!!!!!Glossal Immobilization to Metallic Beam at Hyperborean Temperatures “I triple dog dare you” !!!!!Jean!Wang!and!Zachary!King!BENG!221!October!28,!2011!!2!Table&of&Contents&&Background!and!Motivation!........................................................................!3!Model!and!Assumptions!..............................................................................!3!Model!1:!!1ID!Homogeneous!Model............................................................!5!Model!2:!Nonhomogeneous!Model!with!a!HeatIloss!Term.........................! 8!Conclusion!...................................................................................................! 10!Impact!and!Future!Work!..............................................................................!11!References!................................................... ................................................ !12!Appendix!A:!Analytical!solution!................................................................... !13!Appendix!B:!MATLAB!code!..........................................................................!16!!!3!Background&and&Motivation&&Glossal!immobilization!to!a!metallic!beam!was!a!common!thematic!element!in!blockbuster!comedies!through!the!1980’s!and!1990’s,!and!it!remains!an!important!comedic!tool!for!screenwriters!in!Hollywood.!Here!we!examine!two!landmark!films!in!the!history!of!glossal!immobilization!to!a!metallic!beam:!!1983’s!A"Christmas"Story!and!1994’s!Dumb"and"Dumber.!A"Christmas"Story!depicts!9IyearIold!Ralphie!Parker’s!Christmastime!adventures,!from!his!encounter!with!the!school!bully!to!his!family’s!Christmas!Eve!feast!at!a!local!Chinese!restaurant—the!dogs!got!a!hold!of!the!Christmas!turkey—to!Ralphie’s!inevitable!encounter!with!the!a!real!Red!Ryder!BB!gun.!One!of!the!most!memorable!moments!in!the!movie!is!a!scene!in!which!one!of!Ralphie’s!friends!convinces!another!friend!to!stick!his!tongue!to!the!metal!flagpole!in!the!middle!of!winter.!(The!scene!can!be!viewed!here:!http://youtu.be/ZLZj3zOUZNs.)!Within!a!few!seconds,!the!unfortunate!boy’s!tongue!has!become!frozen!to!the!metal!pole,!and!he!screams!and!wales!until!the!fire!department!shows!up!to!free!him.!Dumb"and"Dumber!contains!a!similar,!though!admittedly!less!realistic,!depiction!of!glossal!immobilization.!In!this!scene,!Harry!Dunne!has!driven!from!Rhode!Island!to!Aspen,!CO,!with!best!friend!Lloyd!Christmas!to!return!a!suitcase!full!of!money,!and!now!he!sits!on!a!ski!lift!with!Mary!Swanson,!the!woman!with!whom!both!men!have!fallen!madly!in!love.!In!a!moment!of!pathetic!abandon,!Harry!notices!frost!on!the!metal!pole!of!the!ski!lift!chair,!and!he!sticks!his!tongue!to!it.!(The!scene!can!be!viewed!here:!http://youtu.be/Iwhpvv2KpsQ.!It’s!pretty!hilarious.)!Again,!the!freezing!process!takes!only!seconds.!As!children,!we!have!often!found!ourselves!wondering!if!these!depictions!of!glossal!immobilization!to!a!metallic!beam!were!realistic.!Lacking!the!vacuous!courage!to!try!such!a!thing,!we!waited!until!graduate!school!to!investigate!the!matter!further.!The!goal!of!this!project!is!to!evaluate!these!two!scenes!by!creating!a!simplified,!mathematical!model!for!glossal!immobilization.!In!this!report,!we!define!a!1Idimensional!model!of!the!tongue!in!contact!with!a!metallic!beam!below!the!freezing!temperature.!We!present!analytical!solutions!and!numerical!approximations!performed!with!MATLAB,!and!we!ultimately!show!that!our!model!demonstrates!the!mechanics!of!the!glossal!immobilization!process!but!does!not!match!the!depictions!of!the!process!seen!in!A"Christmas"Story!and!Dumb"and"Dumber.!!!Model&and&Assumptions&To!approximate!the!mechanics!of!a!tongue!in!contact!with!a!metal!bar,!a!simple,!1Idimensional!model!was!created,!as!shown!in!Figure!1.!!4!!!Figure&1.!A!1Idimensional!model!for!glossal!immobilization!to!a!metallic!beam.!(Image!courtesy!of!Warner!Bros.!Studios)!!Table!1!shows!the!constants!selected!for!both!the!analytical!solutions!and!numerical!approximations.!Thermal!diffusivity,!D,!and!length!of!the!tongue,!L,!were!found!in!literature.!Critical!freezing!distance,!Lcritical,!was!chosen!to!be!the!depth!of!a!lingual!papilla.!The!rational!for!this!distance!is!that!the!saliva!at!the!tip!of!the!tongue!must!freeze!completely!before!the!tongue!becomes!immobilized,!and!this!saliva!should!be!present!at!the!tip!of!the!tongue!to!about!the!depth!of!the!lingual!papillae.!Once!frozen,!the!saliva!forms!to!the!contour!of!the!tip!of!the!tongue,!creating!a!physical!immobilization!to!the!metallic!beam.!Tpole 0 L x)= T(x,t)