Design of double-egg curve in the link roads of transportation networks

Abstract

Original scientific paper The turns from highways to settlement areas are achieved by link roads. For the safety of these turns, turning radii are required to be large. However, it is not always possible to achieve these turnings by means of arcs of circle with large radius, as different factors, such as topography, the state of settlement, problems impossible to overcome and economic conditions, do not allow designing such a route. Instead, for the sake of traffic, linear variation of the line curvature or maintaining the line curvature at constant value is highly desirable. One of the line geometries is the clothoid egg curve. Single and double type clothoid egg curves are used in many applications. In this study, the calculation and design of double-egg curve are explained by equations and figures in detail. For the design of two egg curves used in rotation from main road to connecting road in transportation networks as application, an example is provided for a better understanding of the subject. The main points of rotation geometry with the coordinates of auxiliary points and other intermediate results are given in a table. The main purpose of this study, the theory and calculations of two egg curves will provide basis to practitioners on a sample in a detailed way. By the fulfilment of design and its calculation of this rotation geometry which provides safer and more comfortable driving, it is hoped to be useful for practitioners. Keywords: clothoid; curvature; double-egg curve; egg curve; length of transition curve Projekt dvostrukog kružnog zavoja na prilaznim putevima prometnih mrežaIzvorni znanstveni članak Skretanja s glavnih cesta do naselja postižu se prilaznim putevima. Zbog sigurnosti ovih skretanja, zakretni polumjeri trebaju biti veliki. Međutim, nije uvijek moguće napraviti ova skretanja kružnim lukovima velikog polumjera, budući da različiti čimbenici, kao što su topografija, položaj naselja, problemi koje je nemoguće prevladati te ekonomski uvjeti, ne dopuštaju izradu takve trase. Umjesto toga je, zbog prometa, poželjna linearna varijacija zakrivljenosti linije ili održavanje konstantne vrijednosti zakrivljenosti linije. Takva je klotoidna krivina jajeta. U mnogim se aplikacijama primjenjuje jednostruki ili dvostruki tip takvih klotoidnih zavoja. U ovom se radu proračun i projektiranje dvostruko kružnih zavoja detaljno objašnjavaju jednadžbama i slikama. Primjer projekta dvostruko kružnog zavoja primijenjen u skretanjima s glavne ceste u prometnim mrežama daje se zbog boljeg razumijevanja samog predmeta. U tabeli su prikazane glavne točke geometrije rotacije s koordinatama pomoćnih točaka. Nadamo se da će osnovna svrha ove analize, teorija i detaljni proračuni dvostruko kružnog zavoja i njihova primjena kojom se omogućuje sigurnija i udobnija vožnja, biti od koristi praktičarima.

Numerical Computation of Egg and Double-Egg Curves with Clothoids

“…4. In Table 2, the coordinates of characteristic points obtained with our method are compared with points given in Koç et al (2015). As we can see, our method is accuracy and very useful for obtaining the parametrization of the final curve.…”

“…To show the usefulness of Algorithm 2 and its accuracy for obtaining arcs of clothoids linking circular arcs, we consider the example given in Koç et al (2015): we take circumferences C 1 , C 2 and C 3 of radii R 1 = 200 m, R 2 = 150 m and R 3 = 100 m and centers c 1 =(6736.338,4146.877), c 2 = (6736.461,4196.1287) and c 3 = (6687.231,4198.388). We use Algorithm 2 for linking C 1 with C 2 and C 2 with C 3 , and the final curve is showed in Fig.…”

“…For highway connections and interchanges, shorter links are highly desirable, and it is frequent to have to connect two oriented circumference arcs with a transition curve, avoiding straight segments between them. Different transition curves between circumferences, forming egg and double-egg curves, have been proposed in the literature (Bosurgi and D'Andrea 2012;Koç et al 2015). There are also oval-shaped transition curves that can be used to linking two circumferences with the same orientation (Kobryń 2011;Kobryń 2016b).…”