International Journal of Engineering & Science Research

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IJESR/April 2012/ Volume-2/Issue-4/Article No-1/128-141 ISSN 2277-2685

International Journal of Engineering & Science Research

ESTIMATION OF CENTER OF GRAVITY (CG) FOR SPACECRAFT: A

REVIEW

C. Suresh*1,Jiwan Kumar Pandit

2, K. Ramachandra

1, M. R. Thyagaraj

2

1R. V. College of Engineering, Bangalore, India

2Indian Space Research Organisation, ISRO Satellite Centre, Bangalore, India

ABSTRACT

This paper discusses the importance and role of Centre of Gravity in the design of spacecraft and

in its operation. Currently several methods are practiced to determine the CG of the spacecraft.

This paper reviews differentpractical & virtual methods, its advantages and limitations. The

uncertainties involved in the estimation of spacecraft’s CG are also addressed.

Keywords: Center of gravity, Mass properties, Spacecraft.

1. INTRODUCTION

The Centre of Gravity (CG) is a point in space where, for the purpose of various calculations, the

entire mass of a body is assumed to be concentrated.

Human body while performing different activities, assume different postures wherein the CG of

thebody needs to be balanced, such that its projection on the ground lies in the area under or

between the feet. In Humanoid Robot, it is essential to balance the CG, for the robot to stay on its

feet and perform its operations. CG of an automobile has a profound effect on its fuel economy,

stability, safety, acceleration, braking and manoeuverability. For achieving fine surface finish, in

grinding operation, it becomes essential for the spindle and grinding wheelto have their CGon

the common axis of rotation. During the handling of heavy objects, using Automated Guided

Vehicles and multiple mobile robots, the location of the CG of the object is required to decide the

supporting locations. TheCG of the aircraft shifts due to movement of passengers, crew, fuel

slosh due to manoeuvring and therefore CG,in real time,is required as an input for its control

systems to perform efficiently and in a reliable manner.The CG of the target is aimed, during a

missileattack,to destroy it completely. Foron-orbitspacecraftorientation the propulsive force

should be directed aboutitsCG, and to raise its orbit altitudethe propulsive force must be directed

toitsCG, to avoid any inducedperturbations.

Spacecraft CG estimation on ground and on-orbit conditions becomes imperative for its

successful integration, launch and on-orbit operations. Unlike other systems, spacecraft pose a

unique set of constraints and risks in estimating its CG. To address these issues, new innovative

methods have to be employed. By estimating the CG of a spacecraft more accurately, we can

achieve mass reduction, increased mission life, better spacecraft dynamics on-orbit and more

efficient performance of the spacecraft. Finally it helps to reduce the lifecycle cost of the

spacecraft.

1.1 IMPORTANCE OF CG AND MASS PROPERTIES MEASUREMENT IN A SPACECRAFT


Copyright © 2012 Published by IJESR. All rights reserved 129

For the development of various subsystems of a spacecraft, at different stages, the role of CG is

quite important and briefly discussed as follows:[7,9]

i. Attitude determination:Attitude control simulation models use CG as a parameter to design

and analyse control laws and algorithms. It is also required for reaction wheel sizing.

ii.Stress: Mass and CG of electronic packages are used to analyse package installation and local

attachment analysis.Mass properties are used as an input for FEMs to determine load distribution

in the structural members and optimally design them.

iii. Propulsion:Propulsion group needs CG for thruster alignment to assure adequate torque

control and moment arm determination. Based on mass of spacecraft, propellant quantity is

determined for a specified mission life.

iv. Mechanical ground support equipments (MGSEs) design:CGestimates provide

information for fixing the handling locations for handling and moving flight hardware.

v. Vehicle assembly, integration and test:The location of CG plays a vital role in determining

the integration fixture / adaptors, over which the complete satellite system is to be

integrated.Weight and CG data is used for design of lifting slings.

vi. Launch vehicle interface:It is required to align the spacecraft CG with the thrust line of the

launch vehicle. Alignment between the center of thrust and the center of gravity of the vehicle is

critical to prevent large offset moments from being generated.

vii.Groundcontrollers:Ground controllers need CG to control the satellite, since theCG shifts

due to deployables and continuous utilization of propellant.

viii. Life cycle costing: Component and subsystem weight is used in the cost model.

ix. Program office: The program office requires the mass properties to assure compliance with

requirements and if required to mitigate adverse mass properties trends.

x. From Standardisation point of view:The accommodation of similar payloads can be done on

a standard spacecraft bus such that mass properties are within the specifications of launch

vehicle.

2. PRINCIPLES BASED ON WHICH CENTER OF GRAVITY OF A BODY CAN

BEESTIMATED

Centre of gravity of a body can be estimated by static and dynamic methods.The basic

terminologies used are:

Principal axis: The axis of rotation of the spacecraft about which it spins in free space is called

principal axis. The CG of the spacecraft lies on principal axis.

Moment of Inertia: It describes the distribution of mass about the neutral axis of a section. The

farther the concentration of the mass from the neutral axis, higher the moment of inertia of the

cross section of the body. It is the resistance offered by the cross section of a body to rotational

torque.

Types of unbalance

i.Static unbalance: Is a condition when the CG of the spacecraft is not on its axis of rotation

butaxis of rotation is parallel to principal axis. The amount of unbalance is the product of the

IJESR/April 2012/ Volume-2/Issue

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weight and the distance between axis of rotation and principal axis. Static balancing is done by

placing counter weights at definite distances such that the axis of rotation and principal axis

coincide.

ii. Couple unbalance: Is a condition when th

rotation. To correct couple unbalance, two equal weight must be added on the spacecraft at 180°

angles apart in two correction planes. The distance between these planes is called the couple arm.

iii. Dynamic unbalance: It is the vectorial summation of force and couple unbalance. To correct

for two unrelated correction weights requires two unrelated correction weights in two different

planes at two unrelated angles. The specification of the unbalance is only

location of the correction planes is known. Dynamic unbalance specifies all the unbalance which

exists in a spacecraft. This type of unbalance can be measured on a spinning balancer which

senses centrifugal force due to the couple com

Product of Inertia (POI): The mass distribution resulting in a couple moment when the object is

spinning is the product of inertia. Basically, product of inertia is a measure of dynamic

unbalance.

A. Static Methods of estimating CG

i. By symmetry:For bodies which are homogenous and symmetric about its axes, the geometric

center is the CG of the body.

ii. Bysuspending the body: For bodies which are plane and of uniform thickness, CG can be

found by suspending the body from at least two points. Vertical lines (plumb lines) from the

points of suspensionare projectedon the surface of the body. The point of intersection of the

vertical lines is found and theCG lies, at half the thickness at the point of intersection. (Fig. 1)

Fig. 1.CG location of a Body by suspending it through two points.

iii.Balancing moment method:

edgebears most of the load. The moment acting due to the unbalanced load is balanced using

known weights. These weights are then used to calculate the CG of the body. (Fig.2)

Fig. 2.CGestimation using balancing moment method.

2/Issue-4/Article No-1/128-141 ISSN 2277

Published by IJESR. All rights reserved



Is a condition when the principal axis is not parallel with the axis of



It is the vectorial summation of force and couple unbalance. To correct


planes at two unrelated angles. The specification of the unbalance is only complete if the axial



senses centrifugal force due to the couple component of unbalance.

(POI): The mass distribution resulting in a couple moment when the object is


Static Methods of estimating CG

For bodies which are homogenous and symmetric about its axes, the geometric

For bodies which are plane and of uniform thickness, CG can be



ical lines is found and theCG lies, at half the thickness at the point of intersection. (Fig. 1)


Balancing moment method:In this method the body is balanced about a pivot axis.Knife

dgebears most of the load. The moment acting due to the unbalanced load is balanced using


CGestimation using balancing moment method.

ISSN 2277-2685

130



e principal axis is not parallel with the axis of



It is the vectorial summation of force and couple unbalance. To correct


complete if the axial



(POI): The mass distribution resulting in a couple moment when the object is


For bodies which are homogenous and symmetric about its axes, the geometric

For bodies which are plane and of uniform thickness, CG can be



ical lines is found and theCG lies, at half the thickness at the point of intersection. (Fig. 1)


In this method the body is balanced about a pivot axis.Knife

dgebears most of the load. The moment acting due to the unbalanced load is balanced using




W x a = m x b

a = m x b

W

iv. Multiple point weighing method:The body under consideration is placed on a platform,

which in turn is placed on three or more load measuring instruments like load cells. The

individual readings give the force acting on each supports. By calculating the moment acting

about any fixed point, the CG of the body can be calculated.[4](Fig. 3)

Fig. 3.CG location of a Body using load cell.

The weight of the body is found by adding all the four values of load cells.

W = A + B + C + D

By taking moments about A

x = ( B + C ) l y = ( C + D ) b

W W

B. Dynamic Methods of estimating CG

i. Spin balance method: The test object is mounted on the spin table,which is fixed to the rotor

of the spherical air bearing. The rotor is supported on a vertical shaft which is supported in a

bearing at the lower end.

When the CG of the test object is offset at a given distance from the vertical measuring axis of

the machine, it lies in a certain angular relationship with respect to an arbitrary or geometrical

axis of the test item.

The moment produced by the CG offset is balanced by a moment applied to the spherical

bearing. The stabilizing bearing at the lower end of the shaft supplies this balancing force. As the

test object is rotated, the force on the stabilizing bearing also rotates. The stabilizing bearing is

supported in a flexure and gimbal arrangement so that there is one direction of unrestrained

movement. Aload cell provides the restraint in this direction. The transducer is responsive only

to the force or component of force directed along this single axis.

Measurements are made continuously as the test object rotates. This data is summed to produce a

precise measurement of the force component. The force components provide the resultant force

(moment) and the angle. Once the resultant moment force has been determined, the actual CG



offset with respect to the vertical axis can be obtained by dividing the moment by weight of the

test article.By knowing the CG offset, resultant force and the angle, CG location can be

estimated. This method is used to estimate the height of the CG from a reference point.

Theforce transducers sense the reactions on the bearings which support the part during rotation.

These forces are due to both gravity and centrifugal force (the higher the spin speed, the less

significant the gravity force is). The CG location of the part may then be separated from the

dynamic unbalance of the part using calculations that involve the magnitude of the bearing forces

and their phase relationship. If the POI of the object is high, then CG accuracy will be poor,

because most of the bearing force will be due to POI. Furthermore, air turbulence can cause a

significant deviation.[4]

ii. Moment of Inertia Method:The Spin Table is equipped with an inverted torsion rod which is

used to perform MOI measurements. The instrument oscillates an object about a vertical axis and

measures both moment of inertia and oscillation decay on an essentially frictionless inverted

torsion pendulum.

This measurement is obtained by clamping the lower end of the torsion rod in the torsion rod

chuck. Withthe torsion rod clamped, the test item and spherical support bearing are no longer

free to rotate. They areangularly displaced through a small angle against the elastic restraint of

the torsion rod. When the torsionrod chuck is released, the assembly oscillates about the spin

axis. The oscillation is essentially frictionlessand undamped (with the exception of air drag) due

to the near frictionless environment in the gas-supportedbearing. A photo eye mounted in the

table measures the period of oscillation. The technique is to performall measurements at

specified amplitude. After the average period of oscillations is measured, the grossamount of

inertia of the rotating system can be calculated by subtracting the tare moment of inertia of

thetable and fixturing from the measured gross moment of inertia of the system.

CG is determined on a torsion pendulum by making use of the parallel axis theorem.The

minimum measured moment of inertia of an object occurs when the axis of

measurementcoincides with the CG of the object. Several moment of inertia measurements

arethen made at different object positions to determine the object location resulting in the

smallestmeasured moment of inertia. When the measured moment of inertia is a minimum the

CG of the testobject is coincident with the axis of measurement. This is an extremely tedious

procedure, andrequires some means of determining part position at minimum moment of inertia.

Furthermore, thismethod only works for single axis CG.

Successive moment of inertia measurements are made for at least three positions of the test

object.

This approach of estimating CG is the least accurate of all methods.[4]

3. REVIEW OF THE CG MEASURING INSTRUMENTS CURRENTLY IN USE

3.1. STATIC INSTRUMENTS

Static instruments are used to calculate the CG of the spacecraft along single axis. Repositioning

the spacecraft by rotating it 90° about vertical axis, CG can be estimated along other axes.

3.1.1. Pivot balance instrument



In this instrument a beam is balanced over a knife-edge at the center of length of the beam. This

instrument works on the principle of balancing moment method. (Fig. 3)

The advantage ofthis instrument is that it can be easily constructed with relatively low

investment.

Using this instrument, CG can be found in one direction only. For every axis the object has to be

reoriented. Pivot friction affects the sensitivity of the instrument.Knife-edge has moderate

sensitivity when new, but they rapidlydeteriorate as the edge is worn.

3.1.2. Rotary table with spherical air bearing

Air bearing consists of a hemispherical recess in a block called stator and hemispherical ball

called rotor. These two are separated by an air gap of less than 0.012 mm. Air is introduced into

the gap through jewel orifices that meter the air and provide dynamic centering of the bearing.

About 30 litres of air or nitrogen has to be pumped into this gap per minute to levitate the rotor.

The air bearing acts as pivot and also as a rotary table.

Theadvantagesof this method are that the table can be rotated so that X & Y axes CG can be

measured in single test set-up.

Total time to make a measurement is about 30 seconds. In this machine, the lean error can be

eliminated by recording readings when the table is at two locations 180° apart. The lean error

which is equal for both measurements is therefore subtracted from the result. The bearing acts as

both pivot and rotary table.

This method requires clean room environment for precise measurement and operation. All parts

have to be moved to clean room for measuring CG. Preferably nitrogen is used for levitating the

stator. [8, 10, 4, 11]

3.1.3. Multiple supports weighing method

This method works on the principle of multiple points weighing method discussed earlier.

The advantages of this instrument are that it can measure both weight and CG of the body. For a

given value of accuracy requirement it is the lowest cost instrument. This instrument is the

preferred choice for heavy parts with tight tolerances for estimating CG. This is the fastest CG

measuring method. Boynton claims that the total time to measure CG along two horizontal axes

is less than 30 seconds.[4]

Using this method CG can be estimated only in horizontal axes and to estimate CG along vertical

axis, repositioning is required. It is highly sensitive and correction for lean error caused by

levelling requires significant efforts. The instrument reference coordinates is difficult to define.

Unlike rotary table instruments, these instruments are fixed and spacecraft reorientation is

required for CG estimation along different axes.Fixturing errors can induce uncertainties in CG

estimation.[4, 5]

3.1.4. Multiple points weighing method with spherical air bearing

A combination of multiple point weighing method and spherical gas bearing provides the

advantage of measuring the CG of the spacecraft in all three axes in a single setup.Thebasic

instrument consists of a large weighing platform upon which a spherical air bearingpivot and two



smallermoment scales are mounted. Both momenttransducers are supported on a rigid platform

which remains parallel to the base independent ofthe object weight. Therefore, the lean error

described in the previous case is eliminated.

The weight of the test object is supported primarily by a spherical gas bearing pivot, which is

located near thenominal CG of the object. The two moment transducers support the off axis

components of theCG. Spacecraft CGlocation is measured relative to the “Machine Zero

Reference”.

The third CG coordinate may be measured by tilting the spacecraft through a known

angle(approximately 30 degrees), re-measuring CG, and comparing it with the CG location

beforetilting.Boynton discusses the mathematical model of estimating CG in the tilted position

and he claims thatan accuracy of up to 0.127 mm can be achieved from this instrument.[8, 11]

3.2 DYNAMIC INSTRUMENTS

3.2.1. Spin balance cg instrument

This instrument works on the principle of CG estimation using spin balancing method discussed

earlier. In this method CG can be estimated in vertical axis.

The constraints in this method are that the accuracy achieved is directly proportional to the spin

speed. But spinning spacecraft at high speeds of more than 30 rpm poses risks to the spacecraft’s

deployables’ integrity. Forces on the force transducer will be due to both gravity and centrifugal

force. If the Product of Inertia of the object is high, CG accuracy will be poor, since most of the

bearing force will be due to POI.Air turbulence causes significant error.Fixturing has to be robust

to constrain the test object which will be subject to dynamic forces. Instrument cost is also

high.[4, 10, 11]

3.2.2 Moment of inertia cginstrument

This instrument works on the principle of CG measurement using Moment of Inertia method

discussed earlier. The advantage of this method is that,moment of inertia measuring instrument

can be configured to measure CG of the object.

The limitations in this method are that in every trial to measure the CG, it is required to

reposition the object at three different locations, and hence fixture design is complicated.

Accuracy of this method is poor.Instrument does not give direct CG readout. Lean error

dramatically increases even for slight variation in the level of the apparatus. It is a tedious

procedure. It is the least accurate method of all the methods discussed.[4, 10, 11]

4. UNCERTAINTIES / ERRORS IN CG MEASUREMENT OF A SPACECRAFT

The accuracy, to which we can estimate the CG of the object, depends on the ability of the

measuring instrument. But to achieve the best possible accuracy of the machine, we must avoid

the errors which might creep in due to measuring practices.

The uncertainties commonly encountered while measuring CG can emerge from inaccuracies in

establishing the following elements:

A. Co-ordinate systems



The object must have precisely defined measurement axes. The CG of the object is defined with

reference to the axes. It is a common practice to establish the measuring axes at least ten times

more precisely, than the accuracy to which we intend to estimate the CG.For example if we

intend to measure the CG to an accuracy of 0.1 mm, then the reference axis should be established

to an accuracy of at least 0.01mm[1,2,3,4].

i.Structural or Geometric co-ordinate system:For a spacecraft, the origin is defined on the

separation plane between launch vehicle and spacecraft. Usually it will be at the center of the

interface ring. The Roll axis in this system is typically defined as the longitudinal axes of

symmetry.[6]

ii. Mass properties balancing co-ordinate system: In this system, the origin is considered at the

nominal CG location or the location where we intend to have the CG. Its axes will be parallel to

the Structural or Geometric co-ordinate system, but the directions (+/-) will be opposite. By

defining such a co-ordinate system, positive and negative unbalances can be corrected with the

target being zero.[6]

iii.Mass properties instrument co-ordinate system: Measuring instrument measures the CG of the

object with reference to its own co-ordinate systems.It is very important to align the object

reference axes with that of the instrument. This is exactly the function of the fixtures. The mass

properties instrument co-ordinate system is uniquely defined for every orientation of the

components or systems.[6]

iv. Principal axis co-ordinate system: Once the CG of the spacecraft is estimated, a co-ordinate

system with actual CG as the origin is defined. The offset and angle of inclination of this co-

ordinate system from structural or mass properties balancing co-ordinate system is reported. [6]

Identifying datum surfaces

Once the co-ordinate system is established, datum surfaces have to be identified.

To qualify as datum surfaces,

• Surfaces should be perfectly horizontal.

• Surface geometry should be simple.

• Surfaces should be machined to close tolerances.[4]

Identifying mounting surfaces

Mounting surfaces may be one among the datum surfaces. But mounting surface may be

different from a datum surface. The mounting surface supports the load of the object, and must

ideally fasten the object to the fixture in such a way that the datum surfaces contact with the

reference surfaces of the fixture, as intended.[4]

B. Fixturing errors

Designing fixtures for constraining the object for which CG has to be estimated is a challenging

task. Fixturing error is almost always the major source of measurement error. Error induced by

the fixtures will degrade the accuracy of the measuring instrument.

The functions of fixture in this case are:

� Locate the article to be tested in a repeatable manner.



� Accurately relate the test article coordinate system to the machine system.

� Secure the test article rigidly during measurement.

The other requirements of fixtures are

� To be balanced about the measurement axis.

� To be rigid.

� Have minimum weight.

� Have no detachable parts.

� Have low thermal expansion.

� Have realistic tolerances consistent with required measurement accuracy.

� Provide for verifying the location of datum surfaces.

� Be simple to set up and easy to use.

Failing to meet any of the above constraints will induce errors in the measurement.[4,5]

C. Lean error

In any of the above methods used to measure the CG of the measured body, it has been observed

that the body tilts due to the CG offset. The amount of tilt depends on the weight of the object

and the CG offset. This in turn will introduce an error in CG measurement due to object lean. It

has been experimentally determined that the amount of error induced increases with the degree

of lean and with the height of CG above the datum.

There are three components of lean error.

First, there is the effect of levelling the machine. The sensitivity of the levelling technique, the

operator skill in the levelling process, the stability of the floor on which the machine is mounted,

and CG height of the test part above the machine loading plane,all contribute to the lean effect

due to levelling.

The second type of lean error is caused by the finite stiffness of the measuring system. That is,

allmeasuring systems deflect somewhat under load. For test parts with large CG height, the CG

willlean in the direction of the CG offset causing further CG offset. This effect can be

compensatedfor by measuring the machine stiffness constant, entering the approximate CG

height, andcorrecting the measured reaction force proportionately to compensate for the machine

deflection.

Finally, the part may be caused to lean by inaccuracies in the support fixture. Generally, this

canbe determined by performing optical measurements on the object while supported in

theinstrument.

The effect of lean error can be minimized by designing the fixture to keep the CG height to

aminimum, keeping CG offset minimum, and making the measuring system as stiff as

possibleconsistent with required sensitivity and accuracy.[4,5]

D. The air mass effect

Air has significant mass and alters the mass properties in two ways:

Air trapped inside the payload will increase its mass by an amount equal to the unoccupied

volume in the payload times the density of air. This is called the entrapped air effect.[4]



Air dragged or pushed along by any protrusions on the outer surface of the payload

candramatically increase moment of inertia. This is called the entrained air effect.[4]

Entrapped air effects the CG measurement using both static & dynamic methods and the

entrained air affects CG measurement in dynamic methods only.[4,12]

E. Drafts, temperature changes and vibration

Due to the flow of air in and out of the room, through AC ducts, significant disturbances can be

caused to the functioning of the instrument.

Temperature changes can cause the elements in the instrument, fixtures to alter their dimensions

and can subsequently induce errors in CG measurement.

Vibration affects the functioning of dynamic CG measuring instruments and can significantly

alter its ability to calculate the CG.[4]

F.Liquid Propellant mass

Depending on the mission requirement, the propellant mass can vary from 10% to 40% of the

total weight of the spacecraft. Due to safety concerns, the spacecraft CG is estimated with empty

propellant tanks. To avoid the CG offset due to liquid propellant, the propellant tank is placed

along the primary axis of the spacecraft such that the CG offset can be easily estimated. In orbit,

due to the consumption of propellant, mass of the spacecraft decreases and CG shifts from initial

position.Further due to the attitude changes and fuel slosh, there can be significant variation in

CG location of the spacecraft.[16]

G. Mass of removable items

Prior to satellite integration, certain components which are vulnerable to damage, are covered

with protective covers, like thrusters with thruster protection caps. Also there will be alignment

elements and handling brackets. These components are removed only before placing in the

launch vehicle. It is mandatory and very much essential to retain them even during CG

measurement. The mass of these removable items are up to 3% of the spacecraft mass, and are

distributed throughout the spacecraft. Once they are removed from the spacecraft, it induces

significant uncertainty to the actual CG of the spacecraft.[2]

H. Deployment mechanisms

Due to the deployment of mechanisms and reorientation of these in space for operations, the CG

of the spacecraft shifts. On ground, the spacecraft is placed on the CG measuring machine with

its mechanisms in stowed position. CG of the spacecraft in stowed position is essential for

integrating the spacecraft with the launch vehicle. There are concerns to estimate the CG of the

spacecraft in deployed positions as the mechanisms are vulnerable to damages during handling,

during CG measurement.[2]

5. POTENTIAL OF VIRTUAL METHODS (CAD) AS A CG MEASURING TOOL

Certain CAD software has the ability to estimate the CG of a component, sub system or a

complex system. Co-ordinate systems for estimating the mass properties can be established

accurately. Any surface qualifies as a datum surface. Fabrication of handling equipments to place



the components or subsystems on the measuring instrument can be avoided and this also

enhances the safety of the subsystems since they remain in the same location without transit.

Also fixturing errors and lean error are eliminated. Fuel mass can be considered and its effect on

CG can be estimated.The air mass effect is eliminated. Effects of drafts, temperature changes and

vibration during measurement can be avoided. Mass of removable items can be taken into

consideration. CG of the spacecraft in different deployed configurations can be estimated.

Harnesses can be suitably modelled and simulated for their mass properties. Components

movement to the measuring location or transporting measuring instrument to the locations where

subsystems are integrated becomes obsolete. It aids in compressing development time or time to

realise a spacecraft.

The estimation of CG using CAD package accurately depends on the degree to which the solid

models substitute for real components. To achieve a high degree of similarity, it is imperative

that we know the densities of all the components. In real scenario, collecting density values of

every component and material in a spacecraft is impractical. Although density of majority of

components is known, it varies in different degree even for homogenous materials like metals.

This can induce a significant amount of shift in estimated CG value from actual value.

Also for modelling components, nominal dimensions are used. But in reality the component

dimensions vary over the tolerance band. The location of the components also varies within the

position tolerance band. Tolerance stack up analysis has to be performed in order to fine tune CG

value estimated using CAD. This can increase the duration of estimating the CG and the

advantage of reducing development time may not be realised.

The access to the detailed technical specifications required to generate solid models, for

contractor supplied subsystems, at times becomes inaccessible which poses a critical limitation.

However this limitation can be overcome by positioning a body in the CAD model at the

measured CG location of the subsystem to simulate the exact CG effect of the actual sub system.

6. ESTIMATION OF CG OF FLUID FILLED TANKS USING CAD

The presence of the fluid propellant in the spacecraft significantly increases the difficulty in

reliably estimating its mass properties. The reason is becausethe liquid propellant will deform

continuously when the spacecraft orientation alters and hence its mass properties also

continuously change.

The varying mass properties of the fuel in the tank modify both the low-frequency and high-

frequency dynamics of the structure. The fluid is often modelled using finite element hydro-

elastic methodologies that couple the fluid and structural motion, to predict accurate structural

responses. But for the purpose of estimating the CG of the spacecraft, the CG of the fluid is

assumed to be same as that of the solid having same shape and hence is modelled as solid.[15,

16, 17]

7. OTHER POTENTIAL CONCEPTS FOR MEASURING CG OF SPACECRAFT

7.1.Multiple mobile robots:

Multiple mobile robots are a group of robots which collectively perform a task by co-ordinating



with each other. Jun Sasaki et al., discuss how multiple mobile robots can be used to estimate the

CG of an unsymmetrical body. To achieve this objective, the robots perform tilting operation.

In this method, firstly the robots are positioned around the object of which CG is to be estimated.

The robots end effectors engage with the body at specified locations and lift the object. The

weight is sensed by the robots and the object is placed on ground. The robots are programmed to

estimate the weight distribution and rearrange themselves to strategic positions. The robots again

lift the object as earlier. The weight distribution is sensed and recorded. Then the object is tilted

along a horizontal axis. The resulting changes in the weight distribution is sensed and recorded.

Now three sets of data are available. Location of the robots or end effectors contact points,

weight distribution before tilting and weight distribution after tilting. By using the first two sets

of data, CG along two horizontal axes can be found. By using location data and weight

distribution after tilting, CG height before tilting can be estimated. [14]

The advantages of this method are – the spacecraft CG can be estimated directly. There is no

requirement of fixtures. There are no dynamic loads induced since the spacecraft is not spun. CG

can be estimated in the deployed position as well. This method can be used to estimate the CG of

sub systems individually.

7.2.Photogrammetry:

Photogrammetric technique involves collecting images of object from geometrically varied

positions. Two dimensional measurements of discrete, identifiable points on the images can then

be reduced analytically to three dimensional coordinates and a 3-D image can be generated.

Gary L. Glick et al., discuss video photogrammetry as a method to estimate the CG of spacecraft

subsystems and spacecraft. The authors have combined photogrammetry with a classical

approach to CG determination and achieved rapid and high precision results.

The classical approach followed here to estimate CG is the suspension of the body method

discussed earlier. The authors explain this technique with an example of solar panel wing. Each

wing is suspended by a single support cable at an attach point. Targets on the wing and cable are

measured photogrammetrically. This process is repeated for other attachment points on the same

wing. The data is then analysed to determine the CG of that wing. A robotic video

photogrammetric system is used to speed the acquisition of the data. The CG was determined in

three dimensions to accuracy of the order of +/- 0.025 mm.[13]

This method has the same advantages of multiple mobile robots method.

8. CONCLUSION

The challenge of estimating the CG of a spacecraft was explored and was addressed with

different innovative concepts. Different concepts had unique set of advantages. Of all the

concepts discussed above, CAD method hassignificant advantages. It has the flexibility to

incorporate design modifications even at final stages of spacecraft realisation and estimate CG

changes. CAD has thepotential to cut down spacecraft development costs & time and also avoid

the risks posed by physical estimation to spacecraft’s health. It can be employed to estimate CG

in any stage of product development, right from concept development to on orbit operations.



CAD method is currently implemented on a spacecraft to ascertain its benefits. Multiple mobile

robots have the potential to be used to estimate the CG of nano& micro satellites and also

different subsystems individually. Photogrammetry has the potential to estimate the CG of

spacecrafts over 1000 kg, which haveunsymmetrical shape & mass distribution and poses higher

risks for CG estimation using dynamic measuring systems.

ACKNOWLEDGMENT

The authors express sincere gratitude to Sri K.V. Govinda, Dy. Director, ICA & Sri G.V.C.

Rajan, Group Director, SIG at ISRO Satellite Centre for their valuable guidance, encouragement

and support. The authors are also thankful to Dr.Satyanarayana, Principal, &Dr. H.N. Narasimha

Murthy, Dean, Mechanical Engineering Department, R. V. College of Engineering for their

valuable guidance.

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International Journal of Engineering & Science Research

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