Modeling of Stadia Surveying with Incomplete Intercepts

Observation of the half‐ and quarter‐intercepts in stadia surveying is often necessary for long sights, large vertical angles, and situations in which the line of sight is obstructed. Applying the standard stadia formulas using the doubled half‐intercept or quadrupled quarter‐intercept may produce substantial discrepancies in the horizontal distance and the difference in elevation. This paper develops revised stadia formulas that are explicit functions of the observed half‐ or quarter‐intercept, the vertical angle, and instrument‐related parameters. The formulas are based on the geometric relationships between the actual complete intercept and the observed incomplete intercept. The incomplete intercept can be the lower or upper half‐intercept; or the lower, middle lower, middle upper, or upper quarter‐intercept. The formulas, which involve only a minor modification of the standard stadia formulas, can be easily applied manually or programmed on electronic calculators.