Lecture 2 Medium

Trigonometric Leveling

• Trigonometric leveling determines elevation differences by measuring the inclined slope distance (or horizontal distance) and the zenith (or altitude) angle between points.
• ΔH (difference in elevation) = S * cos Z, where S is the slope distance and Z is the zenith angle (converted to decimal degrees).
• ΔH = H * cot Z (using horizontal distance).
• Zenith angle is the vertical angle, measured from the horizontal, to the target sighted. It starts at 0° (directly above the instrument) and increases as the scope is rotated.
• A zenith angle less than 90° indicates an uphill sight.
• A zenith angle equal to 90° indicates a horizontal sight.
• A zenith angle greater than 90° indicates a downhill sight.
• Instrument and rod height must be equal to eliminate further calculations.
• Curvature and refraction corrections are needed to improve accuracy (especially for longer distances).
• ΔH = SD * cos Z + 0.0206 * (SD/1000)* (sin Z)^2
• This formula is used to correct for curvature and refraction when slope distance (SD) is greater than 1000 ft.
• To increase accuracy, calculate difference in elevation from lower point to higher point and a second time from higher point to lower point.
• Average the calculations to minimize error.

Converting Units

• Convert angles from degrees, minutes, and seconds (DMS) to decimal degrees (DD).
• Example: 88° 46' 38" = 88.77722222°
• To convert from decimal degrees to DMS:
  • Find the whole-number degrees.
  • Multiply the decimal portion by 60 to get minutes.
  • Multiply the decimal portion of the minutes by 60 to get seconds.

Altitude Angles

• Altitude angle = 90°–Zenith angle
• ΔH = H * tan α

Level Vials

• Level vials (tube or circular) are glass tubes filled with a liquid (sensitive alcohol) which levels when horizontal.
• Level vial radius of curvature determines sensitivity (larger radius = higher sensitivity).
• In a bull's-eye level vial when the bubble is centered it means the line of sight is horizontal.

Explore the fundamentals of trigonometric leveling, a technique used to determine elevation differences through inclined slope distances and zenith angles. This quiz covers essential formulas, angle interpretations, and corrections for accuracy in measurements.