Calculate wake fraction (wakeFraction) (dimensionless) using the Holtrop & Mennen method.

calcHMWakeFraction(
  breadth,
  wettedSA,
  maxDraft,
  nProp,
  lwl,
  propDiam,
  formFactor,
  Cf,
  Ca,
  Cbw,
  Cp,
  Cm,
  aftDraft = maxDraft,
  Cstern = 0,
  lcb = 0
)

Arguments

breadth

Moulded breadth (vector of numericals, m)

wettedSA

Wetted hull surface area (vector of numericals, m^2) (see calcHMWettedSA)

maxDraft

Maximum summer load line draft (vector of numericals, m)

nProp

Number of propellers (vector of numericals, see calcPropNum)

lwl

Waterline Length (vector of numericals, m) (see calclwl)

propDiam

Propeller diameter (vector of numericals, m) (see calcPropDia)

formFactor

Form factor (1+k) (vector of numericals, dimensionless) (see calcHMFormFactor)

Cf

Frictional resistance coefficient (vector of numericals, dimensionless) (see calcCf)

Ca

Incremental hull (roughness) resistance coefficient (vector of numericals, dimensionless) (see calcHMCa)

Cbw

Waterline block coefficient (vector of numericals, dimensionless) (see calcCbw)

Cp

Prismatic coefficient (vector of numericals, dimensionless) (see calcCp)

Cm

Midship section coefficient (vector of numericals, dimensionless) (see calcCm)

aftDraft

Aft draft (deviation from actual draft indicates trim) (vector of numericals, m)

Cstern

Afterbody form coefficient:

  • U-Shaped Hull = 10

  • Normal Hull = 0 (default)

Can supply either a vector of numericals, a single number, or rely on the default

lcb

Longitudinal position of center of buoyancy (vector of numericals, see calclcb)

Value

wakeFraction (vector of numericals, dimensionless)

Details

"The speed of advance of the propeller relative to the water in which it is working is lower than the observed speed of the vessel. This difference in speed, expressed as a percentage of the ship speed, is known as the wake fraction coefficient". https://www.wartsila.com/encyclopedia/term/wake-fraction-coefficient

Wake fraction is a component of hull efficiency as well as a component of propeller efficiency.

Actual draft is typically obtained from sources such as AIS messages or ship records.

Note: In "A Statistical Re-Analysis of Resistance and Propulsion Data", the authors re-analyze with the inclusion of Series 64 hull forms for a total of 334 models included in the analysis. They suggest an update of the single screw wake fraction equation but that the original equations should be used for twin screw ships.

Viscous resistance coefficient: Cv = (1+k) * Cf + Ca

We are assuming here that 1+k = 1+k_1 from calcHMFormFactor.

Additionally, we are assuming conventional stern for all single screw ships. Holtrop & Mennen also include an estimation for wake fraction for single screw ships with open stern for fast sailing ships, but that is not included here.

References

Holtrop, J. and Mennen, G. G. J. 1982. "An approximate power prediction method." International Shipbuilding Progress 29.

Holtrop, J. and Mennen, G. G. J. 1984. "A Statistical Re-Analysis of Resistance and Propulsion Data'.

See also

Examples

calcHMWakeFraction(c(32.25,32.20), c(10746.28,8669.7), c(13.57,11.49), c(1,1), c(218.75,209.25), c(6.7,7), c(1.27,1.18), c(0.0015,0.0014), c(0.00033,0.00035), c(0.81,0.65), c(0.81,0.67), c(0.99,0.98), c(13.57,11.49))
#> [1] 0.4427881 NA