Estimate lift, resistance and power for a prismatic hard-chine hull at a user-specified running trim and mean wetted length.
This page checks an entered running condition; it does not solve equilibrium trim or wetted length.
Total Resistance RT: — kN
Effective Power PE: — kW
Delivered Power PD: — kW
Pressure / Trim Drag Rp: — kN
Friction Force Rf: — kN
Predicted Hydrodynamic Lift L: — kN
Vessel Weight W: — kN
Lift-to-Weight Ratio L/W: —
Savitsky Lift Coefficient CLβ: —
Smooth ITTC Coefficient Cf,0: —
Applied Friction Coefficient Cf: —
Reynolds Number: —
Beam Speed Coefficient CV: —
Mean Wetted-Length Ratio λ: —
This calculation checks a user-specified planing attitude. Savitsky lift is evaluated from the entered trim, beam, deadrise and mean wetted length. Friction is estimated with the ITTC-1957 line. The calculator does not solve vertical and longitudinal equilibrium automatically. L/W near 1.00 is a necessary vertical-force consistency check, but it is not sufficient to establish full running equilibrium; trim and wetted length are not altered to force the ratio to 1.00. PE is tow-force power based on the calculated resistance. PD uses the entered overall propulsive efficiency and is not automatically engine brake power; no separate mechanical, gearbox, shaft or service margins are added.
The Savitsky relations describe the hydrodynamic lift and resistance of prismatic hard-chine planing surfaces. This calculator evaluates the trim angle and mean wetted length entered by the user. It calculates the corresponding lift coefficient, hydrodynamic lift, frictional resistance, pressure or trim drag, effective power and delivered power.
The input geometry represents a prismatic V-bottom planing surface with chine beam b, mean wetted length lm, deadrise β and running trim τ. The method first evaluates the Savitsky lift coefficient and predicted lift. It then calculates smooth-water friction using the ITTC-1957 correlation line and combines the horizontal lift component with the horizontal friction component.
The entered displacement mass is converted to vessel weight and compared with the calculated hydrodynamic lift. The calculator does not modify the entered trim or wetted length to make these forces equal.
The dimensionless ratio λ relates mean wetted length to chine beam. The beam speed coefficient CV expresses speed relative to the gravitational scale based on beam.
In these empirical lift equations, τ and β are inserted in degrees. Radian values are used only inside trigonometric functions elsewhere in the calculation.
For a steady condition supported primarily by hydrodynamic lift, calculated lift would normally be expected to be reasonably close to vessel weight. A large difference indicates that the entered trim, speed, displacement and wetted geometry are not mutually consistent within this simplified calculation.
Even when L/W = 1.00, longitudinal moment equilibrium remains untested. A complete Savitsky equilibrium calculation also needs information such as longitudinal centre of gravity, vertical centre of gravity and thrust-line geometry.
The calculator treats ΔCf as a direct user-entered addition to the smooth ITTC-1957 coefficient. It is not a built-in prediction of hull roughness, fouling or correlation allowance.
The wetted-area expression is a mean-length approximation. It does not separately calculate keel wetted length, chine wetted length or the triangular forward wetted region.
Effective power PE is the power associated with the calculated horizontal resistance. Delivered power PD depends directly on the propulsive efficiency entered by the user.
| Symbol | Meaning | Unit |
|---|---|---|
| V | Vessel speed | m/s |
| b | Chine beam | m |
| lm | Mean wetted length | m |
| λ | Mean wetted-length to beam ratio | dimensionless |
| CV | Beam-based speed coefficient | dimensionless |
| τ | Running trim angle | degrees |
| β | Bottom deadrise angle | degrees |
| ρ | Water density | kg/m³ |
| ν | Water kinematic viscosity | m²/s |
| W | Vessel weight | N |
| L | Predicted hydrodynamic lift | N |
| CLβ | Deadrise-corrected Savitsky lift coefficient | dimensionless |
| Re | Reynolds number based on mean bottom velocity and wetted length | dimensionless |
| Cf,0 | Smooth ITTC-1957 coefficient | dimensionless |
| ΔCf | User-entered friction allowance | dimensionless |
| Rp | Horizontal pressure or trim drag | N |
| Rf | Friction-force magnitude along the bottom | N |
| RT | Total calculated horizontal resistance | N |
| PE | Effective power | kW |
| PD | Delivered power | kW |
Evaluate a planing condition with:
Convert speed:
V = 30 × 0.514444 = 15.433 m/s
Calculate dimensionless geometry and speed:
λ = 5.50 / 3.20 = 1.71875
CV = 15.433 / √(9.80665 × 3.20) = 2.755
Calculate lift coefficients:
CL0 = 0.085181
CLβ = 0.058488
Calculate lift and weight:
L = 0.5 × 1025 × 15.433² × 3.20² × 0.058488 = 73.111 kN
W = 7.4552 × 1000 × 9.80665 = 73.111 kN
L/W = 73.111 / 73.111 = 1.000
Calculate friction:
Vm = 15.215 m/s
Re = 15.215 × 5.50 / (1.19 × 10−6) = 7.032 × 107
Cf,0 = 0.002194
Cf = 0.002194 + 0.000400 = 0.002594
S = 3.20 × 5.50 / cos 18° = 18.506 m²
Rf = 5.859 kN
Calculate pressure drag, total resistance and power:
Rp = 73.111 × tan 4° = 5.112 kN
RT = 5.112 + 5.859 × cos 4° = 10.957 kN
PE = 10.957 × 15.433 = 169.11 kW
PD = 169.11 / 0.60 = 281.85 kW
L/W is the first consistency check. A result well below 1.00 means the calculated hydrodynamic lift is lower than the entered vessel weight. A result well above 1.00 means the entered geometry and attitude produce more calculated lift than the entered weight.
This difference should not be corrected by changing displacement merely to obtain a convenient ratio. Instead, check whether speed, running trim, deadrise, beam and mean wetted length represent the same operating condition.
The resistance result represents the horizontal force calculated for the entered attitude. It excludes several components that may be material on a real craft, including appendage drag, aerodynamic drag, spray drag, trim-tab drag, propulsor–hull interaction and added resistance in waves.
The underlying Savitsky lift relation is intended for prismatic hard-chine planing surfaces. The calculator displays extrapolation warnings when the entered condition falls outside the implementation checks of:
These warnings are method-applicability notices, not vessel-acceptance limits.
The calculation does not account for:
This calculator is intended for preliminary educational and engineering checks. It does not replace an approved powering analysis, loading computer, model test, CFD study, classification review or vessel trial.