Notes on Curves for Railways
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NORTH WEST Freight Transport Strategy
NORTH WEST Freight Transport Strategy Department of Infrastructure NORTH WEST FREIGHT TRANSPORT STRATEGY Final Report May 2002 This report has been prepared by the Department of Infrastructure, VicRoads, Mildura Rural City Council, Swan Hill Rural City Council and the North West Municipalities Association to guide planning and development of the freight transport network in the north-west of Victoria. The State Government acknowledges the participation and support of the Councils of the north-west in preparing the strategy and the many stakeholders and individuals who contributed comments and ideas. Department of Infrastructure Strategic Planning Division Level 23, 80 Collins St Melbourne VIC 3000 www.doi.vic.gov.au Final Report North West Freight Transport Strategy Table of Contents Executive Summary ......................................................................................................................... i 1. Strategy Outline. ...........................................................................................................................1 1.1 Background .............................................................................................................................1 1.2 Strategy Outcomes.................................................................................................................1 1.3 Planning Horizon.....................................................................................................................1 1.4 Other Investigations ................................................................................................................1 -
Trigonometry and Spherical Astronomy 1. Sines and Chords
CHAPTER TWO TRIGONOMETRY AND SPHERICAL ASTRONOMY 1. Sines and Chords In Almagest I.11 Ptolemy displayed a table of chords, the construction of which is explained in the previous chapter. The chord of a central angle α in a circle is the segment subtended by that angle α. If the radius of the circle (the “norm” of the table) is taken as 60 units, the chord can be expressed by means of the modern sine function: crd α = 120 · sin (α/2). In Ptolemy’s table (Toomer 1984, pp. 57–60), the argument, α, is given at intervals of ½° from ½° to 180°. Columns II and III display the chord, in units, minutes, and seconds of a unit, and the increase, in the same units, in crd α corresponding to an increase of one minute in α, computed by taking 1/30 of the difference between successive entries in column II (Aaboe 1964, pp. 101–125). For an insightful account on Ptolemy’s chord table, see Van Brummelen 2009, where many issues underlying the tables for trigonometry and spherical astronomy are addressed. By contrast, al-Khwārizmī’s zij originally had a table of sines for integer degrees with a norm of 150 (Neugebauer 1962a, p. 104) that has uniquely survived in manuscripts associated with the Toledan Tables (Toomer 1968, p. 27; F. S. Pedersen 2002, pp. 946–952). The corresponding table in al-Battānī’s zij displays the sine of the argu- ment at intervals of ½° with a norm of 60 (Nallino 1903–1907, 2:55– 56). This table is reproduced, essentially unchanged, in the Toledan Tables (Toomer 1968, p. -
Derailment of Freight Train 9204V, Sims Street Junction, West Melbourne
DerailmentInsert document of freight title train 9204V LocationSims Street | Date Junction, West Melbourne, Victoria | 4 December 2013 ATSB Transport Safety Report Investigation [InsertRail Occurrence Mode] Occurrence Investigation Investigation XX-YYYY-####RO-2013-027 Final – 13 January 2015 Cover photo source: Chief Investigator, Transport Safety (Vic) This investigation was conducted under the Transport Safety Investigation Act 2003 (Cth) by the Chief Investigator Transport Safety (Victoria) on behalf of the Australian Transport Safety Bureau in accordance with the Collaboration Agreement entered into on 18 January 2013. Released in accordance with section 25 of the Transport Safety Investigation Act 2003 Publishing information Published by: Australian Transport Safety Bureau Postal address: PO Box 967, Civic Square ACT 2608 Office: 62 Northbourne Avenue Canberra, Australian Capital Territory 2601 Telephone: 1800 020 616, from overseas +61 2 6257 4150 (24 hours) Accident and incident notification: 1800 011 034 (24 hours) Facsimile: 02 6247 3117, from overseas +61 2 6247 3117 Email: [email protected] Internet: www.atsb.gov.au © Commonwealth of Australia 2015 Ownership of intellectual property rights in this publication Unless otherwise noted, copyright (and any other intellectual property rights, if any) in this publication is owned by the Commonwealth of Australia. Creative Commons licence With the exception of the Coat of Arms, ATSB logo, and photos and graphics in which a third party holds copyright, this publication is licensed under a Creative Commons Attribution 3.0 Australia licence. Creative Commons Attribution 3.0 Australia Licence is a standard form license agreement that allows you to copy, distribute, transmit and adapt this publication provided that you attribute the work. -
Coverrailway Curves Book.Cdr
RAILWAY CURVES March 2010 (Corrected & Reprinted : November 2018) INDIAN RAILWAYS INSTITUTE OF CIVIL ENGINEERING PUNE - 411 001 i ii Foreword to the corrected and updated version The book on Railway Curves was originally published in March 2010 by Shri V B Sood, the then professor, IRICEN and reprinted in September 2013. The book has been again now corrected and updated as per latest correction slips on various provisions of IRPWM and IRTMM by Shri V B Sood, Chief General Manager (Civil) IRSDC, Delhi, Shri R K Bajpai, Sr Professor, Track-2, and Shri Anil Choudhary, Sr Professor, Track, IRICEN. I hope that the book will be found useful by the field engineers involved in laying and maintenance of curves. Pune Ajay Goyal November 2018 Director IRICEN, Pune iii PREFACE In an attempt to reach out to all the railway engineers including supervisors, IRICEN has been endeavouring to bring out technical books and monograms. This book “Railway Curves” is an attempt in that direction. The earlier two books on this subject, viz. “Speed on Curves” and “Improving Running on Curves” were very well received and several editions of the same have been published. The “Railway Curves” compiles updated material of the above two publications and additional new topics on Setting out of Curves, Computer Program for Realignment of Curves, Curves with Obligatory Points and Turnouts on Curves, with several solved examples to make the book much more useful to the field and design engineer. It is hoped that all the P.way men will find this book a useful source of design, laying out, maintenance, upgradation of the railway curves and tackling various problems of general and specific nature. -
Differential and Integral Calculus
DIFFERENTIAL AND INTEGRAL CALCULUS WITH APPLICATIONS BY E. W. NICHOLS Superintendent Virginia Military Institute, and Author of Nichols's Analytic Geometry REVISED D. C. HEATH & CO., PUBLISHERS BOSTON NEW YORK CHICAGO w' ^Kt„ Copyright, 1900 and 1918, By D. C. Heath & Co. 1 a8 v m 2B 1918 ©CI.A492720 & PREFACE. This text-book is based upon the methods of " limits " and ''rates/' and is limited in its scope to the requirements in the undergraduate courses of our best universities, colleges, and technical schools. In its preparation the author has embodied the results of twenty years' experience in the class-room, ten of which have been devoted to applied mathematics and ten to pure mathematics. It has been his aim to prepare a teachable work for begimiers, removing as far as the nature of the subject would admit all obscurities and mysteries, and endeavoring by the introduction of a great variety of practical exercises to stimulate the student's interest and appetite. Among the more marked peculiarities of the work the follow- ing may be enumerated : — i. A large amount of explanation. 2. Clear and simple demonstiations of principles. 3. Geometric, mechanical, and engineering applications. 4. Historical notes at the heads of chapters giving a brief account of the discovery and development of the subject of which it treats. 5. Footnotes calling attention to topics of special historic interest. iii iv Preface 6. A chapter on Differential Equations for students in mathematical physics and for the benefit of those desiring an elementary knowledge of this interesting extension of the calculus. -
Technical Investigation Report on Train Derailment Incident at Hung Hom Station on MTR East Rail Line on 17 September 2019
港鐵東鐵綫 紅磡站列車出軌事故 技術調查報告 Technical Investigation Report on Train Derailment Incident at Hung Hom Station on MTR East Rail Line 事故日期︰2019 年 9 月 17 日 Date of Incident : 17 September 2019 英文版 English Version 出版日期︰2020 年 3 月 3 日 Date of Issue: 3 March 2020 CONTENTS Page Executive Summary 2 1 Objective 3 2 Background of Incident 3 3 Technical Details Relating to Incident 4 4 Incident Investigation 8 5 EMSD’s Findings 19 6 Conclusions 22 7 Measures Taken after Incident 22 Appendix I – Photos of Wheel Flange Marks, Broken Rails, Rail Cracks and Damaged Point Machines On-Site 23 1 Executive Summary On 17 September 2019, a passenger train derailed while it was entering Platform No. 1 of Hung Hom Station of the East Rail Line (EAL). This report presents the results of the Electrical and Mechanical Services Department’s (EMSD) technical investigation into the causes of the incident. The investigation of EMSD revealed that the cause of the derailment was track gauge widening1. The sleepers2 at the incident location were found to have various issues including rotting and screw hole elongation, which reduced the strength of the sleepers and their ability to retain the rails in the correct position. The track gauge under dynamic loading of trains would be even wider, and this excessive gauge widening caused the train to derail at the time of incident. After the incident, MTR Corporation Limited (MTRCL) have reviewed the timber sleeper condition across the entire EAL route and replaced the sleepers of dissatisfactory condition. MTRCL were requested to enhance the maintenance regime to closely monitor the track conditions with reference to relevant trade practices to ensure railway safety. -
Development of Trigonometry Medieval Times Serge G
Development of trigonometry Medieval times Serge G. Kruk/Laszl´ o´ Liptak´ Oakland University Development of trigonometry Medieval times – p.1/27 Indian Trigonometry • Work based on Hipparchus, not Ptolemy • Tables of “sines” (half chords of twice the angle) • Still depends on radius 3◦ • Smallest angle in table is 3 4 . Why? R sine( α ) α Development of trigonometry Medieval times – p.2/27 Indian Trigonometry 3◦ • Increment in table is h = 3 4 • The “first” sine is 3◦ 3◦ s = sine 3 = 3438 sin 3 = 225 1 4 · 4 1◦ • Other sines s2 = sine(72 ), . Sine differences D = s s • 1 2 − 1 • Second-order approximation techniques sine(xi + θ) = θ θ2 sine(x ) + (D +D ) (D D ) i 2h i i+1 − 2h2 i − i+1 Development of trigonometry Medieval times – p.3/27 Etymology of “Sine” How words get invented! • Sanskrit jya-ardha (Half-chord) • Abbreviated as jya or jiva • Translated phonetically into arabic jiba • Written (without vowels) as jb • Mis-interpreted later as jaib (bosom or breast) • Translated into latin as sinus (think sinuous) • Into English as sine Development of trigonometry Medieval times – p.4/27 Arabic Trigonometry • Based on Ptolemy • Used both crd and sine, eventually only sine • The “sine of the complement” (clearly cosine) • No negative numbers; only for arcs up to 90◦ • For larger arcs, the “versine”: (According to Katz) versine α = R + R sine(α 90◦) − Development of trigonometry Medieval times – p.5/27 Other trig “functions” Al-B¯ırun¯ ¯ı: Exhaustive Treatise on Shadows • The shadow of a gnomon (cotangent) • The hypothenuse of the shadow -
Track Report 2009 V1:G 08063 PANDROLTEXT
The Journal of Pandrol Rail Fastenings 2009 DIRECT FIXATION ASSEMBLIES Pandrol and the Railways in China................................................................................................page 03 by Zhenping ZHAO, Dean WHITMORE, Zhenhua WU, RailTech-Pandrol China;, Junxun WANG, Chief Engineer, China Railway Construction Co. No. 22, P. R. of China Korean Metro Shinbundang Project ..............................................................................................page 08 Port River Expressway Rail Bridge, Adelaide, Australia...............................................................page 11 PANDROL FASTCLIP Pandrol, Vortok and Rosenqvist Increasing Productivity During Tracklaying...................................................................................page 14 PANDROL FASTCLIP on the Gaziantep Light Rail System, Turkey ...............................................page 18 The Arad Tram Modernisation, Romania .....................................................................................page 20 PROJECTS Managing the Rail Thermal Stress Levels on MRS Tracks - Brazil ...............................................page 23 by Célia Rodrigues, Railroad Specialist, MRS Logistics, Juiz de Fora, MG-Brazil Cristiano Mendonça, Railroad Specialist, MRS Logistics, Juiz de Fora, MG-Brazil Cristiano Jorge, Railroad Specialist, MRS Logistics, Juiz de Fora, MG-Brazil Alexandre Bicalho, Track Maintenance Manager, MRS Logistics, Juiz de Fora, MG-Brazil Walter Vidon Jr., Railroad Consultant, Ch Vidon, Juiz de Fora, MG-Brazil -
Mathematics Tables
MATHEMATICS TABLES Department of Applied Mathematics Naval Postgraduate School TABLE OF CONTENTS Derivatives and Differentials.............................................. 1 Integrals of Elementary Forms............................................ 2 Integrals Involving au + b ................................................ 3 Integrals Involving u2 a2 ............................................... 4 Integrals Involving √u±2 a2, a> 0 ....................................... 4 Integrals Involving √a2 ± u2, a> 0 ....................................... 5 Integrals Involving Trigonometric− Functions .............................. 6 Integrals Involving Exponential Functions ................................ 7 Miscellaneous Integrals ................................................... 7 Wallis’ Formulas ................................................... ...... 8 Gamma Function ................................................... ..... 8 Laplace Transforms ................................................... 9 Probability and Statistics ............................................... 11 Discrete Probability Functions .......................................... 12 Standard Normal CDF and Table ....................................... 12 Continuous Probability Functions ....................................... 13 Fourier Series ................................................... ........ 13 Separation of Variables .................................................. 15 Bessel Functions ................................................... ..... 16 Legendre -
Tables of Trigonometric Functions in Non-Sexagesimal Arguments
Tables of Trigonometric Functions in Non-Sexagesimal Arguments Excluding the ordinary tables of trigonometric functions in sexagesimal arguments the two principal groups of such tables are those with arguments in A. Radians,—tables of this type have been already listed in RMT 81; and B. Grades. But we shall also consider tables of the trigonometric functions with arguments in C. Mils; Dl. Gones; D2. Cirs; and E. Time. B. Grades. The first stage in the evolution of the centesimal division of the quadrant was by the division of each sexagesimal degree into 100 minutes and each of these minutes into 100 seconds. This was conceived already about 1450 by Theodericus Ruffi, in a Latin codex in Munich.1 The centesimal division of the degree was also presented by Vieta in his Calendarij Gregoriani, 1600, p. "29"(Opera M athematica, 1646, p. 487). It was this source which sug- gested to Henry Briggs the choice of every hundredth of a degree as the unit in the preparation of his wonderful "sine canon";2 see RMT 79. Late in the eighteenth century the centesimal division of the quadrant was definitely in the thought of scholars then in Berlin and especially of Johann Carl Schulze (1749-1790), author of Neue und erweiterte Sammlung logarithmischer, trigonometrischer und anderer zum Gebrauch der Mathematik unentbehrlicher Tafeln [also French t.p.], Berlin, 2v., 1778. He had studied under J. H. Lambert (1728-1778) and became a member of the Academy of Sciences at Berlin, in which Lagrange (following Euler) was director of its mathematical section for a score of years before he moved to Paris in 1787. -
Rail Equipment Catalogue
Version 1.2 Rail Equipment Catalogue Partners in excellence RAIL EQUIPMENT CATALOGUE Contents Contents Rail Pullers and Tampers 1 Welding Equipment 3 Power Units 02800A 60 Ton Bridge Jack / Spreader 15 02800-6 100 Ton Bridge Jack / Spreader 02850 Bridge Jack / Spreader Stool 16 -KIT Rail Saws 02900A Diesel Power Unit 33 01100RM Lightweight Two-Stage Spike Puller 16 00800A Rail Saw 7 00100K Dual Circuit Power Unit 34 03100C Rail Puller 18 03900A Reversing Rail Saw 7 03700A Electric Power Unit 35 08300 Spike Driver 18 Battery-Operated 00100 36 Shearing Machines 01200 Spring Clip Applicator 19 Hydraulic Power Unit EME1 06500 Hydraulic Intensifier 37 Electric Shearing Machines 8 08200 Tamper 19 EME2 EMB1 Ignition 03000 Hydraulic Manifold Circuit 37 Battery Shearing Machines 8 EMB2 Startwel® Ignition System 20 06700 Mobile Diesel Power Unit 38 EGH1 EGH2 Dead Head Rail Welding Traceability App 02050RM Modular Power Unit 39 Cutter TM Hydraulic Shearing Machines 9 05100A Pandrol Connect 22 05100B 06300 Power Unit Mobility Cart 40 EPM2 Hydraulic Hand Pump 9 06600 Power Unit Transport 41 05000 Shearing Machine Twin Power Unit Alignment 05500 42 2 Grinding Equipment W/ Generator BA240 Alignment Beam 10 Magnetic Straight Edge 10 CR57 Profile / Frog Grinders 4 Clipping Equipment A Frame Rail Aligner 11 CR61 Alpha Grinder 25 ap-1 Alignment Plates 11 09200A Precision Frog Grinder 26 Preheaters Clip Driver CD100 45 MR150 Profile Grinder 26 03800B Hydraulic Preheater 12 Clip Driver CD200 IQ 45 Our products stand the test RPLE Profile Grinder 26 Precision Torch Stand 12 Clip Driver CD300 IQ 46 06000 of time. -
Finished Vehicle Logistics by Rail in Europe
Finished Vehicle Logistics by Rail in Europe Version 3 December 2017 This publication was prepared by Oleh Shchuryk, Research & Projects Manager, ECG – the Association of European Vehicle Logistics. Foreword The project to produce this book on ‘Finished Vehicle Logistics by Rail in Europe’ was initiated during the ECG Land Transport Working Group meeting in January 2014, Frankfurt am Main. Initially, it was suggested by the members of the group that Oleh Shchuryk prepares a short briefing paper about the current status quo of rail transport and FVLs by rail in Europe. It was to be a concise document explaining the complex nature of rail, its difficulties and challenges, main players, and their roles and responsibilities to be used by ECG’s members. However, it rapidly grew way beyond these simple objectives as you will see. The first draft of the project was presented at the following Land Transport WG meeting which took place in May 2014, Frankfurt am Main. It received further support from the group and in order to gain more knowledge on specific rail technical issues it was decided that ECG should organise site visits with rail technical experts of ECG member companies at their railway operations sites. These were held with DB Schenker Rail Automotive in Frankfurt am Main, BLG Automotive in Bremerhaven, ARS Altmann in Wolnzach, and STVA in Valenton and Paris. As a result of these collaborations, and continuous research on various rail issues, the document was extensively enlarged. The document consists of several parts, namely a historical section that covers railway development in Europe and specific EU countries; a technical section that discusses the different technical issues of the railway (gauges, electrification, controlling and signalling systems, etc.); a section on the liberalisation process in Europe; a section on the key rail players, and a section on logistics services provided by rail.