digital.library.unt.edu/67531/metadc64105/m2/1/high_res_d/19930090066.pdfld cc to d national...
TRANSCRIPT
c
RESEARCH MEMORANDUM A MJ3THOD FOR RAPID SELECTION OF DESIGN CHARACTERISTICS
OF I -, la-, 2
AND 2 S T A G E TURBINES WITH
OPTIMUM ANNULUS TAPER
%Peggy L. Yohner and R&bert.E, English
F e w i s Flight Propulsion Laboratory Cleveland, Ohia
2, :.,
NATI~NAL ADVISORY COMMITTEE 3 .I, FOR AERONAUTICS cI1 WASHINGTON
February 18, €958
LD cc to d
NATIONAL ADVISORY COMMI- FOR AEXONALJTICS
1-, l$-, AHD 2-SWGE TURBINES WITH O P ! K " ANHULUB 'PAPER
By Peggy L. Yohner and Robert E. English
A method is presented f o r the rapid selection of a turbine design within specified aerodynamic limits. Tables present detailed information on the over-dl design parameters and velocfty-diagram variables of each design. C h a r t s prepared from the tables f a c i l i t a t e the evaluation of turbine diameter and exi t rad ius r a t io fo r a selected number of stages.
r: The turbine annulus was tapered t o yield maximum work output. Aerody- E namic variables accepted as limiting in the turbine designs were: (1)
turbine rotor exit axial Mach number, (2) blade-row entrance relative Mach number, and (3) zero relative velocity change across a blade row. Several examples demonstrate the use of the charts and tables. 4
8
INTRODUCTION
Some of the most important considerations i n t h e i n i t i a l phases of a turbine design are the number of turbine stages, the divfsion of work between the stages, the aerodynamic lhits t o be imposed on the turbine, and the turbine diameter. A rapid, accurate method of estimating the turbine diameter for a selected number of stages and a given s e t of aero- dynamic limits would accelerate this preliminary phase of the design and make it more definitive.
Reference 1 presents a method f o r rapid estimation of the aerodynamic characteristics of I-stage and multistage turbines wi th in specified aero- dynamic limits. Reference 2 contains a similar method for 1-stage tur- bines w i t h downstream stators (hereinafter called "14-stage turbines"). In both analyses, annulus taper is an independent variable whose magnitude is lef t to the designer . Tapering the annulus is especially important at high blade speeds, because turbine work can thereby be increased as much as 85 percent. The selection of annulus taper for maximum turbine work (or, alternatively, minimum turbine diameter f o r a given work output) requires considerable effort, even w i t h the assistance of references 1 and 2.
e
a
NCLASSIFIED
2 NACA RM E57Jo9
The velocity-diagram analysis of the present report considers tu- bines having 1, l*, and 2 stages. The data of references 1 and 2 were extended in the following ways:
(I) The amount of annulus taper was selected to produce maximum w o r k output. For simplicity, the inner w a l l of the tapered annulus w a s assumed t o be conical, even though such a specification probably does not produce tbe greatest turbine work within the specified design limits; and the outer w a l l o f t h e annulus was made cylindrical. rp
LT
0 (2) For 2-stage turbines, deceleration in the second s ta tor w&8 .
avoided. (In ref. 1, exclusion of those turbines w i t h deceleration in the second s ta tor is left t o the designer. )
(3) For those design problems in which turbine diameter ie not speci- f ied and minimum turbine diepeter is desired, charts were prepared t o permit rapid determination of turbine diameter.
(4) The range of blade speed was extended t o both higher and lower values.
(5) The tabulated results were expanded t o present m o r e information on the internal flow of each design.
The turbine aerodynamic variables accepted as l imiting in the design k
were : (I) turbine rotor exit axial Mach number, (2) blade-row entrance relative Mach number, and (3) zero relative velocity change across a 2 blade row. Both the turbine exit axial Mach number and the blade-row entrance relative Mach number were varied to yield turbines of conserva- t ive, moderate, and c r i t i c a l design.
DESCRIPTION OF TABLES AND CHARTS
The symbols used i n t h i s analysis are defined in appendix A. The derivations of the equations and the methods of analyzing the I-, %, and 2-stage turbines are described i n appendixes B, C, and D, respectively.
Assumptions
The following assumptions were made t o simplify the analysis:
(1) There is no radial variation in stagnation state relative t o the stator.
(2) Free-vortex flow conditions prevail at each. axid station.
HACA RM E57J09 - 3
4 (3) ~ n y effects of annulus w a ~ curvature or r a d components of
4 velocity m a y be neglected.
(4) he losses occur as follows:
(a) In a 1-stage turbine, all losses occur i n the rotor.
(b) In a +-stage turbine, the losses corresponding t o the 1
p w r o p i c efficiency d l occur in the rotor; additional losses i n the dOwnstrea3II stator are conaidered in the form of 8 st-ion- pressure Loss coefficient &, = 0.05.
(c) In a 2-stage turbine, the- entropy rise per stage is split, wlth one-third occurring in the stator and two-thirds in the rotor .
(5) TIE constant value f o r the ra t io of specific heats rT is 4/3.
(6) The turbine polytropic efficiency is 0.85.
(7) The amount of exi t w h i r l t o be tolerated in turbines without %,T
%
3 2-
downstream stators can be assigned as a percentage of the turbine work
P d -VeZ,o,Ui
5 (8) In the l*-stage turbines, the downstream stator eliminstes exit Y whirl.
(9) In the 8-stage turbines, the inner annulus d l is a single .
conical surface f’rom the f i r s t - ro tor in le t t o the turbine exit.
The effects of assumptions (4) t o (6) on the results of the analysis are described i n the DISCUSSION.
Organization af Tables
Each of tables I, 11, and III corresponds t o a given number of stages and a particular combination of aerodynamic limits. Table IV summarizes and identifies these tables for easy reference. (In table identification, a Roman numeral corresponds to the number of stages; a letter, t o the exit axial Mach number; and an Arabic numeral, t o other limiting aerodynamic variables. )
Figure 1 shows the geometry of the turbines and the axial stations. Flgure 2 presents typical velocity diagrams of the turbines. The tables were prepared with blade-speed parameter ut as the independent
c
Sa,cr,l L’ variable and exi t rad ius r a t io (?)o as the parameter.
4
Construction of C h a r t s
NACA RM E57J09
Charts were prepared from the tables to facilitate entry into the tEibles. Both the abscisss and the ordinate of the-charts are dimension- less quantities that the designer can evaluate from the requirements of the turbine design. The abscissa and the ordinate were obtained from the t a l e information in the followlug manner:
and.
It can be seen that the abscissa of the charts w 2
%,lRa, cr ,1 3 hasa
close relation to the parameter e described in reference 3, differing only in that parameter e fs expressed in terms of the compressor-Inlet stagnation conditions and this parameter is expressed in terms o f t h e turbine-inlet stagnation conditions. This parameter is useful because it relates the compressor and the turbine in a manner that is independent of
actual diameter. The ordinate of the chart8 --, is also expreesed
i n terms of turbine-inlet st~lgnation conditions and is independent of turbine diameter.
%,cr,l
The chart numbering system parallels that of the tablesJ that is, data in table I(&) are plotted in chart I (a), and BO forth. Each p8rt of charts I and 11 represents information corresponding 10 two parts of tables I and II so that both (g)2,hs limit and &)h 5 1.0 were sat-
isfiedi that is, chart I(a) 1 contains data from both tables I(a) 1 and I(a)3. (Neither table I11 nor chart I11 exceeds either the Mach number limit or the velocity-ratio limit.) Each chart consists of a mid of
ut. -
curves representing constant and ($)o. On charts I and 11, %,cr,l
where applicable, there is an curve representing those design6 for which (E) = limit and
a Z,h = 1.0 simultaneously. Along this
curve, the slapes of some curves are discontinuous because the turbines change f Y o m Mach-number-limited to velocity-ratio-limited.
4
f
NACA RM E57509
1
S
5
DISCUSSION - ..
Annulus Taper
Figure 3 compares the attainable work parameter of high-output 1-stage turbines designed w i t h optimum annulus taper and that attainable from turbines without taper. The m a x i m u m benefit Prom annulus taper is achieved at a combination of high blade speed and low r a d i u s ra t io . For
= 0.5 (fig. 3(a)), when (g)Z,h = 0.8 and a ut = 1.0, there is a,=-,l
a maximum increase of 85 percent in turbfne work; when El = 1.0 and ~.
ut = 1.0, there is a maximum increase of 102 percent in turbine work. %,cr,l In the latter case, '(F) = 1.334 (fig. 4 or table I(c)3), which exceeds
the currently accepted limits; the 85-percent increase of the first example would be the more r ea l i s t i c of the two. Since both the preceding examples
axe extreme, a more typical example m i g h t be cr ,1 = 0.7 and
2,h
"
= 0.5; i n th i s case there is a 26-percent increase in turbine work i
when (F) = 0.8 and 1.0. u 2,h
Rotor Inlet Mach Number Limitation
Figure 3 also shows that, i f rotor inlet Mach number can exceed nor- m a l limits, l u g e amounts of work are available at high blade speeds from turbines limited by velocity ratio. Figure 4 shows the increases in rotor in le t Mach number associated with th i s increase in turbine work for high- output 1-stage turbines. In order to show the potential gain resulting *om elimination of the limit on rotor inlet Mach number, the design
information corresponding t o the complete ranges of ut %,cr, l and
is tabulated for all 1- and lgstage ' turbines l imited by velocity
r a t i o .
Inlet Radius Ratio
Figure 5 shows the variation of turbine work with inlet r a u s r a t i o a for selected high-output 1-stage designs. Figure 6 shows this same
6 0 NACA RM E57JO9
variation for selected high-output 2-stage designs. I n arrow indicates the inlet r a d i u s ratio that corresponds turbine work and is the design value i n the tables. It as the inlet radius r a t i o exceeds the value for m a x i m u m
5
both figures an t o the m a x i m u m can be seen that, work. there can
X
be a sudden decrease in turbine work. This is most c r i t i c a l at high blade speeds and high radius ratios.
- I
A comparison of figures 5 Bnd 6 shows tht the gain i n work from annulus taper i s greater i n a %stage turbine than i n a 1-stage turbine.
For example, when ($)o = 0.5 and a = 0.6, the increase in tur- a,cr , l
bine work is 14 percent for the 1-stage t u r b i n e and 43 percent for the . .
Z-~twe turbine.
Ratio of Specific Bats rr
In 811 e f f o r t t o determine the effect of changes in yT f’rom the assumed value of 4/3, two 1-stage designs were re-evduated fo r UT vsrying from 1.3 t o 1.4. The results are ahom i n figure 7. For low blade speeds, there is no change i n either inlet r a d i u s r a t i o or turbine work. A t higher blade speeds, the effect is still quite small. The maxi- mum error introduced by assuming y, = 4/3 mer this range is 1.6 percent in turbine work and 0.6 in inlet radius ra t io .
Polytropic Efficiency
I n the same way, the effect of varying polytropic efficiency from the assigned value of 0.85 w a s investigated by varying q fYom 0.75 t o 0.90. The results are shown i n figure 8. The effect of varying poly- trapic efficiency is greater at high blade speeds than at low blade speeds. The maximum variation i n turbine work is 4.9 percent when + = 0.4,
P,T.
TT
and 10.3 percent when = 0.8. The maximum var ia t ion in in le t
r a d i u s r a t i o is 2.5 percent when ut = 0.4, and 5.0 percent when &a, c r ,1
%, c r ,1 I T
= 0.8. c r ,I
It should also be noted i n figure 8 that, aa the assigned value of turbine efficiency increases, the maximum turbine-work parameter decreases. This var ia t ion in turbine work is a direct result of the effect of turbine efficiency on turbine pressure ratio. Decreasing turbine efficiency
raises both the pressure r a t i o - and the r a t i o of densities pin PO Pa, o
Pa, In
NACA RM F57J09 7
" across the turbine. This effect can be simply explained by considering a se t of conditions different from those used i n the analysis: For given
and for a given set of turbine exit conditions, the increased density r a t io accompanying lower efficiency decreases the i n l e t axial Mach number and thereby increases the potential turbine work capacity within the specified design limits.
e values of turbine work, blade speed, and in l e t and exit radius ratios,
Loss Assumptions
Assumption (4) i n t he DESCRIPTION OF TABLES awD CHARTS considers that , for 1- and le-stage turbines , the losses in the f i rs t two blade rows are concentrated in the rotor, whereas f o r the 2-stage turbines the losses are divided between the s ta tor and the rotor . In order t o determine the effect of these differing assumptions on the final results, three 1-stage designs were computed with the loss distribution assumed for the E-stage turbines; that is, one-third of the entropy r i s e occurs in t he s t a to r and two-thirds in the ro tor . All three designs were high-output 1-stage t u r -
bines (k) = 0.7 and (E) = 0.8) . The comparative results are
shown in the following table: 3 ,m 2,h
The largest change occurs at a high blade speed and low radius r a t io . Decreasing the blade speed or increasing the radius ratio causes the change in turbine work t o approach 1 percent. In addition it should be noted that, of the two weight-flow parameters, the turbine-exit weight- flow parameter is much less sens i t ive to the loss assumptions and is con- sequently more reliable.
Second-Stage-Stator Velocity Limitations
In o rde r t o determine the e f fec t of the velocity limits of the second-stage s ta tor on design turbine work, these limits were decreased and a selected group of designs w a s recalculated. Figure 9 shows the comparative resul ts . A t high blade speeds the last three blade rows are all limited by Mach number. As the blade speed is decreased, the second rotor becomes limited by velocity ratio whlle the f i rs t rotor and second d
8 __IC__ NACA RM E57J09
s ta tor remain limited by Mach number. A further decrease in blade speed changes the second-stator limitation to velocity ratio, and f ina l ly at low blade speeds the last three blade rows all become limited by velocity I r a t io . The effect of decreasing the mch number l i m i t from 0.8 t o 0.7 is a minor decrease in turbine work (5 percent at the m a x i m u m ) , b u t the e f fec t of decreasing the velocity-ratio l i m i t is a major decrease i n t u r - 8 bine work (31 percent or more). As the blade-speed parameter was decreased t o 0.2, it became impossible t o compute a design f o r @)5,m = 0.6 and (z)t = 0.9. The velocity level at the i n l e t t o the second stator, dic-
tated by the limit imposed, w a s insuff ic ient to pass the necessary mass flow even i n a s t ra ight annulus. It should be noted that at the low blade speeds, where the second s t a to r is limited by velocity ratio, use of ref- erence 1 w i l l yield inappropriate results.
% -
4 VI
Comparison of Work Available
Figure 10 compares the amount of work available in I-, lz, and 2- stage turbines for selected design limitations. It is interest ing to note that at extremely Lar blade speeds there is more work available i n a 1% stage turbine than in a 2-stage turbine. The large work output of the lT-stage turbine results f'rom the large tangential velocity at the inlet
t o the downstream stator . The inlet tangential velocity acceptable by t h i s s t a to r is independent of rotor blade speed and remains high even at low speeds.
1
1
General
The-charts facilitate entry into the tables when turbine blade speed and exit r a d i u s r a t i o are unknown and enable the designer t o determine rapidly which of the many possible designs is most applicable to the given design problem. ..
The turbine design requirements w i l l comonly consist of:
(1) ~ngular velocity CD, r&ans/sec
(2) Work per pound of gas -AH, Btu/ lb
(3) Weight flow w, lb/sec
NACA RM E57J09 9
v) fc Ln d
(4) Turbine-inlet stagnation temperature Tly %
(5) Turbine-inlet stagnation pressure P ~ , Ib/sq ft
These turbine variables are not convertible t o those in the tables without some selection of turbine diameter. However, they are readily expressed i n terms of the charrt variables, namely,
w h e r e
m2
RPa, 1 a, cr, 1 a3 a a,m,l
and
and
With calculated values for these parameters, it is possible to enter any
N of the charts and determine and (F)o. k 8,
In order t o help determine w h i c h of the designs is most applicable, the t i p r a d i u s of the turbine may be calculated by
W
rt = U t aa.cr.1 aa, cr , 1 0)
and compared w i t h a limiting or desired value. All designs with too large a diameter may then be discsrded, and only those that are reasonable should be further investigated through use of the appropriate tables.
Interpolation in Tables
Any of the tables may be entered afrectly if a blade-speed par-ter and ex i t radius r a t i o are k n m for any given set of turbine design limits. In general, lineas interpolation in a given table would be adequate, and no more than one significant figure would be lost in %he result. However, this is not d y s true, and the tabulated resul ts should be scanned i n the region of in te res t to determine the method of interpolation to be used, Fbr example, the pressure ra t ios corresponding to a high blade-
polation is advisable. The turbine characterist ics do not vary l inearly .+ speed parameter are extremely nonlinear, and some other method of inter-
10 - NACA RM E57309
To illustrate the use of the tables, an example requiring direct interpolation is shown. A 1-stage tmbine, with an exit axial Mach number e)3,m of 0.6, a rotor inlet velocity l imitation e)z,a of 0.6, an 4 Ln
exi t radius r a t io of 0.63, and a blade-speed parameter ut of 0.562 is investigated through use of the tables. Table I ( b ) l is indi-
cated. Linear interpolation is used to determine
8l
aa, cr ,I
(e)2, 2, Gl, and %,2-3. Interpolating with respect t o ut %,cr,l
holding e)3 = 0.6 yields - = 0 -980, and holdfug el3 = 0.7 yields -@AH U?
iJ + = 1.221. m n , interpolating with respect
preceding two numbers yields the final 7 =
JAH
ut -&fm UL b
= 0.5246, (.$)2 = Pg -
- 1.61,
t o between the
1.052. In a similar way L
*Bh,2-5 = 77.70.
Design Specifications and h-eliminary Calculations
To illustrate the use of the charts and tables, a turbo jet engine with high weight flow and high compressor pressure ratio is investigated. Four turbine designs we read *om the charts: a high-output 1-stage turbine, a high-output l p t a g e turbine, a conservative 2-stage turbine, and a moderate 2-stage turbine. The f rontal area ( i n proportion t o com- pressor frontal area) of each of these turbine designs is then evaluated and the most applicable ones are chosen. These are further evaluated through the use of the tables.
1
The turbine design requirements are specified by the following conditionsr
J
NACA RM. E57J09 11
Compressor pressure ra t io ,
Compressor polytropic efficiency,
Compressor equivalent w e i g h t flaw,
Compressor equivalent t i p speed,
Turbine-inlet temperature, Tl Compressor-inlet temperature, Tln,C Compressor-inlet pressure, Pin,C
?P,c r-) %At c
( k ) C
The assigned quantities are:
Ratio of turbine t o compressor weight flow, (l+f 1 (1-b) r n
Combustor pressure loss, G3l3 Ratio of specific heats i n compressor, rc Ratio of specific heats in turbine, yr Gas constant, R
9 .o
0.88
1000 f t l s e c
220O0 R 518.7O R 2U6 lb/sq ft
1.0
0.95
1.4
53.4 ft-lb/(lb) (%) 4/3
n
The dimensionless parameters W L and -gJml-3 are then “%,la;,cr,l
calculated for use in entering the charts:
C P,C = (+-)($)
( 3 C%i!2) = ”
= 0.2402 Btu/( lb) (%)
= B9.0) 0.3247 - 1.0](0.2402) (518.7)
= 129.7 Btu/lb
12 NACA RM E57J09
= (2ll6) (9.0) (0.95)
= 18,092 lb/sq f%
p*,1 = 18 092
= 0.1540 lb/cu f't, *om eq. (3)
aa,cr,l - - ,,/2(+)(32.17)(53.4) (2200) = 2078 ft /sec, *om eq. (S)
= 0.0253
-@%-3 (32.17) (778.2) (129.7) z= &a, cr, 1
2 (2078)
= 0.7520
Entry into Charts
All the following values are l inear ly interpolated fYom the charts.
Example 1. - Entry into chart I ( c ) l for a 1-stage turbine with exi t a x i d Mach number of 0.7 and rotor hub i n l e t Mach number limit of 0.8 y i e l d s
The location of limited by Mach
the point OR the chart indicates that the design is number.
e =ample 2. - Entry into char t I I (c) l f o r a lh-stage turbine w i t h
exi t axial Mach number of 0.7 and rotor hub in l e t Mach number limit of 0.8 yields t
(aa,2,11 = 0.593 and ($)o,T = 0.791
The ent i re range of this chart is limited by Mach number.
Example 3. - Entry into chart III(a)l for a 2-stage turbine with exit axial Mach number of 0.5 and rotor hub and second-stage stator hub Mach number limit of 0.6 yields
Example 4. - Entry into chart III(a)2 for a 2-stage turbine with exi t axial Mach number of 0.5 and hub Mach number l i m i t of 0.8 yields
( ) = 0.459 and ($)o,T = 0.533 &a,cr, l T
Evaluation of Turbine f ion ta l Area
NO l imiting value for t ip radius is specified in %his problem, b u t the comparative compressor and turbine t ip areas m a y be evaluated 86
f ollms :
14
Example 1. -
= (4.318)(0.S45)2
= 1.796
Example 2. -
= 1.518
Example 3. -
($)t = (4.318) (0.492)2
= 1.045
=ample 4. - (z)t = (4.318) (0.459j2
NACA FM E57J09
= 0.910
It can be seen from the preceding results that, i f the compressor is not the component which limits the engine frontal area, a conservative 2- stage turbine (example 3) will meet the requirements. However, i f t h e turbine must be no larger than the compressor, increasing the turbine hub Mach number limit t o 0.8 (example 4) will more than satisfy this require- ment. Examples 3 ana 4 are further investigated through the use o r t h e tables.
h 4 cn
NACA RM E57J09 15
i Entry into Tables
II Table 111 yields the -following results:
All of the tabulated values were obtained by linear interpolation from the table except those values marked with a superscript (*) . Example 4 is located in the tab le in 8 region very near the transit ion of the sec- ond stator from velocity-ratio-limited to Mach-number-limited, and l inear
interpolation would yield (z)t 1.0 and e) 0.8. Therefore, the
surrounding points were plotted and cross-plotted, and the desired values were read from the cross plots. In each of the plots, enough points beyond the transition point were plotted t o determine w h e t h e r each point t o be used in cross-plotting was limited by velocity ratio or by Mach number.
a 3,h
It can be seen from the foregoing results that examples 3 and 4 are almost a l ike i n some respects. There is almost the same amount of turning
in this region of the table) and almost the same amount of exi t w h i r l . There is less pressure drop across the turbine and less taper required in example 3. Therefore, i f the additional 4.5 percent in frontal area could be tolerated, example 3 would provide the velocity parameters f o r the f ina l design calculations. If the turbine frontal area is critical, specifying an exi t axial Mach number of 0.5 w i t h a limiting hub inlet re la t ive Mach number of 0.7 would probably yield a turbine of sufficient capabili t ies and frontal area t o satisfy the requirements.
I i n the first rotor (a glance will show this is the most c r i t i c a l blade row
w
C O N C L U D ~ REMARKS
A method was devised f o r the rapid selection of 1-, 15, and %stage turbine designs within specified aerodynamic limits. The turbine annulus was tapered. to y ie ld maximum work output. For given sets of t u r b i n e de- sign l i m i t s , c W t s permit determination of attainable values of blade- speed parameter, ex i t rad ius ratio, and turbine diameter from turbine design data commonly specified in turbojet-engine design. For ranges of blade-speed parameter and exi t r a d i u s ratio, detailed design information is tabulated.
i
Lewis Flight Propulsion Laboratory National Advisory Committee fo r Aeronautics
Cleveland, Ohio, October 17, 1957 -
16
APPEXDIX a
SYMBOLS
A annuler mea, sq ft
at t i p frontal area, sq f t
a sonic velocity, d s , f t /sec
%, cr cr i t ical veloci ty , ,,/s ~RT, ft /sec
b r a t i o of bleed air t o compressor-inlet airflow
cp D
e
f
Q
H
J
P
P
R
specific heat at constant pressure, Btu / ( lb) (%)
diffusion factor of damstream stator blade8
parameteg used in re la t ing compressors and turbines,
fuel-air r a t i o
acceleration due to gravity, 32.17 Ft/sec 2
stagnation specific enthalpy, Btu / lb
mechanical equivalent of heat, 778.2 f t - lb /B tu
stagnation pressure, Ib/sq ft;
static pressure, lb/sq ft
gas C O ~ t ~ t , Ft -lb/ (lb) ( S i )
r ad ius , ft
entropy, N u / (lb) (9)
stagnation temperature, OR s t a t i c temperature, 41 blade velocity, f't/sec
.
NACA RM E57J09 17
* v
w W
w A
a
.
Y
6
qP e
i
velocity of gas, ft /sec
weight-flow ra te of gas, Ib/sec
weight -flow parameter, w/paaa, c&
flow angle of absolute velocity measured from axial direction (fig. 2) ,
(fig. 2) , deg flow angle of relative velocity measured *om axial direction
r a t io of specific heats
r a t io of stagnation pressure to NACA standard sea-level pressure, P/2ll6
polytropic efficiency
r a t i o of stagnation temperature t o NACA stadaxd sea-level t e m - perature, T/518.7
gas density, lb/cu ft
solidity, ratio of blade chord to p i tch
angular velocity, radians/sec
stagnation-pressure loss coefficient of downstream s ta tor blades
Subscripts :
a stagnation condition
B combustor
C compressor
h hub rad ius
i ideal
in i n l e t
m mean radius
0 exit
18
R rotor
S s ta tor
T turbine
t t i p radius
z axial component
e tangential component
Superscripts:
1 relative to ro to r
. r
* stagnation state r e l a t ive t o stator, which would exist if only the axial component of velocity were considered
t
NACA RM E57J09 19
APPENDIX B
The following conditions were assumed in the computations for the 1-stage turbines :
(1) Flow through the turbine is adiabatic.
(2) A t any given axid station, both stagnation pressure P and stagnation temperature T are constant radially.
(3) Free-vortex flow conditions prevail at each axial station; that is J
(4) Tip radius is constant from entrance to exit.
z B
(5) ~ n y effects of annulus w a ~ curvature or radial components of velocity may be neglected.
w (6) The turbine working f l u i d obeys the perfect-gas law; that is, & .* L R t P (B2)
(7) A* the mean r a d i u s pVzA is constant from inlet to ou t le t .
(8) The ent i re loss in the turbine occurs across the rotor.
The following constants were assigned:
(1) Ratio of specFfic heats rT = 4/3
(2) Turbine polytropic efficiency q p , ~ = 0.85
The following quantities were assigned and varied independently:
(1) Exit axia l Mach number J m
20 - (4) Blade-speed parameter
aa,cr,l
NACA RM ES7J09
The general method of solution w a s 88 follows: Values for both in l e t radius r a t i o -h and turbine-work parameter -gJm1-3 were assumed.
For each assumed value of i n l e t r&us ra t io the tursine-work parameter w a s varied unt i l the computed rotor hub i n l e t velocity w a s equal to the assigned limit. This assigned Umit waa either in the f o r m of Mach number
G t ) Z 45
or velocity ratio @)h. i n l e t r a d i u s r a t io was repeatedly
increased by some increment q$)2 , usual ly 0.005, until the value of
turbine-work parameter began t o decrease. The greatest value of turbine work obtained in t h i s manner was taken t o be the maximum turbine work that could be achieved by varying inlet radius ratio. See figures 1(a) and 2(a) for the axial stations and-velocity diagrams, respectively.
Conservation of energy requires that
HI - H3 = Cp,T 1 (T - T3) = -AH
where
Cr i t icd ve loc i ty is defined as
Combination of equations (B3), (M), and (BS) yields
.
21
The definition of total state requires that
As an aid in analysis, a temperature T* was defined
w h i c h is identical t o the relation 7r2
This temperature T* is herein called "axial stagnation teqperature" because equation (B10) indicates that, if the s t a t i c enthalpy i s increased by the kinetic energy contained i n the axla1 component of velocity, the teqera ture reached is T*. Equations (B8), (B9), and (B10) LMJ be com- bined t o produce
c
I
w h e r e
a = d- Equations (B5) and (B12) may be combined t o show that
It is now possible to evaluate the complete velocLty diagrams at the turbine exit in terms of the cri t ical veloci ty aa,cr,3.
22 - NACA RM F57JO9
From the isentropic relation - - -
1 -
and equation (3381, the specific-mass-flow parameter can be expressed
The definition of polytropic efficiency and assumption (8) resu l t in
Pl p3 ” -
From assumption (7)
where
Combination opequations (BZ), (B5), (B17), and (B18) yields
Turbine work also be expressed as
." -
NACA RM E57J09
- Manipulating equation (B20) gives
23
The complete velocity diagrams at the turbine rotor inlet can now be evaluated i n terms of cri t ical . velocity aa,cr,2.
By use of equations (B5) , (B8), and (B12), it is possible t o mite
From
where
equation (B5) it is obvious that
The definit ion of inlet weight-flow parameter is
The combination of equations (B18), (B24), (B25), and (B26) and the w e of assumptions (4) and (8) yield
c
24 NACA RM E57J09
. APpEWDlx c
METHOD OF ANALYZING l*-STAGF, 'TURBINES
The following conditions were assumed i n the computations for the l& stage turbines : I+
cn 4 UI (I t o 7) Same as for 1-stage turbines (appendix B) .
(8) The en t i re loss i n the first stage occurs i n the rotor .
(9) The chord length of the downstream s ta tor blades is constant radial ly .
(10) ~ n n ~ l a r area across the downstream s ta tor is constant.
(11) The gas leaving the damstream stator has only axial velocity; t ha t is, Ve ,4 = 0.
The following constants were assigned:
(1 and 2) same as for 1-stage turbines (appendix B) .
(3) Mean sol idi ty of downstream sta tor blades ~ 3 , ~ = 1.5. . (4) Stagnation-pressure loss coefficient of downstream s ta tor blades
Em = 0.05. 4
(5) Hub diffusion factor of downstream s ta tor blades % = 0.4.
The same quantitieq as for the 1-stage turbines were assigned and varied independently.
tial Mach number at the in le t of the downstream s ta tor @)3,m assumed. The specific-weight-flow parameter downstream of the s ta tor w a s then computed from two independent relations. In one case 5 was used t o determine the pressure ratio through the s ta tor , and in the other % waa used t o determine the velocity leaving the stator. The value of
The general method o f solution w a a as followe: A value for tangen-
was awusted unt i l the two methods of computing
gave ident ical results. Since these computations were indepenaent of both in le t rad ius ra t io and turbine work, this trial-and-error computation was solved, and then the method of solution outlined in appendix B was fo l - II
lowed. The axial stations and Velocity diagrams for l*-stage turbines are given in figures l (b) and 2(b), respectively.
NACA RM FS7J09 .- 25
Born the definit ion of t o t a l state
4
b Lo Lo -8
Equations (E>, (B12), and (C1) may be combined t o y i e l d
where
The specific-mass-flow parameter at the inlet t o the downstream s t a to r may be evaluated from equation (B15), ere
c and
A derivation similar t o that used for equation (B19) incorporating assumption (10) yie lds
D
% * may be solved i n equation (B5) of reference 4 as follows :
26 - NaCA RM E57J09
Incorporating assumption (11) into equation (13) of reference 4 yields
The solution of equation (C8) for is
where *om assumption (9)
By application of atmuraptions (3) and (II), equation (BE) may be written:
L
Equation (C6) y i e l b the specific-weight-flow parameter from the pressure losses, and equation (CU) gives this parameter from the di f - fueion factor.
The use of equations (Bl) through (B6) w i t h (C4) and (C5) permits evduation of the corqplete velocity diagrams at the turbine rotar exit i n terms of the cri t ical veloci ty aa,cr,3.
Equations (B16) through (B27) specify the necessary information t o complete the calculation.
NACA RM E57JO9 C" i- 't
AFTENDM D
27
METEOD OF ANALYZING 2-STAGE TURBINES
The following conditions were assumed i n the computations for the 2-stage turbines :
(1 t o 7) Same as f o r 1-stage turbines (appendix B) . (8) The inner annulus w a l l is a single conical surface *om the
first ro tor in le t to the turbine exit.
(9) The axial lengths of the la& three blade rows axe equal.
(10) One-third of the over-all stage loss occurs i n the stator blade row and two-thirds in the rotor blade row.
(U) The velocity ratio across the hub of each rotor blade row is never greater than 1.0.
The following constants were assigned:
following quantities were assigned and varied independently:
Rotor hub inlet l imit ing Mach number g),,hlimit = F) a 4 P m i t
Second-stage s ta tor hub inlet limiting Mach number @)g,hlimit
(4) Limiting velocity r a t io across tip of second-stage stator
l i m i t
28 - NACA RM E57J09
The general method af solution w a s as follows: Values for inlet radius r a t i o @& turbine-work parameter -gJm1-5, and turbine second-
stage work r a t i o - were assumed. For each assumption of inlet
rad ius ratio and work parameter, the second-stage work r a t i o was varied un t i l the second-stage rotor hub inlet velocity satisfied the assigned limits. These assigned limits were: either the ro to r hub velocity ratio
%,5 m3-5 m1-5 8i 3
G)h = 1.0 and the rotor hub iulet Mach number &)4,hs assigned value,
or e)h s 1.0 and (E) = assigned value. a 4,h
A similar restr ic t ion was put on the velocity into the second-stage stator. The velocity ratio at the t i p k)t w a s assigned, and the hub
in l e t Mach nuuiber (z)3,h w a s evaluated. If t h i s Mach number exceeded its
assigned limit, then Q),,, was set equal t o i t s assigned limit and the
tip velocity ratio was computed.
While the inlet radius r a t io was held constaut, the turbine-work parameter was varied (Kith the i teration j u s t described being carried out for each trial value) un t i l the f i rs t -s tage rotor hub inlet velocity sat- isfied the assigned limits. These assigned linpits were identical to those
for the second-stage rotor; that is, either p) = 1.0 and (9 5.
assigned value, or p) 5 1.0 and (%) = assigned value. h a 2,h
h 2,h
'13ne inlet radius r a t io was successively increased by an arb i t ra ry
increment, G$>, = 0.005, unt i l the value of over-all turbine-work param-
e ter began t o decrease. The greatest value of turbine work obtained in this manner was taken t o be the maximum turbine work that could be achieved by varying i n l e t r&us r a t io .
Figure l(c) shows the assumed 2-stage turbine geometry and axial stations, and figure Z ( c ) shows the velocity diagrams.
NACA RM E57J09 - 29
L - Equation6 (€33) through (B15) permit evaluation of the velocity dia-
- grams, i n terms of the cri t ical velocity, and the specific-mass-flaw
all turbine conditions where necessary. For example, equation (X) would c parameter at the turbine exit by rewriting the equatfons t o apply to over-
become :
Equations (B3) t o (E) combine t o become
and thus necessary temperature ra t ios are defined.
If the expansion across the second turb ine stage w e r e isentropic with the gases expanding from some inlet pressure P3 t o sane ideal exit pressure P5 , iJ this expaneion could be expressed
However, from the definition sion is expressed
P?
of polytropic efficiency the actual expan-
The losses AS that occur during the ac tua l expansion may be expressed in terms of the ideal and actual pressures as
From assumption (10)
30 I NACA RM E57309
Solution of equation (X) for stator pressure ratio yields
p4 ( p5 )" L
" "
p3 '5, i (D7 1
Equations (D2), (M), (D7), and equations (B15) t o (B21) permit 2 evaluation of complete velocity diagrams at the second-stage rotor inlet i n terms of the crf t ical veloci ty aa,cr,4, where
u1
and evaluation of the specific-mass-flow paremeter, where
from assumptions (8) and (9).
Equations (B22) and (B23) define the second-stage rotor hub in le t
velocity i n terms of the specified limits e) and &&. 4 ,h
A derivation similar t o that for (B19) y ie lds
where
f rom a8sumptLons (8) and (9) . From assumption (3) and the velocity diagrams
NACA RM FS7J09
. where
31
. rt - = 2.0 rm 1.0 + - rh
rt
and p) has been assigned. Substitution of (D12) i n (B15) yields v4 t
From equation (D14) ( ) may be evaluated and then vz aa,cr 3 , m
be evaluated from equation (D12).
A derivation similar to (B22) yields
If the result of equation (D15) exceeds the assigned limit, (z) is . set equal t o the l i m i t , and from equation (C1) 3,h
fiom assumption (3) and the velocity diagrams
where
.
32 - NACA RM E57J09
Substitution of equation (D17) i n (B15) yields
may be evaluated f’rom equation (D17). Velocity diagrams and assumption
It is now possible to evaluate the complete velocity diagrsms at the first rotor exit i n terms of the cri t ical veloci ty aa,cr,3.
By repeating the procedure outlined for the second-stage rotor, the specific-mass-flow parameter, the velocity diagrams at the i n l e t t o the f i rs t -s tage rotor in terms of the cr i t ical veloci ty aa,cr,2, and the first-stage rotor hub inlet velocity i n terms of the specified limits
c
and p) may be evaluated. d
2,h h
A derivation similar t o that for equation (B27) yields
1. Cavicchi, Richard H., and English, Robert E. : A Rapid Method for Use i n Design of Turbines Within SpecifTed Aerodynamic Limits. W A TN 2905, 1953.
2. Cavicchi, Richard E., and Constantine, Anita B.: Analysis and Con- struction 09 Design C h a r t s for Turbines with Downstream Stators. NACA RM E54G23a, 1954.
MEA RM E57J09 33
3. Cmicchi, Richard H., and English, Robert E.: Analysis of Limitations Imposed on One-Spml !L!urbojet-Engine Designs by Compressors and Turbines at Flight Mach Numbers of 0, 2 .O, and 2.8. NACA RM E54J?21a, 1954.
4. Lieblein, Seymour, Schwenk, Francis C., and Broderick, Robert L.: Diffusion Factor for Estimating Losses and Limiting Blade Loadings i n Axial-Flow-Compressor Blade Elements. NACA RM F53DO1, 1953.
34
NACA RM S!5'7JOS 35
'%A
- 1 0 - 8 -13 .I - 1 5 . 7 - 1 8 . 9 - 2 2 -6 - 2 7 -1
- 1 0 . 7 - 1 2 . 9 - 1 5 - 4 -18 -3 - 2 1 . 7 - a 5 - 9
- 8 . 9
-1; :: -18.1 - 1 5 - 4
- 2 5 - 2
- 9 -1 -11 -1 -13 - 2 - 1 5 - 6 -18 -3 -21 - 4
- 8 1 . 4
-a5 .o - 9 - 4 -11 . 5 - 1 3 . 7 - 1 6 -1 - 1 8 . 7 - 2 1 . 7 - 2 5 . 2
z UJ P
0 . 4 8 6 3 - 4 0 0 3 - 4 0 7 5 - 5 3 1 3 - 7 5 3 4 . o s 9
- 4 3 2 4 - 4 3 2
0 . 4 6 5 2 .8 9 1 - 4 6 2 2 - 8 4 4
2 - 8 8 4 - 9 9 2
- 4 3 6 3 -1 5 2 - 4 1 4 3 - 5 5 2
0 . 4 0 1 . 3 6 0 - 5 0 1 .a63 - 6 0 i . a a o .70 1 . 2 1 3 - 8 0 1 . 2 a s - 9 0 i . a 6 4
1 . 0 0 1.311
0 . 4 3 5 2 - 7 7 5 a - 5 7 7 2 - 4 9 0 2 - 4 7 5 2 - 5 0 9
* 37 4 2 . 5 8 0 2 - 6 7 6
1.35 0 . 1 8 1 9 0 . 9 8 5 1 - 5 6 - 1 6 9 ~ - 9 0 s 8 4 - 4
7 7 . 8
1.88 .135z . a 2 9 2 . 4 0 - 3 0 8 4 . 7 6 5
9 0 .2
3.31 . O B 1 0 - 6 6 7 101.9 9 6 - 4
5 . 1 0 - 0 5 4 9 - 6 2 9 1 0 8 - 2 9 - 1 0 - 0 3 2 5 - 5 6 1 115.5
1 . 4 6 6 8 0 . 8 0 0 - 4 6 6 9 . B O O
3 . 4 3 3 a - 5 6 6
2 - 2 6 0 2 - 2 0 2
-36 9 . s 4 9 a -1 9 3
2 - 1 8 4
a -380 1 . 4 4 7 1 . 4 0 9 I . 3 9 8
. ) . 4 6 6 6 I O . 9 0 0
c 1.0 -
0.5 0 - 9 0 1 . 2 7 1 0 . 4 6 1 4 0.616 0 . 5 3 5 1 . 0 0 1 . 3 3 0 - 4 5 0 1 - 8 6 0 , 4 9 2 5 -353
- 9 0 1 . 3 7 s - 4 6 0 6 - 8 4 5 .501 3 -721
1 . O O 1.420 - 4 5 7 1 - 8 8 5 - 4 6 7 3 - 6 1 3 3 - 9 4 5
5 .o ea
0.1 0 . 8 0 1 . 5 4 0 0 . 4 6 9 9 0 . 8 0 5 o . s a 2
- 0 - 9 2 5
- 8 3 9
0 - 9 4 1 .8 5 4 . 7 7 1
0 . 9 6 1
-7 8 5 . e 7 0
- 7 0 6
5 . I S 9 - 6 5
3 - 7 5 6 . 0 4
11 - 5 8
0 . 0 8 0 0 - 0 4 5 5
0 . 0 9 0 9
- 0 3 2 8 . o s 9 1
3 - 0 0 4 - 3 9
1 4 - 2 0 7 - 2 5
0 . 0 8 8 6 . 0 6 2 8 - 0 3 9 9
0 - 0 7 2 7 . 0 5 4 4
- 0 2 5 3 . o s 7 5 - 0 1 2 4
0 . o s 3 3 - 0 2 4 1 . O l 6 a . a 0 9 0 . o o 51
0 . 9 9 4 - 8 9 4 - 8 0 4 - 7 2 3. -6 4 6
0 - 9 5 0 -830 - 7 4 0 -6 6 I - 5 9 1
3 - 5 0
8 . 9 6 5 - 2 8
1 7 . 8 9
4 . 2 5 2 - 9 8
11.51 6 -61
2 3 - 4 1
(a) Cmoludsd. M3,m - 0.5
*1 5 %2-3 %h
- - 4 .l
- 8 . 3 - 1 0 . 9 - 1 3 . 9 - 1 7 - 5
- 2 7 .o - 3 3 . 5
- 4 . 3 - 6 . 4 - 8 . 6 -11 .I - 1 4 .O - 1 7 . 4
- 2 6 .6
- 6 . a
- a 1 .e
_I
- 8 % . s - s a . 8 - - 4 . 4 - 6 .7 - 9 .o - 1 1 . 5 - 1 4 . 3 - 1 7 . 6 - 2 1 . 6 - a b .5 - 3 8 . 9 - - 4 . 6 - 7 .o - 9 . 4 - 1 1 . 9 - 1 4 .8 - 1 8 .I
- 2 7 . O - 3 3 . 6
- 4 . 6 - 7 . 3 - 9 .e - 1 2 .6 - 1 5 .6 - 1 8 . 9
- 8 8 . O - 3 4 . 9
- a a .I
-
- a 3 .o
0 . B O O 1 0 . 4 6 8 0 3 . 5 0 0 . 5 0 0
, 5 9 0 . 5 3 5
. 6 4 5
. 7 0 5
. 7 6 5 , 8 2 0 . e 7 5
0 . 6 0 0 . . d o 0 . . 6 1 5 . . 6 6 5 . 7 1 5 .? 6 0 -810 . a 5 5 . 9 0 0
__
) . 4 8 5 I 3 . 1 9 8 3 4 . 2
6 0 . 3 6 8 . 4 7 7 . 7 8 6 .7 9 6 .1
1 0 7 . 3 1 1 9 .O
5 0 . a 0 . 3 3 7 8
. 3 a 1 7
. a 9 9 8
. a 8 7 1
. 1 a a 1
. a 6 8 6
. I 7 6 7
. 0 7 0 7
. 0 3 0 9
0 . 2 8 4 8 . a 6 6 0 . a 4 2 1 . a 1 0 8 . 1 7 2 a . l a 8 6 . 0 8 4 5 . 0 4 6 0 . 0 1 8 5
0 . S I ? . 5 3 8
- 6 0 4 . 5 6 6
, 6 4 2 . 7 1 2 . 7 8 8 . 8 6 7
1 . o a l o . s e a
. 5 5 0
. 5 8 7
. . 6 9 6 , 6 3 5
.771
. 8 6 5
1 . I 5 1 . 9 8 6
o . 5 a 9 . 5 6 4 - 6 1 2
. 7 4 7
. 6 7 2
. 8 4 0
I .lo5 . 9 5 6
1 . 3 1 4
0 . 5 3 6 . 5 8 0 .6 3 9
. 8 0 6
. 7 1 4
1 . O b 8 . 9 1 9
I . a 5 0 1 . s a l
1 . 0 4 1 . 1 0
1 . 5 5 1 . I 9
1 . 6 2 2 . 1 4
5 . 9 1 1 4 . 7 0
1 . 0 6 1 . 1 4
1 . 4 8 I . 8 5
4 . 0 7 7 . 9 7
3 . a 3
I . a 7
a . 5 6
a i . 8 2
~ ~~
. e o 2 . 4 6 7 s
. 7 9 4 . 4 6 7 8
- 8 6 8 . 4 6 7 1 - 9 5 0 . 4 6 3 4
1 . 0 6 7 . 4 6 5 3
1 . 3 6 8 , 4 6 0 7 1 . a 0 5 . 4 6 s 5
I . s a 5 . 4 6 5 7
- 4 6 8 3 . i 7 7 . 4 7 3 . 4 9 1 3 - 4 3 1
J - 2 0 6
- 5 0 7 . S a 6
3 . 7 9 9 4 . 2 7 0
- 5 4 4 . 5 4 7
4 . e 2 1 5 - 4 3 4
1 .OD
1 . 4 8 4 2 .9 9 6 2 , 9 8 3 3 . 0 9 3 3 . 3 0 3
. 5 I 8 3 . 5 8 8
.s 4 0 3 . 9 1 6
. 5 4 6 4 .6 7 8
0.6 o . a o - 3 0
- 6 0 . 4 0
- 6 0 . 7 0 . B O
1 . 0 0 .9 0
0 . 7 o . ao - 3 0 - 4 0 . 6 0 . 60 .7 0 . 8 0
1 .oo - 9 0 .
0.a o . a o -30 . 4 0 - 5 0 - 6 0 .7 0 . 8 0
I .oo .9 0
0.9 o . a o . s o . 4 0
1 .oo
3 8 . 5
7 0 . O
8 6 .6 9 6 . 4
1 1 5 . 4 1 2 6 . 3
5 6 .a
7 8 .a
1 0 5 . a I - 3 . 7 0 0 .roo - 7 0 0
- 7 7 5 . 7 3 5
.a15
. e 5 0
. a g o
. 9 a 5
I . o a I . I 9 1 . 3 6 1 . 6 4 2 . 1 5
11.17 5 . 2 8
3 4 . 3 5
3 . l a
1 . 4 0 6 0 . 4 6 7 9
1 . 3 0 9 . 4 6 ? 0 I . S 9 8 . 4 6 7 5
I . 4 o a .466s 1 . 4 5 6 - 4 6 5 3 1 . 5 3 4 . 4 6 3 7 1 . 6 9 0 . r 6 1 a 1 . 7 3 4 . 4 5 7 3 1 . 8 4 9 - 4 5 0 1
3 . 4 8 3 a . a 6 9 . 4 6 3 a . e 5 4 - 4 3 6 a . e 3 4 . 4 5 6 a . e 6 a . 4 8 1 - 5 1 0 3 . 1 3 1 . s 2 s 3 . 3 8 3 - 5 5 7 3 . 5 3 8 . 5 6 1 3 . 7 7 4
a .9 7 8
0 . 2 2 3 0
. 1 6 0 6
. I 6 2 6
. I 8 0 0
. O B 5 5
. a 0 4 6
. o s s a , 0 9 7 0 . 0 0 9 7
0 . 1 5 4 7 . I 3 0 7 . I 1 8 6
. 0 ? 2 4
. 0 4 9 0
. O a 8 6
. 0 1 3 4
. 0 9 6 a
. o o 4 a 0 . 0 8 0 1
. 0 7 0 0
.057d
. 0 3 1 5
. 0 4 4 s
. o a o ~ , 0 1 0 9 . 0 0 4 6 . 0 0 1 a
4 a . 4 61 .6 7 8 . 9 8 0 . 5 9 7 .o
1 1 4 - 6 1 2 2 -5 1 3 2 . 6
4 6 . B 6 6 .6 8 4 .6 9 8 .l
1 1 5 .I
1 3 0 .6 1 4 0 .I
1 0 5 .a
1 0 s .a 1 2 a .1
- D . a o o
~~
. a 0 0
. a 0 0
.a10
. a 4 0
. E 6 5
. e 9 5
. 9 4 5
. 9 a o
1 . 7 5 9 0 . 4 6 7 8
1 . 7 4 3 . 4 6 6 7
1 . 7 5 8 - 4 6 4 6 1 . 7 3 3 - 4 6 5 8
1 . 7 5 a . 4 6 7 4 3 , 4 8 4 a . 7 4 9
2 . 7 3 8 2 .r a.3
a . 7 4 a
a . 9 1 4 3 . O J 2 3 . 1 6 4
1 . 1 0
1 . 4 8
2 . 5 5 3 . 9 3
1 6 . 5 3 7 . l 2
5 8 . 3 4
I . a 4
I . a 6
3.900 . g o o . g o o
. 9 0 5
. 9 0 0
. 9 3 5 . 9 5 0 . 9 6 5
. 9 a o
3 . 4 8 6 a . 6 4 9 . 4 6 9 1 2 . 6 4 0 - 4 4 5
0 . 5 4 4 . 5 9 7 . 6 6 9
. e 7 3
. 7 6 1
1 . 0 1 2 1 . 1 9 0 1 . 4 3 i I - 7 9 1
1 . l a 1 . 6 8
s . a o 10 . a 7
.II, s a a 6 . 6 5
1 . 3 0
2 . 1 6 3 -16
4 9 .6 7 1 . O 8 9 .6
1 1 7 . 5 1 0 5 . S
i a 5 . 4 1 3 1 .D I 4 0 . 4 1 4 8 . 5
. . . ”
6 1
. .. .
4575 I
. . . .. .
- 0 . 1 0
. I 6
.so
. 4 0
.so
. 6 0
. 7 0
. 0 0
.9 0 1 .oo
. a o
- 3 . 1 0 .I 6
.3 a - 4 0 . I O . 6 0 . T O . e o .9 0
1 . 1 0 .l 6 . B O . s o . 4 0 .EO - 6 0 - 7 0 .eo .9 0
. a o
L.00
L.00
.ao ) . 1 0
.1 6
. 3 0
. 4 0 . B O - 6 0 .I 0 . B O .9 0
L , 0 0
) . 1 0 .11 . P O . 3 0
.so - 4 0
- 7 0 . 6 0
. a 0 -9 0
-
L.op
- F - 0 . a 0 0
. I 9 8
. 7 9 1
. T I 6
. 7 1 T
.747
. T T J
. 9 1 4
. o s 0
1 . 0 8 8 1 . 1 4 0
1 . 0 6 4 1 , 0 1 8 1 . O B 0
1 . o o s - 9 1 1
1 . 0 1 9 1 . 0 0 8 I . 1 6 6
-
1 . a 0 9
. 9 8 a
- I .ma4
1 . S 4 8 1 . 3 4 1 1 . 3 3 1 I . S O 6 1 . 8 7 9 I , 8 3 6 1 . a l a I . a 0 4 1 . a 6 0 1 . S l 6 1 . 3 0 0
1 . 6 4 6 1 . 6 6 3
1 . 6 0 3 1 . 6 3 3
1 . 1 6 3 1 . 6 1 0 1 . 4 7 0 1 . 4 4 7 1 . 4 6 0 I . 4 7 0 1 . s o 0 1 . e 7 0
1 . 9 5 6 1 . 9 6 9
1 . E T 6 1 . B P S 1 . 7 6 4 1 . T O 3 I . 6 6 1 1 . 6 3 0
-
-
I . g a l
I . 6 a 1 -
0 . 5 0 0 . s o 0 . s o 0 .so0 . s o 0 . 5 3 0 . S T 8 .630 . 6 9 0 . 7 5 6 . 0 9 6
> . 6 0 0
, 6 0 0 . 6 0 0
, 6 0 0 , 6 0 0 . 6 1 5 . 6 S 6 . 7 0 0 . 7 1 0 , 8 0 5 . E 6 0
-
- 1 . 7 0 0
. T O O . r o o . 7PO . 7 0 0 . T O O , 7 3 0 . 7 7 Q . a 1 0 . 0 1 0 . a 9 5 -
) . I O 0 . e o 0 . a 0 0 . a 0 0 . e 0 0 . 0 0 0
. a s s , 0 0 6
. E 6 6 , 0 9 8 - . g a s
) . g o 0
. e o 0
. g o o
. g o o
. g o o
.DO0
.BOO
. D E 5
. D O 1
. 9 4 O
. 9 6 0 -
- ele,+ - ) .E94 . E 8 7 . 6 7 T
. 5 1 9
. a 5 1
. S O T
. s o 1
. 4 9 4 , 4 0 8 , 4 6 3 . 4 4 3
L 1 9 3 . 6 8 1 . S T 4 .I41 . S O 7
. 4 7 6
. 4 0 0
. 4 6 1
. 4 6 P
. 4 5 T
. 4 1 8
-
- ) . I 9 8 .sa4 .639 . 5 7 P
. 4 9 7
. 4 4 9
. 4 3 0
. 4 3 4
. 4 P I
. 3 9 0 . 5 7 9
1.899 . 5 8 3 . E T 0 .I 3 5 . 4 9 0 . 4 3 7
. 3 0 4
. s e 9
. I11 . s 8 3
-
. s 7 a
- 1.890 . 5 8 8 . 6 6 9 . 6 S e . 4 8 4 . 4 8 7 . > 6 1 . 3 1 6 .Ill
. 8 7 B
. a s 1 -
-“14
s . B o o 5 .lPO 3 - 1 6 6 3 . 1 0 5 5 . 0 8 9 P . 9 8 9 s , 0 9 8
3 . 6 5 4 s . > l a 4 . o n 1 4 . 1 9 3
8 . 9 S 5
iG-
- a .PIT a , 9 3 8
a , 7 0 6 a . 0 5 8
B . T I 3 8 . T U 7 8 . 0 3 1 3 . O D 7 S .0J9 I . 6 1 0 - a ,719 a . 7 3 6 0 . T I P 8 . 6 6 4 . B . 6 9 6
B . 4 7 4 a . s a 0
a . 4 9 7 P . 5 7 a a . a 0 3
a . s e s a . S T O
a .BO4
a .31a
P . a 1 7
P . 5 6 0
B . 4 4 3
P - 8 6 1 0 . E 9 7
P . 8 6 6
B . 3 4 4 a . a 9 7
a . 4 4 a a , 4 3 0
a . 3 1 6 8 . a 6 0 a , 1 7 8 a , 1 0 3 a .OBI 9 . o a a
- D . 4 1 6 9 . 3 7 8
8 .DO6
- p1 P; -
1 . O l 1 .OB 1 . 0 4 1 . 1 0
1 . 8 9 1 . 4 0 1 . 7 9 9 . 3 6
6 . 4 9 3 . 8 6
1 . 0 1 1 . o > 1 . 0 6 I . 1 3 1 . B 6 1 . 4 1 1 . 6 1 8 . 0 6
4 . 3 9
1 . 1 8
-
a . e a B . a s - 1 .OB 1 . O A 1 . 0 7 1 . 1 7 1 ,ss 1 . s 4 1.87
> . 4 3 5 . 6 0 0 . 6 0
B - 4 8
- I . o a
I . a 0
1 . o s 1 . 0 9
1 . 4 s 1 . 7 9 P . 16
4 . 9 6 B . 9 0
7 . 0 8 5 . 9 3
1 . 0 3 1 . o s 1 . I 1
1 . s a 1 . 9 3
3.10 8 . 6 7
9 . 4 0 6 . 4 9
8 . 8 6
-
I . a 7
-
41 - 0 . 3 9 8 6
. > a l e
. J 0 i l
. 3 6 3 7
. > 4 1 0 ,3138 . U T 8 1 .P337 . 1 8 1 a
. O T 1 9
. l a 4 7
0 .55 ’19 . x 8 0 0 . 3 a 1 3 . S O 1 6 . U 7 6 8 . E 4 0 3 . P 1 4 5 . 1 7 5 0 . 1 3 1 6 . 0 0 7 0 . 0 4 9 4
_1
- 0 . ~ 6 s ~
. a s 9 8 .asus . a 5 3 0 . P O 8 6 . l e 1 6 . 1 6 8 5 . 1 8 0 6 . O E T T , 0 5 6 1 . 0 3 1 P
0 . 1 8 6 5 . I 8 1 9 . 1 7 6 6 . 1 6 9 0 . 1 3 8 6 . 1 1 b 3 . 0 9 4 3 .0781 . O S 0 8
. 0 1 7 1
. O L l 9
3 . 0 9 1 0 . 0 9 1 1
. 0 8 0 9
. O d 1 4
. o s 1 3
. 0 4 9 6
. o s 1 9
. O B 1 8
.0130
. D O 6 0
-
- . 0 9 1 a
-
- ah 0 . 9 9 3
. e 0 4
. e 7 2
. ~ 4 a , 9 0 3 . e 5 9 . 0 1 0 ; . 7 1 0
.6 4 I
. 5 8 7
-
i .7oa
- 4 9 9 1 . 9 8 0 . 9 6 5 . 9 9 6
, 0 9 6 . 7 7 1 . 7 1 1 . 6 6 0 . 6 0 1 . 6 4 6
. . e78
I_
4 9 8 9 - , 9 7 1
, 9 0 9 , 9 5 7
. O S 8
- 7 3 0 . 6 1 8 . 6 1 4 . 6 8 8 . 6 O b
0 . 9 0 6 , 9 6 9 , 9 4 7 , 0 9 1
. 7 6 7
. 6 3 0
.a17 , 6 1 1
. 4 6 6
0 . 9 8 3
. 9 3 T
. 7 9 0
. 7 8 3
.613
. 1 0 e
. 5 3 1
. 4 7 0
. 4 3 0
. T O P
-
. s a 8
. s e a
- . e a r . a l a
0 1 . 0 - 7 . 1 1 4 .6 - S . 4
9 0 . 0 - 4 . 9
6 6 . E - 9 . 6 4 8 . 4 - 7 . 3
6 8 . 7 - 1 9 . 0 6 9 . 1 - 1 4 . 1
0 8 . 4 -81.0 7 5 . 3 - 1 7 . 9
9 0 . 1 - 0 6 . 6 9 1 . 9 - 3 8 . 0
l b . 1 - 0 . 5 8 4 .l - 4 . B 3 1 . 0 - 1 . o 6 0 . 7 - 9.D 16 .8 - 7 . 4
7 1 . 0 - 1 P . S 7 7 . 4 - 1 4 . O 13.9 - 1 1 . 9 9 0 . 9 - 9 1 . 5
1 0 6 ,4 - 3 0 . 9 9 8 . 0 - 0 1 . 0
17 .6 - 9 .6 0 6 . 1 7 3.9. s 4 . I - 1 .I 5 0 - 7 - 7 . I 6 1 .7 - 1 0 . 8
0 6 . 6 - 1 1 . 5 9 9 . s -11.P
1 0 6 . 7 - 8 1 . 6 1 Z 3 . 6 - 3 0 . 4
- 1 9 . 4 - 1 8 . 7
9 8 . 9 - a i . 6
10.0 - 8 . 6 . 0 0 .o - 4 .o 5 4 . a - 7 . 9 S T . 0 - 1 . 3
7 0 . 1 - 1 0 . 5 0 4 . 7 - 1 3 . 1 9 6 . 8 - 1 6 . 8
1 0 8 .6 - 1 8 .T 1 0 0 . a - a 9 .o 1 1 5 .T - a s . a
a o . o - B .7
1 9 3 . 1 - S O . 5
0 9 .T - 4 .1 3 9 . 3 - I * 4 1 1 . 4 - e .I T 4 . U - 1 0 . 9
1 0 3 . 4 - 1 6 - 6 09;s - 1 3 . 7
1 1 4 .a - 1 9 . 4 110 .a - a a .6 1 8 6 . I - 8 6 . J 1 3 1 . 4 - 3 0 . S II
1
. .
. ..
TABm I. - Contkued. 1-STAUE lURBIIIB8
w $s
4 . 6 6 6 4 - 0 9 3 5 . 2 1 2 5 . 5 9 0
r '1
p1 Y;
-gJml-S
.z i . 1 6 7
1 . 3 0 3 1 . 3 9 7
1 . a 9 3
' PV, ,-h, 0 . 5 2 1 3
. 5 1 7 9
- 5 0 4 3 . 5 1 a 7
3 ..29 2 . 3 1 0 . 5 0 . 7 0
.8 0
.9 0 1 .oo
0.6 0 . 6 0 .70 . e o .9 0
1 . o o
, 0 . 7 0 . s o .7 0
.9 0 - 8 0
' 1 . 0 0
y O . 8 0 - 5 0 - 6 0 .7 0
.9 0
.e 0
1 . o o
0 - 9 5 3 8 7 . 7 0 , 1 8 4 8 . 1 3 4 0 . O B 5 0 . 0 4 4 4
- 2 5 . 6
- 3 6 . 2 - 3 0 . 5
11 . o o 5 . 4 1
1 . 5 2 6
1 . 3 6 6 1 . 5 3 1
1 . 4 9 1 I - 4 3 2
0 .5227 3 -6 6 5 1 . 9 9 0 . 1 8 0 6 0 . 9 8 1 I 8 7 . 5 0 . 7 0 5 0 . 5 5 6 . 7 5 0 . 5 5 0 . 7 9 s . 5 3 8 . E 4 0 - 4 9 8 - 8 9 0 - 4 6 9
- 1 7 . 5 - 2 0 . 8 - 2 4 .6 - 2 9 . 2
- 1 7 - 4 - 2 0 . 6 - 2 4 . 2 - 2 6 . 5 - 3 3 . 6
3 . 6 9 7 3 . 7 9 4 3 . 9 5 0 4 . 1 4 2
~~
2 . 6 4 3 . 8 7 6 - 5 4
1 3 - 6 3
~.
. 0 9 8 7
. 1 3 9 9 1 0 0 .a 1 0 8 . 3 , 0 6 1 0
. 0 3 1 1
1 . 5 3 9 0 . 5 2 1 6 . 5 1 6 6 . 5 1 4 4 - 5 0 8 1 . 4 9 8 4
5 - 1 4 1 3 .o 9 1 3 . l o 5 3 . 1 6 2 3 . a 4 a
3 . 0 7 2 . a s
8 . 0 8 4 . 6 4
1 7 . 2 4
0 . 1 2 6 9 -0971 , 0 6 6 6 . 0 4 0 1 . 0 2 0 0
0 . 7 6 6 0 . 5 1 6 . 8 0 0 . 5 0 4 - 6 4 0 . 4 9 4 . 8 7 5 . 4 5 6 . 9 1 5 . 4 2 7
0 . 9 3 3
1 0 7 . O 1 .SI5 1 . 5 2 1 I . 5 4 9 1 . 5 8 9
2 . 9 6 3 a - 7 8 5
1 . 9 6
3 . 6 6 2 . 5 9
0 . 9 7 0 96 . a . e 8 3 I l o a . 6
0 . 1 0 2 1
. 0 5 8 4
. 0 7 9 9
. 0 2 8 7
. 0 3 8 9
. 0 1 1 1
1 . 7 a l
1 .685 1 . 6 9 3
1 . 6 9 1
2 .a2 3 a . 0 7 5 1 . 9 6 2 1.886 1 . 8 3 6
2 . 6 8 9
2 - 6 3 3 2 - 6 4 4
2 . 6 4 1
2 . 7 4 5 2 , 5 6 1 2 - 4 8 8
1 0 9 . 4 1 1 5 .l
1 0 . 2 4 2 2 . 3 0
5 I 3 1
1
o . s a 1 6 . 5 1 8 5
2 . a 6 3 . 0 9 4 . 5 3 7 -32
1 3 . 5 0 2 9 . 8 6
0 . 0 4 7 9 . 0 3 5 9 . o 2 5 3
. 0 0 9 3
. 0 1 6 3
. O D 4 5
0 . 9 2 6 100 .6 . e 3 3 I 1 1 8 . 7
\ 0 .so 0 . 9
.7 0 - 6 0
.9 0
.8 0 . 7 5 0 1 1 9 . 4
. 6 0 5 1 3 1 . 1
. 6 7 3 I 1 2 6 . 2 . 5 4 2 1 3 8 . 3
. 5 1 4 6
. S O 9 3
.so17
. 4 9 0 4
~. . "
2 . 2 6 6 2 . 3 2 9
2 . a 2 1 I 1 .oo 1 . 7 9 9
SLkt a
. .. 1
. . . . . . . .
. +
. . . . I
I
I
. . . . . . .
0 . 8 0 . 1 0 . 1 6
. 3 0
. 4 0
. 6 0 a 6 0 . 70 . B O
1 . O O - 9 0
0 . 6 0 - 1 0 . 1 B .BO . 3 0
.a 0 - 4 0
. 6 0
. 7 0
.BO
.9 0 1 . o o
0 . 7 0 . 1 0 . I 5
.so - 4 0 .so . 6 0 .7 0
.9 0 . B O
1 . o o
. a 0
. a o
~
0.8 0 . 1 0
. B O
.I 6
- 3 0 . 4 0 .no . 6 0 -7 0 . B O
1 .OD - 9 0
0 . 9 0 . 1 0 .I 6
. so
. 8 0
. 4 0
.5 0
.7 0 - 6 0
.e 0
.9 0 1 . o o
. . . . . .
1
- ( 3 P -
).SO0 . 5 0 0 , 5 0 0 .500
. 6 6 5
. 5 3 0
. 6 4 5
.'105
. 7 7 0
. e 3 0
. a 9 0
L600 , 6 0 0 , 6 0 0 , 8 0 0
, 6 6 0 , 7 1 0 . 7 6 0 . a 1 0 * a 6 0 .915
1 7 0 0 . 7 0 0
, 7 0 0 , 7 0 0
. 7 0 0
.750
.7t0
. a 1 0
.a50
. E 9 0
.050
D.100 , 8 0 0 . B O O , 8 0 0 , 1 0 0 .b06 , 8 3 8 .0b6 . e 9 5
. 9 5 0
&DO0 . g o o .p00 .p00 , 9 0 0 , 9 0 0 , 9 0 0 , 9 0 0 . 9 3 5 . 9 5 5 . 9 7 0
-
,110
-
-
.9a0 -
-
I '
.. ..
4 II
. . .
IP. 0
. . -. .. .
457s 1 I CW-6
TABLB I. - Continued. 1STAOE TDRazHEs
( 0 ) Continued. = O.'
@h
3 1
0 , 5 6 1 1 0 . 7 5 0 0 . 6 4 3 5 . 4 9 8 3 . 9 0
* 5 5 4 4 . 5 4 3 4 1 I - 5 6 4 1 6 - 1 6 9 1 1 5 . 3 9 .6 1 a 5 . 8 0 0 6 . 8 5
0 . 1 2 4 8 . 0 7 4 5 . 0 3 5 4
0 . 9 8 5 . 9 0 8 . E 2 8
1 . 3 7 3 1 . 4 5 0
0 . 5 5 9 1 0 . 7 9 5 , 6 1 5 . 5 5 1 8 I A;: r:;;: I 4 . 3 6 8 I 8 . 3 8
4 - 2 2 2 4 . 6 3
. 5 4 0 0 4 - 5 4 1 1 9 . 3 5
0 . 0 9 1 0
. 0 2 4 5
. O S 2 8 0 . 9 3 6
. 8 5 8
. 7 7 9 I I I
0 . 5 6 9 1 0 . 8 0 0 0 . 5 9 5 3 . 4 4 0 3 . 5 5 . 5 5 6 8 . e 4 0 , 5 7 4 5 . 4 2 9 5 . 6 3
- 5 9 6 1 . 5 4 8 8 I I 1::; I 3 . 5 3 2 1 2 4 . 7 9
3 - 4 6 8 1 0 . 5 0
o . 0 9 a 4
. 0 3 4 a , 0 6 0 6
. 0 1 5 5
0 . 9 6 9 -083 . e o 5 , 7 2 8
1 . 6 8 0 1 . 6 9 9
0 . 5 6 4 8 1 0 . 8 2 5 ( 0 . 5 4 7 I 3 . 1 0 4 I 2 . 9 3 0 . 0 7 7 7 0 . 9 9 4 . 9 1 0 .82 9
. 6 ? 7 - 7 5 8
1 0 1 . B 1 - 1 6 . 4 1 0 . 8 0 . 6 0 1 . 9 8 6
. P O 1 .a37
.80 1 . e 5 7
1 . 0 0 1 .831
. 7 0 1 . 9 o a . 5 6 0 0 . a 5 5 .SJ6 2 . 9 7 2 4 . 2 9
' 5 5 4 0 . 5 4 5 2 1 ::!: 1 ::$: 1 2 . 8 7 0 I 1 3 : 5 4 2 . g o 1 7 0 4
, 5 3 1 5 . 9 4 0 . 4 0 0 2 - 8 6 0 3 2 . 5 8
~. . O S 4 8
. 0 1 9 1
. 0 3 4 9
. 0 0 8 5
1 0 7 .9 1 - 1 9 -31
1 2 1 . 8 - 2 6 -6 1 1 4 .6 - a 8 .?
1 3 1 . 6 - 3 1 . 5
0 . 8 6 2 1 10.900 10 .476 I 9 , 8 3 6 I 3 . 5 5 0 . 0 3 4 4 0 . 9 4 4 . 8 5 7 . 7 7 5 .700
. 0 2 3 4 , 0 1 4 4 , 0 0 7 7 , 0 0 3 4 . a 2 9
*, OT. 3
0 - 1 0
. 2 0
.1 5
. s o
. 4 0
. 5 0
. 7 0
. 6 0
. eo
.9 0 1 .oo 0 .10
. I 6
.3 0
. 4 0
. so
. 6 0
. 7 0
. eo 9 0
2 -
- .a o
i 100 - 0 .10
. $ I
. 3 0
. so
. 4 0
. 6 0
.7 0 . B O . g o .
1 . o o 0 . 1 0
. a s
. s o
. so
. 4 0
- 6 0 .70 ,no . 9 0
1 . o o 0 . 1 0
. 1 5
.so .so
.so - 6 0 .t 0 .LO
1 . 0 0 .9 0
. ao
- . s o
-
. 4 0
-
1 . s a 6 1 0 - 5 7 4 3
- D.100
. s o 0
. s o 0
. s o 0 ' : E .630
. 7 s o
. e 2 0
. a 0 0
3 . 6 0 0
. 6 0 0
. 6 0 0
.d 0 0
. 6 0 0
. 7 0 0 , 6 4 0
, 8 0 0 . e 5 0 . 9 0 0
b.700 . 7 0 0 . 7 0 0 .7 0 0
. 7 8 0
. 7 6 0
. 0 0 0
. e 4 0
.930
. a 0 0
-
. 7 5 a
-
. 7 o a
. a 8 0
I . B O O . e o 0 . B O O . B O O . e o 0 .a00 .ea0 . 0 5 0 . e 0 0 .9 1 0 . 9 4 0
I . 9 0 0 . g o o . g o o . 9 0 0 . g o o . g o o . 9 0 0 . P i 0 . P I 0 . 9 6 0 , 9 7 0
-
. ..(
- .691 . 6 8 1 . 6 6 0 . 6 s a . 6 1 a , d.0 7 . 6 4 0 . 6 2 8 .6 4 S . 6 6 6 . 6 a 8 - . 6 9 1
.667
. 6 8 1
.630
. 5 8 3
. S R 9
. 6 4 4
. 6 4 9
. E 9 7
. 6 5 9
, 6 as
- .6 9 a . s e a - 6 6 8 . 6 58 . s o 4 , 6 6 9 . 5 9 1 . B O 8
. b o 9
. 8 1 6
. 6 6 0 -
. 6 9 3
. 6 0 4
. 6 7 a
. 6 3 0
. 5 3 8
.s93
- 5 3 8 . 6 s a ,169 . 5 6 4 . 5 a 5 -
u T
. 6 9 4
. 6 8 7 .
. 6 7 7
. 6 4 8 , 6 0 9 . 5 5 9 - 5 0 0 . 4 8 S - 5 a o . s o a . 6 0 7
*
I h - 1.0 a 4 . 9 0 4
2 6 . 9 4 7 . 0 4 7 8 . 3 1 6 . a d 4 3 . 9 0 5 . 5 6 7 8 . 4 6 4 . 1 6 6 1 . 7 8 4 . 4 9 3 1 . 4 4 4 .171 1 . 8 . 4 . 0 4 7 1 . 1 3 4 . 1 2 8 1 . 0 6 4 . a 1 1 1 . 0 3 4 . 8 4 0 1 . 0 1
3 . 8 6 0 ' 1 . 0 8 3 . 8 3 0 1 . 0 4 3 . 8 1 8 1 . 0 8 3 . 7 4 8 1 . i ~
3 . 0 3 4 a . 0 6 4 . 0 9 9 9 . 9 7 4 . 4 4 5 5 . 1 0 c . a 5 s 1 1 . 4 5 s .si1 4 1 .as 3 . 5 3 8 1 . 0 8
3 . 6 7 4 3 . 6 0 1
1 . 3 4 1.60
3 . 5 8 1
3 . 4 6 8
1 . 0 5
1 . 9 3 3 . 5 0 3 1 . 1 0
3 . 4 0 s 1 . 4 1
3 . 4 0 7 9 . 4 3 3 . 5 4 1 ; 3 . 7 0 3 . 7 3 1 6 . 7 9 3 . P I S 1 6 . 6 1
3 . 3 5 5 1 . 8 0
4 . a m 6 9 . 0 3
3 . ~ 1 1 . 0 s 3.168
1 . 9 9 3 . a a 6 1 . 1 1 3 . 9 1 7 1.07
3 . 1 4 0 a . 0 7 3 . 1 1 7 8 . 9 5
3 . 8 4 6 9 . 1 7
3 . S O 9 1 8 s . 1 1
5 . 0 6 8 1 . 0 8
3.0.5~ 1 . 7 4 8 . 9 7 7 e . 4 s 8 . 9 4 1 3 . 1 5 a . 9 1 a 6 . 6 0 a . g a l i 4 . 3 9
3 . 1 1 7 1 . s e
3.169
8 5 . 7 0 5 . 3 6 5
4 . 7 9
3 . 0 7 1
1 . 3 6 3 . 0 3 5 1 . 1 4 3 . 0 5 4
1 . 0 3
0 . 9 5 5 8 1 4 .61 3 . 0 1 1
4 4 . 6 6
1 . 4 2 5 3 .41b5 . 4 0 9 1 . 3 8 4 1 .3619 . 3 a 9 4 .a548 .190a . l a a d . 0 6 2 4 .0211
.3615
. 3 4 3 7
. 3 5 3 9
. 3 1 6 1
. a 8 1 6
. 1 9 0 9
. e 4 0 5
. 1 3 6 4
. 0 8 3 3
.0597
-
. o l a a
. a 8 6 9
. a 6 9 8
. a 4 a a
. a 0 8 8
- . 0 7 9 4
. 1 7 1 7
.130a , 0 0 0 9
. 0 2 a 4
.0511
. 0 0 6 0 -
.195a
. a 0 1 6
.1866
. 1 6 3 8
.1066
. 1 3 6 1
. 0 7 ? 3
. 0 4 9 6
. 0 1 6 6
. 0 1 0 6
.00p4
.1019
.1039 - . a 9 6 6 .0~a5
. 0 3 a 7
. 0 6 1 8
. 0 4 B 6
.d195
. O O V S
. 0 0 3 4
. 0 0 0 6 -
- FL, -
0 . 7 0 4 . 7 1 0 . 7 1 7 . 7 3 9 . 7 6 8 . a 0 0 . e 6 0
1 . 0 8 0 1 . 1 4 6 1 . s 3 4
0 . 7 0 6 . 7 1 3
. 7 5 0
. 7 8 8
. e 3 7
. 9 0 0
.985 1 . 0 9 3 I . a 4 4 1 . 4 7 0
. 9 a 9
- . 7 a a
- 0 . 7 0 7
. 7 1 6
. 7 6 8 .
. e 1 0
. 9 5 0
. e 7 1
1 . o s 1 1 . 3 7 1 1 . l a b
1 . 6 6 0
. 7 a n
- 0 . 70 0
. 7 1 9
. 7 5 4
. 7 7 6
.058
I . O O B . 9 1 1
1 . 1 s s 1 . 3 3 1 1 . e 9 9
0 . 7 1 0 .795 . 7 4 0 . 7 9 1
. 9 5 6 1 . 0 1 7
t . 4 S B 1 . 7 5 7
I . a s s
-
. a 6 8
1 . a s 1
a . a d o -
1 6 . 8 8 5 . 0
- z . 4 - 3 . 7 3 3 . 1
- 1 5 . 6 7 5 . 7
- 7 .J 4 8 . 6 - 9 . 7 6 0 .O
- 4 . 9
6 9 .e 8 7 . a
- r a .a' - 1 9 . 5
9 6 . a - a r . 4
r a o . e - 3 ~ .I 1 8 . 8 - a .s a 7 . a - 3 . 7 9 5 . 9 - 5 . 0 8 1 . 6 - 7 . 4 6 8 . 8 - 9 . 9 7 7 . 0 - 1 0 . 5 8 3 . I '-16 .6
I O Q .6 - a 3 . 9 9 a . 3 - 1 9 . 1
1 1 4 . 4 - a 9 .-I 19e .1 - 3 7 . 3
19 . 4 - a .5 a 9 .e - 3 .8 . 3 a . 3 - E- .I 1 6 . e - 7 . a 7 a . e - 1 0 . a 0 4 . 5 - 1 9 . 9
101 .P - 1 9 .6 9 9 . b -16.9
1 0 6 .3 -30 . 3
111 .I - 8 9 . 7 1 9 1 . 4 - a 4 . o
1 1 1 .7 - 5 7 . 5
0 6 . 6 - 9 . 6 3 0 . 7
- 1 0 . 5 7 6 . 8 - 7 . 8 5 9 . 4 - 6 .8 4 0 . 6 - 3 . 9
1 0 3 .I - 1 6 . A s a . 6 - 1 3 . 4
111.7 - a o .1 l a o . 7
-38 .s 1 4 8 .I - 5 0 . a 1 3 0 . 7 - a 4 .6
a i . 7 - a . s sa .3 - 4 .o
6 8 . 1 - I .o 4 a ,6 - 6 . 3
8 0 . 8 - 1 0 . 9
1 1 1 . 1 - 1 7 .s 9 6 . 5 - 1 3 . 9
1 8 1 . 6 - 9 1 . O 1 0 9 .I - 9 5 .b 137 .O -31 .I 1 4 6 .O - 4 0 .1
I
. .
CW-6 b c k 4575 8
F
Q1 ($)h
0 . 8 4 3
,771 . B O B
, 7 3 7 . 7 0 4 , 6 7 5 , 6 4 7 ,619 . 5 9 3
0 . 8 4 7 .EO3 , 7 6 0
.688
.613
. 6 4 7
. 582 ,551
0 . 8 4 8 ,795
.?on
. 7 4 6
.697
.617
.580 , 5 4 5 , 5 1 1
0 . 8 4 6 . 7 8 5
, 6 7 7 .630 . 5 8 7 . S 4 6 .SO9 . 4 7 4
- . ? a 0
. 7 a 9
ut an, bp, 1 o . a o
. 3 0
. 4 0
. 5 0
.60
.7 0
. B O
.9 0 1 .oo
9 . 5 7 8
5 . A 9 0
4 .A1 5 4 . 9 6 0
4 . 7 8 9 4 . A 4 7 4 . 9 6 0
7 , 9 0 4
4 . 8 0 5 5 . 7 9 5
3 - 9 6 1 5 . 7 9 . 3 3 . 7 1 5 5 . 6 9 6 3 . 7 1 6
7 . a 5 6
5 .ape
1 . a 6 6
6 . 7 ~ a 4 . 9 7 9 4 . a 9 9 3 , 6 0 6 5 . 3 1 1 5 .130 3 . 0 2 1 a . 9 5 ~ B . 9 a 5
5 . 9 5 5 1 . 4 1 5
3 . 1 6 2 2 . 8 7 0 I! . 6 7 8 R . 5 4 7 2 , 4 5 6 2 . 3 0 1 '
5 . 6 a 7
1 . 1 5 1 . 2 6
1 .61 1 . 4 0
1 . s a a . 4 1 3 . a 3 4 . 7 5 7 . 9 1
1 . 1 8
1 . 4 9 . 1 . 3 1
1 . 7 4
-
a . 1 3 a . 7 4
5 . 7 1 3 . 7 8
9 . 7 4
J . a 1 1 . 3 7 1 . 5 9 1 . 9 1
3 .15 4 . 4 6 6 .91
a . 3 9
l a . o s 1 . a 5
a .11 a .TI 1.71 1 . 4 4
3.87 5 * 3 4 B . 4 9
1 5 .ll
1 . a 8
1 . 8 6
3 . 1 4 4 .39
1 0 . ? 1 6 . 5 A
1 9 . 4 1
1 . 5 a
a . S T
0.2994 . 2 ? 6 A ,8510
. l e 9 6 , 1 5 4 8 . 1 1 9 0 . 0 8 4 3 , 0 5 3 5
. aa19
0. a 4 0 5 . a a 6 s . a n a n .175a . 1 4 6 6 . 11 7 0 . O B 7 8 . a 6 0 7 * 0 3 7 7
0 . 1 9 3 5 . 1 7 a 5 . 1 5 1 1 , 1 3 8 5 , 1 0 5 1
.0601
. 0 4 0 6
. o . s a o
. o a 4 7
0 . 3 3 9 1
, 0 9 9 4 ,116n
* 0 8 2 6 , 0 6 6 0 , 0 5 0 3 . 0 3 6 0 . o a 3 ~ . CJI 4 a
0 , 0 6 7 8 . 0 5 8 5 , 0 4 8 5
. 0 3 0 4
. 0 3 9 1
. 0 1 5 7
. 0 0 6 0
. o a a 5
. 0 1 o a
) . 4 5 0 7 o . a o .30 . 4 0 . 5 0 . 6 0 .70 .8 0 .9 0
1 . o o 0 .EO
. 3 0
. 4 0
.50
.60
.7 0
.80
1 . o o .9 0
o . a o . 3 0 . 4 0 . 5 0 . 6 0 .7 0 .8 0 .9 0
1 . o o
0 . 6 0 0
.670 ,633
. 7 4 0
. ? 7 5
. R l O
. A 4 5
.8 R 0
. 7 a s
a . a 4 6 a , 0 8 8
I . 4 a 6
1 . 7 8 9 1 . 536
1. . 3 6 5 1 . 3 3 7 1 . 3 3 0 1 . 5 3 8
3 . 3 a 3 2 . 4 4 0
1 . 7 6 7 2 . 0 0 8
1 . 5 3 4 1 . 6 2 2
1 .4RO 1 . 4 5 0 1 . 4 5 3
3 . E l l
2 . 3 a l a , 8 3 6
a , 0 2 3
1 . 6 3 0
1 . A 3 7 1 . 7 1 4
1 . 5 7 2 1 . 5 3 0
0 . 4 5 6 . 4 3 9 . 4 4 1
I 4 3 9 ' e44 1
, 4 5 2
, 4 0 6 . 5 8 ?
. 4 2 a
1 1
3 , 4 4 8 8 0.700 0 . 4 3 5 1 - 7 0 5 I - 4 0 7 8 8 . 5 9 5 . 9
1 0 1 . 6 9 8 . A
1 0 5 . 7 1 0 8 . 9 1 1 2 . 4 1 1 6 .l 1 a a . o
- 3 6 . 7 0 . 6 a 6 t
;735 ; a o Q .765 , 4 1 0 . 7 9 0 , 4 0 0 . e 2 0 . 9 9 4 .850 , 3 8 7 , 8 8 0 . 3 7 6 .905 . 3 1 6
I I 1 (.
8 8 . 9 - 3 5 . 6 0 . 6 1 6
1 0 5 . 3 8 7 . 9
1 0 9 . ? 111.9 1 1 6 . O l a o . 3 1 s a . 9 1 8 7 . 6
8 9 . 4 - 3 4 . 6 0 .6071
1 0 8 . 2 9 9 , o
156.7 121.5 1 8 4 . 5 1519.6 sa . 3 1 3 7 . 9
8 8 . 9 - 3 5 . 6 0 . 6 1 6
1 0 5 . 3 8 7 . 9
1 0 9 . ? 111.9 1 1 6 . O l a o . 3 1 s a . 9 1 8 7 . 6
8 9 . 4 - 3 4 . 6 0 .6071
1 0 8 . 2 9 9 , o
156.7 121.5 1 8 4 . 5 1519.6 sa . 3 1 3 7 . 9
0 . 9 o . a o .30 . 4 0 .50 . 6 0 . 7 0 .8 0 .9 0
1 .oo
5 . 3 a 1
5 . a 9 4
a . R I ~ a ,366
5 , 9 8 1
2 , 5 7 1 2 . E 6 6
2 . l o 4 2 ,015
0.841 .? 7 3 ,711
.603 , 6 5 4
, 5 1 4 .557
,476 , 4 4 0
- G ut
- 0 .50
. 6 0
.7 0
.8 0
1 . o o .9 0
43h,2-5 1 a3,h -SJm,-: 9
1 . 6 5 7 1 . 5 3 4 1 . 4 6 5
I . 4 2 1 1 . 4 5 1
I . 4 a 7
2 . l a 7 1 . 8 6 7 1 . 7 1 1 1 .615 1 . 5 5 9
1 . 5 1 2 I . 5 2 7
0.5 0 . 6 5 4 ' 2 . a 6 . 1 6 3 5 1 . 8 3 0 . 1 9 8 1 0 .961
.918 2 -97 . I 2 8 2 4 .a1 , 0 9 4 0
.E78
8.59 . 0 6 2 9 . a 3 9
. 7 6 b 11 . a 7 . a 3 7 8
. 8 o a
1 0 1 . 1 1 0 4 . 5 1 0 7 . 4 110.9 116 .6
9 8 . 1 - 3 9 . 7
5 . 0 5 0 5 . 72A 5 . 6 8 3 5 . ? O R . 4 7 4
0 . 6 0 . 4 u . s o . 7 0 .KO
. 8 0
.9 0 1 .oo
5 . 9 4 8 5.185 4 . 7 5 2 4 . 4 8 7 4 . 3 5 0
4 . a 0 1 4 , 2 4 3
0 . 6 3 8 1 0 .4507 0 .705 0 .524 . 7 3 5 .518 . 7 7 0 , 5 1 9 . B O O . s o 4 .a35 .497 . e 6 5 . 4 6 9 . g o o . 4 5 4
1 . 6 3 0 . 1 8 5 7 0 . 9 9 0 1 . 9 8 . 1 5 6 A . . 9 3 7
3 . 3 8 . 0 9 7 1 . a 4 0 4 . 9 0 . O K 9 7 . 7 9 5 7.86 . 0 4 5 6
1 4 . 4 7 . 0 2 6 4 .751 . 7 1 0
2.51 . l a 6 5 , 8 8 7 1 0 2 . 9
1 0 9 . 2 1 0 5 . 3
1 1 7 . 2
9 9 . 6 - 3 8 .I
118 . z l a 0 . 9
0.7 0 . 4 0 - 5 0 .so .7 0 . 8 0 .9 0
1.00
4 . P l l 4 . 8 7 3 7 . 8 7 7 3 . 6 2 1 3 - 4 5 0 3 . 3 3 6 3 . a 6 0
0 . 6 2 6 1 0.4488 0 . 7 6 0 0 . 4 8 7
. g a o . 4 0 6
1 . 7 5 0 . 1 3 8 R 0 . 9 7 1 2 . 1 6 . I 1 4 6 .910 2 . 8 ' l . 0 9 0 R .a53 3 .a7 . 0 6 8 a . B O O 5 .7.6 . 0 4 7 R .750 9 . 4 7 . 0 3 0 7
17 . 7 9 . D l 7 4 ,708 . 6 5 7
108 .o 110 .6 1 1 4 . 6 117.5 1 8 2 . a
1 1 4 .O 1 1 7 . 8 120 .T. 1 2 4 .I 1 2 8 . 1
0 . 8 0 - 4 0 . 5 0
.70
.6 0
. a 0
. 9 0 1 - 0 0
4 . a 5 3 3 .667 3 . 2 9 3 3 . 0 4 0 2 .E61 2 .7 31 2 .631
0.616( a a 2 . 3 4 7 2 . 1 O B 1 . 9 4 5 1 .a31
1 . 6 8 4 1 . 7 4 8
9 - 0 9 1 2 . 6 4 5 2 . 3 d 9 2 . L A 1
I . E 7 0 1.776
I . q a 8
0 . 4 4 7 2 0 . 8 2 0 0 . 4 3 6 . 8 4 0 . 4 3 0 . 8 6 0 . 4 2 1 . R B S . 4 2 h . g o 5 , 4 1 8
.940 . 3 4 3
. g a s , . 3 9 3
1 .R9 0 . 0 9 1 1 2 . 4 0 . 0 7 3 7 3 . 1 9 .OS70 4 . 5 1 .0418
1 1 . 5 8 .Ol80 6 . e a . o a 8 7
2 2 . 1 4 .0101
0 . 9 4 9 . 8 B O .a17 . 7 5 9 . 7 0 6 . 6 5 6 . 6 0 8
0 . 9 0 . 4 0 . s o .60 .7 0 . 8 0 . 9 0
1 .oo -
0 . 4 4 5 9 0 . 9 0 0 0 . 3 9 6
. P I 5 . 3 4 4
.955 . 7 1 4
. ¶ d o . 3 1 6
. 9 6 5
3 . B i d 3 . a 6 6
2 . 6 4 3 2 . 6 5 A 2 - 3 0 9 2 - 1 9 3
a . P o 0 1 2 1 . 3 1 2 6 .O
1 3 6 . 6 1 3 3 .9
.0187
I SLSP I ,
1
. . .
k
. . . . . I
” . . . . . .. . . .. . . . . . . . .. . ..
I
- 1.0 3.
”OB e 1 1 . 3 4 5
B . 6 6 8 7 , 4 5 7 6 . R 4 0 6 . 5 2 7 6 . 3 9 R 6 . 3 6 9
6 . 1 2 8 6 . 4 a 3
-
- . 5 4 0 , 5 5 5 - 5 7 0 .571 . 5 7 9 . 5 8 a , 5 8 0 . 5 7 1
.48R * 5 1 0
. 6 a 5
-
. b a d
. 5 4 a - 5 5 7
. 5 8 3 , 5 7 1
. 5 67
. E 4 7
(g)je,h
o . 7 a 1
. 7 9 a
. p a 9
. 7 5 ?
. 8 3 7
. B e l
, 9 8 1 1 .os9 1 .lOS
49h.24
- J 9 .7 I .18 o.a93a 1 . 3 8 . a 6 4 4 1 . 5 4 . a 3 1 4
a . 4 0 . 1 5 s 4 5 - 3 8 .116n 5 . 1 0 , 0 7 9 1
1 9 . 3 a . o a 4 1 8 . 9 9 , 0 4 7 7
1 . a 1 0 . a 4 3 2 1 . 5 8 , 8 1 5 9
8 - 7 8 .1177
1 . 8 6 . 1 9 4 6
1 . 6 4 . l o 5 1 2 . 0 5 .1518
6 . 3 1 . 0 5 S J 7 . 9 3 . 0 8 4 7
1 1 . 9 0 . 0 3 1 5 8 7 . A 4 - 0 1 4 7
1 . a 4 O . I S E ~ i . 4 5 . .163P 1 . 7 7 . I 3 7 4 8 . 8 8 .lo96
8 . 0 6 . 0 3 5 4 4 . 7 4 . 0 5 e 9
1 6 .19 . 0 1 9 0
3.14 . 0 8 a a
4 1 . 4 7 .noes I . a a 0 . 1 3 0 7 1 . 5 4 . i n 9 5 1 . 9 7 . O B 9 4 a . 5 7 . a s 9 1 S . 7 0 .0500
10 . 5 8 . a 1 9 5 5 . R 6 .0331
6 4 . 9 5 . 0 0 7 9 a a . a 8 . 0 0 9 8
8 8 . o 9 1 .7 9 5 . 3 9 8 . 9
10 3 ..6 107.7
116 . 9 l l a . o 1 s a . 4
D . i a a
5 - 4 8 4
6 . 9 4 P 5 . 9 5 1
5 . 1 3 4
4 .910 4 . 9 7 9
4 . 9 1 7 4 .B9?
D .717 . 7 6 1 . B O P ,861 , 9 1 8 .PO0
1 . o s 0 1 .131 I . a 3 5
9 1 . B -38. I . 6 5 8 9 6 . 6
1 0 0 .o 104 .E 1 0 8 . 4
1 1 7 . 0
1 0 8 . 7
I t a .6 183.3
. 4 5 6
. 4 9 2
..I74
. 5 1 4
. 5 3 6
. 6 6 1 , 5 4 0
. 5 5 3 , 5 7 7
7 . 7 3 8 5 . E 7 8 5 . n o 7
1 0 0 . 4
1 1 3 . B 1 0 9 . 6
1 2 3 . 4 1 B D , 5 1 3 4 . 2
9 5 . 4
106 . a
119 . a
0 . 7 1 6
. R 2 7
. 7 6 9
. a 9 0
1 . 0 4 1 . 9 6 1
I . 1 3 3 1 . a 4 1 I , 3 7 3
0 . 7 1 9
.8 4 9 , 7 8 0
. 9 2 5 I .ala 1 . I l a 1 . a 3 0 I .J73 1 . 5 5 5
0 . 7 P 3 , 7 9 4 . e 7 4 . 9 6 6
1 . 0 7 1
1 . 3 4 5 1 . 1 9 5
1 . 5 3 8 1 . 7 8 4
- 3 6 .7
- 3 5 .6
- 3 4 . 6
4 . 5 3 1 4 . a s 1 4 ,081
3 . 9 a e T . 9 8 3
5 . R 9 9
1
, 4 6 1
. 4 4 8 , 4 3 4
. 4 7 7
. 4 9 a
. 5 n b
. 5 a 4
. 5 l 8
. 5 8 1
- , 4 6 8 , 4 4 5 . 4 1 6 . 4 0 4 . 4 3 0
. 4 4 4
. 4 4 4
. 4 8 8 . 4 7 a -
6 . 7 R l
4 . s a 9 5 . 1 8 5
1.939 3 . 6 6 3 3 . 4 1 0 S . 3 6 7 3.272 5 . 8 1 1
1 0 5 .7 0 5 .I
1 1 . 1 . 3 1 1 s . 5
1 3 0 . 6 1 2 6 . 5
1 5 5 . R 1 4 1 . 6
9 5 . 6 106 . 6 1 1 6 . 3 l e J . 6
133 . O 1 3 8 . 5
1 4 8 . 3
L a o .6
1 a 7 . 6
1.41 .I . D l 3 9
. .
. . . . . . . . . . ..
L P m
!
: ,
i I
1
I
i.
. .
213 ..ioI..1 *t
3.1 0 .10
. a o . , . I 5
.3n
; .sa .4 0
.60
.7 0
, . 9 0 .0.0
1 .aa 3.6 0 .10
. 1 5
.30
. A 0
. 5 0
. 6 0
. 0 0
. 7 0
-9 0 1 .oo
0.7 0 .10
. s o
.I5
.3Q
.4P . . . 5 a
. 6 0
. 8 0
. aa
. T O
1 . o a . s a
0.8 o .lo .ao . 4 a
. 7 a
.1 I
.30
::a .no
1 .oil .9 0
0.9 0 .10 .15 . a 0 .so . 5 0 .60 - 7 0
.9 n 1.00
.40
.ea
" 1 1
"
1
"
1
. .
"
I
"
6 . 7 0 0
9 . 5 5 8 6 .0 0 0 5 .74 4 s .153 4 .853 4 . 7 3 0
4 . e o 9 4 . . 9 4 8
3 . 7 0 7 9 . 7 7 7 7 . 7 9 0 5 3 6 1
I .sal'
4 . 7 a 6
4 . 7 7 a 4 . a s 7 3 . 9 3 9 3 . 7 8 D 3 . 7 1 1 3 . 7 0 8 3 .7 32
1 .ai8 8 .S4 1 6 . 6 8 7 4 . 9 9 7 4 .1.0s
3 . 3 Y O 5 .160
3 . a 8 6
3 . 0 4 a B . v a a a .9 .53
r . a s % 5 . e 7 8
J . a 0 6
a . 7 1 a a .JBO a .4aa a . 4 n i
0 .Ob8
4 . 4 3 0 3 . 6 7 6
P .9 DB
0 .Be9 6 .411
J .99J 5 .338 0 .P 17
5 . a 4 7
a . 6 a o a , 4 0 8
a .is7 B .Uh4
U .045
- "
"
"
"
"
c
.1.08 0 . a 9 9 4 1 . 1 5 . a 0 8 7 1.18 . a 7 7 8 1.11 . a s 8 4 I . 4 9 . a a s 4
a . 1 3 .16s0 a . 7 4 .1307
1 . 7 4 . 1 9 5 7
J.71 . 0 9 7 9 6.75 .0674 9.90 . 0 4 1 5
%,2J
. 7 4 6 73.1
.733
8 5 . 7 . a 8 1 8 1 . 0 7 7 . a
. 6 3 a 0 9 . a
0 . 7 8 0 6 6 . 8
. 7 0 6
. 6 8 6
9 8 .3 .610
06 . 6
. 5 8 8 g4.9
.568 QV .5
. 5 4 7 105.1
0.773 68.6
.7 4 0
. 7 5 6 7 3 . 4 7 7 . 9
. 7 0 7 ' 8 5 . 9 -8 7 6 . 6 4 6 91 . 4
8 9 .o .618 91.1 .591 9 0 . 1 . 5 6 5 . 101.7 . 1 4 0 1 0 5 . 7 .SI6 110.1
0 . 7 8 3 6 8 . 4 .7 6 3 7 3 . 6
~ . 7 4 S 7 8 . 6
. 6 8 8 9 4 3
.bOO 201.6 , 9 6 9 1 0 4 . 8 . 5 3 9 100.6 . L I O ' 1 1 3 . 4
.
~ . 7 0 5
~ . . d 3 3
, 88.1
9 7 : 0
,483 118.7 1 0 .79.0 6 8 . a
. 7 8 7 73.8
. 7 0 0 8 9 . 5
. E 1 8 9 9 . 0
.611 104.6
. a 4 6 1i1.1
.581 1 0 7 . 9
.513 ,116 .3 t . 4 0 a 119.8
. ~ S P 1 8 5 . 6
0.794 . 7 a e 14.0 . 7 4 3 7 9 . 8 .695 9 0 . 7 .646 100.9 . b o 1 110.5 . B E 0 117.6
- 4 a b IS4 . 7 .IBO 1s1.a .4sa 154.7 . 4 a a 1 1 4 . a
1
. . . ."
I
0 .IO .lb
.30
. 4 0
. 6 0
. 7 0
. B O
. 9 0 I .oo 0 .15
.30
. 4 0
. 6 0
. s o
.80
. T O
1 . o o - 9 0
0 .15
. 30
. 4 0
. s o
. 7 0
. 6 0
. 9 0
. 8 0
1 .oo 0 .I5
. 4 0
. > o
.50
. 6 0
. 7 0
. e o
.9 0 1 .oo
. a n
. B O
- . a o
- . ao
- . a o
- o .ao
, 3 0 . 4 0 .50
.7 0
.BO
. 9 0 1 . o o
. a o
-
+%-s
~ a ' . z a 7 1 s . s o 8 La . x 1 7
x- 8 . e 0 0 7 . S A 4 6 . 5 1 4 6 . 0 4 6 5 . 7 9 4 5 .683 5 . 6 6 6 5 . 7 1 1
1 0 -618 9 . O S 8 7 . 1 6 0 5 . 8 V E
4 .738 5 . 1 6 8
4 . 4 0 e 4 . 3 3 4 4 . e 5 7 4 . a n 4
B . s 7 a
4 . a 9 3
L O . 6 6 4
6 . O S 0 4 . 9 3 4
3 .8 9 0 3 , 6 4 3
3 .365 3 . 4 7 6
3 .E90
9 . a 8 9 7 . a 8 4 5 .SI5 4 . S O 6 3 .Ill 3 , 5 3 1 3 . 0 ' 1 5
a . 7 6 9 2 . a 0 4
a .66P 6 . 4 6 1 4 . 7 4 7 3 .e71
e . 9 4 8 3 . 3 8 3
2 . 4 9 1 a - 6 8 4
a . 3 3 4 a . a 8 2
5 p1
1 . 0 9 I . 1 4
1 . 5 3 1 * s 4
x .81
I . a 0
a . a 4 a . 9 4
6 . 5 7 4 - 1 7
I1 . 9 s
I .l6 1 . a 3 1 . d o 1 . 6 4 1 . 9 8 9 . 6 1 > . . S a
1 4 .81 7 . 9 6 4 . p a
I . I 9
1.4'1 1 . 7 6
a . 8 4
1 . a 7
a .le J . 9 a a .a7
I 8 . 6 0 9 . 7 5
1 . a 8 1 .31 1 . 6 6 1.91 a . 4 3 3 . a s
is .06 a 3 .se 1.31 1.66
4 . 4 2 7 .IO
a .lo a . 7 7 3 . e a a . n 4 5 . 6 0
13.90 s o .so
4 - I . 3 5 0 5 . 3 3 7 a . 3 8 3 8
' . a s 9 5 . a 9 8 8
. a a ~ 9
. l a 4 8
. 1 4 4 6
.lo58 ' . 0 7 0 6 . 0 4 1 4
1 . 9 0 0 6
. a 3 8 1
. a 6 7 1
. a o r s
. 1 4 l a
-
. 1 7 4 6
. 0 7 7 4
.lo05
. O S 0 4
. o a s 9 - ' . a 1 8 3
. a 0 8 9
.la70
. o s a 5
. 1 8 0 4
. 1 5 4 0
, 1 0 0 4 . o 7 5 a
.03s+
. a 1 8 8
.I505
. 1 4 0 7
. l o o 6 -1806
.Ob95
.0811
, 0 4 5 7 .0311 . 0 1 9 4 . 0 1 0 7
' . 0 7 1 9
. a 4 8 6
. 0 6 0 1
. 0 2 8 6
. 0 3 8 0
. 0 1 3 4
.0083
. 0 0 4 5
-
. o a o a
-
- & o . 9 s a
, 9 5 6 . 9 7 4
. E 8 7
. o n 1
. a 5 5
. 7 9 4
. ' I 65
. 7 3 6
. ? l o 0 . 9 8 7
. 9 6 5
, 8 8 1
. B O 4
. 7 6 7 * 7 3 3 , 6 9 9 , 6 6 6
0 . 9 9 5 . 9 6 9 ,919 . 8 7 0
. 7 8 0
.7J8
. 6 9 8
. 6 b 0
. e a 1
- . 9 a a
. e 4 8
-
. e a 4
. 6 a a
1 .PO0 . 9 7 a
. E 5 6
.91P
, 7 5 4 . B O 3
, 7 0 7 .663 , e a 1 , 5 8 1
0 . 9 6 8
. a 4 0
. 9 o a
.I81
. ? a 6
. 6 7 5
.6a8
. 5 8 4
. 6 4 1
-
-
Wh, 2-1
8.5 .6 8 5 .s 86 . 5 e 9 .I 9 1 . a 9 3 . 4 9 7 . 3 9 9 . 5
1 0 0 .I 1 0 3 . 4
lia .O
8 7 . 7 8 9 . 4
9 8 . 7
1 0 1 . 8 9 8 . 6
105 . 3 108 . o 1 1 2 . 4 i 1 7 . S
9 0 . 9 66 . e
1 0 0 . 6 9 7 . 4
1 0 5 . 9
110.7 1 1 4 . I 118.6 1 8 4 . 7
8 6 . O
9 9 . 4 9 0 . 6
1 0 4 . 7 1 0 9 . 9 1 1 8 . 9 11.7 . 4
9 a .9
1 0 7 . a
1 a o .s 1 8 5 . 4
9 0 . a 130 . 6
9 9 . 7 1 0 8 . 7
1 9 2 . 4 1 1 7 . 9
l P 6 . o 1bp.0 1 3 8 . 4
l a 9 . d
- 3 6 : 4
- 3 4 . 8
-33 .I
I
. .
. ,..
0 . 8 0.10 .I 5
. s o
. s o
. 4 0
.7 0
. e o
. e o 1 .Od
.9f l
0 . 6 0 . 1 0 . l b
.IO
. 4 0
. 6 0
.e 0
.7 0
. eo 1 . o o
. 9 0
0 . 7 0 . 1 0 d l 5
. 3 0
. 4 0
. a o
. a o
. a o
2: .7 0 . 0 0 .90
1 . O O
0 . 0 0.10 . I 5
. 3 0
- 6 0 . 6 0 . 7 0
1 .oo .PO
' 0 . 9 0 . 1 0 . l S
.50
. * a
. a o
. 4 a
. e o
. a o
. s a
i t 4 .?
1 . 0 0
I ! :r . . . . .
1 . e ~ a 1 . 6 6 9 1 . 6 7 3 1 .691
3 ,651 a . 7 4 1 a . 3 1 7
1 . 9 6 7 . 7 6 0
1 . E 4 4 . e 3 1
. 0 0 5
. 8 0 1 . 0 0 0
7 . s a 6 o . 5 0 0 8 3 . 7 0 0 s . a 4 5 . 7 0 0
a . d 4 4 .7eo a . s a 5 2 . 1 9 7 .a 1 0
.7ao 0 . 0 9 3 a . o x 0
.e 4 0
1 .pee . 0 6 3 .19,a . s a 6
n . 1 7 7 0 . 4 9 8 ~ 0 . 0 0 0
4 . l o 0 .7UD 9 . i 4 6 .?BO
1 . 9 6 4
S .PO6 .a00 4 . 7 6 4 . e o 0 3 . E 0 7 . B O O 3 . o l e . e 1 0
.8 a 0
.PO0
.PXQ
. 9 4 s
9 . 0 3 0 0 . 4 9 7 1 1 . 9 0 0 6 .S?? .PO0
.goo 4 . 0 9 X S . ( L O
.goo
.9OO S . 0 5 0 .9OP a . 7 7 8 .v 1 0 x . S R 9 . v a & a . I t l o a . ~ L S
. 9 4 O
a . a 5 7 .PUh , 9 6 b
a . 4 6 4 a . e 7 8 . 0 2 a
. n a p a . s a 3 a . e 9 6
a . a 0 1
5 . 3 4 8
P . 1 5 7
_.
!Lrn - . ! I 8 4 . 6 9 0 . 5 9 6 . e o 0 .e 1 9 . 6 P 7
. 6 4 S
.631
, 6 3 7
.a15
. e 1 0
. 5 6 9
. 5 6 8
. 6 7 S
. I 8 0
. 6 9 0 , 6 0 6
. d B 9
. e 0 1
. 6 7 S
. 5 5 6
. s 3 9
. 5 3 7
. 5 6 4
. 5 T P
. 6 O S
..5 0 9
. 5 9 4
. 8 9 9
. 5 9 7
. 5 6 3
. 5 7 7
. I 4 7
.s11
. 4 9 6
.53P
. s a 1
. 5 6 3
.15D
. a 9 *
- . a n 1
. d a 0
. s a 1 -
-
, 6 8 8
- . s e a . S I 1 .SS8 .SO7
.4 .9
. 4 9 1
. * I1
. 4 ? 9
. 5 1 1
. 5 6 3
a a . 4 5 0 15 . e 0 1
1 . 0 9
1 2 . 6 4 6 1 . 1 4
9 . s a 9 1 .80
8 . 0 9 1 1 .36
7 . 3 4 8 1 . 9 6 1.60
6 . 9 4 a 6 . 7 4 4
a . 6 6 3 . e o
6 . 6 7 5 s . 6 a
6 . 7 6 S a 8 . 60 6 . 6 9 8 IO . I S
1 7 . 9 7 6 i .ll 1 0 . 1 4 8 1 .04
1 . 1 7
7 . 6 1 5 1 . 4 3 6 , 4 3 6 1 . 7 1
6 . 4 5 5 9 . 7 9 9
s . l S l S . 0 7 8 1 3 . 4 0
7 .01
5 . 0 7 4 5 8 . 6 1
i a . 7 5 0
a . 9 a a . i 7
s . a s 0 4 . a 7
1 4 . 9 5 1 1 0 . 7 0 4
0 . s a 8 I . 1 9
6 .4Ll1 5 . 3 Q 4 . ' 1 . 8 6
1 . 6 1
4 . I 0 6 a . 4 a , 4 . 4 8 4 3 . Y 8
4 . l a 8 E .11 8 . 9 7
4 . o s 7 I 0 . 4 3 4 .OD1 4 8 . 0 3
1 0 . ? 7 6 9 . 8 a 9 1 .aa
1.13
7 . 4 4 4 I . a s 7
1 . 3 8
4 .?l I 1 .60
4 , 1 0 4 8 . 7 8 D . 0 4
S . 0 6 0 4 .Q1 3 .E30 6 . 4 6 3 . 4 7 8 11.86
I . r a I .ae
4 . a 7 1
3 . s 7 0 0 6 . a 3 1 , a 0 9 7 6 . a 9
i l . 1 4 8 1 . 1 5 0 . i l 9 1 .a4 6 . 6 9 6 1 . 3 6
4 . B E 9 x . a 7 9 . 7 6 6 S . 4 5 0 s . 1 9 7
4 . 9 4 8 . 4 5
~ . o s a 1 . 7 1
s .am
3 . o a n 10 . L a
P . ? a 7 13n .sa a .a913 4 0 .oa
I
Q, - 1 . 3 1 0 s .3S63
. a 8 7 4
. s a i a
. a 4 9 1
. a 0 7 8
. 1 6 4 0
. r a o s
. O B 1 1 , 0 4 7 8 . o a 3 4
. a 8 0 2
. a s 3 7
. l a l a
- 1 . 8 9 3 9
. X 6 5 7
.19E5
. l a 3 5
. O S 6 4
. 0 8 7 8
. o s 1 1 , 0 1 4 3
# . a z o 5 . e 1 0 1 . a 0 4 9 . 1 7 6 7 . 1 4 6 6 . 1 1 5 7 . o e s n . 0 5 8 6 . a s s 9 . 0 1 0 9 . 0 0 7 9
' . 1 6 0 4 . 1 6 0 5 .1400 . 1 1 7 6 . 0 9 4 9 . 0 7 X S . 0 6 1 1 . 0 3 3 9
. 0 0 9 7
. 0 1 9 T
. 0 0 1 7
.003s , 0 7 7 7 . 0 7 1 1 .Ob04 . 0 4 5 1 .os31
-
-
-
. 0 1 4 a
. o a a e
. a 0 7 6
.QO1b
.0011 -
- (82.b - 0 . E 0 7
. 0 8 4
. 0 4 1
. 0 7 7
.911
.95b
1 . 0 4 6 . 9 9 9
1 . 0 9 7
1 . x i 4 1.153 - o . 7 9 a
.01a
.85a
. 0 7 6
. 9 8 3
1 . 0 9 0 .D14
1 . 0 9 1 1 . 1 6 0 1 . a 3 9 i . s 3 a
o . 7 8 a -
. 0 0 4
. 0 x 0
. a 0 0
. 9 3 6 - 9 9 9
t . I 4 8 1 . 9 3 9 1 . 5 4 7 1 . 4 ? 0
0 . 7 7 4 . 0 0 0
. 0 0 ?
1 +031 . P I S
1 ,il7 1 . 3 5 4 1 . 4 7 6 1 . 6 6 0
0 . 7 6 9
. E a 9
.7 9 1
. E 9 1
1 . P a 0 . 9 ? 7
1 . 1 7 3 1 . X 9 ? 1 . 4 4 7
1 .E91 1 .6 3 7
I . a 6 9
- . 0 a 7
I .a16
-
-
SlSP . . .
. . , . . . . . . . . . .. .
* 4575 cw-7
- & I . B a a
.86S
. a 6 9
.BP9
. B O 5
. 7 7 9
. I S 4
.731
. 7 0 9 , 8 0 7 .666
I . a 9 9 . o n 5 . E 6 6 . a 3 4 . a 0 8
.T48
. 7 1 1
. 6 5 1 , 6 1 6
. 6 S l
0 . P I 1
. 8 7 J
. 8 9 0
. a 5 4 , 1 9 7 . 1 6 0 . T U 5 . 6 9 1 . 6 6 8
. I P S
0 . 9 8 0 .a98 .8?6 . a s 1
. 7 4 6
. ' I87
. 7 O I - 6 6 6
.E94 , 6 5 9
0 . 9 P 7 .DO1 . 8 7 6
. 7 7 6
.BPI , 7 8 8
. 6 4 0
. b a s
. 6 0 0
.E61
. s a 5
-
. 7 7 a
-
.ma6
-
, 6 8 9
-
4 _I . S 7 7 0 . 3 6 P 8 .J4BO . $ l I b . a 7 9 9 . a 4 0 8 ,1991 .lSdB . 1 1 4 a . 0 7 5 8 . a 4 4 1
. 3 1 5 9
. 1 0 1 8
. P I S 1
.lo78
. l a 1 8
. l i d 8
, 0 1 5 8 .On88
. 0 3 0 6
. a n 7 1
. n n n e
Pl u; 1 . 1 4 1 .09
1 . n o 1 . s 4 1 . 1 3 1 . 8 1 E .U4
4 . 1 7 6 *s9
In ,OT
1 . l l 1 . 1 7
1 . 4 0 1 . 1 3
1 . 6 4 1 . 9 8 a . 6 8 3 . 4 0 4 . 9 6 8 . 0 6
i s . I 8
a . 9 3
-
I . l a 1 . 1 9 1 . n 7
1 . I 9 1 . 4 8
n . a o Q - 8 6 s . 9 7 5 .96
1 9 . P l 9 . 9 4
I . 1 4 r . n a 1.91 1 .67 1 . 9 5
5 . so P . 4 6
4 . 7 0
1s . 4 5 7 . a 7
0 4 . a a I .16 1 . n 4
1 . 6 6 1 . 5 6
a . e 1 a . l a
9 . l a 5 .90 s - 7 4
1 5 - 9 1 S I .77
5) - a Q,m
. e a 0
. 6 9 8
. 6 9 4
.59O
. 6 8 4
. 6 8 S
. 5 6 ?
. 5 5 9
. 5 4 s
. s o 1
.mas
. 697
. 570 , 6 8 1 .663 . E 4 3 i s 4 0 . 5 n 1
. 4 9 7
. S I 0
. 46U
, 5 1 6 -
- . e a 8 . a 0 1 . 5 7 s , 6 1 6 , 6 1 1 . 5 o s . 4 9 n , 4 9 0
. 4 4 7 , 4 7 1
- . * E O
. s s 4
. 6 0 7
. 6 7 9
. 5 1 9
. 4 6 6
. 4 S 8
. 4 S l - 4 9 7 . 4 1 7 .4OI i 1 7 4
. 6 4 0
.E14
, 5 9 1 , 6 8 6
. 4 6 1 ,196 . 5 6 9 . S 6 0 . 5 6 1 . S O 8
-
% , e 4
7 1 .9 8 1 . 7
8 5 . 4 8 8 . I 9 0 . e 9 s . 6
1 0 0 . o 9 6 .I
1 0 4 . 1 1 0 8 . 9
e a .9
- . s o 0 . s o 0
.SbO
.moo
. 6 4 5 ,681 . 720 . 7 7 6 , 1 1 0 . E 6 1
.sa0 1 1 . 9 6 3 1 s . s 1 4 1 1 , 9 9 9
8 . 7 7 4 7 . 8 6 s 6 , 4 1 1 6 . P O 0 s . I 6 4 5 . 6 6 7 5 6 6 6
17 . e 1 9 1 0 . s o 4
9 . a n 7 r . i 4 a s . 8 6 a
4 . 7 3 5 6 , l b S
4 , 4 8 6 4 . J 4 5 4 . n 7 3 4 .U46
14 . 9 P O 1 0 . 5 4 3
8 , s 3 4
4 . 3 1 0 3 , 9 1 4
3 . 4 9 5 3 , 6 6 1
s . s a 6 3 .31 .8
l a . a 0 9 9 .lo8 7 , 8 5 1 5 . 3 3 5 4 . 3 4 3 3 . 7 4 1 s , 3 1 1 3 . l o 0 n .911 8 . 7 8 1
5 : 7 n s
6 . o a s 4 PI^
9.683
1 1 . a 0 0 8 . 0 1 1
4 . 7 8 7 6 , 4 0 0
S . 9 0 0 3.359
B . 7 1 S n , 111 9 . 3 6 4
0 . 9 a o
a . a 4 1
.I 0 . 1 0 . 1 6
. so
. 4 0
. a 0 - 6 0 . T O
1 . o o .90
.6 0 .IO . l I . a 0
.4 0
. Y O
. s o
. T O
. 6 0
. B O
1 .oo - 9 0
1.7 0 .io .PO . I C
. 4 0
. 10
. s o
. T O
. 6 0
.a 0
.9 0
.ao
.aa
L .ao 1.8' 0 . 1 0
- 1 5 . P O . Y O . 4 0 . I D . 6 0 .7 0 .BO
1 .oo .9 0
1.9 0 . 1 0 . I 5 . a 0 . so . 4 0 . so . B O . T O . 8 0
1 . o o .PO
1 . 4 9 1 s . In9 3 . o o o 1.816 z .Mi s 1 . s o 0 1 . .441 1 . d l 7 1 . * I 7 1 . A 3 1
6 . 4 1 8 4 .601
D . E 7 1 5.138
1 . a s s 1 . 7 0 4 1 . & l S 1 .56-4
I . s a g 1 . 1 1 8
7 . 3 1 1 5 . I 6 6 4 . 0 8 3 e . P O 1
1 . 9 1 8 1 . 7 9 4 1 . 7 1 5 1 .LE9 1 . E 8 3
E . l e 8
4 . 6 3 s 1 . 4 1 5 a . 7 7 9 2 . s e s 0 . a 4 9 i . 9 1 4 1.161
1 , ? I T
9 . 0 7 4 6 . 4 0 9 6 . l a 4
3 . l S 9 3 .813
E . l a 1 P . 4 1 4
8 . O S 7 D , 1 9 7
1 . 9 1 4 1 .E15
a .IPS
-
9 . 1 1 0
-
a , 4 9 6 a . % l a
- I . e a 9
1 . 7 8 9 -
-
7 6 . 4 8 0 .T 1 4 .P 8 9 . 4 9 1 . 8 9 8 . 1
1 0 1 . 9 9 7 . 1
10s .s 1 1 4 . 9 1 0 9 . O
7 5 -1
8 4 . 4 9 s . 1 9 6 .6
1 0 0 .I 101.9 1 0 6 . 7 1 1 1 .I 1 1 6 . 8 1 n o . n
7 4 . O 7 9 . 0
9 s . I 8 4 .o
l o a . 4 1 0 s . e 1 o e . a 1 1 4 . E 1 1 1 . 9 181 . S 1 8 7 . 1
7 s .O 78.1 1 S . 6 9 3 . 8
1 0 3 . 4 1 1 9 .I 1 1 8 . 0 1 8 1 . 8 1 8 8 . 6 I S 1 . e 136 - 4
7 p . n
3 . 5 4 9 5
0 . 6 5 9 ?
0 . 6 S 7 4
, 6 0 0 .moo , 6 0 0 . a 8 5 . 6 6 6 . 7 0 0 7 4.0
. 8 l L
. 8 S h
3 7 5
. a 9 u -
. 7 O O
. 7 0 0
. 7 0 0
. 7 0 0
. I S 0
. 7 6 0
. ? g o
. a 5 5 ,I8A .91s
. B O O . B O O . a 0 0 . I O 0 . a 0 0 .B 86 , 1 6 0 . E 7 0 .a91 . 9 n o . 9 4 O
.DO0
. P O 0 , 9 0 0
, 9 0 0 , 9 0 0 , 9 1 0 . 9 a 6 , 9 4 0 , 9 5 0
. a a a
-
- . g a o
I . P 4 1 7 . n 3 4 1
. 1 9 s 5
.1S61
. l d S l
. l o 7 4
. o s 1 7
. 0 3 5 1
. 0 1 9 7
1 . 1 7 a n . l a n o . I S 1 1
. I O 7 4
.OM61 , 0 1 6 4
. 0 4 8 4
. 0 3 8 B
. o n 0 9
. 0 1 1 1
1 . 0 8 9 6 .0836 . 0 7 1 4 .OM46 . 0 5 1 9 . 0 4 0 a , o s 0 1 . o s 1 3 , 0 1 4 1 . 0 0 1 5 . 0 0 4 6
. a 9 1 4
. 0 8 o a
. 1 a 9 s
- 3 1 . 4 0 . 6 S 6 6
. .
0 .8
- - ut %m,3 - 0 .40
.5 0
.6 0
.7 0
.8 0
.9 0 1 .oo 0 .40 .50 . 6 0 .7 0
.9 0
. 8 0
1 .oo 0 ,40
. 5 0
.60
.7 0
.8 0
1 .oo .9 0
0 .40 . 5 0 .60 .7 0 .a P -9 0
I .oo 0 .40
. 5 0
. 6 0
.7 0
.9 0
.8 0
3 . o o
-
-
-
-
-
"rn1-3
0: 2 .123 1 .e71 1 . 7 2 5
1.596 1,641
I . 576 1.577
2 .422 a .114 1.9a7 1 .e10
I .69 3 1.738
1.667
a .746 a .139 I .eB 1
2 .373
1.986
1 . 8 0 8 1.755
3 .lo9 2 . 6 6 0 2 .371
2 .032 1.926 1 .a43
3 .511 2 .99 6 2 - 6 3 9
2 .I99 2 -054 1.936
a .174
a - 3 8 6
0.5461
0. s4a5
0.5397
0.5374
~~
0 . 5 3 5 6
-EJm14 p1
%,s P; 8 .490 7 . 4 8 5
1 .64
6 .901 2 .oo
6 .563 2.55
6 .385 3.47 5.16
6 .312 6 -307 17 .01
8 .63
5.872 6 .727 1.77
2.20 5.353 2 . 8 8 5 , 0 2 8 4 . e 2 6
4.02
4 . 7 0 4 10 - 5 6 6 .15
4 -631 21 .34
5 .603 4 .e43 a .44
1 .91
4 .366 3.28 4 .052 4 . 7 1 3 .839 5 .690 13 .03
7 .39
3 -581 26 .89
4 -858 4 -1.56 3 - 7 0 5 3 . 3 9 6
4.334
A
"1
0.2623 .a204 .1772 .1344 .0944 .OS96 .03as
O . Z O 8 . 5 .171$
.0999
.I349
. 0 6 8 4
.04aa
. o z a s 0.1540 .la39 .0952 . O S 8 8 , 0 4 6 0
.0145
. o a 7 7
0.0998 .0784 .058? .0413
.0159
.0082
0.0479 .0363 .0264 . 0 1 8 1 -011s . 0 0 6 6 . 0 0 3 4
. oa7o
0 . 9 7 8 .947 .917 .E88 ,860 . a 3 3 -806
0 .976 .938 .go1 . 8 6 5 -830 .796 , 7 6 9
0 .969 .924 . e a 0 .e 3 7 .I97 . 7 5 7 . 7 1 7
0 -957 -905 -855 .BO7 . 7 6 0 .716 .673
0.945 .e 8 4 - 7 7 4
- 6 7 6 .630
. e a 7
.7a4
%,2-3
9 2 . 8
97.9 95.7
1 0 4 .9 101.7
108 .7 114.7
9 9 .o 9 5 - 7
1 0 2 - 6 105 . 5 110 .o 1 1 3 -6 119.2
103.5 99.9
1 1 1 .a 1 1 4 .2 118.7
1 0 7 .a
135.6
1 0 5 - 3 1 0 8 .B 112.3 117.3 l a 1 .I 1 8 4 -7 130.4
106 - 6 1 1 5 - 5 121 .o 1 8 5 .I 1a9.2 1 3 3 .I 139 . 6
-7- -35 . 3 -8657
i- -33 . 5 .a391
7 -31.4 .80li
. . . . . . . . .
I
. .
Gw-7 back
- . .. . . . . ..
4575
3 3 G ut
0 . 5 0 . l o .16 . a0 . s o .40 . 6 P . 60 . 7 0 . B O .9 0
1.00
0 . 8 0 . I O .15 .PP .30 .40 . S O . 60 .70 .no .PO
1 . o o J.7 0 . I O
.15
. a 0
. 3 0
.40
. 6 0
. 6 0
.70
. 8 0 - 9 0
1 . o o J .I 0 . I O
.is
.PO
. 3 0
. 4 0
. 6 0
. 6 0
. 7 0
. B O
.PO I . o o
0.9 0 . 1 0 . I 5 .PO .30 - 4 0 . s o . 6 0 . 7 0
- 9 0 1 . o o
. E n
7 .043 4 .909 3 . 9 6 4 8 . 9 3 9 a . 4 6 1
a . 0 4 7 a .BOO 1 . 9 5 7 1 . P O 6 1 . a 1 8
7 . 9 1 5 5 , 1 8 7 4 . 5 1 8
B . 7 9 9 3.36>
B .a89 8 . 4 8 s
B . 1 6 7
8 .031
I , 0 7 8 -
a . a 8 9
a . o o s n . 7 1 3 6 . s a 8
- 5 . 0 9 1 3 . a 5 5 3 . l a T
B A 6 1 a .a03 a . s g g 8 . a 8 6 ~ . R O S 8 , 1 4 5
I * a 4 4 7 a001 5 . a 6 9 4 , 3 1 7 3 . s a 0
B .a81 3.186
a . s 1 a a . 6 6 9
a . a 9 0 8 . 5 9 1
-
-
5. pJh - 1 . 0
&)4,. m a - . 5 4 6 1 3 .600
. E 4 0 ,580 . 6 8 0 . 6 6 8 . 7 0 6
.?PO
. 7 5 0
. a 3 5
. n e 0
. 5 4 R 5 1.600 . 6 0 0 . 6 0 5 , 640 . d B 0 . 7 1 5 . 7 8 0 . 790
.a66
.88I
. so0
.SSP7 3.700 , 7 0 0 , 7 0 0 .710 . 7 4 0 . 7 7 0 . g o o
.a60
. n > o
. a90
.9BO
' . 5374 Y.100 . e 0 0
, 8 0 0
. e 3 0
.876 ' . a 9 5
.9 P'O
.940
.sa0
.aoo
. n o 8
. a 5 0
> 4 , 8 9 4 17 .310 L3 . 7 8 1 L O . B 4 6
7 .771 0 . 6 S 1
7 , 8 9 8
4 . 9 3 6 6 . 9 0 0 6 . 9 6 8
7 .a43
19 .BE4 L 3 . 8 6 1 L O . 9 8 4
6 .837 0 .165
6 . 1 1 0
5 . 4 3 6 5 . 6 8 6
5 .a96 5 ,as6 5 .sol
1 6 . 1 6 4 1 1 . 6 4 4
6 . 8 6 4 S .710 5 . 0 6 6 4 . 6 7 8
4 . e 6 8 4 .169
- 9 . a s 1
4 .483
A . o g a
l $ .T8J v .a87 7 . 956
4 . 9 7 9 4 .sa0 4 . D O 8 1 .798 1 . 5 7 s
1 .J4V 5 .446
1 1 . 9 0 6 8 . 6 4 3 6 . 9 9 9 5 - 3 30 4 .470
3 . E 5 7 3 . 8 9 5 3 . l o 1 e . 9 5 8
5 , 9 9 1
5 . * s a
a 3 3 0
1 . l o 1 .16 I . a s 1 .40 1,66 8 - 7 0 9.011
11 . a 9
a . o s
6 . l a a s .94 -
1 . 1 s 1 . 1 9 I . a 6 a .47 I . 7e a . a 7 3 - 0 9 4 .ID I .64
1 4 37 .SI I . I 3 1 .P1 1 . 3 1 1 . 56 1 . 9 4
3 . d o 1 . 8 7
8 0 a40 9 . T P
5 5 - 7 1
1 . 1 6 1 .84 1 . 3 5 1 . 6 6 s . l S 0 .91 4 . a 9 6 . 9 8
1 3 - 0 0
8 7 . I 9
1 .16 1 . P I 1 . 3 9 I .77 P .sa 3 . 4 3 5 . J 8
18.37 9 . I D
1 5 1 . I 7
a . 5 8
-
8 9 . a 6 -
4 1 . l a
- 4 x
. s o a m
. 3 5 7 9 - 3 4 0 6
.E603
. a l s o
. l 6 B B
. l a 9 6
.0810
. 0 4 6 8
. o a a > 0.JlSl
. a 9 7 7
.8111
. a 0 6 7
. a 4 6 4
.1664
. 1 8 5 4
.0880
.OS63
. 0 1 5 6
. 0 3 0 a
"
- o . a 4 a a
. a 3 1 6
. a i 6 6
. l a s o
. 1 5 1 9
. o n 7 8
.11v1
. 0 5 n n
. 0 3 5 8
.Dl05
. 0 0 7 6
0 . 1 7 0 9 .1897 . 1 4 7 8 . % a s 9 . 0 9 0 1
. O E P ~ , 0 7 1 3
, 0 1 9 8 . 0 3 4 0
.DO94 .aoss o . a n a v
. a 7 5 5
-
- . 0 8 8 4
.0610 ,0467 . O S 1 8
,0140 . 0 0 7 n
. O D 1 1
. o m a n
. o a 3 4 -
- > . 9 8 1
. 9 3 7
.954 . 9 9 O
1 .OPT 1 . O d 7 1 . 1 1 0 L . 155 L .a04 L , 8 8 8 L ,316
> - 9 0 1 . 9 S O . 9 4 1 .983
1 .OR9 1 . 0 7 9 1 . 1 3 4 1 . 1 9 5 I .a63 1.339 1 . 4 8 9
-
- I . an7 .PO9 . 9 3 3 .PES
1. . l o o 1 .169
1 . 3 5 7 1 . 4 4 3 1 . 5 7 3
D . a 7 8 . g o 3 .989 . 9 8 E
1 . 0 6 4 1 .IS8 I . a 1 3 1.31s 1 . 4 e 9 1 . E 7 8 L. . 7 6 7
0 .871 . e 9 9 .gas . 9 9 6
1 .16J 1.073 1 .E67 1 . 3 9 1 I . 5 4 a 1.714 1 . 9 9 6
I . o > n
I .a47
-
-
-
c_
8S . S 8 4 . 9 8 6 . 6 9 0 . o 9 s . I 9 6 . 4
1 0 0 .5
1 0 8 . 0
119.1 1 1 s . o 103 . 7
0 0 . I 0 5 .P
9 3 . 1 8 9 .O
1 0 0 . 4 9 6 . 3
1 0 4 .1 1 0 8 . 4 113.7
l U S . 4 110.3 -
7 8 . 3
9 6 . a 8 3 .I 0 8 . 4
1 0 0 . I 1 0 4 . 8 109.8 1 1 5 .e 118 . e l a 4 .I 1 3 1 -1
7 6 . 6
6 7 . 4 9 7 . 5
1 O b . 8 1 0 9 . 9 1 1 5 .I 119.8 1 P S .o 1 8 9 - 6 1 3 6 - 9
7 5 .I 8 0 . 9 0 6 . 5
101.0 97.1
116.1 l a r .s 1 8 7 . 8 1 3 1 .a 136 - 9 144 .4
- e a . I
-
-
E F
I: !
. .
52 WCA RM ES/JOS
TABIS 111. - 2-8TME TURBIWES
7 - 9 . h -
5 3 .I 4 7 . 5
6 2 . 5 5 7 . 9
71.8 6 7 .3
7 6 . 7
5 0 .l 5 8 . 7 6 2 . 6
7 0 . 5 6 7 . O
7 8 . 3 7 4 . 9
5 2 . 4
6 8 . O
7 4 . 3 71 . o
0 0 . 8 7 7 . 5
- 6 3 . a
1 2 , 2 0 8 1 0 . 7 5 3 1 0 . 3 5 9 10 . l o 6
1 0 . 0 9 9 10 . s 7 7
1 1 . 2 8 3
2 , 1 4 9 1 . 8 6 8 1 . 7 Q 3 . 1 . 7 4 9 1 . a 2 7 1 . 9 2 5 a .030
1 . 1 8 1 . 4 0
2 - 5 5 1 - 0 1
4 . 3 1 9 . 5 9
30.35
. 1 5 0 9 4 0 6
. a 9 4 0 1 : s a 5
. 6 4 5 6 l i 3 5 e .0160 5 0 5
2 . i l l i . 7 5 2 1 .661 1 - 6 8 5 1 . 7 2 7 1 . 7 8 9 1 . R 4 3
1 1 . 1 2 1
8 - 7 1 4 9 - 4 9 2
1. a s 1 . 5 4
3.12 2 . 0 7
1 4 - 4 0 5 . 7 7
5 1 . 6 4
0 . 6 0 . 2 0 4 . 0 0 4 0 . 4 6 7 4 .30 3 . 4 1 ' 7 . 4 6 6 6 . 4 0 3 .137 . 4 6 5 4 . 5 0 3 . 0 0 9 . 4 6 3 7 - 6 0 3 . 0 2 3 . 4 6 0 8 . 7 0 3 . 0 9 1 . 4 5 5 8 . 0 0 3 - 1 0 5 . 4 4 7 0
6 ;3s9 8 . 5 8 5 8 . 3 9 0
8 - 6 2 1
0 . 7 . 2 0 3 1 0 . 1 2 P
7 - 6 5 3
7 , 0 5 4 7 . 1 9 0
7 .oa1 6 - 8 6 7
a . 6 7 8 1.32 1 . 7 2
3 - 9 1
2 2 . 0 2 7 . 9 0
8 9 . 6 3
a . 4 2
4 - 9 5 9 o . 4 6 7 a 4 . 2 5 2 - 4 6 6 1 3 . 7 5 0 - 4 6 4 8 3 . 5 2 3 . 4 6 2 7 3 . 4 5 7 . 4 5 9 8
3 . 3 6 5 . 4 4 2 5 3 . 4 4 0 . 4 5 3 1
9 . 3 1 9 7 . 9 8 7 6 . 9 3 2
6 . 0 7 7 6 . 3 5 9
5 - 6 3 9 5 . E 9 2
1 * 3 9
a . 9 1 1 . 9 4
5 4 . 4
7 2 . e 6 5 . 9
7 0 . e 7 6 . O
7 9 . 6 0 s . 5
5 . 9 6 4 0 . 4 6 7 0 5 . I 1 2 . 4 6 5 7 4 . 4 3 6 . 4 6 4 0 4 . 0 7 0 . 4 6 1 5 3 . e 9 0 . 4 5 7 3
3 . 6 0 9 . 4 3 7 1 3.771 - 4 5 0 1
1 1 . 0 7 3 4 . 1 9
1 6 0 . 1 3
5 ; 0 3
I I - - 0 . 9 0 . 2 0 7 . 0 3 7 0 . 4 6 6 7 0 . 9 0 0 1 . e 9 1 8 . 6 8 6
- 3 0 5 . 9 8 6 . 4 6 5 2 . 9 0 0 1 . 6 5 6 7 . 3 9 0 5 . 2 0 . 4 0 5 . 5 ' 1 0 . 4 6 3 1 , 9 0 0 1 . 5 ? 1 6 . 4 3 3 1.60 . 5 0 4 . 6 7 0 . 4 6 0 0 . 9 1 5 1 . 5 0 4 5 . 7 6 5 6 . 7 5 .60 4 . 3 9 9 . 4 5 5 1 . 9 5 5 2 . 4 7 0 5 . 3 4 5 1 6 . 0 1 . 7 0 4 . 0 8 6 , 4 4 6 6 , 9 8 0 1 . 4 3 3 5 . 0 4 5 5 4 . 3 1
4
2. (g) .-(3 . I ' e),,, S O . ~ J ' G $ . @),,. @)h 5 1.0 2 . h 3.h
. .- ..
1 2 - 5 5 0
1 3 , 9 2 7 1 2 . 9 1 5
1 4 . 3 7 2 1 4 .I07 1 3 . 6 2 1
1 . 4 8 1 . 0 6 2 3 k . 4 0 7 5 6 .3 6 0 .1 7 6 . S 8 1 .o 8 3 - 6 e a . a
.- 3 - 1 7 3 I O - 4 6 7 5 l 0 . 5 0 0
- <
0 . 5 . 2 0 ~ .~ 3 . 1 4 0 . 4 6 6 7 . 5 1 5 3 . 2 2 8 . 4 6 5 3 . 6 6 0 3 . 4 8 2 . 4 6 2 8 . 7 8 0 5 . 5 9 3 . 4 5 8 6 . 0 7 5 3 . 5 1 7 . 4 5 2 4 . 9 3 0 3 - 4 0 5 - 4 4 1 7 - 9 6 5
2 .236
2 . I 3 6 2 ' . 1 7 9
2 . 0 3 9 2 .131- 2 - 2 1 5
1 ; i 9
s . a 4 B . 1 2
0 . 7 7 2 4 . 6 1 9 8 - 1 4
~. . . 2 4 5 7 . 4 0 1 .1783 . 4 4 3 . l o 4 3 . 4 4 6 - 0 4 9 4 I . 4 4 2
"
"
"
"
1
1 1 . 9 3 4
1 1 . 2 7 7 1 1 . 5 4 0
1 1 . 2 2 0 11.068 1 0 . 6 7 8 10 . l a 2
1 . 7 0 1 . 2 7
2 . 6 5
1 1 - 9 6 4 . 9 ?
3 7 . 8 2 1 7 5 . 0 4
0.6 0 . 2 0 * 3 0 . 4 0 . 5 0 .60 . 7 0 .8 0
0 . 6 0 0 . 6 3 0 . 7 3 0 . 0 3 5 . 9 0 5 . 9 5 0 . 9 8 0
e . a 3 8 a .io8 e . 2 9 7
1 . 9 0 3 1 . 9 3 5
1 . 9 5 9 1 . 9 9 9
2 .333 2 . 1 5 9 1 . 9 6 2
1 . ? E 5 1 . 7 7 5
1 . e o 6 1 . a 2 1
6 0 . 9
8 0 . 7
1 -36 1 . 9 6 3 . 2 0
1 6 . 6 5 8 . 6 1
5 2 4 - 9 8 5 9 . 2 8
1 1 . 3 4 5 10 . 5 8 6
9 . 7 8 5 9 . 4 4 3 8 . 9 2 7
7 . a 9 5 8 . 4 5 5
0 . 7 0 0 .700 .000 . 8 7 5 . 9 3 0 . 9 6 5 . 9 8 5
0 . 7 .80
.7 0
0.8 . 2 0 pi . 7 0
a . 3 6 3 2 ,103 1 . e 2 1 1 . d 9 2 1 .67h 1 . 6 6 6
1 0 . e 6 7
8 . 6 8 4 9 . a 4 3
1 . 4 8 2 . 3 0 5 . 9 7 8 .60
2 3 . 6 4 9 5 - 4 0
1 . 1 1 0 6 0 . 4 4 5 . 0 7 9 6 - 3 3 0 . 0 4 0 5 - 2 9 0 . 0 2 4 1 . a 8 8 . 0 0 9 6 . a 7 9 . O Q 2 7 - 2 2 0
1 . 0 5 7 9 0 . 4 5 0 .0365 - 3 1 3
. 0 0 9 7 .183
.0036 . 1 9 7
. 0 0 0 9 . i s 1
. o a o 3 - 2 0 s
8 . 0 2 9 7 .4 3 4 6 . 9 2 4
2 . 3 7 0 2 . 0 1 4 i .69?
i o . 4 o e 9 . l o o 7 - 9 3 8
2 . 6 9 1 . 6 1
- 5 . 1 4 1 1 . 5 5
1 5 8 . 2 6 3 4 . 4 5
1.615 7 . O O A 6 . 3 4 5 5 ..si2
i . 5 7 7 1 . 5 4 1
. 6 0
NACA RM E57J09 53
v)
d L-
dBh*24 I 0 - 9 5 3
. E 6 2 - 8 0 1 - 7 3 5 . 6 6 1 . 5 8 3 - 5 1 3
1 - 5 2 ? 0 . 2 0 . 0 . 5
- 6 0 0 - 6 0 0 - 6 0 0 . 6 0 0 . 7 0
. 5 7 5 1 . 0 0 0 - 6 0 0 1.000 - 6 0 0 . 9 9 4
- 6 0 0 . a 1 4 - 6 0 0 . 9 0 9
- 6 0 0 . 7 1 0 - 6 0 0 - 6 0 4
0 . 9 0 2 - 8 5 3
. 5 3 5 I 0 - 5 7 4
2 0 0 . 6
4 0 30
6 0 5 0
7 0 8 0
4 .5 .7 - 8 . 3 6 3 . 9 -1 .1 .7 7 5 . 9 - 1 5 . 3 8 6 . 5 - 1 9 . 3
1 1 4 . 4 - 3 0 .3 9 8 . 7 - 2 4 . 2
1 3 1 . 9 - 3 7 . 5
1 .600 1 . O O O
. S O 0 .E67 - 6 0 0 . 9 2 l
. s o 0 - 8 2 0
- 6 0 0 . 6 7 0 . s o 0 . 7 5 5
. 6 0 0 . 5 8 7
. 5 9 5 1 . 0 0 0 - 6 0 0 1 . 0 0 0 - 6 0 0 . 9 6 6
- 6 0 0 . 7 6 1 - 6 0 0 - 8 6 8
- 6 0 0 - 6 5 4 . s o 0 - 5 5 0
;768 - 6 9 9 . 6 2 6 . 5 5 2 490
0 - 8 7 6 . e o 2 - 7 3 4
. 6 0 0 1 . 0 0 0 - 6 0 6 I 1 . o o o
9 0 . 7 7 5 . 3 1 1 0 . 4 9 5 . 9 1 1 8 . O 1 0 3 . 4 1 2 2 . 8 1 0 9 . 7 1 3 0 . 4 1 2 0 . 9 1 4 0 . 2 1 3 7 . 5 1 5 1 - 5 1 5 6 .6
- 6 0 0 ~ . 9 1 6 . 6 0 0 - 8 1 3
. 6 0 0 1 . 7 0 7 , 6 0 0 . 6 0 0 - 6 0 0 . 5 0 0
- 6 6 5 - 5 9 4 - 5 2 7 . 4 7 2
o - 8 5 8
. 7 4 4
. 6 7 3
I
9 4 . o l 7 8 - 9 I
5 3 -3 I - 8 - 7 . 6 0 0 1 . 0 0 0 . 6 0 0 . 9 8 1 . 6 0 0 .E73 . S O 0 . 7 6 3 . 6 0 0 . 6 5 4 - 6 0 0 - 5 4 9 . 6 0 0 - 4 5 4
1 i s ;5 1 0 0 ;1 1 2 9 . 5 1 1 2 .8 1 3 5 . 8 1 2 0 . 3 1 4 1 . 4 1 3 0 . 2 1 4 7 . 4 1 4 5 . 3 1 6 0 . l 1 6 3 . 4
7 4 . 5 - 1 2 . 4 8 7 . 7 - 1 5 . 9
1 1 0 .8 - 2 4 . 7 9 8 . 4 - 1 9 .a ~- " I
- " ;774 - 7 0 0
- 5 6 7 - 6 3 2
. 5 0 6
. 4 5 8 1 2 6 - 8 - 3 0 19 1 4 4 :9 1 -36 . 4
- 5 3 6 - 4 7 4
0 . a 3 9 - 7 4 7 . 6 6 7 - 6 0 1 - 5 4 2 - 4 8 . 9
h 5 0.8; gk. - - 6 3 3 - 7 6 6
. B O O
.BOO
. a 0 0 - 8 0 0
. e o 0 -
. 6 7 a
. e o 0 - 8 0 0 . e o 0
. e o 0
. e o 0
. a 0 0
r " .
3 . 2 0 0 . 5 q- - 8 0 t 6 4 . 6 4 1 - 8
8 8 .Y. 6 0 .6 9 4 . 0 7 4 . 3
1 0 8 5 9 1 8 1 2 3 12 1 0 9 17 1 5 6 . 5 1 3 9 . 5 1 3 9 . 2 1 2 4 . 2
9 3 . 6 6 5 . 8 7 1 . 5 4 6 . 3
1 0 4 . 7 8 1 . 4
1 2 8 - 9 1 1 3 .8 1 1 4 . 4 9 7 . 9
1 4 6 . O 1 2 9 . 2 1 6 2 . 6 1 4 5 . O
- 5 7 5 . 6 5 4 . 6 9 1 .7 9 8 - 8 0 0 - 8 0 0 - 8 0 0
- 5 9 7 - 6 9 1 .I 8 4 . B O O . e o 0 . e o 0
-
. a00
1 . o o o 1 . 0 0 0 1.000
1 . o o o - 8 6 9 . 7 9 7 .7 2 3
1 0 9 . 4 1 0 9 . 7 1 1 6 .I 1 2 3 . 8
1 5 1 . 2 1 3 6 . 2
1 1 3 . 9 1 1 8 . 9
1 3 1 - 2 1 2 1 . 7
1 5 5 - 3 1 4 3 . 9
- 2 9 . 9
1 .o 0 0 1 .o 0 0 1 . 0 0 0
. 7 8 8
.B 9 1
- 7 1 6 . 6 5 0
. 8 0 0 - 7 1 5
- 8 0 0
. B O O
. e o 0
. e o 0
. e o 0
. 7 6 2
. B O O - 8 0 0 . B O O
- 8 0 0 - 8 0 0
- 8 0 0 .8 0 0 . B O O . e o 0 . e o 0 . e o 0
-
-
-
1 , 0 0 0 1 .o 00
. g a s
. 7 8 5 - 7 1 9 . 6 5 1 . 5 9 1
- 7 5 8 . 6 2 1
- 8 0 0 - 8 0 0 . a 0 0 - 8 0 0 . e o 0
1 . 0 0 0 [o . 5 4 5 1 . O O O - 6 0 1 1 0 4 . 9 7 3 . 2
7 7 . 7 5 0 . 6
1 1 0 . 5 8 7 . 3
1 3 5 .F 1 1 8 . 2 1 2 2 . O 1 0 4 - 2
1 5 2 . 5 1 3 4 . 3 1 6 8 . O 1 5 0 . 3
1 2 4 . O 9 8 . 9
1 2 4 . 4 1 3 1 . 2 1 3 9 . 4 1 5 2 . O 1 6 4 .6
1 . 0 0 0 . 6 0 0 1 . 0 0 0 . 7 9 5
. 8 5 8 1 . B O O - 7 1 6 . e 0 0 . 5 8 8 . e o 0
-7 8 3 . 2 5 4 "7 1 1 0 . 3 7 8 . 4 1 1 9 . 7 9 4 . 4 1 2 8 - 5 1 0 8 . 5
1 5 8 . I 1 3 9 . 2 1 4 1 . 0 1 2 2 . 5
1 . o o o . 9 8 8 .8 3 4 . 7 2 4 - 6 6 2 .s 99.
. 6 4 7 - 8 0 0 - 8 0 0 . 8 0 0 .8 0 0 - 8 0 0
3 . 2 0 . 8
. 5 0 ::x I' - 7 0 - 6 0
1 2 8 . 5 1 3 5 . 2 i 4 0 . 3 1 4 6 . 5 . 7 9 5
- 6 7 5 - . e o 0 . s o 0 . B O O .8 0 0 . a 0 0
I ;fEf . 6 0 0
1 0 8 . 9 1 3 2 0
' 1 4 8 : 2 1 1 5 3 . 3 1 5 5 . E 1 6 4 .6
1 .o 0 0 . 9 3 0 . 7 5 0
- 6 1 4 - 6 7 2
.5 5 4 L
54 NACA RM EVJ09
- a2.h
- a 7 .I 1 8 . 5
4 8 . 4 3 5 . o 5 6 . 2 6 1 . 5
7 1 . 4 6 6 .3
7 6 . 8 - a o . e 30.3 38 .P 5 3 . 2
6 6 . 4 7 0 .6
7 9 . a 7 4 . e
1 2 . 9 3 3 .l
6 7 . b 5 7 . 3
7 0 . E
7 6 . 9 7 3 . B
e a .P
- 4 a .s
e a . 4
a 4 .7 - 1 5 .7 4 5 . 3 6 0 . 8 7 1 .7 7 5 . 5 7 7 .e 8 0 . 5 8 4 . 9
a 6 . 4 3 8 .o 4 8 .I 6 3 . 9 7 4 . 8 a 1 . a
-
e a . o 8 a . 6
I 1 - - 1.500
- 5 0 0 . s o 0 - 5 0 0
. 6 5 0 . 5 5 0
- 7 6 5
. 9 4 0 - 8 7 0
0 . 5 .IO a . 4 9 0 . i s a . 4 5 8 .ao a . 4 1 0 . 3 0 a . a g 4 . 4 0 a . a o s . s o a . a 7 9 - 6 0 a . 4 9 0 . 7 0 2 . 7 6 0 . e o a . 9 8 4 i 1 . 6 6 4
1 - 6 1 9 1 . 6 4 3
1 . 5 4 4 1 . 5 6 0
1 . 5 8 9 1 . 6 6 5
1.88V I - 7 7 8
9 . 9 5 8
9 . 6 4 4 9 . e s a 9 . 1 7 6 8 .a13 9 . 1 1 7 9 . 9 6 1
11 .038 1 i . 6 9 6
o . s a 8 a . s a 7 9
. s a e a ; s a 1 4 . s a 4 4
. 4 8 7 a
. 5 8 7 5
. s i 5 9
. S O 5 6
o . s a n .5a7
. 5 a 3
. s a 5
. 5 1 a
. 5 a7
.5 1 9
- 4 7 7 . 4 9 9
. s o 0
. 6 0 0
. 6 0 0
. 6 0 0
.630
. e a 5
. 7 a s
. 9 6 0 - 9 1 0
.7 0 0
.7 0 0
.7 0 0
. 7 0 0
.7 I O
.7 9 5
.E80 . 9 4 5 . 9 7 5
.BOO
. e o 0
. a 0 0
. e o 0
. e o 0
. e 5 5
. 9 6 5
. 9 a 5
- 9 0 0 -900 . 9 0 0 . g o o . g o o . g o o . 9 5 5 . 9 8 5
-
-
. g a o
-
I .?ti8
1 - 5 8 8
I . 6 8 0 1 . 6 5 1
1 - 5 3 5 1 . 5 5 6 1 . S 9 8 1 . 6 6 0 i - 7 1 9
9 - 0 9 7 8 . 9 0 4 8 - 4 9 7 7 . 9 4 7
a .337
8 . 9 4 1 8 . a 1 7
9 . a s 1
7 . 9 4 a
i - 7 3 4 1 . 7 0 7 1 . 6 7 4 1 . a 9 5
1 . a 1 6 1 - 5 4 4 I . 6 7 0
I . 7 5 6 1 . 7 8 8 1 . 6 9 1 1 . d o 3 1 . S O 8
I . s a 0 I . s a 5
o . s a 8 3 . 8 a 7 5
. s a l 3
- 4 9 8 8
3 . s a e o . s a 7 3 . s a 6 3 . s a 3 4
- 5 8 6 7 . 5 3 4 5
. 5 l h 5
. S O 8 0
. 4 6 8 3
. 5 1 9 4 . 5 1 3 4 - 5 0 3 3 . 4 8 5 3 . 4 s ~ a
3 . s a 7 8 . s a 7 0 .sass . 5 2 5 8
. S 1 7 1
. 4 9 7 9
.SO98
. 4 7 6 8 -
a . 4 9 9
7 . 3 4 a
6 . 9 3 3
1 . 4 7 1 1 . 4 5 1 1 . 4 3 9 1 . 4 3 4
1 . 7 7 5 1 . 7 4 4
1 . 6 0 7 1 . 7 0 5
1 . 4 0 3 1 . s o 1 1 . 3 7 5 1 . 3 3 5 -.- . .
- 18 .: 1 9 .I
5 9 .: 4 9 .. 6 4 . I 6 0 - 1
6 9 .I ?4 .I 7 9 . 9
3 0 . 9
S I .I 5 5 .I 6 5 . 1 6 8 -6 7 2 . 6 7 6 .6 8 9 .6
3 5 - 4 4 6 . O 5 5 . J 6 6 . O 6p.5
7 5 .6 7 9 .6 83.7
4 0 . 1 3 b .s
6 9 .l 5 6 .Q
7 6 . 4 7 4 . 5
7 B .6 8 5 . o
5 0 .I 37.3
5 8 . 5 7 1 . f
8 1 . 4 7 9 .s
e 5 . 5
- 4 3 . a
-
7 a .6
-
-
e a . 4 -
-510 .lo . I S
. s o
. 4 0
.6 0
. 5 0
. 7 0
. 8 0
0 . 4 0 . 1 0 .I 5
. s o
. 4 0
. s o
.6 0
. 7 0
.8 0
0 . 7 0 . 1 0 . I 5
. s o
.30
.?) 0
.6 0
.? 0
0 .a 0.10 .1 s . s o . 4 0 . . so .6 0.
. a o
. a o
. a o
.a o
.a 0 '
.7 0
. a o - 0 . 9 0 . 1 0
. 1 5
.30
. s o
. 4 0
. 6 0 '
. 7 0
1 .600 . 6 0 0 . 6 0 0 . 6 4 5 . 7 3 5
. g o o
. 9 5 5
. 9 8 0
1 . 7 0 0 . 7 0 0 . 7 0 0 - 7 1 0 . 7 9 0 a 8 6 5 .93 0 . 9 7 a .os0
i ; a 0 0 .€ loo . B O O . B O O
- 9 0 5 . 8 4 0
. 9 5 5
.OB0
. g o o
. g o o
. 9 0 0
. g o o
.s 0 0
.9 4 0
. 9 7 5
. 9 9 0
.a as
-
-
KACA RM E57J09
56 NACA RM ES/JOS
TABLE R I , - Concluded. 2-STME TtJAwIBs
-gJmllS
1 6 . 7 9 6 1 6 . 6 4 4 1 5 . B 8 9 1 3 - 9 4 2 1 3 - 2 8 4 1 3 . 2 5 2 1 3 . 7 9 7 1 4 . 2 3 1 1 3 . 9 9 3
' PV,
0 . 5 7 4 0 . 5 7 3 3
. 5 6 7 3
. 5 7 0 5
- 5 6 2 1 . 5 5 2 6
- 5 0 6 2 . 5 3 5 5
, 5 7 8 5
ml-3 G *,h
2 7 .P 3 8 . 7 4 6 .7 5 5 . 2 5 9 . 9 6 4 . 7 6 8 . 5 7 3 . * 7 8 .6
- . - 2 . l i s 2 . l i O 2 . o l e 1 . 7 8 7 ¶ . 7 3 8 1 . 7 9 4
1 . 9 6 8 1 . E 7 0
2 - 0 4 8
4 . 1 9 9 4 .161
5 . 4 8 6 3 . 3 1 6
3 . 4 4 9 3 . 3 1 3
3 . 4 9 8 3 . 5 5 8
3 . 9 7 a
. s o 0
. s o 0
. 5 4 0
. 5 0 0
. 6 3 5
. 7 3 5
. 8 4 5
. 9 2 5
. 9 7 0
. 4 0
. 6 0
. 7 0
. 8 0
1 5 . 1 5 ? 1 5 . d o 0 1 4 .081
11 .10 8 1 2 . 1 8 6
1 0 - 9 1 4 1 0 . E O 5
I O .e83 i o - 4 1 8
a o . 4 4 1 . 4 4 9 .o 6 0 - 5 6 4 . 8 6 8 . e 7 6 .P 01 . 8
3 1 . 3 4 8 . a 5 1 . o 6 4 . 1 6 9 . 7
7 s . 4 7 8 . 8
7 9 . 9 8 3 -0
7.a . 2
-
0 . 6 0 . 1 0
. 2 0
. 1 5
.30
. 4 0
.60
. s o
. 7 0
.80
0 . 5 7 3 8 , 5 7 3 0 . 5 7 2 0
. 5 6 5 5
. 5 6 9 3
. 5 5 9 1
. 5 4 7 6
. 5 2 7 1
.4 9.1 3
0 . 5 7 3 6
, 5 7 1 4 , 5 7 2 7
. 5 6 8 0
. 5 6 3 4
, 5 4 2 0 . 5 5 57
. 6 1 7 6
. 4 7 3 5
0 . 5 7 3 5 . 5 7 2 3 - 5 7 0 8 . 5 6 6 6 . 5 6 0 9 . 5 5 1 9
. 5 0 6 7 , 5 3 5 7
5 . 4 5 7 5 .4 .0 0 5 . 0 6 9 4 . 3 8 7 3 . 9 9 9 3 . e 9 0 3 .9 2.9 3 . 9 1 8 3 . 7 5 1
6 .e01 6 . 6 2 0 6 . I 6 9 5 . 3 7 1 4 . 7 3 5 4 . 4 7 5 1
4 . a 4 8 3 . 9 8 5
8 . 2 3 3 7 , 9 1 5 7 . 3 3 1 6 . 3 5 0 5 . 5 3 7 5 . O B 1 4 . e 2 9 4 . 5 5 5
4 . 3 9 a
. 6 0 0
. 6 0 0
. 6 0 0
. 6 1 0
. 6 9 5
. 7 9 0 - 8 8 5 . 9 5 0 . 9 8 0
. 7 0 0
. 7 0 0
. 7 0 0
. 7 0 0
. 7 5 5
. e 4 0
. 9 2 0
. 9 6 5
. 9 9 0
. e 00
.a 0 0
. e o 0
. e 2 0
.8'0 0
. e 9 0
. 9 5 0
. 9 8 0
2 . 1 6 3 2 . 1 4 7 2 . 0 0 9 1 . 7 2 6 1 . 7 0 1 1 . 7 2 7 1 . 7 6 9 1 . a 2 0 1 . E 6 3
2 . 1 9 4
1 . g 7 4
1 .663 1 . 6 9 9
1 - 6 6 3 1 .670 1 .686 1 . 6 9 4
2 . a l e 2 . 1 2 4 1 . 9 4 4 1 . ? l o 1 . d Z 6 1 .601 1 . 5 7 4 1 . 5 5 8
a . 1 3 5 1 3 - 8 8 0
1 2 . 5 9 0 1 3 . 5 1 0
1 0 . 9 6 2 9 , 6 0 4 9 .I41 8- i 9 5 9 8 . 6 1 0 8 - 1 3 2
0 . 7 0 . 1 0
. 6 0
. 5 0
. e 0 0 - 8 - 0.10
. 3 0
.so
. 4 0
. 5 0
.60
3 a . 9
s a . 8 4 4 - 2
7 4 . 3 6 6 . 5
7 6 . S 7 8 . 3 8 2 .?
12 . 8 6 4 i2 . 3 6 ? 1 1 . 4 5 4
9 . 9 5 4
7 - 9 3 9 7 . 5 4 6
a . 6 5 z
7 . l i e I
. g o o
. 9 0 0
. g o o
. g o o
.9 0 0
. 9 3 0
. 9 7 0
. 9 9 0 7
3 4 . 2 4 5 . 5 5 4 . 5 6 6 . 7 7 8 . ? a 1 . 7 8 a . 9 8 5 .O
1 2 .os1 1 1 , 4 5 9 1 0 . 5 5 9
9 - 1 2 2 7 . 9 4 0 7 . 0 5 6 6 . 4 8 5 5 .9RO
9 . 7 4 5
8 . 5 5 3 7 .38.sr 6 . 4 9 2
5 . 2 5 2 5 . 7 1 5
4 - 8 4 4
9 . 2 e a 0 . 5 7 3 3
. 5 7 1 9
. 5 7 0 1
. 5 5 7 9
. 5 6 5 j . -
. S A 7 2
. 5 2 8 6
. 4 9 4 1
2 . 2 3 6 2 ,115 1.920 I , 7 1 8 1 - 5 9 8 1 . 5 3 Q 1 . 4 A Z 1 . 4 4 2
. s o
.6 0
. 7 0
NACA RM E57JoS 57
*h,2-3 %,4-5 %,h % , 3 4 @h N 2 , h @t ' @3,h @h g),,,
4 4 . 1 - 1 5 - 7 1 9 1 . 0 0 0 . 7 4 8 1 . 0 0 0 - 7 8 2 1 . 0 0 0 - 7 . 3 3 1 . 7 4 8 . 5 6 4 . 0 - 8 0 - 7 9 3 1 . 0 0 0 - 7 8 4 1 , 0 0 0 - 8 0 0 . 9 5 7 - 9 . 6 4 1 . 6 6 2 . 9 79 .4
0 . 1 0 0 . 5 0 . 7 0 8 1 . 0 0 0 1 . 0 0 0 0 . 7 2 2 . 0 0 0 0 . 7 3 7 1 - 4 . 9 2 1 . 2 3 2 . 9
9 4 . 1 79 . O 5 7 . 5 - 1 3 . 6
- 8 0 - 8 0 0 - 5 8 0 - 8 0 0 . 7 2 3 - 8 0 0 - 5 7 1 - 4 6 . 3 1 3 7 .6 1 5 7 .3 1 4 9 . 2 - 7 0 . 8 0 0 - 6 8 6 - 8 0 0 - 8 0 3 - 8 0 0 - 6 3 0 - 3 7 .8 1 1 8 . 1 1 3 5 . 1 1 3 3 . 2 .60 , 8 0 0 . 7 9 5 . B O O . a 8 3 - 8 0 0 - 7 0 6 - 2 9 . 9 9 8 . 5 1 1 2 . 7 1 1 8 - 3 - 5 0 . 800 . a 9 2 - 8 0 0 . 930 - 8 0 0 . 7 8 1 - 2 3 . 3 8 2 . 6 9 7 . 7 1 0 9 .I - 4 0 - 8 0 0 - 9 7 0 - 8 0 0 .949 - 8 0 0 - 8 4 4 - 1 8 . 1 7 0 . 0 8 7 . 4 1 0 0 . 7 -30 . 7 7 1 1 . 0 0 0 . 800 . 970 - 8 0 0 . 8 9 6
4 7 . 7
. 2 0 - 7 4 0 1 . 0 0 0 . B O O .998 - 8 0 0 - 9 8 6 - 9 . 7 4 4 . 4 6 7 . 2 8 3 . 9 - 1 5 . 7 2 3 1 . 0 0 0 - 1 5 9 1 . 0 0 0 . 8 0 0 - 9 9 7 - 7 - 4 3 3 . 9 5 2 . 2 6 8 .7 - 1 0 0 . 6 0 0 . 7 1 0 1 . 0 0 0 1 . 0 0 0 0 . 7 2 7 1 . 0 0 0 0 . 7 4 7 .- 4 . 9 2 2 . 7 3 5 . 5
1 0 4 . 9 8 8 - 1 6 3 . 1 - 1 3 . P
- 8 0 - 8 0 0 . 5 4 4 - 8 0 0 - 6 4 9 - 8 0 0 . 5 5 5 - 4 6 . 0 1 4 3 . 8 1 6 4 . 5 1 5 8 . 3 - 7 0 .BOO - 6 4 7 - 8 0 0 - 7 1 9 - 8 0 0 - 6 0 7 - 3 7 - 4 1 2 4 .3 1 4 4 . 1 1 4 1 . 7 - 6 0 - 8 0 0 - 7 5 7 - 8 0 0 - 7 9 7 - 8 0 0 . 6 7 6 -29 .6 1 0 4 . 1 1 2 1 .7 1 2 8 . 3 - 5 0 . 8 0 0 - 8 5 9 - 8 0 0 - 8 5 8 . B O O - 7 5 0 - 2 3 . 1 8 7 . 4 1 0 5 . 7 1 1 8 . 9 - 4 0 - 8 0 0 - 9 4 5 . B O O - 8 9 1 . 8 0 0 . 8 1 5 - 1 8 . 0 7 4 . 5 9 5 . 6 1 1 1 . 4 - 5 0 - 7 8 6 1.000 - 8 0 0 . 9 1 8 - 8 0 0 . 8 7 1
5 0 . 8
.20 . 7 4 7 1 . 0 0 0 - 8 0 0 . 9 8 0 - 8 0 0 - 9 1 2 - 9 . 8 4 6 . 8 7 0 . 1 87.1.
. I 5 - 7 2 7 1.000 - 7 7 1 1 . 0 0 0 - 8 0 0 - 9 7 4 - 7 . 5 3 5 . 7 5 5 . 3 7 1 . 7 0 . 1 0 ' 0 - 7 . 0 . 7 1 2 1 . 0 0 0 1 . 0 0 0 0 . 7 3 2 1 . 0 0 0 0 . 7 5 7 - 5 . 0 2 4 . 0 3 7 . 8
1 1 2 . 8 9 4 . 2 6 7 . 3 - 1 4 . 1
- 8 0 - 8 0 0 - 5 0 5 - 8 0 0 . 5 9 1 - 8 0 0 . 5 4 1 - 4 6 - 5 1 4 9 . 6 1 7 0 . 0 1 6 2 . 6 - 7 0 .800 - 6 0 6 - 8 0 0 - 6 5 1 - 8 0 0 - 5 8 8 - 3 7 . 5 a 3 0 . 6 1 5 2 . 4 1 5 2 . 0 .60 - 8 0 0 . 7 1 6 . 8 0 0 . 7 2 5 . B O O - 6 5 0 - 2 9 . 8 1 0 9 . 8 1 3 0 . 2 1 3 7 . 4 .50 - 8 0 0 - 8 2 8 - 8 0 0 - 7 8 9 - 8 0 0 - 7 2 0 - 2 3 . 3 9 2 . 5 1 1 4 . 1 1 2 9 -1 - 4 0 - 8 0 0 . 9 1 6 . 800 . 8 3 3 . 8 0 0 - 7 8 6 - 1 8 . 2 9 9 . 6 1 0 4 . 4 1 2 2 . 5 -30 - 8 0 0 - 9 9 6 - 8 0 0 - 8 7 3 - 8 0 0 - 8 4 7
5 3 . 6
- 2 0 1 . 0 0 0 - 1 5 6 - 8 0 0 . 959 - 8 0 0 - 8 9 7 - 9 .9 4 9 . 1 7 2 ; 8 9 0 . 2 - 1 5 - 7 3 2 1 . 0 0 0 - 7 8 3 1 . O O O - 8 0 0 - 9 5 0 - ,7 .6 37 .5 58 -1 7 4 . 4 . 1 0 0 . 8 ' 0 0 . 7 1 4 1 . 0 0 0 1 . 0 0 0 0 . 7 3 7 1 . 0 0 0 0 . 7 6 8 - 5 . 1 2 5 . 2 3 9 . 8
1 1 7 . 0 9 7 . 6 6 9 . 9 - 1 4 . 4
- 8 8 4 1 - 8 0 0
- 8 0 0 . 7 8 1 - 8 0 0 - 7 5 7 -18 .7 8 5 . 3 1 1 3 . 9 1 5 3 . 5 '-30 - 9 7 4 - 8 0 0 - 8 0 0 .E45 - 8 0 0 - 8 2 4
- 4 0 1 5 8 . 6 1 2 2 . 5 9 7 . 9 - 2 5 . 7 - 6 9 3
.70 . 8 0 0 - 5 6 5 - 8 0 0 ,598 - 8 0 0 - 5 7 2 - 3 8 . 0 1 3 6 . 5 1 5 9 .2 1 5 8 . 8 - 6 0 - 6 7 4 - 8 0 0 - 8 0 0 . 6 6 5 - 8 0 0 . 6 2 8 ' - 3 0 . 2 1 1 5 . 4 1 3 8 .I 1 4 5 . 7 - 5 0 - 7 8 3 - 8 0 0 - 8 0 0 - 7 3 1 - 8 0 0
5 6 . 0
- 2 0 .165 1 . 0 0 0 - 8 0 0 - 9 3 5 - 8 0 0 - 8 8 2 -10.1 5 1 .2 7 5 . 4 9 3 . 2 - 1 5 "137 1 . 0 0 0 - 7 9 5 1 . 0 0 0 - 8 0 0 - 9 2 6 - 7 . 8 3 9 . 1 6 0 . 6 7 6 . 9 - 1 0 0 . 9 0 0 . 7 1 6 1 . 0 0 0 1 . 0 0 0 0 . 7 T 9 ' 1 . 0 0 0 0 . 7 4 3 - 5 . 3 2 6 . 4 4 1 . 7
1 4 3 . 3 1 2 3 . 0 9 1 . 2 - 1 9 . 4 -30 - 8 0 0 - 9 5 1 - 8 0 0 ' -821. - 8 0 0 - 8 0 1 - 1 4 .8 7 2 . 3 1 0 1 . O 1 2 1 - 5 - 4 0 - 8 0 0 - 8 4 8 . 8 0 0 - 7 4 0 - 8 0 0 - 7 2 8
1 5 2 . 5 1 3 5 . 1 1 0 5 . 6 - 2 4 . 4 - 6 6 6 . a 0 0 - 7 0 - 8 0 0 - 5 8 6 - 8 0 0 - 5 5 3 . 8 Q O - 5 5 9 -38 . 9 1 4 2 . 3 1 6 5 . O 1 6 6 . 3 - 6 0 . 8 0 0 - 6 3 2 - 8 0 0 . 614 - 8 0 0 . - 6 0 9 -3O.a 121 .8 1 4 7 - 5 1 5 7 . 7 - 5 0 - 8 0 0 . 7 4 2 - 8 0 0 - 6 7 6
-
58 0 NACA RM E57J09
TABLE IV. - SUMMARY OF "€BINE DESIGN CONDITIONS
1-Stage turbines IL-Stage turbines 2
Table Table
3,m 3,m
0.5 II(a)2 e1.0 .8 I(a> 2 C1.0 .8 I I ( a ) l C1.0 0.6 0.5 I (a) l 0.01 (1.0 0.6
-" 11(a)3 1.0 -" I(a) 3 1.0
0.6 II(b)2 U . 0 .8 C1.0 .8 II(b)l C1.0 0.5 0.6 I (b ) l 0.02 C1.0 0.6
---
I I ( c )3 1.0 --- I ( 4 3 1.0 --- II(c)2 <1.0 1.0 c1.0 1.0
II(b)3 1.0 "- 1.0
0.7 I I ( c ) l c1.0 0.8 ---- 0.8
(2) 5,m 0.5
0.7
2-Stage turbinee I
3.. 6 5.8
Sl.0 Sl.0
o .01 III( a) 1 IIIr(a) 2
0 -02 I I I ( b ) l [ III(b) 2
c v -4 vi
.
59
Station 1 2 3
(a) 1-Stage turbines.
I 2 3 4
(b) l r S t a g e 1 turbines.
1 2 3 4
i P
5
( c ) 2-Stage turbines.
Figure 1. - Annulus geometry and axial stat ions of turbines.
60 RACA RM $57"
' f 3
(a) 1-stage turbines. ,
R (b) +Stage 1 turbhea.
( c ) 2-Stage turbines.
Figure 2 . - Typical veloclty'dlagrama for turbines.
c
..... .
’ : I
.. . . ~. . . , . . . .. . . . . . - . . . . ..
4575 I
Blade-apsd parameter, q-& ( a ) Turbine-sat radius rat io ($)3 - 0.5 . (b) l’urbim-exlt ~ a d i k ratlo (t)3 - 0.7.
Flgure 3. - Effeot o f a m l u e taper on work output of I-stage turbines. - 0 .7 .
. .
62
Figure 4. - Rotor-inlet Mach numbers for high-output 1-stage turbines with optimum taper limited by
4515 I
(a) mt radius ratio, (21 u 0.5.
(b) Exit radius ratio, ($)3 = 0.7.
Figure 5. - Variation of turbine vork vith lalet radius ra t io In highatput. 1-atage turbines.
. .
64 BACA BM 3257589
.
(a) Exit radius ratio (z)6 - 0.5.
(a ) Inlet radius ratio corresponding to maximum work output.
1.30 1.32 1.34 1.36 1.38 1.40 Ratio of specific heats, yr
(b) Maximum turbine work output.
Figure 7. - Effect of variation i n r a t i o of specific heats on inlet radius ratio and m a x i m work of 1-stage turbines. (2)3,m = 0.7; (2) = 1.0; (2) = 0.6. vg h =t 3
66 - NACA RM E57J09
.75 .80 .€E .90 Turbine polylxopic efficiency, $,T
(b) M a x i m u m turbine work output.
Figure 8. - Effect of. var ia t ion in tur- bine polytropic efficiency on. inlet radius ratio and m a x i m u m work of 1-
I V"\ stage turbines. (-f)3,m = 0.7;
(3) = 1.0; (2) = 0.6. h rt 3
. . . . . . . . . . . . . . .. . . ..
6 CW-9 baok 4575- 8
0 LaQt three blade row 1 M b d by velocity ratlo 0 Pirst rotor limited by Madl mrmber, second 6tdOT
and second lotar limited by velocity ratio 0 First rotor. and second stator l lmited by Mach
mer, semnd rotor United by velocity ratio V Last three blade row llmlted by Mach rider
101 I I I I I I I I I I I I .1 .2 .9 .4 -5 .. .6 .7
Eilade-sgeed parameter, - U t %,cr,l
3
Figure 9. - Effect o f second-stage stator-veloolty limitation on dealepl work of 2-stage
68 - NllCA RM E57
0 .2 .4 .6 .8 1.0
Blade-speed parameter, Ut aa,crjl
Figure 10. - Comparison of work available in 1- 1-, 1 and 2-stwe
turbines for selected aerodynamic limits. = 0.6;
(”) = 0.5; (E) limit = (1) limit = 0.8; rt 0 a in,R,h EL in,S,h
limit -= 1.0.
NACA RM E57J09
. 69
70 RACA RM E57J09
0 .02 .04 -06 .- .08 -10 WaP Dimensionless turbine weight-flow - speed parameter,
Chart I . - 1-Stage turbines.
.
Dimensionlea$- turbine-weight-flow - speed parameter, wmz
72
1.0
1. e
1.4
1.2
1.0
.a
.6
.4
.2
- NACA RM S57JOS
.
y" 01
0 .02 .04 .06 -08 .10 .I2 Mmenslonless turbine veight-flow - speed parameter, m 2
%la:,c,,l
I..($) = 0.6; @h< 1.0. 2, h
(b) (+) = 0.6. 3 , m
C h a r t I. - Continued. 1-Btage turbines.
NACA RM EVJO9 0 73
0 .02 -04 -06 .08 .10
Dimensionlees turbfne weight-flov - speed parameter, m 2 ma, 14, cr, 1
2. (:)z,h d 0.81 (gh 5 1.0.
(a) Concluded. (2)3,LL = 0.6.
Chart I. - Continued. 1-Stage turbines. -
74 NACA RM E57J09
1.
1.
1.
1.
1.
( c , (3) - 0 .7 . a 3,m
Chart I. f Continued. I-8tage turbines. -
.
0
NACA RM ES/JO9 0 75
Dimensionless turbine weight-flow - speed parameter, 4
(c) Concluded. (>)3,m = 0.7.
Chart I. - Concluded. 1-Stage turbfnee.
76
P I
c
0 .02 -04 .06 .08 Dimensionless turbine weight-flow - apeed parameter,
d . .
3 '%,1%,crIl
(a) (2) - 0.5. 3 , m
Chart 11. - l$"e turbines.
.
Lo t- dr LD
c
1.
78
1.
I.
1.
1.
1.
(b) (2) = 0 . 6 .
Ch& 11. - Continued. &Stage turbinea. 3 , m
NACA RM E!5'7Jos
.
(b) Concluded. - 0.6.
chert II. - Continuad. k p . k g e turbines. 1
7 9
80
Chert II. - Continued. $-Stage turbines.
82
2,
2.
2d k
1.
1.
NACA RM EvJO9
0 .01 .02 .03 -04 Dimensionless turbine weight-flow - speed parameter,
w d
Chart 111. - 2-Stage turbines.
.
NACA RM E57J09
2.
2.
2.
1.
1.
0 .01 .02 .a Dimensionless turbine weight-flow - speed parameter, WtJ?
%,l4,Cr,l
Chmt III. - Continued. 2-Stage turbines.
83
84 NACA RM E57J09
n
2.
2 .
1.
1.
0 .01 .02 .03 .04 .os WLU 2 3 Dimensionless turbine weight-flow - speed parameter,
flpa,l%,cr,l
1.
(b) (2) . = 0.6. 5 , m
Chart 111. - Continued. 2-Stage turbines.
a
2.8
2.4
2.0
1.6
1.2
.8
.4
0 .01 .02 .03 Dimensionleas turbine weight-flow -
apeed parameter, W G
*Pa,laZ,cr,L
2. (E) , (I) , (r) < 0.8; * 2,h a 3,h a 4,h-
Chart III. - Continued. 2-Stage turbines.
85
86 '
..
m m
4 0
NACA R?4 E q J O 9
0 . 01 .02 .03 -.04 Mmensio~ees turbine velght-flow - speed pemmter,
' w2 %,laZ,cr,L
Chart 111. - Concluded. 2-8tage turbinee.
.
.
L
J