

1 2 » 02 6500*199 9*233 12*5? 6966*60? 9*417

12.03 6509 .436 9*237 12*53 6976*022 5 *420

12-04 6518.677 • 9*241 . 12 *5 4 6 985* 4 4 6 9*4? 4

12*05 6527.921 9*244 12*55 6994*873 9 • 4 2 7

12*06 6537 * 1 69 9*248 12*56 7004*304 9*431

12.07 6546.422 9*253 12*57 7013*739 9*435

12.08 6555*678 9*256 12*58 7023*176 9*437

12.09 656a . 937 9*259 12*59 7032*618 9*442

12* 10 6574 * 2 0

1

9*264 12*60 7042*062 9 • 44

4

12*11 6583 * 468 9*267 12*61 7051*531 9*449

12*12 6592.739 9*271 12*6? 7060*96? 9 • 451

12.13 6602.014 9*275 12*63 7070*417 9*45 5

12.14 6611*292 9*278 12*64 7079*876 9*459

12.15 6620*575 9*283 12*65 7089*338 9*46?

12 « 16 6629*861 9*286 12*66 7058*803 9*465

12*17 6639* 151 9*290 12*67 7108*272 9*4 69

12.18 6648 444 9*293 12*68 7117*745 5*473

12*19 6657.742 9*298 12*69 7127*220 5*475

12.20 6667*043 9*301 12*70 7136*700 9*480

12.21 6676*347 9* 304 12*71 7146*18? 9*482

12*22 6685.656 9*309 12*72 7155*668 9*486

12*23 6694*968 9.312 12*73 7165*157 9*4 89

12*24 6704 * 284 9*316 12*74 7174*650 9*493

12.25 6713*603 9*319 12*75 7184*146 9*496

12.26 6722 * 926 9.323 12*76 7193*646 9*500

12*27

' 6732*253 9*327 12*77 7203*148 5*502

12*28 6741*584 9.331 12*78 7212*655 9*507

12.29 • ir;: 6750*918 9*334 12*79 7222*164 9*509

12*30 6760*256 9*338 12«8o 7231.677 9*513

12*31 6769*597 9*341 12*81 7241*193 • 9*516

12*3? 6778*942 9 ® 345 12*82 7250*713 9*520

12*33 6788*291 9.349 12*83 7260*236 9*523

12*34 6797*644 9*353 12*84 7269*762 9*526

12*35 6807*000 9.356 12*85 7279*292 9*530

12*36 6816*359 9*359 12*86 7288*825 9*533

12*37 6825*723 9.364 12*87 7298*361 9*536

12.38 6835*090 9*367 12*88 7307*900 9*539

12.39 6844.460 9.370 12*89 7317 * 443 9*543

12.40 6853*834 9.374 12*90 7326*989 9*546

12.41 6863*212 9*378 12*91 7336*538 9*549

12*42 6872*593 9.381 12*9? 7346*091 9*553

12*43 6881*978 9.385 12*93 7355*647 9*556

12.44 6891 . 367 9.389 12*94 7365*206 9*559

12*45 6900*759 9.392 12*95 7374*768 9*56?

12.46 6910* 154 9.395 12*96 7384*334 9*566

12.47 6919*553 9*399 12*97 7393*903 9*569

12.48 6928.956 9.403 12*98 7403*475 9*572

12.49 6938*36? 9*406 12*99 7413*050 9*575

66
S8UNDIM3 TABLE AT *160 DEGREE’S C< TANK Nfi* 4

F.LEV* (M) VOL. ( s

)

0 I FT ELEV. (M> VtjL. (S) D 1 r F «

14.00 8395*708 9.870 14*50 8892*379 9.992

14.01 8405.580 9.872 14*51 8902*373 9*994

14.02 8415.455 9.875 14*52 8912*370 9*997

14.03 8423.332 9. 877 14*53 8922*369 9 .999

14.04 8435.212 . 9.880 14*54 8932*370 10*001

14.05 8445.095 9.883 14*55 8942*373 10*003

14.06 8454.980 9.885 14*56 8952*379 10*006

14.07 8464 . 868 9.888 14*57 8962 » 38 7 10*008

14.08 8474.759 9.891 14*58 8972.397 10*010

14.09 8484.651 9.892 14*59 8982*410 10*013

14.10 8494.547 9.896 14 »60 8992*424 10*014

14.11 8504 . 445 9. 898 14*61 9002*441 10*017

14.12 8514* 345 9.9Q0 14*62 9012*460 10*019

14.13 8524.249 9.904 14*63 9022*482 10*022

14.14 853^.154 9.9C5 14*64 9032*505 10*023

14. 15 8544*062 9.908 14*65 9042*531 10*026

14.16 8553.973 9.911 14*66 9052.559 10*028

14.17 8563.886 9.913 14 • 67 9062 * 589 10*030

14.18 8573.801 9.915 14*68 9072*621 10*032

14.19 8583*719 9.918 14*69 9082*656 10*035

14.20 8593.640 9.921 14*70 9092*692 10*036

' 14.21 8603*563 9.923 14*71 9102*731 10*039

14.22 8613.488 9.925 14.72 9112*772 10*041

14.23 8623.416 9.928 14*73 9122*815 10*043

14.24 8633*347 9.931 14*74 9132.860 10*045

14.25 8643.280 9.933 14*75 9142*908 1C*04S

14.26 8653*215 9.935 14*76 9152.957 10*049

14.27 8663.153" 9.938

~ 14*77 9163*009 10*052

14.28 8673*093 9.940 14*78 9173*063 1C* 054

14.29 8683.035 9.942 14*79 9183*119 1 C * 056

14.30 8692*980 9.945 "'14*80 9193*177 10*058

14.31 8702*928 9.948 14*81 9203*237 10*060

14.32 8712*878 9.950 14*82 9213*299 10*062

14.33 8722*830 9*952 14*83 9223*363 10*064

14.34 8732*785 9.955 14*84 9233*430 10*067

14.35 8742*742 9*957 14*85 9243*458 10*068

14*36 8752*701 9.959* ' 14*86'" 9253*569 1 0 * 07

i

14.37 8762 • 663 9.962 14*87 9263*64

1

10*072

14.38 8772*627 9.964 14*88 9273*716 10*0/5

14.39 8782*593 “9*966” 14*89 9283*792 10*076

14.40 8792.562 9.969 1 4 * 9o 9293*871 10*079

14.41 8802*533 9.971 14 «9l 9303*952 10*081

14.42 8812*507 9.974 14*9? 9314*035 10*083

14.43 8822*483 9.976 14*93 9324*120 10*085

14.44 8832.461 9.978 14*94 9334.2Q6 10*086

14.45 8842*442 9*981 14*95 9344*295 10*089

14.46 8852*424 9.982 14*96 9354*386 10*091

14.47 8862*410 9.986 .. _ ...... 14*97 9364*479 10*093

14.48 8872 • 397 9.987 14*98 9374*574 10*095

14*49 8882*387 9.990 14*99 9384*671 10*097

67
S0UNDING TABLE AT **160 DEGREES C, TANK N0. 4

ELE V « CM) VOL. (S> D 1 FT

.

ELEV. (h) V0L. ( 5

)

D 1 EF • 16.00 10413.592 10*266 16 « 5o 10928*460 10*325

16.01 10423.859 10*267 16*51 10938*786 10*326

16.02 10434 . 127 10*268 16*59 10949*1 14 10*328

16.03 10444.397 10.270 16*53 10959*442 10*328

16.04 10454 . 668 10*271 1 6 * 54 10969*772 10*330

16.05 1 0 4 6 4 .940 10*272 16*55 10980* 1C2 10*330

16*06 10475*213 10*273 16*56 10990*484 10*332

16.07 10485*488 10*275 16*57 11000*766 10*332

16.08 10495.764 10 « 276 16*58 11011*100 10*334

16.09 10506 * 042 10*278 16*59 11021*434 10*334

16.10 10516*321 10*279 16*60 11031*770 10*336

16.11 10526.601 1G.H8Q 16*61 11042. 1C6 i 0 • J 3 6

16.12 10536*882 10*281 16*6P 11052*444 10*338

16.13 10547. 164 10.282 16*63 11062*782 10*338

16.14 10557.448 10*284 16*64 11073*121 10*339

16.15 10567.733 10«285 1 6 « 65 11083*462 10*341

16.16 10578 * C20 10*287 16«66 11093*803 10*341

16.17 10588 * 308 10*288 16*67 11104*145 10*342

16.18 10598*596 10*288 16*68 11114*488 10*343

16*19 10608.887 10*291 16*69 11124*832 1 C * 3 4 4

16.20 10619. 178 10.291 16*70 11135*177 1 0*345

16.21 10629*470 10*292 16*71 11145*523 10*346

16«22 10633*764 10*294 16*72 11155*869 10*346

16.23 1 065q * 053 10*295 16*73 11166*217 10*348

16.24 10660*355 10*296 16*74 11176*566 10*349

16.25 1067 0 * 653 10*298 16*75 11186.915 10*349

16.26 10680*952 10*299 16*76 11197*265 10*350

16*27 10691*251 10*299 16*77 13207*616 10*351

16.28 10701*552 10*301 16*78 11217*968 10*352

16.29 ' 10711*854 10® 3q2 16*79 1 1228 * 32i 10*353

16*30 “ 1o722*158 1 0 » 3q4 16*8q 11238*675 10*354

1

6

« 3

1

10732*462 10*3q4 16®8i 11249*030 10*355

16. 32 X0742#768 10*3q6 16® 82 1 1 259 * 385 1 o « 355

1 6 % 33 1q 753 . o75 10®3q7 16*83 11269*741 10*356

16.34 10763*383 10*308 16*84 11280*098 10*357

16.35 10773*692 10*309 . 16*85 11290*456 10*358

1 6 « 36 10784* C02 10 ® 310 16*86 11300*815 10*359

16.37 10794.313 10*311 16*87 11311*175 10*360

16.38 10804*626 10*313 16*88 11321*535 10*360

16.39 10814.939 10.313 16*89 11331*896 10*361

16.40 10825.254 10.315 16*90 11342*258 10*362

16.41 10835.570 10*316 16*91 11352.621 10*363

16.42 10845*887 10*317 16*92 11362*984 10*363

16.43 10856*204 10.317 16*93 11373*349 10*365

16.44 10866.523 10*319 16*94 11383*714 10*365

16.45 10876*844 10*321 16*95 11394*079 10*365

16.46 10887* 165 10*321 16*96 11404*446 10*367

16.47 10897.487 10-322 16*97 11414*813 10*367

16.48 10907.810 10*323 16*98 11425.181 10*368

16.49 10918. 135 10*325 16*99 11435* 550 10*369

68
SOUNDING TABLE AT -16 0 DEGREES c# talk no. 4

ELEV. (M) VOL* (S) D JEFt ELEV. (M

)

V0L * (5) DlFFo

18 00 12485 112 10 395 18*50 13004*686 10*393

18 01 12495 507 10 395 18.51 13015*077 10*391

18 02 12505 903 10 396 18.5? 13025*469 10*39?

18 03 12516 298 10 395 18*53 1 3035*860 10*391

18 04 12526 694 10 396 18* 5 4 1 3Q4 6 « 2o 1 10*391

18 05 12537 089 10 395 18 < 55 13056*64? 10*391

18 06 12547 4 85 10 396 18*56 13067*033 10*391

18 07 12557 881 10 396 18*57 13077*423 10*390

18 08 12568 277 10 396 18 ‘58 1 3087 * 8 1

3

10*390

18 09 12578 672 10 395 18*59 13098*203 10*390

18 10 12589 C68 10 396 18*60 13108*593 10*390

18 11 12599 464 10 396 1 8*61 13118*982 10*389

18 12 12609 860 10 396 18*62 13129*371 10*389

18 13 12620 256 10 396 18*63 13139*759 10*388

18 14 12630 652 10 396 18.64 13150*148 10*389

IS 15 12641 048 10 396 18*65 13160*536 10*388

IS 16 12651 442 10 394 18*66 13170*923 10*387

18 17 12661 825 10 383 18*67 13181*311 10*388

18 18 12672 207 10 382 18*68 13191*698 10*387

18 19 12682 590 10 383 18*69 13202*100 10*402

IS 20 12692 973 10 383 18*70 13212*501 10*401

18 21 12703 356 10 383 18*71 13222*903 10*402

18 22 12713 738 10 382 18*72 13233*303 10*400

18 23 12724 121 10 383 18*73 13243*704 10*401

18 24 12734 504 10 383 18*74 13254*104 10*400

18 25 12744 886 10 382 18*75 13264*504 10*400

18 26 12755 269 10 383 18*76 13274*903 10*399

18 27 12765 651 10 382 18*77 13285*302 10*399

18 28 12776 033 10 382 18*78 13295*701 10*399

18 29 12786 416 10 383 18*79 13306*099 10*398

18 30 12796 811 10 395 18*80 13316*497 10*398

18 31 12807 206 10 355 18*81 13326*895 10*398

18 32 12817 601 10 395 18*82 13337*292 10*397

18 33 12827 996 10 395 18*83 13347*688 10*396

18 34 12838 390 10 394 18*84 13358*084 10*396

18 35 12848 785 10 395 18*85 13368*480 1 C * 396

18 36 12859 179 10 394

18*86 13378*875 10*395

18 37 12869 574 10 395 18*87 13389*270 10*395

18 38 12879 968 10 394 18*88 13399*664 1 0*394

18 39 12890 362 10 394 18*89 13410*058 10*394

18 40 12900 756 10 394 18*90 13420*45? 10*394

18 41 12911 150 10 334 18*91 13430*844 10*392

18 42 12921 543 10 393 18*92 13441 *237 10*393

18 43 12931 937 10 394 18*93 13451*629 10*392

18 44 12942 330 10 393 18*94 13462*020 10*391

IS 45 12952 723 10 393 18*95 13472*411 10*391

18 46 12963 116 10 393 18*96 5 3482*802 10*391

18 47 12973 509 10 393 _ 18*97 13493*192 10*390

18 48 12983 901 10 392 18*98 13503*581 10*389

18 49 12994 293 10 392 18*99 13513*970 10*389

69
S e U N D I N G TABLE AT «160 DEGREES C , TANK NO • 4

ELEVv(M) VOLi (S^ DjFF* ELE V. { M ) VBL. (S) D I F F e

20.00 14559 417 10.303 20 • 5 o 15072.956 1 C . 237

20*01 14 569 719 10.302 20*51 15083*192 10.236

20*02 14580 020 10.301 20 * 5 ? 15093.426 10*234

20 • 03 14590 320 10.300 20*53 15103.658 10.232

2 0.0 A 14600 618 10.293 20*54 15113*889 10*231

20.05 14610 916 10.298 20*55 15124 0 19 1 C * 230

20 « 06 14621 212 10*296 20*56 15134.347 10*228

20.07 14631 507 10*295 20*57 15144.573 10*226

20*08 14641 800 10.293 20*58 15154 . 798 10*225

20.09 14652 C 93 10.293 20*59 15165*022 10*224

20.10 14662 384 10*291 20*60 15175*244 10*222

20*11 14672 674 10*290 20*61 15185*464 10*220

20*12 14682 963 10*289 20*62 15195*683 10*219

20.13 14693 250 10*287 20*63 15205 * 9 C 0 10*217

20.

1

4 14703 537 10.287 20*64 15216016 10*216

2 C . 15 14713 822 10*285 20*65 15226*330 10*214

20 c 5.6 14 72 4 105 50*283 20 • 66 15236.543 10*213

20.17 1.4734 388 10*283 20*67 15246*754 10*211

20.18 14744 669 10*281 20*68 15256.963 10*209

20*19 14754 949 10*280 20*69 15267071 10*208

20.20 14765 227 10*278 20*70 15277.377 10*206

20.21 14775 505 10*278 20*71 15287.582 1 C . 205

20.22 14785 781 10.276 20*72 15297*785 10*203

20.23 14796 C 56 10*275 20*73 15307.926 10*201

20 »

2

4 14806 329 10*273 20*74 15318086 10.200

20.25 14816 601 10.272 20*75 15328.384 10*198

20»26 14826 872 10*271 20*76 15338.581 10*197

20 « 27 ~ 14837 141

' 10*269 20*77 15348*775 10*194

20 * 28 .14847 409 10*268 20*78 15358.969 10*194

20*29 14857 676 10*267 20*79 15369060 10*191

20*30 14867 941 10*265 20*80 15379*350 10*190

20.31 14878 206 10*265 20*81 15389*538 10*188

20*32 14888 468 10*262 20*82 15399.725 10*187

20*33 14898 729 10*261 20*83 15409 . 9 C 9 10*184

20*34 14908 989 10*260 20*84 15420*093 10*184

20*35 14919 248 10*259 20*85 15430*274 10*181

20*36 14929 505 10 • 257 20 * 86 15440*454 10*180

20*37 14939 761 10*256 20*87 15450*632 10*178

20*38 14950 015 10*254 20*88 15460*808 10*176

20*39 14960 268 10*253 20 * 89 15470*383 10*175

20*4 0 14970 520 10*252 20*90 15481*155 10*172

20*41 1498 c 770 10*250 20 * 9 l 15491*327 10*172

20.42 14991 019 10*249 20*92 15501*496 10*169

20*43 15001 266 10*247 20*93 15511*664 10*168

20*44 15011 512 10*246 20*94 15521.830 10*166

20*45 15021 756 10*244 20*95 15531*994 10*164

20.46 15031 999 10*243 20*96 15542056 10*162

20*47 15042 240 10*241 20*97 15552.317 10*161

20 * 48 15 C 52 480 10*240 20*98 15562.475 10*158

20.49 15062 719 10*239 20*99 15572.632 10*157

70
SOU,\D 1 KG TABLE AT -*60 DEBTEES C# TANK NO * 4

ELEV. ( M) VOL* <S> D jFF. ELF V « (M) VfiL* (s) DlFF.

22*00 16588 203 9*945 22 * 5q 170.82*225 9*816

22.01 16598 145 9.942 22*51 17092.039 9*814

22.02 16608 085 9*940 22*52 17101.850 9*811

22 • 03 16618 022 9.937 22*53 17111*657 9*807

22.04 16627 958 9*936 22*54 1 7121*463 9*806

22*05 16637 890 9.932 22*55 17131*265 9*802

22.06 16647 820 9.930 22*56 17541 *065 9*800

22.07 16657 74 8 9.928 22*57 17150.862 9*797

22*08 16667 673 9*925 22*58 17160*656 9 • 7 9 4

22.09 16677 596 9.923 22*59 17170*^47 9*791

22.10 16687 516 9 » 3 20 22*60 17180*235 9*788

22*1 1 16697 434 9*918 22*61 17190*021 9*786

22.12 16707 349 5.915 22*62 17199*804 5*763

22.13 16717 262 9.913 22*63 17209*584 9.780

22.14 16727 172 9.910 22*64 17219*362 9*778

22.15 16737 080 9.908 22*65 17229*136 9*774

22*16 16746 986 9 >906 22*66 1 7238*908 9*772

22.17 16756 888 9 » 53 C 2 22*67 17248*677 9*769

22.18 16766 789 9.901 22*68 17258*443 9 * 766

22.19 16776 686 9.897 22*69 17268*206 9*7 63

22.20 16786 581 9.895 22 * 7q 17277*966 9.760

22*21 16796 474 9.893 22*7l 17287*724 9*758

22*22 16806 36 4- 9.890 22*79 17297*478 9*754

22.23 16816 252 9.888 22*73 17307*230 9.752

22.24 16826 137 9.885 22*74 17316*979 9*749

22.25 16836 019 9.882 22*75 17326*725 9*746

22.26 16845 899 9.880 22*76 17336.468 9*743

22.27 16855 776 9.877 22*77 17346.208 9.740

22*28 16865 651 9.875 22*78 17355*945 9.737

22*29 '16875 523 9.872 22*79 17365*680 9*735

22*30 1 6885 392 9.865 22*8o 17375.4H 9*731

22*31 16895 259 9*867 22*81 17385*140 9*729

22*32 169Q5 123 9.864 22«&? 17394*865 9*725

22*33 16914 985 9.862 22*83 17404*588 9.723

22.34 16924 844 9*859 22*84 17414* 3CS 9*720

22*35 16934 700 9.856 22*85 17424*025 9.717

22*36 16944 554 9.854 22*86 17433*738 9.713

22.37 16954 405 9.851 22*87 17443*449 9.711

22.38 16964 253 9.848 ‘ 22*88 17453*157 S.705

22.39 16974 099 9.846 22*89 17462*862 9 • 7q5

22.^0 16983 942 9.843 22*9o 17472*564 9.702

22.41 16993 783 9 • 84 % 22*91 17482.263 9*699

22*42 17C03 621 9.838 22*9? 17491.959 9*696

22.43 17013 456 9.835 22*93 17501*652 9*693

22.44 17023 288 9.832 22*9 4 17511*342 9*690

22*45 17033 118 9.830 22*95 17521 *029 9*687

22.46 17042 945 9.827 22*96 17530*713 9*684

22.47 17052 769 9.824 22*97 17540*394 9*681

22*48 17062 591 9.822 22*98 17550*072 9.678

22*49 17072 409 9.818 22*99 17559*747 9*675

71
SOUNDING table: at -160 DEGREES Cx Tank NO. 4

ELEV. (M

J

VOL. (S) DIFF* ELEV. (M) V8L * (SI D 1 EE * 24.00 18520.203 9*337 24*50 18982*231 9*145

2 A. 01 18529*536 9*333 24*51 18991*373 9*142

24 .02 18538 . 865 9.329 24*5? 19000*511 9*138

24.03 18548.191 9*326 24*5? 19009*644 9*133

2'* *04 18557.513 9*322 24*54 19018*774 9*130

24.05 18566 • £31 9*318 24*55 19027*500 9*126

24*06 18576. 146 9*315 24*56 19037*021 9.121

24.07 18585.457 9.311 24*57 19046*139 9*118

24.08 18594 . 764 9.307 24*58 19Q55 *25? 9*113

24.09 18604.068 9 • 3 C 4 24*59 19064*362 9*110

24 . 10 18613.367 9*299 2 4 * 6 0 19073*468 9*106

24.11 18622*663 9.296 24*61 i 9 0 S 2 * 569 5*101

24.12 18631 . S56 9*293 24*62 19091*667 9*098

24 .13 18641 . 244 9*288 24*63 19100*760 9*093

24*14 18650*529 9.285 24*64 19109*849 9*089

24 . 15 18659.810 9.281 24*65 191 1 8*234 9*085

24 *16 18669.087 3*277 24*66 19128*016 9*082

24*17 lS678»36i 9.274 24 • 67 19137*093 9*077

24.18 18687*630 9.269 24*68 19146* 166 9*073

24 . 19 18696*896 9*266 24*69 19155*235 9*069

24.20 187C6* 159 9.263 24*70 19164 . 299 9*064

24.21 18715*417 9.258 24*71 19173*360 9.061

24.22 18724*671 9.254 24*7? 19182*417 9*057

24.23 18733*922 9*251 24*73 19191 * 469 9*052

24.24 18743® 169 9.247 24*74 19200*518 9*049

24.25 18752.412 9.243 24*75 19209*562 9*044

24.26 18761*652 9*240 24*76 19218*602 9*040

24.27 18770*887 9*235 24*77 19227*638 9*036

2^.28 18780*119 9.232 24*78 19236*670 5*03?

24.29 18789*346 9*227 24*79 19245*697 5*027

24.30 18798*570 9*224 24*80 19254*721 9*024

24.31 18807*791 9.221 24*81 19263*740 9*019

24 s 32 18817*007 9*216 24*82 19272*755 9*015

24.33 18826.219 9.212 24*83 19281*766 2*011

24.34 18835*428 9.2C9 24*84 19290*773 9*007

24.35 18844.632 9*204 24*85 19299*775 9*002

24.36 18853*833 9*201 24*86 19308 *774 8*999

24.37 18863*030 9*197 24«87 19317*768 8*994

24.38 18872*223 9*193 24*38 19326*758 8*990

24.39 18881 * 412 9*189 24*89 19335*743 8*985

24.40 18890*597 9*185 24*90 19344*725 8*982

24.41 18899*778 9*181 24*91 19353*702 8*977

24.42 18908*955 9*177 24*92 19362*675 8*973

24.43 18918*129 9*174 24*93 19371 *644 8*969

24.44 18927*298 9*169 24*94 19380*608 8*964

24.45 18936*463 9.165 24*95 19389*569 8*961

24.46 18945.625 9.162 24*96 19398*525 8*956

24.47 18954.782 9.157 24*97 19407*476 8*951

24.48 18963*936 9*154 24*98 19416*424 8*948

24.49 18973*086 9*150 24*99 19425*367 8*243

72
SOUNDING TABLE AT -160 DEGREES Cm TANK NO * 4

elev. (M) V&L • (S) DIFE. ELEV* (M) V3L * (S) DIFE.

26 • CO 20305 443 8*478 26*50 20722*922 8*223

26.01 20313 916 8.473 26*51 20731*141 8*219

2 6 • 0 2 20322 384 8.468 26*52 20739*354 8*213

26.03 20330 847 8.463 26*53 20747 » 562 8*208

26*04 20339 306 8.459 26*54 20755*764 8*202

26 * 05 20347 759 8.453 '26*55 20763*96? 8*198

26 • 06 20356 207 8*448 26*56 20772*154 8*192

26 « 07 20364 650 8*443 26*57 20780*341 8*187

26.03 20373 089 8,439 26*58 20788*522 8*181

26 * 09 20381 52? 8*433 26*59 20796*698 8*176

26.10 2q359 950 8*428 26*60 20804*869 8*171

26*11 2Q398 374 8*424 26*63 208139035 8*166

26*12 20406 792 8*418 26 6 6? 20821 * 195 8*160

26*13 20415 206 8.414 26*63 20829*350 8*155

26*14 20423 614 8.408 26*64 20837*500 8*150

' 26*15 20432 C 1

7

8.403 26*65 20845 *644 8*144

26*16 2Q44C 416 8.399 26*66 20853*783 8*139

26 * 1 7 _ 20448 809 8.393 26*67 20861*916 8*133

26*18 20457 197 8.388" 26*68 20870*045 8* 129

26*19 20465 580 8.383 26*69 20878.167 8*122

26.20 20473 958 8.378 26*70 20886*285 8*118

26*21 20482 331 ’ 8.373 26*71 20894*397 8*112

26.22 20490 699 8*368 26*72 20902*504 8*107

26*23 20499 C62 8*363 26*73 20910*605 8*101

26*24 20507 420 "8.358 26*74 20918*701 8*096

26*25 20515 773 8.353 26*75 20926*791 8*090

26*26 20524 121 8.348 26*76 20934*877 8*086

26*27 20532 463 8.342 " 26*77 20942*956 8*079

26.28 2c540 801 8.338 26*78 1 20951*031 8*075

26*29 20549 133 8.332 26*79 20959*099 8*068

26.3Q - 20557 461 8.328

“ 26»8o 20967*163 8*064

26.31 20565 783 8.322 26.81 20975*221 8*058

26.32 20574 100 8.317 26*82 20983*273 8*052

26*33 2q582 412 8.312 ' 26*83 20^91*321 8*048

26*34 2o59o 718 8.306 26*84 20999*362 8*041

26.35 2Q599 C20 8.302 26*85 21007 * 398 8*036

26*36 2q6o7 316 8.296 26*86 21015*429 8*031

26*37 20615 6q8 8.292 26*87 21023*454 8*025

26*38 20623 894 8.286 26*88 21031*474 8*020

26.39 20632 175 8.281 26*89 21039*488 8.014

26.40 2o64o 451 8.276 26*90 21047*497 8*009

26.41 20648 721 8*270 26*9l 2 1 055 * 5C0 8*003

26*42 2 0 6 5 6> 987 8*266 26*92 21063*498 7*998

26*43 20665 247 8*260 26*93 21071*490 7*992

26*44 20673 502 8*255 26*94 21079*477 7*987

26*45 2o68

1

752 8*250 26*95 21087*458 7*981

26*46 2Q689 996 8*244 26*96 21095*434 7*976

26*47 20698 236 8*240 26*97 21103*404 7*970

26*48 20706 470 8.234 26*98 21111*368 7*964

26 * 49 2q7 1

4

699 8.229 26*99 21119*327 7*959

73
SOUNDING TABLE AT «160 DEGREES C, TANK N 6. 4

ELEV. (M) VOL. 
 DiFF. ELEV. (M) V8l* ( S 5 D I

f

; F , 28.00 21893.436 7.364 28*50 22253-633 7*047

28.01 21900.795 7.359 28*51 22260*673 7*040

28.02 21908.148 7.353 28.52 22267*707 7*034

28.03 21915*494 7*346 28*53 22274.724 7*027

28.04 21922.834 7.340 28*54 22281.754 7*020

28.05 21930.168 7.334 28*55 22288 *768 7 * 0 1

4

28.06 21937.495 7.3?7 28*56 22295 » 776 7*008

28.07 21944.817 7.322 28*57 22302*776 7*000

28.08 21952.132 7.315 28*58 22309-771 6*395

28.09 21959.440 7.308 28*59 22316*758 6*987

28.10 21966.743 7.303 28*60 22323-739 6*98

1

28.11 21974.039 7.296 28*61 22-330 * 7 1

4

6*975

28.12 21981.329 7*290 28*62 22337*682 6*968

28.13 21988*613 7.284 28*63 22344 * 643 6*961

28*14 21995.890 7.277 28*64 22351 * 598 6*955

28.15 22003*16? 7.272 28*65 22358 * 54 6 6-948

28.16 22010.426 7.264 28*66 22365*487 6-941

28.17 22017.685 7.259 28*67 22372*42

2

6-935

28.18 22024.937 7.252 28*68 22379*350 6*928

28.19 22032.183 7 * 2 4 6 28 ® 69 22386*27? 6*922

2 8 « 20 22039.422 7.239 28*70 22393^186 6-914

28.21 2204 6 * 656 7.234 28*71 22400 * 095 6*909

28.22 22053.882 7.226 28*7? 22406-396 6*901

28.23 22061 . 103 7.221 28*73 22413*891 6*895

28*24 22068 .317 7.214 28*74 22420*779 6; e <5 8 8

28.25 22075.525 7.208 28*75 22427*661 6*832

28.26 22082*726 7.201 28.76 22434*536 6.8 75

28.27 22089*921 7.195 28*77 22441*404 6*868

28.28 22097*110 7.189 28*78 22448*265 6*861

2 8 » 2 9 .•22104*292 7.182 28*79 22455* 120 6 » 855

28 . 3q • 22111*468 7*176 28»8o 22461*968 6*848

28.31 22118.638 7.170 28 * 8 i 22468*309 6*841

28.32 22125.801 7*163 28*82 22475*644 6*835

28.33 22132*957 7.156 28*83 22482*472 6*828

28*34 22140* 107 7*150 28*84 22489*293 6*821

28.35 22147.251 7*144 28*85 22496- 1 C 7 6*814

28*36 " 22154*389 7*138" 28*86 22502*915 6*808

28.37 22161*520 7.131 28*87 22509*716 6*801

28.38 22168.644 7*124 28*88 22516.510 6*794

28.39 "22175*762 7.118 28*89" 22523*297 6*787

28.40 22182.874 7*112 28«9o 22530*078 6*781

28.41 22189.979 7.105 28*91 22536*852 6*774

28.42 22 1 97 e 077 7.098 28*92 22543*618 6*766

28.43 22204.170 7.093 28*93 22550*379 6*761

28.44 22211.255 7.085 28*94 22557*132 6*753

28*45 22218.335 7.080 28*95 22563*879 6-74/

28.46 22225.407 7.072 28*96 22570*618 6*739

28.47 22232.473 7*066 23*97 22577*351 6*7 33

28.48 22239.533 ' 7.060 28*98 22584*077 6*72 6

28.49 22246*586 7.053 28*99 22590*797 6*720

74
SOUNDING TABLE AT -160 DEGRESS Ct TANK NO* A

ELEV. (M) VPL* (S) D I F E * ELEV* (N) V0L* ( S > D I FF •

3C « 00 23233*122 5*997 3o«5o 23523.282 5*615

3C.C1 23239*111 5.989 30*51 23528 » 890 5*608

30*02 23245*092 5.981 30*52 23534*489 5*599

3C • 03 23251*066 5*974 30*53 23540*081 5*592

30*04 23257*033 5.967 30*54 2 3 Fj 45*664 5*583

30*05 23262*99? 5*959 30*55 23551 » 2 4 0 5*576

30*06 23268*943 5.951 30*56 23556*809 5*569

30*07 23274*887 5*944 30*57 23562*369 5 * 560

30*08 23280*824 5*937 30*58 23567*921 5*55?

3C • 09 23286*753 5*929 30*59 23573*466 5*545

30*10 23292*674 5.921 3 0 • 6 o 23579*003 5*53 7

30*11 23298*588 5.914 30 * 6

1

23584*532 5*529

30*12 23304 *494 5*906 3Q « 6 2 23590*053 5*521

3C* 13 23310*393 5*899 30*63 23595*566 5*513

30*14 23316*284 5*891 3 0 * 6 4 23601 *07? 5 *506

30 * 1

5

23322*168 5.884 30*65 23606*569 5*4 97

30*16 23328*044 5 c 876 30*66 23612*059 5*4 90

30 *17 23333*913 5*869 30*67 23617 9 5 4

1

5*48?

30*18 23339*774 5*861 30*68 23623*015 5*474

30*19 23345*627 5*853 30*69 23628*481 5*466

30*20 23351*473 5.846 30*70 23633*939 5*458

30*21 23357*311 5*838 3C * 7 l 23639*389 5 * 450

30*22 23363*141 5.830 30*7? 23644*831 5*442

30*23 23368*964 5*823 30*73 23650*265 5*434

30*24 23374*780 5.816 30*74 23655*69? 5*427

30*25 23380*587 5.8C7 30*75 23661*110 5*418

30*26 23386*387 5 * 800 30*76 23666*521 5*411

~~ 3C • 27 23392*180 "5.793 30*77 23671*923 5*402

30*28 23397*964 5.784 30*78 23677.318 5*395

30*29 23403*742 5.778 30*79 23682*704 5*386

30*30 23409*511 "5.769 30*80 23688*083 5*379

30*31 23415*273 5*762 30*8l 23693*454 5*371

30*32 23421*027 5.754 30*82 23698*817 5*363

30*33 23426*773 5 * 746 '” '30*83 23704*171 5*354

3 0 * -3 4 23432*512 5.739 30*84 23709*518 5*347

30*35 23438*243 5*731 30*85 23714*857 5*339

30*36 23443*967 5*724" 30*86 23720*188 5*331

30*37 23449*682 5*715 30*87 23725*510 5*322

30*38 23455*390 5*708 30*88 23730 *825 5*315

30*39 23461*090 5. 7

C0"~ " 30*89 23736*132 5*307

30*40 23466*783 5.693 30*90 23741*430 5*298

30*41 23472*468 5*685 30*91 23746*721 5*291

30*42 23478* 145 5.677 30*92 23752*004 5*283

30*43 23483*814 5.669 30*93 23757*278 5*274

3C • 44 23489*476 5*662 30*94 23762*545 5*267

30*45 23495*130 5.654 30*95 23767*803 5* 258

30*46 23500*776 5*646 30*96 23773*053 5*250

30*47 23506*414 5*638 . .30*97 23778*296 5*243

3G • 4 8 23512*045 5.631 30*38 23783*530 5*234

30*49 23517*667 5*622 30*99 23788*756 5*226

75
SOUND 1NH TABLE AT - 16 o DEGREES C, TANK N0. u

ELEV. (M) VOL. (s> DlFF, ELEV. (M

)

V0L* <S> D I FT , 32.00 24273*879 4.379 32 * 5o 24481*571 3*936

32.01 24278.248 4.369 3 2 • 5

1

24485*498 3.927

32.02 24282.609 4,361 32*5? 24489.416 3.918

32*03 24286*961 4.352 32*53 24493*324 3*908

32-04 24291 * 30

5

4*344 32*54 24497*224 3.900

32*05 24295 .640 4*335 32*55 24 501 * 1 1

5

3*891

32*0 6 24299*966 4*326 32*56 2450 4*996 3*881

32*07 24304*283 4,317 32*57 24508.865 3.873

32.08 24308.591 4.308 32*58 24512*732 3*863

32*02 24312*891 4 .3Q0 32*59 24516-587 3*855

32*10 24317. 182 4*291 32*60 2452Q.432 3.845

32*11 24321*464 4.282 32*61 24524,268 3-836

32.12 24325.738 4*274 32*62 24528. C96 3-828

32*13 24330*003 4 ® 265 32 « 63 24531.914 3.818

3 2 « 1

4

24334.P58 4.255 32*64 24535-723 3-809

32*15 24338*506 4*245 32 * &5 24539,523 3*800

32*16 24342 * 744 4 *238 32*6 6 24543-314 2-791

32.17 2 4 34 o « 973 4*225 3? , 67 24547*096 3*782

32*18 24351.194 4,221 32*68 24550*868 3*772

32*19 24355 » 4Q6 4.212 32*69 24554.632 3.764

32. ?Q 24359.609 4 .203 32*70 24558 ,386 3-754

32.21 24363.803 4 • 194 32*7l 24562-132 3*746

32*22 24367.989 4,186 32*72 24565*868 3*736

32*23 24372* 165 4*176 32*73 24569*595 3.727

32.24 24376*333 4 * 168 32*74 24573,313 3.718

32.25 24380 « 492 4.159 32*75 24577*022 3.709

32*26 24384 « 642 4*150 32*76 24580*721 3.699

32.27 24388*783 4,141 32*77 24584.412 3.691

32.28 24392 « 916 4.133 32*78 24588.093 3-681

32.29 • ' 24397*039 4*123 32*79 24591.765 3.672

32 « 30 ' 24401 * 154 4,115 32*80 24595.428 3-663

32*31 24405*259 4.105 32*81 24599.082 3*654

32.32 244Q9.356 4*097 32*82 24602*726 3 ® 644

32.33 24413*444 4,088 32*83 24606.361 3*635

32.34 24417*523 4,079 32*84 24609.587 3.626

32.35 24421,593 4*070 32*85 24613.604 3-617

32*36 24425 « 654 4 ® 06

1

32 *86 24617.212 3.608

32 , 37 24429*707 4*053 32*87 24620*811 3*599

32*38 24433*750 4.043 32*88 24624*400 3*589

32*39 24437*784 4.034 32*89 24627*980 3 • 58q

32*40 2444 1.810 4.026 32*90 24631.551 3.571

32*41 24445*826 4*016 32*91 24635*112 3*561

32*42 24449*834 4 • 008 32*92 24638-664 3-552

32.43 24453*832 3.998 32*93 24642*207 3.543

32.^4 24457*822 3.990 32*94 24645.741 3.534

32.45 24461.803 3.981 32*95 2464 9* 265 3.524

32.46 24465.774 3*971 32*96 24652-781 3-516

32*47 24469.737 3.963 32*97 24656 286 3-505

32.4 8 24473*691 3.954 32*98 24659.783 3-497

32.49 24477.635 3.944 32*99 24663*270 3*487

76
«. —- S0UND IN

G

table AT -i6o DEGREES C, T Af^ ;K NO. 4

ELEV. (M) VOL. (S) D IFF • ELEV. (M) V0L* <S) DIPT.

34 00 24966 509 2 516 34 • 50 25079*539 2*012

34 01 24969 016 2 5C7 34*51 25081*541 2*002

34 02 24971 513 2 497 34*5? 25083*532 1*991

34 03 24973 999 2 486 34*53 25085*514 1*982

34 04 24976 476 2 477 34*54 25087*485 1*971

34 05 24978 943 2 467 34*55 25089 * 4 4 5 1*960

34 06 24981 400 2 457 34 *56 25091 *396 1*951

34 07 24983 846 2 446 34*57 25093*336 1 *940

34 CS 24986 283 2 437 34*58 25095*266 1*930

34 09 249SS 710 2 427 34*59 25097*185 1*919

34 10 24991 127 2 417 34*60 25099*095 1*910

34 11 24993 534 2 407 34*61 25100*993 1*898

34 12 24995 931 2 397 34*6? 25102*882 1*889

34 13 24998 318 2 387 34*63 25104*760 1*878

34 14 25000 695 2 377 34*64 25106*628 1*868

34 15 25003 062 2 367 34*65 25108*486 1*858

34 16 25005 418 2 356 34 *66 25110*333 1*847

34 17 25007 765 2 347 34*67 25112*170 1*837

34 18 25010 102

' 2 337' 34 * 68 25113*996 1*826

34 19 25012 429 2 327 34*69 25115*812 1 » 8

1

6

34 20 25014 745 2 316 34 *70 25117*618 1*806

34 21 25017 C52 2 307 34 * 7

1

25119*413 1*795

34 22 25019 349 2 297 34*72 25121*198 1*785

34 23 25021 635 2 286 34.73 25122*973 1 *775

34 24

' 25023 911 2 276 34*74 25124*737 1*764

34 25 25026 178 2 267 34*75 25126*491 1*754

34 26 25028 434 2 256 34*76 25128*234 1

* 743

34 27 2503c 680

" 2 246' * 34*77 25129*967 1*733

34 28 25032 916 2 236 34*78 25131*689 1*722

34 29 25035 142 2 226 34*79 25133.4Q1 1*712

" 34 30 25037 358 2 216 ' 34*80 25135*103 1*7 0 2

34 31 25039 563 2 205 34 ® 8

1

25136*794 1*691

34 32 25041 759 2 196 34*83 25138*475 l*68l

-'"34 33 25043 944 2 185' 34*83 25140*145 1*67q

34 34 25046 120 2 176 34*84 25141*805 1*660

34 35 25048 285 2 165 34*85 25143*454 1*649

34 36 H5q5o 440 2 155" 34 « 86 25145*093 1*639

34 37 25052 584 2 144 34*87 25146*721 1*628

34 38 25054 719 2 135 34*88 25148*338 1*617

34 39 25056 844 ?. 125 ~

34*89 " 25149*946 1 *6o8

34 40 25058 958 2 114 34»9o 25151*542 1*596

34 41 25061 062 2 104 34*91 25153*129 1*587

34 42 25063 156 2 094 34*92 25154*704 1*575

34 43 25065 239 2 083 34*93 25156*269 1 *565

34 4 4 25067 313 2 074 34*94 25157*824 1*555

34 45 25069 376 2 063 34*95 25159*368 1*544

34 46 25071 429 2 053 34*96 25160*901 1*533

34 47 25073 472 2 043 34*97 ...... 25162*424 1*523

34 48 25075 505 2 033 34*98 25163.937 1*513

34 49 25077 527 2 022 34*99 25165*438 1*501

_ . _ .. .. ... „ - ....

77
SOUND H.C3 TABLE. AT «160 DEGREES C» TANK NO* 4

ELEV. (M) VOL* (S> D jFF .

36.00 25261.639 .397

36. Ci 25262.023 .384

36.0? 25262.395 .372

3b.03 25262*755 .360

3 6 * C 4 25263. 103 .34 8

36. C 5 25263 • 439 *336

36 *06 25263.763 .324

36.07 25264 . 074 *311

36.08 25264 . 374 *300

36.09 25264.661 .287

36*10 25264.936 .275

3b « 1

1

25265 « 198 . 262

36.1? 25265.449 .251

36.13 25265*687 .238

36. 1

A

25265*914 *227

36.15 25266* 128 * 2 1

4

36.16 25266 * 329 «2C1

36.17 25266*519 *190

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El.EV.(M) VBU* (S) DiFF.

78
MBS-114A irev. •-?•)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 79-1751

II

4. TITLE AND SUBTITLE

Custody Transfer Systems for LNG Ships:

Techniques and Sounding Tables

Tank Survey

5. Publication Date May 1979

7. AUTHOR(S)

R. H. F. Jackson, R. S. Collier, S. Haber, P. V. Tryon

8 . Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, state, ZIP)

The Maritime Administration

Department of Commerce

Washington, DC

13. Type of Report & Period Covered

15. SUPPLEMENTARY NOTES

i Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-word or leae factual summary of moat significant information , If document includes a significant bibliography or

literature surrey, mention it here.) Static measurements of liquefied natural gas (LNG) for custody transfer purposes

require an accurate and precise knowledge of the container volume and the volumeheight relationship. The extremely low temperatures of LNG (less than 150° K)

preclude in situ surveys; however, the increasing value of the cargo requires

more precise and accurate measurements than previously used for bulk marine cargoes.

A description and assessment of the application of photogrammetric techniques to the

ambient temperature survey of a 35-meter diameter spherical aluminum container are presented. Sample sounding tables ( height-volume ) are calculated, and an estimate

of error is given.

17. KEY WORDS c<* to twelve entries; alphabetical order; capitalize only the liret letter of the first key word unless a proper name

separated by semicolons)

Accuracy; statistical analysis; cryogenic; error estimation; liquefied natural gas;

LNG; marine; mathematical modeling; measurement; photogrammetric; precision; ship

cargo; strapping; survey

18. AVAILABILITY \XJ Unlimited 19. SECURITY CLASS 21. NO. OF

(THIS REPORT) PRINTED PAGES

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20402, SO Stock No. SN003-003-

20. SECURITY CLASS

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22. Price

i

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