RU2624997C1 - Method of graduating cylindrical fuel tanks of liquid rockets by trigger levels of controlling sensors - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: method is proposed, consisting in determining the volume of the fuel tank under each i-th trigger level of the controlling sensor V_i, which is predetermined when testing each of the sensors in a vertically mounted chamber when filling and draining it with a liquid. Volumes are calculated by the ratio:

The values of V_ndn and

, as well as the average value of the inner diameter of the tank cylindrical part

are determined by the results of preliminary measurement of the volumes of the constituent elements of the fuel tank by the gas method, incl. the total internal volume of the finally collected fuel tank, internal volumes of the upper and lower bottoms, external volumes of the intra-tank systems. The value

is calculated by the ratio:

EFFECT: invention extends the technological capabilities of the measurement methodology, reduces the labour and time costs on performing control work, improves the quality and correctness of the control results.

2 dwg

Description

The invention relates to the field of engineering, and in particular to methods of graduating volumes by levels, i.e. determination of tank volumes corresponding to control fluid levels. The present invention should expand the technological capabilities of the measurement methodology, reduce labor and time spent on control work, improve the quality and accuracy of the control results.

It is known that the measurement of the total volumes of fuel tanks of liquid rockets and their graduation according to the level of response of level sensors is currently performed by filling the tanks with a process control liquid with a vertical center line. The main disadvantages of this technology is the need to operate large and expensive equipment, as well as the great complexity and duration of the measurement process itself. (see. "New high technology in technology", Encyclopedia, under the editorship of Kasaev KS, t. 1, p. 257, M .. MC "Aspect", 1994).

, где G_i - вес заполняющей среды на i-м уровне заполнения объема бака, ρ(t) - плотность заполняющей среды при температуре испытания t.At present, the leading rocket and space enterprises of Russia (GKNPTs named after MV Khrunichev, GNP RSC "TsSKB-Progress, PO Polet") have created and operate special stands for measuring the volume of fuel tanks of launch vehicles and graduating tanks for levels. The stands work by the method of filling the volumes of vertically installed tanks with a control process fluid, weighing the filling medium and estimating the filling volumes by the ratio

where G _i is the weight of the filling medium at the ith level of filling the tank volume, ρ (t) is the density of the filling medium at the test temperature t.

The following negative aspects of this technology should be noted:

- very long cycles of control and measuring operations: at least 10 ... 15 days of working time are spent for measuring one product;

- the need for significant energy costs - 500.0 ... 1000.0 kWh;

- the accuracy of measuring volumes by reference levels is not high enough, relative random errors reach ± 0.2%;

- distilled or demineralized water with the addition of a corrosion inhibitor (dichromic acid potassium according to GOST 4220-75 or dichromic acid sodium according to GOST 4237-76) is usually used as a control, process fluid, therefore, after the work is completed and the control fluid is drained, internal flushing is required the surfaces of the tank with distilled (desalted) water to remove the corrosion inhibitor and their subsequent drying to remove moisture residues to the degree of dryness of the volume: (dew point in the filling gas - should not be higher than -55 ° C);

- filling the volumes of the fuel tanks with water solutions of the inhibitor for products with high tightness requirements is not permissible due to the danger of possible clogging of micro-leaks and, as a consequence, not revealing them during subsequent tightness monitoring by gas methods;

- the disposal of the used control process fluid, a solution of a corrosion inhibitor in water, is also a big problem.

At present, methods are also known for measuring the internal volumes of capacities by measuring the external contours (see, for example, GOST 8.570-2000 “GSOEI. Steel vertical cylindrical tanks. Verification procedure.”), Including using control and measuring machines, as well as non-contact optical devices (laser theodolites - total stations, laser trackers, laser radars, etc.). The micron accuracy of modern laser radars provides minimal errors in measuring the external geometry of capacities, i.e. minus the shell thicknesses of the internal geometry of the containers, which determines the dimensions of their internal volume.

The use of optical instruments and especially laser radars (for example, a non-contact measuring system based on the MV 300 laser radar) for accurate measurement of the geometric dimensions of large-sized products allows us to estimate the internal volumes of fuel tanks by accurately measuring their outer surfaces, adjusting them to the thickness of the shells. Laser radar MV 300 allows you to determine the distance to almost any surface with a marginal error of 16 μm + 2.5 μm / m (μm / m - additional error depending on the distance of the device from the controlled surface, expressed in meters).

A precision analysis shows that due to the high accuracy of measuring distances using a laser radar, the use of this method allows smaller errors when measuring volumes of tanks with relatively smooth internal and external surfaces in comparison with the method of filling the volume with a control medium.

However, this method is difficult to implement and is not able to provide high accuracy in estimating volumes if the inner and outer surfaces are finned (for example, have a waffle configuration) or are shielded by protective shells.

In recent years, the so-called gas method regulated by OST 92-1039-82. To date, this method has been tested while measuring volumes in the range of 1.0 ... 150.0 m ³ with a relative error not exceeding ± 0.08 ... 0.1%.

The high accuracy of measuring internal volumes by the gas method determines its potential use in the technology of graduating fuel tanks of liquid rockets.

The main advantages in comparison with the traditional method involving the use of control fluid:

- significantly higher productivity of the measuring process (not less than 2 ... 3 times the performance of the measurement method by filling the fuel tanks with a control liquid);

- eliminates the negative impact of the control environment, there is no need for subsequent flushing and drying of the tank;

- incomparably low cost, dimensions and complexity of the necessary technological equipment;

- incomparably small energy costs for measuring operations.

The technical problem to be solved by the present invention is aimed at expanding the technological capabilities of the method for calibrating fuel tanks of liquid rockets, increasing the reliability and accuracy of measurements, reducing labor costs and time required for energy costs to perform test work.

The technical problem is solved in that the determination of the volume of the internal cavity of the fuel tank under each response level of the control sensor V _i , previously estimated when testing each of the sensors in a special vertically mounted process chamber when filling and draining its control liquid, is performed by the calculation method based on the results of preliminary measurements the gas method of the volumes of the main constituent elements of the tank, including its total free volume after final assembly, inside the actual volumes of the upper and lower bottoms of the tank, the external volumes of the internal tank systems (a set of sensors and level alarms, a set of an internal tank cable network, frames, funnel extinguishing devices, etc.), and the value of V _{i is} calculated by the ratio:

, м³, где

, m ³ , where

- среднее значение внутреннего диаметра цилиндрической части бака, м;

- the average value of the inner diameter of the cylindrical part of the tank, m;

h _n - height manageable level with respect to the plane of the lower end of the cylindrical part of the tank, m;

V _NDN - the internal volume of the lower bottom of the fuel tank, m ³ ;

- наружный объем j-го внутрибакового агрегата, расположенного ниже контролируемого уровня, м³;

- the external volume of the j-th internal tank unit located below the controlled level, m ³ ;

n is the total number of tank systems located below the controlled level, units;

рассчитывается:and value

calculated:

, м, где

, m, where

V _about - the free internal volume of the finally assembled fuel tank, measured by the gas method;

V _vdn , V _ndn - internal volumes of the upper and lower bottoms of the fuel tank, respectively, measured by the gas method after trimming the ends of the bottoms for welding with the cylindrical part of the fuel tank, m ³ ;

- наружный объем j-го внутрибакового элемента, измеренный газовым методом;

- the outer volume of the j-th inner tank element, measured by the gas method;

k is the total number of internal tank elements in the volume of the fuel tank.

Distinctive features of the proposed method are:

- application for evaluating the internal and external volumes of the constituent elements of the fuel tank structure of the gas measurement method; due to the sufficiently high accuracy of this method achieved so far (the relative error does not exceed the values ± (0.1 ... 0.2%); at the same time, it is possible to calculate the estimated values of the controlled volumes during graduation with an error of less than ± 0.2%);

- the use of an analytical calculation method for estimating the free volumes of a fuel tank under controlled sensors response levels;

- the ability to verify the correctness of the calculation and analytical estimates of the volume of the tank under the control levels if the sum of the results of the assessment of elementary volumes obtained by measuring its total free volume by the gas method coincides.

Comparison of the claimed technical solution with the prior art in the scientific and technical literature and patent sources shows that the set of essential features of the claimed solution was not known. Therefore, it meets the condition of patentability - “novelty”.

Analysis of the known technical solutions in the art shows that the proposed device has features that are not available in the known technical solutions, and their use in the claimed combination of features makes it possible to obtain a new technical effect, therefore, the proposed technical solution has an inventive step compared to the existing level technicians.

The proposed method can be used instead of the currently used at the enterprises of the rocket and space industry measurement method of filling the volume with a control liquid.

The invention is illustrated in the drawing, where in FIG. 1 is a schematic diagram of a graduated tank, and FIG. 2 - design of a technological chamber.

The following procedure for graduating a fuel tank by the response levels of control sensors without filling its volume with control liquid is regulated.

During the technological process of manufacturing a fuel tank, gas measurements are performed with a relative error within ± 0.1 ... 0.2% of the following structural elements:

- internal volumes of the upper V _vdn and lower V _vdn tank bottoms; measurement of the volumes of the bottoms to be performed after the operation of trimming the butt end to perform welding them with the cylindrical part of the tank;

(расходных и тоннельных трубопроводов, комплекта датчиков и сигнализаторов уровня, комплекта внутрибаковой кабельной системы, силовых шпангоутов, воронкогасительных устройств, внутрибаковых пневмо-гидросистем с арматурой и автоматикой и т.п.);- external volumes of internal tank systems

(consumable and tunnel pipelines, a set of sensors and level alarms, a set of inside tank cable system, power frames, funnel extinguishing devices, inside tank pneumatic and hydraulic systems with fittings and automation, etc.);

- the free internal volume of the finally assembled fuel tank V _about .

The average diameter of the cylindrical part of the tank is determined by the ratio:

, м, где

, m, where

V _about - the free internal volume of the finally assembled fuel tank, measured by the gas method, m ³ ;

V _vdn , V _ndn - internal volumes of the upper and lower bottoms of the fuel tank, respectively, measured by the gas method after trimming the ends of the bottoms for welding with the cylindrical part of the fuel tank, m ³ ;

- наружный объем j-го внутрибакового элемента, измеренный газовым методом, м³;

- the outer volume of the j-th inner tank element, measured by the gas method, m ³ ;

k is the total number of inside tank elements in the volume of the fuel tank, units;

L _C - the measured length of the cylindrical part of the tank, m

According to the test results of sensors that monitor the level of fuel components in the tank, in a special vertically mounted process chamber, when it is filled and the control fluid is drained, the trigger position of each sensor relative to the base level of their installation inside the tank body is set with an error of ± 1.0 mm (axial coordinate sensor response to the liquid level in the fuel tank).

.Then, the coordinates of the response levels of each sensor are calculated relative to the position of the plane of the lower end of the cylindrical part of the fuel tank -

.

For each response level of the control sensor, the value of the free volume of the fuel tank from the response level to the lower point of the tank is calculated by the ratio:

, м³, где

, m ³ , where

V _on - a free internal volume finally assembled fuel tank, measured by gas;

V _vdn , V _ndn - internal volumes of the upper and lower bottoms of the fuel tank, respectively, measured by the gas method after trimming the ends of the bottoms for welding with the cylindrical part of the fuel tank, m ³ ;

- наружный объем j-го внутрибакового элемента, измеренный газовым методом;

- the outer volume of the j-th inner tank element, measured by the gas method;

k is the total number of internal tank elements in the volume of the fuel tank.

When mastering the proposed method in production, the following advantages will be achieved in comparison with the currently used method for estimating the volume of filling with a control liquid:

- higher measurement accuracy: the relative random error in the estimation of volume values will not exceed ± 0.15%;

- significantly higher productivity of the measuring process (not less than 2 ... 3 times the performance of the measurement method by filling the fuel tanks with a control liquid);

- eliminates the negative impact of the control environment, there is no need for subsequent flushing and drying of the tank;

- incomparably low cost, dimensions and complexity of the necessary technological equipment;

- incomparably small energy costs for measuring operations.

The specific implementation of the proposed technique performed on the fuel tank layout with dimensions: inner diameter of the cylindrical part 2 - 1800 mm, its length - L _n = 3600 mm, the bottom 1 - hemispherical shape - convex, the inner radius of the hemisphere - R = 900 mm (see scheme. on fig 1). The thickness of the shells is 3 mm. Structural material - alloy AMg-6. In the inner cavity of the tank are located:

- SURT fuel level control system located in the volume of the cylindrical part of the tank, - 3;

- funnel extinguishing devices - 4;

- internal tank cable network - 5;

- 3 power frames 6 on the inner surface of the cylindrical part of the tank body.

Расстояния между положениями соседних датчиков - 500,0 мм. Конструктивное положение уровней срабатывания датчиков относительно расположения плоскости нижнего торца цилиндрической части (см. схему фиг. 1) соответственно:The fuel level control system (SURT) is located in the volume of the cylindrical part of the tank along its axis and includes seven level 7 sensors, evenly, at equal distances located along the axis of the tank, at distances h ₁ ... h ₇ from the lower end of the cylindrical part of the tank. The lower base end of the SURT is mounted inside the tank - at a distance Δ = 50 mm from the plane of the lower end of the cylindrical part of the tank. The total length of the CURT block

Distances between positions of adjacent sensors are 500.0 mm. The structural position of the sensor response levels relative to the location of the plane of the lower end of the cylindrical part (see the diagram of Fig. 1), respectively:

h ₁ = 350 mm;

h ₂ = 850 mm;

h ₃ = 1350 mm;

h ₄ = 1850 mm;

h ₅ = 2350 mm;

h ₆ = 2850 mm;

h ₇ = 3350 mm.

The gas measurements of the internal volumes of the upper and lower bottoms after trimming before welding with the cylindrical part of the body showed the following results:

- V _int = 1.525 m ³ ;

- V _NDN = 1.528 m ³ .

The gas measurement of the free internal volume of the fuel tank after final assembly showed:

- V _o = 12.22 m ³ .

The gas measurements of the external volumes of the internal tank systems showed the following results:

;- fuel consumption level control system

;

;- funnel extinguishing devices

;

;- inside cable network

;

.- 3 power frames on the inner surface of the cylindrical part of the tank body

.

Total external volume of internal tank systems

.

.

The actual coordinates of the response of the level sensors relative to the base level of the SURT-6 were estimated after testing the system in a special process chamber installed vertically, using HFC 122 as a control liquid, HFC 122 (see diagram in Fig. 2).

The design of the technological chamber includes: a housing 8, a cover 9, a level gauge 10, a control fluid supply valve 11, a control fluid drain 12, a vacuum pump 13 with a valve 14 and a vacuum sensor 15. The controlled system СУРТ 16 is placed in the technological chamber, the chamber is sealed, and atmospheric air is removed from the chamber volume by a vacuum pump 13 through a valve 15 to a residual pressure of less than 0.1 mm Hg. For the control operation, the chamber volume is filled with a previously degassed control fluid (Freon 141b was used as the control fluid). By smoothly lowering the level of the control fluid by draining through valve 12, the fluid level is determined at which the next sensor of the system is triggered, the response time is recorded by the device 17, the coordinate of the response of the sensor is determined relative to the base plane 18.

The error in measuring the position of the sensor response level is not more than ± (0.5 ... 1.0) mm.

The established experimental values of the coordinates of the response of the level sensors h ₁ ... h ₇ :

h ₁ = 351.5 mm;

h ₂ = 848.7 mm;

h ₃ = 1350.6 mm;

h ₄ = 1847.2 mm;

h ₅ = 2346.3 mm;

h ₆ = 2852.5 mm;

h ₇ = 3348.6 mm.

The values of the volume of the internal tank systems under the response levels of the control sensors are calculated:

;-

;

;-

;

;-

;

;-

;

;-

;

;-

;

.-

.

The average diameter of the cylindrical part of the tank is determined by the ratio:

, м,

, m

L _i = 3.602 m - measured length of the cylindrical part of the tank

рассчитываются объемы топливного бака под каждым уровнем срабатывания контрольных датчиков уровня СУРТ.By ratio

the fuel tank volumes are calculated under each response level of the control sensors of the level of the CURT.

;

;

;

;

;

;

;

;

;

;

;

;

.

.

Let us evaluate the achievable accuracy of the fuel tank calibration under the following initial conditions:

- the coordinates of the triggering of the sensors of the SURT block relative to the base of the block were previously set during testing in a special technological chamber with an error of not more than ± (0.5 ... 1.0) mm;

- the coordinates of the binding base of the SURT unit in the fuel tank body relative to the plane of the lower end of the cylindrical part of the tank are set with an error of not more than ± (0.5 ... 1.0) mm;

- the full free volume of the tank and the volumes of the bottoms (upper and lower to the plane of the junction with the cylindrical part) are determined with a relative error within 0.1 ... 0.2%;

- the established tolerance on the length of the cylindrical part of the tank does not exceed a value of ± 3 mm.

In the technological process of manufacturing the tank are measured by the gas method:

- volumes of the upper V _bottom and bottom V bottom _days ;

- the total volume of the fuel tank V _about .

Please note that:

- the measurement of the volumes of the upper V _in and bottom V _in bottoms by the gas method is performed after the trimming of the butt end to weld the bottoms with the cylindrical part of the tank body;

- the measurement of the total volume of the fuel tank V _about is performed after the final assembly of the tank and installation of all internal tank systems.

может быть вычислен, если известны ее объем V_ц и длина L_ц. Если измерены газовым методом значения V_о, V_вдн, V_ндн и

, а также оценены расчетным путем значения внешних объемов внутрибаковых систем под каждым уровнем срабатывания контрольных датчиков:The average diameter of the cylindrical part of the tank

can be calculated if its volume V _c and length L _{c are} known. If measured by the gas method, the values of V _o , V _vdn , V _ndn and

, and also estimated by calculation the values of the external volumes of the internal tank systems under each level of operation of the control sensors:

V _c = V _o -V _vdn -V _vdn + V _wbs

The absolute error in evaluating the value of V _C will be determined:

We make an estimate of ΔV _c.

Values ΔV _о , ΔV _int , ΔV _vat when measuring V _о , V _vd , V _{vdn by the} gas method with a relative error in the range of 0.1 ... 0.2%:

ΔV _about - absolute measurement error by the gas method of the total tank volume:

- with a relative measurement error of volumes ± 0.1%

ΔV _о = 0.001⋅V _о = 0.001⋅12.22 = ± 0.01222 m ³ ;

- with a relative measurement error of the volume of ± 0.2%

ΔV _о = 0.002⋅V _о = 0.002⋅12.33 = + 0.02444 m ³ .

ΔV _VDN - absolute error measurement gas by volume upper bottom:

- with a relative measurement error of volumes ± 0.1%

ΔV = 0,001⋅V _{VDN VDN} = 0,001⋅1,525 = ± 0,001525 m ^3;

- with a relative measurement error of the volume of ± 0.2%

ΔV _vdn = 0.002⋅V _vdn = 0.002⋅1.525 = ± 0.00305 m ³

ΔV _NDN - absolute measurement error of the lower bottom volume using the gas method

- with a relative measurement error of volumes ± 0.1%

ΔV _bpd = 0.001⋅V _bpd = 0.001⋅1.528 = ± 0.001528 m ³ ;

- with a relative measurement error of the volume of ± 0.2%

ΔV _bpd = 0.002⋅V _bpd = 0.002⋅1.5280 = ± 0.003056 m ³ .

ΔV _VSB - the absolute error of measuring the total volume of internal tank systems:

- with an average relative error of volume measurement ± 0.1%

ΔV _VBS = 0.001⋅V _VBS = 0.001⋅0.093 = ± 0.000093 m ³ ;

- with an average relative error of volume measurement ± 0.2%

ΔV _VBS = 0002⋅V _VBS = 0.002⋅0.093 = ± 0.000186 m ³ .

The absolute error of measuring V _c gas method:

- with an average relative error of volume measurement ± 0.1%:

;

;

- with an average relative error of volume measurement ± 0.2%:

.

.

следует также учесть дополнительную ошибку, связанную с неточностью измерения ее длины - ΔL_ц When assessing the measurement error of the average diameter of the cylindrical part of the tank

should also take into account the additional error associated with the inaccuracy of measuring its length - ΔL _c

With the accepted values ΔL = ± 3 mm = ± 0.003 m, d = 1809.7 mm = 1.8097 m, we obtain:

.

.

следует оценивать по значению полной погрешности

Thus, the error in estimating the mean diameter of the cylindrical part of the tank

should be estimated by the value of the total error

.

.

- with a relative measurement error of volumes ± 0.1%

- with a relative measurement error of the volume of ± 0.2%

.

.

оценивается по соотношению:Value

estimated by the ratio:

- with a relative measurement error of volumes ± 0.1%

;

;

- with a relative measurement error of volumes ± 0.1%

.

.

Let us now evaluate the values of the expected error in the calibration of the fuel tank when using volume values below the response plane of the level sensors of the SURT calculated by the results of measurements by the gas method.

The total estimated absolute error in estimating the volume under each plane of operation of each level is determined by:

; где Δh_г=±1,0 мм;- the inaccuracy of determining the axial coordinate of the level sensor when it is calibrated in the process chamber Δh _g ,

; where Δh _g = ± 1.0 mm;

- the error of the axial basic level of the SURT sensor in the volume of the fuel tank relative to the lower end of its cylindrical part Δh _y :

; где Δh_у=±1,0 мм;

; where Δh _y = ± 1.0 mm;

, где- an error in estimating the volume of the cylindrical part of the fuel tank under the plane of operation of the next sensor

where

- длина цилиндрической части бака под i-м уровнем срабатывания очередного датчика;

- the length of the cylindrical part of the tank under the i-th level of operation of the next sensor;

- the error in measuring the volume of the lower bottom by the gas method ΔV _NDN ;

- an error in estimating the external volume of internal tank elements located below the control i-th level of operation of the next sensor -

.

.

.The relative error in estimating the volume δV _i under each plane of operation of the sensors of the level of SURT is determined by:

.

The error value δV _{i is} determined for three positions of the liquid level in the tank volume:

- upper - L _q = 3348.6 mm; V _in = 10.0469 m ³ ;

- Medium - L _q = 1847.2 mm; V _cp = 6.22176 m ³ ;

- lower - L _c = 351.5 mm; V _n = 2.4146 m ³ .

The value ΔV _i L when _i = 3348.6 mm for the case of gas volume measurement with an accuracy of ± 0,1%:

.

.

The value ΔV _i L when _i = 3348.6 mm for the case of gas volume measurement with an accuracy of ± 0,2%:

.

.

The value ΔV _i L when _i = 1847.2 mm for the case of gas volume measurement with an accuracy of ± 0,1%.

.

.

The value ΔV _i L when _i = 1847.2 mm for the case of gas volume measurement with an accuracy of ± 0,2%:

.

.

The value ΔV _i at _n = L 351.5 mm for the case of gas volume measurement with an accuracy of ± 0,1%:

.

.

The value ΔV _i at _n = L 351.5 mm for the case of gas volume measurement with an accuracy of ± 0,2%:

.

.

The performed calculations show that calibration of fuel tanks with setting tank volumes under all controlled levels with a relative error not exceeding ± 0.2% is possible if the relative error of the gas method for measuring the volumes of constituent elements is not more than ± 0.15%. If greater accuracy of measurements by the gas method is achieved, the relative calibration error decreases to a value of ± 0.14 ... 0.15%.

Recent developments of this method of measuring volumes show the possibility of achieving accuracy at which the relative error does not exceed the value of 0.08 ... 0.1%.

The proposed method for calibrating the volumes of fuel tanks of liquid rockets during development in production will provide the necessary measurement accuracy: the relative measurement error is up to ± 0.15%. At the same time, the following advantages will be achieved in comparison with the currently used method of estimating the volume of filling with a control fluid: significantly higher productivity of the measuring process, lower cost, complexity and energy consumption of the necessary technological equipment, the negative impact of the control fluid is eliminated.

Claims (14)

A method for calibrating cylindrical fuel tanks of liquid rockets according to the response levels of control sensors, which consists in determining the volume of the fuel tank under each i-th response level of the control sensor V _i , which is predefined when testing each of the sensors in a special vertically mounted process chamber when filling and draining it control fluid, and calculating its value by the ratio:

where

- the average value of the inner diameter of the cylindrical part of the tank, m;

- the height of the controlled level relative to the plane of the lower end of the cylindrical part of the tank, m;

- internal volume of the bottom of the fuel tank, m ³ ;

- the external volume of the j-th internal tank unit located below the controlled level, m ³ ; n is the total number of tank systems located below the controlled level, units; moreover, the values

and

, as well as the average internal diameter of the cylindrical part of the tank

determined by the results of a preliminary measurement by gas method of the volumes of the constituent elements of the fuel tank, including the total internal volume of the finally assembled fuel tank, the internal volumes of the upper and lower bottoms, the external volumes of the internal tank systems, and the value

calculated by the ratio:

where V _o is the free internal volume of the finally assembled fuel tank, measured by the gas method, m ³ ;

,

- internal volumes of the upper and lower bottoms of the fuel tank, respectively, measured by the gas method after trimming the ends of the bottoms for welding with the cylindrical part of the fuel tank, m ³ ;

- the outer volume of the j-th inner tank element, measured by the gas method, m ³ ; k is the total number of inside tank elements in the volume of the fuel tank, units;

- the measured length of the cylindrical part of the tank, m

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