What Is the Grid-to-Ground Correction? の座標変換

The grid-to-ground correction is the process of multiplying (or dividing) a measured ground distance by a Combined Scale Factor (C) to convert it into a grid distance usable in a State Plane or UTM coordinate computation, or vice versa. The combined factor C accounts for two compounding geometric effects: (1) map projection scale distortion and (2) the sea-level (elevation) flattening effect. Without applying C, all distances in a State Plane project will be systematically shorter or longer than the actual ground measurements.

合成縮尺係数の公式

Step 1, Elevation (Sea Level) Factor:
E = R / (R + H)
(R ≈ 6,371,000 m; H = orthometric height in metres)

Step 2, Grid Scale Factor:
k = from State Plane tables or NGS NCAT (typically 0.9996 to 1.0003)

Step 3, Combined Scale Factor:
C = E ±k

Step 4, Convert ground to grid:
D_grid = D_ground ±C

Step 5, Convert grid to ground:
D_ground = D_grid ÷ C

参照テーブル

Elevation H (m)Elevation Factor ETypical k (SPCS)Combined Factor C1 km ΁E(mm)
0 m (sea level)1.0000000.999960.999960-40 mm
200 m0.9999690.999960.999929-71 mm
500 m0.9999210.999990.999911-89 mm
1,000 m0.9998431.000010.999853-147 mm
2,000 m0.9996861.000010.999696-304 mm

工学的影響

A documented real project showed that neglecting the combined scale factor on a 1-mile survey traverse produced a misclosure of 0.351 feet (107 mm) —yielding a ratio of 1:8,400. This fails the minimum closure requirement for:

  • Cadastral boundary surveys (1:20,000 required)
  • DOT ROW surveys (1:50,000 required)
  • Structural engineering control (1:25,000 required)
Full DOT Grid-to-Ground Requirements

よくあるご質問 (FAQ)

Do I need a grid-to-ground correction for State Plane coordinates?

Yes, always. Even within a single State Plane zone, the two effects (elevation factor and grid scale factor) both apply. At high elevations (1,000+ m), the elevation factor alone can introduce errors of 150+ mm per kilometer if ignored.

When is the combined scale factor exactly 1.000000?

The combined factor C = 1.000 only when the elevation factor and grid scale factor perfectly cancel, this happens at specific elevations and distances from the central meridian. In practice, no real project can assume C = 1 without computing it.

実務リスク警告

誤った測地系（データム）の指定や、グリッド・地上補正（Grid-to-Ground）を適用しない座標変換は、1〜400mの位置ズレを引き起こします。これは測量過失請求や施工紛争の代表的な原因です。

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