Curves & Turnouts Quiz: Versine of Curve Formula

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Questions and Answers

What is the purpose of comparing the proposed and existing versines?

To find the differences in the existing and proposed versines at each station (correct)

To calculate the cumulative versine difference

To determine the final versine at the last station

To identify the correct alignment of the curve

What is the significance of the first summation at any station?

It represents half the slew required at each station

It gives the cumulative versine difference at each station (correct)

It is the final value at the last station

It shows the difference between the proposed and existing versines at that station

What is the process to obtain the cumulative versine difference at Station No. 1?

Multiply the versine difference of Station No. 1 with the cumulative versine difference of Station '0'

Divide the versine difference of Station No. 1 by the cumulative versine difference of Station '0'

Subtract the versine difference of Station No. 1 from the cumulative versine difference of Station '0'

Add the versine difference of Station No. 1 to the cumulative versine difference of Station '0' (correct)

What is the theoretical representation of the second summation at any station?

Half the slew required at each station to obtain the proposed versine Signup and view all the answers

What is the initial value of the second summation at Station '0'?

Zero Signup and view all the answers

What is the purpose of calculating the second summation at each station?

To calculate half the slew required at each station to obtain the proposed versine Signup and view all the answers

What is the significance of the figure against the last station in Column 5?

It is zero, since the sum total of the existing and proposed versines is the same Signup and view all the answers

How is the cumulative versine difference calculated at each station?

By adding the versine difference of the current station to the cumulative versine difference of the previous station Signup and view all the answers

What is shown against Station No. 1 in Column 6?

The first summation for the station Signup and view all the answers

Why do correcting couples need to be applied?

To make the slew at the last station zero Signup and view all the answers

What happens when the final half-throw is negative?

Add to the versines having lower station numbers Signup and view all the answers

What is the purpose of calculating the length of transition?

To realign and/or transition a complete curve Signup and view all the answers

What is the formula to determine the radius of a curve?

R = 125 × C² / V Signup and view all the answers

What is the consequence of not applying correcting couples?

The track beyond the last station will be affected by the slew at the last station Signup and view all the answers

What is the length of the chord used to measure versines of a curve?

20 metres Signup and view all the answers

What is the reference level for a curve?

Inner rail Signup and view all the answers

What is calculated in para 405?

The length of transition Signup and view all the answers

What happens when the final half-throw is positive?

Subtract from the versines having higher station numbers Signup and view all the answers

What is the degree of a curve with a radius of 1750 metres?

1° Signup and view all the answers

How are stations selected for applying correcting couples?

In pairs such that the sum of the product of the differences of the station numbers equals the numerical amount of the half-throw Signup and view all the answers

Why is the chord length used in measuring versines of a curve?

To determine the radius of the curve Signup and view all the answers

What is used to measure the versine of a curve?

A fishing cord or nylon wire Signup and view all the answers

What is the interval at which measuring stations are located for measuring versines of a curve?

10 metres Signup and view all the answers

What is the purpose of checking the radii of turnout and turn-in curves?

To verify the radius of the curve Signup and view all the answers

What is the rate of change of cant and cant deficiency used in formulas (a) and (b)?

35 mm per second Signup and view all the answers

What is the maximum cant gradient used in formula (c)?

1 in 720 Signup and view all the answers

How should the length of transition curve be rounded off?

To the next higher value in multiple of 10 m Signup and view all the answers

What is the minimum length of transition curve allowed in exceptional cases?

2/3 of the desirable length Signup and view all the answers

What is the maximum cant gradient allowed in exceptional cases?

2.8 mm per metre Signup and view all the answers

What is the purpose of reducing the length of transition curve in exceptional cases?

To increase the speed on the transition curve Signup and view all the answers

What is the recommended approach when the length of transition curve is restricted?

Select a lower cant and/or cant deficiency Signup and view all the answers

What is the goal of selecting a lower cant and/or cant deficiency in restricted cases?

To permit the highest speed on the curve as a whole Signup and view all the answers

What is the requirement for altering or inserting points and crossings in existing running lines?

Sanction of the Commissioner of Railway Safety Signup and view all the answers

Under what condition is the sanction of the Commissioner of Railway Safety not required for shifting of points?

When the nature of signalling is not affected Signup and view all the answers

What is the tolerance in gauge at various portions of turnout during new laying or renewal?

As given in Para 520 (3) (a) and Para 525 (1) respectively Signup and view all the answers

What is the recommended gauge in the crossing portion of a turnout?

0 mm to 4 mm with respect to the gauge prescribed in standard drawing Signup and view all the answers

What should be done if the gauge of the track on either side of the points and crossings is maintained wider or tighter than the gauge on the points and crossings?

Bring the gauge of the track to the same gauge as in the points and crossings Signup and view all the answers

What should be done before interlocking work is taken in hand?

Bring the rails to correct level and alignment Signup and view all the answers

Why should the track at turnout be laid to correct gauge?

To avoid future adjustments of gear Signup and view all the answers

What should be done to the cess before running rods and wires?

Clear the cess and bring it to the correct level and section Signup and view all the answers

Study Notes

Curves and Turnouts

Determination of Radius

The radius of a curve is determined by measuring the versine on a chord of known length.
The formula to determine the radius is: R = (125 × C^2) / V, where R is the radius in metres, C is the chord length in metres, and V is the versine in millimetres.

Curve Designation

Curves can be designated by their radius in metres or by their degree.
The degree of a curve is the angle subtended at the centre by a chord of 30.5 metres.
For example, a 1° curve has a radius of 1750 metres.

Measuring Versines

For measuring versines of a curve, 20 metres overlapping chords should normally be used with stations at 10 metres intervals.
For checking the radii of turnout and turn-in curves, overlapping chords of 6 metres should be used, and the versine measuring stations should be located at every 3 metres.

Versine Measurement

The versine is obtained by stretching a fishing/nylon cord or wire stretched between the end of the chord length decided upon, and the measuring distance between the cord/wire and gauge face of the rail at the middle point of the chord.

Reference Rail for Level

The level of the inner rail of any curve is taken as the reference level.

Transition Curves

The length of transition curves is calculated based on the rate of change of cant and cant deficiency.
The formulae for calculating the length of transition curves are based on a rate of change of cant and cant deficiency of 35 mm per second, or a maximum cant gradient of 1 in 720 or 1.4 mm per metre.

Turnouts

Gauge and Super-elevation in Turnouts

It is good practice to maintain a reasonable uniform gauge over turnouts.
Tolerance in gauge at various portions of turnout during new laying/renewal and maintenance shall be as specified.
The gauge in the crossing portion shall be 0 mm to 4 mm with respect to the gauge prescribed in standard drawings.

Interlocking of Points

Before interlocking work is taken in hand, the JE/SSE/P.Way should bring the rails to correct level and alignment, fully ballast and pack the points to be interlocked, mark the locations where the rods and wires have to cross the lines, and ensure that the track at turnout is laid to correct gauge.

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Description

This quiz covers the concepts of curves and turnouts in civil engineering, including the determination of radius measurement and formulas. Test your knowledge of curves and turnouts in civil engineering.

Civil Engineering Chapter 4: Curves & Turnouts

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