# Railway Engineering Questions and Answers – Safe Speed on Curves and Transition Curves

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This set of Railway Engineering Question Paper focuses on “Safe Speed on Curves and Transition Curves”.

1. Which formula was used earlier for the calculation of Safe speed on curves?
a) Martin’s Formula
b) Henry’s equation
c) Bolt’s formula
d) Anderson’s formula

Explanation: Safe speed is the one which protects a carriage from overturning and derailment. Earlier Martin’s formula V = 4.4(R-70)1/2, was used for its calculation on Transitioned curves.

2. Which of the following is the correct revised formula for the calculation of speed at transitioned curves?
a) V = 0.27((Ca + Cd) x R)1/2
b) V = 0.347((Ca + Cd) x R)1/2
c) V = 0.27((Ca + Cd) x R)1/4
d) V = 0.27((Ca + Cd) x R)1/3

Explanation: Martin’s formula which was earlier used was changed by applying some formula based on some theoretical considerations. The revised formula for BG is V = 0.27((Ca + Cd) x R)1/2.

3. Calculate the super elevation for a 2° curve for equilibrium speed of 80kmph.
a) 146.3mm
b) 214mm
c) 100.8mm
d) 78.5mm

Explanation: G = 1750mm, V = 80km/h
R = 1750/2 = 875
Super elevation = GV2/127R
= 1750×802/127×875
= 100.8mm.
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4. On which portion of the track is a Transition curve provided?
a) Between straight line and circular curve
b) Before straight line
c) On one side of circular curve
d) In the middle of circular curve

Explanation: Transition curve is placed in between a straight line and circular curve on both sides. It is provided so that sudden centrifugal force should not come into effect while moving from straight track to circular one.

5. Which of the following is wrong about Transition curves?
a) Degree of curvature is uniform throughout its length
b) Radius of curvature decreases from a specified value to zero
c) Gradual increase in superelevation from zero
d) Should ensure a gradual increase or decrease in centrifugal forces

Explanation: In transition curve the radius of curvature decreases gradually from infinity at the straight line to a desired value at the circular curve. Superelevation increases from zero to specified value.

6. What is the correct formula of shift?
a) S = L2 / 24R
b) S = L2 / 2R
c) S = L2 / 4R
d) S = L2 / 24R2

Explanation: The main curve to be fit in the transition curve is moved inward by shift which is calculated as S = L2 / 24R. Here, L is the length of transition curve in metre.

7. Which of the following is not correct in case of an S-shaped transition curve?
a) Curvature assumes shape of quadratic parabola
b) Shift required is twice
c) Gradient is at centre and twice steeper
d) Desirable when shift is restricted

Explanation: An S-shaped transition curve is desirable when shift is restricted. In this case shift required is half of the shift provided in case of straight line ramp.

8. Which of the following is not a formula used to calculate the length of a transition curve?
a) L = 0.008CaxVm
b) L = 0.008CdxVm
c) L = 0.72Ca
d) L = 0.08CdxVmx S

Explanation: Here Ca is the actual cant, Cd is the cant deficiency. The length of transition curve is taken as the maximum of the following formulae; L = 0.008Cd x Vm, L = 0.008Ca x Vm and L = 0.72Ca.

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