Propeller Design Workshop

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Propeller Design Workshop

• Presented by
• David J. Gall
• Gall Aerospace
• www.PropellerDesignWorkshop.com

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Propeller Design Workshop

• Theory and design of practical propellers, Part
  1. How Propellers Work

How Propellers Work
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How Propellers Work

• 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.

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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

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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!

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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, lets actually climb
• 2400 lbs _at_ 1100 fpm requires 320 lbs. thrust
• Additional 80 Thp, 140 Thp, _at_78 eff. 180 hp

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1. Propeller Aerodynamics

• For a fixed-pitch prop, need 200 hp engine since
  cant get full rpm and power in climb
• 4.25 sq ft. pulling 560 lbs 132 psf!
• Tip speed 905 fps 535 kt

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1. Propeller Aerodynamics

• Thats not the environment wed 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, thats the way
  weve always done it
• At cruise speed a similar analysis would yield
  similar results

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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 cant!
• 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

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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

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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

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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 Res of three to nine million
• There is a significant drop-off below 700,000

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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 airplanes 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! ?

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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

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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

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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 havent gotten the second tool built, yet)

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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 itll do!
• Unfortunately, this introduces waaaaay too many
  variables to isolate subtle propeller design
  changes.

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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 its our turn

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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

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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

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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

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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 couldnt 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

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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!
• Youll see that induced drag IS accounted for

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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

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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! ?)

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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)

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1. Propeller Aerodynamics

• This forum focuses on optimizing a fixed-pitch
  prop for one specific airplane (Bobs 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 itll do it
  really!)
• While still retaining a good climb rate(Theres
  that second design point thing)

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1. Propeller Aerodynamics

• Questions so far?
• How are we doing for time?

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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

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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 775-778 and
  924 instead.
• Thank you, John Crigler!

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1. Propeller Aerodynamics
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1. Propeller Aerodynamics

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

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1. Propeller Aerodynamics
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1. Propeller Aerodynamics
Propeller operating alone. A substantial
cavitating hub vortex is evident.
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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.
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1. Propeller Aerodynamics
Propeller and stator operating together. The hub
vortex has been canceled.
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1. Propeller Aerodynamics
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1. Propeller Aerodynamics

• NASA-CR-145627
• 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

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1. Propeller Aerodynamics

• Questions so far?
• How are we doing for time?

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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 youll find the Epper 1230
  airfoil that Burt Rutan used on some airplanes)

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1. Propeller Aerodynamics
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1. Propeller Aerodynamics

• Questions so far?
• How are we doing for time?

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1. Propeller Aerodynamics

• There are two things above all else that I want
  you to learn from this 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

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1. Propeller Aerodynamics

• Questions so far?
• How are we doing for time?

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2. Best diameter and pitch.
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3. Number of blades.
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4. Determining blade anglesfrom hub to tip.
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5. Angle of attack.
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6. Blade shape and "ellipticloading explained.
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7. Historical notes.
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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
• Froudes and Rankines Actuator Disc Theory
• Drzwieckis Blade Element theory
• Wright Bros. first to combine them
• Predicted and achieved remarkable 66 efficiency

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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

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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 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

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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

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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

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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 werent 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!)

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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 airplanes
  propeller registered the highest efficiency ever
  recorded in the MIT water tunnel 85
• Propellers designed using Larrabees method have
  helped to set many absolute world records

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History

• Late 20th c. Larrabee reigns supreme
• MITs Chrysalis man-powered airplane
• Gossamer Albatross and Gossamer Condor
• More than 400 windmills in Altamonte Pass, CA
• Aerovironments Solar Challenger et. seq.
• Rutans Voyager (propellers by John Roncz)
• And so on, and so on.

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Today

• Larrabee computerized Glauerts work, but.
• What happened to Theodorsens 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???

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Yes!

• !!!
• (Er, at least I think I can)

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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

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8. NACA wind tunnel research.
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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.

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How Propellers Work

• 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.

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Propeller Design 101How Propellers Work

• Propeller Design Workshop
• Gall Aerospace
• www.PropellerDesignWorkshop.com