Cranfield Report a.S.a.E. No 2-1971

8/11/2019 Cranfield Report a.S.a.E. No 2-1971

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C R A NF IE LD R E P O R T A . S . A . E . N O . 2

C R A N F I E L D

I N S T I T U T E O F T E C H N O L O G Y

P I L O T E X P E R I M E N T A L S T U D Y O F T H E V I B R A T I O N

C H A R A C T E R I S T I C S O F

A M A C P H E R S O N S T R U T W H E E L S U S P E N S I O N

by

R. M. STAYNER


2/30

Cranfield Report ASAE No. 2

April.1971

CRANFIELD INSTITUTE OF TECHNOLOGY

PILOT EXPERIMENTAL STUDY OF THE VIBRATION

CHARACTERISTICS OF

A MACPHERSON STRUT WHEEL SUSPENSION

- by -

R.M. Stayner

S U M M A R Y

The vibratory force transmissibility of a strut type wheel suspension has

been investigated in the laboratory. Measurements were made using an electro

hydraulic vibrator and both swept frequency sinusoidal and broad band random

excitation. The development of the test rig and the analysis equipment are

described briefly. The results indicate the importance of non-linearity in

the response of the suspension system and the need for a more satisfactory

theoretical analysis.


3/30

CONTENTS

INTRODUCTION

EXPERIMENTAL DETAILS

Page No.

1

1

General design of the rig

Modifications

Sinusoidal analysis equipment

Swept sinusoidal vibration tests

Constant frequency test

Random vibration tests

1

1

2

2

3

3

CALCULATION OF TRANSMISSIBILITY FUNCTIONS

Swept sine forcing

Random forcing

DISCUSSION OF RESULTS

Raw data

Reduced data

Sing le f requency t e s t

Relevance of theoretical analysis

SUGGESTIONS FOR FUTURE WORK

General investigation of suspension systems

Extensions to theory

Verification of experimental method

Extensions to experiment

Equipment improvements

CONCLUSIONS

5

6

6

6

7

7

7

7

8

TABLES

1.

2.

3.

Force transmissibility from swept sine analysis

Force transmissibility from random analysis

Resonant frequencies: experimental observations

compared with theoretical values

9

10

11

FIGURES

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Block diagram:swept,sinusoidal vibration.

Block diagram: random vibration.

Swept sine vibration response: vector locus

Swept sine amplitude response.

Typical repeatability of consecutive sweeps.

Distortion effects.

Force in strut, 15-200 Hz., 60 lb. input force,

Force in tie-rod, lower link, 15-200 Hz., 60 lb. input force.

Force in strut, 15-200 Hz., 30 lb. input force.

Force in tie-rod, lower link, 15-200 Hz., 30 lb. input force,

Force in strut, tie-rod, 2-50 Hz., small displacement.


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Forceinstrut, tie-rod,4-50Hz ., larger displacement.

Constant frequency responsetovariationsinforcing amplitude.

Strut force, displacement.

Tie-rod force, lower link force.

Responsetorandom forcing,

Displacement p.s.d.,0-25Hz ., larger displacement.

Strut force, input force,0-25H z. , larger displacement.

Tie-rod force, lower link force,

0-25

Hz. , larger displacement.

All forcesanddisplacement p.s.d.0-25Hz, , smaller displacement,

Tie-rod force, input force p,s.d.,0-200 Hz,

Strut force p.s.d.,0-200 Hz.

Force transmissibility functions.

Sinusoidal forcing, 15-200 Hz.,60 lb.input force.

Sinusoidal forcing, 15-200 Hz.,

30 lb.

input force.

Sinusoidal forcing,

2-50

Hz., small displacement.

Sinusoidal forcing,4-50Hz ., large displacement,

Random forcing0-25Hz., (large displacement).

Random forcing0-25Hz ., (small displacement)

Random forcing0-200Hz ., strutand tie rodforce only.

Strut forcefor alltypesofinput.

Tierodforcefor alltypesofinput.

Lower link forcefor alltypesofinput.

Force transducer calibrations.


5/30

- 1 -

The vibratory forces transmitted through an automobile suspension system

may be studied in the laboratory and related to theoretical analysis of the

system. The work reported here concerns the development of experimental

techniques useful in such a laboratory study.

Measurements were made on a test rig in which an electro-hydraulic

vibrator was used to excite a single suspension system in isolation. This rig

was built to validate the theoretical analysis of a student thesis project,

but has not yet been operated successfully. A brief series of experiments

was carried out in which forces transmitted through the suspension system were

analysed, by several techniques, at frequencies in the range 0-200HZ. Two

types of excitation were used; swept sinusoidal and broad band random. For

the former, equipment was available to plot the complete vector locus of the

relationship between two variables, or to track and plot the fundamental

amplitude of a distorted signal. For the randomly excited vibrations, analysis

was restricted to power spectral density functions of single variables.

The details of the experimental techniques, discussed in the next section,

are included as an aid to future, more complete studies using the same or

similar equipment. This leads to the procedures for obtaining transmissibility

functions from the raw data, as required for evaluation of both the suspension

system and the experimental methods. The results are then discussed with

reference to the existing theoretical analysis of the suspension system, and

finally some suggestions are made concerning possible continuation of

experimental and analytical work on this topic. Continuation of such work is

encouraged by indications of variation in the system characteristics observed

during this preliminary investigation. Further experiment is also required

to resolve a certain lack of correlation between results of random and swept

sinusoidal vibration tests.

EXPERIMENTAL DETAILS

General Design of the Rig.

The general design of the rig is fully described in the relevant A.S.A.E.

thesis.*

A stiff frame supports the suspension unit, as on the car, by the top

of the MacPherson strut, the inner pivot of the transverse lower link and the

stabilizer bar. Also attached to the frame and connected to the wheel spindle

is the ram of the electro-hydraulic vibrator. Force transducers are inter

posed between the hydraulic ram and the wheel spindle and between the frame

and suspension system at each attachment point. A displacement transducer

is fitted between the frame and the wheel spindle.

Provision is made for forcing the wheel spindle in each of three directions,

effectively vertically, longitudinally, and laterally, relative to the orient

ation of the suspension as part of the car. Only the first position was used

for the tests described.

Modifications

Modifications made since the rig was originally completed concern the

control and measurement functions. A two channel carrier-amplifier system

was constructed for the input force transducer and for the displacement trans

ducer.

The latter had been replaced by one of the inductive type as the

W.J. Foulkes

(1966).


6/30


7/30

- 3 -

However a source of error was introduced in that the amplitude response of the

tracking filter varies with frequency. This did not affect the vector plotting

function as the output was used to provide phase information only, but for

tracking filter operation it presents a considerable limitation.

Repeatability of measured frequency functions was better for pairs of runs

with the same direction of frequency sweep (fig. 4) than for pairs of runs with

opposite directions of frequency sweep. This suggested a system response for

decreasing frequency sweeps which differs from that for increasing frequency

sweeps. To avoid investigation of this phenomenon at this stage, tests were

restricted to increasing frequency only. The output of each force transducer,

total and fundamental component, was plotted for each of two input force levels,

nominally 60 lb. r.m.s. and 30 lb, r.m.s. (figs. 6 - 9 ) .

To extend the frequency range below 15 HZ , distortion information was

neglected and only total r.m.s. outputs of the transducers were recorded. This

allowed frequencies as low as 2 HZ to be investigated, and the input force level

to be plotted concurrently with each output using the second pen of the X-Y

plotter. The lower level of input force, 30 lb. r.m.s. was used, but only two

of the outputs were obtained, since the system response changed radically during

this series ofruns. The change, which occurred suddenly, is attributed to a

reduction of coulomb friction with increase of working temperature, since

displacement amplitude increased markedly. Fig. 10 shows the responses at the

start of the test, while fig. 11 shows the later responses.

Constant Frequency Test

A constant frequency test was therefore carried out to investigate the effect

of varying the amplitude of the input force. A frequency of 6.5 HZ was chosen

as at this frequency considerable force change had been observed (fig. 12 and

fig.

13). The displacement demand signal was gradually increased from zero, with

the force feedback amplitude control removed. It is to be noted that the chosen

force level for the previous tests, viz. 30 lb., was the maximum for system

operation under friction lock conditions at this frequency.

Random Vibration Tests

Random vibration tests were carried out with demanded displacements of band-

limited white noise. Two ranges were chosen to suit the analysis equipment.

viz.0 - 25 HZ and 0 - 200 HZ. The input frequency content was controlled by

properties of the vibrator/suspension system and no attempt was made to obtain

white noise characteristics for either the input force or the displacement

(fig. 2) . An extended series of tests was not planned and so the most readily

obtainable random excitation was used. All transducer outputs were recorded for

The tracking filter is made up of a set of modular equipment. The performance

was reported to the manufacturer who conducted supervised tests of each component

module. These were all within the quoted specifications. Similar checks were

observed on other modules which, when combined in the tracking filter configuration

had a far better frequency response. No cause could be found for the poor

performance of the A.S.A.E. system, but it is suggested that it be returned to the

manufacturer for a more extended test so that it can be brought up to specification.


8/30

-

4 -

power spectral analysis,andtheir r.m.s, levels for allfrequencies above

2

HZ)

measured with

a

valve voltmeter.

For

the

lower frequency analysis,

0 - 25 HZ

(Figs. 14-17) displacement

and

all

four force signals were recorded

at

each

of two

levels

of thedis

placement signal. These were obtained

for the

same r.m.s. input force

by

approaching this force from firstahigherandthenalower value. Inthisway

it

was

hoped that

the

results could

be

related

to

those obtained with sinusoidal

excitation when

two

types

of

response were observed

for the

same input.

The broader band analysiswas retrictedtoinputand twooutput forces

(figs.18 and 19)

only,

by a

shortage

of

analyser tape loops

and

experimental

time.

CALCULATION

OF

TRANSMISSIBILITY FUNCTIONS

The transmissibility functions were calculated

for

each type

of

excitation

so that

the

random

and

swept sine vibration results could

be

compared.

Comparison

of the

system response

to

different levels

of the

same type

of

forcing

is also simplified.

Swept sine forcing

Fortheresultsof thesinusoidal forcing tests,thetransmissibility ratios

of each output force

to the

input force,

as

functions

of

frequency, (figs.

20 - 23)

were obtained

as

follows:

At each frequencytheamplitudes were read fromtheplotted results. Using

calibrations

of the

transducers,

e.g. in

Ibf./volt

fig. 30, and of the

analyser

plotted output,

in

volts/cm.,

the

measured amplitudes were converted

to Ibf.

Ratios

of two

force levels thus obtained could

be

plotted directly

as

trans

missibility functions. Where suitable, frequency intervals were restricted

to

those marked duringtheexperiment,but forrapidly changing functionsit wasoften

necessary

to

interpolate frequency values, with some lack

of

accuracy.

All values were measured from total signal level curves, corrected where

distortion

was

observed.

A

linear amplitude response

was

assumed

for the

analyser,for thecalculations,but infacttheresponseof thesystemwassome

what non-linear

and

results

for

values outside

the

range

0.025 - 0.075

volts

are

not accurate. Table

1

shows

a

specimen calculation

for

sinusoidally obtained

transmissibility functions.

Random Forcing

Calculation

of

transmissibility functions from

the

results

of the

random

forcing tests

are

complicated

by the

presentation

of the

results

as

power spectral

density functions,

i.e., as

plots

of

mean squared amplitude density.

In

addition

the variance inherent

in the

results must

not be

confused with minor system

resonance effects. Procedure

was as

follows:

The area under each p.s.d. curve

was

measured,

and

that amount

for the

area

above

2 HZ was

used

to

calibrate

the

power density scale.

The

area represents

the mean square signal level,

and the

root mean square level

was

known from

the

voltmeter reading taken during

the

test.

The

resulting values

of for

example

lb2/HZ/cm. were notedforeach variable. Amplitude values were measured from

the p.s.d. curves

as cm. and

ratios calculated

for

each frequency

and

pair

of

curves

in

these units. Square roots then taken yielded transmissibility functions


9/30


10/30

- 6 -

vibrator/suspension system to a demanded white noise displacement control.

The actual displacement cannot be maintained at frequencies above a few HZ ,

while the input force at low frequencies is very low if large displacements are

not allowed. Tie rod and lower link forces are maintained even at low

frequencies and vary little in frequency content with amplitude of forcing.

Strut force increases at low frequencies as displacement level is increased, but

not at frequencies above 10 HZ, although displacement frequency spectra have

similar forms for the two cases.

Reduced Data

The reduction of the raw data to obtain transmissibility functions introduced

little change in the interpretation of the results of the swept sine tests.

Agreement between transmissibility function amplitudes from both sets of results

was good for the tie rod force, but only fair for the low frequency test and so

no comparison can be made. It may be worth noting that the tie rod force

appeared least effected by amplitude variation in all the available raw data.

Reduction of the results of the random vibration tests yielded transmiss

ibility functions which, except for the tie rod, differed considerably from those

obtained in sinusoidal vibration (figs. 27 to

29).

Where comparisons are

available, the form of the transmissibility functions is similar, with main

resonances apparent from the strut force at 20 HZ, and from the tie rod at 25 and

60 HZ, but the vibrator/system response was limited to frequencies below 130 HZ.

The lower frequency random test was less informative. Differences in the forces

appear related to differences in the displacement transfer function, but not to

the results of the sinusoidal tests.

Single Frequency Test.

The results of the test carried out at a single frequency with gradually

increasing amplitude (figs. 12 and 13) bear out the previous observation that two

types of response are possible for one amplitude of input force. In this case

the low frequency swept sine test had been carried out with the input controlled

to be 30 Ibf., which value corresponds to the limit of one type of motion at 6.5

HZ. The sudden increase in displacement amplitude was accompanied by a decrease

in all the force amplitudes, but it is to be noted that the force transmissibility

ratios did not all decrease. The force transmitted through the tie rod increased

considerably.

Relevance of Theoretical Analysis

The relevance of the earlier theoretical analysis of the suspension system

must be questioned in the light of the comparison afforded by table 3, In this

table the predicted resonant frequencies for a simplified model of the suspension

system may be compared with maxima of the force transmissibility functions.

Particularly notable is the lack of predicted resonant conditions between 90 and

200 HZ, when in fact, in addition to those resonances shown, there were several

which did not result in high force transmissibilities but were observed to produce

considerable displacements. The primary standing wave frequency in the main spring

was observed at the calculated frequency, but produced increased force transmiss

ibilities only through the lower link and through the strut in the high friction

state.


11/30

- 7 -

SUGGESTIONS FOR FUTURE WORK

General Investigation of Suspension Systems

The investigation of suspension systems as vibration isolators should be a

feasible experimental task. It should serve as an aid in verifying or modifying

analytical models for an integrated vehicle analysis, and also as a design tool

for the study of components and of temperature and ageing effects. Information

could also be provided of dynamic loading applied to the vehicle structure, i.e.

verification of force analysis procedures. The methods are available for such

work, but further development is still required, as indicated in the following

paragraphs.

Extensions to Theory

The theoretical analysis for the particular suspension used requires

considerable extension to be of any practical value, A more complete model is

required for prediction of many of the frequency effects observed. It should

at least be three dimensional. Further degrees of freedom could be included after

experimental study of individual resonances. Such a study requires the theory

to yield modes of vibration for each resonance, and measurements to be made of

displacements or accelerations of several co-ordinates. To be relevant to the

measurements made and the results sought, the model equations of motion should be

solved for transfer functions or frequency response functions relating forces at

fixtures to force input to the hub. This force input to the hub, which should be

a random function in order to produce realistic operating conditions, must be

related to observed suspension inputs which may be available only in the form of

displacement or acceleration values.

Verification of Experimental Method

Further verification of the experimental method is required before any

weight can be given to the disparity between certain swept sine and random

vibration results. These preliminary tests must be repeated, with a careful

check on transducer calibrations and amplifier settings. What little insight

that has been gained into the response of the system should be used to ensure

that results are obtained from all transducers for each type of forcing. It

would be particularly valuable to include the displacement in the swept sine

test as a record of the system operating conditions. Random analysis should

be carried out with longer sample recordings.

Extensions to the Experiment

Extensions to the experiment can be suggested in many

ways.

Forcing has

so far been limited to one axis only, but the rig was designed for forces to be

applied to the wheel spindle from any of three mutually perpendicular directions.

In the first instance, each axis of forcing could be used, with a range of

pre

loads on the main suspension spring. It would also be possible to force the

system on two axes simultaneously to study the effect of coulomb friction in

the strut on transmission of horizontal forces. Random forcing with amplitude

and frequency parameters similar to road conditions may be obtained using the

equaliser filter set for low frequency shaping. Effect of statistical parameters

of the forcing on system response could be studied and related to swept sinusoidal

responses.

There is much basic information which could be gained from a series

of constant frequency tests, in each of which the variation of system response

with amplitude may be measured.


12/30

- 8 -

Equipment Improvements

Improvements can be made in the laboratory equipment to reduce approximations

involved in some of the measurements and to reduce the labour of data reduction.

The swept sine tests would benefit from incorporation of a dependable

frequency discriminator. A suitable module is available to fit into the

frequency response analyser. The analyser would be far more valuable if the

complete tracking filter arrangement could be brought up to the maker s claimed

performance. This is quite feasible for the frequency response, and surely the

non-linearity of the output amplitude response could be reduced. Random testing

would be facilitated if equalisation filters covering the range 25 - 200 HZ were

added.

Data reduction should be carried out on the digital computer. For swept

sine tests the higih speed data logger could be used to digitise the frequency

response curves instead of recording them on the X-Y plotter. A high speed

analogue-to-digital converter is available which was bought with random signal

analysis in mind. This could be used, either on-line or from magetic tape

recordings of the experiments, to enable the digital computer to be used for cross-

spectral analysis, a function which the existing analogue equipment cannot perform.

A suitable programme ought to be available for such analysis in the computer

library of programmes.

CONCLUSIONS

In conclusion, it is not claimed that the experimental results presented

here are themselves reliable descriptions of the performance of the MacPherson

strut suspension system. Rather it is hoped that as the results of only four

days laboratory measurements they are indicative of the state of development

of the equipment and experimental techniques. Variations were observed in the

response of the suspension system. Since these were such as the equipment was

intended to measure, it is suggested that the work could be continued to some

purpose,


13/30

- 9 -

TABLE 1

Force Transmissibility from Swept Sine Analysis

Assumed sensitivity of analyser graphical output: 1 cm.reps.0.005volts

Transducer calibrations: Input force, f, 1250 Ibf./volt.

Strut force, s, 1545 Ibf./volt

Results, 4 - 5 0 HZ , large displacement amplitude:

Frequency

HZ

4

6

7

10

14

17

20

25

30

40

47

50

Input

cm.

6.1

5.8

4.2

4.3

4.5

4.4

4.5

5.1

4.8

4.5

4.6

4.5

force,

f

Ibf.

38.1

36.2

26.3

26.9

28.1

27.5

28,1

31.9

30.0

28.1

28.75

28.1

Strut force, s

cm. Ibf.

11.4

6.4

3.5

3.0

3.0

4.5

11.2

13.2

11.1

6.1

2.5

3.4

88.0

49.5

27.0

23.2

23.2

34.8

86.5

102.0

85.8

47.1

19.3

26.3

Transmissibility

Ratio s/f

2.31

1,37

1.03

0.86

0.83

1.26

3,08

3.20

2.86

1.68

0.67

0.94


14/30

- 10 -

TABLE 2

Force Transmissibility from Random Analysis

Specimen calculation: Strut force, 0-25 HZ, small displacement case.

Spectral density calibrations:

Input force, F, measured0.030volts r.m.s., calibration

1250 Ibf/volt, thus 37.5 Ibf. r.m.s.

2

Area under p.s.d. curve, 5.6 cm

2 2 2

so 1 cm equivalent to (37.5) /5.6 mean squared Ibf.(lb )

Frequencyaxis:1 cm, represents 2,5 HZ,

(37 5i 2

therefore, on power density

axis,

1 cm. represents ^ /- c lb /HZ

* * ^

6xz.

whence the factor F 100 lb.

/WLlcm.

and F - 10 r.m.s.lb./HZ/cm.

S i m i l a r l y f o r t h e s t r u t f o r c e

e} = 0.666 Ib^/HZ/cm.

and s = 0 .8 1 6 Ib ./HZ/cm.

For calculat

Frequency

HZ

2

4

6

8

10

12

14

16

18

20

22

ion in the table,

Power Densities

Input

force

0.22

0.22

0.30

0.31

0.35

0.42

0.52

0.45

1.15

1.20

1.61

the factor -

0.0816

r

(cm.)

Strut

force

2.5

2.9

3.75

3.75

5.2

4.3

5.0

3.0

6.3

6.2

6.2

Ratio

H2

11.4

13.2

12.5

12.1

14.9

10.2

9.6

6.67

5.5

5.2

3.85

H

3.38

3.63

3.54

3.48

3.86

3.19

3.10

2.58

2.34

2.28

1.96

Transmissibility

0.28

0.30

0.29

0.28

0.32

0.26

0.25

0.21

0.19

0.19

0.16


15/30

- 11 -

TABLE 3

Resonant Frequencies; experimental observations compared with theoretical values

Experimental Observations

Frequency,

HZ

5

15-30

20-25

25

30-35

45

45

80-120

120

180

Transducer

Strut

Strut

Transverse

Link

Tie rod

Strut

Transverse

Link

Tie Rod

Various

Tie rod

All

Conditions

Sweep Range

HZ

0-25

15-200

15-200

0-25,

15-200

15-200

15-200

0-25,

15-200

15-200

15-200

15-200

Displacement

large

small

small

any

large

large

any

various

any

any

Predicted

Frequency

HZ

3 - 4

21.5

34-83

46.5

49

316

Frequencies

Conditions

no friction

friction

locked

damper unlocked,

varies with

damping.

spring surge

any condition

any condition


16/30

^''( l/'.'

DISPLACEMENT

TRANSDUCER

//yy//

VOLTAGE

PROP.

FREQUENCY

nn

X - Y

PLOTTER

TRACKING

FILTER

n

COMPONENT

RESOLVER

JUNCTION

BLOCK

2-BEAM

C.R.O.

- I

CARRIER

AMPLIFIERS

m

VALVE

XTMETER

RG. I . BLOCK D IAGRAM: APPARATUS FOR SWEPT SINUSOIDAL VIBRATION.

RANDOM

SIGNAL

GENERATOR

// /^ ^ / y ^j y /

LOAD

CELL

2

CHANNEL

CARRIER

SYSTEM

- ^

//??/

DISPLACEMENT

TRANSDUCER

UlU

JUNCTION

BLOCK

CARRIER

AMPLIFIERS

X - Y

PLOTTER

NO RATOM ISAC

STATISTICAL ANALYSER

B

VALVE

VOLTMETER

FIG.2. BLOCK DIAGRAM ; APPARATUS FOR RANDOM VIBRATION.


17/30

O O I

FIG.

3. VECTOR LOCUS PLOT STRUT FORCE I5 -200 Hz

RELATIVE TO CONSTANT INPUT FORCE.

20

so K30 20 0

FREQUENCY

Hj

FIG.4.

REPEATABILITY OF AMPLITUDE RESPONSE TO SWEPT SINE FORCING

15-200H2. ( S T R U T FORCE)


18/30

- 0 7 $

TOTAL SIGNAL

FUNDAMENTAL COMPONENT

I

.-

ao o Hz

F1G.S. DISTORTION : FUNDAMENTAL AND TOTAL COMPONENTS OF TRANSDUCER

OUTPUT

( I N P U T F O R C E ) ( N O T E - F R E Q U E N C Y

RESPONSE OF TRACKING FILTER)

' 0 2 5

INPUT FOBCE N OMINAL 60 LB R.M.S.

STRUT FORCE

FIG.

FREQUENCY H j

6. FREQUENCY RESPONSE^ SWEPT SINE FORCING, I5- 200 Hj . 60LB R.M.S. INPUT


19/30

^

0 7 5

i/i -OS

2

TTt ROD FORCE

UOWER LINK FORCE

SO

FREQUENCY Hj

FIG.7. FREQUENCY RESPONSE, SWEPT SINE INPUT F0 RC E7 60L B R.M.S. I S - 2 0 0 H j

075 ..

ui 'OS

2

of

J

r^x

INPUT FREQUENCY

( N O M .

3 0 L B

R.MtS)

STRUT FORCE

^ \

> I ^ -

5 0

FREQUENCY Hj

FIG.

8. FREQUENCY RESPONSE. SWEPT SINE INPUT FORCE 3 0 LB RM.S. I 5 - 2 0 0 H ^.


20/30


21/30

VOLTS R.M.S.

O

s i

>

3)

O

m

&

-

^

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7 - - -

^ i ^ ^

/ r

i

s

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Documents

Cranfield Report a.S.a.E. No 2-1971