Kluyverweg 1 HS D E L R
T H E C O L L E G E O F A E R O N A U T I C S
C R A N F I E L D
A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF
TAIL UNIT FLUTTER ON THE M . S . 760 'PARIS'
by
Report No. 154
THE COLLEGE OF AERONAUTICS CRANFIELD
A Theoretical and Experimental Investigation of Tail Unit F l u t t e r on The M . S . 760 ' P a r i s '
by
-C . G . B . Mitchell, B.A. , D . -C . A e . D . J , J o h n s , M . S c , M . I . A . S .
Summary
After an incident which, it was suspected, was due to s y m m e t r i c elevator flutter, had occurred on the Morane-Saulnier 760 operated by the College of Aeronautics, Cranfield, a theoretical and experimental ln\«stigation of the a i r c r a f t ' s flutter c h a r a c t e r i s t i c s was undertaken.
The theoretical investigation consisted of b i n a r y and t e r n a r y s y m m e t r i c flutter calculations with and without the control circuit Included. These showed the aircraft to be liable to flutter for m a s s distributions s i m i l a r to that which existed at the time of the incident.
The experimental work consisted of flight flutter t e s t s using control jerk excitation with both film and magnetic tape recording. These showed that the a i r c r a f t a s supplied by the m a k e r s had a c r i t i c a l speed for s y m m e t r i c elevator flutter of 380 knots, but that this could be lowered to 240 knots by the installation of a stick force indicator combined with unfavourable d i s t r i -butions of fuel load and fuselage m a s s distribution. The t e s t s also showed the tail unit mode excited by rudder kicks to be safe, but a s doubt exists a s to whether this mode is the most critical a n t i s y m m e t r i c one, further work Is needed on this aspect. A 75 c . p . s . rudder buzz was encountered that was not caused by compressibility effects.
As a r e s u l t of this investigation the elevator m a s s balance was Increased and the aircraft proved to be free from elevator flutter up to at least 400 knots.
A general conclusion reached in this investigation was that static balancing of control surfaces should include the effect of components of the control circuit attached to them if those components contribute to the inertia couplings induced by vibration in other elastic m o d e s .
This report is based on a thesis submitted by M r . Mitchell in partial fulfillment of the r e q u i r e m e n t s for the Diploma of the College of Aeronautics. The investigation was supervised by M r . D . J . Johns, who prepared this r e p o r t .
Introduction 1
Ground Resonance T e s t s 1
2 . 1 . 1 2 . 2 . Discussion on the Ground Resonance Tests 3
Flight T e s t s 4 3 . 1 . Flight T e s t P r o g r a m m e 4
3 . 2 . Excitation of the M . S . 760 5 3 . 3 . Aircraft Instrumentation 5 3 . 4 . Flight Test Techniques 6 3 . 5 . The Effect of Aircraft Configuration
on the F l u t t e r Speed 7 3 . 6 . Flight T e s t s with Increased Elevator ,
Mass Balance 9 Analysis of Flight Records 9 4 . 1 . Analysis of film r e c o r d s 9 4 . 2 . Analysis of Magnetic Tape Records 10
Theoretical Investigation 12 5 . 1 . Symmetric Flutter 12 5 . 2 . F i r s t Flutter Calculation 13
5 . 3 . Second Flutter Calculation 14
Results 16
Discussion 17 7 . 1 . Safety of the Flight T e s t s 17
7 . 2 . Symmetric Flutter 19 7 . 3 . Antisymmetric Vibration 23
7 . 4 . Limited Amplitude Flutter 24
7 . 5 . Instrumentation 25
Conclusions 26 8 . 1 . Conclusions relating specifically to the
M . S . 760 four seat aircraft with tip tanks 26
8.2. General conclusions 26
Acknowledgements 27
References 28
1
-1. Introduction
The College of Aeronautics took delivery of a Morane-Saulnier M . S . 760 • P a r i s ' , r e g i s t r a t i o n G T A P R U , in D e c e m b e r 1958. This i s a straight wing all metal aircraft powered by two Turbomeca ' M a r b o r e ' gas turbines giving 883 l b . t h r u s t each. The aircraft ( F i g u r e s 1 ahd 2) h a s an all up weight of 7650 l b . It s e a t s four crew in a p r e s s u r i s e d cabin ahead of the leading edge of the wing. It has an altitude limitation of 25,000 feet and an
indicated airspeed limit of 350 knots, this latter being said to be set by wing/aileron flutter at 410 knots.
In F e b r u a r y 1960 when a stick force t r a n s d u c e r was fitted to the top of the control column an oscillation of the tail s t r u c t u r e and elevators was noticed. On F e b r u a r y 4th a flight to observe this was m a d e , when it was recorded a s a vibration of the e l e v a t o r s whose amplitude Increased with increasing airspeed from 200 knots up to the maximum the pilot considered safe, 320 knots. It could be greatly reduced, if not entirely stopped, by holding the control column firmly.
The m a n u f a c t u r e r s , when consulted, stated that they had experienced this vibration but that it only occurred when a force t r a n s d u c e r was fitted to the control column.
It was felt advisable to investigate the effect further, particularly a s the a i r c r a f t ' s tailplane is mounted at the top of the fin. In this country in the l a s t ten y e a r s at least five aircraft have been built and flown with this tailplane position. Of these one lost both elevators due to symnaetric flutter (Reference 1) and another lost the complete tailplane due to a n t i - s y m m e t r i c flutter
(Reference 2).
The advent of r e a r mounted jet engines for civil aircraft has meant that s e v e r a l m o r e aircrerft now in the project or construction stage a r e to be fitted with high tailplanes. It is thus of interest to investigate the flutter of the M . S . 760 tall unit with the aims of firstly establishing the safety, or o t h e r -w i s e , of the p a r t i c u l a r aircraft; and secondly, of attempting to l e a r n m o r e about the flutter of high tailplanes that might be applicable to future a i r c r a f t .
This r e p o r t covers the investigation of the tail unit flutter of the M . S . 760. The investigation i s both theoretical and p r a c t i c a l . The f o r m e r consisted mainly of making standard flutter calculations to find the effect of m a s s balance and control circuit on the flutter c h a r a c t e r i s t i c s of the a i r c r a f t . The l a t t e r consisted of flight t e s t s to m e a s u r e the a i r c r a f t ' s damping for s t r u c t u r a l vibrations at various s p e e d s . F r o m these the flutter c h a r a c t e r i s t i c s can be e s t i m a t e d .
The two p a r t s of the investigation must be considered together. In this r e p o r t although the details a r e separated the r e s u l t s a r e brought together whenever this provides a c l e a r e r picture of the behaviour of the a i r c r a f t .
2. Ground Resonance T e s t s
m e a s u r e d in ground resonance t e s t s .
T h r e e s e t s of ground resonance t e s t s were made during this investigation with, in general, the aircraft excited at the tailplane, using Goodman 390A electro-mechanical e x c i t e r s (Figure 3). These sets of t e s t s were each aimed at establishing different aspects of the a i r c r a f t ' s vibration c h a r a c t e r i s t i c s and the r e s u l t s of each set of t e s t s were plotted in such a way a s to highlight the aspect under consideration. In all t e s t s the control column was held in the neutral position fore and aft by an elastic cord. Figure 4 shows the location of m e a s u r e m e n t points for all the t e s t s in which the mode shapes were mapped using a hand-held Lan Elec s e i s m i c a c c e l e r o m e t e r .
Three different s e t s of exciter positions were used in all. F o r most of the t e s t s two e x c i t e r s were attached to the tailplane r e a r s p a r , one at each of the outboard elevator hinge fittings, using brackets which bolted on to the underside of the tailplane below the fittings. The e x c i t e r s were connected in s e r i e s and could be driven either in phase o r in antiphase to give s y m m e -t r i c o r a n -t i s y m m e -t r i c oscilla-tions respec-tively.
To find the effect of exciter position on the r e s u l t s one exciter was fitted to apply a l a t e r a l horizontal force to the fuselage below the fin, instead of the two e x c i t e r s on the tailplane. This could only produce v e r y small vibration amplitudes but the modes excited agreed well both with r e g a r d to mode shape and frequency with those excited on the tailplane t i p s . In addition, in the third s e r i e s of t e s t s the elevators were excited directly at their trailing edge in o r d e r to determine the circuit frequency. Measurements were then only taken for s y m m e t r i c excitation but a scan through the frequency range using a n t i s y m m e t r i c excitation showed that nothing unusual was happening.
The first set of t e s t s were aimed at obtaining a general picture of the a i r c r a f t ' s n o r m a l m.ode shapes and frequencies to guide the positioning of t r a n s d u c e r s and the design of the instrumentation system a s a whole for the flight t e s t s . The aircraft had two n o r m a l control columns fitted, had full main fuel, no fuel in the wing tip t a n k s , and carried no cockpit ballast to r e p r e s e n t the crew. It was supported on i t s undercarriage with the t y r e p r e s s u r e s reduced to about half their norm.al values for this and for both the other ground resonance t e s t s .
The n o r m a l mode frequencies from the t e s t s a r e given in Table 1.
The second set of t e s t s was aimed specifically at measuring s y m m e t r i c modes for use in the flutter calculations. The only modes measured were the wing fundamental bending, fuselage v e r t i c a l bending, elevator rotation and tailplane first overtone bending. These modes were measured with the a i r -craft in each of the following conditions:
(i) Main tank full, tip tanks empty, no nose ballast, (ii) Main tank full, tip tanks empty, 152 lb. nose ballast. (ill) Main tank empty, tip tanks empty, no nose ballast. (iv) Main tank empty, tip tanks empty, 152 l b . nose ballast.
\ 3
-four crew with p a r a c h u t e s . The u n d e r c a r r i a g e was lowered and excitation
was at the tailplane r e a r s p a r t i p s . One n o r m a l control column and the stick force t r a n s d u c e r on a stub stick were fitted.
Table 2 gives the frequencies and, where they can be m e a s u r e d , the dampings of the sjrmmetric naodes excited during the second set of t e s t s and F i g u r e 5 shows the amplitude/frequency response at the tailplane r e a r s p a r tip in condition (i).
As related elsewhere in this r e p o r t it was decided during the investigation to i n c r e a s e the elevator m a s s balance. This had been t r i e d r a t h e r crudely during the second resonance test by attaching clamps to the elevator h o r n s . This showed that increasing the m a s s balance from 5.5 lb. to 7.5 lb. stopped elevator rotation being excited by fuselage v e r t i c a l bending.
Once the elevator m a s s balance had been modified to p e r m i t it to be increased for flight it was n e c e s s a r y to repeat the ground resonance t e s t s to decide what value of m a s s balance was likely to be b e s t , and to confirm that no new i n e r t i a l coupling occurred with the l a r g e r m a s s balance fitted.
F o r this t e s t the aircrsLft was in the same condition a s for case (ii) of the second set of t e s t s . Elevator m a s s balance values of 5.5 lb. ( m a k e r s ) , 6 . 5 l b . and 7.5 l b . were t e s t e d .
2.2 Discussion on the Ground Resonance T e s t s
The behaviour of the aircraft when excited s y m m e t r i c a l l y at frequencies between 15 and 20 c . p . s . is very complicated. There appear to be t h r e e modes in this frequency r a n g e , all containing some fuselage bending and some elevator rotation in varying proportions and with various relative phase. It is difficult, and perhaps not very meaningful, to determine which of these is due to which component of the a i r c r a f t . As the e l e v a t o r phase is 90*' relative to the fuselage for the 18.3 c . p . s . mode this is the circuit resonance frequency, The 19.2 c . p . s . mode is termed elevator rotation (11) for want of a better name.
In the second set of t e s t s only two of these modes could be excited. This difference must be due either to the different control circuit inertia o r the
cockpit ballast causing two of the previous modes to m e r g e into one. Both the modes that could be excited a r e sensitive to the fuselage m a s s distribution,
During the third set of test s it was observed that increasing the elevator m a s s balance to 6 . 5 1b. reduced the elevator rotation caused by fuselage bending, and a further i n c r e a s e to 7.5 lb. prevented it com.pletely. 7.5 l b . is the m a s s n e c e s s a r y to statically balance the elevators and the control run down the fin.
With 5.5 l b . m a s s balance elevator rotation could always be excited by exciters attached to the tailplane, for any value of p o w e r used. With 6.5 lb. and low excitation power a s t r u c t u r a l mode was excited at 15,6 c . p . s . which changed to an elevator rotation mode when the power was increased or the elevator struck a sharp blow. With 7.5 lb. m a s s balance elevator rotation could not be excited from the tailplane. This indicates that 7.5 lb. m a s s balance gives effective dynamic balance of the e l e v a t o r s .
No new couplings w e r e found in the frequency range 10-50 c . p . s . when the elevator m a s s balance was i n c r e a s e d .
Throughout the t e s t s , r e g a r d l e s s of m a s s balance, s y m m e t r i c excitation at about 18 c . p . s . caused a n t i s y m m e t r i c motion of the rudder accompanied by out of phase motion of the rudder pedals. Under a n t i s y m m e t r i c excitation the most e a s i l y excited mode i s fin torsion at 13.0 c . p . s . This gives a v e r y violent v e r t i c a l a s well as fore and aft motion of the tailplane t i p s .
The s t r u c t u r a l damping i s obtained from the response s p e c t r a . Reference 3 shows that the s h a r p e r the resonance peak, the lower is the damping for that mode. The simplest way to evaluate the damping is to m e a s u r e the width of the peak at a height of 1/ V^ that of the top of the peak. If the resonance i s at a frequency of w r a d . / s e c . and the peak width is 6w r a d . / s e c , then the damping is
- Üü
^ ^ 2uThis e x p r e s s i o n is developed in r e f e r e n c e 3 , pages 72-79.
Although t h e r e i s no r e a s o n why the s t r u c t u r a l damping should be the s a m e for all resonance m o d e s , on the M . S . 760 it i s reasonably constant at 4 . 8 p e r cent, except when the main fuel tank is empty, when it is r a t h e r lower.
3 . Flight T e s t s
3 . 1 Flight T e s t P r o g r a m m e
The flight t e s t s divided into t h r e e p h a s e s . The first established the flutter c h a r a c t e r i s t i c s of the basic aircraft with empty wing tip fuel t a n k s . It was initially (and incorrectly) assumed that variation of the contents of the main fuel tank would not affect these c h a r a c t e r i s t i c s . The second phase investigated the effect of variation of t h e contents of the main and wing tip fuel t a n k s , the control column inertia and the aircraft centi-e of gravity on the flutter behaviour.
This second phase became m o r e complicated a s it p r o g r e s s e d and it was found that m o r e aircraft p a r a m e t e r s were significant. It was not completed rigorously but sufficient flights were made to understand how the various p a r a -m e t e r s affected the aircraft,
Both the first and second phases of flight t e s t s used film recording. Before the third phase started the instrumentation system was modified to allow the use of both magnetic tape and film r e c o r d i n g . A m o r e important modification was to the a i r c r a f t itself. The flutter calculations had indicated that an i n c r e a s e of elevator m a s s balance would solve the flutter problem on this aircrsift. After consultation with the m a k e r s the m a s s balance was increased from 5.5 lb. to 7.5 l b .
The t h i r d phase of flight t e s t i n g was, therefore, intended p r i m a r i l y to establish that the aircraft was free from flutter with the increased elevator m a s s balance. In addition it was also an opportunity to gain experience of the use of magnetic tape recording, and to compare this technique with that of recording on film.
5
-3 , 2 . Excitation of the M . S . 760
The best method of excitation a p p e a r s to be to use a sinusoidal exciter fitted with a tJrake. The r e q u i r e d mode can be selected by choice of
frequency, the amplitude r e s p o n s e m e a s u r e d , then the brake is applied and the decay of the oscillations used to m e a s u r e the damping. This method was originally considered for the M . S . 760, but rejected because of lack of e l e c t r i c power in the a i r c r a f t . An e l e c t r i c a l l y driven inertial exciter such a s that
used by the R . A . E . Farnborough for the flutter testing of a Meteor (Reference 4) required a large power surplus to avoid frequency hunting n e a r r e s o n a n c e .
F o r the M . S . 760 at l e a s t 1 H . P . , preferably 2 H. P . , would have been needed. The a i r c r a f t can supply a maximiun of 60 arnps at 28 volts, giving the
equivalent to 2,2 H . P . This ruled out an e l e c t r i c a l l y driven inertial e x c i t e r .
Bonkers w e r e ruled out on the grounds of safety, modification time and expense. An i n e r t i a l exciter on the control column using about \ H . P , was s e r i o u s l y considered. A s it was known that the control column affected the flutter c h a r a c t e r i s t i c s of the M . S . 760 it was decided to use stick j e r k s
initially to investigate the safety of fitting a heavy exciter to the control column. These t e s t s showed that while it would be safe, it would so change the c h a r a c t -e r i s t i c s of th-e control syst-em that th-e r -e s u l t s would not b-e applicabl-e to th-e a i r c r a f t in its n o r m a l configuration.
Use of a solenoid to excite the control system sinusoidally was considered (Reference 5). This reduced the e l e c t r i c a l power required at the expense of a complex control s y s t e m . The design and modification t i m e involved made . this system im.practicable,
This left stick j e r k s a s the only possible method of excitation; a s t h e s e proved very effective during the initial flights it was decided to continue using them throughout the investigation.
3.3 Aircraft Instrumentation
The aircraft was fitted with ten - 9g Lan Elec s e i s m i c a c c e l e r o m e t e r s in the r e a r fuselage and tail unit. Five of these were sensitive to v e r t i c a l (or normal) acceleration, five to l a t e r a l . R . A . E . torsional velocity t r a n s -d u c e r s (Reference 6) were fitte-d to each elevator an-d the r u -d -d e r . Figm'e 6 shows the positions and reference numbers of the a c c e l e r o m e t e r s and velocity t r a n s d u c e r s in the a i r c r a f t . F i g u r e s 7 and 8 show typical installations, The signals from these were integrated once or twice a s n e c e s s a r y to give displacement. This was done using fully t r a n s i s t o r i s e d equipment designed and built by the Department of Flight Instrumentation Section,
F o r the first two phases of flight testing the displacement signals were recorded on a Hussenot A 13 film r e c o r d e r . To avoid overcrowding the film a switching system was used to select six signals at a t i m e . Five switch channels were used. Channels 1 and 2 c a r r i e d the v e r t i c a l a c c e l e r o -m e t e r s and both elevator t r a n s d u c e r s and were used to record s y -m -m e t r i c oscillations. Channels 3, 4 and 5 w e r e used to r e c o r d a n t i s y m m e t r i c oscillations.
between two forms of presentation. These a r e , firstly, spacing the mean points of the signals a c r o s s the film and using small signal amplitude. This gives g r e a t e r clarity at the expense of accuracy. The alternative is to bunch all the t r a c e s at the centre of the film and use the l a r g e s t possible amplitude. The authors chose this l a t t e r alternative. It certainly i s m o r e difficult to identify the signals, p a rti cu la r ly a s it h a s not been possible to use t r a c e identification b r e a k s , but the gain of a factor of four on anapUtude h a s helped the analysis considerably once a t r a c e has been identified.
F o r the final phase of flight testing a magnetic tape r e c o r d e r was installed in addition to the Hussenot A 13. This was to gain experience of the technique of recording on magnetic tape, and to enable the transient response of the a i r -craft to a control j e r k to be analysed electrically,
3.4 Flight Test Techniques
F o r the initial t e s t s the aircraft was flown with a normal control column on the pilot's (port) side and a stub stick on the starboard side. The wing tip fuel tanks were empty. To m e a s u r e the damping in symmetric and a n t i -synamietric modes at a given speed the aircraft was t r i m m e d to that speed. The pilot struck the control column a sharp forward blow with his fist and then left the column free to v i b r a t e . The instrument channel was then
switched from 1 to 2 and the stick j e r k repeated. Next the rudder pedal was kicked and a recording made on each of the three antisymnaetric channels. This completed the m e a s u r e m e n t s at that airspeed,
Measurements were made at between 8,000 and 12,000 feet. This altitude range was chosen a s being small enough to have no effect on flutter speed. The mean altitude of 10,000 feet was decided on a s being sufficient to make it possible to escape from the aircraft if a s t r u c t u r a l failure occurred,
This initial phase was completed in five flights.
These flights showed that two oscillation modes could be excited by control j e r k s . These a r e a s y m m e t r i c fuselage v e r t i c a l bending/elevator rotation mode at 18.3 cycles p e r second with a c r i t i c a l speed of 380 knots equivalent a i r speed, and an a n t i s y m m e t r i c fin bending/torsion mode at 9.5 - 10.5 c . p . s . Over the speed range tested this l a t t e r mode h a s no critical speed for l a r g e amplitude oscillations but has non-linear damping that d e c r e a s e s with decreasing amplitude to zero for an amplitude at the tailplane tip of order 0.03 inches. Thus the
aircraft flutters v e r y gently in this mode throughout its flying life. These r e s u l t s a r e given in g r e a t e r detail and discussed in l a t e r sections.
This stage of the investigation, corresponding to the initial flutter clearance of a prototype, was completed in about one fifth the flying time normally needed to clear a new aircraft. One reason for this was the
reliability of the i n s t r u m e n t s , but a m o r e important one was that the aircraft had previously been flown to 350 knots and so was believed to be saife up to that speed. Also the flutter incident of F e b r u a r y 1960 had shown that if elevator flutter was encountered it was mild at speeds above the c r i t i c a l .
On a prototype being flight flutter tested it is prudent to take r e c o r d s at speeds up to a predetermined one on any one flight. After the flight the
7
-r e c o -r d s , a -r e analysed and it is decided how much this maximum speed can be r a i s e d for the next flight. I n c r e a s e s a r e usually about 10 knots. According to Bisplinghoff (Reference 7, page 554) an aircraft wing can be destroyed in two to t h r e e cycles of flutter 5 knots above its critical speed.
Because the M . S . 760 was believed to be safe, and the flutter was of a control surface r a t h e r than the p r i m a r y s t r u c t u r e , this test procedure was not rigorously followed. The first two flights were exploratory. On the third r e c o r d s were taken up to 300 knots. The fourth increased maximum speed to 330 knots and indicated a flutter speed of at least 360 knots, taking the most p e s s i m i s t i c set of points. The fifth flight concentrated on speeds between 320 knots and the design diving speed of 350 knots.
3,5 The Effect of Aircraft Configuration on the F l u t t e r speed
Once the flutter c h a r a c t e r i s t i c s of the b a s i c a i r c r a f t were known the investigation was concentrated on the effect of two a i r c r a f t p a r a m e t e r s on the flutter speed of the s y m m e t r i c mode. These were the p r e s e n c e or absence of fuel in the wing tip t a n k s , and the moment of inertia and m a s s moment of the control column. It was believed that the f o r m e r would affect the aerodynamic damping by altering the amount of wing flexing that o c c u r r e d , while it was known that adding a m a s s , in this case a force t r a n s d u c e r , to the control column made the aircraft m o r e liable to flutter. Whether this effect was due to stick moment of i n e r t i a (mr^) or the stick m a s s moment (mr) only was not known. As the control column slopes back in the t r i m m e d position it appeared possible for pitching of the aircrEift to cause an i n e r t i a l moment tending to rotate the elevators to act on the control column.
A s e r i e s of stick j e r k s with the wing tip fuel tanks full and then empty showed that tip fuel has a negligible effect on the flutter speed of the aircraft when the t r a n s d u c e r is not fitted to the stick,
To investigate the effect of m a s s e s on the control column on the
s y m m e t r i c flutter speed a siriall r i g was built. This was a ' T ' shaped a r m which would fit onto the stub stick in the aircraft. The stub stick i s a control column about 8 Inches s h o r t e r than the n o r m a l one fitted to the
a i r c r a f t . The upper end is designed to c a r r y the force t r a n s d u c e r or other experimental equipment that might be required. The v e r t i c a l leg of the ' T ' fitted onto the stub stick with the c r o s s piece horizontal fore and aft when the controls v/ere central (Figure 9). Weights were made from mild steel cylinders with central holes so that they could slide on the c r o s s piece. These could be fitted either forward or aft of the stick. They were held in position by a pin that passed through a hole in the weight and the c r o s s piece. There were four holes in the c r o s s piece, two forward and two aft of the stick,
E a r l y t e s t s with a 2 lb. weight on the a r m showed v e r y little variation of aircraft damiping between the weight in the extreme forward and extreme aft positions. It was therefore concluded that the effect of the stick centre of m a s s varying from ahead of to behind the column pivot was unimportant. The same s e r i e s of t e s t s showed that the damping decreased considerably when the a r m alone was fitted to the stick. It increased slightly (relative to that with the a r m only) when a 1 lb. m a s s was fitted. These r e s u l t s
fitted in an attempt to repeat the original flutter incident failed to do so. On t h r e e occasions the a i r c r a f t was flown to 350 knots with no t r a c e of vibration. F r o m stick j e r k s the flutter speed still appeared to be 380 knots, but the damping at s u b c r i t i c a l speeds was reduced. On these flights the effect of changing the a i r c r a f t ' s centre of gravity was investigated qualitatively (owing to an instrument failure no r e c o r d s w e r e obtained), and this appeared to be insignificant. This was l a t e r found to be i n c o r r e c t . The authors were thus forced to the conclusion that something had changed in the a i r c r a f t and that it was no longer flutter prone below 380 knots,
Shortly after this the a i r c r a f t with the t r a n s d u c e r fitted fluttered at 260 knots. This o c c u r r e d on a routine student flight, when the fuel in the main (fuselage) tank was almost exhausted. The incident was repeated and recorded the next day, again with v e r y little fuel in the main tank. The fuel load in this tank had originally been assumed not to affect the flutter c h a r a c t e r i s t i c s of the a i r c r a f t a s the tank has only a small displacement in the fuselage v e r t i c a l bending mode. These r e s u l t s showed that this assumption was not valid.
It m a y be felt that it was r a s h to deliberately fly the a i r c r a f t into a
flutter r e g i m e . The authors do not believe it was a s t h e r e was ample evidence that flutter with the t r a n s d u c e r fitted would not be catastrophic. F r o m the incidents and the flight of F e b r u a r y 1960 it was known that the flutter was mild, probably amplitude limited and could be stopped almost entirely by the pilot holding the control column. It was of the utmost value to get a m e a s u r e m e n t of the flutter raode shape and frequency to confirm that this mode was the one excited by stick j e r k s ,
This flight was made with 99 l b . of ballast fitted in the nose of the a i r -craft. On the next flight, this was not c a r r i e d but the aircraft was excited at intervals as fuel was burnt off. No l a r g e amplitude flutter o c c u r r e d , indicating that the amount of nose ballast c a r r i e d is a significant p a r a m e t e r . The flight also showed that the variation of damping with main fuel tank contents i s complex.
The main tank capacity is 930 l i t r e s . When it contains 600 l i t r e s the damping i s m a r k e d l y reduced compared to the case of a full tank. With 400 l i t r e s the damping i s much the s a m e , but further reducing the contents to 200 l i t r e s causes the damping to i n c r e a s e again. These r e s u l t s a r e given in g r e a t e r detail in a l a t e r section.
This r a t h e r complicated behaviour is supported by further r e c o r d s from the same flight. After excitation the s t r u c t u r a l vibrations decayed to a
certain amplitude and then continued at this amplitude until the control column was held again. This amplitude depends both on speed and main tank contents, points of large Eunplitude corresponding to points of low damping and vice v e r s a .
9
-This behaviour with the t r a n s d u c e r in and without nose ballast is so complex that it cannot be expected that a c c u r a t e predictions of the behaviour of the aircraft in other configurations can be made from it. Similarly, the flutter calculations a r e not sufficiently detailed to predict it. To clear the a i r c r a f t it would be n e c e s s a r y to fly at all possible combinations of fuel s t a t e , ballast and stick i n e r t i a .
F u r t h e r t e s t s to discover the interaction of these p a r a m e t e r s , and p a r t i c u l a r l y to m e a s u r e the variation of flutter c h a r a c t e r i s t i c s with fuel state of the basic aircraft without the t r a n s d u c e r fitted, were left until after the a i r c r a f t had been resonance tested and the magnetic tape r e c o r d e r fitted,
3-. 6. Flight T e s t s with Increased Elevator M a s s Balance
The t e s t techniques used for the third phase of flight testing were identical to those used previously, except for the inclusion of the magnetic tape r e c o r d e r in the instrumentation s y s t e m . The r e c o r d e r was fitted in the s t a r b o a r d r e a r p a s s e n g e r seat with 88 l b . of ballast under the seat. This was the maximum that could be fitted and, together with the r e c o r d e r , was the equivalent of a p a s s e n g e r weighing 134 l b . and a 24 l b . parachute. The difference between this and the standard 165 lb. p a s s e n g e r was not thought to be significant.
F o r the first t h r e e flights of this phase the aircraft was flown with the . stick force t r a n s d u c e r on the port side and a normal control column on s t a r -b o a r d . 99 l-b. of -ballast was fitted to the nose of the a i r c r a f t . This is the condition in which flutter previously occurred at about 250 knots.
The t e s t s were conducted fairly cautiously. The first flight was to 250 knots, the second to 300 knots and the third to 375 knots. The madcers
p e r m i s s i o n had been obtained to exceed the normal Certificate of Airworthiness speed limit of 350 knots. In addition, the aircraft was flown under e x p e r i -mental category B conditions because of the change of m a s s balance.
These t e s t s showed that the damping of the elevator mode was now almost constant at 2 . 5 p e r cent critical throughout the speed range of the a i r c r a f t .
The final flight was made to check that the i n c r e a s e of m a s s balance had also improved the aircraft with n o r m a l control columns. Once m o r e the a i r c r a f t was flown to 375 knots. This flight showed that the aircraft with 7.5 lb. of elevator m a s s balance but otherwise a s supplied by the m a k e r s was now free from flutter up to at least 400 knots.
4 . Analysis of Flight Records
4 . 1 Analysis of film r e c o r d s
If the aircraft can be considered a single degree of freedom system when vibrating, a s it i s if it vibrates in one n o r m a l mode, then the decay of the transient response to an impulse will be exponential. Since the aircraft is
a poorly damped s t r u c t u r e the decay will be an exponentially d e c r e a s i n g oscillation. Thus, if the logarithm of the amplitude of successive peaks of the oscillation is plotted against the number of the peak after the s t a r t of the naotion a straight line should r e s u l t , the slope of which i s related to the damping
by
y - k^°ge^
where y = c / c , A is the amplitude ratio of successive full waves.
The technique of analysing the film r e c o r d obtained from a control j e r k was a s follows. When the t r a c e from the t r a n s d u c e r to be used had been identified the envelopes of its peaks and troughs were sketched in freehand. This is shown for a stick jerk in Figure 10. The height between the envelope lines was then m e a s u r e d at each peak o r trough. The logarithm to base ten of the height was then plotted against the number of the wave, as in Figure 11. The best straight line was then drawn through thé curve and the slope of this line used to determine the damping,
In practice the decay is not exponential, but contains beats depending on the purity of the mode forced. In the vast majority of c a s e s , however, a v e r y good approximation to a straight line was obtained.
There were two exceptions to t h i s . , The mode forced by rudder kicks showed non-linear damping in that the logarithmic plot started steeply downwards immediately sifter the kick and then became l e s s and l e s s steep until at some s m a l l amplitude the slope was z e r o . Figure 12 shows an example of t h i s .
The damping was evaluated from the slope of the curve at an a r b i t r a r y amplitude of 0.316 i n s . peak to peak on the film.
The other i r r e g u l a r i t y was not so e a s y to evaluate. When the t r a n s d u c e r was fitted to the control column and under certain conditions of speed and fuel
state, the oscillation resulting from, a stick jerk did not decay for about half a
second, and then suddenly stopped in a v e r y few cycles. Figure 13 shows a film r e c o r d of a decay of this type, and F i g u r e 14 shows the corresponding logarithmic amplitude plot. It is clearly not possible to fit a straight line to a curve of this type,
The technique of film analysis used does highlight non-linearities in the a i r c r a f t ' s r e s p o n s e . F o r a good, linear t r a c e the damping could be accurately obtained with a repeatability of - 10 per cent. Frequency could be m e a s u r e d to 0.1 c . p . s . for a 20 c . p . s . oscillation. F o r this frequency the phase could be determined to 10° - 20°, the a c c u r a c y depending on the number of modes superimposed on the signals whose phases were being compared,
The highlighting of non-linearities makes the plotting of logarithmic amplitude graphs for each control j e r k v e r y well worth while, even though it i s a lengthy and tedious p r o c e s s . The line obtained makes it possible to estimate the accuracy of the result and the quantity of unwanted modes present. This is not possible if the damping is obtained directly from the flight r e s u l t s by comparison with standard exponential decay c u r v e s ,
4 , 2 Analysis of Magnetic Tape Records
When the aircraft response is recorded on magnetic tape the existence of
11
-s e p a r a t e the variou-s mode-s the -signal from the tape i -s played through a narrow p a s s filter which r e m o v e s all frequencies except the one r e q u i r e d . If the filter h a s a near z e r o damping it will not distort the signal.
In practice the tape is made into an endless loop and played backwards, This is to avoid setting the filter ringing with the initial high amplitude d i s t u r -bance and swamping the interesting part of the decaying oscillation. This technique has been t r i e d on the signals obtained from the M . S . 760 with consid-erable s u c c e s s ,
The endless loop of tape c a r r y i n g the signal to be analysed i s played back-w a r d s through a standard replay unit. The loop i s about four feet long, back-with at least a foot between the splices and the signal. The signal from the tape i s amplified, demodulated and put into the a n a l y s e r . This is a filter whose damping i s kept to z e r o by the use of an anaplifier with variable feed back.
In the equipment used the amplifier is a modified Solartron analogue computer t r a i n e r with the filter components in a separate unit. The output can be permanently recorded on paper by a New Electronic P r o d u c t s Ltd. ultra-violet r e c o r d e r type 1185. The complete set of equipment i s shown in F i g u r e 15. F r o m left to right the units a r e the tape replay deck, demodulator,' a n a l y s e r , oscilloscope and ultra-violet r e c o r d e r .
The system is first used to determine what frequencies a r e present on a tape. The signal is repeatedly put through the filter while the filter frequency is changed by small steps through its full range, from 6 - 5 5 c . p . s . Each time the signal goes through the filter it s e t s it ringing, the amplitude of
oscillation depending on the amplitude of vibration, at the frequency to which the filtej" i s tuned, present in the signal. This procedure provides data from which can be plotted an amplitude/frequency curve s i m i l a r to that obtained from a ground resonance t e s t .
The filter is then tuned to each of the response peaks in turn and at each peak an ultra-violet r e c o r d e r t r a c e is taken of the signal from the filter. These a r e comparatively pure modes and a r e analysed by plotting logarithm of amplitude curves a s before.
As a t e s t of the system the elevator response to a single stick j e r k at 150 knots was analysed. The t r a c e from the film recording of the j e r k i s shown in F i g u r e 16. This contains a 4 c . p . s . component with initial amplitude 3.1 inches and high damping, and a 20 c . p . s , mode whose logarithmic amplitude graph, from the film, is given a s Figure 17, The Initial amplitude is about 0,4 inches,
It will be seen that the damping of the high frequency component is between 3,4 and 4 . 1 per cent c r i t i c a l , and that the decay curve shows beats at 4 c . p . s . indicating a mode with frequency of either 24 or 16 c . p . s . i s also present.
Figure 18 shows the amplitude/frequency curve obtained from the analysis of the magnetic tape recording of the same stick j e r k . Clearly frequencies of 20.0 c . p . s . , 16.8 c . p . s . , 13,3 c , p , s . , 11.5 c , p , s , and l e s s than 6 c , p , s , a r e present. F i g u r e s 19 and 20 show the filtered t r a c e s and the logarithmic
amplitude graphs for the 2 0 , 0 , and 16,8 c . p . s . modes.
In the case of the 20.0 c . p . s . mode the original ratio of wanted to unwanted signal was 1 : 8. After filtering it became 2 : 1, a gain factor of 16. When the t r a c e is analysed the decay is n e a r e r a perfect exponential than the author has ever obtained from a film recording. The decay r a t e s
obtained from film and tape a r e the s a m e , although the range of possible dampings that could be obtained from the film by suitable choice of the best straight line is far g r e a t e r than could be obtained from the tape recording.
The decay of the 16.8 c . p . s . mode is also a near perfect exponential; this i s even m o r e i m p r e s s i v e a s the mode i s quite invisible on the film r e c o r d . The 13.3 c . p . s . mode had a much l e s s perfect decay, but this is hardly
surprising when it is considered that it i s a r a t h e r weaker mode. The 11.5 c , p , 8 . mode i s so heavily damped that its damping cannot be evaluated n u m e r i -cally,
These modes can all be identified a s ones that would be expected to be p r e s e n t . In o r d e r of descending frequency they a r e the control circuit (only one control column fitted), fuselage bending, a low frequency mode predicted by the flutter calculations and observed by Morane-Saulnier but not previously by The College of Aeronautics, and finally at 11.5 c p . s . tailplane bending, It is possible that the last two modes may be r e v e r s e d , tailplane bending o c c u r -ring at 13.3 c p . s ,
5. Theoretical Investigation
The technique of flutter calculations is well established, there being several textbooks (reference 3, 7 and 8) and a very detailed report (reference 9) on the subject. The theoretical investigation of the flutter of the M,S.760 tïdl unit applies the technique to the p a r t i c u l a r aircraft.
F r o m the s t a r t an energy solution of the equations of motion was used. The generalised coordinates needed for Lagrange's equations a r e taken to define m e a s u r e d n o r m a l modes for the aircraft and a control rotation. The g e n e r a l -ised aerodynamic forces on the aircraft a r e obtained in two ways, both attempt-ing to c o r r e c t two-dimensional derivatives to the comparatively low aspect ratio (3.9 for the tailplane) of the M . S . 760 surfaces.
5.1 Symmetric Flutter
F o r s y m m e t r i c flutter the modes used were an elevator rotation (the elevator being assumed torsionally stiff), the wing fundamental flexion mode and the fuselage vertical flexion mode. These were measured modes and each included all p a r t s of the aircraft a s well as the component after which the mode was named. Thus the fuselage vertical flexion mode included wing and tailplane flexion and torsion, and some elevator rotation.
Two sets of calculations were made. The first used modes measured on the third prototype M.S. 760 by O . N . E , R , A . (Reference 10), and aerodynamic forces obtained from the two-dimensional derivatives by a method developed by the first author. The second calculation used modes measured on the College aircraft and aerodynamic t e r m s recommended by Minhinnick (Reference 11).
13
-It was noticed that although the elevators a r e statically balanced when out of the a i r c r a f t , aijd normally r e s t nose down when in the aircraft, they a r e in fact under balanced. This i s due to the control run up the fin which provides an underbalancing moment of 18 lb, in. With the complete circuit connected this i s not apparent a s the sloping back control columns provide an overbalancing moment that o v e r r i d e s the effect of the control run. However, when the aircraft i s oscillating the displacement amplitude is much g r e a t e r at the back of the fuselage than at the control column. Thus the apparent static overbalance becomes a dynamic underbalance for the elastic modes
r e f e r r e d to a s wing fundamental bending and fuselage v e r t i c a l bending. This should be made clear by inspection of F i g u r e 21, which shows a schematic drawing of both the elevator control circuit and main fuel tank disposition relative to the fuselage v e r t i c a l bending mode.
In the flutter calculations the m a s s of the control run up the fin is included in the m a s s distribution for the e l e v a t o r s . This is believed to provide the inertia coupling that causes flutter in this c a s e .
5.2 F i r s t F l u t t e r Calculation
The first calculation used a wing bending mode that included some fuselage bending with a frequency of 10,3 c p . s . (Reference 10, page 50) and a fuselage v e r t i c a l bending mode at 18.3 c . p . s . that included some wing and tailplane flexure and torsion (Reference 10, page 29). These modes were checked for m a s s orthogonality and Broadbent's criterion
a
/a a v r r s s
was evaluated at 0.025. The modes were m e a s u r e d with the wing tip fuel tanks fitted but empty, the main fuel tank full and ballast representing four crew in the cabin.
The procedure for evaluating the aerodynamic derivatives for the M. S. 760 tail unit (tailplane aspect ratio 3 . 9 , t a p e r ratio 0,6) was then a s follows. The steady spanwise lift distribution for this planform was obtained from Reference 12, a s was the steady lift distribution for a rectangular aerofoil of the same aspect r a t i o . The ratio of the dynamic forces at a given spanwise station on a rectangular wing of aspect ratio 3.9 to the two-dimensional dynamic forces was obtained from reference 13 for a chosen mode shape. The ratio of steady lifts at that station obtained from reference 12 is then used to c o r r e c t the ratio of dynamic forces for a rectangular wing to that for a tapered one. The ratio of three-dimensional to two-dimensional forces obtained by this method was assumed to apply to all aerodynamic derivatives at the p a r t i c u l a r station.
When checked against the values of three-dimensional derivatives quoted by Minhinnick (reference 9) those obtained by the method outlined above agreed to within 20 per cent except for the elevator derivatives which were much too small,
A great advantage of t h r e e dimensional derivatives i s that they a r e insensitive to changes of reduced frequency, Minhinnick recommends that in general they should be regarded a s independent of frequency. In view of the work involved the derivatives were evaluated at v = 0.6 and then assumed to apply for all frequencies,
Stiffnesses for the elastic modes were evaluated by equating kinetic to potential energy in the modes excited during ground resonance t e s t s . This is valid so long a s the mode shapes do not change in flight. This assumption i s implicit in the s e m i - r i g i d method used throughout this
investigation. The stiffness of the control circuit was initially taken as z e r o ,
Once the term.8 of the equations of motion were known the solution was comparatively simple, using the F e r r a n t i Pegasus digital computer owned by The College of Aeronautics, The t h r e e simultaneous equations in the t h r e e generalised coordinates a r e solved by equating the determinant of their c o -efficients to z e r o with the speed and frequency a s unknowns,
A p r o g r a m m e was written that expanded the determinant. This gave
r e a l and innaginary equations which were cubic and quadratic in v respectively, and both contained the speed. These were solved by the same p r o g r a m m e by substituting a range of values of speed into the equations and at each speed solving each equation for v . The r e s u l t s were plotted graphically and points at which the r e s u l t s from the two equations coincided were solutions. A developed version of this p r o g r a m m e provides a s i m i l a r solution with the
added facility of being able to solve for damping at points away from the flutter boundary. This is a useful check on the stability of flutter solutions,
This type of calculation, with the circuit stiffness z e r o , is r e f e r r e d to a s the circuit cut c a s e . The r e s u l t s of the calculations a r e shown in Figure 22 where the flutter speed is plotted against the m a s s balance in the elevator horn. The predicted flutter frequency is written alongside the theoretical points,
The solution will be seen to consist of two lobes of instability. The s m a l l e r r e p r e s e n t s a high frequency mode which has both upper and lower critical speeds for all values of m a s s balance between zero and 3.6 lb. The other i s a lower frequency mode which^ has no upper critical speed and extends out to values of m a s s balance of at least seven pounds,
The agreement with the experimental result for the aircraft with the normal control columns fitted is poor both with regard to speed and frequency,
5. 3 Second F l u t t e r Calculation
A further set of calculations w e r e made to attempt to achieve a b e t t e r agreement with experiment. These calculations were the same as the first in principle, but the modes used were measured on the College aircraft and the values of aerodynamic derivatives were as recommended by Minhinnick (Reference 11).
= 15
-The modes used were m e a s u r e d for the aircraft with the main fuel tank empty, four crew and 152 l b . nose ballast. Flight t e s t s had indicated that these conditions would give the aircraft a critical equivalent a i r speed of 640 f t / s e c . at 10,000 feet. The t r a n s d u c e r was fitted to the control column during the mode m e a s u r e m e n t .
The s t r u c t u r a l t e r m s obtained from these modes were all within 15 per cent of those for the first calculation. Broadbent's orthogonality criterion for the wing bending mode with r e s p e c t to the fuselage bending mode was 0.09,
Minhinnick's technique for obtaining aerodynamic derivatives a s s u m e s that the variation of the derivatives with frequency is s m a l l . If this is so then the aerodynamic derivatives obtained from aircraft control and stability t e s t s can be used a s the derivatives for flutter calculations.
The individual derivatives obtained by this method a g r e e with those of the first calculation to within 20 per cent for the main surface and about 50 per cent for the control surface. However, after integration over the a i r -craft the final aerodjTiamic t e r m s in the flutter determinant a r e v e r y different. The t e r m s involving the elastic modes only a r e about 50 per cent l a r g e r in the second calculation, but those involving the elevators a r e quite different.
The boundaries for t e r n a r y flutter obtained by the second calculation a r e shown in F i g u r e 23. It will be seen that again the two lobes a r e p r e s e n t , the high frequency one being r a t h e r l a r g e r this t i m e . The flutter speed at m a s s balance values close to that used on the M . S . 760 i s much lower, 850 f t / s e c . at a m a s s balance of 5 lb. compared with the experimental value of 640 f t / s e c at 5.5 lb,
In addition to the t e r n a r y calculation a binary calculation was also under-taken using another p r o g r a m m e . This solved the s i m p l e r binary flutter
equations directly in t e r m s of speed and frequency. The r e s u l t s of the binary calculation using elevator rotation and fuselage vertical bending a s d e g r e e s of freedom i s shown in Figure 23. It will be noticed that the envelope of the two lobes of the t e r n a r y cal culation is almost identical to the binary curve on F i g u r e 23, but the frequencies around the binary curve in the 5 lb, m a s s
balance regime a r e v e r y much n e a r e r those measured in flight. Using elevator rotation and the wing bending mode as degrees of freedom does not predict flutter at any value of m a s s balance between z e r o and ten pounds,
Since it was known experimentally that the moment of inertia of the control column had a profound effect on the flutter c h a r a c t e r i s t i c s of the aircraft it was clearly n e c e s s a r y to include the control circuit in the calculations. 'This was done using the method developed by Templeton. (Reference 14).
The effect of the control circuit on control surface flutter depends on two p a r a m e t e r s . These a r e the circuit stiffness and the frequency of vibration of the control column if the surface is rigidly clamped. The former was obtained from ground t e s t s c a r r i e d out by Service Technique Aeronautique and described in reference 15. The l a t t e r depends on the moment of inertia of the control column or columns. On the M.S. 760 these moments of inertia were calculated from m e a s u r e m e n t s of the weight and centre of gravity of the control columns. The stick frequencies were then calculated to be 28.2 c . p . s .
for the circuit with two n o r m a l control columns or 19.7 c p . s . for the circuit with one n o r m a l column and the t r a n s d u c e r on its stub stick.
F i g u r e 24 shows the r e s u l t s of the binary calculation with the circuit included. It will be seen that a s the stick inertia i n c r e a s e s and the frequency drops the a i r c r a f t becomes p r o g r e s s i v e l y l e s s flutter prone. There is no indication of an initial lowering of the flutter speed a s the stick inertia i n c r e a s e s .
This r e s u l t does predict that when the pilot g r a s p s the control column he will stop the a i r c r a f t fluttering, a s the m a s s of his hands i n c r e a s e s the moment of inertia of the control column. However, it totally fails to predict the effect of the t r a n s d u c e r on the a i r c r a f t ' s flutter c h a r a c t e r i s t i c s .
8. Results
F i g u r e 23 gives the r e s u l t s of the circuit cut elevator flutter calculations for the a i r c r a f t in the condition that flight t e s t s had shown to be the most flutter p r o n e . It will be seen from the binary calculation that the predicted flutter speed at the value of m a s s balance used in the aircraft is v e r y much higher than that m e a s u r e d in flight, but that only a small change in the position of the flutter boundary would be needed to achieve agreement between theory and p r a c t i c e .
As a check on the calculations, and to enable the effect of s t r u c t u r a l damping to be determined, the six degree of freedom flutter simulator at the R . A . E . , Farnborough was also used to solve the flutter equations. The r e s u l t s a r e given in Table 3.
F i g u r e 25 gives the digitally calculated damping at s u b - c r i t i c a l speeds for a m a s s balance of 4 lb. This was the l a r g e s t m a s s balance at which the high frequency lobe of the t e r n a r y solution was encountered. The damping of the low frequency lobe fell to zero at its critical speed even m o r e suddenly than did that of the high frequency lobe.
Figure 26 shows an example of the response of the aircraft to a stick jerk taken at 10,000 feet altitude and 200 knots with the m a k e r s original m a s s balance, one n o r m a l control columin and one stub stick fitted,
Figure 27 shows the continuous antisymmetric oscillation of the tail unit that o c c u r s in both rough and sniooth s t i r . Figure 28 shows that continuous
self-excited 75 c . p . s . vibration of the rudder also o c c u r s .
A film r e c o r d of limited amplitude flutter with a frequency of 17 c . p . s . has been obtained for the M . S . 760 but is not included here because of its length. This film was of interest since no record of limited amplitude flutter has apparently ever been presented in a published document. Figure 29 i s a logarithmic amplitude plot of the flutter taken at 6000 ft, altitude, a speed of 300 knots with 300 l i t r e s of fuel in the main tank, , The stick force t r a n s d u c e r , one normal control column and 99 lb. of nose ballast were fitted. Figure 29 shows the limiting amplitude most clearly with the initial damping being -0.5 per cent critical. The inset drawing i l l u s t r a t e s the form of the amplitude plot as recorded on film,
17
-Figure 30 shows the variation of limiting amplitude with speed for s i m i l a r aircraft conditions.
Figure 31 shows the variation with speed of the damping of the 18,3 c . p . s , s y m m e t r i c oscillation obtained from stick j e r k s on the basic aircraft. It shows that flutter will occur at 380 knots equivalent a i r speed. When consulted on this the m a k e r s stated that they had encountered elevator flutter at 360 knots on the third prototype M.S. 760. This could be stopped by the pilot grasping the stick.
F i g u r e 32 shows that the effect of fuel in the tip tanks is very slight, possibly beneficial. This would a g r e e with the destabilising effect of wing motion predicted by the flutter calculations, but the measured r e s u l t is not really based on enough m e a s u r e m e n t s to be believed implicitly. It could be due entirely to two inaccurate points at the highest speed,
These r e s u l t s a r e all based on m e a s u r e m e n t s by t r a n s d u c e r 2 at the tailplane tip. Similar r e s u l t s a r e obtained if the t r a c e s from the elevator t r a n s d u c e r o r the r e a r fuselage t r a n s d u c e r 5 a r e used. In general the r e a r fuselage damping is some 20 - 30 per cent g r e a t e r than that of the tailplane tip, while that of the elevators is about 50 per cent l e s s .
F i g u r e s 33 and 34 show the effect of the main fuel tank contents on the damping of s y m m e t r i c vibrations when the stick force t r a n s d u c e r is fitted. The frequency ranges from 17.0 to 17.5 c . p . s . The condition of the aircraft was identical to that in which it fluttered at 240 knots except that no nose ballast was fitted.
F i g u r e 35 shows the effect of varying the vibration frequency by fitting weights to the control column while the aircraft maintained a constant speed of 150 knots. F u l l e r details of this test a r e given in Table 4.
F i g u r e s 36 to 38 show how the damping of s y m m e t r i c vibration is changed by adding 2 . 0 lb, additional m a s s balance to the e l e v a t o r s . It will be seen that the M . S . 760 i s free from s y m m e t r i c elevator flutter up to at least 400 knots with this extra m a s s balance. Tables 5 to 10 give measured dampings, frequencies and phase angles of s y m m e t r i c vibrations for various aircraft configurations.
Figure 39 shows the variation with speed of the damping of the 9 - 1 0 c . p . s . a n t i s y m m e t r i c vibration forced by rudder kicks. Figure 40 shows the variation with speed of the amplitude of the continuous a n t i s y m m e t r i c vibration of the tail unit, as measured at the tailplane tip by t r a n s d u c e r 2. Tables 11 and 12 give details of the r e s u l t s plotted on F i g u r e s 39 and 40 respectively.
7. Discussion
7.1 Safety of the Flight T e s t s
In a flight investigation of this s o r t safety is of paramount importance. In this particular investigation it was most valuable to know that before the investigation commenced the particular aircraft concerned had repeatedly flown to 350 knots with and without the transducer fitted, and would not flutter
catastrophically in this speed range. This made it possible to fly t e s t s that would have been the height of folly on an unproven prototype,
Flight flutter testing is inevitably dangerous in that the aircraft is flown to i t s design speed limits and if anything goes wrong at these speeds it i s m o r e likely to be s e r i o u s . Escape from the aircraft would also be m o r e difficult at high speed. On the other hand, flutter testing in itself will not cause flutter. If an aircraft i s going to flutter at a certain speed it will flutter at that speed, whether or not it is instrumented and tested to detect the onset of this condition.
Thus flight flutter testing can only be beneficial. Dangerous conditions can be detected and avoided, and the safety m a r g i n s at design conditions can be estimated from test r e s u l t s .
F u r t h e r steps can be taken to improve the safety of flight flutter t e s t s . If sufficient theoretical r e s u l t s a r e available, a s they should be in the case of a prototype, then the damping in each mode that should occur at a given speed will be known. If the m e a s u r e d damping does not agree with that calculated it reduces any temptation to use the theoretical work to bias extrapolation of the flight r e s u l t s to a higher speed. On the other hand, if flight and calculated r e s u l t s a g r e e with regard to damping, mode shape and frequency at one speed then it should be safe to consider theoretical r e s u l t s for a higher speed when planning the next flight. This could be most useful in the case of an aircraft for which the damping first fell, and then increased again, as speed was increased,
It is most valuable during flight t e s t s to know how speed, altitude or edr-craft configuration should be changed to reduce the violence of flutter if it o c c u r s . Usually, reducing speed stops flutter, but this need not be so on an aircraft for which the flutter reginae changes rapidly with altitude. Mach Number or fuel load. On the M . S . 760 grasping the control column stops elevator flutter as the calcul-ations predicted, but aircraft could be built such that holding the control column would make a control surface flutter m o r e violent.
Points such a s these must be borne in mind during the planning of a flight t e s t . The pilot must always know that he can r e t r e a t from a dangerous position to one that has been proved safe. The flight must be planned to r e a c h a speed that is certain to be safe, and this speed must not be exceeded. The pilot should be asked to t r i m his speed up to the final one selected r a t h e r than to fly at around the selected speed while he t r i m s the aircraft, as this underlines the need for caution. In a conservatively planned test the odd five or ten knots involved should not be of great p r a c t i c a l significance a s the safety margin should be considerably l a r g e r than t h i s ,
The g r e a t e s t danger in the M . S . 760 investigation has been one of fatigue. Elevator flutter on this aircraft is amplitude limited and can be stopped by the pilot, so will not be catastrophic. On the other hand, the s t r e s s e s induced during fluttering may be sufficient to cause failure by fatigue,
With the stick force transducer fitted to the aircraft and with the m a k e r s eleyator m a s s balance (5.5 lb.) there is slight continuous vibration at speeds above 300 knots. The s t r e s s e s induced by this should not cause damage, but in view of the lack of fatigue test data and the life the aircraft is expected to reach it should not be flown in this condition without special authority and a
19
-r e c o -r d of these flights should be kept. 7.2 Symmetric F l u t t e r
The r e s u l t s from the first phase of flight testing showed beyond doubt that the aircraft a s supplied by the m a k e r s would suffer elevator flutter at 380 knots equivalent a i r speed. This result was l a t e r confirmed by Morane-Saulnier, who had experienced elevator flutter on the third prototype M . S . 760 at 360 knots. The flutter was amplitude limited and could be stopped by the pilot grasping the control column.
The mode that the elevator couples with i s fuselage v e r t i c a l bending at 18.3 c . p . s . Both the frequency and mode shape m e a s u r e d in flight agree with those m e a s u r e d during ground resonance t e s t s .
Phase two of the flight t e s t s showed that the behaviour of the aircraft becomes much naore complicated when the frequency of the control circuit is v a r i e d . The variation of damping with frequency given in F i g u r e 35 could be due to one of two c a u s e s . It could be a r e s u l t of frequency coincidence of the aircraft as a whole with the natural frequency of the fuselage bending mode, or it could be due to some effect directly causing a change in the
damping of the aircraft. One example of this latter is fuel sloshing, an effect that will clearly change the damping of the aircraft a s a whole. It is far from obvious whether this change will account for the effects observed.
The known variation of damping of the elevator mode with main fuel tank contents and with nose ballast could be due to either mechanism. In the first case burning off of fuel or changing the ballast load will change the natural frequency of the fuselage bending mode and so change the degree of frequency coincidence. F r o m the flight r e c o r d s the extreme frequency l i m i t s for the elevator oscillation with the t r a n s d u c e r fitted a r e 17.0 c . p . s , and 17.5 c . p . s . Thus the frequency does not v a r y by m o r e than 0.5 c p . s , through the whole range of speed and naain fuel tank contents.
By the second explanation varying the ballast load will v a r y the mode shape, and hence the amplitude of oscillation at the main tank. Varying the tank
contents will v a r y the sloshing behaviour directly.
The authors feel that the second explanation i s c o r r e c t although it cannot be proved a s yet. The evidence that points towards it is given below,
F r o m the flight triials the damping at a given speed d e c r e a s e s a s the main tank fuel contents fall from full (900 litres) to 600 l i t r e s , r e m a i n s constant for 600 to 400 l i t r e s , and then r i s e s again towards that for the full tank case as the contents fall towards z e r o ,
Now the main tank is basically semi-cylindrical with the axis fore and aft, but it has a projection downwards for about the forward third of its length.
Figure 41 shows t h i s . The tank has baffles at about 1 foot intervals so sloshing of the contents as a whole will not occur; anyway, the frequency of the effect is far too high for this to be happening. However, a frequency of 17,5 c . p . s . is about that at which a fourth harmonic standing wave will form on the surface of the fuel between the baffles. Reference 16 shows that this will happen in c i r c u l a r and annular tanks. Energy dissipation in a wave system of this type
will be proportional to the free surface a r e a in the fuel.
Now, because of the shape of the tank, a s the contents fall from 900 to 600 l i t r e s the free surface a r e a of the fuel i n c r e a s e s considerably. F r o m 600 to 400 l i t r e s t h e r e is little change. By the time the contents a r e down to 300 l i t r e s all the remaining fuel i s in the forward tank section and the surface a r e a i s much reduced.
The flutter calculations show that a s the control colrnnn inertia is increased the unstable region on the flutter diagram i s steadily reduced. This h a s been shown in Figure 24. The calculation thus indicates that grasping the stick and increasing the stick inertia by the m a s s of the pilot's hands will stop the elevator flutter. It gives no suggestion of the initial drop of flutter speed that occurs when the flutter frequency is lowered towards 17.5 c . p . s - One of two conclusions can be drawn from t h i s . Either the calculation is not c o r r e c t , which does not appear likely in view of its accuracy in predicting the flutter speed and frequency, or some effect is occurring which has not been included in the calculation.
If fuel sloshing is occurring it is a s a high, probably fourth, harmonic standing wave between the tank baffles and will cause a positive damping of the a i r c r a f t s t r u c t u r e (reference 16). Energy is absorbed by, and dissipated in, the fuel motion. This a p p e a r s to be a stabilising effect, but in fact need not be s o . Damping, as well as absorbing energy, will cause phase changes in the complete motion of the aircraft. These changes will alter the rate at which the oscillating aircraft absorbs energy from the a i r s t r e a m . If damping i n c r e a s e s this r a t e by m o r e than the r a t e of dissipation due to the damping the overall effect will be destabilising,
This effect has been shown by Broadbent in reference 17, where the introduction of up to 20 p e r cent c r i t i c a l s t r u c t u r a l damping in a wing flutter
problem was found to reduce the flutter speed. However, when the Royal Aircraft Establishment six degree of freedom flutter simulator was used to investigate
the effect of s t r u c t u r a l damping on the M . S . 760 elevator flutter this was found to be very beneficial.
F r o m the flight t e s t s the phase of motion of the elevators relative to that of the tailplane has been observed to v a r y . At 300 knots with the n o r m a l control column fitted the elevators a r e in phase with the tailplane. Fitting the stick force t r a n s d u c e r causes phase changes of 60° to 85°, the exact value depending on the contents of the main fuel tank. Large values of phase angle correspond to points of low aircraft damping.
Thus t h e r e can be no doubt of one link in the mechanism by which the t r a n s d u c e r or main fuel tank contents affect the elevator flutter of the M.S. 760. The mechanisna is one of changing the phase angle between the two significant degrees of freedom of the aircraft to enable it to extract m o r e energy from the a i r s t r e a m .
Two minor pieces of evidence support the case of fuel sloshing. One i s the 'plateau' type of decay curve, an example of which is shown in Figure 13 and 14. These look as though motion of something in the aircraft builds up for about half a second after a stick j e r k . Then, when the amplitude r e a c h e s a critical level, the aircraft changes in some way and becomes v e r y heavily damped. The change does not cause a change of phase angle between the
