Staff Intercept in Gradienter given Horizontal Distance 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 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%

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

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Formula

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Staff Intercept in Gradienter given Horizontal Distance

Formula

`"s"_{"i"} = "D"/((100*cos("x")^2*0.5*sin(2*"x"))/("m"*"c"))`

Example

`"9.6944m"="35.5m"/((100*cos("20°")^2*0.5*sin(2*"20°"))/("3.1"*"2.5m"))`

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Staff Intercept in Gradienter given Horizontal Distance Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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 - (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

Distance between Two Points: 35.5 Meter --> 35.5 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

s_i = D/((100*cos(x)^2*0.5*sin(2*x))/(m*c)) --> 35.5/((100*cos(0.3490658503988)^2*0.5*sin(2*0.3490658503988))/(3.1*2.5))

Evaluating ... ...

s_i = 9.69439969719227

STEP 3: Convert Result to Output's Unit

9.69439969719227 Meter --> No Conversion Required

FINAL ANSWER

9.69439969719227 ≈ 9.6944 Meter <-- Staff Intercept

(Calculation completed in 00.004 seconds)

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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

Staff Intercept in Gradienter given Horizontal Distance Formula

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

What Equipment is needed to Measure Staff Intercept in Gradienter given Horizontal Distance?

The equipment needed to measure Staff Intercept in Gradienter given Horizontal Distance includes a leveling instrument such as a gradienter, a leveling rod, and a measuring tape.

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 Staff Intercept in Gradienter given Horizontal Distance?

Staff Intercept in Gradienter given Horizontal Distance calculator uses Staff Intercept = Distance between Two Points/((100*cos(Vertical Angle)^2*0.5*sin(2*Vertical Angle))/(Revolution of Screw*Distance in One Turn)) to calculate the Staff Intercept, The Staff Intercept in Gradienter given Horizontal Distance formula is defined as the difference between two points in vertical staff due to two vanes or hairs in the telescope. Staff Intercept is denoted by s_i symbol.

How to calculate Staff Intercept in Gradienter given Horizontal Distance using this online calculator? To use this online calculator for Staff Intercept in Gradienter given Horizontal Distance, enter Distance between Two Points (D), Vertical Angle (x), Revolution of Screw (m) & Distance in One Turn (c) and hit the calculate button. Here is how the Staff Intercept in Gradienter given Horizontal Distance calculation can be explained with given input values -> 9.6944 = 35.5/((100*cos(0.3490658503988)^2*0.5*sin(2*0.3490658503988))/(3.1*2.5)).

FAQ

What is Staff Intercept in Gradienter given Horizontal Distance?

The Staff Intercept in Gradienter given Horizontal Distance formula is defined as the difference between two points in vertical staff due to two vanes or hairs in the telescope and is represented as s_i = D/((100*cos(x)^2*0.5*sin(2*x))/(m*c)) or Staff Intercept = Distance between Two Points/((100*cos(Vertical Angle)^2*0.5*sin(2*Vertical Angle))/(Revolution of Screw*Distance in One Turn)). 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 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 Staff Intercept in Gradienter given Horizontal Distance?

The Staff Intercept in Gradienter given Horizontal Distance formula is defined as the difference between two points in vertical staff due to two vanes or hairs in the telescope is calculated using Staff Intercept = Distance between Two Points/((100*cos(Vertical Angle)^2*0.5*sin(2*Vertical Angle))/(Revolution of Screw*Distance in One Turn)). To calculate Staff Intercept in Gradienter given Horizontal Distance, you need Distance between Two Points (D), Vertical Angle (x), Revolution of Screw (m) & Distance in One Turn (c). With our tool, you need to enter the respective value for Distance between Two Points, 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 Staff Intercept?

In this formula, Staff Intercept uses Distance between Two Points, 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 -

Staff Intercept = Distance between Two Points*(tan(Vertical Angle to Upper Vane)-tan(Vertical Angle to Lower Vane))
Staff Intercept = Vertical Distance/((100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(Revolution of Screw*Distance in One Turn))

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