Surveying: measurement theory, instruments, error adjustment and field practice
Scope
The Surveying domain rewards candidates who can defend a number. Expect traverse computation, angle and distance observation, instrument corrections, error propagation, and the tolerance (較差) rules of 作業規程の準則 as applied to 公共測量.
Core rules
- A closed traverse's 閉合差 is the vector gap between computed and known end point; 閉合比 = 閉合差 ÷ 総延長.
- Errors split into 定誤差 (systematic: 器械定数, 気象, 球差・屈折差, 投影) which is corrected, and 偶発誤差 (random) which is averaged down by repetition.
- 較差 limits compare two independent observations (倍角法 vs 方向法, or 往復観測); they are not a comparison with the truth.
- 偏心補正, 器械高・目標高 and 標尺補正 must be applied before coordinates are computed, never afterwards.
- Area by 座標法: S = ½ |Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)| with vertices listed in order.
Worked example
A closed traverse of total length 800 m closes with ΔX = +0.032 m and ΔY = −0.024 m. 閉合差 = √(0.032² + 0.024²) = √0.0016 = 0.040 m. 閉合比 = 0.040 ÷ 800 = 1/20,000, inside the 1/10,000 limit common for 公共測量 traverses. Distribute by the compass rule: the correction to each leg's ΔX is −0.032 × (that leg's length ÷ 800), and the Y correction is +0.024 × (leg ÷ 800). After adjustment the loop closes exactly, and the adjusted coordinates become the skeleton of the 地積測量図.
Traps
- Quoting 閉合比 where the question asks for 較差, or vice versa.
- Sexagesimal slips when subtracting angles across a degree boundary.
- Rounding intermediate coordinates; round only the final 地積 (㎡, two decimals).
- Forgetting that a トータルステーション's 気象補正 uses the mean of instrument-side and target-side temperature and pressure.