Vertical Distance between Instrument Axis and Lower Vane Solution

STEP 0: Pre-Calculation Summary
Formula Used
Vertical Distance = Distance between Two Points*tan(Vertical Angle to Lower Vane)
V = D*tan(θ2)
This formula uses 1 Functions, 3 Variables
Functions Used
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
Variables Used
Vertical Distance - (Measured in Meter) - vertical Distance between center of transit and point on rod intersected by middle horizontal crosshair.
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.
Vertical Angle to Lower Vane - (Measured in Radian) - Vertical angle to lower vane is the angle formed the instrument axis and the lower vane.
STEP 1: Convert Input(s) to Base Unit
Distance between Two Points: 35.5 Meter --> 35.5 Meter No Conversion Required
Vertical Angle to Lower Vane: 19.5 Degree --> 0.34033920413883 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = D*tan(θ2) --> 35.5*tan(0.34033920413883)
Evaluating ... ...
V = 12.5712093248372
STEP 3: Convert Result to Output's Unit
12.5712093248372 Meter --> No Conversion Required
FINAL ANSWER
12.5712093248372 12.57121 Meter <-- Vertical Distance
(Calculation completed in 00.004 seconds)

Credits

Created by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
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Meerut Institute of Engineering and Technology (MIET), Meerut
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13 Stadia Surveying Calculators

Vertical Distance between Center of Transit and Rod Intersected by Middle Horizontal Crosshair
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
Go Horizontal Distance = (Stadia Factor*Rod Intercept*(cos(Vertical Inclination of Line of Sight))^2)+(Instrument Constant*cos(Vertical Inclination of Line of Sight))
Staff Intercept in Gradienter given Horizontal Distance
Go Staff Intercept = Distance between Two Points/((100*cos(Vertical Angle)^2*0.5*sin(2*Vertical Angle))/(Revolution of Screw*Distance in One Turn))
Horizontal Distance using Gradienter
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)
Staff Intercept in Gradienter given Vertical Distance
Go Staff Intercept = Vertical Distance/((100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(Revolution of Screw*Distance in One Turn))
Vertical Distance using Gradienter
Go Vertical Distance = Staff Intercept*(100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(Revolution of Screw*Distance in One Turn)
Distance Equation given Index Error
Go Distance between Two Points = (Multiplying Constant*Staff Intercept/(Revolution of Screw-Index Error))+Additive Constant
Staff Intercept
Go Staff Intercept = Distance between Two Points*(tan(Vertical Angle to Upper Vane)-tan(Vertical Angle to Lower Vane))
Stadia Distance from Instrument Spindle to Rod
Go Stadia Distance = Intercept on Rod*((Focal Length of Telescope/Rod Intercept)+Stadia Constant)
Intercept on Rod between Two Sighting Wires
Go Intercept on Rod = Stadia Distance/((Focal Length of Telescope/Rod Intercept)+Stadia Constant)
Vertical Distance between Instrument Axis and Lower Vane
Go Vertical Distance = Distance between Two Points*tan(Vertical Angle to Lower Vane)
Additive Constant or Stadia Constant
Go Stadia Constant = (Focal Length of Telescope+Distance from Center)
Stadia Interval
Go Stadia Interval = Revolution of Screw*Pitch Screw

Vertical Distance between Instrument Axis and Lower Vane Formula

Vertical Distance = Distance between Two Points*tan(Vertical Angle to Lower Vane)
V = D*tan(θ2)

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.

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.

How to Calculate Vertical Distance between Instrument Axis and Lower Vane?

Vertical Distance between Instrument Axis and Lower Vane calculator uses Vertical Distance = Distance between Two Points*tan(Vertical Angle to Lower Vane) to calculate the Vertical Distance, The Vertical Distance between Instrument Axis and Lower Vane formula is defined as the vertical distance above the plane of the instrument axis to the lower vane of the telescope. The formula is used when the observing point is at the elevation and both the angle by vane is at a higher elevation. Vertical Distance is denoted by V symbol.

How to calculate Vertical Distance between Instrument Axis and Lower Vane using this online calculator? To use this online calculator for Vertical Distance between Instrument Axis and Lower Vane, enter Distance between Two Points (D) & Vertical Angle to Lower Vane 2) and hit the calculate button. Here is how the Vertical Distance between Instrument Axis and Lower Vane calculation can be explained with given input values -> 12.57121 = 35.5*tan(0.34033920413883).

FAQ

What is Vertical Distance between Instrument Axis and Lower Vane?
The Vertical Distance between Instrument Axis and Lower Vane formula is defined as the vertical distance above the plane of the instrument axis to the lower vane of the telescope. The formula is used when the observing point is at the elevation and both the angle by vane is at a higher elevation and is represented as V = D*tan(θ2) or Vertical Distance = Distance between Two Points*tan(Vertical Angle to Lower Vane). 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 & Vertical angle to lower vane is the angle formed the instrument axis and the lower vane.
How to calculate Vertical Distance between Instrument Axis and Lower Vane?
The Vertical Distance between Instrument Axis and Lower Vane formula is defined as the vertical distance above the plane of the instrument axis to the lower vane of the telescope. The formula is used when the observing point is at the elevation and both the angle by vane is at a higher elevation is calculated using Vertical Distance = Distance between Two Points*tan(Vertical Angle to Lower Vane). To calculate Vertical Distance between Instrument Axis and Lower Vane, you need Distance between Two Points (D) & Vertical Angle to Lower Vane 2). With our tool, you need to enter the respective value for Distance between Two Points & Vertical Angle to Lower Vane 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 Distance between Two Points & Vertical Angle to Lower Vane. 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 = Staff Intercept*(100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(Revolution of Screw*Distance in One Turn)
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