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If the vertical curve connects a 1% upgrade with 1.4% downgrade, and the rate of change of grade is to be 0.06% per 20 m stations, the length of a vertical curve is
  • a)
    133.3 m
  • b)
    40 m
  • c)
    400 m
  • d)
    800 m
Correct answer is option 'D'. Can you explain this answer?
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To find the length of a vertical curve, we need to use the formula:

L = (Vf - Vi) / G

where L is the length of the curve, Vf is the final grade, Vi is the initial grade, and G is the rate of change of grade per station.

Given:
- The vertical curve connects a 1% upgrade with a 1.4% downgrade.
- The rate of change of grade is 0.06% per 20 m stations.

Let's calculate the length of the curve using the given values:

1. Calculate the difference in grades:
Vf = 1.4% (downgrade)
Vi = 1% (upgrade)

Vf - Vi = 1.4% - 1% = 0.4%

2. Calculate the length of the curve using the formula:
L = (Vf - Vi) / G

Since the rate of change of grade is given per 20 m stations, we need to convert it to per 1 m station.

0.06% per 20 m = (0.06 / 20)% per 1 m = 0.003% per 1 m

Now, substitute the values into the formula:

L = (0.4%) / (0.003% per 1 m)

Simplifying the expression:
L = (0.4 / 0.003) m

Converting meters to stations:
1 station = 20 m

L = (0.4 / 0.003) m * (1 station / 20 m)
L = 133.33 stations
L ≈ 133.33

Therefore, the length of the vertical curve is approximately 133.33 stations, which is closest to option 'D' - 800 m.
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