0USAARL Report No. 93-4

AD-A259 924

An Automated Method for DeterminingMass Properties

By DTICSELEc-rF ft

Michael B. Deavers S.C

and

A Joseph McEntire

93-01372I I iH 11H Iirllllll 11lli '•5 ? (

Biodynamics Research Division

December 1992

Approvod for publc reease; dutlWrbuilon unlimited.

United States Army Aeromedical Research LaboratoryFort Rucker, Alabama 36362-5292

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4 HN V. BROLTC, MC, SFSDirector, Biodynamics

Research Division

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W. , O.D., Ph.D. DAVID H. EYCha rman, scientific Colonel, MC,dSFSReview Committee Commanding

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"11. TITLE (Include Security Clssfiation) "

An automated method for determining mass properties

12. PERSONAL AUTHOR(S)

Michael B. Deavers and B. Joseph McEntire"13a. TYPE OF REPORT 13b. TIME COVERED 14. DATE OF REPORT (Y.ontkay) 1S. PAGE COUNT

Final I FROM TO 1992 December 22

"16. SUPPLEMENTARY NOTATION

"17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number)

FIELD GROUP SUB-GROUP center-of-mass, mass moments of inertia, impacts, man-20 11 mounted equipment

- 23 02, ,19, ABSTRACT (Continue on revere if neceary and identify by block number)

The U.S. Army Aeromedical Research Laboratory performs mass properties testing with the

KSR330-60 Mass Properties Instrument (MPI). For man-mounted equipment, it is important todefine and measure the mass properties in order to accurately develop math models, under-stand human performance impacts, and to conduct comparative evaluations. Determining massproperties requires a thorough theoretical understanding of the center-of-mass and massmoments of inertia. This report provides the operating theory and procedures to measuremass properties with the MPI.

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Acknowleduments

The authors wish to thank Mr. Troy Bowman forrecommendations towards the operation of the MPI.

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ii

Table of Contents

List of figures .... ....................... ........ 2

Introduction . .. .. .. .. .. .. .. .. .. .. . .. 3

Equipment ............. . . . . . . .. .. . . . . . . . 3

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Center-of-mass . . . . . . . . . . . . . . . . . . . .. 3

Moments of inertia. . . . . . . . . ............... 4

Mass moments of inertia. . . . . . ........... 4

Mass products of inertia .............. 6

Principal moments and axes of inertia .... ....... 9

Procedure of operation ................... 11

Calibration . .. .. .. .. .. .. .. .. .. . .. 12

Measurements . . . . . . . . . . . . . . . . . . . . . . 14

Step 1: Tare measurement. . . . . . . . . . . . . 14

Step 2: Part measurement. .......... . . . 15

Step 3: Calculations. . . . ........... . 15

Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . 15

References . . . . . . . . . . . . . . . . .......... 17

Appendix A: Accuracy of the MPI . . . . . ........... 18

Appendix B: Determination of torsional pendulum physicalconstant . . . . . . . ............ 19

Appendix C: KSR main menu ..................... . 20

Appendix D: Mounting of test fixture. . . . . . ........ 21

Appendix E: Manufacturers' list . . ............... 22

1

List of figures

Figure Page

1 KSR330-60 Mass Properties Instrument setup . . .. 4

2 Moments produced during CM testing ...... ........ 5

3 Inverted torsional pendulum ......... ............ 6

SDifferential mass with respect to the CM ... ..... 7

5 Arbitrary axis with respect to the coordinateaxis ................. .................... 8

6 Direction cosines for principal axis 1 .... ...... 10

7 Relation between coordinate and principal axes . . 11

8 Calibration beam and weights ............. 13

9 MPI setup for CM calibration .... ........... .. 13

D-1 Mounting pattern of test platform ............ ... 21

2

Introduction

Mass property evaluations are an integral part of theengineering analysis performed by the Biodynamics ResearchDivision at the U.S. Army Aeromedical Research Laboratory(USAARL). For man-mounted equipment, it is important to defineand measure the mass properties in order to accurately developmath models, understand human performance impacts, and to conductcomparative evaluations. To measure these properties, the SpaceElectronics KSR330-60 Mass Properties Instrument (MPI) wasselected. The purpose of this paper is to describe the MPI'soperating theory and the procedure to measure mass propertieswith the MPI.

Equipment

The KSR330-60 MPI was designed and produced by SpaceElectronics, Inc. The MPI is capable of testing a 330-lb load.The maximum full-scale moment allowed due to the offset of thepart's CM is 60 in-lb. The accuracies of the MPI are listed inAppendix A. The MPI requires a continuous source of pressurized(70 to 05 PSI) nitrogen or dry clean instrument air. A JUN-AIR2000 oil-less air compressor with an absorption dryer wasselected to supply instrument air to the MPI. The MPI operationis fully automated with a personal computer and a dot matrixprinter. The MPI system setup is shown in Figure 1.

Theory

The MPI is designed to obtain accurate measurements of thecenter-of-mass (CM) and the mass moment of inertia (MOI). The CMis defined as the point in a body at which its entire mass may beassumed to be concentrated. The MOI of a body is defined as ameasure of its resistance to rotational acceleration.

Center-of-mass

For each orthogonal axis of a test part, its CM iscalculated by measuring the force required to balance the testpart on the test platform's pivot axis. This pivot axis servesas the fulcrum for the test platform, which is suspended by arotary gas bearing. The test part's mass and the unknowndistance between the test part's CM location and the testplatform's pivot axis results in a moment applied about the pivotaxis (Figure 2). The MPI measures the force required to balance

* See manufacturer's list.

3

Figure 1. KSR330-60 Mass Properties Instrument setup.

this moment caused by the test part. This balancing force (F1)is sensed by a force transducer located at a known distance (dj)from the fulcrum. From the moment equation,

N1 = Fjdj,

the moment (N1) produced by the transducer relative to the pivotaxis can be determined. In order to balance the test platform,this moment must equal the moment resulting from the cM of thetest part. Since the force applied by the test part (F2) isknown from its mass, the unknown distance from the fulcrum to theCM of the test part (d2) is easily calculated from the followingequation:

FidI - FAd2

or d2 - (Fldl)/F 2 .

Moments of inertia

Mass moments of inertia

The MOI calculations are based on the period of rotationaloscillation of the test platform, which is configured as an

4

F,

F dF2d2

test platform test mass -' 7o ]

fulcrum

pivot axis

Figure 2. Moments produced during CM testing.

inverted torsional pendulum (Figure 3). To begin theoscillation, the platform is rotated slightly and released. Thetest platform's MOI is related directly to the oscillation period(T) by the following equation:

I= CT2,

where C is a physical constant dependent on the torsionalpendulum configuration. This constant is found experimentally asshown in Appendix B.

To determine the MOI of the test part, a tare period (T)must first be measured for the platform and any test fixturenecessary to support the test part. The test part then is addedto the system and another period (Ti) is acquired. Using thecalibration constant, C, the test part MOI then is calculated:

I = C(T? - Tt).

This measurement and calculation provide the part's MOI about asingle axis. This procedure must be repeated for the part's tworemaining axes. These moments, I., I., and I., are used todetermine the part's principal moments of inertia and principalaxes of inertia. The MOIs are mathematically represented by:

5

S= f (y 2 + z 2 ) lm,

S= f (z 2 + x 2) nm,

I"= f (X2 + y2) elM.

where x, y, and z are the distances from the basic coordinateaxes of the CM to the differential mass (dm) (Figure 4).

Rotated and releasedto actuate pendulummotion

dFixed at base

Figure 3. Inverted torsional pendulum.

Mass products of inertia

Along with the MOIs, the products of inertia are required inorder to calculate the principal moments of inertia and theprincipal axes of inertia. The products of inertia, P1 ,, P..,and P,, are mpthematically defined by the following integrals:

Pxy = P. X 'Zf~mS= P . = f xz dr

S= Pzy = fyz & nm

where x, y, and z are the distances from the basic coordinateaxes of the CM to the differential mass (dm) (Figure 4).

6

z

CM X

dx

Figure 4. Differential mass with respect to the CM.

To experimentally determine P., P., and Py, with the NPI,perform the following steps for the x-y plane, the x-z plane, andthe y-z plane.

a. Record the MOIs (Ix,, I,, and I.) that weredetermined during the basic MOI testing.

b. Rotate the test part to an arbitrary axis(remaining within the x-y, y-z, or x-z planes) 60 from thecoordinate axis (Figure 5). In order to simplify thecalculations, a 450 rotation is suggested.

c. Run an MOI test with the test part at thisorientation. The resulting MOI values (Iy,, I,, or Iyz) providethe MOI of the test part with respect to a new coordinate systemwith axes within the x-y, x-z, and y-z planes of the basiccoordinate system.

7

z

ZY Go

le

@00

X¥X

Y

xYFigure 5. Arbitrary axis with respect to the coordinate axis.

d. Having calculated I., In, I=, I", I., and I,, thefollowing transformation equations provide a means of solving forthe products of inertia (Beer and Johnston, 396-397).

= + Cos(20) - P sin(2e)2 2I• I•+1I I• - I

= 2 + 2 cos(20) - Py. sin(20)

Iz= + 2 COS(20) - Py sin(20)2 2

The calculations are simplified by using 450 as the rotationangle (cos(20)=O and sin(20)=1). After rearranging terms andreducing, P., P., and P. are solved by substituting theappropriate values into the following equations:

a

IX; + 1Yp =2 I•÷/_/IX2

P=- 2 IXl

IY + 1rPy = MY ZN 1_ y,

3P'Z 2

Principal moments and axes of inertia

For every three-dimensional object, there is a maximum,intermediate, and minimum MOI about the part's CM. These threemoments are known as the principal MOIs. The axes about whichthese moments act are called principal axes of inertia. Theseaxes define a unique coordinate system about which the productsof inertia are equal to zero.

The principal MOIs are calculated by substituting the basicMOI and products of inertia into the following determinantequation:

XX-I -P. -Plxx,,xi' z

-PzX - PZN IZz-

The solution to this determinant is a cubic equation, whose rootsyield three values for I. These values, I1, 12, and 13, yield themaximum, intermediate, and minimum values, respectively, of thetest part's MOI.

To determine the orientation of the principal axes, thedirection cosines (a, b, and c) for each axis must be determined.Direction cosines are the cosines of the angles between theprincipal axes (1, 2, and 3) and the basic reference axes (x, y,and z) (Figure 6). The direction cosines are calculated bysubstituting the basic MOIs, the products of inertia, and theindividual principal MOIs (I,, 12, and 13) into the equationswhich follow. This substitution yields three equations withthree unknowns. The calculations must be performed three times,once for each of the principal moments of inertia.

(In - I)a - P1~b - PJc = 0

-PYxa + (Iy - I) b - P•zc = 0

-PZa - P1 ,b + (In - I)c = 0.

9

kz

ki ~ -r

Figure 6. Direction cosines for principal axis 1.

The three calculations result in three sets of direction cosines:

(1) a, , b,, c,,

(2) a,, b2, c2,

(3) a,, b3, C3.

10

As a check, substitute each set of the direction cosines into thefollowing equation: 2a2 + b + c = 1.

Each set of direction cosines defines a principal axis (1, 2,or 3) with respect to the basic coordinate axes. The relationbetween the principal axes and the coordinate axes is shown belowin Figure 7 (Meriam and Kraige, 589-606).

z

3

/

2/

22

/X

//

3

Figure 7. Relation between coordinate and principal axes.

Procedure of operation

The procedures to measure the CM and MOI of test parts arerelatively simple, but must be carefully followed in order toensure accuracy. Before operating the MPI, check for correct setupof the entire system as detailed in the MPI Model KSR330-60

12

instruction manual. The initial start up of the system is as

follows:

1. Remove all objects from the MPI test platform.

2. Turn on the MPI, the gas bearing pressure, the aircompressor, and the computer system. Allow at least 10 minutesfor the console to warm up before operation of the MPI.

3. Execute the KSR program. If the program is notinitiated, the rotary gas bearing system will not be supplied airby the compressor.

4. Press any key to display the main menu (Appendix C).

5. Select the update test information menu and enter theappropriate information. It is important to update the test partID before each test performed.

6. Set the gas bearing pressure for the test part. To doso:

a. With the air off, mount the test fixture and thetest part to the test platform.

b. Turn the air on and turn the pressure regulatorcounterclockwise until the bearing pressure gauge reads zero.

c. Slowly turn the regulator clockwise until the testplatform and the test part float freely on the gas bearing.

d. Note the bearing pressure level.

e. Turn the regulator clockwise to get an additional 5psi on the bearing pressure gauge. WARNING: Do not exceed 95psi on the bearing pressure gauge.

f. Turn the air off at the toggle switch to lock thetest platform in place and remove the test part from the fixturein order to prepare for the test sequence.

Calibration

Individual calibrations must be performed for the CM and theMOI. Both require the use of a calibration beam and weights(Figure 8). The calibration beam must be installed with holes A,B, and C in the qOadrant between the +X and +Y axes. Thecomputer will prompt the operator to place specific weights inparticular holes on the calibration beam (Figure 9). The NPIsystem calibration essentially is a comparison of the measured CM

12

Figure 8. Calibration beam and weights.

Figure 9. MPI setup for CM calibration.

13

and OI values of the simple weight against their theoretical CMand OI values. After the sequence is complete, the computerwill display that the calibration was accepted or rejected. Anaccepted calibration indicates the machine is operating correctlyand will provide reliable data. If rejected, the system isfaulty and a diagnosis must be performed to find the source oferror. Possible sources include: floor vibration, air drafts,touching the NPI during testing, improper system setup, etc.

Measurements

In order to measure the CH and OI of a test part, theweight of the part and the estimated height of the part's CMabove the test platform must be entered into the computer. Theweight of the test part is crucial in obtaining accurate resultsand should be checked before each calculation is made. Theestimated CM height has only a minor affect on the actualcalculations of the CM. The measurements consist of three steps:

1. Tare measurement.

2. Part measurement.

3. Calculations.

Step 1: Tare measurement

The tare measurement is perf irmed to eliminate the testfixture from the test part's CH i ,d MOI calculations. Duringthis measurement, the fixture to be used to mount the test partonto the platform should be attached. Test fixtures should befabricated to mount to the test platform (Appendix D). It isimportant to mount the test fixture so that the defined test partcoordinate system aligns with the test platform system. If anoffset is present, it should be noted and be accounted for in theCH and MOI test results.

As with the calibration, individual tare measurements mustbe performed for the CK and the MOI. With the fixture in place,press the moment display button off and then on to zero thedisplay. The operator then should follow the screen prompts toinitiate the tare measurement. The computer will take readingsfrom each quadrant and print the results. All subsequent partmeasurements will compensate for the test fixture's properties.If the fixture is to be placed in a different configuration,another tare measurement must be performed for the new fixtureorientation.

14

SteD 2: Part measurement

The test part now should be installed in the fixture andpart measurement selected from the main menu. Again, the CM andMOI tests are two separate functions. For each test, thecomputer will prompt the operator through the sequence and printthe raw data.

Step 3: Calculations

To obtain the test results, the calculations menu should beselected. The program provides the option to calculate the CMand OI separately or together. After selecting whichcalculations are to be made, be sure to verify that the actualweight of the test part and the estimated CM height are enteredproperly. These values are crucial to obtaining correct data.The computer will perform the calculations and print the data.The MOI is given about the test part's CM and the platform'scoordinate system.

Conclusions

After following the procedure to measure the mass propertiesof a test part, several conclusions were made:

1. The positioning of the fixture is crucial to obtainaccurate results. It is necessary for the test part to bereferenced to the pivot axis of the test platform. If thedefined axis of the test part is not aligned with the pivot axisof the test platform, an offset distance will have to be figuredinto the results from the CM calculations.

2. Vertical components of the test fixture must beperpendicular to the test platform. The MPI is incapable offactoring the lean of the vertical components into thecalculations. Therefore, the results will be erroneous if thefixture is not perpendicular.

3. It is important to update the test information beforeeach test. By changing the test part ID each time, the resultswill be labeled appropriately on the printouts. This is veryimportant when performing a series of tests.

4. Each time calculations are done, the mass of the testpart should be entered. This will minimize the possibility ofhaving the calculations based on the wrong test part weight.

5. The MPI must be absolutely isolated from any vibrationin the surrounding environment. Vibration isolators were addedto the described MPI system.

is

6. A test fixture may require the part to be attached insuch a way that would cause an offset between the center axis ofthe test part and that of the test platform. If this is thecase, be sure to attach the part the same way each time so thatthe offset is always in the same direction.

7. The maximum moment allowed due to the offset of the CMof a test part is 60 lb/in. When designing test fixtures, thisrestriction must be kept in mind.

8. Accurate results are obtained by running both the CM andOI tests together and then performing the calculations for both.

The MPI calculates the MOI results about the test part's CM. Ifthe CM was never determined, the MOI results will be based on theCM of the last part tested and will be wrong.

16

References

Beer, Ferdinand P., and Johnston, Jr., E. Russell. 1977. Vectormechanics for engineers: Statics and dynamics. 3rd ed.New York: McGraw-Hill Book Company.

Meriam, J. L., and Kraige, L. G. 1986. Engineering mechanics:Dynamics. Vol 2. 2nd ed. New York: John Wiley and Sons.

Space Electronics, Inc. n.d. Mass Properties Instrument ModelKSR330-60 instruction manual. Berlin, CT: SpaceElectronics, Inc.

17

A~pendix A.

Accuracy of the MPI

The accuracies of the MPI are as follows:

CM error for 100-lb part with 0.5-in. CM offset

Bearing/machine tolerance ............. .. 0.001000 in.

Sensitivity error (0.003/part weight in lbs. 0.000030 in.

Linearity error (0.03% of full scale). . . . 0.000180 in.

Max uncertainty this example ......... 0.001210 in.

Moment of inertia

Basic accuracy ......... ............... . +0.25%

Tare MOI (typical) .............. 130 lb-in2

MOI error for 800 lb-in2 part:Basic accuracy. . .............. 2.0 lb-in2

i0 s 0 0 . 0 . 0

Determination of torsional pendulum physical constant

The calibration constant primarily is a function of thespring rate of the torsion rod. A calibration weight is placedat a known distance from the center of the test platform and theperiod of oscillation (To) is measured. The weight then isplaced at the center of the platform and a second period (T0) isfound. The difference between the two readings is completely dueto the change in MOI. The 1401 change, I, is defined as I = WR,where W is the calibration weight and R is the offset. Thecalibration constant then is determined:

C = I/ (T.' - T.).

ARoendix C.

KSR main menu

The main menu of the KSR program appears as follows:

>>>>> MAIN MENU <<<<<

Fl: Update test informationF2: Part measurementF3: Tare measurementF4: CalibrationF5: System utilitiesF6: Calculations

<ESC>: Quit

Select function from list

20

Mounting of test fixture

Any part to be tested must be interfaced with the testplatform by means of a test fixture. The fixture must befabricated to fit the hole pattern of the test platform. Thispattern is detailed in Figure D-1 shown below.

+¥Y3/8-16 THREADED INSERTSI DEEP4 @4.0 DIA.4 28.0 DIA

\+ /

Figure D-1. Mounting pattern of test platform.

21

Appendix E.

Manufacturers' list

Space Electronics, Inc.81 Fuller WayBerlin, CT 06037

JUN-AIR (USA) Inc.1303 Barclay Blvd.Buffalo Grove, IL 60089

22

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Reports Section (TSKD)Commander Brooks Air Force Base, TX 78235-5301U.S. Army Health Services CommandATTN: HSOP-SO Dr. Diane DamosFort Sam Houston, TX 78234-6000 Department of Human Factors

ISSM, USCHQ USAF/SGPT Los Angeles, CA 90089-0021Boiling Air Force Base, DC 20332-6188

U.S. Army White SandsU.S. Army Dugway Proving Ground Missile RangeTechnical Library, Building 5330 ATTN: STEWS-IM-STDugway, UT 84022 White Sands Missile Range, NM 88002

U.S. Army Yuma Proving Ground U.S. Army Aviation EngineeringTechnical Library Flight ActivityYuma, AZ 85364 ATTN: SAVTE-M (Tech Lib) Stop 217

Edwards Air Force Base, CA 93523-5000AFFTC Technical library6510 TW/TSTL Ms. Sandra G. HartEdwards Air Force Base, Ames Research CenterCA 93523-5000 MS 262-3

Moffett Field, CA 94035CommanderCode 3431 Commander, Letterman Army InstituteNaval Weapons Center of ResearchChina Lake, CA 93555 ATTN: Medical Research library

Presidio of San Francisco, CA 94129

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Commander Italian Army Liaison OfficeU.S. Army Medical Materiel Building 602

Development Activity Fort Rucker, AL 36362Fort Detrick, Frederick, MD 21702-5009

Directorate of Training Development

Commander Building 502U.S. Army Aviation Center Fort Rucker, AL 36362Directorate of Combat DevelopmentsBuilding 507 ChiefFort Rucker, AL 36362 USAHEL/USAAVNC Field Office

P. 0. Box 716U. S. Army Research Institute Fort Rucker, AL 36362-5349Aviation R&D ActivityATMN: PERI-IR Commander U.S. Army Aviation CenterFort Rucker, AL 36362 and Fort Rucker

ATTN: ATZQ-CGCommander Fort Rucker, AL 36362U.S. Army Safety CenterFort Rucker, AL 36362 Chief

Test & Evaluation Coordinating BoardU.S. Army Aircraft Development Cairns Army Air Field

Test Activity Fort Rucker, AL 36362ATTN: STEBG-MP-PCairns Army Air Field MAJ Terry NewmanFort Rucker, AL 36362 Canadian Army Liaison Office

Building 602Commander U.S. Army Medical Research Fort Rucker, AL 36362

and Development CommandATTN: SGRD-PLC (COL Schnakenberg) German Army Liaison OfficeFort Detrick, Frederick, MD 21702 Building 602

Fort Rucker, AL 36362MAJ John WilsonTRADOC Aviation LO LTC Patrice CottebruneEmbassy of the United States French Army Liaison OfficeAPO New York 09777 USAAVNC (Building 602)

Fort Rucker, AL 36362-5021Netherlands Army Liaison OfficeBuilding 602 Australian Army Liaison OfficeFort Rucker, AL 36362 Building 602

Fort Rucker, AL 36362British Army Liaison OfficeBuilding 602 Dr. Garrison RapmundFort Rucker, AL 36362 6 Burning Tree Court

Bethesda, MD 20817

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Commandant, Royal Air Force DirectorInstitute of Aviation Medicine Army Personnel Research EstablishmentFarnborough Hampshire GUI4 6SZ UK Farnborough, Hants GU14 6SZ UK

Commander U.S. Army Research and TechnologyU.S. Army Biomedical Research Laboratories (AVSCOM)

and Development Laboratory Propulsion Laboratory MS 302-2ATTN: SGRD-UBZ-I NASA Lewis Research CenterFort Detrick, Frederick, MD 21702 Cleveland, OH 44135

Defense Technical Information OCC Dr. Christine SchlichtingSelection Behavioral Sciences DepartmentCameron Station Box 900, NAVUBASE NLONAlexandra, VA 22313 Groton, CT 06349-5900

Commander, U.S. Army Foreign Science Dr. Eugene S. Channingand Technology Center 7985 Schooner Court

AIFRTA (Davis) Frederick, MD 21701-3273220 7th Street, NECharlottesville, VA 22901-5396 LTC Gaylord Lindsey (5)

USAMRDC Liaison at AcademyDirector, of Health SciencesApplied Technology Laboratory ATTN: HSHA-ZAC-FUSARTL-AVSCOM Fort Sam Houston, TX 78234ATTN: Library, Building 401Fort Eustis, VA 23604 Aviation Medicine Clinic

TMC #22, SAAFU.S. Air Force Armament Fort Bragg, NC 28305

Development and Test CenterEglin Air Force Base, FL 32542 Dr. A. Kornfield, President

Biosearch CompanyCommander, U.S. Army Missile 3016 Revere Road

Command Drexel Hill, PA 29026Redstone Scientific Information CenterATIN: AMSMI-RD-CS-R NVEOD

/ILL Documents AMSEL-RD-ASIDRedstone Arsenal, AL 35898 (Attn: Trang Bui)

Fort Belvior, VA 22060Dr. H. Dix ChristensenBio-Medical Science Building, Room 753 CA Av MedPost Office Box 26901 HQ DAACOklahoma City, OK 73190 Middle Wallop

Stockbridge Hants S020 8DY UK

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Commander and Director Col. Otto Schramm FilhoUSAE Waterways Experiment Station c/o Brazilian Army CommissionATTN: CEWES-IM-MI-R Office-CEBW

Alfrieda S. Clark, CD Dept. 4632 Wisconsin Avenue NW3909 Halls Ferry Road Washington, DC 20016Vicksburg, MS 39180-6199

Mr. Richard ThornleyILS Manager, APACHEBox 84Westland Helicopters LimitedYeovil, Somerset BA202YB UK

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