Electronic Distance Measuring Equipments - Problem 5

A 750m. baseline distance is measured with an electronic total station. If the vendor's accuracy specification of the instrument is ±(3mm. + 2ppm). Determine the precision of the measured distance to the nearest thousand.

Solution:

\begin{equation} RA = \frac{e}{b} \end{equation}

\begin{equation} e = \pm A + (B \times C) \end{equation}

\begin{equation} e = \pm 3mm. + [(750mm. \times \frac{1000mm.}{1m.}) \times (2 \times 10^{-6})] \end{equation}

\begin{equation} e = \pm 4.5mm. \end{equation}

\begin{equation} RA = \frac{4.5mm.}{750m. \times \frac{1000mm.}{1m.}} \end{equation}

\begin{equation} RA = \frac{1}{166666.667} \end{equation}

\begin{equation} RA \approx \pm \frac{1}{166000} \end{equation}

Answer: \begin{equation} RA = \pm \frac{1}{166000} \end{equation}