Exact solution of circular vertical curves

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

Emergency services site selection: The integration of analytic hierarchy process and geographic information systems

Bu araştırmada itfaiye istasyonlarının yeni yerlerinin belirlenmesi aşamasında gözönüne alınabilecek ölçütler saptanmış, Analitik Hiyerarşi Yöntemi (AHY) kavramından yararlanılarak herbir ölçüt için ağırlıklar belirlenmiş ve belirlenen ölçüt ağırlıklarına dayanarak Coğrafi Bilgi Sistemleri (CBS) ortamında en uygun yer analizi yapılmıştır. Ayrıca oluşturulan modelin duyarlılığını test etmek amacıyla yine CBS ortamında duyarlılık analizleri gerçekleştirilmiştir. Gerçekleştirilen bu çalışmalar ile karar vericilere özellikle itfaiye istasyonları gibi acil durum servislerinin en uygun yerlerinin belirlenmesinde verecekleri kararlarda destek sağlayacak bir sistem üzerine odaklanılmıştır. Çalışmada izlenen adımlar şu şekilde özetlenmektedir: Çözülecek problemin/amacın belirlenmesi; itfaiye istasyonlarının yeni yerlerinin belirlenmesinde etkili olası ölçütlerin belirlenmesi; verilerin elde edilmesi, hazırlanması ve düzenlenerek CBS ortamına aktarılması; parça parça olan veri gruplarının bir çalışma bölgesi oluşturacak şekilde düzenlenmesi ve herbir ölçüte (tabaka) karşılık gelen verilerin raster veri formatında betimlenmesi; raster veri gruplarının sınıflandırılması; Analitik Hiyerarşi Yöntemi (AHY) yardımıyla tercih matrislerinin oluşturulması; iki karar verici grubun görüşlerine dayanarak oluşturulan tercih matrisinden yararlanarak özdeğer ve özvektörlerin hesaplanması; AHY’nin sonuçların sentezlenmesi özelliğinden faydalanarak ilgili herbir ölçüt için önem/ağırlık değerlerinin belirlenmesi; ölçütlere ağırlıklı toplama işlemi uygulanarak sonuç raster verisinin CBS ortamında elde edilmesi; oluşturulan modelin duyarlılığının (CBS) ortamında test edilmesi ve yeni itfaiye istasyon yerlerinin belirlenmesinde karar vericilere destek sağlayan bir sistemin önerilmesi.  Anahtar Kelimeler: CBS, analitik hiyerarşi yöntemi, yer seçimi, çok ölçütlü karar verme.In the early 1980s Geographical Information Systems (GIS) software emerged as a new information processing technology offering unique capabilities of automating, managing, and analysing a variety of spatial data. Many applications of GIS developed over the last decade provided information necessary for the decision-making in diverse areas including natural resource management, regional planning, and disaster management. Two perspectives on developing better decision support capabilities of GIS can be identified, one based on analytical problem solving as a centrepiece of Spatial Decision Support Systems (SDSS) and another based on integration of GIS and specialized analytical models. According to first perspective, SDSS should offer modelling, optimization, and simulation functions required to generate, evaluate, recommend, and test the sensitivity or problem solution strategies. These capabilities are essential to solving semi-structured spatial decision-making problems. The second perspective on improving the decision support capabilities focuses on the expansion of GIS descriptive, prescriptive, and predictive capabilities by integrating GIS software with other statistical software and analytical models. According to this view, mapping, query, and spatial modelling functions of GIS can provide data display at different scales, preprocessing, and data input for environmental and statistical models. The general objective of Multi-criteria Decision Making (MCDM) is to assist the decision-maker (DM) in selecting the ?best? alternative from the number of feasible choice-alternatives under the presence of multiple choice criteria and diverse criterion priorities. The problem of multicriterion choice in decision making is the paramount challenge faced by individiuals, public and private corporations. The nature of challenge is two-fold: How to identify choice alternatives satisfying the objectives of parties involved in the decision-making process? How to order the set of feasible choice alternatives to identify the most preferred alternative? The challenge of multicriterion choice can be attributed to many spatial decision-making problems involving search and location/allocation of resources. These problems, often analysed in (GIS), include location/site selection for: service facilities, retail outlets, critical areas for specific resource management, and emergency service locations where are key locations for effective emergency management. In this study, the criteria and its priorities/weights that should be considered for finding optimal locations of fire stations are determined; and multi-criteria site analysis is conducted based on mentioned criteria weights in (GIS) environment. Moreover, in order to test the sensitivity and robustness of the model developed, a sensitivity analysis is performed based on the combination of the criterion weights by using (GIS) capabilities. With these analyses performed, it is focused on the creating the model that supports decision makers in decision-making for finding the optimal locations of fire stations. In this study, these steps are followed: Definition of the problem/objective (determining the optimal locations of fire stations); determining the potential criteria in finding the optimal locations of fire stations; data collection and preparation and transfer to (GIS) environment; creation of raster data sets representing the regionalised criteria; classification of raster data sets; establishment of preference matrix, assigning preference values to the relevant criteria by using the pairwise comparison feature of Analytic Hiyerarchy Process (AHP); determination of criteria weights by calculating eigenvalues and eigenvectors of the preference matrix which evaluated by two decision maker group; determining the criteria priorities/weights values by using the synthesis of priorities and calculating the overall composite weights; calculating the result raster (suitability map for potential fire stations) as a weighted summation of all criteria raster data sets; conducting the sensitivity analyses in (GIS) environment in order to test the sensitiveness and robustness of the model developed; offering a system that supports decision makers in determining the optimal locations of fire stations. The integration of the (AHP) and (GIS) combines decision support methodology with powerful visualisation and analysing capabilities which should considerably facilitate finding optimal locations of fire stations and this process improves the decision making in emergency management. Keywords: GIS, Analytic hierarchy process, site selection, multi-criteria decision making

Osteoid Osteoma Treated with Radiofrequency Ablation

Purpose. Our aim is to evaluate the results of treatment with computed tomography (CT) guided percutaneous radiofrequency ablation for osteoid osteomas which were localized in a difficult area for operation. Materials and Methods. Glenoid, distal tibia, humerus shaft, proximal humerus, and in third finger of the hand proximal phalanx were involved in one patient. Proximal femur was involved in three patients, distal femur was involved in three patients, and proximal tibia was involved in two patients. 9 males and 4 females were aged 4 to 34 years (mean age: 18.5 years). All patients had pain and were evaluated with X-rays, CT, bone scintigraphy, and MRI. In all patients, RF ablation was performed with local anesthesia. The lesion heated to 90°C for 6 minutes. Results. All of the patients achieved complete pain relief after ablation and were fully weight bearing without any support. In all patients, there was soft tissue edema after the procedure. During follow-up, all patients were free from the pain and there was no sign about the tumor. There was no other complication after the process. Conclusion. CT guided RFA is a minimally invasive, safe, and cost-effective treatment for osteoid osteoma placed in difficult area for surgery

Characteristics of patients with hepatocellular carcinoma: A multicenter study

Background and Aim: The aim of the present study was to examine the etiology of hepatocellular carcinoma (HCC) by underlying cause and determine the characteristics and clinical features of patients with HCC. Materials and Methods: The study comprised 1802 HCC patients diagnosed and followed up by Liver Diseases Outpatient Clinics in 14 tertiary centers in Turkey between 2001 and 2020. Results: The mean age was 62.3 +/- 10.7 years, and 78% of them were males. Of the patients, 82% had cirrhosis. Hepatitis B virus (HBV) infection was the most common etiology (54%), followed by hepatitis C virus (HCV) infection (19%) and nonalcoholic fatty liver disease (NAFLD) (10%). Of the patients, 56% had a single lesion. Macrovascular invasion and extrahepatic spread were present in 15% and 12% of the patients, respectively. The median serum alpha-fetoprotein level was 25.4 ng/mL. In total, 39% of the patients fulfilled the Milan Criteria. When we compared the characteristics of patients diagnosed before and after January 2016, the proportion of NAFLD-related HCC cases increased after 2016, from 6.6% to 13.4%. Conclusion: Chronic HBV and HCV infections remain the main causes of HCC in Turkey. The importance of NAFLD as a cause of HCC is increasing