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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 1. How Propellers Work Propeller Design Workshop How Propellers Work

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**Outline: Theory and design of practical propellers, Part 1.**

Propeller aerodynamics. Best diameter and pitch. Number of blades. Determining blade angles from hub to tip. Angle of attack. Blade shape and "elliptic" loading explained. Historical notes. NACA wind tunnel research. Introduction to Vortex theory: What all those German guys said (Prandtl, Munk, Betz, Goldstein, Glauert, Theodorsen) translated into plain English. How Propellers Work How Propellers Work

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**1. Propeller Aerodynamics**

How many of you are preparing to design your own airplane? How many of you are prepared to design your own propeller for that airplane? This forum will attempt to provide an overview and some details of propeller design One cannot tell a good prop just by looking, but one can avoid the potentially bad ones How Propellers Work

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**1. Propeller Aerodynamics**

Propeller design has three parts: Aerodynamic design Main aspect of this forum Structural design Secondary Mechanical design Details, details! How Propellers Work

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**1. Propeller Aerodynamics**

Why propeller aerodynamics is important Consider a typical light airplane at climb speed 82kts, L/D = 10, 175 sq ft. wing, 2400 lbs., 13.7 psf 76in, 8in chord, 4.25 sq ft., 240 lbs., 56.5 psf 60 Thp, even more Bhp Now, let’s actually climb fpm requires 320 lbs. thrust Additional 80 Thp, 140 eff. = 180 hp How Propellers Work

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**1. Propeller Aerodynamics**

For a fixed-pitch prop, need 200 hp engine since can’t get full rpm and power in climb 4.25 sq ft. pulling 560 lbs = 132 psf! Tip speed: 905 fps = 535 kt How Propellers Work

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**1. Propeller Aerodynamics**

That’s not the environment we’d normally think of as being within the operating envelope of a little old Skyhawk Just maybe, the airfoil choice is a little more involved than “Use a Clark Y, that’s the way we’ve always done it” At cruise speed a similar analysis would yield similar results How Propellers Work

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**1. Propeller Aerodynamics**

This is high-speed subsonic aerodynamics at the tip, but still low-speed aero at the root How can low-speed aerodynamics possibly support 132 psf loadings? It can’t! Thus, the question of the loading from root to tip becomes important So important that it is the driving factor over all other design factors How Propellers Work

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**1. Propeller Aerodynamics**

The propeller tips must not be allowed to go sonic That does not mean they must be kept below Mach 1.0 That does mean they must be kept much below Mach 1.0 Good rules-of-thumb are 950fps for metal props, 850fps for wood, somewhere in between for composites based on thickness How Propellers Work

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**1. Propeller Aerodynamics**

Notice also that the blade chord is narrow That means the Reynolds’ Numbers are low along the entire blade, even near the tips due to the effect of taper Low Reynolds’ Numbers (Re) put the blades’ airfoil design condition near the bottom of or even below the lower limit of what has been historically researched in wind tunnels How Propellers Work

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**1. Propeller Aerodynamics**

For example, a formula one racer at full race power (4400 rpm) and speed (250 mph) has a propeller blade Re on the order of one million Typical GA airplanes fare slightly better, but many homebuilts fare much worse Typical NACA/NASA wind tunnel airfoil research is at Re’s of three to nine million There is a significant drop-off below 700,000 How Propellers Work

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**1. Propeller Aerodynamics**

As Tim Kern points out on page 90 of the January, 2009 Sport Aviation magazine, “The wrong prop can waste 20% of your airplane’s potential.” That could be 128 knots vs. 160 knots. Think about it. And the rate of climb…? A 5% increase in prop efficiency is equal to a 5% decrease in airframe drag Each requires a new prop…! How Propellers Work

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**1. Propeller Aerodynamics**

Propeller aerodynamic design is more like sailplane design than airplane design There are two design points of interest Sailplane: thermalling (minimum sink), and travelling between thermals (maximize L/D) Propeller: climbing, and cruising Of first concern for each is the distribution of “lift” along the “span” for maximum efficiency How Propellers Work

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**1. Propeller Aerodynamics**

A wing operates in a translating airflow A propeller is a wing operating in a rotating and translating airflow This complicates matters (immensely) When an airplane slows down, the entire wing experiences a uniform change of airspeed and angle of attack across the entire wingspan Not so for a propeller How Propellers Work

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**1. Propeller Aerodynamics**

Because of this complication, we tend to design propellers for a single design point Then we accept whatever performance we get at the other important design point So, we need two tools for propeller design A design tool, to optimize for our design point An analysis tool, to predict off-point performance (I haven’t gotten the second tool built, yet) How Propellers Work

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**1. Propeller Aerodynamics**

The Analysis tool could be a computer tool or it could be a wind tunnel, or… The most common Analysis tool for propeller design is the airplane – carve the prop, mount it, fly it, see what it’ll do! Unfortunately, this introduces waaaaay too many variables to isolate subtle propeller design changes. How Propellers Work

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**1. Propeller Aerodynamics**

So, much good design-tool effort is discounted in the end as just so much “bloviating” “The old ways work, just stick to ‘em” Thus, we have rules-of-thumb and popular wisdom and anecdotal evidence as our most powerful and influential design “experts” Some propeller manufacturers are very enlightened – now it’s our turn How Propellers Work

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**1. Propeller Aerodynamics**

A side note about propeller design methods: There are four ways to design anything “Wing it,” a.k.a. “W.A.G.” – “wild-astute-guess” Also “S.W.A.G.” – “scientific-wild-astute-guess” Cut-and-try (and try, and try again…) Trial-and-error, a.k.a. “Bracketing” or “zeroing-in” Guided by Analysis, usually called “Analytical methods” or “Theoretical methods” How Propellers Work

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**1. Propeller Aerodynamics**

There are three primary Analytical methods Statistical measurement Trial and error (tens or hundreds of times) Variation of parameters Dimensional analysis and Similitude Isolation of physical parameters, comparison with smaller-scale models, discovery of scaling factors First Principles – “Theoretical” Newton, Bernoulli, Einstein, “high-falutin’ stuff” How Propellers Work

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**1. Propeller Aerodynamics**

The “Theoretical” method does not stand alone; It informs the other methods. Likewise, the other methods feed back to theory to guide the evolution of that theory Today, there is essentially one theory of propellers, but many different approaches to that theory having various levels of approximation to cover the “hard parts” How Propellers Work

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**1. Propeller Aerodynamics**

Another side note: There is NO equivalent to Aspect Ratio for props This is not to say one couldn’t calculate an aspect ratio for a propeller blade Rather, the function of the AR in wing aerodynamic calculations is not paralleled anywhere in propeller calculations Thus, the “usual” calculation of induced drag from AR is absent How Propellers Work

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**1. Propeller Aerodynamics**

This is a result of the Vortex theory of lift See NACA Report No. 116 Application of Modern Hydrodynamics to Aeronautics L. Prandtl, Gottingen University This document should be considered required reading! Add NACA Report No. 824 or “Theory of Wing Sections” by Abbott and von Doenhoff to your required reading list, too OH, I could go on and on with the required readings list…! You’ll see that induced drag IS accounted for How Propellers Work

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**1. Propeller Aerodynamics**

Another side note: Everything you read WILL have typographical erors Especialy in the important section, or in the all-important equaations Cross-check and verify from multiple sources Do your own homework Does it make sense? (First principles) Do the units work out? (Dimensional analysis) Look for newer works that cite the older ones How Propellers Work

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**1. Propeller Aerodynamics**

What constitutes the “best prop” for my airplane? Optimization can take many forms Lightest weight Most damage tolerant Lowest cost Easiest to build Coolest looking (Most prevalent! ) How Propellers Work

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**1. Propeller Aerodynamics**

What constitutes the “best prop” for my individual, unique airplane (or type)? Optimized for some specified flight condition Usually, either “climb” or “cruise” In-between sometimes called a “service prop” Racing airplanes optimize for maximum speed Other applications may optimize for maximum static thrust or low-speed thrust (STOL) May optimize for some combination of specified flight conditions (more challenging) How Propellers Work

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**1. Propeller Aerodynamics**

This forum focuses on optimizing a fixed-pitch prop for one specific airplane (Bob’s RV-6) operating at one specific design point: Altitude = 8000 ft density altitude Horsepower = 170 sea-level brake horsepower Speed = 205 mph TAS (he says it’ll do it – really!) While still retaining a good climb rate (There’s that “second design point” thing…) How Propellers Work

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**1. Propeller Aerodynamics**

Questions so far? How are we doing for time? How Propellers Work

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**1. Propeller Aerodynamics**

A propeller is a wing constrained to rotate about one of its wing tips When we think of a propeller we typically think of a two-bladed propeller A two-bladed propeller is two wings each constrained to rotate about one of its wing tips And joined at the central wing “tips” Thus, a two-bladed propeller has four wing tips How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

“Theory of Propellers” Theodore Theodorsen, PhD. McGraw-Hill 1948 (eBay about $165) Save yer sheckels – get NACA Reports and 924 instead. Thank you, John Crigler! How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

MIT Open CourseWare (OCW) “Hydrofoils and Propellers” Prof. J. E. Kerwin, PhD. Kerwin_notes.pdf Free online How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

Propeller operating alone. A substantial cavitating hub vortex is evident. How Propellers Work

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**1. Propeller Aerodynamics**

Pre-swirl stator operating alone. A substantial hub vortex is again evident.The sign of this vortex is opposite from the one shown in the previous figure. How Propellers Work

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**1. Propeller Aerodynamics**

Propeller and stator operating together. The hub vortex has been canceled. How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

NASA-CR Proceedings of the NASA-Industry-University General Aviation Drag Reduction Workshop, 1975 “Propellers of Minimum Induced Loss, and Water Tunnel Tests of Such a Propeller” (p. 273) E. E. Larrabee, Massachusetts Institute of Technology How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

Questions so far? How are we doing for time? How Propellers Work

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**1. Propeller Aerodynamics**

NASA Conference Publication 2085 (Part I) Science and Technology of Low-Speed and Motorless Flight, 1979 “Design of Propellers for Motorsoarers” by E. Eugene Larrabee (p. 285) (This is also where you’ll find the Epper 1230 airfoil that Burt Rutan used on some airplanes) How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

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**1. Propeller Aerodynamics**

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**1. Propeller Aerodynamics**

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**1. Propeller Aerodynamics**

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**1. Propeller Aerodynamics**

How Propellers Work

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**1. Propeller Aerodynamics**

Questions so far? How are we doing for time? How Propellers Work

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**1. Propeller Aerodynamics**

There are two things above all else that I want you to learn from this 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 How Propellers Work

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**1. Propeller Aerodynamics**

Questions so far? How are we doing for time? How Propellers Work

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**2. Best diameter and pitch.**

How Propellers Work

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3. Number of blades. How Propellers Work

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**4. Determining blade angles from hub to tip.**

How Propellers Work

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5. Angle of attack. How Propellers Work

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**6. Blade shape and "elliptic“ loading explained.**

How Propellers Work

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7. Historical notes. How Propellers Work

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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 How Propellers Work

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**History Early 20th c.: Experiment and Analysis**

Scientific method flourishes in experiment Eiffel – wind tunnel investigation of wings and airfoils Lesley & Durand – tests of model propellers 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 See the book “What Engineers Know and How They Know It” How Propellers Work

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**History Early 20th c.: Experiment and Analysis**

Analysis flourishes 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 How Propellers Work

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**History Early-mid 20th c.: Emphasis on simplification**

Creation and use of charts (graphs), tables, and nomograms for rapid calculation Minimal reliance on computation Prefer statistical estimates over iterative solutions Calculus machines more plentiful than calculating machines Planimeter and Integraph for integration Splines and French Curves for drawing derivative curves Slide rules and tables for logarithms, trigonometry, math How Propellers Work

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**History Mid-late 20th c.: Emphasis on computation**

Increasing use of computers Development of discretization into finite elements Direct and iterative solutions of “unsolvable” math Calculating machines more plentiful than mathematicians Mini-computers Programmable pocket calculators Personal computers How Propellers Work

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**History Mid-late 20th c.: Jets and CFD**

Finite element and finite volume methods evolved into Computational Fluid Dynamics – CFD Too bad nobody was interested in propellers any more! (Or weren’t they? Ships have em’ too….) Then came the 1970s “energy crisis” 1980s “un-ducted fans” were all the rage Waaaaaaaaaay loud! Oops! Cancel program (Exception: high-bypass-ratio turbofans are just big, many-bladed, ducted, fixed-pitch propellers… Really!) How Propellers Work

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**History Mid-late 20th c.: NOT Jets and CFD**

BUT: Quietly, Prof. Eugene E. Larrabee of MIT was revolutionizing propeller design for the rest of us His design for a VW powered homebuilt airplane’s propeller registered the highest efficiency ever recorded in the MIT water tunnel – 85% Propellers designed using Larrabee’s method have helped to set many absolute world records How Propellers Work

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**History Late 20th c.: Larrabee reigns “supreme”**

MIT’s “Chrysalis” man-powered airplane Gossamer Albatross and Gossamer Condor More than 400 windmills in Altamonte Pass, CA Aerovironment’s “Solar Challenger” et. seq. Rutan’s “Voyager” (propellers by John Roncz) And so on, and so on…. How Propellers Work

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**Today Larrabee computerized Glauert’s work, but….**

What happened to Theodorsen’s theory? What about CFD? What about super-computers? What about prop-fans? What about this, that, and the other new theory trumpeting itself as the next and way better prop design theory? Can you tie it all together for us, Dave??? How Propellers Work

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**(Er, at least I think I can)**

Yes! !!! (Er, at least I think I can) How Propellers Work

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**!!! Yes! (Er, at least I think I can) NASA CR-145627 p. 273 (1975)**

NASA CP-2085 pt-1 p. 285 (1979) Adkins & Liebeck in Journal of Propulsion & Power EAA Weick TN-212 NASA TM-80403 NASA CP-2126 How Propellers Work

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**8. NACA wind tunnel research.**

How Propellers Work

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**9. Introduction to Vortex theory**

What all those German guys said (Prandtl, Munk, Betz, Goldstein, Glauert, Theodorsen) translated into plain English. How Propellers Work

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**Summary: Theory and design of practical propellers, Part 1.**

Propeller aerodynamics. Best diameter and pitch. Number of blades. Determining blade angles from hub to tip. Angle of attack. Blade shape and "elliptic" loading explained. Historical notes. NACA wind tunnel research. Introduction to Vortex theory: What all those German guys said (Prandtl, Munk, Betz, Goldstein, Glauert, Theodorsen) translated into plain English. How Propellers Work How Propellers Work

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**Propeller Design 101: How Propellers Work**

Propeller Design Workshop Gall Aerospace

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