Given a circular curve connecting 2 tangents that intersect at an angle of 48°. The PI is at station (948+67.32) and the design speed of the highway is 60 mi/h. Determine the point of the tangent and the deflection angles from the PC to full stations for laying out the curve.
What will be an ideal response?
First determine the radius of the curve:
R = u2 / [15(e + fs)]
For u = 60 mi/h, from Table 3.4, fs = 0.12, e = 0.08
R = (60)2 / [15(0.08+0.12)]
R = 1200 ft
The length of the tangent, T, can be found using Equation 15.22,
T = R tan(?/2) = 1200(tan(48°/2))
T = 534.27 ft
The length of the curve, L, is given by Equation 15.26:
L = R?? / 180 = 1200(48)(3.1415926) / 180
L = 1005.30 ft
Station of the PC can be found by subtracting the tangent length from the station
of the PI.
PC = (948+67.32) – (5+34.27) = 943+33.05
Station of the PT can be found by adding the length of the curve to the station of
the PC.
PT = (943+33.05) + (10+5.30) = 953+38.35
First full station is located at 944+00
?1 / ? = l1 / L
?1 / 48 = 66.95 / 1005.3
?1 = 3.197°
The first chord can be found using Equation 15.28,
C1 = 2R sin (?1/2) = 2(1200) sin (3.197° / 2)
C1 = 66.94 ft
The first deflection angle = ?1/2 = 1.5985°
Last full station is located at 953+00
?2 / ? = l2 / L
?2 / 48 = 38.35 / 1005.30
?2 = 1.831°
The last chord can be found using Equation 15.28,
C2 = 2R sin (?2/2) = 2(1200) sin (1.831°/ 2)
C2 = 38.35 ft
For other deflection angles between full stations:
?/48 = 100/1005.3
? = 4.775° ?/2 = 2.3875°
The chords between full stations can be found using Equation 15.28,
C = 2R sin (?/2) = 2(1200) sin (2.3875°) = 99.97 ft
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