PointofSeparation Oncethecoverrotates30°,ittransitions fromrotating aboutafixedhingepintoacylinder rotating onan inclined plane,pointO'.Thecovercontinues rotating aboutthispointuntilthereaction forceparallel to thebasereduces tozero,Figure9.Thecentrifugal forceholdsthecoveronthepointofrotation untilits centerofmassmakesanangleof58.5°withrespect tothetracking mirrorbase.Separation willonly occurwhenthecover's centerofmassandthepointofrotation formalinenormaltothebase.Thatisto saythataslongasthecover's centerofmassisnotdirectly overthepointofrotation, thecentrifugal forceistheonlyforceholding thecoveron.Oncethecover's centerofmasspasses thepointofrotation, thehingenolongersupports areaction force,andthecoverreleases alongalineartrajectory. In hindsight, itisprobably fortunate thattheplanewasinclined. Otherwise, astheparallel, orfriction, component ofthereaction forcesreduced, thecovermayhaveslidtowards thehingepinandadversely affected thefly-away separation. Analysis Approach Theanalysis ofthecover's release wasdoneassuming rigidbodydynamics. Theinertial coordinate system wasselected, whichusesthenormal andtangential directions. Theequations ofmotion pertaining totherotation ofabodyaboutafixedpointweredeveloped. Theseequations weredeveloped usingthedynamic characteristics ofthespringplungers andthecover's geometry, asfollows: theapplied torqueatanypointintimeisequaltothespringforcetimesthedistance between thehingeandplungers. Thetorsional springconstant isequaltotheapplied torquedivided bytheangleofrotation atanypointin time.Usingtheprincipal ofconservation ofenergy andequating theinitialpotential andfinalkinetic energythemaximum angular velocity wasobtained. Themaximum acceleration isobtained bytakingthe maximum torquedivided bythecover's inertia. Assuming theacceleration islinearanddecreasing, theareaundertheacceleration curveisthevelocity fromwhichtherelease timeisestimated. Usingthebasicrelationships theangular velocity and displacement ofthecoverwerecalculated byintegrating theareaundertheappropriate curves. The centrifugal andtangential forceswerealsocalculated atthehingepointusedtodevelop theloadsand frictioninthehinge.Thefollowing twocaseswereanalyzed: Case1.zerog,environment: noairresistance, orbearing friction. Case2.oneg,environment: airresistance including bothfrictionand formdrag,andbearing torquefriction. Analysis andTestResults Thecoverrelease analysis andtestresults areillustrated inFigure 10.Inthe0gcase,theanalysis estimated acoverrelease timeof80mswithanaverage angular velocity of14.4radians persecond. The testresultsshowsthatthecoverrelease took100mswithanaverage angular velocity of10.47radians persecond. Theanalytical prediction agreedtowithinapproximately 20%and27%respectively. Inthelgcase,theanalysis estimated acoverrelease timeof104mswithanaverage velocity of8.2 radians persecond. Thetestresultsshowthatthecoverrelease took120mswithanaverage velocity of 7.52radians persecond. Theanalytical prediction agreed towithinapproximately 15%and9% respectively. Theseerrorsareattributed tofriction inboththeplunger andhingeassemblies, andbasic modeling assumptions. Thismodeling wasdoneassuming planemotion, i.e.,atwo-dimensional representation versesathree-dimensional problem. NASA/C P--2002-211506 71