Geçki düşey geometrisinde, iki doğru parçasını birleştirmek için daire yayı veya 2. derece parabolü kullanılmaktadır. Uygulamada, dairesel düşey kurblara ilişkin kırmızı kot ve kilometre hesaplarında kolaylık amacı ile bazı kabuller yapılarak yaklaşık çözümler uygulanmaktadır. Bir ulaştırma yapısının uygulama projesi, yapının tüm niteliklerini kapsar. Bu niteliklerin en önemlilerinden biri olan “geçki düşey geometrisi”, ulaştırma yapısının gerçek (hatasız) düşey geometrisini temsil eder ve sayısal olarak kilometreler, kırmızı kotlar ve kırmızı çizgi eğimleri ile ifade edilir. Söz konusu sayısal büyüklükleri hata dereceleri bakımından üç ana gruba ayırmak mümkündür: Birinci gruptaki büyüklükler, hesap kolaylığı bakımından yuvarlak sayı seçilirler. İkinci gruptakilerin sayısal inceliği boy kesit çiziminin ölçeğine bağlıdır. İkinci gruptaki büyüklüklerin hataları küçüktür. Üçüncü gruptaki büyüklükler ise, bir hesap işlemi sonunda üretildiklerinden hataları diğer gruptakilerden daha büyüktür. Günümüzde demiryolları ve yüksek standartlı kara yolları için, hesapla bulunan kilometrelerin ve proje kotlarının varsayımlardan kaynaklanan hatalardan arındırılmış mm inceliğinde değerler kabul edilebilir hata sınırları içinde hesaplanmalıdır. Günümüzde bilgisayar teknolojisinin gelişmesi ile birlikte bu yaklaşık çözümlerin önemi kalmamıştır. Ayrıca demiryolları ve yüksek standartlı kara yolları için, hesapla bulunan kilometre ve kırmızı kotların mm inceliğinde değerler olması gerekmektedir. Bu nedenle dairesel düşey kurbların çözümünde kesin çözümün kullanılması daha uygun olacaktır. Bu yazıda düşey kurbların (daire ve 2. derece parabol) kesin çözümlerine ilişkin formüller türetilmiş ve çözümü anlatılmıştır. Örnek olarak alınan bir geçkide düşey geometriye ait ana ve ara noktaların kilometrelerinin ve kırmızı kotlarının, yaklaşık ve kesin hesapları yapılarak aradaki farklar gösterilmiştir. Anahtar Kelimeler: Düşey kurb, geçki, daire, parabol, düşey geçki tasarımı. In the vertical geometry of the routes, circular curves or 2nd degree parabola are used for joining two straight lines. In practice, the approximate solutions are used with the aim of simplifying the calculation of heights and kilometers of circular vertical curves. A transportation practice project covers all properties of the structure. One of the most important properties named "vertical geometry of the route" represents real geometry (with no errors) and is expressed by kilometers, elevations and gradients digitally. Those digital values can be divided into the tree parts by means of error levels: Group 1- The values chosen by creator (designer/drafter) with defined criteria (usually, radiuses of vertical circular curves or the lengths of parabolas in horizon plate, entry and exit gradients of back and forward tangents, kilometers of essential points of vertical curve (EPVC) which consist of beginning of vertical curve (BVC), end of vertical curve (EVC) and point of vertical intersection (PVI). Group 2- The values measured by means of graphically. Group 3- The values determined by calculation. The values in the second group are chosen as rounded numbers in order to simplify the computations. The numbers of the digits of the values in the second group are determined based on the scale of the longitudinal section. In most cases, the scale of the longitudinal section is 1:1000 thus the chainage values of the tangent points are obtained within the precision of 0.25 to 0.5 meters. The values in the group one are free of error while the second group values consist small errors. In third group, since the values in the third group are the products of a computation they have more errors according to the other two groups. In most textbooks the computation of vertical geometry is being thought without taking the errors introduced by omitting and assumptions into account. These errors are mainly introduced by not carrying out the computations using enough degrees of a formula which is in a series form or assuming that slope distances can be used as plane distances (Umar and Yayla 1994; Müller, 1984). The main reason of these assumptions is due to the limitations of the computations before 70s. Nowadays these limitations are over come by means of new computation techniques and instruments. And the computations can even be executed easily by a hand calculator. The results of exact computations of circular and parabolic vertical curves are described. The basic concepts of the subject should be summarized prior to calculations. 1) The vertical geometry is designed by using the longitudinal section of horizontal geometry (original surface). All vertical geometry related calculations are to be carried out on a vertical plane defined by K, H perpendicular coordinate system.2) K axis shows the chainages. The points located on the same vertical line naturally will have the same chainages. All distances used in the calculations must be in horizontal plane.3) H shows the point heights. All distances used in the calculations must be in vertical plane. 4) All computations are carried out in stages. The number and the quality of the input values obtained as 1st, 2nd and 3rd group values should be good enough to achieve an unique solution for the stage calculation of a vertical geometry. If the number and the quality of the values are not suitable, the calculations can not be done. In case of having the number of the initial data more than required number, the obtained results are different depending on the calculation method used. The contradictions adverting to the real value concept as a result of these computations must be prevented. The both methods, approximate solution and the exact solution, were applied to the profile data of sag and crest vertical curves to point out differences between two methods and the initial data. Two points are taken as an initial data on every curve and straight line for each. Nowadays, approximate solutions are not necessary due to the recent developments in computer technology. In addition, for the railroads and high standard roads the level of calculation precision should be in millimeter. For these reasons, the exact solutions are more suitable instead of approximate solutions. In this paper, equations of exact solution of vertical curves are evaluated and the solutions are explained. Differences of project heights and kilometers obtained from approximate and exact solutions are having been shown on a sample route. Keywords: Circular curves, route, circle, parabola, circular route design
