Greenberg, Harry

English

NASA Technical Reports Server

—“kc$?$ Jfdi , . ‘w~
L
.,
,
,:
‘llilllllllillllllnillllili~
u
3 1176 00097 0484 ,
___NATiONAL-” AD,WSORY COMMITTEE FOR AERONA
,, —..
ly/..lrINI]]]] Iuwolrr
ORIGINALLYISSUED
June 1944 as
RestrictedBulletinL4F07
- .-WWCULNCION OF STICKFORCESFOR
AN ELEVATCN3WITHA SPRINGTAB
By H- Greenberg
LangleyMemorialAeronauticalLaboratory
La@ey Field,Va.
NAchA
$?A ;C 4!) m3w’y
WASHINGTON
.MM& ~EMO~ AERONAfij.-CA?.
LmKy’?/’ifTm.-
NACA WARTIME REPORTS are reprints of papers originally issued tu proyu?ie$,~apid distribution of
advance research results to an authorized group requiring them for the wfi ‘effokti They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change in order to expedite general distribution., \f
,.
.-
l.
ii
https://ntrs.nasa.gov/search.jsp?R=19930092911 2020-06-17T01:05:41+00:00Z
wCA RB No, ~~
NATIONAL ADVIS$ORY COMM33!TEE FOR
RESTRICTED BULLETIN
.
CAIMJLA!!?IOWOF STICK FORCES
AERONAUTICS
FOR .- -
AN ELEVATOR WITH A SPRING TAB
By Harry Greenberg
SUMMARY
Formulas for the calculation of’hinge-moment
characteristics of an elevator with a spring tab have
been developed in terms of basic aerodynamic parameters,
spring stiffness, and airspeed. The formulas have been
used in a study of the stick-force gradients on a
pursuit airplane equipped with an elevator with a spring
tab. Charts are presented showing the variation of
stick-force gradient I.naccelerated fll~t over a large
range of speed and the complete range of spring stiffness
for various center-of-gravity locations, altitudes, and
airplane sizes.
It is shown that the stick-force ~vadient for the
elevator with spring tab tends to decrease as the speed
increases and for weak springs tends to approach the value
corresponding to a pure servotab (no spring). This
tendency Is independent of altitude, size, or center.of-
gravlty location although the magnitudes vary with these
parameters. The variation of stick-force ~radlent with
center-of-gravity locatien is less for the spring-tab than
for a linked-tab t~e or balance.
INTRODUCTION
On most types of control surface, balanced or
unbalanced, the control force per unit deflection of the
surface increases approximately as the square of the
speed. On a spring-tab type of balanced control
(reference 1), the amount of aerodynamic balance increases
with speed; this condition results in a control force that
increases less rapidly than the square of the speed. This
type of control can be used to advantage on ailerons since
it reduces the difference between the control force per
unit helix angle pb/2V at the high and low ends of the
speed range.
2 NACi RB NO. L@?~
The question has arisen as to whether the known
advantages of the spring tab on the aileron could be
realized for the elevator. me purpose of this report
Is to analyze the characteristics of the spring-tab
control used as an elevator. Ger.eral expressions, by
which either the static or maneuvering stick forces for
an elevator with a spring tab may be calculated, are
developed and applied to the calculation of maneuvering
forces for a typical pursuit airplane. The maneuvering
stick forces for the same elevator arrangement with a
servotab and with no tab are also presented for comparison.
The effects of variations In spying stiffness, airspeed,
altitude, center-of-~avlty location, airplane stze, and
tab size are considered.
DESCRIPTION W’
In the sprin~-loaded
ETdVATOR-VA3
elevator-tab
SYSTiM
arrangement
referred to h6reifi. the control is connected-directlv
to tho tab, as in & servotab, and to the elevator t~ough
a spring, (See fig. 1.) TMs arrangement gives the
control system characteristics that are between those of
a servocontrolled elevator and an ordinary unbalanced
elevator. A weak spring apy?oachos the case of no spring,
or pw’e servocontrol. A stiff sy’ing approaches the case
of a ri~id connection, or an ordinary unbalanced elevator.
As the speed is :ncreased, the aerodynamic forces
increase while the spring effect remains constant; effec-
tively, the spring becomes weaker in comparison with the
aerodynamic forces and the condition of pure servocontrol
is approached.
In figure 1, BC is an idler that is free to pivot
at the hinqe of the elevator T3. The control rod AC
operates the tab through the linkace i3CDZand operates
the elevator through the spring and crank ;!C-.The
lengths of 3G and qC are ass”xmed.equal in the analysis.
SYMBOLS
wing aspect ratio
tail aspect ratio
NACA RB No. L@~
b wing span
about elevatora .- (& .,.,.,.. .:,...- ..~e
‘Z::ci-i$ent-“
hinge-moment coefficient about tab
c)
Ht
hinge
lpv%tq
lift coefficient of wing
()
L
$$sw
,.
()
%?lift coefficient of tall —
$TFST
pitching-moment coefficient about airplane
center of gravity
(
Pitching moment
++ )
mean chord of wing
mean chord of elevator
mean chord of tab
()W?=stick-force gradient in maneuvers K
stick force
force in spring; positive *en in compression
force in control rod AC at C; positive in
sane sense as F 3
force In control rod AC at A: positive as
In figure 1
acceleration of gravity
hinge moment about elevator hinge
. .-.-,.
RACA IIRBNo. I@~
Ht hinge moment about tab hinge
K llnkage ratio (W2)
kl spring constant, pounds per foot
, 4=k1Z12
=
–d
L
Z*
h
%
z~
‘2
M
m
n
q
r
Sw
se
‘T
%
v
v:
x/c
qseq
lift of wing
length of control stick
distance between wing and tall
lift of tall
length of arm BC
length of arm DE
Mach number
mass of airplane
normal acceleration per g of airplane due to
curvature of fllght path; accelerometer
reading minus component of gravity force
dynamic pressure
gearing ratio between control stick and rod
area of wing
area of elevator
area of tail surface
area ol’tab
airspeed
weight of airplane
distance between center of gravity of airplane
and neutral point in fraction of mean wing
chord
NACA RB HO. 4.F07~ 5
a
-.,
%’
. 6e
angle of attack at wing
r--#-angle..ofu$ttack at tail
. .
deflection of’elevator
deflection of elevator control arm BC
deflection of tab with respect to elevator
angle of pitch of airplane
pitching velocity
nondimensional pftchlng veloclty (66/2V)
(m/pSwb)airplane-density parameter
mass density of air
‘-3?f?nevcr6e) fit, qs e~s a) and D9 are used
as subscripts, a derivative is indicated; for exampl~,
acm b%
%
=— and %1 hen a derivative or coef-ba D9 =~. ...
ficient 1s written with a bar above it
- for example, ~ -
the total derivative or coefficient is indicated, that 3.s,
the resultant or effective value which takes into account
the floating tendency and sprln~ actton of the elevator
witu stick fixed.
All angles are measured in radians.
METHODS OF ANALYSIS
The basic assumptions involved in the analysis sre
as follows:
(1) Id.nkageratio is constant
(2) Aerodynamic derIvatives are constant over the
ra~e of deflections involved
(3) Effect of speed on the aerod~amlc
1s given by the factor
&
derivatives
11-
6 NACA RB No. L4.F07
(J-f.)Effect of power is neglected
(5) Effect of chmges In forward speed durii~ Q
pull-up is neglected
(6) affect of horizontal tall flexibility IS ignored
. .
I
NACA RB No. I@~
k%om the condition for equlllbrlum of the tab,
., .,,.- . . .._- ... ,.. ~
.—---- .
F2Z2 = -
t
t%t + d:%tae + %%~
)
qst~
at %!
Combining expressions (1) to (3) gives
+ %% + =T%-leeu
t =T
7
(3)
I s~q
+ K——
soFe-(%%lt + 6e%t + =T%L ) (5)6t 6e taT
If the values of the aerodynmnlc coefficients on the
right-hand side of’equation (5) are obtained from low-
speed datn, they should be multiplied by —
&
to
I apply to high speeds, according to the Glauert approxi-
mation or, If
,~y? .1,:
k2 =
qse~
..
_ _. .. .
8 NACA RB NO. @~
equatton (5.) ma~ be written as
Stq
+ ~— (%cht + be%t + %Cht ) (6)Se% 8~ 80 %?
Sy su~etItutIng for 5t In term of 8~ and 80 In
equation (6) and solving fcw da, timre is obtained
6= = (‘7)
vihiohdetermines the angle Ee at rhich tbe elevator
floats in response to a control deflection 8s and angle “
of attack ~. The tab angle Is then determtied by the
linkage ratio. Equation (7) cqn be written fn abbreviated
form as
(5e= A8S + 3% (9)
Then, .
i5t ( )=u3s+8e
= II(1 + A)6S +-=% (9)
.
. . . . . -. .—-. — .,----+..
.. - ?-*..: “...’~y.-” ——- --,-.. “ . .. . ..-
,. ~ . .,+-”;+?~>.:“o :- e .. -...-:”..:: ++-. .. . ..... ... . . . . . . ... . . . .-.. .- . . ... . .’.-*.:“”..:+- . “.,.?.:..
iJACARB NO. L@07 9
The stistitutlon of equations (8) and (9) In the expres-
~ion for the control force F5 giv9s
. whioh givgs the fundamental control hinge-moment deriva-
—..—
tlves ~ and Che as96
s %
% = A@eB + K(l + A)Ohe58 e6
e t
and
(11)
(12)
~i~enthe St Zck la f~ed, the glevator movgs ~~th
ch~es in angle of attack in accordance with equation (7).
As a result, the static-stability derivative ~ and
the damping In pitching ~ are affected. T&y may
be calculatedly
(13)
w+)
.. ..- ------- . . .. . ------- ;..-- .. .. . . . ------ ... . . .
.-. I
. .. .. . ..- - . . . . . . .. .- ——. -
—..— ..- —.
10 NACA RB NO- L!+F07
The control effectIveness %/j similarly depends
s
, on the notion of the elevator with respect to the control
arm. The relation is
uquabAuu \
.
~a =~ A + Gm6tK(l + A) (15)
s e
After the five fundamental derivatives are obtained
by equations (11) to (15)3 the stick force per unit
normal acceleration in a pull-up maY be calculated. The
formula fop this stick-f&ce gr~dieht,
from equations on page 14of’reference
which is taken
2, ia
)——C436%08 (16)~ s
for a mass-balanced elevator. In formula (16). total
derivatives are used. Values of T&_ and ‘~ are0= eDQ
The effect of compressibilitymust agah be taken
Tinto account in using formula (16 . All the derivatives
in that expression should be multiplied by
d,+
,if
the data used in computing these derivatives are based
on low-speed measurements. The factor cancels out except
in the second and fourth terms. The corrected formula is ,
(18)
. .
9+
,
..—. ——---
.
*.... . . -------s-----.,. ,..
.. -m—--- .— - .. --
-:. ... ”f .“
--%.. -..L. ..,#.. s..:”’.”’. .. 7.. ,,.m... --:. , .- .- . .
11YACA RB NO. 4.F07
Spring, elevator, and tab deflections corresponding
to any ae(seleration are calwala%ed by the following
formulas$ derived by using equations (2) of reference 2:
8a
m-
(
-= b-~ m ‘
— - 2V2 CLJ3?U3S
.
)+‘AdD6
oomputatlons~ based on t~ioal airplane
have been made to Illustrate the effeot
A number of
oharacteristios.
of spring stlff%ess on the oharaoteristios
with a spring tab. The following airplane dimensions and
of an elevator
derivatives are used:
~/S , pounds per square foot . .
!!t03 ee . . .
l , l
l
9
l
9
9
l
9
l
9
l
9
l
l
l m.8m*9
We*ma l o
l m99m9 l
99=** l m
l *9998 l
l *s*ma 4
.*#m* l m
999999 l
9..9. l *
Zar feet . .
s~# l l , .
b.~.~..
AT.. . . . .
Lh/60 . . . .
c~ l 0 l l l
da~da . . . .
daq@8 . . .
CIUa (for a.g.
point)
0111
Al?!tud;,af;e;
IJ ‘“” ‘ l “
l m
99
ahead of neut;aiiooat~on C).05G
-0.232
‘15.3
“20,000
l 23.3
l m
.9
l m
l *
•~
l *
l a
l mb9
9*9*
l 9**
9999
dimensions and derivativesThe following elevator and tab
are used:
S93 squre feet .
~, feet . . . . .
~/G . . . . . .
~/ST .O . . . .
S+/Se . . . . . .
. . -. ~. . . --- --- .---- .- - -- - --- - —— - -- .- --- --- .—- . ... --- ---- --- - -- . . -- - . --
.- .
.-.
. ..-. ., --- .- ..--”--- -~ ..-sk. -~_ .
—& A-LA.. -.-L-*L. ..,- ‘. ..-A ..- -4-, ---- #M. . . . . . ------ . . .
12
31, foot
K.. .
%
e/3e
% 06
t
%5t
%
‘%
.
l
l
9
l
.
.
l
l
9
l
9
l
w
9
l
l
9
l
l
l
l
l
l
9
l
.
9
l
l
l
l
l
l
.
.
equation
k2
A
= .k2 - 0.622
l amm
l ama
~~:@7 “
-0.115
-0.115
-0.115
-0. 3~5
l m e
(7),
+ 0.130
equation (10),
-0.487~ - 0.0067
~ =a -k2 - 0.622
Fromequations(13) to (15),
l ’. , . .
l .m. .
l .*.9
CJ%6
e
c%5t
%%J!
%qJe
% t“
l
l
l
l
.
FL3No. IJF07
l
9
l
l
l
9
9
s
B
0.115
= -k2 - 0.622
l
.
9
l
l
l
l
9
l
l
8
l
b
mut
l 0.5
00n5
3.09
-ld4
.
-0.0615
+ 0000230.115%
~ = -?E2- 0.622.
K = -0.232 - 0.0635-k2 . 0.622
.
.
k2 + 0.130
— = -1.1OC%lb 0.0615
s -% “ 0.622 -
These values can be sti.stitutedin formulas (17)
to obtain Fn.
.
and (18)
.
..-
... —. +-. —
- . . ...... .“-;...~ ,. .. . ... ., :.+.-.. . ...+-. . . . ..> . . ) ..-. ----————
.
~... - ---
. ..*..
.. <-:-. :: ...,....
-.. .
>*, r.;,; . . .-~. -*. .
. .
lJACARB k!Ol L@?~
rss?mTs
Thecomputed values
13
AWD DISCUSSION
of the sttck=force nad%ent in
mmvmvers Fn for the assumed airplane and 61evator
are plotted as a function OF speed In figure 2, for
variou~ values of the spring constant kl. The top
curve, for ir~laite spring ctlffness, applies to an
ordinary uzzbal.aficedlevatcx’,for wMch the spring Is
replaced by a rigid rod. ~L~~ bottom curve applles to
a pure servocontrol, for tihichtlaespring is removed.
Tli9 Intermediate curves are for the canes in tiich
springs of various stiffnesres are connected between
tha control rod and elevator. The inwease in stick-
force :~adient with speed for veryhi~ and very low
valnes of s;ning stiffness is based on the assumgt~on
of the effect of ccrnpressihilltymentioned previously
and is not important for toe gmrposes of this report.
The Important fact is that %he addition of a spring
reduces the sttck-force gradient in the mannw shown.
A very weak spriag reduces tl?estick-force gradient at
the hQh end of the speed range to a value only slightly
higher than that of the pure s~rvoconti’cl. In the case
corresponding to complete servo-ogeraticn (no s-prlng)in
figure 2, tho stick force is less than the mfnlmum value
considered deelra’ole. This value could be Increased by
using a tab of inc~eased cho~d. Increasing the s-panof
the tab would have no appreciable effect on the s-cick-
force gradients because the i~.creasedforces on the tab
are com~ensated by the reduced deflections needed.
Other methods of reeucing the stick forces, such as the
linked belanclng tab, wculd result in a sll~ht increase
of stisk-force gradient with speed es Is ths case of the
top an~ bottom curves of figure 2.
It is sometimes considered desirable to have direct
control until a certain stick force Is reached after
which the tab controi begins to function. This direct
control is accomplished by preloading the sprhg b~ an
amount that depends on the stick force at which it is
desired to have the tab come into actlan. The stick
fwce varies with acceleration in the manner shown in
fLgure 3. The curve has the slope for infinite syring
stiffness up to a certain polat, as indicated by the
solid line, and then has the slope corresponding to the
spring stiffness used, as Indicated by the dashed line.
. . . . -. . . - . — —- . -- . .-. . .- - -- . -- -... . . -
. . .
---
. .
. . . . .. . . . .-- ..-’ G.A. ALL- “ ---- * .:&. -.. . - -.. ..~a. —:--” “’ “~— --- .-.. — -. -. —-
The point where the slope changes of course depends on
the preload in the sprIng. Such an arrangement might be
useful in maintaining reasonable control forces for pull-
outs at very high speeds. “
The effect of Increased airplane sizs is shown in
f~gure 4. Z!hewing loading and control gearing Zs are
assumed the same as in figure 2, but all lengths are
assumed doubled. The stick-force gradient for pure
servo-operatton
4%=01
is somewhat higher than the
value considered stiab e and any appreciable auount of
sprli~ stiffness would make the stick-force gradient too
large. For this case, a tab with smaller chord could be
used to give lower stick forces.
The effect of altitude on the variation of stlck-
force ~adlent with speed is shown In figure 5. An
Increase in altitude reduces the stick-force gradient by
an amount that does not vary appreciably with speed.
The loss fn stick force in pounds decreases as the spmtng
stiffness is decreased.
The affect of center-of-gravity location on the
stick-force ~adlent for several types of balanced
elevator is shown in figure 6. The elevator with
spring tab shows the smallest change of stick-force
gradients. The llnked-tab balance chosen for comparison
was assumed to be so linked as to give the same stlck-
f’orcegradient as the elevator with spring tab for one(particular center-of-gravity location ~ = 0.05J The
variation of stick-force gradient with-center-o-f-gravity
locatton is less with the spring tab than with the
linked tab because % is r:du.cedas well as ~e5s;
‘a
this condition permits a smaller qeA for a given
u“
stick-force gradient. As shown in eq&tion (18), the
variation in stick-force ~sdlent with ~, which
depends on center-of-~avity location, is &oportlonal
to ~
e~s”
____ .. . . .. .
----
NACA RB No c L4F07
CONCLUSIOIW5
Fomaulas have been develoned for the
15
calculation of
hi~~e-m.omeutcharacteristics o? on elevator with a
spr~~ tab, ‘Theanalysis included basic aerodynamlo
parameters, spring stiffness, and airspeed ti indicated
the following conclusions:
1, The stlclc-forcegrgdients for an elevator with a
spring tab tend to dacrease as the speed increases~ For
a weak sprtng ac hi@ speeds, the stick foroe approaches
that of a pure servocontrol.
2. The variation of stick-force gradient with
cenbm-of-grcvity locatloa M less for an elevator with
a spring tab than vith a Mnksd tab.
5. Increase In altitude reduces the stick-force
~ycdients by a nearly constant mount over the speed
ranges for a piven sari~ stiffness. The amount of
retiuctionin ths sttck-forco ~radicnt decreases as the
spring sttffness decreases.
Langlo~ Memorial Aeronautical Laboratory
Haticmal Advisory Comnittee for Aeronautics
Langlsy Flold, Va.
REFER2XCIS
1, C?tos, S. B.: Notss on the SpringaTab. Rep.
?!o.B.A. 1665, R.A.E.$ April 1941e
2, Creenlmrg, EarP;, and Sternfiold, Leonard: A
Theoretical Wvestigation of Lon@tudinal
St~.bllity of Airplanes with Free Controls
Including Ei?f6ctof Pi?iction in Control
system. NACA ARR No o @l, 19440
3. Harmon, S, N.: Determination of ths Effect of
Horizontal-Tail Floxibllity on Lm@tudinal
Control Characteristics. iWX ACi2ITo,L5i301,
19450
. . . .. -—. ---- .- .-. . . . . . . .-_. ------ --c. -
- ..--—-. . - .. ..
-.
!.
.;
I
I
D“
.
~F
A Uvvuu c
D
B
=&.
F3 f-l fir/4 WJiw NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS
A
I?i.gure1.- Spring-loadedelevator-tab combination.
.
.
NACA RB NO. L4F0’7 Fig. 2
0 200 +00 am
True a~rsipa~ ~ mph
NATIONAL ADVISORY -
COMMITTEE FOR AERONAUTICS.
.
Figure 2.- Variation of
elevator with spring
span, 42 feet.
stick-force gradient with .speedfor
tab.
‘1’ spring stiffness; wing
.
.,
-–....—. ..—.- ... . .... . . . . .. .. . .. ---- .. . ...7..___ ,..––-.. .. ..... _.._
NACA RE? No. L4F07
> t
1
I
1 H
v
I 1 1 1
I
I
1 I
r- 1 /1 l— /aD /oc#fed
I/l I Ziab/”ee ____
.IzmmImI
Fig. 3
0 4 8
. Normal acce/erat/on,
NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS. ‘
Figure 3.- Effect of spring preload on
/6’
9
stick-force gradient.
NACA RB NO. L4F07 Fig. 4
a..
Figure 4.- VarlatLon of stick-force gradient with speed.
kl s spring stiffness; wing span, 84 feet.
ll—lm—m—
,NAC!.4 13B No. L4F07 Fig. !5
.
Q 200 ?00 600
True ajrsp+ bj mph
NATIONAL ADVISORY
COMMITTEE FOR AERONAUT ICS.
Figure 5.- Variati.onof stick-force gradient with speed at
sea level and 20$000 feet. kl, spring stiffness;wing
span, 42 feet.
NACA
NAT IONAL ADVISORY
COMMITTEE FORAERONAUTICS.
l
o .0/ .02 .03 .0+
Center- of- grav]ty A7caf!00, Z/Z
Figure 6.- Variation of stlok-foroe gradient
.05 .
with
‘oenter-of-gravitylocation for vaiious types of
balance. ~


Calculation of stick forces for an elevator with a spring tab

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server