Construction Calculations

Overview

Surveyors perform extensive calculations for construction layout and design support. This includes horizontal and vertical curve computations, earthwork quantities, and coordinate geometry.

Learning Objectives

• Calculate horizontal curve elements
• Compute vertical curve data
• Determine earthwork quantities
• Apply coordinate geometry to construction

Key Concepts

Horizontal Curves

Circular curve calculations using:

• Degree of curve (D) or Radius (R)
• Tangent distance (T = R tan(Δ/2))
• Length of curve (L = πRΔ/180)
• External distance (E = R(sec(Δ/2) - 1))
• Middle ordinate (M = R(1 - cos(Δ/2)))

Vertical Curves

Parabolic vertical curve computations:

• Length based on algebraic difference of grades
• K value (L per percent grade change)
• Elevation at any station
• High/low point location
• Sight distance verification

Earthwork Calculations

Volume computation methods:

• Average end area
• Prismoidal formula
• Grid method for large areas
• Cross-section development
• Mass diagrams for haul optimization

Coordinate Geometry (COGO)

Common construction calculations:

• Inversing between points
• Intersection of lines and curves
• Offset computations
• Curve/line combinations
• Area calculations

Key Terms

• Degree of Curve: Central angle subtended by 100-foot arc
• K Value: Horizontal distance per 1% grade change
• Average End Area: Volume method using cross-section areas

Practice Questions

1. Calculate the tangent distance for a curve with R = 500' and Δ = 30°.
2. How is the high point of a crest vertical curve determined?

Based on CalTrans LS/LSIT Video Exam Preparation Course materials.