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Propeller Design Workshop Presented by David J. Gall Gall Aerospace

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PROPELLER DESIGN WORKSHOP Theory and design of practical propellers, Part 2. Design Methods Propeller Design Methods

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Propeller Aerodynamics Concept There are two things above all else that I wanted you to learn from yesterdays forum: Goldsteins 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

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History The development of propeller design methods has mirrored the technologies of the day 19 th c.: Scientific method still in infancy – Helmholtz Theory of Vorticity Foundation of Hydrodynamics and Aerodynamics – Froudes and Rankines Actuator Disc Theory – Drzwieckis Blade Element theory – Wright Bros. first to combine them Predicted and achieved remarkable ~66% efficiency Propeller Design Methods

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History Early 20 th 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

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History Early 20 th c.: Experiment and Analysis – Analysis flourished in academia and research institutes Lanchester: Concepts of vortex flow and circulation Prandtl: Quantified Lanchesters 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 Goldsteins solution, reformulated Glauert Propeller Design Methods

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

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History The rest of the 20 th century…. Marine propeller theory did not stop in , Lerbs: Non-uniform radial inflow velocity Larrabees 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

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PROPELLER DESIGN METHODS Outline: Theory and design of practical propellers, Part 2. 1.Conventional and computer design methods. 2.Spreadsheets. 3.Helical pitch. 4.Graphical layout. 5.Propellers of "Standard Form." 6.Analytic methods. 7.Computer design methods. 8.Ellippse(TM) propellers. 9.Carter propellers. 10.McGinnis' method. 11.Betz - Goldstein - Theodorsen Theory. 12.Minimum Induced Loss propellers: Larrabee's method. 13.Hepperle/Eppler. 14.Kerwin's method. Propeller Design Methods

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1. Conventional and Computer Design Methods. What is the desired output? Use the tool most appropriate to the task Dont need CAD? Then, dont 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

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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

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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

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Creating a Master with a CNC Router

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2. Spreadsheets Propeller Design Methods I havent 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 Thats why I havent used my cell phone (Excel) Spreadsheets can be useful for some preliminary work, but I find them ungainly

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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 youre an EAA member it is free to download from the magazine archive Propeller Design Methods

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3. Helical pitch Propeller Design Methods

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4. Graphical Layout Propeller Design Methods

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5. Propellers of "Standard Form" Propeller Design Methods

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6. Analytic Methods Archaic; obsolete Propeller Design Methods

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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

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7. Computer Design Methods Larrabees 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 hadnt read Kerwin! It doesnt matter because at the design point the two will give nearly identical results And were only using it for design at that point Propeller Design Methods

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7. Computer Design Methods Helice – With Dr. Susan French – Commercial version of Larrabees 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 cant fact-check this morning Propeller Design Methods

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7. Computer Design Methods Dr. Martin Hepperles JavaProp – Does Adkins and Liebecks version of Larrabee – Doesnt do the hub correctly (tapers to nothing) – Doesnt 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

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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

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7. Computer Design Methods Larrabees 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 As modified by David J. Gall to include Theodorsens theory (abridged) And to include physical (structural) constraints Propeller Design Methods

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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

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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

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7. Computer Design Methods Based on work by Fuhrmann before WWI This work was immensely important in reconciling theoretical and practical aerodynamics It solved dAlemberts 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

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7. Computer Design Methods Trollers body wake adaptation algorithm employs von Karmans adaptation of Prandtls line distribution of Rankines source-sink method to approximate a body of revolution This is probably the first instance of CFD that worked, yet its a footnote in history Lets talk about spinners and inlets and outlets Propeller Design Methods

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8. Ellippse Propellers Propeller Design Methods

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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 Goldsteins work Propeller Design Methods

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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

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

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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

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11. Computer Design Methods Whats your input? – Power – Physical constraints – Design operating conditions (design points) Whats your DATA – Good Goldstein numbers are hard to find Im using values published by Wald – Whats your interpolation scheme Original DTMB documents have complex interpolation Propeller Design Methods

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Propeller Design Workshop David J. Gall Gall Aerospace

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