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Trilateration over triangulation; primary specs

Short answer

Trilateration advantages: speed (EDM measures distances quickly), no baseline is needed, accuracy is 1 part in 100,000 to 1,000,000 without accumulation of angular error, fewer observers and cost, possible in poor visibility, simple computation. Primary triangulation specs: baseline 5–15 km, triangle sides 30–150 km, average triangular closure <1″, maximum 3″, probable baseline error 1 in 1,000,000, discrepancy 5 mm√K.

Explain the advantages of trilateration over triangulation. List out the general specifications of primary triangulation.

Advantages of trilateration over triangulation

  1. Speed: only distances are measured, and EDM takes minutes per side, while observing angles in several sets is slow.
  2. No base line: no separate base line, base extension or check base is needed; every side is measured with high accuracy.
  3. Accuracy: modern EDM gives 1 part in 100,000 to 1,000,000, and there is no accumulation of angular error.
  4. Fewer observers and less cost: the work can be done by a small party, and in many cases no tall towers are needed for signals.
  5. Weather: work is possible in poor visibility or at night, particularly with microwave instruments.
  6. Simple computation: angles are computed from the sides by the cosine rule, and the figure is adjusted by the least squares method.
  7. Strong networks: very long sides and a strong network are possible with the same field effort.

General specifications of primary (first order) triangulation

ItemFirst order (primary)Second order (secondary)Third order (tertiary)
Length of base line5 to 15 km1.5 - 5 km0.5 - 3 km
Length of sides of triangles30 - 150 km8 - 30 km1.5 - 10 km
Average triangular error (closure)less than 1"3"6"
Maximum triangular error3"8"12"
Probable error of base line1 in 1,000,0001 in 500,0001 in 250,000
Discrepancy between two measures of the base5 mm K\sqrt{K}10 mm K\sqrt{K}20 mm K\sqrt{K}
Probable error of computed distances1 in 60,000 to 1 in 250,0001 in 20,000 to 1 in 50,0001 in 5,000 to 1 in 20,000

(KK is the distance in km. The figures are the common textbook values; Survey Department practice may differ slightly.)

✓ Answer checked by Claude Opus 5.5 (high effort)

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