Note on compressibility effects on downwash at the tail at subcritical speeds

iN


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


WAIRTIMEI REPORT
ORIGINALLY ISSUED
March 1915 as
Confidential Bulletin L5C09

NOTE ON COMPRESSIBILITY EFFECTS ON DOWNWASH
AT THE TAIL AT SUBTRITICAL SPEEDS
By Jack N. Nielsan and Harold E. Sveberg


Langley Memorial Aeronautical
Langley Field, Va.


Laboratory


WASHINGTON


NACA WARTIME REPORTS are reprints of papers originally Issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change In crder to expedite general distribution.


I-19


DOCUMENTS DEPARTMENT


49^ V





































Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation


http://www.archive.org/details/noteoncompressib001ang









NA.?A CS IN. L50?' CO'N!IDENTIAL

fTATICiOAL ADVISORY CO.MT:II'T: FOR AiRO'!AUTICS


CONPIDE;ITI.-.L BULLETIN

.iCT' Cr COo'prESSIBILITY IFr CTS C.! DC ,i7' VASP

AT THE TAIl AT SUYlTTTCAI. SEEDS

Py Jac' U. Nielsen and T'arc,!, W. S weber.-r


SU ""'AY


C,]oculations have ben r.iaie to sh.ow the marnitlide
of ths, coi,'press_..bility effects on t- do'.'.:'~sh a. t the
tail at sutcritical rpeed.s. .x'rin:ental -'esu ts of tests
of two sii-.plane models are included to .ive some verifi-
cation. of the theory.

TlIe calculations rhowea tt. ; t tbe effect 01o co.n'Dressi-
bilit;. on the span l':,od distr'.ibut icn ailon: the *;ir-g and
on the downv.ash angle at the tail ,are s,'ll for constant
values of the lift coefficient. The exn erimenta results
confirmed these calculations.


I YTR ODUCTTIOi


A rational solution for the problem of lon.Titudirnal
stability at h-ih speeds requires a ;.owledre of the
effects of comoi-essibilit.r on t'v: o'.in.:as in the recion
of the horizontal tail surfltce. StiirLes of this r ro':lem
for speeds below the critical have e;en re Dorted by euek
in rec rence I and by C-oldstein and Yrje.nr ir reference 2.
In reference 1 the downrw,.ash at the tail is .-.-tumrd to be
unaffected ? by increas- s in "ach nurrber fr con-a .nt
valu.- of the lift coefficient. In reference 2, cn the
basis of the 1Iauert-Pranrdtl t heory, the dc'wnwashh is
found to decrease slightly with increases in .ci nunbcr
for constant values of the lift coefficient. and span
loadin:-. !'o experimental verificiaticnSr of the conclu-
sions stated in these reports ar. civen.

The present paper presents t.h-.-orietical calculations,
based on the methods of reference ., to show the magnitude
of the ccmrpressibility effects on downvwash and gives some
experimental verification of the theory. Calculations


COIFI]TEI'!TDIAL








NACA CB No. L5CO9


have been made to obtain the s p.n load distributions along
the vwinr and the average downwash angles at the tail of a
typical pursuit airplane for a rn-je of lift coefficient
anF cch number. PWind-tunnel test data showing the effect
of compressibility on the average downwash anrles at the
tail have also been included for two airplane models.


SYMBOLS


CL airplane lift coefficient (horizontal tail
removed)


cla


a(t-Oo)


basic section lift coefficient (CL = 0)

additional section lift coefficient

free-stream Mach number

chord

wing span

distance outboard along span from wing
center line

distance from wing quarter-chord line to
elevator hinge line

downwash angle, degrees

angle of attack, degrees

airplane angle of attack for zero an.-leo of
attack of tail, de-rees


it angle of incidence of stabilizer relative
to airplane reference line


THECT, CAL CALCUIATI01-S


The effects of co.p'ressibility on the downwash at
the tail ma' be consilde:.,d the result of two factors?


C flN~TP)~UTIAL


C Or' IPE TOTAL









NTACA CB No. L5CO


the change in span loading along the wing and the change
in downw,,ash for a given span loading. Methods for calcu-
latin; both these changes are given in reference 2 in
which the Glauert-Prandtl theory of compressible flow is
used. According to reference 2, the span loading for any
Mach number may be approximated by using the slope of the
lift curve for compressible flow in the equation of the
lifting-line theory (reference 5). The downwash at a
distance x behind the lifting line may now be determined
by the methods of reference 4 for incompressible flow
except that the distance of the tail behind the lifting
line is increased by the ratio M1/1 Mo *

In order to show the magnitud- of the coioprssibility
effects, calculations have been i'lade in ,ohich the afore-
mentioned methods are used to detcr.mine the span loading
along the wing and the resultant do'nv.ash at the tail of
a hit:h-speed pursuit airplane. The distributions of twist
andc hord along the wing shown in figure 1, which corre-
sponi approximately to the distrIbutions for a modern
pursuit airplane, were used for ,m'. calculations. The
twist st the inboard sections is usad to increase the
critical. sn.-ed of the wing-fusela-'e juncture.

Scan load distribution.- Thec load distribution along
the su. an has teen determined in two parts. The first
part, which i- due to wing twist, is the load distri-
bution at zero lift and is referred to as the basic load
distri''.utlon. This distribution 'has been calculated by
the -ethod of reference 5 using ten harmonics for the
circulation because of the sharp break in the wing twist
distribution. For these calculations, the slope of the
section lift curve was taken as L.67 /I o2 per
radian. Basic load distributions along the wing sran
are given in figure 2 for Mach nuunbers of 0 End 0.8.
Although the slope of the section lift curve for MT = 0.8
is increased 66 percent over that for .oQ = 0, the ordi-
nates of the basic-load-distribution curve show an average
increase of only about 20 percent; that is, the effect of
the increased slope of the section lift curve is dimin-
ished to a large extent as a result of the small span
within which the twist is effected.

The second part of the load distribution is that due
to the untwisted wing operating at a riven lift coeffi-
cient and is referred to as the additional load distribution.


CONFIDENTIAL


C0-PTL'-:TIAL








NACA CB 'To. L5o09


This distribution has been taken from reference 6 for,-a
lift coefficient of 1.0 and is shown plotted in figure 3
for -ach numbers of 0 and 0.8. The additional load
distribution is seen to be almost unaffected by com-
pressibility. This result depends on the wing plan form.
For an elliptical wing, the additional load distribution
remains elliptical regardless of the slope of the section
lift curve. For other than elliptical wings, increasing
the slope of the section lift curve causes the additional
load distribution to become more nearly elliptical but
the effect "'ill normally be small, as in the present case.

The additional load distribution for lift coefficients
other than 1.0 may be obtained si'aply by ntultiplying the
ordinates in figure 5 by the i- t coefficient.- Since the
total load distribution is obtained by adding the addi-
tional load distribution to the basic load distribution,
it may be concluded that below the critical speed the
total load distribution for a -lven lift coefficient will
also be changed very little by compressibility. Span
load distributions for elliptical wings of approximately
zero aerodynamic twist given in reference 7 and calculated
from experimental section-lift-curve slopes show very
small chan-ges with Mach number up to the critical speed.

Downwash at tail.- By using the comr-pressible-flow
span load distributions, calculations have been made by
the method of reference 4 of the aver-aie downwash across
the tail span for a range of lift coefficient and Mach
number. For these calculations, the angle of attack for
zero lift was assumed to be indenpndent of .Tach
number and the distance.-of the tail behind the liftin7l
line was taken as 0.95;/V1 o The downwash angles
were calculated at three points aonr the tail semispan
and the results were averaged to ..?iQ.n the average
downnash .ing-le at the tail. Thi.se results are shown in
figure ;.

The variations of downwash un:le with !Yach number
for constant values of lift coefficient (fig. i) are
small. For low values of the lift coefficient, the
c':anjes in downg.as:h angle with '.ch number are inappre-
ciable except at very "hi-h values of the Mach number
(abova about Mo = 0.7). At the l-rb lift coefficients,
the dowmnvash decreased zlijhtly with increa-irng Mach
nu'b-Jr up to a :-?ch number of a:o-.t 0.7. At Mach numbers


SCTFnDE' TIAL








NACA CB No. L5C09 CONFIDENTIAL 5

higher than about 0.7, the downwash angle decreases more
rapidly than at the lower Mach numbers.

The decrease in downwash angle with Mach number for
constant lift coefficient results from two effects:
(1) the distance from the lifting line to the tail, used
for the downwash computations, increases with increasing
Mach number, and (2) the tail moves farther above the
wake since, for a given lift coefficient, the angle of
attack decreases as the Mach number increases.

It has already been remarked that increasing Mach
number causes the span load distribution to become more
elliptical. For a highly tapered wing, which has pro-
portionately more trailing vorticity inboard than an
elliptical wing, the effect tends to cause a reduction in
downwash; for a rectangular wing, which has proportion-
ately more trailing vorticity outboard, the effect tends
to cause an increase in downwash. In either case, as for
the load distribution itself, computations show that the
effect is small.

Although the change in downwash angle with Yach
number for constant lift coefficient has been shown to be
small, it does not follow that the change in the longi-
tudinal stability characteristics will be small. In
particular, the angle of attack of the wing for a given
lift coefficient will decrease with increasing Mach number
because of the increase in the slope of the lift curve and,
as a result, the angle of attack of the tail for the same
lift coefficient will decrease a corresponding amount.
This decrease in tail angle of attack for a given lift
coefficient will cause an increase in airplane pitching-
moment coefficient and a rearward shift of the neutral
point, Because of the different aspect ratios of the wing
and tail, furthermore, a disproportionate increase in the
wing and tail lift-curve slopes will occur that also
causes a shift of the neutral point.


EXPERIMENTAL RESULTS


An analysis has been made of wind-tunnel test data
obtained at high M'ach numbers to verify experimentally
the theory and calculations presented in the preceding
section. The data were obtained from tests of complete


CONFIDENTIAL








NACA CB No. L5C09


models of the P-51B and XP-58 airplanes in the Ames
16-foot high-speed wind tunnel. Dovwjnash angles were
computed from the results of pitching-moment measurements
with the horizontal tail set at several angles of inci-
dence and with the horizontal tail removed. The inter-
section of the pitching-moment curves for this model with
the tail on and with the tail off gave the airplane angle
of attack for which the tail angle of attack is zero.
The downwash angles were then computed from the relation


a = (att=00) + it


where a(at=Oo) is the airplane angle of attack for
zero tail angle of attack and it is the stabilizer
incidence, relative to the airplane reference axis.

Inasmuch as the wind-tunnel test data were corrected
by incompressible-flow methods, it was necessary to
investigate the effect of compressibility on the wind-
tunnel wall corrections. The effect of the tunnel walls
is to cause an increment of upwash at the wing and an
additional increment of upwash at the tail. These incre-
ments necessitate a correction to the airplane angle of
attack and tail-on pitching-moment coefficient. Goldstein
and Young (reference 2) showed that the correction to the
airplane angle of attack is unchanged for compressible
flow but that the correction to the tail-on pitching-
moment coefficient must be adjusted for compressibility.
This adjustment is made by assuming that the tail is at

a distance x/l M02 instead of a distance x behind
the wing quarter-chord line.

The variation of the downwash angle with Mach number
for several values of the lift coefficient is given in
fi. ure 5 for the P-511 airplane model. In order to show
the limits of the subcritical region and also to facili-
tate the use of the data given in figure 5, curves of
lift coefficient against P'acli number for several angles
of attack are given in figure 6. Similar downwash and
lift data are presented in fi ur,-s 7 and 8 for the XP-58
airplane r-odel. For both airplane r;odels some downwash
exists at z,:ro lift (between 10 and 20). No definite
reason can be given for this apparent discrepancy; it may


COIUPID'IUTIAL


CONFIDEI'TIAL







IIACA CB No. L5C09


result, however, from either the wing twist or inaccu-
racies in the tail settings, or from both. Although the
absolute magnitude of the downwash angles may be in error,
the v-,riation of the dcwnwash an-le with OTach number is
considered accurate.
'Tie results plotted in figures 5 ,nd 7 show that at
low lilt coefficients, which correspond to high-speed
fli.ghit, the change in downwash anLgle with Mach number is
neg.li_ible. At the hit.h lift coefficients, some change
in the do'vnvash angle cith Iach number occurs. This
change i.*F small for the cast of the P-51E airplane model
but a'ou.nts to about 0.50 for the XF-5 airplane model.
The c: ncrimental results, in ,,-nral, agree with the
theory in that the variation of deo~*'.-,ash angle with 1rach
number pt constant lift coefficient ic relatively small.


AT 'Tr.s AT CTTP':CRImICAL SP-'DS


Although the present pa,.'pe.r is primarily concerned
with the dJownwash at subcritical sr,,dr, a few remarks
regarding the downwash at s'uper'p.critical speeds should be
made. Evidence ir available referencess 7 and 8) which
shows that larce changes in rnan lcarding ,may occur at
supercritical speeds. The chanr:cs in span loading may
cause- anpreciable changes in th- iownw'.ash at the tail.
If flow breakdown due to shock occurs first at the inboard
win, sections because of their thickne.rf or because of
wing-fusel.age interference, there '..ill be a shift of the
load outboard and a con.a'seiuent reduction in the downwash
at the teil. Unfortunately, these effects are not well
understood because theory has noc been developed and
wind-tui.nnel test data are insufficient at supercritical
speeds for which conditions the '.':ind-tunnel tare and
interference corrections are not 'ell understood at
present.


CONCLUDI''TG rE'AE IS


Theoretical calculations have shown that the effect
of compressibility at subcritical speeds on the span load
distribution alonr the wing and on the downwsh angle at
the tail is small for constant values of the lift coef-
ficient. ZExpeeimental results o.' the downwash variation


CONFIDENT IAL


CONFIDENTIAL







NACA CB 1%o. L5C09


with MIach number for two airplane models confirmed these
calculations. At supercritical speeds, however, large
changes in the span loading and in the owv;nwvash for
constant values of the lift coefficient may occur.

Langley e :-orial Aeronautical Laboratory
.-tional Adv-sory Committee for A.-ronautics
Langley Field, Va.





1. Husk, D. I.: Compressible Flow behind a Wing. Air-
craft Engineering, vol. XIV, no. 160, June 1942,
p. 160.
2. Goldstein, S., and Young, A. D.: The Linear Pertur-
bation Theory of Compressible Flow, with Applica-
tions to idind-Tunncl Interference. R. & M 1. l. 1909,
British A.R.C., 1943.

5, Glausrt, H.: The Elements of Aerofoil and Airscrew
Theory. Cambridge Univ. Press, 1926, p. 139.

4. Silverstein, Abe, and Katzoff, S.: Design Charts for
Predicting Downwash Angles and .a!-e Characteristics
behind Plain and Flapped wings. HACA Rep. No. 648,
1959.
5. Pearson, H. A.: Span Load Distribution for Tapered
Wings with Partial-Span Flps. NACA Rep. No. 535,
1937.
6. Anderson, 3'S-.,n-i F.: Determination of the Charac-
teristics of Tapered Wings. 1ACA Rep. ir'. 572, 1956.
7. Doshar, John: The Dtcormination of Span Load Distribu-
tion at High Specds by Use of High-Soecd iind-ru.niiel
Section Data. :.CA AiC h. iB22, 1944.

8. Whitcomb, Richard T.: The elationn between Spanwise
Variations in the Critical ]Kach 1.:'.r and Spanv'ise
Load Distributions. i.". CB Ui. L4L07, 1944.


CO1FTIDLE;TIAL


CONFIDENTIAL





NACA CB No. L5C09


4






CM,
IV -- -^ T -



z / / *II


-3-


b,c


-J
O I

i-


z~4 (~J

0


Fig. 1


'0
O

q.)




r0






0
i.JcZ
0





lb
)ZI
Is






t8





NACA CB No. L5C09


6








2o








-2


-6


Spanwise


station DNTAL
bi CONFIDENTIAL


Figure Z.- Effect of Mach number on the
basic span load distribution.


Mach number, M.
0
















NA IISORY
COMMIT FORONAU C


2 .Z .4 .6 .9 1X0


CONFIDENTIAL


Fig. 2






NACA CB No. L5C09


/00



90







0 70

-Q
'60



b50

40



30





20



/10


.4
Spanwise


.6 .8
station ,


/0


CONFIDENTIAL


Figure J.- Effect of Mach number on the
additional span load distribution.


7lach number /1o
0
--- 0 .8


































NATI A. AD ISORY
C MMIfI ro A ONAUnIls
^^^1




---- --- --- -] --- --- -- --- --- ^ --- ----------------
^^'
__ __ ___ ___ ___ S __ ___ ___ ___ ___ ___
^<\






____ ~ ~ ~ ~ ~ ~ ~ AI ___L A___ ISORY^^ __ __ ___ ___ _
C)MR O \ 0AT


0L
0


Fig. 3


CONFIDENTIAL







NACA CB No. L5C09


.3 .4


Mach number


.5 .6 .7 .8

7 'V0 CONFIDENTIAL


Figure 4.-


Calculated variation of the down wash
anqle with Mach number for constant
values of the lift coefficient.


.c,_


--- .6
-- 08- -



-- ---- -- -- -- ._..._ ,..._ .._ .6




-- -- -- -- _-- ^ -.-. 4. --








0

AMI RM IA MSORY
IOM 'ITIE FOR A ROMAUT S


CONFIDENTIAL


Fig. 4






NACA CB No. L5C09


c>,
0b



^J
I)


o


Mach number /0


CONFIDENTIAL


Figure J. Experimental variation of the downwash
anqle with Mach number for constant
values of the liff coefficient. P-5/8 airplane
model


Fig. 5


CONFIDENTIAL






NACA CB No. L5C09


(-)
1.
q)
4U,


0




.2




-.4
..9


.5
lMach


.6 .7
number ,/ N


CONFIDENTIAL
Figure 6. Variation of lift coefficient with
Mach number for the P-5/B
airplane model.


I I.Hn


A


-A


-7




___-4



WTIONAL ADVISOF I
COMM TTEE FO AERON UTS


"7--"


CONFIDENTIAL


Fig. 6


f


?






NACA CB No. L5C09


0 L
.3


.4 .5 .6 .7 .8
Mach number /0
CONFIDENTIAL


Figure 7- Experimental variation of the
downwash angle with Mach number
for constant values of the lift
coefficient. XP-58 airplane model.


Fig. 7


CONFIDENTIAL






NACA CB No. L5C09


-2 L
.3


.4 .5 .6 .7


Mach number IO


CONFIDENTIAL


F-iqure 8.- Variation of liff coefficient with Afach
number for the XP-58 airplane
model.


CONFIDENTIAL


Fig. 8




f
I
!i









































>*




















































































f















f.




UNIVERSITY OF FLORIDA

3 1262 08104 977 6

*I
Ul i RIFYG OF FLOR;DA
FC:LJUMENTS tlEPARTMEkiT
1 .:-\ rj..FSTON SCIEBICE LIBRARY
'O. .OX 117011
C.-A.J'VlILLE, FL 32611-7011 USA













I;