Formulation:

PROP_DESIGN does not rely upon momentum theory, Theodorsen's theory of propellers, or the Betz condition. PROP_DESIGN has no light loading limitations either. Therefore, PROP_DESIGN can easily calculate the static condition. PROP_DESIGN utilizes a novel implementation of lifting-line theory (a.k.a. vortex theory). The formulation is purely analytical with a few exceptions. Empirical data was used to create the airfoil, atmospheric, and stall models. The empirical data, utilized by PROP_DESIGN, is freely available online. Reputable sources were referenced:

  • Airfoil Model; NACA (Predecessor of NASA)
  • Atmospheric Model; United States Committee on Extension to the Standard Atmosphere (COESA)
  • Stall Model; Sandia National Laboratories

You can use your own airfoil and stall models, if desired. You will have to edit and re-compile the Fortran 77 source code, in order to do so, however. Editing the airfoil and stall models is not too difficult, as the source code is very clean. The portions which define the airfoil and stall models only consist of a few lines of code.

Using your own airfoil and stall models will require wind tunnel testing and/or 2D CFD. You need to know Cl, Cd, and Cm (i.e. lift, drag, and pitching moment coefficients) for angles of attack of 0 to 90 degrees. These coefficients must be calculated for Mach numbers of .1 to 1.3 and a wide range of Reynolds numbers. Traditional airfoil analysis programs are not capable of accurately determining this information.

PROP_DESIGN executes quickly, and requires little computational resources, because it does not attempt to solve the Euler, Navier-Stokes, or Boltzmann equations. Rather, the Biot-Savart law and the Kutta-Joukowski theorem are utilized to iterate upon induced angle of attack and circulation. As of May 21, 2013, PROP_DESIGN includes the affect of wake contraction. The affect is very small but included for completeness.

PROP_DESIGN is based on a code called PROPSY, described in the following publications:

  • 'The numerical determination of circulation for a swept propeller', 1996, by Markus Tremmel
  • 'Numerical Determination of Circulation for a Swept Propeller', 2001, by M. Tremmel, D. B. Taulbee, J. R. Sonnenmeier

I have made many corrections and improvements to PROPSY. In fact, at this point, PROP_DESIGN is almost an entirely different program. Therefore, one should not expect the results of the two codes to be the same. Rather than publish these changes via a traditional outlet, I decided to publish them online. This was done to make it easy, and free, for people to obtain them.

Supporting Software:

PROP_DESIGN is used in combination with several other software programs:

  • *.bat, *.DAT, *.plt, *.txt, *.TXT, and *.XYZ files can be viewed with Microsoft Notepad
  • *.f files can be viewed with Force and compiled with Intel Parallel Studio XE
  • *.ods and .odt files can be viewed with LibreOffice
  • *.pdf files can be viewed with Google Chrome
  • *.plt files can be plotted with gnuplot
  • *.XYZ files can be imported into CAD programs such as Rhino

Additionally, while not necessary to utilize PROP_DESIGN, you may find the following software useful as well (listed alphabetically):

  • ANSYS - The hands down leader in CAE software; I have used ANSYS Workbench since it's inception. It's strong points are contact, meshing, and ease of use. It has some frustrating things as well. I prefer Mecway when appropriate to use. ANSYS is one of the most capable CAE programs available, albeit one of the most expensive. However, the student versions of ANSYS are free. The new ANSYS Discovery Live product looks like a real game changer as well
  • Hanley Innovations MultiElement Airfoils - Appears to be the best airfoil analysis program available. Not only can the program calculate subsonic, transonic, and supersonic flow regimes, it can also calculate post stall behavior. Dr. Hanley has a blog post on the topic here; http://hanleyinnovations.blogspot.com/2013/12/through-180-degree-angle-of-attack.html. I haven't used the product personally, however, due to the cost. I recommend using MultiElement Airfoils to create your own airfoil and stall models. I have evaluated everything else available and nothing seems adequate. Otherwise, the best option is wind tunnel testing
  • Keyshot - Rendering program; Easy to use, great results, no expensive GPU required
  • Mathcad - One of a kind general math and scientific documentation program; You can use it to solve common math problems and annotate pictures by placing formulas over them
  • Mecway - FEA program; Very affordable, easy to install, easy to use, can export the cold shape, accurate, great support from the developer. I use it for isotropic materials such as aluminum. Not sure how good it would be for composites. Can perform modal analysis with stress stiffening and spin softening
  • mingw-builds - Windows version of GCC; Contains an open source Fortran compiler called gfortran. The executable files are not as fast as those created with Intel Fortran. However, gfortran is free. This is the version of Fortran that I compare the Intel Fortran compiler against in my Fortran Compiler Comparison
  • MoI - NURBS surface modeler; Fantastic interface, very affordable, very easy to use, the developer offers amazing support, the user community is incredible as well. It's a tough call between Rhino and MoI. I have used both but went with Rhino because it worked with PROP_DESIGN point files out of the box. MoI required a custom script that the developer provided. Also, Rhino has more functionality and a lot of optional 3rd party plugins. MoI is worth checking out however. It may be for you

Limitations:

PROP_DESIGN does not calculate aircraft propeller noise levels. This is due to the fact that an efficient aircraft propeller is also a quiet aircraft propeller. Since you normally strive for an efficient design, there is no additional effort required to achieve a quiet design. To calculate aircraft propeller noise levels, I recommend the procedure described below (the document is based on empirical data collected by Hamilton Standard and also contains information showing what aircraft propeller characteristics increase aircraft propeller noise levels):

  • 'Prediction Procedure for Near-Field and Far-Field Propeller Noise', 1977, SAE AIR1407 1977-05-01

The paper shows that, if you have an efficient design, there is only one variable left that drives noise. This variable is shaft horsepower. Noise is proportional to shaft horsepower. So the higher the shaft horsepower is the more noise the aircraft propeller will make. Again, from an aircraft propeller design point of view, this means that all you need to do is create an efficient design. Shaft horsepower is dictated by the size of the aircraft. The size of the aircraft is dictated by the max. payload. As an example, if you want to fly four people around, that is going to be much quieter than flying four hundred people around. There is nothing you can do about that. This is why it is a waste of time to worry about noise levels. It is more useful to minimize noise by creating an efficient design. PROP_DESIGN_OPT will automatically find the optimum geometry for any operating condition that a solution exists. So PROP_DESIGN makes it very easy to maximize fuel efficiency and minimize noise.

 

Below are the other limitations of PROP_DESIGN:

  • Does not have a GUI
  • Does not export complete CAD files
  • Computes using only one CPU thread
  • Does not look at counter-rotating propellers
  • Does not include stators, nozzles, or diffusers
  • Does not include the affect of back pressure, pitch, or yaw
  • Does not apply to tiltrotors, helicopters, or quadcopters
  • Does not apply to marine propellers or wind turbines

Creating a GUI, exporting complete CAD files, and computing in parallel are outside my programming abilities. PROP_DESIGN already runs very fast using only one CPU thread. So there is little reason to spend the time to re-write or modify the code to run in parallel. I do not believe in using counter-rotating propellers. I don't believe counter-rotating propellers can even work as intended. At their best, it is very easy to prove that they decrease propeller efficiency while increasing noise and cost. I do not believe in using stators, unless they are used in axial flow compressors. In the case of ducted fans, it is easy to prove that stators decrease propeller efficiency and increase cost. The modern turbofan example takes a deeper look into counter-rotating propellers and stators. It is easy to compute the performance of nozzles and diffusers by hand, so there was no reason to include them in PROP_DESIGN. The reference information shows how to perform these calculations. It is best to avoid situations with back pressure, pitch, or yaw. Therefore, I did not specifically address them. I was only interested in creating the best performing propellers. Part of that involves avoiding poor operating conditions as much as possible. This is why I do not believe in tiltrotors, helicopters, and quadcopters. They operate in some of the worst operating conditions, most of the time. Using thrust vectoring nozzles is a much better approach. Thrust vectoring nozzles will increase efficiency, thrust to weight ratio, and safety. They will also decrease cost. Although PROP_DESIGN could be modified to handle marine propellers and wind turbines, I have no interest in these devices. There are many other codes dedicated to marine propellers and wind turbines, so there is little value in expanding the focus of PROP_DESIGN.

Design Process:

The geometry PROP_DESIGN outputs is termed the hot shape. The hot shape is the geometry required to provide the desired aerodynamic performance. FEA is needed to find the corresponding cold shape. Centrifugal force will deform the cold shape into the hot shape, at a user specified shaft angular velocity. The cold shape is the geometry that should be manufactured.

PROP_DESIGN is unproven. It is up to the user to verify his or her design. To do this, I recommend comparing the results you obtain with PROP_DESIGN against test data that you collect. The typical aircraft propeller design process is as follows:

  • Determine the required hot shape, using PROP_DESIGN (or equivalent)
  • Create a hot shape CAD (computer aided design) model, using output from PROP_DESIGN (or equivalent)
  • Perform additional aerodynamic analysis, on the hot shape CAD model, using CFD (computational fluid dynamics) software
  • Perform noise analysis, on the hot shape CAD model, using CAA (computational aeroacoustics) software
  • Use FEA (finite element analysis) software to create a cold shape CAD model that yields the desired hot shape under steady state loads
  • Ensure that the cold shape CAD model can withstand the steady and vibrational loads acting upon it, using FEA software
  • Ensure that the cold shape CAD model is not excited by flutter, using FSI (fluid structural interaction) software
  • Use the cold shape CAD model to manufacture prototype(s)
  • Test prototype(s) to make sure they perform as desired
  • Ensure that the final design meets all applicable regulations (ASTM, EASA, FAA, etc...)

This is an iterative procedure that is usually conducted by a number of qualified engineers. Many of these steps are performed in parallel, in order to save time and money. Many people manufacture the hot shape, this may cause you to miss your performance target. As you can imagine, this process is very complex, time consuming, and expensive. Many people have been killed due to mistakes in this process.

Aerodynamic Performance:

PROP_DESIGN_ANALYSIS and gnuplot can be used to create plots which aid the understanding of aircraft propeller performance. Some of the available plot types are shown below. The performance maps were made with PROP_DESIGN_MAPS_CS. This is the version of PROP_DESIGN that lets you evaluate constant speed propellers. It is available in the PROP_DESIGN_UNDOCUMENTED folder. All of the screenshots below are for the included General Atomics Predator B example.

Aerodynamic Loads:

PROP_DESIGN_ANALYSIS outputs steady state aerodynamic forces and moments along the span (a.k.a. the quarter chord line) of the blade. These are for use with structural analysis software such as FEA. It should be noted that, the affect of centrifugal force is typically much more dominate than the affect of the aerodynamic loads. It is not uncommon to ignore the aerodynamic loads and only apply centrifugal force. For high horsepower engines, aerodynamic loads will become more significant. To be safe, you can run a structural model with and without aerodynamic loads. This will allow you to see how important they are to your specific application. All loads act at the airfoil's quarter chord point.

It is easier to apply thrust and torque force rather than lift and drag. This is because lift and drag vectors change with angle of attack. You should not apply lift and drag with thrust and torque force, since thrust and torque force result from lift and drag. Doing so will cause error.

PROP_DESIGN_ANALYSIS also outputs lift, drag, and pitching moment coefficients along the span of the blade. These coefficients are non-dimensional. They are output for completeness more than anything.

 

The screenshots below indicate load locations and directions. Dark blue arrows designate the thrust vectors, red arrows designate the torque force vectors, and green arrows designate the pitching moment vectors. Vectors are shown in the positive direction. Note, positive pitching moments act to increase angle of attack while negative pitching moments act to decrease angle of attack. The orange line represents the axis of rotation. Notice that, for swept blades:

  • The thrust vectors (dark blue arrows) are parallel to the axis of rotation and perpendicular to the span of the blade
  • The torque force vectors (red arrows) are mutually perpendicular to the thrust vectors and the span of the blade
  • The pitching moment vectors (green arrows) are mutually perpendicular to the thrust and torque force vectors

The magenta lines are mutually perpendicular to the dark blue and light blue lines. The sweep angle (delta) is the angle between the magenta line and the red line. Delta is coded to always be zero at the root of the blade and increase smoothly to the value specified at the tip.

Spanwise distance is shown with the light blue lines, in the pictures below. The light blue lines always start at the axis of rotation and end at the quarter chord points, even though it was not possible to show this in all of the pictures below. The span of the blade can be thought of as a line starting at the axis of rotation and connecting all quarter chord points. Thus the span of the blade is essentially the blade itself and is not shown with a special line. Do not confuse spanwise distance with the span of the blade.


It is worth noting that the load vector orientation is the same for truly swept blades, swept airfoils, or any combination of the two. The PROP_DESIGN mesh is based on a truly swept blade. Thus, the pictures below reflect the internal computations. Applying aerodynamic loads to straight blades is much easier, since all vectors are aligned with the global coordinate system.

Hot Shape CAD Models:

Below are renderings of hot shape aircraft propeller and hot shape fan CAD models. I created them using PROP_DESIGN, Rhino, and KeyShot. The renderings are of four of the included examples; Airbus A400M, Delta Computer Case Fan, General Atomics Predator B, and the Piaggio Avanti II. These renderings should give you an idea of all the different shapes PROP_DESIGN can create.

Four different chord distribution options are available; constant, elliptical aligned along chord / 4, elliptical aligned along chord / 2, and scimitar (elliptical aligned along the trailing edge).