Braille publications, such as Braille books and textbooks, utilize a combination of raised convex dots and lines, and indented concave dots and lines, to create diagrams and graphs. Extensive research has focused on the ease of identifying raised convex stimuli such as convex dots and lines, resulting in the establishment of standards such as the JIS. However, there is limited knowledge regarding the ease of distinguishing concave stimuli, such as concave dots and lines. Hence, quantitative guidelines to determine the most easily identifiable concave stimuli are warranted. Among these stimuli, ruled lines comprising concave lines, frequently used in braille publications for graphs, must be designed and produced considering the distance between concave and convex lines to ensure tactile readability when used as supplements. Therefore, this study specifically targeted ruled lines comprising common concave stimuli in braille publications and aimed to assess the influence of the distance between concave and convex lines on tactile readability. The results indicated that narrow distances, such as 2 mm or 3 mm, were more easily identifiable, while wide distances, particularly 5 mm or 6 mm, posed significant challenges for tactile recognition. These insights may aid in the proofreading process of braille publications.