# Marine Propeller

Propeller that converts rotation into thrust in marine environments

• Library:
• 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, Va.

• 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 kT and kQ 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 CT and CQ 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 Va 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.

• 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.

• nThr is the Rotational speed threshold parameter.

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

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

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

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

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

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

• kThr is the Saturation threshold for nondimensional coefficients parameter.

• J is the advance ratio.

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

• η is the efficiency.

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

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

• β is the advance angle.

• βTLU 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:

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.

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

`$J=\frac{{V}_{a}\epsilon n}{D\left({n}^{2}+{n}_{Thr}^{2}\right)},$`

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

When you set Parameterization to:

• `Polynomial fit`kT and kQ 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 kT and kQ to always be positive. The block calculates the thrust and torque coefficients as

`$\begin{array}{l}{k}_{T}=\sum _{j=1:N}^{N}{p}_{kT,j}{J}^{j}\\ {k}_{Q}=\sum _{j=1:N}^{N}{p}_{kQ,j}{J}^{j}\end{array}$`

where pkT and pkQ represent the polynomial coefficients.

• `Tabulated data for advance ratio` — You specify tabulated values for kT and kQ 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

`$\eta =\frac{{k}_{T}\sqrt{{J}^{2}+{k}_{Thr}^{2}}}{2\pi \sqrt{{k}_{Q}^{2}+{\left(0.01·{k}_{Thr}\right)}^{2}}}.$`

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

`$\beta =\mathrm{arctan}\left(\frac{{V}_{a}}{0.7\pi \epsilon nD}\right),$`

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

`$\begin{array}{l}{C}_{T}^{*}=\frac{T}{\frac{1}{8}\rho {V}_{R}^{2}\pi {D}^{2}}\\ {C}_{Q}^{*}=\frac{Q}{\frac{1}{8}\rho {V}_{R}^{2}\pi {D}^{3}}\end{array}$`

`${V}_{R}^{2}={V}_{A}^{2}+{\left(0.7D\pi \epsilon n\right)}^{2}.$`

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

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

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

`$\eta =\frac{1}{2\pi D}\sqrt{\frac{{V}_{A}^{2}{C}^{*2}+{\left(D\pi {n}_{Thr}{K}_{Thr}\right)}^{2}}{{n}^{2}{C}_{Q}^{*2}+{\left(0.1{n}_{Thr}{K}_{Thr}\right)}^{2}}}.$`

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:

`${V}_{A}=V\left(1-w\right),$`

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 = VR2-VC2.

• 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 kT and kQ matrices.

### 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 Va. To attain negative thrusts and torques, you must include the signs in the values of CT and CQ.

### 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 and Initial Conditions for Blocks with Finite Moist Air Volume.

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.

## Ports

### Inputs

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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```.

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`.

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

#### Dependencies

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

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

#### Dependencies

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

### Outputs

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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```.

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.

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

#### Dependencies

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

### Conserving

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Mechanical rotational conserving port associated with the rod interface.

#### Dependencies

To enable this port, set Rotational connections to `Conserving`.

Mechanical rotational conserving port associated with the case interface.

#### Dependencies

To enable this port, set Rotational connections to `Conserving`.

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

#### Dependencies

To enable this port, set Translational connections to `Conserving`.

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

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### Propeller

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.

Diameter of the propeller.

Nondimensional constant thrust coefficient when using constant coefficients.

#### Dependencies

To enable this parameter, set Parameterization to ```Constant coefficients```.

Nondimensional resistive torque coefficient when using constant coefficients.

#### Dependencies

To enable this parameter, set Parameterization to ```Constant coefficients```.

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```.

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`

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`

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 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 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`

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```.

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`

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`

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`

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`

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```.

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`.

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`.

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`.

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`.

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```.

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

Option to specify a constant or variable fluid density.

Constant fluid density value.

#### Dependencies

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

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.

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.

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`.

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

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

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

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 Va 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 kT 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.

## Version History

Introduced in R2021b

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