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Staff Intercept Formula

GoStaff Intercept in Gradienter given Horizontal Distance Formula

GoStaff Intercept in Gradienter given Vertical Distance Formula

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Staff intercept is the difference in reading between top and bottom cross hairs. Check FAQs

s i = D \cdot (\tan (θ 1) - \tan (θ 2))

s_i - Staff Intercept?D - Distance between Two Points?θ₁ - Vertical Angle to Upper Vane?θ₂ - Vertical Angle to Lower Vane?

Staff Intercept Example

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With units

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Here is how the Staff Intercept equation looks like with Values.

Here is how the Staff Intercept equation looks like with Units.

Here is how the Staff Intercept equation looks like.

3.9827 = 35.5 \cdot (\tan (25) - \tan (19.5))

3.9827m = 35.5m \cdot (\tan (25°) - \tan (19.5°))

3.9827 = 35.5 \cdot (\tan (25) - \tan (19.5))

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Staff Intercept Solution

Follow our step by step solution on how to calculate Staff Intercept?

FIRST Step Consider the formula

s i = D \cdot (\tan (θ 1) - \tan (θ 2))

Next Step Substitute values of Variables

∴

s i = 35.5m \cdot (\tan (25°) - \tan (19.5°))

Next Step Convert Units

∴

s i = 35.5m \cdot (\tan (0.4363rad) - \tan (0.3403rad))

Next Step Prepare to Evaluate

∴

s i = 35.5 \cdot (\tan (0.4363) - \tan (0.3403))

Next Step Evaluate

∴

s i = 3.98271253966168m

LAST Step Rounding Answer

∴

s i = 3.9827m

Staff Intercept Formula Elements

Variables

Functions

Staff Intercept

Staff intercept is the difference in reading between top and bottom cross hairs.

Symbol: s_i

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Staff Intercept

Distance between Two Points

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.

Symbol: D

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance between Two Points

Vertical Angle to Upper Vane

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.

Symbol: θ₁

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Vertical Angle to Upper Vane

Vertical Angle to Lower Vane

Vertical angle to lower vane is the angle formed the instrument axis and the lower vane.

Symbol: θ₂

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Vertical Angle to Lower Vane

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.

Syntax: tan(Angle)

Other Formulas to find Staff Intercept

Go Staff Intercept in Gradienter given Horizontal Distance

s i = \frac{D}{\frac{100 \cdot {\cos (x)}^{2} \cdot 0.5 \cdot \sin (2 \cdot x)}{m \cdot c}}

Go Staff Intercept in Gradienter given Vertical Distance

s i = \frac{V}{\frac{100 \cdot \sin (2 \cdot x) \cdot 0.5 \cdot {\sin (x)}^{2}}{m \cdot c}}

Other formulas in Stadia Surveying category

Go Horizontal Distance between Center of Transit and Rod

H Horizontal = (K \cdot R i \cdot {(\cos (a))}^{2}) + (fc \cdot \cos (a))

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

V = \frac{1}{2 \cdot ((K \cdot R i \cdot \sin (2 \cdot a)) + (fc \cdot \sin (a)))}

Go Additive Constant or Stadia Constant

C = (f + D c)

Go Stadia Distance from Instrument Spindle to Rod

D s = R \cdot ((\frac{f}{R i}) + C)

How to Evaluate Staff Intercept?

Staff Intercept evaluator uses Staff Intercept = Distance between Two Points*(tan(Vertical Angle to Upper Vane)-tan(Vertical Angle to Lower Vane)) to evaluate 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 evaluate Staff Intercept using this online evaluator? To use this online evaluator 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.

FAQs on Staff Intercept

What is the formula to find Staff Intercept?

The formula of Staff Intercept is expressed as Staff Intercept = Distance between Two Points*(tan(Vertical Angle to Upper Vane)-tan(Vertical Angle to Lower Vane)). Here is an example- 3.982713 = 35.5*(tan(0.4363323129985)-tan(0.34033920413883)).

How to calculate Staff Intercept?

With Distance between Two Points (D), Vertical Angle to Upper Vane (θ₁) & Vertical Angle to Lower Vane (θ₂) we can find Staff Intercept using the formula - Staff Intercept = Distance between Two Points*(tan(Vertical Angle to Upper Vane)-tan(Vertical Angle to Lower Vane)). This formula also uses Tangent (tan) function(s).

What are the other ways to Calculate Staff Intercept?

Here are the different ways to Calculate Staff Intercept-

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))

Can the Staff Intercept be negative?

Yes, the Staff Intercept, measured in Length can be negative.

Which unit is used to measure Staff Intercept?

Staff Intercept is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Staff Intercept can be measured.

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Staff Intercept Formula

​GoStaff Intercept in Gradienter given Horizontal Distance Formula

​GoStaff Intercept in Gradienter given Vertical Distance Formula

Staff Intercept Example

Staff Intercept Solution

Staff Intercept Formula Elements

Other Formulas to find Staff Intercept

Other formulas in Stadia Surveying category

How to Evaluate Staff Intercept?

FAQs on Staff Intercept

Variable Name

GoStaff Intercept in Gradienter given Horizontal Distance Formula

GoStaff Intercept in Gradienter given Vertical Distance Formula