Elevation of Lowest Point on Sag Curve Calculator

✖The Elevation of Point of Vertical Curve referred as the vertical line passing through the point of curvature at the start point of the curve.ⓘ Elevation of Point of Vertical Curve [E₀]			+10% -10%
✖The Grade at Beginning of Curve referred as the grade at the beginning of the parabolic curve.ⓘ Grade at Beginning of Curve [G_I]			+10% -10%
✖The Rate of Change of Grade is referred as how quickly the grade (slope) of a roadway change over a specific distance.ⓘ Rate of Change of Grade [R_g]			+10% -10%

✖The Elevation of Lowest Point on a Sag Curve is referred as point at which the tangent intersection points on a vertical curve.ⓘ Elevation of Lowest Point on Sag Curve [E_s]

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Formula

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Elevation of Lowest Point on Sag Curve

Formula

E s = E 0 - (\frac{{G I}^{2}}{2 \cdot R g})

Example

49.0099 m = 50 m - (\frac{10^{2}}{2 \cdot 50.5 m⁻¹})

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Elevation of Lowest Point on Sag Curve Solution

STEP 0: Pre-Calculation Summary

Formula Used

Elevation of Lowest Point on a Sag Curve = Elevation of Point of Vertical Curve-((Grade at Beginning of Curve^2)/(2*Rate of Change of Grade))
E_s = E₀-((G_I^2)/(2*R_g))
This formula uses 4 Variables

Variables Used

Elevation of Lowest Point on a Sag Curve - (Measured in Meter) - The Elevation of Lowest Point on a Sag Curve is referred as point at which the tangent intersection points on a vertical curve.
Elevation of Point of Vertical Curve - (Measured in Meter) - The Elevation of Point of Vertical Curve referred as the vertical line passing through the point of curvature at the start point of the curve.
Grade at Beginning of Curve - The Grade at Beginning of Curve referred as the grade at the beginning of the parabolic curve.
Rate of Change of Grade - (Measured in Per Meter) - The Rate of Change of Grade is referred as how quickly the grade (slope) of a roadway change over a specific distance.

STEP 1: Convert Input(s) to Base Unit

Elevation of Point of Vertical Curve: 50 Meter --> 50 Meter No Conversion Required
Grade at Beginning of Curve: 10 --> No Conversion Required
Rate of Change of Grade: 50.5 Per Meter --> 50.5 Per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_s = E₀-((G_I^2)/(2*R_g)) --> 50-((10^2)/(2*50.5))

Evaluating ... ...

E_s = 49.009900990099

STEP 3: Convert Result to Output's Unit

49.009900990099 Meter --> No Conversion Required

FINAL ANSWER

49.009900990099 ≈ 49.0099 Meter <-- Elevation of Lowest Point on a Sag Curve

(Calculation completed in 00.004 seconds)

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National Institute of Technology (NIT), Warangal

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< Parabolic Curves Calculators

Elevation of Point of Vertical Curvature

Go Elevation of Point of Vertical Curve = Elevation of Point of Vertical Intersection-((1/2)*(Length of Curve*Grade at Beginning of Curve))

Elevation of Point of Vertical Intersection

Go Elevation of Point of Vertical Intersection = Elevation of Point of Vertical Curve+(1/2)*(Length of Curve*Grade at Beginning of Curve)

Length of Curve using Rate of change of Grade in Parabolic Curves

Go Length of Parabolic Curves = (Grade at End of Curve-(-Grade at Beginning of Curve))/Rate of Change of Grade

Distance from Point of Vertical Curve to Lowest Point on Sag Curve

Go Distance from PVC to Lowest Point on a Sag Curve = -(Grade at Beginning of Curve/Rate of Change of Grade)

Elevation of Lowest Point on Sag Curve Formula

Elevation of Lowest Point on a Sag Curve = Elevation of Point of Vertical Curve-((Grade at Beginning of Curve^2)/(2*Rate of Change of Grade))
E_s = E₀-((G_I^2)/(2*R_g))

What is Lowest Point on a Sag Curve?

The Lowest Point on a Sag Curve is the point at which the tangent intersection points of the sag curve.

What is the Point of Curvature?

Point of Curvature can be defined as the point at which the vertical line intersects at the beginning point of the parabolic curve.

How to Calculate Elevation of Lowest Point on Sag Curve?

Elevation of Lowest Point on Sag Curve calculator uses Elevation of Lowest Point on a Sag Curve = Elevation of Point of Vertical Curve-((Grade at Beginning of Curve^2)/(2*Rate of Change of Grade)) to calculate the Elevation of Lowest Point on a Sag Curve, The Elevation of Lowest Point on Sag Curve formula is defined as the elevation from PVC (point of vertical curvature) towards the lowest point of the sag curve. Elevation of Lowest Point on a Sag Curve is denoted by E_s symbol.

How to calculate Elevation of Lowest Point on Sag Curve using this online calculator? To use this online calculator for Elevation of Lowest Point on Sag Curve, enter Elevation of Point of Vertical Curve (E₀), Grade at Beginning of Curve (G_I) & Rate of Change of Grade (R_g) and hit the calculate button. Here is how the Elevation of Lowest Point on Sag Curve calculation can be explained with given input values -> 49.0099 = 50-((10^2)/(2*50.5)).

FAQ

What is Elevation of Lowest Point on Sag Curve?

The Elevation of Lowest Point on Sag Curve formula is defined as the elevation from PVC (point of vertical curvature) towards the lowest point of the sag curve and is represented as E_s = E₀-((G_I^2)/(2*R_g)) or Elevation of Lowest Point on a Sag Curve = Elevation of Point of Vertical Curve-((Grade at Beginning of Curve^2)/(2*Rate of Change of Grade)). The Elevation of Point of Vertical Curve referred as the vertical line passing through the point of curvature at the start point of the curve, The Grade at Beginning of Curve referred as the grade at the beginning of the parabolic curve & The Rate of Change of Grade is referred as how quickly the grade (slope) of a roadway change over a specific distance.

How to calculate Elevation of Lowest Point on Sag Curve?

The Elevation of Lowest Point on Sag Curve formula is defined as the elevation from PVC (point of vertical curvature) towards the lowest point of the sag curve is calculated using Elevation of Lowest Point on a Sag Curve = Elevation of Point of Vertical Curve-((Grade at Beginning of Curve^2)/(2*Rate of Change of Grade)). To calculate Elevation of Lowest Point on Sag Curve, you need Elevation of Point of Vertical Curve (E₀), Grade at Beginning of Curve (G_I) & Rate of Change of Grade (R_g). With our tool, you need to enter the respective value for Elevation of Point of Vertical Curve, Grade at Beginning of Curve & Rate of Change of Grade and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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