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The effect of high speed rotation on the performance of hydrostatic thrust bearings.

KLEMZ, F. B.

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KLEMZ, F. B. (1974). The effect of high speed rotation on the performance of hydrostatic thrust bearings. Masters, Sheffield Hallam University (United Kingdom)..

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"The Effect of High Speed Rotation on The Performance of Hydrostatic Thrust Bear ings ’*

A thesis submitted for the degree of

' MASTER OF PHILOSOPHY

BY

F.B. KLEMZ, C.Eng. , M.I.Mecli.E.

Department of Mechanical and Production Engineering Sheffield Polytechnic

September 19

A&V

O P O C p

Li u . ^RY \

2

SYNOPSIS

Hydrostatic bearings have been the subject of many theoret ical

and experimental investigations. Some investigations have

confirmed that increasing the speed of rotation of a hydros tatic

thrust bearing reduces the load carrying capacity. Previous

theoretical predictions of the pressure distributio n, during

rotation, have not taken into account the radial inertia effects,

with the result that the predicted values of pressure near

the vicinity of the air inlet, have been much higher than those

measured under test.

In this investigation radial and rotational inertia effe cts have

been considered theoretically and experimentally for bo th

'parallel* and 'stepped* bearings using air as the lubricant. The

relevance of compressibility has also been assessed.

3

ACKNOWLEDGEMENTS

The author wishes to express his gratitude to Dr G R Symmons,

Director of Studies, for suggesting this research project an d

for his very helpful supervision.

Sincere thanks are also due to Dr R H Roberts, Manager,

National Centre of Tribology, U.K.A.E.A., Risley, for his

very useful comments and continued interest in this project.

The advice and encouragement given by Mr 0 Bardsley, Head of

Department, is much appreciated.

The assistance given by Mr R Teasdale and Mr D McKay in the

manufacture and construction of the experimental test rig was

a valued contribution.

Thanks are also due to Miss J I Senior for typing this thesis

so ably.

4

LIST OF CONTENTS Page

Title 1

Synopsis 2

Acknowledgements 3

List of Contents 4

Index to figures 6

Symbols 9

CHAPTER 1 INTRODUCTION

1.01 General notes on gas bearings 12

1.02 Review of previous literature 15

1.03 Rotational inertia effects in rotating boundaries 18

CHAPTER 2 APPARATUS

2.01 Design requirements of test equipment 21

2.02 Description of the test equipment 22

2.03 Manufacture of the test equipment 23

2.04 Test procedure 24

CHAPTER 3 ANALYSIS

3.01 Inertia effects in fully developed axisymmetric 43laminar flow

3.02 Solution for the stepped parallel surface hydrost atic 52 thrust bearing

3.03 Theoretical thrust calculated from theoretical 55pressure distribution

3.04 Experimental thrust calculated from the 56experimental pressure distribution

CHAPTER 4 COMPRESSIBILITY

4.01 The relevance of the compressibility term in 58analysing the performance of a hydrostatic thrust bearing

4.02 Theoretical determination of the partial derivati ves 52

T~\and — £

5

CHAPTER 5 EXPERIMENTAL AND THEORETICAL RESULTS

5.01 Introduction 79

5.02 Static case 81

5.03 Static/Dynamic case 83

5.04 Stepped bearing 85

5.05 The zero-flow condition 86

5.06 The Radial Velocity, Axial Velocity and the 86pressure term

av71>3z

5.07 Bearing thrust and Bearing performance 88

CHAPTER 6 SUMMARY

6.01 Errors 129

6.02 Discussion 132

6.03 Conclusions 134

6.04 Further work 134

APPENDICES

1. Compressibility -— complete solution of 137compressibility and viscous terms outlined in(4.01)

2. Computer program and print out of thrust values etc . 142

3 V3. Computer program and print out of V , V and y--z-2- 184-i JC Z d z

values.

4. Computer program and print out of solution to 194equation (33).

5. Computer program and print out of ratio: 198comp.term/viscous term.

STATEMENT OF ADVANCED COURSES OF STUDY ATTENDED 204

REFERENCES 205

6

INDEX TO FIGURES Page

FIG

1 Plate. Arrangement of test apparatus 11

2 Plate. Static and dynamic disc assembly 26

3 Plate. View of test rig from drive side 27

4 Static disc hole co-ordinates 28

5 Arrangement of static pressure holes 29

6 Hydrostatic thrust bearing assembly 30

7 Drive shaft assembly 31

8 Steady for hydrostatic thrust bearing 32

9 Orifice fitting 33

10 Drive arrangement for hydrostatic thrust bearing 34

11 Method of setting air gap 35

12 Design provision for the adjustment of the dynamic 36disc

13 Dynamic disc with central recess 37

14 Instrumentation 38

15 Calibration of tacho-generator output 39

16 Sample results sheet 40

17 Configuration and co-ordinate system 41

18 Configuration of stepped thrust bearing 42

19 Co-ordinates used for employing Simpson’s rule to 57determine experimental thrust

20 Determination of from experimental results. 64Test 13.

3 2 ~21 Determination of from experimcintal results. 6 5

Test 13.

22 Table of results. Test 13. 66


3 2p24 Determination of -—4- from experimental results. 68

Test 14. dr

FIG. PAGE


26 Determination of from experimental results. 70Test 19. or

3 2-27 Determination of t :— *r from experimental results. 71

Test 19. 3r



3 2“30 Determination of -r-r from experimental results. 7 4

Test 20.


32 Variation of compressibility ratio with radius 7 6(Hobson & Lawrie).

33 Variation of compressibility ratio with radius. 77Tests 13 and 14.

34 Variation of compressibility ratio with radius. 78Tests 19 and 20.

35-40 Static Tests 1-12. 90-95

41-46 Static/Dynamic Tests 13-24. 96-102

43A Theoretical dimensionless pressure distribution rad- 98ial term ignored. Test 18.

46A Negative pressure distribution due to radial and 103inertia terms.

47-52 Static/Dynamic Tests, Stepped bearing. 104-107Tests 25-36.

53-58 Relation between static pressure and volume flow 110- 115rate.

59 Suction due to rotation speed of 4000 rev/min. 116

60 Instrumentation used to measure suction due to 117rotational inertia effect.

61 Radial velocity distribution across gap at disc 118radius 95mm.

62 Axial velocity distribution at disc radius 50mm 119

63 Axial velocity distribution at disc radius 25mm 120

64 Change in pressure across gap at disc radius 70mm 121

65 Change in pressure across gap at disc radius 25mm 122

8

FIG.

6 6

67

68

69

70

71

72

PAGE

Relation between Reynolds number and Thrust 123

Relation between Reynolds number and dimensionless 124Thrust.

Relation between Thrust and volume flow rate. 125

Relation between performance and flow rate 126(Theory)

Relation between performance and flow rate 127(Experimental)

Relation between performance and flow rate 128(Stepped bearing)

Proposed instrumentation for continuous 136recording of gap width using pressure transducers

f

9

SYMBOLS

Symbols which only arise once, are defined in the text, and

are not listed.

D disc diameter (D = 2r2)

F total load capacity

Q volume flow rate

R dimensionless radius (£)h

T lubricant temperature

U X W representative velocities

RDl ri/r 2

RD3 r 3/r 2

Ki inertia parameter --- --------560TT2h 2p r2 2

K2 inertia parameter 3pQ 2r 22

Rn

20 p

Re Reynolds number

Reynolds number [£ (« 1) 2hu] see page (46 )

Vr Vz Vq velocity components in the r, z, 9 directions

Vr Vg Ve velocity ratios

R gas constant

p pressure

2h gap between parallel discs

r, 0 , z cylindrical co-ordinates

rj reference radii

r 2 outside radius of bearing

r 3 radius of step

2 rr 1 radius ratioD

p mean pressure across the air gap between discs

I O

mean pressure at reference radius ri

mean pressure at radius r2

mass f low rate

4-ua I • .film thickness in recess,film thickness ratio ( :— : ----- --r-= ----- — :------- )minimum film thickness

rotational speed

co-efficient of dynamic viscosity

density

FIG. I. ARRANGEM ENT OF TEST A P P A R A T U S .

12

CHAPTER 1

GENERAL NOTES ON GAS BEARINGS

1.01 Gas bearings have been in existence for many y ears and

their use is increasing due to the many advantages they have to

offer. They can be operated at very high and very l ow temper

atures. At the upper end of the scale the expectati on is that

some devices may be called upon to function at 1100 -1700°C, while

at the lower end of the scale this could mean -260° C. Gas is the

only known lubricant that could possibly be used fo r such

extremes of temperature, and even with this form of lubrication

care should be taken over possible condensation at low temp

eratures.

Extremely high rotational speeds are possible becau se there isi

no serious problem in keeping the bearing cool. Ult rafuges

using hydrostatic step bearings have been operated at speeds in

excess of 1700 rev/sec. In 1962 there evolved the a ir turbine

dentral drill operating at 8500 rev/sec. Dril l ing s pindles oper

ating at 1700 rev/sec are used in the precision dri l l ing of

electronic printed circuit boards. A small high-spe ed expansion

turbine for liquefying helium, developed by the Bri t ish Oxygen

Co. Ltd. (19), operates at 6000 rev/sec. The bearings, i n this

unit are lubricated by helium gas at a temperature between -260°C

and -223°C.

Gas has an inherent low viscosity, resulting in sma ll fr ict ional

forces giving a low power loss. Large structures hav e been

floated successfully on hydrostat ic-type bearings. The Hale

13

200 inch telescope on Mount Palomer has a mass of 45 3Gg, yet the

coefficient of friction for the entire supporting s ystem is claim

ed to be less than 0.000004. Hydrostatic bearings a re currently

being applied to large radio telescopes and radar a ntennae.

There are two fundamental types of air bearing, the hydrodynamic

bearing and the hydrostatic bearing. The hydrodynam ic bearing

relies on the lubricant being continuously forced t hrough a

converging gap, or in the case of thrust bearings, a series of

converging gaps, in order to generate a force of suf ficient

magnitude to overcome the applied load. With this t ype of

bearing the viscosity of the lubricant is of paramou nt importance

in determining the load capacity. The viscosity of air is about

4000 times less than an S.A.E. 10 oil, therefore th ere are few

applications for air bearings of this type.

%Hydrostatic air bearings rely on an external supply of high

pressure air for their operation. The continuous ai r f low

prevents metal to metal contact within the bearing, when the

bearing is at rest, and when it is rotating at low s peed; thus

eliminating wear which is a troublesome feature of all hydro-

dynamic bearings. This thesis is concerned only wi t h hydrostat ic

thrust bearings.

In practice, a loaded thrust bearing takes up a posi t ion such that

the thrust due to the distr ibuted pressure across t he active faces

of the bearing just balances the applied load. The gap between

the two bearing surfaces changes to accommodate cha nges in the

applied load, with an increase in load producing a d ecrease in the

bearing gap. If, for a given mass f low rate of air, th e applied

load is too great, the two halves of the bearing wil l touch and

failure due to seizure could result. If the flow ra te is

excessive the bearing wil l operate satisfactori ly b ut power wil l

be wasted in pumping more air through the bearing t han is actually

required. It is also known that increasing the spee d of rotat ion

of a loaded thrust bearing causes the bearing * gap ' to reduce.

A designer wil l need to know how the following para meters are

related in determining the load carrying capacity o f a hydrostat ic

thrust bearing; mass flow rate, air viscosity, air density, gap

size, speed of rotation, bearing size and pressure distribution.

The object of this project was to establish how the above

parameters are related, confirming the derived theo ry by means of

a thrust bearing of fixed overall dimensions. Theore tical ly the

following sections have been considered:

(i) The ’formation of an expression for pressure di stribution,

which embraces radial and rotational terms, for bot h

1paral lel-1 and 1 stepped* bearings, for incompress ible

flow.

(ii) Expressions for the radial f low velocity, and the axial

flow velocity, were derived and used to show graphi cal ly

the influence of .rotation on the axial and radial

velocity profiles.

(iii) Compressibi l i ty was taken into account and it s inf luence

on the theoretical pressure distr ibution for a thrus t

bearing was considered.

Theoretical and experimental results have been comp ared graphic

ally, and computer programs have been used to conve rt the results

to non-dimensional form.

REVIEW OF PREVIOUS LITERATURE

1.02 Radial inertia effects only, in stationary bou ndaries.

Brand (1) investigated theoretically the relative i mportance of

the viscous term compared with the radial inertia t erm in the

Navier-Stokes equation and demonstrated by order of magnitude

arguments that inertia forces are not negligible, w hen a suitably

defined Reynolds number was sufficiently large.

The problem of radial flow between two parallel sta tionary

surfaces has been dealt with by Livesey (2). He sug gested that

inertia effects may be significant at low fluid vel ocit ies and

that this could bring about a change in the sign of the radial

pressure gradient. (This type of condition being most likely to

occur in the vicinity of the *.air inlet, when there was a large

bearing gap w id th . ) Livesey derived an expression t hat predicted

the pressure distribution in terms of the volume fl ow rate, fluid

density, gap width and reference radii. The express ion contained

a term due to the inertia effects, in addition to t he well

established viscous term.

Morgan and Saunders (3), using compressed air, conf irmed

experimentally that the viscous term alone could no t predict the

pressure change between two radial points in the pa th of the air

flow. The inclusion of Livesey*s inertia term only part ly

corrected the error existing when the viscous term alone was used.

15

Jackson and Symmons (4) extended the power series a nalysis of Hunt

and Torbe (5) to include an inertia term. The solut ion derived

by Jackson and Symmons showed the inertia effect to be 23 per

cent greater than the inertia effect predicted by L ivesey.

Moller (6 ) considered the analysis of radial f low w ithout swirl,

between parallel discs using air at incompressible speeds.

Approximate solutions were obtained for turbulent a nd laminar

pressure distributions, using an integral momentum method. He.

was able to confirm these results experimentally. M oller showed

that it was possible for the flow to be turbulent thr oughout the

channel, provided that the channel exit Reynolds nu mber was large

enough. In order to achieve turbulence, high flow ra tes were

necessary, and this was facilitated by using a large inlet jet

diameter.

Jackson and Symmons (7), in 1964, investigated expe rimental ly

the principal theories predicting the pressure dist r ibution for

laminar flow between parallel plates. The apparatus they used

was designed with an air inlet jet diameter much sm aller than that

used by Moller; this resulted in a relatively low fl ow rate, which

ensured that the flow was non-turbulent at all radi i, except,

possibly, a small area immediately adjacent to the air inlet. They

found that the various theoretical analyses gave wi dely di f fer ing

results. All the theoretical results predicted high er values

than those shown by experimental results, for all r adii, except for

p

a small area in the vicinity of the air inlet. Jacks on and

Symmons proposed that further investigation was nee ded before a

closer correlation between theoretical and experime ntal results

could be expected, particularly for bearings where the central

16

17

inlet jet was small in diameter.

The relative importance of the basic terms in the N avier Stokes

equation, including the compressibil i ty term, has b een considered

by Hobson and Lawrie (8 ). As well as a theoretical a nalysis,

their work included an experimental investigation o f the radial

flow of air between stationary parallel circular pl ates. First

they considered the problem of incompressible flow. .Starting

with the Navier Stokes equation, and using a transv erse velocity

profi le in parabolic form, they obtained an expressio n which

included pressure, inertia and viscous terms. Their expression

was the same as that obtained by Livesey. By conside ring the

inertia and viscous terms only, they were able to o btain an

estimate of their significance by determining a para meter Kj_,

inertia term/viscous term.

*

Next, using the Characteristic equation for a perfec t gas, the

transverse velocity profile, V r , was written in a fo rm applicable

to compressible flow. The first and second partial derivatives

3 V 3 V(-7r-21) and (-z— j7-) were evaluated and substitute d in the Navier

3r 3r

Stokes equation, which included the compressibil i ty term. The

partial derivatives (-£) and were determined graphi cally

from the experimental pressure distribution. Parame ters, K c ,

inertia term/viscous term and 3 / compressibi l i ty te rm/viscous

te rm, .were evaluated and the results for various fl ow rates, and

flow gap thicknesses analysed. Hobson and Lawrie fo und tWat for

their particular series of tes ts , -t-hat> the signi ficance of the

viscous and radial inertia terms, based on compress ible and

incompressible theory, given by K c and K- respecti vely, di f fered

by less than one per cent. Their investigation did not al low for

18

bearing rotation.

1.03 ROTATIONAL INERTIA EFFECTS IN ROTATING BOUNDAR IES

Osterle and Hughes (9) considered theoretically the effect of

lubricant inertia in hydrostatic thrust bearings, w i th a single

central recess, at normal operating speeds, using b oth compress

ible and incompressible lubricants. In the case of incompressible

lubricants, the inclusion of a rotational inertia te rm reduced

the error in load capacity that would be experience d if the

viscous term alone was used. They calculated that t he same

effect would occur with compressible lubricants whe re the recess

pressure was low, but that this effect would decrease as the

recess pressure increased.

Dowson (10) produced an analysis which included an inertia term *

associated with the effect of rotation on the press ure distr ibution

in a hydrostatic thrust bearing with a single central inlet. This

theory included a solution for a similar bearing wi t h a central

recess. (Dowson*s rotational inertia term was the s ame as that

derived by Osterle and Hughes.) From-the formation of the

continuity term he concluded that for a ‘static' pa rallel surface

bearing the flow is entirely radial, but with rotatio n there is an

axial component present which causes the ' f luid1 to move towards

the moving surface as it spirals between the bearin g surfaces.

Theoretically, it was found that rotation reduces t he load

carrying capacity of a hydrostatic thrust bearing. Dowson's

analysis did not include an inertia term due to rad ial effects.

Experimental work by Coombs and Dowson (11), using oil as the

tyy&cLlum

lubricating •i$te *ar/ confirmed the general theory of Dowson ' s

earlier work. The best correlation between experime ntal and

theoretical results were obtained when thermal effe cts were small.

H.N. Shirman (12), using the basic theory proposed by Dowson,

obtained an expression for the dimensionless pressu re

distribution for a hydrostatic thrust bearing wi th a single central

inlet. Using air as the lubricating tncdium^he showed

experimentally the detrimental effect of rotation o n the load

carrying capacity of a hydrostatic bearing. He did not obtain

a good correlation between experimental and theoreti cal results,

which must have been due partly to the absence of a radial inertia

term in the basic theory, which would have modif ied considerably

the predicted dimensionless pressure in the vicinity of the

central inlet.

iTing and Mayer (13) considered the effects of the l ubricant

rotational inertia and the temperature on the perfo rmance of para

llel stepped hydrostatic thrust bearings. They obta ined

expressions for pressure and temperature distr ibuti ons and load

carrying capacities appertaining to adiabatic f low conditions.

They obtained satisfactory correlation between the experimental

results obtained by Coombs and Dowson and their own theoretical

results, especially when the speed of rotation was high. In

common with Dowson1s work, their theoretical analys is did not

include a radial inertia terra, therefore for isoth ermal

conditions they obtained the same differential equa tion for

the pressure distribution. By introducing an expone ntial

viscosity-temperature relation, and assuming that t he bearing

surfaces were perfect insulators, adiabatic solutio ns were

2 0

obtained. Ting and Mayer made the important observa tion that

the adiabatic analysis should not be applied to bea rings with

extremely small film thicknesses because, under the se conditions,

the assumption that the lubricant wil l carry away m ost of the

heat generated is not true.

21

CHAPTER 2 APPARATUS

2.01 DESIGN REQUIREMENTS OF TEST EQUIPMENT

There were no parts previously manufactured that co uld be used

for the test r i g f so the design was not limited, or assisted, by

existing components.

It was decided to base the design on the following:

(a) No attempt would be made to measure directly th e axial

thrust created by the air flow through the thrust b earing; in

stead the gap width would be adjusted to a predeter mined size,

and the resulting pressure distribution, measured b y a mul t i

tube manometer, used as a measure of the axial thrus t.

(b) The air flow, suitably filtered, would be suppl ied from

the compressed air mains. The amount of air used wo uld compare

with that used in an actual air bearing, i.e. the air consumption

would be as small as possible so that the power requi red to supply

the air was the minimum. With air consumption in mi nd, it was

decided to use a small inlet jet diameter, similar t o that used

by Jackson and Symmons (7).

(c) Particular attention was to be paid to the meth od of supp

orting and adjusting the relative posit ions of the discs. The

following were considered crucial:

i. rigid construction

ii. easy access to discs

iii. disc alignment to be simple but positive

iv. vibration transfer to be avoided

v. axial float, deflection and wobble to be reduced to a minimum.

2 2

vi. no axial thrust to be transmitted to the dynamic d isc by

the drive shaft,

vii. moving parts to be covered by guards which can easily be

removed, to facil i tate adjustment of discs.

2 •02 DESCRIPTION OF THE TEST EQUIPMENT

Plates of the air bearing are shown in FIGS 1, 2 & 3. The

static disc was designed to move axially so that th e air gap size

could be changed. In addition to axial movement the static disc

could be tilted for a few degrees, at any angular po sition, so

that it could be accurately aligned with the dynami c disc. The

dynamic disc had the same degree of movement as the static disc,

but it was intended that once the dynamic disc was correctly

positioned (see 2.04), any adjustment to the air gap s ize would

be made by -moving the static disc only.

The drive shaft was supported by a roller bearing a nd angular

contact bearings. Axial movement of the bearing dri ve shaft was

prevented by pre-loading it axially by means of a c ompression

spring acting against a single row ball thrust bear ing. The

weight of the drive shaft and the dynamic disc was supported by

means of a lathe-type steady. The drive shaft was dr iven by

means of a d.c. motor, 2 h.p. A bearing speed of 400 0 rev/min was

obtained via a vee belt drive. A flexible coupling, designed to

transmit axial torque only, was used to connect the drive from

the motor to the bearing drive shaft. The speed of the bearing

drive shaft was measured using a tachogenerator (SE RVOTECH

PRODUCTS TYPE SA 740A/7) connected to a digital vol tmeter. To

adjust the speed of rotation a Variac was used. The motor drive

2 3

and the hydrostatic bearing assembly were each moun ted on a

separate stand, constructed from 2in x 2in x %in an gle iron.

To measure the mass flow rate of the air passing th rough the

bearing, an orifice plate was used. The orifice pla te was

designed to B.S.1042 Part 1, using D and ^ pressure tappings.

Static pressure readings were taken on a mult i tube w ater-f i l led

manometer. The pressure upstream of the orifice pla ce was meas

ured with a mercury filled manometer. Clean, moistu re free,

air was obtained by a PURAIRE FILTER, NORGREN F41-3 21-AOTB. The

mass flow rate of air was controlled by a pressure r egulator

NORGREN 11-918-100.

A NORGREN 10-way selection switch was used in conjun ction wi th a

pressure transducer (S.E. LABS (Eng.) Ltd. Series No .91 1 25in

W.G.) to enable pressure measurements to be made on a U.V.

recorder. The arrangement of instrumentation is show n in F ig .14.

2 .03 MANUFACTURE OF THE TEST EQUIPMENT

Two discs each 190mm diameter, 30mm thick, made fro m free

cutting stainless steel, were used to form the hydr ostat ic thrust

bearing. A central jet 4.0 mm diameter was machined in the

static disc and an array of static pressure tapping s, each

0.64 mm diameter, were dril led at 1cm, 2cm, 3cm, 4c m, 5cm, 6cm,

7cm and 8cm radius, so that four tappings were avai lable for each

radius as shewn in FIG.5. The discs were ground and lapped to a

surface finish of less than four micro-inches, and were each

tested for flatness using a grade one straight edge. A WADKIN,

numerically controlled point-to-point dri l l ing mach ine,

2 4

incorporating an AIRMEC autoset controller, using a punch tape,

was used when machining the static pressure holes i n the static

disc.

Modifications to the test rig

Before * repeatable1 results could be obtained from the test rig

two modif ications were necessary to the original de sign. A

stiffening plate was placed under the bearing housi ng, and

additional supports were provided to strengthen the bracket

which supports the static disc. These two modif icat ions provided

a more rigid structure, enabling a more accurate air gap width to

be maintained.

2.04 TEST PROCEDURE

Before each series of tests it was necessary to adj ust the

dynamic disc to ensure that it would rotate without wobble i.e.

rotate so that the active face of the disc was, for all angular

positions, perpendicular to the axis of rotation. A djustment of

the dynamic disc was effected as follows:

(a) . The air gap was adjusted to approximately 0.0 01m, using a

feeler guage, and air was allowed to flow, at a low flow rate,

through the hydrostatic bearing via the central inl et.

(b) One of the outer static pressure tapping points was

connected to a 'sensit ive1 manometer (FIG.11) and th e air

flow rate adjusted, so that a mid-scale reading was obtained

on the manometer.

2 5

(c) The dynamic disc was then slowly rotated, by ha nd, and

any error in the initial setting of the disc was sh own by a

change in the manometer reading.

(d) An adjustment to the dynamic disc (FIG.12) was followed by

reducing the size of the air gap to 0.0005m and tes ting as

before.

The thickness of the air gap was adjusted by the ai d of three

studs set in the static disc (FIG.6). These studs w ere adjusted

until the required parallel gap was obtained. It wa s original ly

intended to use slip-blocks, measuring the distance between

anvils set in the static and dynamic discs, to dete rmine the

size of the air gap, but later it was found that th e use of a

feeler guage applied direct to the air gap enabled a more

•parallel1 gap to be obtained. The thickness of eac h feeler *

guage was tested using a Taylor Hobson Talymin Gauge as a compar

ator. The size of each gauge was compared with an I nspection

grade slip block pile, and the error found to lie w ithin the

range ±1%.

Initially a stroboflash was used to calibrate the vo ltage output

from the tachogenerator, but later greater accuracy was obtained

by checking the voltage output of the tachogenerato r wi th the aid

of a synchronous motor. The voltage output was found to be

2.5v per 1000 rev/min - as stated in the manufacture rs speci f i

cation. This value was used when drawing the cal ibr ation curve

shown in FIG.15.

26

FIG. 2 ■ STATIC AND DYNAMIC DISC A S S E M B L Y .

27

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C O N F I G U R A T I O N O F S T E P P E D T H R U S T B E A R I N G

CHAPTER 3 ANALYSTS

t

3.01 INERTIA EFFECTS IN FULLY DEVELOPED AXISYMMETRI C LAMINAR

FLOW

Navi.er Stokes equations in cylindrical co-ordinates for steady

state flow:

V 3Vr + v 3Vr r 3r z Sz

Ya i = - I + iL fjr p 3r p |_

3 V3z ^ + t z i f h ( r V - ) }

+ i l A A ,rV 1 +3 3r *r 3r r 3z ^

v ^ + v ! a + v . M a ^ + 2 | I i ( r v ) i ' r 3r r r z Bz p [_ 3z 3r *r 3r 0

v avz. + v. ^ r 3r z 3z

=-I 2E + H TlfVz. + 1 Ap 3z p L_3zz r 3r 3r '

+ 1 1 A A (rV ) + £¥z. }~3 3z tr 9r lrv-r; a* J 3z

Continuity equation in cylindrical co-ordinates

( pr vr ) + | A ( pve) + £ ( pvz ) = 0

When a gas is being used as the lubricating medium, th e effect of

compressibil i ty should be considered. The relevance of the

compressibil ity term in the full Navier Stokes equa tion, for the

series of tests undertaken in this project, has bee n examined

in Chapter 4, and found to be small enough to justi fy the

assumption of incompressible flow.

4 4

Dowson (10) obtained a solution for the pressure di str ibution in a

hydrostatic thrust bearing which included all but o ne of the

predominant inertia terms, and was applicable to th e case of

rotating boundaries. Beginning with the Navier-Stok es equations

of motion for an incompressible isoviscous fluid, n eglecting body

forces and allowing for axial symmetry, the equatio ns in

cylindrical co-ordinates takes the form:

The continuity equation for an incompressible fluid in cyl indrical

co-ordinates is:

For axial symmetry this reduces to:

1 3'(rVr ) , 3VZ _ nr 3r 3z

An alternative form of this equation is:

(1)

P

(3)

These equations can be nondimensionalized by making the

following substitutions:

4 5

V = v' u r r v e = v ex V = V'W

z zr =

r *Dz = z*2h P = P'Pi

where the representative quantit ies U, X, pt etc. a re selected so

that the primed variables are always £ 1. The equat ions now

become:

|"2U2V 19Vr , WU V 1 3Vr P L"D- r 3 ^ + 2h 2 3i*

2X2 V(j2 D r*

.2p ^ ^D 8r^ D

:32Vv . 1 SVv-1-rF +3r ' * ' r 1 3 r r

+ ( 0 )2 afVjL - v £ l4h 3z r i J

[~2UX V J 3Vp)! , WX V J 3Ve' ^ 2UX V r' Ve’P I D 3r ' 2h Z 3V D r 'u z

4yXD 2

92Vel3r rr

(4)

1 3Ve' . , D . 2 32Vr Vfl'fr ' 3 # " + (4h} 3 ^ F ^ J

p2UW V 1 3VJ ^ W 2 V 1 3VZ' p (“ D" r 3 # ~ + 2h 2 I ? "

.EL £ e !L +2h 3z' D 2

32V z* + 1 3VZ'Sr1'2- r 3rv

+ ■ (Jl)2 H zL'4h ITz1

2U 1 vr* V V + I T r 1 1 ~ 3 F H +

JL 8V*' = o2h 3z'

(5)

The primed quantities are all of the same order of magnitude, and

if only the predominant viscous terms are retained, the

equations of motion are:

Rn

v ' +r dr1

V 1 _ fX )2 V fl'24hU z 3z' VU ; r 1WD

Rn

v . v •r 3r' 4hU z 3z'

3V 01 + Vr V e*

s 2p* (2h) 2 IpL + SlVrlyUD 3f

3 2 V 0'3z

Rn

V, 3VZ' , WD 3VZ'

r 3r* ' 4hU 3zf_2pih 3pf 32V z f

yW 3?™ 3:

(6 )

4 6

Where the Reynolds number R = — (~0 2hU J n y D

With oil as the lubricant in mind, Dowson argued th at the rep

resentative radial velocity U would be small, and s ince h << ^

the Reynolds number Rn would be considerably less t han 1. Also

W 4hsince — = 0 (— ) from equation (5) all the inertia t erms in the

second and third equations of motion can be neglect ed. Similarly,

two inertia terms in the first equation of motion w ere

discounted, and the following equations obtained:

pVQV = "_2E , „ p Vr r 9r *azz

0 =-

9z + V9 2 V ' 9p~

(7)

If air is to be used as the lubricating medium then th e first of

equations (7) can be extended to include an additio nal inertia

9Vterm. pVr wil l be significant when is large and r is small

i.e. in the vicinity of the air inlet. From the conti nuity

9Vr -V, 3VZequat ion,Vr can be written in the form — ^ -- Vr an(

— V 2

these two terms — wil l be the most significant. If the radial

-oV ^2inertia term is included in the first equation of mo tion,

the revised three equations of motion become:

_ pVr _ PV0 r r

o = - IE + ,,i!Vz•'i r~, r. „ Zo Z d Z

-IE +9r M^ z ^

(8)

4 7

The ‘second of equations (8 ) can be integrated dire ctly, and with

the boundary conditions z = - h .. V fi = 0, z =■ +h V fi = fir we obtain

(9)

_ thanIf . the volume flow rate is constant, -Thci* the mean velocity

_ Q4TTrh

Let V _ Qr 47rrh

( 1 0 )

If the third of equations (8 ) is integrated twice wit h respect to

z, the successive equations obtained are:

(11)

and /pdz = yV + Az + B . z

(11A)

where A and B are functions' of r only.

The mean pressure p across the air gap (2h) = _1_2h

hpdz

from equation (11A)-h

pdz = 2Ah (since V = 0 when z = ±h)

A =2h

h

- h

pdz = p

combining the above relationship between A and p in equation (11)

p p (12)

4 8

From equation (12) it will be seen that the pressur e at any

point, at a particular radius, in the air gap, wil l differ from

the mean pressure by an amount which is dependent upo n the local

axial velocity gradient.

If the result expressed in equation (9) is introduc ed into the

first of equations (8 ) and the expression for p in equation (12) is

used to eliminate we find,3r' '

Bp _ pQ2 pP2r ,z2 2z .. fB2vr B2V 7 .3F ” 16rr r dh 2 + ~ (h^ + IT + 1} + y ( ( 1 3 )

INERTIA TERMS VISCOUS TERMS

The second viscous term in equation (13) can be re- written in

terms of V and r from equation (2 ) to give,

Bp - PQ2 , pft2r ,z2 2z n . [~32V r , _3_ rl JL fr-v \3r 16ir2r bh 2 T 4 (hT h * _ [JiT2” Br *r 3r ( r*

INERTIA TERMS VISCOUS TERMS

when the two viscous terms are non-dimensionalised they become:

^W T r"2' and IP "3 ? ” (r 'v r' ) } respectively, the first viscous

term is ( ^ ) 2 times the second viscous term, and sin ce D >> 4h,

the second viscous term may be neglected, so that e quation (14)

becomes

Bp PQ , pft r ,z , 2z , ,, , 3 V r— k— Ttrr + — (i rr + -t— + 1) + \i-rr~7JL (15)3r 16iT^rdh z 4 h z h K3zz

(14)

integrating equation (15) twice with respect to z, and re

arranging

4 9

V r - & S ? - ^ < W - & + $ ♦ C . ♦ 0 ( 1 6 )

introducing the boundary conditions z = - h f Vr = O a nd z = +h,

V = 0 we find r

^ p£32rh j ^ h 2 3p , pO2 , 7 pfi2rh2C = and D = + To —12y 2y 3r 32Trzr dy 48 y

The volume rate of flow, of lubricant, through the bearing can

be evaluated from the integral

+h

Q = 2irr | V^dz

-h

„,no« 0 . 2„ [_|s; 1 1 „ ■ * M W -

fro» above |f - -fifjr * 11,1

*

combining equations (16) and (17) equation (16) bec omes

\T - 1 / „ 2 u 2 w PQ2 , 3prft2 __ 3yQ , PQ2 ,z2 „ ^r 2y (z ~ h } (167rzr “h 2' 10 4-rrrh 32'ir2r ;th 2y }

pft2 ^z4 , z 3 , z 2 n , 7pft2r h 2 pft2rhz ,1QN“ ~ T (12iPr + 3 h + T } + 4 8 y + . 1 2 U ( 1 8 )

integrating (17) with respect to r and introducing the boundary

conditions p = 0 at r = r 2 we obtain:

“ _ 3yQ , , r 2 v PQ2 ,1 ... 1 % 3 p f i 2 , 2 2 * n q )p - g e (~ ) j n F W ^ f t 20 "^o" (r2 r > (19)

writ ing the above equation in dimensionless form, w here

p = i r h 3 P a n f q p = LyQ h

P = i l o q (2^-) - -2 2- ) - 3 i rh ° p f l 2 2 _ R 2 \ ( 2 0 )4 ^ e ' r 3 2 7rh y R2 2} 20yQ (Rz R ; ;

5 0

A further series of equations, giving values of p, P, Vz and

can be obtained by assuming that the radial velocity has a

parabolic distribution based on the 'creeping; f.lo w’ solution.

In this case:

Vr = W F T (h2 - z2) (21)

from equations (9) and (21) , also substituting for the firstdr dr

of equations (8) becomes

| !Vr = I | £ - 9Q2P b „ (h- - 2h 2 z2 + a") ~ ( K + % + 1 )Bzz y 3r 64Tr*-hbr dy ' 4y h ■ h

integrating twice with respect to z, and re-arranging

„ _ z2 Bp 9Q2p ,hl*z 2 _ h 2zu z6*r 2y Br 64Tr2h br yy [ 2 6 30;

fi2rp ,zk , z 3 , z2» , _ . _4y (l 2h7' + 3h + 2 J ClZ ° 2 (22)

introducing the boundary conditions z = -hf = O and z = +h,

Vr = O we find

n ft2rh _ - h2 Bp ,9Q 2 11, , ,Q2rp l lh2vCi = pyr — - and C2 = — rf- + 7 7 -T r E— 3— x ^ 7chb) + (— — - x )12y z 2y Br 64 tt h r y 30 4y 12

fi 2rh 212y

The volume rate of flow, of lubricant, through the bearing can be

evaluated from the integral

+h

Q = 2iTr j Vrdz

-h

hence Q = 2irr ^3y Br 140irzr y 5y

Si

from the above - 1^dr

3 yQ , 27 pQ 2 ; 3 p ^2 r4urh 3 2807T^r dh 2 10

(23)

integrating equation (23) with respect to r and intr oducing the

boundary condition p = 0 at r = r 2 we obtain

3yQ t ,r2vp = w log- ( ~ )

27pQ2 560tt 2h 2 r 2

3 pft ‘ 20

(r 2 2 - r 2) (24)

writ ing the above equation in dimensionless form, wh ere

_ ,rrh3pP = ~ Q m d E = h

P — - loa (R 2 ) — \ — 37rh 5p^ 2 2 _ „ 2 \ (°5>P 4 i0ge R 560¥Hy R^r) 20yQ U a R } Ub)

+ h

from equation (2) -- - - - d z = 0 (since V„ = 0 when z = ±h)J_h r dr . z

integrating with respect to z and introducing the b oundary

conditions z = -h, V = 0, z = Ih, V = 0/ we obtain:Z z

2hl A (r IE) + 9Q2PhL 3yr 3r 3r TOr^r y

2ft 2rph 35y

= 0 (26)

3p _ 27Q p 3pr£lfrom the above equation (2 6) — nrr + — +

^ 3r 280Tr^rdh^ 10(27)

(from equation (24) it can be shown that C = - ^ 3-)

by combining equations (22) and (27) equation (22) becomes

1 /-,2 U 2 \ / 3yQ . 27pQ‘Vr - ^ <z< - h ’) H +4rrrhd "r 280?rzr h 2 + 10 1 6 4irzh br 3y

3'pQ' 2r» 902p) -

rh^z 2 h 2zu . z 6 l lh6* ft3rp ,zh . z 3 . z 2 hz30 30

( — ---------- rj- + — +

4y 12h^ 3h

iiHl + hi.) 12 3 }

(28)

5 2

AXIAL VELOCITY

From equations (2) and (28) equation (2) can be wri t ten in the

form

aVg _ 1 /_ 2 _ b 2 % JL zr.i£x 9Q2p Vh-'z 2 _ h 2z*» , l lh 6 '3z 2yr v ' 3r 1 3r ; 32irzh br liy ^ 2 6 T 30 '

, fi2p , zh z 3 . z 2 hz l lh 2 h 2»2y 3h 2 " 3 " 12 3

replacing (r|£) in the above equation by

av7. = _ 1 /„ 2 _ b 2 \ / 2 7 Q 2 p 3 pft2r _ 9 Q 2 pO r-y h ) ( 1 / /On- 2 „ I- 2 t C )3z 2yr 140 tt r h 5 32iT^hbr ty

,hhz2 h 2z V , l lh6N , ft2p ,zk , z 3 , z 2 hz l lh 2 , h 2N ,OQ7^I 7i “ -- 7 + — oTr) + o",. " VTnTuT + ov~ + ” 7T ~ T~ ~ — To '* “o' {ZOt\)2 6 30 2y 12h 3h 2 3 12 2

Integrating equation (28A) with respect to z and su bstituting

the end conditions V = 0 when z = h. V = 0 when z = - h f it can bez r z r

shown that

v = 1 - v, 2 r \ / 2 7 Q 2p , 3 p ^ 2r . _ 9 Q 2 prr Oli-V. ' O h Z ) ( 1 /I /"wZ Ct U 2 t C ' TOnriiv, b„Hz 2yr 3 140ir r'h 5 32 tt h°r y

,h**z 3 h 2z 5 z 7 l lh6Zv . ft2p ,z 5 , z 1* z 36 " 30 210 " 30 ; 2y ^ O h 2- ' 12h 6

i f i - Z g i * |i, (29,

3 *02 SOLUTION FOR THE STEPPED PARALLEL SURFACE HYDROSTATIC

THRUST BEARING

The configuration of the hydrostatic thrust bearing is shown in

FIG.18. By integrating equation (27) with respect t o r

5 3

-27Q p , 3pr Q , „ ^p = 2 2 " o?;— + C log r + D* 5607r^r h 2020

the above expression can be used to predict the pre ssure

distribution on either side of the step

Let P = i t s p i h i r e ' + -P§5~'' + C > lo3er + D ‘ r 3 5 r 5 r : (30)

*“ a p “ i V S W * + l£f5° - + ° 2 lo9er + ° 2 r 2 r £ r 3 (31)

For the boundary conditions let p = pi at radius ri and p = 0 when

r = r 2 . The additional conditions needed to determi ne C 2 , C 2 , Dj

and D 2 are obtained from the requirements of flow and pre ssure

continuity at the step. The expressions obtained ar e,

PiC, =

(a 3 - 1) log (RD3) + log^ (RD1)(32)

C2 =P i o r

a z (RDT)" (RD3)zk v r & - !) - 1 } “ K" C(RDl)2- 1)

(a 3 - 1) loge (RD3) + loge (RD1)

Di =P* + a J r y ^ F " -

pi i°ger i'

1 + K 1{a , (R15 l ) , ” 4 - U - k 2 ((rdi )2 - 1)(RD3)

(a 3 - 1) log (RD3) + log (RD1) e e

D2 = P! (Kx - K 2) -

I 1 + ~ - V ~ K* ( (RD1) 2-Pi o r log . r^ ---------- - --- - ----- - ---- - --------------------------------

(a 1) loge (RD3) + loge (RD1)

5 4

560tt h p i r 2where K r = 2^z-, ^--2 r K 2 = z RDl = (§L ) and RD3 = £ f )r 2 r 2

The lubricant flow rate through the bearing can be found by solving

the quadratic equation formed by combining equation (32) with the

relation Ci = — >- §- 3—3- A 47rhda

. - 3 UQthus . . 3w 3 = 4 nh a

Pi 1 +27pQ2________ rr 2 *________ ,r2.2 ,l _ 3pfl 2r 2 2 f ,r 1. 2_ -.i5607r2h zPir2z (ar 1)2 r 3 cT2" * 20pi r 2 \

(a 3 - 1 ) log (“ •) + log^ (--) -rie r 2 e r 2

giving the final solution

81y7Tr2 [(a 3 - l)loge (§*-.) + l°ge (-i-)]

2240ha"3~p r /r 2 \ 2_ , 3: 3\ 2 ,11~ my-* i 2ar 1 a' i) - g

J f S l ^ r ;2 Q “ 3 - D l ° g e (l 7 ) + loge (fffi2240ha *p r,r 2 *-(L±) 2 (A

L( ar 1 r 2 a

27Tr2h 2pi rz 2 [l - { (£ 1 ) 2- 1 }]1

- 1 ) - i]

1 4 0 p F (—— ) 2 - (— J 2 ^ - 1 ) - 1]K L ari r 2 a J

(33)

thus for a particular pressure pi at radius r i . there could,

theoretically, be two values of f low rate Q, one of which may be

negative or zero.

The above theoretical relationship between Q, pi and ri etc has

been shown graphically in FIGS. 53 - 58 inclusive.

These graphs have been used to provide the value of the theoretical

static pressure at the datum radius ri in the solut ion of

e q u a t i o n s ( 3 0 ) a n d ( 3 1 ) .

A c o m p u t e r p r i n t o u t o f r e s u l t s a s s o c i a t e d w i t h e q u a t i o n ( 3 3 ) i s

g i v e n i n A p p e n d i x ( 4 ) .

3 . 0 3 T H E O R E T I C A L T H R U S T - C a l c u l a t e d f r o m t h e o r e t i c a l

p r e s s u r e d i s t r i b u t i o n

5 5

4-u 4. 4. • - -27Q2 pt h e s t a t i c p r e s s u r e p = ^ Q ^ r ^ ' a 2 " +

2 n 23 p r f t

20

+ Cilog^r + Di ( r 3 > r > r i )

a n d p =

2 n 2- 2 1 Q p 3 p r f t

5 6 0 'rr 2 r 2 h z 2 0

+ C z l o g ^ r + D 2

T H R U S T ( F ) ’ = i r r ! 2 p i + 2 t t

r 3

.1-2

p r d r + 2 t t

rip r d r

r 3

( r 2 r £ r 3 )

_ 2 ~ 0 j~“ 2 7 Q 2 p / i 3 » , 3 f t 2 / b 4 \F = i r r Fp, + 2i r^ 8y Z§ Z5gl oge (? a-) + w ( r 3 - r , )- 2 7 Q p

' + c i ( 2 1 o g r 3 - 1 ) - — - ( 2 1 o g r i - 1 ) } + ^ - ( r 3 2 - r i 2 )

“ M o ' i f ^ h 7 ' l o g e ( ? 7 ) + ^ k i r 2 " ~ + c 2 { E 4 - ( 2 1 o 9 e . r 2 " 1 )

r 3( 2 i o g r 3 - 1 ) } + % - ( r 2 2 - r 3 2 ) (34)

A c o m p u t e r p r i n t o u t e m p l o y i n g t h i s e q u a t i o n i s s h o w n i n

A p p e n d i x ( 2 ) .

5 6

3.04 EXPERIMENTAL' THRUST - Calculated from the experime ntal

pressure distribution

The value of the 'experimental* thrust has been cal culated by

using Simpson's Rule to evaluate the integral 2tt p r dr, where the

static pressure value p is determined experimentall y. The

co-ordinates used when applying Simpson's rule are shown in FIG. (19)

•The pressures PB, PC etc are in inches of H 20.

B — the element width is 0.0095m.

The experimental thrust (THE) has been calculated f rom the equation:

THE = 2 tt249.1 x B

x {2 ((PC x RC) + (PE x RE) + (PG x RG)

+ (PJ x RJ)) + 4.0((PB x RB) + (PD x RD) X (PF x RF)

+ (PH x RH) X (PK x RK) 1 Newtons>i] (35)

A computer print-out employing this equation is sho wn in Appendix

(2).

5 7

C O -O ftP U M A T g S U S E D P O R E M P L O Y IN G S IM P S O N S R U L E

T O P g T E ^ ^ M E : S t t P E R C E N T A L . T H R U S T ,

F IG . N °I 9 .

RADIUS

5 8

CHAPTER 4 ' COMPRESSIBILITY

4.01 THE RELEVANCE OF THE COMPRESSIBILITY TERM IN A NALYSING

THE PERFORMANCE OF A HYDROSTATIC THRUST BEARING

The Navier Stokes equations (1) used in the earlier analysis

(CHAPTER 3) omitted the compressibil i ty terms, whic h in the r

direction takes the form — (? + -i - Y^) the omission of3 <3r r 3r r '

this term is justified if the fluid flow is radial, a nd the

density of the lubricant constant. Under these cond itions the

continuity equation takes the form = 0 which when

J\ 2 TT T ■ T\ TT TT

differentiated with respect to r becomes -t-y 1 + — ~C- - —£ = 0 ,* 3rz r 3r r 2 '

hence the compressibil ity term = 0. If the fluid is a ssumed to

have axial as well as radial flow then the continuity equation

97 v 3Vtakes the form -?r—- + — + 2- = 0 if this equation is non-

dr r dz3V

dimensionalised, it can be shown that the omission of — 2- isd Z

justified if is >> 1 .

Hobson and Lawrie ( 8 ) considered the effect of inertia and

compressibil ity in an externally pressurised gas lubr ication thrust

bearing, assuming the flow to be isothermal.

Starting with the Navier Stokes equation in the for m

Pv iYr = _3 e + + I £Yr - Yc) + u(iivc -+ i iYr - Yr + iffep r 3r 3r 3 ^ 3 7 ^ r 3r r * } y ^dr2- r 3r r^ air /

INERTIA PRESSURE COMPRESSIBILITY VISCOUS

and using the transverse velocity profile in parabo lic form

V r = I f e i F (h* - z2>

5 9

by differentiating with respect to r they obtained:

= - c (h 2 - z 2 ) (—— v + -b 3r [ pr^ p r 3r ; '

l ^ ^ c m 2 - z2) ] - ^ + - 2 3r ]_Pr

s p + _ 3 _ f 8 P ^ 2p zr 3r p^r 3r

■ -i ' 'if?!p 2 aP*j

ana afVr = - 2C3z pr

where p is replaced by ^ and C = and is constant for iso*3mRT8 i T h '

thermal flow and a given film thickness and mass fl ow rate. When

the above is substituted in the full Navier Stokes e quation the

following differential equation is obtained:

(h 2 - z 2 )2 (rrr + ^rr-.l§) = -§£ + ^ ( h 2 - z2)3tflC » 2 2 \ 2 / 187rh 3 Z p r 3 ^ p ^ P ;3r

t -

1 I E + 2 Sjd 2 1_ 8^ 'r 3r p r 3r p r 3 r _

+

y c T ( h 2+ z2) (— r-r 4^ + —i— (4") L p r 3r p r 3r

•p r 3r ‘ prj

integrating this equation over the film thickness, 2h, and

substituting for C the following differential equat ion is obtained:

•3m2R T , 1 1 3px = ju VnnRTl" 1 3p 2_ f 3p _2___ 1 (i!P\407r2h p r 3 p 2r 3 3r 3r ‘ 12tr _pzr* 3r pPr 3r p^: 3r

INERTIA PRESSURE COMPRESSIBILITY

umRT ^ | £ + 2 (DC )2 _ 34tt Lpz r A 3r p 3r 3r p r 3rz h^pr_

VISCOUS

From their experimental radial pressure distributio n, values of

(■ |£)were determined graphically and then, in turn, plotted against

the radius. The second partial derivative they esti mated from the

resulting curve. These results were substituted in the final

differential equation and the relevance of the comp ressibi l i ty

term determined, for different radii, from the rati o compressibi l i ty

term/viscous term. For their series of tests they f ound this

— I*ratio to be very small (less than 10 per cent ) .

A graph showing the relevance of the compressibi l i t y term for

two values of R , is shown in FIG.32. e

3mIf instead of the transverse velocity profi le V r =

we substitute equation (18) replacing p by ^ etc.K1

t(h 2 - z2 ) ,

„ _ I f 2 /^2rt 3prfi 2 3ymRT , m 2RT ,z2 _ , .r 2y n ; 16TTzr^h2p 10RT " 4iThdr p j “ 32ir2r*py ;

prQ2 (Z1* z 3 z2 , 7pft 2r h 2 pft2rhz4yRT 12h 2 3h 2 } 48yRT 12yRT

which has already been shown, allows for the rotati onal and

radial inertia effects. The following equations are obtained for

the compressibil i ty and viscous terms (see Appendix 1 for the

complete solut ion.)

•u-i-o. y r 2 h 3 rm2RTcompressibil i ty term - ^ ” 3 7 ™

12 + IP _p r “ p 2r 4 3r

1 3 P ,p 2r 3 dr*

r 3 p 3 v3r( I ? ) +3 3£

p 2r l+ dr+

3fi10RT

3ytfiRTTtFE3- p r ‘

+p 2r 2 3r

61

7h 3 Q2 24y&T

+ r^fil + -1[-2h3{A2RT ,3r 3r v rL 3y 16 tt h I Pr

1 ; 3p p 2r 3 3r

3fl10RT

ft*

p + r ■ IE3r

, 3ymRT+ . -v:"3—4Trh

i. i appr p 2r 3r

i ft 2 RT I + V*w 2 1 . l£

pr715" p 2r 3 3r

4yRTp + r 9p

3r. . a . , — 2 u 3 h +30 24yRT11,3 . 7ft 2h :

p + r3£3r

32 tt y

2h 3 fm2RT

s

4h

J r 3 J

3 y+

3P 2pr167Tzh zr p 10RT

3yihRT_ 4TThdrp>

rtizRTh _ H P zp r h d , 7P 2h 3pr 247Tzy r dp 120yRT ^ 24yRT

+

r 2 h 3 frfi2RTViscous term = y

12[pr

. 3 3p 1 32P ■ 2 r3p 2 ,+ tnnnr + - ■ 3--r [ ovrj +

3 3p p 2 3?J

+ 3P:10RT

21 e + rlig'3r IE*

3ymRT4iTh 3

p 2r^ 3r p zr d 3r r p ^3r

? +2 + 1pr p zr z

3 £ ___ 1_ 3^3r p 2r 3r'

2 rlE)rp^ S r '

3 3p 3rJ

1 3plj _ ift2RTp zr 2 3r

4h3

TIP. h2 i, 3

32?rzy12

[pr

120yRT z 3r r 3rr

p zr 4 3r ; ‘ r 3p J 3r

7h 3.Q2+

24yRT 2H + r5123r

I1J 2hr i 3u

fm 2RT *• 1 6 7 r 2 h 2 pr

3p3r

+ 3P'10RT

p + r3p3r

+3ymRT47rh'

1 , 1 IP. P ? p r 3r

tft2RTf 3 H 1 9P1 i 1 n 2 fn + r 3fi] l lh 3 , 7fl 2h 3 fD + r^ l

32 trzy p r 4 p zr “ 3ry 3J 4yRTU T i. _

3r J 30 ' 24yRT p + 3r

} +

}2h ;

4 f -rTt 3y 16 tt

fa2 RT 3P2pr 3ymRT^ h 2r 3p 10RT 47rhdrp^

tfi2RTh _ H P 2p r h 3 , 247rzy r 3p 120yRT

7P2h 3pr i 2h24yRT * y

rm 2RT 3prP16irzr dh zp 10RT

2 _ 3yifiRT ~ 24Trh3rp

m zR T______ 2prP2h8TTz r dpyh 3yRT

The relevance of the compressibil i ty term compared with the

viscous term can be obtained from the ratio compres sibi l i ty term/

viscous term.

Graphs showing the relevance of the compressibil i ty term for

four different values of R are shown in FIGS. 33 and 34.e

6 2

4.02 THEORETICAL DETERMINATION OF PARTIAL’ DERIVATIV ES

‘ p a n d• 9r

For a plain thrust bearing, i.e. one without a centra l recess,

it has been shown (23) that

9 p 3yQ , 27pQ29r 4Trrhd 280iTzr 3h z

'3'p'fl r 10

(23A)

If this equation is differentiated with respect to r, then,

32P _ 3yQ 81'p'Q9rz 4Trr 2h 3 2807Tzr Hh

+3pft‘

10

These two equations were used to determine, theoret ically, the9~

values of and ■ *— ?, enabling a check to be made on th e dr; dr

graphically determined values shown in FIGS. 26-31 in clusive.

EXAMPLE

Test No .19

when r = 0.06m

|£ = -28770 N / m 3

32P = 9 p r

391800 N/m'

(-28300 N / m 3 graphically)

(382000 N /m 4 graphically)

Test No.20

when r = 0.06m

9r2

25890 N / m :

= 456500 N /m 4

(-23500 N / m 3 graphically)

(468000 N /m 4 graphically)

6 3

RADIAL POSITION OF MAXIMUM STATIC PRESSURE p

From equation (23A)

3p = -3yQ 27pQ2 , 3pft2r3r irrrh3* ”280?7rThT 10

for p to be a maximum = 0 ^ 9r

3y0 _ 27pQ2 , 3 p ft 2 r“ TnrhJ 2807rzr bh 2 10

multiplying both sides of the above equation by r

3yQr 2 _ 27pQ2 3pft 2r lf4iThb 280'nr2Trz" 10

Let A = r 2

, 3pft2A 2 3yQA 2 7 p Q 2 _then ---- + 2 8 ^ - ^ - 0

• & 2 - 5 y Q A + Q 2 = n2Trhd pftz 287rzh 2ftz

The solution for this quadratic equation, and hence the value of

r from r = /A, for tests 19 and 20, is given in the computer pr in t

out Appendix (3). The theoretical position of the p (max) for

Tests 19 and 20 is shown in FIG.44.

Note: p(max) and P(max) wil l occur at the same radi us for any

one test.

2 4 0 0

22 00

2 0 0 0

( 8 0 0

1 6 0 0

1 4 0 0

1200

P( n / t?)

iO O O

8 0 0

6 0 0

4 0 0

200

6 4

F 1G .N ° 2 Q.,

6 5

T E S T N ° I 3

F iG . N ° 2 1.

6 6

• r

(cm ) '

e

( d e g r e e s )

~o7’

( 1 5 0 0 0 t a n © )

0 1

( d e g r e e s )

/ - J & x i o 6

( 3 0 0 0 0 0 t a n 04 )

1 - 0 - 6 2 - 0 - 2 8 2 0 0 7 6 »0 - ! • 2 0 3

1 • 5 — 6 6 * 0 — 3 3 6 0 0 - 7 0 - 5 - 0 • 8 4 7

2 - 0 ~~ 6 0 • 0 - 3 7 2 0 0 ~ 5 0 * O - 0 - 3 5 8

3 - 0 - 6 9 - 0 - 3 9 1 0 0 - 2 9 - 0 —* 0 * 1 6 6

4 - 0 — 6 9 * 0 - 3 9 1 0 0 ' 5 2 - 5 0 * 3 9 1

5 - 0 - 6 5 - 0 - 3 2 2 0 0 6 1 - 0 0 . 5 4 1

6- O - 6 ! - O - 2 7 1 0 0 5 4 - 0 ■ 0 * 4 1 3

7 - 0 — 5 9 * 5 - 2 5 4 0 0 5 0 - 0 0 - 3 5 8

8 • O 1 wt «£s 0 - 2 0 6 0 0 4 7 - 0 0 - 3 2 2

6 • 5 - 5 1 - 5 - 1 8 8 0 0 4 6 0 0 - 3 1 1

C O M P R E S S IB IL IT Y T E S T N ° I 3

T A & LE OF & £ £U L T S

F I G . H°22.

O 0 - 0 2 0 - 0 4 0 - 0 6 0 . 0 8

r (m}D E T E R M IN A T IO N O F P R O M £ X P E R lte £ W T A L R E S U L T- - - - - - - - - - - - - - - - - c? r - - - - - - - - - - - - - - - - - - - :- - - - - - - - - i~

F I G . N ° 2 3 .

60

T E S T N ° i4

O

- 4 0 0 0

- B O O O

- 12000

- 1 6 0 0 0

■ $«/«?)- 20000

- 2 4 0 0 0

- 2 8 0 0 0

- 3 2 0 0 0

- 3 6 0 0 0

0-02 0 - 0 4 0 - 0 6

f(m)

0 * 0 8

D E T E R /V\ I N A T SO N O P F R O M E X P E R IM E N T A L . R E S U L T S---------------------------------------------- d r ------------------- ■---------------------------------------------------

F IG . N ° 2 4 .

6 9

■ r( c m ) '

©

(degrees!

\opor

( < 5 0 0 0 t a n © )

cL

( d e g r e e s )

4 * i o s* CJf

( s O O O O O ta n 0()

1 .0 * - 6 6 * 5 - 3 4 5 0 0 - 5 8 * 0 — 0 . 4 8

1 - 5 6 0 * O ~ 6 7 1 3 0 - 4 0 - 5 ' . — O - 2 5 6

2 - 0 6 8 • 5

.......... —

— 3 8 0 8 0 - 27 * 5 - 0 - 1 5 6

3 - 0 - 6 9 - 5 - 4 0 S 2 0 - 3 - O — 0 * 0 1 6

4 - 0 - 6 7 - 5 ~ 3 6 2 1 0 ! 8 - O 0 * 0 9 0

5 - 0 - 2 7 - 5 - 2 8 8 2 0 4 2 - 0 0 - 2 7 0

6 - O - 5 8 - 5 — 2 4 4 8 0 6 9 • O O * 7 B 2

7 - 0 - 5 3 - 0 - 1 9 9 0 0 61 • 5 0 5 5 2

8 - 0 - 4 8 - 0 - 1 6 6 6 0 6 0 - 0 O . 5 1 9

8 - 5 - 4 2 - 0 - 1 3 5 1 0 5 7 . 0 0 - 4 6 2

C O M P R E S S IB IL IT Y T E S T N ° 14

T A B L E O F R E S U L T S

F I G . 2 5 .

7 0

r (m )

D E T E R M IN A T IO N OF - |£ - F R O M E X P E R IM E N T A L R E S U LTS . ----------------------------------- d r ------------------ -----------------

FIG. N° 26.

“7 OI d

r

(cm) ‘

©

{degrees)

i[L% r

( 1 5 0 0 0 t o n e )

CL

(d e g re e s )

>7 6<3 E? v* [ O

( 7 5 0 0 0 0 ter? 0\)

1*0 7 EL O 7 0 7 0 0 8 5 - 0 — 8 - 5 7 3

1 .5 4 8 - 0 . 1 6 6 7 0 - 8 4 - 0 - 7 1 3 6

2 0 - 4 3 - 0 1 4 0 0 0 8 2 • O - 5 3 3 6

3 - 0 - 7 1 - 0 - 4 3 7 0 0 3 0 - 0 0 - 4 3 3

4-0 - 6 8 - O - 3 7 1 0 0 3 5 - 0 0 - 5 2 5

5 - 0 - 6 5 - 0 , - 3 2 2 0 0 2 9 - 0 0 - 4 1 6

6 0 — 6 2 - 0 - 2 8 3 0 0 2 7 - Q 0 - 3 8 2

7 0 - 5 8 - 0 - 2 4 0 0 0 2 5 - 0 0 - 3 4 9

8 - 0 ~ 5 5 - 0 - 2 1 4 0 0 2 2 - 2 0 - 3 1 1

8 - 5 - 5 2 . 0 - 1 9 2 0 0

.

21 -O

........ . .

0 - 2 8 8

C O M P R E S S I B I L I T Y " S T N ° ny

TAB LE? O P R E S U L T S

F I G . N ° 2 8 .

7 3

s>,=r (m)

PETER/VMNATION OF -g£ Pft.OfA E X P E R I M E N T A L R E S U L T S

D E T E R M IN A T IO N OF FR O M E X P E R IM E N T A L R E S U L T S----------------------------------------o r i ---------------------------------------------------------------------

K j n . m o o r \I i u. IS w .

r

( c m )

©

(d eg rees )

e).[33 r

( i S G O O t a n © )

OC

(d egrees)f f e x l Obfz

( 7 5 0 0 0 0 ta n

1 . 0 7 - 2 5 4 4 2 0 0 - 8 3 - 0 6 - 1 0 8

1 .5 6 0 - 0 2 6 O O O 81*5 - 5 . 1 0 8

2 - 0 - 2 2 - 5 - 6 2 0 0 - 8 3 . 5 - 6 - 5 8 2

3 - 0 - 7 1 . 5 4 4 8 0 0 3 0 - 0 0 - 4 3 3

4 « 0 - 6 6 . 0 - 3 3 7 0 0 4 2 • O ' 0 - 6 7 5

5 - 0 — 6 1 * 5 - 2 7 6 0 0 3 6 - 0 0 - 5 4 5

6 - 0 - 5 7 -5 - 2 3 5 0 0 3 2 - 0 0 - 4 6 8

7 - 0 - 5 3 - 0 - 1 9 9 0 0 3 2 - 0 0 2 7 3

8 * 0 - 5 0 - 5 - 1 8 1 0 0 1 6 - 0 0 - 2 1 5

8 - 5 - 4 5 . 0 - 1 5 0 0 0 8 i -5 0 - 2 0 1

TABtfc Oh kESUL i £

F I G . N °3 I .

CO

MP

RE

SS

IBIL

ITY

T

ER

MV

ISC

OU

S

TER

M

perc

ent

x I

O

7 6

V A R I A T I O N O F C O M P R E S S IB IL I T Y R A T IO W 1TM R A P iU S

^H O g > & O M <£• L.&wgis'j

F I G . N ° 3 2 .

5

O

5

10

15

2 0

25

30

35

40

45

50

7 7

T E S T N ° G R A P H

13 O

14

V A R I A T I O N OP C O M P R E S S I B I L I T Y R A TIO W IT H RADIUS

F I G . N °3 3 .o

CO

MP

RE

SS

IBIL

ITY

T

ER

MV

ISC

OU

S

TER

M

pe

rce

nt

x I

O

7 8

F I G . N ° 3 4 .

7 9

CHAPTER 5 EXPERIMENTAL AND THEORETICAL- RESULTS

5.01 INTRODUCTION

The results of 36 tests were used to test the theor ies outl ined in

Chapter 3. 12 tests were used for each of the follo wing:

(i) Plain thrust bearing (static)

(ii) Plain thrust bearing (static/dynamic)

(iii) Stepped thrust bearing (static/dynamic)

In each of the 36 tests the theoretical determinatio n of the

dimensionless pressure distr ibution was calculated from equations

(30) and (31). The theoretical relation between p 1 , r, and Q was

evaluated using equation (33). Equation (33) has be en shown in

graphical form in FIGS.53-58 inclusive.

*

Graphs in dimensionless form, were used to show the change in

pressure as the air lubricant flows through the bear ing. The

effect of a change in flow rate, Q, and gap thicknes s (2h), or

alternatively the dimensionless constant R = on the■ e iryh

dimensionless pressure profile can be seen. The vis cous flow

3 rline P - P 2 = loge was included, where appropriate, so that

its limitations for the design of thrust bearings c ould be seen.

In practice, thrust bearings would be operated with gap sizes

which would be regulated by changing either the bea ring load or the

volume flow rate of the lubricant. The constant gap size (2h)

used for this series of tests were, in general, lar ger than those

used in practice, and this had the effect of produc ing extreme

conditions regarding the radial inertia effect, par t icular ly in

the central area of the disc.

8 0

In the static tests, comparisons between experiment al and

theoretical results were made to test the effect of the radial

inertia term responsible for the deviation of the

dimensionless pressure values from the viscous flow solution.

In the dynamic tests there were two inertia terms t o be taken

into account, the radial inertia term — - and a rotat ional ' r

inertia term -. Tests 13-24 inclusive show the rele vance of r

these two effects.

The value of the experimental thrust was calculated by usingf r 2 _

Simpson's Rule to determine the value 2ir prdr. These thrustr l

values were based on the static pressure readings f rom each of

the 36 tests. The theoretical thrust values, for all tests were

calculated from equation (34). Theoretical thrust v alues for

Tests 1-24 inclusive are shown graphically in F IG. 66 .

Thrust values from F I G .66 were used in formulating equations

(1') (21) (3') shown in FIG.67, these equations were then used

in predicting thrust values for flow rates in exces s of those

employed in Tests 1-24 inclusive, and are shown in FIG. 68 .

Theoretically the rotation term (r 22 - r 2 ) is independent of

gap size (2h) and flow rate Q. The magnitude of the rotat ional

inertia term for the zero flow condition, at 4000 rev/min was

examined experimentally. The effect of varying the gap size (2h)

on the magnitude of the rotation term was investigat ed and the

results are shown graphically in FIG.59.

Results from tests with a stepped bearing enabled eq uations (30)

and (31) to be tested more rigorously than those ob tained from

the plain bearing tests. The theoretical analysis o f the

81

stepped bearing was based on the assumption that th e air would

expand in two stages; the inner stage through a gap w idth

(2ah) and the outer stage through a gap width (2h). FIGS. 47-52

inclusive enable the theoretical and experimental r esults to be

compared, and the two stage expansion is clearly ev ident.

5.02 STATIC CASE

FIGS. 35-40 inclusive record the experimental and t heoretical

results for tests 1-12 inclusive. In these tests th ree

different gap widths were used 0.2mm, 0.25mm and 0. 3mm. For

each gap width four different air flow rates were e mployed.

The significance of the Reynolds number in predict i ng the

form of the dimensionless pressure distr ibution is readily

seen — the smaller the Reynolds number, the smaller the

deviation from the Viscous flow line. A high Reynol ds number is

therefore associated with a high value for the dimen sionless radial

inertia term (jh~ - br~ r) / which could be wri t ten in the5607rhy R R 2

27 1 1form 5 gQRe (pT- ~ r “2*) * T^e 9 raPhs shown in FIGS. 35-40 inclusive

are in dimensionless form, to enable comparisons to be made between

thrust bearings when different parameters are used. When actual

pressure values are required however, it is prefera ble to use

the radial inertia term in the form t t t P- zttt z*) . See560ir^h r z r 2 -

equation (24). The value of the dimensionless radia l inert ia term

is proportional to the Reynolds number, or but the va lue of the

radial inertia term in dimensionalised form is propo rt ional to

(2) 2 . Therefore, for a given flow rate, if the gap width is

halved, the Reynolds number is doubled and the valu e of the

radial inertia term, in dimensionalised form, is incr eased by a

factor 4.

8 2

The correlation between theoretical and experimenta l results

was not the same for each test, neither was it the same at

different radii for any one test. In general the lo wer the

Reynolds number the closer the correlation between experimental

and theoretical results. This can be seen by compar ing F IG.35

with.FIG.37. For the higher Reynolds numbers, assoc iated with

higher gap widths, the theoretical prediction of di mensionless

pressure compared with experimental results was hig her for the

outer three-quarters of the disc, and lower for the inner

quarter of the disc, as shown in FIG.37-40 inclusive . The

significance of the accumulative effects of experim ental error_ dimensioned

in the theoretical prediction of ■d-imcns-ionlcaa p ressure d is

tribution is considered in Chapter 6 .

The results of the thrust calculations based on equ ations

(34) and . (35) are shown in Appendix (2). The perce ntage

error, based on the relation:

■ theoretical thrust - experimental thrustpercentage error = --------- jt ---- r-. =— ----------------* • 3 theoretical thrust

ranges from 0.4% to 17%.

Theoretically, the higher the Reynolds number the g reater the

radius at which the maximum static pressure (p) occ urs. (See

8 3

4.02). Experimentally it was shown that the radial position of

the (p) maximum was different for each test. If Tes t No.2

(Re = 78060) is compared with Test No.12 (R = 38150 0) the

radial position of the (p) maximum was greater for test No .12

than for Test No.2 - confirming the theoretical pre diction for

these two tests.

5.03 •STATIC/DYNAMIC CASE

The results from Test No.13-No.24 inclusive are shown in FIGS.

41-46 inclusive. In these tests three different gap widths

were used, 0.2mm, 0.25mm and 0.3mm. For each gap wi dth two

different air flow rates were employed. The dynamic tests

were at 4000 rev/min. '

The equation for the theoretical dimensionless pres sure

distribution from Chapter 3 is:

P P — Inrr ) 27pQ / 1 _ 1 \ _. 3tT h pfi 2 _ p 2 \P - P 2 - T loge (— ) - — — {-p (R 2 R )

VISCOUS TERM RADIAL INERTIA ROTATIONAL INERTIATERM TERM

The radial and rotational inertia terms, when expre ssed in

dimensionalised form, become (~ 4 ~ ~ — z-) and560tt h r r 2

- ~ - ( r 22 - r 2) respectively. The form of the negative press ure

distributions, due to both these terms, for Test No .13 and

Test No.15 are shown in FIG.46A. This graph shows the relative

importance of these two terms. In the centre of the disc i.e.

when r is small, the radial term has its highest val ue. In one

case (Test No.23) the negative pressure effect is la rge enough

8 4

to overcome the positive pressure effect due to the Viscous term,

and a pocket of sub-atmosphere pressure is induced in the centre of

the disc.

The negative pressure distribution due to the rotat ional term

also has its highest value in the centre of the dis c, but theuniform

distribution of negative pressure is more -even- than with the

radial term. The correlation between experimental a nd theoretical

results, for the dimensionless pressure distributio n, followed a

similar pattern to those in the static case. The di stort ion of the

pressure distr ibution curve, due to the adverse eff ect of the

rotational term, reduced the thrust on the bearing by 5N, which is

13.5% of the maximum thrust generated. (Theoretical ly if the

rotation speed were 40,000 rev/min the reduction in thrust would

be 500N since the magnitude of the rotation term is propor tional

to ft2 ) .

8 5

5.04 ' STEPPED BEARING

Results associated with experimental Tests 25-36 in clusive are

shown in graphical form in FIGS.47-52 inclusive. The effect of

the introduction of a step in the bearing was to exte nd the area

over which high pressure acted. At the same time ho wever, in vicinity

the "VQcimity of the air inlet, pronounced fall-off in static

•pressure could occur due to radial inertia effects .

Equations (30) and (31) were used to determine the dimensionless

pressure distribution and equations (34) and (35) r espect ively to

determine the theoretical and experimental thrusts. The percentage

error in determining the bearing thrust varied from 3.3% in Test 33

to 30% in Test 36. Theoretically the suction effect induced by a

rotational speed of 4000 rev/min reduced the bearing thrust by 5N,

for every test. The highest thrust recorded was for Tests 27 and 28.

In Test 2 7 - (Re = 182 200/109 300) the theoretical and experimental

thrusts were 38.2 and 36.8N respectively. In Test 2 8 the theore

tical and experimental thrusts were 33.2 and 32N re spectively.

This represents a 13% reduction in thrust, due to a rotation speed

of 4000 rev/min, for both experimental and theoretical res ults.

The logical reason for providing a step is to extend the area over

which the high inlet pressure of the incoming air c an act before it

begins to escape through the narrower air gap. Incre asing the size

of the air gap, by the provision of a step and for a given flow

rate, results in a decrease in the Reynolds number; thus the

effect of radial inertia in decreasing the static p ressure is

reduced. However the size of step chosen for Tests 25-36 inclusive

only part ly reduces the radial inertia effect. This means that

some decrease in pressure across the stepped portion of the disc

8 6

is unavoidable.

Where the Reynolds numbers are in excess of 200 000 (see Tests

31-36), the correlation between the experimental an d theoretical

pressure profiles, for the stepped area of the disc , shows

considerable variation, due to an overestimation of the value of

the radial inertia term. This is consistent with the pressure

distribution profile for Test 23 and 24 where the Rey nolds number

is 31140.

5.05 THE ZERO-FLOW CONDITION

To test the significance of the rotational inertia term, as

contained in equation (24), tests were carried out, in a plain

thrust bearing, with the dynamic disc rotating at 4000 rev/min. The

air inlet to the bearing was blocked so that a zero- f low condit ion

(Q = 0) existed. Under these conditions equation (2 4 ) is reduced

to p = -3pfi 2 (r 22 ~ r 2) i.e. theoretically, a suction effect is 20

produced which is independent of gap size. The instru mentation

was arranged as shown in FIG.60. Tests at gap widths of 0.2mm,

0.25mm, 0.3mm, 0.35mm, 0.4mm, and 0.45mm were run. Only when a

gap width of 0.45mm was tried was there a noticeable change in the

suction effect, where the theoretical value tends t o overestimate

the suction effect. The results are tabulated in FI G.59.

5.06 THE RADIAL VELOCITY, AXIAL VELOCITY AND THE PRESSU RE

TERM------- d Z— -

FIGS. 61-65 inclusive show how the magnitude of the theoretical

radial velocity, axial velocity and the pressure te rm p3Vz are3z

influenced by h, Q f Q, r and z. The radial velocity components

8 7

shown in FIG.61 were calculated from equation (28). The axial

velocity components shown in FIG.62 and 63 were calc ulated from

equation (29) . The pressure term components (y- -2-) shown ina Z

FIG.64 and 65 were calculated by mult iplying equatio n (28A) by

y. These calculations are tabulated in Appendix 3.

The effect of rotation was to induce a flow in the a xial direction

towards the dynamic disc while at the same time the profi le of

the radial velocity curve was distorted so that its maximum value wa

nearer the dynamic disc than the static disc. The v al idity of

the graphs shown depend on the flow being laminar. To assist the

air to flow, without swirl, into the gap separating the static and

dynamic discs, a radius was machined at the exit fr om the air inl

port, but this could not be expected to eliminate t urbulence

completely. Therefore the calculated values for V , V andJ. z

9Vy- -2- for small values of r are ' ideal 1 values only.

d Z *

The variation in pressure across the gap was very sm all. e.g.

in Test 20 when z = 0 and r = 70mm (FIG. 64) y-^2- = 1.99 x 10” 3N /m2 .d Z

The value of p, at the same position in the air gap, was 545N/m2 .

This justifies the interchange of by -|£, as in the theory

outl ined in Chapter 1. (see the first of equations ( 8 ) and equation

(15)).

8 8

5 .07 BEARING THRUST AND BEARING PERFORMANCE

Curves of Reynolds number /Thrust shown in FIG. 66 were based on values

tabulated in Appendix (2) . These graphs were replo tted In dimensionless

form,in FIG.67. The dimensionless thrust TD was obt ained by mul t i

plying the thrust (T) by The straight line laws asso ciated with

equations 1 1 2 1 and 3 1 (FIG. 67) were used to obtain the relationships

between T and Q shown in F IG. 68 .

viz. consider Test No.7.

h = 0.125mm Q = 0.00213 m 3/s p = 1.24 kg /m 3

y = 0.000018 Ns/m 2 r 2 = 95mm

from equation 2 1 Rp = -6.15 x 10 11 x TD + 100.35 x 101*

. PQ_ _ .6.15 X K T - X T x r, + 3 ,. x 10 ,'' irph ViQ

*

substituting values for p, Q etc in the above equat ion

37.4 x lO 4 = -15200T + 100.35 x 10 4

T = 41.4N

(Results given in Appendix 2 are 41.IN (Theory), 38. 9N

(Experiment)).

In determining the performance of thrust bearings tw o things should

be considered: (a) the thrust that the bearings can support,

(b) the volume flow rate of the lubricant required. If the

measure of performance is taken as the ratio Thrust/V olume flow

rate per second, then the bearing giving the best p erformance

wil l be one that has the smallest air gap with the smallest f low

8 9

rate. See FIGS. 69, 70 and 71.

When the gap and flow rate are small we have the pa radoxical

situation, where, if the volume of air flowing thro ugh a rotating

bearing is increased, this could result in an improv ement in

performance. This is because, theoretically, the su ction caused

by the rotational inertia effect is independent of f low rate,

so that as the flow rate increases the percentage r eduction in

thrust due to the rotational inertia effect decreas es.

For the series of tests undertaken the performance of the stepped

thrust bearings was not as good as that of the plai n bearings,

however, the stepped bearing is able to provide init ial ' l i f t 1

to separate contacting surfaces immediately before the bearing is

rotated. This is an important feature if wear is to be avoided

in practice.

9 0

S T A T I C T E S T S

oC. ~ I • O

n =■ O- OOOl m

Ra - 950

o3 *m / see Re TH E O R Y E X P E R IM E N T

0 .000503 ! 78400 o

0-000356 78060 --------------- A

2? loci J R

o IC O 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0

R

DIMEM6i0K1 LESS PStgSSURg PISTRlSUTtOM T E S i S h'° 1 & N°2

FIG. N®35.

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P - R 2.1 oa Eza

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9 2

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puwewsioMuess pressure Disraie-'.’Tio.'-i T E S T S N °5 & N °6

F I G . N °3 7 .

oc. « i ♦ o

h - O . O O O I 2 5 m

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F IG . N ° 3 8 .

94 '


DC - I . O

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A

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9 9S T A T IC A N D D YN A M IC T E S T S

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DIMENSIOMUSSS pr essur e DIST&'&UTIOM T E S T S N ° 17 & N ’"' i 6

FIG . N ° 4 3 .

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PIMSNSIOMLSSS PRESSURE DISTRI&UTIOW T E S T S N ° 21 & N °2 2

F I G . N °4 E .

102S T A T IC A N D D Y N A M IC T E S T S

rv/ —Vv. -- NO

h = Q . Q O G i S m

- 6 3 3

o - 0 - 0 0 2 1 3 rn/s

J3 (fc11 3 1 1 4 0 0

rcv/m inSPEED T H E O R Y E X P E R IM E N T

Z E R O --------------- O

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piAASfrigtotMLsss p r e s s u r e TESTS N° 23 & N °2 4

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S T E P P E D B E A R IN G

■ OL - 1 - 6 6 7 [ r 3 = 4 5 m m ]

h - 0 - 0 0 0 1 m

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Re “ 1 2 8 7 0 0 / 7 7 2 0 0

R

DIMEMSIOMLESS PRESSURE PiSTKlBUTIQ-M T E S T S N °2 5 5 . N °2 6

F IG . N °4 7 .

! O S

S T A T IC A i I D D Y N A M IC T E S T S


oC — 1 -6 6 7 [ r 3 = 4 5 f i im ]

h = O - O O O I m

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Fl~ “ 1 8 2 2 0 0 / 1 0 9 3 0 0 e /

R

D(MEMS(OML£SS PRESSURE D iSTC iBU T iO ^i T E S T S N ° 2 7 & N u 2 8iO

F I G . M °4 8 .

1 0 6


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STEPPED B E A R IN G

OC - 1 - 5 3 3 [ H*= 4 5 m m

= O . Q O O I 2 5 m

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= 2 0 5 2 0 0 / 1 3 4 0 0 0

rcv/m inSPEED

TH E O R Y E X P E R IM E N T

Z E R OC

4 0 0 0 A

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P&ESSUKlT T E S T S N ° 2 9 a N ° 3 0

F IG . N °4 9 ,

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oC = 1 - 5 3 3 [r3 “ 4 5 m m

h « 0-000125 mR

O ** 0 - 0 0 1 8 4 m ' V sec

Re - 322000 j 210000

R

DiMENSlOMLSSS PRESSURE DISTRIBUTION T E S T S N ° 3 \ & N °3 2

1 0 8

STATIC A N D D Y N A M IC T E S T S


DC =• 1 - 4 4 5 [ r 3 = 4 5 m m ] '

h “ 0 - 0 0 0 1 5 m

R

0

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D!M£n s io ml .£S5 PRS&suKS DisTOiew-'TioM T E S T S N ° 3 3 & M ° 3 4

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1 0 9

S T A T IC A N D D Y N A M I C T E S T S

S T E P P E D B E A P J N G

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h = O - O O O S 5 m

*= 6 3 3C,

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Re - 3 8 6 0 0 0 / 2 6 7 0 0 0

F IG . N ° 5 2

TA

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a /V O L U M E FLO W R A T E m /s e c « 10

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F IG . N °5 4 .

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EXPERIMENTAL RESULT^

0^ Q h ( mrnj GRAPH

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D IS C R A D IU S ( c m s')

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F I G . N ° 61 .

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F IG . N ° 6 6 .

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RELATION &ETW g £ N PERFOR/AfeMCE & F L O W RATS ( STEPPED SEAR I MG)

129

CHAPTER 6 SUMMARY

6.01 ERRORS

The errors arising from this project can be classif ied into two

groups; namely, errors in the physical measurements and errors in

the theoretical computat ions.

Errors in the physical measurements

If the axis of rotation of the dynamic disc is not p arallel to

the axis of generation of the static disc, then thi s misal ighment

can cause a vibration to be superimposed on the air passing

through the bearing. A vibration of this type was d etected by

the pressure transducer during pressure measurement s associated

with the zero flow condition; but the variation in pressure

produced was too small to have any significant effe ct on the

static disc, therefore a major error, due to squeez e-fi lm

effects, can be discounted.

The volume flow rate, Q, was measured using an orif ice plate whose

design was based on BS 1042. From details given in Appendix D of

this standard it was apparent that an error of ±1.3 per cent in

the flow rate could be expected.

The setting of the distance between the discs, 2h, wa s subject

to error from three sources (a) feeler gauge size, ±1% error,

(b) error in interpreting the ff ee l ! when setting th e gap with

the feeler gauges, ±1%, (c) alignment error, ±1% erro r. Giving

a total of ±3% error.

1 3 0

The speed of rotation of the dynamic disc was measu red by means

of a tachogenerator, the output of which was fed to a digital

voltmeter. A speed tolerance of ±2% was estimated. The step in

the stepped disc was set to an accuracy of ±1%. The sta tic

pressure p measured from the static disc tappings h ave an

estimated tolerance of ±2%. The values of temperature, atmos

pheric pressure, density and viscosity were recorde d to an

estimated tolerance of 0 .1%, 0 .1%, 0 .2% and 0 .2% res pectively.

The tolerance on the radial positions of the static pressure

tappings (set by a numerically controlled machine tool) was

±0.1%. The outer diameter of the disc r 2 was manufa ctured to

very close limits. It wil l be assumed that the size attributed

to r 2 is correct.

'Accumulative' effect of errors' in physical measureme nts

Equation (24) is made up of three terms, if each ter m is considered

separately, the possible error associated with each term can be

calculated.

VISCOUS TERM

hence percentage error = ±10.3%

RADIAL INERTIA TERM

hence percentage error = ±8.9

I 31

ROTATIONAL INERTIA TERM

Let W = (r22 - r 2)

then = — + 2^ - 2—W p - f i r

hence percentage error - ±4.3

The above analysis suggests that in determining the value of the

static pressure, theoretical predictions should cor relate with

experimental results to within ±10%.

Errors in the theoretical computations

The equations used for determining the static press ure in a

thrust bearing at any radius, rely on the solution of a

quadratic equation (33), by means of a computer progra m,

Appendix (4), to provide the necessary relationship between p

and Q at the reference radii r i . The graphs (FIGS.5 3-58

inclusive) show how p and Q are related, but these graphs were

not relied on exclusively to provide an accurate fo recast of p

and Q values. To avoid errors due to interpolation, the computer

program was used to predict values of Q for part icu lar values of

p to suit each particular test run.

SoThe graphical determination of the partial derivati ves •— and

8 2 p■5— 5- could be subject to considerable error part ic ularly in the dr

vicinity of the air inlet — where rapid changes in pr essure take

place, an error of 5% and 10% respectively will be a ssumed.

(see 4.02).

1 3 2

Some of the theoretical and experimental curves obt ained by Jackson

& Symmons (7) and Shirman (12) for non-rotating hyd rostatic bearings

show the same general form as those found in this r eport. If the *

graph associated with the Reynolds number 174800 (J ackson &

•Symmons (7) FIG.3 p . 63) is compared with Test 5, F IG.37, both

theoretical graphs overestimate the values of the d imensionless

pressure for all but the inner quarter of the disc, where the

dimensionless pressure is underestimated.

The curves associated with parallel circular plates "without a central

recess (shown by Coombs and Dowson (11)) do not al l ow for radial

inertia effects. This would appear to be justified if the flow

rates employed were small. In their experimental te sts Coombs

and Dowson used a thrust bearing with an outside dia meter of 5.25in

(r2 = 66.7mm) with an oil supply hole 0.25in diamete r. If we

assume the following: 2h = 0.25mm, p = 900kg/m3, ft = 419rad/s

(4000 rev/min) , y = 0.02Ns/m2 and Q = 0.00015m3/s, t he relative

magnitudes of the Viscous, Radial, and Rotational t erms, when

calculated from equation (24), are:

VISCOUS RADIAL ROTATIONAL

1 0.05 0.56 when r = 15mm

1 0.032 0.48 when r = 30mm

From these results it is clear that if Coomes and Dow son used the

test conditions assumed above, the omission of the radial inertia

term did not seriously affect their results.

6.02 DISCUSSION

1 3 3

If, however, air is the lubricant, its low absolute v iscosity value

greatly reduces the value of the viscous term. The value of the

radial and rotational terms will also be reduced (b ecause of the

air's lower density value), but not by the same mag nitude as the

viscous term. This means that the radial term can b e significant

(in relation to the viscous term) -part icularly whe n Q and h are

large and r is small. The effect of omitting the radi al inertia term

when calculating the value of dimensionless pressur e is shown in

FIG.43A.

The maximum theoretical thrust of 57.4N (12.81bf), recorded in

Test 4, is small by practical standards, but if higher thrusts

were obtained by reducing the size of the air gap, the effect of

rotation, the main interest of this thesis, would b e eclipsed by

the resulting high value of the viscous flow term. The low thrust

values are due to the fact that the pressure change across the disc

was relatively small, and so it follows that the cha nge in gas

density, which is proportional to the absolute press ure, was too

small to effect the accuracy of the theory based on incompressible

flow.

The use of a pressure transducer, connected to a U.V . recorder,

to measure the suction effect experienced during th e zero f low

condition, proved very effective. The U.V. recorder was used to

record the high pressures experienced in Tests 1-36 , but without

success; the sensitivity of the recorder had been r educed to

such an extent to cope with the higher range in pre ssure ----

that small pressure changes could not be measured a ccurately. The

radial pressure distribution for Tests 1-36 was the refore measured

using a water fil led manometer.

1 3 4

6.03 CONCLUSIONS

It has been established both theoretically and exper imentally that

the faster a hydrostatic thrust bearing is rotated, the smaller the

load it can sustain for fixed flow and gap width co nditions. The •

tests in which suction effects alone were considere d were signifi-

. cant in showing the non-dependence of the rotatio nal inertia term on

gap thickness and flow rate.

There has not been complete agreement between exper imental results

and theoretical predictions, this is due mainly to t he accumulative

effect of errors in the physical measurements discu ssed in (6 .0 1 )

and partly to the inadequacy of the theory employed , to really

predict how the air pressure changes as it passes th rough the

bearing part icularly in the vicinity of the air inl et where

turbulence could exist. However since the theoretic al results

were tested under extreme conditions, sufficient ac curacy exists

for the designer to use these equations to include the effects of

rotation on hydrostatic thrust pads.

6.04 FURTHER WORK

Modif ication to existing test rig

The principal error due to physical measurement was in the

determination of the gap thickness (2h). This error would be

reduced considerably if three pressure transducers w ere used

(FIG.72), to monitor continuously the gap width. The three

transducers could be connected via transducer conve rters to the

same U.V. recorder and readings from each channel c ould be

! 3 5

recorded simultaneously on the same trace.

Design of new test rig

T h e . p r o p o s e d r ig w o u ld b e

arranged. so that the dynamic disc rotates with its axis of

rotation in a vertical plane. The dynamic disc would be above

the static disc, supported only by the air which flows radially from

the centre of the two discs. The thrust provided by the escapi ng

air would always be equal to the weight of the dynamic disc. The

effect of rotation would be to reduce the size of the air gap .

The design could include:

(a) Very high speed rotation by the use of air jets, to inves

tigate the effects of high shear rates on viscosity.

(b) Use of thermocouples, to measure changes in air temperature,

to test the validity of isothermal theory.

(c) The use of pressure transducers to measure pressure, an d

changes in the air gap size.

(d) An electro-magnet positioned above the rotating d isc which

could be used to induce a pure squeeze film effect at any

frequency.

136

RELATIVE POSITIONS OR PRESSURE

TRA N SD UCERS ISsi STATIC D ISC .

“E

/

DVMA/VtICDISC

STATIC

DISC

T R A N S D U C E R C O M V E PITS P.

*

U V RECORDS

P R O P O S E D IM S T R U M g N T A T i OM POP , C O N T IN U O U S RECORDS M O

O F G A P W IP T M U S IN G P R E S S U R E T R A N S D U C E R S ,

F I G . N ° 7 2 .

1 3 7

APPENDIX I COMPRESSIBILITY

Complete solution of compressibil i ty and viscous te rms outl ined in

(4.01).

From equation (18)

v = -L (72 - h 2w pQ2 . + 3r^ 2 - 3^Q, _ pQ2 , rz2 - -nr 2 y i6TTzr sh z 10 4irhdr 32iT2r dy h7*

prfi’2'^1* . z 3 z2» 7pfi2rh 2 pft2rhz4y 3h 2 48y 12y

and from the perfect gas equation p = ^

\ 7 = _ L /~2 _ ^2 \ /iti2RT 3prQ2 _ 3ymRT , __ m 2RT /z2 _r 2 y l ' 16TT2r ;,h 2p 10RT 4irharpJ l 2F zF JpiI(h7' ;

prfi2 ,z4 z 3 z2» 7p£22rh2 pft2rhz~4yRT I2ET2" * 3h 2 j 48yRT 12yRT

Differentiating with respect to r we obtain

3Vr _ 1 f„z _ u2 \ t 3 1 3p^ , 3ft2 , „ 3p x9r 2y “ * 16TTkh 2 ( pr^ p7^ 3rJ 10R T (p 3rJ

3ym RT, 1 1 3p. m 2RT , 3 _____ 1 9£w z2 _ , , _47rh3 p r2 p 2r 3r 32ir2y p r 4 p ^ r d 3r h7"

R L _ (p + r i E ) ( ^ ! _ + l l + l l ) + Z ff-J}.2. ( p + r i E ) + (p + r l E ) g f h z _4yRT p r 3r ; ll2h^ 3h 2 ' 48y RT lp r 3r ; 'P r 3 r ;12yRT

Differentiating again with respect to r we obtain

i l^E = i - ( z2 - h 2){n i i | T .(12 + 3£ _ 1. 3fp + 2 ,3p}2 +3r 2y 167rzh z p r b p r 4 3r p zr d 3r r 3p 3r

Iz— r IE) + j_?2 ,, (lE + lE + r2l#) - + T _ 1 _ U p +p r 3r IoRt 3r 3r 3r*- 4'irhcl p r J p 2r 2 3r p^r 3r

in2h2 . Bp rl!Px . ^Zhz fr9p , rllP)48yRT Br 3r^} 12 £T(23r Bpr)

Differentiating V twice with respect to z we obtain

8zV r _ 1 ,ifrzRT 3prflz _ 3yifoRT . _ A ZRT __ _ pr.fl2 ,z2 2z3z y 16TT2r dh zp 10RT '4irh Jrp 16Tr2r 3pyh2 4yRT Ti2" "H"

Substituting these equations in the compressibil i ty term we

obtain

u ,32vr i avr vr . _ v3 (3 P ^ h i 8F P r) “ 3

W - h ’H * 25T '121_2y

, 3 3p'z t t t v — — r + z z r z n r —16Trzh z p r b p zr H 3r

1 B2p 2 ____ /3P\2 , 3 ___ Bp. 3ft2 ,03p 92PV 3 y A R T , 2 _p 2r d Br2" , r dp d Br p 2r lt Br 10RT 8r r 8r z ” 47rh3_ p r 3

1 Bp 1 32p 2 /Bp. 2 , 1 Bp. m 2RT ,12 , 3 Bpp 2r 2 Br p zr "Br2" r p 3 Br p zr z Br 32nzy p r b" ‘ p zr 4 Br

2 _ 1 ________ B 2 p . 3 ^ _____ _ B p . / Z 2 _ n _ f i 2 _ / 9 B d „ B ^ d ^ f z u

r 3p 3 Br p 2r 3 Br2 p 2r** Br h^ 4yRT Br “ Br 12h2

Z l + 2l) + 7n2h 2 ■ 3p 3fp. a zhz . 3p 32p , Iri_. 2 _ h 2 .3h 2 ■ 48yRT 3r 3r^J 12yRT l 3r 3r^) r i2p ( '

i-m 2RT . 3 _ 1 Bp. 3ft2 , Bp. _ 3ymRT , 1 _ 1 Bp. • »16TT2h 2 p r 1* p zr 3 Br 10RT ^ Br 4ttIP p r z p 2r 3r

^ - Jk... 12) (?L— - l) _ (n + r-^) (- -r + + _—_)32 tt y v pr^ p r 3r ; ' 4yRT ™ r 3r' ^IFh^ 3h 2 ;

2u2, 3px , ft2hz , _3px 1 rl , 2 u 2 i ,it2RT

(p + + T o'TTprp (p. + rT£)> “ trz-{oT7(z2 - h z) (1Cwa u r ^ +7ftzh48yRT Br7 ‘ 12yRTv ' J-3r/J r ^ y 11 7 v167Tzh zr 5p

3<?2nr _ 3ymRT . _ it2RT , z2 _ , • f i V z 1*' 'z + *L\ +^ 4TThTrp 32,irzy r ;5p h 7 4yRT 12h2 3h 2

I 3 9

7Q2h 2pr p'ft2'rhz,” 4 8y RT 12yRT _

Integrating the above equation over the film thickn ess 2h between

limits of z = h and z = -h giving a final equation

. • . • y F -2h3'r* 2RT ,12 , 3 3p 1 :32p ,compressibil i ty term = 3 (^pr - prpr -57 - prp- g£* r -

2 f8P '2 , 3 3£, 3n2 , 3p 3fp. _ 3plhRT ,2 ___ 1 JLB _r 3p 3 3r p zr 4 3r 10R T ' 3r 3rz 4nhJ pr° ‘ p zr 2 3r

1 A!p + ^ ( l E ) 2 + i _ ^ ) } - e!1t (12 ■ 3 _ _ Bjd ' 2 . ^ _p r 3r2 r p j Br p 2r z Br 32Tr2y pr p 2r 4 3r r dp Br

I _ ( i L?£ ) + 3 ... v iE) (_il1) _ i l ^ h i (2 3p B^p, 7h3Q 2 (2 3p A 32p,p 2r 3 Br p r Br 3 ; 120yRT^ Br dir* 2 4 y R T U 3r ‘ Br2

l f 2h3 rft2RT , 3 _ 1_ 3p, ' 3fl2 , ^ Bp, , 3ytfiRT,l ^ 1 Bp,-,r 3y 16772h 2 ' p r 4 p 2r d Br' 10RT^p r 8r 4iTh3 ^pr2’ Br'

m 2RT ,3 1. __ 3p, , 4. . _ Q2 , , Bp, 11,3 . 7ft2h 3 , Bp,,3 2 7T2 y prv p zr* 3r 3 4 tFI t p 3r 30 24yRT p r 3r /^

■ 1 f 2 h 3 ,ift2RT 3fl2pr _ 3ymRT . ifr2RTh _ llft2p r h 3 7Q2h 3p r -Tr2" 3y 16Tr2h zr dp 10RT “ 47rhJrp 24TT2y r dp " 120yRT 24 yRT _

J\TT 2 TT ^2 , 7

Substituting for V r , anc d~zz^ viscosity term we

obtain •

„73'2v£ + I - Z r + 3*v r x _ 1Ifl_#„2 __ 1 2 \ rift2 RT ,12 , _3___ 3£y Br2 r 3r iF Br2 y [2y * 167T2h 2 (pr° p'r" 3r

1 32p 2 /3p,2 , 3 Bp, , 3ft2 ,n3p , 32p x 3ymRT ,2tF y- d aV*' + TT3--3- fc:) + ^2— rr + T ^ m (2v- + r-r- ) - -J^T-T ” (-p"r' 3rz r^p 3r p zr 4 Br' 1 0 R T v 3r Br^^ 47rh3 vp F

h - T - I s - K - + ^ - ( ^ ) 2 + K - t , 1 2 3 . 3 p +

P^r 3r p zr 3r2 r p ^ B r ' . p 2r 2 3rK 32*rr2y pr17 p 2 3r

2 /3p,2 1 32p , 3 Bp, /z2 i , Q2 /03p , 32p N ,zTrTzrri-Kb) - -7 —t + z^r=r o£) (ct - 1 ) - -5775™ (2yS + r r f ) (T 7"r p 3 3r p zr J 3r^ p^ r4 Br7 'h* ; 4y R T v 9r v12h

1 4 0

zl +" zl) + I R ! h i (oi£ + rilE) + £lh .2 ( 2^E + ri!B) + I { l - (z2 - h 2)3h 2 ; 48yRT Br rJ P r) 12 yRTU 3r bF2 r^2y^ }

'rih2RT / 3 1 Bp. , 3,Q2 , Bp. 3ymRT , 1 1 Bp. -i16ir'zh z p r 4 p2rlcT Br 10RT^p r 3r 4irh7~ p r 2 p 2r Br

ART , 3 1 9pN ,z2 __ t N 'ft2' , 9px fzM , z 3 , z2 ,32rFy'(‘"prir " p ^ F Br* " * 4y ^ T (p r 3r) (l 2 h r 3h 2 *

7ft2h 2 , _3p^ , ft2hz , J p \ 1 1 rl ,„2 ^ 2 \'/A2RT48yRT(p r 3r 12yRT p Br* * r 2" * 2 y (z " * (167rzh 2r 3p

on2„„ _ 3yART \ m 2RT ,z2 , N Q2p r fz k , z 3 , z2x ,pr 47rhdrp 32Tr2y r dp^hr 4y R T (12h2* 3h 2.

7fi2h 2pr p F r h z . l,ih2RT 3prft2 3yftRT . tfi2RT/ D i. T5m ' 10,,T3rn J ‘ T /~\T3m “ A d —~ / _ 148yRT T 12yRT J ‘ y v16TT z r 3h zp ' 10RT rrh2r p / 16Trzr 3pyhz

+ 2 z +

4 y RT hT h _

integrating the above equation over the film thickn ess 2h between

limits of z = h and z = -h giving a final equation

, [~ 2 h 3 rrti2RT .12 , 3 Bp 1 32p ^ 2 ,8p.2Viscose term = y -■ =— — zttt-(— 5 * + ~~2— «r r~ “ — 2—3- + “ 3— *-(v )|_ 3y 16ir h" p r & p zr 4 Br p 2r 3 Br^ r 3p- Br

3 Bp. 3ft2 /?8p . 8 2p . _ 3ymRT .2 1 Bp _ 1 32pp 2r^ Br 10RT Br r 3r 4Trh3 p r 3 p 2r 2 Br p 2r Br2*

2 /Bp\ 2 , 1 Bpvi m 2RT ,12 , _3___ Bp , __2___ ,Bp. 2 _ 1 ____ /82p.r p 3 Br p zr z Br 327r2y p r s -r p zr 4 Br **" r zp 3 Br p zr 3 3rz

•3 ; Bp. , 4h. _ Ilft2h 3 / nBp , „8 2p. ■ 7h3ft2 ,03p A 3 2 p. A 1p zr'r Br* ( 3 * 120yRT Br Br2** 2TyRf (23r r 3lF* r

f.2h3 rm 2RT , 3 _ 2. __ .Bp. , 3ft_2 . Bp. , 3ym R T ,l*• 3y IGtt2!!2* p r k p 2r 3 Br lOl T p Br 4Trh° p r 2

7ft2h 3 , _9p. i _ 1 / 2h3 ,it \2RT , 3ft2pr _ 3ymRT . in2RTh24yRT ^ r 3r F " 1 3y 167r2h 2r 3p 10RT 4iTh3rp 24TTzy r 3p

H ^ 2p th 3 7ft2h 3p r -. 2 h .ifo2RT 3prft2 _ 3yART . _ m 2RT120yfcr 24yRT y 16TT2r dh 2p 10RT 4TTh3rp 8irzr 3pyh

• 2prft2hl 3yRT J

These equations have been used to calculate the rat io viscous

term/compressibil i ty term for Tests 13, 14, 19 and 20 (se e

Appendix 5).

C O M P U T E R P R O G R A M <£ P R IN T O U T OF T M P U 5 T V A L U E S E T C .

1 4 2

F L O W C H A R T N° 1 A A P P E N D IX 2

143

F L O W C M A R T M ° 1 &.

1

14 4

/ / J O B 1 1 S 1 3 K L E M Z . F . / T H R U S T B E A M I N G I N N E R *

* J O B 1 9 7 0

/ / O P T I O N L I N K

/ / E X E C F O R T R A N

0 0 0 1 N J B R = 0

0 0 0 2 1 R E A D ! 1 , 5 0 ) P P , H , 3 , S P E E , A L P H 4 , T E S T

0 0 0 3 5 0 F Q R M A T [ F 7 . 3 , F 7 . 6 , F 8 . 7 , F 5 . 1 , F 6 . 4 , F 4 . 1 )

0 0 0 4 W R I T E ( 3 y 3 0 0 )

0 0 0 5 3 0 0 F O R M A T { * 0 ' 6 X , * P * , 8 X , * H * , 1 I X , * Q 1 , 6 X , * S P E E » , 3 X ,

* A L P H A * j 3 X » 1 T E S T 1 )

0 0 0 6 W R I T E ! 3 , 4 0 0 ) P P , H , 9 , S P E E , A L P H A , T E S T

0 0 0 7 4 0 0 F O R M A T { ' ' 3 X , F 8 . 1 , 2 K , = 8 . 6 , 2 X , F 9 . 7 , 2 X , F 5 . 1 , 2 X ,

F 6 . 4 , 2 X , F 5 . 2 )

0 0 0 8 R 1 = 0 . 0 1

0 0 0 9 R 2 = 0 . 0 9 5

0 0 1 0 R 3 = 0 . 0 4 5

0 0 1 1 R D 1 = R 1 / R 2

0 0 1 2 R D 3 = R 3 / R 2

0 0 1 3 P I = 3 . 1 4 1 5 9

0 0 1 4 V I S = 1 . 8 / 1 0 0 0 0 0 . 0

0 0 1 5 D E M = 1 . 2 4

0 0 1 6 D R 1 = ( R 3 - R 1 ) / 1 0 . 0

0 0 1 7 R = R 1

0 0 1 8 WR 1 TF: { 3 , 1 0 )

0 0 1 9 1 0 F O R M A T ! 1 0 ' 3 X , ' R » , 8 X , • R / H * , 8 X , • I P K 1 , 8 X , 1 I P D * 8 X ,

' I P R K * , 6 X , * I P R O 1 )

0 0 2 . 0 F i = l . Q / ( { A L P H A * R D 1 ) * # 2 )

0 0 2 1 F 2 = ( 1 . 0 / ( A L P H A * * 2 ) ) - 1 . 0

0 0 2 2 F 3 = ( R D 1 * R D 1 ) - 1 . D

0 0 2 3 DM = A L 3 G ( R 0 3 ) * ( { A L P H A « * 3 ) - 1 . 0 )

0 0 2 4 B 4 = DM + A L O ' G ( R D 1 )

0 0 2 5 F D l = - 3 . 0 * V I S * Q / ( 4 . 0 » P I «■ ( ( A L P H A * H ) * * 3 ) )

0 0 2 6 F D 2 = 3 . 0 * D E N * R 2 & R 2 * S ? E E * S P E E * ( 1 . 0 - ( R D 1 & R D 1 ) ) / 2 0 . 0

0 0 2 7 P P D = ( 1 . 0 - ( F D 2 / I F D 1 * B 4 ) ) > * F D 1 * B 4

0 0 2 8 C O 1 = 2 7 . 0 * D E N # Q * 3 / ( 5 5 O . O * P I # P I * H * H * P P * R 2 » R 2 )

0 0 2 9 C 0 2 = 3 . 9 * D E N * ( S P E E * * 2 ) « R 2 * R 2 / ( 2 0 . 0 * P P )

0 0 3 0 C D 2 = 3 . 0 * D E N * { S P E E * * 2 ) * R 2 * R 2 / { 2 0 . 0 * P P D )

0 0 3 1 C 1 = P P * ( 1 . 0 + C 0 1 * ( F 1 - F 2 / ! R Q 3 « R D 3 ) - 1 . 0 ) - C 0 2 * F 3 ) / B 4

0 0 3 2 C 2 = C 1 * ( 4 L P H A * * 3 )

1 4 5

0 0 3 3 D 1 = P P * { 1 . 0 + C 0 1 * F 1 - C 0 2 * R : ) 1 * R D 1 ) - C 1 * A L O G ( R 1 )

0 0 3 4 D 2 = P P * ( C 0 1 - C 0 2 ) - C 2 * A L 0 G ( R 2 )

0 0 3 5 2 D R Z = R / R 2

0 0 3 6 B 1 = A L 0 G ( R Z ) + D M

0 0 3 7 Q 2 = D M <-( ( R Z * R Z ) - ( R D 1 * R D 1 ) )

0 0 3 f t B 3 = ( ( 1 . 0 - ( R D 1 * R D 1 ) ) * A L O G ( R Z ) ) - { ( 1 . 0 ^ { R Z * R Z ) )

* A L 0 G ( R D 1 ) )

0 0 3 9 D K = P I -«• { H * * 3 ) / ( V I S * Q )

0 0 4 0 P R = - C 0 1 / ( ( R Z * A L P H A ) * * 2 ) + ( C Q 2 * R Z * R Z ) + ( C 1 »

( A L O G ( R ) ) / P P ) + ( 0 1 / P P )

0 0 4 1 P R I D = ( B 1 + C D 2 * ( B 2 + B 3 ) ) / B 4

0 0 4 2 DC = P I * H * H * H * P P / ( \ / I S * Q )

0 0 4 3 R F = D E N * Q / { P I * V I S * H * A L P H A )

0 0 4 4 C P K = P R * P P

0 0 4 5 C P D = P R I D * P P D

0 0 4 6 D P K = C P K * D K

0 0 4 7 D P D = C P D * D K

C I P K = S T A T I C P R E S S U R E S E E E Q U A T I O N ( 3 0 )

C I P D = “ " S T A T I C P R E S S U R E , R A D I A L I N E R T I A T E R M

N E G L E C T E D

C I P R D = I P D I N D I M E N S I O N L E S S F O R M

C ' I P R K = I P K I N D I M E N S I O N L E S S F O R M

C R F = D F N * Q / ( P I * V I S * H * A L P H A )

C Q = C H E C K O N V O L U M E F L O W R A T E B A S E D O N Q

= Q K

C P P D = T H E Q R E T I C A L P R E S S J R E P A T R A D I U S = 1 C M I F

R A D I A L I N E R T I A T E R M

C C l S ' D l _= C O N S T A N T S D F I N T E G R A T I O N

( S E E E Q U A T I O N 3 0 )

0 0 4 8 H R = R / H . . . . . . .

0 0 4 9 W R I T E ( 3 , 1 3 ) R , H R , C P K , C P D , D P K , D P D _

0 0 5 0 1 3 F O R M A T ( 1 * I X , F 5 . 3 , 4 X , F 7 . 3 , 4 X , F 7 . 1 , 4 X , F 7 . 1 i

F 6 . 3 , 4 X f F 6 . 3 )

0 0 5 1 I F ( R - R 3 ) 2.1 , 2 2 , 2 2

0 0 5 2 2 1 R = R + D R 1

0 0 5 3 I F ( R - R 3 ) 2 0 , 2 2 , 2 2

0 0 5 4 2 2 W R I T E ( 3 , 3 0 )

0 0 5 5 3 0 F O R M A T ( * 0 « 6 X , ' C l * , 1 9 X , ? D l * , 1 9 X , * Q • , 1 8 X , ’ P P D *

, I 8 X , 1 R E ’ )

0 0 5 6 Q:< = - ( C l * 4 . 0 * P I * ( H * A L P H A ) t t * 3 ) / ( 3 . 0 * V I S )

0 0 5 7 W R I T F ( 3 , 1 1 ) C 1 , D l , Q K , P P D , R E

0 0 5 8 11 FORMA T ( 1 1 I X , E 1 6 . 8 , 4 X , E 16. 8 , 4X , E 1 6 . 8 , 4 X , E 1 6 . 8 ,

4 X , E 1 6 . 8 )

0 0 5 9 I F ( N J 3 R - 3 6 ) 1 5 0 , 1 0 0 , 1 0 0

0 0 6 0 1 5 0 N U B R = N U B R + 1

0 0 6 1 I F ( NUB R- 3 6 ) 1 , 1 0 0 , 1 0 00 0 6 2 1 0 0 C O N T I N U E

0 0 6 3 E N D

1 4 6

/ / J G B 1 1 S 1 3 K L E M Z . F . / T H R U S T B E A R I N G C U T E R *

* J C B 1 1 4 5

/ / C P T I C N L I N K

/ / E X E C F C R T R A N

C C 0 1 N U B R = 0

C 0 0 2 1 R E A D ( 1 , l l ) P P f H , Q , S P E E , A L P H A , P B , P C , P C . P E » P F , P G T P H

0 0 0 3 1 1 F C R M A T ( F 7 . 0 , F 7 . 6 , F 8 . 7 , F 5 . 1 , F 6 . 4 , 7 F 5 . 2 )

C C 0 4 R E A D ( 1 , 1 3 ) P J , P K , T E S T

0 0 0 5 1 3 • F O R M A T ( 2 F 5 . 2 , F 4 . 1 )

C O 0 6 h R I T E ( 3 » 3 0 0 )

0 0 0 7 3 0 0 F O R M A T ( 1 0 * 6 X , ' P * , 9 X , ' H « , 7 X , * Q * , 7 X , • S P E E * , 3 X ,

’ A L P H A * , 5 X , ' P B * , 4 X ,

/ * P C * , 6 X , ’ P D » , 5 X , * P E * , 5 X , * P F * T 5 X , ’ P G • , 5 X , » P H * >

0 0 0 8 W R I T E ( 3 , 2 C 0 ) P P , H , Q , S P E E , A L P H A , P B , P C , P D , P E , P F , P G , P H

0 0 0 9 2 0 0 FORMA T ( * 1 I X f F 8 . 1 , 2 X , F 8 . 6 , 2 X , F 9 . 7 , 2 X , F 5 . 1 , 2 X , F 6 . 4 ,

7 ( 2 X » F 5 . 2 ) )

0 0 1 0 ' W R I T E ( 3 » 4 0 0 )

0 0 1 1 4 OC F O R M A T ( * C * 4 X , * P J * t 5 X , * P K * , 4 X , » T E S T * )

0 0 1 2 W R I T G ( 3 , 2 1 0 ) P J , P K , T E S T

0 0 1 3 2 1 0 F O R M A T ( / 1 H , 2 ( 2 X , F 5 . 2 ) , 2 X , F 4 . 1 )

0 0 1 4 R 1 = 0 . 0 1

0 0 1 5 R 2 = 0 . 0 9 5

CO 1 6 R 3 = 0 . 0 4 5

0 0 1 7 R B = 0 . 0 0 9 5

0 0 1 8 R C = 0 . C 1 9

0 0 1 9 R D = 0 . 0 2 8 5

0 0 2 0 R W = 0 . 0 3 8 0

0 0 2 1 R F = 0 . 0 4 7 5

0 0 2 2 R G = 0 . 0 5 7

C 0 2 3 R h = 0 . 0 6 6 5

C 0 2 4 R J = 0 . 0 7 6

0 0 2 5 R K = 0 . 0 8 5 5

0 0 2 6 B = C . C C 9 5

0 0 2 7 R D 1 = R 1 / R 2

0 0 2 8 R D 3 = R 3 / R 2

0 0 2 9 P I = 3 . 1 4 1 5 9

0 0 3 0 V I S = 1 . 8 / 1 C C C C 0 . 0

C 0 3 1 L5EN = 1 . 2 4

0 0 3 2 x D R 2 = ( R 2 - R 3 ) / 1 0 o 0

0 0 3 3 R = R 3

0 0 3 4 W R I T E ( 3 » 1 4 )

0 0 3 5 1 4 F O R M A T ( * 0 * 3 X f * R * , 8 X , 1 R . / H * , 8 X , 1 O P K * , 8 X » * CI P C ' 8 X ,

' 0 P R K * , 6 X , * C P R D * )

0 0 3 6 D C = P I * H * H * H * F P / ( V I S * Q )

0 0 3 7 , R E = D E N * Q / ( P I * V I S * H )

0 0 3 8 F 1 = 1 . Q / { ( A L P H A * R D 1 ) * * 2 )

0 0 3 9 F 2 = ( 1 . 0 / ( A L P H A * * 2 ) ) - 1 . 0

0 0 4 0 F 3 = ( R D 1 * R C 1 ) — 1 . 0

0 0 4 1 OM = A L O G ( R D 3 ) * ( ( A L P H A * * 3 ) - 1 . 0 )

0 0 4 2 B 4 = 0 M + A L C G ( R D 1 )

0 0 4 3 F D 1 = - 3 . 0 * V I S * G / ( 4 . 0 * P I * ( ( A L P H A * H ) * * 3 ) )

0 0 4 4 F 0 2 = 3 . 0 « D E N * K 2 * R 2 * S P E E * S P E E * ( 1 . C ~ ( R D 1 * R D 1 ) ) / 2 C . 0

0 0 4 5 P P C = ( 1 . 0 - ( F D 2 / ( F C 1 * B 4 > ) ) * F D 1 * B 4

0 0 4 6 C 0 1 = 2 7 . 0 * D E N # Q * Q / ( 5 6 0 . 0 * P I * P I P * * R 2 * R 2 )

0 0 4 7 C C 2 = 3 * 0 * D F N*- ( S P E E * * 2 ) * R 2 * R2 / ( 2 0 . C * P P )C 0 4 8 C D 2 = 3 . C * C E . \ * ( S P E E * * - 2. ) * R 2 * R 2 / ( 2 0 . C * P P C )

! 4 7

0 0 4 9 C 1 = P P * ( 1 . 0 + C 0 1 * ! F 1 - F 2 / ( R D 3 * R D 3 ) - 1 . 0 ) ~ C C 2 * F 3 ) / B 4

0 0 5 0 C 2 = C 1 * ! A L P H A * * 3 )

0 0 5 1 . D 1 = P P * ( 1 . 0 + C 0 1 * F l - C 0 2 * R T n * R D l ) - C 1 * A L C G { R 1 )

0 0 5 2 D I = C l / 2 . 0

0 0 5 3 D 2 = P P * ( C 0 I - C G 2 ) - C 2 * A L 0 G ( R 2 )

0 0 5 4 G 1 = 2 7 . 0 * C * C * D E N / ( 5 6 0 . 0 * ( ( P I * H ) * * 2 ) )

0 0 5 5 G 2 = ( 3 . 0 * S P E E * * 2 ) / 8 0 • 0

C 0 5 6 2 4 R Z = R / R 2

0 0 5 7 B 1 = A L 0 G ( R Z ) + D M

0 0 5 8 B 2 = D H * ( { R Z * R Z ) - { R D 1 * R D 1 ) )

0 0 5 9 B 3 = ( ( 1 . 0 - ! R D 1 * R D 1 ) ) * A L 0 G ( R Z ) ) - ( ( 1 . 0 - ( R Z * R Z ) ) * A L 0 G ( R D 1 ) ) '

0 0 6 0 B 6 = ! A L P H A * * 3 ) * ( 1 . Q - ! R D 1 * R D 1 ) ) * A L C G ( R Z )

C 0 6 1 8 7 = ! { ! A L P H A * * 3 ) - 1 . C ) * A L 0 G ! R D 2 ) ) + A L C G ! R D l )

0 0 6 2 P S = - ( C C 1 / ! R Z * R Z ) ) + ( C 0 2 * R Z * R Z ) + ( C 2 * ( A L C G ( R ) ) / P P ) + ( D 2 / P P )

0 0 6 3 P S I D = ! ! A L P H A * * 3 ) * A L G G ( R Z ) / B 4 ) + ( C D 2 / B 4 ) * ( B 6 - ( < 1 . 0 - ( R Z * R Z )

) * B 7 ) )

0 0 6 4 : T T H = P I * R 1 * R 1 * P P + 2 . 0 * P I * ( { - G 1 / ( A L P H A * * 2 ) ) * A L G G ! R 3 / R 1 ) + G 2 *

{ R 3 * * 4 - r i * * 4 ) + c 1 * ( ( R 3 * R 3 / 4 . 0 ) * { 2 . 0 * A L C G ( R 3 ) - 1 . 0 ) - ( R 1 * R 1 /

4 . 0 ) * ( 2 • 0 * AL C G ( R 1) - 1 . 0 ) ) + D I * ( R 3 * R 3 - R 1 * R 1 ) - G 1 * A L C G ( R 2 / R 3 )+ G 2 * ( R 2 * * 4 - R 3 * * 4 ) + C 2 * ( ( R . 2 * R 2 / 4 . 0 ) * ( 2 . 0 * A L 0 G ( R 2 ) - 1 . 0 ) -

( R 3 * R 3 / 4 . 0 ) * { 2 . C * A L Q G ( R 3 ) - 1 . 0 ) J + D 2 / 2 . 0 * ( R 2 * R 2 - R 3 * R 3 ) )

0 0 6 5 0 P K = P S * P P

0 0 6 6 C PC = P S I D * P PD

0 0 6 7 ' C K = P l « ( H * * 3 ) / ( V I S * Q )

0 0 6 8 D P K = G F K * D K

C 0 6 9 D P D = 0 P D * D K

C 0 7 0 T H E = ( ( 2 4 9 . 1 * B / 3 • C ) * ( 2 • .0 * ( P C * R C + P E * R W + P G * R G + P J * R J ) + 4 . 0 *

/ ( P B * R B + P D * R D + P F * R F + P h : * R H + P K * R K ) ) ) * 2 . C * P I

C P D T = P E R C E N T D I F F I N T H R U S T B A S E D QN T H E T H E O R E T I C A L T H R U S T

C R E = D F N * G / ( P I * V I S * H * A L P H A )

C T T F = T H E 0 R E T I C A L T H R U S T ( T H R U S T )

C T H E = E X P E R I M E N T A L T H R U S T ( T H R U S T X )

C C 2 & 02 = C O N S T A N T S O F I N T E R G R A T I C N ( S E E E Q U A T I O N 3 1 )

0 0 7 1 P D T = ( T T H - T H E ) * 1 0 0 . 0 / T T H

0 0 7 2 H R = R / H

0 0 7 3 W R I T E ( 3 , 1 5 ) R , H R f C P K , C P C , D P K , D P D

C C P K = S T A T I C P R E S S U R E S E E E Q U A T I O N ( 3 1 )

C C P C = S T A T I C P R E S S U R E , R A D I A L I N E R T I A T E R M N E G L E C T E D

C O P R K = 0 P K I N D I M E N S I O N L E S S F O R M

C O P R D = O P D I N D I M E N S I C N L E S S F O R M

0 0 7 4 1 5 F O R M A T ( 1 ' 1 X , F 5 . 3 , 4 X , F 7 . 3 , 4 X , F 7 . 1 , 4 X , F 7 . 1 , 4 X , F 6 . 3 , 4 X f F 6 . 3 )

0 0 7 5 I F ( R - R 2 ) 2 3 , 2 5 , 2 5

0 0 7 6 2 3 R = R + D R 2

0 0 7 7 I F ( R - R 2 ) 2 4 , 2 5 , 2 5

0 0 7 8 2 5 C O N T I N U E

0 0 7 9 L R I T E ( 3 , 3 0 )

0 0 8 0 3 0 F O R M A T ( ! C * 8 X , ’ C 2 1 , 1 5 X , 1 D 2 * , 1 4 X , » R E 1 , 1 3 X , ’ T H R U S T * , 9 X , *

T H R U S T X * , 9 X » 1 P C T * )

0 0 8 1 - W R I T E ! 3 , 1 2 ) C 2 , D 2 , R E , T T H , T H E , P D T

0 0 8 2 1 2 F O R M A T ! 1 ' 1 X , 6 E 1 6 . 8 )

0 0 8 3 I F ( N U B R - 3 6 ) 1 5 0 , 1 C C , I C O

0 0 8 4 1 5 0 N U 6 R = N U B R + 1

0 0 8 5 I F ( N U i 3 R — 3 6 ) 1 , 1 0 0 , 1 0 0 ......................... .

C 0 8 6 1 0 0 C O N T I N U E

C C 8 7 E N G .

1 4 8

p H Q S P E E A L P H A T E S T

2 6 7 5 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 3 5 6 0 0 * 0 1 . 0 0 0 0 1 . 0 0

R R / H I P K I P D ' I P R K I P R D

0 * 0 1 0 1 0 0 . 0 0 0 2 6 7 5 . 0 3 4 4 4 . 0 1 . 3 1 1 1 . 6 8 8

0 . 0 1 3 1 3 5 . 0 0 0 2 5 6 3 . 7 2 9 8 4 . 9 1 . 2 5 7 1 . 4 6 3

0 . 0 1 7 1 7 0 . 0 0 0 2 3 6 7 . 6 2 6 3 2 . 3 1 . 1 6 1 1 . 2 9 0

0 . 0 2 0 2 0 5 . 0 0 0 2 1 6 5 . 0 2 3 4 5 . 9 1 . 0 6 1 1 . 1 5 0

0 . 0 2 4 2 4 0 . 0 0 0 1 9 7 4 . 0 2 1 0 4 c 7 0 . 9 6 8 1 . 0 3 2

0 . 0 2 7 2 7 5 . 0 0 0 1 7 9 8 . 1 1 8 9 6 . 5 0 . 8 8 2 0 . 9 3 0

0 . 0 3 1 3 1 0 . 0 0 0 1 6 3 6 . 9 1 7 1 3 . 2 0 . 8 0 3 0 . 8 4 0

0 . 0 3 4 3 4 5 . 0 0 0 1 4 8 9 . 1 1 5 4 9 . 6 0 . 7 3 0 0 . 7 6 0

0 * 0 3 8 3 8 0 . 0 0 0 1 3 5 3 . 1 1 4 0 1 . 7 0 . 6 6 3 0 . 6 8 7

0 . 0 4 1 4 1 5 . 0 0 0 1 2 2 7 . 3 1 2 6 7 . 0 0 . 6 0 2 0 . 6 2 1

0 . 0 4 5 4 5 0 . 0 0 0 1 1 1 0 . 4 1 1 4 3 . 1 0 . 5 4 4 0 . 5 6 0

. C l D l Q K

- 0 • 1 5 2 5 4 3 7 5 E 0 4 - 0 . 3 5 8 2 1 8 7 0 E 0 4 0 . 3 5 4 9 8 5 0 1 E - 0 3

P P D RE

0 . 3 4 4 4 0 2 3 4 E 0 4 0 . 7 8 0 6 3 8 1 3 E 0 5

P H 0 S P E E A L P H A T E S T

3 6 0 0 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 5 8 3 0 0 . 0 1 . 0 0 0 0 2 . 0 0

R R / H I P K I P D I P R K I P R D

0 . 0 1 0 1 0 0 . 0 0 0 3 6 0 0 . 0 5 6 4 0 . 1 1 . 0 7 8 1 . 6 8 8

0 . 0 1 3 1 3 5 . 0 0 0 3 7 7 7 . 9 4 8 8 8 . 2 1 . 1 3 1 1 . 4 6 3

0 . 0 1 7 1 7 0 . 0 0 0 3 6 1 8 . 1 4 3 1 0 . 7 1 . 0 8 3 1 . 2 9 0

0 . 0 2 0 2 0 5 . 0 0 0 3 3 7 1 . 9 3 8 4 1 . 7 1 . 0 0 9 1 . 1 5 0

0 . 0 2 4 2 4 0 . 0 0 0 3 1 0 9 . 7 3 4 4 6 . 8 0 . 9 3 1 1 . 0 3 2

0 . 0 2 7 2 7 5 . 0 0 0 2 8 5 4 . 1 3 1 0 5 . 7 0 . 8 5 4 0 . 9 3 0

0 . 0 3 1 3 1 0 . 0 0 0 2 6 1 2 . 2 2 8 0 5 * 6 0 . 7 8 2 0 . 8 4 0

0 . 0 3 4 3 4 5 . 0 0 0 2 3 8 5 . 7 2 5 3 7 . 6 0 . 7 1 4 0 . 7 6 0

0 . 0 3 8 3 8 0 . 0 0 0 2 1 7 4 . 2 2 2 9 5 . 5 0 , 6 5 1 0 , 6 8 7

0 . 0 4 1 4 1 5 . 0 0 0 1 9 7 6 . 6 2 0 7 4 . 8 0 . 5 9 2 0 . 6 2 1

0 . 0 4 5 4 5 0 . 0 0 0 1 7 9 1 . 8 1 8 7 2 . 0 0 . 5 3 6 0 . 5 6 0

C l D l • Q K

- 0 . 2 5 0 3 4 8 9 3 E 0 4 - 0 . 5 8 7 0 0 8 9 8 E 0 4 0 . 5 8 2 5 8 7 6 7 E - 0 3

P P D

0 . 5 6 4 0 0 7 0 3 E 0 4

RE0 • 1 2 7 8 4050E 06

1 4 9

p H Q S P E E A L P H A P B P C

• 2 6 7 5 . 0 O . O O O i O O 0 . 0 0 0 3 5 6 0 0 . 0 1 . 0 0 0 0 9 . 0 0 8 . 1 0

P J P K T E S T P D P E ' P F P G P H

6 . 3 0 4 . 9 0 3 . 8 0 2 . 8 0 2 . 0 0

1 . 2 0 0 . 4 0 1 . 0

R R / H G P K O P D Q P R K O P R O

0 . 0 4 5 4 5 0 . 0 0 0 1 1 1 0 . 4 1 1 4 3 . 1 0 . 5 4 4 0 . 5 6 0

0 . 0 5 0 5 0 0 . 0 0 0 9 5 6 . 9 9 8 1 . 9 0 . 4 6 9 0 . 4 8 1

0 . 0 5 5 5 5 0 . 0 0 0 8 1 6 . 8 8 3 6 . 1 0 . 4 0 0 0 . 4 1 0

0 . 0 6 0 6 0 0 . 0 0 0 6 8 8 . 2 7 0 3 . 0 0 . 3 3 7 0 . 3 4 5

0 . 0 6 5 6 4 9 . 9 9 9 5 6 9 . 2 5 8 0 . 5 0 . 2 7 9 0 . 2 8 5

0 . 0 7 0 6 9 9 . 9 9 9 4 5 8 . 7 4 6 7 . 2 0 . 2 2 5 0 . 2 2 9

0 . 0 7 5 7 4 9 . 9 9 9 3 5 5 a 5 3 6 1 . 6 0 . 1 7 4 0 . 1 7 7

0 . 0 8 0 7 9 9 . 9 9 9 2 5 8 . 7 2 6 2 . 9 0 . 1 2 7 0 . 1 2 9

0 . 0 8 5 8 4 9 . 9 9 9 1 6 7 . 5 1 7 0 . 2 0 . 0 8 2 0 . 0 8 3

0 . 0 9 0 8 9 9 . 9 9 9 8 1 . 5 8 2 . 7 0 . 0 4 0 0 . 0 4 1

0 . 0 9 5 9 4 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

- 0 • 1 5 2 5 4 3 7 5 E 0 4 - 0 . 3 5 8 2 1 8 8 5 E 0 4 0 . 7 8 0 6 3 8 1 3 E 0 5

T H R U S T T H R U S T X P O T

0 . 2 0 2 9 9 6 5 2 E 0 2 0 . 1 8 0 0 5 1 2 7 E 0 2 0 . 1 1 3 0 3 2 7 3 E 0 2

P H Q S P E E A L P H A P B P C

3 6 0 0 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 5 8 3 0 o « o f—• c 0 0 0 0 1 2 . 0 0 « ro o

P J P K T E S T P D PE P F P G P H

1 0 . 0 0 8 . 0 0 6 . 3 0 4 . 7 0 3 . 4 0

2 . 2 0 1 . 1 0 2 . 0

R R / H Q P K O P D O P R K O P R D

0 . 0 4 5 4 5 0 . 0 0 0 1 7 9 1 . 8 1 . 8 7 2 . 0 0 . 5 3 6 0 . 5 6 0

0 . 0 5 0 5 0 0 . 0 0 0 1 5 4 7 . 3 1 6 0 8 . 0 0 . 4 6 3 0 . 4 8 1

0 . 0 5 5 5 5 0 . 0 0 0 1 3 2 3 . 0 1 3 6 9 . 2 0 . 3 9 6 0 . 4 1 0

0 . 0 6 0 6 0 0 . 0 0 0 1 1 1 6 . 1 1 1 5 1 . 2 0 . 3 3 4 0 . 3 4 5

0 . 0 6 5 6 4 9 . 9 9 9 9 2 4 . 1 9 5 0 . 7 0 . 2 7 7 0 . 2 8 5

0 . 0 7 0 6 9 9 . 9 9 9 7 4 5 . 3 7 6 5 . 1 0 . 2 2 3 0 . 2 2 9

0 . 0 7 5 7 4 9 . 9 9 9 5 7 8 . 0 5 9 2 . 2 0 . 1 7 3 0 . 1 7 7

0 . 0 8 0 7 9 9 . 9 9 9 4 2 0 . 9 4 3 0 . 5 0 . 1 2 6 0 . 1 2 9

0 . 0 8 5 8 4 9 . 9 9 9 2 7 2 . 8 2 7 8 . 7 0 . 0 8 2 0 . 0 8 3

0 . 0 9 0 8 9 9 . 9 9 9 1 3 2 . 8 1 3 5 . 5 0 . 0 4 0 0 . 0 4 1

0 . 0 9 5 9 4 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 0 0 . 0 0 0

C 2 0 2 R E

- 0 . 2 5 0 3 4 8 9 3 E 0 4 - 0 . 5 8 7 0 0 9 3 8 E 0 4 0 . 1 2 7 8 4 0 5 0 E 0 6

THRUST THRUST X POT0 « 3218 4 8 3 0 E 02 0 . 2981 3934 E 02 0 . 7 3 6 6 4989E 01

I 5 0


3 8 6 0 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 7 3 7 0 0 . 0 1 . 0 0 0 0 3 . 0 0

R R / H I P K I P D • I P R K I P R D

0 . 0 1 0 1 0 0 . 0 0 0 3 8 6 0 . 0 7 1 2 9 . 9 0 . 9 1 4 1 . 6 8 8

0 . 0 1 3 1 3 5 . 0 0 0 4 3 9 6 . 6 6 1 7 9 . 5 1 . 0 4 1 1 . 4 6 3

0 . 0 1 7 1 7 0 . 0 0 0 4 3 3 5 . 1 5 4 4 9 . 4 1 . 0 2 7 1 . 2 9 0

0 . 0 2 0 2 0 5 . 0 0 0 4 0 9 9 . 1 4 8 5 6 . 5 0 . 9 7 1 1 . 1 5 0

0 . 0 2 4 2 4 0 . 0 0 0 3 8 1 2 . 7 4 3 5 7 . 3 0 . 9 0 3 1 . 0 3 2

0 . 0 2 7 2 7 5 . 0 0 0 3 5 1 8 . 7 3 9 2 6 . 1 0 . 8 3 3 0 . 9 3 0

0 . 0 3 1 3 1 0 . 0 0 0 3 2 3 2 . 8 3 5 4 6 . 7 0 . 7 6 6 0 . 8 4 0

0 . 0 3 4 3 4 5 . 0 0 0 2 9 6 0 . 7 3 2 0 7 . 9 0 . 7 0 1 0 . 7 6 0

0 . 0 3 8 3 8 0 . 0 0 0 2 7 0 4 . 0 2 9 0 1 . 9 0 . 6 4 0 0 . 6 8 7

0 . 0 4 1 4 1 5 . 0 0 0 2 . 4 6 2 . 4 2 6 2 2 . 9 0 . 5 8 3 0 . 6 2 1

0 . 0 4 5 4 5 0 . 0 0 0 2 2 3 5 . 1 2 3 6 6 . 4 0 . 5 2 9 0 * 5 6 0

. C l D l Q K

- 0 . 3 1 5 9 8 8 4 8 E 0 4 - 0 . 7 4 0 1 5 1 9 5 E 0 4 0 . 7 3 5 3 3 7 6 1 E - 0 3

P P D

0 . 7 1 2 9 9 0 2 3 E 0 4

R E

0 . 1 6 1 6 0 9 6 9 E 0 6

P H Q S P E E A L P H A T E S T

3 1 7 5 . 0 0 . 0 0 0 1 0 0 0 . 0 0 1 1 4 5 0 0 . 0 1 . 0 0 0 0 4 . 0 0


0 . 0 1 0 1 0 0 . 0 0 0 3 1 7 5 . 0 1 1 0 7 7 . 0 0 . 4 8 4 1 . 6 8 8

0 . 0 1 3 1 3 5 . 0 0 0 5 2 8 8 . 9 9 6 0 0 . 4 0 . 8 0 6 1 . 4 6 3

0 . 0 1 7 1 7 0 . 0 0 0 5 7 6 9 . 2 8 4 6 6 . 1 0 . 8 7 9 1 . 2 9 0

0 . 0 2 0 2 0 5 . 0 0 0 5 7 1 0 . 3 7 5 4 5 . 0 0 . 8 7 0 1 . 1 5 0

0 . 0 2 4 2 4 0 . 0 0 0 5 4 4 9 . 1 6 7 6 9 . 4 0 . 8 3 1 1 . 0 3 2

0 . 0 2 7 2 7 5 . 0 0 0 5 1 1 0 . 9 6 0 9 9 . 6 0 . 7 7 9 0 . 9 3 0

0 . 0 3 1 3 1 0 . 0 0 0 4 7 4 7 . 7 5 5 1 0 . 2 0 . 7 2 4 0 . 8 4 0

0 . 0 3 4 3 4 5 . 0 0 0 4 3 8 2 . 9 4 9 8 3 . 8 0 . 6 6 8 0 . 7 6 0

0 . 0 3 8 3 8 0 . 0 0 0 4 0 2 6 . 8 4 5 0 8 . 4 0 . 6 1 4 0 . 6 8 7

0 . 0 4 1 4 1 5 . 0 0 0 3 6 8 4 . 0 4 0 7 4 . 9 0 . 5 6 2 0 . 6 2 1

0 . 0 4 5 4 5 0 . 0 0 0 3 3 5 6 . 3 3 6 7 6 . 5 0 . 5 1 2 0 . 5 6 0

Cl- 0 . 4 8 9 8 8 0 4 7 E 0 4 -0

D l

1 1 4 4 3 1 8 8 E 0 5

Q K

0 . 1 1 4 0 0 0 1 5 E - 0 2

P P D

0 . 1 1 0 7 6 9 8 0 E 05R E

0 . 2 5 1 0 7 6 1 9 E 06


. 3 8 6 0 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 7 3 7 0 0 . 0 1 . 0 0 0 0 1 4 . 5 0 1 6 . 1 0

P J P K T E S T P D P E ' P F P G P H

1 3 . 2 0 1 0 . 5 0 8 . 1 0 6 . 1 0 4 . 3 0

2 . 7 0 1 . 3 0 3 . 0

R R / H O P K O P D O P R K OP- RD

0 . 0 4 5 4 5 0 . 0 0 0 2 2 3 5 . 1 2 3 6 6 . 4 0 . 5 2 9 0 . 5 6 0

0 . 0 5 0 5 0 0 . 0 0 0 1 9 3 3 . 0 2 0 3 2 . 8 0 . 4 5 8 0 . 4 8 1

0 . 0 5 5 5 5 0 . 0 0 0 1 6 5 4 . 7 . 1 7 3 0 . 9 0 . 3 9 2 0 . 4 1 0

0 . 0 6 0 6 0 0 . 0 0 0 1 3 9 7 . 1 1 4 5 5 . 4 0 . 3 3 1 0 . 3 4 5

0 . 0 6 5 6 4 9 . 9 9 9 1 1 5 7 . 7 1 2 0 1 . 9 0 . 2 7 4 0 . 2 8 5

0 . 0 7 0 6 9 9 . 9 9 9 9 3 4 . 3 9 6 7 . 2 0 . 2 2 1 0 . 2 2 9

0 . 0 7 5 7 4 9 . 9 9 9 7 2 4 . 9 7 4 8 . 7 0 . 1 7 2 0 . 1 7 7

0 . 0 8 0 7 9 9 . 9 9 9 5 2 8 . 1 5 4 4 . 3 0 . 1 2 5 0 . 1 2 9

0 . 0 8 5 8 4 9 . 9 9 9 3 4 2 . 4 3 5 2 . 3 0 . 0 8 1 0 . 0 8 3

0 . 0 9 0 8 9 9 . 9 9 9 1 6 6 . 7 1 7 1 . 2 0 . 0 3 9 0 . 0 4 1

0 . 0 9 5 9 4 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

- * 0 . 3 1 5 9 8 8 4 8 E 0 4 - 0 . 7 4 0 1 5 2 3 4 E 0 4 0 . 1 6 1 6 0 9 6 9 E 0 6

T H R U S T T H R U S T X P D T

0 . 3 9 6 4 5 4 3 2 E 0 2 0 . 3 8 1 5 7 3 0 3 E 0 2 0 . 3 7 5 3 5 9 3 4 E 0 1


3 1 7 5 . 0 0 . 0 0 0 1 0 0 0 . 0 0 1 1 4 5 0 0 . 0 1 . 0 0 0 0 1 6 . 8 0 1 9 . 2 0

P J P K T E S T P D P E P F PG P H

1 7 . 4 0 1 3 . 4 0 1 0 . 6 0 8 . 0 0 5 . 7 0

3 . 5 0 1 . 9 0 4 . 0

R R / H O P K O P D O P R K O P R D

0 . 0 4 5 4 5 0 . 0 0 0 3 3 5 6 . 3 3 6 7 6 . 5 0 . 5 1 2 0 . 5 6 0

0 . 0 5 0 5 0 0 . 0 0 0 2 9 1 4 . 6 3 1 5 8 . 1 0 . 4 4 4 0 . 4 8 1

0 . 0 5 5 5 5 0 . 0 0 0 2 5 0 2 . 9 2 6 8 9 . 1 0 . 3 8 2 0 . 4 1 0

0 . 0 6 0 6 0 0 . 0 0 0 2 1 1 8 . 6 2 2 6 1 . 0 0 . 3 2 3 0 . 3 4 5

0 . 0 6 5 6 4 9 . 9 9 9 1 7 5 9 . 1 1 8 6 7 . 2 0 . 2 6 8 0 . 2 8 5

0 . 0 7 0 6 9 9 . 9 9 9 1 4 2 1 . 9 1 5 0 2 . 6 0 . 2 1 7 0 . 2 2 9

0 . 0 7 5 7 4 9 . 9 9 9 . 1 1 0 4 . 8 1 1 6 3 . 1 0 . 1 6 8 0 . 1 7 7

0 . 0 8 0 7 9 9 . 9 9 9 8 0 5 . 8 8 4 5 . 6 0 . 1 2 3 0 . 1 2 9

0 . 0 8 5 8 4 9 . 9 9 9 5 2 3 . 0 5 4 7 . 3 0 . 0 8 0 0 . 0 8 3

0 . 0 9 0 8 9 9 . 9 9 9 2 5 4 . 8 2 6 6 . 0 0 . 0 3 9 0 . 0 4 1

0 . 0 9 5 9 4 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

- 0 . 4 8 9 0 8 0 4 7 E 0 4 - 0 . 1 1 4 4 3 1 9 5 E 0 5 0 . 2 5 1 0 7 6 1 9 E 0 6

THRUST THRUST X PDT0® 5 7 4 4 4 2 2 9 E 02 0 . 4 9 5 3 2 9 2 8 E 02 0 . 1 3 7 7 2 I 3 8 E 02

1 5 2


9 5 0 . 0 0 . 0 0 0 1 2 5 0 . 0 0 1 0 4 0 0 0 . 0 1 . 0 0 0 0 5 . 0 0


0 . 0 1 0 8 0 . 0 0 0 9 5 0 . 0 5 1 5 1 . 3 0 . 3 1 1 1 . 6 8 8

0 . 0 1 3 1 0 8 . 0 0 0 2 1 6 3 . 0 4 4 6 4 . 6 0 . 7 0 9 1 . 4 6 3

0 . 0 1 7 1 3 6 . 0 0 0 2 4 9 1 . 0 3 9 3 7 . 2 0 . 8 1 6 1 . 2 9 0

0 . 0 2 0 1 6 4 . 0 0 0 2 5 2 0 . 3 3 5 0 8 . 8 0 . 8 2 6 1 . 1 5 0

0 . 0 2 4 1 9 2 . 0 0 0 2 4 3 3 . 2 3 1 4 8 . 1 0 . 7 9 8 1 . 0 3 2

0 . 0 2 7 2 2 0 . 0 0 0 2 2 9 8 . 5 2 8 3 6 . 6 0 . 7 5 3 0 . 9 3 0

0 . 0 3 1 2 4 8 . 0 0 0 2 1 4 5 . 5 2 5 6 2 . 5 0 . 7 0 3 0 . 8 4 0

0 . 0 3 4 2 7 6 . 0 0 0 1 9 8 7 . 3 2 3 1 7 . 7 0 . 6 5 1 0 . 7 6 0

0 . 0 3 8 3 0 4 . 0 0 0 1 8 3 0 . 5 2 0 9 6 . 6 0 . 6 0 0 0 . 6 8 7

0 . 0 4 1 3 3 2 . 0 0 0 1 6 7 7 . 9 1 8 9 5 . 0 0 . 5 5 0 0 . 6 2 1

0 . 0 4 5 3 6 0 . 0 0 0 1 5 3 1 . 0 1 7 0 9 . 8 0 . 5 0 2 0 . 5 6 0

C l D l Q K

- 0 . 2 2 6 3 9 1 6 7 E 0 4 - 0 . 5 2 8 2 5 1 9 5 E 0 4 0 . 1 0 2 8 9 7 7 3 E - 0 2

P P D R E

0 . 5 1 5 1 3 3 2 0 E 0 4 0 . 1 8 2 4 4 1 3 8 E 0 6


- 2 7 5 0 . 0 0 . 0 0 0 1 2 5 0 . 0 0 1 7 1 0 0 0 . 0 1 . 0 0 0 0 6 . 0 0


0 . 0 1 0 8 0 . 0 0 0 • 2 7 5 0 . 0 8 4 7 0 . 0 - 0 . 5 4 8 1 . 6 8 8

0 . 0 1 3 1 0 8 . 0 0 0 1 2 3 8 . 3 7 3 4 0 . 9 0 . 2 4 7 1 . 4 6 3

0 . 0 1 7 1 3 6 . 0 0 0 2 6 6 9 . 5 6 4 7 3 . 6 0 . 5 3 2 1 . 2 9 0

0 . 0 2 0 1 6 4 . 0 0 0 3 1 9 1 . 0 5 7 6 9 . 3 0 . 6 3 6 1 . 1 5 0

0 . 0 2 4 1 9 2 . 0 0 0 3 3 2 8 . 1 5 1 7 6 . 2 0 . 6 6 3 1 . 0 3 2

0 . 0 2 7 2 2 0 . 0 0 0 3 2 8 5 . 5 4 6 6 4 , 1 0 . 6 5 5 0 . 9 3 0

0 . 0 3 1 2 4 8 . 0 0 0 3 1 5 4 . 7 4 2 1 3 . 3 0 . 6 2 9 0 . 8 4 0

0 . 0 3 4 2 7 6 . 0 0 0 2 9 7 9 . 9 3 8 1 0 . 9 0 . 5 9 4 0 . 7 6 0

0 . 0 3 8 3 0 4 . 0 0 0 2 7 8 4 . 1 3 4 4 7 . 3 0 . 5 5 5 0 . 6 8 7

0 . 0 ^ 1 3 3 2 . 0 0 0 2 5 7 9 . 8 3 1 1 5 . 9 0 . 5 1 4 0 . 6 2 1

0 . 0 4 5 3 6 0 . 0 0 0 2 3 7 3 . 9 2 8 1 1 . 2 0 . 4 7 3 0 . 5 6 0

C l D l Q K

- 0 • 3 7 5 8 1 4 8 7 E 0 4 - 0 . 8 7 2 0 6 0 9 4 E 0 4 0 . 1 7 0 8 1 2 3 4 E - 0 2

P P D

0 . 8 4 6 9 9 7 6 6 E 0 4

RE0 . 2 9 9 9 7 5 7 5 E 06

1 5 3


9 5 0 . 0 0 . 0 0 0 1 2 5 0 . 0 0 1 0 4 0 0 0 . 0 1 . 0 0 0 0 7 . 4 0 9 . 3 0

P J P K T E S T P D P E " P F P G P H

8 . 1 0 6 . 8 0 5 . 3 0 4 . 0 0 2 . 9 C

1 . 8 0 0 . 8 0 5 . 0


0 . 0 4 5 3 6 0 . 0 0 0 1 5 3 1 . 0 1 7 0 9 . 8 0 . 5 0 2 0 . 5 6 0

0 . 0 5 0 4 0 0 . 0 0 0 1 3 3 1 . 8 1 4 6 8 . 7 0 . 4 3 7 0 . 4 8 1

0 . 0 5 5 4 4 0 . 0 0 0 1 1 4 5 . 2 1 2 5 0 . 6 0 . 3 7 5 0 . 4 1 0

0 . 0 6 0 4 8 0 . 0 0 0 9 7 0 . 3 1 0 5 1 . 5 0 . 3 1 8 0 . 3 4 5

0 . 0 6 5 5 2 0 . 0 0 0 8 0 6 . 3 8 6 8 . 3 0 . 2 6 4 0 . 2 8 5

0 . 0 7 0 5 5 9 . 9 9 9 6 5 2 . 2 6 9 8 . 8 0 . 2 1 4 0 . 2 2 9

0 . 0 7 5 5 9 9 . 9 9 9 5 0 7 . 1 5 4 0 . 9 0 . 1 6 6 0 . 1 7 7

0 . 0 8 0 6 3 9 . 9 9 9 3 7 0 . 0 3 9 3 . 2 0 . 1 2 1 0 . 1 2 9

0 . 0 8 5 6 7 9 . 9 9 9 2 4 0 . 2 2 5 4 . 5 0 . 0 7 9 0 . 0 8 3

0 . 0 9 0 7 1 9 . 9 9 9 1 1 7 . 1 1 2 3 . 7 0 . 0 3 8 0 . 0 4 1

0 . 0 9 5 7 5 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 0 0 . 0 0 0

C 2 D 2

—0 . 2 2 6 3 9 1 6 7 E 0 4 - 0 . 5 2 8 2 5 1 9 5 E 0 4

R E

0 . 1 8 2 4 4 1 3 8 E 0 6

T H R U S T

2 5 8 0 7 2 6 6 E 0 2

T H R U S T X

0 . 2 4 0 6 9 6 1 1 E 0 2

P O T

0 c 6 7 3 3 2 0 2 9 E 0 1

P H Q S P E E A L P H A iPB P C

- 2 7 5 0 . 0 0 . 0 0 0 1 2 5 0 . 0 0 1 7 1 0 0 0 . 0 1 . 0 0 0 0 7 . 2 0 1 2 . 8 0

P J P K T E S T P D P E P F P G P H

1 0 . 4 0 9 . 6 0 7 . 8 0 6> . 0 0 4 . 4 0

2 . 8 0 1 . 3 0 6 . 0


0 . 0 4 5 3 6 0 . 0 0 0 2 3 7 3 . 9 2 8 1 1 . 2 0 . 4 7 3 0 . 5 6 0

0 . 0 5 0 4 0 0 . 0 0 0 2 0 8 4 . 3 2 4 1 4 . 8 0 . 4 1 6 0 , 4 8 1

0 . 0 5 5 4 4 0 . 0 0 0 1 8 0 4 . 8 2 0 5 6 . 2 0 . 3 6 0 0 . 4 1 0

0 . 0 6 0 4 8 0 . 0 0 0 1 5 3 7 . 7 1 7 2 8 . 9 0 . 3 0 7 0 . 3 4 5

0 . 0 6 5 5 2 0 . 0 0 0 1 2 8 3 . 5 1 4 2 7 . 7 0 . 2 5 6 0 . 2 8 5

0 . 0 7 0 5 5 9 . 9 9 9 1 0 4 1 . 9 1 1 4 8 . 9 0 . 2 0 8 0 . 2 2 9

0 . 0 7 5 5 9 9 . 9 9 9 8 1 2 . 5 8 8 9 . 4 0 . 1 6 2 0 . 1 7 7

0 . 0 8 0 6 3 9 . 9 9 9 5 9 4 . 3 6 4 6 . 5 0 . 1 1 8 0 . 1 2 9

0 . 0 8 5 6 7 9 . 9 9 9 3 8 6 . 7 4 1 8 . 5 0 . 0 7 7 0 . 0 8 3

0 . 0 9 0 7 1 9 . 9 9 9 1 8 8 . 8 2 0 3 . 4 0 . 0 3 8 0 . 0 4 1

0 . 0 9 5 7 5 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

- 0 . 3 7 5 8 1 4 8 7 E 0 4 - 0 . 8 7 2 0 6 1 3 3 E 0 4 0 . 2 9 9 9 7 5 7 5 E 0 6

THRUST THRUST X POT0 . 3 6 6 5 1 4 2 8E 02 0 . 3 4 1 0 8 0 1 7 E 02 0 . 6 9 3 9 4 5 9 8 E 01

1 5 4


.. - 6 8 0 0 . 0 0 . 0 0 0 1 2 5 0 . 0 0 2 1 3 0 0 0 . 0 1 . 0 0 0 0 7 . 0 0


0 , 0 1 0 8 0 . 0 0 0 - 6 8 0 0 . 0 1 0 5 5 0 . 3 - 1 . 0 8 8 1 . 6 8 8

0 * 0 1 3 1 0 8 . 0 0 0 - 2 7 4 . 3 9 1 4 3 . 9 - 0 . 0 4 4 1 . 4 6 3

0 . 0 1 7 1 3 6 . 0 0 0 2 2 0 5 . 8 8 0 6 3 . 6 0 . 3 5 3 1 . 2 9 0

0 . 0 2 0 . 1 6 4 . 0 0 0 3 2 2 5 . 6 7 1 8 6 . 3 0 . 5 1 6 1 . 1 5 0

0 . 0 2 4 1 9 2 . 0 0 0 3 6 1 5 . 5 6 4 4 7 . 6 0 . 5 7 9 1 . 0 3 2

0 . 0 2 7 2 2 0 . 0 0 0 3 7 0 2 . 8 5 8 0 9 . 6 0 . 5 9 3 - 0 . 9 3 0

0 . 0 3 1 2 4 8 . 0 0 0 3 6 3 4 . 5 5 2 4 8 . 2 0 . 5 8 2 0 . 8 4 0

0 . 0 3 4 2 7 6 . 0 0 0 3 4 8 3 . 7 4 7 4 6 , 9 0 . 5 5 8 0 . 7 6 0

0 . 0 3 8 3 0 4 . 0 0 0 3 2 8 8 . 7 4 2 9 4 . 0 0 . 5 2 6 0 . 6 8 7

0 . 0 4 1 3 3 2 . 0 0 0 3 0 7 0 . 8 3 8 8 1 . 1 0 . 4 9 1 0 . 6 2 1

0 . 0 4 5 3 6 0 . 0 0 0 2 8 4 2 . 5 3 5 0 1 . 7 0 . 4 5 5 0 « d 6 0

C l D l Q K

- 0 . 4 7 0 5 7 3 8 3 E 0 4 - 0 . 1 0 8 8 1 8 3 6 E 0 5 0 . 2 1 3 8 8 1 4 4 E - 0 2

P P D R E

0 . 1 0 5 5 0 3 2 0 E 0 5 0 . 3 7 3 6 5 4 0 6 E 0 6


- 1 3 1 5 0 . 0 0 . 0 0 0 1 2 5 0 . 0 0 2 6 1 0 0 0 . 0 1 . 0 0 0 0 8 . 0 0


0 . 0 1 0 8 0 . 0 0 0 -iM f « it K -K- <- 1 2 9 2 7 . 9 - 1 . 7 1 7 1 . 6 8 8

0 . 0 1 3 1 0 8 . 0 0 0 —2 9 5 9 . 8 1 1 2 0 4 . 5 - 0 . 3 8 7 1 . 4 6 3

0 . 0 1 7 1 3 6 . 0 0 0 1 0 6 5 . 0 9 8 8 0 . 8 0 . 1 3 9 1 . 2 9 0

0 . 0 2 0 1 6 4 . 0 0 0 2 8 4 0 . 7 8 8 0 5 . 7 0 . 3 7 1 I . 1 5 0

0 . 0 2 4 1 9 2 . 0 0 0 3 6 3 2 . 0 7 9 0 0 . 5 0 . 4 7 4 1 . 0 3 2

0 . 0 2 7 2 2 0 . 0 0 0 3 9 4 0 . 8 7 1 1 8 . 8 0 . 5 1 5 0 . 9 3 0

0 . 0 3 1 2 4 8 . 0 0 0 3 9 9 4 . 8 6 4 3 0 . 9 0 . 5 2 2 0 . 8 4 0

0 . 0 3 4 2 7 6 . 0 0 0 3 9 0 8 . 0 5 8 1 6 . 6 0 . 5 1 0 0 . 7 6 0

0 . 0 3 8 3 0 4 . 0 0 0 3 7 4 1 . 3 5 2 6 1 . 7 0 . 4 8 9 0 . 6 8 7

0 . 0 4 1 3 3 2 . 0 0 0 3 5 2 9 . 3 4 7 5 5 . 8 0 . 4 6 1 0 . 6 2 1

0 . 0 4 5 3 6 0 . 0 0 0 3 2 9 2 . 2 4 2 9 0 . 8 0 . 4 3 0 0 . 5 6 0

C l D l ' Q K

- 0 . 5 7 5 9 7 4 6 1 E 0 4 - 0 . 1 3 2 6 5 1 0 5 E 0 5 0 . 2 6 1 7 8 7 3 3 E - 0 2

P P D

0 . 1 2 9 2 7 8 5 9 E 0 5

RE0 . 4 5 7 8 5 7 7 5 E 06

1 5 5


- 6 8 0 0 . 0 0 . 0 0 0 1 2 5 0 . 0 0 2 1 3 0 0 0 . 0 1 . 0 0 0 0 4 . 6 0 1 5 . 2 0


1 3 . 5 0 1 1 . 4 0 9 . 2 0 7 . 2 0 4 . 2 0

3 . 3 0 1 . 5 0 7 . 0


0 . 0 4 5 3 6 0 . 0 0 0 2 8 4 2 . 5 3 5 0 1 . 7 0 . 4 5 5 0 . 5 6 0

0 . 0 5 0 4 0 0 . 0 0 0 2 5 1 1 . 7 3 0 0 7 . 9 0 . 4 0 2 0 . 4 8 1

0 . 0 5 5 4 4 0 . 0 0 0 2 1 8 5 . 3 2 5 6 1 . 3 0 . 3 5 0 0 . 4 1 0

0 . 0 6 0 4 8 0 . 0 0 0 1 8 6 8 . 7 2 1 5 3 . 5 0 . 2 9 9 0 . 3 4 5

0 . 0 6 5 5 2 0 . 0 0 0 1 5 6 4 . 4 1 7 7 8 . 4 0 . 2 5 0 0 . 2 8 5

0 . 0 7 0 ' 5 5 9 . 9 9 9 1 2 7 3 . 0 1 4 3 1 . 1 0 . 2 0 4 0 . 2 2 9

0 . 0 7 5 5 9 9 . 9 9 9 9 9 4 . 6 1 1 0 7 . 8 0 . 1 5 9 0 . 1 7 7

0 . 0 8 0 6 3 9 . 9 9 9 7 2 8 . 7 8 0 5 . 4 0 . 1 1 7 0 . 1 2 9

0 . 0 8 5 6 7 9 . 9 9 9 4 7 4 . 8 5 2 1 . 2 0 . 0 7 6 0 . 0 8 3

0 . 0 9 0 7 1 9 . 9 9 9 2 3 2 . 2 2 5 3 . 4 0 . 0 3 7 0 . 0 4 1

0 . 0 9 5 7 5 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 0 2 R E

~ 0 . 4 7 0 5 7 3 8 3 E 0 4 - 0 . 1 0 8 8 1 8 4 8 E 0 5 0 . 3 7 3 6 5 4 0 6 E 0 6


0 . 4 1 0 9 1 5 2 2 E 0 2 0 . 3 8 9 4 8 3 1 8 E 0 2 0 . 5 2 1 5 6 8 3 0 E 0 1

P H Q S P E E A L P H A P 3 P C

- 1 3 1 5 0 . 0 0 . 0 0 0 1 2 5 0 . 0 0 2 6 1 0 0 0 . 0 1 . 0 0 0 0 0 . 5 0 1 6 . 9 0


1 5 . 5 0 1 3 . 0 0 1 0 . 6 0 8 . 2 0 6 . 1 0

3 . 9 0 1 . 9 0 8 . 0


0 . 0 4 5 3 6 0 . 0 0 0 3 2 9 2 . 2 4 2 9 0 . 8 0 . 4 3 0 0 . 5 6 0

0 . 0 5 0 4 0 0 . 0 0 0 2 9 3 3 . 1 3 6 8 5 . 8 0 . 3 8 3 0 . 4 8 1

0 . 0 5 5 4 4 0 . 0 0 0 2 5 6 7 . 5 3 1 3 8 . 5 0 . 3 3 5 0 . 4 1 0

0 . 0 6 0 4 8 0 . 0 0 0 2 2 0 5 . 8 2 6 3 8 . 8 0 . 2 8 8 0 . 3 4 5

0 . 0 6 5 5 2 0 . 0 0 0 1 8 5 3 . 3 2 1 7 9 . 2 0 . 2 4 2 0 . 2 8 5

0 . 0 7 0 5 5 9 . 9 9 9 1 5 1 2 . 6 1 7 5 3 . 6 0 . 1 9 8 0 . 2 2 9

0 . 0 7 5 5 9 9 . 9 9 9 1 1 8 4 . 7 1 3 5 7 . 4 0 . 1 5 5 0 . 1 7 7

0 . 0 8 0 6 3 9 . 9 9 9 8 6 9 . 8 9 8 6 . 8 0 . 1 1 4 0 . 1 2 9

0 . 0 8 5 6 7 9 . 9 9 9 5 6 7 . 7 6 3 8 * 7 0 . 0 7 4 0 . 0 8 3

0 . 0 9 0 7 1 9 . 9 9 9 2 7 8 . 0 3 1 0 . 5 0 . 0 3 6 0 . 0 4 1

0 . 0 9 5 7 5 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

- 0 . 5 7 5 9 7 4 6 I E 0 4 - 0 . 1 3 2 6 5 1 1 3 E 0 5 0 . 4 5 7 S 5 7 7 5 E 0 6


0 * 4 3 3 9 0 9 9 I E 0 2 0 . 4 5 7 4 7 3 3 0 E 0 2 - 0 . 5 4 3 0 4 7 8 1 E 0 1

156

p H Q S P E E A L P H A T E S T; 1 3 . 0 0 . 0 0 0 1 5 0 0 . 0 0 1 0 3 8 0 0 . 0 1 . 0 0 0 0 9 . 0 0

R R / H I P K I P O I P R K I P R D

0 . 0 1 0 6 6 . 6 6 7 1 3 . 0 2 9 7 5 . 4 0 . 0 0 7 1 . 6 8 8

0 . 0 1 3 9 0 . 0 0 0 9 3 8 . 0 2 5 7 8 . 7 0 . 5 3 2 1 . 4 6 3

0 . 0 1 7 1 1 3 . 3 3 3 1 2 3 0 . 8 2 2 7 4 . 1 0 . 6 9 8 1 . 2 9 0

0 . 0 2 0 1 3 6 . 6 6 7 1 3 0 4 . 7 2 0 2 6 . 6 0 . 7 4 0 1 . 1 5 0

0 . 0 2 4 1 . 6 0 . 0 0 0 1 2 8 9 . 6 1 8 1 8 . 3 0 . 7 3 2 1 . 0 3 2

0 . 0 2 7 1 8 3 . 3 3 3 1 2 3 5 . 3 1 6 3 8 . 4 0 . 7 0 1 0 . 9 3 0

0 . 0 3 1 2 0 6 . 6 6 7 1 1 6 3 . 7 1 4 8 0 . 1 0 • 6 6 0 0 . 8 4 0

0 . 0 3 4 2 3 0 . 0 0 0 1 0 8 4 . 9 1 3 3 8 . 7 0 . 6 1 6 0 . 7 6 0

0 . 0 3 8 2 5 3 . 3 3 3 1 0 0 4 . 1 1 2 1 1 . 0 0 . 5 7 0 0 . 6 8 7

0 . 0 4 1 2 7 6 . 6 6 7 9 2 3 . 8 1 0 9 4 . 5 0 . 5 2 4 0 . 6 2 1

0 . 0 4 5 3 0 0 . 0 0 0 8 4 5 . 3 9 8 7 . 5 0 . 4 8 0 0 . 5 6 0

C l D 1 Q K

- 0 . 1 2 7 9 9 8 2 4 E 0 4 - 0 . 2 9 8 0 7 7 9 3 E 0 4 0 . 1 0 0 5 2 9 4 7 E - 0 2

P P D R E

0 ® 2 9 7 5 3 6 1 3 E 0 4 0 . 1 5 1 7 4 2 1 3 E 0 6


- 2 8 4 8 . 0 0 . 0 0 0 1 5 0 0 . 0 0 1 7 1 0 0 0 . 0 1 . 0 0 0 0 1 0 . 0 0


0 . 0 1 0 6 6 . 6 6 7 - 2 8 4 8 . 0 4 9 0 1 . 6 - 0 . 9 8 1 1 . 6 8 8

0 . 0 1 3 9 0 . 0 0 0 4 6 . 7 4 2 4 8 . 2 0 . 0 1 6 1 . 4 6 3

0 . 0 1 7 1 1 3 . 3 3 3 1 1 3 6 . 7 3 7 4 6 . 3 0 . 3 9 2 1 . 2 9 0

0 ; 0 2 0 1 3 6 . 6 6 7 1 5 7 6 . 9 3 3 3 8 . 7 0 . 5 4 3 1 . 1 5 0

0 . 0 2 4 1 6 0 . 0 0 0 1 7 3 7 . 7 2 9 9 5 . 5 0 . 5 9 9 1 . 0 3 2

0 . 0 2 7 1 8 3 . 3 3 3 1 7 6 5 . 0 2 6 9 9 . 1 0 . 6 0 8 0 . 9 3 0

0 . 0 3 1 2 0 6 * 6 6 7 1 7 2 4 . 0 2 4 3 8 . 3 0 . 5 9 4 0 . 8 4 0

0 . 0 3 4 2 3 0 . 0 0 0 1 6 4 7 . 2 2 2 0 5 . 4 0 . 5 6 7 0 . 7 6 0

0 . 0 3 8 2 5 3 . 3 3 3 1 5 5 1 . 5 1 9 9 5 . 0 0 . 5 3 4 Go 6 8 7

0 . 0 4 1 2 7 6 . 6 6 7 1 4 4 6 . 4 1 8 0 3 . 2 0 . 4 9 8 0 . 6 2 1

0 . 0 4 5 3 0 0 . 0 0 0 1 3 3 7 . 1 1 6 2 6 . 9 0 . 4 6 1 0 . 5 6 0

C l 0 1 Q K

- 0 . 2 1 9 3 0 5 1 0 E 0 4 - 0 . 5 0 7 4 9 4 1 4 E 0 4 0 . 1 7 2 2 4 1 5 2 E - 0 2

P P D R E

0 . 4 9 0 1 6 0 5 5 E 0 4 0 . 2 4 9 9 7 9 8 1 E 0 6


1 3 . 0 0 . 0 0 0 1 5 0 0 . 0 0 1 0 3 8 0 0 . 0 • 1 . 0 0 0 0 3 . 6 0 5 . 1 8


4 . 6 5 3 . 8 0 3 . 0 5 2 . 3 0 1 . 6 51 . 0 5 0 . 5 5 9 . 0


0 . 0 4 5 3 0 0 . 0 0 0 8 4 5 . 3 9 8 7 . 5 0 . 4 8 0 0 . 5 6 0

0 . 0 5 0 3 3 3 . 3 3 3 7 3 7 . 7 8 4 8 . 3 0 . 4 1 9 0 . 4 8 1

0 . 0 5 5 3 6 6 . 6 6 7 6 3 5 . 8 7 2 2 . 3 0 . 3 6 1 0 . 4 1 0

0 . 0 6 0 4 0 0 * 0 0 0 5 3 9 . 8 6 0 7 . 3 0 . 3 0 6 0 . 3 4 5

0 . 0 6 5 4 3 3 . 3 3 3 4 4 9 . 2 5 0 1 . 5 0 . 2 5 5 0 . 2 8 5

0 . 0 7 0 4 6 6 . 6 6 6 3 6 3 . 8 4 0 3 . 6 0 . 2 0 6 0 . 2 2 9

0 . 0 7 5 5 0 0 . 0 0 0 2 8 3 . 1 3 1 2 . 4 0 . 1 6 1 0 . 1 7 7

0 . 0 8 0 5 3 3 . 3 3 3 2 0 6 . 8 2 2 7 . 1 0 . 1 1 7 0 . 1 2 9

0 . 0 8 5 5 6 6 . 6 6 6 1 3 4 . 4 1 4 7 . 0 0 . 0 7 6 0 . 0 8 3

0 . 0 9 0 5 9 9 . 9 9 9 6 5 . 5 7 1 . 5 0 . 0 3 7 0 . 0 4 1

0 . 0 9 5 6 3 3 . 3 3 3 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

“ 0 . 1 2 7 9 9 8 2 4 E 0 4 - 0 . 2 9 8 0 7 8 2 2 E 0 4 0 . 1 5 1 7 4 2 1 3 E 0 6


0 . 1 3 8 4 1 3 0 6 E 0 2 0 • 1 3 7 8 2 5 7 9 E 0 2 0 • 4 2 4 2 8 2 9 7 E 0 0


“ 2 8 4 8 . 0 0 . 0 0 0 1 5 0 0 . 0 0 1 7 1 0 0 o » o h-*

6 0 0 0 0 1 * 5 0 7 . 1 0


6 . 5 5 5 . 5 5 4 . 5 5 3 . 5 0 2 . 5 0

1 . 6 0

o.

ooCO.

o

R R / H O P K O P D D P R K O P R D

0 . 0 4 5 3 0 0 . 0 0 0 1 3 3 7 . 1 1 6 2 6 . 9 0 . 4 6 1 0 . 5 6 0

0 . 0 5 0 3 3 3 . 3 3 3 1 1 7 9 . 9 1 3 9 7 . 5 0 . 4 0 6 0 . 4 8 1

0 . 0 5 5 3 6 6 . 6 6 7 1 0 2 5 . 6 1 1 9 0 . 0 0 . 3 5 3 0 . 4 1 0

0 . 0 6 0 4 0 0 . 0 0 0 8 7 6 . 3 1 0 0 0 . 5 0 . 3 0 2 0 . 3 4 5

0 . 0 6 5 4 3 3 . 3 3 3 7 3 3 . 1 8 2 6 . 2 0 . 2 5 3 0 . 2 8 5

0 . 0 7 0 4 6 6 • 6 6 6 5 9 6 . 3 6 6 4 . 9 0 . 2 0 5 0 . 2 2 9

0 . 0 7 5 5 0 0 . 0 0 0 4 6 5 . 7 5 1 4 . 7 0 . 1 6 0 0 . 1 7 7

0 . 0 8 0 5 3 3 . 3 3 3 3 4 1 . 1 3 7 4 . 2 0 . 1 1 7 0 . 1 2 9

0 . 0 8 5 5 6 6 . 6 6 6 2 2 2 . 2 2 4 2 . 2 0 . 0 7 7 0 . 0 8 3

0 . 0 9 0 5 9 9 . 9 9 9 1 0 8 . 6 1 1 7 . 7 0 . 0 3 7 0 . 0 4 1

0 . 0 9 5 6 3 3 . 3 3 3 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

- 0 . 2 1 9 3 0 5 1 0 E 0 4 - 0 . 5 0 7 4 9 4 5 3 E 0 4 0 . 2 4 9 9 7 9 8 1 E 0 6


0 • 1 9 6 0 9 3 9 0 E 0 2 0 . 1 9 5 3 0 6 5 5 E 0 2 0 . 4 0 1 5 1 8 5 8 E 0 0

1 5 8


- 6 0 5 0 . 0 0 . 0 0 0 1 5 0 0 . 0 0 2 1 3 0 0 0 . 0 1 . 0 0 0 0 1 1 . 0 0

R R / H I P K I P D ‘ I P R K I P R D

0 , 0 1 0 6 6 . 6 6 7 - 6 0 5 0 . 0 6 1 0 5 . 5 - 1 . 6 7 3 1 . 6 8 8

0 . 0 1 3 9 0 . 0 0 0 - 1 3 4 1 . 2 5 2 9 1 . 6 - 0 . 3 7 1 1 . 4 6 3

0 . 0 1 7 1 1 3 . 3 3 3 5 1 7 . 0 4 6 6 6 . 4 0 . 1 4 3 1 . 2 9 0

0 . 0 2 0 1 3 6 . 6 6 7 1 3 3 5 . 6 4 1 5 8 . 7 0 . 3 6 9 1 . 1 5 0

0 . 0 2 4 1 6 0 . 0 0 0 1 6 9 9 . 3 3 7 3 1 . 2 0 . 4 7 0 1 . 0 3 2

0 . 0 2 7 1 8 3 . 3 3 3 1 8 4 0 . 2 3 3 6 2 . 0 0 . 5 0 9 0 . 9 3 0

0 . 0 3 1 2 0 6 . 6 6 7 1 8 6 3 . 5 3 0 3 7 . 1 0 . 5 1 5 0 . 8 4 0

0 . 0 3 4 2 3 0 . 0 0 0 1 8 2 1 . 8 2 7 4 7 . 0 0 . 5 0 4 0 . 7 6 0

0 . 0 3 8 2 5 3 . 3 3 3 1 7 4 3 . 4 2 4 8 5 . 0 0 . 4 8 2 0 . 6 8 7

0 . 0 4 1 2 7 6 . 6 6 7 1 6 4 4 . 1 2 2 4 6 . 0 0 . 4 5 5 0 . 6 2 1

0 . 0 4 5 3 0 0 . 0 0 0 1 5 3 3 . 3 2 0 2 6 . 4 0 . 4 2 4 0 . 5 6 0

C l D 1 Q K

- 0 . 2 6 7 8 0 8 6 7 E 0 4 - 0 . 6 1 6 8 5 4 3 0 E 0 4 0 . 2 1 0 3 3 6 1 1 E - 0 2

P P D R E

0 * 6 1 0 5 5 0 7 8 E 0 4 0 . 3 1 1 3 7 8 3 8 E 0 6


- 1 0 6 5 0 . 0 0 . 0 0 0 1 5 0 0 . 0 0 2 6 1 0 0 0 . 0 1 . 0 0 0 0 1 2 . 0 0


0 . 0 1 0 6 6 . 6 6 7 7 4 8 1 . 4 - 2 . 4 0 4 1 . 6 8 8

0 . 0 1 3 9 0 . 0 0 0 - 3 3 7 1 . 1 6 4 8 4 . 1 - 0 . 7 6 1 1 . 4 6 3

0 . 0 1 7 1 1 3 . 3 3 3 - 4 2 0 . 7 5 7 1 8 . 0 - 0 . 0 9 5 1 . 2 9 0

0 . 0 2 0 1 3 6 . 6 6 7 9 3 8 . 7 5 0 9 5 . 9 0 . 2 1 2 1 . 1 5 0

0 . 0 2 4 1 6 0 . 0 0 0 1 5 9 4 . 5 4 5 7 2 . 1 0 . 3 6 0 1 . 0 3 2

0 . 0 2 7 1 8 3 . 3 3 3 1 9 0 0 . 7 4 1 1 9 . 7 0 . 4 2 9 0 . 9 3 0

0 . 0 3 1 2 0 6 • 6 6 7 2 0 1 9 . 0 3 7 2 1 . 6 0 . 4 5 6 0 . 8 4 0

0 . 0 3 4 2 3 0 . 0 0 0 2 0 3 0 . 8 3 3 6 6 . 1 0 . 4 5 8 0 . 7 6 0

0 . 0 3 8 2 5 3 . 3 3 3 1 9 8 0 . 3 3 0 4 5 . 0 0 . 4 4 7 0 . 6 8 7

0 . 0 4 1 2 7 6 . 6 6 7 1 8 9 2 . 5 2 7 5 2 . 2 0 . 4 2 7 0 . 6 2 1

0 . 0 4 5 3 0 0 . 0 0 0 1 7 8 2 . 4 2 4 8 3 . 1 0 . 4 0 2 0 . 5 6 0

C l D i Q K

- 0 . 3 3 2 5 5 2 3 9 E 0 4 - 0 . 7 6 2 4 6 6 4 1 E 0 4 0 . 2 6 1 1 8 5 7 4 E - - 0 2

P P D R E

0 . 7 4 8 1 3 9 8 4 E 0 4 0 • 3 8 1 5 4 8 1 3 E 0 6

p H Q S P E E A L P H A P B P C- 6 0 5 0 . 0 0 . 0 0 0 1 5 0 0 . 0 0 2 1 3 0 0 0 . 0 ' 1 . 0 0 0 0 - 1 . 6 6 8 . 1 3

P J P K T E S T P D P E P F PQ P H7 . 6 5 6 . 5 0 5 . 3 5 4 . 1 0 3 . 0 0

1 . 9 5 0 . 9 5 1 1 . 0


0 . 0 4 5 3 0 0 . 0 0 0 1 5 3 3 . 3 2 0 2 6 . 4 0 . 4 2 4 0 . 5 6 0

0 . 0 5 0 3 3 3 . 3 3 3 1 3 6 5 . 7 1 7 4 0 . 7 0 . 3 7 8 0 . 4 8 1

0 . 0 5 5 3 6 6 . 6 6 7 1 1 9 5 . 2 1 4 8 2 . 2 0 . 3 3 1 0 . 4 1 0

0 . 0 6 0 4 0 0 . 0 0 0 1 0 2 6 . 7 1 2 4 6 . 3 0 . 2 8 4 0 . 3 4 5

0 . 0 6 5 4 3 3 . 3 3 3 8 6 2 . 5 1 0 2 9 . 2 0 . 2 3 9 0 . 2 8 5

0 . 0 7 0 4 6 6 « 6 6 6 7 0 3 . 9 8 2 8 . 2 0 . 1 9 5 0 . 2 2 9

0 . 0 7 5 5 0 0 . 0 0 0 5 5 1 . 3 6 4 1 . 1 0 . 1 5 2 0 . 1 7 7

0 . 0 8 0 5 3 3 . 3 3 3 4 0 4 . 7 4 6 6 . 1 0 . 1 1 2 0 . 1 2 9

0 . 0 8 5 5 6 6 . 6 6 6 2 6 4 . 2 3 0 1 . 6 0 . 0 7 3 0 . 0 8 3

0 . 0 9 0 5 9 9 . 9 9 9 1 2 9 . 3 1 4 6 * 6 0 . 0 3 6 0 . 0 4 1

0 . 0 9 5 6 3 3 . 3 3 3 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 0 2 R E

- 0 . 2 6 7 8 0 8 6 7 E 0 4 - 0 . 6 1 6 8 5 4 6 9 E 0 4 0 . 3 1 1 3 7 8 3 8 E 0 6

T H R U S T T H R U S T X - ....................P D T

0 . 2 0 2 6 7 4 4 1 E 0 2 0 . 2 2 3 7 8 3 4 2 E 0 2 - 0 . 1 0 4 1 5 2 3 I E 0 2


- 1 0 6 5 0 • 0 0 . 0 0 0 1 5 0 0 . 0 0 2 6 1 0 0 0 . 0 1 . 0 0 0 0 6 . 1 2 8 . 9 5


8 . 7 5 7 . 3 5 5 . 8 5 4 . 5 5 3 . 4 0

2 . 2 5 1 . 1 0 1 2 . 0

R R / H O P K D P D O P R K O P R D

0 . 0 4 5 3 0 0 . 0 0 0 1 7 8 2 . 4 2 4 8 3 . 1 0 . 4 0 2 0 . 5 6 0

0 . 0 5 0 3 3 3 . 3 3 3 1 6 0 4 . 1 2 1 3 3 . 0 0 . 3 6 2 0 . 4 8 1

0 . 0 5 5 3 6 6 . 6 6 7 1 4 1 4 . 5 1 8 1 6 . 3 0 . 3 1 9 0 . 4 1 0

0 . 0 6 0 4 0 0 . 0 0 0 1 2 2 2 . 0 1 5 2 7 . 1 0 . 2 7 6 0 . 3 4 5

0 . 0 6 5 4 3 3 . 3 3 3 1 0 3 1 . 1 1 2 6 1 . 1 0 . 2 3 3 0 . 2 8 5

0 . 0 7 0 4 6 6 « 6 6 6 8 4 4 • 5 1 0 1 4 . 8 0 . 1 9 1 0 . 2 2 9

0 . 0 7 5 5 0 0 . 0 0 0 6 6 3 . 3 7 8 5 . 6 0 . 1 5 0 0 . 1 7 7

0 . 0 8 0 5 3 3 . 3 3 3 4 8 8 . 1 5 7 1 . 1 0 . 1 1 0 0 . 1 2 9

0 . 0 8 5 5 6 6 • 6 6 6 3 1 9 . 3 3 6 9 . 6 0 . 0 7 2 0 . 0 8 3

0 . 0 9 0 5 9 9 . 9 9 9 1 5 6 . 6 1 7 9 . 7 0 . 0 3 5 0 . 0 4 1

0 . 0 9 5 6 3 3 . 3 3 3 0 . 0 . 0 . 0 0 . 0 0 0 0 . 0 0 0

C 2 0 2 R E

- 0 . 3 3 2 5 5 2 3 9 E 0 4 - 0 . 7 6 2 4 6 6 4 1 E 0 4 0 . 3 8 1 5 4 8 1 3 E 0 6


0 . 2 0 6 7 9 4 7 4 E 0 2 0 . 2 6 6 7 2 4 5 5 E 0 2 - 0 . 2 8 9 8 0 3 3 1 E 0 2

! 6 0


; 3 1 0 0 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 4 4 1 0 0 . 0 1 . 0 0 0 0 1 3 . 0 0

R . R / H . I P K I P D I P R K - I P R D

0 , 0 1 0 1 0 0 . 0 0 0 3 1 0 0 . 0 4 2 6 6 . 3 1 . 2 2 7 1 . 6 8 8

0 , 0 1 3 1 3 5 . 0 0 0 3 0 6 3 . 1 3 6 9 7 . 6 1 . 2 1 2 1 . 4 6 3

0 . 0 1 7 1 7 0 . 0 0 0 2 8 6 5 . 2 3 2 6 0 . 8 1 . 1 3 4 1 . 2 9 0

0 . 0 2 0 2 0 5 . 0 0 0 2 6 3 7 . 8 2 9 0 6 . 0 1 . 0 4 4 1 . 1 5 0

0 . 0 2 4 2 4 0 . 0 0 0 2 4 1 5 . 0 2 6 0 7 . 3 0 . 9 5 6 1 . 0 3 2

0 . 0 2 7 2 7 5 . 0 0 0 2 2 0 5 . 8 2 3 4 9 . 3 0 . 8 7 3 0 . 9 3 0

0 . 0 3 1 3 1 0 . 0 0 0 2 0 1 2 . 1 2 1 2 2 . 3 0 . 7 9 6 0 . 8 4 0

0 . 0 3 4 3 4 5 . 0 0 0 1 8 3 3 . 0 1 9 1 9 . 5 0 . 7 2 5 0 . 7 6 0

0 . 0 3 8 3 8 0 . 0 0 0 1 6 6 7 . 4 1 7 3 6 . 4 0 • 6 6 0 0 . 6 8 7

0 . 0 4 1 4 1 5 . 0 0 0 1 5 1 3 . 6 1 5 6 9 . 5 0 . 5 9 9 0 . 6 2 1

0 . 0 4 5 4 5 0 . 0 0 0 1 3 7 0 . 5 1 4 1 6 . 0 0 . 5 4 2 0 . 5 6 0

C l

- G . 1 8 9 4 4 7 9 5 E 0 4

D 1

- 0 . 4 4 4 6 3 1 6 4 E 0 4

Q K

0 . 4 4 0 8 6 4 8 2 E - 0 3

P P D R E

O c 4 2 6 6 3 2 8 1 E 0 4 0 . 9 6 7 0 2 6 2 5 E 0 5


2 8 0 9 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 4 4 1 0 4 1 9 . 0 1 . 0 0 0 0 1 4 . 0 0


0 . 0 1 0 1 0 0 . 0 0 0 2 8 0 9 . 0 3 9 7 4 . 9 1 . 1 1 2 1 . 5 7 3

0 . 0 1 3 1 3 5 . 0 0 0 2 7 7 4 . 8 3 4 0 8 . 9 1 . 0 9 8 1 * 3 4 9

0 . 0 1 7 1 7 0 . 0 0 0 2 5 8 0 . 2 2 9 7 5 . 5 1 . 0 2 1 1 . 1 7 8

0 . 0 2 0 2 0 5 . 0 0 0 2 3 5 7 . 1 2 6 2 5 . 0 0 . 9 3 3 1 . 0 3 9

0 . 0 2 4 2 4 0 . 0 0 0 2 1 3 9 , 4 2 3 3 1 . 4 0 . 8 4 7 0 . 9 2 3

0 . 0 2 7 2 7 5 . 0 0 0 1 9 3 6 . 1 2 0 7 9 . 3 0 , 7 6 6 0 . 8 2 3

0 . 0 3 1 3 1 0 . 0 0 0 1 7 4 9 . 0 1 8 5 8 . 9 0 . 6 9 2 0 . 7 3 6

0 . 0 3 4 3 4 5 . 0 0 0 1 5 7 7 . 4 1 6 6 3 . 7 0 . 6 2 4 0 * 6 5 8

0 . 0 3 8 3 8 0 . 0 0 0 1 4 2 0 , 0 1 4 8 8 . 9 0 . 5 6 2 0 . 5 8 9

0 . 0 4 1 4 1 5 . 0 0 0 1 2 7 5 . 3 1 3 3 1 . 0 0 . 5 0 5 0 . 5 2 7

0 . 0 4 5 4 5 0 . 0 0 0 1 1 4 2 . 0 1 1 8 7 . 4 0 . 4 5 2 0 . 4 7 0

C l D 1 Q K

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0 . 0 4 5 4 5 0 . 0 0 0 1 3 7 0 . 5 1 4 1 6 . 0 0 . 5 4 2 0 . 5 6 0

0 . 0 5 0 5 0 0 . 0 0 0 1 1 3 1 . 9 1 2 1 6 . 3 0 . 4 6 8 0 . 4 8 1

0 . 0 5 5 5 5 0 . 0 0 0 1 0 0 9 . 5 1 0 3 5 . 7 0 . 4 0 0 0 . 4 1 0

0 . 0 6 0 6 0 0 . 0 0 0 8 5 0 . 9 8 7 0 . 8 0 . 3 3 7 0 . 3 4 5

0 . 0 6 5 6 4 9 . 9 9 9 7 0 4 . 1 7 1 9 . 2 0 . 2 7 9 0 . 2 8 5

0 . 0 7 0 6 9 9 . 9 9 9 5 6 7 . 6 5 7 8 . 7 0 . 2 2 5 0 . 2 2 9

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0 . 0 3 0 7 9 9 . 9 9 9 3 2 0 . 2 3 2 5 . 7 0 . 1 2 7 0 . 1 2 9

0 . 0 8 5 8 4 9 . 9 9 9 2 0 7 . 5 2 1 0 . 8 0 . 0 8 2 0 . 0 8 3

0 . 0 9 0 8 9 9 . 9 9 9 1 0 0 . 9 1 0 2 . 5 0 . 0 4 0 0 . 0 4 1

0 . 0 9 5 9 4 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

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6 . 7 5 5 . 3 0 4 . 0 0 2 . 9 0 1 . 9 0

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0 . 0 4 5 4 5 0 . 0 0 0 1 1 4 2 . 0 1 1 8 7 . 4 0 . 4 5 2 0 . 4 7 0

0 . 0 5 0 5 0 0 . 0 0 0 9 6 9 . 0 1 0 0 3 . 3 0 . 3 8 3 0 . 3 9 7

0 . 0 5 5 5 5 0 . 0 0 0 8 1 3 . 7 8 3 9 . 8 0 . 3 2 2 0 . 3 3 2

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0 . 0 7 0 6 9 9 . 9 9 9 4 3 2 . 9 4 4 4 . 0 0 . 1 7 1 0 , 1 7 6

0 . 0 7 5 7 4 9 . 9 9 9 3 2 9 . 0 3 3 6 . 9 0 . 1 3 0 0 . 1 3 3

0 . 0 8 0 7 9 9 , 9 9 9 2 3 4 . 5 2 3 9 . 9 0 . 0 9 3 0 , 0 9 5

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C 2 D 2 R E

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0 . 1 9 9 0 9 8 3 6 E 0 2 0 . 1 8 8 2 4 4 0 2 E 0 2 0 . 5 4 5 1 7 4 6 9 E 0 1

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0 . 0 1 0 1 0 0 . 0 0 0 3 8 0 0 . 0 6 5 2 0 . 4 0 . 9 8 4 1 . 6 8 8

0 . 0 1 3 1 3 5 . 0 0 0 4 1 7 2 . 6 5 6 5 1 . 2 1 . 0 8 0 1 . 4 6 3

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0 . 0 3 4 3 4 5 . 0 0 0 2 7 3 3 . 4 2 9 3 3 . 7 0 . 7 0 8 0 . 7 6 0

0 . 0 3 8 3 8 0 . 0 0 0 2 4 9 4 . 1 2 6 5 3 . 9 0 . 6 4 6 0 . 6 8 7

0 . 0 4 1 4 1 5 . 0 0 0 2 2 6 9 . 7 2 3 9 8 . 7 0 . 5 8 8 0 . 6 2 1

0 . 0 4 3 4 5 0 . 0 0 0 2 0 5 9 . 0 2 1 6 4 . 2 0 . 5 3 3 0 . 5 6 0

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0 . 6 5 2 0 4 2 5 8 E 0 4 0 • 1 4 7 7 9 5 0 6 E 0 6

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0 . 0 1 7 1 7 0 . 0 0 0 3 7 7 7 . 6 4 6 9 8 . 3 0 . 9 7 8 1 . 2 1 7

0 . 0 2 0 2 0 5 . 0 0 0 3 5 3 7 . 0 4 1 6 0 . 4 0 . 9 1 6 1 . 0 7 7

0 . 0 2 4 2 4 0 . 0 0 0 3 2 6 2 . 5 3 7 0 8 . 9 0 . 8 4 5 0 . 9 6 0

0 . 0 2 7 2 7 5 . 0 0 0 2 . 9 8 7 . 9 3 3 2 0 . 5 0 . 7 7 4 0 . 8 6 0

0 . 0 3 1 3 1 0 . 0 0 0 2 7 2 5 . 0 2 9 8 0 . 2 0 . 7 0 6 0 . 7 7 2

0 . 0 3 4 3 4 5 . 0 0 0 2 4 7 7 . 8 2 6 7 7 . 9 0 . 6 4 2 0 . 6 9 3

0 . 0 3 8 3 8 0 . 0 0 0 2 2 4 6 . 8 2 4 0 6 . 3 0 . 5 8 2 0 . 6 2 3

0 . 0 4 1 4 1 5 . 0 0 0 2 0 3 1 . 4 2 1 6 0 . 2 0 . 5 2 6 0 . 5 5 9

0 . 0 4 5 4 5 0 . 0 0 0 1 8 3 0 . 6 1 9 3 5 . 6 0 . 4 7 4 0 . 5 0 1

C l

0 . 2 8 9 6 8 9 5 3 E 0 4

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0 . 6 7 4 1 3 6 9 1 E - 0 3

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1 2 . 0 0 9 . 5 0 7 . 4 0 5 . 5 0 3 . 9 0

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0 . 0 4 5 4 5 0 . 0 0 0 2 0 5 9 . 1 2 1 6 4 . 2 0 . 5 3 3 0 . 5 6 0

0 . 0 5 0 5 0 0 . 0 0 0 1 7 7 9 . 7 1 8 5 9 . 0 0 . 4 6 1 0 . 4 8 1

0 . 0 5 5 5 5 0 . 0 0 0 1 5 2 2 . 7 1 5 8 3 . 0 0 . 3 9 4 0 . 4 1 0

0 . 0 6 0 6 0 0 . 0 0 0 1 2 8 5 . 2 1 3 3 0 . 9 0 . 3 3 3 0 . 3 4 5

0 . 0 6 5 6 4 9 . 9 9 9 1 0 6 4 . 6 1 0 9 9 , 1 0 . 2 7 6 0 . 2 8 5

0 . 0 7 0 6 9 9 . 9 9 9 8 5 8 . 9 8 8 4 . 5 0 . 2 2 2 0 . 2 2 9

0 . 0 7 5 7 4 9 . 9 9 9 6 6 6 . 3 6 8 4 . 7 0 . 1 7 3 0 . 1 7 7

0 . 0 8 0 7 9 9 . 9 9 9 4 8 5 . 3 4 9 7 . 7 0 • 1.2 6 0 . 1 2 9

0 . 0 8 5 8 4 9 . 9 9 9 3 1 4 , 6 3 2 2 . 1 0 . 0 8 1 0 . 0 8 3

0 . 0 9 0 8 9 9 . 9 9 9 1 5 3 . 1 1 5 6 . 6 0 . 0 4 0 0 . 0 4 1

0 . 0 9 5 9 4 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 0 2 R E 1

- 0 . 2 8 9 6 7 0 0 9 E 0 4 - * 0 . 6 7 8 7 9 8 8 3 E 0 4 0 • 1 4 7 7 9 5 0 6 E 0 6 :


0 • 3 6 7 1 7 3 9 2 E 0 2 0 . 3 4 7 1 0 7 0 9 E 0 2 0 . 5 4 6 5 2 1 1 9 E 0 1


3 5 0 9 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 6 7 4 0 4 1 9 . 0 1 . 0 0 0 0 1 3 . 3 0 1 3 . 2 0


1 0 . 5 0 8 . 7 0 6 . 6 0 4 . 8 0 3 . 4 0

2 . 0 0 0 . 9 0 1 6 . 0 ....... - - ■ • -


0 . 0 4 5 4 5 0 . 0 0 0 1 8 3 0 . 6 1 9 3 5 . 6 0 . 4 7 4 0 . 5 0 1

0 . 0 5 0 5 0 0 . 0 0 0 1 5 6 6 . 7 1 6 4 5 . 9 0 . 4 0 6 0 , 4 2 6

0 . 0 5 5 5 5 0 . 0 0 0 1 3 2 6 . 9 1 3 8 7 . 0 0 . 3 4 4 0 . 3 5 9

0 . 0 6 0 6 0 0 . 0 0 0 1 1 0 8 . 1 1 1 5 3 . 8 0 . 2 8 7 0 . 2 9 9

0 . 0 6 5 6 4 9 . 9 9 9 9 0 8 . 0 9 4 2 . 4 0 . 2 . 3 5 0 . 2 4 4

0 . 0 7 0 6 9 9 . 9 9 9 7 2 4 . 3 7 4 9 . 8 0 . 1 8 8 0 . 1 9 4

0 . 0 7 5 7 4 9 . 9 9 9 5 5 5 . 3 5 7 3 . 6 0 . 1 4 4 0 . 1 4 9

0 . 0 8 0 7 9 9 . 9 9 9 3 9 9 . 6 4 1 2 . 0 0 . 1 0 3 0 . 1 0 7

0 . 0 8 5 8 4 9 . 9 9 9 2 5 5 . 8 2 6 3 . 4 0 . 0 6 6 0 . 0 6 8

0 . 0 9 0 8 9 9 , 9 9 9 1 2 2 . 9 1 2 6 . 4 0 . 0 3 2 0 . 0 3 3

0 . 0 9 5 9 4 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 0 0 . 0 0 0

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R R / H I P K I P D ’ I P R K I P R D

0 . 0 1 0 8 0 . 0 0 0 1 5 8 0 . 0 2 5 7 0 . 7 1 . 0 3 8 1 . 6 8 8

0 . 0 1 3 1 0 8 . 0 0 0 1 7 0 3 . 0 2 2 2 8 . 0 1 . 1 1 9 1 . 4 6 3

0 . 0 1 7 1 3 6 . 0 0 0 1 6 4 7 . 1 1 9 6 4 . 8 1 . 0 8 2 1 . 2 9 0

0 . 0 2 0 1 6 4 . 0 0 0 1 5 4 2 . 7 1 7 5 1 . 0 1 . 0 1 3 1 . 1 5 0

0 . 0 2 4 1 9 2 . 0 0 0 1 4 2 7 . 0 1 5 7 1 . 0 0 . 9 3 7 1 . 0 3 2

0 . 0 2 7 2 2 0 . 0 0 0 1 3 1 2 . 2 1 4 1 5 . 6 0 . 8 6 2 0 * 9 3 0

0 . 0 3 1 2 4 8 . 0 0 0 1 2 0 2 . 6 1 2 7 8 . 8 0 . 7 9 0 0 . 8 4 0

0 . 0 3 4 2 7 6 . 0 0 0 1 0 9 9 . 4 1 1 5 6 . 6 0 . 7 2 2 0 . 7 6 0

0 . 0 3 8 3 0 4 . 0 0 0 1 0 0 2 . 6 1 0 4 6 . 3 0 . 6 5 9 0 . 6 8 7

0 . 0 4 1 3 3 2 . 0 0 0 9 1 2 . 1 9 4 5 . 7 0 . 5 9 9 0 . 6 2 1

0 . 0 4 5 3 6 0 . 0 0 0 8 2 7 . 2 8 5 3 . 2 0 . 5 4 3 0 . 5 6 0

C l

- 0 . 1 1 6 0 5 3 3 7 E 0 4

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0 . 5 2 7 4 7 6 1 9 E - 0 3

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2 5 7 0 7 1 2 9 E 0 4

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0 . 0 1 0 8 0 . 0 0 0 1 2 8 9 . 0 2 2 7 9 . 3 0 . 8 4 7 1 . 4 9 7

0 . 0 1 3 1 0 8 . 0 0 0 1 4 1 4 . 6 1 9 3 9 . 3 0 . 9 2 9 1 . 2 7 4

0 . 0 1 7 1 3 6 . 0 0 0 1 3 6 2 . 2 1 6 7 9 . 5 0 . 8 9 5 1 . 1 0 3

0 . 0 2 0 1 6 4 . 0 0 0 1 2 6 2 . 0 1 4 7 0 . 0 0 . 8 2 9 0 . 9 6 6

0 . 0 2 4 1 9 2 . 0 0 0 1 1 5 1 . 3 1 2 9 5 . 1 0 . 7 5 6 0 . 8 5 1

0 . 0 2 7 2 2 0 . 0 0 0 1 0 4 2 . 4 1 1 4 5 . 6 0 . 6 8 5 0 . 7 5 2

0 . 0 3 1 2 4 8 . 0 0 0 9 3 9 . 5 1 0 1 5 . 5 0 . 6 1 7 0 . 6 6 7

0 . 0 3 4 2 7 6 . 0 0 0 8 4 3 . 7 9 0 0 . 8 0 . 5 5 4 0 . 5 9 2

0 . 0 3 8 3 0 4 . 0 0 0 7 5 5 . 3 7 9 8 . 7 0 . 4 9 6 0 . 5 2 5

0 . 0 4 1 3 3 2 . 0 0 0 6 7 3 . 8 7 0 7 . 2 0 . 4 4 3 0 . 4 6 5

0 . 0 4 5 3 6 0 . 0 0 0 5 9 8 . 7 6 2 4 . 7 0 . 3 9 3 - 0 . 4 1 0

C l D 1 Q K

- 0 . 1 1 6 0 7 2 9 5 E 0 4 - 0 . 3 0 1 5 3 4 9 4 E 0 4 0 . 5 2 7 5 6 5 6 0 E - 0 3

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0 . 0 5 0 4 0 0 . 0 0 0 7 1 4 . 7 7 3 2 . 9 0 . 4 6 9 0 . 4 8 1

0 . 0 5 5 4 4 0 . 0 0 0 6 1 1 . 3 6 2 4 . 1 0 . 4 0 2 0 . 4 1 0

0 . 0 6 0 4 8 0 . 0 0 0 5 1 5 . 9 5 2 4 . 7 0 . 3 3 9 0 . 3 4 5

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0 . 0 7 0 5 5 9 . 9 9 9 3 4 4 . 7 3 4 8 . 7 0 . 2 2 6 0 . 2 2 9 :

0 . 0 7 5 5 9 9 . 9 9 9 2 6 7 . 3 2 6 9 . 9 0 . 1 7 6 0 . 1 7 7

0 . 0 8 0 6 3 9 . 9 9 9 1 9 4 . 7 1 9 6 . 2 0 . 1 2 8 0 . 1 2 9

0 . 0 8 5 6 7 9 . 9 9 9 1 2 6 . 2 1 2 7 . 0 0 . 0 8 3 0 . 0 8 3

0 . 0 9 0 7 1 9 . 9 9 9 6 1 . 4 6 1 . 7 0 . 0 4 0 0 . 0 4 1

0 . 0 9 5 7 5 9 . 9 9 9 0 . 0 0 . 0 0 . 0t

0 . 0 0 0

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4 . 3 0 3 . 2 0 2 . 4 0 1 . 7 0 1 . 1 0

0 . 7 0 0 . 3 0 1 8 . 0 ■ - -


0 . 0 4 5 3 6 0 . 0 0 0 5 9 8 . 7 6 2 4 . 7 0 . 3 9 3 0 . 4 1 0

0 . 0 5 0 4 0 0 . 0 0 0 5 0 1 . 7 5 1 9 . 9 0 . 3 3 0 0 . 3 4 1

0 . 0 5 5 4 4 0 . 0 0 0 4 1 5 . 5 4 2 8 . 2 0 . 2 7 3 0 . 2 8 1

0 . 0 6 0 4 8 0 . 0 0 0 3 3 8 . 8 3 4 7 . 6 0 . 2 2 3 0 . 2 2 8

0 . 0 6 5 5 2 0 . 0 0 0 2 7 0 . 6 2 7 6 . 6 0 . 1 7 8 0 . 1 8 2

0 . 0 7 0 5 5 9 . 9 9 9 2 1 0 . 0 2 1 4 . 0 0 . 1 3 8 0 . 1 4 1

0 . 0 7 5 5 9 9 . 9 9 9 1 5 6 . 4 1 5 8 . 9 0 . 1 0 3 0 , 1 0 4

0 . 0 8 0 6 3 9 . 9 9 9 1 0 9 . 0 1 1 0 . 5 0 . 0 7 2 0 . 0 7 3

0 . 0 8 5 6 7 9 . 9 9 9 6 7 . 4 6 8 . 2 0 . 0 4 4 0 . 0 4 5

0 . 0 9 0 7 1 9 . 9 9 9 3 1 . 2 3 1 . 5 0 . 0 2 1 0 . 0 2 1

0 . 0 9 5 7 5 9 . 9 9 9 - 0 . 0 0 . 0 - 0 . 0 0 0 0 . 0 0 0

C 2 D 2 R E

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0 . 0 1 0 8 0 . 0 0 0 1 4 0 0 . 0 4 2 3 9 . 9 0 . 5 5 8 1 . 6 8 8

0 . 0 1 3 1 0 8 . 0 0 0 2 1 2 0 . 9 3 6 7 4 . 7 0 . 8 4 5 1 . 4 6 3

0 . 0 1 7 1 3 6 . 0 0 0 2 2 6 5 . 6 3 2 4 0 . 6 0 . 9 0 2 1 . 2 9 0

0 . 0 2 0 1 6 4 . 0 0 0 2 2 2 2 . 6 2 8 8 8 . 0 0 . 8 8 5 1 . 1 5 0

0 . 0 2 4 1 9 2 . 0 0 0 2 1 1 0 . 7 2 5 9 1 . 1 0 . 8 4 1 1 . 0 3 2

0 . 0 2 7 2 2 0 . 0 0 0 1 9 7 3 . 7 2 3 3 4 . 8 0 . 7 8 6 0 . 9 3 0

0 . 0 3 1 2 4 8 . 0 0 0 ■ 1 8 2 9 . 7 2 1 0 9 . 1 0 . 7 2 9 0 . 8 4 0

0 . 0 3 4 2 7 6 . 0 0 0 1 6 8 6 . 7 1 9 0 7 . 7 0 . 6 7 2 0 . 7 6 0

0 . 0 3 8 3 0 4 . 0 0 0 1 5 4 7 . 9 1 7 2 5 . 7 0 . 6 1 6 0 . 6 8 7

0 . 0 4 1 3 3 2 . 0 0 0 1 4 1 5 . 0 1 5 5 9 . 7 0 . 5 6 3 0 . 6 2 1

0 . 0 4 5 3 6 0 . 0 0 0 1 2 8 8 . 3 1 4 0 7 . 3 0 . 5 1 3 0 . 5 6 0

C l

- 0 * 1 8 6 9 6 9 5 1 E 0 4 - 0

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0 . 8 4 9 7 9 8 5 5 E - 0 3

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0 • 4 2 3 9 9 4 1 4 E 0 4

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0 * 1 5 0 1 6 3 3 1 E 0 6

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1 1 0 9 * 0 0 . 0 0 0 1 2 5

R R / H

0 . 0 1 0 8 0 . 0 0 0

0 . 0 1 3 1 0 8 . 0 0 0

0 . 0 1 7 1 3 6 . 0 0 0

0 . 0 2 0 1 6 4 . 0 0 0

0 . 0 2 4 1 9 2 . 0 0 0

0 . 0 2 7 2 2 0 . 0 0 0

0 . 0 3 1 2 4 8 . 0 0 0

0 . 0 3 4 2 7 6 . 0 0 0

0 . 0 3 8 3 0 4 . 0 0 0

0 . 0 4 1 3 3 2 . 0 0 0

0 . 0 4 5 3 6 0 . 0 0 0

C l

- 0 . 1 8 6 9 8 9 1 I E 0 4

Q S P E E

0 . 0 0 0 8 5 6 0 4 1 9 . 0

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1 1 0 9 . 0 3 9 4 8 . 5

1 8 3 2 . 6 3 3 8 5 . 0

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1 . 0 0 0 0 2 0 . 0 0

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0 . 4 4 2 1 . 5 7 2

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0 . 7 7 3 1 . 0 3 8

0 . 7 3 1 0 . 9 2 2

0 . 6 7 9 0 . 8 2 2

0 . 6 2 4 0 . 7 3 5

0 . 5 7 0 - 0 . 6 5 8

0 . 5 1 8 0 . 5 8 9

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0 . 4 2 2 0 . 4 6 9

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0 . 0 4 5 3 6 0 . 0 0 0 1 2 8 8 . 3 1 4 0 7 . 3 0 . 5 1 3 0 . 5 6 0

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0 . 0 5 5 4 4 0 . 0 0 0 9 5 9 . 4 1 0 2 9 . 3 0 . 3 8 2 0 . 4 1 0

0 . 0 6 0 4 8 0 . 0 0 0 8 1 1 . 8 8 6 5 . 5 0 . 3 2 3 0 . 3 4 5

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0 . 0 7 5 5 9 9 . 9 9 9 4 2 2 . 9 4 4 5 . 2 0 . 1 6 8 0 . 1 7 7

0 . 0 8 0 6 3 9 . 9 9 9 3 0 8 . 4 3 2 3 . 7 0 . 1 2 3 0 . 1 2 9

0 . 0 8 5 6 7 9 . 9 9 9 2 0 0 . 1 2 0 9 . 5 0 . 0 8 0 0 . 0 8 3

0 . 0 9 0 7 1 9 . 9 9 9 9 7 . 5 1 0 1 . 8 0 . 0 3 9 0 . 0 4 1

0 . 0 9 5 7 5 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

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0 . 2 2 1 9 3 4 8 1 E 0 2 0 . 2 1 7 6 2 4 6 6 E 0 2 D . 1 9 4 2 0 7 8 6 E 0 1


1 1 0 9 . 0 0 . 0 0 0 1 2 5 0 . 0 0 0 8 5 6 0 4 1 9 . 0 1 . 0 0 0 0 6 . 6 0 7 . 8 0

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0 . 0 5 5 4 4 0 . 0 0 0 7 6 3 . 6 8 3 3 . 4 0 . 3 0 4 0 . 3 3 2

0 . 0 6 0 4 8 0 . 0 0 0 6 3 4 . 7 6 8 8 . 3 0 . 2 5 3 0 . 2 7 4

0 . 0 6 5 5 2 0 . 0 0 0 5 1 7 . 1 5 5 8 . 0 0 . 2 . 0 6 0 . 2 2 2

0 . 0 7 0 5 5 9 . 9 9 9 4 0 9 . 8 4 4 0 . 4 0 . 1 6 3 0 . 1 7 5

0 . 0 7 5 5 9 9 . 9 9 9 3 1 2 . 0 3 3 4 . 2 0 . 1 2 4 0 . 1 3 3

0 . 0 8 0 6 3 9 . 9 9 9 2 2 2 . 7 2 3 7 . 9 0 . 0 8 9 0 . 0 9 5

0 . 0 8 5 6 7 9 . 9 9 9 1 4 1 . 4 1 5 0 . 7 0 . 0 5 6 0 . 0 6 0

0 . 0 9 0 7 1 9 . 9 9 9 6 7 . 3 7 1 . 6 0 . 0 2 7 0 . 0 2 9

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C 2 D 2 R E

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R R / H I P K 1 P D I P R K I P R D

0 . 0 1 0 6 6 . 6 6 7 5 5 0 . 0 2 3 4 1 . 9 0 . 3 9 7 1 . 6 8 8

0 . 0 1 3 9 0 . 0 0 0 1 0 5 0 . 8 2 0 2 9 . 7 0 . 7 5 8 1 . 4 6 3

0 . 0 1 7 1 1 3 . 3 3 3 1 1 7 6 . 7 1 7 8 9 . 9 0 . 8 4 8 1 . 2 9 0

0 . 0 2 0 1 3 6 . 6 6 7 1 1 7 7 . 4 1 5 9 5 . 2 0 . 8 4 9 1 . 1 5 0

0 . 0 2 4 1 6 0 . 0 0 0 1 1 3 0 . 1 1 4 3 1 . 2 0 . 8 1 5 1 . 0 3 2

0 . 0 2 7 1 8 3 . 3 3 3 1 0 6 3 . 7 1 2 8 9 . 6 0 . 7 6 7 0 . 9 3 0

0 . 0 3 1 2 0 6 . 6 6 7 9 9 0 . 5 1 1 6 5 . 0 0 . 7 1 4 0 . 8 4 0

0 . 0 3 4 2 3 0 . 0 0 0 9 1 6 . 0 1 0 5 3 . 7 0 . 6 6 0 0 . 7 6 0

0 . 0 3 8 2 5 3 . 3 3 3 8 4 2 . 6 9 5 3 . 2 0 . 6 0 8 0 . 6 8 7

0 . 0 4 1 2 7 6 . 6 6 7 7 7 1 . 7 8 6 1 . 5 0 . 5 5 6 0 . 6 2 1

0 . 0 4 5 3 0 0 . 0 0 0 7 0 3 . 6 7 7 7 . 3 0 . 5 0 7 0 . 5 6 0

C l 0 1 Q K

- 0 . 1 0 3 3 6 9 1 2 E 0 4 - 0 . 2 4 1 3 2 6 7 3 E 0 4 0 . 8 1 1 8 5 7 4 0 E - 0 3

P P D R E

0 . 2 3 4 1 8 7 8 7 E 0 4 0 . 1 1 9 4 3 4 7 5 E 0 6


2 5 9 . 0 0 . 0 0 0 1 5 0 0 . 0 0 0 8 1 7 0 4 1 9 . 0 1 . 0 0 0 0 2 2 . 0 0


0 . 0 1 0 6 6 » 6 6 7 2 5 9 . 0 2 0 5 0 . 4 0 . 1 8 7 1 . 4 7 8

0 . 0 1 3 9 0 . 0 0 0 7 6 2 . 4 1 7 4 0 . 9 0 . 5 5 0 1 . 2 5 5

0 . 0 1 7 1 1 3 . 3 3 3 8 9 1 . 8 1 5 0 4 . 6 0 . 6 4 3 1 . 0 8 5

0 . 0 2 0 1 3 6 . 6 6 7 8 9 6 . 7 1 3 1 4 . 2 0 . 6 4 7 0 . 9 4 8

0 . 0 2 4 1 6 0 . 0 0 0 8 5 4 . 5 1 1 5 5 . 3 0 . 6 1 6 0 . 8 3 3

0 . 0 2 7 1 8 3 . 3 3 3 7 9 4 . 0 1 0 1 9 . 6 0 . 5 7 2 0 . 7 3 5

0 . 0 3 1 2 0 6 . 6 6 7 7 2 7 . 4 9 0 1 . 6 0 . 5 2 4 0 . 6 5 0

0 . 0 3 4 2 3 0 . 0 0 0 6 6 0 . 3 7 9 7 . 8 0 . 4 7 6 0 . 5 7 5

0 . 0 3 8 2 5 3 . 3 3 3 5 9 5 . 3 7 0 5 . 6 0 . 4 2 9 0 . 5 0 9

0 . 0 4 1 2 7 6 . 6 6 7 5 3 3 . 4 6 2 3 . 0 0 . 3 8 5 0 . 4 4 9

0 . 0 4 5 3 0 0 . 0 0 0 4 7 5 . 1 5 4 8 . 7 0 . 3 4 3 0 . 3 9 6

C l D l Q K

- 0 . 1 0 3 3 8 8 6 5 E 0 4 - 0 . 2 7 0 8 4 3 5 I E 0 4 0 . 8 1 2 0 1 1 0 7 E — 0 3

P P D R E

0 . 2 0 5 0 4 3 9 0 E 0 4 0 . 1 1 9 4 3 4 7 5 E 0 6

I 6 9


. 5 5 0 . 0 0 . 0 0 0 1 5 0 0 . 0 0 0 8 1 7 0 0 . 0 1 . 0 0 0 0 3 . 6 5 4 . 6 0

P D P E • P F PG P HP J P K T E S T 4 < 0 5

3 . 3 5 2 . 6 5 - 1 . 9 5 1 . 3 5

0 . 9 0 0 . 4 5 2 1 . 0


0 . 0 4 5 3 0 0 . 0 0 0 7 0 3 . 6 7 7 7 . 3 0 . 5 0 7 0 . 5 6 0

0 . 0 5 0 3 3 3 . 3 3 3 6 1 1 . 5 6 6 7 . 7 0 . 4 4 1 0 . 4 8 1

0 . 0 5 5 3 6 6 . 6 6 7 5 2 5 . 5 5 6 8 . 5 0 . 3 7 9 0 . 4 1 0

0 . 0 6 0 4 0 0 . 0 0 0 4 4 5 . 0 4 7 8 . 0 0 . 3 2 1 0 * 3 4 5

0 . 0 6 5 4 3 3 . 3 3 3 3 6 9 . 7 3 9 4 . 8 0 . 2 6 7 0 . 2 8 5

0 . 0 7 0 4 6 6 . 6 6 6 2 9 8 . 9 3 1 7 . 7 0 . 2 1 6 0 . 2 2 9

0 . 0 7 5 5 0 0 . 0 0 0 2 3 2 . 3 2 4 5 . 9 0 . 1 6 7 0 . 1 7 7

0 . 0 8 0 5 3 3 . 3 3 3 1 6 9 . 5 1 7 8 . 8 0 . 1 2 2 0 . 1 2 9

0 . 0 8 5 5 6 6 . 6 6 6 1 1 0 . 0 1 1 5 . 7 0 . 0 7 9 0 . 0 8 3

0 . 0 9 0 5 9 9 . 9 9 9 5 3 . 6 5 6 . 2 0 . 0 3 9 0 . 0 4 1

0 . 0 9 5 6 3 3 . 3 3 3 0 . 0 0 . 0 0 * 0 0 . 0 0 0

C 2 D 2 R E

- 0 . 1 0 3 3 6 9 1 2 E 0 4 - 0 . 2 4 1 3 2 7 1 7 E 0 4 0 * 1 1 9 4 3 4 7 5 E 0 6


0 . 1 1 9 4 9 7 1 3 E 0 2 0 . 1 1 9 2 1 7 9 8 E 0 2 0 . 2 3 3 6 0 3 8 9 E 0 0


2 5 9 . 0 0 . 0 0 0 1 5 0 0 . 0 0 0 8 1 7 0 4 1 9 . 0 1 . 0 0 0 0 2 * 6 0 3 . 6 0


3 . 1 5 2 . 5 0 1 . 9 0 1 . 3 5 0 . 8 8

0 . 5 2 0 . 3 0 2 2 . 0


0 . 0 4 5 3 0 0 . 0 0 0 4 7 5 . 1 5 4 8 . 7 0 . 3 4 3 0 . 3 9 6

0 . 0 5 0 3 3 3 . 3 3 3 3 9 8 . 6 4 5 4 . 6 0 . 2 8 7 0 * 3 2 8

0 . 0 5 5 3 6 6 . 6 6 7 3 2 9 . 6 3 7 2 . 6 0 . 2 3 8 0 . 2 6 9

0 . 0 6 0 4 0 0 * 0 0 0 2 6 7 . 9 3 0 0 . 9 0 . 1 9 3 0 * 2 1 7

0 . 0 6 5 4 3 3 . 3 3 3 2 1 3 . 0 2 3 8 . 0 0 . 1 5 4 0 * 1 7 2

0 . 0 7 0 4 6 6 . 6 6 6 1 6 4 . 3 1 8 3 . 0 0 . 1 1 8 0 . 1 3 2

0 . 0 7 5 5 0 0 . 0 0 0 1 2 1 . 3 1 3 4 . 9 0 . 0 8 7 0 . 0 9 7

0 . 0 8 0 5 3 3 . 3 3 3 8 3 . 8 9 3 . 0 0 . 0 6 0 0 . 0 6 7

0 . 0 8 5 5 6 6 . 6 6 6 5 1 . 3 5 6 . 9 0 . 0 3 7 0 . 0 4 1

0 . 0 9 0 5 9 9 . 9 9 9 2 3 . 4 2 6 . 0 0 . 0 1 7 0 . 0 1 9

0 . 0 9 5 6 3 3 . 3 3 3 - 0 . 0 0 . 0 - 0 . 0 0 0 0 . 0 0 0

C 2 D 2 R E

- 0 • 1 0 3 3 8 8 6 5 E 0 4 - 0 . 2 7 0 8 4 3 6 5 E 0 4 0 . 1 1 9 4 3 4 7 5 E 0 6


0 . 6 9 6 6 5 6 5 1 E 0 1 0 . 8 5 0 1 5 7 5 5 E 0 1 - 0 . 2 2 0 3 3 9 5 1 E 0 2 .4

1 7 0


; - 6 0 5 0 . 0 0 . 0 0 0 1 5 0 0 . 0 0 2 1 3 0 0 0 . 0 1 . 0 0 0 0 2 3 . 0 0


0 . 0 1 0 6 6 . 6 6 7 - 6 0 5 0 . 0 6 1 0 5 . 5 - 1 . 6 7 3 1 . 6 8 8

0 . 0 1 3 9 0 . 0 0 0 - 1 3 4 1 . 2 5 2 9 1 . 6 - 0 . 3 7 1 1 . 4 6 3

0 . 0 1 7 1 1 3 . 3 3 3 5 1 7 . 0 4 6 6 6 * 4 0 . 1 4 3 1 . 2 9 0

0 . 0 2 0 1 3 6 . 6 6 7 1 3 3 5 . 6 4 1 5 8 . 7 0 . 3 6 9 1 . 1 5 0

0 . 0 2 4 . 1 6 0 . 0 0 0 1 6 9 9 . 3 3 7 3 1 . 2 0 . 4 7 0 1 . 0 3 2

0 . 0 2 7 1 8 3 . 3 3 3 1 8 4 0 . 2 3 3 6 2 . 0 0 . 5 0 9 0 . 9 3 0

0 . 0 3 1 2 0 6 . 6 6 7 1 8 6 3 . 5 3 0 3 7 . 1 0 . 5 1 5 0 . 8 4 0

0 . 0 3 4 2 3 0 . 0 0 0 1 8 2 1 . 8 2 7 4 7 . 0 0 . 5 0 4 0 . 7 6 0

0 . 0 3 8 2 5 3 . 3 3 3 1 7 4 3 . 4 2 4 8 5 . 0 0 . 4 8 2 0 . 6 8 7

0 . 0 4 1 2 7 6 . 6 6 7 1 6 4 4 . 1 2 2 4 6 . 0 0 . 4 5 5 0 . 6 2 1

0 . 0 4 5 3 0 0 . 0 0 0 1 5 3 3 . 3 2 0 2 6 . 4 0 . 4 2 4 0 . 5 6 0

C l D 1 Q K

- 0 . 2 6 7 8 0 8 6 7 E 0 4 - 0 . 6 1 6 8 5 4 3 0 E 0 4 0 . 2 1 0 3 3 6 1 I E - 0 2 .

P P D R E

0 . 6 1 0 5 5 0 7 8 E 0 4 0 . 3 1 1 3 7 8 3 8 E 0 6


- 6 3 4 1 . 0 0 . 0 0 0 1 5 0 0 . 0 0 2 1 3 0 0 4 1 9 . 0 1 . 0 0 0 0 2 4 . 0 0


0 . 0 1 0 6 6 . 6 6 7 - 6 3 4 1 . 0 5 8 1 4 . 1 - 1 . 7 5 4 1 . 6 0 8

0 . 0 1 3 9 0 . 0 0 0 1 6 2 9 . 6 5 0 0 2 . 9 - 0 . 4 5 1 1 . 3 8 4

0 . 0 1 7 1 1 3 . 3 3 3 2 3 2 . 0 4 3 8 1 . 2 0 . 0 6 4 1 . 2 1 2

0 . 0 2 0 1 3 6 . 6 6 7 1 0 5 4 . 9 3 8 7 7 . 7 0 . 2 9 2 1 . 0 7 2

0 . 0 2 4 1 6 0 . 0 0 0 1 4 2 3 . 7 3 4 5 5 . 3 0 . 3 9 4 0 . 9 5 6

0 . 0 2 7 1 8 3 . 3 3 3 1 5 7 0 . 4 3 0 9 2 . 0 0 . 4 3 4 0 . 8 5 5

0 . 0 3 1 2 0 6 . 6 6 7 1 6 0 0 . 4 2 7 7 3 . 8 0 . 4 4 3 0 . 7 6 7

0 . 0 3 4 2 3 0 . 0 0 0 1 5 6 6 . 2 2 4 9 1 . 2 0 . 4 3 3 0 . 6 8 9

0 . 0 3 8 2 5 3 . 3 3 3 1 4 9 6 . 0 2 2 3 7 . 4 0 . 4 1 4 0 . 6 1 9

0 . 0 4 1 2 7 6 • 6 6 7 1 4 0 5 . 8 2 0 0 7 . 6 0 . 3 8 9 0 . 5 5 5

0 . 0 4 5 3 0 0 . 0 0 0 1 3 0 4 . 8 1 7 9 7 . 9 0 . 3 6 1 0 . 4 - 9 7

C l D 1 Q K

- 0 . 2 6 7 8 2 8 3 0 E 0 4 - 0 • 6 4 6 3 7 1 4 8 E 0 4 0 . 2 1 0 3 5 1 4 7 E - 0 2

PPD0 . 5 8 1 4 0 7 0 3 E 04

R E

D . 3 1 1 3 7 8 3 8 E 0 6

171


- 6 0 5 0 . 0 0 . 0 0 0 1 5 0 0 . 0 0 2 1 3 0 0 0 . 0 1 . 0 0 0 0 - 1 . 6 6 8 . 1 5


7 . 6 5 6 . 6 5 5 . 3 0 4 . 0 0 2 . 9 5

2 . 0 0 1 . 1 5 2 3 . 0


0 . 0 4 5 3 0 0 . 0 0 0 1 5 3 3 . 3 2 0 2 6 . 4 0 . 4 2 4 0 . 5 6 0

0 . 0 5 0 3 3 3 . 3 3 3 1 3 6 5 . 7 1 7 4 0 . 7 0 . 3 7 8 0 . 4 8 1

0 . 0 5 5 3 6 6 . 6 6 7 1 1 9 5 . 2 1 4 8 2 . 2 0 . 3 3 1 0 . 4 1 0

0 . 0 6 0 4 0 0 . 0 0 0 1 0 2 6 . 7 1 2 4 6 . 3 0 . 2 8 4 0 . 3 4 5

0 . 0 6 5 4 3 3 . 3 3 3 8 6 2 . 5 1 0 2 9 . 2 0 . 2 3 9 0 . 2 8 5

0 . 0 7 0 4 6 6 . 6 6 6 7 0 3 . 9 8 2 8 . 2 0 . 1 9 5 0 . 2 2 9

0 . 0 7 5 5 0 0 . 0 0 0 5 5 1 . 3 6 4 1 . 1 0 . 1 5 2 0 . 1 7 7

0 . 0 8 0 5 3 3 . 3 3 3 4 0 4 . 7 4 6 6 . 1 0 . 1 1 2 0 . 1 2 9

0 . 0 8 5 5 6 6 • 6 6 6 2 6 4 . 2 3 0 1 . 6 0 . 0 7 3 0 . 0 8 3

0 . 0 9 0 5 9 9 . 9 9 9 1 2 9 . 3 1 4 6 . 6 0 . 0 3 6 0 . 0 4 1

0 . 0 9 5 6 3 3 . 3 3 3 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 . D 2 R E j

- 0 . 2 6 7 8 0 8 6 7 E 0 4 - 0 . 6 1 6 8 5 4 6 9 E 0 4 0 . 3 1 1 3 7 8 3 8 E 0 6 !


0 . 2 0 2 6 7 4 4 1 E 0 2 0 , . 2 2 6 4 5 7 6 7 E 0 2 - 0 . 1 1 7 3 4 7 1 5 E 0 2i


- 6 3 4 1 . 0 0 . 0 0 0 1 5 0 0 . 0 0 2 1 3 0 0 4 1 9 . 0 1 . 0 0 0 0 - 2 . 7 0 7 . 1 0


6 . 7 0 5 . 8 0 4 . 5 5 3 . 5 0 2 . 4 5

1 . 5 5 0 . 7 5 2 4 . 0 —


0 . 0 4 5 3 0 0 . 0 0 0 1 3 0 4 . 8 1 7 9 7 . 9 0 . 3 6 1 0 . 4 9 7

0 . 0 5 0 3 3 3 . 3 3 3 1 1 5 2 . 8 1 5 2 7 . 6 0 . 3 1 9 0 . 4 2 2

0 . 0 5 5 3 6 6 * 6 6 7 9 9 9 . 4 1 2 8 6 . 3 0 . 2 7 6 0 . 3 5 6

0 . 0 6 0 4 0 0 . 0 0 0 8 4 9 . 7 1 0 6 9 . 1 0 . 2 3 5 0 . 2 9 6

0 . 0 6 5 4 3 3 . 3 3 3 7 0 5 . 9 8 7 2 . 4 0 . 1 9 5 0 . 2 4 1

0 . 0 7 0 4 6 6 • 6 6 6 5 6 9 . 3 6 9 3 . 5 0 . 1 5 7 0 . 1 9 2

0 . 0 7 5 5 0 0 . 0 0 0 4 4 0 . 3 5 3 0 . 1 0 . 1 2 2 0 . 1 4 7

0 . 0 8 0 5 3 3 . 3 3 3 3 1 9 . 0 3 8 0 . 3 0 . 0 8 8 0 . 1 0 5

0 . 0 8 5 5 6 6 . 6 6 6 2 0 5 . 4 2 4 2 . 9 0 . 0 5 7 0 . 0 6 7

0 . 0 9 0 5 9 9 . 9 9 9 9 9 . 1 1 1 6 . 4 0 . 0 2 7 0 . 0 3 2

0 . 0 9 5 6 3 3 . 3 3 3 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

- 0 . 2 6 7 8 2 8 3 0 E 0 4 - 0 • 6 4 6 3 7 1 4 8 E 0 4 0 . 3 1 1 3 7 8 3 8 E 0 6

THRUST THRUST X PDT0 . 1 5 2 8 4 2 5 7 E 02 0 . 1 8 7 30225E 02 - 0 . 2 2 5 4 5 8 5 3 E 02

1 7 2


. 1 9 0 0 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 5 8 7 0 0 . 0 1 . 6 6 7 5 2 5 . 0 0


0 . 0 1 0 1 0 0 . 0 0 0 1 9 0 0 . 0 2 7 0 3 . 1 0 . 5 6 5 0 . 8 0 4

0 . 0 1 3 1 3 5 . 0 0 0 2 0 7 6 . 1 2 5 3 9 . 8 0 . 6 1 7 0 . 7 5 5

0 . 0 1 7 1 7 0 . 0 0 0 2 1 0 3 . 3 2 4 1 4 . 4 0 . 6 2 5 0 . 7 1 8

0 . 0 2 0 2 0 5 . 0 0 0 2 0 8 2 . 9 2 3 1 2 . 5 0 . 6 1 9 0 . 6 8 8

0 . 0 2 4 2 4 0 . 0 0 0 2 0 4 5 . 7 2 2 2 6 . 8 0 . 6 0 8 0 . 6 6 2

0 . 0 2 7 2 7 5 . 0 0 0 2 0 0 3 . 0 2 1 5 2 . 7 0 . 5 9 6 0 . 6 4 0

0 . 0 3 1 3 1 0 . 0 0 0 1 9 5 9 . 2 2 0 8 7 . 6 0 . 5 8 3 0 . 6 2 1

0 . 0 3 4 3 4 5 . 0 0 0 1 9 1 6 . 3 2 0 2 9 . 4 0 . 5 7 0 0 . 6 0 3

0 . 0 3 8 3 8 0 . 0 0 0 1 8 7 5 . 0 1 9 7 6 . 8 0 . 5 5 7 0 . 5 8 8

0 . 0 4 1 4 1 5 . 0 0 0 1 8 3 5 . 6 1 9 2 8 . 9 0 . 5 4 6 0 . 5 7 4

0 . 0 4 5 4 5 0 . 0 0 0 1 7 9 8 . 2 1 8 8 4 . 8 0 . 5 3 5 0 . 5 6 0

C l D 1 Q K

—0 . 5 4 2 1 1 2 7 9 E 0 3 0 . 1 5 4 1 3 8 6 7 E 0 3 0 . 5 8 4 9 2 7 3 9 E - 0 3

P P D

0 . 2 7 0 3 0 7 6 9 E 0 4

R E

7 7 1 9 2 0 0 0 E 0 5

P

1 6 0 9

H

. 0 0 . 0 0 0 1 0 0

Q

0 . 0 0 0 5 8 7 0

S P E E

4 1 9 . 0

A L P H A T E S T

1 . 6 6 7 5 2 6 . 0 0


0 . 0 1 0 1 0 0 . 0 0 0 1 6 0 9 . 0 2 4 1 1 . 6 0 . 4 7 8 0 . 7 1 7

0 . 0 1 3 1 3 5 . 0 0 0 1 7 8 7 . 7 2 2 5 1 . 1 0 . 5 3 2 0 . 6 6 9

0 . 0 1 7 1 7 0 . 0 0 0 1 8 1 8 . 4 2 1 2 9 . 1 0 . 5 4 1 0 . 6 3 3

0 . 0 2 0 2 0 5 . 0 0 0 1 8 0 2 . 3 2 0 3 1 . 6 0 . 5 3 6 0 . 6 0 4

0 . 0 2 4 2 4 0 . 0 0 0 1 7 7 0 . 2 1 9 5 0 . 9 0 . 5 2 6 0 . 5 8 0

0 . 0 2 7 2 7 5 . 0 0 0 1 7 3 3 . 3 1 8 8 2 . 7 0 . 5 1 5 0 . 5 6 0

0 . 0 3 1 3 1 0 . 0 0 0 1 6 9 6 . 2 1 8 2 4 . 2 0 . 5 0 4 0 . 5 4 2

0 . 0 3 4 3 4 5 . 0 0 0 1 6 6 0 . 7 1 7 7 3 . 5 0 . 4 9 4 0 . 5 2 7

0 . 0 3 8 3 8 0 . 0 0 0 1 6 2 7 . 7 1 7 2 9 * 2 0 . 4 8 4 0 . 5 1 4

0 . 0 4 1 4 1 5 . 0 0 0 1 5 9 7 . 4 1 6 9 0 . 4 0 . 4 7 5 0 . 5 0 3

0 . 0 4 5 4 5 0 . 0 0 0 1 5 6 9 . 9 1 6 5 6 . 2 0 . 4 6 7 0 . 4 9 2

C l

0 • 5 4 2 2 0 1 1 7 E 0 3 - 0 ,D 1

1 4 0 5 3 3 6 9 E 0 3

QK0 . 5 8 5 0 2 3 Q 8 E - 0 3

PPD0 . 2 4 1 1 6 3 7 0 E 04

R E

0 . 7 7 1 9 2 O O O E 0 5

1 7 3


1 9 0 0 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 5 8 7 0 0 . 0 1 . 6 6 7 5 7 . 5 9 7 . 8 2

P J P K T E S T P D P E • P F PG PH

7 . 5 6 7 . 1 0 6 . 2 0 4 • 6 0 3 . 3 2

2 . 0 5 0 . 9 5 2 5 . 0

R R / H □ P K O P D O P R K O P R D

0 . 0 4 - 5 4 5 0 . 0 0 0 1 7 9 8 . 2 1 8 8 4 . 8 0 . 5 3 5 0 . 5 6 0

0 . 0 5 0 5 0 0 . 0 0 0 1 5 5 3 . 0 1 6 1 9 . 0 0 . 4 6 2 0 . 4 8 1

0 . 0 5 5 5 5 0 . 0 0 0 1 3 2 7 . 9 1 3 7 8 . 6 0 . 3 9 5 0 . 4 1 0

0 . 0 6 0 6 0 0 . 0 0 0 1 1 2 0 . 2 1 1 5 9 . 1 0 . 3 3 3 0 . 3 4 5

0 . 0 6 5 6 4 9 . 9 9 9 9 2 7 . 6 9 5 7 . 2 0 . 2 7 6 0 . 2 8 5

0 . 0 7 0 6 9 9 , 9 9 9 7 4 8 . 1 7 7 0 . 3 0 . 2 2 2 0 . 2 2 9

0 . 0 7 5 7 4 9 . 9 9 9 5 8 0 . 2 5 9 6 . 3 0 . 1 7 3 0 . 1 7 7

0 . 0 8 0 7 9 9 . 9 9 9 4 2 2 . 5 4 3 3 . 5 0 . 1 2 6 0 . 1 2 9

0 . 0 8 5 8 4 9 . 9 9 9 2 7 3 . 8 2 8 0 . 6 0 . 0 8 1 0 . 0 8 3

0 . 0 9 0 8 9 9 . 9 9 9 1 3 3 . 3 1 3 6 . 4 0 . 0 4 0 0 . 0 4 1

0 . 0 9 5 9 4 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0.000

C 2 D 2 R E

- 0 . 2 5 1 3 5 4 4 9 E 0 4 - 0 • 5 8 9 3 4 4 9 2 E 19 4 0 . 1 2 8 7 1 7 6 3 E 0 6- - - -


0 . 2 7 5 8 7 6 3 I E 0 2 0 . 2 5 8 1 7 3 9 8 E 0 2 0 . 6 4 1 6 7 6 3 3 E 0 1


1 6 0 9 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 5 8 7 0 4 1 9 . 0 1 . 6 6 7 5 6 . 6 4

0000.o

P J P K T E S T P D P E P F Pr*U P H

6 . 5 6 6 . 1 5 5 . 1 5 3 . 9 0 2 . 6 0

1 . 6 0 0 . 7 2 2 6 . 0 -


0 . 0 4 5 4 5 0 . 0 0 0 1 5 6 9 . 9 1 6 5 6 . 2 0 . 4 6 7 0 . 4 9 2

0 . 0 5 0 5 0 0 . 0 0 0 1 3 4 0 . 2 1 4 0 6 . 0 0 . 3 9 8 0 . 4 1 8

0 . 0 5 5 5 5 0 . 0 0 0 1 1 3 2 . 2 1 1 8 2 . 7 0 . 3 3 7 0 . 3 5 2

0 . 0 6 0 6 0 0 . 0 0 0 9 4 3 . 2 9 8 2 . 0 0 . 2 8 0 0 . 2 9 2

0 . 0 6 5 6 4 9 . 9 9 9 7 7 1 . 0 8 0 0 . 5 0 . 2 2 9 0 . 2 3 8

0 . 0 7 0 6 9 9 . 9 9 9 6 1 3 . 5 6 3 5 . 6 0 . 1 8 2 0 . 1 8 9

0 . 0 7 5 7 4 9 . 9 9 9 4 6 9 . 3 4 8 5 . 3 0 . 1 4 0 0 . 1 4 4

0 . 0 8 0 7 9 9 . 9 9 9 3 3 6 . 3 3 4 7 . 8 0 . 1 0 0 0 . 1 0 3

0 . 0 8 5 8 4 9 . 9 9 9 2 1 5 . 1 2 2 1 . 8 0 . 0 6 4 0 . 0 6 6

0 . 0 9 0 8 9 9 . 9 9 9 1 0 3 . 1 1 0 6 . 2 0 . 0 3 1 0 . 0 3 2

0 . 0 9 5 9 4 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 0,

0 . 0 0 0

C 2 D 2 R E

- 0 . 2 5 1 3 9 5 4 6 E 0 4 - 0 . 6 1 8 9 1 1 7 2 E 0 4 0 . 1 2 8 7 1 7 6 3 E 0 6

THRUST THRUST X PDT0« 2260 6659E 02 0 . 2 1 4 7 6 1 9 6 E 02 0 . 5 0 0 0 5 7 3 2 E 01

1 7 4


• 2 2 4 0 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 8 3 1 0 0 . 0 1 . 6 6 7 5 2 7 . 0 0


0 . 0 1 0 1 0 0 . 0 0 0 2 2 4 0 . 0 3 8 2 6 . 7 0 . 4 7 0 0 . 8 0 4

0 . 0 1 3 1 3 5 . 0 0 0 2 6 8 7 . 6 3 5 9 5 . 5 0 . 5 6 4 0 . 7 5 5

0 . 0 1 7 1 7 0 . 0 0 0 2 8 1 4 . 8 3 4 1 8 . 0 0 . 5 9 1 0 . 7 1 8

0 . 0 2 0 2 0 5 . 0 0 0 2 8 3 3 . 0 3 2 7 3 . 8 0 . 5 9 5 0 . 6 8 8

0 . 0 2 4 2 4 0 . 0 0 0 2 8 0 8 . 3 3 1 5 2 . 4 0 . 5 9 0 0 . 6 6 2

0 . 0 2 7 2 7 5 . 0 0 0 2 7 6 5 . 6 3 0 4 7 . 6 0 . 5 8 1 0 . 6 4 0

0 . 0 3 1 3 1 0 . 0 0 0 2 7 1 5 . 7 2 9 5 5 . 3 0 . 5 7 0 0 . 6 2 1

0 . 0 3 4 3 4 5 . 0 0 0 2 6 6 3 . 3 2 8 7 2 . 9 0 . 5 5 9 0 . 6 0 3

0 . 0 3 3 3 8 0 . 0 0 0 2 6 1 1 . 1 2 7 9 8 . 5 0 . 5 4 8 0 . 5 8 8

0 . 0 4 1 4 1 5 . 0 0 0 2 5 6 0 . 0 2 7 3 0 . 6 0 . 5 3 8 0 . 5 7 4

0 . 0 4 5 4 5 0 . 0 0 0 2 5 1 0 . 6 2 6 6 8 . 3 0 . 5 2 7 0 . 5 6 0

C l

- 0 . 7 7 0 9 1 3 3 3 E 0 3

D 1

0 . 1 9 4 2 3 6 0 8 E 0 3

Q K

0 . 8 3 1 7 9 8 4 2 E - 0 3

P P D R E

0 . 3 8 2 6 6 7 3 6 E 0 4 0 • 1 0 9 2 7 8 6 3 E 0 6

P

1 9 4 9

H

. 0 0 . 0 0 0 1 0 0

Q

0 . 0 0 0 8 3 1 0

S P E E

4 1 9 . 0

A L P H A T E S T

1 . 6 6 7 5 2 8 . 0 0


0 . 0 1 0 1 0 0 . 0 0 0 1 9 4 9 . 0 3 5 3 5 . 2 0 . 4 0 9 0 . 7 4 2

0 . 0 1 3 1 3 5 . 0 0 0 2 3 9 9 . 3 3 3 0 6 . 8 0 . 5 0 4 0 . 6 9 5

0 . 0 1 7 1 7 0 . 0 0 0 2 5 2 9 . 9 3 1 3 2 . 7 0 . 5 3 1 0 . 6 5 8

0 . 0 2 0 2 0 5 . 0 0 0 2 5 5 2 . 4 2 9 9 2 . 8 0 . 5 3 6 0 . 6 2 9

0 . 0 2 4 2 4 0 . 0 0 0 2 5 3 2 . 8 2 8 7 6 . 5 0 . 5 3 2 0 . 6 0 4

0 . 0 2 7 2 7 5 . 0 0 0 2 4 9 6 . 0 2 7 7 7 . 6 0 . 5 2 4 0 . 5 8 3

0 . 0 3 1 3 1 0 . 0 0 0 2 4 5 2 . 7 2 6 9 2 . 0 0 . 5 1 5 0 . 5 6 5

0 . 0 3 4 3 4 5 . 0 0 0 2 4 0 7 . 3 2 6 1 7 . 1 0 . 5 0 6 0 . 5 5 0

0 . 0 3 8 3 8 0 . 0 0 0 2 3 6 3 . 8 2 5 5 0 . 9 0 . 4 9 6 0 . 5 3 6

0 . 0 4 1 4 1 5 . 0 0 0 2 3 2 1 . 8 2 4 9 2 . 2 0 . 4 8 8 0 . 5 2 3

0 . 0 4 5 4 5 0 . 0 0 0 . 2 2 8 2 . 3 2 4 3 9 . 7 0 . 4 7 9 0 . 5 1 2

C l

- 0 . 7 7 1 0 0 1 4 6 E 0 3

D 1

- 0 • 1 0 0 4 3 6 2 8 E 0 3

' Q K

0 . 8 3 1 8 9 3 4 1 E - 0 3

P P D R E

0 . 3 5 3 5 2 3 3 4 E 0 4 0 . 1 0 9 2 7 8 6 3 E 0 6

1 7 5

P H Q S P E E A L P H A P B PC

. • ■ 2 2 4 0 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 8 3 1 0 0 . 0 1 . 6b 7 5 1 0 . 0 9 1 1 . 0 0

P J P K T E S T P D P E P F P G P H1 0 . 7 0 1 0 . 1 8 8 . 8 5 6 . 5 0 4 . 8 0

3 . 0 0 1 . 3 8 2 7 . 0


0 . 0 4 5 4 5 0 . 0 0 0 2 5 1 0 . 6 2 6 6 8 . 3 0 . 5 2 7 0 . 5 6 0

0 . 0 5 0 5 0 0 . 0 0 0 2 1 7 3 . 3 2 2 9 2 . 0 0 . 4 5 6 0 . 4 8 1

0 . 0 5 5 5 5 0 . 0 0 0 1 8 6 1 . 6 1 9 5 1 . 7 0 . 3 9 1 0 . 4 1 0

0 . 0 6 0 6 0 0 . 0 0 0 1 5 7 2 . 7 1 6 4 1 • 0 0 . 3 3 0 0 . 3 4 5

0 . 0 6 5 6 4 9 . 9 9 9 1 3 0 3 . 8 1 3 5 5 . 1 0 . 2 7 4 0 . 2 8 5

0 . 0 7 0 6 9 9 . 9 9 9 1 0 5 2 . 5 1 0 9 0 . 5 0 . 2 2 1 0 . 2 2 9

0 . 0 7 5 7 4 9 . 9 9 9 8 1 6 . 9 8 4 4 . 1 0 . 1 7 2 0 . 1 7 7

0 . 0 8 0 7 9 9 . 9 9 9 5 9 5 . 2 6 1 3 . 7 0 . 1 2 5 0 . 1 2 9

0 . 0 8 5 8 4 9 . 9 9 9 3 8 6 . 0 3 9 7 . 2 0 . 0 8 1 0 . 0 8 3

0 . 0 9 0 8 9 9 . 9 9 9 1 8 8 . 0 1 9 3 . 1 0 . 0 3 9 0 . 0 4 1

0 . 0 9 5 9 4 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

- 0 . 3 5 7 4 3 9 5 0 E 0 4 - 0 e 8 3 6 7 3 3 9 8 E 0 4 0 . 1 8 2 2 2 2 0 6 E 0 6


0 . 3 8 2 4 7 9 2 5 E 0 2 0 . 3 6 7 8 6 1 9 4 E 0 2 0 . 3 8 2 1 7 2 5 8 E 0 1 '


1 9 4 9 . 0 0 . 0 0 0 1 0 0 0 . 0 0 0 8 3 1 0 4 1 9 . 0 1 . 6 6 7 5 8 . 9 4 9 . 8 5

P J P K T E S T< P D

9 . 5 4

P E

9 . 0 5

P F PG

7 . 7 5 5 . 6 5

P H

4 . 0 0

2 . 5 2 1 . 2 0 2 8 . 0


0 . 0 4 5 4 5 0 . 0 0 0 2 2 8 2 . 3 2 4 3 9 . 7 0 . 4 7 9 0 . 5 1 2

0 . 0 5 0 5 0 0 . 0 0 0 1 9 6 0 . 5 2 0 7 9 . 0 0 . 4 1 2 0 . 4 3 7

0 . 0 5 5 5 5 0 . 0 0 0 1 6 6 5 . 9 1 7 5 5 . 8 0 . 3 5 0 0 . 3 6 9

0 . 0 6 0 6 0 0 . 0 0 0 1 3 9 5 . 7 1 4 6 3 . 8 0 . 2 9 3 0 . 3 0 7

0 . 0 6 5 6 4 9 . 9 9 9 - 1 1 4 7 . 2 1 1 9 8 . 4 0 . 2 4 1 O c 2 5 2

0 . 0 7 0 6 9 9 . 9 9 9 9 1 8 . 0 9 5 5 . 8 0 . 1 9 3 0 . 2 0 1

0 . 0 7 5 7 4 9 . 9 9 9 . 7 0 6 . 0 7 3 3 . 1 0 . 1 4 8 0 . 1 5 4

0 . 0 8 0 7 9 9 . 9 9 9 5 0 9 . 6 5 2 8 . 0 0 . 1 0 7 0 . 1 1 1

0 . 0 8 5 8 4 9 . 9 9 9 3 2 7 . 3 3 3 8 . 4 0 . 0 6 9 0 . 0 7 1

0 . 0 9 0 8 9 9 . 9 9 9 1 5 7 . 8 1 6 2 . 9 0 . 0 3 3 0 . 0 3 4

0 . 0 9 5 9 4 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 0 0 . 0 0 0

C 2 D 2 R E

- 0 • 3 5 7 4 8 0 3 7 E 0 4 - 0 . 8 6 6 3 0 0 3 9 E 0 4 0 . 1 8 2 2 2 2 0 6 E 0 6

THRUST THRUST X PDT0 . 3 3 2 6 6 9 5 3 E 02 0 . 3 2 0 3 4 4 2 4 E 02 0 . 3 7 0 4 9 6 3 7 E 01


6 5 5 . 0 0 . 0 0 0 1 2 5 0 . 0 0 1 1 7 0 0 0 . 0 1 * 5 3 3 4 2 9 . 0 0


0 . 0 1 0 8 0 . 0 0 0 6 5 5 . 0 2 9 9 7 . 3 0 . 1 9 1 0 . 8 7 3

0 . 0 1 3 1 0 8 . 0 0 0 1 4 5 8 . 9 2 7 8 3 . 1 0 . 4 2 5 0 . 8 1 1

0 . 0 1 7 1 3 6 . 0 0 0 1 7 5 1 . 4 2 6 1 8 . 5 0 . 5 1 0 0 . 7 6 3

0 . 0 2 0 1 6 4 . 0 0 0 1 8 6 1 . 3 2 4 8 4 . 8 0 . 5 4 2 0 . 7 2 4

0 . 0 2 4 1 9 2 . 0 0 0 1 8 9 3 . 8 2 3 7 2 . 3 0 . 5 5 2 0 . 6 9 1

0 . 0 2 7 2 2 0 . 0 0 0 1 8 8 9 . 8 2 2 7 5 . 1 0 . 5 5 1 0 . 6 6 3

0 . 0 3 1 2 4 8 . 0 0 0 1 8 6 7 . 6 2 1 8 9 . 5 0 . 5 4 4 0 . 6 3 8

0 . 0 3 4 2 7 6 . 0 0 0 1 8 3 6 . 3 2 1 1 3 . 2 0 . 5 3 5 0 . 6 1 6

0 . 0 3 8 3 0 4 . 0 0 0 1 8 0 0 . 5 2 0 4 4 . 2 0 . 5 2 5 0 . 5 9 6

0 . 0 4 1 3 3 2 . 0 0 0 1 7 6 2 . 7 1 9 8 1 . 3 0 . 5 1 4 0 . 5 7 7

0 . 0 4 5 3 6 0 . 0 0 0 1 7 2 4 . 4 1 9 2 3 . 5 0 . 5 0 2 0 . 5 6 0

C l D l Q K

- 0 • 7 1 5 5 1 7 5 8 E 0 3 - 0 . 3 8 3 0 3 4 4 2 E 0 3 0 . 1 1 7 2 5 5 0 7 E - 0 2

P P D R E

0 ® 2 9 9 7 3 1 7 9 E 0 4 0 . 1 3 3 8 5 0 6 9 E 0 6

P hi Q S P E E A L P H A T E S T

3 6 4 . 0 0 . 0 0 0 1 2 5 0 . 0 0 1 1 7 0 0 4 1 9 . 0 1 . 5 3 3 4 3 0 . 0 0


0 . 0 1 0 8 0 . 0 0 0 3 6 4 . 0 2 7 0 5 . 9 0 . 1 0 6 0 . 7 8 8

0 . 0 1 3 1 0 8 . 0 0 0 1 1 7 0 . 5 2 4 9 4 . 3 0 . 3 4 1 0 . 7 2 7

0 . 0 1 7 1 3 6 . 0 0 0 1 4 6 6 . 5 2 3 3 3 . 2 0 . 4 2 7 0 . 6 8 0

0 . 0 2 0 1 6 4 . 0 0 0 1 5 8 0 . 7 2 2 0 3 . 8 0 . 4 6 1 0 . 6 4 2

0 . 0 2 4 1 9 2 . 0 0 0 1 6 1 8 . 2 2 0 9 6 . 4 0 . 4 7 1 0 . 6 1 1

0 . 0 2 7 2 2 0 . 0 0 0 1 6 2 0 . 1 2 0 0 5 . 1 0 . 4 7 2 0 . 5 8 4

0 . 0 3 1 2 4 8 . 0 0 0 1 6 0 4 . 6 1 9 2 6 . 2 0 . 4 6 8 0 . 5 6 1

0 . 0 3 4 2 7 6 . 0 0 0 1 5 8 0 . 8 1 8 5 7 . 3 0 . 4 6 1 0 . 5 4 1

0 . 0 3 8 3 0 4 . 0 0 0 1 5 5 3 . 3 1 7 9 6 . 6 0 . 4 5 3 0 . 5 2 3

0 . 0 4 1 3 3 2 . 0 0 0 1 5 2 4 - 6 1 7 4 2 . 8 0 . 4 4 4 0 . 5 0 8

0 . 0 4 5 3 6 0 . 0 0 0 1 4 9 6 . 1 1 6 9 4 . 9 0 . 4 3 6 0 . 4 9 4

C l D l Q K

- 0 . 7 1 5 6 2 2 0 7 E 0 3 - 0 * 6 7 7 7 8 1 4 9 E 0 3 0 . 1 1 7 2 7 2 2 3 E - 0 2

P P D R E

0 . 2 7 0 5 8 7 7 7 E 0 4 0 . 1 3 3 8 5 0 6 9 E 0 6

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P J P K T E S T . P D P E P F P G ■ PH

6 . 8 5 6 . 4 2 5 . 2 5 4 . 1 0 3 . 0 2

1 . 9 2 0 . 9 4 2 9 . 0


0 . 0 4 5 3 6 0 . 0 0 0 1 7 2 4 . 4 1 9 2 3 . 5 0 . 5 0 2 0 . 5 6 0

0 . 0 5 0 4 0 0 . 0 0 0 1 5 0 2 . 4 1 6 5 2 . 2 0 . 4 3 8 0 . 4 8 1

0 . 0 5 5 4 4 0 . 0 0 0 1 2 9 3 . 3 1 4 0 6 . 9 0 . 3 7 7 0 . 4 1 0

0 . 0 6 0 4 8 0 . 0 0 0 1 0 9 6 . 9 1 1 8 2 . 9 0 . 3 2 0 0 . 3 4 5

0 . 0 6 5 5 2 0 . 0 0 0 9 1 2 . 2 9 7 6 . 9 0 . 2 6 6 0 . 2 8 5

0 . 0 7 0 5 5 9 . 9 9 9 7 3 8 . 3 7 8 6 . 1 0 . 2 1 5 0 . 2 2 9

0 . 0 7 5 5 9 9 . 9 9 9 5 7 4 . 3 6 0 8 . 5 0 . 1 6 7 0 . 1 7 7

0 . 0 8 0 6 3 9 . 9 9 9 4 1 9 . 2 4 4 2 . 4 0 . 1 2 2 0 . 1 2 9

0 . 0 8 5 6 7 9 . 9 9 9 2 7 2 . 3 2 8 6 . 3 0 . 0 7 9 0 . 0 8 3

0 . 0 9 0 7 1 9 . 9 9 9 1 3 2 . 8 1 3 9 . 2 0 . 0 3 9 0 . 0 4 1

0 . 0 9 5 7 5 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 0 0 . 0 0 0

C 2 D 2 R E

- 0 . 2 5 7 9 8 0 0 8 E 0 4 - 0 . 6 0 1 3 7 3 0 5 E 0 4 0 • 2 0 5 2 4 6 5 6 E 0 6


0 • 2 5 9 0 5 3 6 5 E 0 2 0 • 2 2 8 0 2 0 9 4 E 0 2 0 . 1 1 9 7 9 2 6 I E 0 2


3 6 4 . 0 0 . 0 0 0 1 2 5 0 . 0 0 1 1 7 0 0 4 1 9 . 0 1 . 5 3 3 4 4 . 2 4 6 . 0 6

P J P K T E S T P D P E P F P G PH

6 . 0 6 5 . 9 0 4 . 9 0 3 . 5 0 2 . 4 2

1 . 5 0 0 . 6 8 3 0 . 0


0 . 0 4 5 3 6 0 . 0 0 0 1 4 9 6 . 1 1 6 9 4 . 9 0 . 4 3 6 0 . 4 9 4

0 . 0 5 0 4 0 0 . 0 0 0 1 2 8 9 . 6 1 4 3 9 . 2 0 . 3 7 6 0 . 4 1 9

0 . 0 5 5 4 4 0 . 0 0 0 1 0 9 7 . 6 1 2 1 1 . 0 0 . 3 2 0 0 . 3 5 3

0 . 0 6 0 4 8 0 . 0 0 0 9 1 9 . 9 1 0 0 5 . 8 0 . 2 6 8 0 . 2 9 3

0 . 0 6 5 5 2 0 . 0 0 0 7 5 5 . 6 8 2 0 . 1 0 . 2 2 0 0 . 2 3 9

0 . 0 7 0 5 3 9 . 9 9 9 6 0 3 . 7 6 5 1 . 4 0 . 1 7 6 0 . 1 9 0

0 . 0 7 5 5 9 9 . 9 9 9 4 6 3 . 4 4 9 7 . 5 0 . 1 3 5 0 . 1 4 5

0 . 0 8 0 6 3 9 . 9 9 9 3 3 3 . 6 3 5 6 . 7 0 . 0 9 7 0 . 1 0 4

0 . 0 8 5 6 7 9 . 9 9 9 2 1 3 . 6 2 2 7 . 5 0 . 0 6 2 0 . 0 6 6

0 . 0 9 0 7 1 9 . 9 9 9 1 0 2 . 6 1 0 9 . 0 0 . 0 3 0 0 . 0 3 2

0 . 0 9 5 7 5 9 . 9 9 9 0 . 0 0 . 0 0 . 0!

0 . 0 0 0

C 2 D 2 R E

- 0 . 2 5 8 0 1 7 7 5 E 0 4 - 0 . 6 3 0 9 3 2 0 3 E 0 4 0 • 2 0 5 2 4 6 5 6 E 0 6


0 . 2 0 9 2 4 0 1 I E 0 2 0 . 1 9 6 5 1 1 9 9 E 0 2 0 . 6 0 8 3 0 2 0 2 E 0 1

1 7 8


: - 1 0 1 0 . 0 0 . 0 0 0 1 2 5 0 . 0 0 1 8 3 5 0 0 . 0 1 . 5 3 3 4 3 1 . 0 0

R R / H I P K I P D I P R K , I P R D

0 . 0 1 0 8 0 . 0 0 0 • 1 0 1 0 . 0 4 7 0 0 . 9 - 0 . 1 8 8 0 . 8 7 3

0 . 0 1 3 1 0 8 . 0 0 0 1 1 5 4 . 8 4 3 6 4 . 9 0 . 2 1 5 0 . 8 1 1

0 . 0 1 7 1 3 6 . 0 0 0 2 0 1 8 . 2 4 1 0 6 . 7 0 . 3 7 5 0 . 7 6 3

0 . 0 2 0 1 6 4 . 0 0 0 2 4 0 5 . 6 3 8 9 7 . 1 0 . 4 4 7 0 . 7 2 4

0 . 0 2 4 1 9 2 . 0 0 0 2 5 8 3 . 8 3 7 2 0 . 6 0 . 4 8 0 0 . 6 9 1

0 . 0 2 7 2 2 0 . 0 0 0 2 6 5 8 . 9 3 5 6 8 . 2 0 . 4 9 4 0 . 6 6 3

0 . 0 3 1 2 4 8 . 0 0 0 2 6 7 9 . 3 3 4 3 4 . 0 0 . 4 9 8 0 . 6 3 8

0 . 0 3 4 2 7 6 . 0 0 0 2 6 6 9 . 1 3 3 1 4 . 2 0 . 4 9 6 0 . 6 1 6

0 . 0 3 8 3 0 4 . 0 0 0 2 6 4 1 . 3 3 2 0 6 . 0 0 . 4 9 1 0 . 5 9 6

0 . 0 4 1 3 3 2 . 0 0 0 2 6 0 3 . 3 3 1 0 7 . 4 0 . 4 8 4 0 . 5 7 7

0 . 0 4 5 3 6 0 . 0 0 0 2 5 5 9 . 6 3 0 1 6 . 7 0 . 4 7 5 0 . 5 6 0

C l

■ 0 • 1 1 3 5 6 7 0 2 E 0 4

0 1

• 0 • 6 8 8 0 6 6 4 1 E 0 3

Q K

0 . 1 8 6 1 0 7 4 2 E - 0 2

P P D

0 . 4 7 0 0 9 2 1 9 E 0 4

R E

2 0 9 9 2 8 1 9 E 0 6

P

- 1 3 0 1

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0 . 0 0 1 8 3 5 0 4 1 9 . 0

A L P H A T E S T

1 . 5 3 3 4 3 2 . 0 0


0 . 0 1 0 8 0 . 0 0 0 - 1 3 0 1 . 0 4 4 0 9 . 5 - 0 . 2 4 2 0 . 8 1 9

0 . 0 1 3 1 0 8 . 0 0 0 8 6 6 . 4 4 0 7 6 . 1 0 . 1 6 1 0 . 7 5 7

0 . 0 1 7 1 3 6 . 0 0 0 1 7 3 3 . 3 3 8 2 1 . 5 0 . 3 2 2 0 . 7 1 0

0 . 0 2 0 1 6 4 . 0 0 0 2 1 2 4 . 9 3 6 1 6 . 1 0 . 3 9 5 0 . 6 7 2

0 . 0 2 4 1 9 2 . 0 0 0 2 3 0 8 . 2 3 4 4 4 . 7 0 . 4 2 9 0 . 6 4 0

0 . 0 2 7 2 2 0 . 0 0 0 2 3 8 9 . 2 3 2 9 8 . 2 0 . 4 4 4 0 . 6 1 3

0 . 0 3 1 2 4 8 . 0 0 0 2 4 1 6 . 3 3 1 7 0 . 7 0 . 4 4 9 0 . 5 8 9

0 . 0 3 4 2 7 6 . 0 0 0 2 4 1 3 . 5 3 0 5 8 . 4 0 . 4 4 8 0 . 5 6 8

0 . 0 3 8 3 0 4 . 0 0 0 2 3 9 4 . 0 2 9 5 8 . 5 0 . 4 4 5 0 . 5 5 0

0 . 0 4 1 3 3 2 . 0 0 0 2 3 6 5 . 2 2 8 6 8 . 9 0 . 4 3 9 0 . 5 3 3

0 . 0 4 5 3 6 0 . 0 0 0 2 3 3 1 . 3 2 7 8 8 . 1 0 . 4 3 3 0 . 5 1 8

C l

- 0 . 1 1 3 5 7 7 4 4 E 0 4

D l

- 0 . 9 8 2 8 1 2 5 0 E 0 3

Q K

0 . 1 8 6 1 2 4 4 9 E - 0 2

P P D

0 . 4 4 0 9 4 8 0 5 E 0 4

R E

0 . 2 0 9 9 2 8 1 9 E 0 6

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9 . 9 3 9 . 5 7 8 . 0 0 5 . 7 0 4 . 0 0

2 . 5 5 1 . 2 0 3 1 . 0


0 . 0 4 5 3 6 0 . 0 0 0 2 5 5 9 . 6 3 0 1 6 . 7 0 . 4 7 5 0 . 5 6 0

0 . 0 5 0 4 0 0 . 0 0 0 2 2 5 0 . 7 2 5 9 1 . 3 0 . 4 1 8 0 . 4 8 1

0 . 0 5 5 4 4 0 . 0 0 0 1 9 5 1 . 0 2 2 0 6 . 6 0 . 3 6 2 0 . 4 1 0

0 . 0 6 0 4 8 0 . 0 0 0 1 6 6 3 . 7 1 8 5 5 . 3 0 . 3 0 9 0 . 3 4 5

0 . 0 6 5 5 2 0 . 0 0 0 1 3 8 9 . 6 1 5 3 2 . 1 0 . 2 5 8 0 . 2 8 5

0 . 0 7 0 5 5 9 . 9 9 9 1 1 2 8 . 7 1 2 3 2 . 9 0 . 2 1 0 0 . 2 2 9

0 . 0 7 5 5 9 9 . 9 9 9 8 8 0 . 5 9 5 4 * 4 0 . 1 6 4 0 . 1 7 7

0 . 0 8 0 6 3 9 . 9 9 9 6 4 4 . 3 6 9 3 . 8 0 . 1 2 0 0 . 1 2 9

0 . 0 8 5 6 7 9 . 9 9 9 4 1 9 . 4 4 4 9 . 1 0 . 0 7 8 0 . 0 8 3

0 . 0 9 0 7 1 9 . 9 9 9 2 0 4 . 9 2 1 8 . 3 0 . 0 3 8 0 . 0 4 1

0 . 0 9 5 7 5 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 0 0 . 0 0 0

C 2 D 2 R E

- 0 . 4 0 9 4 6 6 2 1 E 0 4 - 0 . 9 4 9 3 6 8 7 5 E 0 4 0 . 3 2 1 9 0 3 8 I E 0 6 ;


0 • 3 7 0 8 1 6 6 5 E 0 2 0 . 3 1 8 0 6 5 3 4 E 0 2 0 , . 1 4 2 2 5 7 0 8 E 0 2


- 1 3 0 1 . 0 0 . 0 0 0 1 2 5 0 . 0 0 1 8 3 5 0 4 1 9 . 0 1 . 5 3 3 4 3 . 2 9 8 . 7 0


9 . 1 0 8 . 7 0 7 . 1 5 5 . 1 5 3 . 6 5

2 . 3 0 1 . 0 0 3 2 . 0

R R / H . . O P K O P D O P R K O P R D

0 . 0 4 5 3 6 0 . 0 0 0 2 3 3 1 . 3 2 7 0 8 . 1 0 . 4 3 3 0 . 5 1 8

0 . 0 5 0 4 0 0 . 0 0 0 2 0 3 7 . 8 2 3 7 8 . 3 0 . 3 7 9 0 . 4 4 2

0 . 0 5 5 4 4 0 . 0 0 0 1 7 5 5 . 3 2 0 1 0 . 6 0 . 3 2 6 0 . 3 7 4

0 . 0 6 0 4 8 0 . 0 0 0 1 4 8 6 . 7 1 6 7 8 . 1 0 . 2 7 6 0 . 3 1 2

0 . 0 6 5 5 2 0 . 0 0 0 1 2 3 3 . 0 1 3 7 5 . 4 0 . 2 2 9 G o 2 5 5

0 . 0 7 0 5 5 9 . 9 9 9 9 9 4 . 1 1 0 9 8 . 2 0 . 1 8 5 0 . 2 0 4

0 . 0 7 5 5 9 9 . 9 9 9 • 7 6 9 . 6 8 4 3 . 3 0 . 1 4 3 0 . 1 5 7

0 . 0 8 0 6 3 9 . 9 9 9 5 5 8 . 7 6 0 8 . 1 0 . 1 , 0 4 0 . 1 1 3

0 . 0 8 5 6 7 9 . 9 9 9 3 6 0 . 7 3 9 0 . 3 0 . 0 6 7 0 . 0 7 3

0 . 0 9 0 7 1 9 . 9 9 9 1 7 4 . 7 1 8 8 . 1 0 . 0 3 2 0 . 0 3 5

0 . 0 9 5 7 5 9 . 9 9 9 0 . 0 0 . 0 0 . 0 0 0 0 . 0 0 0

C 2 D 2 R E •

- 0 . 4 0 9 5 0 3 8 I E 0 4 - 0 . 9 7 8 9 2 8 1 3 E 0 4 0 . 3 2 1 9 0 3 8 I E 0 6


0 . 3 2 1 0 0 2 2 0 E 0 2 0 • 2 8 5 5 9 6 0 I E 0 2 0 . 1 1 0 2 9 8 8 5 E 0 2

1 8 0


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0 . 0 1 0 6 6 • 6 6 7 - 1 1 9 8 . 0 2 7 1 9 . 7 - 0 . 4 1 2 0 . 9 3 5

0 . 0 1 3 9 0 . 0 0 0 2 9 6 . 3 2 5 0 2 . 4 0 . 1 0 2 0 . 8 6 0

0 . 0 1 7 1 1 3 . 3 3 3 8 9 8 . 4 2 3 3 5 . 5 0 . 3 0 9 0 . 0 0 3

0 . 0 2 0 1 3 6 . 6 6 7 1 1 7 3 . 0 2 1 9 9 . 9 0 . 4 0 3 0 . 7 5 6

0 . 0 2 4 1 6 0 . 0 0 0 1 3 0 3 . 2 2 0 8 5 . 8 0 . 4 4 8 0 . 7 1 7

0 . 0 2 7 1 8 3 . 3 3 3 1 3 6 1 . 9 1 9 8 7 . 2 0 . 4 6 8 0 . 6 8 3

0 . 0 3 1 2 0 6 . 6 6 7 1 3 8 2 . 4 1 9 0 0 . 5 0 . 4 1 5 0 . 6 5 3

0 . 0 3 4 2 3 0 . 0 0 0 1 3 8 1 . 2 1 8 2 3 . 1 0 . 4 7 5 0 . 6 2 7

0 . 0 3 8 2 5 3 . 3 3 3 1 3 6 7 . 5 1 7 5 3 . 1 0 . 4 7 0 0 . 6 0 2

0 . 0 4 1 2 7 6 . 6 6 7 1 3 4 6 . 4 1 6 8 9 . 3 0 . 4 6 3 0 . 5 8 1

0 . 0 4 5 3 0 0 . 0 0 0 1 3 2 0 . 9 1 6 3 0 . 7 0 . 4 5 4 0 . 5 6 0

C l 0 1 Q K

- 0 . 7 2 1 0 1 9 5 3 E 0 3 - 0 . 7 2 7 8 5 9 3 8 E 0 3 0 . 1 7 0 6 8 2 4 4 E : - 0 2

P P D R E

0 . 2 7 1 9 6 9 7 3 E 0 4 0 . 1 7 3 4 6 1 1 3 E 0 6

P H . - Q S P E E .... A L P H A . J E S T . __ -

- 1 4 8 9 . 0 0 . 0 0 0 1 5 0 0 . 0 0 1 7 1 4 0 4 1 9 . 0 1 . 4 4 4 5 3 4 . 0 0


0 . 0 1 0 6 6 . 6 6 7 - 1 4 8 9 . 0 2 4 2 8 . 3 - 0 . 5 1 2 0 . 8 3 5

0 . 0 1 3 9 0 . 0 0 0 8 . 0 2 2 1 3 . 7 0 . 0 0 3 0 . 7 6 1

0 . 0 1 7 1 1 3 . 3 3 3 6 1 3 . 5 2 0 5 0 . 2 0 . 2 1 1 0 . 7 0 5

0 . 0 2 0 1 3 6 . 6 6 7 8 9 2 . 4 1 9 1 9 . 0 0 . 3 0 7 0 . 6 5 9

0 . 0 2 4 1 6 0 . 0 0 0 1 0 2 7 . 7 1 8 0 9 . 9 0 . 3 5 3 0 . 6 2 2

0 . 0 2 7 1 8 3 . 3 3 3 1 0 9 2 . 3 1 7 1 7 . 2 0 . 3 7 5 0 . 5 9 0

0 . 0 3 1 2 0 6 . 6 6 7 1 1 1 9 . 3 1 6 3 7 . 2 0 . 3 8 5 0 . 5 6 3

0 . 0 3 4 2 3 0 . 0 0 0 1 1 2 5 . 7 1 5 6 7 . 2 0 . 3 8 7 0 . 5 3 9

0 . 0 3 8 2 5 3 . 3 3 3 1 1 2 0 . 2 1 5 0 5 . 5 0 . 3 8 5 0 . 5 1 7

0 . 0 4 1 2 7 6 . 6 6 7 . 1 1 0 8 . 2 1 4 5 0 . 8 0 . 3 8 1 0 . 4 9 9

0 . 0 4 5 3 0 0 . 0 0 0 1 0 9 2 . 6 1 4 0 2 . 1 0 . 3 7 5 0 . 4 8 2

C l D 1 Q K

- 0 . 7 2 1 1 3 6 9 6 E 0 3 - 0 • 1 0 2 2 6 6 4 3 E 0 4 0 . 1 7 0 7 1 0 2 2 E : ~ 0 2

P P D R E

0 . 2 4 2 8 2 5 7 6 E 0 4 0 . 1 7 3 4 6 1 1 3 E 0 6

p H Q S P E E A L P H A k P B P C

- 1 1 9 8 . 0 0 . 0 0 0 1 5 0 0 . 0 0 1 7 1 4 0 0 . 0 1 . 4 4 4 5 1 * 5 6 5 . 6 0


6 . 2 0 5 . 8 4 4 . 8 0 3 . 5 0 2 . 5 5

1 . 6 2 0 . 7 5 3 3 . 0

R R / H , O P K O P D O P R K O P R D

0 . 0 4 5 3 0 0 . 0 0 0 1 3 2 0 . 9 1 6 3 0 . 7 0 . 4 5 4 0 . 5 6 0

0 . 0 5 0 3 3 3 . 3 3 3 1 1 6 6 . 1 1 4 0 0 . 7 0 . 4 0 1 0 . 4 8 1

0 . 0 5 5 3 6 6 . 6 6 7 1 0 1 3 . 9 1 1 9 2 . 7 0 . 3 4 8 0 . 4 1 0

0 . 0 6 0 4 0 0 . 0 0 0 8 6 6 . 6 1 0 0 2 . 9 0 . 2 9 8 0 . 3 4 5

0 . 0 6 5 4 3 3 . 3 3 3 7 2 5 . 1 8 2 8 . 2 0 . 2 4 9 0 . 2 8 5

0 . 0 7 0 4 6 6 . 6 6 6 5 8 9 . 9 6 6 6 . 4 0 . 2 0 3 0 . 2 2 9

0 . 0 7 5 5 0 0 . 0 0 0 4 6 0 . 8 5 1 5 . 9 0 . 1 5 8 0 . 1 7 7

0 . 0 8 0 5 3 3 . 3 3 3 3 3 7 . 5 3 7 5 . 0 0 . 1 1 6 0 . 1 2 9 f

0 . 0 8 5 5 6 6 * 6 6 6 2 1 9 . 9 2 4 2 . 7 0 . 0 7 6 0 . 0 8 3

0 . 0 9 0 5 9 9 . 9 9 9 1 0 7 . 5 1 1 8 . 0 0 . 0 3 7 0 . 0 4 1

0 . 0 9 5 6 3 3 . 3 3 3 0 . 0 0 . 0 0 . 0 0 0 0 . 0 0 0

C 2 D 2 R E

- 0 . 2 1 7 3 1 9 8 0 E 0 4 - 0 . 5 0 2 7 8 0 0 8 E 0 4 0 . 2 5 0 5 6 4 5 0 E 0 6


0 . 1 8 7 8 0 2 4 3 E 0 2 0 . 1 9 4 0 2 5 8 8 E 0 2 - 0 . 3 3 1 3 8 2 7 5 E 0 1


- 1 4 8 9 . 0 0 . 0 0 0 1 5 0 0 . 0 0 1 7 1 4 0 4 1 9 . 0 - 1 . 4 4 4 5 0 . 7 8 5 . 0 5

P J P K T E S T P D P E P F P G PH

5 . 2 0 5 . 0 6 4 . 0 2 2 . 9 5

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R R / H - O P K O P D O P R K O P R D

0 . 0 4 5 3 0 0 . 0 0 0 1 0 9 2 . 6 1 4 0 2 . 1 0 . 3 7 5 0 . 4 8 2

0 . 0 5 0 3 3 3 . 3 3 3 9 5 3 . 3 1 1 8 7 . 7 0 * 3 2 8 0 . 4 0 8

0 . 0 5 5 3 6 6 . 6 6 7 8 1 8 . 2 9 9 6 . 8 0 . 2 8 1 0 . 3 4 3

0 . 0 6 0 4 0 0 . 0 0 0 6 8 9 . 6 8 2 . 5 . 7 0 . 2 3 7 0 . 2 8 4

0 . 0 6 5 4 3 3 . 3 3 3 5 6 8 . 5 6 7 1 * 4 0 . 1 9 5 0 . 2 3 1

0 . 0 7 0 4 6 6 . 6 6 6 4 5 5 . 3 5 3 1 . 7 0 . 1 5 6 0 . 1 8 3

0 . 0 7 5 5 0 0 . 0 0 0 • 3 4 9 . 8 4 0 4 . 9 0 . 1 2 0 0 . 1 3 9

0 . 0 8 0 5 3 3 . 3 3 3 2 5 1 . 9 2 8 9 . 3 0 . 0 8 7 0 . 0 9 9

0 . 0 8 5 5 6 6 • 6 6 6 1 6 1 . 1 1 8 4 . 0 0 . 0 5 5 0 . 0 6 3

0 . 0 9 0 5 9 9 . 9 9 9 7 7 . 3 8 7 . 8 0 . 0 2 7 0 . 0 3 0

0 . 0 9 5 6 3 3 . 3 3 3 - 0 . 0 0 . 0 - 0 . 0 0 0 0 . 0 0 0

C 2 D 2 R E

- 0 . 2 1 7 3 5 5 2 0 E 0 4 - 0 « 5 3 2 3 3 4 3 8 E 0 4 0 * 2 5 0 5 6 4 5 0 E 0 6

THRUST THRUST X PDT0. 13798 6 0 6 E 02 0 . 1 6 2 4 4 1 5 6 E 02. - 0 . 1 7 7 2 3 1 6 0 E 02

1 8 2


: - 5 0 8 0 . 0 0 . 0 0 0 1 5 0 0 . 0 0 2 6 3 8 0 0 . 0 1 . 4 4 4 5 3 5 . 0 0


0 . 0 1 0 6 6 . 6 6 7 - 5 0 8 0 . 0 4 1 8 5 . 9 - 1 . 1 3 4 0 . 9 3 5

0 . 0 1 3 9 0 . 0 0 0 1 3 6 1 . 1 3 8 5 1 . 4 - 0 . 3 0 4 0 . 8 6 0

0 . 0 1 7 1 1 3 . 3 3 3 2 0 2 . 6 3 5 9 4 . 5 0 . 0 4 5 0 . 8 0 3

0 . 0 2 0 1 3 6 . 6 6 7 9 6 4 . 9 3 3 8 5 . 9 0 . 2 1 5 0 . 7 5 6

0 . 0 2 4 1 6 0 . 0 0 0 1 3 6 7 . 5 3 2 1 0 . 3 0 . 3 0 5 0 . 7 1 7

0 . 0 2 7 1 8 3 . 3 3 3 1 5 8 7 . 8 3 0 5 8 . 5 0 . 3 5 5 0 . 6 8 3

0 . 0 3 1 2 0 6 . 6 6 7 1 7 0 7 . 7 2 9 2 5 . 0 0 . 3 8 1 0 . 6 5 3

0 . 0 3 4 2 3 0 . 0 0 0 1 7 6 8 . 8 2 8 0 5 . 8 0 . 3 9 5 0 . 6 2 7

0 . 0 3 8 2 5 3 . 3 3 3 1 7 9 4 . 0 2 6 9 8 . 2 0 . 4 0 1 0 . 6 0 2

0 . 0 4 1 2 7 6 . 6 6 7 1 7 9 6 . 6 2 6 0 0 . 0 0 . 4 0 1 0 . 5 8 1

0 . 0 4 5 3 0 0 . 0 0 0 1 7 8 4 . 6 2 5 0 9 . 7 0 . 3 9 8 0 . 5 6 0

C l

- 0 . 1 1 1 1 0 2 6 4 E 0 4

01- 0 * 1 2 1 7 3 9 5 8 E 0 4

Q K

0 . 2 6 3 0 0 6 2 9 E - 0 2

P P D

0 . 4 1 8 5 8 5 5 5 E 0 4

R E

0 . 2 6 6 9 7 2 3 1 E 0 6


- 5 3 7 1 . 0 0 . 0 0 0 1 5 0 0 . 0 0 2 6 3 8 0 4 1 9 . 0 1 . 4 4 4 5 3 6 . 0 0


0 . 0 1 0 6 6 . 6 6 7 - 5 3 7 1 . 0 3 8 9 4 . 4 - 1 . 1 9 9 0 . 8 7 0

0 . 0 1 3 9 0 . 0 0 0 - 1 6 4 9 . 5 3 5 6 2 . 7 - 0 . 3 6 8 0 . 7 9 6

0 . 0 1 7 1 1 3 . 3 3 3 - 8 2 . 3 3 3 0 9 . 3 - 0 . 0 1 8 0 . 7 3 9

0 . 0 2 0 1 3 6 . 6 6 7 6 8 4 . 3 3 1 0 4 . 9 0 . 1 5 3 0 . 6 9 3

0 . 0 2 4 1 6 0 . 0 0 0 1 0 9 2 . 0 2 9 3 4 . 4 0 . 2 4 4 0 . 6 5 5

0 . 0 2 7 1 8 3 . 3 3 3 1 3 1 8 . 2 2 7 8 8 . 5 0 . 2 9 4 0 . 6 2 3

0 . 0 3 1 2 0 6 . 6 6 7 1 4 4 4 . 7 2 6 6 1 . 7 0 . 3 2 3 0 . 5 9 4

0 . 0 3 4 2 3 0 . 0 0 0 1 5 1 3 . 3 2 5 5 0 . 0 0 . 3 3 8 0 . 5 6 9

0 . 0 3 8 2 5 3 . 3 3 3 1 5 4 6 . 8 2 4 5 0 . 6 0 . 3 4 5 0 . 5 4 7

0 . 0 4 1 2 7 6 . 6 6 7 1 5 5 8 . 4 2 3 6 1 . 5 0 . 3 4 8 0 . 5 2 7

0 . 0 4 5 3 0 0 . 0 0 0 1 5 5 6 . 3 2 2 8 1 . 2 0 . 3 4 8 0 . 5 0 9

C l

“ 0 • 1 1 1 1 1 4 4 0 E 0 4

D 1

- 0 . 1 5 1 2 1 9 7 8 E 0 4

Q K

0 . 2 6 3 0 3 4 0 9 E - 0 2

PPD0 . 3 8 9 4 4 1 9 2 E 04

RE0 • 26 697231E 06

1 8 3


- 5 0 8 0 . 0 0 . 0 0 0 1 5 0 0 . 0 0 2 6 3 8 0 0 . 0 • 1 . 4 4 4 5 ” 3 . 1 2 7 . 7 0


9 . 1 4 8 . 9 2 6 . 8 5 5 . 0 0 3 . 6 0

2 . 3 5 1 . 1 5 3 5 . 0


0 . 0 4 5 3 0 0 . 0 0 0 1 7 8 4 . 6 2 5 0 9 . 7 0 . 3 9 8 0 . 5 6 0

0 . 0 5 0 3 3 3 . 3 3 3 1 6 0 7 . 6 2 1 5 5 . 9 0 . 3 5 9 0 . 4 8 1

0 . 0 5 5 3 6 6 . 6 6 7 1 4 1 8 . 5 1 8 3 5 . 7 0 . 3 1 7 0 . 4 1 0

0 . 0 6 0 4 0 0 . 0 0 0 1 2 2 6 . 0 1 5 4 3 . 5 0 . 2 7 4 0 . 3 4 5

0 . 0 6 5 4 3 3 . 3 3 3 1 0 3 4 . 9 1 2 7 4 . 6 0 . 2 3 1 0 . 2 8 5

0 . 0 7 0 4 6 6 . 6 6 6 8 4 7 . 9 1 0 2 5 . 7 0 . 1 8 9 0 . 2 2 9

0 . 0 7 5 5 0 0 . 0 0 0 6 6 6 . 1 7 9 4 . 0 0 . 1 4 9 0 . 1 7 7

0 . 0 8 0 5 3 3 . 3 3 3 4 9 0 . 3 • 5 7 7 . 2 0 . 1 0 9 0 . 1 2 - 9

0 . 0 8 5 5 6 6 . 6 6 6 3 2 0 . 7 3 7 3 . 6 0 . 0 7 2 0 . 0 8 3

0 . 0 9 0 5 9 9 . 9 9 9 1 5 7 . 3 1 8 1 . 6 0 . 0 3 5 0 . 0 4 1

0 . 0 9 5 6 3 3 . 3 3 3 0 . 0 0 . 0 0 . 0 0 . 0 0 0

C 2 D 2 R E

” 0 . 3 3 4 8 7 0 3 1 E 0 4 - 0 . 7 6 7 4 8 4 3 8 E 0 4 0 . 3 8 5 6 4 1 3 8 E 0 6


0 • 2 2 8 9 8 7 2 7 E 0 2 0 . 2 7 1 2 8 2 3 5 E 0 2 ” 0 . 1 8 4 7 0 4 7 4 E 0 2


” 5 3 7 1 . 0 0 . 0 0 0 1 5 0 0 . 0 0 2 6 3 8 0 4 1 9 . 0 1 . 4 4 4 5 - 3 . 9 8 7 . 2 3

P J P K T E S T i P D P E P F PG P H

8 . 0 0 7 . 9 5 5 . 9 0 4 . 3 0 3 . 1 0

2 . 0 0 0 . 9 0 3 6 . 0


0 . 0 4 5 3 0 0 . 0 0 0 1 5 5 6 . 3 2 2 8 1 . 2 0 . 3 4 8 0 . 5 0 9

0 . 0 5 0 3 3 3 . 3 3 3 1 3 9 4 . 7 1 9 4 2 . 8 0 . 3 1 1 0 . 4 3 4

0 . 0 5 5 3 6 6 . 6 6 7 1 2 2 2 . 7 1 6 3 9 . 8 0 . 2 7 3 0 . 3 6 6

0 . 0 6 0 4 0 0 , 0 0 0 1 0 4 9 . 0 1 3 6 6 . 3 0 . 2 3 4 0 . 3 0 5

0 . 0 6 5 4 3 3 . 3 3 3 8 7 0 . 3 1 1 1 7 . 9 0 . 1 9 6 0 . 2 5 0

0 . 0 7 0 4 6 6 . 6 6 6 7 1 3 . 3 8 9 1 . 0 0 . 1 5 9 0 . 1 9 9

0 . 0 7 5 5 0 0 . 0 0 0 5 5 5 . 2 6 8 3 . 0 0 . 1 2 4 0 . 1 5 3

0 . 0 8 0 5 3 3 . 3 3 3 4 0 4 . 7 4 9 1 . 5 0 . 0 9 0 0 . 1 1 0

0 . 0 8 5 5 6 6 • 6 6 8 2 6 2 . 0 3 1 4 . 8 0 . 0 5 9 0 . 0 7 0

0 . 0 9 0 5 9 9 . 9 9 9 1 2 7 . 2 1 5 1 . 4 0 . 0 2 8 0 . 0 3 4

0 . 0 9 5 6 3 3 . 3 3 3 0 . 0 0 . 0 0 . 0 0 0 0 . 0 0 0

C 2 D 2 R E

“ 0 . 3 3 4 9 0 5 7 9 E 0 4 - 0 . 7 9 7 0 3 7 S 9 E 0 4 0 • 3 3 5 6 4 1 3 8 E 0 6

THRUST THRUST X PDT0 . I 7 9 1 7 2 8 2 E 02 0 . 2 3 2 3 1 5 0 6 E 02 - 0 . 2 9 6 5 9 7 6 0 E 02

C O M P U T E R P R O G R A M a n d p r i n t o u t O F V r , _VH _ J L h J n % v a l u e s .

' ^

1 8 4

FLOW' CHART N- ^ a . A P P E N D IX 3

1 8 5

F L O W Q U A R T N ° Z b .

/■ 1 8 6

/ / J O B 1 1 S 1 3 R K L E M Z

* J O B 2 9 2 5



C

0 0 0 1

0 0 0 2

0 0 0 3

0 0 0 4

0 0 0 5

0 0 0 6

0 0 0 7

0 0 0 8

0 0 0 9

0010 0011 00120 0 1 3

0 0 1 4

0 0 1 5

0 0 1 6

0 0 1 7

0 0 1 8

0 0 1 9

0020 0021 00220 0 2 3

0 0 2 4

0 0 2 5

0 0 2 6

0 0 2 7

0 0 2 8

0 0 2 9

0 0 3 0

0 0 3 1

0 0 3 2

0 0 3 3

0 0 3 4

0 0 3 5

4 0

4 1

4 2

4 3

4 4

1 6

8 0

8 1

1 5

11

F / R A D I A L V E L O C I T Y A X I A L V E L O C I T Y

T E S T S ( 1 9 ) & ( 2 0 )

S P E E = 0 • 0

G O T O 4

I F ( S P E E - 1 . 0 ) 8 , 1 0 2 , 1 0 2

S P E E = 4 0 0 0 . 0 * 2 . 0 * P 1 / 6 0 . 0

0 = 0 . 0 0 0 8 5 6

R 1 = 0 . 0 1

R 2 = 0 . 0 9 5

P I = 3 . 1 4 1 5 9

H = 0 . 0 0 0 1 2 5

V I S = 1 . 8 / 1 0 0 0 0 0 . 0

D E N=1 . 2 4

D O 1 0 0 1 = 1 , 5

G O T 0 ( 4 0 , 4 1 , 4 2 , A 3 , 4 4 ) , I

R = 0 . 0 1

G O T O 1 6

R = 0 . 0 2 5

G O T O 1 6

R = 0 « 0 5

G O T O 1 6

R = 0 . 0 7

G O T O 1 6

R = R 2

W R I T E ( 3 , 8 0 ) S P E E

F O R M A T ( 1 * 5 0 X , ' S P E E D = 1 F 5 . 1 )

W R I T E ( 3 , 8 1 ) R

F O R M A T { ' * 5 0 X , * R A D I U S = * F 5 . 3 )

E = 0 . 7 5 * V I S * Q / ( P I * R * H * H * H )

F = 2.7 • 0 * D E N * Q * Q / ( 2 8 0 . 0 * P I * P I * R * R * R * H * H )

G = 0 . 3 * D E N * S P E E * S P E E * R

P R = - E + F + G

P R = S L O P E O F P R E S S U R E D I S T R I B U T I O N C U R V E

Z = -HW R I T E ( 3 , 1 5 )

F O R M A T ( * 0 * 9 X , 1 V R « 1 4 X , * Z * 2 2 X , * V Z * , 1 4 X

/ , 1 V R B 1 , 1 2 X , * V R I 1 , 1 2 X , • V R C • , 1 5 X , • D V Z • )

~ A 1 = ( Z * Z - H * H ) / ( 2 . 0 * V I S )

A 2 = 9 . 0 * Q * Q * D E N / ( 6 4 . 0 * P I * P I * r l * « 6 * R * R * R * V I S )

1 8 7

0 0 3 6 A 3 = ( H * * 4 ) * Z * Z / 2 . 0 _ .....

. 0 0 3 7 A 4 = ( Z * * 4 ) * H * H / 6 . 0

0 0 3 8 A 5 = ( Z * * 6 ) / 3 0 . 0

0 0 3 9 A 6 = ( H * * 6 J * 1 1 . 0 / 3 0 . 0

0 0 4 0 B 1 = R * D E N * S P E E * * 2 / ( 4 8 . 0 * V I S ) ‘

0 0 4 1 B 2 = ( Z * * 4 ) / ( H * H ) + 4 . 0 * Z * Z * Z / H + 6 . 0 * Z * Z - 4 . 0 * Z * H

- 7 . 0 * H * H

0 0 4 2 C l = ( 1 . 0 / ( 2 . 0 * R * V I S ) } * ( ( ( Z * * 3 ) / 3 . 0 ) - ( H * H * Z ) )

0 0 4 3 C 2 = 2 7 . 0 * Q * Q * D E N / ( 1 4 0 . 0 * P I * P I * R * R * R * H * H )

0 0 4 4 C 3 = 3 . 0 * D E N * S P E E * S P E E * R / 5 . 0

0 0 4 5 C 4 = 9 . 0 * Q * Q * D E N / ( 3 2 . 0 * P I * P I * ( H * * 6 ) * ( R * * 4 ) * V I S )

0 0 4 6 C 5 = ( H * * 4 ) * ( Z * Z * Z ) / 6 . 0

0 0 4 7 C 6 = H * H * ( Z * * 5 ) / 3 0 . 0

0 0 4 3 C 7 = ( Z * * 7 ) / 2 1 0 . 0

0 0 4 9 C 8 = 1 1 . 0 * Z * ( H * * 6 ) / 3 0 . 0

0 0 5 0 C 9 = D E N * S P E E * S P E E / ( 1 2 0 . 0 * V I S )

0 0 5 1 C 1 0 = ( Z * * 5 ) / ( H * H )

0 0 5 2 C 1 1 = 5 . 0 * ( Z * * 4 ) / H

0 0 5 3 C 1 2 = 1 0 . 0 * ( Z * * 3 )

0 0 5 4 ' C 1 3 = 1 0 . 0 * ' h * Z * Z

0 0 5 5 . C 1 4 = 3 5 . 0 * H * H * Z

0 0 5 6 C 1 5 = 5 . 0 * H * H * H

0 0 5 7 V R = A 1 * { - E + F + G ) - A 2 * ( A 3 - A 4 + A 5 - A 6 ) - B 1 * B 2

0 0 5 8 V Z = - C 1 * ( - C 2 + C 3 ) - C 4 * ( C 5 - C 6 + C 7 - C 8 ) + C 9 * ( C 1 0 +

C 1 1 + C 1 2 - C 1 3 - C 1 4 + C 1 5 )

0 0 5 9 V R B = ( H * H - Z * Z ) * 3 . 0 * Q / ( 8 . 0 * P I * H * H * H * R )

0 0 6 0 V R I = A 1 * ( - E + F ) - A 2 * ( A 3 - A 4 + A 5 - A 6 )

0 0 6 1 _ D V Z = - V I S * ( ( A 1 / R ) * ( C 2 + ' C 3 ) - C 4 M ( H * * 4 ) * ( Z * Z ) /

2 . 0 - ( H * H ) * ( Z * * 4 ) / 6 . 3 - H Z * * 6 ) / 3 0 . 0 - ( H * * 6 )

* 1 1 . 0 / 3 0 . 0 ) + C 9 * 6 0 « 0 * ( ( Z * * 4 ) / { H * H * 1 2 . 0 ) +

{ Z * * 3 ) / ( 3 . 0 * H ) + ( Z * Z ) / 2 . 0 - H * Z / 3 « 0 - ( H * H ) *

1 1 . 0 / 1 2 . 0 + ( H * H ) / 3 . O H

C V R = R A D I A L V E L O C I T Y B A S E D O N E Q U A T I O N ( 2 8 )

C V Z = R A D I A L V E L O C I T Y B A S E D O N E Q U A T I O N ( 2 9 )

C V R B = R A D I A L V E L O C I T Y B A S E D O N E Q U A T I O N ( 2 1 )

C V R I = R A D I A L V E L O C I T Y B A S E D O N E Q U A T I O N ( 2 3 )

( S P E E D = Z E R O )

C V R C = R A D I A L V E L O C I T Y B A S E D O N E Q U A T I O N ( 1 8 )

C D V Z = E Q U A T I O N ( 2 8 A ) * V I S

0 0 6 2 F C = D E N * Q * Q / ( 1 6 . 0 * P I * P I * R * R * R * H * H ) ■

0 0 6 3 0 1 = ( D E N * Q * Q * Z * Z ) / ( 3 2 . Q * P I * P I * R * R * R * H * H * V I S )

0 0 6 4 D 2 = D E N * S P E E * S P E E * R / ( 4 . 0 * V I S )

0 0 6 5 D 3 = ( Z * * 4 ) / ( 1 2 . 0 * H * H ) + ( Z * * 3 ) / ( 3 . 0 * H ) + ( Z * I ) / 2 . 0

0 0 6 6 D 4 = D E N * S P E E * S P E E * R * H * Z / ( 1 2 . O ' * V I S )

0 0 6 7 D 5 = 7 . 0 * D E N * S P E E * S P E E * R * H * H / ( 4 8 . 0 * V I S )

0 0 6 0 D 6 = D E N * Q * Q / ( 3 2 . Q * P I * P I * R * R * R * V I S )

0 0 6 9 P R C = —E + F C + G

0 0 7 0 _ „ V R C = ( A 1 * P R C ) - D 1 - D 2 * D 3 + D 4 + D 5 + D 6

1 8 8

■ 0 0 7 1 Z 1 = H

0 0 7 2 Z D = H / 1 0 . 0

0 0 7 3 W R I T E ( 3 , 2 0 ) V R , Z , V Z , V R B , V R I , V R C , D V Z

0 0 7 4 2 0 F O R M A T ( • • 4 X , F 9 . 4 , 6 X , F 1 0 . 7 , 8 X , E 1 6 . 4 , 6 X , F 9 , 4 ,

6 X » F 9 * 4 » 6 X » F 9 . 4 ,

/ 6 X , E 1 6 « 8 )

0 0 7 5 I F { Z - Z 1 ) 1 0 , 1 1 , 1.1

0 0 7 6 1 0 Z = 2 + Z D

0 0 7 7 I F ( Z - Z l ) 1 1 , 1 1 , 1 2

0 0 7 8 1 2 W R I T E F 3 , 3 1 ) P R

0 0 7 9 3 1 F O R M A T ( * 0 ' 7 X » * D P / D R = * F 8 • 1 )

0 0 8 0 F 1 = ( 3 . 0 # D E N * S P E E * * 2 ) / 1 0 . 0

0 0 8 1 F 3 = 2 7 . 0 * D E N * Q * Q / ( 2 8 0 . 0 * P I * P I * H * H )

0 0 8 2 F 2 = 3 . 0 * V I S * Q / ( 4 . 0 * P I * H * H * H )

0 0 8 3 F 4 = S Q R T { ( 9 . . 0 * D E N * Q * H ) / ( 7 0 • 0 * P I * V I S ) )

0 0 8 4 F 5 = F 4 / H

0 0 8 5 I F ( F 1 ) 9 4 , 9 4 , 9 9

0 0 8 6 9 4 W R 1 T E (. 3 , 1 0 3 ) F 5

0 0 8 7 1 0 3 F O R M A T { 2 2 X , * P I S A M A X W H E N D I M E N S I O N L E S S

R A D I U S = • F 5 . 1 )

0 0 8 8 GO T O 9 5

0 0 8 9 9 9 F K 1 = F 2 / F 1 ....................

0 0 9 0 F K 2 = F 3 / F 1

0 0 9 1 F K 3 = ( F K 1 * * 2 ) - 4 . 0 * F K 2

0 0 9 2 I F ( F K 3 ) 9 1 t 9 2 , 9 3

0 0 9 3 9 3 F K 4 = S Q R T ( F K 3 )

0 0 9 4 S 0 1 = ( F K 1 + F K 4 J / 2 . 0

0 0 9 5 S Q 2 = ( F K l - F K 4 ) / 2 . 0

0 0 9 6 S Q 3 = ( S Q R T ( S Q 1 ) ) / H

0 0 9 7 S Q 4 - ( S 0 R T ( S Q 2 ) ) / H

0 0 9 8 W R I T E I 3 , 9 8 ) S Q 3 , S Q 4

0 0 9 9 9 8 F O R M A T ( 2 ( 1 0 X , 1 P I S A M A X W H E N D I M E N S I O N L E S S

R A D I U S . = * E 1 0 . 4 ) )

0 1 0 0 G O T O 9 5

0 1 0 1 9 2 O Q = F K 1 / 2 . 0

0 1 0 2 Q Q 1 = 0 Q / H

0 1 0 3 W R I T E ( 3 , 9 7 ) 0 0 . 1

0 1 0 4 9 7 F O R M A T { 1 5 X , * P I S . A M A x W H E N D I M E N S I O N L E S S

R A D I U S = f F 5 . 1 )

0 1 0 5 G O T O 9 5

0 1 0 6 9 1 W R I T F ( 3 , 9 6 )

0 1 0 7 9 6 F O R M A T ( 1 0 X , ' N O R E A L S O L U T I O N ' )

0 1 0 8 9 5 C O N T I N U E

0 1 0 9 1 0 0 C O N T I N U E

0 1 1 0 1 0 1 G O T O 7

0 1 1 1 1 0 2 C O N T I N U E

0 1 1 2 E N D

189

S P E E D = 0 . 0

R A D I U S = 0 . 0 1 0

v z V R BV R I V R C D VZ

V R Z 0 . 0 0 0 3 0 . 0 0 0 0 - 0 . 1 0 7 0 8 6 4 5 E - 0 5

0 . 0 0 0 3 - 0 . 0 0 0 1 2 5 0 - 0 • 8 5 8 3 E - 0 5 0 * 07 . 0 1 5 1 1 5 . 5 3 1 1 0 . 3 0 6 5 7 1 4 6 E - 0 1

7 . 0 1 5 1 - 0 . 0 0 0 1 1 2 5 - 0 . 1 1 6 6 E - 0 1 i 1 5 . 5 3 1 01 7 . 0 3 2 9 2 9 . 4 2 7 3 0 . 4 4 6 1 9 5 1 6 E - 0 1

1 7 . 0 3 2 9 - 0 . 0 0 0 1 0 0 0 - 0 . 3 8 7 1 E - 0 1 2 9 . 4 2 7 22 9 . 3 9 3 4 4 1 . 6 8 8 6 0 . 4 4 2 6 2 6 1 0 E - 0 1

2 9 . 3 9 3 4 - 0 . 0 0 0 0 8 7 5 - ■ 0 . 7 0 3 I E - 0 1 4 1 . 6 8 8 54 3 . 1 6 3 8 5 2 . 3 1 5 1 0 . 3 2 9 2 6 1 3 1 E - 0 1

4 3 . 1 6 8 8 - 0 . 0 0 0 0 7 5 0 - 0 • 9 7 6 5 E - 0 1 5 2 . 3 1 5 05 7 . 2 9 3 3 6 1 . 3 0 6 7 0 . 1 4 4 4 7 9 4 6 E - 0 1

5 7 . 2 9 3 3 - 0 . 0 0 0 0 6 2 5 - 0 . 1 1 4 4 E 0 0 6 1 • 3 0 6 67 0 . 6 7 5 1 6 8 . 6 6 3 5 - 0 . 7 2 4 2 1 8 0 4 E - 0 2

7 0 . 6 7 5 1 - 0 . 0 0 0 0 5 0 0 - 0 . 1 1 7 D E 0 0 ' 6 8 . 6 6 3 48 2 . 2 9 1 5 7 4 . 3 8 5 5 — 0 . 2 8 4 6 2 4 1 4 E - 0 1

8 2 . 2 9 1 5 - 0 . 0 0 0 0 3 7 5 - 0 . 1 0 4 4 E 0 0 7 4 . 3 8 5 39 1 . 2 6 6 3 7 8 . 4 7 2 6 - 0 . 4 6 0 5 7 9 6 9 E - 0 1

9 1 . 2 6 6 3 - 0 . 0 0 0 0 2 5 0 - 0 • 7 8 2 8 E - 0 1 7 8 . 4 7 2 59 6 . 9 3 0 9 8 0 . 9 2 4 8 — 0 . 5 7 6 2 2 4 7 0 E - 0 1

9 6 . 9 3 0 9 - 0 . 0 C 0 0 1 2 5 - 0 . 4 1 8 8 E - 0 1 8 0 . 9 2 4 7 '9 3 . 8 6 6 4 8 1 . 7 4 2 2 - 0 . 6 1 6 4 8 2 8 3 E - 0 1

9 8 . 8 6 6 4 0 . 0 0 0 0 0 0 0 0 . 2 3 6 7 E - 0 6 8 1 . 7 4 2 19 6 . 9 3 0 7 8 0 . 9 2 4 8 — 0 . 5 7 6 2 2 4 7 0 E - 0 1

9 6 . 9 3 0 7 0 . 0 0 0 0 1 2 5 0 . 4 1 8 8 E - 0 1 8 0 . 9 2 4 79 1 . 2 6 6 2 7 8 . 4 7 2 5 - 0 . 4 6 0 5 7 8 2 8 E - 0 1

9 1 . 2 6 6 2 0 . 0 0 0 0 2 5 0 0 . 7 8 2 8 E - 0 1 7 8 . 4 7 2 48 2 . 2 9 1 3 7 4 . 3 8 5 4 - 0 . 2 8 4 6 1 8 5 1 E - 0 1

8 2 . 2 9 1 3 0 . 0 0 0 0 3 7 5 0 . 1 0 4 4 E 0 0 7 4 . 3 8 5 37 0 . 6 7 5 0 6 8 . 6 6 3 5 - 0 . 7 2 4 2 0 4 2 6 E - 0 2

7 0 . 6 7 5 0 0 . 0 0 0 0 5 0 0 0 . 1 1 7 0 E 0 0 6 8 • 6 6 3 35 7 . 2 9 3 2 6 1 . 3 0 6 7 0 . 1 4 4 4 8 0 1 3 E - 0 1

5 7 . 2 9 3 2 0 . 0 0 0 0 6 2 5 0 . 1 1 4 4 E 0 0 6 1 . 3 0 6 54 3 . 1 6 3 7 5 2 . 3 1 5 0 0 . 3 2 9 2 6 0 6 0 E - 0 1

4 3 . 1 6 8 7 0 . 0 0 0 0 7 5 0 0 . 9 7 6 4 E - 0 1 5 2 . 3 1 4 92 9 . 3 9 3 2 4 1 . 6 8 8 5 0 • 4 4 2 6 2 7 5 2 E - 0 1

2 9 . 3 9 3 2 0 . 0 0 0 0 8 7 5 0 • 7 0 3 1 E - 0 1 4 1 . 6 8 8 41 7 . 0 3 2 9 2 9 . 4 2 7 2 0 . 4 4 6 1 9 0 9 5 E - 0 1

1 7 . 0 3 2 9 0 . 0 0 0 1 0 0 0 0 . 3 8 7 1 E - 0 1 2 9 . 4 2 7 17 . 0 1 5 0 1 5 . 5 3 1 0 0 . 3 0 6 5 7 7 7 9 E - 0 1

7 . 0 1 5 0 0 . 0 0 0 1 1 2 5 0 . 1 1 6 6 E - 0 1 1 5 . 5 3 1 0

D P / D R = 3 7 9 8 0 7 . 4

P I S A M A X W H E N ’b l M E N S I ON L E S S R A D I U S

S P E E D =

R A D I U S =

= 1 3 8 . 9

0 . 0

0 . 0 2 5

V Z V R B.........V R I V R C D V Z

V R Z 0 . 0 0 0 0 0 . 0 0 0 0 - 0 . 2 7 4 1 4 1 1 4 E - 0 7

0 . 0 0 0 0 - 0 . 0 0 0 1 2 5 0 - 0 • 1 7 8 8 E - 0 6 0 . 0 5 . 6 6 7 4 6 . 2 1 2 4 0 . 7 8 4 8 2 7 4 0 E - 0 35 . 6 6 7 4 - 0 . 0 0 0 1 1 2 5 - 0 • 2 9 8 4 E - 0 3 6 . 2 1 2 4

1 0 . 9 7 7 6 1 1 . 7 7 0 9 0 . 1 1 4 2 2 6 5 5 E - 0 21 0 . 9 7 7 6 - 0 . 0 0 0 1 0 0 0 - 0 . 9 9 1 0 E - 0 3 1 1 . 7 7 0 9

1 5 . 8 8 3 5 1 6 . 6 7 5 4 0 . 1 1 3 3 1 2 9 2 E - 0 21 5 . 8 8 8 5 - 0 . 0 0 0 0 8 7 5 - 0 . 1 8 0 0 E - 0 2 1 6 . 6 7 5 4

2 0 . 3 4 0 6 2 0 . 9 2 6 0 0 . 8 4 2 9 2 3 3 0 E - 0 3

2 0 . 3 4 0 6 - 0 . 0 0 0 0 7 5 0 - 0 . 2 5 0 0 E - 0 2 2 0 . 9 2 6 02 4 . 2 6 5 3 2 4 . 5 2 2 6 0 . 3 6 9 8 8 7 3 3 E - 0 3

2 4 . 2 6 5 8 - 0 . 0 0 0 0 6 2 5 - 0 . 2 9 2 6 E - 0 2 2 4 . 5 2 2 62 7 . 5 9 4 1 2 7 . 4 6 5 3 - 0 . 1 8 5 3 7 8 8 1 E - 0 3

2 7 . 5 9 4 1 - 0 . 0 0 0 0 5 0 0 - 0 . 2 9 9 4 E - 0 2 2 7 • 4 6 5 43 0 . 2 6 0 1 2 9 . 7 5 4 1 - 0 . 7 2 8 6 1 2 7 7 E - 0 3

3 0 . 2 6 0 1 - 0 . 0 0 0 0 3 7 5 - 0 . 2 6 7 4 E - 0 2 2 9 . 7 5 4 13 2 . 2 0 7 7 3 1 . 3 8 9 0 - 0 . 1 1 7 9 0 5 6 5 E - 0 2

3 2 . 2 0 7 7 - 0 . 0 0 0 0 2 5 0 - 0 . 2 0 0 4 E - 0 2 3 1 . 3 8 9 03 3 . 3 9 4 2 3 2 . 3 6 9 9 - 0 . 1 4 7 5 1 0 7 2 E - 0 2

3 3 . 3 9 4 2 - 0 . 0 0 0 0 1 2 5 - 0 . 1 0 7 2 E - 0 2 3 2 . 3 6 9 93 3 . 7 9 2 8 3 2 . 6 9 6 8 - 0 . 1 5 7 8 1 6 7 5 E - 0 2

3 3 . 7 9 2 8 0 . 0 0 0 0 0 0 0 0 • 6 0 6 0 E - 0 8 3 2 . 6 9 6 83 3 . 3 9 4 2 3 2 . 3 6 9 9 - 0 . 1 4 7 5 1 1 1 6 E - 0 2

3 3 . 3 9 4 2 0 . 0 0 0 0 1 2 5 0 . 1 0 7 2 E - 0 2 3 2 . 3 6 9 93 2 . 2 0 7 7 3 1 . 3 8 8 9 - 0 . 1 1 7 9 0 5 6 5 E - 0 2

3 2 . 2 0 7 7 0 . 0 0 0 0 2 5 0 0 . 2 0 0 4 E - 0 2 3 1 . 3 8 9 03 0 . 2 5 0 1 2 9 . 7 5 4 1 - 0 . 7 2 8 5 9 9 7 3 E - 0 3

3 0 . 2 6 0 1 0 . 0 C 0 0 3 7 5 0 . 2 6 7 4 E - 0 2 2 9 . 7 5 4 12 7 . 5 9 4 0 2 7 . 4 6 5 3 - 0 . 1 8 5 3 7 8 8 1 E - 0 3

2 7 . 5 9 4 0 0 . 0 0 0 0 5 0 0 0 • 2 9 9 4 E - 0 2 2 7 • 4 6 5 32 4 . 2 6 5 7 2 4 . 5 2 2 6 0 . 3 6 9 8 8 7 3 3 E - 0 3

2 4 . 2 6 5 7 0 . 0 0 0 0 6 2 5 0 . 2 9 2 8 E - 0 2 2 4 . 5 2 2 62 0 . 3 4 0 6 2 0 . 9 2 5 9 0 . 8 4 2 9 2 3 3 0 E - 0 3

2 0 . 3 4 0 6 0 . 0 0 0 0 7 5 0 0 . 2 5 0 0 E - 0 2 2 0 . 9 2 6 01 5 . 8 8 8 5 1 6 . 6 7 5 4 0 . 1 1 3 3 1 3 8 1 E - 0 2

1 5 . 8 8 8 5 0 . 0 0 0 0 8 7 5 0 • 1 8 0 0 E - 0 2 1 6 . 6 7 5 41 1 0 . 9 7 7 6 1 1 . 7 7 0 9 : 0 . 1 1 4 2 2 5 6 7 E - 0 2

1 0 . 9 7 7 6 0 . 0 0 0 1 0 0 0 0 • 9 9 0 9 E - 0 3 1 1 . 7 7 0 95 . 6 6 7 4 6 . 2 1 2 4 0 . 7 8 4 8 4 4 1 6 E - 0 3

5 . 6 6 7 4 0 . 0 0 0 1 1 2 5 0 . 2 9 8 5 E - 0 3 6 . 2 1 2 4

D P / D R = - 3 8 9 7 2 . 5P I S A MAX WHEN DI MENSI DNL ESS RADI US =1 3 8 . 9

1 9 0

S P E E D = : 0 . 0

R A D I U S = 0 . 0 5 0

V R Z V Z V R B

0 . 0 0 0 0 - 0 . 0 0 0 1 2 5 0 - 0 . 7 4 5 I E - 0 8 0 . 0

3 . 0 3 8 1 - 0 . 0 0 0 1 1 2 5 - 0 • 1 8 6 5 E - 0 4 3 . 1 0 6 2

5 . 7 8 6 3 - 0 . 0 0 0 1 0 0 0 - 0 . 6 1 9 3 E - 0 4 5 . 8 8 5 4

8 . 2 3 9 3 - 0 . 0 0 0 0 3 7 5 - 0 . 1 1 2 5 E - 0 3 8 . 3 3 7 7

1 0 . 3 8 9 8 - 0 . 0 0 0 0 7 5 0 - 0 . 1 5 6 2 E - 0 3 1 0 . 4 6 3 0

1 2 . 2 2 9 2 - 0 . 0 0 0 0 6 2 5 - 0 . 1 8 3 0 E - 0 3 1 2 . 2 6 1 3

1 3 . 7 4 8 8 - 0 . 0 0 0 0 5 0 0 - 0 . 1 8 7 1 E - 0 3 1 3 . 7 3 2 7

1 4 . 9 4 0 3 - 0 . 0 0 0 0 3 7 5 - 0 . 1 6 7 1 E - 0 3 1 4 . 8 7 7 1

1 5 . 7 9 6 8 - 0 . 0 0 0 0 2 5 0 - 0 • 1 2 5 2 E - 0 3 1 5 . 6 9 4 5

1 6 . 3 1 3 0 - 0 . 0 0 0 0 1 2 5 - 0 . 6 7 0 0 E - 0 4 1 6 . 1 8 4 9

1 6 . 4 8 5 4 0 . 0 0 0 0 0 0 0 0 * 3 7 8 8 E - 0 9 1 6 . 3 4 8 4

1 6 . 3 1 3 0 0 . 0 0 0 0 1 2 5 0 • 6 7 0 0 E - 0 4 1 6 . 1 8 4 9

1 5 . 7 9 6 8 0 . 0 0 0 0 2 5 0 0 • 1 2 5 2 E - 0 3 1 5 . 6 9 4 5

1 4 . 9 4 0 3 0 . 0 0 0 0 3 7 5 0 . 1 6 7 1 E - 0 3 1 4 . 8 7 7 1

1 3 . 7 4 0 8 0 . 0 0 0 0 5 0 0 0 • 1 8 7 I E - 0 3 1 3 . 7 3 2 7

1 2 . 2 2 9 2 0 . 0 0 0 0 6 2 5 0 • 1 8 3 0 E - 0 3 1 2 . 2 6 1 3

1 0 . 3 8 9 8 0 . 0 0 0 0 7 5 0 0 . 1 5 6 2 E - 0 3 1 0 . 4 6 3 0

8 . 2 3 9 3 0 . 0 0 0 0 8 7 5 0 . 1 1 2 5 E - 0 3 8 . 3 3 7 7

5 . 7 8 6 3 0 . 0 0 0 1 0 0 0 0 . 6 1 9 3 E - 0 4 5 . 8 8 5 4

3 . 0 3 0 1 0 . 0 0 0 1 1 2 5 0 . 1 8 6 5 E - 0 4 3 . 1 0 6 2

D P / D R = - 3 3 1 2 1 . 6

P I S A M A X W H E N D I M E N S I O N L E S S R A D I U S = 1 3 8 . 9

^— S P E E D =

R A D I U S ^

0 . 0

0 . 0 7 0

V R Z V Z V R B

0 . 0 0 0 0 - 0 . 0 0 0 1 2 5 0 - 0 . 2 7 9 4 E - 0 8 0 . 0

2 . 1 9 3 9 . - 0 . 0 0 0 1 1 2 5 - 0 . 4 8 5 6 E - 0 5 2 . 2 1 8 7

4 . 1 6 7 7 - 0 . 0 0 0 1 0 0 0 - 0 . 1 6 1 2 E - 0 4 4 . 2 0 3 9

5 . 9 1 9 7 - 0 . 0 0 0 0 8 7 5 - 0 • 2 9 2 8 E - 0 4 5 . 9 5 5 5

7 . 4 4 6 9 - 0 . 0 0 0 0 7 5 0 - 0 • 4 0 6 7 E - 0 4 7 . 4 7 3 6

8 . 7 4 6 4 - 0 . 0 0 0 0 6 2 5 - 0 . 4 7 6 4 E - 0 4 8 . 7 5 8 1

9 . 8 1 4 9 - 0 . 0 0 0 0 5 0 0 - 0 • 4 8 7 I E - 0 4 9 . 8 0 9 1

1 0 . 6 4 9 5 - 0 . 0 0 0 0 3 7 5 - 0 . 4 3 5 0 E - 0 4 1 0 . 6 2 6 5

1 1 . 2 4 7 6 - 0 . 0 0 0 0 2 5 0 - 0 . 3 2 6 0 E - 0 4 1 1 . 2 1 0 3

1 1 . 6 0 7 3 - 0 . 0 0 0 0 1 2 5 - 0 . 1 7 4 4 E - 0 4 1 1 . 5 6 0 7

1 1 . 7 2 7 4 0 . 0 0 0 0 0 0 0 0 . 9 8 6 0 E - 1 0 1 1 . 6 7 7 4

1 1 . 6 0 7 3 0 . 0 0 0 0 1 2 5 0 . 1 7 4 4 E - 0 4 1 1 . 5 6 0 7

1 1 . 2 4 7 6 0 . 0 0 0 0 2 5 0 0 . 3 2 6 0 E - 0 4 1 1 . 2 1 0 3

1 0 . 6 4 9 5 0 . 0 0 0 0 3 7 5 0 • 4 3 5 0 E - 0 4 ' 1 0 . 6 2 6 5

9 . 8 1 4 9 0 . 0 0 0 0 5 0 0 0 . 4 8 7 I E - 0 4 9 . 8 0 9 0

8 . 7 4 6 4 0 . 0 0 0 0 6 2 5 0 • 4 7 6 4 E - 0 4 8 . 7 5 8 1

7 . 4 4 6 9 0 . 0 0 0 0 7 5 0 0 • 4 0 6 7 E - 0 4 7 . 4 7 3 6

5 . 9 1 9 6 0 . 0 0 0 0 8 7 5 0 . 2 9 2 8 E - 0 4 5 . 9 5 5 5

4 . 1 6 7 7 0 . 0 0 0 1 0 0 0 0 • 1 6 1 2 E - 0 4 4 . 2 0 3 9

2 . 1 9 3 9 0 . 0 0 0 1 1 2 5 0 . 4 8 5 7 E - 0 5 2 . 2 1 8 7

D P / D R = - 2 5 2 4 8 . 4P I S A MAX WHEN DI MENSI ONL ESS RADI US =1 3 8 . 9

V R I

0 . 0 0 0 0

3 . 0 3 8 1

5 . 7 8 6 3

8 . 2 3 9 3

1 0 . 3 8 9 8

1 2 . 2 2 9 2

1 3 . 7 4 8 8

1 4 . 9 4 0 3

■ 1 5 . 7 9 5 8

1 6 . 3 1 3 0

1 6 . 4 3 5 4

1 6 . 3 1 3 0

1 6 . 7 9 6 8

1 4 . 9 4 0 3

1 3 . 7 4 3 3

1 2 . 2 2 9 2

1 0 . 3 8 9 8

8 . 2 3 9 3

5 . 7 8 6 3

3 . 0 3 8 1

V R C

0.03 . 1 0 6 2

5 . 8 8 5 4

8 . 3 3 7 7

1 0 . 4 6 3 0

1 2 . 2 6 1 3

1 3 . 7 3 2 7

1 4 . 8 7 7 1

1 5 . 6 9 4 5

1 6 . 1 8 4 9

1 6 . 3 4 8 4

1 6 . 1 8 4 9

1 5 . 6 9 4 5

1 4 . 8 7 7 1

1 3 . 7 3 2 7

1 2 . 2 6 1 3

1 0 . 4 6 3 0

8 . 3 3 7 7

5 . 8 8 5 4

3 . 1 0 6 2

D V Z

- 0 . 1 7 1 3 3 8 2 1 E - 0 8

0 . 4 9 0 5 1 4 5 0 E - 0 4

0 . 7 1 3 9 1 5 9 4 E - 0 4

0 . 7 0 8 1 9 7 4 8 E - 0 4

0 . 5 2 6 8 1 6 1 5 E - 0 4

0 . 2 3 1 1 6 5 9 0 E - 0 4

■ 0 . 1 1 5 8 7 5 4 9 E - 0 4

• 0 . 4 5 5 3 9 9 4 2 E - 0 4

- 0 . 7 3 6 9 2 3 9 8 E - 0 4

- 0 . 9 2 1 9 5 8 4 2 E - 0 4

■ 0 . 9 8 6 3 7 1 1 6 E - 0 4

• 0 . 9 2 1 9 5 5 6 5 E - 0 4

- 0 . 7 3 6 9 2 1 2 1 E - 0 4

• 0 . 4 5 5 3 8 8 5 I E - 0 4

■ 0 . 1 1 5 8 7 0 0 0 E - 0 4

0 . 2 3 1 1 7 1 4 3 E - 0 4

0 . 5 2 6 8 1 8 7 7 E - 0 4

0 . 7 0 8 2 0 5 7 7 E - 0 4

0 . 7 1 3 9 0 7 6 5 E - 0 4

0 . 4 9 0 5 2 5 2 7 E ~ 0 4

V R I

0 . 0 0 0 0

2 . 1 9 3 9

4 . 1 6 7 7

5 . 9 1 9 7

7 . 4 4 6 9

7 4 6 4

8 1 4 9

6 4 9 5

2 4 7 6

6 0 7 3

7 2 7 4

1 1 . 6 0 7 3

1 1 . 2 4 7 6

1 0 . 6 4 9 5

: 9 . 8 1 4 9

; 3 . 7 4 6 4

7 . 4 4 6 9

5 . 9 1 9 6

: 4 . 1 6 7 7

2 . 1 9 3 9

8

9

10

1 1

1 1

1 1

V R C

0 . 0 0 0 0

2 . 2 1 8 7

4 . 2 0 3 9

5 . 9 5 5 5

7 . 4 7 3 6

8 . 7 5 8 1

9 . 8 0 9 1

0 . 6 2 6 5

1 . 2 1 0 3

1 . . 5 6 0 7

1 . 6 7 7 4

1 . 5 6 0 7

1 . 2 1 0 3

0 . 6 2 6 5

9 . 8 0 9 0

8 . 7 5 8 1

7 . 4 7 3 6

• 5 . 9 5 5 5

4 . 2 0 3 9

2 . 2 1 8 7

D V Z

- 0 . 4 4 6 0 0 7 9 0 E - 0 9

0 . 1 2 7 6 8 4 7 6 E - 0 4

0 . 1 8 5 8 3 6 9 8 E - 0 4

0 . 1 8 4 3 5 0 2 1 E - 0 4

0 . 1 3 7 1 3 3 5 1 E - 0 4

0 . 6 0 1 7 3 1 1 5 E - 0 5

- 0 . 3 0 1 6 5 6 9 3 E - 0 5

- 0 . 1 1 8 5 4 5 1 7 E - 0 4

- 0 . 1 9 1 8 2 9 3 1 E - 0 4

- 0 . 2 3 9 9 9 6 1 5 E - 0 4

- 0 . 2 5 6 7 6 4 0 3 E - Q 4

■ 0 . 2 3 9 9 9 6 1 5 E - 0 4

- 0 . 1 9 1 8 2 9 3 1 E ~ 0 4

- 0 . 1 1 8 5 4 2 4 2 E - 0 4

■ 0 . 3 0 1 6 2 9 4 6 E - 0 5

0 . 6 0 1 7 3 1 1 5 E - 0 5

0 • 1 3 7 1 3 2 8 2 E - Q 4

0 . 1 8 4 3 5 0 9 4 E - 0 4

0 . 1 8 5 8 3 5 2 3 E - 0 4

0 . 1 2 7 6 8 7 6 7 E - Q 4

191

S P E E D =

R A D I U S = 0

0 . 0

. 0 9 5

V R Z V Z V R B

0 . 0 0 0 0 - 0 . 0 0 0 1 2 5 0 - 0 . 6 9 8 5 E - 0 9 , 0 . 0

1 . 6 2 4 9 - 0 . 0 0 0 1 1 2 5 - 0 . 1 4 3 1 E - 0 5 1 . 6 3 4 8

3 . 0 8 3 1 - 0 . 0 0 0 1 0 0 0 - 0 . 4 7 5 3 E - 0 5 3 . 0 9 7 6

4 . 3 7 3 9 - 0 . 0 0 0 0 8 7 5 - 0 . 8 6 3 2 E - 0 5 4 . 3 8 8 3

5 . 4 9 6 2 - 0 . 0 0 0 0 7 5 0 - 0 . 1 1 9 9 E - 0 4 5 . 5 0 6 8

6 . 4 4 8 6 - 0 . 0 0 0 0 6 2 5 - 0 . 1 4 0 4 E - 0 4 6 . 4 5 3 3

7 . 2 3 0 1 - 0 . 0 0 0 0 5 0 0 - 0 . 1 4 3 6 E - 0 4 7 . 2 2 7 7

7 . 8 3 9 3 - 0 . 0 0 0 0 3 7 5 - 0 . 1 2 8 2 E - 0 4 7 . 8 3 0 0

8 . 2 7 5 2 - 0 . 0 0 0 0 2 5 0 - 0 • 9 6 1 0 E - 0 5 8 . 2 6 0 3

8 . 5 3 7 1 - 0 . 0 0 0 0 1 2 5 - 0 . 5 1 4 1 E - 0 5 8 . 5 1 8 4

8 . 6 2 4 4 0 . 0 0 0 0 0 0 0 0 . 2 9 0 6 E - 1 0 8 . 6 0 4 4

8 . 5 3 7 1 0 . 0 0 0 0 1 2 5 0 • 5 1 4 1 E - 0 5 8 . 5 1 8 4

8 . 2 7 5 2 0 . 0 0 0 0 2 5 0 0 . 9 6 1 0 E - 0 5 8 . 2 6 0 3

7 . 8 3 9 3 0 . 0 0 0 0 3 7 5 0 . 1 2 8 2 E - 0 4 7 . 8 3 0 0

7 . 2 3 0 1 0 . 0 0 0 0 5 0 0 0 • 1 4 3 6 E - 0 4 7 . 2 2 7 7

6 . 4 4 8 6 0 . 0 0 0 0 6 2 5 0 . 1 4 0 4 E - 0 4 6 . 4 5 3 3

5 . 4 9 6 2 0 . 0 0 0 0 7 5 0 0 . 1 1 9 9 E - 0 4 5 . 5 0 6 8

4 . 3 7 3 9 0 . 0 0 0 0 8 7 5 0 • 8 6 3 2 E - 0 5 4 . 3 8 8 3

3 . 0 8 3 1 0 . 0 0 0 1 0 0 0 0 . 4 7 5 2 E - 0 5 3 . 0 9 7 6

1 . 6 2 4 9 0 . 0 0 0 1 1 2 5 0 • 1 4 3 1 E - 0 5 1 . 6 3 4 8

D P / D R = - - 1 9 1 6 2 . 0

P I S A M A X W H E N ‘ D I M E N S I O N L E S S R A D I U S = 1 3 8 . 9

S P E E D = 4 1 8 . 9

R A D I U S = 0 . 0 1 0

V R z ” V Z V R B

0 . 0 0 0 3 - 0 . 0 0 0 1 2 5 0 - 0 . 1 0 5 8 E - 0 4 0 . 0

6 . 9 9 2 8 - 0 . 0 0 0 1 1 2 5 - 0 . 1 1 6 3 E - 3 I 1 5 . 5 3 1 0

1 6 . 9 9 3 7 - 0 . 0 0 0 1 0 0 0 - 0 . 3 8 6 1 E - 0 1 2 9 . 4 2 7 2

2 9 . 3 4 3 0 - 0 . 0 0 0 0 8 7 5 - 0 . 7 0 0 9 E - 0 1 4 1 . 6 8 8 5

4 3 . 1 1 2 4 - 0 . 0 0 0 0 7 5 0 - 0 . 9 7 2 9 E - 0 1 5 2 . 3 1 5 0

5 7 . 2 3 5 7 - 0 . 0 0 0 0 6 2 5 - 0 . 1 1 3 9 E 0 0 6 1 . 3 0 6 6

7 0 . 6 2 0 9 - 0 . 0 0 0 0 5 0 0 - 0 . 1 1 6 3 E 0 0 6 8 . 6 6 3 4

8 2 . 2 4 4 6 - 0 . 0 0 0 0 3 7 5 - 0 . 1 0 3 7 E 0 0 7 4 . 3 8 5 3

9 1 . 2 3 0 0 - 0 , 0 0 0 0 2 5 0 - 0 • 7 7 4 I E - 0 1 7 3 . 4 7 2 5

9 6 . 9 0 7 9 - 0 . 0 0 0 0 1 2 5 - 0 . 4 0 9 3 E - 0 1 8 0 . 9 2 4 7

9 8 . 8 5 8 6 0 . 0 0 0 0 0 0 0 0 . - 9 8 3 9 E - 0 3 8 1 . 7 4 2 1

9 6 . 9 3 8 9 0 . 0 0 0 0 1 2 5 0 « 4 2 8 6 E - 0 1 8 0 . 9 2 4 7

9 1 . 2 9 0 4 0 . 0 0 0 0 2 5 0 0 . 7 9 2 2 E - 0 1 7 8 . 4 7 2 4

8 2 . 3 3 0 3 0 . 0 0 0 0 3 7 5 0 . 1 0 5 3 E 0 0 7 4 . 3 0 5 3

7 0 . 7 2 6 5 0 . 0 0 0 0 5 0 0 0 . 1 1 7 7 E 0 0 6 8 . 6 6 3 3

5 7 . 3 5 3 7 0 . 0 0 0 0 6 2 5 0 . 1 1 5 0 E 0 0 6 1 . 3 0 6 5

4 3 . 2 3 3 2 0 . 0 0 0 0 7 5 0 0 . 9 8 0 9 E - 0 1 5 2 . 3 1 4 9

2 9 . 4 5 5 2 0 , 0 C 0 0 8 7 5 0 . 7 0 6 0 E - 0 1 4 1 . 6 8 8 4

1 7 . 0 8 4 5 0 . 0 0 0 1 0 9 0 0 . 3 8 8 6 E - 0 1 2 9 . 4 2 7 1 .

7 . 0 4 6 5 0 . 0 0 0 1 1 . 2 5 0 . 1 1 7 1 E - 0 1 1 5 . 5 3 1 9

D ' P / D R = 3 8 0 4 6 Q . 1

P I S A M A X W H E N D I M E N S I O N L E S S R A D I U S = 0 . i 3 5 2 E 0 4

V R I V R C D V Z

0 . 0 0 9 0 - 0 . 0 0 0 0 - 0 . 1 3 1 4 7 4 1 8 E - 0 9

1 . 6 2 4 9 1 . 6 3 4 8 0 . 3 7 6 3 8 8 2 0 E - 0 5

3 . 0 8 3 1 3 . 0 9 7 6 0 . 5 4 7 8 1 0 6 7 E - 0 5

4 . 3 7 3 9 4 . 3 8 8 3 0 . 5 4 3 4 2 9 8 1 E - 0 5

5 . 4 9 6 2 5 . 5 0 6 8 0 . 4 0 4 2 4 8 5 7 E - 0 5

6 . 4 4 8 6 6 . 4 5 3 3 0 . 1 7 7 3 8 2 7 5 E - 0 5

7 . 2 3 9 1 7 . 2 2 7 7 - 0 . 8 8 9 1 3 6 8 0 E - 0 6

7 . 8 3 9 3 7 . 8 3 0 0 - 0 • 3 4 9 4 4 7 4 2 E - 0 5

3 . 2 7 5 2 8 . 2 6 9 3 - 0 . 5 6 5 4 6 9 4 2 E - 0 5

8 . 5 3 7 1 8 . 5 1 8 4 - 0 . 7 0 7 4 5 2 1 8 E - 0 5

8 . 6 2 4 4 8 . 6 0 4 4 - 0 . 7 5 6 8 7 8 6 7 E - 0 5

8 . 5 3 7 1 8 . 5 1 8 4 - 0 . 7 0 7 4 5 5 6 4 E - 0 5

8 . 2 7 5 2 8 . 2 6 0 3 —0 . 5 6 5 4 7 1 1 5 E - 0 5

7 . 8 3 9 3 7 . 8 3 0 0 — 0 . 3 4 9 4 4 3 9 6 E - 0 5

7 . 2 3 9 1 7 . 2 2 7 7 - 0 . 8 8 9 1 3 6 8 0 E - 0 6

6 • 4 4 8 6 6 . 4 5 3 3 0 . 1 7 7 3 8 6 1 2 E - 0 5

5 . 4 9 6 2 5 . 5 0 6 8 0 . 4 0 4 2 4 6 8 4 E - 0 5

4 . 3 7 3 9 4 . 3 8 8 3 0 . 5 4 3 4 3 1 5 4 E - 0 5

3 . 0 8 3 1 3 . 0 9 7 6 0 . 5 4 7 8 0 5 4 8 E - 0 5

1 . 6 2 4 9 1 . 6 3 4 8 0 . 3 7 6 3 9 6 2 0 E - 0 5

V R I V R C - D V Z

0 . 0 0 0 3 0 . 0 0 0 1 - 0 . 1 0 7 1 6 3 7 6 E - 0 5

7 . 0 1 5 1 1 5 . 5 0 8 7 0 . 3 0 9 6 4 1 5 8 E - 0 1

1 7 . 0 3 2 9 2 9 . 3 8 8 2 0 . 4 5 2 1 2 9 5 4 E - 0 1

2 9 . 3 9 3 4 4 1 . 6 3 8 2 0 . 4 5 1 2 1 3 7 2 E - 0 1

4 3 . 1 5 8 3 5 2 . 2 5 8 7 0 . 3 4 0 2 . 8 2 6 9 E - 0 1

5 7 . 2 9 3 3 6 1 . 2 4 9 2 0 . 1 5 7 7 0 3 2 4 E - 0 1

7 0 . 6 7 5 1 6 8 . 6 0 9 3 - 0 . 5 7 2 4 2 2 8 9 E - 0 2

8 2 . 2 9 1 5 7 4 . 3 3 8 6 - 0 . 2 6 7 7 5 4 3 1 E - 0 1

9 1 . 2 6 6 3 7 8 . 4 3 6 3 - 0 . 4 4 2 3 0 6 9 6 E - 0 1

9 6 . 9 3 0 9 8 0 . 9 0 1 9 - 0 . 5 5 6 8 6 2 1 7 E - 0 1

9 8 . 8 5 5 4 8 1 . 7 3 4 4 - 0 . 5 9 6 3 7 2 2 2 E - 0 1

9 5 . 9 3 9 7 8 0 . 9 3 3 0 - 0 . 5 5 5 7 4 0 2 6 E - 0 1

9 1 . 2 6 6 2 7 8 . 4 9 6 7 - 0 . 4 4 0 1 2 9 8 6 E - 0 1

8 2 . 2 9 1 3 7 4 . 4 2 4 5 - 0 . 2 6 4 6 5 5 0 9 E - 0 1

7 0 . 6 7 5 0 6 8 . 7 1 5 1 - 0 . 5 3 4 3 3 4 0 3 E - 0 2

5 7 . 2 9 3 2 6 1 . 3 6 7 2 0 . 1 6 1 9 5 3 3 1 E - 0 1

4 3 . 1 6 8 7 5 2 . 3 7 9 6 0 . 3 4 4 6 3 3 3 9 E - 0 1.

2 9 . 3 9 3 2 4 1 . 7 5 0 5 ~ 0 . 4 5 5 2 6 0 5 4 E - 0 1

1 7 . 0 3 2 9 2 9 . 4 7 8 8 0 . 4 5 5 3 8 0 8 4 E - 0 1

7 . 0 1 5 0 1 5 . 5 6 2 5 0 . 3 1 1 5 8 5 6 3 E - 0 1

I S A M A X W H E N D I M E N S I O N L E S S R A D I U S = 0 . 1 3 9 7 E 0 3

1 9 2

S P E E D = 4 1 8 . 9

•• R A D I U S = 0 . 0 2 5

V R Z V Z V R B

0 . 0 0 0 0 - 0 . 0 0 0 1 2 5 0 - 0 . 2 0 8 6 E - 0 6 0 . 0

5 . 6 1 1 5 - 0 . 0 0 0 1 1 2 5 - 0 . 2 6 9 3 E - 0 3 6 . 2 1 2 4

1 0 . 8 7 9 9 - 0 . 0 0 0 1 0 0 0 - 0 . 8 8 3 9 E - 0 3 1 1 . 7 7 0 9

1 5 . 7 6 2 6 - 0 . 0 0 0 0 8 7 5 - 0 . 1 5 8 0 E - 0 2 1 6 . 6 7 5 4

2 0 . 1 9 9 6 - 0 . 0 0 0 0 7 5 0 - 0 . 2 1 4 5 E - 0 2 2 0 . 9 2 6 0

2 4 . 1 2 1 9 - 0 . 0 0 0 0 6 2 5 - 0 . 2 4 3 0 E - 0 2 2 4 . 5 2 2 6

2 7 . 4 5 8 6 - 0 . 0 0 0 0 5 0 0 - 0 . 2 3 5 6 E - 0 2 2 7 . 4 6 5 4

3 0 . 1 4 2 8 - 0 . 0 0 0 0 3 7 5 - 0 . 1 9 0 8 E - 0 2 2 9 . 7 5 4 1

3 2 . 1 1 7 1 - 0 . 0 0 0 0 2 5 0 - 0 . 1 1 3 4 E - 0 2 3 1 . 3 8 9 0

3 3 ' . 3 3 6 8 - 0 . 0 0 0 0 1 2 . 5 - 0 . 1 2 7 2 E - 0 3 3 2 . 3 6 9 9

3 3 . 7 7 3 1 0 . 0 0 0 0 0 0 0 0 . 9 8 3 7 E - 0 3 3 2 . 6 9 6 8

3 3 . 4 1 4 7 0 . 0 0 0 0 1 2 5 0 . 2 0 5 5 E - 0 2 3 2 . 3 6 9 9

3 2 . 2 6 8 2 0 . 0 0 0 0 2 5 0 0 . 2 9 4 7 E - 0 2 3 1 . 3 8 9 0

3 0 . 3 5 7 6 0 . 0 0 0 0 3 7 5 0 . 3 5 3 7 E - 0 2 2 9 . 7 5 4 1

2 7 . 7 2 2 9 0 . 0 0 0 0 5 0 0 0 . 3 7 4 4 E - 0 2 2 7 . 4 6 5 3

2 4 . 4 1 7 0 0 . 0 0 0 0 6 2 5 0 . 3 5 3 7 E - 0 2 . 2 4 . 5 2 2 6

2 0 . 5 0 1 7 0 . 0 0 0 0 7 5 0 0 . 2 9 5 I E - 0 2 2 0 . 9 2 6 0

1 6 . 0 4 3 5 0 . 0 0 0 0 8 7 5 0 • 2 0 9 2 E ~ 0 2 1 6 . 6 7 5 4

1 1 . 1 0 6 5 0 . 0 0 0 1 0 0 0 0 . 1 1 3 9 E - 0 2 1 1 . 7 7 0 9

5 . 7 4 6 0 0 . 0 0 0 1 1 2 5 0 . 3 4 0 4 E - 0 3 6. * 2 1 2 4

D P / D R = - 3 7 3 4 0 . 7

P I S A M A X W H E N D I M E N S I 0 N L E S S R A D I U S = 0 • 1 3 5 2 E 0 4 P

S P E E D = 4 1 8 . 9

R A D I U S = 0 . 0 5 0

I S A

V R Z V Z V R B

0 . 0 0 0 0 - 0 . 0 0 0 1 2 5 0 - 0 . 3 7 2 5 E - 0 8 0 . 0

2 . 9 2 6 3 - 0 . 0 0 0 1 1 2 5 0 • 1 0 4 7 E - 0 4 3 . 1 0 6 2

5 . 5 9 0 8 - 0 . 0 0 0 1 0 0 0 0 . 4 5 1 6 E - 0 4 5 . 8 8 5 4

7 . 9 8 7 5 - 0 . 0 0 0 0 8 7 5 0 * 1 Q 7 5 E - 0 3 8 . 3 3 7 7

1 0 . 1 0 7 8 - 0 . 0 0 0 0 7 5 0 0 . 1 9 8 3 E - 0 3 1 0 . 4 6 3 0

1 1 . 9 4 1 5 - 0 . 0 0 0 0 6 2 5 0 . 3 1 5 0 E - 0 3 1 2 . 2 6 1 3

1 3 . 4 7 7 8 - G . 0 0 0 0 5 0 0 0 . 4 5 1 4 E - 0 3 1 3 . 7 3 2 7

1 4 . 7 0 5 8 - 0 . 0 0 0 0 3 7 5 0 . 5 9 8 S E - 0 3 1 4 . 8 7 7 1

1 5 . 6 1 5 5 - 0 . 0 0 0 0 2 5 0 0 . 7 4 5 0 E - 0 3 1 5 . 6 9 4 5

1 6 . 1 9 8 1 - 0 . 0 0 0 0 1 2 5 0 . 8 7 7 8 E - 0 3 1 6 . 1 8 4 9

1 6 . 4 4 6 1 0 . 0 0 0 0 0 0 0 0 . 9 8 3 7 E - 0 3 1 6 . 3 4 8 4

1 6 . 3 5 3 9 0 . 0 0 0 0 1 2 5 0 • 1 0 5 0 E - 0 2 1 6 . 1 8 4 9

1 5 . 9 1 7 7 0 . 0 0 0 0 2 5 0 0 • 1 0 6 8 E - 0 2 1 5 . 6 9 4 5

1 5 . 1 3 5 4 0 . 0 0 0 0 3 7 5 0 . 1 0 3 1 E - 0 2 1 4 . 8 7 7 1

1 4 . 0 0 6 6 0 . 0 0 0 0 5 0 0 0 . 9 3 6 7 E - 0 3 1 3 . 7 3 2 7

1 2 . 5 3 1 7 0 . 0 0 0 0 6 2 5 0 . 7 9 1 7 E - 0 3 1 2 . 2 6 1 3

1 0 . 7 1 2 1 0 . 0 0 0 0 7 5 0 0 . 6 0 7 5 E - 0 3 1 0 . 4 6 3 0

8 . 5 4 9 4 0 . 0 0 0 0 8 7 5 0 . 4 0 4 2 E - 0 3 8 . 3 3 7 7

6 . 0 4 4 1 0 . 0 0 0 1 0 0 3 0 • 2 0 9 8 E - 0 3 5 . 8 8 5 4

3 . 1 9 5 4 0 . 0 0 0 1 1 2 5 0 . 6 0 5 5 E - 0 4 3 . 1 0 6 2

D P / D R = -

P I S

2 9 3 5 8 . 1

A M A X W H E N D I M E N S I O N L E S S R A D I U S = 0 . 1 3 5 2 E 0 4

i

P

V R I V R C D V Z

0 . 0 0 0 0 0 . 0 0 0 0 - 0 . 2 8 1 8 7 0 7 4 E - 0 7

5 . 6 6 7 4 6 . 1 5 6 5 0 . 1 0 9 1 9 0 0 5 E - 0 2

1 0 . 9 7 7 6 1 1 . 6 7 3 1 0 . 1 7 3 5 8 1 8 3 E - 0 2

1 5 . 8 8 3 5 1 6 . 5 4 9 5 0 . 1 9 9 2 0 5 7 1 E - 0 2

2 0 . 3 4 0 6 2 0 . 7 8 5 0 0 . 1 9 4 5 2 6 7 7 E - 0 2

2 4 . 2 6 5 8 2 4 . 3 7 8 8 0 . 1 6 9 2 5 0 1 8 E - 0 2

2 7 . 5 9 4 1 2 7 . 3 2 9 8 0 . 1 3 3 2 8 3 6 5 E - 0 2

3 0 . 2 6 0 1 2 9 . 6 3 6 8 0 . 9 5 8 6 5 2 2 4 E - 0 3

3 2 . 2 0 7 7 3 1 . 2 9 8 3 0 . 6 4 8 5 1 5 3 0 E - 0 3

3 3 . 3 9 4 2 3 2 . 3 1 2 4 0 . 4 6 1 4 5 5 9 0 E - 0 3

3 3 . 7 9 2 8 3 2 . 6 7 7 2 0 . 4 3 3 2 0 0 2 7 E - 0 3

3 3 . 3 9 4 2 3 2 . 3 9 0 3 0 . 5 7 3 6 3 9 9 9 E - 0 3

3 2 . 2 0 7 7 3 1 . 4 4 9 4 0 . 8 6 6 0 7 9 4 7 E - 0 3

3 0 . 2 6 0 1 2 9 . 8 5 1 6 0 . 1 2 6 8 0 2 5 3 E - 0 2

2 7 . 5 9 4 0 2 7 . 5 9 4 2 0 . 1 7 1 3 5 8 1 4 E - 0 2

2 4 . 2 6 5 7 2 4 . 6 7 3 8 0 . 2 1 1 7 4 4 0 1 E - 0 2

2 0 . 3 4 0 6 2 1 . 0 8 7 1 0 . 2 3 8 0 4 0 0 7 E - 0 2

1 5 . 8 8 3 5 1 6 . 8 3 0 4 0 . 2 3 9 6 6 0 2 9 E - 0 2

1 0 . 9 7 7 6 1 1 . 8 9 9 8 0 . 2 0 6 2 1 6 2 4 E - 0 2

5 . 6 6 7 4 6 . 2 9 1 1 0 . 1 2 8 5 6 8 9 0 E - 0 2

W H E N D I M E N S I O N L E S S R A D I U S = 0 • 1 3 9 7 E 0 3 f

V R I V R C D V Z

0 . 0 0 0 0 0 . 0 - 0 . 2 4 8 6 3 4 3 I E - 0 8

3 . 0 3 8 1 2 . 9 9 4 4 0 . 3 5 6 1 2 6 5 8 E - 0 3

5 . 7 8 6 3 5 . 6 9 0 0 0 . 6 6 4 9 4 6 8 6 E - 0 3

8 . 2 3 9 3 8 . 0 8 5 9 0 . 9 2 9 7 5 0 0 4 E - 0 3

1 0 . 3 8 9 3 1 0 . 1 8 1 0 0 . 1 1 5 5 0 3 0 9 E - 0 2

1 2 . 2 2 9 2 ~- 1 1 . 9 7 3 6 0 . 1 3 4 5 7 4 1 3 E - 0 2

1 3 . 7 4 3 8 1 3 . 4 6 1 7 0 . 1 5 0 6 6 3 6 2 E - 0 2

1 4 . 9 4 0 3 1 4 . 6 4 2 5 0 . 1 6 4 1 7 3 8 7 E - 0 2

1 5 . 7 9 6 8 1 5 . 5 1 3 2 0 . 1 7 S 3 8 8 7 6 E - 0 2

1 6 . 3 1 3 0 1 6 . 0 7 0 0 0 . 1 8 4 4 3 8 0 5 E - 0 2

1 6 . 4 8 5 4 1 6 . 3 0 9 1 0 . 1 9 1 2 7 4 2 6 E - 0 2

1 6 . 3 1 3 0 1 6 . 2 2 5 8 0 . 1 9 5 6 5 6 4 4 E - 0 2

1 5 . 7 9 6 8 1 5 . 8 1 5 4 0 . 1 9 7 1 4 5 5 8 E - 0 2

1 4 . 9 4 0 3 1 5 . 0 7 2 2 0 . 1 9 5 1 0 9 4 7 E - 0 2

1 3 . 7 4 8 9 1 3 . 9 9 0 5 0 . 1 8 8 7 3 8 0 8 E - 0 2

1 2 . 2 2 9 2 1 2 . 5 6 3 8 0 . 1 7 7 0 6 7 8 9 E - 0 2

1 0 . 3 8 9 8 1 0 . 7 8 5 3 0 . 1 5 9 0 1 6 7 9 E - 0 2

3 . 2 3 9 3 8 . 6 4 7 7 0 . 1 3 3 4 2 9 1 9 E - 0 2

5 . 7 8 5 3 6 . 1 4 3 2 0 . 9 9 1 2 9 8 5 8 E - 0 3

3 . 0 3 8 1 3 . 2 6 3 6 0 . 5 4 9 8 9 8 9 5 E - 0 3

I S A MAX WHEN DI MENS I ONLESS RADI US = 0 . 1 3 9 7 E 03

1 9 3

S P E E D = 4 1 8 * 9

R A D I U S = 0 • 0 7 0

V R Z V Z

0 . 0 0 0 0 - 0 . 0 0 0 1 2 5 0 0 . 0

2 . 0 3 7 4 - 0 . 0 0 0 1 1 2 5 0 . 2 4 2 7 E - 0 4

3 . 8 9 4 1 - 0 . 0 0 0 1 0 0 0 0 . 9 0 9 6 E - 0 4

5 . 5 6 7 1 - 0 . 0 0 0 0 8 7 5 0 . 1 9 0 7 E - 0 3

7 . 0 5 2 0 - 0 . 0 0 0 0 7 5 0 0 • 3 1 3 9 E - 0 3

8 . 3 4 3 6 - 0 . 0 0 0 0 6 2 5 . 0 • 4 5 0 3 E - 0 3

9 . 4 3 5 5 - 0 . 0 0 0 0 5 0 0 0 . 5 8 9 8 E - 0 3

1 0 . 3 2 1 2 - 0 . 0 0 0 0 3 7 5 0 . 7 2 2 2 E - 0 3

1 0 . 9 9 3 8 - 0 . 0 0 0 0 2 5 0 0 • 8 3 7 7 E - 0 3

1 1 . 4 4 6 5 - 0 . 0 0 0 0 1 2 5 0 . 9 2 7 4 E - 0 3

1 1 . 6 7 2 3 0 . O O O O O O D 0 . 9 8 3 7 E - 0 3

1 1 . 6 6 4 6 0 . 0 0 0 0 1 2 5 0 . 1 0 0 1 E - 0 2

1 1 . 4 1 6 9 0 . 0 0 0 0 2 5 0 0 • 9 7 5 4 E - 0 3

1 0 . 9 2 2 7 0 . 0 0 0 0 3 7 5 0 * 9 0 6 9 E - 0 3

1 0 . 1 7 5 8 0 . 0 0 0 0 5 0 0 0 . 7 9 6 3 E - 0 3

9 . 1 6 9 8 0 . 0 0 0 0 6 2 5 0 . 6 5 6 3 E - 0 3

7 . 8 9 8 1 0 . 0 0 0 0 7 5 0 0 . 4 9 1 9 E - 0 3

6 . 3 5 3 7 0 . 0 0 0 0 8 7 5 0 . 3 2 0 9 E - 0 3

4 . 5 2 8 7 0 . 0 0 0 1 0 0 0 0 . 1 6 4 0 E - 0 3

2 . 4 1 4 2 0 . 0 0 0 1 1 2 5 0 . 4 6 7 6 E - 0 4

D P / D R = - 2 0 6 7 9 . 5

P I S A M A X W H E N D I M E N S I O N L E S S R A D I U S = 0 . 1 3 5 2 E D A

S P E E D = 4 1 8 • 9

R A D I U S = 0 . 0 9

V R Z V Z

0 . 0 0 0 0 - 0 . 0 0 0 1 2 5 0 0 . 7 4 5 1 E - 0 8

1 . 4 1 2 6 - 0 . 0 0 0 1 1 2 5 0 . 2 7 6 9 E - 0 4

2 . 7 1 1 7 - 0 . 0 0 0 1 0 0 0 0 • 1 0 2 3 E - Q 3

3 . 8 9 5 4 - 0 . 0 0 0 0 8 7 5 0 . 2 1 1 4 E - 0 3

4 . 9 6 0 3 - 0 . 0 0 0 0 7 5 0 0 • 3 4 2 6 E - 0 3

5 . 9 0 2 0 - 0 . 0 0 0 0 6 2 5 0 « 4 8 3 9 E - 0 3

6 . 7 1 5 1 - 0 . 0 0 0 0 5 9 0 0 . 6 2 4 2 E - 0 3

7 . 3 9 3 7 - 0 . 0 0 0 0 3 7 5 0 . 7 5 2 9 E - 0 3

7 . 9 3 0 7 - 0 . 0 0 0 0 2 5 0 0 • 8 6 0 7 E - 0 3

8 . 3 1 8 7 - 0 . 0 0 0 0 1 2 5 0 . 9 3 9 7 E - 0 3

8 . 5 4 9 7 0 . 0 0 0 0 0 0 0 0 . 9 8 3 7 E - 0 3

8 . 6 1 4 B 0 . 0 0 0 0 1 2 5 0 . 9 8 8 5 E - 0 3

8 . 5 0 4 8 0 . 0 0 0 0 2 5 0 0 . 9 5 2 4 E - 0 3

8 . 2 1 0 0 0 . 0 0 0 0 3 7 5 0 . 8 7 6 3 E - 0 3

7 . 7 1 9 9 0 . 0 0 0 0 5 0 0 0 . 7 6 4 0 E - 0 3.

7 . 0 2 3 3 0 . 0 0 0 0 6 2 5 0 • 6 2 2 7 E - 0 3

6 . 1 0 8 6 0 . 0 0 0 0 7 5 0 0 • 4 6 3 2 E - 0 3

4 . 9 6 3 0 0 . 0 0 0 0 8 7 5 0 . 3 0 0 3 E - 0 3

3 . 5 7 3 0 0 . 0 0 0 1 0 0 0 0 . 1 5 2 6 E - 0 3

1 . 9 2 3 9 0 . 0 0 0 1 1 2 5 0 . 4 3 3 3 E - 0 4

D P / D R = - 1 2 9 6 1 . 3

P I S A M A X W H E N D I M E N S I O N L E S S R A D I U S = 0 . 1 3 5 2 E 0 4

V R B V R I ■ V R C D V Z

0 . 0 0 . 0 0 0 0 - 0 . 0 0 0 0 - 0 . 1 2 1 8 9 6 8 7 E - 0 8

2 . 2 1 8 7 2 . 1 9 3 9 2 . 0 6 2 2 0 . 3 1 9 8 4 3 6 5 E - 0 3

4 . 2 0 3 9 4 . 1 6 7 7 3 . 9 3 0 2 0 . 6 1 2 1 3 8 7 7 E - 0 3

5 . 9 5 5 5 5 . 9 1 9 7 5 . 6 0 2 9 0 . 8 7 7 3 5 5 4 7 E - 0 3

7 . 4 7 3 6 7 . 4 4 5 9 7 . 0 7 8 7 0 . 1 1 1 6 0 6 2 7 E - 0 2

8 . 7 5 8 1 . 8 . 7 4 6 4 8 . 3 5 5 3 0 . 1 3 2 8 6 4 1 5 E - 0 2

9 . 8 0 9 1 9 . 8 1 4 9 9 . 4 2 9 6 0 . 1 5 1 5 2 0 7 1 E - 0 2

0 . 6 2 6 5 1 0 . 6 4 9 5 1 0 . 2 9 8 1 0 . 1 6 7 5 4 2 3 7 E - 0 2

1 . 2 1 0 3 1 1 . 2 4 7 6 1 0 . 9 5 6 5 0 . 1 8 0 8 3 9 7 0 E - 0 2

1 . 5 6 0 7 L I . 6 0 7 3 1 1 . 3 9 9 8 0 • 1 9 1 2 5 7 6 6 E - 0 2

1 . 6 7 7 4 1 1 . 7 2 7 4 1 1 . 6 2 2 4 0 . 1 9 8 5 7 0 3 6 E - 0 2

1 . 5 6 0 7 1 1 . 6 0 7 3 1 1 . 6 1 7 9 0 • 2 0 2 4 7 6 0 2 E - 0 2

1 . 2 1 0 3 1 1 . 2 4 7 6 1 1 . 3 7 9 6 0 . 2 0 2 5 9 6 4 9 E - 0 2

0 . 6 2 6 5 1 0 . 6 4 9 5 1 0 . 8 9 9 7 0 . 1 9 8 4 7 7 9 7 E - 0 2

9 . 8 0 9 0 9 . 8 1 4 9 1 0 . 1 7 0 0 0 . 1 8 9 5 9 5 2 0 E - 0 2

8 . 7 5 8 1 8 . 7 4 5 4 9 . 1 8 1 5 0 . 1 7 5 3 5 7 8 9 E - 0 2

7 . 4 7 3 6 7 . 4 4 6 9 7 . 9 2 4 8 0 • 1 5 5 1 1 9 8 5 E - 0 2

5 . 9 5 5 5 5 . 9 1 9 6 6 . 3 8 9 5 0 * 1 2 8 1 9 0 6 4 E - 0 2

4 . 2 0 3 9 ; 4 . 1 6 7 7 4 . 5 6 4 8 0 . 9 3 8 4 9 1 2 0 E - 0 3

2 . 2 1 8 7 2 . 1 9 3 9 2 . 4 3 9 0 0 . 5 1 3 6 1 5 3 2 E - 0 3

p I S A M A X W H E M D I M E N S I O N L E S S R A D I U S = 0 . 1 3 9 7 E 0 3

V R BV R I V R C D V Z

0 . 0 i 0 . 0 0 0 0 - 0 . 0 0 0 0 - 0 . 9 0 4 4 3 4 7 5 E - 0 9

1 . 6 3 4 8 1 . 6 2 4 9 1 . 4 2 2 5 0 . 3 1 0 8 3 9 1 5 E - 0 3

3 . 0 9 7 6 3 . 0 8 3 1 2 . 7 2 6 2 0 . 5 9 9 0 3 3 4 3 E - 0 3

4 . 3 8 8 3 4 . 3 7 3 9 3 . 9 0 9 8 0 . 8 6 4 3 5 5 1 4 E - 0 3

5 . 5 0 6 8 5 . 4 9 5 2 4 . 9 7 1 0 0 . 1 1 0 6 3 9 2 1 E - 0 2

6 • 4 5 3 3 6 . 4 4 8 6 5 . 9 0 6 7 0 . 1 3 2 4 3 9 8 4 E - 0 2

7 . 2 2 7 7 7 . 2 3 0 1 6 . 7 1 2 8 0 . 1 5 1 7 3 3 5 0 E - 0 2

7 . 8 3 0 0 7 . 8 3 9 3 7 . 3 8 4 4 0 . 1 6 8 3 7 8 3 7 E - 0 2

8 . 2 6 0 3 8 . 2 7 5 2 7 . 9 1 5 8 0 . 1 8 2 1 9 2 5 2 E - 0 2

8 . 5 1 8 4 8 . 5 3 7 1 8 . 3 0 0 1 0 . 1 9 2 9 5 0 2 0 E - 0 2

8 . 6 0 4 4 8 . 6 2 ^ 4 8 . 5 2 9 7 0 . 2 0 0 3 8 1 1 3 E - 0 2

8 . 5 1 8 4 8 . 5 3 7 1 8 . 5 9 6 1 0 . 2 0 4 1 6 8 5 2 E - 0 2

8 . 2 6 0 3 8 . 2 7 5 2 8 . 4 8 9 9 0 . 2 0 3 9 4 9 2 8 E - 0 2

7 . 8 3 0 0 7 . 8 3 9 3 8 . 2 0 0 8 0 . 1 9 9 3 1 3 R 6 E - 0 2

7 . 2 2 7 7 7 . 2 3 0 1 7 . 7 1 7 5 0 . 1 8 9 8 0 7 8 9 E - 0 2

6 « 4 5 3 3 6 . 4 4 8 6 7 . 0 2 8 0 0 . 1 7 4 9 3 3 5 8 E - 0 2

5 . 5 0 6 8 5 . 4 9 6 2 6 . 1 1 9 3 0 . 1 5 4 1 5 2 8 4 E - 0 2

4 . 3 8 8 3 4 . 3 7 3 9 4 . 9 7 7 3 0 . 1 2 6 8 9 0 5 6 E - 0 2

3 . 0 9 7 6 | 3 . 0 8 3 1 3 . 5 8 7 4 0 . 9 2 5 3 8 5 8 6 E - 0 3

1 . 6 3 4 8 ' 1 . 6 2 4 9 1 . 9 3 3 8 0 . 5 0 4 6 1 0 8 3 E - 0 3

p I S A M A X W H E N D I M E N S I O N L E S S R A D I U S = 0 . 1 3 9 7 E 0 3

FLOW CMAPT N9 3 a A P P E N D I X 4

C O M P U T E R P R O G R A M & P R IN T O U T OP S O L U T IO N T O E Q U A T IO N

1 9 4

PBLl N T

W % t T £

F K l £KZl

a a u a x i o m s t o

F O R M < a u & D £ A “n C

Vi A . D C — L O O P

4 C O R P 'G 2 A J i f ^O

t o D i P ^ e e e N T

V / V l -U S S O F fa

CO M PU TE

V A L U E O F

a

c o m p a r e

V a l u e 's

- — < i ---------- — -

MG

Y

^ E N P

F L O W C H A R T NJ 3 r

1 9 6

/ / J O B 1 1 S 1 3 R K L E M Z . F / V O L U M E F L O W A I R B E A R I N G

* J O B 2 8 7 5



O O O l

0 0 0 20 0 0 3

0 0 0 4

0 0 0 5

0 0 0 6

0 0 0 7

0 0 0 8

0 0 0 9

0010 0011 00120 0 1 3

0 0 1 4

0 0 1 5

0 0 1 60 0 1 7

0 0 1 8

0 0 1 9

0 0 2 0 00 21 0 02 20 0 2 3

0 0 2 4

0 0 2 5

0 0 2 6

0 0 2 7

0 0 2 8

0 0 2 9

0 0 3 0

0 0 3 1

0 0 3 2

0 0 3 3

0 0 3 4

A L P H A = 1 . 0

G O T O 7 1

7 0 A L P H A = 1 * 5 3 3 4

7 1 R 1 = 0 . 0 1

R 2 = 0 • 0 9 5

R 3 = 0 . 0 4 5

P I = 3 . 1 4 1 5 9

S P E E = 4 0 0 0 . 0 * 2 . 0 * P I / 6 0 « 0

H = 0 . 0 0 0 1 2 5

D E N = 1 . 2 4

R D 1 = R 1 / R 2

R D 3 = R 3 / R 2

V I S = 1 . 8 / 1 0 0 0 0 0 . 0

R B = ( R D 1 * R D 1 J - 1 . 0

D M = A L O G ( R D 3 ) * ( ( A L P H A * * 3 ) - 1 . 0 >

B 4 = 0 M + A L 0 G ( R D 1 )

R A = ( 1 . 0 / ( R D 1 * R D 1 ) ) - 1 . 0

D O 1 0 0 1 = 1 , 1 0

3 0 T O ( 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , 1 8 , 1 9 , 2 0 ) , I

1 1 P P = - 2 5 0 • 0

3 0 T O 8 0

1 2 P P = - 3 0 0 • 0

G O T O 8 0

1 3 P P = 3 5 0 . 0

GO r o 3 0

1 4 P P = 4 0 0 . 0

G O T O 8 0

1 5 P P = 4 5 0 . 0

GO T O 8 0

1 6 P P = 5 0 0 . 0

G O T O 8 0

1 7 P P = 5 5 0 . 0

G O T O 8 0

1 8 P P = 6 0 0 . 0

197

0 0 3 5 G O T O 8 0

0 0 3 6 1 9 P P = 6 5 0 . 0

0 0 3 7 GO T O 8 0

0 0 3 8 2 0 P P = 7 0 0 . 0

0 0 3 9 8 0 C Q 2 = 3 . 0 * D E N * ( S P E E * * 2 ) * R 2 * R 2 / ( 2 0 . 0 * P P )

0 0 4 0 F 3 = C 0 2 * R B

0 0 4 1 F I = - 3 . 0 * V I S * B 4 / ( 4 . 0 * P I * P P # ( H * A L P H A ) * * 3 )

0 0 4 2 F 4 = 2 7 . 0 * D E N / ( ( 5 6 0 . 0 * ( P I * H * R 2 ) * * 2 ) * P P )

0 0 4 3 F 5 = 1 • 0 / ( { A L P H A * R D l - ) * * 2 )

0 0 4 4 F 6 = ( ( 1 . 0 / ( A L P H A * * 2 ) ) - 1 . 0 ) / ( R D 3 * R D 3 )

0 0 4 5 F 2 = F 4 *• ( F 5 - F 6 - 1 . 0 )

0 0 4 6 F K 1 = F 1 / F 2

0 0 4 7 F K 2 = ( 1 . 0 - F 3 ) / F 2

0 0 4 8 W R I T F ( 3 , 9 9 ) F K 1 , F K 2

0 0 4 9 9 9 F O R M A T ( 1 0 X f E 1 0 . 4 t 2 0 X » E 1 0 * 4 )

C S O L U T I O N ! O F Q U A D R A T I C

0 0 5 0 F K 3 = F K l * F K i - 4 . 0 » F K 2

0 0 5 1 I F ( F K 3 ) 9 1 , 9 2 , 9 3

0 0 5 2 9 3 F K 4 = S Q R T ( E K 3 >

0 0 5 3 S Q l = ( F K l + F K 4 > / 2 . 0

0 0 5 4 S Q 2 = ( F K l - F K 4 ) / 2 . 0

0 0 5 5 W R I T E ( 3 t 9 8 ) S Q 1. > S Q 2 t P P

0 0 5 6 9 8 F D R M A T ( 2 6 X , E 1 0 . 4 , 2 0 X , E 1 0 . 4 , 1 0 X , F 5 . 0 )

0 0 5 7 GO T O 1 0 0

0 0 5 8 9 2 0 Q = F K 1 / 2 . 0

0 0 5 9 W R I T E ( 3 » 9 7 ) 0 Q

0 0 6 0 9 7 F O R M A T ( 1 5 X , E 1 6 . 8 )

0 0 6 1 GO T O 1 0 0

0 0 6 2 9 1 W R T T E ( 3 j 9 6 )

0 0 6 3 9 6 F O R M A T ( 1 0 X » 1 MO R E A L S O L U T I O N )

0 0 6 4 1 0 0 C O N T I N U E

0 0 6 5 W R I T E ( 3 , 3 0 ) A L P H A

0 0 6 6 3 0 F O R M A T ( ’ O ' 2 5 X » 1 A L P H A = « F 6 . 4 )

0 0 6 7 I F ( A L P H A ~ 1 . 0 ) 7 0 , 7 0 7 l 0 1

0 0 6 8 1 0 1 C O N T I N U E

0 0 6 9 E N D

1 9 8

F K 1 F K 2 .

. . . . Q . V! Q - P

0 . 1 2 9 2 E - 0 2

0 . 1 2 8 4 E - 0 2

0 . 1 0 7 6 E - 0 7' 0 . 8 3 8 7 E - 0 5

h

- 2 5 0 .

O * 1 2 9 2 E - 0 2

0 . 1 2 9 4 E - 0 2

— • 2 2 7 7 E - 0 8- • 1 7 6 0 E - 0 5 - 3 0 0 .

0 . 1 2 9 2 E - 0 2

0 . 1 1 4 6 E - 0 2

0 . 1 6 7 3 E - 0 60 • 1 4 6 0 E - 0 3 3 5 0 .

0 . 1 2 9 2 E - 0 2

0 • 1 1 3 3 E - 0 2

0 • 1 8 0 3 E - 0 60 . 1 5 9 2 E - 0 3 4 0 0 .

0 • 1 2 9 2 E - 0 2

0 . 1 1 1 9 E - 0 2

0 . 1 9 3 3 E - 0 S0 . 1 7 2 8 E - 0 3 4 5 0 .

0 . 1 2 9 2 E - 0 2

0 . 1 1 0 5 E - 0 2

0 • 2 0 6 4 E - 0 60 . 1 8 6 7 E - 0 3 5 0 0 .

0 • 1 2 9 2 E - 0 2

0 . 1 0 9 I E - 0 2

0 . 2 1 9 4 E - 0 60 . 2 0 1 2 E - 0 3 5 5 0 .

0 . 1 2 9 2 E - 0 2

0 • 1 0 7 6 E - 0 2

0 . 2 3 2 5 E - 0 60 . 2 1 6 1 E - 0 3 6 0 0 .

0 . 1 2 9 2 E - 0 2

0 • 1 0 6 0 E - 0 2

0 • 2 4 5 5 E - 0 60 • 2 3 1 5 E - 0 3 6 5 0 .

0 . 1 2 9 2 E - 0 2

0 . 1 0 4 4 1 : - 0 2

A L P H A = 1 . 0 0 0 0

0 . 2 5 8 6 E - 0 60 . 2 4 7 6 E - 0 3 7 0 0 .

0 . 1 4 9 3 E - 0 2

0 . 1 4 7 7 E - 0 2

0 . 2 4 0 5 E - 0 70 . 1 6 2 9 E - 0 4 - 2 5 0 .

0 . 1 4 9 3 E - 0 2

0 . 1 4 9 6 E - 0 2

- . 5 0 8 7 E - 0 8- • 3 3 9 9 E - 0 5 - 3 0 0 .

0 . 1 4 9 3 E - 0 2

0 . 1 1 7 5 E - 0 2

0 . 3 7 3 7 E - 0 60 . 3 1 8 1 E - 0 3 3 5 0 .

0 . 1 4 9 3 E - 0 2

0 • 1 1 3 9 E - 0 2

0 • 4 0 2 9 E - 0 60 . 3 3 3 6 E - 0 3 4 0 0 .

0 . 1 4 9 3 E - 0 2

0 . 1 1 0 0 E - 0 2

0 . 4 3 2 0 E - 0 60 . 3 9 2 6 E - 0 3 4 5 0 .

0 . 1 4 9 3 E - 0 2

0 . 1 0 5 7 E - 0 2

0 . 4 6 1 I E - 0 60 . 4 3 6 5 E - 0 3 5 0 0 .

0 . 1 4 9 3 E - 0 2

0 . 1 0 0 5 E - 0 2

0 . 4 9 0 3 E - 0 60 . 4 8 7 7 E - 0 3 5 5 0 .

0 . 1 4 9 3 E - 0 2

0 . 9 4 1 0 E - 0 3

0 • 5 1 9 4 E - 0 60 . 5 5 2 0 E - 0 3 6 0 0 .

0 . 1 4 9 3 E - 0 2

0 • 8 3 9 8 E - 0 3

0 . 5 4 8 6 E - 0 60 . 6 5 3 2 E - 0 3 6 5 0 .

0 . 1 4 9 3 E - 0 2 Oo 5 7 7 7 E - 0 6

N D R E A L S O L U T I O N

A L P H A = 1 . 5 3 3 4

9 9

C O M P U T E R P R O G R A M ■ & P R IN T O U T O P RA.T1Q ! C O M P T E R M I V IS C O U S T E R M

F L O W C M A R T N °4 . A P P E N D IX 5

2 0 0

/ / J O B 1 1 S 1 3 R K L E M Z . F / \ l A y / I E R S T O K E S E Q U A T I O N

* J O B 2 7 2 1

/ / O P T I O N ! L I N K

/ / E X E C F O R T R A N !

0 0 0 1 N J B R = 0

0 0 0 2 W R I T E ( 3 , 1 2 )

0 0 0 3 1 2 F O R M A T ( ' O ' 4 X , ’ C O M ' , 1 3 X , ' C 0 M H ' , 1 1 X , ' V F T 5 , 1 1 X

• V F T H * , 1 1 X , * C Q V ' , 1 1 X , r ’ C O V N * , 9 X , 1 R» )

0 0 0 4 1 R E A D ( 1 » 1 1 ) P S , D Q , P R » P R 2 » S , R , M

0 0 0 5 1 1 F 0 R M A T ( F 8 . 0 , F 8 . 7 , F 8 . 0 , F 9 . 0 , F 5 . 1 : F 5 . 3 , F 7 . 6 )

C T E S T N U M B E R S 1 3 , 1 4 , 1 9 & 2 0

0 0 0 5 P 4 = 1 0 1 3 0 0 . 0

0 0 0 7 P - P S + P A

0 0 0 8 P I = 3 . 1 4 1 5 9

0 0 0 9 V l S = 0 . 0 0 0 0 1 8

0 0 1 0 T = 2 9 3 . 0

0 0 1 1 H = 0 * 0 0 0 1 2 5

0 0 1 2 P 2 R 2 = P R * P R

0 0 1 3 . R R = 2 B 7 • 0

0 0 1 4 DM = D Q * P / ( R ' R * T )

0 0 1 5 A l = 3 7 0 3 7 . 0 * H * * 3

0 0 1 6 A 2 = ( 1 . 8 1 7 * D M * D M * T ) / ( H * H )

0 0 1 7 A 3 = 1 2 . 0 / ( P * ( R * * 5 ) )

0 0 1 8 A 4 = ( 6 . 0 * P R ) / ( P * P * ( R # * 4 ) )

0 0 1 9 A 5 = P R 2 / ( P * P * ( R * * 3 ) )

0 0 2 0 A 6 = 2 . 0 * P 2 R 2 / ( ( R * P ) * * 3 )

0 0 2 1 A 7 = S * S / ( 9 5 6 . 9 0 f i - T )

0 0 2 2 A B = 2 . 0 * P R

0 0 2 3 A 9 = R * P R 2

0 0 2 4 A 1 0 = D M * T / { 8 1 1 . 0 * ( H * * 3 ) )

0 0 2 5 A 1 1 = 2 . 0 / ( P * ( R * * 3 ) )

0 0 2 5 A 1 2 = 2 . 0 * P R / ( P * P * R * R )

0 0 2 7 A 1 3 = P R 2 / ( P * P * R )

0 0 2 8 A 1 4 = 2 . 0 * P 2 R 2 / ( R * ( P * * 3 ) )

0 0 2 9 A 1 5 = 6 7 3 1 3 • 0 # D M * D M * T * H

0 0 3 0 A 1 6 = S * S * ( M * * 3 ) * 1 7 . 7 4 4 / T

0 0 3 1 A 1 7 = 5 6 . 4 5 * S * S * ( H * * 3 ) / T

0 0 3 2 A 1 8 = P R 2 / ( P * P * R * R * R )

0 0 3 3 A 1 9 = D M O M * R R * T / ( 8 . 0 * P I * P I * R * R * R * P * V I S * H )

2 0 1

0 0 3 4

0 0 3 5

0 0 3 6

0 0 3 7

0 0 3 8

0 0 3 9

0 0 4 0

0 0 4 1

0 0 4 2

0 0 4 3

0 0 4 4

0 0 4 5

0 0 4 6

0 0 4 7

0 0 4 8

0 0 4 9

0 0 5 0

0 0 5 1

0 0 5 2

0 0 5 3

0 0 5 4

0 0 5 5

0 0 5 6

0 0 5 7

0 0 5 3

0 0 5 9

0 0 6 0

0 0 6 1

0 0 6 2

0 0 6 3

0 0 6 4

0 0 6 5

A 2 0 = S * S * H * * 3 ) * 3 8 . 7 2 / T

B 1 = 1 • 0 / R

B 2 = 3 7 0 3 7 . 0 * ( H * » 3 )

B 3 = 3 . 0 / ( P » ( R * » 4 ) )

B 4 = P R / ( P * P * { R * * 3 ) )

B 5 = R * P R

B 6 = 1 . 0 / ( P * R * R )

B 7 = P . R / ( P * P * R )

C 1 = 1 . 0 / ( R * R )

C 2 = l . 8 7 * D M * D M * T / ( H * H * P * ( R * * 3 ) )

C 3 = S * S * P * R / ( 9 5 6 . 9 * T )

C 4 = D M * T / { 8 1 1 . 0 * ( H * * 3 ) * R * P )

C 5 = 6 7 3 1 3 . 0 * D M * D M * T * H / { P * { R * * 3 ) )

C 7 = 3 7 0 3 7 . 0 * ( H * * 3 )

A = - A 1 * { 4 2 * ( A 3 * 4 4 - 4 5 * 4 6 ) * 4 7 * ( 4 8 * 4 9 ) - 4 1 0 * ( A 1 1

+ 4 1 2 - 4 1 3 * 4 1 4 ) ) + A 1 5 * ( 4 3 * 4 4 + A 6 - 4 1 8 ) • - 4 1 6 * ( 4 8 + 4 9 ) +

4 1 7 * ( A & + A 9 )

B = B 1 « { - 8 2 * ( A 2 * ( - 6 3 - 3 4 J + 4 7 * ( P + B 5 ) + 4 1 0 * { 8 6 + B 7 ) ).

- A 1 5 M B 3 + 3 4 ) + 4 2 0 * ( P + 3 5 ) )

C = C 1 * ( - G 7 * ( C 2 + C 3 - C 4 ) * C 5 * { 4 2 0 * P * R ) )

C 0 M = V I S * ( A + B - C ) / 3 . D

C 0 M H = V I S * D M * R . R * T * { 4 1 2 / 2 . Q + A l 4 - A 1 3 ) / { 6 . 0 * P I )

V 1 = 1 2 9 . 0 5 * P * R * S * S * H / r

V 2 = 3 . 0 / ( H * H * P * . R )

V F T H = V I S * D M * R R * r * { A 1 2 / 2 . 0 + A l 4 - A 1 3 - V 2 ) / ( 2 . 0 * P I )

V T = 2 . 0 * H * ( A 2 / ( P * ( R * * 3 ) ) * A 7 * P * R - A 1 0 / ( R * P ) ) / V I S -

A 1 9 - V 1

V F T = V I S M A + 3 - C + V T )

C O V H = C O M H / V F T H

C 0 V = C 3 M / V F T

C C Q M = C O M P R E S S I B I L I T Y T E R M

C C 3 M H = C Q M P R E S S I 3 I L I T Y T E R M ( H O B S O N & L A W R I E )

C V F T = V I S C O U S T E R M

C V F T H = V I S C O U S F L O W T E R M ( H O B S O N & L A W R I E )

C C D V = C Q M / V F T

C C 0 V H = C 3 M H / V F T H

W R I T E ( 3 , 1 0 ) C O M , C O M H , V F T , 7 F T H , C O V , C O V H , R

1 0 F O R M A T * * 0 * I X , 6 ( E 1 0 . 4 , 5 X ) f F 5 . 3 )

I F ( N U B R - 4 0 ) 7 7 * 3 4 5 , 3 4 5

7 7 N J B R = N U 3 R + 1

I F ( N J B R - 4 0 ) 1 , 3 4 5 , 3 4 5

3 4 5 C O N T I N U E

E N D

2 0 2

C O M C O M W V F T v 'f t h c o v C O V W R

0 . 6 1 7 7 E - 0 4 0 . 1 2 4 7 E - 0 4 - • 4 7 1 OE 0 2 4 7 0 8 E 0 2 - . 1 3 1 2 E - 0 5 2 6 4 3 E - 0 6 0 . 0 1 0 x

0 . 1 0 8 5 E - 0 4 0 . 4 3 4 7 E - 0 5 - • 3 1 3 9 E 0 2 3 1 3 9 E 0 2 - • 3 4 5 9 E - 0 6 - . 1 3 3 5 E - 0 6 0 . 0 1 5 I

0 . 3 3 7 7 E - 0 5 0 . 1 8 3 3 E - 0 5 - • 2 3 5 4 E 0 2 - . 2 3 5 4 E 0 2 - * 1 4 3 5 E - 0 6 - . 7 7 8 5 E - 0 7 0 . 0 2 0

- • 2 8 6 9 E - 0 6 - . 4 8 9 6 E - 0 6 - . 1 5 6 9 E 0 2 - . 1 5 5 9 E 0 2 0 . 1 8 2 3 E - 0 7 0 . 3 1 1 9 E - 3 7 0 . 0 3 0

- • 2 3 5 7 E - 0 6 2 8 3 6 E - 0 6 - • 1 1 7 7 E 0 2 - . 1 1 7 7 E 0 2 0 . 2 0 0 3 E - 0 7 0 . 2 4 0 9 E - 0 7 0 . 0 4 0 \

- . 1 5 0 4 E - 0 6 1 6 6 0 E - 0 6 9 4 1 5 E 0 1 - • 9 4 1 7 E 0 1 | 0 . 1 5 9 7 E - 0 7 0 . 1 7 6 3 E - 0 7 0 . 0 5 0 I

- . I D 5 5 E - 0 6 - . 1 1 1 8 E - 0 6 - • 7 8 4 6 E 0 1 - . 7 8 4 7 E 0 1 ; 0 . 1 3 4 5 E - 3 7 0 . 1 4 2 5 E - 0 7 0 . 0 6 0

- . 7 5 1 3 E - 0 7 - • 7 8 0 4 E - 0 7 - . 6 7 2 5 E 0 1 - ♦ 5 7 2 6 E 0 1 ! 0 . 1 1 1 7 E - 0 7 0 . 1 1 5 0 E - D 7 0 . 0 7 0

- . 5 5 7 8 E - 0 7 5 7 2 7 E - 0 7 5 8 8 4 E 0 1 5 8 3 5 E 0 1 0 . 9 4 7 9 E - 0 8 0 . 9 7 3 1 E - 0 8 0 . 0 8 0

- . 4 6 9 0 E - 0 7 - • 4 8 0 0 E - 0 7 5 5 3 8 E 0 1 - • 5 5 3 9 E 0 1 0 . 8 4 6 9 E - 0 8 0 . 8 6 6 6 E - 0 8 0 . 0 3 5 *

0 . 5 7 5 7 E ” 0 4 0 . 8 3 9 0 E - 0 5 - • 4 7 1 1 E 0 2 - . 4 7 0 8 E 0 2 1 2 2 2 E - 0 5 1 7 3 2 E - 0 6 0 . 0 1 0 \

0 . 1 0 1 1 E - 0 4 0 . 3 6 2 1 E - 0 5 - • 3 1 4 2 E 0 2 - . 3 1 3 9 E 0 2 - • 3 2 1 9 E - 0 5 - . 1 1 5 4 E - D 6 0 . 0 1 5

0 . 4 0 2 4 E - 0 5 0 . 2 4 8 4 E - 0 5 2 3 5 8 E 0 2 - • 2 3 5 4 E 0 2 - . 1 7 0 7 E - 0 5 1 0 5 5 E - 0 6 0 . 0 2 0

- • 2 9 7 6 E - 0 6 - . 4 9 9 9 E - 0 6 - • 1 5 7 5 E 0 2 - • 1 5 6 9 E 0 2 0 . 1 B 9 D E - 0 7 _ 0 . 3 1 8 5 E - 0 7 0 . 0 3 0

- • 2 5 0 2 E - Q 6 - . 2 9 3 1 E - 0 5 - . 1 1 3 4 E 0 2 - . 1 1 7 7 E 0 2 0 . 2 1 1 3 E - 0 7 0 . 2 5 3 2 E - 0 7 0 . 0 4 0

- . 9 4 2 D E - 0 6 9 5 7 8 E - 0 6 - • 9 5 D 4 E 0 1 - • 9 4 1 7 E 0 1 0 • 9 9 1 2 E - 0 7 0 . . 1 0 1 7 E - 0 5 0 . 0 5 0

- . 1 0 7 2 E - 0 6 - . 1 1 3 5 E - Q 6 - • 7 9 5 2 E 0 1 - . 7 8 4 7 E 0 1 0 . 1 3 4 3 E - 0 7 • 0 . 1 4 4 6 E - 0 7 0 . 0 6 0

- . 5 0 1 9 E - Q 7 - • 6 3 D 9 E - 0 7 - • 6 8 4 9 E 0 1 - • 5 7 2 6 E 0 1 0 . 8 7 8 7 E - G 3 0 . 9 3 7 9 E - 0 8 0 . 0 7 0

- . 4 2 2 7 E - 0 7 - . 4 3 7 6 E - 0 7 6 0 2 6 E 0 1 5 8 8 5 E 0 1 0 . 7 3 1 5 E - 0 8 0 . 7 4 3 6 E - 0 3 0 . 0 8 0

3 4 2 7 E - 0 7 3 5 3 6 E - 0 7 - • 5 6 8 9 E 0 1 5 5 3 9 E 0 1 0 . 6 0 2 4 E - 0 8 0 . 6 3 8 4 E - 0 8 0 . 0 8 5 J

61 oN 1S

31

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1

2 0 3

C O M C D M H V F T V F T H - C O V C U V H R

0 . 1 2 5 2 E - 0 4 - • 6 4 9 1 E - 0 6 - . 2 4 2 6 E 0 2 - . 2 4 2 6 E 0 2 - • 5 1 6 3 E - 0 6 0 . 2 6 7 6 5 - 0 7 0 . 0 1 0

0 . 1 3 6 1 E - 0 5 - . 3 7 1 1 5 - 3 6 - • 1 6 1 7 E 0 2 - . 1 6 1 7 E 0 2 - . 8 4 1 5 E - 0 7 0 . 2 2 9 5 5 - 0 7 0 . 0 1 5

0 . 1 1 0 1 E - 3 6 3 0 3 3 E - D S - . 1 2 1 3 E 0 2 - . 1 2 1 3 E 0 2 - . 9 0 3 1 E - 3 3 0 . 2 4 7 3 E - 3 7 0 . 3 2 0

- • 9 6 8 6 E - 0 7 - . 1 5 0 7 E - 0 6 - • 8 3 8 4 E 0 1 - • 8 0 8 6 E 0 1 0 . 1 1 9 8 E - 0 7 3 . 1 8 6 4 E - 0 7 0 . 0 3 0

- . 1 2 4 5 E - 0 6 - • 1 3 7 2 E - 0 6 - . 6 0 6 3 E 0 1 — • 6 0 6 4 E 0 1 0 . 2 0 5 3 E - 0 7 3 • 2 2 6 2 E - 0 7 0 . 0 4 0

- . 9 1 6 6 E - D 7 - . 9 5 8 2 E - D 7 - . 4 8 5 3 E 0 1 - . 4 8 5 I E 0 1 0 . 1 8 9 0 E - 3 7 0 . 1 9 7 5 5 - 3 7 . 0 . 3 5 3

- . 5 5 7 8 5 - 0 7 - • 5 8 4 6 E - 0 7 - • 4 0 4 2 E 0 1 - • A 0 4 3 E 0 1 0 . 1 4 0 5 E - 0 7 0 . 1 4 4 6 E - 0 7 0 . 0 6 0

- . 4 1 0 7 E - 0 7 - • 4 1 8 4 E - 3 7 - • 3 4 6 5 E 0 1 - . 3 4 6 5 E 0 1 • 0 . 1 1 8 5 E - 0 7 3 . 1 2 0 3 5 - 3 7 0 . 0 7 0

- • 2 9 1 9 E - 0 7 - . 2 9 5 9 5 - 0 7 - . 3 0 3 1 E% 0 1 - • 3 0 3 2 E 0 1 0 . 9 6 3 0 5 - 3 3 • 0 . 9 7 5 3 5 - 0 8 0 . 3 3 3

- • 2 5 3 4 5 - 0 7 - . 2 5 6 4 E - 3 7 - . 2 8 5 3 E 0 1 - • 2 8 5 4 E 3 1 0 . 8 8 8 1 5 - 0 8 0 . 3 9 8 4 E - 0 8 0 . 0 8 5

0 * 1 1 9 5 E - 0 4 - . 1 1 9 7 E - 0 5 - • 2 4 2 8 E 0 2 - . 2 4 2 6 E 0 2 - • 4 9 2 1 E - 0 6 3 . 4 9 3 5 E - 0 7 0 . 0 1 0

0 . 6 3 6 1 E - 0 6 - . 1 1 2 1 E - 0 5 - • 1 6 2 3 E 0 2 - • 1 6 1 7 E 3 2 - . 3 7 4 2 E - 0 7 3 . 6 9 3 3 5 - 0 7 0 . 0 1 5

0 . 5 8 3 5 E - 0 7 - • 3 5 0 6 E - 0 5 - . 1 2 1 6 E 0 2 - . 1 2 1 3 E 0 2 - . 4 7 9 3 5 - 3 8 0 . 2 8 9 1 5 - 0 7 0 . 0 2 0

- • 1 2 2 2 E - 0 6 - . 1 7 6 3 E - D 6 - . 8 1 3 8 E 0 1 - . 3 0 8 6 E 0 1 0 . 1 5 0 2 5 - 0 7 0 . 2 1 7 5 E - 0 7 0 . 0 3 0

- • 8 7 7 1 E - 0 7 - . 1 0 3 4 E - 3 6 - . 6 1 3 5 E 0 1 - . 6 0 6 4 E 0 1 0 . 1 4 3 0 5 - 0 7 3 . 1 6 5 3 5 - 3 7 0 . 0 4 3

- . 6 4 2 8 E - 3 7 - . 6 8 4 2 5 - 3 7 - . 4 9 4 0 E 0 1 - . 4 8 5 I E 0 1 1 0 . 1 3 0 1 5 - 0 7 0 . 1 4 1 3 5 - 0 7 0 . 3 5 0

- . 7 9 4 5 E - 0 7 - . 8 1 1 3 E - 3 7 - • 4 1 4 9 E 0 1 • - • 4 0 4 3 E 0 1 0 . 1 9 1 5 5 - 0 7 0 . 2 0 3 7 5 - 0 7 0 . 0 6 0

- • 4 8 2 3 E - 3 7 - . 4 9 3 1 E - 3 7 - . 3 5 8 9 E 0 1 - . 3 4 5 5 E 0 1 0 . 1 3 4 4 5 - 0 7 3 . 1 4 1 4 E - 3 7 0 . 3 7 3

- . 3 7 0 3 E - Q 7 - . 3 7 4 3 E - 3 7 - • 3 1 7 3 E 0 1 - . 3 0 3 2 5 0 1 0 . 1 1 6 7 E - 0 7 3 . 1 2 3 4 E - 0 7 0 . 0 3 0

- • 2 9 8 6 E - 0 7 - • 3 0 1 5 E - 0 7 - • 3 0 0 4 E 0 1 - . 2 8 5 4 5 0 1 0 . 9 9 4 1 E - 0 8 0 . 1 0 5 7 E - 0 7 0 . 0 8 5

\

TES

T N°

1

4.

TES

T N

°I3

2 0 4

STATEMENT OF ADVANCED COURSES OF STUDY ATTENDED

Three advanced courses of study were attended, at S heffield

Polytechnic, during the period in which the research was being

carried out. These were:

(1) Instrumentation and Control.

(2) Course on Tribology: Lubrication Theories.

(3) Preparation of scientific programs in BASIC and FORTRAN IV

for use on I.B.M.1130 and I.B.M. 370/135 digital co mputers.

2 0 5

2 .

3.

4.

5.

6 .

7.

8 .

9.

1 0 .

11 .

1 2 .

13.

14.

15.

16.-

17.

18.

1.

REFERENCES

BRAND R.S. Journ. App. Mech. Vol .22 ASME Trans. Vol .77 1955 p .363

LIVESEY J.L. Int.J.Mech.Sci. Vol.l 1960 p . 84

MORGAN P.G. and SAUNDERS A. In t .J .Mech.Sci . Vol .2 19 60 p . 8

JACKSON J.D. and SYMMONS G.R. Int.J.Mech.Sci. Vol .7 . 1965p.239

HUNT J.B. and TORBE I. Int. J.Mech. Sci. Vol. 4.. 1962 p . 503

MOLLER P.S. The Aeronautical Quarterly Vo l .14 1963

JACKSON J.D. and SYMMONS G.R. App. Sci.Res. Section A Vol .151964 p .59.

HOBSON B.D. and LAWRIE J.M. A Method of Analysing t he effect of inertia and compressibil ity in an externally pressurised gas lubricated thrust bearing.

Conference on Externally Pressurised Bearings held at the Institution of Mechanical Engineers, London,Nov.1971 p .368.

OSTERLE J.F. and HUGHES W.F. Wear Vol.l 1957/58 p .4 65

DOWSON D. Journ. Basic Eng. ASME Trans. Vo l .83 1961 (SeriesD. No.2) p .227

COOMBS J.A. and DOWSON D. Inst.Mech.Eng. Proceeding s Vo l .1791964/65 p .96

SHIRMAN H.N. MSc Thesis Inertia Effects in Hydrosta ticThrust Bearings. The Victoria University of Manchester. Jan.1969

TING L.L. and MAYER J.E. The Effects of Temperature and Inertia on Hydrostatic Bearing Performance.

Journal of Lubrication Techno logy Vol .93 No.2 p.307 1971

FULLER D.F. Theory and Practice of Lubrication for EngineersJohn Wiley & Sons 1965

POWELL J.W. The Design of Aerostatic bearingsPOWELL J.W. The Machinery Publishing Co. 1970

GRASSAM N.S. and POWELL J.W. Gas Lubricated Bearing sButterworths 1964

NEALE M.J. Tribology Handbook Butterworths 1973

BAIRD D.C. Experimentation: An Introduction To Meas urement Theory and Design.Prentice-Hall 1963

2 0 6

19. A Large Tank of Liquid Helium for Nuclear Exper imentsNew Scientist (No.325) Feb.1963 p .277

20. PINKUS 0. and STERNLICHT B. Theory of Hydrodyna mic Lubrication McGraw-Hil l 1961

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