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In order to allow smooth movement of Locomotive with a maximum permissible speed of 120 kmph on a Broad Gauge track in transition curve, the radius of curvature by Martin’s formula will be
- a)786 m
- b)687 m
- c)575 m
- d)638 m
Correct answer is option 'B'. Can you explain this answer?
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In order to allow smooth movement of Locomotive with a maximum permiss...
Concept:
We know that by Martin’s formula for a Broad Gauge track in a transition curve. For speed greater than 100 kmph.
Speed. 
Where V is speed in kmph
R is the radius of curvature in m.
Calculation:
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In order to allow smooth movement of Locomotive with a maximum permiss...
Formula should be at least 610 meters. Martin formula is used to calculate the minimum radius required for a transition curve based on the maximum permissible speed and the rate of change of centrifugal force. The formula is:
R = V² / (127 * a)
Where R is the radius of curvature in meters, V is the maximum permissible speed in kmph, and a is the rate of change of centrifugal force in m/s² per degree of curvature. For a Broad Gauge track, the rate of change of centrifugal force is typically 0.00075 m/s² per degree of curvature.
Plugging in the values for a maximum permissible speed of 120 kmph and a rate of change of centrifugal force of 0.00075 m/s² per degree of curvature, we get:
R = (120² * 1000) / (127 * 0.00075 * 57.3)
R = 609.79 meters
Therefore, the minimum radius required for a transition curve to allow smooth movement of Locomotive with a maximum permissible speed of 120 kmph on a Broad Gauge track is 610 meters.
R = V² / (127 * a)
Where R is the radius of curvature in meters, V is the maximum permissible speed in kmph, and a is the rate of change of centrifugal force in m/s² per degree of curvature. For a Broad Gauge track, the rate of change of centrifugal force is typically 0.00075 m/s² per degree of curvature.
Plugging in the values for a maximum permissible speed of 120 kmph and a rate of change of centrifugal force of 0.00075 m/s² per degree of curvature, we get:
R = (120² * 1000) / (127 * 0.00075 * 57.3)
R = 609.79 meters
Therefore, the minimum radius required for a transition curve to allow smooth movement of Locomotive with a maximum permissible speed of 120 kmph on a Broad Gauge track is 610 meters.
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