A little bit about me ...

• I came from a really small fishing village ...

• I didn't speak English at all ...

• ... but I really loved airplanes ...

• ... and I was good at math & science

My career with NASA • Intern graduate student (airfoils) 1982 • Hired fulltime as an aerodynamlcist 1983 • Aircraft: F-8 Oblique Wing, Deep Stall

Schwlezer, hypersonlcs (M 14.2), F-18 HARV, SR-71A, F-106 Eclipse, X-37, X-38, X-36, X-48, Mars airplanes, ...

• Chief of Aerodynamics 2002 • Deputy Director of Research/Engineering 2004 • Washington DC, Special Assistant to the

Associate Administrator of Aero 2008 • Project Manager 2009 • Associate Director of Research 2012 • Chief Scientist 2014

1

https://ntrs.nasa.gov/search.jsp?R=20180004149 2020-04-20T11:22:16+00:00Z

On the Minimum Induced Drag of Wings

Albion H. Bowers NASA Armstrong Chief Scientist

NASA Neil A. Armstrong Flight Research Center

Flying wings are so elegant and elemental ...

Yet they are difficult to fly and handle poorly. Why?

Lift ------r

Where does lift come from? You should wonder about this ...

Imagination vs Knowledge

• Requirements and Assumptions

• Concepts and Solutions

2

Questions vs Answers

• "The important and difficult job is never to find the right answers, it is to find the right question.• -Peter Drucker, Concept of the Corporation and Management

• • ... question the unquestionable." -Ratan Tata, CEO Tata Group

• 'They get a kick out of screwing with the status quo. They can't bear it. So they spend a tremendous amount of time thinking about how to change the world. As they brain storm, they like to ask: if we did this, what would happen?" -Meg Whitman, colounder of ebay, PayPal, and Skype

Flying wings are so elegant and elemental. .•

Yet they are difficult to fly and handle poorly. Why?

Birds

~ ­J..,,,. -

---i ~-- .

3

- -• Birds tum and maneuver without a vertical tall

• Birds have slender tips that cany little load

• Birds gracefully fly formation with overlapped wingtips

• Birds have narrow wingtips without tip stall

Prandtl Lifting Line Theory

• Prandtl' s "vortex ribbons"

• Elliptical spanload for a given span (1920)

• "the downwash produced by the longitudinal vortices must be uniform at all points on the aerofoils in order that there may be a minimum of drag for a given total lilt." y = c

LudwlJPr.ar.dtl

Thlt II UMI ICCllptad th1<1ry and 1h• slllnderd for the minimum drqofwlnp, But whit Is• wln-1 Is It only aeroctvnamlc7 What about the strvcturei'

Wilbur & Orville Wright

• Flying experiments 1899 to 1905

-4:Lx:i. ~'i;tJ •

Patent H:Zl,!91

Wingtip vortices

'I'

4

Wingtip vortices Elliptical Spanload

5

Fundamental Assumptions

Minimum Induced Drag & Bending Moment

• Prandtl (1933) Constrain minimum induced drag Constrain integrated wing bending moment 22% increase In span with 11 o/o decrease in induced drag

Birds

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6

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----

-

Horten Applies a Bell Spanload

«1» ~ Hll193SJ

~Hm(l9lll

~HDC(11,1J

~(194') I

• Horten Spanload (1934-1954) use twist to achieve spanload induced thrust at tips no structural implications

Prandtl & Horten

. • V . F ~ V d ~ B $

A .. g, DI ,. "' .. .. ,n

"' ""

7

,-

,...-

0

Jones Spanload

I I ,...-c-~=-st:~

L rl ! ,- 1-4 ....

.,, 11'1--- I\ "';flEw-• -~

I I I ..

i i'i~ I , '""'-I ~ ·-• . .. .. 1.0 l,R , ...

• Minimize induced drag (1950) Constrain wing root bending moment 30% increase in span with 17% decrease in induced drag

• "Hence, for a minimum induced drag with a given total lilt and a given bending moment the downwash must show a II near variation along the span." y = bx+ c

Winglets

• Richard Whitcomb's Winglets - induced thrust on wingtips - induced drag decrease is about half or the span "extension" - reduced wing root bending stress

t---__)f, ~-i ..

!Klein and Viswanathan

: \. I 1 '-- ! I - -.... ...... • .!.. I " ... 1-i•! ...

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uo 1.11 lOI \.12 '·1' 1.lD 1,... UI m1 ,,. UI

'3,.i .... ., ...

• Minimize induced drag (1975) Constrain bending moment Constrain shear stress 16% increase in span with 7% decrease in induced drag

• "Hence the required downwash-distribution is parabolic.• y = ax2 + bx + c

Whitcomb's Winglets

• ~~ ........ a.. ... ~ ·==-~ ... MC,1 ....... ...... .,.._ ..... _

8

Prandtl 1920

Elliptical Spanload

Bird Flight Model

• Minimum Structure

• Flight Mechanics Implications

• Empirical evidence

PrandtI(1920) vs Prandtl(1933)

== ......... ······_ .. -: _ - -·-------- - ~ . :::·-- · ·· · .. :: .. ~:: _ , t t• . .. . . .. .. .. ,. , . , . . ' •

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:... - --1 11 I II P tl!.: .. 111.t'U .. II"••

Prandtl 1933

Bell Spanload

dw

...

How do birds turn & maneuver?

• "First the tail is tilted downward on the side away from the direction of the tum •.• Perheps the tail functions as a rudder in starting the tum .. ." (Kolo rd, 1950)

• Alleviating the load on the tips allows the bird to tum (bank and yaw) correctly (Hoey, 1992)

• • ... the tall wes loaded upward and the same clockwise tail rotation produced a right force, thus a left tum ... • (Hoey, 1992)

clL 0--·' -..., ,. __ .....

Spanload, Downwash, Induced Drag

~~ ___ ,.,..~ ,,,,,,-;/ ~

.,.. .. /'·

.,..,, • All wings dictate 3 solutions • Spanload • Downwash • Induced Drag

9

'!wist

Horten H Xe Example

• Horten H Xe looUaunched ultralight sailplane 1950

• 24 degree leading edge sweep angle

• Chord; root - 63 inches tip -15. 75 Inches

• Span: 49.2 feel

Calculation Method

• Taper • Twist • Control Surface Deflections • Central Difference Angle

RO U274 R1 ...... A1 B.,71S9

•• &.1441 .. L9030 AS ...... .. U:ZS) R7 1.6801 .. IASISS R9 8.1492 R1D l.?522 R11 7.2592 R12 6.i534 R11 5.9$7$1 A14 S.ti1&2 A1S 4.1927 R16 !.1251 A17 1.9l94 R18 o.&519 R19 -0.6417 Rl0-1.6726

Prandtl Wing

• 24 degree leading edge sweep angle

• Chord: root - 15. 75 inches tip - 3.875 inches

• Span; 147.6 inches

+--- 3750 ----+

Symmetrical Spanloads

• Elevon Trim • CG Location

--~ .. L-.._.--... '--...,.'---'---,...'--... ~-,---;.._-,,,~,

-

10

Asymmetrical Spanloads

• Clila (roll due to aileron) • Cnoa (yaw due to aileron)

induced component profile component change with lift

• cnaa/Clila • CL(Lift Coefficient)

Increased lift: increased CIJ3 increased Cnl3" Decreased lift: decreased Gip decreased Cnp•

g. Q 0, .966 .01514 ,0005' .174 ,01384 ,CIOOJ7 _,n .01345 JIOOZJ .390 .013&4 .IIOCI03 ,IOI .01345 .Jl00I$

Dr Edward Uden's Results

• Spanload and Induced Drag • Eleven Configurations • Induced Yawing Moments

Elevon Config cnaa S load I -.002070 bell II .001556 1>en Ill .002788 bell

IV -.019060 elliptical V -.015730 elliptical VI . 001842 bell VII .002823 bell VIII .004528 bell IX .005408 bell X .004132 bell XI .005455 bell

Performance Comparison

• MaxUD:31.9 • Min sink: 89.1 fpm • Does not include pilot drag

• Prediicted UD: 30 • Predicted sink: 90 fpm

·. ______ ...

•Mitteleffekt"

• Artifact of spanload approximations • Effect on spanloads

increased load at tips decreased load near centerline

• Upwash due to sweep unaccounted for

, .. :~::::~·--r···· .. r·•~-••-:·-··· ..... , .. ... ,.,_ .. ,,,..,, .... ,_

~ ' ' . ; ; . - . :

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-- ...... -•-·l ....... ~ ........ : ..... __ .. ;_. ____ , __ : __ ·•·'•-•

: - t i : ' . i . ... _____ ;

11

Kucheman

• Effect on spanloads increased load at tips decreased load near centerline

• Upwash due to sweep unaccounted for • Residual (Kucheman)

:: =r=r.:···T·····r····1 :::: :::::.::::::::~::::::~:; ....... _ . .:. ............. .!

... l_: _LL!-\· ... i ········:····) ..... ) ..... . 1 .... _ i ..... ,

~ ... 1.~l~~~~~~.;

Prandtl's Bell Spanload

Elliptical Half-Lemniscate

• Minimum induood drag for given control power (roll) • Dr Richard Eppler: FS-24 Phoenix

Prandtl's Spanload

sl = (1 - x2) 312 -~ II I • ,r l ' i

w = 3/2 (x2 - ½)

lim L(x)=O x: 0--, b/2

lim x: 0-+ b/2 dx

lim

x:Q--,b/2 J1.W1!lll!L = lim J1.llWOO_

dx x:00-->b/2 dx

(1)

(2)

(3)

12

Mike Allen

- = ,,.. ............

) ..

13

F

Spanload Spedding's Gliding Falcon

• Spedding photograpgh's a gliding falcon's wake with He bubbles • Vortex cores are 0.76 b apart • Elliptical spanload is assumed, so the vortex cores are assumed to

come from the wingtips

!

.. t• M U •• 12 ... ,

14

B

•

•I' J,

.. I' I.,

Henningsson 2014 (PLOS One)

Portugal, et al 2014 (Nature)

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,.:.~ ~ --~'::J:W.:~~-- 24.000L/:=:::. : : ~: ;~:: :t,r~: !1i", " 20,000 ' ' ' ' • ' ,._ "ii : t i -~-; ' 11.000

~ :- : ~ : : ~: : 12.0001'-------~ ~ , , , ~ ~ Dfolar10ttotio9 2.0m

Henningsson 2014 (PLOS One)

-.......... }~::,._ 0.1 ~ ·

Upwash and Wing Beats

I: -, Speakman&. aa.nkS •

1991 -, ..!" .............. . . .:· . .,,..,..,

15

Upwash and Wing Beats CFD

- ~le::= -- ,. - ~L -•- ILL/\ I f \

•.... J \ ...... , - -- , .L ... -.. .

'1Y!!IE.• ~ - ..... .... .

.... •· ..... . - -- .

........ ""'""

Pointy Wings and Wing Stall Nachtigall 1966 (J of Exp Bio)

: :_;

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u -------.. ; - ~- -·•--,. .

1 I l -l t f ':' I • IOU:U DM2U61Jta~ll

16

Effect of Sideslip

:.I

• Wingtwist • Sideslip is imposed • Distorts the bell spanload and the induced drag/thrust profile

PRANDTL-D Proverse Yaw?

What would Proverse Yaw look like?

•

Flight Data

• Measurement of proverse yaw would be the final hurdle to achieve

• Icing on the cake: measure Cnda (yawing moment due to aileron deflection)

• NOT ONE SECOND OF FLIGHT DATA EXISTS TO PROVE ANY OF THIS IS TRUE

17

Proverse Yaw Revalidated Proverse Yaw

• ... until June 26"1, 2013

• Roll and Yaw are the same sign

• From Uden: Cnda Is +ve ,~

• uncertainty ..

Inertias; conflaurzitlon changes, turbulence~ and slope of Cnda

Spanload, Downwash, Induced Drag Elliptical Spanload Flow

• All wings dictate 3 solutions

• Spanload • Downwash • Induced Drag

18

Bell Spanload Flow

Induced/ ~

• The aerodynamic testbed • wing pressures ·FOSS

resultant

lift

Prandtl 3

19

Wind Tunnel Test

• NASA Langley • 12-ft low speed tunnel • 52 runs, 6 component force-moment

The Future: Prandtl-M on Mars?

Das kleiner Prandtl Falke

The Future: Prandtl-M on Mars?

The Mars Mission

• Deploy cubesat from large Mars rover

• Use Exobrake parachute for Mars atmosphere entry

• Deploy Prandtl-m (2 lbm, 2 fl span) from cubesat at 15,000 ft agl

• Glide 5 mins, 22 miles, Mach 0.6

• Crash land on Mars • Transmit images & data back

20

The Mars Mission

• Deploy cubesat from large Mars rover

• Use Exobrake parachute for Mars atmosphere entry

• Deploy Prandtl-m (2 lbm, 2 fl span) from cubesat at 15,000 fl agl

• Glide 5 mins, 22 miles, Mach 0.6 • Crash land on Mars • Transmit images & data back

Prandtl Propulsion

• Propulsion systems currenHy use "minimum induced loss· • What ii we switched to minimum torque for a given ihrust? + 15.4%

an&le

radius

•

... ~

... I

-i

'I

Prandtl Propulsion

rtdhlS

Prandtl Prop 1

--­~-.,ww.•Aall!.HNW ------· kfjaal--.c:.i. . =~~

.

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s J"

__ , I I

I

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21

Prandtl Prop 2

... ,1 ===I -~ ... -_.,......,..,,...,..

·1 .. l"nlflt,_..,...,.

/~ ii- ---_, ---

~ -I f- --- . /,,,.---\ "'!

1-- ~ /---\ . 'i - -~~ ... . . . . ,; . . ' . . __ ., --.. I ......... ~ ...... ,

··--- .I .,,,..-·,_ I

~1ap.,,_.01m~ . - - ut.HD!a /. ' I . \

.~ ~.:.... \ -·~·-··· -----1'lwilil ....... I

·t ii' I I

I. I l

!.\ ' ' / I

l I I

•I ' /

") . .•

i ., ~

,. o; ' . . . . . . . __ ., . . . . ' . --.. CodvllRIMr

Prandtl 3 Team Prandtl Interns Spring 2016

22

2016 Interns & MARTI PRANDTL-D

• Videos

- TEDxNASA 2011 http://www.youtube.comtwatch?v=2230maQ9uL Y

- NASA Aero Academy 2013 http://www.youtube.com/walch?v=Hrol6wBFGpY

Red Jense:n: pllot, erclneer

PRANDTL-D Aircraft

23

Control of Yaw

• You Have Three Choioes:

• 1/ drag a vertical tail around with you all the time } to create a yawing moment

• 2/ manipulate drag at the wing tips to control yaw

•OR·

• 3/ manipulate THRUST at the wing tips to control yaw

• Biological vs Mechanical Flight

Current Design Options

Prandtl, Horten, Jones, and Birds

Biological Flight

• Mechanical Flight (11 O yrs)

• Vertabrate Flight (128 My)

~ ~7Jf ~ = . • 0 •H • • -

• l -: , -~-

•·,,,..,.-rr· .. · · 1 '7 '!- . . - . n,, · _· ,4

' ' . · . . 1

... • . . . . . ··-·

I II I • .a ,I Ill ..

24

Efficiency

• Efficiency: 12.5% increase in wing efficiency

• 20-30% increase in efficiency by eliminating the tail

• 15.4% increase in propulsive efficiency

• TOTAL EFFICIENCY INCREASE: 69%

• CY2011: world jet fuel consumption $134B

• $558 in jet fuel saved

• CY2011 World GDP: $69.7T

• World power production: $12.0T

• $1.85T savings in world power production

Prandtl 3c cFOSS

.. __ _

Prandtl 3 & 3c

• The aerodynamic testbed - wing pressures -FOSS

25

Concluding Remarks • Birds as as the first model for flight

• Applied approach gave Immediate solutions, departure from bird flight

• Eventual m981ing of theory and applicalions (applied theory)

• Spanload evolution (Prandll/Horten/Jones/KlelnNiswana1han/Whilcomb/Bowers)

• Solve plllformance, structure and control with ONE spanload soluti011!

• 12.5% Increase In LID, ~2% increase in prop efficiency, 20-30% decrease in drag eliminating the tall, -'IS-62% reduction in total aero efficiency

• Assumptions and Solutions

• The Wrights disintegrated the flight of birds, and Prandtl/Horten/Jones reintegrated 1he flight of birds ...

• Thanks: Red Jensen, Brian Eslinger, Dr Christian Gelzer, Dr Oscar Murillo, Hayley Foster & Steve Craft, Dr Bob Liebeck, NaUn Ratnayake, Mike Allen, Walter Horten, Georgy Dez-Falvy, Rudi Opitz, Bruce Cannichael, R.T. Jones, Russ Lee, Bob Hoey, Phil Barnes, Dan & Jan Armstrong, Dr PhD Burgers, Ed L.ockhan, Andy Kesckes, Dr Paul MecCready, Reinhold Stadler, Dr Edward Uden & Dr Ka~ Nickel

References • Andera0t1, Jahn Jr; • A History ot Aerodymrnlcs-: and Its blpact on Flying Macldnes'"; Canbtidge Unlveflity

Presa; Cambtldge, Unitor:1 Kingdom. • Prand\l, l...UdW%i! "'AA:,tic:stioneofModem Hydrodynamics to Aeroneutic:l";NACA Report No. 1t&; 1921. • Munk, Max M.: "Tho Minimum Induced Drag 01 Aetcfails .. : NACA Report No. 121, 1923. • Nii:i:cil. K'ar1; a,d Wohffar1, MlchaeS; with Brown, Erie M. (trr,slator): '"Tailless Alrerefl In Theory and

Practice": AIM Ed.Jc;atlon Series, AIM, 1994. • Prand11, Lu.dwig: '"UbarTragllugal kleinsten lncuzierten Widntamlas,.; Zeltsdu1ft tur AU91Dcknik und

t.lot<muflechlffahrt, Jg 24 Nr 11pg305-3081833: Munchen, Oeustchland. • Horten, A&lmar; and sem,gar, Pt!ltar: ._.,ith SQQtt, J"1 (lr811Ma1or): '"'Nur11ugel: the Story of Horten f!ylng

Wings 1933-1960'";Weishap1Vedag; Graz, Austria; 1985. • Hortc,n, Roimar; unpubllehed personal notes. • Uden, Edward; unpublished personal nulos. • Jonu, RobertT.: "The Spw,wiee Ditb1bullon at Ufl ror Minimum Induced Drag at wngs-Having a 13iwin

Uh andaGIYen Bllndng Moment•; NACA Technical Note 22-49, DK 1950. • Klein, Nmin md Vilw.arudhan, Sathy; "Approxlm81e Solution tor Minim.im lnduc«i Drag al Wrg& with a

Given Structural Watd'lt·: Journal or Aircraft, Feb 197S, Vol 12 No 2, AIAA.

• :~~~~~~A ~=~~=\:i~~~l~~~nnaf RBSUlts al High Subscole Speed& for

• JanN. RobertT; •Minimizing induced Drag.": Soaring. October 1979, SoartngSoclaly at .-.m.ria • Kofotd, Cal; '"Caflfatni• Conder"; Audaban $pedal Report No 4, 1950, Dover, NY. • Hoey, Robert; '"Research on 1het 8tm1ity and Control ot Soa'I~ Blrdl"; AIM Report 82-4122-CP, AIM,

1982 • Lee, flusaeU; "Qroy the Wmg: Aeimar Horten" a Epic Quest ~ Stabilize and Control the AII-Wi,g Alrcratt.'"

Smlthsonla, lnllfWtlon Sdiola1v Prea (Aowmai & l.Jfflefleld), Washin"on D.C., 2011. • 8-illg, G. R .. Tho wake of ak .... l (lolcol/nllOOCfJ/u{J In gldlngni,,t. J. BK/J· 8tol.,127, 45-57 (1887). • Partugal, S. J. at al., Upwash uptoltcion 111d downwash avolda,ce ~ flap phl5ing in lbil fcml.don flli,.t.

Nalun,li08, 399-002(2014).

NASA Aero Academies & Others • 2014 NASA Aero Academy

- Brian Plank, Joe Lorenzetti, Kathleen Glasheen, Bryce Doerr, Cynthia Farr, Nancy Pinon, Heather Laffoon, Jack Toth, Leo Banuelos

• 2013 NASA Aero Academy - Eric Gutierrez, Louis Edelman, Kristyn Kadala, Nancy Pinon, Cody Karcher, Andy Putch, Hovig Yaralian, Jacob Hall

• 2012 NASA Aero Academy - Steffi Valkov, Juliana Plumb (Ulrich), Luis Andrade, Stephanie Reynolds, Joey Wagster, Kimmy Callan, Javier Rocha, Sanel Horozovic, Ronalynn Ramos, Nancy Pinon

• Mike Allen, Alex Stuber, Matt Moholt, Dave Voracek, Jaiwon Shin, Ross Hathaway, Brian Eslinger, Oscar Murillo, Lesli Monforton, Rad Jensen, Aamod Samuel, Brad Neal, Brad Flick, Chris Acuff, Rick Howard (NPS), Marko Stamenovic, Jim Murray, Nalin Ratnayaka, Eric Nisbet, Jeromy Robbins, Nelson Brown, Curtis Stump, Andrew Burrell, Anthony MacPharson, Brian Taylor, Chris Miller, Victor Loera, Cameron Law, Koen vander Kerckhove, Bob Hoey, Russ Lee, Reinhold Stadler, Edward Uden, Paul MacCready, Karl Nickel, Walter Horten, Diego Roldan Knellinger, Michael Cox, Jeff Jennings, Phil Barnes

Full-Scale Wing =::==;,=;c========

26

1i ~,..,;,, W~i!! r.rc" hui!d '3 ship, don't drum up peopl<:! to collect wooci s no don't assign them 1.aslts ,ind work, but rnth~r tc,u:h them to long for the endless immensity of the sea ...

- Antoine de Saint-Exupery

27

r~ _,•·· N\4. ,~ .

' ) '

Questions?

Questions?

[Q1 . ARMSTRONG ,.

- · - ·-- _-,-.,.._. ' .. /

The End

www.noso.gov

28