Distance for small errors under Curvature and Refraction Calculator

✖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 [c]			+10% -10%

✖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 for small errors under Curvature and Refraction [D]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Levelling Formulas PDF PDF Image

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 00.020 seconds)

You are here -

Home » Engineering » Civil » Surveying Formulas » Vertical Control » Levelling » Distance for small errors under Curvature and Refraction

Credits

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< Levelling Calculators

Distance between Two points under Curvature and Refraction

LaTeX 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

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

Error Due to Curvature Effect

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

Combined Error Due to Curvature and Refraction

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

Distance for small errors under Curvature and Refraction Formula

LaTeX Go

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)

Home

FREE PDFs

🔍 Search