# 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,*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.*Quadrant*is the relative two-dimensional location of the propeller operating condition where the vertical axis is*V*and the horizontal axis is_{a}*ω*.*First quadrant*:*+V*,_{a}*+ω**Second quadrant*:*+V*,_{a}*-ω**Third quadrant*:*-V*,_{a}*-ω**Fourth quadrant*:*-V*,_{a}*+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)*.*n*is the_{Thr}**Rotational speed threshold**parameter.*k*is the thrust coefficient. This value is equivalent to the_{T}**kT**parameter.*k*is the torque coefficient. This value is equivalent to the_{Q}**kQ**parameter.*p*is the_{kT}**kT polynomial fit coefficients**parameter.*p*is the_{kQ}**kQ polynomial fit coefficients**parameter.*k*is the nondimensional coefficient threshold. This value is equivalent to the_{Thr}**Saturation threshold for nondimensional coefficients**parameter.*J*is the advance ratio.*V*is the advance velocity. You can specify the advance velocity using the_{a}**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:

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

where the propeller rotational speed *n* is linearized with the
angular speed threshold *n _{Thr}* for
smoothing.

When you set **Parameterization** to ```
Polynomial
fit
```

, the block calculates the thrust and torque coefficients as:

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

respectively, where *p _{kT}* and

*p*represent the polynomial coefficients.

_{kQ}When you set **Efficiency sensor** to
`On`

, the block outputs the smoothed efficiency:

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

**Propeller Parameterizations**

You can choose different options to parameterize the propeller
*k _{T}* and

*k*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

_{Q}*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*k*and_{T}*k*as constants._{Q}`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*k*. The block saturates_{T}= .063J^{3}-.19J^{2}-.25J+.37*J*to be between 0 and the first positive root of the polynomial and restricts*k*and_{T}*k*to always be positive._{Q}`Tabulated coefficients`

— You can specify tabulated values for*k*and_{T}*k*for given values of_{Q}*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:

$${V}_{A}=V(1-w),$$

where:

*V*is the vessel velocity. You can specify the vessel velocity relative to the reference using the**R2**and**C2**ports, where*V*=*V*-_{R2}*V*.._{C2}*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 *k _{T}* and

*k*matrices.

_{Q}### 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

### Outputs

### Conserving

## Parameters

## Model Examples

## 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.

## See Also

**Introduced in R2021b**