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Propeller Design Workshop

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1 Propeller Design Workshop
Presented by David J. Gall Gall Aerospace

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

3 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 additive Propeller Design Methods

4 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% efficiency Propeller Design Methods

5 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 & props Propeller Design Methods

6 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 Notice that only Prandtl’s name appears prominently under both headings Propeller Design Methods

7 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

8 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 incorrectly Propeller Design Methods

9 Propeller Design Methods
Outline: Theory and design of practical propellers, Part 2. 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 Methods Propeller Design Methods

10 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 “app” Propeller Design Methods

11 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 machine Propeller Design Methods

12 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

13 Creating a Master with a CNC Router

14 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 non-linear 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 ungainly Propeller Design Methods

15 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

16 3. Helical pitch Propeller Design Methods

17 4. Graphical Layout Propeller Design Methods

18 5. Propellers of "Standard Form"
Propeller Design Methods

19 6. Analytic Methods Archaic; obsolete Propeller Design Methods

20 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 CFD Propeller Design Methods

21 7. Computer Design Methods
Larrabee’s method is technically a “blade-element” 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 point Propeller Design Methods

22 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 morning Propeller Design Methods

23 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 believe Propeller Design Methods

24 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

25 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) constraints Propeller Design Methods

26 7. Computer Design Methods
Additional Guidance from “The Aerodynamics of Propellers” by Quentin R. Wald, Progress in Aerospace Sciences 42 (2006) An excellent article, well worth the $35 from Propeller Design Methods

27 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

28 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 drag Propeller Design Methods

29 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

30 8. Ellippse™ Propellers Propeller Design Methods

31 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 work Propeller Design Methods

32 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

33 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 loading Propeller Design Methods

34 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

35 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 interpolation Go to Excel spreadsheet for Goldstein Go to Excel spreadsheet for Power & Altitude Go to Excel spreadshet for inflow velocity Go to Mathcad for inflow velocity Go to Mathcad for Larrabee propellers Sorry, no bibliography today. Please me or keep checking the website Propeller Design Methods

36 Propeller Design Workshop
David J. Gall Gall Aerospace


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