Tacheometry: Simple Guide with Examples

Welcome to an introduction to Tacheometry, a revolutionary method in land surveying.Traditional surveying relied heavily on measuring tapes and chains, which was time-consuming and often difficult in rough terrain.Tacheometry introduces a more efficient approach using specialized instruments: the theodolite and leveling staff.This method is particularly valuable when surveying rough or hilly terrain, where direct measurements would be challenging or impossible.The key to tacheometry lies in its optical principle. The telescope of the instrument contains special stadia hairs that allow for precise distance measurements.This method offers several key advantages over traditional surveying techniques, making it an invaluable tool in modern land surveying.The tacheometer's telescope contains three parallel stadia hairs - one central and two outer cross-hairs.A leveling staff with clear graduated markings is used to take readings.The surveyor takes three readings where the stadia hairs intersect the staff.The instrument must be perfectly level for accurate measurements.To calculate the distance, we first find the difference between the upper and lower staff readings.This difference is then multiplied by the multiplication constant, which is typically one hundred.The stadia hairs create three lines of sight to the leveling staff, allowing us to measure the interval.For accurate readings, the leveling staff must be held perfectly vertical, which can be checked with a plumb line.These basic principles and equipment form the foundation of tacheometric surveying.There are three main methods of tacheometric measurement, each with its own unique characteristics and applications.Stadia tacheometry is the most common method. It uses parallel stadia hairs in the telescope to measure the intercept length on a vertical staff.Tangential tacheometry involves measuring two vertical angles to different points on the staff. This method can be more precise but takes longer to perform.Wedge tacheometry uses an optical wedge for measurement. While it offers the highest precision, it's typically reserved for specialized applications.Each method offers different levels of accuracy. Stadia tacheometry provides accuracy of one in four hundred, tangential one in five hundred, and wedge tacheometry can achieve one in one thousand.Now that we understand the different types of tacheometric measurements, let's look at how to perform them in the field.To begin the field procedure, the surveyor sets up the tacheometer at a known point and carefully levels the instrument.A leveling staff is held vertically at the target point where measurements are needed.Looking through the telescope, the surveyor sees three horizontal cross-hairs: upper, center, and lower stadia hairs.The surveyor records three readings where these cross-hairs intersect the staff. In our example, these are two point eight five zero, two point five zero zero, and two point one five zero meters.To calculate the horizontal distance, we first find the staff interval by subtracting the lower reading from the upper reading.This interval is then multiplied by one hundred, which is the standard multiplication constant for most tacheometers.For elevation differences, we must also consider the vertical angle between the horizontal line of sight and the target point.The elevation difference is calculated using trigonometry, specifically the sine of the vertical angle multiplied by the horizontal distance.Tacheometry finds its primary applications in several key areas of surveying.It excels in topographic surveys, allowing efficient mapping of terrain and creation of contour maps, especially in challenging landscapes.For preliminary surveys of roads and railways, it provides quick and efficient measurements across varied terrain.However, tacheometry has important limitations we must consider.The method's accuracy is limited to approximately one in four hundred, making it unsuitable for precise engineering surveys that require higher accuracy.Weather conditions can significantly impact the reliability of tacheometric measurements.In modern surveying, traditional tacheometry has largely been replaced by total stations, which offer higher accuracy, digital readings, and automated calculations.