Vertical 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%

✖vertical Distance between center of transit and point on rod intersected by middle horizontal crosshair.ⓘ Vertical Distance using Gradienter [V]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Photogrammetry Stadia and Compass Surveying Formulas PDF PDF Image

Vertical Distance using Gradienter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vertical Distance = Staff Intercept*(100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(Revolution of Screw*Distance in One Turn)
V = s_i*(100*sin(2*x)*0.5*sin(x)^2)/(m*c)
This formula uses 1 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)

Variables Used

Vertical Distance - (Measured in Meter) - vertical Distance between center of transit and point on rod intersected by middle horizontal crosshair.
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

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

Evaluating ... ...

V = 1.45532645013249

STEP 3: Convert Result to Output's Unit

1.45532645013249 Meter --> No Conversion Required

FINAL ANSWER

1.45532645013249 ≈ 1.455326 Meter <-- Vertical Distance

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Surveying Formulas » Photogrammetry Stadia and Compass Surveying » Stadia Surveying » Vertical Distance using Gradienter

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!

< 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)

Vertical Distance using Gradienter Formula

LaTeX Go

Vertical Distance = Staff Intercept*(100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(Revolution of Screw*Distance in One Turn)
V = s_i*(100*sin(2*x)*0.5*sin(x)^2)/(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 Tangential Method?

In this method, stadia hairs are not used to bisect the staff for observations. Two vanes at a constant distance apart are fixed on the staff. Each vane is bisected by the cross-hair and the staff reading and vertical angle corresponding to each vane are recorded. This method is preferred when the telescope is not equipped with a stadia diaphragm.

How to Calculate Vertical Distance using Gradienter?

Vertical Distance using Gradienter calculator uses Vertical Distance = Staff Intercept*(100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(Revolution of Screw*Distance in One Turn) to calculate the Vertical Distance, The Vertical Distance using Gradienter formula is defined as the vertical length in the staff from the surface of the Earth of the considered point. Vertical Distance is denoted by V symbol.

How to calculate Vertical Distance using Gradienter using this online calculator? To use this online calculator for Vertical 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 Vertical Distance using Gradienter calculation can be explained with given input values -> 1.455326 = 3*(100*sin(2*0.3490658503988)*0.5*sin(0.3490658503988)^2)/(3.1*2.5).

FAQ

What is Vertical Distance using Gradienter?

The Vertical Distance using Gradienter formula is defined as the vertical length in the staff from the surface of the Earth of the considered point and is represented as V = s_i*(100*sin(2*x)*0.5*sin(x)^2)/(m*c) or Vertical Distance = Staff Intercept*(100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(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 Vertical Distance using Gradienter?

The Vertical Distance using Gradienter formula is defined as the vertical length in the staff from the surface of the Earth of the considered point is calculated using Vertical Distance = Staff Intercept*(100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(Revolution of Screw*Distance in One Turn). To calculate Vertical 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 Vertical Distance?

In this formula, Vertical Distance uses Staff Intercept, Vertical Angle, Revolution of Screw & Distance in One Turn. We can use 2 other way(s) to calculate the same, which is/are as follows -

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))))
Vertical Distance = Distance between Two Points*tan(Vertical Angle to Lower Vane)

Home

FREE PDFs

🔍 Search