Horizontal Distance using Gradienter Calculator

✖Staff intercept is the difference in reading between top and bottom cross hairs.ⓘ Staff Intercept [s_i]			+10% -10%
✖Vertical Angle is the angle between horizontal distance and slope distance.ⓘ Vertical Angle [x]			+10% -10%
✖Revolution of screw is the number of revolutions made for the micrometer screw.ⓘ Revolution of Screw [m]			+10% -10%
✖Distance in One Turn is the distance by which the line of sight moves by one revolution of the screw.ⓘ Distance in One Turn [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.ⓘ Horizontal Distance using Gradienter [D]

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Horizontal Distance using Gradienter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance between Two Points = Staff Intercept*(100*cos(Vertical Angle)^2*0.5*sin(2*Vertical Angle))/(Revolution of Screw*Distance in One Turn)
D = s_i*(100*cos(x)^2*0.5*sin(2*x))/(m*c)
This formula uses 2 Functions, 5 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

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.
Staff Intercept - (Measured in Meter) - Staff intercept is the difference in reading between top and bottom cross hairs.
Vertical Angle - (Measured in Radian) - Vertical Angle is the angle between horizontal distance and slope distance.
Revolution of Screw - Revolution of screw is the number of revolutions made for the micrometer screw.
Distance in One Turn - (Measured in Meter) - Distance in One Turn is the distance by which the line of sight moves by one revolution of the screw.

STEP 1: Convert Input(s) to Base Unit

Staff Intercept: 3 Meter --> 3 Meter No Conversion Required
Vertical Angle: 20 Degree --> 0.3490658503988 Radian (Check conversion here)
Revolution of Screw: 3.1 --> No Conversion Required
Distance in One Turn: 2.5 Meter --> 2.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D = s_i*(100*cos(x)^2*0.5*sin(2*x))/(m*c) --> 3*(100*cos(0.3490658503988)^2*0.5*sin(2*0.3490658503988))/(3.1*2.5)

Evaluating ... ...

D = 10.9857240599276

STEP 3: Convert Result to Output's Unit

10.9857240599276 Meter --> No Conversion Required

FINAL ANSWER

10.9857240599276 ≈ 10.98572 Meter <-- Distance between Two Points

(Calculation completed in 00.022 seconds)

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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

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< Stadia Surveying Calculators

Vertical Distance between Center of Transit and Rod Intersected by Middle Horizontal Crosshair

LaTeX Go Vertical Distance = 1/(2*((Stadia Factor*Rod Intercept*sin(2*Vertical Inclination of Line of Sight))+(Instrument Constant*sin(Vertical Inclination of Line of Sight))))

Horizontal Distance between Center of Transit and Rod

LaTeX Go Horizontal Distance = (Stadia Factor*Rod Intercept*(cos(Vertical Inclination of Line of Sight))^2)+(Instrument Constant*cos(Vertical Inclination of Line of Sight))

Stadia Distance from Instrument Spindle to Rod

LaTeX Go Stadia Distance = Intercept on Rod*((Focal Length of Telescope/Rod Intercept)+Stadia Constant)

Additive Constant or Stadia Constant

LaTeX Go Stadia Constant = (Focal Length of Telescope+Distance from Center)

Horizontal Distance using Gradienter Formula

LaTeX Go

Distance between Two Points = Staff Intercept*(100*cos(Vertical Angle)^2*0.5*sin(2*Vertical Angle))/(Revolution of Screw*Distance in One Turn)
D = s_i*(100*cos(x)^2*0.5*sin(2*x))/(m*c)

What is Gradienter ?

It is mainly used in setting out gradients, but is also used in tacheometry. When the tangent screw actuating the vertical circle of a theodolite is provided with a micrometer head and a scale for counting the whole turns by which it has been turned, it is called gradienter. The pitch of the screw is kept such that when moved by one revolution, the line of sight moves by tan–1 0.01.

What is Tacheometry?

Tacheometry is a branch of surveying in which the horizontal and vertical distances are determined by angular observations with a tacheometer, the chaining operation being altogether eliminated Tacheometry is not as accurate as is changing, but it is far more rapid in rough and difficult country where levelling is tedious and chaining is both inaccurate and slow.

How to Calculate Horizontal Distance using Gradienter?

Horizontal Distance using Gradienter calculator uses Distance between Two Points = Staff Intercept*(100*cos(Vertical Angle)^2*0.5*sin(2*Vertical Angle))/(Revolution of Screw*Distance in One Turn) to calculate the Distance between Two Points, The Horizontal Distance using Gradienter formula is defined as the length of the space between the instrument and the considered point. The vertical angle here represents the angle between the instrument axis and the observation made to lower point of vertical staff. Distance between Two Points is denoted by D symbol.

How to calculate Horizontal Distance using Gradienter using this online calculator? To use this online calculator for Horizontal Distance using Gradienter, enter Staff Intercept (s_i), Vertical Angle (x), Revolution of Screw (m) & Distance in One Turn (c) and hit the calculate button. Here is how the Horizontal Distance using Gradienter calculation can be explained with given input values -> 10.98572 = 3*(100*cos(0.3490658503988)^2*0.5*sin(2*0.3490658503988))/(3.1*2.5).

FAQ

What is Horizontal Distance using Gradienter?

The Horizontal Distance using Gradienter formula is defined as the length of the space between the instrument and the considered point. The vertical angle here represents the angle between the instrument axis and the observation made to lower point of vertical staff and is represented as D = s_i*(100*cos(x)^2*0.5*sin(2*x))/(m*c) or Distance between Two Points = Staff Intercept*(100*cos(Vertical Angle)^2*0.5*sin(2*Vertical Angle))/(Revolution of Screw*Distance in One Turn). Staff intercept is the difference in reading between top and bottom cross hairs, Vertical Angle is the angle between horizontal distance and slope distance, Revolution of screw is the number of revolutions made for the micrometer screw & Distance in One Turn is the distance by which the line of sight moves by one revolution of the screw.

How to calculate Horizontal Distance using Gradienter?

The Horizontal Distance using Gradienter formula is defined as the length of the space between the instrument and the considered point. The vertical angle here represents the angle between the instrument axis and the observation made to lower point of vertical staff is calculated using Distance between Two Points = Staff Intercept*(100*cos(Vertical Angle)^2*0.5*sin(2*Vertical Angle))/(Revolution of Screw*Distance in One Turn). To calculate Horizontal Distance using Gradienter, you need Staff Intercept (s_i), Vertical Angle (x), Revolution of Screw (m) & Distance in One Turn (c). With our tool, you need to enter the respective value for Staff Intercept, Vertical Angle, Revolution of Screw & Distance in One Turn 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 Staff Intercept, Vertical Angle, Revolution of Screw & Distance in One Turn. We can use 1 other way(s) to calculate the same, which is/are as follows -

Distance between Two Points = (Multiplying Constant*Staff Intercept/(Revolution of Screw-Index Error))+Additive Constant

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