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(7) :. ': '.. .:; -:~. -" -"'" :--,,' . . : ': '. ' . ", Abstract' \. I. :.. ". •. ,.... - ~ .... .. \. -. ,.. .'. .. •. .... ., :. .". ' , .\ ! ,. ' : ,'. \. ".. .. ". " ,' ~' -/;. .~. I. " ,':':,::,:.:.',~:. ,. : '.. . ·' ...T.:~. :& . . .... .;'.~. . :. ", . . ' :. ' , ', . '" -. . '. ,In', Canada's ~orthern .Regions · 'floating ide sh4i'ets are of~en ' used'. , • ,': ,.,~;::' . . . . . -. , . .... ... '. . . '. '. ... ". " ',:.'. ,_ ~ as I~oii\ds .for ' vehi9ular t;oaffic, incl~ding 'larqe 'tru~k~, an~ ~_~".' .' ". '. '.'< , :'. ~ways for' airct"aft~.. 'operators ha~e " found,,' that: : a ~r;tioal . sp·eed. :,,;, ;' .::. ' e~ists for movement over the~, ro~ds ~rid. runway~·. . Movement over '." -, . , . the ice she~t. ~t', .th~s· crit.~ciai- spee,d · c~u~es ' ··ia;-ge .'· .~~~litud~ W.~B~.~ : t~. be generated in ~ the . slieet . near the load. .' Thus, . it . is 'very . ' '.. . . ~. . ' •. i ' ..important that. . operators avoid this speed'. · . .......--... . '. •• ' :- .. _' t ' .. .. . . ,,~. :: " .. I- .. .'. .. ,. .. ',. .. ','. ,. ". '. ' . , '. '. .-,. ,-.'. ' ,. '. ... '.. ;.. t. •. '. .. oj. . , . . . .. ,. .. '. ". '. ',.. '\. '. -. '. •. E~e~~iment~l work .1~~!:l been d~ne ' o~ . ~\is- ph~riom!!ric:m.' ~ a~~.:' .. '.. •. '. .. ', . .. " ". ,,. .. .. .'. :. .. ' ' . ~ .-. :.;. ..:,;, ;". :{:~','I. ''''~. '..1. \. <:':. " :.'. . "' ."researchers have developed theoretical ·m eans , :'t o .deterfnine thi~ . ,:,' :', . . ' c~itf,c~l '~P:~~d!,: "'lVnt'i l qu~te : ~~ce~tlY "(mid .1~80S~):~·~~~~:~~____ b~d, ,be~~. "', ' ~. .. ' ,'. '. ,. ' .. " ..no ,.· mea:~ure'ments 'or J?r~¢lic:~i~ns ' of th~ . w~:e p~tterns geh~r~t~d-'+~~~ .::J .:,: ': '/ ," lc:;:~ sheets,.',and. the ,11mited , predictions y~re ~Qnflict-ing.' · . . ~. ; . ' :: :'::. ,:. .. . :' '' '. \-> ' .~: ', : .' .',' " ,',,; ''' : ':: ':: .'.',' .' '..' " .',. . ," '. ""'''< , ",' '.' .' ,,' ~n '1:hfsi :',thesi's,' ,an .exper·imenta~ "'approach ' ~ae(taken , t;es-deterl1lJ.ne· . ' ,. ~~. •,. ' , ':,.' '. . . ' the wave' pa.t ter{ls gen~rated in ' "a:-: float~ng ~ce_ ' sbee..t .by, a m6vi.nq ','" - " ': , c, : ,. " lo~d·.. ,Several ¢lifferent moving :loads were used, ·and the ice was .' . . :' ,. ~ ~ 1), "~' : :'-'" '. ', '" , ..1~odelled in var.ious ways: . EG/AD/.S model" ice! .· styrofoa~ ·she,e..tinqJ ' " . ':; ;: .: . ', ~ ._.,--- and ,- po1-yet-hy-~~hee1::ing -'-:--Th.eoret1ca~ .predictions of ehe, , . 'll .....,~; • • \ . , • ',' • , I . • ' , ' , . patterns w.ere, ~_lso produced. "T17.e generated p~tterns ~greed · wi t~. ' ',~,'. ' ..the 'llredict1ons ~ . " . .. " ' . ,'" ' ~'; ,. ~,. •. • •. ~" ,. '\ .. .. .... .:. '.. t. .'. .. .. '.. .. '. '. •. . ' ..... , ". .. '. '\....,. •. ' .. ' .. ". .. ,. "_ _. '.. .. •. I. ••. ". . ; . ,. t,...... .. ... .. •. ..',. .. I. .. •. .. ,. '. . ',. •. .. '. .. :. ". ,.. .. .. .. I :'. , .. ~.. : ," ••. ~~. , ~ .!. _. , ........... .. ~--r-'. ..... '.. _. .. • ". >;, ' . . -:. '. ... ".,. .. .'. " . ).. ". ... . ,. -. ..'." ,. ,:. ,". ,. ,~ ::.. ,. :". ~". ". , J:-, ,' '.. ': ~~ ' - '.'. '. -:. .. , l.. '. •. wa~ ·a:l.s~ . d~~.~in~d that .'1:he' d~fl~ctlon '~ep~essio"ncaused: by ~~e)o:ad , ~t' ~sieeds less, ~~~n ~~ c.x:it~:al chanq~d shape'· .~~h ,... , {t. .. ','. '. . C'. ". -. ,. .',.. speed. ' , The, ~ests also indicated that .t he c,r itical ' speed :'is ' muc~ '. of "sheet' ~h~racte~istics . '. :: m~~e ' a ."f~ctioh' , . , '.than iO~d . ~ ,. :'. ~haracteris~ics ~. -. ,. '. i,. .. ". , f ,. .. ,. ,". -.. ". .~.. . . ,,:-4.
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(9) /;ji~i'fl :~;j~j~~7'j~~~~:~~;;:(;;!;:'::1'~?P:1!:~:?0~:~~')~J:'!f~fj~!t::1?:;;,\~~i;j);?r~';,~i~,)~;~;':?;\:'~T:'?:$:i~t;r:;{!y~". ", ,,'. 'I. ,c, j ' " ",. ,',. • , ', \. ". ,. , ,', , ' " ". il"!\~ ~! '~:', ,:,,'" • ,,'., : ' ,.. ' '\.. " ,. •. •• t. .. ,', ". .~ :. .. ". .. ". '" ' ," ". ~r t~,,:::,: .'. LIST. .... , LIST ~. , , " ,. ". " " " '". '.. -. ,. ". ,' -. O~,~ {AB'~S , ~_. '1ii"J"I\'X~ ~1 ',; ,~f~i '. ,,. '-::',. i:i'-'~",:. ~~f:'<'" ~ ~( ...." , ' " , .. ':',". ' ,'. :. ,',. .. ' ... i,, \.....: ". , 1, -. q '. •. I. .- 1'.1'.- ::;, General"" . '". ..". :. .. S~Op~(' O'f . ,w.~rk,,~ . '.: . ' .. .. ". .. .. -.' "CHAPTER. ~l}:;::. ~·!". L·: ,.'. ~~L>',,)f '::•.',.:,. '~. .. , 0'. ~'.!;':,~,. .. ... •. '. .. .' ,' c,. ', ". .'. ,. ,,' .. ':. :'.a,. .. o. " ., ,':. 'f ". ,,'.' .. .: .;. " ,. ' I. ". ~:.. , " ". :~,. ". ,. '. . ,'. ~~ " " , ', \ ,' . . ,' " ~.. ,. ,'. ,-. • ". •. ~. ,. "".. .. ,. . 33 ,. ". ,. .. ).9. '. .,. .. ;". \. .. PRED~CTIONS'OFGENERATED, ' WAYE PATTERNS :. 3{. ... .'. " '. ' \. w~v~ :.'patt;ern.... .'Predictions'." :. ". ". ". H~~h""s~eed' A~'" i~e '- Br~~~i~9.·. '. '.. '.4 :'. ,.. ~..... :,. ", .. ,q. ~~~1" - ~.1•. r~J.' _". .. " G~ne'r'Eil ' . . .' :. t$:~~,{' ~. .. ". ,. -,. t. ' :"'L/ 0 " \. .. ~.;..•,,_#,. ~I. .. I ... .. '. . ..... . '''EXp'e~ime~tai'. 'wo~lt· on critical ' speed ," .. ,2'.4 .:,. '. ,,'. ,~. .' .. . '. ' ,. Theoretlcal' ,Work , on ', Criti'cal ' Speed. ..::: ,.:' :. :.,. -. '. \'~ ",'. \'. ~". ;;}. ,. l:,\":,.. ,. ". '. '. ,. :. 2.2. ". ~-;-'-:.:'. \ \. .:',. ". ,. -.. .... ",'. -General. "~.~': - '. '. CHAPT~R: :, 2 :. ~:J-t • ~. ~~:{~.";... .. ". ... ". i: ;::., :', ','. ,- '. .,. .'. ". ~". ,,'.. \,.. ". ". CHAPTER l ' :;, ' INTRODUCTION ' .. .". '~'t::. ,. ....;... ~~~~~'1~,:<: :;, . ',' ' " ," , '::', ~i'\ .' ''. .. ". '". ':,;': .' ~,;~. "!X",;' :,:-. ". ". ". .,. . ,.,,'. _<. '~QF 'FIGtnU:~ ' ". ' ,' , Y""~. ,. :. <'. NOMENCLATURE. f -. ",. . :.. '. ". '.'. , ",. ," '. -~~.~F'Co~~:''': ~ ":.' ",','::, ~,'" " ~" ~'>}.~lt. .. .. ". .. .'. . ... .•. .'. } ' . , '". ,. ''' " ". ,. 3~ '. " ',. .. " ,. ,. ". . ,. -- -". \. ,. \ ". ". ". .' ,. '. . . "r \' ": ~ . ,' '. . . , ~ ,' :. ,.. .... \ :. '. ., .. ,. . ",' ". ' ," .. ~,. ',. . ." .. ..... :.. .' ,. '. ... " ' ". ,. '. :. ' 0 , :' . , .. ..". 'r. '\ '. ~ .". .'. :,,'. \. ;.I. ,~'. ••. u.~ ... ;:.' r ' . , \ . I~:..~;t· ...' ~' •.; ·'riJ~f(~;: ~;-:h,: .f~;~:r::~'" t_~. d'," ~ . -\~''';'''. ... ~ !:~("~ ,··~t),:,,~ ~~:'~i d·i~~..;.. ,,:$b~~~~,,: \t-.
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(14) .it~'ij~'(,~'tf.. <: ·!)t;'~J(,~'\'('~~r:;i;~\~~;.ry"~:':'In~c~r/,;~:?,ri!'~1~~)/f.7":·~~~~(~}·;~~~t:711~·PT'Z;!i".;\" J:~''!04~~ ';~ :~': '. ~~~!. , '. '. "' ~S~ -P~ , FlGURE~ " , . :', " , ". ' (.. ~. •. .. ~:~~ :~.' ~L':· ~.:. '--. ~ :'. ; '". j". ,:: :~~qur~.:.7 .:. : .Cri~i~~l. ~p~e~ ..fC?r. .... '. p.:fq~r~ ,2". ';:!:;~'-'-:., ',-. ',~ ~'i9ure. ,. . .- .-. '. < ~ .;'(. .. .. \~'. .. va~~~~~ .an~ h.:. 3. ~.,~.·:., t· ' . ;hqi,r'e6 " t{:~.~> " .';, Fi~~e . 7..,,; :'. : Detie~ti~rl' 'Aml'i:ifi,c~ti'~n ' Factor, . v~rs~·~ VIVc. .. '~:.'. . R/,·. d". " ;-. ". . ....... j.". t":<:~~. ','..- :' .\~'. ___. ,.. ',' ~ ::~l~.);~. . . " . ,. r. :,~~v:e; pat~~;rn,~ ·!frE!d;'~!~d .. b~ . S~.i~r.ot.. : ' · ,:':';·~.,:;(::1. '.·wave ,p~ttern.s , :pr~dicte~, .bY·'Davis '.e~'. ,.~. 'r-~ ..,. ' :.. '. . .. . : '.. ..' '.. 'l. .:. .",. .. ~:.~:/,:.",:,'. : · ~~~17e , ~ , ...:/ay.~· : l?a~~~.~Ge:~~e~ry: ~~>':: '.>.'. ': , :'-.Fi'gUre '-io·:; ~~ivi~· ·, wedq~ · · · '. :: ':' '.:, ;. .. c. t .' .. '. .. ....,. .. .-. .. " > '.. ./. .. ... ff>~.: F.i~e.12. ~::~;:..":' .. •. " .. ,. ". ". •. ~:' _~,.~__.,'. ·"': :'~: "':~;.'..:,~'L·r.~:·. '.. .. . •. . ••. 3 1.1.1.1. 4""" " ....:. ". ". •. •. wave:pa"1;~",,~ f!>rPlate';i th tnertia. '. ll.7". 1'3. : ·':.Fiqure:, 17,. l~O 1.2'1;. 1.25. . .'. - ~ ':'.. .". ._'._. ¥'~~~.,.':'. ' , ..' .- r~~~~'. ~.~'." '.LO~d C~ll output ·.at·, :c~~t~ca~ , .S~eed ." :tl,,> ',"', " (J-a.t :'uary 2, ·1987) >- ". ': .. : .'. ~ty. ". ~i, ~'?'!~. .' . : ,). ,' I;~:.,}j ' . ', . ·, :~~A _ ....... . 1:16 :'-- ", ' ';' .~~~. ;\'.~.:: , '. ~ , ;.. ".'- .,'. ,: :,..( .~.~.',' ." ·I?e~ember.' ~~~,:. " 19~~ '.'.. '.. ...... ." '.' ., ' ,~:. ' ''}. , ~. ~:}'.~:..-, ': '. .' i.' Fi9-Ur~ '.18- ,-' ,.' wa~e~",in' ~~~ :; ~heet;' at' '~D -': :~~i:\':'>:',:·. ': .:. : ~~qU·~~~.i.9 '.-: .::H~vekc;af~·: ~~·s ·i~,~~n.~~'.-: ?v'er ..Ige. ' ~d!.<;.·,. ". '1.1.9 ", . "'- '. .' .":p miumatic' rfube.-AcV. Model. ~;i/:" : '. . Fi~re .. .. 2P~~~:~~it ". <'.., '.'. :' ."'i::~staric";GVer - .." ... ,': ", . }~e .,' '.". ... '. ; "·t.~. :;. ':" .<~. ... , i,~.-5: ..:~...:/.:.',:: :.:.:,. :..(.;.,:. .. ,cti~i'ca~: '~P~'~d ~e~su.s: Sh'e'e~ Thickness Fiqi,re .14 piotSh~~~q ;Shad~zone . : . ~~:", .: ··~-~.i~r·~ 1~ ' '. ':.:~~rfa~~ T:~n~i~'n- w~v~- Patte~;; y:·~.'·,'·, : ".; .' '.' ":Fi~u~.~:·,.i6·,' .:Air. Ce1-l " Mo~el ....... . , ". j.F: '. '~'.: ' 1i~re. .. '.,. . , , ~. '~'::,;~(). ..... :t\\'L"~<",,- '.~ " ,' : Fiqu~~.· ' ~( '<~~i~': ~i~'~~ ~~~~e" ~~~t~~~ :" ~N~: ~n~r~i~) ~,'il!. ' : ...>~~. 1.06. . .- '.:H. ·~~rs~: ~,Ni, ,~ -: ~. .. .. .~. :,:::f.; " . .',i'~. ~. . ' ': .. ~~;;~~,~, . :: .Fiqure, .s· •. ~; ' ./~~. ....106 '.. •. .. , " .: · . ~l~. 1.05":. ' . '. l. '5. ~~? ~':'. ". . , ~x. ,. , - Crl tica~ .Spee~:r. f~.r .variC?us . H: and .L · .. '4 ,. . '.. ". .. ,. .·,Fi.qur.~ .' F~~~..encv versus V~hicle Speed . 'F iqure R/A 'versus V/V' ,\. :k::. l' !< '.. : ,:. '.. /'. ..... 1.27' ..... <:~,j; ' . ,"':;::';\~. 128. .. .'. '129.: ," ', <,"_). ,J:'. ,:'"; 'J_:?".~,:!_;,r'·.~):'1; ... 13(( .'. ,.. " . . ' <~"J. . '... l/~. , Fiqu~a·, 22 s!iriqle IIn~~!>TireHq~el~ <.'use~in: . J{~ . ...', - _. 131 ' .- ...'.,'.... ;:;;:;1; f~!.\.L,·· "}.' ',>.:: ,<, < :':>~ ': . '.•.';'.~ '. ,,' .., . '.,. '.' .' . . <'. !f·:,-· ... ,· .' ; , ..<. .,' .:.',:': .' ,,' " ~::· ~~yrO~~~\~h~et.. :r~~t,~ . :' ·<·: ':.. ~. .". •. • • • ....
(15) .. .. F:r~S ; ·f~ont~d·.. r.. Lis'r". OF. ". .. . ". . , : ...:.....~ .. ;. c.-. ,. ". .. ..' ". \. ~. .. . . .. ,. :~. I.. . . .•. .. . :... .. .\. e,. ' •. !. :...P:i~~23 ' .' Roller .Model. Used: i~' Styrofoam' Sheet Tests ' \. ... ... :. Figu17e. 24. Lap. Fiqu~e 25. r;:':"..... .. \. ~ '. .'. ••. ~. ... '. ;. .. •. I. •. ••. Join~ in styrofoam ·.Sheet. '.-. :,·t.~}.-.·~.·:·' <·· , ' ': .. F·. i~'.~·r·e ':I. sen~Qrs '. .. - ... . 'sa~tiona'l ' ·.~i~w. :ot' ~pp;~a~u~ 'for TO~ing MC?~els:. .' 2~8. . s,t yrofoam Sheet·. T~sts. 31. . _,. .. ~;,,;' I~~. . Figur'e '. •. ,:;(.'> ".. F~~~e .' 35 -. ....Fi9l;1r. '~136. 0('; \.. . . . ,.,. ~L:',':: .:. ~utputs. I?efl,e ct!6ricsehsor (~.o ;A~jacent. Channels). ,. ~\>':" '.. ~ ·~.~i:.,-f.~,f,. '.'. ' : 13? 138. ' . .•.••... .. .::. 'fi. ~..' , \i ":~!. 140 II. ~,. •. ' ,; '.:",. • ; -, .. ,'z::,£. "./:~. 14·2. •. ·Load gell < ? u t p u t . . . - .~~11er Resis:tance' :. "149 .. •. . •. Figure 38 .. open wa.t er 'wave pat;tern.s. ·151 ". t. .:. >, :.t~. • . W':-~. ':' '~~~5. \,·~~.,·.:~1,. 152. I. •. .. ' :.~.·>~;i. ,':. I. ..150 .. '~i:~. /.1~. 148 .,. Deflection . Patterns' below' .. Critical Speed .. I. ".}J~. ' .. F:i'gure ·37. .'. .:,:, ;~~. 141 ·. ..... : ·F~~re.· ·39~ , :w~~.~ · , patt~'in1il 'in -:p~iY'e~hYlene . ·~~!!·et 'r. . :' :·.I.:~·~. 136. 13!. Styro~oam Sheet ·. Wave ·Patterns.· from. '. ;:::. ). : , Roll~r" riefl'8C?t:i tins' .'. .. 'T'. ~i·/:'. ·.:, . . .. ~\« .'. ~4. '. ·1 35. \.'. ~~. TW'0 ,'T ire', Daf1e.c tion ·s .. ~f;r/·,~ ' , ,~ ' ~_ ' figUr~ ~;'.. '. :.:.. 134. r...... Photo showing. ~~'d:;,",:' :' , I,,::~., F:i.~re : 32' ~:,:'.'. 132. •. 133 .. .~i~~e ·.· 3~c. ·.· .si~qi.~ .· T~ra ·~e~l~q,ti·on~... ,;-. •. I'. F~:f~' :: .... ; . Figur~., 29 •• : .~e~lec~ion sen.~or· :,9~tput' . ~/:L··< ".'. •. 'Loc~n ~f ~efieytion. Sensors' O~~Sheet. F~gure 27 Figure. . '.. Arr.a~g.~~nt (;f ' cuts ' in ' Sl),eet. •. FigUre 26. ~;:." .•. :. .. . '. ~ ..... ..:,· .·,~.;,·.;:_,~l.;~r:. l;,:.{.-;,' ...' '. < ~< ..,'\l~ Ql. ~ ,~,:,. ~:.<.':. ' • •. lY;,. )~;/;~.,. I. I. . •. ". .. i~;1.'. .. rr-.. ". ·.. '. ", . ...; '. t~~:. ·" · ,',;': : . :" v'~" '" I. .i·..... '. ,I. .. .. "l~'~. ... , ' ,.. , '. ~. .. ." ,l<i>. .". ,. ". .. < :j;~. '. ,.,. ': ' df~. '.\'. ~. .. ". ,. .," "ii;'. .;'. :\:,~:. *' . ,,., .. i~tQj~i~~~}·,.:,i~~;i~':!;(,~>+;g'hk:;'£~:';' ;G.:·: ;:~·')t,:;:j'~ ~'i:';~;. ');~\'<i;:(~\~ji.~l{~" .i'$>:;;;c~,i,-;,;~G;'~;~.
(16) ... .p. i' . '. Cush-ion ~i~~ter. ,Dc. , ' .. Depress~o~~ .Diam~~e:. ','. -.. .. .. .. Energy'. ~. .. ". '.. ,...,. Tr~nsmitted. .. ,.. o I. .. ,. '. ~. ..':-. ". Characteristic. L. r.. ~ngth ', .. , ',. Fr9u~ ,N~er: " ' " , ,.j :. " .. ". . ", ,," j Pres~ure ' " • .'. ... '. •. P' , ". " :' ,. . . ', . iJ ': ':. •. •. . ', . , '. •. ".. .. 1. .~. .. ". ". -:Towing , ..R,sist;~nce ' .. .- .. R. / '. ". ', -'. ". ' .'. " .. ". ~ ". sur~ace .. v... .. .. 'Interface- , Pressure. s. ~. \. ', .. ;. P. .I. ". #. Tension ... o. .'. Velo,c ity. ,. t I. "critical. ". 0 '. Yr. '.. .......'rr-.. "',. ,". x. 0 ". ,.. •. ... velQcj.~y. .,. t,. Resonan~ , velqcity. .'. . .. '. '. ... ~. Weight, ,. '. ". l. t ,. .' 'D~sta.nce (WaVe,' 'Pattern GeometrY). -. -t', •. .' • • • .J. ,. ,\,;. . -. o .. ". ". '. , ' 0 :' •. ". ". \'. ,;. ". I. .,. ". -'. '. ... •. ~:.. . ... .". ,, '.. .. ". -.. .. " ,. ~. ... ::.~~. . :-.~:.". ..... .-. \. Water Dept·li " , :4 ' , . , Spring . 'c onstant. ..'. I. ... . ...... .. ,-. younq i s·... Modu~us. E. '.~ ' .',:, '~. <' , -. ,Energy Absorbed. '.. . ,... ·: .:' ·~)S -,. ". . ... : :. " ". ".
(17) (:t'i~~:~:,o""?r!t~1';r,?\,;:::;,,;:":ir'C'(:':':':~Wi;';' )~2:~~:~;?~~~(:'~ ."~;':i)1;:~;:.;:l~~;;:l;t)}yr:~i:'~~/~~))~;:~(~ ~t;:..... dN~~~TURE(~ont~d'l. .. c.::_~:, ....' .. . 't. fi. ,f, . ' I', .. ':i~~~. , •.. q. ' G'~~itati~nal Ac:~eleratibn' - -. h. ,Ice Thickness. ,- .'/.':~~\. ". '. ' h·w. ..: .. -.~~\;.~ •. .. '.. ... Load. q. ~: :"~:~~. \(. ). Wave Number. '-,. '": ... .. " .'~. Time. t. .. ':.~. ~'.. Velocity ,Vector •. '. ," ". x, y,. Verticai 'Deflection of Ice. ~ationary . cart~sian. Z-. .. ~eiociiy~ iotent.ial ".. a. Ice Sheet :'Density' (mass/ar'e a)'. "i. .. ". .. .. / ,'. 'j .. ,. . ,. PW '·. \.. .. ... V. " '". .. ~. #. '. \. r. '. .... . '. ,. ,~.~:. ,. "t.,. <,. '. ". • .'. .. -.... '-. Densi, ' ".t y ,' of " ,Flu~d .' 'Water ,,?ens1ty -. ,p f , .. r-. ~. . Density" of"I,e e. ,ip l.-. :_!"& .. ".. ~. ,. .. Vehicie. A. ,. At' ,. ~eiqht. .. . I. ~~lEmqth '. .. ,". \.. '_. 't. , ~: ' ~. Circular Frequency ". ,... .. ,. ;. ;. ~. : "'~,. Coordinate System. ". :-;"". "'\-,. .. Angle. '0. ... ,,;-. . ;"'::" ~ \'. ,.. w'. .. .,:-,. ~. ',~ ~~:~~. I. .;. ,:,,;~. ". ,~-.~~j. v. Wave Hei9ht~. 7\': , .'. :\',. ,.;rj. '\ ., xU. ',.. It..
(18) .. ". ... , ', '. .. . ,. -. .' ... '". 1 :--. ". ~. .,. , -:'. ,. .... '. ." .. \. \. ,. . '. . ..>-...., : .'. \. ". \". .-"':" .. .: '. .. '.: ,". '-. ~. .\.. r '", '. \". I. .. , ... '--........... ... '. ~. , CHAPTER l ' . INTRODUCTION ,. " ,. :" ' ". ... ' '! : ~ .. --. #. ., .. ... " ,. .~. ". ','. .". ... .... " ". • • oJ ',. .,. . ... . ,. .". ... The' ability ·to ·transport ~ople and' goods over ' floati~g ice' . , . .. .. :, ',. ':. ,. ... .... ,. '. ., .. ·. ;:. .. '.. ~. " '. '. '. ,. ,. ' ". •. '. J. •. ~fl~ating .. '11. .. ' .. .". ii. ... ' . ... •. ,'. -:'. . ' .. '. ". ;. w" ,. '. •. ... ... ". ". .. '. '. .. ~ :.. •. •. •. ~ .. ';.. ". •. .. ,. "'~ . : " ,. ", '. . . . ... ' :.. ',. : '. ~she·ets. , . '. '. '.. :.. ' .. .... _ -. •. •. •. ':. ,:. •. I. ~. ..... ". " :.. : ... ' ~~ I". , .(7,,. .. ,. ". '. .. .. .. '. ., . . , .. '. .. 0. ... .. 'f. '. ' .. ~ .. .:. . ... .•. .. .. .. I. ~. ' ., . . .. 'r. -. .. '. ,. I '. :. .. I. •. runways', '. tW~~ ' ccin:dition~ ' ' :~ust ... :. '. :. ,. : ••. "'~ oS. ' , ,'. •. •. •. ~. .. ' • •. ..... ,. .. . .. .. ". •. , ,'. .. .."'.:::</.::~; ' 'I~. . ..:~'~ _. .... ". I. •. ~:. _.,. ~.'. ~ ~ ':':~. .. •. ,. .. '.. - '. :. _. .. •. '. !. ". .' ..... oJ ,. t. ,;. .•. be ,consider.ed~...''!..' Firs't, the stati~ ,. . . . . . . . , :: . . . . _ ._ '. ,.. •. .. ". .. .. _. .. ,. ~,. :. ".. ' ". ,, ' ,. ". To 'predic;t ··~he . Sate use . of these.'·float'inq . ih~. · ro~ds and •. .. ,. ''-. t. _). '. .... .. ..,'. ~';" .~. ,.). •. . : '_~ ", ' : ". ;. :' •. .. .. ~. .... ,- ' ;,.-./. : . ... condition ~st. b~ con'sidered~. · ~ 'Th'is is' ~ bearing capaci:'ey : .' . , <:~; ..' .. " ... . ' '. " :' , ; . ' ' . . . ' ' . : .' ~ . . \. . ' - . : ....: . .' problem : and: invo'l ves': 'thedeterm'i,ri'ation of :the maximum sta1;ic or··· · . ..> /~. ,. .. .:. ". ;,::. .- : .. ·0. ,' ,. 'f ' • •. • •. ..... i~. . ~(.::' .; :. . ' .,. .. .. •. ,. ; '. .. ~. : ",. , '. ". ,. ' .'. ,:'. '. ' ,. ,. • • ••. : ~.. .. ,:. , ". .. '. '.';. . ,. I . ... ... :. , .'. .'. .'. . ~ . ~I.... ., ::. : , 0. -. ~ . : ..~ , ~~s~-.s~at~~ . loa~ .·~~.~.i~ .·~~~.e.~\~a~ ..:s~;PPO~. i ..~Ji~S . P~Ob~~~, .~a~~:...-'>. ". .':,< .~. ~.';f. ;;.::: ...... i ... ~'~:. ::. -,\. .. ..to . al.low . '-.conv~n'tlona~ :aircraft access to ... .. :~~,~. " .. q~111a~a foz: .. '. ". .. · sit~~ oth·erWise . -i~access.ib.i'e·. · ,". ". >.::-. .. ". ~~ads •. "Th~Y ': ar~' 'us~d ·by.-mi~i~q, . 'l~'~q_in~ ' ~nd" oil'. .. - :f loating": ice. '. ': ! '," ". --'. .. -~e~sible" , _: Winter ian.d inq .s trips: are' ~is~~ 's~t' ·uP. o~ · ' ... •. '.. " ," ',. . '. '. •. ·..-,. ~ .. '. • J. •. ...' ~ '·companie·~ . :t~ 'qet to ' s'i1:es- whi~h ~o~id ' b~ ot~e'~is'e . ". .:. •. iceroa~~ays,' liaye "been· u~ed in ~eve.r~llocations. : .. by .' a. !i'-;';a~he.r. ". '... ' ,'. •. is of .great importance.. ". . ::::e::~:;: qo:::~:~i:d~:::·· :::l::::::~:~n:: .:::~:~d . ... '. . -... ' -- ." ~. .. •. Nort~. • sheets in the Canadian. ". -l. ~.. · .. '. : '" •. •. ~.. been.. ~e' subject · Qt. much study • .: Kerr (19'15). has developed bqth, .. . '". , .~, :>.:;. . " ,. '. .. ... l~. , J. '. ". .~ .~ :. •. ', '. ••. •. •. ~. ". '. :. ~ ,,'. :.'\~. •. ' ,0,':.. ". :.. .. .. "'.~. ' . . : .... -. =: . :'. ". ... / .: .theor~t;ica!'.. and .: .mRiri~.al · formulae. giving :.th~ ..allowable··load " ".' : '. .: ,: .~ '~.~5:;;:. ", ::,. ;~<~~. ~~ile~~cal ~ro~..rties,!~1:J,e i~~: i~e thi~es~, ·~~d : . . . .j;~i ' ... -',:" (in':' ~• .:c~'s~ ~~t : lung 'cSurat;lon ~oads' ;~~et:~ .q~~ep : can c~me . ~'rito :- ." . -: . '.:'? :;;.;~ .:baseil :. ".. _. -. •. t. ,.
(19) .v·~.:t~:r1Vl:'& ~ .... . .,rl~'~~l~~:,'Ir::i.~~'.•~ ;.;'f4.~~!l..~ .. .... ~. or? • ':"'~Mr.i\!.."i' -, ,';,'';T.:tiJ! '~I tlt;-Y ." ~*-'~t~~'l'l.~', . .... .. t~\}.~ />~,~~~ fr:··~;:·r~~{i~~:~~l;:':~t.:: , ~:.J:J,~j ~..~~";- .~ tf.\~'i~t-:~;t':.?~~!~. 4\..t.....,,::~I~;')~i.~·: .....F\ . 1'-< ~. ",\.. f'~(~. .. ". ... ". •. ', ' ,-. ','. 2 "f .'. ,, ...,. ,. ~,. :. / 0,. ,. ... . ... "i '-. '. ~.. :.,.:. I. .'. , .' '. ..... ~,.'. ....... .... . . ". ~.' ". / : ',. •. () .. •. ;J.:ft). ,. ~ .I. •. . : :.. .. .: ". .. ". ... ". ,.~.. " ,;'". /. 'II. ,. ". . •. se~ondiY, · the dynamicc:.ori.d.:tiO~ ~"'~t' :be ~~onsidered.~ . :. ~a~s' .. ',:',,:/;~:. m~vinq. over· a float~l1c{~ice she$t.at"'high' speeds', generate', .'. ..' .' :.:f. ie/sllee!: intii~ vici"ity o~tha ' .. .' . . '. . 'load,," ,At' a . certain "critical, speed" ,'the' ampli'tu~e , o':f th9s'a .' . .. '. ,... ,.. ,~. ,':. •. "". •. ~.. I. " '. :. .. ' , '. •. ,',. ". •. '.. ".. '_. \. .. ". .. ,',. ••••. ' . '. ~·.,; ·I ,'.. for: the , sallie load •. ' Thus, ". it ca,n b. seeri th.at"a ·l.oad which is. l>.;' ·· ~. .•... a. maximUm, ,'and. det~rinine~ ' to 'be, .sa~e 1~. a " Bta~ic. .Coil~~ti~n \qould ~be. ·r· • •~. ~-w.1 .' L' •. , ',. :;-".. ..., ".' ". . . . . \' -. 'c:iuite. '. ::;. !. '.. .,. ·'Sev~ral , . ispects ..... ... w. •. . '.: ,:. ".. . \,0': ::.. ,.. ';. . ,.. .. ' . ":'" . '." '-:..,".' ~'. '. .. . .... '.. ,I'.' ,:' . ~,':. .1: '.:' . '. ' .. :. . .... ~ '. ,. . ,' . '.. , .1'. ot this 'critical' speed phenomenon will be ' : ,'.. •. •. •. ,. ... •. . ,' " , ,- el(amined ''in .. ' . 'tliis' thesis •. .--,;". <.. unsafe:. i.,~/· ·· ~'."j" :-.~~>. .' .~. ... ;. " ,. if~t ~er~ . t~:.t~avel\~ ~he crfttc~l ' ~~eed·. "" Alt~~~9h ((,'.. t~~ns~~rt o;~~ato~s·~q~~er·al~~..·~~· ·t o 8.foi~. ~h~" crit'~~~i" '~p~ed, . ;~;.:<~, ,.. ". th~" cari~~i~~:': ~~~,S~ ':' ~~ar~ .: ~as' 'r~~en~l~" used, hov~~~~af~' ~o ' ta·~~ . , • ;,-.;.:,\ ':' ~ ad~a~t'aq~ of the Ph~~~~~no~'." fo-~~ic~b~a~lng . putposa~ ~ .. . , :>.-". ..... ... \. ;~<:-:.'(' '.::. ~. . . ... ,~s·. ". , '<~{. '. ' ". ",. ~he d~fl~ction under ~e' loa~ is :\. .. . . grea:~.~st, ~~d.· ca~. be :two',t~ ..thr:ee: ~~~es the -~t~tiC defla~tion '\.. .wave!?. ',.'1. ~. -to. -. fl~iair~?;aVi;y~~v~s6n-~~. '" .. .,. t, " .0. ). '.<i:',. /. ;,..-. ,,' . ). .". ~"'.;}'i>fj. . .r.HH'/,' ·:;,"'* ...£_t~'1·",;'&;t-,,~;J~:J.s~i\. .",. ,. .. .. .' •• '. ':'. ... .'. ~. . . ./. .. ,". .. .. ~,;,:,;: : -.. -. '.. ··~~eri~~n~~lly·.·~;d ~~heor~~ical,iy'~'" i~. ,," ' '. ttnderstci6d. ,This. ~~;:'~;'.:.'t. ~.:. ' ..,:, ,,'..:~~~itic~i ~pe'ed. .. thesis. ,.,'.:' . " ;. -. .,.. '. -;. ' ~ell. ... .. :~ .:.. '.- :~:<~5. ,. :.....:;:;,:~'. :t~e '::;'l. a~4~, ~t th~" · · ... ,,".;'-J;~. __ '-'". .' f~~ .~ -~~m~c,~.~.:" ~ ~..': .-; ,. . _, . .:,;.;.':,) ;.:,;.,~:; I.' . ~~~~'t~te " ~QfJ,u~~_ . : • \/ .. ' : . : " ~ .. . . . . li.. I.. '", •. .. .. dOneOD. P\lenomenon ...a~:· ~~mo~i~:L:-~ersitY. ., ,". •. , " ., '. ' ",':. . ...... work. .. -:. ~ . ...:.. ". .. '. ii': s~il~. ~ot. 'r~pO~so~ recen~. ':'. ',!'" '., . N~t~onai . Resea~c~' .~ouncil: ~ s·. .,. ,. ...-;-.. Although m~ny ·:~ese~rch~rs · : have .·_s.tUdie;d 'this pheno~enon. ..'. ~.;,.}.~ .:.:~~:':";.". '.'. .'. ,/. '.. (\.;:: ~,': -'.. ~{',. .. :. • " ':,. .". t. •. .. •. ' .. ,. •. •. 1. •. , 1. '. •. ,. ,,.....:. ". .. '. ~. ~,: ":V"-~;"1....~t.~· I~ .. ,.... fJ '~~~;~t~;.:!~; :":,~,, ~'i'·;:)i-~r..:.~·':.,; ,: ,%~·;'tt ';. ':'.~~" 1,l;_~ .•} ~ <: ~",. ' ''\1:'lt~;:!':'':;:\1:'' \.~~/~ ~ij 'ft : ~ ;,.!. fj.::·· ; ~~\ "I:~ :'rr.f.fr"·~M)';~! ll~f~f.~~,j':' :.; r~\~ ;:~/;. :~t;" .;g:').~' ~ J'..\lt'~~ r'~:i1~:'(~r,: ;.~\';'.!'~.~ . .~. . '~~l(.:J,'J:jYt;,,,' -;. .. . , .ON" '1!~" .... ,:"..'~~~';'':.:('"'' ...... ~•.~~~~}l ,..1;,.. ..... ' .. ~ ,,· .. ··t !l \...::,.' ,~ I~;}.~W.·;;:' .. ·1..... !. of. •••. -J . ....... ! ' .. '. ~..
(20) !l;:(!:\,;::~:'~i ~'~:;~;1~?rir:1:;?:~:~~}"r}";ft~':c;'t:!'~~5'i7:1.:';'i{;~" <~:"~i::! ;'7f~fs'~~~~~l';rW~: ~~i?','r~':':'?!;~;t~:~'iI';~ 0". _. •. •. '. ,. '. >.'.. . ' .' '. :. - .. 3 . '- . ;. .. •. ~ ,.. . '. understand. '.. wa~":",,indUC~bY a, '-;OVin!ll~ad, .:';a must ~!1';~~~~d h~~ha. .\ :,:.,::. ". '\ ,' ot. ,. , :00: •..•, '. .~. ... ,. '\ '". Under the action. '.:' :'.' .. ",. :t :r:. \. .. .I .. ,. . .. .. .. ,. :. '1". ' .. 'fl~at~ri~>ice ' sh~ee~ by .a ~o~inq ~9~~. . This th~s~s w~l;L st~dy ''-. \. I: .:'.,. In pre~io~s' studies; ..," ,. 4. ' ". ,. ",;. ' . ~.f , .> .. . ' • . •• :,.. •' :. :':',, • . '. ' .. •. ,. '.. ". .'. . .. '- '.. ,. ' .. . '. J' ". . '. . '_. obtain' ililpr~ved c1ata:~:, by ' ~s'inq :'mli~tJple ··s~risor~ ,•.'. '. It ·.'w ill.· ~:ls'ci'. .. ' '" .'. •. ' ,'. - .. t -. ,". •. -.. ~.. ". I. •. I. l ,. •. .,. . . .. .. .. • .'. .'. :\". '. .. ' ,. .. .. ... . : 1 .' ;. . " ''\.'/.~ ~. .. ~t1;.empt . ~o-p.redict: - ,~ese' "q~ner'a~~d :' wav~ ·,.,p. ~tt~rn~. ·. T~~' 'onlY ' ':" '.' . :. . .... ,'.' . ' .. , ". ". ,. ••. ..... •. •. •. ,'". ,' .. .. .. :. ,. : '.. •. ". .-.. .'. .. ~. • '. '. ~. •. : :,.. •• J. ':... 1,. .. ,. .. :. ". '.~J.. :' ~ .. ... ;~.. h\. 't.".;,~. (1'9-8~)~) -~'a~d" :'~re ' ~onfl:i6ti~~~.· "·~ ~n. · p~~d·i~~~·~r .·, · · . '~~': '. . .:.>f,j. . fampli~udes as ·well · tis .th~· ~rest· .-,l~atter.n~? ~plit~de :.,.. ,. . ...... ",'. tJ. .:~--:. .. k:~~. ·p.rf1d'ic~i~ns~· '.' ~~w~v:er,· . ~~ii,' b~ ' ~xPe<?te~ . ~ ;1?~. ·p~.or ·du.e . t6 : . . '. ::," :'.: . ... '. '..:,:1.-:'.:'; . (i~~si~~~i~~.·. · an~. ':no~-:-li~~'~r ' fa/~t'o.rs~ . · b.O~·. :~f :·. ~hi~h'; (a;e .'·' i~~~e~.. ' .... .L,~ " For .this p.aBoil. ' i~~as ,de~ide~ :tC! con;"eritFat~ol1 he wav~ : ': " t;. .;. . '. ,, ' ... 1t. .. '. . '. . crest; patter.n.s ., . . ~ .. .. ~~... /f. . .". .. . \,. . . .;.. . . .' '; : .' ... '.' ·: :··.C.:~. ... : ' ,;. ". ..... '" _. ". ... ". :..... '.. ". '. ,. .. I'. ;:'-".: .....~~;: .~' ~.:. ':~h~ "th~si~ ·iJ.~~9.~lni·z·e~ int~: 's.ix>na~r(eha~~~s~. · ·, :. · .'. ., : '. '.,. ( . :. .. ". .. . \:: ' :. ... .. '. : ". •. .. • ,. •. .. ••. 0 • • ·•. ..... .. ': .. , .\. "". ?;~":" :-'-' .. .: "': ',': '.. .. the ·critieal ·sp&ed ·phenomenori• •. : ," on. •. J ' .. ). .. .. •. ". •• •. .,. ~ ' ;':-< ""i..'. .. ., . . . . .. .. -.},:'; :- .,'.>.'. '.:........:..~·~p~~r .- . ~', i.~ .. ~n' :l~~r~du~tic;n~' ..~ha~~~r • '. . . •. . .. ; .. .. ,1\';;[. ~b~~8 ~..va patte~si, ~d~aiL~. , i.~woul~ ~~ke 1;oprec1~~ttl1e~~a~~'. ,'. .,'. ' ... I. ". " . ~nd ' ~~V;:~ et · ~i. .) ".'. ,~. .... .' ·. :.pr~<;lic~ion~,·· in :~he litei:"~~ure ar~ . Ctuit;f!!' r.ecfint~'JS~iribrot ,.c.~~83). " " ". ". \. " l"'~:' :. '. u~;inJ"inqle "~nsor~. TJli;' dat~' wal. n~~'~ffi.Ci~nt~o : ' ~ I ' <.-':: -,~,' de~~,~i~~, ,t~e ·. ·w~~;e::p~~~e~~ · .~~~~te~ ..· ~'. Th·~ '~~~~.i~· .~iii· ~~t:Y-~·to. .. ' .. \.~.-'. ,'. ,:'.. ':.~)'. \.:>;. -: .. .. ' " . 6 :\ ". ~ .. : ...... :. ,, ' .. . . ','. , ' . . .~: .. . . 'data 'on .wave generati.on in . floating ice. she.~ts was ' obt~in~.d ' . ' . r. ; 'L". "j}:. ice 's heet de:forms · under .the moving load. · · · · ~~at ,.is ·· 'to .'s ay, we .. ' " w~ve ' pattern··.· qeneration 'in iC$' ·sheets.. ". ·!L;;:,,:;:;~. . · ~~qui~~ a~'' un~er~t~nd'in~ o;:' ~hii !w~y~ 'pat~~~s ~enera~~~ i~ ' ~ .. \:. -. fee. ".. '". .'~ ·: .:'r~;{f. . :..... . '" ,T',~:' . ... ... . " ( ; 'I ' . " h6w :' a'~ .~i~~in~ ' ' :h~et fai~s". •. .. '. ,. .. .2.:is. ~:. iit~~a~i~t!<~e~+~wJ ..".'; :~. "',:',''~:Jr ~~. ".. -"_.. .. .. .. •. , .• . .,. .Tranflport ·.over 'iee is . ': . ~ : :,:. :....:.:: : ~ ';:,:,~~; . .' . _. . :' :<' ;~ ..:., .: '.: " . ', ',' '- :::'" .'. , . . ...,' ·"\·.:r:~~. ..':-: : .:": , '. " . " ;.' . l .. ·. .·.. ·, . .·. · · · . ..."'... fri:~ ; ;<"'~'. : . ~:" , ' '..:. ~.~~e~.a~ . ~~ ':'.~~ .'. ¥q'~ ~l?ee.~ :~.~r ;~~~~.op · Veh~~~e . · l~~,>~ "'~~~ , ~~~ak~~~.•:·.'_..:'.· ': ~:' . ~;.Xt~ ~~:,C:~. · :". ~'~ '.,". ~ a;~': 2,t~}~~.~i' ~lUi' ~" .: (t:;~'~,:\.~,:, .\\;\;~!!;'~~;:,\::':;ij· ,';;;:Ij'!. I;~:V; ~\~~;:~';.~t.... '~~J.~;,:r.Sf:':·: i\ \';~~f~~! /).\:,:~.:\.i~A~;(~~~{(:·:~· ·:(jS~~4;~'-.':: \:~:. .';::'~~' ~';'·'\;f"i;f·l~!i;" ~k,t,,~! l'f.f!.\ :f' '01 ' ...... :n ' ·'r{:;.t;, ,v] "''!. ::''-' .... , ", l. ' .- .. t.. ~~J It:~~(. f:' ''''''.~:. ':..."'~~~~-..:r.i '-'··~;t'l/.~{j. ~ ."'". ~.\~ '~.';. ~~. J. • •-. I.
(21) f~;:{i '~(0(·tr.);~;'~';: :j:'~~">SJ\';:'!~';';\~?{" ':" :0i;;'f:f~;'T~~;f~~~X;~t'y. i&~;,:~;:;;,1~~':t::rh':(':4)~'>':'"Y 1~:1'~'l" ':':~" 'l!~:";'~\ ;:t\ . _.. ... '~ ". .' ::' . -. ,. '. chapt~r : 3. _.. .. \' ".. ,. '. ". contains wave pattern . ~. ". ./ ". - -' -:...--.:.. ". ... , :. ". .. ,. .. ''. ,. . '.. 'predi~tions . ' .' ~ ~.. ',. r. ~.. .' ~.. ,'. .. ,. .. ', N'/;:~,t, >. ;. '. :. ". .:.::y. reported .in ... '. .' .. '.". :". Qfo. literai,;re~nd ~~~ some- de~elope~at. Kem~riai univ~rs~t;' FO,r - ~Ms, ~ ,i ,c e. Newfoun,d land... ,plates ' lllld'-:thin '.'~ia'"tes· ~ .'. ,.. '. •. wa.~, model,l~das. •. .'. '. _. .. •. •. ".. •. :ri. t~lck. membranes,. 'Tie var~'ous '~ode~s 'are compa.red ~. ••. .. . . ' ;;:~. •. ~:. ' ,' .>:!.. •. ')"\~~. J .. 1. .,,';.;;,. chapter 5 .describe'~ ' t~e ~xp~i!ment,~i ' ~ork' ·which. was done. . The , •. ... .experi~ental. •. I'. •. •. ,'-,'. '. :. :'. ... . _ ' '. . . " . .. .. rs:.. .. a~e. ·.Q.escrib'ed •.'· .. facilltie,s'. ,,, , ' .:. .. '. '. • .. \. '". . . '". ' .--.~. . ... . " ,-,>:. ,:. . .,. .' .~~.:~. .. ~xperilt\&n:t;s ". Eac,h . set of. :-.' ..'~ .",. .. ,. .,,' ,- , ". .. . ' .'. .......~} .:..,:·I,.!} .. :",:, /{.~~ ..", .. :.,:,j,:~~ ,. '. , . ~~e~ii~~.~ta~ ·.~~~~~~tu:~ ~~.~~'. ~~st~~ei: n1;a~l~~ .1!iO~~OW~~ br... . ..exper mental , procedures, ,presentat d SCUS3,.L.on .o f '. ' :' '. _ ' . : o;rl'.' and ,. . . . . '. . .. . . . - ': '. .. . \ ' . : ' . . '. .: .. \ ·res,.h ts ~ .'C hapt'e r 6 co~tains ,concl~sioi1s . and -.suqqeliitlonll .tor ~ 1" • ': . ' .. , . . . '.. '.. ,: ,-, '. .. '. ' . .... .. -. . 'r '. :'. ~. is ,tr~a1;~d . sep,a~~teiy· • .. ,. 'Inc~u4elf'iS ':.a .. d~~<?ripti~)n ot" the , ,:.. '.. :... ". ,. ". I. f'. '. f~t.ure .. _,' I. .:. '. .. ~. work .. ·. \. . .. ... ',.. ...... '. '.. ,' .. I. ... .. :. '. ,. ',. ". -. .. •. •. •. t'•.. •. . ~h~J?~e;, . 4 .t)~l~nes . th~ obj ~cti~~s o~ ·~he~e.~i~erita.l ' work,.:. '. • .. ... .. ..':, ,, ';~'''.,~;~ . ' .". ". .'. .. "". .". .:: ... .... ". .. ". ... ' . , ::.,. .. ': ' ;'. .. . ... .. :,. . '. . .. ~.. to •. ,". .. ". ". 1. I. . '.. ,. ' ". ','. ... ...... .,. . " -' ,. ... "". ~-:. . '.. ". .. .: ..:' :. . .;. \'. '.. .. '. ./. ".. .. ~. .. .. '.. )-. .. ... :. . .. .. .. ':. ,. ". ,". .:. •. -. ... '1. .. .'. ,. ,..,.,. ". . .. ,'. ,. . . . .,. ,. "'. 'i.ci t, : .,' •. . '. ;.,~.. .-' --'-.-~ .. ,-'. ."'". !.••j. '. ,. .. '.. .:. J . .... : :'1:~. .. '.. ~ . ~.;~ ' .. ! .. ,. .. '. ':' ,-. '-. ,.'. .. t.:"': t. , ., 0. ... '. .~. " : i~. .. .... .. ..... " ~1:. .'. .... ,...... .. ". ,. .. ...'. . . ; . .... ,.. .rr ', q:,. ,." ':;f'~.
(22) ·. .. " • . ', Or .' ......•.JHAPT \. ," ,. ,. .~'.. 'I '.. .. . .. ~ ~'TERA~. . ~ .,. ". REVIEW_,. I. 2 • 1 .. General. 1 .. ',-:',;:~.,.. 2. ~. :. .' " . .. ER. . . \,'. . ' . . t . ,,'. ... . ... .;. • . ' f. ".. ,. ~. ".', !. '''\. ••. .. I. ,:. .. .. . ',. ~. .. .. .". '. .. ~. .. ". ,. 1. :----. .... .. ••. .. '. .~. . ... ... ,. 'A i s~ationar}" load . restinq on a f~oatinq ice 'sheet. create~ -a. '. 0. ,. •. .. - .'. , bOWl.-sh~ped "depression" centered ' at ,'t he ·l. .oad .. .. If'he ' load moves " . . . . . .. .. .... .'. '. ': .' a~. low 'O'elocities, ..:8. ,Hqua$i-statlc"conditicSn ' exists . where ·'.the . i . :. p. .. .. .. ' .. .ff. -. ::. .. ... ..... .. '. ~. :. .... ". ... .. '. .. . • :'. .. ". ~. .. ". _. -:.. •. •. 0. bC?wl-sh~ped ·~eprefl1s.ion : moves_' witil ' the . load.; - -1;f, •. ~ :' .. •. •. •. , " .. l. .. ". • '. .. '. '' .. •. ~. •. •. • .-:. 1. ..... •. howe.ver, . .t~e .. _. '. .. •. . loa~ '~ove' s ' 'a. t hi~h v~io~i ti~s, flexur~l' qrav!t.y. wav~Ei' ·' a~e ' . ,' .... . .. . . 'I . .: ,. .. 6f the ' load. :In: ". .' . · ~~~~s. ~ ;~'~~di ti~~ ~ '. 1;wo ';d~~~l~~~' "wa~~' .·~~~s .are~ gerie~a~~~ ~." .': :'s~or~'. '. ' . ':q~nerated ·.' iri :tli~ : id~:' ~h~~t · in ' the'" vi~ihity ' . : '. · ." ~.' '. ~:'.. , I :. .: ' . ·. , ,. ...... ,. -;"". ,1'. :'. ~;.. -. '. ~. .. ~. :. : "' :. .. . .. :::-: I .. ": ' ". ' .. .. . •. .. '. ~, " : ~ :. ' i . .. . ,." . obse~eij · in. ... •. •. ,_ • . : .. .. '. ':. •. <'. ,. •. '. .. .. '. ,;. •. ;. ,' ". :'. '". .. ;'.. ,. '. .. .. . .. ... •. \. .. . ; '.. ' .. .. fol-low. ~t~; · ·.It has . been . . :.. ., } ,. '. •. '.. " : -. . .'. ". •. •. .. .. •. - '. .. • ~ .. f•. .. ", ". ~,-. ". . ~. . :-. .'. •. '.. -. .. .' ... -. '. ./ ."'.'.. .. . ~,. :. . ,. '. :', ~.~ .. . . .. . ... . '. '. .. :. . .. ,' .. ". .. ,. '. .. .,. ". '. '. ~. ". ". .. •••. :. . . .: .. . .'. . .. ". ·.a. .. ,. ".. I.,. ~.. ' ... .". : .. .. .. ... •. ,. ". ",. ~. ',. '. ••. . ,. .... \. .. •. .. ,. _. .". ~. . ". •. •. ". ,. ..". .. ,. ,. '. .. .. .. ... . '. ", \. '. .. •. '. .~,. . . . . . . ...,. .. •. .. .. '.. .,. .. .. ". .. .. ~. , ',. ' .:. .. ~. .' ' .' . .~ .. ..,. '. '. .,. ~. .. '.. '.. '~J"~'. ,. /.. .. '. .. •. '. .. '.... ... . .. ,. "At[". ... '... ... ". ,':'. . ' ..... :< :" '~". '. ' . c. ..: ~.~~;. ~ ~. ': ~:.,'.: :~.::;".:;'". ... '<. .,. .. '. ". ' :' ~".;;~:~ ••; .' t '·,.t. ". .L..~ "'. F l'· 'J :..'-;l '~ '" ·~.. 1t \~~·~<'fJl. \ ..i,;tf ~~[~l"~ ' ~r~oI\.~~ ~t,,; ... tt~.;i'" · ~ll . ~'O!iJ ~ ". '''.'-J'-.f. ;. ... . ' 1I:ri'\". 4'. ~. ~.. , ''''~:l. :.. ,'< "C:~~·. '. .;. (,. ". . . '; ... :~.. .,'.". ,. ~"1(.. ~ . ~" ~! '({ l,.) .! 't .t ~'i!.jI.~ :~ . · J I',./ 1I" A"' 'f. ;.,''''''·''~;·(lr~ C,'; ,,;:r~· \; •. $,' ~,..) I~. ,. ;. •• !~. <A /\ ..'· .).• r '~ ( ~ It~J "" '~' l'; ..-.?'I "~-l~ ... ':\.' '1;'·.!.~Wi.. a~~~t ,, ~:. ~ ~, ~ . . l!l''' (' !./ t Y' i...· · \:'t~yP~;.:.· ~ ;~ ~"t:;.'J Lr.";-.~r:i.t~!V~;~~.~ : l J ~"'''.. :\', '.1. ,' ' .. -,. . . ','" . . .. ' , ,.,. ". 18 ..·••v:.yll.. . ' .J. .. ,.. .. ,. '. ... ..... .. ... .. , -,~"" !,. .~ . .. ';'. ' . '. . .. . " ; .. ... '. ' . . ' . :.. . . ,...... : .. ' .. . . , ' ., .... . ,. ;. .. ', ". ',". ",. .. '.. "maxi~~ ('EyX-e; 1977) • . '. .. . ....~: . . ,.. ~t:~. .. .. wav~s: .. (as well as d·et~ei:t:i?n ..'o t .1;he :ic$ sheet under theloa~).. .'; '..·is. 1.',. \. . - ., . . , •. .. .:. .. • ". •. '.. .:.. . 'verocit" 'and' at · this .velocity .the.· amplitUde ,·O f. thtl generateci. . .. ;~;~.: ..'-. .: . . ~<\. .. ~.. ". l~boratorY_ . ·. . , '. .... :,'. ,. by a load moving at . coristant sp.e ed 'are fixed . relative. .. 4. .. ' . '!. ';:(~,';. {"". .' .:' ., : ; . .. There ' is . a "cert~in ·cut-off.: velocity ·.below which no waves are ' : ., ' . .' '. .:',. , ', ... ,,', :.!.. ' . " "', . ' . ~ , . . ' qener~ted .. bythe :' moving . load. ~This velocity;; is' also ·a. critical . " ,. \' . :':,:.; ' . ~ :',. '. (mlit~~et ai · l986)·: that:. th~\iave""patterns .. ". '~.';~: '. .'. ... . -. ". ',.,.. :.. . 'to .i~ .. " ':.. .' ~. , .. ". I .... ~. •. . . •. • .. .. ~Emerate4. ,.. ". .. . . .. ". ". .. ... '. ..... .... '. the. field . . (Eyre, '1977-) - and 'in. : . ~xperi~ent~··.·. ..,. ,' .: .. wa~_el·enqth, · .low~requency -.~aves. '.. '. ': ...... ... '. '.. .' . . ::' . .. , ... . . . . '.:' . .... .' .... - : :. ' wave -l.e'nqth, hiqh·.·freqUency. waves' precede ' the: . load 'and lonqer·. ... ". '.. '. - J-. .. ' .:'. ;. ... ;. ."1..
(23) ,. •. I.!.!>~ ;; '. ~. •. ".. •. r. '. •. :>. ". ~! .. :/~-t~. • 1 -. /. ,'.. .. Theoret'ical Work on" critical ~~ee.d ·. . . ' 2.2. ",. :;";.. . ~.:' ,~... ,. i. .. ' ':." : I~~;'. - ... .:.. . .. t. .. .. •. .. ,. '...: '. .:'; ~.'t. . ,. ~6vi~c;:i l.oad :w as fil::st ·9bse~e.d. ,.. •• '. '.. I. .. .'. ' I.vanov. .. •. shor~lY. .-. ·II·. ,. '. after . the' .. ,. .. '.. w~:r;,. '. .. ' .~.. : ~' .:'" . . : '.. '.. , ,. ". .' . ' " -2 '. .. .. ':, ',, '. .. .. ':. .~. ". .... ". .. '.. , . .... .. .. ~. '. .. ,. '. !' -, :' . '. ,". ,. ,. .. '. ... i·. ,.. .. ". '. ,~. ..~:}~, .. '.. .,. ... ,.. ~,. I '". ----:-~-] :=-:...: .: .~. ,,_ .' ...c'-:'. ....... ,- ... ,:, .,' .... '. . on a . thi!l : pIa te :t;"es~inq on.a ·, Winkler ·foundation. . He" ;. ,. ",,. _. \-. .. .. .. .. .,. '. ....... ". .. ..... .. .. ". ~. .. .'. ; .'. :. iricor,reQtlY'. analy~ed .1:he· 'sin~larities "in ·his· results·'.and 'caine .~ ~,:.'. " ' .0 '. ". ~. ~:.. ~:'. -. , '. .,. '. #. ,:. ,,'. . '. ,. .. •. , '.: ~'. .- .. . : •. ••. ,". ,. ,~. ,. ,,". .'. 0. ... ~ ., ~~~'i~~ti~ns~ '~~er 'th~ load. ~~'~a~lie· ' infi~~te~ . Th'~S incor.;e~t . .~ . . '" ~n~~ysi~W~:S' ' po~rited' ~ut ' ~y N~V~l~' (~970j ~ .: 'Liv~~le'Y ·~~e~te~. t~e :. - .. ,. ,~. ,. ... '. •. .'". -. •. •. \I. •. ,. •. ',. .. 0,. ". .,'. -. - ",. '". '," ,. . .. ,'., "< .' :............. . . .. " ....: '. :.. ': " t "~ ....... .': .. :.\ ..:. " "' ,,, ', ~ ". :.'. ,. ',':. '",. ... . :. ,-. . ~:~. .'.. '.. water ba~'e : .as · a" seri~s of .ideal·. spri~cjs' and the aQtion ot·.'the . .. . -: . . :' , . '. - ~" .. -. .' . ..:. .... , - . ' . water 'on .thE. sheet . was ~epres.ented by -simp~e Kw:terms1 J( being ,, ". r,. .,~. •. '.'~. .:. ','.< :.. ':'. '.. :. '. . . ·i. . .... , . ' . • , '. '.: . • . . . .. . \. a· spring constant and w ~ . being the '.: vertical ·~ defiection ~ . The. :;~.:(. \. '. ·to the erroneous. conclusion that at velocities above critical,. :. ... distributed: .rec~an~la~·.. ipad trave~linq, 'at a .~~nst:~n~ . velocity·· .. '. , ' . 4,'.:. ,." ... ~>:~.. '. ... '.. i~~~·1~~f~~~:r~e.x~en~~--'-thI~ .s9'iu~ion'~'t:o ' }i ·~nl~f·~~iY~·-·.- ;-.'.-'. .. • <. ~ '':. . ..... ,. -'-'- ' - -Lr-c '. . ... I ,. bp and : down 'on. ",. .-.t. / ". .....<. ~. .,'. '. ' .. .. ." .'d~fiE!~tio'~ ~ '.. -\,-~'-'".-. -. .':. 'fo~ndat¥n ·.a~s~mes ' iC!undati~~" 'pr'es'su~e ~roporttPnai to. i,.. .. n. • ' .. ..'. ~ .. \.. ,' .. '. . -.;. ' ~h: ' resti~~'on a .' .'Wi~kl~r ;foundation. ·· .' T~e ..i.n:~iate ,'..... . ' . . . . .' .. ' ~inki~r ';'. .; '. "a. '. 0". \.. HOl~ ".(1.~5~) .. cons:id~~ed" ~ \~ad~ ~:9vin~ yer~ic~ilY'. . .. ., i. ~ (.. ". ... di~cu~:e~" ~he" d~fo~ation'" "~f'· ice ·~~~~B .~ '~~~in9 .lo~ds. ;. '.. ., .. ,.. .... . ' o.*". ·Assoc. -(1.946)'. ptlblislled :the' first paper which': ... &c. ~,. :. the Russiana' 6n · . ~n fce .S heet ·. by. oy~r L~~e. ~~~e;ja . . . .. during " . ~~x:ld: wai-.. .. - .'. "":-. ,. ',;' ' .. : - .~.. ". : :~. I. ,. . "';. ~~:. Th~ generat:i,on of ' ~aves in a ' floating, i.ca sheet induced by a . .. :.'. .:'~ ;~. A'. " . . " .~ <,;:~'~ ....-..';. ,,. .. ... ~' i!-· :.. J' ". ". ,~. ":I!..~~. •• '. ./. '........ ... '. .t,'.' ,. : , ' ,,'.. ,",. '. ':i', ;.. ': :.-:.,". ',:, . y.: ". .. .. ,' .:" • .'. , .. . ' ', .• ':. .'~· ,·· · · :~ 'A .'. . ". ~ inertia . of· the .' water and' the loa,ti was not c:.~nsid..r'd : and, . tb~s ... .. .:.>.~. ;i,~. ; ... fN<' . ·\e~uit~olStain4us~~9~i.. ' ioYP'; !'~: ~~ly:i;aC;"~ ~. ~~8id.~.d " , .. ' : , ~::~ if(~;.!:~·.. ~' . ...... ..·'.':<'i ~' . """. .. ...:. .•...... .,.:;, "~.-:'. \_ ' .,. '". >.(.;tj. ' . ...... '. '~ ~ i~'i)]~!}si,~f~:~:,~ ,~,;'_,L;,;",:',.::;;;;,,:'i);:.• :,LA.,.,. /,,':, .~.:';~" ;:'l)'X', :,~,; ; •. :j:.•.: ,::~;"/..',;;j~: ~J~ \ \, '" 1. ~ "~~';l!, , 1..~~1 ;~ . .....,1't.ol • .c;:..;';)~ '{ , t~·;4~'(.~' ~ft~ ·· " . ~.! ,.. .... .'. l'. -;h .1. ~... t.~~r.}I'1.,,' . . . h ,. •. .'i ',.,. .. t- -:-. :":' :' i· j.{ J J • •~.,~:; 1,,$ 'fV";~;~" · ' t,~·J~'~~.~\. •••. *'1./"' " -: i"\Co''r, "'~,ti ~.• ~ ·'':..''):ri; ~ f~ "'\: :.;tt"~ ~. "l. ..,.. ~ ~. •. ..... ;i;-.1 ~\~ '~l ~~ ' ~l i~'-tl~-"\ ,,,,-t ;. '\'I· I~";'~ .!" h"~""" 1-f;{jl~:tot.. - ·""'(t\~t><'.1'5·\\) t,; ,..~. ' j ' j'. w, -...t,·,··\tt"",•.t:.h#".
(24) .. .. .. . . .. . .. . '. :" ,. :". ' 1 °. .. . '" qUelli:attve .• ~. ... .. ,-. ~. J. at'bes~" .\. ... -. •. I. J. I. t. :,. .. ;L.:·. . ": . .. 0',.-. .. ... ,. .. ...,. .. .. ... .. '. •. •. '.. '. • • ,.. .. '. ... .... ". 'l:h'e :' respo~s~:. ?\'. .. '. ;:: . ", :'.' ..... '.:' '.:'. ~':_j.. ,. rio~( consi~er.eg,.. moving. l:~ad, .. :it.. fs·. .·:..,~'··.·d~~~rib:~ :·~h~· ·. ~~~·p·· ~~~~ :,:(:i. ~~i~diriq· . -. ineit·i. ~'. .. : .:.: .... . '" '.< '.,< ':"'; .. ':: " .' ".: ... :.... ~ I. .. .. •. '. ~ -"': .' .' ../ . . :~ .:... n~cess~~ to .. eff~ctS) . Of ' .~h~ >.... :' .' ..... : ..: . .... : ': "':': ',.; ......., .- ..... •. ,. base:.,w ith .equations of hydrodynamics • . ' .. .' .. .. ~. .. --.:.--- ---- , - -. ". -. . '. ',,'. .~. .. ' ;.. '. .. . .. .. ..~. .. •. :'. '- .. $. .. '. ,'. . '• • •. •. •. ' ," " .. c: ·. . :--. '. she~ts to,· w~ter·. ,waves. : .. floating 'iee. :. ,. -. ;. ;.. ". ': ~~. . :.;<, ..-. ....:~:. .:. ~.' ~\~. .:. oC:1. '.' .. '.,: :'~. li'q"u'-~~ ' ..:..' . ;".:f.-..:.): . . .:." ... .. ...;>.:; . . .' .. .- ;'.:. :~" :~. '. ..'.,'·. -~r.e·enhill· .' (18·87).~ .'. Thi~ :~heory ' outiineq t;~e response of '.'. '.' '". ~.!\. .. ... .. '.. ~f th~'~ liltid·:.h~~~ '~a~ .·.stlll b.~~~q d~scr.ibed by ' '.. she~t ·to".·a·. ·.,... floatiriq·· ice. .. r:~·.'· .. ,. ".t. lj\:·.::·~ -. ".,, . . . :.': . :.'..:'. :. ".':. . .. .. '. ...: ': :.',: ~ .: . .:.:-". -.; '" .:.. '":.:", ~ .:'. L',': f:' .' .'.' . ......:' .' . ~ ·.\~ ' .' J}~~<;. ;..... :"" -T~e .'.th~~r~"· ~·f :*l~~'~~l~ w.~v~~· . 1~.'· i~e .'~o~\rs! was.'~~e~en~~d ~::"::::: .. ~.. ',. '. ....", . .' .. ,'. :. . .. . ': :. '.. '. .' _, ,': :':. ".' .. ': '..: : ._.. 7;;. :... " ". ~. '.. ~r:··. ··. .. ,.,. .. ,.':.... : './. , ",', \. .:', ~' . s~~~le J(~ ,:~erma.· · ~:> ~o-· .do··a ~I~~~~'e~~ ~'~~~;~is' of·· t~e~.· ~s~:o~~~· 9f 'a " ~' .'. ". \-,).. '. ,.. , ' .; -. ~. ,. ... . . ., ~V:~J? '. though·. ine~ia . e\fects ·,()t . t~e loa<:ll(e.re. . ~:;~::: . . . . ~:~::: ~:.. . . ' • , , '•. fo~.~~~tion.·arid analyzed, the. effects o~: ·.a m.~ving'. lo~d, :incluC;ling . -. :1\.',", '.'. ,~. , - : .... , ... :. :. '-. tyPe:, l.an~lVsis;as .e;en<led W.'. ..\. '..i\,. Til is. I.. ~/.<. '.. r:-f":, :: :~.':" ' :" -.... .. . ,. J. ,:, •. '. ~. (19.58) '", He ..considered 'a plate. resting o.n.. a Winkle;-. f.isz·cz~~: •. ~ ~.'. '.. /. .. . , .... .. .'0':'. . .. /i •. . .. , . .,:..I. ..t. .. , ,. '. .. ". ... /. Q". '~. by ' -. '. >. ".<q . '.::): !,. .. "'.r'-:,?:.. ~ .. .. _. .'. .: .. ..'-i~. _ .. . ...r. .. ";:. . wilson. (1955) " attempted >'" '.. !:oan"i!.~' ~~p~o~l~m Of~a;;e~ .in <i?-ec:u~edbY ,~OVirlq IQ~dS. ... .' ~Y. '}lpp~r:i~q Gree~~~~:-':s :th~ory.~ ~~~ :~ th.~~rY by . ~e~z (1.884) . ~~\:> ',;' '.:. :. '. ' ~d~.~i~C?~~~n ·, .ti~:· ~i~~t~ng · .~l~t~s .bY · staot~·~ l~ad~>' to :the , .cr;~i~al. •. '.':'.~::~. it~:l~.; .: ~ ' ". ".:.::'.:.~. {~:;:~'~ >."::". tr".. \~ ". ~;~.~...... : .' .,,' · ';p~e~' :. problem.~: " .". '; ".' ". ":,'. ';!;'., .... . ,. '.. ,. .. • .'. .. ,'. .. . .. .. ')Ie ~b~ained ' ; the . foliowi~q. ·-exP~~_~si~n .foor the .. crltic·al.·;~ velocity.:: ' .. ". .. .. :... ... ;.. .',. ;itt;:::/' · ... / · ; ~ . ' :, ,., .. ... . ... '. '. .. , ' . " .<.. . •. .. .. . -: . ',. . . .. ;.. ';~;\,;: •. •. ... . ; ,, ' -. .. '. .' <':~~. - . .. ' jC ' 1. '. ~ ... .. .. ". ¥ • • • • .,;:.. . .... ..: .:. <::'!i~. , ,' )';~ ,./· ~t~~. . ,.
(25) ". ·t~.:". .. ~ 'A-r. •. ' c:o~. , Vc:';". .. •. I •. :·ir"<~ !;W'~(. h~.l 01.~ +0.. 5 h 1/ 4). I. (2-1). :::. \~here. .. .. :It ~. ~. water d e p t h ' . .. Q. ":"/ :'". ~t\". I •. hi. I7EipropertiE;swer,;. ~,'.~,ir:;~,·;:.· ~.,; '.;, .';.:. ~.:. . ' ','. ". '1. ·'". oknass of ;shea.t. ::&.t. ,',. ,as f01J.oWS:· •. e ~ • ,,". ~:. . ,12 (1-. ,2 ) t:·:··,-;- ,',. 'I X. '10 9,. / ..... \. ~:,' .. where '. :~~~. :". '. .. d~.. .' E. 6. fV ':. ' ''}~J. 'I. ,~)~. •. :.,". ne em '.. .\ ". .... ;. .. .,. •. ,'\, , :. •I. Young • s .lllodul us. ::a J. __? ", - ' .'. ~'. ... " • '.'. • ;·::t~~·. :. '. \ _. ~" l ~.. . ~--. .:·!~~i. \ .. :' \'. a1sQ ca,;~ied. :i~SO~. rr( .. seriJ". :ut. two. .::~ ;. .~"'j,.;-':' . ." ';y.. ... , Chel~ea ,.~~.c~l!l"; inF~rI1ary; 9\~4. :xperi~ents. of. '~:M. on lakes in. ,:.~ ,':.~ /'\~.,f:.j,\. 1. and Mia e Lacs it•• t .. ' .~ .~ra.l~e,~di ~~~~~~.ta' In F~bruary" ':1955. .1'he results showed ~h~. .criti.';a~. ~~~.~~. .' 0:,(:. ~ ': a - Peiisson' s RatY~. :t.;.. '. ~ ,:.'.: "':.,'~,. •.' '.' . ' .. .'1<. ~:'.. ",. -.!.. /. c';..,:~ ;,.~.:'i~,.1. . ".,~ ";::~~. I . '. ... . '. ". u. .,(:~:(~ <. .>-.: j!.~ , i ". :.;: ~ .,. ". •.. ~. ~ ,,:~. ',::,~~~. , ",. •, /. 8.0. '. v. ·. -. :::!.. J. <,' : :(. h". . .:·.·.:.:.:::.. :. ' ~ t, ~~. :.: /:~. .,. •. ~·i::···:~'~·. ~.;:.~ :_.~·,\"'_~·,! ·:". ~. " ... -. ~-. ':. ir~:.:·· :'. '> "'";'.:. (0. 0150. ".,. ~'.. •.·f,•.. k. . ., ". j;:<~_ .. ~~.:~~. '". 'I. ~. ;; ~. ... ~;;~~~ -:;h~~Om'i'~ori · ;;'e~weiL · Tti~author. ,.',•..-.. .. . ..:. concluded, tha t~"~. ~~i;;> ' ,'" ,::o~t:s~~::;~:i:::~::er:::~t:~:.::::~:::::·d:::~1::: .\:\~ f;.:~I~ ...; •• ~., ~"i,:.". :. .. '.. ~ ,,. _ '.. .'. • "l. .(. -. .. .:·; ..', .~;:~~n ( id~l. :.. ~\Ht/:·~.~. .',. , .'.' : .. .. . . ) ..... .,. ,". ;'.. ~•. •. '. . .,. \' .. " ••. I.. •. I. >. •. ', ', '. " -,. !.. t. ,. •. ' ,. r,. ~~. ....... ". .,. •. "'....... ,., ' ,I. >'0:. ~. :!.... (._. •• .'. ,. .. · " ,. . ' ...... /~. ' .. :" ,fX. , ' .. .. ~. ,I :.' . :. .~ i' .';.~:~.~.t.~. ' . ,". ,.... .. "". ~'-. I. .... 1),10), J iL. _t:• • ·L- · I.·. .. ~ '.f~ ,'.~~~\tt.'i~ ' to '''J~'';''!': r':V~i~~ 'l ~ ~·'1.....·,. · .. ,.... AVI:A, l't;!....:;,~ lt. " .. .. ,.. ... "'-I~iwtl,mt! ~. "nli: 1l::... .. I"T. ,,;t;. '. 'jI. 'r',. "'.<~J~. ,... ~ j~! . ..... :;:j~. ,. ' .. ,'.Y'> • •~ ~~ ':'I~ ' .... r~·~. .., . .. .. I,. ~. ... .,.. !'. ' .. "'0 .. •. .1 .'. .,'. • •. .. • •. .... .,. .', :l ," ~ :~ ". ·. .!i,'~J. .... . 1:.
(26) ~ '. ', ,'. :. .. ... A, . , I, ". . - f. I:.. -.~-. ,I,. ). ' ..of. . ' .'. .. ., ~. _•. .. .. ' ~. : I.. ~t:>.. ~" ". .. '" . .: .. '. , t. '- .9. ..:.!. -.. . ..... . ... .. '." ,. .. '. .. .'. '.,'t .. , ,. --.. ' .:. '. 'A"~ut (i9!56 )w!>,,' had ;..orki>d ,w!i:h wilson on the 19 55,' fl~:Ld t e s t s , ',:» 'attempted to ,'improve on Wilsolilsapproacit'.' 'Acco~.:1irig to Nevel. I';. "11. I~~ I '~::7:::h::~~;:~:::~~:::::~~~::~::::;::r:~::::::~, \"'~li f~~":: /' ,, Th_e./lrsts~s~e~.ti; formul~tio;, ~t ~e: ~ri~i~a~ ,':;:~ speed'. ~l'!\"~: ~":.~ ;.:'.~ '. :,:::'"~:.'.:' " ;~ _. l. ,. '. ...•.. :~~ ;/.". _. ,. H~ uses ,. ,,~: ,!>. p",;~. theo~ a~~ :e~a;.~o"s 6t hYd~~~~~~ci to,!odel the' ::;~em:;~e!di~{er~n:ia~' e~a:t.~~ ~Orthe m;tion o~:. t~e~~a;te , . ,. , ', ;. 'l';:.::. "<:' r~~. 1. phen.omenonforml"linq • oads. on,:f oatinq ice sh,'1"tS, H ',8:'t~ib\ite~" ~~ Khei.sin (,1963)'~ :', His ·" anal.ysis is linear.. ". < .\., " .' ~ .. f! -: . . . . . . : .. '. tii'~'. ". _,. . '.. .. q. .-. ,. , ' 2' '.8.1: .. ". ,. .. '.,. '.. 'l here, .. .. '.. '. -. D. '. '. .. ... :.. ,. -:--. ". ." I •. .. ,. I,. i ". i. .... .: .,... .. .. ~. ". : v4. '.. ,. , ,. -. •. '.-flo .. ,. +. ~. ,. '. , •. ~ ... ! .... ','-. .. "\. '. ... ". , J.'. ', '. ; ,. ". .. · 8y~.··. :. II '. :". '". ". ,. •. -. 11 ". ice' ·thfcmess. :' ". \. " '. ..' r. .. ... '\ ,. .. .. ". .. • '. :. " ". ". ". . "',- :,! '.. . "'cw-' -. 00:. ·1 '. . ,'. I. '.. ..... .. . '. " :~. '. ' . :. '. . ,;' ". ... ". ,". .. ~:. ~' I. '~v," "" !·~"';;~J.;';~,!.~!;f'·i;;:}~itr:C;";"'-':':!•.'' ; i'i ., {i·;:;r::.,;:!,.,;~,::y'i].>.\, 2-~'~':\~; '':v,I;;;~::::';'~';, Sj,'';:f;;:gf~l;':!; ,'-;: ;;.0':!>~,.';'~ ' ' ''.l~ :-: \~,;.) ~ (~I'~;:t{;'~~;f::t:~::}k'::" ~:::;' f'·,~ 'J(~:1~;~·· . • . (' ' -)ro r. \ ... ;. ......,... '\ .• ' .. , .. ~. ~. ~' \. '~" "''';. h-'~. ~". ,~. ~. ~.. ~r' ~ " 'J t:. \'. ,. \. ~:,. '. '. \,. ,. ,'.',0'. '-.... \. . ' :.. ". ,. '. "" ~ ;:.'. ~". ~". ;.: ~. .' \'.~:'. .... , , ':4;;:,: .... ". ~. " ". j~·i~".: "" .' ~ ., \,t ". .. .... ". ". ~->:.,; .C,'" . '. ~~~f;.: ', .:·,·". 'z' '. ~. " , 8 W' fi'~:. ·P ., .s· ' +','. ••. ~11J:>:~f\: " ~~\ 'l'". ,. .,.. ,. 'r ". -i-f'~. Ai.. _. •.:1". ". ":.. ' .~,.
(27) .. vertical deflection of ice. interface. pr~ssure. •. .:' : ". ,. ,. .'. .. t:. ". ': '/" ,.". r. :·.:':;~'I~ ,';. ~. ....•.. ·,tima '. '.. ". -'. ~. I. :. .I:~ .~ i'l. :",:: ). . ~). ". load. ...:.... .'. ". "-. The liquid which '6UPP,o rts. .. '. , ~he pl~te !. and ' iJ:tcompres.sible • .:.'. -. -'. is ~~sumed. ~. I. ,. ,.. to. , be inviscid' ,". ;Its !notion 'is' assumed to be irr,o tational.. the . continuity" equation becomeS.. Tn~s,. . \. :, '. ~:}i. .:. ". -.. ~. ,. (pressure of water 'On .. ice). mass , density of ice. ". q: ,. ". '". -' .,. .,. .-. •. ",. ','. :.\~.
(28) ;. .". .~. " ' , :.. ... ,. .'". ,. .. , .I-< ~ti. ". ,>;~~~ ~: ;{~. ,. For an i~rotationai f1ow:. .. .; .c"'~,. '~ :~;. ;'. ,.:.".'1. •. o. .: : ~.. (2-5). • .... .. .7.. ' '';~~. . . .:.. V must take the form;". .\. ,. ~. :.. . ... ,'. .' ..' ,- .!.'.. v; . .. . ,,~ .. ,,', where ' V is .". - '.-. ,.. the velocity . vector. . 4. ". . ",.. ,-;,. ". ,. ,. -~.,. ~. is. the pressu're at the 'plate liquid interface.. :.:. '.. ,, ' ,. ·.:.Next , - Bernouifi -.' is ·. ~qu:~ti~n for unsteady flow. o ,. '. ....'.'?. r_,.~~. u~ed. to solve : ~. ('~ ,. . '. ••. ~.~. I.
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