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Reduced Distance Formula

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Reduced distance is the distance which is reduced over the ellipsoid between the projections of the two points onto the ellipsoid. Check FAQs

K = R \cdot \sqrt{\frac{(D - (H 2 - H 1)) \cdot (D + (H 2 - H 1))}{(R + H 1) \cdot (R + H 2)}}

K - Reduced Distance?R - Earth Radius in km?D - Distance Traveled?H₂ - Elevation of b?H₁ - Elevation of a?

Reduced Distance Example

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Here is how the Reduced Distance equation looks like with Values.

Here is how the Reduced Distance equation looks like with Units.

Here is how the Reduced Distance equation looks like.

49.2136 = 6370 \cdot \sqrt{\frac{(50 - (100 - 101)) \cdot (50 + (100 - 101))}{(6370 + 101) \cdot (6370 + 100)}}

49.2136m = 6370 \cdot \sqrt{\frac{(50m - (100m - 101m)) \cdot (50m + (100m - 101m))}{(6370 + 101m) \cdot (6370 + 100m)}}

49.2136 = 6370 \cdot \sqrt{\frac{(50 - (100 - 101)) \cdot (50 + (100 - 101))}{(6370 + 101) \cdot (6370 + 100)}}

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Reduced Distance Solution

Follow our step by step solution on how to calculate Reduced Distance?

FIRST Step Consider the formula

K = R \cdot \sqrt{\frac{(D - (H 2 - H 1)) \cdot (D + (H 2 - H 1))}{(R + H 1) \cdot (R + H 2)}}

Next Step Substitute values of Variables

∴

K = 6370 \cdot \sqrt{\frac{(50m - (100m - 101m)) \cdot (50m + (100m - 101m))}{(6370 + 101m) \cdot (6370 + 100m)}}

Next Step Prepare to Evaluate

∴

K = 6370 \cdot \sqrt{\frac{(50 - (100 - 101)) \cdot (50 + (100 - 101))}{(6370 + 101) \cdot (6370 + 100)}}

Next Step Evaluate

∴

K = 49.2135529834565m

LAST Step Rounding Answer

∴

K = 49.2136m

Reduced Distance Formula Elements

Variables

Functions

Reduced Distance

Reduced distance is the distance which is reduced over the ellipsoid between the projections of the two points onto the ellipsoid.

Symbol: K

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Reduced Distance

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

Distance Traveled

Distance Traveled defines how much path an object has covered to reach its destination in a given period.

Symbol: D

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance Traveled

Elevation of b

Elevation of b represents the vertical height of a point. Here consider a point B one surface of earth, then elevation at B gives the height of point above sea level.

Symbol: H₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Elevation of b

Elevation of a

Elevation of a is the vertical height of a point above the sea level. Here considering a point A, Elevation at A gives the height of point A from sea level.

Symbol: H₁

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Elevation of a

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.

Syntax: sqrt(Number)

Other formulas in EDM Lines category

Go Spheroidal Distance

S = K + (\frac{K^{3}}{24 \cdot R^{2}})

Go Spheroidal Distance for Tellurometers

S = K + (\frac{K^{3}}{43 \cdot R^{2}})

Go Spheroidal Distance for Geodimeters

S = K + (\frac{K^{3}}{38 \cdot R^{2}})

How to Evaluate Reduced Distance?

Reduced Distance evaluator uses Reduced Distance = Earth Radius in km*sqrt(((Distance Traveled-(Elevation of b-Elevation of a))*(Distance Traveled+(Elevation of b-Elevation of a)))/((Earth Radius in km+Elevation of a)*(Earth Radius in km+Elevation of b))) to evaluate the Reduced Distance, The Reduced Distance formula is defined as the means of the process of converting a measured slope distance between two points to the ‘reduced’ distance over the ellipsoid between the projections of the two points onto the ellipsoid. It is useful to start by thinking of the simple geometry which would arise if the earth were flat. Reduced Distance is denoted by K symbol.

How to evaluate Reduced Distance using this online evaluator? To use this online evaluator for Reduced Distance, enter Earth Radius in km (R), Distance Traveled (D), Elevation of b (H₂) & Elevation of a (H₁) and hit the calculate button.

FAQs on Reduced Distance

What is the formula to find Reduced Distance?

The formula of Reduced Distance is expressed as Reduced Distance = Earth Radius in km*sqrt(((Distance Traveled-(Elevation of b-Elevation of a))*(Distance Traveled+(Elevation of b-Elevation of a)))/((Earth Radius in km+Elevation of a)*(Earth Radius in km+Elevation of b))). Here is an example- 49.21355 = 6370*sqrt(((50-(100-101))*(50+(100-101)))/((6370+101)*(6370+100))).

How to calculate Reduced Distance?

With Earth Radius in km (R), Distance Traveled (D), Elevation of b (H₂) & Elevation of a (H₁) we can find Reduced Distance using the formula - Reduced Distance = Earth Radius in km*sqrt(((Distance Traveled-(Elevation of b-Elevation of a))*(Distance Traveled+(Elevation of b-Elevation of a)))/((Earth Radius in km+Elevation of a)*(Earth Radius in km+Elevation of b))). This formula also uses Square Root (sqrt) function(s).

Can the Reduced Distance be negative?

No, the Reduced Distance, measured in Length cannot be negative.

Which unit is used to measure Reduced Distance?

Reduced Distance is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Reduced Distance can be measured.

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Reduced Distance Formula

Reduced Distance Example

Reduced Distance Solution

Reduced Distance Formula Elements

Other formulas in EDM Lines category

How to Evaluate Reduced Distance?

FAQs on Reduced Distance

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