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Quiz AnswersWhat can be done to improve the safety of ahorizontal curve?
Make it less sharp Widen lanes and shoulders on curve
Add spiral transitions Increase superelevation
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Quiz Answers! Increase clear zone
"! Improve horizontal and vertical
ali#nment$! Assure ade%uate surface draina#e
&! Increase skid resistance on down#radecurves
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(ome of )our Answers *ecrease posted speed Add rumble strips
+i##er or better si#ns ,uardrail +etter lane markers
(i#ht distance *ecrease radius
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(uperelevation and (piral(uperelevation and (piral-urves-urves-. /' 0ecture 1&-. /' 0ecture 1&
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bectives1! *efine superelevation runoff len#th andmethods of attainment 3for simple andspiral curves4
2! -alculate spiral curve len#th
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ther Issues 5elatin# to
6orizontal -urves 1! 7eed to coordinate withvertical and topo#raphy
2! 7ot always needed
MAXIMUM CENTERLINE DEFLECTION
NOT REQUIRING HORIZONTAL CURVE
Design Speed, mph M!im"m De#$e%&i'n
() )*+-
+ +*.)-
+) (*.)-
. (*/)-
.) /*/)-
) /*/)-
)) /*-
0 /*-
0) *.)-
1 *.)-
S'"2%e3 Ohi' DOT Design Mn"$, Fig"2e ((4/E
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Attainment of (uperelevation 8
,eneral 1! 9an#ent to superelevation2! Must be done #radually over a distance without
appreciable reduction in speed or safety andwith comfort
'! -han#e in pavement slope should be consistentover a distance
/! Methods 3.:hibit '8'$ p! 1&"4a! 5otate pavement about centerline
b! 5otate about inner ed#e of pavementc! 5otate about outside ed#e of pavement
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(uperelevation
9ransition (ection; 9an#ent 5unout (ection <(uperelevation 5unoff (ection
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9an#ent 5unout (ection; 0en#th of roadway needed toaccomplish a chan#e in outside8lane
cross slope from normal crossslope rate to zero
>or rotation about
centerline
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(uperelevation 5unoff
(ection; 0en#th of roadway needed toaccomplish a chan#e in outside8lane
cross slope from to fullsuperelevation or vice versa
; >or undivided hi#hways with cross8
section rotated about centerline
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(ource@ A olicyon ,eometric*esi#n of6i#hways and(treets 39he,reen +ook4!Washin#tonB *-!AmericanAssociation of(tate 6i#hwayand9ransportation
fficialsB 21/th .d!
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(ource@ A olicyon ,eometric*esi#n of6i#hways and(treets 39he,reen +ook4!Washin#tonB *-!AmericanAssociation of(tate 6i#hwayand
9ransportationfficialsB 21/th .d!
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( - l9 * i M l li
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1/
(ource@ -al9rans *esi#n Manual onlineBhttp@CCwww!dot!ca!#ovCh%CoppdChdmCpdfCchp?2??!pdf
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1(ource@ Iowa *9 (tandard 5oadlans
(ame as point . of ,+
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Attainment 0ocation 8
W6.5.1! (uperelevation must be attained over alen#th that includes the tan#ent and thecurve 3why4
2! 9ypical@ ""D on tan#ent and ''D oncurve of len#th of runoff if no spiral
'! Iowa uses $D and 'D if no spiral
/! (uper runoff is all attained in (piral ifused 3see lab manual 3Iowa (piral len#th E5unoff len#th4
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1$
Minimum 0en#th of 5unofffor curve
; 0r based on draina#e and aesthetics; rate of transition of ed#e line from 7-
to full superelevation traditionally taken
at !D 3 1 foot rise per 2 feet alon#the road4; current recommendation varies from
!'D at & mph to !&D for 1mph
3with further adustments for numberof lanes4
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Minimum 0en#th of 9an#ent 5unout
0t E e7- : 0r
ed
where
; e7- E normal cross slope rate 3D4; ed E desi#n superelevation rate
; 0r E minimum len#th of superelevation runoff 3ft4
35esult is the ed#e slope is same as for 5unoff
se#ment4
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1=
0en#th of (uperelevation5unoff
F E multilane adustment factorAdusts for total width
r
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5elative ,radient 3,4; Ma:imum lon#itudinal slope
; *epends on desi#n speedB hi#her
speed E #entler slope! >or e:ample@; >or 1 mphB , E !$&D
; >or & mphB , E !'D
; (ee tableB ne:t pa#e
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Ma:imum 5elative,radient 3,4
(ource@ A olicy on ,eometric *esi#n of6i#hways and (treets 39he ,reen +ook4!Washin#tonB *-! American Association of
(tate 6i#hway and 9ransportation fficialsB21 /th .d!
M l il Ad
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Multilane Adustment
; 5unout and runoff must be adusted formultilane rotation!
; (ee Iowa *9 manual section 2A82 and(tandard 5oad lan 582
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0en#th of (uperelevation5unoff .:ample
>or a /8lane divided hi#hway with cross8sectionrotated about centerlineB desi#n superelevationrate E /D! *esi#n speed is mph! What is the
minimum len#th of superelevation runoff 3ft4
0r E 12eF
,
;
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2/
0r E 12eF E 3124 3!/4 31!4
, ! 0r E 144 feet
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9an#ent runout len#th.:ample continued
; 0t E 3e7- C ed 4 : 0r
as defined previouslyB if 7- E 2D9an#ent runout for the e:ample is@
09 E 2D C /D G 1//H E $2 feet
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2"
>rom previous e:ampleB speed E mphB e E /D
>rom chart runoff E 1// feetB same as from calculation
(ource@ A olicy on ,eometric*esi#n of 6i#hways and(treets 39he ,reen +ook4!Washin#tonB *-! American
Association of (tate 6i#hwayand 9ransportation fficialsB21 /th .d!
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27
(piral -urve(piral -urve9ransitions9ransitions
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(piral -urve 9ransitions; ehicles follow a transition path asthey enter or leave a horizontal
curve; -ombination of hi#h speed and sharp
curvature can result in lateral shifts
in position and encroachment onadoinin# lanes
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Minimum 0en#th of (piral
ossible .%uations@0ar#er of 314 0 E '!1 '
5-
Where@0 E minimum len#th of spiral 3ft4
E speed 3mph4
5 E curve radius 3ft4
- E rate of increase in centripetal acceleration3ftCs'4 use 18' ftCs' for hi#hway4
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'1
Minimum 0en#th of (piral
r 324 0 E 32/pmin541C2
Where@
0 E minimum len#th of spiral 3ft45 E curve radius 3ft4
pmin E minimum lateral offset between the
tan#ent and circular curve 3!"" feet4
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'2
Ma:imum 0en#th of (piral
; (afety problems may occur whenspiral curves are too lon# J drivers
underestimate sharpness ofapproachin# curve 3drivere:pectancy4
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''
Ma:imum 0en#th of (piral
0 E 32/pma:541C2
Where@0 E ma:imum len#th of spiral 3ft4
5 E curve radius 3ft4
pma: E maximum lateral offset between thetan#ent and circular curve 3'!' feet4
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0en#th of (piralo AA(69 also provides recommended spiral
len#ths based on driver behavior ratherthan a specific e%uation! (ee 9able 1"!12of te:t and the associated tan#ent runout
len#ths in 9able 1"!1'!o Superelevation runoff length is set equalto the spiral curve length when spirals areused!
o *esi#n 7ote@ >or construction purposesBround your desi#ns to a reasonable valuesKe!#!0s E 1/$ feetB round it to0s E 1 feet!
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'(ource@ Iowa *9*esi#n Manual
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'"(ource@ Iowa *9*esi#n Manual
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'$(ource@ Iowa*9 *esi#nManual
SPIRAL TERMI!L!"#
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'&(ource@ Iowa *9 *esi#n Manual
SPIRAL TERMI!L!"#
Att i t f l ti
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Attainment of superelevationon spiral curves
(ee sketches that follow@
7ormal -rown 3*9 J pt A4
1! 9an#ent 5unout 3sometimes known as crownrunoff4@ removal of adverse crown 3*9 J A to +4+ E 9(
2! oint of reversal of crown 3*9 J -4 note A to + E+ to -
'! 0en#th of 5unoff@ len#th from adverse crownremoved to full superelevated 3*9 J + to *4B * E(-
/! >ully superelevate remainder of curve and thenreverse the process at the -(!
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/(ource@ Iowa *9 (tandard 5oad lans 582
$ith Spirals
(ame as point . of ,+
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/1
$ith Spirals
9an#ent runout 3A to +4
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/2
$ith Spirals
5emoval of crown
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/'
$ith Spirals
9ransition ofsuperelevation >ull superelevation
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//
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/
9ransition .:ample,iven@
; I L station 2/<$/!2/
; * E / 35 E 1B/'2!/ ft4∀∆ E !/1$
; 0 E 1'&!/2 ft
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/"
With no spiral N; 9 E $2!' ft
; - E I J 9 E 2'& <21!=/
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>or@
; *esi#n (peed E mph
; superelevation E !/
; normal crown E !2
5unoff len#th was found to be 1//H9an#ent runout len#th E
!2C !/ G 1// E $2 ft!
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/&
Where to start transition for superelevation?
Osin# 2C' of 0r on tan#entB 1C' on curve for
superelevation runoff@*istance before - E 0t < 2C' 0rE$2 <2C' 31//4 E 1"&
(tart removin# crown at@
- station J 1"&H E 2'&<21!=/ 8 1"&! E(tation E 2'"< '!=/
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/=
0ocation .:ample J with spiral
; (peedB e and 7- as before and∀∆ E !/1$
; I L (tation 2/<$/!2/; 5 E 1B/'2!/H
; 0r was 1//HB so set 0s E 1H
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0ocation .:ample J with spiral
(ee Iowa *9 desi#n manual for moree%uations@
http@CCwww!dot!state!ia!usCdesi#nCPtoc!htm-hapterP2
; (piral an#le Rs E 0s G * C2 E ' de#rees
; E !" 3calculated4; 9s E 35 < p 4 tan 3delta C24 < k E &2$!"' ft
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; 9( station E I J 9sE 2/<$/!2/ J & < 2$!"'
E 2'$</"!"15unoff len#th E len#th of spiral9an#ent runout len#th E 0t E 3e7- C ed 4 : 0r E 2D C /D G 1H E $H9herefore@ 9ransition from 7ormal crown be#ins
at 32'$</"!"14 J 3<$!4 E 2'"<$1!"1
0ocation .:ample J with spiral
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2
With spiralsB the central an#le for thecircular curve is reduced by 2 G Rs
0c E 33delta J 2 G Rs4 C *4 G 1
0c E 3!/1$82G'4C/4G1 E 12'!/2 ft9otal len#th of curves E 0c <2 G 0s E 1'!/2
erify that this is e:actly 1 spiral len#thlon#er than when spirals are not used
3e:tra credit for who can tell me whyBprovide a one8pa#e memo by Monday4
0ocation .:ample J with spiral
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Also note that the tan#ent len#th witha spiral should be lon#er than thenon8spiraled curve by appro:imately S
of the spiral len#th used! 3#ood checkJ but why???4
0ocation .:ample J with spiral