T.C.K.`da köprülü kavşaklarda klotoid uygulaması

Abstract

Klotoid, sarılma noktası, etrafında sonsuz sayıda dönme yapan bir eğriden ibarettir. Klotoidde eğrilik yarıçapı, eğrin nin uzunluğu ile orantılı olarak azalır. Bu eğrinin aeçiş eğ risi için uygun olan kısmı başlangıçtan itibaren alınan belir li bir kısmıdır. Eğri üzerindeki herhangi bir noktanın e&rilik yarıçanı R ve bu noktanın başlangıç noktasına olan uzaklığı ise R.L=Sab'it ' = A2 dir. A değerine klotoidin parametresi denir ve aynı bir klotoidde A Parametresi sabit kalır. Parametrenin değişmesi ile klotoidin şekli değişmez sadece büyüklüğü değişir. A= 1 alınır sa buna birim klotoid adı verilir. Uygulamada kolaylık olsun diye birim klotoide göre cetveller hazırlanmıştır. Uygulanan, klotoidin değerlerini bulmak için birim klotoiddeki uzunluklar A ile çarpılır açılar ise değiştirilmez. Geçiş eğrisi olarak klotoidin ve kurp yarıçapının seçilmesi klotoid pistoleleri ile grafik olarak yapılır. Bu pistoleler üzerinde klotoidin Paramet resi ve her noktanın eğrilik yarıçapı ve geçiş eğrisinin son nok tasında daire kurbunun yarıçapı yazılıdır. Bunlar değişik para metrelere ve kurb yarıçaplarına göre hazırlanmıştır. Bu pistole ler kesişen almymanlar üzerine oturtulur ve uygun A Parametresi ve R kurp yarıçapı deneme yolu ile bulunmuş olur. Rakordman kurbu geçki elemanı olan klotoid, pratik gerek-. şiirlere iyi bir şekilde cevap verme ve hareket diinatmiğinaen;.dfc)lıay.ı yol inşaatında tercih edilmektedir. Kioto idlerden yar.arianılarak hazırlanan güzergah projeleri ve aplikasyonları ile yüzlerce ve hatta binlerce metre uzunluğunda ve birleştikleri daire yayları ile aynı Önemde rakordman kurplarına sahip bulunan güzergahlar gerçekleş tirilebilmektedir. Böyle güzergahlar, yumuşak, güzel ve ekonomik bir şekilde çevre araziye, mevcut bina ve tesislere ve serbest yol kesimleri ile düğüm noktalarındaki (kavşaklar, ayrıl ma yerleri, birleşme noktaları) hareket hızına uyma özelliği sağ layabilmektedir. VII

The clothoid bay be called the ideal transition curve since it possesses the property that LR is constant and when a. vehicle is travelling over it with constant velecity, the centrifugal fora for setting out this curve can only be expressed, as infinite series and so the calculations are somewhat tedious if special tables are not available. Using sijmbals, at any point on the wrve, rt is constand- and so rl = RL. It can be shown that it, 1= f (*C) is the intrinsic equation of any wrve, the radius of mrvature at any point is given by the formula1 r- -£t- and so in the clothoid 2 Integrating. 1 /Z` RL.t* constant. The constant of integration disappears if Z is zero when is zero and the intriosil equation of the mrve can be written 1 - /JÎ&/[2~Z = A /JIx Where A is equal to vRL, a constant if the length and minimum radius of the curve are known. in the early days of roads the alignment on a horizantal plase consisted of a number of circular arcs with straight lengths tangential to them. In eithes case a sudden centrifugal force come into action when the vehicle passed the tangent point, cousing a heavy lurch. With the coming of trans it ionwrves cant and curvature could be introduced together so that is become possible for a vehicle to run right through a curve from straight to straight under equilibrium conditions. It has already been stated that the centrifugal force acting on a vehicle. If the centrifugal force is to increase at a constant rate, force must vary directly with time, and if the speed of the vehicle is constant, the distance measured from the beginning of the curve must also vary with time. The ideal wrve is therefore one in which the radius of curvatwe varies inversely as the distance travelled *. along the wrve measured from its beginning. The jerk of the force experienced on entering a circular curve directly from a straight in a vehicle can be most unpleasant, A road vehicle traces out a transition curve when entering a curve, whether one' is provided or not, since' to- pass from a straight to a circular are would involve an instant^s^ous mevement of the steering-whell. If a transition curve is..- provided the driver has no difficulty in keepino- his vehicle to.its proper path. VIÎIThedliotihojdcurve strats from a radius of infinity and gradually sharpen. In its firts' partion the wrve is very similar in shape. The spiral, however, continues to decrease in radius while the parabola does not. For motorway work the spiral is generally used, but sometimes on low speed. urban reads and junctions the parabola is more useful. The curve can be set out by deflection angle in the same there, iş no simple sub- chord deflection to use. for each succesive point nn the curve. This can be overcome in various ways, of which the two most simple are the use of convenient formulae and recourse to tables of prepared data. These tables were calculated for certain de signed speeds of traffic and provided all the necessary data for setting out in imperial units. There are certain terms and relationships which must be understood to use the tables and to set in the necessary centre line pegs. The start peg, for example, when coming off the straight, is no langer marked point of chancre in alignment from' tangent to change from tangent to spiral. The point of change from straight to wrve is also moved back along the tangent by insertion of the spiral lead-in to the main curve. Consequently the tangent length in curcular curves will be increased by an amount denoted a constant in both tables. This also has the effect of movning the circular part of the curve towards the centre by an amount. The radius of the new circular curve is derived from the application of the shift to the original circular wrve darius; this new radius. is denoted by P. Both figures are tabulated for all lengths of transition spiral.. The setting out procodure is similar to.that for circular curves a.nd is made diffucult in the same way by the chainage '.... convention. While it is possible to extract the deflection angles direct from the table, they must be adjusted to suit the differing lesghts of the spiral from the origin, caused by the odd chainage and the inital und final sub-chards. Both sets -of tables show methode of calculating deflection for add chard lengths and have tables of corrections for approximations made.-. For setting out the clothoid, same methods can be used as in circular curves, the angles of course being different. The clothaid can also be set. out by offsets from a tangent. To illustrate the methed of carrying out the calculations and the use of the tables, two eamples can be worked out, the first giving the calculations for setting out the curve and the secont.the method of finding the distance from apex to the tangent point. If it is not considered necessary to drive pegs at even chainages, the calculation can be simplistsed by using a fixed set of angles and calculating the length of chord required. The cherd telgth. Should be made short enough for there to be no appreciable diffrence between the sum of the cord lengths and the curve length. IX