Elevation of Lowest Point on Sag Curve Calculator

✖Elevation of PVC(point of vertical curvature) can be described as the vertical line passing through the point of curvature.ⓘ Elevation of PVC [E₀]			+10% -10%
✖Grade at beginning of Curve can be described as the grade at the beginning of the parabolic curve.ⓘ Grade at beginning of Curve [G_I]			+10% -10%
✖Rate of Change of Grade is a rate that describes how one grade changes in relation to another.ⓘ Rate of Change of Grade [R_g]			+10% -10%

✖Elevation of Lowest Point on a Sag Curve can be described as the point at which the tangent intersection point.ⓘ 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"}-(("G"_{"I"}^2)/(2*"R"_{"g"}))`

Example

`"49.0099m"= "50m"-((("10")^2)/(2*"50.5m⁻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 PVC-((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) - Elevation of Lowest Point on a Sag Curve can be described as the point at which the tangent intersection point.
Elevation of PVC - (Measured in Meter) - Elevation of PVC(point of vertical curvature) can be described as the vertical line passing through the point of curvature.
Grade at beginning of Curve - Grade at beginning of Curve can be described as the grade at the beginning of the parabolic curve.
Rate of Change of Grade - (Measured in Per Meter) - Rate of Change of Grade is a rate that describes how one grade changes in relation to another.

STEP 1: Convert Input(s) to Base Unit

Elevation of PVC: 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 00.020 seconds)

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Created by M Naveen

National Institute of Technology (NIT), Warangal

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National Institute of Technology Karnataka (NITK), Surathkal

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< 7 Parabolic Curves Calculators

Elevation of PVC given Elevation of Lowest Point on Sag Curve

Go Elevation of PVC = Elevation of Lowest Point on a Sag Curve+((Grade at beginning of Curve^2)/(2*Rate of Change of Grade))

Elevation of Lowest Point on Sag Curve

Go Elevation of Lowest Point on a Sag Curve = Elevation of PVC-((Grade at beginning of Curve^2)/(2*Rate of Change of Grade))

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

Elevation of Point of Vertical Curvature

Go Elevation of PVC = Elevation of PVI-(1/2)*(Length of Parabolic Curves*(-Grade at beginning of Curve))

Elevation of Point of Vertical Intersection

Go Elevation of PVI = Elevation of PVC+(1/2)*(Length of Curve*Grade at beginning of Curve)

Rate of Change of Grade given Distance from PVC to Lowest Point on Sag Curve

Go Rate of Change of Grade = -(Grade at beginning of Curve/Distance from PVC to lowest point on a sag curve)

Distance from PVC 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 PVC-((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 point of the sag 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 PVC-((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 PVC (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 PVC-((Grade at beginning of Curve^2)/(2*Rate of Change of Grade)). Elevation of PVC(point of vertical curvature) can be described as the vertical line passing through the point of curvature, Grade at beginning of Curve can be described as the grade at the beginning of the parabolic curve & Rate of Change of Grade is a rate that describes how one grade changes in relation to another.

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 PVC-((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 PVC (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 PVC, 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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