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L=(g2−g1)/r is equation for find out length for vertical, so in this equation ‘r’ is notified by______
Rate of change of grade
total change of grade
Chain length
All of the above
Rate of change of grade
In surveying and highway engineering, vertical curves are provided to connect two intersecting gradients smoothly. The equation L=rg2−g1 determines the length of a vertical curve, where r denotes the rate of change of grade per unit length or per chain.
In surveying and highway engineering, vertical curves are provided to connect two intersecting gradients smoothly. The equation L=rg2−g1 determines the length of a vertical curve, where r denotes the rate of change of grade per unit length or per chain.
L=rg2−g1=rN — Length of vertical curve, where N is the total change of grade and r is the rate of change of grade
N=∣g1−g2∣ — Total deviation or change in grade
Vertical curves (usually parabolic) ensure a gradual transition in elevation to maintain comfortable riding conditions and adequate sight distance. The length of the curve (L) is directly proportional to the total change in grade (N=g2−g1) and inversely proportional to the maximum permissible rate of change of grade (r).
A rate of change of grade (r) typically ranges between 0.05% to 0.1% per 20 m or 30 m chain for summit curves.
Parabolic curves are preferred for vertical alignment because they provide a constant rate of change of grade throughout the length of the curve.
Ensures smooth transition between two different gradients.
Improves driver comfort and safety by preventing sudden vertical accelerations.
Requires larger land area and earthwork volumes to achieve smooth vertical transitions.
Designing for adequate sight distance at low values of r can significantly increase construction cost.
Design of summit and valley vertical curves in highway engineering.
Railway track gradient transition design.
Option B represents the numerator (g2−g1), which is the algebraic difference or total change of grade (N).
Option C refers to the unit length (such as 20 m or 30 m) used to measure distances along the survey line, not 'r'.
A is correct — The variable 'r' in the equation represents the rate of change of grade per unit distance.
For competitive exams like GATE and SSC JE, remember that parabolic vertical curves maintain a constant rate of change of grade (r=dx2d2y), which makes calculation of elevations straightforward.