In an attempt to develop a method for the design of the aerial rope way, the traditional theories of rope way were examined and compared. The resulting formulas of the traditional and approximate parabolic curve theory were summarized and those of the catenary curve theory as an exact ones were summarized and newly developed when necessary. In particular, it was found that the resulting formulas from both of these theories can fully be expressed with only three dimensionless parameters $U^{*}$, $V^{*}$, and $W^{*}$, improving compactness and generality of these formulas. Comparision of the theories were done through error analysis, and it was shown that the error of the approximate parabolic curve is of order $U^{*2}$ and $V^{*}$. From this, it was concluded that the traditional parabolic curve theory has its limitation when the rope way becomes larger or steeper, leading to the necessity of the use of catenary curve theory.ve theory.