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REPORT No. 648
DESIGN CHARTS FOR PREDICTING DOWNWASH
ANGLES AND WAKE CHARACTERISTICS BEHIND
PLAIN AND FLAPPED WINGS
By ABE SILVERSTEIN and S. KATZOFF
Langley Memorial Aeronautical Laboratory
111 ():_4--3!_-- I
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
HEADQUARTERS, NAVY BUILDING, WASHINGTON, D. C.
LABORATORIES, LANGLEY FIELD, VA.
Created by act of Congress approved March 3, 1915, for the supervision and direction of the scientific
study of the problems of flight (U. S. Code, Title 50, Sec. 151). Its membership was increased to 15 by
act approved March 2, 1929. The members are appointed by the President, and serve as such without
compensation.
JOSEPH S. AMES, Ph. D., Chairman,
Baltimore, Md.
I)AVID W. TAYLOR, D. Eng., Vice Chairman,
Washington, D. C.
WII.LIS RAY GREGt;, So. D., Chairman, Exeeuti_e Commillee,
Chief, United States Weather Bureau.
WILLIAM P. MACCRACKEN, J. D., Vice ('hairman, Executive
Committee,
Washington, D. C.
CIIARLES G. ABBOT, So. D.,
Secretary, Smithsonian Institution.
LYMAN J. BRIGGS, Ph. D.,
Director, National Bureau of Standards.
ARTHUR B. COOK, Rear Admiral, United States Navy,
Chief, Bureau of Aeronautics, Navy Department.
HARRY F. GUGGENHEIM, M. A.,
Port Washington, Long Island, N. Y.
SYDNEY M. KRAUS, Captain, United States Navy,
Bureau of Aeronautics, Navy Department.
CHARLES A. LINDBERGH, LL.D.,
New York City.
DENIS MULLIGAN, J. S. D.,
Director of Air Commerce, Department of Commerce.
AUGUSTINE W. ROBINS, Brigadier General, United States
Army,
Chief Mat6riel Division, Air Corps, Wright Field,
Dayton, Ohio.
EDWARD P. WARNER, Sc. D.,
Greenwich, Conn.
OSCAR WESTOVER, Major General, United States Army,
Chief of Air Corps, War Department.
ORVILLE WRIGHT, Sc. D.,
Dayton, Ohio.
GEORGE W. LEWIS, Director of Aeronautical Research
JOlIN F. VICTORY, Secretary
HENRY J. E. REID, Engineer-in-Charge, Langley Memorial Aeronautical Laboratory, Langley Field, Va.
JOHN J. IDE, Technical Assistant in Europe, Paris, France
TECHNICAL COMMITTEES
AERODYNAMICS AIRCRAFT STRUCTURES
POWER PLANTS FOR AIRCRAFT AIRCRAFT ACCIDENTS
AIRCRAFT MATERIALS INVENTIONS AND DESIGNS
Coordination of Research Needs of Military and Civil Aviation
Preparation of Research Programs
Allocation of Problems
Prevention of Duplication
Consideration of Inventions
LANGLEY MEMORIAL AERONAUTICAL LABORATORY
LANGLEY FIELD, VA.
Unified conduct, for all agencies, of
scientific research on the fundamental
problems of flight.
OFFICE OF AERONAUTICAL INTELI,IGENCE
WASHINGTON, D. C.
Collection, classification, compilation,
and dissemination of scientific and tech-
nical information on aeronautics.
REPORT No. 648
DESIGN CHARTS FOR PREDICTING DOWNWASH ANGLES AND WAKECHARACTERISTICS BEHIND PLAIN AND FLAPPED WINGS
l]_, +\I+I: _II+\I,:RSTEIN altd _. I_+',TZOFF
SUMMARY
l+,'quatiol_s aml desigl_ c/torts are given for predicting
the doumwash al+gles a_(1 the wake charachristics .for
power-off eoT+ditio_+s behimt plain and flapped wings oJthe types used in modern desig_ practice. The dou,mrash
charts cover the cases of elliptical wings amt wil_gs of taper
ratios 1, 2, 3, aTM 5, with aspect ratios of 6, 9, arid 12,
hadr_g flaps em, eri_g O, gO, 70, aTM 100 }>ereel_t of the
,_pa_. Curves of the spa_ load distributio_+s for all these
cases are i*wluded. Data o_ the lift aml tile drag q[
flaplJed airfoil secti+ms aml curces for fiI_di,_g the coldribu-
tion of the flap to the total wb_g lljt .for diff_re?it types offlap al_dJor the entire ra,ge of flap spans are ah.o inel'uded.
The wake width, and the distribution of dyrmmie pressure
across the wake are given in terms of the profile-dra 9 eo-
eflieiel_t and the distance behind the whig. A method ofestimating the wake position is olso give_+.
The equatlons and the charts are based on theory that
has been show_t ia a previous report to be in a.qreemeT_t withexperime_ t.
INTRODUCTION
In a recent paper (reference 1) methods are developed
for predicting <lownwash angles and wake characteristics
for power-oil' comlitions behind airfoils of known st)anloading. The calcuhttion of do_vtm"tsh involves several
simplifying assumptions that nre shown to be justified.Wake characteristics are given by eml)irical expressions
derived from experimental data and are in agreement
with available them'y.
In or<ler to m,_ke the methods of reference 1 readily
al)l)lieable for design purl)oses , charts hqve been 1)re-
pared covering the range of modern design practice.
These ehurts are given in the present paper, lnchtded
are curves of the lift and the (lr,_g of flapped airfoil sec-tions and charts f()r llnding the contributions of the
difl'erent types of tl'tl) to tim total wing lift. lnforma-
lion is also l)rcset,tt_<l for determining the l)osili(m of the
wake, its width, :tl.I the (list t'ibtltioI_ <,f dynamicpressure across it.
The downwash charts are for elliptical uings and for
wings of taper ratios i, 2, 3, and 5, with aspect ratios
of 6, 9, and 12, having llaps covering 0, 4(1, 70, and 100
percent of the span. The explanatory text accompany-ing the charts is suitMently complete to permit their
use without study of reference 1.
SYMBOLS
CL, lift c(,elfMent.
C lift coeflicien! at . 1)articular angle of attack.l'tc_
ttaps up.
CVr' increase of lift coeflMent, at the same angle of
attack, Ul)On deflecting the flal).c. section lift ('oetIi('ient.
Ac+, increment of section lift ('oetlieient corresponding
to a tlap delleetion (two-dimensional).c<,, section protile-drag coefficient.
c, wing chord.
(7, flap chord.
b, wing span.
bl, flap span.
S, wing area.
x, longitudinal distance fi'om quarter-chord point.
y, lateral distance from symmetry plane.
z, vertical distance from quarter-chord point.
s, vortex senfisI)an, in wing senfispnns.I', vortex strength.
v,, induced vertical velocity.g, downwash f'wtor.
e, downwash angle.
h, downward displacement, measured normal to therelqtive wind, of the center line of the wake and
the trailing vortex sheet from its origin at thetrailing edge.
m, vertietfl distance of the elevator hinge axis fromthe wake origin, measured perpendicular to therelative wind.
,_, distance behiml !he trailing edge..(-, wake half-width.
i", vertical distance from wake center line.
+7, loss in dynami<: t)ressure at wake center, fraction
of free-stream (lyImmie pressure q.
v', loss in dymtmic pressure, fraction of free-streamdynamic l)r(,ssure %
k, correction for hw, ling wake origin.
5z, ttap angle.
1
2 REPORTNO.648---NATIONALA])VISORY COMMITTH.] FOR AERONAUTICS
RESUMI_ OF THEORY
Downwash, plain wings.- The downwash behind a
wing is mainly a function of the wing loading and is amanifestation of the associated vortex system. This
vortex system comprises the bound, or lifting, vortex
considered localized at the quarter-chord line and thevortex sheet that is shed from the trailing edge. If the
strength of the bound vortex at distance s from theairfoil center is F, the vorticity per unit spanwise length
in the sheet as it leaves the trailing edge is --dF/ds.
A first approximation to the downwash is obtained
by assuming the sheet to originate at the quarter-chordline and to extend unchanged indefinitely downstrc'un,
the vortex system thereby consisting of elementary
U-vortices (or horseshoe vorticcs) of scmispan s and
strength -- (dI'/ds)ds to which the Biot-Savart equation
is applicable. The actual sheet, however, does not
extend unaltered from the lifting line to infinity be-
cause, as a result of the air motions that the vortex
system itself creates, it is rapidly displaced downwardand deformed.
For purposes of calculation of tile downwash angleat the tail, a satisfactory second approximation is ob-
tained by neglecting the defornmtion and consideringthe entire sheet to be unifornfiy displaced downward
by an amount equal to the displacemel_t of the center ofthe sheet near the tail. This displttccment, fm'ther-
more, can be readily calculated since the sheet follows
the downflow which, with reasonable accuracy, may be
taken as that given by lhe first approximation. Inas-much as the downwash depends to a predominant extent
on the trailing vortex sheet, a vertical displacement ofthe sheet causes a vertical displacement of the entire
downwash pattern by the same amount.The strength of tile vortex system is proportional to
C_.; hence, the downwash angle e and the displacement
h must also be proportional to CL. At higher lifts,
however, there are three disturbing effects, all of whichtend to increase the downwash above the sheet and to
decrease it below. These factors are: (1) The effect of
the strong tip vortices that, owing to the curvature of
the sheet, are above the center; (2) the effect of the
bound vortex that, owing to the downward displace-ment of the sheet relative to it, similarly contributes
more to the downwash above than below it; and (3)
the flow of air into the wttke, which is coincident with
the trailing vortex sheet.Downwash, flapped wings.--The effect of a flap on
the downwash depends upon its effect on the span load
distribution. The change in loading upon lowering a
given flap is nearly independent of the angle of attack,
and the absolute change in tim lift coefficient at any
section c_ is approximately proportional to the total
increase in the wing lift coefficient CLf The resultant
loading and vortex systems being the sums of those of
the plain wing and of the flap, the resultant downwash
is the sum of that due to the plain wing at the given
attitude and that due to the flap. The component
due to the flap is proportional to (,_:. The vortex-
sheet origin lies between the trailing edges of the plain
wing and of the flap. Its vertical displacement is, like
the downwash, the sum of that due to the plain wing
and that due to the flap.
For wings with flaps, increased importance attaches
to the three disturbing effects mentioned for plain wings.
The wake, in particular, requires consideration where
high-drag flaps are used.The wake.--The wake is characterized by a loss in
total pressure, the deficiency being a maximum at its cen-
ter and decreasing to zero at a fairly well-defined wake
edge. Its center line coincides with that of the trailingvortex sheet. On account of turbulent mixing with
the surrounding air, the maximum total-pressure lossdecreases with distance downstream, whereas the width
of the wake increases. The integrated loss in total
1)ressure across the wake remains nearly constant and is
proportional to the profile drag of the wing section fromwhich the wake was shed.
DOWNWASH CHARTS
Plan forms.--The downwash charts of figures 1 to 15
contain four groups of diagrams. In the first column
of each chart are shown the plan forms of the wings
for which the computations were made. Consistent
with the assumption made in the calculations that there
is no sweepback of the lifting line, the quarter-chordline is drawn perpendicular to the center line in every
case. The tips are shown rounded for a spanwise
distance equal to the tip chord, as was done in refer-
ence 2. Although the flap chord is shown as 20 per-
cent of the wing chord, the actual value of c:/c is
immaterial as long as it is constant over the entire span
of the flap. In actual practice, this condition is not
always maintained. As long as the variation of c:/cremains within the usual limits, however, this source
of error is of secondary importance.
Span load distributions.--The span load distributionsare shown in the second column of each figure. The
distribution for the plain wing was obtained fromreference 2. The distributions for the flap conditions
were coral)uteri by the Lotz method (reference 3).In the computations, the Fourier coetficients for the
chord distribution were found by Pearson's system
(reference 4) "rod the Fourier coefficients for the angle
distribution were forum by the usual method of integra-tion. Ten terlns of the series for the loading were
derived, which arc adequate to give the shape of the
loading curve except near the flap tip, where a reason-
able number of terms does not suffice to give the shape
accurately. The curves are therefore more or less
arbitrarily drawn in this region, the main condition
being tlmt the slope be infinite at the position of the
flap tip.
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16 REPORT NO. 648--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
DESIGNCHARTSFORPREDICTINGDOWNWASHANGLESAN]) WAKECIIARACTERISTICS 17
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18 I{Ir, POIVI" NO. 648--NATIONAl, AI)VISOI{Y (:OMMITTF, E lrOR AERONAUTICS
Undisplaced downwash-contour charts.--The down-wash-contour charts shown in tile fourth column are
drawn for C_,, =1.0 and Cz,F=I.O. For othcrlift mwf-
tieients, tile downwash angles can be obt'dned by
multiplying the angles on the contour charts by the
particular wdues of UL_ or Ctl. In the derivation of
these charts, tim tr,dling vortex sheet was assumed to
start at the quartcr-chor(l line and to extend unclm.n/cd
indetlnitely downstream. As Mrea,ly explained, the
vortex system is thereby assumed to be m'tde ttl) of
U-vortices of strength -- (dr /ds)ds, where r is lhe
strength of the bound vortex. The downflow velocity
at a point (x, z) in the symmetry phme is given by the
equation
1 F 1 dl'W= -- -T 1 8_-
7tO,to (18
In the actual computation, the indicated integr._tion
was replaced by a summation, i. e., the smooth span
load distributions were '_pproximated by st;el)wise
distributions of 5 to 7 steps, so tlmt equ.Ltion ([) was
effectively replaced by
x 1 1 ,1
where (AF)n is the rise of the nth step 'rod s, is the
corresponding sam/span. Figure 16 illustrales the
substitution of "t stepwise distrihution tara ,()ntinl,)U_
span load distribution.('urw_s of tile function
sF x / 1 1 \, I -]
were fotmd useful in these COmlnflations. They are
reproduced in figure 17.
The longitudinal component of lhe in,luted tlow
generally being negligible compared with the free-
stream velocity V, it follows that the tangent of the
do'_llwash attgle is very nearly v:/I'. The downwash-
contour charts have been constructed on this basis;
only hMf of each chart is shown, for the nxis is a line
of symmetry when the longitudinal components of the
induced velocities are neglected.
Displacement of the center line.--The downwash-
contour charts just (Inscribed require a vertical dis-
placement, as has already been mentioned, because the
trailing vortex sheet undergoes downward displacement
as it proceeds downstream. The downward displace-
ment is given by the equation
rh= tan _ dx (3)d T.E.
The curves shown in the third cohmm of tigures 1 to
15 are plots of this integral as a function of :r, for
(_r., 1.0=amt ('L/= 1.0. For other lift coefficients, dis-
1)lacc, mcnts are obtained t)3, multiplying tile values on
|he C]l:Lrts t)3" tim imrrtieuhlr values of ('r_ or Co/.
Origin of the trailing vortex sheet,--For a plain wing,
the sheet is considered to be shed at the t,r,dling
edge. For a wing with .t flal) , the origin is be-.
Iween the trailing edges of the flap and the wing,
-b
I
. S 4 _ -_
(_rh
.Z
I I 1 I II0 .2 .4 .6 .8 /.0
O/stance from c-cn/er" //r:,,2, se'mi._pom
I¢IGUEE 16.-- Illustration of tile substitution of six U-vortices for Ihe aCIilll[ vortex
system. CL, 1.0; taper, 3:1; aspect ratio, 9.
the distance below the trailing edge of the wing, in
sere/spans, being given by the formula
ho= (c/2) sin 5i+kcb/2 (4)
which is based on the available experimental data.
The factor k is given in figure 18.
Contribution of the flap to the total lift.--Figure 19
shows the theoretical contribution of the tlap to the
wing lift. coefficient. The values of 6_/Ac z were derived
incidental to the computations of sp'm load distribu-
tion, coming directly out of the first term of the Fourier
series for the loading. It must be noted that they
correspond, as do the span load distributions them-
selves, to flaps of uniform c/c or, stated differently, to
flaps of uniform Act. VChere Ac_ is not uniform, an
average Act weighted according to chord will usually be
satisfactory.
DESIGN CHARTS FOR PREDICTING DOWNWASH ANGLES AND WAKE CHARACTERISTICS 19
\/
1
io .2 .# .5 .8 /.o o .2 .4 6 .,9 /.o
U - voF_ex sefzl/soorT, 8
Fl_r:R_ 17.- Curves of Ihe g funclion for various values of x and z. (a) x:0.4. (b) z=0.6. (c) z=[).9. (d) .t:=1.2. (e) x=l.C,. (f) z=2.,5.
T _ of the curves of figure 19, (later are presented i. figure 20
for the increment of section lift coefficient 5cz obtained
t)v deflecting the various flal)s. It, re.st be f_()te(I tlmt! [ : i i "
t i I these increments are ._'cctiol_ char,_cteristics 'tml gwethe increase in lift eoetticient whel_ the tl'q) is lowered i.
two-dimensional flow. The data were obtained m'finly
from N. A. (I. A. results ,m(] from referen('c 5. No al-
tempt has been made here to give _Lcomplete 1)resenta-r
! i tion of the lift increments due to tlaps. The d'lta givent
_o 40 eo eo /o0 are best applicable _/t abo.t 3 ° to 4 ° beh)w maximum
F/op def/ecfton. 5.e .deq. lift; however, they apl)ly with re_somd,le a(.c.ra('y at
lower angles, for the increments are ne,lrly c()nst2mt
I
FIGUitE 18. Curve .f the k factor for localing the wake origin for wings with flaps.
2O REPORT NO. 648--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
over the entire useful range. The coefficients for the
0.20c external-airfoil flap arc based on the combined
chord of the wing and flap; those for the 0.26c Fowler
; rl/,p_,coZ?._.._._, i
4
....... (aJ -- _
0
Toper rof/o
O_
3.-_-'-r'-._
• 511,p/,_of.J/.. .
C_s.4 _,_ ,c,t
- Ib)
0 -EIh)o f/col
Tof_r rot/bI:1 , z .
3.'/-_"- "-
Ellipt/co/_/
.2 / "_ (c)
J I0 .8 .4 .6 .8 LO
Flop sport, b///b
FI(IURE 19. -I,ifl iucreinents fl)r wings with partial-span flalm (_t] .[ tl. (ID .1 =9.
(c) .4 - 12.
flap are based on the chord of the plain wing. In the
case of the Fowler flap, simply extending the flap, with
_s= 0 °, increases the lift coefficient by about 26 percent,
because the effective chord is increased by this amount.
Accordingly, the total increment in lift coefficient onextending t,be flap is 26 percent of the lift coefl_cientfor the plain wing at the particular angle of attack, plus
the further increment given in figure 20 for the particu-
lar 8s.
Variation of downwash across the tail span.--The
discussion thus far has been concerned with the calcula-
/.4--
l.z .........
Lt? ....
/ t
/ FIoD 5 A,'rfo;'/ !.S ..... _ ' ,I t_e lhschmess _¢
IV.'
rll
20 30 40 50 60 70Flop ongle, _, .de(7.
(a) Different types of flap on wings 0.12cthick.(b) Comparison of flapped wings O.12cand 0.21cthick.
I,'IC._RE20.--increment in section lift coefficient due to flap•
tion of the downwash in the plane of symmetry and it
has been tacitly implied that the downwash so derived
applies over the entire tail span. In order to investi-
gate the error thereby involved, calculations of down-
wash were made for points on the vortex sheet, 0.75
b/2 back from the quarter-chord line, which is approxi-
mately the usual longitudinal position of the tail. The
calculations showed that, for some cases, considerable
DESIGNCItARTSFORPREDICTINGDOWNWASHANGLESANDWAKECHARACTERISTICS
1.04- Toper- re/so
Elhpt/col tI.O0
21
L C
.88
1.16
Ploln o/,-foil
i
1.04
1.00
dil[eren('e exists beiweeti the downw_tsh at the center
of the tail and the avera/e downwaql <>ver the t,dl.The correction fact<irs have been ph>tte(1 in tigure 21for all eases.
METHODS (iF APPLICATION
Downwash, plain wings. Tim downwash at the tailof an a.irplane with a wing haviil/lieither twist nor a flap
is obtained from the ehllrts 7iron in ti/ure_ 1 t.o 15 in
the foliowin 7 lllll:llllel';
.2 .3 .4
1. For each angle of atttlek under consi(|erlttion, tind
the |onTit.udinal dist, ailee x of the elevlttor=liin_e axis
fronl the qull.rter-ehord point of the 1'oo{ section <qnd
tile. vertical distlulee m of-the hinge axis from the trail-
ing edge, (it" wake oriTin. ('onsi(ler m ((} tm neTa.tive if
the }linTe ,i.xis lies below the lrliilin 7 edTe.
7. Find t|le ([owliwilrll (lisphleement 1t. of the wllke
center lille li.t (listitlice .r from tile <[u'/rter-clior(t poinl
by multipiyiilK the value lit. dislnnee x on tim eorre-
spondili 7 disl)hicemelit chart by the lift eoeltlcienl ('L.
22 REPORT NO. 648--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
3. Locate the point (x, Im+hl) on thc downwash-contour chart and multiply the corresponding down-
wash angle by the lift coefficient and by the correction
factor of figure 21.Downwash, flapped wings.--For an airplane with
flaps down, it is first necessary to separate the lift co-efficient into two parts. The part CL. is the lift coeffi-
cient at the particular angle of attack, with flaps up.
The part CL I is the increase, at the particular angle of
attack, on lowering the flap; it may be obtained by the
use of figures 19 and 20. Derivation of the downwash
proceeds in the following manner:l. Find the longitudinal distance x of the hinge axis
from the quarter-chord point of the root section, andthe vertical distance m of the hinge axis from the wake
origin. The wake origin in this case is not the trailing
edge but a point below the trailing edge, as previously
explained. (See equation (4).)2. Find the contribution h_ of the plain wing to the
downward displacement of the wake center line at dis-
tance x from the quarter-chord point by multiplying the
value on the corresponding displacement chart (plain
w_ing), at distance x, by CL_.
3. Find the contribution h2 of the flap to the down-
ward displacement by multiplying the value on the
corresponding displacement chart (flap), at distance x,
by CL r
4. Locate the point @, Im+h,+h21) on the contour
charts for the plain wing and for the flap; multiply the
corresponding downwash angles, respectively, by CL_
and CL r and by the correction factors of figure 21 and
add in order to get the desired downwash.
This procedure completes the computation of the
downwash, except for the wake effect, which increasesthe downwash above the wake center line and decreases
the downwash below it. The amount of this correctionwill be discussed in the next section. There are two
other reasons, previously mentioned, for making still
further corrections, seldom exceeding 0.5 °, positive
above the wake and negative below it. Interference of
the fuselage, the nacelles, and the wing-fuselage junc-
tures is only partly predictable; however, for the modern
airplane with efficient wing-fuselage junctures andstreamline fuselages, it is likely to be of small im-
portance.For wings or for flap spans other than those covered
by the charts, a linear interpolation is usually permis-sible. For a wing with appreciable aerodynamic twist,
the downwash due to the twist will have to be computed
from the span load distribution at C_.--0 and appliedas an additive correction. Dihedral and sweepback
may be neglected.
WAKE CHARTS AND FORMULAS
The center line of the wake coincides with the center
line of the trailing vortex sheet; hence no new data are
required for locating it. The wake half-width, in
chord lengths, is given by the formula
_ = 0.68c,_0! _(_+ 0.15)_ _ (5)
in which _ is in chord lengths. It will be noted that the
unit of length in this and the other wake equations is
the chord rather than the sere,span. Curves of this
equation are plotted in figure 22 for different values
of the parameter c_0.
o�
o / 2 3Di._tonce from ;rE., _ ,chord lengihs
FII;IrRE 22. -Relstinn between wake width and distance from trailin_ edge.
_-= 0.6S_aol/l(6+0,15) 1/2
The maximum loss of dynamic pressure in the wakeoccurs at the wake center and its value _ i_ given by the
forinula2.42Cd0__
(6)6+0.3
Curves of this equation are plotted in figure 23 for dif-
ferent values of the parameter cd0- The distribution of
dynamic pressure within the wake is given by the equa-tion
, =cos t' 77 (7)
which is plotted in figure 24.The effect of the wake on the downwash in and near
it is negligible for low profile-drag coefficients as, for
example, in the case of plain wings at low angles of
attack. It must, however, be taken into account for
wings with high-drag flaps and it may be approximately
DESIGN CIIARTS FOR PREDICTING DOWNWASH ANGLES AND WAKE CHARACTERISTICS 23
computed for such cases, as exphtined in reference 1.
Results of some of these conqmtations are shown in
l.
I
i
0 / 2 3 dD_fonce from r_, _ ,chord lengths
],'I(;):l_E 2:C |_.elatioll between nlaxinltlm ]oss Of dynanlic pressure ill the _ake _Lild
distance from the trailing e,lge.
2 4o_ tl+',• _ d0/
,_+().3
Lt
p,¢
J' ll,IJIH ,' '_t \;il i_tioll ,)f ,13 rt;_rllit _)1_,_111'13 IH_'q lJ.i_l-i}:q'_ I}lq' x,t,_tl,.4,.
,7_ ir
zO
tigm'e 25. Figure 25 ('t) shows the c()mputed effectat the ut)per edge of tile w,tke for three distances behind
the trailing edge; at the lower edge of the wake, it is the
same ill magnitude but opposite in sign. The effect
diminishes with distance from the wake; for points only
:t short distance outside the wake (i. e., for the most
usual tail positions), however it, is nearly equal t() that
_-¢'3
_o
_. / •
g_
./ .2
profNe-_r_ coefficient, c-_o
...... __
i
--- )--
:
- f-- (b)--
./ .e .3 .5Oistonce from w_l<e ce_#et- /me, _',chord length
(a) At the upper edge of the wake.
(b) Within the wake.
FIGUICE 25.--Wake effect on downwash. The clIcets are equal, bllt or opposite sign,
below the wake center.
at the wake edge near it. Figure 25 (b) shows some
typical variations of the effect within the wake.In order to facilitate the application of the preceding
equations, which involve c_0, some section profile-drag
c
LJ
24
20
/6
/2- .
08
04
0
I Flop tvpe ] c./c A_PFo/I th_ckne55
-- PIo_nondspht 0.2|--i0., 'c ] t ]
...... I " .2 .2 ',..j i ,l-d , L.-d--[x/ernolotrfo/I .2l I ./ " [ _ )" i
I0 20 30 40 50 _0 /0Flop onqle, d, , de 9.
I"II;I!IIE 2G. -Section i,rofih,-(lrat: (_oellieicllts for (lill'erent llal)S.
eoelficients for the different flaps are presented in figure
26. These do.ttt apply particularly in the higher lift
range, about 3 ° to 4 ° below the stall. They were col-lected mainly from N. A. C. A. results and fromreference 5.
24 REPOI{T NO. 648- NATIONAl, ADVISOIRY COMMITTI,:E FOR AEI{ONAI;TI('S
EXAMPLE OF APPLICATION TO DESIGN
For purposes of illustration, some spccinwn calcula-
tions will be made for a nlidwing monoplane (fig. 27).
The wing is of aspect rlttio 9, taper ratio 3 : 1, and has 'lsplit tlap of 0.70b si)an and 0.20c chord. This case is
covered by figure 8. The tail span is 0.3b.
The ease of the airplane with flaps up will be con-
sidered first. It will be _lSSumed that, when the air-
plane is operating at the attitude shown in figure 27 (a),
_o,4" e
rn=.02 b/2 ] edge
- "Wc,/Te ¢,
{c)
m _-./3b/2 -_
(a) Flap up.
(b) Flap down.
(c) Flap down, tail in the wake.
FI[;URE 271--lllustration for the si)e'cilncn calculations of downwash anti wake.
the lift coefficient C_. is 0.9. The steps outlined under
Methods of Application are as follows:
1. x-0.68 b/2. m----O.O1 b/2.
2. The downward displacement of the trailing vortex
sheet at x=0.68 b/2 is, for CL--1.0, 0.05 b/2, so tluith=0.9X0.05=0.045 b/2.
3. Reference to the downwash-contour .chart shows
that the downwash at point (x, Ira-i-hi), or (0.68, 0.04),
for CL= 1.0 is 5.6 °. Multiplying by Cr (0.9) and by tile
correction factor of figure 21 (0.95) gives, for thedownwash,
_=0.9X0.95X 5.6_4.8 °
The center of the wake passes mq h. semispans I)elowthe hinge axis, as shown, and its half-widttl ,{-at this
point is obtained from tim section l)rofile-dnlg cocflicien t
(assulne cao=O.Ol5 ) anti the distance behind the trailing
edge (}----1.29c), where c may be taken as the ]"lot chord.
By equation (5) or figure 22,
_'=0.68X0.015_"_X 1.44_=0.1 chord
The edges of the wake are shown in the figure.The tail lies outside the wake and, inasmuch as
tim wake is too slight to affect, the downwash, it requiresno further consideration.
The airplane at the same attitude, with flaps down,
8I=60 °, is shown in figure 27(b). From figure 20,
kc, is seen to be 1.13 (assuming the wing thickness to
|)e 0.12c); from figure 19, CLI/Ac_ is 0.67, so that CLI----
0.76. Tlle contribution of the plain wing, CL., is 0.9
as before, since the angle of attack is the same. The
steps outlined in Methods of Application are as follows:
1. x=0.68 b/2, as before.
m=0.023 b/2.
(The wake origin, as indicated by equation (4)
and figure 18, is (0.1 c)si_11_ 60°j_O.Ol_e semi-b/2
Sll'ms below ttl(_ wing trailing edge, at the
loc_Ltion shown. For this wing, b/2--3c.)
2. The contribution 1,, of the plain wing to the
downward disl)lacenlent is the same as before:
h1-_0.045 b/2.
3. F,w the flap (,ontl'il)ulion, lhe elmrt shows that,
for (_)_s-_ 1.0 and d:=-().(i_'_/)/2, the disl)hlcenlcnt
is 0.07 b/2.
1_:-- 0.76 X 0.07---- 0.053 b/2.
4. Tile point (x, ]m-]-/_,÷h_]) is thus (0.68, 0.12).Refercnce to the downwash-contour chart for
the plain wing and to figure 21 shows that the
plain-wing contribution to the downwash attllis point is _-0.9X0.95X5.0=4.3 °. Sim-
ilarly, the flap contribution to the downwashat this point is " °*_=0. _6 X0.94 X 6.8----4.9 .
The sum is E,-t-,2=4.3+4.9----9.2 °, to which
a wake correction should be applied, as de-
rived in the next paragraph.
The center of the wake in this case passes m-]-h,-]-
h_=0.12 b/2 or 0.36c below the hinge axis, as shown.
Figure 26 gives %=0.17 and, with }----1.29c as before,
figure 22 or equation (5) gives the wake half-width:
_'----0.68 X 0.17 _ X 1.44_=0.34c
The edges of the wake are shown in the figure. There is
no effect on the dynamic pressure at the tail, for it liesoutside the wake. The increase in downwash at the
upper edge is found from figure 25 to be 1.5 °. The
effect at the tail, which is only a small distance from theedge, may be considered to be the same. The down-wash is thus 9.2+1.5----10.7 ° .
If the relative positions of the wing and tail are such
that the tail lies within the wake, as is shown for exam-
ple in figure 27 (e), the average loss of dynamic pressure
at the tail is also required. The loss at the hhlge axis
may be used for this value although the average overthe tail surface may be somewhat different.
I)ESIGN C.IIAtlTS FOR PIIEDICTIN(I DOWNWASH AN(',I,ES AND WAKE CHAItACTI':RISTI('S 2,_
The COlnlmtation of tile downwash l)roeeeds ns before:
.,. 11.1;8 b/2
'm ..... 0.13 b/2
hl--0.045 b/2
h_-0.053 b/2
[m+h, _h._! :0.03 b/2: 0.09c
el_ 0.gx0.95XS.7 =-4.9 °
e_ =: 0.94 ).(0.76 )/. 7.8-- 5.6 °
ell _.,= 10.5 °, whi(.h is llm downwash un(.of
re<'ted fro' wake effect.
The wake effect at the hinge axis is seen, by interpo-
lating between the two curves of figure 25(b), to be
about 1.6 °, which must now be subtracted from the 1)re-
ceding value, for the t,dl hies below the _wd_e center.
The corrected downwash is 10.5--1.6:8.9 °.
The computation of thc dynamic l)ressure at this
point is as follows:
_- 1.2,(t( .
c,t, ().17
i" -0.34c• !
==0.09c, =0.26
2.42_0.17 _
.)(V l._,)@().:_ 0.63, from tigurc 2;_ m"
(_q mttion ({i).
_r _ ortit:().63 cos" (0.26))-_0.o3, from figllre 24
equation (7).
The dynamic 1)rcssure _Jt this point is 1--n', or 0.47q.
]_AN(;LI,]Y _IEMOR1AI_ AEI{ONA1Jq'ICAI, ]_,AI{OI{A'I'OItY,
NATIONAL AI)VISORY COMMITTEE FOR AERONAUTI('S 7
I,AN(ZLEV Flr:Lt), V*., July 1.4, 1,9,_38.
REFERENCES
1. Silverslein, At)c, ]{atzotf, S., and Bullivant, W. Kenneth.1)ownwash mM Wake behi||d Plain and Flapped Airfoils.
T. It. No. 651, N. A. C. A., 1939.
2. Anderson, Raymond F.: Detcrlnination of the Characteristics
of Tapered Wings. T. tt. No. 572. N. A. C. A., 1936.
3. I,otz, Irn|gard: Berechnung der Auftriebsverteihmg beliebiggcformtcr 1,'liigel. Z.F.M., 22. Jahrg., 7. Heft, 14. April
1931, S. 189-195.I. Pearson, I I. A.: Span Load l)istribution for Tapered Wing._
with |)arlial-Sl)an Flaps. T. ]l. No. 585, N. A. ('. A., 1937.
5. Clark, K. W., and Kirkby, F. W.: Wind Tunnel Testsofthe
Characteristics of Wing Flaps and Their Wakes• R. &
M. No. 1698, British A. R. C., 1936.
US. GOVERNMENT pRiNTING OFFICE:I939
