Staff Intercept Calculator

✖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.ⓘ Distance between Two Points [D]			+10% -10%
✖Vertical Angle to Upper Vane is the angle made between the instrument axis and the line formed to sight the object through the upper vane.ⓘ Vertical Angle to Upper Vane [θ₁]			+10% -10%
✖Vertical angle to lower vane is the angle formed the instrument axis and the lower vane.ⓘ Vertical Angle to Lower Vane [θ₂]			+10% -10%

✖Staff intercept is the difference in reading between top and bottom cross hairs.ⓘ Staff Intercept [s_i]

⎘ Copy

👎

Formula

✖

Staff Intercept

Formula

`"s"_{"i"} = "D"*(tan("θ"_{"1"})-tan("θ"_{"2"}))`

Example

`"3.982713m"="35.5m"*(tan("25°")-tan("19.5°"))`

Calculator

LaTeX

Reset

👍

Download Photogrammetry Stadia and Compass Surveying Formulas PDF

Staff Intercept Solution

STEP 0: Pre-Calculation Summary

Formula Used

Staff Intercept = Distance between Two Points*(tan(Vertical Angle to Upper Vane)-tan(Vertical Angle to Lower Vane))
s_i = D*(tan(θ₁)-tan(θ₂))
This formula uses 1 Functions, 4 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

Staff Intercept - (Measured in Meter) - Staff intercept is the difference in reading between top and bottom cross hairs.
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 Upper Vane - (Measured in Radian) - Vertical Angle to Upper Vane is the angle made between the instrument axis and the line formed to sight the object through the upper vane.
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 Upper Vane: 25 Degree --> 0.4363323129985 Radian (Check conversion here)
Vertical Angle to Lower Vane: 19.5 Degree --> 0.34033920413883 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

s_i = D*(tan(θ₁)-tan(θ₂)) --> 35.5*(tan(0.4363323129985)-tan(0.34033920413883))

Evaluating ... ...

s_i = 3.98271253966168

STEP 3: Convert Result to Output's Unit

3.98271253966168 Meter --> No Conversion Required

FINAL ANSWER

3.98271253966168 ≈ 3.982713 Meter <-- Staff Intercept

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Surveying Formulas » Photogrammetry Stadia and Compass Surveying » Stadia Surveying » Staff Intercept

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!

< 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

Staff Intercept Formula

Staff Intercept = Distance between Two Points*(tan(Vertical Angle to Upper Vane)-tan(Vertical Angle to Lower Vane))
s_i = D*(tan(θ₁)-tan(θ₂))

What are the Advantages and Disadvantages of Subtense method over Stadia Method?

Advantages: Field work for long sights is more accurate as it is easier to intersect a fixed vane with a movable wire than to read the staff graduations. This is very effective in setting out curves for railways, etc.
Disadvantages: The calculations in the subtense method are more time consuming as the number of revolutions of the micrometer screw and index error come in the denominator.

How to Calculate Staff Intercept?

Staff Intercept calculator uses Staff Intercept = Distance between Two Points*(tan(Vertical Angle to Upper Vane)-tan(Vertical Angle to Lower Vane)) to calculate the Staff Intercept, The Staff Intercept formula is defined as the difference in reading between top and bottom crosshairs. Here it is the distance between the two vanes. Staff Intercept is denoted by s_i symbol.

How to calculate Staff Intercept using this online calculator? To use this online calculator for Staff Intercept, enter Distance between Two Points (D), Vertical Angle to Upper Vane (θ₁) & Vertical Angle to Lower Vane (θ₂) and hit the calculate button. Here is how the Staff Intercept calculation can be explained with given input values -> 3.982713 = 35.5*(tan(0.4363323129985)-tan(0.34033920413883)).

FAQ

What is Staff Intercept?

The Staff Intercept formula is defined as the difference in reading between top and bottom crosshairs. Here it is the distance between the two vanes and is represented as s_i = D*(tan(θ₁)-tan(θ₂)) or Staff Intercept = Distance between Two Points*(tan(Vertical Angle to Upper Vane)-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 Upper Vane is the angle made between the instrument axis and the line formed to sight the object through the upper vane & Vertical angle to lower vane is the angle formed the instrument axis and the lower vane.

How to calculate Staff Intercept?

The Staff Intercept formula is defined as the difference in reading between top and bottom crosshairs. Here it is the distance between the two vanes is calculated using Staff Intercept = Distance between Two Points*(tan(Vertical Angle to Upper Vane)-tan(Vertical Angle to Lower Vane)). To calculate Staff Intercept, you need Distance between Two Points (D), Vertical Angle to Upper Vane (θ₁) & Vertical Angle to Lower Vane (θ₂). With our tool, you need to enter the respective value for Distance between Two Points, Vertical Angle to Upper Vane & 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 Staff Intercept?

In this formula, Staff Intercept uses Distance between Two Points, Vertical Angle to Upper Vane & Vertical Angle to Lower Vane. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

Home

FREE PDFs

🔍 Search