# Propeller Performance Curves

Propeller Performance Curves are essential to the VTOL simulation. The App will ask for an input of RPM, Velocity at the disk (m/s), and Thrust (N). For a set of data, you have the ability to enter curves for multiple RPM.

## Background

TS Aero uses actuator disks to model propeller physics. Each propeller has unique performance characteristics in the form of thrust and torque. These vary as a function of velocity magnitude normal to the propeller plane, as well as the rate of rotation of the propeller. During a simulation setup the user inputs a desired rotation rate for each or all of the propellers. However, in order to calculate the thrust each propeller is expected to provide, data is required to help the solver understand its primary performance characteristics. Hence the requirement that propeller performance curves be provided for the project.

### Data Format

The data required for the actuator disk model is simply Thrust vs. Disk Velocity for 2 or more RPMs. The required units for these 3 inputs are Revolutions/minute, meters/second, and Newtons. It is expected that users will want to run the propellers at RPMs that do not exactly match a curve, therefore TS Aero interpolates between provided data to calculate performance curves for arbitrary RPMs.

**Note: **Due to the inaccuracies of extrapolation, it is requested that the uploaded performance curves encompass the RPM range that will be desired in the simulations.

### Calculating UDisk

Performance data can come in a variety of formats, some manufacturers provide data in terms of Thrust Coefficient vs Advance Ratio while others provide data as Massflow vs Pressure Jump.

In the former case, the Thrust Coefficient for propellers is usually expressed as

Where CT is the thrust coefficient, ρ is the density, n is the revolutions per second and D is the disk diameter. From here it is simple to solve for T. It is advised that ρ and D are in metric units to obtain T in terms of Newtons.

The Advance Ratio can be expressed as

Where J is the advance ratio and U∞ is the freestream velocity. However, the app requires that the data is uploaded in terms of Udisk instead of U∞. Using equations derived from Actuator Disk theory, Udisk can be written in terms of U∞, thrust density and disk area as follows

**Note: **This equation may not be valid for ALL cases and users should use discretion when applying it to their projects.

## Common Issues

### Run setup has failed to save

While it is possible to setup cases with propellers that have no performance curves associated with them, an error will occur when the user attempts to save the run. If such an error does occur, simply update the propeller(s) with valid performance curves. After doing so, clicking the browser reload button while on the desired run will show that the run has been saved.

### Case has meshed but failed to run

It is important to provide performance curves that match your propeller. Generally larger propellers will provide more thrust and will have data at lower RPMs. Conversely, smaller propellers will provide less thrust but will tend to operate at higher RPMs. If for example a case is setup with a series of 4 inch diameter propellers but draws its performance curves from the data of a 20 inch diameter propeller, the simulation may error out as the physical dimensions of the propeller would likely require a non-realistic mass flow to achieve the thrust derived from the incorrect performance curve.

For some experimental data on a variety of propellers please visit UIUC's Propeller Database

## Sample Prop Curve

This example excel sheet below can allow for generating a prop thrust curve of your propeller size, by interpolating sample data from an APC propeller and applying a similar thrust curve to the user's input radius and density, so that there is a similar pressure jump across both propeller sizes.

**Note: **Please be advised that data generated from this excel sheet can only be used as a placeholder and results using data generated from this excel sheet is not representative of your vehicle performance.

**Please download excel sheet**.

- To download, hover over excel sheet and click on
**Pop Out**in Top Right corner of sheet. - Click
**Download**on Top Right.