Sentidos y acepciones

The Permanent Way is designed using standard geometric shapes. Circular curves and straight lines form the basis of the track with transitions forming a gradual joining of the two.

The following terms and definitions are essential knowledge to help understand the basics of track geometry.

C8-1 Simple geometry

Figure 211 – Geometry terms

C8-1.1 Circle

Is a shape, formed by a continuous line that is always the same distance from the centre point.

C8-1.2 Tangent

Is a straight line that touches a circle at one point (in rail terms, tangent track is straight track).

Radius Mid Ordinate

Chord

Arc

Versine

Tangent Diameter

Tangent point

C8-1.3 Circumference

Is the continuous line that forms a circle.

C8-1.4 Arc

Is any part of a circumference.

C8-1.5 Diameter

Is a straight line drawn from one point to another point on the circumference (through the centre).

C8-1.6 Chord

Is a straight line drawn from one point to another point on the circumference (not through the centre).

C8-1.7 Radius

Any straight line drawn from the centre of a circle to a point on its circumference.

The plural of radius is radii. The radius of a circle is a constant length.

C8-1.8 Middle Ordinate

The distance measured at right angles from the centre of a chord to the circumference.

C8-1.9 Versine

Distance measured at right angles from any given point on the chord to the circumference.

C8-1.10 Tangent Point (TP)

Is the point where a straight line touches a circle. In railway terms, the tangent point is the point where the straight meets the curve.

C8-1.11 Transition Point (TRS)

Is the point at which the transition meets the circular curve.

C8-1.12 Compound Tangent Point (CTP)

Is the point where two curves of different radii meet in a non-transitioned compound curve.

C8-1.13 Compound Transition (CTRS)

Are used to connect transitioned compound curves and reverse curves. The CTRS is the point where the transition begins to join one radius curve to another.

C8-2 Curves

Curves are provided in a railway route to change direction. This allows the line to:

• follow the natural contour of the country, reducing construction costs by avoiding heavy earthworks, etc., and

• be lengthened to obtain grades at locations where a grade on a straight line between two points would be excessively steep for traffic.

In general practice, curves are always located with the greatest possible radius consistent with economical layout.

In heavy and mountainous country, relatively sharp curves occur and are responsible for reduction of the maximum permissible speed for the line.

Curved tracks introduce problems not associated with straight tracks caused by the action and effects of vehicles entering and travelling around curves.

When a vehicle moves in a straight line there is no change of direction; but when it enters a curve it changes direction. How quickly it changes direction depends on speed and curve radius. The faster the change the greater the forces exerted. Large accelerations and forces are undesirable for passenger comfort and, ultimately, safe operation of trains.

Once a vehicle has fully entered a circular curve the rate of change of direction becomes constant, but as it moves out of the curve back into a straight, or into another curve a similar change occurs, which produces the same conditions of acceleration and force.

In order to remove these effects, a transition curve is used (See Section C8-2.4). This curve has the effect of gradually increasing the amount of displacement in a given length.

The displacement takes place at a slower rate and, consequently, the forces exerted on the vehicle are more uniformly and evenly applied, and reach their maximum as the vehicle reaches the commencement of the circular curve.

When a vehicle travels on a straight track, its weight is uniformly distributed through the wheels to both rails, but when it enters a curve this distribution is altered and the load on the outer rail is increased. The amount of increase depends on the speed of the vehicle and the radius of the curve. It is possible with excessive speed to reach a condition where the whole of the weight is carried on the outer rail, and in such an extreme case, overturning may occur.

To counteract the increased loading on the outer rail, the outer rail is raised above the level of the inner rail. This is known as “superelevation” (or cant) (See Section C8-2.5) and its effect is to permit higher speeds on curves, due to the increased stability against overturning, and to improve the riding of vehicles entering and running on curves.

As superelevation is only necessary on curved tracks, it is difficult to suitably arrange its application at the tangent points of circular curves where the change of direction and increased loading of the outer rail both occur at the one time and give rise to rough riding and difficulty in maintaining correct alignment.

This condition is improved by using transition curves.

When a curved track is laid accurately to a position set out by a surveyor, it represents an almost perfect circular curve of given radius; but under traffic conditions distortion occurs and while the general average radius remains, it becomes a series of “flats” and “sharps”.

In such a curve, a “flat” is a portion of the curve where the radius was greater than the given radius, and a “sharp” is a portion of smaller radius.

The two types of curves found in tracks are described as “circular” and “transition” a circular curve being a curve of constant radius and a transition curve, a curve of varying radius.

Conventions

When describing the rails of tracks on curves, the rail of greater radius is called the

“Outer Rail” and the rail of smaller radius is called the “Inner Rail”.

The length of radius is given in metres and with any increase or decrease of this length, the curve is referred to as “flatter” or “sharper” respectively.

It is usual to speak of a curve by its radius. That is, a 400metre curve is a curve having a radius of 400 metres.

Figure 212 – Basic track geometry The various forms curves take in track layouts are:

1. Simple curves.

2. Compound curves.

3. Reverse curves with length of straight.

4. Direct reverse curves.

5. Transition curves.

C8-2.1 Circular Curve (Arc)

A Circular curve is a curve with a constant radius.

Simple curves are of one radius between their tangent points with straights and are used to provide a change of direction.

With flat curves, the change of direction at the tangent point is very gradual, but as the radius decreases and the curves become sharper, the rate of change of direction increases rapidly and introduces several unfavourable conditions from the action of vehicles entering the curve.

These conditions make sharp circular curves unsuitable for high speeds, and can only be overcome by the introduction of “transitions”.

C8-2.2 Compound Curve

A Compound curve is a curve formed when 2 or more circular curves of different radii are joined so that they follow the same direction.

When flat and sharp curves are compounded similar conditions are set up at the compound tangent point as at the tangent points of simple curves due to the alteration of change of direction caused by the difference of radius.

When the difference in radius is not great, compound curves are satisfactory, but where large differences occur transitions are necessary to remove these conditions.

The limits of change of radius for compound curves vary with the maximum permissible speed for the line.

C8-2.3 Reverse Curve

A Reverse curve is a curve formed when 2 curves (circular or compound) are joined so that the direction is changed.

Where a length of straight occurs between the two curves it is desirable that it should be sufficiently long to allow vehicles to complete one change of direction before commencing the other; so that the minimum length should be at least equal to the overall length of the longest vehicle.

Direct reverse curves should be avoided where possible in favour of a layout including a length of straight as above, owing to the undesirable reverse in change of direction.

C8-2.4 Transition

Transitions are curves of gradually changing radius introduced between straights and circular curves, and between compound circular curves to make the change of direction gradual and to simplify the application of “superelevation”. The form of transition curve adopted on this system is described as a Cubic Parabola.

The transition commences from the straight as a curve of infinite radius (that is, a radius so great that the curve may be considered straight), and the radius decreases gradually until it coincides with the radius of the circular curve which it joins.

This provides a gradual uniform rate of change of direction between the straight and the circular curve and removes the effect of the abrupt change which occurs at the tangent

Due to the gradual change of radius, transition curves allow the application of superelevation that matches the radius as it changes.

C8-2.5 Superelevation

This is the deliberate raising of the outer rail above the level of the inner rail on curves, to even out the centrifugal forces, allowing faster speeds, smoother running and less wear and tear.

When there are variations in superelevation on curves the chances of a derailment are greater. This is because the rolling stock lack a differential and so want to run straight ahead.

The amount of superelevation at any point in the transition is based on the radius of the curve and the required average speed of trains around the curve.

Curve charts or “F Sheets” (also known as “G” sheets) are available and show details of:

• The radius of the curve.

• The amount of superelevation.

• The ramp rate (used to calculate the length of the transition).

• The location in kilometres of the TP and the TRS.

Superelevation is applied gradually and evenly from the straight to the curve to ensure trains travel smoothly.

If incorrect superelevation is applied to the track the following can occur:

1. Increased wear on the low rail. This is caused by too much of superelevation being applied to curves.

2. Increased wear on the high rail. This is caused by not enough superelevation on curves.

3. Possible derailments. This can be caused by sudden changes in superelevation.

4. Reduction in clearance. This can be caused by changes in super. eg.

platforms, structures etc. Overhead wiring is also affected.

C8-3 Grade

The term “Gradient”, more commonly called “grade”, is the rate of which the finished surface of a track rises or falls in its length.

Grades are expressed as a percentage (%) indicating the rise in every 100 m of length.

Thus, a grade of 2.5% (1 in 40) is a rise or fall of 2.5m in l00m of horizontal distance, as in Figure 214.

The direction of a grade. is described with the direction of traffic as a “rising grade” or a

“falling grade”, and with the increase or decrease of the rate of grade so it is referred to as a “steeper” or “flatter” grade respectively.

Figure 213 – Rising grade

Figure 214 – Falling grade

The steepest rising grade in the direction of traffic on any section of line is called the

“ruling grade” and this determines the heaviest loads that can be hauled through the section by the various types of locomotives.

The highest point on a grade is known as the “summit” or “top” of the grade and the commencement of a rising grade is called the “foot” or “bottom” of the grade.

In cases where the grades meet eases are introduced between the angles of the grades.

C8-4 Track Geometry terms

C8-4.1 Datum rail

This is the rail that is used as a reference when measuring the track.

On TANGENT TRACK either track can be used as the datum rail although the DOWN rail is normally used. Make sure you use the same rail for the whole length of track being measured.

On CURVED TRACK the inner or low rail is used as the datum rail when lifting and levelling.

On CURVED TRACK the outer or high rail is used as the datum rail when lining track.

C8-4.2 Longitudinal rail level (Top)

The level (height) of the rail when you look along its length. The common term used is

"TOP."

If there is too much variation in top the following can occur:

1. Rough riding - Variation in longitudinal rail level causes rough riding and it results in higher maintenance of rolling stock.

2. This also results in passenger discomfort and speed restrictions causing delays.

1 60

Falling grade 1.67%

1

40 Rising grade

2.5%

C8-4.3 Rail level

Rail level is the height of the running surface (top) of the rail when it is measured to survey marks.

C8-4.4 Cross-level

This is the level of one rail compared to the other when you measure across the track.

C8-4.5 Twist

This is a variation in cross level when measured at different points along the track (usually every 2 metres for a short twist and every 14 metres for a long twist.)

If twists are left in the track the following can occur:

• Derailments - Because of the rigid nature of the track and vehicle suspensions the wheel travel cannot compensate for sudden changes in cross-level and the wheel may “float” and derail.

• Oscillations or swaying movements (rock and roll) - This swaying of rolling stock may result in derailments.

• Increased track maintenance - The pounding of track from the rolling stock as it travels along is increased, resulting in more rail wear and more maintenance.

C8-4.6 Track gauge

The track gauge is the distance between the two rails of a track. The standard gauge is 1435mm.

It is measured between the two gauge faces 16mm below the running surface.

C8-4.7 Survey

Tells us exactly where the track should be (alignment and rail level).

For alignment measurement, the datum rail is normally the closest rail to the survey mark.

For alignment measurement, the datum rail is the low rail on curves.

C8-4.8 Alignment

This is the horizontal (or lateral) position of the track as compared with the permanent survey marks and is measured using a plum bob and tape from the gauge face of the nearest rail to the survey mark.

Cross level

Alignment Rail level

Figure 215 - Good track line - Poor track alignment

C8-4.9 Line

This is the horizontal smoothness of the track, without reference to the permanent survey marks.

The datum rail is the high rail on curves and either rail on straight track.

Figure 216 - Good track alignment - Poor track line

C8-4.10 Track Centres

This is the distance between two tracks and is measured from centre line to centre line or from one rail of one track to the corresponding rail of the other track.

C8-4.11 Structure Clearance

Is the distance from a fixed object at the side of the track to the centre line of the track and is normally measured from the closest point of the structure to the gauge face of the nearest rail.

Survey Mark

9 Good track line 8 Poor track line

9 9 9

Survey Mark 9 Good track alignment

Correct alignment distance 8 Poor track alignment Incorrect alignment distance 98

98

Track Centres

Structure Clearance

In document Sandra Viviana Mahecha Mahecha (página 92-98)