Fletcher, Herman S

Jaquet, Byron M

English

NASA Technical Reports Server

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NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS 
TECHNICAL NOTE 3843 
EXPERIMENTAL STEADY-STATE YAWlliG 
DERN ATNES OF A 600 DELTA-WING MODEL AS AFFECTED BY 
CHANGES IN VERTICAL POSITION OF THE WrnG AND rn RATIO 
OF FUSELAGE DIAMETER TO WJNG SPAN 
By Byron M. Jaquet and Her man S. TIetcher 
Langley Aer onautical Laboratory 
Langley Field, Va. 
~ 
Was hington 
October 1956 
r 
https://ntrs.nasa.gov/search.jsp?R=19930084620 2020-06-17T19:00:58+00:00Z

D 
NATIONAL ADV~SORY COMMITTEE FOR AERONAUTICS 
TECHNICAL NOTE 3843 
EXPERIMENTAL STEADY-STATE YAWING 
DERIVATIVES OF A 600 DELTA-WING MODEL AS AFFECTED BY 
CHANGES IN VERTICAL POSITION OF THE WING AND IN RATIO 
OF FUSELAGE DIAMETER TO WING SPAN 
By Byron M. Ja~uet and Herman S. Fletcher 
SUMMARY 
An investigation was made in the Langley stability tunnel to deter-
mine the effects on the steady-state yawing derivatives of the vertical 
position of the wing for a 600 delta-wing model having ratios of fuselage 
diameter to wing span of 0.123, 0.165, and 0.246. The test Mach number 
was 0.13 and the Reynolds number was 1.65 X 106 . The results of the 
investigation indicated that for angles of attack below the stall the 
steady-state damping in yaw decreased (the values of the yawing-moment 
coefficient due to yawing became less negative) when the wing was raised 
from a low to a middle or high position on each of the three fuselage 
sizes investigated. With the vertical tail on or off, the steady-state 
damping in yaw increased with an increase in fuselage size. The results 
of calculations of the oscillatory damping in yaw for the model with the 
large fuselage indicated that the effects of wing position would be oppo-
site to those determined under steady-state conditions. For angles of 
attack below the stall, raising the wing produced a positive increment in 
the rolling moment due to yawing, and fuselage size had little effect on 
this parameter. 
INTRODUCTION 
Preliminary stability analyses of new airplane designs are, in many 
cases, made with stability derivatives which have been estimated by vari-
ous means, such as in reference 1 . As shown in references 2 and 3 the 
degree of accuracy of some of these estimated derivatives is always a 
matter of Question; this is especially true in the moderate and high 
ranges of angle of attack or when a design departs from a simple body of 
revolution (ref. 4). Experience has shown, however, that in order to 
obtain more accurate estimates of the dynamic stability of a given deSign, 
it is necessary to use stability derivatives which are determined 
experimentally. 
2 NAeA TN 3843 
The present experimental investigation was undertaken, as a con-
tinuation of the work of reference 5, to show some effects of airplane 
design variables on the lateral derivatives of airplane models; namely, 
the effects on the steady-state yawing derivatives of changes in verti-
cal position of the wing for a 600 delta-wing model having ratios of 
fuselage diameter to wing span of 0.123, 0.165, and 0.246. The deriv-
atives were obtained at a Mach number of 0.13 and a Reynolds number 
of 1.65 X 106 • 
SYMBOLS 
The data presented herein are referred to the stability system of 
axes shown in figure 1. The center of gravity was located at the pro-
jection of the wing 0.25 mean aerodynamic chord on a plane passing 
through the fuselage center line of each model. The coefficients and 
symbols used herein are defined as follows: 
b 
S 
c 
c 
p 
lift coefficient, Lift qs 
side-force coefficient, Side force 
<lS 
rolling-moment coefficient, Rolling moment 
qSb 
yawing-moment coefficient, Yawing moment 
qSb 
wing span, ft 
wing area, sq ft 
local chord parallel to plane of symmetry, ft 
l b / 2 mean aerodynamic chord, ~ 0 c2dy, ft 
dynamic pressure, py2 ~, lb/sq ft 
mass density of air, slugs/cu ft 
NACA TN 3843 
v 
y 
(l, 
f3 
t 
~ 
r 
rb 
2V 
Cyr 
Cl = r 
CIlr = 
• - £§. 
f3 - dt 
dCy 
~ 
2V 
dCl 
~ 
2V 
dCn 
()rQ 
2V 
airspeed, ft/sec 
spanwise distance measured from and perpendicular to plane 
of symmetry, ft 
angle of attack of fuselage center line, deg 
angle of Sideslip, radians 
time, sec 
angle of yaw, radians 
yawing angular velocity, d~/dt, radians/sec 
yawing-angular-velocity parameter, radians 
= (dCn) _ (~) (}!:Q ~ 
2V (j) 2V (j) 
3 
4 NACA TN 3843 
Subscripts: 
~ .. 
ill measured under oscillatory conditions 
v vertical tail 
APPARATUS, MODELS, AND TESTS 
The tests of the present investigation were made in the 6- by 6-foot 
curved-flow test section of the Langley stability tunnel, in which the 
airstream is curved about a strut-supported model in order to simulate 
an airplane in curved flight. (See ref. 6.) The strut was rigidly 
attached to an electromechanical balance system. 
The models used for the present investigation consisted of a 
3-percent-thick, 600 delta wing mounted in a low, middle, or high posi-
tion on each of three fuselages which had ratios of maximum fUselage 
diameter to wing span of 0.123, 0.165, and 0.246. The fUselage fineness 
ratios corresponding to the ratios of fuselage diameter to wing span 
were 12, 9, and 6, respectively. The length of each fUselage was 
54.00 inches. A single vertical tail was common to all configurations, 
and this was the vertical tail designated as V3 in reference 5. Since 
the fuselage diameter at the base varied when the ratio of fuselage diam-
eter to wing span was changed, the overall span of the vertical tail 
also varied. The exposed area of the tail, however, was approximately 
the same for all models. The models did not have a horizontal tail. A 
drawing of the models is presented as figure 2, and additional data may 
be obtained from table I and from reference 5. 
In order to obtain the steady-state yawing derivatives, the models 
were tested, tail on and off, through a range of angle of attack from _40 
to 360 at values of ~~ of 0, -0.0316, -0.0670, and -0.0881. The angle of 
sideslip was 00 for all tests. The Mach number was 0.13, and the Reynolds 
number was 1.65 X 106 • 
CORRECTIONS 
The angle of attack was corrected for the effects of the jet bound-
aries by the methods of reference 7. Corrections were applied to the 
derivatives to account for the pressure gradient associated with curved 
flow. (See ref. 6.) Blockage corrections were considered to be neg-
ligible and hence were not applied. The effects of the support strut on 
NACA TN 3843 5 
the derivatives were not determined but, on the basis of past experience~ 
they were not expected to influence the accuracy of the data presented 
herein. 
RESULTS AND DISCUSSION 
Presentation of Results 
The relation between the angle of attack and the lift coefficient 
is presented in figure 3 for each configuration. The effect of the verti-
cal position of the wing on the steady-state yawing derivatives for the 
model with each of the three fuselage sizes is shown in figure 4 with 
the vertical tail on and in figure 5 with the vertical tail off. The 
effects of the wing position and the fuselage size on the value of Cr 
and CDr at an angle of attack of 00 are summarized in figure 6. 
Effect of Wing Position and Fuselage Size on 
The effects of vertical position of the wing on the derivatives 
r 
C~ (figs. 4 and 5) and -C l (ref. 5) are similar in the low and mod-r ~ 
erate ranges of angle of attack since an upward displacement of the wing 
produces a positive increment in these derivatives. In the low range 
of angle of attack, the data of figures 4 and 5 indicate that an increase 
in the ratio of fuselage diameter to wing span increases the magnitude 
of the effect on Cr
r 
produced by raising the wing. However, the data 
of figure 6, where the derivatives Crr and CDr are plotted against 
the ratio of wing height to wing span, indicate that only a small part 
of this increase is caused by the increase in fuselage diameter since 
the variation of Cl with ratio of wing height to wing span was about r 
the same for all fuselage sizes. The major increase in Crr was caused 
by the increased wing height in terms of wing span since the ratio of 
wing height to fuselage diameter was 0.333 for all models. The tail 
contribution to C~r decreases slightly as the wing is moved from the 
low to the middle or high position and is essentially unaffected by 
changes in fuselage size (fig. 6). For the range of wing positions and 
fuselage sizes investigated, the value of Crr near ~ = 00 varies 
linearly with changes in wing position. 
6 
Effect of Wing Position and Fuselage Size on 
With the tail on and for angles of attack below the 
the wing decreases the value (becomes less negative) of 
increasing the fuselage size increases the value of Cnr 
NACA TN 3843 
stall, raising 
Cnr, and 
( fig. 4). Wi th 
the tail off, the effects of the wing position are smaller and somewhat 
different from the tail-on results in the low range of angle of attack 
inasmuch as the midwing position has the least value of Cnr 
(figs. 5 and 6) and the high and low positions have values of Cnr which 
are nearly e~ual for a given fuselage size. With the tail off (fig. 5), 
the effects of fuselage size on Cnr are similar to those with tail on. 
The tail contribution to Cnr decreases as the wing is raised and 
slightly increases as the fuselage size is increased (fig. 6). 
Comparison of Steady-State and Oscillatory Damping in Yaw 
The results of an investigation of a 450 swept-wing model (ref. 8) 
have indicated that raising the wing increased the damping in yaw deter-
mined under oscillatory conditions Cnr,m - Cn~,m' whereas in the present 
investigation the steady-state damping in yaw Cnr , as determined from 
curved-flow tests, decreased when the wing was raised. 
In order to indicate whether differences exist in the steady and 
oscillatory damping in yaw for the present models, calculations were 
made, by using the method of reference 8, and the sidewash data from 
reference 5, to determine the effect of wing position on the oscillatory 
damping in yaw for the model with the largest fuselage diameter. Since 
it was shown in reference 8 that almost e~ual values of the steady-state 
and oscillatory damping in yaw were obtained when the tail was removed 
(~ = 00 ), it was assumed that a similar circumstance occurred for the 
present investigation. In effect, therefore, the steady-state value of 
Cnr and the value of Cny determined under pure yawing oscillatory 
conditions (no sideslipping) were assumed to be e~ual. The total oscil-
latory damping in yaw was obtained by the addition of the steady-state 
damping in yaw of the wing-fUselage combination and the tail contribution 
to the oscillatory damping in yaw as expressed by (Cnr - CnQ ). ,m I-',m v 
The calculated results are shown in figure 6 and indicate that under 
.oscillatory conditions, where the angle of sideslip is changing as well 
as the angle of yaw, the ~ contribution to the damping is quite appre-
ciable, as was noted in reference 8, and the effects of wing position 
may be opposite to those for the steady-state condition. The results 
• 
NACA TN 3843 7 
of additional calculations (not presented) indicate that the effect of 
fuselage size on the tail contribution to the oscillatory damping in yaw 
was negligibly small for the models of this investigation at an angle of 
attack of 00 • 
CONCLUSIONS 
Results of an investigation made in the Langley stability tunnel 
to determine the effects of wing position and fuselage size on the 
steady-state yawing derivatives of a 600 delta-wing model indicated the 
following conclusions: 
1. For angles of attack below the stall, the steady-state damping 
in yaw decreased (the values of the yawing-moment coefficient due to 
yawing became less negative) when the wing was raised from a low to a 
middle or a high position on fuselages having ratios of the maximum diam-
eter to wing span of 0.123, 0.165, and 0.246. This was the result of 
a decrease in the tail contribution to the steady-state damping in yaw 
when the wing was raised since the effect of wing position on the damping 
in yaw for the wing-fuselage combination was small. With the vertical 
tail on or off, the steady-state damping in yaw increased with an increase 
in fuselage size. 
2. The results of calculations of the oscillatory damping in yaw 
for the model with the large fuselage indicated that the effects of wing 
position would be opposite to those determined under steady-state 
conditions. 
3. For angles of attack below the stall, raising the wing produced 
a positive increment in the rolling moment due to yawing, and fuselage 
size had little effect on this parameter. 
Langley Aeronautical Laboratory, 
National Advisory Committee for Aeronautics, 
Langley Field, Va., July 25, 1956. 
8 NACA TN 3843 
REFEREN"CES 
1. Campbell, John P., and McKinney, Marion 0.: Summary of Methods for 
Calculating Dynamic Lateral Stability and Response and for Estimating 
Lateral Stability Derivatives. NACA Rep. 1098, 1952. (Supersedes 
NACA TN 2409.) 
2. Letko, William, and Riley, Donald R.: Effect of an Unswept Wing on 
the Contribution of Unswept-Tail Configurations to the Low-Speed 
Static- and Rolling-Stability Derivatives of a Midwing Airplane 
Model. NACA TN 2175, 1950. 
3. Letko, William: Effect of Vertical-Tail Area and Length on the Yawing 
Stability Characteristics of a Model Having a 450 Sweptback Wing. 
NACA TN 2358, 1951. 
4. Letko, William, and Williams, James L.: Experimental Investigation 
at Low Speed of Effects of Fuselage Cross Section on Static Longi-
tudinal and Lateral Stability Characteristics of Models Having 00 
and 450 Sweptback Surfaces. NACA TN 3551, 1955. 
5. Goodman, Alex, and Thomas, David F., Jr.: Effects of Wing Position 
and Fuselage Size on the Low-Speed Static and Rolling Stability 
Characteristics of a Delta-Wing Model. NACA Rep. 1224, 1955. 
(Supersedes NACA TN 3063.) 
6. Bird, John D., Jaquet, Byron M., and Cowan, John W.: Effect of Fuse-
lage and Tail Surfaces on Low-Speed Yawing Characteristics of a 
Swept-Wing Model As Determined in Curved-Flow Test Section of the 
Langley Stability Tunnel. NACA TN 2483, 1951. (Supersedes NACA 
RM LBG13.) 
7. Silverstein, Abe, and White, James A.: Wind-Tunnel Interference With 
Particular Reference to Off-Center Positions of the Wing and to the 
Downwash at the Tail. NACA Rep. 547, 1936. 
8. Fisher, Lewis R., and Fletcher, Herman S.: Effect of Lag of Sidewash 
on the Vertical-Tail Contribution to Oscillatory Damping in Yaw of 
Airplane Models. NACA TN 3356, 1955. 
D 
I 
.. 
NACA TN 3843 
TABLE 1.- GEOMETRIC CHARACTERISTICS OF MODELS 
Fuselage: 
Fineness ratio • • • • • • • 
Maximum diameter, in. • ••• 
Ratio of maximum diameter to 
wing span •• • • • • • • 
Wing: 
12 
4.5 
0.123 
9 
6.0 
0.165 
Aspect ratio . . . . . . . . . . . . . . . . . 
Taper ratio • • • • • • . . • • • • • • . . • • • 
Leading-edge sweep angle, deg • • • • • • • • • • • • • • • 
Dihedral angle, deg • • • • • • • • • 
Tw'ist, deg . . . . . . . • . . . . ..•. 
AJ:oea, sq in. . . • • . • . • . • • • • • . . . • • . 
NACA airfoil section parallel to plane of symmetry • • • • • 
Vertical tail: 
Aspect ratio • • • • • • • 
Taper ratio • • • • • • • 
Leading-edge sweep angle, deg •••• 
Area for 12.00-inch span, sq in •• 
NACA airfoil section parallel to root 
Tail length from center of gravity to 0.25 
chord of tail, in. • • • • • • • • 
Ratio of tail area to wing area 
Ratio of tail length to wing span 
. . . 
. . 
mean aerodynamic 
. . . . . . . . . 
9 
6 
9.0 
0.246 
2.31 
o 
60 
o 
o 
576.7 
65A003 
2.18 
o 
42.5 
66.0 
65-006 
21.5 
0.115 
0.59 
CL 
r,Cn 
Cy 
,.& 
, 
~ 
Figure 1.- Stability system of axes. Arrows indicate positive angles, 
velocities, and coefficients. 
x 
t-' 
o 
~ 
~ 
~ 
\..N 
~ 
\..N 
---- -------~--------------------- --------------------------------------
NACA TN 3843 11 
12.00 
Wmg 
poslflon 4.50maxlmum dIameter 5 .12 
~~~==~====~====~-~~====_=-~. ~-====~_-~=-=-7t~--=~7_-~-~-~N~~O~O=-=- --J2.J2 
600maxlmum dIameter 
900 maxImum dIameter 
/ 
E co::. :..-_-_-;::: := ____ -~= -: :-. ------- -::--:=-======"' _____ _ 6.23 
4.46 
1-' ------------~--~-----------
-------- - --------------
--~ -=-=-=-=--""- ------_-=::-===----
1-------- 27. 00 ~ 54.00 
/ 
/ 
'/ 
, 
:/ 
/ 
/ 
f-''''-<:----t--'-'<:-- C r 21.10 -----"i 
'. 
c/4 
t-- --15.80-----l 
II. 20----+-----------3/.60 ~ ________________ ~'-------------.J.. 
Figure 2 .- Details of models. Dimensions are in inches. 
I 
1.4 
1.2 
1.0 
.8 
~-.J 
...... ~ ·6 
~ 
~ ~ 4 
~ 
~ 
...... 
a 
-4 
-4 
i i i 
a 
-4 a 4 8 12 16 20 24 28 32 36 
4 8 12 16 20 24 28 32 36 
Angle of attack, Q7, deg 
(a) Vertical tail on. 
Figure 3.- Variation of lift coefficient with angle of attack for the 
various models. Ratios of fuselage diameter to wing span are 0.123, 
0.165, and 0.246. 
f-' 
f\) 
~ 
~ 
~ 
\.>J 
~ 
\.>J 
..-~-------
/,4 
1.2 
1.0 
~-....J .8 
..... 'a; 
.6 
i::i 
'i:: 
-...: 
~ 4 \.) 
;:::: 
.... 
.2 -....J 
0 
~2 
-4 
-4 o 4 
-4 0 4 8 
8 12 16 20 24 
Angle of attock, a:: deg 
16 
32 
(b) Vertical tail off. 
Figure 3.- Concluded. 
- -- - .-----~-~~-----~ 
~ (") 
:t> 
1-3 
21 
\>l 
~ 
\>l 
t--' 
\>l 
14 
CY. r 
I 
I 
NACA TN 3843 
.2 
./. 
o 7. 
r 
-:I 
Angle of attock, X, deg 
(a) Ratio of fuselage diameter to wing span of 0.123. 
Figure 4.- Variation of yawing derivatives with angle of attack for the 
various models with a vertical tail on. 
NACA TN 3843 15 
.2 
./ 
0 7r 
-./ 
.3 
... :2 
Angle of attack~ a; deq 
(b) Ratio of fuselage diameter to wing span of 0.165. 
Figure 4.- Continued. 
16 NACA TN 3843 
.2 
./ 
o c;. 
r 
2 
Angle of attack, ex:, deg 
(c) Ratio of fuselage diameter to wing span of 0.246. 
Figure 4.- Concluded. 
D 
NACA TN 3843 
1.2 
.8 
.4 
CY,-
0 
.3 
-.4 
.2 
-.8 
.I 
0 
-.1 
~2 
.3 
~3 
.I 
Cn 
0 
'f' 
... ,/ 
... :2 
Angle of CTItock, X, deg 
(a) Ratio of fuselage diameter to wing span of 0.123. 
Figure 5.- Variation of yawing derivatives with angle of attack for the 
various models without a vertical tail. 
17 
7r 
18 NACA TN 3843 
.2 
./ 
c. 
o tr 
Angle of attock, X, deg 
(b) Ratio of fuselage diameter to wing span of 0.165. 
Figure 5.- Continued. 
NACA TN 3843 19 
.2 
./ 
o Cf. r 
~I 
Angle of ottoc~ a; deg 
(c ) Ratio of fuselage diameter to wing span of 0.246 . 
Figure 5. - Concluded. 
20 
J 
o 
-J 
o 
-.1 
-.3. 
-4 
-.08 -.06 
Low 
-.04 -. 02 
Fuselage dIameter 
Wing span 
o 
o 
o 
o 
0.123 
0./65 
0246 
Tallon 
Tat! off 
.02 
MId 
Wing heIght 
Wing span 
.04 
NACA TN 3843 
.06 
HIgh 
.08 
Figure 6.- Summary of effects of wing position and fuselage size on the 
steady-state yawing derivatives of a 60° delta-wing model. a = 0°. 
NACA - Langley Fie ld, Va. 


Experimental Steady-state Yawing Derivatives of a 60 Degree Delta-wing Model as Affected by Changes in Vertical Position of the Wing and in Ratio of Fuselage Diameter to Wing Span

Experimental Steady-state Yawing Derivatives of a 60 Degree Delta-wing Model as Affected by Changes in Vertical Position of the Wing and in Ratio of Fuselage Diameter to Wing Span

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