Surveying Quick Formula Sheet

1. Fundamental Principles & Measurements

• Scale Relation: $1 \text{ cm} = k \text{ meters}$

• Shrunk Scale: $\text{Shrunk Scale} = \text{Original Scale} \times \text{Shrinkage Factor}$

• Shrinkage Factor (SF): $\frac{\text{Shrunk Length}}{\text{Actual Length}}$

• True Length ($L$): $L = \left( \frac{l'}{l} \right) \times L'$

  (Jahan $l'$ = galat chain length, $l$ = sahi chain length, $L'$ = measured length)

2. Chain Surveying Corrections

• Temperature Correction ($C_t$): $\alpha (T_m - T_o) L$

• Pull Correction ($C_p$): $\frac{(P_m - P_o) L}{AE}$

• Sag Correction ($C_s$): $\frac{W^2 L}{24 P^2}$ (Hamesha Negative)

• Slope Correction ($C_{sl}$): $\frac{h^2}{2L}$ (Hamesha Negative)

3. Compass Surveying (Bearings)

• Fore Bearing (FB) & Back Bearing (BB): $\text{BB} = \text{FB} \pm 180^\circ$

• Magnetic Declination: $\text{True Bearing (TB)} = \text{Magnetic Bearing (MB)} \pm \text{Declination}$

  (East ke liye $+$, West ke liye $-$)

• Included Angle (Clockwise): $\text{FB of next line} - \text{BB of previous line}$

4. Levelling & Curvature

• Height of Instrument (HI): $\text{RL of BM} + \text{BS}$

• New RL: $\text{HI} - \text{IS}$ (Intermediate Sight) ya $\text{HI} - \text{FS}$ (Fore Sight)

• Curvature Correction ($C_c$): $-0.0785 D^2$ (meters mein)

• Refraction Correction ($C_r$): $+0.0112 D^2$ (meters mein)

• Combined Correction ($C$): $-0.0673 D^2$ (meters mein, $D$ is in km)

5. Tacheometry (Distance & Elevation)

• Horizontal Distance ($D$): $ks + c$

  • Multiplicative Constant ($k$): $f/i$ (Target value = 100)

  • Additive Constant ($c$): $f+d$ (Anallatic lens ke liye = 0)

• Staff at Angle $\theta$ (Horizontal): $D = ks \cos^2 \theta + c \cos \theta$

6. Area & Volume Calculation

• Trapezoidal Rule (Area): $A = \frac{d}{2} [ (O_1 + O_n) + 2(O_2 + O_3 + ... + O_{n-1}) ]$

• Simpson’s 1/3rd Rule (More Accurate): $A = \frac{d}{3} [ (\text{First} + \text{Last}) + 4(\sum \text{Even}) + 2(\sum \text{Odd}) ]$

  (Note: Simpson's rule ke liye offsets ki sankhya hamesha Odd honi chahiye)