Road surveys are fundamental in building technology for designing and constructing safe, efficient transport routes. In Kenya, where infrastructure development is rapidly expanding, precise surveying methods like tachometry ensure that roads conform to topographical and engineering requirements. These surveys help professionals address challenges posed by varied terrain and urban settings, enabling the delivery of durable road networks that support economic growth and connectivity. This chapter explores tachometry survey techniques, a vital tool for rapid and accurate distance and elevation measurements in road construction projects.

1.1 Tachometry Survey

Tachometry survey is a rapid surveying method that combines angular and stadia measurements to determine horizontal distances and elevations without the need for chaining or taping. It is especially useful in building technology for road surveys where quick and accurate data collection over uneven terrain is critical. Tachometry allows surveyors to efficiently map out road alignments, slopes, and gradients, which are essential for designing safe and cost-effective roads. In Kenya, tachometry is widely applied in county governments and private construction firms to expedite road project planning and monitoring.

1.1.1 Principles of Tachometry Survey

Tachometry survey is based on measuring horizontal angles, vertical angles, and stadia intervals using a theodolite equipped with a stadia diaphragm. The method relies on the principle that the horizontal distance to a staff can be computed from the stadia intercept and the instrument constants. It enables simultaneous determination of distance and elevation differences, reducing field time compared to conventional chaining and leveling.

Components of Tachometry Measurement

• Horizontal Angle Measurement: Determines the angular direction of the target staff relative to a reference direction, critical for plotting road alignments.
• Vertical Angle Measurement: Measures the angle of elevation or depression to the staff, used to compute height differences along slopes.
• Stadia Intercept: The difference between the upper and lower stadia hair readings on the leveling staff, which correlates to the distance.
• Instrument Constants: Two constants, the multiplying constant (usually 100) and the additive constant (usually zero or a small correction), are used in distance calculation.
• Staff Reading: The actual readings taken on the graduated staff at the stadia hairs, which are essential for computing distances and elevations.

Tachometry combines these measurements so that horizontal distances and height differences are calculated directly from the angles and stadia readings, enabling efficient data collection during road surveys.

1.1.2 Equipment Used in Tachometry Survey

The theodolite must be carefully set up on a tripod over a known point and precisely levelled using the instrument’s leveling screws and the plumb bob. The levelling staff is held vertically at the target points along the road alignment. Accurate readings of stadia hairs and angles are taken and recorded immediately for calculation.

1.1.3 Procedure for Conducting Tachometry Survey in Road Works

Tachometry survey in road projects follows a systematic procedure to ensure accurate mapping of the terrain and road alignment. The steps below describe a typical workflow used by surveyors in Kenyan road construction sites.

1. Station Setup: Select and prepare a known survey station along the proposed road route. Set up the theodolite on a tripod directly over the station using a plumb bob and level it precisely.
2. Instrument Calibration: Check the theodolite for proper functioning, zero the horizontal circle, and ensure stadia hairs are visible and clear.
3. Targeting the Staff: Position the levelling staff vertically at the point to be surveyed along the road alignment or slope.
4. Angle Measurement: Measure and record the horizontal angle from a reference direction and the vertical angle to the staff.
5. Stadia Reading: Note the staff readings at the upper and lower stadia hairs to determine the stadia intercept.
6. Recording Data: Enter all measurements – horizontal angle, vertical angle, upper and lower stadia readings – into the field book or digital device.
7. Moving to Next Point: Relocate the staff to the next point along the road alignment and repeat the measurement process.
8. Calculations: After fieldwork, compute horizontal distances and elevation differences using the tachometry formulas.

This procedure allows surveyors to capture detailed topographical data necessary for designing road gradients, curves, and drainage features.

1.1.4 Calculations in Tachometry Survey

The key calculations in tachometry survey involve determining the horizontal distance, vertical height difference, and reduced level of points from the measured angles and stadia readings. These calculations enable the plotting of road profiles and layouts.

Formulas Used

• Horizontal Distance (D) = k × s + C
  • Where k is the multiplying constant, typically 100
  • s is the stadia intercept (difference between upper and lower stadia hair readings)
  • C is the additive constant (usually zero or small correction)
• Vertical Height Difference (Δh) = D × tan(V) + (HI - HR)
  • Where V is the vertical angle (positive for elevation, negative for depression)
  • HI is the height of instrument above the datum
  • HR is the height of the staff reading at the point

Step-by-Step Calculation Example

Suppose a theodolite set up at a station has an instrument height (HI) of 1.5 m. The stadia readings on the staff are 1.2 m (upper hair) and 0.8 m (lower hair), the vertical angle measured is +5°, and the staff is held vertically.

1. Calculate stadia intercept:
   s = 1.2 - 0.8 = 0.4 m
2. Calculate horizontal distance:
   D = 100 × 0.4 + 0 = 40 m
3. Calculate vertical height difference:
   Δh = 40 × tan(5°) + (1.5 - 0)
   tan(5°) ≈ 0.0875
   Δh = 40 × 0.0875 + 1.5 = 3.5 + 1.5 = 5.0 m

The reduced level (RL) of the point can then be found if the RL of the instrument station is known by adding or subtracting Δh accordingly.

This method allows quick determination of distances and elevations essential for road design, especially over uneven terrain.

Chapter Summary

This chapter focused on essential techniques for conducting road surveys, beginning with tachometry survey, which involves rapid measurement of distances and elevations using specialized instruments to efficiently gather field data. It then explored the scaling of survey maps and photographs, emphasizing the importance of accurately converting measurements from maps or aerial images to real-world dimensions to ensure precision in planning and design. The chapter also covered the process of setting circular curves, detailing the geometric principles and procedures necessary to establish smooth, safe road alignments that accommodate vehicle turning requirements. Finally, it examined the plotting of traverse details, which involves accurately recording and representing a series of connected survey lines to create reliable frameworks for further road design and construction activities. Each topic built upon the previous to provide a comprehensive understanding of the practical and theoretical aspects of road surveying.