# Propeller

Marine propeller that converts torque into thrust

• Library:
• Simscape / Driveline / Engines & Motors

## Description

The Propeller block represents a propeller with fixed or controllable blades that converts rotational mechanical energy into translational mechanical energy. You can parameterize the propeller by using constants, polynomials, or tabulated data to characterize the thrust and torque coefficients. Propellers that allow negative pitch or are designed to operate in reverse may include thrust and torque coefficient curves specific to the astern direction, which you can use in the parameterization.

You can include the wake effects of the vessel hull in the block. You can specify a constant wake fraction or enable a physical signal port, and the block will calculate 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.

• 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.

### Equations

The block equations refer to these quantities:

• T(t) is the smoothed propeller thrust.

• Q(t) is the smoothed propeller torque.

• ρ, ρ(t) is the fluid density, which can function with time. You can specify the fluid density with the Density parameter or the Rho port.

• P is the pitch.

• D is the propeller diameter. This value is equivalent to the Propeller diameter parameter.

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

• n(t) is the propeller angular speed in revolutions per second, which serves to consistently nondimensionalize the torque and thrust. Here, ω = 2πn(t).

• nThr is the Rotational speed threshold parameter.

• kT is the thrust coefficient. This value is equivalent to the kT parameter.

• kQ is the torque coefficient. This value is equivalent to the kQ parameter.

• pkT is the kT polynomial fit coefficients parameter.

• pkQ is the kQ polynomial fit coefficients parameter.

• kThr is the nondimensional coefficient threshold. This value is equivalent to the Saturation threshold for nondimensional coefficients parameter.

• J is the advance ratio.

• Va is the advance velocity. You can specify the advance velocity using the Va port.

• η is the smoothed efficiency.

The block smooths the propeller thrust and torque with respect to the rotational speed 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 uses coefficients of thrust and torque to parameterize the performance of the propeller. You can provide static coefficients, or you can specify the coefficients as a polynomial that acts as a function of the advance ratio. The block defines the advance ratio as:

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

where the propeller rotational speed n is linearized with the angular speed threshold nThr for smoothing.

When you set Parameterization to ```Polynomial fit```, the block calculates the thrust and torque coefficients as:

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

respectively, where pkT and pkQ represent the polynomial coefficients.

When you set Efficiency sensor to `On`, the block outputs the smoothed efficiency:

`$\eta =\frac{|J|}{2\pi }\frac{{k}_{T}}{\sqrt{{k}_{Q}^{2}+{\left(0.1{k}_{Thr}\right)}^{2}}}.$`

Propeller Parameterizations

You can choose different options to parameterize the propeller kT and kQ based on the fidelity you desire or the type of information that is available to you. If you want to parameterize the propeller performance as a function of J, you can set Parameterization to ```Polynomial fit``` or `Tabulated coefficients`. If you want to use an asymmetrical parameterization for negative values of J, you must set Parameterization to `Tabulated coefficients`.

• `Constant coefficients` — This simple parameterization does not function with J. You specify kT and kQ as constants.

• `Polynomial fit` — You can specify a vector of polynomial coefficients in descending degree. For example, if you enter `[.063, -.19, -.25, .37]` for the kT polynomial fit coefficients (pN...p0) parameter, the block interprets this vector as kT = .063J3-.19J2-.25J+.37. 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.

• `Tabulated coefficients` — You can specify tabulated values for kT and kQ for given values of J and P/D. You must select this option if you want to use negative coefficients.

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 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 using the R2 and C2 ports, where V = VR2-VC2..

• w is the wake fraction. This is equivalent to 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

• 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 coefficients`, the block assumes identical torque and thrust coefficients in the first quadrant and third quadrant as well as identical torque and thrust coefficients in the second quadrant and fourth quadrant.

### Variables

Use the Variables tab to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.

## 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.

#### Dependencies

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

### Outputs

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

#### 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, set Efficiency sensor to `On`.

### Conserving

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Mechanical rotational conserving port associated with the rod interface.

Mechanical rotational conserving port associated with the case interface.

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.

Diameter of the propeller.

Nondimensional constant thrust coefficient.

#### Dependencies

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

Nondimensional constant torque coefficient.

#### 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``` or ```Tabulated coefficients```.

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

#### Dependencies

To enable this parameter, set:

• Parameterization to `Polynomial fit` or ```Tabulated coefficients```.

• 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 coefficients```

• 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 coefficients```

• Blade pitch type to `Controlled`

Tabulated advance ratios. Each element has a corresponding element in the kQ table, kQ(J) and kQ table, kQ(J) parameters.

#### Dependencies

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

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

#### Dependencies

To enable this parameter, set:

• Parameterization to ```Tabulated coefficients```

• 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 coefficients```

• 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.

#### Dependencies

To enable this parameter, set:

• Parameterization to ```Tabulated coefficients```

• 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.

#### Dependencies

To enable this parameter, set:

• Parameterization to ```Tabulated coefficients```

• 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 coefficients```.

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 coefficients```.

### 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`.

Option 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 block 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. A wake fraction of `0` is equivalent to the open water condition.

#### Dependencies

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

Option 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.

#### Dependencies

To enable this parameter, set Parameterization to ```Polynomial fit``` or ```Tabulated coefficients```.

Option 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 also generates 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 coefficients```.

## 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.