Survey Mathematics

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Essential formulas and calculations for traverse, areas, curves, and trigonometry

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8 cards in this deck

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Cards (8)

1
Front

Latitude and Departure formulas?

Back

Latitude (ΔN) = L × cos(Az) Departure (ΔE) = L × sin(Az) Memory aid: Lat = N/S = Cosine Dep = E/W = Sine — Ghilani Elementary Ch. 10

2
Front

Closure error formula?

Back

Error = √[(ΣLat)² + (ΣDep)²] Relative Precision = Error / Total Length Example: Error=0.05, Length=5000 Precision = 1:100,000 — Ghilani Elementary Ch. 10

3
Front

Bearing to Azimuth conversions?

Back

NE: Az = bearing angle SE: Az = 180° - bearing SW: Az = 180° + bearing NW: Az = 360° - bearing Back Az = Forward Az ± 180° — Kavanagh Ch. 6

4
Front

Coordinate area formula?

Back

Area = ½|Σ(Xi×Yi+1 - Xi+1×Yi)| (Shoelace / Cross-multiply method) Go around polygon, close to start. — Ghilani Elementary Ch. 12

5
Front

Law of Cosines and Sines?

Back

COSINES: a² = b² + c² - 2bc×cos(A) (Find side from 2 sides + included angle) SINES: a/sin(A) = b/sin(B) = c/sin(C) (Find parts from AAS, ASA cases) — Ghilani Elementary Ch. 2

6
Front

Horizontal curve: Radius from Degree?

Back

Arc definition: R = 5729.578 / D Chord definition: R = 50 / sin(D/2) — Ghilani Elementary Ch. 24

7
Front

Horizontal curve: Tangent distance?

Back

T = R × tan(Δ/2) Other formulas: L = R × Δ (radians) LC = 2R × sin(Δ/2) E = R × [1/cos(Δ/2) - 1] — Kavanagh Ch. 17

8
Front

Slope to horizontal distance?

Back

HD = SD × cos(vertical angle) VD = SD × sin(vertical angle) Or: HD = √(SD² - VD²) — Ghilani Elementary Ch. 6