Savitsky Planing Resistance Calculator

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.

Operating Condition

Hull Geometry
Required for the lift-to-weight consistency check.

Water and Friction Inputs
Use a value consistent with the selected water condition.
Added directly to the smooth ITTC-1957 coefficient.
Specified Running Condition Results

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 C:

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.


Report: Savitsky Planing Resistance

Savitsky Planing Hull Resistance at a Specified Running Condition

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.

Note: This is a running-condition check, not a complete equilibrium solver. It does not calculate trim, wetted length, sinkage, centre of pressure or longitudinal moment balance. A value of L/W close to 1.00 indicates approximate vertical-force consistency, but it does not by itself prove that the entered attitude is a stable or achievable operating condition.

What the calculator determines

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.

Calculation method

Speed coefficient and wetted-length ratio

Formula
λ = lm / b
CV = V / √(g b)

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.

Savitsky lift coefficient

Formula
CL0 = τ1.1 [0.012 λ0.5 + 0.0055 λ2.5 / CV2]
C = CL0 − 0.0065 β CL00.6
L = 0.5 ρ V2 b2 C

In these empirical lift equations, τ and β are inserted in degrees. Radian values are used only inside trigonometric functions elsewhere in the calculation.

Lift-to-weight comparison

Formula
W = Δ × 1000 × g
Lift-to-weight ratio = L / W

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.

Friction calculation

Formula
Vm = V √[1 − A / (λ cos τ)]
where
A = 0.012 τ1.1 √λ − 0.0065 β (0.012 √λ τ1.1)0.6
Re = Vm lm / ν
Cf,0 = 0.075 / [log10(Re) − 2]2
Cf = Cf,0 + ΔCf

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.

Resistance and power

Formula
S ≈ b lm / cos β
Rf = 0.5 ρ V2 S Cf
Rp = L tan τ
RT = Rp + Rf cos τ
PE = RT V
PD = PE / ηD

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.

Symbols and units

Symbols used by the planing-condition calculation
Symbol Meaning Unit
VVessel speedm/s
bChine beamm
lmMean wetted lengthm
λMean wetted-length to beam ratiodimensionless
CVBeam-based speed coefficientdimensionless
τRunning trim angledegrees
βBottom deadrise angledegrees
ρWater densitykg/m³
νWater kinematic viscositym²/s
WVessel weightN
LPredicted hydrodynamic liftN
CDeadrise-corrected Savitsky lift coefficientdimensionless
ReReynolds number based on mean bottom velocity and wetted lengthdimensionless
Cf,0Smooth ITTC-1957 coefficientdimensionless
ΔCfUser-entered friction allowancedimensionless
RpHorizontal pressure or trim dragN
RfFriction-force magnitude along the bottomN
RTTotal calculated horizontal resistanceN
PEEffective powerkW
PDDelivered powerkW

Worked example

Worked Example

Evaluate a planing condition with:

  • Speed: 30.00 kn
  • Running trim: 4.00°
  • Chine beam: 3.20 m
  • Mean wetted length: 5.50 m
  • Deadrise: 18.00°
  • Displacement mass: 7.4552 t
  • Water density: 1025 kg/m³
  • Kinematic viscosity: 1.19 × 10−6 m²/s
  • Friction allowance: 0.0004
  • Propulsive efficiency: 0.60

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

C = 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

How to interpret the results

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.

Input guidance

  • Enter running trim, not static trim measured while the vessel is stopped.
  • Use the chine beam associated with the approximately prismatic planing surface.
  • Enter mean wetted length for the evaluated operating condition. Do not automatically substitute overall vessel length or waterline length.
  • Use displacement mass for the same loading condition as the entered running geometry.
  • Keep water density and kinematic viscosity consistent with the assumed water temperature and salinity.
  • Set ΔCf to zero when no separate friction allowance is to be applied.
  • Enter ηD as a decimal. For example, 0.60 represents 60%.

Applicability and limitations

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:

  • 0.60 ≤ CV ≤ 13.00
  • λ ≤ 4.00
  • 2° ≤ τ ≤ 15°

These warnings are method-applicability notices, not vessel-acceptance limits.

The calculation does not account for:

  • automatic solution of trim or sinkage
  • longitudinal centre of gravity and moment equilibrium
  • vertical centre of gravity or thrust-line moment
  • warped, stepped or strongly non-prismatic bottoms
  • catamarans or tunnel hulls
  • trim tabs, interceptors or lifting appendages
  • spray and whisker-spray corrections
  • air resistance and superstructure drag
  • propeller or waterjet interaction
  • porpoising and dynamic stability
  • waves, accelerations or slamming loads
Result Check: A plausible L/W value does not verify porpoising stability, manoeuvring safety, structural loads or seakeeping. Final design and powering work should be checked against suitable model tests, validated numerical analysis, trial data or a complete recognised planing-hull calculation.

Common input errors

  • Entering trim in radians instead of degrees
  • Using overall length as mean wetted length
  • Entering displacement in kilograms instead of tonnes
  • Entering efficiency as 60 instead of 0.60
  • Combining seawater density with an unrelated viscosity value
  • Using static deadrise or beam values from a different hull station
  • Adding a large ΔCf without a defined technical basis
  • Treating L/W = 1.00 as proof of complete dynamic equilibrium

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References

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.