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The surveyor can establish curves of short radius, usually less than one tape length, by holding one end of the tape at the center of the circle and swinging the tape in an arc, marking as many points as desired. As the radius and length of curve increases, the tape becomes impractical, and the surveyor must use other methods.
An alternate formula for the length of curve is by ratio and proportion with its degree of curve. $\dfrac{L_c}{I} = \dfrac{1 \, station}{D}$ $L_c = \dfrac{1 \, station \times I}{D}$
the formula is L = R px0(t)2. + y0(t)2 + z0(t)2 dt. 7.1. Because a parameter change t = t(s) corresponds to a substitution in the inte-gration which does not change the integral, we immediately see \path independence of arc length": The arc length is independent of the parameterization of the curve. De nition:
Surveying Reference Formulas. October 11, 2010. The morning and afternoon FS exam books will include reference material similar to the material shown here. Basic theories, conversions, formulas, and definitions that examinees are expected to know have not been included.
A compound curve consists of two (or more) circular curves between two main tangents joined at point of compound curve (PCC). Curve at PC is designated as 1 ( R 1 , L 1 , T 1 , etc) and curve at PT is designated as 2 ( R 2 , L 2 , T 2 , etc).
Since the ends of the chords lie on the circumference of the curve, the surveyor defines the arc in the field. The length of the chords varies with the degree of curve. To reduce the discrepancy between the arc distance and chord distance, the surveyor uses the following chord lengths:
Survey mathematics generally consists of applications of formulas and equations that have been adapted to work toward the specific needs of the surveyor such as: Units of measurement and conversions. Check and adjustment of raw field data. Closure and adjustment of survey figures.
