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Vertical Distance using Gradienter Formula

GoVertical Distance between Center of Transit and Rod Intersected by Middle Horizontal Crosshair Formula

GoVertical Distance between Instrument Axis and Lower Vane Formula

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vertical Distance between center of transit and point on rod intersected by middle horizontal crosshair. Check FAQs

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

V - Vertical Distance?s_i - Staff Intercept?x - Vertical Angle?m - Revolution of Screw?c - Distance in One Turn?

Vertical Distance using Gradienter Example

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Here is how the Vertical Distance using Gradienter equation looks like with Values.

Here is how the Vertical Distance using Gradienter equation looks like with Units.

Here is how the Vertical Distance using Gradienter equation looks like.

1.4553 = 3 \cdot \frac{100 \cdot \sin (2 \cdot 20) \cdot 0.5 \cdot {\sin (20)}^{2}}{3.1 \cdot 2.5}

1.4553m = 3m \cdot \frac{100 \cdot \sin (2 \cdot 20°) \cdot 0.5 \cdot {\sin (20°)}^{2}}{3.1 \cdot 2.5m}

1.4553 = 3 \cdot \frac{100 \cdot \sin (2 \cdot 20) \cdot 0.5 \cdot {\sin (20)}^{2}}{3.1 \cdot 2.5}

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Vertical Distance using Gradienter Solution

Follow our step by step solution on how to calculate Vertical Distance using Gradienter?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = 3m \cdot \frac{100 \cdot \sin (2 \cdot 20°) \cdot 0.5 \cdot {\sin (20°)}^{2}}{3.1 \cdot 2.5m}

Next Step Convert Units

∴

V = 3m \cdot \frac{100 \cdot \sin (2 \cdot 0.3491rad) \cdot 0.5 \cdot {\sin (0.3491rad)}^{2}}{3.1 \cdot 2.5m}

Next Step Prepare to Evaluate

∴

V = 3 \cdot \frac{100 \cdot \sin (2 \cdot 0.3491) \cdot 0.5 \cdot {\sin (0.3491)}^{2}}{3.1 \cdot 2.5}

Next Step Evaluate

∴

V = 1.45532645013249m

LAST Step Rounding Answer

∴

V = 1.4553m

Vertical Distance using Gradienter Formula Elements

Variables

Functions

Vertical Distance

vertical Distance between center of transit and point on rod intersected by middle horizontal crosshair.

Symbol: V

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Vertical Distance

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

Vertical Angle

Vertical Angle is the angle between horizontal distance and slope distance.

Symbol: x

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Vertical Angle

Revolution of Screw

Revolution of screw is the number of revolutions made for the micrometer screw.

Symbol: m

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Revolution of Screw

Distance in One Turn

Distance in One Turn is the distance by which the line of sight moves by one revolution of the screw.

Symbol: c

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance in One Turn

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.

Syntax: sin(Angle)

Other Formulas to find Vertical Distance

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 Vertical Distance between Instrument Axis and Lower Vane

V = D \cdot \tan (θ 2)

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 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)

Go Intercept on Rod between Two Sighting Wires

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

How to Evaluate Vertical Distance using Gradienter?

Vertical Distance using Gradienter evaluator uses Vertical Distance = Staff Intercept*(100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(Revolution of Screw*Distance in One Turn) to evaluate the Vertical Distance, The Vertical Distance using Gradienter formula is defined as the vertical length in the staff from the surface of the Earth of the considered point. Vertical Distance is denoted by V symbol.

How to evaluate Vertical Distance using Gradienter using this online evaluator? To use this online evaluator for Vertical Distance using Gradienter, enter Staff Intercept (s_i), Vertical Angle (x), Revolution of Screw (m) & Distance in One Turn (c) and hit the calculate button.

FAQs on Vertical Distance using Gradienter

What is the formula to find Vertical Distance using Gradienter?

The formula of Vertical Distance using Gradienter is expressed as Vertical Distance = Staff Intercept*(100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(Revolution of Screw*Distance in One Turn). Here is an example- 1.455326 = 3*(100*sin(2*0.3490658503988)*0.5*sin(0.3490658503988)^2)/(3.1*2.5).

How to calculate Vertical Distance using Gradienter?

With Staff Intercept (s_i), Vertical Angle (x), Revolution of Screw (m) & Distance in One Turn (c) we can find Vertical Distance using Gradienter using the formula - Vertical Distance = Staff Intercept*(100*sin(2*Vertical Angle)*0.5*sin(Vertical Angle)^2)/(Revolution of Screw*Distance in One Turn). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Vertical Distance?

Here are the different ways to Calculate Vertical Distance-

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

Can the Vertical Distance using Gradienter be negative?

No, the Vertical Distance using Gradienter, measured in Length cannot be negative.

Which unit is used to measure Vertical Distance using Gradienter?

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

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: Value
: Unit

Vertical Distance using Gradienter Formula

​GoVertical Distance between Center of Transit and Rod Intersected by Middle Horizontal Crosshair Formula

​GoVertical Distance between Instrument Axis and Lower Vane Formula

Vertical Distance using Gradienter Example

Vertical Distance using Gradienter Solution

Vertical Distance using Gradienter Formula Elements

Other Formulas to find Vertical Distance

Other formulas in Stadia Surveying category

How to Evaluate Vertical Distance using Gradienter?

FAQs on Vertical Distance using Gradienter

Variable Name

GoVertical Distance between Center of Transit and Rod Intersected by Middle Horizontal Crosshair Formula

GoVertical Distance between Instrument Axis and Lower Vane Formula