Aerodynamics, Aeroelasticity, and Stability of Hang Gliders

Aerodynamics, Aeroelasticity, and Stability of Hang Gliders

-
NASA Technical Memorandum 8 1 2 6 9
-
-
-
-
- -
- --
-
--
-
-
-
-
-
-
-
Aerodynamics, Aeroelasticity, and
Stability of Hang Gliders
Experimental Results
-
llan M. Kroo
(NASA-TB-81209)
AEBOCYYAHICS,
A E P O B L A S l I C I T i , A N D STAidlLITY OF UAIG
GLlDE61S.
E P P E B I d b Y T A L RESULTS (YASA)
lug p
HC A36/MP A 3 1
CSCL 0 1 A
ldl-24025
Unclas
G3/OL
ULU33
J
April 1981
National Aeronaut~csand
Space Admtn~stration
NASA Technical MmOrmhrn 81269
Aerodynamics, Aerodasticity, and
Stability of Hang Gliders
Experimental Results
-
llan M. Kroo, Stanford University, Stanford, California
and
Ames Research Center. Moffett Field, California
Nat~onz'Aerwauttcs and
Space 4d~;rii>tra?10n
1
*-.,
. I "
*
_
.
. . .-
.
.....--
.---
_I___
.
-
.
a
"%-
t;b
h
.t
!f
LIST OF SYl4BOLS
.[
*
A
cross-sectional a r e a
@
%
.-
.
___*.
..
'0'
I -
:-f
'f
5
;;
-- -_-
AR
aspect r a t i o .
i
ii
b
I
i
drag
qs
C~0
CD a t zero l i f t
CL
l i f t coefficient ,
lift
qs
CL0
CL a t which CD
i s miniwrm
r o l l i n g moment
qSb
moment
pitching-moment coef f ic!.ent ,
qs
awing moment
yawing-ment
coefficient,
qSb
s i d e force
side-f orce c o e f f i c i e n t ,
rolling-moment c o e f f i c i e n t ,
-
qs
mean geometric chord,
S
root chord
diameter
Young' s modulus
equivalent f l a t - p l a t e drag a r e a
constant in 3-parameter drag polar
c h a r a c t e r i s t i c length
MAC
.t
. .
S
drag c o e f f i c i e n t ,
1:
mean aerodynamic chord,
$ lobla
c2dy
iii
1
3 PV'
pressure,
q
dyn..ic
RC
~ a p a o l d ah e r ,
@!i
planform area
tension
tunnel airspeed
angle of a t t a c k (measured with respect to keel)
angle of s i d e s l i p
strain
sweep angle
taper r a t i o ,
&
r
a i r density
stress
Subscripts:
B
body a x i s system ( f i g . 6 6 )
S
s t a b i l i t y a x i s system ( f i g . 6 5 )
W
wind a x i s system ( f i g . 10)
c/4
quarter-chord l i n e
f
f u l l - s c a l e value
1.e.
leading edge
m
model value
P
r a t e of change with r o l l r a t e
a
r a t e of change with
a
B
r a t e of change with
$
I l a n M. Xroo**
Ames Research Center
One-f i f th-scale models of t h r e e b a s i c u l t r a l i g h t g l i d e r designs vere
t e s t e d i n a 2- by 3-m (7- by 10-ft) wind tunnel a t h s Research Center. The
models vere constructed t o simulate t h e elastic p r o p e r t i e s of f u l l - s c a l e
g l i d e r s and were t e s t e d a t Reynolds numbers c l o s c t o f u l l - s c a l e values
(1.0x106 to 5 . 0 ~ 1 0 ~ ) .Twenty-four minor modifications were made t o t h e b a s i c
configuratirrns i n order t o evaluate t h e e f f e c t s of t w i s t , r e f l e x , dihedral,
and various s t a b i l i t y enhancement devises. Longitudinal and l a t e r a l data were
obtained a t several speeds through an angle of a t t a c k range of -30° t o +4S0
with s i d e s l i p angles of up t o 20°.
Modern g l i d e r configurations e x h i b i t much more s t a b l e and l i n e a r p i t c h i n e
c h a r a c t e r i s t i c s than the e a r l y "Rogallo designs" which a r e shown t o
have p o t e n t i a l l y dangerous c h a r a c t e r i s t i c s a t low angles of a t t a c k . The
importance of v e r t i c a l center of gravity displacement i s discussed. Large
d e s t a b i l i z i n g moments a t negative angles of a t t a c k associated with low c e n t e r
of gravity contribute t o t h e p o s s i b i l i t v of tumbling.
moate7.t
L a t e r a l data i n d i c a t e t h a t e f f e c - i - ~ edihedral is l o s t a t low angles of
a t t a c k f o r nearly a l l of t h e configurations tested. The appearance of l a t e r a l
d a t a depends g r e a t l y on t h e chosen reference axis system f o r these g l i d e r s
which operate a t unusuallv l a r g e angles of a t t a c k , hence demonstrating t h e
need f o r a dynamic analysis.
Drag data suggest t h a t lift-dependent viscous drag is a l a r g e p a r t of t h e
g l i d e r ' s t o t a l drag a s i s expected f o r t h i n , cambered s e c t i o n s at these r e l a t ively low Reynolds numbers.
*.This work was supported by the NASA University Grants Program, NSG 2359,
with technical a s s i s t a n c e from Ames Research Center personnel and t h e Army
Aeromechanics Laboratory. Technical monitor: W
r Eonald Cif f one; f a c u l t y
advisor: Prof. Holt Ashley.
.
**Research A s s i s t a n t , Department of Aeronautics and Astronautics, Stanford
University.
In the laot 10 years hang glfding has evolved from an obscure aport to a
popular, world-vide activity with sooe 40 glider manufacturing corporations
and with participants nubering in the tens of thousands. Performance gains
have made possible 150-b (10hile) flights at altitudes up ta 6,000 rr
(19,000 it) and aultihour flight8 are now cwaon. The requirements associated
with performance, stability, and controllability have become more demanding as
thermal soaring and limited acrobatic maneuvers have replaced the original
short glides frola sand dunes.
These requirements have been met largely by a design evolution based on
trial and error rather than conventional analytical and wind-tunnel work.
Although the results of NASA wind-tmnel studies of the Rogallo wing
(refs. 1-8) in the 1%0's could be used to obtain sooe idea of the characteristics of older hang glider designs, relatively little accurate data exist on
the aerodynamic properties of modern gliders w N c h bear little resemblance to
the original Rogallo designs. Hence, most of the analytical work w N c h has
been done on glider dynamics is based on unrepresentative data. Only in the
last 2 years have data from contenrporary d e s i ~ sbecae available. The data
base remains extremely limited despite the need for a quantitative understanding of the properties of these aircraft to increase their performance and
safety
.
In 1979, NASA-supported work (under grant NSG-2359) began on a program
of research aimed at the development of quantitative tools to be used in predicting the aerodynamic characteristics of these ultralight gliders and
assisting in their design (ref. 9). The investigation consists of two closely
related phases:
1) Wind-tunnel studies of elastically-scaled models.
2) Development of analytical methods to predict the aerodynamic and
structural properties of modern hang glider designs.
The empirical results will be used in verification and refinement of
the analytical work to allow development of an analysis method with a broad
range of applicability. The results also make it possible to identify design
variables which are effective in improving the controllability and performance
of these gliders. This report details the first portion of this work which
was conducted in the Army Aeromechanics Laboratory 7- by 10-ft Wind Tunnel
No. 2 at Ames Research Center. The assistance of personnel associated with
this facility is gratefully acknowledged. Uany useful sug~estionshave been
provided by members of the project Advisory Committee, whose help is also
greatly appreciated: Dr. Bolt Ashley (faculty advisor), Mr. Donald Ciffone
(technical monitor), Dr. Robert Ormiston, Mr. Gary Valle, Dr. Robert Jones,
Dr. W. Hewitt Phillips, Dr. Paul MacCready, and Dr. Peter Lissaman.
. .
2
I
I
TESTING PROCEDURE
Model Construction
SuizZing- Unavailability of large-ecale wind-tunnel f a c i l i t i e s d i c t a t e d
t h e use of s c a l e models r a t h e r than a c t u a l production g l i d e r s . To properly
d u p l i c a t e t h e aerodynamlc c h a r a c t e r i s t i c s of t h e f u l l - s c a l e a i r c r a f t , i t i s
necessary t h a t these models operate a t t h e same Reynolds number and r d n
geanetrically s i m i l a r m d e r corresponding loads. Reynolds nunber equivalence
is especially important i f t h e r a t h e r complex separated-flow e f f e c t s , apparent
a t higher angles of a t t a c k and s i d e s l i p , a r e t o be sinulated. Recent experimental inveetigations ( r e f s . 10-12) have demonstrated t h e importance of e l a s t i c
scaling. The f l i g h t c h a r a c t e r i s t i c s of tiris type of g l i d e r have been shovn t o
vary conrliderably w i t h changes i n loading. This is caused by t h e f l e x i b i l i t y
of t h e frame and deformation of t h e f a b r i c sail, w h ~ c hn e c e s s i t a t e s accurate
modelin,: cf t h e e l a s t i c p r o p e r t i e s I n addition t o ge-tric
and aerodynamlc
similarity
.
These combined requirements place severe c o n s t r a i l d e on model construction. Since a v a i l a b l e wind tunnels operate a t e s s e n t i a l l y sea-level condiF experienced by t h e g l i d e r
t i o n s , it follows t h a t any r e s u l t a n t force ,
model must equal t h e corresponding Ff a t f u l l scale. Force e q u a l i t y can be
reasoned f r a a the f a c t t h a t
where t h e product of speed and t y p i c a l length, v t , must be t h e same a t both
scales. With a i r d e n s i t i e s
and f o r c e s proportional t o
pv2a2
then
The combination of equal force and equal s t r a i n requirements leads t o
d i f f i c u l t i e s i n t h e construction of e l a s t i c a l l y scaled models. I f t h e leading
edges of both model and f u l l - s c a l e g l i d e r s a r e constructed of tubes with c i r cular c r o s s s e c t i o n s of radius r propol-tional t o 1 f o r aerodynamic slmilari t y , t h e s t r a i n i n these tubes is proportional t o F r 2 / ~ 1 ,with EI t h e
f a m i l i a r bending r i g i d i t y . The severe requirement on model construction is t o
ensure that
I f t h e same construction and material were employed on t h e model one would
have
This f a c t o r of 25 a t one-fifth s c a l e is q u i t e unacceptable. Since weight is
not believed t o be a very s i g n i f i c a n t f a c t o r , t h e s i t u a t i o n can be a l l e v i a t e d
with t h e use of s o l i d rods of s t i f f e r material on the model. Models cons t r u c t e d of steel i n t h i s manner approach t h e desired s t i f f n e s s :
The requirement of equal s t r a i n s , therefore, can be met by allowing largerthan-scale rod diameters o r by some relaxing of t h e Reynolds number requirement. I f the rod diameters a r e geometrically scaled, a reduction i n Reynolds
number by approximately 0.54 i s required.
Scaling of cables t o simulate aerodynamic and s t r u c t u r a l p r o p e r t i e s of
the f u l l - s c a l e g l i d e r is amre d i f f i c u l t . Geometrically s i m i l a r model cables
would have a cross-sectional a r e a 1/25 times t h a t of t h e f u l l - s c a l e model,
whereas ( i f the Reynolds number were reduced a s above) t h e forces they experience would be lower by a f a c t o r of 3.4.
To duplicate t h e s t r e t c h i n g of t h e
cables, then, t h e requirement i s t h a t
Since f u l l - s c a l e cables a r e nominally 3.2 mm (0.125 i n . ) , adequate model
s t r u c t u r a l s t r e n g t h a s w e l l a s simulated cable s t r e t c h i n g w i l l be ensured i f
1.6-mm (0.063-in.) cables a r e used. I f t h e cables were geometrically scaled,
they would be 0.6 rn (0.025 i n . ) i n diameter. Hence, an a r t i f i c i a l l y high drag
i s produced. It is believed t h a t the l a r g e r cables s u b s t a n t i a l l y a f f e c t only
t h e drag measurements, which may be corrected accordingly.
Further d i f f i c u l t i e s associated with e l a s t i c s c a l i n g include properly
modeling the cable attachments and s a i l stretching. Small d i f f e r e n c e s i n
attachment geometry (absence of s t a i n l e s s - s t e e l thimbles) lead t o some modeling discrepancies. Exact modeling of s a i l s t r e t c h i n g i s a l s o d i f f i c u l t . It
requires s p e c i a l tightly-woven f a b r i c , s t i f f thread, and scaled s t i t c h i n g .
Simultaneous s c a l i n g of s a i l t e n s i l e p r o p e r t i e s and bending r i g i d i t y r e q u i r e s
t h e s e l e c t i o n of a material with proper values of Young's modulus and thickness. I f s a i l material is used (fixed E), t h e thickness required t o duplic a t e s t r e t c h i n g v a r i e s with t h e inverse of t h e s c a l e f a c t o r . This r e s c l t s i n
a very t h i c k sail with larger-than-scale bending r i g i d i t y . Preliminary
-
a n a l y s i s shaved t h a t f o r t h e models t e s t e d t h e c o n t r i b u t i o n of sail s t r e t c h i n g
480 ~ / m * (10 l b / f t 2 ) elont o t h e o v e r a l l deformation would be mall [ a t q
g a t i o n s of 0.4% f o r t h e standard and 1.41 f o r t h e low-billow models were
predicted]
3.8-oz. Dacron s a i l c l o t h was s e l e c t e d f o r use on t h e g l i d e r
models as a compromise based on required s t r e n g t h , e l a s t i c i t y , and bending
r i g i d i t y . No attempt was made t o simulate t h e mass p r o p e r t i e s of t h e s a i l
material.
-
Although some d i s c r e p a n c i e s e x i e t e d i n modeling t h e e l a s t i c p r o p e r t i e s of
t h e f u l l - s c a l e g l i d e r , t h e predominant e l a s t i c deformations a s s o c i a t e d w i t h
leading-edge bending were modeled c a r e f u l l y . Further d e t a i l s of nodel cons t r u c t i o n a r e shown i n f i g u r e s 1-4.
Mode2 configurations- A wide v a r i e t y of hang g l i d e r designs a r e comnon
today. It i s no longer p o s s i b l e t o test a "standard" c o n f i g u r a t i o n and use
the r e s u l t s t o predict universal c h a r a c t e r i s t i c s f o r these a i r c r a f t . P~wever,
s u f f i c i e n t s i m i l a r i t y does e x i s t s o t h a t c e r t a i n c h a r a c t e r i s t i c s may b e determined from t e s t s on a small group w i t h d i f f e r e n t b u t c a r e f u l l y s e l e c t e d
geometries.
I n p a r t i c u l a r , t h e e f f e c t of v a r i o u s modifications including fixed-twist
r i b s ( f i g . 5 ) , l u f f l i n e s ( f i g . 6 ) , and k e e l pockets ( f i g . 7) as w e l l a s t h e
e f f e c t s of b a t t e n f l e x i b i l i t y , d i h e d r a l , and sweep were i n v e s t i g a t e d .
Three b a s i c models were constructed w i t h p r o j e c t e d planforms shown i n
f i g u r e s 2-4.
The f i r s t model i s a "standard Rogallo" configuration, represent a t i v e of t h e e a r l y hang g l i d e r designs. This model was s e l e c t e d p r i m a r i l y
because of t h e r e l a t i v e l y l a r g e amount of f u l l - s c a l e d a t a which e x i s t f o r t h i s
configuration. Results from t h e present i n v e s t i g a t i o n could be compared w i t h
previous s t u d i e s t o v e r i f y t h e b a s i c techniques used i n t h e reduced-scale
tests.
The second mo'el i s most r e p r e s e n t a t i v e of present g l i d e r designs, and a
majority of t h e d a t a were obtained with t h i s model. The t h i r d configuration
was t e s t e d t o o b t a i n a b e t t e r i d e a of t h e e f f e c t s of sweep on hang g l i d e r
designs. A summary of t h e b a s i c model geometric p r o p e r t i e s i s included i n
f i g u r e s 2-4.
A t o t a l of 2 7 d i f f e r e n t c o n f i g u r a t i o n s were t e s t e d and a r e
s u m a r i z e d i n t a b l e 1.
Balance and Support System
The model support system permitted an angle-of-attack range of +45" t o
-30" ( s e e f i g s . 8, 9). The model was supported i n t h r e e places: t h e p i l o t
attachment point a t t h e apex of t h e t r i a n g u l a r c o n t r o l frame and a t each end
of t h e h o r i z o n t a l segment of t h e frame ( c o n t r o l b a r ) . Angle-of-attack changes
were made by r o t a t i n g t h e model about an a x i s j u s t below t h e c o n t r o l bar.
This placed t h e s a i l g e n e r a l l y a h v e t h e tunnel c e n t e r l i n e , which complicated
w a l l c o r r e c t i o n s but s u b s t a n t i a i t y reduced s t r u t i n t e r f e r e n c e e f f e c t s . The
s t r u t r o t a t e d about its v e r t i c a l axis t o o b t a i n s i d e s l i p a n g l e s of 220'.
The 6-cmponznt balance system of t h e Army's 2- by 3-m (7- by 10-ft)
wind-tunnel f a c i l i t y at h e o Research Center waa u d . Readings from a t r a i n gauge balances were averaged f o r each data point and recorded on a PDP-11
computer which a l s o provided on-line uncorrected d a t a reduction. The following = a l e r e s o l u t i o n s were a v a i l a b l e and were e f f e c t 1 aly reduced by averaging:
Lift
Drag
Side force
pitching moment
Rolling moment
Yawing moment
20.9 N
r
.09N
f .09N
+ .16 Nm
+ .14 Nm
r.14Nm
(0.2 l b )
( .02 l b )
( .02 l b )
( .12 f t / l b )
( .10 f t l l b )
(.lOft/lb)
Angle-of-attack measurements were made with an Angle I n d i c a t i n g D i g i t a l Servo
attached t o t h e support s t r u c t u r e , a s shown i n f i g u r e 9. The output from t h i s
servo was input d i r e c t l y t o t h e d i g i t a l deta a c q u i s i t i o n system.
In addition t o t h e six-component force d a t a , photographs of wool t u f t
p a t t e r n s were taken t o provide information on s t a l l c h a r a c t e r i s t i c s and b a s i c
flow properties. Photographs of t h e s a i l shape change with angle of a t t a c k
were a l s o recorded f o r comparison with f u t u r e a n a l y t i c a l work.
Data AnalysCs
Scale outputs were converted t o standard f o r c e s and moments i n nondimens i o n a l c o e f f i c i e n t form using projected a r e a , mean geometric chord, and ~lpan
a s references. Except where otherwise noted, t h e reference center about which
moment.8 were computed i s t h e p i l o t t e t h e r point near t h e apex of t h e c o n t r o l
frame 12.54 cm (1.00 i n . ) below t h e k e e l ] . Reference c e n t e r l o c a t i o n s a r e
shown f o r each model i n f i g u r e s 2-4.
Angle of a t t a c k i s measured w i t h respect
t o f!te kec. i n a l l cases. [Note t h a t the s a i l root chord i n some cases is not
p a r a l l e l t o t h e keel ( f i g . 7 ) . 1 Moments a r e presented with respect t o a windaxes system ( f i g . 10) unless otherwise specified. The importance of t h e choice
of reference axes and moment c e n t e r is d i s c u s . + ~ di n a l a t e r section.
Weight tares- Wind-off measurements of weight t a r e s with and without model
were made f o r various angles of a t t a c k and s i d e s l i p , f i t t o a two-dimensional
least-squares approximation, and subtracted from t h e data.
A e m d y d c tares- Model-off runs were made t o determine t h e aerodynamic
f o r c e s exerted on t h e strut-mounting system a t various angles of a t t a c k , sides l i p , and dynamic pressure. A three-dimensional least-squares approximat!.on
of these t a r e s was subtracted f rcm t h e data. No other c o r r e c t i o n f o r s t r u t
interference was made.
!Mtml boundm)y oorrsotions- Longitudinal and l a t e r a l d a t a were corrected
f o r blocking, streamline curvature, and induced angle e f f e c t s according t o
procedures described i n references 13-16 f o r these yawed, swept models, off
t h e tunnel c e n t e r l i n e . Maximm model span was about 70% of t h e tunnel span.
b
This resulted i n an induced upwaeh of about 0.75. a t t h e root q u a r t e r chord of
t h e model. The e f f e c t of increased upwarh a t the t i p s is negligible a t lowl i f t coefficiente. A t t h e higher CL an e f f e c t i v e decrease i n warhout i r
induced. This is p a r t i a l l y compensated by t h e a e r o e l a r t i c respome ( g r e a t e r
geometric washout). The spanwise v a r i a t i o n of boundary-induced v e l o c i t i e s was
small, only s l i g h t l y a f f e c t i n g t h e g l i d e r s t a l l i n g behavior. A t CL of 1.0
an e f f e c t i v e decrease i n washout of l e s s than O.SO was induced.
Uncertainties a r e introduced i n t o t h e d a t a from s e v e r a l sources: 1 ) .--ale
n o n l i n e a r i t i e s , 2) weight t a r e and aerodynamic t a r e f i t t e d curve e r r o r s ,
3) moment arm measurement u n c e r t a i n t i e s , 4) support system f l e x i b i l i t y ,
5) minimMl measurement accuracy of s c a l e s , 6) noise i n zero readings, 7) measurement accuracy of Angle Indicating D i g i t a l Servo, 8) h y s t e r e s i s i n s c a l e
balance system, and 9) model centering, The n e t u n c e r t a i n t i e s i n t h e s i x components of forces and moments a r e approximately:
Values i n parentheses i n d i c a t e u n c e r t a i n t i e s during yaw sweep i n which l a r g e
weight t a r e s and h y s t e r e s i s e f f e c t s appeared during t u r n t a b l e rot--tion.
Some previous i n v e s t i g a t i o n s ( r e f s . 10-12 and 17, 18) have shown t h a t
r e s u l t s vary considerably with dynamic pressure. I n t h i s investigat' 3, data
were obtained a t dynamic pressures ranging from 240 N/m2 (5.0 p s f ) o 963 N/m2
(20.0 p s f ) . The Reynolds number corresponding t o the tunnel conditions a t
20 t o 40 m/sec (65 t o 130 f t / s e c ) i s 1 . 3 5 ~ 1 0t~o 2 . 7 0 ~ 1 0 per
~ m. S k c o . t h e
models were constructed f o r e l a s t i c s i m i l a r i t y a t a Reynolds nuqn!,er of 0 54
times the f u l l - s c a l e value, these conditions correspond t o f c l l - s c a l e veioci t i e s of 7 t o 15 m/sec (24 t o 48 f t / s e c ) based on equivalent e l a s t i c
def ormat f ons.
Because of t h e l a r g e amount of tunnel time required t o generate data on
the number of configurations shown i n t a b l e 1 with a three-dimensional test
matrix (a, 8, q ) , some of t h e t e s t rune were made a t only one dynamic pressure
and a r e intended t o demonstrate configuration-dependent trends r a t h e r than t o
e s t a b l i s h a comprehensive data base on a very limited number of configurations.
Model s t r u c t u r a l considerations a l s o limited t e s t i n g a t t h e high dynamic
pressures. The 1.6-mm (1116-in.) high-strength b o l t s were required t o withstand s t r e s s e s s i m i l a r t o t h e 8(5/16-in.) a i r c r a f t b o l t s used on f u l l s c a l e g l i d e r s and s a i l material was required t o withstand f u l l - l u f f i n g , low
angle-of-attack measurements at tunnel speeds up to 40 m/eec (130 ft/sec).
These revere conditions reoulted in a sail failure at the trailing edge of the
first model and two bolt failures with subsequent models. The latter two
structural failures occurred at highly stresssd areas which were recagnieed
during model construction as potential problems, and safety wires at these
joints prevented major damage to the models.
PRESENTATION OF RESULTS
Figures 11-13 are installation photographs of the three models tested.
Measured aerodynamic characteristics of these configurations are outlined
below and are presented in figures 14-64. Table 1 describes the coqfigurations.
Description
Selected tuft photographs
stall behavior
Configurations
-
1, 2A, 31
Longitudinal characteristics of
basic models variation
with q and a
Lift
Drag
Moment
1, 2B,C,H, 3H
Variation of C, with reference
center location
1, 2E
Pitching-moment variation with
sideslip
1, 2A, 38,I
-
Lffect of modifications on
longitudinal characteristics
Lift
Drag
Moment
Lateral characteristics of basic
models vs a
Figures
2D-C.L-P, 3B-E,H,G
1,2B-G,L-P, 3B,E,H
2B-G,L,N,PS 3B-E,H,G
36-40
41-48
49-55
1, 2A,H,N,Q, 38,I
56-64
DISCUSS ION OF RESULTS
General R e s u l t s
Lift curve- Figure 19 shows t h a t a l a r g e range of n e a r l y l i n e a r CL vs a
e x i s t s even f o r t h e high-billow "standard" design. A l i f t curve s l o p e of
about 2.2/rad, a r e l a t i v e l y l a r g e CL of 1.4 a t 37'. a break i n t h e l i n e a r
curve a t about 10' due t o l u f f i n g , and a s h i f t i n t h e curve n e a r a = 0' when
t h e s a i l c o l l a p s e s i n f r o n t of t h e c r o s s bar a r e a l l apparent i n t h e f i g u r e
and agree well with previous r e s u l t s .
-
The second model e x h i b i t s a very l i n e a r l i f t curve from CL
0 (where
l u f f - l i n e tension diminishes r a p i d l y ) up t c bout CL = 0.8. The curve
reaches a maximum of 0.92 f o r t h e b a s i c c o n f i g u r a t i o n ( f i g . 20).
In c o n t r a s t t o t h e above, t h e v a r i a t i o n of CL w i t h a f o r t h e t h i r d
model is more nonlinear ( f i g . 21). This i s probably a r e s u l t of higher s a i l
t e n s i o n and a correspoildingly g r e a t e r deformation with loading. This t r e n d i s
a l s o v i s i b l e i n t h e v a r i a t i o n w i t h dynamic pressure. The highly r e f l e x e d
a i r f o i l combined with an e a r l y r o o t s t a l l r e s u l t s i n a r e l a t i v e l y low CLma
of 0.83 a t 24'.
Drag data- Drag d a t a f o r t h e b a s i c c o n f i g u r a t i o n s a r e given in f i g u r e s 22-24. Data on o t h e r c o n f i g u r a t i o n s a r e presented i n f i g u r e s 41-48. A s
mentioned previously, drag r e s u l t s must be c o r r e c t e d f o r two e f f e c t s : 1) t h e
use of larger-than-scale c a b l e s , and 2 ) t h e absence of p i l o t drag. R e s u l t s
from t h i s i n v e s t i g a t i o n , t o g e t h e r with r e s u l t s i n r e f e r e n c e s 10-12 and 19-21
were used t o approximate t h e r e l a t i v e ,:ontributions of v a r i o u s g l i d e r compon e n t s t o t h e t o t a l drag of t h e g l i d e r .
Cables: It i s d i f f i c u l t t o e s t i m a t e t h e a c t u a l d r a g of c a b l e s in t h e
v i c i n i t y of t h e g l i d e r . When t h e d a t a f o r i s o l a t e d c a b l e s from r e f e r e n c e 19
a r e used, a drag c o e f f i c i e n t of 1.0 per u n i t l e c g t h based on diameter appears
reasonable. For conventional u l t r a l i g h t designs t h i s may be expressed approximately a s :
of equivaient f l a t - p l a t e drag a r e a , o r about 0.08 m2 (0.86 f t 2 ) f o r a t y p i c a l
10-m (33-ft) span g l i d e r . The d a t a resented here must, t h e r e f o r e , be cotr e c t e d t o account f o r t h e large-diameter c a b l e s as follows:
Standard:
Model 2:
Model 3:
-0.0050
-0.0056
-0.0055
P i l o t and harness: Estimates of p i l o t and h a r n e s s drag from r e f e r ences 10 and 12 vary from 0.12 m2 (1.3 f t 2 ) t o 0.23 m2 ( 2 * 5 f t 2 ) . A f u l l s c a l e p i l o t drag a r e a of 0.21 m2 (2.3 f t 2 ) l e a d s t o t h e iollowing c o r r e c t i o n &
which must be added t o t h e model data:
Standard:
Wodel2:
Xodel 3:
0.0115
0.0110
0.0118
Cross bar: The drag of t h e c r o s s b a r v a r i e s with its d i s t a n c e from t h e
s a i l and with the l i f t c o e f f i c i e n t of t h e g l i d e r . A rough approxiaation t o
its drag i r o n reference 19 i s
Control frame: Approximately 0.186 n2 (2.0 f t 2 ) of p a r a s i t i c dray area
is due t o t h e c o n t r o l bar and ldngpost ( r e f . 19).
S a i l drag: The remaining drag on the g l i d e r is the viscous and induced
drag of t h e l i f t i n g surface. E d n a t i o n of section c h a r a c t e l ~ s t i c sin the
Reynolds nlrmber r m g e of 5x10' t o 1x10' ( r e f s . 19-21) shows t h a t p r o f i l e drag
v a r i e s rapidly with l i f t c o e f f i c i e n t (especially f o r t h i n sections). The drag
data obtained here f o r the second amdel is p l o t t e d v s cL2 i n f i g u r e 44. The
curve i s c l e a r l y not l i n e a r and much g r e a t e r success w a s achieved ir. f i t t i n g
data t o a three-paraaeter drag polar. This is p a r t l y due t o the l a r g e amount
of t w i s t i n these wings and p a r t l y t o t h e highly c d e r e d s e c t i o n s which
achieve minimm drag a t a r e l a t i v e l y high CL. This l a r g e lift-dependent
viscous drag makes the usual r e l a t i o n f o r drag: CD = C D +
~ c L 2 / n ~unsuit~
-
able over the large CL range i n which hang g l i d e r s operate, and d a t a wer+
f i t t o t h e form CD CDdn + K (CL - c
~ ( f i~g s . )45-48).
~
Apparent i n these f i g u r e s i s t h e influence of twist on drag (see espe, t w i s t produces a more
c i a l l y f i g . 44). In addition t o an increment i n CD
min
rapid increase i n drag with l i f t f o r t h e configurations t e s t e d here.
Fcr convenience i n data i n t e r p r e t a t i o n the drag p o l a r s f o r many configurat i o n s were f i t t o a three-parameter drag polar in t h e range 0.2 < CL < 0.8
and a r e susnsrarized below. (Note that C
has not been corrected f o r p i l o t
Dmin
o r oversized cables.)
Configuration
C
Dpia
K
CLo
-
0.44
.27
.28
.35
.30
-28
.21
-25
Cornpent s
0.45 <
< 1.1
6 config. avg.
Pitching mmentStandard: The v a r i a t i o n of C,,, with a is shown i n f i g u r e 25. Thc
highly nonlinear character of t h e curve is a t t r i b u t e d primarily t o deformation
of t h e f l e x i b l e sail. Figure 25 i n d i c a t e s t h a t a negative p i t c h i n g mosent is
present throughout t h e e n t i r e range of a tested. This is i n agreement with
results from references 1-7 and implies t h a t soclle *'bar pressure" corresponding
t o a rearward center-of-gravity s h i f t is required t o trim this g l i d e r a t the
desired CL. The slope of C, v s a changes s e v e r a l times throughout t h e
angle-of-attack range. During these t e s t s s i g n i f i c a n t changes i n s a i l shape
were observed t o coincide with d i s c a n t i n u i t i e s i n t h e pitching-mament curve.
Trailing-edge l u f f i n g began a t about 22", appearing a s high-f requency
motion of the t r a i l i n g edge from midspan t o t i p s . The l u f f i n g spread forward
and a t about 16" lau-frequency "rippling" extended t o t h e c r o s s bar. A t 13O
large-scale motion of the s a i l from t h e c r o s s bar, a f t , was observed w h i l e
the forward s a i l portion r d n e d i n f l a t e d . From 13' t o 10' t h e sail maintained t h i s general shape while t h e amplitude of t h e l u f f i n g increased. A t
about 10" t h e forward portion of t h e s a i l became s l a c k and a l s o experienced
large-scale l u f f i n g . From 10' t o 2' t h e s a i l was f u l l y l u f f i n g with l a r g e
amplitudes. The s a i l appeared t o l i e almost uniformly i n t h e plane of t h e
frame. A t about 2" t h e forward portion of t h e - s a i l began t o i n f l a t e on t h e
opposite s i d e of t h e f r a a e i n t e r m i t t e n t l y . By -2' i t had s t a b i l i z e d i n t h i s
position, forming a highly cambered surface between t h e leading edges and
cross bar while t h e s a i l a f t of t h e c r o s s bar remained l u f f i n g . The r e a r
portion of t h e s a i l continued t o l u f f extensively t o -25" where only highfrequency l u f f i n g of the t r a i l i n g edge persisted.
The pitching-moment: curve c l e a r l y r e f l e c t s these observed changes In s a i l
shape. The slope of C,
v s a increases a s t h e t r a i l i n g edge begins l u f f i n g ,
corresponding t o a decrease i n the l o c a l l i f t - c u r v e slope near t h e t r a i l i n g
edge. A s t h e e n t i r e r e a r portion of the s a i l begins l u f f i n g $ becomes
more positive.
The r e a r portion of the s a i l may be regarded a s analogous t o a h o r i z o n t a l
s t a b i l i z e r ; although "fixed1' under tension a t high CL, i t becartes unloaded a t
low-lift c o e f f i c i e n t s and is f r e e t o move downward. This corresponds t o a
"stick-free" horizontal c o n t r o l surface i n t h e analogy, with subsequent reduct i o n i n longitudinal s t a t i c s t a b i l i t y . When the forward s a i l p a r t begins t o
e n t e r global l u f f i n g , the r e a r s a i l i s no longer more "free" than t h e forward
s e c t i o ~since
~
t h e s a i l i n f r o n t of the c r o s s bar a l s o changes i t s incidence
with a. Thus, Cma becomes more nepative when t h e forvard s a i l a r e a begins
-.
l u f f i n g ( a t -10').
A t 2 " , when t h e s a i l begins t o i n f l a t e negatively near t h e
nose, t h e s t i c k - f r e e analogy again holds and
becomes positive. A s sail
teqsion a t t u e t r a i l i n g edge increases and l u f f i n g subsides, t h e g l i d e r
becomes "stable" again near -25".
The physical i n t e r p r e t a t i o n cf t h e n o n l i n e a r i t i e s i n pitching moment
a p p l i e s not only t o t h e standard configuration but t o many f l e x i b l e g l i d e r s
i n whtch s u f f i c i e n t sail slackness e x i s t s f o r large-scale l u f f i n g . The i n l t i a l d e s t a b i l i z i n g break i n C
due t o l u f f i n g occurs on many g l i d e r s
'Ra
although t h e subsequent i n c r e a s e i n s t a b i l i t y is o f t e n prevented w i t h t h e usa
of b a t t e n s and r o o t c a r which prevent forward a d 1 l u f f i n g . This i n c r e a s e
in s t a b i l i t y a t about 10' on t h e "etandard" i n t h e f u l l - l u f f i n g c o n d i t i o n may
r e s u l t i n a s t a b l e trim point a t law CL f o r s u f f i c l e n t l y a f t center-ofg r a v i t y p o s i t i o n s . Such s t a b l e " f u l l - l u f f dives" Prate reported w i t h t h e s e
e a r l y designs ( r e f s . 22-26) and, although t h e m e c h m i m was not f u l l y understood, c o r r e c t i v e measures have v i r t u a l l y eliminated t h i s probleae I n c u r r e n t
designs, a s seen i n pitching-mment d a t a f o r o t h e r models t e s t e d here.
Also apparent i n t h e pitching-aoment d a t a f o r t h e "standard" i s a l a r g e
nose-dawn moment a t stall. Tuft s t u d i e s I n d i c a t e t h a t t h i s is due t o leadingedge s e p a r a t i o n a t t h e higher CL w i t h s e c t i o n s j u s t inboard of midspan
s t a l l i n g f i r s t ( f i g . 14).
Models 2 and 3: Features of t h e pitching-moment curves f e r models 2
and 3 w i l l be discussed i n d e t a i l i n t h e following s e c t i o n s i n terms of t h e
e f f e c t s of c o n f i g u r a t i o n changes. I n general, t h e v a r i a t i o n of & with a
d i f f e r s g r e a t l y from t h e o r i g i n a l standard configuration. Lover sail f u l l ness, t h e use of b a t t e n s , r e f l e x , and fixed minim- t w i s t produce a much more
l i n e a r pitching-moment curve. Host of t h e s e c o n f i g u r a t i o n s were found t o be
s t a b l e and trimmed "hands-off" i n t h e d e s i r e d CL range, although considera b l e v a r i a t i o n s were produced with changes i n t w i s t and l u f f - l i n e arrangement.
C ~ Z C Cof mfemnce csnters/azes systems- The b a s i c r e f e r e n c e c e n t e r s
about which moments a r e measured i n t h i s r e p o r t a r e shown i n f i g u r e s 2-4.
These c e n t e r s correspond t o p i l o t t e t h e r p o s i t i o n s , the point a t which t h e
p i l o t ' s harness i s a t t a c h e d t o t h e g l i d e r . This p o i n t has been chosen h e r e
and i n many previous s t u d i e s ( r e f s . 10-12, 27, 28) s i n c e it corresponds
a p p r o x h a t e l y t o t h e g l i d e r ' s c e n t e r of r o t a t i o n when no p i l o t c o n t r o l f o r c e
is present. ?hat is, although t h e c e n t e r of g r a v i t y of t h e ->ilot-plus-glider
system is located below t h e k e e l , r o t a t i o n s occur about a point near t h e k e e l
i f t h e p i l o t i s f r e e t o swing about t h e t e t h e r point.
A measure of "hands-on" s t a b i l i t y , corresponding t o t h e c a s e in which the
p i l o t ' s p o s i t i o n is f i x e d with r e s p e c t t o t h e c o n t r o l b a r , is obtained from a
p l o t of % about t h e combined p i l o t and g l i d e r c e n t e r of g r a v i t y . In this
case t h e reference c e n t e r is located below t h e keel. As can be seen from
f i g u r e s 22 and 23 t h e two curves a r e s u b s t a n t i a l l y d i f f e r e n t . ( I n t h e s e f i g u r e s t h e reference p o i n t w a s f i x e d r e l a t i v e t o t h e g l i d e r a t t h e combined
p i l o t l g l i d e r c e n t e r of g r a v i t y , which was a s s m e d t o l i e 24.4 cm (3.6 i n . )
v e r t i c a l l y below t h e models' k e e l a t an angle of a t t a c k of 2 S 0 . ) The e f f e c t s
of t h e low-center-of-gravity p o s i t i o n a r e (1) increased s t a b i l i t y a t high CL,
2) somewhat l a r g e r C, (due t o drag), 3) decreased s t a b i l i t y a t negative
-
0
angles of a t t a c k .
Simple geometric c o n s i d e r a t i o n s show t h a t t h e v e r t i c a l 1 displaced c e n t e r
of g r a v i t y i n t r o d u c e s a p i t c h i n g moment which v a r i e s w i t h a1, i n c r e a s i n g t h e
s t a b i l i t y a t p o s i t i v e angles and c o n t r i b u t i n g l a r g e d e s t a b i l i z i n g nroments a t
negative angles. It i s p o s s i b l e t h a t t h i s e f f e c t is a major c o n t r i b u t o r t o
t h e "tmibling" phenoaenon discussed i n r e f e r e n c e s 12, 22, and 28 and c-tlly
reported with e a r l y high-performance hang g l i d e r s . The r a p i d nose-down
p i t c h i n g v e l o c i t y which may continue f o r s e v e r a l r o t a t i o n 8 begin8 v f t h an
encounter w i t h h negative v e r t i c s l gust o r gradient. I n r e f e r e n c e 12 the
cause of t h i s phenoaena i e described a s a s s o c i a t e d w i t h a e r o e l a s t i c &format i o n s of t h e s a i l vhich result i n l a r g e , negative p i t c h i n g moments when t h e
forward s a i l p o r t i o n collapses. R e s u l t s of the present i n v e s t i g a t i o n show
t h a t t h e n e g a t i v e value of t h e p i t c h i n g moment down t o -30° is comparable t o
t h a t i n t h e normal f l y i n g regime. The f a c t t h a t many of t h e hang g l i d e r s
which have reported t rnsbling problems used r e l a t i v e l y t i g h t sails, which would
not produce sudden nose-down moments a t negative a n g l e s of a t t a c k , a l s o indic a t e s t h a t another e f f e c t rnay be important. I n t h e observed c a s e s of tmmbling
with hang g l i d e r s " p i l o t s have maintained t h e i r g r i p on t h e c o n t r o l bar"
( r e f . 28) and t h e v e h i c l e i,. reference 22 v h i c h e x h i b i t e d t m b l i n g had a
c e n t e r of g r a v i t y fixed a t a point 25% of t h e k e e l l e n g t h below t h e keel.
The importance of v e r t i c a l center-of-gravity l o c a t i o n
t h e pitchingmoment c h a r a c t e r i s t i c s of t h e g l i d e r and t h e e f f e c t of r e f e r e n c e c e n t e r locat i o n on t h e appearance of moment d a t a i n d i c a t e s t h a t c a r e should be taken i n
drawing conclusions about s t a b i l i t y without c a r r y i n g out a dynamic analysis.
The United S t a t e s Hang Gliding Association has developed pitching-moment
requirements f o r g l i d e r c e r t i f i c a t i o n i n an apparently s u c c e s s f u l s e l f r e g u l a t i o n program. Among t h e s e e m p i r i c a l l y determined requirements is a
minimm pitching-moment c o e f f i c i e n t a t zero l i f t of 0.05 based on M C and
measured about t h e p i l o t t e t h e r point. The above c o n s i d e r a t i o n s i n d i c a t e why
such a l a r g e p i t c h i n g moment a t zero l i f t i s a reasonable requirement and why
demonstrated a b i l i t y t o recover from near-zero angle-of - a t t a c k c c n d i t i o n s ( a s
was once the requirement) is not s u f f i c i e n t t o ensure l o n g i t u d i n a l s t a b i l i t y .
~ 1 . )
.
Similar considerat ions apply t o t h e choice of r e f e r e n c e a x e s sys. as. A
wind-axes system, shown i n f i g u r e 10, was used t o d e f i n e t h e moments and
f o r c e s i n t h e report. l b o o t h e r r e f e r e n c e systems, o f t e n used i n tbe present a t i a n of wind-tunnel d a t a andlor dynamic a n a l y s e s , a r e t h e s t a b i l i t y - and
body-axes systems, shown i n f i g u r e s 65 and 66. I n t h e symmetric f l i g h t cond i t i o n i B = 0) no d i f f e r e n c e between these systems e x i s t s f o r l o n g i t u d i n a l
data. In g e n e r a l , however, major d i f f e r e n c e s appear f o r l a t e r a l c o e f f i c i e n t s ,
e s p e c i a l l y a t high angles of a t t a c k o r s i d e s l i p . The transformations between
t h e t h r e e systems f o r use i n comparing t h e s e d a t a w i t h r e s u l t s of o t h e r
s t u d i e s and i n f u t u r e dynamics work a r e included i n t h e appendix. Of s p e c i a l
i n t e r e s t i s t h e f a c t t h a t wind axes and s t a b i l i t y axes produce t h e same value
of yawing-moment c o e f f i c i e n t while body axes and s t a b i l i t y axes provide ident i c a l measurements of p i t c h i n g amment and s i d e force. When yawing--moment d a t a
a r e expressed i n body axes, a s i n r e f e r e n c e s 2 and 5, most g l i d e r s e x h i b i t
negative v a l u e s of CnB (usually i n d i c a t i v e of d i r e c t i o n a l i n s t a b i l i t y ) a t
higher a n g l e s of a t t a c k .
I n s t a b i l i t y and wind axes, however, C
appears t o
"0
increase w i i h a. Variation i n t h e appearance of l a t e r a l d e r i v a t i v e s v s angle
of a t t a c k , depending on t h e axes system chosen, i s demonstrated i n f i g u r e s 56
and 57, i n whlch l a t e r a l d e r i v a t i v e s a r e expressed in wind axes and body axes,
r e s p e c t i v e l y . Conclusions concerning the d i r e c t i o n a l s t a b i l i t y of t h e s e
g l i d e r s without a study of t h e dynamics cannot be made with c e r t a i n t y .
InfZwmce of changes h d
e pmsarre- C h t q e s In a a i l shape due t o
s t r u c t u r a l e l a s t i c i t y together with Reynolds-nubardependent flaw c h a r a c t e r
i s t i c s a r e expected t o produce c h a q e s i n aerodynaric c o e f f i c i e n t s with
dynamic pressure. Figures 19-29 i l l u s t r a t e t h e e f f e c t s of airspeed on t h e
c h a r a c t e r i s t i c s of models t e s t e d here. In a g r e e ~ e n twith previous f u l l - s c a l e
tests, p i t c h i n w e n t c o e f f i c i e n t appears t o b e most atrongly a f f e c t e d by
.hanges I n dynamic pressure. L i f t and drag c o e f f i c i e n t s do not ap?ear t o be
:f fected g r e a t l y i n the range of speeds employed here.
S i r i l a r e f f e c t s a r e observed with t h e second rodel. Larger v a r i a t i o n s i n
aerodynamic c h a r a c t e r i s t i c s with q appear in t h e d a t a a t lw angles of
a t t a c k . This is expected because of t h e r e l a t i v e l y f l e - ' b l e b a t t e n s wkase
shapes vary g r e a t l y with loading a t t h e angles where l u f r l i n e s a r e ef*.ective.
Monotonicity of p i tching-mment c o e f f i c i e n t changes v s q was investigated
and presented i n f i g u r e 29. I n these runs, a v a r i e t y of dynamic pressures was
used while the model a t t i t u d e was fixed. A t those angles tested, pitchingPoaaent c o e f f i c i e n t does not vary g r e a t l y with q, but a steady decrease i n the
magnitude of Cm is observed f o r a l l a - e s p e c i a l l y a t t h e lower angles
where luf f - l i n e s a r e i n tension.
with
lift
low
This
The t h i r d model exhibited l a r g e r v a r i a t i o n s i n aerodynamic p r o p e r t i e s
dyr.amic pressure throughout t h e range of angle of a t t a c k tested. Lower
c o e f f i c i e n t s a t given a and smaller pitching-moraent c o e f f i c i e n t s a t
CL were obtained a t higher tunnel speeds, a s shown i n f i g u r e s 21 and 28.
general trend a l s o appears in f u l l - s c a l e r e s u l t s .
Since "speed s t a b i l i t y " and "angle-of-attack s t a b i l i t y " a r e both d e s i r a b l e , i t is not possible t o i n f e r longitudinal s t a b i l i t y c h a r a c t e r i s t i c s by
inspection of a s i n g l e p l o t of C,,, v s a a t fixed q o r C, v s CL a t
fixed load. Although much can be s a i d from such d a t a , t h e importance of a
dynamic a n a l y s i s is again demonstrated.
Sepa*. $ion phenomena- The appearance of separated f l w on the models was
~,~b$erved
with t h e use of wool t u f t s attached t o t h e s a i l upper surface (and
lower surface i n some cases). Runs with and without t u f t s indicated t h a t
t h e i r presence had a n e g l i g i b l e e f f e c t on c o e f f i c i e n t data.
S t a l l behavior of the first model i s s\rmprarized i n f i g u r e s 14(a)-14(g),
which a r e traced from photographs of the t u f t e d model. Separation occurs
f i r t : t a t a sectioi-. near the midspan, spreading outward quickly. The root
sezt ion remi f s \ s attached t o very high angles.
S m t a t i o n from t h e second b a s i c configuration with a minimum of 24' of
n e g a t i v e t i p incidence (with respect t o t h e keel) begins a t t h e root chord and
s l c . 1 ~spreads toward t h e t i p s . The flow a t t h e wingtips remains attached up
t . a keel incidence of 39'.
This is primarily due t o t h e f a c t t h a t t h e t i p s
Arc allowed t o t w i s t under the applied loads and assuned a shape with a l a r g e
amciur.t of washout (>30°) a t t h e extreme angles of a t t a c k . However, even when
the washout w e b fixed a t 12', separation occurred f i r s t a t the r o o t , spreading more rspldly toward t h e t i p s a s a was increased. The process is shown
i n figure 15. Also apparent from these s t u d i e s is t h e e f f e c t of s i d e s l i p on
s t a l l c h a r a c t e r i s t i c s . Figure 16 i l l u s t r a t e s t h e eta11 behavior a t a s i d e s l i p
a n g l e of 20'. A s expected, the t r a i l i n g - w i n g s t a l l occurs at a much lower
a n g l e than t h a t of t h e leading wing, although t h e e f f e c t on the lateral deriva t i v e s does not appear s i g n i f i c a n t .
The t h i r d model demonstrated s i m i l a r s t a l l i n g c h a r a c t e r i s t i c s with a r o o t
s t a l l occurring a t 29'.
I n c r e a s i n g t i p washout w i t h a n g l e of a t t a c k prevented
t i p s t a l l up t o 40". Despite t h e l o v e r sweep angle, observed behavior i n t h e
s i d e s l ! -ping condition was s i m i l a r t o t h a t of model 2. On t h e t h i r d model,
t h e lower s u r f a c e of the s a i l was a l s o t u f t e d during one of t h e tests. The
s t i f f , highly cambered b a t t e n / r i b s which extended t o t h e leading edge of t h i s
model produced an a i r f o i l shape with pronounced lower-surface s e p a r a t i o n a t
a n g l e s of a t t a c k up t o 20°. The flow p a t t e r n i n f e r r e d from t u f t observations
is shown i n f i g u r e 18. Host of t h e lover-surface flow remains separated up
t o 5" where flow begins t o r e a t t a c h some d i s t a n c e a f t of t h e l e a d i n g edge.
Reattachment l o c a t i o n moves toward t h e leading edge as incidence is increased
with lower s u r f a c e s near t h e wingtips remaining separated up t o 20° (due t o
lower l o c a l incidence with washout).
The appearance of lower-surface s e p a r a t i o n suggests that s u t tantial performance l o s s e s may be a s s o c i a t e d with the use of p r o f i l e s s i m i l a r t o those
t e s t e d . Eppler ( r e f . 21) d i s c u s s e s th!s problem i n t h e design of a i r f o i l s
f o r use on u l t r a l i g h t g l i d e r s . In o r d e r t o obtain low-section drag a t high
CL and l a r g e maxifaun-lift c o e f f i c i e n t s , a l a r g e amount of camber i s required
on these t h i n s e c t i o n s . Since camber g e n e r a l l y c r e a t e s a l a r g e , n e g a t i v e
, a i r f o i l s w i t h l a r g e nose camber and r e f l e x appear d e s i r a b l e , y e t t h i s
L o
l a r g e nose camber r e s u l t s i n poor low-lift d r a g c h a r a c t e r i s t i c s . The s o l u t i o n
seems t o r e q u i r e t h e use of s e c t i o n s w i t h g r e a t e r thickness. Many r e c e n t
g l i d e r designs employ double-surface a i r f o i l s and may overcame t h e observed
d i f f i c u l t i e s i n obtainin; t h e required maximum l i f t , low-pitching moment, and
low-sec t i o n drags.
LutemZ data- The v a r i a t i o n of
C
afl
( e f f e c t i v e d i h e d r a l ) with angle of
a t t a c k is shown i n f i g u r e s 56-64.
~ h e s ecurves were obtained from tests a t
a f i x e d yaw angle of 20" a f t e r yaw runs showed ,hat t h e c o e f f i c i e n t s were
l i n e a r i n 0 up t o t h i s angle. A l l g l i d e r s t e s t e d showed a decrease in
C
with SL as expected from simple sweep theory with C
b e c m i n g posiaB
t~
t i v e a t low angles of a t t a c k . The l o s s of e f f e c t i y e d i h e d r a l a t l o w - l i f t
c o e f f i c i e n t s may be a t t r i b u t e d t o t h e l a c k of geometric d i h e d r a l combined w i t h
the high t w i s t of t h e s e wings. (At low angle of a t t a c k t h e s e c t i o n CL near
t h e t i p s i s negative. producing, according t o sweep theory, an adverse r o l l
due t o s i d e s l i p . ) This behavior has been reported i n r e f e r e n c e 12 and appears
t o be c h a r a c t e r i s t i c of a majority of hang-glider designs. The magnitude of
C
a t a given Ct is g r e a t e s t f o r model 1 and least f o r model 3, r e f l e c t i n g
Ra
th; expected dependence on sweep angle.
Figures 56-64 a l s o show t h e behavior of
Cn
B
, the
yawing-mueent coeffi-
c i e n t due t o s i d e s l i p d e r i v a t i v e , a s a function of incidence angle.
In t h e
chosen reference axes syrtem, C,
to a
of 0.8 and maintains t
CL
ha value of
C,
8
up t o 45'.
The t h i r d model
demonstrates'similar behavior with a roughly parabolic v a r i a t i o n of
CL
up
f o r the f i r a t model increases w i t h CL
through s t a l l but w i t h a generally lower value of
Cn
B
C
"8
than model 1.
wlth
The
second model's yaw s t i f f n e s s does not change monotonically with CL but
out t o s t a l l a s indicated in figmaintains a small p o s i t i v e value of
ure 5 9 .
Values of
f i g u r e 56.
Cn
cna
6
f o r m d e l 1 i n t h e body-axes system a r e given in
The v a r i a t i o n of C, with a a t 20° of s i d e s l i p is compared with t h e
The e f f e c t is model dependent and no general
syumetric data i n f i g u r e s 32-35.
conclusions a r e apparent from t h e d a t a expressed i n t h i s form. It should be
noted t h a t t h e p o s i t i v e increments i n C, due t o s i d e s l i p f o r t h e f i r s t model
appear a s negative increments a t t h e higher angles of a t t a c k when expressed i n
body axes, &gain i n d i c a t i n g t h e necessity of more thorough a n a l y s i s t o a s s e s s
t h e importance of these r e s u l t s . Coupling of longitudinal and l a t e r a l motion,
a s suggested by t h e change i n C, with 0, is a r e s u l t of a e r o e l a s t i c d i s t o r t i o n of the s a i l which changes t h e l i f t d i s t r i b u t i o n of the wing i n such a way
a s t o produce a (sometimes large) pitching moment. Reference 1 2 i n d i c a t e s
t h a t i n same cases a l a r g e nose-down pitching moment i s produced, increasing
t h e p o s s i b i l i t y of p i t c h divergence a t l o v CL. Results from s i m i l a r t e s t s
with the second model i n d i c a t e a l e s s important e f f e c t , while the pitching
moment of the t h i r d model appears s i g n i f i c a n t l y a l t e r e d a t 20" of s i d e s l i p .
I n f a c t , a s t a b l e ( i n a) C, = 0 point appears a t t h i s condition. The point
is not a c t u a l l y a t r i m point s i n c e C, is nonzero a t this a t t i t u d e and a corr e c t i v e yawing moment w i l l tend t o reduce 0 and hence increase k.
E f f e c t s of Configuration Changes
A major goal of t h i s experimental i n v e s t i g a t i o n was t h e a n a l y s i s of
e f f e c t s on the aerodynamic p r o p e r t i e s of u l t r a l i g h t g l i d e r s of various design
modifications. Full-scale t e s t s have shown t h a t r a t h e r l a r g e d i f f e r e n c e s
e x i s t i n d a t a obtained from g l i d e r s with very s i m i l a r geometries due t o d i f ferences i n s a i l and c a b l e tension, small v a r i a t i o n s i n s a i l shape, leadingedge s t i f f n e s s , e t c . D i f f i c u l t i e s associated v i t h e l a s t i c s c a l i n g of small
models may a l s o lead t o sod d i f f e r e n c e s between these r e s u l t s and t h e prope r t i e s of a p a r t i c u l a r f u l l - s c a l e vehicle. Conclusions drawn from comparative
s t u d i e s of modifications t o a b a s i c configuration a r e less a f f e c t e d by such
d i f f i c u l t i e s , and i t is believed t h a t general r e s u l t s obtained from these
model t e s t s w i l l be e s p e c i a l l y useful i n f u l l - s c a l e applications.
Washout- Figures 36-55 i l l u s t r a t e t h e e f f e c t s of various modifications on
t h e longitudinal c h a r a c t e r i s t i c s of models 2 and 3. I n these f i g u r e s , d a t a on
configurations 2A-P may be compared t o obtain an idea of the e f f e c t s of t w i s t
on l i f t , drag, and moment c h a r a c t e r i s t i c s of a t y p i c a l contemporary g l i d e r . A
primary e f f e c t of washout on t h i s swept wing i a , of course, on pitching
moment. When the minimtun washout of t h e t i p is constrained by a r j b fixed
t o t h e leading edge ( f i g . S), t h e p i t c h i n g moment a t low a n g l e s of a t t a c k i s
increased g r e a t l y . Fixing t h e incidence of t h e t i p a t a n g l e s below 20°, as is
accomplished by t h e " f l o a t i n g t i p " arrangement of c o n f i g u r a t i o n s 2A-D, H-Q,
a l s o Increases t h e g l i d e r ' s l o n g i t u d i n a l s t a b i l i t y i n t h i s range. A t higher
a n g l e s of a t t a c k t h e l o c a l t i p incidence i n c r e a s e s t o approximately 30' w i t h
respect t o t h e k e e l on t h i s model.
This condition prevents t h e t i p from
s t a l l + . n g , i n c r e a s e s t h e drag, and decreases C
The e f f e c t s of wing t w i s t
Lmax'
on l a t e r a l d e r i v a t i v e s were not evaluated s y s t e m a t i c a l l y i n t h e present study
but a l e believed t o be responsible f o r t h e l o s s of e f f e c t i v e d i h e d r a l d i s cur.s;d previously.
Lu;f lines- Luff l i n e s o r r e f l e x b r i d l e s a r e l i 5 e s connected t o a p o i n t
on t h r upper-wing s t r u c t u r e ( u s u a l l y t h e upper wires near t h e kingpost) and t o
t h e ends of one o r more p a i r s of b a t t e n s near t h e t r a i l i n g edge ( s e e f i g . 6).
A t normal f l y i n g a t t i t u d e s t h e t r a i l i n g edge of t h e s a i l l i e s above t h e plane
of t h e frame and l u f f l i n e s remain slack. A s t h e angle of a t t a c k i s decreased
t o very low and negative angles, t h e s a i l t r a i l i n g edge moves toward -he frame
plane and l u f f l i n e s t i g h t e n , preventing f u r t h e r displacement of t h e t r a i l i n g
edge. I f t h e b a t t e n s a r e f l e x i b l e , a l a r g e amount of r e f l e x o r negative camb e r i s produced along with a s t r o n g l y s t a b i l i z i n g (nose-up) p i t c h i n & moment.
Thus, a very l a r g e Cm
a t low and n e g a t i v e angles of a t t a c k i s achieved w i t h
0
a very small performance l o s s i n t h e normal f l i g h t regime. Luff l i n e s a r e now
incorporated on nearly a l l flexible-wing hang g l i d e r s and play a l a r g e r o l e i n
t h e e l i m i n a t i o n of t h e (once common) tumbling and high-speed s t a b i l i t y problems. Their e f f e c t s a r e i l l u s t r a t e d i n f i g u r e s 36-55. Luff-line l e n g t h
determines t h e angle a t which t h e i r e f f e c t s become important and, t o some
e x t e n t , t h e magnitude of Cm produced. Other f a c t o r s which appear t o a f f e c t
t h e i n f l u e n c e of l u f f l i n e s a r e i l l u s t r a t e d i n t h e f i g u r e s and include:
1) luf £ - l i n e b a t t e n s t i f f n e s s - g l i d e r s with l u f f l i n e s a t t a c h e d t o i n f l e x i b l e
b a t t e n s r e q u i r e l a r g e dynamic p r e s s u r e s t o produce r e f l e x and seem l e s s e f f e c t i v e i n generating C, ; 2) chord of b a t t e n t o which l u f f l i n e s a r e s t t a c h e d
0
-
l a r g e r chord l e a d s t o i a r g e r camber change f o r given b a t t e n s t i f f n e s s as w e l l
a s g r e a t e r c o n t r i b u t i o n t o g l i d e r C,;
3) spanwise l o c a t i o n of l u f f l i n e s and
model sweep - l u f f l i n e s which a r e located some d i s t a n c e fram t h e r o o t chord
on swept wings may increase t h e wing washout i n a d d i t i o n t o i n c r e a s i n g t h e
These f a c t o r s must be considered simultaneously i n t h e
local section's
evaluation of l u f f - l i n e e f f e c t i v e n e s s . For example, l u f f l i n e s l o c a t e d ne:r
the r o o t of a highly swept wing with r e l a t i v e l y s t i f f b a t t e n s nay reduce t h e
washout by holding t h e r o o t chord a t a more negative incidence w i t h r e s p e c t
t o t h e f i x e d t i p a n g l e , while producing l i t t l e r e f l e x change. I n g e n e r a l ,
however, c o n f i g u r a t i o n s s i m i l a r t o those conanonly flown employ l u f f l i n e s
v'lich a r e capable of generating C, of approximately +O. 1 t o +0.2.
.
Bat &enf l d b i l i t y - The e f f e c t of b a t t e n f l e x i b i l i t y on l o n g i t u d i n a l
c h a r a c t e r i s t i c s of t h e second model a r e shown i n f i g u r e s 37(b) and 51. The
primar;. impact of b a t t e n f l e x i b i l i t y i s t1,at a s s o c i a t e d w i t h l u f f l i n e s d i s cussed above. Batten s t i f f n e s s a l s o i n f l u e n c e s s e c t i o n camber ' i n t h e absence
of l u f f l i n e s . S t i f f e r ( s t r a i g h t ) b a t t e n s reduce s a i l camber and subsequent
v a r i a t i a n s i n C, and CL v s a a r e apparent i n f i g u r e s 37(b) and 51. Runs
a t high speeds w i t h t h e most f l e x i b l e b a t t e n s produced large-amplitude f l u t t e r
( d i s t i n c t from t h e aerodynamic l u f f i n g observed on t h e f i r s t model) and proh i b i t e d tests of t h i s configuration a t a l l but t h e l a r g e r angles of a t t a c k .
Ref Zex and r i b camber- S t e e l music wire (1/8-in.) r i b s with various
anaunts of r e f l e x and camber were s u b s t i t u t e d f o r f l e x i b l e b a t t e n s i n s e v e r a l
runs with Plodel 3. Results a r e presented i n f i g u r e s 40, 43, and 53. Data f o r
models with highly cambered s e c t i o n s show an increase i n drag a t low CL
associated 'with lower surf ace separation discussed previously. A higher
and lower drag a t h i g h - l i f t c o e f f i c i e n t s is obtained with this configuc
~
x
r a t i o n , however. Tests with r i b s having g r e a t e r nose camber and increased
with an a d d i t i o n a l
trailing-edge r e f l e x show t h e expected increase i n C
low-angle-of-attack
drag penalty.
mo
.%eep- A comparison of t h e r e s u l t s from models 2 and 3 demonstrates t h e
general e f f e c t of sweep on t h e s t a t i c longitudinal and l a t e r a l c h a r a c t e r i s t i c s
of these designs. Basic d i f f e r e n c e s l i e i n t h e method by which t h e l a r g e C,
required a t zero l i f t i s obtained. Highly swept g l i d e r s m y r e l y on t h e
pitching moment produced by t w i s t , while g l i d e r s with very low sweep must
employ s e c t i o n s which a r e highly reflexed a t low angles of attack. P a r t of
t h e motivation f o r designs with r e l a t i v e l y low sweep includes: 1) more
d e s i r a b l e s t a l l i n g c h a r a c t e r i s t i c s ; 2) lower t w i s t drag, i f required C
can
mo
be achieved without large washout; 3) p l a s t i c deformation of t h e t i p s ,
decreasing washout a t high speeds, and increasing wa: ~ u at t high angles of
a t t a c k w i l l not r e s u l t i n such d e s t a b i l i z i n g changes Ln pitching moment;
4) lower e f f e c t i v e d i h e d r a l a t high CL may improve l a t e r a l control. Higher
sweep designs e x h i b i t g r e a t e r d i r e c t i o n a l s t a b i l i t y and some washout may be
used t o simultaneously reduce t i p - s t a l l tendencies, produce C,
and improve
spanwise l i f t d i s t r i b u t i o n .
and
1'
1
~1
Performance comparisons show t h a t t h e second
Results of present t e s t s i n d i c a t e generally l a r g e r values of
C
n,
f o r t h e higher sweep model.
mo8el exceeded t h e maximum L/D of t h e lower sweep design. This i s a t t r i b uted t o two f a c t o r s . The a i r f o i l shape of t h e basic low-sweep configuration
was highly reflexed and cambered. Resulting lower surface separation
increased the p r o f i l e drag of t h i s design r e l a t i v e t o t h a t of t h e f l a t t e r s a i l
of model 2. Low leading-edge sweep a l s o reduces t h e e f f e c t i v e t o r s i o n a l
r i g i d i t y of t h e wing and without some leading-edge r e s t r a i n t , very l a r g e s a i l
tension i s required t o a t t a i n a " f l a t " s a i l . A s no r e s t r a i n t fixed t o t h e
leading edge was employed here, a r e s u l t i n g nonopt imal twist d i s t r i b u t i o n produced high induced drag and premature root s t a l l with correspondingly low
Therefore, these d a t a should not be used d i r e c t l y t o a s s e s s t h e r e l a C h X .
t i o n between sweep and p o t e n t i a l performance. It i s shown, however, that i t
i e not d i f f i c u l t t o obtain t h e required C, through t h e use of r e f l e x r a t h e r
than t w i s t .
o
S a i l fuZZnea8 ( b i Z h ) - No t e s t s were run i n which billow was systematic a l l y varied. Comparison of r e s u l t s from t h e standard configuration and t h e
second model i n d i c a t e t h a t much of t h e n o n l i n e a r i t y i n the aerodynamic
c h a r a c t e r i s t i c s of t h e s e a i r c r a f t i s a r e s u l t of larae sail f u l l n e s s . Higher
sail tension allows t h e g l i d e r t o approach more c l o a e l y an optimal apanwise
load d i s t r i b u t i o n and reduces t h e drag s u b s t a n t i a l l y a t low a n g l e s of a t t a c k ,
a s can be seen frocn f i g u r e s 45 and 46.
KeeZ pocketa- The second model was t e s t e d with and without a "keel
pocket ,'I s h a m i n f i g u r e 7. The k e e l pocket provides a means of a t t a c h i n g
t h e s a i l a t t h e keel i n such a way t h a t i t is f r e e t o s l i d e l a t e r a l l y as loading changes. This technique i s used t o decrease t h e r o l l damping. CQn. and t o
i n c r e a s e the e f f e c t i v e n e s s of t h e "weight-shift" c o n t r o l method. ~ l t & o u i~th
is intended t o change d q i n g d e r i v a t i v e s , i t s e f f e c t on s t a t i c d e r i v a t i v e s
was evaluated here ( s e e f i g . 52). Major changes i n t h e g l i d e r geometry w i t h
the a d d i t i o n of a keel pocket a f f e c t s t a t i c r e s u l t s a s follows: By reducing
the incidence of the root s e c t i c a with r e s p e c t t o the k e e l ( t o which a n g l e
of a t t a c k is r e f e r r e d ) the z e r o - l i f t incidence is increased. Because of
the reduced r o o t incidence, the t w i s t (washout) i s reduced a s t i p washout
c o n s t r a i n t r i b s were not a l t e r e d . The r o o t chord is r a i s e d o u t of t h e plane
of the frame which introduces approximately 2 * of anhedral. The k e e l pocket
a l s o adds some l a t e r a l a r e a a f t of t h e reference c e n t e r and thus a f f e c t s
directional stability.
Figure 42 i l l u s t r a t e s t h e i n f l u e n c e of t h e k e e l pocket on p i t c h i n g moment
vs CL. The increment i n pitching-moment c o e f f i c i e n t a t low
t h e f l e x i b l e r i b s e c t i o n and trailing-edge support wire ( f i g . 7 which
is duea c t i n
a manner s i m i l a r t o l u f f l i n e s . A l a r g e amount of r e f l e x i s produced a t t h e
root chord a s t h e t r a i l i n g edge i s held f i x e d and t h e (negative) camber of t h e
f l e x i b l e r i b i n c r e a s e s under negative load. The s h i f t i n Cm curve a t t h e
l a r g e r values of CL and t h e higher CL
due t o reduced t w i s t a r e apparent
max
i n f i g u r e 50. L a t e r a l d e r i v a t i v e s vary i n t h e manner shown i n f i g u r e 65.
Included i n t h i s d a t a i s a small i n c r e a s e i n C
due t o anhedral. The value
i
s
not
measurably
changed.
Of
CnB
Dihedral- The l o s s of e f f e c t i v e d i h e d r a l a t low angles of a t t a c k
(CLg > 0) suggests t h a t t h e incorporation of geometric d i h e d r a l might improve
t h e l a t e r a l c h a r a c t e r i s t i c s of g l i d e r s a t high speeds. T h e o r e t i c a l considerat i o n s a l s o suggest t h a t t h e low values of C
might be increased with
"6
d i h e d r a l . These ~ s s e r t i o n swere t e s t e d by introducing 3.5" of d i h e d r a l (per
s i d e ) t o t h e second and t h i r d models. Figures 34, 35, and 61--4 surm~arlzet h e
r e s u l t s . The general conclusion from these d a t a is t h a t t h i s amount of geometric d i h e d r a l i s i n s u f f i c i e n t t o s i g n i f i c a n t l y a l t e r e i t h e r
8 In
C1fi Or
t h e d e s i r e d range of l i f t c o e f f i c i e n t s . Figure 53 i n d i c a t e s t h a t t h e inclusion of t h i s amount of d i h e d r a l does decrease t h e angle a t which C
becomes
20
p o s i t i v e (by approximately 5') but t h e c h a r a c t e r of t h e curve remains
unaltered. A small e f f e c t on t h e p i t c h i n g moment c o e f f i c i e n t a t 20' of
s i d e s l i p i s i n d i c a t e d i n f i g u r e s 34 and 35 b u t , again, t h e e f f e c t is small.
Comparison with Previouo Work
Results of f u l l - r c a l e wind-tunnel t e a t s of varlouo configurations
reported i n references 1-12 and 17 agree well with tho- prenented here.
f o r mcdel I l i e w e l l within t h e range of values
Values of C
and CL
Lpax
u
obtained i n these investigatione. The general c h a r a c t e r i s t i c s of pitching
moment v s angle of attack-are observed i n each of t h e s t u d i e s I n t h e range in
which d a t a a r e a v a i l a b l e , although some d i f f e r e n c e s art expected i n l i g h t of
d i s s i m i l a r i t i e s , i n p a r t i c u l a r model construction methods.
Although most of t h e data a v a i l a b l e f o r comparison are found i n NASA
r e p o r t s on designs s i m i l a r t o t h e standard configuration, some r e s u l t s f o r
more contemporary designs a r e a v a i l a b l e (refs. 10-12). The e f f e c t s of l u f f
l i n e s and fixed t w i s t r i b s have been investigated previously i n tests of production g l i d e r s using "t e s t vehicles." Gliders a r e mounted on automotiSes or
on c a r r i a g e s i n f r o n t of t h e c a r and simple balances used t o determine t h e
pitching moment a t a given angle of incidence. A sample of such d a t a is shown
i n f i g u r e 35, kindly provided by M r . T m P r i c e , former president of t h e Hang
Glider Manufacturers Association. The b a s i c behavior of C, v s a a s
a f f e c t e d by l u f f l i n e s and fixed t i p s a l s o appears i n t h e wind-tunnel tests of
f i g u r e 49(a), although t h e data a t negative angles of a t t a c k d i f f e r . This
d i f f e r e n c e i s probably due t o t h e influence of the large keel pocket with
f l e x i b l e root batten of configuration 2E which increases t h e root r e f l e x a t
low CL; t h i s was not incorporated i n t h e configuration of f i g u r e 55. Differences i n moment reference center a l s o contribute t o this discrepancy.
i s observed between t h e present t e s t s and
c~,x
the data i n references 10 and 11. Although t h e value of
for the f i r s t
Some disagreement i n
model i s i n good agreement with previous d a t a , values of
C - ~C
x
f o r the
Lmax
second and t h i r d models appear lower than expected. The discrepancy i s part i a l l y due t o the d i f f i c u l t y of producing "clean," r i p p l e s s s a i l s a t these
small scales. Such imperfections may lead t o e a r l y separation. The somewhat
lower Reynolds number involved i n these t e s t s might be expected t o reduce
C
while values i n reference 10 may be overestimated due t o l a r g e blocking
Lmx
effects.
A comparison of l a t e r a l d e r i v a t i v e s measured here and i n references 2 , 3,
8, and 12 f o r t h e standard configuration i n d i c a t e t h e same general behavior
with angle of attack. Differences a r e due p a r t l y t o small differences i n
reference center location with i n s u f f i c i e n t information a v a i l a b l e t o r e l a t e
a l l data t o t h e same reference a s w e l l a s d i f f e r e n c e s i n t h e individual model
geometries (see f i g . 56).
S t a t i c l o n g i t u d l n o l and l a t e r a l aerodynem?~c h a r a c t e r i s t i c s of 27 v a r i a t i o n s of 3 b a s i c u l t r a l i g h t g l i d e r c o n f i g u r a t i o n s v e r e determined from windtunnel t e s t s of 115-size, e l a s t i c a l l y s c a l e d models. The importance of sweep,
t w i s t , l u f f l i n e s , b a t t e n f l e x i b i l i t y , r e f l e x , k e e l pockets, and d i h e d r a l a r e
discussed a s they r e l a t e t o t h e d a t a obtained here. Modern g l i d e r configurat i o n s e x h i b i t much more s t a b l e and l i n e a r pitching-moment c h a r a c t e r i s t i c s than
o l d e r Rogallo designs which a r e shown t o have p o t e n t i a l l y dangerous charact e r i s t i c s a t low angles of a t t a c k . Fixing t h e c e n t e r of g r a v i t y v e r t i c a l l y
below t h e keel may produce l n r g e d e s t a b i l i z i n g moments a t negative angles of
a t t a c k and may c o n t r i b u t e t o t h e p o s s i b i l i t y of tumbling.
Differences i n t h e appearance of l a t e r a l d e c i v a t i v e s depending on choice
of r e f e r e n c e axes system a r e important f o r t h e s e gliders which f r y at
unusually l a r g e angles of a t t a c k , thus demonstrating t h e need f o r a f u l l
dynamic a n a l y s i s i n t h e assessment of g l i d e r ~ t a b i l i t y . V a r i a t i o n s of yitchi n g moment w i t h s i d e s l i p and dynamic pressure complicate t h e a n a l y s i s of
l o n g i t u d i n a l s t a b i l i t y but a r e important f o r some of t h e s e configurations.
A l l g l i d e r s t e s t e d demonstrated a l o s s of e f f e c t i v e d i h e d r a l (associated w i t h
p o s i t i v e values of Cg ) a t low a n g l e s of a t t a c k . This i s a t t r i b u t e d t o t h e
B
i n f l u e n c e of sweep and t w i s t on C
and t h e l a c k of geometric d i h e d r a l .
The d a t a presented here a r e intended t o provide s o w b a s i c information on
t h e aerodynamic c h a r a c t e r i s t i c s of modern hang g l i d e r s and t h e e f f e c t s of
v a r i r u s design modifications. Results form a base of empirical d a t a from
which a n a l y t i c a l work on s t a b i l i t y and c o n t r o l , necessary f o r a c o r r e c t i n t e r p r e t a t i o n of t h e s e d a t a , may proceed. Such work, planned f o r f u t u r e publicat i o n , involves t h e development of more r e f i n e d performance and s t a b i l i t y
p r e d i c t i o n methods i n a form which may be used i n the design of s a f e r and more
e f f i c i e n t ultralight gliders.
APP WDIX
TRANSFORMATIONS BETWEW AXES SYSTgEiS
The following relations may be uaed to transform the data (expressed i n
t h i s report i n wind axes) t o s t a b i l i t y or body axes. (Note that b$ = Ms
while NS = Nw.)
LB = 4J
-
D~ ' 45
YB
YW cos 0
MB = k+
COB
0
tB =
-MW s i n
NB =
-%
- 41 s i n B
+ % sin 0
0 cos a + % cos
0 cos n
- NW sin
+ % cos
0 sin a
+ NW cos
sin 0 sin a
Ls ' LW
Ds = l'w
YS = YW
%
=
COB
0
- I+,
% cos 6 + gw
as = -% s i n 0
Ns ' NW
+
s i n f3
sin
B
cos B
a
REFERENCES
1.
Polhamus, E. C.; and Naeseth, R. L.:
Experimental and T h e o r e t i c a l S t u d i e s
of t h e E f f e c t s of Careber and Twist on t h e Aerodynamic C h a r a c t e r i s t i c s
of Parawings Having Nominal Aspect R a t i o s of 3 and 6. NASA 'IN 11-972,
1963.
2.
E f f e c t s of Aspect Ratio and Canopy Shape on Low-Speed AeroBugg, F. M.:
dynamic C h a r a c t e r i s t i c s of 50 Swept Parawings. NASA TN D-2922, 1965.
3.
Naeseth, R. L.; and Gainer, T. G..
Low-Speed I n v e s t i g a t i o n of t h e E f f e c t s
of Wing Sweep on t h e Aerodynamic C h a r a r r ~ r i s t i c sof Parawings Having
Equal Length Leading Edges and Keel. NASA TN D-1957, 1963.
4.
Johnson, J. L., J r . , and Hassel, J.: Full-Scale Wind Tunnel Investigat i o n o f a Flexible-Wing Manned Test Vehicle. NASA "iN D-1046, 1963.
5.
Job ?on, J. L . , J r . : Low-Speed Wind Tunnel I n v e s t i g a t i o n t o D e t e m i x e
t h e F l i g h t C h a r a c t e r i s t i c s of a Model of a Parawing U t i l i t y 7ehicle.
NASA TN D-1255, 1362.
6.
Johnson, J. L., Jr.: Low-Speed Force and F l i g h t I n v e s t i g a t i o n s cf a
Model of a Modified Psrawing U t i l i t y Vehicle. NASA TN D-2492, 1965.
7.
T u r n e l l , J. A , ; and Nielsen, J. N . :
Aerodynamics of F l e x i b l e Wings a t
Low Speeds, P a r t IV - E ~ ~ e r i m e n t Pr-gram
al
and Comparison w i t h Theory.
VIDYA Report No. 172, Feb. 1965.
8.
Chambers, J.; and Iioisseau, P.: A a e o r e t i c a l Analysis of t h e Dynamic
L a t e r a l S t a b i l i t y and Control of a Parawing Vehicle. NASA TN 0-3461,
1966.
9.
Kroo, I. ; and Chang, L. : A n a l y t i c a l and Scale-Model Research Aimed a t
Improved Hang Glider Design. Proc. of t h e Third I n t e r n a t i o n a l Symposium on t h e Technology and Science of Low-Speed and Motorless F l i g h t .
NASA CP-2085, 1979.
1
Ormiston, R.:
Wind Tunnel Tebts of Four F l e x i b l e Wing U l t r a l i g h t Gliders.
NASA CP-2085, 1979.
1:.
Experimental Study of t h e k l i g h t Envelope and Research of
LaBurthe, C.:
S a f e t y Requirements f o r Hang Gliders. NASA CP-2085, 1979.
12.
LaBurthe, C.; and Walden, S.:
l e g e r s de formule ROGALLO
ONERA RT 815134 SY, 1978.
13,
G i l l i s , C.; Polhamus, E.; and Gray, J.: C h a r t s f o r Determining JetBoundary Corrections f o r Complete Models i n 7-by-10 Foot Closed
Rectangular Wind Tunnels. NACA ARR L5G31, 1945.
Etude d e s e c u r i t e s u r des planeurs u l t r a e t mecanique du v o l .
- Aeroilynamigue
b t t o f f , S.; and Rannah, H.: Calculation of Tunnel-Induced Upwash Veloct t i e a f o r Sktcpt and Y
d Wings. NACA 'LN-1748, 1948.
Weinberg, .I.: Wind Tunnel Wall Corrections i n the h e r 7-by-10 Foot Wind
Tunnels. km f o r P i l e s , NACA h e s Aeroruutlcal Laboratory, 1950.
Pope, A.; and Harper, J.:
Inc., 1966.
Lou-Speed W i n d Tunnel Testing.
Wiley and Sons,
i n * ~ e e t i g a t i o acf t h e Steady-State
R i g m a t i , N.; and Pflugehaupt, H.:
Behavior of l k o Delta-Wing Hang Gliders. NASA TT F-17394, 1977.
Theoretical and Rxperimental Aerodynarics of an E l a s t i c
Ormiston, R.:
Sailwing. Ph.D. Thesis, Dept. of Aerospace and Xechanical Sciences,
Princeton Univ. , I%?.
Hoerner, S.:
Fluid Dpnaric Drag, Pub. by Author, 1965.
Schmitz, F.: Aerodynaaics of t h e Xodel Airplane.
Measurements. Berlin, 1942.
P a r t I, A i r f o i l
Eppler, K.:
Same New A i r f o i l s . In: Tech. and Science of Low Speed and
Hotorless Flight. NASA CP-2085, 1979.
Libby, C.; and Johnson, J.:
Parawing Airplane Model.
S t a l l i n g and Tumbling of a Radio-Controlled
NASA TN D-2291.
P h i l l i p s , W. H.: Recovery from a V e r t i c a l Dive.
Hang Gliding), Aug. 1975.
P h i l l i p s , U. H.:
N o v . 1975.
Ground S u e r (now
More on Dive Recovery o r Lack Thereof.
Ground S k i m e r ,
S t a b i l i t y and Control of Hang Gliders. Paper presented
P h i l l i p s , W. H.:
a t Society of Automotive Engineers Meeting, Sept. 1976.
Jones, R. T.: Dynamics of U l t r a l i g h t A i r c r a f t - Dive Recovery of Hang
Gliders. NASA 2M(-73229, 1977.
Valle, G.:
Flight Testing f o r HGIYA C e r t i f i c a t i o n and HGHA Specification
and Compliance Program. Hang Gliding, Jan. 1977.
A Preliminary Analysis of t h e Longitudinal Dynamics of UltraValle, G.:
l i g h t Gliders. Hang Gliding, March 1979.
TABLE 1.- DESCRIPTION OF CONFIGURATIONS
Conf iguration
planform
B.sic
I
geometry
Tip
1
1
Standard.
( f i g . 2)
2A
30° sweep 21° min t i p
(fig. 3)
washout
2B
24' min t i p
washout
i
1
1
2C
2D
i
2E
.
i
I
i
Bat t e n s
I
2H
21
2J
None
No
No
Spruce
To f i r s t
b a t t e n set
Yes
No
To f i r s t
b a t t e n set
None
21" min t i p
washout
No f i x e d
twist t i p s
I
To f i r s t
b a t t e n set
Shortened
luff lines
9
24' min t i p
washout
To f i r s t
b a t t e n set
Cambered r i b s
replace batten
set 2
F l e x i b l e plast i c b a t t e n s !.n
s e t s 1, 2, 3
Plastic battens
i n set 1; spruce
i n sets 2 and 3
2K
Rigid cambered
r i b s sets 1 , 2 . 3
2L
Spruce
2M
Kee 1
Ipocltet Dihedral
None
2F
2G
Luff
lines
I
I
I
I
I
I
I
t
i
I
No
Plastic battens
set 1
2N
Spruce
I
To 2nd
b a t t e n set
I
t
NOTES :
1. Batten sets a r e numbered from t h e root with the p a i r of b a t t e n s c l o s e s t
t o the root labeled B e t 1.
2. Tip t w i s t is measured w.r.t t h e keel reference; t h e l a r g e keel pocket
produces a 9' angle between root chord and keel.
3. Since dihedral w a s added by simply lengthening t h e lower wires and
tightening t h e upper wires, some a d d i t i o n a l billow was introduced. This is
r e f l e c t e d i n t h e drag data.
Figure 2
conf
.- Model 1 "rtandardcharacterieticr.
fguration" planfonn and geoaatr ' c
ft)
WING:
Figure 3.- Model 2 planfonn and geometric characterletice.
,..,
'
,
..
., .
. '.'*
I
.. . nn*
'
Figure 6 . - Luff l i n e geometry.
:
luff lines
l u f f line8
with l u f f
lGI.
angler of attack
s a i l shape a t p o ~ i t i v e
i'..'d:3,UP
,'-
tb(klR I?.
A ~m
P
:
..
1.1)
i.,F.,,,-,s
-
.
>.\
-
:,isr t ~ f t p . ~ Lt ~ B ~ I I s.t . 1 1 1 ~ 1 . t t - dL : L ~ I ~i p l r . 1 ~
ion.
(d)
F i g n r t - 14
1
= 35."
.- Cnntinucd.
(0
= 3S.b
Figure 1 4 . - C o n t inucd
.
..
...
8
$.*
4
4..
-1.
4
* e.
*'
r r *.
8
-.
P4
1 1
*
i
.
-8.
%
.
E
d
o m m m s
N * U m m
~ a ) f i h r n
c
0
r(
U
-.2,
M'
v*
q b
2
8
.
C O O
(d
LC
. O N 0
"-cOddN
r(
0 0 . .
II
I1
II
I1
1
M
tu
c
It
0
cl
a - u u - W C r
am
0
. a +x n
51
%a
?
..
v
.4
2
3
t.
t
C
cl
0
C
.
0
aJ
I :
-1
U
Id
1
i
.a
1
-
0
U?
4
d
m
.
[O
.c
Q)
-
0
4
I
Ln
.
$
4'
a
L.r
a
U
ii*.
C
'0
0
'b
r-l
I
tu
'
0
U
U
aJ
(c;
u
W
I
4 b
F:
I
0\
4
aJ
Id
%
rl
*
R
1
.
Cr.
-
k
t
.:tr
i
,8
t*.
-- b-,L
'
4
e
-...t..:
I
M--
3
psf
C
N/mL
-
4
.6
,
4 b
i'
t'
h
t
i
#4.
I
.2
:I'b
a.
/"
0;;
4
,-),
/
h
a
a;:' ;
. I
-.
1c*
:,I;i
.Y&
-10
#, ,
$
M
40
I *
a/;:
'
-,2
+!,;
..
:
'&'
I .
tie.'
' I '
a;!
74
*
..
,.
;;*;.'
,,
,'
J
'
B'
,
,
a
t:i
t
1.
::'I :
,i
;
,
f
Conf ig. 2H
.
;:/
;I
;
' #'/;
r:t:
;I
-,6.,
./?
,
I
'
'
'
I
4' ,;
.!
.:
Figure 20.- Effect of dynamic pressure on CL
56
vs
a, configurstion 2H.
x/mL
Figure 22.- Effect of
psf
q
on drag, configuration 1.
Config. 1
Pig. 58
.
W A R ISON OF LATERAL MTA
W I T H PREVIOUS WORK
REF, 3
+ REF, 2
0 REF. 8
4 REFe 12
X THIS REWRT
1C
3
20
40
58
a
Figure 56.- Cornpariron of lateral data with previous work.
9L
C
"6
4-
- -
f-
-
+
Config. 2N
WITHOUT DIHUlRAL
X
WITH
Config.DIHEDRAL
24
+
+-
- - a .
-t
x
Figure 61.- Effect of dihedral on lateral derivatives.
99
Symbol
+
0
vith
(
pocket
i
Figure 62.- Effect of keel pocket on lateral characterietics.
from yaw sweepa.)
Conf ig.
2K
q(psf)
2N
5.
A
(Derivatives
10.