The most important ideas are elevation, horizontal distance, vertical difference, slope, and direction. Leveling problems often use height of instrument, backsight, foresight, and reduced level to find unknown elevations. Slope and grade describe how much height changes over a run, while bearings and azimuths describe direction.
Careful units, signs, and instrument readings are essential for accurate engineering work.
Key Facts
- Height of instrument is found by HI = known elevation + backsight.
- Unknown elevation is found by elevation = HI - foresight.
- Rise or fall between two points is vertical difference = ending elevation - starting elevation.
- Percent grade is percent grade = rise / run x 100.
- Slope ratio can be written as slope = rise / run, with rise and run in the same units.
- Horizontal distance from stadia readings is approximately distance = stadia interval x stadia factor, often D = (upper reading - lower reading) x 100.
- Azimuth is measured clockwise from north from 0 degrees to 360 degrees.
- A closed level loop error is closure error = final calculated benchmark elevation - known benchmark elevation.
Vocabulary
- Benchmark
- A benchmark is a fixed point with a known elevation used as a reference in leveling.
- Backsight
- A backsight is a rod reading taken on a point of known elevation to find the height of instrument.
- Foresight
- A foresight is a rod reading taken on a point whose elevation is being calculated.
- Height of Instrument
- Height of instrument is the elevation of the line of sight through the level.
- Grade
- Grade is the steepness of a surface, usually written as a percent using rise divided by run times 100.
- Azimuth
- Azimuth is a direction angle measured clockwise from north between 0 degrees and 360 degrees.
Common Mistakes to Avoid
- Adding the foresight instead of subtracting it is wrong because an elevation is found by elevation = HI - foresight.
- Mixing feet and meters in one formula is wrong because rise, run, and distance calculations require consistent units.
- Forgetting the sign of rise or fall is wrong because a negative vertical difference means the ending point is lower than the starting point.
- Using percent grade = run / rise x 100 is wrong because grade compares vertical change to horizontal distance, so percent grade = rise / run x 100.
- Reading an azimuth counterclockwise from north is wrong because azimuths are measured clockwise from north from 0 degrees to 360 degrees.
Practice Questions
- 1 A benchmark elevation is 124.65 m and the backsight is 1.42 m. What is the height of instrument?
- 2 The height of instrument is 126.07 m and the foresight to Point A is 2.18 m. What is the elevation of Point A?
- 3 A road rises 3.6 m over a horizontal distance of 120 m. What is the percent grade?
- 4 Why is it important to use a benchmark when beginning a leveling survey?