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Distance between Two points under Curvature and Refraction Formula

GoDistance for small errors under Curvature and Refraction Formula

GoDistance to Visible Horizon Formula

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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. Check FAQs

D = {(2 \cdot R \cdot c + (c^{2}))}^{\frac{1}{2}}

D - Distance between Two Points?R - Earth Radius in km?c - Error due to Curvature?

Distance between Two points under Curvature and Refraction Example

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Here is how the Distance between Two points under Curvature and Refraction equation looks like with Values.

Here is how the Distance between Two points under Curvature and Refraction equation looks like with Units.

Here is how the Distance between Two points under Curvature and Refraction equation looks like.

35.4964 = {(2 \cdot 6370 \cdot 0.0989 + ({0.0989}^{2}))}^{\frac{1}{2}}

35.4964m = {(2 \cdot 6370 \cdot 0.0989 + ({0.0989}^{2}))}^{\frac{1}{2}}

35.4964 = {(2 \cdot 6370 \cdot 0.0989 + ({0.0989}^{2}))}^{\frac{1}{2}}

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Distance between Two points under Curvature and Refraction Solution

Follow our step by step solution on how to calculate Distance between Two points under Curvature and Refraction?

FIRST Step Consider the formula

D = {(2 \cdot R \cdot c + (c^{2}))}^{\frac{1}{2}}

Next Step Substitute values of Variables

∴

D = {(2 \cdot 6370 \cdot 0.0989 + ({0.0989}^{2}))}^{\frac{1}{2}}

Next Step Prepare to Evaluate

∴

D = {(2 \cdot 6370 \cdot 0.0989 + ({0.0989}^{2}))}^{\frac{1}{2}}

Next Step Evaluate

∴

D = 35.496419273076m

LAST Step Rounding Answer

∴

D = 35.4964m

Distance between Two points under Curvature and Refraction Formula Elements

Variables

Distance between Two Points

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.

Symbol: D

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance between Two Points

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.

Symbol: R

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Earth Radius in 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.

Symbol: c

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Error due to Curvature

Other Formulas to find Distance between Two Points

Go Distance for small errors under Curvature and Refraction

D = \sqrt{2 \cdot R \cdot c}

Go Distance to Visible Horizon

D = \sqrt{\frac{h}{0.0673}}

Other formulas in Levelling category

Go Error Due to Curvature Effect

c = \frac{D^{2}}{2 \cdot R}

Go Combined Error Due to Curvature and Refraction

c_r = 0.0673 \cdot D^{2}

Go Correction on Refraction Error

c r = 0.0112 \cdot D^{2}

Go Height of Observer

h = 0.0673 \cdot D^{2}

How to Evaluate Distance between Two points under Curvature and Refraction?

Distance between Two points under Curvature and Refraction evaluator uses Distance between Two Points = (2*Earth Radius in km*Error due to Curvature+(Error due to Curvature^2))^(1/2) to evaluate the Distance between Two Points, Distance between Two points under Curvature and Refraction is defined as the length of space between two specified points. If the distance is too long, then curvature effects must be considered. Distance between Two Points is denoted by D symbol.

How to evaluate Distance between Two points under Curvature and Refraction using this online evaluator? To use this online evaluator for Distance between Two points under Curvature and Refraction, enter Earth Radius in km (R) & Error due to Curvature (c) and hit the calculate button.

FAQs on Distance between Two points under Curvature and Refraction

What is the formula to find Distance between Two points under Curvature and Refraction?

The formula of Distance between Two points under Curvature and Refraction is expressed as Distance between Two Points = (2*Earth Radius in km*Error due to Curvature+(Error due to Curvature^2))^(1/2). Here is an example- 35.49642 = (2*6370*0.0989+(0.0989^2))^(1/2).

How to calculate Distance between Two points under Curvature and Refraction?

With Earth Radius in km (R) & Error due to Curvature (c) we can find Distance between Two points under Curvature and Refraction using the formula - Distance between Two Points = (2*Earth Radius in km*Error due to Curvature+(Error due to Curvature^2))^(1/2).

What are the other ways to Calculate Distance between Two Points?

Here are the different ways to Calculate Distance between Two Points-

Distance between Two Points=sqrt(2*Earth Radius in km*Error due to Curvature)
Distance between Two Points=sqrt(Height of Observer/0.0673)

Can the Distance between Two points under Curvature and Refraction be negative?

Yes, the Distance between Two points under Curvature and Refraction, measured in Length can be negative.

Which unit is used to measure Distance between Two points under Curvature and Refraction?

Distance between Two points under Curvature and Refraction is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Distance between Two points under Curvature and Refraction can be measured.

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