UNIT 3 PART 1

Pacing

• Definition: Measuring distances by counting the number of normal steps or paces.

• Key Relationships:

  • $1\text{ step} = 1\text{ pace}$

  • $1\text{ stride} = 2\text{ paces}$

• Pacing Formulas:

  • $\text{Pace Factor (PF)} = \frac{\text{Known Length}}{\text{Mean Number of Paces}}$

  • $\text{Paced Distance (PD)} = \text{Pace Factor} \times \text{Mean Number of Paces}$

  • $\text{Relative Precision (RP)} = \frac{|\text{Tape Distance} - \text{Pace Distance}|}{\text{Tape Distance}}$

• Factors Affecting Pace Length:

  • Speed of pacing

  • Roughness of ground

  • Weight of clothing and shoes

  • Fatigue of the pacer

  • Slope of terrain (going downhill produces fewer steps)

  • Age and sex of individual

• Mechanical Counters:

  • Passometer: Automatically registers the number of paces.

  • Pedometer: Automatically calculates distance based on an input pace factor.

Taping

• Definition: Measuring horizontal distances by stretching a calibrated tape between two points.

• Composition of Taping Party:

  1. Head Tapeman: Carries the forward end of the tape and holds the zero mark.

  2. Rear Tapeman: Holds the trailing end of the tape at the starting point.

  3. Recorder: Records distance measurements and field notes.

  4. Flagman: Directs alignment and marks measured points.

• Types of Tapes:

  • Steel Tape: Standard surveying tape; prone to corrosion.

  • Invar Tape: Made of $35\%$ nickel and $65\%$ steel; has a very low coefficient of thermal expansion, but is expensive.

  • Lovar Tape: Properties and cost fall between steel and Invar tapes.

  • Other Tapes: Linen/cloth, non-metallic, fiberglass, wires, builder's, phosphor bronze, and nylon-coated steel tapes.

• Standard Conditions for Steel Tapes:

  • Temperature: $20\,^\circ\text{C}$ ($68\,^\circ\text{F}$)

  • Pull/Tension: $50\,\text{N}$ ($10\,\text{lbs}$)

  • Support: Supported throughout its entire length.

Taping Errors & Slope Corrections

• Sources of Taping Errors: Incorrect tape length, temperature variation, non-standard pull, sag due to weight/wind, poor alignment, tape not horizontal, improper plumbing, faulty marking, and incorrect reading.

• Slope Taping Formulas:

  • Horizontal distance ($d$) from slope distance ($s$):
    $d = s \cdot \cos(\theta)$
    $d = \sqrt{s^2 - h^2}$

  • Slope Corrections ($C_h$) (Always subtracted from slope distance):

  • Gentle Slope ($\theta < 11.31^\circ$):
    $C_h = \frac{h^2}{2s}$

  • Steep Slope ($11.31^\circ \le \theta \le 16.7^\circ$):
    $C_h = \frac{h^2}{2s} + \frac{h^4}{8s^3}$

  • Very Steep Slope ($\theta > 16.7^\circ$):
    $C_h = s(1 - \cos(\theta))$

Taping Corrections

• Incorrect Tape Length Correction ($C_l$):

  • Tape Correction: $C = \text{True Length} - \text{Nominal Length}$

  • Total Correction: $C_l = C \times \frac{\text{Measured Length}}{\text{Nominal Length}}$

  • Application Rules:

  • Measuring: If tape is too long, add ($+$); if too short, subtract ($-$).

  • Laying Out: If tape is too long, subtract ($-$) ; if too short, add ($+$).

• Temperature Correction ($C<em>t$):
  $C</em>t = \alpha \cdot L \cdot (T<em>m - T</em>s)$

  • $\alpha$ = Coefficient of thermal expansion ($0.0000116\,^\circ\text{C}^{-1}$ for steel)

  • $L$ = Measured length

  • $T_m$ = Measurement temperature

  • $T_s$ = Standard temperature ($20\,^\circ\text{C}$)

• Pull Correction ($C<em>p$):
  $C</em>p = \frac{(P<em>m - P</em>s)L}{AE}$

  • $P_m$ = Applied pull during measurement

  • $P_s$ = Standard pull ($50\,\text{N}$)

  • $A$ = Cross-sectional area of tape

  • $E$ = Modulus of elasticity

• Sag Correction ($C<em>s$) (Always subtracted):
  $C</em>s = \frac{W^2 L}{24 P^2} = \frac{w^2 L^3}{24 P^2}$

  • $W$ = Total unsupported weight of tape

  • $w$ = Weight per unit length ($W = w \cdot L$)

  • $P$ = Applied tension/pull

• Normal Tension ($P_n$):

  • The tension required to equate pull elongation with sag shortening ($C<em>p = C</em>s$), eliminating the combined error of sag and pull.