UNCLASSIFIED AD NUMBER AD116273 CLASSIFICATION CHANGES TO: unclassified FROM: confidential LIMITATION CHANGES TO: Approved for public release, distribution unlimited FROM: Distribution authorized to U.S. Gov't. agencies and their contractors; Administrative/Operational Use; OCT 1956. Other requests shall be referred to Office of Naval Research, Arlington, VA 22203-1995. AUTHORITY 31 Oct 1968, DoDD 5200.10; ONR ltr, 28 Jul 1977 THIS PAGE IS UNCLASSIFIED
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UNCLASSIFIED AD NUMBER CLASSIFICATION CHANGESi l0 steady aerodT.amic force - also system input: if[ - fore-aft force duo to change in gyrobar tilt, lb/rad il• Xwm fore-aft force
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UNCLASSIFIED
AD NUMBERAD116273
CLASSIFICATION CHANGES
TO: unclassified
FROM: confidential
LIMITATION CHANGES
TO:
Approved for public release, distributionunlimited
FROM:
Distribution authorized to U.S. Gov't.agencies and their contractors;Administrative/Operational Use; OCT 1956.Other requests shall be referred to Officeof Naval Research, Arlington, VA22203-1995.
AUTHORITY31 Oct 1968, DoDD 5200.10; ONR ltr, 28 Jul1977
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I
STABILITY ANALYSES 'JF FLYINGPLATFORM IN HOVERING AND
FORWARD FLIGHT
October 12, 1956
1 Report No. "12
, 0. * T. PALBBACHTEK
A.PPROVED: 41ý4•G. J. SISSINGH
No. of pages •_1
* lI ADVANrED RESEARCH DIVISION1.. OF
HILLER HELAICOPTERS
. S 4i -.Ont hels eie,1e 15 Sftm In ae J WI
N. WVINT 06510.'17, psg•AmO 6. USe "Wr
-t a•-- 7 "m er•hIs lo"av
'I
This r~port is prepared in partial sat. 6faction3
I Iof Phase III of' Contract Nonr 1357(00)
;ia'
-i I
II F
as(
: I
Ii
i "
* I
I J
)'I
Iim 1 •mm •1m
L: LIST OF SMOIBS
f~P A =( 2 Z2) dma = distance from center of platform to pilot's platform supportf ~ ~~~spring ft. Also F2+ +2 ]
S= K 2 + - S + 22
a, ` fore-aft tilt of gyrobar tip path plane; + aft
B =S(z xC. ) dmb - distaunce from pilots platform to pilut o.g. Also = 22S
b lateral tilt of grobar tip path plane; + to right
C z5(x + y2 ) dm
c = distance from total e.g. to pilot's platform
D jfyzdmn (alsoii d = dist•ace from total c.g. to e.g. -f platform less pilot
E = zx dm
FFgj [ acceleration of gravity - Ft/sec'
°• I I :distaice from bottom of duct to c.g., ft.SL h distance from point of appliocit..,r of ,.-rocjyai.i drag
r. force to e.g., ft.t L hf = distrce from bottom of d, .c. .•o p,.. platform, f ..
I . See following table for numerical derivatives., V.FIDF.NTT-AL 7
r f Numerical calculations based on Hiller report No. 680.2 will show the
following variations of the stability derivatives and constants with
center of gravity location (See also P.epore . fD No, 111):
hf I uKB 2g
31 109 7.56 -. 0748 +.0343 -. 222
32.2 112.5 7.8 -. 070?4 0 -. 222
33.0 U5 7.98 -. 0748 -. 224 -. 222
34 118 8.18 -. 0748 -. 0491 -. 222
71 m 114.43 slugs
i h Fortunately, A/KB2 does not change with e.g. locationswhich greatly
I sinplifies the problem of determining the effect of e.g. (Mu) variation.
b I In the range of e.g. locations considered, Mu changes sign making the
SI rsystem -regenerative feedback.
Figure I shows the root locus of the system. Positive Mu variations areL • L shown in red and negative Mu variations i., blue. At a gain of .00529
neutral stability exists at a frequency of 0.13+ rad/sec. Increasing
the c.g. location height (i.e., raising the pilot),makes Mu less posi-
[ I rtive and the platform ztable. Theoreticallyat a gain of .00081 the
oscillitory roots would be .5 critically damped,which would give a mcs-
j•_ onable response. (The real pole at 0.24 wou .1 affect the response only
slightly).
I II 8LI fO1JFTDENTIAL
Vihe!f, at neutral stability is
('02)(L-3 .07 t-b/t/seý;.
At .5 damping
fT -00081)(1 4 .j43) .00274s Ft-lb/kt/sec..
" Although this represents a 6.5 to I change inWif, from Figure 2 it is1 • seen to occur over a very small range of Ce.g. Variations near zero M4 [? The analysis thus shows that the platform is theoretically very sensi-
S�F tive to vertical c.go location, stable only for a very small range of
'I ~Positive N 's near zero, and unstable for all negative s
The Platform as designed has a c.g. location of 19.5 inches above thebottom of the duct, and 1 "3/1..42 .+902 (Ref e Fiure 3).
: [1 The resulting stability equation is
S3 295 3 + .0161* + .q 6-69+S.-906] [(S -. 305+. 91 t II
which would give an unstable response.
II Ill
¶ JONFIDENTIAL
IV. TWO DEGREE OF FREEDC( ANALYSIS WITH Xaj
1 The transverse component of the
1- H h angular velocity at Xu due to a
zr rotation q about the c.g. is h(-.
The fore-aft force due to this rotation is Xuh" ,and hence
L X Xuh
[ With reference to Figure 3, the following table can be constructed:
$ [hf R ifxU h(ft) Xq
31 1234.83 -. 222 2. -. 532
32.2 35. -. 222 2.414 -. 5
33 35.6 -. 222 2.465 -. 5h8
34 35.96 -. 222 2.1495 -. 5514
Ave. -51
j7 If Xq ii not neglected, the equations are then
S. ., (XqS..g) X
i Nu KB'S•-- So (1?)
The block diagram for this syatem is
X0 1LL L
1. 0
I'ir IDM",A
SLONFIDENTIAL
where the outer loop has been made regenerative 0X nowever, is nega-
-r Since the gain is one, the pole at +3.66 goes to infinity and does
not enter into the response. The unstable roots of the helicopter will
i j tstill be present with the additional possibility of an aperiodic root from
Ithe small spring loop pole. If the spring cons ant is greater than 2370
Ft-lb/rad, the spring pole will be to the left •f .222 and the possibility
I of divergent aperiodic motion is eliminated. The system, howeve,, is still
I unstable and the conclusion is reached that mountLig the pitot on springs
does not appear to be a promising method of improving stability.
SJFID!NTIAL 18
i '0.FIDENTIAL
; bar VII. IN PLANE ANALYSIS OF GYROBAR STABILIZING DEVICE
In this section a free pivoted, air damped Crrobar is analyzed. The
bar senses rate of pitching motion (;), and by linkages, controls vanes
[ located below the platform that set up correcting moments. An identical
system controls the roll rate (%). Pitch alone 1ill be analyzed here
£ and in Section VIII. coupled roll and pitch will be considered.
F i If 61 is the amplitude of the flapping deflection of the pitch control
bar, and 82 the flapping amplitude of the roll control bar then*
61 + MK61 + 2 61 -220sin!1 + 2IWcosY.,(28)
S+22i°sT, + 2M.sinll1
62 + 2K262 ++ 2K2Qco9T
2, er 2 2° 2 2 (29)
Under the sssumptions
I ti a -alcos~ - bsinTl
2 -alcosl 2 blsin! 2
where +a1 is + tilt back
+bl is + tilt to right
"* "The Frequency Response of the Ordinary Rotor Blade, the Hiller ServoBlade, an6 the Young-Bell Stabiliser" by 0. J. 3issingh,Royal Aircraft Establishment Repo-t No. Aero 2307, May 1950.
• • 3NFID•IIAL 19
LO0NPIDENTIAL
Ii
the abufe two equations reduce to
E$[ 22S -2128 225+212 2 -S [S.2K] = 0 (30)
+2123 +22S S [-S+2Y] 22S+2K22 0
If only a pitch (0 sensing) bar is considered, the equation representing
the bar is
'U~ +a, + 00 (31)
This, together with the platform equation (page 7 ), result in the follow-
"ing group representing the system:
S-X. s -Ua (
I0 S S+g =0
where X and N are the force and moment derivatives set up by bar
motion.
"P t If the angle of attack of the vane is denoted by a, the linkage ratio n
•i is defined by
aa
4 I- thenX 1aX aXnal 1 .a,
= Mau i Mea Maal
IJONFIDMNIAL 20
L
L ONFIDENTIAL
If it is assumed that
M. = I L
• L
where L is the distance from the vane to the e.g. (3.04 ft. with hf
19.5"), then
x
[ al Uconstant
•a,
[ The block diagram for the system is
1, 2
IKBSL•V sx -,U
Nt !O.L.T.F. - "V
LAJ1I r) -uJ
Ma. (33):S S + .25
" II $![. [s.., 52][-.o, .,]I~~ IS.9
9 o.305) 2 .
The system is very sensitive to changes in K2. 'A value cf KX2 .4 and4- aI/B2 of about 3.0 results in a reasonable x ;ponse (Sec Fig. 4). With
2 - 2550 rpm (267 rad/sec) K .0015, a very small value.
S- 2
j , 3NFIDENTIAL 21
. - w ( .(
If -3.0 then
•Na (3)(5.62)(14 -43) l4.25 Ft'Ib/degree
The X realizable from the present vane configuration is about 6.4Ft-lb/
degree. Therefore, the linkage ratio is
5.n .6 ls2 -. 65
j [ If the bar were allowed 15 maximum deflection, the vanes would then be
at approximately 160, which is about stall.
- I
Ei
t i,
U.
-ONMIENTIAL 22
j 1 .
;- .:
RONFIDENTIAL
VIII. COUPLED PITCH AND ROLL ANALYSIS OF GYROBAR STABILIZING DEVICE
vL The Uyrobars couple the pitch and roll responses of the platform. The
six equations are then
u v a, b
S-ZU 0 0 -(XS-g 0 -X
0 -v(YPS~g) 0 0 -1 -O
S-Lv KA2S2 - 0•Lb o " -0 (31
4 !.u 0 0 100
-4 2 [S2+QK W
If sy etry is assumed andX t= -! =O then
AlLt u¥
:11 u v
J Xal - -Tbl
i = IIiS; The six uluations can be reduced to the following four:
38+3.55 x 1(15][In order to remove the theoretical instabili" I.-Iue to he assumption of tmMetry., it will be necessary to make Ma Ib . Since the system is sensitive
- to changes in that derivative, flight tests wf'l2 be made to determine th...9efactors (values of the linkage ratio, for example) that Will spread the
'*roots sufficiLently tc achieve good response.,
~J~IflN~tAL25
iL3ON7IDET=AL
IX. ORARB FLIGHT ANALYSISi A Zq, 0
The equations of motion for the platform in forward flight are the con-
[• ventional vertical plane motion equations of the airplane. These are