Deviation Angle given Total Length of Valley Curve Calculator

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Vertical alignment

Design of Transition Curves and Setback Distances

Design of Superelevation

Marshall Mix Design

Pavement Materials

Sight Distance

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Length of Valley Curve

Length of Summit Curve greater than Sight Distance

Length of Summit Curve Less than Sight Distance

Length of Summit Curve with Grade Angles

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Design of Valley Curve

Length of Valley Curve greater than Stopping Sight Distance

Length of Valley Curve Less than Stopping Sight Distance

✖Length of Curve is the distance along the road where the alignment changes from upward to downward slope, creating a valley-shaped concave.ⓘ Length of Curve [L_s]			+10% -10%
✖Rate of Change of Acceleration refers to how quickly the acceleration of an object changes over time.ⓘ Rate of Change of Acceleration [C_a]			+10% -10%
✖Design speed refers to the intended or planned operating speed for a particular section of a roadway or railway.ⓘ Design Speed [v]			+10% -10%

✖Deviation Angle is the angle between the reference direction and the observed direction.ⓘ Deviation Angle given Total Length of Valley Curve [N]

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Formula

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Deviation Angle given Total Length of Valley Curve

Formula

`"N" = ("L"_{"s"}/2)^2*"C"_{"a"}/"v"^3`

Example

`"0.4116rad"=("7m"/2)^2*"4.2m/s"/("5m/s")^3`

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Deviation Angle given Total Length of Valley Curve Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deviation Angle = (Length of Curve/2)^2*Rate of Change of Acceleration/Design Speed^3
N = (L_s/2)^2*C_a/v^3
This formula uses 4 Variables

Variables Used

Deviation Angle - (Measured in Radian) - Deviation Angle is the angle between the reference direction and the observed direction.
Length of Curve - (Measured in Meter) - Length of Curve is the distance along the road where the alignment changes from upward to downward slope, creating a valley-shaped concave.
Rate of Change of Acceleration - (Measured in Meter per Second) - Rate of Change of Acceleration refers to how quickly the acceleration of an object changes over time.
Design Speed - (Measured in Meter per Second) - Design speed refers to the intended or planned operating speed for a particular section of a roadway or railway.

STEP 1: Convert Input(s) to Base Unit

Length of Curve: 7 Meter --> 7 Meter No Conversion Required
Rate of Change of Acceleration: 4.2 Meter per Second --> 4.2 Meter per Second No Conversion Required
Design Speed: 5 Meter per Second --> 5 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N = (L_s/2)^2*C_a/v^3 --> (7/2)^2*4.2/5^3

Evaluating ... ...

N = 0.4116

STEP 3: Convert Result to Output's Unit

0.4116 Radian --> No Conversion Required

FINAL ANSWER

0.4116 Radian <-- Deviation Angle

(Calculation completed in 00.004 seconds)

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< 12 Design of Valley Curve Calculators

Total Length of Valley Curve

Go Length of Curve = 2*sqrt((Deviation Angle*Design Speed^3)/Rate of Change of Acceleration)

Design Speed given Total Length of Valley Curve

Go Design Speed = ((Length of Curve/2)^2*Rate of Change of Acceleration/Deviation Angle)^(1/3)

Rate of Change of Acceleration given Total Length of Valley Curve

Go Rate of Change of Acceleration = (Length of Curve/2)^2*Deviation Angle*Design Speed^3

Deviation Angle given Total Length of Valley Curve

Go Deviation Angle = (Length of Curve/2)^2*Rate of Change of Acceleration/Design Speed^3

Design Speed given Length of Valley Curve

Go Design Speed = (Length of Curve*Radius of Curve*Rate of Change of Acceleration)^(1/3)

Radius of Curve given Length of Valley Curve

Go Radius of Curve = (Design Speed^3)/(Length of Curve*Rate of Change of Acceleration)

Rate of Change of Acceleration

Go Rate of Change of Acceleration = (Design Speed^3)/(Length of Curve*Radius of Curve)

Length of Valley Curve

Go Length of Curve = (Design Speed^3)/(Radius of Curve*Rate of Change of Acceleration)

Time given Rate of Change of Acceleration

Go Time = ((Design Speed^2)/Radius of Curve)/Rate of Change of Acceleration

Length of Valley Curve given Time and Design Speed

Go Length of Curve = Design Speed*Time

Design Speed given Length of Valley Curve and Time

Go Design Speed = Length of Curve/Time

Time given Length of Valley Curve and Design Speed

Go Time = Length of Curve/Design Speed

Deviation Angle given Total Length of Valley Curve Formula

Deviation Angle = (Length of Curve/2)^2*Rate of Change of Acceleration/Design Speed^3
N = (L_s/2)^2*C_a/v^3

Difference between Length of Valley Curve and Total Length of Valley Curve

"Length of Valley Curve" refers to the curve segment itself, while "Total Length of Valley Curve" includes the approach and departure sections, providing a comprehensive view of the entire transition.

How to Calculate Deviation Angle given Total Length of Valley Curve?

Deviation Angle given Total Length of Valley Curve calculator uses Deviation Angle = (Length of Curve/2)^2*Rate of Change of Acceleration/Design Speed^3 to calculate the Deviation Angle, The Deviation Angle given Total Length of Valley Curve formula is defined as one-fourth of the square of the length of the curve divided by the rate of change of acceleration, all divided by the cube of the design speed. Deviation Angle is denoted by N symbol.

How to calculate Deviation Angle given Total Length of Valley Curve using this online calculator? To use this online calculator for Deviation Angle given Total Length of Valley Curve, enter Length of Curve (L_s), Rate of Change of Acceleration (C_a) & Design Speed (v) and hit the calculate button. Here is how the Deviation Angle given Total Length of Valley Curve calculation can be explained with given input values -> 0.4116 = (7/2)^2*4.2/5^3.

FAQ

What is Deviation Angle given Total Length of Valley Curve?

The Deviation Angle given Total Length of Valley Curve formula is defined as one-fourth of the square of the length of the curve divided by the rate of change of acceleration, all divided by the cube of the design speed and is represented as N = (L_s/2)^2*C_a/v^3 or Deviation Angle = (Length of Curve/2)^2*Rate of Change of Acceleration/Design Speed^3. Length of Curve is the distance along the road where the alignment changes from upward to downward slope, creating a valley-shaped concave, Rate of Change of Acceleration refers to how quickly the acceleration of an object changes over time & Design speed refers to the intended or planned operating speed for a particular section of a roadway or railway.

How to calculate Deviation Angle given Total Length of Valley Curve?

The Deviation Angle given Total Length of Valley Curve formula is defined as one-fourth of the square of the length of the curve divided by the rate of change of acceleration, all divided by the cube of the design speed is calculated using Deviation Angle = (Length of Curve/2)^2*Rate of Change of Acceleration/Design Speed^3. To calculate Deviation Angle given Total Length of Valley Curve, you need Length of Curve (L_s), Rate of Change of Acceleration (C_a) & Design Speed (v). With our tool, you need to enter the respective value for Length of Curve, Rate of Change of Acceleration & Design Speed 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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