Propeller Design

Propeller Design Workshop

Presented byDavid J. Gall

Gall [email protected]

www.PropellerDesignWorkshop.com

mailto:[email protected]

http://www.propellerdesignworkshop.com/

PROPELLER DESIGN WORKSHOPTheory and design of practical propellers, Part 2. Design Methods

Propeller 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 additive


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


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


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


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


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

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.


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

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


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 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

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


3. Helical pitch


4. Graphical Layout


5. Propellers of "Standard Form"


6. Analytic Methods

• Archaic; obsolete


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



• 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



• 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



• 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



• 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.comPropeller 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



• 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


http://www.sciencedirect.com/


• “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!!)



• 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



• 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


8. Ellippse™ Propellers


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


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


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



• 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



• 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


Propeller Design Workshop

David J. GallGall Aerospace

[email protected]

mailto:[email protected]

http://www.propellerdesignworkshop.com/

Documents

Propeller Design