The in-flight calibration of sideslip vanes using the "flat turn" technique

:LFT

T H E COLLEGE OF AERONAUTICS

C R A N F I E L D

THE IN-FLIGHT CALIBRATION O F SIDESLIP VANES

USING THE " F L A T T U R N " TECHNIQUE

by

W. G. B r a d l e y

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 T h e I n - F l i g h t C a l i b r a t i o n of S i d e s l i p V a n e s U s i n g t h e " F l a t T u r n " T e c h n i q u e . - b y W. G. B r a d l e y , B . S c . ( E n g . ) , G r a d . R. A e . S. SUMMARY

T h e "flat t u r n " t e c h n i q u e for the c a l i b r a t i o n of s i d e s l i p v a n e s i s d e s c r i b e d in P a r t A . D e t a i l s a r e given in P a r t B of the in-flight c a l i b r a t i o n s of s i d e s l i p v a n e s mounted on a de Havilland " D O V E " MK. 5 " A i r c r a f t , and a M o r a n e - S a u l n i e r M . S . 760 ' P A R I S I' a i r c r a f t .

Summary

P a r t A Theory and description of method 1 Definitions, conventions and notation 1

Theory of the method 2 2.1 The relation between heading, track and sideslip 2

2.2 Measurement of track 2 Manoeuvre technique 5 Method of calculation 6 Determination of the zero reading 7

P a r t B Sideslip vane calibrations carried out on a de Havilland 'DOVE' aircraft and a

Morane-Saulnier M.S. 760 «PARIS' aircraft. 7

Introduction 7 Instrumentation 7 Test technique 8 Analysis 8 Results 8 Discussion 9 Conclusion 10. Referrnces 1 1 . Figures

The in-flight calibration of sideslip vanes

P a r t A. Theory and description of method

1. Definitions, conventions and notation 1.1 F r e e - s t r e a m velocity V

This is the aircraft speed vector. 1. 2 Axes system

See fig. 6. 1, 3 Sideslip angle p

Sideslip angle is the angle between the speed vector, V, and the aircraft plane of symmetry. Ox. zi measured towards the plane of symmetry. Sideslip is positive when the speed vector is to the right of O^, zj i - c . when sideslipping to starboard.

1.4 Heading C

The angle between geographical North and H^i z the projection of Oxj^ in the horizontal plane. Heading angle is positive when 'measured clockwise from geographical North

1.5 Track R.

_ The angle between geographical North and the projection of the speed vector V on the horizontal plane. Track is positive in the clockwise sense.

1. 6 Longitudinal attitude 6

The angle between the longitudinal reference axis Oxj and the horizontal plane, positive when the aircraft is pitched nose up.

1. 7 Lateral attitude A.

The angle between the lateral reference Oyj and the horizontal plane, positive when the aircraft is banked to starboard.

1. 8 Angle of bank ^

The angle between the lateral reference axis Oyj and the intersection Hy, z^^ of the plane Oy z with the horizontal plane, positive when the aircraft is banked to starboard.

1. 9 Pendulum Angle P

The angle between the pendulum m a s s and the aircraft reference axis Oz^^. The angle is positive when the m a s s is to the right of Oz , to an observer looking towards the aircraft nose.

1.10 L a t e r a l Acceleration yn

The l a t e r a l acceleration of the a i r c r a f t ' s centre of gravity normal to the flight path. It is positive towards the starboard wing tip, i . e . positive when the aircraft is turning to starboard.

1.11 Vane angle or dp^?

This is the indicated sideslip value measured by either a sideslip vane or by a differential p r e s s u r e sensing device. In the case of a vane it is positive when the vane nose is pointing to starboard.

2. Theory of the method

This method was developed in France by A. Boisson (ref. 1), 2.1 The relationship between heading, track, and sideslip

Consider the projection of the speed vector V and of the body axis Ox^ on the horizontal plane, as shown in Fig. 1.

Call the projections V and Hx z. The angle between these projections is designated /?„.

ri

It can be seen that - B = C - R or /9jj = R - C

When the aircraft is in level flight with the lateral attitude A equal to zero then ^ „ =fi For such a flight path it follows that

/9 = R - C (1).

Hence, finding the angle of sideslip requires determination of the angles of track and heading.

Change in heading angle is easily measured by a directional gyro.

2.2 Measurement of track

The test technique requires the aircraft to be flown with a continuously varying angle of sideslip. The manoeuvre must be at constant altitude with the wings level. This ineans that the aircraft executes a flat sliding turn.

Fig. 2 shows the projections Hx z and Hy z on the horizontal plane passing through the a i r c r a f t ' s c. g. O, The flight path will remain in this plane as long as the altitude is kept constant.

The angle between Hx z and the speed vector V will be equal to the sideslip angle P , provided that the wings are level.

If the speed is assunaed constant, the only acceleration then lies in the horizontal plane normal to the flight path and is designated y , where

VN

= v f (2,

In p r a c t i c e , the acceleration is measured along Hy, z, and not normal to the flight path; denote this acceleration y'j^, where

^N = >'N ^°^ ^

T h e a r g u m e n t up t o now s p e c i f i e s that the wings should r e m a i n l e v e l . Now c o n s i d e r t h e g e n e r a l c a s e when t h i s i s not s o , and the effect of bank angle m u s t be included in t h e a n a l y s i s . T o m a k e a l l o w a n c e for bank a n g l e , a bank angle g y r o m u s t be used t o c o r r e c t the l a t e r a l a c c e l e r a t i o n s e n s i n g d e v i c e .

2 . 2 . 1 M e a s u r e m e n t of t r a c k u s i n g a p e n d u l u m

F i g . 3 s h o w s the p l a n e Oy z . T h e a x i s Oy m a k e s the angle of bank ^ with the h o r i z o n t a l Hy z .

Suppose a pendulum m a s s i s f r e e t o r o t a t e about O and i s c o n s t r a i n e d t o m o v e in the p l a n e Oy z T h e angle which t h e pendulum m a k e s with t h e a x i s Oz i s P , T h i s a n g l e w i l l depend on the a c c e l e r a t i o n s due t o g r a v i t y g, and t h e l a t e r a l a c c e l e r a t i o n y a c t i n g on t h e p e n d u l u m .

T h e p r o j e c t i o n of g in t h e p l a n e Oy^ z i s along the p e r p e n d i c u l a r t o Hy z and h a s t h e v a l u e g c o s 6, 6 b e i n g the longitudinal attitude a n g l e .

T h e p r o j e c t i o n of y,, in the p l a n e Oy z along Hy z is e q u a l t o y . T h e o t h e r p r o j e c t i o n of y ^ in t h e p l a n e Oy z along t h e v e r t i c a l i s e q u a l t o y' sin/5 s i n 6 and i s a s s u m e d t o be n e g l i g i b l e .

T h e p e n d u l u m m a s s o r i e n t a t e s i t s e l f a c c o r d i n g t o the d i r e c t i o n of the r e s u l t a n t of t h e v e c t o r s g c o s 6 and y .

It can be s e e n f r o m fig. 3 that t h e r e i s a r e l a t i o n s h i p tan ( ^ - P ) g c o s 6 s/ y cos/9 g c o s VT— C O S P dt g COS 6 o r dR fi

dT = s [

2 . 2 . 2 Measurement of t r a c k using an accelerometer

Consider a s p r i n g - m a s s type accelerometer mounted at or near the aircraft e.g. O, as shown in fig. 4. Assume that the aircraft is turning to starboard, i . e . it has a l a t e r a l acceleration y' , towards the starboard wing tip.

N ^ The accelerometer m a s s is subjected to an acceleration - y ' along Hy z hich has a component - y* cos <l> along Oy .

w

The m a s s is also subjected to a component of the gravitational acceleration •g', of value g cos 6 sin^ along Oy .

The resultant acceleration on the accelerometer Ay. is then Ay^.g, where Ay. is the indicated acceleronieter output, and is given by

Ay^ • g = y ^ cos 0 - g cos 6 sin^ o r

but

• _ Ayi+ cos 9 sin <p

^N ^ S[ cos<t>

V N = -^^ COS/9

= VTTCOS P

at

hence — = g A^ + cos6 sin i> | (4) ' V cos <p cos/S

Combining equations (1) and (3), and integrating ( 1^^) with respect to t i m e , the final equation for the pendulum is

A [tan (^ - P)

cos 6

/9 dt - C (5)

Similarly, for the accelerometer

/9 = / g fAyi + s i n ^ c o s e l d t - C (6) o L V cos 0 c o s ^ J

All values on the right hand side of the equations are referred to an initial steady state condition, so the above equations become

and for the accelerometer ^ /

AAyj + sin M> cos 6

V cos t4 cos ^P dt LC (8)

2 . 2 . 3 Simplified formulae

If the longitudinal attidude Q is small and the sideslip angle P is l e s s than 8 or so, equations (2) and (4) can respectively be reduced to

dR tan ( » - P) , ^.

— = g — for the pendulum (9)

dR

dT = e

(Ay^- + sin^ )

V for the accelerometer (10)

If the accelerometer is calibrated in degrees and not in units of ' g ' , then Ay^ = sin * say

and equation (6) can be closely approximated by

dR

dt

(sin * + sin ^ ) V

2 . 2 . 4 Notes on calculation

If the sideslip angle is greater than 8 , then equations (3) or (4) should be used to compute true sideslip. It should be noted that true sideslip ^ a p p e a r s in the integration t e r m on the right hand side of each equation. However, it is sufficiently accurate to use the indicated value of sideslip for this part of the computation.

By measuring the various quantities in the equations, <P , P, Ay^, or P , at successive time intervals (dR/dt) can be calculated and integrated with respect to time

to give R = f (t). Aircraft true airspeed V is easily determined and 't» can be found from

the C L / O relationship.

Changes in track A R, and heading AC, can then be used to determine P, the true sideslip angle. This can then be related to the sideslip vane angle (or if the sideslip is measured by a differential p r e s s u r e device, dp^ ) and a calibration curve obtained.

3. Manoeuvre technique

The pilot flies the aircraft at the desired indicated airspeed in a straight and level trimmed condition. P a r t of the initial t r i m is recorded and then the pilot s t a r t s to execute a flat sliding turn. This is done by a progressive application of either rudder or rudder t r i m tab. When the maximum sideslip angle is reached the control deflection is reduced to zero at the same rate at which it was applied. The pilot r e - t r i m s the aircraft in a straight and level condition. The pilot endeavours to maintain the wings level throughout the manoeuvre. Successive turns are carried out to port and starboard.

4. Method of calculation

The following assumes that a photographic trace method of recording is used. 4.1 Find the vane angle or dpys heading angle C, pendulum angle P or indicated

lateral acceleration Ay. , and bank angle <f> as functions of time. Trace reading should commence just before sideslip begins to increase and end just after it r e t u r n s to

z e r o .

4.2 All quantities, with the exception of the vane angle or dp/9 , should be normalised with respect to their initial steady state readings at t = o. This means that (dR/dt)j_Q However, the value of sideslip used in the computation of (dR/dt) i . e . the vane angle or dp o , should be normalised.

4 . 3 VHTJ ^^ computed at each time interval and integrated, either numerically or

graphically, to give R = f (t).

4.4 ^ is then calculated by equation (1) for each reading taken.

4 . 5 A calibration curve can then be drawn by plotting the vane angle or dnj against 4.6 It will usually be found that the test points lie on two lines on the calibration curve. One line is formed by the points for increasing sideslip and the other for decreasing sideslip.

(ss)

\dt

This fact a r i s e s from the basic assumption that V-— } is z e r o . This is

\dt {=Q

almost invariably untrue, since it is nearly impossible for a pilot to fly an absolutely constant heading. Any e r r o r in (dR/dt)t=o gives r i s e to an e r r o r in calculated or true sideslip which is proportional to time when (dR/dt) is integrated.

It is plain, therefore, that( — J must be known exactly, and the following procedure is suggested, ^ ^^"^ This is shown graphically in Fig. 5. Take two points having the same vane angle or dpa , one near the beginning and one near the end of the manoeuvre. Denote these points by 1 and 2, recorded at times tj and t2. Since the vane angle, and hence the angle of sideslip, is the same at tj^ and t2 it follows that the change in true track from ti to t2 is equal to the change in heading C during the same tiixie interval. Any difference between the change in heading C and the change in measured track R must come from assuming C^H/^j^)^,^ to be zero and hence

F o r each analysis point throughout the manoeuvre it is then possible to apply a correction quantity to the sideslip angle having a value

( d t ) t - o

where t is counted from t = o . This should bring all points of the calibration on to a single curve.

5. Determination of the zero reading

It can easily be seen that this technique only yields the slope of the vane angle-sideslip relationship. A pendulum can be used to find the zero reading on the calibration, i . e . the vane angle for which true sideslip is z e r o .

A ground shot should be taken on the t r a c e r e c o r d e r , together with a reading of the inclination of the aircraft's lateral axis. In this way it is possible to ntieasure the pendulum angle P with respect to the aircraft's true vertical axis. It should be noted that for the determination of track R, P need not be determined absolutely, since changes in P a r e of primary interest. However, for the determination of the zero reading, the instrument mounting e r r o r must be taken into account to find the absolute value of P , i . e . P ' Taking this into account, the t r a c e s must be examined at or near the trim condition, to find a point where P ' = O. At this instant, sideslip is zero and the vane angle at this time must be the zero reading on the calibration.

PART B. Sideslip vane calibrations carried out on a de Havilland 'DOVE' aircraft and a Morane-Saulnier M.S. 760 'PARIS' aircraft.

6. Introduction

Details are given of work carried out on two College of Aeronautics aircraft in order to verify the 'flat-turn' technique and to calibrate the sideslip vanes mounted on each aircraft.

T e s t s were carried out throughout the speed range for each aircraft, i . e . for the DOVE 90, 120 and 150 Kts. A . S . I . R . at 5,000 and 10,000 ft, , and for the PARIS 110, 160, 220, and 290 Kts. A . S . I . R . at 10,000 and 22,000 ft.

7. Instrumentation 7,1 Sideslip vane angle

On both aircraft, sideslip vane angle was measured by a simple balanced vane using an Elliott type W/121 A . C . inductive pick-off. The vanes were mounted on short probes in front of the aircraft nose, the DOVE probe being 3 feet long, and that of the PARIS 2 feet long. Range was t 15° in both cases.

7.2 Bank angle.

Bank angle was measured by a Smiths Series 7, cageable 2-axis free gyro, with Elliott inductive pick-offs mounted on the gimbals. Range used was t 5°.

7. 3 Lateral acceleration

The a i r c r a f t ' s lateral acceleration was measured with an R. A . E . type IT-1-40-31 t 0.5 g s p r i n g - m a s s accelerometer. The accelerometer was used in conjunction with a c a r r i e r amplifier and demodulator. Although the instrument has a low natural frequency, a low-pass filter was used for additional smoothing. Range was t 15° of bank ( i t 0.26 g).

7.4 Pendulum level

An S . F - I . M . type J . 32 pendulum was used for this measurement. Calibrated range was t 12°.

7. 5 Heading angle

Heading angle was measured by a basically simple directional gyro. The instrument was modified by the addition of m i r r o r s on the gimbal axis and the gyro was fixed to the back of the A. 13 r e c o r d e r . Calibrated range was t 30°. 7.6 Recording

The above quantities were recorded on a Hussenot-Beaudouin type A. 13 photographic t r a c e r e c o r d e r . Paper transport speed was | inch per second.

8. Test technique

The aircraft was initially trimmed in level flight at the desired airspeed, and thirty seconds was allowed for the t r i m to completely stabilise. Ten seconds before the manoeuvre commenced, the heading and bank angle gyros were uncaged and recording began. The pilot then progressively applied rudder angle (in the case of the PARIS) or rudder t r i m tab (in the case of the DOVE) whilst maintaining the wings approximately level. Upon reaching the maximum sideslip angle the control surface deflection was eased off at approximately the same rate at which it was

applied, until the aircraft was trimmed once m o r e , after which recording ceased. Successive turns were carried out to port and starboard, the average time for the manoeuvre being 25 to 30 seconds.

9. Analysis

The t r a c e s were read on Benson-Lehner OSCAR trace reading equipment. A type-written print-out and paper tape punch-out of the results were obtained in this way. For the main body of the work the t r a c e s were read every half second.

The paper tape was then used, with a suitable programme, as the input to the College of Aeronautics "Pegasus" computer. In this way the first plot-out was obtained (in the manner of fig. 5). From this graph (dR/dt)t=o was determined and the output tapes for the first computation used as input tapes for a re-computation, together with a subsidiary correction programme to give the final values of vane angle and sideslip.

10. Results

Fig. 7 shows the final calibration curve obtained for the 'DOVE'. It can be seen that the sideslip vane o v e r - r e a d s by about 20% throughout the range.

Fig. 8 shows the equivalent curve for the 'PARIS'. The noticeable feature of the graph is the appreciable change in slope with indicated airspeed. The amount the vane o v e r - r e a d s varies from 5% at 290 Kts. A . S . I . R . to 30% at 110 Kts. A . S . I . R .

On both aircraft no change in the calibration was noted with altitude change at constant indicated airspeed, and the zero readings were invariant with airspeed and altitude. Fig. 9 shows the results of a typical calibration run, both before and after correction for (dR)

drt=o

The fact that the 'PARIS' calibration is incidence (viz. indicated airspeed) dependent, whereas the 'DOVE' calibration is not, can perhaps be explained as

follows:-The 'DOVE' probe is 50% longer than that of the 'PARIS'; the fuselage fineness ratio is 2, whereas that of the 'PARIS' is 3. This suggests that the 'PARIS' vane is influenced more by the aircraft fuselage than the 'DOVE'. If, then, any incidence effect is present on the vane due to its proximity to the aircraft fuselage, it would seem logical to expect that the 'PARIS' should be more affected by change in flow distribution around the aircraft nose than the 'DOVE'. This argument, however, does not mean that the vane zero reading is dependent on incidence.

Adamson's report (ref. 2) gives theoretical values for the ratio between vane angle and sideslip for various vane positions, and fuselage fineness r a t i o s . Data pertaining to both 'PARIS' and 'DOVE' have been applied to Adamson's curves and compared with the 'flat turn' results in the table below.

Aircraft 'DOVE' 'PARIS' Sideslip/Vane Angle 0.80 0.806 0,75 0.740* Method Theory Flat Turns Theory Flat Turns

* The 'PARIS' slope quoted is that appropriate to 160 kts.

11.2 General

At the beginning of the work on this topic a pendulum was used for the measurement of t r a c k . At the lower airspeeds the pendulum, being undamped, exhibited a low frequency oscillation of about 0. 5 c. p. s. In order to achieve integration accuracy, this necessitated reading the t r a c e s every 0.1 second. The accelerometer, being electrically damped and having a low pass filter, had no such oscillation. A check was made to find the relationship between the final answers derived from the two s y s t e m s . The result was that with the same reading interval of 0.1 seconds, the maximuna difference was 0.15° at the maximum sideslip angle of 13°. With this and the labour involved in mind, it was decided to use the accelerometer system at a reading interval of 0. 5 second.

The t r a c e reading interval is largely a compromise between the range of sideslip to be calibrated, the time taken to execute the manoeuvre, and the trace reading labour available. It is considered that a 0.5 second time interval is about the maximum desirable for a sideslip range of t 130 or so, a manoeuvre time of 30 seconds, and an acute labour shortage.

The time taken to execute the manoeuvre is a compromise between doing the manoeuvre slowly enough to keep the lateral accelerometer output or pendulum output "on t r a c e " , and quickly enough to minimise the drift of the free gyros.

It is worth noting that variations in heading are the same whether they are referred to the air or ground. The track is calculated from the true airspeed and lateral acceleration which is referred to the ground axis , The air is moving and, since the accelerations due to viscosity and coriolis are zero, it makes no difference whether the aircraft acceleration is referred to air or ground. All quantities are measured relative to the air and hence the wind has no effect on the calculations.

It was found that the best results were obtained from manoeuvres that were carried out smoothly without any jerky control movements. On large aircraft it would be advisable to use rudder t r i m to apply sideslip.

12. Conclusions

The 'flat turn' technique provides a reasonably simple and quick method of accurately calibrating sideslip measuring devices. The above results show the importance of carrying out such calibrations whenever an accurate knowledge of sideslip is required. This is of particular importance with fuselage-mounted devices.

Since each test run is quite brief, the complete airspeed/altitude/Mach No. envelope can be covered with comparatively few flights; also a number of repeat runs can be used as a check on accuracy. The use of a digital computer greatly reduces the amount of manual analysis involved.

It is of prime importance that particular attention should be given to the instrumentation requirements for this exercise.

1 3 . References

1. Boisson, A. Etalonnage d'incidence et de

derapage. AGARD Report 77, 1956.

2. Adamson, D. E r r o r s involved in the measurement

of sideslip and dynamic head in the neighbourhood of an aircraft body. R . A . E , TN. Aero. 1895, 1947.

ACKNOWLEDGEMENTS

The author wishes to thank Dr. S. Kirkby and Mr. J. A.Milner, Department of Mathematics, for their assistance in preparing the computer programme.

F I G . l . J COS e FIG. 4. H x . i FIG. 2. H j i l i SIDESLIP g FIG. 5. cot e FIG. 3.

. • I 12 - l O / / 1 - 6 -t / 1 - Ï / / Ul < • . o | . » - 6 - * / • 2 / 2 i . - s — ^ -1 6 1 ! • - I O . - 1 3 - - I 4 -\7

4°

FIG 8 DOVE - SIDESLIP VANE CAUBRATION 9 7 -z

1 J

FIG. 9. DOVE . TYPICAL CALIBRATION RUN 120KTS. I . A . S . AT 5 0 0 0 f t .