4- steps in hoist design

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    1

    Steps in Design of a Hoisting System

    ©Dr. B. C. Paul 1999 major revision 2012

    With Credit to Dr. H. Sevim for Oriinal Boo! 

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    2

    Steps in Design of Hoisting

    System Determine the "erforman#e re$uirements

    % &suall' means "rodu#tion

    % #an also involve fiurin a##e"ta(le sto""in

    distan#es ) num(er of levels to (e served under

    *hat #onditions

    Sele#t hoist t'"e to meet #onstraints

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    +

    Once Upon a Mine

    Dar! Bla#! #oal mine *ill "rodu#e + million

    tons of #oal from a sinle level. ,he hoistin

    distan#e from loadin "o#!et to dum" (in is1000 ft. ,he mine o"erates 2-0 da's "er 'ear

    + "rodu#tion shifts "er da' *ith hours of

    o"eration ea#h "rodu#tion shift. ,he "ea! "rodu#tion *ill (e a(out -000 tons "er shift.

    ,he averae "rodu#tion is /000 tons "er shift.

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    /

    Your Mission Jim, Should you

    decide to accept it  Desin a hoistin s'stem for the Dar! Bla#! Coal

    ine.

    irst Ste" is to esta(lish the "erforman#ere$uirement.

    ,he fundamental Ca"a#it' $uation is

    % 3 4 P 5 ,

    % 3 is re$uirement in ,ons Per Hour 

    % P is Produ#tion "er shift

    % , is the averae shift "rodu#tion time

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    -

    Which Production Numer Do

    We Use! 6#tual "rodu#tion is a distri(ution ) not an

    averae num(er 

    7f *e desin on averae then all the num(ers

    a(ove the mean *ill o "ast #a"a#it' ) *e8ll

    loose our hih values and not meet

     "rodu#tion 7f *e desin on a "ea! that is seldom

    a#hieved *e8ll "a' (i (u#!s

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     Decision "riteria

    7f "ea! a""roa#hes 2 times averae ) need to

    #onsider #ost of *or! sto""ae vs. ta!e *or!

    sto""aes 7f "ea! is some*hat #lose to averae then

    desin for the "ea! 

    7n e:am"le the "ea! is 12-; of the averae<*hi#h is not #onsidered a sinifi#ant

    deviation. Desin for the Pea!=

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    What if #ife had not een so

     $ind! Cal#ulate the #ost of a "rodu#tion sto""ae

    % a' (e #ost of lost "rodu#tion

    % a' in#lude "enalties on #ontra#ts% a' in#lude idle la(or #ost

    Cal#ulate the amorti>ed #ost of the ne:t

    in#rement of "rodu#tion #a"a#it' Che#! multi"le "oints and o for minimum

    total #ost.

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    ?

     Pic% production capacity 6""l' formula

    %  1/ t"h 4 -000 t5shift 5 hours "rod time

    Other desin de#isions need to (e made

    % 7s this a @eo"e or a Drum HoistA

    % One evel so @eo"e *on8t (e too tri#!'

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     &nput My Hoist Distance and

     Production 'ate (arget 

    9

    ' S"readsheet is

    O"ti)Hoist.

     e:t ets loo! at some fi:ed

    C'#le time elements

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     )lements

    Ho* on *ill it ta!e for the ore "o#!et doors to

    o"en and dro" a load into the s!i"A

    On#e the S!i" is in "osition ho* lon *ill it ta!eto de"osit the load into the dum" "oint #huteA

    % 6(out ? se#onds to load

    % 10 se#onds to dum" is reasona(le

    % our load and unload times ma' de"end on other

    desin elements of the s'stem.

    10

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    "reep (ime

    Hoists and levators slo* to near

    sto" as the' line u" *ith a set level

    % Pull a*a' fromthe loadin "oint% Or line u" *ith dum" "oint

    % Will &suall' ta!e a (it more time to

    line u" *ith the unload "oint

    % 2 se#onds to "ull a*a' from load and

    / to line u" *ith dum" is reasona(le.

    116 fo*l Beast

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     No* We Need to Pic% a Pea%

    Speed and a 'ate of S%ip +cceleration

    12

    ,he ma:imum s"eed *e lift at is safet' related. or men there are reulations.

    or materials there are uidelines Esho*n in "in!F

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    "onsiderations

    ,his is a @eo"e Hoist

    % ,he ro"e is just sittin over a fri#tion *heel

    % 7f 7 G"eel out and the ro"e starts to sli" 7 have

    a major hoistin a##ident

    Hih s"eed and hih a##eleration in#rease

     "rodu#tion% But the' also #ause a (i in#rease in motor si>e

    and ener' (ill.

    1+

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     &m going to go for modest speed

    and particularly modestacceleration

    1/

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    -eometry "onsiderations

    1-

    ,*o S!i"s S!i" and Counter)*eiht

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    Stopping "onsiderations

    1

    7f m' #ontrols miss

    Sto""in the s!i" at

    ,he dum" "oint I ho*

    ar do 7 have for an

    meren#' sto" (efore

    ,he over)*iend turns

    7nto a disasterA

    Dum"

    Chute

    oadin #hute

    Shaft Bottom

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    -etting Our .irst )stimate

    1

    &sin a ord(er a""ro:imation of the #'#le time the "roram estimates the si>e

    Of s!i" that *ill (e needed to a#hieve the "rodu#tion taret usin the distan#e<

    S"eed and a##eleration #onditions s"e#ified.

    E,his "art of the s"readsheet is inde"endent of *hether the hoist *as a @eo"e or 

    6 drum hoistF.

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    Our Ne/t (as% is to -et Our

     )/act "ycle (ime

    1?

    ,he onl' missin

    Pie#e of information

    Was *hat is the

    Cree" s"eed E2 ft5se#

    7s reasona(leF.

    E7 *ant8s 'ou mone' for m' fa!e

    Jlo(al *armin initiativeF

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     Ne/t We Must 0alance S%ip Si1e,

    Weight, 'ope Diameters andWheel Si1es

    19

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     .irst We Need to Pic% + S%ip Si1e

    20

    We have alread' (een iven a first uess s!i" si>e. We tr' a(out that si>e

    6nd then #he#! the a#tual hourl' "rodu#tion a#hieva(le in the red (o: E*e

     o* have fiured the e:a#t #'#le time tooF.

    6s #an (e seen a 1 ton s!i" *ill et me m' 20 tons5hour.

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     Ne/t &ll -o for S%ip Weight 

    21

    7n eneral a s!i" heav' enouh to handle the (anin of ore loadin and

    &nloadin *ill *eiht a(out -; of the load *eiht.

    O"ti)Hoist estimates this for us (ut leaves us a 'ello* (lan! to #hoose theWeiht. 6 hiher *eiht usuall' means *e are just addin *eihts to our 

    S!i".

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     Ne/t We -o .or 'ope Si1ing 

    22

    @eo"e hoists usuall' have multi"le ro"es in even num(ers< 2< /< < and ? (einCommon. Where that 12 #ame from is unsure.

    We need to #onsider (oth hoistin ro"es and tail ro"es. Sometimes tail ro"es

    6re used and *orn)out hoist ro"es *hi#h #an #ause tail ro"es to (e the same

    6s hoist ro"es.

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     My .irst -uess is 2 ropes

    3(his is a relati4ely modest depth5

    2+

    ,he red (o: estimates that 7 *ill need a 1.0/ in#h ro"e to rea#h needed

    Safet' fa#tors for this de"th.

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     .rom Here & Need to -o +nd

     )nter My 'ope Properties

    2/

    7 enter m' ro"e si>e< it8s *eiht and it8s strenth. E7 have the advantae of Havin an estimate of *hat si>e ro"e to tr'F.

    ,he s"readsheet then #om"ares the a#hieved fa#tor of safet' to *hat is re$uired

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    Where Do & -et (hese 'ope

     Properties

    2-

    ,he s"readsheet has a

    Ko"e "ro"erties ta(le

    Kiht (elo* for me to

    oo! thins u" on.

    78m loo!in for 1.0/

    lattened strand

    7 o for 1.12-

    Weiht 2.2? l(s5ft

    Strenth -.9 tons

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     )nter My 'ope and "hec% My

     .actor of Safety

    2

    6 fa#tor of safet' #learl' meets a .-

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     & Wonder &f & "ould -et +*ay

    *ith a 6 inch rope

    2

    eee I one in#h ro"e is a no"e.

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    What if & Use High Strength

    Steal!

    2?

    Oh so #lose (ut still no"e to the ro"e

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    With Hoist 'ope Selected & can

    no* pic% the Wheel for My Hoist .rame

    29

    7 need a .- ft *heel Esee "i#! re#ommendationF to avoid (endin m' ro"e to

    Shar". Eou #an see *h' 7 *anted a smaller ro"e I it *ould have allo*ed me

    ,o use a smaller lo*er inertia *heelF.

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     No* & Need to Deal *ith (ail

     'ope Sim"le #ase is to et used ro"e

    6lso easiest to have just one tail ro"e so

    have less s*inin and tanlin.

     um(er of tail ro"es is #ommonl' less than

    num(er of hoist ro"es.

    +0

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     &m going to try straight across

    Using my *orn7out hoist ropes for tail ropes8

    +1

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     No* &ll "hec% "onditions at My

     $eope Wheel 

    +2

    ,1 is the *eiht of the heav' loaded side. ,2 is the *eiht of the lihter em"t'

    Side.

    Kemem(er I onl' fri#tion sto"s the ro"e from sli""in. ,he ratio of ,1 to ,2

    ust therefor not (e more than 1.-

    Of #ourse 1.9- is reater than 1.- so life is su#!in riht no*.

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     +nother Parameter is (read

     Pressure

    ++

    @eo"e *heels are normall' lined *ith a leather li!e fri#tional material. Sin#e *eDon8t *ant the ro"es to #ut the material to "ie#es *e need to limit the load to

    6(out +00 "si or less.

    Well at least one thin *or!ed.

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    So What Do & Do No*

    ither ,1 is to (i or ,2 is too little

    7 #ould loo! at ro"e *eiht (ut the ro"e *eiht

    shifts (a#! and forth from ,1 to ,2 de"endin on*here *e are

    % ,he ,1 and ,2 ratios are "i#!ed (' the s"readsheet to (e

    *orst #ase

    7 #ould ma!e m' s!i" lihter % But a liht dut' s!i" #ould et (eat to "ie#es

    % 6nd a lihter s!i" *ould also redu#e ,2

    +/

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     &dea

    7f m' s!i"s *ere heavier then the s!i"s *ould

    a##ount for a hiher "er#entae of the *eiht.

    Sin#e s!i"s are the for ,1 and ,2 ma!in it alarer "ro"ortion *ill even the ratio

    E7 #ould ma!e a similar arument for "i#!in

    heavier ro"es (ut ro"es are e:"ensive and (iro"es for larer hiher inertia *heelsF.

    +-

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     Putting 9 tons of Dead Weight on

     My s%ips made it more e4en

    +

    Of #ourse 78m still not there 'et.

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    O% : +dding 6;8; dead *eight

    tons to the s%ip did it

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    So What "an & Do With My (read

     Pressure 7 #an8t #hane m' ,1 and ,2

    But 7 #an s"read the load over a reater area

    % ,hat unfortunatel' *ould mean ettin a (ier

    @eo"e *heel

    +?

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    (here : + 6= ft Wheel Spreads

    the #oad 

    +97 !no* I the inertia situation su#!s.

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    "ome to (hin% +out &t : (he

     .actor of Safety Suc%s (oo

    /0

    Ho* "rofound I 7 "ut more *eiht on the ro"e *ithout strenthenin the ro"e

    6nd 7 et into safet' fa#tor trou(le.

    EWhere the

    one' JoesF

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    (a%e + #ittle Weight Off the S%ip

    and Put + #ittle More On the 'ope

    /1

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    (ime to Pic% Out Our Motor 

    /2

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    /+

     #oo%ing at Hoist Duty "ycle

    Hoist doesn8t al*a's run at a sinle s"eed

    7nitial a##eleration ) time it starts to move )

     (ut its (' the loadin "o#!et so *e don8tGfloor it

    Cree" 1 ) #arefull' #ree"s "ast the loadin

    area to avoid tearin somethin u" ain a##eleration ) after #lear of loadin area

    ) hit it u" to full s"eed

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    //

     Hoist Duty "ycle

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    /-

     Duty "ycle "ontinued 

    Kun at ull S"eed ) until 'ou et #lose

    enouh to the to" that 'ou8d (etter slo* do*n

    or 'ouLll "ut the s!i" u" some"la#e interestin ain De#eleration ) slo* do*n to #ree"

    s"eed (efore 'ou ta!e out the dum" (in

    Cree" 2 ) move slo*l' into dum" "osition inal De#eleration ) sto" to dum"

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    /

    What Si1e Motor!

    Ke$uired horse"o*er for motor varies

    reatl' throuh hoistin #'#le

    6djustments are made (' #al#ulatin theKoot ean S$uared EKSF Horse"o*er

    re$uirements

    ,his re$uires ta!in horse"o*er duties atmulti"le "oints throuh the hoistin #'#le

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    (he Spreadsheet Does Your

    "alculations

    /

    ,he otor Si>in is

    6 fun#tion of somethin

    Called W I *hat is

    that.A

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    /?

    (he Mystery of the ))W (erm

    W stands for e$uivalent effe#tive *eiht Hoist #ontains motors< ears< and lare

    *heels that #ontri(ute inertia to the s'stem

    durin a##eleration Could o throuh lon hand and #al#ulate

    inertia of ever'thin Eif 'ou8re sadisti#

    enouhF

    6lternative is to use manufa#tures ta(les that

    redu#e inertia to an e$uivalent load on a ro"e.

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    /9

     Norderg )>ui4alent )ffecti4e

    Weight "hart 

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     'eading the "hart 

    -0

    We !no* it is

    6 @eo"e hoist

    So 7 *ill use

    ,he @eo"e line

    7 !no* 7 have

    6 10ft *heel

    So 7 start at

    10 and read u"

    ,o the @eo"e

    ine

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     & (hen 'ead O4er to the

     )>ui4alent )ffecti4e Weight 

    -1

    78ll (e #onservative

    7n m' readin and

    Call it +

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     )nter the Numer and -et Motor 

    Si1ing 

    -2

    Of #ourse understandin

    What all these HP1< HP6

    6nd ,S stuff is *ould

    6dd a lot of understandin

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    @eo"e Hoist -+

    (he Horsepo*er Demand of a

     $eope Hoist O4er (ime #oo%s #i%e (his

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    -/

    Understanding $eope Duty

    "ycles3 ) Wh' is there a stead' flat line for Horse"o*er re$uired in a @eo"eHoist Dut' C'#le

    6 ) Horse"o*er is an ener' out"ut "er unit time. 7t ta!es ener' tolift the s!i" load u" the shaft as it travels at full stead' s"eed.

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    --

     $eope Duty "ycles3 ) Wh' is there a slo"ed line leadin u"*ard from *hen the hoist starts

    6 ) When the hoist is o"eratin at less than full s"eed the load is

    trans"orted a lesser distan#e "er unit time and thus the ener' out"ut "er

    unit time is less. ,he line has a linear slo"e (e#ause the a##eleration rate is

    a #onstant.

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    -

    (he $eope Duty "ycle3 ) Wh' is there a "ea! that dro"s shar"l' to the flat line forHorse"o*er to run the @eo"e

    6 ) ou must add additional for#e to a##elerate the load. 6t the end

    of the a##eleration "eriod the additional for#e is no loner needed.

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    -

     $eope Duty "ycles3 ) Wh' is there a (i dro" in horse"o*er at the end of the full s"eed runfor the hoist

    6 ) When the hoist de#elerates< the momentum of the load "rovides "art of

    the ener' to !ee" the load movin u" the shaft.

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    -?

     $eope "ycles3 ) Wh' does the line slo"e do*n at the end of the Hoist

    C'#le

    6 ) ,he load is slo*in do*n and a##umulatin less "otential

    ener' "er unit of time.

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    -9

     $eope "ycles3) Wh' the funn' dashed lines that sho* more "o*er

     (ein used at the start and less (ein re#overed at the end.

    6 ) ri#tional losses

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    @eo"e Hoist 0

     +pproach to +ttac%ing the 'MS

     Horsepo*er 'e>uirements We *ill #al#ulate #om"onents of Horse"o*er

    re$uirements% HP

    1 *ill (e the horse"o*er to a##elerate the load

    % HP+ *ill (e the horse"o*er to move the load at full s"eed u"

    the shaft

    % HP2 *ill (e the horse"o*er re#overed from momentum *hen

    the load is de#elerated

    % HP *ill (e the horse"o*er still re$uired to lift the load after

    de#eleration starts

    % HP/ and HP- *ill #over fri#tional losses

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    You "an See (hose Horsepo*ers

    "alculated8

    1

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    @eo"e Hoist 2

     Horsepo*er ?6 3.or $eope

     Hoists5 HP1 4 ,S M N2 5 E--0 M M ,aF

    % Where ,S is the ,otal Sus"ended oad

    % N is the Nelo#it'% is the a##eleration of ravit'

    % ,a is the a##eleration time to et the hoist to full

    s"eed and in#ludes time to a##elerate to #ree" s"eed

    Einitial a##eleration t1F and then to a##elerate to fulls"eed Et+F

    % ,a 4 t1  t+

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    @eo"e Hoist +

    (otal Suspended #oad 

    ,S 4 W 2000 M S 2ME2000MSWF Ko"e Weiht E(oth sidesF

    % S and SW are the s!i" *eiht and load in tons

    % K is the ro"e *eiht% Be#ause of tail ro"e there is a full lenth of ro"e on (oth s!i" sides

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    @eo"e Hoist /

     Horsepo*er ?@ 7 Po*er to #ift a

     #oaded S%ip at .ull Speed  HP+ 4 N M 2000 M S 5 --0

    %  ote that the s!i" *eiht term is missin

    % 7 have a s!i" oin do*n to (alan#e a s!i"#omin u"

     

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    @eo"e Hoist -

     Horsepo*er ?A 7 Negati4e

     Horsepo*er from Momentum During Deceleration HP2 4 ) ,S M N2 5 E--0 M M ,r F

    % Where ,r  is time durin de#eleration

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    @eo"e Hoist

     Horsepo*er ?2 7 #osses in -ears

    and Dri4es Derived em"iri#all' rather than (' "h'si#s

    fundamentals

    HP/ 4 0.111 M E2000 M S M N 5 --0F

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    @eo"e Hoist

     +pproach to 'MS Horsepo*er

    "ontinued  We *ill add the different fundamental #om"onents

    of horse"o*er to et the horse"o*er needs at

    various #ardinal "oints durin the lift

    We *ill la(el these #ardinal "oints 6 throuh

    % :am"le D is the "ea! "o*er re$uired at the heiht of

    the a##eleration "hase

    We *ill "ut the horse"o*er values at the #ardinal "oints into the KS horse"o*er e$uation and use

    that to si>e the motor.

    "alculate Horsepo*er at @

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    @eo"e Hoist ?

    "alculate Horsepo*er at @

    "ardinal Points Point 6 ) Pea! of the 6##eleration Phase HP6 4 HP1  HP+  HP/

    Point B ) Durin ull S"eed Kun

    HPB 4 HP+  HP/

    Point C ) 6t 7nitiation of De#eleration

    HPC 4 HP2  HP+  HP/

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    Yip : (here are the 4alues

    9

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    @eo"e Hoist 0

    One More Monster Po*er Sin% 

    ,hese Bi otors have an 6rmature to Sin!

    a Battleshi"= ) ta!es a lot of inertia to s"in

    the thin u" or do*n HP- Eto s"in it u"F 4 0.- M HP6 M 1.2 5 ,a

    HP9 Eto s"in do*nF 4 )0.- M HP6 M 1.2 5 ,r 

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    (hose "alculations are Done (oo

    1

    " ti " di l P i t f

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    @eo"e Hoist 2

    "orrecting "ardinal Points for

     +rmature +cceleration Point D is the revision of 6 "ea! of

    a##eleration

    HPD 4 HP6  HP-

    Point is revision of C initiation of

    De#eleration

    HP 4 HPC  HP9

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     +nd the "alculations +re (here

    +

    'MS )>uations Depend on

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    @eo"e Hoist /

     'MS )>uations Depend on

     Motor (ype or 6C otor 

    HPrms 4 E HPD2 M ,a  HPB2M ,fs  HP2M ,r F5

    E 0.- M ,a  ,sf   0.- M ,r   0.2- M tr F Q0.-

    % Where% ,a is a##eleration time

    % ,sf is full s"eed time

    % ,r is de#eleration time

    % tr  is the rest time

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    -

     'MS Horsepo*er for D" Motors

     umerator is the same as 6C

    Denominator is #haned to

    E 0.- M ,a  ,sf   0.- M ,r   0.- Mtr F

    KS HP DC 4 umerator5

    DenominatorQ0.-

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     #oo%s #i%e & Need +out 6A==

     HP 

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    (ime to Pic% the Motors

    7 need to #hoose the num(er and si>e of motor and the inertia of the rotor 

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    "onsider Pic%s

    ?

    78d rather o 6C *ith fre$uen#' #ontrol. 78d li!e to do 2 00 h" motors (ut

    With a 10 ft diameter @eo"e *heel 78ll still need ear redu#tion so 7 *ould

    Onl' et a(out 9/; transmission I ' "i#! a 12-0 t*o "ole 6C

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     Plug7&n My Motor Parameters

    and -ear 'eduction )fficiency

    9

    O! I ,hat seems to *or! 

    Eote that there are limits to ho* mu#h 'ou #an turn do*n the s"eed of 6 motor *ith varia(le fre$uen#' drivesF

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    Our #ast (as% is to Si1e the 0ra%e

    ?0

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    We Want (*o (hings .rom Our

     0ra%e Hold the ma:imum "ossi(le u(alan#ed load

    *ith a 1.- fa#tor of safet'

    7f a full s"eed load "asses the ore dum"s"eed it must "erform an emeren#' sto"

     (efore the s!i" #rashes into the to" of the

    headframe.

    ?1

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    ?2

     Ne/t Step is to Design the

     0ra%ing System Durin Clut#hin O"erations the Bra!e must hold the

    load so it doesnLt o to the shaft (ottom

    Desin "ra#ti#e is to rate the (ra!e and #lut#h to hold

    the ma:imum load "lus -0;

    BK 4 CK 4 ED52F M E 2000MS 2000MSW H M Wr  M

    nF M E1.-F R&nits are ft)l(s

    % D is drum or *heel diameter 

    % BK and CK are Bra!e and Clut#h Katins in ftMl(s tor$ue

    %  ote this is the load on one side of a drum hoist if the other is

    #lut#hed

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    (he Spreadsheet 'uns the

    "alculation

    ?+

    7 need to set m' (ra!e ratin to at least this si>e.

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     & .ill &n the Numers

    ?/

    Bra!e ratin #omes from the re#ommendation

    ass of the rotor #ame from the motor s"e#ifi#ation list

    ,he ear ratio and s"eed *ere *or!ed to et a *or!a(leKatio and a motor s"eed that *as *ithin the turn)do*n

    imit for the motor.

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    ?-

     +nother .actor is 0ra%e

     Performance During an )mergency Stop Desin is done on *orst #ase s#enario

    % ma:imum un(alan#ed load travelin at full s"eed

    % dis#overed *ith a minimum toleran#e distan#e

     (efore 'ou ride into the head frame or #rash into the

     (ottom

    ust either desin for a toleran#e distan#e 'our (ra!e #an sto" in or si>e u" the (ra!e for the

    toleran#e 'ou have.

    D i " t

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    ?

     Design "oncept 

    6ssume the Bra!e must fiht aainst thema:imum un(alan#ed load

    % Su(tra#t un(alan#ed load from (ra!e #a"a#it'

    % ,his leaves the net for#e availa(le for the emeren#'

    sto"

    &se e*tons Se#ond a*

    % @no* the net for#e availa(le

    % @no* total mass in motion% Solve for the de#eleration rate

    Cal#ulate the time and distan#e to sto"

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    ?

     .ormula

    oo! at a:imum differential load

    % W 4 E,1 ) ,2F M 2000

    % ,1 4 a: load 4 S SW EH M Wr  M n52000F% ,2 4 in Balan#in oad 4 SW

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    (he Spreadsheet +pplies the

     .ormula to -et the DifferentialWeight8

    ??

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    ?9

    (he Mass that must e Stopped 

    ,o use e*tonLs a* to et or#e Ke$uirements

    the load must (e in mass% eans *e must use slus ) some ho* a s'stem made (' @ins usin slus

    sounds *ron

    4 E W M K 2  WK 2m M JK 2F 5 K 2  ,1 M2000

    ,2 M 2000 Q 5 +2.2% Where K is the Drum or Wheel Kadius D52

    % WK 2m is the inertia of the motor rotor in ft 2

    % JK is the ear ratio of the motor to the drive

    %  ote that the K 2 terms are needed to #onvert rotatin inertia to e$uivalent

    mass

    Sol4ing for the Deceleration 'ate

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    90

    Sol4ing for the Deceleration 'ate DK 4 E B ) W F 5

    % DK 4 De#eleration Kate

    % 4 ass to (e sto""ed

    % W 4 et un(alan#ed load E,1 ) ,2F M 2000

    % B 4 Bra!e Katin in l(s linear for#e

    % Jet B 4 BK 5 K I  BK is the Bra!e Katin in tMl(s

    6""l'in the De#eleration Kate% ,ime to Sto" 4 , 4 N 5 DK 

    % Bra!in Distan#e 4 S 4 EN52F M ,

    Che#! Bra!in Distan#e 6ainst 6vaila(le or ma!e

    sure 'ou have the distan#e

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    @eo"e Hoist 91

    (he -ear 'atio Prolem

    JK 4 N 5 ND

    % N is r"m of motor at rated travel s"eed

    % ND is r"m of Drum ND 4 N 5 E"i M D F R remem(er 7 need r"m

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    Sol4ing for the Mass to e

    Stopped 

    @eo"e Hoist 92

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    "hec% Out Our Stopping

     Distance

    u" I We 6""ear to Be O@