Connecting the arcs of two circular curves in the design and reconstruction of highways
DOI:
https://doi.org/10.31548/zemleustriy2026.01.0%25pKeywords:
circular curve, solution search, optimization, clothoid, direct insertion, geometric connection conditionsAbstract
The safety and conditions of road transport traffic significantly depend on the influence of curved sections. For practical use, methods for designing horizontal curves are constantly being improved. At present, there are no simple and reliable methods for designing transition curves for connecting two one-way circular curves in scientific publications. Existing methods for finding optimal transition curves use iterative processes and specially developed software products. Therefore, improving the methodology for solving the problem of connecting circular curves is of practical importance. The paper considers the main options for forming curved sections with two circular curves - connecting by straight inserts, arcs of circles of larger radius and clothoids, as well as searching for a clothoid that is common to two circular curves and ensures the preservation of their centers. It is proved that with a known position of the centers and arcs of circular curves of given radii , the search for the optimal clothoid can be performed by the standard function "Solution Search" of the " Microsoft" menu. Excel ". Possible options for the location of the extreme points of the clothoid on existing or designed circular curves are given by the directional angles between the centers of the curves and the starting and ending points of the circular curves. Examples of calculations of direct inserts and clothoids for connecting two circular curves are given.
Received: 02.02.2026;
Accepted: 17.02.2026;
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