Surveying & Geomatics: Formulas, Tricks & Solved
Examples
COMPLETE ENGINEERING EXAM & PREPARATION GUIDE
SECTION 1: FUNDAMENTALS & BASIC SURVEYING
1. Fundamental Principles & Direct Measurements
Key Rules & Formulas:
• Principle 1: Work from whole to part (prevents accumulation of errors).
• Principle 2: Locate a new point with at least two reference points (linear or angular measurements).
• Tape Temperature Correction (C ):
t
Ct = α · L · (Tm − T0)
Where α = thermal expansion coefficient, L = measured length, Tm = measured temperature, T0 = standard
temperature.
• Pull/Tension Correction (C ):
p
Cp = [(P − P0) · L] / [A · E]
• Sag Correction (C ): (Always subtractive!)
s
Cs = (W2 · L) / (24 · P2)
Civil Engineering Surveying & Geomatics Page 1 of 7
, WORKED EXAMPLE: SAG & TEMPERATURE CORRECTION
Problem: A 30 m steel tape was standardized at 20°C with a pull of 100 N. A line measured 30 m at 35°C
under a pull of 150 N. Calculate the true length if α = 11.5 × 10−6 /°C, A = 0.03 cm2, and E = 2 × 105 N/mm2.
1. Temperature Correction:
Ct = (11.5 × 10−6) × 30 × (35 − 20) = +0.005175 m
2. Pull Correction:
Cp = [(150 − 100) × 30] / [(3 mm2) × (200,000 N/mm2)] = ,000 = +0.0025 m
3. Corrected Length:
Ltrue = 30 + 0.005175 + 0.0025 = 30.007675 m
2. Compass Surveying
Key Formulas & Rules:
• Fore Bearing (FB) & Back Bearing (BB) Relationship:
BB = FB ± 180°
(Use +180° if FB < 180°, use −180° if FB > 180°)
• True Bearing (TB) Formula:
True Bearing = Magnetic Bearing ± Magnetic Declination
(Use + for East Declination, − for West Declination)
• Local Attraction Check Shortcut:
If |FB − BB| = 180° ⟹ Both stations are FREE from local attraction!
Civil Engineering Surveying & Geomatics Page 2 of 7
Examples
COMPLETE ENGINEERING EXAM & PREPARATION GUIDE
SECTION 1: FUNDAMENTALS & BASIC SURVEYING
1. Fundamental Principles & Direct Measurements
Key Rules & Formulas:
• Principle 1: Work from whole to part (prevents accumulation of errors).
• Principle 2: Locate a new point with at least two reference points (linear or angular measurements).
• Tape Temperature Correction (C ):
t
Ct = α · L · (Tm − T0)
Where α = thermal expansion coefficient, L = measured length, Tm = measured temperature, T0 = standard
temperature.
• Pull/Tension Correction (C ):
p
Cp = [(P − P0) · L] / [A · E]
• Sag Correction (C ): (Always subtractive!)
s
Cs = (W2 · L) / (24 · P2)
Civil Engineering Surveying & Geomatics Page 1 of 7
, WORKED EXAMPLE: SAG & TEMPERATURE CORRECTION
Problem: A 30 m steel tape was standardized at 20°C with a pull of 100 N. A line measured 30 m at 35°C
under a pull of 150 N. Calculate the true length if α = 11.5 × 10−6 /°C, A = 0.03 cm2, and E = 2 × 105 N/mm2.
1. Temperature Correction:
Ct = (11.5 × 10−6) × 30 × (35 − 20) = +0.005175 m
2. Pull Correction:
Cp = [(150 − 100) × 30] / [(3 mm2) × (200,000 N/mm2)] = ,000 = +0.0025 m
3. Corrected Length:
Ltrue = 30 + 0.005175 + 0.0025 = 30.007675 m
2. Compass Surveying
Key Formulas & Rules:
• Fore Bearing (FB) & Back Bearing (BB) Relationship:
BB = FB ± 180°
(Use +180° if FB < 180°, use −180° if FB > 180°)
• True Bearing (TB) Formula:
True Bearing = Magnetic Bearing ± Magnetic Declination
(Use + for East Declination, − for West Declination)
• Local Attraction Check Shortcut:
If |FB − BB| = 180° ⟹ Both stations are FREE from local attraction!
Civil Engineering Surveying & Geomatics Page 2 of 7
