I

AD/A-002 918
CRITERIA OF THE LONGITUDINAL STABILITY
OF THE EKRANOFLAN

R. D. Irodov
Foreign Technology Division
Wright-Patterson Air Force Base, Ohio
20 November 1974

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 FTD-MT- 2t-2792-7t

EDITED MACHINE TRANSLATION

FTD-MT-24-2792-7i< 20 November 1972*

CRITERIA OF THE LONGITUDINAL STABILITY

OF THE EKRANOPLAN

By: R. D. Irodov

English pages: l^l

Source: Uchenyye Zaplskl Tsagl, Vol. 1, No. 1,
1970, pp. 63-72
Country of Origin: USSR
Requester: AFFDL/PTB
This document Is a SYSTRAN machine aided
translation, post-edited for technical accuracy
by: Robert D. Hill
Approved for public release;
distribution unlimited.

THIS TRANSLATION IS A RENDITION OF THE ORIGI-

NAL FOREIGN TEXT WITHOUT ANY ANALYTICAL OR
EDITORIAL COMMENT. STATEMENTS OR THEORIES PREPARED BY:
ADVOCATEOORIMPLIEDARE THOSE OF THE SOURCE
AND DO NOT NECESSARILY REFLECT THE POSITION TRANSLATION DIVISION
OR OPINION OF THE FOREIGN TEC OOLOGY Dl- FOREIGN TECHNOLOGY DIVISION
VISION. WP.AFB. OHIO.

FTD-MT- 2^-2792-7^ /a Date 20 NOV 197^

 All figures, graphs, tables, equations, etc. merged Into
this translation were extracted from the best quality
copy available.

U. S-. BOARD ON GEOGRAPHIC NAMES TRANSLITERATION SYSTEM

Block Ita lie Tranallteraitlon Block Italic Transliterat.

A a A A, a P p P P R, r
5 6 B B, b C e C f S, 8
B a B V. v T T T m T, t
r r r G, g V y y y U, u
a a B Df d * ♦ 0 * P, f
E • B Ye, ye; E, e* X X X X Kh, kh
» M m M Zh, zh II u u ¥ Ts, ts
3 i 3 Z, 2 M •1 V V Ch, ch
M N H 1, 1 111 111 w m Sh, ah
n ■ R Y, y 111 III m -1 Shch, shch
K K K K, k •h • "b 1 ii
JI Jl n L* 1 y u hi M Y, y
M M M M, m b 1 h 1 i
H N H N, n 8 1 9 • E, e
0 e 0 0, 0 10 » 10 » Yu, yu
n n n P, P n a * • Ya, ya

* ye initially, after vowels, and after ^, L; £ elsewhere.

wHen written as 6 in Russian, transliterate äs y6 or 6.
The use of diacritical marks is preferred, but such mark:
may be omitted when expediency dictates.

FTD-MT-24-2792-71*
 FOLLOWING ARE THE CORRESPONDING RUSSIAN AND ENGLISH

DESIGNATIONS OP THE TRIQONOICTRIC FUNCTIONS

Russian English

sin ■in
OOtt cos
tg tan
ctg eot
§•0 ■ae
cossc e«e
sh sinh
eh coeh
th tanh
eth ooth
■eh ■aeh
csch ■■oh
are •in ■ln-;
are cos coo
are tg tan":
are etg eot
are •ae ■ae'
are eoaae GBG'

are ■h ■inh-J
are eh
are th taah**^
are eth coth-1
are ■eh ■och"^
are eaeh e^eh"1

ret curl
lg log
•

FTD-MT-2^-2792-7i4 11
/
 GREEK ALPHABET

Alpha A a « Nu N V
Beta B 6 XI ^2 (
Gamma r Y Omlcron 0 0
Delta A 6 PI n ir
Epsilon E e < Rho p P 9
Zeta z C Sigma z 0 <
Eta H n Tau T T
Theta 0 e • Upsllon T U
Iota I \ Phi ♦ <P ♦
Kappa K H K S Chi X X
Lambda A \ Psl f *
Mu M M Omega Q 01

PTD-MT-24-2792-74 111
CRITERIA OF THE LONGITUDINAL STABILITY
OF THE EKRANOPLAN

R. D. Irodov

Examined are some questions of the

longitudinal stability of the ekranoplan*
directly connected with the selection of
its aerodynamic design.

The ekranoplan is a flight vehicle which uses the effect

of a considerable increase in the lift properties and lift-drag
ratio of a wing in flight near the surface (screen). The favorable
effect of the screen appears greater, the less the height of the
location above it of the trailing edge of the wing expressed in
parts of a chord. With the assigned wing area and the assigned
absolute distance from the screen to the trailing edge of the
wing, determined by the possible height of the uneveness of the
screen, the effect of the screen will be greater, the less the
wing aspect ratio. This fact defines the design of the ekranoplan
as a flight vehicle with a low aspect-ratio wing [1]. Some
features of the aerodynamic characteristics of the ekranoplan lead
to the need for the introduction of new stability criteria and
the appearance in connection with this of additional requirements

•Translator's Note. This term is a transliteration from the

Russian and not listed in dictionaries; it is believed to be some
kind of air-cushion vehicle which moves over the surface on an
air cushion.

PTJ-MT-24-2792-7^
for Its aerodynamic design.

1. The equations of pltehlng of the ekranoplan do :v*. »iiff^i

In form from similar equations fttr an aircraft and are written In
the form [2]

dV

^- = -fr(rt»~C086), (1)

2
where g Is the force of gravity [m/s ],
n and n y - ratio to the weight of the aircraft of the sum
of projections of the thrust of the engines and
aerodynamic forces on the horizontal and vertical
axes of a high-speed coordinate system,
t - time [sj,
V - flight speed [m/s],
6 - flight path angle [rad],
♦ - pitch angle [rad],
H - flight altitude (distance from the center of
gravity of the ekranoplan to the surface of the
screen) [m],
M - pitching moment [kgf'm].

The weight of the ekranoplan 0 and Its moment of Inertia I

in the analysis of motion during short time Intervals can be
considered to be constant. The effect of the aerodynamic forces
on the ekranoplan Is assigned by dependences n , n and M on the
parameters which determine the flight conditions, taking into
account the obvious equation of constraint *=e+a, where a is the
angle of attack.

When evaluating the stability of the aircraft, the dominant

role is played by the examination of motion at a constant velocity

FTD-MT-24-2792-71*
;

(short-period motion). Let us write the equations of the short-

period motion of the ekranoplar. in increments, being based on the
same assumptions as tnose In the case of an aircraft [2]: V-ccnst ;
6*9 MCX +Ae; n y -n y HCX +An y*; H»H MUX +AH; ♦«♦ wax +A»;' M^-M
z z MCX fAK a •

The initial mode is the horizontal steady flight: 6 „ »0;

M z MCX «0;* n y MCX
„ -1.

As a result of these assumptions the first equation of

system
jm (1) becomes identical
j (n =0), and the other three are
written in the form

A6 fy-An,,

A'a + Ad-4-AAf, (2)

Ä//r= 1/A6

(the dot denotes differontiatIon with respect to time).

Assuming further that the angles of attack a and the devia-

tions of the stabilizer $ and flight altitude H in the process
of the disturbed motion are changed within such limits, and that
increases in the aerodynamic coefficients Ac and Am M/iy —-^-SAc,;

AAft—J-j-5^ Am,, where p is the air density [kg«s /m ], b. - the

average aerodynamic chord of the wing [m], S - the wing area
[m ] J can be considered linearly dependent on them, let us write
•

A«Js=mjA«4:/n;Ai-fmjA9+ m'*mt4-m» AH.

Here w "-TT- is the angular rate of rotation of the ekranoplan,

$ is the angle of deflection of the stabilizer. After substituting
the expressions for Ac and Am into the system and after excluding

fTD-MT-2Ü-2792-7^
an increase In the flight path angle A8, we will obtain the system
Of two linear differential second-order equations with constant
coefficients.

Converting in this system to a new time unit T . dependent

on parameters of the ekranoplan and flight conditions T'r—> ^nu
m
- 20/S
i\j [s], introducing the differential operator with respect to
the dlmenslonless time D=d/dT and after designating for brevity

a^ _"*+"■:
'* i. ■

r d* bA ,

" bA '

20/S is the relative density of the ekranoplan;

«»=
tgbA
e IM - dlmensionless moment of inertia;
i<~

*,- Xf, — - reserve of the longitudinal static stability with

4 respect to the angle of attack is the distance
in parts of thü MAC_of the center of gravity
of the ekranoplan fx ) up to the point of the
application of a lift increment because of a
change in the angle of attack x„ :
m«
A
"' — xFH—~kr
c
~ reserve of the longitudinal static stability
r with respect to the height above the screen is
the distance in the fractions of the MAC from
the center of gravity of the ekranoplan to the
point of application of a lift increment because
of a change in flight altitude (Xpn);

»«=*t
x -| mT«
~ - reserve of the longitudinal static stability with
^ respect to overload (x , Xp and x„n by
definition are positive with the locatior of the
center of gravity and foci behind the leading
 edge of the MAC of the wlnp), let un write the
system of equations of the disturbed motion of the
ekranoplan (2) in the following form convenient
for analysis:

In the absence of the effect of the screen. I.e., the

effect of the flight altitude on aerodynamic coefficient;-, (o ■
n y
■m «0), this system falls Into two independent equations: the
equation of the short-period motion

(!)• + 210 +-J) At«•£-«; AfW

ar.d the equation which describes a change in the altitude depending

on the change in the angle of attack,

0«Afl-,»e;it(t), i.e.. iV^nnytefiJiW

or the equations which describe a change in the angle of attack

and flight altitude In the s.^ort-perlod motion,

(D* + 2ID +-J) A« --f. »ijAt(t).

(D« + 2U) + OD»AÄ-^Lr;«ijAt(t).

2
With 2C>0 and WQ>0 In the Isotropie atmosphere at constant
velocity, the aircraft is stable with respect to angle of attack
and Is neutral In flight altitude. Consequently, for the precise
maintaining of constant altitude of the flight, there must either
be the pilot's virtually continuous Interference in the aircraft
control or the introduction of stabilization of the aircraft with
r'eipeot to the altitude by the means of automatic control.

tfltn Mlgtot near the .icreon (I.e., the earth's «urTaro

" filter the ♦'crces and monujit:-. which act on the aircraft depend
JuLatantlr-ily not only on the angle of attack but also on the
tltlttttf«« Therefore, the system which describes the motion cC
tn<~ eKranopl'!.- at constant velocity does not break up into two
niept ident second-order equations. By eliminating an Increase in
i e an^ie cf attack from the system. It Is possible to write one
•quatlon of :ne fouith order, which describes a change In the flight
..titude of tb« ekranoplan In the short-period notion

ri^llar y 1*. Is possible to write the equation which describes

.' change in tn-j angle of attach of the ekranoplan:

*^-(D,-Kf)«;A?(T).

2. Le* ta ft^'te the characteristic equation of the system

In v;^ otanuard fom:

wher«
 D(c . m )
where ■ =- Is the Jacoblan functions c„(a, H) and m (o, H).
D(o. I) y z

The stability of motion in the case of the equation of the

fourth order will be provided for with

Au Au At, At>0 and -4,^,-^4-^a>0.

For all the aircraft designs In the field of flight angles

of attack, Inequality co>0 Is fulfilled. The conditions of the
stabilization of ekranoplan outside the effect of the screen la
the fulfillment of Inequality o <0.

From tests of profiles, wings and layouts of aircraft near

the screen, it is known that usually the lift coefficient at the
assigned angle of attack is Increased with the approach toward
I
the screen (Fig. 1), I.e., c <0.

From equations for the calculation of coefficients of A., it

Is evident that under these assumptions conditions A1>0, A-X)
and A^>0 are always satisfied. Consequently, the stability
conditions of the short-period motion of the ekranoplan with
flight near the screen are reduced to two inequalities: Ai.>0
2 2
and A^A^-AjA^-A'X).

The satisfaction of the first condition ensures the

aperiodic stability of the ekranoplan (i.e., the absence of the
nonnegative real roots of the characteristic equation), and the
satisfaction of the second condition ensures its oscillatory
stability (I.e., the absence of the nonnegative real parts of the
complex roots of the characteristic equation).
 M . 1 N.l#i 'HJS-.Sj'SO'tv'fl ! ! 1 After substituting
**i /\ ivnsa J i i i M i i i LiJ the expressions which
n "^^V^^ ' ! ^ >~-,J*.-ff
"^ 1 1 determine the coefficients
h ^ ^^3nZZZZZ
■^ « **
if1 "SNJ y^r-fg^g, In terms of arodynamlc
derivatives. It is possible
# *^^5:
ttJI
' ..r^SM* rr
1 ■' ,u
"L---i-i^'*^'
ff to write the stability
criteria of the ekranoplan
■ -4- { i [ i 7*/^'
41 ■«s^^:: In the short-period motion
in the following form:
^ 4/ 44 Ofi 41 (ff ft tf t.8 IS
*
mI aperiodic stability -
8.1
%•-%*<« (3)
-r-r. i i »^
'0.1-■ ttt<2rf JF or, at any sign by deriv-
-at '/ 1 1 ative c ,
Figure 1
.<0; (3a)
0(«;»)

oscillatory stability -

/
w
i
-*

Thus in order to insure the aperiodic stability of the

ekr-anoplar-, it 1? necessary by the selection of the aerodynamic
layout to insure the position of the focus In altitude above the
screen (Xtä) in front of the focus with respect to the angle of
attack (xp ). To provile for oscillatory stability, it is necessary
to select centering x in an appropriate manner.

Consequently, unlike the aircraft the longitudinal static

stability of hhich in the absence of the compressibility effect
of the air, with any aerodynamic layout, can always be provided
 for by the selection of centering, the longitudinal aperodlc
(static) stability of the ekranoplan under these conditions can
be provided for only with a iirflnHo rorm fco the floltvtiM .UMV-
JynamJ c layout. If Llir notnHtyit.'iwto la.Vvtul oT Lh»' fKraiuip l.i;i h«
^uch that the foeUfl lit aitltu.h above the r.creen Is placrd behind
the focus with respect to the angle of attack, then by the
' selection of the center-of-^ravlty location the aperiodic stability
of the ekranoplan cannot be Insured.

In model tests with a screen In wind tunnels understood by

the height of the model above the screen usually Is the distance
fron the screen to the trailing edge of the wing at the place of
its Intersection with the mean aerodynamic chord.

Unaer conditions of considerable dependence of the aerodynamic

characteristics of the ekranoplan on flight altitude, the deriv-
atives ca and m^ and the focus for the angle of attack x,, prove
y z ■ Fa ^
to be dependent on the point with respect to which there occurs
the rotation of the ekranoplan with a change in the angle of
attack. The focus In altitude xpn does not depend on the position
on the MAC of this point. If values c\ m°| and ÜL, , determined
with the rotation of the ekranoplan relative to the trailing edge
of the wing, are assigned, then their values with the rotation
of the ekranoplan relative to the center of gravity can be
calculated according to the equations

1- f
*;..
(i--*r)
X

x
F7t

JC. n».K
^Fn CZXt*9. K ' ■a

fyt.«
(in the calculation of the derivatives rn z a. H and m-z the moiuont
ta measured relative to the centei' of gravity of the ekrano^lan
x T ,' and therefore both derivatives depend on the centering).

It Itl obvious that with the center-of-gravity displacement

of tlie ekranoplan forward chordwise, its focus with respect to
the angle of attack is displaced to the side of the focus In
nltitude above the screen and In the limit coincides with it with
x -*~c». Thus, the use for evaluation of the static longitudinal
stability of the ekranoplan of data of model tests in wind tunnels
In which the angle of attack was changed with the rotation of the
model relative to the trailing edge of the wing cannot lead to an
inaccurate qualitative evaluation - the order of location of the
foci on the MAC of the wing does not depend on the center of
rotation of th« wing with a change in the angle of attack, I.e.,
on the centering of the ekranoplan.

The account of velocity change in the examination of the

disturbed motion of the ekranoplan virtually does not change the
condition of the aperiodic stability - the maximum rear centering,
letenr.ined not allowing for a cnange in the flight speed, is
somewhat displaced back in comparison with the actual, and with
sufficiently forward centering the ekranoplan again loses
oscillatory stability«

2. Let us coi.sldex for an example the longitudinal static

[aperiodic) stabiXity In flight nefj? the screen of a delta-wing
airplane, which has an elevator unit on its fuselage, the
aerodynamic characteristics of which were given In Pig. 1.
Figure 2 gives these characteristics reconstructed into the
impendence m c ) with n=const and a=ccnst- (H - distance from the
• y
center of gravity of the model to the screen). The slope tangents
of these curves are the reserves of stability in angle of attack
m 'y '■*T"*Pa and in hei ht
ß of the rii ht
e above the screen

10 ■

■
 c (R)
■ * '^T'^FR*
res ectivel
P y » with the centering I "O.S!» It If»
evident that at all the height within limitt- \S( tho iM'i\vi vV
the screen and at all atlt't«^
of attack the negative tlopo fm ■

of the curve a«const Is more ^1 1 W-s'

oc'7°ja'\
y row

4
than the slope of the curvp
R*const: this: means thai the
w ^
a / If/vs'
focup In angüe of attack of t T^&^f'
the aircraft Is located In
ott
V Mtvvfe w °.
front of the focus in height,
•not
qir* Ji6 \XV\///'I
d'/ t
■>

\^ ♦xv 20W\
1
V
which indicates the aperiodic
w«
-DM
R'O.SS H,
instability of the aircraft 11 L
with flight near the screen. Figure 2

Taklnr Into account thai' I ho i'iu;u:- in .iii)-, lo of ntiach of

wing» of small aspect ration with the approach toward the ucrcon
only very Insignificantly Is displaced back so that the Isolated
wing can be considered neutral in height above the screen or
weakly unstable, the considerable instability of the aircraft of
a normal configuration with the low-positioned elevator unit can
be explained by the fact that with the setting of the elevator
unit in the lower position the focus In height above the screen
is shifted back more than is the focus in angle of attack.

The setting of the fin on fuselage in front of wing (canard

configuration), obviously, will lead to a shift in the focus In
angle of attack forward and virtually will not change the position
of focus In height above the screen, since the fin will undergo
considerably less ground effect, since it lies above the wing at
positive angles of attack, and its area is considerably less than
the wing area. Hence it follows that the aircraft designed in
a canard configuration will also be aperlodically unstable In
flight near the screen.

Thus, the ekranoplar. for providing longitudinal static

11
stability In flight near the screen must have a special aerodynamic
design distinct from designs characteristic for aircraft with a
low aspeot^ratio wing.

One of the possible aerodynamic designs of the okran.-pla:-.,

proposed by Lippish [!]> ha;' highly positioned elovatox' unit.
Such a fin shifts the focus In anrlo-of attack consUlorahly BKMV
than does the focus iri height abi»vo tho scn^Mi, t^tiU'O It is lo^uto^l
In a zone of a sufficiently weak efiVct of tin,' scivon (at UMi-i
at sufficiently small angles of attack). Thlf design ensures the
position Of focus in angle of attack behind focus in height above
the screen under conditions of the maximum lift-drag ratio.

Another configuration can l>e "bob-tallod" with ovorfiow in tho

ro t part (aircraft of "Drarun" .i-^'- typo). With l lie appiwich inward
the screen the overlow Lnuigniflcnntly chungcu tho position of
the focus In angle of attack (x., ) but noticeably shifts forward
tho focus In the height of the flight (^i.-rj^ because of a docroase
In the relative distance from the ..CIVMI ef tho wing iviitor
section with overflow in front.

4. For the practical problsms of the «valuation of the static

ibilit> o'' -he ekranopian Laced on materials of tests of Lttf
i'l In a .■.InJ tunnel. It pi eves to be possible M write the
■nj.titl n .i' •.h.- ap*»;lodlc longitudinal ütaLllJf 'the
• rancplan '-ja) m another fen, which nn.kes U ^ul*s»iDle to mane
■:.■-.. J nations aocordln^ to only one derivative defined a/ the :Oope
of Che experisMnta] curve, virtually wlthl,ia tiic »*idit.ioni 1
.; '.traction of curves obtained a;: a ro-ilt of mini, I let:-.,
rhe : til Ine-juall ty

D(cy, m,)
<0
D(a. H)

m ' wrlttei in dry of the following four foims

FTD-Kr-2U-27 ^2-7^ 12
 da dl^csO
mr<0;
dm, dm,
~d'a~ d/l
'f

(here c y r. n ly the eoeii'u-1 Mil of lil't In n liot'lsvnitai lUondy

flight). It i:? most convenient to m-e one of the i:uU two
lüequaiitleö. Since under cruising condition? of the flit"!".;
c P <0.and c a >ü, the stability criteria can be written In the 'V
y * y *
dm, dm,
~3r <0; <0.
V'rr.o dft l»,-»,r H

.■.'ith rn <ü criterion ^0 can bo used. The derivative?

dH K o
can be found as ^iopco of curves of m^Ca) at c "conat, n (fll
with c -const or c (R) witlj in »0. as is shown on Fig?. S-".
y y s * "

.:% ftywA*^7"
M
vNss.
^ ^.
c, *c0nt YXA ^/
ry r*/»i; «••v'l
«^
/
«t
:„
—
—
^^
v s
.'\ 1 1

i
::
*■

^ 1 1 __
^* -. ^ ''S I q
i
^
V ^, i *•
«? * "■>=

v. ii
«/
^5^
^ ^ mir
^S £J
fcjj 1
■
/#•« ^ 1 '
./ «' ■ ES: -1 11 :i'' 1^1
■«/
/ /'i^ -
^a
Uss:
dmt
«/ d oc
/
4
*V>»
i
•^z
dmt\
dt
>
«
i "i
rf I
M ^f#*.<^ • "'. cmtt

Figure 3 Figure H

Since tne stability cf the ekranoplan la catinatcd inuhM1

conditions of steady flight, the txamlnation of otablliiy,
strictly ipeaking, makes senae only with i'i. = o, I.e., ;ii iv-iiii
of balancins.

F'i"u-UT-2H-2792-7i* 13
 * *t.\ Figure 5
V
*J »^
i iK l ■ **■»>-.
^ « »Af*)
^ ^
4 ^H
■

ß.e fe * - es
FN '•
< —. __
4* sj l
^*
\
r~ ~ — «•
V 1 Kmi
0
V
— -
m;
5 ' ~" — •B*r\
-</
-^1 -•
-^ 5 •'
— —
"i

In the analysis of the stability of the aircraft, usually

th« assumption Is made that the control-surface deflection dee?
n;4. change the position of focus in angle of attack, or. In ether
woi'ds, the slope of tho curves m (a). Accepting this tesurjptlcn
for tne ekranoplan and assuming additionally that the control
it flection do-r not change the position of the focus In height
;»l ■. - the acroiMi, w«> obtain the po.n-lblllty of Jud^ln^ tho
Ltablilty in slope of the appropriate curve III,.UX) or nir.(lP with
.. = c, r n and the arbltrarji value of th«^ pltehin;- montent.

hLbLIOÜRAPHY

GeJiabvni ti. M. 3J-P»IIOII,IIIII.-. .1., .Cy.ioctpociiHC'. I9W.

„. Otir <• .T a v c K M ft H. ß, K<JI<ltl f. C. npO.ao.lbii«*
in« fi'iiiBOCif. i yiitjjB.irfCMOCTb caxo.ier» M., 06opoMrM3, l9ol.

Manascript sutsiiitted
Nove/nber 6, 196f)

F'i D-MT-2^-2792-7^ lH
 nv /nw0\ 7/g
imi amttama DOCUMINT CONTHOL DATA R&D
' fCMpfiiM mttmt
Foreign Technology Division UNCLASP irii:n
Air Force Systems command
U. S. Air Force
• ■■•oar TITWC

CKiTilRIA OF THE LONGITUDINAL STABILITY OF THE EKRANOPLAN

4 cttc«i»«ivi WQTH fflfgm ml twßmi m$ wclim»» <■!»»)

h Translation
- .j 'MoaTti rn»i Miaw. mim» IMMml, lm»i mmm»<

R. D. Iiodov
• SITSS1 D*r| lb. NO or act

A?7Q
»«▼■•et «a
•• ceaTatet •MAHT MO
£& 2

• -.o.tcT»o 75007185 FTD-MT-24-2792-74

Ml* >«yan)

Approved for public release; distribution unlimited.

it

Foreign Technology Division

Wright-Patterson AFB, Ohio

20

Reproduced by
NATIONAL TECHNICAL
INFORMATION SERVICE
U S 0«partm«nt of Commwtm
Sp.mgMd, VA. 32151

DD ;r..l473 I

UNCLASSIFIED
5»runiv ClKtifn anon