Highway geometric design – differential grade on a curve after superelevation If the original longitudinal gradient is x% and, after providing proper superelevation along the curved portion, the effective gradient is y%, the differential grade along the curve equals:

Introduction / Context:
On a curved highway with superelevation, the longitudinal profile perceived along an edge (or control line) can differ from the original centerline grade. Designers sometimes compute a “differential grade” to capture the change between the original gradient and the gradient after fully applying superelevation.

Given Data / Assumptions:

• x% = original (centerline) longitudinal gradient of the alignment.
• y% = effective gradient along the curve after providing superelevation.
• Sign convention: grades are algebraic; here we report the algebraic difference.

Concept / Approach:
The differential grade is simply the algebraic difference between two grades describing the same reach: original and modified. It quantifies how the profile grade line effectively changes due to the cross fall transitioning to full superelevation through the curve.

Step-by-Step Solution:
Define differential grade DG = original grade − modified grade.DG = x% − y%.Choose the option that reflects this algebraic difference.

Verification / Alternative check:
In many layout computations, one may use absolute difference |x − y| to check vertical conflicts. The algebraic form (x − y)% is the clean expression.

Why Other Options Are Wrong:

• (x + y)% or (y + x)%: addition has no physical basis here.
• (y − x)%: sign-reversed relative to the definition above.
• (x × y)%: multiplication of percentages is not meaningful in this context.

Common Pitfalls:
Ignoring sign convention or mixing up which line (edge vs. centerline) is being referenced. Always track which grade is being compared.

Final Answer:
(x - y)%