Experimental study of the aerodynamic characteristics of a model of an air cushion vehicle in hovering flight

,

fI

EXPERIMENTAL STUDY OF THE AERODYNAMIC CHARACTERISTICS OF A MODEL OF AN AIR CUSHION VEHICLE IN HOVERING FLIGHT

by

B. W. Gowans

o

ACKNOWLEDGEMENTS

The author wishes to express his gratitude to Dr. G. N. Patterson, the Director of the Institute for Aerospace Studies, for the opportunity to conduct this research.

This investigation was suggested and supervised by Prof-essor B. Etkin. His guidance and many suggestions during the entire project are gratefully acknowledged.

The author is indebted to G. Kurylowich for his assistance in the experimental work. Thanks go also to D. Surry for his assistance with the experimental work and for his many suggestions as to the con-struction and operation of the model.

This study was made possible by 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 Flight

Dynamics Laboratory.

SUMMARY

A self-propelled model of an Air Cushion Vehicle has been built and flight tested on the UTIAS Circular Track Facility. A detailed study of the flow through the model has been made, and the jet mass and momentum fluxes have been measured.

An augmentation curve and the basic static and dynamic stability characteristics in pitch have been obtained for the model while

in hovering flight.

TABLE OF CONTENTS NOTATION I INTRODUCTION II MODEL III IV 2. 1 Construction

2. 2 Specifications and Performance 2. 3 Moments of Inertia

MODEL CALIBRATION

3. 1 Pressure Rise Across Fan 3. 2 Measurement of Fan R. P. M. 3. 3 Inlet Mass Flow

3. 4 Propulsion Duct Thrust and Mass Flow 3.5 Exit Jet Mass Flow and Momentum

Flux Distribution 3. 6 Fan Efficiency

AUGMENTATION CURVE V STATIC STABILITY IN PITCH

1 1 2 2 3 3 4 5 5 5 7 7

5. 1 Free Flight Tests (five degrees of freedom) 8 5.2 Rotation about Pitch Axis (one degree of freedom) 9 VI THRUST ~ING DYNAMOMETER

VII STATIC THRUST IN HOVERING FLIGHT

VIII DYNAMIC MEASUREMENT OF PITCH STIFFNESS

8

IX

AND DAMPING

8. 1 Experimental Procedure 8. 2 Equations of Motion

8. 3 Determination of Stability Derivatives by Analogue Simulation 8.4 Results and Discussion

CONCL USIONS

APPENDIX I _. Model Data

APPENDIX II - Derivation of Augmentation Factor for Inviscid 3

Dimensional Thick -Jet Flow iv 9 9 10 10 11 11 12 13 14

REFERENCES

TABLES

FIGURES

v

A.B.C AL a b c De

.

'

d Fb h hl

?r

J Jl L M Me Mq m n P.Q.R ~

1>

(Ap) P NOTATION Moments of Inertia Augmentation factor Area

Distance between front and rear jet Wing chord

Equivalent diameter of circular model Propeller diameter

Pressure thrust on nozzle base He ight above ground

Angular momentum terms Advance ratio

Total jet momentum thrust with ambient exit pressure Momentum thrust of annular jet

Lift

Pitching moment ~M

a

e ft lbs/radian

~ ~

ft lbs/radian/ sec. Mass flow. or model Mass. Revolutions per second Angular velocities Power

Propeller pitch Fan pre ssure rise Static pre s sure

Pe Jet exit statie pressure

PT Total pressure

Q Equivalent volume flow

q Angular velocity in pitch

R Radius of a,nnular jet in cross section

Ro Radius of inlet bellmouth

.,

r Radius

ro Radius of annular nozzle base

T Thrust. or Period of oscillation

t Jet thickne s s

V Equivalent velocity

V e ' Equivalent jet velocity at nozzle exit

f

₀ Average inlet equivalent velocity

V·

J Average jet exit equivalent velocity

01,(3

Computer constants

W Angular distanee (see Fig.

7)

I,e>

.

Euler Angles

~

Fan' Efficiency

~1 Elemental length of jet sheet _~

1'0

Angle of nozzle exit

f

Density of air

e

Pitch angle

, - - - --- --- - - . _ - - - -- - --- _._ -- - - .

....

'

..

1. INTRODUCTION

A preliminary investigation into the feasibility of using a circular track for dynamic testing of models of Air Cushion Vehicles indicated the need for a high performance seU -propelled model. (Ref. 1)

To meet this re'quirement a second GETOL model was designed and built.

Many difficulties were experienced with this model, especially mechan-ical and structural ones associated with the unconventional power instal-lation. Measurements of the momentum flux distribution of the wing

slot established that the distribution was poor both spanwise and at the wing tips. A number of improvements were incorporated and trimmed stabie flights were finally obtained. However the weight accumulation

resulting from repairs, changes, and balancing for trim reduced the

hl

c

to an unacceptably low value.

In order to avoid the difficulties experienced with the GETOL model, attention was shifted to a more conventional Air Cushion Vehicle. A preliminary model was built from a commercially available model kit. This model performed fairly well af ter some ;major

modific-ations to the stability jets. It flew at a height of about one inch above

ground at speeds of about ten feet per second. It was thought that by

using a higher performance engine, redesigning the propulsion system and modifying the internal air flow system (mainly by the addition of fairings to reduce the pressure losses) a higher forward speed could be achieved and the overall efficiency increased.

This report describes the construction and c.alibration of the model, and the measurement of its augment at ion and basic pitching stability characteristics while in hovering flight.

u.

MODEL

2.1 Construction

The model was constructed by the author; Figures 1 and 2 show it during construction. Figure 1 shows the model before the engine, propulsion duct and inlet bellmouth were installed. Figure 2 shows it with the engine and propulsion duct in place before the final top

decking and inlet bellmouth had been installed. Figure 3 shows the model

in its completed form. It was constructed entirely from balsa wood

except for the plywood engine mount, and was finished with model air-plane dope and then coated with a plastic finish to fuel-proof it.

Provision was made for additional weights to be added to the front and rear in order that the centre of gravity, all up weight, and pitching moment of inertia of the model could easily be varied.

2. 2 . Specifications and Performance

The principal dimensions of the model are summarized in Fig. 4 and Appendix I.

The model is powered by a Cox "Special 15" model airplane engine with a displacement of .15 cubic inches capable of developing .46 horsepower at 18, 000 R. P. M. The horsepower versus R. P. M. curve for this engine is shown in Fig. 5. The curve was obtained from Ref. 2 and is considered to be very reliable for the fuel used. The nitromethane content of the fuel used was 30% and that normally used in the model is 25%. This difference in nitromethane content should not change the curve by more than 5 percent.

Air is supplied to the peripheral and stability jets by a simple axial fan. The fan is an 8 inch diameter two bladed propeller with a 3 1/2 inch pitch. For forward propulsion some of the air is bIed off behind the fan and out through a propulsion duct. Additional propulsion for forward flight can be gained from the peripheral jet by flying the mod-el in a nose down attitude.

The model in its normal configuration (weight 2. 6 Ibs) will fly at a height above ground of 11/2 inches and at a speed of 15 feet

per seconde lt will fly at speeds up to 20 feet per second when flying in

a nose down attitude.

2. 3 Moments of Inertia

The moments of inertia of the model about its C. G. werè found by setting up a bifilar pendulum and supporting it from two fine copper wires equidistant from the C. G. Figure 6 shows the model sus-pended for measuring the pitching moment of inertia. The model was

s.et in rotational mot ion about the two wires and the period of oscillation,

T, was recorded. The bifilar suspension theory gives the moment of inertia as

I

₌

T 2 mga2

,

16

TI

2.1

where m

₌

mass of body

g

=

acceleration of gravity (32. 2 ft/ sec)

a

=

distance between wires

.i..

=

length of wire s

The measured periods and calculated moments of inertia

are recorded in Appendix 1.

'

.

lIL MODEL CALIBRATION*

3.1 Pressure Rise Across Fan

The static pressure rise across the fan was measured by

use of built-in wall taps. In all. six sets of pressure taps were in stalle d;

the position of these are shown in Fig. 4 and 7. The measured pressure rise across the fan at these stations is plotted in Fig. 8. The high

pressure rise noted at stations. A and B is caused by the presence of the

propulsion duet scoop situated behind the fan in this region. The average pressure rise was calculated to be 7. 76 P. S. F.

The inlet wall velocities. at these six stations,were

calculated from the statie pressure measurements in front of the fan and

are shown in Fig. 9.

During all tests when the model engine was running its

R. P. M. was obtained. (see 3.2) For a fixed geometry. the fan v~lume

flow veries as the R. P. M. and the pressure rise as the (R. P. M.) . Using this fact all pressure measurements and volume flow calculations were corrected to a common R. P. M. value. (In thiscase to 13.500 R. P. M. ). The R. P. M. of the engine did not vary more than 500 from the value of 13. 500 during any of the tests.

3.2 Measurement of Fan R. P. M.

The engine R. P .. M. was obtained during flight from the sound equipment shown in Fig. 10. Also shown in Fig. 10 is a block diagram of the electronie equipment. The microphone and sound level meter "listen" to the engine noise and pick up the distinct "pops" made

by the single cycle engine. This signalor series of pulses is now paseed

through a 1/3 octave filter which produces a good periodic signal at the engine frequency. The counter counts the number of pulses per second and this figure is then displayed.

This system was devised by the Aeródynamie nois.e group

at UTIAS.

*

All velocities quoted were obtained from measured values of the

dynam-ic pressure by using the standard density

f!

= •

002378 slugs/ cu. ft.

Hence the velocities and volume flows are'tequivalent' values, i. e. true

values time J~' The jet momenta are of course correct.

3

3. 3 !nIet Mas s Flow

In order to calculate the inlet mass flow a special static

pressure rake was constructed (see Fig. U) and static pressure

measure-ments were made at four different angular positions. Figtir:'e,12 shows

the pressure rake held in one of these positions. The iniét velocity

distributions were then calculated from these measurements by assuming the inlet total pressure to be atmospheric. The profiles so obtained are

shown in Figs. 13 to 16. The inlet wall velocities were taken from Fig. 9.

AU velocities were corrected to 13,500 R. P. M.

manner;

Q

=

=

=

where I (W)=

The inlet volume flow, Q, was calculated in the foUowing

S

Vda

=

R

r

2_rT"

r

₀

J

J

V(r,W) o 0 2Tr

f

I(tA) dW 0 R

[0

_{V(r,W) rdr} 0 rdrd-W (1) (2) (3)

(4)

I( W) was calculated numerically from the inlet velocity data for eight

stations around the fan and is plotted on Fig. 17. The volume flow was then found by graphically integrating Eq. 3 from Fig. 17. The inlet

volume flow was calculated to be 16. 6 cubic feet per seconde (Corrected

to 13,500 R. P. M.)

Assuming standard density for air the inlet mass flow is

m =

I'

Q = 39.4 x 10 -3 slugs/ sec.

The average inlet velocity, V 0 was calculated to be

_ Qinlet

V o

=

ainlet

=

47.5 ft/sec.

3.4 Propulsion Duet Thrust and Mass Flow

The propulsion duet on the model is made up of two simil-ar portions. one situated on the port and the other on the stsimil-arbosimil-ard side of the model. The exit area of eaeh duet is 1. 6 in. 2 The exit velocity of the air leaving eaeh duet was measured at 3 positions with a pilot-statie probe. The average velocity from the port duet was found to be 79. 4 feet per seeond and that of the starboard to be 74. 1 feet per seeond.

Thus the exit volume flow from the port duet is

Q

=

a V

=

O. 884 ft. 3/ sec.

The exit mass flow from the port duet. assuming standard density. is

m

=I'Q

=

2.10x10- 3 slugs/see.

The port thrust is

T = mV = O. 167 Ibs. or 2. 67 oZ.

Similarly the starboard volume flow was ealeulated to be 0.- 824 eubie feet per seeond and the thrust 2. 32 oz.

The total mass flow out the propulsion duet is 4.06 x 10- 3 slugs per seeond and the total duet thrust 4. 99 oZ.

3.5 Exit Jet Mass Flow and Momentum Flux Distribution

In order to obtain a qualitative idea of the momentum flux distribution of the peripheral and stability jets. flow visualization studies were conducted. These tests were made by holding the model above a ground board eoated with lamp blaek and kerosene. The resulting streak patterns are shown in Figs. 18 to 20 and indieate the exit flow distribution to be reasonably uniform at 9

=

O.

A quantitative knowledge of the momentum flux was required in order to non-dimensionalize the measured force and moment data. To aehieve this an exhaustive probing of the peripheral and stability jets was undertaken. In all. 116 stations were traversed using the total pressure probing system shown in Fig. 21. The positions of the stations traversed are shown in Fig. 22. The model was attaehed to a earriage whieh was moved in • 05 inch intervals aeross the stationary probes. The pressure readings on the manometer board were photographed at eaeh interval. In

all. four different traverses were made to eompletely probe fr'ont. rear.

port and starboard jets. Typical velocity profiles across the jets are shown in Fig. 23 and 24.

The volume flow per unit length at each station was found

numerically by integrating the velocity versus gap distance profiles. It

is shown in Figs. 25 to 33. The large dips present in some of these

profiles (e. g. at the 12. 3 inch position of Fig. 25) occur at .stations where the probes were situated at positions where the balsa bulkheads blocked the jets. The total volume flow out the stability and peripheral jets was then obtained by integrating the volume flow distributions from Figs. 25 to 33.

The total volume flow out the stability jets was calculated

to be 5.80 cubic feet per second andthat out the 'peripheral jet to be 8. 75

cubic feet per seconde

The total mass flow out the model

0:.

e. propulsion duet,

stability and peripheral jets) assuming standard density was calculated

to be 38.7 x 10- 3 slugs per second which compares very favorably with

the previously calculated inlet flow value of 39.4 x 10- 3 slugs per seconde

(see 3. 3)

In calculating the velocities of the stability and peripheral jets from measured total pressure values it was assumed that the static pressure was atmospheric. This assumption, while being nearly valid for the peripheral jet, might be que stioned when used in calculating the stability jet velocities. However, the excellent agreement between the calculated inlet and exit mass flow values would indicate the assumption is justified.

The above calculations show that 10.6% of the mass flow goes into the propulsion system while 35. 6% is used in the stability jets and 53.8% for maintaining the peripheral jet.

The momentum thrust of the peripheral and stability jets was calculated in a similar manner to the mass flow, only (velocity)2 profiles were used in place of velocity profiles during the calculations. The momentum thrust from the stability jets was calculated to be 0.70

Ibs. and that from the peripher'al jet to be 1. 14 Ibs! The total momentum

thrust of the model at 13, 500 R. P. M. is 1. 84 Ibs.

An average jet exit velocity was calculated to be V·

J =

~

_SVda V2 da

=

53 •. 2 ft/ sec

6

3. 6 Fan Efficiency

The average pressure rise across the fan was found to be 7.76 P. S. F., when corrected to 13,500 R. P. M. (from Fig. 8)

The in1et area of the fan is • 35 ft 2• Thus

Thrust T = a(A P) = 2. 76 Ibs.

and output power,

_

f>

out = T(V 0) = 129 ft. 1bs/ sec.

(V 0 from sec. 3. 3)

oroutputhorsepower = 129/ 550 = .235

From the engine H. P.

at 13, 500 R. P. M. is .408 and

curve (Fig. 5) the input horsepower

Fan Efficiency ~ =

CP

out

Fin

=

57. 8%

Figure 34 shows the variation in propeller efficiency with

advance ratio,

& '

for different pitch to diameter ratios for a two bladed

propeller (from Ref. 3). The.ip/ d value for the propeller used in this fan is 0.437. When the engine is operating at 13, 500 R. P. M. the average

inlet velocity is 47. 5 ft/ sec (from 3. 3) and the advance ratio,

9- '

is

~

=

~d

=.316

From Fig. 34 the propeller efficiency for these values is 61% which agrees very favorably with that calculated from the flow measurements above.

The measured fan efficiency value of 57.8% is considered to be quite acceptable for this model as little de sign work went into match-ing the fan and horsepower characteristics.

IV AUGMENTATION CURVE

A lift augmentation curve was obtained for the model,

while in hovering flight, and is shown in Fig. 35. The data for this curve was obtained in the following manner. The model was restrained from forward flight by attaching a light cable to the rear. For various ail up

wèights, the height above ground was obtained by measuring the heights,

of'

the front and rear target points (see Fig. 3 and 4 for target points)

above ground with a scale. The height above ground is taken to be the height of the base of the model at its centre line above ground. Augment-ation is defined as lift (equal to the model weight in this case) divided by

momentum thrust. In order to correct the augmentation value s for the

differences in R. P. M. the lift was divided by the calculated momentum

thrust cor'responding to the actua1 R. P. M. of the engine. Thus the

au gment at ion curve obtained is independent of the engine R. P. M. 7

The augmentation factor for the model is shown in Fig. 36 together with other' published data and a theoretical relationship derived in Appendix II for comparison. It is seen that the augmentation for the UTIAS model falls below that predicted by theory and the NASA and DTMB models. Viscous losses in the air cushion would explain part of the dis -crepancy between the experimental values and those predicted by theory. Also the theory does not take into account the stability jets and is derived for a circular planform. Neither the NASA nor the DTMB model used stability jets and they were not free flight models. It is believed that the lower augmentation obtained for the UTIAS model can be explained by the large percentage of air (35%) used for maintaining the stability jets. It

was, in fact, noted that for a given weight the model would hover at a higher height when the stability jets were partially sealed off. The dotted line in Fig. 36 shows the augmentation for the UTIAS model based on the peripheral jet momentum flux only. This curve agrees much more clo se-ly with the other data shown especialse-ly that of NASA and tends to confirm the above explanation.

V STATIC STABILITY IN PITCH

5.1 Free Flight Tests (five degrees of freedom)

The static stability in pitch was obtained in much the same way as the augmentation data. The model was prevented from forward flight by a cable attached to its rear. The pitching moment on the model was varied by shifting small weights a given distance from front to rear and vice versa. For each different pitching moment the angle of pitch was obtained from measurements of the height above ground of the front and rear target points.

The restraining cab1e was attached to the model at one end and to a thrust ring dynamometer (see VI for a description of the dynamo -meter) on the other, thus enabling the restoring moment caused by the cab1e to be ca1culated. Figure 37 shows the forces acting on the model during the pitchirig tests.

Figure 38 shows the non-dimensional pitching moment versus angle of pitch curve obtained for two different h/ De values; It is seen from Fig. 38 that the pitching moment increases as h/De decreases, as expected and found by other investigations. (see for example Ref .. 8). Figure 38 shows the pitching moment to have a fairly large negative slope thus giving the model very good stability in pitch.

Figure 39 shows the pitching moment data for the UTIAS model along with experimental results obtained for other similar vehicles. The pitching moment slopes from Fig. 39 evaluated at zero pitching

moment are tabulated in Table I for comparison. The data obt ained for the UTIAS model' is in general agreement with that of the other air cushion.

vehicles. The best agreement is with the DTMB 7 foot flight test model which utilizes an elaborate stability jet system. As noted by Stanton-Jones (Ref. 9) the pitching stability has been found to be sensitive to quite small changes in geometry and even identical models can give quite large variations. The results from Fig. 39 appear to verify this statement.

5. 2 Rotation about Pitch Axis (one degree of freedom)

In order to 'obtain the static stability in pitch for a greater and more accurately defined

hl

De range <Df values the model was set up in a pitehing rig as shown in Fig. 44. In this configuration all motion except pitch is restrained. As in 5.1 the pitching moment on the model was varied by moving small weights from front to rear and vice versa. The angle of pitch was obtained as in 5.1 for each different pitching moment. These tests were conducted at five different h/De values and the non-dimensional values are plotted in Fig. 40. The pitching moment

slopes evaluated at zero pitching moment from Fig. 40 are tabulated in Table II and plotted in Fig. 50 as a function of

hl

De.

The results obtained by this method are considered to be ·more accurate than those of 5.1 as the

hl

De value can be accurately

controlled and no correction for thrust is necessary. VI THRUST RING DYNAMOMETER

In order to measure the static thrust of the model while in hovering flight a thrust ring dynamometer was designed and built. Figure 41 shows a diagram of the dynamometer along with a block diagram of the

associated electronics

anq

its calibration curve. Figure 42 shows a photograph of the dynamometer and recording instrument. The dynamo-meter consists of a linear variable differential transformer mounted in a proving ring. The transformer is rigidly attached to one side of the ring and the movable core to the other. The extens'ion of the resilient proving ring causes the core position to vary with respect to the trans-former. The magnitude of this variation is proportional to the applied load. (Hooke's law) When the core is moved a voltage is induced in the

secondary coH which produces an electrical signal proportional to the force acting on the ring. The 1000 cycle a. c. input voltage to the primary coil is supplied by a power supply in the demodulator unit and the d. c. output voltage is recorded on a recording galvano,meter instrument ..

VII STATIe THRUST IN HOVERING FLIGHT

The thrust values obtained from the thrust ring dynam-ometer and recorder during the pitching tests 'enabled astatic thrust versus angle of pitch curve to be obtained. This curve is shown in Fig. 43 for the two different

hl

De values.

From these results it is seen that the statie thrust in

-creases with decreasing angle of pitch and this was confirmed by flight tests as the model flew faster in a nose down attitude.

If it is assumed that the increased thrust obtained from flying the model in a nose down attitude is due to the forward component

of the lift vector then

T = L sine (5)

or T~

La

(for small value s of

e

) (6)

and

~

T =

a.

L

+e"

(7)

or approximately _{l!~ L} (8)

~.

From Fig. 43 at an all up weight of 3. 25 Ibs 'OT

I

~e

=

2.77 Ibs and

at 4.20 Ibs

0

T 1'08 = 4.56 Ibs. The rough agreement between Eq. 8 and the measured slopes ipdicates that the principle souree of thrust is the inclined lift vector, as suggested above. The residual discrepancy

sugge sts that when at an angle

e

an asymmetrie flow pattern in the

cushion develops, with a consequent alteration of the pressure distrib

u-tion on the vehicle.

VIII DYNAMIC MEASUREMENT OF PITCH STIFFNESS AND DAMPING

8.1 Experimental Procedure

The model was set up in a specially designed rig to r e-strain motion in all degrees of freedom except pitch. (see Fig. 44). The model was allowed to pitch about its C. G. position which was placed at the centre line. With the engine running the model was tilted

to an initial pitch angle and then released and allowed to return to its reference state. This mot ion was recorded by a high speed 16 M. M. movie camera. The pitch angle transients were then obt ained by a frame

by frame analysis of the movie fllm. The pitch angle was obtained from measurements of the relative height of the front and rear target points. The target points were measured against a reference grid (see Fig. 44)

and corrections were made for parallax _.

The experiment was repeated at four different h/ De

values for both positive and negative initial angles of pitch. 8. 2 Equations of Motion

The dynamics of an air cushion vehicle while in hovering

'li

ght and restrained in all degrees of freedom but pitch is now investig

-àted. For this case only the pitching moment equation need be considered.

10

Assuming a restoring moment proportional to displacement and damping proportional to rate. the perturbation pitching moment is given by

(9) whence the one-degree of freedom pitch equation is

ë. _

~è_

Me 9

=

0

B

B

(10)

Equation 10 is used to describe the pitch transients obtained in 8. 1

8. 3 Determination of Stability Derivatives by Analogue Simulation

In order to obtain the stability derivatives from the ex-perimental data obtained from 8. 1. Eqn. 10 was set up on the UTIAS Pace analogue computer. Figure 45 shows the computer diagram of Eqn. 10. With this program the computer plots the pitch angle versus time on an x-y plotter. The values of the constants in Eqn. 10 (i. e. Me / Band M /B) ean be varied by changing the values of 0( and

/3

on t.he

com-pu~er.

(see Fig. 44). The pitch transients obtained from 8. 1 were placed on the x-y plotter and the best fit of Eqn. 10 was superimposed on them. This was done by matching the initial pitch angle and varying the constants

cf.. and

(3

until the best fit curve was obtained. The values of these constants were recorded and the associated stability derivatives calcul-ated from them.

8.4 Results and Discussion

Typical experimental curves obtained Jrom 8.2 are shown.

in Figs. 46 to 49 along with the best fit curve of Eqn. 10. The experimen-tal points. in general. show fairly good agreement with the theoretical curve. It is possible that better agreement could have be;n obtained if some additional terms had been added to Eqn. 10 (eg. Mqq) however it was felt that the aceuracy of the data did not warrant these refinements at present. The values obtained for

Me

and Mq are tabulated in Table UI. Four values were obtained for eaeh h/ De ratio. two for an initial positive pitch angle and two for an initial negative pitchangle.

The mean non-dimensionalized values obtained for Me

from Table IU are plotted in Fig. 50 as a function of h/ De• Me increases as h/ Oe decreases as expected and found in Sec. V. :Also;plötted in Fig. 50 are the values of Me obtained statically from Sec. V. The static values show the same trend as the dynamic values but differ in magnitude. lt is possible that this difference is due to a frequency dependence of Me. However it is difficult to draw definite conclusionsfrom the limfted test data available and further experimental testingin this region would clarify

this discrepancy. It can be seen from Fig. 50 that Me becomes high1y dependent on h/ De at lower values of hl De •

Figure 51 shows the mean non-dimensionalized values of Mq plotted as a function of h/ De • The large scatter. shown as an error

bar. makes it difficult to draw any significant conclusion~ However. Mq

does show a definite increasing trend as h/ De decreases.

'.IX CONCLUSIONS

This s~udy has produced a high-performance self-propelled

model of an Air Cushion Vehicle. A calibration of the model has shown the uniformity of the jet momentum flux to be adequate and the fan effic-iency reasonable.

The augmentation. although be10w that of other experimen-tal models and that predicted by theory, is sufficient to allow the model to fly at suitable heights above ground for future experimenta1 investig-ations in connection with the UTIAS Track Facility.

Investigations into the pitch stability of the model have shown.ït to be sufficient for the h/ De range of interest.

o x Dimensions APPENDIX I Model Data Length Wiqth Base Area Equivalent Diameter Inlet Fan Area

Exit area of Peripheral jets Exit area of Stability jets.

Exit area of Propulsion ducts Perimeter of Peripheral jets For a Fan R. P. M. of 13, 500:

o

Inlet mass flow = 39.4 x 10- 3 slugs/ sec Jet momentum thrust = 1. 84 Ibs.

Moments of Inertia 29 1/2 inches 20 inches 2. 68 feet 2. 22 inches O. 35 ft2 0.101 ft 2 O. 0734 ft2 0.014 ft2 6. 08 feet

oThe measu~ed periods, and values required to calculate the model moments of inertia are recorded in the table below.

Pe.r~od m a Moment

(sec.) (Ibs. ) (in. ) (in. ) C. G. Position (slug ft. 2)

.

1. 485 2.60 6 ·10 • 6" fwd.

cl

Ixx=A=. Ol Q9 ( / 1. 95 2.60 9 1/4

I

D

• 6" fwd.

ct

Izz=C=. 0445 2.67 2. 60 6 1/8 10 · 6" fwd.

ei.

Iyy=B=. 0367 2.70 2. 89 6 1/8 10 at

ct

Iyy=B=. 0416

x~ value used in calculations of VIII

o

APPENDIX II

Derivation of Augmentation factor for Inviscid 3 Dimensional Thick-JetFlow

The solution for the augmentation factor for a 3 dimension-al thick jet has been presented by Pinnes (Ref. 11).

From Fig. 52, by equating the pressure and centrifugal forces acting on the element, one obtains

V 2

.0

S.a

&

R(

R1

=

(P + dP, R)

'J -

p~..Q

(11)

,- dR

or

Bernoulli's equation gives

dP = fJV 2 dR R 1/2fv2

=

PT -P Combining 12 and 13 dR

=

2 R

Integrating Equation 14 between Rl and R 2 as shown in Fig. 53 we get

(12)

(13)

(14)

P

=

1/2".0 V2 [ 1 -

(:~)

2

J

(15) Equation 15 assumes a constant curvature for all particles of the jet. From geometrical consideration (see Fig. 53) .

R

2

=

_h_-,--.,.--__

l-sinYo ( 16)

(17) By neglecting any variation of jet momentum per foot of circumference' we get

(18)

Substituting 16, 17 and 18 into 15 one obtains

\ (1

.

~

sin

"t

0) -

(.!-.)(

1 -

sinr

0 \

2

J

L

.

.2.

h / ro · ro 2 h/ro ) . 14

/

and the base thrust is

Fb = J

[(1 -

sin

r

0)

-(~)(

1 -

Sinr

o )

2J

1. .h/ro ro 2 h/ro

(20)

Equation 20 is the solution for an ambient exit pressure but

in

this case there exists a non-ambient exit pressure which causes a reduction

in

jet exit velocity. The new jet momentum is approximately

r

R2

J1

= .)

;0

V_e2 _21TrodR

Rl and from 12

The velocity V_{e at any radius R is given by} 1/2fJVe2

=

1/2fv2

(~)2

or

Using Eq. 23, Eq. 21 can be integrated to give

I t

J

=

JO - R2) and the total thru st is

and

=

cos 'to + I-sin

'(0

2 h/ ro _ 2

(!...)(

I-sin

't

0\

cos

'(0

ro 2 h/ro / (21)

(22)

(23) (24) (25) 1rto) ( I-sin

1)

0)

2 (26) ~

2 h/

ro

For the UTIAS model it is assumed De

=

2ro .

., 0

Also QO= -25 , De

=

22 in, t

=

.02"

When these values are substituted into Eq. 26 we get AL = 906

+ .

356 . h/De .0118 h/De . 018 ( . 356 )2 h/De Eqn. 27 is plotted in Fig. 36.

15

1. 2. 3.

4.

5. 6. 7.

8.

Liiva, J. Warring, R. H. Warring, R. H. T inajero, A. A. Vog1er, R. D. Fresh, J. N. Tinajero, A. A. Stanton-Jones, R. Johnson, A. E. REFERENCES

A Facility for Dynamics Testing of Mode1s of Airborne Vehic1es with Ground Effect, UTIA Technical Note No. 53, Oct. 1961.

Engine Ana1ysis - Cox Special 15. Aeromodeller Magazine, Feb. 1963. Airscrews For the Aeromodeller. Harborough Publishing Co. 1942.

Preliminary Investigations of Plan Form Effect on Augmentation Parameter for Periphera1-Jet Ground-Effect Machines. DTMB Aero Report 979. Feb. 1960.

Effects of Various Arrangements of Slotted and Round Jet Exits on the Lift and Pitching Moment Characteristics of a Rectangu1ar Based Model at Zero Forward Speed. NASA TND 660. Feb. 1961.

Aerodynamic Response of a 7 foot Gem F1ying over Uneven Surfaces. DTMB Aero Report

1434 1960.

The Deve10pment of the Saunders Roe Hover-craft SRNI-Symposium on Ground Effect Phen-omena, Princeton University. Oct. 1959. Hovering and Wind Tunnel Investigations of The David Tay10r Model Basin 3-foot Diameter Powered Annu1ar Jet Model 430. DTMB Aero Report 1041. Oct. 1962.

9. Stanton-Jones, R. Some Design Prob1ems of Hovercraft. IAS

10. Etkin, B.

11. Pinnes, R. W.

Paper No. 61-45. Jan. 1961.

Dynamics of Flight-Stability and ControL John Wiley and Sons, N. Y., 1959.

A Power Plant Man' s Look at the Ground Effect Machine. NAVAER Research Division, Report No. DR-1958, April 1959.

TABLE I

. ,

~

Ó(~b

i

)]

from Figure 39.

oe

M=o

Comparison of value s of

Vehicle t/De h/De

[

Ó(L;~

·

de

M=o , UTIAS .009 .059 -.400 UTIAS .009 .045 -.670 DTMB (Ref. 6) .032 .051 -. 7-46 SRN -1 (Ref. 7) .029

-

-.430 DTMB (Ref. 8) .025 • 130 -.287 TABLE II

·

-tOr~b)

j

Tabulated values of for UTIAS model from Fig. 40.

.084 .066 .055 .046 .027 M=o . -. 131 -.230 -. 310 -.516 -. 969

TABLEIII

Tabulated values of Me ' and Mer- obtained from Dynamic tests.

Me

(~b)

M,,-tMt)Lt,

2

IV

J]

Run- h/De ft. Ibs. / rad ft. Ibs trad/sec .~ -L .085 -1. 32 -.228 -.270 -1. 10 2 .085 -1. 33 -.229 -.202 -.822 3 .085 -1. 34 -.231 -. 141 -. 575 I 4 .085 -1. 38 -.238 -. 191 -. 778 Meanl-4 .085 -1. 34 -.231 -.201 -. 818 ~- .067 -1. 56 -.236 -.219 -. 783 6 .067 -1. 77 -.268 -. 182 -. 651 7 .067 -2.02 -.306 -. 169 -. 605 8 .067 -2.03 -. 308 -.244 -. 872 Mean5-8 • 067 -1. 85 -.280 -.204 -.730 9 .056 -2. 16 -.275 -. 171 -. 514 10 .056 -2. 59 -. 329 ..:. 211 -. 635 11 .056 -2.59 -. 329 -. 162 -.487 .-12 .056 -2. 36 -.300 -. 162 -.487 Mean9-12 .056 -2.45 -. 311 -. 177 -. 532 . 13- .043 -5. 16 -.532 -.348 -.846 14 .043 -4.25 -.437 -.262 -.637 15 .043 -3. 36 --. 346 -.234 -.569 16 .043 -4. 14 -.426 -.244 -.594 Mean13-16 .043 -4. 30 -.443 -. 272 -. 661

FAN PRESSURE PROBES

VENTRAL FIN

1

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I

FRONT TARGET POINT REAR TARGET POINT

CUT-AWAY SlDE VIEW OF MODEL

~~---l'.*~---~~

T

.---#-~ BA L..:iA BULKHEAD

PERIPHERAL JET

CUT-AWAY PLAN VIEW OF MODEL

Po!

ti

I=Q .5 .4 .3 .2 I I I I I I I I I I 10 11 12 13 14 15 16 17 18 19 R. P. M. (THOUSANDS)

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FRONT

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