Vertical Curve Design – Deviation Angle Between Two Ascending Grades Two ascending gradients, 1 in 50 and 1 in 30, meet at a summit. What is the deviation angle A (algebraic difference of grades) to be used in vertical curve computations? Provide the closest standard expression.

Introduction / Context:
In geometric design of highways, the deviation angle A between two grades governs the required length of a vertical curve for comfort and sight distance. A is defined as the algebraic difference of grades, taking sign into account (ascending positive, descending negative). This question deals with computing A for two ascending grades meeting at a summit point.

Given Data / Assumptions:

• Grade 1: +1 in 50.
• Grade 2: +1 in 30.
• Both are ascending (same sign).
• Summit curve design context.

Concept / Approach:

Express each grade as a percentage: g = rise/run × 100. For 1 in N ascending, g = (1/N) × 100 %. The deviation angle A (for vertical curves) equals the absolute algebraic difference |g2 − g1| when both grades have the same sign. This A then enters formulas for curve length based on sight distance or comfort criteria.

Step-by-Step Solution:

Verification / Alternative check:

If one grade were descending, A would be the sum of absolute values. Here, since both are ascending, only the difference is taken, giving a relatively small A and therefore a shorter summit curve than if grades opposed each other.

Why Other Options Are Wrong:

• 3.33% and 2.00%: These are the individual grades, not the deviation angle.
• 5.33%: Sum of 3.33% and 2.00%, applicable only if grades had opposite signs (one up, one down).

Common Pitfalls:

Forgetting to convert to percentage; adding instead of subtracting when grades have the same sign; mixing up algebraic difference (A) with the actual curve gradient at any point.

Final Answer:

A = 1.33% (equivalently, about 1 in 75)