Hassell, J. L., Jr.

Johnson, J. L., Jr.

English

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.NASA - La,-=gle'/
DY_AHiC 5TABiLiTf AHil CO.hTROL CHARACTERi_I-'iCS OF PARAWiNGS
Cy Joseph L. Johnson, Jr. and James L. Hassell,
,
L
I ,gTRODUCTION
Jr.
Recently, the Langley _esearch Center has conducted several
investig_t?on_ to determine the dynamic stability &nd control character-
istics of models employing the parzwing concept. These investigations
have ccnsis ted of fcee-fligh¢ model tests conducted in the Langley fuli-
T
scale tunnel and o=ztdoocs using the drop-model technique w_th uncontrolled
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end radio. • _. =_ _ed mode|s.
The mc_eis usecJ in the dynami_ stability zt;_ie_ h_ve varied from
small-scale, simple rese=rc_ configurations to larg_=scale, i_f_at_le
conf_guratior, s similar to thope currently being consiaered for recovery
system appi:ca_ions Control for _st of the n_<lel flight tests was
Z
obtained from th_ center--of-g,'avity-shift control system bu_ a few tests
we_ ,.ede in which ctte_ method: of control we, e evaluated. Th_s paper
prese,_ts a brief s_m&ry of the dynamic stability 3nd conCrol information
obtaineO in Eh_se te_ts and includes _he results of related analytical
ctudias and _o-ce test ;nvestigations.
LONG=TUDINAL STAPlLITY CK'_E_CTERISTICS
S_e static longitudinal stability informo_ion obt_;ne_ in recent ;orce
test investigatioqs of parawings are presented in figures 1 to 3. Bzsic
pitching moment data fnr a parawin 9 configurat_or, havinE a low center of
gravity posit:un is presented in _;_re I for an ang|_-of-attack :'pnqe o_
vhe keel from -10 ° _c 50° . These data sh_'_ :Ca¢ic ;ongitudinal stability
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over most of the positive angle-or-attack range _ith an ir.crease in
s_atic stab_lil¥ above the stall. For some para_ings, |ongitudinal
instability _r _itch-up h_s c_curred near the stall, in the low positive
_g!e-of-attack range_ paraw[_g coqfigurations have _een Found to have
very low static stobi]:ty and instability at iow negative angles of attack
This static instability, oitStr at ;owor high angles of attacZ_ can lead
to dy_a_ic stability prObg_as. One problem of this type is _ tendency
towar_ an end _ver end tumblin 9 qK,tion which may occur _nder _e co_lditio_.s
of flight. Some static force test i_formation related to th_ tu_,_li0g
problem is presented in figure 2.
: The dat_ of figure 2 s;._-_ static pi_hing moment characteristics G_
a 3_0 ° a_g_-o_-attack range for a par_ing configuration _ith low center
oc gravity together _ith simila| date for _ conventional d_ta _ing
configuration witf, the c_ter of gravity in the plane of the wing. Notice
£he ,_ear 0° and. of course, _60 ° a_gle of _t_acK _h_ch aiso corresponds
i
to O°) both configurations have a stable trim point. In the case of the
conventional _ng, a _isturbance which oitches the wing a_a¥ from its trim
point is opposed by large restoring _oments _hich are _mnetrical a_
positive or negative anglss of attack. In the case of _he parawing, however.
there is a region of static longitudinal instohility at lo_ _egative a_gle_
of ottack _nd ia_e differences in the magnitude of the positive o,_d
h_gativ_ pitching n_,_ents over the angle-of-attack r_nge. The Static
instability at low negative angles of attac_ is re_at_d to the |¢,:ersal in
the fabric as the wing pitches through zero _ngle of _ttack. _:'_ large
asyn_nctr¥ in th_ positive an_ negative pit_,ing moments is reiated to _he
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Ic_ center-of-gravity _ffset. A parawing configurat:on which pitches
downward through "ts trim point to i.a_ negativ_ angles of attack wi !i
encounter the region of static Iongitudin_! instabillty and will therefore
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tend to ?it_-h downward to e_'en higher negative angles of attack, if the
pi'.chin 9 ,_otion is great enough to ._vercome.the restorin_i moments Jr, the
f;rst half of:the cycle, then the Ditching motion _iii continue with
energy being fed into _he system as the configLration seeks its staole
t_im point near 0° angle of at_'ck, lhis energy acts as a oriving force
which tends to pitch the co_figur_tion ti, roug h its stable trim pcint and
i_to the region of static instability. From these ,esults "e Can be seen
hew ._ steady, nose-do_m tumbling n_tion could b_ established for a c_f!g-
urati_l of this type. It should be pointed out, h_.mver, that predictm_ns
of a tumb!in_ motion cannot be_ mar:e _ased on static data alo,ze. There are
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other fa_tors, such _ dampiPa in pitch and nlass and inertia characteris_;cs
whi=i, must L-e consid_.red in determining stable and unstable boundaries _n
a d_amic st_ility problem of Lhis type. ,t should also be pointed out
_hat the data presenteJ in Figure 2 apply to configurations h_ving rigid
connections between Lhe center of qrav;ty o¢ payload and the parawing _d
therefore are not d;rect|y applicable to r_covery system.s where f',_.xible
.-isers are involved unless the risers are ir tension.
Presented in figure 3 is the-low sub._ic parawing data from the
previous _igure togetherwith data at a Hath number of _.5 for the micro-
meteoroid parawing cot, figuration. It is i_teresting to note the general
similarity in the static pitching characteristics.for the two cases in tha _
the Hach nu_moer 4_5 data shov; static instability _t Ic_ negative ang;es of
r
I
i\
attack and unsymmetrical pitching moment variations over th_ angle-of-
attack ran e,e. - Based on "these data it we,Jld-appear that the micrc_r=.teoroid
r.
configuration ._ay have tumbling problems similar to-thOs_ encountered with
the low subsor-;¢ models. Analysis m_de by _the 7-x lO-f_t tunnels b,-a, ch
: has indicated that the bui ld-up in dynamic pressure _4_;ch occurs when
thi s- configuration enters the otmo__phere acts to orevent tumb I in9 bu_ there
.ace cr',-ical cond_.tions in this speed range where _-umbling may occur_.
?.
LATERAL STABI LITY C-'._.RACTERISTlr.S -"
r
: To date, the dynamic lateral" stabi li_y _c'naracteri sties oF par_inc.s
:have been found to _e generally satisfactory-. Presente_ in ,_igura _ are
? : _
: some statFc and dynam|c lateral sta:ai I "t-.: .erivativ_ _hi ch v_.re measurea
for a pa.-awing configuration at various _.enter of gravity locations h_.low
the parawin9 keel. P._esented in this f:.gure are _.e _:-=tic lateral
stabillt_ derivatives Cn/_ and C_p . the yawing derivatives Cn - Cn_
. |° _
and C?_. _ C_/_, the rolling derivatives Cnp and (;_), and the ra_io of
yav:;.ng iner_i_ to roiling ir, e'-tia IZ/IX. _ome signifi-cant char,ges in
these derivatives as the center of gravity was Iowere6 (tha_ .is, i_.creasing
Z/b) are the incFease_ in directiona: stability and positive dihedral _ffect.
the increase in _amping in roll. _nd the decrease in the rad!o of IZ/IX . _
.--_ _.
The effect of th_ changes in these derivatives on the calculated Dutch roll
damping is presented in figure 5. Plotted in figure 5 is the calculaced
D, tch rol l damping, l/c1/2 (one over cycles to da_) to one-hat( amp] itude),
aga;nst Z/b. Although the dat_ sh_ tha_ the damping for the configuration
with the low.center of gravity (Z/b =-.5) i_ only ,_bout one-fourth of the
va_ue for the configuration wi_h the center of gra_'ityon the keel (Zib = 0),
-5-
T..fit: UOIlYJd_Ili_ I._ OL! I I _vVtlOIV_.t q;'.i _._'.JVrV I ut LII_ I*=_., 1,_rvtlI.U! --V! --_! uv * 4 7 wwlvl w. wv=,_
/
Reducing t_hegeometr_c dihedral by 18°, which has b_en suggested as a
possible means of impro_ng_latera.l C_ntro] (as wi-I1 be discussed later);
increased the damping for this condition. I-t shou'id b_ _.ogfn_ed out that
the values of damping shown _.ere _.o not take into account the effeG_._ of
-_'_bodi_:s beneath the parawing, ip case_ w_.z_re large destabi lizing-bodies are
Used,: the Dutch roll damping could Ix_ssjbly be reduced down into the
unstabie regi on.
CONTROL CHARACTER! ST I CS "
Aswas po_nte_ out i,_ the INTRODUCTION, control for most parawfng -
flight :tests to date was obtained f_rom the center-of-gravity-shift contro!
system. Lon9itudin3iiy , this control system has been found to be.generally
effective l)ut in .,.ome cases large _tick forces and unstable stick force
gradient3 have beer, encountered. _- Presented in figure 6 are calculat_l.
data which show the ,,ari_tion in ]o._9,tudina] stick force with lift
(. coeffirient for a control s,_st_n of this type using several different riser
arrangements. These r=.sults, which were presented by Hewes at _he Apollo
o- .
Co,_ference last year, s_;ow unstable stick force gradients and indicate that
the 9radiants c_n be altere_ _preciai);y b.vchanging the- ;iser lengths and
attachzn__nt points. Analysis ;._dicates that the stick force gradients _ould
h_ve been n;¢de stable in these cases by proper arraogement of the ;isers.
it is, of course, desirable to have the stick force gr_.dien_t"stable from
handl_=_g qualities cons!derations_ano t'o keep the _radients low fran con_ro]
- powe=" ,'equi ren_.ts.
.-. 3.
3
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L- ._,
In the analysis of this type of control system it was found that the
s,gnif;cant _sctor involved in determing the stick force characteristics
- _s the Cmo _ the wing_ $_e infor_tion to i!lustrate this point is
presented in figure 7. On the left :;de ,_f-thi;; ;gure is a Plot of the
pitching moment coefficient (raft-fred to th_ parawing-keel) against lift
coefficient and, on ti_e right s_de_ is a plot of Cm _ga'nsL stick force
: • O
gradient. The date pre_enLed are for the Ryan F!ex-Wing configuration and
I
for an inflatable parawing of the t,F;obeing consio_red for recovery system
app!icatio.s. _n the cas_ of the _'yan _l_-Wiag, it,was found that at
moderate lift coefNcients this configuration had posit-i've values of Cmo
whZch produ,_d a high stable _tick force gredient. In order to reduce the
Z i
stick forces in this case.:the gradient '_as lowered by reducing Cmo throu3h
trailing-edge m_lifications to the _ing so that in the final arrangement _he
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stick forces were in a more tolerable region. Based on these_data, it
ap_ars that par_wing_ for recovery syst._ms,' which have been found tO have
: c
negati_e values of Cm° , wil'l have hig h unstable stick _orce gredi_ntg
un_._ss some means is used to redu_ these values of _no, either by changes
in the _in_ itse'f or _y changes in the rigging as ir¢:,tioned earlier.
: From the lateral control standpoint, there t,as been so_ i.ndicat_on
of possible _roblems in the use of the center-of-gravity-sh_ft control
i
system. An eqjation for calculating the net roll;n_ moment produced by
t;,is type of control _/stem is presePted in figure 8. This equation is
C_net -_in _ Z/b (1 - -C_t _ L/D). The CL sin ¢ Z/b term in this
T
equation's derive_ grem the fact that whet, the wing Ts banked, the lift ,_
vector is tilted and has e component wh;ch produces _ rol'i£ 0 I_ent about
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: /
the center of gravity through the _oment 6rm Z/_. The-term (1 - - L/D)
is called the roli!ng effectiveness factor and_is derived fl-mm--the fact that
the lift comp_nentTwhich produces rol] is rearwar¢; of the center of _ravit'/
and_also produces an adverse yawihg moment through the arm X/b. When the
sideslip angle resultin 9 from this adverse yatmsng ,_oment is taken into4,ccount,
;ll:::can be shown, that _he favorable rolling mom6nt produced by the lift vector'
i+_ reduced through the effect:;.ve dlhedral i)arameter C . For configuratiorLs
having _high ratios cf -CI_/Cn/_. and low values of 'L/D, .the roi ! ing
effectiveness term becomes smalt and th_.refor_= the net rol ling moment produced
in such ases is reduced. Presellted in f:igure 9 are some data showlng the
_ffect of leading-e_lge, thickness on these j)arameters. Plotted in this figure
are values of C_, -C_ , L/D and the rolling effectiveness t'actor
_1 - =C_/_n_/ L/D) for a parawing with .a leading edge thickness of 1.5
percent of the keel _.-.d another having a leading edge thickness of:7 percent
of the keel. These resu_t'_ i;_dicate that the rol =ing m_..nt produced:by
: banking the win 9 is reduced by about 50 percent a_ moderate lift coefficients
for eith_,- _ing_-nL that the rolling effectiveness for the wing'_ith the
thir; ieading edges decreases rapidly with increasing lift coefficient and
t .]
approaches zero near maximum lift :o_fficient. It is slgnifica,¢ to note.
that for the tn;ck !eading-edge _onfiguration, which is repres=nta¢ive of :
inflatable parawings no_ being C_sidered for _ecovery systems, iF, ere is an
l.lcre_se in effectiveness with increasing 1|ft coefficient.
In discussing lateral control characteristics, another fac+or which
m_st be ¢_=s_de,-ed.is that of lateral hinge moments. 'Some.indication of
the lateral hinge momentcharacteristics involved in the center-of-grav!¢y-
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sPift control system was obtained in the force :est Investigation nf
the Rvan F]e_-Wing airplane. Some of the re_uiLs obtained in this
investigation are presented }n figure 10. Plotted in this figure is
rolling moment coefficient agsinst roll hinge moment coefflci_n_. The
horizontal dashed line plotted n this figure represents the"v_lue of C_
required ¢o produce a pb/2V of 0.09 based on a v_ll_e of damping in rol 1.
of -.15. This value of pb/2V is the ,;,inimum value specifled in the
hahdling qualities requirements for a light liaison airpla_e_ It is
presented he;'e merely to establish e Yeference for purposes of comparison _
and is not intended to imply that this value of pb/ZV is a valid
specification for parawing app!:_atior.s. For recover'/ syst_ applications,
a sm_iler value may well prove to be acceptable. Considerably more
research and flight experience _illl be required to esl__ .sh the proper
criterion for this case. The solid circ]e at the lower right, vfhich
represents _asured data, shows that 5° Of wing bank pro6_ces only about
one-third of the roiling effectiveness requircd by the pb/2V = _09
criterion. The stick force corresponding _.o the hinge n_)ment for this
condition w_s about 70 potmds.. Analysis indicated that reduc;n] CZ_
by using 18° negative geometric dihedral angle of the w_ng would improve
the re]ling effectiveness and reduce the hinge n_nents. It _'_ alsu
estimated that increasing Z/b up to C.5, which is a value representative
of parawing recovery systems, _ould substantialiy increase the roiling
moments-without increasing th_ hinye _,x_ent_,
Because of the problems _hat h_ve been encounteredwith the center-
of-gravity-shilL control system, so_e attention has recently been given to
other methods of control for para_;n0z. Presented in fi9ure 1!
the alternative control methods that have been prcposed.
_re some of
These methcds are:
?I
t
•1
(
I
"t
4;
-r
.?
-)-
1 Tr=|l;_ =d_ _1_ rnn_ In this =ontroi system the
tension i_ Increased or dec,'eased in,-a cab|e ;n the'parawing
trailing edge to provide pitch _r roll COrLrclo
2. Trailin 9 edge risers. In thls control system rlsers_ ¢-e
attached to the parawina troill_g edge arfl pu'l_l do_ or -
released to provide control. _
3. fllnged ),adi.ng-edgeor keel ntmb_rs. _ln this control systam..
: hinges areplaced in the-wing leading edges or _el and the .-
aft portion of these memb_rs deflected for c_ntrol.
4. Auxiliary surfzces. This control _ system.Is c_-n_erned
prlmarii',, with sutfaces pieced at ¢h¢ rear-of the wing _ t0
prov;de directiona! control.
k
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(
Some p':_n_sing, resu!ts havebeen obt_ined with a wing-tip control
sys - in tests in the Langley full-s, e tunnel with t;,_ Ryan FleJc-Wing
cirplan_ In order to show how these results c_npard with t;'cse for th_
: ; T
center-of-g, 'ity-shift control _ystem, data for I_th types o_ c_sntrol are
presented in fi:, -e !2, Plotted in .'his figure are the dat._ for the wing :
bank control systr,. :rom figure 10 for comparison pqrposes. Also plotted
o• c
are ._.asured da_.a fo," _ and 10 deflection of the aft 2S-percent of the
wing !eading edges for cont=:c.. These result_ show that w!th about 7°
deflection of the wing t ip._a pb/2V of .09 could P,_: pro_Jce6 with a .
hi._ge _ent coefficient considerably i_:ss- than that produced _y banking
the _in_. The _t.ick fo. ce corresponding to the hir, q_ n_ment for 7 ° de:lection
of the wing tip w_s about 30 pounds on the lyon Fiex-Winc airplane.
SUetI_RY
1. P_,awing confiq.ure_;ons ger,a:'ally have ;ati_actory dynamic
ioP£itudi_] ,:_abilitv ch._racceristlcc iF, the nomal operationsl angl_-ot:-
attack r'_nge but tt,ere m_, t= problems at extreme angtes of attack (either
high or low) b_c=use or" static ])ngitudina', lnstab!iity,
!
4
C
?i. -- " _ • . _-
. . ...
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- I0-
e Lateral Iy. parawin9 con_ig'jratibns 9enerall¥ have _at,sf_ct,_r¥
dynamic stabi 1;tf characteristics.
3. F.'om the cemtroi standpoint, the use of the cen_er-_f-gr_v;ty--
"shift :o.troi :-/stem_may _ 9ene:aii¥ sat'sfactor_ .:or _ recover_, sbstem._
?-_FplicaLions but this type of c_tro _ system may introd_:ce-some s'..:ck-
force problem_ -_ncL Lay , ecGme inadequate_ for conf i gurat i._s hav i n9 h i9 h
ratio_ of dil_dral effecc to-direction.a| s_bility and iow velues of L/D.
_,_-.
°
¢.1
o"[ime. sec
:- 2.
'" ALTITUDE U3ED
•., _ -,
DESCENT


Dynamic stability and control characteristics of parawings

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