Distance Equation given Index Error Calculator

✖Multiplying constant is used in stadia work, by which the staff intercept is multiplied to determine the distance between the staff and the theodolite.ⓘ Multiplying Constant [K_M]			+10% -10%
✖Staff intercept is the difference in reading between top and bottom cross hairs.ⓘ Staff Intercept [s_i]			+10% -10%
✖Revolution of screw is the number of revolutions made for the micrometer screw.ⓘ Revolution of Screw [m]			+10% -10%
✖Index error is the error formed during stadia survey.ⓘ Index Error [e]			+10% -10%
✖Additive constant is the sum of focal length of the object lens and distance from the center of the object lens to the center of the instrument.ⓘ Additive Constant [C_add]			+10% -10%

✖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 Equation given Index Error [D]

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Distance Equation given Index Error

Formula

`"D" = ("K"_{"M"}*"s"_{"i"}/("m"-"e"))+"C"_{"add"}`

Example

`"35.5m"=("12"*"3m"/("3.1"-"1.5"))+"13"`

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Download Photogrammetry Stadia and Compass Surveying Formulas PDF

Distance Equation given Index Error Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance between Two Points = (Multiplying Constant*Staff Intercept/(Revolution of Screw-Index Error))+Additive Constant
D = (K_M*s_i/(m-e))+C_add
This formula uses 6 Variables

Variables Used

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.
Multiplying Constant - Multiplying constant is used in stadia work, by which the staff intercept is multiplied to determine the distance between the staff and the theodolite.
Staff Intercept - (Measured in Meter) - Staff intercept is the difference in reading between top and bottom cross hairs.
Revolution of Screw - Revolution of screw is the number of revolutions made for the micrometer screw.
Index Error - Index error is the error formed during stadia survey.
Additive Constant - Additive constant is the sum of focal length of the object lens and distance from the center of the object lens to the center of the instrument.

STEP 1: Convert Input(s) to Base Unit

Multiplying Constant: 12 --> No Conversion Required
Staff Intercept: 3 Meter --> 3 Meter No Conversion Required
Revolution of Screw: 3.1 --> No Conversion Required
Index Error: 1.5 --> No Conversion Required
Additive Constant: 13 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D = (K_M*s_i/(m-e))+C_add --> (12*3/(3.1-1.5))+13

Evaluating ... ...

D = 35.5

STEP 3: Convert Result to Output's Unit

35.5 Meter --> No Conversion Required

FINAL ANSWER

35.5 Meter <-- Distance between Two Points

(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

Distance Equation given Index Error Formula

Distance between Two Points = (Multiplying Constant*Staff Intercept/(Revolution of Screw-Index Error))+Additive Constant
D = (K_M*s_i/(m-e))+C_add

What are some common applications of Stadia Surveying?

Stadia Surveying is commonly used in civil engineering, construction, and land surveying to measure distances and heights in the field. It can be used to measure the height of buildings, the length of roads, or the slope of land.

How to Calculate Distance Equation given Index Error?

Distance Equation given Index Error calculator uses Distance between Two Points = (Multiplying Constant*Staff Intercept/(Revolution of Screw-Index Error))+Additive Constant to calculate the Distance between Two Points, The Distance Equation given Index Error formula is defined as a distance when a number of revolutions of the screw and index error are already established. Distance between Two Points is denoted by D symbol.

How to calculate Distance Equation given Index Error using this online calculator? To use this online calculator for Distance Equation given Index Error, enter Multiplying Constant (K_M), Staff Intercept (s_i), Revolution of Screw (m), Index Error (e) & Additive Constant (C_add) and hit the calculate button. Here is how the Distance Equation given Index Error calculation can be explained with given input values -> 35.5 = (12*3/(3.1-1.5))+13.

FAQ

What is Distance Equation given Index Error?

The Distance Equation given Index Error formula is defined as a distance when a number of revolutions of the screw and index error are already established and is represented as D = (K_M*s_i/(m-e))+C_add or Distance between Two Points = (Multiplying Constant*Staff Intercept/(Revolution of Screw-Index Error))+Additive Constant. Multiplying constant is used in stadia work, by which the staff intercept is multiplied to determine the distance between the staff and the theodolite, Staff intercept is the difference in reading between top and bottom cross hairs, Revolution of screw is the number of revolutions made for the micrometer screw, Index error is the error formed during stadia survey & Additive constant is the sum of focal length of the object lens and distance from the center of the object lens to the center of the instrument.

How to calculate Distance Equation given Index Error?

The Distance Equation given Index Error formula is defined as a distance when a number of revolutions of the screw and index error are already established is calculated using Distance between Two Points = (Multiplying Constant*Staff Intercept/(Revolution of Screw-Index Error))+Additive Constant. To calculate Distance Equation given Index Error, you need Multiplying Constant (K_M), Staff Intercept (s_i), Revolution of Screw (m), Index Error (e) & Additive Constant (C_add). With our tool, you need to enter the respective value for Multiplying Constant, Staff Intercept, Revolution of Screw, Index Error & Additive Constant 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 Distance between Two Points?

In this formula, Distance between Two Points uses Multiplying Constant, Staff Intercept, Revolution of Screw, Index Error & Additive Constant. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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