CURVAS ESPIRAL

8/16/2019 CURVAS ESPIRAL

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Camino tipo C

Curva de PI 2Vp = 60 Km/hr Gc = 6

KmPI = 0+693.724∆ = 48°51'00''Sc = 8.10%> 7% → curva con espiral

Rc=1145.92

Gc

= 190.99

¿=8VSc = 38.88

Gc≤ ¿

40

θe=¿

= 5°49'55''

∆c=∆−2θe = 37°11'10''

Lc=20∆c

Gc

= 123.95

LT = Lc+2≤¿ = 201.71

Xc=( ¿100 )(100−0.00305 θe2 ) = 38.84

Yc=( ¿100 ) (0.582θe−0.0000126 θe3 ) = 1.32

K = Xc− Rc sinθe = 19.43

P=Yc− Rc (1−cosθe ) = 0.33

T L= Xc−Yc ( 1

tan θe ) = 25.93

Tc=Yc

(

1

sinθe

)

= 12.98

CLe=√ Xc2+Yc

2 = 38.86

∅c=θe

3

= 1°56'38''

Xc=cos∅cCLe = 38.84

Yc=sin ∅cCLe = 1.32

STe=

[( Rc+ P )

(tan

∆

2

)]+ K

= 106.32



KmTE= KmPI −STe = 0+587.41

KmEC = KmTE+¿ = 0+626.29

KmCE= KmEC +¿ = 0+750.24

KmET = KmCE+¿ = 0+789.12

Ke=θe

¿2

= 0.00386

kilometr

aje

cuerd

a

L L2 Ѳ=Ke

L2

Ø=ϴ/3

KmTE=

!"#$%&'

--- --- 0.00 0.00 0°00'00

''+591.29 3.89 3.89 15.1165 0.0583

2

0°01'10

''+595.18 3.89 7.78 60.4662 0.2332

8

0°04'40

''+599.07 3.89 11.66 136.048

9

0.5248

8

0°10'30

''

+602.96 3.89 15.55 241.8647

0.93312

0°18'40''

+606.85 3.89 19.44 377.913

6

1.4580

0

0°29'10

''+610.73 3.89 23.33 544.195

6

2.0995

2

0°41'59

''+614.62 3.89 27.22 740.710

7

2.8576

8

0°57'09

''

+618.51 3.89 31.10 967.4588

3.73248

1°14'39''

+622.40 3.89 34.99 1224.44

01

4.7239

2

1°34'29

''KmEC=

!(2(%2)

3.89 38.88 1511.65

44

5.8320

0

1°56'38

''

Kilometraj

e

cer!a "

#arcial

" total



KmEC=

!(2(%2)

---- --- ---- Dm = 0°09'0

0''+640 13.71 2°03'2

6''

2°03'26''

+660 20 3°00'00''

5°03'26'' D13.71

= 2°03'26''

+680 20 3°00'0

0''

8°03'26''

+700 20 3°00'0

0''

11°03'26

''

D20 = 3°00'0

0''+720 20 3°00'0

0''

14°03'26

''

+740 20 3°00'00'' 17°03'26'' D10.24 = 1°32'09''KmCE=

!$"%2&

10.23

5

1°32'0

9''

18°35'35

''

Kilometraj

e

cer!a $ $2 =Ke$2

&=/3

KmCE=

!$"%2&

3.89 38.88 1511.65

44

5.8320 1°56'38

''+754.13 3.89 34.99 1224.44

01

4.7239 1°34'29

''+758.01 3.89 31.10 967.458

8

3.7325 1°14'39

''+761.90 3.89 27.22 740.710

7

2.8577 0°57'09

''+765.79 3.89 23.33 544.195

6

2.0995 0°41'59

''+769.68 3.89 19.44 377.913

6

1.4580 0°29'10

''+773.57 3.89 15.55 241.864

7

0.9331 0°18'40

''+777.45 3.89 11.66 136.048

9

0.5249 0°10'30

''+781.34 3.89 7.78 60.4662 0.2333 0°04'40



''+785.23 3.89 3.89 15.1165 0.0583 0°01'10

'' KmET=

!$#)%'2

---- --- 0.00 0.00 0°00'00

''

Camino tipo C

Curva de PI 3Vp =60 Km/hr Gc =8

KmPI =1+277.59∆ =108°27'00''

Sc =9.40%> 7% → curva conespiral

Rc=1145.92

Gc

=143.24

¿=8VSc =45.12

Gc≤ ¿

40

θe=¿

=9°01'26''

∆c=∆−2θe =90°24'07''

Lc=20∆c

Gc

=226.01

LT = Lc+2≤¿ =316.25

Xc=( ¿100 ) (100−0.00305θe2 ) =45.01

Yc=( ¿100 ) (0.582θe−0.0000126 θe3 ) =2.37

K = Xc− Rc sinθe =22.54

P=Yc− Rc (1−cosθe ) =0.59

T L= Xc−Yc ( 1

tan θe ) =30.11

Tc=Yc ( 1

sin θe ) =15.08

CLe=√ Xc2+Yc2 =45.07



∅c=θe

3

=3°00'29''

Xc=cos∅cCLe =45.01

Yc=sin∅cCLe =2.37

STe=[ ( Rc+ P )( tan ∆2 )]+ K =222.15

KmTE= KmPI −STe =

1+055.44

KmEC = KmTE+¿ =1+100.56

KmCE= KmEC +¿ =1+326.56

KmET = KmCE+¿ =1+371.68

Ke=θe

¿2

=0.00443

kilometra

je

cuerd

a

L L2 Ѳ=KeL2

Ø=ϴ/3

KmTE

=

1

+

055.44 --- --- 0.00 0.00 0°00'0

+ 059.95 4.51 4.51 20.3581 0.0902

4

0°01'4

+ 064.46 4.51 9.02 81.4326 0.3609

6

0°07'1

+ 068.97 4.51 13.54 183.2233 0.8121

6

0°16'1

+ 073.48 4.51 18.05 325.7303 1.4438

4

0°28'5

+ 078.00 4.51 22.56 508.9536 2.2560

0

0°45'0

+ 082.51 4.51 27.07 732.8932 3.2486

4

1°04'5

+ 087.02 4.51 31.58 997.5491 4.4217

6

1°28'2

+ 091.53 4.51 36.10 1302.921

2

5.7753

6

1°55'3

+ 096.04 4.51 40.61 1649.009

7

7.3094

4

2°26'1

KmEC 1 100.56 4.51 45.12 2035.814 9.0240 3°00'2



= + 4 0

(ilometraj

e

cer!a "

#arcial

" total

KmEC=

1+

100.56 ---- --- ----

+ 120 19.443 3°53'1

9''

3°53'19'' Dm= 0°12'00''

+ 140 20 4°00'0

0''

7°53'19''

+ 160 20 4°00'0

0''

11°53'19

''

D19.44

=

3°53'19''

+ 180 20 4°00'0

0''

15°53'19

''+ 200 20 4°00'0

0''

19°53'19

''

D20= 4°00'00''

+ 220 20 4°00'0

0''

23°53'19

''+ 240 20 4°00'0

0''

27°53'19

''

D26.56

=

5°18'44''

+ 260 20 4°00'0

0''

31°53'19

''+ 280 20 4°00'0

0''

35°53'19

''+ 300 20 4°00'0

0''

39°53'19

''KmCE

=

1

+

326.56 26.562 5°18'4

4''

45°12'04

''

(ilometraje cer!a $ $

2

=Ke$

2

&=

KmCE

=

1

+

326.56 4.51 45.12 2035.814

4

9.0240 3°00'2

+ 331.07 4.51 40.61 1649.009

7

7.3094 2°26'1

+ 335.59 4.51 36.10 1302.921

2

5.7754 1°55'3

+ 340.10 4.51 31.58 997.5491 4.4218 1°28'2

+ 344.61 4.51 27.07 732.8932 3.2486 1°04'5+ 349.12 4.51 22.56 508.9536 2.2560 0°45'0



+ 353.63 4.51 18.05 325.7303 1.4438 0°28'5+ 358.15 4.51 13.54 183.2233 0.8122 0°16'1+ 362.66 4.51 9.02 81.4326 0.3610 0°07'1+ 367.17 4.51 4.51 20.3581 0.0902 0°01'4

KmET =

1+

371.68 ---- --- 0.00 0.00 0°00'0

Camino tipo CCurva de PI "

Vp = 60 Km/hr Gc = 11

KmPI = 2+662.62∆ = 62°04'

Sc = 10.00%> 7% → curva con espiral

Rc=1145.92

Gc

= 104.17

¿=8VSc = 48.00

Gc≤ ¿

40

θe=¿

= 13°12'00''

∆c=∆−2θe = 35°40'00''

Lc=20∆c

Gc

= 64.85

LT = Lc+2≤¿ = 160.85

Xc=( ¿100 )(100−0.00305θe2 ) = 47.74

Yc=( ¿100 )(0.582θe−0.0000126θe3 ) = 3.67


P=Yc− Rc (1−cosθe ) = 0.92

T L= Xc−Yc ( 1

tan θe ) = 32.08

Tc=Yc ( 1

sinθe ) = 16.09

CLe=√ Xc2+Yc

2

= 47.89



∅c=θe

3

= 4°24'00''



STe=[ ( Rc+ P )( tan ∆2 )]+ K = 87.19

KmTE= KmPI −STe =

2+575.43

KmEC = KmTE+¿ = 2+623.43

KmCE= KmEC +¿ = 2+688.28

KmET = KmCE+¿ = 2+736.28

Ke=θe

¿2

= 0.00573

(ilometraj

e

cer!a $ $2 =Ke$2

&=/

KmTE

=

2

+

575.43 --- --- 0 0 0°00'0

+ 580.23 4.8 4.8 23.04 0.132 0°02'3

+ 585.03 4.8 9.6 92.16 0.528 0°10'3

+ 589.83 4.8 14.4 207.36 1.188 0°23'4

+ 594.63 4.8 19.2 368.64 2.112 0°42'1

+ 599.43 4.8 24 576 3.3 1°06'0

+ 604.23 4.8 28.8 829.44 4.752 1°35'0

+ 609.03 4.8 33.6 1128.96 6.468 2°09'2

+ 613.83 4.8 38.4 1474.56 8.448 2°48'5

+ 618.63 4.8 43.2 1866.24 10.692 3°33'5

KmEC

=

2

+

623.43 4.8 48 2304 13.2 4°24'0

(ilometraj

e

cer!a "

#arcial

" total Dm= 0°16'30''

KmEC

=

2

+

623.43 ---- --- ----

+ 640 16.5678

4°33'22''

4°33'22''

D16.57=

4°33'22''



+ 660 20 5°30'0

0''

10°03'2

2''+ 680 20 5°30'0

0''

15°33'2

2''

D20= 5°30'00''

KmCE=

2+

688.28 8.28078

2°16'38''

17°50'00''

D8.28= 2°16'38''

(ilometraj

e

cer!a $ $2 =Ke$2

&=/

KmCE

=

2

+

688.28 4.8 48 2304 13.2 4°24'0

+ 693.08 4.8 43.2 1866.24 10.692 3°33'5

+ 697.88 4.8 38.4 1474.56 8.448 2°48'5

+ 702.68 4.8 33.6 1128.96 6.468 2°09'2

+ 707.48 4.8 28.8 829.44 4.752 1°35'0

+ 712.28 4.8 24 576 3.3 1°06'0

+ 717.08 4.8 19.2 368.64 2.112 0°42'1

+ 721.88 4.8 14.4 207.36 1.188 0°23'4

+ 726.68 4.8 9.6 92.16 0.528 0°10'3

+ 731.48 4.8 4.8 23.04 0.132 0°02'3

KmET

=

2

+

736.28 ---- --- 0 0 0°00'0

Camino tipo C

Curva de PI )Vp = 60 Km/hr Gc = 5

KmPI = 4+488.47∆ = 58°33'Sc = 7.40%> 7% → curva con espiral

Rc=1145.92

Gc

= 229.18

¿=8VSc = 35.52



Gc≤ ¿

40

θe=¿

= 4°26'24''

∆c=∆−2θe = 49°40'12''

Lc=20∆c

Gc= 198.68

LT = Lc+2≤¿ = 269.72

Xc=( ¿100 )(100−0.00305θe2 ) = 35.50

Yc=( ¿100 )(0.582θe−0.0000126θe3 ) = 0.92


P=Yc− Rc (1−cosθe ) = 0.23

T L= Xc−Yc ( 1

tan θe ) = 23.68

Tc=Yc ( 1

sinθe ) = 11.85

CLe=√ Xc2+Yc

2 = 35.51

∅c=θe

3= 1°28'48''



STe=[ ( Rc+ P )( tan ∆2 )]+ K = 146.37

KmTE= KmPI −STe =

4+342.10

KmEC = KmTE+¿ = 4+377.62

KmCE= KmEC +¿ = 4+576.30

KmET = KmCE+¿ = 4+611.82

Ke=θe

¿2

= 0.00352



(ilometra je

cer!a

$$2

=Ke$2 &=/3

Km)*

=

4

+ 342.10 --- --- 0.00 0.00 0°00'00''

+ 345.66 3.55 3.55 12.6167 0.0444

0 0°00'53''

+ 349.21 3.55 7.10 50.4668 0.1776

0 0°03'33''

+ 352.76 3.55 10.66 113.550

30.3996

0 0°08'00''

+ 356.31 3.55 14.21 201.867

30.7104

0 0°14'12''

+ 359.86 3.55 17.76 315.417

61.1100

0 0°22'12''

+ 363.42 3.55 21.31 454.201

31.5984

0 0°31'58''

+ 366.97 3.55 24.86 618.218

52.1756

0 0°43'31''

+ 370.52 3.55 28.42 807.469

12.8416

0 0°56'50''

+ 374.07 3.55 31.97 1021.95

303.5964

0 1°11'56''Km*

=4+

377.62 3.55 35.52 1261.67

044.4400

0 1°28'48''

(ilometra je

cer!a

" #arcial

" total

Km*=

4+

377.62 ---- --- ---- Dm =0°07'30''

+ 380 2.37 0°17'4

9''0°17'49'

'

+ 400 20 2°30'0

0''2°47'49'

'D2.38

=0°17'49''

+ 420 20 2°30'0

0''5°17'49'

'

+ 440 20 2°30'0

0''7°47'49'

'D20

=2°30'00''

+ 460 20 2°30'0

0''10°17'4

9''+ 480 20 2°30'0 12°47'4 D16.30 =



0'' 9'' 2°02'17''

+ 500 20 2°30'0

0''15°17'4

9''

+ 520 20 2°30'0

0''

17°47'4

9''+ 540 20

2°30'00''

20°17'49''

+ 560 20 2°30'0

0''22°47'4

9''Km*

=4+

576.30 16.30 2°02'1

7''24°50'0

6''

(ilometra

je

cer!

a $

$2

=Ke$2 &=/3

Km*=

4+

576.30 3.55 35.52 1261.67

04 4.4400 1°28'48''

+ 579.86 3.55 31.97 1021.95

30 3.5964 1°11'56''

+ 583.41 3.55 28.42 807.469

1 2.8416 0°56'50''

+ 586.96 3.55 24.86 618.218

5 2.1756 0°43'31''

+ 590.51 3.55 21.31 454.2013

1.5984 0°31'58''

+ 594.06 3.55 17.76 315.417

6 1.1100 0°22'12''

+ 597.62 3.55 14.21 201.867

3 0.7104 0°14'12''

+ 601.17 3.55 10.66 113.550

3 0.3996 0°08'00''

+ 604.72 3.55 7.10 50.4668 0.1776 0°03'33''

+ 608.27 3.55 3.55 12.6167 0.0444 0°00'53''Km*)

=4+

611.82 ---- --- 0.00 0.00 0°00'00''

CURVAS ESPIRAL

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