Development and testing of a fixed-base hovercraft simulator

•

DEVELOPMENT .AND TEST:mG OF A FIXED-BASE HOVERCRAFT SIMULATOR

by

.

, Andrew

J.

Fraser

Kl-

'I' ~'I'I! ( I -

DelFT

2 ~Ov. 1976

..

..

DEVELOPMENT AND TESTING OF A FIXED-BASE HOVERCRAFT SIMULATOR

by

Andrew J. Fraser

December,

1975

DrI.AS Technical Note No.

197

CN ISSN 0082-5263

Ack;nowledgement

The author wishes to express hls thanks to his supervisor, Dr. L. D. Reid, farhis assistance and helpful suggestiens during work on this project,

and throughout the preparation of the final report.

Thanks is awed as well to the three test subjects, W. Pinchin, G • Rao

and D. Venturi for re-arranging their schedules to take part in the test program whenever free time could be found on the computer.

Finally , credit is due to W. Graf for developing and programing

clipping and plotting subroutines for the display. These have beceme a part

of the UTIAS computer subroutine library and have found applicatien in at least

ene other simulation project.

Financial suppert for this work was provided by the Canadian Def~nce

...

\

..

Summary

The Design and Development of a Fixed Base Hovercraft Simulator is a continuation of the work begun by Band and teported, in Ref. 1.

Electrical measurements of control posi tion at the pilot f s work

station are fed to an analogue co~uter where the equations of metion of the

yehicle under study are progra.med. The outputs frem the analogue co~uter­

vehicle position, orientation,and speed, are fed to a digital ce~uter via

an analogue to <ligital converter. The digital co~uter then generates" in proper orientation and perspective, a 'wire-frame' image of a road lined with telephone poles and clisplays it on a cathode ray tube. ,As the vehicle meves forward, the poles move towards the operator and,off the CRT or 'front windew' •

They are then picked up and displayed in their correct posi tion on peripheral

displays or 'side windows' •

In order to assess the effectiveness of the peripheral units, an

automobile simulation was programed and a tracking task carried out. When

tested to the

95%

confidence level, the

8-1/2%

i~rovement in tracking

performance with the peripheral units functioning was feund to be significant. In addition, subjective comments from these involved in the test program indicated peripheral units facilitated the adjustment to the small display and made i t easier to project into the task.

"

..

2.

3.

4.

5.

6.

7.

TABLE OF CONTENTS

Acknow1edgement

Summary

Tab1e of Contents

Notation

INTRODUCTION

VISUAL DISPLAY

2.1 Three Dimensiona1 Viewing Transformation

2.2 Two Dimensional Screen Projection

2.3 Axis Location

SIMPLIFIED DISPLAY GENERATION AND COMPUTER PROORAMMING

3.1 Display Limitat:i,.ons

3.2 Vehic1e Operatiilg Restrictions

3.3 Display Generation

3.4 Subroutines and Program Organization

3.5 Program Evaluation

PERIPHERAL DISPLAY SYSTEM

4.1 Requirement for Periphera1 Displays

4.2 Design of Peripheral Display

4.3 Programming for the Peripheral Display

é:ONTROL SYSTEM

SIMULATION TEST PROGRAM

6.1 Automobile Simulation

6

.

• 2 Vehic1e Dynamics

6

·

.3 Tracking Task and Measure;ments

6.4 Nu;merical Test Results

6.5 Subjective Impressions

ÇONCLUSIONS

REFERENCES

APPEND!x A APPENDIX B

TABLES

FIGURES

i i

iii

iv

v 1 2 2

4

5

6

6

6 7 9 10 10 10

11

12

12

13

13

13

14

15

15

16

17

A

FE

FE'

F

0

F

s Fv Ty

G

₅ G'If! 5 H

~B'

S Tx ' Ty ' u, v, w u , e v , 0 V W

x,

y,

z

x sp

x

,

s v.p. ex: 5 T

z

w 0 NOTATION

'Perpendicular distanc~ from CRT to observer . Body-fixed coordinate frame

Intermediate coordinate frame

Earth-fixed reference frame; Object Space Screen coordinate frame

Viewing coordinate frame

Laplace transfer function of vehicle dynamics; T

=

f(5)

Y

Laplace trans,fer ;func'tion of vehicle dynamics ; 'If!

=

f( 5) CRT screen height

Eulerian transformation from F

B, te FE

Sealing factor - reselutien of

DIA

converter COIIIponents of vehicle transla'tion in F

o Vehicle velocity camponents in

F

_B

Vehicle velocity cOIIIponents in

F

o Tota.:!,. speed ef vehicle

CRT screen width Coerdinates in F o

Peripheral screen coordinate

Screen coordinates of vanishing point

Performance Score - standard deviation ef vehicle lateral position, T_y' with respect te road centre line Steering wheel angle

Actual road wheel' angle Disturbanee road wheel angle

5 s

e

ti>

'Ij! 'lj!e Subscripts B

B'

o s

v

Commanded road wheel angle Pitch

Bank Reading

Standard deviation of he'ading'angle

BOdy-fixed coordinate frame •

Intermed1ate coordinate frame Object space reference frame Screen frame

Viewing frame

..

'

,

1. INTRODUCTION

The requirement to provide a relatively simple and inexpensive ground effect vehicle simulator for the purpose of pilot controllability studies

necessi tated a careful review of the desired display information • ' Aircraft simulators have successfully made use of astandard instrument presentation from which the operator deri ves his performance information • ACV' showever, cannot make use of this form of instrumentation as their operation relies heavily on visual cues taken from the real world.

Real world presentations can become very complex and costly if i t

is desired to maintain'a high degree of authenticity. Thus, for this simulation, a simple presentation was designed that would provide the operator with as many as possible of the visual cues required for actual operations, but at the same time, avoid the complexity of real world displays.

For a typical tracking problem, lateral position error provides the operator with an important visual cue. As a feedback ef the effects of corre, c-tive action, heading angle and sideways velocity must be introduced. These 'I, can be c0nstrued as first and' second order rate feedbacks. A forward speed indication allews the operator to anticipate cont rol effectiveness while pitch, roll and he ave , though not directly produced in the simple tracking problem of an ACV, will often indicate the operating regime of the vehicle. Finally, a requirement exists for some sort of preview to allow the operator to plant,his course by mentally integrating his path to some aiming point further along the road. Thus, maximum usefulness is ensured by incorporating all of these in a single display.

A si~le perspective view of a road lined with telephone poles ,was chosen for a display to be projected on a Cathode Ray Tube. The display depicted a herizon line to give pitch and roll information, road side lines to indicate lateral position, heading and he ave information, and a moving

'telephone pole' display along the road side lines to suggest vehicle velocity. Thus, this si~lified wire-frame display provided all of the important visual

cues used in the control ef a hovercraft.

The persp~ctive display was generated by an HP2l00A digital co~uter while the vehicle equations of motion were programed on a TR-48 analogue

computer. An analogue to digital çonverter provided the necessary interface. Potentiometers were mounted on the operator' s controls to transfer control position information to the analogue computer.

Since li ttle information was available to determine how influential peripheral motion ,sensation was during tracking problems, i t was decided to

incorporate a peripheral display that, in effect, carried the moving poles from the two dimensional display, located in front of the operator, through his peripheral vision field. Experimentation and subjecti ve questioning were used to evaluate the usefulness of the peripheral displays both in control and motivation.

2. VISUAL DISPLAY

2.1 Three Dimensional Viewing Transformation

Development of a two dimensional picture from a three dimensional scene for the purpose of vehicle simulation involves three distinct steps. First, the real world scene must be defined in terms of an earth-fixed

coordinate system within which the vehicle is free to move. Second, a

transformation is used to map the real world scene into a viewing coordinate system, as would be seen by an observer, reflecting his displacement and orientation with respect to the real world. Finally, the three dimensional viewing coordinate system must be reduced to a two dimensional image on a

screen.

Beginning with the most general case (see Fig. la), the coordinates of all the points forming the î'eal world scene, in this case a road lined

with telephone poles, are defined in an earth-fixed reference frame, Fo, termed Object Space. No restrictions on the orientation and posi tîon of F 0 need be

made, however for convenience in establishing vehicle orientation, the z-axis is directed vertically downward. A second axis system, FB" parallel to Fo_ and located g,t the vehicle centre of gravity, is located by coordinates (Tx,Ty , Tz ) in the F 0 frame, representing co~onents of the vehicle translation. Thus,

using column ma-trix notation, the transformation that maps the gener al coor-dinate (x,y,z) of the Fo frame into the FB' frame is given by:

~, x - T _X

YB' = Y T _Y (2.1.1)

ZB' z

-

T _z

Now a body-fixed axis system, FB' is located at the vehicle centre of gravity such that th~ x-axis is aligned with some convenient forward facing, longitudinal axis of the vehicle, and the xz-plane lies in the vehicle plane of symmetry. Next the vehicle rotations must be applied. Using the Euler angle representation, and following the notation of Ref. 2 as depicted in Fig. 1 b,

these are:

(i)

A

rotation

*

(azimuth) about the ZB' axis, bringing the axes to an intermediate F2 frame.

(ii)

(iii)

A rotation 8 (elevation) about the Y2 axis of F2' bringing the axes to the Fs frame.

A rotation ~ (banj() about the Xs axis of Fs, carrying the body-fixed frame, FB' to its final orientation.

The restrietions to these angles noted in Ref. 2 apply, however for

'

.

From the foregoing, Object Space coordinates may be mapped into the body-fixed frame by:

x

B x - T x

~B

=

LBB' Y T _Y (2.1.2)

zB z

-

T _z

where LBB' is the Eulerian Transformation and is given by:

cose cofrI/J cose sin7fJ -sine

LBB'

sir4J sineco:!tIjJ sincp sine sin7fJ sincp cose

(2.1.3)

=

_-

_{coscp sirtl/J + coscp cos7fJ}

coscp sine cos7fJ coscp sine sin7fJ coscp èose

+ sincp sirtl/J

-

sincp cos7fJ

Since the image is to be projected on a Cathode Ray TUbe, it is

desirab1e to convert the body-fixed frame to a viewing axis system a1igned with the conventiona1 osci11oscope axes, that is, with the x-axis projecting hori-zontal1y to the right, the y-axis vertica11y up, and the z-axis forward into

the screen. This is done only for convenienc~ and the transformation,

o

1

o

T =

o

o

-1 (2.1.4)

1

o

o

generates the required 1eft-handed axis system so that the Object Space coor-dinates (x,y,z) are transformed to F , the viewing frame by:

v · z v = _{T LBB'} x -Y z -T x (2.1.5) T Y T z

Equation 2.1.5 is based on the assumption that the observer's eye position is at the vehic1e centre of gravity and the CRT is located direct1y

in front of him. If the observer were to be located anyWhere other than at the

c. of g., the above equation would have to be modified to ref1ect his

displace-ment. For such a displacement defined in Fv by

(Dv

_{x ' Dv , Dv ), Object Space}

x x - D v D v v x yv

=

yv D _v (2.1.6) D y z z - D v D v v

z

where x , _Yv'

z

are determined from Eq. 2.1.

5.

v v

Equation 2.1.5 is expanded and presented in Tab1e 1.

2.2 Two Dimensional Screen Projection

With the origin of the vi ewingr frame at the ob server 's eye, three dimensional coordinates are reduced to a two dimensiona1 screen projection by the geometry of similar triangles. Referring to Fig. 2, a pair of screen coordinates (x', y'), rnay be calculated from the viewing coordinates as:

s s X x'

=

A...:!

s z v yv y'

=

A-s z v (2.2.7)

where A is the perpendicular distanee from the screen centre to the observer ' s eye position. \ Since the units of these screen coordinates are the same as the units of A, generality is preserved by nondimensionalizing the horizontal screen coordinate by the screen width, W, and the vertica1 coordinate by H, the screen height. Thus, screen coordinates are expressed in terms of screen fractions. Though not essentia1, it was found convenient to retain a first quadrant display on the screen, that is, the screen coordinate origin is located at the lower left-hand corner. This was imp1emented by adding one screen semi-dimension to each of the equations giving, in this frame:

Ax

11 V +

1:

Xs

=

WZ

2

v

(2.2.8)

For examp1e, the coordinates of the upper right-hand corner of the CRT are given as (1,1).

Again, in keeping with the generalized approach, i t is desirab1e to incorporate the resolution of the digi tal to ana10gue converter to be used. This is done by multiplying Eqs. 2.2.8 by a sealing factor, S, equal to the maximum number of points the DIA converter is capable of resolving. Screen

, ,.,

coordinates (xs ' y s) are now in integer munbers and when sUi table round-off is applied, are given by:

8 +

~

2

(

A Y)

.

Y = _ _ v_ 8+~ s H z 2 , v

Equations 2.2.9. represent the final transformation, carrying viewing coordinates into the F s or screen frame, and when the CRT axes are scaled so that the

maximum DIA output voltage produces a full screen deflectio~, _{the x s ' Ys}

coor-dinate of the upper right-hand corner of the s'creen becomes (8,8).

The screen used in this simulation was

8

inches high by 10 inches

wide, and the resolution of the high speed DIA converter was one part in

256.

The distance A, from the observer' s eye to the screen was set at

18

inches.

This gave an included viewing angle of

39°

across the screen diagonal and

represented a compromise between "window" size and ease of viewing. Tt should

be noted that to retain image fideli ty, the observer must remain at thi s di stance

fram the screen. 8hould he move closer to the screen, the perspective view will

appear as through a telephoto lens, while moving further from the screen gi yes a wide angle lens effect. For the purpose of computer programming, all simulation

constants were reduced to their numeric~:. values;

2.3 Axis Location

The derivations presented thus far have general application. For the restricted case of the straight line tracking problem, considerable simplification

can be achievedthrough th~ appropriate placement of the Object 8pace reference

frame.

The on.gLn of the Object 8pace axes is loc ated on the road centreline such that the xy-plane lies on the road surface, and the x-axis is directed

along the centreline (see Fig.

3).

Road side lines are located by the road

semi-width dimension, RW, perpendicular to the x-axis. ' The lateral posi tion of the'

poles, WP, is similarly defined, and the position of the pole tops above the

ground plane, and hencetheir height, HP, is expressed in the negative z-direction. For long term motion studies, calculations are further reduced by

permitting the Objec't 8pace frame to move along the road centreline so that the origin of FB, the body fixed frame, always lies in the yz-plane. This eliminates Tx ' or translation in the x-direction from all equations. The poles, which give the only indication of forward motion, are positioned in the x-direc'tion as a

func'_{tiE>ll of time and vehicle forward velocity. Tz ' measured along the negative}

z-axis, identifies the height of the vehicle certtre of gravity above the ground

plane, and T_y defines the vehicle lateral position with respect to the road

centre-line.

As a consequence of the ch0ice ofaxis locations, ~ becomes the heading

3.

SIMPL;rFIED DISPLAY GENERATION AND COMPUTER PROGRAMMING 3.1 Display Limitations

Two problems arise in the generation of pictorial informatibn. First, the display must be refreshed to avoid flicker or fade, and second, the

information must be continually upçiated. Since the simulator is ex:pected to operate in real time at an update rate sufficient to provide current and continuous information, time is at a premium.

Now straight lines in Object Space remain straight lines when Ilrojected onto a two dimensional screen, and the wire frame display chosen yields only straight lines. Thus it is merely necessary to calculate the screen coordinates of the end points of any line, determine the intersection of the line wi th the screen edges (known as clipping) and project this portion of the line onto the screen. Use of a vector generator would simplify this last step, however the cost was judged prohi bit i ve .

Instead, it was decided that, af ter the screen intersection points were calculated, the line in between would be digi tized by linear interpolation

and stored in an array in core. Eachcoordinate pair is called up'in turn to drive the oscilloscope deflection plates. Between coordinate pairs, a blanking pulse shuts off the CRT electron beambo eliminate beam 'wander' associated with

a coordinate change.

The interface hardware provides a refresh rate of once every 40 ms. and provision is made for a variable update rate. Floating point multiplication and division ha,rdware were added to the computer for additional time savings.

3.2 Vehicle Operating Restrictions

A survey was made of typical operational envelopes for hovercraft, and it was found that maximum. roll and pi tch excursions of .05 radians could be ex:pected while sideslip angles of the order of .80 radians were not uncommon during some manoeuvres. Simple 'tracking tasks, however, would yield sideslip angles closer to a more reasonable .40 radians in the presence of modest cross-winds.

Reading angles greater than .27 radians result in a display wi th the vanishing point entirely off the screen for the straight road case and viewing

constants previously selected. Tracking under these conditions would be un-natural,as in real life, the operato:r would shift his gaze to the side window, if necessary, in order to select an aiming point several hundred feet down his proposed path. This loss of the appropriate rate feedback cue is the most

severe limi tation imposed on this simulation and ·can be rectified by choosing a larger display, or providing CRT side "windows" with the appropriate images generated on them.

For the purpose of this study, it was decided to accept present equip-ment limi tations and impose appropriate restrictions on the vehicle operation.'

-cp

±

.1 radians

,S ± .1 radians

î/J

±

.3

radians

These limi'tations ensure th at the vanishing point is normallyon the screen.

3.3

'

Display Generation

Much simplification of the calculations can be achie'Ved wi th only slight loss of image fidelity through the following considerations.

8ince all combinations of bank and pitch produce a horizon line that intersects thé sides of the CRT screen, the followihg equations, based

on small angle approximations and derived in Appendix

B,

can be used to

generate the endpoints, (xs , Ys ) and

(X

_{S2 ' YS2)' of the horizon}. line, in the screen coord,inate system. Rote

~hat

no further clipping of the line is necessary.

x

=

0 sJ. YSl,

= (-

AS -

Xirp)~

2 H +~ 2

(3.3.1)

y . = (- AS +

Xi

rp )

~

+

~

S2 2 H 2

The subscripts 1 and 2 are used for the first and second point of each coordinate pair that defines the end.points of a line throughout the text and computer program.

8ince the road is straight, both side lines converge to a connnon van-ishing point. The screen coordinat'es of the vanishing point, rray be calculated by using small angle approximations in the exact equations of Table 1. The

resultant equations are substituted into Eqs. 2.2.9 where y

=

0 and z

=

0 (sinee the vanishing point lies on the road centre line) and letting x ~ 00 so that the vanishing point equations are:

x s v.p. - A (rpS _ 011)8

+

~

- Til

'f 2 y s =

~

(-S - I

rpî/J)

8 +

~

v.p.

The left and rignt foreground endpoints of the road side lines must be calculated using some finite positive x-distance. A value of 10 feet was

subs ti tuted into the small angle approximations of Table 1 where all double and triple angle produets are dropped. Considerable computational time saving is effected by this simplification and Eqs. 2.2.9 convert the points into screen coordinates. As these lines extend below the CRT window, they must be clipped before being digitized. The vanishing point is the second point in each case, of the coordinate pairs that define the lines forming the road side lines.

Rather than calculating coordinates for each individual pole top and base from lengthy equations, screen coordinates for a pair of imaginary control poles located at x·

=

100 fee·t are calculated and stored without being displayed. Again small angle approximations are used in Table 1, rejecting all higher

order products . From these four coordinate pairs, and the vanishing point coordinates, the coordinate pairs for each pole top and base can be calculated by linearly interpolating along the four 'rays' joining the vanishing point and the two end points on each of the control poles. Where XP is the dis·tance to

the real pole under consideration, and 100 is the distance tE> the con trol pole

(xp

and 100 are in the x-direction of Object Space) , the proportionality constant K (computer variable

AK)

is determined as:

K

=

(Xp - 100)

XP (3.3.4a)

If the screen coordinates of the Pole Base of the Left control pole are given as (PBLX,PBLY), then the screen coordinates of the-real pole at XP are determined to be:

x = K(x PBLX) + PBLX

s~ s

v.p.

(3.3.4b)

Ys~ K(y - PBLY) + PBLY s

v.p.

Similar forms of 3.3 .4b hold for the remaining three coordinate pairs, and the deri vations for the three equations may be found in Appendix B.

Pole positioning is achieved by setting a fixed reference distance, REFXP, as the nominal furthest x-distance in Object Space at which the first pole pair is to appear in the display, in this study, 700 feet. A variable reference distance XPl (also in Fo) is th en initially set equal to this fixed reference distance. The first pole pair appears at this variable reference

dis·tance and subsequent pole pairs are calculated at XPl minus integral multiples of the pole spacing, SP, until a pole has a negative x-coordinate, in which case it is ignored. The display information is updated af ter an elapsed time interval. llt, and the variable reference dlstance is reduced by a distance V!:s.t, where V is

the velocity component of the vehicle in the x-direction, and pole pair calcula-tion proceeds as ·before. When the variable reference distance is reduc'ed from the fixed reference distance by a value equal to the pole spacing, the variable reference distance is incremented by one pole spacing to reset it to the fixed reference distance. Thus, poles appear continually at some fixed distance down the road and move toward the observer so th at no time is wastea. calculating poles at a distance beyond the resolution of the screen. The operation niay

3.4

Subroutines and Program Organization

A listing of the Fortran prcgram appears as Appendix A and a flow chart is shown as Fig.

4.

The subroutines are written in assembler language and their listings are not incorporated in this report.

The program begins by reading the selected simulation constants from the teletype. These, of course, may be varied to suit the particular simulation.

The first subroutine called, STIME, is used to define the time interval between updates in 10 ros.· increments and sets up the interrupt locations. Subroutine TIME ini tially sets the 10 ms. interval counter, NPASS, to 0, then usesthe time base generator (TBG) to time intervals

between caUs to TIME. The program is used with the interrupt system on so .

that when a fixed time unit of 10 ros. has elapsed, the TBG interrupts what-ever calculations are in progress, and increments NPASS by one interval before returning control to the main program. At the end of the update

calculations, PTIME provides a waiting loop, effectively halting the program until the specified time interval IUPDT has elapsed. If a longer period of time has already elapsed during the updatecalculations, the program immedi-ately continues wi th the plotting routine, and when finished, returns to the beginning, resetting NPASS to 0 again through TIME. This waiting loop intro-duces a pure time delay in displaying current information to the operator, but its estimated duration of about 50 milliseconds is of no significance to a human operator. SREG causes the elapsed time interval to be displayed in the S register of the computer

epu

for monitoring the speed of the update c.alculations. PLTIN and MPIN set up the appropriate interrupt locations.

The current values of ~, 8, ~, _{Ty , Tz , and V are read from the}

AID

converter through subroutine SAMP. These readings are scaled for the simula-tien bystatements within the program.

Initially, two core locations, IBUFAl and IBUFA2, are established through subroutine BUFA. These are the entry points to two arrays, IBUFA and IBUFB of 2000 words each. While the program calculates the digitized .line information and stores it in one buffer, the other buffer is available as the data source for the plotting process that interrupts every 40 ros. to refresh the display. This procedure uses direct memory access (DMA). Upon completion of an updated array, that is, when the entire display has been recalculated and stored in the first buffer, the entry adress locations are interchanged so that the plotting subroutine, PLOT, now displays the most recent informa-tion.

m

isthe counter used to keep track of the number of points to be plotted or displayed.

Subreutine POINT clips and digitizes each line, storing the coor-dinates in the current buffer. It requires only the end points of each line defined in screen coordinates. POINS is a separate entry point to subroutine POINT for use when i t is known that a line will not need to be clipped. The horizon line is the only line that falls into this category but the resultant

3.5 Program Evaluation

Using an IBM 1130 computer and a CALCOMP plotter, plots were made of the screen images produced by both the approximate approach as described

above, and the exact transformation based on the equations of Table 1. The

results of these plots are shown in Figs. 5a through 5c. As can be seen, for moderate heading angle and side position excursions, the difference in

the two methods would be less than the resolution of the

Dj

A converter . As

the vehicle operating maxima are· approached, errors become more apparent but

i t is judged that these errors would be of no practical significance in a

tracking problem.·

In the actual program used for the di splay (Appendix A), pole tops

were given the same xs coordinate as their respec"tive bases. If this was not

done, it was found that the discrete nature of the digitization and

DjA

con-version created I sawtooth I poles, causing some distraction to the operator.

The horizon line provides the most powerful rolling cue in any event, and i t was judged that the inconsistency of vertical poles in a banked attitude was barely noticeable. This is exemplified in Fig. 5d.

To save plotting time, program PLOT was modified to plot only every

second dot across the screen, gi ving 128 points along each axis. As far as

calculating the position ofpoints on the screen, the resolution still remained

fixed at one part in 256. None of the subjec"ts later tested made any connnent

on the slightly perceptible discrete points making up the display, though one favoured changing the focus of the CRT to obtain a more homogeneous image.

The calculation ofthe distance travelled down the road between information updates, that is, over an interval Llt, is based on a computed constant velocity for that interval. The resulting staircase integration gives an accumulating error in the x-direction, which is not significant for tracking problems.

Finally, i t was found that co~lete updates required ab out 50 ms.

of calculation time. Since the present refresh rate of once every 40 ms.

produces no flicker or fade, the possibility remains to suppress the refresh

completely, and plot the image at the maximum update rate. A slight time

saving would result. The entire refresh operation is estimated to take ab out

5 ms. wi th the display chosen, but could be expec"ted to rise with a greater

number of points. No jerkiness or discontinuity could be detected in the

image for the update rate achieved wi th the screen resolution used in the

simulation, even at the extremes of the operating limitations chosen.

4. PERIPHERAL DISPLAY SYSTEM

4.1

Requirement for Periphe ral Displays

Extensive research has been carried out to determine the limits

of peripheral vision and the usefulness of information presented within the

perip~eral field (Ref. 3). To date, no information has been presented

con-cerning the enhancement of two dimensional displays af ter the fashion proposed

in this report. The small size of the display used in this simulator gives rise to the well known problem of apparent motion reversal (Ref. 4). Subjects

initially fe el they are moving in the opposite sense to that actually depic ted

on the display. In real life si tuations, the imposing size of the real world,

through both forward and peripheral vision, leaves no doubt that i t is the vehicle and hence the operator, that is moving, not the visual image. But in the case of small displays, the small size of the image may cause the operator

to believe that he is controlling the image, and hence the control system

appears reversed. As wi th the artificial horizon in aircraft, training can

overcome this deficiency but the use of peripheral displays was proposed as a means of extending the size of the simulation, and minimizing these effects •

4.2 Design of Peripheral Display

The function of the peripheral display units is to create a third dimension in the simulation by carrying the motion of the poles from the screen in front of the operator, through his peripheral vision field. As reported

in Ref. 3, cOlour, shape, and motion discrimination deteriorate ·towards the

limits of the peripheral field. However, as the forward part of these units

lies within the central viewing field, a certain fidelity of simulation must be preserved.

The original method proposed by Band in Ref. 1 suggested using motor

driven cylinders wi th sli t-shaped apertures, rotating about a long-filament

light bulb. Operation would be at a constant velocity and would connnence on

a trigger signal from the digi tal computer. Even at modest simulation spe eds

of up to 30 mph, rotational speeds of from 0 to 60 rpm would be required for

the motor system. The long time constants associated with such a system and

the accUIPulating positional error on each single sweep at the cons tant veloci ty,

required an alternative approach.

Instead, a system was developed using galvanometers to posi tion the

vertical light beam on the peripheral screen. Fi ve flashlight bulbs connected

in parallel and located behind a narrow slit made from steel shim-stock, gave a vertical line light source. This was focused through a lens and directed onto al" diameter, front- surface mirror mounted onthe galvanometer. The

galvanometer had a swing of ± 15°',. gi ving a light swing of 60° of arc for

display purposes. The vertical line or pole was focused onto the rèar of: a

piece of plexiglass made translucent by sanding. Right- and left-hand units

were mounted in plywood boxes and located at the operator' s eye level at a 40° angle to the CRT (see Fig. 4c and 6).

The galvanometers selec·ted were General Scanning G- 330 units. These

are not tangent corrected, that is, the mirror angular position is directly proportional to applied current. The natural frequency of the units wi th the 1" diameter mirror installed was 112 Hz., well above the operating frequencies anticipated in most simulation situations, so that mirror position can be considered directly proportional to the applied voltage. Mirror posi tion was calculated digitally and an output voltage is generated at the low speed

(50 !-lS. conversiontime) Multiprogrammer DIA converter. A locally manufactured buffer provided the nécessary voltage-to-current impedance transfer,smoothed

out the step output of the DIA converter, and incorporated a gain adjustment

for accurate calibration and matching of the units.

The calculated step response time constant for a. full 60° swing of

detectable· in the periphery so that no shuttering or light control was used during the 'flyback' or reset motion of the light beam that occurs as

sub-sequent poles are picked up and displayed. As reported in Ref. 3, angular motions in the peripheral field of between 9000

and 1200<> per second are detectable, but shape and direction of motion are not discriminable. The angular sweep rate during reset was equal to l1500

jsec. During the test program, no subject commented on any .11eficiency in this respect, and only with concentration could this motion be detected.

4.3 Programming for the Peripheral Display

Programming for the peripheral motion is straightforward, and both the geometry and the flow chart are shown in Fig. 4c. Basically, the program tests the screen coordinate, xs~, of the base of a pole to see if i t lies

within the viewing angle included by the 'side window' . (This angle is defined by integer screen coordinate cons tants, Xs of 426 and 2613 for the right-hand

side.) If i t _{does, the peripheral screen coordinate x sp is calculated as a} function of xs₁ , and the digital to analogue conversion number, NDAR, which

incorporates the tangent correction and

Dj

A sealing, is detemined next. If the pole does not fall within the lateral viewing angle, NDAR is set equal to 1750, a value that holds the light beam beyond the aft limits of the peripheral

screen and out of sight until a pole is to be displayed.

The variable, IPASR, ensures that in the event two poles fall within the limi ts of the screen, the pole farthest forward on the unit, or closest to the central vision field, is displayed. The flow chart of Fig. 4c shows the programming for the right"'hand uni t only. However the left-hand unit is similar as can be seen in the listing of Appendix A. Subroutine MjNTR controls the

Dj

A interface operation.

5 • CONTROL SYSTEM

I t has been observed (Ref. 5) that control feel can have a pronounced effect on pilot opinions of vehicle s tabili ty and control. Thus it was necessary to develop some sort of control system that at least approximated the feelof the vehicle being simulated.

Many different control layouts and configurations may be found in

hovercraft, of ten completely different for vehicles of similar size. To avoid having to rebuild acontrol system for each simulation, the more common aircraft configuration of wheel and rudder pedals was adopted here. .A survey made of hovercraft control configurations indicated all vehicles had at least

one of these controls.

A simple lever and spring arrangement about the axis of the wheel permitted a 'ground-adjustable' control feel. By varying the length of the lever arm, the spring constant, and the spring preload, widely different, nonlinear force gradients could be achieved. A similar Slfstem was developed for the rudder pedals. A diagram of the control wheel configuration as well as a force gradient curve used in the simulation of Section 6 are shown in Fig. 6b.

Potentiometers, motmted on the controls , provided control posi tion information directly to the analogue computer. The choice of lk pots on the controls feeding operational amplifiers with lOOk input impedance, ensured th at na significant electrical loading -effects would be present.

A special simulator booth housed the controls and displays while the computing and recording facilities were located in a separate room. Figure

7

shows pictures of the booth and associated facilities.

6.

SIMULATION TEST PROORAM

6.1

Automobile Simulation

To determine the .authenticity of the display and the usefulness of the peripheral units, Ç3. simulation test·program was required. Though the

simulator was developed for hovercraft studies, the general tmavailabili ty of test subjects with sui table experience rtiled out suéh a-simulation. Instead, it was decided to simulate the dynamics of an automobile. Subjects with

driving experience were readily available so that meaningful comparisons could

be made. .

The automobile-simulation method of Ref.

6

was used with the addition of a

3

ó

deadband at the steering wheel input to closer approximate the character-istics of an actual car. Vehicle dynamic charactercharacter-istics representative of a full size North American sedan travelling at 30 mph were taken from Ref.

7.

These values are summarized in Table 2.

6.2 Vehicle Dynamics

I t was assumed that the origin of the viewing axis system, Fv, and

hence the driver's eye position, was located at the vehicle centre of gravity. This assumption was not necessary but for any other location, the program would

have to be modified to incorporate Eq~ 2.1.6. In fact, for more complicated studies, to locate the eye at other than the centre of gravity might give rise to false-impressions of motion. For example, if a vehicle pitched about its

centre of gravity while the operator was located well forward of this point, the operator would see a combined pitch and heave IIlotion on the display. On such a small display, this might lead to confusion in interpreting the actual motion _

of the vehicle, -though in a real world situation, such subjectj,ve ambiguity may not exist. I t is suggested that this simplification be employed routinely.

Secondly, programming can be kept to a minimum by assuming vehicle lateral velocity, v, (in FB) and vehicle total veloci~y V, correspond to V_{o and}

Uo respectively, in Object Space (see Table 2 and Fig.

3),

keeping in mind that the maximum heading angle was restricted to 0.3 radians. These assumptions are similar to those of Ref.

6,

and are compatible with the small angle approxima-tions used in generating the display. The analogue programming for this simula-tion appears in Fig.

8.

A Pace TR-48 analogue computer having a 10 volt reference voltage was used and the variables in Fig. 8 are defined in terms of machine

6.3 Tracking Task and Measurements

The task each subject was required to perform was that of simply 'driving' the vehicle down the centre of the lane while an external disturbance was applied (see Fig. 5c for display geometry parameters).

The potentiometer signal for steering wheel angle, ex s' was scaled to simulate a 20:1 gear ratio from steering wheel angle to commanded road wheel angle (Le. 5_s = .05CXs). This resultant command signal, 5_{s ,} was passed through the diode deadband circuit shown in Fig.

7 ,

equivalent to a 30

deadband at the steering wheel. The modified command angle was then sun:n:ned wi th a disturbance an,gle, 5d' ·to gi ve the final road wheel angle, 5, as the input to the vehicle dynamics .

The disturbance was a random-appearing signal composed of four non-harmonically related sine waves of 6.28, 3.00, 1.20, and 0.50 rad/sec, and all

of a.:rtqlli tude equal to 0.20 X 10-3 radians of road wheel angle. The RMS value

of the noise signal was 2.83 x 10-3 radians, which was equivalent to 3.250

of steering wheel angle. This input noise could be interpreted as road surface roughness continually disturbing the road wheel angle. Ten separate three minute records of disturbance .were stored on tape, ensuring a random phase relationship between sine waves, and a typical time trace of this noise appears in Fig.

9.

Three modes of operation of the simulator were tested: Mode A: Full display and operating peripheral units. Mode B: Full display without peripheral units.

Mode C: Partial display consisting of road side lines and horizon line but no poles and no peripheral units, that is, no forward lID tion cues were

present.

OVer a period of several days, three subjects underwent a series of sessions in the simulator lasting about 45 minutes each. The first few sessions provided training, allowing subjects to become familiar wi th both the display and the vehicle dynamics , while the last three sessions formed the data base for the experimental test results . The number of training sessions was adjusted from subject to subject to ensure each individual' s learning curve had 'flattened out' • Learning curves and test runs are shown in Fig. 10 for all three subjects tested.

From the Mean and Mean Square~ _{values of the lateral position, Ty ,}

computed over a fixed time interval on the analogue computer (see Fig. 8), a performance score,

Y

_{e ,} was calculated as the standard deviation of side position. Similarly, the standard deviation of heading angle,

?/Je,

was determined as a measure of the control activity used by individuals while tracking.

During sessions, subjects were given a program of two minute runs, out of which 100 seconds of data weré recorded. Each session began with sufficient unrecorded warm-up runs for the operator to feel comfortable in the simulator, and during the training sessions, the various modes were tested in a random order. Throughout the actual test portion, randomized groups of three runs for a partic-ular mode were recorded with the results of the first run dropped during data

reduction to help eliminate any adaptation effects between modes. A total of 27 test runs was completed for each subject.

After the training period and af ter the last test session, subjects were questioned about their impressions 0f the simulator, and suggestions for

improvement were· invited.

6.4

Numerical Test Results

The 27 test runs were divided equally among the

3

modes for

9

runs

under each set of conditions. When these ;were subdivided into 'groUps of

3,

with the first run of each group eliminated, six independent test runs per

subject for each mode remained. Mean values of the p~rformance _{score Ye for}

each mode are shown in Fig. 11, by subj ect, along .wi th the 'standard· deviation.

Mean values of the test results are swrnnari,zed, again by subjéct, -in Table

3'-It can be seen from the mean·lateral position .in this table, that subjects 1

and

3

tended to favour the left-hand side of the road, while subj ect 2 showed

no di~~inct preference.

The average of the performance scores for all three subjects shows an 8-1/2% improvement in traeking performance in going from Mode B to A, and

a 13-1/2% improvement in tracking performance in going from Mode C to A. An

analysis of variance of the performance score was campleted to determine the

significance 0f this observed improvement, and when 'tested at the

5%

level, the

differences were found to be significant. A su:rmna.ry 0f the analysis of the

variance is shown in Table

4,

and a time record of operator performance is shown

in Fig.

9.

6.5

Subjective I~ressions

Though dri ving experience of the test subje cts varied from "no dri ving experience within the past two years" to "daily commuting of 20 miles" , their subjective assessments 0f the simulator were in close agreement.

The initial tendency to fixate on the motion of the vanishing point

to the exclusion of the road side line cues, resulted in inadvertent control reversal, which was most pronounced (and persistent) in Mode C displays. With training, subjects found the 'real world' aiming point some two or three pole

spacings down the road (200' to 300'), and were then able to project 'into' the simulati on.

When asked if the driving task simulated a ri de over a rough country road, all subjects stated that the lack 0f kinesthetic cues detracted signifi-cantly from such a s imul at i on , but no subject noted any periodic nature to the bumpiness or disturbance input. Control of the vehicle i t's elf was termed

some-what sluggish, but it was' judged that if appropriate kinesthetic cues could be

incorporated, i t would indeed be reali stic.

During Mode C tests, simulations having no forward metion cues, subjects agreed that they lost all feeling of a real world operation, and were just

controlling an instrument. In general, subjects felt that the motion cues of the poles on the CRT display were essential to the simulation, and that the peripheral

displays enhanced their abili ty to interpret the display as a real world simulation. The two subjects who favoured the left-hand side of the road said they lacked an indication as to where the centre of the vehicle was with respect tothe c:entre of the road.

7 •

CONCLUSIONS

Operation of the sys·tem has been found satisfactory and reliable. No

programming or mechanical defect~ arose during the test program.

Tt is suggested that ·the introduction of vibrations at the operator' s

seat be considered as a method of masking any anticipated kinesthetic c\les. This would be more applicable to vehicles with surface contact than to

hover-craft, but greater environment al fidelity with respect to noise and engine vibration could be easily achieved, and would probably be beneficial. Only a larger display or the inclusion of peripheral CRT displays can eliminate the

restric·tion on heading angle, necessitated by the loss of path preview at large

heading angles.. Tt is possible that some tracking problems or performance

evaluations would not require heading angles that exceed the capabili ties 'of

this si1llulator, so that this restriction might pose no problem.

Use of peripheral displays to complement the motion depicted on a small two dimensional screen creates a more compelling simulated real world. Operator performance improves under these conditions, and subjects are more

easily able to project into the task. In effect, use of peripheral units .

1. 2.

3.

4.

5.

6.

Band, D. Etkin, B. Vallerie, L. L. Bernotat, R. K. Gartner,

K.

R. ed. Van Cott, H. P. Kinkade, R.

G.

ed. Weir, D.

H.

Wojcik, C.

K.

.Al.len, R. W. et al Newman, W. M. Sproull, R. F. Peatman, J. B. Kingslake, R. Winer, B. J. REFERENCES

"A Pr~liminary S tudy of the Feasi bili ty of an .A.:ir Cushion Vehicle Simulator". UTIAS 'rN No. 189, April 1974.

"Dynamics of AtJ!l.Ospheric Flight". Wiley, 1972. "Peripheral Vision Displays". NASA CR-808, June 1967.

"Displays and Controls". Swets &. Zeitlinger, N.V. Amsterdam, 1972 (pp. 39-132).

"Huma.n Engineering Guide to Equipment Design". U.S. Government Printing Office, Washington, D.C. Lib. of Con., No. 72-600054, 1972 (pp. 668-699).

"Measurement of Driver Describing Functions in Simulated Steering Control Tasks". Seventh Annual Conference on Manua1 Control, NASA SP.;.281, June 1971 (pp. 209-218).

".Al.coho1 Effects on Driving Behaviour and Performance in a Car Simulator". IEEE Trans. Syst., Man, Cybern., Vol. SM;-5, Sept. 1975 (pp. 498-505).

Additional Reading

"Principles of Interactive Cony;mter Graphics". McGraw-HilI, 1973.

"Design of Digi tal Systems". McGraw-Hi11, 1972. "App1ied Optics and Optical Engineering". Vol. I, Academie Press, 1965.

"Statistical Principles in Experimental Design". McGraw-Hi11, 1971.

APPENDIX A

0060 XSvp=ePHI*THETA-PSI>*460.8+127.

0061 YSVP=127.-eTHETA+PHI*PSI~*576.

""62 C

0063 C

0064 C ****ROAD SIDE LINE CAl.. CUI.ATI ON S

0065 C 0066 PI0=-10.*PSI 0067 TI0="; 10'-* TH ETA 0068 RYI = RW+"TY 0069 RY2=RW-TY 0070 XSI=epI0+RY2-TZ*PHI>*46.08+127. 0071 YS1= e Tl0+RY2*PHI+TZ >*57.6+ 127.

0072 CAl..L POINT eXSVP,YSVP,XSI,YSI;IPT, IBFAI >

0073 XS1=epI0-RY1-TZ*PHI)*46.08+127.

0074 YS1'" e TI0";RY li1iPHI+TZ >*57''- 6+ 127.

0075 CAl..L POINT eXS1,YS1,XSVl',YSVP~'IPT, IBFA1 >

0076 C

0077 C

0078 C ****CONTROL POLE CAl..CULATION

0079 C 0080 Pl=-100.*PSI 0081 T1=";100.-*THETA 0082 WYl=WP+TY 0083 WY2=WP-TY 0084 HZl=HP+TZ 0085 HZ2=HP-TZ 0086 PTLy=eTl-WY1*PHI-HZ2>*5.76+127. 0087 PBLX::: ep l-WY 1-TZ*PHI >*4. '6+ 127. 0088 PBL Y= e T l-WY1i1iPHI+TZ >*5''-76+ 127. 0089 PTRy=eTl+WY2*PHI-HZ2>*5.76+127. 0090 PBRX=epl+WY2-TZ*PHI>*4.6+127. 0091 PBRY= e T 1 +WY2*PHI+TZ >* 5''-7 6+ 127. 0092 C

•

0093 C 0094 C ****POLE DISTRIBUTION 0095 C 9096 XP=XP1 0097 IPASL=0 9098 IPASR=0 8999 88 CONTINUE 0100 AK=(XP-100.>/XP 0101 XS1=AK*eXSVP-PBLX>+PBLX 9102 YS1=AK*eYSVP-PBLY>+PBLY 0103 XS2=XS1 9104 YS2=AK*eYSVP-PTLY>+PTLY 8105 1 Fe I PASL > 30, 30, 45 0106 30 IFe-172.-XSI> 40,40,32 0107 32 lFeXSI+2359. > 40,40,34 0108 34 lPASL= 1 0109 xsp=e-20.50*XSl-3519.94>/(513;82-XSI) 0110 NDAl..=";1680.+3208.6*ATANeXSP/9.>

•

8111 GO TO 45 0112 40 NDAl..=1750 0113 45. CONTINUE

8114 CALL POINT (XS2, YS2, XSI, YS I, I PT, 1 BFAI)

0115 XSI=AK*(XSVP-PBRX)+PBRX 0116 YSI-AK*(YSVP-PBRY)+PBRY 8117 XS2-XSl 9118 YS2-AK*(YSVP-PTRY)+PTRY 8119 1 Fe 1 PASR) SB, SB, 65 A-l

•

1313131 131302 01303 0004 0005 0006 0007 0008 0009 0010 0011 0012 131313 0014 13015 01316 0017 0018 01319 013213 0021 0022 0023 0024 0025 0026 0027 01328 0029 131330 01331 0032 111033 0034 11111135 011136 0037 111038 01339 004111 0041 0042 111043 111044 01345 1311146 011147 1311148 0049 0050 131351 13052 0053 0054 0055 13056 0057 11111158 131359 C*****PERSPECTIVE 24 OCTOBER 75 C C C

C***** SIMULATION CON STANTS C WRI TEC 2" 200) 21313 FORMATC"UPDATE RATE? .... ) READ< 1,,*) UPDAT WRITE<2,,201) 201 FORMATC "RW" WP" HP? .... ) READCI,,*) RW"WP"HP WRI TEC 2" 202) 202 FORMATC "SP" REFXP? .... ) READC I" * ) SP" REFXP WRI TE C 2" 203)

C C

203 FORMAT< "TYMAX" VMAX? .... ) READ(1" *) TYMAX "VMAX I UPDT=- UPDAT 110. XP I =REFXP CALL STIMECIUPDT) CALL BUFACIBFA1"IBFA2) CALL PLTIN CALL MPIN C***** SAMPLING C 10 CALL SAMP C C CALL TIMECNPASS) CALL SREG<NPASS) IPT=0 C ****SCALING C C C PHI=!21.1*FLOATCIANDCIBUF(1),,177700B»/32704. THETA=0.I*FLOAT(IANDCIBUFC2),,1777!21I1lB»/327~4. PSI=0.3*FLOATCIANDCIBUF(3)" 177700B»/32704. TY=TYMAX*FLOATC IAND( I BUF( 4)" 177700B) )/327134. TZ=3!21.*FLOAT(IAND(IBUF(5),,177700B»/32704. V=VMAX*FLOAT(IAND(IBUF(6),,177700B»/32704. DELT=FLOAT(NPASS)*0.01

C ****HORIZON LINE CALCULATION C C C XSI=0. XS2=255. YDUM I = 1"27. -576. *THETA YDUM2= 160"'-*PHI

YSI =YDUM 1 ;';YDUM2 YS2=YDUM 1 +YDUM2

CALL POIN S(XS I, YSl" XS2" YS2" IPT" I BFAI) C ****VANISHING POINT CALCULATION

C

A-2

0120 0121 0122 0123 0124 0125 0126 0127 0128 0129 0130 0131 0132 0133 0134 0135 0136 0137 0138 0139 0140 0141 0142 0143 0144 0145 50 IFeXSI-426.) 60~60~52 52 IFe2613.-XS1) 60~60~54 54 I PASR= 1 XSp=e-8727.7+20.5*XSl)/e259.8+XSl) NDAR=-1680'-+3208. 6*ATAN(XSPJ9.) GO TO 65 60 N DAR= 1750 65 CONTINUE

CALL POINT eXS2~YS2~XSl~YS1~IPT~ IBFAl) XP=XP-SP I FeXP)85~ 85~ 80 85 CONTINUE 86 XPl=XPI-V*DELT IFeXPl-eREFXP-SP»90~90~95 90 XP1=XPl+SP 95 IFeXPI-eREFXP+SP»100~ 100~97 97 XPl=XPl-SP 1 00 I BF D= I BF A 1 I BFAI = I BFA2 IBFA2=IBFD CALL PTIME

CALL PLOT e IPT~ IBFA2) CALL MCNTReNDAL~NDAR) GO TO 10

END ENDS

APPENDIX B 1. Derivation of Equations 3.3.1

This derivation assumes that zero elevation of the vehicle corresponds to a horizontal Zv viewing axis but may be easily modified for other si tuations.

With no elevation and no bank, and '\.ll1der the assumption made above, the integer screen coordinates for the left-hand side of the horizon line are

(0,

8/2), and for the right-hand side, (8, 8/2). Note that the Xs coordinates

ofthe ends of the horizon line xS:L' xSE remain constant due to the vehicle

operating restrietions • .

With reference to Fig. B-l, the change in YS:L and YS2 due to vehicle elevation are calculated as:

8A tan8

- H

(B.l.l)

Now the position of the horizon line on the screen is independent of

the heading angle of the vehicle, so that at some given angle of elevation, a

rollof angle

cp

about the oZv axis produces a rotation of the displayed horizon

. line of

cpcos9 •

Examining Fig. B-2, it can be seen that the roll effect on the inter-section points of the horizon line with the screen edge can be calculated as:

by , S:L

W . 8

!:::"y = ± - tan(cpcose)

-S2 2 H (B.1.2)

The vehicle operating restrietions of 8ection 3.2 ensure that the

horizon line infersects only the sides of the CRT. 8umming these effects , and

using small angle approximation, the screen coordinat es for the end points of the horizon line are given as:

x 0 S:L YS:L (- A8 -

~

cp )

~

+~ 2 x 8 S2 Y _S2

=

(- Ae +

~

cp )

~

+~ ₂ 2. Derivation of Eg,uations 3.3.4

The integer screen coordinates of the Pole Top ef the Right-hand control

pole are given as

(PTRX,

PTRY). These are calcUïate~by using the small angle

approximaUons of Table 1, dropping all higher order angle produets , then

In order to simplify the notation for the following development define the coorcUDates of the top of the right-hand control pole by:

F

(x'

y'

z')

V' v' v' v

F

(x' y')

s s' s

and the cQordinates of the top of a general right-hand display pole by:

F o(xp ' yp' z_P . ) F (x , v vP YVP' z vP ) F (x s sp' Ysp' zsp) Define l:sx.. ~

(x

- x')

v vp v ba. ==

(z

z')

v vP v !:::ix. _s ==

(x

_sp

- x')

_s

x

= (

~

x;v-)

S

+

§. s W z 2 v Using B .•

2.2

i t can be shown that

where l:sx..

~

AS (

~

_

x~)

s

W

z

z'

vP v AS

x

S -.-~=x --2 W z s~ vp

(B.2.l)

(B.2.2)

(B.2.3)

(B.2.4)

and Thus Fram B.2.1 and B.2.3,

x'

AB v S W

Z'

=, PI'RX -

'2

v

&

=x -PI'RX s s~ & AB ( !:::.xv

+

x~ x~

) s =

W

!:::.z + z' -

Z'

v v v = AB !:::.zv ( !:::.xv _

x~)

W

z

&

z'

p v v

Now using Table 1, for Tx = 0 and small angles, i t follows that

z'

=

x' + (y' - T )~ - (z' - T )9

v

Y

z

z

=

x + (y - T )~ - (z - T )9

vp P P Y p z

But for the present display

Thus, from B.2.9 and B.2.l0

y'

=

y p z'

=

z p !:::.z =

(z

- z')

v vp v =

(x

- x')

p (B.2.5) (B.2.6) (B.2.7) (B.2.8) (B.2.l0) (B.2.ll)

Also, except when the pole is quite close to the vehicle, (from B.2.9)

z ~ x

Thus, substituting B.2.11 and B.2.l2 in B.2.8 obtain

where

and fram B.2.6 and B~2.l3,

X SJ. (x - Xl) K

=

--'p"----x p ( & .

XI)

AS v v =P.rRX+-K _W - - -_{f:yz, Z I} V V (B.2.l3) (B.2.l4) (B.2.l5)

Noting toot a straight line earl be drawn through the top of the control pole, the top of the gener al display pole and the vanishing point, it follows that

(x - Xl) ::; VI> v =

(z

-

Zl)

VI> V (x" - Xl) V V

(z"

Zl)

V V

where (") denotes the vanishing point. Now, sinee Z"

»

z I v · v' (fram 2.2.9), and x" x"

SA

v

SA

v

W

(z" - Zl)

~

Til

zrr

v v v XII S :::: S -

'2

.

Xl

SA

v W

(z" _

Z I) ~ 0 v v

Substituting B.2.5, B.2.l6, B.2.l7 and B.2.18 into B.2.15 obtain

x = Pl'RX

+

K(x" - PTRX) SJ. s (B.2.l6) (B.2.l7) (B.2.l8) (B.2.19) Replaeing x" by Xs to eorrespond to the notation of Seetion 3.3 obtain

s v.p.

x

=

K(x - PTRX) + PTRX

SJ. s v.p. (B.2.29)

__ z -- v

A

---,

,

- - - -

--

---

e

__ ---\6.

y .

~

__ ---- s

.& __ ---:-

_ _ _ _ _ _ _ _ _

}_,2_ _ _ _ _ _ Horizontal Observer CRT Screen Figure B-l CRT Screen

---.---1~s2

i

due to

e

j

-t

_ _

6

y 5 due to <f> 2 (xs ' y s )

~\.

_.1

2 2 'vI . Figure B-2

..

Xv = _{Cx - Tx) {Sin<t>SineCOSIjJ - COS<t>SinljJ}} + _{Cy - Ty) {Sin<t>SineSinljJ} + COS<t>COSIjJ} + Cz - T z) {Sin<t>cose}

Yv

=

-~X

_{- Tx) {COS<t>SineCOSIjJ} + Sin<t>SinljJ} + Cy - T_y) {COS<t>SineSinljJ - Sin<t>COSIjJ} + Cz - T_z) {Cos<t>cose})

Zv = ex - T) {cosecosljJ} + Cy - Ty) {COSeSinljJ} - Cz - T z) {Sine}

Exact Viewing Transformation Equations

--\---4---(>

Xo '

Road

~

t

v

Automobi1e Motion Vectors

[ s - Y

v

-N

_v

t.

Automobi1e Latera1-Directiona1

~~trix

t.

T 2 2

G

_~

Y _ 9O.9(s

_- +

2(.36)(7.6)8

+

7.6 )

₂

8

2

(s2

+

2(.94)(5.6)s

+

5.6 )

19.5(s

+

6.1)

Automobi1e Transfer Functions

Vehic1e: Uorth American Sedan

Speed

Y

_ó Y v Y r

N

_ó N v N r

44 fps

90.9 ft/sec

2

- rad

-1

-5.6

sep I

2.87 ft/sec - rad

19.5

sec -2

0.094 rad/ft -

sec -1

-4.86 sec

Automobile Dynamie Parameters

Y -2 _(Y0: 1 + YCX2) v mV N 2 (b Y CX2 - a Y ) v

IV

CX1 ZZ N -2 (a2y + b2y ) r

IV

CX1 CX2

zz

Yb

=

~Y

_{m CX1} No 2a _I Y _CX1 ZZ

m is the total vehicle mass

V is the nominal forward velocity Y

CX1 is the side force due to fronttire slip angle Y

CX2 is the side force due to rear tire slip angle

a is the distanee of the e.g. af't of the front a.xle

b is the di stance of the e.g. ahead of the rear a.xle

1 is the total vehicle yaw moment of inertia

zz

Subject 1

Subject 2

I

.

Subject 3

NODE

A B C

units

y .684

.835

.855

_ft.

e

(.139 )

(.142)

(.092 )

-

-.519

-.379

-.686

T

_{(.183 )}

(.199)

(.105 )

ft.

Y

1.47

1.74

1.59

_rad.

""e

(.288)

.

(.251)

(.141 )

Y

_e

_{(.116 )}

.734

_{( .077)}

.775

_{(.128 )}

.855

ft.

-

-.039

-.066

.119

T

(.369 )

(.231)

(.329)

ft.

Y

1.79

1.73

1.97

_rad.

""e

(.412)

(.110)

( .368)

Y

_e

_{(.157 )}

.708

_(.101)

.716

.751

ft.

(.139)

-

-.134

-.432

-.010

T

(.339 )

( .178)

(.275)

ft.

Y

""e

1.35

1.33

1.30

_rad.

(.095 )

( .115)

(.162)

Summary of Test Resu1ts

Brackets indicate standard deviation.

Mean Va1ues are for 6 runs.

TABLE 3

x 10

2

x 10

2

x 10

2

DEGREES

MEM

SOURCE OF

VARIATION

OF

SQUARES

F-RATIOS

FREEDOM

SUBJECTS

2

.0252

1.644

MODES

2

.0571

3.706*

INTERACTION

4

.0108

0.705

SUBJECTS x MODES

EX:PERIMENTAL ERROR

45

.0153

TOTAL

53

0.1084

*Significant at the 5 percent level.

ANALYSIS OF VARIANCE OF PERFORMANCE SCORES Y

(2

.

factor - fixed factor)

e

--~ . .. --~--- ---x (x,y,Z)

r

t ... . Z (T T T ) : x' y' Zo ; C B,

n

rt

.

r'

.,/

,

y ... _ ... ; I

I

I I / Ze' I I I

~

L'---xe

I Ye I

,

I

,

I Yv I I Ze I I I I I

L----...

Zv Axis Transformation

FIGURE 1a

Ye'

~~~---I---AG~

')

The Euler Angles

(from Ref. 2 )

F IGU RE 1b