An investigation was undertaken to determine the effectiveness of four analytical methods (empirical, modified empirical, vortex-lattice, and an inviscid, three dimensional, potential flow, wing body program) to estimate the lateral and longitudinal static stability characteristics of an isolated V-tail wind tunnel model. The experimental tests were conducted in the V/STOL tunnel at a Mach number of 0.18. Angle-of-attack data were obtained from -12 deg to 8 deg at 0 deg sideslip. Sideslip sweeps from -5 deg to 10 deg were made at angles of attack of 4 deg, 0 deg and -4 deg. The V-tail dihedral angles were 45 deg, 50 deg, 55 deg, and 60 deg

Freeman, C. E.

Yeager, W. T., Jr.

English

NASA Technical Reports Server

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E
' i+
NASA
Technical Memorandum 78729
AVRADCOM
Technical Report 78-34
Analysis of Stability Contributions
of High Dihedr_ V-T"a_
Carl E. Freeman and William T. Yeagcr, Jr.
Structures Laboratory. A VRADCOM Research and Techuologj Laboratories
Langley Research Ceuter
Hamptou, Virgiuia
National Aeronautics
and Space Administration
ttci, mti_ md Ta_W_.a
IMormmtkm OfWce
1978
SU_@UtRY
A__ investigation was undertaken to determine the effectiveness of four ana-
lytic_l _ethods (empirical. modified empirical, vortex-lattice, and an inviscid,
three-dimen._ional, potential-flow, wing-body program) to estimate the lateral and
longitudinal _tatic stability characteristics of an isolated V-tail wind-tunnel
model. The experimental tests were conducted in the Langley V/STOL tunnel at
e Mach number of 0.]8. Angle-of-attack data were obtained fro_ -]2 r_ to 8° at
0° side_lip. Sideslip sweeps frcm -5 ° to 10° were made at angles of attack of
4 ° , 0 °, and-4 ° . The V-tail dihedral angles were 45 ° , 50 ° , 55 ° , and 60 ° . Of
the methods used, a combination of the modified empirical and vortex-lattice
methods correlated with the experir_ental results best except for predicting
static directional stability oontributions at high dihedrel a_Jles. The
invisci@, three-dimensional, potential-flow, wing-bo¢_ program oorrelated bet-
at high 8|bearal aagles.
Conventionally powered, single-rotc_ helicopters have experienced direc-
tioaat _trol proble_r 1bile cqperattng in l_Ic_i_y, Ieft-rear-quarteriflg
winds in ground effect_ im_ d_-l¢__ _ma_4. £J_ \ira ._J_l_ ef_
{_fs, I anc_ 2). Investigations have been conducted to determine the source
of these directional control problems and possible means of alle_iating
{raft. 3 to 5). Reference 4 shows that a V-t}_pe empennage can present signif-
icant advantages over conventional horizontal-vertical control suEfaoes for
helicopter directional control at low speeds. Th_ prinoipal _c]vantages are
smaller adverse fin forces and increased tail-tutor efficient.
An important aspect of designing a V-type e_pennage is the ability to pre-
dict _ts aerodynamic characteristics in ter_ of longitudinal and directional
static stability. Previous work in this _rea, such as references 6 and 7, used
a sipplified method to predict the aerodynamic characteristics of lifting sur-
faces with increasing dihedral angle. The accuracy of this method was found to
be deficient for V-tails with @ihedral angles greater than 40° .
An investigation was conducted to evaluate the effectiveness of the simpli,
fled method of references 6 and 7 and of more sophisticated vortex-lattice and
inviscid-flow paneling methods in determining the effects of dihedral on the
static stability characteristics of an isolated V-tail. Wind-tunnel tests of a
helicopter V-type empennage were conducted and the results were used as a basis
for comparison with the analytical methods.
SYMBOLS
Units used for physical quantities defined in this paper are given in the
International System of Units (SI) and parenthetically in U.S. Customary Units.
Measurements and calculations were made in U.S. Customary Urits. Conversion
factor_ are presented in reference 8. The positive directions of forces are
shown in figure I.
c section lift coefficient
CL
cM
Cy
Cyc
F L
Fy
iv
R
S
6
r
total lift coefficient (stability axis), FL,/q S
lift-curve _lope, dCL/da, per deg
side-force coefficient (body axis), Fy/q_S
_lope of side-force curve, dCy/d_, per deg
lift force, N (ibf)
side force, N tlbf)
incidence angle, deg
correction factor foc Cy8 (ref. 6)
dynamic pressure, Pa [Ibf/ft 2)
total V-tail area, 0.244 m 2 (2.625 ft 2)
angle of attack, deg
angle of sideslip, deg
dihedral angle, deg
Subscript:
N normal to _urface
APPARATUS AND EXPERIMENTaJL TEST PROCEDL_ES
The experimental data presented in this report were obtained on the tail-
alone configuration shown in figure 2. Dimensions and geometric data are given
in figure ]. The model was mounted on a six-component strain-gage balance. A
bluff forebody was attached to the strut to close off the tail cone. Transition
grit was applied to the tail surfaces.
The tests were conducted in the Langley V/STOL tunnel, which is an atmo-
spheric, closed-circuit wind tunnel. The test section measures 4.2 m (]4.50 ft)
by 6.63 m (2].75 ft[. Data were obtained eta free-stream dynamic pressure of
2.30 kPa (48 Ibf/ftL), which corresponds to a Mach number of 0.]8. Model angle-
of-ettack sweeps were made from -12 ° to 8° at _ = 00. Sideslip sweeps were
made frG_ -5 ° to ]0 ° at _ = 4° , 0 °, and -4 ° . Pitch measurements were made
using an internal pitch accelerometer. Yaw an_]e was measured externally.
2
The strut support was held parallel to the test-section center line for the
sideslip sweeps to minimize strut interference on the model. No wall _ _rrec-
tions were made.
The incidence angle and dihedral angle of each tail surface of the model
could be independently varied. For this investigation th_ incidence angle of
both tail surfaces was fixed at 5°, as shown in figure 1. Four ,_ihedral angles
were tested: 45 °, 50 O, 55 ° , and 60 °. The experimental data presented in this
report are the result of subtracting tail-cone data from data for the tail cone
plus the tail surfaces to obtain data for the tail surfaces.
ANALYTICAL HETHODS
Experimental data were coe_pared with results from four analytical methods
to determine the ability of rheim methods to predict the effects of dihedral
angle on the static stability characteristics of an isolated V-tall. _be four
analytical method_ used were (1) the simplified analysis of reference 6w the
Pureer-Calptmll amthoS; (2) a sodtfied version of the Purser-Campbell aethcds
(3) the vortez-latttce meth(xY of reference 9; ar_ (4) the tnvilcid, three-
dimensional (3-0)• [x>tentlal-flow program of reference 10.
The asmm_ttmm m_e by the Purser_ll method are basically there is
no lnte¢ference between the tai] surfacem bath dihedral, and lift and aide force
are simple 9eomtric functions of dihedral; and the lift-curve slope nomal to
the tail surface vith dihedral is equal to the lift-curve slope of the tail sur-
faces at 0 ° dihedral. 1_ese _ioms simplify the expressions for the tail
contribution to longitudinal and directicmal stability Is)
Cl_) cos 2 F
CYB = -K(CI,a} sin2 r
N
{1)
(2)
The modified Purser-Campbell mthod sakes use of equations (1)
the same value of K used in the Purser-Cempkmll method# but
(_taine_] by using the vortex-lattice aethnd of reference 9.
and (2) and uses
(_) is
The vortex-lattice method of reference 9 used 6 chordwtse and ]0 spanwise
rows of panels to Bode1 the V-tail. The left surface of the V-tail was modeled
from the dihedral hinge line to the tip; the right surface wee modeled from the
dihedral hinge line to the mi6point of the tail-rotor gearbox fairing. The
spamelse loads were stained frmm the po/nt 6.25 cw (2.46 in.) from the dihedral
hlnge llne to the outboard end of each respective surface. This irJbcard point
represents the juncture of the tail surfaces and the tail cone. The vortex-
lattice method has a potentlal deficiency in its ability to model this V-tall
configuration. This potential deficiency Bay arise because the experimental
V-tail model uses a relatively thick (15 percent) airfoil section, _hereas the
vortex-lattice method is based on thin-airfoil assumptions.
The inviscid, three-dimensional, potential-flow pzo_ram utilizes source
panels to represent nonliftir_ surfaces and doublet panels on source panels
to represent lifting I "_rfaces. Neumann boundary conditions of tangential fl_
are assumed. The V-tail configuration as _eled for this program, is shaem in
f-gure 3. Discrete components were used for the modelir_ to allow for easier
alterations in the paneling scheme when dihedral angle was changed. A total of
860 panels was used to mo_el the lifting surface and three chor_ise panels
behind each lifting surface were used to model the wake. A cosine distribution
of panels was used on the lifting surfaces. Doublet panels alone were extended
2.54 am (].O in.) into the body, and loa_ were sungned for the tail surfaces
only.
RESULTS N_ DISCUSSION
Experimental data from the wind-tunnel test of the isolated V-tail ace pre-
sented in figures 4 to 7. In figure 4 longitudinal aerodynamic data are pre-
sented in the form of CL as a function of _ for dihedral angles of 45 °, 50 °,
55 °, and 60 °. Jm expected, the lift-curve slope decreases with increasing dihe-
dral because of the reduction in projected horizontal surface area. Also, as
dlhedra/ an_le increases, the lift curwm beo0me nonlinear over the anqle-of-
attack range t_sted.
In figure 5 longitudlr_L1 aerodlmmaic data are presented fo_ three tail con-
figuratlona- right and left surfaces together at F = 55 o, left surface only at
r = 55 ° , a_d right surface only at F = 55 ° . alac shown in figure 5 (as the
dashed line) is the mm of the lift coefficients of the individual surfaces.
This figuze indicates that a benefic.al interference occ_s betwa_m the two tail
surfaces, since CL_ of the total c_:figuration is greater than that of the sum
of the individual tail surfaces. In a(Mitton, the interference between the tail
surfaces appears to be nonlinear with changes in angle of attack.
Figures 6 and 7 present lateral stability data in the form of Cy as a
function of B. In figure 6 the data are presented for three angles of attack
at each of the four dihedral angles tested. For the three values of angle of
attack, the value of Cy_ became more negative as dihedral angle was increased.
In contrast to the lift curves, the side-force curves became more linear with
increasing dihedral angle over the range of sideslip angles tested.
In figure 7 are presented the lateral stability data for three tail con-
figurations: right and left surfaces together at F = 55 o, left surface only
at F - 55 ° , and right surface only at F - 55 ° . &leo shown is the sum of the
sid_,-force coefficients of the individual surfaces (dashed line). In contrast
to the longitudinal aerodynamic data, a r_nbeneficial interference occurred
between the two tail surfaces, since the value of C¥_ is less negative for
the total configuration than for the sum of the individual tall surfaces.
4
The primary results of this investigation are susmarized in figure 8 as a
c<mparison of calculated values of CLQ and -CyB with values of these deriv-
atives determined from the wind-tunnel data shown in figures 4 and 6(b). The
values of CL_ were obtained at 8 = 0° between a = -5° and 5°, and the
values of -CyB were obtained at a = 0° between B = -5 ° and 5° . The four
analytical methods were described earlier.
shown in figure 8, the best correlations with the experimental values
of CLa were obtained with the modified Purser-Campbell and vortex-lattice
methods. The other two methods gave values of CLa higher than the measured
values; the least satisfactory correlation was obtained with the Purser-Campbell
smtbod.
Figure 8 also shows the variation of -C_ with increasing dtb_Iral m_le.
TWo of the _tstrtbuticns of -¢_ (Purser-Campkmll M modified Purser-Cmsp_ll
neW, ks) were predicted by use of equation (2}. As previously sho_ in equa-
tion (2), the value of -C_ predicted is dependent on l and (CLef. for any
given dihedral angle. The value of I {0.65} was detara/ned from figure 2 of
refereJ_e 6. mind (_ _ _ne_ am l:_'evtmmly deserlbe_, l_r the
N
Purser-C2mpbell s_th_, the results do net correlate well with the experimental
data; for the modified Purser-Cap, bell method, the correlation with the experi-
nmntal data is such better. However, neither of the two methods using equa-
tion (2} predicts: the reduction in the slope of -Cy B versus F shown by the
experimental data at the higher dihedral angles. Both the vortex-lattice and
3-4) potential flow methods correlate the experimental data better, particularly
in predicting the reduction in -CyB as F approaches the value where the two
surfaces would converge into one, as described in reference 6. This reduction in
-Cy_ at the higher dihedral angles is due to increased interference between the
two V-tail surfaces, which is more accurately predicted by these more SOl_histi-
cared methods. Changing the value of K or (CL_ _ in equation (2) will still
N
not enable the nodified Purser-Cmq_bell method to accurately predict the reduc-
tion in -Cy8 i_dicatad by the experimental results, since the results frou
equation {2) will still follow a sine-squared distribution of dihedral angle.
5
ODNCLUDINC I_MARKS
An investigation was ur_ertak_n to determine the ability of four analyti-
cal methods to accuzately predict the lateral and longitudinal 3tdtic stability
characteristics of an isolated V-tail model. It was detezwined frcn this inves-
tigation that a simplified prediction method used in conjunction _ith a vortex-
lattice method gave adequate results for the longitudinal static stability
characteristics at ,_derate dihedral angles. This combination of methods was
deficient in the prediction of tail contribution to static directional stabil-
ity at high dihedral angles. A more sophisticate_ method based on an inviscid,
three-dimensional, wing-body, potential-flow program sufficiently predicted the
tail contributions to static directional stability at the higher dihedral angles.
However, this metho_ was deficient iu the prediction of longitudinal static sta-
bility characteristics.
Langley Research Center
National Aeronautics and Space A_tn_stration
• lmptcm, YJ_ 23665
July 20, '!978
6
REFERNICES
I. Connor, William J.: The Huey Cobra in Vietnam. 1968 Report to the Aero-
space Profession, Tech. Rev., vol. 9, no. 2, Soc. Exp. Test Pilots, 1968,
pp. 25-32.
2. Lynn, R. R.; Robinson, F. D.; Batra, N. N.; and Duhon, Jo No: Tail Rotor
Design. Pt. I: Aerodynamics. J. _verican Helicopter Sot., vol. 15,
no. 4, Oct. 1970, l:_- 2-15.
3. Huston, Robert J.; and Morris, Charles E. K., Jr.: A Wind-Tunnel Investi-
gation of Helicopter Directional Control in Rearward Flight in Ground
Effect. NASA TN I>-6118, ]971.
4. Ye_er, William T., Jr.; Young, Warren H., Jr.; and Nantay, Wayne R.: A
Wind-Ttmnel Investigation of Parameters Affecting Helicopter Directional
Contr¢.l at Low Speeds in Ground Effect° _ TN D-7694, 1974.
5. Wlesmer, Walme; and Iohlef, Gary: Tail _otor Deaign_ide. USJU_I_L Tech.
Rep. 73-99, U.S. Army, Jun. 1974. (Avatlab2e fr_ _ as AD 775 391.)
6. Purser, Paul Lz ar£ Caupi_ll, Oclm P.: _per_bwntal Verlfl©at/cm of a
Simplified Vee-Yall Theory m_ Analysis of .Ivsllable Data on Cc_lete
Node/s With Vee TaiLs. _ Rep. 823, 1945. (Supersedes _ ACR LSA03.)
7. Scha&e, Ik0bert 0.: Effect of Gecsmtrlc Dihedral on the Aer_Ic Charac-
teristics of Two Isolated Vee-Yail Surfaces. IOtC_ YN 1369, 1947.
8. J_ffichtly,E. &.: The Internatlo_l Systmm of Onits - Physical Constants and
Conversion Factocs (Secoe_ Itevlslcm). _ SP-7012, 1%73.
9. Tulinius, J.: Unified Subsonic, Transonic, and Supersonic MAR Vortex Lat-
tice. TFD-72-523, Los Angeles Div., North R_erican Rockwell, Apr. 27,
1972.
10. Hess, John L.: Calculatio_ of Potential Flow About Arbitrary Three-
DiBenslonal Lifting Bodies. Rep. No. _ J5679-01 (Contract
N00019-71-C-0524), McDom_ll Douglas Corp., Oct. 1972. (&vailable
from DOC as AD 755 480.)
7
rib
Flgure 2.-V-tail without fuselage.
L--76-4116
OlUG'INAL PAGE IS
OF POOR QUALITY
Figure 3.- V-tail paneling gecmetryo
10
CL
.3
.i
-.4 0
-15 -_o_ _ d
5
Figure 4.- Zffect of dihedzal o_ v-tail lift coefficient-
10
11
CL
.3 . l--
i
2- !
1
!
T
l
I
+
Configuration
0 Both
El Left only
0 Right only
Leftonly + Right only
t
+
J
1 •
.1
-.3 ;i;: '::
[ i i _ " ' _ _ '
-.4
-15
2;:it::i ',!;!i.i_!-r .... v ..............
i
" i!ii':-i,+ _J,_t_f_-i:i : _; :;;i _ ;_ ;,_1:_[. • :.
• i_ + ........ ,:. ,i;+.i_;_ .........
t- ; _" ; ; _.. , _ . . •
..... I ..... ;1; .......... +' _+': ...... ;'
......... +.......+;
, ' "'" '''+ " !++1;; ii,+ ; i : + +
"+itl+i':_:+'+i ;+; " ;! + +'I ; I + ,7
' I ll + _ .+;i• ,i+ .... _- i ili• , ;+_+ +
, ,+. ++_ .+++, i+ .... t '
: : _+-:?-I P • _+ i + : + : - i , + _ + t + , + + + + ; ,
---; '--+.-_ 4..._. ; + _.,...u.._._ -++.._-+7-+-- +-+_,+--__.+__+_._
+; + PI t fit i+ i: + ;, + + ; r .... ' ' +"
: i ! ,1! , T_, ;, + •
..... ; '' ' ++'::; ++!;I;;I;L;];;
.... ;,...:_;_);._.; ..... +, ..... :.,
• +
-10 -5 0 5
_ d_
+! t.
" , •1 j+: ;;l;i_it_ ¸ il _! __ :!,-, ¸
10
Figure 5.- Comparison of lift coef, _cient for the V-tail at 55 ° dihedral
and left and right surfaces alone at 5._° dihedral.
12
Cy
_I
-.3
-lO -5 0 5 lO 15
_, d_
(a) _ ,= 4o,,
Figure 6.- Effect of dihedral on V-tail side-force coefficient.
13
Cy
' I ' ' r,,eg "1
........ 0 45
.2 _' z_ 60 ....
.1
0
15
(b) a = 0°.
Figure 6.- Continued°
14
Cy
.... i .........
(C) O, '= -40.
Figure 6.- Concluded.
15
4_m.
.2
.I
Cy
0
Configu ration
0 Bo(h
E] Left only
0 Rightonly
..... Left only + Right only
-5 10 15
"a_ ,31 == 4 0.
Figure 7.- Comparison of side-force coefficient for the V-tail at
55 o dihedral and left and right surfaces alone at 55 ° dihedral.
16
Cy
0
Configuration
0 Both
[3 Left only
0 Right only
Left only + Right on ly
0
(b) a = 0°.
5
Figuze 7.- Continued.
lO 15
17
iCy
.4
°
Configu ration
Both
Left only
Right only
..... Left only + Right only
(c) a - -4o.
Figure 7.- Conolucled.
18
.03 ..............................................
Ct
i
i
0 _
0 Experimental ...... 7- ---T- ............
Purser-Campbell Iref. O_ : I '
....... Modified Purser-Campbell _ " ..........
Vortex-Lattice (ref. 9)
.... 3-.D Potential Flow (ref. 10)
.031 - -T...... T...... T..... _- T T .... ] I _- _-----_
I i , i | ! I i i J..---'l"_ _ '
I i i _ i i i k......¢- I I
I
!
, i i
' _ i
i IO,o 'so '.............. ,. ................. J 60 70
F, deg
Figure 8.- Comparison of experimentally determined V-tail and -C¥_
with values predicted by tour analytical methods CLa
19



Analysis of stability contributions of high dihedral V-tails

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