Length of Curve when S is Less than L Calculator

✖Sight Distance SSD is s the minimum distance between two vehicles moving along a curve, when the driver of one vehicle can just see the other vehicle on the road.ⓘ Sight Distance SSD [SD]			+10% -10%
✖Upgrade is the gradient or the slope which is towards the crest of a curve. Mentioned by %.ⓘ Upgrade [g₁]			+10% -10%
✖Downgrade is the gradient or the slope which is guided to the downward direction of a curve. Mentioned by %.ⓘ Downgrade [g₂]			+10% -10%
✖Height of Observer is the length or vertical length of the observer.ⓘ Height of Observer [H]			+10% -10%
✖Height of Object is the vertical distance of the object which is being observed.ⓘ Height of Object [h₂]			+10% -10%

✖Length of Curve is determined by the permissible rate of change of grade or from centrifugal consideration as appropriate.ⓘ Length of Curve when S is Less than L [L_c]

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Length of Curve when S is Less than L

Formula

`"L"_{"c"} = "SD"^2*(("g"_{"1"})-("g"_{"2"}))/(200*(sqrt("H")+sqrt("h"_{"2"}))^2)`

Example

`"705.2362m"=("490m")^2*(("2.2")-("-1.5"))/(200*(sqrt("1.2m")+sqrt("2m"))^2)`

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Download Surveying Vertical Curves Formulas PDF

Length of Curve when S is Less than L Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Curve = Sight Distance SSD^2*((Upgrade)-(Downgrade))/(200*(sqrt(Height of Observer)+sqrt(Height of Object))^2)
L_c = SD^2*((g₁)-(g₂))/(200*(sqrt(H)+sqrt(h₂))^2)
This formula uses 1 Functions, 6 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Length of Curve - (Measured in Meter) - Length of Curve is determined by the permissible rate of change of grade or from centrifugal consideration as appropriate.
Sight Distance SSD - (Measured in Meter) - Sight Distance SSD is s the minimum distance between two vehicles moving along a curve, when the driver of one vehicle can just see the other vehicle on the road.
Upgrade - Upgrade is the gradient or the slope which is towards the crest of a curve. Mentioned by %.
Downgrade - Downgrade is the gradient or the slope which is guided to the downward direction of a curve. Mentioned by %.
Height of Observer - (Measured in Meter) - Height of Observer is the length or vertical length of the observer.
Height of Object - (Measured in Meter) - Height of Object is the vertical distance of the object which is being observed.

STEP 1: Convert Input(s) to Base Unit

Sight Distance SSD: 490 Meter --> 490 Meter No Conversion Required
Upgrade: 2.2 --> No Conversion Required
Downgrade: -1.5 --> No Conversion Required
Height of Observer: 1.2 Meter --> 1.2 Meter No Conversion Required
Height of Object: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_c = SD^2*((g₁)-(g₂))/(200*(sqrt(H)+sqrt(h₂))^2) --> 490^2*((2.2)-((-1.5)))/(200*(sqrt(1.2)+sqrt(2))^2)

Evaluating ... ...

L_c = 705.236154560732

STEP 3: Convert Result to Output's Unit

705.236154560732 Meter --> No Conversion Required

FINAL ANSWER

705.236154560732 ≈ 705.2362 Meter <-- Length of Curve

(Calculation completed in 00.004 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 19 Surveying Vertical Curves Calculators

Sight Distance when Length of Curve is Less

Go Sight Distance SSD = 0.5*Length of Curve+(100*(sqrt(Height of Observer)+sqrt(Height of Object))^2)/((Upgrade)-(Downgrade))

Length of Curve when Sight Distance is More

Go Length of Curve = 2*Sight Distance SSD-(200*(sqrt(Height of Observer)+sqrt(Height of Object))^2)/((Upgrade)-(Downgrade))

Length of Curve when S is Less than L

Go Length of Curve = Sight Distance SSD^2*((Upgrade)-(Downgrade))/(200*(sqrt(Height of Observer)+sqrt(Height of Object))^2)

Velocity given Length

Go Vehicle Velocity = sqrt((Length of Curve*100*Allowable Centrifugal Acceleration)/(Upgrade-(Downgrade)))

Sight Distance when S is Less than L and h1 and h2 are same

Go Sight Distance SSD = sqrt((800*Height of Vertical Curves*Length of Curve)/((Upgrade)-(Downgrade)))

Sight Distance when S is Less than L

Go Sight Distance = (1/Tangential Correction)*(sqrt(Height of Observer)+sqrt(Height of Object))

Allowable Centrifugal Acceleration given Length

Go Allowable Centrifugal Acceleration = ((Upgrade)-(Downgrade))*Vehicle Velocity^2/(100*Length of Curve)

Length of Curve Based on Centrifugal Ratio

Go Length of Curve = ((Upgrade)-(Downgrade))*Vehicle Velocity^2/(100*Allowable Centrifugal Acceleration)

Upgrade given Length based on Centrifugal Ratio

Go Upgrade = (Length of Curve*100*Allowable Centrifugal Acceleration/Vehicle Velocity^2)+(Downgrade)

Sight Distance when Length of Curve is Less and Both Height of Observer and Object is Same

Go Sight Distance SSD = (Length of Curve/2)+(400*Height of Vertical Curves/((Upgrade)-(Downgrade)))

Downgrade given Length based on Centrifugal Ratio

Go Downgrade = Upgrade-(Length of Curve*100*Allowable Centrifugal Acceleration/Vehicle Velocity^2)

Length of Curve when S is Less than L and h1 and h2 are same

Go Length of Curve = ((Upgrade)-(Downgrade))*Sight Distance SSD^2/(800*Height of Vertical Curves)

Length of Curve when Height of Observer and Object are Same

Go Length of Curve = 2*Sight Distance SSD-(800*Height of Vertical Curves/((Upgrade)-(Downgrade)))

Length of Curve given Change in Grade where S is more than L

Go Length of Curve = 2*Sight Distance SSD-(800*Height of Vertical Curves/Change in Grade)

Length given S is Less than L and Change of Grade

Go Length of Curve = Change in Grade*Sight Distance SSD^2/(800*Height of Vertical Curves)

Tangential Correction

Go Tangential Correction = (Upgrade-Downgrade)/4*Number of Chords

Permissible Grade given Length

Go Permissible Rate = Change in Grade/Length of Vertical Curve

Change of Grade given Length

Go Change in Grade = Length of Vertical Curve*Permissible Rate

Length of Vertical Curve

Go Length of Vertical Curve = Change in Grade/Permissible Rate

Length of Curve when S is Less than L Formula

Length of Curve = Sight Distance SSD^2*((Upgrade)-(Downgrade))/(200*(sqrt(Height of Observer)+sqrt(Height of Object))^2)
L_c = SD^2*((g₁)-(g₂))/(200*(sqrt(H)+sqrt(h₂))^2)

How the Valley or Vertical Curve should be designed?

The valley curve should be designed such that there is enough headlight sight distance. Improperly designed valley curves results in extreme riding discomfort as well as accident risks especially at nights. The length of valley curve for various cases were also explained in the section. The concept of valley curve is used in underpasses.

What is the difference between Crest and Sag Vertical Curves?

Crest vertical curves are used to transition from a descending grade to an ascending grade, while sag vertical curves are used to transition from an ascending grade to a descending grade. Crest curves are typically longer and flatter than sag curves due to the need for drivers to be able to see over the crest of the curve, whereas sag curves are steeper and shorter.

How to Calculate Length of Curve when S is Less than L?

Length of Curve when S is Less than L calculator uses Length of Curve = Sight Distance SSD^2*((Upgrade)-(Downgrade))/(200*(sqrt(Height of Observer)+sqrt(Height of Object))^2) to calculate the Length of Curve, The Length of Curve when S is Less than L is defined for a situation where the sight distance is slightly less than the length of curve. ie. the vehicles can see eachother. Length of Curve is denoted by L_c symbol.

How to calculate Length of Curve when S is Less than L using this online calculator? To use this online calculator for Length of Curve when S is Less than L, enter Sight Distance SSD (SD), Upgrade (g₁), Downgrade (g₂), Height of Observer (H) & Height of Object (h₂) and hit the calculate button. Here is how the Length of Curve when S is Less than L calculation can be explained with given input values -> 705.2362 = 490^2*((2.2)-((-1.5)))/(200*(sqrt(1.2)+sqrt(2))^2).

FAQ

What is Length of Curve when S is Less than L?

The Length of Curve when S is Less than L is defined for a situation where the sight distance is slightly less than the length of curve. ie. the vehicles can see eachother and is represented as L_c = SD^2*((g₁)-(g₂))/(200*(sqrt(H)+sqrt(h₂))^2) or Length of Curve = Sight Distance SSD^2*((Upgrade)-(Downgrade))/(200*(sqrt(Height of Observer)+sqrt(Height of Object))^2). Sight Distance SSD is s the minimum distance between two vehicles moving along a curve, when the driver of one vehicle can just see the other vehicle on the road, Upgrade is the gradient or the slope which is towards the crest of a curve. Mentioned by %, Downgrade is the gradient or the slope which is guided to the downward direction of a curve. Mentioned by %, Height of Observer is the length or vertical length of the observer & Height of Object is the vertical distance of the object which is being observed.

How to calculate Length of Curve when S is Less than L?

The Length of Curve when S is Less than L is defined for a situation where the sight distance is slightly less than the length of curve. ie. the vehicles can see eachother is calculated using Length of Curve = Sight Distance SSD^2*((Upgrade)-(Downgrade))/(200*(sqrt(Height of Observer)+sqrt(Height of Object))^2). To calculate Length of Curve when S is Less than L, you need Sight Distance SSD (SD), Upgrade (g₁), Downgrade (g₂), Height of Observer (H) & Height of Object (h₂). With our tool, you need to enter the respective value for Sight Distance SSD, Upgrade, Downgrade, Height of Observer & Height of Object and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Length of Curve?

In this formula, Length of Curve uses Sight Distance SSD, Upgrade, Downgrade, Height of Observer & Height of Object. We can use 6 other way(s) to calculate the same, which is/are as follows -

Length of Curve = ((Upgrade)-(Downgrade))*Vehicle Velocity^2/(100*Allowable Centrifugal Acceleration)
Length of Curve = 2*Sight Distance SSD-(200*(sqrt(Height of Observer)+sqrt(Height of Object))^2)/((Upgrade)-(Downgrade))
Length of Curve = 2*Sight Distance SSD-(800*Height of Vertical Curves/((Upgrade)-(Downgrade)))
Length of Curve = 2*Sight Distance SSD-(800*Height of Vertical Curves/Change in Grade)
Length of Curve = ((Upgrade)-(Downgrade))*Sight Distance SSD^2/(800*Height of Vertical Curves)
Length of Curve = Change in Grade*Sight Distance SSD^2/(800*Height of Vertical Curves)

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