## 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, it 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:

Using your own airfoil and stall models will require wind tunnel testing 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:

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

Using your own airfoil and stall models will require wind tunnel testing 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

## LIMITATIONS:

PROP_DESIGN does not apply to the design of:

- Helicopters
- Marine propellers
- Quadcopters
- Tiltrotor aircraft (i.e. aircraft like the Bell Boeing V-22 Osprey)
- Wind turbines

- Aircraft maneuvers
- Back pressure (i.e. fans operating near a ceiling or wall, computer case fans with filters attached, fans attached to CPU or GPU coolers)
- Counter-rotation
- Nozzles
- Pitched and/or yawed propeller axis of rotation (i.e. aircraft like the Northrop Grumman E-2 Hawkeye)
- Stators
- The affect of wind

## 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 Fortran
- *.ods files can be viewed with LibreOffice Calc
- *.odt files can be viewed with LibreOffice Writer
- *.pdf files can be viewed with Sumatra PDF
- *.plt files can be plotted with gnuplot
- *.XYZ files can be imported into Rhino

## NOTES:

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):

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:

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

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
- Create a hot shape CAD (computer aided design) model, using output from PROP_DESIGN
- 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...)

## BENCHMARKING:

The benchmarking versions of PROP_DESIGN were specifically designed to make it easy to benchmark x86 processors, test Fortran compilers and compiler options, and burn-in/load/stress test x86 processors. PROP_DESIGN and the benchmarking versions of PROP_DESIGN utilize the floating-point unit (FPU) of x86 processors.