static investigation of a cruciform nozzle with multiaxis thrust-vectoring and reverse thrust

7/27/2019 Static Investigation of a Cruciform Nozzle With Multiaxis Thrust-Vectoring and Reverse Thrust

1/82


2/82

NASATechnicalPaper3188

1992

Aeronautics andof Management

Sta t i c Pe r fo rmance of aCruciform Nozzle WithMult iaxis Thrust Vectoringa n d Reverse -ThrustCapabil i t ies

David J. Winga n d Scott C. AsburyLangley Research CenterHampton, Virginia


3/82

SummaryA multiaxis thrust-vectoring nozzle designed to

have equal flow-turning capability in pitch and yawwas conceived and experimentally tested for inter-nal static performance at Langley Research Center.The cruciform-shaped, convergent-divergent, nozzleturned the flow for thrust vectoring by deflectingthe divergent surfaces of the nozzle, called flaps.Methods for eliminating physical interference be-tween pitch and yaw flaps at the larger multiaxisdeflection angles were studied. These methods in-cluded restricting the pitch flaps from the path of theyaw flaps and shifting the flow path at the throatoff the nozzle centerline to permit larger pitch-flapdeflections without interfering with the operation ofthe yaw flaps. Two flap widths were tested at bothdry and afterburning power settings. Vertical- andreverse-thrust configurations at dry power were alsotested.

Despite the complex internal geometry, this cruci-form nozzle had only slightly lower unvectored thrustefficiency than existing axisymmetric and nonax-isymmetric nozzle designs. Thrust losses in single-axis thrust vectoring were primarily the result ofcomplex flow interactions between shearing flowswithin the nozzle. Splitting the flow, a consequenceof the cruciform cross section, caused these inter-actions. Thrust losses in multiaxis thrust vector-ing were primarily the result of turning supersonicflow. More equal pitch and yaw thrust-vector angleswere achieved by the nozzle with narrow divergentflaps than by the nozzle with wide divergent flaps.However, the narrow-flap nozzle had thrust losses1 to 2 percent higher than those of the wide-flapnozzle. The shifted-throat nozzle design had largerthrust-vector angles at the nozzle pressure ratio ofpeak resultant thrust efficiency than the restricted-flap nozzle design but had 1.5- to 2.0-percent-lowerpeak thrust performance. The vertical- and reverse-thrust configurations had performance similar to thatof existing nozzles of similar design.Introduction

Military aviation history has shown that fighteraircraft with better maneuver performance have anadvantage over their opponents in close-in air-to-airengagements. Maximizing this maneuverability in-cludes maintaining attitude control into and beyondthe angle-of-attack range of aerodynamic control sur-face effectiveness. The elevators and rudders of con-ventionally configured aircraft (control surfaces aftof the wing) lose effectiveness at high angles of at -tack, generally before the wing stalls; this effect oc-curs because the elevators and rudders are located in

the separated wake of the wing. Although the wingmay still be producing sufficient lift, asymmetricalflow situations and ineffective aerodynamic controlsurfaces cause the aircraft attitude to diverge.

A supplemental source of a tti tude control can beachieved through deflection of the engine thrust toproduce the necessary forces and moments to main-tain or augment aircraft control. The primary ad-vantage of this technique, known as thrust vectoring,is that it is independent of angle of att ack, within thelimits of inlet capability. When the thrust is deflectedin the vertical or horizontal planes, the normal- andside-force components produce the necessary pitchand yaw moments that are usually supplied by thetail surfaces.

The concept of deflecting the engine thrust to pro-duce useful forces may be extended to include deflect-ing the thrust vertically downward to supplement orreplace th e wing lift for such applications as short andvertical takeoffs and landings. This extension of theconcept assumes proper balance can be maintainedthrough reaction control jets. In addition, deflectingthe thrust forward produces reverse thrust that canbe used in flight or upon landing. Other applicationsand benefits of thrust-vectoring technology can befound in references 1 to 12. The applications citedin these references document the need to develop ex-tremely versatile nozzles.

Various nozzle concepts for thrust vectoring havebeen investigated over the past 12 years at Lang-ley Research Center (refs. 13 to 24). In particular,both axisymmetric and two-dimensional (2-D) noz-zles have been studied. These studies emphasized2-D nozzles because their geometry accommodates alarger variety of devices in the development of vec-tored thrust. These devices include internal diver-gent flaps, external vanes, and plugs. Early researchwas limited to single-plane vectoring in the pitch di-rection (refs. 16 to 19). More recent experimentsadded yaw capability to pitch-vectoring nozzles toobta in multiaxis vectoring (refs. 20 to 24). Resultsshow that , in some cases, performance in one of thevectoring directions is compromised by the devicesneeded to provide vectoring in the other direction.For instance, physical interference between pitch andyaw flaps can limit the range of available multiaxisvector angles. Also, combining pitch and yaw vec-toring with dissimilar vectoring methods or in anasymmetrical fashion may favor one direction overthe other.

A multiaxis thrust-vectoring nozzle concept de-signed to reduce this compromise has been in-vestigated experimentally to evaluate its internal


4/82

performance and to assess its potential. The uniquegeometry associated with this nozzle allows for a newapproach to achieve large-angle multiaxis thrust vec-toring without physical interference of the divergentflaps. The nozzle is a nonaxisymmetric, convergent-divergent design with symmetry about the verticaland horizontal axes. Thrust is vectored through thedeflection of the nozzle divergent flaps (either topand bottom or side flaps) about a hinge line near thethroat plane, the location of minimum cross-sectionalflow area in the nozzle. Corner pieces between adja-cent pitch and yaw vector flaps contain exhaust flowat the nozzle corners. The resulting geometry is anozzle with a cruciform cross section at the nozzleexit. To turn the flow in the pitch direction, thetop and bottom flaps are rotated in the same direc-tion through the same angle; a similar movement ofthe side flaps provides yaw vectoring. The designincludes two additional capabilities to meet possibleperformance needs of futu re fighter aircraft. First ,the nozzle can operate in a vertical-thrust mode forshort and vertical takeoffs and landings, and second,th e nozzle can operate in a thrust-reversing capacity.

This cruciform nozzle, so named for its distinctivecross-sectional shape at the nozzle exit, was testedfor internal performance in the sta tic test facilities ofthe Langley l6-Foot Transonic Tunnel. The nozzlewas tested unvectored, vectored in one and two direc-tions, and configured in vertical- and reverse-thrustmodes at nozzle pressure ratios up to 8. Divergentflap width, nozzle expansion ratio , and nozzle powersetting were varied as test parameters. In addition,several methods of achieving increased multiaxis vec-toring capability at large divergent flap angles in drypower operation were examined.Symbols

All forces and moments (with the exception of re-sultant thrust) are referred to the model centerline(body axis). The model (balance) moment referencecenter was located at model stat ion (Sta .) 29.39. Ref-erence 25 contains a discussion of the data reductionprocedure and definitions of the force and momentterms and the propulsion relationships.A linear nozzle dimension measured fromnozzle centerline to convergent flap

surface at nozzle connection station(Sta . 42.24) (fig. 6(a) and table 2), in.cross-sectional area at nozzle exitplane, in2cross-sectional area at nozzle throa tplane, in2

A,

A t

linear nozzle dimension measured fromnozzle connection stat ion (Sta . 42.24)to corner convergent point (fig. 6(a)and table 2), in.flap width (fig. 6(a) and table 2), in.linear nozzle dimension on vertical-thrust and thrust-reverser configura-tions measured from flap closure pointto aft surface of model flap (fig. 6(c)and table 2), in.longitudinal length of cutout ontransition section used for vertical-thrust configurations (fig. 6(e) andtable 2 ), in.measured axial thrust, lbfideal isentropic thrust,

normal force measured by balance, lbfresultant thrust,d m , bfside force measured by balance, lbflongitudinal length of cutout ontransition section used for thrust-reverser configurations (fig. 6(e) andtable 2), in.acceleration of gravity, 32.174 ft/sec2reference length, 1.0 in.pitching moment measured by balance,in-lbfyawing moment measured by balance,in-lbfnozzle pressure ratio , p t , j / p adesign nozzle pressure ratio (NPR forfully expanded flow at nozzle exit)atmospheric pressure, psiaverage jet total pressure, psigas constant (for y = 1.3997),1716 ft2/sec2-Rjet tota l temperature, ORideal isentropic weight-flow rate (forNPR > 1.89),

2


5/82

WPX

Y

Yb

Yt

z

zb

Zl

zr

zt

Y

measured weight-flow rate, lbf/seclongitudinal thrust-reverser dimensionmeasured from downstream portcorner without port extension to aftsurface of corner piece (fig. 6(d) andtable 2), in.linear thrust-reverser dimensionmeasured from nozzle centerline tocenter of internal radius (fig. 6(d) andtable 2), in.linear nozzle dimension measuredfrom nozzle centerline to center ofbottom-flap throat radius (fig. 6(a)and table 2 ) , in.linear nozzle dimension measured fromnozzle centerline to center of left-flapthroat radius (fig. 6(a) and table 2),in.linear nozzle dimension measured fromnozzle centerline to center of right-flapthroat radius (fig. 6(a) and table 2),in.linear nozzle dimension measured fromnozzle centerline to center of top-flapthroat radius (fig. 6(a) and table 2),in.linear vertical-thrust configurationdimension measured from nozzlecenterline to downstream port corner(fig. 6(c) and table 2 ) , in.linear nozzle dimension from nozzlecenterline to trai ling edge of bottomflap (fig. 6(a) and table 2), in.linear nozzle dimension from nozzlecenterline to trai ling edge of left flap(fig. 6(a) and table 2), in.linear nozzle dimension from nozzlecenterline to tra iling edge of r ight flap(fig. 6(a) and tab le 2), in.linear nozzle dimension from nozzlecenterline to trai ling edge of top flap(fig. 6(a) and table 2), in.ratio of specific heats, 1.3997 for airpitch thrust-vector angle, measuredfrom centerline, positive deflectiondownward, tan-' z,egn

6 P geometric vector angle in pitch plane,measured from centerline, positivedeflection downward, deggeometric vector angle in yaw plane,measured from centerline, positivedeflection to left looking upstream,

6 yaw thrust-vector angle, measured

6 V , Y

degfrom centerline, positive deflection toleft looking upstream, tan-' E , degS

Abbreviations:A/B afterburning powerC-D convergent-divergentSERN single-expansion-ramp nozzleSta. model station , in.2-D two-dimensionalTest Facility

The test was conducted in two phases in th e stat ictest facilities of the Langley l6-Foot Transonic Tun-nel. The dry power nozzles were tested in the modelpreparation area, a facility normally used for modelsetup and calibration before entrance into the windtunnel. However, because the model preparationarea has a high-pressure air supply and a data ac-quisition system, it can be used to test the internalperformance of nozzles at wind-off conditions. Theair system uses the same supply of clean, dry air usedin the wind tunnel propulsion simulations; the systemincludes the same valving, filters, and heat exchangerto provide an air supply at a constant total temper-ature of about 530"R. The model was mounted ona sting-strut support system in a soundproof roomwith an air exhaust duct opposite the jet. The con-trol room is adjacent to the test area, and a windowbetween the rooms allows for model observation dur-ing testing.

The afterburning power nozzles were tested in thestatic test stand of the l6-Foot Transonic Tunnel.The static test stand is separate from the wind tunneland thus has its own air supply system, valving,filters, and heat exchanger. The model was attachedto a dolly-mounted strut support system, and the airexhausted into a vented room. Reference 26 providesdetails of both facilities.Propulsion Simulation System

Figure l (a) shows the propulsion simulation sys-tem with a typical cruciform nozzle configuration

3


6/82

installed and figure l ( b ) shows the internal de-tails of the test hardware. High-pressure, constant-temperature air is supplied to the propulsion simula,tion system so th at the forces and moments producedby the nozzle can be measured accurately. As shownin figure l( b) , air is supplied through six lines in th esupport strut to an annular high-pressure plenum.The air flows radially out of the high-pressure plenumthrough eight equally spaced sonic nozzles into a low-pressure plenum. This flow transfer design (perpen-dicular to th e nozzle axis) minimizes th e force on thebalance caused by axial momentum transfer of theflow across the force balance. Flexible bellows actas seals between the metric (supported by the forcebalance) and nonmetric portions of the model andminimize forces caused by pressurization. The airthen passes through a choke plate for flow straight-ening, through an instrumentation section, through acircular-to-octagonal transition section, and into thenozzle; the air then exhausts to atmospheric pres-sure. Th e instrumentation section includes an iron-constantan thermocouple for to tal temperature mea-surements and a rake of nine pitot probes for totalpressure measurements.Nozzle Design

The cruciform nozzle is a fully variable, non-axisymmetric, convergent-divergent nozzle designedto turn the flow in both pitch and yaw directionsthrough the deflection of divergent flaps into or awayfrom the flow. Figure 2 is a close-up of a typicalmodel, and figures 3 and 4 show external and inter-nal views of the various configurations tested. In-terchangeable blocks are used to simulate deflectabledivergent flaps in the model. Th e goal of th e design isto accomplish multiaxis thrust vectoring while min-imizing the physical interference between the pitchand yaw flaps. Each of the four divergent flaps movesin a channel and has a pivot point near the throatplane. (See fig. 3(c).) Th e channel sidewalls ex-tend to the nozzle exit plane t o provide flow contain-ment. Th e nozzle is designed to operate in both dryand afterburning (A/B) power modes. Operation inA/B mode requires th at the throat be widened to ac-commodate the lower density flow that results fromthe higher exhaust gas temperatures associated withafterburning.

In the A/B power mode, the pitch (top and bot-tom) and yaw (side) flaps do not physically interferewith each other at normal vectoring angles. In thedry power mode, the flaps do not interfere at low mul-tiaxis vectoring angles; the flaps do, however, inter-fere with each other at higher angles (Le., angles usu-ally greater than lo", but actual size depends on the

specific geometry). The pitch and yaw flaps are freefrom physical interference until an inward-deflectedflap moves into the path of an adjacent flap. Twoconcepts for eliminating this physical interference athigher multiaxis vectoring angles have been investi-gated and are subsequently described.

The nozzle is also designed to have the multi-functional capabilities of providing vertical thrust forshort and vertical takeoffs and landings and reversethrust for aircraft deceleration. In the vertical-thrustmode, th e divergent flaps move together to close theexit. The convergent bottom flap pivots open abouta hinge point at the throat and thus creates a ven-tra l port . (See fig. 5(a).) Th e designed turning anglein the vertical-thrust mode is 90'. In the thrust-reverser mode, the divergent flaps close in the sameway. However, the reverser is deployed by the leftand right convergent flaps th at pivot open about thehinge point at the throa t. (See fig. 5(b).) The de-signed turning angle in reverse mode is 120". Thetotal port areas of both the vertical-thrust and thethrust-reverser configuration are scheduled to main-tain a sufficient air flow through the engine.

A model of the nozzle was built with interchange-able blocks used to represent flaps for each vectoringconfiguration. Th e nominal throat area was 4 in2in dry power mode and 8 in2 in A/B power mode.Port areas of 4 in2 were used in both vertical-thrustand thrust-reverser configurations. Model dimen-sions and configuration specifications are presentedin tables 1 and 2 and in figure 6. The model wastested both with narrow flaps and with wide flapsto investigate the effect of flap width on nozzle per-formance and thrust-vectoring capability. Th e cross-sectional flow areas for the two configurations withdifferent flap width were kept as nearly equal as pos-sible. All yaw flaps were arbitrarily chosen to haveunrestricted freedom of movement; any restrictionsof movement necessary to eliminate flap interferencewere applied to the pitch flaps. Th e nozzle was oth-erwise symmetrical, so th e pitch- and yaw-vectoringresults were interchangeable if desired. The modelwas built so that pitch vectoring deflected the flowdown t o give a positive force (up) and yaw vectoringdeflected the flow to the right to give a negative force(left) looking upstream. Th e nominal geometric flapangle in thrust vectoring was 20" for both pitch andyaw. The L-shaped corner pieces (fig. 2) that formedthe flap channels were designed for static (no externalflow) tests only; actual flight nozzle hardware wouldhave smoothly faired external surfaces and little orno base area.

As mentioned previously, two concepts for ex-tending the multiaxis vectoring angles beyond the

4


7/82

A configuration called restricted flapgs. 3(d) and 4 (d)) allowed the trailing edge of thepitch flap to move to the edge of the yaw flap

restricted th e trailing edge from movingal-wed. The bottom flap was then ro tated through the20" angle. Another configuration called shifted

(figs. 3(d) and 4(d )) moved t he top and bot-convergent flaps so tha t the throat plane shiftedThis movement allowed the top pitch Aap to

ate closer t o 20" before being restr icted by the yawShifting the flow passage to allow greater

gles represents a new approach t o handlef flap interference. The restricted-flapshifted-throat configurations were each tested at

a ratios and a t two flap widths.The vertical-thrust and thrust-reverser configura-

ere tested with and without port length exten-s to assess their effect on nozzle performance. At extension of 1.500 in. was tested on the vertical-

rus t configurations, and port extensions of 0.750ons. (See figs. 5(a), 5(b), 6(c), and 6(d).)

The weight-flow rate of a ir t o the nozzle waslibrated venturi system upstream of the

pressure plenum. The air supply in the modelarea was connected to the same multiple

as that used for the l6-Foot Tran-ic Tunnel. The air supply in the static test s tand

a separa te pair of critical venturis.rs. Forces and moments werea six-component strain-gauge balance

the nozzle centerline.

Each da ta point is the average steady-sta te valuef 10 frames per second. All dat a were taken inorder of the average jet tota l pressure p t j .

at a obtained from this test are given in table 3.f th e da ta presented are plotted as a function

f nozzle pressure ratio (NPR ), the ratio of jet tota lto atmospheric pressure. T he NPR range of

o 8 corresponds typically to th e operationaJ NPR0.2 to 1 .3 .The strain-gauge balance measurements, from

h the actual nozzle thrus t components are subse-

interactions. Although the bellows arrangement isdesigned to eliminate pressure and momentum inter-actions with the balance, small bellows tares on thesix balance components still exist. These tares resultfrom a small pressure difference between the endsof the bellows, which occurs when internal velocitiesare high, and from small differences in the springconstants of the forward and aft bellows, which oc-cur when the bellows are pressurized. These bellowstares are determined from tests of s tandard axisym-metric calibration nozzles with known performanceover a range of expected internal pressures and lon-gitudinal and lateral forces and moments. The bal-ance data are then corrected in a manner similar totha t discussed in reference 16 to obtain th rus t alongthe body axis F a , normal force Fn, and side forceF,. The resultant thrust ratio F r I F i , axial thrustratio F a / F i , normal-force ratio Fn IF i , and resultantpitch and yaw thrust-vector angles 6 and 6 are thendetermined from these corrected balance da ta. Ref-erences 25 and 26 contain a more detailed discussionof thi s da ta reduction process.

The discharge coefficient w p / w i is the ratio ofmeasured weight-flow rate from upstream venturimeasurements to ideal weight-flow rate, which is cal-culated from total pressure and temperature mea-surements and the geometric nozzle throat area. Thisdischarge coefficient is a measure of the nozzle effi-ciency in passing weight flow. The ideal weight-flowcalculation is sensitive to the throat area of the noz-zle used in the calculation; thus, a small discrepancybetween measured and actual throat area can signif-icantly change the discharge coefficient level. Sincethe throat areas of the cruciform nozzle are difficultto measure, nominal values are used in the calcula-tions and are listed in table 1.

The basic performance parameters presented inthis report are resultant thrust ratio F r / F i , axialthrust ratio F,/Fi, discharge coefficient w,/wi, andresultant pitch and yaw thrust-vector angles 6 and6,. The normal-force ratio Fn /F i is used t o comparesingle and multiaxis thrust-vectoring capability. Al-though pitching-moment and yawing-moment ratiosM,/F iL and M 2 / F i L were measured and recordedin table 3 , they are not discussed because this reportemphasizes forces. Rolling-moment data are not in-cluded because they are not relevant to this nozzledesign.Discussion of Results

Basic DataThe basic da ta for each configuration of this

investigation are presented in figures 7 to 10 for5


8/82

the dry power configurations and in figure 11 forthe afterburning power configurations with nominaldivergent flap deflections of 20". In general, manyof the basic data show trends that are consistentwith previous studies (refs. 13 to 15). One trendis the occurrence of peak values of F r / F i (for theunvectored nozzle) at slightly higher values of NPRthan that of the NPRd listed in table 1. The NPRdis the design NPR and is calculated from the nozzlearea ratio ( A e / A t , atio of nozzle exit plane area tonozzle throat plane area) with the assumption thatthe nozzle expands isentropically (ref. 27). Thrus tlosses at nozzle pressure ratios below and aboveNPRd are associated with nozzle overexpansion andunderexpansion.

The deflection of divergent flaps for thrust vector-ing generally results in a decrease in resultant thrustratio. In some cases, particularly at larger area ra-tios ( A e / A t = 1.5 and 1.4), two local maximumsoccur in Fr/Fi with the deflection of the divergentflaps; one occurs at high NPR and one occurs at lowNPR. (See figs. 8 and 10.) The same behavior ispresent in the axial thrust ratio. In addition, someperformance curves ( F a / F i and Fr/Fi) have multi-ple distinct local peaks with the deflection of flaps.Two possible explanations exist for this behavior.First, at low NPR's, internal exhaust flow separa-tion probably occurs in the divergent channel. Thelarge-area-ratio configurations are the most suscep-tible to separation. As shown by the data in refer-ence 28, internal flow separation can cause disconti-nuities in the thrust ratio curves. Second, when thedivergent flaps are deflected for thrust vectoring, theflaps have unequal lengths referenced t o the flow cen-terline. Therefore, near the nozzle exi t, part of theexhaust flow is bounded by a solid surface and part isunbounded. In th is case, the nozzle geometry is simi-lar to tha t of a single-expansion-ramp nozzle (SERN)designed to allow partially unbounded expansion. Asshown in reference 23, these nozzles either have dis-continuities in their thrust ratio performance curvesor have two distinct performance peaks.

The discharge coefficient is relatively constantwith NPR's above the choked flow condition(NPR > 1.89). The deflection of divergent flapsfor thrust vectoring generally results in a decreasein discharge coefficient. This decrease is most likelya result of a decrease in effective nozzle throat area.The throats of two-dimensional convergent-divergent(2-D C-D) nozzles with divergent flap thrust vector-ing have been shown to pivot and translate onto thedivergent flaps and decrease in area (ref. 19). Thesame phenomenon is believed to occur here. In some

cases of multiaxis thrust vectoring, the decrease indischarge coefficient is nearly 11percent.

In general, the resultant pitch and yaw thrust-vector angles show a dependency on NPR. The trendin pure pitch vectoring is an increase in pitch thrust-vector angle with increasing values of NPR in thelow-NPR range, probably as the low-energy sepa-rated exhaust flow begins to reattach on the di-vergent flap. The resultant pitch thrust-vector an-gle generally reaches a maximum value and thendecreases as NPR increases. The resultant thrust-vector angles in multiaxis thrust vectoring generallyshow effective thrust vectoring (lit tle adverse flowseparation and therefore large angles) at low NPR's.

The thrust-vector angles in single-axis and multi-axis thrust vectoring are less than the nominal flapdeflection angle of 20". This apparent deficiency inthrust vectoring is caused by the divergent channelgeometry of the cruciform nozzle. Sketches of crosssections at the exit planes of the narrow- and wide-flap configurations are shown in figure 12. The de-flection of the pitch flaps divides the exhaust flowinto a center region that is deflected and side re-gions tha t are not. The resultant thrus t vector equalsthe sum of these components and thus has an an-gle smaller than the flap deflection angle becauseof t he undeflected exhaust regions. A more realis-tic thrust-vector angle for comparison than 20" isan area-weighted flap deflection angle. The percent-ages of the area a t the exit plane enclosed betweenopposing divergent flaps are 65 and 75 percent forthe narrow- and wide-flap configurations. Therefore,13" and 15" are more appropriate angles by whichto judge thrust-vectoring capability for the narrow-and wide-flap configurations. (These angles are 65and 75 percent of 20".) As shown in the basic data(figs. 7 to lo) , thrust-vector angles of these magni-tudes are reached and occasionally exceeded, whichdemonstrates that the flaps are turn ing the flow effec-tively. A similar argument concerning exhaust flowsplitting and regional contribution applies in multi-axis thrust vectoring as well.

In the afterburning configuration, the percent-ages of enclosed area a t the exit planes are 57 and63 percent for the narrow- and wide-flap configura-tions. Therefore, the equivalent thrust-vector anglesfor comparison are 11.4" and 12.6'. As shown infigure 11, these angles are achieved only in multi-axis thrust vectoring, with the exception that theangle for the wide-flap configuration at Ae /A t = 1.2also surpasses 12.6" in single-axis thrust vectoring.An obvious drawback to the cruciform design is thatlarge flap deflections are necessary to produce thedesired thrust-vector angle.

6


9/82

Summary DataSince applications of the cruciform nozzle would

normally be with it operating at peak thrust effi-ciency, the data are summarized and the configura-tions are compared at peak resultant thrust ratio. Infigure 13, the data are arranged by power setting,flap width, and area ratio. The bars in the bar chartare composed of data from the unvectored, pitch-vectoring, and multiaxis-vectoring configurations ofthe basic pitch, restricted-flap, and shifted-throatconcepts.

Peak resultant thrust ratios of 2-D C-D nozzlestypically range from 0.985 to 0.995 (refs. 19 and 24).The peak resultant thrust ratios measured for the un-vectored cruciform nozzle range from 0.981 to 0.990;this performance is up t o 1.4 percent lower than thatof typical 2-D C-D nozzles. The slightly lower per-formance of the cruciform nozzle may be a result ofadditional surface friction losses because of a largerinternal surface area. A decrease in peak resultantthrust ratio occurs with the addition of pitch thrustvectoring and again with the addition of yaw thrustvectoring. The decreases in peak resul tant thrustratio for the pitch-vectoring cruciform nozzles arelarger than t he decreases for pitch-vectoring 2-D C-Dnozzles th at deflect internal divergent flaps for thrustvectoring. These decreases are probably a result ofinternal flow interactions and shear losses in the com-plex flow field of the cruciform nozzle. As previ-ously discussed, deflecting the divergent flaps createsa region of deflected flow and regions of undeflectedflow; shear losses between these flows contribute tothe overall decrease in thrust efficiency of the noz-zle. Adding yaw vectoring to pitch vectoring resultsin an additional decrease in peak resultant thrust ra-tio; this decrease is generally greater than that ofpure pitch vectoring. These losses are partially at-tributable to adverse interactions in the complex in-ternal flow field of the cruciform nozzle.

Another probable contributor to the large lossesin multiaxis thrust vectoring is localized supersonicflow turning, an inefficient process because of th eoblique shocks that are formed in the divergentchannel. Studies of internal pitch thrust-vectoring2-D C-D nozzles have shown that flow turning is al-most entirely subsonic because the throat is inclinedtoward the direction of flow turning. The same phe-nomenon probably occurs in the single-axis thrust-vectoring configuration of the cruciform nozzle; th atis, the throat in pitch vectoring is inclined so thatmost of the exhaust flow passing through the throatis already turned in the pitch plane and can expandwithout further changes in direction. In multiaxisthrust vectoring, the throat of t he cruciform nozzle

is inclined in both the pitch and the yaw plane, soexhaust flow passing through the throat moves in adirection roughly 45" from both the vertical and thehorizontal plane or along the bisector of the pitchand yaw channels. However, because nearly all flowexits the nozzle through the pitch and yaw channels,the flow must be redirected after passing through thethroat to follow the walls of the channels. In otherwords, the channel sidewalls are turning supersonicflow, and this action is shown in the thrust perfor-mance as a significant decrease in F,/Fi. Since thethroat of the pitch-vectoring nozzle turns most of theexhaust flow in the correct direction for expansion,supersonic readjustments are seldom necessary, andmost of the losses are from shear.

A comparison of the data in figure 13 shows tha tthe restricted-flap configurations have up t o 2 percenthigher peak resultant thrust ratios in both single-axis and multiaxis thrust vectoring than t he shifted-throat configurations. The larger thrust losses forthe shifted-throat configurations may be related tothroat inclination. When the throat is shifted, theexhaust flow first turns in the opposite direction ofvectoring upstream of the throat and then turnsback through a greater angle in the direction ofthrust vectoring. A throat plane tha t is inclined tothe oncoming flow may still be relatively orthogonalto the nozzle axis. Additional flow turning in thesupersonic region is necessary for the flow to expanddown the pitch channel and thus results in supersonicturning losses.

The effect of area ratio A,/At on the peak resul-tant thrust ratio is generally small. Increasing theflap width increases the peak resultant t hrus t ratios,particularly in single-axis thrust vectoring. As theflap width is increased, the geometry approaches tha tof a 2-D C-D nozzle, and therefore the performanceis expected to also approach that of a 2-D C-D noz-zle. In general, the peak resultant thrust ratios ofthe wide-flap nozzle are 1 to 2 percent higher thanthose of the narrow-flap nozzle. Previous researchon pitch-vectoring 2-D C-D nozzles has shown thatthrust vectoring can be accomplished with almost nolosses in thrust (ref. 19).

The peak resultant thrust ratios of the nozzlein the afterburning mode are generally similar tothose of the dry power mode. The most significantdifference is tha t t he benefit of having wider flapsshown for the dry power mode is not present duringvectoring operation. In the afterburning mode, thewide-flap configuration does not approximate thegeometry of a 2-D C-D nozzle any more than doesthe narrow-flap configuration. The thrust vectoring

7


10/82

losses associated with the cruciform geometry aretherefore still dominant.

A comparison of the effects of various thrust-vectoring configurations on the pitch thrust-vectorangles of the pitch-vectoring nozzle is shown in fig-ure 14. Th e most significant effects occur at lowrange of NPR's. Here the shifted-throat configura-tion provides the most pitch vectoring for the narrow-flap nozzle, and the basic pitch configuration providesthe most pitch vectoring for the wide-flap nozzle.In both situations the angle of the inward-deflectedpitch flap with respect t o th e oncoming flow is largertha n th at for any other configuration of the same flapwidth. This large flap deflection reduces the adverseflow separation from the opposite flap at low NPR's.Above a certain NPR, pitch vector angles of th e vari-ous pitch-vectoring configurations differ by less thanlo . The peak resultant thrust ratios occur in thisregion of NPR's.

The effect on the nozzle normal-force ratio F,/Fiof adding yaw thrust vectoring to pitch thrust vec-toring is presented in figure 15 and figure 16 for th edry power and afterburning power modes. As shownin figure 15, the coupling between pitch and yaw de-flections on the dry power nozzle is dependent ongeometry and NPR. For example, the narrow-flapconfiguration at A J A t = 1.3 has a small decreasein normal-force ratio caused by the addition of yawvectoring to pitch vectoring over a large NPR range.The wide-flap configuration at A , / A t = 1.2, how-ever, has a large decrease in normal-force ratio. Theeffect of adding yaw vectoring to the pitch-vectoringafterburning configurations, shown in figure 16, isto increase the normal-force ratio across the NPRrange. The exception is the wide-flap configurationat Ae /A t = 1.2.

The yaw thrust-vector angles produced in mul-tiaxis thrust vectoring by the restricted-flap andshifted-throat configurations are presented in fig-ure 17. The method of thrust vectoring has littleeffect on the yaw thrust-vector angles produced bythe nozzle.

The multiaxis thrust-vectoring capability of thecruciform nozzle is summarized in figure 18. Thethrust-vector angles are presented for the condition ofpeak resultant thrust ratio; as previously discussed,this condition represents a realistic operational con-figuration. The conditions of equal pitch and yawthrust-vector angles, shown as 45" lines through theplots, represent the goal of the cruciform nozzle de-sign to provide equal levels of thrust vectoring inpitch and yaw.

In dry power operation, equal thrust-vector anglesare not achieved because of the asymmetry requiredto allow multiaxis thrust vectoring. Wi th t he excep-tion of the narrow-flap configuration at Ae /A t = 1.3,the ability of the shifted-throat configuration to pro-duce equal pitch and yaw thrust-vector angles isequal to or greater than that of the restricted-flapconfiguration. Equal pitch and yaw thrust-vector an-gles are produced by the afterburning configurationsof the cruciform nozzle because of nozzle symmetry.The divergent flaps of t he afterburning configurationsdo not physically interfere and therefore do not needmodifications.

Figure 18(a) shows that the shifted-throat config-uration generally provides larger pitch thrust-vectorangles than those of the restricted-flap configurationsand that the benefits are greater for the wide-flapnozzle. Shifting the throat also generally produces alarger yaw thrust-vector angle. More equal thrust-vector angles are achieved by the narrow-flap nozzle.Increasing the area ratio Ae/At increases the mag-nitude of both the pitch and the yaw thrust-vectorangle. Moreover, increasing the flap width decreasesthe pitch thrust-vector angle. In afterburning oper-ation (fig. 18(b)), ncreasing the flap width increasesboth the pitch and the yaw thrust-vector angle.

Vertical-Thrust ModeThe thrust performance, discharge coefficient,

and resultant thrust-vector angles for the nozzle inthe vertical-thrust mode (fig. 5(a) ) are shown in fig-ure 19. Th e length-to-width ratios for the port open-ings associated with the narrow- and wide-flap con-figurations are about 2.6 and 1.5. Both have the samephysical port area of 4 in2.

A s shown in figure l9(a), the resultant thrustratios for both nozzles are high, considering thatthe internal geometry is not specifically designedto turn the flow smoothly in the vertical-thrustmode. The resultant thrust ratio of the narrow-flap configuration varies from 0.964 at NPR = 3.0to 0.955 at NP R = 6.6. The wide-flap resultantthrust ratio varies from 0.974 at NPR = 2.5 to 0.960at NP R = 5.5. Thrust performance for a similar90' flow-turning nozzle with a rectangular port and asharp upstream port corner was measured by Re andMason (ref. 29). The resultant thrust ratios rangingfrom 0.980 at NPR = 3 to 0.950 at NP R = 7 thatwere obtained for tha t nozzle are comparable to thoseof the current nozzle.

The discharge coefficient in the vertical-thrustmode shows a dependence on NPR t ha t is not presentin the cruise configuration. Th e narrow-flap nozzle

8


11/82

discharge coefficient is 0.826 at NPR = 2.0 and in-creases to 0.865 at NPR = 6.6. The wide-flap nozzledischarge coefficient is 0.796 at NPR = 2.0 and in-creases to 0.848 at NPR = 6.0. This variation of dis-charge coefficient is the result of changes in the effec-tive exit area of the port . The variance of dischargecoefficient with NPR suggests that the flow patternin the nozzle does not stabilize until the discharge co-efficient levels out at about NPR = 3.5. The nozzletested by Re and Mason achieved discharge coeffi-cients from 0.750 at NPR = 2 to 0.840 at NPR = 7(ref. 29); these coefficients are slightly lower than thevalues measured for the current nozzle.

The low discharge coefficients of t he vertical-thrust nozzles suggest that the effective port area forthe flow is smaller than the actual port area used inthe ideal weight-flow calculation (4 n2). A flow sep-aration region probably exists on the upstream wallof the port at the sharp corner (fig. 5(a)) and thusreduces the effective port area and consequently theweight flow through the nozzle. Re and Mason con-cluded that a corner radius on the upstream port cor-ner increases discharge coefficient by 5 to 10 percent(ref. 29). The asymptotic behavior of discharge coef-ficient with increasing NPR supports the theory of aseparated region, since a separation region would di-minish in size at higher pressure ratios because of theadded energy in the flow. As shown in figure 19(a),the wide-flap nozzle has a 2-percent-lower dischargecoefficient than the narrow-flap nozzle. If the regionsof separated flow in the two ports extend the samedistance from the upstream wall, the wide-flap con-figuration loses more effective port area than doesthe narrow-flap configuration. This difference resultsin a lower discharge coefficient.

Th e resultant thrust-vector angle also shows a de-pendence on the port width and NPR. The wide-flapnozzle deflects the thrust up to 87', about 2 morethan does the narrow-flap nozzle. Possible reasons forbetter thrust deflection of t he wide-flap configurationare tha t the wide-flap nozzle has more surface area onthe external expansion surface to turn the flow andthat the longer port length of the narrow-flap con-figuration probably allows more mass flow to escapethe port before being turned. Despite the increase inthrust-vector angle with NPR, neither nozzle is capa-ble of completely deflecting the thrust 90" (vertical).

In figure 19(b) , the performance data are pre-sented for the same configurations as those presentedin figure 19(a) with a 1.500-in. port length extensioninstalled (fig. 5(a)). The resultant thrust ratios anddischarge coefficients are not significantly affected bythe presence of the port extension. The resultantthrust-vector angle, however, is greatly increased.

The port extension increases the thrust-vector an-gle beyond the geometric angle of go", particularlyat high NPR's. At NPR = 6, the narrow-flap noz-zle deflects the thrust 92" and the wide-flap nozzledeflects the thrust 97'. This overdeflection is possi-ble because the flow outside of the port is physicallybounded on only one side, similar to the flow for theSERN geometry.

Thrust-Reverser ModeIn thrust-reverser mode, the nozzle exit is closed

off by the divergent flaps, and the side (right and left)convergent flaps are pivoted open as though hinged atthe throat to permit th rust reversing. To investigatethe possible necessity of a longer port length, twoport length extensions to the downstream walls weretested (fig. 5(b)): a short port length extension of0.750 in. and a long port length extension of 1.500 in.

The effects of the thrust-reverser port length onaxial thrus t rat io and discharge coefficient are shownin figure 20. Large negative values of Fa/F i representdesirable results for thrust reversers. In general, thetarget level of Fa/Fi is equal to the cosine of theport angle, in this case -0.5 ( ~ 0 ~ 1 2 0 " ) .he axialthrust ratios show that virtually no net axial thrust(i.e., reverse thrust ) is produced without the por textensions installed. Each port causes the thrust todeflect about 90, which cancels (or spoils) the thrustof the opposite port. The configurations with theport extensions do produce reverse thrust, and thisresult indicates the existence of a minimum requiredport length extension for reversing the thrust.

The wide-flap reverser produces significantlymore reverse thrust than does the narrow-flap re-verser. Similar to the vertical-thrust mode, thelonger port of the narrow-flap configuration proba-bly allows more mass flow to escape the port beforebeing turned. In fact, the wide-flap reverser withthe long port extension installed produces more re-verse thrust than expected, as shown by compari-son of the maximum F,/Fi (-0.62) with the targetof -0.5. This behavior has occurred in previousthrust-reverser tests (refs. 29 and 30). The low axialthrust ratio at low NPR is partially caused by thesharp upstream port corner. Re and Mason (ref. 29)concluded that increasing the corner radius raises thethrust efficiency at low NPR's because the larger ra-dius allows a smoother transition of the flow throughthe port; thus, separation at the corner is reduced.

Discharge coefficient is significantly affected bythe addition of the port extensions. The dischargecoefficient decreases about 10 percent when the shortport length extension is installed, but only an addi-tional decrease of 0 to 1percent occurs when the long

9


12/82


13/82

of Fighter Aircraft Design, AGARD-R-740, Oct,. 1987,pp. 7A-1-7A-7.12. Nguyen, Luat T.; and Gilber t, William P.: Impact

of Emerging Technologies on Future Combat AircraftAgility. AIAA-90-1304, May 1990.13. Berrier, Bobby L.: Results From NASA Langley Exper-

imental Studies of Multiaxis Thrust Vectoring Nozzles.SAE Tech. Pap er Ser. 881481, Oct. 1988.14. Capone, Francis J.; and Berrier, Bobby L. : Investigation

of Ax isy mm etr ic and Nona xisymm etric Nozzles Installedon a 0.10-Scale F-18 Prototype Airplane Model. NASATP-1638, 1980.

15. Leavi tt, Laurence D.: Summa ry of Nonaxisymmetric Noz-zle Internal Performance From the NASA Lang1e.y StaticTes t Facility. AIAA-85-1347, Ju ly 1985.16. Capone, Francis J.: Static Performance of Five Twin-Engine Nonax isymm etric Nozzles W ith Vectoring and Re-versing Capability. NASA TP-1224, 1978.17. Capone, Francis 3.; Mason, Mary L. ; and Leavitt, Lau-rence D.: A n Experimental Invest igation of Thrust Vector-ing Tw o-Dime nsional Convergent-Divergent Nozzles In-

stalled in a Twin-E ngine F ighter Model at High, Anglesof Attack. NASA TM-4155, 1990.

18. Willard, C. M.; Capone, F. J.; Konarski, M.; and Stevens,H. L.: Static Performance of Vectoring/Reversing Non-Axisymmetric Nozzles. AIAA Paper 77-840, .July 1977.19. Re, Richard J.; and Leavitt, Laurence D.: Static InternalPerformance Including Thrust Vectoring and Reversing of

Two-Dime nsional Convergent-Divergen t Nozzles. NASATP-2253, 1984.20. Berrier, Bobby L.; and Mason, Mary L.: Static Perfor-mance of an Axisymm etric Nozzle W ith Post-Exit Vanes

for Multiaxis Thrust Vectoring. NASA TP-2800, 1988.21. Capone, Francis J.; and Bare, E. Ann: Multiaxis Control

Power &om Thrust Vectoring for a Supersonic Fighter

Aircraft Model at Mach 0.20 to 2.47. NASA TP-2712,1987.22. Lacey, David W.; and Murphy, Richard D.: Jet EngineThrust Turning b y the Use of Small Externally MountedVanes. DTNSRDC-82/080, U.S. Navy, Jan. 1983. (Avail-able from DTIC as AD BO70 970L.)23. Schirmer, Albert0 W.; and Capone, Francis J.: Paramet-ric Study of a Simultaneous Pitch/Yaw Thrust Vector-

ing Single Expansion Ramp Nozzle. AIAA-89-2812, July1989.24. Taylor, John G.: Static Investigation of a Two-Dimensional C onvergent-Divergent Exhaust Nozzle Wzth

Mu ltiaxis Thr ust- Vectoring Capability. NASA TP-2973,1990.25. Mercer, Charles E.; Berrier, Bobby L.; Capone, FrancisJ.; Grayston, Alan M.; and Sherman, C. D.: Computa-tions for the l6-Foot Transonic Tunn el-NA SA, LangleyResearch Center. NASA TM-86319, 1984.26. Staff of the Propulsion Aerodynamics Branch: A User'sGuide to the Langley 16-Foot Transonic FunnelComplex-Revision 1. NASA TM-102750, 1990.27. Liepmann, H. W.; and Roshko, A.: Elements of Gasdy-namics. John Wiley & Sons, Inc., c.1957.28. Berrier, Bobby L.; and Re, Richard J.: Investigation

of Convergent-Divergent Nozzles Applicable to Reduced-Power Supersonic Cruise Aircraft. NASA TP-1766, 1980.29. Re, Richard J.; and Mason, Mary L.: Effect of VaryingInternal Geometry on the Static Performance of Rectan-

gular Thrust-R everse r Ports. NASA TM-89061, 1987.30. Berrier, Bobby L.; a nd Capone, Francis J .: Effect ofPort Corner Geometry on the Internal Performance of

a Rotating- Vane-Type Thrust Reverser. NASA TP-2624,1986.

11


14/82

Table 1. Cruciform Nozzle Configurations

(a) Unvectored and vectored configurations

I ParameterConfiguration

123456

10111 2161718192021222 324252627282930313233343536373839404142

Yaw, deg000

- 00

-2000

-20000

-200

-2000

-20000- 00- 000

-20000-200- 000

-20

DescriptionBaseline

Basic pitchRestricted flapRestricted flapShifted throatShifted throatA/B baseline

A/B pitchA/B pitch-yawBaseline


A/B pitchA/B pitch-yawBaseline


A/B pitchA/B pitch-yaw

BaselineBasic pitch

Restricted flapRestricted flapShifted throatShifted throatA/B baseline

A/B pitchA/B pitch-yaw

12


15/82

Configuration43444950454647485152

Table 1. Concluded

(b) Vertical- and reverse-thrust configurations

Flap widthNarrowWide

NarrowWide

NarrowWideNarrowWide

NarrowWide

Port area, in24.004.004.004.004.004.004.004.004.004.00

ParameterOperat ionVerticalVerticalVerticalVerticalReverserReverserReverserReverserReverserReverser

Angle, deg90909090

120120120120120120

Extension, in.00

1.51.51.51.500

0.750.75

13


16/82

Table 2. Cruciform Nozzle Dimensions[Dimensions in inches]

"

Configuration

"

123456101112161718192021222324252627282930313233343536373839404142

Y

(a) Unvectored and vectored configurations

""

Yt1.5451.5451.5451.5451.9711.9712.3522.3522.3521.5451.5451.5451.5451.9711.9712.3542.3542.3541.5101.5101.5101.5101.7071.7072.1252.1252.1251.5101.5101.5101.5101.7071.7072.1252.1252.125

Yb1.5451.5451.5451.5451.5451.5452.3522.3522.3521.5451.5451.5451.5451.1181.1182.3542.3542.3541.5101.5101.5101.5101.3131.3132.1252.1252.1251.5101.5101.5101.5101.3131.3132.1252.1252.125

ParameterYl

1.5451.5451.5451.5451.5451.5452.3522.3522.3521.5451.5451.5451.5451.5451.5452.3542.3542.3541.5101.5101.5101.5101.5101.5102.1252.1252.1251.5101.5101.5101.5101.5101.5102.1252.1252.125

Yr1.5451.5451.5451.5451.5451.5452.3522.3522.3521.5451.5451.5451.5451.5451.5452.3542.3542.3541.5101.5101.5101.5101.5101.5102.1252.1252.1251.5101.5101.5101.5101.5101.5102.1252.1252.125

zt1.2803.2173.6173.6173.6443.6442.2511.1751.1751.4420.3670.6180.6180.7930.7932.5751.4821.4821.1450.0920.8120.8120.8120.8121.8830.8180.8181.2670.2030.8120.8120.8120.8122.1281.0461.046

zb12802.3752.3752.3751.9481.9482.2513.3393.3391.4422.5302.5302.5302.1072.1072.5753.6413.6411.1452.2422.2422.2422.0472.0471.8832.9772.9771.2672.3612.3612.3612.1652.1652.1283.2113.211

Z l1.2801.2801.2803.2171.2803.2172.2512.2511.1751.4421.4421.4420.3671.4420.3672.5752.5751.4821.1451.1451.1450.0921.1450.0921.8831.8830.8181.2671.2671.2670.2031.2670.2032.1282.1281.046

z r1.2801.2801.2802.3751.2802.3752.2512.2513.3391.4421.4421.4422.5301.4422.5302.5752.5753.6411.1451.1451.1452.2421.1452.2421.8831.8832.9771.2671.2671.2672.3611.2672.3612.1282.1283.211

14


17/82

Configuration43444546474849505152

Table 2. Concluded

(b) Vertical- and reverse-thrust configurations

OperationVerticalVerticalReverserReverserReverserReverserVerticalVerticalReverserReverser

A2.1262.0302.1262.0302.1262.0302.1262.0302.1262.030

B1.5591.3351.5591.3351.5591.3351.5591.3351.5591.335

ParameterE

2.4241.649

2.4241.649

1.5451.510

1.5451.5101.5451.510

1.510

Yt1.5451.510

1.5451.510

z2.8902.8302.4602.4032.4602.4032.8902.8302.4602.403

15


18/82

Table 3. Cruciform Nozzle DataConfiguration 1

NPR

2.002.503.003.513.984.525.015.536.007.018.01

NPR2.002.523.013.514.014.505.015.525.997.038.01

NPR2.002.502.993.514.014.505.015.526.017.008.02

16

W d W i

0.97440.97540.97270.97410.97 190.97280.97200.96980.97050.97 100.9702

wdwi0.94820.94870.94380.94250.94150.94 110.94080.94070.94050.93970.9390

Wdwi0.%340.96470.%270.%150.%130.%020.%050.95990.95950.95880.9582

F P i0.90490.93490.95340.96520.974 10.97700.97900.98 170.98 130.97870.9787

F P i0.91710.91190.92940.93980.94600.95280.95760.96150.96300.96340.9630

F P i0.92200.94 180.92090.93820.94590.95400.95930.96490.%720.%9 10.9702

F P i 4 ZY0.90480.93490.95340.96520.974 10.97700.97900.98170.98 130.97870.9787

Fapi0.91130.88790.90290.91270.9 1430.92340.93010.93520.93790.94000.9406

Fapi0.92160.94070.90450.91980.92210.927 10.93370.94040.94350.94660.9487

-1.00 -0.34-0.33 -0.120.10 -0.230.09 -0.160.18 -0.140.17 -0.080.18 -0.030.14 -0.010.15 0.010.11 0.040.09 0.06

Configuration 246.45

13.0913.7013.7814.8614.2713.7813.4313.0912.6712.38

6,-0.141.390.360.240.280.070.150.090.090.060.03

Configuration 3%1.812.63

10.7311.3612.8813.6513.2712.9412.7112.3612.10

6,-0.48-0.691.560.300.330.460.160.130.140.120.09

[email protected] 10.00290.00300.00240.00250.00190.0015

F P i0.10300.20650.22010.22390.24260.23490.22800.22330.21810.21 130.2065

Fnpi0.029 10.04320.17130.18480.21090.22510.22020.21600.21280.20750.2035

MyPiL

0.22740.0950-0.007 1-0.0070-0.024 1-0.0304-0.0343-0.0403-0.0444-0.0482-0.03%

My/FiL-1.6641-3.2247-3.4004-3.4205-3.6984-3.5302-3.3797-3.2703-3.1793-3.0250-2.9205

MyFiL-0.5065-0.6030-2.6537-2.8730-3.2761-3.4650-3.3760-3.2783-3.2048-3.0863-2.9909

F P i-0.0054-0.0020-0.0038-0.0027-0.0023-0.0013-0.0005-0.00020.00010.00070.0010

[email protected] 150.00570.00380.00450.00120.00250.00150.00150.00100.0005

F P i-0.0077-0.01 140.02460.00480.00530.00740.00260.00210.00240.00200.0015

m5i1-0.0742-0.0860-0.0317-0.0286-0.0218-0.0213-0.0155-0.0126-0.0110-0.0069-0.006 1

m5110.0696

-0.3068-0.0452-0.0233-0.03220.01720.00660.01300.01390.01820.0185

M P i L0.05930.1447

-0.4089-0.0732-0.0690-0.1063-0.0169-0.0127-0.0156-0.0056-0.0042


19/82


20/82

Table 3. ContinuedConfiguration 10

NPR1.992.502.993.503.994.494.995.495.99

NPR2.012.563.013.494.004.495.005.486.00

NPR

1.992.492.993.494.004.504.975.515.99

wdwi0.97 170.97340.97410.9748097420.97470.97410.974309733

w d w i0.95400.95590.95690.95750.95840.95870.95870.95990.9594

W d W i

0.90723.9 1 00.91480.91640.91700.9 1800.91840.91870.9180

F P i0.93 190.95770.97 100.98020.98460.98560.98560.98430.9833

F P i0.95670.%260.95470.95680.95860.%130.%270.%300.%27

F P i0.93310.90670.91780.93020.93690.94 150.94340.94360.9438

FdFi0.93190.95770.97100.98020.98460.98560.98560.98430.9833

0.95560.95800.94250.94170.94220.94550.94750.94830.9484

FaFi0.91010.84050.85660.87780.89000.89780.90220.90460.9062

4 40.48 0.080.01 0.08

-0.06 0.03-0.08 0.07-0.07 0.06-0.11 0.04-0.08 0.08-0.07 0.10-0.06 0.11

Configuration 114 6Y2.76 -0.065.65 0.269.10 1.00

10.20 0.4110.60 0.3910.40 0.4310.19 0.4110.01 0.449.88 0.50

Configuration 124 6,9.28 -8.89

16.10 -15.8415.28 -15.1613.91 -13.9413.10 -13.0912.60 -12.5612.24 -12.1611.94 -11.7811.73 -11.54

F#i0.00790.0002-0.0011-0.0014-0.0012-0.0019-0.0014-0.0012-0.0011

F P i0.04610.09470.15090.16950.17640.17360.17020.16730.1651

FnFi0.14870.24260.23410.21730.20710.20070.19570.19130.1881

MyFiL0.08740.10620.08770.07040.06020.05620.04820.04630.0426

MyFiL-0.4603-1.3015-2.2663-2.6016-2.7186-2.6574-2.5784-2.5064-2.4492

MyFiL-2.1449-3.7120-3.5897-3.2840-3.0707-2.9374-2.8394-2.7527-2.6916

F P i0.00130.0013O.ooo60.00130.001 10.00070.00130.00170.0019

F P i-0.00100.00440.01650.00670.00640.007 10.00680.00730.0083

F P i-0.1423-0.23 85-0.2321-0.2179-0.2070-0.2001-0.1944-0.1886-0.1850

m5i1-0.0276-0.0323-0.0217-0.0224-0.0236-0.0174-0.0147-0.0119-0.0066

m5110.0234

-0.08 13-0.2760-0.1114-0.1009-0.0953-0.0875-0.08 15-0.0837

m5112.15353.76233.62683.31803.10762.96992.87582.78822.725 1

18


21/82


NPR2.012.523.003.504.014.505.035.516.016.998.00

NPR2.012.503.013.504.014.515.025.516.007.008.00

NPR2.012.523.013.514.024.505.005.515.997.057.93

W $ w iO.% 140.96260.%110.%070.95890.95840.95750.95700.95670.95530.9546

wp/wi0.93890.93900.93900.93720.93790.93690.93590.93500.93490.93340.9322

Wpfwi0.95260.9560.95360.95270.94990.95120.95070.95040.94980.95070.9457

F R i0.87340.91790.93490.94750.95840.96570.97170.97530.97800.98 100.9832

F R i0.94730.94650.93690.92290.93460.93870.94690.95300.9560.%040.%33

F R i0.8970.94090.94390.93920.93290.93660.94490.95150.95670.%110.9683

FdFi 6, 40.87330.9 1790.93490.94750.95840.96570.97 170.97530.97800.98100.9832

0.94690.94530.92960.90030.91010.90890.91800.92520.92940.93530.9393

F$Fi0.8%60.94080.94230.93040.91470.91410.92060.92730.93320.93860.9465

-0.10 -0.40-0.23 -0.09-0.11 -0.100.04 -0.050.01 0.16-0.13 0.24-0.12 0.22-0.15 0.23-0.20 0.22-0.21 0.20-0.21 0.19

Configuration 17

1.62 -0.352.94 -0.277.13 -0.2912.71 0.5413.15 0.3114.48 0.2714.20 0.3013.87 0.1813.56 0.1513.14 0.1412.80 0.10

Configuration 1891.81-0.773.297.8511.3312.6013.0012.9312.7312.4312.18

%0.54-0.2-0.05-0.160.190.180.30.330.250.140.13

F P i-0.0015-0.0037-0.0018O.OOO60.0002-0.0021-0.0021-0.0025-0.0033-0.0035-0.0036

Fnpi0.02680.04850.1 1630.2030.21260.23470.23230.22840.2242-0.21830.2134

F P i0.0283-0.01260.05420.12820.18320.20430.2 1250.21290.21080.20690.2043

MyFiL0.05680.12310.0930.04520.05630.08270.07520.07 70.06370.05170.0465

My/FiL-0.57 0-0.7801-1.7797-3.14 7-3.2631-3.6166-3.5463-3.4571-3.3712-3.2379-3.1270

MYIF$.--0.4510.3644-0.6877-1.9019-2.8282-3.1929-3.3102-3.3113-3.2639-3.1514-3.0921

F P i-0.006-0.00 5-0.0016-0.OOO90.00270.0040.00370.00390.00370.00340.0032

F P i-0.0058-0.0044-0.00460.00840.00490.00430.00470.00300.00240.00220.0016

F P i0.0085-0.0035-0.0008-0.00250.00300.00280.00490.00530.004 10.00230.0022

m5i1-0.0034-0.0328-0.0069-0.0062-0.0490-0.0636-0.05 0-0.048-0.0407-0.0346-0.0339

m511-0.0084-0.00420.0309-0.1564-0.0890-0.0653-0.0690-0.0358-0.0245-0.0174-0.0 39

M#iL-0.18440.0194-0.00870.0113-0.0556-0.0520-0.0807-0.085-0.0572-0.0283-0.0234

19


22/82

Table 3 . ContinuedConfiguration 19

NPR2.022.5 13.033.514.034.515.005.516.007.018.02

NPR2.022.543.023.504.024.515.035.525.996.997.98

NPR2.002.503.514.024.535.055.526.047.018.013.01

20

wpfwi0.91440.91740.91650.91510.91620.91610.91530.91460.9 1390.91340.9124

W d W i

0.92310.92510.92350.92320.92260.92170.92170.92060.91970.91920.9178

W p k

0.88600.88820.88860.88870.88970.89030.88920.88690.88840.88730.8909

F P i0.89480.87860.89840.91520.92920.93400.93750.93980.94120.94400.9480

F P i0.87820.89030.89600.91470.92990.93900.94320.94730.95 180.956 10.9589

F P i0.89 120.88920.91 120.91660.92290.928 10.93010.93250.93220.93320.9192

0.86250.83790.86010.87080.86380.86220.87080.879 10.88490.89400.9024

0.87350.88000.86860.88900.90420.91250.91500.9 1950.92400.93000.9340

Fa&0.84840.85040.85430.85730.86660.86870.87030.87530.88080.88610.8639

13.6911.5611.4912.5715.5416.0715.3514.6014.0113.1712.60

-7.45-13.51-12.58-13.19-15.77-16.73-16.16-15.32-14.71-13.80-13.03

Configuration 204 SY5.57 -2.048.61 -1.27

14.16 1.0613.62 0.4313.48 -0.2413.63 -0.0514.02 0.1713.92 0.1213.88 0.0813.43 -0.0113.10 0.06

Configuration 21

16.24 -7.7913.18 -11.0816.50 -12.5915.83 -14.0814.82 -14.2215.13 -14.6515.37 -14.4514.92 -14.1913.83 -13.7212.93 -13.3616.51 -11.90

F#i0.21000.17 140.17490.19420.24020.24830.23900.22900.22080.20930.2018

F n p i0.08520.13320.21910.2 1540.21680.22130.22860.22790.22830.22200.2173

FnR0.24700.19910.25300.243 10.22930.23490.23930.23320.21680.20350.2561

My/FiL-3.4767-2.7164-2.6694-2.9350-3.6553-3.7820-3.6026-3.4 192-3.2718-3.0498-2.9059

My/FiL-1.5000-2.1937-3.5909-3.5192-3.5402-3.5775-3.6908-3.6821-3.6477-3.5305-3.4263

MyFiL-4.2180-4.1093-3.3271-3.8883-3.6168-3.6901-3.7583-3.6402-3.3482-3.0966-3.8963

F P i-0.1127-0.2012-0.1919-0.204 1-0.2439-0.2592-0.2523-0.2408-0.2324-0.2196-0.2088

F P i-0.0311-0.01950.01600.0067

-0.0037-0.00070.00270.00200.0013

-0.00020.0010

F P i-0.1161-0.1665-0.1908-0.2151-0.2196-0.2270-0.2243-0.2213-0.2151-0.2104-0.1820

M P i L1.7 1043.04852.84053.03213.69593.96683.83483.60903.44603.18252.9719

M#iL0.34990.2327

-0.2914-0.13010.045 1

-0.0018-0.0399-0.0125-0.00120.02400.0047

M P i L1.81912.58272.87463.26133.29703.40243.34133.27803.14693.03402.5199


23/82


NPR1.992.482.993.493.984.505.005.495.995.98

NPR2.002.512.993.504.004.504.995.505.99

NPR2.002.513.013.503.994.515.015.506.01

Wpfwi0.97760.97700.97820.97810.97820.97810.97800.97780.97700.977

wpfwi0.%100.96350.96430.96490.96450.%540.%670.96860.%94

Wpfwi0.94270.95050.95140.95250.95250.95300.95360.95530.9545

[email protected].%240.97 80.97590.97990.98 00.9808

[email protected].%300.%660.95670.95900.%150.%19

F P i0.%5 10.97080.%970.96690.%280.93830.94030.94070.9407

0.8787 0.800.9009 0.590.9318 0.360.9497 0.210.9624 0.150.9718 0.140.9759 0.130.9798 0.170.9810 0.170.9808 0.14

6Y-0.200.020.040.02-0.00.070.070.090.140.14

Configuration 23

0.92030.94 10.95250.95750.95960.94530.94760.95020.9507

Fapi0.95830.96140.95550.94850.94090.90570.90790.90850.9086

1.42 0.543.78 0.095.06 0.076.14 0.036.89 0.088.83 -0.418.87 0.018.78 0.108.77 0.20

Configuration 244 6,5.15 -4.417.10 -6.845.85 -5.498.08 -7.888.82 -8.6110.90 -10.7710.89 -10.6710.93 -10.5910.93 -10.53

F P i0.0 230.00920.00580.0350.00240.00240.00220.00300.00290.0024

F P i0.02280.06220.08440.10310.11600.14680.14780.14670.1467

F n R0.08650.09850.11910.13470.14610.17440.17460.17540.1755

My/FiL-0.02390.01720.03640.03520.03970.03240.03500.02740.02930.0302

My/FiL-0.0901-0.7840-1.1788-1.4888-1.705-2.1766-2.1983-2.1895-2.1882

My/FiL-1.1218-1.3876-1.7240-1.9854-2.1623-2.6068-2.6029-2.6016-2.5984

F P i-0.0030.0003O.OOO60.0003-0.oO010.0010.0010.00150.00230.0025

F P i0.00880.00150.0012O.OOO60.0013-0.00680.00020.00170.0033

F P i-0.0739-0.0925-0.1147-0.1312-0.1425-0.1723-0.1711-0.1698-0.1689

m5i10.0572-0.0282-0.0401-0.0318-0.0299-0.0284-0.0257-0.0246-0.020-0.0209

m511-0.1773-0.0267-0.0332-0.0285-0.02620.09970.0052-0.0010-0.0226

m5111.12191.39471.73271.98802.16492.63292.61332.59162.5929

21


24/82


NP R2.012.503.013.524.024.515.025.516.007.017.99

NPR

2.002.503.033.504.004.505.015.525.997.018.00

IW R2.022.503.003.514.014.505.015.506.007.008.00

2 2

WpJwi0.97 120.97040.97010.%920.%860.%770.%760.%740.%760.%780.%75

wpfwi0.92380.92330.924 10.92730.92790.92770.92730.92740.927 10.92670.9264

wpfwi0.97210.97240.97240.97210.97080.9702O.%%0.%920.%890.%750.%67

F P i0.92900.95010.96780.97750.98 160.98380.98470.98420.98300.98030.9777

F P i0.92020.94180.95600.%380.%7 10.%930.%970.%990.%930.%640.9643

F P i0.92050.929 10.92660.94700.95950.96360.97020.97380.97650.98010.98 16

F$Fi 4 6,0.92830.95000.96770.97750.98160.98380.98470.98420.98300.98030.9777

Fapi0.86670.88540.91250.92700.93470.93890.93960.94130.94210.941 10.9404

Fapi0.91940.92780.90920.92740.938 10.93 130.93930.944 10.94780.95290.9555

-1.20 -1.83-0.27 -0.63-0.05 -0.45-0.07 -0.26-0.06 -0.17-0.03 -0.10-0.08 -0.03-0.10 -0.01-0.12 0.00-0.11 0.00-0.06 0.00

Configuration 26SP

19.6319.9317.3515.8814.8614.4014.3013.9413.6113.1312.80

6,-0.4 1-0.050.070.000.200.270.260.210.200.140.12

Configuration 276,2.293.07

11.1011.6812.1414.8814.5014.1913.9313.5213.24

6 Y-1.680.32

-0.78-0.34-0.170.340.150.090.1 10.060.05

F,/Fi-0.0194-0.0045-0.o009-0.0012-0.001 1-0.0005-0.0014-0.0017-0.0020-0.0019-0.001 1

F P i0.30920.32100.28500.26370.24800.24100.23%0.23370.22810.21950.2 137

Fnpi0.03670.04970.17840.19180.20170.24750.24300.23870.23510.22910.2249

MyPiL0.27%0.05040.01670.02010.01700.00150.0056

-0.0039-0.0131-0.0205-0.0228

MyF&-4.9288-5.0370-4.3533-3.9475-3.6411-3.4769-3.4190-3.2950-3.1898-3.0219-2.8976

MyFiI--0.8108-0.7769-2.7502-3.0066-3.1212-3.8255-3.7680-3.7104-3.6316-3.5057-3.4070

F P i-0.0297-0.0105-0.0076-0.0045-0.0029-0.0017-0.0005-0.0002O.oo00O.oo000.0001

F P i-0.0063-0.00080.001 10.00010.00330.00440.00430.00340.00320.00230.0020

F P i-0.02700.0052

-0.0123-0.0055-0.00270.00550.00250.00150.00180.00 10O.OOO9

0.38860.09080.06400.03330.02240.0094

-0.0067-0.0043-0.001 1O.OOO90.0035

m511-0.0054-0.0468-0.0789-0.0408-0.0880-0.1016-0.0893-0.0682-0.0634-0.0480-0.0465

M P i L0.2653

-0.12410.16830.06570.0296

-0.0988-0.048 1-0.0225-0.0300-0.0222-0.0234


25/82

NPR2.022.513.023.504.014.515.025.506.006.507.008.00

NPR1.992.513.013.504.014.505.015.606.007.008.01

NPR2.012.503.023.514.014.515.025.506.007.008.00

~

wdwi0.91920.91990.91970.9 1870.9 1920.9 1 60.9 1 70.91850.91830.91790.91800.9172

wdwi0.96000.%060.96070.95940.95910.95810.95760.95750.95700.95880.9597

wdwi0.90210.90270.90300.90 180.90 150.90110.90070.90050.90020.89%0.8988

~~

F P i0.89090.91250.92400.93020.93770.94060.94060.94330.94540.94780.94960.9520

F P i0.91730.91890.93700.95050.%070.96740.97280.97610.97730.97950.9801

F P i0.90790.91500.92260.92800.93460.93890.93950.94170.94200.94230.9433

FdFi0.83990.86880.88180.87900.88500.89000.89520.90190.90700.91210.91520.9199

0.9 1410.89780.90620.91540.92230.93100.93840.94360.94590.95010.9519

F$Fi0.84960.86550.86360.87160.88140.88950.89450.89930.90240.90660.9098


4.28 -19.066.71 -16.638.10 -15.578.68 -17.25

10.04 -16.8310.73 -15.8810.95 -14.4810.65 -13.6010.32 -12.9910.02 -12.459.84 -12.169.55 -11.67

Configuration 294 SY4.66

12.2914.6815.6116.2515.7615.2714.8 114.5614.0913.79

1.330.4 11.330.51

-0.050.060.130.180.140.130.08

Configuration 30

6.01 -19.8910.06 -16.3610.93 -17.8711.07 -17.1611.26 -16.2211.06 -15.4010.90 -14.4210.86 -13.7310.69 -13.0810.46 -12.1610.22 -11.65

F#i0.06290.10230.12550.13420.15670.16860.17310.16%0.16520.16110.15880.1548

F#i0.07450.19570.23740.25580.26880.26280.25620.24%0.24570.23840.2335

F#i0.08950.15350.16670.17050.17550.17380.17230.17250.17030.16740.1641

MyPiL-0.9098-1.4408-1.7581-1.8760-2.2599-2.4607-2.5454-2.48 10-2.3987-2.3 133-2.2578-2.1629

MyP&-1.4237-3.1893-3.8804-4.1530-4.3320-4.20644.0645-3.9291-3.8540-3.7143-3.6086

M y @ --1.5033-2.4182-2.58 13-2.6100-2.6688-2.6255-2.5933-2.5857-2.5498-2.4787-2.4043

F P i-0.2903-0.2594-0.2458-0.2730-0.2676-0.2532-0.23 11-0.2183-0.2093-0.2013-0.1972-0.1901

F P i0.02120.00650.02100.0082

-0.0008O.ooo90.00220.00300.00230.002 10.0014

F P i-0.3074-0.254 1-0.2784-0.269 1-0.2564-0.2450-0.2300-0.2198-0.2097-0.1953-0.1875

M7iFIL4.39793.85973.61164.09893.99723.72693.32953.10142.92492.77102.67592.5230

m511-0.3696-0.1252-0.3726-0.15840.0002

-0.0234-0.0362-0.0500-0.0398-0.0329-0.0295

m5114.72183.78244.21274.04033.79953.59033.3 1083.11062.925 12.63652.4749

23


26/82


NPR2.002.522.983.493.994.524.995.506.02

NPR2.012.503.003.504.014.505.005.505.99

NPR2.012.502.993.504.004.505.005.516.00

W p h0.97930.98 140.98250.98350.98350.98280.98280.98220.9809

W p h

0.95540.95610.95630.95620.95620.95590.95530.95490.9540

WpJWi

0.89350.89650.89910.89970.90030.90020.89970.89930.8986

F P i0.94170.%600.9780.98600.98890.98940.98840.98660.9850

F P i0.95520.94670.9536O.% 180.%630.96780.%800.%7 10.%57

F P i0.91760.93970.95180.95 170.95070.95150.95230.95120.9508

F$Fi 40.9416 0.700.9660 0.560.9781 0.400.9860 0.300.9888 0.290.9894 0.240.9884 0.220.9866 0.210.9850 0.22

40.360.09-0.01-0.03-0.04-0.06-0.010.020.05

Configuration 32Fapi 40.94780.91890.92240.93250.93910.94260.9440.94400.9436

FaFi0.85970.88540.88590.88780.89480.90160.90590.90780.9093

7.11 -0.0613.90 -0.0914.68 -0.1814.18 0.0013.62 0.0013.10 0.1012.76 0.1312.53 0.1412.27 0.18

Configuration 33

15.08 -14.4914.26 -13.9615.60 -15.4415.29 -15.2614.24 -14.2513.40 -13.4512.90 -12.9112.52 -12.4412.28 -12.10

FdFi0.01 140.00950.00690.00520.00510.00420.00380.00360.0038

F,JFi0.11830.22740.24 170.23570.22750.2 1940.21370.20980.2053

FnFi0.23 160.22500.24740.24270.22700.21480.20750.20160.1980

My/FiL0.0472-0.0234-0.0195-0.0140-0.0139-0.0095-0.0100-0.01 3-0.0124

My/FiL-1.7383-3.4237-3.7231-3.5951-3.4069-3.2631-3.1423-3.0424-2.9733

MyFiL-3.3716-3.2030-3.5831-3.5175-3.2222-3.0064-2.8712-2.7 6-2.6948

F P i0.00600.0016-0.0002-0.0005-0.oo06-0.0010-0.00010.00030.0008

[email protected]

F P i-0.2221-0.2201-0.2446-0.2422-0.2272-0.2156-0.2077-0.2002-0.1949

-0.1400-0.0668-0.0424-0.0378-0.0258-0.021-0.0138-0.0137-0.0110

m511-0.0195-0.03 10.0143-0.0247-0.0288-0.0335-0.0322-0.0246-0.0239

m5113.31983.23453.61463.56053.2683.05542.91832.80022.7221

24


27/82


NPR2.003.002.493.514.024.515.005.516.027.017.99

NPR2.012.523.003.514.034.515.015.506.007.018.00

NPR2.002.493.003.504.014.514.995.506.007.008.00

Wdwi0.97550.97500.97350.97330.97250.97200.97150.97130.97 00.97080.9704

W d W i

0.94410.94660.94560.94490.94540.94430.94410.94400.94380.94290.9421

W d W i

0.97010.97130.97 50.97 100.%99O.%%0.%910.%860.%840.%750.%72

F P i0.90800.95210.93340.%3 10.97210.97840.98 90.98380.98500.98490.9848

F P i0.92760.94760.93830.95 10.9570.%040.96360.9660.%790.%940.9698

F P iO.% 130.%760.%590.95720.9470.95760.96430.%730.%810.97500.9784

0.9039 0.010.9521 0.190.9334 0.110.9631 0.250.9721 0.250.9784 0.220.9819 0.180.9838 0.130.9850 0.090.9849 0.060.9848 0.08

F$Fi0.9 1860.93320.89880.91230.91850.91880.92470.92890.93240.93630.9382

F P i0.96 20.96720.96590.95170.92790.93640.94 30.94120.93830.94570.9500

-5.40 0.0002-0.36 0.0031-0.43 0.0018-0.21 0.0043-0.17 0.0043-0.15 0.0038-0.12 0.0031-0.09 0.0022-0.09 0.0016-0.09 0.0010-0.11 0.0014

Configuration 3597.9710.0016.6716.4116.3216.9316.3415.9415.5615.0314.66

6,0.0-0.21-0.60-0.080.01-0.0-0.06-0.040.040.070.05

Configuration 366,-0.150.486.0911.5512.0712.5313.3214.2614.1013.83

-1.624-0.48-0.17-0.25-0.57-0.13-0.08-0.05-0.040.060.0-0.03

FnFi0.12870.16450.26910.26870.26890.27%0.27 10.26530.25%0.25 30.2455

F P i-0.0025-0.02730.0080.10160.18970.20030.20930.22290.23850.23750.2339

MyPiL-0.0085-0.0275-0.0210-0.0464-0.0495-0.0434-0.0386-0.0363-0.0392-0.0453-0.0457

MyF&-2.1205-2.60294.1126-4.1037-4.0627-4.1942-4.0342-3.91 3-3.8072-3.6400-3.5141

M y F$ --0.10550.4420-0.0178-1.5246-2.8988-3.0740-3.1944-3.4094-3.6953-3.6478-3.5660

F P i-0.0854-0.0059-0.0070-0.0036-0.0028-0.0026-0.0020-0.0016-0.0016-0.0016-0.0019

F P i0.0002-0.0035-0.0094-0.00120.0002-0.0002-0.OOO9-0.OOO6O.OOO60.0012O.OOO9

F P i-0.0080-0.0028-0.0043-0.0095-0.0021-0.0012-0.oo09-0.00070.0oO90.0002-0.oo04

m5i11.28390.04160.04330.01250.01460.01500.01380.01530.01650.01880.0247

m511-0.074-0.0500.1201-0.01 2-0.0228-0.0078o.Ooo1-0.oo04-0.0086-0.0209-0.0200

m511-0.0128-0.0526-0.01460.1 1390.0020.00420.0020.0085-0.0130-0.0030-0.001

25


28/82


NPR2.022.513.013.514.004.525.005.506.027.018.01

IWR1.992.513.003.514.014.505.025.516.017.008.01

NPR1.992.502.993.504.004.495.015.506.007.017.99

W d W i

0.93240.93260.93 130.93070.93080.92990.93070.93020.93020.92890.928 1

wp/Wi

0.%580.%7 10.%630.%540.%5 10.96440.96450.96420.96400.%300.%22

W d W i0.92140.92190.91990.9 1%0.91980.92000.92040.9 1970.92000.9 1 70.9177

F P i0.88290.9 1620.91780.92690.93700.94520.93980.94040.94400.95050.9545

F P i

0.90700.93640.93970.93720.95 130.%040.%600.%860.97100.97530.978 1

F P i0.90010.91 160.91430.92460.92790.93340.93270.935 10.936 10.94200.9455

F$Fi0.8410.88190.86600.86770.86990.87660.87530.88160.89050.90270.9098

0.90380.93460.93000.91040.92330.93 130.93490.93480.93690.94160.9459

Fa&0.85460.86240.85190.85740.85160.86040.86460.87 110.87660.88900.8%2

6 , 49.62 -14.948.62 -13.339.92 -16.92

12.29 -17.0211.98 -18.7412.52 -18.6013.33 -17.2713.08 -16.1512.54 -15.2511.96 -14.1811.55 -13.65

Configuration 38

4.043.048.20

13.7413.9414.1614.5915.1915.2415.1014.75

-2.53-1.80-0.82-0.25-0.050.02-0.120.050.080.070.07

Configuration 39

8.15 -16.5811.15 -15.6614.55 -16.2214.61 -17.1514.47 -19.1614.17 -18.6014.50 -17.3014.47 -16.3114.07 -15.5413.26 -14.5312.77 -13.95

F#i0.14 50.13370.15140.18910.18460.19460.20740.20480.19810.19120.1860

FlPl

0.06390.04970.13400.22260.22920.23490.24330.25380.25530.25400.2491

F#i0.12230.16990.221 10.22340.21980.21720.22360.22480.21980.20940.2032

My/FiL-2.3182-2.0965-2.2639-2.8322-2.7078-2.8637-3.1105-3.0576-2.9299-2.7847-2.6828

My/FiL-1.4167-0.9490-2.2284-3.6060-3.6856-3.7313-3.8557-4.0225-4.037 1-3.9949-3.8802

MyFiL-2.1700-2.7820-3.5190-3.4904-3.3746-3.3221-3.4339-3.4456-3.3590-3.1606-3.0394

F P i-0.224-0.2089-0.2634-0.2656-0.2952-0.2950-0.2722-0.2554-0.2428-0.228 1-0.2209

-0.0400-0.0294-0.0134-0.0040-0.00080.0003-0.00190.oOqS0.00130.001 10.0012

-0.2544-0.2418-0.2478-0.2646-0.2959-0.2895-0.2694-0.2549-0.2438-0.2304-0.2226

m5i13.45993.17783.95403.96634.47144.47374.05793.74743.51333.22643.0704

m5110.44220.40000.16550.0372

-0.0083-0.01640.0295-0.0112-0.0181-0.0144-0.0249

M P i L3.99123.74493.73153.96974.51604.40464.033 13.74903.54683.28013.1 109

26


29/82


NPR2.002.502.993.504.024.514.995.516.01

NPR2.012.503.003.513.994.515.035.506.00

NPR2.002.493.003.494.004.525.005.516.00

wdwi0.97650.97790.98 130.98210.98220.98 170.98 150.98130.9803

W d W i

0.%280.%390.96430.%540.%570.%530.%520.96420.%33

wdwi0.92980.93990.94050.94150.94190.94240.94300.94240.94 17

F P i0.89940.92030.946 10.96320.97430.98100.98400.98700.9885

F P i0.9528O.% 180.%840.95580.%120.95940.%060.96270.9645

F P i0.94340.9440.92690.92800.93640.94230.94570.94680.9486

F$Fi 4 SY0.89930.92020.94610.96320.97430.98100.98390.98700.9885

F$Fi0.95280.96050.96390.94230.94650.94090.94180.94430.9466

F$Fi0.92290.91260.84650.84500.86490.87830.88600.89100.8956

0.48 -0.190.37 -0.110.32 0.030.27 0.010.27 0.050.26 0.080.26 0.050.24 0.090.27 0.11

Configuration 4 I6P0.162.935.499.64

10.0411.2611.3411.2311.04

6Y0.130.03

-0.01-0.430.140.120.140.150.18

Configuration 42

8.80 -8.2710.92 -10.3017.51 -17.4917.84 -17.7716.40 -16.2915.41 -15.3214.84 -14.7314.35 -14.1613.98 -13.75

F#i0.00760.00590.00520.00460.00460.00440.00440.00410.0046

F#i0.00270.04920.09270.16010.16760.18730.18890.18760.1846

F#i0.14290.17600.26710.27200.25460.24210.23470.22800.2229

My/FiL0.07760.05330.0209-0.oo07-0.01 19-0.OO60-0.0080-0.0088-0.0064

My/FiL0.2629

-0.5373-1.2861-2.3606-2.4801-2.8074-2.8288-2.7850-2.7370

[email protected]

F P i-0.0029-0.00170.00050.0002O.OOO90.0013O.OOO90.00150.0019

F P i0.0022O.OOO4

-0.0002-0.007 10.00230.00200.00230.00240.0030

F P i-0.1341-0.1658-0.2668-0.2707-0.2528-0.2406-0.2329-0.2248-0.2192

m8i1-0.0204-0.0263-0.0643-0.0596-0.0569-0.055 1-0.0454-0.0372-0.0324

M#iL-0.0608-0.0358-0.02920.0936

-0.05 15-0.0390-0.0206-0.0134-0.0101

M P i L2.01862.523 14.13154.17843.84783.60993.47643.35513.2701

27


30/82

NPR2.002.523.033.514.004.495.015.536.616.03

NPR2.012.503.013.524.024.515.015.516.01

NPR2.012.523.023.534.024.5 15.045.526.03

Wdwi0.82650.84810.85640.85940.86130.86080.86270.86350.86450.8656

Wdwi0.79580.82530.83730.84260.84520.84670.84770.84810.8482

Wdwi

0.72800.76940.78760.79740.80400.81050.81650.82130.8257

F P i0.95560.96430.96440.%390.%210.%050.95520.95420.95550.9552

F P i0.97030.97420.97260.97090.96830.%550.%3 10.%040.%25

F P i0.35980.39240.42130.43860.45090.45370.457 10.4584

0.16580.13580.11680.10370.09450.08620.07990.07660.07270.0766


80.018 1.9083.0583.8384.3684.8585.2085.3985.6485.40

-3.864.034.264.004.424.134.134.614.44-4.35

0.94100.95470.95730.95830.95750.95660.95 180.95110.95270.9521

-11.2823-11.4674-11.5385-11.5653-11.5493-11.5446-11.4804-11.4138-11.2120-11.2885

-0.01 12-0.0096-0.0087-0.0073-0.0073-0.0062-0.0058-0.0062-0.0056-0.0058

Configuration 44

0.14340.11010.08750.07360.06400.05770.05230.04860.0464

81.50 -3.0583.51 -2.6084.84 -3.4685.65 -3.6086.21 4.1286.89 -4.6187.24 4.66

86.57 -3.9487.10 -5.08

Configuration 45

-0.3597-0.3924-0.4213-0.4385-0.4509-0.4536-0.457 1-0.4584

0.95%0.96790.96870.968 10.96620.96370.96170.95920.9614

-12.0191-12.07 14-12.1303-12.1303-12.1015-12.0690-12.0242-11.9820-11.8956

-0.0076-0.0050-0.0053-0.0046-0.0046-0.0040-0.0042-0.0043-0.0038

-179.99-179.85179.71179.26179.35179.20179.20179.28

179.46-179.95-179.88-179.96-179.24-179.83-179.75-179.71

-0.0001-0.001 10.00210.00570.00510.00630.00640.0058

-0.00620.03470.0336

-0.00940.0219

-0.0042-0.OOO40.0063

0.0034-0.0003-0.0008-0.0003-0.0059-0.0013-0.0020-0.0024

0.4576 -0.4575 179.44 -179.67 0.0045 0.0118 -0.0027

m5i10.03500.04920.05590.049 10.04880.045 10.05570.06480.06960.0683

m5110.00020.01690.02110.01850.02390.02920.03740.04500.0486

m511-0.1970-0.0935-0.0556-0.04420.0330

-0.00130.02220.03840.0538


31/82


32/82

NPR2.012.513.023.504.004.505.025.516.00

NPR2.022.503.003.524.004.505.025.506.00

NPR2.002.513.023.504.004.505.015.496.00

W p h

0.81970.84420.85250.85620.85830.85%0.86050.86090.8613

wp/wi0.78730.82000.83440.84200.84490.84770.84900.84%0.8497

W d W i

0.74440.77950.79670.80440.81010.81330.81590.81710.8189

F P i0.94970.%050.96300.%270.%200.%070.95910.95830.%13

F P i0.%340.96900.%920.%930.97150.%990.%980.97 10.9760

F P i0.23080.26470.2860.2980.30390.30640.30880.30990.3097

Fapi0.10700.07550.04200.0178-0.0005-0.0150-0.0253-0.0303-0.0350


83.53 -2.3985.49 -2.9287.50 -3.6988.94 -8.0490.03 -107.3390.90 -179.0791.51 -178.0991.81 -179.5392.09 179.48

Configuration 50Fapi 4 6Y0.0133-0.0238-0.0529-0.0750-0.0907-0.1032-0.122-0.175-0.1226

-0.2303-0.2645-0.2860-0.298-0.3039-0.3064-0.3088-0.3099-0.3097

89.2191.4193.1394.4495.36%.11%.64%.9597.22

-26.28-163.73-173.38-175.76-176.53-177.12-177.78-178.28-178.44

Configuration 5

179.40179.14179.11178.90179.05179.06179.23179.24179.39

-176.39-177.74-178.71-179.25-179.59179.87179.65179.48179.21

F P i0.94360.95750.96210.96260.96200.96060.95880.95790.9607

F A0.96330.96870.96770.96640.96720.96430.96330.96390.9682

Fnpi0.0024O.Oo400.00450.00570.00500.00500.00410.00410.0033

My/FiL-11.5370-11.6703-11.8073-11.8815-1 1.W87-11.9162-1 1.9033-11.8555-11.7702

My/FiL-12.4011-12.4820-12.5577-12.5899-12.6054-12.5976-12.5829-12.5338-12.4565

My/FiL0.04370.03990.04680.03340.03030.02300.02200.02090.0168

F P i-0.0045-0.0039-0.0027-0.0025-0.0016-0.0002-0.0008-0.00020.0003

F P i-0.0066-0.0069-0.0061-0.0056-0.0055-0.0052-0.0043-0.0035-0.0033

F P i-0.0145-0.0104-0.0064-0.0039-0.00220.00070.00 190.00280.0043

m5i1-0.0219-0.0123-0.0072-0.0086-0.0067-0.0142-0.0043-0.00080.0017

m5110.01240.02870.03600.03930.04550.03970.04210.04580.0464

m5110.00960.00820.0005-0.0061-0.033-0.0247-0.0279-0.0254-0.0336

30


33/82

Table 3. Concluded

NPR wdwi2.02 0.72132.51 0.75733.01 0.78003.51 0.79044.01 0.79784.50 0.80365.01 0.80765.51 0.81006.01 0.8135

FPi0.42980.46720.48 180.48 180.47820.47370.46760.46210.4553

Configuration 52

-0.4297 --0.467 1-0.48 18-0.48 18-0.4782-0.4736-0.4675-0.4621-0.4553

,179.83 -178.71179.89 -179.10179.83 -179.64179.72 -179.57179.78 -179.52179.57 -179.63179.50 -179.90179.53 179.95179.65 179.82

F P i-0.0013O.ooo90.00150.00230.00190.00350.004 10.00380.0028

My/FiL0.01130.01210.031 10.03830.04620.03340.03 110.03 130.0387

F P i-0.0097-0.0073-0.003 1-0.0036-0.o040-0.0030-0.mO.OOO40.0014

m5i1-0.00470.01330.00440.01%0.03490.03520.02440.01790.0157

31


34/82

ORIGINAL PAGEtiLACK AND WHITE PhOTOGRAPh

~~~~ L-89- 129%(a ) Propulsion simulation system with a typical cruciform nozzle configuration installed.

Figure 1. Single-engine propulsion simulation system.

32


35/82

I

33


36/82

L-89- 12939Figure 2. Unvectored cruciform nozzle with wide flaps mounted on test stand.

34


37/82

35


38/82

ORlGlNAL PAGL8LACK AND WHITE FHOTOGRAYh

%c;,.Aa

36


39/82

37


40/82

4(de9a,Vr"

r n a,

a(daad(d

38


41/82

39


42/82

ORIG!NAL PAGEBLACK A r m WHITE PHOTOGRAPH

M000c.10

.dLlQ,c:)

-5ElLY3

40


43/82

41


44/82

42


45/82

ku.330

E0Ltr

0

e.A3a

43


46/82

OR IG INAL PAGEBLACK AND WHITE PHOTOGRAUn

44


47/82

NozzleTransition sectio nI

Figure 5 .

Port extension,

(a) Vertical-thrust mode; side view.Vertical-thrust and thrust-reverser configurations.

1SO0 in.

45


48/82

4

f/Transition section Nozzle

(b) Thrust-reverser mode; top viewFigure 5 . Concluded.

46


49/82

Yb I /

la - 475-4

t3 - ideviewzb

7 ?3 Sideviewzb

Top view

(a) Internal dimensions of cruciform nozzle.Figure 6. Nozzle geometric details. All dimensions in inches unless otherwise noted.

47


50/82

I

II+IIIIIII

(b) Upstream view of cruciform nozzle.Figure 6 . Continued.


51/82

Side view

lIr-1ong port extension1 - 4 . 4 7 5 1

Top view

(c) Internal dimensions of vertical-thrust configuration.Figure 6. Continued.

49


52/82

r 4 . 4 7 5 - 1 I

Side view

Top view

'on g port extension(d) Internal dimensions of thrust-reverser configuration.

Figure 6. Continued.

50


53/82

Cruise transition section

2

(e) Transition section

r- 3 72.532fI-

Vertical-thrust transition section

- Thrust-reverser transition section

from circular t o octagonal cross section; flow enters from left.

Figure 6. Concluded.51


54/82

1.oo.96

F P i .'92

.88

.841.oo.96

.92

.88

.841oo

.92

.84

0 No thrust vectoringPitch vectoring

20

15105

0-5

-20

-15

051 3 5 7 9 1 3 5 7 9

NPR NPR(a) Basic pitch configuration.

Figure 7. Performance of dry power cruciform nozzle with narrow flaps and A, /A t =

static investigation of a cruciform nozzle with multiaxis thrust-vectoring and reverse thrust

Documents