the horten

8/12/2019 The Horten

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Toward the theory of Flying WingsTranslated from the German by Yoram Leshinski (Many thanks!)

Aerodynamics

From Lilienthal (1892) to Junkers (1910), the creation of lift was the leading thought that gave allconstructs their form !ven the em"ennage should create lift #he making of airfoils for wings andem"ennage reflected the strong cam$er of a $ird%s airfoil, that Lilienthal had reali&ed and measured as $est for creating ma'imum lift

#he creation of lift was em"hasi&ed in 182 through $ *agnus *agnus, who as an artiller officerstudied the flight of rotating "ro+ectiles in crosswinds, gave the correct e'"lanation for the "ro+ectilesmissing the targets otation and crosswind gave a force "er"endicular to the flight direction- Lift #hat "henomenon (known toda as the *agnus effect) can $e clearl o$served on .cut. tennis $alls or.sliced. golf $alls / clinder revolving on its a'is (with circular flow lines, whose s"eed is inversel "ro"ortional to the radius) will $e $rought into a "arallel flow, so that the local s"eeds overla" /n

asmmetric flow line is created in regards to the hori&ontal, that means lift, a smmetr remains inregard to the verticals, and so no resistance is created f ou envision the image distorted through amathematical trick, then from the circle ou will get the Joukowski /irfoil #his transformation is alsoeasil achieved through drawing

f ou write the circulation then the lift is (discovered inde"endentl $ utta and

Joukowski)- or when the stagnation "ressure, is introduced and su$stituted

with where with and

#he flow lines of the rotating clinder in a "arallel flow can $e easil made visi$le through e'"erimentsin a hdrodnamic tank, f instead of a rotating clinder, a cam$ered "late is su$merged in the waterflow, then the "icture of the flow lines, a little $it further from the clinder or the "late, remainsunchanged $ecause of smmetr "rinci"les around the vertical, the lift can $e viewed as an effect onthe clinder a'is and also on the middle of a cam$ered "late, that is 0 of the airfoil #he lift is then "resent, even so the /3/ is &ero, its coefficient stated as clo #he circulation $elonging to each

cam$ering resulting through this, that the down flow direction at the trailing edge, in clinder and "late,must $e the same 4ou can make it visi$le, with the same e'"eriment configuration, that a flat "late, oreven $etter, one with a smmetrical airfoil envelo"ing it, will create the same flow line image (this willalwas take "lace when the lines are viewed a little $it further out from the clinder area and the downflow angle is now through the given angle of the flat "late)

/nchor on the s"ot of the clinder a'is the "oint of 02 t (t 5 airfoil length) of the turna$lesmmetrical airfoil, and ou will also see that no moment is created, and it can $e "erceived that the liftaffects at t 6 7 #his occur in all /3/, as long as the flow does not $ecome tur$ulent and detaches nt67 "oint the moment does not change when the /3/ changes (ie moment 5 &ero) #herefore, ou callthat "oint the eutral oint of the airfoil /lso in the "revious e'am"le, ou can give the cam$ered "late, envelo"ed with a smmetrical airfoil, an e'tra /3/, through which the down flow direction andwith it the circulation, and with it the lift, will $e increased /t the same time, the neutral "oint remains



inside t67, et a moment e'ists in all /3/, cmo

5 cao

: t67, in which t67 of the leverage arm of the &ero

lift in t62 indicates to the neutral "oint 02 t n other cam$ered airfoil centre lines, c mo must $e

calculated or in wind tunnel measured f ou $end the centre line in the front (at the airfoil nose), thec

ao will $e raised, c

mo stas small f ou $end the centre line in the $ack, c

ao is raised together with

cmo #hrough com$ination this $rings ou to a ;<form centre line, where c mo 5 0 and through this, a

.fi'ed "ressure "oint. airfoil can $e constructed

=ith that, the lift and the moment in two<dimensional flow are e'"lained, $ut a resistant is not etevident /s said in the first cha"ter, randtl e'"lained this from the friction, which develo"s on the to"surface of a flow<surrounded $od, and is therefore called friction resistance #he flow "attern of themotionless clinder in the "arallel stream is e'"erimentall difficult to show, as the friction on the to"surface of the local s"eeds changes o""osite the theoretical, where$ the "ressure distri$ution shiftsand, finall, even the se"aration of the stream follows Friction resistance to the clinder to" surfaceand the friction of the air laers $etween the streamlines changes the "icture $ehind the $od (thesmmetr is distur$ed), and there$ causes air resistance 3n the front side of the clinder is theadditional flow "ressure >" 5 ? in the center #he flow "ressure is reduced on $oth sides to &ero when

the clinder is raised u" to the angle of @0 degrees, thus the local velocit is that of the free unim"airedflow /ccording to the Aernoulli law, the "ressure reduces itself u" to a clinder angle of 90 degrees,since the s"eed rises #he "ressure field on the front of the clinder can $e divided into its com"onentsin the direction of the flow, which results, $etween the clinder angle 0 to @0 degrees in "ressurecom"onents to the rear, and from @0 to 90 degrees in suction com"onent to the front Aoth eliminatethemselves "erfectl, so that half of the clinder e'"eriences no "ressure resistant $etween 0 and B90degrees

Junkers was "erfectl right to "ro+ect a thick athick wing, the volume s"an<wise, laid outtransverse to the flight direction / "ressure

resistance does not e'ist #herefore, if onedistorts the circle (clinder) through the samemathematical e?uation and a smmetricalJoukowski airfoil develo"s, then on the rear side,the se"aration is "revented and with that, theresistance is e?ual to the friction resistance #husthe measurements resulted, with the accurac of1910, in air resistance inde"endent from theairfoil thickness #oda we know that this fact isonl "artiall correct #he $oundar laer, thelaminar tur$ulence and the mach num$er

e'ercise influence, where as the aforementioneda""lies onl in a certain area and doesn%tgenerall a""l evertheless, Junkers couldreduce air resistance through the self<su""ortingwing and "revent the need of wires and struts#he thicker wing ended u" resulting in lessresistance #oda there are hardl an strutted or $raced air"lanes left, there$ "roving Junkers%

Fig. 1 deal flow around a clinder and accordinglthe theoretical "ressure flow, that doesn%t "roduce an

force com"onent in the flow direction n addition the "ressure flow is drawn in with su"ercritical, tur$ulent $oundar laer and with su$<critical, laminar<se"arated flow, to which the flow "attern no longer fitand with the vorte' formation resistance occurs #heclinder can $e transformed mathematicall andgra"hicall easil into a airfoil, in which the flowse"aration is avoided, and therefore no "ressureresistance occurs

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develo"ment correct

#he mach num$er, the relation of flight s"eed to the s"eed of sound, was stated with the resistantestimation f one imagines the front<"ro+ecting surface multi"lied $ the rate of v of the flight, thenone receives a volume which, "er second from the front to the rear, must $e led "ast the air"lane #hisoccurs, as is ver well visi$le on the clinder in the hdrodnamic tank, at high s"eeds near the largest

cross<section #here will $e, as stated a$ove, no e'tra resistance added to the friction f ou think ofthe air as com"ressi$le (as is necessar at high s"eeds), then the volume to $e trans"orted is multi"lied $ the densit C and ou receive mass #he trans"ortation of that air mass "ast the air"lane (from thefront to the rear) is therefore different from the .volume trans"ort. n the "lace of the highest velocit(connected with the $iggest negative "ressure $ the Aernoulli e?uation), the negative "ressure nowalso changes the densit (reduced), so that, in order to trans"ort the mass of air, high s"eeds must againnow $e increased #he "roduct C : v now $ecomes instrumental, and we have to e'amine if it has a

ma'imum (whether there is a s"eed at which /t a higher s"eed the densit decline will $e

larger, since it corres"onds with the s"eed increase and, with that, less air mass flows laterall $ theair"lane t is easil derived that the ma'imum e'isted and the a""ro"riate s"eed is that of the sound

#his locall occurring s"eed of sound, at further increase of the flight s"eed, makes the continuit ofthe flow not "ossi$le #herefore the flight mach num$er, at which locall the s"eed of sound occurs, iscalled critical and the s"eed range $eginning with it transonic (to a""ro'imatel mach num$er 1@) /t*ach 1@, "urel su"ersonic flow $egins #he transonic stream is still toda in a research status 3n theother hand, the su"ersonic flow is eas to calculate

#he air"lane%s volume distri$ution "er"endicular to the flight direction (as found in a thick wing, "atented $ Junkers), loses its "hsical foundation with the critical mach num$er Dowever, this isshifted $ the swee" of the wing to higher values, u" to a""ro'imatel * 5 0 9 n the su"ersonicrange different laws a""l, since air is com"ressed, which leads to energ loss Dere the Junkers "atentcannot $e a""lied an longer Furthermore, it is "ractical to kee" the front<"ro+ecting surface small, that

is, to la out the s"ace in longitudinal direction /fter a suggestion from D *ultho"" (to me in 19),it is $est to calculate the cross<sections of the air"lane as at * 5 1 #he factor .cte.

is o$tained from the desired air"lane volume, the largest cross<section area sma'

(surface) in 0 of

the total length of the air"lane E in the a$ove e?uation is set from <1 to 1 #he shift of the critical

mach num$er $ the swee"<angle follows onl a""ro'imatel the factor , where as the swee"<

angle refers to the minimum airfoil "ressure, as is "hsicall necessar #he influence of the wing<ta"ering on the shifting of the critical mach num$er is not et investigated, $ut is, with an increase ofthe ta"ering, to $e e'"ected, which is es"eciall "rominent in the delta wing / thickening of the wingaround 1 diminishes the critical mach num$er around a""ro'imatel 1 3ne ma conclude from

this that the swee" is more effective

For the "erformance calculation in the transonic flight it make sense to set the thrust in relationshi" tothe front<"ro+ecting surface and so to define a cali$rated load #he thrust at travel height and thenum$er of revolutions of the engines at travel s"eed are to $e considered #he thrust must $e divided $

sma' and one receives so the dimension da 6 m2 #he cali$rated load and the s"ace distri$ution

according to the *ultho"" e?uation is, with that, o""osed to the Junkers "atent and $anishes the wingonl air"lane into the su$sonic fling range #he tail<less air"lane however, which re"resents onl a



"artial solution in the su$sonic to the wing<onl air"lane, is, in the transonic or su"ersonic, a must forflight "erformance and safe controlla$ilit #he swe"t wing does not onl shift the critical machnum$er to higher value t diminishes the resistance +um" near the s"eed of sound and reduces the liftcolla"se, that the strait wing suffers #hat%s wh an air"lane without swee" a$ove the critical machnum$er (or close to * 5 1) is uncontrolla$le ;ince in su"ersonic flight the flow is two dimensional,the side "ro"ortion can $e ke"t small =ith strong swee" ou get the delta air"lane, which is

controlla$le in the whole transonic area #he su"ersonic aircraft is therefore o"timal with regards to theresistance and for safet reasons (controlla$ilit) a tail<less delta air"lane #he wing thickness should $e, as is static<constructive necessar, as small as "ossi$le #he fuselage must haven the volume for thefulfillment of the mission, "refera$l with round cross<section, in order to form a "ressuri&ed ca$in,which is unavoida$le with the travel heights in the stratos"here Junkers could not "ossi$l foresee thisdevelo"ment of aviation 1910 t a""eared onl after the end of the war, 197 and later, and can $e seenin the construction e'am"les of the .*irages. and .Goncorde., which re"resent o"timal configuration#he tail<less air"lane, which Junker did not "atented and did not use in his "ro+ects J1000 and H @8,was now the $est solution in the su"ersonic

n the su$sonic area however the tail<less air"lane is a "artial solution of the wing< onl air"lane andwas "ro$a$l understood as such, so that the flight characteristics and the controlla$ilit could $estudied

For "erformance com"arison to the tail air"lane the wing<onl air"lane is to $e considered, asa""ro"riate for the mission #he attem"ts of different designers with tail<less gliders and sail<"lanes inthe twenties have so their +ustification, also then when the wing was connected with struts to thefuselage and thus ha""ened what Junkers wanted to eliminate with his "atent #he flight characteristics("articularl in stretched flight) where with these sam"les further develo"ed #he strutted swe"t wingwas also com$ined with tail air"lanes (falcon, su"er<falcon), although the strut force com"onent in thewing had to $e led over diagonals and secondar s"ars, which generall are not intended for it t is notto $e said that the tail<less air"lane is staticall more difficult than a tail air"lane, $ut onl that thetem"orar solution with struts (in regards to the Junkers "atent) had led to illogical sstems and thatthe, $ Junkers alread 191I constructed, cantilever wings meant a large ste" ahead in the direction ofthe wing<onl air"lane

Lift distribution

/ir resistance in the su$sonic region, in which from now on the wing<onl air"lane is to $e seen, wasclarified $ two messages in the Lifting =ing #heor $ L randtl ("u$lished 1918) #he divertedinduced resistance $ecomes a minimum, if the lift is distri$uted over the s"an in the form of a halfelli"se, in the case of a given s"an and a constant weight of the air"lane f now the wing has the formof an elli"se, then (without washout) the lift coefficient is same in ever "lace of the s"an Glose to thema' lift a local flow se"aration can $ring a rolling moment around the longitudinal a'is of theair"lane, which the "ilot can $arel ad+ust with the aileron, $ecause the whole wing is close to the ma'lift #he elli"tical wing was therefore s"arsel used for reasons of the flight characteristics and "roduction #he wing ti" (according to the suggestion of /hl$orn) was made thicker, similar to theanonia<;amen #hrough that the local coefficient of lift at the wing ti" is smaller than in the other "laces of the wing (even at elli"tical lift distri$ution), so that a flow se"aration is not to $e e'"ectedthere #ail<less air"lanes, according to the anonia "rinci"le, can have elli"tical lift distri$ution

#he lift was according to the mathematical derivative from the circulation of utta<Joukowski in wings"an direction as constant, $ecause the created vorte' could not change L randtl e'"lained, in Jul



1918 in Hoettingen, that the a$ove "ro$lem could not a""l in three dimensions, $ecause the $entcarring vorte' at the wing ti" induced on the carring line of the vorte' center, in 167 of the de"th , adownward s"eed w n the model of the .horseshoe vorte'., w $ecomes infinite at the wing ti"s, whichis "hsicall im"ossi$le randtl assem$led therefore the carring vorte' from man single vortices,

each resem$ling a horseshoe, and "roofed- if varies the intensit over the wing s"an ("ro"ortionall

to an elli"se), then the down<wash w is constant over the wing s"an, the wing ti" e'cluded De derived

an e?uation, from which the induced down<wash can $e calculated and from it the resistance, whichwas this wa calculated with the lift #he down<draft s"eed w of the vorte' center multi"lied $ the lift,re"resents an energ "er second, hence a "erformance, that must $e e?uivalent to another force timess"eed, therefore resistance times airs"eed #he elli"tical lift distri$ution with constant down<wash overthe wing s"an or constant a

i(induced /3/), resulted in a minimum for this .induced resistance. #he

e?uation from randtl, in the meantime, can not generall $e solved /t the wing ti"s, for which randtlhad re?uired that , the down<wash remains undetermined

4ou could kee" this &one small, "oint like, if , however, the down<wash at the wing ti" was

first ascertained when #wo different lift distri$utions result from it, those with "er"endicular

tangent at the wing ti" and those with hori&ontal tangent Gonse?uentl, different authors tried todescri$e the lift distri$ution "recisel enough to $e acce"ted $ the scientist ;chrenk gave 192 thesim"lest solution, to take the average value $etween the de"th distri$ution and the e?ual area elli"se,which results in a good a""ro'imation and is still com"letel sufficient toda for the calculation ofem"enage loads #his a""ro'imation had to fail, if the wing had a wash<out Li""isch, in 19@2, cameu" with an a""ro'imation method (;"ort Fling 19@2), in which the wash<out where included

De also mentioned the lift distri$ution with &ero<tangent at the wing ti", later termed $ me (Dorton) as $ell distri$ution n 19@8 *ultho"" succeeded to se"arate the critical wing ti" and to give a solution tothe e?uation for the determination of the lift distri$ution $ linear e?uations at certain "oints of thewing s"an (Lufo 19@8)

(#hese "a"ers of Li""isch and *ultho"", as dissertation recogni&ed, would have $een enough to $ereceived with honour in ever universit, however $oth were missing in the fulfillment of formalities ofthe curriculum, in order to receive acknowledgment)



Fig. 2 Lift distribution along the wing span. =ith a

central angle δ , which indicates the coordinates from

00 to 1800 as 4 5 cos δ in s"an direction, and which

descri$es the elli"tical lift distri$ution with cl t 5 c : :

t : e : sin δ , can also define the $ell distri$ution with

cl t 5 c : t : e sin@

δ n the case of a narrowing wing,in the e'am"le is the wing of the D re"resented, ouget without washout a .ormal >istri$ution., whichhas less lift at the wing ti" than elli"tical wing withthe same area, however $oth distri$utions have muchmore lift there, than the stretched $ell distri$ution=ith tail<less air"lanes, whose wing is arranged afterthe volume curve, the $ell distri$ution is necessar, to "revent to high lift values at the wing ti" ;ince the

distri$ution of sin2 δ is theoreticall not "ossi$le, was

the D after the c : t 5 c : t : e : sin

@ δ

curveconstructed, with which in 4 5 1 a &ero<tangent isavaila$leK contrar to the elli"tical and normaldistri$utions, with which at the wing ti" a vertical

tangent occurs #he distri$ution of sin7 δ , that leads

to larger induced resistance and those with sin2, δ are

also drawn in, since these have likewise &ero<tangents,

the curve sin2, δ remained however onl an attem"t,

$ecause the flight characteristics worsened and alarger a$ilit was re?uired $ the "ilots $eing, even sothe "erformance im"roved do to the smaller induced

resistance

De selected these "oints according to a central angle d (as cos d ), the elli"tical distri$ution wasaccording to "ro"ortionall to sin d =ith given chord length and local wash<out angels could so the liftdistri$ution with sufficient accurac $e determined and com"arative calculations showed that thedifferences were small o""osite the calculation "rocedures of Li""isch, which was onl ana""ro'imation solution 3n the other hand, the local /3/ could, for an intended lift distri$ution withgiven de"th, $e determined, that is a total /3/ and a washout !'ce"t for the smmetrical distri$utionsof the straight flight, ou could also asmmetricall calculated the aileron deflection and the rollresistance, which was im"ortant for the air"lane laout ;ince these calculations can toda $e moreeasil e'ecuted with com"uters, it is not worth it to go into greater detail with the method and onl theresults are shown, which were derived at different distri$utions (a""lied to the sam"le D with a ta"er

of the wing troot 6 tti" 5 8, as"ect ratio $26F 5 87 and ) =ith the designations of *ultho""

is the $ell distri$utioncl: t 5 cte sin@d /lso was investigated cl : t 5 cte : sin7d and clt 5 sin2d, as

well as the normal distri$ution (without washout), and necessar washout and induced resistancedistri$utions for cl 5 1

t results-



DistributionForm

LiftCenter

Cwi/Cwi

ell.

YClmax Yaw

Normal 0.385 ./. 0.88 negative

Ellise sin 0.!"# # 0.88 negative

$ell sin3 0.333 #.33 0.3% ositive

$ell sin! 0.30& #.5! 0."& ositive

$ell sin".5 0.35# #."3 0.!%5 0

egative aw meant that an aileron deflection "roduces a moment around the vertical a'is o""osing theturn, which must $e $alanced with the rudder

Fig. 3 #he necessarwashout (to give the D the $ell distri$ution) is recordedin the a$ove gra"hs t isunderstanda$le that with a cltotal smaller than one, "ro"ortionall also thewashout $ecomes smaller#he rudder kinetics has to

ada"t to the gra"h in such amanner that with the rudderdeflection the washout gra"his "reserved for a modified cltotal, thus with the rudderdeflection a varia$le washoutis arranged

ickel has, in 1878 (#M$ingen >iss), calculated >istri$utions, which resulted in a minimum of theinduced resistance Nnfortunatel without s"ecifing the resistance distri$ution and without the datawhich are necessar for the a""lication #he occu"ing authorities had for$idden the aviation research

at that time t would $e to $e welcomed, if toda the work were concluded n the distri$utions of ickel is the vertical tangent 4 5 1 allowed, so that ?uite different lift distri$utions develo" than thosefor the $ell form / gra"h, which >r arl ickel gave the author (Dorton) in /rgentina, is shown (Fig)



Fig. 4 Local lift coefficient atdifferent lift distri$utionscalculated for the wing of theD at cl<total 5 10 4indicates the center of lift ins"an direction Glose to it

should, with increase of the/3/, the se"aration the flowof take "lace first, so thatfrom the locall decreased liftno moment will occur #hecenter of lift and the GH ofthe air"lane must corres"ondin '<direction, if at the wholewing cm0 5 0 and no rudderdeflections e'ist #heelli"tical lift distri$ution has

its ma' cl with 4 5 088,their center with 4 5 0,721,therefore it is ?uite unsuita$lefor this wing sha"e #he $elldistri$ution with the ma' liftcoefficient in 4 5 0,@I andcenter of lift in 0@@ fulfills?uite well this condition(small differences arecontrolla$le), if the wing ti"swith their rudders o"erate in

strong flow #he wing ti"must $e well "rotectedagainst flow se"aration,which the $ell distri$utionensures at all ta"ers, u" to thetriangle wing

!ven if these distri$utions could not $e used, it can nevertheless $e said without closer investigation,that a calculation is necessar of the negative c l values occurring at the wing ti", $ecause a se"aration

of the current on the wing ti" lower surface (>unne) would influence the e?uili$rium and thecontrolla$ilit articularl with the ta"ering of the wing the danger e'ists, which must $e "ointed out

!ven more flow se"aration is to $e e'"ected $ the use of Frise t"e ailerons in which the de"loedaileron leading edge is su""osed to do +ust that /ilerons, which are deflected in the same direction aselevators, are necessar, in order to change washout "ro"ortionall to the lift coefficient, as >unne wasfirst to show !ven with e'cessive ta"er can this sstem "revent ti""ing and ensure controlla$ilit, evenin the e'treme flight

Aecause of the, towards the wing ti", diminishing lift, the reduced lifting vorte' trails off in singlevortices in flight direction to the rear #hese induce a down wash at the "lace of the main vorte'according to the radtl%s lifting wing theor n the case of a swe"t wing the segments differ from those



of the strait wing, so that with it shifts occur and the wing ti"s receive less down wash n addition, thelifting single vortices influence each other at the swee" $end (that is right and left), and there, throughthe local

Fig. #he inducedresistance distri$utions of all $ell distri$utions show

"ro"ulsion at the wing ti"#his is favora$le withaileron deflection, since the4aw changes its valuearound the vertical a'is, thus $ecomes "ositive f therudder kinetics "reserves the $ell distri$ution at all cl<value, then the 4aw isavoided, or even "ositive, atall cl<value #his is, on the

one hand, favored $ the "ilot, on the other hand alarge "art of the ruddereffect is there$ su"erfluous

down draft, create a .lift hole. =hether the .u" wash. at the wing ti"s and the .down wash. at the rooteliminate each other, could not $e "roven Dowever, different lift distri$ution than those of the straightnon swe"t wing develo"s, with other lift centers of that of the half wing / o"e, due to wind tunnelmeasurements, gave the correction as such, that with c l total 5 1 a > cl : t is to $e deducted according to

the formula > cl : t 5 2 (1 < ) (1 < cos +), where$ + the swee"<angle of the t 6 7 < line is #his

em"irical formula gives a correction in such a manner that cl : t+ 5 cl : t1 < > cl : t !ven if the "hsical $asis is not contained in it, nevertheless the e'"eriments in the wind tunnel confirmed thea""ro'imation

f the lift distri$ution has a turning "oint (as with the $ell distri$ution), the vortices going off to the rear



Fig. ! 3"timal liftdistri$utionaccording to ickel /t a givenlift and longitudinalforce the inducedresistance isminimal

are stronger inside then outside #herefore the induction is so, that the down wash in the core of thevortices transforms at the wing ti" into u" wash ;tarting from 0I of the half s"an outward the $elldistri$ution has u" wash and the additional distri$utions $ aileron deflection, which causes a momentaround the vertical a'is, changes likewise it%s sign t is understanda$le that the "ilot, with the sam"le of4aw, draws a conclusion on the lift distri$ution and thus on the GH of the air"lane =ith the reali&ationof 4aw thus can $ecome .$alanced. =ool tuff e'"eriment ("hotogra"hed at the wing end of an D )acknowledged that with .more correctl. "osition of the center of gravit (thus $ell lift distri$ution) the

=ool tuffs was "ointing in flight direction, even if there is no lift and thus no cross "ressure slo"e andno cross flow /lso, the "hotogra"hing of the =ool tuffs at the wing ti" served to determined the GH,that is the $alancing

Fig. " =ith the .o$ot., installedat thewing ti" of the D , =ool tuffs could $e "hotogra"hed, which dis"laed the flowdirection there =ith $ell distri$utionand local cl 5 0 a vorte' is not availa$lethere, the direction of flow on to" and $ottom side are the same (#he sheet

metal at the other wing ti" serves for themoment $alance around the verticala'is #he asmmetr is caused $ thetu$ing and the Gamera) =ool<tufts onthe white<"ainted wing root werelikewise "hotogra"hed, in order to makethe center effect visi$le #his howeverwas without success, since the currentalwas fitted and so it could $e "roven

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that the center effect results from the ai<distri$ution and not $ a se"aration ofthe flow

Flaps

Junkers $uilt in 192, for the first time on the # 29 air"lane, landing fla"s in form of an au'iliar wing,which divided, worked at the same time at the outer wing also as aileron #he ma' lift coefficientalmost dou$led itself during o"timal au'iliar wing "osition =ith the same landing s"eed one couldthus almost dou$le the weight6s?f, or to $uild a wing onl half as large with same fling weight #hisJunkers dou$le<wing, caused different landing fla"s sstems to $e ignored, seemed to out<date thewing<onl idea, $ecause the wing could, and had to, $ecome smaller n addition it $ecame o$vious thatthe occurring "itch<moment needed an em"ennage for the $alancing t is therefore understanda$le thatJunkers, after the H @8 (which also had these landing fla"s), develo"ed the tail (.normal.) air"lane Ju2, in order to use the "ossi$ilities that his au'iliar wings invention $rought #oda these dou$le<wings are not used an more, although their advantages in relation to other sstems continue to e'istand the "ossi$ilities with Laminar airfoil were not et sufficientl e'amined #herefore, in the

develo"ment of the wing<onl, landing fla" com$inations had to $e included, with which we dealt inthe "receding sections

t must $e still "ointed out however that the airfoils of the tail air"lanes at that time with a""ro'imatelcircularl curved center line, after integration of the landing fla"s (that caused the ma'imum lift forlanding), were changed to airfoils with small airfoil moments, which are also suita$le for tail<lessair"lanes

/ su$stantial feature in the difference of the wing sha"ing of $oth $uilding methods was there$omitted ow it had to $e "roven that landing fla"s are also usea$le with the onl<wing #he >CL alsoannounced a "atent for a fla" form, which "roduced no moment Dowever it was overseen that a lift

increase at the wing root of the swe"t wing results in a $ackwards acting moment, that the airfoilmoment of the fla" is however to"<heav (thus o""osite)had $een ignored #here are "ossi$ilities,however, of com$ining the moments in such a wa that the resulting moment $ecomes &ero /lso, theta"er "las an im"ortant role, $ecause the "ointed wing with same landing fla" s"an has more wingarea influenced $ the landing fla", than the rectangle wing (at the same time less surface at the wingti" $urdened with small lift coefficient) #he "olar, which are measured with the a""ro"riate rudderdeflections, are called e?uili$rium<"olar Later investigations resulted in that landing fla"s at the deltawing root are alread sufficient, in order to raise the lift over the whole s"an #he induction causes thatai dro"s more strongl towards the wing ti"s which therefore increases the effective /3/

Fig. # Landing fla" order of the DC$ #hese landing

fla"s had a full moment $alance around the hori&ontala'is of the air"lane n 197@, the DCc was assigned to the/erodnamic La$orator Hoettingen from the esearch<nstitute, in order to make takeoff and landingmeasurements and determine the ma' lift, which is the $ase for "erformance com"arisons with tail air"lanes

Dowever, since fla" foils have a smaller ma' /3/, landing fla"s in mid<s"an can cause "rematurelocal se"arations and thus "revent the effectiveness of the fla" sstem =ind tunnel measurements

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/theory/theory_pic__2.jpg



$efore 197, using such landing fla"s, led to the wrong o"inion that the delta wing was unsuita$le forlanding fla"s t should $e "ointed out that the delta wing with a small fla" in the correct "lace (thewing root) increases the lift in such a wa that it is suita$le for almost all aircraft designs, with theflight characteristics not $eing com"romised / strong ta"er is therefore, as stated, advantages n orderto get a ?ualit gra"h with ma' landing lift to resistance in the high<s"eed flight (to $e used as aardstick), one can refer the ma' landing lift to the air<surrounded surface (without fla"s), since the

resistance in the high<s"eed flight is mostl friction resistance =ith the wing<onl, the value 10 can $eeasil achieved =ith the tail air"lane, the fuselage and the em"ennage would have to $e added assurface Dowever, all these com"arisons have their draw$acks n this case, the $oundar laer is notincluded, which can have su$stantial differences in the drag coefficients at enold num$ers $etweenthree and twelve million during a laminar flow #he swee" does not "revent the laminar effect, as wasshown with gliders

$otes to the theoretical basis of the interpretation of the % &&

=as it in the delta, with inner elevators, mainl the local airfoil moment ,which at large airfoil lengthcaused the control moment , an increased swee" had to take over now this

function

>uring the transfer of the elevators into the aileron at the wing ti"s, the local de"ths remained small

with large ta"er, so that the second integral ($ecause of t2) can $e neglected #he first, however,contains ', the distance of the wing com"onent (re"resented $ the t67 <"oint) to the GH For it to $ecome reall effective, ', which is the swee", must $e large #he D , therefore, was su""osed to

receive a stronger swee" and larger ta"er =hen the lift distri$ution considera$l influences the altitudecontrol, it is reasona$le to assume that the wash<out of the wing must change "ro"ortionall with thelift coefficient For $alance reasons, the centre of lift must corres"ond with the GH of each half<wingin longitudinal directionK in addition, the wash<out changes with the rudder deflection For e'am"le,with c

l 5 0, the com$ined aileron<elevators in &ero "osition and the wings have a rigid wash<out of

0 f the "ilot wants to fl now with c l 5 10, the elevator deflection must $e as large as the

$asic wash<out, thus o ;o the term Caria$le =ash<3ut develo"ed n the ideal case, without chordmoments, one has to multi"l the lift distri$ution onl with one factor, in this e'am"le 2 #he form andits GH remain unchanged / "rere?uisite for it is that the wing de"th at the end in the rudder area is

small ($ ta"er or high as"ect ratio), or that the value $ecomes &ero, as for e'am"le with a

rotation of the whole wing ti" For a later "ro+ect, the D , the aileron<elevator would have to $edivided into several fla"s, which would have to o"erate with different deflection angles, in order tore"resent the necessar wash<out form more e'actl =ould one then transition to the half of the wing<de"th, thus receive dou$le the D as"ect ratio (D C), then the local chord moment would have onlone fourth of the value of the D $ecause of the de"th s?uare, with which c m is connected #he

altitude control, due to the wash<out change, would then $e more "ro"ortionall to cl n other words,

the distur$ance $ the local moments (caused $ the fla" deflection) will $e less significant For the D



, with smaller as"ect ratio, another solution would $e a rotating wing ti" #he wash<out would then

get a ste" $ut with the chord moment of the fla" deflection would e?ual &ero #hese

considerations "resu""ose a airfoil whose cma

5 0, throughout the whole wing

n com$ination with the first "oint (the lift hole at the head of the swee") one could now $ring the

rudders into neutral "osition and measure the s"eed of the air"lane, so that the c l can $e calculated and

check the com"liance with the design lift coefficient

n addition, one can go the other wa, calculate out of the design lift coefficient the s"eed, then correctthe GH "osition in such a wa that the flown and the theoretical s"eed corres"ond with the neutralrudder "ositionK this "rocess was later called .$alancing out $ the neutral rudder "osition.

Fig. ' #he wing<ti" of the D #he wash<out ste" o$tained $the deflected aileron is visi$le at 4 5 09

>uring flight testing of the D the ?uestion came u" in 19@7- which form of the lift distri$ution shouldthe new construction, the D , receiveO #he aileron aw moments had $een the determining factor with

the D for the controlla$ilit #he $ell lift distri$ution with the &ero

tangent in 5 1 had resulted in a defined descending flow over the whole s"an and with that an

induced /3/ From the turning "oint of the lift distri$ution to the outside the induced /3/ changedit%s sign, even so the lift remained "ositive =ith the calculation of the induced resistance distri$utioncl:t:ai in wing s"an direction the wing ends received "ro"ulsion =ith 4 5 0I changed a i it%s sign, that

was something newK one could use negative induced resistance for the com"ensation of aileron aw fthe aileron would $e enough from 4 5 0I to 1, then the induced aw moments would have the o""ositesign #hus the correction of the aileron deflection would $e reduced or even unnecessar $ a fullrudder deflection, the rudder could then $ecome much smaller ;ince the lift distri$ution form doesn%tchange much $ varia$le wash<out during the elevator deflection, then this effect is attaina$le with alllift coefficients thus all s"eeds /ileron and rudders will then $e se"arate and inde"endent, as long asthe $ell distri$ution (the turning "oint) was achieved #hat was the theor of the lift distri$ution for theD

#he washout ste" at the transition from ailerons to the fi'ed, immova$le wing ti" (called ear) at 4 509 had a good affect on the aw in the D and it should therefore remain Aesides, the aileron<elevator, which reaches from 4 5 0I to 09, a""eared as ?uite small t was designated therefore fromhalf the s"an and u" (4 5 0 to 4 5 09) t also resulted that wing washout needed for the $elldistri$ution $ecame smaller with larger ta"er of the wing com"ared with a small ta"er or with therectangle wing #hus a large ta"er was not onl advantages for the wing volume, $ut also for thenecessar washout #he calculation of the local c l load resulted, that with increased ta"er of t root 6 twing<



ti"s5 8 it reached a ma'imum at 4 5 0@I #hat, however, is almost at the lift center, which is in the

$ell at 4 5 0@@ / se"aration of the flow starting at 450@I should therefore hardl resulted in achange in GH, at least it should $e controlla$le #hat means .;"in resistance. or at least controlla$ilitin the e'treme flight #he disadvantage of the $ell distri$ution, an a$out @@ higher induced resistancewith same s"an com"ared to a wing with elli"tical lift distri$ution,had to $e acce"ted $ecause of the

flight characteristicsK that is, in order

to kee" same cwi, the s"an of the $ell distri$ution must $e around1 larger than with the elli"ticaldistri$ution at a given wing area

#he airfoil distri$ution over thewing s"an, however, is likewisedetermined $ the $ell distri$ution,as the airfoil at the wing ti" can $esmmetrical, $ecause there cl is

alwas small, and even a trianglewing has near 4 5 1 a small c

l #he

se"aration of the flow is thereforethere not to $e feared

=ithin the range from 4 5 0@ to 07should the se"aration $egin, even ata cam$er of the airfoil middle line

within this area is this fulfilled #he ma' cam$er can, at last, $e at the wing root t is o$vious to sha"ethe wing linear from the root airfoil to the wing ti" airfoil and to use a fi'ed<"ressure<"oint airfoil at theroot(c

mo 5 0) =ith the formulas of Airn$aum for c

aoand c

mothe center line of the root airfoil was

drawn and modified "oint for "oint in such a wa, until cm0 5 0 was achieved

Attempt of a repetition( % )&* + ,olonia +

Aeside the $uilding the D EC c and the D3 @@ there was a third attem"t to $uild Dorton t"e inHerman after the ;econd =orld =ar- it was the D EC which was almost read for flight at the end ofthe war

#he motivating force in the /erodnamic /ssociation olon was ! Gilsik #he "ro+ect was "ursued inan e'tensive corres"ondence across the /tlantic awa Lack of funds led after five ears, in 19, forcancellation of the work /t this time the fuselage mocku" was finished =ind tunnel e'"eriments with

models, $uilding of the devices and man detail investigations had "receded

3riginall the .Golonia. was su""osed to get the airfoil of the D C #hat%s how the D EC was $uilttoward end of the war 19@ the airfoil was changed to one with a larger laminar e'tension,unfortunatel in vain

;"ecial features of this design were the wing narrowing near the center "iece, the small fins on thewing at 70 meters of the half s"an and the rear of the fuselage develo"ed as the dive $rake

,oordinates of the % &&& root-rib. (#hrough multi"lication of@6@2 ou get the coordinates of the D )



n Januar 19 the "ro+ect D EC .Golonia. was given u", even though after thorough testing of the "rotot"e in an im"roved version with 1 meters wing s"an could $e counted on having a lift6drag ratioof @8 to 70 #hese where e'cellent "erformances for that time for a 1<*eter<Hlider with rigid airfoil

Engineering department

Chance Vought Aircraft'tratfor() Conne*ti*ut

#itle!'cer"t from LHA<176/dvance e"ort

Ten ears /e0elopment of the Flying Wing %igh-peed Fighter

a"er "resented $ the Dorten Arothers, Aonn $efore the

Fling =ing ;eminar, /"ril 17, 197@

Ten ears /e0elopment of the Flying Wing %igh-peed Fighter

A Dorten Arothers, Aonn

e"ort o LHA 17

/fter three ears of fling activities which were used to "re"are the $efore the glider e'aminations, andaside from worksho" "ractice for the theoretical $asis of air"lane construction, we decided in 1928 togo into the construction of all<wing air"lanes

#he develo"ment stage of the model lasted five ears, until enough confidence was gained to assumethe res"onsi$ilit for the construction, to stud the flight characteristics of all<wing full<scaleair"lanes #he construction of models, which was su""lemented $ continued designs of largeair"lanes, after sstematic stud, gave us the e'"erience for this full<scale construction #he results ofthe model construction ver soon showed, the necessit for o$serving enolds% laws of similarit asthe are "resented in the recentl "u$lished $ook $ F = ;chmit&, ./erodnamics of the flingmodel. ("u$lisher Colkmann) /fter these relationshi"s had $een cleared u", sstematic work, "articularl in the field of flight characteristics, could follow t was shown at that time that thea""arentl "ro$lematic sta$ilit a$out the lateral a'is of tailless self<sta$ili&ing wings does not give risean "articular need for attention Furthermore, it was shown the center of gravit location was "ossi$le

in front of the G<"oint (see the work .;ta$ilit consideration in swe"t $ack wings. in this re"ort) u"onwhich the calculations of the times were $ased #he models were usuall $alanced at the G<"oint /rear location of the center of gravit had the accom"aning t"ical characteristics (.falling off.), aforward location of even 10 "ercent to 1 "ercent of the measure of swee" $ack had o$+ectionless flightcharacteristics For this reason considered the "ro$lem of sta$ilit a$out the lateral a'is as solved, andturned our com"lete attention in the construction of models to the moments a$out the verticala'is !ven toda it is our view that the essential "ro$lem in the construction of air"lanes is thesta$ili&ing a$out the vertical a'is 3f course, the model flights were made onl with glider modelswhich, in order to fill the enolds% similarit laws, had s"ans of @ to 7 meters and weights of 10<1



kg Flights were tied to hill countr /fter the start of such a model, a$solute adherence to the coursewas necessar, and a turning meant contact with the ground against the direction of sus"ension at alarge angle, hence fracture For this "ur"ose models have to $e $uilt in such a wa that turning does nottake "lace n contrast to the construction to full<scale models, the sail"lane model had to $e neutral inits moments a$out the vertical a'is in awed flow #he full<scale air"lane, when in awed flow,demands all weather<cocking effect of the side surfaces which lie $ehind the center gravit #he

sail"lane model in contrast, cannot, as alread stated, turn like a weather vane, $ut must use the awedflow to raise the de"ressed area n other words it must "ossess a "ositive rolling moment due aw, $utno awing moment

n 19@@ the real develo"ment $egan with the construction of the sail"lane of 12 m s"an at the "arentalresidence #his model .Dorten . was intentionall so designed in its side areas that in awed flow nomoments resulted a$out the vertical a'is >irectional control was alread then, as in all later t"es,accom"lished through $raking of one wing #he fla" arrangements of the lateral control services, whichwhen not actuated, form the surface of the wing, have $een develo"ed in various was in the course oftime #his de"ends and the control forces availa$le to "roduce the drag re?uired in each case, as well ason the effect of other distur$ances on wing, which the evoke 3n all models arranged in such a wathat the created neither lift nor negative lift at the wing ti"sK that is, fla"s on the underside of the wing,

de"ending on the method of attachment, were over<dimensioned $ 20 "ercent to 0 "ercent com"aredto the to" side fla"s *oreover, it was "ossi$le to "roduce the aileron $ehavior in the same wa as isdone in the conventional air"lane, that is, the maneuver and action are the same as usual /t that timewe naturall discussed the advisa$ilit of such a steering a$out the vertical a'is, and found that e'istsKthat is, we discuss the ?uestion whether the "roduct of flight time ' drag is smaller with this form ofcontrol than with the conventional arrangement t is clear that the rudders in the normal arrangementcause a relativel small drag when dis"laced and that the lift com"onent "er"endicular to the surface,amounting to from ten to twent times the drag, acts on the lever of the fuselage in the conventionalair"lane and thus "roduces the awing moment #he added drag caused $ the movement of the aileronin the conventional air"lane surel is smaller, in general, and that other $raking fla"s at the wing ti"s,which a""ear in our models, where it is e'actl this drag, acting on the lever of the semi<s"an, which

must "roduce the awing moment =hen the are not dis"laced, however, these fla"s do not "roducean additional drag since the form "art of the contour of the wing n discussing the "ractica$ilit ofthis form of control the ?uestion now arises concerning the fre?uenc of their use, in order to determinefrom this the "roduct of drag ' time /ccording to our test and counts in 19@7, one achieves a reductionin drag with his form of control of 0 to I0 of that of the surface controls on sail"lanes in thermalflights /ccording to later e'"eriences with "owered air"lanes this reduction increases to 9 n thesecom"arisons the shortened high<s"eed flight condition is not taken into considerationK instead drag forthe whole flight is considered For the "urel high<s"eed flight conditions, however, the saving is100

n contrast to the aileron develo"ment, the model .Dorten . showed an incom"lete vertical and lateralswing #he advantage of the fling wing does not stand out so much in the case of the sail"lane as in

the develo"ment direction of the high<s"eed fighter

n order to su""l advance work for this, "rofiles were develo"ed whose mean cam$er linesmathematicall is a""ro'imatel the .constant center of "ressure. t"e rofiles of this t"e whichwere tested, $rought out all their weaknessesK $e it in the distri$ution of thickness, which makes thestatics un"leasantK $e it in the form which causes too high local velocities, or, as is "articularl the casewith /merican wing sections, where too little em"hasis is "laced on the flow +uncture at the trailingedge #hus there came into $eing after man estimates, a mean cam$er line with a mathematicallconstant center of "ressure, which o$tains its cam$er for the "articular a""lication through a change in



the scale of the ordinates #he .teardro". which is "laced on the mean cam$er line unfortunatel couldnot $e taken over either, since the "rofile forms from which a good flow +uncture can $e e'"ected,a""ro'imatel the Joukowsk<forms, $ecome so shar" at their trailing edge that their incor"orationdoes not a""ear "ossi$le #he other forms, however, are right awa so $lunt, that the characteristic ofthe mean cam$er line is lost through the $ad flow +uncture at the trailing edge which is then to $ee'"ected #hus here too, satisfactor com$inations had to $e found through suita$le com"romises

*uch more "reliminar work was necessar order to make a "ro+ect of fling<wing high<s"eed fighter(see a lecture on the as"ect ratio considerations of this "ro$lem in e"ort /@761 of the Lilienthal;ociet, " )

#he design resulting from these considerations, the model .Dorten C. was com"leted in 19@ /llattem"ts to interest the aircraft industr, or other national s"ecialists, in it, remained unsuccessful withthe e'ce"tion of the >namit Go #roisdorf, which is not an aircraft construction firm f we wanted tosta in the countr, and this we considered necessar for national reasons, we had to acce"t thisoffer =ith it we took over as a further "ro$lem, the use of fa$ric in air"lane control surfacearrangements /s a result, in s"ite of good flight sta$ilit, $ad controlla$ilit was encountered, so thatwe would not assume res"onsi$ilit for flights $ other "ilots /fter the "artici"ation at the hoensail"lane contest it was dismantled in order to make wa for new constructions #he flightcharacteristics themselves were so good, that even then an instrument flight of @67 of an hour was madethrough clouds

/fter the hoen sail"lane com"etition of 19@7 < at that time the .;ta$ilit Gonsiderations in ;we"t$ack=ings. was com"leted P it was $oth logical to "rove the inde"endence of the lift slo"e distri$ution ofthe "latform, and its de"endence on the center of gravit location in swe"t$ack wings, $ incor"oratingan e'treme ta"er ratio of 1 to 10 For this reason alone the model .Dorten . was $uilt, again in the "arental house, since it was not "ossi$le to o$tain an kind of hel" or worksho" facilities for this "ro$lem /fter more than a ear%s construction time, the "roof could $e attem"ted, and the hundreds of "ilots and several thousand hours on this model alwas confirmed the correctness of these "rinci"les #he elevator and aileron arrangements of this air"lane, according to e'"erience, were $uilt

in such a wa to ever air"lane "ilot and sail"lane "ilot even with the least fling e'"erience (1 to 2hours in the air) could fl it without re<schooling, so that soaring on instruments, and cross<countrflights u" to 270 kilometers (10 miles), followed re"eatedl =ith this the aerodnamic "ro$lem wasin itself solved n order to decrease the flight e'"ense the air"lane is e?ui""ed with a 0 horse"owerDirth motor, with which it flew a$out 80 hours #he work was then interru"ted $ the draft

Aefore this, all variations of the sail"lane and "owered air"lane were worked out as "ro+ects, and eventhe "rone "ilot "osition was treated #he resulting designs of the models .Dorten and C. were set $ack, even though the ielded advantages in "erformance over the com"arison sail"lanes

#he dou$le "ro$lem and the draft made construction ver difficult, so that the twin<engined model.Dorten C. could not $e $roken in until 1<162 ears later in *a of 19@I

#he flight results were satisfactor, even if (we were working with an all<fa$ric air"lane) difficultiesarose the gluing of materials which would have $een shortened the lifes"an, and which furtherstrengthened us in our search for a sho" were sim"le wood construction could $e undertaken #heair"lane itself was ?uickl evaluated, and in a landing received damage which made it%s reconstructionseem im"ractical =e succeeded in the winter of 19@I<19@8 in constructing a sho" in which theair"lane could $e created anew in the mi'ed wood<steel tu$ing construction #his new craft has "roveditself $ man hours in the air with various "ilots, and is e'tensivel descri$ed in maga&ines

#he real "ro+ect, the fighter air"lane, could not $e constructed with such sim"le means For this reasonwe $usied ourselves constructivel in the field of sail"lanes #hus in 19@8, the old "ro+ect .Dorten @.,



sitting the "ilot in the fling wing, was studied further #his model was re"roduced in a$out 20s"ecimens $ the various glider clu$s, and is well enough known /t the "artici"ation in the hoensail"lane com"etition of 19@8<19@9, the advantages of the fling wings were shown, and re"eatedaltitude flights over ,000 meters (20,000 feet), and distance flights over @00 kilometers (18 miles)were made #he results showed that such flight characteristics had $een achieved that it was called thea""ro"riate tool for instrument flight #his was "artl achieved $ constructing the elevators and

rudders in a "articular wa !ach one has two fla"s, of which the outer forms the function of clim$ingcontrol and the inner "erforms the function of diving control A means of the activation then, thefunction other elevators divided into its main actions, that is, with this arrangement at deflections of thediving controls the total incidence in the wing is maintained, and thus transcends the neutral sta$ilitwhich necessaril a""ears high<s"eed and diving flight with wing fla" controls /t the deflections ofthe clim$ controls, however, onl the outside fla" deflects u"ward (the inside fla" onl accom"anies itthree or four degrees) so that the wing elements with large cords are not e?ui""ed with controls andconse?uentl can maintain their full lift coefficients Gonversel the wing ti"s, which $ecause of thecontrol deflections work at lower lift coefficients, form a smaller fraction of the totalarea Gonse?uentl, the ma'imum lift of the whole wing for this control arrangement is high, althougha .falling<off. $ecause of the ca decrease at the wing ti"s, is not to $e feared /t the deflections of the

ailerons a differential action is effected $ this arrangement #he aileron deflection itself is, as weknow, com"osed of diving control deflection on one side and of clim$ing control deflection on theother side, where the control fla"s must $e so dimensioned that a moment a$out the lateral a'is is not "roduced n the case of single<fla" control with differential transmission, this action cannot $eo$tained, and the "ilot will counteract the "itching moments resulting from the aileron deflection $ a "ushing of the control column, and thus will eliminate the differential action of the arrangement #heonl "ossi$ilit of reali&ing differential controls in tailless air"lanes lies in the two<or<more fla"sstem Aut this arrangement also $rings with it to further advantage, es"eciall for high<s"eedflight #hrough the method of actuation the transmission can $e selected in such a wa that it is small inthe vicinit of the control stick neutral "ositionK that it is, relativel large stick movements areaccom"anied $ small fla" deflections, while with larger deflections the transmission ratio increases of

its own accord #his transmission characteristic, which we have called ."rogressive controls. for short,will $e "resu""osed for the reali&ation of high<s"eed aircraft

#hrough this and other e'am"les there arose the o""ortunit to $ring construction to such maturit thatthe res"onsi$ilities for the $uilding of high<s"eed com$at aircraft from constructive "oints of viewcould $e assumed at antime

3ther e'am"les of construction of all<wing sail"lanes, for instance, a ara$ola for s"ecial "ur"oses,trans"ort sail"lanes for 1I "ersons with 27m s"an, arose incidentall

n the Fall of 19@8 we again su$mitted a design for a twin<engined air"lane which was first to $e "owered $ two /s 10c motors =e were referred to several industrial firms who, although the wereagreea$le to a "ersonal entr into their factories, could not $e dealt with regarding the carring out of

the fling<wing "ro+ect in the form which would $e necessar for the reali&ation of such a "ro$lem #hus this "ro+ect, the .Dorten C., also had to $e set $ack

n 19@9 then, the o""ortunit of working in the main direction of develo"ment was not o"en to us, sowe decided to $uild a high<"erformance sail"lane with "rone "ilot%s "osition, the .Dorten C. #hroughthis arrangement for the "ilot it was "ossi$le to hold the wing thickness, and with it the chord of theroot, so that with a 20m s"an, an as"ect ratio a""ro"riate to soaring was o$tained Dere for the firsttime the fling wing had o""ortunit to "rove that it $rings with it the "erformance advantages for eventhis "ro$lem Gom"arison flights with corres"onding conventional aircraft "rove the correctness of this "oint of view



#he work was again interru"ted $ the war until 1971, when in the Fall $ virtue of the announcementof a similar aircraft $ the orthro" Go, N;/, a re"air contract for our old twin<engined "lane,.Dorten C., was received and was added to our e'"eriences #his air"lane and shown interestingresults in the increase of the ma'im lift, "articularl through the arrangement of it%s landing aids t was "ossi$le, $ the use of cam$ered and s"lit fla"s, to sur"ass a total c

a of 1 without slats, with and angle

of swee"$ack of 72 degrees #he use of landing fla"s on swe"t$ack wings, and their action, ields the

$asis for "erformance com"arisons with conventional aircraft #he landing aids of the model .DortenC., however were not et sufficientl develo"ed that the could $e used for final com"arisons, and "arallel com"arisons on sail"lanes with cam$ered fla"s and retracta$le center slats (similar to the>uck) "ermit measurements of ma'im lift of 18, even though these e'"eriments were unfortunatelcarried out the wings with onl 27 degrees of swee"$ack A skillful use of these landing aidcom$inations ma $e assumed that even with 70 degrees of swee"$ack a ma'imum lift for the wholeair"lane of 20 will $e attained, a value which toda is "resent onl a few conventional air"lanes nthis connection the flight e'"eriences with the model .Dorten . ma $e interesting, which is sta$leeven with full landing fla" deflection and makes "ossi$le $ dive<like a""roaches to the "oint oflanding, and after "ulling out, s"ot<landing the air"lane in the narrowest of s"aces #he controlcharacteristics with de"ressed fla"s, were here$ shown to $e ade?uate and the moment a$out the

lateral a'is is not distur$edt should $e mentioned that almost all or air"lanes are e?ui""ed with triccle landing gears and that thenose wheel in all cases is free<swiveling #hrough this arrangement of the wheels, for which the all<wing air"lane is well "redis"osed, the ground characteristics will $e a""recia$l im"roved overconventional aircraft

*an individual e'"eriences have occurred in o"eration of air"lanes during the course of theears #hus, to give a few e'am"les, the flight of a sail"lane without "ilot%s cano", through which alarger area of se"aration was created on the u""er surfaces 3n the flight under consideration, it was "ossi$le to land the aircraft without a trou$le, even though the landing s"eed was a$out 20 kilometers "er hour higher n another case a "iece of cowling from the to"side of the air"lane flew into the

"ro"eller, in the takeoff of .Dorten C. and forced the "ilot to sto" one engine #he "ilot continued toclim$ on one engine without cowling and concluded his local flight, and even for lack of flinge'"erience, turned towards the dead engine and landed smoothl n another case an air"lane iced u"heavil in clouds #he "ilot could not notice this until he left the cloud /ccording to his re"ort, theaircraft had at the leading edge a cm laer of ice #he sole result was an increased rate of sink, $utthere was known nose heaviness, as is usual with straight wings #he loosening of the laers of ice onthe swe"t$ack wing in such cases also leads one to e'"ect sim"lified methods of deicing

#he studies undertaken so far aim at the develo"ment of the fling<wing fighter #he assume that the "ower "lants are availa$le which can $e $uilt into the wing, and that conse?uentl in the nacelles willnot $e necessar !ven though the fighter air"lane with "ro"eller and reci"rocating engine has not et $een created in this form, the "ro$lem can nevertheless $e considered as solved $ the e'"eriments and

flight characteristics studies #his line of develo"ment will surel come when it $ecomes necessar tofl economicall, and this is onl the case with long<range air"lanes in time of war

n order to o$tain criteria for the com"arison of "erformance with conventional air"lanes one mustselect a reference carefull and determine the other ?uantities from it #he landing s"eed is fre?uentltaken as this reference ?uantitK that is, the wing loading is chosen de"ending on the ma'imum liftattaina$le, so that the air"lanes to $e com"ared have e?ual landing s"eeds #his t"e of com"arison forthe fighter "ro$lem, or even the long<range fighter air"lane, is not ?uite right, for the dis"osa$le loadsamount to 0 "ercent of the fling weight, and it is no "ro$lem to negotiate a landing with an air"lanethus lightened #he conditions are different, however, at the takeoff For this, aids have $een created in



the form of concrete stri"s, takeoff rockets, cata"ults, etc, which facilitate the takeoff t is, therefore,more "ur"oseful to introduce the s"eed of takeoff as the reference ?uantitK that is, to select a wingloading de"endent on the lift coefficients attaina$le at takeoff #he landing fla"s and then are e'tendedin takeoff "osition, and there is no reason wh in this configuration the conventional air"lane shouldo$tain higher lift coefficient than the swe"t$ack wing efinements, such as .increase in dnamic headthrough the sli"stream of the conventional aircraft. or $etter .o"erating efficienc of "usher

"ro"ellers., "articularl at the takeoff of fling<wings, are not to $e considered hereAased in these assum"tions one can easil estimate the advantage in "erformance of the all wingconstruction over the conventional air"lane Nnder similar conditions it manifests itself in a gain ofs"eed of 8 to 10 "ercent, or $ an increase in useful load of a$out 20 "ercent #o name other advantagesof this t"e of construction the "ilot%s visi$ilit is ?uoted, which corres"onds to that of a "ul"it, $utwithout the distur$ance of the usual engine nacelles Further the "ossi$ilit of using $raking "ro"ellersshould $e "ointed out, which could $e actuated without tail $lanketing, and it should $e also mentionedthat a swe"t$ack wing without "rotrusions is suited toward warding off ca$le $arriers, $alloon $arrages,etc

#his develo"ment, and its effects on armament, can now $e surveed down to its smallestconse?uences, and shows that the advantages of the fling wing com"ared to the conventionalconstruction, in this arrangement lies with the limits given / different status o$tains for thedevelo"ment of a high<s"eed fighter or fighter<$om$er with +et "ro"ulsion, which now im"ends, $ecause of the develo"ment of corres"onding tools !ven more than in the "revious "ro$lems, thereference ?uantit must here $e taken as the s"eed of the takeoff #he "erformance of +et "ower "lantsat the start and at low s"eeds is $ad >is"osa$le loads are large #he landing s"eed here reall no longeroffers a reference ?uantit Aecause the "erformance of the "ower "lants increases with the increasings"eed, and on the other hand the s"ecific fuel consum"tion decreases with increase in s"eed, theaerodnamic develo"ment of the nacelle is im"erative as a "resu""osition for the econom of +et "ro"ulsion ;ince studies $ Ausemann show that the swe"t$ack wing has advantages at high *achnum$ers, and it will $e even "ossi$le to o$tain s"eeds with the swe"t$ack wings which the straightwing cannot achieve $ecause the local a""earance of sonic s"eeds, swee"$ack $ecomes necessar for

high<s"eed flight #he conventional air"lane as a swe"t$ack wing air"lane shows "oor flightcharacteristics in low s"eed flight, since $een here the swe"t$ack wing is not .free. $ut .$ound. (see.;ta$ilit Gonsiderations and ;we"t$ack =ings. in this re"ort) *oreover, the conventional air"lanewould have to show nacelle $odies on the wing, which, as can $e seen from the a$ove mentioned stud $ Ausemann, does awa with the advantages of the swe"t$ack wing #he fling wing, therefore, has to $e "resu""osed here #he working out of a corres"onding "ro+ect shows that the single seat fighter with

two #L<"ower"lants and 1000 kg of ammunition results a 70 to 7 m2 wing area is taken at the smallestconstruction #he installation of the "ower "lants and fuel as well as armament, landing gear, and "ilotin the wing alone, "resu""oses a 1@ "ercent "rofile thickness at the root, were the outer "anel can, ofcourse, $ecome thinner #he s"ace for a ma'imum of 7<o$m of fuel "er "ower "lant would $e createdin the outer wing, of which, $ecause of takeoff weight, one would onl use half at first =ith this theo$+ective would $ecome- 1000 kg $om$s < 1000 k"h (2 m"h) ma'imum s"eed and 1000 km radiusof action

n summar it ma $e said that the form of the high<s"eed air"lane cannot $e determined from the "ointof view of giving the o"timum sha"e to a given s"ace, as for instance in a s"indle<like fuselage #hisfuselage, it is true, has the least drag, $ut it does not "roduce the lift necessar for flight and must $ee?ui""ed with wings and control surfaces #he necessar s"ace, therefore, is to $e sha"ed in such a wathat it has an ade?uate L6> ratio for all "ossi$le flight conditions f, in addition, the sha"e has the?ualit of avoiding as nearl as "ossi$le the local velocit of sound at high *ach num$ers, a direction



of develo"ment is o$tained which must, for "ractical reasons, $e created

olutions for the ell-haped Lift /istribution

einhold tadler

Appendi A1 Appendi A2 Appendi A3 Appndi A4

his formula now has to $e solved for the $ell sha"ed lift distri$ution-

+E,u. 00-0&

+E,u. 00-0%

For this the term is s"lit u" in several "arts, which can $e integrated se"eratel #hecalculation is descri$ed in the Appendi A1 #he final solution is-

or +E,u. 00-08

#his gives the re?uired calculation method for the geometrical twist , which can $e

transformed, using e?uation (!?u 00<0@)-

+E,u. 00-0a

+E,u. 00-0b

Appendi A1( olution of 56uation 77-7"

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+E,u. 00-0%

#he integration is transformed into a set of terms, which can $e solved se"eratel /n integrata$le

solution was first "resented $ >r *artin *aurer@

, *unich, in 199 and confirmed $ the solution of>r arl ickel, Frei$urg iAr, 1998 #he solution of >r *aurer is $asis for the here descri$edcalculation-

+E,u. #-0#a

+E,u. #-0#b

+E,u. #-0#*

#he following transformations can $e used-

+E,u. #-0"

+E,u. #-03a

+E,u. #-03b

#his leads to a new formula for the integration (!?u 00<0I)-

+E,u. #-0!

;olutions for the integrations are given in *ultho"", res"ectvel Aronstein7 -

+$ro. "%5

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+1ul. 0

!?uation !?u /1<07 now gives-

+E,u. #-05

and from this-

+E,u. # 0&

+E,u. #-0%a

+E,u. #-0%b

+E,u. #-0%*

#his gives the re?uired solution, which can $e now written as e?uation !?u 00<08-

+E,u. 00-0%

or +E,u. 00-08

Appendix A2: Halfspan Center of Lift for the Bell-Shaped Distribution2e formula for total lift is +2ru*4enbro(t

+2ru. 5.!"

For a s6metri*al lift (istribution onl6 te alfsan ma6 be use(



wit 7 +E,u. 00-0#

f te sanwise *ontrol oints are arange( along a 9*entral-angle9 similar to te 1ulto-ro*e(ure) te

following terms *an be written

an( +1ul. 0%

2is gives te following solution for one si(e +alfsan

wit +E,u. 00-0"

+E,u. 00-03

2e rolling-moment of te alfwing is

+E,u. "-0#

2is gives now

+E,u. "-0"

**or(ingl6 to $ronstein +$ro. 35& tis gives

+E,u. "-03

2e alfsan *enter of lift is ten

Appendix A3: Soe Coents on the Bell-Shaped LiftDistribution



n man6 *ases te (is*ussion about te bell sae( lift (istribution *on*entrates on te aero(6nami* oint ofview. For te swet fl6ing wing) tis (istribution as some a(vantages) but brings some (rawba*4s wit rese*tto erforman*e.

:nfortunatel6) one ver6 imortant oint is misse( in all tis (is*ussion) te matemati*s. **or(ingl6 to ;eimar<=;2EN) te bell sae( lift (istribution was alrea(6 use( on te < ) long before 1ulto resente( is*alv*ulation meto(. n exa*t solution of te +unswet lifting line was onl6 available for te elliti*al lift(istribution + ) n># at tis time. For arbitrar6 wing la6out onl6 aroximate meto(s as '*ren4 or

Liis* were available. solution for oter fun*tions seem ossible) but were not resente( at

tis time. solution of iger or(ers sow tat te lift (istribution a**or(ingl6 te ower n>" is 6si*all6 notossible. t re,uires an in(efinite twist at te wing ti. Next ossibilit6 is te ower n>3) an( tris is te bellsae( lift (istribution. 2e re,uire( wing twist in*lu(es te in(u*e( angle of atta*4 wi* follows a simlefun*tion . 2wist at te ti is te +negative same on as at te root.

2e re*onstru*tion of tis solution was tri*46 but for a matemati*ian li4e ;. <orten ossible. t enables a fastmeto( to *al*ulate te re,uire( basi* twist) ma4ing te la6out in(een(ent from a meto( li4e 1ultio?s.:nfortunatel6 we miss te final verifi*ation tat ;eimar <orten as use( tis simle meto(. 2e surviving*al*ulations give no (es*rition ow te twist was (erive(. Neverteless) te twist fits well wit te bell sae) atleast for some of te airlanes.

'tress *al*ulations ten were erforme( using te well establise( Liis* meto(.

+C ;. '2DLE;) &-0#-#5

rev. 0# 8-0#-05

rev. 03 -0#-0"

Appendix A!: "eoetr# to the Bell-Shaped LiftDistribution

'ene @ing 'e*tion xle

Nullauftriebsri*tung Dire*tion for Aero Lift Flow



The /esign8 ,onstruction and Flying of a Flying Wingy Art 9resse

/5&:$

#he design of a Fling =ing is a different aerodnamic challenge than for a conventional "lanform #he ke issue is longitudinal ("itch) sta$ilit /lmost as im"ortant is aw sta$ilit andcontrol will deal with the "itch "ro$lem first

#he "ro$lem arises $ecause there is no conventional hori&ontal sta$ili&er For conventionalconfigurations the e'istence of that sta$ili&er wa $ehind the GH reduces the sta$ilit "ro$lem to amatter of ad+usting the relative incidence of the wing and tail and the "osition of the GH =hether ornot the wing is sta$le $ itself is unim"ortant For a fling wing the "itch sta$ilit of the wing alone isof "rimar im"ortance Cirtuall all conventional wing sections, when right side u", are unsta$le Athe same token the same sections fling u"side down are sta$le $ut not ver efficient Aecause of these "eculiarities, a good "art of the aerodnamic design involved selecting airfoil sections and thedetermining the re?uired twist or washout #he other "art was the "lanform or laout of the com"letewing

used the com"uter for much of this "rocess #he necessar calculations can $e done with a handcalculator $ut the com"uter s"eeds u" the "rocess immensel and makes changes a "iece of cake For

the design "ur"ose needed several ma+or software elements #he are-

1 / source of airfoil section coordinates2 / wa to anal&e the sections to determine how the $ehave at the low s"eeds (enolds

um$er) that our models fl at@ / wa to estimate the "erformance of the com"lete wing7 /nd finall a wa to draw the wing ri$s or tem"lates that will $e re?uired



A&F;&L 5,T&;$

#he Nniversit of llinois >e"t of /eronautical and /stronautical !ngineering has "u$lished a largenum$er of airfoil sections ;ome these have $een tested in their low s"eed wind tunnel (a fellow clu$mem$er, on Ao&&onetti has contri$uted a model wing for this "ro+ect) #he airfoil sections are

availa$le on the nternet1 Niuc stands for the Nof llinois at Nr$ana<Gham"aign and rof ;elig is thechairman of the /""lied /erodnamics Hrou" #he file to download is .coord90@07targ&. =hat to

do ne't is a $it involved which %ll descri$e later

A&F;&L 5,T&;$ A$AL&

#he airfoil section analsis used is $ased on /;/ #* 80210 ./ Gom"uter rogram for the >esignand /nalsis of Low ;"eed /irfoils. $ ichard !""ler and >an * ;omers , /ugust 1980 !""leris6was a "rofessor of aeronautics at the Nniversit of ;tuttgart in Herman and is the guru of thesail"lane design folks ;omers works(ed) at /;/ Langle

#he com"uter "rogram develo"ed in #* 80210 has $een reworked for use on a G $ a com"ancalled ./irware. and is called ./irfoil<ii. #he com"an is located at 3 Ao' 29 Ganton, G#

0019 /s stated in the title the software works $oth in the design mode and the analsis mode n thedesign mode ou s"ecif a desired velocit distri$ution over the wing (determined $ guess and $goll) and the "rogram gives ou $ack a wing section, including the coordinates n the analsis modeou "rovide section coordinates and the "rogram gives $ack the aerodnamic "erformance (lift, drag,moments etc +ust like in a wind tunnel test) #here is other software availa$le at the uiuc location onthe nternet (for a "rice) For all know it ma $e the same as /irfoil<ii am not a$out to s"end moremone to find out have tried ./irfoil<ii. and it works fine

3-/&<5$&;$AL W&$: A$AL&

Nltimatel, selected the method develo"ed in 19@I $ a /le'ander at /G/2 and ada"ted it for

use here

& =L;TT&$:

#he ri$ or tem"late "lotting was done with a software, software called .Gom"ufoil@ . #his is a ratherwell known at least to the sail"lane weenies t can $e made to acce"t the airfoil section data that isdownloaded from the N of llinois #he same data was loaded into >esign Gad which used to do theoverall design of the fling wing

#he software comes "reloaded with a lot of airfoils including, $elieve, some of those in the N ofllinois list #he software has "rovisions for modifing the airfoils and out"utting coordinates #hese

revised coordinates can then $e fed $ack into /F3L<ii to get its characteristics used this feature toe'amine refle'ed trailing edges which is a wa to get sta$le sections for a fling wing

/5&:$ =;,5/>5

#he airfoil coordinate data that used are availa$le on the nternet at the NNG source cited earlierunder the filename .coord90@07targ&. #he downloaded file is a list of airfoil id num$ers that can $eclicked on to get the coordinate listing #his listing does not give an clue as to what the airfoil lookslike ight ne't to the :dat file is a :gif file $ the same name A clicking on this filename ou get a

http://www.uiuc.edu/ph/www/m-selig



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"icture of the airfoil selected the file .e@2dat. and .e@2gif. #he accom"aning one linedescri"tion sas that this is a fling wing airfoil #his is a$out as good a clue that the file "rovides as towhat the airfoil is good for #here is no aerodnamic "erformance data Aoth of these files can $e savedto disk and6or "rinted out saved them to a flo"" for further use #o see what the files look like afterthe have $een saved and ou a no longer in our nternet $rowser a viewer is needed For the data filethe viewer (and editor) must $e /;G editor, the >3; .!ditor. works fine or the =indows .note"ad.

editor is 3 also For the gif file, .Cuerint<ro. which is a useful shareware gra"hics viewer, issuggested #he data shown in this column was im"orted using the standard =orderfect .gra"hics .menu Aecause = does not acce"t :gif files had to re<save the file as a :"c' file #hismani"ulation can easil $e done in Cuerint<ro #he airfoil coordinates are shown $elow n order touse the coordinates to "lot the airfoil in >esignGad some more mani"ulation is re?uired n the .Files.menu of >esignGad, select .File Gonvert. #he in"ut filename is (in this case) e""l@2t't #he in"utfile t"e is .'. and the out"ut file t"e is dw2 Ae sure to edit e""l@2t't to remove the header whichnames the airfoil t"e >esignGad does not recogni&e the te't and will return an error if it is left in fou neglect to s"ecif where ou want the converted file to go ou will have to look for it Nsuall itgoes in the director that >esignGad is in 4ou can now load the file into a >esignGad window in theusual wa For some unfathoma$le reason when ou do this into an em"t window the airfoil shows u"as a small s"ot one unit wide in a screen that is several hundred units wide ;et a "oint on the s"ot and.&oom. with a factor of a$out 100 and the airfoil shows u" as a reasona$le si&e /t this "oint ou havean airfoil that can $e mani"ulated for air"lane design "ur"oses For airfoil "erformance we need to getthe coordinate data into ./F3L<ii.

#he interesting feature of the "articular airfoil that chose is the slightl refle'ed trailing edge #his hasconsidera$le effect on the sta$ilit of the airfoil t is found on most sections that are used for flingwings

n order to calculate the airfoil "ro"erties the airfoil coordinates for all of the sections of the wing arere?uired .Gom"uFoil. "erforms this task t also has the ver useful ca"a$ilit to .loft. theintermediate ri$s when "rovided the root and ti" ri$ coordinates and "ut all the s"ars and sheetingcutouts in the right "lace /s ou might imagine this is an enormous time saver for ta"ered wings

chose old faithful Glark<4 for the root section and the !""ler @2 as the ti" section to illustrate the "rocess t would $e hard to find two more different sections to tr to loft together t turned out thatthis com$ination leads to worka$le design

For "reliminar design selected a wing with an 80. s"an, an as"ect ratio of eight, an area of 800s?uare inches, a ta"er ratio of 162 and a swee" of 20 #his gives a root chord of 1@@@@., a ti" chord of. and a mean chord of 10. #his also turned out to $e a worka$le configuration and $ecame "ermanent

had the "rogram generate all twent one ri$s for a 2. s"acing #he "rogram will "rint out the ri$s full scale with most an "rinter f the ri$si&e is too $ig for a sheet of "a"er it will tile the out"ut which can then

$e "asted together /s noted a$ove used the airfoil coordinatesgenerated $ the "rogram to get the airfoil aerodnamic "ro"erties onl used three of the sectionsK root, 27. and 70.(ti") s"an stations t

turned out that onl three sections ade?uatel descri$e the "erformance of the wing =hereintermediate data are re?uired the can $e gotten $ inter"olation #hese three sections are shown infigure 1

#he ./irfoil<ii. "rogram re?uires the in"ut airfoil coordinates in a ver s"ecific format t must $e/;G without ta$s and in two arras of ten columns each as shown in earlier n addition the arramust start with the coordinates of the trailing edge, work forward over the to" of the airfoil to the

$igure %@ing irfoil 'e*tions

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leading edge then over the $ottom, and $ack to the trailing edge n the te't s"lit the arra into two "arts for s"ace reasons For in"ut to .airfoil<ii. the file must not $e s"lit in this manner) #he num$er ofcoordinate "oints must $e divisi$le $ 7 #he trailing edge is listed twice, at the start and at the end /t"ical listing will have 9 (81) lines .Gom"uFoil. "uts a num$er of e'traneous elements in the filewhich have to $e removed eg.eof. characters, ta$s and la$els f this is not done "ro"erl ./irfoil<ii.will re+ect it

/irfoil<ii is a F3#/ "rogram that originall re?uired the old A* card for in"uts #he author did aminimal amount of work to ada"t the code to an interactive G "rogram that that runs in >3; Aecauseof this the in"ut routine is tedious and not intuitive $ut once set u" it is acce"ta$le #he out"ut of the "rogram is two forms #he visual out"ut is a gra"hics "lot on screen #his can $e "lotted immediatel ifou live in the old =indows @1 or >3; world found to m chagrin that gra"hics driver in =indows9 will not acce"t the out"ut for "rinting have not $een a$le to find the author of the "rogram to seeif he has written an u"grade Fortunatel the "rogram also has a ta$ular out"ut of all of the results in

minute detail #his ta$ular out"ut can $e co"ied to a s"read sheet where the data can $e mani"ulated and "lotted used Lotus $ut an s"read sheet should work aswell t should $e noted that the out"ut is an /;G file without an s"ecialcharacters #he ta$les are s"ace delimited which, if there are no te't characters,

allows the num$ers to $e acce"ted as num$ers (and not te't) ran /irfoil<ii for thethree airfoils shown in Figure 1 then mani"ulated and mi'ed the ta$ular results sothat could "lot the data in a conventional "lot for aerodnamic data $ut with thedata for all three on the same gra"h #his allows for a visual com"arison of the datavariation along the s"an #he Lift Goefficient for the three sections are shown in

figure 2

#he to" curve is for i$ 0 (root ri$) and the others are in se?uence #he curve for the ti" ri$ (ri$ 70)dis"las some strange characteristics *ost interesting are the $reaks in the curve at $oth high and lowangles of attack the other is the $reak in the slo"e at a$out angle of attack do not know whether toattri$ute these anomalies to the refle'ed trailing edge or to the strong "ossi$ilit that the calculationsfail at the low enolds um$er at the ti" (e520000) t ma in fact $e a com$ination of these

"ro$lems ;ections with refle'ed trailing edges are known to have "oor "erformance (as do ordinarairfoils such and the Glark<4 when u"side down) their chief advantage is the "ositive moment a$outthe aerodnamic center which makes the solution to the sta$ilit "ro$lem a $it sim"ler for fling wings

#he data for i$ 0 (Glark<4) is ver close to the e'"erimental data for the root enolds um$er(e500000) #his gives me some confidence in the results for the other sections #he lofted section(i$ 27) falls where it should, midwa $etween the root and ti" and is well $ehaved f ou e'aminethe "rofiles closel ou can see the start of the develo"ment of the refle' #he ke is the curve of thelower surface of ri$ 27 #he lower surface for the Glark<4 is essentiall flat from the 20 "oint to thetrailing edge

For the com"lete wing calculations the onl data of im"ortance from these curves is the 0<

interce"t "oint and the slo"e of the straight "ortions of the curve #he nonlinear "ortions of the curveare much more difficult to deal with analticall for the com"lete wing (in other words too damn hard)and not reall needed for determining the "itch sta$ilit of models

$igure 2

$igure 3





#he other section "erformance "arameters are the >rag and itching moment Goefficients #hese areshown for all three sections in figures @ and 7 n figure @ the drag is "lotted vs angle of attack n theworking range of angle of attack (<2 to deg) the drag for the three sections is virtuall identical(e'ce"t for the anomalous $ehavior of ri$ 70 at the e'tremes) t is also almost constant in that region ata$out 001 #his is in accord with first order theor

#he moment coefficients a$out the 2 chord "oint "resented in figure 7 are

roughl constant for small angles of attack f the were calculated a$out theaerodnamic center the would $e constant (ote- the ri$s start with 0 at the to"and work down) /gain e'ce"t for the e'tremities the curves $ehaveas e'"ected For the com"lete wing the num$ers that need are the constantmoment a$out the aerodnamic center #o get these "lotted the moment versuslift and took the value of moment at cl50 for each of the ri$s se"aratel

;ome comments on the software are in order #he .com"uFoil. software is e'cellent and "rovidesmuch more ca"a$ilit than have used so far n "articular it draws all the ri$s including cutouts forsheeting, s"ars, leading edges and +ig alignment holes with washout if desired t contains a ver largeli$rar of wing sections and a "rofile generator for /G/ sections t is availa$le from the author- /demonstration "rogram is availa$le at his we$ site .htt"-66ourworldcom"uservecom6home"ages6com"ufoil6.

#he .airfoil<ii. "rogram has limitations at low e t calculates the $oundar laer thickness using thevelocit and "ressure distri$utions $ased on no $oundar laer (1st a""ro') #he $oundar laer effectsthe "ressure and velocit and strictl s"eaking the calculations of the velocit and "ressure should $ere"eated with the sha"e changed $ the .dis"lacement thickness. For a "recise solution this is re"eateduntil no more change is noted ;uch a "rogram is availa$le from roof >rela at *# #he license forthe "rogram to non commercial users is Q000RRR

/nother "rogram called .anda. is availa$le from >eskto" /eronautics nc t has a we$ "age andsearching for the name will get ou there have talked to them and used their demonstration "rogramwhich is availa$le on the nternet n terms of accurac it seems to $e no $etter than .airfoil<ii. t uses

the same first a""ro'imation for the $oundar laer t is easier to use in the sense that it isinteractive 4ou can change the sha"e of the section on the screen with the mouse and watch the "ressure and velocit distri$ution "lots change with little dela f had not alread s"ent a $unch ofmone for .airfoil<ii. "ro$a$l would go for .anda. $ut as it is got all needed from .airfoil<ii. / $ig "ro$lem is that there is no technical su""ort or u"dates that ou would ordinaril e'"ect

#he wing data "resented a$ove a""lies onl to wing sections /nother wa to look at it is that thea""l to wings of infinite as"ect ratio don%t know how to $uild such a wing so we have to find a wato ad+ust the data to account for the fact that a real wing is finite Like everthing else in this world thiswill $e an a""ro'imate solution

#he earliest reference that have that treats this "ro$lem is a $ook $ D Hlauert7 "u$lished in 192

and re"u$lished "eriodicall ever since #here have $een numerous e'tensions of Hlauert%s work #heone that is classic and is the $asis for what a""ears in most earl te'ts is the "reviousl cited work $a /nderson at /G/ /nderson%s "a"er is suita$le for almost anthing that we design in the modelworld sa almost $ecause it falls a"art com"letel for things like the fling lawnmower and otherver low as"ect ratio fling machines t also has "ro$lems for swe"t wings $ecause of the .cross flow.or flow along the wing which increases with swee" angle evertheless for swee" angles of u" toaround 20 it gives reasona$le results

struggled for $it for a wa to "resent the calculations in some intelligi$le

$igure !

$igure &

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and $rief wa and gave u" #he method involves length s"readsheet arras using num$ers that aree'tracted from /nderson%s "a"er #his would take more time and s"ace than can $e +ustified Ariefl themethod adds u" the characteristics of each section (as determined $ airfoil<ii) #he angle of attack ofeach section is modified $ the local circulation (also known as downwash) to account for the "resenceof the rest of the wing .Lifting line theor. "rovides the $asis for estimating the downwash ote- thedownwash is a result of the vorte' flow around the wing which can $e made visi$le $ smoke or

condensation that man of ou ma have o$served in full scale aircraft t is interesting to note thatnone of this would ha""en and air"lanes would never fl if it were not for the $oundar laer whichgenerates the skin friction drag (Look u" >%/lem$ert%s arado' as an e'ercise for the reader)

#he result of these calculations is the lift and moment coefficient curves for the com"lete, finite wingwith the dimensions used last month to generate the airfoil sections / sketch of the "lanform isshown in Fig #he aerodnamic data are shown in figures and I ote that the curves do not e'tendinto the nonlinear or stall region

t ma not $e a""arent $ut the whole reason for this e'ercise is to make surethat the final wing is sta$le in straight and level flight A that mean thatwhen "ut into a level flight attitude it will continue that wa for some timewithout immediatel falling off into a s"iral dive or some other wildgration From the moment curve in fig , alread know that theconfiguration is sta$le in "itch $ecause the slo"e of the curve is negative (itslo"es u" to the left) #his means that if the wing is distur$ed in "itch themoment increases in the "ro"er direction to return the wing to the startingangle =hat is missing is "ro"er location of the GH so that the moments are&ero and the lift is su""orting the weight #o determine this needed to knowthe weight (gravit) also needed to know the cruise s"eed of the wing (oralternativel a .design lift coefficient.) ;trictl s"eaking if were doing this.$ the $ook. would determine this using the thrust availa$le from theengine com"ared to the thrust re?uired $ the drag !nough is enough, a goodol% ;=/H will get around these "ro$lems ever time #o $egin with "icked

a light wing loading of 18 o& "er s?uare foot Nsing the dimensions on fig 1this works out to a gross weight of 2 "ounds easona$le lift coefficients for straight and level flight

range around 01 to 0@ #he formula for lift is- L5GL/C26@87 for lift in "ounds, C in m"h and / in

s?uare feet For the two values of GL the e?uation gives C5@8 and m"h res"ectivel #hese are a $it

high $ut not unreasona$le #he onl wa to change them is to decrease the wing loading or increase thewing trim G

L For the moment at least will go with these #he moment coefficients G

*corres"onding

to the a$ove lift coefficients are <08 and <2 res"ectivel #he formula for moment is *5(G*/C26@87)

(mac) where mac is the mean aerodnamic chord, in this case 10@I. (For some reason this dimensiongot lost in the translation from >esignGad to =orderfect and is missing on the figure) lugging in the

moment coefficients and the corres"onding s"eeds gives <@9 and <718 "ound<feet for the low andhigh s"eeds res"ectivel #he negative sign indicates that these are nose down moments and the area$out the 167 chord "oint of the root chord ($ definitions that used in the original e?uations that didn%t show) #his nose down moment must $e counteracted $ a nose u" moment of the weight of thewing acting at the GH /t this "oint had not decided where the GH would $e $ut have com"lete Ocontrol of its location when do the detail design #he "rocedure is to "ick the desired GH so that theair"lane trims out the desired s"eed and then tr to $uild it so it falls at that "oint f it doesn%t work outthat is what those little lead weights are for #he e?uation for the GH location is 12(*6=eight)5'GH,

where * is in "ound<feet, =eight is in "ounds and 'GH is in inches #he negative sign indicates that the

$igure '

$igure (





GH should $e aft of the 167 chord "oint /gain "lugging the num$ers gives I@. and 80. for the lowand high s"eeds res"ectivel #hese are the locations shown on the "lanform in fig 1

#he change in the "itching moment $etween low and high s"eed was a little $it disconcerting *osthigh "erformance aero$atic air"lanes (model or full scale) e'hi$it little or no trim change with s"eed(desira$le) ;"ort "lanes $oth model and full scale are generall designed to "itch u" when the s"eedincreases n this case had a design that tucks under as s"eed increases (think a$out itR) #his was not

goodR #he onl eas wa could come u" with to reduce this tendenc was to change the twist orwashout (increase itO) had to do a little re"rogramming to investigate this "ro$lem

#he "ro$lem is easil cured of course $ a $it of u"<elevator (elevon) trim #his solution is e?uivalentto increasing the twist of the wing (more washout) #hat is nice $ut<<how muchO #he s"readsheetdevelo"ed for the initial calculations had twist included as a fi'ed num$er =hat was needed was thesame s"readsheet with twist as a varia$le "arameter *aking this change was not a $ig deal ttook a$out an hour do it and verif the results #he results are summari&ed in Figure 8, which "lots thetrim GH "osition as a function of airs"eed for a range of twist angles #he original laout had a twist of< (the triangle sm$ol) #he desired curve should $e at or a$ove the hori&ontal line (the curve la$eledwith the diamond or < 7@ ) #he hori&ontal curve was arrived at $ cut and tr t re"resents the

neutral case where if s"eed increases (as in a dive) the air"lane will continue

in the dive with no tendenc to recover For the case where tw5 <Io as thes"eed increases in the dive the nose will tend to rise, which increases theangle of attack, which increases the drag, which slows the "lane downetc ote that this effect is fairl sensitive to the angle of twist 3ne degreemakes a su$stantial difference #his has two im"lications 3ne the $uilderhad $etter $e accurate #o a certain e'tent an inaccuracies can $e accounted

for $ trimming out the air"lane during the first few flights (if it survives) #he other im"lication is thatthe design twist can $e changed in flight $ the wing twisting under the flight loads on it #he flingwing configuration is notorious for its fle'i$ilit "ro$lems $ecause of the increased moment arm of theti" caused $ swee" #his twist under load is resisted $ the torsional stiffness of the wing Dightorsional stiffness can achieved $ full sheeting the wing #his was not desira$le for weightdistri$ution reasons #he .><tu$e. method works almost as well and was selected here

#he remaining aerodnamic design "ro$lems are the sta$ilit in roll and aw will take care of the roll "ro$lem $ ar$itraril using a few degrees of dihedral #he aw sta$ilit is not so easil $rushedaside n a conventional laout the aw sta$ilit is "rovided $ the fin at the end of a long fuselage #hesi&e of the fin (including the rudder "art) is not too critical since the fuselage $ehind the GH itself actsas a fin For the fling wing it would $e nice if could avoid "utting an .ugl. stick and fin $ehind thewing $ut that is what usuall is done /nother "ossi$ilit is turned u" winglets at the ti" of thewing /fter diligentl reviewing all of the aero te'ts that are on m $ookshelf find onl two that are

remotel useful 3ne of these has $een referred to $efore and it in turn refers to a much earlier work

$ Hrant (Hrant%s $ook is a classic and is in the .must read. class for anone interested in the

technical histor of modeling) Aecause the .Genter of Lateral /rea. (GL/) "rinci"le of lateral sta$ilitreferred to in the references re?uires that $oth the GH and the GL/ $e determined and these in turnre?uire a laout of the air"lane in some detail am going to do the detailed laout first and mani"ulateit to get the GH and GL/ .right.

=ower =arameters

!lectric "ower was new to me so looked to the nternet for some hel" found a useful $it of software

$igure )











called .*otoGalcI . #his is shareware and the "rice was Q@N; t is a simulation that calculates the "erformance of electric sstems (motors, gear$o'es, controls and "ro"s) t has a large data$ase ofmotors and other com"onents that can $e selected to for a sstem t is well worth the "rice fordesigners decided to tr to si&e an electric sstem that would $e roughl com"ara$le to the @0 cu in

glow engine #he stum$ling $lock is that the electric motor out"ut is e'"ressedin watts and the glow engine is defined $ dis"lacement whereas reall

needed the "ower #o make a long stor short assumed that the glow engines"ecific "ower is 2 D6cu in ("ossi$l too high) For the @0 engine the "owerwould $e ) 0 D #he electric e?uivalent of this is 77I watts measured at theshaft /n e'act re"lacement for the glow engine is "ro$a$l not "ossi$le $ut should $e a$le to get a reasona$le a""ro'imation

ran the *otoGalc "rogram using an /stro Go$alt 0 I# S0 (there are manothers in the data$ase "rovided) #he "rogram allows a range of num$er of cells and "ro" diametersand "itches and gear ratios #he out"uts are /m"s, =atts<in, =atts<out, !fficienc, *, #hrust, *Dand running time used a gear ratio of 7-1, "ro" diam range of from 11. to 1., "itch range of I. to10. and num$er of cells from 8 to 1 #he "rogram out"utted 1@8 "ossi$ilities for each cell si&e Forthis "arameter used 1I /D and /D

#he com$ination that came closest to the 77I watts out"ut that assumed for the glow engine 1@ cellswith a 17'10 "ro" running and 0I * t ran with an efficienc of 80 and consumed 72am"sR Nnfortunatel it onl ran for 2 minutes Nsing /D cells the results were almost the same $utthe running time increased to I minutes #he weight of the cells is a serious "ro$lem icad cellsweigh roughl 1 o&6/D #his results in a weight for the 1I/D cell sstem of 21 l$s and for the/D sstem of 1 l$s not including the weight of the motor and controlsR

#hese weights were too high for this first go around com"leted the design using the 7 glowengine ma reconsider and redesign it in the future for electric $ut some of the flight "arameters willhave to change if it is to get off the ground

3ne of the interesting $ut sometimes frustrating as"ects of design es"eciall when doing it $ one%s

lonesome is that fre?uentl occurs that some additional data is re?uired that re?uires a diversion #hishas ha""ened once $efore and now it is a$out to ha""en again Aefore could do a detailed laout needed to know what is to $e .laid out. alread had most of the airframe stuff $ut what a$out theinsidesO #he driving item was the "ower "lant f a design .team. had done this +o$ there would have $een a ower lants gu who would have all the necessar data lined u" for the detailer to add to thelaout /s it is had not even selected the t"e of "ower "lant want to use much less do have all ofthe dimensional and weight data

Aoth conventional glow engines and electric motors were candidates for this a""lication #he $ig?uestion was .what ;i&e.O #o answer this ?uestion for the glow engine without resorting to a lot ofdetailed calculations used a figure have had in m files for some ears #he "lot is shown in Figure

9 unning the num$ers for m wing and a @0 and a 7 cu in engine got a wing cu$ic loading of Io&6cu ft and engine dis"lacement loadings of 1@ and 208 l$s6cu in for the 7 and @0 cu in enginesres"ectivel f these "oints were "lotted on figure 2 the would lie in the .scale.<.trainer. region sus"ected that the @0 engine would $e marginal for takeoff on our grass stri" so for glow "ower selected a 7 Aesides alread had one of those and could weigh all of the "ieces for that setu"

/5TA&L5/ /5&:$

$igure *+o,er +araeters









Figure 10 is a thum$nail of the final structural design t would $e nice ifthe e?ui"ment could $e housed in the wing without the ugl central ."od. $ut not "ossi$le /s it is the "od is "rett crowded /s noted earlier could have gone either with glow or electric "ower settled on glow $ecause of the $atter si&e and weight #he entire control is with a singlecontrol surface in each wing #he are controlled with one servo each #he

servos res"ond to aileron and elevator in"uts that are mi'ed $ thetransmitter

=hile was com"leting the drawing also did a weight and $alance =ith afull 8 o& fuel tank the revised estimated weight was "ounds #his was well $elow the to l$sthat "ulled out of m ear for the initial aerodnamic design #he GH came out at 79. aft of the midri$ 167 chord reference "oint #he desired value is 2@. #wo o& of lead in the nose will fi' that smalldiscre"anc also moved the "osition of the Genter of Lateral /rea (GL/) rearward $ adding to thefin area #he distance of the GL/ aft of the GH is now a$out 12 inches #his is not much $ut it willhave to do for the time $eing

#hose of ou who read ./ir and ;"ace. from the ;mithsonian ma have read the article on the orthro" Fling =ing "rogram of the late %70s found the article terrifingR

,;$T>,T&;$

3ne of the nice things a$out fling wings is that once ou finish the wing the air"lane is almostcom"lete #he construction is relativel straightforward and since the em"hasis of this discussion isdesign do not cover the details will $e ha"" to res"ond to ?uestions via email

F&$AL /5TA&L

Figure 11 shows the com"leted with the covering and all the insides com"leted

covered the =ing with ;ig .;u"ercoat. mostl $ecause had some left over from a long forgotten "ro+ect find the .;u"ercoat. easier to a""l than .*onocoat. mostl $ecause it shrinks more and at alower tem"erature #he slightl lower weight is insignificant "refer the .fa$ric and do"e. covering $ut went with the film t"e for weight reasons #his is in s"ite of the fact that find thefa$ric anddo"e easier to a""l al$eit more time consuming

e'"ected the visi$ilit of the model in flight will $e a "ro$lem !'ce"t for the to" and $ottom , the."resented area. is small and at an distance the model will $e difficult to see #o hel" this a $it covered the $ottom with midnight $lue and the to" with cu$ ellow #he fins hel" some in the sideview $ut the are ugl and if can get awa with it some da will remove them #he are held in onl $ some ta$s of covering material

Figure 11

Finished, ead to Fl

/s it turns out the weight is a non<issue #he final all u" em"t weight is 7 l$s 9 o& less muffler #his is

$igure %Flying Wing

,onstruction =lans

http://www.nurflugel.com/Nurflugel/Papers/Art_Kresse/Wing_photo_300.gif

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well $elow m initial .guess. of l$s and a later revision of 3n to" of this the center of gravitfell well within the limits calculated for sta$ilit =#D3N# A/LL/;#

/fter a few false starts figured out how to "rogram m Futa$a transmitter for .elevons. t works asadvertised Dowever as the initial flight tests showed that more so"histicated "rogramming wasre?uired

FL&:%T T5T&$:

#he first successful flight of the Fling =ing took "lace on Fe$ 2I, 1998 =itnesses "resent were Ao$4ount, at Freeman, >ave ;tudenick and several other clu$ mem$ers Ao$ 4ount assisted in thetest #he events, attem"ts and ad+ustments leading u" to this successful flight are descri$ed $elow

Flight test ?1

reflight checkout 3, Gontrols set at ma'imum deflection in $oth directions #he control deflection at

the in$oard end of the elevon was a$out @67.#a'i test 3, controlled well on ground /ccelerated smoothl and tracked 3 to liftoff Liftoffnormal, clim$ normal to a$out 20 to @0<ft altitude /t this "oint angle of attack increased leading to ana""arent stall /ircraft tum$led over nose u" several times and into the ground o recover "ossi$le>amage minimal ose cone re"aired

/nalsis- $ehavior sm"tomatic of fling wings in stall region caused $ over control and lack of "itchsta$ilit in stall ;olution- decrease control deflection to "reclude inadvertent stall /dd u"thrust toengine ("usher) to hold nose down /dd nose weight to increase "itch sta$ilit

Flight test ?2

Aehaved as $efore on ground #ake off as $efore, no "itch u" or "itch insta$ilit noted $ut aircraftrolled right which could not $e sto""ed with left aileron Grash caused minor damageP$roken "ro" and $ent landing gear

/nalsis- nsufficient roll control due to reduced aileron mode deflection ;olution- ncrease aileronmode deflection without increasing elevator mode deflection #his re?uired some cogitation since thetwo controls are cou"led #he desired effect was o$tained $ "utting the elevator on .low rate. andaileron on .high rate. n retros"ect this seems rather o$vious $ut at the time it was not clear how therate switches work in the elevon mode #he manual did not "rovide a clue also added e'"onential tothe aileron control to "reclude over control ( ho"e)

n addition added a differential to the .aileron. mode to minimi&e or eliminate an adverse aw #hisis a known "ro$lem with high as"ect ratio wings /lthough 10 is not a "articularl high as"ect ratio, did notice what seemed to $e "ronounced adverse aw on the second flight #he flight was ver shortso am not sure it ha""ened used a$out @ to 1 differential using the ./#C. mode in the transmitter had no idea what is the .correct. differential to use so this was an e'"eriment

Flight test ? 3

#he weather this morning was "artiall cloud, tem"erature in the high forties with wind from the



south (cross wind, what else) at from 0 to knots, a $eautiful da for fling had set u" the controls $efore leaving home so there was little to do $ut fuel u" and fl

#he first attem"t was little more than scurring a$out the runwa, $ut it would not lift off even with fullu" elevator ;itting on the ground the aircraft was slightl nose downR =ith the "itch control surfacesso close to the cg fore and aft the did not generate enough moment to raise the nose wheel off theground Ao$ 4ount noticed that the nose wheel was $ent rearward somewhat (not corrected from the

"revious test attem"t) #his leads to the nose down attitude and also a tendenc of the nose wheel to.dig in. to the rough turf #his was easil corrected with some gentle metal $ending

#he ne't attem"t was successfulR #he aircraft tracked down the runwa with no noticea$le effect of thecrosswind / touch of u" elevator and it was air$orne /lmost no trim changes were re?uired to get astraight and level flight at a$out half throttle #he aircraft is ver sensitive to "itch control ase'"ected /$out three notches of u" trim caused nearl vertical flight attitude

For this first flight stuck to straight and level flight and gentle turns /s far as could tell the aircraftwent where it was "ointed which is the desired situation 3nl ver small control movements werere?uired to achieve this situation /t no time did let it get near stall attitude #his is the $ad conditionfor fling wings since the tend to tum$le when stalled have alread demonstrated this on the first

test flight/fter a$out five minutes of this landed the aircraft using a rather flat long a""roach !ven with this,the low sink rate at idle throttle resulted in a high a""roach ather than tr a go<around, killed theengine and landed safel al$eit a $it long

Nnder the conditions and constraints of this flight test the aircraft e'hi$its good flight characteristicswith no vices e'ce"t for the minor re?uirement that the takeoff attitude $e "arallel to the ground orslightl nose high t remains to $e seen what ha""ens in some of the more violent maneuvers that wesu$+ect models to #here was no noticea$le adverse aw so the differential settings must have $een atleast a""ro'imatel correct

#he control settings that "roduced these results are-

Ghannel 1 /ileron mode/#C5100!E5<2>658/#C(u" surface)5100, (dn surface)5@0

Ghannel 2 !levator mode/#C5110!E50>6570/#C (u")5100, (dn)5@0

For this test set the aileron on full rate and the elevator on low rate

ationale

n the case of a conventional "lanform the various control surfaces are all a$out the same distance fromthe a'es through the cg a$out which the "rovide control (ailerons from the roll a'is, elevator from the "itch a'is etc) #hus the surfaces "rovide roughl the same res"onse a$out each a'is n the case of thefling wing the same surfaces control $oth roll and "itch Dowever, the distance to the "itch a'is ismuch less than the distance to the roll a'is /erodnamic control surfaces are velocit control devices,that is, the cause the control surface (and whatever it is attached to) to move with a linear velocit that



is "ro"ortional to the deflection /ngular velocit (which is what we notice from the ground) is linearvelocit divided $ distance of the control surface to the a'is of rotation #herefor the short distance ofthe "itch control to its a'is leads to ver sensitive "itch control in com"arison to the same deflection forroll control ho"e this makes sense

ome ;bser0ations

#he "rogramma$le transmitter reall demonstrated its value with these control "ro$lems rovidingelevon control with different throw for the elevator and aileron modes along with e'"onential anddifferential ailerons would $e a nightmare to do mechanicall #he Futa$a manual does not descri$ethese com$inations and is rather dense in an case $ut an hour or two e'"erimentation got me what needed

was ver fortunate on the first two flights that the were not catastro"hic %m not sure that if theresulted in total loss of the aircraft that would $e enthusiastic enough to start from scratch

t might $e o$served that should have $een smart enough to work through the rationale $efore the firstflight and avoided all the "ro$lems Nnfortunatel %m not that smart (=e grow too soon old and too

late smart) /t least learn from m mistakes

ubse6uent Acti0ities

#he design of .*od 1. descri$ed a$ove was followed $ .*od 2. which has the followings"ecifications-

'an 39

;oot Cor( "09

2i Cor( #09

'wee "0 (eg +"5B *or( line

;oot 'e*tion #5B Clar4 Y

2i 'e*tion #5B Eler 3"5

2wist #0 (eg total aero(6nami*

Die(ral " (eg

@eigt 8 lbs

ower "-='35s) " *6*) us-ull



#he laout of this design is much the same as for *od 1 $ut the as"ect ratio is rather than 8 for *od1

Nsing the control lessons learned from *od 1 resulted in a com"letel successful first flight #he onl.disconcerting. feature of $oth designs is their ver low sink rate at idle "ower which makes themdifficult to land in a &ero wind condition ;"oilers will $e used in an future design

,opy of letter from Flight Lt. .,. ForbesMay 21, 1950

Dear Hollis:

Thank you for your letter of last Sunday. Immediately after! I "ot

your letter, I tele#honed Ha$krid"e %ir&raft 'td. $ho re#aired the

Horten! to ask them to fi( the &enter of "ra)ity atta&hments for

you. Ho$e)er, the Horten is no$ some$here in #a&kin" &ases on its $ay

to you, as far as I &an find out. %ll I &an do us to ha)e the #ro#eratta&hments made, and I e(#e&t one to *e sent me tomorro$ mornin" to

)erify if it is the &orre&t ty#e. If it is I+ll ha)e t$o made $ithout

delay only a matter of days and shi##in" o)er to you *y air. They

should rea&h you *efore the Horten, I re&kon.

The ty#e of releases you re-uire are definitely not the ty#e $hi&h

released automati&ally *e&ause they mi"ht release at inter)als and

this $ould not *e satisfa&tory. The manual ty#e is not so &riti&al.

%t the end I+ll #ut a )ery rou"h sket&h to sho$ you ho$ to *uild u#

the release me&hanism. If I had the e(a&t measurements here I $ould

do it for you, *ut is not a diffi&ult o* on&e you see the releasefittin"s and method of atta&hment.

/ou ha)e to atta&h the releases on the main s#ar on the e(tremities

of the &enter se&tion *oth at, as near as #ossi*le, the same an"le

so the one le)er in the &o&k#it o#erates the release hooks the same

amount and it at e(a&tly the same time. This is all &ommon sense and

$e #erfe&tly o*)ious to you see the $hole outfit.

I *elie)e I ha)e on the eihe the only real &enter of "ra)ity

atta&hment in e(isten&e. The hook is situated a*o)e the skid on the

fusela"e, makin" an an"le *et$een a line dra$n from the hook to the

&enter of "ra)ity and the horiontal of 0 de"rees. The is the

o#timum an"le as far as safety is &on&erned. I ha)e had a laun&h to

3400 feet on o&&asion and 2000 feet is normal. In &ontest flyin" I

only use aeroto$in" $hen it is laid do$n in the re"ulations. I

#refer to sit in my ma&hine and takeoff $hen I feel it is the

o##ortune moment, and literally no time at all I+m at 2000 feet. If I

fail on the first attem#t I &an land *a&k at the takeoff #oint and *e

immediately off a"ain. The time $asted aeroto$in" is amain"

&om#ared to $in&h to$in", then I am suffi&iently oldfashioned in

some $ays to )ie$ aeroto$in" the same $ay as a "ood ya&htsman )ie$s



a ya&ht $ith a en"ine installed as a means of "ettin" air*orne,

I mean.

6o$, mu&h nonsense has *een $ritten a*out &enter of "ra)ity laun&hin"

and one of the $orst arti&les on the su*e&t $as $ritten *y one of my

7erman instru&tors in 7ermany, and #ossi*ly the one to $hi&h you

refer as ha)in" a##eared in 8Sail#lane and 7lider8.

There is no dan"er at all from #ilot or "lider #oint of )ie$ if the

elementary #rin&i#les are o*ser)ed. %t no #osition e)er on takeoff

should a #ilot *e una*le to land after a &a*le *reak or #o$er

failure. In other $ords at ea&h #oint on the &lim*, es#e&ially at the

early sta"es, he should *e in su&h a #osition that if anythin" "oes

$ron", his air s#eed and an"le of &lim* are su&h as to ena*le him to

land strai"ht ahead $ithout trou*le.

The same arti&le in 8Sail#lane8 stressed the dan"er an"le as far as

strainin" the ma&hine is &on&erned. This is #erfe&tly true, *ut it is

so easily o*)iated *y the introdu&tion of a $eak link link in the

"lider end of the &a*le. It is a##arent that any strain felt *y the

ma&hine in rou"h air &onditions is felt e-ually $ell *y ea&h #oint

alon" the &a*le. If the $eak link is the &orre&t *reakin" strain that

must *reak *efore stru&tural dama"e &an result of the "lider.

In the &ase of a normal "lider I re&ommend a 1.4 7. $eak link and for

the Horten 1.3 7. link. This is *ased on the ma(imum allu# $ei"ht of

the ma&hine in -uestion. If these fi"ures are adhered to, and if the

ma&hine &onforms to normal %ir e"istration oard re-uirements

stru&tural dama"e &annot #ossi*ly result, irres#e&ti)e of an"le or

rate of &lim*.

The te&hni-ue I su""est for ;. of 7. takeoff in the Horten is to hold

the sti&k &entral and allo$ the *uildu# of s#eed to lift the ma&hineoff the "round. Hold the ma&hine off the "round and #arallel to it

until a*out <0 k#h air s#eed is rea&hed. =ase the &ontrol sti&k *a&k

"ently, maintainin" air s#eed on the &lim*. The $in&h dri)er should

*e #ro"ressi)ely throttlin" *a&k until at the ma(imum hei"ht the

$in&h has literally sto##ed #ullin". %t this #oint the "lider is

flyin" strai"ht and le)el at <0 k#h and the &a*le is released $ithout

any tension on it. This, *y the $ay, is almost $ord for $ord out

instru&tional #atter at the s&hool.

/ou $ill *e! re-uired! to hold a sli"ht for$ard #ressure on the

sti&k at the moment of lea)in" the "round to #re)ent assumin" a

sudden &lim*in" attitude, due to the lo$ #osition of atta&hment.

>or landin" I su""est use s#oilers as re-uired on the a##roa&h,

kee#in" a 55?0 k#h on the &lo&k. hen almost on the "round ease this

s#oilers and hold off a*out three or four in&hes from a "round and

allo$ the ma&hine to settle on it as the s#eed falls off. %s soon as

you tou&hdo$n kee# the sti&k $here it is and #ull s#oilers fully

out. /ou+ll find that this the #od $ill in)aria*ly tou&h first if you

land at the stallin" s#eed and this is the ni&est $ay of landin". It



falls "ently onto his skid and #ulls u# literally si( or se)en yards.

/ou mention Hanna eis&h. She is a )ery "ood friend of mine and s#ent

all of her )a&ations $ith my $ife and me the last t$o years in

7ermany. e still &orres#ond re"ularly.

I for"ot to mention the o#eration of the under&arria"e last time I

$rote to you. Do not #ush the le)er for$ard after "ettin" air*orne,

*ut ust #ush in the kno* $ith your ri"ht thum* and let the le)er fly

for$ard. If you do this the $heel falls &orre&tly. If you #ush the

le)er for$ard manually it does not o#erate &orre&tly at least it

did not $ith me. >or landin" ust #ull the under&arria"e handle *a&k

until the s#rin"loaded #lun"er &li&ks home. I hate like Hell to ha)e

to land $ithout the front skid fully do$n@@@

There is )ery little room in this ma&hine, #rimarily *e&ause it $as

*uilt around Horten+s test #ilot $ho $as only a*out 5 feet 3 in&hes

tall. Ho$e)er if it fits it $ill fit you okay. I ha)e an %meri&an

A*ser)er ty#e #ara&hute $hi&h slin"s )ery lo$ on the *a&k ust on

your *ottom. The *ase of the #ara&hute fits a re&ess on the hood. %

small #a&ked seatty#e #ara&hute should fit e-ually $ell *et$een your

knees and *ottom.

I also for"ot to mention that $ould fittin" the hood you ha)e to

o#erate the le)er in front, under left, to lo&k it home. This le)er

also o#erates the safety harness. I+m only tellin" you these details

to sa)e your time to ha)in" to find them our for yourself.

/ou ask a*out doin" a fe$ ho#s first. I su""est you "o to an airfield

first to ha)e aeroto$ to a fe$ thousand feet to a&&ustom yourself to

the flyin" the thin". The only #art of the fli"ht $hi&h mi"ht *e

likely to dama"e ma&hine is the initial takeoff and only then if

really &arelessly &arried out. hy, then, #reudi&e this *eautifulma&hine *y ho##in" itB Mu&h *etter to "et off the "round for the

first time and really "et used to it.

I didn+t realie the &limati& &onditions $hen I asked you a*out

flyin" the in" $hen I "et a&ross. Af &ourse it $ill *e im#ossi*le

*ut, any$ay, thank you for the offer.

I am sorry to hear you+ll $on+t *e takin" #art in the 6ationals this

year, *ut I kno$ *y *itter e(#erien&e ho$ mu&h it &osts to kee# a

family, &ar, and sail#lane. Still, I mana"e someho$, and I &urtail

the other a&ti)ities to flyin" in &ontests. It is all "rand fun and I

meet su&h mar)elous #eo#le.

Clease let me kno$ $ho+s flyin" in S$eden this year from your #art of

the $orld. I kno$ Caul M&;ready is flyin" a eiher, *ut $ho else is

flyin" $hatB

My $ife is no$ in ;hi&a"o and is or"aniin" for me my tour of the

States at the end of the year. I shall &ertainly look you u# if it

&an #ossi*ly *e arran"ed. The only reasons for his t$omonth tri# are

to )isit my #arentsinla$ $hom I ha)en+t met yet, and, of &ourse, to



)isit isho#, $ith ho#es of flyin" there if it is all #ossi*le. %lso

to study &onditions in the States $ith a )ie$ to settlin" there $hen

I lea)e the %ir >or&e if I lea)e it@

/ou seem to *e $orried a*out ho$ to "et the Horten from Detroit MI,

to alley ;ity. hy not aeroto$ itB, and &all in here and there at

)arious air sho$s $ith it, and let it earn its kee#B It is a money

s#inner and al$ays attra&ts *i" &ro$ds. This is only an idea for itis $orth.

Cerha#s you &an assist me, sin&e your *usiness is my ho**y. I am a

keen #hoto"ra#her *oth still and mo)ie. %t the moment I ha)e three or

four reels of %"fa &olor mo)ie film $hi&h I ust &annot "et #ro&essed

in his &ountry. There are shots of a Standin" a)e at home in

S&otland, one or to #ersonal shots and one $hole reel of the Horten

in fli"ht. ;ould you #ossi*ly #ro&ess them for me, or if not, "i)e me

the address of a firm in the states $ho &ould do it for meB I $ill *e

mu&h o*li"ed if you &ould, that mi"ht *e a hel# to you to see the

films *efore you a&tually fly the Horten. I &annot tell you $hat they

$ill *e like as I didn+t take them and the $eather for #hoto"ra#hy$as dreadful.

If you+re interested, I use a 'ei&a 3&, a Su#er Ikonta and a

ollefle( for the still #hoto"ra#hy, and a Siemens 1? mm mo)ie $ith a

set off four lenses. The latter is an e(&ellent &amera and I+)e had

some mar)elous results $ith it. In &onun&tion $ith this I ha)e a

eiss Ikon #roe&tor.

6o more for no$, *ut I $ill "et those t$o releases off to you as soon

as #ossi*le.

/ours Sin&erely,

Ea&k >or*es

C.S. I ust &annot dra$ you a #i&ture of the release me&hanism, *ut

I+ll "et an a&&urate dra$in" of that fitted to the other one, $hi&h

is e(a&tly the same in e)ery res#e&t as your one. This $ill not take

lon" I #romise you.

Ea&k

,opy of letter from

lac@burn and :eneral Aircraft Ltd.



12th May, 1950

Dear Mr. urtton:

/ou $ill ha)e re&ei)ed my &a*le of May 11th as follo$s:

8Horten fli"ht tested "reat su&&ess May <th sto# $ill ad)ise

shi##in" date8

and naturally you $ill $ish to ha)e more am#le information as to $hat

has *een ha##enin" o)er here $ith the Horten I "lider and I feel I+m

#ro*a*ly the *est #erson to su##ly this information.

The air&raft $as assem*led at the ;olle"e of %eronauti&s at ;ranfield

last $eek *y Mr. H.=. olton of the Ha$krid"e %ir&raft ;o. 'td.,

Denham. Mr. olton has maintained a life lon" interest in "liders and

is one of the *est en"ineers of its field. He "a)e his undi)ided

attention to the ri""in" and assem*ly of the Horten I and $as

e(tremely &areful on the &ontrol adustments. hen the air&raft

rea&hes you I $ould stron"ly ad)ise that the indi)idual adustmentsare not &han"ed, sin&e the air&raft flies #erfe&tly as ri""ed.

The #ilot for the o&&asion $as >li"ht 'ieutenant >or*es, ;hief >lyin"

Instru&tor at the .%.> 7lider S&hool at Detlin", Maidstone, Fent and

he made t$o #erfe&t fli"hts and $as &om#letely satisfied $ith the

air&raft. Moreo)er he said that $as a thousand #ities that it $as

lea)in" the &ountry for %meri&a and I should think it is ust a*out

the most effi&ient "lider in the $orld and one $ith $hom ne$ re&ords

are *ound to *e &reated. In&identally the air&raft to$ed off *y a

Moth.

In )ie$ of the hi"hly su&&essful fli"hts, durin" the &ourse of $hi&hsuffi&ient o*ser)ations $ere made to satisfy the ritish 7lider

%sso&iation, the air&raft $as immediately dismantled so as to *e

a)aila*le for the trans#ortation &om#any $hi&h is handlin" the

#a&kin" and shi##in" for formalities. I ho#e to ad)ise you a fe$ days

as to the shi##in" date and anti&i#ated arri)al date of arri)al in

Detroit.

The air&raft is, of &ourse, sensiti)e on the &ontrols, sin&e the

lon"itudinal, lateral, and dire&tional deri)ati)es ha)e )ery lo$

)alues. ;onse-uently, )ery small mo)ements are re-uired to maneu)er

the air&raft. >or*es states that it turns )ery ni&ely on aileron

a##li&ation only and that at the ;.7. #osition as flo$n the stall isstrai"htfor$ard and inno&uous. >or information you $ill find the

follo$in" fi"ures useful:

ei"ht em#ty 5?0 #ounds

ei"ht as flo$n <20 #ounds

7ross affe&ti)e #roe&ted $in" area 2001 s-uare feet

Croe&ted $in" s#an ??.42 feet



Standard mean &ord len"th 3.03 feet

distan&e of -uarter standard mean &ord #oint aft of datum 4.20 feet

;.7. as flo$n 4.54G feet aft of datum 1? S.M.;.

;.7. em#ty 4.<?G feet aft of datum 23 S.M.;

The datum referred to is the leadin" ed"e of the $in" on the &enter

line of the air&raft and su&h is the most for$ard #oint. The&hara&teristi& of some tailless air&raft of the ;.7. is too far aft

is a #eriodi& lon"itudinal os&illation, $hi&h is only &ured *y

for$ard mo)ement of the &enter of "ra)ity. %s stated earlier this

#arti&ular air&raft flies #erfe&tly and there is no hint of su&h

os&illation, neither $ould $e e(#e&t it $ith a 1? S.M.; #osition of

the &enter of "ra)ity.

I en&lose some &o#ies of #hoto"ra#hs, taken on the o&&asion of the

test fli"hts, $hi&h are not )ery "ood, *ein" #urely amateur

efforts. The o&&asion $as one of )ery "reat interest to the students

of the ;olle"e of %eronauti&s and it $as indeed a )ery #retty #ie&e

of flyin".

/ours Sin&erely,

>.>. ;ro&om*e!.

GMeasured normal to the $in" hin"e from a(is.

.he Horten H / Series0ltra Light $l#ing 1ing Sailplanes

Albion H Bo,ersASA Dr#den $light 4esearch Center

5d,ards CA

Soaring Societ# of AericaSoaring Hoebuilders Association

.ehachapi6 CASepteber &-(6 %**)



;"anload Distor

•3"timum s"an load develo"ment

•Aell<sha"ed s"an load

Dorten ;ail"lane Distor

•!arl ;ail"lanes•Digh "erformance sail"lanes

•Later (/rgentine) sail"lanes

•Foot<launched sail"lanes

Dorten D Ec /nalsis

nalytical pan Load %istory

•



=randtl Lifting line theory

,irculation

pan load

&nduced /rag

• <un@ ;ptimum pan Load

5lliptical

• chren@

Approimate <ethod

Accomodate taper8 twist8 and surface deflections

• <ulthopp

implified theory Addition of control points

,oincident with circulation 0orte

ell 0s. 5lliptical pan Loads

<un@$ic@el

•



5lliptical span load

• ;ptimum

• <inimum induced drag

%orten

• ell-shaped span load• ub-optimal induced drag

• &nduced thrust at wing tips

• pro0erse yaw with roll command

+<itteleffe@t+

Artifact of span load approimations

5ffect

on span

loads

•

increased loads at tips

• decreased load near centerline

>pwash due to sweep is unaccounted for



,alculation <ethod B<ulthoppC

• Taper

• Twist• ,ontrol urface

/eflections

• ,entral /ifference

Angle

• /r. 5dward >denDs

results

sinnBEC

n 2.( ad0erse

yaw n GH 2.(

pro0erse yaw

as n increases8

induced drag

increases

n H 3 near

optimum



>densD esults

• pan

Loading and &nduced /rag

• 5le0on ,onfigurations

• &nduced awing <oments5le7onConfigurationI

II

III

I

I

II

III

IJ

J

JI

Cn8a.0020<0

.00155?

.002<

.0190?0

.015<30

.001942

.00223

.004529

.00540

.004132

.005455

Span Load*ell

*ell

*ell

elli#ti&

elli#ti&

*ell

*ell

*ell

*ell

*ell

*ell



5arly %orten ailplanes

• D Gontrol

surfacelaout

#wistdistri$ution

• D

!levons

Aell ;ha"e;"an Load

• D

m"rovederformance

m"rovedDandling

ilotosition

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/ho_i/ho_i.html

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/ho_ii/ho_ii.html

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/ho_iii/ho_iii.html

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_8/Ho_III_Schematic.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_8/ho_iii_e_in_flight.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_8/ho_ii_plans.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_8/ho_ii_pic_1.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_8/ho_i_plans.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_8/ho_i_horten_brothers.jpg

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/ho_i/ho_i.html

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/ho_ii/ho_ii.html

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/ho_iii/ho_iii.html



%igh =erformance %orten ailplanes

Later %orten ailplanes BArgentinaC

• D C

Digh as"ectratio

Digh "erformance

!'tensivetesting

*a' L6>- @I(design), @2(>F;), 29

(*;N)

• D C

!'tremehigh as"ect

ratio

erformanceham"ered $

structure

• Dorten .mini<tail.

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/ho_iv/ho_iv.html

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/ho_vi/ho_vi.html

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_9/ho_vi_plans.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_9/ho_vi_si.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_9/ho_iv_plans.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_9/Img0068.jpg

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/ho_iv/ho_iv.html

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/ho_vi/ho_vi.html



>ltra Light %orten ailplanes

% ) =iernifero eries

• D ECa ( /e @7Glen /ntu)

#wo<seattandem

;im"lecontrolsstem

• D EC$ ( /e @7mGlen /ntu)

;ingle seater(.mono"la&a.)

Digh "erformance

• D ECc ( /e 71Nru$u)

#wo<seatside<$<side

;im"lecontrolsstem

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_10/ho_xv_c_plans.gif

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_10/ho_xv_c_4.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_10/ho_xv_m_plans.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_10/ho_xv_a_and_b_1.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_10/ho_xv_a_plans.gif



%orten % )c Analysis

• < a Llita

=nemanufa*ture(

Flown

extensivel6 Non-bell san

loa(

Frise elevons

• < b

Never*omlete(

$ell sanloa(

• < *

Design

stu(6 <ig

erforman*e

• Elevon DesignCange

http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/ho_x_piernifero/ho_x_piernifero.html



http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_11/bowers_ho_xb_3.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_11/ho_x_c.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_11/Ho_Xb_plans.gif

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_11/bowers_ho_xa_2.jpg

http://www.nurflugel.com/Nurflugel/Papers/Al_Bowers_Horten_X_Series/bowers_2_11/ho_x_a_plans.jpg






/irfoil

/irfoil *ean Gam$er

#wist >istri$ution (einhold ;tadler)

rofile >rag Gom"onents

• Local lift coefficients

• !levon deflections

• Local enolds num$ers

• roverse6/dverse "rofile awing moments

%orten % )c Analysis



•Corte' Lattice /nalsis

;"an loads(longitudinal trim Tassmetrical roll)

roverse6/dverse

induce awingmoments

•acce"ta$lehandling?ualities

•

"roverse6adverse aw

Force vectors on ti"s (twist T u"wash)

@20 "anels

•70 s"anwise

•8 chordwise

ymmetrical pan Loads

Center



Longitudinal Trim

!levon #rim

GH Location

Assymetrical pan Loads



oll

,ontrol

• Glda(roll due

toaileron)

• Gnda(awdue toaileron)

induced com"onent

rofuile com"onent

#otal

Ghange with lift

CL&&.%%!.58"

.30.#8

Cl.0#38!.0#38!.0#3!5

.0#38!.0#3!5

Cn.00055.0003%.000"#

.00003-.000#5



• Gnda6Glda

• GL (Lift Goefficient)

ncreased lift-

• increased Gl$

• increased Gn$:

>ecreased lift-• decreased Gl$

• decreased Gn$:

Airfiol Analysis

•rofile Gode (>r ichard !""ler)

•Fla" 3"tion (elevon deflections)

•*atched Local Lift Goefficients (local angles of attack)

•rofile >rag

•ntegrated Lift Goefficients

*atch rofile results to Corte' Lattice;e"aration differences in lift

=erformance Analysis



•*a'imumL6>- @19(does notinclude "ilotdrag)

•*a'imumsink- 891 f"m(doesn notinclude "ilotdrag)

•L6> enaltAell vs!lli"tical

/ssumesame-

•

as"ect ratio

•wing area

•airfoils

*a' L6> ($ell)- @19@

*a' L6> (elli"tical)- @98

U1@

,oncluding emar@s

• Aell ;"an Load

"roverse aw

induced drag "enalt

• m"ortance of Gnda6Glda

• 3"timi&ation of sinn (u"wash distri$utionO)

• !ffect of GL on Gn$:

• Gnda Gom"onents

• D Ec has ver high "erformance for an ultra light sail"lane



• #hanks- Aruce Garmichael, >r aul *acGread, einhold ;tadler, Hregg*acherson, Juan *anuael *ascarello, uss Lee, Heoff ;teele, >oug Aullard,

>avid Lednicer, Jan ;cott, >r >avid *hra, >r arl ickel

eferences

• Dorten, eimarK adn ;elinger, eterK with ;cott, Jan (translator)- .urflugel- the;tor of Dorten Fling =ings 19@@ < 190.K =eisha"t CerlagK Hra&, /ustriaK198

• ickel, arlK and =ohlfarht, *ichaelK with Arown, !ric (translator)- .#ailless/ircraft in #heor and ractice.K ///K ew 4ork, 4K 1997

• acher, Dans- .*itteilungen- Flugtechnischen Fachgru""en und/r$eitsgemeinschaften.K FFH< >armstadt, 1977

• Horgfalv, >es&o- .erformance /nalsis of the Dorten C Fling =ing.KGongress of the 3;#CK Gologne, HermanK June 190

• Dorten, eimar- .Lift >istri$ution on Fling =ing /ircraft.K #echnical ;oaring,Col 10 o 7

• randtl, Ludwig- ./""lications of *odern Ddrodnamics to /eronautics.K /G/ e"ort o 11K 1921

• *unk, *a' *- .#he *inimum nduced >rag of /erofoils.K /G/ e"ort 121,192@

• ;chrenk, 3skar- ./ ;im"le /""ro'imation *ethod for 3$taining the ;"anwiseLift >istri$ution.K /G/ #* 1910, 1970

• *ultho"", Dans- .*ethods for Galculating the Lift >istri$ution of =ings(;u$sonic Lifting ;urface #heor).K /G * 2887K 190

9arl $ic@el Frei$urg den 11 Iuly 1''"

;chlier$ergstrasse 88 ><I9100Frei$urg i Ar F0I1 < 70 @1 9

H!*/4



;n the importance of the correct ,.:. location

in flying wings would like to dedicate this lecture to the memor of obert 9ronfeld. De was one ofthe most successful and famous sail"lane "ilots in the late 20s and @0s De was killednearl e'actl ;o ears ago while testing a fling wing #he reason for this accident wasmost "ro$a$l a wrong GH location of his tailless glider

Aefore come to the histor of ronfeld%s fatal flight, would like to treat this su$+ect ofthe GH location a little more general For sim"licit, in the following onl swept bac@

flying wings are regarded Dence, eg fling "lanks are notconsidered

Tail-hea0iness

Let%s first assume, that our fling wing is tail-hea0y8 ie that the GH istoo far $ackwards Dence, in e?uili$rium flight we need additional lift atthe $ack for the $alance of "itching moments >ue to the $ack swee" and

to the location of the elevons at the ti"s this lift has to $e added at the wingti"s, hence, $oth elevons have to go down there < see the sketch

ow, this is a ver unwelcome situation-

First( #his additional lift ma lead to separation of the flow at the ti" and, hence,to wingtip-stall with a su$se?uent roll-o0er which ma result in a spin.

econd( f this flow se"aration ha""ens simultaneousl at $oth wingti"s, then a.rearup-stall+ ma result, which is es"eciall dangerous near the ground

Third( f this flow se"aration ha""ens simultaneousl at $oth wingti"s, then a .rearup-

stall+ ma result, which is es"eciall dangerous near the ground

Forth( Aoth elevons down means that the wing has negati0e twist. ;uch wings withnegative washout, however, have a tendenc for spiral instability. #his ma not $e as

dangerous, $ut it is un"leasant during instrument flight

Fifth( #his negative twist unfortunatel am"lifies the unfavora$le ad0erse yaw8 whichis a nuisance for an fling wing #hus control around the vertical a'is is weakened

3""osite to "o"ular $elief tail<heaviness gives no ad0antage for the performance. f thelift distri$ution of the wing is chosen o"timal for the correct GH "osition, then tail<heaviness gives more induced drag, ie a loss

http://www.nurflugel.com/Nurflugel/Papers/Dr_Nickel_Paper/Nickel_1.GIF



$ose-hea0iness

3$viousl in this case everthing is reversed /ssume, that our flingwing is nose hea0y8 ie if the GH is too much in front #hen, ine?uili$rium flight we need less lift at the $ack for the $alance of "itching

moments >oe to the $ack swee" this negative lift has to $e "ut at the wingti"s, hence, $oth elevons have to go u" there < see the sketch

#he conclusion from this is now o$vious-

First( #his negative lift "revents the separation of the flow at the ti" and sto"s, hence,an wingtip-stall. #herefore, noroll-o0er should $e o$served and a spin-proof aircraftcan $e e'"ected R

econd( ;ince no flow se"aration at the wingti"s occurs, also no +rear-up+

stall should $e o$served

Third( Aoth elevons u" means that the wing has positi0e twist. ;uch wings with "ositive washout, however, have a tendenc for spiral stability while circling. #his ises"eciall im"ortant and "leasant for sail"lanes, es"eciall during instrument flight

Let me tell ou, as an e'am"le, m own e'"erience while fling the %orten %

&&&f ("rone "ilot "osition) n 1971 entered a cumulus cloud with this shi", even thatm turn<indicator was not working /t that time had not nor have now < an instrumentflight rating Aut had trust in the words of %einJ cheidhauer who had told me- . Inthe cloud keep the stick completely back and well centered . . . and wait until the round

appears aain". t worked, after a rise of 1000 meters came out on to" of the cloud#he Dorten did the constant circling herself never fling faster than I0 km6hGom"letel safeR =ith which other sail"lane of that time would that have $een "ossi$leO=ith noneR

Fourth( A this "ositive twist the ad0erse yaw is dam"ened or even com"letelannihilated #his strengthens the control around the vertical a'is

Fifth( #here is, however, a "rice to $e "aid for all these ver favora$le flightcharacteristics- f the lift distri$ution of the wing is chosen o"timal for the correct GH

"osition, then nose<heaviness gives more induced drag, ie gives a loss f the nose<heaviness is ver large, then this loss ma also $e ver su$stantial

ow ou ma ask- "#hy would anybody in his riht mind mo$e the c . of a flyin wintoo much backward %". have seen this done ver often, it ha""ened twice during thelast two ears with a disastrous result in one case #he .normal. reason for doing so isthe o$servation, that the elevons are in .u".<"osition during .normal. flight #heo$vious reaction is then- .&h. the airplane is nose'hea$y otherwise the ele$ons would

be in neutral position". #hen, the GH is moved hack, then wingti" stall and6or lateralinsta$ilit occurs, then the "lane goes into a s"in or an other un"leasant flight situationand ver often crashes



f moving the GH $ack is wrong, what should then he done in such a caseO =h, thesolution should $e o$vious to an aeronautical engineer-

When the flying wing in normal flight has the ele0ons up8 then the fied twist of the

wing8 the build-in wash out8 is too small and should be increased R

Aut, whenever suggested this remed, then invaria$l came the re"l- .#ell but this

would deteriorate the performances of the airplane". #his is trueK $ut flying with the

ele0ons up deteriorates the performance e0en more R

Aut, ou know, no$od ever did $elieve me RRR /nd so, fling wings again and againhave $een fling with GH aft and crashed

$urflKgel =apers

A etrospecti0e( Flying Wing /esign &ssues

Albion %. owers

$AA /ryden Flight esearch ,enter8 5dwards8 ,A

/a0id A. Lednicer

Analytic <ethods8 &nc.8 edmond8 WA

=resented to the members of The Wing &s The Thing BTW&TTC on eptember 278 1''"8 at

:illespie Field in 5l ,aon8 ,A.

/l Aowers whose "resentation for the da would $e an engineering and historical analsis and "ers"ective of fling wings, including designs $ orthro", Li""isch and Dorten

/l started with a little $ackground a$out himself De $uilt the usual $alsa models when he was oungand a$out the time he should have gotten into radio control models a new movement was $eginning in;outhern Galifornia #his resulted he his first $am$oo and "lastic hang glider, which his father ?uicklcut u" into si' foot chunks Dowever, his father did go out and $u some aluminum tu$ing and $uilt a.real. hang glider from an original set of Fle'iFlier "lans /l flew hang gliders until a$out 19I whenhe moved into sailing, sail"laning and college /fter college he went to work for /;/ where he istoda

#he "a"er he was "resenting toda was not solel his work t was a colla$oration with >avid Ledniceras a co<author #he had $een friends for a while $efore discovering the were $oth fling wing nutsand took the o""ortunit of the fling wing sm"osium to "ut together this "a"er

/s an introduction, /l commented that the num$er one thing ou need to think a$out when ou have aconventional air"lane is that ou have a tail that serves one function and wing that servesanother =hen ou "ut these elements together ou end u" with having to make com"romises #heseare in "erformance, sta$ilit, control and structure, or how do ou "ut all the "ieces into one worka$leunit and what is the configuration ou are left to work with #here are things like "lanks, .$oards.,



swe"t (fore or aft) wings, deltas, etc De went on to "resent a short chronolog of wing designs $Dorten, Li""isch, orthro" and the ;A<1@ as a recent e'am"le, +ust to la some groundwork for the restof the "a"er



#he first com"romise to $e discussed is "erformance t%s reall im"ortant to understand "rofiledrag 4ou look at the "olar for lift to dragK the drag $ucket and minimum drag De showed an e'am"leof a laminar drag $ucket that has a "oint where drag dro"s off shar"l indicating there are significantamounts of laminar flow develo"ing #he new com"uter airfoil design "rograms can come u" withlarger drag $uckets, in fact ou can design them so the entire o"erating range is within the $ucket Dowever, ou have to know what that o"erating range is and $e ver careful in how ou select

it, $ecause if ou get outside of what the airfoil can handle ou can face severe "ro$lems and theirconse?uences

/ high L6> airfoil ma not $e the $est airfoil for our air"lane, since there are other com"romises thatcome along which can kind of contaminate what ou have to do #hese are s"anload and trimissues e't ou look for the "itching moment and there are two was ou can go with this 3ne is with



a smmetrical airfoil which has no "itching moment, $ut somehow ou have to trim it to "roduce "ositive lift Dowever, if no "itching occurs then ou have a &ero lift airfoil which is not veruseful #he Dorten and Li""isch a""roaches were to use cam$ered and refle'ed airfoils, the refle' tohel" control the "itching moment caused $ the cam$er #he good news is ou end u" with a low "itching moment and it ha""ens at some "ositive lift coefficient which is ver $eneficial

#he ne't thing to look at in airfoil selection is skin friction Laminar flow is usuall a good thing and

tur$ulent flow is sometimes good and $ad 4ou want to avoid laminar se"aration and minimi&e theamount of tur$ulent flow ou have to have #his gets into $oundar laer control issues and mostaircraft we see have natural transition "oints on the wing

De then moved on to discuss interference drag which is hard to understand since it is verconfiguration de"endent #his is drag created at corners and other intersections of surfaces likewinglets or the fuselage #he air flow doesn%t +ust flow through the corner, $ut rather it $uilds u" acirculation region #his is "utting energ into the air to make it use this swirling motion and that energis coming from the vehicle that is "roducing the flow and this is drag

#here is another t"e of drag created $ lift, which is induced drag 3ne wa one to look at this isthrough the lifting line theor "ut forth $ Ludwig randtl De thought ou could descri$e a wing as aseries of vortices /ir goes over the to" faster and along the $ottom slower and along with this ouhave the motion of the airfoil through the air Aut given this condition, if ou remove the motion of theairfoil through the air, what do ou have left overO t turns out what ou have is this faster motiongoing forward over the to", $ut the motion on the $ottom is going slower so ou su$tract it out as aconstant, so ou a result ou can think of as a little $it of motion going $ackwards #his is calledcirculation and it is ver difficult to calculate, $ut there are some a""ro'imations which hel" to arriveat a solution 3ne of these was ;chrenk%s a""ro'imation since it accommodated ta"er and twist of anormal wing and it would also com"are control surface deflections #he one thing it didn%t do for ou

was the effect of swee" #his came u" later ver strongl for the Dortens $ecause the found with theirswe"t wings the couldn%t find everthing that was going on

#he affect of swee" was called the middle effect $ the Dortens and it influenced their designs over theears =ith more modern techni?ues availa$le through the introduction of digital com"uters in the %0sand %I0s, circulation calculations can $e done much more ?uickl eliminating the need fora""ro'imations Gom"utational fluid dnamics (GF>) has now $een introduced, $ut /l commentedthat, although not readil advertised, it is still an a""ro'imation of what is actuall going on, es"eciallin the tur$ulent flow region 4ou can%t descri$e the flow motion of the air in a tur$ulent region due do



its chaotic characteristics and the need to average it all out

;till talking a$out "erformance, /l moved on to lift and s"anloading Ludwig randtl said if ou candescri$e what this induced loss can $e , then what is the minimum induced loss ou can get, or theo"timum solutionO !lli"tical s"anloading was found to $e the minimum induced drag that could $eo$tained and this was the acce"ted theor for almost 80 ears ;ome recent develo"ments have shownthat "ure elli"tical is not reall ?uite the o"timum due to the effect of drag on the s"anloading t can $e

calculated, $ut it is com"letel configuration de"endent, however, for all "ractical "ur"oses the lookelli"tical and elli"tical is still o"timum

#he Dortens came u" with a $ell sha"ed s"anload distri$ution #he $ell curve shows a download at the

wingti"s $ut a lot of lift near the centerline and this has a drag "enalt associated with it #he furtherou get from the elli"tical distri$ution the more drag "enalt ou have to incur, so ou have to considerthe com"lete configuration f ou have a conventional design with a tail, it has to have a download inorder to trim the air"lane, and that download has to $e included in the induced drag calculations t can $e com"ensated for $ the designer $ looking at the far field wake and how it rolls u" and whether ithas an discontinuities that can cause additional drag #hese discontinuities caused $ control surfacesand other design im"erfections need to $e minimi&ed to achieve the lowest drag com"onent

;wee" in the fling wing is analogous to a tail in that it allows for trimming the aircraft t also allowsfor ad+ustments to the dam"ening as descri$ed $ rv Gulver a$out 10 ears ago ;wee" also allows for



"utting fla"s on the aircraft which can $e used for increasing the lift, $ut ou need to $e a$le to trim forthe effects of the fla" during de"loment #here are three was to go with this, one of them not $eingver desira$le #his is the adverse fla" affect where the nose goes over in a tuck as the fla"s are "utdown and is one of the "ro$lems that orthro" never ?uite overcame in his designs /l related a stora$out Ao$ Doover tring to takeoff in the 9<* on !dwards 12,000% runwa with the fla"s down #heaircraft +ust wouldn%t come off the runwa so he thought ma$e he had some t"e of trim "ro$lem and

retracted the fla"s in an effort to solve it #he instant the fla"s came u" the aircraft lea"ed into the air,so o$viousl there was a trim "ro$lem associated with the fla"s and the overall wing design

n modern times, designers have figured out ou can actuall use fla"s on a swe"t fling wing to ouradvantage 4ou can make the fla" work as a trim device, and lan roo integrated them in a wa thatthe nose goes u" and the aircraft slows when the fla"s are "ut down #his can $e seen in the Aright;tar ;=F# Gonversel, ou should $e a$le to make it $alance out so that ou get no "itching momentas in the Flair @0 #his is an e'am"le of having a clear set of criteria in mind $efore starting the designof the aircraft

/l then moved on to sta$ilit, not sta$ilit /> control De +oked a$out a gu in his office saing itshould $e sta$ilit 3 control since ou can%t have $oth De went on to descri$e the differences $etween static sta$ilit, neutral sta$ilit and dnamic sta$ilit 4ou can have a dnamicall sta$lesstem where there is enough dam"ing to remove an oscillations that ma occur and return the aircraftto a trimmed condition 4ou can have neutral sta$ilit where the oscillation doesn%t dam"en $ut it alsodoesn%t grow and get worse over time t%s the dnamic insta$ilit that gives ou the $iggest headachesince ou can $e staticall sta$le and end u" with something like flutter and have the whole thing comea"art in ver short order

De went on to cover the five classical modes of sta$ilit, the first two $eing longitudinal #here is theshort "eriod (arl ickel calls it "ecking) where when ou "ut in a "ulse the aircraft%s angle of attacktries to come $ack 4ou cannot afford to have dnamic insta$ilit here since there is no reaction time tocorrect the condition $efore it might $ecome destructive #hen there is the "hugoid t"e which lasts alonger time, ma$e u" to one or two minutes t can $e dnamicall unsta$le since ou have "lent of

time to recogni&e the condition and correct for it $efore it $ecomes a real "ro$lem#here are three directional modes #he first is roll control which is the result of a standard roll in"utthat sta$ili&es into a constant velocit movement #hen there is dutch roll, also known as the dihedralaffect, where the aircraft gets hit $ a gust and rolls $ack #his can $e dam"ed or undam"ed and mahave more affect on fling wings, such as was seen on the orthro" wings #he weren%t reallunsta$le, $ut rather the had a limit ccle that means the oscillation would $uild u" to a certain si&e andthen +ust sta there #he last mode is s"iral which can $e sta$le or unsta$le #here are a lot of aircraftthat are unsta$le in this mode, $ut $ecause it $uilds u" so slowl it is controlla$le and not a real "ro$lem, like in a Gessna 1I2 #he Dorten was s"irall sta$le as demonstrated when it went into theclouds during a contest at hVn #he "ilots (;cheidhauer and Alech) sim"l held the stick in a constant "osition and the aircraft continued in a controlled manner until coming out of the clouds

For the sail"lane "ilot there are two new modes that need to $e considered #hese concern theattachment of the tow ro"e which affects $oth the longitudinal and lateral modes De noted these modeshad not reall $een descri$ed until a$out five ears ago and there still is no "hsical flight data forthem #here has $een some ground testing and measurements taken, $ut flight data is +ust now $eginning to $e gathered for analsis

;taing with sta$ilit, he went on to talk a$out linearit #his is where the restoring force is "ro"ortional to the dis"lacement ear the outer, ragged edge of the envelo"e ou can get non<linearit,like stalls #here are fi'es for some of these non<linearit%s so ou can get the aircraft to work like ou



want it too >evices like fences, fla"s, vorte' generators and tur$ulators can $e "laced on the airfoil toad+ust for the "ro$lem Dorten "ut large wing fences on the D Ea to hel" the elevon control authorit

/l then moved on to the area of control De related this to making crosswind landings where ou wouldneed a @<a'is control sstem #he Dortens used a $lended surface where the had multi"le trailingedge surfaces that all moved in "itch or roll, $ut the didn%t move "ro"ortionall to eachother Dowever, what ou notice a$out the sstem is that no matter what trim angle of attack ou use all

the control surfaces have some deflection since ou can%t choose a trim angle of attack where the areall at &ero when tested (the aircraft was out of rig) orthro" was an airfoil aerodnamicist and what hedid was use the middle surfaces for "itch and roll, and the out$oard surfaces trimmed onl in "itch ands"lit to act as drag rudders f the stick is "ulled all the wa $ack what ou have done is inducemechanical washout in the middle section and washin at the ti"s #his is a good reci"e for loosing theti" and having a stall6s"in "ro$lem 3ne of the solutions was to tr and "ut slots out towards the ti"s,which hel"ed the stall "ro$lem $ut not that of s"in Dowever, when the airflow over the slots se"aratesit does so with a lot of hsteresis and a small decrease in angle of attack doesn%t result in airflowreattachment t takes a large change in the angle of attack to get the flow to reattach #his was acharacteristic of the t"e of slots that he used #he good news was, of course that it hel"ed the stall

#he ne't thing on his agenda was adverse aw /s most sail"lane "ilots know this is the effect ou getwhen in"utting a roll to right and having the nose move towards the left $ecause of the aileron%sdeflection Dorten had "ostulated that if ou use a $ell sha"ed lift distri$ution ou wouldn%t have this "ro$lem, and this has $een "roven to $e the case #his is $ecause the ti"s are loaded down so ou endu" with a little $it of "ro<verse aw /nother solution is to "ut verticals on the surface, $ut now ouhave additional "rofile drag from the surface and interference drag from the corners and +oints

/nother thing ou can encounter is control force reversal orthro" overcame this "ro$lem $ using ahdraulic control sstem Dorten never seemed to have this "ro$lem throughout his designs, $ut /ldidn%t have an answer as to wh this was the case Dorten had o$viousl found something that worked, $ut a""arentl it%s not discussed or defined in his works

De now moved on to trim, which will also have an effect on the drag "olar "erformance Dere he was

working from information in arl ickel%s $ook f ou have a sta$le air"lane, such as a fling "lank,when ou deflect the elevator down the drag "olar goes u" along with the lift coefficient, e'ce"t ouare trimming the nose down #hese reactions are one of the reasons fling wings have "erformance "ro$lems 4ou can have a unsta$le aircraft that can $e made to "erform in the $etter "art of the "olar $using an artificial control sstem (active flight controls) lan roo has done this with an G model thatwas 8 unsta$le, $ut one of the other "ro$lems he encountered was getting actuators that were fastenough 3ne of the advantages of this t"e of control sstem is that ou can make the lift distri$utionwhat ou want it $e through control surface movements unavaila$le with a manual control sstem

ow he moved into the area of structures =hat can ou $uild versus what to do ou wantaerodnamicall deall, in order to carr the load, ou want something that has a thick center sectionand thin ti"s #his has adverse affects aerodnamicall on airfoil thickness and chord and the stallcomes sooner due to the thin ti"s #a"er ratio is one method for hel"ing solve this "ro$lem and ickeland =ohlfarht favor a low ta"er design since ou can get ver close to an elli"tical s"anloaddistri$ution 3$viousl Dorten favored the high ta"er ratio, $ut this has it "ro$lems with ti" stall thatneed to $e overcome in some other fashion /n elli"tical "lanform is another wa of controlling theta"er ratio

deall ou want to $uild a s"anloader where the local lift distri$ution carries the load as much as "ossi$le, in other words, "ut the load where the lift is #he Dortens understood this conce"t when the $uilt some cargo carring gliders where the ammunition storage $as were evenl distri$uted across the



s"an t ended u" fling at nearl three times its gross weight due to this distri$ution method

3nce ou have our s"anloader, the ne't issue $ecomes one of the s"ar thickness ratio #here is someevidence that ou can get energ e'traction from a ver fle'i$le s"ar, fle'i$le in $ending not torsion,when "assing through gusts #hen ou have the controvers $etween monoco?ue or s"ace frameconstruction and whether or not the skin or the s"ar carries the load Location of the fore and aft s"arsare also a function of the aerodnamic design and can create a com"romise $etween low or high as"ect

ratio wings de"ending on where the "ilot is located in relation to the s"ars

ow it is all coming together, $ut it is also where the headaches $egin, "erformance 4ou have to "ick as"anloader, elli"tical or $ell, $ut most "eo"le don%t think a$out "icking one or the other since the "ro$a$l alread have one in mind $efore starting their "ro+ect f ou use elli"tical then ou use ta"erand twist at our design "oints to control the s"anloading #his elli"tical s"anloading causes adverseaw in roll, $ecause ou have a fairl large load out at the ti" as soon as ou deflect the aileron to liftthe wing t increases the s"anload locall, increasing the induced drag and ou end u" going the wrongwa #he first thought is to "ut verticals like winglets which can $e good things, some of the time 3fcourse ou now have the "rofile, induced and interference drag mentioned earlier and ou cannotcontrol the angle of the winglet other than the toe<in #his toe<in angle corres"onds to a certains"anload and lift coefficient, and this should coincide with the ta"er and twist design "oints Forsail"lanes this $ecomes more difficult since the o"erate over a wide s"eed range throughout the flight,versus something like a "assenger +et that has them set for o"timum "erformance at cruise where thes"end most of there time

/l felt that Dorten, with his $ell sha"ed s"anloader, was willing to suffer some of the induced drag to "revent adverse aw without having vertical surfaces, a design com"romise hiloso"hicall, he $elieved the Dorten sat down and figured this would $e more advantageous than havingverticals =hen Dorten received his h>, his teacher was Ludwig randtl who came u" with theelli"tical s"anload distri$ution, et Dorten threw out the idea and "roceeded with his own designtheories

3ne of the things /l felt didn%t ha""en during the earl ears of fling wing develo"ment was a cross<

fertili&ation of ideas $etween the various designers #here wasn%t a great deal of discussion $etween thedesigners, and this was "artl due to the large distances se"arating them and the lack of ?uicktrans"ortation #here are com"romises to $e made and the designer has to understand this right fromthe start For instance, orthro" used linear twist at certain design "oints and straight lined everthingin<$etween which was ver sim"le and eas De used a smmetrical airfoil which caused most of histrim "ro$lems, $ut it was laminar flow with &ero "itching moment at &ero lift

#here was another issue on the orthro" designs concerning "ower"lant sta$ilit #he "ro"ellers on theEA<@ were a sta$ili&ing influence on the design since the were aft of the center of gravit 3n theother hand, the +et engine intakes in the leading edge of the 4A <79 caused a $ending of the airflowforward of the GH and created a desta$ili&ing influence #herefore, orthro" had to "ut the verticaltails on the 4A<79 to hel" recover some of the directional sta$ilit ;ome "eo"le said the verticals wereto re"lace the lost area of the "ro"eller shaft housings, $ut /l indicated the verticals containedsignificantl more area then what was lost from the nacelles

/l felt that John orthro" full understood the conce"t of s"anloading since he located $om$ $asalong the wing out to the aileron $reaks De also "ut some heav electric gun turrets far out on thewing De used a monoco?ue stressed skinned construction which was a $eautiful design

n contrast, the later model Dorten designs with their $ell sha"e lift distri$ution were giving awa "erformance and drag, $ut had minimal adverse aw #he ?uestion is whether or not this was a goodcom"romise, and Dorten thought it was since he wouldn%t have to use verticals Dere is where /l



wished Dorten and orthro" could have gotten together and discussed airfoils Dorten didn%t haveaccess to the same t"e of airfoils as orthro", and therefore use Hoettingen models which were notanalticall designed like the orthro" laminar flow sections Dorten did tr to use a <1 laminar flowairfoil on the D C$ which su$se?uentl s"un and crashed killing the "ilot #he *ustang airfoil wasdesigned for higher s"eeds and enolds num$ers than a sail"lane, therefore, were notcom"ati$le #his e'"erience turned Dorten off to laminar airfoils for the rest of his career, mainl

$ecause he didn%t understand how the worked Dad he $een a$le to sit down with orthro", it mighthave $een a different stor Dorten, in turn, might have $een a$le to hel" orthro" with flight controlselection and configuration, $oth designers there$ $enefiting from the e'change

/l went on to talk a$out the ;A<1@ /lthough it "erforms well, he noted it had some handling "ro$lems #he used an o"timum modified elli"tical s"an at their design "oint since the includedwinglets t had low ta"er with twist for s"anload control of the lift distri$ution #he winglets also usedrudders which hel"ed in modifing the design "oint and used a large radius in designing the +oining "oint to minimi&e interference drag /lthough the control mechanisms are ver com"licated, the allowfor ver good control surface selection to o"timi&e "erformance n order to overcome an flutter "ro$lems the $uilt u" a unidirectional, monolithic car$on fi$er s"ar (one "iece) #his controlled the $ending moment and then the used cross<"ls in the skin to "rovide the necessar torsional

stiffness #he results of all this stiffness to control "ossi$le flutter gave them an overstrength s"ar thattested at 1 Hs without failure

/t this "oint /l talked a little $it a$out the $lended wing $od aircraft "ro+ect started $ /;/Langle a few ears ago #his is sort of how /l got interested in fling wings and s"anloaderaircraft De covered the "ro$lem of how $ig the s"an has to $e in order to have sufficient airfoil de"thand chord to handle u" to 800 "assengers 3ne wa >ouglas overcame the "ro$lem was to have a largecenter section that ta"ered ?uickl to winglet ti"s /s he e'"lained earlier this t"e of design leads to

ti" stalls, $ut in this case the use of active flight control sstems would $e a$le to overcome the "ro$lem

3ne of the unusual things a$out >ouglas% design conce"t was the use of $oundar laer control to "rovide the engine air n this wa almost the whole wing%s surface $ecomes an engine inlet (suckingair through a "erforated skin) while at the same time maintaining the laminar laer over a larger "ortionof the wing De mentioned the "ro$lem of air"ort infrastructure and its im"act on the designconsiderations since the "assenger gate sstems can onl handle aircraft with a limited amount ofs"an #hen there is "assenger acce"tance if ou tr something like folding the wings to kee" the s"anwithin the desired gate limitations lan roo at ;tanford has $een involved in the "ro+ect and $uilt two



different G models for testing, one of which is a$out 2@% in s"an and will $e instrumented for futuretesting 3ne of the $igger "ro$lems that ma need to $e overcome is the "ressuri&ation ccling and,how long a structure that is not a tu$e will last

#he thing that /l wanted us to get from this "resentation was that ou%ve got integrated sstems andeverthing is a com"romise t could $e $oundar laer control instead of engine inlets, or what ou dofor s"anloading 3"timal "erformance is not alwas "ossi$le, and "erha"s not alwas desira$le, and

sometimes ou have to com"romise on sta$ilit or the control sstem For control sstems, he felt theDorten designs offered some of the $est com$inations and that Dorten reall knew what he was doingin this res"ect

N"on com"leting the formal "art of the "resentation, he showed some color slides of com"uter aided "ictures of "ressure distri$ution, skin friction coefficient and laminar flow on several different t"es offling wings, like the 9<* and Dorten C (S2) which showed the middle effect mentioned earlier(see note $elow) De also showed some slides of what is ha""ening in /rgentina at this time in tring torestore the Dorten D Cc Nru$u, and a few historical shots of Dorten%s work while in /rgentina

(ote This section was titled "*istorical +lyin #in ,ircraft ,nalysis -sin the /,01& 2anel

Method" by 3a$id Lednicer. /lides for the 4'M and *orten I included pressure isobars and skin

friction coefficient distribution in color and a wake roll up slide for the *orten. Graphs included those for semispan fraction (win twist)5 6 mean aerodynamic chord5 lift coefficient5 semispan fraction

(circulation distribution) and5 induced dra coefficient.)

eferences

Dorten, eimarK and ;elinger, eterK with ;cott, Jan (translator)- .urflugel- #he ;tor of DortenFling =ings 19@@ < 190.K =eisha"t CerlagK Hra&, /ustriaK 198

*alone, !dward- .orthro" Fling =ings.K =orld =ar u$licationsK Gorona >el *ar, G/K 198@

ickel, arlK and =ohlfarht, *ichaelK with Arown, !ric (translator)K .#ailless /ircraft in #heor andractice.K ///K ew 4ork, 4K 1997

acher, DansK .*itteilungen- Flugtechnischen Fachgru""en und /r$eitsgemeinschaften.K FFH <>armstadt, 1977

Ford, >anK .Fling =ing.K ;mithsonian /ir T ;"aceK Jul 199I

Aal&er, HeraldK .#he Fling =ing%s Nnsung rotot"es.K =ings, /"r 199I

Li""isch, /le'anderK .!in >reieck Fleight.K *otor$uch CerlagK 19I

Horgfalv, >es&oK .erformance /nalsis of the Dorten C Fling =ing.K Gongress of the 3;#CKGologne, HermanK Jun 190

uhlman, AillK and uhlman, Aunn (A<;?uared)K .3n the =ing- ;=F#.K G ;oaring >igestK Jun1997



*ai, D NlvK .#he !ffect of /eroelasticit N"on !nerg etrieval of a ;ail"lane enetrating a Hust.K#echnical ;oaring, Col 10 o 7

anonmousK .urflugel ennaisanceO.K /erokurier, *a 1988

Dorten, eimarK .Lift >istri$ution on Fling =ing /ircraft.K #echnical ;oaring, Col 10 o 7

van >am, GK .;we"t =ing<#i" ;ha"es for Low<;"eed /ir"lanes.K ;/!81II0, 3ct 198

Gulver, rvK .#ailless Fling =ings.K #echnical ;oaring, Col 11

;chuemann, =ilK ./ ew =ing lanform with m"roved Low<;"eed erformance.K ;oaring, Fe$ 198@

anonmousK .Jahre /kademische Fliegergru""e Araunschweig !C 1922 < 1988%K /kafliegAraunschweigK 1988

>e*atteis, HK and de ;ocio, LK .>namics of a #owed ;ail"lane.K /// 91<282K 1991

the horten

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