18 superelevation and spiral curves

7/25/2019 18 Superelevation and Spiral Curves

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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



2

Quiz Answers! Increase clear zone

"! Improve horizontal and vertical

ali#nment$! Assure ade%uate surface draina#e

&! Increase skid resistance on down#radecurves



'

(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



4

(uperelevation and (piral(uperelevation and (piral-urves-urves-. /' 0ecture 1&-. /' 0ecture 1&



bectives1! *efine superelevation runoff len#th andmethods of attainment 3for simple andspiral curves4

2! -alculate spiral curve len#th



"

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


http://slidepdf.com/reader/full/18-superelevation-and-spiral-curves 9/54 =

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



(ource@ A olicyon ,eometric*esi#n of6i#hways and(treets 39he,reen +ook4!Washin#tonB *-!AmericanAssociation of(tate 6i#hwayand9ransportation

fficialsB 21/th .d!



(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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(ource@ -al9rans *esi#n Manual onlineBhttp@CCwww!dot!ca!#ovCh%CoppdChdmCpdfCchp?2??!pdf



1(ource@ Iowa *9 (tandard 5oadlans

(ame as point . of ,+



1"

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



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



1&

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



1=

0en#th of (uperelevation5unoff

F E multilane adustment factorAdusts for total width

r



2

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



21

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



22

Multilane Adustment

; 5unout and runoff must be adusted formultilane rotation!

; (ee Iowa *9 manual section 2A82 and(tandard 5oad lan 582



2'

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

,

;



2/

0r E 12eF E 3124 3!/4 31!4

, ! 0r E 144 feet



2

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



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!



27

(piral -urve(piral -urve9ransitions9ransitions



2&

(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



'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



'2

Ma:imum 0en#th of (piral

; (afety problems may occur whenspiral curves are too lon# J drivers

underestimate sharpness ofapproachin# curve 3drivere:pectancy4



''

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



'/

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!



'(ource@ Iowa *9*esi#n Manual



'"(ource@ Iowa *9*esi#n Manual



'$(ource@ Iowa*9 *esi#nManual

SPIRAL TERMI!L!"#



'&(ource@ Iowa *9 *esi#n Manual

SPIRAL TERMI!L!"#

Att i t f l ti



'=

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 -(!



/(ource@ Iowa *9 (tandard 5oad lans 582

$ith Spirals

(ame as point . of ,+



/1

$ith Spirals

9an#ent runout 3A to +4



/2

$ith Spirals

5emoval of crown



/'

$ith Spirals

9ransition ofsuperelevation >ull superelevation



//



/

9ransition .:ample,iven@

; I L station 2/<$/!2/

; * E / 35 E 1B/'2!/ ft4∀∆ E !/1$

; 0 E 1'&!/2 ft



/"

With no spiral N; 9 E $2!' ft

; - E I J 9 E 2'& <21!=/



/$

>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!



/&

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'"< '!=/



/=

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




(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

http://www.dot.state.ia.us/design/00_toc.htm






1

; 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




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




'

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




7otes J Iowa *9

(ource@ Iowa *9 (tandard 5oad lans

18 superelevation and spiral curves

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