Reduced Distance 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%
✖Distance Traveled defines how much path an object has covered to reach its destination in a given period.ⓘ Distance Traveled [D]			+10% -10%
✖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.ⓘ Elevation of b [H₂]			+10% -10%
✖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.ⓘ Elevation of a [H₁]			+10% -10%

✖Reduced distance is the distance which is reduced over the ellipsoid between the projections of the two points onto the ellipsoid.ⓘ Reduced Distance [K]

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Formula

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Reduced Distance

Formula

`"K" = "R"*sqrt((("D"-("H"_{"2"}-"H"_{"1"}))*("D"+("H"_{"2"}-"H"_{"1"})))/(("R"+"H"_{"1"})*("R"+"H"_{"2"})))`

Example

`"49.21355m"="6370"*sqrt((("50m"-("100m"-"101m"))*("50m"+("100m"-"101m")))/(("6370"+"101m")*("6370"+"100m")))`

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Reduced Distance Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
K = R*sqrt(((D-(H₂-H₁))*(D+(H₂-H₁)))/((R+H₁)*(R+H₂)))
This formula uses 1 Functions, 5 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

Reduced Distance - (Measured in Meter) - Reduced distance is the distance which is reduced over the ellipsoid between the projections of the two points onto the ellipsoid.
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.
Distance Traveled - (Measured in Meter) - Distance Traveled defines how much path an object has covered to reach its destination in a given period.
Elevation of b - (Measured in Meter) - 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.
Elevation of a - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Earth Radius in km: 6370 --> No Conversion Required
Distance Traveled: 50 Meter --> 50 Meter No Conversion Required
Elevation of b: 100 Meter --> 100 Meter No Conversion Required
Elevation of a: 101 Meter --> 101 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K = R*sqrt(((D-(H₂-H₁))*(D+(H₂-H₁)))/((R+H₁)*(R+H₂))) --> 6370*sqrt(((50-(100-101))*(50+(100-101)))/((6370+101)*(6370+100)))

Evaluating ... ...

K = 49.2135529834565

STEP 3: Convert Result to Output's Unit

49.2135529834565 Meter --> No Conversion Required

FINAL ANSWER

49.2135529834565 ≈ 49.21355 Meter <-- Reduced Distance

(Calculation completed in 00.004 seconds)

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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!

< 4 EDM Lines Calculators

Reduced Distance

Go 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)))

Spheroidal Distance for Tellurometers

Go Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(43*Earth Radius in km^2))

Spheroidal Distance for Geodimeters

Go Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(38*Earth Radius in km^2))

Spheroidal Distance

Go Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(24*Earth Radius in km^2))

Reduced Distance Formula

How does Electronic Distance Measurement work?

Electronic distance measurement (EDM) is a way of determining the length between two points by looking a phase changes that occur as electronic energy waves, which travel from one end of a straight line to the other. But when large variations occur in the terrain or when there's a great deal of obstruction, this method isn’t as effective. So, this method of measurement is avoided in difficult terrain.

How to Calculate Reduced Distance?

Reduced Distance calculator 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 calculate 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 calculate Reduced Distance using this online calculator? To use this online calculator 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. Here is how the Reduced Distance calculation can be explained with given input values -> 49.21355 = 6370*sqrt(((50-(100-101))*(50+(100-101)))/((6370+101)*(6370+100))).

FAQ

What is 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 and is represented as K = R*sqrt(((D-(H₂-H₁))*(D+(H₂-H₁)))/((R+H₁)*(R+H₂))) or 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))). 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, Distance Traveled defines how much path an object has covered to reach its destination in a given period, 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 & 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.

How to calculate 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 is calculated using 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 calculate Reduced Distance, you need Earth Radius in km (R), Distance Traveled (D), Elevation of b (H₂) & Elevation of a (H₁). With our tool, you need to enter the respective value for Earth Radius in km, Distance Traveled, Elevation of b & Elevation of a 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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