Naval Architecture, Ship Propulsion & Noon-Report Performance
Marine Propeller Apparent vs True Wake Slip Formula
Calculate Theoretical Screw Pitch Velocity V_p (m/s), Ship Speed Over Water V_s (m/s), Bridge Noon-Report Apparent Slip (%), and Hydrodynamic True Slip (%) inside the Taylor Stern Wake.
Why a ship can log NEGATIVE Apparent Slip in following seas—yet True Slip inside the stern wake w is ALWAYS positive!
A ship propeller of geometric face pitch P (m/rev) turning at shaft speed N (RPM) advances theoretically through a solid nut at Pitch Velocity V_p = (P * N) / 60 m/s. Comparing V_p against Ship GPS/Log Speed V_s = Knots * (1,852 / 3,600) m/s defines Bridge Noon-Report Apparent Slip S_app = ((V_p - V_s) / V_p) * 100! However, the propeller operates behind the hull inside a dragged boundary-layer wake where water inflows slower at Advance Velocity V_a = V_s * (1 - w), governed by Taylor Wake Fraction w (0.20–0.35 on full-bodied tankers/bulkers)! Consequently, True Hydrodynamic Slip S_true = ((V_p - V_a) / V_p) * 100 = (1 - (1 - S_app/100) * (1 - w)) * 100 is substantially higher than Apparent Slip—and tracking rising S_true flags barnacle hull fouling early!
Verify on a Panamax Container/Cargo Vessel Noon Report—Propeller_Pitch P = 5.20 m (B2), Shaft_RPM N = 105.0 RPM (B3 -> Pitch Speed V_p = 9.10 m/s in E2), Ship_Speed = 16.0 knots (B4 -> V_s = 8.23 m/s in E3), and Taylor_Wake_Fraction w = 0.22 (B5): Apparent Slip is only 9.55% (E4), whereas True Hydrodynamic Slip seen by the propeller blades hits 29.45% (E5)!
| Propeller Slip Noon-Report KPI (Pitch=5.2 m, 105 RPM, 16.0 kn, Wake w=0.22) | Formula | Verified Output |
|---|---|---|
| Theoretical Pitch Speed Vp (m/s) | (Propeller_Pitch_m * Shaft_RPM) / 60 | 9.10 m/s |
| Ship Speed Over Water Vs (m/s) | Ship_Speed_Knots * (1852 / 3600) | 8.23 m/s (7.20 m/s @ 14.0 kn) |
| Apparent Slip S_app (%) | ((Vp - Vs) / Vp) * 100 | 9.55% (20.85% @ 14.0 kn fouled) |
| True Wake-Adjusted Slip (%) | ((Vp - Vs * (1 - Wake_w)) / Vp) * 100 | 29.45% (38.27% @ 14.0 kn fouled!) |
Taylor-Wake True Hydrodynamic Propeller Slip Formula
Validate Pitch P > 0.5 m, Shaft_RPM > 0, Ship_Knots > 0, and Taylor_Wake_Fraction w in [0, 0.55]!
=LET(pt_m, B2, rp_m, B3, kn_s, B4, wk_w, B5, IF(OR(pt_m <= 0.5, rp_m <= 0, kn_s <= 0, wk_w < 0, wk_w > 0.55), "Invalid Propulsion Input", LET(vp_m, (pt_m * rp_m) / 60, vs_m, kn_s * (1852 / 3600), va_m, vs_m * (1 - wk_w), ROUND(((vp_m - va_m) / vp_m) * 100, 2))))Hull Biofouling / Head-Sea Speed Loss Slip Surge Check (Set Ship Speed = 14.0 Knots)
Hold Shaft_RPM constant at 105 RPM while hull fouling / head seas slow Ship_Speed B4 from 16.0 to 14.0 knots (V_s = 7.20 m/s in E3): Apparent Slip E4 more than doubles to 20.85% and True Propeller Slip E5 surges to 38.27%—increasing cavitation risk on blade suction faces!
=IF(ISTEXT(E5), E5, LET(vp_m, (B2 * B3) / 60, vs_m, B4 * (1852 / 3600), ROUND(((vp_m - vs_m) / vp_m) * 100, 2)))Try the example
Use the original values or change them to test your understanding.