Propeller Design WorkshopPresented by David J. Gall Gall Aerospace David@Gall.com www.PropellerDesignWorkshop.com

Theory and design of practical propellers, Part 2. Design Methods

PROPELLER DESIGN WORKSHOPPropeller Design Methods

Propeller Aerodynamics Concept There are two things above all else that I wanted you to learn from yesterday s forum: Goldstein s function does for propellers what elliptical loading does for wings - efficiency Caveat: Different for each advance ratio and number of blades

Each blade is a complete wing unto itself, with a tip vortex from each end, hub and tip Hub vortices are additivePropeller Design Methods

History The development of propeller design methods has mirrored the technologies of the day 19th c.: Scientific method still in infancy Helmholtz Theory of Vorticity Foundation of Hydrodynamics and Aerodynamics

Froude s and Rankine s Actuator Disc Theory Drzwiecki s Blade Element theory Wright Bros. first to combine them Predicted and achieved remarkable ~66% efficiencyPropeller Design Methods

History Early 20th c.: Experiment and Analysis Scientific method flourished in experiment Eiffel wind tunnel investigation of wings and airfoils Lesley & Durand tests of model propellers See the book What Engineers Know and How They Know It

Prandtl et. al Gottingen tunnel: wings and airfoils Weick et. al Langley propeller tunnel Tests of full-scale propellers

N.A.C.A. Variable-density tunnel Model and full-scale propeller tests Investigation of effect of Reynolds number on wings & propsPropeller Design Methods

History Early 20th c.: Experiment and Analysis Analysis flourished in academia and research institutes Lanchester: Concepts of vortex flow and circulation Prandtl: Quantified Lanchester s description Gave us the concepts of downwash and induced drag

Munk: Applied vortex theory to the optimization of wings gave us the elliptic lift distribution

Betz: Applied vortex theory to the optimization of propellers described the propeller analog of elliptic lift (thrust) distribution

Goldstein: Exact solution of Betz propeller distribution Glauert: Comprehensive reformulation and consolidation Theodorsen: Extended Goldstein s solution, reformulated Glauert

Propeller Design Methods

History The rest of the 20th century . Airplane propeller theory all but stopped in 1948 A smattering of papers on Theodorsens s Theory Larrabee s wonderful works (Glauert re-hashed) Some stuff on hub effects and ducted fans

Propeller Design Methods

History The rest of the 20th century . Marine propeller theory did not stop in 1948 1952, Lerbs: Non-uniform radial inflow velocity Larrabee s similar-appearing radially-graded momentum theory is like Lerbs theory in the same way a Yugo was like a real car

1955, Theodorsen was a no-show 1961, Kerwin: Vortex-lattice lifting-line solution But marine engineers have formulated the solution to the optimization problem incorrectlyPropeller Design Methods

Outline: Theory and design of practical propellers, Part 2.1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Conventional and computer design methods. Spreadsheets. Helical pitch. Graphical layout. Propellers of "Standard Form." Analytic methods. Computer design methods. Ellippse(TM) propellers. Carter propellers. McGinnis' method. Betz - Goldstein - Theodorsen Theory. Minimum Induced Loss propellers: Larrabee's method. Hepperle/Eppler. Kerwin's method.

PROPELLER DESIGN METHODSPropeller Design Methods

1. Conventional and Computer Design Methods. What is the desired output? Use the tool most appropriate to the task Don t need CAD? Then, don t use CAD! Very often, the computer is only needed to generate some numeric output Thereafter, a drawing can be made by hand You might not even need the computer my cell phone could do it if there was an appPropeller Design Methods

Desired Output Full-size template at each 'X radius station of: Pressure-side ( thrust face ) including datum Suction-side ( camber face ) including datum Profiles modified to account for thickness of subsequent laminations (glass, carbon, etc.) X could be linear inches or percent radius

CAD files to send to the jobber ? G-codes to go directly to the milling machinePropeller Design Methods

Creating a Master Blade Templates are glued to 1/8 masonite and mounted in a pressure side and suction side array Used to make guide cuts in the prop blank using a propeller duplicator

Creating a Master with a CNC Router

2. Spreadsheets I haven t been able to get Excel to do native iteration Neither have I been able to get it to integrate or interpolate using splines or other nonlinear interpolation schemes That s why I haven t used my cell phone (Excel) Spreadsheets can be useful for some preliminary work, but I find them ungainlyPropeller Design Methods

3. Helical pitch Better to use NACA TN-212, available as: Design and Build Your Own Propeller by Fred Weick, Sport Aviation, December 1960 If you re an EAA member it is free to download from the magazine archive

Propeller Design Methods

3. Helical pitch

Propeller Design Methods

4. Graphical Layout

Propeller Design Methods

5. Propellers of "Standard Form"

Propeller Design Methods

6. Analytic Methods Archaic; obsolete

Propeller Design Methods

7. Computer Design Methods Blade-element theory + momentum (classical) Vortex-lattice lifting line theory (Kerwin, et seq.) Some lit. on corrections for blade curvature

Vortex lattice lifting surface theory (panel) Low-order panels use linear approximation Requires lots and lots of panels (fine grid) Higher-order panel methods now investigated

RANS Reynolds Averaged Navier-Stokes CFDPropeller Design Methods

7. Computer Design Methods Larrabee s method is technically a bladeelement method + momentum theory Larrabee laments that a lifting-line theory of the propeller does not exist I guess Larrabee hadn t read Kerwin! It doesn t matter because at the design point the two will give nearly identical results And we re only using it for design at that pointPropeller Design Methods

7. Computer Design Methods Helice With Dr. Susan French Commercial version of Larrabee s method for wind turbines Q-Prop Dr. Marc Drela with Dr. Larrabee Xrotor Dr. Marc Drela DFDC Ducted Fan Design Code Sorry, my internet is down so I can t fact-check this morningPropeller Design Methods

7. Computer Design Methods Dr. Martin Hepperle s JavaProp Does Adkins and Liebeck s version of Larrabee Doesn t do the hub correctly (tapers to nothing) Doesn t do Theodorsen

Bates Engineering Prop Optimizer Pro Appears to be a Monte Carlo method

Other web resources: Be careful what you believePropeller Design Methods

7. Computer Design Methods NISA Software (free evaluation version) Alibre Design (low-cost full 3D like SolidWorks) Google Sketch-Up MatLab, Octave Mathcad, Mathematica, (TK! Solver) NIST Handbook of Mathematical Functions Java, Processing, SmallBasic, GNU tools, Mac WolframAlpha.com

Propeller Design Methods

7. Computer Design Methods Larrabee s method as implemented here is actually the algorithm from Design of Optimum Propellers by Adkins & Liebeck, published in Journal of Propulsion and Power, Vol. 10, No. 5, Sept.-Oct. 1994 As modified by David J. Gall to include Theodorsen s theory (abridged) And to include physical (structural) constraintsPropeller Design Methods

7. Computer Design Methods Additional Guidance from The Aerodynamics of Propellers by Quentin R. Wald, Progress in Aerospace Sciences 42 (2006) 85-128 An excellent article, well worth the $35 from www.ScienceDirect.com

Propeller Design Methods

7. Computer Design Methods Wake occurs ahead of airplanes as well as behind them it influences inflow to the prop The wake adaptation algorithm used here is an implementation of a method given in Influence of Fuselage on Propeller Design by Theodor Troller, translated from the original German and published as NACA Technical Memorandum No. 492 (replete with typos!!)Propeller Design Methods

7. Computer Design Methods Based on work by Fuhrmann before WWI This work was immensely important in reconciling theoretical and practical aerodynamics It solved d Alembert s Paradox (complaint) It showed that the parasite drag is the sum of the (theoretically calculated) pressure drag, the skin friction drag, and the BL wake dragPropeller Design Methods

7. Computer Design Methods Troller s body wake adaptation algorithm employs von Karman s adaptation of Prandtl s line distribution of Rankine s source-sink method to approximate a body of revolution This is probably the first instance of CFD that worked, yet it s a footnote in history Let s talk about spinners and inlets and outlets

Propeller Design Methods

8. Ellippse Propellers15 10

5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

-5

-10

Propeller Design Methods

8. Ellippse Propellers Arbitrarily forces an elliptical lift distribution from tip-to-tip (across the hub) without regard for the reversal of circulation across the hub Arbitrarily imposes an elliptical distribution vs. solving for the shape of the distribution curve as a function of the Betz condition Ignores the fundamental importance and the overarching achievement of Goldstein s workPropeller Design Methods

9. Carter Propellers Apparently designed using the idea that the aft-ward acceleration of air should be constant along the blade, vs. Betz condition of aft-ward velocity being constant Static thrust measurement is not adequate to predict in-flight performance

Propeller Design Methods

10. McGinnis Method Designed for constant Reynolds Number (Re) along the blade from hub to tip I don t know whether there s any consideration for the loading distribution along the blade I can do a constant Re prop very easily using Larrabee s method while still retaining consideration for the optimum loadingPropeller Design Methods

11. Computer Design Methods Betz - Goldstein - Theodorsen Theory Minimum Induced Loss (MIL) Propellers: Larrabee's method Lerbs radially non-uniform inflow method Kerwin's method Vortex Lattice Lifting Line and Vortex Lattice Lifting Surface

Propeller Design Methods

11. Computer Design Methods What s your input? Power Physical constraints Design operating conditions (design points)

What s your DATA Good Goldstein numbers are hard to find I m using values published by Wald

What s your interpolation scheme Original DTMB documents have complex interpolationPropeller Design Methods

Propeller Design WorkshopDavid J. Gall Gall Aerospace David@Gall.com www.PropellerDesignWorkshop.com