Line-of-sight measurement is a technique that uses the crosshair reticle on a telescope and a leveling staff to determine the horizontal distance and elevation difference between two points. By applying optical and geometric principles, this method allows for the simultaneous calculation of both distance and height. It is particularly useful in topographic surveys and broken terrain measurements.
One of the key advantages of line-of-sight measurement is its simplicity and speed. It does not require physical contact with the ground, making it ideal for areas where the surface is uneven or difficult to access. However, its accuracy is relatively low, typically ranging from 1/200 to 1/300, which makes it unsuitable for high-precision applications.
The "thumb distance estimation" method is a basic visual technique used to estimate distances. This method relies on the principle of right-angle trigonometry. To use it, extend your arm forward, raise your thumb, and align it with the target using one eye. Then switch eyes and measure how far the target appears to move relative to your thumb. Multiply this estimated distance by 10 to get an approximate distance to the target. While this method is quick and easy, it requires individual calibration due to variations in arm length and eye spacing. With training, most people can achieve an error margin of about 5 meters within 200 meters.
Line-of-sight measurement works by using the telescope’s crosshairs and the principle of triangulation to calculate both distance and elevation. The process involves measuring the interval between the upper and lower crosshairs on a leveling staff, which is then used in conjunction with known constants to compute the actual distance.
**Horizontal Line of Sight**
As shown in Figure (1), when using a theodolite at point A to measure the horizontal distance (D) and elevation difference (h) between points A and B, the telescope's line of sight is aligned with the target at point B. The crosshair reticle captures the image of the staff at points M and N. The vertical distance between these two points, called the line-of-sight interval (l), is used in calculations.
Using similar triangles, the formula for horizontal distance is derived as D = Kl + C, where K is the multiplying constant and C is the additive constant. In modern instruments, K is typically set to 100, and C is nearly zero, simplifying the equation to D = 100 × l. The elevation difference (h) is calculated using the instrument height (i) and the middle wire reading (v).
**Tilting Line of Sight**
When measuring on uneven terrain, the telescope must be tilted to capture the line-of-sight interval. In such cases, the line of sight is no longer perpendicular to the staff, so adjustments are necessary. By calculating the angle of inclination (α), the horizontal distance and elevation difference can still be determined using adjusted formulas.
For example, the slant range (D') is calculated as D' = Kl cos α, and the true horizontal distance becomes D = D' × cos α. The elevation difference is then h = D tan α + i - v. These equations ensure accurate results even when the line of sight is not horizontal.
**Observation and Calculation**
During fieldwork, the instrument is placed at point A, and the height (i) of the instrument is measured. The telescope is then aimed at the target at point B, and the readings from the upper, middle, and lower crosshairs are recorded. The line-of-sight interval (l) is calculated as the difference between the upper and lower readings. After adjusting the vertical index level, the vertical angle (α) is determined, and the final distance and elevation are computed using the appropriate formulas.
This method remains widely used in surveying due to its efficiency and practicality, especially in areas where traditional methods are impractical.
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