Wave propulsion hull

A Vessel/WaveHull driven by one propeller and one rudder behind it.

Collaboration diagram for Wave propulsion hull:

Everything of Vessel/WaveHull (states, waves, parameters, outputs, visualization) plus the loads of a propeller turning at PropellerSpeed and a rudder at RudderAngle, both on the centreline. The inputs act directly (no servo or engine dynamics).

Propeller

The open-water thrust coefficient is K_T(J) = KT0 + KT1 J + KT2 J^2 with the advance ratio J = u_P / (n D) and the inflow u_P = (1 - WakeFraction) u. Multiplied out, so it stays finite at n = 0:

T = Rho D^4 KT0 n|n| + Rho D^3 KT1 |n| u_P + Rho D^2 KT2 sign(n) u_P^2

The hull feels (1 - ThrustDeduction) T in surge and the pitch moment PropellerZ T. The polynomial describes the first quadrant (n >= 0, u >= 0); outside it the thrust is an extrapolation.

Rudder

The MMG normal-force model. The rudder sits in the slipstream, whose speed at the rudder follows from actuator-disc theory:

u_R = u_P + SlipstreamFactor (sqrt(u_P^2 + 8 T / (Rho pi D^2)) - u_P)   (T > 0; else u_P)
v_R = v + RudderX r

With U_R^2 = u_R^2 + v_R^2, the angle of attack alpha_R = delta + atan(v_R / u_R) and Fujii's lift slope f_alpha = 6.13 Lambda / (Lambda + 2.25) of the aspect ratio Lambda, the normal force is F_N = Rho / 2 RudderArea f_alpha U_R^2 sin(alpha_R), and on the hull

X_R = -F_N sin(delta)
Y_R = -(1 + HullInteraction) F_N cos(delta)
N_R = -(RudderX + HullInteraction x_H) F_N cos(delta),   x_H = -0.45 Length
K_R =  RudderZ F_N cos(delta),   M_R = -RudderZ F_N sin(delta)

A positive RudderAngle turns the vessel to starboard (positive yaw rate) and heels it to starboard when the rudder is below the CG. There is no stall: the force follows sin(alpha_R) at any angle.

Model notes

• Positions are from the CG: x forward, z down. The defaults put the propeller and the rudder at the aft end of the waterplane, half the draught below the CG.
• The Jacobian of the loads with respect to (u, v, r) is exact (automatic differentiation), with PropellerSpeed and RudderAngle held at their values at the start of the step.

Example configuration excerpt

<Lib
  LibName               = "marine_elements"
  SimObject             = "Vessel/WavePropulsionHull"
  Name                  = "Boat"
  Length                = "20"
  Breadth               = "6"
  Mass                  = "150000"
  RollInertia           = "6.0e5"
  PitchInertia          = "4.5e6"
  YawInertia            = "4.5e6"
  GMT                   = "0.8"
  GML                   = "25"
  RollQuadraticDamping  = "2.0e5"
  SurgeQuadraticDamping = "1.5e3"
  PropellerDiameter     = "1.4"
  KT0                   = "0.45"
  KT1                   = "-0.35"
  KT2                   = "-0.1"
  WakeFraction          = "0.2"
  ThrustDeduction       = "0.15"
  RudderArea            = "1.5"
  RudderAspectRatio     = "1.5"
/>
...
<Connection
  Boat.PropellerSpeed = "4"
  Boat.RudderAngle    = "0"
/>

Input Ports

Name	Width	Description
PropellerSpeed	1	Propeller speed n [rev/s].
RudderAngle	1	Rudder angle delta [rad], positive turns to starboard.

Output Ports

Those of Vessel/WaveHull, and:

Name	Width	Description
Thrust	1	Open-water propeller thrust T [N].
RudderForce	2	Rudder surge and sway force X_R, Y_R on the hull [N].

Configuration parameters

Those of Vessel/WaveHull, and:

Name	Width	Description
PropellerDiameter	1	Propeller diameter D [m]. Required.
KT0	1	Thrust coefficient K_T at J = 0. Required.
KT1	1	Linear coefficient of K_T(J). Required.
KT2	1	Quadratic coefficient of K_T(J). Required.
WakeFraction	1	Wake fraction w (Default: 0).
ThrustDeduction	1	Thrust deduction t (Default: 0).
PropellerX	1	Propeller position forward of the CG [m] (Default: Lcf - Length / 2).
PropellerZ	1	Propeller position below the CG [m] (Default: draught / 2).
RudderArea	1	Rudder area A_R [m^2]. Required.
RudderAspectRatio	1	Rudder aspect ratio Lambda (span^2 / area). Required.
RudderX	1	Rudder position forward of the CG [m] (Default: PropellerX).
RudderZ	1	Rudder position below the CG [m] (Default: PropellerZ).
HullInteraction	1	Hull-rudder interaction factor a_H (Default: 0).
SlipstreamFactor	1	Fraction of the slipstream acceleration reached at the rudder (Default: 0.5).

Full example file

<Contents>
   <!--
   Three WavePropulsionHull hulls of 12, 20 and 40 m in a 1.5 m irregular sea, drawn in the ocean
   of the environment.
 
   The sea is a JONSWAP spectrum, mean period 6 s, travelling south (MainDirectionDeg 180). Each
   hull steams in a turning circle, so it stays in view and meets the waves from every direction:
   the 12 and 40 m hulls to starboard, the 20 m hull to port.
 
   The 12 and 40 m hulls are the 20 m workboat Froude-scaled by 0.6 and 2: lengths, GM and the
   propeller diameter scale by s, areas and the resistance by s^2, mass by s^3, inertias and
   RollQuadraticDamping by s^5, and the propeller speed by s^-1/2. Each starts at about its
   straight-course speed. Added mass and the sway and yaw damping take their defaults.
   SampleLevel grows with the length so the sample spacing stays below the shortest waves with
   energy (about 6 m; see "Short waves" in the WaveHull documentation).
 
   The live view needs a visualization build and the <Visualization> observer below;
   simulationSpeed="1" runs it in real time. The camera starts at NED (-30, 0, 0) looking north
   towards the hulls.
   -->
   <OBJECTS>
      <Lib
         LibName               = "marine_elements"
         SimObject             = "Vessel/WavePropulsionHull"
         Name                  = "Small"
         Length                = "12"
         Breadth               = "3.6"
         Mass                  = "32400"
         RollInertia           = "46656"
         PitchInertia          = "349920"
         YawInertia            = "349920"
         GMT                   = "0.48"
         GML                   = "15"
         RollQuadraticDamping  = "15552"
         SurgeQuadraticDamping = "540"
         PropellerDiameter     = "0.84"
         KT0                   = "0.45"
         KT1                   = "-0.35"
         KT2                   = "-0.1"
         WakeFraction          = "0.2"
         ThrustDeduction       = "0.15"
         RudderArea            = "0.54"
         RudderAspectRatio     = "1.5"
         HullInteraction       = "0.2"
         SampleLevel           = "2"
      />
      <Lib
         LibName               = "marine_elements"
         SimObject             = "Vessel/WavePropulsionHull"
         Name                  = "Medium"
         Length                = "20"
         Breadth               = "6"
         Mass                  = "150000"
         RollInertia           = "6.0e5"
         PitchInertia          = "4.5e6"
         YawInertia            = "4.5e6"
         GMT                   = "0.8"
         GML                   = "25"
         RollQuadraticDamping  = "2.0e5"
         SurgeQuadraticDamping = "1.5e3"
         PropellerDiameter     = "1.4"
         KT0                   = "0.45"
         KT1                   = "-0.35"
         KT2                   = "-0.1"
         WakeFraction          = "0.2"
         ThrustDeduction       = "0.15"
         RudderArea            = "1.5"
         RudderAspectRatio     = "1.5"
         HullInteraction       = "0.2"
         SampleLevel           = "3"
      />
      <Lib
         LibName               = "marine_elements"
         SimObject             = "Vessel/WavePropulsionHull"
         Name                  = "Large"
         Length                = "40"
         Breadth               = "12"
         Mass                  = "1.2e6"
         RollInertia           = "1.92e7"
         PitchInertia          = "1.44e8"
         YawInertia            = "1.44e8"
         GMT                   = "1.6"
         GML                   = "50"
         RollQuadraticDamping  = "6.4e6"
         SurgeQuadraticDamping = "6.0e3"
         PropellerDiameter     = "2.8"
         KT0                   = "0.45"
         KT1                   = "-0.35"
         KT2                   = "-0.1"
         WakeFraction          = "0.2"
         ThrustDeduction       = "0.15"
         RudderArea            = "6.0"
         RudderAspectRatio     = "1.5"
         HullInteraction       = "0.2"
         SampleLevel           = "4"
      />
      <Lib
         LibName                    = "environment"
         SimObject                  = "Environment"
         Name                       = "Environment"
         Waves.Spectrum             = "JONSWAP"
         Waves.Theory               = "Airy"
         Waves.Hs                   = "1.5"
         Waves.MeanPeriod           = "6"
         Waves.MainDirectionDeg     = "180"
         Waves.DirectionCosinePower = "10"
         Waves.NumWaves             = "40"
         Bathymetry.Depth           = "1000"
         Visual.WorldRadius         = "500"
      />
   </OBJECTS>
 
   <INTERCONNECTIONS>
      <Connection
         Small.PropellerSpeed  = "5.16"
         Small.RudderAngle     = "0.35"
         Medium.PropellerSpeed = "4"
         Medium.RudderAngle    = "-0.35"
         Large.PropellerSpeed  = "2.83"
         Large.RudderAngle     = "0.35"
      />
   </INTERCONNECTIONS>
 
   <INITIALIZATION>
      <InitialCondition
         Small.Pose      = "40,-70,0"
         Small.Velocity  = "2.42,0,0"
         Medium.Pose     = "40,40,0"
         Medium.Velocity = "3.13,0,0"
         Large.Pose      = "40,85,0"
         Large.Velocity  = "4.42,0,0"
      />
   </INITIALIZATION>
 
   <SIMULATION simulationSpeed="1">
      <Timing TStart="0" TEnd="600"/>
      <Integrator Method="RK45_i">
         <StepControl StepMax="0.05" StepMin="1e-10" AbsTol="1e-3" RelTol="1e-3"/>
      </Integrator>
   </SIMULATION>
 
   <OBSERVERS>
      <FileOutput TOutput="0, 0:0.5:600, 600" Select="objects:all"/>
      <Visualization frameRate="25"/>
   </OBSERVERS>
</Contents>

This SimObject is referred to as Vessel/WavePropulsionHull