Open-water propeller performance from the classic MARIN Wageningen B-series regression. The workhorse first-pass tool for screw-propeller selection.
Formula
$$ K_T = \frac{T}{\rho n^2 D^4}, \quad K_Q = \frac{Q}{\rho n^2 D^5}, \quad \eta_O = \frac{J \cdot K_T}{2\pi K_Q} $$
Symbol legend
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $K_T$ | Thrust coefficient | - | Oosterveld & van Oossanen |
| $K_Q$ | Torque coefficient | - | Oosterveld & van Oossanen |
| $\eta_O$ | Open-water efficiency | - | result |
| $J$ | Advance ratio $V_A / (n D)$ | - | derived |
| $T$ | Thrust | kN | result |
| $Q$ | Shaft torque | kN·m | result |
| $\rho$ | Sea-water density | kg / m³ | 1025 default |
| $n$ | Shaft rotation rate | rev / s | engine / gearbox |
| $D$ | Propeller diameter | m | propeller drawing |
| $P/D$ | Pitch ratio | - | propeller drawing |
| $A_E/A_O$ | Expanded area ratio | - | propeller drawing |
| $Z$ | Number of blades | - | propeller drawing |
The B-series covers $Z = 2..7$, $P/D = 0.5..1.4$, $A_E/A_O = 0.30..1.05$. KT is a 39-term polynomial and KQ a 47-term polynomial in J, P/D, A_E/A_O, Z; see Oosterveld & van Oossanen (1975) for the full table.
Typical operating ranges
- Tanker / bulker: D = 7–9 m, P/D = 0.65–0.75, $A_E/A_O$ = 0.50–0.60, 4 blades, $\eta_O$ ≈ 0.55–0.60.
- Container: D = 8–10 m, P/D = 0.9–1.1, $A_E/A_O$ = 0.65–0.80, 5 blades, $\eta_O$ ≈ 0.60–0.65.
- Ro-Pax: D = 5–7 m, P/D = 0.9–1.1, 4–5 blades, $\eta_O$ ≈ 0.58–0.62.
Sources
- Oosterveld & van Oossanen - Wageningen B-series polynomials (International Shipbuilding Progress, 1975).
- MARIN - Wageningen Propeller Series.
- Carlton - Marine Propellers and Propulsion.