A horizontal curve is to be designed for a two-lane road in mountainous terrain. The following data are known: Intersection angle: 40 degrees, tangent length = 436.76 ft, station of PI: 2700+10.65, fs = 0.12, e = 0.08. Determine: (a) design speed (b) station of the PC (c) station of the PT (d) deflection angle and chord length to the first 100 ft station

Question

What will be an ideal response?

Answer 1

(a) From the given horizontal curve data, the radius can be calculated, from which
design speed for the curve can be derived.
The radius can be found by rearranging Equation 15.22,
R = T / (tan ?/2) = 436.76 / tan (40°/2) = 436.76 / 0.3640 = 1200 ft
The design speed can then be found:
R = u2 / [15(e + fs)]
(1200) = u2 / [ 15 (0.08+0.12) ]
u2 = 3600
u = 60 mi/h
(b) Station of the PC can be found by subtracting the tangent length from the
station of the PI.
PC = (2700+10.65) – (4+36.76) = 2695+73.89
(c) The length of the curve can be found using Equation 15.26,
L = ?R?/180 = (3.1415926)(1200)(40)/180 = 837.76 ft
Station of the PT can be found by adding the length of the curve to the
station of the PC.
PT = (2695+73.89) + (8+37.76) = 2704+11.65
(d) Deflection angle and chord length to the first full station
To find the deflection angle to the first full station, use Equation 15.27,
?1/2 = 180 l1 / 2?R = (180)(100–73.89)/(2)(3.1415926)(1200) = 0.6233°
The chord to the first full station can be found using Equation 15.28,
C1 = 2R sin (?1/2) = (2)(1200) sin (1.24666/2) = 26.11 ft