A Reformulation of the Lambert Conformal Conic Projection with Application to Bulgarian National Mapping

This paper revisits the Lambert conformal conic (LCC) projection and rederives its equations using a new notation, V, defined as the reciprocal of the commonly used U, which simplifies the expressions. Based on the resulting distortion formulas, conditions determining whether the projection has two, one, or no standard parallels are obtained. An optimal LCC configuration is defined by requiring equal local linear scale factors at the bounding parallels and symmetric maximum and minimum distortions about unity. Applied to the territory of Bulgaria (φS ≈ 41°14′, φN ≈ 44°13′), this criterion yields optimized standard parallels at φ1 ≈ 41°40′ and φ2 ≈ 43°47′. The corresponding local linear scale factors range from ca. 0.999832 to 1.000168, i.e., symmetric distortions of approximately ±1.7 × 10−4. Compared with existing implementations such as BGS2000 and BGS2005, the proposed configuration slightly reduces the distortion range and provides a more balanced distribution of scale over the country.