Calculo de Curvas Horizontales

Calculo de curvas horizontales

CURVA PI1

Calculo de los principales elementos de una curva.

T ¿ Rtg( ∆2 )= 45 tg( 502 )=20.98 m

CL ¿2 Rsen(∆2 ) = 45∗2 sen ( 502 )=38.04 m

M ¿ R(1−cos (∆2 ))= 45 (1−cos ( 502 )) = 4.22 m

E¿ R( 1

cos (∆2 )−1)=

45 ( 1

cos( 502 )−1)= 4.65 m

LC=π∗R∗∆180

= π∗45∗50180

=39.27m

Calculo de progresivas

Prog Pc= Prog PI -T

Prog Pc= 0+112-20.98 = Km 0+091.02

Prog Pt= Prog PC +LC

Prog Pc= 0+112 + 39.27= Km 0 + 130.29

ESTACA PROGRESIVA PARCIAL ACUMULADO Φ α CPC 0 + 091.02 - - - - -1 0 + 100.00 8.98 8.98 11.4394904 5.71974522 8.972 0 + 110.00 10 18.98 24.1783439 12.089172 18.853 0 + 120.00 10 28.98 36.9171975 18.4585987 28.48

4 0 + 130.00 10 38.98 49.656051 24.8280255 37.78PT 0 + 130.29 0.29 39.27 50.0254777 25.0127389 38.04

CURVA PI2


T ¿ Rtg( ∆2 )= 25 tg( 252 )= 5.54 m

CL ¿2 Rsen(∆2 ) = 25∗2 sen (252 )= 10.82 m

M ¿ R(1−cos (∆2 ))= 25(1−cos ( 252 )) = 0.59 m

E¿ R( 1

cos (∆2 )−1)=

25( 1

cos ( 252 )−1)= 4.65 m

LC=π∗R∗∆180

= π∗25∗25180

=10.91m


Prog Pc= Prog PI -T

Prog Pc = Km 0 + 206 – 5.54 = 200.46


Prog Pc= 0 + 200.46 + 10.91= Km 0 + 211.37

ESTACA PROGRESIVA PARCIAL ACUMULADO Φ α CPC 0 + 200.46 - - - - -1 0 + 210.00 9.54 9.54 21.8751592 10.9375796 9.48

PT 0 + 211.37 1.37 10.91 25.0165605 12.5082803 10.82

CURVA PI3


T ¿ Rtg( ∆2 )= 45 tg( 672 )= 29.78 m

CL ¿2 Rsen(∆2 ) = 45∗2 sen ( 672 )= 49.67 m

M ¿ R(1−cos (∆2 ))= 45 (1−cos ( 672 )) = 7.48 m

E¿ R( 1

cos (∆2 )−1)=

45 ( 1

cos( 672 )−1)= 8.96 m

LC=π∗R∗∆180

= π∗45∗67180

=52.62m


Prog Pc= Prog PI -T

Prog Pc= 0 + 303 -29.78 = Km 0 + 273.22


Prog Pc= 0 + 273.22 + 52.62= Km 0 + 325.84

ESTACA PROGRESIVA PARCIAL ACUMULADO Φ α CPC 0 + 273.22 - - - - -1 0 + 280 6.78 6.78 8.63694268 4.31847134 6.782 0 + 290 10 16.78 21.3757962 10.6878981 16.683 0 + 300 10 26.78 34.1146497 17.0573248 26.394 0 + 310 10 36.78 46.8535032 23.4267516 35.775 0 + 320 10 46.78 59.5923567 29.7961783 44.70

PT 0 + 325.84 5.84 52.62 67.0318471 33.5159236 49.67CURVA PI4


T ¿ Rtg( ∆2 )= 45 tg( 882 )= 43.46 m

CL ¿2 Rsen(∆2 ) = 45∗2 sen ( 882 )= 62.52 m

M ¿ R(1−cos (∆2 ))= 45 (1−cos ( 882 )) = 12.63 m

E¿ R( 1

cos (∆2 )−1)=

45 ( 1

cos( 882 )−1)= 17.56 m

LC=π∗R∗∆180

= π∗45∗88180

=69.12m


Prog Pc= Prog PI -T

Prog Pc= 0 + 402 – 43.46 = Km 0 + 358.54


Prog Pc= 0 + 358.54 + 69.12= Km 0 + 427.66

CURVA PI5


T ¿ Rtg( ∆2 )= 45 tg ( 272 ) = 10.80 m CL ¿2 Rsen(∆2 ) = 45∗2 sen ( 272 )= 21.01 m

ESTACA PROGRESIVA PARCIAL ACUMULADO Φ α C

PC 0 + 358.54 - - - - -

1 0 + 360 1.46 1.46 1.85987261 0.92993631 1.46

2 0 + 380 20 21.46 27.3375796 13.6687898 21.25

3 0 + 400 20 41.46 52.8152866 26.4076433 40.02

4 0 + 420 20 61.46 78.2929936 39.1464968 56.80

PT 0 + 427.66 7.66 69.12 88.0509554 44.0254777 62.52

M ¿ R(1−cos (∆2 ))= 45 (1−cos ( 272 )) = 1.28 m

E¿ R( 1

cos (∆2 )−1)=

45 ( 1

cos( 502 )−1)= 4.65 m

LC=π∗R∗∆180

= π∗45∗27180

=21.21m


Prog Pc= Prog PI -T

Prog Pc= 0 + 513 – 10.80 = Km 0 + 502.20


Prog Pc= 0 + 502.20 + 21.21 = Km 0 + 523.41

ESTACA PROGRESIVA PARCIAL ACUMULADO Φ α CPC 0 + 502.20 - - - - -1 0 + 510 7.8 7.8 9.93630573 4.96815287 7.802 0 + 520 10 17.8 22.6751592 11.3375796 17.68

PT 0 + 523.41 3.41 21.21 27.0191083 13.5095541 21.01

CURVA PI6


T ¿ Rtg( ∆2 )= 45 tg( 582 )= 24.94 m

CL ¿2 Rsen(∆2 ) = 45∗2 sen ( 582 ) = 43.63m

M ¿ R(1−cos (∆2 ))= 45 (1−cos ( 582 )) = 5.64 m

E¿ R( 1

cos (∆2 )−1)=

45 ( 1

cos( 582 )−1) = 6.45 m

LC=π∗R∗∆180

= π∗45∗58180

=45.55m


Prog Pc= Prog PI -T

Prog Pc= 0 + 625 – 24.94 = Km 0 + 600.06


Prog Pc= 0 + 600.06 + 45.55 = Km 0 + 645.61

ESTACA PROGRESIVA PARCIAL ACUMULADO Φ α CPC 0 + 600.06 - - - - -1 0 + 610 9.94 9.94 12.6624204 6.33121019 9.392 0 + 620 10 19.94 25.4012739 12.7006369 19.253 0 + 630 10 29.94 38.1401274 19.0700637 28.884 0 + 640 10 39.94 50.8789809 25.4394904 38.16

PT 0 + 645.61 5.61 45.55 58.0254777 29.0127389 43.63

CURVA PI7


T ¿ Rtg( ∆2 )= 45 tg( 552 ) = 23.43 m

CL ¿2 Rsen(∆2 ) = 45∗2 sen ( 552 ) = 41.56 m

M ¿ R(1−cos (∆2 ))= 45 (1−cos ( 552 )) = 5.08 m

E¿ R( 1

cos (∆2 )−1)=

45 ( 1

cos( 552 )−1)= 5.73 m

LC=π∗R∗∆180

= π∗45∗55180

=43.20m


Prog Pc= Prog PI -T

Prog Pc= 0 + 770 – 23.43 = Km 0 + 746.57


Prog Pc= 0 + 746.57 + 43.20 = Km 0 + 789.77


PC 0 + 746.57 - - - - -

1 0 + 750 3.43 3.43 4.36942675 2.18471338 3.44

2 0 + 760 10 13.43 17.1082803 8.55414013 13.38

3 0 + 770 10 23.43 29.8471338 14.9235669 23.17

4 0 + 780 10 33.43 42.5859873 21.2929936 32.66

PT 0 + 789.77 9.77 43.2 55.0318471 27.5159236 41.56

CURVA PI8


T ¿ Rtg( ∆2 )= 35 tg( 702 )= 24.51 m

CL ¿2 Rsen(∆2 ) = 35∗2 sen (702 ) = 40.15 m

M ¿ R(1−cos (∆2 ))= 35(1−cos (702 )) = 6.33 m

E¿ R( 1

cos (∆2 )−1)=

35( 1

cos ( 702 )−1)= 4.65 m

LC=π∗R∗∆180

= π∗35∗70180

=42.76m


Prog Pc= Prog PI -T

Prog Pc= 0 + 820 – 24.51 = Km 0 + 795.49 Prog Pt= Prog PC +LC

Prog Pc= 0 + 795.49 + 42.76 = Km 0 + 838.25

ESTACA PROGRESIVA PARCIAL ACUMULADO Φ α CPC 0 + 795.49 - - - - -1 0 + 800 4.51 4.51 7.3867152 3.6933576 4.512 0 + 810 10 14.51 23.7652411 11.8826206 14.413 0 + 820 10 24.51 40.1437671 20.0718835 24.014 0 + 830 10 34.51 56.522293 28.2611465 33.13

PT 0 + 838.25 8.25 42.76 70.0345769 35.0172884 40.15

CURVA PI9


T ¿ Rtg( ∆2 )= 25 tg( 752 )= 19.18 m

CL ¿2 Rsen(∆2 ) = 25∗2 sen (752 ) = 30.44 m

M ¿ R(1−cos (∆2 ))= 35(1−cos (702 )) = 5.17 m

E¿ R( 1

cos (∆2 )−1)=

35( 1

cos ( 752 )−1) = 6.51 m

LC=π∗R∗∆180

= π∗25∗75180

=32.72m


Prog Pc= Prog PI -T

Prog Pc= 0 + 862 – 19.18 = Km 0 + 842.82


Prog Pc= 0 + 842.82 + 32.72 = Km 0 + 875.54


PC 0 + 842.82 - - - - -

1 0 + 850 7.18 7.18 16.4636943 8.23184713 7.17

2 0 + 860 10 17.18 39.3936306 19.6968153 16.85

3 0 + 870 10 27.18 62.3235669 31.1617834 26.61

PT 0 + 875.54 5.54 32.72 75.0267516 37.5133758 30.44

Calculo del peralte Vd Rmin

CURVA SENTIDO ∆ Rmin.(°) PERALTE (%) Vd. (Km/h) ∆vel.C-1 I 58 45 9.6 39.72 -C-2 D 25 25 12 30 9.72C-3 D 67 45 9.6 39.72 9.72C-4 I 88 45 9.6 39.72 1C-5 I 27 45 9.6 39.72 1C-6 D 58 45 9.6 39.72 1C-7 I 55 45 9.6 39.72 1C-8 D 70 35 10.8 40.57 0.85C-9 I 75 25 12 30 10.57

Calculo de Curvas Horizontales

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