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Which is the length of parabolic vertical curve when it has two uniform grade are + 1.9% and -1.5% with change of grade is 0.25% for 100m chain length.
1360m
1360m
1360km
All of the above
1360m
The length of a vertical curve is calculated based on the total change in grade and the rate of change of grade per unit chain length. Here, the total algebraic change in grade N=(+1.9%)тИТ(тИТ1.5%)=3.4%. Dividing the total grade change by the rate of change per 100┬аm chain length gives 13.6 chain lengths, which equals 1360┬аm.
The length of a vertical curve is calculated based on the total change in grade and the rate of change of grade per unit chain length. Here, the total algebraic change in grade N=(+1.9%)тИТ(тИТ1.5%)=3.4%. Dividing the total grade change by the rate of change per 100┬аm chain length gives 13.6 chain lengths, which equals 1360┬аm.
N=g1тАЛтИТg2тАЛ тАФ Total algebraic change in grade
L=(rNтАЛ)├Чl тАФ Length of vertical curve (L), where r is rate of change of grade and l is chain length
Vertical curves are designed as simple parabolas in highway and railway engineering to provide a gradual change in gradient between two intersecting grade lines. The parabolic shape ensures a constant rate of change of grade per unit distance, leading to a smooth transition and comfortable vertical motion for vehicles.
Algebraic difference in grades: N=(+1.9%)тИТ(тИТ1.5%)=3.4%.
Rate of change of grade (r) = 0.25% per 100┬аm chain length.
Number of chains required = rNтАЛ=0.253.4тАЛ=13.6 chains.
Total curve length = 13.6├Ч100┬аm=1360┬аm.
Provides a constant rate of change of grade, ensuring uniform acceleration and comfort.
Parabolic profile simplifies vertical survey calculations and field layout.
Requires sufficient sight distance, which can significantly lengthen summit curves.
Cannot easily be adjusted if ground profiles change abruptly.
Design of summit and sag vertical curves on highways.
Gradient transitions in railway track design.
Option A (1360┬аm) correctly gives the length in meters.
Option B repeats 1360┬аm, while Option C incorrectly uses kilometers (1360┬аkm).
A is correct тАФ The total grade change of 3.4% divided by 0.25% per chain yields 13.6 chain lengths, which equals 1360┬аm.
Always convert grade differences into a single signed algebraic difference (g1тАЛтИТg2тАЛ) before applying the rate of change formula to avoid sign errors.