Answer / Explanation
To be able to answer the question above, we need to understand that as related to the question, the transition curves used between tangents and circular curves or between two circular curves have significantly different radii.
Hence,
To calculate the minimum length of spiral curve necessary:
We must recall the formula: Ls = 3.15V³ / RC
Where:
Ls = length of spiral (ft)
V = design speed (mph)
R = curve radius (ft)
C = rate of increase of lateral acceleration (ft/s³) *design value = 1 ft/s³
But before we ca continue with the above formula, we need to calculate the absolute difference in the grade of the sag curve as shown below:
Utilizing the formula:
G = (I(G₂) - (G₁)I)
G = (I+3.0) - (+1.0)I)
G = +2.0%
Now, moving forward to determine the value of K by using the formula below or relation as follows:
K = L / G
That is:
K = 420 / 2.0
K = 210
Now that we understand that K = 210, we now refer to the table of interpolation to calculate the value of the design speed:
Therefore:
V = ( 75 + (80 - 75 / 231 - 206) x ( 210 - 206)
Solving the above further, we arrive at:
V = 75.8 m/h
Now, also referring back to the question which states that for e = 6%
Also, referencing the interpolation table to check for the value of e, we have:
Rv = 2587.616 feet
Therefore, R = 2587.616 feet + 12 / 2
R = 2593.616 feet
Now, to calculate the length of the horizontal curve as follows,
we have:
Ls = 3.15V³ / RC = (π / 180 ) RC
Therefore,
Ls = (π / 180 ) x 2593.616 x 37°
Ls = 1674.88 feet
Hence, we can conclude that the length of horizontal curve is 1674.88 ft
