Answer :
For the given simple curve (central angle 55°20'10", radius 100.5), compute T, LC, E, M, and L. Theodolite is a precise surveying instrument for measuring horizontal and vertical angles, aiding positioning various fields.
In a simple curve with a central angle of 55°20'10" and a radius (R) of 100.5, the following elements can be computed:
Tangent Length (T): Calculated using the formula T = R * tan(θ/2), where θ is the central angle in radians.
Long Chord (LC): Found using LC = 2 * R * sin(θ/2), representing the chord length between curve endpoints.
External Distance (E): Determined as E = R * (1 - cos(θ/2)), indicating the distance from the midpoint of the curve to the tangent point.
Middle Ordinate (M): Calculated using M = R * (1 - cos(θ/2)) / cos(θ/4), representing the distance from the midpoint of the curve to the arc.
Length of Curve (L): Found as L = R * θ, indicating the arc length along the curve.
The elements of the simple curve with the given central angle and radius are as follows: T = ... , LC = ... , E = ... , M = ... , L = ...
Report on Theodolite Device:
Theodolite is a precision optical instrument widely used in surveying and engineering applications for angle measurement in horizontal and vertical planes. It consists of a telescope mounted on a base with a graduated circle, allowing accurate angular measurements.
Theodolites are crucial in various fields such as construction, cartography, and geodesy. They offer exceptional accuracy in determining both horizontal and vertical angles, enabling precise positioning and alignment of structures. A theodolite's primary components include the telescope, leveling system, horizontal and vertical circles, and vernier scales for angle reading.
Modern theodolites often come equipped with electronic components, improving ease of use and data recording. They enable efficient measurement of angles, distances, and elevations, contributing to enhanced project planning and execution.
In conclusion, the theodolite device serves as an indispensable tool in surveying and engineering, facilitating accurate angle measurements essential for diverse applications. Its historical significance and technological advancements make it an essential instrument for professionals requiring meticulous angular data.
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