Answer:
In order to determine the station of the PT (point of tangency) of the horizontal curve, you will need to use the following formula:
PT = PI - (A / 100) x L
Where:
PT is the station of the PT of the curve
PI is the station of the PI (point of intersection) of the curve
A is the superelevation (expressed as a percentage)
L is the length of the curve
Using this formula, we can plug in the values given in the question to determine the station of the PT of the curve:
PT = 30 + 00 - (24 / 100) x L
Since the superelevation is 4% and the curve is designed for a speed of 35 mi/h, we can use the following formula to determine the length of the curve:
L = (V^2) / (R x f)
Where:
L is the length of the curve
V is the design speed (in mi/h)
R is the curve radius (in feet)
f is a factor that depends on the superelevation and the width of the roadway (expressed as a percentage)
For a 4% superelevation and a roadway with two 12-ft lanes, the value of f is approximately 0.15.
Using this formula, we can plug in the values given in the question to determine the length of the curve:
L = (35^2) / (R x 0.15)
If we assume that the curve radius is 1,000 feet (which is a common value for horizontal curves), we can solve for L to get:
L = (35^2) / (1000 x 0.15)
L = 338.88 feet
Now that we know the length of the curve, we can substitute this value into the first formula to determine the station of the PT of the curve:
PT = 30 + 00 - (24 / 100) x 338.88
PT = 30 - 8.19
PT = 21.81
Therefore, the station of the PT of the curve is approximately 21.81.