Surveying Calculations

Overview

Fundamental surveying calculations include traverse computations, coordinate transformations, area determinations, and error analysis. Proficiency in these calculations is essential for professional practice.

Learning Objectives

• Perform traverse computations and adjustments
• Calculate areas using various methods
• Apply coordinate transformations
• Understand error analysis fundamentals

Key Concepts

Traverse Computations

Standard traverse calculations:

• Latitude = Distance × cos(Bearing)
• Departure = Distance × sin(Bearing)
• Closure calculations
• Angular and linear misclosure
• Adjustment methods (Compass, Transit, Crandall)

Area Calculations

Methods for computing area:

• Coordinate method (Double Meridian Distance)
• Triangle subdivision
• Planimeter (analog method)
• CAD/software computation
• Section breakdown for irregular shapes

Coordinate Transformations

Converting between systems:

• Translation (shifting origin)
• Rotation (changing orientation)
• Scale factor application
• Conformal transformation
• Grid-to-ground conversions

Error Analysis

Understanding measurement uncertainty:

• Random vs. systematic errors
• Error propagation
• Standard deviation calculations
• Confidence intervals
• Proper rounding and significant figures

Key Terms

• Latitude (Traverse): North-south component of a line
• Departure: East-west component of a line
• Error of Closure: Difference between computed and known position

Practice Questions

1. Calculate the latitude and departure for a line with bearing N 45° E and distance 100.00'.
2. What is the area enclosed by coordinates (0,0), (100,0), (100,100), (0,100)?

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