二度分帶TM投影為臺灣大地基準TWD 67與TWD 97所使用的地圖投影系統，主要針對臺灣國土範圍的狹長特性與需求所建立。內政部設定該投影系統的中央經線投影尺度比為0.9999，但遍尋文獻無法找到其來源。本研究以臺灣本島為研究範圍，根據二度分帶TM投影的長度及面積變形理論推導最佳的中央經線尺度比，同時分析探討現今所使用的中央經線投影尺度比是否使投影后擁有最佳的長度與面積變形。

經實驗分析結果顯示：在臺灣本島地區(緯度範圍: 21.5˚N ~25.5˚N，經度範圍120˚E~122˚E)，現今使用的中央經線投影尺度比0.9999會使得投影后平均的Airy長度變形量為4.686895×10^(-9)，平均的面積變形量為0.000066；而本研究依最佳化理論所推導出的中央經線投影尺度比0.999933則會使得投影后平均的Airy長度變形量為3.602558×10^(-9)，面積變形量為1.340164×10^(-7)，即臺灣本島地區若使用最佳的中央經線投影尺度比0.999933會較使用現行的投影尺度比0.9999的面積變形減少了兩百萬平方公尺，顯示本研究所得之中央經線投影尺度比會使得二度分帶TM地圖投影結果有較小的變形。

TWD 67 and TWD 97 are two current geodetic datums in Taiwan and both use the Transverse Mercator projection in 2°zones (2°TM) as their map projection system, which is established for the narrow feature of the national territory of Taiwan. The ministry of the interior in Taiwan set the value of the projection scale factor along the central meridian of 2°TM to 0.9999, but it is unable to find the sources of this numeric value. The main purpose in this study is to derive the optimal value of projection scale factor along the central meridian for the 2°TM by the length and areal distortions based on the map projection theory, then to analyze whether the current value of the scale factor along the central meridian results in the optimal length and areal distortions or not.

After analyzing, the results show that the average Airy length distortion and the areal distortion of the current value of scale factor in Taiwan island (Latitude range is 21.5˚N ~25.5˚N, Longitude range is 120˚E~122˚E) are 4.686895×10^(-9) and 0.000066, respectively, while the optimal value of scale factor derived in this study is 0.999933 and the average Airy length distortion and the areal distortion are 3.602558×10^(-9) and 1.340164×10^(-7). If using the optimal value of scale factor, the areal distortion will decrease about 2 million square meters than the current value of scale factor. It is shown that our optimal projection scale factor results in minimal distortions in both the distances and areas.

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