Error Due to Curvature Effect Calculator

✖Distance between Two Points is defined as the length of space between two points. For finding the distance when curvature effects are considered, the value must be considered in kilometres.ⓘ Distance between Two Points [D]			+10% -10%
✖Earth radius in km is the distance from the center of Earth to a point on or near its surface. Approximating earth as a spheroid, the radius ranges from 6,357 km to 6,378 km.ⓘ Earth Radius in km [R]			+10% -10%

✖Error due to Curvature is the error formed during the surveying when the geodetic shape of the earth is considered or the curvature effect of the earth is considered. It should be taken in meters.ⓘ Error Due to Curvature Effect [c]

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Formula

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Error Due to Curvature Effect

Formula

`"c" = "D"^2/(2*"R")`

Example

`"0.098921"=("35.5m")^2/(2*"6370")`

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Error Due to Curvature Effect Solution

STEP 0: Pre-Calculation Summary

Formula Used

Error due to Curvature = Distance between Two Points^2/(2*Earth Radius in km)
c = D^2/(2*R)
This formula uses 3 Variables

Variables Used

Error due to Curvature - Error due to Curvature is the error formed during the surveying when the geodetic shape of the earth is considered or the curvature effect of the earth is considered. It should be taken in meters.
Distance between Two Points - (Measured in Meter) - Distance between Two Points is defined as the length of space between two points. For finding the distance when curvature effects are considered, the value must be considered in kilometres.
Earth Radius in km - Earth radius in km is the distance from the center of Earth to a point on or near its surface. Approximating earth as a spheroid, the radius ranges from 6,357 km to 6,378 km.

STEP 1: Convert Input(s) to Base Unit

Distance between Two Points: 35.5 Meter --> 35.5 Meter No Conversion Required
Earth Radius in km: 6370 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

c = D^2/(2*R) --> 35.5^2/(2*6370)

Evaluating ... ...

c = 0.0989207221350079

STEP 3: Convert Result to Output's Unit

0.0989207221350079 --> No Conversion Required

FINAL ANSWER

0.0989207221350079 ≈ 0.098921 <-- Error due to Curvature

(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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< 17 Levelling Calculators

Difference in Elevation between Two Points using Barometric Levelling

Go Distance between Points = 18336.6*(log10(Height of point A)-log10(Height of point B))*(1+(Temperature at Lower Ground Level+Temperature at Higher level)/500)

Difference in Elevation between Ground Points in short lines under Trigonometric levelling

Go Elevation Difference = Distance between Points*sin(Measured Angle)+Height of point A-Height of point B

Distance between Two points under Curvature and Refraction

Go Distance between Two Points = (2*Earth Radius in km*Error due to Curvature+(Error due to Curvature^2))^(1/2)

Distance for small errors under Curvature and Refraction

Go Distance between Two Points = sqrt(2*Earth Radius in km*Error due to Curvature)

Angle of Dip for Compass Surveying

Go Dip Angle = Distance between Two Points/Earth Radius in km*(180/pi)

Error Due to Curvature Effect

Go Error due to Curvature = Distance between Two Points^2/(2*Earth Radius in km)

Distance to Visible Horizon

Go Distance between Two Points = sqrt(Height of Observer/0.0673)

Permissible Closing Error for Rough Levelling

Go Closing Error = 100*sqrt(Distance between Two Points)

Permissible Closing Error for Ordinary Levelling

Go Closing Error = 24*sqrt(Distance between Two Points)

Permissible Closing Error for Accurate Levelling

Go Closing Error = 12*sqrt(Distance between Two Points)

Permissible Closing Error for Precise Levelling

Go Closing Error = 4*sqrt(Distance between Two Points)

Reduced Level given Height of Instrument

Go Reduced Level = Height of Instrument-Back Sight

Back Sight given Height of Instrument

Go Back Sight = Height of Instrument-Reduced Level

Height of Instrument

Go Height of Instrument = Reduced Level+Back Sight

Correction on Refraction Error

Go Refraction Correction = 0.0112*Distance between Two Points^2

Height of Observer

Go Height of Observer = 0.0673*Distance between Two Points^2

Combined Error Due to Curvature and Refraction

Go Combined Error = 0.0673*Distance between Two Points^2

Error Due to Curvature Effect Formula

Error due to Curvature = Distance between Two Points^2/(2*Earth Radius in km)
c = D^2/(2*R)

What is Curvature Effect during Surveying?

In case of a long sight the horizontal line is not a level line due to curvature of the earth. The vertical distance between a horizontal line and the level line represents the effect of curvature of the earth.

How to Calculate Error Due to Curvature Effect?

Error Due to Curvature Effect calculator uses Error due to Curvature = Distance between Two Points^2/(2*Earth Radius in km) to calculate the Error due to Curvature, The Error Due to Curvature Effect is the error obtained during measuring the distance between two points when the shape of earth is considered in effect. Error due to Curvature is denoted by c symbol.

How to calculate Error Due to Curvature Effect using this online calculator? To use this online calculator for Error Due to Curvature Effect, enter Distance between Two Points (D) & Earth Radius in km (R) and hit the calculate button. Here is how the Error Due to Curvature Effect calculation can be explained with given input values -> 0.098921 = 35.5^2/(2*6370).

FAQ

What is Error Due to Curvature Effect?

The Error Due to Curvature Effect is the error obtained during measuring the distance between two points when the shape of earth is considered in effect and is represented as c = D^2/(2*R) or Error due to Curvature = Distance between Two Points^2/(2*Earth Radius in km). Distance between Two Points is defined as the length of space between two points. For finding the distance when curvature effects are considered, the value must be considered in kilometres & Earth radius in km is the distance from the center of Earth to a point on or near its surface. Approximating earth as a spheroid, the radius ranges from 6,357 km to 6,378 km.

How to calculate Error Due to Curvature Effect?

The Error Due to Curvature Effect is the error obtained during measuring the distance between two points when the shape of earth is considered in effect is calculated using Error due to Curvature = Distance between Two Points^2/(2*Earth Radius in km). To calculate Error Due to Curvature Effect, you need Distance between Two Points (D) & Earth Radius in km (R). With our tool, you need to enter the respective value for Distance between Two Points & Earth Radius in km 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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