1. UNIT III GEOMETRIC DESIGN OF TRACKS

2. Gradients
Any departure of track from the level is known as grade or gradient.
Purpose of providing gradient:
To provide uniform rate of rise or fall,
To reduce cost of earth work,
To reach different stations at different level.

3. Types of gradient
1) Ruling gradient: The steepest gradient allowed on the track section. It determines the max load that the locomotive can haul that section. The steep gradient needs more powerful locomotives, smaller train loads, lower speed, resulting in costly hauling.
–In plains:   1 in 150 to 1 in 200
–In hilly regions:   1 in 100 to 1 in 150

4. 2) Momentum Gradient: The gradient on a section which are steeper than the ruling gradient acquire sufficient momentum to negotiate them are known as momentum gradient.
3) Pusher gradient: As stated above a ruling gradient limits the maximum weight of a train which can be hauled over the section by a locomotive. If the ruling gradient is so severe on a section that it needs the help of extra engine to pull the same load than this gradient is known as pusher of helper gradient. In Darjeeling Railways 1 in 37 pusher gradient is used on Western Ghat BG Track.  

5. 4) Gradient at stations: at stations gradient are provided sufficient low due to following reason:
–To prevent movement of standing vehicle
–To prevent additional resistance due to grade.
On Indian railways, maximum gradient permitted is 1 in 400 in station yards.

6. Grade compensation on curves
If a curve is provided on a track with ruling gradient, the resistance of the track will be increased this curve. In order to avoid resistance beyond the allowable limits, the gradients are reduced on curves. The reduction in gradient is known as grade compensation for curves.
•BG track:  0.04% per degree of curve
•MG track:   0.03 % per degree of curve
 •NG track:   0.02 % per degree of curve

7. Degree of curve
A curve is defined by its degree or radius. The degree of a curve is the angle subtended at the center by a chord of 100 feet or 30.48m.
If R is the radius of curve,
Circumference of the curve= 2 ∏ R
Angle subtended at the center by the circle = 360 degree
Angle subtended by the arc of 30.48m = 1750/R
Thus, a 1 degree curve has a radius of 1750 m.

8. Superelevation on Curves
Cant is defined as the difference in height between the inner and outer rails on the curve. It is provided by gradually raising the outer rail above the inner rail level. The inner rail is considered as the reference rail and normally is maintained at its original level. The inner rail is known as the gradient rail.

9. Function of superelevation:
Neutralizes the effect of lateral force.
– It provides better load distribution on the two rails.
– It reduces wear and tear of rails and rolling stock.
– It provides smooth running of trains and comforts to the passengers.

10. Speeds
Equilibrium speed: It is the speed at which the effect of centrifugal force is exactly balanced by the superelevation provided. It can also be said that when the speed of a vehicle running on a curved track is such that the resultant weight of the vehicle and the effect of radical acceleration is perpendicular to the plane of rails and the vehicle is not subjected to an unbalanced radical acceleration, is in equilibrium then its particular speed is called equilibrium speed.

11. Maximum permissible speed:
: This is the highest speed which may be allowed or permitted on a curved track taking into consideration of the radius of curvature, actual cant, cant deficiency, cant excess and the length of the transition curve. When, the maximum permissible speed on the curve is less than the maximum sanctioned speed of the section of a line, permanent speed restriction become necessary on such curves  

12. Cant deficiency
Cant deficiency is the difference between the equilibrium cant (theoritical) necessary for the maximum permissible speed on a curve and the actual cant provided there. As per Indian Railways, Cant deficiency is recommended as follow: 
  BG Track:          75 mm
  MG track:          50 mm
  NG track:          40 mm

13. Cant Excess
When a train travels on a curved rack at a speed lower than the equilibrium speed, then the cant excess occurs. It is the difference between the actual cant provided and the theoretical cant required for such lower speeds. Maximum value for cant excess is
BG track:       75 mm
MG Track:      65 mm

14. Centrifugal Force
When a body moves on a circular curve, it has a tendency to move in a straight direction tangential to the curve. This tendency of the body is due to the fact that the body is subjected to a constant radial acceleration.

15. SUPER ELEVATION
The cant of a railway track (also referred to as superelevation) or a road (sometimes referred to as camber or cross slope) is the difference in elevation (height) between the two edges. This is normally done where the railway or road is curved; raising the outer rail or the outer edge of the road provides a banked turn, allowing vehicles to traverse the curve at higher speeds than would otherwise be possible.

17. FUNCTIONS The main functions of cant are to:
better distribute load across both rails
reduce rail- and wheel-wear
neutralize the effect of lateral forces
improve passenger comfort

18. superelevation is determined by the following formula
where Ea is the height in inches that the outside rail is "superelevated" above the inside rail on a curve, Eu is the unbalanced superelevation or cant deficiency in inches and d is the degree of curvaturein degrees per 100 feet (30 m). Vmax is in miles per hour.

19. unbalanced superelevation of 3 inches, the formula is:

20. TRANSITION CURVE
A track transition curve, or spiral easement, is a mathematically calculated curve on a section of highway, or railroad track, where a straight section changes into a curve. It is designed to prevent sudden changes in centripetal force. In plan (i.e., the horizontal curve) the start of the transition is at infinite radius and at the end of the transition it has the same radius as the curve itself, thus forming a very broad spiral. At the same time, in the vertical plane, the outside of the curve is gradually raised until the correct degree of bank is reached.