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7/23/2019 Elemente de Calcul Balistic
1/13
7
Aiahalta ca nfinui gfioston
Oltr`cunara
Gfiostonf raprazolt ` rfhur f hanflonoo ta`ratona nfra stucofz iamoiahonroo uluo n`rp mrau frulnft sug ul fluhot ulmjo dfca `roz`lt) pranuh ohonfraf pr`oantoiuiuo l oltaro`rui avoo o pa nurgf gfioston6,
Cft`rot r`iuiuo ohp`rtflt) gfiostonf f fkuls s doa roconft if rflmui catool) fvlc ul `goant ca narnatfra gola cadolot) hat`ca pr`proo ca narnatfratoolodon) prolnopoo o iamoto pr`proo,
@ pfrta col cftaia toolodona fia gfiostonoo sult d`i`sota o fpionfta ca ntra`rmflaia ca urhrora palfi) ca ntra nroholfioston) l narnatfraf codarotai`roldrfnoulo if f nr`r svrora s(fu d`i`sot frha ca d`n) `ro iamft ca fnastaf s(fun`hos fita dfpta olnroholfta ca iama,
@cft nu nrataraf luhruiuo oldrfnouloi`r svrota nu fkut`rui frhai`rca d`n) o(f dnut i`n l nfcrui tajlonoo nroholfiostona ` l`u rfhur ; Gfiostonfkuconofr,
Gfiostonf kuconofr asta ` rfhur raiftov tlr f tajlonoo nroholfiostona)na traguoa s ol pfsui nu cazv`itfraf gfiostonoo malarfia) pranuh o nucazv`itfraf tajlonoo hoiotfra l naaf na provata n`lstrunof frhai`r ca d`np`rtfgoia o f hulooao d`i`sota if fnastaf,
Uulntui ca pianfra l n`lstotuoraf gfiostonoo kuconofra nf rfhur f tajlonoonroholfiostona asta iamft) l prolnopfi) ca casn`paroraf hat`cai`r ca ocaltodonfraolcovocufi f frhao ca d`n cup mi`flaia o tuguroia frsa, Cfn stucoahcodarotaia iunrro ca spanofiotfta fpruta ca(f iulmui tohpuiuo) v`h n`lstftf n)l fdfrf aiahaltai`r ca l`utfta o f codarotai`r oltarpratro fia doanruo fut`r) l
t`fta fnasta iunrro casn`paroh fnaiafo prolnopoo ca gfz fia gfiostonoo ofnaiafo ramuio malarfia nu provora if ocaltodonfraf nroholfioston, Fnast dfpt sacft`rafz lasnjohgroo nfrfntarai`r malarfia fia dal`halai`r gfiostona) nfrafu rhfs if dai) njofr cfn s(fu pr`cus ulaia h`codonro pr`cusa ca pr`nasuitoolao o tajlonoo,
l sotufof fntufi) f fsnalsouloo dal`haluiuo oldrfno`lfi o ohpionot fnrataroo luhruiuo oldrfnouloi`r n`hosa nu frha ca d`n) asta ca lan`ltastftr`iui ca`sagot ca ohp`rtflt caolut ca axpartozf nroholfioston l malarfi o
6Tfsoia Hnaifru Gfiostonf kuconofr) Gunurato 6?=7
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axpartozf gfioston`(kuconofr l pfrtonuifr) paltru s`iuo`lfraf nfuzai`r palfiao svroraf fntai`r ca kustooa,
l prolnopou) gfiostonf malarfi p`fta dohprot l trao pro costolnta; gfiostonf oltaro`fr ( stucofz trflsd`rhfraf alarmoao njohona f puigaroo
l alarmof hanflon *nolaton/ na sarvata if pr`puisfraf pr`oantoiuiuo)pranuh o urhaia nrafta pa pr`oantoi o tugui ca nfrtu ca ntra ulaiapoasa fia frhao2
gfiostonf axtaro`fr ( stucofz n`hp`rtfhaltui o trfoant`rofpr`oantoiuiuo, Af vozafz hsurfraf votazao pr`oantoiuiuo ca if oaoraf colafv pl if i`voraf oltao) pranuh o stucoui trfoant`roao casnros ca
pr`oantoi2 gfiostonf tarholfi*f oltao/ ( stucofz n`hp`rtfhaltui pr`oantoiuiuo nfra
f ftols oltf) pranuh o rafnooia dozo`i`mona o go`i`mona pa nfra iapr`v`fn l n`rpui vontohao,
Axpartozf gfiostonfra nf `goant ocaltodonfraf topuiuo ca frh) ca d`n sfunu far n`hprohft o f dfgronfltuiuo fnastaof) cup urhaia nrafta pa tug opr`oantoi) ocaltodonfraf topuiuo ca hulooa o f dfgronfltuiuo fnastaof)
ocaltodonfraf dfnt`roi`r supiohaltfro fo hpunrooca pa frhf o ca pa `goantaca hgrnholta pranuh o aiunocfraf tutur`r hprakurroi`r oldrfnouloi`rn`hosa nu frha ca d`n sfu nu far n`hprohft,
Qlaia coltra naia hfo dranvalt s`ionotfta `goantova l nfcrui axpartozaogfiostona sult;
sostahui) h`caiui o hfrnf frhao nu nfra fr do putut s doa trfsa tuguroiaca nfrtua sfu pr`oantoiaia roconfta ca if i`nui dfptao2
cfn tuguroia ca nfrtua sfu pr`oantoiaia roconfta ca if i`nui dfptao)
axtrfsa col n`rpui vontohao fu d`st trfsa nu ` fluhot frh2 costflf ca if nfra s(f trfs 2 coranof ca trfmara) p`zoof vontohao o f trmt`ruiuo 2 cfn ` fluhot frh asta l stfra l`rhfi ca dulno`lfra o cfn asta
p`sogoi s sa caniflaza d`nui dr fno`lfraf trmfnouiuo2 cfn ` fluhot frh f sudarot h`codonro df ca stfraf l nfra f d`st
pus if cosp`zooa ca dfgronflt p`trovot sn`puiuo o castolfoao paltru nfraf d`st pr`cus2
cfn frhf f sudarot camrfcro cft`rot d`i`soroo lcaiulmfta) prololtarvaloa nu snuia fnjoat`fra sfu ca fit mal) prol axpulara if fmalo
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njohono n`r`zovo sfu cft`rot ul`r n`lcooo ohpr`proo ca ltraolaraaxpi`ftfra sosfu cap`zotfra2
cfn cosp`zotovui ca n`lstrunoa frtozflfi pus if cosp`zooa n`lstotuoafrh l laiasui iamoo 2
stfraf ca dulno`lfra) nfiogrui o adonfnotftaf ulao frha ca d`n can`lstrunoa frtozflfi2
cfn pa afvf frhao) pa lnrnt`r) nuo parnut`r axost urha fiarazocuuroi`r ca hpunfra cfn fnasta urha pr`vol ca if ` hulooasohoifr nu naf pus if cosp`zooa paltru n`hpfrfoa o cfn trfmaraf astaca cft ranalt 2
cfn huloof n`rp caiont asta sfu lu fpt paltru f sa adantuf trfmaro nuaf2
cfn huloof n`rp caiont f d`st n`ldano`lft olcustrofi sfu frtozflfi2 cfn tugui nfrtu o pr`oantoiui fu dnut n`rp n`hul lfolta ca trfmara 2 cfn hfo huita drfmhalta pr`vol col fnaifo pr`oantoi2 cohalsoulaf fionai`r axtrfsa col n`rpui vontohao sfu roconfta ca if i`nui
dfptao o cfn fu d`st n`ldano`lfta olcustrofi sfu frtozflfi2 raiavfraf saroao ulao frha ca d`n 2 cfn vontohf f d`st hpunft proltr(ul d`n trfs corant sfu prol ron`at2 cfn ul `rodonou ca hpuntur asta ca oltrfra sfu ca oaora,
l prfnton sa p`t ltilo o fita fspanta iamfta ca frhaia ca d`n o huloof
fnast`rf cfr naia aluharfta sult nai hfo cas ltilota,Ualtru aiunocfraf covarsai`r hprakurro iamfta ca olvastomfraf
nroholfiostonf f ul`r oldrfnoulo svrota nu frha ca d`n) traguoa s sa ol n`ltca aiahaltaia trfmaroo,
Coltra aiahaltaia trfmaroo) nu vfi`fra ca ocaltodonfra nroholfioston) doa camal) doa olcovocufi) halo`lh;
votazf mi`luiuo2
ranuiui frhao2
trfoant`rof2
gtfof frhao2
putaraf ca ptrulcara,,atn,
Asta tout n dal`halui trfmaroo nu ` frh ca d`n n`lst l pr`puisfrafmi`luiuo col nflfiui avoo cft`rot prasouloo mfzai`r razuitfta col frcarafpuigaroo axpi`zova, Urasoulaf ca d`rfra asta d`frta hfra) doolc lanasfrptrulcaroo mi`luiuo ltra pioluroia avoo, l n`ltolufra) prasoulaf nrata rfpocpa prohoo naltohatro pfrnuro ca mi`l,
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Totazf hfxoh f mi`luiuo sa lramostrafz if murf avoo) ofr prasoulafsnfca l h`haltui oaoroo mi`luiuo col afv, Asta ohp`rtflt dfptui n votazfmi`luiuo asta n`lcoo`lft ca topui frhao) iulmohaf avoo) nfltotftaf ca puigara
o mrautftaf mi`luiuo,
^(f `gsarvft n) nu nt afvf frhao asta hfo iulm nu ftt hfo huit tohpprasoulaf mfzai`r vf fno`lf fsuprf mi`luiuo o crapt urhfra) nu ftt vf do hfohfra votazf oloofi f mi`luiuo,
Nftam`roo ca frhfhalt Uost`i hotrfioar Uunhotrfioar Hotrfioar Uun sahofut`hft
nu iulat
Iulmohaf proo mjoltuota *hh, >4? 133 115 1?5
Totazf oloofi f mi`luiuo *h/s =61 =31 :71 :15
Srfoant`rof pr`oantoiuiuo
Srfoant`rof asta cruhui pfrnurs ca naltrui ca mrautfta fi mi`luiuo
*pr`oantoiuiuo/ l far) ca if oaoraf col afv pl if pulntui ca ncara
7
,
7Hflufi ca pramftora hoiotfrf malarfif f tolaratuiuo paltru fpfrfraf pftroao) H,Fp,L,) Gunurasto 6?:>) p,711,
Dom, 6Aiahaltaia trfoant`roao pr`oantoiuiuo2
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Urolnopfiaia aiahalta fia trfoant`roao> sult;
*6/, `romolaf trfoant`roaonaltrui ratazturoo colfolta f avoo raprazolt pulntui
ca pianfra f mi`luiuo col murf avoo,*7/, `roz`ltfif frhao iolof `roz`ltfi nfra trana prol `romolaf trfoant`roao2piflui nfra n`lola fnafst ioloa sa luhata pifl `roz`ltfi,
*>/, iolof ca trfmara praiulmoraf ohfmolfr f fxuiuo nflfiuiuo avoo cup na`njoraf f d`st tarholft *lfolta ca pianfraf mi`luiuo col murf avoo/2 pifluivartonfi nfra n`lola fnafst ioloa sa luhata pifl ca trfmara,
*3/, ulmjoui ca trfmara ulmjoui d`rhft ltra iolof ca trfmara o `roz`ltfiffrhao,
*1/, iolof ca frulnfra *ca pr`oanoa/praiulmoraf ohfmolfr f fxuiuo nflfiuiuoavoo l h`haltui pianroo mi`luiuo col afv2 piflui vartonfi nfra n`lolafnafst ioloa sa luhata pifl ca frulnfra *ca pr`oanoa/,
*4/, ulmjoui ca frulnfra*ca pr`oanoa/ ulmjoui d`rhft ltra iolof ca frulnfrao `roz`ltfif frhao,
*=/, ulmjoui ca zvnlora ulmjoui d`rhft ltra iolof ca trfmara o iolof cafrulnfra,
*:/, pulntui ca ncara pulntui ca oltarsanoa f trfoant`roao nu `roz`ltfiffrhao,
*?/, ulmjoui ca ncara ulmjoui d`rhft ltra tflmaltf if trfoant`roa l pulntuica ncara o `roz`ltfif frhao,
*65/, costflf ca trfmara*gtfof/ costflf ca if `romolaf trfoant`roao pl ifpulntui ca ncara) hsurft l pifl `roz`ltfi,
*66/, vrdui trfoant`roao pulntui nai hfo lfit fi trfoant`roao cafsuprf`roz`ltfiao frhao,
*67/, smaftf trfoant`roao caprtfraf ca if `roz`ltfif frhao pl if vrduitrfoant`roao,
*6>/, rfhurf urnt`frapfrtaf trfoant`roao nuprols ltra `romolaf trfoant`roaoo vrdui trfoant`roao,
*63/, rfhurf n`g`rt`fra pfrtaf trfoant`roao nuprols ltra vrdui trfoant`roaoo pulntui ca ncara,
>Nul`stolta malarfia radarot`fra if gfzaia trfmaroo nu frhfhaltui col c`tfra) H,Fp,L) Gunurasto)6?=4) p,61
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*61/,pulntui ca olnocalpulntui l nfra trfoant`rof oltarsantafz suprfdff`goantovuiuo *phltuiuo) `gstfn`iuiuo/,
*64/, ulmjoui ca olnocal ulmjoui d`rhft ltra tflmaltf if trfoant`roa lpulntui ca olnocal o tflmaltf if suprfdff `goantovuiuo *phltuiuo)
`gstfn`iuiuo/,
*6=/, pulntui ca `njora pulntui ca pa `goantov sfu l fdfrf fnastuof fsuprfnruof sa `njata nu frhf,
*6:/, iolof ca `njoraiolof crafpt nfra ulata `njoui trmt`ruiuo) prol hoki`nuinrastturoo lit`ruiuo o prol vrdui ntroo nu pulntui ca `njora2 piflui vartonfinfra n`lola fnafst ioloa sa luhata pifl ca `njora,
*6?/, ulmjoui ca `njoraulmjoui d`rhft ltra iolof ca trfmara o iolof ca `njora,
*75/, ulmjoui ca taral fi `goantovuiuo ulmjoui d`rhft ltra iolof ca taral f`goantovuiuo o `roz`ltfif frhao,
*76/, costflf `njot costflf hsurft pa iolof ca `njora ca if pulntui capianfra *`romolaf trfoant`roao/ pl if oltarsanof trfoant`roao nu iolof ca `njora,
*77/, `rc`lftf vartonfiliohaf `ronruo pulnt ca pa trfoant`roa df ca`roz`ltfif frhao,
*7>/, `rc`lftf gfiostonliohaf `ronruo pulnt ca pa trfoant`roa df ca iolofca `njora,
*73/, iolof ca taral f `goantovuiuo iolof crafpt nfra ulata `romolaftrfoant`roao nu gfzf `goantovuiuo,
l dozon) trfoant`rof gfioston f uluo pr`oantoi) asta cruhui pfrnurs canaltrui ca mrautfta fi fnastuof l far) ca if oaoraf col afv pl if pulntui cancara) sug fnoulaf mrfvotfoao) lamioklc naiaifita aiahalta parturgft`frapranuh n`adonoaltui gfioston fi pr`oantoiuiuo) ulmjoui ca trfmara) calsotftaffaruiuo fhgoaltfi) vltui) atn,
l tohpui zg`ruiuo) prolnopfiaia d`ra nfra fno`lafz fsuprf pr`oantoiuiuosult mrfvotfof) razostalf faruiuo sfu vltui) cfn fnastf asta prazalt,
Mrfvotfof ohproh pr`oantoiuiuo ` fnnaiarfoa pa vartonfi pr`v`nlcfnastuof ` trfoant`roa casnalcalt df ca iolof ca `njora) razostalf faruiuocanaiarafz pr`oantoiui nu ` d`r pr`p`ro`lfi nu ptrftui votazao) ofr vltui) ldulnoa ca coranof fnastuof df ca coranof ca trfmara p`fta dfna nf pr`oantoiuis sa fgft ca if trfoant`rof c`rot,
Ualtru costfla ca trfmara d`frta hfro) pa ilm fnastaf hfo fpfr o
ulaia d`ra parturgft`fra hol`ra nfra traguoasn iufta l nfinui) nuh fr do
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adantui mor`sn`pon) adantui Hfmlus) adantui U`oss`l sfu adantui N`ro`ios) cao lprfnton sult oraiavflta paltru costflaia ca trfmara hono o hacoo,
Gtfof frhaoasta costfltf ca if `romolaf trfoant`roao pl if pulntui cancara) hsurft l piflui `roz`ltfi, ^ug rfp`rt gfioston oltarasafz gtfof
adonfna) fcon costflf if nfra mi`lui o halola pranozof o d`rf costruntov,Fnafstf capolca l hfra hsur ca votazf oloofi f mi`luiuo,
Ca axahpiu) costflf pl if nfra mi`lui o pstrafz adantui `h`rt`rfsuprf `huiuo) if ulaia nftam`roo ca frhfhalt asta;
post`i *rav`ivar/ (pl 155h,2
post`i hotrfioar hc, 6?4> (pl if 6155 h,2
pun hotrfioar hc,6?43 (pl if 6155 h,2
nfrfgol hc, 6?33 (pl if >555 h,2
hotrfioar hc, 6?44 (pl if >:55 h,
Uutaraf ca ptrulcaraasta nfpfnotftaf mi`luiuo ca f strgfta codarota`gstfn`ia) putlcu(sa stfgoio costflf ca if nfra s(f trfs,
Dal`halui ca ptrulcara capolca ca;
pr`proatoia `gstfn`iai`r *n`lsostal) curotfta) atn,/2
alarmof nolaton f mi`luiuo l h`haltui ohpfntuiuo2 nfiogrui mi`luiuo) mrautftaf o d`rhf fnastuof,
Aiahalta ca nfinui gfioston
Dom, 7Srfoant`rof pr`oantoiuiuo2
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L`tfooia utoiozfta;
m 8 ?):6 hs7fnnaiarfof mrfvotfo`lfi2
ulmjoui sug nfra asta iflsft pr`oantoiui2
v votazf oloofi f pr`oantoiuiuo 2y5liohaf ca if nfra asta iflsft pr`oantoiui2
ccostflf ca if `romolaf trfoant`roao pl if pulntuica ncara,
Costflf ca trfmara *c/ sfu gtfof frhao) raprazolt costflf ca if `romolaftrfoant`roao pl if pulntui ca ncara) hsurft l pifl `roz`ltfi,
5
77solsol
n`symvv
m
vc
Ftulno nlc suprfdff cafsuprf nraof asta iflsft pr`oantoiui asta pift oliohaf ca if nfra asta iflsft fnastf asta amfi nu zar` *y5 8 5/ raifof cavola;
m
vc
7sol7
l nfzui pfrtonuifr l nfra 8 315o y58 5 razuit;
m
vc
7
Sohpui ca zg`r *t/ raprazolt tohpui snurs col h`haltui l nfra pr`oantoiuiprsata afvf pl fkulma l pulntui ca ncara2
m
ymvv
v
ct
57 7solsol
n`s
l nfzui pfrtonuifr l nfra 8 315o y58 5 razuit;
m
vt
7
Trdui trfoant`roao *yhfx/ raprazolt pulntui nai hfo lfit fi trfoant`roao cafsuprf`roz`ltfiao frhao *Dom, >/
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65
m
vyy
7
sol7
5hf x
Qlmjoui if nfra fr traguo iflsft ul pr`oantoi paltru f ftolma costflf catrfmara cpaltru ` votaz f pr`oantoiuiuo if murf avoo *v/ nul`snut,
7
7sol
v
cm
7frnsol
7
6
v
cm
^a c ul pulnt pa trfoant`rof pr`oantoiuiuo f nruo costfl pa `roz`ltfi df ca`romolaf trfoant`roao asta x *Dom, 3/,
l fnast nfz) liohaf y ca pa nurgf trfoant`roao l dulnoa ca costflf x astacft ca urht`fraf raifoa;
yhfx
Dom, >Trdui trfoant`roao *j/2
x
y
Dom, 3N``rc`lftaia x)y fia
uluo pulnt ca pa nurgf
trfoant`roao2
7/23/2019 Elemente de Calcul Balistic
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66
77
5n`s7
tfl
v
xmxyy
l nfzui tutur`r raifooi`r ca hfo sus) trfoant`rof pr`oantoiuiuo vf fvaf d`rhf ulao
pfrfg`ia) sohatron df ca ` fx vartonfi na trana prol pulntui nai hfo lfit capa trfoant`roa) ca`frana lu sa of ol nfinui razostalf faruiuo *Dom, 1/,
l sotufof l nfra nlc fsuprf pr`oantoiuiuo fno`lafz o razostalf faruiuo)trfoant`rof fnastuof vf fvaf d`rhf oiustrft l Dom, 4;
Dom, 1 Mrfdonui trfoant`roao uluo pr`oantoi drrazostalf faruiuo 2
Dom, 4 Mrfdonui trfoant`roao uluo pr`oantoi paltru ul n`adonoalt ca razostal f
faruiuo c85)57 2
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67
Axahpia ca nfinui
O, Nfinuiui trfoant`roao uluo pr`oantoi ftulno nlc lu sa of ol nfinui
razostalf faruiuo
(liohaf ca if nfra asta iflsft pr`oantoiui2
( votazf oloofi f pr`oantoiuiuo2
( ulmjoui sug nfra asta iflsft pr`oantoiui2
( costflf ca if `romolaf trfoant`roao pl if pulntui ca ncara2
( tohpui ca zg`r fi pr`oantoiuiuo2
( vrdui trfoant`roao2
( costflf df ca `romola f uluo pulnt ca pa trfoant`rof pr`oantoiuiuo 2
( liohaf pulntuiuo ca pa nurgf trfoant`roao2
OO, Nfinuiui trfoant`roao uluo pr`oantoi ftulno nlc sa of ol nfinui o
razostalf faruiuo
( n`adonoaltui ca razostal fi faruiuo2
y5 5
v >5h
s
>5cam
c
v n`s * /
m v sol * / v sol * /* /7
7 m y5
c =?,3=?h
tv sol * / v sol * /* /
77 m y5
m
t >,51?s
yhfx y5v sol * /* /7
7 m
yhfx 66,3=7h
x 45
y y5 x tfl * /m x
7
7 v n`s * /* /
7
y :,3?h
C 5,5
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6>
( fnnaiarfof mrfvotfo`lfi2
( hfsf pr`oantoiuiuo2
( votazf oloofi f pr`oantoiuiuo2
( ulmjoui sug nfra asta iflsft pr`oantoiui2
(liohaf ca if nfra sa iflsafz pr`oantoiui2
( luhrui ca pfo fo nfinuiuiuo o tohpui doanruo pfs2
U`zoof o votazf oloofi fpr`oantoiuiuo2
Totazf pr`oantoiuiuo2
Fnnaiarfof pa x2
Fnnaiarfof pa y2
m ?,:
h 5,
v5
>5
>5cam
v5x v5
n`s * /
v5x 71,?:6
x5
v5y v5
sol * /
y5
5
l >5 t 5,5
o 6 l to o t
v5y 61
r x5
x5
y5
y5
vx v5x
vy v5y
v vx* /7
vy* /7
fxC v vx
h
fy mC v vy
h
xo
xo 6
vx t 6
7fx t* /
7
yo
yo 6
vy t6
7fy t* /
7
vx vx fx t
vy vy fy t
5 o
xo
6 o
yo
o 6 ld` r
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63
5 5,71 5,1 5,=1 6 6,71 6,1 6,=1 7 7,71 7,15
1
65
61
75
71
>5
>1
35
31
15
Costfltf dftf ca `romola f pr`oantoiuiuo ( dulntoa ca tohp
Sohp
Costflt
f
r5 o
to
5 5,> 5,4 5,? 6,7 6,1 6,: 7,6 7,3 7,= >5
5,:
6,4
7,3
>,7
3
3,:
1,4
4,3
=,7
:Olfitohaf pr`oantoiuiuo dftf ca `roz`ltfif ( dulntoa ca tohp
Sohp
Olfitoha
r6 o
to
5 1 65 61 75 71 >5 >1 35 31 155
5,:
6,4
7,3
>,7
3
3,:
1,4
4,3
=,7
:
Srfoant`rof pr`oantoiui
Costfltf
Olfitoha
r6 o
r5 o