Otoyol güzergahları için geçiş eğrilerinin karşılaştırılması ve bir uygulama (Kınalı-E5 kavşağının geometrik çözümü)
The Comparison of the transition curves among their own kins for the route of high speed reads and an application (The geometrical analysing of the crossroad of Kınalı-E5 on the Sakarya-Edirne highway)
- Tez No: 18759
- Danışmanlar: PROF.DR. EMİRHAN ALGÜL
- Tez Türü: Yüksek Lisans
- Konular: Jeodezi ve Fotogrametri, Geodesy and Photogrammetry
- Anahtar Kelimeler: Geçiş eğrileri, Klotoid, Kübik parabol, Otoyollar, Transition elements, Clothoid, Cubic parabola, Motorways
- Yıl: 1991
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Bu çalışmada, otoyol güzergahlarının projelendirilmesinde kullanılan birleştirme eğrilerinden klotoid, lemniskat, kübik parabol ve 2R yarıçaplı dairenin bağıntıları ve özellikleri incelenerek çeşitli uygulamaları gösterilmiştir. 3. Bölümde birleştirme eğrilerinin benzer ve farklı yanları incelenerek birbirleriyle olan karşılaştırmaları yapılmıştır. Bölüm 5'te otoyollarda ve kavşaklarda klotoidin uygulanmasında karşılaşılan problemler incelenmiştir. Edirne-Sakarya otoyolunda Kınalı-E5 kavşağının geometrik çözümü yapılmış ve elde edilen sonuçlar şekillerle ve tablolarla sayısal olarak gösterilmiştir. 8. Bölümde bu çalışmadan elde edilen sonuçlar açıklanmıştır. Ekler bölümünde klotoid hesaplamalarında kullanılan tablolar verilmiştir. Ayrıca, geometrik çözümü yapılmış bir güzergahın ara noktalarının ve offset noktalarının koordinatlarını ve kutupsal aplikasyon elemanlarını veren bir program ilave edilmiştir. v
Özet (Çeviri)
SUMMARY THE COMPARISON OF THE TRANSITION CURVES AMONG THEIR OWN KINDS FOR THE ROUTE OF HIGH SPEED ROADS, AND AN APPLICATION (The geometrical analysing of the crossroad of Kxnali-E5 on the Sakarya-Edirne Highway) Transition curves are introduced at the beginnings and ends of horizontal circular curves as easements from the straight into the circular arc. without transitions the steering must be turned instantly from straight ahead to the position for the curve, and the centrifugal force which is absent on the straight but present on the- circular arc must also be developed at the same instant of passing the TC point. On roads of slight curvature or generous width, or at low speeds, the driver can adopt his individual transition path without difficulty, but on high speed roads with restricted lane widths, or on fixed rail tracks, some concession must be made to these effects and a transition curve introduced between tangent and circular curve [_l]. When a car traveling on a straight stretch of highway reaches a circular path, the steering wheel must be set at a new angle depending upon the radius of the curve. This movement cannot be done instantly but in a measurable time interval, thus creating a demond for a transition curve, the length of which equals speed x time [2j- The requirement of a transition curve is that it shall have a curvature increasing linearly to match the uniform rate of application of süpere lavat ion angle and rate of turn of steering whell. Four curves may be used as a transition curve. - the clothoid - the lemniscate - the cubic parabola - transition curve with radius 2R The most useful curve for direct calculation of the transition is the cubic parabola, but for all practical purposes the first three curves are the same at the curvatures and lengths used in high speed roads [l]. VIThe beginning and points of the transitions to a circular curve are denoted in a similar manner to the tangent points in simple curvature. They are; TS back tangent to lead-in spiral SC lead-in spiral to circular curve CS circular curve to run-out spiral ST run-out spiral to forward tangent. spiral angles are measured relative to the tangent at TS or ST. clothoid is a curve that rotates infinite circula tions around the points of rotation. Only a short part of this curve from its beginning is used in the construc tion of highways and railways. The radius of curvature of clothoid, at the beginning, has infinite value, and the radius decreases proportionally with its own length. The formula of clothoid as follows: A2=R.L where A denotes parameter of clothoid, R denotes the radius of curve, and L is the length of transition curve. The values of length L and radius R change in each point on curve. However, this change is surrounded on the condi tion that the production of length L and radius R must be equal to a constant value as A2. So it's possible to calculate an unknown value by helping any given two values. It is accepted that the curvatures of the ideal transition curve varry in proportion the length of curves. According to the this definition, the most appropriate curve is the clothoid. Lemniscate is the most similar curve to the ideal transition curve. According to polar coordinates, the equation of lemniscate is; S2 = A2. Sin 2a where S and a are the polar coordinates of a point on the curve. A is a parameter which determines the size of curve. Practically, the cubic parabola is one of the most appointed curves. Applications of these curves are easier than 'the others, but, the value of ignorance raise if the spiral angles are greater than twelve degrees. In this point, the curve differs from ideal transition curve. In that case, it is feasible to use the clothoids or lemniscates. vixThe formula of the cubic parabola as follows; X3 Y= * 6.R.L Transition curve with radius 2R is not an exact transitional curve. However, it can provide the reducing of effect of centrifugal force to half. The equation of this curve can be.formulated as follows: X2 Y= - 4R The advantages and disadvantages of transitional curves, providing that comparing each other, in terms of similarities and differences has been reseached. As a resault, the best ideal transition curve is clothoid as it was explained above for the high speed roads. Unit clothoid and norm clothoid tables which are used in calculations of clotoit and clotoit pistoles are analyzed. In addition, different applications of clothoids which are used in the preparation of projects, have been explained at the following sections. At the stage of project properation, it is likely to encounter some various methods of use of the clotoit which are 1) The use of.clothoid as a transition curve between an alligment an a circle. 2) The use of clothoid as a transition curve between two circles with different directions. 3) The use of clothoid as a transition curve (egg line-Eilinie) between two circles with same directions. 4) A number of curve tyoes between two alligments 5) Various tynes of clothoid. At the first method of use quoted above all the elements of clothoid can be computed providing that two of the elements at the transition point of curve are known. These known elements are to be demonstrated in tables. The transition curve combining two circles with different direction eachother is called as S-curve. Especially S-curves placed between two circles with different direction at high speed roads are of importanece, The existence of an interval alligment in an S-curve is of objection. They are supposed to consist of two clothoid branches with the same parameteres, if possible. In order vmto figure out the problem with the purpose of determination of the parameter A, the following method can be used. R= - Rl+R2 -\ L <k2T. 3R Rl+R2 a^/l.r1 If D is known instead of T; T2=D. (2R1+2R2+D) first, the value of T is computed with above formula, where, D is the distance between two curves, T is the length of tangent. Egg line which is used as a transition curve between two circles with same directions at the high speed roads, is not used too much. Solution of the problem is close to S-curve solution. Sametimes, the length of the clothöid and curves may be required to be in proportion each other on the route which is in the form of Alligment-clothoid-circle- clothoid-alligment. In this manner,' some different combinations of curves may emerge. These are as follows; 1. Asymetric position (clothoid-circle-clothöid) 2. Symetric clothöid. branches. 3. The concrete curves with having equal length 4.“Some curves.”5.“Symetric some curves”Some deviations which may occured to calculate the pretty mistake can be neglected, when the project is prepared. On that condition, it is required to direct combining of the different parametric part of clothoid each other. The norm parameters should be prefered in the series of clothoids which are formed in this aim as above. At the sixth chapter, the manner of application was explained. The coordinates of transition points are defined after the horizantal geometrical solution of the route. The applications of any given point on the clothöid is calculated with in the same way of the applications of the curves. Shortly, the using of same application methods can be determined whether the application is verticullar or having polar coordinates. IXIt wanted to be shown as an example of the calcula tion of curves in practical in which is used construction of crossroads those contribute the important role about application of curves, by giving an example as the crossroads of Kınalı-E5 on Sakarya-Edirne Highway. In added chapter, the tables, those are used for calculation of the clotoids, where offered. Moreover», a program that permits to calculating of which any given points on the curve, the coordinates of offset points and the elements of applications of polar coordinates, is introduced. This program can only be used in the programing of Cassio Fx-850p. When the program runs, the consecutive stages are as follows: At the first stage, the coordinates of the station point are input. One of the option of the clotoid, or circle, is choosen. At the following stages, the kilometer of starting point and its coordinates, tangent of bearing, radius of the curve or parameter of the clotoid, the length of the curve, the kilometer of the first application point and application step are entered into the computer. The distance of the left and the rihgt of offset points, from the exe, can be input if it is necessary. At the final production of the computer, any given points on the curve which have demonded intensity and coordinates of the offset points with the elements of polar application can be obtained. x
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