| SE382110B | 1976-01-12 |
| 1. | Method for calibrating cylindrical tanks for determining the volume thereof, c h a r a c t e r i z e d i n that a number of survey stations (A, B, C) are established outside the tank for fixing a base polygon by measuring the distance between said stations and the angles therebetween, that from a first survey station (A) there are measured directions, level by level, to a first tankwall profile (T) and to a second tankwall profile (T) , as well as the direction to a second survey station (B) for orientation in the base polygon (A, B, C), and that corresponding measurements are tanken from the other survey stations, for on the basis of the direction observations to determine the angle (TAT) between every pair of tankwall profiles at same level, so that for every level there can be calculated a mean radius (r_) which constitutes the basis for the calculation of volume. |
| 2. | Method as claimed in claim 1, c h a r a c t e r i z e d i n that the direction measurements are carried out in only one telescope position for each station, the zenith distance possibly being used as identification of the level. |
| 3. | Method as claimed in claim l or 2, c h a r a c t e ¬ r i z e d i n that the survey stations are established outside the tank and so far from the tank that visibility exists between the stations. |
| 4. | Method as claimed in claim 1 or 2, c h a r a c t e ¬ r i z e d i n that three survey stations (A' , B' , C') are established outside the tank, but so close to the tank that visibility does not exist between said stations (Fig. 6) . |
| 5. | Method as claimed in claim 4, c h a r a c t e r i z e d i n that the three survey stations (A', B', C) are arranged at a distance from the tank wall corresponding to approx. 1/13 1/8 of the tank diameter. OM . |
| 6. | Method as claimed in claim 4 or 5, c h a r a c t e ¬ r i z e d i n that the positions of the survey stations (A1, B* , C) are referred to respective outer stations (A, B, C) , which are mutually observable. |
| 7. | Method as. claimed in claim 1, c h a r a c t e r i z e d i n that at the inside of the tank there are established four survey stations (Al, Bl, Cl, Dl) which constitute the corners of an approximate square, that in the areas of the survey stations (W, N, E, S) and in the areas therebetween (NW, NE, SE, SW) there are distributed measuring points in a plurality of evently distributed columns, that from the .stations there are observed measuring point data related to a local coordinate system, and .that a mean centre is determined on the basis of individual radii calculated on the basis of the observations. |
| 8. | Method as claimed in claim 7, c h a r a c t e r i z e d i n that the measuring points are marked by means of a light spot. |
The present invention relates to a method for calibrating cylindrical tanks for determining the volume thereof.
There are previously known methods for measuring cylin¬ drical tanks for determining volume tables, and one of these known methods will be discussed in the following.
In the known method the circumference of the tank is divided into several parts which are measured by tape (strapped), which is stretched between the points of measurements, the readings being performed simultaneously by two persons. These two persons must perform the readings in baskets which are hoisted up and down along the tank.
The measurements are made above and below each horizontal joint line, i.e. on large tanks with 10 rings there will be made 20 circle measurements. After correction for plate thickness temperature and tape scale error etc. the volume tables are calculated by integration of horizontal areas.
The above-mentioned method suffers from the following drawbacks:
- 6-7 persons are necessary to perform the work,
- the work conditions can be dangerous, especially in strong winds, in rainy weather or when there is ice formation on the tank,
- communication is difficult due to positions and distances between the persons involved,
- during measurements the tape position will be dependent on eye sight estimate (from the ground) ,
- observation data give little room for verification and satisfactory documentation.
An object of the present invention is to give instructions for a method for calibrating cylindrical tanks in which the measurements can be performed by only two persons and in less time than by the above-described known method. AnotherObject of the present invention is to give instructions for a method for calibrating cylindrical tanks which can be performed without any danger for the persons involved and under more comfortable
O P
working conditions. Yet another object of the invention is to provide a method for calibrating cylindrical tanks which can be used for external measurement as well as internal measurement of tanks.
These objects are achieved according to the present invention by means of the features stated in the claims.
Further objects and advantages of the present invention will appear from the following description taken in connection with the drawing, which depicts the theoretical background of the invention as well as various embodiments thereof.
Fig. 1 depicts diagrammatically a closed curve referred to different coordinate systems.
Fig. 2 and 3 illustrate diagrammatically how the closed curves can be related to circumscribed triangles.
Fig. 4 illustrates diagrammatically a first -embodiment of the method according to the invention.
Fig. 5 illustrates results of the measurements carried out in accordance with the present invention.
Fig. 6 illustrates diagrammatically a second embodiment of the method according to the invention.
Fig. 7 illustrates diagrammatically a third embodiment of the method according to the invention, in which the measurements are performed within the tank.
With reference to Fig. 1 there will in the following be discussed the theoretic basis of the present invention.
A closed curve can be described mathematically by the Fourier series: r ■ = r Q + a. λ sin(V* - f ± ) + a 2 sin2(V- f 2 ) + a 3 sin 3(Y*- f 3 ) + a sin n(y- f ) n n
In descriptions of physical conditions the amplitudes a, .... will usually decrease as order increases, and in practice it will suffice with limitation to a given order.
From a geometric point of view the curve is generated by varying the angle when r = the sum of a constant r_ and sinus formed components with periods of 1, 1/2, 1/3 revolution etc., with phase angles f and amplitudes a.
OMPI
In connection with tanks the amplitudes of the components will be small in realtion to r Q . The area which is limited by the closed curve, is therefore very nearly equal to the area of the circle with radius r n in as much that the integral of each component for a complete revolution is equal to 0.
If three points are evenly distributed on the curve, 120 apart, then the mean value of the distances from these three points to an approximate center will remain almost con¬ stant even when the approximate center is moved a bit. This is so because: - s±n f + sin(^+ 120°) + sin( + 240°) = 0 for all lvalues (first order component) .
With three evenly distributed points this involves in other words that the mean is compensated for translation.
With an elliptic form the second order component will dominate. In the same way the mean will be compensated for the elliptic form because: sin f+ sin( V+ 240°) + si.n ( f + 480°) = 0 for all values (second order component) .
The main error source in the mean will be the third order component. This is so because the amplitude usually decreases when the order increases, and also because the next following orders will be partly compensated for.
The error will as a maximum be equal to the third order component amplitude, but also depend on the random positioning of the three points in relation to the phase angle. In this connection reference should be made to Figs. 2 and 3 which disclose extreme cases..
In a similar manner as discussed in connection with the use of three points which are evenly distributed on the curve, it can in connection with the use of six evenly distributed points be shown that the mean is compensated for the fifth and lower order components and that the sixth order component will be the main source of error.
In practical execution of the method it is not necessary to demand absolute even distribution of the points. Even with
irregular positioning of the points most of the compen¬ sating effect will be retained.
In the embodiments of the method, which will be described in the following, six tangent points are measured on the tank curve. However, in the first embodiment, which will be discussed as the basic version, the points will be placed in pairs and in each pair the points will be so close that analytically they will be of the same value as three single points.
Reference being had to Fig. 4, a first embodiment of the method according to the invention,in the following designated as the basic version, will be further discussed.
In Fig. 4, 1 designates the cylindrical tank which is to be calibrated or measured. Outside the tank there are established three survery stations A, B and C, respectively, the survey stations being located so far from the tank wall that visibility exists therebetween.
The angles of the triangle A-B-C are measured with a theodolite in four complete sets. The lengths of the sides of the triangle are mutually observed with an electronic range instrument.
From each observation station directions are measured to a second station and to the left tank wall profile,level by level, whereafter the right tank wall profile is measured in the same way.
The essential purpose of this measurement is to determine the angle between the left and the right profile of the tank 1 as this is observed from the respective survey stations. The profile angle, i.e. the angle T1A-A-T2A for station A, will not be effected by collimation nor error in the horizontal axis of the theodolite, because the zenith distance will be equal at the same level for both profiles. If required, the zenith distance can be used as identification of the level.
The further calibration takes place with an outspring in the triangle, the number of measurements making the triangle overdetermined. However, the measurements can be adjusted in
a simple manner and will give an indication of the accuracy. The angle sum error is distributed evenly onto the angles giving the form of the triangle. The measured lengths of the triangle sides are divided by the sinus of the opposite adjusted angle. The three values are then averaged, whereupon the final.side lengths are found by sinus proportions. In Fig. 5 there are shown results of a specific measurement series, the main values thereof appearing from the below table.
STATION OBSERVED ADJUSTED SINUS ADJUSTED PROP. SIDE
A 102?1798 102?1791 93,643 m 93,586 m
B 61,4883 61,4876 93,640 m 77,022 m
C 36,3340 36,3333 93,638 m 50,588 m
Sum 200?0021 200?0000 Mean 93,640 m
MEAN
A - CENTRE 32,394 32,414 m 32,404 m
B - CENTRE 40,643 m 40,604 m 40,623 m
C - CENTRE 55,557 ' 55,514 m 55,535 m
If all observations from one station to the tank are averaged, the direction to a mean centre will appear therefrom The three directional lines will not intersect accurately in one point, because of tank wall irregularities and random observation errors. The discrepancies can be adjusted in a simple manner as illustrated in Fig. 5, in which the measured angles-only are indicated by arcs.
The adjusted distance from one station to the mean centr multiplied by sinus of half of the profile angle, gives the radius r. The mean of the radii, determined from the three stations, is the radius r Q , which is the basis of the further calculation of volume values.
The determination of the mean centre is not critical because the mean radius r Q is well compensated for translation. The adjusted distance between the mean centre and the stations must, however, be geometrically synonymous.
Below there is given a table for the tank circumference values which have been calculated.
Tank 503 OUTER CIRCUMFERENCES
TAPE
St. A St. B St. C MEAN MEASURED
1 57,567 57,514 57,526 57,536 m
2 57,557 57,500 57,507 57,521 m 57,534 m
3 57,553 57,500 57,512 57,522 m 57,534 m
4 57,583 57,477 57,490 57,517 m
5 57,577 57,469 57,500 57,515 m
6 57,566 57,459 57,509 57,511 m
7 56,568 57,453 57,517 56,513
8 57,592 57,383 57,504 57,493 m
9 57,574 57,371 57,479 57,475 m
10 57,615 57,390 57,482 57,496 m
11 57,597 57,400 57,500 57,499 m
12 57,550 57,382 57,471 57,468 m 57,474 m
Because the volume calculations are adapted to tape measurements, the values of the above table express the circum¬ ferences of the tank rather than the radii.
In Fig. 6 there is diagrammatically illustrated the principle of a second embodiment of the method according to the invention. If the survey stations are established as close to the tank as possible, and visibility exists therebetween, then the six above-mentioned tangent points discussed above, will coincide in pairs and consitute three points. If the triangle is made very large, i.e. if survey stations are established at a great distance from the tank, the six tangent points will be distributed more evenly on the circum¬ ference of the tank. However, the measurement accuracy will decrease with increasing distance from the tank, and the observations may be more difficult to perform because of space problems on the measuring site.
By modifying the above discussed basic version it is possible to achieve six evenly distributed tangent points. This involves compensation of the Fourier series components of fifth and lower orders, a fact which reduces errors due to irregularities in the tank body.
In the embodiment illustrated in Fig. 6 the wall profile observations are performed from the inner stations A 1 , B* and C, which are determined from the outer stations A, B and C. The directions A A', B B' and C C* are observed in four complete sets included in the measurement of the main triangle. The sets also include observations between the survey stations and the tank wall profiles at different levels for easy determination of the mean centre of the tank. The distances A A 1 , B B 1 and C C are mutually observed with an electronic range instrument. Even distribution of the tangent points is achieved when the inner stations A', B' and C are established at a distance of approximately 1/13 of the tank diameter from the tank wall. The aiming towards the tank wall profiles will then become very steep and the theodolite must be equipped with a zenith ocular.- This method retains most of the compensatory effect even when the inner stations A', B' and C must be established further.away, for example at distances corre¬ sponding to 1/8 of the tank diameter, from the tank.
•It is emphasized that the accuracy of this method is essentially dependent upon the standard of the regularity achieved during the construction of the tank. If there is used a theodolite of the type "Wild T2" and a tellurometer "MA 100" for the measurements, then the random observation errors will play an insignificant role.
The above discussed embodiments of the present invention result in .a simplified and very accurate measuring method of cylindrical tanks, the method according to the invention resulting in a standard deviation for linear dimensions of approx. 0,3 /oo in connection with the discussed basic version. ' Further, the amplitude of the components show a significant decrease as order increases.
OM
To give an estimate of the accuracy of the advanced verstion of the method described in connection with Fig. 6, compared with the basic version according to Fig. 5, it is necessary to perform two totally independent measurements on a number of tanks. The results presently in hand indicate an achieved accuracy of 0,1 to 0,2 /oo when using the embodiment according to Fig. 6.
In connection with Fig. 7 there is described a third embodiment of the method according to the invention, the measurements here being performed inside the tank in question.
Within the tank 1' there were established four survey stations Al, Bl, Cl and Dl, forming an approximate square. The survey stations were arranged approx. 1 from the wall. Further, on the tank wall there were arranged measuring points in eight columns which were evenly distributed on the tank wall, each point being determined by simultaneous theodolite observations from two stations. One of the theodolites was equipped with a laser. The laser beam projected a spot on the wall, said spot being observed from the other theodolite. The points in each column were measured from two stations in such a way that the directions gave a good intersection and that a too acute angle to the wall was avoided. In all, 128 points were determined on the wall. The measurements were performed in 6 hours by two surveyors and two assistants. On the basis of the measurements a mean centre was determined, and the individual radii calculated from co-ordinates. The mean radii were then corrected for temperature and liquid pressure before the further calculations of the tank volume sections were performed.
The standard deviation of linear dimensions was estimated to + 0,15 °/oo.