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Question 1
ప్రశ్న 1
A railway alignment contains a circular curve, a compound curve and a reverse curve. Which statement correctly distinguishes these horizontal curve arrangements?
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Explanation:
A simple circular railway curve has constant radius and curvature over its circular portion. A compound curve joins circular arcs of different radii curving in the same general direction. A reverse curve changes the direction of curvature from one side to the other. Transitions may be required between the relevant circular arcs to control changes in curvature and cant. Correct identification of the curve arrangement is necessary before selecting its geometric and operating requirements.
వివరణ:
Question 2
ప్రశ్న 2
Which statement correctly explains the conventional degree-of-curve definition and the preferred description of railway curves under the Indian Railways Permanent Way Manual?
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Explanation:
The traditional Indian railway degree-of-curve convention uses a chord approximately 30.5 m long. The central angle subtended by that chord defines the degree of curvature. A larger degree corresponds to a sharper curve with a smaller radius. The familiar approximate relationship is D = 1750/R when R is measured in metres. The current permanent-way manual requires railway curves to be described by their radius in metres.
వివరణ:
Question 3
ప్రశ్న 3
Using the conventional Indian railway approximation D = 1750/R, where D is the degree of curve and R is the radius in metres, what is the degree of a curve having a radius of 700 m?
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Explanation:
The question gives the approximate relationship between degree and radius. Substituting R = 700 m gives D = 1750/700. The result is 2.5 degrees. This degree is a conventional measure of curve sharpness rather than the total angular deflection of the entire alignment. The radius in metres remains the preferred quantity for describing the curve in the current Indian Railways manual.
వివరణ:
Question 4
ప్రశ్న 4
A railway horizontal curve is described by a conventional degree of curve of 3 degrees. Using R = 1750/D, what is its approximate radius?
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Explanation:
The approximate relationship is R = 1750/D. The given degree of curve is 3 degrees. Therefore R = 1750/3 = approximately 583.33 m. The radius rounded to one decimal place is 583.3 m. This calculation uses the conventional railway approximation and not an independent cant or speed criterion.
వివరణ:
Question 5
ప్రశ్న 5
During a railway curve survey, a 20 m chord has a measured versine of 50 mm. Using the standard approximate relation R = 125C^2/v, where C is in metres and v is in millimetres, what is the curve radius?
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Explanation:
Versine is the mid-chord offset between a chord and the curved rail alignment. The approximate radius relation is R = 125C squared divided by v. Here C = 20 m and v = 50 mm. Substitution gives R = 125 times 400 divided by 50 = 1000 m. The formula is the standard small-versine approximation used in railway curve measurement.
వివరణ:
Question 6
ప్రశ్న 6
A railway curve has a radius of 500 m. Using a 20 m chord and the approximate relation v = 125C^2/R, what versine should be expected?
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Explanation:
The standard approximate versine formula is v = 125C squared divided by R. The chord length is 20 m, giving C squared = 400. The curve radius is 500 m. Therefore v = 125 times 400 divided by 500 = 100 mm. For the same chord length, a sharper curve produces a larger versine.
వివరణ:
Question 7
ప్రశ్న 7
An engineer is conducting a routine versine survey of an Indian Railways plain-track curve. Which method is consistent with the current permanent-way guidance?
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Explanation:
Versine measurements provide a practical method for evaluating horizontal track curvature. The Indian Railways manual normally specifies overlapping 20 m chords on plain-track curves. Measurement stations are located at 10 m intervals for that arrangement. The chord or wire must be correctly positioned relative to the rail gauge face. Consistent measurements help identify curvature variations and determine whether curve realignment is necessary.
వివరణ:
Question 8
ప్రశ్న 8
A train negotiates a horizontal railway curve of radius 800 m at a constant speed of 72 km/h. What is the magnitude of its centripetal acceleration using a = v^2/R?
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Explanation:
The train speed must first be converted into metres per second. Dividing 72 km/h by 3.6 gives 20 m/s. The centripetal acceleration is then 20 squared divided by 800. This equals 400/800 = 0.50 m/s². Cant helps manage the lateral effects experienced by the vehicle but does not remove the geometric requirement for centripetal acceleration.
వివరణ:
Question 9
ప్రశ్న 9
The operating speed on a railway circular curve increases from 60 km/h to 90 km/h without changing the radius. By what factor does the required centripetal acceleration increase?
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Explanation:
Centripetal acceleration is proportional to the square of speed for a fixed curve radius. The final-to-initial speed ratio is 90/60 = 1.5. Squaring this ratio gives 2.25. Therefore the required centripetal acceleration increases by a factor of 2.25. This explains why increased operating speeds can create significant additional demands on cant, transition geometry and vehicle dynamics.
వివరణ:
Question 10
ప్రశ్న 10
Why is a transition curve introduced between a straight railway track and a circular curve intended for relatively high-speed operation?
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Explanation:
A transition curve provides a gradual change from zero curvature on the tangent to the curvature of the circular arc. It permits cant to be introduced progressively over an appropriate distance. This reduces sudden lateral acceleration and roll demands on the vehicle. Indian Railways commonly uses cubic-parabola transitions for this purpose. A suitable transition improves running quality and can influence the maximum permissible speed over the entire curve.
వివరణ:
Question 11
ప్రశ్న 11
In an ideal railway transition whose curvature increases linearly with distance from the tangent point, what is the instantaneous radius at the midpoint of a transition leading to a circular curve of radius R?
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Explanation:
Curvature is the reciprocal of radius. At the beginning of an ideal transition from a straight track, curvature is zero. At the end of the transition, curvature reaches 1/R. Linear curvature variation gives a midpoint curvature of 1/(2R). The corresponding midpoint radius is therefore 2R, using the stated idealized transition model.
వివరణ:
Question 12
ప్రశ్న 12
A railway cubic-parabola transition is represented by y = x^3/(6RL), where x is the distance from its beginning, R is the circular-curve radius and L is transition length. For x = 30 m, R = 600 m and L = 90 m, what is the offset y approximately?
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Explanation:
The specified cubic-parabola equation is y = x cubed divided by 6RL. Cubing x = 30 m gives 27000 cubic metres. The denominator is 6 times 600 times 90 = 324000 square metres. The resulting offset is 27000/324000 = approximately 0.08333 m. This equals about 83.3 mm and represents the offset under the stated transition geometry.
వివరణ:
Question 13
ప్రశ్న 13
To accommodate a cubic-parabola railway transition, the circular curve is shifted inward by S = L^2/(24R). If L = 120 m and R = 600 m, what is the shift?
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Explanation:
The transition shift is calculated using S = L squared divided by 24R. The transition length is 120 m, so L squared is 14400 m². The denominator is 24 times 600 = 14400 m. Therefore S = 14400/14400 = 1.00 m. The shift is a geometric inward adjustment of the circular alignment needed to accommodate the transition.
వివరణ:
Question 14
ప్రశ్న 14
For cubic-parabola transitions, shift is given by S = L^2/(24R). If transition length is doubled while the circular-curve radius remains unchanged, what happens to the shift?
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Explanation:
The shift equation contains the square of transition length. When L is doubled, L squared increases by a factor of four. The radius and the constant 24 are unchanged. Consequently the required shift becomes four times the original value. This is an important consideration when modifying transition lengths in a restricted railway corridor.
వివరణ:
Question 15
ప్రశ్న 15
Using the ordinary Indian Railways desirable-transition criteria, calculate the adopted length for actual cant C_a = 80 mm, cant deficiency C_d = 90 mm and maximum speed V = 100 km/h. Take the maximum of 0.0056 C_a V, 0.0056 C_d V and 0.72 C_a, then round upward to the next multiple of 10 m.
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Explanation:
The cant-rate criterion gives 0.0056 times 80 times 100 = 44.8 m. The cant-deficiency-rate criterion gives 0.0056 times 90 times 100 = 50.4 m. The cant-gradient criterion gives 0.72 times 80 = 57.6 m. The greatest of these three lengths is 57.6 m. Rounding upward to the next multiple of 10 m gives 60 m, assuming the stated cant deficiency is authorized for the relevant rolling stock.
వివరణ:
Question 16
ప్రశ్న 16
Cant increases uniformly from zero to 90 mm over a 75 m railway transition. If a train passes through the transition at 54 km/h, what is its rate of change of cant?
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Explanation:
The train speed of 54 km/h is equivalent to 15 m/s. The time required to traverse 75 m is 75/15 = 5 seconds. The cant changes by 90 mm during this period. Therefore the rate of change of cant is 90/5 = 18 mm/s. The calculation assumes constant speed and a uniform cant run-off along the transition.
వివరణ:
Question 17
ప్రశ్న 17
A railway curve has 120 mm cant introduced uniformly over a transition length of 96 m. What is the average longitudinal cant gradient expressed in millimetres per metre?
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Explanation:
The longitudinal cant gradient is the cant change divided by transition length. The total cant change is 120 mm. The transition length is 96 m. Dividing 120 by 96 gives 1.25 mm/m. This corresponds approximately to a gradient of 1 in 800 and satisfies a limiting gradient of 1 in 720 if that is the applicable design criterion.
వివరణ:
Question 18
ప్రశ్న 18
Two reverse railway curves have actual cant magnitudes of 60 mm and 80 mm, with corresponding cant deficiencies of 60 mm and 50 mm. At a uniform maximum speed of 100 km/h, calculate the desirable common-transition length using all three ordinary criteria: L1 = 0.0056(C_a1 + C_a2)V, L2 = 0.0056(C_d1 + C_d2)V and L3 = 0.72(C_a1 + C_a2). Round the largest result upward to the next multiple of 10 m. What length is obtained?
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Explanation:
Reverse railway curves bend in opposite directions, so their actual cant magnitudes are added when evaluating the common transition. The cant-rate criterion gives 0.0056 times 140 times 100 = 78.4 m, while the cant-deficiency-rate criterion gives 0.0056 times 110 times 100 = 61.6 m. The ordinary cant-gradient criterion gives 0.72 times 140 = 100.8 m. The governing unrounded length is therefore 100.8 m, not 78.4 m. Rounding upward to the next multiple of 10 m gives 110 m, subject to other applicable reverse-curve layout conditions.
వివరణ:
Question 19
ప్రశ్న 19
Two circular railway curves of similar flexure are connected by a common transition at a uniform speed of 100 km/h. Their actual cants are 130 mm and 70 mm, while their cant deficiencies are 80 mm and 50 mm. Calculate the desirable transition length using L1 = 0.0056|C_a1 - C_a2|V, L2 = 0.0056|C_d1 - C_d2|V and L3 = 0.72|C_a1 - C_a2|. Round the greatest length upward to the next multiple of 10 m. What length results?
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Explanation:
A compound railway curve joins circular arcs of different radii bending in the same direction. The absolute difference in actual cant is 60 mm, giving a cant-rate transition length of 0.0056 times 60 times 100 = 33.6 m. The difference in cant deficiency is 30 mm, giving a deficiency-rate length of 16.8 m. The ordinary cant-gradient criterion gives 0.72 times 60 = 43.2 m, which governs the desirable length. Rounding 43.2 m upward to the next multiple of 10 m gives 50 m, subject to other applicable compound-curve layout requirements.
వివరణ:
Question 20
ప్రశ్న 20
A proposed railway alignment passes close to a fixed structure on the inside of a sharp horizontal curve. Which clearance assessment is most appropriate?
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Explanation:
A railway vehicle does not follow a curved track as a perfectly flexible line. Its body geometry can create inward mid-throw and outward end-throw relative to the track centreline. Cant and vehicle movement may introduce additional clearance considerations. Indian Railways requires extra clearances on curves according to the applicable Schedule of Dimensions. The necessary allowance must be determined for the actual curve and vehicle conditions rather than using a universal arbitrary value.
వివరణ:
Question 21
ప్రశ్న 21
On a circular railway curve, the outer and inner running paths are separated by an effective transverse distance G = 1750 mm. The track length along the curve is L = 210 m and its radius is R = 700 m. Using the idealized relation d = LG/R, what is the accumulated difference in running-path lengths?
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Explanation:
The outer running path of a railway curve is longer than the inner running path. The problem supplies the geometric relation d = LG/R. Substituting L = 210 m, G = 1750 mm and R = 700 m gives d = 210 times 1750 divided by 700. This equals 525 mm. In traditional fish-plated track, the accumulated difference is relevant to the arrangement of rail joints and the use of suitable cut rails.
వివరణ:
Question 22
ప్రశ్న 22
For a railway circular curve of radius 700 m, the ordinary gradient-compensation rule is 70/R percent. If the ruling gradient is 0.60%, what maximum gradient remains after providing this curvature compensation?
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Explanation:
Curvature adds resistance to the movement of a train on a gradient. The specified ordinary compensation is 70/R percent. At R = 700 m, the compensation is 70/700 = 0.10%. Subtracting 0.10% from the ruling gradient of 0.60% leaves 0.50%. This represents the compensated gradient under the stated rule and applies where the gradient-plus-curvature condition requires compensation.
వివరణ:
Question 23
ప్రశ్న 23
An engineer is considering additional gauge allowance on a sharp railway curve. Which engineering approach is correct?
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Explanation:
Sharp railway curves can create more demanding wheel–rail contact and vehicle-negotiability conditions. The required track gauge must remain within the applicable railway provisions. Special sleeper or rail-seat arrangements may be approved where a particular gauge allowance is needed. The amount is not determined by an unrestricted universal widening rule. Gauge maintenance must also consider rail wear, wheel profiles and compatibility with the relevant vehicle fleet.
వివరణ:
Question 24
ప్రశ్న 24
A railway curve develops abrupt changes in measured versines, local alignment irregularities and nonuniform cant after repeated traffic loading. Which maintenance response is most appropriate?
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Explanation:
Smooth railway running requires curvature and cant to change without abrupt irregularities. Versine surveys reveal differences between the measured and desired horizontal alignment. Curve realignment calculations establish the required lateral movement or slew at each location. The cant profile should be restored in accordance with the corrected curvature. Final inspection must verify that the resulting geometry satisfies the applicable maintenance and operating requirements.
వివరణ:
Question 25
ప్రశ్న 25
A railway circular curve satisfies the equilibrium-cant and cant-deficiency calculations for a proposed train speed, but its transitions are short, nearby structures have limited clearance and rail alignment is irregular. Which decision best represents safe geometric-design practice?
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Explanation:
Railway curve safety depends on more than the theoretical equilibrium-cant calculation. Short transitions can cause excessive rates of change of cant or cant deficiency. Inadequate clearances can create conflicts between vehicle movement and fixed structures. Irregular alignment can increase dynamic forces and degrade riding quality. The final permitted speed must therefore reflect the combined geometric, vehicle, structural and maintenance constraints.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: B. A simple circular curve has constant radius, a compound curve joins arcs of different radii bending in the same direction, and a reverse curve joins arcs bending in opposite directions. సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: D. Degree of curve is conventionally the central angle subtended by a 30.5 m chord, while the manual specifies that curves should be described by their radius in metres. సమాధానం: D.
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Question 3 ప్రశ్న 3Answer: A. 2.5 degrees. సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: C. 583.3 m. సమాధానం: C.
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Question 5 ప్రశ్న 5Answer: B. 1000 m. సమాధానం: B.
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Question 6 ప్రశ్న 6Answer: A. 100 mm. సమాధానం: A.
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Question 7 ప్రశ్న 7Answer: C. Normally use overlapping 20 m chords with measurement stations at 10 m intervals, taking the relevant readings at the gauge face of the rail. సమాధానం: C.
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Question 8 ప్రశ్న 8Answer: D. 0.50 m/s². సమాధానం: D.
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Question 9 ప్రశ్న 9Answer: A. 2.25 times. సమాధానం: A.
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Question 10 ప్రశ్న 10Answer: C. To introduce curvature and cant progressively, reducing abrupt changes in lateral acceleration and vehicle roll response. సమాధానం: C.
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Question 11 ప్రశ్న 11Answer: B. 2R. సమాధానం: B.
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Question 12 ప్రశ్న 12Answer: D. 0.0833 m. సమాధానం: D.
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Question 13 ప్రశ్న 13Answer: A. 1.00 m. సమాధానం: A.
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Question 14 ప్రశ్న 14Answer: C. It becomes four times the original shift. సమాధానం: C.
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Question 15 ప్రశ్న 15Answer: B. 60 m. సమాధానం: B.
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Question 16 ప్రశ్న 16Answer: D. 18 mm/s. సమాధానం: D.
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Question 17 ప్రశ్న 17Answer: A. 1.25 mm/m. సమాధానం: A.
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Question 18 ప్రశ్న 18Answer: C. 110 m. సమాధానం: C.
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Question 19 ప్రశ్న 19Answer: B. 50 m. సమాధానం: B.
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Question 20 ప్రశ్న 20Answer: D. Provide the applicable additional clearance for curved-track vehicle overhang, cant-related effects and the specified Schedule of Dimensions requirements. సమాధానం: D.
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Question 21 ప్రశ్న 21Answer: C. 525 mm. సమాధానం: C.
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Question 22 ప్రశ్న 22Answer: B. 0.50%. సమాధానం: B.
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Question 23 ప్రశ్న 23Answer: D. Follow the applicable railway gauge and Schedule of Dimensions provisions and use an approved track arrangement where additional gauge allowance is justified by sharp-curve negotiability. సమాధానం: D.
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Question 24 ప్రశ్న 24Answer: A. Survey the existing versines, determine the corrected alignment and required slews, then restore smooth curvature and corresponding cant using approved methods. సమాధానం: A.
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Question 25 ప్రశ్న 25Answer: C. Assess the entire curve, including transitions, cant-change rates, clearances, wheel–rail behaviour and alignment condition, and revise the geometry or speed as necessary. సమాధానం: C.