of trigonometrical leveling can be seen from Figure 2. When measuring the vertical angle α and the horizontal distance S is used, then the difference in elevation hAB between ground points A and B is therefore:
hAB=S×tanα+i – v
where i is the vertical height of the measuring center of the instrument above A and v is the vertical height of the center of the target above B. The vertical angles are positive for angles of elevation and negative for angles of depression. The zenith angles are always positive, but naturally when greater than 90° they will produce a negative result. Trigonometrical leveling method of determining difference in elevation is limited to horizontal distance less than 300 m when moderate precision is sufficient, and to proportionately shorter distances as high precision is desired. For the distance beyond 300 m the effects of curvature and refraction must be considered and applied. To eliminate the uncertainty in the curvature and refraction correction, vertical-angle observations are made at both ends of the line as close in point of time as possible. This pair of observations is termed reciprocal vertical-angle observation. The correct difference in elevation between the two ends of the line is the mean of the two values computed both ways either with or without taking into account curvature and refraction.The important notes should be mentioned here is that surveyors used to working with spirit levels have referenced orthometric heights (H) to the “average” surface of the earth, as depicted by MSL. However, the elevation coordinate (h) given by GPS solutions refers to the height from the surface of the ellipsoid to the ground station.
32