⚓ Bollard Pull Calculator

BV Rules and Formulas - Marine Towing Calculation

Input Parameters

Calculation Results

Reynolds Number (R)
1.07e+8
Friction Coefficient (Cf)
0.002063
Hull Fouling Addition (ΔCf)
0.001650
Total Friction Coefficient (Cft)
0.004113
Wetted Surface Area (Sw)
798.45 m²
Frictional Resistance (Rf)
11,135 N
Wave Resistance (Rv)
4,419 N
Total Hydrodynamic Resistance (Rh)
15,554 N
Aerodynamic Resistance (Ra)
42,620 N
Tow Line Resistance (Rr)
0.05 N
Total Resistance (Rtot)
58,174 N
Bollard Pull Coefficient (Cef)
40.0%
Required Static Bollard Pull (Rt)
14.8 tonnes
Status
✓ Satisfied

📐 Formulas Used

  1. Reynolds Number: R = v × L / ν
  2. Friction Coefficient: Cf = 0.075 / [log₁₀(R) - 2]²
  3. Hull Fouling Addition: ΔCf = 0.008 × N × Cf
  4. Total Friction Coefficient: Cft = Cf + ΔCf + 0.0004
  5. Wetted Surface Area: Sw = 1.7 × L × T + B × L
  6. Frictional Resistance: Rf = ½ × Cft × ρsw × Sw × v²
  7. Wave Resistance: Rv = (Rv/D) × D
  8. Hydrodynamic Resistance: Rh = Rf + Rv
  9. Aerodynamic Resistance: Ra = ½ × Cx × Ch × ρair × S × Vw²
  10. Tow Line Resistance: Rr = 4.6×10⁻³ × d × v² × (l + (71.6 × Z/P))
  11. Total Resistance: Rtot = Rh + Ra + Rr
  12. Bollard Pull Coefficient: Cef = 1 - (V + Vc)/Vfr
  13. Required Static Bollard Pull: Rt = Rtot / (Cef × g)

Note: All resistance values are in Newtons (N), bollard pull values are in tonnes-force. g = 9810 N/tonne