Understanding Intercept on a Vertical Staff
When using a tachometer for surveying, the intercept observed on a vertical staff is crucial for calculating distances. In this case, the intercept is noted as 0.75 m.
Key Factors to Consider
- Intercept Definition: The intercept on a vertical staff refers to the distance between the line of sight of the instrument and the reading on the staff.
- Vertical Distance: The vertical distance from the line of sight to the ground is equal to the intercept. Here, it is 0.75 m.
Calculating the Horizontal Distance
To find the horizontal distance between the tachometer and the staff station:
- Tachometer Height: Assume the tachometer is set up at a height above the ground.
- Line of Sight: The line of sight is horizontal when the instrument is perfectly leveled.
- Elevation of Staff Station: The staff station’s elevation can be derived from the intercept. The effective height can be calculated if the height of the tachometer is known.
Using the Right Triangle Formula
In surveying, the relationship between the vertical distance (intercept) and horizontal distance can often be represented using trigonometric principles, specifically in a right triangle.
- Tangent Relationship: If the angle of elevation is known, the formula can be used:
- tan(angle) = vertical distance / horizontal distance.
- Final Calculation: Rearranging gives horizontal distance = vertical distance / tan(angle).
In this case, without specific angle information, only the intercept provides a direct measurement of vertical offset. For precise calculations, further data about instrument height and angle is needed.
Conclusion
The horizontal distance can be calculated accurately by integrating the height of the tachometer and the angle of elevation, alongside the intercept noted.