Method for thermally gauging the tank of a spacecraft and a spacecraft equipped with means for implementing such a method

Abstract

Disclosed is a method for gauging the liquid propellant tank of a spacecraft during a phase of high-thrust along an axis, the tank being thermally conductive and having a known geometry. The method includes steps of: attaching, on a wall of the tank, a heating member and at least one temperature sensor in proximity to the heating member and in a plane of interest perpendicular to the thrust axis; during the high-thrust phase, heating the wall of the tank and acquiring temperature measurements of the wall of the tank at rapid frequency; determining the instant I when the temperature measured by the sensor changes, such change indicating the presence of the liquid-gas interface in the tank in the plane of interest; and determining the volume of liquid propellant present in the tank at instant I.

Claims

1. A method for gauging the liquid propellant tank of a spacecraft, said propellant tank comprising a thermally-conductive wall, having a known geometry and containing a volume of liquid propellant, and said spacecraft being equipped with means of propulsion capable of exerting, according to a given thrust axis, a high thrust allowing said spacecraft to achieve an acceleration of greater than or equal to 0.05 m/s.sup.2, said method comprising steps of: during a phase of high-thrust along said thrust axis exerted by said means of propulsion supplied with liquid propellant from said propellant tank, remotely controlling said spacecraft in which are attached, on an outer surface of said wall of the tank, a heating member and at least two temperature sensors, each of which is in a known position in proximity to said heating member and arranged on the outer surface of the wall of the propellant tank in a position for measuring the temperature of said wall, in a plane perpendicular to said thrust axis, referred to as plane of interest, in which the liquid-gas interface in said tank is likely to be located at some time during a phase of high-thrust exerted by said means of propulsion along said thrust axis, said temperature sensors being aligned along a so-called measurement axis, the heating member having a height, measured along said measurement axis, that is greater than the height occupied by said temperature sensors along said measurement axis, and a height of the heating member protruding beyond an end temperature sensor being greater than a distance between adjacent temperature sensors arranged along said measurement axis, further comprising the steps of: heating the wall of the tank using the heating member; and acquiring measurements of a temperature of the wall of the tank using a first of said temperature sensors, at an acquisition rate of one measurement every 30 seconds or less; determining a moment I at which the temperature measured by said temperature sensor changes, which corresponds to a moment at which a break of slope occurs on a digital curve representing the temperature recorded by said temperature sensor as a function of time, such a change indicating a presence, in the plane of interest associated with said first temperature sensor, of the liquid-gas interface in the tank; and determining, from a geometrical data of the tank and the known position of the first temperature sensor on the wall of the tank, the volume of liquid propellant present in said tank at the moment I.

2. The method according to claim 1, wherein determining the moment I at which the temperature measured by said temperature sensor changes is carried out by detecting the moment at which a break of slope occurs on a digital curve representing the temperature recorded by said temperature sensor as a function of time.

3. The method according to claim 1, wherein, in said spacecraft, a plurality of temperature sensors are attached on the outer surface of the wall of the tank, each of said plurality of temperature sensors being arranged on the outer surface of the wall of the propellant tank in a position for measuring the temperature of said wall, in proximity to the heating member and in a plane perpendicular to said thrust axis, referred to as the plane of interest associated with each respective temperature sensor of said plurality of temperature sensors, in which the liquid-gas interface in said tank is likely to be located at some time during a phase of high-thrust exerted by said means of propulsion along said thrust axis, said method comprising, for at least one of said plurality of temperature sensors, steps of: determining the moment I at which the temperature measured by said at least one of said plurality of temperature sensors changes, which corresponds to the moment at which a break of slope occurs on a digital curve representing the temperature recorded by said at least one of said plurality of temperature sensors as a function of time, said change indicating the presence of the liquid-gas interface in the plane of interest associated with said at least one of said plurality of temperature sensors; and determining, from the geometrical data of the tank and the known position of the at least one of said plurality of temperature sensors on the wall of the tank, the volume of liquid propellant present in said tank at the moment I.

4. The method according to claim 3, wherein, in said spacecraft, said plurality of temperature sensors are aligned along a so-called measurement axis, parallel to said thrust axis.

5. The method according to claim 1, wherein, in said spacecraft, said temperature sensors are situated at an equal distance from said heating member.

6. The method according to claim 5, wherein, in said spacecraft, said temperature sensors are aligned along a so-called measurement axis, and the heating member has a height, measured along said measurement axis, that is greater than the height occupied by said temperature sensors along said measurement axis.

7. The method according to claim 6, wherein, in said spacecraft, a distance between adjacent temperature sensors arranged along said measurement axis is equal to a distance between two additional adjacent temperature sensors, and a height of the heating member protruding beyond an end temperature sensor is greater than said distance.

8. The method according to claim 5, wherein, in said spacecraft, the distance between two adjacent temperature sensors along said measurement axis, measured according to an axis parallel to the thrust axis, is between 10 and 50 mm.

9. The method according to claim 5, wherein determining the moment I at which the temperature measured by a first of said temperature sensors changes is carried out by: for said first temperature sensor and for a temperature sensor arranged upstream of said first temperature sensor in the direction of the thrust exerted by the means of propulsion along the thrust axis, remotely controlling said spacecraft in order to carry out simultaneous acquisitions of measurements of the temperature of the wall of the tank, at an acquisition rate of one measurement every 30 seconds or less, for each pair of simultaneous acquisitions, determining the difference between the temperature measured by said upstream temperature sensor and the temperature measured by said first temperature sensor, and determining the moment at which said difference is the highest.

10. The method according to claim 1, further comprising a second heating member, wherein, in said spacecraft, the two heating members are attached on the outer surface of the wall of the tank, on opposing side of said temperature sensor and at an equal distance from said temperature sensor.

11. The method according to claim 1, wherein said spacecraft is remotely controlled by a control device, whereby control signals are successively determined and sent to said spacecraft by the control device in order to carry out the steps of heating the wall of the tank using the heating member and of acquiring measurements of the temperature of the wall of the tank using said temperature sensor.

12. A computer program product, comprising a set of program code instructions which, when executed by a processor, implement the steps of a method for gauging the liquid propellant tank of a spacecraft according to claim 1.

13. The method of claim 1, wherein a proximity location of the at least one temperature sensor is at a location close enough to the heating member wherein the at least one temperature sensor can measure a rise in the temperature of the wall of the tank caused by the heating of the wall by the heating member.

14. A spacecraft comprising: a propellant tank comprising a thermally-conductive wall and having a known geometry, containing a volume of liquid propellant, means of propulsion capable of exerting, according to a given thrust axis, a high thrust allowing said spacecraft to achieve an acceleration of greater than or equal to 0.05 m/s.sup.2, and supplied with liquid propellant from said propellant tank, and a heating member attached on an outer surface of said wall of the tank, wherein the spacecraft comprises at least two temperature sensors attached on said outer surface in proximity to said heating member, said temperature sensors being aligned along a so-called measurement axis parallel to said thrust axis, and each being arranged on the outer surface of the wall of the propellant tank in a position for measuring the temperature of said wall, in a plane perpendicular to said thrust axis, referred to as the plane of interest associated with said temperature sensor, in which the liquid-gas interface in said tank is likely to be located at some time during a phase of high-thrust exerted by said means of propulsion along said thrust axis, and wherein the heating member has a height, measured along said measurement axis, that is greater than the height occupied by said temperature sensors along said measurement axis, and a height of the heating member protruding beyond an end temperature sensor is greater than a distance between adjacent temperature sensors arranged along said measurement axis.

15. The spacecraft according to claim 14, wherein said temperature sensors are situated at an equal distance from said heating member.

16. The spacecraft according to claim 14, wherein the heating member has a height, measured along an axis parallel to said thrust axis, that is greater than the height occupied by said temperature sensors along said measurement axis.

17. The spacecraft according to claim 14, further comprising a second heating member, wherein the two heating members are attached to the outer surface of the wall of the tank, on opposing side of said temperature sensors and at an equal distance from said temperature sensors.

18. The spacecraft according to claim 14, comprising telemetry means suitable for transmitting the temperature values recorded by said temperature sensors to a remote receiver.

19. A system comprising: the spacecraft according to claim 14, and computing means for determining, from the temperature values recorded by at least one of said temperature sensors, a moment I at which the liquid-gas interface in the tank is located in the plane of interest associated with said temperature sensor, and the volume of liquid propellant present in the tank.

20. The system according to claim 19, wherein: the spacecraft comprises telemetry means suitable for transmitting the temperature values recorded by said temperature sensors to a remote receiver, and the system comprises the remote receiver capable of receiving the temperature values transmitted by said telemetry means of the spacecraft, and of transferring them to said computing means.

21. The spacecraft of claim 14, wherein a proximity location of the at least two temperature sensors is at a location close enough to the heating member wherein the at least two temperature sensors can measure a rise in the temperature of the wall of the tank caused by the heating of the wall by the heating member.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The features and advantages of the invention will be better understood upon reading the description of the example embodiments provided hereafter for illustrative purposes only and in no way limiting the scope of the invention, with reference to FIGS. 1 to 7, wherein:

(2) FIG. 1 shows a diagrammatic view of the propellant tank of a spacecraft equipped with a heating member and a set of temperature sensors for implementing a gauging method according to the invention;

(3) FIG. 2 shows a set of heating members and temperature sensors, equipping the propellant tank of a spacecraft for implementing a gauging method according to the invention;

(4) FIG. 3 shows a graph illustrating the change, as a function of time, in the temperature recorded by a temperature sensor of FIG. 2, during the implementation of a gauging method according to the invention;

(5) FIG. 4 shows a graph illustrating the change, as a function of time, in the temperatures recorded by all of the temperature sensors of FIG. 2, during the implementation of a gauging method according to the invention during an apogee motor firing;

(6) FIG. 5 shows a graph illustrating the change, as a function of time, in the temperatures recorded by two adjacent temperature sensors in FIG. 2, as well as the difference between the temperatures recorded by these two sensors, during the implementation of a gauging method according to the invention;

(7) FIG. 6 shows an expanded view of the area A in FIG. 1, showing the meniscus shape of the liquid surface in the tank;

(8) and FIG. 7 shows a graph illustrating the change, as a function of time, in the temperature recorded by a temperature sensor of FIG. 2, and also of the derivative of the temperature measured with respect to time (moving average of 5 values), during the implementation of a gauging method according to the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

(9) It should be noted straight away that the drawings are not to scale, and that some elements and some distances have been purposefully enlarged in order to facilitate the understanding of the invention.

(10) The method for gauging the propellant tank of a spacecraft, such as a satellite, this tank containing a volume of liquid propellant, is intended to be implemented for a spacecraft equipped with means of propulsion capable of exerting a high thrust along a given thrust axis 12, i.e. so as to apply an acceleration of greater than or equal to 0.05 m/s.sup.2 to the spacecraft. Typically, such a thrust is implemented during apogee motor firings with the purpose of bringing the telecommunications satellite from the orbit into which it was injected by the launch vehicle into the mission geostationary orbit thereof.

(11) The means of propulsion of the spacecraft can be of a type conventional in itself, operating by consumption of liquid fuel.

(12) One example of a tank 10 of a spacecraft to which the present invention applies is shown in FIG. 1. This tank is externally delimited by a wall 11 made of a thermally-conductive material, for example titanium or aluminium, preferably having a thermal conductivity of greater than or equal to 5 W.Math.m.sup.−1.Math.K.sup.−1. For example, the wall 11 can have a thickness of 1 mm, with a thermal conductivity of 5 W.Math.m.sup.−1.Math.K.sup.−1.

(13) The tank 10 has a known geometry, this geometry of course not being limited to the specific shape shown in FIG. 1.

(14) FIG. 1 shows the thrust axis 12. The high thrust exerted by the means of propulsion of the spacecraft is exerted along this axis 12, in the direction given the reference numeral 13 in this figure.

(15) The tank 10 contains a volume of liquid propellant 14 and a volume of gas 15.

(16) During a phase of high-thrust exerted by the means of propulsion of the satellite along the thrust axis 12, and in the direction 13, consuming liquid propellant, the volume of liquid propellant 14 is pressed against the bottom 17 of the tank. The liquid-gas interface 16 in the tank 10 is planar and substantially perpendicular to the thrust axis 12, in this case perpendicular to the plane of FIG. 1, and it moves substantially perpendicularly to the thrust axis 12, and in the direction 13, towards the bottom 17 of the tank. During this displacement, the liquid-gas interface 16 is thus successively located in a plurality of planes perpendicular to the thrust axis 12.

(17) The method according to the invention implements at least one heating member 18, which is attached on the outer surface of the wall 11 of the tank, such that it is capable of heating said wall 11. Said heating member 18 can be of any type conventional in itself, in particular of the electrical resistor type. It preferentially has a power output that lies in the range 1 to 10 W.

(18) The heating member 18 is preferably attached to the wall 11 of the tank 10 such that it extends over a certain height thereof, this height being measured parallel to the thrust axis 12, and such that it covers a plurality of the planes in which the liquid-gas interface 16 in the tank 10 is likely to be located at some point during an operating phase of the spacecraft, during which the means of propulsion exert a high thrust, for example during an apogee motor firing.

(19) The heating member 18 is associated with at least one temperature sensor 191, for example a thermistor, which is itself also attached to the outer surface of the wall 11 of the tank 10, in the vicinity of the heating member 18. In the embodiment shown in FIG. 1, a plurality of such temperature sensors, more specifically four temperature sensors 191, 192, 193, 194 (such a number in no way limiting the scope of the invention), are thus associated with the heating member 18. These temperature sensors 191, 192, 193, 194 are aligned along a so-called measurement axis 20. This measurement axis is preferably substantially parallel to the thrust axis 12.

(20) Each temperature sensor 191, 192, 193, 194 is arranged close enough to the heating member to be capable of measuring a rise in the temperature of the wall 11 of the tank 10 caused by the heating of said wall 11 by the heating member 18. Each temperature sensor is furthermore arranged in a plane perpendicular to the thrust axis 12, referred to as the plane of interest associated with the temperature sensor, in which the liquid-gas interface 16 in the tank 10 is likely to be situated momentarily during the phase of high-thrust, as the volume of liquid propellant 14 contained in the tank 10 lowers.

(21) The known geometric data of the tank 10 can thus be used to associate, by easy calculation, each temperature sensor 191, 192, 193, 194 with a volume of liquid corresponding to the volume of liquid propellant 14 remaining in the tank 10 when the free liquid surface, i.e. the liquid-gas interface 1, is located in the plane of interest associated with the temperature sensor.

(22) This volume can be easily converted into the mass of liquid propellant remaining in the tank 10, using the known density of the liquid propellant used.

(23) FIG. 2 shows a front view of one example arrangement of the different elements attached to the wall 11 of the tank 10 for implementing a gauging method according to the invention. Thus, in this figure, the wall 11 of the tank 10 extends in the plane of the figure.

(24) In this example embodiment, two heating members 18 are implemented, which heating members can be identical or different from one another, and preferably extend substantially parallel to one another, preferentially along an axis that is substantially parallel to the thrust axis 12.

(25) Four temperature sensors successively called C1, C2, C3 and C4, respectively having the reference numerals 191, 192, 193, 194 in the order beginning with the temperature sensor located the furthest from the bottom 17 of the tank 10, to the temperature sensor located the closest to said bottom 17, are arranged between the two heating members 18. These temperature sensors can be identical or different from one another.

(26) The temperature sensors 191, 192, 193, 194 are all situated at an equal distance from each heating member 18. This distance, denoted as d, is for example equal to 5 mm.

(27) The temperature sensors 191, 192, 193, 194 are aligned along a so-called measurement axis 20, which does not lie in a plane parallel to the plane of the liquid-gas interface in the tank 10 during a phase of high-thrust exerted by the means of propulsion of the spacecraft along the thrust axis 12. Preferably, the measurement axis 20 is substantially parallel to the thrust axis 12. In the specific view shown in FIG. 2, the thrust axis 12 and the measurement axis 20 are superimposed on one another.

(28) The distance between two temperature sensors 191, 192, 193, 194 adjacent along the measurement axis 20 measured along the thrust axis 12, denoted as e, is preferentially even, and is preferably of between 10 and 50 mm. It is, for example, equal to 25 mm.

(29) The height of each heating member 18, measured along the measurement axis 20, projecting beyond each of the end temperature sensors 191, 194, denoted as h, is preferably greater than the distance e between two adjacent temperature sensors 191, 192, 193, 194, in particular 1.5 times greater. Thus, the edge effects that could occur at the end temperature sensors 191, 194 are advantageously avoided. By way of example, the height of the heating members 18 projecting beyond each of the end temperature sensors 191, 194 can be equal to 37.5 mm.

(30) These different elements can be arranged in any relevant area of the tank 10 as a function of the needs of the mission of the spacecraft. They can, for example, be arranged near the diaphragm conventionally equipping the tank 10.

(31) According to one specific example embodiment, the method for gauging the tank 10 according to the invention, using the elements described with reference to FIG. 2, is carried out as follows.

(32) In the full description hereinbelow, the quantified results are provided for the following operational configuration: the distance e between two adjacent temperature sensors is 25 mm; the heating member projects beyond the end temperature sensors 191, 194 by a height h of 37.5 cm; the distance d between the temperature sensors 191, 192, 193, 194 and the heating members 18 is equal to 5 mm. Each heating member 18 has a power output of 1.5 W.

(33) During an apogee motor firing, i.e. a phase of high-thrust exerted along the thrust axis 12 by the means of propulsion of the spacecraft, more specifically, for the quantified examples provided hereafter, a phase of thrust allowing the spacecraft to undergo an acceleration of 0.117 m/s.sup.2, creating gravity conditions in the tank, this phase lasting for 2,818 s, the wall 11 of the tank 10 is heated by the heating members 18.

(34) The heating members 18 can also be activated either before implementing the phase of high-thrust or during this phase.

(35) The completion of this step, as for the other steps implemented in the spacecraft, one example embodiment of which will be described hereafter, is controlled remotely by a control device situated remotely therefrom, for example on the Earth's surface.

(36) This remote control device is configured such that it controls the different steps of the method implemented by the spacecraft. For this purpose, the control device and the spacecraft each comprise conventional remote communication means.

(37) The control device is suitable for determining control signals that are sent to the spacecraft. These control signals are, for example, determined as a function of measurement signals received from the spacecraft, which are determined by different sensors (gyroscope, star sensor, etc.) thereof.

(38) According to the invention, for at least one of the temperature sensors 191, 192, 193, 194, preferably for a plurality and preferentially for all of these temperature sensors, a series of instant acquisitions is then carried out, at a fast rate, of the temperature of the wall 11 of the tank 10. In the quantified examples presented herein, the acquisitions are carried out at a rate of one acquisition every 4 seconds. They are preferably simultaneously carried out for all temperature sensors 191, 192, 193, 194.

(39) The data recorded by the temperature sensors 191, 192, 193, 194 is preferably transmitted, by the telemetry means of the spacecraft, to the remote control device, in particular situated on the Earth's surface. This device preferably comprises computing means configured such that they can implement the different computing steps of the gauging method according to the invention.

(40) The remote control device comprises, for example, at least one processor and at least one electronic memory in which a computer program product is stored, in the form of a set of program code instructions to be executed in order to implement the different steps of a gauging method according to the invention.

(41) In one alternative embodiment, the control device further comprises one or more programmable logic devices of the FPGA, PLD type, etc., and/or application-specific integrated circuits (ASIC) suitable for implementing all or part of said steps of the gauging method. In other words, the control device comprises a set of means designed as software (specific computer program product) and/or hardware (FPGA, PLD, ASIC, etc.) to implement the different steps of a method for gauging the liquid propellant tank of a spacecraft according to the invention.

(42) During the phase of high-thrust, a high quantity of liquid propellant is consumed by the means of propulsion, so much so that the volume of liquid propellant 14 in the tank falls quickly. As described hereinabove, the liquid propellant is pressed towards the bottom 17 of the tank 10, and the free surface of the liquid 16 is planar, and substantially perpendicular to the thrust axis 12.

(43) For each temperature sensor, when the liquid-gas interface 16 is located in the plane of interest associated with the sensor, a sudden increase occurs in the temperature measured. The thermal inertia of the wall 11 of the tank 10 indeed differs depending on whether liquid is or is not in contact with said wall 11.

(44) On a digital curve representing the temperature recorded by the temperature sensor as a function of time, as shown in FIG. 3, for example for the temperature sensor C1 191, a break of slope occurs, indicated by the circle given the reference numeral 30 in this figure.

(45) FIG. 4 shows a graph illustrating the change, as a function of time, of the temperature recorded by each of the temperature sensors C1 191, C2 192, C3 193 and C4 194.

(46) This graph shows the start of the apogee motor firing and the end of the apogee motor firing. The heating members 18 are in operation throughout all the duration of the apogee motor firing. They have been activated prior to the start of the firing.

(47) As can be seen on the curves, at the time of the start of the apogee motor firing, the temperature of the wall 11 of the tank situated at the location of the temperature sensors falls rapidly. Indeed, the liquid propellant has been pressed towards the bottom 17 of the tank 10, and fully occupies the part of the tank in which the temperature sensors are situated. The thermal inertia of the wall 11 at this location is thus high. During the apogee motor firing, a sudden break of slope is successively seen on each of the curves. Each sudden break of slope indicates the moment at which the liquid-gas interface 16 in the tank 10 is located in the plane of interest associated with a temperature sensor 191, 192, 193, 194. Logically, this interface is firstly located in the plane of interest associated with the temperature sensor C1 191 situated the furthest from the bottom 17 of the tank 10, then in the plane of interest associated with the temperature sensor C2 192 immediately adjacent thereto, then in the plane of interest associated with the following temperature sensor C3 193, and finally in the plane of interest associated with the temperature sensor C4 194 situated the closest to the bottom 17 of the tank 10.

(48) The gauging method according to the invention comprises a step of determining the moment at which the temperature recorded by one of the temperature sensors 191, 192, 193, 194 changes.

(49) This moment can be determined by analysing the difference between the temperatures recorded by two temperature sensors associated with separate planes of interest, which advantageously allows a particularly reliable and accurate result to be obtained. More particularly, the moment at which the temperature recorded by a temperature sensor, for example the sensor C2 192, changes can be determined by analysing the difference between the temperature recorded by this sensor C2 192 and the temperature recorded by a temperature sensor situated upstream in the direction of thrust 13, i.e. a temperature sensor situated further from the bottom 17 of the tank 10 than the temperature sensor C2 192, which is preferably adjacent thereto. In the specific embodiment shown in the figures, this is the adjacent sensor C1 191. Indeed, at the wall 11 of the tank 10, a cold area forms immediately below the liquid-gas interface 1, and a hot area, which becomes increasingly hotter over time, forms above this interface.

(50) FIG. 5 shows a graph representing, as a function of time, the change in the temperature recorded by the temperature sensor C1 191, in the temperature recorded by the temperature sensor C2 192, and in the difference between these two temperatures. The moment at which this difference is at the highest, which is shown by a circle given the reference numeral 31 in this figure, corresponds to the moment at which the thermal inertia of the wall 11 of the tank 10 begins to change at the location of the temperature sensor C2 192, which means that the liquid-gas interface 16 in the tank 10 is located at the level of this sensor. Then, the temperature difference begins to decrease, the two sensors are both located in an area of the wall 11 of the tank 10 that is no longer in contact with the liquid.

(51) Thus, by studying the temperature differences recorded by two separate temperature sensors, the moment I can advantageously be accurately determined, at which moment the liquid-gas interface 16 in the tank is located in the plane of interest associated with the temperature sensor which, among these two temperature sensors, is situated the closest to the bottom 17 of the tank 10.

(52) As a function of the acceleration to which the spacecraft is subjected, the liquid-gas interface 16 in the tank 10 can take on a curved shape, referred to as a meniscus, the level of liquid being higher against the wall 11 of the tank 10 than at the centre thereof. This meniscus shape is classically all the more pronounced as the acceleration of the spacecraft is low. This meniscus shape is shown in FIG. 6, which provides an expanded view of the area A of FIG. 1.

(53) The change in thermal inertia of the wall of the reactor does not occur exactly at the free liquid surface, but slightly higher, at the peripheral edge of the meniscus.

(54) A person skilled in the art is capable of determining, as a function of the specific conditions, the height of this meniscus, and of providing, according to this height, the adequate correction to the volume of propellant actually contained in the tank at the moment I determined according to the invention, in order to improve the accuracy of the gauging method according to the invention.

(55) The moment at which the temperature recorded by one of the temperature sensors 191, 192, 193, 194 changes, which indicates the presence of the liquid-gas interface 16 in the tank 10 in the plane of interest associated with said temperature sensor, can otherwise be determined by detecting the break of slope on the digital curve showing the temperature recorded by the temperature sensor as a function of time. This detection can be carried out according to any method conventional in itself for a person skilled in the art. For example, it can be carried out by analysing the temperature derivative with respect to time. By way of example, FIG. 7 shows a graph representing the change as a function of time, on the one hand in the temperature recorded by the temperature sensor C2 192, and on the other hand in the temperature derivative with respect to time.

(56) On the derivative curve, a circle given the reference numeral 32 indicates the moment at which the thermal inertia of the wall 11 of the tank 10, at the location of the temperature sensor 192, begins to decrease. This corresponds to the presence of the outer edge of the meniscus at the location of the temperature sensor. A circle given the reference numeral 33 further indicates the moment at which the thermal inertia of the wall 11 of the tank 10, at the location of the temperature sensor 192, reaches its maximum value. The free liquid surface 16 in the tank 10 and almost all of the meniscus are then located below the plane of interest associated with the temperature sensor.

(57) As stated hereinabove, based on the knowledge obtained by the method according to the invention of the moment I at which the liquid-gas interface 16 in the tank 10 is located in the plane of interest associated with a temperature sensor, for example the temperature sensor C2 192, the corresponding volume of liquid propellant can be easily determined, from the geometrical data of the tank 10, and the known position of the temperature sensor on this tank 10, in a subsequent step of the gauging method according to the invention.

(58) A corresponding mass of propellant can thus be easily determined therefrom.

(59) By way of example, the method according to the invention was applied under the aforementioned operating conditions, using the apparatus specified below.

(60) The tank 10 has the shape of a spherical cylinder of radius 343 mm. The assembly of one or more heating members and of one or more temperature sensors is arranged 55 mm from the bottom of the cylindrical portion.

(61) The propellant analysed is NTO (Nitrogen Tetra Oxide).

(62) Under the thrust conditions applied, the height of the meniscus is 1.26 cm.

(63) The results obtained using the method according to the invention were used to determine a mass of propellant remaining in the tank of the spacecraft after the apogee motor firing, by combining these results with the data produced by the Dead Reckoning method, according to equation (1):
m.sub.BOL=m.sub.TM−(t.sub.finLAE−t.sub.TM)*{dot over (m)}.sub.LAE  (1)

(64) wherein the different parameters are as defined hereinabove.

(65) The results obtained were compared to the forecasts obtained using the Dead Reckoning (DR) method. The difference between: the data obtained using the method according to the invention for each of the temperature sensors C1, C2, C3 and C4 by, on the one hand the method of analysing the temperature derivative with respect to time, described hereinabove, and on the other hand the method of determining the moment at which the difference between the temperatures recorded by separate temperature sensors is at its maximum, also described hereinabove, then the application of the equation (1) hereinabove; and the data derived from the Dead Reckoning forecasts (reference remaining mass (DR)), was calculated.

(66) The results obtained are presented in Table 1 hereinbelow.

(67) TABLE-US-00001 TABLE 1 Comparison of the mass data obtained by implementing methods according to specific embodiments of the invention and forecast data obtained by the Dead Reckoning (DR) method Reference Determination using the Determination using the remaining derivative method difference method mass Difference Difference Sensor (DR) (kg) Mass (kg) with DR (kg) Mass (kg) with DR (kg) C4 338.132 337.929 −0.203 337.032 −1.100 C3 351.381 350.72 −0.661 350.541 −0.840 C2 364.629 363.511 −1.118 362.613 −2.016 C1 377.879 372.531 −5.348 — —

(68) The results obtained are shown to be very similar, regardless of the method according to the invention used (derivative or difference method).

(69) Thus, by combining the gauging of the tank using the method according to the invention, with the Dead Reckoning method, knowledge of the quantity of propellant remaining at the end of the apogee motor firing is significantly improved. The method according to the invention thus advantageously allows the forecasts produced using the conventional Dead Reckoning method to be refined as regards the mass of liquid propellant remaining in the tank at the end of the apogee motor firing, thus at the start of the actual mission of the spacecraft.