Calculos de curvas simples

Datos:

Camino: Tipo A4

Vp = 90 Km/h

Pl = 2 + 582.16

∆T = 19° 0’ 35.45’’

Grado sexagesimal = 19.00984722

Memoria de Cálculo

1.- Radio mínimo (Rmin)

Rmin = 0.0282 * Vp²

Rmin = 0.0282 * (90)²

Rmin = 228.42 m

2.- Grado máximo (Gmax)

Gmax = 1145.92 / Rmin

Gmax = 1145.92 / 228.42

Gmax = 5.016723579°

3.- Propuesta del grado de curvatura (Gc) para una curva espiral

40% Gmax = 0.4 * Gmax

40% Gmax = 0.4 * 5.016723579

40% Gmax = 2.006689432

40% Gmax = 2° 0’ 24.08’’

Curva espiral Gc > 40%Gmax

Gcprop = 2° 15’ 0’’

Gcprop = 2.25

Ac = 100 cm

Le = 89 m

Sc = 7.3

Sn = 2%

N = (Sn * Le) / Sc

N = (2 * 89) / 7.3

N = 24.38 m

4.- Calculo de elementos de la curva espiral

Gc = 2.25

Radio de curvatura (Rc)

Rc = 1145.92 / Gc

Rc = 1145.92 / 2.25

Rc = 509.30

Ángulo de la espiral (θe)

θe = (Le * Gc) / 40

θe = (89 * 2.25) / 40

θe = 5.00625

θe = 5° 0’ 22.5’’

Coordenadas CE o EC

Xc = (Le * (100 – (0.00305 * θe²))) / 100

Xc = (89 * (100 – (0.00305 * (5° 0’ 22.5’’)²))) / 100

Xc = 88.93

Yc = (Le * ((0.582 * θe) – (0.00001266 * θe³))) / 100

Yc = (89 * ((0.582 * 5° 0’ 22.5’’) – (0.00001266 * (5° 0’ 22.5’’)³))) / 100

Yc = 2.59

Coordenadas PC o PT

P = Yc – (Rc * (1 - Cosθe))

P = 2.59 – (509.30 * (1 – Cos(5° 0’ 22.5’’)))

P = 0.65

K = Xc – (Rc * Senθe)

K = 88.93 – (509.30 * Sen(5° 0’ 22.5’’))

K = 44.49

Subtangente (Ste)

Ste = ((Rc + P) * Tg(∆T / 2)) + K

Ste = ((509.30 + 0.65) * Tg(19° 0’ 35.45’’ / 2)) + 44.49

Ste = 129.87

Angulo de la curva simple (∆C)

∆C = ∆T - 2θe

∆C = 19° 0’ 35.45’’ – 2(5° 0’ 22.5’’)

∆C = 8° 59’ 50.45’’

∆C = 8.99

Longitud de la curva simple (Lc)

Lc = 20∆C / Gc

Lc = 20(8.99) / 2.25

Lc = 79.98

Longitud total de la curva espiral (LTce)

LTce = (2 * Le) + Lc

LTce = (2 * 89) + 79.98

LTce = 257.98

Cuerda larga de la espiral (Cle)

Cle = √ (Xc² + Yc²)

Cle = √ ((88.93)² + (2.59)²)

Cle = 88.97

Tangente larga (TL)

TL = Xc – (Yc / Tgθe)

TL = 88.93 – (2.59 / Tg(5° 0’ 22.5’’))

TL = 59.36

Tangente corta (Tc)

Tc = Yc / Senθe

Tc = 2.59 / Sen(5° 0’ 22.5’’)

Tc = 29.68

Kilometrajes de los puntos de la curva espiral TE, EC, CE, ET

Km TE = Km Pl – Ste

Km TE = 2 + 582.16 – 129.87

Km TE = 2 + 452.29

Km EC = Km TE + Le

Km TE = 2 + 452.29 + 89

Km TE = 2 + 541.29

Km CE = Km EC + Lc

Km TE = 2 + 541.29 + 79.98

Km TE = 2 + 621.27

Km ET = Km CE + Le

Km TE = 2 + 621.27 + 89

Km TE = 2 + 710.27

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