Dynamic Analysis of High-Speed Railway Alignment : Theory and Practice

__Dynamic Analysis of High-Speed Railway Alignment: Theory and Practice__ elaborates on the dynamic analysis theory and method on spatial alignment parameters of high-speed railways, revealing the interaction mechanism between vehicle-track dynamic performance and track parameters of high-speed railways. It ascertains the influence rules of track structure and track geometry on vehicle-track dynamic performance, establishes the relationship models between vehicle-track dynamic performance and curve dynamic characteristic parameters, and defines the calculation relationship between lateral acceleration of car body on curves and track parameters. This book can be used as a reference book for scientific researchers, engineering technicians and management engaged in railway engineering, and will be very helpful for railway technicians who want to learn more about route planning, design, and construction and maintenance technologies of high-speed railways. Front Cover Dynamic Analysis of High-Speed Railway Alignment Dynamic Analysis of High-Speed Railway Alignment: Theory and Practice Copyright Contents 1 - Introduction 1.1 TARGET SPEED FOR HIGH-SPEED RAILWAY 1.1.1 THE PRINCIPLE OF DETERMINING TARGET SPEED FOR HIGH-SPEED RAILWAY 1.1.1.1 Comply With the Requirements of Macroeconomic Development 1.1.1.2 Comply With China's National Conditions 1.1.1.3 To Market Demand, Taking into Account Long-Term Development 1.1.1.4 Pay Attention to Economic Investment Projects 1.1.1.5 Consider Regional Differences 1.1.2 THE INFLUENCE FACTOR OF TARGET SPEED FOR HIGH-SPEED RAILWAYS 1.1.2.1 The Economy Speed of High-Speed Railway 1.1.2.2 The Suitable Speed Range of Technical Characteristics of High-Speed Rail System 1.1.2.2.1 The Limit Speed of Adhesion Railway 1.1.2.2.2 The Speed Determined by Traction Characteristics 1.1.2.3 The Effect of the Target Speed Value on the Use of High-Speed Railway 1.1.2.3.1 The Effect of Target Speed Value on the Investment in Civil Engineering 1.1.2.3.2 The Effect of Target Speed Value on Transportation Costs 1.1.2.4 The Effect of the Target Speed Value on Passenger Fares 1.1.2.4.1 Government Pricing 1.1.2.4.2 Cost Pricing 1.1.2.4.3 Priced by Customer's Payment Willingness 1.1.2.4.4 Pricing by Comparing With Other Modes of Transportation 1.1.2.4.5 The Maximum Profit Pricing Rule 1.1.2.5 The Impact of Target Speed Value on the Utility Value of Transportation of High-Speed Railway 1.1.2.7 The Design Speed and Experience of the High-Speed Railway Around the World 1.1.2.8 Summary of Research and Application in China 1.1.2.9 Research Steps of the Target Speed Value 1.2 THE BACKGROUND AND OVERVIEW OF HIGH-SPEED RAIL CURVE PARAMETERS 1.2.1 BACKGROUND 1.2.2 RESEARCH SITUATION 1.3 PRINCIPLE OF MINIMUM CURVE RADIUS BASED ON OPTIMAL DYNAMICS PERFORMANCE 2 - Models for Vehicle–Track Dynamic Simulation on Horizontal Curve Sections of High-Speed Railways 2.1 ALIGNMENT MODELS 2.1.1 THE LINE SPACE COORDINATE SYSTEM 2.1.2 LINE SPACE LINEAR MODEL 2.2 VEHICLE MODELS 2.2.1 VEHICLE SYSTEM DYNAMICS MODEL TO SIMPLIFY TOPOLOGY 2.2.2 THE EQUATIONS OF VEHICLE MOTION 2.3 TRACK STRUCTURE MODELS 2.3.1 BALLASTED TRACK STRUCTURE MODEL AND DYNAMIC EQUATIONS 2.3.1.1 The Equations of Rail Motion 2.3.1.2 The Motion Equations for the Sleeper 2.3.1.3 The Equations of Motion for the Track Bed 2.3.2 THE STRUCTURE MODELS AND DYNAMIC EQUATIONS OF THE SLAB TRACK 2.4 WHEEL–RAIL THREE-DIMENSIONAL DYNAMICALLY COUPLING MODEL 2.4.1 GEOMETRIC PARAMETERS OF THE WHEEL–RAIL SPATIAL CONTACT 2.4.2 CONTACT FORCE 2.4.2.1 Normal Force of the Wheel Set 2.4.2.2 Creep Force of Wheel and Rail 2.5 TRACK IRREGULARITY EXCITATION MODEL 2.5.1 GEOMETRICAL IRREGULARITY [62] OF THE TRACK 2.5.1.1 Vertical Irregularity of the Track 2.5.1.2 Horizontal Irregularity of the Track 2.5.1.3 Irregularity of Track Direction 2.5.1.4 Irregularity of the Gauge 2.5.2 THE MODEL [22] OF RANDOM IRREGULARITY OF THE TRACK 2.6 SOLUTION METHOD FOR THE VEHICLE–TRACK COUPLING MODEL 2.6.1 NUMERICAL INTEGRATION METHOD 2.6.1.1 The System Numerical Integration Method 2.6.1.2 Numerical Simulation of Track Random Irregularity 2.6.2 WHEEL–RAIL EXCITATION INPUT MODEL 2.6.3 DATA STORAGE FORMAT 2.6.4 FLOWCHART OF THE SYSTEM 2.6.5 PROGRAM VERIFICATION 3 - The Effect Law of the Curve Parameters of a High-Speed Railway on Vehicle–Line Dynamic Performance 3.1 THE CALCULATION PARAMETERS OF THE CURVE AND THE DYNAMIC PERFORMANCE EVALUATION INDEX OF THE VEHICLE–LINE SYSTEM 3.1.1 THE CALCULATION PARAMETERS AND CALCULATION CONDITIONS 3.1.1.1 Computation of Speed 3.1.1.2 The Value Range of the Actual Superelevation 3.1.1.3 Unbalanced Superelevation 3.1.1.4 Evaluation of the Length of the Transition Curve 3.1.2 EVALUATION INDEX OF THE DYNAMIC PERFORMANCE OF THE VEHICLE SYSTEM 3.1.2.1 Derailment Coefficient 3.1.2.2 Rate of Wheel Load Reduction 3.1.2.3 Evaluation Index for Vehicle Riding Comfort 3.1.2.4 Vertical Wheel Rail Force 3.1.2.5 Lateral Wheel Rail Force 3.1.2.6 Axle Lateral Force 3.2 THE INFLUENCE LAW OF CURVE NEGOTIATION SPEED ON THE VEHICLE–TRACK SYSTEM DYNAMIC CHARACTERISTICS 3.2.1 THE SIMULATION CALCULATION RESULTS 3.2.2 THE INFLUENCE LAW OF CURVE NEGOTIATION SPEED ON THE VEHICLE–TRACK SYSTEM DYNAMIC CHARACTERISTICS 3.3 THE INFLUENCE LAW OF CURVE RADIUS ON THE VEHICLE–TRACK SYSTEM DYNAMIC CHARACTERISTICS 3.3.1 THE SIMULATION CALCULATION RESULTS 3.3.2 THE INFLUENCE LAW OF CURVE RADIUS ON THE VEHICLE–TRACK SYSTEM DYNAMIC CHARACTERISTICS 3.4 THE INFLUENCE LAW OF THE ACTUAL ELEVATION OF THE CURVE ON THE VEHICLE–TRACK SYSTEM DYNAMIC CHARACTERISTICS 3.4.1 THE SIMULATION CALCULATION RESULTS 3.4.2 THE INFLUENCE LAW OF THE ACTUAL ELEVATION OF CURVE ON THE VEHICLE–TRACK SYSTEM DYNAMIC CHARACTERISTICS 3.5 THE INFLUENCE LAW OF THE UNBALANCED SUPERELEVATION ON THE VEHICLE–TRACK SYSTEM DYNAMIC CHARACTERISTICS 3.5.1 THE ANALYSIS OF THE INFLUENCE OF THE FORM OF UNBALANCED SUPERELEVATION ON THE VEHICLE–TRACK DYNAMIC CHARACTERISTICS 3.5.1.1 The Simulation Calculation Results 3.1.5.2 Analysis of the Influence Law 3.5.2 THE INFLUENCE LAW OF UNBALANCED SUPERELEVATION ON THE VEHICLE–TRACK DYNAMIC CHARACTERISTICS 3.5.2.1 The Simulation Calculation Results 3.5.2.2 Analysis of the Influencing Laws 4 - Dynamic Analysis of High-Speed Railway Curves: Theory and Practice 4.1 THE VEHICLE–TRACK DYNAMIC CHARACTERISTICS AND THE RELATIONSHIP MODEL OF CURVE PARAMETER ON HIGH-SPEED RAILWAY 4.1.1 THE LAW OF THE INFLUENCE OF THE TRACK STRUCTURE STATE ON THE VEHICLE–TRACK DYNAMIC CHARACTERISTICS 4.1.1.1 The Law of Ideal Track Geometry 4.1.1.2 Track is Under the Condition of Random Irregularity 4.1.2 THE RELATIONSHIP BETWEEN THE DEFICIENT SUPERELEVATION AND LATERAL ACCELERATION OF VEHICLE BODY 5 - The High-Speed Railway Comfort Degree: Experiment of Passenger in Curve 5.1 THEORY AND METHOD 5.1.1 EXPERIMENT THEORY 5.1.2 IMPLEMENTATION METHOD FOR TEST 5.1.2.1 The Choice of Test Curves 5.1.2.2 Investigation on the Comfort of Passengers 5.1.2.3 Experimental Data Processing 5.1.2.4 Analysis of Test Data 5.1.2.4.1 Analysis of Riding Comfort of Passengers 5.1.2.4.2 Analysis of the Lateral Acceleration Measured by the Track Inspection Car 5.1.2.4.3 Analysis of the Relationship Between Passenger Comfort and Curve Cant Deficiency 5.2 CASE STUDIES OF PASSENGER COMFORT TEST ON CURVES 5.2.1 GUANG-SHEN TEST 5.2.1.1 Test Implementation 5.2.1.1.1 Test Curve Selection 5.2.1.1.2 Passenger Comfort Survey 5.2.1.1.3 Velocity and Lateral Acceleration Measurement 5.2.1.2 Test Data Analysis 5.2.1.2.1 Analysis of the Investigation on Passenger Riding Comfort 5.2.1.2.2 Analysis of the Lateral Acceleration Measured by the Track Inspection Car 5.2.1.2.3 Analysis of the Relationship Between Passenger Comfort and Curve Cant Deficiency 5.2.1.3 Test Conclusion 5.2.2 SUINING–CHONGQING TEST 5.2.2.1 Test Measurement Project 5.2.2.1.1 Collection of the Data of Testing Curves 5.2.2.1.2 Degree of Passenger Comfort Survey 5.2.2.1.3 Measurement of Speed and Horizontal Lateral Acceleration 5.2.2.2 Test Data Analysis 5.2.2.2.1 Analysis of Survey of the Degree of Passenger Comfort 5.2.2.2.2 Analysis of Actual Lateral Acceleration 5.2.2.2.3 Analysis of the Relationship of the Degree of Passenger Comfort and the Curve Deficient Superelevation 5.2.2.3 Test Conclusion 5.2.3 RESEARCH ON WUHAN–GUANGZHOU RAILWAY 5.2.3.1 Passenger Survey 5.2.3.2 The Collection and Analysis of Track Geometry Inspection Vehicle Data 5.2.4 RESEARCH ON BEIJING–SHANGHAI HIGH-SPEED RAILWAY 6 - Calculation Method for Minimum Curve Radius of High-Speed Railways 6.1 PRINCIPLE OF CALCULATION OF MINIMUM CURVE RADIUS OF HIGH-SPEED RAILWAYS 6.1.1 CALCULATION FORMULA OF TRADITIONAL THEORY 6.1.1.1 Minimum Curve Radius With Maximum Running Speed for Passenger Trains 6.1.1.2 Minimum Curve Radius of a High-Speed Line With High and Medium Running Speeds on One Line 6.1.2 MODIFIED METHOD OF TRADITIONAL THEORY FORMULA 6.1.2.1 Modified Method of “Code for Design of High Speed Railway (Try Out)” 6.1.2.1.1 The Physical Meaning of [h+hq] and [hq+hg] Is Undefined 6.1.2.1.2 The Determination Method of Δh Is Unscientific 6.1.2.2 Modified Method Based on Vehicle–Line Dynamic Performance Evaluation 6.1.2.3 Modified Method of High-Speed Railway in Foreign Countries 6.1.3 CALCULATION METHOD FOR MINIMUM CURVE RADIUS BASED ON THE BEST VEHICLE–LINE DYNAMIC PERFORMANCE 6.2 METHOD TO DETERMINE ALLOWABLE ACTUAL SUPERELEVATION OF EXTERNAL RAILS ON A CURVE 6.2.1 THE MAXIMUM ALLOWED SUPERELEVATION DETERMINED BY SAFETY CONDITIONS 6.2.2 THE MAXIMUM ALLOWED SUPERELEVATION DETERMINED BY COMFORT 6.2.3 ENGINEERING APPLICATION PRACTICE AT HOME AND ABROAD 6.2.4 VEHICLE–LINE DYNAMIC SIMULATION ANALYSIS 6.2.5 SUGGESTIONS ON ALLOWABLE VALUE OF SUPERELEVATION 6.3 DETERMINATION METHOD OF DEFICIENT SUPERELEVATION 6.3.1 THE TEST OF THE RIDE COMFORT OF PASSENGERS 6.3.1.1 Passengers’ Ride Comfort Test 6.3.1.2 Relevant Foreign Research 6.3.2 VEHICLE–TRACK DYNAMIC SIMULATION ANALYSIS 6.3.3 FOREIGN ENGINEERING PRACTICE 6.3.4 THE SUGGESTIONS FOR ALLOWABLE VALUE OF DEFICIENT SUPERELEVATION 6.4 THE METHOD FOR DETERMINING THE ALLOWABLE VALUE OF THE SURPLUS SUPERELEVATION 6.4.1 PASSENGER RIDE COMFORT TEST 6.4.2 RELATED RESEARCH RESULTS 6.4.3 THE SURPLUS SUPERELEVATION'S IMPACT ON RAIL WEAR 6.4.4 ANALYSIS OF VEHICLE–TRACK DYNAMICS SIMULATION 6.4.5 SUGGESTIONS FOR THE ALLOWED SURPLUS SUPERELEVATION VALUE 6.5 MINIMUM CURVE RADIUS CALCULATION METHOD FOR HIGH-SPEED RAILWAY BASED ON DYNAMIC ANALYSIS 6.5.1 HIGH-SPEED RAILWAY SPEED MATCHING MODE 6.5.2 CALCULATION AND ANALYSIS OF THE MINIMUM CURVE RADIUS 6.5.3 MINIMUM CURVE RADIUS OF HIGH-SPEED RAILWAYS IN FOREIGN COUNTRIES 6.5.4 RECOMMENDED VALUE OF THE MINIMUM CURVE RADIUS 6.6 CALCULATION METHOD FOR MAXIMUM CURVE RADIUS OF HIGH-SPEED RAILWAYS 6.6.1 MAXIMUM CURVE RADIUS LIMITED TO ACCURACY OF SETTING OUT 6.6.2 THE MAXIMUM CURVE RADIUS ADAPTED TO THE ACCURACY OF TRACK GEOMETRIC STATE DETECTION 6.6.3 TRAIN–LINE DYNAMIC SIMULATION ANALYSIS 6.6.4 THE MAXIMUM CURVE RADIUS OF THE HIGH-SPEED TEST LINES IN FOREIGN COUNTRIES 6.6.5 RECOMMENDED VALUE OF THE MAXIMUM CURVE RADIUS APPENDIX 7 - The Length of the Transition Curve 7.1 THE EASEMENT CURVE LENGTH CALCULATION PRINCIPLE 7.1.1 EASEMENT CURVE LENGTH SHOULD MEET ULTRAHIGH TIME-VARYING RATE WHILE NOT MAKING PASSENGERS UNCOMFORTABLE 7.1.2 EASEMENT CURVE LENGTH OF DEFICIENT TIME-VARYING SUPERELEVATION RATE 7.1.3 EASEMENT CURVE LENGTH SHOULD MEET THE CONDITION THAT ULTRAHIGH SLOPES CANNOT CAUSE WHEELS TO DERAIL (VEHICLE DERAILMENT SAFETY) 7.1.4 MINIMUM EASEMENT CURVE LENGTH CALCULATION 7.2 TRANSITION CURVE ULTRAHIGH TIME-VARYING RATE ALLOWABLE VALUE 7.2.1 THE LARGEST ULTRAHIGH TIME-VARYING RATE PERMITTED BY COMFORT TEST 7.2.2 CAR-LINE DYNAMICS SIMULATION ANALYSIS 7.2.3 DOMESTIC AND INTERNATIONAL RELATED RESEARCH AND ENGINEERING PRACTICE 7.2.3.1 Japanese Shinkansen Easement Curve on Ultrahigh Time-Varying Rate Standard Has Experienced Three Stages 7.2.3.2 The Research and Practice of Our Country 7.2.4 PROPOSAL ALLOWING THE VALUE OF ULTRAHIGH TIME-VARYING RATE 7.3 MAXIMUM DEFICIENT SUPERELEVATION TIME-VARYING RATE B ALLOWED VALUE 7.3.1 EXPERIMENT TO DETERMINE COMFORT OF MAXIMUM ULTRAHIGH TIME-VARYING RATE 7.3.2 CAR-LINE DYNAMICS SIMULATION ANALYSIS 7.3.3 RELATED RESEARCH AND ENGINEERING PRACTICE AT HOME AND ABROAD 7.3.3.1 Related Research and Engineering Practice in Foreign Countries 7.3.3.2 Research and Engineering Practice in China 7.3.4 SUGGESTIONS ABOUT ULTRAHIGH TIME-VARYING RATE VALUE 7.4 MAXIMUM ALLOWABLE VALUE OF ULTRAHIGH SLOPE I0 7.4.1 TRAFFIC SAFETY ALLOWABLE ULTRAHIGH SLOPE 7.4.2 ULTRAHIGH SLOPES AS DETERMINED BY PASSENGER COMFORT 7.4.3 OVERSEAS RELATED RESEARCH AND ENGINEERING PRACTICES 7.4.4 RESEARCH AND ENGINEERING PRACTICE IN CHINA 7.4.5 ULTRAHIGH SLOPE ALLOWABLE VALUE SUGGESTION 7.5 MINIMUM TRANSITION CURVE LENGTH CALCULATION 7.6 THREE PARABOLIC EASEMENT CURVE ERROR ANALYSIS AND CORRECTION METHOD 7.6.1 ERROR OF THE APPROXIMATE FORMULA OF THE EASEMENT CURVE 7.6.2 MODIFIED THREE PARABOLIC 8 - The Minimum Length of the Intermediate Straight Line and Circular Curve 8.1 CALCULATION PRINCIPLES OF THE MINIMUM LENGTH OF THE INTERMEDIATE STRAIGHT LINE AND CIRCULAR CURVE 8.1.1 ENSURING THE LINE MAINTENANCE REQUIREMENTS 8.1.2 VEHICLE LATERAL SWING DOES NOT AFFECT THE SMOOTH RUNNING OF THE TRAIN 8.1.3 THE VIBRATION OF VEHICLE DOES NOT AFFECT THE COMFORT OF PASSENGERS 8.2 THE MINIMUM LENGTH OF INTERMEDIATE STRAIGHT LINE AND CIRCULAR CURVE AT HOME AND ABROAD 8.3 VEHICLE LINE DYNAMICS SIMULATION ANALYSIS 8.4 THE RECOMMENDED VALUES OF MINIMUM LENGTH OF THE INTERMEDIATE STRAIGHT LINE AND INTERMEDIATE CIRCULAR CURVE 9 - The Radius of Vertical Curve 9.1 THE MINIMUM RADIUS OF VERTICAL CURVE REQUIRED BY PASSENGER COMFORT CONDITION 9.1.1 CALCULATION PRINCIPLES 9.1.2 THE VALUES OF VERTICAL CENTRIFUGAL ACCELERATION LIMIT 9.1.2.1 Foreign Research and Engineering Practice 9.1.2.1.1 French Test on Vertical Acceleration 9.1.2.1.2 The Value of Vertical Centrifugal Acceleration Limit on Foreign High-Speed Railway 9.1.3 VEHICLE LINE DYNAMICS SIMULATION ANALYSIS 9.1.4 THE RADIUS OF VERTICAL CURVE OF PASSENGER COMFORT REQUIREMENT 9.2 THE MINIMUM RADIUS OF VERTICAL CURVE OF RUNNING SAFETY REQUIREMENTS 9.3 THE MAINTENANCE CONDITIONS 9.4 THE STANDARDS OF MINIMUM RADIUS OF VERTICAL CURVE 10 - The Maximum Gradient 10.1 THE MAXIMUM CALCULATED GRADIENT 10.1.1 CALCULATION MODEL OF MAXIMUM GRADIENT OF DESIGN LINE 10.1.1.1 The Design Principle of the Maximum Gradient of Design Line 10.1.1.2 The Maximum Calculated Gradient 10.1.2 THE MAXIMUM CALCULATED GRADIENT OF THE TUNNEL SECTION 10.1.2.1 Calculation Method of Additional Air Resistance 10.1.2.2 Calculation Model of Air Additional Resistance for a Single-Line Tunnel 10.1.2.3 The Maximum Calculated Gradient of the Tunnel Section 10.1.3 CALCULATION AND ANALYSIS OF MAXIMUM CALCULATED GRADIENT 10.1.3.1 Maximum Calculated Gradient of Ordinary Passenger Locomotives 10.1.3.1.1 Calculation Results 10.1.3.1.2 Comprehensive Analysis Carriage Return 10.1.3.2 The Maximum Calculated Gradient of Electric Multiple Units 10.1.3.2.1 Computational Data Carriage Return 10.1.3.2.2 Calculate the Relationship Between Grade and Velocity 10.1.3.2.3 Comprehensive Analysis 10.1.4 CALCULATION AND ANALYSIS OF ADDITIONAL AIR RESISTANCE IN TUNNEL 10.1.4.1 Electric Traction 10.1.4.1.1 Air Resistance Calculation Formula 10.1.4.1.2 Comprehensive Analysis 10.1.4.2 Electric Multiple Units 10.1.4.2.1 Air Resistance Calculation Formula 10.1.4.2.2 Tunnel Air Resistance Calculation 10.1.4.2.3 Comprehensive Analysis 10.1.5 THE MAXIMUM CALCULATED GRADE VALUE OF PASSENGER DEDICATED LINE 10.2 INFLUENCE OF ENGINEERING ECONOMIC CONDITIONS ON MAXIMUM GRADIENT 10.2.1 THE IMPACT ON THE NUMBER OF PROJECTS 10.2.2 IMPACT ON OPERATING EXPENSES 10.3 THE APPLICATION OF THE MAXIMUM GRADIENT AT HOME AND ABROAD 10.3.1 THE APPLICATION OF THE MAXIMUM GRADIENT ABROAD 10.3.2 APPLICATION OF MAXIMUM GRADIENT IN CHINA 10.3.2.1 Beijing–Shanghai Passenger Line 10.3.2.2 Beijing–Tianjin Intercity Passenger Dedicated Line 10.3.2.3 Shijiazhuang–Taiyuan Passenger Dedicated Line 10.3.2.4 Wuhan–Guangzhou Passenger Dedicated Line 10.3.2.5 Comparison and Selection 10.3.2.6 Shenyang–Harbin Passenger Line 10.3.2.7 Beijing–Zhengzhou Passenger Line 10.4 PRINCIPLE OF MAXIMUM GRADIENT 11 - The Minimum Length of Grade Section 11.1 THE MINIMUM LENGTH OF GRADE SECTION REQUIRED FOR THE LONGITUDINAL FORCE CONDITION OF THE COUPLER 11.2 THE MINIMUM LENGTH OF GRADE SECTION THAT MEETS THE REQUIREMENT OF THE STABLE OPERATION OF THE TRAIN 11.2.1 THE CALCULATION PRINCIPLE 11.2.1.1 Ensure that the Vertical Curve at the Ends of the Slope Section Does Not Overlap the Middle of the Slope Section 11.2.1.2 The Vertical Vibration Generated on the Vertical Curve of the Vehicle Will Not Affect Passenger Comfort 11.2.2 THE SIMULATION OF VEHICLE VIBRATION DECAY TIME 11.2.3 DOMESTIC AND INTERNATIONAL RESEARCH AND ENGINEERING PRACTICE 11.2.4 THE MINIMUM LENGTH OF GRADE SECTION TO ENSURE THAT THE VEHICLE VIBRATION DOES NOT OVERLAP 11.3 THE LENGTH OF GRADE SECTION OF THE PASSENGER TRAINS MEETS THE REQUIREMENT WHEN THE TRAIN CROSSES TWO KNICK POINTS AT DIFFER ... 11.4 THE EFFECT OF THE MINIMUM LENGTH OF GRADE SECTION ON THE ECONOMY OF THE PASSENGER-DEDICATED LINE 11.5 THE VALUE OF THE MINIMUM LENGTH OF GRADE SECTION 11.6 THE LIMITATION OF THE MAXIMUM LENGTH OF GRADE SECTION 11.6.1 FOREIGN RESEARCH AND ENGINEERING PRACTICE 11.6.2 THE SIMULATION ANALYSIS OF THE LENGTH OF GRADIENT SECTION 11.6.3 REQUIREMENTS OF THE MAXIMUM LENGTH OF GRADIENT SECTION OF THE MAXIMUM SLOPE 12 - Overview of Design Method and Standard Proposed Values of Main Technical Parameters for Spatial Line Shape of ... 12.1 THE MINIMUM CURVE RADIUS STANDARD AND ITS PARAMETER VALUE 12.2 THE MINIMUM TRANSITION CURVE LENGTH STANDARD AND ITS PARAMETER VALUE 12.3 THE MINIMUM RECOMMENDED VALUE OF THE LENGTH OF THE INTERMEDIATE STRAIGHT LINE AND THE CIRCULAR CURVE 12.4 THE STANDARD OF THE MINIMUM VERTICAL CURVE RADIUS 12.5 THE DESIGN PRINCIPLES FOR MAXIMUM DESIGN SLOPE 12.6 DESIGN PRINCIPLES OF MINIMUM LENGTH OF GRADE SECTION Bibliography Index A B C D E F G H I J K L M N O P R S T U V W Back Cover Dynamic Analysis of High-Speed Railway Alignment: Theory and Practice elaborates on the dynamic analysis theory and method on spatial alignment parameters of high-speed railways, revealing the interaction mechanism between vehicle-track dynamic performance and track parameters of high-speed railways. It ascertains the influence rules of track structure and track geometry on vehicle-track dynamic performance, establishes the relationship models between vehicle-track dynamic performance and curve dynamic characteristic parameters, and defines the calculation relationship between lateral acceleration of car body on curves and track parameters. This book can be used as a reference book for scientific researchers, engineering technicians and management engaged in railway engineering, and will be very helpful for railway technicians who want to learn more about route planning, design, and construction and maintenance technologies of high-speed railways. Presents the dynamic effects between the running speed of high-speed trains on curves and spatial curve technical parameters Provides dynamic analysis, theory and methods on curve parameters of high-speed railways and improves the calculation theory on spatial alignment of high-speed railways Covers minimum curve radius, transition curve length, minimum radius of vertical curve, steepest slope, minimum slope length and length of intermediate straight line