Abramovitz, Marvin

Van Dyke, Rudolph D , Jr

English

NASA Technical Reports Server

. 
RESEARCH MEMORANDUM 
THE EFFECT OF STICK-FORCE GR.ADlENT AND STICK GEAXNG 
ON THE TUCKING ACCURACY OF A FIGHTER AIRPLANE 
By Marvin Abramovitz and Rudolph D. Van Dyke, Jr. 
Ames Aeronautical Laboratory 
Moffett Field, Calif. 
NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS 
WASH I NGTON 
December 17,1954 
COPY 
RM A54128 
https://ntrs.nasa.gov/search.jsp?R=19930088495 2020-06-17T07:09:12+00:00Z
NACA RM ~54128 
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
THE EFFECT OF STICK-FORCE GRADIXNT AND STICK GRARING 
ON THE TRACKING ACCURACY OF A .FIGEPER AIRPLANE 
By Marvin Abramovitz and Rudolph D. Van Dyke, Jr. 
SUMMARY 
Steady straight-and-level and steady turning tracking runs against 
an aerial target were made with an F+lH airplane, equipped with a fixed 
optical sight and having various combinations of maneuvering stick-force 
and stick+leflection gradients. 
Over the complete range of contiol-system parameters covered (stick- 
force variation of 0.2 to 5.9 pounds per g and stick4eflection variation 
of 0.07 to 0.70 inch per g), excellent tracking could be accomplished, 
with standard deviations of pitch afm wander of less than 2 mils. Spectral 
densities of control--surface motion and stick-force variation indicated 
no significant or systematic variation of pilot's behavior or method of 
moving the controti with the variations in the control--system characte? 
istics. 
INTRODUCTION 
This investigation is an extension of prevfous studies of the 
influence of various aerodynamic factors on the tracking accuraoy of 
fighter airplanes (refs. 1 and 2). In these studies it was found that, 
in steady msneuvers with a fixed optical sight, excellent tracking was 
possible with a number of different airplane configurations and over a 
large variation of flight conditions. However, since all the configura- 
tions tested met United States Air Force handling-gualities specifica- 
tions (ref. 3) over most of their operatfng range, only a relatively small 
variation in controLforce gradLent was covered., especially in the low 
force range. For this reason, the present investigation was undertaken 
in which the effect of variations in the elevator control-force gradient 
on the tracking performance was studied. 
The scope of the investigation was limited for the most part to the 
region of low to moderate stick-force gradients. In addition, the effects 
2 b .._ _ NACA RM A54128 
of various ratios of stick-t-levator deflection were investigated. It 
was felt that the region of very low forces and very small stick deflec- 
tions, where problems of high control sensitivity could exist, was of 
particular interest. Previous results (ref. 1 for the F-8&L at high Mach 
numbers) indicated that satisfactory tracking could be achieved with 
stick-force gradients high enough to be objectionable to the pilot (and 
lying outside the satisfactory limits as set forth in reference 3), even 
though it required the use of the adjustable stabilizer as a primsry cop 
trol to correct for gross errors. 
AZ 
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NOTATION 
normal acceleration factor, g units 
frequency, cps 
elevator stick force, lb 
G-y(f) = 4J," [Y(t)-T] [y(t+r)-Tj cos (27cf~) dT, power spectral 
density, (units of y)s/cps 
acceleration of gravity, f-t/se@ 
pressure altitude, ft 
Mach number 
‘t 
8 
G/as, normalized power spectral density, per cps 
time, set 
elevator stick deflection, measured at stick grip, in. 
elevator deflection, deg 
A( ) indicates changes in ( ) from t&m value 
pitch aim error, mils 
standard deviation, units of y 
. n - pi z yl, mesn, units of y - -m 
i=1 
NACA BM A54I28 
Test Equipment 
AnF+lH airplane, equipped with a Navy Mark 8 Mod 5 fixed optical 
sight (identical to the one described in reference l), was used as a 
test vehicle. The airplane was provided with a control--stick assembly 
that was modified by the addition of linksges connected by a lead screw 
drive so that the ratio of control--stick to elevator deflections could 
be varied in flight from approximately half to twice normal. In addttion, 
various amounts of ballast were added to the tail cmartment in order to 
vary the maneuvering elevator-angle gradient. Byuslngvsrious conibina- 
tions of stick-to-elevator-deflection ratios and ballast the range of 
maneuvering stick-force and stick--deflection gradients shown on figure 1 
was obtained. In providing the above modifications, a direct mechanical 
link between the stick and elevator was maintained so that whatever stick 
forces were present were primarily a result of the elevator hinge moments, 
as is the case for the normalE'+lE airplane and other airplanes not 
equipped with fully powered controls. 
c 
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Test Procedures 
I 
The standerdfzed gunnery maneuver described in reference lwas used 
for the present tests, In this maneuver the fighter tracks the target at 
a range of approximately one thousand feet in straight and level flight 
for a period of about thirty seconds, after which the terget breaks as 
rapidly as possfble into a steady turn.of a gfven normal acceleration and 
the fighter again tracks the tsrget for about thirty seconds after steady 
conditions have been reached. In this report no data concerning the 
transition region from steady straight to steady turning tracking have 
been presented. In general, as was found for the normal F+l configura- 
tion in reference 1, the transitfon regions were of short duration with 
only slight increases in the aim wander over the complete range of 
control-system parameters covered. In addition, since the results of 
reference 1 indicated very little varfation of aim wander with speed, 
altitude, and normal acceleratfon in the turn, the madority of the data 
for the present tests were taken at a Mach nuuiber of 0.5, an altftude of 
20,000 feet, and a target turn of approximately three g. Also, since 
the results of both references 1 and 2 indicated very little vsriatfon 
of aim wander in smooth air with the alrplarxdynamic response character- 
istics, it was felt that the variation of longitudinal period and dsmp- 
ing due to the variation in static margin in the present tests would not 
significantly affect the results. The period, computed from wind&unnel 
derivatives, varied from 1.7 second for the normal F-5lH to 2.7 seconds 
for the resr center-of--gravity location. The cycles to demp to half- 
amplitude were computed to vary from 0.20 for the normalF+lH to 0.09 
for the rear center of gravity, 
4 
Method of Analysis 
NACAHM A54i28 
c 
The methods of analysis discussed in reference 1 were also applied 
to the data gathered in the present tests. Means, standard deviations, 
and power spectral densities of aim wander, elevator movements, and stick- 
force variations during tracking in steady straight and steady turning 
flight were computed using IHM electronic equipment. 
In computing the spectral densities, corrections for the effect of 
the mean on the low frequency points were applied. This was done because, 
with the method of computation used (ref. 4), the effect of the me= is 
carried over to the second frequency point and tends to obscure the low 
frequency content of the wander about the mean. This is especially true 
of the elevator-movement and stick-force spectra for the steady turns 
where relatively large means occur. 
The results are plotted as normalized power spectral densities. 
This is done in order to emphasize the relative variation in frequency 
content between runs, since in some cases the levels of the spectral 
densities for identical conditions are quite different due to differ- 
ences in the standard deviation. The normalized spectral density is: 
s =-$ (1) 
The area under S equals unity and the actual spectral density (with 
the effect of the mean suppressed) can be obtained by multiplying the 
ordinates by the square of the standard deviation. 
RESULTS AND DISCUSSION 
Means and standard deviations of aim wander, elevator movement, and 
stick-force variation for the various test conditions are listed in 
table I. On figure 2 are plotted standard deviations of pitch aim wander 
as a function of both stick-force gradient and stick-deflection gradient. 
It can be seen that there is no significant variation of aim wander with 
these quantities over the range covered in the present studies. 
On figure 3 are plotted the standard deviations of elevator move- 
ment and on figure 4 are the standard deviations of stick-force varia- 
tion. It can be seen that, like the aim wander, there is very little 
systematic variation of elevator movement with either stick-force or 
stick-deflection gradient. However, the standard deviations of stick- 
force variation, if separated according to center-of--gravity position, 
apparently increase systematically with stick-force gradient and decrease 
with stickileflection gradient. This can be explained by considering 
’ 
NACARM A54I28 5 
+ 
3 
the control friction involved. For the normal F-5ZIH control- to elevator 
deflection gearing, 3 pounds of control friction sre present, as felt at 
the stick grip. As the gearing is varied, the control friction varies in 
inverse proportion to the gearing. Since at both centeMf-gravity pos& 
tfons the control--stick- to elevator--deflection gearing is 2.20 times the 
normal gearing for the points of maxm stick--deflection gradient and 
0.46 times the normal gearing for the points of min3mum stick-deflection 
gradient, the corresponding control frfctions ere 1.36 pounds and 6.52 
pounds, respectively. Figure 5, in which the control-force standard 
deviations sre replotted versus control friction, clearly shows the effect 
of the amount of control friction on the stick-force standard deviations. 
However, since*a large portion of the stick-force varfations 33e within 
the friction band, the same trend does not carry through to the elevator 
motions (figa 3) or to the aim wander (fig. 2). 
It should be emphasized that the control system used in these tests 
was conventional in the sense that a direct link existed between the 
control stick and the elevator. The friction was due to control cables, 
fittings, etc. The test result8 would not necesstiily apply to a system 
with powered controls, especially if the friction forces should arise 
in a hydraulic control valve. Reference 5 compares the effects on the 
general handling qualities of various type8 of friction and breakout force. 
. 
Apparently, a human pilot can readily adapt himself to variations 
in COntzOl ChasaCteriStiCS 80 that he applies Whatever Stick force8 and 
deflections are necessary to maintain small aim Wander. It should be 
pointed out that the lower force gradients tested were definitely cow 
sfdered unsatisfactory by the pilot from a-general handling qualities 
point of view (and are outside the satisfactory limits as set forth in 
reference 3). NeVe&heh8S, even though the pflot felt it required 
more concentration and effort to track at these conditions, excellent 
accuracy was obtained. Of the veriou8 conditions tested, the pilot 
commented most favorably on a stick-force gradient of 1.2 pounds per g 
and a stick--deflection gradient of 0.70 inch per g- Note that this is 
the largest stick-deflection gradient tested and that a minimum Of co?+ 
trol friction i8 present. However, it should be potited out that this 
condition should not be considered an optimum s-e points ly5ng between 
the test extremes were not fnvestigated. 
In an effort to correlate the pilot's opinions with experimental data, 
Spectral densities of elevator movement and Stick-force variations, in 
addition to the amender spectral densities, were computed. It was 
felt that perhaps significant VSJ?&atiOnS in the frequency Content of the 
control movements would occur which would be indicative of variations in 
the pilot's effort. Figures 6, 7, and 8 are normalized spectral densities 
of aimwander, elevator movement, and stick-force verfation for two repr, 
sentative steady turning runs. Figure8 9 through 12 are normalizedspec- 
tral densities of elevator movement and etick-force vaiation for several 
extreme values of test conditions, In general, there is uttle significant 
6 NACA RM A54128 
variation in the results. It is seen that variations between runs at the 
same conditions are as large as variati.ons between conditions. In addi- 
tion, no correlation between the shape of the curve (i.e., whether the 
amplitude falls off steadfly with increasing frequency or whether it peaks 
at an intermediate frequency) and the resulting standard deviation of aFm 
wander was found. Apparently, the variations in control--system parameters 
covered in the tests had no significant or consistent effect on the behavior 
of the pilot, even though they affected hi8 op&ions on the effort required 
to track. He could track with excellent accuracy whether ft required more 
or less effort on his part. 
CONCLUSIONS 
The results of the investigation indicated that: 
1. Over a range of stick-force and 8tiCk4SplaCement gradients of 
0.2 to 5.9 pounds per g and 0.07 to 0.70 inch per g, respectfvely, excel- 
lent tracking, with standard deviatfons of pitch aim wander of less than 
2 mils, could be accomplished. 
2. Over the range of control-system parameters investigated, spectral 
densities of control-surface movement and stick-force variation indicated 
no systematic variation of the pilot's behavior or method of control. 
Ames Aeronautical Laboratory 
National Advisory Committee for Aeronautics 
Moffett Field, Calif., Sept. 28, 1954 
REFERENCES 
1. Rathert, George A., Jr., Gadeberg, Burnett L., and Ziff, Howard L.: 
An Analysis of the Tracking Performances of Two StraIghtWing and 
Two SwepHing Fighter Airplanes With Fixed Sights in a Standard- 
ized Test Maneuver. NACA RM A53Hl2, 1953. 
2. McNeill, Walter E., Drinkwater, Fred J., III, and Van Dyke, Rudolph 
D ., Jr.: A Flight Study of the Effects on Tracking Performance 
of Changes in the Iateral-X&cillatory Cha3XCteriStiCS of a Fighter 
Airplane. NACA RM A53H10, 1953. 
3. Anon.: Flying Qualities of Piloted Airplanes. U. S. Air Force 
Specification No. 1815&B, June 1, 19.48. 
l 
. . 
, 
m 
NACA RM A54128 7 
4. Tukey, John W.: The Sampling Theory of Power Spectrum Estimates. 
Symposium on Applfcations of Autocorrelation Analy8i8 to Physical 
Problems. Office of Naval Research, Navy Dept., June 13-14, 1949, 
PP. 4747. 
5. Phillips, William H., Brown, B. Porter, and Matthews, James T., Jr.: 
Review and Investigation of Unsatisfactory Control Chmacteristics 
Involving Instability of Pilo-kAirpLane Combinatfon and Methods for 
Predicting These Difficulties from Ground TeSt8. NACA RM L53J?l?a, 
1953. 
NACA RM ~54128 
TABLE I.- MEANS AND STANDAFtDDEVIATIONS OF PITCHAIMWANIER, 
EIEVATOR MCIVWENT, AND STICK-FORCE VARIATION 
1 a.69 1.10 1 -.53 1.05 l-08 2.76 0.045 o*040 0.64 
0.2 0.34, 
2.72 .035 "-:g "12 
z 1.38 1.06 .71 .g5 l-O1 
1 .79 2.73 .44 -:g -059 .53 .98 .gt3 -- 
-- -- -- 
1 -.14 .37 -- 1 -1.17 .g2 -7-r -- -- -- -- 
1 -.23 .54 2.61 Xl 
.oyo -- -- 
-- -- 
1 .Q 1.46 -- -- -- -- 
.5 .l6. 
2 -.6g 1.54 2.42  .m 4.39 1.14 1.14 
.ll .go 
1s ZI 
-- -- 
2 .13 .41 4 e.04 1.91 l-21 .076 -- -- - - - - -- 
:: 
-- 
:g ,:g 
-- 1.54 .og4 -- -_ 
-- -- -- 
1 
1 
1.2 -70 
i 
1 -.84 1.41 2.82 1 .052 
.19 
.62 ILo2 
2 . 81 .037 .045 
:g ;*;z 1.47 . 
1.1 .07 
: .m .062 g-57 2.06 
.061 9.94 2.06 
2.06 
1 .49 2.09 2*5g 1 .063 -5.28 -15 .72 1 * 41 2.64 .04g .77 -035 -3.30 -96 -87 
2.7 .32 
: .71 l 48 1.00 6 1.03 1.37 .048 6 - 9 .O& ;:z ;I$ 1.23 
1 --- -- 
-- -- 1 aal .01g .01g --- -- 1:: Ol8 -- -- 
5.7 .52' 
: II- - yx 1.46 -1.39 -029 -- . -1.94 .ti3 -046 -- -- 
1 -22 .&i 1 -. I.8 .73 '7a 2.60 .036 2.61 .036 -036 2:: ;I$,9 1.54 
5.9 .15 
: -075 .057 20.48 17*SQ 2.E -039 1.48 
1.80 
Trap1 referenue 1. 
IUCA RM A54128 9 
. 
8 
6 
4 
2 
0 
M ~0.5, h,=ZO,OOO ft 1 
Normal F-5lH 
0 .2 .4 .6 .8 
AK/AA, , in-/g 
Figure l.- Variation of longitudinal control pammeters. 
10 NACA RM A54128 
MzO0.5, h,=zo,ooo ft 
Straight 8 level 
---- 
4 6 
AFs/% , lb/g 
8 IO 
3 
v-l 2 - .- 
E 
I&- l 
A&AA, , in./g 
Figure 2.- Average standard deviations of aim wander. 
NACA RM A54128 
. 
.4 
.3 ’ 
MzOo.5, h, =20,000 ft 
Straight 6 level 
- - - - 
iiT 
Steady turns 
m .2 
6 
.3 
.2 
.I 
I-- 
0 
0 .2 .4 .6 .8 
Ax/AA, , in/g 
Figure 3.- Average standard deviations of elevator movement. 
NACA RM A54128 
M-0.5, h,=20,000 ft 
Straight # level 
- - - - Steady turns 
0 2 4 6 8 IO 
&/AA,, lb/g 
I 
0 
0’ .2 .4 .6 
Ax&A, h/g 
Figure 4.- Average standard deviations of control-force.variations. 
NACA RM A54128 
t 
2 
I 
0 
0 2 4 6 8 
Control friction, lb 
Figure 5.- Average standard deviation. of control-force va?3ations. 
c 
” 
14 
2.8 
2.4 
1.6 
.8 
4-i 
MaO0.5, h, = 20,000 ft 
AF,/AA, = 0.50 
I 
Axs/AA, = .16 
NACA RM A54120 
2 3 4 5 
f, CPS 
Figure 6.- Normalized spectral densities of aim wander in steady 
turning tracking. 
NACA FM A54128 
. 
* 
2.4 
2.0 
I.6 
.8 
.4 
0 
t-l-i Ms0.5, h, = 20,000 ft A&/A A, = 0.50 Ax,/AA, = .I6 I+ 
. 
r 4g, - = 0.98 
I 
0 I 2 3 4 
f, CPS 
-Tgizig 
Figure 7.- Normalized spectral densities of elevator movement in 
steady turning tracking. 
16 NACA RM A54128 
c 
1.6 
% 
.8 
M=O.5, hp20,OOO ft 
P 
l 
I 2 3 4 
f, CPS 
Kpz$ 
Figure 8.- Normalized spectral density of stick-force variation in 
steady turning tracking. 
iC NACA RM A54128 17 
1.6 
.8 
M - 0.5, h, = 20,000 ft 
AF,/AA, = i.10 
AX/AA, = .OT 
2 3 4 
f, CPS 
yiGzzy 
Figure 9.- Normalized spectral densities of elevator movement in 
steady turning trachfng with low control gearing. 
18 NACA RM A54128 
2.0 
1.6 
I.2 
sFs . 
.8 
.4 
0 
--l-4 MsO.5, h,~20,000 ft AF,/AA, = 1.10 Ax=/AA, = .07 I-H -. 
n - - n-1 
0 I 2 3 
f, CPS 
Figure lO.- Normalized spectral densities of stick-force variation in 
steady turning tracking with low control gearing. 
. 
NACA RM A54I28 19 
2.8 
2.4 
1.6 
.8 
MaO.5, h,~20,000 ft 
AF,/AA, = 1.20 
Ax~/AA, = JO t-l-i 
2 3 4 
f, CPS K5izJ75 
Figure ll.-. Rormalized spectral densities of elevator movement in 
steady turning tracking with high control gearing, 
20 
2.4 
2.0 
SFs 1.2 
.8 
.4 
0 
NACA FM A54128 
. 
4-4 M-0.5, h,~20,000 ft AF,/AA, = 1.20 Axs/AA, = .70 
0 2 3 4 
f, CPS -KiGz&G5 
Figure 12.- Normalized spectral densities of stick-force variation 
in steady turning flight with high control gearing. 
& 
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?acr-langley - 1%17-54 I 560 



The effect of stick-force gradient and stick gearing on the tracking accuracy of a fighter airplane

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