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CivilAdvanced Survey
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L=(g2тИТg1)/rL = ( g_{2} - g_{1} ) / rL=(g2тАЛтИТg1тАЛ)/r is equation for find out length for vertical, so in this equation тАШrтАЩ is notified by______

A

Rate of change of grade

B

total change of grade

C

Chain length

D

All of the above

Correct Answer

тЪЩя╕П TE тАв Technical Concept & PrincipleCivilAdvanced Survey
Option A

Rate of change of grade

Quick Summary:

In surveying and highway engineering, vertical curves are provided to connect two intersecting gradients smoothly. The equation L=g2тИТg1rL = \frac{g_2 - g_1}{r}L=rg2тАЛтИТg1тАЛтАЛ determines the length of a vertical curve, where rrr denotes the rate of change of grade per unit length or per chain.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

In surveying and highway engineering, vertical curves are provided to connect two intersecting gradients smoothly. The equation L=g2тИТg1rL = \frac{g_2 - g_1}{r}L=rg2тАЛтИТg1тАЛтАЛ determines the length of a vertical curve, where rrr denotes the rate of change of grade per unit length or per chain.

ЁЯФв Key Formulas

L=g2тИТg1r=NrL = \frac{g_2 - g_1}{r} = \frac{N}{r}L=rg2тАЛтИТg1тАЛтАЛ=rNтАЛ тАФ Length of vertical curve, where NNN is the total change of grade and rrr is the rate of change of grade

N=тИгg1тИТg2тИгN = |g_1 - g_2|N=тИгg1тАЛтИТg2тАЛтИг тАФ Total deviation or change in grade

тЪЩя╕П Working Principle

Vertical curves (usually parabolic) ensure a gradual transition in elevation to maintain comfortable riding conditions and adequate sight distance. The length of the curve (LLL) is directly proportional to the total change in grade (N=g2тИТg1N = g_2 - g_1N=g2тАЛтИТg1тАЛ) and inversely proportional to the maximum permissible rate of change of grade (rrr).

ЁЯУМ Key Points
  • тЦ╕

    A rate of change of grade (rrr) typically ranges between 0.05% to 0.1% per 20 m or 30 m chain for summit curves.

  • тЦ╕

    Parabolic curves are preferred for vertical alignment because they provide a constant rate of change of grade throughout the length of the curve.

тЬЕ Advantages
  • тЦ╕

    Ensures smooth transition between two different gradients.

  • тЦ╕

    Improves driver comfort and safety by preventing sudden vertical accelerations.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Requires larger land area and earthwork volumes to achieve smooth vertical transitions.

  • тЦ╕

    Designing for adequate sight distance at low values of rrr can significantly increase construction cost.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Design of summit and valley vertical curves in highway engineering.

  • тЦ╕

    Railway track gradient transition design.

ЁЯУД Additional Information
  • тЦ╕

    Option B represents the numerator (g2тИТg1)(g_2 - g_1)(g2тАЛтИТg1тАЛ), which is the algebraic difference or total change of grade (NNN).

  • тЦ╕

    Option C refers to the unit length (such as 20 m or 30 m) used to measure distances along the survey line, not 'r'.

ЁЯУК Diagram / Illustration
Vertical Curve Length FormulagтВВ - gтВБ (Total Change of Grade)r (Rate of Change of Grade)L = Length of Vertical Curve
тЬЕ

A is correct тАФ The variable 'r' in the equation represents the rate of change of grade per unit distance.

Core Concepts Used
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Vertical Curves Rate of Change of Grade Summit and Valley Curves
ЁЯТб EXAM TIP

For competitive exams like GATE and SSC JE, remember that parabolic vertical curves maintain a constant rate of change of grade (r=d2ydx2r = \frac{d^2y}{dx┬▓}r=dx2d2yтАЛ), which makes calculation of elevations straightforward.

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