Distance for small errors under Curvature and Refraction Solution

STEP 0: Pre-Calculation Summary
Formula Used
Distance between Two Points = sqrt(2*Earth Radius in km*Error due to Curvature)
D = sqrt(2*R*c)
This formula uses 1 Functions, 3 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
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.
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.
STEP 1: Convert Input(s) to Base Unit
Earth Radius in km: 6370 --> No Conversion Required
Error due to Curvature: 0.0989 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
D = sqrt(2*R*c) --> sqrt(2*6370*0.0989)
Evaluating ... ...
D = 35.4962814953905
STEP 3: Convert Result to Output's Unit
35.4962814953905 Meter --> No Conversion Required
FINAL ANSWER
35.4962814953905 35.49628 Meter <-- Distance between Two Points
(Calculation completed in 00.019 seconds)

Credits

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

Distance for small errors under Curvature and Refraction Formula

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

How does Curvature and Refraction Affect Distance Measurements for Small Errors?

Curvature and refraction can cause small errors in distance measurements, especially over long distances. These errors arise because light rays traveling through the atmosphere are bent due to variations in the refractive index of air. Additionally, the curvature of the earth can cause objects at a distance to appear higher than they actually are, leading to an overestimation of the distance between them. To correct for these errors, surveyors and engineers use sophisticated instruments and techniques that take into account the effects of curvature and refraction on their measurements.

How to Calculate Distance for small errors under Curvature and Refraction?

Distance for small errors under Curvature and Refraction calculator uses Distance between Two Points = sqrt(2*Earth Radius in km*Error due to Curvature) to calculate the Distance between Two Points, Distance for small errors under Curvature and Refraction is defined as the length between two points if the error due to curvature is considered as very small when compared with the radius of earth. Distance between Two Points is denoted by D symbol.

How to calculate Distance for small errors under Curvature and Refraction using this online calculator? To use this online calculator for Distance for small errors under Curvature and Refraction, enter Earth Radius in km (R) & Error due to Curvature (c) and hit the calculate button. Here is how the Distance for small errors under Curvature and Refraction calculation can be explained with given input values -> 35.49628 = sqrt(2*6370*0.0989).

FAQ

What is Distance for small errors under Curvature and Refraction?
Distance for small errors under Curvature and Refraction is defined as the length between two points if the error due to curvature is considered as very small when compared with the radius of earth and is represented as D = sqrt(2*R*c) or Distance between Two Points = sqrt(2*Earth Radius in km*Error due to Curvature). 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 & 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.
How to calculate Distance for small errors under Curvature and Refraction?
Distance for small errors under Curvature and Refraction is defined as the length between two points if the error due to curvature is considered as very small when compared with the radius of earth is calculated using Distance between Two Points = sqrt(2*Earth Radius in km*Error due to Curvature). To calculate Distance for small errors under Curvature and Refraction, you need Earth Radius in km (R) & Error due to Curvature (c). With our tool, you need to enter the respective value for Earth Radius in km & Error due to Curvature 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 Distance between Two Points?
In this formula, Distance between Two Points uses Earth Radius in km & Error due to Curvature. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Distance between Two Points = (2*Earth Radius in km*Error due to Curvature+(Error due to Curvature^2))^(1/2)
  • Distance between Two Points = sqrt(Height of Observer/0.0673)
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