Length of vertical curve from grades and specified rate of change A +0.8% grade meets a −0.7% grade. If the specified rate of change of grade is 0.05% per 30 m, determine the required length of the vertical curve.

Introduction / Context:
Vertical curves provide a gradual transition between grades. The length depends on the algebraic difference of entering and leaving grades and the allowable rate of change of grade. Designers often specify the permissible change per a fixed chainage (e.g., per 30 m), from which the total curve length is computed easily.

Given Data / Assumptions:

• Entering grade g1 = +0.8%.
• Leaving grade g2 = −0.7%.
• Rate of change of grade = 0.05% per 30 m.
• Algebraic grade difference A = g1 − g2.

Concept / Approach:

For a parabolic vertical curve, the rate of change of grade r per unit length equals A / L, where L is the curve length. If a specification gives r per 30 m, then (A / L) * 30 = r_30. Solve for L using consistent percent units throughout.

Step-by-Step Solution:

Verification / Alternative check:

Check units: percent cancels, leaving metres; a larger A or smaller permissible r_30 would increase L, which matches design intuition.

Why Other Options Are Wrong:

600, 700, 800, 1000 m do not satisfy (A/L)*30 = 0.05% with A = 1.5%.

Common Pitfalls:

Mixing percent and decimal grade forms; inserting 30 m incorrectly (using per-metre value without converting); using A = |g1| + |g2| with wrong sign handling.

Final Answer:

900 m