Characteristics of a rectangular wing with a peripheral jet in ground effect. Part III

•

CHARACTERISTICS OF A RECTANGULAR WING WITH A PERIPHERAL JET IN GROUND EFFECT, PART III

by

D. SURRY

ACKNOWLEDGEMENTS

The author wishes to express his gratitude to Dr. G .. N.

Patterson for the opportunity to carry out this research at the U. T. 1. A. S. The project was initiated and supervised by Professor B. Etkin, to whom the author is particularly indebted. The ideas and under-standing generated by many discussions with Professor Etkin are deeply appreciated.

Thanks also go to Mr. Karl Dau and Mr. Bruce Gowans for their help with this research.

The work was made possible through the joint financial support of the Defence Research Board and National Research Council of Canada, and the United States Air Force through contract No. AF-33(657)-8451 of the Control Criteria Branch, Flight Control Division, Air Force

SUMMARY

Lift, qrag, and pitching moment were measured on a rec-tangular wing with a peripheral jet in ground effect for three angles of attack, three heights above ground, and for a range of forward speeds necessary for take-off calculations. Furthermore, nine configurations were tested in this fashion - each with different jet angles and different ratios of L. E. to T. E. jet strengths. Wherever possible, procedures were automated and on-line data reduction was used. Some flow visualiza-tion tests were made on specific configuravisualiza-tions .

The results were used to study an integrated lift and pro-pulsion system for air-cushion take-off and landing. These calculations showed little advantage to be gained from using variabie jet strengths and angles during take-off at constant height when compared to fixed configura-tion results. The latter used angle of attack, or diversion ofthrust from the cushion to direct forward thrust as means for keeping the height con-stant. A simple take-off procedure in which the height is allowed to in-crease naturally, led to slightly poorer results, but all the take -off pro-cedures studied provided short-field performance.

TABLE OF CONTENTS

Page

NOTATION vi

1. INTRODUCTION 1

11. EXPERIMENTAL APPROACH 1

III. DESCRIPTION OF APPARA TUS 4

3. 1 Force and Pressure Measurements 4

3.2 Output Data 5

3.3 The Wing 5

3.4 Jet Air Supply 5

3.5 Automatic Traversing Gear 5

IV. EXPERIMENTAL PROCEDURE 7

4. 1 Jet Momentum Flux 7

4.2 Description of Configurations Tested 10

4.3 Wind Tunnel Tests 10

4.4 Flow Visualization Tests 10

V. REDUCTION OF DATA 10

5. 1 Inlet Forces 10

5. 2 Presentation of Results 11

5.3 Definition of q

Iq.

'

11

J

VI. DISCUSSION OF RESULTS 12

6. 1 Hovering Cases 12

6.2 Je:t Flap Cases 13

6.3 Intermediate Cases 14

6.4 Experimental Error 15

VII. APPLICATION OF RESULTS TO TAKE-OFF PERFORM- 15 ANCE - PHASE I, ACCELERATION

7.1 Case 1 16 7.2 Case 2 17 7.3 Case 3 17 9 7.4 Case 4 18 7.5 Case 5 19 7.6' Comparison of. Cases 19 J

VIII. TAKE-OFF PERFORMANCE --PhaseS Il and III 20

8. 1 Phase lIl, Climb-out 20

8.2 Phase II - Transition to Climb-out 21

IX. CONCL USIONS REFERENCES FIGURES

24 25

a al , f

,

1f

A· ₁ A· J c

c

D e g h hl I NOTATION acceleration

functions - see text inlet area of wing

true area of peripheral slot

arbitrary area of peripheral slot:: 5.50 ins. 2 aspect ratio

chord length configuration

lift coefficient ::

L/

qS drag coefficient :: D / qS

pitching moment coefficient - M / qSc

thrust coefficient :: T / qS blowing coefficient :: J / qS

drag ::-T

momentum drag

voltage (species defined by subscript) acceleration due to gravity

height of wing above ground measured from the bottom surface at mid-chord

height of wing above ground measured from the line parallel to the chord line joining the two jet exits; hl :: h

+ .

15 ins. (due to cambered bottom of wing)

j J J 1 J 2 J 3 J D JT J. 1 k, k 1, k 2 K

""'

WEL

.t

L . Mc/2 m n Pi PG q q. J

jet momentum flux per unit slot length in the plane normal to both the wing and the peripheral slot;

j = 2

J:j

cos2

,p

dx

o

total outlet jet momentum flux, in the plane normal to both the wing and the peripheral slot. J

=

J1

+

J2

+

J3

L. E. momentum flux T. E. momentum flux total tip momentum flux

momentum flux used for direct thrust

total vehicle rnomentum flux

=

J

+

J_D

total inlet jet momentum flux

constants of proportionality - see text true loss factor for wing as defined in text estimated loss factor for wing

total length of the peripheral slot

total lift (experimental inlet forces have been corrected for)

pitching moment about mid-chord jet mass flow

load factor

=

L / W

ave rage static pressure at the air inlet

g~uge pressure upstream of ejector which controls inlet conditions to wing and hence J

pressure difference obtained from

~-sens

in

g

holes in the traversing gear probe indicating a

bep

dynamic press ure of free stream

dynamic pressure at the centre of the air inlet

... qjmax q. J qjE q/q.l J Rl R2 R3 R s S T t

x

x Xl y

w

w

v

_J

·

..

maximum dynamic pressure at the peripheral slot at a partic ular s

ave rage dynamic pressure at the peripheral slot

qj

=

~.

qj cos 2

cjJ

(s) (dAj/Aj)

=

J /2Aj

J_ _

estimated qj using ~E; qjE = Pi - qic (KE - 1)

a parameter proportional to Cf' using qj defined with

Aj = Aj'

ground run distance to accelerate to any poinLor qS/JT

. horizontal distance required for Phase II

horizontal distance required for Phase III

total horizontal distance required to clear 50 ft

=

Rl

+

R2

+

R3

spanwise distance along the peripheral slot (arbitary zero) wing area

thrust (horizontal force in forward direction of an integrated

propulsion configuration). T

=

TT

-(TD -

D

_MoM)

total thrust (total horizontal force in forward direction) direct thrust as provicled by a separate propulsion unit time

slot width measured perpendicularly to jet sheet

distance to a point in the jet measured perpendicularly to the jet sheet from an arbitrary zero.

distance to a point in the jet parallel to wing chord line height above slot

weight

wing loading W / S.

jet exit velocity free stream velocity

Subscripts 1

2

angle of attack (geometrie)

jet sheet exit angle measured from the norm al to the chord line and positive in the rearward direction (see Fig. 7) local jet exit angle in the plane of the jet sheet (see Fig. 7)

angle of misalignment between the probe and the flow in the ~ direction

air mass density

deflection angle for jet flap measured from wing plane;

b

=

90 -

6;2.

computer sealing constants eonfiguration parameter

climb angle relative to horizontal

L

.

Eo}

_{unless otherwise defined}

1. INTRODUCTION

The potentialities of the GETOL (Ground Effect Take -Off and Landing) concept have been investigated to some extent (Refs. 8 to 11); however, no firm conclusions as to its feasibility have been reached. An aircraft using GETOL would be equipped with a peripheral jet issuing from the under surface of the wing, which would replace the conventional under-carriage as a means of support. As the take-off proceeds, the peripheral jet distribution could be altered so as to produce more thrust at the

ex-pense of 'cushion lift', since an increasing proportion of the aircraft

weight can be supported by 'natural' wing lift.

It is the aim of the present work to provide a more

definit-ive assessment of the aerodynamic aspects of the GETOL concept. This report continues the study of the basic performance and stability

charact-eristics of a representative GETOL wing (rectangular, AR

=

4) made by

Dau (Ref. 1) and Davis (Ref. 2) and previously published as Parts land II. Much of the analysis used here was initiated in these reports. In particu-lar, Part II provided a preliminary estimate of the take-off distance re-quired by a GETOL vehicle using the test wing and subject to the limitations provided by the extent of the available data, which was obtained for only two configurations. They were

Test 1. Test 2.

h=h

j1 =

h

e l

=

e2

=

0 91

=

62

=

300

Neither configuration appeared especially suited for take-off, and so the approach of Part III was to carry out an experimental pro-gram designed to exploit the advantages of a combined lifting and propulsive system.

1I. EXPERIMENT AL APPROACH

Since this research effort was primarily intended to examine the possibility of using the 'cushion' as an integrated lift and propulsion system for take-off, it is thought ne.cessary at this point to explain in gen-eral terms the expected method of analysis, for the experimental program reflects this approach.

Firstly, for ease of reference, a take -off can be divided into three distinct phases. Phase I consists of the ground run, Phase Il is the transition from ground run to climb and Phase III is the steady climb to a required height - say fifty feet. Of course, these separations are

somewhat arbitrary as, in general, the height of the vehicle could be

allowed to increase throughout the take-off. This report is mainly con-cerned with Phase I under the conditions outlined below.

The non-dimensional aerodynamic parameters of interest,

such as LIJ, TIJ _{etc. (sayÎl i )} can be thought of as functions of the

follow-ing form

11·

₁

=

11':

₁

In particular, for Phase I we impose the condition of L = W, and we

de-sire that the thrust be maximized for all points on the best take-off run.

It is clear that a true optimization over all variables would

require an extremely extensive test program, and would not necessarily

lead to physically desirable results. That is, some parameters rnay be

predetermined, and their non-optimization justified by the gain in

sim-licity of the final system. It is in this light that the following program was

proposed.

Phase I was considered to take place with height, angle of

attack and total installed thrust all held constant; and was considered to

progress from an initial hovering condition through various intermediate

configurations determined by best acceleration to a final state capable of

transition to flight independent of ground proximity. Variation of angle of

attack was prohibited because of the inherent decrease in ground clearance,

and constant height was maintained for best efficiency (see section 6).

Also, the leading edge jet angle was not disturbed from its value during

hovering (gl~ 300 ). Steady climb (Phase lIl) would utilize a jet flap.

Both of the terminal states (the initial ground cushion and the jet flap)

were predetermined on the basis of existing knowledge to give good

per-formance.

Thus, we may now write for Phase I,

1I

i

=

lI

i (qS/J; 2Aj/S, JJ./J2,

9

2 )

=

Îl

_i (qSI J,

JA-

)

where){ is a configuration parameter, indicating a particular set of

(2Aj I S, J 1 IJ 2'

e

2).

The end conditions are:

hovering: qs/J

=

0

jet flap:

Since the hovering case is predetermined, then for 0(

=

constant we have

the common augmentation curve

LIJ

=

LIJ (h Ic, A· IS)

=

WiJ

Thus, the choosing of a height during the take-off run deter-mines the initial proportion of thrust taken by the cushion, the remainder being used as direct thrust.

Since the criterion for best take-off distance under the above conditions is maximum acceleration at any point or velocity along the path,

then the. best performance occurs when T

Iw

is maximized at all points

during Phase 1. The actual distance is also influenced by the speed which

the vehic1e must be accelerated to in order to make the required transition

to Phase III - i. e.

(qS/J)T.O. -

but th is is independent of the optimization

of the acceleration previous to this. This assumes that the end point is

not fixed - i. e., if necessary, at transition speed, a step change can be

made to the configuration required for Phase 11. Thus, a plot of shortest

distance for Phase I as a function of transition speed can be produced.

The acceleration at a. point is given by

,

alg

=

TT/w

=

TD/W+ T/w -

Droom

Iw

=

JD/W

+(J

IW)(T IJ) -

(JT

IW)(Dmom I

JT)

(1)

Now, assuming that the forward propulsive and jet curtain air is exhaust-ed at the same speexhaust-ed.

(2)

then if there are no changes in the jet exit velocity, the momentum drag

would be dependent only on the forward velocity of the vehicle. i. e. a

con-stant at a given point. Thus the maximization of lal requires maximization of

al _JD J T

- - -

+

-g

under the conditions

W W J

=~G

J 1 -JT

=

ga.

(J:'

;)=

al g 0(

=

constant

=

0

JT/W

=

constant h/c

=

constant

:

~

(qS

f)

J '

6

₁

=

constant

=

300 J

T

= J + JD

LIJ =(W/JT)(JT/J)

(3 )

(4)

(5)

sec-11fum. 7. Thus, ideally, to study this restricteà optimization, we require

experimentally TIJ and LI J as functions of qSI J and

JL

In this work, 9 configurations we're examined in detail.

Each was to some extent an intuitive choice based on the scheme sketched

in Fig. 1. However, the testing of one configuration (value off'-) also

helped to indicate the choice of the next. No systematic variation of

J-L

due to varying 2Aj

Is

alone was carried out.

,

Figure 1 shows that from an initial hovering condition, the

rear jet is slowly strengthened and is diverted rearward as the take-off

proceeds until a speed is reached at which transition to Phase II is possible.

The details of the transition are not shown in the sketch, but are discussed

in Section 8. It leads to a steady climb using a jet flap arrangement.

Al-so, throughout the take-off, some of thrust may be used as an

independ-ent source of propulsion. This is not shown in the sketch.

IIl. DESCRIPTION OF APP ARA TUS

The development and initial testing of the wing was

report-ed in Ref. 1. However, several changes in the data reduction system

were incorporated due to the number of configurations proposed. Both. for

convenience and continuity, a brief discus sion of the apparatus and

pro-cedure retained from parts land II will be included here.

3.1 Force and Pressure Measurements

The wing was tested using the UTIAS subsonic wind

tunnel (0-200 ft. sec.). The present tests initiated the use of a new

electronics system which was incorporated to tq.ke advantage of the on

line data reduction capability of a Pace analogue computer recently

in-stalled in the subsonic laboratory .

The aerodynamic forces on the wing were measured on a

six-component balance using flat steel springs, whose deflections are

converted into voltage signals by differential tr~nsformers. The

excita-tion for the differential transformers and the necessary demodulation

and amplification of the error signals is provided by transistorized

de-modulators, whose filtered outputs are transmitted directly to the

analo-gue computer.

Pressure signals are also converted to electrical signals

thröugh the use of strain gauge pressure transducers and suitable high

ga in amplification systems. The initial two hovering configurations were

tested using high gain amplification obtained by increasing the feedback impedance of the standard an.alogue amplifiers to provide gains of 3000.

This resulted in a noisy signal which requi!'ed heavy filtering with the

associated penalties placed on response time. In all of the remaining

tests, Offner high gain, high stability D. C. amplifiers were used which

~.

eliminated the disadvantages of the previous system. 3.2 Output Data

. The output data was produced in final coefficient form and was recorded in two ways.

For the first two configurations (hovering), the outputs were plotted against time using an x-y plotter. For all other configurations, which required runs at different tunnel speeds, the outputs were recorded simultaneously using five channels of a Honeywell light-spot galvanometer recorder.

3.3 The Wing

The mechanical details of the wing are shown in Fig. 2. Figure 3 is a schema tic cross - section of the blowing wing as installed in the wind tunnel. The ground board extended

17

ins. in front of the L.E. and 23" beind the T. E. of the wing. Figure 4 is a photo of the wing mount-ed upside down on the preliminary test stand.

The dimensions of the wing are as follows: Planform Span Chord AR Profile Length of either L. E. or T.E. slot

Length of either tip slot Area of inlet to wing The outlet area ratio. varied in each test. the jet was. 10 ins.

3. 4 Jet Air Supply

rectangular 25 ins. 6 ins.

4.17

NACA 0015 24.5 ins. 5.70 ins. 6.79 ins. 2

The approximate thickness of

Low pressuTe high speed air from an ejector (ReL 3) is directed through the central air supply tube into the hollow wing and ejected through the peripheral slot (see Fig. 3). The jet exit speeds pro-duced were of the same order of magnitude as the maximum tunnel speed. 3.5 Automatic Traversing Gear

For each configuration tested the momentum flux as a function of the inlet conditions is required. Also, a knowledge of the uni-formity of the jet sheet is desired: The momentum flux determination

required approximately sixty total head traverses across the slot for each configuration, as explained in detail in Refs. 1 and 2. To simplify the measurement of the outlet momentum flow, an automatic traversing ge ar

system (see Fig. 3) was developed. An electric motor drives a probe through the jet at variable rates of traverse (approxirnately 40 to 300 secs.

per inch). The maximum traversable distance is 1. 25". The displace-ment is converted in to an electrical output by means of a 15 turn potentio

-meter coupled'directly to the drive shaft. The dynamic pressure in the jet is measured continuously by means of a pressure transducer. Thus, two signals are available to the analogue computer:

Since the momentum flux per unit length (in the plane nor-mal to both the wing and the peripheral slot) is

then j

=

2

jX

q. cos2

1J

dx J

X

= 2

C;8

2

cp

i

qj dx (if cos ~

~:

dx--- j Xeq: de_x

~q

0 J

is constant through the

jet)

Since the computer integrates with respect to time only, cuit (Fig. 5) generates the expression

,the analogue cir

-f

:q.

d;; dt

o

J

The outputs obtained directly are a num erical value of

j/qji: and an x-y plot of the non-dimensional dynamic pressure profile,

qj / qjE' A conservative estirnate of the accuracy of the analogue system

is aoout 2%, as found by comparing the numerical integral provided by the circuit and an area integration of the plotted pressure profile, assuming

the latter perfect.

The probe is mounted so that its tip is both at the centre of

its circular arc guide and also on the axis of its supporting shaft. This allows rotation of the probe about two axes with negligible motion of the probe tip. The complete traversing gear can be moved by hand to the per

i-pheral jet station of interest by means of the steel guide rails seen in Fig. 3.

. ,

IV. EXPERIMENT AL PROCEDURE 4. 1 Jet Momentum Flux

As mentioned in Refs. 1 and 2, it is thought that the

varia-tion of momentum flux per unit 'slot length has a considerable effect on the

wing behaviour. In order to examine the flow in the jet more c1osely, a new 5-hole probe was designed (Fig. 6) which would serve to measure both

the angles ~ and 9 (defined in Fig. 7), and the total head present at any

point in the peripheral jet. Because of the steep gradients existing in the dynamic pressure profile, the centre 'hole' was made a slit .007 ins. wide

to minimize the 'dx' over which the probe averages.

The probe alignment for zero pressure differential - i. e.

the zero errors- for the ~ and 9 angle sensors was found by calibrating

the probe in the wind tunnel air stream. It should be noted that care must

be taken in interpreting a null on a probe of this type since the probe is

only aligned with the flow at a null reading if there is negligible velocity

gradient (rigorously, total pressure gradient) between the two angle

sens-ing holes. This is the case for ~ as is shown in Fig. 8 which shows

the maximum non-dimensional dynamic pressure* versus s as taken from

the plotted jet profiles for configuration 1. The distance between the

q;

or 9 sensing holes on the probe is approximately 1/16 in. From Fig. 8,

the wave-Iength characteristic of the fluctuation in total pressure with s is at least an order of magnitude larger) as would be expected. However, the jet profiles obtained (see Fig. 9) indicate that generally this

assump-tion is questionabl~ for 9 measurements, considering that the probe size

is an appreciabIe fraction of the jet width.

Consequently, the probe was not directly used for the angle measurement. Instead, the probé was aligned carefully by eye with a tuft held in the flow (out of the probe's region of influence). In this

manner the probe acted merely as a convenient protractor. The

q;-

sensi-tivity of the probe enabled angles to beobtained to~~ 0 at the point of

maxi-mum dynamic pressure. The tuft measurement was estimated as accurate

to ~2°. Due to the very narrow slit opening, the total pressure probe's

response time was of the order of 5 secs. to 980/0 of true value when

sub-jected to a step input. This characteristic is showr.. in Fig. 10

accom-panied by two other traces indicating the response time of the associated

pressure and electronics system omitting only the probe, and of the electronics system alone. This large response time required compara-tively slow rates of traverse to be used (approx. 100 secs. /inch), although the major effect of speeding the traverse was only a distortion of the plott-ed profile. The numerical value of the integral was relatively unaffectplott-ed

*

Note: that in plots where the ordinates are j / qjE or equivalent, no

num-erical values are given although strict proportionality is maintained graphically.

due to the near syrnrnetry of the true profiles. This effect can be seen in Fig. 11. Figure lla shows profiles obtained frorn the tip jet. The tips dis-played an alrnost perfect square jet profile when exarnined close to the jet

exist. (This was not the case for leading and trailing edge jets - see Fig.

9). Also presented (Fig. 11b) are normalized values of the momenturn

integral I(X) plotted versus traversing rate. The effect of rate is seen to

be of the order of ~%. This also acts as a check on repeatability since six

runs are invol ved.

In addition, the decay in the value of I(X) obtained with in-creasing height of the probe above the slot was exarnined. A plot of nor-malized integral values versus height of the traverse above the slot is

shown ~n Fig. 12b accornpanied, by the decay in the shape of the associated

tip jet profile (Fig. 12a). The severe gradients in the tip jets provided a conservative test (note that the inboard edge of the jet is more ragged than the outboard edge due to the jet not completely filling the slot). Figure 12 shows that for working heights of about 1/8 ins. above the jet exit, up to 4% error can be introduced.

The calibration of a given con~iguration consisted of dete~­

rnining the component of the total outlet momenturn flux in the plane nor-mal to both the wing and slot as a function of the inlet conditions Pi and qic

In the experimental procedure, the form of f(Pi' qic) was

assurned and used to delete any effects of changes of inlet conditions on J

by

dividing the inst:ntaneous

=valu[e~

: : : : :

Ij

X

qj

dx ds

f( Pi' qic) f( Pi, qic

o 0

This definition of JassUllles that 9 and

~

variation at any

station is neglibible - i. e. that they are only functions of s, and not of x.

. The 5 - hole probe used with the traversing gear enabled

this· assumption to be checkedfor

~

as follows. The probe was aligned

with the flow at a particular station (i. e. frorn rneasured values

ot

9 and

r/;

for tue central region of the jet) and then a traverse was made in which

.L1 PlP / qj was plotted against Xl. The calibration of 6. p

P /

qj versus

ö.tj;

was done in the central region of the jet for several values of blowing

pressure .. It was found to be approxirnately linear and independent of qj'

The results obtained for typical trailing edge and t~p stations are shown in

Fig. 13. The change in

rj;

through the major part of the jet is of the

order of 50 . These angle deviations cause negligible change in the dynarnic

pressure integral if the probe is set approxirnately at the mean angle

be-cause of the insensitivity of the total head probe to m isalignrn ent. Figure

5 and ~Oo respectively. Similar results are obtained for 9 misalignments. The form of the function f(pi, qic) used to nondimensionalize

qj and J was changed between configurations Il and lIl. In Refs . .1 and -2

and for the two hovering cases presented here, f = qic' and this appears

adequate for the jet distributions of these tests. However it was found that for the higher internal losses associated with the jet flap cases, J / qic

was -no longer independent of qic~ Figure 15a shows qj/qic at a particular

point in the peripheral jet as a function of PC (Pa is a gauge pressure

up-~tream of the ejector, and hence controls qic). Since qj

=

J/2Aj and

qj

=

k2qj (k2 is a function of position in the jet), then the ratio qj / qic at a

point is proportional tq J /qic. The working range shown in Fig. 15 is that used over all configurations. For any particular test, Pa was controlled

to within

:t

2 psi of the desired pressure. The failure of the assumption

f

=

qic in this te~t led to the use of f = qj instead. To find this function,

the assumption was made that the loss factor K for the internal flow in a

given configuration is constant, i. e.

K

=

loss in total pressure between inlet and outlet

representative dynamic pressure

=

Pi

+

qic - qj

qic

Thus, f(p. q- )

=

q--

=

p- - q- (K - 1)

l' IC J I 1C '

K is also plotted for configuration III in Fig. 15b and is seen to be virtually

constant for the range of blowing pressures used. Similar plots are shown in Fig. 16 for configuration 5 which has a jet distribution similar to those

'\ used in early tests. Here it can be seen th at the loss factor concept bears

little advantage over the assumption of constant qj / qic.

Since qj = J /2Aj determines K, and J is unknown during

calibration, then the best available form of f(Pi, qic) during the initial

cali-bration is that using an estimated value of K = KE based on previous

con-figurations. During tunnel running the trl.{e value of K was used. It was

found as follows. The calibration supplied kiE

=

J /qjE from which a value

of J was determined by using an average value of qjE corresponding to an average set of (Pi. qic) which were monitored throughout the calibration. (They remained virtually constant). The value of J so obtained provided

an accurate value for. qj and hence k2. Then a series of values of K were

calculated as a function of pa from

K

=

Pi

+

1 - k 2 _J q'

qic qic

Figure 15b shows such arelation. The value of K used during tunnel test-ing was that correspondtest-ing to the Pa used in the test.

Note that the inlet conditions were held virtually constant during a given test. and that if no change in inlet conditions occurred the

4. 2 Description of Configurations Tested

Nine configurations in all were tested. Two of these were similar hovering cases differing only in momentum flux distribution. They are all detailed in Fig 17 which records J 1

IJ

2, 92, 2Aj

Is,

etc. for each test.

In some cases with the wing blowing into free air on the cali-bration rig, parts of the jet sheet would attach to the undersurface of the wing - particularly the centre T.E. for the hovering cases, and the centre and tips of the L. E. when J 1 was smal!. To obtain calibrations in these cases it was necessary to use a ground board on the calibration stand, the supports for which are shown in Fig. 3. An end view of the wing while us-ing this technique is shown in Fig. 18 The centre wedge was used to pre-vent cross flows and thus compensate for the inability to use smaller wing-to-board distances because of the clearance required for the traversing gear. The effect of the internal cushion pressure and jet sheet angle change induced by the presence of the groundboard was negligible.

4. 3 Wind Tunnel Tests

Each configuration, after calibration, was tested in the wind tunnel. For the hovering cases,

LIJ, DIJ

,

M_c

l2lJ

o,

were recorded for various heights at zero wind speed. For the rernaining cases,

LIJ, DIJ,

M c /2/Jc, q,

q/ëi{

wer~recorded

simultaneously for three heights and a

continuous range of

q/qj

from zero to roughly .20. In this range of tunnel speeds (approx. 0 to 100 ft.

I

sec) the speed range is continuously variabie by means of a rheostat contro!. Thus, a run consisted merely of slowly decreasing the tunnel speedfrom the highestrequired while continuously re-cording the required data. The effect of the rate of change of tunnel speed on the tests is considered negligible, being of the order of O. 5 ft.

I

sec. 2 For all configurations, three angles of attack - 0 and

±

30 - were tested at each height.

4.4 Flow Visualization Tests

Extensive tuft studies were carried out for the first hover-ing configuration, with tufts on both the whover-ing and the ground board, and 'one on the end of a th in wire enabling arbitrary positions in the flow pattern ,to be appraised. These provided a qualitative understanding of the flow for

hl

c ~ 0, 1. Lampblack and kerosene flow visualization was done for the jet flap case. Examples of these are shown in Figs. 19, 20 and 21. The results of these tests are discussed in Section VI.

V. REDUCTION OF DATA

5. 1 Inlet Forces

..

wing have been removed as shown by the data reduction equations developed in Ref. 1 and which were also 4sed here.

The momentum drag associated with an actual aircraft in flight is estimated and included in conjunction with the take -off performance

calculations. It does not appear'in the recorded aerodynamic variables.

No corrections have been made for the interference effects of the tunnel walls, wing support struts, and air supply tube.

5.2 Presentation of Results

Two hovering cases were studied. The jet angle and

mo-mentum flux distributions are shown in Figs. 23 and 24. The aerodynamic

parameters are plotted as functions of non-dimensional height in Figs. 25

to 27.

All data obtained for the other configurations which were tested at forward speed was in the form of simultaneous five channel traces.

It was c~nverted. to x/y plots .of LIJ, .D/J, Mc/2/J~i a~d q versu.s

q/qj'.

To do thlS as qUlckly as posslble, pOllltS were copled dlrectly usmg

trans-l4/scent graph paper and a 'light box'. Due to the arbitrary form of the

re-sulting scales and zero lines, and to the large number and specialized nature of the curves, the results are not presentE1d in detail here. An

ex-ample is shown in Fig. 22. Since the particular take-off ca1culations

pre-sented in this paper deal extensive~y with only one height and angle of

attack, the relevant data for take-off performance is just TIJ, LIJ

=1i

i

(qS/J,.).l-)' These are presented in Figs. 28 and 29. The other data is

ava:j.lable and is being used for further work not presented here. When more than one run was taken for identical conditions, Figs. 28 and 29 re-prèsent the ave rage values obtained.

5.3 Definition of

q/qj'

Due to the variation of jet exit area from configuration to configuration that was required to change the momentum distribution, and because of the difficulty in measuring it - especially when the flow is re-stricted by a throat prior to the geometrical jet exit as was sometimes the case at the T .E. - it was decided to use a constant value for the exit area

in tl~e analogue computation of

q/qj.

The area chosen arbitrarily was

Aj' :: 5. 50 ins. 2 which corresponds to th at used in Ref. 1.

This means that

ql

qj' is actually a constant times

1/9-t

i. e.

To calculatethe true

q/qj

ratio, the true effective outlet areas, . Aj> were calculated ad hoc by means of a relation derived in Ref. 1

between the inlet and outlet normal momentum fluxes as Ai

J=1.05Ji A.

J

Ji is a known value, calibrated in terms of the inlet qic (see Ref. 1). Ai is

a geometrical constant and J is measured during calibration. The 1. 05

factor arises from consideration of the non-uniformities of the inlet and

outlet dynamic pressure distributions. Agreement between the value cal-culated by the above method and that geometrically measured for

configura-tion II (in which the jet exit area appeared geometrically defip.ed was

with-in 2%.

VI. DISCUSSION OF RESULTS

The results obtained for the limiting configurations - the hovering ground cushion and jet flap - offer a direct comparison with prior work.

6. 1 Hovering Cases

The

LIJ

curves for the hovering cases for

0<.

=

0 are com-pared in Fig. 30 with those obtained previously at UTIAS and with ideal thick jet theory. The experimental curves obtained here compare favour-ably. The effect of toeing in of the jets produces a substantial increase in lift over the results presented in Ref. 1 for h'

Ic

,/.2, but for h'

Ic

= .10 where the later take-off calculations were made, the present .cases give slightly poorer lift augmentations.

DIJ

vs. h'

Ic

results given for Cl and C2 in Fig. 26, show similar drag values for the two configurations, except that C2, due to a reduced T .E. toe-in angle and slightly altered momentum flux distribution, gives reduced drag values. The high drag recorded for both configurations

at rÁ

=

-3, and the associated high nose up moments seen in Fig. 27 may

be the result of the T. E. jet attaching to the bottom surface of the wing for part of the chord. The jet flow, on separation from the bottom surface, would form a stagnation point on the ground causing part of the T. E. jet to pass beneath the L. E. The resulting high pressure area at the L. E. and

low pressure at the T. E. would result in the nose up moment observed,

and the T. E. j et flow would c ontribute to the drag value. Som e tuft studie s (detailed later) indicated this type of flow regime.

The _{M/J c} results in Fig. 27 appear as.two curves for each

value of 0( , due to the existence of two alternative values of moment. 'A

typical record, Fig. 31, shows this double valued moment. Switching be-tween values occurred spontaneously, but could also be triggered off by de-flecting the rear jet slightly with a ruler. This result was attributed to changes in the degree of attachment of the rear jet to the wing at the T. E. over the central portion of the wing. However this may be a peculiarity of

this experimental set-up, since the attachment was encouraged by the jet

distribution's large values of spanwise components (indicated by

rp

F

0).

Flow visualisation with tufts confirmed this idea. For heights of about 1/2 chord, attachment took place over roughly the central 4" of the span at the

T. E. The flow remained attached for about 1

I

3 of the chord, af ter which

it separated and formed a partial cushion over the remainder of the chord.

As the height was r.educed, the attachment became less severe, although

observation was only possible down to

hl

c ~ O. 1.

The quality of the flow was degraded by two mechanisms.

Firstly, even though the distribution of the normal component of the jet momentum was reasonably uniform at the jet exit, the spa,nwise components caused a convectiQn of the normal momentum away from the central part

ofthe wing .and .towards the tips. Thus, if the distribution of the normal

jet momentum could be re-evaluated where the jet sheet crosses an

imaginary plane parallel to the wing plane and.a distance 'y' above it, then

the distribution would become increasingly non-uniform as y-increases,

and would leave a gap in the jet sheet at the wing's centre. This effect is also evident in the jet flap flow pictures (Figs. 20 and 21). This weakening of the jet sheet mayalso have helped the initial breakdown of the jet sheet

at the centre of the wing when forward speed is increased, as observed in

Refs. 1 and 2. '

Secondly, the entrainment effects of the spanwise compon-ents cause a jet pump action on the cushion air inducing secondary flow

to-wards the tips, and thus requiring air to enter the chshion at the centre.

This encourages the attachment of the jets as observed. These effects, in addition to the square cornerinefficiençy discussed in Ref. 1, undoubtedly

cause the experimental results to be conservative. The high drag and

pitch-ing moment values for 0( = - 3 must be assumed to be associated with this

particular test configuration.

T,he jet distribution of Cl showed the tips to be particularly

weak, and the in:ternal cushion flow resulted in a large 'outflow fI'om the

tips. Thus.it was hoped that C2 with stronger tips and a more Uniform

dis-tribution would improve the performance. The results appear in Figs. 23

to 27. Some gain in LIJ was obtained, as shown in Fig. 30, but waS not

considered significant enough to warrant the effort required to improve the

jet distribution, especially with the inherent spanwise components, and the

mechanical difficulties involved in changing the distribution. The fluètuations

. in moment were still apparent. For, all remaining configurations (af ter C3)

only two or three improvements to the jet distribution were made before

final calibra tion.

6. 2 Jet Flap Cases

C 9 was a conventional jet flap. CB inc1uded tip jets as weIl.

The results in the form of CL vs. Cfo for 0/... : 0, are shown in Fig. 34.

Figure 35 gives similar data for 0(,. :

!

3 for C 9 only. Figure 34 includes

results obtained from Refs. 4, 5, and 6, although the latter are for hïgher heights. Considering the differences in AR, jet geometry, and height, the experimental results for CL (C,.Ao(.. ) shown here appear reasonable as does

a comparison of CT IC)), . vs,C)A-'(0<,. : 0) in Fig. 36 with Ref. 4. In

general for 0<. : 0, CL increased with height for constant C""'" as expected,

although for C9 at high Cp.- for

0/.:

0, -3 CL increased from

h'/c :

.108

to h'

Ic:

.240 and then decreased for h'

Ic :

.509. This is probably due to

the jet distribution which tends to leave a gap at large heights, or may be

an effect of the very low q used to obtain these high C~ 's - i. e.

measure-ment errors increase, as do Reynolds' Number effects. Unfortunately

measurements were not taken witltout ground. The TIJ values of Fig. 36

follow the normal trend-increasing with decreasing height (~ef. 7). C8

gives improved lift over C9 but suffers in thrust recovery. Figure 29 shows that C9 has a 68% thrust recovery at zero forward speed compared to 46% for C8.

As previously mentioned, the lampblack and kerosene pic-tures of Figs. 20 and 21 show the 'hole' in the jet sheet caused by the severe spanwise jet velocity components. Figurs 19 and 20, for two different

heights, compare the flow pattern observed at zero forward speed to that

obtained at C"u.

=.

94. At C ~ : (X) there appea~s to be a second

stagna-tion line where the porstagna-tion of the jet flap turned forward meets the induced wind caused by the jet pump action of this configuration. At C.,u. : . 94,

the jet sheet begins to break: in the middle between h'

Ic

= .

108 and .240.

Similar results are shown in Fig. 21 for C,P-' : .36. At low heights the jet

sheet is complete but definitely weakened in the central region, whereas at higher heights a complete break in the flap has been produced.

6.3 Intermediéite Cases

The results for all cases tested at forward speed are shown

in Figs. 28 and 29 for

0<

=

0 as graphs of LIJ vs. 11Cp' . Each

configura-tion shown here is intended as an intermediate configuraconfigura-tion, so that only

one point, or qS/J would be used in a general T.O. run. Thus the peculial'i,

-ties of each configuration are not discussed in detail. The momentum flux and angle distributions follow the same general trend as the configurations

dealt with previously. The moment results and the results for 0(

=

±

3

were taken primarily for stability and control studies and are not presented

here since this matter is to be dealt with in a subsequent paper.

Note that the configuration numbers are roughly based on the

values of 92, Cl being the most negative 92. Thus, Fig. 28 shows that

backward deflection of the T. E. jet affects the lift predominantly at low

speeds, whereas the thrust curves tend to increase uniformly over the

- - - ---~

6.4 Experimental Error

The random error was reduced to effectively zero because of the large number of data points él;ssociated with the continuous trace

technique. The systematic error introduced into the system originated from, (a) inlet momentum calibration (applies to lift only) ....

i"5%

(b) outlet momentum calibration . . . + 0, -2%

(c) balance calibration . . . 2-2%

(d) analogue representation of force reduction equations .... ~2%

(e) output recorder .. ... . . . .... i"1 %

The total resulting percent errors are then estimated to be

M D

. . . +7%, -5%

Je J

Note that the inlet momentum is a correction to the measured lift force, and

as such contributes differing magnitudes depending on the value of LIJ. On

the average, the total error in LIJ is estimated to be

LIJ . . . . +9%, -7%

VII. APPLICATION OF RESULTS TO TAKEOFF PERFORMANCE -PHASE I, ACCELERATION

As discussed in Section II, the prime purpose of this work is

to study the advantages of a restricted optimization of an integrated

propul-sive system. In this section several other programs of operation during

Phase I are also investigated for comparison. All of these programs can be

envisaged as differing in their method of control during Phase 1. The

con-trols are effectively the parameters that are unrestricted and whose values

are allowed to vary during the run such as to determine the best performance.

The available parameters are (h/c, 91' 92, J1/J2'0( , 2Aj/S ) where the

combination (92' J 1 I J2, 2Aj IS) is designated by ~. In this context all

restricted parameters are kept constant during any particular run.

All cases investigated here will assume 91 as fixed and 2Aj

Is

as inherent in the particular results available, so that neither enters

direct-ly into any of the take-off programs. Also, particular values of hl

Ic

= .108

and JT/W = 0.7 will be used as representative values. This value of the

total installed thrust is about 2/3 of that required for VTOL.

Case Control Parameters Fixed Parameters 1

_{f t}

h/c, JIJT, 2 0(

,P-,

h/c, JIJT 3 _JIJT

,p-,

h/c ,0<-4

,p-,

_JIJT hl c, 0( 5 h/c

p,

JIJT ,0(

Each of these cases may have a wide variety of subcases determined by the particular values of the fixed parameters. These will be described under the individual cases, and then discussed collectively.

7. 1 Case 1 -

fL

control

This was considered the primary optimization case, case 4 being overly complicated. Essentially under the conditions (5) and for the

particular values hl Ic

=

•

108, JT/W

=

0.7, from (3), the function to be

optimized is simply TIJ (qSI J,

P. ).

The constant value of JIJT used

dur-ing the run was determined by the hoverdur-ing C2, since at hl Ic = .108,

LIJ

=

WiJ

=

2.67 and thus JIJT =

1/(0.

7,'x 2.67)

=

0.535.

Now any intermediate configuration must give

LIJ

=

WiJ

=

2.67

Thus, for a given.)L , LIJ

=

2.67 defines the particular value of qS/J at

which the configuration can operate and hence a particular value of

TIJ = T*/J. If all possible,;-t- were examined, and the resulting T*/J

points plotted vs. qS/J, then it would be expected that the points would define

an envelope of (T*

I

J)max which would in turn give the maximum

accelera-tion at a given speed and determine the...,.u. pattern, or patterns, req~ired

to attain this acceleration (Note that

JA-

is a lumped variabie -

JA-

=

(92, J 11 J 2, 2Aj IS) - and thus two different ~ could give the same results

in the two dimensional plot of T*/J (qS/J,,)J.). This approach provided Fig.

37 which shows the T*/J points obtained (rom the experimental configurations.

Their envelope should be a conservative estimate of the true envelope if a large number of results were available. Points in a group joined by dotted lines were obtained for the same configuration on different runs. Especially

for the low speed results for C3, the slope of LIJ

=

L/J(qS/J) is nearly.

horizontal (see Fig. 28) leading to a large separation in the abscissae

qS/J on Fig. 37. Since the parameter 2Aj/S was not kept constant from

configuration to ~onfiguration, _{the variation of q/<ij corresponding to the}

T*/J points is also plotted on Fig. 39. This was used to determine the

momentum drag during the acceleration. It is not implied that qj would be

varied during t!Ie ground-run. The curve serves to indicate the variation

of the momentum drag. The corresponding variation in J2IJ and 92 are shown in Fig. 38.

Using equations (1) and (2) and the curves of Fig. 37, the

plot of l/a/g vs. qS/JT (Fig. 39a) was calculated, where

JD JT J 1

=

=

O. 7

-

- -

=

.325 W W W 2.67 and

(j*

)~At

- .7

(qn'"

alg

=

. 325

+ .

7

Now the curve of Fig. 39a may be integrated to yield the ground-run dis-tance, Rl, required to reach a given speed.

Since a

=

~ dV2 dR1

_~S/J"T

V'l.

f

(:/g)

Rl

=

f

2!

dV2

=

J_T d

(fT~

~gS () 0 or

{WJ;

Rl

=

1 JT

(a~

g) d

(~~ ~

(6 ) w

_<Z~

w

0

The coordinate qS/ JT has been introduced for easier interpretation when

J /J T is not fixed. R1/W (qS/JT) is plotted in Fig. 39b. To find a

particular ground run, only the transition speed is required (see Section 8).

7. 2 Case 2 -

ol...

control

The use of angle of attack variation to keep the vehicle at

constant height is somewhat fallacious, since at h/c = .10, an 0<. = 20

re-duces the ground clearance at the T. E. by 17%. However, this case has

been examined in Ref. 2, and the most promising results are repeated here

in Fig. 40 (Case, 2, Ref. 2, h'/c = .108). The angle of attack program is

described in Ref. 2, Fig. 106(b). It uses negative angles of attack up to

2.50 _{to maintain constant height as speed increases. The configuration}

used is that of Test 1 (91, 92

=

0,

h

=

j2 ), in order to provide a trimmed

hovering configuration. 7.3 Case 3 - J /JT control

This program supplies the minimum quantity of air to the cushion at any speed to maintain constant height - so that as the available

into direct thrust. A number of subcases were examined using different basic configurations. The most important is that using Test 1, and the

re-sults in Fig. 41 show R1/w and the required JIJT program. In this case

( Y2.

. a I g

=

J

nl

w

+

TI

w -

O. 7

~

Iqj ') (7 )

Jn/W is a function of forward speed, as determined by

Jn/W

=

0. 7 - J/W

=

0. 7 - 1/~/J)

Similar plots are shown in Fig. 42, using C5 and C6 as constant configura-tions for the whole run. The reason for examining these will be evident af ter discussion of Case 4.

7.4 Case4-jl-, JIJTcontrol

The relaxation of the fixed JIJT restriction of Case 1 leads to the most general case of interest. The only remaining restrictions are geometrical,·

h/c,

and 0( Angle of attack control has already been criticized. hl c control does not lead to an improvement of results. This latter statement can be shown in examples such as Case 5 or simply

intuitively, since as the ground clearance is increased, the advantages in lift to be gained from ground effect decrease, requiring more cushion power which might otherwise have been used for propulsion.

With both'p- and JIJT free, the function to be maximized is

a'/g

as given by (3). This is done by a method similar to that used when only "'" was free, except that each configuration contributes a curve given by

a'/g

=

Jn/W

+ T/w

where JD/W

=

0.7 .. 1/(L/J).

The required optimum would be the envelope of all such curves. It should be noted in Fig. 43, however, that the curves are fairly flat, so that a good approximation to the envelope of the available data is one of the individual curves A, B, C or F up to qS/JT ~ 1. O. In mOpt

cases, transition to Phase II is made below this speed. Each of the curves represent a fixed configuration, thrust diversion acceleration (Case 3) with momentum drag omitted. Figures 41 and 42 give R1/w (qS/JT) for B,

C and F. Curve A leads to slightly poorer results due to a larger jet area and hence higher momentum drag contr.ibution, and this is not included.

A comparison of the results of Fig. 41 with those of Fig. 39b indicate little to be gained by

)J-

control. Furthermore, the general

(fo '

JIJT) con-trol is so weU approximated by constant,)A- , JIJT control that no actual calculation was done for Case 4.

7. 5 Case 5 - hl c control

The final case attempted was to examine the simplest

possible method of take off - i. e. keeping configuration and propulsion

con-trols all fixed and allowing height to increase as the run progressed. The configuration examined was that of Test 1, with the minimum initial cush-ion thrust as determined by hovering. The results are shown in Fig. 44. Figure 44b shows that the height begins to increase quite rapidly above

qS/JT

=

0.7.

7.6 Comparison of Cases

From the above calculations using the available data, we may conclude th at a good approximation to the optimum T.O. run is that

using a fixed configuration with

JIJT

control at constant height. Angle of

attack control gives comparable ground-run distances but contains a height penalty. The simplest type of control is that of variable height and offers reasonable results as long as the transition speed does not become too high.

The similarity of the required ground-run distances to reach relatively low speeds is due to the large weight of the momentum drag term

in th is regime. All configurations examine have similar hovering

efficiencies, and thus similar magnitudes of direct thrust. At the lower speeds,the contribution to thrust or drag of the basic configuration is

small compared to the direct:.thrust minus momentum drag term. However,

as forward speed increases this latter term becomes small, whereas the basic configuration thrust (or drag) term is increasing and becoming more important.

The momentum drag used for any particular configuration

is determined by the mass flow and hence the outlet area - i. e. for

con-stant cushion thrust, J, and speed V eX>

J VeX> JD Voo

+

-W Y _J W V' _J

and the resultant thrust

=

_{JD/W +(T/J)(J/W)-}

Dmorr/W

= JD (1 - VeX> )

+

~

(

~

_

VeX»

W Y. W J V·

J J

Here we have taken Vj to be the same for both the cushion jet and the pro-pulsive jet. Thus,for constant J and JD, the resultant thrust increases with increased jet exit velocity; however, the energy requirements became higher with increasing Vj - the energy remaining in the jets at the exit be-ing tJT Vj. Obviously, from an aerodynamic point of view for constant

JT/W, increased acceleration will be obtained from increased ~ i. e. re-duced jet exit areas (assuming that changes in the parameter q/ q. are not very im,portant so long as C.P' is kept constant). However, the tuel con-sumpti6n is at the same time worsened. In the cases presented here,'

fairly low exit veloeities ar'e used and hence large momentum drags are incurred. The cO,nservative viewpoint is furthered by the assumption of

the total thrust contributing to the momentum drag. Further work

involv-ing optimization of the complete system is required to fully determine the potentialities of the concept.

VIII. TAKE-OFF PERFORMANGE - Phases Il and III

To place the overall take-off performance to 50 ft. in pers-pec'tive, a simple estimate of the Phase II and III performance is given. Phase lil will be dealt with first since it may be treated in the same manner as Phase I ,- i. e. a plot of climb-out angle attainable with a jet flap con~ figuration vs. tr.ansition speed will be produced.

8.

1

.

Phase lIl, Climb-out

Since the jet flap data obtained here does not include a case without ground present, the data used was obtained from Ref. 4. The jet flap tested in Ref. 4 had an aspect ratio 8.3, and a value of

2Aj/S = .55 x 10- 2 . This leads to higher exit velocities than have been: used in the foregoing, and thus a lower momentum drag if all thrusting devices are assumed to have the same Vj. This is the case shown in Fig. 45a, which gives the climb-out angle

't

vs climb -out speed assum-ing constant speed durassum-ing Phase lIl. i. e.

sin

't

₌

TT

-W

TD T

Ih

=

_{- + -}

_{- 0.7}

(i )

W W

For all cases, the minimum thrust is invested in the jet flap, since this leads to maximum angles of climb, and thus J /JT is a function of qS/JT for all cases as shown in Fig. 4,5b,i. e.

J

=

W • C)A-

=

1. 43

C~

JT JT CL CL

If the clim b angle '( is known, then the ground distance

required to attain 50 ft. assuming transition from Phase II to Phase III at

h'

is

and hl requires a particular 'e. We thus choose a representative aircraft

of 20, 000 ibs weight, 20 psf wing loading, and an AR

=

4. 17. This

im-lies S

=

1000 ft and è

=

15.5 ft.

Note that regardless of the speed at which the transition to Phase III is undertaken, acceleration or deceleration could be used to attain the correct speed for maximum climb angle.

8.2 Phase II - Transition to Climb-out

The difficulty posed by the transition between the ground cushion vehicle and steady climb with the jet flap is due to the differing lift performance characteristics of these two fundamental configurations. The ground effect vehicle gives high lift coefficients near the ground, but they faU off rapidly with height. The jet flap gives high lift coefficients away

from the ground but they decrease as the ground is approached. Thus if

transition is made directly to the jet flap near the ground a higher speed is required than that which is necessary to just fly the aircraft out of ground influence. In Fact, Fig. 45 shows that flight away from the ground using the jet flap data of Ref. 4 is possible for qS/JT ~ .2. If no intermediate configurations are used, transition requires a height and speed point at which flight is possible with both the jet flap and the Phase I machine.

If we assume that in the actual application of this concept,

JIJT

=

~ is the maximum cushion thrust obtainable - i. e. that the engines

producing the cushion thrust and the direct propulsion engines are independ-ent - then at any speed, there is a maximum height attainable with the

ground cushion configuration, which is that at which LIJ

=

1 I 0.35

=

2.86.

This leads directly to a height-speed envelope ACD shown inFig. 46 and is just the flight path followed by Case 5, variabie height control. If the jet

flap regime is approached similarly, then JIJT

=

~ defines an allowable

height speed envelope ECG where LIJ = 2.86. The ove"rlapping part of the regimes where LIJ ~ 2..86 is seen in Fig. 46 to exist for qS/JT

2.

.84. The jet flap curve was drawn to provide the best fit to the available data.

The take-off as seen in Fig. 46 would proceed along the arc AC for Case 5, and then at C a transition would be made to a jet flap configuration with

JIJT

= ~

and rotation would be initiated at constant speed. This rotation

would continue until the required steady climb angle of Phase III is reached. Cases 1 to 4 would be similar beyond point C, however they would proceed

at constant height along AB, and then at point B, it is assumed that JIJT =

t

is put into a Test 1 configuration, and rotation takes place at constant speed to point C.

Throughout the rotation calculations, no use is made of the

excess thrust which exists at qS/JT = 0.84 (of the order of . 25W). In an

actual transition, to keep the speed constant, the pilot would incorporate additional angle of attack so that excess thrust would be used by the

additional drag, and thus the load factor would be increased over the values used here, resulting in a more rapid transition to climb-out.

The rotation from B to C was assumed to occur at a constant

load factor of n

=

1. 22. Actually, n

=

1. 22 is available for

eX

=

0 only at

hl/C = . 108 and would fal! off to n = 1 at point C. However, sufficient excess·

thrust exists to support an angle of attack of nearly 100 _{whereas only about}

30 _{is required to keep n = 1. 22.}

Thus, the distan~e required is

where h 'I = (.215 - .108) 15.5 = 1.66 ft.

=

[~

(0.84) (0.7) (20Q

~

=

99.4 ft/sec.

Thus, = 68 ft.

In order to· calculate the horizontal distance required from

C to the point at which steady climb is reached, the variation of n with

height was plotted in Fig. 47a. These values also assume constant speed,

~

=

0 except that an angle of attack increment to n shown by the dashed

lines near n

=

1 was used in order to initiate the rotation (equivalent to

ei..

~ 20 ).

The equations describing unaccelerated flight along a curved vertical planar path are

dh

d't

dR dh

=

=

v

2 sin

't

(n(h) - cost) g

eot "

which were integrated stepwise in the form

A h

=

v

2 g

4'1

sin (

't

+ --Z-) • 0.

t

n(h) - cos (

't

+

4'( ) 2

A R

=

c.o

+ (

'6

-'r

4- )

&>. h

Fig. 47b shows the results in the form of height attained versus angle of clim'b.

The maximum angle of climb at qS/JT = 0.84 is found from

Fig. 45 to be 23.30 . However, this requires J /JT = .06. If J /JT remains

at 0.5, then a lower angle is obtained for which

L

';;P W, but a/ g = 0, - i. e.

rotation could continue but forward speed would begin to decrease. At this

point 'in the climb,

à

change could be made to decrease J /JT and hence

keep a/ g ~ 0 so that rotation could continue. In the present calculatio~s,

the simpier conservative viewpoint is taken that rotation is stopped at this

lower angle and Phase III begins. Since qS/JT = .84, Cp = J /qS =(1/.841

.60, and from Ref. 4, TT/W = . 254 = sin

't .

Thus the limiting climb

angle for J/JT =

t

is 14.70_{. This is'reachèd at a height of 18.4 ft. and}

requires a horizontal distance of 189 ft. from point C. Phase III then

re-quires only (50 - 18.4)

c..ot

14.7 = 121 ft.

Thus, in summary, the distance required to clear 50 ft from point C is 310 ft. andfrom point B is 378 ft.

The distanc~s required to reach qS/JT = 0.84 and the total

distance to 50 ft. are listed below for all cases

8. 3 Case Rl 1 750 2 780 3 (test 1 resul~) 805 5 900

Discussion of Take-Off Resu~ts

R2+R3 378 378 378 310

*

R 1128 1158 '1183 1210

, The results in the previous table show shor~-field take-off per- '

formance for all cases examined under the assumptions stated. The small

distance penalty associated with Case 5 indicates that the mor~ complex

programs are not justif~ed.

Several conservative assumptions have been made throughout

these ca1culations. The most notabie is that all results ,assumed

1. _

2

-):C It is considered that the assumption concerning momentum drag used in

these calculations is unduly conservative. Later ca1culations (see Ref. 12) were made in which only the cushion jets are assumed to contribute to Dmom'