Answer :
To calculate the various parameters and sketch the horizontal curve, we'll use the given information about the tangents, deflection angle, and radius. Let's go step by step:
Given:
Station of intersection (PI) = 132+11.00
Deflection angle (δ) = 55°18'
Radius of the curve (R) = 2000 ft
Step 1: Calculate the degree of curve (D):
D = δ / 100
Note: The deflection angle is given in degrees and minutes, so we need to convert it to decimal degrees before dividing by 100.
Step 2: Calculate the external distance (E):
E = R * sin(D)
Note: The external distance represents the distance from the tangent point to the curve.
Step 3: Calculate the middle ordinate (M):
M = R * (1 - cos(D))
Note: The middle ordinate represents the distance from the curve to the midpoint of the long chord.
Step 4: Calculate the tangent distance (T):
T = R * tan(D/2)
Note: The tangent distance is the distance from the PI to the tangent point on the curve.
Step 5: Calculate the length of the curve (LC):
LC = D * R
Step 6: Calculate the beginning and end stations:
Begin Station = PI - T
End Station = PI + LC
Now, let's substitute the given values into these formulas and calculate the parameters:
Step 1: Degree of Curve (D):
Convert the deflection angle to decimal degrees:
δ = 55 + 18/60 = 55.3°
D = 55.3 / 100 = 0.553
Step 2: External Distance (E):
E = 2000 ft * sin(0.553)
Step 3: Middle Ordinate (M):
M = 2000 ft * (1 - cos(0.553))
Step 4: Tangent Distance (T):
T = 2000 ft * tan(0.553/2)
Step 5: Length of Curve (LC):
LC = 0.553 * 2000 ft
Step 6: Begin and End Stations:
Begin Station = 132+11.00 - T
End Station = 132+11.00 + LC
Now that we have calculated these parameters, we can sketch the curve using the given information and label the relevant points and distances accordingly.
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