Marine Propeller

Propeller that converts rotation into thrust in marine environments

Since R2021b

• 

Libraries:
Simscape / Driveline / Engines & Motors

Description

The Marine Propeller block represents a propeller that converts a rotational mechanical motion into thrust for marine applications. You can configure the propeller with fixed or controllable blades. You can parameterize the propeller by using constants, polynomials, or tabulated data to characterize the thrust and torque coefficients. You can provide tabulated advance velocity data, or you can provide tabulated advance angle data to parameterize all four operational quadrants. Propellers that allow negative pitch or that can operate in reverse may include thrust and torque coefficient curves specific to the astern direction, which you can also specify in the block.

You can also include the wake effects of the vessel hull in the block. When you specify a constant wake fraction or enable a physical signal port, and the block calculates the wake effects automatically.

You can use a physical signal to control the blade pitch.

This terminology is helpful for understanding the block:

• Wake fraction is the difference between the vessel velocity and the advance velocity expressed as a ratio of the vessel velocity.

• Advance velocity is the speed of the flow through the propeller, V_a.

• Advance ratio is the speed of the flow through the propeller with respect to the propeller tip angular speed expressed as a ratio. The block uses this to determine k_T and k_Q when you set Parameterization to Polynomial fit or Tabulated data for advance ratio.

• Advance angle is the angular location of the propeller operational conditions on a four quadrant plot. The block uses this to determine C_T and C_Q when you set Parameterization to Tabulated data for advance ratio.

• Quadrant is the relative two-dimensional location of the propeller operating condition where the vertical axis is V_a and the horizontal axis is ω.

• Pitch is the ideal translational propeller advance distance for a single revolution.

• Open water is when the effects of the hull are not present.

The block equations refer to these quantities:

• T is the propeller thrust.

• Q is the propeller torque.

• ρ is the fluid density. You can specify the fluid density using the Density parameter or the Rho port.

• P is the pitch.

• D is the Propeller diameter parameter, where one represents

• ω is the propeller angular speed input at port R. For more information about using angular units in Simscape™, see Angular Units.

• n is the propeller angular speed in revolutions per second, which consistently nondimensionalizes the torque and thrust. The block defines ω = 2πn.

• n_Thr is the Rotational speed threshold parameter.

• ε is the Propeller direction parameter.

• k_T is the thrust coefficient with respect to the propeller rotational speed.

• k_Q is the resistive torque coefficient with respect to the propeller rotational speed.

• p_kT is the polynomial thrust coefficient vector or 2-D matrix.

• p_kQ is the polynomial resistive torque coefficient vector or 2-D matrix.

• C_T is the thrust coefficient with respect to the relative advance velocity.

• C_Q is the torque coefficient with respect to the relative advance velocity.

• k_Thr is the Saturation threshold for nondimensional coefficients parameter.

• J is the advance ratio.

• V_a is the advance velocity. Specify the advance velocity using the Va port.

• V_R is the relative advance velocity at a blade section at 70% of the blade radius.

• η is the efficiency.

• C_T^* is the thrust coefficient based on the blade relative advance velocity at 70% blade radius.

• C_T,TLU^* is the reference thrust coefficient vector or 2-D matrix.

• C^*_Q is the torque coefficient based on the blade relative advance velocity at 70% blade radius.

• C^*_Q,TLU is the reference torque coefficient vector or 2-D matrix.

• β is the advance angle.

• β_TLU is the reference advance angle.

Parameterizations

The propeller performance depends on the thrust and resistive torque coefficients. The Parameterization parameter gives you different options to control these coefficients. The propeller output depends on the quadrant where the propeller operates. The block defines the four quadrants as:

• First quadrant: +V_a, +n

• Second quadrant: +V_a, -n

• Third quadrant: -V_a, -n

• Fourth quadrant: -V_a, +n

The figure shows a visual representation of the quadrants.

When you set Parameterization to Constant coefficients, you specify the thrust and resistive torque coefficients directly. Otherwise, the block computes these coefficients depending on the Parameterization setting.

Advance Ratio

When you set Parameterization to Polynomial fit or Tabulated data for advance ratio, the block uses the advance ratio, J. The block uses a numerically smoothed version of the fundamental thrust and torque equations such that

$$\begin{array}{l}T=k_T\rho D^{4}n\sqrt{n^2+n_{thr}^2}\\ Q=k_Q\rho D^{5}n\sqrt{n^2+n_{thr}^2}\end{array}$$

The block defines the advance ratio as

$$J=\frac{V_a\epsilon n}{D(n^2+n_{Thr}^2)},$$

where the angular speed threshold n_Thr linearizes the propeller rotational speed, n, for smoothing.

When you set Parameterization to:

• Polynomial fit — k_T and k_Q vary with time according to the values you specify for the polynomial coefficient parameters. The block saturates J to be between 0 and the first positive root of the polynomial and restricts k_T and k_Q to always be positive. The block calculates the thrust and torque coefficients as

  $$\begin{array}{l}{k}_T={\displaystyle \sum _{j=1:N}^N{p}_{kT,j}{J}^j}\\ k_Q={\displaystyle \sum _{j=1:N}^N{p}_{kQ,j}{J}^j}\end{array}$$

  where p_kT and p_kQ represent the polynomial coefficients.

• Tabulated data for advance ratio — You specify tabulated values for k_T and k_Q for given values of J or J and P/D, depending on the Blade pitch type parameter.

This basis of the propeller efficiency is the fundamental relationship

$$\eta =\frac{Powe{r}_{out}}{Powe{r}_{in}}=\frac{T{V}_A}{2\pi nQ}=\frac{J}{2\pi }\frac{k_T}{k_Q}.$$

When Efficiency sensor is on, and you set Parameterization to Constant, the block calculates the smoothed efficiency as

$$\eta =\frac{k_T\sqrt{J^2+k_{Thr}^2}}{2\pi k_Q}.$$

When Efficiency sensor is on, and you set Parameterization to Polynomial fit or Tabulated data for advance velocity, the block calculates the smoothed efficiency as

$$\eta =\frac{k_T\sqrt{J^2+k_{Thr}^2}}{2\pi \sqrt{k_Q^2+{\left(0.01·k_{Thr}\right)}^2}}.$$

Advance Angle

When you set Parameterization to Tabulated data for advance angle, the block uses thrust and torque coefficients with respect to relative advance angle. The block defines the advance angle as

$$\beta =\arctan \left(\frac{V_a}{0.7\pi \epsilon nD}\right),$$

where β is cyclic. You must ensure that the coefficient extrapolation and cycle wrapping occur as expected. The block defines the thrust and torque coefficients for relative advance velocity as

$$\begin{array}{l}{C}_T^{*}=\frac{T}{\frac{1}{8}\rho V_R^2\pi D^2}\\ C_Q^{*}=\frac{Q}{\frac{1}{8}\rho V_R^2\pi D^3}\end{array}$$

where V_R is the relative advance velocity at a blade section at 70% of the blade radius, such that

$$V_R^2=V_A^2+{\left(0.7D\pi \epsilon n\right)}^2.$$

Rearranging the coefficient equations yields the block equations for thrust and torque with respect to relative advance velocity:

$$\begin{array}{l}T=C_T^{*}\frac{1}{8}\rho V_R^2{D}^2\\ Q=C_Q^{*}\frac{1}{8}\rho V_R^2{D}^3\end{array}$$

When you set Blade pitch to:

• Constant, the block calculates the thrust and torque coefficients as

  $$\begin{array}{l}{C}_T^{*}=tablelookup\left({\beta }_{TLU},C_{T,TLU}^{*},\beta ,\text{interpolation = }interp\_method,\text{extrapolation = }extrap\_method\right)\\ C_Q^{*}=tablelookup\left({\beta }_{TLU},C_{Q,TLU}^{*},\beta ,\text{interpolation = }interp\_method,\text{extrapolation = }extrap\_method\right)\end{array}$$

• Controlled, the block calculates the thrust and torque coefficients as

  $$\begin{array}{l}{C}_T^{*}=tablelookup\left(P/D_{TLU},{\beta }_{TLU},C_{T,TLU}^{*},P/D,\beta ,\text{interpolation = }interp\_method,\text{extrapolation = }extrap\_method\right)\\ C_Q^{*}=tablelookup\left(P/D_{TLU},{\beta }_{TLU},C_{Q,TLU}^{*},P/D,\beta ,\text{interpolation = }interp\_method,\text{extrapolation = }extrap\_method\right)\end{array}$$

The basis of the propeller efficiency is the fundamental relationship

$$\eta =\frac{Powe{r}_{out}}{Powe{r}_{in}}=\frac{T{V}_A}{2\pi \epsilon nQ}=\frac{V_A{C}_T^{*}}{2\pi \epsilon nD{C}_Q^{*}}.$$

When Efficiency sensor is on, the block calculates the smoothed efficiency as

$$\eta =\frac{1}{2\pi D}\sqrt{\frac{V_A^2{C}^{*2}+{\left(D\pi n_{Thr}{K}_{Thr}\right)}^2}{n^2{C}_Q^{*2}+{\left(0.1n_{Thr}{K}_{Thr}\right)}^2}}.$$

Environment Interaction

When you set Translational connections to Conserving, the block uses a constant wake fraction to relate the vessel velocity to the advance velocity. You input the thrust and velocity of the vessel by using the R2 and C2 ports. The block computes the advance velocity as:

$$V_A=V(1-w),$$

where:

• V is the vessel velocity. You can specify the vessel velocity relative to the reference by using the R2 and C2 ports, where V = V_R2-V_C2.

• w is the Wake fraction parameter.

When you set Translational connections to Physical connections, you can use the Va port to supply the advance velocity as a physical signal. The block outputs the propeller thrust as a physical signal from the Th port.

Controlled Pitch

When you set Blade pitch type to Controlled, you can parameterize the propeller over a range of pitch-diameter ratios, P/D. You must specify the P/D range as a vector in the Pitch-diameter ratio vector, P/D parameter, where each element corresponds to a row in the k_T and k_Q matrices.

Inertia

You can optionally include translational and rotational propeller inertia. To simulate inertia, set Rotational connections or Translational connections to Conserving, and select Model inertia. When you select Model inertia and set Rotational connections to Conserving, set the initial rotational velocity or torque on the shaft in the Initial Targets section, or set an algebraically linked variable to high priority to initialize the rotational inertia. When you select Model inertia and set Translational connections to Conserving, set the initial translational velocity or thrust in the Initial Targets section, or set an algebraically linked variable to high priority to initialize the translational mass.

Note

For rotational conserving connections, the block logs Q, the aerodynamic torque, and Inertia.t.

For translational conserving connections, the block logs thrust, the aerodynamic thrust, and mass.f.

You can use an Ideal Torque Sensor or Ideal Force Sensor blocks to log the sum of the inertia and the aerodynamic torque or force, respectively.

Assumptions and Limitations

• The block treats the fluid velocity and propeller rotational velocity as quasi-steady in time. Fluid flows uniformly over the propeller.

• When you set Parameterization to Polynomial fit, the block assumes that the propeller torque and thrust coefficients are symmetric with the first quadrant.

• When you set Parameterization to Tabulated data for advance ratio, the block assumes the torque and thrust coefficients are identical in the first and third quadrants and the second and fourth quadrants.

• When you set Parameterization to Tabulated data for advance angle, the block removes the sign from V_a. To attain negative thrusts and torques, you must include the signs in the values of C_T and C_Q.

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Examples

Ship Propeller

A marine propeller represented by a Propeller block from the Simscape™ Driveline™ library that propels a ship. The propeller starts from rest while the current pushes the ship forward. The ship accelerates as the Ideal Angular Velocity Source starts up the propeller. After 500 seconds, the propeller spins at a constant speed, and the ship approaches a constant speed. Ship motion is resisted by a drag force that increases quadratically with ship speed.

• Open Model

Ports

Inputs

Va — Advance velocity, m/s

physical signal

Physical signal input port associated with the speed of the flow through the propeller.

Dependencies

To enable this port, set Translational connections to Physical signals.

PR — Blade pitch diameter ratio, unitless

physical signal

Physical signal input port associated with the blade pitch for a given propeller diameter.

Dependencies

To enable this port, set Blade pitch type to Controlled.

Rho — Variable density, kg/m^3

physical signal

Physical signal input port associated with the fluid density, in kg/m³.

Dependencies

To enable this port, set Fluid density specification to Variable.

w — Propeller rotational velocity, rad/s

physical signal

Physical signal port associated with the propeller rotational velocity, in rad/s.

Dependencies

To enable this port, set Rotational connections to Physical signals.

Outputs

Th — Propeller thrust, N

physical signal

Physical signal output port associated with the thrust generated by the propeller, in N.

Dependencies

To enable this port, set Translational connections to Physical signals.

E — Efficiency, unitless

physical signal

Physical signal output port associated with the efficiency of the propeller. The efficiency signal is a function of the absolute value of the advance ratio.

Dependencies

To enable this port, select Efficiency sensor.

Q — Propeller resistive drag, N*m

physical signal

Physical signal port associated with the propeller resistive drag, in N*m.

Dependencies

To enable this port, set Rotational connections to Physical signals.

Conserving

R1 — Rod interface

mechanical rotational

Mechanical rotational conserving port associated with the rod interface.

Dependencies

To enable this port, set Rotational connections to Conserving.

R2 — Vessel velocity and thrust

mechanical translational

Mechanical translational conserving port associated with the vessel velocity and thrust.

Dependencies

To enable this port, set Translational connections to Conserving.

C2 — Reference current

mechanical translational

Mechanical translational conserving port associated with the motion of the current that the propeller pushes against.

Dependencies

To enable this port, set Translational connections to Conserving.

Parameters

Propeller

Parameterization — Propeller parameterization

Constant coefficients (default) | Polynomial fit | Tabulated data for advance ratio | Tabulated data for advance angle

Option to parameterize the propeller by constant, polynomial, or tabulated thrust and torque coefficients. Choose from these settings:

• Constant coefficients — Use constant coefficients of thrust and torque with respect to the advance ratio.

• Polynomial fit — Use polynomial coefficients to parameterize the advance ratio.

• Tabulated data for advance ratio — Use tabulated advance ratio data to parameterize the advance ratio.

• Tabulated data for advance angle — Use thrust and torque coefficients with respect to the relative advance velocity at 70% of the blade radius.

To learn more, see Parameterizations.

Propeller direction — Positive thrust direction

Negative rotational velocity generates positive thrust for positive thrust coefficients (default) | Positive rotational velocity generates positive thrust for positive thrust coefficients

Whether negative or positive rotational velocity generates positive thrust for positive thrust coefficients.

Propeller diameter — Propeller diameter

0.2 m (default) | positive scalar

Diameter of the propeller.

Thrust coefficient, kT — Coefficient of thrust

0.25 (default) | positive scalar

Nondimensional constant thrust coefficient when using constant coefficients.

Dependencies

To enable this parameter, set Parameterization to Constant coefficients.

Resistive torque coefficient, kQ — Coefficient of torque

0.05 (default) | positive scalar

Nondimensional resistive torque coefficient when using constant coefficients.

Dependencies

To enable this parameter, set Parameterization to Constant coefficients.

Blade pitch type — Constant or controllable blade pitch

Constant (default) | Controlled

Type of blade to model. Select Constant for a blade with constant pitch or Controlled for a blade with variable pitch that you specify using the PR port.

Dependencies

To enable this parameter, set Parameterization to Polynomial fit, Tabulated data for advance ratio, or Tabulated data for advance angle.

kT polynomial coefficients (pN...p0) — Coefficient of thrust polynomial coefficients

[.063, -.19, -.25, .37] (default) | vector

Vector of nondimensional polynomial thrust coefficients. Specify the elements in descending order. The block uses these coefficients to generate a lookup table. For more information, see Using Lookup Tables in Equations.

Dependencies

To enable this parameter, set:

• Parameterization to Polynomial fit

• Blade pitch type to Constant

kQ polynomial coefficients (pN...p0) — Coefficient of torque polynomial coefficients

[.0043, -.021, -.03, .05] (default) | vector

Vector of nondimensional polynomial thrust coefficients. Specify the elements in descending order. The block uses these coefficients to generate a lookup table. For more information, see Using Lookup Tables in Equations.

Dependencies

To enable this parameter, set:

• Parameterization to Polynomial fit

• Blade pitch type to Constant

Pitch-diameter ratio vector, P/D — Pitch-diameter ratio values for thrust and torque coefficients

[-.5, .5, .7, .9, 1.1, 1.4] (default) | vector

Ratios of the blade pitch to the diameter. Each element has a corresponding row in the Table of kT polynomial coefficients (P/D, pN...p0) and Table of kQ polynomial coefficients (P/D, pN...p0) parameters.

Dependencies

To enable this parameter, set:

• Parameterization to Polynomial fit, Tabulated data for advance ratio, or Tabulated data for advance angle

• Blade pitch type to Controlled

Table of kT polynomial coefficients (P/D, pN...p0) — Polynomial thrust coefficients for controllable pitch propellers

[.04, -.1, -.24, .12; .118, -.24, -.24, .19; .082, -.21, -.25, .28; .063, -.19, -.25, .37; .055, -.17, -.25, .45; .064, -.21, -.19, .55] (default) | matrix

Table of polynomial thrust coefficient vectors for the given P/D ratios.

Dependencies

To enable this parameter, set:

• Parameterization to Tabulated data for advance ratio

• Blade pitch type to Controlled

Table of kQ polynomial coefficients (P/D, pN...p0) — Polynomial torque coefficients for controllable pitch propellers

[.02, -.06, -.02, .02; .04, -.034, -.016, .018; .0076, -.02, -.023, .031; .0043, -.021, -.03, .05; .0047, -.024, -.036, .073; .0045, -.025, -.044, .11] (default) | matrix

Table of polynomial torque coefficient vectors for the given P/D ratios.

Dependencies

To enable this parameter, set:

• Parameterization to Tabulated data for advance ratio

• Blade pitch type to Controlled

Advance ratio vector, J — Range of advance ratios for tabulated thrust and torque coefficients

[0, .3, .5, .7, .9, 1.2, 1.5] (default) | vector

Tabulated advance ratios. Each element has a corresponding element in the Thrust coefficient vector, kT(J) and Resistive torque coefficient vector, kQ(J) parameters or a column in the Thrust coefficients table, kT(P/D, J) and Resistive torque coefficients table, kQ(P/D, J) parameters.

Dependencies

To enable this parameter, set Parameterization to Tabulated data for advance ratio.

Thrust coefficient vector, kT(J) — Tabulated thrust coefficient values for given advance ratio

[.37, .28, .21, .12, .033, -.098, -.23] (default) | vector

Tabulated thrust coefficient values as a function of the advance ratio.

Dependencies

To enable this parameter, set:

• Parameterization to Tabulated data for advance ratio

• Blade pitch type to Constant

Resistive torque coefficient vector, kQ(J) — Tabulated torque coefficient values for given advance ratio

[.049, .039, .03, .02, .0096, -.0093, -.028] (default) | vector

Tabulated torque coefficient values as a function of the advance ratio.

Dependencies

To enable this parameter, set:

• Parameterization to Tabulated data for advance ratio

• Blade pitch type to Constant

Thrust coefficient table, kT(P/D, J) — Tabulated thrust coefficient values for given pitch-diameter ratio and advance ratio

[.12, .04, -.02, -.083, -.15, -.24, -.33; (default) | matrix | ...

Tabulated thrust coefficient values as a function of the pitch-diameter ratio and the advance ratio. The columns correspond to the elements in the Advance ratio vector, J parameter and the rows correspond to the elements in the Pitch-diameter ratio vector, P/D parameter.

The default value is [.12, .04, -.02, -.083, -.15, -.24, -.33; .19, .1, .029, -.047, -.12, -.23, -.35; .28, .19, .12, .032, -.054, -.18, -.31; .37, .28, .21, .12, .033, -.098, -.23; .45, .36, .29, .21, .13, -.0057, -.16; .54, .47, .41, .33, .25, .13, .0029].

Dependencies

To enable this parameter, set:

• Parameterization to Tabulated data for advance ratio

• Blade pitch type to Controlled

Resistive torque coefficient table, kQ(P/D, J) — Tabulated torque coefficient values for given pitch-diameter ratio and advance ratio

[.02, .0091, -.0025, -.017, -.032, -.056, -.078; (default) | matrix | ...

Tabulated torque coefficient values as a function of the pitch-diameter ratio and the advance ratio. The columns correspond to the elements in the Advance ratio vector, J parameter and the rows correspond to the elements in the Pitch-diameter ratio vector, P/D parameter.

The default value is [.02, .0091, -.0025, -.017, -.032, -.056, -.078; .017, .011, .006, .0009, -.0041, -.012, -.019; .03, .022, .015, .0074, -.0008, -.013, -.026; .049, .039, .03, .02, .0096, -.0093, -.028; .072, .06, .05, .038, .025, .0042, -.015; .11, .097, .085, .071, .057, .033, .0065].

Dependencies

To enable this parameter, set:

• Parameterization to Tabulated data for advance ratio

• Blade pitch type to Controlled

Advance angle vector, β — Rising advance angles

linspace(0, 360, 10) deg (default) | vector of length N

Tabulated advance angles. Use a monotonically increasing vector where the elements are in the range [0, 360] deg. During simulation, the propeller advance angle can be in the range [0, 360) deg, where the block wraps the angle between 0 and 360 degrees.

When you set Extrapolation method to Linear or Nearest:

• If the first element is not 0, then the block extrapolates based on the first one or two elements when β is less than the first element.

• If the last element is not equivalent to 360 deg, then the block extrapolates nased on the last one or two elements when β is greater than the last element.

Dependencies

To enable this parameter, set Parameterization to Tabulated data for advance angle.

Thrust coefficient vector, Ct(β) — Tabulated thrust coefficients for given advance angle

0.2 * sind(linspace(0, 360, 10) - 200) (default) | vector of length N

Tabulated thrust coefficients as a function of the advance angle. This coefficient depends on the blade relative advance velocity at 70% of the blade radius. The elements in this vector must correspond one-to-one with the Advance angle vector, β parameter.

Dependencies

To enable this parameter, set Parameterization to Tabulated data for advance angle and set Blade pitch type to Constant.

Torque coefficient vector, Cq(β) — Tabulated torque coefficients for given advance angle

0.015 * sind(linspace(0, 360, 10) - 200) (default) | vector of length N

Tabulated resistive torque coefficient as a function of advance angle. This coefficient is based on blade relative advance velocity at 70% of the blade radius. The elements in this vector must correspond one-to-one with the Advance angle vector, β parameter.

Dependencies

To enable this parameter, set Parameterization to Tabulated data for advance angle and set Blade pitch type to Constant.

Thrust coefficient table, Ct(P/D, β) — Tabulated thrust coefficients for given pitch-diameter ratio and advance angle

[0.15 * sind(linspace(0, 360, 10) - 200); 0.20 * sind(linspace(0, 360, 10) - 200); (default) | M-by-N matrix

Tabulated thrust coefficients as a function of pitch-diameter ratio and advance angle. The default value is [0.15 * sind(linspace(0, 360, 10) - 200); 0.20 * sind(linspace(0, 360, 10) - 200); 0.25 * sind(linspace(0, 360, 10) - 200); 0.30 * sind(linspace(0, 360, 10) - 200); 0.35 * sind(linspace(0, 360, 10) - 200); 0.40 * sind(linspace(0, 360, 10) - 200)].

Dependencies

To enable this parameter, set Parameterization to Tabulated data for advance angle and set Blade pitch type to Controlled.

Torque coefficient table, Cq(P/D, β) — Tabulated torque coefficients for given pitch-diameter ratio and advance angle

[0.010 * sind(linspace(0, 360, 10) - 200); 0.015 * sind(linspace(0, 360, 10) - 200); (default) | M-by-N matrix | ...

Tabulated torque coefficients as a function of pitch-diameter ratio and advance angle. The deafult value is [0.010 * sind(linspace(0, 360, 10) - 200); 0.015 * sind(linspace(0, 360, 10) - 200); 0.020 * sind(linspace(0, 360, 10) - 200); 0.025 * sind(linspace(0, 360, 10) - 200); 0.030 * sind(linspace(0, 360, 10) - 200); 0.035 * sind(linspace(0, 360, 10) - 200)].

Dependencies

To enable this parameter, set Parameterization to Tabulated data for advance angle and set Blade pitch type to Controlled.

Interpolation method — Method of interpolation between breakpoint values

Linear (default) | Smooth

Method to use for lookup table breakpoint interpolation. The block uses the tablelookup function to model nonlinearity by using array data to map input values to output values:

• Linear — Select this option for the lowest computational cost.

• Smooth — Select this option to produce a continuous curve with continuous first-order derivatives.

For more information, see tablelookup.

Dependencies

To enable this parameter, set Parameterization to Tabulated data for advance ratio or Tabulated data for advance angle.

Extrapolation method — Method of handling input values that fall outside range of breakpoint data set

Linear (default) | Nearest | Error

Method to use for lookup table breakpoint extrapolation. This method determines the output value when the input value is outside the range specified in the argument list. The block uses the tablelookup function to model nonlinearity by using array data to map input values to output values:

• Linear — Select this option to produce a curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.

• Nearest — Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.

• Error — Select this option to avoid extrapolating when you want your data to be within the table range. If the input signal is outside the range of the table, the simulation stops and generates an error.

Dependencies

To enable this parameter, set Parameterization to Tabulated data for advance ratio or Tabulated data for advance angle.

Environment and Dynamics

Fluid density specification — Fluid density selection

Constant (default) | Variable

Option to specify a constant or variable fluid density.

Fluid density — Constant fluid density value

1000 kg/m^3 (default) | positive scalar

Constant fluid density value.

Dependencies

To enable this parameter, set Fluid density specification to Constant.

Rotational connections — Rotational motion input option

Physical signals (default) | Conserving

Whether to simulate propeller rotational velocity and resistive drag torque as physical signal inputs and outputs, respectively, or as rotational connections. This setting determines the color of the hub in the icon, which indicates whether the block is in the rotational conserving or physical signal domain.

Translational connections — Translational motion input option

Conserving (default) | Physical signals

Whether to simulate advance velocity and propeller thrust as physical signal inputs and outputs, respectively, or as translational connections. This setting determines the color of the of the blades in the icon, which indicates whether the block is in the translational conserving or physical signal domain. When you select Conserving, the constant wake fraction reduces the advance velocity relative to the vessel velocity.

Wake fraction — Wake adjusted percentage of vessel velocity

0.2 (default) | nonnegative scalar

Reduction to vessel velocity with respect to the advance velocity. Use a value of 0 for open water.

Dependencies

To enable this parameter, set Translational connections to Conserving.

Model inertia — Inertia option

off (default) | on

Whether to simulate inertia due to the motion of the rotor. The block applies rotational inertia at port R1 and translational inertia at port R2.

Dependencies

To enable this parameter, set Rotational connections or Translational connections to conserving.

Propeller inertia — Propeller inertia

0.1 kg*m^2 (default) | positive scalar

Inertia of the propeller assembly. The block applies the inertia at port R1.

Dependencies

To enable this parameter, set Rotational connections to conserving and select Model inertia.

Propeller mass — Propeller mass

10 kg (default) | positive scalar

Mass of the propeller assembly. The block applies the translational inertia at port R2.

Dependencies

To enable this parameter, set Translational connections to conserving and select Model inertia.

Advanced

Efficiency sensor — Operating efficiency output option

off (default) | on

Whether to enable the efficiency port E, which outputs a positive-valued efficiency signal.

Rotational speed threshold — Rotational speed smoothing point

0.001 Hz (default) | positive scalar

Saturation threshold value, n_Thr, beyond which the block applies smoothing up to the point of saturation.

Saturation threshold for nondimensional coefficients — Nondimensional coefficient smoothing point

0.001 (default) | positive scalar

Saturation threshold value, k_Thr, where the block applies smoothing to nondimensional coefficients.

Check if operating beyond normal propeller operation — Operating bounds tolerance

Warning (default) | None | Error

Whether to generate a warning or error when the propeller exceeds the operating parameters. The block checks whether the propeller is operating in the first quadrant. If either V_a or n(t) are not positive, the propeller generates thrust and torque coefficients with the appropriate signs and a warning or error, depending on the parameter setting. As you raise the value for the Rotational speed threshold parameter, the trigger becomes less sensitive.

When you set Parameterization to Polynomial fit, the block generates a warning or error when the propeller exceeds the first positive root of the k_T parameter.

The block approximates the hydrodynamics using symmetric or asymmetric behavior with respect to the first quadrant.

Dependencies

To enable this parameter, set Parameterization to Polynomial fit or Tabulated data for advance ratio.

References

[1] Bernitsas, Michael M., D. Ray, P. Kinley. "Kt, Kq and Efficiency Curves for the Wageningen B-Series Propellers." Report 237. Department of Naval Architecture and Marine Engineering. College of Engineering. University of Michigan, 1981.

[2] Carlton, J. S. Marine Propellers and Propulsion. Second edition. Oxford: Elsevier, 2007.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2021b

R2023a: Port and Parameter Updates

Port C1 is no longer required and has been removed.

The Propeller direction parameter is new.

R2023a: New Inertia Option

To model inertia, select Model inertia and set Rotational connections or Translational connections to Conserving to enable the Propeller inertia or Propeller mass parameters, respectively.

R2022b: Name change

The block name changed from Propeller to Marine Propeller.

R2022b: Advance angle support

To independently parameterize the four quadrants, set Parameterization to Tabulated data for advance angle. This setting enables these parameters:

• Advance angle vector, β

• Thrust coefficient vector, Ct(β)

• Torque coefficient vector, Cq(β)

• Thrust coefficient table, Ct(P/D, β)

• Torque coefficient table, Cq(P/D, β)

The setting previously named Tabulated coefficients is now Tabulated data for advance ratio.