Cálculo de DISTANCIA horizontal, vertical y DESNIVEL con 2 ÁNGULOS en una misma mira con TEODOLITO

Summary

The video demonstrates how to calculate the horizontal distance, vertical distance, target-point elevation, and difference in elevation using a theodolite and two observations of the same stationary leveling rod.

Because the rod remains at the same point, both observations refer to the same target elevation and horizontal distance. The vertical distances differ because the observations use different angles and middle-wire readings.

Given information

• Elevation of the instrument’s line of sight: 37.36 m
• Instrument height: 1.50 m
• Instrument station elevation: 35.86 m
• Observation 1
  • Zenith angle: 85° 46′ 30″
  • Middle-wire reading: 1 m
  • Elevation angle: 4° 13′ 30″
• Observation 2
  • Zenith angle: 84° 01′ 40″
  • Middle-wire reading: 3 m
  • Elevation angle: 5° 58′ 20″

Method and calculations

1. Convert zenith angles to elevation angles

Subtract each zenith angle from 90°:

• (90° - 85°46′30″ = 4°13′30″)
• (90° - 84°01′40″ = 5°58′20″)

2. Express the target elevation

For an elevation angle (\alpha), the vertical rise is:

[ V = D\tan(\alpha) ]

where (D) is the horizontal distance.

The target elevation is the instrument-axis elevation plus the vertical rise, minus the middle-wire reading:

[ \text{Target elevation} = 37.36 + D\tan(\alpha) - \text{rod reading} ]

3. Set the two target-elevation expressions equal

Since the rod is stationary, both observations must give the same target elevation:

[ 37.36 + D\tan(4°13′30″) - 1 = 37.36 + D\tan(5°58′20″) - 3 ]

Solving for the horizontal distance, the video reports:

[ D \approx 65.062\text{ m} ]

4. Calculate the vertical rises

• First angle: approximately 4.8006 m
• Second angle: approximately 6.806 m

5. Calculate the target-point elevation

Using either observation, the video reports a target elevation of approximately 41.160 m. Small differences when using rounded intermediate values are attributed to rounding in the presentation.

6. Calculate the difference in elevation

The video reports a difference of approximately 5.606 m, later rounded to about 5.600 m.

Note on the subtitles

Some figures in the auto-generated subtitles appear inconsistent. The stated station elevation (35.86 m) and target elevation (41.160 m) differ by 5.300 m, not the reported 5.606 m. Therefore, the reported elevation difference does not match those two listed elevations.

Speakers and sources

• Speaker: One unnamed presenter/instructor explaining the surveying calculation
• Source/channel: Estudio Facil