Railway Curves Transition Curves Transition Curves An easement
![Railway Curves Railway Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-1.jpg)
![Transition Curves Transition Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-2.jpg)
![Transition Curves An easement curve, introduced between straight & curved track to facilitate gradual Transition Curves An easement curve, introduced between straight & curved track to facilitate gradual](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-3.jpg)
![Key Design Parameters for Transition Curves Rate of Change of Actual Cant (RCa) mm/s, Key Design Parameters for Transition Curves Rate of Change of Actual Cant (RCa) mm/s,](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-4.jpg)
![Requirements from Transition Curves • Curvature shall vary uniformly with distance – Curvature = Requirements from Transition Curves • Curvature shall vary uniformly with distance – Curvature =](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-5.jpg)
![Transition Curves • The spiral (Clothoid), which changes the direction angle uniformly along length, Transition Curves • The spiral (Clothoid), which changes the direction angle uniformly along length,](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-6.jpg)
![Transition Curves • There is not much difference in the layout of a spiral Transition Curves • There is not much difference in the layout of a spiral](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-7.jpg)
![Desirable Versine and Cant Diagram Cubic Parabola – Curvature changes linearly v Ca Transition Desirable Versine and Cant Diagram Cubic Parabola – Curvature changes linearly v Ca Transition](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-8.jpg)
![Shift Transition Curves Inserting Transition Curves Shift Transition Curves Inserting Transition Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-9.jpg)
![Shift Due to Transition Curve Circular Curve With Transition Extended Circular Curve C D Shift Due to Transition Curve Circular Curve With Transition Extended Circular Curve C D](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-10.jpg)
![Length of Transition Curve Length of Transition Curve](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-11.jpg)
![](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-12.jpg)
![Length of Transition Curve • Comfort Criteria: Rate of Change of Cd (RCd) – Length of Transition Curve • Comfort Criteria: Rate of Change of Cd (RCd) –](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-13.jpg)
![Length of Transition Curve • Comfort Criteria: Rate of Change of Cd (RCd) – Length of Transition Curve • Comfort Criteria: Rate of Change of Cd (RCd) –](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-14.jpg)
![Length of Transition Curve • Comfort Criteria: Rate of Change of Ca (RCa) – Length of Transition Curve • Comfort Criteria: Rate of Change of Ca (RCa) –](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-15.jpg)
![Length of Transition Curve • Safety Criteria (Twist) – Cant gradient causes twist in Length of Transition Curve • Safety Criteria (Twist) – Cant gradient causes twist in](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-16.jpg)
![Length of Transition Curve • Length of transition will be maximum of L 1 Length of Transition Curve • Length of transition will be maximum of L 1](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-17.jpg)
![Length of Transition Curve • Length of transition will be maximum of L 1 Length of Transition Curve • Length of transition will be maximum of L 1](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-18.jpg)
![Length of Transition Curve • In exceptional circumstances, minimum length of transition will be Length of Transition Curve • In exceptional circumstances, minimum length of transition will be](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-19.jpg)
![Procedure to find Speed on Curve • Find equilibrium cant for the maximum speed Procedure to find Speed on Curve • Find equilibrium cant for the maximum speed](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-20.jpg)
![Procedure to find Speed on Curve • Cant to be Provided shall also be Procedure to find Speed on Curve • Cant to be Provided shall also be](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-21.jpg)
![Exercise Find Maximum Permissible Speed for – BG route having Speed Potential = 130 Exercise Find Maximum Permissible Speed for – BG route having Speed Potential = 130](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-22.jpg)
![Exercise Find Desirable and Minimum Transition Length for – BG route having Speed Potential Exercise Find Desirable and Minimum Transition Length for – BG route having Speed Potential](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-23.jpg)
![Exercise Calculate Shift for – BG route having Speed Potential = 130 Kmph Rajdhani Exercise Calculate Shift for – BG route having Speed Potential = 130 Kmph Rajdhani](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-24.jpg)
![Desirable Versine and Cant Diagram V Transition Ca Transition Desirable Versine and Cant Diagram V Transition Ca Transition](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-25.jpg)
![If there is no Transition Curve ? v Transition Ca Transition How to introduce If there is no Transition Curve ? v Transition Ca Transition How to introduce](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-26.jpg)
![~2 m ? V Virtual Transition ~2 m ? V Virtual Transition](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-27.jpg)
![Virtual Transition • If there is no space for transition, circular curve immediately follows Virtual Transition • If there is no space for transition, circular curve immediately follows](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-28.jpg)
![Reverse and Compound Curves Reverse and Compound Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-29.jpg)
![Reverse Curves Length of intermediate Transition will be Maximum of L 1 = 0. Reverse Curves Length of intermediate Transition will be Maximum of L 1 = 0.](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-30.jpg)
![Reverse Curves • For high speeds in Group A and B routes a straight Reverse Curves • For high speeds in Group A and B routes a straight](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-31.jpg)
![Compound Curves Compound Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-32.jpg)
![Compound and Reverse Curves • For Compound Curves: Length of Intermediate Transition shall be Compound and Reverse Curves • For Compound Curves: Length of Intermediate Transition shall be](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-33.jpg)
![Vertical curves Vertical curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-34.jpg)
![Types of Vertical Curves Types of Vertical Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-35.jpg)
![Vertical curves • Vertical Curves to be provided, if ; Algebraic Difference between the Vertical curves • Vertical Curves to be provided, if ; Algebraic Difference between the](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-36.jpg)
![Vertical curves • Important issues – Vertical acceleration – Drainage (Sag) – Ventilation (Summit) Vertical curves • Important issues – Vertical acceleration – Drainage (Sag) – Ventilation (Summit)](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-37.jpg)
![Vertical curves • Shall be as flat as possible to reduce Discomfort to passengers Vertical curves • Shall be as flat as possible to reduce Discomfort to passengers](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-38.jpg)
![Effects of curve: Curve Resistance Effects of curve: Curve Resistance](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-39.jpg)
![Compensation for Curvature on gradient • Known as Grade Compensation – Reduction in ruling Compensation for Curvature on gradient • Known as Grade Compensation – Reduction in ruling](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-40.jpg)
![Check Rails on Curves Check Rails on Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-41.jpg)
![Check Rails on Curves CLEARANCE Too Much Wear on Outer Rail in Sharp Curves; Check Rails on Curves CLEARANCE Too Much Wear on Outer Rail in Sharp Curves;](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-42.jpg)
![Thank You Thank You](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-43.jpg)
![IRPWM Provisions • Inspections – AEN to inspect one curve in each PWI jurisdiction IRPWM Provisions • Inspections – AEN to inspect one curve in each PWI jurisdiction](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-44.jpg)
![IRPWM Provisions (BG) • Lateral wear on Rails in Curves (301(b)(iv)) – Group A IRPWM Provisions (BG) • Lateral wear on Rails in Curves (301(b)(iv)) – Group A](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-45.jpg)
![IRPWM Provisions (BG) • Cut in rails in SWR track (424) – To make IRPWM Provisions (BG) • Cut in rails in SWR track (424) – To make](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-46.jpg)
![IRPWM Provisions (BG) After relaying • On curves, Versine variation over Theoretical versine on IRPWM Provisions (BG) After relaying • On curves, Versine variation over Theoretical versine on](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-47.jpg)
![IRPWM Provisions (BG) In-service • Gauge (224(2)(e)(v)) – On straight : (-) 6 mm IRPWM Provisions (BG) In-service • Gauge (224(2)(e)(v)) – On straight : (-) 6 mm](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-48.jpg)
![IRPWM Provisions (BG) In-service tolerances (speed >100 kmph, <140 kmph) • Twist (607(2)(iii)) – IRPWM Provisions (BG) In-service tolerances (speed >100 kmph, <140 kmph) • Twist (607(2)(iii)) –](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-49.jpg)
![IRPWM Provisions (BG) In-service tolerances (speed >100 kmph, <140 kmph) • Alignment defect (607(2)(i)) IRPWM Provisions (BG) In-service tolerances (speed >100 kmph, <140 kmph) • Alignment defect (607(2)(i))](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-50.jpg)
![IRPWM Provisions • Radius of curve (401(1)) R = 125*C 2/V • For measuring IRPWM Provisions • Radius of curve (401(1)) R = 125*C 2/V • For measuring](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-51.jpg)
![IRPWM Provisions • Safe speed on a Curve (405(1)(a)) V = 0. 27 √{R IRPWM Provisions • Safe speed on a Curve (405(1)(a)) V = 0. 27 √{R](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-52.jpg)
![IRPWM Provisions • Curve boards(409(1)) – Curve board shall be provided at tangent point IRPWM Provisions • Curve boards(409(1)) – Curve board shall be provided at tangent point](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-53.jpg)
![Curve Board Curve Board](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-54.jpg)
![IRPWM Provisions • Super-elevation marking on rails (409(3)) – Value of super-elevation shall be IRPWM Provisions • Super-elevation marking on rails (409(3)) – Value of super-elevation shall be](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-55.jpg)
![Lead Curve following Turnout • Minimum radius of lead curve (410(2)) : 350 m Lead Curve following Turnout • Minimum radius of lead curve (410(2)) : 350 m](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-56.jpg)
![Lead portion and Turn-in curves The variation in versine on two successive stations in Lead portion and Turn-in curves The variation in versine on two successive stations in](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-57.jpg)
![Thank You Thank You](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-58.jpg)
![Extra Clearances on curves Lean and Sway Extra Clearances on curves Lean and Sway](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-59.jpg)
![Clearances on curves : Lean L = H * Ca/G H = height of Clearances on curves : Lean L = H * Ca/G H = height of](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-60.jpg)
![Clearances on curves : Additional Allowance due to Lurch & Sway • Inside of Clearances on curves : Additional Allowance due to Lurch & Sway • Inside of](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-61.jpg)
![Extra Clearances on Curves: Platforms and structures Extra Clearances on Curves: Platforms and structures](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-62.jpg)
![Clearance On Curves : Effect of Chords Clearance On Curves : Effect of Chords](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-63.jpg)
![Over-Throw and End-Throw on Curves Vo=14. 7852/8*R Over Throw (Vo) 14. 785 m 21. Over-Throw and End-Throw on Curves Vo=14. 7852/8*R Over Throw (Vo) 14. 785 m 21.](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-64.jpg)
![Extra Clearances due to Curvatures • Platforms/ structures – Inside of curve • (VO Extra Clearances due to Curvatures • Platforms/ structures – Inside of curve • (VO](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-65.jpg)
![Extra Clearances on Curved Parallel Tracks Extra Clearances on Curved Parallel Tracks](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-66.jpg)
![Extra Clearances due to Curvatures • Between Adjacent Tracks VO + VE + 2 Extra Clearances due to Curvatures • Between Adjacent Tracks VO + VE + 2](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-67.jpg)
![Thank You Thank You](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-68.jpg)
![Turnouts taking off from curve Turnouts taking off from curve](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-69.jpg)
![Turnouts taking off from curve Straight Main Line Curved main Line Re Rs R Turnouts taking off from curve Straight Main Line Curved main Line Re Rs R](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-70.jpg)
![Turnouts on Curves Similar Flexure ML T/O Contrary Flexure ML 74 Turnouts on Curves Similar Flexure ML T/O Contrary Flexure ML 74](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-71.jpg)
![Resultant Lead Radius in Similar Flexure Turnouts Main line with Radius R 1 and Resultant Lead Radius in Similar Flexure Turnouts Main line with Radius R 1 and](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-72.jpg)
![Resultant Lead Radius in Contrary Flexure Turnouts Main line with Radius R 1 and Resultant Lead Radius in Contrary Flexure Turnouts Main line with Radius R 1 and](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-73.jpg)
![](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-74.jpg)
![Equivalent Curvature • The train moving on the turnout side experiences dual curvature • Equivalent Curvature • The train moving on the turnout side experiences dual curvature •](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-75.jpg)
![Turnouts in Similar Flexure Re=Rm*Rs/(Rm+Rs) Re: Equivalent Radius Rm: Main Line Radius Rs: Switch Turnouts in Similar Flexure Re=Rm*Rs/(Rm+Rs) Re: Equivalent Radius Rm: Main Line Radius Rs: Switch](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-76.jpg)
![Turnouts in Contrary Flexure Re=Rm*Rs/(Rm-Rs) Re: Equivalent Radius Rm: Main Line Radius Rs: Switch Turnouts in Contrary Flexure Re=Rm*Rs/(Rm-Rs) Re: Equivalent Radius Rm: Main Line Radius Rs: Switch](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-77.jpg)
![Speed on Curve having Turnouts • Trains move on main line as well as Speed on Curve having Turnouts • Trains move on main line as well as](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-78.jpg)
![Calculation of Cant • Similar flexure Turnout: – Calculate equilibrium super elevation for turnout Calculation of Cant • Similar flexure Turnout: – Calculate equilibrium super elevation for turnout](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-79.jpg)
![Calculation of Cant T/O • Contrary flexure– Calculate equilibrium super elevation for turnout side Calculation of Cant T/O • Contrary flexure– Calculate equilibrium super elevation for turnout side](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-80.jpg)
![Turnouts in Contrary Flexure • Curves of contrary flexure – Equilibrium super elevation for Turnouts in Contrary Flexure • Curves of contrary flexure – Equilibrium super elevation for](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-81.jpg)
![Thank You Thank You](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-82.jpg)
- Slides: 82
![Railway Curves Railway Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-1.jpg)
Railway Curves
![Transition Curves Transition Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-2.jpg)
Transition Curves
![Transition Curves An easement curve introduced between straight curved track to facilitate gradual Transition Curves An easement curve, introduced between straight & curved track to facilitate gradual](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-3.jpg)
Transition Curves An easement curve, introduced between straight & curved track to facilitate gradual change of Curvature & Super-elevation from Straight Track to Curved Track
![Key Design Parameters for Transition Curves Rate of Change of Actual Cant RCa mms Key Design Parameters for Transition Curves Rate of Change of Actual Cant (RCa) mm/s,](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-4.jpg)
Key Design Parameters for Transition Curves Rate of Change of Actual Cant (RCa) mm/s, Cant Deficiency (RCd) mm/s, Cant Gradient (i) mm/m;
![Requirements from Transition Curves Curvature shall vary uniformly with distance Curvature Requirements from Transition Curves • Curvature shall vary uniformly with distance – Curvature =](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-5.jpg)
Requirements from Transition Curves • Curvature shall vary uniformly with distance – Curvature = 1/R – Versine shall vary uniformly • Cant shall vary uniformly • Transition shall be tangential to the straight as well as circular curve – Radius infinity at junction with straight – Radius R at junction with circular curve
![Transition Curves The spiral Clothoid which changes the direction angle uniformly along length Transition Curves • The spiral (Clothoid), which changes the direction angle uniformly along length,](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-6.jpg)
Transition Curves • The spiral (Clothoid), which changes the direction angle uniformly along length, is the ideal transition –i. e. L ∝ 1/R • Cubic Parabola – rate of change of curvature uniform with the distance on X direction –i. e. X ∝ 1/R
![Transition Curves There is not much difference in the layout of a spiral Transition Curves • There is not much difference in the layout of a spiral](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-7.jpg)
Transition Curves • There is not much difference in the layout of a spiral and cubic parabola until the deflection from straight is approximately 4 M and deflection angle upto 12° • On Indian Railways for Transition Curves, it is cubical parabola with the equation: Y = KX 3 (Y= X 3/6 R*L)
![Desirable Versine and Cant Diagram Cubic Parabola Curvature changes linearly v Ca Transition Desirable Versine and Cant Diagram Cubic Parabola – Curvature changes linearly v Ca Transition](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-8.jpg)
Desirable Versine and Cant Diagram Cubic Parabola – Curvature changes linearly v Ca Transition Cant variation – Linear Transition Cubic Parabola – Ease in setting/laying/maintaining
![Shift Transition Curves Inserting Transition Curves Shift Transition Curves Inserting Transition Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-9.jpg)
Shift Transition Curves Inserting Transition Curves
![Shift Due to Transition Curve Circular Curve With Transition Extended Circular Curve C D Shift Due to Transition Curve Circular Curve With Transition Extended Circular Curve C D](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-10.jpg)
Shift Due to Transition Curve Circular Curve With Transition Extended Circular Curve C D Circular Curve Without Transition B E Transition Curve Tangent H S S/2 A L/2 F Shift = S = L 2/24 R L/2 G BG=L 2/6 R DE=L 2/8 R
![Length of Transition Curve Length of Transition Curve](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-11.jpg)
Length of Transition Curve
![](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-12.jpg)
![Length of Transition Curve Comfort Criteria Rate of Change of Cd RCd Length of Transition Curve • Comfort Criteria: Rate of Change of Cd (RCd) –](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-13.jpg)
Length of Transition Curve • Comfort Criteria: Rate of Change of Cd (RCd) – Rate of Change of ULA less than 0. 03 g / s taken as 0. 3 m/s 3 – Rate of Change of Cd over Transition where,
![Length of Transition Curve Comfort Criteria Rate of Change of Cd RCd Length of Transition Curve • Comfort Criteria: Rate of Change of Cd (RCd) –](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-14.jpg)
Length of Transition Curve • Comfort Criteria: Rate of Change of Cd (RCd) – Rate of Change of Cd , however, normally shall not exceed 35 mm/sec – Under Exceptional Circumstances it can be increased to 55 mm/sec
![Length of Transition Curve Comfort Criteria Rate of Change of Ca RCa Length of Transition Curve • Comfort Criteria: Rate of Change of Ca (RCa) –](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-15.jpg)
Length of Transition Curve • Comfort Criteria: Rate of Change of Ca (RCa) – For slower speeds, the actual cant causes similar comfort problems – Rate of change of Ca is just noticeable at 6575 mm/sec but normally shall not exceed 35 mm /sec – Under Exceptional Circumstances it can be increased to 55 mm /sec
![Length of Transition Curve Safety Criteria Twist Cant gradient causes twist in Length of Transition Curve • Safety Criteria (Twist) – Cant gradient causes twist in](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-16.jpg)
Length of Transition Curve • Safety Criteria (Twist) – Cant gradient causes twist in track – Critical - longest rigid wheel base – Cant gradient (i) • Limited to 1. 4 mm/m or 1 in 720 • In Exceptional Cases 2. 8 mm/M or 1 in 360 • Future Layouts with 1 in 1200
![Length of Transition Curve Length of transition will be maximum of L 1 Length of Transition Curve • Length of transition will be maximum of L 1](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-17.jpg)
Length of Transition Curve • Length of transition will be maximum of L 1 = C a * V m / R Ca or L 2 = C d * V m / R Cd or L 3 = Ca / i
![Length of Transition Curve Length of transition will be maximum of L 1 Length of Transition Curve • Length of transition will be maximum of L 1](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-18.jpg)
Length of Transition Curve • Length of transition will be maximum of L 1 = 0. 008 Ca* Vm (m, mm, kmph, RCa=35 mm/s) L 2 = 0. 008 Cd*Vm (m, mm, kmph, RCd=35 mm/s) L 3 = 0. 72 Ca (m, mm, i = 1 in 720) or or
![Length of Transition Curve In exceptional circumstances minimum length of transition will be Length of Transition Curve • In exceptional circumstances, minimum length of transition will be](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-19.jpg)
Length of Transition Curve • In exceptional circumstances, minimum length of transition will be maximum of 2/3 rd of L 1 or 2/3 rd of L 2 or ½ of L 3
![Procedure to find Speed on Curve Find equilibrium cant for the maximum speed Procedure to find Speed on Curve • Find equilibrium cant for the maximum speed](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-20.jpg)
Procedure to find Speed on Curve • Find equilibrium cant for the maximum speed – Find minimum cant required by deducting the cant deficiency from equilibrium cant • Find cant required for booked speed of goods trains. – Add cant excess and find out the maximum cant permissible • The cant to be provided shall be between the two values computed above
![Procedure to find Speed on Curve Cant to be Provided shall also be Procedure to find Speed on Curve • Cant to be Provided shall also be](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-21.jpg)
Procedure to find Speed on Curve • Cant to be Provided shall also be less than the Maximum Permissible as per IRPWM • Corresponding to actual cant provided, find maximum speed • Find out the desirable/ minimum transition length • If shift is not possible, restrict length of transition and work out cant and speed permissible corresponding to the reduced length available
![Exercise Find Maximum Permissible Speed for BG route having Speed Potential 130 Exercise Find Maximum Permissible Speed for – BG route having Speed Potential = 130](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-22.jpg)
Exercise Find Maximum Permissible Speed for – BG route having Speed Potential = 130 Kmph Rajdhani Route (Group “A”), and Degree of Curve = 2° Speed of Goods Train = 65 Kmph Cd = 100 mm and Cex = 75 mm SE = 140 mm Max. Speed = 123. 73 Kmph ≈ 120 Kmph
![Exercise Find Desirable and Minimum Transition Length for BG route having Speed Potential Exercise Find Desirable and Minimum Transition Length for – BG route having Speed Potential](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-23.jpg)
Exercise Find Desirable and Minimum Transition Length for – BG route having Speed Potential = 130 Kmph Rajdhani Route (Group “A”), and Degree of Curve = 2° Desirable Length L 1 = 134. 4 m Speed of Goods Train = 65 Kmph L = 96. 0 m Cd = 100 mm and Cex = 75 mm SE = 140 mm Max. Speed = 120 Kmph 2 L 3 = 100. 8 m Minimum Length L 1 = 89. 6 m L 2 = 64. 0 m L 3 = 50. 4 m
![Exercise Calculate Shift for BG route having Speed Potential 130 Kmph Rajdhani Exercise Calculate Shift for – BG route having Speed Potential = 130 Kmph Rajdhani](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-24.jpg)
Exercise Calculate Shift for – BG route having Speed Potential = 130 Kmph Rajdhani Route (Group “A”), and Degree of Curve = 2° Speed of Goods Train = 65 Kmph Cd = 100 mm; and Cex = 75 mm SE = 140 mm Max. Speed = 120 Kmph Desirable Length of Transition L 1 = 140 m Minimum Length of Transition L 1 = 90 m 0. 933 m and 0. 385 m
![Desirable Versine and Cant Diagram V Transition Ca Transition Desirable Versine and Cant Diagram V Transition Ca Transition](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-25.jpg)
Desirable Versine and Cant Diagram V Transition Ca Transition
![If there is no Transition Curve v Transition Ca Transition How to introduce If there is no Transition Curve ? v Transition Ca Transition How to introduce](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-26.jpg)
If there is no Transition Curve ? v Transition Ca Transition How to introduce V and Ca ?
![2 m V Virtual Transition ~2 m ? V Virtual Transition](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-27.jpg)
~2 m ? V Virtual Transition
![Virtual Transition If there is no space for transition circular curve immediately follows Virtual Transition • If there is no space for transition, circular curve immediately follows](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-28.jpg)
Virtual Transition • If there is no space for transition, circular curve immediately follows the straight, the distance between bogie centers becomes the transition virtually • For BG • For MG - 14. 6 M - 13. 7 M • Cant is provided in virtual transition length • half in straight and half in circular curve • @1 in 360 (max. cant gradient) max. cant = 14. 6 * 2. 8 = 40 mm
![Reverse and Compound Curves Reverse and Compound Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-29.jpg)
Reverse and Compound Curves
![Reverse Curves Length of intermediate Transition will be Maximum of L 1 0 Reverse Curves Length of intermediate Transition will be Maximum of L 1 = 0.](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-30.jpg)
Reverse Curves Length of intermediate Transition will be Maximum of L 1 = 0. 008 * (Ca 1+Ca 2) * Vm L 2 = 0. 008 * (Cd 1+Cd 2) * Vm L 3 = 0. 72 * (Ca 1+Ca 2) Constant roll velocity during intermediate transition
![Reverse Curves For high speeds in Group A and B routes a straight Reverse Curves • For high speeds in Group A and B routes a straight](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-31.jpg)
Reverse Curves • For high speeds in Group A and B routes a straight of 50 m length shall be kept – One cycle of oscillation for passenger coach (1. 5 sec) • Otherwise, increase the transition length to eliminate the straight • If neither of the above two are possible than speed restriction of 130 KMPH on BG
![Compound Curves Compound Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-32.jpg)
Compound Curves
![Compound and Reverse Curves For Compound Curves Length of Intermediate Transition shall be Compound and Reverse Curves • For Compound Curves: Length of Intermediate Transition shall be](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-33.jpg)
Compound and Reverse Curves • For Compound Curves: Length of Intermediate Transition shall be Maximum of • L 1 = 0. 008 * (Ca 1 - Ca 2) * Vm • L 2 = 0. 008 * (Cd 1 - Cd 2) * Vm • L 3 = 0. 72 * (Ca 1 - Ca 2) If length is coming less than virtual transition then common transition is deleted and the cant is run out on the length of virtual transition
![Vertical curves Vertical curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-34.jpg)
Vertical curves
![Types of Vertical Curves Types of Vertical Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-35.jpg)
Types of Vertical Curves
![Vertical curves Vertical Curves to be provided if Algebraic Difference between the Vertical curves • Vertical Curves to be provided, if ; Algebraic Difference between the](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-36.jpg)
Vertical curves • Vertical Curves to be provided, if ; Algebraic Difference between the Grades ≥ 0. 4% (4 mm/m) • Not allowed in – Points and Crossing – Un-ballasted deck girder bridges – Transition portion of horizontal curves
![Vertical curves Important issues Vertical acceleration Drainage Sag Ventilation Summit Vertical curves • Important issues – Vertical acceleration – Drainage (Sag) – Ventilation (Summit)](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-37.jpg)
Vertical curves • Important issues – Vertical acceleration – Drainage (Sag) – Ventilation (Summit) in Tunnels ?
![Vertical curves Shall be as flat as possible to reduce Discomfort to passengers Vertical curves • Shall be as flat as possible to reduce Discomfort to passengers](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-38.jpg)
Vertical curves • Shall be as flat as possible to reduce Discomfort to passengers • Vertical Acceleration 0. 3 – 0. 45 m/s 2 2 • Radius Rv ≥ Vm / am Route A B C, D, E & MG Minimum Radius (m) 4, 000 3, 000 2, 500
![Effects of curve Curve Resistance Effects of curve: Curve Resistance](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-39.jpg)
Effects of curve: Curve Resistance
![Compensation for Curvature on gradient Known as Grade Compensation Reduction in ruling Compensation for Curvature on gradient • Known as Grade Compensation – Reduction in ruling](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-40.jpg)
Compensation for Curvature on gradient • Known as Grade Compensation – Reduction in ruling gradient • to allow for the effect of curve or – Increase in actual gradient • to get “Compensated Gradient” to get combined effect of curve + gradient • 70/R % or 0. 04% Per Degree of Curve
![Check Rails on Curves Check Rails on Curves](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-41.jpg)
Check Rails on Curves
![Check Rails on Curves CLEARANCE Too Much Wear on Outer Rail in Sharp Curves Check Rails on Curves CLEARANCE Too Much Wear on Outer Rail in Sharp Curves;](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-42.jpg)
Check Rails on Curves CLEARANCE Too Much Wear on Outer Rail in Sharp Curves; and CHECK RAIL • Para 426 of IRPWM • Clause 4, Chapter 1, BG : SOD Risk of derailment • On Curves of 8 Degrees & above • Minimum Clearance = 44 mm • Clearance = 44 + (G*-1676)/2 • G*: Actual wide gauge on the Curve • Lubrication of outer Rail for all Curves with Radius less than 600 m
![Thank You Thank You](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-43.jpg)
Thank You
![IRPWM Provisions Inspections AEN to inspect one curve in each PWI jurisdiction IRPWM Provisions • Inspections – AEN to inspect one curve in each PWI jurisdiction](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-44.jpg)
IRPWM Provisions • Inspections – AEN to inspect one curve in each PWI jurisdiction every quarter (107(4)) – PWI in-charge and his assistant shall inspect curves once in six months alternately except at group A and B routes where inspection is to be done once in four months (124(4), 139(4)) – For Concrete Sleeper track, once in six months by rotation (124 A, 139 A)
![IRPWM Provisions BG Lateral wear on Rails in Curves 301biv Group A IRPWM Provisions (BG) • Lateral wear on Rails in Curves (301(b)(iv)) – Group A](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-45.jpg)
IRPWM Provisions (BG) • Lateral wear on Rails in Curves (301(b)(iv)) – Group A and B : 8 mm – Group C and D : 10 mm • Minimising wear on outer Rail (427(2)) – Rail flange lubricators shall be provided in curves less than 600 m radius – First one shall be ahead of the curve
![IRPWM Provisions BG Cut in rails in SWR track 424 To make IRPWM Provisions (BG) • Cut in rails in SWR track (424) – To make](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-46.jpg)
IRPWM Provisions (BG) • Cut in rails in SWR track (424) – To make the joints square when the gain of inner rail becomes equal to pitch of the first bolt hole – Gain of inner rail given by: d= LG/R, L is length of curve. • On curves less than 400 m radius, the joints shall be laid staggered
![IRPWM Provisions BG After relaying On curves Versine variation over Theoretical versine on IRPWM Provisions (BG) After relaying • On curves, Versine variation over Theoretical versine on](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-47.jpg)
IRPWM Provisions (BG) After relaying • On curves, Versine variation over Theoretical versine on 20 m chord (316) – 600 m radius and more – Less than 600 m radius : 5 mm : 10 mm • Gauge in Track on curves (403(1)) – More than 350 m radius : -5 mm to + 3 mm – Less than 350 m radius : upto +10 mm
![IRPWM Provisions BG Inservice Gauge 2242ev On straight 6 mm IRPWM Provisions (BG) In-service • Gauge (224(2)(e)(v)) – On straight : (-) 6 mm](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-48.jpg)
IRPWM Provisions (BG) In-service • Gauge (224(2)(e)(v)) – On straight : (-) 6 mm to (+) 6 mm – On Curves with radius 440 m or more: (-) 6 mm to (+) 15 mm – On curves radius less than 440 m: upto (+) 20 mm
![IRPWM Provisions BG Inservice tolerances speed 100 kmph 140 kmph Twist 6072iii IRPWM Provisions (BG) In-service tolerances (speed >100 kmph, <140 kmph) • Twist (607(2)(iii)) –](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-49.jpg)
IRPWM Provisions (BG) In-service tolerances (speed >100 kmph, <140 kmph) • Twist (607(2)(iii)) – On straight/curves • Upto 2 mm/M • At Isolated Locations : upto 3. 5 mm/M – On transitions • Upto 1 mm/M • At Isolated Locations : upto 2. 1 mm/M
![IRPWM Provisions BG Inservice tolerances speed 100 kmph 140 kmph Alignment defect 6072i IRPWM Provisions (BG) In-service tolerances (speed >100 kmph, <140 kmph) • Alignment defect (607(2)(i))](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-50.jpg)
IRPWM Provisions (BG) In-service tolerances (speed >100 kmph, <140 kmph) • Alignment defect (607(2)(i)) on 7. 5 m chord – On straight • Upto 5 mm • At Isolated Locations : upto 10 mm – On curves • Upto ± 5 mm over average versine • At Isolated locations upto ± 7 mm over average versine • Chord to chord ≤ 10 mm
![IRPWM Provisions Radius of curve 4011 R 125C 2V For measuring IRPWM Provisions • Radius of curve (401(1)) R = 125*C 2/V • For measuring](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-51.jpg)
IRPWM Provisions • Radius of curve (401(1)) R = 125*C 2/V • For measuring versine (401(3)) – Normal: • 20 m chord overlapping with stations at 10 m – P & Cs: (for lead and turn-in curve) • 6 m chord overlapping with stations at 1. 5 m (This shall be 3 m as per para 237 (4) (b) and (c) of IRPWM)
![IRPWM Provisions Safe speed on a Curve 4051a V 0 27 R IRPWM Provisions • Safe speed on a Curve (405(1)(a)) V = 0. 27 √{R](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-52.jpg)
IRPWM Provisions • Safe speed on a Curve (405(1)(a)) V = 0. 27 √{R (Ca + Cd)} • Non transitioned Curve (405(2)(a)) Length of virtual transition : 14. 6 m • Inner rail is taken as reference; and outer rail is raised by amount of superelevation (402)
![IRPWM Provisions Curve boards4091 Curve board shall be provided at tangent point IRPWM Provisions • Curve boards(409(1)) – Curve board shall be provided at tangent point](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-53.jpg)
IRPWM Provisions • Curve boards(409(1)) – Curve board shall be provided at tangent point on outside of the curve • Curve posts (409(2)) – Rail posts indicating beginning and end of transition, painted red and white respectively shall be provided (at beginning/end of virtual transition of nontransitioned curves).
![Curve Board Curve Board](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-54.jpg)
Curve Board
![IRPWM Provisions Superelevation marking on rails 4093 Value of superelevation shall be IRPWM Provisions • Super-elevation marking on rails (409(3)) – Value of super-elevation shall be](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-55.jpg)
IRPWM Provisions • Super-elevation marking on rails (409(3)) – Value of super-elevation shall be marked on the inside face of the web of inner rail at every versine stations in transition portion – Value of cant as above shall be marked at the beginning and end of the circular curve – For longer curves, the value of super-elevation shall be repeated as above at intervals not exceeding 250 m
![Lead Curve following Turnout Minimum radius of lead curve 4102 350 m Lead Curve following Turnout • Minimum radius of lead curve (410(2)) : 350 m](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-56.jpg)
Lead Curve following Turnout • Minimum radius of lead curve (410(2)) : 350 m • Minimum radius of turn in curves : 220 m in exceptional circumstances (with PSC/ST sleepers and full ML ballast profile) • There shall be no change in super-elevation 20 m on either side of the toe of switch and nose of crossing (412) • Turnout followed by reverse curve, change in cant behind crossing is permitted. Cant limited to 65 mm, run out at 2. 8 mm/m (414(2))
![Lead portion and Turnin curves The variation in versine on two successive stations in Lead portion and Turn-in curves The variation in versine on two successive stations in](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-57.jpg)
Lead portion and Turn-in curves The variation in versine on two successive stations in lead curve and turn in curve portions should not be more than 4 mm; and versine at each station should also not be beyond ± 3 mm. from its designed value (IRPWM Para 237(4)(d))
![Thank You Thank You](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-58.jpg)
Thank You
![Extra Clearances on curves Lean and Sway Extra Clearances on curves Lean and Sway](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-59.jpg)
Extra Clearances on curves Lean and Sway
![Clearances on curves Lean L H CaG H height of Clearances on curves : Lean L = H * Ca/G H = height of](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-60.jpg)
Clearances on curves : Lean L = H * Ca/G H = height of the structure or maximum height of vehicle whichever is less
![Clearances on curves Additional Allowance due to Lurch Sway Inside of Clearances on curves : Additional Allowance due to Lurch & Sway • Inside of](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-61.jpg)
Clearances on curves : Additional Allowance due to Lurch & Sway • Inside of a Curve – ¼ of lean due to super-elevation • Outside of a Curve – Not to be considered if lean is there • We do not take advantage of the extra clearance given by lean away from outer side structures
![Extra Clearances on Curves Platforms and structures Extra Clearances on Curves: Platforms and structures](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-62.jpg)
Extra Clearances on Curves: Platforms and structures
![Clearance On Curves Effect of Chords Clearance On Curves : Effect of Chords](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-63.jpg)
Clearance On Curves : Effect of Chords
![OverThrow and EndThrow on Curves Vo14 78528R Over Throw Vo 14 785 m 21 Over-Throw and End-Throw on Curves Vo=14. 7852/8*R Over Throw (Vo) 14. 785 m 21.](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-64.jpg)
Over-Throw and End-Throw on Curves Vo=14. 7852/8*R Over Throw (Vo) 14. 785 m 21. 340 m End Throw (VE) VE=(21. 342 -14. 7852)/8*R
![Extra Clearances due to Curvatures Platforms structures Inside of curve VO Extra Clearances due to Curvatures • Platforms/ structures – Inside of curve • (VO](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-65.jpg)
Extra Clearances due to Curvatures • Platforms/ structures – Inside of curve • (VO + L + S - 51) mm – Outside of curve • (VE – 25) mm
![Extra Clearances on Curved Parallel Tracks Extra Clearances on Curved Parallel Tracks](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-66.jpg)
Extra Clearances on Curved Parallel Tracks
![Extra Clearances due to Curvatures Between Adjacent Tracks VO VE 2 Extra Clearances due to Curvatures • Between Adjacent Tracks VO + VE + 2](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-67.jpg)
Extra Clearances due to Curvatures • Between Adjacent Tracks VO + VE + 2 * (L/4) • In new works, if c/c track is 5300 mm, extra clearance is to be provided for curves beyond 5° only.
![Thank You Thank You](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-68.jpg)
Thank You
![Turnouts taking off from curve Turnouts taking off from curve](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-69.jpg)
Turnouts taking off from curve
![Turnouts taking off from curve Straight Main Line Curved main Line Re Rs R Turnouts taking off from curve Straight Main Line Curved main Line Re Rs R](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-70.jpg)
Turnouts taking off from curve Straight Main Line Curved main Line Re Rs R Rm
![Turnouts on Curves Similar Flexure ML TO Contrary Flexure ML 74 Turnouts on Curves Similar Flexure ML T/O Contrary Flexure ML 74](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-71.jpg)
Turnouts on Curves Similar Flexure ML T/O Contrary Flexure ML 74
![Resultant Lead Radius in Similar Flexure Turnouts Main line with Radius R 1 and Resultant Lead Radius in Similar Flexure Turnouts Main line with Radius R 1 and](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-72.jpg)
Resultant Lead Radius in Similar Flexure Turnouts Main line with Radius R 1 and Degree D 1 Turnout Laid on Straight Lead curve with Radius R & Degree D Lead curve with resultant Radius R 2 & resultant Degree D 2 For similar flexure, D 2 = D 1 + D 1750/R 2 = 1750/R 1 + 1750/R 1/R 2= 1/R 1 + 1/R 75
![Resultant Lead Radius in Contrary Flexure Turnouts Main line with Radius R 1 and Resultant Lead Radius in Contrary Flexure Turnouts Main line with Radius R 1 and](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-73.jpg)
Resultant Lead Radius in Contrary Flexure Turnouts Main line with Radius R 1 and Degree D 1 Turnout Laid on Straight Lead curve with radius R & degree D For contrary flexure, D 2 = D 1 - D, 1750/R 2 = 1750/R 1 - 1750/R, 1/R 2= 1/R 1 - 1/R Lead curve with resultant Radius R 2 & resultant Degree D 2 76
![](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-74.jpg)
![Equivalent Curvature The train moving on the turnout side experiences dual curvature Equivalent Curvature • The train moving on the turnout side experiences dual curvature •](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-75.jpg)
Equivalent Curvature • The train moving on the turnout side experiences dual curvature • Due to the main line curve • Due to the turnout itself • The curvatures get added up • Curvature=1/Radius
![Turnouts in Similar Flexure ReRmRsRmRs Re Equivalent Radius Rm Main Line Radius Rs Switch Turnouts in Similar Flexure Re=Rm*Rs/(Rm+Rs) Re: Equivalent Radius Rm: Main Line Radius Rs: Switch](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-76.jpg)
Turnouts in Similar Flexure Re=Rm*Rs/(Rm+Rs) Re: Equivalent Radius Rm: Main Line Radius Rs: Switch Radius
![Turnouts in Contrary Flexure ReRmRsRmRs Re Equivalent Radius Rm Main Line Radius Rs Switch Turnouts in Contrary Flexure Re=Rm*Rs/(Rm-Rs) Re: Equivalent Radius Rm: Main Line Radius Rs: Switch](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-77.jpg)
Turnouts in Contrary Flexure Re=Rm*Rs/(Rm-Rs) Re: Equivalent Radius Rm: Main Line Radius Rs: Switch Radius
![Speed on Curve having Turnouts Trains move on main line as well as Speed on Curve having Turnouts • Trains move on main line as well as](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-78.jpg)
Speed on Curve having Turnouts • Trains move on main line as well as the turnout side • Allowable cant to be found after checking for both the tracks • Similar flexure: turnout side train moves with slower speed and more cant is there on main line so check for cant excess • Contrary flexure: Turnout side train with Negative cant. Check for cant deficiency
![Calculation of Cant Similar flexure Turnout Calculate equilibrium super elevation for turnout Calculation of Cant • Similar flexure Turnout: – Calculate equilibrium super elevation for turnout](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-79.jpg)
Calculation of Cant • Similar flexure Turnout: – Calculate equilibrium super elevation for turnout side as per maximum speed permitted on turnout side (i. e. Ceqto) Ceqto = GV 2/127 Rto (Rto is the resultant radius of Lead curve) – Add 75 mm of cant excess, this is the super elevation which can be provided on turnout side (i. e. Ca). Ca = Ceqto + 75 mm – Speed for main line can be calculated by taking Ca as calculated above and taking Cd as 75 mm. Ca + Cd = GV 2/127 Rm ML T/O
![Calculation of Cant TO Contrary flexure Calculate equilibrium super elevation for turnout side Calculation of Cant T/O • Contrary flexure– Calculate equilibrium super elevation for turnout side](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-80.jpg)
Calculation of Cant T/O • Contrary flexure– Calculate equilibrium super elevation for turnout side as per maximum speed permitted on turnout side (i. e. Ceqto) Ceqto = GV 2/127 Rto (Rto is the resultant radius of Lead curve) – Deduct it from 75 mm i. e. cant deficiency, this is the super elevation which can be provided on main line (i. e. Ca) Ca =75 mm - Ceqto – Speed for main line can be calculated by taking Ca as calculated above and taking Cd as 75 mm. Ca + Cd = GV 2/127 Rm ML
![Turnouts in Contrary Flexure Curves of contrary flexure Equilibrium super elevation for Turnouts in Contrary Flexure • Curves of contrary flexure – Equilibrium super elevation for](https://slidetodoc.com/presentation_image_h2/c1a8ddc073bce1675e4bd1ae2348660b/image-81.jpg)
Turnouts in Contrary Flexure • Curves of contrary flexure – Equilibrium super elevation for turnout side C = G * V 2 / (127 R) $ V: Speed in KPMH for Turnout, R: Metres, C: mm, G: mm – Super-elevation For Main Line (Negative Super-elevation For Turnout) is 75 - C ($ The old formula in SOD has been revised in CS No. 3)
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